LMFDB - Embedded newform 374.2.g.c.103.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [374,2,Mod(69,374)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(374, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("374.69"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$374 = 2 \cdot 11 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	374.g (of order $5$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [4,1,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.98640503560$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} - x^{3} + x^{2} - x + 1$ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			103.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	374.103
Dual form			374.2.g.c.69.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.80902 + 1.31433i) q^{5} +(-1.30902 + 0.951057i) q^{6} +(0.500000 + 1.53884i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 + 0.224514i) q^{9} -2.23607 q^{10} +(-1.69098 - 2.85317i) q^{11} -1.61803 q^{12} +(-1.50000 - 1.08981i) q^{13} +(-0.500000 + 1.53884i) q^{14} +(-1.11803 - 3.44095i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.809017 + 0.587785i) q^{17} +(0.118034 + 0.363271i) q^{18} +(-0.454915 + 1.40008i) q^{19} +(-1.80902 - 1.31433i) q^{20} -2.61803 q^{21} +(0.309017 - 3.30220i) q^{22} +2.00000 q^{23} +(-1.30902 - 0.951057i) q^{24} +(-0.572949 - 1.76336i) q^{26} +(-4.42705 + 3.21644i) q^{27} +(-1.30902 + 0.951057i) q^{28} +(0.927051 + 2.85317i) q^{29} +(1.11803 - 3.44095i) q^{30} +(5.85410 + 4.25325i) q^{31} -1.00000 q^{32} +(5.23607 - 1.17557i) q^{33} -1.00000 q^{34} +(-2.92705 - 2.12663i) q^{35} +(-0.118034 + 0.363271i) q^{36} +(0.0729490 + 0.224514i) q^{37} +(-1.19098 + 0.865300i) q^{38} +(2.42705 - 1.76336i) q^{39} +(-0.690983 - 2.12663i) q^{40} +(-1.54508 + 4.75528i) q^{41} +(-2.11803 - 1.53884i) q^{42} +10.9443 q^{43} +(2.19098 - 2.48990i) q^{44} -0.854102 q^{45} +(1.61803 + 1.17557i) q^{46} +(2.92705 - 9.00854i) q^{47} +(-0.500000 - 1.53884i) q^{48} +(3.54508 - 2.57565i) q^{49} +(-0.500000 - 1.53884i) q^{51} +(0.572949 - 1.76336i) q^{52} +(4.04508 + 2.93893i) q^{53} -5.47214 q^{54} +(6.80902 + 2.93893i) q^{55} -1.61803 q^{56} +(-1.92705 - 1.40008i) q^{57} +(-0.927051 + 2.85317i) q^{58} +(-1.85410 - 5.70634i) q^{59} +(2.92705 - 2.12663i) q^{60} +(-10.2082 + 7.41669i) q^{61} +(2.23607 + 6.88191i) q^{62} +(-0.190983 + 0.587785i) q^{63} +(-0.809017 - 0.587785i) q^{64} +4.14590 q^{65} +(4.92705 + 2.12663i) q^{66} +11.9443 q^{67} +(-0.809017 - 0.587785i) q^{68} +(-1.00000 + 3.07768i) q^{69} +(-1.11803 - 3.44095i) q^{70} +(-3.30902 + 2.40414i) q^{71} +(-0.309017 + 0.224514i) q^{72} +(2.54508 + 7.83297i) q^{73} +(-0.0729490 + 0.224514i) q^{74} -1.47214 q^{76} +(3.54508 - 4.02874i) q^{77} +3.00000 q^{78} +(-3.80902 - 2.76741i) q^{79} +(0.690983 - 2.12663i) q^{80} +(-2.38197 - 7.33094i) q^{81} +(-4.04508 + 2.93893i) q^{82} +(-1.73607 + 1.26133i) q^{83} +(-0.809017 - 2.48990i) q^{84} +(0.690983 - 2.12663i) q^{85} +(8.85410 + 6.43288i) q^{86} -4.85410 q^{87} +(3.23607 - 0.726543i) q^{88} +3.29180 q^{89} +(-0.690983 - 0.502029i) q^{90} +(0.927051 - 2.85317i) q^{91} +(0.618034 + 1.90211i) q^{92} +(-9.47214 + 6.88191i) q^{93} +(7.66312 - 5.56758i) q^{94} +(-1.01722 - 3.13068i) q^{95} +(0.500000 - 1.53884i) q^{96} +(14.3992 + 10.4616i) q^{97} +4.38197 q^{98} +(0.118034 - 1.26133i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q + q^{2} - 2 q^{3} - q^{4} - 5 q^{5} - 3 q^{6} + 2 q^{7} + q^{8} - q^{9} - 9 q^{11} - 2 q^{12} - 6 q^{13} - 2 q^{14} - q^{16} - q^{17} - 4 q^{18} - 13 q^{19} - 5 q^{20} - 6 q^{21} - q^{22} + 8 q^{23}+ \cdots - 4 q^{99}+O(q^{100})$ 4 * q + q^2 - 2 * q^3 - q^4 - 5 * q^5 - 3 * q^6 + 2 * q^7 + q^8 - q^9 - 9 * q^11 - 2 * q^12 - 6 * q^13 - 2 * q^14 - q^16 - q^17 - 4 * q^18 - 13 * q^19 - 5 * q^20 - 6 * q^21 - q^22 + 8 * q^23 - 3 * q^24 - 9 * q^26 - 11 * q^27 - 3 * q^28 - 3 * q^29 + 10 * q^31 - 4 * q^32 + 12 * q^33 - 4 * q^34 - 5 * q^35 + 4 * q^36 + 7 * q^37 - 7 * q^38 + 3 * q^39 - 5 * q^40 + 5 * q^41 - 4 * q^42 + 8 * q^43 + 11 * q^44 + 10 * q^45 + 2 * q^46 + 5 * q^47 - 2 * q^48 + 3 * q^49 - 2 * q^51 + 9 * q^52 + 5 * q^53 - 4 * q^54 + 25 * q^55 - 2 * q^56 - q^57 + 3 * q^58 + 6 * q^59 + 5 * q^60 - 14 * q^61 - 3 * q^63 - q^64 + 30 * q^65 + 13 * q^66 + 12 * q^67 - q^68 - 4 * q^69 - 11 * q^71 + q^72 - q^73 - 7 * q^74 + 12 * q^76 + 3 * q^77 + 12 * q^78 - 13 * q^79 + 5 * q^80 - 14 * q^81 - 5 * q^82 + 2 * q^83 - q^84 + 5 * q^85 + 22 * q^86 - 6 * q^87 + 4 * q^88 + 40 * q^89 - 5 * q^90 - 3 * q^91 - 2 * q^92 - 20 * q^93 + 15 * q^94 + 25 * q^95 + 2 * q^96 + 33 * q^97 + 22 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/374\mathbb{Z}\right)^\times$ .

$n$	$35$	$309$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−0.500000	+	1.53884i	−0.288675	+	0.888451i	0.696598	+	0.717462i	$0.254696\pi$
$3$	−0.500000	+	1.53884i	−0.288675	+	0.888451i	−0.985273	+	0.170989i	$0.945304\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−1.80902	+	1.31433i	−0.809017	+	0.587785i	−0.913545	−	0.406737i	$-0.866667\pi$
$5$	−1.80902	+	1.31433i	−0.809017	+	0.587785i	0.104528	+	0.994522i	$0.466667\pi$
$6$	−1.30902	+	0.951057i	−0.534404	+	0.388267i
$7$	0.500000	+	1.53884i	0.188982	+	0.581628i	0.999994	−	0.00340203i	$-0.00108290\pi$
$7$	0.500000	+	1.53884i	0.188982	+	0.581628i	−0.811012	+	0.585030i	$0.801083\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	0.309017	+	0.224514i	0.103006	+	0.0748380i
$10$	−2.23607			−0.707107
$11$	−1.69098	−	2.85317i	−0.509851	−	0.860263i
$11$	−1.69098	−	2.85317i	−0.509851	−	0.860263i
$12$	−1.61803			−0.467086
$13$	−1.50000	−	1.08981i	−0.416025	−	0.302260i	0.360011	−	0.932948i	$-0.382773\pi$
$13$	−1.50000	−	1.08981i	−0.416025	−	0.302260i	−0.776037	+	0.630688i	$0.782773\pi$
$14$	−0.500000	+	1.53884i	−0.133631	+	0.411273i
$15$	−1.11803	−	3.44095i	−0.288675	−	0.888451i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.809017	+	0.587785i	−0.196215	+	0.142559i
$17$	−0.809017	+	0.587785i	−0.196215	+	0.142559i
$18$	0.118034	+	0.363271i	0.0278209	+	0.0856239i
$19$	−0.454915	+	1.40008i	−0.104365	+	0.321201i	−0.989581	−	0.143979i	$-0.954010\pi$
$19$	−0.454915	+	1.40008i	−0.104365	+	0.321201i	0.885216	+	0.465180i	$0.154010\pi$
$20$	−1.80902	−	1.31433i	−0.404508	−	0.293893i
$21$	−2.61803			−0.571302
$22$	0.309017	−	3.30220i	0.0658826	−	0.704031i
$23$	2.00000			0.417029			0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000			0.417029			0.208514	+	0.978019i	$0.433137\pi$
$24$	−1.30902	−	0.951057i	−0.267202	−	0.194134i
$25$		0			0
$26$	−0.572949	−	1.76336i	−0.112365	−	0.345823i
$27$	−4.42705	+	3.21644i	−0.851986	+	0.619004i
$28$	−1.30902	+	0.951057i	−0.247381	+	0.179733i
$29$	0.927051	+	2.85317i	0.172149	+	0.529820i	0.999492	−	0.0318771i	$-0.0101485\pi$
$29$	0.927051	+	2.85317i	0.172149	+	0.529820i	−0.827343	+	0.561697i	$0.810149\pi$
$30$	1.11803	−	3.44095i	0.204124	−	0.628230i
$31$	5.85410	+	4.25325i	1.05143	+	0.763907i	0.972483	−	0.232972i	$-0.0748451\pi$
$31$	5.85410	+	4.25325i	1.05143	+	0.763907i	0.0789443	+	0.996879i	$0.474845\pi$
$32$	−1.00000			−0.176777
$33$	5.23607	−	1.17557i	0.911482	−	0.204641i
$34$	−1.00000			−0.171499
$35$	−2.92705	−	2.12663i	−0.494762	−	0.359466i
$36$	−0.118034	+	0.363271i	−0.0196723	+	0.0605452i
$37$	0.0729490	+	0.224514i	0.0119927	+	0.0369099i	0.956874	−	0.290504i	$-0.0938229\pi$
$37$	0.0729490	+	0.224514i	0.0119927	+	0.0369099i	−0.944881	+	0.327414i	$0.893823\pi$
$38$	−1.19098	+	0.865300i	−0.193203	+	0.140370i
$39$	2.42705	−	1.76336i	0.388639	−	0.282363i
$40$	−0.690983	−	2.12663i	−0.109254	−	0.336249i
$41$	−1.54508	+	4.75528i	−0.241302	+	0.742650i	0.754921	+	0.655816i	$0.227675\pi$
$41$	−1.54508	+	4.75528i	−0.241302	+	0.742650i	−0.996223	+	0.0868346i	$0.972325\pi$
$42$	−2.11803	−	1.53884i	−0.326820	−	0.237448i
$43$	10.9443			1.66899			0.834493	−	0.551019i	$-0.185761\pi$
$43$	10.9443			1.66899			0.834493	+	0.551019i	$0.185761\pi$
$44$	2.19098	−	2.48990i	0.330303	−	0.375366i
$45$	−0.854102			−0.127322
$46$	1.61803	+	1.17557i	0.238566	+	0.173328i
$47$	2.92705	−	9.00854i	0.426954	−	1.31403i	−0.474156	−	0.880441i	$-0.657247\pi$
$47$	2.92705	−	9.00854i	0.426954	−	1.31403i	0.901111	−	0.433589i	$-0.142753\pi$
$48$	−0.500000	−	1.53884i	−0.0721688	−	0.222113i
$49$	3.54508	−	2.57565i	0.506441	−	0.367951i
$50$		0			0
$51$	−0.500000	−	1.53884i	−0.0700140	−	0.215481i
$52$	0.572949	−	1.76336i	0.0794537	−	0.244533i
$53$	4.04508	+	2.93893i	0.555635	+	0.403693i	0.829859	−	0.557973i	$-0.188421\pi$
