LMFDB - Embedded newform 475.2.l.c.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(101,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("475.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.l (of order $9$, degree $6$, 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:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 15 x^{16} - 14 x^{15} + 72 x^{14} - 51 x^{13} + 231 x^{12} - 93 x^{11} + 438 x^{10} + \cdots + 1 $ x^18 - 3x^17 + 15x^16 - 14x^15 + 72x^14 - 51x^13 + 231x^12 - 93x^11 + 438x^10 - 156x^9 + 582x^8 - 138x^7 + 437x^6 - 132x^5 + 198x^4 - 16x^3 + 15x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			101.1
Root			$-0.644984 + 1.11715i$ of defining polynomial
Character	$\chi$	$=$	475.101
Dual form			475.2.l.c.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.75422 + 1.47196i) q^{2} +(3.10785 + 1.13116i) q^{3} +(0.563307 - 3.19467i) q^{4} +(-7.11687 + 2.59033i) q^{6} +(-1.46955 + 2.54534i) q^{7} +(1.42431 + 2.46697i) q^{8} +(6.08105 + 5.10261i) q^{9} +O(q^{10})$	\(q+(-1.75422 + 1.47196i) q^{2} +(3.10785 + 1.13116i) q^{3} +(0.563307 - 3.19467i) q^{4} +(-7.11687 + 2.59033i) q^{6} +(-1.46955 + 2.54534i) q^{7} +(1.42431 + 2.46697i) q^{8} +(6.08105 + 5.10261i) q^{9} +(0.288800 + 0.500217i) q^{11} +(5.36437 - 9.29136i) q^{12} +(-0.629967 + 0.229289i) q^{13} +(-1.16873 - 6.62820i) q^{14} +(-0.0331972 - 0.0120828i) q^{16} +(0.269572 - 0.226198i) q^{17} -18.1783 q^{18} +(-3.86230 + 2.02056i) q^{19} +(-7.44633 + 6.24822i) q^{21} +(-1.24292 - 0.452386i) q^{22} +(0.715571 - 4.05820i) q^{23} +(1.63598 + 9.27810i) q^{24} +(0.767594 - 1.32951i) q^{26} +(8.16613 + 14.1442i) q^{27} +(7.30371 + 6.12854i) q^{28} +(2.30426 + 1.93351i) q^{29} +(-0.148853 + 0.257821i) q^{31} +(-5.27762 + 1.92090i) q^{32} +(0.331720 + 1.88128i) q^{33} +(-0.139933 + 0.793600i) q^{34} +(19.7266 - 16.5526i) q^{36} +8.30595 q^{37} +(3.80111 - 9.22966i) q^{38} -2.21721 q^{39} +(-2.51099 - 0.913926i) q^{41} +(3.86534 - 21.9215i) q^{42} +(1.14578 + 6.49806i) q^{43} +(1.76071 - 0.640846i) q^{44} +(4.71826 + 8.17226i) q^{46} +(-8.45135 - 7.09153i) q^{47} +(-0.0895041 - 0.0751029i) q^{48} +(-0.819160 - 1.41883i) q^{49} +(1.09366 - 0.398058i) q^{51} +(0.377639 + 2.14170i) q^{52} +(0.713104 - 4.04421i) q^{53} +(-35.1449 - 12.7917i) q^{54} -8.37237 q^{56} +(-14.2890 + 1.91071i) q^{57} -6.88822 q^{58} +(0.467725 - 0.392468i) q^{59} +(0.178325 - 1.01133i) q^{61} +(-0.118383 - 0.671381i) q^{62} +(-21.9243 + 7.97978i) q^{63} +(6.46593 - 11.1993i) q^{64} +(-3.35108 - 2.81189i) q^{66} +(2.55547 + 2.14429i) q^{67} +(-0.570776 - 0.988612i) q^{68} +(6.81438 - 11.8028i) q^{69} +(-2.29645 - 13.0238i) q^{71} +(-3.92671 + 22.2695i) q^{72} +(6.70827 + 2.44161i) q^{73} +(-14.5704 + 12.2261i) q^{74} +(4.27938 + 13.4770i) q^{76} -1.69763 q^{77} +(3.88946 - 3.26364i) q^{78} +(-1.44931 - 0.527504i) q^{79} +(5.24435 + 29.7422i) q^{81} +(5.75009 - 2.09286i) q^{82} +(6.65930 - 11.5342i) q^{83} +(15.7664 + 27.3082i) q^{84} +(-11.5749 - 9.71246i) q^{86} +(4.97418 + 8.61554i) q^{87} +(-0.822680 + 1.42492i) q^{88} +(6.17500 - 2.24752i) q^{89} +(0.342150 - 1.94043i) q^{91} +(-12.5615 - 4.57203i) q^{92} +(-0.754252 + 0.632892i) q^{93} +25.2640 q^{94} -18.5749 q^{96} +(-9.34414 + 7.84066i) q^{97} +(3.52545 + 1.28316i) q^{98} +(-0.796200 + 4.51548i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9	$ 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9} + 18 q^{12} + 3 q^{13} - 12 q^{14} - 3 q^{16} - 24 q^{17} - 48 q^{18} - 21 q^{21} - 9 q^{22} + 9 q^{23} - 15 q^{24} + 3 q^{26} + 24 q^{27} + 12 q^{28} + 15 q^{29} - 18 q^{31} - 15 q^{32} + 33 q^{33} - 12 q^{34} + 75 q^{36} - 36 q^{37} + 33 q^{38} + 36 q^{39} - 30 q^{41} + 9 q^{42} + 36 q^{43} + 42 q^{44} + 9 q^{46} - 21 q^{47} - 33 q^{48} + 9 q^{49} - 45 q^{51} + 39 q^{52} + 12 q^{53} - 66 q^{54} - 72 q^{57} - 12 q^{58} + 18 q^{59} - 30 q^{61} + 24 q^{62} - 54 q^{63} + 36 q^{64} + 39 q^{66} - 51 q^{68} + 15 q^{69} - 12 q^{71} + 66 q^{72} - 24 q^{73} - 15 q^{74} - 33 q^{76} + 60 q^{77} + 48 q^{78} - 51 q^{79} + 27 q^{81} + 15 q^{82} + 48 q^{84} + 63 q^{86} + 15 q^{87} + 27 q^{88} - 54 q^{89} + 30 q^{91} + 42 q^{92} - 72 q^{93} + 30 q^{94} - 66 q^{96} - 27 q^{97} + 3 q^{98} - 93 q^{99}+O(q^{100}) $ 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9 + 18 * q^12 + 3 * q^13 - 12 * q^14 - 3 * q^16 - 24 * q^17 - 48 * q^18 - 21 * q^21 - 9 * q^22 + 9 * q^23 - 15 * q^24 + 3 * q^26 + 24 * q^27 + 12 * q^28 + 15 * q^29 - 18 * q^31 - 15 * q^32 + 33 * q^33 - 12 * q^34 + 75 * q^36 - 36 * q^37 + 33 * q^38 + 36 * q^39 - 30 * q^41 + 9 * q^42 + 36 * q^43 + 42 * q^44 + 9 * q^46 - 21 * q^47 - 33 * q^48 + 9 * q^49 - 45 * q^51 + 39 * q^52 + 12 * q^53 - 66 * q^54 - 72 * q^57 - 12 * q^58 + 18 * q^59 - 30 * q^61 + 24 * q^62 - 54 * q^63 + 36 * q^64 + 39 * q^66 - 51 * q^68 + 15 * q^69 - 12 * q^71 + 66 * q^72 - 24 * q^73 - 15 * q^74 - 33 * q^76 + 60 * q^77 + 48 * q^78 - 51 * q^79 + 27 * q^81 + 15 * q^82 + 48 * q^84 + 63 * q^86 + 15 * q^87 + 27 * q^88 - 54 * q^89 + 30 * q^91 + 42 * q^92 - 72 * q^93 + 30 * q^94 - 66 * q^96 - 27 * q^97 + 3 * q^98 - 93 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	−1.75422	+	1.47196i	−1.24042	+	1.04084i	−0.242928	+	0.970044i	$0.578108\pi$
$2$	−1.75422	+	1.47196i	−1.24042	+	1.04084i	−0.997491	+	0.0707907i	$0.977448\pi$
$3$	3.10785	+	1.13116i	1.79432	+	0.653078i	0.998894	+	0.0470226i	$0.0149733\pi$
$3$	3.10785	+	1.13116i	1.79432	+	0.653078i	0.795423	+	0.606055i	$0.207249\pi$
$4$	0.563307	−	3.19467i	0.281653	−	1.59734i
$5$		0			0
$5$		0			0
$6$	−7.11687	+	2.59033i	−2.90545	+	1.05750i
$7$	−1.46955	+	2.54534i	−0.555438	+	0.962047i	0.442431	+	0.896802i	$0.354116\pi$
$7$	−1.46955	+	2.54534i	−0.555438	+	0.962047i	−0.997869	+	0.0652445i	$0.979217\pi$
$8$	1.42431	+	2.46697i	0.503569	+	0.872206i
$9$	6.08105	+	5.10261i	2.02702	+	1.70087i
$10$		0			0
$11$	0.288800	+	0.500217i	0.0870766	+	0.150821i	0.906274	−	0.422690i	$-0.138914\pi$
$11$	0.288800	+	0.500217i	0.0870766	+	0.150821i	−0.819198	+	0.573511i	$0.805581\pi$
$12$	5.36437	−	9.29136i	1.54856	−	2.68218i
$13$	−0.629967	+	0.229289i	−0.174721	+	0.0635934i	−0.427900	−	0.903826i	$-0.640746\pi$
$13$	−0.629967	+	0.229289i	−0.174721	+	0.0635934i	0.253178	+	0.967420i	$0.418524\pi$
$14$	−1.16873	−	6.62820i	−0.312356	−	1.77146i
$15$		0			0
$16$	−0.0331972	−	0.0120828i	−0.00829929	−	0.00302070i
$17$	0.269572	−	0.226198i	0.0653808	−	0.0548610i	−0.609512	−	0.792777i	$-0.708634\pi$
$17$	0.269572	−	0.226198i	0.0653808	−	0.0548610i	0.674892	+	0.737916i	$0.264190\pi$
$18$	−18.1783			−4.28467
$19$	−3.86230	+	2.02056i	−0.886071	+	0.463549i
$19$	−3.86230	+	2.02056i	−0.886071	+	0.463549i
$20$		0			0
$21$	−7.44633	+	6.24822i	−1.62492	+	1.36347i
$22$	−1.24292	−	0.452386i	−0.264991	−	0.0964489i
$23$	0.715571	−	4.05820i	0.149207	−	0.846194i	−0.814686	−	0.579903i	$-0.803091\pi$
$23$	0.715571	−	4.05820i	0.149207	−	0.846194i	0.963893	−	0.266291i	$-0.0857983\pi$
$24$	1.63598	+	9.27810i	0.333943	+	1.89388i
$25$		0			0
$26$	0.767594	−	1.32951i	0.150538	−	0.260739i
$27$	8.16613	+	14.1442i	1.57157	+	2.72204i
$28$	7.30371	+	6.12854i	1.38027	+	1.15818i
$29$	2.30426	+	1.93351i	0.427891	+	0.359043i	0.831155	−	0.556041i	$-0.187680\pi$
$29$	2.30426	+	1.93351i	0.427891	+	0.359043i	−0.403264	+	0.915083i	$0.632125\pi$
$30$		0			0
$31$	−0.148853	+	0.257821i	−0.0267348	+	0.0463061i	−0.879083	−	0.476668i	$-0.841844\pi$
$31$	−0.148853	+	0.257821i	−0.0267348	+	0.0463061i	0.852348	+	0.522974i	$0.175178\pi$
$32$	−5.27762	+	1.92090i	−0.932961	+	0.339570i
$33$	0.331720	+	1.88128i	0.0577450	+	0.327488i
$34$	−0.139933	+	0.793600i	−0.0239983	+	0.136101i
$35$		0			0
$36$	19.7266	−	16.5526i	3.28777	−	2.75877i
$37$	8.30595			1.36549			0.682745	−	0.730657i	$-0.260786\pi$
$37$	8.30595			1.36549			0.682745	+	0.730657i	$0.260786\pi$
$38$	3.80111	−	9.22966i	0.616622	−	1.49725i
$39$	−2.21721			−0.355037
$40$		0			0
$41$	−2.51099	−	0.913926i	−0.392151	−	0.142731i	0.138416	−	0.990374i	$-0.455799\pi$
$41$	−2.51099	−	0.913926i	−0.392151	−	0.142731i	−0.530567	+	0.847643i	$0.678021\pi$
$42$	3.86534	−	21.9215i	0.596436	−	3.38255i
$43$	1.14578	+	6.49806i	0.174730	+	0.990945i	0.938455	+	0.345403i	$0.112258\pi$
$43$	1.14578	+	6.49806i	0.174730	+	0.990945i	−0.763724	+	0.645543i	$0.776631\pi$
$44$	1.76071	−	0.640846i	0.265437	−	0.0966112i
$45$		0			0
$46$	4.71826	+	8.17226i	0.695669	+	1.20493i
$47$	−8.45135	−	7.09153i	−1.23276	−	1.03441i	−0.998055	−	0.0623379i	$-0.980144\pi$
$47$	−8.45135	−	7.09153i	−1.23276	−	1.03441i	−0.234701	−	0.972068i	$-0.575411\pi$
$48$	−0.0895041	−	0.0751029i	−0.0129188	−	0.0108402i
$49$	−0.819160	−	1.41883i	−0.117023	−	0.202690i
$50$		0			0
$51$	1.09366	−	0.398058i	0.153142	−	0.0557393i
