LMFDB - Embedded newform 352.2.n.a.45.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [352,2,Mod(45,352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(352, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

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

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

chi := DirichletCharacter("352.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 352 = 2^{5} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	352.n (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			45.4
Character	$\chi$	$=$	352.45
Dual form			352.2.n.a.133.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38982 + 0.261511i) q^{2} +(-0.342954 + 0.827965i) q^{3} +(1.86322 - 0.726908i) q^{4} +(-3.84471 + 1.59253i) q^{5} +(0.260125 - 1.24041i) q^{6} +(0.897811 - 0.897811i) q^{7} +(-2.39946 + 1.49753i) q^{8} +(1.55341 + 1.55341i) q^{9} +(4.92700 - 3.21877i) q^{10} +(0.382683 + 0.923880i) q^{11} +(-0.0371463 + 1.79198i) q^{12} +(-5.54640 - 2.29739i) q^{13} +(-1.01301 + 1.48259i) q^{14} -3.72945i q^{15} +(2.94321 - 2.70879i) q^{16} -4.00902i q^{17} +(-2.56520 - 1.75274i) q^{18} +(-0.186560 - 0.0772758i) q^{19} +(-6.00593 + 5.76199i) q^{20} +(0.435448 + 1.05126i) q^{21} +(-0.773467 - 1.18395i) q^{22} +(-3.01858 - 3.01858i) q^{23} +(-0.416995 - 2.50025i) q^{24} +(8.71008 - 8.71008i) q^{25} +(8.30932 + 1.74253i) q^{26} +(-4.30281 + 1.78228i) q^{27} +(1.02020 - 2.32545i) q^{28} +(0.573587 - 1.38476i) q^{29} +(0.975291 + 5.18328i) q^{30} -7.34100 q^{31} +(-3.38217 + 4.53442i) q^{32} -0.896183 q^{33} +(1.04840 + 5.57184i) q^{34} +(-2.02203 + 4.88161i) q^{35} +(4.02354 + 1.76517i) q^{36} +(7.53146 - 3.11963i) q^{37} +(0.279495 + 0.0586123i) q^{38} +(3.80432 - 3.80432i) q^{39} +(6.84036 - 9.57877i) q^{40} +(-3.37501 - 3.37501i) q^{41} +(-0.880113 - 1.34720i) q^{42} +(-4.25260 - 10.2667i) q^{43} +(1.38460 + 1.44322i) q^{44} +(-8.44627 - 3.49856i) q^{45} +(4.98469 + 3.40590i) q^{46} +1.83246i q^{47} +(1.23339 + 3.36586i) q^{48} +5.38787i q^{49} +(-9.82771 + 14.3833i) q^{50} +(3.31933 + 1.37491i) q^{51} +(-12.0042 - 0.248837i) q^{52} +(-1.62721 - 3.92842i) q^{53} +(5.51407 - 3.60229i) q^{54} +(-2.94261 - 2.94261i) q^{55} +(-0.809765 + 3.49876i) q^{56} +(0.127963 - 0.127963i) q^{57} +(-0.435055 + 2.07457i) q^{58} +(-10.8958 + 4.51318i) q^{59} +(-2.71097 - 6.94880i) q^{60} +(0.503786 - 1.21625i) q^{61} +(10.2027 - 1.91975i) q^{62} +2.78934 q^{63} +(3.51482 - 7.18652i) q^{64} +24.9830 q^{65} +(1.24554 - 0.234361i) q^{66} +(-3.37475 + 8.14737i) q^{67} +(-2.91419 - 7.46971i) q^{68} +(3.53451 - 1.46404i) q^{69} +(1.53367 - 7.31337i) q^{70} +(-1.94936 + 1.94936i) q^{71} +(-6.05363 - 1.40107i) q^{72} +(0.977092 + 0.977092i) q^{73} +(-9.65159 + 6.30530i) q^{74} +(4.22448 + 10.1988i) q^{75} +(-0.403776 - 0.00836995i) q^{76} +(1.17305 + 0.485892i) q^{77} +(-4.29247 + 6.28222i) q^{78} +16.2913i q^{79} +(-7.00195 + 15.1016i) q^{80} +2.41675i q^{81} +(5.57327 + 3.80807i) q^{82} +(12.9260 + 5.35414i) q^{83} +(1.57551 + 1.64221i) q^{84} +(6.38449 + 15.4135i) q^{85} +(8.59522 + 13.1568i) q^{86} +(0.949820 + 0.949820i) q^{87} +(-2.30177 - 1.64373i) q^{88} +(-0.494066 + 0.494066i) q^{89} +(12.6537 + 2.65359i) q^{90} +(-7.04225 + 2.91699i) q^{91} +(-7.81852 - 3.43006i) q^{92} +(2.51763 - 6.07809i) q^{93} +(-0.479208 - 2.54680i) q^{94} +0.840334 q^{95} +(-2.59441 - 4.35541i) q^{96} -10.4601 q^{97} +(-1.40899 - 7.48819i) q^{98} +(-0.840701 + 2.02963i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 16 q^{10} - 16 q^{14} - 16 q^{20} + 24 q^{24} - 48 q^{27} + 40 q^{28} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 56 q^{36} - 16 q^{38} - 48 q^{39} - 64 q^{40} - 104 q^{48} - 80 q^{50} + 32 q^{51} + 64 q^{54}+ \cdots + 56 q^{98}+O(q^{100}) $ 160 * q - 16 * q^10 - 16 * q^14 - 16 * q^20 + 24 * q^24 - 48 * q^27 + 40 * q^28 + 80 * q^30 - 48 * q^31 - 48 * q^35 + 56 * q^36 - 16 * q^38 - 48 * q^39 - 64 * q^40 - 104 * q^48 - 80 * q^50 + 32 * q^51 + 64 * q^54 - 40 * q^56 + 8 * q^58 + 32 * q^59 - 8 * q^60 - 64 * q^61 + 24 * q^62 - 24 * q^64 + 48 * q^68 - 64 * q^69 - 24 * q^70 + 32 * q^71 + 72 * q^72 - 128 * q^78 - 16 * q^80 + 40 * q^82 - 80 * q^83 - 152 * q^84 - 64 * q^86 - 112 * q^87 + 144 * q^90 - 72 * q^92 + 96 * q^94 + 56 * q^96 + 56 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$.

$n$	$133$	$287$	$321$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

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 $

$2$	−1.38982	+	0.261511i	−0.982754	+	0.184916i
$2$	−1.38982	+	0.261511i	−0.982754	+	0.184916i
$3$	−0.342954	+	0.827965i	−0.198005	+	0.478026i	−0.991430	−	0.130643i	$-0.958296\pi$
$3$	−0.342954	+	0.827965i	−0.198005	+	0.478026i	0.793425	+	0.608668i	$0.208296\pi$
$4$	1.86322	−	0.726908i	0.931612	−	0.363454i
$5$	−3.84471	+	1.59253i	−1.71941	+	0.712201i	−0.719563	+	0.694427i	$0.755658\pi$
$5$	−3.84471	+	1.59253i	−1.71941	+	0.712201i	−0.999842	+	0.0177738i	$0.994342\pi$
$6$	0.260125	−	1.24041i	0.106195	−	0.506396i
$7$	0.897811	−	0.897811i	0.339341	−	0.339341i	−0.516778	−	0.856119i	$-0.672869\pi$
$7$	0.897811	−	0.897811i	0.339341	−	0.339341i	0.856119	+	0.516778i	$0.172869\pi$
$8$	−2.39946	+	1.49753i	−0.848337	+	0.529456i
$9$	1.55341	+	1.55341i	0.517804	+	0.517804i
$10$	4.92700	−	3.21877i	1.55806	−	1.01786i
$11$	0.382683	+	0.923880i	0.115383	+	0.278560i
$11$	0.382683	+	0.923880i	0.115383	+	0.278560i
$12$	−0.0371463	+	1.79198i	−0.0107232	+	0.517300i
$13$	−5.54640	−	2.29739i	−1.53830	−	0.637183i	−0.557142	−	0.830417i	$-0.688102\pi$
$13$	−5.54640	−	2.29739i	−1.53830	−	0.637183i	−0.981153	+	0.193234i	$0.938102\pi$
$14$	−1.01301	+	1.48259i	−0.270739	+	0.396238i
$15$		−	3.72945i		−	0.962939i
$16$	2.94321	−	2.70879i	0.735802	−	0.677196i
$17$		−	4.00902i		−	0.972331i	−0.873867	−	0.486165i	$-0.838395\pi$
$17$		−	4.00902i		−	0.972331i	0.873867	−	0.486165i	$-0.161605\pi$
$18$	−2.56520	−	1.75274i	−0.604624	−	0.413124i
$19$	−0.186560	−	0.0772758i	−0.0427999	−	0.0177283i	0.361181	−	0.932496i	$-0.382374\pi$
$19$	−0.186560	−	0.0772758i	−0.0427999	−	0.0177283i	−0.403981	+	0.914768i	$0.632374\pi$
$20$	−6.00593	+	5.76199i	−1.34297	+	1.28842i
$21$	0.435448	+	1.05126i	0.0950225	+	0.229405i
$22$	−0.773467	−	1.18395i	−0.164904	−	0.252420i
$23$	−3.01858	−	3.01858i	−0.629417	−	0.629417i	0.318504	−	0.947921i	$-0.396820\pi$
$23$	−3.01858	−	3.01858i	−0.629417	−	0.629417i	−0.947921	+	0.318504i	$0.896820\pi$
$24$	−0.416995	−	2.50025i	−0.0851188	−	0.510362i
$25$	8.71008	−	8.71008i	1.74202	−	1.74202i
$26$	8.30932	+	1.74253i	1.62959	+	0.341739i
$27$	−4.30281	+	1.78228i	−0.828077	+	0.343001i
$28$	1.02020	−	2.32545i	0.192799	−	0.439469i
$29$	0.573587	−	1.38476i	0.106512	−	0.257144i	−0.861633	−	0.507531i	$-0.830558\pi$
$29$	0.573587	−	1.38476i	0.106512	−	0.257144i	0.968146	+	0.250388i	$0.0805581\pi$
$30$	0.975291	+	5.18328i	0.178063	+	0.946333i
$31$	−7.34100			−1.31848			−0.659241	−	0.751932i	$-0.729122\pi$
$31$	−7.34100			−1.31848			−0.659241	+	0.751932i	$0.729122\pi$
$32$	−3.38217	+	4.53442i	−0.597888	+	0.801579i
$33$	−0.896183			−0.156005
$34$	1.04840	+	5.57184i	0.179800	+	0.955562i
$35$	−2.02203	+	4.88161i	−0.341785	+	0.825143i
$36$	4.02354	+	1.76517i	0.670590	+	0.294195i
$37$	7.53146	−	3.11963i	1.23816	−	0.512864i	0.335024	−	0.942210i	$-0.391256\pi$
$37$	7.53146	−	3.11963i	1.23816	−	0.512864i	0.903140	+	0.429345i	$0.141256\pi$
$38$	0.279495	+	0.0586123i	0.0453400	+	0.00950817i
$39$	3.80432	−	3.80432i	0.609179	−	0.609179i
$40$	6.84036	−	9.57877i	1.08156	−	1.51454i
$41$	−3.37501	−	3.37501i	−0.527088	−	0.527088i	0.392615	−	0.919703i	$-0.371570\pi$
$41$	−3.37501	−	3.37501i	−0.527088	−	0.527088i	−0.919703	+	0.392615i	$0.871570\pi$
$42$	−0.880113	−	1.34720i	−0.135804	−	0.207877i
$43$	−4.25260	−	10.2667i	−0.648516	−	1.56566i	−0.814904	−	0.579595i	$-0.803211\pi$
$43$	−4.25260	−	10.2667i	−0.648516	−	1.56566i	0.166389	−	0.986060i	$-0.446789\pi$
$44$	1.38460	+	1.44322i	0.208736	+	0.217573i
$45$	−8.44627	−	3.49856i	−1.25910	−	0.521534i
$46$	4.98469	+	3.40590i	0.734952	+	0.502173i
$47$			1.83246i			0.267292i	0.991029	+	0.133646i	$0.0426684\pi$
$47$			1.83246i			0.267292i	−0.991029	+	0.133646i	$0.957332\pi$
$48$	1.23339	+	3.36586i	0.178025	+	0.485821i
$49$			5.38787i			0.769696i
$50$	−9.82771	+	14.3833i	−1.38985	+	2.03410i
$51$	3.31933	+	1.37491i	0.464799	+	0.192526i
$52$	−12.0042	−	0.248837i	−1.66468	−	0.0345075i
$53$	−1.62721	−	3.92842i	−0.223514	−	0.539610i	0.771848	−	0.635807i	$-0.219332\pi$
$53$	−1.62721	−	3.92842i	−0.223514	−	0.539610i	−0.995362	+	0.0961961i	$0.969332\pi$
$54$	5.51407	−	3.60229i	0.750370	−	0.490210i
$55$	−2.94261	−	2.94261i	−0.396782	−	0.396782i
$56$	−0.809765	+	3.49876i	−0.108209	+	0.467541i
$57$	0.127963	−	0.127963i	0.0169492	−	0.0169492i
$58$	−0.435055	+	2.07457i	−0.0571255	+	0.272405i
$59$	−10.8958	+	4.51318i	−1.41851	+	0.587566i	−0.954486	−	0.298256i	$-0.903595\pi$
$59$	−10.8958	+	4.51318i	−1.41851	+	0.587566i	−0.464024	+	0.885822i	$0.653595\pi$
$60$	−2.71097	−	6.94880i	−0.349984	−	0.897086i
$61$	0.503786	−	1.21625i	0.0645031	−	0.155724i	−0.888341	−	0.459184i	$-0.848142\pi$
$61$	0.503786	−	1.21625i	0.0645031	−	0.155724i	0.952844	+	0.303460i	$0.0981418\pi$
$62$	10.2027	−	1.91975i	1.29574	−	0.243808i
