LMFDB - Embedded newform 930.2.o.d.161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(161,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("930.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.o (of order $6$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			161.1
Character	$\chi$	$=$	930.161
Dual form			930.2.o.d.491.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.71477 + 0.244025i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.244025 + 1.71477i) q^{6} +(0.0693993 + 0.120203i) q^{7} +1.00000i q^{8} +(2.88090 - 0.836897i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.71477 + 0.244025i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.244025 + 1.71477i) q^{6} +(0.0693993 + 0.120203i) q^{7} +1.00000i q^{8} +(2.88090 - 0.836897i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-1.29408 + 2.24142i) q^{11} +(1.71477 - 0.244025i) q^{12} +(-1.11900 - 0.646055i) q^{13} +(0.120203 - 0.0693993i) q^{14} +(1.60705 + 0.646055i) q^{15} +1.00000 q^{16} +(3.25621 + 5.63993i) q^{17} +(-0.836897 - 2.88090i) q^{18} +(-2.87607 - 4.98149i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-0.148337 - 0.189186i) q^{21} +(2.24142 + 1.29408i) q^{22} +4.55419 q^{23} +(-0.244025 - 1.71477i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.646055 + 1.11900i) q^{26} +(-4.73588 + 2.13810i) q^{27} +(-0.0693993 - 0.120203i) q^{28} +3.95424 q^{29} +(0.646055 - 1.60705i) q^{30} +(0.735196 - 5.51901i) q^{31} -1.00000i q^{32} +(1.67210 - 4.15931i) q^{33} +(5.63993 - 3.25621i) q^{34} -0.138799i q^{35} +(-2.88090 + 0.836897i) q^{36} +(3.55974 - 2.05521i) q^{37} +(-4.98149 + 2.87607i) q^{38} +(2.07649 + 0.834774i) q^{39} +(0.500000 - 0.866025i) q^{40} +(0.0318057 + 0.0183630i) q^{41} +(-0.189186 + 0.148337i) q^{42} +(0.173390 - 0.100107i) q^{43} +(1.29408 - 2.24142i) q^{44} +(-2.91338 - 0.715677i) q^{45} -4.55419i q^{46} -8.23865i q^{47} +(-1.71477 + 0.244025i) q^{48} +(3.49037 - 6.04549i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-6.95996 - 8.87660i) q^{51} +(1.11900 + 0.646055i) q^{52} +(-1.48496 + 2.57203i) q^{53} +(2.13810 + 4.73588i) q^{54} +(2.24142 - 1.29408i) q^{55} +(-0.120203 + 0.0693993i) q^{56} +(6.14742 + 7.84031i) q^{57} -3.95424i q^{58} +(11.6793 - 6.74303i) q^{59} +(-1.60705 - 0.646055i) q^{60} -12.4057i q^{61} +(-5.51901 - 0.735196i) q^{62} +(0.300530 + 0.288213i) q^{63} -1.00000 q^{64} +(0.646055 + 1.11900i) q^{65} +(-4.15931 - 1.67210i) q^{66} +(-5.56780 + 9.64371i) q^{67} +(-3.25621 - 5.63993i) q^{68} +(-7.80940 + 1.11134i) q^{69} -0.138799 q^{70} +(-9.28503 - 5.36071i) q^{71} +(0.836897 + 2.88090i) q^{72} +(7.32249 + 4.22764i) q^{73} +(-2.05521 - 3.55974i) q^{74} +(-1.06872 - 1.36303i) q^{75} +(2.87607 + 4.98149i) q^{76} -0.359234 q^{77} +(0.834774 - 2.07649i) q^{78} +(11.0043 - 6.35336i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(7.59921 - 4.82204i) q^{81} +(0.0183630 - 0.0318057i) q^{82} +(5.41461 - 9.37837i) q^{83} +(0.148337 + 0.189186i) q^{84} -6.51243i q^{85} +(-0.100107 - 0.173390i) q^{86} +(-6.78064 + 0.964936i) q^{87} +(-2.24142 - 1.29408i) q^{88} +6.31328 q^{89} +(-0.715677 + 2.91338i) q^{90} -0.179343i q^{91} -4.55419 q^{92} +(0.0860836 + 9.64327i) q^{93} -8.23865 q^{94} +5.75213i q^{95} +(0.244025 + 1.71477i) q^{96} -0.338364 q^{97} +(-6.04549 - 3.49037i) q^{98} +(-1.85229 + 7.54032i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{4} - 8 q^{7} + 8 q^{9}+O(q^{10}) $ 36 * q - 36 * q^4 - 8 * q^7 + 8 * q^9	$ 36 q - 36 q^{4} - 8 q^{7} + 8 q^{9} - 18 q^{10} + 36 q^{16} - 4 q^{18} - 4 q^{19} + 72 q^{21} - 18 q^{22} + 18 q^{25} + 8 q^{28} + 52 q^{31} - 36 q^{33} + 18 q^{34} - 8 q^{36} - 54 q^{37} - 8 q^{39} + 18 q^{40} + 12 q^{42} - 18 q^{43} + 4 q^{45} - 62 q^{49} - 10 q^{51} - 18 q^{55} + 12 q^{57} + 88 q^{63} - 36 q^{64} - 4 q^{66} + 10 q^{67} + 46 q^{69} + 16 q^{70} + 4 q^{72} + 24 q^{73} + 4 q^{76} + 92 q^{78} + 42 q^{79} + 4 q^{81} - 12 q^{82} - 72 q^{84} - 16 q^{87} + 18 q^{88} + 8 q^{90} + 48 q^{93} - 92 q^{94} - 80 q^{97} - 18 q^{99}+O(q^{100}) $ 36 * q - 36 * q^4 - 8 * q^7 + 8 * q^9 - 18 * q^10 + 36 * q^16 - 4 * q^18 - 4 * q^19 + 72 * q^21 - 18 * q^22 + 18 * q^25 + 8 * q^28 + 52 * q^31 - 36 * q^33 + 18 * q^34 - 8 * q^36 - 54 * q^37 - 8 * q^39 + 18 * q^40 + 12 * q^42 - 18 * q^43 + 4 * q^45 - 62 * q^49 - 10 * q^51 - 18 * q^55 + 12 * q^57 + 88 * q^63 - 36 * q^64 - 4 * q^66 + 10 * q^67 + 46 * q^69 + 16 * q^70 + 4 * q^72 + 24 * q^73 + 4 * q^76 + 92 * q^78 + 42 * q^79 + 4 * q^81 - 12 * q^82 - 72 * q^84 - 16 * q^87 + 18 * q^88 + 8 * q^90 + 48 * q^93 - 92 * q^94 - 80 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.71477	+	0.244025i	−0.990026	+	0.140888i
$3$	−1.71477	+	0.244025i	−0.990026	+	0.140888i
$4$	−1.00000			−0.500000
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	0.244025	+	1.71477i	0.0996230	+	0.700054i
$7$	0.0693993	+	0.120203i	0.0262305	+	0.0454325i	0.878843	−	0.477112i	$-0.158316\pi$
$7$	0.0693993	+	0.120203i	0.0262305	+	0.0454325i	−0.852612	+	0.522544i	$0.824983\pi$
$8$			1.00000i			0.353553i
$9$	2.88090	−	0.836897i	0.960301	−	0.278966i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−1.29408	+	2.24142i	−0.390181	+	0.675813i	−0.992473	−	0.122463i	$-0.960921\pi$
$11$	−1.29408	+	2.24142i	−0.390181	+	0.675813i	0.602292	+	0.798275i	$0.294254\pi$
$12$	1.71477	−	0.244025i	0.495013	−	0.0704441i
$13$	−1.11900	−	0.646055i	−0.310355	−	0.179183i	0.336730	−	0.941601i	$-0.390679\pi$
$13$	−1.11900	−	0.646055i	−0.310355	−	0.179183i	−0.647085	+	0.762418i	$0.724012\pi$
$14$	0.120203	−	0.0693993i	0.0321256	−	0.0185477i
$15$	1.60705	+	0.646055i	0.414939	+	0.166811i
$16$	1.00000			0.250000
$17$	3.25621	+	5.63993i	0.789748	+	1.36788i	0.926121	+	0.377225i	$0.123122\pi$
$17$	3.25621	+	5.63993i	0.789748	+	1.36788i	−0.136374	+	0.990657i	$0.543545\pi$
$18$	−0.836897	−	2.88090i	−0.197259	−	0.679035i
$19$	−2.87607	−	4.98149i	−0.659815	−	1.14283i	−0.980663	−	0.195703i	$-0.937301\pi$
$19$	−2.87607	−	4.98149i	−0.659815	−	1.14283i	0.320848	−	0.947131i	$-0.396032\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$	−0.148337	−	0.189186i	−0.0323697	−	0.0412838i
$22$	2.24142	+	1.29408i	0.477872	+	0.275899i
$23$	4.55419			0.949613			0.474807	−	0.880090i	$-0.342518\pi$
$23$	4.55419			0.949613			0.474807	+	0.880090i	$0.342518\pi$
$24$	−0.244025	−	1.71477i	−0.0498115	−	0.350027i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−0.646055	+	1.11900i	−0.126702	+	0.219454i
$27$	−4.73588	+	2.13810i	−0.911420	+	0.411478i
$28$	−0.0693993	−	0.120203i	−0.0131152	−	0.0227163i
$29$	3.95424			0.734285			0.367142	−	0.930165i	$-0.380336\pi$
$29$	3.95424			0.734285			0.367142	+	0.930165i	$0.380336\pi$
$30$	0.646055	−	1.60705i	0.117953	−	0.293406i
$31$	0.735196	−	5.51901i	0.132045	−	0.991244i
$31$	0.735196	−	5.51901i	0.132045	−	0.991244i
$32$		−	1.00000i		−	0.176777i
$33$	1.67210	−	4.15931i	0.291075	−	0.724044i
$34$	5.63993	−	3.25621i	0.967239	−	0.558436i
$35$		−	0.138799i		−	0.0234612i
$36$	−2.88090	+	0.836897i	−0.480151	+	0.139483i
$37$	3.55974	−	2.05521i	0.585217	−	0.337875i	−0.177987	−	0.984033i	$-0.556959\pi$
$37$	3.55974	−	2.05521i	0.585217	−	0.337875i	0.763204	+	0.646158i	$0.223625\pi$
$38$	−4.98149	+	2.87607i	−0.808105	+	0.466560i
$39$	2.07649	+	0.834774i	0.332504	+	0.133671i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	0.0318057	+	0.0183630i	0.00496721	+	0.00286782i	0.502482	−	0.864588i	$-0.332420\pi$
$41$	0.0318057	+	0.0183630i	0.00496721	+	0.00286782i	−0.497514	+	0.867456i	$0.665754\pi$
$42$	−0.189186	+	0.148337i	−0.0291920	+	0.0228889i
$43$	0.173390	−	0.100107i	0.0264418	−	0.0152662i	−0.486721	−	0.873558i	$-0.661807\pi$
$43$	0.173390	−	0.100107i	0.0264418	−	0.0152662i	0.513163	+	0.858291i	$0.328474\pi$
$44$	1.29408	−	2.24142i	0.195090	−	0.337906i
$45$	−2.91338	−	0.715677i	−0.434302	−	0.106687i
$46$		−	4.55419i		−	0.671478i
$47$		−	8.23865i		−	1.20173i	−0.799350	−	0.600866i	$-0.794823\pi$
$47$		−	8.23865i		−	1.20173i	0.799350	−	0.600866i	$-0.205177\pi$
$48$	−1.71477	+	0.244025i	−0.247506	+	0.0352220i
$49$	3.49037	−	6.04549i	0.498624	−	0.863642i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$	−6.95996	−	8.87660i	−0.974589	−	1.24297i
$52$	1.11900	+	0.646055i	0.155177	+	0.0895917i
$53$	−1.48496	+	2.57203i	−0.203975	+	0.353295i	−0.949806	−	0.312840i	$-0.898720\pi$
$53$	−1.48496	+	2.57203i	−0.203975	+	0.353295i	0.745831	+	0.666136i	$0.232053\pi$
$54$	2.13810	+	4.73588i	0.290959	+	0.644471i
$55$	2.24142	−	1.29408i	0.302233	−	0.174494i
$56$	−0.120203	+	0.0693993i	−0.0160628	+	0.00927387i
$57$	6.14742	+	7.84031i	0.814245	+	1.03847i
$58$		−	3.95424i		−	0.519218i
$59$	11.6793	−	6.74303i	1.52051	−	0.877868i	0.520804	−	0.853676i	$-0.325632\pi$
$59$	11.6793	−	6.74303i	1.52051	−	0.877868i	0.999707	−	0.0241912i	$-0.00770104\pi$
$60$	−1.60705	−	0.646055i	−0.207469	−	0.0834053i
$61$		−	12.4057i		−	1.58839i	−0.607662	−	0.794196i	$-0.707892\pi$
$61$		−	12.4057i		−	1.58839i	0.607662	−	0.794196i	$-0.292108\pi$
$62$	−5.51901	−	0.735196i	−0.700915	−	0.0933700i
$63$	0.300530	+	0.288213i	0.0378633	+	0.0363115i
$64$	−1.00000			−0.125000
