LMFDB - Embedded newform 1155.2.c.e.694.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(694,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1155.694");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.c (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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15194 x^{12} + 40320 x^{10} + 61593 x^{8} + 48545 x^{6} + \cdots + 100 $ x^20 + 33x^18 + 456x^16 + 3426x^14 + 15194x^12 + 40320x^10 + 61593x^8 + 48545x^6 + 15624x^4 + 2116*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			694.2
Root			$-2.51841i$ of defining polynomial
Character	$\chi$	$=$	1155.694
Dual form			1155.2.c.e.694.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51841i q^{2} +1.00000i q^{3} -4.34238 q^{4} +(-2.17741 - 0.508790i) q^{5} +2.51841 q^{6} -1.00000i q^{7} +5.89907i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.51841i q^{2} +1.00000i q^{3} -4.34238 q^{4} +(-2.17741 - 0.508790i) q^{5} +2.51841 q^{6} -1.00000i q^{7} +5.89907i q^{8} -1.00000 q^{9} +(-1.28134 + 5.48362i) q^{10} -1.00000 q^{11} -4.34238i q^{12} -1.93158i q^{13} -2.51841 q^{14} +(0.508790 - 2.17741i) q^{15} +6.17150 q^{16} +2.73533i q^{17} +2.51841i q^{18} -5.74934 q^{19} +(9.45516 + 2.20936i) q^{20} +1.00000 q^{21} +2.51841i q^{22} +3.98220i q^{23} -5.89907 q^{24} +(4.48227 + 2.21569i) q^{25} -4.86452 q^{26} -1.00000i q^{27} +4.34238i q^{28} +0.897314 q^{29} +(-5.48362 - 1.28134i) q^{30} +10.2982 q^{31} -3.74421i q^{32} -1.00000i q^{33} +6.88868 q^{34} +(-0.508790 + 2.17741i) q^{35} +4.34238 q^{36} +3.09664i q^{37} +14.4792i q^{38} +1.93158 q^{39} +(3.00139 - 12.8447i) q^{40} +7.83869 q^{41} -2.51841i q^{42} +4.01145i q^{43} +4.34238 q^{44} +(2.17741 + 0.508790i) q^{45} +10.0288 q^{46} +3.41906i q^{47} +6.17150i q^{48} -1.00000 q^{49} +(5.58002 - 11.2882i) q^{50} -2.73533 q^{51} +8.38767i q^{52} +9.17420i q^{53} -2.51841 q^{54} +(2.17741 + 0.508790i) q^{55} +5.89907 q^{56} -5.74934i q^{57} -2.25980i q^{58} -9.82410 q^{59} +(-2.20936 + 9.45516i) q^{60} +1.57645 q^{61} -25.9350i q^{62} +1.00000i q^{63} +2.91353 q^{64} +(-0.982771 + 4.20586i) q^{65} -2.51841 q^{66} -5.66006i q^{67} -11.8778i q^{68} -3.98220 q^{69} +(5.48362 + 1.28134i) q^{70} -5.57815 q^{71} -5.89907i q^{72} -9.45961i q^{73} +7.79861 q^{74} +(-2.21569 + 4.48227i) q^{75} +24.9658 q^{76} +1.00000i q^{77} -4.86452i q^{78} +13.4115 q^{79} +(-13.4379 - 3.13999i) q^{80} +1.00000 q^{81} -19.7410i q^{82} +8.24025i q^{83} -4.34238 q^{84} +(1.39171 - 5.95595i) q^{85} +10.1025 q^{86} +0.897314i q^{87} -5.89907i q^{88} -9.21337 q^{89} +(1.28134 - 5.48362i) q^{90} -1.93158 q^{91} -17.2922i q^{92} +10.2982i q^{93} +8.61058 q^{94} +(12.5187 + 2.92521i) q^{95} +3.74421 q^{96} +15.8647i q^{97} +2.51841i q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) $ 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	