LMFDB - Embedded newform 475.2.n.b.39.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(39,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("475.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.n (of order $10$, degree $4$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.2
Character	$\chi$	$=$	475.39
Dual form			475.2.n.b.134.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49821 - 2.06211i) q^{2} +(-0.334580 - 0.108712i) q^{3} +(-1.38963 + 4.27683i) q^{4} +(0.909940 + 2.04255i) q^{5} +(0.277096 + 0.852813i) q^{6} -3.13524i q^{7} +(6.05293 - 1.96672i) q^{8} +(-2.32693 - 1.69061i) q^{9} +O(q^{10})$	\(q+(-1.49821 - 2.06211i) q^{2} +(-0.334580 - 0.108712i) q^{3} +(-1.38963 + 4.27683i) q^{4} +(0.909940 + 2.04255i) q^{5} +(0.277096 + 0.852813i) q^{6} -3.13524i q^{7} +(6.05293 - 1.96672i) q^{8} +(-2.32693 - 1.69061i) q^{9} +(2.84868 - 4.93656i) q^{10} +(-2.77438 + 2.01571i) q^{11} +(0.929882 - 1.27987i) q^{12} +(-2.67292 + 3.67896i) q^{13} +(-6.46521 + 4.69725i) q^{14} +(-0.0823986 - 0.782317i) q^{15} +(-5.84797 - 4.24880i) q^{16} +(5.19907 - 1.68928i) q^{17} +7.33126i q^{18} +(0.309017 + 0.951057i) q^{19} +(-10.0001 + 1.05328i) q^{20} +(-0.340837 + 1.04899i) q^{21} +(8.31321 + 2.70113i) q^{22} +(2.90205 + 3.99433i) q^{23} -2.23899 q^{24} +(-3.34402 + 3.71719i) q^{25} +11.5910 q^{26} +(1.21510 + 1.67244i) q^{27} +(13.4089 + 4.35681i) q^{28} +(-1.15345 + 3.54997i) q^{29} +(-1.48977 + 1.34199i) q^{30} +(3.31233 + 10.1943i) q^{31} +5.69588i q^{32} +(1.14738 - 0.372807i) q^{33} +(-11.2728 - 8.19015i) q^{34} +(6.40389 - 2.85288i) q^{35} +(10.4640 - 7.60255i) q^{36} +(-5.79814 + 7.98045i) q^{37} +(1.49821 - 2.06211i) q^{38} +(1.29425 - 0.940327i) q^{39} +(9.52492 + 10.5738i) q^{40} +(-8.84399 - 6.42553i) q^{41} +(2.67377 - 0.868762i) q^{42} -1.54557i q^{43} +(-4.76548 - 14.6666i) q^{44} +(1.33579 - 6.29121i) q^{45} +(3.88886 - 11.9687i) q^{46} +(5.50650 + 1.78917i) q^{47} +(1.49472 + 2.05730i) q^{48} -2.82974 q^{49} +(12.6753 + 1.32660i) q^{50} -1.92315 q^{51} +(-12.0199 - 16.5440i) q^{52} +(4.68652 + 1.52274i) q^{53} +(1.62828 - 5.01133i) q^{54} +(-6.64170 - 3.83264i) q^{55} +(-6.16613 - 18.9774i) q^{56} -0.351798i q^{57} +(9.04854 - 2.94005i) q^{58} +(8.14886 + 5.92049i) q^{59} +(3.46034 + 0.734723i) q^{60} +(-2.11434 + 1.53616i) q^{61} +(16.0592 - 22.1036i) q^{62} +(-5.30047 + 7.29547i) q^{63} +(0.0495926 - 0.0360312i) q^{64} +(-9.94665 - 2.11194i) q^{65} +(-2.48779 - 1.80748i) q^{66} +(-6.95171 + 2.25875i) q^{67} +24.5830i q^{68} +(-0.536738 - 1.65191i) q^{69} +(-15.4773 - 8.93130i) q^{70} +(1.01372 - 3.11992i) q^{71} +(-17.4097 - 5.65675i) q^{72} +(-6.52537 - 8.98140i) q^{73} +25.1434 q^{74} +(1.52294 - 0.880164i) q^{75} -4.49693 q^{76} +(6.31973 + 8.69836i) q^{77} +(-3.87811 - 1.26008i) q^{78} +(-2.64141 + 8.12943i) q^{79} +(3.35708 - 15.8109i) q^{80} +(2.44169 + 7.51474i) q^{81} +27.8641i q^{82} +(16.1490 - 5.24713i) q^{83} +(-4.01271 - 2.91540i) q^{84} +(8.18128 + 9.08221i) q^{85} +(-3.18713 + 2.31559i) q^{86} +(0.771845 - 1.06235i) q^{87} +(-12.8288 + 17.6574i) q^{88} +(-7.30488 + 5.30731i) q^{89} +(-14.9745 + 6.67101i) q^{90} +(11.5344 + 8.38024i) q^{91} +(-21.1158 + 6.86095i) q^{92} -3.77089i q^{93} +(-4.56043 - 14.0356i) q^{94} +(-1.66139 + 1.49659i) q^{95} +(0.619209 - 1.90573i) q^{96} +(0.580951 + 0.188762i) q^{97} +(4.23954 + 5.83523i) q^{98} +9.86356 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9}+O(q^{10}) $ 96 * q + 26 * q^4 - 4 * q^5 - 2 * q^6 + 28 * q^9	$ 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9} + 28 q^{10} - 15 q^{11} - 85 q^{12} + 10 q^{14} - 10 q^{15} - 42 q^{16} + 20 q^{17} - 24 q^{19} - 16 q^{21} - 35 q^{23} - 24 q^{24} - 8 q^{25} + 28 q^{26} + 15 q^{27} + 30 q^{28} + 28 q^{29} - 64 q^{30} - 8 q^{31} + 25 q^{33} - 8 q^{34} + 33 q^{35} - 42 q^{36} - 55 q^{37} - 6 q^{39} - 48 q^{40} - 27 q^{41} + 210 q^{42} - 4 q^{44} + 15 q^{45} + 10 q^{46} - 115 q^{48} - 150 q^{49} + 9 q^{50} + 60 q^{51} - 5 q^{52} + 40 q^{53} + 47 q^{54} + 33 q^{55} - 12 q^{56} + 60 q^{58} + 25 q^{59} + 170 q^{60} + 26 q^{61} - 110 q^{62} - 30 q^{63} + 62 q^{64} - 15 q^{65} - 41 q^{66} + 35 q^{67} + 14 q^{69} - 20 q^{70} - 38 q^{71} - 60 q^{73} + 6 q^{74} - 151 q^{75} - 104 q^{76} + 115 q^{78} + 8 q^{79} - 63 q^{80} - 67 q^{81} + 160 q^{83} + 18 q^{84} - 8 q^{85} - 10 q^{87} - 120 q^{88} + 76 q^{89} + 108 q^{90} - 8 q^{91} + 85 q^{92} + 58 q^{94} + q^{95} - 6 q^{96} - 10 q^{97} + 10 q^{98} - 112 q^{99}+O(q^{100}) $ 96 * q + 26 * q^4 - 4 * q^5 - 2 * q^6 + 28 * q^9 + 28 * q^10 - 15 * q^11 - 85 * q^12 + 10 * q^14 - 10 * q^15 - 42 * q^16 + 20 * q^17 - 24 * q^19 - 16 * q^21 - 35 * q^23 - 24 * q^24 - 8 * q^25 + 28 * q^26 + 15 * q^27 + 30 * q^28 + 28 * q^29 - 64 * q^30 - 8 * q^31 + 25 * q^33 - 8 * q^34 + 33 * q^35 - 42 * q^36 - 55 * q^37 - 6 * q^39 - 48 * q^40 - 27 * q^41 + 210 * q^42 - 4 * q^44 + 15 * q^45 + 10 * q^46 - 115 * q^48 - 150 * q^49 + 9 * q^50 + 60 * q^51 - 5 * q^52 + 40 * q^53 + 47 * q^54 + 33 * q^55 - 12 * q^56 + 60 * q^58 + 25 * q^59 + 170 * q^60 + 26 * q^61 - 110 * q^62 - 30 * q^63 + 62 * q^64 - 15 * q^65 - 41 * q^66 + 35 * q^67 + 14 * q^69 - 20 * q^70 - 38 * q^71 - 60 * q^73 + 6 * q^74 - 151 * q^75 - 104 * q^76 + 115 * q^78 + 8 * q^79 - 63 * q^80 - 67 * q^81 + 160 * q^83 + 18 * q^84 - 8 * q^85 - 10 * q^87 - 120 * q^88 + 76 * q^89 + 108 * q^90 - 8 * q^91 + 85 * q^92 + 58 * q^94 + q^95 - 6 * q^96 - 10 * q^97 + 10 * q^98 - 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	−1.49821	−	2.06211i	−1.05939	−	1.45813i	−0.880371	−	0.474286i	$-0.842706\pi$
$2$	−1.49821	−	2.06211i	−1.05939	−	1.45813i	−0.179024	−	0.983845i	$-0.557294\pi$
$3$	−0.334580	−	0.108712i	−0.193170	−	0.0627647i	0.210834	−	0.977522i	$-0.432382\pi$
$3$	−0.334580	−	0.108712i	−0.193170	−	0.0627647i	−0.404004	+	0.914757i	$0.632382\pi$
$4$	−1.38963	+	4.27683i	−0.694813	+	2.13842i
$5$	0.909940	+	2.04255i	0.406937	+	0.913456i
$5$	0.909940	+	2.04255i	0.406937	+	0.913456i
$6$	0.277096	+	0.852813i	0.113124	+	0.348159i
$7$		−	3.13524i		−	1.18501i	−0.805567	−	0.592505i	$-0.798139\pi$
$7$		−	3.13524i		−	1.18501i	0.805567	−	0.592505i	$-0.201861\pi$
$8$	6.05293	−	1.96672i	2.14004	−	0.695340i
$9$	−2.32693	−	1.69061i	−0.775642	−	0.563537i
$10$	2.84868	−	4.93656i	0.900832	−	1.56108i
$11$	−2.77438	+	2.01571i	−0.836508	+	0.607758i	−0.921393	−	0.388632i	$-0.872948\pi$
$11$	−2.77438	+	2.01571i	−0.836508	+	0.607758i	0.0848852	+	0.996391i	$0.472948\pi$
$12$	0.929882	−	1.27987i	0.268434	−	0.369467i
$13$	−2.67292	+	3.67896i	−0.741334	+	1.02036i	0.257207	+	0.966356i	$0.417198\pi$
$13$	−2.67292	+	3.67896i	−0.741334	+	1.02036i	−0.998541	+	0.0540025i	$0.982802\pi$
$14$	−6.46521	+	4.69725i	−1.72790	+	1.25539i
$15$	−0.0823986	−	0.782317i	−0.0212752	−	0.201993i
$16$	−5.84797	−	4.24880i	−1.46199	−	1.06220i
$17$	5.19907	−	1.68928i	1.26096	−	0.409710i	0.399123	−	0.916897i	$-0.369315\pi$
$17$	5.19907	−	1.68928i	1.26096	−	0.409710i	0.861836	+	0.507187i	$0.169315\pi$
$18$			7.33126i			1.72800i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$20$	−10.0001	+	1.05328i	−2.23609	+	0.235520i
$21$	−0.340837	+	1.04899i	−0.0743767	+	0.228908i
$22$	8.31321	+	2.70113i	1.77238	+	0.575882i
$23$	2.90205	+	3.99433i	0.605119	+	0.832875i	0.996165	−	0.0874961i	$-0.0278865\pi$
$23$	2.90205	+	3.99433i	0.605119	+	0.832875i	−0.391046	+	0.920371i	$0.627887\pi$
$24$	−2.23899			−0.457033
$25$	−3.34402	+	3.71719i	−0.668804	+	0.743439i
$26$	11.5910			2.27318
$27$	1.21510	+	1.67244i	0.233846	+	0.321861i
$28$	13.4089	+	4.35681i	2.53404	+	0.823361i
$29$	−1.15345	+	3.54997i	−0.214191	+	0.659213i	0.785019	+	0.619472i	$0.212653\pi$
$29$	−1.15345	+	3.54997i	−0.214191	+	0.659213i	−0.999210	+	0.0397408i	$0.987347\pi$
$30$	−1.48977	+	1.34199i	−0.271994	+	0.245013i
$31$	3.31233	+	10.1943i	0.594911	+	1.83095i	0.555167	+	0.831739i	$0.312654\pi$
$31$	3.31233	+	10.1943i	0.594911	+	1.83095i	0.0397441	+	0.999210i	$0.487346\pi$
$32$			5.69588i			1.00690i
$33$	1.14738	−	0.372807i	0.199734	−	0.0648974i
$34$	−11.2728	−	8.19015i	−1.93326	−	1.40460i
$35$	6.40389	−	2.85288i	1.08245	−	0.482225i
$36$	10.4640	−	7.60255i	1.74400	−	1.26709i
$37$	−5.79814	+	7.98045i	−0.953208	+	1.31198i	−0.00311994	+	0.999995i	$0.500993\pi$
$37$	−5.79814	+	7.98045i	−0.953208	+	1.31198i	−0.950088	+	0.311983i	$0.899007\pi$
$38$	1.49821	−	2.06211i	0.243042	−	0.334518i
$39$	1.29425	−	0.940327i	0.207246	−	0.150573i
$40$	9.52492	+	10.5738i	1.50602	+	1.67187i
$41$	−8.84399	−	6.42553i	−1.38120	−	1.00350i	−0.996767	−	0.0803465i	$-0.974397\pi$
$41$	−8.84399	−	6.42553i	−1.38120	−	1.00350i	−0.384432	−	0.923153i	$-0.625603\pi$
$42$	2.67377	−	0.868762i	0.412572	−	0.134053i
$43$		−	1.54557i		−	0.235697i	−0.993032	−	0.117849i	$-0.962400\pi$
$43$		−	1.54557i		−	0.235697i	0.993032	−	0.117849i	$-0.0375998\pi$
$44$	−4.76548	−	14.6666i	−0.718423	−	2.21108i
$45$	1.33579	−	6.29121i	0.199128	−	0.937839i
$46$	3.88886	−	11.9687i	0.573381	−	1.76469i
$47$	5.50650	+	1.78917i	0.803206	+	0.260977i	0.681718	−	0.731615i	$-0.261233\pi$
$47$	5.50650	+	1.78917i	0.803206	+	0.260977i	0.121488	+	0.992593i	$0.461233\pi$
$48$	1.49472	+	2.05730i	0.215744	+	0.296946i
$49$	−2.82974			−0.404249
$50$	12.6753	+	1.32660i	1.79256	+	0.187609i
$51$	−1.92315			−0.269294
$52$	−12.0199	−	16.5440i	−1.66686	−	2.29424i
$53$	4.68652	+	1.52274i	0.643744	+	0.209165i	0.612654	−	0.790352i	$-0.290102\pi$