$65$	0.646055	+	1.11900i	0.0801333	+	0.138795i
$66$	−4.15931	−	1.67210i	−0.511976	−	0.205821i
$67$	−5.56780	+	9.64371i	−0.680215	+	1.17817i	0.294700	+	0.955590i	$0.404780\pi$
$67$	−5.56780	+	9.64371i	−0.680215	+	1.17817i	−0.974915	+	0.222577i	$0.928553\pi$
$68$	−3.25621	−	5.63993i	−0.394874	−	0.683941i
$69$	−7.80940	+	1.11134i	−0.940142	+	0.133789i
$70$	−0.138799			−0.0165896
$71$	−9.28503	−	5.36071i	−1.10193	−	0.636200i	−0.165203	−	0.986260i	$-0.552828\pi$
$71$	−9.28503	−	5.36071i	−1.10193	−	0.636200i	−0.936727	+	0.350060i	$0.886161\pi$
$72$	0.836897	+	2.88090i	0.0986293	+	0.339518i
$73$	7.32249	+	4.22764i	0.857033	+	0.494808i	0.863018	−	0.505174i	$-0.168572\pi$
$73$	7.32249	+	4.22764i	0.857033	+	0.494808i	−0.00598452	+	0.999982i	$0.501905\pi$
$74$	−2.05521	−	3.55974i	−0.238914	−	0.413811i
$75$	−1.06872	−	1.36303i	−0.123405	−	0.157389i
$76$	2.87607	+	4.98149i	0.329908	+	0.571417i
$77$	−0.359234			−0.0409385
$78$	0.834774	−	2.07649i	0.0945196	−	0.235116i
$79$	11.0043	−	6.35336i	1.23809	−	0.714809i	0.269383	−	0.963033i	$-0.413180\pi$
$79$	11.0043	−	6.35336i	1.23809	−	0.714809i	0.968703	+	0.248224i	$0.0798469\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	7.59921	−	4.82204i	0.844356	−	0.535782i
$82$	0.0183630	−	0.0318057i	0.00202786	−	0.00351235i
$83$	5.41461	−	9.37837i	0.594330	−	1.02941i	−0.399311	−	0.916816i	$-0.630751\pi$
$83$	5.41461	−	9.37837i	0.594330	−	1.02941i	0.993641	−	0.112595i	$-0.0359161\pi$
$84$	0.148337	+	0.189186i	0.0161849	+	0.0206419i
$85$		−	6.51243i		−	0.706372i
$86$	−0.100107	−	0.173390i	−0.0107948	−	0.0186972i
$87$	−6.78064	+	0.964936i	−0.726960	+	0.103452i
$88$	−2.24142	−	1.29408i	−0.238936	−	0.137950i
$89$	6.31328			0.669206			0.334603	−	0.942359i	$-0.391398\pi$
$89$	6.31328			0.669206			0.334603	+	0.942359i	$0.391398\pi$
$90$	−0.715677	+	2.91338i	−0.0754390	+	0.307098i
$91$		−	0.179343i		−	0.0188003i
$92$	−4.55419			−0.474807
$93$	0.0860836	+	9.64327i	0.00892645	+	0.999960i
$94$	−8.23865			−0.849752
$95$			5.75213i			0.590156i
$96$	0.244025	+	1.71477i	0.0249057	+	0.175013i
$97$	−0.338364			−0.0343557			−0.0171778	−	0.999852i	$-0.505468\pi$
$97$	−0.338364			−0.0343557			−0.0171778	+	0.999852i	$0.505468\pi$
$98$	−6.04549	−	3.49037i	−0.610687	−	0.352580i
$99$	−1.85229	+	7.54032i	−0.186162	+	0.757831i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$			14.8778i			1.48039i	0.672390	+	0.740197i	$0.265268\pi$
$101$			14.8778i			1.48039i	−0.672390	+	0.740197i	$0.734732\pi$
$102$	−8.87660	+	6.95996i	−0.878915	+	0.689138i
$103$	0.482953	−	0.836499i	0.0475868	−	0.0824227i	−0.841251	−	0.540645i	$-0.818180\pi$
$103$	0.482953	−	0.836499i	0.0475868	−	0.0824227i	0.888838	+	0.458222i	$0.151514\pi$
$104$	0.646055	−	1.11900i	0.0633509	−	0.109727i
$105$	0.0338704	+	0.238008i	0.00330541	+	0.0232272i
$106$	2.57203	+	1.48496i	0.249818	+	0.144232i
$107$	−5.45398	+	3.14886i	−0.527256	+	0.304411i	−0.739898	−	0.672719i	$-0.765126\pi$
$107$	−5.45398	+	3.14886i	−0.527256	+	0.304411i	0.212642	+	0.977130i	$0.431793\pi$
$108$	4.73588	−	2.13810i	0.455710	−	0.205739i
$109$	−9.55027			−0.914750			−0.457375	−	0.889274i	$-0.651210\pi$
$109$	−9.55027			−0.914750			−0.457375	+	0.889274i	$0.651210\pi$
$110$	−1.29408	−	2.24142i	−0.123386	−	0.213711i
$111$	−5.60262	+	4.39289i	−0.531777	+	0.416955i
$112$	0.0693993	+	0.120203i	0.00655762	+	0.0113581i
$113$	16.0187	+	9.24841i	1.50691	+	0.870018i	0.999968	+	0.00804031i	$0.00255934\pi$
$113$	16.0187	+	9.24841i	1.50691	+	0.870018i	0.506947	+	0.861977i	$0.330774\pi$
$114$	7.84031	−	6.14742i	0.734312	−	0.575758i
$115$	−3.94404	−	2.27709i	−0.367784	−	0.212340i
$116$	−3.95424			−0.367142
$117$	−3.76441	−	0.924734i	−0.348020	−	0.0854917i
$118$	−6.74303	−	11.6793i	−0.620746	−	1.07516i
$119$	−0.451958	+	0.782814i	−0.0414309	+	0.0717604i
$120$	−0.646055	+	1.60705i	−0.0589765	+	0.146703i
$121$	2.15070	+	3.72512i	0.195518	+	0.338647i
$122$	−12.4057			−1.12316
$123$	−0.0590206	−	0.0237270i	−0.00532171	−	0.00213940i
$124$	−0.735196	+	5.51901i	−0.0660226	+	0.495622i
$125$		−	1.00000i		−	0.0894427i
$126$	0.288213	−	0.300530i	0.0256761	−	0.0267734i
$127$	8.87111	−	5.12174i	0.787183	−	0.454481i	−0.0517866	−	0.998658i	$-0.516492\pi$
$127$	8.87111	−	5.12174i	0.787183	−	0.454481i	0.838970	+	0.544178i	$0.183158\pi$
$128$			1.00000i			0.0883883i
$129$	−0.272897	+	0.213972i	−0.0240272	+	0.0188392i
$130$	1.11900	−	0.646055i	0.0981428	−	0.0566628i
$131$	−7.39021	+	4.26674i	−0.645686	+	0.372787i	−0.786802	−	0.617206i	$-0.788264\pi$
$131$	−7.39021	+	4.26674i	−0.645686	+	0.372787i	0.141115	+	0.989993i	$0.454931\pi$
$132$	−1.67210	+	4.15931i	−0.145537	+	0.362022i
$133$	0.399194	−	0.691424i	0.0346145	−	0.0599541i
$134$	9.64371	+	5.56780i	0.833090	+	0.480985i
$135$	5.17044	+	0.516286i	0.445001	+	0.0444348i
$136$	−5.63993	+	3.25621i	−0.483620	+	0.279218i
$137$	−3.60675	+	6.24708i	−0.308146	+	0.533724i	−0.977957	−	0.208808i	$-0.933042\pi$
$137$	−3.60675	+	6.24708i	−0.308146	+	0.533724i	0.669811	+	0.742532i	$0.266375\pi$
$138$	1.11134	+	7.80940i	0.0946033	+	0.664780i
$139$		−	0.410130i		−	0.0347868i	−0.999849	−	0.0173934i	$-0.994463\pi$
$139$		−	0.410130i		−	0.0347868i	0.999849	−	0.0173934i	$-0.00553676\pi$
$140$			0.138799i			0.0117306i
$141$	2.01044	+	14.1274i	0.169310	+	1.18974i
$142$	−5.36071	+	9.28503i	−0.449861	+	0.779182i
$143$	2.89616	−	1.67210i	0.242189	−	0.139828i
$144$	2.88090	−	0.836897i	0.240075	−	0.0697414i
$145$	−3.42448	−	1.97712i	−0.284387	−	0.164191i
$146$	4.22764	−	7.32249i	0.349882	−	0.606014i
$147$	−4.50994	+	11.2184i	−0.371974	+	0.925278i
$148$	−3.55974	+	2.05521i	−0.292608	+	0.168938i
$149$	18.3111	−	10.5719i	1.50011	−	0.866088i	0.500108	−	0.865963i	$-0.333294\pi$
$149$	18.3111	−	10.5719i	1.50011	−	0.866088i	1.00000		0.000124352i	$-3.95825e-5\pi$
$150$	−1.36303	+	1.06872i	−0.111291	+	0.0872606i
$151$			16.1753i			1.31632i	0.752876	+	0.658162i	$0.228666\pi$
$151$			16.1753i			1.31632i	−0.752876	+	0.658162i	$0.771334\pi$
$152$	4.98149	−	2.87607i	0.404053	−	0.233280i
$153$	14.1009	+	13.5230i	1.13999	+	1.09327i
$154$			0.359234i			0.0289479i
$155$	−3.39620	+	4.41201i	−0.272790	+	0.354381i
$156$	−2.07649	−	0.834774i	−0.166252	−	0.0668354i
$157$	22.4522			1.79188			0.895939	−	0.444176i	$-0.146504\pi$
$157$	22.4522			1.79188			0.895939	+	0.444176i	$0.146504\pi$
$158$	−6.35336	−	11.0043i	−0.505446	−	0.875459i
$159$	1.91873	−	4.77282i	0.152165	−	0.378509i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	0.316057	+	0.547427i	0.0249088	+	0.0431433i
$162$	−4.82204	−	7.59921i	−0.378855	−	0.597050i
$163$	−14.7360			−1.15421			−0.577105	−	0.816670i	$-0.695818\pi$
$163$	−14.7360			−1.15421			−0.577105	+	0.816670i	$0.695818\pi$
$164$	−0.0318057	−	0.0183630i	−0.00248361	−	0.00143391i
$165$	−3.52774	+	2.76602i	−0.274634	+	0.215335i
$166$	−9.37837	−	5.41461i	−0.727903	−	0.420255i
$167$	4.66240	+	8.07551i	0.360787	+	0.624902i	0.988091	−	0.153873i	$-0.0491748\pi$
$167$	4.66240	+	8.07551i	0.360787	+	0.624902i	−0.627303	+	0.778775i	$0.715841\pi$
$168$	0.189186	−	0.148337i	0.0145960	−	0.0114444i
$169$	−5.66523	−	9.81246i	−0.435787	−	0.754805i
$170$	−6.51243			−0.499480
$171$	−12.4547	−	11.9442i	−0.952432	−	0.913398i
$172$	−0.173390	+	0.100107i	−0.0132209	+	0.00763308i
$173$	0.626926	+	0.361956i	0.0476643	+	0.0275190i	0.523643	−	0.851938i	$-0.324573\pi$
$173$	0.626926	+	0.361956i	0.0476643	+	0.0275190i	−0.475978	+	0.879457i	$0.657906\pi$
$174$	0.964936	+	6.78064i	0.0731516	+	0.514039i
$175$	−0.0693993	+	0.120203i	−0.00524609	+	0.00908650i
$176$	−1.29408	+	2.24142i	−0.0975452	+	0.168953i
$177$	−18.3818	+	14.4128i	−1.38166	+	1.08333i
$178$		−	6.31328i		−	0.473200i
$179$	−0.272448	−	0.471894i	−0.0203638	−	0.0352711i	0.855664	−	0.517532i	$-0.173149\pi$
$179$	−0.272448	−	0.471894i	−0.0203638	−	0.0352711i	−0.876028	+	0.482261i	$0.839816\pi$
$180$	2.91338	+	0.715677i	0.217151	+	0.0533434i
$181$	−13.2629	−	7.65732i	−0.985822	−	0.569164i	−0.0817989	−	0.996649i	$-0.526067\pi$
$181$	−13.2629	−	7.65732i	−0.985822	−	0.569164i	−0.904023	+	0.427485i	$0.859400\pi$
$182$	−0.179343			−0.0132938
$183$	3.02732	+	21.2730i	0.223786	+	1.57255i
$184$			4.55419i			0.335739i
$185$	−4.11043			−0.302205
$186$	9.64327	−	0.0860836i	0.707079	−	0.00631195i
$187$	−16.8552			−1.23258
$188$			8.23865i			0.600866i
$189$	−0.585673	−	0.420884i	−0.0426015	−	0.0306148i
$190$	5.75213			0.417304
$191$	17.5360	+	10.1244i	1.26886	+	0.732579i	0.974773	−	0.223199i	$-0.0716500\pi$
$191$	17.5360	+	10.1244i	1.26886	+	0.732579i	0.294090	+	0.955778i	$0.404983\pi$
$192$	1.71477	−	0.244025i	0.123753	−	0.0176110i
$193$	−5.98112	−	10.3596i	−0.430531	−	0.745701i	0.566389	−	0.824138i	$-0.308340\pi$
$193$	−5.98112	−	10.3596i	−0.430531	−	0.745701i	−0.996919	+	0.0784377i	$0.975007\pi$
$194$			0.338364i			0.0242931i
$195$	−1.38090	−	1.76118i	−0.0988885	−	0.126121i
$196$	−3.49037	+	6.04549i	−0.249312	+	0.431821i
$197$	−0.549043	+	0.950970i	−0.0391177	+	0.0677538i	−0.884921	−	0.465740i	$-0.845788\pi$
$197$	−0.549043	+	0.950970i	−0.0391177	+	0.0677538i	0.845804	+	0.533494i	$0.179121\pi$
$198$	7.54032	+	1.85229i	0.535867	+	0.131637i
$199$	−10.7314	−	6.19578i	−0.760730	−	0.439207i	0.0688281	−	0.997629i	$-0.478074\pi$