$53$	4.04508	+	2.93893i	0.555635	+	0.403693i	−0.274224	+	0.961666i	$0.588421\pi$
$54$	−5.47214			−0.744663
$55$	6.80902	+	2.93893i	0.918128	+	0.396285i
$56$	−1.61803			−0.216219
$57$	−1.92705	−	1.40008i	−0.255244	−	0.185446i
$58$	−0.927051	+	2.85317i	−0.121728	+	0.374640i
$59$	−1.85410	−	5.70634i	−0.241384	−	0.742902i	−0.996210	−	0.0869778i	$-0.972279\pi$
$59$	−1.85410	−	5.70634i	−0.241384	−	0.742902i	0.754827	−	0.655924i	$-0.227721\pi$
$60$	2.92705	−	2.12663i	0.377881	−	0.274546i
$61$	−10.2082	+	7.41669i	−1.30703	+	0.949610i	−0.999998	−	0.00208984i	$-0.999335\pi$
$61$	−10.2082	+	7.41669i	−1.30703	+	0.949610i	−0.307029	+	0.951700i	$0.599335\pi$
$62$	2.23607	+	6.88191i	0.283981	+	0.874003i
$63$	−0.190983	+	0.587785i	−0.0240616	+	0.0740540i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	4.14590			0.514235
$66$	4.92705	+	2.12663i	0.606478	+	0.261770i
$67$	11.9443			1.45923			0.729613	−	0.683861i	$-0.239700\pi$
$67$	11.9443			1.45923			0.729613	+	0.683861i	$0.239700\pi$
$68$	−0.809017	−	0.587785i	−0.0981077	−	0.0712794i
$69$	−1.00000	+	3.07768i	−0.120386	+	0.370510i
$70$	−1.11803	−	3.44095i	−0.133631	−	0.411273i
$71$	−3.30902	+	2.40414i	−0.392708	+	0.285319i	−0.766564	−	0.642168i	$-0.778035\pi$
$71$	−3.30902	+	2.40414i	−0.392708	+	0.285319i	0.373856	+	0.927487i	$0.378035\pi$
$72$	−0.309017	+	0.224514i	−0.0364180	+	0.0264592i
$73$	2.54508	+	7.83297i	0.297880	+	0.916779i	0.982239	+	0.187634i	$0.0600820\pi$
$73$	2.54508	+	7.83297i	0.297880	+	0.916779i	−0.684359	+	0.729145i	$0.739918\pi$
$74$	−0.0729490	+	0.224514i	−0.00848015	+	0.0260992i
$75$		0			0
$76$	−1.47214			−0.168866
$77$	3.54508	−	4.02874i	0.404000	−	0.459118i
$78$	3.00000			0.339683
$79$	−3.80902	−	2.76741i	−0.428548	−	0.311358i	0.352520	−	0.935804i	$-0.385325\pi$
$79$	−3.80902	−	2.76741i	−0.428548	−	0.311358i	−0.781068	+	0.624446i	$0.785325\pi$
$80$	0.690983	−	2.12663i	0.0772542	−	0.237764i
$81$	−2.38197	−	7.33094i	−0.264663	−	0.814549i
$82$	−4.04508	+	2.93893i	−0.446705	+	0.324550i
$83$	−1.73607	+	1.26133i	−0.190558	+	0.138449i	−0.678974	−	0.734162i	$-0.737575\pi$
$83$	−1.73607	+	1.26133i	−0.190558	+	0.138449i	0.488416	+	0.872611i	$0.337575\pi$
$84$	−0.809017	−	2.48990i	−0.0882710	−	0.271670i
$85$	0.690983	−	2.12663i	0.0749476	−	0.230665i
$86$	8.85410	+	6.43288i	0.954762	+	0.693675i
$87$	−4.85410			−0.520414
$88$	3.23607	−	0.726543i	0.344966	−	0.0774497i
$89$	3.29180			0.348930			0.174465	−	0.984663i	$-0.444180\pi$
$89$	3.29180			0.348930			0.174465	+	0.984663i	$0.444180\pi$
$90$	−0.690983	−	0.502029i	−0.0728360	−	0.0529185i
$91$	0.927051	−	2.85317i	0.0971813	−	0.299093i
$92$	0.618034	+	1.90211i	0.0644345	+	0.198309i
$93$	−9.47214	+	6.88191i	−0.982215	+	0.713621i
$94$	7.66312	−	5.56758i	0.790390	−	0.574252i
$95$	−1.01722	−	3.13068i	−0.104365	−	0.321201i
$96$	0.500000	−	1.53884i	0.0510310	−	0.157057i
$97$	14.3992	+	10.4616i	1.46202	+	1.06222i	0.982832	+	0.184502i	$0.0590673\pi$
$97$	14.3992	+	10.4616i	1.46202	+	1.06222i	0.479184	+	0.877715i	$0.340933\pi$
$98$	4.38197			0.442645
$99$	0.118034	−	1.26133i	0.0118629	−	0.126768i
$100$		0			0
$101$	−1.35410	−	0.983813i	−0.134738	−	0.0978930i	0.518375	−	0.855154i	$-0.326537\pi$
$101$	−1.35410	−	0.983813i	−0.134738	−	0.0978930i	−0.653113	+	0.757261i	$0.726537\pi$
$102$	0.500000	−	1.53884i	0.0495074	−	0.152368i
$103$	−2.26393	−	6.96767i	−0.223072	−	0.686545i	−0.998482	−	0.0550862i	$-0.982457\pi$
$103$	−2.26393	−	6.96767i	−0.223072	−	0.686545i	0.775410	−	0.631458i	$-0.217543\pi$
$104$	1.50000	−	1.08981i	0.147087	−	0.106865i
$105$	4.73607	−	3.44095i	0.462193	−	0.335803i
$106$	1.54508	+	4.75528i	0.150072	+	0.461874i
$107$	3.61803	−	11.1352i	0.349769	−	1.07648i	−0.609213	−	0.793007i	$-0.708514\pi$
$107$	3.61803	−	11.1352i	0.349769	−	1.07648i	0.958981	−	0.283470i	$-0.0914856\pi$
$108$	−4.42705	−	3.21644i	−0.425993	−	0.309502i
$109$	−0.0901699			−0.00863671			−0.00431836	−	0.999991i	$-0.501375\pi$
$109$	−0.0901699			−0.00863671			−0.00431836	+	0.999991i	$0.501375\pi$
$110$	3.78115	+	6.37988i	0.360519	+	0.608298i
$111$	−0.381966			−0.0362546
$112$	−1.30902	−	0.951057i	−0.123690	−	0.0898664i
$113$	1.35410	−	4.16750i	0.127383	−	0.392045i	−0.866945	−	0.498405i	$-0.833919\pi$
$113$	1.35410	−	4.16750i	0.127383	−	0.392045i	0.994328	+	0.106359i	$0.0339194\pi$
$114$	−0.736068	−	2.26538i	−0.0689391	−	0.212173i
$115$	−3.61803	+	2.62866i	−0.337383	+	0.245123i
$116$	−2.42705	+	1.76336i	−0.225346	+	0.163723i
$117$	−0.218847	−	0.673542i	−0.0202324	−	0.0622690i
$118$	1.85410	−	5.70634i	0.170684	−	0.525311i
$119$	−1.30902	−	0.951057i	−0.119997	−	0.0871832i
$120$	3.61803			0.330280
$121$	−5.28115	+	9.64932i	−0.480105	+	0.877211i
$122$	−12.6180			−1.14238
$123$	−6.54508	−	4.75528i	−0.590150	−	0.428769i
$124$	−2.23607	+	6.88191i	−0.200805	+	0.618014i
$125$	−3.45492	−	10.6331i	−0.309017	−	0.951057i
$126$	−0.500000	+	0.363271i	−0.0445435	+	0.0323628i
$127$	0.763932	−	0.555029i	0.0677880	−	0.0492509i	−0.553375	−	0.832932i	$-0.686660\pi$
$127$	0.763932	−	0.555029i	0.0677880	−	0.0492509i	0.621163	+	0.783681i	$0.286660\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−5.47214	+	16.8415i	−0.481795	+	1.48281i
$130$	3.35410	+	2.43690i	0.294174	+	0.213730i
$131$	−7.56231			−0.660722			−0.330361	−	0.943855i	$-0.607170\pi$
$131$	−7.56231			−0.660722			−0.330361	+	0.943855i	$0.607170\pi$
$132$	2.73607	+	4.61653i	0.238144	+	0.401817i
$133$	−2.38197			−0.206543
$134$	9.66312	+	7.02067i	0.834766	+	0.606493i
$135$	3.78115	−	11.6372i	0.325430	−	1.00157i
$136$	−0.309017	−	0.951057i	−0.0264980	−	0.0815524i
$137$	5.09017	−	3.69822i	0.434883	−	0.315961i	−0.348716	−	0.937229i	$-0.613382\pi$
$137$	5.09017	−	3.69822i	0.434883	−	0.315961i	0.783598	+	0.621268i	$0.213382\pi$
$138$	−2.61803	+	1.90211i	−0.222862	+	0.161919i
$139$	−4.63525	−	14.2658i	−0.393157	−	1.21001i	−0.930387	−	0.366578i	$-0.880529\pi$
$139$	−4.63525	−	14.2658i	−0.393157	−	1.21001i	0.537230	−	0.843436i	$-0.319471\pi$
$140$	1.11803	−	3.44095i	0.0944911	−	0.290814i
$141$	12.3992	+	9.00854i	1.04420	+	0.758656i
$142$	−4.09017			−0.343239
$143$	−0.572949	+	6.12261i	−0.0479124	+	0.511998i
$144$	−0.381966			−0.0318305
$145$	−5.42705	−	3.94298i	−0.450692	−	0.327447i
$146$	−2.54508	+	7.83297i	−0.210633	+	0.648261i
$147$	2.19098	+	6.74315i	0.180709	+	0.556166i
$148$	−0.190983	+	0.138757i	−0.0156987	+	0.0114058i
$149$	−8.39919	+	6.10237i	−0.688088	+	0.499925i	−0.876031	−	0.482255i	$-0.839818\pi$
$149$	−8.39919	+	6.10237i	−0.688088	+	0.499925i	0.187943	+	0.982180i	$0.439818\pi$
$150$		0			0
$151$	3.01722	−	9.28605i	0.245538	−	0.755688i	−0.750010	−	0.661427i	$-0.769951\pi$
$151$	3.01722	−	9.28605i	0.245538	−	0.755688i	0.995548	−	0.0942611i	$-0.0300489\pi$
$152$	−1.19098	−	0.865300i	−0.0966015	−	0.0701851i
$153$	−0.381966			−0.0308801
$154$	5.23607	−	1.17557i	0.421934	−	0.0947302i
$155$	−16.1803			−1.29964
$156$	2.42705	+	1.76336i	0.194320	+	0.141181i
$157$	−4.04508	+	12.4495i	−0.322833	+	0.993578i	0.649576	+	0.760296i	$0.274946\pi$
$157$	−4.04508	+	12.4495i	−0.322833	+	0.993578i	−0.972409	+	0.233281i	$0.925054\pi$
$158$	−1.45492	−	4.47777i	−0.115747	−	0.356232i
$159$	−6.54508	+	4.75528i	−0.519059	+	0.377118i
$160$	1.80902	−	1.31433i	0.143015	−	0.103907i
$161$	1.00000	+	3.07768i	0.0788110	+	0.242555i
$162$	2.38197	−	7.33094i	0.187145	−	0.575973i
$163$	0.0450850	+	0.0327561i	0.00353133	+	0.00256566i	0.589550	−	0.807732i	$-0.299305\pi$
$163$	0.0450850	+	0.0327561i	0.00353133	+	0.00256566i	−0.586018	+	0.810298i	$0.699305\pi$
$164$	−5.00000			−0.390434
$165$	−7.92705	+	9.00854i	−0.617120	+	0.701314i
$166$	−2.14590			−0.166554
$167$	0.954915	+	0.693786i	0.0738935	+	0.0536868i	0.624119	−	0.781329i	$-0.285458\pi$
$167$	0.954915	+	0.693786i	0.0738935	+	0.0536868i	−0.550225	+	0.835016i	$0.685458\pi$
$168$	0.809017	−	2.48990i	0.0624170	−	0.192100i
$169$	−2.95492	−	9.09429i	−0.227301	−	0.699561i
$170$	1.80902	−	1.31433i	0.138745	−	0.100804i
$171$	−0.454915	+	0.330515i	−0.0347882	+	0.0252751i
$172$	3.38197	+	10.4086i	0.257872	+	0.793650i
$173$	2.20820	−	6.79615i	0.167887	−	0.516702i	−0.831351	−	0.555748i	$-0.812432\pi$
$173$	2.20820	−	6.79615i	0.167887	−	0.516702i	0.999237	+	0.0390461i	$0.0124319\pi$
$174$	−3.92705	−	2.85317i	−0.297709	−	0.216298i
$175$		0			0
$176$	3.04508	+	1.31433i	0.229532	+	0.0990712i
$177$	9.70820			0.729713
$178$	2.66312	+	1.93487i	0.199609	+	0.145025i
$179$	5.13525	−	15.8047i	0.383827	−	1.18130i	−0.553501	−	0.832849i	$-0.686708\pi$
$179$	5.13525	−	15.8047i	0.383827	−	1.18130i	0.937328	−	0.348449i	$-0.113292\pi$
$180$	−0.263932	−	0.812299i	−0.0196723	−	0.0605452i