$63$	2.78934			0.351424
$64$	3.51482	−	7.18652i	0.439352	−	0.898315i
$65$	24.9830			3.09875
$66$	1.24554	−	0.234361i	0.153315	−	0.0288479i
$67$	−3.37475	+	8.14737i	−0.412291	+	0.995359i	0.572230	+	0.820093i	$0.306079\pi$
$67$	−3.37475	+	8.14737i	−0.412291	+	0.995359i	−0.984521	+	0.175266i	$0.943921\pi$
$68$	−2.91419	−	7.46971i	−0.353398	−	0.905835i
$69$	3.53451	−	1.46404i	0.425505	−	0.176250i
$70$	1.53367	−	7.31337i	0.183309	−	0.874114i
$71$	−1.94936	+	1.94936i	−0.231346	+	0.231346i	−0.813254	−	0.581908i	$-0.802306\pi$
$71$	−1.94936	+	1.94936i	−0.231346	+	0.231346i	0.581908	+	0.813254i	$0.302306\pi$
$72$	−6.05363	−	1.40107i	−0.713427	−	0.165118i
$73$	0.977092	+	0.977092i	0.114360	+	0.114360i	0.761971	−	0.647611i	$-0.224232\pi$
$73$	0.977092	+	0.977092i	0.114360	+	0.114360i	−0.647611	+	0.761971i	$0.724232\pi$
$74$	−9.65159	+	6.30530i	−1.12197	+	0.732976i
$75$	4.22448	+	10.1988i	0.487801	+	1.17766i
$76$	−0.403776	−	0.00836995i	−0.0463163	−	0.000960099i
$77$	1.17305	+	0.485892i	0.133681	+	0.0553725i
$78$	−4.29247	+	6.28222i	−0.486027	+	0.711321i
$79$			16.2913i			1.83291i	0.400138	+	0.916455i	$0.368962\pi$
$79$			16.2913i			1.83291i	−0.400138	+	0.916455i	$0.631038\pi$
$80$	−7.00195	+	15.1016i	−0.782842	+	1.68841i
$81$			2.41675i			0.268527i
$82$	5.57327	+	3.80807i	0.615465	+	0.420531i
$83$	12.9260	+	5.35414i	1.41882	+	0.587693i	0.954563	−	0.298010i	$-0.0963227\pi$
$83$	12.9260	+	5.35414i	1.41882	+	0.587693i	0.464253	+	0.885702i	$0.346323\pi$
$84$	1.57551	+	1.64221i	0.171902	+	0.179180i
$85$	6.38449	+	15.4135i	0.692495	+	1.67183i
$86$	8.59522	+	13.1568i	0.926846	+	1.41873i
$87$	0.949820	+	0.949820i	0.101831	+	0.101831i
$88$	−2.30177	−	1.64373i	−0.245369	−	0.175223i
$89$	−0.494066	+	0.494066i	−0.0523708	+	0.0523708i	−0.732807	−	0.680436i	$-0.761790\pi$
$89$	−0.494066	+	0.494066i	−0.0523708	+	0.0523708i	0.680436	+	0.732807i	$0.261790\pi$
$90$	12.6537	+	2.65359i	1.33382	+	0.279713i
$91$	−7.04225	+	2.91699i	−0.738228	+	0.305784i
$92$	−7.81852	−	3.43006i	−0.815137	−	0.357608i
$93$	2.51763	−	6.07809i	0.261066	−	0.630268i
$94$	−0.479208	−	2.54680i	−0.0494265	−	0.262682i
$95$	0.840334			0.0862164
$96$	−2.59441	−	4.35541i	−0.264791	−	0.444523i
$97$	−10.4601			−1.06206			−0.531031	−	0.847352i	$-0.678195\pi$
$97$	−10.4601			−1.06206			−0.531031	+	0.847352i	$0.678195\pi$
$98$	−1.40899	−	7.48819i	−0.142329	−	0.756422i
$99$	−0.840701	+	2.02963i	−0.0844936	+	0.203986i
$100$	9.89741	−	22.5603i	0.989741	−	2.25603i
$101$	−1.95492	+	0.809753i	−0.194521	+	0.0805734i	−0.477818	−	0.878459i	$-0.658572\pi$
$101$	−1.95492	+	0.809753i	−0.194521	+	0.0805734i	0.283296	+	0.959032i	$0.408572\pi$
$102$	−4.97284	−	1.04285i	−0.492385	−	0.103257i
$103$	−4.60213	+	4.60213i	−0.453461	+	0.453461i	−0.896502	−	0.443040i	$-0.853900\pi$
$103$	−4.60213	+	4.60213i	−0.453461	+	0.453461i	0.443040	+	0.896502i	$0.353900\pi$
$104$	16.7488	−	2.79338i	1.64235	−	0.273914i
$105$	−3.34834	−	3.34834i	−0.326764	−	0.326764i
$106$	3.28886	+	5.03429i	0.319442	+	0.488973i
$107$	−1.00349	−	2.42264i	−0.0970109	−	0.234205i	0.867923	−	0.496699i	$-0.165455\pi$
$107$	−1.00349	−	2.42264i	−0.0970109	−	0.234205i	−0.964934	+	0.262494i	$0.915455\pi$
$108$	−6.72155	+	6.44855i	−0.646782	+	0.620512i
$109$	0.713821	+	0.295674i	0.0683716	+	0.0283205i	0.416607	−	0.909087i	$-0.363219\pi$
$109$	0.713821	+	0.295674i	0.0683716	+	0.0283205i	−0.348236	+	0.937407i	$0.613219\pi$
$110$	4.85924	+	3.32019i	0.463310	+	0.316568i
$111$			7.30567i			0.693424i
$112$	0.210468	−	5.07442i	0.0198873	−	0.479488i
$113$		−	3.75880i		−	0.353598i	−0.984247	−	0.176799i	$-0.943426\pi$
$113$		−	3.75880i		−	0.353598i	0.984247	−	0.176799i	$-0.0565742\pi$
$114$	−0.144383	+	0.211310i	−0.0135227	+	0.0197910i
$115$	16.4127	+	6.79837i	1.53049	+	0.633952i
$116$	0.0621267	−	2.99707i	0.00576832	−	0.278271i
$117$	−5.04705	−	12.1846i	−0.466600	−	1.12647i
$118$	13.9630	−	9.12190i	1.28540	−	0.839739i
$119$	−3.59935	−	3.59935i	−0.329951	−	0.329951i
$120$	5.58495	+	8.94866i	0.509834	+	0.816897i
$121$	−0.707107	+	0.707107i	−0.0642824	+	0.0642824i
$122$	−0.382112	+	1.82211i	−0.0345948	+	0.164966i
$123$	3.95186	−	1.63691i	0.356327	−	0.147596i
$124$	−13.6779	+	5.33623i	−1.22831	+	0.479208i
$125$	−11.6540	+	28.1353i	−1.04237	+	2.51649i
$126$	−3.87669	+	0.729443i	−0.345363	+	0.0649839i
$127$	−6.01852			−0.534057			−0.267028	−	0.963689i	$-0.586042\pi$
$127$	−6.01852			−0.534057			−0.267028	+	0.963689i	$0.586042\pi$
$128$	−3.00563	+	10.9072i	−0.265663	+	0.964066i
$129$	9.95891			0.876833
$130$	−34.7219	+	6.53331i	−3.04531	+	0.573009i
$131$	5.36135	−	12.9434i	0.468423	−	1.13087i	−0.496428	−	0.868078i	$-0.665355\pi$
$131$	5.36135	−	12.9434i	0.468423	−	1.13087i	0.964851	−	0.262796i	$-0.0846446\pi$
$132$	−1.66979	+	0.651443i	−0.145337	+	0.0567008i
$133$	−0.236875	+	0.0981168i	−0.0205397	+	0.00850781i
$134$	2.55969	−	12.2059i	0.221123	−	1.05443i
$135$	13.7047	−	13.7047i	1.17951	−	1.17951i
$136$	6.00362	+	9.61949i	0.514807	+	0.824865i
$137$	−14.1588	−	14.1588i	−1.20967	−	1.20967i	−0.971134	−	0.238536i	$-0.923333\pi$
$137$	−14.1588	−	14.1588i	−1.20967	−	1.20967i	−0.238536	−	0.971134i	$-0.576667\pi$
$138$	−4.52949	+	2.95908i	−0.385576	+	0.251893i
$139$	−2.70482	−	6.53001i	−0.229420	−	0.553868i	0.766687	−	0.642021i	$-0.221904\pi$
$139$	−2.70482	−	6.53001i	−0.229420	−	0.553868i	−0.996107	+	0.0881527i	$0.971904\pi$
$140$	−0.219011	+	10.5654i	−0.0185098	+	0.892936i
$141$	−1.51721	−	0.628450i	−0.127772	−	0.0529250i
$142$	2.19949	−	3.21904i	0.184577	−	0.270136i
$143$		−	6.00338i		−	0.502028i
$144$	8.77988	+	0.364156i	0.731656	+	0.0303463i
$145$			6.23745i			0.517992i
$146$	−1.61351	−	1.10247i	−0.133535	−	0.0912408i
$147$	−4.46097	−	1.84779i	−0.367934	−	0.152403i
$148$	11.7651	−	11.2873i	0.967086	−	0.927806i
$149$	−3.64062	−	8.78923i	−0.298251	−	0.720042i	−0.999971	−	0.00758931i	$-0.997584\pi$
$149$	−3.64062	−	8.78923i	−0.298251	−	0.720042i	0.701720	−	0.712453i	$-0.252416\pi$
$150$	−8.53839	−	13.0698i	−0.697156	−	1.06714i
$151$	−7.70423	−	7.70423i	−0.626961	−	0.626961i	0.320341	−	0.947302i	$-0.396202\pi$
$151$	−7.70423	−	7.70423i	−0.626961	−	0.626961i	−0.947302	+	0.320341i	$0.896202\pi$
$152$	0.563367	−	0.0939590i	0.0456951	−	0.00762108i
$153$	6.22767	−	6.22767i	0.503477	−	0.503477i
$154$	−1.75740	−	0.368540i	−0.141615	−	0.0296978i
$155$	28.2240	−	11.6908i	2.26700	−	0.939024i
$156$	4.32292	−	9.85370i	0.346110	−	0.788928i
$157$	−1.27902	+	3.08783i	−0.102077	+	0.246436i	−0.966664	−	0.256047i	$-0.917580\pi$
$157$	−1.27902	+	3.08783i	−0.102077	+	0.246436i	0.864587	+	0.502483i	$0.167580\pi$
$158$	−4.26034	−	22.6420i	−0.338934	−	1.80130i
$159$	3.81065			0.302205
$160$	5.78225	−	22.8197i	0.457127	−	1.80406i
$161$	−5.42023			−0.427174
$162$	−0.632006	−	3.35885i	−0.0496550	−	0.263897i
$163$	−8.77312	+	21.1802i	−0.687164	+	1.65896i	0.0632557	+	0.997997i	$0.479852\pi$
$163$	−8.77312	+	21.1802i	−0.687164	+	1.65896i	−0.750419	+	0.660962i	$0.770148\pi$
$164$	−8.74172	−	3.83508i	−0.682613	−	0.299469i
$165$	3.44556	−	1.42720i	0.268236	−	0.111107i
$166$	−19.3651	−	4.06101i	−1.50302	−	0.315196i
$167$	3.39362	−	3.39362i	0.262606	−	0.262606i	−0.563506	−	0.826112i	$-0.690548\pi$
$167$	3.39362	−	3.39362i	0.262606	−	0.262606i	0.826112	+	0.563506i	$0.190548\pi$
$168$	−2.61914	−	1.87037i	−0.202071	−	0.144302i
$169$	16.2922	+	16.2922i	1.25324	+	1.25324i
$170$	−12.9041	−	19.7525i	−0.989701	−	1.51495i
$171$	−0.169764	−	0.409846i	−0.0129822	−	0.0313417i
$172$	−15.3865	−	16.0379i	−1.17321	−	1.22288i
$173$	1.92599	+	0.797769i	0.146430	+	0.0606533i	0.454695	−	0.890647i	$-0.349748\pi$
$173$	1.92599	+	0.797769i	0.146430	+	0.0606533i	−0.308265	+	0.951301i	$0.599748\pi$
$174$	−1.56847	−	1.07169i	−0.118905	−	0.0812449i
$175$		−	15.6400i		−	1.18227i
$176$	3.62891	+	1.68256i	0.273539	+	0.126828i
$177$		−	10.5691i		−	0.794425i
$178$	0.557461	−	0.815868i	0.0417835	−	0.0611519i
$179$	3.30292	+	1.36811i	0.246872	+	0.102258i	0.502688	−	0.864468i	$-0.332344\pi$
$179$	3.30292	+	1.36811i	0.246872	+	0.102258i	−0.255817	+	0.966725i	$0.582344\pi$
$180$	−18.2804	−	0.378938i	−1.36254	−	0.0282444i
$181$	−1.58408	−	3.82432i	−0.117744	−	0.284259i	0.854009	−	0.520258i	$-0.174164\pi$
$181$	−1.58408	−	3.82432i	−0.117744	−	0.284259i	−0.971753	+	0.235998i	$0.924164\pi$
$182$	9.02466	−	5.89573i	0.668953	−	0.437021i
$183$	0.834234	+	0.834234i	0.0616683	+	0.0616683i
$184$	11.7634	+	2.72255i	0.867207	+	0.200709i
$185$	−23.9881	+	23.9881i	−1.76364	+	1.76364i
$186$	−1.90957	+	9.10586i	−0.140017	+	0.667674i
$187$	3.70385	−	1.53419i	0.270853	−	0.112191i
$188$	1.33203	+	3.41428i	0.0971482	+	0.249012i
$189$	−2.26296	+	5.46327i	−0.164606	+	0.397394i
$190$	−1.16792	+	0.219756i	−0.0847295	+	0.0159428i
$191$	−19.1422			−1.38508			−0.692539	−	0.721380i	$-0.743508\pi$
$191$	−19.1422			−1.38508			−0.692539	+	0.721380i	$0.743508\pi$
$192$	4.74476	+	5.37479i	0.342424	+	0.387892i
$193$	13.3485			0.960846			0.480423	−	0.877037i	$-0.340483\pi$
$193$	13.3485			0.960846			0.480423	+	0.877037i	$0.340483\pi$
$194$	14.5377	−	2.73543i	1.04375	−	0.196392i
$195$	−8.56801	+	20.6850i	−0.613568	+	1.48128i
$196$	3.91649	+	10.0388i	0.279749	+	0.717058i
$197$	−8.82956	+	3.65732i	−0.629080	+	0.260573i	−0.674362	−	0.738401i	$-0.735581\pi$