$199$	−10.7314	−	6.19578i	−0.760730	−	0.439207i	−0.829558	+	0.558421i	$0.811407\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	7.19421	−	17.8955i	0.507440	−	1.26225i
$202$	14.8778			1.04680
$203$	0.274422	+	0.475312i	0.0192606	+	0.0333604i
$204$	6.95996	+	8.87660i	0.487294	+	0.621486i
$205$	−0.0183630	−	0.0318057i	−0.00128253	−	0.00222141i
$206$	−0.836499	−	0.482953i	−0.0582817	−	0.0336489i
$207$	13.1202	−	3.81139i	0.911915	−	0.264910i
$208$	−1.11900	−	0.646055i	−0.0775887	−	0.0447959i
$209$	14.8875			1.02979
$210$	0.238008	−	0.0338704i	0.0164241	−	0.00233728i
$211$	9.89042	+	17.1307i	0.680884	+	1.17933i	0.974711	+	0.223468i	$0.0717378\pi$
$211$	9.89042	+	17.1307i	0.680884	+	1.17933i	−0.293827	+	0.955859i	$0.594929\pi$
$212$	1.48496	−	2.57203i	0.101988	−	0.176648i
$213$	17.2299	+	6.92663i	1.18057	+	0.474605i
$214$	3.14886	+	5.45398i	0.215251	+	0.372826i
$215$	−0.200214			−0.0136545
$216$	−2.13810	−	4.73588i	−0.145480	−	0.322235i
$217$	0.714425	−	0.294643i	0.0484983	−	0.0200017i
$218$			9.55027i			0.646826i
$219$	−13.5881	−	5.46258i	−0.918197	−	0.369127i
$220$	−2.24142	+	1.29408i	−0.151116	+	0.0872470i
$221$		−	8.41477i		−	0.566039i
$222$	4.39289	+	5.60262i	0.294832	+	0.376023i
$223$	−10.3976	+	6.00306i	−0.696275	+	0.401994i	−0.805958	−	0.591972i	$-0.798350\pi$
$223$	−10.3976	+	6.00306i	−0.696275	+	0.401994i	0.109684	+	0.993967i	$0.465016\pi$
$224$	0.120203	−	0.0693993i	0.00803141	−	0.00463694i
$225$	2.16523	+	2.07649i	0.144348	+	0.138432i
$226$	9.24841	−	16.0187i	0.615195	−	1.06555i
$227$	−10.6047	−	6.12264i	−0.703860	−	0.406374i	0.104923	−	0.994480i	$-0.466540\pi$
$227$	−10.6047	−	6.12264i	−0.703860	−	0.406374i	−0.808784	+	0.588106i	$0.799874\pi$
$228$	−6.14742	−	7.84031i	−0.407123	−	0.519237i
$229$	11.7063	−	6.75865i	0.773576	−	0.446624i	−0.0605728	−	0.998164i	$-0.519293\pi$
$229$	11.7063	−	6.75865i	0.773576	−	0.446624i	0.834149	+	0.551539i	$0.185959\pi$
$230$	−2.27709	+	3.94404i	−0.150147	+	0.260062i
$231$	0.616005	−	0.0876622i	0.0405301	−	0.00576775i
$232$			3.95424i			0.259609i
$233$			1.77466i			0.116262i	0.998309	+	0.0581310i	$0.0185141\pi$
$233$			1.77466i			0.116262i	−0.998309	+	0.0581310i	$0.981486\pi$
$234$	−0.924734	+	3.76441i	−0.0604518	+	0.246087i
$235$	−4.11933	+	7.13488i	−0.268715	+	0.465429i
$236$	−11.6793	+	6.74303i	−0.760256	+	0.438934i
$237$	−17.3196	+	13.5799i	−1.12503	+	0.882111i
$238$	0.782814	+	0.451958i	0.0507423	+	0.0292961i
$239$	−0.668618	+	1.15808i	−0.0432493	+	0.0749099i	−0.886840	−	0.462077i	$-0.847104\pi$
$239$	−0.668618	+	1.15808i	−0.0432493	+	0.0749099i	0.843590	+	0.536987i	$0.180438\pi$
$240$	1.60705	+	0.646055i	0.103735	+	0.0417027i
$241$	18.2787	−	10.5532i	1.17744	−	0.679793i	0.222017	−	0.975043i	$-0.428736\pi$
$241$	18.2787	−	10.5532i	1.17744	−	0.679793i	0.955420	+	0.295249i	$0.0954028\pi$
$242$	3.72512	−	2.15070i	0.239460	−	0.138252i
$243$	−11.8542	+	10.1231i	−0.760449	+	0.649398i
$244$			12.4057i			0.794196i
$245$	−6.04549	+	3.49037i	−0.386232	+	0.222991i
$246$	−0.0237270	+	0.0590206i	−0.00151278	+	0.00376302i
$247$			7.43239i			0.472912i
$248$	5.51901	+	0.735196i	0.350458	+	0.0466850i
$249$	−6.99627	+	17.4031i	−0.443370	+	1.10288i
$250$	−1.00000			−0.0632456
$251$	−0.477311	−	0.826727i	−0.0301276	−	0.0521826i	0.850568	−	0.525864i	$-0.176258\pi$
$251$	−0.477311	−	0.826727i	−0.0301276	−	0.0521826i	−0.880696	+	0.473682i	$0.842925\pi$
$252$	−0.300530	−	0.288213i	−0.0189316	−	0.0181557i
$253$	−5.89349	+	10.2078i	−0.370521	+	0.641761i
$254$	−5.12174	−	8.87111i	−0.321366	−	0.556623i
$255$	1.58920	+	11.1673i	0.0995194	+	0.699326i
$256$	1.00000			0.0625000
$257$	−4.58756	−	2.64863i	−0.286164	−	0.165217i	0.350047	−	0.936732i	$-0.386166\pi$
$257$	−4.58756	−	2.64863i	−0.286164	−	0.165217i	−0.636211	+	0.771515i	$0.719499\pi$
$258$	0.213972	+	0.272897i	0.0133213	+	0.0169898i
$259$	0.494086	+	0.285261i	0.0307010	+	0.0177252i
$260$	−0.646055	−	1.11900i	−0.0400666	−	0.0693974i
$261$	11.3918	−	3.30929i	0.705134	−	0.204840i
$262$	4.26674	+	7.39021i	0.263600	+	0.456569i
$263$	−5.08186			−0.313361			−0.156680	−	0.987649i	$-0.550079\pi$
$263$	−5.08186			−0.313361			−0.156680	+	0.987649i	$0.550079\pi$
$264$	4.15931	+	1.67210i	0.255988	+	0.102910i
$265$	2.57203	−	1.48496i	0.157998	−	0.0912205i
$266$	−0.691424	−	0.399194i	−0.0423940	−	0.0244762i
$267$	−10.8259	+	1.54060i	−0.662531	+	0.0942832i
$268$	5.56780	−	9.64371i	0.340107	−	0.589083i
$269$	0.318041	−	0.550863i	0.0193913	−	0.0335867i	−0.856167	−	0.516699i	$-0.827161\pi$
$269$	0.318041	−	0.550863i	0.0193913	−	0.0335867i	0.875558	+	0.483113i	$0.160494\pi$
$270$	0.516286	−	5.17044i	0.0314201	−	0.314663i
$271$		−	26.1027i		−	1.58562i	−0.609466	−	0.792812i	$-0.708616\pi$
$271$		−	26.1027i		−	1.58562i	0.609466	−	0.792812i	$-0.291384\pi$
$272$	3.25621	+	5.63993i	0.197437	+	0.341971i
$273$	0.0437643	+	0.307533i	0.00264873	+	0.0186127i
$274$	6.24708	+	3.60675i	0.377400	+	0.217892i
$275$	−2.58817			−0.156072
$276$	7.80940	−	1.11134i	0.470071	−	0.0668946i
$277$		−	3.68011i		−	0.221116i	−0.993870	−	0.110558i	$-0.964736\pi$
$277$		−	3.68011i		−	0.221116i	0.993870	−	0.110558i	$-0.0352638\pi$
$278$	−0.410130			−0.0245979
$279$	−2.50082	−	16.5150i	−0.149720	−	0.988728i
$280$	0.138799			0.00829480
$281$		−	9.84129i		−	0.587082i	−0.955946	−	0.293541i	$-0.905166\pi$
$281$		−	9.84129i		−	0.587082i	0.955946	−	0.293541i	$-0.0948337\pi$
$282$	14.1274	−	2.01044i	0.841276	−	0.119720i
$283$	21.5285			1.27973			0.639867	−	0.768486i	$-0.278989\pi$
$283$	21.5285			1.27973			0.639867	+	0.768486i	$0.278989\pi$
$284$	9.28503	+	5.36071i	0.550965	+	0.318100i
$285$	−1.40367	−	9.86361i	−0.0831460	−	0.584270i
$286$	−1.67210	−	2.89616i	−0.0988732	−	0.171253i
$287$			0.00509752i			0.000300897i
$288$	−0.836897	−	2.88090i	−0.0493146	−	0.169759i
$289$	−12.7058	+	22.0072i	−0.747402	+	1.29454i
$290$	−1.97712	+	3.42448i	−0.116101	+	0.201092i
$291$	0.580218	−	0.0825694i	0.0340130	−	0.00484030i
$292$	−7.32249	−	4.22764i	−0.428517	−	0.247404i
$293$	2.79603	−	1.61429i	0.163346	−	0.0943077i	−0.416099	−	0.909319i	$-0.636603\pi$
$293$	2.79603	−	1.61429i	0.163346	−	0.0943077i	0.579444	+	0.815012i	$0.303270\pi$
$294$	11.2184	+	4.50994i	0.654270	+	0.263025i
$295$	−13.4861			−0.785189
$296$	2.05521	+	3.55974i	0.119457	+	0.206905i
$297$	1.33623	−	13.3820i	0.0775361	−	0.776500i
$298$	−10.5719	−	18.3111i	−0.612416	−	1.06074i
$299$	−5.09613	−	2.94225i	−0.294717	−	0.170155i
$300$	1.06872	+	1.36303i	0.0617025	+	0.0786943i
$301$	0.0240663	+	0.0138947i	0.00138716	+	0.000800878i
$302$	16.1753			0.930781
$303$	−3.63056	−	25.5120i	−0.208570	−	1.46563i
$304$	−2.87607	−	4.98149i	−0.164954	−	0.285708i
$305$	−6.20287	+	10.7437i	−0.355175	+	0.615182i
$306$	13.5230	−	14.1009i	0.773056	−	0.806093i
$307$	3.93178	+	6.81003i	0.224398	+	0.388669i	0.956139	−	0.292914i	$-0.0946250\pi$
$307$	3.93178	+	6.81003i	0.224398	+	0.388669i	−0.731740	+	0.681583i	$0.761292\pi$
$308$	0.359234			0.0204692
$309$	−0.624028	+	1.55226i	−0.0354997	+	0.0883050i
$310$	4.41201	+	3.39620i	0.250585	+	0.192891i
$311$			15.4244i			0.874636i	0.899307	+	0.437318i	$0.144072\pi$
$311$			15.4244i			0.874636i	−0.899307	+	0.437318i	$0.855928\pi$
$312$	−0.834774	+	2.07649i	−0.0472598	+	0.117558i
$313$	8.34344	−	4.81709i	0.471599	−	0.272278i	−0.245310	−	0.969445i	$-0.578890\pi$
$313$	8.34344	−	4.81709i	0.471599	−	0.272278i	0.716909	+	0.697167i	$0.245556\pi$
$314$		−	22.4522i		−	1.26705i
$315$	−0.116160	−	0.399865i	−0.00654488	−	0.0225299i
$316$	−11.0043	+	6.35336i	−0.619043	+	0.357405i
$317$	−2.47546	+	1.42921i	−0.139036	+	0.0802722i	−0.567904	−	0.823095i	$-0.692246\pi$
$317$	−2.47546	+	1.42921i	−0.139036	+	0.0802722i	0.428869	+	0.903367i	$0.358912\pi$
$318$	−4.77282	−	1.91873i	−0.267646	−	0.107597i
$319$	−5.11712	+	8.86311i	−0.286504	+	0.496239i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	8.58394	−	6.73049i	0.479109	−	0.375659i
$322$	0.547427	−	0.316057i	0.0305069	−	0.0176132i
$323$	18.7302	−	32.4416i	1.04217	−	1.80510i
$324$	−7.59921	+	4.82204i	−0.422178	+	0.267891i
$325$		−	1.29211i		−	0.0716734i
$326$			14.7360i			0.816150i
$327$	16.3766	−	2.33051i	0.905625	−	0.128877i
$328$	−0.0183630	+	0.0318057i	−0.00101393	+	0.00175618i
$329$	0.990312	−	0.571757i	0.0545977	−	0.0315220i
$330$	2.76602	+	3.52774i	0.152265	+	0.194195i
$331$	3.62142	+	2.09083i	0.199051	+	0.114922i	0.596213	−	0.802826i	$-0.296671\pi$
$331$	3.62142	+	2.09083i	0.199051	+	0.114922i	−0.397162	+	0.917749i	$0.630005\pi$
$332$	−5.41461	+	9.37837i	−0.297165	+	0.514705i
$333$	8.53525	−	8.90001i	0.467729	−	0.487717i
$334$	8.07551	−	4.66240i	0.441872	−	0.255115i
$335$	9.64371	−	5.56780i	0.526892	−	0.304201i
$336$	−0.148337	−	0.189186i	−0.00809243	−	0.0103209i
$337$			25.8541i			1.40836i	0.710019	+	0.704182i	$0.248686\pi$
$337$			25.8541i			1.40836i	−0.710019	+	0.704182i	$0.751314\pi$
$338$	−9.81246	+	5.66523i	−0.533727	+	0.308148i
$339$	−29.7253	−	11.9500i	−1.61446	−	0.649033i
$340$			6.51243i			0.353186i
$341$	11.4190	+	8.78994i	0.618374	+	0.476002i
$342$	−11.9442	+	12.4547i	−0.645870	+	0.673471i
$343$	1.94051			0.104778
