LMFDB - Embedded newform 930.2.h.c.371.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(371,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("930.371");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.h (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} + 10x^{12} - 42x^{10} + 82x^{8} - 378x^{6} + 810x^{4} - 1458x^{2} + 6561 $ x^16 - 2x^14 + 10x^12 - 42x^10 + 82x^8 - 378x^6 + 810x^4 - 1458*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			371.3
Root			$1.39665 + 1.02439i$ of defining polynomial
Character	$\chi$	$=$	930.371
Dual form			930.2.h.c.371.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.02439 + 1.39665i) q^{3} -1.00000 q^{4} -1.00000i q^{5} +(1.39665 + 1.02439i) q^{6} +0.608912 q^{7} +1.00000i q^{8} +(-0.901245 - 2.86143i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.02439 + 1.39665i) q^{3} -1.00000 q^{4} -1.00000i q^{5} +(1.39665 + 1.02439i) q^{6} +0.608912 q^{7} +1.00000i q^{8} +(-0.901245 - 2.86143i) q^{9} -1.00000 q^{10} -1.47420 q^{11} +(1.02439 - 1.39665i) q^{12} +4.49416i q^{13} -0.608912i q^{14} +(1.39665 + 1.02439i) q^{15} +1.00000 q^{16} -0.826092 q^{17} +(-2.86143 + 0.901245i) q^{18} -0.806422 q^{19} +1.00000i q^{20} +(-0.623764 + 0.850435i) q^{21} +1.47420i q^{22} +1.31909 q^{23} +(-1.39665 - 1.02439i) q^{24} -1.00000 q^{25} +4.49416 q^{26} +(4.91963 + 1.67250i) q^{27} -0.608912 q^{28} -1.72571 q^{29} +(1.02439 - 1.39665i) q^{30} +(-4.31145 + 3.52298i) q^{31} -1.00000i q^{32} +(1.51016 - 2.05894i) q^{33} +0.826092i q^{34} -0.608912i q^{35} +(0.901245 + 2.86143i) q^{36} -2.79329i q^{37} +0.806422i q^{38} +(-6.27676 - 4.60378i) q^{39} +1.00000 q^{40} +7.02031i q^{41} +(0.850435 + 0.623764i) q^{42} +12.7290i q^{43} +1.47420 q^{44} +(-2.86143 + 0.901245i) q^{45} -1.31909i q^{46} +4.11787i q^{47} +(-1.02439 + 1.39665i) q^{48} -6.62923 q^{49} +1.00000i q^{50} +(0.846241 - 1.15376i) q^{51} -4.49416i q^{52} -7.69407 q^{53} +(1.67250 - 4.91963i) q^{54} +1.47420i q^{55} +0.608912i q^{56} +(0.826092 - 1.12629i) q^{57} +1.72571i q^{58} +10.3075i q^{59} +(-1.39665 - 1.02439i) q^{60} +7.71695i q^{61} +(3.52298 + 4.31145i) q^{62} +(-0.548779 - 1.74236i) q^{63} -1.00000 q^{64} +4.49416 q^{65} +(-2.05894 - 1.51016i) q^{66} +4.39502 q^{67} +0.826092 q^{68} +(-1.35127 + 1.84231i) q^{69} -0.608912 q^{70} +4.02425i q^{71} +(2.86143 - 0.901245i) q^{72} -4.96332i q^{73} -2.79329 q^{74} +(1.02439 - 1.39665i) q^{75} +0.806422 q^{76} -0.897658 q^{77} +(-4.60378 + 6.27676i) q^{78} +4.39776i q^{79} -1.00000i q^{80} +(-7.37552 + 5.15769i) q^{81} +7.02031 q^{82} -2.04878 q^{83} +(0.623764 - 0.850435i) q^{84} +0.826092i q^{85} +12.7290 q^{86} +(1.76780 - 2.41020i) q^{87} -1.47420i q^{88} -12.1395 q^{89} +(0.901245 + 2.86143i) q^{90} +2.73655i q^{91} -1.31909 q^{92} +(-0.503750 - 9.63048i) q^{93} +4.11787 q^{94} +0.806422i q^{95} +(1.39665 + 1.02439i) q^{96} +2.89218 q^{97} +6.62923i q^{98} +(1.32861 + 4.21831i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 20 q^{7} - 4 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 - 20 * q^7 - 4 * q^9	$ 16 q - 16 q^{4} - 20 q^{7} - 4 q^{9} - 16 q^{10} + 16 q^{16} + 12 q^{18} - 4 q^{19} - 16 q^{25} + 20 q^{28} - 4 q^{31} - 16 q^{33} + 4 q^{36} - 4 q^{39} + 16 q^{40} + 12 q^{45} + 4 q^{49} + 52 q^{51} - 12 q^{63} - 16 q^{64} + 4 q^{66} + 112 q^{67} - 4 q^{69} + 20 q^{70} - 12 q^{72} + 4 q^{76} - 28 q^{78} - 32 q^{81} + 32 q^{82} - 24 q^{87} + 4 q^{90} + 16 q^{93} - 8 q^{94} + 8 q^{97}+O(q^{100}) $ 16 * q - 16 * q^4 - 20 * q^7 - 4 * q^9 - 16 * q^10 + 16 * q^16 + 12 * q^18 - 4 * q^19 - 16 * q^25 + 20 * q^28 - 4 * q^31 - 16 * q^33 + 4 * q^36 - 4 * q^39 + 16 * q^40 + 12 * q^45 + 4 * q^49 + 52 * q^51 - 12 * q^63 - 16 * q^64 + 4 * q^66 + 112 * q^67 - 4 * q^69 + 20 * q^70 - 12 * q^72 + 4 * q^76 - 28 * q^78 - 32 * q^81 + 32 * q^82 - 24 * q^87 + 4 * q^90 + 16 * q^93 - 8 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.02439	+	1.39665i	−0.591433	+	0.806354i
$3$	−1.02439	+	1.39665i	−0.591433	+	0.806354i
$4$	−1.00000			−0.500000
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	1.39665	+	1.02439i	0.570179	+	0.418206i
$7$	0.608912			0.230147			0.115074	−	0.993357i	$-0.463290\pi$
$7$	0.608912			0.230147			0.115074	+	0.993357i	$0.463290\pi$
$8$			1.00000i			0.353553i
$9$	−0.901245	−	2.86143i	−0.300415	−	0.953809i
$10$	−1.00000			−0.316228
$11$	−1.47420			−0.444488			−0.222244	−	0.974991i	$-0.571338\pi$
$11$	−1.47420			−0.444488			−0.222244	+	0.974991i	$0.571338\pi$
$12$	1.02439	−	1.39665i	0.295716	−	0.403177i
$13$			4.49416i			1.24646i	0.782040	+	0.623228i	$0.214179\pi$
$13$			4.49416i			1.24646i	−0.782040	+	0.623228i	$0.785821\pi$
$14$		−	0.608912i		−	0.162739i
$15$	1.39665	+	1.02439i	0.360613	+	0.264497i
$16$	1.00000			0.250000
$17$	−0.826092			−0.200357			−0.100178	−	0.994969i	$-0.531941\pi$
$17$	−0.826092			−0.200357			−0.100178	+	0.994969i	$0.531941\pi$
$18$	−2.86143	+	0.901245i	−0.674445	+	0.212425i
$19$	−0.806422			−0.185006			−0.0925030	−	0.995712i	$-0.529487\pi$
$19$	−0.806422			−0.185006			−0.0925030	+	0.995712i	$0.529487\pi$
$20$			1.00000i			0.223607i
$21$	−0.623764	+	0.850435i	−0.136117	+	0.185580i
$22$			1.47420i			0.314300i
$23$	1.31909			0.275050			0.137525	−	0.990498i	$-0.456085\pi$
$23$	1.31909			0.275050			0.137525	+	0.990498i	$0.456085\pi$
$24$	−1.39665	−	1.02439i	−0.285089	−	0.209103i
$25$	−1.00000			−0.200000
$26$	4.49416			0.881378
$27$	4.91963	+	1.67250i	0.946783	+	0.321873i
$28$	−0.608912			−0.115074
$29$	−1.72571			−0.320456			−0.160228	−	0.987080i	$-0.551223\pi$
$29$	−1.72571			−0.320456			−0.160228	+	0.987080i	$0.551223\pi$
$30$	1.02439	−	1.39665i	0.187027	−	0.254992i
$31$	−4.31145	+	3.52298i	−0.774359	+	0.632746i
$31$	−4.31145	+	3.52298i	−0.774359	+	0.632746i
$32$		−	1.00000i		−	0.176777i
$33$	1.51016	−	2.05894i	0.262885	−	0.358415i
$34$			0.826092i			0.141674i
$35$		−	0.608912i		−	0.102925i
$36$	0.901245	+	2.86143i	0.150207	+	0.476904i
$37$		−	2.79329i		−	0.459215i	−0.973283	−	0.229607i	$-0.926256\pi$
$37$		−	2.79329i		−	0.459215i	0.973283	−	0.229607i	$-0.0737442\pi$
$38$			0.806422i			0.130819i
$39$	−6.27676	−	4.60378i	−1.00509	−	0.737195i
$40$	1.00000			0.158114
$41$			7.02031i			1.09639i	0.836351	+	0.548194i	$0.184685\pi$
$41$			7.02031i			1.09639i	−0.836351	+	0.548194i	$0.815315\pi$
$42$	0.850435	+	0.623764i	0.131225	+	0.0962489i
$43$			12.7290i			1.94115i	0.240804	+	0.970574i	$0.422589\pi$
$43$			12.7290i			1.94115i	−0.240804	+	0.970574i	$0.577411\pi$
$44$	1.47420			0.222244
$45$	−2.86143	+	0.901245i	−0.426556	+	0.134350i
$46$		−	1.31909i		−	0.194490i
$47$			4.11787i			0.600653i	0.953836	+	0.300327i	$0.0970957\pi$
$47$			4.11787i			0.600653i	−0.953836	+	0.300327i	$0.902904\pi$
$48$	−1.02439	+	1.39665i	−0.147858	+	0.201589i
$49$	−6.62923			−0.947032
$50$			1.00000i			0.141421i
$51$	0.846241	−	1.15376i	0.118497	−	0.161559i
$52$		−	4.49416i		−	0.623228i
$53$	−7.69407			−1.05686			−0.528431	−	0.848976i	$-0.677219\pi$
$53$	−7.69407			−1.05686			−0.528431	+	0.848976i	$0.677219\pi$
$54$	1.67250	−	4.91963i	0.227598	−	0.669477i
$55$			1.47420i			0.198781i
$56$			0.608912i			0.0813693i
$57$	0.826092	−	1.12629i	0.109419	−	0.149180i
$58$			1.72571i			0.226597i
$59$			10.3075i			1.34192i	0.741492	+	0.670962i	$0.234119\pi$
$59$			10.3075i			1.34192i	−0.741492	+	0.670962i	$0.765881\pi$
$60$	−1.39665	−	1.02439i	−0.180306	−	0.132248i
$61$			7.71695i			0.988054i	0.869446	+	0.494027i	$0.164476\pi$
$61$			7.71695i			0.988054i	−0.869446	+	0.494027i	$0.835524\pi$
$62$	3.52298	+	4.31145i	0.447419	+	0.547555i