$197$	−8.82956	+	3.65732i	−0.629080	+	0.260573i	0.0452822	+	0.998974i	$0.485581\pi$
$198$	0.637656	−	3.04068i	0.0453162	−	0.216092i
$199$	5.29988	−	5.29988i	0.375699	−	0.375699i	−0.493849	−	0.869548i	$-0.664410\pi$
$199$	5.29988	−	5.29988i	0.375699	−	0.375699i	0.869548	+	0.493849i	$0.164410\pi$
$200$	−7.85591	+	33.9431i	−0.555497	+	2.40014i
$201$	−5.58835	−	5.58835i	−0.394172	−	0.394172i
$202$	2.50523	−	1.63665i	0.176267	−	0.115154i
$203$	−0.728281	−	1.75823i	−0.0511153	−	0.123403i
$204$	7.18409	+	0.148920i	0.502987	+	0.0104265i
$205$	18.3507	+	7.60111i	1.28167	+	0.530885i
$206$	5.19264	−	7.59966i	0.361789	−	0.529493i
$207$		−	9.37819i		−	0.651830i
$208$	−22.5474	+	8.26230i	−1.56338	+	0.572887i
$209$		−	0.201931i		−	0.0139679i
$210$	5.52923	+	3.77798i	0.381553	+	0.260705i
$211$	−13.0590	−	5.40921i	−0.899018	−	0.372385i	−0.115175	−	0.993345i	$-0.536743\pi$
$211$	−13.0590	−	5.40921i	−0.899018	−	0.372385i	−0.783842	+	0.620960i	$0.786743\pi$
$212$	−5.88745	−	6.13670i	−0.404352	−	0.421471i
$213$	−0.945458	−	2.28254i	−0.0647817	−	0.156397i
$214$	2.02822	+	3.10462i	0.138646	+	0.212227i
$215$	32.7000	+	32.7000i	2.23012	+	2.23012i
$216$	7.65541	−	10.7201i	0.520885	−	0.729411i
$217$	−6.59083	+	6.59083i	−0.447415	+	0.447415i
$218$	−1.06941	−	0.224263i	−0.0724294	−	0.0151890i
$219$	−1.14410	+	0.473900i	−0.0773109	+	0.0320232i
$220$	−7.62175	−	3.34374i	−0.513858	−	0.225435i
$221$	−9.21031	+	22.2357i	−0.619552	+	1.49573i
$222$	−1.91051	−	10.1536i	−0.128225	−	0.681465i
$223$	−5.12326			−0.343079			−0.171539	−	0.985177i	$-0.554874\pi$
$223$	−5.12326			−0.343079			−0.171539	+	0.985177i	$0.554874\pi$
$224$	1.03450	+	7.10760i	0.0691207	+	0.474896i
$225$	27.0607			1.80405
$226$	0.982966	+	5.22407i	0.0653859	+	0.347500i
$227$	−8.16677	+	19.7163i	−0.542048	+	1.30862i	0.381228	+	0.924481i	$0.375501\pi$
$227$	−8.16677	+	19.7163i	−0.542048	+	1.30862i	−0.923276	+	0.384138i	$0.874499\pi$
$228$	0.145407	−	0.331442i	0.00962980	−	0.0219503i
$229$	24.2496	−	10.0445i	1.60246	−	0.663759i	0.610696	−	0.791865i	$-0.290890\pi$
$229$	24.2496	−	10.0445i	1.60246	−	0.663759i	0.991760	+	0.128106i	$0.0408899\pi$
$230$	−24.5887	−	5.15644i	−1.62133	−	0.340006i
$231$	−0.804603	+	0.804603i	−0.0529390	+	0.0529390i
$232$	0.697420	+	4.18164i	0.0457878	+	0.274538i
$233$	−5.36587	−	5.36587i	−0.351530	−	0.351530i	0.509149	−	0.860679i	$-0.329960\pi$
$233$	−5.36587	−	5.36587i	−0.351530	−	0.351530i	−0.860679	+	0.509149i	$0.829960\pi$
$234$	10.2009	+	15.6147i	0.666855	+	1.02076i
$235$	−2.91824	−	7.04527i	−0.190365	−	0.459582i
$236$	−17.0206	+	16.3293i	−1.10795	+	1.06295i
$237$	−13.4886	−	5.58716i	−0.876178	−	0.362925i
$238$	5.94373	+	4.06119i	0.385275	+	0.263248i
$239$		−	10.0311i		−	0.648859i	−0.945910	−	0.324429i	$-0.894828\pi$
$239$		−	10.0311i		−	0.648859i	0.945910	−	0.324429i	$-0.105172\pi$
$240$	−10.1023	−	10.9765i	−0.652099	−	0.708533i
$241$		−	3.40844i		−	0.219557i	−0.993956	−	0.109778i	$-0.964986\pi$
$241$		−	3.40844i		−	0.219557i	0.993956	−	0.109778i	$-0.0350141\pi$
$242$	0.797838	−	1.16767i	0.0512870	−	0.0750607i
$243$	−14.9094	−	6.17569i	−0.956440	−	0.396170i
$244$	0.0545664	−	2.63234i	0.00349325	−	0.168519i
$245$	−8.58034	−	20.7148i	−0.548178	−	1.32342i
$246$	−5.06432	+	3.30848i	−0.322889	+	0.210941i
$247$	0.857205	+	0.857205i	0.0545427	+	0.0545427i
$248$	17.6144	−	10.9933i	1.11852	−	0.698078i
$249$	−8.86608	+	8.86608i	−0.561865	+	0.561865i
$250$	8.83935	−	42.1507i	0.559049	−	2.66585i
$251$	22.1810	−	9.18765i	1.40005	−	0.579919i	0.450285	−	0.892885i	$-0.351322\pi$
$251$	22.1810	−	9.18765i	1.40005	−	0.579919i	0.949765	+	0.312965i	$0.101322\pi$
$252$	5.19717	−	2.02759i	0.327391	−	0.127726i
$253$	1.63364	−	3.94396i	0.102706	−	0.247955i
$254$	8.36468	−	1.57391i	0.524847	−	0.0987557i
$255$	−14.9514			−0.936296
$256$	1.32496	−	15.9450i	0.0828100	−	0.996565i
$257$	8.95551			0.558629			0.279315	−	0.960200i	$-0.409893\pi$
$257$	8.95551			0.558629			0.279315	+	0.960200i	$0.409893\pi$
$258$	−13.8411	+	2.60436i	−0.861711	+	0.162140i
$259$	3.96099	−	9.56267i	0.246124	−	0.594195i
$260$	46.5488	−	18.1603i	2.88684	−	1.12625i
$261$	3.04212	−	1.26009i	0.188303	−	0.0779975i
$262$	−4.06649	+	19.3912i	−0.251228	+	1.19799i
$263$	−8.40692	+	8.40692i	−0.518393	+	0.518393i	−0.917085	−	0.398692i	$-0.869464\pi$
$263$	−8.40692	+	8.40692i	−0.518393	+	0.518393i	0.398692	+	0.917085i	$0.369464\pi$
$264$	2.15036	−	1.34206i	0.132345	−	0.0825980i
$265$	12.5123	+	12.5123i	0.768622	+	0.768622i
$266$	0.303556	−	0.198311i	0.0186122	−	0.0121592i
$267$	−0.239627	−	0.578511i	−0.0146649	−	0.0354043i
$268$	−0.365528	+	17.6335i	−0.0223282	+	1.07714i
$269$	13.8915	+	5.75404i	0.846979	+	0.350830i	0.763602	−	0.645688i	$-0.223429\pi$
$269$	13.8915	+	5.75404i	0.846979	+	0.350830i	0.0833777	+	0.996518i	$0.473429\pi$
$270$	−15.4632	+	22.6311i	−0.941062	+	1.37728i
$271$		−	11.4588i		−	0.696071i	−0.937481	−	0.348035i	$-0.886849\pi$
$271$		−	11.4588i		−	0.696071i	0.937481	−	0.348035i	$-0.113151\pi$
$272$	−10.8596	−	11.7994i	−0.658459	−	0.715443i
$273$		−	6.83113i		−	0.413439i
$274$	23.3810	+	15.9756i	1.41250	+	0.965121i
$275$	11.3803	+	4.71386i	0.686256	+	0.284257i
$276$	5.52136	−	5.29711i	0.332347	−	0.318848i
$277$	−4.50720	−	10.8813i	−0.270811	−	0.653796i	0.728707	−	0.684825i	$-0.240121\pi$
$277$	−4.50720	−	10.8813i	−0.270811	−	0.653796i	−0.999518	+	0.0310292i	$0.990121\pi$
$278$	5.46689	+	8.36823i	0.327882	+	0.501893i
$279$	−11.4036	−	11.4036i	−0.682715	−	0.682715i
$280$	−2.45857	−	14.7413i	−0.146928	−	0.880960i
$281$	12.3298	−	12.3298i	0.735535	−	0.735535i	−0.236176	−	0.971710i	$-0.575894\pi$
$281$	12.3298	−	12.3298i	0.735535	−	0.735535i	0.971710	+	0.236176i	$0.0758941\pi$
$282$	2.27300	+	0.476667i	0.135355	+	0.0283851i
$283$	−19.2143	+	7.95881i	−1.14217	+	0.473102i	−0.871901	−	0.489683i	$-0.837113\pi$
$283$	−19.2143	+	7.95881i	−1.14217	+	0.473102i	−0.270269	+	0.962785i	$0.587113\pi$
$284$	−2.21508	+	5.04909i	−0.131441	+	0.299608i
$285$	−0.288196	+	0.695767i	−0.0170713	+	0.0412137i
$286$	1.56995	+	8.34365i	0.0928330	+	0.493370i
$287$	−6.06024			−0.357725
$288$	−12.2977	+	1.78992i	−0.724650	+	0.105472i
$289$	0.927731			0.0545724
$290$	−1.63116	−	8.66897i	−0.0957851	−	0.509059i
$291$	3.58734	−	8.66060i	0.210293	−	0.507693i
$292$	2.53080	+	1.11029i	0.148104	+	0.0649746i
$293$	−10.3779	+	4.29866i	−0.606282	+	0.251130i	−0.664638	−	0.747166i	$-0.731414\pi$
$293$	−10.3779	+	4.29866i	−0.606282	+	0.251130i	0.0583560	+	0.998296i	$0.481414\pi$
$294$	6.68318	+	1.40152i	0.389771	+	0.0817381i
$295$	34.7037	−	34.7037i	2.02053	−	2.02053i
$296$	−13.3997	+	18.7640i	−0.778842	+	1.09064i
$297$	−3.29323	−	3.29323i	−0.191093	−	0.191093i
$298$	7.35830	+	11.2634i	0.426255	+	0.652473i
$299$	9.80738	+	23.6771i	0.567176	+	1.36928i
$300$	15.2848	+	15.9318i	0.882466	+	0.919826i
$301$	−13.0356	−	5.39951i	−0.751358	−	0.311223i
$302$	12.7223	+	8.69278i	0.732084	+	0.500214i
$303$		−	1.89631i		−	0.108940i
$304$	−0.758410	+	0.277913i	−0.0434978	+	0.0159394i
$305$			5.47840i			0.313692i
$306$	−7.02676	+	10.2840i	−0.401693	+	0.587895i
$307$	0.336941	+	0.139565i	0.0192302	+	0.00796542i	0.392278	−	0.919847i	$-0.371687\pi$
$307$	0.336941	+	0.139565i	0.0192302	+	0.00796542i	−0.373048	+	0.927812i	$0.621687\pi$
$308$	2.53885	+	0.0526283i	0.144664	+	0.00299877i
$309$	−2.23208	−	5.38872i	−0.126979	−	0.306554i
$310$	−36.1691	+	23.6290i	−2.05427	+	1.34204i
$311$	−8.55750	−	8.55750i	−0.485251	−	0.485251i	0.421553	−	0.906804i	$-0.361485\pi$
$311$	−8.55750	−	8.55750i	−0.485251	−	0.485251i	−0.906804	+	0.421553i	$0.861485\pi$
$312$	−3.43124	+	14.8254i	−0.194256	+	0.839323i
$313$	8.02855	−	8.02855i	0.453801	−	0.453801i	−0.442813	−	0.896614i	$-0.646020\pi$
$313$	8.02855	−	8.02855i	0.453801	−	0.453801i	0.896614	+	0.442813i	$0.146020\pi$
$314$	0.970114	−	4.62602i	0.0547467	−	0.261061i
$315$	−10.7242	+	4.44211i	−0.604240	+	0.250284i
$316$	11.8422	+	30.3543i	0.666178	+	1.70756i
$317$	−3.13176	+	7.56073i	−0.175897	+	0.424653i	−0.987099	−	0.160114i	$-0.948814\pi$
$317$	−3.13176	+	7.56073i	−0.175897	+	0.424653i	0.811202	+	0.584767i	$0.198814\pi$
$318$	−5.29614	+	0.996527i	−0.296993	+	0.0558825i
$319$	1.49885			0.0839198
$320$	−2.06871	+	33.2275i	−0.115644	+	1.85747i
$321$	2.35001			0.131165
$322$	7.53317	−	1.41745i	0.419807	−	0.0789913i
$323$	−0.309800	+	0.747925i	−0.0172378	+	0.0416156i
$324$	1.75675	+	4.50294i	0.0975974	+	0.250163i
$325$	−68.3201	+	28.2991i	−3.78972	+	1.56975i
$326$	6.65425	−	31.7310i	0.368545	−	1.75742i
$327$	−0.489616	+	0.489616i	−0.0270758	+	0.0270758i
$328$	13.1524	+	3.04403i	0.726218	+	0.168078i
$329$	1.64520	+	1.64520i	0.0907029	+	0.0907029i
$330$	−4.41550	+	2.88461i	−0.243065	+	0.158792i
$331$	2.89511	+	6.98941i	0.159130	+	0.384173i	0.983255	−	0.182234i	$-0.0583329\pi$
$331$	2.89511	+	6.98941i	0.159130	+	0.384173i	−0.824125	+	0.566407i	$0.808333\pi$
$332$	27.9761	+	0.579921i	1.53539	+	0.0318273i
$333$	16.5455	+	6.85338i	0.906690	+	0.375563i
$334$	−3.82906	+	5.60400i	−0.209517	+	0.306637i
$335$		−	36.6986i		−	2.00506i
$336$	4.12926	+	1.91456i	0.225270	+	0.104448i
$337$			35.2575i			1.92060i	0.278973	+	0.960299i	$0.410006\pi$
$337$			35.2575i			1.92060i	−0.278973	+	0.960299i	$0.589994\pi$