$53$	4.68652	+	1.52274i	0.643744	+	0.209165i	0.0310901	+	0.999517i	$0.490102\pi$
$54$	1.62828	−	5.01133i	0.221581	−	0.681956i
$55$	−6.64170	−	3.83264i	−0.895567	−	0.516793i
$56$	−6.16613	−	18.9774i	−0.823984	−	2.53596i
$57$		−	0.351798i		−	0.0465968i
$58$	9.04854	−	2.94005i	1.18813	−	0.386047i
$59$	8.14886	+	5.92049i	1.06089	+	0.770783i	0.974253	−	0.225457i	$-0.0723876\pi$
$59$	8.14886	+	5.92049i	1.06089	+	0.770783i	0.0866381	+	0.996240i	$0.472388\pi$
$60$	3.46034	+	0.734723i	0.446728	+	0.0948524i
$61$	−2.11434	+	1.53616i	−0.270714	+	0.196685i	−0.714857	−	0.699271i	$-0.753508\pi$
$61$	−2.11434	+	1.53616i	−0.270714	+	0.196685i	0.444143	+	0.895956i	$0.353508\pi$
$62$	16.0592	−	22.1036i	2.03952	−	2.80716i
$63$	−5.30047	+	7.29547i	−0.667797	+	0.919143i
$64$	0.0495926	−	0.0360312i	0.00619908	−	0.00450389i
$65$	−9.94665	−	2.11194i	−1.23373	−	0.261954i
$66$	−2.48779	−	1.80748i	−0.306226	−	0.222486i
$67$	−6.95171	+	2.25875i	−0.849287	+	0.275950i	−0.701147	−	0.713016i	$-0.747328\pi$
$67$	−6.95171	+	2.25875i	−0.849287	+	0.275950i	−0.148140	+	0.988966i	$0.547328\pi$
$68$			24.5830i			2.98113i
$69$	−0.536738	−	1.65191i	−0.0646156	−	0.198866i
$70$	−15.4773	−	8.93130i	−1.84989	−	1.06749i
$71$	1.01372	−	3.11992i	0.120307	−	0.370266i	−0.872710	−	0.488239i	$-0.837639\pi$
$71$	1.01372	−	3.11992i	0.120307	−	0.370266i	0.993017	+	0.117972i	$0.0376395\pi$
$72$	−17.4097	−	5.65675i	−2.05175	−	0.666654i
$73$	−6.52537	−	8.98140i	−0.763737	−	1.05119i	−0.996894	−	0.0787542i	$-0.974906\pi$
$73$	−6.52537	−	8.98140i	−0.763737	−	1.05119i	0.233158	−	0.972439i	$-0.425094\pi$
$74$	25.1434			2.92286
$75$	1.52294	−	0.880164i	0.175854	−	0.101633i
$76$	−4.49693			−0.515833
$77$	6.31973	+	8.69836i	0.720200	+	0.991270i
$78$	−3.87811	−	1.26008i	−0.439110	−	0.142676i
$79$	−2.64141	+	8.12943i	−0.297182	+	0.914633i	0.685298	+	0.728263i	$0.259672\pi$
$79$	−2.64141	+	8.12943i	−0.297182	+	0.914633i	−0.982480	+	0.186369i	$0.940328\pi$
$80$	3.35708	−	15.8109i	0.375333	−	1.76772i
$81$	2.44169	+	7.51474i	0.271298	+	0.834971i
$82$			27.8641i			3.07707i
$83$	16.1490	−	5.24713i	1.77258	−	0.575947i	0.774207	−	0.632932i	$-0.218149\pi$
$83$	16.1490	−	5.24713i	1.77258	−	0.575947i	0.998375	+	0.0569856i	$0.0181489\pi$
$84$	−4.01271	−	2.91540i	−0.437823	−	0.318097i
$85$	8.18128	+	9.08221i	0.887384	+	0.985104i
$86$	−3.18713	+	2.31559i	−0.343677	+	0.249696i
$87$	0.771845	−	1.06235i	0.0827505	−	0.113896i
$88$	−12.8288	+	17.6574i	−1.36756	+	1.88228i
$89$	−7.30488	+	5.30731i	−0.774316	+	0.562574i	−0.903268	−	0.429077i	$-0.858839\pi$
$89$	−7.30488	+	5.30731i	−0.774316	+	0.562574i	0.128952	+	0.991651i	$0.458839\pi$
$90$	−14.9745	+	6.67101i	−1.57845	+	0.703186i
$91$	11.5344	+	8.38024i	1.20914	+	0.878488i
$92$	−21.1158	+	6.86095i	−2.20148	+	0.715304i
$93$		−	3.77089i		−	0.391023i
$94$	−4.56043	−	14.0356i	−0.470372	−	1.44766i
$95$	−1.66139	+	1.49659i	−0.170455	+	0.153547i
$96$	0.619209	−	1.90573i	0.0631977	−	0.194503i
$97$	0.580951	+	0.188762i	0.0589866	+	0.0191659i	0.338362	−	0.941016i	$-0.390127\pi$
$97$	0.580951	+	0.188762i	0.0589866	+	0.0191659i	−0.279375	+	0.960182i	$0.590127\pi$
$98$	4.23954	+	5.83523i	0.428259	+	0.589447i
$99$	9.86356			0.991325
$100$	−11.2509	−	19.4673i	−1.12509	−	1.94673i
$101$	−0.179373			−0.0178483			−0.00892416	−	0.999960i	$-0.502841\pi$
$101$	−0.179373			−0.0178483			−0.00892416	+	0.999960i	$0.502841\pi$
$102$	2.88128	+	3.96574i	0.285289	+	0.392667i
$103$	−11.0943	−	3.60476i	−1.09315	−	0.355187i	−0.293690	−	0.955901i	$-0.594883\pi$
$103$	−11.0943	−	3.60476i	−1.09315	−	0.355187i	−0.799464	+	0.600714i	$0.794883\pi$
$104$	−8.94353	+	27.5254i	−0.876985	+	2.69908i
$105$	−2.45275	+	0.258340i	−0.239364	+	0.0252114i
$106$	−3.88133	−	11.9455i	−0.376988	−	1.16025i
$107$		−	0.852837i		−	0.0824468i	−0.999150	−	0.0412234i	$-0.986874\pi$
$107$		−	0.852837i		−	0.0824468i	0.999150	−	0.0412234i	$-0.0131255\pi$
$108$	−8.84127	+	2.87270i	−0.850752	+	0.276426i
$109$	−0.824041	−	0.598701i	−0.0789288	−	0.0573452i	0.547621	−	0.836726i	$-0.315534\pi$
$109$	−0.824041	−	0.598701i	−0.0789288	−	0.0573452i	−0.626550	+	0.779381i	$0.715534\pi$
$110$	2.04734	+	19.4380i	0.195206	+	1.85334i
$111$	2.80751	−	2.03977i	0.266477	−	0.193607i
$112$	−13.3210	+	18.3348i	−1.25872	+	1.73248i
$113$	3.97716	−	5.47410i	0.374140	−	0.514960i	−0.579880	−	0.814702i	$-0.696901\pi$
$113$	3.97716	−	5.47410i	0.374140	−	0.514960i	0.954020	+	0.299742i	$0.0969006\pi$
$114$	−0.725446	+	0.527067i	−0.0679442	+	0.0493644i
$115$	−5.51793	+	9.56218i	−0.514549	+	0.891678i
$116$	−13.5797	−	9.86626i	−1.26085	−	0.916059i
$117$	12.4394	−	4.04179i	1.15002	−	0.373664i
$118$		−	25.6740i		−	2.36348i
$119$	−5.29630	−	16.3003i	−0.485511	−	1.49425i
$120$	−2.03735	−	4.57326i	−0.185984	−	0.417479i
$121$	0.234937	−	0.723061i	0.0213579	−	0.0657328i
$122$	6.33546	+	2.05852i	0.573586	+	0.186369i
$123$	2.26049	+	3.11130i	0.203822	+	0.280536i
$124$	−48.2022			−4.32868
$125$	−10.6354	−	3.44791i	−0.951260	−	0.308390i
$126$	22.9853			2.04769
$127$	−4.60662	−	6.34047i	−0.408772	−	0.562626i	0.554147	−	0.832419i	$-0.313045\pi$
$127$	−4.60662	−	6.34047i	−0.408772	−	0.562626i	−0.962918	+	0.269793i	$0.913045\pi$
$128$	10.6856	+	3.47197i	0.944484	+	0.306881i
$129$	−0.168021	+	0.517117i	−0.0147935	+	0.0455296i
$130$	10.5471	+	23.6752i	0.925043	+	2.07645i
$131$	−2.32566	−	7.15763i	−0.203193	−	0.625365i	−0.999783	−	0.0208442i	$-0.993365\pi$
$131$	−2.32566	−	7.15763i	−0.203193	−	0.625365i	0.796589	−	0.604521i	$-0.206635\pi$
$132$			5.42523i			0.472205i
$133$	2.98179	−	0.968843i	0.258554	−	0.0840093i
$134$	15.0729	+	10.9511i	1.30210	+	0.946032i
$135$	−2.31037	+	4.00372i	−0.198845	+	0.344585i
$136$	28.1473	−	20.4502i	2.41361	−	1.75359i
$137$	−3.06649	+	4.22067i	−0.261988	+	0.360596i	−0.919665	−	0.392705i	$-0.871539\pi$
$137$	−3.06649	+	4.22067i	−0.261988	+	0.360596i	0.657676	+	0.753301i	$0.271539\pi$
$138$	−2.60227	+	3.58172i	−0.221520	+	0.304896i
$139$	−2.70160	+	1.96283i	−0.229147	+	0.166485i	−0.696434	−	0.717621i	$-0.745231\pi$
$139$	−2.70160	+	1.96283i	−0.229147	+	0.166485i	0.467288	+	0.884105i	$0.345231\pi$
$140$	3.30228	+	31.3528i	0.279093	+	2.64979i
$141$	−1.64786	−	1.19724i	−0.138775	−	0.100826i
$142$	−7.95239	+	2.58389i	−0.667349	+	0.216835i
$143$		−	15.5947i		−	1.30409i
$144$	6.42473	+	19.7733i	0.535394	+	1.64777i
$145$	−8.30056	+	0.874268i	−0.689324	+	0.0726040i
$146$	−8.74425	+	26.9120i	−0.723679	+	2.22726i
$147$	0.946774	+	0.307625i	0.0780886	+	0.0253725i
$148$	−26.0738	−	35.8875i	−2.14325	−	2.94993i
$149$	−15.3244			−1.25542			−0.627712	−	0.778446i	$-0.716008\pi$
$149$	−15.3244			−1.25542			−0.627712	+	0.778446i	$0.716008\pi$
$150$	−4.09668	−	1.82180i	−0.334493	−	0.148750i
$151$	7.35113			0.598227			0.299113	−	0.954218i	$-0.403309\pi$
$151$	7.35113			0.598227			0.299113	+	0.954218i	$0.403309\pi$
$152$	3.74092	+	5.14893i	0.303429	+	0.417634i
$153$	−14.9538	−	4.85877i	−1.20894	−	0.392808i
$154$	8.46869	−	26.0639i	0.682426	−	2.10029i
$155$	−17.8083	+	16.0418i	−1.43040	+	1.28851i
$156$	2.22310	+	6.84199i	0.177990	+	0.547798i
$157$			14.9106i			1.19000i	0.803726	+	0.594999i	$0.202848\pi$
$157$			14.9106i			1.19000i	−0.803726	+	0.594999i	$0.797152\pi$
$158$	20.7212	−	6.73271i	1.64849	−	0.535626i
$159$	−1.40248	−	1.01896i	−0.111224	−	0.0808087i
$160$	−11.6341	+	5.18291i	−0.919759	+	0.409745i
$161$	12.5232	−	9.09863i	0.986965	−	0.717072i
$162$	11.8380	−	16.2937i	0.930085	−	1.28015i
$163$	−2.29018	+	3.15216i	−0.179381	+	0.246897i	−0.889233	−	0.457454i	$-0.848762\pi$
$163$	−2.29018	+	3.15216i	−0.179381	+	0.246897i	0.709853	+	0.704350i	$0.248762\pi$
$164$	39.7708	−	28.8951i	3.10557	−	2.25633i
$165$	1.80553	+	2.00435i	0.140560	+	0.156039i
$166$	−35.0147	−	25.4397i	−2.71767	−	1.97450i
$167$	−8.39224	+	2.72680i	−0.649411	+	0.211006i	−0.615154	−	0.788407i	$-0.710906\pi$
$167$	−8.39224	+	2.72680i	−0.649411	+	0.211006i	−0.0342564	+	0.999413i	$0.510906\pi$
$168$			7.01979i			0.541588i
$169$	−2.37301	−	7.30337i	−0.182539	−	0.561797i
$170$	6.47124	−	30.4777i	0.496322	−	2.33754i
$171$	0.888806	−	2.73547i	0.0679687	−	0.209186i
$172$	6.61014	+	2.14777i	0.504019	+	0.163766i
$173$	−6.36943	−	8.76676i	−0.484258	−	0.666525i	0.495058	−	0.868860i	$-0.335147\pi$
$173$	−6.36943	−	8.76676i	−0.484258	−	0.666525i	−0.979316	+	0.202335i	$0.935147\pi$
$174$	−3.34708			−0.253741
$175$	11.6543	+	10.4843i	0.880982	+	0.792539i
$176$	24.7888			1.86853
$177$	−2.08282	−	2.86675i	−0.156554	−	0.215478i
$178$	21.8885	+	7.11200i	1.64061	+	0.533067i
$179$	−3.04196	+	9.36220i	−0.227367	+	0.699764i	0.770676	+	0.637228i	$0.219919\pi$
$179$	−3.04196	+	9.36220i	−0.227367	+	0.699764i	−0.998043	+	0.0625361i	$0.980081\pi$
$180$	25.0502	+	14.4554i	1.86713	+	1.07744i
$181$	−2.00861	−	6.18186i	−0.149299	−	0.459494i	0.848240	−	0.529612i	$-0.177662\pi$
$181$	−2.00861	−	6.18186i	−0.149299	−	0.459494i	−0.997539	+	0.0701181i	$0.977662\pi$
$182$		−	36.3406i		−	2.69374i
$183$	0.874416	−	0.284115i	0.0646387	−	0.0210024i
$184$	25.4216	+	18.4699i	1.87411	+	1.36162i
$185$	−21.5764	−	4.58125i	−1.58633	−	0.336821i
$186$	−7.77599	+	5.64959i	−0.570163	+	0.414248i
$187$	−11.0191	+	15.1665i	−0.805797	+	1.10908i
$188$	−15.3040	+	21.0641i	−1.11616	+	1.53626i
$189$	5.24350	−	3.80963i	0.381409	−	0.277110i
$190$	5.57524	+	1.18377i	0.404470	+	0.0858800i
$191$	10.1059	+	7.34237i	0.731237	+	0.531275i	0.889955	−	0.456049i	$-0.150736\pi$
$191$	10.1059	+	7.34237i	0.731237	+	0.531275i	−0.158717	+	0.987324i	$0.550736\pi$