$63$	−0.548779	−	1.74236i	−0.0691396	−	0.219516i
$64$	−1.00000			−0.125000
$65$	4.49416			0.557432
$66$	−2.05894	−	1.51016i	−0.253437	−	0.185887i
$67$	4.39502			0.536937			0.268469	−	0.963288i	$-0.413482\pi$
$67$	4.39502			0.536937			0.268469	+	0.963288i	$0.413482\pi$
$68$	0.826092			0.100178
$69$	−1.35127	+	1.84231i	−0.162674	+	0.221788i
$70$	−0.608912			−0.0727789
$71$			4.02425i			0.477590i	0.971070	+	0.238795i	$0.0767524\pi$
$71$			4.02425i			0.477590i	−0.971070	+	0.238795i	$0.923248\pi$
$72$	2.86143	−	0.901245i	0.337222	−	0.106213i
$73$		−	4.96332i		−	0.580912i	−0.956888	−	0.290456i	$-0.906193\pi$
$73$		−	4.96332i		−	0.580912i	0.956888	−	0.290456i	$-0.0938071\pi$
$74$	−2.79329			−0.324714
$75$	1.02439	−	1.39665i	0.118287	−	0.161271i
$76$	0.806422			0.0925030
$77$	−0.897658			−0.102298
$78$	−4.60378	+	6.27676i	−0.521276	+	0.710703i
$79$			4.39776i			0.494787i	0.968915	+	0.247393i	$0.0795740\pi$
$79$			4.39776i			0.494787i	−0.968915	+	0.247393i	$0.920426\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−7.37552	+	5.15769i	−0.819502	+	0.573077i
$82$	7.02031			0.775264
$83$	−2.04878			−0.224883			−0.112442	−	0.993658i	$-0.535867\pi$
$83$	−2.04878			−0.224883			−0.112442	+	0.993658i	$0.535867\pi$
$84$	0.623764	−	0.850435i	0.0680583	−	0.0927901i
$85$			0.826092i			0.0896022i
$86$	12.7290			1.37260
$87$	1.76780	−	2.41020i	0.189528	−	0.258401i
$88$		−	1.47420i		−	0.157150i
$89$	−12.1395			−1.28679			−0.643395	−	0.765535i	$-0.722475\pi$
$89$	−12.1395			−1.28679			−0.643395	+	0.765535i	$0.722475\pi$
$90$	0.901245	+	2.86143i	0.0949996	+	0.301621i
$91$			2.73655i			0.286868i
$92$	−1.31909			−0.137525
$93$	−0.503750	−	9.63048i	−0.0522365	−	0.998635i
$94$	4.11787			0.424726
$95$			0.806422i			0.0827372i
$96$	1.39665	+	1.02439i	0.142545	+	0.104551i
$97$	2.89218			0.293657			0.146828	−	0.989162i	$-0.453094\pi$
$97$	2.89218			0.293657			0.146828	+	0.989162i	$0.453094\pi$
$98$			6.62923i			0.669653i
$99$	1.32861	+	4.21831i	0.133531	+	0.423956i
$100$	1.00000			0.100000
$101$		−	7.94461i		−	0.790518i	−0.918570	−	0.395259i	$-0.870655\pi$
$101$		−	7.94461i		−	0.790518i	0.918570	−	0.395259i	$-0.129345\pi$
$102$	−1.15376	−	0.846241i	−0.114239	−	0.0837904i
$103$	17.7611			1.75005			0.875026	−	0.484076i	$-0.160844\pi$
$103$	17.7611			1.75005			0.875026	+	0.484076i	$0.160844\pi$
$104$	−4.49416			−0.440689
$105$	0.850435	+	0.623764i	0.0829940	+	0.0608732i
$106$			7.69407i			0.747314i
$107$			14.9547i			1.44572i	0.690994	+	0.722861i	$0.257173\pi$
$107$			14.9547i			1.44572i	−0.690994	+	0.722861i	$0.742827\pi$
$108$	−4.91963	−	1.67250i	−0.473392	−	0.160936i
$109$	0.702538			0.0672909			0.0336454	−	0.999434i	$-0.489288\pi$
$109$	0.702538			0.0672909			0.0336454	+	0.999434i	$0.489288\pi$
$110$	1.47420			0.140559
$111$	3.90124	+	2.86143i	0.370290	+	0.271595i
$112$	0.608912			0.0575368
$113$		−	18.0546i		−	1.69844i	−0.528043	−	0.849218i	$-0.677074\pi$
$113$		−	18.0546i		−	1.69844i	0.528043	−	0.849218i	$-0.322926\pi$
$114$	−1.12629	−	0.826092i	−0.105486	−	0.0773706i
$115$		−	1.31909i		−	0.123006i
$116$	1.72571			0.160228
$117$	12.8597	−	4.05034i	1.18888	−	0.374454i
$118$	10.3075			0.948884
$119$	−0.503017			−0.0461115
$120$	−1.02439	+	1.39665i	−0.0935137	+	0.127496i
$121$	−8.82674			−0.802431
$122$	7.71695			0.698660
$123$	−9.80490	−	7.19155i	−0.884078	−	0.648440i
$124$	4.31145	−	3.52298i	0.387180	−	0.316373i
$125$			1.00000i			0.0894427i
$126$	−1.74236	+	0.548779i	−0.155221	+	0.0488891i
$127$		−	12.2598i		−	1.08788i	−0.839124	−	0.543941i	$-0.816932\pi$
$127$		−	12.2598i		−	1.08788i	0.839124	−	0.543941i	$-0.183068\pi$
$128$			1.00000i			0.0883883i
$129$	−17.7779	−	13.0394i	−1.56525	−	1.14806i
$130$		−	4.49416i		−	0.394164i
$131$		−	8.39502i		−	0.733476i	−0.930324	−	0.366738i	$-0.880474\pi$
$131$		−	8.39502i		−	0.733476i	0.930324	−	0.366738i	$-0.119526\pi$
$132$	−1.51016	+	2.05894i	−0.131442	+	0.179207i
$133$	−0.491040			−0.0425786
$134$		−	4.39502i		−	0.379672i
$135$	1.67250	−	4.91963i	0.143946	−	0.423414i
$136$		−	0.826092i		−	0.0708368i
$137$	−7.20588			−0.615640			−0.307820	−	0.951445i	$-0.599599\pi$
$137$	−7.20588			−0.615640			−0.307820	+	0.951445i	$0.599599\pi$
$138$	1.84231	+	1.35127i	0.156828	+	0.115028i
$139$		−	5.10841i		−	0.433290i	−0.976251	−	0.216645i	$-0.930489\pi$
$139$		−	5.10841i		−	0.433290i	0.976251	−	0.216645i	$-0.0695113\pi$
$140$			0.608912i			0.0514625i
$141$	−5.75121	−	4.21831i	−0.484339	−	0.355246i
$142$	4.02425			0.337707
$143$		−	6.62529i		−	0.554035i
$144$	−0.901245	−	2.86143i	−0.0751037	−	0.238452i
$145$			1.72571i			0.143312i
$146$	−4.96332			−0.410767
$147$	6.79092	−	9.25869i	0.560106	−	0.763644i
$148$			2.79329i			0.229607i
$149$		−	19.0749i		−	1.56268i	−0.624106	−	0.781340i	$-0.714537\pi$
$149$		−	19.0749i		−	1.56268i	0.624106	−	0.781340i	$-0.285463\pi$
$150$	−1.39665	−	1.02439i	−0.114036	−	0.0836412i
$151$		−	6.08960i		−	0.495565i	−0.968816	−	0.247783i	$-0.920298\pi$
$151$		−	6.08960i		−	0.495565i	0.968816	−	0.247783i	$-0.0797018\pi$
$152$		−	0.806422i		−	0.0654095i
$153$	0.744511	+	2.36380i	0.0601902	+	0.191102i
$154$			0.897658i			0.0723353i
$155$	3.52298	+	4.31145i	0.282973	+	0.346304i
$156$	6.27676	+	4.60378i	0.502543	+	0.368598i
$157$	18.5675			1.48185			0.740924	−	0.671589i	$-0.234388\pi$
$157$	18.5675			1.48185			0.740924	+	0.671589i	$0.234388\pi$
$158$	4.39776			0.349867
$159$	7.88174	−	10.7459i	0.625063	−	0.852205i
$160$	−1.00000			−0.0790569
$161$	0.803212			0.0633020
$162$	5.15769	+	7.37552i	0.405226	+	0.579475i
$163$	2.83067			0.221715			0.110858	−	0.993836i	$-0.464640\pi$
$163$	2.83067			0.221715			0.110858	+	0.993836i	$0.464640\pi$
$164$		−	7.02031i		−	0.548194i
$165$	−2.05894	−	1.51016i	−0.160288	−	0.117566i
$166$			2.04878i			0.159016i
$167$	−1.65895			−0.128373			−0.0641867	−	0.997938i	$-0.520445\pi$
$167$	−1.65895			−0.128373			−0.0641867	+	0.997938i	$0.520445\pi$
$168$	−0.850435	−	0.623764i	−0.0656125	−	0.0481245i
$169$	−7.19751			−0.553655
$170$	0.826092			0.0633584
$171$	0.726784	+	2.30752i	0.0555786	+	0.176460i
$172$		−	12.7290i		−	0.970574i
$173$			7.01005i			0.532965i	0.963840	+	0.266482i	$0.0858614\pi$
$173$			7.01005i			0.532965i	−0.963840	+	0.266482i	$0.914139\pi$
$174$	−2.41020	−	1.76780i	−0.182717	−	0.134017i
$175$	−0.608912			−0.0460294
$176$	−1.47420			−0.111122
$177$	−14.3960	−	10.5589i	−1.08207	−	0.793658i
$178$			12.1395i			0.909898i
$179$	3.40754			0.254691			0.127346	−	0.991858i	$-0.459354\pi$
$179$	3.40754			0.254691			0.127346	+	0.991858i	$0.459354\pi$
$180$	2.86143	−	0.901245i	0.213278	−	0.0671748i
$181$			8.95446i			0.665580i	0.943001	+	0.332790i	$0.107990\pi$
$181$			8.95446i			0.665580i	−0.943001	+	0.332790i	$0.892010\pi$
$182$	2.73655			0.202847
$183$	−10.7779	−	7.90518i	−0.796722	−	0.584368i
$184$			1.31909i			0.0972449i
$185$	−2.79329			−0.205367
$186$	−9.63048	+	0.503750i	−0.706141	+	0.0369368i
$187$	1.21782			0.0890561
$188$		−	4.11787i		−	0.300327i
$189$	2.99562	+	1.01840i	0.217899	+	0.0740780i
$190$	0.806422			0.0585040
$191$			4.19751i			0.303721i	0.988402	+	0.151861i	$0.0485265\pi$
$191$			4.19751i			0.303721i	−0.988402	+	0.151861i	$0.951474\pi$
$192$	1.02439	−	1.39665i	0.0739291	−	0.100794i
$193$	6.54326			0.470994			0.235497	−	0.971875i	$-0.424328\pi$
$193$	6.54326			0.470994			0.235497	+	0.971875i	$0.424328\pi$
$194$		−	2.89218i		−	0.207647i
$195$	−4.60378	+	6.27676i	−0.329684	+	0.449488i
$196$	6.62923			0.473516
$197$	1.09242			0.0778319			0.0389160	−	0.999242i	$-0.487610\pi$