$338$	−26.9038	−	18.3827i	−1.46337	−	0.999885i
$339$	3.11215	+	1.28910i	0.169029	+	0.0700141i
$340$	23.0999	+	24.0779i	1.25277	+	1.30581i
$341$	−2.80928	−	6.78220i	−0.152131	−	0.367277i
$342$	0.343121	+	0.525219i	0.0185539	+	0.0284006i
$343$	11.1220	+	11.1220i	0.600530	+	0.600530i
$344$	25.5786	+	18.2661i	1.37911	+	0.984843i
$345$	−11.2576	+	11.2576i	−0.606090	+	0.606090i
$346$	−2.88541	−	0.605093i	−0.155120	−	0.0325300i
$347$	1.64689	−	0.682162i	0.0884094	−	0.0366204i	−0.338040	−	0.941132i	$-0.609764\pi$
$347$	1.64689	−	0.682162i	0.0884094	−	0.0366204i	0.426450	+	0.904511i	$0.359764\pi$
$348$	2.46016	+	1.07930i	0.131878	+	0.0578563i
$349$	−3.48800	+	8.42077i	−0.186708	+	0.450753i	−0.989322	−	0.145745i	$-0.953442\pi$
$349$	−3.48800	+	8.42077i	−0.186708	+	0.450753i	0.802614	+	0.596499i	$0.203442\pi$
$350$	4.09003	+	21.7369i	0.218622	+	1.16189i
$351$	27.9597			1.49238
$352$	−5.48356	−	1.38947i	−0.292274	−	0.0740589i
$353$	−19.9158			−1.06001			−0.530005	−	0.847995i	$-0.677810\pi$
$353$	−19.9158			−1.06001			−0.530005	+	0.847995i	$0.677810\pi$
$354$	2.76394	+	14.6893i	0.146902	+	0.780725i
$355$	4.39030	−	10.5991i	0.233013	−	0.562542i
$356$	−0.561415	+	1.27970i	−0.0297549	+	0.0678237i
$357$	4.21454	−	1.74572i	0.223057	−	0.0923934i
$358$	−4.94825	−	1.03769i	−0.261523	−	0.0548435i
$359$	−5.99230	+	5.99230i	−0.316261	+	0.316261i	−0.847329	−	0.531068i	$-0.821791\pi$
$359$	−5.99230	+	5.99230i	−0.316261	+	0.316261i	0.531068	+	0.847329i	$0.321791\pi$
$360$	25.5057	−	4.25387i	1.34427	−	0.224199i
$361$	−13.4062	−	13.4062i	−0.705589	−	0.705589i
$362$	3.20170	+	4.90088i	0.168278	+	0.257584i
$363$	−0.342954	−	0.827965i	−0.0180004	−	0.0434569i
$364$	−11.0009	+	10.5541i	−0.576604	+	0.553184i
$365$	−5.31268	−	2.20058i	−0.278078	−	0.115184i
$366$	−1.37760	−	0.941277i	−0.0720083	−	0.0492013i
$367$			31.8089i			1.66041i	0.557457	+	0.830206i	$0.311777\pi$
$367$			31.8089i			1.66041i	−0.557457	+	0.830206i	$0.688223\pi$
$368$	−17.0610	−	0.707625i	−0.889366	−	0.0368875i
$369$		−	10.4856i		−	0.545856i
$370$	27.0661	−	39.6125i	1.40710	−	2.05935i
$371$	−4.98791	−	2.06606i	−0.258959	−	0.107264i
$372$	0.272691	−	13.1549i	0.0141384	−	0.682051i
$373$	5.45793	+	13.1766i	0.282601	+	0.682259i	0.999895	−	0.0145116i	$-0.00461935\pi$
$373$	5.45793	+	13.1766i	0.282601	+	0.682259i	−0.717294	+	0.696771i	$0.754619\pi$
$374$	−4.74650	+	3.10085i	−0.245436	+	0.160341i
$375$	−19.2982	−	19.2982i	−0.996555	−	0.996555i
$376$	−2.74416	−	4.39691i	−0.141519	−	0.226753i
$377$	−6.36269	+	6.36269i	−0.327695	+	0.327695i
$378$	1.71641	−	8.18477i	0.0882828	−	0.420979i
$379$	−10.5001	+	4.34929i	−0.539354	+	0.223408i	−0.635695	−	0.771941i	$-0.719286\pi$
$379$	−10.5001	+	4.34929i	−0.539354	+	0.223408i	0.0963405	+	0.995348i	$0.469286\pi$
$380$	1.56573	−	0.610845i	0.0803202	−	0.0313357i
$381$	2.06408	−	4.98312i	0.105746	−	0.255293i
$382$	26.6042	−	5.00588i	1.36119	−	0.256123i
$383$	21.5385			1.10057			0.550283	−	0.834978i	$-0.314520\pi$
$383$	21.5385			1.10057			0.550283	+	0.834978i	$0.314520\pi$
$384$	−7.99995	−	6.22922i	−0.408246	−	0.317883i
$385$	−5.28382			−0.269288
$386$	−18.5521	+	3.49078i	−0.944276	+	0.177676i
$387$	9.34236	−	22.5544i	0.474899	−	1.14651i
$388$	−19.4895	+	7.60353i	−0.989430	+	0.386011i
$389$	13.7475	−	5.69439i	0.697025	−	0.288717i	−0.00589865	−	0.999983i	$-0.501878\pi$
$389$	13.7475	−	5.69439i	0.697025	−	0.288717i	0.702924	+	0.711265i	$0.251878\pi$
$390$	6.49868	−	30.9892i	0.329073	−	1.56920i
$391$	−12.1016	+	12.1016i	−0.612002	+	0.612002i
$392$	−8.06849	−	12.9280i	−0.407520	−	0.652962i
$393$	8.87802	+	8.87802i	0.447837	+	0.447837i
$394$	11.3151	−	7.39206i	0.570047	−	0.372407i
$395$	−25.9443	−	62.6351i	−1.30540	−	3.15151i
$396$	−0.0910586	+	4.39277i	−0.00457586	+	0.220745i
$397$	−1.93299	−	0.800669i	−0.0970138	−	0.0401844i	0.333649	−	0.942697i	$-0.391720\pi$
$397$	−1.93299	−	0.800669i	−0.0970138	−	0.0401844i	−0.430663	+	0.902513i	$0.641720\pi$
$398$	−5.97993	+	8.75188i	−0.299747	+	0.438692i
$399$		−	0.229774i		−	0.0115031i
$400$	2.04185	−	49.2294i	0.102092	−	2.46147i
$401$			32.4724i			1.62160i	0.585327	+	0.810798i	$0.300966\pi$
$401$			32.4724i			1.62160i	−0.585327	+	0.810798i	$0.699034\pi$
$402$	9.22824	+	6.30541i	0.460263	+	0.314485i
$403$	40.7161	+	16.8652i	2.02821	+	0.840114i
$404$	−3.05383	+	2.92979i	−0.151934	+	0.145763i
$405$	−3.84874	−	9.29169i	−0.191246	−	0.461708i
$406$	1.47198	+	2.25317i	0.0730531	+	0.111823i
$407$	5.76433	+	5.76433i	0.285727	+	0.285727i
$408$	−10.0236	+	1.67174i	−0.496241	+	0.0827637i
$409$	1.81196	−	1.81196i	0.0895957	−	0.0895957i	−0.660888	−	0.750484i	$-0.729820\pi$
$409$	1.81196	−	1.81196i	0.0895957	−	0.0895957i	0.750484	+	0.660888i	$0.229820\pi$
$410$	−27.4920	−	5.76531i	−1.35774	−	0.284728i
$411$	16.5788	−	6.86718i	0.817773	−	0.338733i
$412$	−5.22947	+	11.9201i	−0.257638	+	0.587262i
$413$	−5.73037	+	13.8343i	−0.281973	+	0.680743i
$414$	2.45250	+	13.0340i	0.120534	+	0.640588i
$415$	−58.2234			−2.85808
$416$	29.1762	−	17.3795i	1.43048	−	0.852101i
$417$	6.33425			0.310189
$418$	0.0528072	+	0.280649i	0.00258289	+	0.0137270i
$419$	−0.982856	+	2.37283i	−0.0480157	+	0.115920i	−0.946068	−	0.323970i	$-0.894982\pi$
$419$	−0.982856	+	2.37283i	−0.0480157	+	0.115920i	0.898052	+	0.439890i	$0.144982\pi$
$420$	−8.67264	−	3.80477i	−0.423182	−	0.185654i
$421$	34.0463	−	14.1025i	1.65932	−	0.687312i	0.661292	−	0.750128i	$-0.270008\pi$
$421$	34.0463	−	14.1025i	1.65932	−	0.687312i	0.998025	+	0.0628165i	$0.0200083\pi$
$422$	19.5643	+	4.10279i	0.952374	+	0.199721i
$423$	−2.84656	+	2.84656i	−0.138405	+	0.138405i
$424$	9.78734	+	6.98931i	0.475315	+	0.339431i
$425$	−34.9189	−	34.9189i	−1.69382	−	1.69382i
$426$	1.91093	+	2.92508i	0.0925849	+	0.141721i
$427$	−0.639655	−	1.54426i	−0.0309551	−	0.0747322i
$428$	−3.63076	−	3.78447i	−0.175499	−	0.182929i
$429$	4.97059	+	2.05889i	0.239982	+	0.0994039i
$430$	−53.9987	−	36.8959i	−2.60405	−	1.77928i
$431$			18.1310i			0.873341i	0.899622	+	0.436670i	$0.143842\pi$
$431$			18.1310i			0.873341i	−0.899622	+	0.436670i	$0.856158\pi$
$432$	−7.83626	+	16.9010i	−0.377022	+	0.813152i
$433$		−	24.1360i		−	1.15990i	−0.814651	−	0.579951i	$-0.803072\pi$
$433$		−	24.1360i		−	1.15990i	0.814651	−	0.579951i	$-0.196928\pi$
$434$	7.43652	−	10.8837i	0.356965	−	0.522433i
$435$	−5.16439	−	2.13916i	−0.247614	−	0.102565i
$436$	1.54494	+	0.0320253i	0.0739890	+	0.00153373i
$437$	0.329884	+	0.796410i	0.0157805	+	0.0380975i
$438$	1.46616	−	0.957832i	0.0700560	−	0.0457670i
$439$	24.6438	+	24.6438i	1.17619	+	1.17619i	0.980708	+	0.195477i	$0.0626256\pi$
$439$	24.6438	+	24.6438i	1.17619	+	1.17619i	0.195477	+	0.980708i	$0.437374\pi$
$440$	11.4673	+	2.65404i	0.546683	+	0.126526i
$441$	−8.36958	+	8.36958i	−0.398552	+	0.398552i
$442$	6.98585	−	33.3123i	0.332283	−	1.58450i
$443$	16.5509	−	6.85561i	0.786357	−	0.325720i	0.0468790	−	0.998901i	$-0.485072\pi$
$443$	16.5509	−	6.85561i	0.786357	−	0.325720i	0.739478	+	0.673181i	$0.235072\pi$
$444$	5.31055	+	13.6121i	0.252028	+	0.646002i
$445$	1.11272	−	2.68635i	0.0527481	−	0.127345i
$446$	7.12043	−	1.33979i	0.337162	−	0.0634408i
$447$	8.52574			0.403254
$448$	−3.29649	−	9.60778i	−0.155745	−	0.453925i
$449$	−7.06601			−0.333466			−0.166733	−	0.986002i	$-0.553322\pi$
$449$	−7.06601			−0.333466			−0.166733	+	0.986002i	$0.553322\pi$
$450$	−37.6096	+	7.07666i	−1.77293	+	0.333597i
$451$	1.82654	−	4.40966i	0.0860084	−	0.207643i
$452$	−2.73230	−	7.00348i	−0.128517	−	0.329416i
$453$	9.02103	−	3.73663i	0.423845	−	0.175562i
$454$	6.19435	−	29.5379i	0.290715	−	1.38628i
$455$	22.4300	−	22.4300i	1.05153	−	1.05153i
$456$	−0.115414	+	0.498672i	−0.00540477	+	0.0233524i
$457$	−20.2012	−	20.2012i	−0.944972	−	0.944972i	0.0535914	−	0.998563i	$-0.482933\pi$
$457$	−20.2012	−	20.2012i	−0.944972	−	0.944972i	−0.998563	+	0.0535914i	$0.982933\pi$
$458$	−31.0759	+	20.3016i	−1.45208	+	0.948632i
$459$	7.14522	+	17.2501i	0.333510	+	0.805165i
$460$	35.5224	+	0.736350i	1.65624	+	0.0343325i
$461$	−32.0930	−	13.2934i	−1.49472	−	0.619134i	−0.522383	−	0.852711i	$-0.674957\pi$
$461$	−32.0930	−	13.2934i	−1.49472	−	0.619134i	−0.972338	+	0.233577i	$0.924957\pi$
$462$	0.907844	−	1.32867i	0.0422367	−	0.0618153i
$463$			20.7579i			0.964700i	0.875979	+	0.482350i	$0.160217\pi$
$463$			20.7579i			0.964700i	−0.875979	+	0.482350i	$0.839783\pi$
$464$	−2.06284	−	5.62937i	−0.0957647	−	0.261337i
$465$			27.3779i			1.26962i
$466$	8.86085	+	6.05438i	0.410471	+	0.280464i
$467$	−16.8131	−	6.96422i	−0.778018	−	0.322266i	−0.0419028	−	0.999122i	$-0.513342\pi$
$467$	−16.8131	−	6.96422i	−0.778018	−	0.322266i	−0.736116	+	0.676856i	$0.763342\pi$
$468$	−18.2609	−	19.0340i	−0.844110	−	0.879847i
$469$	4.28491	+	10.3447i	0.197859	+	0.477673i
$470$	5.89826	+	9.02853i	0.272066	+	0.416455i
$471$	−2.11797	−	2.11797i	−0.0975909	−	0.0975909i
$472$	19.3854	−	27.1459i	0.892285	−	1.24949i
$473$	7.85778	−	7.85778i	0.361301	−	0.361301i
$474$	20.2079	+	4.23776i	0.928178	+	0.194647i
$475$	−2.29803	+	0.951877i	−0.105441	+	0.0436751i
$476$	−9.32278	−	4.08999i	−0.427309	−	0.187465i
$477$	3.57474	−	8.63018i	0.163676	−	0.395149i
$478$	2.62324	+	13.9415i	0.119984	+	0.637669i
$479$	17.0743			0.780143			0.390071	−	0.920785i	$-0.372450\pi$
$479$	17.0743			0.780143			0.390071	+	0.920785i	$0.372450\pi$