$344$	0.100107	+	0.173390i	0.00539740	+	0.00934858i
$345$	7.31881	+	2.94225i	0.394031	+	0.158406i
$346$	0.361956	−	0.626926i	0.0194589	−	0.0337037i
$347$	−12.4503	−	21.5645i	−0.668366	−	1.15764i	−0.978361	−	0.206905i	$-0.933661\pi$
$347$	−12.4503	−	21.5645i	−0.668366	−	1.15764i	0.309995	−	0.950738i	$-0.399673\pi$
$348$	6.78064	−	0.964936i	0.363480	−	0.0517260i
$349$	27.1625			1.45398			0.726988	−	0.686650i	$-0.240920\pi$
$349$	27.1625			1.45398			0.726988	+	0.686650i	$0.240920\pi$
$350$	0.120203	+	0.0693993i	0.00642513	+	0.00370955i
$351$	6.68078	+	0.667098i	0.356594	+	0.0356071i
$352$	2.24142	+	1.29408i	0.119468	+	0.0689748i
$353$	8.61106	+	14.9148i	0.458320	+	0.793834i	0.998872	−	0.0474763i	$-0.0151179\pi$
$353$	8.61106	+	14.9148i	0.458320	+	0.793834i	−0.540552	+	0.841311i	$0.681785\pi$
$354$	14.4128	+	18.3818i	0.766032	+	0.976984i
$355$	5.36071	+	9.28503i	0.284517	+	0.492798i
$356$	−6.31328			−0.334603
$357$	0.583979	−	1.45264i	0.0309075	−	0.0768818i
$358$	−0.471894	+	0.272448i	−0.0249404	+	0.0143993i
$359$	−18.1276	−	10.4660i	−0.956737	−	0.552372i	−0.0615698	−	0.998103i	$-0.519611\pi$
$359$	−18.1276	−	10.4660i	−0.956737	−	0.552372i	−0.895167	+	0.445730i	$0.852944\pi$
$360$	0.715677	−	2.91338i	0.0377195	−	0.153549i
$361$	−7.04352	+	12.1997i	−0.370712	+	0.642092i
$362$	−7.65732	+	13.2629i	−0.402460	+	0.697081i
$363$	−4.59699	−	5.86292i	−0.241279	−	0.307723i
$364$			0.179343i			0.00940013i
$365$	−4.22764	−	7.32249i	−0.221285	−	0.383277i
$366$	21.2730	−	3.02732i	1.11196	−	0.158240i
$367$	−21.8135	−	12.5941i	−1.13866	−	0.657404i	−0.192560	−	0.981285i	$-0.561679\pi$
$367$	−21.8135	−	12.5941i	−1.13866	−	0.657404i	−0.946098	+	0.323881i	$0.895012\pi$
$368$	4.55419			0.237403
$369$	0.106997	+	0.0262840i	0.00557004	+	0.00136829i
$370$			4.11043i			0.213691i
$371$	−0.412221			−0.0214015
$372$	−0.0860836	−	9.64327i	−0.00446322	−	0.499980i
$373$	−11.6188			−0.601597			−0.300798	−	0.953688i	$-0.597253\pi$
$373$	−11.6188			−0.601597			−0.300798	+	0.953688i	$0.597253\pi$
$374$			16.8552i			0.871563i
$375$	0.244025	+	1.71477i	0.0126014	+	0.0885506i
$376$	8.23865			0.424876
$377$	−4.42480	−	2.55466i	−0.227889	−	0.131572i
$378$	−0.420884	+	0.585673i	−0.0216479	+	0.0301238i
$379$	−12.5544	−	21.7449i	−0.644878	−	1.11696i	−0.984330	−	0.176338i	$-0.943575\pi$
$379$	−12.5544	−	21.7449i	−0.644878	−	1.11696i	0.339452	−	0.940623i	$-0.389758\pi$
$380$		−	5.75213i		−	0.295078i
$381$	−13.9621	+	10.9474i	−0.715301	+	0.560852i
$382$	10.1244	−	17.5360i	0.518011	−	0.897222i
$383$	−5.90538	+	10.2284i	−0.301751	+	0.522648i	−0.976533	−	0.215369i	$-0.930904\pi$
$383$	−5.90538	+	10.2284i	−0.301751	+	0.522648i	0.674782	+	0.738017i	$0.264238\pi$
$384$	−0.244025	−	1.71477i	−0.0124529	−	0.0875067i
$385$	0.311106	+	0.179617i	0.0158554	+	0.00915412i
$386$	−10.3596	+	5.98112i	−0.527290	+	0.304431i
$387$	0.415742	−	0.433508i	0.0211333	−	0.0220365i
$388$	0.338364			0.0171778
$389$	−6.14668	−	10.6464i	−0.311649	−	0.539792i	0.667070	−	0.744995i	$-0.267548\pi$
$389$	−6.14668	−	10.6464i	−0.311649	−	0.539792i	−0.978720	+	0.205203i	$0.934215\pi$
$390$	−1.76118	+	1.38090i	−0.0891808	+	0.0699248i
$391$	14.8294	+	25.6853i	0.749955	+	1.29896i
$392$	6.04549	+	3.49037i	0.305344	+	0.176290i
$393$	11.6314	−	9.11990i	0.586724	−	0.460038i
$394$	0.950970	+	0.549043i	0.0479092	+	0.0276604i
$395$	−12.7067			−0.639345
$396$	1.85229	−	7.54032i	0.0930812	−	0.378915i
$397$	−6.77103	−	11.7278i	−0.339828	−	0.588600i	0.644572	−	0.764544i	$-0.277036\pi$
$397$	−6.77103	−	11.7278i	−0.339828	−	0.588600i	−0.984400	+	0.175944i	$0.943702\pi$
$398$	−6.19578	+	10.7314i	−0.310567	+	0.537917i
$399$	−0.515803	+	1.28305i	−0.0258224	+	0.0642329i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−27.0123			−1.34893			−0.674464	−	0.738308i	$-0.735625\pi$
$401$	−27.0123			−1.34893			−0.674464	+	0.738308i	$0.735625\pi$
$402$	−17.8955	−	7.19421i	−0.892545	−	0.358815i
$403$	−4.38827	+	5.70080i	−0.218595	+	0.283977i
$404$		−	14.8778i		−	0.740197i
$405$	−8.99213	+	0.376405i	−0.446822	+	0.0187037i
$406$	0.475312	−	0.274422i	0.0235894	−	0.0136193i
$407$			10.6385i			0.527329i
$408$	8.87660	−	6.95996i	0.439457	−	0.344569i
$409$	12.3475	−	7.12882i	0.610543	−	0.352497i	−0.162635	−	0.986686i	$-0.551999\pi$
$409$	12.3475	−	7.12882i	0.610543	−	0.352497i	0.773178	+	0.634189i	$0.218666\pi$
$410$	−0.0318057	+	0.0183630i	−0.00157077	+	0.000906885i
$411$	4.66032	−	11.5925i	0.229877	−	0.571815i
$412$	−0.482953	+	0.836499i	−0.0237934	+	0.0412114i
$413$	1.62107	+	0.935923i	0.0797675	+	0.0460538i
$414$	−3.81139	−	13.1202i	−0.187319	−	0.644821i
$415$	−9.37837	+	5.41461i	−0.460366	+	0.265793i
$416$	−0.646055	+	1.11900i	−0.0316755	+	0.0548635i
$417$	0.100082	+	0.703280i	0.00490104	+	0.0344398i
$418$		−	14.8875i		−	0.728170i
$419$		−	19.9657i		−	0.975389i	−0.873014	−	0.487694i	$-0.837838\pi$
$419$		−	19.9657i		−	0.975389i	0.873014	−	0.487694i	$-0.162162\pi$
$420$	−0.0338704	−	0.238008i	−0.00165271	−	0.0116136i
$421$	−12.8991	+	22.3420i	−0.628666	+	1.08888i	0.359154	+	0.933278i	$0.383065\pi$
$421$	−12.8991	+	22.3420i	−0.628666	+	1.08888i	−0.987820	+	0.155602i	$0.950268\pi$
$422$	17.1307	−	9.89042i	0.833910	−	0.481458i
$423$	−6.89491	−	23.7348i	−0.335242	−	1.15402i
$424$	−2.57203	−	1.48496i	−0.124909	−	0.0721161i
$425$	−3.25621	+	5.63993i	−0.157950	+	0.273577i
$426$	6.92663	−	17.2299i	0.335596	−	0.834790i
$427$	1.49121	−	0.860950i	0.0721646	−	0.0416643i
$428$	5.45398	−	3.14886i	0.263628	−	0.152206i
$429$	−4.55822	+	3.57401i	−0.220073	+	0.172555i
$430$			0.200214i			0.00965517i
$431$	20.9306	−	12.0843i	1.00819	−	0.582081i	0.0975312	−	0.995232i	$-0.468905\pi$
$431$	20.9306	−	12.0843i	1.00819	−	0.582081i	0.910662	+	0.413152i	$0.135572\pi$
$432$	−4.73588	+	2.13810i	−0.227855	+	0.102870i
$433$			16.7926i			0.806999i	0.914980	+	0.403500i	$0.132206\pi$
$433$			16.7926i			0.806999i	−0.914980	+	0.403500i	$0.867794\pi$
$434$	−0.294643	−	0.714425i	−0.0141433	−	0.0342935i
$435$	6.35467	+	2.55466i	0.304683	+	0.122487i
$436$	9.55027			0.457375
$437$	−13.0981	−	22.6867i	−0.626569	−	1.08525i
$438$	−5.46258	+	13.5881i	−0.261012	+	0.649264i
$439$	−4.21190	+	7.29522i	−0.201023	+	0.348182i	−0.948858	−	0.315702i	$-0.897760\pi$
$439$	−4.21190	+	7.29522i	−0.201023	+	0.348182i	0.747835	+	0.663884i	$0.231093\pi$
$440$	1.29408	+	2.24142i	0.0616930	+	0.106855i
$441$	4.99595	−	20.3376i	0.237903	−	0.968455i
$442$	−8.41477			−0.400250
$443$	−4.93112	−	2.84698i	−0.234285	−	0.135264i	0.378263	−	0.925698i	$-0.376522\pi$
$443$	−4.93112	−	2.84698i	−0.234285	−	0.135264i	−0.612547	+	0.790434i	$0.709855\pi$
$444$	5.60262	−	4.39289i	0.265889	−	0.208478i
$445$	−5.46746	−	3.15664i	−0.259182	−	0.149639i
$446$	6.00306	+	10.3976i	0.284253	+	0.492341i
$447$	−28.8197	+	22.5969i	−1.36312	+	1.06880i
$448$	−0.0693993	−	0.120203i	−0.00327881	−	0.00567906i
$449$	−27.1961			−1.28346			−0.641731	−	0.766930i	$-0.721783\pi$
$449$	−27.1961			−1.28346			−0.641731	+	0.766930i	$0.721783\pi$
$450$	2.07649	−	2.16523i	0.0978865	−	0.102070i
$451$	−0.0823184	+	0.0475265i	−0.00387622	+	0.00223794i
$452$	−16.0187	−	9.24841i	−0.753457	−	0.435009i
$453$	−3.94717	−	27.7369i	−0.185454	−	1.30319i
$454$	−6.12264	+	10.6047i	−0.287350	+	0.497704i
$455$	−0.0896715	+	0.155316i	−0.00420387	+	0.00728131i
$456$	−7.84031	+	6.14742i	−0.367156	+	0.287879i
$457$		−	22.1433i		−	1.03582i	−0.855435	−	0.517910i	$-0.826710\pi$
$457$		−	22.1433i		−	1.03582i	0.855435	−	0.517910i	$-0.173290\pi$
$458$	−6.75865	−	11.7063i	−0.315811	−	0.547001i
$459$	−27.4798	−	19.7479i	−1.28265	−	0.921751i
$460$	3.94404	+	2.27709i	0.183892	+	0.106170i
$461$	9.56201			0.445347			0.222674	−	0.974893i	$-0.428522\pi$
$461$	9.56201			0.445347			0.222674	+	0.974893i	$0.428522\pi$
$462$	−0.0876622	−	0.616005i	−0.00407841	−	0.0286591i
$463$		−	6.71621i		−	0.312129i	−0.987747	−	0.156064i	$-0.950119\pi$
$463$		−	6.71621i		−	0.312129i	0.987747	−	0.156064i	$-0.0498807\pi$
$464$	3.95424			0.183571
$465$	4.74708	−	8.39436i	0.220141	−	0.389279i
$466$	1.77466			0.0822096
$467$			5.96215i			0.275895i	0.990440	+	0.137948i	$0.0440506\pi$
$467$			5.96215i			0.275895i	−0.990440	+	0.137948i	$0.955949\pi$
$468$	3.76441	+	0.924734i	0.174010	+	0.0427458i
$469$	−1.54561			−0.0713694
$470$	7.13488	+	4.11933i	0.329108	+	0.190010i
$471$	−38.5004	+	5.47890i	−1.77401	+	0.252454i
$472$	6.74303	+	11.6793i	0.310373	+	0.537582i
$473$			0.518187i			0.0238262i
$474$	13.5799	+	17.3196i	0.623746	+	0.795515i
$475$	2.87607	−	4.98149i	0.131963	−	0.228567i
$476$	0.451958	−	0.782814i	0.0207155	−	0.0358802i
$477$	−2.12551	+	8.65253i	−0.0973203	+	0.396172i
$478$	1.15808	+	0.668618i	0.0529693	+	0.0305819i
$479$	−31.3148	+	18.0796i	−1.43081	+	0.826078i	−0.997182	−	0.0750143i	$-0.976100\pi$
$479$	−31.3148	+	18.0796i	−1.43081	+	0.826078i	−0.433627	+	0.901092i	$0.642766\pi$
$480$	0.646055	−	1.60705i	0.0294882	−	0.0733515i
$481$	−5.31113			−0.242167
$482$	−10.5532	−	18.2787i	−0.480687	−	0.832573i
$483$	−0.675553	−	0.861589i	−0.0307387	−	0.0392036i
$484$	−2.15070	−	3.72512i	−0.0977591	−	0.169324i
$485$	0.293032	+	0.169182i	0.0133059	+	0.00768216i
$486$	10.1231	+	11.8542i	0.459194	+	0.537719i