$181$	−13.6353	+	9.90659i	−1.01350	+	0.736351i	−0.964940	−	0.262469i	$-0.915463\pi$
$181$	−13.6353	+	9.90659i	−1.01350	+	0.736351i	−0.0485601	+	0.998820i	$0.515463\pi$
$182$	2.42705	−	1.76336i	0.179905	−	0.130709i
$183$	−6.30902	−	19.4172i	−0.466376	−	1.43536i
$184$	−0.618034	+	1.90211i	−0.0455621	+	0.140226i
$185$	−0.427051	−	0.310271i	−0.0313974	−	0.0228116i
$186$	−11.7082			−0.858487
$187$	3.04508	+	1.31433i	0.222679	+	0.0961132i
$188$	9.47214			0.690827
$189$	−7.16312	−	5.20431i	−0.521040	−	0.378558i
$190$	1.01722	−	3.13068i	0.0737970	−	0.227124i
$191$	5.66312	+	17.4293i	0.409769	+	1.26114i	0.916847	+	0.399239i	$0.130726\pi$
$191$	5.66312	+	17.4293i	0.409769	+	1.26114i	−0.507078	+	0.861900i	$0.669274\pi$
$192$	1.30902	−	0.951057i	0.0944702	−	0.0686366i
$193$	17.2533	−	12.5352i	1.24192	−	0.902307i	0.244194	−	0.969726i	$-0.421477\pi$
$193$	17.2533	−	12.5352i	1.24192	−	0.902307i	0.997725	+	0.0674194i	$0.0214766\pi$
$194$	5.50000	+	16.9273i	0.394877	+	1.21531i
$195$	−2.07295	+	6.37988i	−0.148447	+	0.456873i
$196$	3.54508	+	2.57565i	0.253220	+	0.183975i
$197$	−8.23607			−0.586796			−0.293398	−	0.955990i	$-0.594786\pi$
$197$	−8.23607			−0.586796			−0.293398	+	0.955990i	$0.594786\pi$
$198$	0.836881	−	0.951057i	0.0594745	−	0.0675886i
$199$	13.0902			0.927938			0.463969	−	0.885852i	$-0.346425\pi$
$199$	13.0902			0.927938			0.463969	+	0.885852i	$0.346425\pi$
$200$		0			0
$201$	−5.97214	+	18.3803i	−0.421242	+	1.29645i
$202$	−0.517221	−	1.59184i	−0.0363915	−	0.112002i
$203$	−3.92705	+	2.85317i	−0.275625	+	0.200253i
$204$	1.30902	−	0.951057i	0.0916495	−	0.0665873i
$205$	−3.45492	−	10.6331i	−0.241302	−	0.742650i
$206$	2.26393	−	6.96767i	0.157736	−	0.485460i
$207$	0.618034	+	0.449028i	0.0429563	+	0.0312096i
$208$	1.85410			0.128559
$209$	4.76393	−	1.06957i	0.329528	−	0.0739837i
$210$	5.85410			0.403971
$211$	−11.7812	−	8.55951i	−0.811048	−	0.589261i	0.103086	−	0.994672i	$-0.467128\pi$
$211$	−11.7812	−	8.55951i	−0.811048	−	0.589261i	−0.914134	+	0.405412i	$0.867128\pi$
$212$	−1.54508	+	4.75528i	−0.106117	+	0.326594i
$213$	−2.04508	−	6.29412i	−0.140127	−	0.431266i
$214$	9.47214	−	6.88191i	0.647502	−	0.470438i
$215$	−19.7984	+	14.3844i	−1.35024	+	0.981005i
$216$	−1.69098	−	5.20431i	−0.115057	−	0.354108i
$217$	−3.61803	+	11.1352i	−0.245608	+	0.755904i
$218$	−0.0729490	−	0.0530006i	−0.00494073	−	0.00358965i
$219$	−13.3262			−0.900504
$220$	−0.690983	+	7.38394i	−0.0465861	+	0.497825i
$221$	1.85410			0.124720
$222$	−0.309017	−	0.224514i	−0.0207399	−	0.0150684i
$223$	−8.40983	+	25.8828i	−0.563164	+	1.73324i	0.110181	+	0.993912i	$0.464857\pi$
$223$	−8.40983	+	25.8828i	−0.563164	+	1.73324i	−0.673345	+	0.739329i	$0.735143\pi$
$224$	−0.500000	−	1.53884i	−0.0334077	−	0.102818i
$225$		0			0
$226$	3.54508	−	2.57565i	0.235816	−	0.171330i
$227$	−1.79180	−	5.51458i	−0.118926	−	0.366016i	0.873820	−	0.486250i	$-0.161635\pi$
$227$	−1.79180	−	5.51458i	−0.118926	−	0.366016i	−0.992746	+	0.120234i	$0.961635\pi$
$228$	0.736068	−	2.26538i	0.0487473	−	0.150029i
$229$	0.190983	+	0.138757i	0.0126205	+	0.00916934i	0.594078	−	0.804408i	$-0.297517\pi$
$229$	0.190983	+	0.138757i	0.0126205	+	0.00916934i	−0.581457	+	0.813577i	$0.697517\pi$
$230$	−4.47214			−0.294884
$231$	4.42705	+	7.46969i	0.291279	+	0.491470i
$232$	−3.00000			−0.196960
$233$	−10.0451	−	7.29818i	−0.658075	−	0.478120i	0.207937	−	0.978142i	$-0.433325\pi$
$233$	−10.0451	−	7.29818i	−0.658075	−	0.478120i	−0.866012	+	0.500022i	$0.833325\pi$
$234$	0.218847	−	0.673542i	0.0143065	−	0.0440308i
$235$	6.54508	+	20.1437i	0.426954	+	1.31403i
$236$	4.85410	−	3.52671i	0.315975	−	0.229569i
$237$	6.16312	−	4.47777i	0.400338	−	0.290862i
$238$	−0.500000	−	1.53884i	−0.0324102	−	0.0997483i
$239$	7.48936	−	23.0499i	0.484446	−	1.49097i	−0.348335	−	0.937370i	$-0.613253\pi$
$239$	7.48936	−	23.0499i	0.484446	−	1.49097i	0.832781	−	0.553602i	$-0.186747\pi$
$240$	2.92705	+	2.12663i	0.188940	+	0.137273i
$241$	24.0902			1.55178			0.775892	−	0.630866i	$-0.217300\pi$
$241$	24.0902			1.55178			0.775892	+	0.630866i	$0.217300\pi$
$242$	−9.94427	+	4.70228i	−0.639242	+	0.302274i
$243$	−3.94427			−0.253025
$244$	−10.2082	−	7.41669i	−0.653513	−	0.474805i
$245$	−3.02786	+	9.31881i	−0.193443	+	0.595357i
$246$	−2.50000	−	7.69421i	−0.159394	−	0.490565i
$247$	2.20820	−	1.60435i	0.140505	−	0.102083i
$248$	−5.85410	+	4.25325i	−0.371736	+	0.270082i
$249$	−1.07295	−	3.30220i	−0.0679954	−	0.209268i
$250$	3.45492	−	10.6331i	0.218508	−	0.672499i
$251$	−8.09017	−	5.87785i	−0.510647	−	0.371007i	0.302422	−	0.953174i	$-0.402205\pi$
$251$	−8.09017	−	5.87785i	−0.510647	−	0.371007i	−0.813069	+	0.582167i	$0.802205\pi$
$252$	−0.618034			−0.0389325
$253$	−3.38197	−	5.70634i	−0.212622	−	0.358754i
$254$	0.944272			0.0592489
$255$	2.92705	+	2.12663i	0.183299	+	0.133175i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−2.44427	−	7.52270i	−0.152469	−	0.469253i	0.845426	−	0.534092i	$-0.179346\pi$
$257$	−2.44427	−	7.52270i	−0.152469	−	0.469253i	−0.997896	+	0.0648394i	$0.979346\pi$
$258$	−14.3262	+	10.4086i	−0.891913	+	0.648012i
$259$	−0.309017	+	0.224514i	−0.0192014	+	0.0139506i
$260$	1.28115	+	3.94298i	0.0794537	+	0.244533i
$261$	−0.354102	+	1.08981i	−0.0219184	+	0.0674578i
$262$	−6.11803	−	4.44501i	−0.377973	−	0.274614i
$263$	0.381966			0.0235530			0.0117765	−	0.999931i	$-0.496251\pi$
$263$	0.381966			0.0235530			0.0117765	+	0.999931i	$0.496251\pi$
$264$	−0.500000	+	5.34307i	−0.0307729	+	0.328843i
$265$	−11.1803			−0.686803
$266$	−1.92705	−	1.40008i	−0.118155	−	0.0858447i
$267$	−1.64590	+	5.06555i	−0.100727	+	0.310007i
$268$	3.69098	+	11.3597i	0.225463	+	0.693903i
$269$	−12.0623	+	8.76378i	−0.735452	+	0.534337i	−0.891283	−	0.453447i	$-0.850194\pi$
$269$	−12.0623	+	8.76378i	−0.735452	+	0.534337i	0.155832	+	0.987784i	$0.450194\pi$
$270$	9.89919	−	7.19218i	0.602445	−	0.437702i
$271$	2.36475	+	7.27794i	0.143648	+	0.442103i	0.996835	−	0.0795026i	$-0.0253332\pi$
$271$	2.36475	+	7.27794i	0.143648	+	0.442103i	−0.853187	+	0.521606i	$0.825333\pi$
$272$	0.309017	−	0.951057i	0.0187369	−	0.0576663i
$273$	3.92705	+	2.85317i	0.237676	+	0.172682i
$274$	6.29180			0.380101
$275$		0			0
$276$	−3.23607			−0.194788
$277$	−1.88197	−	1.36733i	−0.113076	−	0.0821548i	0.529810	−	0.848116i	$-0.322263\pi$
$277$	−1.88197	−	1.36733i	−0.113076	−	0.0821548i	−0.642886	+	0.765962i	$0.722263\pi$
$278$	4.63525	−	14.2658i	0.278004	−	0.855609i
$279$	0.854102	+	2.62866i	0.0511337	+	0.157373i
$280$	2.92705	−	2.12663i	0.174925	−	0.127090i
$281$	−19.9894	+	14.5231i	−1.19247	+	0.866377i	−0.993523	−	0.113635i	$-0.963751\pi$
$281$	−19.9894	+	14.5231i	−1.19247	+	0.866377i	−0.198942	+	0.980011i	$0.563751\pi$
$282$	4.73607	+	14.5761i	0.282029	+	0.867995i
$283$	10.1008	−	31.0871i	0.600431	−	1.84794i	0.0748468	−	0.997195i	$-0.476153\pi$
$283$	10.1008	−	31.0871i	0.600431	−	1.84794i	0.525584	−	0.850742i	$-0.323847\pi$
$284$	−3.30902	−	2.40414i	−0.196354	−	0.142660i
$285$	5.32624			0.315499
$286$	−4.06231	+	4.61653i	−0.240209	+	0.272981i
$287$	−8.09017			−0.477548
$288$	−0.309017	−	0.224514i	−0.0182090	−	0.0132296i
$289$	0.309017	−	0.951057i	0.0181775	−	0.0559445i
$290$	−2.07295	−	6.37988i	−0.121728	−	0.374640i
$291$	−23.2984	+	16.9273i	−1.36577	+	0.992294i
$292$	−6.66312	+	4.84104i	−0.389930	+	0.283300i
$293$	−0.954915	−	2.93893i	−0.0557867	−	0.171694i	0.919281	−	0.393602i	$-0.128771\pi$
$293$	−0.954915	−	2.93893i	−0.0557867	−	0.171694i	−0.975067	+	0.221909i	$0.928771\pi$
$294$	−2.19098	+	6.74315i	−0.127781	+	0.393269i
$295$	10.8541	+	7.88597i	0.631950	+	0.459139i
$296$	−0.236068			−0.0137212
$297$	16.6631	+	7.19218i	0.966892	+	0.417333i
$298$	−10.3820			−0.601411
$299$	−3.00000	−	2.17963i	−0.173494	−	0.126051i
$300$		0			0
$301$	5.47214	+	16.8415i	0.315409	+	0.970728i
$302$	7.89919	−	5.73910i	0.454547	−	0.330248i
$303$	2.19098	−	1.59184i	0.125869	−	0.0914490i
$304$	−0.454915	−	1.40008i	−0.0260912	−	0.0803004i
$305$	8.71885	−	26.8339i	0.499240	−	1.53650i
$306$	−0.309017	−	0.224514i	−0.0176653	−	0.0128346i
$307$	19.6525			1.12163			0.560813	−	0.827942i	$-0.310489\pi$
$307$	19.6525			1.12163			0.560813	+	0.827942i	$0.310489\pi$
$308$	4.92705	+	2.12663i	0.280745	+	0.121176i
$309$	11.8541			0.674356
$310$	−13.0902	−	9.51057i	−0.743472	−	0.540164i
$311$	−0.489357	+	1.50609i	−0.0277489	+	0.0854023i	−0.963972	−	0.266004i	$-0.914296\pi$
$311$	−0.489357	+	1.50609i	−0.0277489	+	0.0854023i	0.936223	+	0.351407i	$0.114296\pi$
$312$	0.927051	+	2.85317i	0.0524839	+	0.161529i
$313$	14.7361	−	10.7064i	0.832932	−	0.605160i	−0.0874554	−	0.996168i	$-0.527874\pi$