$197$	1.09242			0.0778319			0.0389160	+	0.999242i	$0.487610\pi$
$198$	4.21831	−	1.32861i	0.299782	−	0.0944205i
$199$			15.7637i			1.11746i	0.829349	+	0.558731i	$0.188712\pi$
$199$			15.7637i			1.11746i	−0.829349	+	0.558731i	$0.811288\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	−4.50222	+	6.13829i	−0.317562	+	0.432962i
$202$	−7.94461			−0.558981
$203$	−1.05080			−0.0737520
$204$	−0.846241	+	1.15376i	−0.0592487	+	0.0807793i
$205$	7.02031			0.490320
$206$		−	17.7611i		−	1.23747i
$207$	−1.18883	−	3.77449i	−0.0826292	−	0.262345i
$208$			4.49416i			0.311614i
$209$	1.18883			0.0822329
$210$	0.623764	−	0.850435i	0.0430438	−	0.0586856i
$211$	18.2443			1.25599			0.627993	−	0.778219i	$-0.283876\pi$
$211$	18.2443			1.25599			0.627993	+	0.778219i	$0.283876\pi$
$212$	7.69407			0.528431
$213$	−5.62045	−	4.12240i	−0.385107	−	0.282462i
$214$	14.9547			1.02228
$215$	12.7290			0.868108
$216$	−1.67250	+	4.91963i	−0.113799	+	0.334738i
$217$	−2.62529	+	2.14519i	−0.178217	+	0.145625i
$218$		−	0.702538i		−	0.0475818i
$219$	6.93200	+	5.08438i	0.468421	+	0.343571i
$220$		−	1.47420i		−	0.0993905i
$221$		−	3.71259i		−	0.249736i
$222$	2.86143	−	3.90124i	0.192046	−	0.261834i
$223$		−	3.41852i		−	0.228921i	−0.993428	−	0.114461i	$-0.963486\pi$
$223$		−	3.41852i		−	0.228921i	0.993428	−	0.114461i	$-0.0365140\pi$
$224$		−	0.608912i		−	0.0406846i
$225$	0.901245	+	2.86143i	0.0600830	+	0.190762i
$226$	−18.0546			−1.20098
$227$			5.73684i			0.380767i	0.981710	+	0.190384i	$0.0609732\pi$
$227$			5.73684i			0.380767i	−0.981710	+	0.190384i	$0.939027\pi$
$228$	−0.826092	+	1.12629i	−0.0547093	+	0.0745902i
$229$			19.6437i			1.29809i	0.760750	+	0.649045i	$0.224831\pi$
$229$			19.6437i			1.29809i	−0.760750	+	0.649045i	$0.775169\pi$
$230$	−1.31909			−0.0869785
$231$	0.919553	−	1.25371i	0.0605021	−	0.0824881i
$232$		−	1.72571i		−	0.113298i
$233$		−	7.05243i		−	0.462020i	−0.972951	−	0.231010i	$-0.925797\pi$
$233$		−	7.05243i		−	0.462020i	0.972951	−	0.231010i	$-0.0742030\pi$
$234$	−4.05034	−	12.8597i	−0.264779	−	0.840666i
$235$	4.11787			0.268620
$236$		−	10.3075i		−	0.670962i
$237$	−6.14212	−	4.50503i	−0.398973	−	0.292633i
$238$			0.503017i			0.0326058i
$239$	−19.6785			−1.27290			−0.636449	−	0.771319i	$-0.719597\pi$
$239$	−19.6785			−1.27290			−0.636449	+	0.771319i	$0.719597\pi$
$240$	1.39665	+	1.02439i	0.0901532	+	0.0661242i
$241$		−	6.59262i		−	0.424668i	−0.977197	−	0.212334i	$-0.931894\pi$
$241$		−	6.59262i		−	0.424668i	0.977197	−	0.212334i	$-0.0681065\pi$
$242$			8.82674i			0.567404i
$243$	0.351941	−	15.5845i	0.0225770	−	0.999745i
$244$		−	7.71695i		−	0.494027i
$245$			6.62923i			0.423526i
$246$	−7.19155	+	9.80490i	−0.458516	+	0.625138i
$247$		−	3.62419i		−	0.230602i
$248$	−3.52298	−	4.31145i	−0.223710	−	0.273777i
$249$	2.09876	−	2.86143i	0.133003	−	0.181335i
$250$	1.00000			0.0632456
$251$	−8.85000			−0.558607			−0.279304	−	0.960203i	$-0.590104\pi$
$251$	−8.85000			−0.558607			−0.279304	+	0.960203i	$0.590104\pi$
$252$	0.548779	+	1.74236i	0.0345698	+	0.109758i
$253$	−1.94461			−0.122256
$254$	−12.2598			−0.769248
$255$	−1.15376	−	0.846241i	−0.0722512	−	0.0529937i
$256$	1.00000			0.0625000
$257$			10.2443i			0.639019i	0.947583	+	0.319510i	$0.103518\pi$
$257$			10.2443i			0.639019i	−0.947583	+	0.319510i	$0.896482\pi$
$258$	−13.0394	+	17.7779i	−0.811800	+	1.10680i
$259$		−	1.70087i		−	0.105687i
$260$	−4.49416			−0.278716
$261$	1.55529	+	4.93799i	0.0962698	+	0.305654i
$262$	−8.39502			−0.518646
$263$	−8.47245			−0.522433			−0.261217	−	0.965280i	$-0.584124\pi$
$263$	−8.47245			−0.522433			−0.261217	+	0.965280i	$0.584124\pi$
$264$	2.05894	+	1.51016i	0.126719	+	0.0929437i
$265$			7.69407i			0.472643i
$266$			0.491040i			0.0301076i
$267$	12.4356	−	16.9547i	0.761049	−	1.03761i
$268$	−4.39502			−0.268469
$269$	−23.9937			−1.46292			−0.731462	−	0.681883i	$-0.761161\pi$
$269$	−23.9937			−1.46292			−0.731462	+	0.681883i	$0.761161\pi$
$270$	−4.91963	−	1.67250i	−0.299399	−	0.101785i
$271$		−	28.4163i		−	1.72617i	−0.505060	−	0.863084i	$-0.668530\pi$
$271$		−	28.4163i		−	1.72617i	0.505060	−	0.863084i	$-0.331470\pi$
$272$	−0.826092			−0.0500892
$273$	−3.82199	−	2.80330i	−0.231318	−	0.169663i
$274$			7.20588i			0.435323i
$275$	1.47420			0.0888976
$276$	1.35127	−	1.84231i	0.0813368	−	0.110894i
$277$		−	5.61368i		−	0.337294i	−0.985677	−	0.168647i	$-0.946060\pi$
$277$		−	5.61368i		−	0.337294i	0.985677	−	0.168647i	$-0.0539397\pi$
$278$	−5.10841			−0.306382
$279$	13.9664	+	9.16182i	0.836148	+	0.548504i
$280$	0.608912			0.0363895
$281$		−	5.84072i		−	0.348428i	−0.984708	−	0.174214i	$-0.944261\pi$
$281$		−	5.84072i		−	0.348428i	0.984708	−	0.174214i	$-0.0557385\pi$
$282$	−4.21831	+	5.75121i	−0.251197	+	0.342480i
$283$	4.18725			0.248906			0.124453	−	0.992225i	$-0.460282\pi$
$283$	4.18725			0.248906			0.124453	+	0.992225i	$0.460282\pi$
$284$		−	4.02425i		−	0.238795i
$285$	−1.12629	−	0.826092i	−0.0667155	−	0.0489335i
$286$	−6.62529			−0.391762
$287$			4.27475i			0.252331i
$288$	−2.86143	+	0.901245i	−0.168611	+	0.0531064i
$289$	−16.3176			−0.959857
$290$	1.72571			0.101337
$291$	−2.96273	+	4.03936i	−0.173678	+	0.236791i
$292$			4.96332i			0.290456i
$293$		−	4.57441i		−	0.267240i	−0.991033	−	0.133620i	$-0.957340\pi$
$293$		−	4.57441i		−	0.267240i	0.991033	−	0.133620i	$-0.0426601\pi$
$294$	−9.25869	−	6.79092i	−0.539978	−	0.396055i
$295$	10.3075			0.600127
$296$	2.79329			0.162357
$297$	−7.25251	−	2.46560i	−0.420834	−	0.143068i
$298$	−19.0749			−1.10498
$299$			5.92823i			0.342838i
$300$	−1.02439	+	1.39665i	−0.0591433	+	0.0806354i
$301$			7.75081i			0.446750i
$302$	−6.08960			−0.350417
$303$	11.0958	+	8.13839i	0.637438	+	0.467538i
$304$	−0.806422			−0.0462515
$305$	7.71695			0.441871
$306$	2.36380	−	0.744511i	0.135129	−	0.0425609i
$307$	11.2585			0.642554			0.321277	−	0.946985i	$-0.395888\pi$
$307$	11.2585			0.642554			0.321277	+	0.946985i	$0.395888\pi$
$308$	0.897658			0.0511488
$309$	−18.1943	+	24.8060i	−1.03504	+	1.41116i
$310$	4.31145	−	3.52298i	0.244874	−	0.200092i
$311$		−	13.1382i		−	0.744998i	−0.928033	−	0.372499i	$-0.878501\pi$
$311$		−	13.1382i		−	0.744998i	0.928033	−	0.372499i	$-0.121499\pi$
$312$	4.60378	−	6.27676i	0.260638	−	0.355352i
$313$			1.16595i			0.0659033i	0.999457	+	0.0329516i	$0.0104907\pi$
$313$			1.16595i			0.0659033i	−0.999457	+	0.0329516i	$0.989509\pi$
$314$		−	18.5675i		−	1.04783i
$315$	−1.74236	+	0.548779i	−0.0981707	+	0.0309202i
$316$		−	4.39776i		−	0.247393i
$317$			27.7221i			1.55703i	0.627628	+	0.778513i	$0.284026\pi$
$317$			27.7221i			1.55703i	−0.627628	+	0.778513i	$0.715974\pi$
$318$	−10.7459	−	7.88174i	−0.602600	−	0.441986i
$319$	2.54404			0.142439
$320$			1.00000i			0.0559017i
$321$	−20.8864	−	15.3194i	−1.16576	−	0.855047i
$322$		−	0.803212i		−	0.0447613i
$323$	0.666179			0.0370672
$324$	7.37552	−	5.15769i	0.409751	−	0.286538i
$325$		−	4.49416i		−	0.249291i
$326$		−	2.83067i		−	0.156776i
$327$	−0.719673	+	0.981197i	−0.0397980	+	0.0542603i
$328$	−7.02031			−0.387632
$329$			2.50742i			0.138239i
$330$	−1.51016	+	2.05894i	−0.0831314	+	0.113341i
$331$		−	26.0335i		−	1.43093i	−0.698649	−	0.715464i	$-0.746215\pi$
$331$		−	26.0335i		−	1.43093i	0.698649	−	0.715464i	$-0.253785\pi$
$332$	2.04878			0.112442
$333$	−7.99280	+	2.51744i	−0.438003	+	0.137955i
$334$			1.65895i			0.0907737i
$335$		−	4.39502i		−	0.240126i
$336$	−0.623764	+	0.850435i	−0.0340291	+	0.0463950i
$337$		−	15.8543i		−	0.863641i	−0.901959	−	0.431821i	$-0.857871\pi$
$337$		−	15.8543i		−	0.863641i	0.901959	−	0.431821i	$-0.142129\pi$
$338$			7.19751i			0.391493i
