LMFDB - Embedded newform 930.2.o.d.161.11

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			161.11
Character	$\chi$	$=$	930.161
Dual form			930.2.o.d.491.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-1.40749 + 1.00944i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.00944 - 1.40749i) q^{6} +(-2.21698 - 3.83992i) q^{7} -1.00000i q^{8} +(0.962053 - 2.84156i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-1.40749 + 1.00944i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.00944 - 1.40749i) q^{6} +(-2.21698 - 3.83992i) q^{7} -1.00000i q^{8} +(0.962053 - 2.84156i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(0.0757934 - 0.131278i) q^{11} +(1.40749 - 1.00944i) q^{12} +(-0.295242 - 0.170458i) q^{13} +(3.83992 - 2.21698i) q^{14} +(-1.72364 + 0.170458i) q^{15} +1.00000 q^{16} +(3.50983 + 6.07921i) q^{17} +(2.84156 + 0.962053i) q^{18} +(3.09517 + 5.36099i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(6.99655 + 3.16674i) q^{21} +(0.131278 + 0.0757934i) q^{22} -4.85473 q^{23} +(1.00944 + 1.40749i) q^{24} +(0.500000 + 0.866025i) q^{25} +(0.170458 - 0.295242i) q^{26} +(1.51431 + 4.97060i) q^{27} +(2.21698 + 3.83992i) q^{28} +10.2242 q^{29} +(-0.170458 - 1.72364i) q^{30} +(-3.15848 + 4.58519i) q^{31} +1.00000i q^{32} +(0.0258392 + 0.261281i) q^{33} +(-6.07921 + 3.50983i) q^{34} -4.43396i q^{35} +(-0.962053 + 2.84156i) q^{36} +(-3.45531 + 1.99493i) q^{37} +(-5.36099 + 3.09517i) q^{38} +(0.587617 - 0.0581117i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-0.0353071 - 0.0203846i) q^{41} +(-3.16674 + 6.99655i) q^{42} +(6.78199 - 3.91558i) q^{43} +(-0.0757934 + 0.131278i) q^{44} +(2.25394 - 1.97984i) q^{45} -4.85473i q^{46} -0.796378i q^{47} +(-1.40749 + 1.00944i) q^{48} +(-6.32999 + 10.9639i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-11.0767 - 5.01345i) q^{51} +(0.295242 + 0.170458i) q^{52} +(6.46710 - 11.2014i) q^{53} +(-4.97060 + 1.51431i) q^{54} +(0.131278 - 0.0757934i) q^{55} +(-3.83992 + 2.21698i) q^{56} +(-9.76802 - 4.42114i) q^{57} +10.2242i q^{58} +(1.54372 - 0.891267i) q^{59} +(1.72364 - 0.170458i) q^{60} +12.6420i q^{61} +(-4.58519 - 3.15848i) q^{62} +(-13.0442 + 2.60547i) q^{63} -1.00000 q^{64} +(-0.170458 - 0.295242i) q^{65} +(-0.261281 + 0.0258392i) q^{66} +(-3.90015 + 6.75526i) q^{67} +(-3.50983 - 6.07921i) q^{68} +(6.83298 - 4.90056i) q^{69} +4.43396 q^{70} +(6.62466 + 3.82475i) q^{71} +(-2.84156 - 0.962053i) q^{72} +(4.70206 + 2.71474i) q^{73} +(-1.99493 - 3.45531i) q^{74} +(-1.57795 - 0.714201i) q^{75} +(-3.09517 - 5.36099i) q^{76} -0.672130 q^{77} +(0.0581117 + 0.587617i) q^{78} +(13.6994 - 7.90934i) q^{79} +(0.866025 + 0.500000i) q^{80} +(-7.14891 - 5.46746i) q^{81} +(0.0203846 - 0.0353071i) q^{82} +(-1.37723 + 2.38544i) q^{83} +(-6.99655 - 3.16674i) q^{84} +7.01967i q^{85} +(3.91558 + 6.78199i) q^{86} +(-14.3905 + 10.3208i) q^{87} +(-0.131278 - 0.0757934i) q^{88} +0.746707 q^{89} +(1.97984 + 2.25394i) q^{90} +1.51161i q^{91} +4.85473 q^{92} +(-0.182955 - 9.64192i) q^{93} +0.796378 q^{94} +6.19034i q^{95} +(-1.00944 - 1.40749i) q^{96} -6.38190 q^{97} +(-10.9639 - 6.32999i) q^{98} +(-0.300117 - 0.341668i) 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
$3$	−1.40749	+	1.00944i	−0.812614	+	0.582802i
$3$	−1.40749	+	1.00944i	−0.812614	+	0.582802i
$4$	−1.00000			−0.500000
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	−1.00944	−	1.40749i	−0.412103	−	0.574605i
$7$	−2.21698	−	3.83992i	−0.837939	−	1.45135i	−0.891615	−	0.452795i	$-0.850427\pi$
$7$	−2.21698	−	3.83992i	−0.837939	−	1.45135i	0.0536754	−	0.998558i	$-0.482906\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.962053	−	2.84156i	0.320684	−	0.947186i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	0.0757934	−	0.131278i	0.0228526	−	0.0395818i	−0.854373	−	0.519660i	$-0.826059\pi$
$11$	0.0757934	−	0.131278i	0.0228526	−	0.0395818i	0.877226	+	0.480079i	$0.159392\pi$
$12$	1.40749	−	1.00944i	0.406307	−	0.291401i
$13$	−0.295242	−	0.170458i	−0.0818853	−	0.0472765i	0.458498	−	0.888695i	$-0.348388\pi$
$13$	−0.295242	−	0.170458i	−0.0818853	−	0.0472765i	−0.540384	+	0.841419i	$0.681721\pi$
$14$	3.83992	−	2.21698i	1.02626	−	0.592513i
$15$	−1.72364	+	0.170458i	−0.445043	+	0.0440120i
$16$	1.00000			0.250000
$17$	3.50983	+	6.07921i	0.851259	+	1.47442i	0.880072	+	0.474840i	$0.157494\pi$
$17$	3.50983	+	6.07921i	0.851259	+	1.47442i	−0.0288127	+	0.999585i	$0.509173\pi$
$18$	2.84156	+	0.962053i	0.669762	+	0.226758i
$19$	3.09517	+	5.36099i	0.710080	+	1.22990i	0.964827	+	0.262887i	$0.0846747\pi$
$19$	3.09517	+	5.36099i	0.710080	+	1.22990i	−0.254746	+	0.967008i	$0.581992\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$	6.99655	+	3.16674i	1.52677	+	0.691038i
$22$	0.131278	+	0.0757934i	0.0279886	+	0.0161592i
$23$	−4.85473			−1.01228			−0.506140	−	0.862451i	$-0.668928\pi$
$23$	−4.85473			−1.01228			−0.506140	+	0.862451i	$0.668928\pi$
$24$	1.00944	+	1.40749i	0.206052	+	0.287303i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	0.170458	−	0.295242i	0.0334295	−	0.0579016i
$27$	1.51431	+	4.97060i	0.291429	+	0.956593i
$28$	2.21698	+	3.83992i	0.418970	+	0.725677i
$29$	10.2242			1.89860			0.949298	−	0.314379i	$-0.101796\pi$
$29$	10.2242			1.89860			0.949298	+	0.314379i	$0.101796\pi$
$30$	−0.170458	−	1.72364i	−0.0311212	−	0.314693i
$31$	−3.15848	+	4.58519i	−0.567280	+	0.823525i
$31$	−3.15848	+	4.58519i	−0.567280	+	0.823525i
$32$			1.00000i			0.176777i
$33$	0.0258392	+	0.261281i	0.00449802	+	0.0454833i
$34$	−6.07921	+	3.50983i	−1.04258	+	0.601931i
$35$		−	4.43396i		−	0.749476i
$36$	−0.962053	+	2.84156i	−0.160342	+	0.473593i
$37$	−3.45531	+	1.99493i	−0.568050	+	0.327964i	−0.756370	−	0.654144i	$-0.773029\pi$
$37$	−3.45531	+	1.99493i	−0.568050	+	0.327964i	0.188320	+	0.982108i	$0.439696\pi$
$38$	−5.36099	+	3.09517i	−0.869667	+	0.502103i
$39$	0.587617	−	0.0581117i	0.0940940	−	0.00930532i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−0.0353071	−	0.0203846i	−0.00551404	−	0.00318353i	0.497240	−	0.867613i	$-0.334347\pi$
$41$	−0.0353071	−	0.0203846i	−0.00551404	−	0.00318353i	−0.502754	+	0.864429i	$0.667680\pi$
$42$	−3.16674	+	6.99655i	−0.488638	+	1.07959i
$43$	6.78199	−	3.91558i	1.03424	−	0.597121i	0.116046	−	0.993244i	$-0.462978\pi$
$43$	6.78199	−	3.91558i	1.03424	−	0.597121i	0.918197	+	0.396123i	$0.129645\pi$
$44$	−0.0757934	+	0.131278i	−0.0114263	+	0.0197909i
$45$	2.25394	−	1.97984i	0.335998	−	0.295136i
$46$		−	4.85473i		−	0.715790i
$47$		−	0.796378i		−	0.116164i	−0.998312	−	0.0580818i	$-0.981502\pi$
$47$		−	0.796378i		−	0.116164i	0.998312	−	0.0580818i	$-0.0184984\pi$
$48$	−1.40749	+	1.00944i	−0.203154	+	0.145700i
$49$	−6.32999	+	10.9639i	−0.904284	+	1.56627i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	−11.0767	−	5.01345i	−1.55104	−	0.702023i
$52$	0.295242	+	0.170458i	0.0409426	+	0.0236382i
$53$	6.46710	−	11.2014i	0.888325	−	1.53862i	0.0464704	−	0.998920i	$-0.485203\pi$
$53$	6.46710	−	11.2014i	0.888325	−	1.53862i	0.841855	−	0.539704i	$-0.181464\pi$
$54$	−4.97060	+	1.51431i	−0.676413	+	0.206071i
$55$	0.131278	−	0.0757934i	0.0177015	−	0.0102200i
$56$	−3.83992	+	2.21698i	−0.513131	+	0.296256i
$57$	−9.76802	−	4.42114i	−1.29381	−	0.585595i
$58$			10.2242i			1.34251i
$59$	1.54372	−	0.891267i	0.200975	−	0.116033i	−0.396135	−	0.918192i	$-0.629649\pi$
$59$	1.54372	−	0.891267i	0.200975	−	0.116033i	0.597110	+	0.802159i	$0.296315\pi$
$60$	1.72364	−	0.170458i	0.222521	−	0.0220060i
$61$			12.6420i			1.61865i	0.587364	+	0.809323i	$0.300166\pi$
$61$			12.6420i			1.61865i	−0.587364	+	0.809323i	$0.699834\pi$
$62$	−4.58519	−	3.15848i	−0.582320	−	0.401128i
$63$	−13.0442	+	2.60547i	−1.64342	+	0.328258i
$64$	−1.00000			−0.125000
$65$	−0.170458	−	0.295242i	−0.0211427	−	0.0366202i
$66$	−0.261281	+	0.0258392i	−0.0321615	+	0.00318058i
$67$	−3.90015	+	6.75526i	−0.476479	+	0.825286i	−0.999637	−	0.0269500i	$-0.991421\pi$
$67$	−3.90015	+	6.75526i	−0.476479	+	0.825286i	0.523158	+	0.852236i	$0.324754\pi$
$68$	−3.50983	−	6.07921i	−0.425630	−	0.737212i
$69$	6.83298	−	4.90056i	0.822594	−	0.589959i
$70$	4.43396			0.529959
$71$	6.62466	+	3.82475i	0.786202	+	0.453914i	0.838624	−	0.544711i	$-0.183361\pi$
$71$	6.62466	+	3.82475i	0.786202	+	0.453914i	−0.0524218	+	0.998625i	$0.516694\pi$
$72$	−2.84156	−	0.962053i	−0.334881	−	0.113379i
$73$	4.70206	+	2.71474i	0.550335	+	0.317736i	0.749257	−	0.662279i	$-0.230411\pi$
$73$	4.70206	+	2.71474i	0.550335	+	0.317736i	−0.198922	+	0.980015i	$0.563744\pi$
$74$	−1.99493	−	3.45531i	−0.231905	−	0.401672i
$75$	−1.57795	−	0.714201i	−0.182206	−	0.0824688i
$76$	−3.09517	−	5.36099i	−0.355040	−	0.614948i
$77$	−0.672130			−0.0765963
$78$	0.0581117	+	0.587617i	0.00657986	+	0.0665345i
$79$	13.6994	−	7.90934i	1.54130	−	0.889870i	0.542543	−	0.840028i	$-0.317462\pi$