$480$	16.9109	+	12.6136i	0.771872	+	0.575730i
$481$	−48.9395			−2.23145
$482$	0.891344	+	4.73713i	0.0405996	+	0.215770i
$483$	1.85889	−	4.48776i	0.0845824	−	0.204200i
$484$	−0.803497	+	1.83150i	−0.0365226	+	0.0832500i
$485$	40.2160	−	16.6580i	1.82612	−	0.756402i
$486$	22.3365	+	4.68414i	1.01320	+	0.212477i
$487$	2.45962	−	2.45962i	0.111456	−	0.111456i	−0.649179	−	0.760635i	$-0.724888\pi$
$487$	2.45962	−	2.45962i	0.111456	−	0.111456i	0.760635	+	0.649179i	$0.224888\pi$
$488$	0.612549	+	3.67277i	0.0277288	+	0.166258i
$489$	−14.5277	−	14.5277i	−0.656964	−	0.656964i
$490$	17.3423	+	26.5461i	0.783446	+	1.19923i
$491$	−7.05204	−	17.0251i	−0.318254	−	0.768334i	−0.999347	−	0.0361365i	$-0.988495\pi$
$491$	−7.05204	−	17.0251i	−0.318254	−	0.768334i	0.681093	−	0.732197i	$-0.261505\pi$
$492$	6.17332	−	5.92258i	0.278315	−	0.267010i
$493$	−5.55154	−	2.29952i	−0.250029	−	0.103565i
$494$	−1.41553	−	0.967196i	−0.0636879	−	0.0435162i
$495$		−	9.14218i		−	0.410910i
$496$	−21.6061	+	19.8852i	−0.970142	+	0.892871i
$497$			3.50031i			0.157010i
$498$	10.0037	−	14.6409i	0.448277	−	0.656073i
$499$	18.2420	+	7.55607i	0.816623	+	0.338256i	0.751593	−	0.659627i	$-0.229286\pi$
$499$	18.2420	+	7.55607i	0.816623	+	0.338256i	0.0650296	+	0.997883i	$0.479286\pi$
$500$	−1.26228	+	60.8937i	−0.0564507	+	2.72325i
$501$	1.64594	+	3.97365i	0.0735352	+	0.177530i
$502$	−28.4250	+	18.5698i	−1.26867	+	0.828810i
$503$	20.6710	+	20.6710i	0.921673	+	0.921673i	0.997148	−	0.0754744i	$-0.0240471\pi$
$503$	20.6710	+	20.6710i	0.921673	+	0.921673i	−0.0754744	+	0.997148i	$0.524047\pi$
$504$	−6.69291	+	4.17712i	−0.298126	+	0.186064i
$505$	6.22652	−	6.22652i	0.277077	−	0.277077i
$506$	−1.23909	+	5.90863i	−0.0550842	+	0.262671i
$507$	−19.0768	+	7.90187i	−0.847231	+	0.350934i
$508$	−11.2138	+	4.37491i	−0.497534	+	0.194105i
$509$	13.4177	−	32.3931i	0.594728	−	1.43580i	−0.284162	−	0.958776i	$-0.591715\pi$
$509$	13.4177	−	32.3931i	0.594728	−	1.43580i	0.878890	−	0.477025i	$-0.158285\pi$
$510$	20.7799	−	3.90996i	0.920148	−	0.173136i
$511$	1.75449			0.0776140
$512$	2.32834	+	22.5073i	0.102899	+	0.994692i
$513$	0.940462			0.0415224
$514$	−12.4466	+	2.34196i	−0.548995	+	0.103300i
$515$	10.3648	−	25.0229i	0.456728	−	1.10264i
$516$	18.5557	−	7.23921i	0.816868	−	0.318688i
$517$	−1.69297	+	0.701252i	−0.0744568	+	0.0308410i
$518$	−3.00434	+	14.3263i	−0.132003	+	0.629460i
$519$	−1.32105	+	1.32105i	−0.0579877	+	0.0579877i
$520$	−59.9456	+	37.4127i	−2.62879	+	1.64065i
$521$	−11.1740	−	11.1740i	−0.489540	−	0.489540i	0.418621	−	0.908161i	$-0.362513\pi$
$521$	−11.1740	−	11.1740i	−0.489540	−	0.489540i	−0.908161	+	0.418621i	$0.862513\pi$
$522$	−3.89849	+	2.54685i	−0.170632	+	0.111473i
$523$	−9.94627	−	24.0124i	−0.434920	−	1.04999i	−0.977680	−	0.210101i	$-0.932621\pi$
$523$	−9.94627	−	24.0124i	−0.434920	−	1.04999i	0.542760	−	0.839888i	$-0.317379\pi$
$524$	0.580702	−	28.0137i	0.0253681	−	1.22379i
$525$	12.9494	+	5.36381i	0.565158	+	0.234096i
$526$	9.48564	−	13.8826i	0.413593	−	0.605312i
$527$			29.4302i			1.28200i
$528$	−2.63765	+	2.42757i	−0.114789	+	0.105646i
$529$		−	4.77636i		−	0.207668i
$530$	−20.6619	−	14.1178i	−0.897497	−	0.613236i
$531$	−23.9365	−	9.91481i	−1.03875	−	0.430266i
$532$	−0.370029	+	0.355000i	−0.0160428	+	0.0153912i
$533$	10.9654	+	26.4729i	0.474965	+	1.14667i
$534$	0.484326	+	0.741363i	0.0209589	+	0.0320819i
$535$	7.71624	+	7.71624i	0.333602	+	0.333602i
$536$	−4.10333	−	24.6031i	−0.177237	−	1.06269i
$537$	−2.26550	+	2.26550i	−0.0977635	+	0.0977635i
$538$	−20.8115	−	4.36434i	−0.897247	−	0.188160i
$539$	−4.97774	+	2.06185i	−0.214407	+	0.0888101i
$540$	15.5729	−	35.4970i	0.670151	−	1.52755i
$541$	−15.5346	+	37.5038i	−0.667884	+	1.61242i	0.117259	+	0.993101i	$0.462589\pi$
$541$	−15.5346	+	37.5038i	−0.667884	+	1.61242i	−0.785143	+	0.619314i	$0.787411\pi$
$542$	2.99659	+	15.9257i	0.128715	+	0.684066i
$543$	3.70967			0.159197
$544$	18.1786	+	13.5592i	0.779400	+	0.581345i
$545$	−3.21530			−0.137728
$546$	1.78641	+	9.49407i	0.0764515	+	0.406309i
$547$	11.6710	−	28.1762i	0.499014	−	1.20473i	−0.451001	−	0.892523i	$-0.648933\pi$
$547$	11.6710	−	28.1762i	0.499014	−	1.20473i	0.950015	−	0.312203i	$-0.101067\pi$
$548$	−36.6732	−	16.0889i	−1.56660	−	0.687283i
$549$	2.67192	−	1.10674i	0.114035	−	0.0472347i
$550$	−17.0493	−	3.57538i	−0.726985	−	0.152455i
$551$	−0.214017	+	0.214017i	−0.00911743	+	0.00911743i
$552$	−6.28848	+	8.80594i	−0.267655	+	0.374806i
$553$	14.6265	+	14.6265i	0.621981	+	0.621981i
$554$	9.10980	+	13.9445i	0.387038	+	0.592444i
$555$	−11.6345	−	28.0882i	−0.493857	−	1.19228i
$556$	−9.78640	−	10.2007i	−0.415036	−	0.432607i
$557$	1.25311	+	0.519054i	0.0530958	+	0.0219930i	0.409073	−	0.912502i	$-0.365852\pi$
$557$	1.25311	+	0.519054i	0.0530958	+	0.0219930i	−0.355977	+	0.934495i	$0.615852\pi$
$558$	18.8312	+	12.8668i	0.797186	+	0.544696i
$559$			66.7131i			2.82166i
$560$	7.27198	+	19.8448i	0.307297	+	0.838598i
$561$			3.59282i			0.151689i
$562$	−13.9119	+	20.3606i	−0.586838	+	0.858862i
$563$	−36.3004	−	15.0361i	−1.52988	−	0.633698i	−0.550340	−	0.834941i	$-0.685502\pi$
$563$	−36.3004	−	15.0361i	−1.52988	−	0.633698i	−0.979541	+	0.201243i	$0.935502\pi$
$564$	−3.28373	−	0.0680691i	−0.138270	−	0.00286622i
$565$	5.98600	+	14.4515i	0.251833	+	0.607978i
$566$	24.6231	−	16.0861i	1.03499	−	0.676149i
$567$	2.16978	+	2.16978i	0.0911223	+	0.0911223i
$568$	1.75819	−	7.59662i	0.0737719	−	0.318747i
$569$	25.4263	−	25.4263i	1.06593	−	1.06593i	0.0682591	−	0.997668i	$-0.478256\pi$
$569$	25.4263	−	25.4263i	1.06593	−	1.06593i	0.997668	−	0.0682591i	$-0.0217445\pi$
$570$	0.218591	−	1.04236i	0.00915579	−	0.0436597i
$571$	−19.3328	+	8.00791i	−0.809053	+	0.335121i	−0.748576	−	0.663049i	$-0.769262\pi$
$571$	−19.3328	+	8.00791i	−0.809053	+	0.335121i	−0.0604768	+	0.998170i	$0.519262\pi$
$572$	−4.36391	−	11.1856i	−0.182464	−	0.467695i
$573$	6.56489	−	15.8490i	0.274252	−	0.662103i
$574$	8.42267	−	1.58482i	0.351555	−	0.0661490i
$575$	−52.5842			−2.19291
$576$	16.6236	−	5.70366i	0.692649	−	0.237653i
$577$	5.89239			0.245304			0.122652	−	0.992450i	$-0.460860\pi$
$577$	5.89239			0.245304			0.122652	+	0.992450i	$0.460860\pi$
$578$	−1.28938	+	0.242612i	−0.0536313	+	0.0100913i
$579$	−4.57793	+	11.0521i	−0.190252	+	0.459309i
$580$	4.53406	+	11.6218i	0.188266	+	0.482568i
$581$	16.4121	−	6.79813i	0.680890	−	0.282034i
$582$	−2.72093	+	12.9748i	−0.112786	+	0.537824i
$583$	3.00669	−	3.00669i	0.124524	−	0.124524i
$584$	−3.80772	−	0.881271i	−0.157564	−	0.0364673i
$585$	38.8088	+	38.8088i	1.60455	+	1.60455i
$586$	13.2993	−	8.68830i	0.549388	−	0.358910i
$587$	10.9671	+	26.4769i	0.452660	+	1.09282i	0.971307	+	0.237829i	$0.0764357\pi$
$587$	10.9671	+	26.4769i	0.452660	+	1.09282i	−0.518648	+	0.854988i	$0.673564\pi$
$588$	−9.65496	−	0.200139i	−0.398164	−	0.00825361i
$589$	1.36954	+	0.567281i	0.0564309	+	0.0233744i
$590$	−39.1567	+	57.3075i	−1.61206	+	2.35931i
$591$		−	8.56486i		−	0.352311i
$592$	13.7162	−	29.5828i	0.563734	−	1.21585i
$593$		−	0.690760i		−	0.0283661i	−0.999899	−	0.0141831i	$-0.995485\pi$
$593$		−	0.690760i		−	0.0283661i	0.999899	−	0.0141831i	$-0.00451476\pi$
$594$	5.43823	+	3.71580i	0.223133	+	0.152461i
$595$	19.5705	+	8.10636i	0.802312	+	0.332329i
$596$	−13.1723	−	13.7299i	−0.539557	−	0.562399i
$597$	2.57050	+	6.20573i	0.105204	+	0.253984i
$598$	−19.8224	−	30.3423i	−0.810597	−	1.24079i
$599$	−7.17363	−	7.17363i	−0.293106	−	0.293106i	0.545200	−	0.838306i	$-0.316454\pi$
$599$	−7.17363	−	7.17363i	−0.293106	−	0.293106i	−0.838306	+	0.545200i	$0.816454\pi$
$600$	−25.4095	−	18.1453i	−1.03734	−	0.740781i
$601$	−14.1340	+	14.1340i	−0.576539	+	0.576539i	−0.933948	−	0.357409i	$-0.883660\pi$
$601$	−14.1340	+	14.1340i	−0.576539	+	0.576539i	0.357409	+	0.933948i	$0.383660\pi$
$602$	19.5292	+	4.09543i	0.795951	+	0.166917i
$603$	−17.8986	+	7.41384i	−0.728887	+	0.301915i
$604$	−19.9550	−	8.75444i	−0.811956	−	0.356213i
$605$	1.59253	−	3.84471i	0.0647455	−	0.156310i
$606$	0.495905	+	2.63554i	0.0201448	+	0.107061i
$607$	6.03089			0.244786			0.122393	−	0.992482i	$-0.460943\pi$
$607$	6.03089			0.244786			0.122393	+	0.992482i	$0.460943\pi$
$608$	0.981379	−	0.584583i	0.0398002	−	0.0237080i
$609$	1.70552			0.0691110
$610$	−1.43266	−	7.61402i	−0.0580068	−	0.308283i
$611$	4.20988	−	10.1636i	0.170314	−	0.411173i
$612$	7.07660	−	16.1305i	0.286054	−	0.652036i
$613$	25.0313	−	10.3683i	1.01100	−	0.418771i	0.185183	−	0.982704i	$-0.440712\pi$
$613$	25.0313	−	10.3683i	1.01100	−	0.418771i	0.825821	+	0.563933i	$0.190712\pi$
$614$	−0.504787	−	0.105858i	−0.0203715	−	0.00427208i
$615$	−12.5869	+	12.5869i	−0.507553	+	0.507553i
$616$	−3.54232	+	0.590792i	−0.142724	+	0.0238037i
$617$	2.77948	+	2.77948i	0.111898	+	0.111898i	0.760839	−	0.648941i	$-0.224788\pi$
$617$	2.77948	+	2.77948i	0.111898	+	0.111898i	−0.648941	+	0.760839i	$0.724788\pi$
$618$	4.51141	+	6.90566i	0.181475	+	0.277786i
$619$	−7.77398	−	18.7680i	−0.312462	−	0.754351i	−0.999613	−	0.0278356i	$-0.991139\pi$
$619$	−7.77398	−	18.7680i	−0.312462	−	0.754351i	0.687150	−	0.726516i	$-0.258861\pi$
$620$	44.0895	−	42.2987i	1.77068	−	1.69876i
$621$	18.3684	+	7.60842i	0.737097	+	0.305315i
$622$	14.1313	+	9.65555i	0.566614	+	0.387152i
$623$			0.887155i			0.0355431i