$313$	14.7361	−	10.7064i	0.832932	−	0.605160i	0.920387	+	0.391008i	$0.127874\pi$
$314$	−10.5902	+	7.69421i	−0.597638	+	0.434209i
$315$	−0.427051	−	1.31433i	−0.0240616	−	0.0740540i
$316$	1.45492	−	4.47777i	0.0818454	−	0.251894i
$317$	4.92705	+	3.57971i	0.276731	+	0.201057i	0.717490	−	0.696569i	$-0.245291\pi$
$317$	4.92705	+	3.57971i	0.276731	+	0.201057i	−0.440759	+	0.897625i	$0.645291\pi$
$318$	−8.09017			−0.453674
$319$	6.57295	−	7.46969i	0.368014	−	0.418223i
$320$	2.23607			0.125000
$321$	15.3262	+	11.1352i	0.855427	+	0.621504i
$322$	−1.00000	+	3.07768i	−0.0557278	+	0.171513i
$323$	−0.454915	−	1.40008i	−0.0253121	−	0.0779028i
$324$	6.23607	−	4.53077i	0.346448	−	0.251709i
$325$		0			0
$326$	0.0172209	+	0.0530006i	0.000953779	+	0.00293543i
$327$	0.0450850	−	0.138757i	0.00249320	−	0.00767329i
$328$	−4.04508	−	2.93893i	−0.223352	−	0.162275i
$329$	15.3262			0.844963
$330$	−11.7082	+	2.62866i	−0.644515	+	0.144703i
$331$	7.47214			0.410706			0.205353	−	0.978688i	$-0.434166\pi$
$331$	7.47214			0.410706			0.205353	+	0.978688i	$0.434166\pi$
$332$	−1.73607	−	1.26133i	−0.0952791	−	0.0692243i
$333$	−0.0278640	+	0.0857567i	−0.00152694	+	0.00469944i
$334$	0.364745	+	1.12257i	0.0199580	+	0.0614243i
$335$	−21.6074	+	15.6987i	−1.18054	+	0.857711i
$336$	2.11803	−	1.53884i	0.115548	−	0.0839507i
$337$	−7.87132	−	24.2254i	−0.428778	−	1.31964i	−0.899330	−	0.437271i	$-0.855945\pi$
$337$	−7.87132	−	24.2254i	−0.428778	−	1.31964i	0.470551	−	0.882373i	$-0.344055\pi$
$338$	2.95492	−	9.09429i	0.160726	−	0.494664i
$339$	5.73607	+	4.16750i	0.311540	+	0.226347i
$340$	2.23607			0.121268
$341$	2.23607	−	23.8949i	0.121090	−	1.29398i
$342$	−0.562306			−0.0304060
$343$	14.8992	+	10.8249i	0.804480	+	0.584489i
$344$	−3.38197	+	10.4086i	−0.182343	+	0.561195i
$345$	−2.23607	−	6.88191i	−0.120386	−	0.370510i
$346$	5.78115	−	4.20025i	0.310797	−	0.225807i
$347$	8.04508	−	5.84510i	0.431883	−	0.313781i	−0.350519	−	0.936556i	$-0.613995\pi$
$347$	8.04508	−	5.84510i	0.431883	−	0.313781i	0.782401	+	0.622775i	$0.213995\pi$
$348$	−1.50000	−	4.61653i	−0.0804084	−	0.247472i
$349$	1.08359	−	3.33495i	0.0580034	−	0.178516i	−0.917857	−	0.396911i	$-0.870082\pi$
$349$	1.08359	−	3.33495i	0.0580034	−	0.178516i	0.975860	+	0.218395i	$0.0700821\pi$
$350$		0			0
$351$	10.1459			0.541548
$352$	1.69098	+	2.85317i	0.0901297	+	0.152074i
$353$	36.5410			1.94488			0.972441	−	0.233149i	$-0.0749029\pi$
$353$	36.5410			1.94488			0.972441	+	0.233149i	$0.0749029\pi$
$354$	7.85410	+	5.70634i	0.417441	+	0.303289i
$355$	2.82624	−	8.69827i	0.150001	−	0.461656i
$356$	1.01722	+	3.13068i	0.0539126	+	0.165926i
$357$	2.11803	−	1.53884i	0.112098	−	0.0814441i
$358$	13.4443	−	9.76784i	0.710552	−	0.516246i
$359$	6.60081	+	20.3152i	0.348378	+	1.07220i	0.959751	+	0.280853i	$0.0906175\pi$
$359$	6.60081	+	20.3152i	0.348378	+	1.07220i	−0.611373	+	0.791343i	$0.709383\pi$
$360$	0.263932	−	0.812299i	0.0139104	−	0.0428119i
$361$	13.6180	+	9.89408i	0.716739	+	0.520741i
$362$	−16.8541			−0.885832
$363$	−12.2082	−	12.9515i	−0.640765	−	0.679779i
$364$	3.00000			0.157243
$365$	−14.8992	−	10.8249i	−0.779859	−	0.566601i
$366$	6.30902	−	19.4172i	0.329778	−	1.01495i
$367$	9.06231	+	27.8909i	0.473049	+	1.45589i	0.848572	+	0.529081i	$0.177463\pi$
$367$	9.06231	+	27.8909i	0.473049	+	1.45589i	−0.375523	+	0.926813i	$0.622537\pi$
$368$	−1.61803	+	1.17557i	−0.0843459	+	0.0612808i
$369$	−1.54508	+	1.12257i	−0.0804339	+	0.0584387i
$370$	−0.163119	−	0.502029i	−0.00848015	−	0.0260992i
$371$	−2.50000	+	7.69421i	−0.129794	+	0.399463i
$372$	−9.47214	−	6.88191i	−0.491107	−	0.356810i
$373$	4.56231			0.236227			0.118114	−	0.993000i	$-0.462315\pi$
$373$	4.56231			0.236227			0.118114	+	0.993000i	$0.462315\pi$
$374$	1.69098	+	2.85317i	0.0874386	+	0.147534i
$375$	18.0902			0.934172
$376$	7.66312	+	5.56758i	0.395195	+	0.287126i
$377$	1.71885	−	5.29007i	0.0885251	−	0.272452i
$378$	−2.73607	−	8.42075i	−0.140728	−	0.433117i
$379$	29.0066	−	21.0745i	1.48997	−	1.08252i	0.515797	−	0.856711i	$-0.327496\pi$
$379$	29.0066	−	21.0745i	1.48997	−	1.08252i	0.974170	−	0.225814i	$-0.0725043\pi$
$380$	2.66312	−	1.93487i	0.136615	−	0.0992567i
$381$	0.472136	+	1.45309i	0.0241883	+	0.0744438i
$382$	−5.66312	+	17.4293i	−0.289750	+	0.891760i
$383$	−23.3713	−	16.9803i	−1.19422	−	0.867651i	−0.200515	−	0.979691i	$-0.564262\pi$
$383$	−23.3713	−	16.9803i	−1.19422	−	0.867651i	−0.993704	+	0.112040i	$0.964262\pi$
$384$	1.61803			0.0825700
$385$	−1.11803	+	11.9475i	−0.0569803	+	0.608899i
$386$	21.3262			1.08548
$387$	3.38197	+	2.45714i	0.171915	+	0.124904i
$388$	−5.50000	+	16.9273i	−0.279220	+	0.859351i
$389$	0.826238	+	2.54290i	0.0418919	+	0.128930i	0.969815	−	0.243841i	$-0.0784076\pi$
$389$	0.826238	+	2.54290i	0.0418919	+	0.128930i	−0.927923	+	0.372771i	$0.878408\pi$
$390$	−5.42705	+	3.94298i	−0.274809	+	0.199661i
$391$	−1.61803	+	1.17557i	−0.0818275	+	0.0594512i
$392$	1.35410	+	4.16750i	0.0683925	+	0.210490i
$393$	3.78115	−	11.6372i	0.190734	−	0.587019i
$394$	−6.66312	−	4.84104i	−0.335683	−	0.243888i
$395$	10.5279			0.529714
$396$	1.23607	−	0.277515i	0.0621148	−	0.0139456i
$397$	24.7082			1.24007			0.620035	−	0.784574i	$-0.287119\pi$
$397$	24.7082			1.24007			0.620035	+	0.784574i	$0.287119\pi$
$398$	10.5902	+	7.69421i	0.530837	+	0.385676i
$399$	1.19098	−	3.66547i	0.0596237	−	0.183503i
$400$		0			0
$401$	−4.39919	+	3.19620i	−0.219685	+	0.159610i	−0.692185	−	0.721720i	$-0.743352\pi$
$401$	−4.39919	+	3.19620i	−0.219685	+	0.159610i	0.472500	+	0.881331i	$0.343352\pi$
$402$	−15.6353	+	11.3597i	−0.779816	+	0.566569i
$403$	−4.14590	−	12.7598i	−0.206522	−	0.635609i
$404$	0.517221	−	1.59184i	0.0257327	−	0.0791971i
$405$	13.9443	+	10.1311i	0.692896	+	0.503419i
$406$	−4.85410			−0.240905
$407$	0.517221	−	0.587785i	0.0256377	−	0.0291354i
$408$	1.61803			0.0801046
$409$	−31.7254	−	23.0499i	−1.56872	−	1.13974i	−0.928368	−	0.371662i	$-0.878788\pi$
$409$	−31.7254	−	23.0499i	−1.56872	−	1.13974i	−0.640353	−	0.768081i	$-0.721212\pi$
$410$	3.45492	−	10.6331i	0.170626	−	0.525133i
$411$	3.14590	+	9.68208i	0.155176	+	0.477582i
$412$	5.92705	−	4.30625i	0.292005	−	0.212154i
$413$	7.85410	−	5.70634i	0.386475	−	0.280791i
$414$	0.236068	+	0.726543i	0.0116021	+	0.0357076i
$415$	1.48278	−	4.56352i	0.0727868	−	0.224015i
$416$	1.50000	+	1.08981i	0.0735436	+	0.0534325i
$417$	24.2705			1.18853
$418$	4.48278	+	1.93487i	0.219260	+	0.0946375i
$419$	6.70820			0.327717			0.163859	−	0.986484i	$-0.447606\pi$
$419$	6.70820			0.327717			0.163859	+	0.986484i	$0.447606\pi$
$420$	4.73607	+	3.44095i	0.231096	+	0.167901i
$421$	−6.78115	+	20.8702i	−0.330493	+	1.01715i	0.638406	+	0.769699i	$0.279594\pi$
$421$	−6.78115	+	20.8702i	−0.330493	+	1.01715i	−0.968900	+	0.247454i	$0.920406\pi$
$422$	−4.50000	−	13.8496i	−0.219057	−	0.674187i
$423$	2.92705	−	2.12663i	0.142318	−	0.103400i
$424$	−4.04508	+	2.93893i	−0.196447	+	0.142727i
$425$		0			0
$426$	2.04508	−	6.29412i	0.0990847	−	0.304951i
$427$	−16.5172	−	12.0005i	−0.799324	−	0.580743i
$428$	11.7082			0.565937
$429$	−9.13525	−	3.94298i	−0.441054	−	0.190369i
$430$	−24.4721			−1.18015
$431$	24.4164	+	17.7396i	1.17610	+	0.854484i	0.991726	−	0.128372i	$-0.0409752\pi$
$431$	24.4164	+	17.7396i	1.17610	+	0.854484i	0.184371	+	0.982857i	$0.440975\pi$
$432$	1.69098	−	5.20431i	0.0813575	−	0.250393i
$433$	−3.10739	−	9.56357i	−0.149332	−	0.459596i	0.848211	−	0.529659i	$-0.177680\pi$
$433$	−3.10739	−	9.56357i	−0.149332	−	0.459596i	−0.997543	+	0.0700630i	$0.977680\pi$
$434$	−9.47214	+	6.88191i	−0.454677	+	0.330342i
$435$	8.78115	−	6.37988i	0.421024	−	0.305892i
$436$	−0.0278640	−	0.0857567i	−0.00133445	−	0.00410700i
$437$	−0.909830	+	2.80017i	−0.0435231	+	0.133950i
$438$	−10.7812	−	7.83297i	−0.515143	−	0.374274i
$439$	−29.0902			−1.38840			−0.694199	−	0.719783i	$-0.744241\pi$
$439$	−29.0902			−1.38840			−0.694199	+	0.719783i	$0.744241\pi$
$440$	−4.89919	+	5.56758i	−0.233560	+	0.265424i
$441$	1.67376			0.0797030
$442$	1.50000	+	1.08981i	0.0713477	+	0.0518372i
$443$	1.80902	−	5.56758i	0.0859490	−	0.264524i	−0.898840	−	0.438276i	$-0.855589\pi$
$443$	1.80902	−	5.56758i	0.0859490	−	0.264524i	0.984789	+	0.173752i	$0.0555892\pi$
$444$	−0.118034	−	0.363271i	−0.00560165	−	0.0172401i
$445$	−5.95492	+	4.32650i	−0.282290	+	0.205096i
$446$	−22.0172	+	15.9964i	−1.04255	+	0.757454i
$447$	−5.19098	−	15.9762i	−0.245525	−	0.755648i
$448$	0.500000	−	1.53884i	0.0236228	−	0.0727034i
$449$	−16.2984	−	11.8415i	−0.769168	−	0.558833i	0.132541	−	0.991178i	$-0.457686\pi$