$79$	13.6994	−	7.90934i	1.54130	−	0.889870i	0.998757	−	0.0498417i	$-0.0158717\pi$
$80$	0.866025	+	0.500000i	0.0968246	+	0.0559017i
$81$	−7.14891	−	5.46746i	−0.794323	−	0.607496i
$82$	0.0203846	−	0.0353071i	0.00225110	−	0.00389902i
$83$	−1.37723	+	2.38544i	−0.151171	+	0.261836i	−0.931658	−	0.363336i	$-0.881638\pi$
$83$	−1.37723	+	2.38544i	−0.151171	+	0.261836i	0.780487	+	0.625172i	$0.214971\pi$
$84$	−6.99655	−	3.16674i	−0.763386	−	0.345519i
$85$			7.01967i			0.761390i
$86$	3.91558	+	6.78199i	0.422228	+	0.731321i
$87$	−14.3905	+	10.3208i	−1.54283	+	1.10650i
$88$	−0.131278	−	0.0757934i	−0.0139943	−	0.00807960i
$89$	0.746707			0.0791508			0.0395754	−	0.999217i	$-0.487399\pi$
$89$	0.746707			0.0791508			0.0395754	+	0.999217i	$0.487399\pi$
$90$	1.97984	+	2.25394i	0.208693	+	0.237586i
$91$			1.51161i			0.158459i
$92$	4.85473			0.506140
$93$	−0.182955	−	9.64192i	−0.0189715	−	0.999820i
$94$	0.796378			0.0821401
$95$			6.19034i			0.635115i
$96$	−1.00944	−	1.40749i	−0.103026	−	0.143651i
$97$	−6.38190			−0.647983			−0.323992	−	0.946060i	$-0.605025\pi$
$97$	−6.38190			−0.647983			−0.323992	+	0.946060i	$0.605025\pi$
$98$	−10.9639	−	6.32999i	−1.10752	−	0.639426i
$99$	−0.300117	−	0.341668i	−0.0301629	−	0.0343389i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$			4.63251i			0.460952i	0.973078	+	0.230476i	$0.0740283\pi$
$101$			4.63251i			0.460952i	−0.973078	+	0.230476i	$0.925972\pi$
$102$	5.01345	−	11.0767i	0.496405	−	1.09675i
$103$	−6.44116	+	11.1564i	−0.634666	+	1.09927i	0.351920	+	0.936030i	$0.385529\pi$
$103$	−6.44116	+	11.1564i	−0.634666	+	1.09927i	−0.986586	+	0.163244i	$0.947804\pi$
$104$	−0.170458	+	0.295242i	−0.0167148	+	0.0289508i
$105$	4.47582	+	6.24075i	0.436796	+	0.609035i
$106$	11.2014	+	6.46710i	1.08797	+	0.628141i
$107$	−7.29005	+	4.20891i	−0.704756	+	0.406891i	−0.809116	−	0.587649i	$-0.800054\pi$
$107$	−7.29005	+	4.20891i	−0.704756	+	0.406891i	0.104361	+	0.994540i	$0.466720\pi$
$108$	−1.51431	−	4.97060i	−0.145714	−	0.478296i
$109$	4.76919			0.456806			0.228403	−	0.973567i	$-0.426650\pi$
$109$	4.76919			0.456806			0.228403	+	0.973567i	$0.426650\pi$
$110$	0.0757934	+	0.131278i	0.00722662	+	0.0125169i
$111$	2.84955	−	6.29578i	0.270468	−	0.597569i
$112$	−2.21698	−	3.83992i	−0.209485	−	0.362838i
$113$	13.5788	+	7.83972i	1.27739	+	0.737499i	0.976367	−	0.216119i	$-0.0693400\pi$
$113$	13.5788	+	7.83972i	1.27739	+	0.737499i	0.301019	+	0.953618i	$0.402673\pi$
$114$	4.42114	−	9.76802i	0.414078	−	0.914859i
$115$	−4.20432	−	2.42736i	−0.392054	−	0.226353i
$116$	−10.2242			−0.949298
$117$	−0.768404	+	0.674957i	−0.0710390	+	0.0623998i
$118$	0.891267	+	1.54372i	0.0820478	+	0.142111i
$119$	15.5625	−	26.9550i	1.42661	−	2.47096i
$120$	0.170458	+	1.72364i	0.0155606	+	0.157346i
$121$	5.48851	+	9.50638i	0.498956	+	0.864216i
$122$	−12.6420			−1.14456
$123$	0.0702714	−	0.00694941i	0.00633616	−	0.000626607i
$124$	3.15848	−	4.58519i	0.283640	−	0.411762i
$125$			1.00000i			0.0894427i
$126$	−2.60547	−	13.0442i	−0.232113	−	1.16207i
$127$	12.1984	−	7.04278i	1.08244	−	0.624945i	0.150884	−	0.988551i	$-0.451788\pi$
$127$	12.1984	−	7.04278i	1.08244	−	0.624945i	0.931553	+	0.363606i	$0.118455\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−5.59302	+	12.3572i	−0.492438	+	1.08799i
$130$	0.295242	−	0.170458i	0.0258944	−	0.0149501i
$131$	−1.83163	+	1.05749i	−0.160030	+	0.0923936i	−0.577876	−	0.816124i	$-0.696118\pi$
$131$	−1.83163	+	1.05749i	−0.160030	+	0.0923936i	0.417846	+	0.908518i	$0.362785\pi$
$132$	−0.0258392	−	0.261281i	−0.00224901	−	0.0227416i
$133$	13.7238	−	23.7704i	1.19001	−	2.06115i
$134$	−6.75526	−	3.90015i	−0.583565	−	0.336922i
$135$	−1.17387	+	5.06182i	−0.101031	+	0.435652i
$136$	6.07921	−	3.50983i	0.521288	−	0.300966i
$137$	−8.98731	+	15.5665i	−0.767837	+	1.32993i	0.170896	+	0.985289i	$0.445334\pi$
$137$	−8.98731	+	15.5665i	−0.767837	+	1.32993i	−0.938733	+	0.344644i	$0.888000\pi$
$138$	4.90056	+	6.83298i	0.417164	+	0.581661i
$139$		−	5.72097i		−	0.485246i	−0.970121	−	0.242623i	$-0.921992\pi$
$139$		−	5.72097i		−	0.485246i	0.970121	−	0.242623i	$-0.0780078\pi$
$140$			4.43396i			0.374738i
$141$	0.803898	+	1.12089i	0.0677004	+	0.0943963i
$142$	−3.82475	+	6.62466i	−0.320966	+	0.555929i
$143$	−0.0447547	+	0.0258392i	−0.00374258	+	0.00216078i
$144$	0.962053	−	2.84156i	0.0801711	−	0.236797i
$145$	8.85446	+	5.11212i	0.735323	+	0.424539i
$146$	−2.71474	+	4.70206i	−0.224673	+	0.389145i
$147$	−2.15799	−	21.8213i	−0.177988	−	1.79979i
$148$	3.45531	−	1.99493i	0.284025	−	0.163982i
$149$	14.6868	−	8.47941i	1.20319	−	0.694661i	0.241925	−	0.970295i	$-0.422221\pi$
$149$	14.6868	−	8.47941i	1.20319	−	0.694661i	0.961263	+	0.275634i	$0.0888878\pi$
$150$	0.714201	−	1.57795i	0.0583142	−	0.128839i
$151$			6.58155i			0.535599i	0.963475	+	0.267799i	$0.0862965\pi$
$151$			6.58155i			0.535599i	−0.963475	+	0.267799i	$0.913704\pi$
$152$	5.36099	−	3.09517i	0.434834	−	0.251051i
$153$	20.6511	−	4.12487i	1.66954	−	0.333476i
$154$		−	0.672130i		−	0.0541617i
$155$	−5.02792	+	2.39165i	−0.403852	+	0.192102i
$156$	−0.587617	+	0.0581117i	−0.0470470	+	0.00465266i
$157$	−4.31735			−0.344562			−0.172281	−	0.985048i	$-0.555114\pi$
$157$	−4.31735			−0.344562			−0.172281	+	0.985048i	$0.555114\pi$
$158$	7.90934	+	13.6994i	0.629233	+	1.08986i
$159$	2.20474	+	22.2940i	0.174847	+	1.76803i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	10.7628	+	18.6418i	0.848229	+	1.46918i
$162$	5.46746	−	7.14891i	0.429564	−	0.561671i
$163$	−13.7076			−1.07367			−0.536833	−	0.843689i	$-0.680379\pi$
$163$	−13.7076			−1.07367			−0.536833	+	0.843689i	$0.680379\pi$
$164$	0.0353071	+	0.0203846i	0.00275702	+	0.00159177i
$165$	−0.108263	+	0.239196i	−0.00842829	+	0.0186214i
$166$	−2.38544	−	1.37723i	−0.185146	−	0.106894i
$167$	−10.0226	−	17.3596i	−0.775572	−	1.34333i	−0.934473	−	0.356035i	$-0.884128\pi$
$167$	−10.0226	−	17.3596i	−0.775572	−	1.34333i	0.158901	−	0.987295i	$-0.449205\pi$
$168$	3.16674	−	6.99655i	0.244319	−	0.539796i
$169$	−6.44189	−	11.1577i	−0.495530	−	0.858283i
$170$	−7.01967			−0.538384
$171$	18.2113	−	3.63754i	1.39265	−	0.278170i
$172$	−6.78199	+	3.91558i	−0.517122	+	0.298560i
$173$	3.40914	+	1.96827i	0.259192	+	0.149644i	0.623966	−	0.781452i	$-0.285520\pi$
$173$	3.40914	+	1.96827i	0.259192	+	0.149644i	−0.364774	+	0.931096i	$0.618854\pi$
$174$	−10.3208	−	14.3905i	−0.782417	−	1.09094i
$175$	2.21698	−	3.83992i	0.167588	−	0.290271i
$176$	0.0757934	−	0.131278i	0.00571314	−	0.00989545i
$177$	−1.27309	+	2.81274i	−0.0956911	+	0.211419i
$178$			0.746707i			0.0559680i
$179$	−8.59467	−	14.8864i	−0.642396	−	1.11266i	−0.984896	−	0.173145i	$-0.944607\pi$
$179$	−8.59467	−	14.8864i	−0.642396	−	1.11266i	0.342501	−	0.939518i	$-0.388726\pi$
$180$	−2.25394	+	1.97984i	−0.167999	+	0.147568i
$181$	−1.68735	−	0.974191i	−0.125420	−	0.0724111i	0.435978	−	0.899958i	$-0.356403\pi$
$181$	−1.68735	−	0.974191i	−0.125420	−	0.0724111i	−0.561397	+	0.827546i	$0.689736\pi$
$182$	−1.51161			−0.112048
$183$	−12.7614	−	17.7935i	−0.943349	−	1.31533i
$184$			4.85473i			0.357895i
$185$	−3.98985			−0.293340
$186$	9.64192	−	0.182955i	0.706980	−	0.0134149i
$187$	1.06409			0.0778139
$188$			0.796378i			0.0580818i
$189$	15.7295	−	16.8345i	1.14415	−	1.22453i
$190$	−6.19034			−0.449094
$191$	15.3677	+	8.87254i	1.11197	+	0.641995i	0.939338	−	0.342992i	$-0.111440\pi$
$191$	15.3677	+	8.87254i	1.11197	+	0.641995i	0.172629	+	0.984987i	$0.444774\pi$
$192$	1.40749	−	1.00944i	0.101577	−	0.0728502i
$193$	−9.44857	−	16.3654i	−0.680123	−	1.17801i	−0.974943	−	0.222454i	$-0.928593\pi$
$193$	−9.44857	−	16.3654i	−0.680123	−	1.17801i	0.294820	−	0.955553i	$-0.404740\pi$
$194$		−	6.38190i		−	0.458194i
$195$	0.537947	+	0.243482i	0.0385232	+	0.0174361i
$196$	6.32999	−	10.9639i	0.452142	−	0.783133i
$197$	7.36648	−	12.7591i	0.524840	−	0.909049i	−0.474742	−	0.880125i	$-0.657459\pi$
$197$	7.36648	−	12.7591i	0.524840	−	0.909049i	0.999582	−	0.0289241i	$-0.00920811\pi$
$198$	0.341668	−	0.300117i	0.0242813	−	0.0213284i
$199$	8.06105	+	4.65405i	0.571433	+	0.329917i	0.757721	−	0.652578i	$-0.226313\pi$
$199$	8.06105	+	4.65405i	0.571433	+	0.329917i	−0.186289	+	0.982495i	$0.559646\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	−1.32962	−	13.4449i	−0.0937843	−	0.948332i
$202$	−4.63251			−0.325942
$203$	−22.6669	−	39.2603i	−1.59091	−	2.75553i
$204$	11.0767	+	5.01345i	0.775521	+	0.351012i
$205$	−0.0203846	−	0.0353071i	−0.00142372	−	0.00246595i
$206$	−11.1564	−	6.44116i	−0.777304	−	0.448777i
$207$	−4.67050	+	13.7950i	−0.324623	+	0.958818i
$208$	−0.295242	−	0.170458i	−0.0204713	−	0.0118191i
$209$	0.938373			0.0649086
$210$	−6.24075	+	4.47582i	−0.430653	+	0.308861i
$211$	−8.47373	−	14.6769i	−0.583355	−	1.01040i	−0.995078	−	0.0990921i	$-0.968406\pi$
$211$	−8.47373	−	14.6769i	−0.583355	−	1.01040i	0.411723	−	0.911309i	$-0.364927\pi$