$487$	−1.86997	−	1.07963i	−0.0847364	−	0.0489226i	0.457033	−	0.889450i	$-0.348912\pi$
$487$	−1.86997	−	1.07963i	−0.0847364	−	0.0489226i	−0.541769	+	0.840527i	$0.682245\pi$
$488$	12.4057			0.561581
$489$	25.2689	−	3.59595i	1.14270	−	0.162615i
$490$	3.49037	+	6.04549i	0.157679	+	0.273108i
$491$	−2.38639	+	4.13336i	−0.107696	+	0.186536i	−0.914837	−	0.403824i	$-0.867681\pi$
$491$	−2.38639	+	4.13336i	−0.107696	+	0.186536i	0.807140	+	0.590360i	$0.201014\pi$
$492$	0.0590206	+	0.0237270i	0.00266086	+	0.00106970i
$493$	12.8759	+	22.3016i	0.579899	+	1.00442i
$494$	7.43239			0.334399
$495$	5.37429	−	5.60396i	0.241556	−	0.251879i
$496$	0.735196	−	5.51901i	0.0330113	−	0.247811i
$497$		−	1.48812i		−	0.0667513i
$498$	17.4031	+	6.99627i	0.779851	+	0.313510i
$499$	11.4636	−	6.61852i	0.513181	−	0.296285i	−0.220959	−	0.975283i	$-0.570919\pi$
$499$	11.4636	−	6.61852i	0.513181	−	0.296285i	0.734140	+	0.678998i	$0.237585\pi$
$500$			1.00000i			0.0447214i
$501$	−9.96559	−	12.7099i	−0.445230	−	0.567838i
$502$	−0.826727	+	0.477311i	−0.0368986	+	0.0213034i
$503$	8.00686	−	4.62276i	0.357008	−	0.206119i	−0.310759	−	0.950489i	$-0.600583\pi$
$503$	8.00686	−	4.62276i	0.357008	−	0.206119i	0.667768	+	0.744370i	$0.267250\pi$
$504$	−0.288213	+	0.300530i	−0.0128380	+	0.0133867i
$505$	7.43889	−	12.8845i	0.331026	−	0.573354i
$506$	10.2078	+	5.89349i	0.453793	+	0.261998i
$507$	12.1091	+	15.4437i	0.537783	+	0.685879i
$508$	−8.87111	+	5.12174i	−0.393592	+	0.227240i
$509$	6.81409	−	11.8024i	0.302029	−	0.523130i	−0.674566	−	0.738214i	$-0.735669\pi$
$509$	6.81409	−	11.8024i	0.302029	−	0.523130i	0.976595	+	0.215084i	$0.0690026\pi$
$510$	11.1673	−	1.58920i	0.494498	−	0.0703708i
$511$			1.17358i			0.0519162i
$512$		−	1.00000i		−	0.0441942i
$513$	24.2716	+	17.4424i	1.07162	+	0.770101i
$514$	−2.64863	+	4.58756i	−0.116826	+	0.202349i
$515$	−0.836499	+	0.482953i	−0.0368606	+	0.0212815i
$516$	0.272897	−	0.213972i	0.0120136	−	0.00941961i
$517$	18.4663	+	10.6615i	0.812145	+	0.468892i
$518$	0.285261	−	0.494086i	0.0125336	−	0.0217089i
$519$	−1.16336	−	0.467687i	−0.0510660	−	0.0205292i
$520$	−1.11900	+	0.646055i	−0.0490714	+	0.0283314i
$521$	−32.0945	+	18.5298i	−1.40609	+	0.811805i	−0.995008	−	0.0997951i	$-0.968181\pi$
$521$	−32.0945	+	18.5298i	−1.40609	+	0.811805i	−0.411079	+	0.911600i	$0.634848\pi$
$522$	−3.30929	−	11.3918i	−0.144844	−	0.498605i
$523$		−	29.4901i		−	1.28951i	−0.764388	−	0.644756i	$-0.776959\pi$
$523$		−	29.4901i		−	1.28951i	0.764388	−	0.644756i	$-0.223041\pi$
$524$	7.39021	−	4.26674i	0.322843	−	0.186394i
$525$	0.0896715	−	0.223056i	0.00391359	−	0.00973498i
$526$			5.08186i			0.221579i
$527$	33.5208	−	13.8246i	1.46019	−	0.602210i
$528$	1.67210	−	4.15931i	0.0727687	−	0.181011i
$529$	−2.25939			−0.0982343
$530$	−1.48496	−	2.57203i	−0.0645026	−	0.111722i
$531$	28.0036	−	29.2004i	1.21525	−	1.26719i
$532$	−0.399194	+	0.691424i	−0.0173073	+	0.0299771i
$533$	−0.0237270	−	0.0410964i	−0.00102773	−	0.00178008i
$534$	1.54060	+	10.8259i	0.0666683	+	0.468480i
$535$	6.29771			0.272274
$536$	−9.64371	−	5.56780i	−0.416545	−	0.240492i
$537$	0.582342	+	0.742708i	0.0251299	+	0.0320502i
$538$	−0.550863	−	0.318041i	−0.0237494	−	0.0137117i
$539$	9.03365	+	15.6467i	0.389107	+	0.673953i
$540$	−5.17044	−	0.516286i	−0.222500	−	0.0222174i
$541$	0.929363	+	1.60970i	0.0399564	+	0.0692066i	0.885312	−	0.464997i	$-0.153945\pi$
$541$	0.929363	+	1.60970i	0.0399564	+	0.0692066i	−0.845356	+	0.534204i	$0.820611\pi$
$542$	−26.1027			−1.12121
$543$	24.6114	+	9.89410i	1.05618	+	0.424597i
$544$	5.63993	−	3.25621i	0.241810	−	0.139609i
$545$	8.27077	+	4.77513i	0.354281	+	0.204544i
$546$	0.307533	−	0.0437643i	0.0131612	−	0.00187294i
$547$	−14.1962	+	24.5886i	−0.606986	+	1.05133i	0.384748	+	0.923022i	$0.374288\pi$
$547$	−14.1962	+	24.5886i	−0.606986	+	1.05133i	−0.991734	+	0.128309i	$0.959045\pi$
$548$	3.60675	−	6.24708i	0.154073	−	0.266862i
$549$	−10.3823	−	35.7397i	−0.443107	−	1.52533i
$550$			2.58817i			0.110360i
$551$	−11.3727	−	19.6980i	−0.484492	−	0.839165i
$552$	−1.11134	−	7.80940i	−0.0473016	−	0.332390i
$553$	1.52739	+	0.881838i	0.0649511	+	0.0374996i
$554$	−3.68011			−0.156353
$555$	7.04846	−	1.00305i	0.299190	−	0.0425771i
$556$			0.410130i			0.0173934i
$557$	2.75277			0.116638			0.0583192	−	0.998298i	$-0.481426\pi$
$557$	2.75277			0.116638			0.0583192	+	0.998298i	$0.481426\pi$
$558$	−16.5150	+	2.50082i	−0.699137	+	0.105868i
$559$	−0.258698			−0.0109418
$560$		−	0.138799i		−	0.00586531i
$561$	28.9029	−	4.11311i	1.22028	−	0.173655i
$562$	−9.84129			−0.415130
$563$	−29.4580	−	17.0076i	−1.24151	−	0.716784i	−0.272105	−	0.962268i	$-0.587720\pi$
$563$	−29.4580	−	17.0076i	−1.24151	−	0.716784i	−0.969401	+	0.245484i	$0.921053\pi$
$564$	−2.01044	−	14.1274i	−0.0846548	−	0.594872i
$565$	−9.24841	−	16.0187i	−0.389084	−	0.673913i
$566$		−	21.5285i		−	0.904908i
$567$	1.10700	+	0.578802i	0.0464898	+	0.0243074i
$568$	5.36071	−	9.28503i	0.224931	−	0.389591i
$569$	−3.13648	+	5.43255i	−0.131488	+	0.227744i	−0.924250	−	0.381787i	$-0.875309\pi$
$569$	−3.13648	+	5.43255i	−0.131488	+	0.227744i	0.792762	+	0.609531i	$0.208642\pi$
$570$	−9.86361	+	1.40367i	−0.413141	+	0.0587931i
$571$	30.5621	+	17.6451i	1.27899	+	0.738423i	0.976662	−	0.214782i	$-0.0689042\pi$
$571$	30.5621	+	17.6451i	1.27899	+	0.738423i	0.302324	+	0.953205i	$0.402238\pi$
$572$	−2.89616	+	1.67210i	−0.121094	+	0.0699139i
$573$	−32.5410	−	13.0819i	−1.35942	−	0.546504i
$574$	0.00509752			0.000212767
$575$	2.27709	+	3.94404i	0.0949613	+	0.164478i
$576$	−2.88090	+	0.836897i	−0.120038	+	0.0348707i
$577$	−16.6655	−	28.8655i	−0.693795	−	1.20169i	−0.970585	−	0.240758i	$-0.922604\pi$
$577$	−16.6655	−	28.8655i	−0.693795	−	1.20169i	0.276790	−	0.960930i	$-0.410729\pi$
$578$	22.0072	+	12.7058i	0.915377	+	0.528493i
$579$	12.7843	+	16.3048i	0.531297	+	0.677606i
$580$	3.42448	+	1.97712i	0.142194	+	0.0820955i
$581$	1.50308			0.0623583
$582$	−0.0825694	−	0.580218i	−0.00342261	−	0.0240508i
$583$	−3.84333	−	6.65684i	−0.159174	−	0.275698i
$584$	−4.22764	+	7.32249i	−0.174941	+	0.303007i
$585$	2.79771	+	2.68305i	0.115671	+	0.110930i
$586$	−1.61429	−	2.79603i	−0.0666856	−	0.115503i
$587$	38.7354			1.59878			0.799391	−	0.600811i	$-0.205156\pi$
$587$	38.7354			1.59878			0.799391	+	0.600811i	$0.205156\pi$
$588$	4.50994	−	11.2184i	0.185987	−	0.462639i
$589$	−29.6074	+	12.2107i	−1.21995	+	0.503132i
$590$			13.4861i			0.555212i
$591$	0.709424	−	1.76468i	0.0291818	−	0.0725892i
$592$	3.55974	−	2.05521i	0.146304	−	0.0844688i
$593$			1.94011i			0.0796706i	0.999206	+	0.0398353i	$0.0126833\pi$
$593$			1.94011i			0.0796706i	−0.999206	+	0.0398353i	$0.987317\pi$
$594$	−13.3820	−	1.33623i	−0.549068	−	0.0548263i
$595$	0.782814	−	0.451958i	0.0320922	−	0.0185285i
$596$	−18.3111	+	10.5719i	−0.750054	+	0.433044i
$597$	19.9139	+	8.00563i	0.815021	+	0.327649i
$598$	−2.94225	+	5.09613i	−0.120318	+	0.208396i
$599$	1.34831	+	0.778446i	0.0550904	+	0.0318065i	0.527292	−	0.849684i	$-0.323207\pi$
$599$	1.34831	+	0.778446i	0.0550904	+	0.0318065i	−0.472202	+	0.881490i	$0.656541\pi$
$600$	1.36303	−	1.06872i	0.0556453	−	0.0436303i
$601$	19.4855	−	11.2500i	0.794830	−	0.458896i	−0.0468299	−	0.998903i	$-0.514912\pi$
$601$	19.4855	−	11.2500i	0.794830	−	0.458896i	0.841660	+	0.540007i	$0.181579\pi$
$602$	0.0138947	−	0.0240663i	0.000566306	−	0.000980871i
$603$	−7.96950	+	32.4423i	−0.324543	+	1.32115i
$604$		−	16.1753i		−	0.658162i
$605$		−	4.30140i		−	0.174877i
$606$	−25.5120	+	3.63056i	−1.03636	+	0.147481i
$607$	11.9076	−	20.6245i	0.483314	−	0.837124i	−0.516503	−	0.856286i	$-0.672766\pi$
$607$	11.9076	−	20.6245i	0.483314	−	0.837124i	0.999816	+	0.0191616i	$0.00609972\pi$
$608$	−4.98149	+	2.87607i	−0.202026	+	0.116640i
$609$	−0.586560	−	0.748088i	−0.0237686	−	0.0303140i
$610$	10.7437	+	6.20287i	0.434999	+	0.251147i
$611$	−5.32262	+	9.21906i	−0.215330	+	0.372963i
$612$	−14.1009	−	13.5230i	−0.569994	−	0.546633i
$613$	29.6934	−	17.1435i	1.19931	−	0.692420i	0.238906	−	0.971043i	$-0.423211\pi$
$613$	29.6934	−	17.1435i	1.19931	−	0.692420i	0.960401	+	0.278622i	$0.0898778\pi$
$614$	6.81003	−	3.93178i	0.274831	−	0.158674i
$615$	0.0392498	+	0.0500585i	0.00158271	+	0.00201856i
$616$		−	0.359234i		−	0.0144739i
$617$	31.1992	−	18.0128i	1.25603	−	0.725170i	0.283730	−	0.958904i	$-0.408428\pi$
$617$	31.1992	−	18.0128i	1.25603	−	0.725170i	0.972300	+	0.233734i	$0.0750946\pi$
$618$	1.55226	+	0.624028i	0.0624411	+	0.0251021i
$619$		−	34.6062i		−	1.39094i	−0.718555	−	0.695470i	$-0.755196\pi$
$619$		−	34.6062i		−	1.39094i	0.718555	−	0.695470i	$-0.244804\pi$
$620$	3.39620	−	4.41201i	0.136395	−	0.177190i
$621$	−21.5681	+	9.73732i	−0.865496	+	0.390745i
$622$	15.4244			0.618461
$623$	0.438137	+	0.758876i	0.0175536	+	0.0304037i
$624$	2.07649	+	0.834774i	0.0831260	+	0.0334177i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−4.81709	−	8.34344i	−0.192530	−	0.333471i
$627$	−25.5287	+	3.63292i	−1.01952	+	0.145085i
$628$	−22.4522			−0.895939
$629$	23.1825	+	13.3844i	0.924347	+	0.533672i
$630$	−0.399865	+	0.116160i	−0.0159310	+	0.00462793i
$631$	27.7348	+	16.0127i	1.10411	+	0.637455i	0.937296	−	0.348534i	$-0.113320\pi$