$624$	0.891822	−	21.5020i	0.0357015	−	0.860770i
$625$		−	65.1415i		−	2.60566i
$626$	−9.05873	+	13.2578i	−0.362060	+	0.529890i
$627$	0.167192	+	0.0692532i	0.00667701	+	0.00276571i
$628$	−0.138534	+	6.68305i	−0.00552812	+	0.266683i
$629$	−12.5067	−	30.1938i	−0.498674	−	1.20391i
$630$	13.7431	−	8.97825i	0.547538	−	0.357702i
$631$	−21.3352	−	21.3352i	−0.849341	−	0.849341i	0.140710	−	0.990051i	$-0.455062\pi$
$631$	−21.3352	−	21.3352i	−0.849341	−	0.849341i	−0.990051	+	0.140710i	$0.955062\pi$
$632$	−24.3966	−	39.0902i	−0.970445	−	1.55493i
$633$	8.95727	−	8.95727i	0.356020	−	0.356020i
$634$	2.37538	−	11.3271i	0.0943384	−	0.449855i
$635$	23.1394	−	9.58466i	0.918260	−	0.380356i
$636$	7.10010	−	2.77000i	0.281537	−	0.109837i
$637$	12.3781	−	29.8833i	0.490437	−	1.18402i
$638$	−2.08314	+	0.391967i	−0.0824725	+	0.0155181i
$639$	−6.05631			−0.239584
$640$	−5.81421	−	46.7214i	−0.229827	−	1.84683i
$641$	21.8354			0.862446			0.431223	−	0.902245i	$-0.358082\pi$
$641$	21.8354			0.862446			0.431223	+	0.902245i	$0.358082\pi$
$642$	−3.26610	+	0.614552i	−0.128903	+	0.0242544i
$643$	−2.68795	+	6.48928i	−0.106002	+	0.255912i	−0.967977	−	0.251039i	$-0.919228\pi$
$643$	−2.68795	+	6.48928i	−0.106002	+	0.255912i	0.861975	+	0.506951i	$0.169228\pi$
$644$	−10.0991	+	3.94001i	−0.397960	+	0.155258i
$645$	−38.2891	+	15.8599i	−1.50763	+	0.624481i
$646$	0.234978	−	1.12050i	0.00924509	−	0.0440855i
$647$	2.04417	−	2.04417i	0.0803645	−	0.0803645i	−0.665782	−	0.746146i	$-0.731902\pi$
$647$	2.04417	−	2.04417i	0.0803645	−	0.0803645i	0.746146	+	0.665782i	$0.231902\pi$
$648$	−3.61915	−	5.79889i	−0.142174	−	0.227802i
$649$	−8.33927	−	8.33927i	−0.327345	−	0.327345i
$650$	87.5525	−	57.1973i	3.43409	−	2.24346i
$651$	−3.19662	−	7.71733i	−0.125285	−	0.302466i
$652$	−0.950240	+	45.8407i	−0.0372143	+	1.79526i
$653$	5.25389	+	2.17623i	0.205600	+	0.0851625i	0.483107	−	0.875561i	$-0.339508\pi$
$653$	5.25389	+	2.17623i	0.205600	+	0.0851625i	−0.277507	+	0.960724i	$0.589508\pi$
$654$	0.552440	−	0.808520i	0.0216021	−	0.0316156i
$655$			58.3018i			2.27804i
$656$	−19.0755	−	0.791180i	−0.744774	−	0.0308904i
$657$			3.03565i			0.118432i
$658$	−2.71678	−	1.85630i	−0.105911	−	0.0723663i
$659$	22.1396	+	9.17053i	0.862437	+	0.357233i	0.769660	−	0.638454i	$-0.220426\pi$
$659$	22.1396	+	9.17053i	0.862437	+	0.357233i	0.0927768	+	0.995687i	$0.470426\pi$
$660$	5.38241	−	5.16379i	0.209510	−	0.201000i
$661$	9.89386	+	23.8859i	0.384827	+	0.929054i	0.991017	+	0.133734i	$0.0426969\pi$
$661$	9.89386	+	23.8859i	0.384827	+	0.929054i	−0.606191	+	0.795319i	$0.707303\pi$
$662$	−5.85150	−	8.95696i	−0.227425	−	0.348122i
$663$	−15.2516	−	15.2516i	−0.592324	−	0.592324i
$664$	−39.0335	+	6.51005i	−1.51479	+	0.252639i
$665$	0.754461	−	0.754461i	0.0292567	−	0.0292567i
$666$	−24.7876	−	5.19817i	−0.960501	−	0.201425i
$667$	−5.91143	+	2.44859i	−0.228891	+	0.0948099i
$668$	3.85622	−	8.78991i	0.149202	−	0.340092i
$669$	1.75704	−	4.24188i	0.0679312	−	0.164001i
$670$	9.59709	+	51.0046i	0.370768	+	1.97048i
$671$	1.31646			0.0508212
$672$	−6.23963	−	1.58105i	−0.240699	−	0.0609903i
$673$	−38.4004			−1.48023			−0.740113	−	0.672482i	$-0.765228\pi$
$673$	−38.4004			−1.48023			−0.740113	+	0.672482i	$0.765228\pi$
$674$	−9.22021	−	49.0017i	−0.355149	−	1.88748i
$675$	−21.9540	+	53.0017i	−0.845011	+	2.04004i
$676$	42.1989	+	18.5130i	1.62303	+	0.712040i
$677$	32.3083	−	13.3826i	1.24171	−	0.514333i	0.337462	−	0.941339i	$-0.390432\pi$
$677$	32.3083	−	13.3826i	1.24171	−	0.514333i	0.904249	+	0.427006i	$0.140432\pi$
$678$	−4.66246	−	0.977755i	−0.179061	−	0.0375505i
$679$	−9.39120	+	9.39120i	−0.360401	+	0.360401i
$680$	−38.4015	−	27.4232i	−1.47263	−	1.05163i
$681$	−13.5236	−	13.5236i	−0.518225	−	0.518225i
$682$	5.67802	+	8.69141i	0.217423	+	0.332811i
$683$	4.51448	+	10.8989i	0.172742	+	0.417035i	0.986412	−	0.164292i	$-0.0525338\pi$
$683$	4.51448	+	10.8989i	0.172742	+	0.417035i	−0.813670	+	0.581327i	$0.802534\pi$
$684$	−0.614229	−	0.640233i	−0.0234856	−	0.0244799i
$685$	76.9848	+	31.8882i	2.94144	+	1.21838i
$686$	−18.3661	−	12.5491i	−0.701221	−	0.479126i
$687$			23.5226i			0.897443i
$688$	−40.3266	−	18.6976i	−1.53744	−	0.712840i
$689$			25.5269i			0.972499i
$690$	12.7021	−	18.5901i	0.483562	−	0.707714i
$691$	−10.8731	−	4.50380i	−0.413633	−	0.171332i	0.166155	−	0.986100i	$-0.446865\pi$
$691$	−10.8731	−	4.50380i	−0.413633	−	0.171332i	−0.579788	+	0.814767i	$0.696865\pi$
$692$	4.16845	+	0.0864086i	0.158461	+	0.00328476i
$693$	1.06743	+	2.57702i	0.0405485	+	0.0978927i
$694$	−2.11049	+	1.37876i	−0.0801130	+	0.0523372i
$695$	20.7985	+	20.7985i	0.788931	+	0.788931i
$696$	−3.70144	−	0.856673i	−0.140303	−	0.0324721i
$697$	−13.5305	+	13.5305i	−0.512504	+	0.512504i
$698$	2.64558	−	12.6155i	0.100137	−	0.477505i
$699$	6.28300	−	2.60250i	0.237645	−	0.0984357i
$700$	−11.3689	−	29.1409i	−0.429702	−	1.10142i
$701$	5.16521	−	12.4699i	0.195087	−	0.470982i	−0.795819	−	0.605534i	$-0.792960\pi$
$701$	5.16521	−	12.4699i	0.195087	−	0.470982i	0.990907	+	0.134552i	$0.0429595\pi$
$702$	−38.8591	+	7.31178i	−1.46664	+	0.275965i
$703$	−1.64614			−0.0620855
$704$	7.98454	+	0.497109i	0.300929	+	0.0187355i
$705$	6.83406			0.257385
$706$	27.6794	−	5.20819i	1.04173	−	0.196013i
$707$	−1.02814	+	2.48215i	−0.0386672	+	0.0933509i
$708$	−7.68280	−	19.6927i	−0.288737	−	0.740096i
$709$	−28.4754	+	11.7949i	−1.06941	+	0.442966i	−0.846784	−	0.531937i	$-0.821464\pi$
$709$	−28.4754	+	11.7949i	−1.06941	+	0.442966i	−0.222630	+	0.974903i	$0.571464\pi$
$710$	−3.32996	+	15.8790i	−0.124971	+	0.595929i
$711$	−25.3070	+	25.3070i	−0.949088	+	0.949088i
$712$	0.445614	−	1.92537i	0.0167001	−	0.0721562i
$713$	22.1594	+	22.1594i	0.829875	+	0.829875i
$714$	−5.40095	+	3.52839i	−0.202125	+	0.132047i
$715$	9.56056	+	23.0812i	0.357545	+	0.863190i
$716$	7.14857	+	0.148184i	0.267155	+	0.00553790i
$717$	8.30541	+	3.44021i	0.310171	+	0.128477i
$718$	6.76119	−	9.89529i	0.252325	−	0.369289i
$719$			14.4753i			0.539836i	0.962883	+	0.269918i	$0.0869966\pi$
$719$			14.4753i			0.539836i	−0.962883	+	0.269918i	$0.913003\pi$
$720$	−34.3360	+	12.5821i	−1.27963	+	0.468909i
$721$			8.26368i			0.307756i
$722$	22.1381	+	15.1264i	0.823896	+	0.562946i
$723$	2.82207	+	1.16894i	0.104954	+	0.0434733i
$724$	−5.73143	−	5.97408i	−0.213007	−	0.222025i
$725$	−7.06540	−	17.0574i	−0.262402	−	0.633495i
$726$	0.693168	+	1.06104i	0.0257259	+	0.0393789i
$727$	5.82601	+	5.82601i	0.216075	+	0.216075i	0.806842	−	0.590767i	$-0.201175\pi$
$727$	5.82601	+	5.82601i	0.216075	+	0.216075i	−0.590767	+	0.806842i	$0.701175\pi$
$728$	12.5293	−	17.5452i	0.464367	−	0.650267i
$729$	5.09981	−	5.09981i	0.188882	−	0.188882i
$730$	7.95917	+	1.66910i	0.294582	+	0.0617763i
$731$	−41.1594	+	17.0488i	−1.52234	+	0.630572i
$732$	2.16078	+	0.947953i	0.0798646	+	0.0350374i
$733$	18.2674	−	44.1014i	0.674722	−	1.62892i	−0.0987644	−	0.995111i	$-0.531489\pi$
$733$	18.2674	−	44.1014i	0.674722	−	1.62892i	0.773487	−	0.633813i	$-0.218511\pi$
$734$	−8.31837	−	44.2088i	−0.307037	−	1.63178i
$735$	20.0938			0.741170
$736$	23.8968	−	3.47816i	0.880849	−	0.128207i
$737$	−8.81865			−0.324839
$738$	2.74209	+	14.5731i	0.100938	+	0.536442i
$739$	9.15283	−	22.0969i	0.336692	−	0.812847i	−0.661336	−	0.750089i	$-0.730010\pi$
$739$	9.15283	−	22.0969i	0.336692	−	0.812847i	0.998029	−	0.0627578i	$-0.0199896\pi$
$740$	−27.2581	+	62.1325i	−1.00203	+	2.28403i
$741$	−1.00372	+	0.415754i	−0.0368725	+	0.0152731i
$742$	7.47261	+	1.56707i	0.274328	+	0.0575289i
$743$	32.3211	−	32.3211i	1.18575	−	1.18575i	0.207514	−	0.978232i	$-0.433463\pi$
$743$	32.3211	−	32.3211i	1.18575	−	1.18575i	0.978232	−	0.207514i	$-0.0665373\pi$
$744$	3.06116	+	18.3543i	0.112228	+	0.672903i
$745$	27.9942	+	27.9942i	1.02563	+	1.02563i
$746$	−11.0314	−	16.8859i	−0.403888	−	0.618236i
$747$	11.7623	+	28.3966i	0.430359	+	1.03898i
$748$	5.78590	−	5.55090i	0.211553	−	0.202961i
$749$	−3.07601	−	1.27413i	−0.112395	−	0.0465556i
$750$	31.8678	+	21.7744i	1.16365	+	0.795090i
$751$		−	35.2204i		−	1.28521i	−0.766198	−	0.642604i	$-0.777854\pi$
$751$		−	35.2204i		−	1.28521i	0.766198	−	0.642604i	$-0.222146\pi$
$752$	4.96374	+	5.39331i	0.181009	+	0.196674i
$753$			21.5160i			0.784087i
$754$	7.17911	−	10.5069i	0.261448	−	0.382640i
$755$	41.8897	+	17.3513i	1.52452	+	0.631478i
$756$	−0.245107	+	11.8243i	−0.00891447	+	0.430044i
$757$	11.9509	+	28.8520i	0.434362	+	1.04864i	0.977865	+	0.209235i	$0.0670975\pi$
$757$	11.9509	+	28.8520i	0.434362	+	1.04864i	−0.543503	+	0.839407i	$0.682903\pi$
$758$	13.4559	−	8.79063i	0.488741	−	0.319290i
$759$	2.70520	+	2.70520i	0.0981925	+	0.0981925i
$760$	−2.01635	+	1.25842i	−0.0731406	+	0.0456478i
$761$	11.4005	−	11.4005i	0.413269	−	0.413269i	−0.469607	−	0.882876i	$-0.655604\pi$
$761$	11.4005	−	11.4005i	0.413269	−	0.413269i	0.882876	+	0.469607i	$0.155604\pi$
$762$	−1.56556	+	7.46544i	−0.0567144	+	0.270444i
$763$	0.906336	−	0.375417i	0.0328116	−	0.0135910i
$764$	−35.6661	+	13.9146i	−1.29036	+	0.503412i
$765$	−14.0258	+	33.8613i	−0.507104	+	1.22426i
$766$	−29.9348	+	5.63255i	−1.08159	+	0.203512i
$767$	70.8010			2.55647
$768$	12.7475	+	6.56544i	0.459987	+	0.236910i
$769$	−12.9977			−0.468710			−0.234355	−	0.972151i	$-0.575298\pi$
$769$	−12.9977			−0.468710			−0.234355	+	0.972151i	$0.575298\pi$