$212$	−6.46710	+	11.2014i	−0.444163	+	0.769312i
$213$	−13.1850	+	1.30392i	−0.903421	+	0.0893428i
$214$	−4.20891	−	7.29005i	−0.287715	−	0.498338i
$215$	7.83117			0.534081
$216$	4.97060	−	1.51431i	0.338207	−	0.103036i
$217$	24.6091	+	1.96305i	1.67057	+	0.133260i
$218$			4.76919i			0.323010i
$219$	−9.35847	+	0.925496i	−0.632387	+	0.0625392i
$220$	−0.131278	+	0.0757934i	−0.00885076	+	0.00510999i
$221$		−	2.39311i		−	0.160978i
$222$	6.29578	+	2.84955i	0.422545	+	0.191250i
$223$	−21.5409	+	12.4367i	−1.44249	+	0.832821i	−0.998015	−	0.0629710i	$-0.979942\pi$
$223$	−21.5409	+	12.4367i	−1.44249	+	0.832821i	−0.444473	+	0.895792i	$0.646609\pi$
$224$	3.83992	−	2.21698i	0.256565	−	0.148128i
$225$	2.94189	−	0.587617i	0.196126	−	0.0391744i
$226$	−7.83972	+	13.5788i	−0.521490	+	0.903248i
$227$	21.1435	+	12.2072i	1.40334	+	0.810221i	0.994734	−	0.102488i	$-0.0326802\pi$
$227$	21.1435	+	12.2072i	1.40334	+	0.810221i	0.408610	+	0.912709i	$0.366014\pi$
$228$	9.76802	+	4.42114i	0.646903	+	0.292797i
$229$	−8.99933	+	5.19577i	−0.594693	+	0.343346i	−0.766951	−	0.641706i	$-0.778227\pi$
$229$	−8.99933	+	5.19577i	−0.594693	+	0.343346i	0.172258	+	0.985052i	$0.444894\pi$
$230$	2.42736	−	4.20432i	0.160056	−	0.277224i
$231$	0.946015	−	0.678476i	0.0622432	−	0.0446404i
$232$		−	10.2242i		−	0.671255i
$233$			13.8174i			0.905207i	0.891712	+	0.452603i	$0.149505\pi$
$233$			13.8174i			0.905207i	−0.891712	+	0.452603i	$0.850495\pi$
$234$	−0.674957	−	0.768404i	−0.0441233	−	0.0502321i
$235$	0.398189	−	0.689684i	0.0259750	−	0.0449900i
$236$	−1.54372	+	0.891267i	−0.100488	+	0.0580165i
$237$	−11.2977	+	24.9610i	−0.733865	+	1.62139i
$238$	26.9550	+	15.5625i	1.74723	+	1.00876i
$239$	0.937720	−	1.62418i	0.0606561	−	0.105059i	−0.834103	−	0.551609i	$-0.814014\pi$
$239$	0.937720	−	1.62418i	0.0606561	−	0.105059i	0.894759	+	0.446550i	$0.147347\pi$
$240$	−1.72364	+	0.170458i	−0.111261	+	0.0110030i
$241$	3.75160	−	2.16599i	0.241662	−	0.139524i	−0.374278	−	0.927316i	$-0.622110\pi$
$241$	3.75160	−	2.16599i	0.241662	−	0.139524i	0.615940	+	0.787793i	$0.288776\pi$
$242$	−9.50638	+	5.48851i	−0.611093	+	0.352815i
$243$	15.5811	+	0.478986i	0.999528	+	0.0307269i
$244$		−	12.6420i		−	0.809323i
$245$	−10.9639	+	6.32999i	−0.700456	+	0.404408i
$246$	0.00694941	+	0.0702714i	0.000443078	+	0.00448034i
$247$		−	2.11038i		−	0.134280i
$248$	4.58519	+	3.15848i	0.291160	+	0.200564i
$249$	−0.469520	−	4.74771i	−0.0297546	−	0.300874i
$250$	−1.00000			−0.0632456
$251$	1.41418	+	2.44943i	0.0892620	+	0.154606i	0.907199	−	0.420701i	$-0.138216\pi$
$251$	1.41418	+	2.44943i	0.0892620	+	0.154606i	−0.817937	+	0.575307i	$0.804882\pi$
$252$	13.0442	−	2.60547i	0.821708	−	0.164129i
$253$	−0.367956	+	0.637319i	−0.0231332	+	0.0400679i
$254$	7.04278	+	12.1984i	0.441903	+	0.765399i
$255$	−7.08595	−	9.88011i	−0.443739	−	0.618716i
$256$	1.00000			0.0625000
$257$	6.04700	+	3.49124i	0.377202	+	0.217777i	0.676600	−	0.736351i	$-0.263453\pi$
$257$	6.04700	+	3.49124i	0.377202	+	0.217777i	−0.299398	+	0.954128i	$0.596786\pi$
$258$	−12.3572	−	5.59302i	−0.769324	−	0.348206i
$259$	15.3207	+	8.84542i	0.951983	+	0.549627i
$260$	0.170458	+	0.295242i	0.0105713	+	0.0183101i
$261$	9.83627	−	29.0528i	0.608850	−	1.79832i
$262$	−1.05749	−	1.83163i	−0.0653321	−	0.113159i
$263$	17.4149			1.07385			0.536924	−	0.843630i	$-0.319586\pi$
$263$	17.4149			1.07385			0.536924	+	0.843630i	$0.319586\pi$
$264$	0.261281	−	0.0258392i	0.0160808	−	0.00159029i
$265$	11.2014	−	6.46710i	0.688094	−	0.397271i
$266$	23.7704	+	13.7238i	1.45746	+	0.841463i
$267$	−1.05098	+	0.753757i	−0.0643191	+	0.0461292i
$268$	3.90015	−	6.75526i	0.238240	−	0.412643i
$269$	−8.86812	+	15.3600i	−0.540699	+	0.936517i	0.458166	+	0.888867i	$0.348507\pi$
$269$	−8.86812	+	15.3600i	−0.540699	+	0.936517i	−0.998864	+	0.0476505i	$0.984827\pi$
$270$	−5.06182	−	1.17387i	−0.308053	−	0.0714395i
$271$			7.23882i			0.439727i	0.975531	+	0.219863i	$0.0705612\pi$
$271$			7.23882i			0.439727i	−0.975531	+	0.219863i	$0.929439\pi$
$272$	3.50983	+	6.07921i	0.212815	+	0.368606i
$273$	−1.52588	−	2.12757i	−0.0923503	−	0.128766i
$274$	−15.5665	−	8.98731i	−0.940405	−	0.542943i
$275$	0.151587			0.00914103
$276$	−6.83298	+	4.90056i	−0.411297	+	0.294979i
$277$		−	1.92186i		−	0.115473i	−0.998332	−	0.0577367i	$-0.981612\pi$
$277$		−	1.92186i		−	0.115473i	0.998332	−	0.0577367i	$-0.0183884\pi$
$278$	5.72097			0.343121
$279$	9.99046	+	13.3862i	0.598113	+	0.801412i
$280$	−4.43396			−0.264980
$281$		−	4.20127i		−	0.250627i	−0.992117	−	0.125313i	$-0.960006\pi$
$281$		−	4.20127i		−	0.250627i	0.992117	−	0.125313i	$-0.0399936\pi$
$282$	−1.12089	+	0.803898i	−0.0667483	+	0.0478714i
$283$	0.572852			0.0340525			0.0170263	−	0.999855i	$-0.494580\pi$
$283$	0.572852			0.0340525			0.0170263	+	0.999855i	$0.494580\pi$
$284$	−6.62466	−	3.82475i	−0.393101	−	0.226957i
$285$	−6.24879	−	8.71283i	−0.370146	−	0.516104i
$286$	−0.0258392	−	0.0447547i	−0.00152790	−	0.00264640i
$287$			0.180769i			0.0106704i
$288$	2.84156	+	0.962053i	0.167440	+	0.0566895i
$289$	−16.1379	+	27.9516i	−0.949285	+	1.64421i
$290$	−5.11212	+	8.85446i	−0.300194	+	0.519952i
$291$	8.98245	−	6.44216i	0.526561	−	0.377646i
$292$	−4.70206	−	2.71474i	−0.275167	−	0.158868i
$293$	18.8306	−	10.8719i	1.10010	−	0.635141i	0.163850	−	0.986485i	$-0.447609\pi$
$293$	18.8306	−	10.8719i	1.10010	−	0.635141i	0.936246	+	0.351344i	$0.114275\pi$
$294$	21.8213	−	2.15799i	1.27264	−	0.125857i
$295$	1.78253			0.103783
$296$	1.99493	+	3.45531i	0.115953	+	0.200836i
$297$	0.767305	+	0.177943i	0.0445236	+	0.0103253i
$298$	8.47941	+	14.6868i	0.491199	+	0.850782i
$299$	1.43332	+	0.827526i	0.0828908	+	0.0478570i
$300$	1.57795	+	0.714201i	0.0911028	+	0.0412344i
$301$	−30.0710	−	17.3615i	−1.73327	−	1.00070i
$302$	−6.58155			−0.378726
$303$	−4.67625	−	6.52021i	−0.268644	−	0.374576i
$304$	3.09517	+	5.36099i	0.177520	+	0.307474i
$305$	−6.32101	+	10.9483i	−0.361940	+	0.626899i
$306$	4.12487	+	20.6511i	0.235803	+	1.18054i
$307$	5.01125	+	8.67974i	0.286007	+	0.495379i	0.972853	−	0.231424i	$-0.0743386\pi$
$307$	5.01125	+	8.67974i	0.286007	+	0.495379i	−0.686846	+	0.726803i	$0.741005\pi$
$308$	0.672130			0.0382981
$309$	−2.19589	−	22.2045i	−0.124920	−	1.26317i
$310$	−2.39165	−	5.02792i	−0.135837	−	0.285567i
$311$		−	33.6401i		−	1.90755i	−0.300517	−	0.953776i	$-0.597159\pi$
$311$		−	33.6401i		−	1.90755i	0.300517	−	0.953776i	$-0.402841\pi$
$312$	−0.0581117	−	0.587617i	−0.00328993	−	0.0332672i
$313$	7.16424	−	4.13628i	0.404947	−	0.233796i	−0.283669	−	0.958922i	$-0.591552\pi$
$313$	7.16424	−	4.13628i	0.404947	−	0.233796i	0.688616	+	0.725126i	$0.258218\pi$
$314$		−	4.31735i		−	0.243642i
$315$	−12.5993	−	4.26570i	−0.709893	−	0.240345i
$316$	−13.6994	+	7.90934i	−0.770650	+	0.444935i
$317$	−22.3713	+	12.9161i	−1.25649	+	0.725438i	−0.972391	−	0.233356i	$-0.925029\pi$
$317$	−22.3713	+	12.9161i	−1.25649	+	0.725438i	−0.284104	+	0.958794i	$0.591696\pi$
$318$	−22.2940	+	2.20474i	−1.25018	+	0.123635i
$319$	0.774931	−	1.34222i	0.0433878	−	0.0751498i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	6.01202	−	13.2829i	0.335558	−	0.741378i
$322$	−18.6418	+	10.7628i	−1.03886	+	0.599789i
$323$	−21.7270	+	37.6323i	−1.20893	+	2.09392i
$324$	7.14891	+	5.46746i	0.397162	+	0.303748i
$325$		−	0.340916i		−	0.0189106i
$326$		−	13.7076i		−	0.759196i
$327$	−6.71259	+	4.81422i	−0.371207	+	0.266227i
$328$	−0.0203846	+	0.0353071i	−0.00112555	+	0.00194951i
$329$	−3.05803	+	1.76555i	−0.168595	+	0.0973381i
$330$	−0.239196	−	0.108263i	−0.0131673	−	0.00595970i
$331$	10.4215	+	6.01687i	0.572818	+	0.330717i	0.758274	−	0.651936i	$-0.226043\pi$
$331$	10.4215	+	6.01687i	0.572818	+	0.330717i	−0.185456	+	0.982653i	$0.559376\pi$
$332$	1.37723	−	2.38544i	0.0755854	−	0.130918i
$333$	2.34450	+	11.7377i	0.128478	+	0.643222i
$334$	17.3596	−	10.0226i	0.949878	−	0.548412i
$335$	−6.75526	+	3.90015i	−0.369079	+	0.213088i
$336$	6.99655	+	3.16674i	0.381693	+	0.172760i
$337$			4.89013i			0.266382i	0.991090	+	0.133191i	$0.0425224\pi$
$337$			4.89013i			0.266382i	−0.991090	+	0.133191i	$0.957478\pi$
$338$	11.1577	−	6.44189i	0.606898	−	0.350393i
$339$	−27.0258	+	2.67268i	−1.46784	+	0.145160i
$340$		−	7.01967i		−	0.380695i
$341$	0.362543	+	0.762167i	0.0196328	+	0.0412736i
$342$	3.63754	+	18.2113i	0.196696	+	0.984753i
$343$	25.0961			1.35506
$344$	−3.91558	−	6.78199i	−0.211114	−	0.365660i
$345$	8.36781	−	0.827526i	0.450508	−	0.0445525i
$346$	−1.96827	+	3.40914i	−0.105815	+	0.183276i
$347$	−2.42056	−	4.19254i	−0.129943	−	0.225067i	0.793712	−	0.608294i	$-0.208146\pi$
$347$	−2.42056	−	4.19254i	−0.129943	−	0.225067i	−0.923654	+	0.383227i	$0.874813\pi$
$348$	14.3905	−	10.3208i	0.771413	−	0.553252i
$349$	11.9589			0.640144			0.320072	−	0.947393i	$-0.396293\pi$
$349$	11.9589			0.640144			0.320072	+	0.947393i	$0.396293\pi$