$449$	−16.2984	−	11.8415i	−0.769168	−	0.558833i	−0.901709	+	0.432344i	$0.857686\pi$
$450$		0			0
$451$	16.1803	−	3.63271i	0.761902	−	0.171058i
$452$	4.38197			0.206110
$453$	12.7812	+	9.28605i	0.600511	+	0.436297i
$454$	1.79180	−	5.51458i	0.0840932	−	0.258812i
$455$	2.07295	+	6.37988i	0.0971813	+	0.299093i
$456$	1.92705	−	1.40008i	0.0902424	−	0.0655650i
$457$	−28.5066	+	20.7112i	−1.33348	+	0.968831i	−0.333825	+	0.942635i	$0.608339\pi$
$457$	−28.5066	+	20.7112i	−1.33348	+	0.968831i	−0.999657	+	0.0261958i	$0.991661\pi$
$458$	0.0729490	+	0.224514i	0.00340868	+	0.0104908i
$459$	1.69098	−	5.20431i	0.0789283	−	0.242916i
$460$	−3.61803	−	2.62866i	−0.168692	−	0.122562i
$461$	−3.05573			−0.142319			−0.0711597	−	0.997465i	$-0.522670\pi$
$461$	−3.05573			−0.142319			−0.0711597	+	0.997465i	$0.522670\pi$
$462$	−0.809017	+	8.64527i	−0.0376389	+	0.402214i
$463$	13.0902			0.608352			0.304176	−	0.952616i	$-0.401619\pi$
$463$	13.0902			0.608352			0.304176	+	0.952616i	$0.401619\pi$
$464$	−2.42705	−	1.76336i	−0.112673	−	0.0818617i
$465$	8.09017	−	24.8990i	0.375173	−	1.15466i
$466$	−3.83688	−	11.8087i	−0.177740	−	0.547028i
$467$	−19.7533	+	14.3516i	−0.914073	+	0.664113i	−0.942042	−	0.335496i	$-0.891096\pi$
$467$	−19.7533	+	14.3516i	−0.914073	+	0.664113i	0.0279685	+	0.999609i	$0.491096\pi$
$468$	0.572949	−	0.416272i	0.0264846	−	0.0192422i
$469$	5.97214	+	18.3803i	0.275768	+	0.848725i
$470$	−6.54508	+	20.1437i	−0.301902	+	0.929160i
$471$	−17.1353	−	12.4495i	−0.789551	−	0.573642i
$472$	6.00000			0.276172
$473$	−18.5066	−	31.2259i	−0.850933	−	1.43577i
$474$	7.61803			0.349908
$475$		0			0
$476$	0.500000	−	1.53884i	0.0229175	−	0.0705327i
$477$	0.590170	+	1.81636i	0.0270220	+	0.0831652i
$478$	19.6074	−	14.2456i	0.896821	−	0.651579i
$479$	−12.9443	+	9.40456i	−0.591439	+	0.429705i	−0.842830	−	0.538180i	$-0.819112\pi$
$479$	−12.9443	+	9.40456i	−0.591439	+	0.429705i	0.251391	+	0.967886i	$0.419112\pi$
$480$	1.11803	+	3.44095i	0.0510310	+	0.157057i
$481$	0.135255	−	0.416272i	0.00616709	−	0.0189804i
$482$	19.4894	+	14.1598i	0.887716	+	0.644963i
$483$	−5.23607			−0.238249
$484$	−10.8090	−	2.04087i	−0.491319	−	0.0927668i
$485$	−39.7984			−1.80715
$486$	−3.19098	−	2.31838i	−0.144746	−	0.105164i
$487$	8.39919	−	25.8500i	0.380603	−	1.17138i	−0.559016	−	0.829157i	$-0.688821\pi$
$487$	8.39919	−	25.8500i	0.380603	−	1.17138i	0.939620	−	0.342220i	$-0.111179\pi$
$488$	−3.89919	−	12.0005i	−0.176508	−	0.543235i
$489$	−0.0729490	+	0.0530006i	−0.00329887	+	0.00239677i
$490$	−7.92705	+	5.75934i	−0.358108	+	0.260180i
$491$	5.82624	+	17.9313i	0.262934	+	0.809229i	0.992162	+	0.124958i	$0.0398795\pi$
$491$	5.82624	+	17.9313i	0.262934	+	0.809229i	−0.729228	+	0.684271i	$0.760120\pi$
$492$	2.50000	−	7.69421i	0.112709	−	0.346882i
$493$	−2.42705	−	1.76336i	−0.109309	−	0.0794175i
$494$	2.72949			0.122806
$495$	1.44427	+	2.43690i	0.0649152	+	0.109530i
$496$	−7.23607			−0.324909
$497$	−5.35410	−	3.88998i	−0.240164	−	0.174490i
$498$	1.07295	−	3.30220i	0.0480800	−	0.147975i
$499$	5.65248	+	17.3965i	0.253040	+	0.778776i	0.994210	+	0.107458i	$0.0342712\pi$
$499$	5.65248	+	17.3965i	0.253040	+	0.778776i	−0.741170	+	0.671317i	$0.765729\pi$
$500$	9.04508	−	6.57164i	0.404508	−	0.293893i
$501$	−1.54508	+	1.12257i	−0.0690293	+	0.0501527i
$502$	−3.09017	−	9.51057i	−0.137921	−	0.424477i
$503$	−6.05573	+	18.6376i	−0.270012	+	0.831010i	0.720485	+	0.693471i	$0.243919\pi$
$503$	−6.05573	+	18.6376i	−0.270012	+	0.831010i	−0.990496	+	0.137539i	$0.956081\pi$
$504$	−0.500000	−	0.363271i	−0.0222718	−	0.0161814i
$505$	3.74265			0.166546
$506$	0.618034	−	6.60440i	0.0274750	−	0.293601i
$507$	15.4721			0.687142
$508$	0.763932	+	0.555029i	0.0338940	+	0.0246254i
$509$	−2.92705	+	9.00854i	−0.129739	+	0.399296i	−0.994735	−	0.102483i	$-0.967321\pi$
$509$	−2.92705	+	9.00854i	−0.129739	+	0.399296i	0.864995	+	0.501780i	$0.167321\pi$
$510$	1.11803	+	3.44095i	0.0495074	+	0.152368i
$511$	−10.7812	+	7.83297i	−0.476930	+	0.346510i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−2.48936	−	7.66145i	−0.109908	−	0.338261i
$514$	2.44427	−	7.52270i	0.107812	−	0.331812i
$515$	13.2533	+	9.62908i	0.584010	+	0.424308i
$516$	−17.7082			−0.779560
$517$	−30.6525	+	6.88191i	−1.34809	+	0.302666i
$518$	−0.381966			−0.0167826
$519$	9.35410	+	6.79615i	0.410600	+	0.298318i
$520$	−1.28115	+	3.94298i	−0.0561823	+	0.172911i
$521$	10.9828	+	33.8015i	0.481164	+	1.48087i	0.837460	+	0.546498i	$0.184039\pi$
$521$	10.9828	+	33.8015i	0.481164	+	1.48087i	−0.356296	+	0.934373i	$0.615961\pi$
$522$	−0.927051	+	0.673542i	−0.0405759	+	0.0294801i
$523$	−5.35410	+	3.88998i	−0.234119	+	0.170097i	−0.698659	−	0.715455i	$-0.746220\pi$
$523$	−5.35410	+	3.88998i	−0.234119	+	0.170097i	0.464540	+	0.885552i	$0.346220\pi$
$524$	−2.33688	−	7.19218i	−0.102087	−	0.314192i
$525$		0			0
$526$	0.309017	+	0.224514i	0.0134738	+	0.00978928i
$527$	−7.23607			−0.315208
$528$	−3.54508	+	4.02874i	−0.154280	+	0.175328i
$529$	−19.0000			−0.826087
$530$	−9.04508	−	6.57164i	−0.392893	−	0.285454i
$531$	0.708204	−	2.17963i	0.0307334	−	0.0945878i
$532$	−0.736068	−	2.26538i	−0.0319126	−	0.0982169i
$533$	7.50000	−	5.44907i	0.324861	−	0.236025i
$534$	−4.30902	+	3.13068i	−0.186469	+	0.135478i
$535$	8.09017	+	24.8990i	0.349769	+	1.07648i
$536$	−3.69098	+	11.3597i	−0.159426	+	0.490663i
$537$	21.7533	+	15.8047i	0.938724	+	0.682023i
$538$	−14.9098			−0.642808
$539$	−13.3435	−	5.75934i	−0.574743	−	0.248072i
$540$	12.2361			0.526557
$541$	−11.1910	−	8.13073i	−0.481138	−	0.349567i	0.320628	−	0.947205i	$-0.396106\pi$
$541$	−11.1910	−	8.13073i	−0.481138	−	0.349567i	−0.801766	+	0.597638i	$0.796106\pi$
$542$	−2.36475	+	7.27794i	−0.101574	+	0.312614i
$543$	−8.42705	−	25.9358i	−0.361639	−	1.11301i
$544$	0.809017	−	0.587785i	0.0346863	−	0.0252011i
$545$	0.163119	−	0.118513i	0.00698725	−	0.00507653i
$546$	1.50000	+	4.61653i	0.0641941	+	0.197569i
$547$	−5.57953	+	17.1720i	−0.238563	+	0.734222i	0.758065	+	0.652179i	$0.226145\pi$
$547$	−5.57953	+	17.1720i	−0.238563	+	0.734222i	−0.996629	+	0.0820439i	$0.973855\pi$
$548$	5.09017	+	3.69822i	0.217441	+	0.157980i
$549$	−4.81966			−0.205698
$550$		0			0
$551$	−4.41641			−0.188145
$552$	−2.61803	−	1.90211i	−0.111431	−	0.0809593i
$553$	2.35410	−	7.24518i	0.100107	−	0.308096i
$554$	−0.718847	−	2.21238i	−0.0305409	−	0.0939952i
$555$	0.690983	−	0.502029i	0.0293306	−	0.0213099i
$556$	12.1353	−	8.81678i	0.514649	−	0.373915i
$557$	−1.65654	−	5.09831i	−0.0701899	−	0.216022i	0.909808	−	0.415029i	$-0.136229\pi$
$557$	−1.65654	−	5.09831i	−0.0701899	−	0.216022i	−0.979998	+	0.199007i	$0.936229\pi$
$558$	−0.854102	+	2.62866i	−0.0361570	+	0.111280i
$559$	−16.4164	−	11.9272i	−0.694340	−	0.504468i
$560$	3.61803			0.152890
$561$	−3.54508	+	4.02874i	−0.149674	+	0.170094i
$562$	−24.7082			−1.04225
$563$	26.7984	+	19.4702i	1.12942	+	0.820569i	0.985610	−	0.169036i	$-0.0540655\pi$
$563$	26.7984	+	19.4702i	1.12942	+	0.820569i	0.143807	+	0.989606i	$0.454066\pi$
$564$	−4.73607	+	14.5761i	−0.199424	+	0.613765i
$565$	3.02786	+	9.31881i	0.127383	+	0.392045i
$566$	26.4443	−	19.2129i	1.11154	−	0.807578i
$567$	10.0902	−	7.33094i	0.423747	−	0.307870i
$568$	−1.26393	−	3.88998i	−0.0530334	−	0.163220i
$569$	−8.88197	+	27.3359i	−0.372351	+	1.14598i	0.572897	+	0.819627i	$0.305820\pi$
$569$	−8.88197	+	27.3359i	−0.372351	+	1.14598i	−0.945248	+	0.326352i	$0.894180\pi$
$570$	4.30902	+	3.13068i	0.180485	+	0.131130i
$571$	−43.0132			−1.80004			−0.900022	−	0.435844i	$-0.856450\pi$
$571$	−43.0132			−1.80004			−0.900022	+	0.435844i	$0.856450\pi$
$572$	−6.00000	+	1.34708i	−0.250873	+	0.0563244i
$573$	−29.6525			−1.23875
$574$	−6.54508	−	4.75528i	−0.273187	−	0.198482i
$575$		0			0
$576$	−0.118034	−	0.363271i	−0.00491808	−	0.0151363i
$577$	17.9443	−	13.0373i	0.747030	−	0.542749i	−0.147875	−	0.989006i	$-0.547243\pi$
$577$	17.9443	−	13.0373i	0.747030	−	0.542749i	0.894905	+	0.446257i	$0.147243\pi$
$578$	0.809017	−	0.587785i	0.0336507	−	0.0244486i
$579$	10.6631	+	32.8177i	0.443144	+	1.36386i
$580$	2.07295	−	6.37988i	0.0860745	−	0.264910i
$581$	−2.80902	−	2.04087i	−0.116538	−	0.0846696i
$582$	−28.7984			−1.19373
$583$	1.54508	−	16.5110i	0.0639909	−	0.683815i
$584$	−8.23607			−0.340811
$585$	1.28115	+	0.930812i	0.0529692	+	0.0384843i
$586$	0.954915	−	2.93893i	0.0394472	−	0.121406i
$587$	14.8369	+	45.6632i	0.612384	+	1.88472i	0.434501	+	0.900671i	$0.356925\pi$
$587$	14.8369	+	45.6632i	0.612384	+	1.88472i	0.177882	+	0.984052i	$0.443075\pi$
$588$	−5.73607	+	4.16750i	−0.236551	+	0.171865i
$589$	−8.61803	+	6.26137i	−0.355100	+	0.257995i
$590$	4.14590	+	12.7598i	0.170684	+	0.525311i