$52$	0.377639	+	2.14170i	0.0523691	+	0.297000i
$53$	0.713104	−	4.04421i	0.0979523	−	0.555515i	−0.895850	−	0.444356i	$-0.853433\pi$
$53$	0.713104	−	4.04421i	0.0979523	−	0.555515i	0.993803	−	0.111159i	$-0.0354563\pi$
$54$	−35.1449	−	12.7917i	−4.78261	−	1.74073i
$55$		0			0
$56$	−8.37237			−1.11880
$57$	−14.2890	+	1.91071i	−1.89263	+	0.253080i
$58$	−6.88822			−0.904468
$59$	0.467725	−	0.392468i	0.0608926	−	0.0510950i	−0.611833	−	0.790987i	$-0.709568\pi$
$59$	0.467725	−	0.392468i	0.0608926	−	0.0510950i	0.672726	+	0.739892i	$0.265123\pi$
$60$		0			0
$61$	0.178325	−	1.01133i	0.0228322	−	0.129488i	−0.971261	−	0.238016i	$-0.923503\pi$
$61$	0.178325	−	1.01133i	0.0228322	−	0.129488i	0.994093	+	0.108529i	$0.0346139\pi$
$62$	−0.118383	−	0.671381i	−0.0150346	−	0.0852655i
$63$	−21.9243	+	7.97978i	−2.76220	+	1.00536i
$64$	6.46593	−	11.1993i	0.808242	−	1.39992i
$65$		0			0
$66$	−3.35108	−	2.81189i	−0.412489	−	0.346120i
$67$	2.55547	+	2.14429i	0.312200	+	0.261967i	0.785401	−	0.618988i	$-0.212457\pi$
$67$	2.55547	+	2.14429i	0.312200	+	0.261967i	−0.473201	+	0.880955i	$0.656901\pi$
$68$	−0.570776	−	0.988612i	−0.0692167	−	0.119887i
$69$	6.81438	−	11.8028i	0.820355	−	1.42090i
$70$		0			0
$71$	−2.29645	−	13.0238i	−0.272538	−	1.54564i	−0.746675	−	0.665189i	$-0.768351\pi$
$71$	−2.29645	−	13.0238i	−0.272538	−	1.54564i	0.474137	−	0.880451i	$-0.342760\pi$
$72$	−3.92671	+	22.2695i	−0.462767	+	2.62448i
$73$	6.70827	+	2.44161i	0.785143	+	0.285769i	0.703316	−	0.710878i	$-0.251702\pi$
$73$	6.70827	+	2.44161i	0.785143	+	0.285769i	0.0818275	+	0.996647i	$0.473924\pi$
$74$	−14.5704	+	12.2261i	−1.69378	+	1.42125i
$75$		0			0
$76$	4.27938	+	13.4770i	0.490878	+	1.54591i
$77$	−1.69763			−0.193463
$78$	3.88946	−	3.26364i	0.440395	−	0.369535i
$79$	−1.44931	−	0.527504i	−0.163060	−	0.0593489i	0.259201	−	0.965824i	$-0.416541\pi$
$79$	−1.44931	−	0.527504i	−0.163060	−	0.0593489i	−0.422260	+	0.906475i	$0.638763\pi$
$80$		0			0
$81$	5.24435	+	29.7422i	0.582706	+	3.30469i
$82$	5.75009	−	2.09286i	0.634991	−	0.231118i
$83$	6.65930	−	11.5342i	0.730953	−	1.26605i	−0.225524	−	0.974238i	$-0.572409\pi$
$83$	6.65930	−	11.5342i	0.730953	−	1.26605i	0.956476	−	0.291809i	$-0.0942573\pi$
$84$	15.7664	+	27.3082i	1.72026	+	2.97957i
$85$		0			0
$86$	−11.5749	−	9.71246i	−1.24815	−	1.04732i
$87$	4.97418	+	8.61554i	0.533288	+	0.923683i
$88$	−0.822680	+	1.42492i	−0.0876980	+	0.151897i
$89$	6.17500	−	2.24752i	0.654549	−	0.238236i	0.00666773	−	0.999978i	$-0.497878\pi$
$89$	6.17500	−	2.24752i	0.654549	−	0.238236i	0.647881	+	0.761741i	$0.275655\pi$
$90$		0			0
$91$	0.342150	−	1.94043i	0.0358671	−	0.203412i
$92$	−12.5615	−	4.57203i	−1.30963	−	0.476667i
$93$	−0.754252	+	0.632892i	−0.0782123	+	0.0656279i
$94$	25.2640			2.60578
$95$		0			0
$96$	−18.5749			−1.89579
$97$	−9.34414	+	7.84066i	−0.948754	+	0.796099i	−0.979087	−	0.203441i	$-0.934787\pi$
$97$	−9.34414	+	7.84066i	−0.948754	+	0.796099i	0.0303336	+	0.999540i	$0.490343\pi$
$98$	3.52545	+	1.28316i	0.356124	+	0.129618i
$99$	−0.796200	+	4.51548i	−0.0800211	+	0.453822i
$100$		0			0
$101$	0.545793	−	0.198653i	0.0543085	−	0.0197667i	−0.314723	−	0.949184i	$-0.601912\pi$
$101$	0.545793	−	0.198653i	0.0543085	−	0.0197667i	0.369032	+	0.929417i	$0.379689\pi$
$102$	−1.33258	+	2.30810i	−0.131945	+	0.228536i
$103$	−3.23555	−	5.60414i	−0.318809	−	0.552193i	0.661431	−	0.750006i	$-0.269949\pi$
$103$	−3.23555	−	5.60414i	−0.318809	−	0.552193i	−0.980240	+	0.197813i	$0.936616\pi$
$104$	−1.46292	−	1.22753i	−0.143451	−	0.120370i
$105$		0			0
$106$	4.70199	+	8.14409i	0.456698	+	0.791024i
$107$	9.18942	−	15.9165i	0.888374	−	1.53871i	0.0465776	−	0.998915i	$-0.485169\pi$
$107$	9.18942	−	15.9165i	0.888374	−	1.53871i	0.841797	−	0.539795i	$-0.181498\pi$
$108$	49.7860	−	18.1206i	4.79066	−	1.74366i
$109$	−0.435803	−	2.47156i	−0.0417424	−	0.236733i	0.956797	−	0.290756i	$-0.0939067\pi$
$109$	−0.435803	−	2.47156i	−0.0417424	−	0.236733i	−0.998540	+	0.0540230i	$0.982796\pi$
$110$		0			0
$111$	25.8136	+	9.39539i	2.45012	+	0.891771i
$112$	0.0795397	−	0.0667417i	0.00751579	−	0.00630650i
$113$	11.3386			1.06665			0.533325	−	0.845911i	$-0.320942\pi$
$113$	11.3386			1.06665			0.533325	+	0.845911i	$0.320942\pi$
$114$	22.2535	−	24.3847i	2.08423	−	2.28384i
$115$		0			0
$116$	7.47492	−	6.27220i	0.694029	−	0.582359i
$117$	−5.00083	−	1.82015i	−0.462327	−	0.168273i
$118$	−0.242793	+	1.37695i	−0.0223509	+	0.126758i
$119$	0.179600	+	1.01856i	0.0164639	+	0.0933713i
$120$		0			0
$121$	5.33319	−	9.23735i	0.484835	−	0.839759i
$122$	1.17582	+	2.03658i	0.106454	+	0.184383i
$123$	−6.76997	−	5.68068i	−0.610428	−	0.512210i
$124$	0.739805	+	0.620770i	0.0664364	+	0.0557468i
$125$		0			0
$126$	26.7140	−	46.2700i	2.37987	−	4.12206i
$127$	18.0347	−	6.56408i	1.60032	−	0.582468i	0.620826	−	0.783949i	$-0.286797\pi$
$127$	18.0347	−	6.56408i	1.60032	−	0.582468i	0.979493	+	0.201480i	$0.0645752\pi$
$128$	3.19181	+	18.1017i	0.282119	+	1.59998i
$129$	−3.78945	+	21.4911i	−0.333643	+	1.89218i
$130$		0			0
$131$	−5.24756	+	4.40322i	−0.458481	+	0.384711i	−0.842572	−	0.538584i	$-0.818959\pi$
$131$	−5.24756	+	4.40322i	−0.458481	+	0.384711i	0.384091	+	0.923295i	$0.374515\pi$
$132$	6.19692			0.539373
$133$	0.532827	−	12.8002i	0.0462019	−	1.10991i
$134$	−7.63916			−0.659923
$135$		0			0
$136$	0.941977	+	0.342852i	0.0807738	+	0.0293993i
$137$	−2.29941	+	13.0406i	−0.196452	+	1.11413i	0.713884	+	0.700264i	$0.246934\pi$
$137$	−2.29941	+	13.0406i	−0.196452	+	1.11413i	−0.910336	+	0.413870i	$0.864177\pi$
$138$	5.41946	+	30.7353i	0.461335	+	2.61636i
$139$	−2.73439	+	0.995237i	−0.231928	+	0.0844149i	−0.455370	−	0.890302i	$-0.650493\pi$
$139$	−2.73439	+	0.995237i	−0.231928	+	0.0844149i	0.223442	+	0.974717i	$0.428271\pi$
$140$		0			0
$141$	−18.2438	−	31.5992i	−1.53641	−	2.66114i
$142$	23.1990	+	19.4663i	1.94682	+	1.63357i
$143$	−0.296629	−	0.248901i	−0.0248054	−	0.0208142i
$144$	−0.140220	−	0.242868i	−0.0116850	−	0.0202390i
$145$		0			0
$146$	−15.3617	+	5.59121i	−1.27134	+	0.462732i
$147$	−0.940899	−	5.33610i	−0.0776040	−	0.440114i
$148$	4.67880	−	26.5348i	0.384595	−	2.18115i
$149$	8.32247	+	3.02913i	0.681804	+	0.248156i	0.659622	−	0.751598i	$-0.270716\pi$
$149$	8.32247	+	3.02913i	0.681804	+	0.248156i	0.0221819	+	0.999754i	$0.492939\pi$
$150$		0			0
$151$	8.37160			0.681271			0.340636	−	0.940195i	$-0.389358\pi$
$151$	8.37160			0.681271			0.340636	+	0.940195i	$0.389358\pi$
$152$	−10.4858	−	6.65027i	−0.850508	−	0.539408i
$153$	2.79348			0.225839
$154$	2.97801	−	2.49884i	0.239975	−	0.201363i
$155$		0			0
$156$	−1.24897	+	7.08324i	−0.0999973	+	0.567113i
$157$	2.75519	+	15.6255i	0.219888	+	1.24705i	0.872219	+	0.489115i	$0.162680\pi$
$157$	2.75519	+	15.6255i	0.219888	+	1.24705i	−0.652331	+	0.757934i	$0.726209\pi$
$158$	3.31887	−	1.20797i	0.264035	−	0.0961008i
$159$	6.79088	−	11.7622i	0.538552	−	0.932799i
$160$		0			0
$161$	9.27793	+	7.78511i	0.731203	+	0.613552i
$162$	−52.9791	−	44.4548i	−4.16243	−	3.49270i
$163$	4.86130	+	8.42002i	0.380766	+	0.659507i	0.991172	−	0.132582i	$-0.0423269\pi$
$163$	4.86130	+	8.42002i	0.380766	+	0.659507i	−0.610406	+	0.792089i	$0.708994\pi$
$164$	−4.33415	+	7.50697i	−0.338440	+	0.586195i
$165$		0			0
$166$	5.29612	+	30.0358i	0.411059	+	2.33123i
$167$	−0.0489947	+	0.277863i	−0.00379132	+	0.0215017i	−0.986645	−	0.162887i	$-0.947919\pi$
$167$	−0.0489947	+	0.277863i	−0.00379132	+	0.0215017i	0.982853	+	0.184389i	$0.0590305\pi$
$168$	−26.0200	−	9.47052i	−2.00749	−	0.730666i
$169$	−9.61429	+	8.06735i	−0.739561	+	0.620565i
$170$		0			0
$171$	−33.7969	−	7.42063i	−2.58452	−	0.567470i
$172$	21.4046			1.63208
$173$	−11.5894	+	9.72470i	−0.881129	+	0.739355i	−0.966411	−	0.257002i	$-0.917265\pi$
$173$	−11.5894	+	9.72470i	−0.881129	+	0.739355i	0.0852817	+	0.996357i	$0.472821\pi$
$174$	−21.4075	−	7.79171i	−1.62290	−	0.590688i
$175$		0			0
$176$	−0.00354334	−	0.0200953i	−0.000267089	−	0.00151474i
$177$	1.89756	−	0.690657i	0.142630	−	0.0519129i
$178$	−7.52403	+	13.0320i	−0.563950	+	0.976790i
$179$	7.22664	+	12.5169i	0.540145	+	0.935558i	0.998895	+	0.0469929i	$0.0149638\pi$
$179$	7.22664	+	12.5169i	0.540145	+	0.935558i	−0.458751	+	0.888565i	$0.651703\pi$
$180$		0			0
$181$	−5.33540	−	4.47693i	−0.396577	−	0.332768i	0.422592	−	0.906320i	$-0.361120\pi$
$181$	−5.33540	−	4.47693i	−0.396577	−	0.332768i	−0.819169	+	0.573552i	$0.805565\pi$
$182$	2.25604	+	3.90757i	0.167229	+	0.289648i
$183$	1.69819	−	2.94135i	0.125534	−	0.217431i
$184$	11.0307	−	4.01483i	0.813192	−	0.295978i
$185$		0			0
$186$	0.391527	−	2.22046i	0.0287082	−	0.162812i
$187$	0.191000	+	0.0695184i	0.0139673	+	0.00508369i
$188$	−27.4158	+	23.0046i	−1.99950	+	1.67778i
$189$	−48.0022			−3.49165
$190$		0			0
$191$	5.49050			0.397279			0.198639	−	0.980073i	$-0.436348\pi$