$350$	3.83992	+	2.21698i	0.205252	+	0.118503i
$351$	0.400191	−	1.72565i	0.0213606	−	0.0921086i
$352$	0.131278	+	0.0757934i	0.00699714	+	0.00403980i
$353$	−1.15263	−	1.99642i	−0.0613484	−	0.106259i	0.833720	−	0.552187i	$-0.186207\pi$
$353$	−1.15263	−	1.99642i	−0.0613484	−	0.106259i	−0.895068	+	0.445929i	$0.852873\pi$
$354$	−2.81274	−	1.27309i	−0.149496	−	0.0676638i
$355$	3.82475	+	6.62466i	0.202996	+	0.351600i
$356$	−0.746707			−0.0395754
$357$	5.30548	+	53.6482i	0.280796	+	2.83936i
$358$	14.8864	−	8.59467i	0.786771	−	0.454242i
$359$	−10.5554	−	6.09415i	−0.557091	−	0.321637i	0.194886	−	0.980826i	$-0.437566\pi$
$359$	−10.5554	−	6.09415i	−0.557091	−	0.321637i	−0.751977	+	0.659189i	$0.770900\pi$
$360$	−1.97984	−	2.25394i	−0.104346	−	0.118793i
$361$	−9.66013	+	16.7318i	−0.508428	+	0.880623i
$362$	0.974191	−	1.68735i	0.0512024	−	0.0886851i
$363$	−17.3212	−	7.83980i	−0.909125	−	0.411483i
$364$		−	1.51161i		−	0.0792296i
$365$	2.71474	+	4.70206i	0.142096	+	0.246117i
$366$	17.7935	−	12.7614i	0.930082	−	0.667049i
$367$	−25.0740	−	14.4765i	−1.30885	−	0.755665i	−0.326946	−	0.945043i	$-0.606020\pi$
$367$	−25.0740	−	14.4765i	−1.30885	−	0.755665i	−0.981904	+	0.189377i	$0.939353\pi$
$368$	−4.85473			−0.253070
$369$	−0.0918912	+	0.0807161i	−0.00478366	+	0.00420191i
$370$		−	3.98985i		−	0.207423i
$371$	−57.3497			−2.97745
$372$	0.182955	+	9.64192i	0.00948576	+	0.499910i
$373$	−17.3060			−0.896073			−0.448036	−	0.894015i	$-0.647876\pi$
$373$	−17.3060			−0.896073			−0.448036	+	0.894015i	$0.647876\pi$
$374$			1.06409i			0.0550227i
$375$	−1.00944	−	1.40749i	−0.0521274	−	0.0726824i
$376$	−0.796378			−0.0410701
$377$	−3.01862	−	1.74280i	−0.155467	−	0.0897589i
$378$	16.8345	+	15.7295i	0.865875	+	0.809039i
$379$	−12.7591	−	22.0994i	−0.655391	−	1.13517i	−0.981796	−	0.189941i	$-0.939170\pi$
$379$	−12.7591	−	22.0994i	−0.655391	−	1.13517i	0.326404	−	0.945230i	$-0.394163\pi$
$380$		−	6.19034i		−	0.317558i
$381$	−10.0599	+	22.2263i	−0.515385	+	1.13869i
$382$	−8.87254	+	15.3677i	−0.453959	+	0.786280i
$383$	10.8456	−	18.7852i	0.554186	−	0.959878i	−0.443781	−	0.896135i	$-0.646363\pi$
$383$	10.8456	−	18.7852i	0.554186	−	0.959878i	0.997966	−	0.0637424i	$-0.0203036\pi$
$384$	1.00944	+	1.40749i	0.0515129	+	0.0718256i
$385$	−0.582081	−	0.336065i	−0.0296656	−	0.0171274i
$386$	16.3654	−	9.44857i	0.832977	−	0.480919i
$387$	−4.60172	−	23.0384i	−0.233919	−	1.17111i
$388$	6.38190			0.323992
$389$	−10.6493	−	18.4451i	−0.539941	−	0.935205i	−0.998907	−	0.0467513i	$-0.985113\pi$
$389$	−10.6493	−	18.4451i	−0.539941	−	0.935205i	0.458965	−	0.888454i	$-0.348220\pi$
$390$	−0.243482	+	0.537947i	−0.0123292	+	0.0272400i
$391$	−17.0393	−	29.5129i	−0.861713	−	1.49253i
$392$	10.9639	+	6.32999i	0.553759	+	0.319713i
$393$	1.51052	−	3.33734i	0.0761959	−	0.168346i
$394$	12.7591	+	7.36648i	0.642795	+	0.371118i
$395$	15.8187			0.795924
$396$	0.300117	+	0.341668i	0.0150814	+	0.0171695i
$397$	−5.77806	−	10.0079i	−0.289992	−	0.502282i	0.683815	−	0.729655i	$-0.260319\pi$
$397$	−5.77806	−	10.0079i	−0.289992	−	0.502282i	−0.973808	+	0.227374i	$0.926986\pi$
$398$	−4.65405	+	8.06105i	−0.233286	+	0.404064i
$399$	4.67867	+	47.3100i	0.234227	+	2.36846i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−1.19650			−0.0597505			−0.0298752	−	0.999554i	$-0.509511\pi$
$401$	−1.19650			−0.0597505			−0.0298752	+	0.999554i	$0.509511\pi$
$402$	13.4449	−	1.32962i	0.670572	−	0.0663155i
$403$	1.71410	−	0.815351i	0.0853852	−	0.0406155i
$404$		−	4.63251i		−	0.230476i
$405$	−3.45740	−	8.30941i	−0.171800	−	0.412898i
$406$	39.2603	−	22.6669i	1.94846	−	1.12494i
$407$			0.604809i			0.0299793i
$408$	−5.01345	+	11.0767i	−0.248203	+	0.548376i
$409$	−10.7369	+	6.19894i	−0.530904	+	0.306518i	−0.741385	−	0.671080i	$-0.765831\pi$
$409$	−10.7369	+	6.19894i	−0.530904	+	0.306518i	0.210480	+	0.977598i	$0.432497\pi$
$410$	0.0353071	−	0.0203846i	0.00174369	−	0.00100672i
$411$	−3.06391	−	30.9818i	−0.151132	−	1.52822i
$412$	6.44116	−	11.1564i	0.317333	−	0.549637i
$413$	−6.84479	−	3.95184i	−0.336810	−	0.194457i
$414$	−13.7950	−	4.67050i	−0.677987	−	0.229543i
$415$	−2.38544	+	1.37723i	−0.117096	+	0.0676057i
$416$	0.170458	−	0.295242i	0.00835738	−	0.0144754i
$417$	5.77499	+	8.05220i	0.282802	+	0.394318i
$418$			0.938373i			0.0458973i
$419$			14.9065i			0.728232i	0.931354	+	0.364116i	$0.118629\pi$
$419$			14.9065i			0.728232i	−0.931354	+	0.364116i	$0.881371\pi$
$420$	−4.47582	−	6.24075i	−0.218398	−	0.304517i
$421$	−1.94022	+	3.36057i	−0.0945607	+	0.163784i	−0.909425	−	0.415868i	$-0.863478\pi$
$421$	−1.94022	+	3.36057i	−0.0945607	+	0.163784i	0.814864	+	0.579652i	$0.196811\pi$
$422$	14.6769	−	8.47373i	0.714462	−	0.412495i
$423$	−2.26295	−	0.766158i	−0.110029	−	0.0372519i
$424$	−11.2014	−	6.46710i	−0.543986	−	0.314070i
$425$	−3.50983	+	6.07921i	−0.170252	+	0.294885i
$426$	−1.30392	−	13.1850i	−0.0631749	−	0.638815i
$427$	48.5444	−	28.0271i	2.34923	−	1.35633i
$428$	7.29005	−	4.20891i	0.352378	−	0.203445i
$429$	0.0369087	−	0.0815456i	0.00178197	−	0.00393706i
$430$			7.83117i			0.377652i
$431$	−13.7921	+	7.96285i	−0.664341	+	0.383557i	−0.793929	−	0.608011i	$-0.791968\pi$
$431$	−13.7921	+	7.96285i	−0.664341	+	0.383557i	0.129588	+	0.991568i	$0.458634\pi$
$432$	1.51431	+	4.97060i	0.0728572	+	0.239148i
$433$		−	23.2577i		−	1.11769i	−0.829271	−	0.558847i	$-0.811244\pi$
$433$		−	23.2577i		−	1.11769i	0.829271	−	0.558847i	$-0.188756\pi$
$434$	−1.96305	+	24.6091i	−0.0942293	+	1.18127i
$435$	−17.6229	+	1.74280i	−0.844956	+	0.0835610i
$436$	−4.76919			−0.228403
$437$	−15.0262	−	26.0261i	−0.718800	−	1.24500i
$438$	−0.925496	−	9.35847i	−0.0442219	−	0.447165i
$439$	−5.97131	+	10.3426i	−0.284995	+	0.493626i	−0.972608	−	0.232451i	$-0.925325\pi$
$439$	−5.97131	+	10.3426i	−0.284995	+	0.493626i	0.687613	+	0.726078i	$0.258659\pi$
$440$	−0.0757934	−	0.131278i	−0.00361331	−	0.00625843i
$441$	25.0647	+	28.5349i	1.19356	+	1.35880i
$442$	2.39311			0.113829
$443$	25.6238	+	14.7939i	1.21742	+	0.702879i	0.964366	−	0.264573i	$-0.0852310\pi$
$443$	25.6238	+	14.7939i	1.21742	+	0.702879i	0.253056	+	0.967452i	$0.418564\pi$
$444$	−2.84955	+	6.29578i	−0.135234	+	0.298784i
$445$	0.646667	+	0.373353i	0.0306550	+	0.0176987i
$446$	−12.4367	−	21.5409i	−0.588893	−	1.01999i
$447$	−12.1120	+	26.7601i	−0.572878	+	1.26571i
$448$	2.21698	+	3.83992i	0.104742	+	0.181419i
$449$	6.67722			0.315117			0.157559	−	0.987510i	$-0.449638\pi$
$449$	6.67722			0.315117			0.157559	+	0.987510i	$0.449638\pi$
$450$	0.587617	+	2.94189i	0.0277005	+	0.138682i
$451$	−0.00535209	+	0.00309003i	−0.000252020	+	0.000145504i
$452$	−13.5788	−	7.83972i	−0.638693	−	0.368749i
$453$	−6.64369	−	9.26346i	−0.312148	−	0.435235i
$454$	−12.2072	+	21.1435i	−0.572913	+	0.992314i
$455$	−0.755803	+	1.30909i	−0.0354326	+	0.0613710i
$456$	−4.42114	+	9.76802i	−0.207039	+	0.457430i
$457$		−	1.89621i		−	0.0887011i	−0.999016	−	0.0443506i	$-0.985878\pi$
$457$		−	1.89621i		−	0.0887011i	0.999016	−	0.0443506i	$-0.0141219\pi$
$458$	−5.19577	−	8.99933i	−0.242782	−	0.420511i
$459$	−24.9023	+	26.6518i	−1.16234	+	1.24400i
$460$	4.20432	+	2.42736i	0.196027	+	0.113176i
$461$	−15.9746			−0.744010			−0.372005	−	0.928231i	$-0.621330\pi$
$461$	−15.9746			−0.744010			−0.372005	+	0.928231i	$0.621330\pi$
$462$	0.678476	+	0.946015i	0.0315656	+	0.0440126i
$463$			32.0164i			1.48793i	0.668219	+	0.743964i	$0.267057\pi$
$463$			32.0164i			1.48793i	−0.668219	+	0.743964i	$0.732943\pi$
$464$	10.2242			0.474649
$465$	4.66251	−	8.44162i	0.216219	−	0.391471i
$466$	−13.8174			−0.640078
$467$		−	6.35865i		−	0.294243i	−0.989118	−	0.147122i	$-0.952999\pi$
$467$		−	6.35865i		−	0.294243i	0.989118	−	0.147122i	$-0.0470009\pi$
$468$	0.768404	−	0.674957i	0.0355195	−	0.0311999i
$469$	34.5862			1.59704
$470$	0.689684	+	0.398189i	0.0318127	+	0.0183671i
$471$	6.07663	−	4.35812i	0.279996	−	0.200811i
$472$	−0.891267	−	1.54372i	−0.0410239	−	0.0710555i
$473$		−	1.18710i		−	0.0545830i
$474$	−24.9610	−	11.2977i	−1.14650	−	0.518921i
$475$	−3.09517	+	5.36099i	−0.142016	+	0.245979i
$476$	−15.5625	+	26.9550i	−0.713304	+	1.23548i
$477$	−25.6076	−	29.1529i	−1.17249	−	1.33482i
$478$	1.62418	+	0.937720i	0.0742882	+	0.0428903i
$479$	0.544866	−	0.314579i	0.0248956	−	0.0143735i	−0.487501	−	0.873123i	$-0.662091\pi$
$479$	0.544866	−	0.314579i	0.0248956	−	0.0143735i	0.512396	+	0.858749i	$0.328758\pi$
$480$	−0.170458	−	1.72364i	−0.00778030	−	0.0786732i
$481$	1.36020			0.0620199
$482$	2.16599	+	3.75160i	0.0986581	+	0.170881i
$483$	−33.9663	−	15.3736i	−1.54552	−	0.699524i
$484$	−5.48851	−	9.50638i	−0.249478	−	0.432108i
$485$	−5.52689	−	3.19095i	−0.250963	−	0.144894i
$486$	−0.478986	+	15.5811i	−0.0217272	+	0.706773i
$487$	13.7023	+	7.91102i	0.620910	+	0.358483i	0.777223	−	0.629225i	$-0.216628\pi$