$770$	7.34358	−	1.38178i	0.264644	−	0.0497957i
$771$	−3.07133	+	7.41485i	−0.110611	+	0.267039i
$772$	24.8712	−	9.70313i	0.895136	−	0.349223i
$773$	−2.66928	+	1.10565i	−0.0960073	+	0.0397675i	−0.430170	−	0.902748i	$-0.641546\pi$
$773$	−2.66928	+	1.10565i	−0.0960073	+	0.0397675i	0.334163	+	0.942515i	$0.391546\pi$
$774$	−7.08601	+	33.7898i	−0.254701	+	1.21455i
$775$	−63.9407	+	63.9407i	−2.29682	+	2.29682i
$776$	25.0986	−	15.6643i	0.900987	−	0.562315i
$777$	6.55912	+	6.55912i	0.235307	+	0.235307i
$778$	−17.6174	+	11.5093i	−0.631616	+	0.412629i
$779$	0.368836	+	0.890449i	0.0132149	+	0.0319036i
$780$	−0.928025	+	44.7690i	−0.0332286	+	1.60299i
$781$	−2.54696	−	1.05498i	−0.0911373	−	0.0377503i
$782$	13.6543	−	19.9837i	0.488279	−	0.714616i
$783$			6.98067i			0.249469i
$784$	14.5946	+	15.8576i	0.521235	+	0.566344i
$785$		−	13.9087i		−	0.496422i
$786$	−14.6606	−	10.0172i	−0.522926	−	0.357301i
$787$	−28.0036	−	11.5995i	−0.998222	−	0.413477i	−0.177077	−	0.984197i	$-0.556664\pi$
$787$	−28.0036	−	11.5995i	−0.998222	−	0.413477i	−0.821145	+	0.570720i	$0.806664\pi$
$788$	−13.7929	+	13.2327i	−0.491352	+	0.471395i
$789$	−4.07744	−	9.84382i	−0.145161	−	0.350449i
$790$	52.4378	+	80.2671i	1.86565	+	2.85577i
$791$	−3.37469	−	3.37469i	−0.119990	−	0.119990i
$792$	−1.02220	−	6.12899i	−0.0363223	−	0.217784i
$793$	−5.58839	+	5.58839i	−0.198450	+	0.198450i
$794$	2.89589	+	0.607293i	0.102771	+	0.0215520i
$795$	−14.6508	+	6.06858i	−0.519612	+	0.215230i
$796$	6.02234	−	13.7274i	0.213456	−	0.486555i
$797$	−2.45181	+	5.91918i	−0.0868474	+	0.209668i	−0.961336	−	0.275378i	$-0.911197\pi$
$797$	−2.45181	+	5.91918i	−0.0868474	+	0.209668i	0.874489	+	0.485046i	$0.161197\pi$
$798$	0.0600883	+	0.319345i	0.00212710	+	0.0113047i
$799$	7.34637			0.259896
$800$	10.0362	+	68.9541i	0.354833	+	2.43790i
$801$	−1.53497			−0.0542357
$802$	−8.49189	−	45.1310i	−0.299859	−	1.59363i
$803$	−0.528799	+	1.27663i	−0.0186609	+	0.0450514i
$804$	−14.4746	−	6.35013i	−0.510479	−	0.223952i
$805$	20.8392	−	8.63187i	0.734485	−	0.304234i
$806$	−60.9987	−	12.7919i	−2.14859	−	0.450576i
$807$	−9.52829	+	9.52829i	−0.335412	+	0.335412i
$808$	3.47812	−	4.87051i	0.122360	−	0.171344i
$809$	−4.02527	−	4.02527i	−0.141521	−	0.141521i	0.632797	−	0.774318i	$-0.281907\pi$
$809$	−4.02527	−	4.02527i	−0.141521	−	0.141521i	−0.774318	+	0.632797i	$0.781907\pi$
$810$	7.77895	+	11.9073i	0.273324	+	0.418381i
$811$	−7.60419	−	18.3581i	−0.267019	−	0.644641i	0.732321	−	0.680959i	$-0.238437\pi$
$811$	−7.60419	−	18.3581i	−0.267019	−	0.644641i	−0.999340	+	0.0363181i	$0.988437\pi$
$812$	−2.63502	−	2.74658i	−0.0924711	−	0.0963860i
$813$	9.48746	+	3.92983i	0.332740	+	0.137825i
$814$	−9.51884	−	6.50397i	−0.333635	−	0.227964i
$815$		−	95.4030i		−	3.34182i
$816$	13.4938	−	4.94470i	0.472378	−	0.173099i
$817$			2.24398i			0.0785069i
$818$	−2.04446	+	2.99215i	−0.0714829	+	0.104618i
$819$	−15.4708	−	6.40822i	−0.540594	−	0.223921i
$820$	39.7168	+	0.823297i	1.38697	+	0.0287508i
$821$	−0.400889	−	0.967831i	−0.0139911	−	0.0337775i	0.916730	−	0.399508i	$-0.130819\pi$
$821$	−0.400889	−	0.967831i	−0.0139911	−	0.0337775i	−0.930721	+	0.365731i	$0.880819\pi$
$822$	−21.2458	+	13.8797i	−0.741033	+	0.484111i
$823$	−6.32356	−	6.32356i	−0.220425	−	0.220425i	0.588252	−	0.808678i	$-0.299816\pi$
$823$	−6.32356	−	6.32356i	−0.220425	−	0.220425i	−0.808678	+	0.588252i	$0.799816\pi$
$824$	4.15081	−	17.9344i	0.144600	−	0.624776i
$825$	−7.80583	+	7.80583i	−0.271764	+	0.271764i
$826$	4.34638	−	20.7259i	0.151230	−	0.721145i
$827$	−14.2700	+	5.91085i	−0.496218	+	0.205540i	−0.616735	−	0.787171i	$-0.711545\pi$
$827$	−14.2700	+	5.91085i	−0.496218	+	0.205540i	0.120517	+	0.992711i	$0.461545\pi$
$828$	−6.81709	−	17.4737i	−0.236910	−	0.607252i
$829$	−3.28911	+	7.94062i	−0.114236	+	0.275789i	−0.970649	−	0.240502i	$-0.922688\pi$
$829$	−3.28911	+	7.94062i	−0.114236	+	0.275789i	0.856413	+	0.516291i	$0.172688\pi$
$830$	80.9203	−	15.2261i	2.80879	−	0.528504i
$831$	10.5551			0.366153
$832$	−36.0049	+	31.7844i	−1.24824	+	1.10193i
$833$	21.6001			0.748399
$834$	−8.80349	+	1.65647i	−0.304840	+	0.0573590i
$835$	−7.64302	+	18.4519i	−0.264498	+	0.638554i
$836$	−0.146786	−	0.376243i	−0.00507669	−	0.0130127i
$837$	31.5870	−	13.0837i	1.09180	−	0.452240i
$838$	0.745479	−	3.55484i	0.0257521	−	0.122800i
$839$	2.77178	−	2.77178i	0.0956926	−	0.0956926i	−0.657640	−	0.753332i	$-0.728445\pi$
$839$	2.77178	−	2.77178i	0.0956926	−	0.0956926i	0.753332	+	0.657640i	$0.228445\pi$
$840$	13.0484	+	3.01998i	0.450214	+	0.104199i
$841$	18.9175	+	18.9175i	0.652329	+	0.652329i
$842$	−43.6305	+	28.5034i	−1.50361	+	0.982293i
$843$	5.98009	+	14.4372i	0.205965	+	0.497244i
$844$	−28.2638	−	0.585886i	−0.972881	−	0.0201670i
$845$	−88.5843	−	36.6928i	−3.04739	−	1.26227i
$846$	3.21182	−	4.70063i	0.110425	−	0.161611i
$847$			1.26970i			0.0436273i
$848$	−15.4305	−	7.15442i	−0.529884	−	0.245684i
$849$		−	18.6382i		−	0.639663i
$850$	57.6629	+	39.3995i	1.97782	+	1.35139i
$851$	−32.1512	−	13.3174i	−1.10213	−	0.456516i
$852$	−3.42080	−	3.56562i	−0.117195	−	0.122156i
$853$	−12.4483	−	30.0529i	−0.426222	−	1.02899i	−0.980475	−	0.196644i	$-0.936996\pi$
$853$	−12.4483	−	30.0529i	−0.426222	−	1.02899i	0.554253	−	0.832349i	$-0.313004\pi$
$854$	1.29285	+	1.97898i	0.0442404	+	0.0677193i
$855$	1.30538	+	1.30538i	0.0446432	+	0.0446432i
$856$	6.03580	+	4.31027i	0.206299	+	0.147322i
$857$	3.39304	−	3.39304i	0.115904	−	0.115904i	−0.646776	−	0.762680i	$-0.723883\pi$
$857$	3.39304	−	3.39304i	0.115904	−	0.115904i	0.762680	+	0.646776i	$0.223883\pi$
$858$	−7.44667	−	1.56163i	−0.254225	−	0.0533131i
$859$	43.4342	−	17.9910i	1.48195	−	0.613846i	0.512406	−	0.858743i	$-0.328754\pi$
$859$	43.4342	−	17.9910i	1.48195	−	0.613846i	0.969549	+	0.244898i	$0.0787543\pi$
$860$	84.6974	+	37.1576i	2.88816	+	1.26706i
$861$	2.07838	−	5.01766i	0.0708312	−	0.171002i
$862$	−4.74146	−	25.1989i	−0.161495	−	0.858279i
$863$	−1.10072			−0.0374691			−0.0187345	−	0.999824i	$-0.505964\pi$
$863$	−1.10072			−0.0374691			−0.0187345	+	0.999824i	$0.505964\pi$
$864$	6.47122	−	25.5387i	0.220155	−	0.868846i
$865$	−8.67532			−0.294970
$866$	6.31182	+	33.5448i	0.214484	+	1.13990i
$867$	−0.318169	+	0.768129i	−0.0108056	+	0.0260870i
$868$	−7.48926	+	17.0711i	−0.254202	+	0.579432i
$869$	−15.0512	+	6.23439i	−0.510576	+	0.211487i
$870$	7.73701	+	1.62251i	0.262309	+	0.0550084i
$871$	37.4354	−	37.4354i	1.26845	−	1.26845i
$872$	−2.15557	+	0.359508i	−0.0729966	+	0.0121745i
$873$	−16.2489	−	16.2489i	−0.549940	−	0.549940i
$874$	−0.666751	−	1.02060i	−0.0225532	−	0.0345224i
$875$	14.7970	+	35.7232i	0.500232	+	1.20767i
$876$	−1.78723	+	1.71464i	−0.0603848	+	0.0579322i
$877$	−30.5531	−	12.6555i	−1.03171	−	0.427347i	−0.198378	−	0.980126i	$-0.563567\pi$
$877$	−30.5531	−	12.6555i	−1.03171	−	0.427347i	−0.833328	+	0.552779i	$0.813567\pi$
$878$	−40.6952	−	27.8060i	−1.37340	−	0.938406i
$879$		−	10.0668i		−	0.339543i
$880$	−16.6316	−	0.689817i	−0.560652	−	0.0232537i
$881$			34.3011i			1.15563i	0.816166	+	0.577817i	$0.196095\pi$
$881$			34.3011i			1.15563i	−0.816166	+	0.577817i	$0.803905\pi$
$882$	9.44352	−	13.8210i	0.317980	−	0.465377i
$883$	16.2016	+	6.71091i	0.545226	+	0.225840i	0.638257	−	0.769823i	$-0.279656\pi$
$883$	16.2016	+	6.71091i	0.545226	+	0.225840i	−0.0930311	+	0.995663i	$0.529656\pi$
$884$	−0.997594	+	48.1251i	−0.0335527	+	1.61862i
$885$	16.8317	+	40.6353i	0.565790	+	1.36594i
$886$	−21.2100	+	13.8563i	−0.712565	+	0.465512i
$887$	1.91165	+	1.91165i	0.0641869	+	0.0641869i	0.738472	−	0.674285i	$-0.235548\pi$
$887$	1.91165	+	1.91165i	0.0641869	+	0.0641869i	−0.674285	+	0.738472i	$0.735548\pi$
$888$	−10.9405	−	17.5297i	−0.367138	−	0.588257i
$889$	−5.40349	+	5.40349i	−0.181227	+	0.181227i
$890$	−0.843980	+	4.02455i	−0.0282903	+	0.134903i
$891$	−2.23278	+	0.924849i	−0.0748011	+	0.0309836i
$892$	−9.54578	+	3.72414i	−0.319616	+	0.124693i
$893$	0.141605	−	0.341864i	0.00473862	−	0.0114400i
$894$	−11.8493	+	2.22957i	−0.396299	+	0.0745681i
$895$	−14.8775			−0.497300
$896$	7.09408	+	12.4911i	0.236997	+	0.417297i
$897$	−22.9673			−0.766856
$898$	9.82052	−	1.84784i	0.327715	−	0.0616632i
$899$	−4.21070	+	10.1655i	−0.140435	+	0.339039i
$900$	50.4202	−	19.6706i	1.68067	−	0.655688i
$901$	−15.7491	+	6.52351i	−0.524680	+	0.217330i
$902$	−1.38540	+	6.60631i	−0.0461287	+	0.219966i
$903$	8.94122	−	8.94122i	0.297545	−	0.297545i
$904$	5.62890	+	9.01908i	0.187215	+	0.299970i
$905$	12.1807	+	12.1807i	0.404900	+	0.404900i
$906$	−11.5605	+	7.55236i	−0.384071	+	0.250910i
$907$	−21.9008	−	52.8733i	−0.727205	−	1.75563i	−0.651693	−	0.758483i	$-0.725941\pi$
$907$	−21.9008	−	52.8733i	−0.727205	−	1.75563i	−0.0755125	−	0.997145i	$-0.524059\pi$
$908$	−0.884565	+	42.6724i	−0.0293553	+	1.41613i
$909$	−4.29467	−	1.77891i	−0.142445	−	0.0590027i
$910$	−25.3081	+	37.0394i	−0.838954	+	1.22784i
$911$		−	6.62785i		−	0.219590i	−0.993954	−	0.109795i	$-0.964980\pi$
$911$		−	6.62785i		−	0.219590i	0.993954	−	0.109795i	$-0.0350195\pi$
$912$	0.0299976	−	0.723248i	0.000993319	−	0.0239491i
$913$			13.9910i			0.463036i
$914$	33.3589	+	22.7933i	1.10342	+	0.753935i
$915$	−4.53593	−	1.87884i	−0.149953	−	0.0621126i
$916$	37.8809	−	36.3424i	1.25162	−	1.20079i
$917$	−6.80729	−	16.4342i	−0.224796	−	0.542707i