$191$	5.49050			0.397279			0.198639	+	0.980073i	$0.436348\pi$
$192$	32.7634	−	27.4918i	2.36450	−	1.98405i
$193$	−6.08625	−	2.21521i	−0.438098	−	0.159455i	0.113549	−	0.993532i	$-0.463778\pi$
$193$	−6.08625	−	2.21521i	−0.438098	−	0.159455i	−0.551647	+	0.834078i	$0.686000\pi$
$194$	4.85048	−	27.5085i	0.348244	−	1.97499i
$195$		0			0
$196$	−4.99412	+	1.81771i	−0.356723	+	0.129837i
$197$	−4.64727	+	8.04931i	−0.331104	+	0.573490i	−0.982729	−	0.185052i	$-0.940755\pi$
$197$	−4.64727	+	8.04931i	−0.331104	+	0.573490i	0.651624	+	0.758542i	$0.274088\pi$
$198$	−5.24991	−	9.09310i	−0.373095	−	0.646219i
$199$	−18.6201	−	15.6242i	−1.31995	−	1.10757i	−0.986317	−	0.164863i	$-0.947282\pi$
$199$	−18.6201	−	15.6242i	−1.31995	−	1.10757i	−0.333630	−	0.942704i	$-0.608274\pi$
$200$		0			0
$201$	5.51646	+	9.55478i	0.389101	+	0.673942i
$202$	−0.665031	+	1.15187i	−0.0467914	+	0.0810451i
$203$	−8.30765	+	3.02374i	−0.583083	+	0.212225i
$204$	−0.655601	−	3.71810i	−0.0459012	−	0.260319i
$205$		0			0
$206$	13.9250	+	5.06827i	0.970198	+	0.353123i
$207$	25.0588	−	21.0269i	1.74171	−	1.46147i
$208$	0.0236836			0.00164216
$209$	−2.12615	−	1.34845i	−0.147069	−	0.0932739i
$210$		0			0
$211$	18.3601	−	15.4060i	1.26396	−	1.06059i	0.268715	−	0.963220i	$-0.413401\pi$
$211$	18.3601	−	15.4060i	1.26396	−	1.06059i	0.995248	−	0.0973716i	$-0.0310435\pi$
$212$	−12.5182	−	4.55626i	−0.859755	−	0.312925i
$213$	7.59504	−	43.0736i	0.520404	−	2.95136i
$214$	7.30832	+	41.4475i	0.499586	+	2.83330i
$215$		0			0
$216$	−23.2622	+	40.2913i	−1.58279	+	2.74147i
$217$	−0.437495	−	0.757764i	−0.0296991	−	0.0514403i
$218$	4.40254	+	3.69417i	0.298178	+	0.250201i
$219$	18.0864	+	15.1763i	1.22217	+	1.02552i
$220$		0			0
$221$	−0.117957	+	0.204307i	−0.00793463	+	0.0137432i
$222$	−59.1124	+	21.5152i	−3.96736	+	1.44400i
$223$	−3.57177	−	20.2565i	−0.239183	−	1.35648i	−0.833622	−	0.552336i	$-0.813737\pi$
$223$	−3.57177	−	20.2565i	−0.239183	−	1.35648i	0.594438	−	0.804141i	$-0.297374\pi$
$224$	2.86640	−	16.2562i	0.191520	−	1.08616i
$225$		0			0
$226$	−19.8904	+	16.6901i	−1.32309	+	1.11021i
$227$	−12.6949			−0.842593			−0.421297	−	0.906923i	$-0.638425\pi$
$227$	−12.6949			−0.842593			−0.421297	+	0.906923i	$0.638425\pi$
$228$	−1.94500	+	46.7250i	−0.128811	+	3.09444i
$229$	5.76019			0.380644			0.190322	−	0.981722i	$-0.439047\pi$
$229$	5.76019			0.380644			0.190322	+	0.981722i	$0.439047\pi$
$230$		0			0
$231$	−5.27596	−	1.92029i	−0.347133	−	0.126346i
$232$	−1.48793	+	8.43845i	−0.0976872	+	0.554012i
$233$	0.482485	+	2.73631i	0.0316087	+	0.179262i	0.996525	−	0.0832967i	$-0.0265449\pi$
$233$	0.482485	+	2.73631i	0.0316087	+	0.179262i	−0.964916	+	0.262558i	$0.915434\pi$
$234$	11.4517	−	4.16810i	0.748624	−	0.272477i
$235$		0			0
$236$	−0.990333	−	1.71531i	−0.0644652	−	0.111657i
$237$	−3.90753	−	3.27881i	−0.253821	−	0.212981i
$238$	−1.81434	−	1.52241i	−0.117606	−	0.0986834i
$239$	−9.72936	−	16.8518i	−0.629340	−	1.09005i	−0.987684	−	0.156460i	$-0.949992\pi$
$239$	−9.72936	−	16.8518i	−0.629340	−	1.09005i	0.358344	−	0.933590i	$-0.383341\pi$
$240$		0			0
$241$	6.80304	−	2.47610i	0.438222	−	0.159500i	−0.113481	−	0.993540i	$-0.536200\pi$
$241$	6.80304	−	2.47610i	0.438222	−	0.159500i	0.551704	+	0.834040i	$0.313978\pi$
$242$	4.24147	+	24.0546i	0.272652	+	1.54629i
$243$	−8.83644	+	50.1140i	−0.566858	+	3.21481i
$244$	−3.13042	−	1.13938i	−0.200404	−	0.0729412i
$245$		0			0
$246$	20.2378			1.29031
$247$	1.96983	−	2.15847i	0.125337	−	0.137340i
$248$	−0.848051			−0.0538513
$249$	33.7432	−	28.3139i	2.13839	−	1.79432i
$250$		0			0
$251$	2.57969	−	14.6301i	0.162829	−	0.923446i	−0.788447	−	0.615103i	$-0.789114\pi$
$251$	2.57969	−	14.6301i	0.162829	−	0.923446i	0.951275	−	0.308343i	$-0.0997745\pi$
$252$	13.1427	+	74.5359i	0.827911	+	4.69532i
$253$	2.23664	−	0.814070i	0.140616	−	0.0511801i
$254$	−21.9746	+	38.0612i	−1.37881	+	2.38817i
$255$		0			0
$256$	−12.4313	−	10.4311i	−0.776958	−	0.651946i
$257$	−15.1338	−	12.6988i	−0.944021	−	0.792128i	0.0342591	−	0.999413i	$-0.489093\pi$
$257$	−15.1338	−	12.6988i	−0.944021	−	0.792128i	−0.978281	+	0.207285i	$0.933537\pi$
$258$	−24.9865	−	43.2779i	−1.55559	−	2.69436i
$259$	−12.2060	+	21.1414i	−0.758445	+	1.31367i
$260$		0			0
$261$	4.14641	+	23.5155i	0.256657	+	1.45557i
$262$	2.72397	−	15.4484i	0.168288	−	0.954407i
$263$	11.1365	+	4.05337i	0.686709	+	0.249942i	0.661725	−	0.749746i	$-0.269824\pi$
$263$	11.1365	+	4.05337i	0.686709	+	0.249942i	0.0249835	+	0.999688i	$0.492047\pi$
$264$	−4.16859	+	3.49786i	−0.256559	+	0.215278i
$265$		0			0
$266$	17.9067	+	23.2386i	1.09793	+	1.42485i
$267$	21.7333			1.33005
$268$	8.28982	−	6.95598i	0.506381	−	0.424904i
$269$	10.2199	+	3.71975i	0.623120	+	0.226797i	0.634234	−	0.773141i	$-0.281315\pi$
$269$	10.2199	+	3.71975i	0.623120	+	0.226797i	−0.0111138	+	0.999938i	$0.503538\pi$
$270$		0			0
$271$	−1.01974	−	5.78324i	−0.0619448	−	0.351307i	−0.999989	−	0.00478962i	$-0.998475\pi$
$271$	−1.01974	−	5.78324i	−0.0619448	−	0.351307i	0.938044	−	0.346517i	$-0.112636\pi$
$272$	−0.0116821	+	0.00425195i	−0.000708333	+	0.000257812i
$273$	3.25830	−	5.64353i	0.197201	−	0.341562i
$274$	−15.1616	−	26.2607i	−0.915947	−	1.58647i
$275$		0			0
$276$	−33.8676	−	28.4183i	−2.03859	−	1.71058i
$277$	−11.9064	−	20.6224i	−0.715385	−	1.23908i	−0.962811	−	0.270176i	$-0.912918\pi$
$277$	−11.9064	−	20.6224i	−0.715385	−	1.23908i	0.247426	−	0.968907i	$-0.420415\pi$
$278$	3.33176	−	5.77079i	0.199826	−	0.346109i
$279$	−2.22075	+	0.808285i	−0.132953	+	0.0483908i
$280$		0			0
$281$	−1.23971	+	7.03074i	−0.0739549	+	0.419419i	0.925243	+	0.379375i	$0.123861\pi$
$281$	−1.23971	+	7.03074i	−0.0739549	+	0.419419i	−0.999198	+	0.0400440i	$0.987250\pi$
$282$	78.5166	+	28.5777i	4.67559	+	1.70178i
$283$	−20.4796	+	17.1844i	−1.21739	+	1.02151i	−0.218428	+	0.975853i	$0.570093\pi$
$283$	−20.4796	+	17.1844i	−1.21739	+	1.02151i	−0.998957	+	0.0456547i	$0.985463\pi$
$284$	−42.9003			−2.54567
$285$		0			0
$286$	0.886725			0.0524332
$287$	6.01628	−	5.04825i	0.355130	−	0.297989i
$288$	−41.8951	−	15.2486i	−2.46869	−	0.898530i
$289$	−2.93052	+	16.6198i	−0.172383	+	0.977634i
$290$		0			0
$291$	−37.9092	+	13.7978i	−2.22228	+	0.808843i
$292$	11.5789	−	20.0553i	0.677607	−	1.17365i
$293$	0.536685	+	0.929566i	0.0313535	+	0.0543058i	0.881276	−	0.472601i	$-0.156685\pi$
$293$	0.536685	+	0.929566i	0.0313535	+	0.0543058i	−0.849923	+	0.526907i	$0.823352\pi$
$294$	9.50508	+	7.97571i	0.554348	+	0.465153i
$295$		0			0
$296$	11.8302	+	20.4906i	0.687618	+	1.19099i
$297$	−4.71676	+	8.16967i	−0.273694	+	0.474053i
$298$	−19.0582	+	6.93662i	−1.10401	+	0.401827i
$299$	0.479716	+	2.72061i	0.0277427	+	0.157337i
$300$		0			0
$301$	−18.2235	−	6.63283i	−1.05039	−	0.382310i
$302$	−14.6856	+	12.3227i	−0.845062	+	0.709091i
$303$	1.92095			0.110356
$304$	0.152631	−	0.0204097i	0.00875400	−	0.00117058i
$305$		0			0
$306$	−4.90037	+	4.11190i	−0.280135	+	0.235062i
$307$	−24.4039	−	8.88231i	−1.39281	−	0.506940i	−0.466772	−	0.884378i	$-0.654583\pi$
$307$	−24.4039	−	8.88231i	−1.39281	−	0.506940i	−0.926035	+	0.377438i	$0.876805\pi$
$308$	−0.956284	+	5.42336i	−0.0544894	+	0.309025i
$309$	−3.71640	−	21.0768i	−0.211419	−	1.19901i
$310$		0			0
$311$	−9.52546	+	16.4986i	−0.540139	+	0.935548i	0.458756	+	0.888562i	$0.348295\pi$
$311$	−9.52546	+	16.4986i	−0.540139	+	0.935548i	−0.998896	+	0.0469862i	$0.985038\pi$
$312$	−3.15798	−	5.46978i	−0.178785	−	0.309666i
$313$	11.7965	+	9.89844i	0.666777	+	0.559493i	0.912110	−	0.409946i	$-0.134453\pi$
$313$	11.7965	+	9.89844i	0.666777	+	0.559493i	−0.245332	+	0.969439i	$0.578897\pi$
$314$	−27.8333	−	23.3549i	−1.57073	−	1.31800i
$315$		0			0
$316$	−2.50161	+	4.33291i	−0.140726	+	0.243745i
$317$	24.0001	−	8.73532i	1.34798	−	0.490624i	0.435663	−	0.900110i	$-0.356514\pi$
$317$	24.0001	−	8.73532i	1.34798	−	0.490624i	0.912317	+	0.409485i	$0.134292\pi$
$318$	5.40077	+	30.6293i	0.302860	+	1.71761i
$319$	−0.301700	+	1.71103i	−0.0168920	+	0.0957991i
$320$		0			0
$321$	46.5635	−	39.0714i	2.59892	−	2.18075i
$322$	−27.7349			−1.54560
$323$	−0.584120	+	1.41833i	−0.0325013	+	0.0789180i
$324$	97.9707			5.44282
$325$		0			0
$326$	−20.9217	−	7.61489i	−1.15875	−	0.421750i
$327$	1.44133	−	8.17420i	0.0797058	−	0.452034i
$328$	−1.32179	−	7.49625i	−0.0729837	−	0.413911i
$329$	30.4700	−	11.0902i	1.67987	−	0.611421i
$330$		0			0
$331$	−2.26589	−	3.92464i	−0.124545	−	0.215718i	0.797010	−	0.603966i	$-0.206414\pi$
$331$	−2.26589	−	3.92464i	−0.124545	−	0.215718i	−0.921555	+	0.388248i	$0.873080\pi$
$332$	−33.0969	−	27.7716i	−1.81643	−	1.52416i
$333$	50.5089	+	42.3820i	2.76787	+	2.32252i
$334$	−0.323056	−	0.559550i	−0.0176768	−	0.0306172i
$335$		0			0
$336$	0.322693	−	0.117451i	0.0176043	−	0.00640746i
$337$	−3.53193	−	20.0306i	−0.192397	−	1.09114i	−0.916078	−	0.401001i	$-0.868662\pi$