$487$	13.7023	+	7.91102i	0.620910	+	0.358483i	−0.156313	+	0.987708i	$0.549961\pi$
$488$	12.6420			0.572278
$489$	19.2934	−	13.8371i	0.872476	−	0.625734i
$490$	−6.32999	−	10.9639i	−0.285960	−	0.495297i
$491$	−14.6796	+	25.4258i	−0.662481	+	1.14745i	0.317481	+	0.948265i	$0.397163\pi$
$491$	−14.6796	+	25.4258i	−0.662481	+	1.14745i	−0.979962	+	0.199186i	$0.936170\pi$
$492$	−0.0702714	+	0.00694941i	−0.00316808	+	0.000313304i
$493$	35.8854	+	62.1553i	1.61620	+	2.79934i
$494$	2.11038			0.0949506
$495$	−0.0890749	−	0.445951i	−0.00400362	−	0.0200440i
$496$	−3.15848	+	4.58519i	−0.141820	+	0.205881i
$497$		−	33.9175i		−	1.52141i
$498$	4.74771	−	0.469520i	0.212750	−	0.0210397i
$499$	7.99202	−	4.61419i	0.357772	−	0.206560i	−0.310331	−	0.950629i	$-0.600440\pi$
$499$	7.99202	−	4.61419i	0.357772	−	0.206560i	0.668103	+	0.744069i	$0.267107\pi$
$500$		−	1.00000i		−	0.0447214i
$501$	31.6303	+	14.3163i	1.41314	+	0.639605i
$502$	−2.44943	+	1.41418i	−0.109323	+	0.0631178i
$503$	29.0229	−	16.7564i	1.29407	−	0.747130i	0.314694	−	0.949193i	$-0.398098\pi$
$503$	29.0229	−	16.7564i	1.29407	−	0.747130i	0.979372	+	0.202063i	$0.0647647\pi$
$504$	2.60547	+	13.0442i	0.116057	+	0.581035i
$505$	−2.31626	+	4.01187i	−0.103072	+	0.178526i
$506$	−0.637319	−	0.367956i	−0.0283323	−	0.0163576i
$507$	20.3299	+	9.20160i	0.902883	+	0.408657i
$508$	−12.1984	+	7.04278i	−0.541219	+	0.312473i
$509$	−1.90683	+	3.30273i	−0.0845188	+	0.146391i	−0.905186	−	0.425015i	$-0.860269\pi$
$509$	−1.90683	+	3.30273i	−0.0845188	+	0.146391i	0.820667	+	0.571406i	$0.193602\pi$
$510$	9.88011	−	7.08595i	0.437498	−	0.313771i
$511$		−	24.0741i		−	1.06497i
$512$			1.00000i			0.0441942i
$513$	−21.9603	+	23.5030i	−0.969570	+	1.03768i
$514$	−3.49124	+	6.04700i	−0.153992	+	0.266722i
$515$	−11.1564	+	6.44116i	−0.491610	+	0.283831i
$516$	5.59302	−	12.3572i	0.246219	−	0.543994i
$517$	−0.104547	−	0.0603602i	−0.00459797	−	0.00265464i
$518$	−8.84542	+	15.3207i	−0.388645	+	0.673153i
$519$	−6.78517	+	0.671012i	−0.297836	+	0.0294542i
$520$	−0.295242	+	0.170458i	−0.0129472	+	0.00747507i
$521$	−1.54506	+	0.892043i	−0.0676905	+	0.0390811i	−0.533463	−	0.845823i	$-0.679110\pi$
$521$	−1.54506	+	0.892043i	−0.0676905	+	0.0390811i	0.465773	+	0.884904i	$0.345776\pi$
$522$	29.0528	+	9.83627i	1.27161	+	0.430522i
$523$			10.0624i			0.440000i	0.975500	+	0.220000i	$0.0706057\pi$
$523$			10.0624i			0.440000i	−0.975500	+	0.220000i	$0.929394\pi$
$524$	1.83163	−	1.05749i	0.0800152	−	0.0461968i
$525$	0.755803	+	7.64256i	0.0329859	+	0.333549i
$526$			17.4149i			0.759326i
$527$	−38.9601	−	3.10782i	−1.69713	−	0.135379i
$528$	0.0258392	+	0.261281i	0.00112450	+	0.0113708i
$529$	0.568361			0.0247114
$530$	6.46710	+	11.2014i	0.280913	+	0.486556i
$531$	−1.04745	−	5.24402i	−0.0454553	−	0.227571i
$532$	−13.7238	+	23.7704i	−0.595004	+	1.03058i
$533$	0.00694941	+	0.0120367i	0.000301012	+	0.000521369i
$534$	−0.753757	−	1.05098i	−0.0326183	−	0.0454804i
$535$	−8.41782			−0.363934
$536$	6.75526	+	3.90015i	0.291783	+	0.168461i
$537$	27.1239	+	12.2766i	1.17048	+	0.529776i
$538$	−15.3600	−	8.86812i	−0.662218	−	0.382332i
$539$	0.959543	+	1.66198i	0.0413305	+	0.0715864i
$540$	1.17387	−	5.06182i	0.0505153	−	0.217826i
$541$	−18.1365	−	31.4134i	−0.779751	−	1.35057i	−0.932085	−	0.362239i	$-0.882012\pi$
$541$	−18.1365	−	31.4134i	−0.779751	−	1.35057i	0.152334	−	0.988329i	$-0.451321\pi$
$542$	−7.23882			−0.310934
$543$	3.35832	−	0.332117i	0.144119	−	0.0142525i
$544$	−6.07921	+	3.50983i	−0.260644	+	0.150483i
$545$	4.13024	+	2.38460i	0.176920	+	0.102145i
$546$	2.12757	−	1.52588i	0.0910515	−	0.0653015i
$547$	−3.68662	+	6.38542i	−0.157629	+	0.273021i	−0.934013	−	0.357239i	$-0.883718\pi$
$547$	−3.68662	+	6.38542i	−0.157629	+	0.273021i	0.776384	+	0.630260i	$0.217052\pi$
$548$	8.98731	−	15.5665i	0.383919	−	0.664967i
$549$	35.9230	+	12.1623i	1.53316	+	0.519074i
$550$			0.151587i			0.00646368i
$551$	31.6458	+	54.8121i	1.34815	+	2.33507i
$552$	−4.90056	−	6.83298i	−0.208582	−	0.290831i
$553$	−60.7424	−	35.0697i	−2.58303	−	1.49131i
$554$	1.92186			0.0816521
$555$	5.61567	−	4.02752i	0.238372	−	0.170959i
$556$			5.72097i			0.242623i
$557$	36.6396			1.55247			0.776234	−	0.630445i	$-0.217127\pi$
$557$	36.6396			1.55247			0.776234	+	0.630445i	$0.217127\pi$
$558$	−13.3862	+	9.99046i	−0.566684	+	0.422930i
$559$	−2.66977			−0.112919
$560$		−	4.43396i		−	0.187369i
$561$	−1.49769	+	1.07414i	−0.0632327	+	0.0453501i
$562$	4.20127			0.177220
$563$	11.0257	+	6.36572i	0.464680	+	0.268283i	0.714010	−	0.700135i	$-0.246877\pi$
$563$	11.0257	+	6.36572i	0.464680	+	0.268283i	−0.249330	+	0.968419i	$0.580210\pi$
$564$	−0.803898	−	1.12089i	−0.0338502	−	0.0471981i
$565$	7.83972	+	13.5788i	0.329820	+	0.571264i
$566$			0.572852i			0.0240788i
$567$	−5.14564	+	39.5725i	−0.216096	+	1.66189i
$568$	3.82475	−	6.62466i	0.160483	−	0.277964i
$569$	7.33515	−	12.7049i	0.307506	−	0.532615i	−0.670310	−	0.742081i	$-0.733839\pi$
$569$	7.33515	−	12.7049i	0.307506	−	0.532615i	0.977816	+	0.209465i	$0.0671724\pi$
$570$	8.71283	−	6.24879i	0.364940	−	0.261733i
$571$	−25.3027	−	14.6085i	−1.05888	−	0.611347i	−0.133761	−	0.991014i	$-0.542705\pi$
$571$	−25.3027	−	14.6085i	−1.05888	−	0.611347i	−0.925123	+	0.379667i	$0.876039\pi$
$572$	0.0447547	−	0.0258392i	0.00187129	−	0.00108039i
$573$	−30.5862	+	3.02479i	−1.27776	+	0.126362i
$574$	−0.180769			−0.00754513
$575$	−2.42736	−	4.20432i	−0.101228	−	0.175332i
$576$	−0.962053	+	2.84156i	−0.0400856	+	0.118398i
$577$	6.00180	+	10.3954i	0.249858	+	0.432767i	0.963486	−	0.267758i	$-0.0862826\pi$
$577$	6.00180	+	10.3954i	0.249858	+	0.432767i	−0.713628	+	0.700525i	$0.752949\pi$
$578$	−27.9516	−	16.1379i	−1.16263	−	0.671246i
$579$	29.8187	+	13.4963i	1.23922	+	0.560889i
$580$	−8.85446	−	5.11212i	−0.367661	−	0.212269i
$581$	12.2132			0.506688
$582$	6.44216	+	8.98245i	0.267036	+	0.372335i
$583$	−0.980328	−	1.69798i	−0.0406010	−	0.0703230i
$584$	2.71474	−	4.70206i	0.112337	−	0.194573i
$585$	−1.00294	+	0.200328i	−0.0414663	+	0.00828253i
$586$	10.8719	+	18.8306i	0.449113	+	0.777886i
$587$	−19.2966			−0.796456			−0.398228	−	0.917286i	$-0.630375\pi$
$587$	−19.2966			−0.796456			−0.398228	+	0.917286i	$0.630375\pi$
$588$	2.15799	+	21.8213i	0.0889941	+	0.899895i
$589$	−34.3572	−	2.74065i	−1.41566	−	0.112926i
$590$			1.78253i			0.0733858i
$591$	2.51135	+	25.3944i	0.103303	+	1.04458i
$592$	−3.45531	+	1.99493i	−0.142012	+	0.0819909i
$593$		−	4.53781i		−	0.186346i	−0.995650	−	0.0931728i	$-0.970299\pi$
$593$		−	4.53781i		−	0.186346i	0.995650	−	0.0931728i	$-0.0297009\pi$
$594$	−0.177943	+	0.767305i	−0.00730110	+	0.0314829i
$595$	26.9550	−	15.5625i	1.10505	−	0.637998i
$596$	−14.6868	+	8.47941i	−0.601594	+	0.347330i
$597$	−16.0438	+	1.58664i	−0.656631	+	0.0649368i
$598$	−0.827526	+	1.43332i	−0.0338400	+	0.0586127i
$599$	−1.76009	−	1.01619i	−0.0719153	−	0.0415203i	0.463611	−	0.886039i	$-0.346553\pi$
$599$	−1.76009	−	1.01619i	−0.0719153	−	0.0415203i	−0.535526	+	0.844518i	$0.679887\pi$
$600$	−0.714201	+	1.57795i	−0.0291571	+	0.0644194i
$601$	−26.6292	+	15.3744i	−1.08623	+	0.627133i	−0.932569	−	0.360991i	$-0.882438\pi$
$601$	−26.6292	+	15.3744i	−1.08623	+	0.627133i	−0.153657	+	0.988124i	$0.549105\pi$
$602$	17.3615	−	30.0710i	0.707603	−	1.22560i
$603$	15.4433	+	17.5814i	0.628900	+	0.715971i
$604$		−	6.58155i		−	0.267799i
$605$			10.9770i			0.446279i
$606$	6.52021	−	4.67625i	0.264865	−	0.189960i
$607$	−16.7594	+	29.0282i	−0.680244	+	1.17822i	0.294662	+	0.955601i	$0.404793\pi$
$607$	−16.7594	+	29.0282i	−0.680244	+	1.17822i	−0.974906	+	0.222615i	$0.928541\pi$
$608$	−5.36099	+	3.09517i	−0.217417	+	0.125526i
$609$	71.5345	+	32.3775i	2.89872	+	1.31200i
$610$	−10.9483	−	6.32101i	−0.443284	−	0.255930i
$611$	−0.135749	+	0.235124i	−0.00549181	+	0.00951209i
$612$	−20.6511	+	4.12487i	−0.834770	+	0.166738i
$613$	38.7543	−	22.3748i	1.56527	−	0.903710i	0.568564	−	0.822639i	$-0.307499\pi$
$613$	38.7543	−	22.3748i	1.56527	−	0.903710i	0.996708	−	0.0810710i	$-0.0258340\pi$
$614$	−8.67974	+	5.01125i	−0.350286	+	0.202238i
$615$	0.0643315	+	0.0291173i	0.00259410	+	0.00117412i
$616$			0.672130i			0.0270809i
$617$	−12.3320	+	7.11990i	−0.496469	+	0.286637i	−0.727254	−	0.686368i	$-0.759204\pi$
$617$	−12.3320	+	7.11990i	−0.496469	+	0.286637i	0.230785	+	0.973005i	$0.425871\pi$
$618$	22.2045	−	2.19589i	0.893196	−	0.0883317i
$619$			17.4299i			0.700566i	0.936644	+	0.350283i	$0.113915\pi$
$619$			17.4299i			0.700566i	−0.936644	+	0.350283i	$0.886085\pi$
$620$	5.02792	−	2.39165i	0.201926	−	0.0960510i
$621$	−7.35155	−	24.1309i	−0.295008	−	0.968340i
$622$	33.6401			1.34884
$623$	−1.65543	−	2.86729i	−0.0663235	−	0.114876i
$624$	0.587617	−	0.0581117i	0.0235235	−	0.00232633i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	4.13628	+	7.16424i	0.165319	+	0.286341i
$627$	−1.32075	+	0.947234i	−0.0527457	+	0.0378289i