$ 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} - 2 q^{10} - 20 q^{11} - 6 q^{14} + 2 q^{15} + 38 q^{16} + 2 q^{19} + 4 q^{20} + 20 q^{21} - 18 q^{24} + 12 q^{25} + 20 q^{26} - 38 q^{29} + 6 q^{30} + 20 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} + 2 q^{40} + 12 q^{41} + 26 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{49} - 6 q^{50} + 26 q^{51} - 6 q^{54} + 2 q^{55} + 18 q^{56} - 22 q^{59} + 16 q^{60} + 34 q^{61} - 26 q^{64} - 28 q^{65} - 6 q^{66} - 26 q^{69} - 6 q^{70} + 72 q^{71} - 72 q^{74} - 8 q^{75} + 44 q^{76} + 4 q^{79} - 8 q^{80} + 20 q^{81} - 26 q^{84} - 16 q^{85} + 52 q^{86} + 6 q^{89} + 2 q^{90} + 16 q^{94} + 14 q^{95} + 62 q^{96} + 20 q^{99}+O(q^{100}) $ 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9 - 2 * q^10 - 20 * q^11 - 6 * q^14 + 2 * q^15 + 38 * q^16 + 2 * q^19 + 4 * q^20 + 20 * q^21 - 18 * q^24 + 12 * q^25 + 20 * q^26 - 38 * q^29 + 6 * q^30 + 20 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 + 2 * q^40 + 12 * q^41 + 26 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^49 - 6 * q^50 + 26 * q^51 - 6 * q^54 + 2 * q^55 + 18 * q^56 - 22 * q^59 + 16 * q^60 + 34 * q^61 - 26 * q^64 - 28 * q^65 - 6 * q^66 - 26 * q^69 - 6 * q^70 + 72 * q^71 - 72 * q^74 - 8 * q^75 + 44 * q^76 + 4 * q^79 - 8 * q^80 + 20 * q^81 - 26 * q^84 - 16 * q^85 + 52 * q^86 + 6 * q^89 + 2 * q^90 + 16 * q^94 + 14 * q^95 + 62 * q^96 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$		−	2.51841i		−	1.78078i	−0.455195	−	0.890392i	$-0.650431\pi$
$2$		−	2.51841i		−	1.78078i	0.455195	−	0.890392i	$-0.349569\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−4.34238			−2.17119
$5$	−2.17741	−	0.508790i	−0.973769	−	0.227538i
$5$	−2.17741	−	0.508790i	−0.973769	−	0.227538i
$6$	2.51841			1.02814
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$			5.89907i			2.08563i
$9$	−1.00000			−0.333333
$10$	−1.28134	+	5.48362i	−0.405195	+	1.73407i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$		−	4.34238i		−	1.25354i
$13$		−	1.93158i		−	0.535725i	−0.963457	−	0.267863i	$-0.913683\pi$
$13$		−	1.93158i		−	0.535725i	0.963457	−	0.267863i	$-0.0863173\pi$
$14$	−2.51841			−0.673073
$15$	0.508790	−	2.17741i	0.131369	−	0.562206i
$16$	6.17150			1.54287
$17$			2.73533i			0.663415i	0.943382	+	0.331708i	$0.107625\pi$
$17$			2.73533i			0.663415i	−0.943382	+	0.331708i	$0.892375\pi$
$18$			2.51841i			0.593594i
$19$	−5.74934			−1.31899			−0.659495	−	0.751709i	$-0.729230\pi$
$19$	−5.74934			−1.31899			−0.659495	+	0.751709i	$0.729230\pi$
$20$	9.45516	+	2.20936i	2.11424	+	0.494028i
$21$	1.00000			0.218218
$22$			2.51841i			0.536926i
$23$			3.98220i			0.830346i	0.909742	+	0.415173i	$0.136279\pi$
$23$			3.98220i			0.830346i	−0.909742	+	0.415173i	$0.863721\pi$
$24$	−5.89907			−1.20414
$25$	4.48227	+	2.21569i	0.896453	+	0.443139i
$26$	−4.86452			−0.954010
$27$		−	1.00000i		−	0.192450i