$337$	−3.53193	−	20.0306i	−0.192397	−	1.09114i	0.723681	−	0.690135i	$-0.242449\pi$
$338$	4.99072	−	28.3038i	0.271459	−	1.53952i
$339$	35.2388	+	12.8259i	1.91391	+	0.696605i
$340$		0			0
$341$	−0.171955			−0.00931191
$342$	70.2101	−	36.7305i	3.79653	−	1.98616i
$343$	−15.7585			−0.850880
$344$	−14.3986	+	12.0819i	−0.776320	+	0.651410i
$345$		0			0
$346$	6.01601	−	34.1185i	0.323423	−	1.83422i
$347$	−4.73475	−	26.8521i	−0.254175	−	1.44150i	−0.798182	−	0.602416i	$-0.794205\pi$
$347$	−4.73475	−	26.8521i	−0.254175	−	1.44150i	0.544008	−	0.839080i	$-0.316906\pi$
$348$	30.3258	−	11.0377i	1.62563	−	0.591682i
$349$	−6.31115	+	10.9312i	−0.337828	+	0.585135i	−0.984024	−	0.178036i	$-0.943026\pi$
$349$	−6.31115	+	10.9312i	−0.337828	+	0.585135i	0.646196	+	0.763171i	$0.276359\pi$
$350$		0			0
$351$	−8.38750	−	7.03795i	−0.447692	−	0.375658i
$352$	−2.48504	−	2.08520i	−0.132453	−	0.111142i
$353$	15.3996	+	26.6728i	0.819636	+	1.41965i	0.905950	+	0.423384i	$0.139158\pi$
$353$	15.3996	+	26.6728i	0.819636	+	1.41965i	−0.0863140	+	0.996268i	$0.527509\pi$
$354$	−2.31212	+	4.00471i	−0.122888	+	0.212848i
$355$		0			0
$356$	−3.70166	−	20.9931i	−0.196187	−	1.11263i
$357$	−0.593991	+	3.36869i	−0.0314373	+	0.178290i
$358$	−31.1015	−	11.3200i	−1.64377	−	0.598282i
$359$	−13.2039	+	11.0794i	−0.696877	+	0.584749i	−0.920883	−	0.389839i	$-0.872531\pi$
$359$	−13.2039	+	11.0794i	−0.696877	+	0.584749i	0.224007	+	0.974588i	$0.428086\pi$
$360$		0			0
$361$	10.8347	−	15.6080i	0.570245	−	0.821475i
$362$	15.9493			0.838278
$363$	27.0237	−	22.6756i	1.41838	−	1.19016i
$364$	−6.00630	−	2.18612i	−0.314816	−	0.114584i
$365$		0			0
$366$	1.35056	+	7.65943i	0.0705951	+	0.400365i
$367$	−28.2788	+	10.2927i	−1.47614	+	0.537272i	−0.949761	−	0.312975i	$-0.898674\pi$
$367$	−28.2788	+	10.2927i	−1.47614	+	0.537272i	−0.526383	+	0.850248i	$0.676452\pi$
$368$	−0.0727893	+	0.126075i	−0.00379440	+	0.00657210i
$369$	−10.6061	−	18.3702i	−0.552129	−	0.956315i
$370$		0			0
$371$	9.24594	+	7.75826i	0.480025	+	0.402789i
$372$	1.59701	+	2.76610i	0.0828010	+	0.143416i
$373$	−3.06676	+	5.31178i	−0.158791	+	0.275034i	−0.934433	−	0.356139i	$-0.884093\pi$
$373$	−3.06676	+	5.31178i	−0.158791	+	0.275034i	0.775642	+	0.631173i	$0.217426\pi$
$374$	−0.437385	+	0.159195i	−0.0226166	+	0.00823178i
$375$		0			0
$376$	5.45728	−	30.9498i	0.281438	−	1.59611i
$377$	−1.89494	−	0.689702i	−0.0975944	−	0.0355215i
$378$	84.2063	−	70.6575i	4.33110	−	3.63423i
$379$	30.8958			1.58701			0.793505	−	0.608564i	$-0.208254\pi$
$379$	30.8958			1.58701			0.793505	+	0.608564i	$0.208254\pi$
$380$		0			0
$381$	63.4741			3.25187
$382$	−9.63153	+	8.08181i	−0.492792	+	0.413501i
$383$	4.37066	+	1.59079i	0.223330	+	0.0812855i	0.451262	−	0.892392i	$-0.350974\pi$
$383$	4.37066	+	1.59079i	0.223330	+	0.0812855i	−0.227932	+	0.973677i	$0.573196\pi$
$384$	−10.5563	+	59.8677i	−0.538698	+	3.05511i
$385$		0			0
$386$	13.9373	−	5.07277i	0.709391	−	0.258197i
$387$	−26.1895	+	45.3615i	−1.33129	+	2.30586i
$388$	19.7847	+	34.2681i	1.00442	+	1.73970i
$389$	−12.3923	−	10.3984i	−0.628315	−	0.527219i	0.272090	−	0.962272i	$-0.412285\pi$
$389$	−12.3923	−	10.3984i	−0.628315	−	0.527219i	−0.900405	+	0.435053i	$0.856730\pi$
$390$		0			0
$391$	−0.725059	−	1.25584i	−0.0366678	−	0.0635105i
$392$	2.33347	−	4.04169i	0.117858	−	0.204136i
$393$	−21.2894	+	7.74870i	−1.07391	+	0.390870i
$394$	−3.69596	−	20.9609i	−0.186200	−	1.05599i
$395$		0			0
$396$	13.9770	+	5.08720i	0.702368	+	0.255641i
$397$	7.61069	−	6.38613i	0.381970	−	0.320511i	−0.431506	−	0.902110i	$-0.642017\pi$
$397$	7.61069	−	6.38613i	0.381970	−	0.320511i	0.813475	+	0.581600i	$0.197573\pi$
$398$	55.6619			2.79008
$399$	16.1350	−	39.1782i	0.807762	−	1.96137i
$400$		0			0
$401$	−9.90801	+	8.31381i	−0.494783	+	0.415172i	−0.855737	−	0.517412i	$-0.826896\pi$
$401$	−9.90801	+	8.31381i	−0.494783	+	0.415172i	0.360954	+	0.932584i	$0.382451\pi$
$402$	−23.7413	−	8.64114i	−1.18411	−	0.430981i
$403$	0.0346570	−	0.196550i	0.00172639	−	0.00979083i
$404$	−0.327180	−	1.85553i	−0.0162778	−	0.0923162i
$405$		0			0
$406$	10.1226	−	17.5329i	0.502376	−	0.870141i
$407$	2.39876	+	4.15478i	0.118902	+	0.205945i
$408$	2.53970	+	2.13106i	0.125734	+	0.105503i
$409$	−4.78036	−	4.01120i	−0.236373	−	0.198341i	0.516905	−	0.856043i	$-0.327084\pi$
$409$	−4.78036	−	4.01120i	−0.236373	−	0.198341i	−0.753278	+	0.657702i	$0.771529\pi$
$410$		0			0
$411$	−21.8973	+	37.9272i	−1.08011	+	1.87081i
$412$	−19.7260	+	7.17968i	−0.971830	+	0.353717i
$413$	0.311617	+	1.76727i	0.0153337	+	0.0869616i
$414$	−13.0079	+	73.7714i	−0.639302	+	3.62566i
$415$		0			0
$416$	2.88429	−	2.42020i	0.141414	−	0.118660i
$417$	−9.62385			−0.471282
$418$	5.71459	−	0.764149i	0.279510	−	0.0373758i
$419$	−30.5403			−1.49199			−0.745995	−	0.665951i	$-0.768026\pi$
$419$	−30.5403			−1.49199			−0.745995	+	0.665951i	$0.768026\pi$
$420$		0			0
$421$	−34.3641	−	12.5075i	−1.67480	−	0.609578i	−0.682219	−	0.731148i	$-0.738985\pi$
$421$	−34.3641	−	12.5075i	−1.67480	−	0.609578i	−0.992583	+	0.121569i	$0.961207\pi$
$422$	−9.53063	+	54.0509i	−0.463944	+	2.63115i
$423$	−15.2078	−	86.2478i	−0.739430	−	4.19351i
$424$	10.9926	−	4.00099i	0.533850	−	0.194305i
$425$		0			0
$426$	50.0794	+	86.7401i	2.42636	+	4.20257i
$427$	2.31212	+	1.94010i	0.111891	+	0.0938880i
$428$	−45.6716	−	38.3230i	−2.20762	−	1.85241i
$429$	−0.640329	−	1.10908i	−0.0309154	−	0.0535470i
$430$		0			0
$431$	−22.4618	+	8.17542i	−1.08195	+	0.393796i	−0.820631	−	0.571458i	$-0.806378\pi$
$431$	−22.4618	+	8.17542i	−1.08195	+	0.393796i	−0.261314	+	0.965254i	$0.584156\pi$
$432$	−0.100192	−	0.568216i	−0.00482048	−	0.0273383i
$433$	2.54471	−	14.4318i	0.122291	−	0.693547i	−0.860589	−	0.509300i	$-0.829904\pi$
$433$	2.54471	−	14.4318i	0.122291	−	0.693547i	0.982880	−	0.184247i	$-0.0589845\pi$
$434$	1.88286	+	0.685305i	0.0903802	+	0.0328957i
$435$		0			0
$436$	−8.14132			−0.389898
$437$	5.43611	+	17.1198i	0.260044	+	0.818953i
$438$	−54.0664			−2.58339
$439$	−13.0414	+	10.9430i	−0.622433	+	0.522283i	−0.898567	−	0.438836i	$-0.855391\pi$
$439$	−13.0414	+	10.9430i	−0.622433	+	0.522283i	0.276134	+	0.961119i	$0.410947\pi$
$440$		0			0
$441$	2.25836	−	12.8078i	0.107541	−	0.609896i
$442$	−0.0938107	−	0.532027i	−0.00446212	−	0.0253059i
$443$	−33.8207	+	12.3097i	−1.60687	+	0.584854i	−0.980818	−	0.194926i	$-0.937553\pi$
$443$	−33.8207	+	12.3097i	−1.60687	+	0.584854i	−0.626054	+	0.779780i	$0.715331\pi$
$444$	44.5562	−	77.1736i	2.11454	−	3.66250i
$445$		0			0
$446$	36.0825	+	30.2768i	1.70856	+	1.43365i
$447$	22.4385	+	18.8282i	1.06131	+	0.890542i
$448$	19.0040	+	32.9160i	0.897856	+	1.55513i
$449$	−1.77883	+	3.08102i	−0.0839481	+	0.145402i	−0.904942	−	0.425534i	$-0.860086\pi$
$449$	−1.77883	+	3.08102i	−0.0839481	+	0.145402i	0.820994	+	0.570936i	$0.193420\pi$
$450$		0			0
$451$	−0.268014	−	1.51998i	−0.0126203	−	0.0715731i
$452$	6.38713	−	36.2232i	0.300425	−	1.70380i
$453$	26.0177	+	9.46966i	1.22242	+	0.444923i
$454$	22.2697	−	18.6865i	1.04517	−	0.877001i
$455$		0			0
$456$	−25.0656	−	32.5292i	−1.17380	−	1.52332i
$457$	4.61695			0.215972			0.107986	−	0.994152i	$-0.465560\pi$
$457$	4.61695			0.215972			0.107986	+	0.994152i	$0.465560\pi$
$458$	−10.1046	+	8.47879i	−0.472158	+	0.396188i
$459$	5.40074	+	1.96571i	0.252085	+	0.0917514i
$460$		0			0
$461$	−5.06596	−	28.7305i	−0.235945	−	1.33811i	−0.840614	−	0.541634i	$-0.817806\pi$
$461$	−5.06596	−	28.7305i	−0.235945	−	1.33811i	0.604669	−	0.796477i	$-0.293305\pi$
$462$	12.0818	−	4.39741i	0.562096	−	0.204586i
$463$	−8.81888	+	15.2747i	−0.409848	+	0.709877i	−0.994872	−	0.101138i	$-0.967752\pi$
$463$	−8.81888	+	15.2747i	−0.409848	+	0.709877i	0.585024	+	0.811016i	$0.301085\pi$
$464$	−0.0531328	−	0.0920288i	−0.00246663	−	0.00427233i
$465$		0			0
$466$	−4.87413	−	4.08988i	−0.225790	−	0.189460i
$467$	8.47175	+	14.6735i	0.392026	+	0.679009i	0.992717	−	0.120473i	$-0.0384410\pi$
$467$	8.47175	+	14.6735i	0.392026	+	0.679009i	−0.600691	+	0.799482i	$0.705108\pi$
$468$	−8.63180	+	14.9507i	−0.399005	+	0.691097i
$469$	−9.21333	+	3.35338i	−0.425432	+	0.154845i
$470$		0			0
$471$	−9.11226	+	51.6782i	−0.419871	+	2.38120i
$472$	1.63439	+	0.594870i	0.0752290	+	0.0273811i
$473$	−2.91954	+	2.44978i	−0.134240	+	0.112641i
$474$	11.6809			0.536523
$475$		0			0
$476$	3.35514			0.153782
$477$	24.9724	−	20.9544i	1.14341	−	0.959434i
$478$	41.8726	+	15.2404i	1.91521	+	0.697078i
$479$	−2.51117	+	14.2416i	−0.114738	+	0.650714i	0.872141	+	0.489255i	$0.162731\pi$
$479$	−2.51117	+	14.2416i	−0.114738	+	0.650714i	−0.986879	+	0.161459i	$0.948380\pi$
$480$		0			0
$481$	−5.23248	+	1.90447i	−0.238580	+	0.0868362i
$482$	−8.28927	+	14.3574i	−0.377566	+	0.653964i
$483$	20.0282	+	34.6898i	0.911312	+	1.57844i