$339$	25.2159	+	18.4950i	1.36954	+	1.00451i
$340$		−	0.826092i		−	0.0448011i
$341$	6.35594	−	5.19358i	0.344193	−	0.281248i
$342$	2.30752	−	0.726784i	0.124776	−	0.0393000i
$343$	−8.29900			−0.448104
$344$	−12.7290			−0.686299
$345$	1.84231	+	1.35127i	0.0991866	+	0.0727499i
$346$	7.01005			0.376863
$347$	25.9222			1.39158			0.695789	−	0.718246i	$-0.255055\pi$
$347$	25.9222			1.39158			0.695789	+	0.718246i	$0.255055\pi$
$348$	−1.76780	+	2.41020i	−0.0947640	+	0.129201i
$349$	23.6456			1.26572			0.632860	−	0.774266i	$-0.281881\pi$
$349$	23.6456			1.26572			0.632860	+	0.774266i	$0.281881\pi$
$350$			0.608912i			0.0325477i
$351$	−7.51648	+	22.1096i	−0.401200	+	1.18012i
$352$			1.47420i			0.0785751i
$353$	4.03503			0.214763			0.107381	−	0.994218i	$-0.465753\pi$
$353$	4.03503			0.214763			0.107381	+	0.994218i	$0.465753\pi$
$354$	−10.5589	+	14.3960i	−0.561201	+	0.765137i
$355$	4.02425			0.213585
$356$	12.1395			0.643395
$357$	0.515287	−	0.702538i	0.0272719	−	0.0371822i
$358$		−	3.40754i		−	0.180094i
$359$			33.1132i			1.74765i	0.486244	+	0.873823i	$0.338367\pi$
$359$			33.1132i			1.74765i	−0.486244	+	0.873823i	$0.661633\pi$
$360$	−0.901245	−	2.86143i	−0.0474998	−	0.150810i
$361$	−18.3497			−0.965773
$362$	8.95446			0.470636
$363$	9.04203	−	12.3278i	0.474584	−	0.647043i
$364$		−	2.73655i		−	0.143434i
$365$	−4.96332			−0.259792
$366$	−7.90518	+	10.7779i	−0.413210	+	0.563368i
$367$			14.5621i			0.760133i	0.924959	+	0.380066i	$0.124099\pi$
$367$			14.5621i			0.760133i	−0.924959	+	0.380066i	$0.875901\pi$
$368$	1.31909			0.0687625
$369$	20.0881	−	6.32702i	1.04575	−	0.329372i
$370$			2.79329i			0.145216i
$371$	−4.68501			−0.243234
$372$	0.503750	+	9.63048i	0.0261182	+	0.499317i
$373$	8.90617			0.461144			0.230572	−	0.973055i	$-0.425940\pi$
$373$	8.90617			0.461144			0.230572	+	0.973055i	$0.425940\pi$
$374$		−	1.21782i		−	0.0629722i
$375$	−1.39665	−	1.02439i	−0.0721225	−	0.0528993i
$376$	−4.11787			−0.212363
$377$		−	7.75561i		−	0.399434i
$378$	1.01840	−	2.99562i	0.0523811	−	0.154078i
$379$	−23.9647			−1.23098			−0.615492	−	0.788143i	$-0.711043\pi$
$379$	−23.9647			−1.23098			−0.615492	+	0.788143i	$0.711043\pi$
$380$		−	0.806422i		−	0.0413686i
$381$	17.1226	+	12.5588i	0.877218	+	0.643409i
$382$	4.19751			0.214763
$383$	−1.37487			−0.0702525			−0.0351262	−	0.999383i	$-0.511183\pi$
$383$	−1.37487			−0.0702525			−0.0351262	+	0.999383i	$0.511183\pi$
$384$	−1.39665	−	1.02439i	−0.0712723	−	0.0522757i
$385$			0.897658i			0.0457489i
$386$		−	6.54326i		−	0.333043i
$387$	36.4230	−	11.4719i	1.85148	−	0.583150i
$388$	−2.89218			−0.146828
$389$	−7.52414			−0.381489			−0.190745	−	0.981640i	$-0.561090\pi$
$389$	−7.52414			−0.381489			−0.190745	+	0.981640i	$0.561090\pi$
$390$	6.27676	+	4.60378i	0.317836	+	0.233122i
$391$	−1.08969			−0.0551082
$392$		−	6.62923i		−	0.334826i
$393$	11.7249	+	8.59979i	0.591442	+	0.433802i
$394$		−	1.09242i		−	0.0550355i
$395$	4.39776			0.221275
$396$	−1.32861	−	4.21831i	−0.0667654	−	0.211978i
$397$	−8.55964			−0.429596			−0.214798	−	0.976658i	$-0.568909\pi$
$397$	−8.55964			−0.429596			−0.214798	+	0.976658i	$0.568909\pi$
$398$	15.7637			0.790165
$399$	0.503017	−	0.685810i	0.0251824	−	0.0343334i
$400$	−1.00000			−0.0500000
$401$	28.2196			1.40922			0.704610	−	0.709595i	$-0.251122\pi$
$401$	28.2196			1.40922			0.704610	+	0.709595i	$0.251122\pi$
$402$	6.13829	+	4.50222i	0.306150	+	0.224550i
$403$	−15.8329	−	19.3764i	−0.788691	−	0.965205i
$404$			7.94461i			0.395259i
$405$	5.15769	+	7.37552i	0.256288	+	0.366492i
$406$			1.05080i			0.0521505i
$407$			4.11787i			0.204115i
$408$	1.15376	+	0.846241i	0.0571196	+	0.0418952i
$409$			22.3167i			1.10349i	0.834013	+	0.551745i	$0.186038\pi$
$409$			22.3167i			1.10349i	−0.834013	+	0.551745i	$0.813962\pi$
$410$		−	7.02031i		−	0.346709i
$411$	7.38164	−	10.0641i	0.364109	−	0.496424i
$412$	−17.7611			−0.875026
$413$			6.27637i			0.308840i
$414$	−3.77449	+	1.18883i	−0.185506	+	0.0584277i
$415$			2.04878i			0.100571i
$416$	4.49416			0.220345
$417$	7.13464	+	5.23301i	0.349385	+	0.256262i
$418$		−	1.18883i		−	0.0581474i
$419$			33.8502i			1.65369i	0.562429	+	0.826845i	$0.309867\pi$
$419$			33.8502i			1.65369i	−0.562429	+	0.826845i	$0.690133\pi$
$420$	−0.850435	−	0.623764i	−0.0414970	−	0.0304366i
$421$	−14.2200			−0.693041			−0.346521	−	0.938042i	$-0.612637\pi$
$421$	−14.2200			−0.693041			−0.346521	+	0.938042i	$0.612637\pi$
$422$		−	18.2443i		−	0.888117i
$423$	11.7830	−	3.71121i	0.572908	−	0.180445i
$424$		−	7.69407i		−	0.373657i
$425$	0.826092			0.0400713
$426$	−4.12240	+	5.62045i	−0.199731	+	0.272312i
$427$			4.69894i			0.227398i
$428$		−	14.9547i		−	0.722861i
$429$	9.25320	+	6.78689i	0.446749	+	0.327674i
$430$		−	12.7290i		−	0.613845i
$431$		−	8.94068i		−	0.430657i	−0.976542	−	0.215329i	$-0.930918\pi$
$431$		−	8.94068i		−	0.430657i	0.976542	−	0.215329i	$-0.0690823\pi$
$432$	4.91963	+	1.67250i	0.236696	+	0.0804681i
$433$		−	13.7885i		−	0.662632i	−0.943520	−	0.331316i	$-0.892507\pi$
$433$		−	13.7885i		−	0.662632i	0.943520	−	0.331316i	$-0.107493\pi$
$434$	2.14519	+	2.62529i	0.102972	+	0.126018i
$435$	−2.41020	−	1.76780i	−0.115560	−	0.0847595i
$436$	−0.702538			−0.0336454
$437$	−1.06375			−0.0508859
$438$	5.08438	−	6.93200i	0.242941	−	0.331224i
$439$	−16.5736			−0.791016			−0.395508	−	0.918462i	$-0.629431\pi$
$439$	−16.5736			−0.791016			−0.395508	+	0.918462i	$0.629431\pi$
$440$	−1.47420			−0.0702797
$441$	5.97456	+	18.9690i	0.284503	+	0.903288i
$442$	−3.71259			−0.176590
$443$			12.5190i			0.594796i	0.954754	+	0.297398i	$0.0961189\pi$
$443$			12.5190i			0.594796i	−0.954754	+	0.297398i	$0.903881\pi$
$444$	−3.90124	−	2.86143i	−0.185145	−	0.135797i
$445$			12.1395i			0.575470i
$446$	−3.41852			−0.161872
$447$	26.6409	+	19.5402i	1.26007	+	0.924219i
$448$	−0.608912			−0.0287684
$449$	28.1935			1.33053			0.665266	−	0.746606i	$-0.268318\pi$
$449$	28.1935			1.33053			0.665266	+	0.746606i	$0.268318\pi$
$450$	2.86143	−	0.901245i	0.134889	−	0.0424851i
$451$		−	10.3493i		−	0.487332i
$452$			18.0546i			0.849218i
$453$	8.50503	+	6.23814i	0.399601	+	0.293093i
$454$	5.73684			0.269243
$455$	2.73655			0.128291
$456$	1.12629	+	0.826092i	0.0527432	+	0.0386853i
$457$			1.42648i			0.0667280i	0.999443	+	0.0333640i	$0.0106221\pi$
$457$			1.42648i			0.0667280i	−0.999443	+	0.0333640i	$0.989378\pi$
$458$	19.6437			0.917888
$459$	−4.06407	−	1.38164i	−0.189694	−	0.0644893i
$460$			1.31909i			0.0615031i
$461$	16.3493			0.761463			0.380732	−	0.924686i	$-0.375672\pi$
$461$	16.3493			0.761463			0.380732	+	0.924686i	$0.375672\pi$
$462$	−1.25371	−	0.919553i	−0.0583279	−	0.0427815i
$463$			16.4367i			0.763878i	0.924188	+	0.381939i	$0.124744\pi$
$463$			16.4367i			0.763878i	−0.924188	+	0.381939i	$0.875256\pi$
$464$	−1.72571			−0.0801140
$465$	−9.63048	+	0.503750i	−0.446603	+	0.0233609i
$466$	−7.05243			−0.326697
$467$			6.41513i			0.296857i	0.988923	+	0.148428i	$0.0474215\pi$
$467$			6.41513i			0.296857i	−0.988923	+	0.148428i	$0.952579\pi$
$468$	−12.8597	+	4.05034i	−0.594441	+	0.187227i
$469$	2.67618			0.123575
$470$		−	4.11787i		−	0.189943i
$471$	−19.0204	+	25.9323i	−0.876413	+	1.19490i
$472$	−10.3075			−0.474442
$473$		−	18.7650i		−	0.862816i
$474$	−4.50503	+	6.14212i	−0.206923	+	0.282117i
$475$	0.806422			0.0370012
$476$	0.503017			0.0230558
$477$	6.93424	+	22.0160i	0.317497	+	1.00804i
$478$			19.6785i			0.900074i
$479$		−	22.2928i		−	1.01858i	−0.860594	−	0.509291i	$-0.829908\pi$
$479$		−	22.2928i		−	1.01858i	0.860594	−	0.509291i	$-0.170092\pi$
$480$	1.02439	−	1.39665i	0.0467569	−	0.0637479i