$28$			4.34238i			0.820632i
$29$	0.897314			0.166627			0.0833135	−	0.996523i	$-0.473450\pi$
$29$	0.897314			0.166627			0.0833135	+	0.996523i	$0.473450\pi$
$30$	−5.48362	−	1.28134i	−1.00117	−	0.233940i
$31$	10.2982			1.84961			0.924803	−	0.380447i	$-0.124230\pi$
$31$	10.2982			1.84961			0.924803	+	0.380447i	$0.124230\pi$
$32$		−	3.74421i		−	0.661890i
$33$		−	1.00000i		−	0.174078i
$34$	6.88868			1.18140
$35$	−0.508790	+	2.17741i	−0.0860012	+	0.368050i
$36$	4.34238			0.723730
$37$			3.09664i			0.509085i	0.967062	+	0.254542i	$0.0819248\pi$
$37$			3.09664i			0.509085i	−0.967062	+	0.254542i	$0.918075\pi$
$38$			14.4792i			2.34883i
$39$	1.93158			0.309301
$40$	3.00139	−	12.8447i	0.474561	−	2.03093i
$41$	7.83869			1.22420			0.612099	−	0.790781i	$-0.290326\pi$
$41$	7.83869			1.22420			0.612099	+	0.790781i	$0.290326\pi$
$42$		−	2.51841i		−	0.388599i
$43$			4.01145i			0.611740i	0.952073	+	0.305870i	$0.0989473\pi$
$43$			4.01145i			0.611740i	−0.952073	+	0.305870i	$0.901053\pi$
$44$	4.34238			0.654638
$45$	2.17741	+	0.508790i	0.324590	+	0.0758459i
$46$	10.0288			1.47867
$47$			3.41906i			0.498721i	0.968411	+	0.249360i	$0.0802204\pi$
$47$			3.41906i			0.498721i	−0.968411	+	0.249360i	$0.919780\pi$
$48$			6.17150i			0.890779i
$49$	−1.00000			−0.142857
$50$	5.58002	−	11.2882i	0.789134	−	1.59639i
$51$	−2.73533			−0.383023
$52$			8.38767i			1.16316i
$53$			9.17420i			1.26017i	0.776525	+	0.630087i	$0.216981\pi$
$53$			9.17420i			1.26017i	−0.776525	+	0.630087i	$0.783019\pi$
$54$	−2.51841			−0.342712
$55$	2.17741	+	0.508790i	0.293602	+	0.0686052i
$56$	5.89907			0.788296
$57$		−	5.74934i		−	0.761519i
$58$		−	2.25980i		−	0.296727i
$59$	−9.82410			−1.27899			−0.639494	−	0.768796i	$-0.720856\pi$
$59$	−9.82410			−1.27899			−0.639494	+	0.768796i	$0.720856\pi$
$60$	−2.20936	+	9.45516i	−0.285227	+	1.22066i
$61$	1.57645			0.201843			0.100922	−	0.994894i	$-0.467821\pi$
$61$	1.57645			0.201843			0.100922	+	0.994894i	$0.467821\pi$
$62$		−	25.9350i		−	3.29375i
$63$			1.00000i			0.125988i
$64$	2.91353			0.364192
$65$	−0.982771	+	4.20586i	−0.121898	+	0.521673i
$66$	−2.51841			−0.309995
$67$		−	5.66006i		−	0.691486i	−0.938329	−	0.345743i	$-0.887627\pi$
$67$		−	5.66006i		−	0.691486i	0.938329	−	0.345743i	$-0.112373\pi$
$68$		−	11.8778i		−	1.44040i
$69$	−3.98220			−0.479401
$70$	5.48362	+	1.28134i	0.655418	+	0.153149i
$71$	−5.57815			−0.662005			−0.331002	−	0.943630i	$-0.607387\pi$
$71$	−5.57815			−0.662005			−0.331002	+	0.943630i	$0.607387\pi$
$72$		−	5.89907i		−	0.695212i
$73$		−	9.45961i		−	1.10716i	−0.832795	−	0.553582i	$-0.813261\pi$
$73$		−	9.45961i		−	1.10716i	0.832795	−	0.553582i	$-0.186739\pi$
$74$	7.79861			0.906570
$75$	−2.21569	+	4.48227i	−0.255846	+	0.517567i
$76$	24.9658			2.86378
$77$			1.00000i			0.113961i
$78$		−	4.86452i		−	0.550798i
$79$	13.4115			1.50892			0.754458	−	0.656348i	$-0.227900\pi$