$484$	−26.5061	−	22.2412i	−1.20482	−	1.01097i
$485$		0			0
$486$	−58.2649	−	100.918i	−2.64295	−	4.57772i
$487$	−0.165966	+	0.287462i	−0.00752064	+	0.0130261i	−0.869761	−	0.493473i	$-0.835727\pi$
$487$	−0.165966	+	0.287462i	−0.00752064	+	0.0130261i	0.862241	+	0.506499i	$0.169061\pi$
$488$	2.74891	−	1.00052i	0.124437	−	0.0452915i
$489$	5.58376	+	31.6671i	0.252506	+	1.43203i
$490$		0			0
$491$	3.14034	+	1.14299i	0.141721	+	0.0515824i	0.411907	−	0.911226i	$-0.364863\pi$
$491$	3.14034	+	1.14299i	0.141721	+	0.0515824i	−0.270186	+	0.962808i	$0.587085\pi$
$492$	−21.9615	+	18.4279i	−0.990100	+	0.830792i
$493$	1.05852			0.0476733
$494$	−0.278313	+	6.68594i	−0.0125219	+	0.300815i
$495$		0			0
$496$	0.00805671	−	0.00676038i	0.000361757	−	0.000303550i
$497$	36.5247	+	13.2939i	1.63836	+	0.596313i
$498$	−17.5159	+	99.3375i	−0.784905	+	4.45142i
$499$	−2.44695	−	13.8773i	−0.109540	−	0.621235i	−0.989309	−	0.145833i	$-0.953414\pi$
$499$	−2.44695	−	13.8773i	−0.109540	−	0.621235i	0.879769	−	0.475402i	$-0.157697\pi$
$500$		0			0
$501$	−0.466576	+	0.808133i	−0.0208451	+	0.0361047i
$502$	17.0097	+	29.4617i	0.759180	+	1.31494i
$503$	2.83896	+	2.38217i	0.126583	+	0.106216i	0.703881	−	0.710318i	$-0.251449\pi$
$503$	2.83896	+	2.38217i	0.126583	+	0.106216i	−0.577299	+	0.816533i	$0.695893\pi$
$504$	−50.9128	−	42.7209i	−2.26784	−	1.90294i
$505$		0			0
$506$	−2.72527	+	4.72030i	−0.121153	+	0.209843i
$507$	−39.0052	+	14.1967i	−1.73228	+	0.630500i
$508$	−10.8110	−	61.3124i	−0.479662	−	2.72030i
$509$	6.13731	−	34.8064i	0.272032	−	1.54277i	−0.476204	−	0.879335i	$-0.657988\pi$
$509$	6.13731	−	34.8064i	0.272032	−	1.54277i	0.748236	−	0.663433i	$-0.230901\pi$
$510$		0			0
$511$	−16.0729	+	13.4867i	−0.711021	+	0.596618i
$512$	0.399682			0.0176636
$513$	−60.1192	−	38.1287i	−2.65433	−	1.68342i
$514$	45.2401			1.99546
$515$		0			0
$516$	66.5222	+	24.2121i	2.92848	+	1.06588i
$517$	1.10655	−	6.27554i	0.0486659	−	0.275998i
$518$	−9.70742	−	55.0535i	−0.426520	−	2.41891i
$519$	−47.0185	+	17.1133i	−2.06388	+	0.751191i
$520$		0			0
$521$	−2.52454	−	4.37264i	−0.110602	−	0.191569i	0.805411	−	0.592717i	$-0.201945\pi$
$521$	−2.52454	−	4.37264i	−0.110602	−	0.191569i	−0.916013	+	0.401148i	$0.868611\pi$
$522$	−41.8876	−	35.1479i	−1.83337	−	1.53838i
$523$	−17.8994	−	15.0194i	−0.782686	−	0.656752i	0.161238	−	0.986916i	$-0.448451\pi$
$523$	−17.8994	−	15.0194i	−0.782686	−	0.656752i	−0.943924	+	0.330164i	$0.892896\pi$
$524$	11.1109	+	19.2446i	0.485380	+	0.840704i
$525$		0			0
$526$	−25.5023	+	9.28209i	−1.11195	+	0.404718i
$527$	0.0181920	+	0.103172i	0.000792454	+	0.00449423i
$528$	0.0117189	−	0.0664612i	0.000510000	−	0.00289235i
$529$	5.65596	+	2.05860i	0.245911	+	0.0895043i
$530$		0			0
$531$	4.84687			0.210336
$532$	−40.5922	−	8.91262i	−1.75989	−	0.386411i
$533$	1.79139			0.0775939
$534$	−38.1249	+	31.9906i	−1.64982	+	1.38437i
$535$		0			0
$536$	−1.65014	+	9.35839i	−0.0712751	+	0.404221i
$537$	8.30062	+	47.0752i	0.358198	+	2.03144i
$538$	−23.4033	+	8.51811i	−1.00899	+	0.367242i
$539$	0.473147	−	0.819515i	0.0203799	−	0.0352990i
$540$		0			0
$541$	24.3992	+	20.4734i	1.04900	+	0.880219i	0.992988	−	0.118211i	$-0.0377160\pi$
$541$	24.3992	+	20.4734i	1.04900	+	0.880219i	0.0560152	+	0.998430i	$0.482160\pi$
$542$	10.3016	+	8.64403i	0.442490	+	0.371293i
$543$	−11.5175	−	19.9488i	−0.494262	−	0.856086i
$544$	−0.988197	+	1.71161i	−0.0423686	+	0.0733845i
$545$		0			0
$546$	2.59131	+	14.6961i	0.110898	+	0.628934i
$547$	−5.15875	+	29.2567i	−0.220572	+	1.25093i	0.650399	+	0.759593i	$0.274602\pi$
$547$	−5.15875	+	29.2567i	−0.220572	+	1.25093i	−0.870971	+	0.491334i	$0.836510\pi$
$548$	40.3651	+	14.6917i	1.72431	+	0.627599i
$549$	6.24483	−	5.24003i	0.266523	−	0.223639i
$550$		0			0
$551$	−12.8065	−	2.81186i	−0.545576	−	0.119789i
$552$	38.8231			1.65242
$553$	3.47251	−	2.91378i	0.147666	−	0.123906i
$554$	51.2418	+	18.6505i	2.17706	+	0.792384i
$555$		0			0
$556$	1.63915	+	9.29611i	0.0695156	+	0.394243i
$557$	−20.3389	+	7.40274i	−0.861785	+	0.313664i	−0.734836	−	0.678245i	$-0.762741\pi$
$557$	−20.3389	+	7.40274i	−0.861785	+	0.313664i	−0.126950	+	0.991909i	$0.540519\pi$
$558$	2.70590	−	4.68676i	0.114550	−	0.198407i
$559$	−2.21174	−	3.83085i	−0.0935467	−	0.162028i
$560$		0			0
$561$	0.514963	+	0.432105i	0.0217418	+	0.0182435i
$562$	−8.17427	−	14.1583i	−0.344811	−	0.597230i
$563$	−2.96419	+	5.13413i	−0.124926	+	0.216378i	−0.921704	−	0.387894i	$-0.873203\pi$
$563$	−2.96419	+	5.13413i	−0.124926	+	0.216378i	0.796778	+	0.604272i	$0.206536\pi$
$564$	−111.226	+	40.4830i	−4.68346	+	1.70464i
$565$		0			0
$566$	10.6308	−	60.2904i	0.446847	−	2.53420i
$567$	−83.4107	−	30.3590i	−3.50292	−	1.27496i
$568$	28.8585	−	24.2151i	1.21088	−	1.01605i
$569$	−5.27877			−0.221297			−0.110649	−	0.993860i	$-0.535293\pi$
$569$	−5.27877			−0.221297			−0.110649	+	0.993860i	$0.535293\pi$
$570$		0			0
$571$	16.5322			0.691852			0.345926	−	0.938262i	$-0.387565\pi$
$571$	16.5322			0.691852			0.345926	+	0.938262i	$0.387565\pi$
$572$	−0.962251	+	0.807424i	−0.0402337	+	0.0337601i
$573$	17.0636	+	6.21065i	0.712843	+	0.259454i
$574$	−3.12301	+	17.7115i	−0.130352	+	0.739263i
$575$		0			0
$576$	96.4654	−	35.1105i	4.01939	−	1.46294i
$577$	18.1317	−	31.4050i	0.754832	−	1.30741i	−0.190625	−	0.981663i	$-0.561052\pi$
$577$	18.1317	−	31.4050i	0.754832	−	1.30741i	0.945458	−	0.325745i	$-0.105615\pi$
$578$	−19.3229	−	33.4683i	−0.803728	−	1.39210i
$579$	−16.4094	−	13.7691i	−0.681950	−	0.572224i
$580$		0			0
$581$	19.5723	+	33.9003i	0.811998	+	1.40642i
$582$	46.1911	−	80.0054i	1.91468	−	3.31633i
$583$	2.22893	−	0.811263i	0.0923127	−	0.0335991i
$584$	3.53125	+	20.0267i	0.146124	+	0.828711i
$585$		0			0
$586$	−2.30975	−	0.840680i	−0.0954148	−	0.0347282i
$587$	20.4165	−	17.1315i	0.842680	−	0.707093i	−0.115485	−	0.993309i	$-0.536842\pi$
$587$	20.4165	−	17.1315i	0.842680	−	0.707093i	0.958165	+	0.286217i	$0.0923977\pi$
$588$	−17.5771			−0.724867
$589$	0.0539709	−	1.29655i	0.00222383	−	0.0534234i
$590$		0			0
$591$	−23.5481	+	19.7592i	−0.968640	+	0.812785i
$592$	−0.275734	−	0.100359i	−0.0113326	−	0.00412473i
$593$	4.80721	−	27.2630i	0.197408	−	1.11956i	−0.711539	−	0.702647i	$-0.752001\pi$
$593$	4.80721	−	27.2630i	0.197408	−	1.11956i	0.908947	−	0.416911i	$-0.136887\pi$
$594$	−3.75123	−	21.2743i	−0.153915	−	0.872895i
$595$		0			0
$596$	14.3652	−	24.8812i	0.588421	−	1.01918i
$597$	−40.1951	−	69.6199i	−1.64507	−	2.84935i
$598$	−4.84616	−	4.06641i	−0.198174	−	0.166288i
$599$	−26.3171	−	22.0826i	−1.07529	−	0.902272i	−0.0797652	−	0.996814i	$-0.525417\pi$
$599$	−26.3171	−	22.0826i	−1.07529	−	0.902272i	−0.995521	+	0.0945415i	$0.969862\pi$
$600$		0			0
$601$	−8.44516	+	14.6274i	−0.344485	+	0.596666i	−0.985260	−	0.171063i	$-0.945280\pi$
$601$	−8.44516	+	14.6274i	−0.344485	+	0.596666i	0.640775	+	0.767729i	$0.278613\pi$
$602$	41.7313	−	15.1890i	1.70084	−	0.619056i
$603$	4.59845	+	26.0791i	0.187263	+	1.06202i
$604$	4.71578	−	26.7445i	0.191882	−	1.08822i
$605$		0			0
$606$	−3.36977	+	2.82757i	−0.136887	+	0.114862i
$607$	4.71187			0.191249			0.0956245	−	0.995417i	$-0.469515\pi$
$607$	4.71187			0.191249			0.0956245	+	0.995417i	$0.469515\pi$
$608$	16.5024	−	18.0828i	0.669262	−	0.733356i
$609$	−29.2393			−1.18483
$610$		0			0
$611$	6.95008	+	2.52962i	0.281170	+	0.102338i
$612$	1.57359	−	8.92424i	0.0636084	−	0.360741i
$613$	7.12765	+	40.4229i	0.287883	+	1.63267i	0.694802	+	0.719201i	$0.255492\pi$
$613$	7.12765	+	40.4229i	0.287883	+	1.63267i	−0.406919	+	0.913464i	$0.633397\pi$
$614$	55.8842	−	20.3402i	2.25530	−	0.820864i
$615$		0			0
$616$	−2.41794	−	4.18800i	−0.0974216	−	0.168739i
$617$	4.96251	+	4.16404i	0.199783	+	0.167638i	0.737191	−	0.675685i	$-0.236152\pi$
$617$	4.96251	+	4.16404i	0.199783	+	0.167638i	−0.537408	+	0.843323i	$0.680596\pi$
$618$	37.5436	+	31.5028i	1.51022	+	1.26723i
$619$	18.3222	+	31.7349i	0.736429	+	1.27553i	0.954093	+	0.299509i	$0.0968230\pi$
$619$	18.3222	+	31.7349i	0.736429	+	1.27553i	−0.217664	+	0.976024i	$0.569844\pi$
$620$		0			0
$621$	63.2433	−	23.0187i	2.53787	−	0.923708i
$622$	−7.57557	−	42.9632i	−0.303753	−	1.72267i
$623$	−3.35379	+	19.0203i	−0.134367	+	0.762032i
$624$	0.0736049	+	0.0267900i	0.00294656	+	0.00107246i
$625$		0			0
$626$	−35.2637			−1.40942
$627$	−5.08244	−	6.59579i	−0.202973	−	0.263410i
$628$	51.4703			2.05389
$629$	2.23905	−	1.87879i	0.0892769	−	0.0749122i
$630$		0			0
$631$	−2.62539	+	14.8893i	−0.104515	+	0.592734i	0.886898	+	0.461965i	$0.152856\pi$
$631$	−2.62539	+	14.8893i	−0.104515	+	0.592734i	−0.991413	+	0.130769i	$0.958256\pi$
$632$	−0.762919	−	4.32673i	−0.0303473	−	0.172108i
$633$	74.4872	−	27.1111i	2.96060	−	1.07757i
$634$	−29.2433	+	50.6509i	−1.16140	+	2.01160i
$635$		0			0
$636$	−33.7509	−	28.3203i	−1.33831	−	1.12297i