$631$	27.7348	+	16.0127i	1.10411	+	0.637455i	0.166809	+	0.985989i	$0.446654\pi$
$632$	6.35336	+	11.0043i	0.252723	+	0.437729i
$633$	−21.1402	−	26.9618i	−0.840246	−	1.07163i
$634$	1.42921	+	2.47546i	0.0567610	+	0.0983130i
$635$	−10.2435			−0.406500
$636$	−1.91873	+	4.77282i	−0.0760827	+	0.189255i
$637$	−7.81144	+	4.50994i	−0.309501	+	0.178690i
$638$	8.86311	+	5.11712i	0.350894	+	0.202589i
$639$	−31.2356	−	7.67308i	−1.23566	−	0.303542i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−22.3307	+	38.6779i	−0.882010	+	1.52769i	−0.0329073	+	0.999458i	$0.510477\pi$
$641$	−22.3307	+	38.6779i	−0.882010	+	1.52769i	−0.849103	+	0.528228i	$0.822857\pi$
$642$	−6.73049	−	8.58394i	−0.265631	−	0.338781i
$643$			44.6908i			1.76243i	0.472714	+	0.881216i	$0.343274\pi$
$643$			44.6908i			1.76243i	−0.472714	+	0.881216i	$0.656726\pi$
$644$	−0.316057	−	0.547427i	−0.0124544	−	0.0215717i
$645$	0.343322	−	0.0488573i	0.0135183	−	0.00192375i
$646$	−32.4416	−	18.7302i	−1.27640	−	0.736929i
$647$	25.8469			1.01615			0.508073	−	0.861314i	$-0.330358\pi$
$647$	25.8469			1.01615			0.508073	+	0.861314i	$0.330358\pi$
$648$	4.82204	+	7.59921i	0.189428	+	0.298525i
$649$			34.9041i			1.37011i
$650$	−1.29211			−0.0506807
$651$	−1.15318	+	0.679584i	−0.0451966	+	0.0266350i
$652$	14.7360			0.577105
$653$		−	31.9363i		−	1.24976i	−0.780719	−	0.624882i	$-0.785147\pi$
$653$		−	31.9363i		−	1.24976i	0.780719	−	0.624882i	$-0.214853\pi$
$654$	−2.33051	−	16.3766i	−0.0911301	−	0.640374i
$655$	8.53349			0.333431
$656$	0.0318057	+	0.0183630i	0.00124180	+	0.000716956i
$657$	24.6335	+	6.05126i	0.961044	+	0.236082i
$658$	−0.571757	−	0.990312i	−0.0222894	−	0.0386064i
$659$			23.2040i			0.903901i	0.892043	+	0.451951i	$0.149272\pi$
$659$			23.2040i			0.903901i	−0.892043	+	0.451951i	$0.850728\pi$
$660$	3.52774	−	2.76602i	0.137317	−	0.107667i
$661$	−16.3429	+	28.3067i	−0.635665	+	1.10100i	0.350708	+	0.936485i	$0.385941\pi$
$661$	−16.3429	+	28.3067i	−0.635665	+	1.10100i	−0.986374	+	0.164520i	$0.947393\pi$
$662$	2.09083	−	3.62142i	0.0812623	−	0.140750i
$663$	2.05342	+	14.4294i	0.0797481	+	0.560393i
$664$	9.37837	+	5.41461i	0.363951	+	0.210127i
$665$	−0.691424	+	0.399194i	−0.0268123	+	0.0154801i
$666$	−8.90001	−	8.53525i	−0.344868	−	0.330734i
$667$	18.0084			0.697286
$668$	−4.66240	−	8.07551i	−0.180394	−	0.312451i
$669$	16.3646	−	12.8312i	0.632694	−	0.496082i
$670$	−5.56780	−	9.64371i	−0.215103	−	0.372569i
$671$	27.8064	+	16.0541i	1.07346	+	0.619760i
$672$	−0.189186	+	0.148337i	−0.00729801	+	0.00572222i
$673$	17.0895	+	9.86660i	0.658750	+	0.380329i	0.791800	−	0.610780i	$-0.209144\pi$
$673$	17.0895	+	9.86660i	0.658750	+	0.380329i	−0.133051	+	0.991109i	$0.542477\pi$
$674$	25.8541			0.995864
$675$	−4.21959	−	3.03234i	−0.162412	−	0.116715i
$676$	5.66523	+	9.81246i	0.217893	+	0.377402i
$677$	4.74370	−	8.21634i	0.182315	−	0.315779i	−0.760353	−	0.649510i	$-0.774974\pi$
$677$	4.74370	−	8.21634i	0.182315	−	0.315779i	0.942669	+	0.333730i	$0.108307\pi$
$678$	−11.9500	+	29.7253i	−0.458936	+	1.14159i
$679$	−0.0234822	−	0.0406724i	−0.000901165	−	0.00156086i
$680$	6.51243			0.249740
$681$	19.6788	+	7.91113i	0.754093	+	0.303155i
$682$	8.78994	−	11.4190i	0.336584	−	0.437256i
$683$			24.1664i			0.924703i	0.886697	+	0.462352i	$0.152994\pi$
$683$			24.1664i			0.924703i	−0.886697	+	0.462352i	$0.847006\pi$
$684$	12.4547	+	11.9442i	0.476216	+	0.456699i
$685$	6.24708	−	3.60675i	0.238689	−	0.137807i
$686$		−	1.94051i		−	0.0740889i
$687$	−18.4244	+	14.4462i	−0.702936	+	0.551157i
$688$	0.173390	−	0.100107i	0.00661044	−	0.00381654i
$689$	3.32334	−	1.91873i	0.126609	−	0.0730979i
$690$	2.94225	−	7.31881i	0.112010	−	0.278622i
$691$	−12.4677	+	21.5948i	−0.474295	+	0.821503i	−0.999567	−	0.0294313i	$-0.990630\pi$
$691$	−12.4677	+	21.5948i	−0.474295	+	0.821503i	0.525272	+	0.850935i	$0.323964\pi$
$692$	−0.626926	−	0.361956i	−0.0238321	−	0.0137595i
$693$	−1.03492	+	0.300642i	−0.0393133	+	0.0114204i
$694$	−21.5645	+	12.4503i	−0.818578	+	0.472606i
$695$	−0.205065	+	0.355183i	−0.00777855	+	0.0134729i
$696$	−0.964936	−	6.78064i	−0.0365758	−	0.257019i
$697$			0.239176i			0.00905942i
$698$		−	27.1625i		−	1.02812i
$699$	−0.433063	−	3.04315i	−0.0163799	−	0.115102i
$700$	0.0693993	−	0.120203i	0.00262305	−	0.00454325i
$701$	3.71436	−	2.14449i	0.140290	−	0.0809962i	−0.428212	−	0.903678i	$-0.640857\pi$
$701$	3.71436	−	2.14449i	0.140290	−	0.0809962i	0.568502	+	0.822682i	$0.307523\pi$
$702$	0.667098	−	6.68078i	0.0251780	−	0.252150i
$703$	−20.4761	−	11.8219i	−0.772270	−	0.445870i
$704$	1.29408	−	2.24142i	0.0487726	−	0.0844766i
$705$	5.32262	−	13.2399i	0.200462	−	0.498645i
$706$	14.9148	−	8.61106i	0.561326	−	0.324082i
$707$	−1.78836	+	1.03251i	−0.0672581	+	0.0388315i
$708$	18.3818	−	14.4128i	0.690832	−	0.541667i
$709$			30.0757i			1.12952i	0.825257	+	0.564758i	$0.191031\pi$
$709$			30.0757i			1.12952i	−0.825257	+	0.564758i	$0.808969\pi$
$710$	9.28503	−	5.36071i	0.348461	−	0.201184i
$711$	26.3853	−	27.5129i	0.989528	−	1.03182i
$712$			6.31328i			0.236600i
$713$	3.34822	−	25.1346i	0.125392	−	0.941298i
$714$	−1.45264	−	0.583979i	−0.0543636	−	0.0218549i
$715$	−3.34419			−0.125066
$716$	0.272448	+	0.471894i	0.0101819	+	0.0176355i
$717$	0.863927	−	2.14901i	0.0322640	−	0.0802561i
$718$	−10.4660	+	18.1276i	−0.390586	+	0.676515i
$719$	16.9853	+	29.4193i	0.633443	+	1.09716i	0.986843	+	0.161683i	$0.0516922\pi$
$719$	16.9853	+	29.4193i	0.633443	+	1.09716i	−0.353400	+	0.935472i	$0.614974\pi$
$720$	−2.91338	−	0.715677i	−0.108575	−	0.0266717i
$721$	0.134066			0.00499289
$722$	12.1997	+	7.04352i	0.454027	+	0.262133i
$723$	−28.7686	+	22.5569i	−1.06992	+	0.838900i
$724$	13.2629	+	7.65732i	0.492911	+	0.284582i
$725$	1.97712	+	3.42448i	0.0734285	+	0.127182i
$726$	−5.86292	+	4.59699i	−0.217593	+	0.170610i
$727$	−7.64523	−	13.2419i	−0.283546	−	0.491116i	0.688710	−	0.725037i	$-0.258178\pi$
$727$	−7.64523	−	13.2419i	−0.283546	−	0.491116i	−0.972256	+	0.233921i	$0.924844\pi$
$728$	0.179343			0.00664690
$729$	17.8570	−	20.2516i	0.661371	−	0.750059i
$730$	−7.32249	+	4.22764i	−0.271018	+	0.156472i
$731$	1.12919	+	0.651939i	0.0417647	+	0.0241128i
$732$	−3.02732	−	21.2730i	−0.111893	−	0.786274i
$733$	−7.52100	+	13.0268i	−0.277795	+	0.481154i	−0.970836	−	0.239743i	$-0.922937\pi$
$733$	−7.52100	+	13.0268i	−0.277795	+	0.481154i	0.693042	+	0.720897i	$0.256270\pi$
$734$	−12.5941	+	21.8135i	−0.464855	+	0.805152i
$735$	9.51492	−	7.46045i	0.350963	−	0.275183i
$736$		−	4.55419i		−	0.167870i
$737$	−14.4104	−	24.9595i	−0.530813	−	0.919396i
$738$	0.0262840	−	0.106997i	0.000967527	−	0.00393862i
$739$	−21.7153	−	12.5374i	−0.798812	−	0.461194i	0.0442436	−	0.999021i	$-0.485912\pi$
$739$	−21.7153	−	12.5374i	−0.798812	−	0.461194i	−0.843056	+	0.537826i	$0.819246\pi$
$740$	4.11043			0.151102
$741$	−1.81369	−	12.7449i	−0.0666276	−	0.468195i
$742$			0.412221i			0.0151331i
$743$	42.6682			1.56534			0.782672	−	0.622434i	$-0.213856\pi$
$743$	42.6682			1.56534			0.782672	+	0.622434i	$0.213856\pi$
$744$	−9.64327	+	0.0860836i	−0.353539	+	0.00315598i
$745$	−21.1439			−0.774652
$746$			11.6188i			0.425393i
$747$	7.75022	−	31.5497i	0.283566	−	1.15434i
$748$	16.8552			0.616288
$749$	−0.757005	−	0.437057i	−0.0276604	−	0.0159697i
$750$	1.71477	−	0.244025i	0.0626147	−	0.00891055i
$751$	13.8231	+	23.9422i	0.504411	+	0.873665i	0.999987	+	0.00510032i	$0.00162349\pi$
$751$	13.8231	+	23.9422i	0.504411	+	0.873665i	−0.495576	+	0.868564i	$0.665043\pi$
$752$		−	8.23865i		−	0.300433i
$753$	1.02022	+	1.30117i	0.0371790	+	0.0474174i
$754$	−2.55466	+	4.42480i	−0.0930352	+	0.161142i
$755$	8.08763	−	14.0082i	0.294339	−	0.509810i
$756$	0.585673	+	0.420884i	0.0213007	+	0.0153074i
$757$	−29.7395	−	17.1701i	−1.08090	−	0.624057i	−0.149760	−	0.988722i	$-0.547850\pi$
$757$	−29.7395	−	17.1701i	−1.08090	−	0.624057i	−0.931139	+	0.364665i	$0.881183\pi$
$758$	−21.7449	+	12.5544i	−0.789811	+	0.455997i
$759$	7.61504	−	18.9423i	0.276409	−	0.687561i
$760$	−5.75213			−0.208652
$761$	−0.261502	−	0.452935i	−0.00947944	−	0.0164189i	0.861247	−	0.508187i	$-0.169684\pi$
$761$	−0.261502	−	0.452935i	−0.00947944	−	0.0164189i	−0.870726	+	0.491768i	$0.836351\pi$
$762$	10.9474	+	13.9621i	0.396582	+	0.505794i
$763$	−0.662782	−	1.14797i	−0.0239943	−	0.0415594i
$764$	−17.5360	−	10.1244i	−0.634432	−	0.366289i
$765$	−5.45023	−	18.7617i	−0.197053	−	0.678329i
$766$	10.2284	+	5.90538i	0.369568	+	0.213370i
$767$	−17.4255			−0.629197
$768$	−1.71477	+	0.244025i	−0.0618766	+	0.00880551i
$769$	−7.69298	−	13.3246i	−0.277416	−	0.480499i	0.693326	−	0.720624i	$-0.256145\pi$
$769$	−7.69298	−	13.3246i	−0.277416	−	0.480499i	−0.970742	+	0.240126i	$0.922811\pi$
$770$	0.179617	−	0.311106i	0.00647294	−	0.0112115i
$771$	8.51296	+	3.42232i	0.306587	+	0.123252i
$772$	5.98112	+	10.3596i	0.215265	+	0.372850i
$773$	−28.7485			−1.03401			−0.517007	−	0.855981i	$-0.672954\pi$
$773$	−28.7485			−1.03401			−0.517007	+	0.855981i	$0.672954\pi$
$774$	−0.433508	−	0.415742i	−0.0155821	−	0.0149435i
$775$	5.14720	−	2.12281i	0.184893	−	0.0762535i
$776$		−	0.338364i		−	0.0121466i
$777$	−0.916858	−	0.368588i	−0.0328921	−	0.0132230i
$778$	−10.6464	+	6.14668i	−0.381691	+	0.220369i