$591$	4.11803	−	12.6740i	0.169393	−	0.521339i
$592$	−0.190983	−	0.138757i	−0.00784935	−	0.00570289i
$593$	−37.1803			−1.52681			−0.763407	−	0.645918i	$-0.776475\pi$
$593$	−37.1803			−1.52681			−0.763407	+	0.645918i	$0.776475\pi$
$594$	9.25329	+	15.6129i	0.379667	+	0.640606i
$595$	3.61803			0.148325
$596$	−8.39919	−	6.10237i	−0.344044	−	0.249963i
$597$	−6.54508	+	20.1437i	−0.267872	+	0.824427i
$598$	−1.14590	−	3.52671i	−0.0468593	−	0.144218i
$599$	35.6803	−	25.9233i	1.45786	−	1.05920i	0.473945	−	0.880554i	$-0.342830\pi$
$599$	35.6803	−	25.9233i	1.45786	−	1.05920i	0.983914	−	0.178642i	$-0.0571705\pi$
$600$		0			0
$601$	−1.00000	−	3.07768i	−0.0407909	−	0.125541i	0.928587	−	0.371114i	$-0.121024\pi$
$601$	−1.00000	−	3.07768i	−0.0407909	−	0.125541i	−0.969378	+	0.245573i	$0.921024\pi$
$602$	−5.47214	+	16.8415i	−0.223028	+	0.686408i
$603$	3.69098	+	2.68166i	0.150308	+	0.109205i
$604$	9.76393			0.397289
$605$	−3.12868	−	24.3970i	−0.127199	−	0.991877i
$606$	2.70820			0.110013
$607$	−21.1803	−	15.3884i	−0.859683	−	0.624597i	0.0681154	−	0.997677i	$-0.478301\pi$
$607$	−21.1803	−	15.3884i	−0.859683	−	0.624597i	−0.927799	+	0.373081i	$0.878301\pi$
$608$	0.454915	−	1.40008i	0.0184492	−	0.0567809i
$609$	−2.42705	−	7.46969i	−0.0983491	−	0.302687i
$610$	22.8262	−	16.5842i	0.924207	−	0.671476i
$611$	−14.2082	+	10.3229i	−0.574802	+	0.417618i
$612$	−0.118034	−	0.363271i	−0.00477124	−	0.0146844i
$613$	−11.6738	+	35.9281i	−0.471499	+	1.45112i	0.379123	+	0.925346i	$0.376226\pi$
$613$	−11.6738	+	35.9281i	−0.471499	+	1.45112i	−0.850622	+	0.525778i	$0.823774\pi$
$614$	15.8992	+	11.5514i	0.641639	+	0.466178i
$615$	18.0902			0.729466
$616$	2.73607	+	4.61653i	0.110239	+	0.186005i
$617$	18.2918			0.736400			0.368200	−	0.929747i	$-0.379974\pi$
$617$	18.2918			0.736400			0.368200	+	0.929747i	$0.379974\pi$
$618$	9.59017	+	6.96767i	0.385773	+	0.280281i
$619$	1.51722	−	4.66953i	0.0609823	−	0.187684i	−0.915924	−	0.401351i	$-0.868541\pi$
$619$	1.51722	−	4.66953i	0.0609823	−	0.187684i	0.976907	+	0.213667i	$0.0685407\pi$
$620$	−5.00000	−	15.3884i	−0.200805	−	0.618014i
$621$	−8.85410	+	6.43288i	−0.355303	+	0.258143i
$622$	−1.28115	+	0.930812i	−0.0513696	+	0.0373222i
$623$	1.64590	+	5.06555i	0.0659415	+	0.202947i
$624$	−0.927051	+	2.85317i	−0.0371117	+	0.114218i
$625$	20.2254	+	14.6946i	0.809017	+	0.587785i
$626$	18.2148			0.728009
$627$	−0.736068	+	7.86572i	−0.0293957	+	0.314127i
$628$	−13.0902			−0.522355
$629$	−0.190983	−	0.138757i	−0.00761499	−	0.00553261i
$630$	0.427051	−	1.31433i	0.0170141	−	0.0523641i
$631$	1.48936	+	4.58377i	0.0592904	+	0.182477i	0.976315	−	0.216353i	$-0.0694163\pi$
$631$	1.48936	+	4.58377i	0.0592904	+	0.182477i	−0.917025	+	0.398830i	$0.869416\pi$
$632$	3.80902	−	2.76741i	0.151515	−	0.110082i
$633$	19.0623	−	13.8496i	0.757659	−	0.550471i
$634$	1.88197	+	5.79210i	0.0747424	+	0.230034i
$635$	−0.652476	+	2.00811i	−0.0258927	+	0.0796896i
$636$	−6.54508	−	4.75528i	−0.259530	−	0.188559i
$637$	−8.12461			−0.321909
$638$	9.70820	−	2.17963i	0.384351	−	0.0862923i
$639$	−1.56231			−0.0618039
$640$	1.80902	+	1.31433i	0.0715077	+	0.0519534i
$641$	2.07295	−	6.37988i	0.0818766	−	0.251990i	−0.901735	−	0.432288i	$-0.857706\pi$
$641$	2.07295	−	6.37988i	0.0818766	−	0.251990i	0.983612	+	0.180298i	$0.0577063\pi$
$642$	5.85410	+	18.0171i	0.231043	+	0.711077i
$643$	−29.2705	+	21.2663i	−1.15432	+	0.838660i	−0.989049	−	0.147589i	$-0.952849\pi$
$643$	−29.2705	+	21.2663i	−1.15432	+	0.838660i	−0.165267	+	0.986249i	$0.552849\pi$
$644$	−2.61803	+	1.90211i	−0.103165	+	0.0749538i
$645$	−12.2361	−	37.6587i	−0.481795	−	1.48281i
$646$	0.454915	−	1.40008i	0.0178984	−	0.0550856i
$647$	−22.4164	−	16.2865i	−0.881280	−	0.640287i	0.0523099	−	0.998631i	$-0.483342\pi$
$647$	−22.4164	−	16.2865i	−0.881280	−	0.640287i	−0.933590	+	0.358344i	$0.883342\pi$
$648$	7.70820			0.302807
$649$	−13.1459	+	14.9394i	−0.516022	+	0.586422i
$650$		0			0
$651$	−15.3262	−	11.1352i	−0.600683	−	0.436421i
$652$	−0.0172209	+	0.0530006i	−0.000674424	+	0.00207566i
$653$	−1.11803	−	3.44095i	−0.0437521	−	0.134655i	0.926794	−	0.375569i	$-0.122553\pi$
$653$	−1.11803	−	3.44095i	−0.0437521	−	0.134655i	−0.970546	+	0.240914i	$0.922553\pi$
$654$	0.118034	−	0.0857567i	0.00461549	−	0.00335335i
$655$	13.6803	−	9.93935i	0.534535	−	0.388362i
$656$	−1.54508	−	4.75528i	−0.0603254	−	0.185663i
$657$	−0.972136	+	2.99193i	−0.0379266	+	0.116726i
$658$	12.3992	+	9.00854i	0.483371	+	0.351189i
$659$	21.7984			0.849144			0.424572	−	0.905394i	$-0.360425\pi$
$659$	21.7984			0.849144			0.424572	+	0.905394i	$0.360425\pi$
$660$	−11.0172	−	4.75528i	−0.428845	−	0.185099i
$661$	−8.76393			−0.340877			−0.170439	−	0.985368i	$-0.554518\pi$
$661$	−8.76393			−0.340877			−0.170439	+	0.985368i	$0.554518\pi$
$662$	6.04508	+	4.39201i	0.234949	+	0.170700i
$663$	−0.927051	+	2.85317i	−0.0360037	+	0.110808i
$664$	−0.663119	−	2.04087i	−0.0257340	−	0.0792011i
$665$	4.30902	−	3.13068i	0.167097	−	0.121403i
$666$	−0.0729490	+	0.0530006i	−0.00282672	+	0.00205373i
$667$	1.85410	+	5.70634i	0.0717911	+	0.220950i
$668$	−0.364745	+	1.12257i	−0.0141124	+	0.0434335i
$669$	−35.6246	−	25.8828i	−1.37733	−	1.00069i
$670$	−26.7082			−1.03183
$671$	38.4230	+	16.5842i	1.48330	+	0.640227i
$672$	2.61803			0.100993
$673$	−29.3156	−	21.2990i	−1.13003	−	0.821017i	−0.144334	−	0.989529i	$-0.546104\pi$
$673$	−29.3156	−	21.2990i	−1.13003	−	0.821017i	−0.985700	+	0.168512i	$0.946104\pi$
$674$	7.87132	−	24.2254i	0.303192	−	0.933129i
$675$		0			0
$676$	7.73607	−	5.62058i	0.297541	−	0.216176i
$677$	35.3885	−	25.7113i	1.36009	−	0.988165i	0.361653	−	0.932313i	$-0.382212\pi$
$677$	35.3885	−	25.7113i	1.36009	−	0.988165i	0.998439	−	0.0558521i	$-0.0177875\pi$
$678$	2.19098	+	6.74315i	0.0841442	+	0.258969i
$679$	−8.89919	+	27.3889i	−0.341519	+	1.05109i
$680$	1.80902	+	1.31433i	0.0693726	+	0.0504022i
$681$	9.38197			0.359518
$682$	15.8541	−	18.0171i	0.607085	−	0.689909i
$683$	−20.6180			−0.788927			−0.394464	−	0.918912i	$-0.629070\pi$
$683$	−20.6180			−0.788927			−0.394464	+	0.918912i	$0.629070\pi$
$684$	−0.454915	−	0.330515i	−0.0173941	−	0.0126376i
$685$	−4.34752	+	13.3803i	−0.166110	+	0.511235i
$686$	5.69098	+	17.5150i	0.217283	+	0.668728i
$687$	−0.309017	+	0.224514i	−0.0117897	+	0.00856574i
$688$	−8.85410	+	6.43288i	−0.337559	+	0.245251i
$689$	−2.86475	−	8.81678i	−0.109138	−	0.335893i
$690$	2.23607	−	6.88191i	0.0851257	−	0.261990i
$691$	7.33688	+	5.33056i	0.279108	+	0.202784i	0.718528	−	0.695498i	$-0.244816\pi$
$691$	7.33688	+	5.33056i	0.279108	+	0.202784i	−0.439420	+	0.898282i	$0.644816\pi$
$692$	7.14590			0.271646
$693$	2.00000	−	0.449028i	0.0759737	−	0.0170572i
$694$	9.94427			0.377479
$695$	27.1353	+	19.7149i	1.02930	+	0.747829i
$696$	1.50000	−	4.61653i	0.0568574	−	0.174989i
$697$	−1.54508	−	4.75528i	−0.0585243	−	0.180119i
$698$	2.83688	−	2.06111i	0.107378	−	0.0780143i
$699$	16.2533	−	11.8087i	0.614756	−	0.446646i
$700$		0			0
$701$	8.69756	−	26.7683i	0.328502	−	1.01103i	−0.641332	−	0.767263i	$-0.721618\pi$
$701$	8.69756	−	26.7683i	0.328502	−	1.01103i	0.969835	−	0.243763i	$-0.0783819\pi$
$702$	8.20820	+	5.96361i	0.309799	+	0.225082i
$703$	−0.347524			−0.0131071
$704$	−0.309017	+	3.30220i	−0.0116465	+	0.124456i
$705$	−34.2705			−1.29070
$706$	29.5623	+	21.4783i	1.11259	+	0.808345i
$707$	0.836881	−	2.57565i	0.0314742	−	0.0968675i
$708$	3.00000	+	9.23305i	0.112747	+	0.346999i
$709$	−11.2812	+	8.19624i	−0.423673	+	0.307816i	−0.779114	−	0.626882i	$-0.784331\pi$
$709$	−11.2812	+	8.19624i	−0.423673	+	0.307816i	0.355441	+	0.934699i	$0.384331\pi$
$710$	7.39919	−	5.37582i	0.277687	−	0.201751i
$711$	−0.555728	−	1.71036i	−0.0208414	−	0.0641433i
$712$	−1.01722	+	3.13068i	−0.0381220	+	0.117327i
$713$	11.7082	+	8.50651i	0.438476	+	0.318571i
$714$	2.61803			0.0979775
$715$	−7.01064	−	11.8290i	−0.262183	−	0.442378i
$716$	16.6180			0.621045
$717$	31.7254	+	23.0499i	1.18481	+	0.860813i
$718$	−6.60081	+	20.3152i	−0.246340	+	0.758157i
$719$	−12.1525	−	37.4015i	−0.453211	−	1.39484i	−0.873223	−	0.487321i	$-0.837974\pi$
$719$	−12.1525	−	37.4015i	−0.453211	−	1.39484i	0.420012	−	0.907519i	$-0.362026\pi$
$720$	0.690983	−	0.502029i	0.0257514	−	0.0187095i
$721$	9.59017	−	6.96767i	0.357157	−	0.259489i
$722$	5.20163	+	16.0090i	0.193584	+	0.595792i
$723$	−12.0451	+	37.0710i	−0.447962	+	1.37868i
$724$	−13.6353	−	9.90659i	−0.506750	−	0.368176i
$725$		0			0
$726$	−2.26393	−	17.6538i	−0.0840224	−	0.655194i
$727$	−40.3050			−1.49483			−0.747414	−	0.664359i	$-0.768705\pi$
$727$	−40.3050			−1.49483			−0.747414	+	0.664359i	$0.768705\pi$