$637$	0.841366	+	0.705990i	0.0333361	+	0.0279723i
$638$	−1.98932	−	3.44561i	−0.0787580	−	0.136413i
$639$	52.4905	−	90.9162i	2.07649	−	3.59659i
$640$		0			0
$641$	−1.83609	−	10.4130i	−0.0725210	−	0.411287i	−0.999358	−	0.0358234i	$-0.988595\pi$
$641$	−1.83609	−	10.4130i	−0.0725210	−	0.411287i	0.926837	−	0.375464i	$-0.122517\pi$
$642$	−24.1708	+	137.080i	−0.953946	+	5.41010i
$643$	−3.28323	−	1.19500i	−0.129478	−	0.0471261i	0.276469	−	0.961023i	$-0.410836\pi$
$643$	−3.28323	−	1.19500i	−0.129478	−	0.0471261i	−0.405946	+	0.913897i	$0.633058\pi$
$644$	30.0972	−	25.2545i	1.18599	−	0.995168i
$645$		0			0
$646$	−1.06306	−	3.34786i	−0.0418254	−	0.131720i
$647$	−21.5689			−0.847961			−0.423981	−	0.905671i	$-0.639368\pi$
$647$	−21.5689			−0.847961			−0.423981	+	0.905671i	$0.639368\pi$
$648$	−65.9036	+	55.2997i	−2.58894	+	2.17238i
$649$	0.331398	+	0.120619i	0.0130085	+	0.00473471i
$650$		0			0
$651$	−0.502513	−	2.84989i	−0.0196950	−	0.111696i
$652$	29.6376	−	10.7872i	1.16070	−	0.422459i
$653$	−13.9890	+	24.2297i	−0.547432	+	0.948181i	0.451017	+	0.892515i	$0.351061\pi$
$653$	−13.9890	+	24.2297i	−0.547432	+	0.948181i	−0.998449	+	0.0556654i	$0.982272\pi$
$654$	9.50371	+	16.4609i	0.371625	+	0.643673i
$655$		0			0
$656$	0.0723150	+	0.0606795i	0.00282343	+	0.00236914i
$657$	28.3347	+	49.0772i	1.10544	+	1.91468i
$658$	−37.1267	+	64.3053i	−1.44735	+	2.50688i
$659$	−5.32402	+	1.93779i	−0.207395	+	0.0754854i	−0.443629	−	0.896211i	$-0.646309\pi$
$659$	−5.32402	+	1.93779i	−0.207395	+	0.0754854i	0.236234	+	0.971696i	$0.424087\pi$
$660$		0			0
$661$	−0.0226150	+	0.128256i	−0.000879623	+	0.00498859i	−0.985244	−	0.171153i	$-0.945251\pi$
$661$	−0.0226150	+	0.128256i	−0.000879623	+	0.00498859i	0.984365	+	0.176142i	$0.0563618\pi$
$662$	9.75178	+	3.54936i	0.379014	+	0.137950i
$663$	−0.597696	+	0.501527i	−0.0232126	+	0.0194777i
$664$	37.9395			1.47234
$665$		0			0
$666$	−150.988			−5.85068
$667$	9.49542	−	7.96760i	0.367664	−	0.308507i
$668$	0.860080	+	0.313044i	0.0332775	+	0.0121120i
$669$	11.8129	−	66.9944i	0.456714	−	2.59015i
$670$		0			0
$671$	0.557385	−	0.202871i	0.0215176	−	0.00783177i
$672$	27.2968	−	47.2794i	1.05300	−	1.82384i
$673$	−20.7160	−	35.8812i	−0.798543	−	1.38312i	−0.920565	−	0.390590i	$-0.872271\pi$
$673$	−20.7160	−	35.8812i	−0.798543	−	1.38312i	0.122021	−	0.992528i	$-0.461062\pi$
$674$	35.6801	+	29.9391i	1.37434	+	1.15321i
$675$		0			0
$676$	20.3567	+	35.2589i	0.782951	+	1.35611i
$677$	9.63213	−	16.6833i	0.370193	−	0.641193i	−0.619402	−	0.785074i	$-0.712625\pi$
$677$	9.63213	−	16.6833i	0.370193	−	0.641193i	0.989595	+	0.143881i	$0.0459582\pi$
$678$	−80.6956	+	29.3708i	−3.09910	+	1.12798i
$679$	−6.22544	−	35.3062i	−0.238911	−	1.35493i
$680$		0			0
$681$	−39.4540	−	14.3601i	−1.51188	−	0.550279i
$682$	0.301647	−	0.253112i	0.0115507	−	0.00969216i
$683$	−14.0647			−0.538170			−0.269085	−	0.963116i	$-0.586721\pi$
$683$	−14.0647			−0.538170			−0.269085	+	0.963116i	$0.586721\pi$
$684$	−42.7445	+	103.790i	−1.63438	+	3.96851i
$685$		0			0
$686$	27.6439	−	23.1960i	1.05545	−	0.885626i
$687$	17.9018	+	6.51572i	0.682996	+	0.248590i
$688$	0.0404779	−	0.229561i	0.00154320	−	0.00875195i
$689$	0.478063	+	2.71123i	0.0182127	+	0.103290i
$690$		0			0
$691$	5.66284	−	9.80833i	0.215425	−	0.373126i	−0.737979	−	0.674823i	$-0.764220\pi$
$691$	5.66284	−	9.80833i	0.215425	−	0.373126i	0.953404	+	0.301697i	$0.0975531\pi$
$692$	24.5388	+	42.5025i	0.932825	+	1.61570i
$693$	−10.3234	−	8.66232i	−0.392152	−	0.329054i
$694$	47.8311	+	40.1350i	1.81564	+	1.52350i
$695$		0			0
$696$	−14.1695	+	24.5423i	−0.537094	+	0.930275i
$697$	−0.883620	+	0.321612i	−0.0334695	+	0.0121819i
$698$	−5.01924	−	28.4655i	−0.189981	−	1.07744i
$699$	−1.59572	+	9.04980i	−0.0603558	+	0.342295i
$700$		0			0
$701$	−11.8225	+	9.92029i	−0.446531	+	0.374684i	−0.838147	−	0.545445i	$-0.816361\pi$
$701$	−11.8225	+	9.92029i	−0.446531	+	0.374684i	0.391615	+	0.920129i	$0.371916\pi$
$702$	25.0731			0.946323
$703$	−32.0800	+	16.7827i	−1.20992	+	0.632972i
$704$	7.46945			0.281516
$705$		0			0
$706$	−66.2756	−	24.1224i	−2.49432	−	0.907857i
$707$	−0.296434	+	1.68116i	−0.0111485	+	0.0632265i
$708$	−1.13751	−	6.45114i	−0.0427503	−	0.242449i
$709$	−17.9320	+	6.52671i	−0.673450	+	0.245116i	−0.656033	−	0.754733i	$-0.727767\pi$
$709$	−17.9320	+	6.52671i	−0.673450	+	0.245116i	−0.0174175	+	0.999848i	$0.505544\pi$
$710$		0			0
$711$	−6.12166	−	10.6030i	−0.229580	−	0.397644i
$712$	14.3397	+	12.0324i	0.537401	+	0.450933i
$713$	0.939777	+	0.788566i	0.0351949	+	0.0295320i
$714$	−3.91660	−	6.78374i	−0.146575	−	0.253875i
$715$		0			0
$716$	44.0582	−	16.0359i	1.64653	−	0.599289i
$717$	−11.1753	−	63.3782i	−0.417349	−	2.36690i
$718$	6.85407	−	38.8714i	0.255792	−	1.45067i
$719$	10.7312	+	3.90584i	0.400207	+	0.145663i	0.534279	−	0.845308i	$-0.320583\pi$
$719$	10.7312	+	3.90584i	0.400207	+	0.145663i	−0.134072	+	0.990972i	$0.542805\pi$
$720$		0			0
$721$	19.0192			0.708314
$722$	3.96810	+	43.3281i	0.147677	+	1.61250i
$723$	23.9437			0.890475
$724$	−17.3078	+	14.5230i	−0.643239	+	0.539742i
$725$		0			0
$726$	−14.0278	+	79.5558i	−0.520622	+	2.95259i
$727$	1.89714	+	10.7592i	0.0703609	+	0.399036i	0.999566	+	0.0294711i	$0.00938231\pi$
$727$	1.89714	+	10.7592i	0.0703609	+	0.399036i	−0.929205	+	0.369565i	$0.879507\pi$
$728$	5.27432	−	1.91969i	0.195479	−	0.0711486i
$729$	−38.8479	+	67.2865i	−1.43881	+	2.49209i
$730$		0			0
$731$	1.77872	+	1.49252i	0.0657883	+	0.0552029i
$732$	−8.44003	−	7.08203i	−0.311953	−	0.261759i
$733$	11.7865	+	20.4147i	0.435343	+	0.754036i	0.997324	−	0.0731146i	$-0.0232939\pi$
$733$	11.7865	+	20.4147i	0.435343	+	0.754036i	−0.561981	+	0.827150i	$0.689961\pi$
$734$	34.4568	−	59.6810i	1.27182	−	2.20286i
$735$		0			0
$736$	4.01888	+	22.7922i	0.148138	+	0.840132i
$737$	−0.334591	+	1.89756i	−0.0123248	+	0.0698975i
$738$	45.6456	+	16.6136i	1.68024	+	0.611557i
$739$	−1.72100	+	1.44409i	−0.0633081	+	0.0531218i	−0.673893	−	0.738829i	$-0.735379\pi$
$739$	−1.72100	+	1.44409i	−0.0633081	+	0.0531218i	0.610585	+	0.791951i	$0.290935\pi$
$740$		0			0
$741$	8.56350	−	4.48000i	0.314588	−	0.164577i
$742$	−27.6393			−1.01467
$743$	20.6210	−	17.3031i	0.756511	−	0.634788i	−0.180705	−	0.983537i	$-0.557838\pi$
$743$	20.6210	−	17.3031i	0.756511	−	0.634788i	0.937216	+	0.348750i	$0.113394\pi$
$744$	−2.63561	−	0.959285i	−0.0966263	−	0.0351691i
$745$		0			0
$746$	−2.43899	−	13.8322i	−0.0892976	−	0.506432i
$747$	99.3502	−	36.1605i	3.63503	−	1.32304i
$748$	0.329680	−	0.571023i	0.0120543	−	0.0208787i
$749$	27.0086	+	46.7803i	0.986874	+	1.70932i
$750$		0			0
$751$	−26.1495	−	21.9420i	−0.954209	−	0.800676i	0.0257926	−	0.999667i	$-0.491789\pi$
$751$	−26.1495	−	21.9420i	−0.954209	−	0.800676i	−0.980001	+	0.198991i	$0.936234\pi$
$752$	0.194876	+	0.337534i	0.00710638	+	0.0123086i
$753$	24.5664	−	42.5502i	0.895248	−	1.55062i
$754$	4.33935	−	1.57940i	0.158030	−	0.0575182i
$755$		0			0
$756$	−27.0400	+	153.351i	−0.983434	+	5.57733i
$757$	17.7079	+	6.44514i	0.643604	+	0.234253i	0.643142	−	0.765747i	$-0.277631\pi$
$757$	17.7079	+	6.44514i	0.643604	+	0.234253i	0.000462353		1.00000i	$0.499853\pi$
$758$	−54.1979	+	45.4775i	−1.96856	+	1.65182i
$759$	7.87198			0.285735
$760$		0			0
$761$	−10.8012			−0.391544			−0.195772	−	0.980649i	$-0.562721\pi$
$761$	−10.8012			−0.391544			−0.195772	+	0.980649i	$0.562721\pi$
$762$	−111.347	+	93.4315i	−4.03369	+	3.38467i
$763$	6.93139	+	2.52282i	0.250933	+	0.0913322i
$764$	3.09283	−	17.5403i	0.111895	−	0.634587i
$765$		0			0
$766$	−10.0087	+	3.64286i	−0.361628	+	0.131622i
$767$	−0.204663	+	0.354486i	−0.00738994	+	0.0127998i
$768$	−26.8354	−	46.4802i	−0.968338	−	1.67721i
$769$	37.4804	+	31.4498i	1.35158	+	1.13411i	0.978486	+	0.206313i	$0.0661464\pi$
$769$	37.4804	+	31.4498i	1.35158	+	1.13411i	0.373091	+	0.927795i	$0.378298\pi$
$770$		0			0
$771$	−32.6692	−	56.5847i	−1.17655	−	2.03785i
$772$	−10.5053	+	18.1957i	−0.378094	+	0.654878i
$773$	−25.1420	+	9.15095i	−0.904296	+	0.329137i	−0.751973	−	0.659194i	$-0.770898\pi$
$773$	−25.1420	+	9.15095i	−0.904296	+	0.329137i	−0.152323	+	0.988331i	$0.548675\pi$
$774$	−20.8284	−	118.124i	−0.748662	−	4.24588i
$775$		0			0
$776$	−32.6516	−	11.8842i	−1.17212	−	0.426619i
$777$	−61.8489	+	51.8974i	−2.21882	+	1.86181i
$778$	37.0448			1.32812
$779$	11.5448	−	1.54376i	0.413636	−	0.0553110i
$780$		0			0
$781$	5.85150	−	4.91000i	0.209383	−	0.175693i
$782$	3.12046	+	1.13575i	0.111587	+	0.0406145i
$783$	−8.53090	+	48.3811i	−0.304869	+	1.72900i
$784$	0.0100504	+	0.0569988i	0.000358944	+	0.00203567i
$785$		0			0
$786$	25.9404	−	44.9301i	0.925263	−	1.60260i
$787$	10.9173	+	18.9093i	0.389160	+	0.674045i	0.992337	−	0.123563i	$-0.0394321\pi$
$787$	10.9173	+	18.9093i	0.389160	+	0.674045i	−0.603177	+	0.797607i	$0.706099\pi$