$779$		−	0.211253i		−	0.00756893i
$780$	1.38090	+	1.76118i	0.0494443	+	0.0630603i
$781$	24.0312	−	13.8744i	0.859903	−	0.496465i
$782$	25.6853	−	14.8294i	0.918503	−	0.530298i
$783$	−18.7268	+	8.45458i	−0.669241	+	0.302142i
$784$	3.49037	−	6.04549i	0.124656	−	0.215910i
$785$	−19.4442	−	11.2261i	−0.693992	−	0.400676i
$786$	−9.11990	−	11.6314i	−0.325296	−	0.414877i
$787$	−34.1679	+	19.7269i	−1.21795	+	0.703186i	−0.964480	−	0.264156i	$-0.914907\pi$
$787$	−34.1679	+	19.7269i	−1.21795	+	0.703186i	−0.253475	+	0.967342i	$0.581573\pi$
$788$	0.549043	−	0.950970i	0.0195588	−	0.0338769i
$789$	8.71424	−	1.24010i	0.310235	−	0.0441488i
$790$			12.7067i			0.452085i
$791$			2.56733i			0.0912839i
$792$	−7.54032	−	1.85229i	−0.267934	−	0.0658183i
$793$	−8.01479	+	13.8820i	−0.284614	+	0.492965i
$794$	−11.7278	+	6.77103i	−0.416203	+	0.240295i
$795$	−4.04808	+	3.17401i	−0.143571	+	0.112571i
$796$	10.7314	+	6.19578i	0.380365	+	0.219604i
$797$	−10.6929	+	18.5207i	−0.378763	+	0.656036i	−0.990883	−	0.134729i	$-0.956984\pi$
$797$	−10.6929	+	18.5207i	−0.378763	+	0.656036i	0.612120	+	0.790765i	$0.290317\pi$
$798$	1.28305	+	0.515803i	0.0454195	+	0.0182592i
$799$	46.4654	−	26.8268i	1.64383	−	0.949064i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	18.1879	−	5.28357i	0.642640	−	0.186686i
$802$			27.0123i			0.953836i
$803$	−18.9518	+	10.9418i	−0.668795	+	0.386129i
$804$	−7.19421	+	17.8955i	−0.253720	+	0.631125i
$805$		−	0.632115i		−	0.0222791i
$806$	5.70080	+	4.38827i	0.200802	+	0.154570i
$807$	−0.410944	+	1.02222i	−0.0144659	+	0.0359837i
$808$	−14.8778			−0.523399
$809$	15.5907	+	27.0039i	0.548140	+	0.949407i	0.998402	+	0.0565104i	$0.0179974\pi$
$809$	15.5907	+	27.0039i	0.548140	+	0.949407i	−0.450262	+	0.892897i	$0.648669\pi$
$810$	0.376405	+	8.99213i	0.0132255	+	0.315951i
$811$	−18.3000	+	31.6966i	−0.642601	+	1.11302i	0.342249	+	0.939609i	$0.388811\pi$
$811$	−18.3000	+	31.6966i	−0.642601	+	1.11302i	−0.984850	+	0.173408i	$0.944522\pi$
$812$	−0.274422	−	0.475312i	−0.00963032	−	0.0166802i
$813$	6.36971	+	44.7602i	0.223396	+	1.56981i
$814$	10.6385			0.372878
$815$	12.7617	+	7.36799i	0.447024	+	0.258089i
$816$	−6.95996	−	8.87660i	−0.243647	−	0.310743i
$817$	−0.997364	−	0.575829i	−0.0348934	−	0.0201457i
$818$	−7.12882	−	12.3475i	−0.249253	−	0.431719i
$819$	−0.150092	−	0.516670i	−0.00524463	−	0.0180539i
$820$	0.0183630	+	0.0318057i	0.000641265	+	0.00111070i
$821$	−13.4659			−0.469963			−0.234982	−	0.972000i	$-0.575503\pi$
$821$	−13.4659			−0.469963			−0.234982	+	0.972000i	$0.575503\pi$
$822$	−11.5925	−	4.66032i	−0.404334	−	0.162547i
$823$	9.06292	−	5.23248i	0.315913	−	0.182393i	−0.333656	−	0.942695i	$-0.608282\pi$
$823$	9.06292	−	5.23248i	0.315913	−	0.182393i	0.649570	+	0.760302i	$0.274949\pi$
$824$	0.836499	+	0.482953i	0.0291408	+	0.0168245i
$825$	4.43812	−	0.631578i	0.154516	−	0.0219887i
$826$	0.935923	−	1.62107i	0.0325649	−	0.0564041i
$827$	10.8412	−	18.7775i	0.376985	−	0.652957i	−0.613637	−	0.789588i	$-0.710294\pi$
$827$	10.8412	−	18.7775i	0.376985	−	0.652957i	0.990622	+	0.136631i	$0.0436275\pi$
$828$	−13.1202	+	3.81139i	−0.455957	+	0.132455i
$829$			9.97742i			0.346530i	0.984875	+	0.173265i	$0.0554317\pi$
$829$			9.97742i			0.346530i	−0.984875	+	0.173265i	$0.944568\pi$
$830$	5.41461	+	9.37837i	0.187944	+	0.325528i
$831$	0.898039	+	6.31055i	0.0311526	+	0.218911i
$832$	1.11900	+	0.646055i	0.0387944	+	0.0223979i
$833$	45.4615			1.57515
$834$	0.703280	−	0.100082i	0.0243526	−	0.00346556i
$835$		−	9.32479i		−	0.322698i
$836$	−14.8875			−0.514894
$837$	8.31842	+	27.7093i	0.287527	+	0.957773i
$838$	−19.9657			−0.689704
$839$		−	51.6912i		−	1.78458i	−0.451464	−	0.892289i	$-0.649098\pi$
$839$		−	51.6912i		−	1.78458i	0.451464	−	0.892289i	$-0.350902\pi$
$840$	−0.238008	+	0.0338704i	−0.00821207	+	0.00116864i
$841$	−13.3640			−0.460826
$842$	22.3420	+	12.8991i	0.769955	+	0.444534i
$843$	2.40152	+	16.8756i	0.0827129	+	0.581226i
$844$	−9.89042	−	17.1307i	−0.340442	−	0.589663i
$845$			11.3305i			0.389779i
$846$	−23.7348	+	6.89491i	−0.816018	+	0.237052i
$847$	−0.298514	+	0.517042i	−0.0102571	+	0.0177658i
$848$	−1.48496	+	2.57203i	−0.0509938	+	0.0883238i
$849$	−36.9164	+	5.25349i	−1.26697	+	0.180299i
$850$	5.63993	+	3.25621i	0.193448	+	0.111687i
$851$	16.2117	−	9.35983i	0.555730	−	0.320851i
$852$	−17.2299	−	6.92663i	−0.590286	−	0.237302i
$853$	−50.4561			−1.72758			−0.863792	−	0.503849i	$-0.831917\pi$
$853$	−50.4561			−1.72758			−0.863792	+	0.503849i	$0.831917\pi$
$854$	−0.860950	−	1.49121i	−0.0294611	−	0.0510281i
$855$	4.81394	+	16.5713i	0.164633	+	0.566728i
$856$	−3.14886	−	5.45398i	−0.107626	−	0.186413i
$857$	8.64284	+	4.98994i	0.295234	+	0.170453i	0.640300	−	0.768125i	$-0.278810\pi$
$857$	8.64284	+	4.98994i	0.295234	+	0.170453i	−0.345066	+	0.938578i	$0.612143\pi$
$858$	3.57401	+	4.55822i	0.122015	+	0.155615i
$859$	36.6353	+	21.1514i	1.24998	+	0.721677i	0.971106	−	0.238650i	$-0.0767048\pi$
$859$	36.6353	+	21.1514i	1.24998	+	0.721677i	0.278876	+	0.960327i	$0.410038\pi$
$860$	0.200214			0.00682724
$861$	−0.00124393	−	0.00874110i	−4.23929e−5	−	0.000297896i
$862$	−12.0843	−	20.9306i	−0.411593	−	0.712900i
$863$	−8.76573	+	15.1827i	−0.298389	+	0.516825i	−0.975768	−	0.218810i	$-0.929783\pi$
$863$	−8.76573	+	15.1827i	−0.298389	+	0.516825i	0.677379	+	0.735634i	$0.263116\pi$
$864$	2.13810	+	4.73588i	0.0727398	+	0.161118i
$865$	−0.361956	−	0.626926i	−0.0123069	−	0.0213161i
$866$	16.7926			0.570635
$867$	16.4173	−	40.8379i	0.557562	−	1.38693i
$868$	−0.714425	+	0.294643i	−0.0242491	+	0.0100008i
$869$			32.8871i			1.11562i
$870$	2.55466	−	6.35467i	0.0866110	−	0.215444i
$871$	12.4607	−	7.19421i	0.422216	−	0.243767i
$872$		−	9.55027i		−	0.323413i
$873$	−0.974794	+	0.283176i	−0.0329918	+	0.00958405i
$874$	−22.6867	+	13.0981i	−0.767387	+	0.443051i
$875$	0.120203	−	0.0693993i	0.00406361	−	0.00234612i
$876$	13.5881	+	5.46258i	0.459099	+	0.184564i
$877$	−21.9817	+	38.0735i	−0.742270	+	1.28565i	0.209189	+	0.977875i	$0.432917\pi$
$877$	−21.9817	+	38.0735i	−0.742270	+	1.28565i	−0.951459	+	0.307774i	$0.900416\pi$
$878$	7.29522	+	4.21190i	0.246202	+	0.142145i
$879$	−4.40063	+	3.45044i	−0.148430	+	0.116380i
$880$	2.24142	−	1.29408i	0.0755581	−	0.0436235i
$881$	5.41706	−	9.38263i	0.182505	−	0.316109i	−0.760228	−	0.649657i	$-0.774913\pi$
$881$	5.41706	−	9.38263i	0.182505	−	0.316109i	0.942733	+	0.333548i	$0.108246\pi$
$882$	−20.3376	−	4.99595i	−0.684801	−	0.168223i
$883$		−	23.3128i		−	0.784538i	−0.919850	−	0.392269i	$-0.871690\pi$
$883$		−	23.3128i		−	0.784538i	0.919850	−	0.392269i	$-0.128310\pi$
$884$			8.41477i			0.283019i
$885$	23.1255	−	3.29094i	0.777357	−	0.110624i
$886$	−2.84698	+	4.93112i	−0.0956462	+	0.165664i
$887$	17.6083	−	10.1662i	0.591229	−	0.341346i	−0.174354	−	0.984683i	$-0.555784\pi$
$887$	17.6083	−	10.1662i	0.591229	−	0.341346i	0.765583	+	0.643337i	$0.222450\pi$
$888$	−4.39289	−	5.60262i	−0.147416	−	0.188012i
$889$	1.23130	+	0.710890i	0.0412964	+	0.0238425i
$890$	−3.15664	+	5.46746i	−0.105811	+	0.183270i
$891$	0.974199	+	23.2731i	0.0326369	+	0.779678i
$892$	10.3976	−	6.00306i	0.348137	−	0.200997i
$893$	−41.0408	+	23.6949i	−1.37338	+	0.792920i
$894$	22.5969	+	28.8197i	0.755753	+	0.963874i
$895$			0.544897i			0.0182139i
$896$	−0.120203	+	0.0693993i	−0.00401570	+	0.00231847i
$897$	9.45671	+	3.80172i	0.315750	+	0.126936i
$898$			27.1961i			0.907545i
$899$	2.90714	−	21.8235i	0.0969587	−	0.727855i
$900$	−2.16523	−	2.07649i	−0.0721742	−	0.0692162i
$901$	−19.3414			−0.644356
$902$	0.0475265	+	0.0823184i	0.00158246	+	0.00274090i
$903$	−0.0446590	−	0.0179535i	−0.00148616	−	0.000597455i
$904$	−9.24841	+	16.0187i	−0.307598	+	0.532775i
$905$	7.65732	+	13.2629i	0.254538	+	0.440873i
$906$	−27.7369	+	3.94717i	−0.921497	+	0.131136i
$907$	0.665627			0.0221018			0.0110509	−	0.999939i	$-0.496482\pi$
$907$	0.665627			0.0221018			0.0110509	+	0.999939i	$0.496482\pi$
$908$	10.6047	+	6.12264i	0.351930	+	0.203187i
$909$	12.4512	+	42.8615i	0.412979	+	1.42162i
$910$	0.155316	+	0.0896715i	0.00514866	+	0.00297258i
$911$	25.9660	+	44.9745i	0.860293	+	1.49007i	0.871646	+	0.490136i	$0.163053\pi$
$911$	25.9660	+	44.9745i	0.860293	+	1.49007i	−0.0113524	+	0.999936i	$0.503614\pi$
$912$	6.14742	+	7.84031i	0.203561	+	0.259618i
$913$	14.0139	+	24.2728i	0.463792	+	0.803312i
$914$	−22.1433			−0.732435
$915$	8.01479	−	19.9367i	0.264961	−	0.659085i
$916$	−11.7063	+	6.75865i	−0.386788	+	0.223312i
$917$	−1.02575	−	0.592218i	−0.0338733	−	0.0195568i
$918$	−19.7479	+	27.4798i	−0.651777	+	0.906967i
$919$	−3.34135	+	5.78738i	−0.110221	+	0.190908i	−0.915859	−	0.401500i	$-0.868489\pi$
$919$	−3.34135	+	5.78738i	−0.110221	+	0.190908i	0.805638	+	0.592408i	$0.201822\pi$
$920$	2.27709	−	3.94404i	0.0750735	−	0.130031i
$921$	−8.40393	−	10.7182i	−0.276919	−	0.353177i
$922$		−	9.56201i		−	0.314908i
$923$	6.92663	+	11.9973i	0.227993	+	0.394895i
$924$	−0.616005	+	0.0876622i	−0.0202651	+	0.00288387i
$925$	3.55974	+	2.05521i	0.117043	+	0.0675750i
$926$	−6.71621			−0.220708
$927$	0.691277	−	2.81405i	0.0227045	−	0.0924257i
$928$		−	3.95424i		−	0.129804i
$929$	−10.6588			−0.349704			−0.174852	−	0.984595i	$-0.555945\pi$