$481$	12.5535			0.572391
$482$	−6.59262			−0.300286
$483$	−0.822804	+	1.12180i	−0.0374389	+	0.0510439i
$484$	8.82674			0.401215
$485$		−	2.89218i		−	0.131327i
$486$	−15.5845	−	0.351941i	−0.706927	−	0.0159643i
$487$			25.4115i			1.15150i	0.817624	+	0.575752i	$0.195291\pi$
$487$			25.4115i			1.15150i	−0.817624	+	0.575752i	$0.804709\pi$
$488$	−7.71695			−0.349330
$489$	−2.89971	+	3.95344i	−0.131130	+	0.178781i
$490$	6.62923			0.299478
$491$	21.8676			0.986870			0.493435	−	0.869783i	$-0.335741\pi$
$491$	21.8676			0.986870			0.493435	+	0.869783i	$0.335741\pi$
$492$	9.80490	+	7.19155i	0.442039	+	0.324220i
$493$	1.42559			0.0642055
$494$	−3.62419			−0.163060
$495$	4.21831	−	1.32861i	0.189599	−	0.0597168i
$496$	−4.31145	+	3.52298i	−0.193590	+	0.158187i
$497$			2.45041i			0.109916i
$498$	−2.86143	−	2.09876i	−0.128224	−	0.0940475i
$499$			4.19112i			0.187620i	0.995590	+	0.0938101i	$0.0299047\pi$
$499$			4.19112i			0.187620i	−0.995590	+	0.0938101i	$0.970095\pi$
$500$		−	1.00000i		−	0.0447214i
$501$	1.69941	−	2.31697i	0.0759242	−	0.103514i
$502$			8.85000i			0.394995i
$503$			32.1810i			1.43488i	0.696620	+	0.717440i	$0.254686\pi$
$503$			32.1810i			1.43488i	−0.696620	+	0.717440i	$0.745314\pi$
$504$	1.74236	−	0.548779i	0.0776107	−	0.0244446i
$505$	−7.94461			−0.353530
$506$			1.94461i			0.0864484i
$507$	7.37307	−	10.0524i	0.327449	−	0.446442i
$508$			12.2598i			0.543941i
$509$	26.5526			1.17692			0.588461	−	0.808525i	$-0.299734\pi$
$509$	26.5526			1.17692			0.588461	+	0.808525i	$0.299734\pi$
$510$	−0.846241	+	1.15376i	−0.0374722	+	0.0510893i
$511$		−	3.02222i		−	0.133695i
$512$		−	1.00000i		−	0.0441942i
$513$	−3.96730	−	1.34874i	−0.175160	−	0.0595483i
$514$	10.2443			0.451855
$515$		−	17.7611i		−	0.782647i
$516$	17.7779	+	13.0394i	0.782626	+	0.574029i
$517$		−	6.07056i		−	0.266983i
$518$	−1.70087			−0.0747319
$519$	−9.79057	−	7.18104i	−0.429758	−	0.315213i
$520$			4.49416i			0.197082i
$521$		−	33.6814i		−	1.47561i	−0.675013	−	0.737805i	$-0.735862\pi$
$521$		−	33.6814i		−	1.47561i	0.675013	−	0.737805i	$-0.264138\pi$
$522$	4.93799	−	1.55529i	0.216130	−	0.0680730i
$523$		−	38.1411i		−	1.66779i	−0.551920	−	0.833897i	$-0.686105\pi$
$523$		−	38.1411i		−	1.66779i	0.551920	−	0.833897i	$-0.313895\pi$
$524$			8.39502i			0.366738i
$525$	0.623764	−	0.850435i	0.0272233	−	0.0371160i
$526$			8.47245i			0.369416i
$527$	3.56165	−	2.91031i	0.155148	−	0.126775i
$528$	1.51016	−	2.05894i	0.0657211	−	0.0896037i
$529$	−21.2600			−0.924347
$530$	7.69407			0.334209
$531$	29.4942	−	9.28960i	1.27994	−	0.403134i
$532$	0.491040			0.0212893
$533$	−31.5504			−1.36660
$534$	−16.9547	−	12.4356i	−0.733700	−	0.538143i
$535$	14.9547			0.646546
$536$			4.39502i			0.189836i
$537$	−3.49065	+	4.75913i	−0.150633	+	0.205371i
$538$			23.9937i			1.03444i
$539$	9.77280			0.420944
$540$	−1.67250	+	4.91963i	−0.0719729	+	0.211707i
$541$	−14.9304			−0.641909			−0.320954	−	0.947095i	$-0.604004\pi$
$541$	−14.9304			−0.641909			−0.320954	+	0.947095i	$0.604004\pi$
$542$	−28.4163			−1.22059
$543$	−12.5062	−	9.17288i	−0.536693	−	0.393646i
$544$			0.826092i			0.0354184i
$545$		−	0.702538i		−	0.0300934i
$546$	−2.80330	+	3.82199i	−0.119970	+	0.163566i
$547$	−13.0258			−0.556942			−0.278471	−	0.960445i	$-0.589828\pi$
$547$	−13.0258			−0.556942			−0.278471	+	0.960445i	$0.589828\pi$
$548$	7.20588			0.307820
$549$	22.0815	−	6.95486i	0.942415	−	0.296826i
$550$		−	1.47420i		−	0.0628601i
$551$	1.39165			0.0592863
$552$	−1.84231	−	1.35127i	−0.0784139	−	0.0575138i
$553$			2.67785i			0.113874i
$554$	−5.61368			−0.238503
$555$	2.86143	−	3.90124i	0.121461	−	0.165599i
$556$			5.10841i			0.216645i
$557$	−38.1075			−1.61467			−0.807334	−	0.590094i	$-0.799090\pi$
$557$	−38.1075			−1.61467			−0.807334	+	0.590094i	$0.799090\pi$
$558$	9.16182	−	13.9664i	0.387851	−	0.591246i
$559$	−57.2060			−2.41956
$560$		−	0.608912i		−	0.0257312i
$561$	−1.24753	+	1.70087i	−0.0526707	+	0.0718108i
$562$	−5.84072			−0.246376
$563$			21.1070i			0.889556i	0.895641	+	0.444778i	$0.146717\pi$
$563$			21.1070i			0.889556i	−0.895641	+	0.444778i	$0.853283\pi$
$564$	5.75121	+	4.21831i	0.242170	+	0.177623i
$565$	−18.0546			−0.759563
$566$		−	4.18725i		−	0.176003i
$567$	−4.49104	+	3.14058i	−0.188606	+	0.131892i
$568$	−4.02425			−0.168854
$569$	41.9852			1.76011			0.880056	−	0.474871i	$-0.157505\pi$
$569$	41.9852			1.76011			0.880056	+	0.474871i	$0.157505\pi$
$570$	−0.826092	+	1.12629i	−0.0346012	+	0.0471750i
$571$		−	12.3205i		−	0.515595i	−0.966199	−	0.257798i	$-0.917003\pi$
$571$		−	12.3205i		−	0.515595i	0.966199	−	0.257798i	$-0.0829968\pi$
$572$			6.62529i			0.277017i
$573$	−5.86244	−	4.29989i	−0.244907	−	0.179631i
$574$	4.27475			0.178425
$575$	−1.31909			−0.0550100
$576$	0.901245	+	2.86143i	0.0375519	+	0.119226i
$577$	10.3379			0.430372			0.215186	−	0.976573i	$-0.430964\pi$
$577$	10.3379			0.430372			0.215186	+	0.976573i	$0.430964\pi$
$578$			16.3176i			0.678722i
$579$	−6.70286	+	9.13862i	−0.278561	+	0.379788i
$580$		−	1.72571i		−	0.0716561i
$581$	−1.24753			−0.0517562
$582$	4.03936	+	2.96273i	0.167437	+	0.122809i
$583$	11.3426			0.469762
$584$	4.96332			0.205384
$585$	−4.05034	−	12.8597i	−0.167461	−	0.531684i
$586$	−4.57441			−0.188967
$587$	37.0267			1.52826			0.764128	−	0.645065i	$-0.223170\pi$
$587$	37.0267			1.52826			0.764128	+	0.645065i	$0.223170\pi$
$588$	−6.79092	+	9.25869i	−0.280053	+	0.381822i
$589$	3.47685	−	2.84101i	0.143261	−	0.117062i
$590$		−	10.3075i		−	0.424354i
$591$	−1.11907	+	1.52573i	−0.0460324	+	0.0627601i
$592$		−	2.79329i		−	0.114804i
$593$			4.28501i			0.175964i	0.996122	+	0.0879822i	$0.0280419\pi$
$593$			4.28501i			0.175964i	−0.996122	+	0.0879822i	$0.971958\pi$
$594$	−2.46560	+	7.25251i	−0.101165	+	0.297574i
$595$			0.503017i			0.0206217i
$596$			19.0749i			0.781340i
$597$	−22.0164	−	16.1482i	−0.901071	−	0.660903i
$598$	5.92823			0.242423
$599$			18.2340i			0.745021i	0.928028	+	0.372511i	$0.121503\pi$
$599$			18.2340i			0.745021i	−0.928028	+	0.372511i	$0.878497\pi$
$600$	1.39665	+	1.02439i	0.0570179	+	0.0418206i
$601$			40.0825i			1.63500i	0.575929	+	0.817500i	$0.304640\pi$
$601$			40.0825i			1.63500i	−0.575929	+	0.817500i	$0.695360\pi$
$602$	7.75081			0.315900
$603$	−3.96099	−	12.5760i	−0.161304	−	0.512135i
$604$			6.08960i			0.247783i
$605$			8.82674i			0.358858i
$606$	8.13839	−	11.0958i	0.330599	−	0.450737i
$607$	−0.491040			−0.0199307			−0.00996535	−	0.999950i	$-0.503172\pi$
$607$	−0.491040			−0.0199307			−0.00996535	+	0.999950i	$0.503172\pi$
$608$			0.806422i			0.0327047i
$609$	1.07643	−	1.46760i	0.0436193	−	0.0594703i
$610$		−	7.71695i		−	0.312450i
$611$	−18.5064			−0.748688
$612$	−0.744511	−	2.36380i	−0.0300951	−	0.0955510i
$613$			15.5986i			0.630022i	0.949088	+	0.315011i	$0.102008\pi$
$613$			15.5986i			0.630022i	−0.949088	+	0.315011i	$0.897992\pi$
$614$		−	11.2585i		−	0.454354i
$615$	−7.19155	+	9.80490i	−0.289991	+	0.395372i
$616$		−	0.897658i		−	0.0361677i
$617$			39.2031i			1.57826i	0.614229	+	0.789128i	$0.289467\pi$
$617$			39.2031i			1.57826i	−0.614229	+	0.789128i	$0.710533\pi$
$618$	24.8060	+	18.1943i	0.997842	+	0.731882i
$619$		−	28.9628i		−	1.16411i	−0.813148	−	0.582057i	$-0.802248\pi$
$619$		−	28.9628i		−	1.16411i	0.813148	−	0.582057i	$-0.197752\pi$
$620$	−3.52298	−	4.31145i	−0.141486	−	0.173152i
$621$	6.48945	+	2.20618i	0.260413	+	0.0885311i
$622$	−13.1382			−0.526793
$623$	−7.39192			−0.296151
$624$	−6.27676	−	4.60378i	−0.251272	−	0.184299i
$625$	1.00000			0.0400000
$626$	1.16595			0.0466006
$627$	−1.21782	+	1.66037i	−0.0486352	+	0.0663089i