$728$	2.42705	+	1.76336i	0.0899525	+	0.0653543i
$729$	9.11803	−	28.0624i	0.337705	−	1.03935i
$730$	−5.69098	−	17.5150i	−0.210633	−	0.648261i
$731$	−8.85410	+	6.43288i	−0.327481	+	0.237929i
$732$	16.5172	−	12.0005i	0.610494	−	0.443550i
$733$	−12.3885	−	38.1280i	−0.457581	−	1.40829i	−0.868078	−	0.496428i	$-0.834645\pi$
$733$	−12.3885	−	38.1280i	−0.457581	−	1.40829i	0.410496	−	0.911862i	$-0.365355\pi$
$734$	−9.06231	+	27.8909i	−0.334496	+	1.02947i
$735$	−12.8262	−	9.31881i	−0.473103	−	0.343729i
$736$	−2.00000			−0.0737210
$737$	−20.1976	−	34.0790i	−0.743987	−	1.25532i
$738$	−1.90983			−0.0703018
$739$	13.6180	+	9.89408i	0.500947	+	0.363960i	0.809379	−	0.587287i	$-0.199804\pi$
$739$	13.6180	+	9.89408i	0.500947	+	0.363960i	−0.308431	+	0.951247i	$0.599804\pi$
$740$	0.163119	−	0.502029i	0.00599637	−	0.0184549i
$741$	1.36475	+	4.20025i	0.0501352	+	0.154300i
$742$	−6.54508	+	4.75528i	−0.240278	+	0.174572i
$743$	−11.1631	+	8.11048i	−0.409535	+	0.297545i	−0.773414	−	0.633902i	$-0.781452\pi$
$743$	−11.1631	+	8.11048i	−0.409535	+	0.297545i	0.363878	+	0.931446i	$0.381452\pi$
$744$	−3.61803	−	11.1352i	−0.132644	−	0.408235i
$745$	7.17376	−	22.0786i	0.262826	−	0.808896i
$746$	3.69098	+	2.68166i	0.135136	+	0.0981824i
$747$	−0.819660			−0.0299898
$748$	−0.309017	+	3.30220i	−0.0112988	+	0.120740i
$749$	18.9443			0.692209
$750$	14.6353	+	10.6331i	0.534404	+	0.388267i
$751$	7.89261	−	24.2910i	0.288005	−	0.886389i	−0.697476	−	0.716608i	$-0.745694\pi$
$751$	7.89261	−	24.2910i	0.288005	−	0.886389i	0.985482	−	0.169782i	$-0.0543062\pi$
$752$	2.92705	+	9.00854i	0.106739	+	0.328508i
$753$	13.0902	−	9.51057i	0.477032	−	0.346584i
$754$	4.50000	−	3.26944i	0.163880	−	0.119066i
$755$	6.74671	+	20.7642i	0.245538	+	0.755688i
$756$	2.73607	−	8.42075i	0.0995098	−	0.306260i
$757$	−14.6074	−	10.6129i	−0.530915	−	0.385732i	0.289785	−	0.957092i	$-0.406416\pi$
$757$	−14.6074	−	10.6129i	−0.530915	−	0.385732i	−0.820700	+	0.571360i	$0.806416\pi$
$758$	35.8541			1.30228
$759$	10.4721	−	2.35114i	0.380114	−	0.0853410i
$760$	3.29180			0.119406
$761$	0.145898	+	0.106001i	0.00528880	+	0.00384254i	0.590427	−	0.807091i	$-0.298960\pi$
$761$	0.145898	+	0.106001i	0.00528880	+	0.00384254i	−0.585138	+	0.810934i	$0.698960\pi$
$762$	−0.472136	+	1.45309i	−0.0171037	+	0.0526397i
$763$	−0.0450850	−	0.138757i	−0.00163219	−	0.00502335i
$764$	−14.8262	+	10.7719i	−0.536394	+	0.389713i
$765$	0.690983	−	0.502029i	0.0249825	−	0.0181509i
$766$	−8.92705	−	27.4746i	−0.322547	−	0.992699i
$767$	−3.43769	+	10.5801i	−0.124128	+	0.382027i
$768$	1.30902	+	0.951057i	0.0472351	+	0.0343183i
$769$	−42.8885			−1.54660			−0.773300	−	0.634040i	$-0.781395\pi$
$769$	−42.8885			−1.54660			−0.773300	+	0.634040i	$0.781395\pi$
$770$	−7.92705	+	9.00854i	−0.285671	+	0.324645i
$771$	12.7984			0.460922
$772$	17.2533	+	12.5352i	0.620959	+	0.451153i
$773$	7.92047	−	24.3767i	0.284880	−	0.876769i	−0.701555	−	0.712615i	$-0.747511\pi$
$773$	7.92047	−	24.3767i	0.284880	−	0.876769i	0.986435	−	0.164154i	$-0.0524894\pi$
$774$	1.29180	+	3.97574i	0.0464327	+	0.142905i
$775$		0			0
$776$	−14.3992	+	10.4616i	−0.516901	+	0.375550i
$777$	−0.190983	−	0.587785i	−0.00685148	−	0.0210867i
$778$	−0.826238	+	2.54290i	−0.0296221	+	0.0911673i
$779$	−5.95492	−	4.32650i	−0.213357	−	0.155013i
$780$	−6.70820			−0.240192
$781$	12.4549	+	5.37582i	0.445672	+	0.192362i
$782$	−2.00000			−0.0715199
$783$	−13.2812	−	9.64932i	−0.474630	−	0.344839i
$784$	−1.35410	+	4.16750i	−0.0483608	+	0.148839i
$785$	−9.04508	−	27.8379i	−0.322833	−	0.993578i
$786$	9.89919	−	7.19218i	0.353092	−	0.256537i
$787$	27.6976	−	20.1235i	0.987311	−	0.717324i	0.0279807	−	0.999608i	$-0.491092\pi$
$787$	27.6976	−	20.1235i	0.987311	−	0.717324i	0.959331	+	0.282285i	$0.0910923\pi$
$788$	−2.54508	−	7.83297i	−0.0906649	−	0.279038i
$789$	−0.190983	+	0.587785i	−0.00679918	+	0.0209257i
$790$	8.51722	+	6.18812i	0.303029	+	0.220164i
$791$	7.09017			0.252097
$792$	1.16312	+	0.502029i	0.0413296	+	0.0178388i
$793$	23.3951			0.830785
$794$	19.9894	+	14.5231i	0.709396	+	0.515406i
$795$	5.59017	−	17.2048i	0.198263	−	0.610190i
$796$	4.04508	+	12.4495i	0.143374	+	0.441261i
$797$	43.5066	−	31.6094i	1.54108	−	1.11966i	0.591429	−	0.806357i	$-0.298564\pi$
$797$	43.5066	−	31.6094i	1.54108	−	1.11966i	0.949653	−	0.313305i	$-0.101436\pi$
$798$	3.11803	−	2.26538i	0.110377	−	0.0801937i
$799$	2.92705	+	9.00854i	0.103552	+	0.318699i
$800$		0			0
$801$	1.01722	+	0.739054i	0.0359417	+	0.0261132i
$802$	−5.43769			−0.192012
$803$	18.0451	−	20.5070i	0.636797	−	0.723675i
$804$	−19.3262			−0.681584
$805$	−5.85410	−	4.25325i	−0.206330	−	0.149908i
$806$	4.14590	−	12.7598i	0.146033	−	0.449443i
$807$	−7.45492	−	22.9439i	−0.262425	−	0.807662i
$808$	1.35410	−	0.983813i	0.0476371	−	0.0346104i
$809$	25.9336	−	18.8419i	0.911778	−	0.662445i	−0.0296860	−	0.999559i	$-0.509451\pi$
$809$	25.9336	−	18.8419i	0.911778	−	0.662445i	0.941464	+	0.337114i	$0.109451\pi$
$810$	5.32624	+	16.3925i	0.187145	+	0.575973i
$811$	4.70163	−	14.4701i	0.165096	−	0.508115i	−0.833947	−	0.551845i	$-0.813924\pi$
$811$	4.70163	−	14.4701i	0.165096	−	0.508115i	0.999043	+	0.0437301i	$0.0139242\pi$
$812$	−3.92705	−	2.85317i	−0.137812	−	0.100127i
$813$	−12.3820			−0.434255
$814$	0.763932	−	0.171513i	0.0267758	−	0.00601154i
$815$	−0.124612			−0.00436496
$816$	1.30902	+	0.951057i	0.0458248	+	0.0332936i
$817$	−4.97871	+	15.3229i	−0.174183	+	0.536081i
$818$	−12.1180	−	37.2955i	−0.423697	−	1.30401i
$819$	0.927051	−	0.673542i	0.0323938	−	0.0235355i
$820$	9.04508	−	6.57164i	0.315868	−	0.229492i
$821$	11.4721	+	35.3076i	0.400380	+	1.23224i	0.924692	+	0.380717i	$0.124323\pi$
$821$	11.4721	+	35.3076i	0.400380	+	1.23224i	−0.524311	+	0.851527i	$0.675677\pi$
$822$	−3.14590	+	9.68208i	−0.109726	+	0.337701i
$823$	−2.19098	−	1.59184i	−0.0763729	−	0.0554881i	0.548944	−	0.835859i	$-0.315030\pi$
$823$	−2.19098	−	1.59184i	−0.0763729	−	0.0554881i	−0.625317	+	0.780371i	$0.715030\pi$
$824$	7.32624			0.255222
$825$		0			0
$826$	9.70820			0.337792
$827$	3.52786	+	2.56314i	0.122676	+	0.0891292i	0.647431	−	0.762124i	$-0.275843\pi$
$827$	3.52786	+	2.56314i	0.122676	+	0.0891292i	−0.524755	+	0.851253i	$0.675843\pi$
$828$	−0.236068	+	0.726543i	−0.00820393	+	0.0252491i
$829$	0.729490	+	2.24514i	0.0253362	+	0.0779769i	0.962925	−	0.269769i	$-0.0869473\pi$
$829$	0.729490	+	2.24514i	0.0253362	+	0.0779769i	−0.937589	+	0.347746i	$0.886947\pi$
$830$	3.88197	−	2.82041i	0.134745	−	0.0978980i
$831$	3.04508	−	2.21238i	0.105633	−	0.0767467i
$832$	0.572949	+	1.76336i	0.0198634	+	0.0611334i
$833$	−1.35410	+	4.16750i	−0.0469169	+	0.144395i
$834$	19.6353	+	14.2658i	0.679913	+	0.493986i
$835$	−2.63932			−0.0913374
$836$	2.48936	+	4.20025i	0.0860962	+	0.145269i
$837$	−39.5967			−1.36866
$838$	5.42705	+	3.94298i	0.187474	+	0.136208i
$839$	−8.76393	+	26.9726i	−0.302565	+	0.931198i	0.678010	+	0.735052i	$0.262842\pi$
$839$	−8.76393	+	26.9726i	−0.302565	+	0.931198i	−0.980575	+	0.196145i	$0.937158\pi$
$840$	1.80902	+	5.56758i	0.0624170	+	0.192100i
$841$	16.1803	−	11.7557i	0.557943	−	0.405369i
$842$	−17.7533	+	12.8985i	−0.611819	+	0.444512i
$843$	−12.3541	−	38.0220i	−0.425498	−	1.30955i
$844$	4.50000	−	13.8496i	0.154896	−	0.476722i
$845$	17.2984	+	12.5680i	0.595082	+	0.432352i
$846$	3.61803			0.124391
$847$	−17.4894	−	3.30220i	−0.600941	−	0.113465i
$848$	−5.00000			−0.171701
$849$	42.7877	+	31.0871i	1.46847	+	1.06691i
$850$		0			0
$851$	0.145898	+	0.449028i	0.00500132	+	0.0153925i
$852$	5.35410	−	3.88998i	0.183429	−	0.133269i
$853$	40.0795	−	29.1195i	1.37230	−	0.997032i	0.374743	−	0.927129i	$-0.377731\pi$
$853$	40.0795	−	29.1195i	1.37230	−	0.997032i	0.997554	−	0.0699033i	$-0.0222691\pi$
$854$	−6.30902	−	19.4172i	−0.215890	−	0.664441i
$855$	0.388544	−	1.19581i	0.0132879	−	0.0408960i
$856$	9.47214	+	6.88191i	0.323751	+	0.235219i
$857$	36.3607			1.24206			0.621029	−	0.783788i	$-0.286715\pi$
$857$	36.3607			1.24206			0.621029	+	0.783788i	$0.286715\pi$
$858$	−5.07295	−	8.55951i	−0.173188	−	0.292217i
$859$	11.6525			0.397577			0.198789	−	0.980042i	$-0.436299\pi$
$859$	11.6525			0.397577			0.198789	+	0.980042i	$0.436299\pi$
$860$	−19.7984	−	14.3844i	−0.675119	−	0.490503i
$861$	4.04508	−	12.4495i	0.137856	−	0.424278i
$862$	9.32624	+	28.7032i	0.317653	+	0.977635i
$863$	−41.0517	+	29.8258i	−1.39741	+	1.01528i	−0.402409	+	0.915460i	$0.631827\pi$
$863$	−41.0517	+	29.8258i	−1.39741	+	1.01528i	−0.995005	+	0.0998215i	$0.968173\pi$
$864$	4.42705	−	3.21644i	0.150611	−	0.109426i
$865$	4.93769	+	15.1967i	0.167887	+	0.516702i