$788$	23.0971	+	19.3807i	0.822799	+	0.690410i
$789$	30.0257	+	25.1945i	1.06894	+	0.896949i
$790$		0			0
$791$	−16.6627	+	28.8607i	−0.592458	+	1.02617i
$792$	−12.2736	+	4.46722i	−0.436123	+	0.158736i
$793$	0.119548	+	0.677993i	0.00424529	+	0.0240762i
$794$	−3.95066	+	22.4053i	−0.140204	+	0.795135i
$795$		0			0
$796$	−60.4029	+	50.6840i	−2.14092	+	1.79645i
$797$	13.0244			0.461347			0.230673	−	0.973031i	$-0.425907\pi$
$797$	13.0244			0.461347			0.230673	+	0.973031i	$0.425907\pi$
$798$	29.3646	+	92.4773i	1.03949	+	3.27366i
$799$	−3.88234			−0.137347
$800$		0			0
$801$	49.0187	+	17.8413i	1.73199	+	0.630393i
$802$	5.14319	−	29.1685i	0.181612	−	1.02997i
$803$	0.716015	+	4.06072i	0.0252676	+	0.143300i
$804$	33.6318	−	12.2410i	1.18610	−	0.431706i
$805$		0			0
$806$	0.228518	+	0.395804i	0.00804919	+	0.0139416i
$807$	27.5543	+	23.1208i	0.969959	+	0.813892i
$808$	1.26745	+	1.06351i	0.0445886	+	0.0374143i
$809$	4.51134	+	7.81388i	0.158610	+	0.274721i	0.934368	−	0.356310i	$-0.115965\pi$
$809$	4.51134	+	7.81388i	0.158610	+	0.274721i	−0.775757	+	0.631031i	$0.782632\pi$
$810$		0			0
$811$	21.0062	−	7.64565i	0.737629	−	0.268475i	0.0542386	−	0.998528i	$-0.482727\pi$
$811$	21.0062	−	7.64565i	0.737629	−	0.268475i	0.683391	+	0.730053i	$0.260505\pi$
$812$	4.98009	+	28.2435i	0.174767	+	0.991153i
$813$	3.37259	−	19.1269i	0.118282	−	0.670810i
$814$	−10.3236	−	3.75749i	−0.361843	−	0.131700i
$815$		0			0
$816$	−0.0411159			−0.00143934
$817$	−17.5551	−	22.7823i	−0.614175	−	0.797052i
$818$	14.2901			0.499642
$819$	11.9819	−	10.0540i	0.418681	−	0.351315i
$820$		0			0
$821$	−6.05598	+	34.3451i	−0.211355	+	1.19865i	0.675766	+	0.737116i	$0.263813\pi$
$821$	−6.05598	+	34.3451i	−0.211355	+	1.19865i	−0.887121	+	0.461537i	$0.847298\pi$
$822$	−17.4148	−	98.7645i	−0.607412	−	3.44481i
$823$	−4.74344	+	1.72647i	−0.165346	+	0.0601809i	−0.423367	−	0.905958i	$-0.639152\pi$
$823$	−4.74344	+	1.72647i	−0.165346	+	0.0601809i	0.258021	+	0.966139i	$0.416930\pi$
$824$	9.21684	−	15.9640i	0.321084	−	0.556134i
$825$		0			0
$826$	−3.14800	−	2.64149i	−0.109533	−	0.0919090i
$827$	−38.4862	−	32.2938i	−1.33830	−	1.12296i	−0.982060	−	0.188569i	$-0.939615\pi$
$827$	−38.4862	−	32.2938i	−1.33830	−	1.12296i	−0.356237	−	0.934395i	$-0.615941\pi$
$828$	−53.0581	−	91.8993i	−1.84390	−	3.19372i
$829$	−8.13553	+	14.0911i	−0.282559	+	0.489406i	−0.972014	−	0.234922i	$-0.924516\pi$
$829$	−8.13553	+	14.0911i	−0.282559	+	0.489406i	0.689456	+	0.724328i	$0.257850\pi$
$830$		0			0
$831$	−13.6758	−	77.5595i	−0.474409	−	2.69051i
$832$	−1.50544	+	8.53778i	−0.0521918	+	0.295994i
$833$	−0.541758	−	0.197184i	−0.0187708	−	0.00683201i
$834$	16.8823	−	14.1659i	0.584587	−	0.490527i
$835$		0			0
$836$	−5.50551	+	6.03276i	−0.190412	+	0.208648i
$837$	−4.86222			−0.168063
$838$	53.5743	−	44.9542i	1.85069	−	1.55292i
$839$	20.3201	+	7.39592i	0.701528	+	0.255335i	0.668063	−	0.744105i	$-0.267124\pi$
$839$	20.3201	+	7.39592i	0.701528	+	0.255335i	0.0334650	+	0.999440i	$0.489346\pi$
$840$		0			0
$841$	−3.46462	−	19.6488i	−0.119470	−	0.677545i
$842$	78.6926	−	28.6418i	2.71193	−	0.987061i
$843$	−11.8058	+	20.4482i	−0.406612	+	0.704272i
$844$	−38.8746	−	67.3329i	−1.33812	−	2.31769i
$845$		0			0
$846$	153.631	+	128.912i	5.28196	+	4.43209i
$847$	15.6748	+	27.1495i	0.538592	+	0.932869i
$848$	−0.0725383	+	0.125640i	−0.00249098	+	0.00431450i
$849$	−83.0858	+	30.2408i	−2.85150	+	1.03786i
$850$		0			0
$851$	5.94350	−	33.7072i	0.203740	−	1.15547i
$852$	−133.328	−	48.5273i	−4.56773	−	1.66252i
$853$	30.2607	−	25.3918i	1.03611	−	0.869397i	0.0445424	−	0.999007i	$-0.485817\pi$
$853$	30.2607	−	25.3918i	1.03611	−	0.869397i	0.991565	+	0.129610i	$0.0413726\pi$
$854$	−6.91172			−0.236514
$855$		0			0
$856$	52.3542			1.78943
$857$	9.54432	−	8.00863i	0.326028	−	0.273570i	−0.465051	−	0.885284i	$-0.653964\pi$
$857$	9.54432	−	8.00863i	0.326028	−	0.273570i	0.791079	+	0.611714i	$0.209520\pi$
$858$	2.75581	+	1.00303i	0.0940817	+	0.0342429i
$859$	5.73773	−	32.5403i	0.195769	−	1.11026i	−0.715551	−	0.698561i	$-0.753824\pi$
$859$	5.73773	−	32.5403i	0.195769	−	1.11026i	0.911319	−	0.411700i	$-0.135065\pi$
$860$		0			0
$861$	24.4081	−	8.88381i	0.831825	−	0.302759i
$862$	27.3689	−	47.4044i	0.932189	−	1.61460i
$863$	−4.43310	−	7.67835i	−0.150904	−	0.261374i	0.780656	−	0.624961i	$-0.214885\pi$
$863$	−4.43310	−	7.67835i	−0.150904	−	0.261374i	−0.931560	+	0.363587i	$0.881552\pi$
$864$	−70.2673	−	58.9612i	−2.39054	−	2.00590i
$865$		0			0
$866$	16.7791	+	29.0622i	0.570176	+	0.987573i
$867$	−27.9073	+	48.3368i	−0.947781	+	1.64161i
$868$	−2.66725	+	0.970799i	−0.0905323	+	0.0329511i
$869$	−0.154694	−	0.877311i	−0.00524762	−	0.0297607i
$870$		0			0
$871$	−2.10152	−	0.764892i	−0.0712074	−	0.0259174i
$872$	5.47656	−	4.59538i	0.185460	−	0.155619i
$873$	−96.8300			−3.27720
$874$	−34.7359	−	22.0302i	−1.17496	−	0.745181i
$875$		0			0
$876$	58.6715	−	49.2312i	1.98232	−	1.66337i
$877$	10.4313	+	3.79669i	0.352241	+	0.128205i	0.512080	−	0.858938i	$-0.328875\pi$
$877$	10.4313	+	3.79669i	0.352241	+	0.128205i	−0.159839	+	0.987143i	$0.551097\pi$
$878$	6.76972	−	38.3930i	0.228467	−	1.29570i
$879$	0.616444	+	3.49603i	0.0207921	+	0.117918i
$880$		0			0
$881$	−20.9588	+	36.3016i	−0.706119	+	1.22303i	0.260168	+	0.965563i	$0.416222\pi$
$881$	−20.9588	+	36.3016i	−0.706119	+	1.22303i	−0.966286	+	0.257470i	$0.917111\pi$
$882$	14.8910	+	25.7919i	0.501405	+	0.868458i
$883$	−20.3742	−	17.0960i	−0.685646	−	0.575325i	0.232004	−	0.972715i	$-0.425472\pi$
$883$	−20.3742	−	17.0960i	−0.685646	−	0.575325i	−0.917650	+	0.397390i	$0.869916\pi$
$884$	0.586248	+	0.491921i	0.0197177	+	0.0165451i
$885$		0			0
$886$	41.2094	−	71.3768i	1.38446	−	2.39795i
$887$	19.5566	−	7.11802i	0.656646	−	0.239000i	0.00785834	−	0.999969i	$-0.497499\pi$
$887$	19.5566	−	7.11802i	0.656646	−	0.239000i	0.648788	+	0.760970i	$0.275276\pi$
$888$	13.5884	+	77.0634i	0.455996	+	2.58608i
$889$	−9.79506	+	55.5506i	−0.328516	+	1.86311i
$890$		0			0
$891$	−13.3630	+	11.2129i	−0.447676	+	0.375645i
$892$	−66.7249			−2.23412
$893$	46.9705	+	10.3131i	1.57181	+	0.345114i
$894$	−67.0764			−2.24337
$895$		0			0
$896$	−50.7654	−	18.4771i	−1.69595	−	0.617276i
$897$	−1.58657	+	8.99787i	−0.0529739	+	0.300430i
$898$	−1.41470	−	8.02315i	−0.0472091	−	0.267736i
$899$	−0.841496	+	0.306280i	−0.0280655	+	0.0102150i
$900$		0			0
$901$	−0.722559	−	1.25151i	−0.0240719	−	0.0416938i
$902$	2.70751	+	2.27187i	0.0901502	+	0.0756450i
$903$	−49.1332	−	41.2276i	−1.63505	−	1.37197i
$904$	16.1497	+	27.9721i	0.537131	+	0.930338i
$905$		0			0
$906$	−59.5796	+	21.6852i	−1.97940	+	0.720443i
$907$	0.139827	+	0.792997i	0.00464287	+	0.0263310i	0.987041	−	0.160467i	$-0.0513001\pi$
$907$	0.139827	+	0.792997i	0.00464287	+	0.0263310i	−0.982398	+	0.186798i	$0.940189\pi$
$908$	−7.15115	+	40.5562i	−0.237319	+	1.34590i
$909$	4.33264	+	1.57695i	0.143705	+	0.0523042i
$910$		0			0
$911$	33.6958			1.11639			0.558196	−	0.829709i	$-0.311494\pi$
$911$	33.6958			1.11639			0.558196	+	0.829709i	$0.311494\pi$
$912$	0.497441	+	0.109221i	0.0164719	+	0.00361666i
$913$	7.69283			0.254595
$914$	−8.09913	+	6.79598i	−0.267895	+	0.224791i
$915$		0			0
$916$	3.24475	−	18.4019i	0.107210	−	0.608016i
$917$	−3.49613	−	19.8276i	−0.115453	−	0.654764i
$918$	−12.3675	+	4.50141i	−0.408189	+	0.148569i
$919$	7.14677	−	12.3786i	0.235750	−	0.408331i	−0.723740	−	0.690072i	$-0.757579\pi$
$919$	7.14677	−	12.3786i	0.235750	−	0.408331i	0.959490	+	0.281741i	$0.0909120\pi$
$920$		0			0
$921$	−65.7964	−	55.2097i	−2.16806	−	1.81922i
$922$	51.1770	+	42.9426i	1.68542	+	1.41424i
$923$	4.43290	+	7.67801i	0.145911	+	0.252725i
$924$	−9.10669	+	15.7733i	−0.299588	+	0.518902i
$925$		0			0
$926$	−7.01363	−	39.7763i	−0.230482	−	1.30713i
$927$	8.92017	−	50.5888i	0.292977	−	1.66155i
$928$	−15.8751	−	5.77806i	−0.521125	−	0.189674i
$929$	11.3513	−	9.52484i	0.372423	−	0.312500i	−0.437296	−	0.899317i	$-0.644064\pi$
$929$	11.3513	−	9.52484i	0.372423	−	0.312500i	0.809719	+	0.586818i	$0.199619\pi$
$930$		0			0
$931$	6.03067	+	3.82476i	0.197647	+	0.125352i
$932$	9.01339			0.295244
$933$	−48.2663	+	40.5002i	−1.58017	+	1.32592i
$934$	−36.4602	−	13.2704i	−1.19301	−	0.434221i
$935$		0			0
$936$	−2.63245	−	14.9294i	−0.0860444	−	0.487982i
$937$	−45.6316	+	16.6085i	−1.49072	+	0.542577i	−0.953639	−	0.300954i	$-0.902695\pi$
$937$	−45.6316	+	16.6085i	−1.49072	+	0.542577i	−0.537080	+	0.843531i	$0.680473\pi$
$938$	11.2261	−	19.4442i	0.366546	−	0.634877i
$939$	25.4650	+	44.1066i	0.831017	+	1.43936i
$940$		0			0
$941$	14.5770	+	12.2315i	0.475195	+	0.398736i	0.848685	−	0.528898i	$-0.177395\pi$
$941$	14.5770	+	12.2315i	0.475195	+	0.398736i	−0.373490	+	0.927634i	$0.621839\pi$
$942$	−60.0835	−	104.068i	−1.95763	−	3.39071i