$628$	−18.5675			−0.740924
$629$			2.30752i			0.0920067i
$630$	0.548779	+	1.74236i	0.0218639	+	0.0694172i
$631$		−	49.1763i		−	1.95768i	−0.204635	−	0.978838i	$-0.565601\pi$
$631$		−	49.1763i		−	1.95768i	0.204635	−	0.978838i	$-0.434399\pi$
$632$	−4.39776			−0.174934
$633$	−18.6893	+	25.4808i	−0.742831	+	1.01277i
$634$	27.7221			1.10098
$635$	−12.2598			−0.486515
$636$	−7.88174	+	10.7459i	−0.312531	+	0.426103i
$637$		−	29.7928i		−	1.18043i
$638$		−	2.54404i		−	0.100719i
$639$	11.5151	−	3.62683i	0.455530	−	0.143475i
$640$	1.00000			0.0395285
$641$	−23.9489			−0.945923			−0.472962	−	0.881083i	$-0.656815\pi$
$641$	−23.9489			−0.945923			−0.472962	+	0.881083i	$0.656815\pi$
$642$	−15.3194	+	20.8864i	−0.604610	+	0.824320i
$643$			3.61654i			0.142622i	0.997454	+	0.0713111i	$0.0227183\pi$
$643$			3.61654i			0.142622i	−0.997454	+	0.0713111i	$0.977282\pi$
$644$	−0.803212			−0.0316510
$645$	−13.0394	+	17.7779i	−0.513427	+	0.700002i
$646$		−	0.666179i		−	0.0262105i
$647$	3.48391			0.136967			0.0684833	−	0.997652i	$-0.478184\pi$
$647$	3.48391			0.136967			0.0684833	+	0.997652i	$0.478184\pi$
$648$	−5.15769	−	7.37552i	−0.202613	−	0.289738i
$649$		−	15.1953i		−	0.596469i
$650$	−4.49416			−0.176276
$651$	−0.306740	−	5.86412i	−0.0120221	−	0.229833i
$652$	−2.83067			−0.110858
$653$		−	29.3349i		−	1.14796i	−0.818868	−	0.573982i	$-0.805398\pi$
$653$		−	29.3349i		−	1.14796i	0.818868	−	0.573982i	$-0.194602\pi$
$654$	0.981197	+	0.719673i	0.0383678	+	0.0281415i
$655$	−8.39502			−0.328021
$656$			7.02031i			0.274097i
$657$	−14.2022	+	4.47316i	−0.554079	+	0.174515i
$658$	2.50742			0.0977495
$659$			30.4356i			1.18560i	0.805348	+	0.592802i	$0.201978\pi$
$659$			30.4356i			1.18560i	−0.805348	+	0.592802i	$0.798022\pi$
$660$	2.05894	+	1.51016i	0.0801440	+	0.0587828i
$661$	3.48471			0.135540			0.0677698	−	0.997701i	$-0.478412\pi$
$661$	3.48471			0.135540			0.0677698	+	0.997701i	$0.478412\pi$
$662$	−26.0335			−1.01182
$663$	5.18518	+	3.80315i	0.201376	+	0.147702i
$664$		−	2.04878i		−	0.0795082i
$665$			0.491040i			0.0190417i
$666$	2.51744	+	7.99280i	0.0975489	+	0.309715i
$667$	−2.27637			−0.0881415
$668$	1.65895			0.0641867
$669$	4.77447	+	3.50190i	0.184592	+	0.135391i
$670$	−4.39502			−0.169794
$671$		−	11.3763i		−	0.439178i
$672$	0.850435	+	0.623764i	0.0328062	+	0.0240622i
$673$		−	35.7954i		−	1.37981i	−0.723900	−	0.689905i	$-0.757652\pi$
$673$		−	35.7954i		−	1.37981i	0.723900	−	0.689905i	$-0.242348\pi$
$674$	−15.8543			−0.610687
$675$	−4.91963	−	1.67250i	−0.189357	−	0.0643745i
$676$	7.19751			0.276827
$677$	−33.5556			−1.28965			−0.644824	−	0.764331i	$-0.723069\pi$
$677$	−33.5556			−1.28965			−0.644824	+	0.764331i	$0.723069\pi$
$678$	18.4950	−	25.2159i	0.710296	−	0.968412i
$679$	1.76109			0.0675842
$680$	−0.826092			−0.0316792
$681$	−8.01234	−	5.87677i	−0.307033	−	0.225198i
$682$	−5.19358	−	6.35594i	−0.198872	−	0.243381i
$683$			23.7290i			0.907964i	0.891011	+	0.453982i	$0.149997\pi$
$683$			23.7290i			0.907964i	−0.891011	+	0.453982i	$0.850003\pi$
$684$	−0.726784	−	2.30752i	−0.0277893	−	0.0882301i
$685$			7.20588i			0.275322i
$686$			8.29900i			0.316857i
$687$	−27.4353	−	20.1228i	−1.04672	−	0.767733i
$688$			12.7290i			0.485287i
$689$		−	34.5784i		−	1.31733i
$690$	1.35127	−	1.84231i	0.0514419	−	0.0701355i
$691$	14.6081			0.555720			0.277860	−	0.960622i	$-0.410375\pi$
$691$	14.6081			0.555720			0.277860	+	0.960622i	$0.410375\pi$
$692$		−	7.01005i		−	0.266482i
$693$	0.809010	+	2.56858i	0.0307317	+	0.0975723i
$694$		−	25.9222i		−	0.983995i
$695$	−5.10841			−0.193773
$696$	2.41020	+	1.76780i	0.0913586	+	0.0670083i
$697$		−	5.79942i		−	0.219669i
$698$		−	23.6456i		−	0.894999i
$699$	9.84975	+	7.22444i	0.372552	+	0.273254i
$700$	0.608912			0.0230147
$701$		−	15.8165i		−	0.597380i	−0.954350	−	0.298690i	$-0.903450\pi$
$701$		−	15.8165i		−	0.597380i	0.954350	−	0.298690i	$-0.0965497\pi$
$702$	22.1096	+	7.51648i	0.834474	+	0.283691i
$703$			2.25257i			0.0849574i
$704$	1.47420			0.0555610
$705$	−4.21831	+	5.75121i	−0.158871	+	0.216603i
$706$		−	4.03503i		−	0.151860i
$707$		−	4.83757i		−	0.181935i
$708$	14.3960	+	10.5589i	0.541033	+	0.396829i
$709$			16.5034i			0.619800i	0.950769	+	0.309900i	$0.100296\pi$
$709$			16.5034i			0.619800i	−0.950769	+	0.309900i	$0.899704\pi$
$710$		−	4.02425i		−	0.151027i
$711$	12.5839	−	3.96346i	0.471932	−	0.148641i
$712$		−	12.1395i		−	0.454949i
$713$	−5.68721	+	4.64715i	−0.212988	+	0.174037i
$714$	−0.702538	−	0.515287i	−0.0262918	−	0.0192841i
$715$	−6.62529			−0.247772
$716$	−3.40754			−0.127346
$717$	20.1585	−	27.4839i	0.752833	−	1.02641i
$718$	33.1132			1.23577
$719$	−14.3937			−0.536795			−0.268397	−	0.963308i	$-0.586494\pi$
$719$	−14.3937			−0.536795			−0.268397	+	0.963308i	$0.586494\pi$
$720$	−2.86143	+	0.901245i	−0.106639	+	0.0335874i
$721$	10.8149			0.402769
$722$			18.3497i			0.682904i
$723$	9.20757	+	6.75342i	0.342433	+	0.251163i
$724$		−	8.95446i		−	0.332790i
$725$	1.72571			0.0640912
$726$	−12.3278	−	9.04203i	−0.457529	−	0.335581i
$727$	−36.9796			−1.37150			−0.685748	−	0.727839i	$-0.740525\pi$
$727$	−36.9796			−1.37150			−0.685748	+	0.727839i	$0.740525\pi$
$728$	−2.73655			−0.101423
$729$	21.4055	+	16.4561i	0.792796	+	0.609487i
$730$			4.96332i			0.183701i
$731$		−	10.5153i		−	0.388922i
$732$	10.7779	+	7.90518i	0.398361	+	0.292184i
$733$	23.1070			0.853478			0.426739	−	0.904375i	$-0.359662\pi$
$733$	23.1070			0.853478			0.426739	+	0.904375i	$0.359662\pi$
$734$	14.5621			0.537495
$735$	−9.25869	−	6.79092i	−0.341512	−	0.250487i
$736$		−	1.31909i		−	0.0486225i
$737$	−6.47914			−0.238662
$738$	−6.32702	−	20.0881i	−0.232901	−	0.739453i
$739$			12.0209i			0.442194i	0.975252	+	0.221097i	$0.0709638\pi$
$739$			12.0209i			0.442194i	−0.975252	+	0.221097i	$0.929036\pi$
$740$	2.79329			0.102684
$741$	5.06172	+	3.71259i	0.185947	+	0.136385i
$742$			4.68501i			0.171992i
$743$	−47.8691			−1.75615			−0.878074	−	0.478525i	$-0.841172\pi$
$743$	−47.8691			−1.75615			−0.878074	+	0.478525i	$0.841172\pi$
$744$	9.63048	−	0.503750i	0.353071	−	0.0184684i
$745$	−19.0749			−0.698851
$746$		−	8.90617i		−	0.326078i
$747$	1.84645	+	5.86244i	0.0675583	+	0.214495i
$748$	−1.21782			−0.0445281
$749$			9.10607i			0.332729i
$750$	−1.02439	+	1.39665i	−0.0374055	+	0.0509983i
$751$	15.5167			0.566212			0.283106	−	0.959089i	$-0.408635\pi$
$751$	15.5167			0.566212			0.283106	+	0.959089i	$0.408635\pi$
$752$			4.11787i			0.150163i
$753$	9.06587	−	12.3603i	0.330379	−	0.450435i
$754$	−7.75561			−0.282443
$755$	−6.08960			−0.221623
$756$	−2.99562	−	1.01840i	−0.108950	−	0.0370390i
$757$			48.4424i			1.76067i	0.474355	+	0.880334i	$0.342681\pi$
$757$			48.4424i			1.76067i	−0.474355	+	0.880334i	$0.657319\pi$
$758$			23.9647i			0.870438i
$759$	1.99204	−	2.71593i	0.0723065	−	0.0985820i
$760$	−0.806422			−0.0292520
$761$	−14.5191			−0.526318			−0.263159	−	0.964752i	$-0.584764\pi$
$761$	−14.5191			−0.526318			−0.263159	+	0.964752i	$0.584764\pi$
$762$	12.5588	−	17.1226i	0.454959	−	0.620287i
$763$	0.427784			0.0154868
$764$		−	4.19751i		−	0.151861i
$765$	2.36380	−	0.744511i	0.0854634	−	0.0269179i
$766$			1.37487i			0.0496760i
$767$	−46.3237			−1.67265
$768$	−1.02439	+	1.39665i	−0.0369645	+	0.0503972i
$769$	12.3810			0.446471			0.223236	−	0.974764i	$-0.428338\pi$
$769$	12.3810			0.446471			0.223236	+	0.974764i	$0.428338\pi$
$770$	0.897658			0.0323493
$771$	−14.3076	−	10.4941i	−0.515276	−	0.377937i
$772$	−6.54326			−0.235497
$773$	22.9171			0.824271			0.412136	−	0.911122i	$-0.364783\pi$
$773$	22.9171			0.824271			0.412136	+	0.911122i	$0.364783\pi$