$866$	3.10739	−	9.56357i	0.105593	−	0.324983i
$867$	1.30902	+	0.951057i	0.0444565	+	0.0322996i
$868$	−11.7082			−0.397402
$869$	−1.45492	+	15.5474i	−0.0493546	+	0.527410i
$870$	10.8541			0.367989
$871$	−17.9164	−	13.0170i	−0.607074	−	0.441065i
$872$	0.0278640	−	0.0857567i	0.000943596	−	0.00290409i
$873$	2.10081	+	6.46564i	0.0711017	+	0.218829i
$874$	−2.38197	+	1.73060i	−0.0805712	+	0.0585384i
$875$	14.6353	−	10.6331i	0.494762	−	0.359466i
$876$	−4.11803	−	12.6740i	−0.139135	−	0.428215i
$877$	−14.4828	+	44.5734i	−0.489049	+	1.50514i	0.336981	+	0.941511i	$0.390594\pi$
$877$	−14.4828	+	44.5734i	−0.489049	+	1.50514i	−0.826030	+	0.563626i	$0.809406\pi$
$878$	−23.5344	−	17.0988i	−0.794249	−	0.577056i
$879$	5.00000			0.168646
$880$	−7.23607	+	1.62460i	−0.243928	+	0.0547652i
$881$	48.8885			1.64710			0.823548	−	0.567246i	$-0.191991\pi$
$881$	48.8885			1.64710			0.823548	+	0.567246i	$0.191991\pi$
$882$	1.35410	+	0.983813i	0.0455950	+	0.0331267i
$883$	−8.36068	+	25.7315i	−0.281359	+	0.865935i	0.706107	+	0.708105i	$0.250450\pi$
$883$	−8.36068	+	25.7315i	−0.281359	+	0.865935i	−0.987466	+	0.157830i	$0.949550\pi$
$884$	0.572949	+	1.76336i	0.0192704	+	0.0593081i
$885$	−17.5623	+	12.7598i	−0.590350	+	0.428915i
$886$	4.73607	−	3.44095i	0.159111	−	0.115601i
$887$	2.58359	+	7.95148i	0.0867485	+	0.266985i	0.985016	−	0.172466i	$-0.0551733\pi$
$887$	2.58359	+	7.95148i	0.0867485	+	0.266985i	−0.898267	+	0.439450i	$0.855173\pi$
$888$	0.118034	−	0.363271i	0.00396096	−	0.0121906i
$889$	1.23607	+	0.898056i	0.0414564	+	0.0301198i
$890$	−7.36068			−0.246731
$891$	−16.8885	+	19.1926i	−0.565788	+	0.642978i
$892$	−27.2148			−0.911218
$893$	11.2812	+	8.19624i	0.377509	+	0.274277i
$894$	5.19098	−	15.9762i	0.173612	−	0.534324i
$895$	11.4828	+	35.3404i	0.383827	+	1.18130i
$896$	1.30902	−	0.951057i	0.0437312	−	0.0317726i
$897$	4.85410	−	3.52671i	0.162074	−	0.117753i
$898$	−6.22542	−	19.1599i	−0.207745	−	0.639374i
$899$	−6.70820	+	20.6457i	−0.223731	+	0.688574i
$900$		0			0
$901$	−5.00000			−0.166574
$902$	15.2254	+	6.57164i	0.506951	+	0.218812i
$903$	−28.6525			−0.953495
$904$	3.54508	+	2.57565i	0.117908	+	0.0856650i
$905$	11.6459	−	35.8424i	0.387123	−	1.19144i
$906$	4.88197	+	15.0251i	0.162192	+	0.499177i
$907$	−26.0795	+	18.9479i	−0.865956	+	0.629154i	−0.929499	−	0.368825i	$-0.879760\pi$
$907$	−26.0795	+	18.9479i	−0.865956	+	0.629154i	0.0635424	+	0.997979i	$0.479760\pi$
$908$	4.69098	−	3.40820i	0.155676	−	0.113105i
$909$	−0.197561	−	0.608030i	−0.00655268	−	0.0201671i
$910$	−2.07295	+	6.37988i	−0.0687176	+	0.211491i
$911$	−21.1074	−	15.3354i	−0.699319	−	0.508085i	0.180391	−	0.983595i	$-0.442264\pi$
$911$	−21.1074	−	15.3354i	−0.699319	−	0.508085i	−0.879710	+	0.475510i	$0.842264\pi$
$912$	2.38197			0.0788748
$913$	6.53444	+	2.82041i	0.216258	+	0.0933421i
$914$	−35.2361			−1.16551
$915$	36.9336	+	26.8339i	1.22099	+	0.887100i
$916$	−0.0729490	+	0.224514i	−0.00241030	+	0.00741815i
$917$	−3.78115	−	11.6372i	−0.124865	−	0.384294i
$918$	4.42705	−	3.21644i	0.146114	−	0.106158i
$919$	1.71885	−	1.24882i	0.0566995	−	0.0411946i	−0.559074	−	0.829117i	$-0.688843\pi$
$919$	1.71885	−	1.24882i	0.0566995	−	0.0411946i	0.615774	+	0.787923i	$0.288843\pi$
$920$	−1.38197	−	4.25325i	−0.0455621	−	0.140226i
$921$	−9.82624	+	30.2421i	−0.323786	+	0.996509i
$922$	−2.47214	−	1.79611i	−0.0814155	−	0.0591518i
$923$	7.58359			0.249617
$924$	−5.73607	+	6.51864i	−0.188703	+	0.214447i
$925$		0			0
$926$	10.5902	+	7.69421i	0.348015	+	0.252847i
$927$	0.864745	−	2.66141i	0.0284020	−	0.0874122i
$928$	−0.927051	−	2.85317i	−0.0304319	−	0.0936599i
$929$	15.6631	−	11.3799i	0.513890	−	0.373363i	−0.300407	−	0.953811i	$-0.597123\pi$
$929$	15.6631	−	11.3799i	0.513890	−	0.373363i	0.814297	+	0.580448i	$0.197123\pi$
$930$	21.1803	−	15.3884i	0.694531	−	0.504606i
$931$	1.99342	+	6.13512i	0.0653318	+	0.201071i
$932$	3.83688	−	11.8087i	0.125681	−	0.386807i
$933$	−2.07295	−	1.50609i	−0.0678653	−	0.0493070i
$934$	−24.4164			−0.798929
$935$	−7.23607	+	1.62460i	−0.236645	+	0.0531301i
$936$	0.708204			0.0231484
$937$	−17.2082	−	12.5025i	−0.562168	−	0.408439i	0.270084	−	0.962837i	$-0.412949\pi$
$937$	−17.2082	−	12.5025i	−0.562168	−	0.408439i	−0.832252	+	0.554398i	$0.812949\pi$
$938$	−5.97214	+	18.3803i	−0.194997	+	0.600140i
$939$	9.10739	+	28.0297i	0.297208	+	0.914714i
$940$	−17.1353	+	12.4495i	−0.558890	+	0.406058i
$941$	−33.3156	+	24.2052i	−1.08606	+	0.789067i	−0.978729	−	0.205157i	$-0.934230\pi$
$941$	−33.3156	+	24.2052i	−1.08606	+	0.789067i	−0.107328	+	0.994224i	$0.534230\pi$
$942$	−6.54508	−	20.1437i	−0.213250	−	0.656317i
$943$	−3.09017	+	9.51057i	−0.100630	+	0.309707i
$944$	4.85410	+	3.52671i	0.157988	+	0.114785i
$945$	19.7984			0.644041
$946$	3.38197	−	36.1401i	0.109957	−	1.17502i
$947$	28.2492			0.917976			0.458988	−	0.888442i	$-0.348212\pi$
$947$	28.2492			0.917976			0.458988	+	0.888442i	$0.348212\pi$
$948$	6.16312	+	4.47777i	0.200169	+	0.145431i
$949$	4.71885	−	14.5231i	0.153180	−	0.471440i
$950$		0			0
$951$	−7.97214	+	5.79210i	−0.258514	+	0.187822i
$952$	1.30902	−	0.951057i	0.0424255	−	0.0308239i
$953$	−2.25329	−	6.93491i	−0.0729912	−	0.224644i	0.907905	−	0.419176i	$-0.137681\pi$
$953$	−2.25329	−	6.93491i	−0.0729912	−	0.224644i	−0.980896	+	0.194532i	$0.937681\pi$
$954$	−0.590170	+	1.81636i	−0.0191075	+	0.0588067i
$955$	−33.1525	−	24.0867i	−1.07279	−	0.779427i
$956$	24.2361			0.783850
$957$	8.20820	+	13.8496i	0.265334	+	0.447693i
$958$	−16.0000			−0.516937
$959$	8.23607	+	5.98385i	0.265957	+	0.193229i
$960$	−1.11803	+	3.44095i	−0.0360844	+	0.111056i
$961$	6.60081	+	20.3152i	0.212929	+	0.655329i
$962$	0.354102	−	0.257270i	0.0114167	−	0.00829472i
$963$	3.61803	−	2.62866i	0.116590	−	0.0847072i
$964$	7.44427	+	22.9111i	0.239764	+	0.737917i
$965$	−14.7361	+	45.3530i	−0.474371	+	1.45996i
$966$	−4.23607	−	3.07768i	−0.136293	−	0.0990228i
$967$	−24.2918			−0.781171			−0.390586	−	0.920567i	$-0.627728\pi$
$967$	−24.2918			−0.781171			−0.390586	+	0.920567i	$0.627728\pi$
$968$	−7.54508	−	8.00448i	−0.242508	−	0.257274i
$969$	2.38197			0.0765198
$970$	−32.1976	−	23.3929i	−1.03380	−	0.751101i
$971$	−14.4336	+	44.4221i	−0.463197	+	1.42557i	0.398039	+	0.917369i	$0.369691\pi$
$971$	−14.4336	+	44.4221i	−0.463197	+	1.42557i	−0.861236	+	0.508206i	$0.830309\pi$
$972$	−1.21885	−	3.75123i	−0.0390945	−	0.120321i
$973$	19.6353	−	14.2658i	0.629477	−	0.457342i
$974$	21.9894	−	15.9762i	0.704584	−	0.511911i
$975$		0			0
$976$	3.89919	−	12.0005i	0.124810	−	0.384125i
$977$	−23.5172	−	17.0863i	−0.752383	−	0.546638i	0.144182	−	0.989551i	$-0.453945\pi$
$977$	−23.5172	−	17.0863i	−0.752383	−	0.546638i	−0.896564	+	0.442913i	$0.853945\pi$
$978$	−0.0901699			−0.00288332
$979$	−5.56637	−	9.39205i	−0.177902	−	0.300171i
$980$	−9.79837			−0.312998
$981$	−0.0278640	−	0.0202444i	−0.000889630	−	0.000646354i
$982$	−5.82624	+	17.9313i	−0.185923	+	0.572211i
$983$	7.78773	+	23.9682i	0.248390	+	0.764466i	0.995060	+	0.0992717i	$0.0316513\pi$
$983$	7.78773	+	23.9682i	0.248390	+	0.764466i	−0.746670	+	0.665194i	$0.768349\pi$
$984$	6.54508	−	4.75528i	0.208650	−	0.151593i
$985$	14.8992	−	10.8249i	0.474728	−	0.344910i
$986$	−0.927051	−	2.85317i	−0.0295233	−	0.0908634i
$987$	−7.66312	+	23.5847i	−0.243920	+	0.750708i
$988$	2.20820	+	1.60435i	0.0702523	+	0.0510413i
$989$	21.8885			0.696015
$990$	−0.263932	+	2.82041i	−0.00838831	+	0.0896386i
$991$	−50.6656			−1.60945			−0.804723	−	0.593650i	$-0.797686\pi$
$991$	−50.6656			−1.60945			−0.804723	+	0.593650i	$0.797686\pi$
$992$	−5.85410	−	4.25325i	−0.185868	−	0.135041i
$993$	−3.73607	+	11.4984i	−0.118561	+	0.364892i
$994$	−2.04508	−	6.29412i	−0.0648662	−	0.199638i
$995$	−23.6803	+	17.2048i	−0.750717	+	0.545428i
$996$	2.80902	−	2.04087i	0.0890071	−	0.0646675i
$997$	−5.61146	−	17.2703i	−0.177717	−	0.546955i	0.822031	−	0.569443i	$-0.192841\pi$
$997$	−5.61146	−	17.2703i	−0.177717	−	0.546955i	−0.999747	+	0.0224880i	$0.992841\pi$
$998$	−5.65248	+	17.3965i	−0.178926	+	0.550678i
$999$	−1.04508	−	0.759299i	−0.0330650	−	0.0240231i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	374.2.g.c.103.1	yes	4
11.3	even	5	inner	374.2.g.c.69.1	✓	4
11.5	even	5		4114.2.a.f.1.1		2
11.6	odd	10		4114.2.a.k.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
374.2.g.c.69.1	✓	4	11.3	even	5	inner
374.2.g.c.103.1	yes	4	1.1	even	1	trivial
4114.2.a.f.1.1		2	11.5	even	5
4114.2.a.k.1.1		2	11.6	odd	10

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	374.2.g.c.103.1

Level	$374$
Weight	$2$
Character	374.103
Analytic conductor	$2.986$
Analytic rank	$0$
Dimension	$4$
Inner twists	$2$