$628$	4.31735			0.172281
$629$	−24.2551	−	14.0037i	−0.967116	−	0.558365i
$630$	4.26570	−	12.5993i	0.169950	−	0.501970i
$631$	−23.7443	−	13.7088i	−0.945247	−	0.545739i	−0.0536458	−	0.998560i	$-0.517084\pi$
$631$	−23.7443	−	13.7088i	−0.945247	−	0.545739i	−0.891601	+	0.452821i	$0.850418\pi$
$632$	−7.90934	−	13.6994i	−0.314617	−	0.544932i
$633$	26.7422	+	12.1039i	1.06291	+	0.481086i
$634$	−12.9161	−	22.3713i	−0.512962	−	0.888476i
$635$	14.0856			0.558968
$636$	−2.20474	−	22.2940i	−0.0874235	−	0.884013i
$637$	3.73775	−	2.15799i	0.148095	−	0.0855028i
$638$	1.34222	+	0.774931i	0.0531390	+	0.0306798i
$639$	17.2415	−	15.1447i	0.682064	−	0.599116i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	2.37909	−	4.12071i	0.0939686	−	0.162758i	−0.815209	−	0.579167i	$-0.803378\pi$
$641$	2.37909	−	4.12071i	0.0939686	−	0.162758i	0.909178	+	0.416408i	$0.136711\pi$
$642$	13.2829	+	6.01202i	0.524234	+	0.237275i
$643$		−	25.8635i		−	1.01996i	−0.860187	−	0.509979i	$-0.829653\pi$
$643$		−	25.8635i		−	1.01996i	0.860187	−	0.509979i	$-0.170347\pi$
$644$	−10.7628	−	18.6418i	−0.424115	−	0.734588i
$645$	−11.0223	+	7.90511i	−0.434002	+	0.311263i
$646$	−37.6323	−	21.7270i	−1.48062	−	0.854839i
$647$	40.9260			1.60897			0.804483	−	0.593975i	$-0.202442\pi$
$647$	40.9260			1.60897			0.804483	+	0.593975i	$0.202442\pi$
$648$	−5.46746	+	7.14891i	−0.214782	+	0.280836i
$649$		−	0.270209i		−	0.0106066i
$650$	0.340916			0.0133718
$651$	−36.6186	+	22.0785i	−1.43520	+	0.865323i
$652$	13.7076			0.536833
$653$		−	5.44033i		−	0.212897i	−0.994318	−	0.106448i	$-0.966052\pi$
$653$		−	5.44033i		−	0.212897i	0.994318	−	0.106448i	$-0.0339479\pi$
$654$	−4.81422	−	6.71259i	−0.188251	−	0.262483i
$655$	−2.11499			−0.0826393
$656$	−0.0353071	−	0.0203846i	−0.00137851	−	0.000795883i
$657$	12.2377	−	10.7495i	0.477439	−	0.419377i
$658$	−1.76555	−	3.05803i	−0.0688284	−	0.119214i
$659$		−	5.45615i		−	0.212542i	−0.994337	−	0.106271i	$-0.966109\pi$
$659$		−	5.45615i		−	0.212542i	0.994337	−	0.106271i	$-0.0338910\pi$
$660$	0.108263	−	0.239196i	0.00421415	−	0.00931069i
$661$	11.9479	−	20.6944i	0.464721	−	0.804920i	−0.534468	−	0.845189i	$-0.679488\pi$
$661$	11.9479	−	20.6944i	0.464721	−	0.804920i	0.999189	+	0.0402687i	$0.0128214\pi$
$662$	−6.01687	+	10.4215i	−0.233852	+	0.405044i
$663$	2.41571	+	3.36828i	0.0938184	+	0.130813i
$664$	2.38544	+	1.37723i	0.0925729	+	0.0534470i
$665$	23.7704	−	13.7238i	0.921776	−	0.532188i
$666$	−11.7377	+	2.34450i	−0.454827	+	0.0908477i
$667$	−49.6359			−1.92191
$668$	10.0226	+	17.3596i	0.387786	+	0.671665i
$669$	17.7646	−	39.2488i	0.686817	−	1.51745i
$670$	−3.90015	−	6.75526i	−0.150676	−	0.260978i
$671$	1.65962	+	0.958182i	0.0640689	+	0.0369902i
$672$	−3.16674	+	6.99655i	−0.122159	+	0.269898i
$673$	−13.8591	−	8.00156i	−0.534229	−	0.308437i	0.208508	−	0.978021i	$-0.433139\pi$
$673$	−13.8591	−	8.00156i	−0.534229	−	0.308437i	−0.742737	+	0.669583i	$0.766473\pi$
$674$	−4.89013			−0.188361
$675$	−3.54751	+	3.79673i	−0.136544	+	0.146136i
$676$	6.44189	+	11.1577i	0.247765	+	0.429141i
$677$	19.6399	−	34.0172i	0.754821	−	1.30739i	−0.190642	−	0.981660i	$-0.561057\pi$
$677$	19.6399	−	34.0172i	0.754821	−	1.30739i	0.945463	−	0.325729i	$-0.105610\pi$
$678$	−2.67268	−	27.0258i	−0.102644	−	1.03792i
$679$	14.1485	+	24.5060i	0.542971	+	0.940453i
$680$	7.01967			0.269192
$681$	−42.0818	+	4.16163i	−1.61258	+	0.159474i
$682$	−0.762167	+	0.362543i	−0.0291849	+	0.0138825i
$683$			36.1528i			1.38335i	0.722210	+	0.691674i	$0.243127\pi$
$683$			36.1528i			1.38335i	−0.722210	+	0.691674i	$0.756873\pi$
$684$	−18.2113	+	3.63754i	−0.696326	+	0.139085i
$685$	−15.5665	+	8.98731i	−0.594764	+	0.343387i
$686$			25.0961i			0.958175i
$687$	7.42164	−	16.3973i	0.283153	−	0.625596i
$688$	6.78199	−	3.91558i	0.258561	−	0.149280i
$689$	−3.81872	+	2.20474i	−0.145481	+	0.0839938i
$690$	0.827526	+	8.36781i	0.0315034	+	0.318557i
$691$	−8.55414	+	14.8162i	−0.325415	+	0.563635i	−0.981596	−	0.190968i	$-0.938837\pi$
$691$	−8.55414	+	14.8162i	−0.325415	+	0.563635i	0.656181	+	0.754603i	$0.272171\pi$
$692$	−3.40914	−	1.96827i	−0.129596	−	0.0748222i
$693$	−0.646624	+	1.90990i	−0.0245632	+	0.0725509i
$694$	4.19254	−	2.42056i	0.159147	−	0.0918833i
$695$	2.86048	−	4.95450i	0.108504	−	0.187935i
$696$	10.3208	+	14.3905i	0.391208	+	0.545471i
$697$		−	0.286186i		−	0.0108400i
$698$			11.9589i			0.452650i
$699$	−13.9478	−	19.4478i	−0.527556	−	0.735584i
$700$	−2.21698	+	3.83992i	−0.0837939	+	0.145135i
$701$	−23.8746	+	13.7840i	−0.901732	+	0.520615i	−0.877762	−	0.479098i	$-0.840964\pi$
$701$	−23.8746	+	13.7840i	−0.901732	+	0.520615i	−0.0239700	+	0.999713i	$0.507631\pi$
$702$	1.72565	+	0.400191i	0.0651306	+	0.0151042i
$703$	−21.3895	−	12.3493i	−0.806722	−	0.465761i
$704$	−0.0757934	+	0.131278i	−0.00285657	+	0.00494773i
$705$	0.135749	+	1.37267i	0.00511260	+	0.0516978i
$706$	1.99642	−	1.15263i	0.0751362	−	0.0433799i
$707$	17.7885	−	10.2702i	0.669004	−	0.386250i
$708$	1.27309	−	2.81274i	0.0478455	−	0.105709i
$709$		−	5.11133i		−	0.191960i	−0.995383	−	0.0959800i	$-0.969402\pi$
$709$		−	5.11133i		−	0.191960i	0.995383	−	0.0959800i	$-0.0305985\pi$
$710$	−6.62466	+	3.82475i	−0.248619	+	0.143540i
$711$	−9.29532	−	46.5368i	−0.348602	−	1.74527i
$712$		−	0.746707i		−	0.0279840i
$713$	15.3336	−	22.2598i	0.574247	−	0.833638i
$714$	−53.6482	+	5.30548i	−2.00773	+	0.198553i
$715$	−0.0516783			−0.00193266
$716$	8.59467	+	14.8864i	0.321198	+	0.556331i
$717$	0.319683	+	3.23259i	0.0119388	+	0.120723i
$718$	6.09415	−	10.5554i	0.227432	−	0.393923i
$719$	2.77625	+	4.80860i	0.103537	+	0.179330i	0.913139	−	0.407648i	$-0.133651\pi$
$719$	2.77625	+	4.80860i	0.103537	+	0.179330i	−0.809603	+	0.586978i	$0.800317\pi$
$720$	2.25394	−	1.97984i	0.0839994	−	0.0737841i
$721$	57.1196			2.12725
$722$	−16.7318	−	9.66013i	−0.622694	−	0.359513i
$723$	−3.09390	+	6.83563i	−0.115063	+	0.254220i
$724$	1.68735	+	0.974191i	0.0627098	+	0.0362055i
$725$	5.11212	+	8.85446i	0.189860	+	0.328846i
$726$	7.83980	−	17.3212i	0.290962	−	0.642849i
$727$	8.19462	+	14.1935i	0.303922	+	0.526408i	0.977021	−	0.213145i	$-0.0683705\pi$
$727$	8.19462	+	14.1935i	0.303922	+	0.526408i	−0.673099	+	0.739552i	$0.735037\pi$
$728$	1.51161			0.0560238
$729$	−22.4137	+	15.0540i	−0.830138	+	0.557557i
$730$	−4.70206	+	2.71474i	−0.174031	+	0.100477i
$731$	47.6073	+	27.4861i	1.76082	+	1.01661i
$732$	12.7614	+	17.7935i	0.471675	+	0.657667i
$733$	2.14291	−	3.71164i	0.0791504	−	0.137092i	−0.823733	−	0.566978i	$-0.808113\pi$
$733$	2.14291	−	3.71164i	0.0791504	−	0.137092i	0.902884	+	0.429885i	$0.141446\pi$
$734$	14.4765	−	25.0740i	0.534336	−	0.925497i
$735$	9.04177	−	19.9768i	0.333511	−	0.736855i
$736$		−	4.85473i		−	0.178948i
$737$	0.591211	+	1.02401i	0.0217775	+	0.0377198i
$738$	−0.0807161	−	0.0918912i	−0.00297120	−	0.00338256i
$739$	28.4832	+	16.4448i	1.04777	+	0.604931i	0.922024	−	0.387132i	$-0.126534\pi$
$739$	28.4832	+	16.4448i	1.04777	+	0.604931i	0.125746	+	0.992062i	$0.459868\pi$
$740$	3.98985			0.146670
$741$	2.13031	+	2.97034i	0.0782588	+	0.109118i
$742$		−	57.3497i		−	2.10537i
$743$	−21.0480			−0.772176			−0.386088	−	0.922462i	$-0.626174\pi$
$743$	−21.0480			−0.772176			−0.386088	+	0.922462i	$0.626174\pi$
$744$	−9.64192	+	0.182955i	−0.353490	+	0.00670745i
$745$	16.9588			0.621323
$746$		−	17.3060i		−	0.633619i
$747$	5.45338	+	6.20840i	0.199529	+	0.227154i
$748$	−1.06409			−0.0389069
$749$	32.3238	+	18.6621i	1.18109	+	0.681900i
$750$	1.40749	−	1.00944i	0.0513942	−	0.0368596i
$751$	−11.6044	−	20.0995i	−0.423452	−	0.733440i	0.572823	−	0.819679i	$-0.305848\pi$
$751$	−11.6044	−	20.0995i	−0.423452	−	0.733440i	−0.996274	+	0.0862395i	$0.972515\pi$
$752$		−	0.796378i		−	0.0290409i
$753$	−4.46299	−	2.02001i	−0.162640	−	0.0736133i
$754$	1.74280	−	3.01862i	0.0634691	−	0.109932i
$755$	−3.29078	+	5.69979i	−0.119764	+	0.207437i
$756$	−15.7295	+	16.8345i	−0.572077	+	0.612266i
$757$	−13.9874	−	8.07560i	−0.508379	−	0.293513i	0.223788	−	0.974638i	$-0.428158\pi$
$757$	−13.9874	−	8.07560i	−0.508379	−	0.293513i	−0.732167	+	0.681125i	$0.761491\pi$
$758$	22.0994	−	12.7591i	0.802687	−	0.463432i
$759$	−0.125442	−	1.26845i	−0.00455326	−	0.0460418i
$760$	6.19034			0.224547
$761$	16.7904	+	29.0818i	0.608652	+	1.05422i	0.991463	+	0.130389i	$0.0416226\pi$
$761$	16.7904	+	29.0818i	0.608652	+	1.05422i	−0.382811	+	0.923827i	$0.625044\pi$
$762$	−22.2263	−	10.0599i	−0.805172	−	0.364432i
$763$	−10.5732	−	18.3133i	−0.382776	−	0.662987i
$764$	−15.3677	−	8.87254i	−0.555984	−	0.320997i
$765$	19.9468	+	6.75329i	0.721178	+	0.244166i
$766$	18.7852	+	10.8456i	0.678736	+	0.391868i
$767$	−0.607694			−0.0219425
$768$	−1.40749	+	1.00944i	−0.0507884	+	0.0364251i
$769$	−11.8914	−	20.5965i	−0.428815	−	0.742730i	0.567953	−	0.823061i	$-0.307736\pi$