$192$	−0.0205097	+	0.00666400i	−0.00148016	+	0.000480933i
$193$		−	20.0284i		−	1.44168i	−0.693103	−	0.720838i	$-0.743757\pi$
$193$		−	20.0284i		−	1.44168i	0.693103	−	0.720838i	$-0.256243\pi$
$194$	−0.481138	−	1.48079i	−0.0345437	−	0.106315i
$195$	3.09835	+	1.78793i	0.221878	+	0.128036i
$196$	3.93228	−	12.1023i	0.280877	−	0.864451i
$197$	−3.36999	−	1.09498i	−0.240102	−	0.0780138i	0.186494	−	0.982456i	$-0.440287\pi$
$197$	−3.36999	−	1.09498i	−0.240102	−	0.0780138i	−0.426596	+	0.904442i	$0.640287\pi$
$198$	−14.7777	−	20.3397i	−1.05020	−	1.44548i
$199$	−4.66230			−0.330502			−0.165251	−	0.986252i	$-0.552843\pi$
$199$	−4.66230			−0.330502			−0.165251	+	0.986252i	$0.552843\pi$
$200$	−12.9305	+	29.0767i	−0.914322	+	2.05603i
$201$	2.57145			0.181376
$202$	0.268739	+	0.369888i	0.0189084	+	0.0260252i
$203$	11.1300	+	3.61636i	0.781174	+	0.253819i
$204$	2.67246	−	8.22497i	0.187109	−	0.575863i
$205$	5.07698	−	23.9111i	0.354592	−	1.67003i
$206$	9.18819	+	28.2783i	0.640172	+	1.97025i
$207$		−	14.2007i		−	0.987020i
$208$	31.2623	−	10.1577i	2.16765	−	0.704312i
$209$	−2.77438	−	2.01571i	−0.191908	−	0.139429i
$210$	4.20746	+	4.67080i	0.290342	+	0.322316i
$211$	−1.24516	+	0.904659i	−0.0857201	+	0.0622793i	−0.629820	−	0.776741i	$-0.716871\pi$
$211$	−1.24516	+	0.904659i	−0.0857201	+	0.0622793i	0.544100	+	0.839021i	$0.316871\pi$
$212$	−13.0250	+	17.9274i	−0.894563	+	1.23126i
$213$	−0.678343	+	0.933659i	−0.0464793	+	0.0639733i
$214$	−1.75864	+	1.27773i	−0.120218	+	0.0873437i
$215$	3.15690	−	1.40638i	0.215299	−	0.0959140i
$216$	10.6441	+	7.73341i	0.724241	+	0.526192i
$217$	31.9616	−	10.3849i	2.16969	−	0.704976i
$218$			2.59624i			0.175840i
$219$	1.20687	+	3.71438i	0.0815530	+	0.250994i
$220$	25.6210	−	23.0795i	1.72737	−	1.55602i
$221$	−7.68190	+	23.6424i	−0.516740	+	1.59036i
$222$	−8.41247	−	2.73338i	−0.564608	−	0.183452i
$223$	3.83014	+	5.27174i	0.256485	+	0.353022i	0.917769	−	0.397114i	$-0.129988\pi$
$223$	3.83014	+	5.27174i	0.256485	+	0.353022i	−0.661284	+	0.750136i	$0.729988\pi$
$224$	17.8580			1.19319
$225$	14.0656	−	2.99620i	0.937707	−	0.199747i
$226$	−17.2468			−1.14724
$227$	−2.09142	−	2.87860i	−0.138813	−	0.191059i	0.733951	−	0.679203i	$-0.237674\pi$
$227$	−2.09142	−	2.87860i	−0.138813	−	0.191059i	−0.872763	+	0.488143i	$0.837674\pi$
$228$	1.50458	+	0.488868i	0.0996433	+	0.0323761i
$229$	4.45556	−	13.7128i	0.294431	−	0.906167i	−0.688980	−	0.724780i	$-0.741941\pi$
$229$	4.45556	−	13.7128i	0.294431	−	0.906167i	0.983412	−	0.181387i	$-0.0580586\pi$
$230$	27.9853	−	2.94759i	1.84529	−	0.194358i
$231$	−1.16884	−	3.59732i	−0.0769041	−	0.236686i
$232$			23.7562i			1.55967i
$233$	−3.02274	+	0.982149i	−0.198027	+	0.0643427i	−0.406351	−	0.913717i	$-0.633199\pi$
$233$	−3.02274	+	0.982149i	−0.198027	+	0.0643427i	0.208325	+	0.978060i	$0.433199\pi$
$234$	−26.9714	−	19.5959i	−1.76318	−	1.28102i
$235$	1.35611	+	12.8753i	0.0884631	+	0.839895i
$236$	−36.6448	+	26.6240i	−2.38537	+	1.73308i
$237$	1.76753	−	2.43279i	0.114813	−	0.158027i
$238$	−25.6781	+	35.3429i	−1.66446	+	2.29094i
$239$	−4.63628	+	3.36845i	−0.299896	+	0.217887i	−0.727549	−	0.686056i	$-0.759341\pi$
$239$	−4.63628	+	3.36845i	−0.299896	+	0.217887i	0.427653	+	0.903943i	$0.359341\pi$
$240$	−2.84204	+	4.92506i	−0.183453	+	0.317911i
$241$	4.49732	+	3.26749i	0.289698	+	0.210478i	0.723136	−	0.690705i	$-0.242700\pi$
$241$	4.49732	+	3.26749i	0.289698	+	0.210478i	−0.433439	+	0.901183i	$0.642700\pi$
$242$	−1.84301	+	0.598832i	−0.118473	+	0.0384944i
$243$		−	8.98146i		−	0.576161i
$244$	−3.63175	−	11.1774i	−0.232499	−	0.715559i
$245$	−2.57489	−	5.77989i	−0.164504	−	0.369263i
$246$	3.02915	−	9.32275i	0.193131	−	0.594397i
$247$	−4.32487	−	1.40524i	−0.275185	−	0.0894130i
$248$	40.0986	+	55.1910i	2.54626	+	3.50463i
$249$	−5.97355			−0.378558
$250$	8.82412	+	27.0971i	0.558086	+	1.71377i
$251$	24.1737			1.52583			0.762914	−	0.646500i	$-0.223768\pi$
$251$	24.1737			1.52583			0.762914	+	0.646500i	$0.223768\pi$
$252$	−23.8358	−	32.8072i	−1.50152	−	2.06666i
$253$	−16.1028	−	5.23211i	−1.01237	−	0.328940i
$254$	−6.17305	+	18.9987i	−0.387332	+	1.19208i
$255$	−1.74995	−	3.92812i	−0.109586	−	0.245989i
$256$	−8.88761	−	27.3532i	−0.555475	−	1.70958i
$257$		−	24.9236i		−	1.55469i	−0.629073	−	0.777346i	$-0.716565\pi$
$257$		−	24.9236i		−	1.55469i	0.629073	−	0.777346i	$-0.283435\pi$
$258$	1.31808	−	0.428271i	0.0820602	−	0.0266630i
$259$	25.0206	+	18.1786i	1.55471	+	1.12956i
$260$	22.8545	−	39.6053i	1.41738	−	2.45622i
$261$	8.68562	−	6.31047i	0.537626	−	0.390608i
$262$	−11.2755	+	15.5194i	−0.696602	+	0.958791i
$263$	14.7525	−	20.3050i	0.909676	−	1.25206i	−0.0576014	−	0.998340i	$-0.518345\pi$
$263$	14.7525	−	20.3050i	0.909676	−	1.25206i	0.967277	−	0.253722i	$-0.0816547\pi$
$264$	6.21183	−	4.51316i	0.382311	−	0.277766i
$265$	1.15417	+	10.9581i	0.0709003	+	0.673149i
$266$	−6.46521	−	4.69725i	−0.396407	−	0.288007i
$267$	3.02103	−	0.981593i	0.184884	−	0.0600725i
$268$		−	32.8701i		−	2.00786i
$269$	1.62440	+	4.99938i	0.0990412	+	0.304817i	0.988286	−	0.152615i	$-0.0487693\pi$
$269$	1.62440	+	4.99938i	0.0990412	+	0.304817i	−0.889245	+	0.457432i	$0.848769\pi$
$270$	11.7175	−	1.23417i	0.713106	−	0.0751089i
$271$	−7.09360	+	21.8319i	−0.430906	+	1.32619i	0.466319	+	0.884617i	$0.345580\pi$
$271$	−7.09360	+	21.8319i	−0.430906	+	1.32619i	−0.897225	+	0.441574i	$0.854420\pi$
$272$	−37.5814	−	12.2109i	−2.27871	−	0.740397i
$273$	−2.94815	−	4.05779i	−0.178430	−	0.245588i
$274$	13.2977			0.803345
$275$	1.78482	−	17.0535i	0.107628	−	1.02836i
$276$	7.81080			0.470155
$277$	13.5984	+	18.7166i	0.817051	+	1.12457i	0.990197	+	0.139678i	$0.0446067\pi$
$277$	13.5984	+	18.7166i	0.817051	+	1.12457i	−0.173146	+	0.984896i	$0.555393\pi$
$278$	8.09512	+	2.63026i	0.485513	+	0.157753i
$279$	9.52704	−	29.3212i	0.570369	−	1.75541i
$280$	33.1515	−	29.8629i	1.98118	−	1.78465i
$281$	2.39241	+	7.36307i	0.142719	+	0.439244i	0.996711	−	0.0810429i	$-0.0258251\pi$
$281$	2.39241	+	7.36307i	0.142719	+	0.439244i	−0.853992	+	0.520287i	$0.825825\pi$
$282$			5.19179i			0.309166i
$283$	14.9539	−	4.85882i	0.888918	−	0.288827i	0.171263	−	0.985225i	$-0.445215\pi$
$283$	14.9539	−	4.85882i	0.888918	−	0.288827i	0.717655	+	0.696398i	$0.245215\pi$
$284$	11.9347	+	8.67105i	0.708193	+	0.514532i
$285$	0.718565	−	0.320115i	0.0425641	−	0.0189620i
$286$	−32.1579	+	23.3641i	−1.90153	+	1.38155i
$287$	−20.1456	+	27.7280i	−1.18916	+	1.63673i
$288$	9.62952	−	13.2539i	0.567425	−	0.780994i
$289$	10.4234	−	7.57301i	0.613138	−	0.445471i
$290$	14.2388	+	15.8068i	0.836132	+	0.928209i
$291$	−0.173854	−	0.126312i	−0.0101915	−	0.00740455i
$292$	47.4797	−	15.4271i	2.77854	−	0.902803i
$293$			32.2752i			1.88554i	0.333449	+	0.942768i	$0.391788\pi$
$293$			32.2752i			1.88554i	−0.333449	+	0.942768i	$0.608212\pi$
$294$	−0.784109	−	2.41324i	−0.0457301	−	0.140743i
$295$	−4.67793	+	22.0317i	−0.272360	+	1.28274i
$296$	−19.4004	+	59.7084i	−1.12763	+	3.47048i
$297$	−6.74230	−	2.19070i	−0.391228	−	0.127118i
$298$	22.9592	+	31.6006i	1.32999	+	1.83057i
$299$	−22.4519			−1.29843
$300$	1.64799	+	7.73647i	0.0951468	+	0.446665i
$301$	−4.84574			−0.279304
$302$	−11.0135	−	15.1588i	−0.633758	−	0.872293i
$303$	0.0600147	+	0.0195000i	0.00344776	+	0.00112024i
$304$	2.23373	−	6.87470i	0.128113	−	0.394291i
$305$	−5.06161	−	2.92084i	−0.289827	−	0.167247i
$306$	12.3846	+	38.1157i	0.707978	+	2.17893i
$307$			0.999183i			0.0570264i	0.999593	+	0.0285132i	$0.00907726\pi$
$307$			0.999183i			0.0570264i	−0.999593	+	0.0285132i	$0.990923\pi$
$308$	−45.9835	+	14.9409i	−2.62015	+	0.851339i
$309$	3.32005	+	2.41216i	0.188871	+	0.137223i
$310$	59.7605	+	12.6888i	3.39417	+	0.720673i
$311$	6.13864	−	4.45998i	0.348090	−	0.252902i	−0.399977	−	0.916525i	$-0.630982\pi$
$311$	6.13864	−	4.45998i	0.348090	−	0.252902i	0.748067	+	0.663623i	$0.230982\pi$
$312$	5.98465	−	8.23716i	0.338814	−	0.466337i
$313$	9.92108	−	13.6552i	0.560773	−	0.771837i	−0.430652	−	0.902518i	$-0.641716\pi$
$313$	9.92108	−	13.6552i	0.560773	−	0.771837i	0.991425	+	0.130681i	$0.0417163\pi$
$314$	30.7474	−	22.3393i	1.73517	−	1.26068i
$315$	−19.7245	−	4.18804i	−1.11135	−	0.235969i
$316$	−31.0976	−	22.5937i	−1.74938	−	1.27100i
$317$	5.85027	−	1.90087i	0.328584	−	0.106763i	−0.140079	−	0.990140i	$-0.544736\pi$
$317$	5.85027	−	1.90087i	0.328584	−	0.106763i	0.468663	+	0.883377i	$0.344736\pi$
$318$			4.41867i			0.247787i
$319$	−3.95557	−	12.1740i	−0.221470	−	0.681613i
$320$	0.118722	+	0.0685092i	0.00663675	+	0.00382978i
$321$	−0.0927132	+	0.285342i	−0.00517475	+	0.0159262i
$322$	−37.5247	−	12.1925i	−2.09117	−	0.679463i
$323$	3.21320	+	4.42259i	0.178787	+	0.246080i
$324$	−35.5323			−1.97402
$325$	−4.73710	−	22.2383i	−0.262767	−	1.23356i
$326$	9.93128			0.550043
$327$	0.210622	+	0.289896i	0.0116474	+	0.0160313i
$328$	−66.1693	−	21.4997i	−3.65359	−	1.18712i
$329$	5.60948	−	17.2642i	0.309261	−	0.951807i
$330$	1.42814	−	6.72614i	0.0786165	−	0.370262i
$331$	7.31431	+	22.5111i	0.402031	+	1.23732i	0.923349	+	0.383962i	$0.125440\pi$
$331$	7.31431	+	22.5111i	0.402031	+	1.23732i	−0.521318	+	0.853362i	$0.674560\pi$
$332$			76.3580i			4.19069i
$333$	26.9837	−	8.76752i	1.47870	−	0.480457i
$334$	18.1963	+	13.2204i	0.995657	+	0.723387i
$335$	−10.9392	−	12.1439i	−0.597675	−	0.663492i
$336$	6.45015	−	4.68631i	0.351884	−	0.255659i
$337$	8.18956	−	11.2720i	0.446113	−	0.614023i	−0.525443	−	0.850829i	$-0.676101\pi$