$774$	−11.4719	−	36.4230i	−0.412349	−	1.30920i
$775$	4.31145	−	3.52298i	0.154872	−	0.126549i
$776$			2.89218i			0.103823i
$777$	2.37552	+	1.74236i	0.0852211	+	0.0625067i
$778$			7.52414i			0.269754i
$779$		−	5.66134i		−	0.202838i
$780$	4.60378	−	6.27676i	0.164842	−	0.224744i
$781$		−	5.93254i		−	0.212283i
$782$			1.08969i			0.0389673i
$783$	−8.48984	−	2.88624i	−0.303402	−	0.103146i
$784$	−6.62923			−0.236758
$785$		−	18.5675i		−	0.662703i
$786$	8.59979	−	11.7249i	0.306744	−	0.418213i
$787$			39.3350i			1.40214i	0.713091	+	0.701071i	$0.247295\pi$
$787$			39.3350i			1.40214i	−0.713091	+	0.701071i	$0.752705\pi$
$788$	−1.09242			−0.0389160
$789$	8.67910	−	11.8330i	0.308984	−	0.421267i
$790$		−	4.39776i		−	0.156465i
$791$		−	10.9937i		−	0.390890i
$792$	−4.21831	+	1.32861i	−0.149891	+	0.0472103i
$793$	−34.6812			−1.23157
$794$			8.55964i			0.303770i
$795$	−10.7459	−	7.88174i	−0.381118	−	0.279537i
$796$		−	15.7637i		−	0.558731i
$797$	−15.3571			−0.543977			−0.271989	−	0.962300i	$-0.587681\pi$
$797$	−15.3571			−0.543977			−0.271989	+	0.962300i	$0.587681\pi$
$798$	−0.685810	−	0.503017i	−0.0242774	−	0.0178066i
$799$		−	3.40174i		−	0.120345i
$800$			1.00000i			0.0353553i
$801$	10.9407	+	34.7364i	0.386571	+	1.22735i
$802$		−	28.2196i		−	0.996469i
$803$			7.31692i			0.258208i
$804$	4.50222	−	6.13829i	0.158781	−	0.216481i
$805$		−	0.803212i		−	0.0283095i
$806$	−19.3764	+	15.8329i	−0.682503	+	0.557689i
$807$	24.5790	−	33.5108i	0.865221	−	1.17963i
$808$	7.94461			0.279490
$809$	−17.3663			−0.610565			−0.305282	−	0.952262i	$-0.598751\pi$
$809$	−17.3663			−0.610565			−0.305282	+	0.952262i	$0.598751\pi$
$810$	7.37552	−	5.15769i	0.259149	−	0.181223i
$811$	26.2911			0.923207			0.461603	−	0.887086i	$-0.347274\pi$
$811$	26.2911			0.923207			0.461603	+	0.887086i	$0.347274\pi$
$812$	1.05080			0.0368760
$813$	39.6876	+	29.1094i	1.39190	+	1.02091i
$814$	4.11787			0.144331
$815$		−	2.83067i		−	0.0991540i
$816$	0.846241	−	1.15376i	0.0296244	−	0.0403896i
$817$		−	10.2649i		−	0.359124i
$818$	22.3167			0.780285
$819$	7.83044	−	2.46630i	0.273618	−	0.0861796i
$820$	−7.02031			−0.245160
$821$	35.2252			1.22937			0.614684	−	0.788773i	$-0.289284\pi$
$821$	35.2252			1.22937			0.614684	+	0.788773i	$0.289284\pi$
$822$	−10.0641	−	7.38164i	−0.351025	−	0.257464i
$823$			31.9544i			1.11386i	0.830559	+	0.556931i	$0.188021\pi$
$823$			31.9544i			1.11386i	−0.830559	+	0.556931i	$0.811979\pi$
$824$			17.7611i			0.618737i
$825$	−1.51016	+	2.05894i	−0.0525769	+	0.0716829i
$826$	6.27637			0.218383
$827$	−18.8953			−0.657054			−0.328527	−	0.944495i	$-0.606552\pi$
$827$	−18.8953			−0.657054			−0.328527	+	0.944495i	$0.606552\pi$
$828$	1.18883	+	3.77449i	0.0413146	+	0.131173i
$829$		−	40.8083i		−	1.41733i	−0.705545	−	0.708665i	$-0.749298\pi$
$829$		−	40.8083i		−	1.41733i	0.705545	−	0.708665i	$-0.250702\pi$
$830$	2.04878			0.0711143
$831$	7.84034	+	5.75061i	0.271978	+	0.199486i
$832$		−	4.49416i		−	0.155807i
$833$	5.47635			0.189744
$834$	5.23301	−	7.13464i	0.181204	−	0.247052i
$835$			1.65895i			0.0574103i
$836$	−1.18883			−0.0411164
$837$	−27.1029	+	10.1209i	−0.936814	+	0.349828i
$838$	33.8502			1.16934
$839$		−	17.9983i		−	0.621369i	−0.950513	−	0.310684i	$-0.899442\pi$
$839$		−	17.9983i		−	0.621369i	0.950513	−	0.310684i	$-0.100558\pi$
$840$	−0.623764	+	0.850435i	−0.0215219	+	0.0293428i
$841$	−26.0219			−0.897308
$842$			14.2200i			0.490054i
$843$	8.15743	+	5.98319i	0.280957	+	0.206072i
$844$	−18.2443			−0.627993
$845$			7.19751i			0.247602i
$846$	−3.71121	−	11.7830i	−0.127594	−	0.405107i
$847$	−5.37471			−0.184677
$848$	−7.69407			−0.264215
$849$	−4.28938	+	5.84811i	−0.147211	+	0.200707i
$850$		−	0.826092i		−	0.0283347i
$851$		−	3.68462i		−	0.126307i
$852$	5.62045	+	4.12240i	0.192553	+	0.141231i
$853$	−26.6003			−0.910776			−0.455388	−	0.890293i	$-0.650499\pi$
$853$	−26.6003			−0.910776			−0.455388	+	0.890293i	$0.650499\pi$
$854$	4.69894			0.160795
$855$	2.30752	−	0.726784i	0.0789154	−	0.0248555i
$856$	−14.9547			−0.511140
$857$		−	29.6814i		−	1.01390i	−0.861976	−	0.506949i	$-0.830773\pi$
$857$		−	29.6814i		−	1.01390i	0.861976	−	0.506949i	$-0.169227\pi$
$858$	6.78689	−	9.25320i	0.231701	−	0.315899i
$859$		−	35.1459i		−	1.19916i	−0.800314	−	0.599581i	$-0.795334\pi$
$859$		−	35.1459i		−	1.19916i	0.800314	−	0.599581i	$-0.204666\pi$
$860$	−12.7290			−0.434054
$861$	−5.97032	−	4.37902i	−0.203468	−	0.149237i
$862$	−8.94068			−0.304521
$863$	30.0613			1.02330			0.511650	−	0.859194i	$-0.329034\pi$
$863$	30.0613			1.02330			0.511650	+	0.859194i	$0.329034\pi$
$864$	1.67250	−	4.91963i	0.0568996	−	0.167369i
$865$	7.01005			0.238349
$866$	−13.7885			−0.468552
$867$	16.7156	−	22.7899i	0.567691	−	0.773985i
$868$	2.62529	−	2.14519i	0.0891083	−	0.0728124i
$869$		−	6.48318i		−	0.219927i
$870$	−1.76780	+	2.41020i	−0.0599340	+	0.0817136i
$871$			19.7519i			0.669269i
$872$			0.702538i			0.0237909i
$873$	−2.60657	−	8.27577i	−0.0882189	−	0.280092i
$874$			1.06375i			0.0359818i
$875$			0.608912i			0.0205850i
$876$	−6.93200	−	5.08438i	−0.234211	−	0.171785i
$877$	10.8508			0.366405			0.183202	−	0.983075i	$-0.441354\pi$
$877$	10.8508			0.366405			0.183202	+	0.983075i	$0.441354\pi$
$878$			16.5736i			0.559333i
$879$	6.38883	+	4.68598i	0.215490	+	0.158054i
$880$			1.47420i			0.0496953i
$881$	37.1225			1.25069			0.625345	−	0.780349i	$-0.284958\pi$
$881$	37.1225			1.25069			0.625345	+	0.780349i	$0.284958\pi$
$882$	18.9690	−	5.97456i	0.638721	−	0.201174i
$883$		−	31.4405i		−	1.05806i	−0.848604	−	0.529029i	$-0.822556\pi$
$883$		−	31.4405i		−	1.05806i	0.848604	−	0.529029i	$-0.177444\pi$
$884$			3.71259i			0.124868i
$885$	−10.5589	+	14.3960i	−0.354935	+	0.483915i
$886$	12.5190			0.420585
$887$		−	8.82989i		−	0.296479i	−0.988952	−	0.148239i	$-0.952639\pi$
$887$		−	8.82989i		−	0.296479i	0.988952	−	0.148239i	$-0.0473606\pi$
$888$	−2.86143	+	3.90124i	−0.0960232	+	0.130917i
$889$		−	7.46514i		−	0.250373i
$890$	12.1395			0.406919
$891$	10.8730	−	7.60346i	0.364259	−	0.254726i
$892$			3.41852i			0.114461i
$893$		−	3.32074i		−	0.111124i
$894$	19.5402	−	26.6409i	0.653522	−	0.891006i
$895$		−	3.40754i		−	0.113901i
$896$			0.608912i			0.0203423i
$897$	−8.27964	−	6.07282i	−0.276449	−	0.202766i
$898$		−	28.1935i		−	0.940828i
$899$	7.44030	−	6.07964i	0.248148	−	0.202767i
$900$	−0.901245	−	2.86143i	−0.0300415	−	0.0953809i
$901$	6.35601			0.211749
$902$	−10.3493			−0.344595
$903$	−10.8252	−	7.93987i	−0.360238	−	0.264222i
$904$	18.0546			0.600488
$905$	8.95446			0.297656
$906$	6.23814	−	8.50503i	0.207248	−	0.282561i
$907$	49.6736			1.64938			0.824692	−	0.565582i	$-0.191348\pi$
$907$	49.6736			1.64938			0.824692	+	0.565582i	$0.191348\pi$
$908$		−	5.73684i		−	0.190384i
$909$	−22.7329	+	7.16004i	−0.754003	+	0.237483i
$910$		−	2.73655i		−	0.0907158i
$911$	12.9885			0.430329			0.215164	−	0.976578i	$-0.430971\pi$
$911$	12.9885			0.430329			0.215164	+	0.976578i	$0.430971\pi$
$912$	0.826092	−	1.12629i	0.0273546	−	0.0372951i
$913$	3.02031			0.0999578
$914$	1.42648			0.0471838
$915$	−7.90518	+	10.7779i	−0.261337	+	0.356305i
$916$		−	19.6437i		−	0.649045i
$917$		−	5.11183i		−	0.168807i
$918$	−1.38164	+	4.06407i	−0.0456008	+	0.134134i
$919$	−29.5455			−0.974615			−0.487307	−	0.873231i	$-0.662021\pi$
$919$	−29.5455			−0.974615			−0.487307	+	0.873231i	$0.662021\pi$
$920$	1.31909			0.0434893
$921$	−11.5331	+	15.7241i	−0.380027	+	0.518126i
$922$		−	16.3493i		−	0.538436i
$923$	−18.0856			−0.595296
$924$	−0.919553	+	1.25371i	−0.0302511	+	0.0412441i
$925$			2.79329i			0.0918429i