$918$	−14.4417	−	22.1060i	−0.476647	−	0.729608i
$919$	−18.7044	−	18.7044i	−0.617000	−	0.617000i	0.327760	−	0.944761i	$-0.393706\pi$
$919$	−18.7044	−	18.7044i	−0.617000	−	0.617000i	−0.944761	+	0.327760i	$0.893706\pi$
$920$	−49.5624	+	8.26609i	−1.63403	+	0.272525i
$921$	−0.231111	+	0.231111i	−0.00761535	+	0.00761535i
$922$	48.0800	+	10.0828i	1.58343	+	0.332059i
$923$	15.2904	−	6.33347i	0.503288	−	0.208469i
$924$	−0.914283	+	2.08403i	−0.0300777	+	0.0685595i
$925$	38.4274	−	92.7719i	1.26348	−	3.05032i
$926$	−5.42840	−	28.8498i	−0.178388	−	0.948063i
$927$	−14.2980			−0.469608
$928$	4.33912	+	7.28438i	0.142439	+	0.239121i
$929$	35.5849			1.16750			0.583751	−	0.811933i	$-0.301585\pi$
$929$	35.5849			1.16750			0.583751	+	0.811933i	$0.301585\pi$
$930$	−7.15961	−	38.0504i	−0.234773	−	1.24772i
$931$	0.416352	−	1.00516i	0.0136454	−	0.0329429i
$932$	−13.8983	−	6.09732i	−0.455254	−	0.199724i
$933$	10.0201	−	4.15048i	0.328045	−	0.135881i
$934$	25.1885	+	5.28223i	0.824193	+	0.172840i
$935$	−11.7970	+	11.7970i	−0.385803	+	0.385803i
$936$	30.3570	+	21.6785i	0.992251	+	0.708584i
$937$	−26.0899	−	26.0899i	−0.852319	−	0.852319i	0.138099	−	0.990418i	$-0.455901\pi$
$937$	−26.0899	−	26.0899i	−0.852319	−	0.852319i	−0.990418	+	0.138099i	$0.955901\pi$
$938$	−8.66052	−	13.2567i	−0.282776	−	0.432848i
$939$	3.89393	+	9.40079i	0.127074	+	0.306783i
$940$	−10.5586	−	11.0056i	−0.344384	−	0.358964i
$941$	−12.6855	−	5.25453i	−0.413537	−	0.171293i	0.166208	−	0.986091i	$-0.446848\pi$
$941$	−12.6855	−	5.25453i	−0.413537	−	0.171293i	−0.579745	+	0.814798i	$0.696848\pi$
$942$	3.49748	+	2.38973i	0.113954	+	0.0778617i
$943$			20.3755i			0.663516i
$944$	−19.8433	+	42.7976i	−0.645845	+	1.39294i
$945$		−	24.6085i		−	0.800515i
$946$	−8.86605	+	12.9758i	−0.288260	+	0.421881i
$947$	13.8154	+	5.72254i	0.448941	+	0.185958i	0.595687	−	0.803217i	$-0.296880\pi$
$947$	13.8154	+	5.72254i	0.448941	+	0.185958i	−0.146746	+	0.989174i	$0.546880\pi$
$948$	−29.1936	−	0.605160i	−0.948165	−	0.0196547i
$949$	−3.17458	−	7.66411i	−0.103051	−	0.248788i
$950$	2.94494	−	1.92390i	0.0955464	−	0.0624197i
$951$	−5.18597	−	5.18597i	−0.168167	−	0.168167i
$952$	14.0266	+	3.24637i	0.454605	+	0.105215i
$953$	−22.2490	+	22.2490i	−0.720715	+	0.720715i	−0.968751	−	0.248036i	$-0.920215\pi$
$953$	−22.2490	+	22.2490i	−0.720715	+	0.720715i	0.248036	+	0.968751i	$0.420215\pi$
$954$	−2.71137	+	12.9293i	−0.0877840	+	0.418601i
$955$	73.5960	−	30.4845i	2.38151	−	0.986454i
$956$	−7.29170	−	18.6902i	−0.235830	−	0.604485i
$957$	−0.514039	+	1.24100i	−0.0166165	+	0.0401158i
$958$	−23.7302	+	4.46510i	−0.766689	+	0.144261i
$959$	−25.4239			−0.820980
$960$	−26.8017	−	13.1083i	−0.865022	−	0.423070i
$961$	22.8902			0.738395
$962$	68.0173	−	12.7982i	2.19297	−	0.412631i
$963$	2.20452	−	5.32218i	0.0710397	−	0.171505i
$964$	−2.47762	−	6.35069i	−0.0797988	−	0.204542i
$965$	−51.3211	+	21.2579i	−1.65208	+	0.684315i
$966$	−1.40993	+	6.72332i	−0.0453639	+	0.216319i
$967$	−17.1060	+	17.1060i	−0.550092	+	0.550092i	−0.926467	−	0.376375i	$-0.877170\pi$
$967$	−17.1060	+	17.1060i	−0.550092	+	0.550092i	0.376375	+	0.926467i	$0.377170\pi$
$968$	0.637763	−	2.75559i	0.0204985	−	0.0885679i
$969$	−0.513008	−	0.513008i	−0.0164802	−	0.0164802i
$970$	−51.5370	+	33.6687i	−1.65475	+	1.08104i
$971$	19.8669	+	47.9630i	0.637560	+	1.53921i	0.829920	+	0.557883i	$0.188386\pi$
$971$	19.8669	+	47.9630i	0.637560	+	1.53921i	−0.192359	+	0.981325i	$0.561614\pi$
$972$	−32.2688	−	0.668905i	−1.03502	−	0.0214551i
$973$	−8.29113	−	3.43430i	−0.265801	−	0.110099i
$974$	−2.77523	+	4.06166i	−0.0889240	+	0.130144i
$975$		−	66.2720i		−	2.12240i
$976$	−1.81180	−	4.94431i	−0.0579944	−	0.158264i
$977$		−	5.29010i		−	0.169245i	−0.996413	−	0.0846227i	$-0.973031\pi$
$977$		−	5.29010i		−	0.169245i	0.996413	−	0.0846227i	$-0.0269685\pi$
$978$	23.9900	+	16.3918i	0.767117	+	0.524151i
$979$	−0.645528	−	0.267386i	−0.0206312	−	0.00854570i
$980$	−31.0448	−	32.3592i	−0.991691	−	1.03368i
$981$	0.649554	+	1.56816i	0.0207387	+	0.0500676i
$982$	14.2534	+	21.8178i	0.454843	+	0.696233i
$983$	7.33701	+	7.33701i	0.234014	+	0.234014i	0.814366	−	0.580352i	$-0.197085\pi$
$983$	7.33701	+	7.33701i	0.234014	+	0.234014i	−0.580352	+	0.814366i	$0.697085\pi$
$984$	−7.03101	+	9.84573i	−0.224140	+	0.313871i
$985$	28.1227	−	28.1227i	0.896063	−	0.896063i
$986$	8.31702	+	1.74415i	0.264868	+	0.0555449i
$987$	−1.92640	+	0.797940i	−0.0613179	+	0.0253987i
$988$	2.22028	+	0.974056i	0.0706364	+	0.0309889i
$989$	−18.1540	+	43.8276i	−0.577264	+	1.39364i
$990$	2.39078	+	12.7060i	0.0759839	+	0.403824i
$991$	6.78925			0.215668			0.107834	−	0.994169i	$-0.465609\pi$
$991$	6.78925			0.215668			0.107834	+	0.994169i	$0.465609\pi$
$992$	24.8285	−	33.2871i	0.788305	−	1.05687i
$993$	−6.77988			−0.215153
$994$	−0.915368	−	4.86481i	−0.0290337	−	0.154303i
$995$	−11.9363	+	28.8167i	−0.378405	+	0.913551i
$996$	−10.0747	+	22.9643i	−0.319228	+	0.727652i
$997$	46.1921	−	19.1334i	1.46292	−	0.605960i	0.497686	−	0.867357i	$-0.334183\pi$
$997$	46.1921	−	19.1334i	1.46292	−	0.605960i	0.965231	+	0.261397i	$0.0841833\pi$
$998$	−27.3291	−	5.73114i	−0.865088	−	0.181416i
$999$	−26.8464	+	26.8464i	−0.849382	+	0.849382i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.n.a.45.4	✓	160
32.5	even	8	inner	352.2.n.a.133.4	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.2.n.a.45.4	✓	160	1.1	even	1	trivial
352.2.n.a.133.4	yes	160	32.5	even	8	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:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38982 + 0.261511i) q^{2} +(-0.342954 + 0.827965i) q^{3} +(1.86322 - 0.726908i) q^{4} +(-3.84471 + 1.59253i) q^{5} +(0.260125 - 1.24041i) q^{6} +(0.897811 - 0.897811i) q^{7} +(-2.39946 + 1.49753i) q^{8} +(1.55341 + 1.55341i) q^{9} +(4.92700 - 3.21877i) q^{10} +(0.382683 + 0.923880i) q^{11} +(-0.0371463 + 1.79198i) q^{12} +(-5.54640 - 2.29739i) q^{13} +(-1.01301 + 1.48259i) q^{14} -3.72945i q^{15} +(2.94321 - 2.70879i) q^{16} -4.00902i q^{17} +(-2.56520 - 1.75274i) q^{18} +(-0.186560 - 0.0772758i) q^{19} +(-6.00593 + 5.76199i) q^{20} +(0.435448 + 1.05126i) q^{21} +(-0.773467 - 1.18395i) q^{22} +(-3.01858 - 3.01858i) q^{23} +(-0.416995 - 2.50025i) q^{24} +(8.71008 - 8.71008i) q^{25} +(8.30932 + 1.74253i) q^{26} +(-4.30281 + 1.78228i) q^{27} +(1.02020 - 2.32545i) q^{28} +(0.573587 - 1.38476i) q^{29} +(0.975291 + 5.18328i) q^{30} -7.34100 q^{31} +(-3.38217 + 4.53442i) q^{32} -0.896183 q^{33} +(1.04840 + 5.57184i) q^{34} +(-2.02203 + 4.88161i) q^{35} +(4.02354 + 1.76517i) q^{36} +(7.53146 - 3.11963i) q^{37} +(0.279495 + 0.0586123i) q^{38} +(3.80432 - 3.80432i) q^{39} +(6.84036 - 9.57877i) q^{40} +(-3.37501 - 3.37501i) q^{41} +(-0.880113 - 1.34720i) q^{42} +(-4.25260 - 10.2667i) q^{43} +(1.38460 + 1.44322i) q^{44} +(-8.44627 - 3.49856i) q^{45} +(4.98469 + 3.40590i) q^{46} +1.83246i q^{47} +(1.23339 + 3.36586i) q^{48} +5.38787i q^{49} +(-9.82771 + 14.3833i) q^{50} +(3.31933 + 1.37491i) q^{51} +(-12.0042 - 0.248837i) q^{52} +(-1.62721 - 3.92842i) q^{53} +(5.51407 - 3.60229i) q^{54} +(-2.94261 - 2.94261i) q^{55} +(-0.809765 + 3.49876i) q^{56} +(0.127963 - 0.127963i) q^{57} +(-0.435055 + 2.07457i) q^{58} +(-10.8958 + 4.51318i) q^{59} +(-2.71097 - 6.94880i) q^{60} +(0.503786 - 1.21625i) q^{61} +(10.2027 - 1.91975i) q^{62} +2.78934 q^{63} +(3.51482 - 7.18652i) q^{64} +24.9830 q^{65} +(1.24554 - 0.234361i) q^{66} +(-3.37475 + 8.14737i) q^{67} +(-2.91419 - 7.46971i) q^{68} +(3.53451 - 1.46404i) q^{69} +(1.53367 - 7.31337i) q^{70} +(-1.94936 + 1.94936i) q^{71} +(-6.05363 - 1.40107i) q^{72} +(0.977092 + 0.977092i) q^{73} +(-9.65159 + 6.30530i) q^{74} +(4.22448 + 10.1988i) q^{75} +(-0.403776 - 0.00836995i) q^{76} +(1.17305 + 0.485892i) q^{77} +(-4.29247 + 6.28222i) q^{78} +16.2913i q^{79} +(-7.00195 + 15.1016i) q^{80} +2.41675i q^{81} +(5.57327 + 3.80807i) q^{82} +(12.9260 + 5.35414i) q^{83} +(1.57551 + 1.64221i) q^{84} +(6.38449 + 15.4135i) q^{85} +(8.59522 + 13.1568i) q^{86} +(0.949820 + 0.949820i) q^{87} +(-2.30177 - 1.64373i) q^{88} +(-0.494066 + 0.494066i) q^{89} +(12.6537 + 2.65359i) q^{90} +(-7.04225 + 2.91699i) q^{91} +(-7.81852 - 3.43006i) q^{92} +(2.51763 - 6.07809i) q^{93} +(-0.479208 - 2.54680i) q^{94} +0.840334 q^{95} +(-2.59441 - 4.35541i) q^{96} -10.4601 q^{97} +(-1.40899 - 7.48819i) q^{98} +(-0.840701 + 2.02963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 16 q^{10} - 16 q^{14} - 16 q^{20} + 24 q^{24} - 48 q^{27} + 40 q^{28} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 56 q^{36} - 16 q^{38} - 48 q^{39} - 64 q^{40} - 104 q^{48} - 80 q^{50} + 32 q^{51} + 64 q^{54}+ \cdots + 56 q^{98}+O(q^{100}) \) 160 * q - 16 * q^10 - 16 * q^14 - 16 * q^20 + 24 * q^24 - 48 * q^27 + 40 * q^28 + 80 * q^30 - 48 * q^31 - 48 * q^35 + 56 * q^36 - 16 * q^38 - 48 * q^39 - 64 * q^40 - 104 * q^48 - 80 * q^50 + 32 * q^51 + 64 * q^54 - 40 * q^56 + 8 * q^58 + 32 * q^59 - 8 * q^60 - 64 * q^61 + 24 * q^62 - 24 * q^64 + 48 * q^68 - 64 * q^69 - 24 * q^70 + 32 * q^71 + 72 * q^72 - 128 * q^78 - 16 * q^80 + 40 * q^82 - 80 * q^83 - 152 * q^84 - 64 * q^86 - 112 * q^87 + 144 * q^90 - 72 * q^92 + 96 * q^94 + 56 * q^96 + 56 * q^98

Introduction

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