$337$	8.18956	−	11.2720i	0.446113	−	0.614023i	0.971557	+	0.236806i	$0.0761006\pi$
$338$	−11.5051	+	15.8354i	−0.625793	+	0.861331i
$339$	−1.92578	+	1.39916i	−0.104594	+	0.0759919i
$340$	−50.2120	+	22.3690i	−2.72313	+	1.21313i
$341$	−29.7384	−	21.6062i	−1.61042	−	1.17004i
$342$	−6.97245	+	2.26548i	−0.377027	+	0.122503i
$343$		−	13.0748i		−	0.705971i
$344$	−3.03970	−	9.35523i	−0.163890	−	0.504400i
$345$	2.88571	−	2.59945i	0.155361	−	0.139950i
$346$	−8.53528	+	26.2689i	−0.458860	+	1.41222i
$347$	−3.93748	−	1.27936i	−0.211375	−	0.0686798i	0.201416	−	0.979506i	$-0.435446\pi$
$347$	−3.93748	−	1.27936i	−0.211375	−	0.0686798i	−0.412790	+	0.910826i	$0.635446\pi$
$348$	3.47093	+	4.77733i	0.186061	+	0.256092i
$349$	−25.3994			−1.35960			−0.679798	−	0.733399i	$-0.737933\pi$
$349$	−25.3994			−1.35960			−0.679798	+	0.733399i	$0.737933\pi$
$350$	4.15920	−	39.7401i	0.222319	−	2.12420i
$351$	−9.40069			−0.501772
$352$	−11.4812	−	15.8026i	−0.611952	−	0.842279i
$353$	−25.9607	−	8.43513i	−1.38175	−	0.448957i	−0.478504	−	0.878085i	$-0.658821\pi$
$353$	−25.9607	−	8.43513i	−1.38175	−	0.448957i	−0.903243	+	0.429129i	$0.858821\pi$
$354$	−2.79106	+	8.58999i	−0.148343	+	0.456553i
$355$	7.29502	−	0.768358i	0.387179	−	0.0407802i
$356$	−12.5474	−	38.6169i	−0.665011	−	2.04669i
$357$			6.02953i			0.319117i
$358$	23.8634	−	7.75368i	1.26122	−	0.409795i
$359$	−6.31602	−	4.58886i	−0.333347	−	0.242191i	0.408503	−	0.912757i	$-0.366051\pi$
$359$	−6.31602	−	4.58886i	−0.333347	−	0.242191i	−0.741849	+	0.670567i	$0.766051\pi$
$360$	−4.28757	−	40.7074i	−0.225975	−	2.14547i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	−9.73835	+	13.4037i	−0.511836	+	0.704482i
$363$	−0.157210	+	0.216381i	−0.00825139	+	0.0113571i
$364$	−51.8694	+	37.6853i	−2.71870	+	1.97525i
$365$	12.4073	−	21.5009i	0.649426	−	1.12541i
$366$	−1.89593	−	1.37748i	−0.0991020	−	0.0720018i
$367$	4.02232	−	1.30693i	0.209964	−	0.0682213i	−0.202147	−	0.979355i	$-0.564792\pi$
$367$	4.02232	−	1.30693i	0.209964	−	0.0682213i	0.412110	+	0.911134i	$0.364792\pi$
$368$		−	35.6890i		−	1.86042i
$369$	9.71623	+	29.9035i	0.505807	+	1.55671i
$370$	22.8790	+	51.3566i	1.18942	+	2.66990i
$371$	4.77417	−	14.6934i	0.247863	−	0.762843i
$372$	16.1275	+	5.24013i	0.836170	+	0.271688i
$373$	−4.74036	−	6.52454i	−0.245446	−	0.337828i	0.668464	−	0.743745i	$-0.266952\pi$
$373$	−4.74036	−	6.52454i	−0.245446	−	0.337828i	−0.913910	+	0.405917i	$0.866952\pi$
$374$	47.7839			2.47085
$375$	3.18357	+	2.30979i	0.164399	+	0.119277i
$376$	36.8493			1.90036
$377$	−9.97709	−	13.7323i	−0.513846	−	0.707249i
$378$	−15.7117	−	5.10505i	−0.808124	−	0.262576i
$379$	2.25551	−	6.94175i	0.115858	−	0.356574i	−0.876267	−	0.481826i	$-0.839974\pi$
$379$	2.25551	−	6.94175i	0.115858	−	0.356574i	0.992125	+	0.125252i	$0.0399739\pi$
$380$	−4.09193	−	9.18520i	−0.209912	−	0.471191i
$381$	0.852000	+	2.62219i	0.0436493	+	0.134339i
$382$		−	31.8399i		−	1.62907i
$383$	−19.2675	+	6.26039i	−0.984523	+	0.319891i	−0.756664	−	0.653804i	$-0.773172\pi$
$383$	−19.2675	+	6.26039i	−0.984523	+	0.319891i	−0.227858	+	0.973694i	$0.573172\pi$
$384$	−3.19775	−	2.32330i	−0.163184	−	0.118560i
$385$	−12.0163	+	20.8233i	−0.612405	+	1.06126i
$386$	−41.3008	+	30.0068i	−2.10215	+	1.52730i
$387$	−2.61296	+	3.59643i	−0.132824	+	0.182817i
$388$	−1.61461	+	2.22232i	−0.0819694	+	0.112821i
$389$	13.0170	−	9.45738i	0.659986	−	0.479508i	−0.206672	−	0.978410i	$-0.566263\pi$
$389$	13.0170	−	9.45738i	0.659986	−	0.479508i	0.866658	+	0.498902i	$0.166263\pi$
$390$	−0.955082	−	9.06784i	−0.0483625	−	0.459168i
$391$	21.8355	+	15.8644i	1.10427	+	0.802298i
$392$	−17.1282	+	5.56530i	−0.865106	+	0.281090i
$393$			2.64762i			0.133555i
$394$	2.79099	+	8.58979i	0.140608	+	0.432747i
$395$	−19.0083	+	2.00208i	−0.956411	+	0.100735i
$396$	−13.7067	+	42.1848i	−0.688786	+	2.11986i
$397$	27.7668	+	9.02198i	1.39358	+	0.452800i	0.907108	−	0.420899i	$-0.138285\pi$
$397$	27.7668	+	9.02198i	1.39358	+	0.452800i	0.486468	+	0.873699i	$0.338285\pi$
$398$	6.98510	+	9.61417i	0.350132	+	0.481915i
$399$	−1.10297			−0.0552177
$400$	35.3493	−	7.52997i	1.76747	−	0.376499i
$401$	5.17391			0.258373			0.129186	−	0.991620i	$-0.458763\pi$
$401$	5.17391			0.258373			0.129186	+	0.991620i	$0.458763\pi$
$402$	−3.85258	−	5.30262i	−0.192149	−	0.264471i
$403$	−46.3579	−	15.0626i	−2.30925	−	0.750322i
$404$	0.249262	−	0.767150i	0.0124013	−	0.0381671i
$405$	−13.1274	+	11.8252i	−0.652308	+	0.587600i
$406$	−9.21776	−	28.3694i	−0.457470	−	1.40795i
$407$		−	33.8282i		−	1.67680i
$408$	−11.6407	+	3.78229i	−0.576300	+	0.187251i
$409$	12.3357	+	8.96242i	0.609962	+	0.443163i	0.849401	−	0.527748i	$-0.176964\pi$
$409$	12.3357	+	8.96242i	0.609962	+	0.443163i	−0.239439	+	0.970911i	$0.576964\pi$
$410$	−56.9137	+	25.3546i	−2.81077	+	1.25218i
$411$	1.48482	−	1.07879i	0.0732409	−	0.0532126i
$412$	30.8339	−	42.4392i	1.51908	−	2.09083i
$413$	18.5622	−	25.5486i	0.913385	−	1.25717i
$414$	−29.2835	+	21.2757i	−1.43920	+	1.04564i
$415$	25.4121	+	28.2106i	1.24743	+	1.38480i
$416$	−20.9549	−	15.2246i	−1.02740	−	0.746449i
$417$	1.11728	−	0.363027i	0.0547135	−	0.0177775i
$418$			8.74103i			0.427538i
$419$	1.14024	+	3.50931i	0.0557046	+	0.171441i	0.975038	−	0.222039i	$-0.0712711\pi$
$419$	1.14024	+	3.50931i	0.0557046	+	0.171441i	−0.919333	+	0.393480i	$0.871271\pi$
$420$	2.30354	−	10.8490i	0.112401	−	0.529377i
$421$	−6.35497	+	19.5586i	−0.309722	+	0.953227i	0.668150	+	0.744026i	$0.267086\pi$
$421$	−6.35497	+	19.5586i	−0.309722	+	0.953227i	−0.977873	+	0.209201i	$0.932914\pi$
$422$	3.73101	+	1.21228i	0.181623	+	0.0590128i
$423$	−9.78843	−	13.4726i	−0.475930	−	0.655061i
$424$	31.3620			1.52307
$425$	−11.1064	+	24.9749i	−0.538740	+	1.21146i
$426$	2.94161			0.142521
$427$	4.81624	+	6.62898i	0.233074	+	0.320799i
$428$	3.64744	+	1.18512i	0.176306	+	0.0572852i
$429$	−1.69532	+	5.21766i	−0.0818508	+	0.251911i
$430$	−7.62980	−	4.40283i	−0.367942	−	0.212324i
$431$	12.2537	+	37.7131i	0.590241	+	1.81657i	0.577118	+	0.816661i	$0.304177\pi$
$431$	12.2537	+	37.7131i	0.590241	+	1.81657i	0.0131224	+	0.999914i	$0.495823\pi$
$432$		−	14.9431i		−	0.718950i
$433$	−5.22512	+	1.69774i	−0.251103	+	0.0815883i	−0.431864	−	0.901939i	$-0.642144\pi$
$433$	−5.22512	+	1.69774i	−0.251103	+	0.0815883i	0.180761	+	0.983527i	$0.442144\pi$
$434$	−69.3000	−	50.3494i	−3.32651	−	2.41685i
$435$	2.87224	+	0.609855i	0.137714	+	0.0292403i
$436$	3.70565	−	2.69231i	0.177469	−	0.128938i
$437$	−2.90205	+	3.99433i	−0.138824	+	0.191075i
$438$	5.85130	−	8.05362i	0.279586	−	0.384817i
$439$	−15.5888	+	11.3260i	−0.744015	+	0.540558i	−0.893966	−	0.448135i	$-0.852088\pi$
$439$	−15.5888	+	11.3260i	−0.744015	+	0.540558i	0.149951	+	0.988693i	$0.452088\pi$
$440$	−47.7395	−	10.1364i	−2.27589	−	0.483233i
$441$	6.58459	+	4.78399i	0.313552	+	0.227809i
$442$	60.2624	−	19.5804i	2.86639	−	0.931347i
$443$			14.8981i			0.707829i	0.935278	+	0.353915i	$0.115150\pi$
$443$			14.8981i			0.707829i	−0.935278	+	0.353915i	$0.884850\pi$
$444$	4.82238	+	14.8418i	0.228860	+	0.704358i
$445$	−17.4874	−	10.0913i	−0.828984	−	0.478372i
$446$	5.13254	−	15.7963i	0.243033	−	0.747979i
$447$	5.12724	+	1.66594i	0.242510	+	0.0787962i
$448$	−0.112966	−	0.155485i	−0.00533716	−	0.00734597i
$449$	11.7034			0.552316			0.276158	−	0.961112i	$-0.410939\pi$
$449$	11.7034			0.552316			0.276158	+	0.961112i	$0.410939\pi$
$450$	−27.2517	−	24.5159i	−1.28466	−	1.15569i
$451$	37.4886			1.76527
$452$	17.8850	+	24.6166i	0.841240	+	1.15787i
$453$	−2.45954	−	0.799153i	−0.115559	−	0.0375475i
$454$	−2.80259	+	8.62549i	−0.131532	+	0.404814i
$455$	−6.62144	+	31.1851i	−0.310418	+	1.46198i
$456$	−0.691887	−	2.12941i	−0.0324006	−	0.0997188i
$457$			7.36463i			0.344503i	0.985053	+	0.172251i	$0.0551041\pi$
$457$			7.36463i			0.344503i	−0.985053	+	0.172251i	$0.944896\pi$
$458$	−34.9526	+	11.3568i	−1.63323	+	0.530668i
$459$	9.14260	+	6.64249i	0.426740	+	0.310045i
$460$	−33.2280	−	36.8871i	−1.54926	−	1.71987i
$461$	21.8612	−	15.8831i	1.01818	−	0.739749i	0.0522688	−	0.998633i	$-0.483355\pi$
$461$	21.8612	−	15.8831i	1.01818	−	0.739749i	0.965908	+	0.258884i	$0.0833548\pi$
$462$	−5.66690	+	7.79982i	−0.263648	+	0.362881i
$463$	11.5588	−	15.9094i	0.537185	−	0.739372i	−0.451019	−	0.892514i	$-0.648939\pi$
$463$	11.5588	−	15.9094i	0.537185	−	0.739372i	0.988204	+	0.153142i	$0.0489393\pi$
$464$	21.8285	−	15.8593i	1.01336	−	0.736250i
$465$	7.70223	−	3.43128i	0.357183	−	0.159122i
$466$	6.55400	+	4.76176i	0.303608	+	0.220584i
$467$	7.12108	−	2.31378i	0.329524	−	0.107069i	−0.139582	−	0.990210i	$-0.544576\pi$
$467$	7.12108	−	2.31378i	0.329524	−	0.107069i	0.469107	+	0.883142i	$0.344576\pi$
$468$			58.8176i			2.71885i
$469$	7.08172	+	21.7953i	0.327004	+	1.00641i
$470$	24.5186	−	22.0864i	1.13096	−	1.01877i
$471$	1.62096	−	4.98880i	0.0746899	−	0.229872i
$472$	60.9684	+	19.8098i	2.80630	+	0.911822i
$473$	3.11542	+	4.28800i	0.143247	+	0.197163i
$474$	−7.66481			−0.352056
$475$	−4.56862	−	2.03168i	−0.209623	−	0.0932197i
$476$	77.0736			3.53266
$477$	−8.33083	−	11.4664i	−0.381442	−	0.525010i
$478$	13.8922	+	4.51386i	0.635416	+	0.206459i
$479$	10.9285	−	33.6345i	0.499337	−	1.53680i	−0.310750	−	0.950492i	$-0.600580\pi$
$479$	10.9285	−	33.6345i	0.499337	−	1.53680i	0.810087	−	0.586310i	$-0.199420\pi$
$480$	4.45599	−	0.469333i	0.203387	−	0.0214220i
$481$	−13.8618	−	42.6622i	−0.632043	−	1.94523i
$482$		−	14.1693i		−	0.645396i
$483$	−5.17913	+	1.68280i	−0.235659	+	0.0765701i