$929$	−10.6588			−0.349704			−0.174852	+	0.984595i	$0.555945\pi$
$930$	−8.39436	−	4.74708i	−0.275262	−	0.155663i
$931$	−40.1541			−1.31600
$932$		−	1.77466i		−	0.0581310i
$933$	−3.76394	−	26.4493i	−0.123226	−	0.865912i
$934$	5.96215			0.195087
$935$	14.5971	+	8.42762i	0.477375	+	0.275613i
$936$	0.924734	−	3.76441i	0.0302259	−	0.123044i
$937$	−10.1412	−	17.5650i	−0.331297	−	0.573824i	0.651469	−	0.758675i	$-0.274153\pi$
$937$	−10.1412	−	17.5650i	−0.331297	−	0.573824i	−0.982767	+	0.184851i	$0.940820\pi$
$938$			1.54561i			0.0504658i
$939$	−13.1316	+	10.2962i	−0.428535	+	0.336005i
$940$	4.11933	−	7.13488i	0.134358	−	0.232714i
$941$	−15.3368	+	26.5640i	−0.499964	+	0.865963i	−1.00000		4.17483e-5i	$-0.999987\pi$
$941$	−15.3368	+	26.5640i	−0.499964	+	0.865963i	0.500036	+	0.866005i	$0.333320\pi$
$942$	5.47890	+	38.5004i	0.178512	+	1.25441i
$943$	0.144849	+	0.0836286i	0.00471693	+	0.00272332i
$944$	11.6793	−	6.74303i	0.380128	−	0.219467i
$945$	0.296766	+	0.657333i	0.00965379	+	0.0213830i
$946$	0.518187			0.0168477
$947$	23.6453	+	40.9549i	0.768369	+	1.33085i	0.938447	+	0.345424i	$0.112265\pi$
$947$	23.6453	+	40.9549i	0.768369	+	1.33085i	−0.170077	+	0.985431i	$0.554402\pi$
$948$	17.3196	−	13.5799i	0.562514	−	0.441055i
$949$	−5.46258	−	9.46147i	−0.177323	−	0.307132i
$950$	−4.98149	−	2.87607i	−0.161621	−	0.0933119i
$951$	3.89609	−	3.05484i	0.126339	−	0.0990600i
$952$	−0.782814	−	0.451958i	−0.0253711	−	0.0146480i
$953$	−53.3463			−1.72806			−0.864028	−	0.503444i	$-0.832066\pi$
$953$	−53.3463			−1.72806			−0.864028	+	0.503444i	$0.832066\pi$
$954$	8.65253	+	2.12551i	0.280136	+	0.0688158i
$955$	−10.1244	−	17.5360i	−0.327619	−	0.567453i
$956$	0.668618	−	1.15808i	0.0216246	−	0.0374550i
$957$	6.61188	−	16.4469i	0.213732	−	0.531654i
$958$	18.0796	+	31.3148i	0.584125	+	1.01174i
$959$	−1.00122			−0.0323312
$960$	−1.60705	−	0.646055i	−0.0518673	−	0.0208513i
$961$	−29.9190	−	8.11511i	−0.965128	−	0.261778i
$962$			5.31113i			0.171238i
$963$	−13.0771	+	13.6360i	−0.421404	+	0.439413i
$964$	−18.2787	+	10.5532i	−0.588718	+	0.339897i
$965$			11.9622i			0.385078i
$966$	−0.861589	+	0.675553i	−0.0277212	+	0.0217356i
$967$	1.32180	−	0.763144i	0.0425064	−	0.0245411i	−0.478596	−	0.878035i	$-0.658854\pi$
$967$	1.32180	−	0.763144i	0.0425064	−	0.0245411i	0.521103	+	0.853494i	$0.325521\pi$
$968$	−3.72512	+	2.15070i	−0.119730	+	0.0691261i
$969$	−24.2014	+	60.2007i	−0.777462	+	1.93392i
$970$	0.169182	−	0.293032i	0.00543211	−	0.00940868i
$971$	−41.8314	−	24.1513i	−1.34243	−	0.775054i	−0.355268	−	0.934764i	$-0.615611\pi$
$971$	−41.8314	−	24.1513i	−1.34243	−	0.775054i	−0.987164	+	0.159711i	$0.948944\pi$
$972$	11.8542	−	10.1231i	0.380224	−	0.324699i
$973$	0.0492989	−	0.0284627i	0.00158045	−	0.000912473i
$974$	−1.07963	+	1.86997i	−0.0345935	+	0.0599177i
$975$	0.315308	+	2.21568i	0.0100979	+	0.0709585i
$976$		−	12.4057i		−	0.397098i
$977$		−	45.8703i		−	1.46752i	−0.679408	−	0.733761i	$-0.737763\pi$
$977$		−	45.8703i		−	1.46752i	0.679408	−	0.733761i	$-0.262237\pi$
$978$	−3.59595	−	25.2689i	−0.114986	−	0.808010i
$979$	−8.16991	+	14.1507i	−0.261111	+	0.452258i
$980$	6.04549	−	3.49037i	0.193116	−	0.111496i
$981$	−27.5134	+	7.99259i	−0.878435	+	0.255184i
$982$	4.13336	+	2.38639i	0.131901	+	0.0761529i
$983$	−1.90512	+	3.29977i	−0.0607639	+	0.105246i	−0.894807	−	0.446453i	$-0.852687\pi$
$983$	−1.90512	+	3.29977i	−0.0607639	+	0.105246i	0.834043	+	0.551699i	$0.186020\pi$
$984$	0.0237270	−	0.0590206i	0.000756391	−	0.00188151i
$985$	0.950970	−	0.549043i	0.0303004	−	0.0174940i
$986$	22.3016	−	12.8759i	0.710229	−	0.410051i
$987$	−1.55864	+	1.22210i	−0.0496120	+	0.0388997i
$988$		−	7.43239i		−	0.236456i
$989$	0.789652	−	0.455906i	0.0251095	−	0.0144970i
$990$	−5.60396	−	5.37429i	−0.178106	−	0.170806i
$991$			11.1470i			0.354098i	0.984202	+	0.177049i	$0.0566550\pi$
$991$			11.1470i			0.354098i	−0.984202	+	0.177049i	$0.943345\pi$
$992$	−5.51901	−	0.735196i	−0.175229	−	0.0233425i
$993$	−6.72013	−	2.70158i	−0.213257	−	0.0857320i
$994$	−1.48812			−0.0472003
$995$	6.19578	+	10.7314i	0.196420	+	0.340209i
$996$	6.99627	−	17.4031i	0.221685	−	0.551438i
$997$	−23.4726	+	40.6557i	−0.743384	+	1.28758i	0.207562	+	0.978222i	$0.433447\pi$
$997$	−23.4726	+	40.6557i	−0.743384	+	1.28758i	−0.950946	+	0.309357i	$0.899886\pi$
$998$	−6.61852	−	11.4636i	−0.209505	−	0.362874i
$999$	−12.4642	+	17.3443i	−0.394350	+	0.548750i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.o.d.161.1	✓	36
3.2	odd	2	inner	930.2.o.d.161.13	yes	36
31.26	odd	6	inner	930.2.o.d.491.4	yes	36
93.26	even	6	inner	930.2.o.d.491.10	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.o.d.161.1	✓	36	1.1	even	1	trivial
930.2.o.d.161.13	yes	36	3.2	odd	2	inner
930.2.o.d.491.4	yes	36	31.26	odd	6	inner
930.2.o.d.491.10	yes	36	93.26	even	6	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.71477 + 0.244025i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.244025 + 1.71477i) q^{6} +(0.0693993 + 0.120203i) q^{7} +1.00000i q^{8} +(2.88090 - 0.836897i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.71477 + 0.244025i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.244025 + 1.71477i) q^{6} +(0.0693993 + 0.120203i) q^{7} +1.00000i q^{8} +(2.88090 - 0.836897i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-1.29408 + 2.24142i) q^{11} +(1.71477 - 0.244025i) q^{12} +(-1.11900 - 0.646055i) q^{13} +(0.120203 - 0.0693993i) q^{14} +(1.60705 + 0.646055i) q^{15} +1.00000 q^{16} +(3.25621 + 5.63993i) q^{17} +(-0.836897 - 2.88090i) q^{18} +(-2.87607 - 4.98149i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-0.148337 - 0.189186i) q^{21} +(2.24142 + 1.29408i) q^{22} +4.55419 q^{23} +(-0.244025 - 1.71477i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.646055 + 1.11900i) q^{26} +(-4.73588 + 2.13810i) q^{27} +(-0.0693993 - 0.120203i) q^{28} +3.95424 q^{29} +(0.646055 - 1.60705i) q^{30} +(0.735196 - 5.51901i) q^{31} -1.00000i q^{32} +(1.67210 - 4.15931i) q^{33} +(5.63993 - 3.25621i) q^{34} -0.138799i q^{35} +(-2.88090 + 0.836897i) q^{36} +(3.55974 - 2.05521i) q^{37} +(-4.98149 + 2.87607i) q^{38} +(2.07649 + 0.834774i) q^{39} +(0.500000 - 0.866025i) q^{40} +(0.0318057 + 0.0183630i) q^{41} +(-0.189186 + 0.148337i) q^{42} +(0.173390 - 0.100107i) q^{43} +(1.29408 - 2.24142i) q^{44} +(-2.91338 - 0.715677i) q^{45} -4.55419i q^{46} -8.23865i q^{47} +(-1.71477 + 0.244025i) q^{48} +(3.49037 - 6.04549i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-6.95996 - 8.87660i) q^{51} +(1.11900 + 0.646055i) q^{52} +(-1.48496 + 2.57203i) q^{53} +(2.13810 + 4.73588i) q^{54} +(2.24142 - 1.29408i) q^{55} +(-0.120203 + 0.0693993i) q^{56} +(6.14742 + 7.84031i) q^{57} -3.95424i q^{58} +(11.6793 - 6.74303i) q^{59} +(-1.60705 - 0.646055i) q^{60} -12.4057i q^{61} +(-5.51901 - 0.735196i) q^{62} +(0.300530 + 0.288213i) q^{63} -1.00000 q^{64} +(0.646055 + 1.11900i) q^{65} +(-4.15931 - 1.67210i) q^{66} +(-5.56780 + 9.64371i) q^{67} +(-3.25621 - 5.63993i) q^{68} +(-7.80940 + 1.11134i) q^{69} -0.138799 q^{70} +(-9.28503 - 5.36071i) q^{71} +(0.836897 + 2.88090i) q^{72} +(7.32249 + 4.22764i) q^{73} +(-2.05521 - 3.55974i) q^{74} +(-1.06872 - 1.36303i) q^{75} +(2.87607 + 4.98149i) q^{76} -0.359234 q^{77} +(0.834774 - 2.07649i) q^{78} +(11.0043 - 6.35336i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(7.59921 - 4.82204i) q^{81} +(0.0183630 - 0.0318057i) q^{82} +(5.41461 - 9.37837i) q^{83} +(0.148337 + 0.189186i) q^{84} -6.51243i q^{85} +(-0.100107 - 0.173390i) q^{86} +(-6.78064 + 0.964936i) q^{87} +(-2.24142 - 1.29408i) q^{88} +6.31328 q^{89} +(-0.715677 + 2.91338i) q^{90} -0.179343i q^{91} -4.55419 q^{92} +(0.0860836 + 9.64327i) q^{93} -8.23865 q^{94} +5.75213i q^{95} +(0.244025 + 1.71477i) q^{96} -0.338364 q^{97} +(-6.04549 - 3.49037i) q^{98} +(-1.85229 + 7.54032i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{4} - 8 q^{7} + 8 q^{9}+O(q^{10}) \) 36 * q - 36 * q^4 - 8 * q^7 + 8 * q^9	\( 36 q - 36 q^{4} - 8 q^{7} + 8 q^{9} - 18 q^{10} + 36 q^{16} - 4 q^{18} - 4 q^{19} + 72 q^{21} - 18 q^{22} + 18 q^{25} + 8 q^{28} + 52 q^{31} - 36 q^{33} + 18 q^{34} - 8 q^{36} - 54 q^{37} - 8 q^{39} + 18 q^{40} + 12 q^{42} - 18 q^{43} + 4 q^{45} - 62 q^{49} - 10 q^{51} - 18 q^{55} + 12 q^{57} + 88 q^{63} - 36 q^{64} - 4 q^{66} + 10 q^{67} + 46 q^{69} + 16 q^{70} + 4 q^{72} + 24 q^{73} + 4 q^{76} + 92 q^{78} + 42 q^{79} + 4 q^{81} - 12 q^{82} - 72 q^{84} - 16 q^{87} + 18 q^{88} + 8 q^{90} + 48 q^{93} - 92 q^{94} - 80 q^{97} - 18 q^{99}+O(q^{100}) \) 36 * q - 36 * q^4 - 8 * q^7 + 8 * q^9 - 18 * q^10 + 36 * q^16 - 4 * q^18 - 4 * q^19 + 72 * q^21 - 18 * q^22 + 18 * q^25 + 8 * q^28 + 52 * q^31 - 36 * q^33 + 18 * q^34 - 8 * q^36 - 54 * q^37 - 8 * q^39 + 18 * q^40 + 12 * q^42 - 18 * q^43 + 4 * q^45 - 62 * q^49 - 10 * q^51 - 18 * q^55 + 12 * q^57 + 88 * q^63 - 36 * q^64 - 4 * q^66 + 10 * q^67 + 46 * q^69 + 16 * q^70 + 4 * q^72 + 24 * q^73 + 4 * q^76 + 92 * q^78 + 42 * q^79 + 4 * q^81 - 12 * q^82 - 72 * q^84 - 16 * q^87 + 18 * q^88 + 8 * q^90 + 48 * q^93 - 92 * q^94 - 80 * q^97 - 18 * q^99

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