$769$	−11.8914	−	20.5965i	−0.428815	−	0.742730i	−0.996768	+	0.0803311i	$0.974402\pi$
$770$	0.336065	−	0.582081i	0.0121109	−	0.0209768i
$771$	−12.0353	+	1.19022i	−0.433441	+	0.0428646i
$772$	9.44857	+	16.3654i	0.340061	+	0.589004i
$773$	−32.4861			−1.16844			−0.584222	−	0.811594i	$-0.698600\pi$
$773$	−32.4861			−1.16844			−0.584222	+	0.811594i	$0.698600\pi$
$774$	23.0384	−	4.60172i	0.828099	−	0.165406i
$775$	−5.55013	−	0.442730i	−0.199367	−	0.0159033i
$776$			6.38190i			0.229097i
$777$	−30.4927	+	3.01554i	−1.09392	+	0.108182i
$778$	18.4451	−	10.6493i	0.661290	−	0.381796i
$779$		−	0.252374i		−	0.00904225i
$780$	−0.537947	−	0.243482i	−0.0192616	−	0.00871806i
$781$	1.00421	−	0.579781i	0.0359335	−	0.0207462i
$782$	29.5129	−	17.0393i	1.05538	−	0.609323i
$783$	15.4827	+	50.8207i	0.553305	+	1.81618i
$784$	−6.32999	+	10.9639i	−0.226071	+	0.391567i
$785$	−3.73894	−	2.15868i	−0.133448	−	0.0770464i
$786$	3.33734	+	1.51052i	0.119039	+	0.0538786i
$787$	−28.3409	+	16.3627i	−1.01025	+	0.583266i	−0.911264	−	0.411824i	$-0.864892\pi$
$787$	−28.3409	+	16.3627i	−1.01025	+	0.583266i	−0.0989821	+	0.995089i	$0.531559\pi$
$788$	−7.36648	+	12.7591i	−0.262420	+	0.454525i
$789$	−24.5113	+	17.5793i	−0.872625	+	0.625841i
$790$			15.8187i			0.562803i
$791$		−	69.5220i		−	2.47192i
$792$	−0.341668	+	0.300117i	−0.0121406	+	0.0106642i
$793$	2.15493	−	3.73245i	0.0765239	−	0.132543i
$794$	10.0079	−	5.77806i	0.355167	−	0.205056i
$795$	−9.23762	+	20.4095i	−0.327625	+	0.723850i
$796$	−8.06105	−	4.65405i	−0.285716	−	0.164958i
$797$	26.5414	−	45.9710i	0.940144	−	1.62838i	0.174949	−	0.984578i	$-0.444024\pi$
$797$	26.5414	−	45.9710i	0.940144	−	1.62838i	0.765195	−	0.643799i	$-0.222643\pi$
$798$	−47.3100	+	4.67867i	−1.67476	+	0.165623i
$799$	4.84135	−	2.79515i	0.171275	−	0.0988854i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	0.718372	−	2.12181i	0.0253824	−	0.0749705i
$802$		−	1.19650i		−	0.0422500i
$803$	0.712771	−	0.411518i	0.0251531	−	0.0145222i
$804$	1.32962	+	13.4449i	0.0468921	+	0.474166i
$805$			21.5256i			0.758679i
$806$	0.815351	+	1.71410i	0.0287195	+	0.0603765i
$807$	−3.02328	−	30.5709i	−0.106424	−	1.07615i
$808$	4.63251			0.162971
$809$	1.51461	+	2.62337i	0.0532507	+	0.0922329i	0.891422	−	0.453174i	$-0.149708\pi$
$809$	1.51461	+	2.62337i	0.0532507	+	0.0922329i	−0.838171	+	0.545407i	$0.816375\pi$
$810$	8.30941	−	3.45740i	0.291963	−	0.121481i
$811$	−13.3664	+	23.1513i	−0.469357	+	0.812951i	−0.999386	−	0.0350289i	$-0.988848\pi$
$811$	−13.3664	+	23.1513i	−0.469357	+	0.812951i	0.530029	+	0.847979i	$0.322181\pi$
$812$	22.6669	+	39.2603i	0.795454	+	1.37777i
$813$	−7.30717	−	10.1886i	−0.256274	−	0.357328i
$814$	−0.604809			−0.0211985
$815$	−11.8712	−	6.85382i	−0.415829	−	0.240079i
$816$	−11.0767	−	5.01345i	−0.387761	−	0.175506i
$817$	41.9828	+	24.2388i	1.46879	+	0.848007i
$818$	−6.19894	−	10.7369i	−0.216741	−	0.375406i
$819$	4.29531	+	1.45424i	0.150090	+	0.0508154i
$820$	0.0203846	+	0.0353071i	0.000711860	+	0.00123298i
$821$	−9.87519			−0.344647			−0.172323	−	0.985040i	$-0.555127\pi$
$821$	−9.87519			−0.344647			−0.172323	+	0.985040i	$0.555127\pi$
$822$	30.9818	−	3.06391i	1.08061	−	0.106866i
$823$	31.0805	−	17.9443i	1.08340	−	0.625500i	0.151587	−	0.988444i	$-0.451562\pi$
$823$	31.0805	−	17.9443i	1.08340	−	0.625500i	0.931811	+	0.362944i	$0.118228\pi$
$824$	11.1564	+	6.44116i	0.388652	+	0.224388i
$825$	−0.213357	+	0.153018i	−0.00742813	+	0.00532741i
$826$	3.95184	−	6.84479i	0.137502	−	0.238161i
$827$	26.0638	−	45.1438i	0.906326	−	1.56980i	0.0871986	−	0.996191i	$-0.472209\pi$
$827$	26.0638	−	45.1438i	0.906326	−	1.56980i	0.819127	−	0.573612i	$-0.194458\pi$
$828$	4.67050	−	13.7950i	0.162311	−	0.479409i
$829$		−	46.6111i		−	1.61887i	−0.587210	−	0.809435i	$-0.699774\pi$
$829$		−	46.6111i		−	1.61887i	0.587210	−	0.809435i	$-0.300226\pi$
$830$	−1.37723	−	2.38544i	−0.0478044	−	0.0827997i
$831$	1.94001	+	2.70500i	0.0672981	+	0.0938354i
$832$	0.295242	+	0.170458i	0.0102357	+	0.00590956i
$833$	−88.8688			−3.07912
$834$	−8.05220	+	5.77499i	−0.278825	+	0.199971i
$835$		−	20.0452i		−	0.693693i
$836$	−0.938373			−0.0324543
$837$	−27.5741	−	8.75616i	−0.953100	−	0.302657i
$838$	−14.9065			−0.514938
$839$			18.4085i			0.635530i	0.948169	+	0.317765i	$0.102932\pi$
$839$			18.4085i			0.635530i	−0.948169	+	0.317765i	$0.897068\pi$
$840$	6.24075	−	4.47582i	0.215326	−	0.154431i
$841$	75.5352			2.60466
$842$	−3.36057	−	1.94022i	−0.115813	−	0.0668645i
$843$	4.24094	+	5.91324i	0.146066	+	0.203663i
$844$	8.47373	+	14.6769i	0.291678	+	0.505201i
$845$		−	12.8838i		−	0.443215i
$846$	0.766158	−	2.26295i	0.0263411	−	0.0778020i
$847$	24.3358	−	42.1509i	0.836189	−	1.44832i
$848$	6.46710	−	11.2014i	0.222081	−	0.384656i
$849$	−0.806283	+	0.578261i	−0.0276716	+	0.0198459i
$850$	−6.07921	−	3.50983i	−0.208515	−	0.120386i
$851$	16.7746	−	9.68482i	0.575026	−	0.331991i
$852$	13.1850	−	1.30392i	0.451710	−	0.0446714i
$853$	−15.2054			−0.520622			−0.260311	−	0.965525i	$-0.583825\pi$
$853$	−15.2054			−0.520622			−0.260311	+	0.965525i	$0.583825\pi$
$854$	28.0271	+	48.5444i	0.959068	+	1.66115i
$855$	17.5902	+	5.95543i	0.601572	+	0.203672i
$856$	4.20891	+	7.29005i	0.143858	+	0.249169i
$857$	20.7182	+	11.9617i	0.707722	+	0.408603i	0.810217	−	0.586130i	$-0.199349\pi$
$857$	20.7182	+	11.9617i	0.707722	+	0.408603i	−0.102495	+	0.994733i	$0.532683\pi$
$858$	0.0815456	+	0.0369087i	0.00278392	+	0.00126004i
$859$	1.89573	+	1.09450i	0.0646815	+	0.0373439i	0.531992	−	0.846749i	$-0.321444\pi$
$859$	1.89573	+	1.09450i	0.0646815	+	0.0373439i	−0.467310	+	0.884093i	$0.654777\pi$
$860$	−7.83117			−0.267041
$861$	−0.182475	−	0.254430i	−0.00621874	−	0.00867094i
$862$	−7.96285	−	13.7921i	−0.271216	−	0.469760i
$863$	−8.56123	+	14.8285i	−0.291428	+	0.504767i	−0.974148	−	0.225913i	$-0.927464\pi$
$863$	−8.56123	+	14.8285i	−0.291428	+	0.504767i	0.682720	+	0.730680i	$0.260797\pi$
$864$	−4.97060	+	1.51431i	−0.169103	+	0.0515178i
$865$	1.96827	+	3.40914i	0.0669230	+	0.115914i
$866$	23.2577			0.790328
$867$	−5.50164	−	55.6318i	−0.186846	−	1.88935i
$868$	−24.6091	−	1.96305i	−0.835286	−	0.0666302i
$869$		−	2.39790i		−	0.0813433i
$870$	−1.74280	−	17.6229i	−0.0590865	−	0.597474i
$871$	2.30297	−	1.32962i	0.0780332	−	0.0450525i
$872$		−	4.76919i		−	0.161505i
$873$	−6.13972	+	18.1345i	−0.207798	+	0.613761i
$874$	26.0261	−	15.0262i	0.880347	−	0.508269i
$875$	3.83992	−	2.21698i	0.129813	−	0.0749476i
$876$	9.35847	−	0.925496i	0.316194	−	0.0312696i
$877$	−13.5369	+	23.4467i	−0.457110	+	0.791737i	−0.998807	−	0.0488364i	$-0.984449\pi$
$877$	−13.5369	+	23.4467i	−0.457110	+	0.791737i	0.541697	+	0.840574i	$0.317782\pi$
$878$	−10.3426	−	5.97131i	−0.349046	−	0.201522i
$879$	−15.5294	+	34.3105i	−0.523793	+	1.15726i
$880$	0.131278	−	0.0757934i	0.00442538	−	0.00255500i
$881$	19.4785	−	33.7378i	0.656249	−	1.13666i	−0.325330	−	0.945600i	$-0.605476\pi$
$881$	19.4785	−	33.7378i	0.656249	−	1.13666i	0.981579	−	0.191056i	$-0.0611911\pi$
$882$	−28.5349	+	25.0647i	−0.960819	+	0.843972i
$883$		−	20.2262i		−	0.680665i	−0.940305	−	0.340332i	$-0.889460\pi$
$883$		−	20.2262i		−	0.680665i	0.940305	−	0.340332i	$-0.110540\pi$
$884$			2.39311i			0.0804891i
$885$	−2.50890	+	1.79936i	−0.0843357	+	0.0604850i
$886$	−14.7939	+	25.6238i	−0.497010	+	0.860847i
$887$	−22.5371	+	13.0118i	−0.756721	+	0.436893i	−0.828117	−	0.560555i	$-0.810588\pi$
$887$	−22.5371	+	13.0118i	−0.756721	+	0.436893i	0.0713964	+	0.997448i	$0.477254\pi$
$888$	−6.29578	−	2.84955i	−0.211272	−	0.0956248i
$889$	−54.0874	−	31.2274i	−1.81403	−	1.04733i
$890$	−0.373353	+	0.646667i	−0.0125148	+	0.0216763i
$891$	−1.25960	+	0.524097i	−0.0421981	+	0.0175579i
$892$	21.5409	−	12.4367i	0.721244	−	0.416411i
$893$	4.26937	−	2.46492i	0.142869	−	0.0824855i
$894$	−26.7601	−	12.1120i	−0.894993	−	0.405086i
$895$		−	17.1893i		−	0.574576i
$896$	−3.83992	+	2.21698i	−0.128283	+	0.0740641i
$897$	−2.85272	+	0.282116i	−0.0952495	+	0.00941959i
$898$			6.67722i			0.222822i
$899$	−32.2931	+	46.8801i	−1.07704	+	1.56354i
$900$	−2.94189	+	0.587617i	−0.0980629	+	0.0195872i
$901$	90.7938			3.02478
$902$	−0.00309003	−	0.00535209i	−0.000102887	−	0.000178205i
$903$	59.8501	−	5.91881i	1.99169	−	0.196966i
$904$	7.83972	−	13.5788i	0.260745	−	0.451624i
$905$	−0.974191	−	1.68735i	−0.0323832	−	0.0560894i
$906$	9.26346	−	6.64369i	0.307758	−	0.220722i
$907$	30.7364			1.02058			0.510292	−	0.860001i	$-0.329537\pi$
$907$	30.7364			1.02058			0.510292	+	0.860001i	$0.329537\pi$
$908$	−21.1435	−	12.2072i	−0.701672	−	0.405111i
$909$	13.1635	+	4.45672i	0.436607	+	0.147820i
$910$	−1.30909	−	0.755803i	−0.0433959	−	0.0250546i
$911$	20.8174	+	36.0567i	0.689710	+	1.19461i	0.971932	+	0.235264i	$0.0755954\pi$
$911$	20.8174	+	36.0567i	0.689710	+	1.19461i	−0.282222	+	0.959349i	$0.591071\pi$
$912$	−9.76802	−	4.42114i	−0.323452	−	0.146399i