$484$	2.76593	+	2.00957i	0.125724	+	0.0913440i
$485$	0.143074	+	1.35838i	0.00649664	+	0.0616810i
$486$	−18.5208	+	13.4561i	−0.840119	+	0.610382i
$487$	4.68043	−	6.44206i	0.212091	−	0.291918i	−0.689696	−	0.724099i	$-0.742256\pi$
$487$	4.68043	−	6.44206i	0.212091	−	0.291918i	0.901787	+	0.432181i	$0.142256\pi$
$488$	−9.77679	+	13.4566i	−0.442575	+	0.609152i
$489$	1.10893	−	0.805681i	0.0501473	−	0.0364342i
$490$	−8.06102	+	13.9692i	−0.364160	+	0.631064i
$491$	5.35998	+	3.89425i	0.241893	+	0.175745i	0.702126	−	0.712053i	$-0.252234\pi$
$491$	5.35998	+	3.89425i	0.241893	+	0.175745i	−0.460233	+	0.887798i	$0.652234\pi$
$492$	−16.4477	+	5.34419i	−0.741521	+	0.240935i
$493$			20.4050i			0.918997i
$494$	3.58182	+	11.0237i	0.161154	+	0.495980i
$495$	8.97524	+	20.1468i	0.403407	+	0.905532i
$496$	23.9431	−	73.6893i	1.07508	−	3.30875i
$497$	−9.78170	−	3.17827i	−0.438769	−	0.142565i
$498$	8.94963	+	12.3181i	0.401043	+	0.551988i
$499$	−16.4682			−0.737219			−0.368609	−	0.929584i	$-0.620166\pi$
$499$	−16.4682			−0.737219			−0.368609	+	0.929584i	$0.620166\pi$
$500$	29.5254	−	40.6945i	1.32041	−	1.81992i
$501$	3.10431			0.138690
$502$	−36.2172	−	49.8487i	−1.61645	−	2.22486i
$503$	33.6667	+	10.9390i	1.50113	+	0.487745i	0.940346	−	0.340220i	$-0.110502\pi$
$503$	33.6667	+	10.9390i	1.50113	+	0.487745i	0.560779	+	0.827965i	$0.310502\pi$
$504$	−17.7353	+	54.5835i	−0.789992	+	2.43134i
$505$	−0.163219	−	0.366379i	−0.00726315	−	0.0163037i
$506$	13.3362	+	41.0445i	0.592865	+	1.82465i
$507$			2.70153i			0.119979i
$508$	33.5186	−	10.8909i	1.48715	−	0.483203i
$509$	13.7620	+	9.99868i	0.609990	+	0.443184i	0.849411	−	0.527732i	$-0.176958\pi$
$509$	13.7620	+	9.99868i	0.609990	+	0.443184i	−0.239421	+	0.970916i	$0.576958\pi$
$510$	−5.47843	+	9.49374i	−0.242589	+	0.420390i
$511$	−28.1589	+	20.4586i	−1.24567	+	0.905035i
$512$	−29.8817	+	41.1286i	−1.32060	+	1.81765i
$513$	−1.21510	+	1.67244i	−0.0536479	+	0.0738400i
$514$	−51.3952	+	37.3408i	−2.26695	+	1.64703i
$515$	−2.73225	−	25.9408i	−0.120397	−	1.14309i
$516$	−1.97813	−	1.43720i	−0.0870824	−	0.0632691i
$517$	−18.8836	+	6.13565i	−0.830499	+	0.269846i
$518$		−	78.8306i		−	3.46362i
$519$	1.17803	+	3.62561i	0.0517099	+	0.159147i
$520$	−64.3600	+	6.77880i	−2.82237	+	0.297270i
$521$	2.22165	−	6.83752i	0.0973321	−	0.299557i	−0.890522	−	0.454939i	$-0.849661\pi$
$521$	2.22165	−	6.83752i	0.0973321	−	0.299557i	0.987854	+	0.155382i	$0.0496609\pi$
$522$	−26.0258	−	8.45628i	−1.13912	−	0.370121i
$523$	−13.6367	−	18.7693i	−0.596292	−	0.820726i	0.399070	−	0.916920i	$-0.369333\pi$
$523$	−13.6367	−	18.7693i	−0.596292	−	0.820726i	−0.995363	+	0.0961945i	$0.969333\pi$
$524$	33.8438			1.47847
$525$	−2.75953	−	4.77480i	−0.120436	−	0.208389i
$526$	−63.9735			−2.78938
$527$	34.4420	+	47.4054i	1.50032	+	2.06501i
$528$	−8.29385	−	2.69483i	−0.360943	−	0.117278i
$529$	−0.425381	+	1.30919i	−0.0184948	+	0.0569212i
$530$	20.8675	−	18.7975i	0.906428	−	0.816512i
$531$	−8.95254	−	27.5531i	−0.388507	−	1.19570i
$532$			14.0989i			0.611267i
$533$	47.2785	−	15.3617i	2.04786	−	0.665390i
$534$	−6.55029	−	4.75907i	−0.283459	−	0.205945i
$535$	1.74196	−	0.776030i	0.0753116	−	0.0335507i
$536$	−37.6359	+	27.3441i	−1.62562	+	1.18109i
$537$	2.03556	−	2.80171i	0.0878408	−	0.120903i
$538$	7.87557	−	10.8398i	0.339540	−	0.467337i
$539$	7.85078	−	5.70393i	0.338157	−	0.245685i
$540$	−13.9127	−	15.4448i	−0.598706	−	0.664636i
$541$	−0.0716227	−	0.0520369i	−0.00307930	−	0.00223724i	0.586245	−	0.810134i	$-0.300606\pi$
$541$	−0.0716227	−	0.0520369i	−0.00307930	−	0.00223724i	−0.589324	+	0.807897i	$0.700606\pi$
$542$	55.6474	−	18.0809i	2.39026	−	0.776642i
$543$			2.28668i			0.0981310i
$544$	9.62194	+	29.6133i	0.412537	+	1.26966i
$545$	0.473049	−	2.22793i	0.0202632	−	0.0954339i
$546$	−3.95064	+	12.1588i	−0.169072	+	0.520350i
$547$	−14.6955	−	4.77485i	−0.628333	−	0.204158i	−0.0224963	−	0.999747i	$-0.507161\pi$
$547$	−14.6955	−	4.77485i	−0.628333	−	0.204158i	−0.605836	+	0.795589i	$0.707161\pi$
$548$	−13.7898	−	18.9800i	−0.589071	−	0.810786i
$549$	7.51697			0.320817
$550$	−37.8402	+	21.8692i	−1.61351	+	0.932506i
$551$	−3.73266			−0.159017
$552$	−6.49767	−	8.94328i	−0.276559	−	0.380651i
$553$	25.4877	+	8.28147i	1.08385	+	0.352164i
$554$	18.2224	−	56.0829i	0.774197	−	2.38273i
$555$	6.72100	+	3.87840i	0.285291	+	0.164629i
$556$	−4.64046	−	14.2819i	−0.196799	−	0.605686i
$557$			27.5833i			1.16874i	0.811487	+	0.584370i	$0.198658\pi$
$557$			27.5833i			1.16874i	−0.811487	+	0.584370i	$0.801342\pi$
$558$	−74.7370	+	24.2835i	−3.16387	+	1.02800i
$559$	5.68608	+	4.13118i	0.240496	+	0.174730i
$560$	−49.5711	−	10.5253i	−2.09476	−	0.444774i
$561$	5.33555	−	3.87650i	0.225267	−	0.163666i
$562$	11.5991	−	15.9648i	0.489279	−	0.673435i
$563$	−8.32669	+	11.4607i	−0.350928	+	0.483011i	−0.947593	−	0.319479i	$-0.896492\pi$
$563$	−8.32669	+	11.4607i	−0.350928	+	0.483011i	0.596665	+	0.802490i	$0.296492\pi$
$564$	7.41031	−	5.38390i	0.312030	−	0.226703i
$565$	14.8001	+	3.14246i	0.622645	+	0.132204i
$566$	−32.4235	−	23.5571i	−1.36286	−	0.990178i
$567$	23.5605	−	7.65527i	0.989448	−	0.321491i
$568$		−	20.8784i		−	0.876037i
$569$	8.89095	+	27.3635i	0.372728	+	1.14714i	0.944999	+	0.327074i	$0.106063\pi$
$569$	8.89095	+	27.3635i	0.372728	+	1.14714i	−0.572271	+	0.820065i	$0.693937\pi$
$570$	−1.73667	−	1.00216i	−0.0727412	−	0.0419759i
$571$	12.4200	−	38.2248i	0.519761	−	1.59966i	−0.254689	−	0.967023i	$-0.581973\pi$
$571$	12.4200	−	38.2248i	0.519761	−	1.59966i	0.774449	−	0.632636i	$-0.218027\pi$
$572$	66.6957	+	21.6707i	2.78869	+	0.906099i
$573$	−2.58303	−	3.55524i	−0.107908	−	0.148522i
$574$	87.3606			3.64636
$575$	−24.5522	−	2.56963i	−1.02390	−	0.107161i
$576$	−0.176313			−0.00734638
$577$	11.9241	+	16.4121i	0.496406	+	0.683244i	0.981553	−	0.191188i	$-0.0612341\pi$
$577$	11.9241	+	16.4121i	0.496406	+	0.683244i	−0.485147	+	0.874432i	$0.661234\pi$
$578$	−31.2327	−	10.1481i	−1.29911	−	0.422107i
$579$	−2.17732	+	6.70110i	−0.0904864	+	0.278488i
$580$	7.79558	−	36.7150i	0.323694	−	1.52451i
$581$	−16.4510	−	50.6310i	−0.682503	−	2.10053i
$582$			0.547748i			0.0227049i
$583$	−16.0716	+	5.22198i	−0.665618	+	0.216273i
$584$	−57.1615	−	41.5303i	−2.36536	−	1.71853i
$585$	19.5746	+	21.7302i	0.809312	+	0.898435i
$586$	66.5550	−	48.3550i	2.74936	−	1.99753i
$587$	−2.06405	+	2.84092i	−0.0851923	+	0.117257i	−0.849486	−	0.527611i	$-0.823088\pi$
$587$	−2.06405	+	2.84092i	−0.0851923	+	0.117257i	0.764294	+	0.644868i	$0.223088\pi$
$588$	−2.63132	+	3.62171i	−0.108514	+	0.149357i
$589$	−8.67178	+	6.30042i	−0.357315	+	0.259604i
$590$	52.4404	−	23.3618i	2.15894	−	0.961789i
$591$	1.00849	+	0.732713i	0.0414839	+	0.0301398i
$592$	67.8147	−	22.0343i	2.78717	−	0.905605i
$593$			0.441554i			0.0181325i	0.999959	+	0.00906623i	$0.00288591\pi$
$593$			0.441554i			0.0181325i	−0.999959	+	0.00906623i	$0.997114\pi$
$594$	5.58390	+	17.1855i	0.229110	+	0.705129i
$595$	28.4749	−	25.6503i	1.16736	−	1.05156i
$596$	21.2952	−	65.5399i	0.872285	−	2.68462i
$597$	1.55991	+	0.506846i	0.0638429	+	0.0207438i
$598$	33.6377	+	46.2983i	1.37555	+	1.89328i
$599$	33.9488			1.38711			0.693554	−	0.720404i	$-0.256044\pi$
$599$	33.9488			1.38711			0.693554	+	0.720404i	$0.256044\pi$
$600$	7.48724	−	8.32278i	0.305665	−	0.339776i
$601$	−33.5747			−1.36954			−0.684770	−	0.728760i	$-0.740097\pi$
$601$	−33.5747			−1.36954			−0.684770	+	0.728760i	$0.740097\pi$
$602$	7.25993	+	9.99243i	0.295893	+	0.407261i
$603$	19.9948	+	6.49670i	0.814250	+	0.264566i
$604$	−10.2153	+	31.4395i	−0.415656	+	1.27926i
$605$	1.69067	−	0.178072i	0.0687353	−	0.00723965i
$606$	−0.0497036	−	0.152972i	−0.00201907	−	0.00621406i
$607$			35.1447i			1.42648i	0.700919	+	0.713241i	$0.252773\pi$
$607$			35.1447i			1.42648i	−0.700919	+	0.713241i	$0.747227\pi$
$608$	−5.41711	+	1.76013i	−0.219693	+	0.0713825i
$609$	−3.33074	−	2.41992i	−0.134968	−	0.0980602i
$610$	1.56027	+	14.8136i	0.0631733	+	0.599786i
$611$	−21.3007	+	15.4759i	−0.861735	+	0.626087i
$612$	41.5603	−	57.2028i	1.67997	−	2.31229i
$613$	3.31384	−	4.56111i	0.133845	−	0.184221i	−0.736834	−	0.676074i	$-0.763680\pi$
$613$	3.31384	−	4.56111i	0.133845	−	0.184221i	0.870679	+	0.491852i	$0.163680\pi$
$614$	2.06042	−	1.49699i	0.0831519	−	0.0604134i
$615$	−4.29807	+	7.44826i	−0.173315	+	0.300343i
$616$	55.3601	+	40.2215i	2.23052	+	1.62057i
$617$	−33.0372	+	10.7344i	−1.33003	+	0.432153i	−0.885927	−	0.463824i	$-0.846477\pi$
$617$	−33.0372	+	10.7344i	−1.33003	+	0.432153i	−0.444102	+	0.895976i	$0.646477\pi$
$618$		−	10.4602i		−	0.420772i
$619$	−2.94513	−	9.06416i	−0.118375	−	0.364319i	0.874261	−	0.485456i	$-0.161346\pi$
$619$	−2.94513	−	9.06416i	−0.118375	−	0.364319i	−0.992636	+	0.121136i	$0.961346\pi$
$620$	−43.8610	−	98.4553i	−1.76150	−	3.95406i
$621$	−3.15400	+	9.70701i	−0.126566	+	0.389529i
$622$	−18.3939	−	5.97655i	−0.737530	−	0.239638i
$623$	16.6397	+	22.9026i	0.666655	+	0.917572i
$624$	−11.5640			−0.462930
$625$	−2.63506	−	24.8607i	−0.105403	−	0.994430i
$626$	−43.0224			−1.71952
$627$	0.709122	+	0.976022i	0.0283196	+	0.0389786i
$628$	−63.7703	−	20.7202i	−2.54471	−	0.826827i
$629$	−16.6637	+	51.2856i	−0.664425	+	2.04489i
$630$	20.9152	+	46.9486i	0.833282	+	1.87048i
$631$	−12.3533	−	38.0196i	−0.491778	−	1.51354i	−0.821919	−	0.569605i	$-0.807096\pi$
$631$	−12.3533	−	38.0196i	−0.491778	−	1.51354i	0.330141	−	0.943932i	$-0.392904\pi$
$632$			54.4018i			2.16399i