$943$	−5.50569	+	9.53613i	−0.179290	+	0.310539i
$944$	−0.0202693	+	0.00737740i	−0.000659708	+	0.000240114i
$945$		0			0
$946$	1.51551	−	8.59490i	0.0492736	−	0.279444i
$947$	−38.1018	−	13.8679i	−1.23814	−	0.450646i	−0.361763	−	0.932270i	$-0.617825\pi$
$947$	−38.1018	−	13.8679i	−1.23814	−	0.450646i	−0.876378	+	0.481624i	$0.840047\pi$
$948$	−12.6758	+	10.6363i	−0.411692	+	0.345451i
$949$	−4.78582			−0.155354
$950$		0			0
$951$	84.4697			2.73912
$952$	−2.25696	+	1.89381i	−0.0731484	+	0.0613788i
$953$	−35.5481	−	12.9385i	−1.15152	−	0.419118i	−0.305457	−	0.952206i	$-0.598809\pi$
$953$	−35.5481	−	12.9385i	−1.15152	−	0.419118i	−0.846060	+	0.533088i	$0.821032\pi$
$954$	−12.9630	+	73.5170i	−0.419694	+	2.38020i
$955$		0			0
$956$	−59.3164	+	21.5894i	−1.91843	+	0.698251i
$957$	−2.87309	+	4.97634i	−0.0928738	+	0.160862i
$958$	−16.5579	−	28.6792i	−0.534962	−	0.926582i
$959$	−29.8136	−	25.0166i	−0.962732	−	0.807828i
$960$		0			0
$961$	15.4557	+	26.7700i	0.498570	+	0.863549i
$962$	6.37560	−	11.0429i	0.205558	−	0.356036i
$963$	137.097	−	49.8993i	4.41789	−	1.60798i
$964$	−4.07814	−	23.1283i	−0.131348	−	0.744911i
$965$		0			0
$966$	−86.1958	−	31.3727i	−2.77330	−	1.00940i
$967$	−21.5070	+	18.0465i	−0.691618	+	0.580336i	−0.919375	−	0.393382i	$-0.871305\pi$
$967$	−21.5070	+	18.0465i	−0.691618	+	0.580336i	0.227758	+	0.973718i	$0.426861\pi$
$968$	30.3844			0.976591
$969$	−3.41972	+	3.74722i	−0.109857	+	0.120378i
$970$		0			0
$971$	−26.9547	+	22.6176i	−0.865016	+	0.725835i	−0.963043	−	0.269349i	$-0.913191\pi$
$971$	−26.9547	+	22.6176i	−0.865016	+	0.725835i	0.0980264	+	0.995184i	$0.468747\pi$
$972$	155.120	+	56.4590i	4.97548	+	1.81092i
$973$	1.48511	−	8.42250i	0.0476106	−	0.270013i
$974$	−0.131992	−	0.748566i	−0.00422931	−	0.0239856i
$975$		0			0
$976$	−0.0181396	+	0.0314187i	−0.000580633	+	0.00100569i
$977$	26.6516	+	46.1619i	0.852659	+	1.47685i	0.878799	+	0.477191i	$0.158345\pi$
$977$	26.6516	+	46.1619i	0.852659	+	1.47685i	−0.0261400	+	0.999658i	$0.508322\pi$
$978$	−56.4079	−	47.3318i	−1.80372	−	1.51350i
$979$	2.90759	+	2.43976i	0.0929269	+	0.0779749i
$980$		0			0
$981$	9.96127	−	17.2534i	0.318039	−	0.550859i
$982$	−7.19127	+	2.61741i	−0.229483	+	0.0835249i
$983$	8.82370	+	50.0417i	0.281432	+	1.59608i	0.717757	+	0.696293i	$0.245169\pi$
$983$	8.82370	+	50.0417i	0.281432	+	1.59608i	−0.436325	+	0.899789i	$0.643720\pi$
$984$	4.37156	−	24.7924i	0.139360	−	0.790352i
$985$		0			0
$986$	−1.85687	+	1.55810i	−0.0591349	+	0.0496200i
$987$	107.241			3.41352
$988$	−5.78599	−	7.50883i	−0.184077	−	0.238888i
$989$	27.1903			0.864603
$990$		0			0
$991$	52.8203	+	19.2250i	1.67789	+	0.610703i	0.993018	−	0.117960i	$-0.0376354\pi$
$991$	52.8203	+	19.2250i	1.67789	+	0.610703i	0.684873	+	0.728662i	$0.259858\pi$
$992$	0.290343	−	1.64662i	0.00921840	−	0.0522801i
$993$	−2.60263	−	14.7603i	−0.0825920	−	0.468403i
$994$	−83.6404	+	30.4426i	−2.65291	+	0.965581i
$995$		0			0
$996$	−71.4458	−	123.748i	−2.26385	−	3.92110i
$997$	−28.7054	−	24.0867i	−0.909110	−	0.762834i	0.0628394	−	0.998024i	$-0.479984\pi$
$997$	−28.7054	−	24.0867i	−0.909110	−	0.762834i	−0.971949	+	0.235190i	$0.924429\pi$
$998$	24.7194	+	20.7420i	0.782479	+	0.656578i
$999$	67.8275	+	117.481i	2.14597	+	3.71693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.l.c.101.1		18
5.2	odd	4		475.2.u.b.424.1		36
5.3	odd	4		475.2.u.b.424.6		36
5.4	even	2		95.2.k.a.6.3	✓	18
15.14	odd	2		855.2.bs.c.766.1		18
19.4	even	9		9025.2.a.cc.1.2		9
19.15	odd	18		9025.2.a.cf.1.8		9
19.16	even	9	inner	475.2.l.c.301.1		18
95.4	even	18		1805.2.a.v.1.8		9
95.34	odd	18		1805.2.a.s.1.2		9
95.54	even	18		95.2.k.a.16.3	yes	18
95.73	odd	36		475.2.u.b.149.1		36
95.92	odd	36		475.2.u.b.149.6		36
285.149	odd	18		855.2.bs.c.586.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.6.3	✓	18	5.4	even	2
95.2.k.a.16.3	yes	18	95.54	even	18
475.2.l.c.101.1		18	1.1	even	1	trivial
475.2.l.c.301.1		18	19.16	even	9	inner
475.2.u.b.149.1		36	95.73	odd	36
475.2.u.b.149.6		36	95.92	odd	36
475.2.u.b.424.1		36	5.2	odd	4
475.2.u.b.424.6		36	5.3	odd	4
855.2.bs.c.586.1		18	285.149	odd	18
855.2.bs.c.766.1		18	15.14	odd	2
1805.2.a.s.1.2		9	95.34	odd	18
1805.2.a.v.1.8		9	95.4	even	18
9025.2.a.cc.1.2		9	19.4	even	9
9025.2.a.cf.1.8		9	19.15	odd	18

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.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.75422 + 1.47196i) q^{2} +(3.10785 + 1.13116i) q^{3} +(0.563307 - 3.19467i) q^{4} +(-7.11687 + 2.59033i) q^{6} +(-1.46955 + 2.54534i) q^{7} +(1.42431 + 2.46697i) q^{8} +(6.08105 + 5.10261i) q^{9} +O(q^{10})\)	\(q+(-1.75422 + 1.47196i) q^{2} +(3.10785 + 1.13116i) q^{3} +(0.563307 - 3.19467i) q^{4} +(-7.11687 + 2.59033i) q^{6} +(-1.46955 + 2.54534i) q^{7} +(1.42431 + 2.46697i) q^{8} +(6.08105 + 5.10261i) q^{9} +(0.288800 + 0.500217i) q^{11} +(5.36437 - 9.29136i) q^{12} +(-0.629967 + 0.229289i) q^{13} +(-1.16873 - 6.62820i) q^{14} +(-0.0331972 - 0.0120828i) q^{16} +(0.269572 - 0.226198i) q^{17} -18.1783 q^{18} +(-3.86230 + 2.02056i) q^{19} +(-7.44633 + 6.24822i) q^{21} +(-1.24292 - 0.452386i) q^{22} +(0.715571 - 4.05820i) q^{23} +(1.63598 + 9.27810i) q^{24} +(0.767594 - 1.32951i) q^{26} +(8.16613 + 14.1442i) q^{27} +(7.30371 + 6.12854i) q^{28} +(2.30426 + 1.93351i) q^{29} +(-0.148853 + 0.257821i) q^{31} +(-5.27762 + 1.92090i) q^{32} +(0.331720 + 1.88128i) q^{33} +(-0.139933 + 0.793600i) q^{34} +(19.7266 - 16.5526i) q^{36} +8.30595 q^{37} +(3.80111 - 9.22966i) q^{38} -2.21721 q^{39} +(-2.51099 - 0.913926i) q^{41} +(3.86534 - 21.9215i) q^{42} +(1.14578 + 6.49806i) q^{43} +(1.76071 - 0.640846i) q^{44} +(4.71826 + 8.17226i) q^{46} +(-8.45135 - 7.09153i) q^{47} +(-0.0895041 - 0.0751029i) q^{48} +(-0.819160 - 1.41883i) q^{49} +(1.09366 - 0.398058i) q^{51} +(0.377639 + 2.14170i) q^{52} +(0.713104 - 4.04421i) q^{53} +(-35.1449 - 12.7917i) q^{54} -8.37237 q^{56} +(-14.2890 + 1.91071i) q^{57} -6.88822 q^{58} +(0.467725 - 0.392468i) q^{59} +(0.178325 - 1.01133i) q^{61} +(-0.118383 - 0.671381i) q^{62} +(-21.9243 + 7.97978i) q^{63} +(6.46593 - 11.1993i) q^{64} +(-3.35108 - 2.81189i) q^{66} +(2.55547 + 2.14429i) q^{67} +(-0.570776 - 0.988612i) q^{68} +(6.81438 - 11.8028i) q^{69} +(-2.29645 - 13.0238i) q^{71} +(-3.92671 + 22.2695i) q^{72} +(6.70827 + 2.44161i) q^{73} +(-14.5704 + 12.2261i) q^{74} +(4.27938 + 13.4770i) q^{76} -1.69763 q^{77} +(3.88946 - 3.26364i) q^{78} +(-1.44931 - 0.527504i) q^{79} +(5.24435 + 29.7422i) q^{81} +(5.75009 - 2.09286i) q^{82} +(6.65930 - 11.5342i) q^{83} +(15.7664 + 27.3082i) q^{84} +(-11.5749 - 9.71246i) q^{86} +(4.97418 + 8.61554i) q^{87} +(-0.822680 + 1.42492i) q^{88} +(6.17500 - 2.24752i) q^{89} +(0.342150 - 1.94043i) q^{91} +(-12.5615 - 4.57203i) q^{92} +(-0.754252 + 0.632892i) q^{93} +25.2640 q^{94} -18.5749 q^{96} +(-9.34414 + 7.84066i) q^{97} +(3.52545 + 1.28316i) q^{98} +(-0.796200 + 4.51548i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9	\( 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9} + 18 q^{12} + 3 q^{13} - 12 q^{14} - 3 q^{16} - 24 q^{17} - 48 q^{18} - 21 q^{21} - 9 q^{22} + 9 q^{23} - 15 q^{24} + 3 q^{26} + 24 q^{27} + 12 q^{28} + 15 q^{29} - 18 q^{31} - 15 q^{32} + 33 q^{33} - 12 q^{34} + 75 q^{36} - 36 q^{37} + 33 q^{38} + 36 q^{39} - 30 q^{41} + 9 q^{42} + 36 q^{43} + 42 q^{44} + 9 q^{46} - 21 q^{47} - 33 q^{48} + 9 q^{49} - 45 q^{51} + 39 q^{52} + 12 q^{53} - 66 q^{54} - 72 q^{57} - 12 q^{58} + 18 q^{59} - 30 q^{61} + 24 q^{62} - 54 q^{63} + 36 q^{64} + 39 q^{66} - 51 q^{68} + 15 q^{69} - 12 q^{71} + 66 q^{72} - 24 q^{73} - 15 q^{74} - 33 q^{76} + 60 q^{77} + 48 q^{78} - 51 q^{79} + 27 q^{81} + 15 q^{82} + 48 q^{84} + 63 q^{86} + 15 q^{87} + 27 q^{88} - 54 q^{89} + 30 q^{91} + 42 q^{92} - 72 q^{93} + 30 q^{94} - 66 q^{96} - 27 q^{97} + 3 q^{98} - 93 q^{99}+O(q^{100}) \) 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9 + 18 * q^12 + 3 * q^13 - 12 * q^14 - 3 * q^16 - 24 * q^17 - 48 * q^18 - 21 * q^21 - 9 * q^22 + 9 * q^23 - 15 * q^24 + 3 * q^26 + 24 * q^27 + 12 * q^28 + 15 * q^29 - 18 * q^31 - 15 * q^32 + 33 * q^33 - 12 * q^34 + 75 * q^36 - 36 * q^37 + 33 * q^38 + 36 * q^39 - 30 * q^41 + 9 * q^42 + 36 * q^43 + 42 * q^44 + 9 * q^46 - 21 * q^47 - 33 * q^48 + 9 * q^49 - 45 * q^51 + 39 * q^52 + 12 * q^53 - 66 * q^54 - 72 * q^57 - 12 * q^58 + 18 * q^59 - 30 * q^61 + 24 * q^62 - 54 * q^63 + 36 * q^64 + 39 * q^66 - 51 * q^68 + 15 * q^69 - 12 * q^71 + 66 * q^72 - 24 * q^73 - 15 * q^74 - 33 * q^76 + 60 * q^77 + 48 * q^78 - 51 * q^79 + 27 * q^81 + 15 * q^82 + 48 * q^84 + 63 * q^86 + 15 * q^87 + 27 * q^88 - 54 * q^89 + 30 * q^91 + 42 * q^92 - 72 * q^93 + 30 * q^94 - 66 * q^96 - 27 * q^97 + 3 * q^98 - 93 * q^99

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