$913$	0.208770	+	0.361601i	0.00690929	+	0.0119672i
$914$	1.89621			0.0627212
$915$	−2.15493	−	21.7903i	−0.0712398	−	0.720366i
$916$	8.99933	−	5.19577i	0.297346	−	0.171673i
$917$	8.12138	+	4.68888i	0.268191	+	0.154840i
$918$	−26.6518	−	24.9023i	−0.879640	−	0.821900i
$919$	16.1588	−	27.9879i	0.533029	−	0.923234i	−0.466226	−	0.884665i	$-0.654387\pi$
$919$	16.1588	−	27.9879i	0.533029	−	0.923234i	0.999256	−	0.0385687i	$-0.0122798\pi$
$920$	−2.42736	+	4.20432i	−0.0800278	+	0.138612i
$921$	−15.8150	−	7.15807i	−0.521121	−	0.235867i
$922$		−	15.9746i		−	0.526094i
$923$	−1.30392	−	2.25845i	−0.0429189	−	0.0743377i
$924$	−0.946015	+	0.678476i	−0.0311216	+	0.0223202i
$925$	−3.45531	−	1.99493i	−0.113610	−	0.0655928i
$926$	−32.0164			−1.05212
$927$	25.5049	+	29.0360i	0.837689	+	0.953667i
$928$			10.2242i			0.335627i
$929$	−23.4654			−0.769876			−0.384938	−	0.922942i	$-0.625777\pi$
$929$	−23.4654			−0.769876			−0.384938	+	0.922942i	$0.625777\pi$
$930$	8.44162	+	4.66251i	0.276812	+	0.152890i
$931$	−78.3695			−2.56846
$932$		−	13.8174i		−	0.452603i
$933$	33.9577	+	47.3480i	1.11172	+	1.55010i
$934$	6.35865			0.208062
$935$	0.921528	+	0.532044i	0.0301372	+	0.0173997i
$936$	0.674957	+	0.768404i	0.0220616	+	0.0251161i
$937$	−12.9271	−	22.3904i	−0.422310	−	0.731463i	0.573855	−	0.818957i	$-0.305447\pi$
$937$	−12.9271	−	22.3904i	−0.422310	−	0.731463i	−0.996165	+	0.0874943i	$0.972114\pi$
$938$			34.5862i			1.12928i
$939$	−5.90827	+	13.0537i	−0.192809	+	0.425990i
$940$	−0.398189	+	0.689684i	−0.0129875	+	0.0224950i
$941$	−27.4893	+	47.6128i	−0.896125	+	1.55213i	−0.0637183	+	0.997968i	$0.520296\pi$
$941$	−27.4893	+	47.6128i	−0.896125	+	1.55213i	−0.832406	+	0.554166i	$0.813037\pi$
$942$	4.35812	+	6.07663i	0.141995	+	0.197987i
$943$	0.171406	+	0.0989614i	0.00558175	+	0.00322263i
$944$	1.54372	−	0.891267i	0.0502438	−	0.0290083i
$945$	22.0394	−	6.71438i	0.716943	−	0.218419i
$946$	1.18710			0.0385960
$947$	−0.435118	−	0.753646i	−0.0141394	−	0.0244902i	0.858869	−	0.512195i	$-0.171168\pi$
$947$	−0.435118	−	0.753646i	−0.0141394	−	0.0244902i	−0.873009	+	0.487705i	$0.837834\pi$
$948$	11.2977	−	24.9610i	0.366932	−	0.810697i
$949$	−0.925496	−	1.60301i	−0.0300429	−	0.0520358i
$950$	−5.36099	−	3.09517i	−0.173933	−	0.100421i
$951$	18.4493	−	40.7617i	0.598260	−	1.32179i
$952$	−26.9550	−	15.5625i	−0.873615	−	0.504382i
$953$	20.8903			0.676705			0.338352	−	0.941019i	$-0.390130\pi$
$953$	20.8903			0.676705			0.338352	+	0.941019i	$0.390130\pi$
$954$	29.1529	−	25.6076i	0.943862	−	0.829077i
$955$	8.87254	+	15.3677i	0.287109	+	0.497287i
$956$	−0.937720	+	1.62418i	−0.0303280	+	0.0525297i
$957$	0.264186	+	2.67141i	0.00853992	+	0.0863543i
$958$	0.314579	+	0.544866i	0.0101636	+	0.0176038i
$959$	79.6987			2.57360
$960$	1.72364	−	0.170458i	0.0556303	−	0.00550150i
$961$	−11.0480	−	28.9645i	−0.356386	−	0.934339i
$962$			1.36020i			0.0438547i
$963$	4.94645	+	24.7643i	0.159397	+	0.798018i
$964$	−3.75160	+	2.16599i	−0.120831	+	0.0697618i
$965$		−	18.8971i		−	0.608320i
$966$	15.3736	−	33.9663i	0.494638	−	1.09285i
$967$	10.7519	−	6.20759i	0.345756	−	0.199622i	−0.317058	−	0.948406i	$-0.602695\pi$
$967$	10.7519	−	6.20759i	0.345756	−	0.199622i	0.662815	+	0.748784i	$0.269362\pi$
$968$	9.50638	−	5.48851i	0.305547	−	0.176407i
$969$	−7.40709	−	74.8993i	−0.237950	−	2.40611i
$970$	3.19095	−	5.52689i	0.102455	−	0.177458i
$971$	−12.9054	−	7.45095i	−0.414155	−	0.239112i	0.278419	−	0.960460i	$-0.410190\pi$
$971$	−12.9054	−	7.45095i	−0.414155	−	0.239112i	−0.692573	+	0.721347i	$0.743523\pi$
$972$	−15.5811	−	0.478986i	−0.499764	−	0.0153635i
$973$	−21.9681	+	12.6833i	−0.704264	+	0.406607i
$974$	−7.91102	+	13.7023i	−0.253486	+	0.439050i
$975$	0.344135	+	0.479835i	0.0110211	+	0.0153670i
$976$			12.6420i			0.404661i
$977$			17.5311i			0.560869i	0.959873	+	0.280434i	$0.0904785\pi$
$977$			17.5311i			0.560869i	−0.959873	+	0.280434i	$0.909522\pi$
$978$	13.8371	+	19.2934i	0.442461	+	0.616934i
$979$	0.0565955	−	0.0980262i	0.00180880	−	0.00313293i
$980$	10.9639	−	6.32999i	0.350228	−	0.202204i
$981$	4.58822	−	13.5519i	0.146490	−	0.432680i
$982$	−25.4258	−	14.6796i	−0.811370	−	0.468445i
$983$	16.8589	−	29.2005i	0.537715	−	0.931350i	−0.461311	−	0.887238i	$-0.652621\pi$
$983$	16.8589	−	29.2005i	0.537715	−	0.931350i	0.999027	−	0.0441118i	$-0.0140458\pi$
$984$	−0.00694941	−	0.0702714i	−0.000221539	−	0.00224017i
$985$	12.7591	−	7.36648i	0.406539	−	0.234715i
$986$	−62.1553	+	35.8854i	−1.97943	+	1.14282i
$987$	2.52192	−	5.57190i	0.0802736	−	0.177356i
$988$			2.11038i			0.0671402i
$989$	−32.9247	+	19.0091i	−1.04694	+	0.604454i
$990$	0.445951	−	0.0890749i	0.0141733	−	0.00283099i
$991$		−	7.56119i		−	0.240189i	−0.992762	−	0.120095i	$-0.961680\pi$
$991$		−	7.56119i		−	0.240189i	0.992762	−	0.120095i	$-0.0383198\pi$
$992$	−4.58519	−	3.15848i	−0.145580	−	0.100282i
$993$	−20.7419	+	2.05124i	−0.658223	+	0.0650942i
$994$	33.9175			1.07580
$995$	4.65405	+	8.06105i	0.147543	+	0.255553i
$996$	0.469520	+	4.74771i	0.0148773	+	0.150437i
$997$	3.25273	−	5.63389i	0.103015	−	0.178427i	−0.809911	−	0.586553i	$-0.800484\pi$
$997$	3.25273	−	5.63389i	0.103015	−	0.178427i	0.912925	+	0.408126i	$0.133818\pi$
$998$	4.61419	+	7.99202i	0.146060	+	0.252983i
$999$	−15.1484	−	14.1540i	−0.479274	−	0.447814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.o.d.161.11	yes	36
3.2	odd	2	inner	930.2.o.d.161.2	✓	36
31.26	odd	6	inner	930.2.o.d.491.11	yes	36
93.26	even	6	inner	930.2.o.d.491.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.o.d.161.2	✓	36	3.2	odd	2	inner
930.2.o.d.161.11	yes	36	1.1	even	1	trivial
930.2.o.d.491.2	yes	36	93.26	even	6	inner
930.2.o.d.491.11	yes	36	31.26	odd	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.40749 + 1.00944i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.00944 - 1.40749i) q^{6} +(-2.21698 - 3.83992i) q^{7} -1.00000i q^{8} +(0.962053 - 2.84156i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-1.40749 + 1.00944i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.00944 - 1.40749i) q^{6} +(-2.21698 - 3.83992i) q^{7} -1.00000i q^{8} +(0.962053 - 2.84156i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(0.0757934 - 0.131278i) q^{11} +(1.40749 - 1.00944i) q^{12} +(-0.295242 - 0.170458i) q^{13} +(3.83992 - 2.21698i) q^{14} +(-1.72364 + 0.170458i) q^{15} +1.00000 q^{16} +(3.50983 + 6.07921i) q^{17} +(2.84156 + 0.962053i) q^{18} +(3.09517 + 5.36099i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(6.99655 + 3.16674i) q^{21} +(0.131278 + 0.0757934i) q^{22} -4.85473 q^{23} +(1.00944 + 1.40749i) q^{24} +(0.500000 + 0.866025i) q^{25} +(0.170458 - 0.295242i) q^{26} +(1.51431 + 4.97060i) q^{27} +(2.21698 + 3.83992i) q^{28} +10.2242 q^{29} +(-0.170458 - 1.72364i) q^{30} +(-3.15848 + 4.58519i) q^{31} +1.00000i q^{32} +(0.0258392 + 0.261281i) q^{33} +(-6.07921 + 3.50983i) q^{34} -4.43396i q^{35} +(-0.962053 + 2.84156i) q^{36} +(-3.45531 + 1.99493i) q^{37} +(-5.36099 + 3.09517i) q^{38} +(0.587617 - 0.0581117i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-0.0353071 - 0.0203846i) q^{41} +(-3.16674 + 6.99655i) q^{42} +(6.78199 - 3.91558i) q^{43} +(-0.0757934 + 0.131278i) q^{44} +(2.25394 - 1.97984i) q^{45} -4.85473i q^{46} -0.796378i q^{47} +(-1.40749 + 1.00944i) q^{48} +(-6.32999 + 10.9639i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-11.0767 - 5.01345i) q^{51} +(0.295242 + 0.170458i) q^{52} +(6.46710 - 11.2014i) q^{53} +(-4.97060 + 1.51431i) q^{54} +(0.131278 - 0.0757934i) q^{55} +(-3.83992 + 2.21698i) q^{56} +(-9.76802 - 4.42114i) q^{57} +10.2242i q^{58} +(1.54372 - 0.891267i) q^{59} +(1.72364 - 0.170458i) q^{60} +12.6420i q^{61} +(-4.58519 - 3.15848i) q^{62} +(-13.0442 + 2.60547i) q^{63} -1.00000 q^{64} +(-0.170458 - 0.295242i) q^{65} +(-0.261281 + 0.0258392i) q^{66} +(-3.90015 + 6.75526i) q^{67} +(-3.50983 - 6.07921i) q^{68} +(6.83298 - 4.90056i) q^{69} +4.43396 q^{70} +(6.62466 + 3.82475i) q^{71} +(-2.84156 - 0.962053i) q^{72} +(4.70206 + 2.71474i) q^{73} +(-1.99493 - 3.45531i) q^{74} +(-1.57795 - 0.714201i) q^{75} +(-3.09517 - 5.36099i) q^{76} -0.672130 q^{77} +(0.0581117 + 0.587617i) q^{78} +(13.6994 - 7.90934i) q^{79} +(0.866025 + 0.500000i) q^{80} +(-7.14891 - 5.46746i) q^{81} +(0.0203846 - 0.0353071i) q^{82} +(-1.37723 + 2.38544i) q^{83} +(-6.99655 - 3.16674i) q^{84} +7.01967i q^{85} +(3.91558 + 6.78199i) q^{86} +(-14.3905 + 10.3208i) q^{87} +(-0.131278 - 0.0757934i) q^{88} +0.746707 q^{89} +(1.97984 + 2.25394i) q^{90} +1.51161i q^{91} +4.85473 q^{92} +(-0.182955 - 9.64192i) q^{93} +0.796378 q^{94} +6.19034i q^{95} +(-1.00944 - 1.40749i) q^{96} -6.38190 q^{97} +(-10.9639 - 6.32999i) q^{98} +(-0.300117 - 0.341668i) 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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