$926$	16.4367			0.540143
$927$	−16.0071	−	50.8220i	−0.525742	−	1.66921i
$928$			1.72571i			0.0566491i
$929$	−25.2035			−0.826899			−0.413450	−	0.910527i	$-0.635676\pi$
$929$	−25.2035			−0.826899			−0.413450	+	0.910527i	$0.635676\pi$
$930$	0.503750	+	9.63048i	0.0165186	+	0.315796i
$931$	5.34596			0.175207
$932$			7.05243i			0.231010i
$933$	18.3494	+	13.4586i	0.600733	+	0.440616i
$934$	6.41513			0.209909
$935$		−	1.21782i		−	0.0398271i
$936$	4.05034	+	12.8597i	0.132390	+	0.420333i
$937$	15.7891			0.515806			0.257903	−	0.966171i	$-0.416968\pi$
$937$	15.7891			0.515806			0.257903	+	0.966171i	$0.416968\pi$
$938$		−	2.67618i		−	0.0873804i
$939$	−1.62842	−	1.19439i	−0.0531414	−	0.0389773i
$940$	−4.11787			−0.134310
$941$	6.24146			0.203466			0.101733	−	0.994812i	$-0.467561\pi$
$941$	6.24146			0.203466			0.101733	+	0.994812i	$0.467561\pi$
$942$	25.9323	+	19.0204i	0.844918	+	0.619718i
$943$			9.26046i			0.301562i
$944$			10.3075i			0.335481i
$945$	1.01840	−	2.99562i	0.0331287	−	0.0974476i
$946$	−18.7650			−0.610103
$947$	−23.5542			−0.765410			−0.382705	−	0.923871i	$-0.625007\pi$
$947$	−23.5542			−0.765410			−0.382705	+	0.923871i	$0.625007\pi$
$948$	6.14212	+	4.50503i	0.199487	+	0.146316i
$949$	22.3060			0.724082
$950$		−	0.806422i		−	0.0261638i
$951$	−38.7179	−	28.3983i	−1.25552	−	0.920876i
$952$		−	0.503017i		−	0.0163029i
$953$	−13.8604			−0.448981			−0.224491	−	0.974476i	$-0.572072\pi$
$953$	−13.8604			−0.448981			−0.224491	+	0.974476i	$0.572072\pi$
$954$	22.0160	−	6.93424i	0.712795	−	0.224504i
$955$	4.19751			0.135828
$956$	19.6785			0.636449
$957$	−2.60609	+	3.55312i	−0.0842429	+	0.114856i
$958$	−22.2928			−0.720246
$959$	−4.38775			−0.141688
$960$	−1.39665	−	1.02439i	−0.0450766	−	0.0330621i
$961$	6.17720	−	30.3783i	0.199264	−	0.979946i
$962$		−	12.5535i		−	0.404742i
$963$	42.7917	−	13.4778i	1.37894	−	0.434316i
$964$			6.59262i			0.212334i
$965$		−	6.54326i		−	0.210635i
$966$	1.12180	+	0.822804i	0.0360935	+	0.0264733i
$967$			57.1337i			1.83730i	0.395077	+	0.918648i	$0.370718\pi$
$967$			57.1337i			1.83730i	−0.395077	+	0.918648i	$0.629282\pi$
$968$		−	8.82674i		−	0.283702i
$969$	−0.682428	+	0.930417i	−0.0219227	+	0.0298893i
$970$	−2.89218			−0.0928624
$971$		−	17.5332i		−	0.562667i	−0.959610	−	0.281334i	$-0.909223\pi$
$971$		−	17.5332i		−	0.562667i	0.959610	−	0.281334i	$-0.0907768\pi$
$972$	−0.351941	+	15.5845i	−0.0112885	+	0.499873i
$973$		−	3.11057i		−	0.0997203i
$974$	25.4115			0.814236
$975$	6.27676	+	4.60378i	0.201017	+	0.147439i
$976$			7.71695i			0.247014i
$977$		−	45.4019i		−	1.45254i	−0.687412	−	0.726268i	$-0.741253\pi$
$977$		−	45.4019i		−	1.45254i	0.687412	−	0.726268i	$-0.258747\pi$
$978$	3.95344	+	2.89971i	0.126417	+	0.0927226i
$979$	17.8961			0.571962
$980$		−	6.62923i		−	0.211763i
$981$	−0.633158	−	2.01026i	−0.0202152	−	0.0641826i
$982$		−	21.8676i		−	0.697823i
$983$	8.59753			0.274219			0.137109	−	0.990556i	$-0.456219\pi$
$983$	8.59753			0.274219			0.137109	+	0.990556i	$0.456219\pi$
$984$	7.19155	−	9.80490i	0.229258	−	0.312569i
$985$		−	1.09242i		−	0.0348075i
$986$		−	1.42559i		−	0.0454001i
$987$	−3.50198	−	2.56858i	−0.111469	−	0.0817588i
$988$			3.62419i			0.115301i
$989$			16.7907i			0.533913i
$990$	−1.32861	−	4.21831i	−0.0422261	−	0.134067i
$991$			3.10155i			0.0985238i	0.998786	+	0.0492619i	$0.0156869\pi$
$991$			3.10155i			0.0985238i	−0.998786	+	0.0492619i	$0.984313\pi$
$992$	3.52298	+	4.31145i	0.111855	+	0.136889i
$993$	36.3596	+	26.6685i	1.15384	+	0.846298i
$994$	2.45041			0.0777224
$995$	15.7637			0.499744
$996$	−2.09876	+	2.86143i	−0.0665016	+	0.0906677i
$997$	27.4863			0.870501			0.435250	−	0.900309i	$-0.356660\pi$
$997$	27.4863			0.870501			0.435250	+	0.900309i	$0.356660\pi$
$998$	4.19112			0.132668
$999$	4.67178	−	13.7420i	0.147809	−	0.434777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.h.c.371.3	✓	16
3.2	odd	2	inner	930.2.h.c.371.14	yes	16
31.30	odd	2	inner	930.2.h.c.371.6	yes	16
93.92	even	2	inner	930.2.h.c.371.11	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.h.c.371.3	✓	16	1.1	even	1	trivial
930.2.h.c.371.6	yes	16	31.30	odd	2	inner
930.2.h.c.371.11	yes	16	93.92	even	2	inner
930.2.h.c.371.14	yes	16	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.02439 + 1.39665i) q^{3} -1.00000 q^{4} -1.00000i q^{5} +(1.39665 + 1.02439i) q^{6} +0.608912 q^{7} +1.00000i q^{8} +(-0.901245 - 2.86143i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.02439 + 1.39665i) q^{3} -1.00000 q^{4} -1.00000i q^{5} +(1.39665 + 1.02439i) q^{6} +0.608912 q^{7} +1.00000i q^{8} +(-0.901245 - 2.86143i) q^{9} -1.00000 q^{10} -1.47420 q^{11} +(1.02439 - 1.39665i) q^{12} +4.49416i q^{13} -0.608912i q^{14} +(1.39665 + 1.02439i) q^{15} +1.00000 q^{16} -0.826092 q^{17} +(-2.86143 + 0.901245i) q^{18} -0.806422 q^{19} +1.00000i q^{20} +(-0.623764 + 0.850435i) q^{21} +1.47420i q^{22} +1.31909 q^{23} +(-1.39665 - 1.02439i) q^{24} -1.00000 q^{25} +4.49416 q^{26} +(4.91963 + 1.67250i) q^{27} -0.608912 q^{28} -1.72571 q^{29} +(1.02439 - 1.39665i) q^{30} +(-4.31145 + 3.52298i) q^{31} -1.00000i q^{32} +(1.51016 - 2.05894i) q^{33} +0.826092i q^{34} -0.608912i q^{35} +(0.901245 + 2.86143i) q^{36} -2.79329i q^{37} +0.806422i q^{38} +(-6.27676 - 4.60378i) q^{39} +1.00000 q^{40} +7.02031i q^{41} +(0.850435 + 0.623764i) q^{42} +12.7290i q^{43} +1.47420 q^{44} +(-2.86143 + 0.901245i) q^{45} -1.31909i q^{46} +4.11787i q^{47} +(-1.02439 + 1.39665i) q^{48} -6.62923 q^{49} +1.00000i q^{50} +(0.846241 - 1.15376i) q^{51} -4.49416i q^{52} -7.69407 q^{53} +(1.67250 - 4.91963i) q^{54} +1.47420i q^{55} +0.608912i q^{56} +(0.826092 - 1.12629i) q^{57} +1.72571i q^{58} +10.3075i q^{59} +(-1.39665 - 1.02439i) q^{60} +7.71695i q^{61} +(3.52298 + 4.31145i) q^{62} +(-0.548779 - 1.74236i) q^{63} -1.00000 q^{64} +4.49416 q^{65} +(-2.05894 - 1.51016i) q^{66} +4.39502 q^{67} +0.826092 q^{68} +(-1.35127 + 1.84231i) q^{69} -0.608912 q^{70} +4.02425i q^{71} +(2.86143 - 0.901245i) q^{72} -4.96332i q^{73} -2.79329 q^{74} +(1.02439 - 1.39665i) q^{75} +0.806422 q^{76} -0.897658 q^{77} +(-4.60378 + 6.27676i) q^{78} +4.39776i q^{79} -1.00000i q^{80} +(-7.37552 + 5.15769i) q^{81} +7.02031 q^{82} -2.04878 q^{83} +(0.623764 - 0.850435i) q^{84} +0.826092i q^{85} +12.7290 q^{86} +(1.76780 - 2.41020i) q^{87} -1.47420i q^{88} -12.1395 q^{89} +(0.901245 + 2.86143i) q^{90} +2.73655i q^{91} -1.31909 q^{92} +(-0.503750 - 9.63048i) q^{93} +4.11787 q^{94} +0.806422i q^{95} +(1.39665 + 1.02439i) q^{96} +2.89218 q^{97} +6.62923i q^{98} +(1.32861 + 4.21831i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 20 q^{7} - 4 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 - 20 * q^7 - 4 * q^9	\( 16 q - 16 q^{4} - 20 q^{7} - 4 q^{9} - 16 q^{10} + 16 q^{16} + 12 q^{18} - 4 q^{19} - 16 q^{25} + 20 q^{28} - 4 q^{31} - 16 q^{33} + 4 q^{36} - 4 q^{39} + 16 q^{40} + 12 q^{45} + 4 q^{49} + 52 q^{51} - 12 q^{63} - 16 q^{64} + 4 q^{66} + 112 q^{67} - 4 q^{69} + 20 q^{70} - 12 q^{72} + 4 q^{76} - 28 q^{78} - 32 q^{81} + 32 q^{82} - 24 q^{87} + 4 q^{90} + 16 q^{93} - 8 q^{94} + 8 q^{97}+O(q^{100}) \) 16 * q - 16 * q^4 - 20 * q^7 - 4 * q^9 - 16 * q^10 + 16 * q^16 + 12 * q^18 - 4 * q^19 - 16 * q^25 + 20 * q^28 - 4 * q^31 - 16 * q^33 + 4 * q^36 - 4 * q^39 + 16 * q^40 + 12 * q^45 + 4 * q^49 + 52 * q^51 - 12 * q^63 - 16 * q^64 + 4 * q^66 + 112 * q^67 - 4 * q^69 + 20 * q^70 - 12 * q^72 + 4 * q^76 - 28 * q^78 - 32 * q^81 + 32 * q^82 - 24 * q^87 + 4 * q^90 + 16 * q^93 - 8 * q^94 + 8 * q^97

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