$633$	0.514951	−	0.167318i	0.0204675	−	0.00665028i
$634$	−12.6847	−	9.21599i	−0.503775	−	0.366014i
$635$	8.75898	−	15.1787i	0.347589	−	0.602348i
$636$	6.30683	−	4.58218i	0.250082	−	0.181695i
$637$	7.56366	−	10.4105i	0.299683	−	0.412479i
$638$	−19.1778	+	26.3960i	−0.759258	+	1.04503i
$639$	−7.63343	+	5.54601i	−0.301974	+	0.219397i
$640$	2.63160	+	24.9852i	0.104023	+	0.987626i
$641$	−32.2817	−	23.4540i	−1.27505	−	0.926378i	−0.275658	−	0.961256i	$-0.588896\pi$
$641$	−32.2817	−	23.4540i	−1.27505	−	0.926378i	−0.999392	+	0.0348775i	$0.988896\pi$
$642$	0.727310	−	0.236317i	0.0287046	−	0.00932670i
$643$			29.1803i			1.15076i	0.817887	+	0.575379i	$0.195145\pi$
$643$			29.1803i			1.15076i	−0.817887	+	0.575379i	$0.804855\pi$
$644$	21.5107	+	66.2032i	0.847642	+	2.60877i
$645$	−1.20913	+	0.127353i	−0.0476093	+	0.00501451i
$646$	4.30582	−	13.2519i	0.169410	−	0.521391i
$647$	13.8094	+	4.48695i	0.542904	+	0.176400i	0.567614	−	0.823295i	$-0.307866\pi$
$647$	13.8094	+	4.48695i	0.542904	+	0.176400i	−0.0247108	+	0.999695i	$0.507866\pi$
$648$	29.5587	+	40.6841i	1.16118	+	1.59822i
$649$	−34.5420			−1.35589
$650$	−38.7605	+	43.0860i	−1.52031	+	1.68997i
$651$	−11.8227			−0.463366
$652$	−10.2988	−	14.1751i	−0.403331	−	0.555138i
$653$	−24.7371	−	8.03758i	−0.968039	−	0.314535i	−0.218015	−	0.975945i	$-0.569958\pi$
$653$	−24.7371	−	8.03758i	−0.968039	−	0.314535i	−0.750024	+	0.661411i	$0.769958\pi$
$654$	0.282242	−	0.868650i	0.0110365	−	0.0339669i
$655$	12.5036	−	11.2633i	0.488557	−	0.440093i
$656$	24.4186	+	75.1527i	0.953386	+	2.93422i
$657$			31.9309i			1.24574i
$658$	−44.0049	+	14.2981i	−1.71549	+	0.557396i
$659$	17.9594	+	13.0483i	0.699598	+	0.508288i	0.879801	−	0.475342i	$-0.157676\pi$
$659$	17.9594	+	13.0483i	0.699598	+	0.508288i	−0.180203	+	0.983629i	$0.557676\pi$
$660$	−11.0813	+	4.93663i	−0.431339	+	0.192158i
$661$	40.9907	−	29.7815i	1.59435	−	1.15837i	0.696982	−	0.717088i	$-0.254526\pi$
$661$	40.9907	−	29.7815i	1.59435	−	1.15837i	0.897371	−	0.441277i	$-0.145474\pi$
$662$	35.4620	−	48.8093i	1.37827	−	1.89703i
$663$	5.14042	−	7.07517i	0.199637	−	0.274777i
$664$	87.4292	−	63.5210i	3.39291	−	2.46509i
$665$	4.69216	+	5.20887i	0.181954	+	0.201991i
$666$	−58.5068	−	42.5077i	−2.26709	−	1.64714i
$667$	−17.5271	+	5.69491i	−0.678653	+	0.220508i
$668$		−	39.6814i		−	1.53532i
$669$	−0.708389	−	2.18020i	−0.0273879	−	0.0842913i
$670$	−8.65275	+	40.7520i	−0.334285	+	1.57439i
$671$	2.76955	−	8.52380i	0.106917	−	0.329058i
$672$	−5.97492	−	1.94137i	−0.230487	−	0.0748899i
$673$	19.1640	+	26.3770i	0.738718	+	1.01676i	0.998691	+	0.0511426i	$0.0162863\pi$
$673$	19.1640	+	26.3770i	0.738718	+	1.01676i	−0.259973	+	0.965616i	$0.583714\pi$
$674$	−35.5137			−1.36794
$675$	−10.2801	−	1.07591i	−0.395681	−	0.0414120i
$676$	34.5328			1.32819
$677$	−4.32400	−	5.95148i	−0.166185	−	0.228734i	0.717800	−	0.696249i	$-0.245149\pi$
$677$	−4.32400	−	5.95148i	−0.166185	−	0.228734i	−0.883985	+	0.467515i	$0.845149\pi$
$678$	5.77044	+	1.87493i	0.221612	+	0.0720062i
$679$	0.591816	−	1.82142i	0.0227118	−	0.0698998i
$680$	67.3829	+	38.8838i	2.58401	+	1.49112i
$681$	0.386811	+	1.19048i	0.0148226	+	0.0456194i
$682$			93.6943i			3.58774i
$683$	6.98210	−	2.26862i	0.267163	−	0.0868064i	−0.172372	−	0.985032i	$-0.555143\pi$
$683$	6.98210	−	2.26862i	0.267163	−	0.0868064i	0.439535	+	0.898225i	$0.355143\pi$
$684$	10.4640	+	7.60255i	0.400101	+	0.290691i
$685$	−11.4112	−	2.42291i	−0.436001	−	0.0925748i
$686$	−26.9616	+	19.5888i	−1.02940	+	0.747902i
$687$	−2.98148	+	4.10365i	−0.113750	+	0.156564i
$688$	−6.56682	+	9.03845i	−0.250358	+	0.344588i
$689$	−18.1288	+	13.1713i	−0.690653	+	0.501788i
$690$	−9.68374	−	2.05612i	−0.368654	−	0.0782751i
$691$	29.5879	+	21.4969i	1.12558	+	0.817780i	0.985045	−	0.172296i	$-0.0551185\pi$
$691$	29.5879	+	21.4969i	1.12558	+	0.817780i	0.140533	+	0.990076i	$0.455119\pi$
$692$	46.3451	−	15.0584i	1.76178	−	0.572436i
$693$		−	30.9246i		−	1.17473i
$694$	3.26098	+	10.0363i	0.123785	+	0.380971i
$695$	−6.46746	−	3.73210i	−0.245325	−	0.141566i
$696$	2.58258	−	7.94836i	0.0978924	−	0.301282i
$697$	−56.8350	−	18.4668i	−2.15278	−	0.699481i
$698$	38.0536	+	52.3763i	1.44035	+	1.98247i
$699$	1.11812			0.0422912
$700$	−61.0347	+	35.2742i	−2.30690	+	1.33324i
$701$	32.3396			1.22145			0.610725	−	0.791843i	$-0.290878\pi$
$701$	32.3396			1.22145			0.610725	+	0.791843i	$0.290878\pi$
$702$	14.0842	+	19.3852i	0.531574	+	0.731649i
$703$	−9.38158	−	3.04826i	−0.353833	−	0.114967i
$704$	−0.0649607	+	0.199928i	−0.00244830	+	0.00753508i
$705$	0.945971	−	4.45526i	0.0356273	−	0.167795i
$706$	21.5004	+	66.1713i	0.809177	+	2.49039i
$707$			0.562379i			0.0211504i
$708$	15.1550	−	4.92414i	0.569558	−	0.185061i
$709$	−1.24909	−	0.907519i	−0.0469107	−	0.0340826i	0.564083	−	0.825718i	$-0.309230\pi$
$709$	−1.24909	−	0.907519i	−0.0469107	−	0.0340826i	−0.610993	+	0.791636i	$0.709230\pi$
$710$	−12.5139	−	13.8920i	−0.469639	−	0.521356i
$711$	19.8901	−	14.4510i	0.745936	−	0.541954i
$712$	−33.7780	+	46.4914i	−1.26588	+	1.74234i
$713$	−31.1068	+	42.8149i	−1.16496	+	1.60343i
$714$	12.4336	−	9.03350i	0.465314	−	0.338070i
$715$	31.8529	−	14.1902i	1.19123	−	0.530683i
$716$	−35.8133	−	26.0199i	−1.33841	−	0.972410i
$717$	1.91739	−	0.622999i	0.0716064	−	0.0232663i
$718$			19.8994i			0.742639i
$719$	3.14888	+	9.69127i	0.117434	+	0.361423i	0.992447	−	0.122676i	$-0.0391475\pi$
$719$	3.14888	+	9.69127i	0.117434	+	0.361423i	−0.875013	+	0.484099i	$0.839147\pi$
$720$	−34.5418	+	31.1153i	−1.28730	+	1.15960i
$721$	−11.3018	+	34.7833i	−0.420900	+	1.29540i
$722$	2.42415	+	0.787656i	0.0902177	+	0.0293135i
$723$	−1.14950	−	1.58215i	−0.0427503	−	0.0588407i
$724$	29.2300			1.08632
$725$	−9.33875	−	16.1588i	−0.346832	−	0.600122i
$726$	0.681735			0.0253016
$727$	1.64509	+	2.26428i	0.0610131	+	0.0839773i	0.838433	−	0.545004i	$-0.183472\pi$
$727$	1.64509	+	2.26428i	0.0610131	+	0.0839773i	−0.777420	+	0.628982i	$0.783472\pi$
$728$	86.2986	+	28.0401i	3.19844	+	1.03924i
$729$	6.34867	−	19.5392i	0.235136	−	0.723674i
$730$	−62.9259	+	6.62776i	−2.32899	+	0.245304i
$731$	−2.61090	−	8.03552i	−0.0965676	−	0.297205i
$732$			4.13454i			0.152817i
$733$	−42.7659	+	13.8955i	−1.57959	+	0.513241i	−0.961952	−	0.273218i	$-0.911912\pi$
$733$	−42.7659	+	13.8955i	−1.57959	+	0.513241i	−0.617642	+	0.786459i	$0.711912\pi$
$734$	−8.72132	−	6.33641i	−0.321910	−	0.233881i
$735$	0.233167	+	2.21375i	0.00860048	+	0.0816555i
$736$	−22.7512	+	16.5297i	−0.838622	+	0.609294i
$737$	14.7337	−	20.2792i	0.542724	−	0.746996i
$738$	47.1073	−	64.8376i	1.73404	−	2.38671i
$739$	−9.35084	+	6.79378i	−0.343976	+	0.249913i	−0.746338	−	0.665568i	$-0.768190\pi$
$739$	−9.35084	+	6.79378i	−0.343976	+	0.249913i	0.402361	+	0.915481i	$0.368190\pi$
$740$	49.5764	−	85.9125i	1.82247	−	3.15820i
$741$	1.29425	+	0.940327i	0.0475454	+	0.0345438i
$742$	−37.4521	+	12.1689i	−1.37491	+	0.446735i
$743$			34.3349i			1.25962i	0.776748	+	0.629812i	$0.216868\pi$
$743$			34.3349i			1.25962i	−0.776748	+	0.629812i	$0.783132\pi$
$744$	−7.41628	−	22.8250i	−0.271894	−	0.836804i
$745$	−13.9443	−	31.3009i	−0.510879	−	1.14677i
$746$	−6.35227	+	19.5503i	−0.232573	+	0.715786i
$747$	−46.4483	−	15.0920i	−1.69946	−	0.552187i
$748$	−49.5521	−	68.2026i	−1.81180	−	2.49374i
$749$	−2.67385			−0.0977003
$750$	−0.00660845	−	10.0254i	−0.000241307	−	0.366076i
$751$	20.1801			0.736383			0.368192	−	0.929750i	$-0.379977\pi$
$751$	20.1801			0.736383			0.368192	+	0.929750i	$0.379977\pi$
$752$	−24.6000	−	33.8590i	−0.897071	−	1.23471i
$753$	−8.08802	−	2.62796i	−0.294744	−	0.0957680i
$754$	−13.3697	+	41.1477i	−0.486896	+	1.49851i
$755$	6.68909	+	15.0151i	0.243441	+	0.546454i
$756$	9.00662	+	27.7195i	0.327568	+	1.00815i
$757$		−	5.91886i		−	0.215125i	−0.994198	−	0.107562i	$-0.965695\pi$
$757$		−	5.91886i		−	0.215125i	0.994198	−	0.107562i	$-0.0343045\pi$
$758$	−17.6939	+	5.74909i	−0.642671	+	0.208816i
$759$	4.81888	+	3.50112i	0.174914	+	0.127083i
$760$	−7.11294	+	12.3262i	−0.258014	+	0.447119i
$761$	−39.4085	+	28.6319i	−1.42856	+	1.03791i	−0.438274	+	0.898842i	$0.644410\pi$
$761$	−39.4085	+	28.6319i	−1.42856	+	1.03791i	−0.990283	+	0.139066i	$0.955590\pi$
$762$	4.13076	−	5.68550i	0.149642	−	0.205964i
$763$	−1.87707	+	2.58357i	−0.0679546	+	0.0935315i
$764$	−45.4455	+	33.0181i	−1.64416	+	1.19455i
$765$	−3.68274	−	34.9650i	−0.133150	−	1.26416i
$766$	41.7763	+	30.3523i	1.50944	+	1.09667i
$767$	−43.5625	+	14.1543i	−1.57295	+	0.511082i
$768$			10.1180i			0.365103i
$769$	2.76159	+	8.49931i	0.0995856	+	0.306493i	0.988422	−	0.151732i	$-0.0484852\pi$
$769$	2.76159	+	8.49931i	0.0995856	+	0.306493i	−0.888836	+	0.458225i	$0.848485\pi$
$770$	60.9429	−	6.41889i	2.19623	−	0.231321i
$771$	−2.70948	+	8.33894i	−0.0975797	+	0.300319i
$772$	85.6581	+	27.8320i	3.08290	+	1.00170i
$773$	−24.2359	−	33.3579i	−0.871706	−	1.19980i	−0.978650	−	0.205535i	$-0.934107\pi$
$773$	−24.2359	−	33.3579i	−0.871706	−	1.19980i	0.106944	−	0.994265i	$-0.465893\pi$
$774$	11.3310			0.407284
$775$	−48.9706	−	21.7774i	−1.75908	−	0.782266i
$776$	3.88770			0.139560
$777$	−6.39518	−	8.80221i	−0.229426	−	0.315778i
$778$	−39.0043	−	12.6733i	−1.39837	−	0.454358i
$779$	3.37810	−	10.3967i	0.121033	−	0.372502i
$780$	−11.9522	+	10.7666i	−0.427958	+	0.385506i
$781$	3.47639	+	10.6992i	0.124395	+	0.382848i
$782$		−	68.7954i		−	2.46012i
$783$	−7.33867	+	2.38448i	−0.262263	+	0.0852143i
$784$	16.5482	+	12.0230i	0.591009	+	0.429393i
$785$	−30.4557	+	13.5678i	−1.08701	+	0.484255i
$786$	5.45969	−	3.96670i	0.194741	−	0.141487i
$787$	14.1826	−	19.5207i	0.505557	−	0.695839i	−0.477606	−	0.878574i	$-0.658495\pi$
$787$	14.1826	−	19.5207i	0.505557	−	0.695839i	0.983162	+	0.182735i	$0.0584952\pi$
$788$	9.36605	−	12.8913i	0.333652	−	0.459232i
$789$	−7.14327	+	5.18989i	−0.254307	+	0.184765i
$790$	32.6069	+	36.1976i	1.16010	+	1.28785i
$791$	−17.1626	−	12.4694i	−0.610233	−	0.443360i
$792$	59.7034	−	19.3988i	2.12147	−	0.689307i
$793$		−	11.8846i		−	0.422035i
$794$	−22.9962	−	70.7750i	−0.816104	−	2.51171i
$795$	0.805105	−	3.79182i	0.0285541	−	0.134482i
$796$	6.47886	−	19.9399i	0.229637	−	0.706750i
$797$	−4.82287	−	1.56705i	−0.170835	−	0.0555076i	0.222351	−	0.974967i	$-0.428627\pi$
$797$	−4.82287	−	1.56705i	−0.170835	−	0.0555076i	−0.393186	+	0.919459i	$0.628627\pi$
$798$	1.65248	+	2.27445i	0.0584973	+	0.0805146i
$799$	31.6511			1.11974
$800$	−21.1727	−	19.0472i	−0.748568	−	0.673419i
$801$	25.9705			0.917623
$802$	−7.75161	−	10.6692i	−0.273719	−	0.376742i
$803$	36.2077	+	11.7646i	1.27774	+	0.415164i
$804$	−3.57336	+	10.9977i	−0.126023	+	0.387858i
$805$	29.9797	+	17.3000i	1.05665	+	0.609746i
$806$	38.3932	+	118.162i	1.35234	+	4.16208i
$807$		−	1.84928i		−	0.0650978i
$808$	−1.08574	+	0.352777i	−0.0381960	+	0.0124106i
$809$	36.9129	+	26.8188i	1.29779	+	0.942899i	0.999931	−	0.0117119i	$-0.00372810\pi$
$809$	36.9129	+	26.8188i	1.29779	+	0.942899i	0.297857	+	0.954610i	$0.403728\pi$
$810$	44.0525	+	9.35354i	1.54785	+	0.328650i
$811$	11.5979	−	8.42639i	0.407258	−	0.295890i	−0.365233	−	0.930916i	$-0.619011\pi$
$811$	11.5979	−	8.42639i	0.407258	−	0.295890i	0.772491	+	0.635026i	$0.219011\pi$
$812$	−30.9331	+	42.5758i	−1.08554	+	1.49412i
$813$	4.74675	−	6.53334i	0.166476	−	0.229134i
$814$	−69.7574	+	50.6817i	−2.44499	+	1.77639i
$815$	−8.52238	−	1.80953i	−0.298526	−	0.0633851i
$816$	11.2465	+	8.17107i	0.393707	+	0.286045i
$817$	1.46992	−	0.477607i	0.0514261	−	0.0167094i
$818$		−	38.8652i		−	1.35889i
$819$	−12.6720	−	39.0004i	−0.442796	−	1.36278i
$820$	95.2088	+	54.9409i	3.32483	+	1.91862i
$821$	4.10139	−	12.6228i	0.143140	−	0.440538i	−0.853627	−	0.520884i	$-0.825602\pi$
$821$	4.10139	−	12.6228i	0.143140	−	0.440538i	0.996767	+	0.0803457i	$0.0256024\pi$
$822$	−4.44915	−	1.44562i	−0.155182	−	0.0504217i
$823$	16.9710	+	23.3586i	0.591573	+	0.814231i	0.994904	−	0.100823i	$-0.0321477\pi$
$823$	16.9710	+	23.3586i	0.591573	+	0.814231i	−0.403331	+	0.915054i	$0.632148\pi$
$824$	−74.2426			−2.58636
$825$	−2.45107	+	5.51172i	−0.0853354	+	0.191893i
$826$	−80.4941			−2.80075
$827$	14.3652	+	19.7720i	0.499526	+	0.687539i	0.982109	−	0.188311i	$-0.0603014\pi$
$827$	14.3652	+	19.7720i	0.499526	+	0.687539i	−0.482583	+	0.875850i	$0.660301\pi$
$828$	60.7342	+	19.7337i	2.11066	+	0.685794i
$829$	4.72666	−	14.5472i	0.164164	−	0.505243i	−0.834810	−	0.550538i	$-0.814423\pi$
$829$	4.72666	−	14.5472i	0.164164	−	0.505243i	0.998974	+	0.0452945i	$0.0144226\pi$
$830$	20.1005	−	94.6679i	0.697700	−	3.28597i
$831$	−2.51505	−	7.74052i	−0.0872460	−	0.268516i
$832$			0.278757i			0.00966418i
$833$	−14.7120	+	4.78022i	−0.509741	+	0.165625i
$834$	−2.42252	−	1.76007i	−0.0838852	−	0.0609461i
$835$	−13.2061	−	14.6603i	−0.457014	−	0.507342i
$836$	12.4762	−	9.06448i	0.431498	−	0.313502i
$837$	−13.0245	+	17.9267i	−0.450194	+	0.619638i
$838$	5.52826	−	7.60900i	0.190971	−	0.262848i
$839$	−17.3926	+	12.6365i	−0.600460	+	0.436260i	−0.846042	−	0.533116i	$-0.821021\pi$
$839$	−17.3926	+	12.6365i	−0.600460	+	0.436260i	0.245582	+	0.969376i	$0.421021\pi$
$840$	−14.3383	+	6.38758i	−0.494717	+	0.220393i
$841$	12.1897	+	8.85631i	0.420333	+	0.305390i
$842$	49.8530	−	16.1982i	1.71805	−	0.558228i
$843$		−	2.72362i		−	0.0938063i
$844$	−2.13877	−	6.58246i	−0.0736195	−	0.226578i
$845$	12.7582	−	11.4926i	0.438895	−	0.395358i
$846$	−13.1169	+	40.3696i	−0.450968	+	1.38794i
$847$	−2.26697	−	0.736583i	−0.0778940	−	0.0253093i
$848$	−20.9368	−	28.8171i	−0.718974	−	0.989582i
$849$	−5.53149			−0.189840
$850$	68.1407	−	14.5151i	2.33721	−	0.497863i
$851$	−48.7030			−1.66952
$852$	−3.05046	−	4.19859i	−0.104507	−	0.143841i
$853$	32.8233	+	10.6649i	1.12385	+	0.365161i	0.811235	−	0.584720i	$-0.198796\pi$
$853$	32.8233	+	10.6649i	1.12385	+	0.365161i	0.312614	+	0.949880i	$0.398796\pi$
$854$	6.45395	−	19.8632i	0.220850	−	0.679705i
$855$	6.39608	−	0.673676i	0.218741	−	0.0230392i
$856$	−1.67729	−	5.16216i	−0.0573285	−	0.176439i
$857$		−	55.4898i		−	1.89550i	−0.319021	−	0.947748i	$-0.603354\pi$
$857$		−	55.4898i		−	1.89550i	0.319021	−	0.947748i	$-0.396646\pi$
$858$	13.2993	−	4.32121i	0.454031	−	0.147524i
$859$	12.8596	+	9.34307i	0.438765	+	0.318781i	0.785144	−	0.619313i	$-0.212589\pi$
$859$	12.8596	+	9.34307i	0.438765	+	0.318781i	−0.346379	+	0.938095i	$0.612589\pi$
$860$	1.62791	+	15.4559i	0.0555113	+	0.527041i
$861$	9.75467	−	7.08718i	0.332438	−	0.241531i
$862$	59.4098	−	81.7706i	2.02351	−	2.78512i
$863$	30.8036	−	42.3975i	1.04857	−	1.44323i	0.158522	−	0.987355i	$-0.449327\pi$
$863$	30.8036	−	42.3975i	1.04857	−	1.44323i	0.890045	−	0.455873i	$-0.150673\pi$
$864$	−9.52602	+	6.92106i	−0.324082	+	0.235459i
$865$	12.1108	−	20.9871i	0.411778	−	0.713583i
$866$	11.3293	+	8.23118i	0.384984	+	0.279707i
$867$	−4.31072	+	1.40064i	−0.146400	+	0.0475681i
$868$			151.125i			5.12953i
$869$	−9.05826	−	27.8785i	−0.307281	−	0.945712i
$870$	−3.04564	−	6.83657i	−0.103257	−	0.231781i
$871$	10.2715	−	31.6125i	0.348037	−	1.07115i
$872$	−6.16534	−	2.00324i	−0.208785	−	0.0678383i
$873$	−1.03271	−	1.42140i	−0.0349518	−	0.0481070i
$874$	12.5846			0.425681
$875$	−10.8100	+	33.3446i	−0.365445	+	1.12725i
$876$	−17.5629			−0.593394
$877$	−0.817343	−	1.12498i	−0.0275997	−	0.0379877i	0.794994	−	0.606617i	$-0.207474\pi$
$877$	−0.817343	−	1.12498i	−0.0275997	−	0.0379877i	−0.822594	+	0.568629i	$0.807474\pi$
$878$	46.7107	+	15.1772i	1.57641	+	0.512207i
$879$	3.50869	−	10.7986i	0.118345	−	0.364229i
$880$	22.5563	+	50.6324i	0.760374	+	1.70682i
$881$	9.24405	+	28.4502i	0.311440	+	0.958513i	0.977195	+	0.212343i	$0.0681094\pi$
$881$	9.24405	+	28.4502i	0.311440	+	0.958513i	−0.665755	+	0.746170i	$0.731891\pi$
$882$		−	20.7456i		−	0.698540i
$883$	21.9760	−	7.14042i	0.739550	−	0.240294i	0.0850713	−	0.996375i	$-0.472888\pi$
$883$	21.9760	−	7.14042i	0.739550	−	0.240294i	0.654479	+	0.756081i	$0.272888\pi$
$884$	−90.4398	−	65.7083i	−3.04182	−	2.21001i
$885$	3.96025	−	6.86283i	0.133122	−	0.230692i
$886$	30.7215	−	22.3205i	1.03211	−	0.749870i
$887$	1.98307	−	2.72946i	0.0665849	−	0.0916463i	−0.774426	−	0.632665i	$-0.781961\pi$
$887$	1.98307	−	2.72946i	0.0665849	−	0.0916463i	0.841011	+	0.541019i	$0.181961\pi$
$888$	12.9820	−	17.8682i	0.435647	−	0.599617i
$889$	−19.8789	+	14.4429i	−0.666717	+	0.484398i
$890$	5.39059	+	51.1798i	0.180693	+	1.71555i
$891$	−21.9217	−	15.9270i	−0.734404	−	0.533575i
$892$	−27.8688	+	9.05512i	−0.933117	+	0.303188i
$893$			5.78988i			0.193751i
$894$	−4.24632	−	13.0688i	−0.142018	−	0.437088i
$895$	−21.8908	+	2.30567i	−0.731727	+	0.0770702i
$896$	10.8855	−	33.5020i	0.363658	−	1.11922i
$897$	7.51195	+	2.44078i	0.250817	+	0.0814953i
$898$	−17.5341	−	24.1336i	−0.585121	−	0.805349i
$899$	−40.0100			−1.33441
$900$	−6.73171	+	64.3198i	−0.224390	+	2.14399i
$901$	26.9379			0.897432
$902$	−56.1658	−	77.3056i	−1.87012	−	2.57399i
$903$	1.62129	+	0.526788i	0.0539530	+	0.0175304i
$904$	13.3075	−	40.9563i	0.442601	−	1.36219i
$905$	10.7990	−	9.72780i	0.358972	−	0.323363i
$906$	2.03697	+	6.26914i	0.0676737	+	0.208278i
$907$		−	22.1836i		−	0.736595i	−0.929708	−	0.368297i	$-0.879941\pi$
$907$		−	22.1836i		−	0.736595i	0.929708	−	0.368297i	$-0.120059\pi$
$908$	15.2176	−	4.94449i	0.505013	−	0.164089i
$909$	0.417389	+	0.303251i	0.0138439	+	0.0100582i
$910$	74.2275	−	33.0677i	2.46062	−	1.09618i
$911$	21.7940	−	15.8342i	0.722066	−	0.524612i	−0.164977	−	0.986297i	$-0.552755\pi$
$911$	21.7940	−	15.8342i	0.722066	−	0.524612i	0.887044	+	0.461685i	$0.152755\pi$
$912$	−1.49472	+	2.05730i	−0.0494951	+	0.0681242i
$913$	−34.2268	+	47.1092i	−1.13274	+	1.55909i
$914$	15.1867	−	11.0338i	0.502330	−	0.364964i
$915$	1.37598	+	1.52751i	0.0454886	+	0.0504979i
$916$	52.4557	+	38.1113i	1.73319	+	1.25923i
$917$	−22.4409	+	7.29149i	−0.741064	+	0.240786i
$918$		−	28.8049i		−	0.950702i
$919$	−17.6344	−	54.2732i	−0.581706	−	1.79031i	−0.612115	−	0.790769i	$-0.709681\pi$
$919$	−17.6344	−	54.2732i	−0.581706	−	1.79031i	0.0304087	−	0.999538i	$-0.490319\pi$
$920$	−14.5935	+	68.7314i	−0.481135	+	2.26601i
$921$	0.108623	−	0.334306i	0.00357924	−	0.0110158i
$922$	−65.5053	−	21.2840i	−2.15730	−	0.700950i
$923$	8.76845	+	12.0687i	0.288617	+	0.397247i
$924$	17.0094			0.559568
$925$	−10.2758	−	48.2396i	−0.337866	−	1.58611i
$926$	−50.1245			−1.64719
$927$	19.7214	+	27.1441i	0.647735	+	0.891531i
$928$	−20.2202	−	6.56995i	−0.663761	−	0.215669i
$929$	4.53102	−	13.9450i	0.148658	−	0.457522i	−0.848805	−	0.528706i	$-0.822678\pi$
$929$	4.53102	−	13.9450i	0.148658	−	0.457522i	0.997463	+	0.0711835i	$0.0226776\pi$
$930$	−18.6152	−	10.7421i	−0.610418	−	0.352246i
$931$	−0.874438	−	2.69124i	−0.0286585	−	0.0882019i
$932$		−	14.2926i		−	0.468169i
$933$	−2.53872	+	0.824879i	−0.0831139	+	0.0270053i
$934$	−15.4401	−	11.2179i	−0.505216	−	0.367061i
$935$	−41.0051	−	8.70648i	−1.34101	−	0.284732i
$936$	67.3456	−	48.9294i	2.20126	−	1.59931i
$937$	−25.0710	+	34.5073i	−0.819034	+	1.12730i	0.170833	+	0.985300i	$0.445354\pi$
$937$	−25.0710	+	34.5073i	−0.819034	+	1.12730i	−0.989866	+	0.142003i	$0.954646\pi$
$938$	34.3344	−	47.2572i	1.12106	−	1.54300i
$939$	−4.80387	+	3.49022i	−0.156768	+	0.113899i
$940$	−56.9502	−	12.0921i	−1.85751	−	0.394399i
$941$	29.3147	+	21.2984i	0.955631	+	0.694307i	0.952132	−	0.305687i	$-0.0988862\pi$
$941$	29.3147	+	21.2984i	0.955631	+	0.694307i	0.00349908	+	0.999994i	$0.498886\pi$
$942$	−12.7160	+	4.13167i	−0.414309	+	0.134617i
$943$		−	53.9730i		−	1.75760i
$944$	−22.4993	−	69.2457i	−0.732290	−	2.25376i
$945$	12.5526	+	7.24358i	0.408337	+	0.235634i
$946$	4.17478	−	12.8487i	0.135734	−	0.417746i
$947$	−2.06965	−	0.672470i	−0.0672545	−	0.0218523i	0.275197	−	0.961388i	$-0.411257\pi$
$947$	−2.06965	−	0.672470i	−0.0672545	−	0.0218523i	−0.342451	+	0.939536i	$0.611257\pi$
$948$	7.94844	+	10.9401i	0.258153	+	0.355317i
$949$	50.4839			1.63878
$950$	2.65522	+	12.4649i	0.0861466	+	0.404414i
$951$	−2.16403			−0.0701734
$952$	−64.1163	−	88.2485i	−2.07802	−	2.86015i
$953$	−36.5568	−	11.8780i	−1.18419	−	0.384767i	−0.350268	−	0.936649i	$-0.613910\pi$
$953$	−36.5568	−	11.8780i	−1.18419	−	0.384767i	−0.833922	+	0.551883i	$0.813910\pi$
$954$	−11.1636	+	34.3581i	−0.361436	+	1.11239i
$955$	−5.80139	+	27.3229i	−0.187729	+	0.884149i
$956$	−7.96360	−	24.5095i	−0.257561	−	0.792692i
$957$			4.50319i			0.145567i
$958$	−85.7313	+	27.8558i	−2.76985	+	0.899980i
$959$	13.2328	+	9.61420i	0.427310	+	0.310459i
$960$	−0.0322741	−	0.0358282i	−0.00104164	−	0.00115635i
$961$	−67.8725	+	49.3123i	−2.18944	+	1.59072i
$962$	−67.2062	+	92.5014i	−2.16681	+	2.98236i
$963$	−1.44181	+	1.98449i	−0.0464618	+	0.0639492i
$964$	−20.2241	+	14.6937i	−0.651374	+	0.473251i
$965$	40.9090	−	18.2246i	1.31691	−	0.586672i
$966$	11.2295	+	8.15874i	0.361305	+	0.262503i
$967$	31.6672	−	10.2893i	1.01835	−	0.330881i	0.248175	−	0.968715i	$-0.420169\pi$
$967$	31.6672	−	10.2893i	1.01835	−	0.330881i	0.770174	+	0.637834i	$0.220169\pi$
$968$		−	4.83869i		−	0.155521i
$969$	−0.594285	−	1.82902i	−0.0190912	−	0.0587566i
$970$	2.58678	−	2.33018i	0.0830565	−	0.0748175i
$971$	12.5715	−	38.6911i	0.403439	−	1.24166i	−0.518753	−	0.854924i	$-0.673603\pi$
$971$	12.5715	−	38.6911i	0.403439	−	1.24166i	0.922192	−	0.386733i	$-0.126397\pi$
$972$	38.4122	+	12.4809i	1.23207	+	0.400324i
$973$	6.15393	+	8.47016i	0.197286	+	0.271541i
$974$	−20.2965			−0.650342
$975$	−0.832617	+	7.95545i	−0.0266651	+	0.254778i
$976$	18.8915			0.604701
$977$	5.08742	+	7.00223i	0.162761	+	0.224021i	0.882606	−	0.470114i	$-0.155787\pi$
$977$	5.08742	+	7.00223i	0.162761	+	0.224021i	−0.719845	+	0.694135i	$0.755787\pi$
$978$	−3.32281	−	1.07965i	−0.106252	−	0.0345232i
$979$	9.56856	−	29.4490i	0.305813	−	0.941194i
$980$	28.2977	−	2.98050i	0.903938	−	0.0952085i
$981$	0.905312	+	2.78627i	0.0289044	+	0.0889586i
$982$		−	16.8873i		−	0.538895i
$983$	−25.7957	+	8.38152i	−0.822754	+	0.267329i	−0.689990	−	0.723819i	$-0.742385\pi$
$983$	−25.7957	+	8.38152i	−0.822754	+	0.267329i	−0.132764	+	0.991148i	$0.542385\pi$
$984$	19.8016	+	14.3867i	0.631253	+	0.458632i
$985$	−0.829944	−	7.87973i	−0.0264442	−	0.251069i
$986$	42.0774	−	30.5710i	1.34002	−	0.973580i
$987$	−3.75364	+	5.16644i	−0.119480	+	0.164450i
$988$	12.0199	−	16.5440i	0.382404	−	0.526335i
$989$	6.17352	−	4.48532i	0.196306	−	0.142625i
$990$	28.0981	−	48.6921i	0.893017	−	1.54754i
$991$	7.19726	+	5.22912i	0.228629	+	0.166108i	0.696202	−	0.717846i	$-0.254872\pi$
$991$	7.19726	+	5.22912i	0.228629	+	0.166108i	−0.467574	+	0.883954i	$0.654872\pi$
$992$	−58.0655	+	18.8666i	−1.84358	+	0.599016i
$993$		−	8.32692i		−	0.264247i
$994$	8.10111	+	24.9327i	0.256952	+	0.790816i
$995$	−4.24241	−	9.52298i	−0.134493	−	0.301899i
$996$	8.30100	−	25.5479i	0.263027	−	0.809515i
$997$	−3.86060	−	1.25439i	−0.122267	−	0.0397268i	0.247245	−	0.968953i	$-0.420475\pi$
$997$	−3.86060	−	1.25439i	−0.122267	−	0.0397268i	−0.369511	+	0.929226i	$0.620475\pi$
$998$	24.6728	+	33.9593i	0.781005	+	1.07496i
$999$	−20.3921			−0.645178

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.n.b.39.2	✓	96
25.9	even	10	inner	475.2.n.b.134.2	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.n.b.39.2	✓	96	1.1	even	1	trivial
475.2.n.b.134.2	yes	96	25.9	even	10	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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.49821 - 2.06211i) q^{2} +(-0.334580 - 0.108712i) q^{3} +(-1.38963 + 4.27683i) q^{4} +(0.909940 + 2.04255i) q^{5} +(0.277096 + 0.852813i) q^{6} -3.13524i q^{7} +(6.05293 - 1.96672i) q^{8} +(-2.32693 - 1.69061i) q^{9} +O(q^{10})\)	\(q+(-1.49821 - 2.06211i) q^{2} +(-0.334580 - 0.108712i) q^{3} +(-1.38963 + 4.27683i) q^{4} +(0.909940 + 2.04255i) q^{5} +(0.277096 + 0.852813i) q^{6} -3.13524i q^{7} +(6.05293 - 1.96672i) q^{8} +(-2.32693 - 1.69061i) q^{9} +(2.84868 - 4.93656i) q^{10} +(-2.77438 + 2.01571i) q^{11} +(0.929882 - 1.27987i) q^{12} +(-2.67292 + 3.67896i) q^{13} +(-6.46521 + 4.69725i) q^{14} +(-0.0823986 - 0.782317i) q^{15} +(-5.84797 - 4.24880i) q^{16} +(5.19907 - 1.68928i) q^{17} +7.33126i q^{18} +(0.309017 + 0.951057i) q^{19} +(-10.0001 + 1.05328i) q^{20} +(-0.340837 + 1.04899i) q^{21} +(8.31321 + 2.70113i) q^{22} +(2.90205 + 3.99433i) q^{23} -2.23899 q^{24} +(-3.34402 + 3.71719i) q^{25} +11.5910 q^{26} +(1.21510 + 1.67244i) q^{27} +(13.4089 + 4.35681i) q^{28} +(-1.15345 + 3.54997i) q^{29} +(-1.48977 + 1.34199i) q^{30} +(3.31233 + 10.1943i) q^{31} +5.69588i q^{32} +(1.14738 - 0.372807i) q^{33} +(-11.2728 - 8.19015i) q^{34} +(6.40389 - 2.85288i) q^{35} +(10.4640 - 7.60255i) q^{36} +(-5.79814 + 7.98045i) q^{37} +(1.49821 - 2.06211i) q^{38} +(1.29425 - 0.940327i) q^{39} +(9.52492 + 10.5738i) q^{40} +(-8.84399 - 6.42553i) q^{41} +(2.67377 - 0.868762i) q^{42} -1.54557i q^{43} +(-4.76548 - 14.6666i) q^{44} +(1.33579 - 6.29121i) q^{45} +(3.88886 - 11.9687i) q^{46} +(5.50650 + 1.78917i) q^{47} +(1.49472 + 2.05730i) q^{48} -2.82974 q^{49} +(12.6753 + 1.32660i) q^{50} -1.92315 q^{51} +(-12.0199 - 16.5440i) q^{52} +(4.68652 + 1.52274i) q^{53} +(1.62828 - 5.01133i) q^{54} +(-6.64170 - 3.83264i) q^{55} +(-6.16613 - 18.9774i) q^{56} -0.351798i q^{57} +(9.04854 - 2.94005i) q^{58} +(8.14886 + 5.92049i) q^{59} +(3.46034 + 0.734723i) q^{60} +(-2.11434 + 1.53616i) q^{61} +(16.0592 - 22.1036i) q^{62} +(-5.30047 + 7.29547i) q^{63} +(0.0495926 - 0.0360312i) q^{64} +(-9.94665 - 2.11194i) q^{65} +(-2.48779 - 1.80748i) q^{66} +(-6.95171 + 2.25875i) q^{67} +24.5830i q^{68} +(-0.536738 - 1.65191i) q^{69} +(-15.4773 - 8.93130i) q^{70} +(1.01372 - 3.11992i) q^{71} +(-17.4097 - 5.65675i) q^{72} +(-6.52537 - 8.98140i) q^{73} +25.1434 q^{74} +(1.52294 - 0.880164i) q^{75} -4.49693 q^{76} +(6.31973 + 8.69836i) q^{77} +(-3.87811 - 1.26008i) q^{78} +(-2.64141 + 8.12943i) q^{79} +(3.35708 - 15.8109i) q^{80} +(2.44169 + 7.51474i) q^{81} +27.8641i q^{82} +(16.1490 - 5.24713i) q^{83} +(-4.01271 - 2.91540i) q^{84} +(8.18128 + 9.08221i) q^{85} +(-3.18713 + 2.31559i) q^{86} +(0.771845 - 1.06235i) q^{87} +(-12.8288 + 17.6574i) q^{88} +(-7.30488 + 5.30731i) q^{89} +(-14.9745 + 6.67101i) q^{90} +(11.5344 + 8.38024i) q^{91} +(-21.1158 + 6.86095i) q^{92} -3.77089i q^{93} +(-4.56043 - 14.0356i) q^{94} +(-1.66139 + 1.49659i) q^{95} +(0.619209 - 1.90573i) q^{96} +(0.580951 + 0.188762i) q^{97} +(4.23954 + 5.83523i) q^{98} +9.86356 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9}+O(q^{10}) \) 96 * q + 26 * q^4 - 4 * q^5 - 2 * q^6 + 28 * q^9	\( 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9} + 28 q^{10} - 15 q^{11} - 85 q^{12} + 10 q^{14} - 10 q^{15} - 42 q^{16} + 20 q^{17} - 24 q^{19} - 16 q^{21} - 35 q^{23} - 24 q^{24} - 8 q^{25} + 28 q^{26} + 15 q^{27} + 30 q^{28} + 28 q^{29} - 64 q^{30} - 8 q^{31} + 25 q^{33} - 8 q^{34} + 33 q^{35} - 42 q^{36} - 55 q^{37} - 6 q^{39} - 48 q^{40} - 27 q^{41} + 210 q^{42} - 4 q^{44} + 15 q^{45} + 10 q^{46} - 115 q^{48} - 150 q^{49} + 9 q^{50} + 60 q^{51} - 5 q^{52} + 40 q^{53} + 47 q^{54} + 33 q^{55} - 12 q^{56} + 60 q^{58} + 25 q^{59} + 170 q^{60} + 26 q^{61} - 110 q^{62} - 30 q^{63} + 62 q^{64} - 15 q^{65} - 41 q^{66} + 35 q^{67} + 14 q^{69} - 20 q^{70} - 38 q^{71} - 60 q^{73} + 6 q^{74} - 151 q^{75} - 104 q^{76} + 115 q^{78} + 8 q^{79} - 63 q^{80} - 67 q^{81} + 160 q^{83} + 18 q^{84} - 8 q^{85} - 10 q^{87} - 120 q^{88} + 76 q^{89} + 108 q^{90} - 8 q^{91} + 85 q^{92} + 58 q^{94} + q^{95} - 6 q^{96} - 10 q^{97} + 10 q^{98} - 112 q^{99}+O(q^{100}) \) 96 * q + 26 * q^4 - 4 * q^5 - 2 * q^6 + 28 * q^9 + 28 * q^10 - 15 * q^11 - 85 * q^12 + 10 * q^14 - 10 * q^15 - 42 * q^16 + 20 * q^17 - 24 * q^19 - 16 * q^21 - 35 * q^23 - 24 * q^24 - 8 * q^25 + 28 * q^26 + 15 * q^27 + 30 * q^28 + 28 * q^29 - 64 * q^30 - 8 * q^31 + 25 * q^33 - 8 * q^34 + 33 * q^35 - 42 * q^36 - 55 * q^37 - 6 * q^39 - 48 * q^40 - 27 * q^41 + 210 * q^42 - 4 * q^44 + 15 * q^45 + 10 * q^46 - 115 * q^48 - 150 * q^49 + 9 * q^50 + 60 * q^51 - 5 * q^52 + 40 * q^53 + 47 * q^54 + 33 * q^55 - 12 * q^56 + 60 * q^58 + 25 * q^59 + 170 * q^60 + 26 * q^61 - 110 * q^62 - 30 * q^63 + 62 * q^64 - 15 * q^65 - 41 * q^66 + 35 * q^67 + 14 * q^69 - 20 * q^70 - 38 * q^71 - 60 * q^73 + 6 * q^74 - 151 * q^75 - 104 * q^76 + 115 * q^78 + 8 * q^79 - 63 * q^80 - 67 * q^81 + 160 * q^83 + 18 * q^84 - 8 * q^85 - 10 * q^87 - 120 * q^88 + 76 * q^89 + 108 * q^90 - 8 * q^91 + 85 * q^92 + 58 * q^94 + q^95 - 6 * q^96 - 10 * q^97 + 10 * q^98 - 112 * q^99

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