$79$	13.4115			1.50892			0.754458	+	0.656348i	$0.227900\pi$
$80$	−13.4379	−	3.13999i	−1.50240	−	0.351062i
$81$	1.00000			0.111111
$82$		−	19.7410i		−	2.18003i
$83$			8.24025i			0.904485i	0.891895	+	0.452243i	$0.149376\pi$
$83$			8.24025i			0.904485i	−0.891895	+	0.452243i	$0.850624\pi$
$84$	−4.34238			−0.473792
$85$	1.39171	−	5.95595i	0.150952	−	0.646014i
$86$	10.1025			1.08938
$87$			0.897314i			0.0962021i
$88$		−	5.89907i		−	0.628842i
$89$	−9.21337			−0.976615			−0.488307	−	0.872672i	$-0.662386\pi$
$89$	−9.21337			−0.976615			−0.488307	+	0.872672i	$0.662386\pi$
$90$	1.28134	−	5.48362i	0.135065	−	0.578024i
$91$	−1.93158			−0.202485
$92$		−	17.2922i		−	1.80284i
$93$			10.2982i			1.06787i
$94$	8.61058			0.888114
$95$	12.5187	+	2.92521i	1.28439	+	0.300120i
$96$	3.74421			0.382142
$97$			15.8647i			1.61081i	0.592723	+	0.805406i	$0.298053\pi$
$97$			15.8647i			1.61081i	−0.592723	+	0.805406i	$0.701947\pi$
$98$			2.51841i			0.254398i
$99$	1.00000			0.100504
$100$	−19.4637	−	9.62138i	−1.94637	−	0.962138i
$101$	−17.6934			−1.76056			−0.880281	−	0.474453i	$-0.842646\pi$
$101$	−17.6934			−1.76056			−0.880281	+	0.474453i	$0.842646\pi$
$102$			6.88868i			0.682081i
$103$		−	10.6962i		−	1.05393i	−0.849888	−	0.526964i	$-0.823330\pi$
$103$		−	10.6962i		−	1.05393i	0.849888	−	0.526964i	$-0.176670\pi$
$104$	11.3945			1.11733
$105$	−2.17741	−	0.508790i	−0.212494	−	0.0496528i
$106$	23.1044			2.24410
$107$			5.79452i			0.560177i	0.959974	+	0.280089i	$0.0903638\pi$
$107$			5.79452i			0.560177i	−0.959974	+	0.280089i	$0.909636\pi$
$108$			4.34238i			0.417846i
$109$	9.96757			0.954721			0.477360	−	0.878708i	$-0.341594\pi$
$109$	9.96757			0.954721			0.477360	+	0.878708i	$0.341594\pi$
$110$	1.28134	−	5.48362i	0.122171	−	0.522842i
$111$	−3.09664			−0.293920
$112$		−	6.17150i		−	0.583152i
$113$			8.06070i			0.758287i	0.925338	+	0.379144i	$0.123781\pi$
$113$			8.06070i			0.758287i	−0.925338	+	0.379144i	$0.876219\pi$
$114$	−14.4792			−1.35610
$115$	2.02610	−	8.67090i	0.188935	−	0.808566i
$116$	−3.89648			−0.361779
$117$			1.93158i			0.178575i
$118$			24.7411i			2.27760i
$119$	2.73533			0.250747
$120$	12.8447	+	3.00139i	1.17256	+	0.273988i
$121$	1.00000			0.0909091
$122$		−	3.97014i		−	0.359440i
$123$			7.83869i			0.706791i
$124$	−44.7185			−4.01584
$125$	−8.63243	−	7.10501i	−0.772108	−	0.635492i
$126$	2.51841			0.224358
$127$			18.2960i			1.62351i	0.583998	+	0.811755i	$0.301488\pi$
$127$			18.2960i			1.62351i	−0.583998	+	0.811755i	$0.698512\pi$
$128$		−	14.8259i		−	1.31044i
$129$	−4.01145			−0.353188
$130$	10.5921	+	2.47502i	0.928986	+	0.217073i
$131$	2.32349			0.203004			0.101502	−	0.994835i	$-0.467635\pi$
$131$	2.32349			0.203004			0.101502	+	0.994835i	$0.467635\pi$
$132$			4.34238i			0.377956i
$133$			5.74934i			0.498531i
$134$	−14.2543			−1.23139
$135$	−0.508790	+	2.17741i	−0.0437897	+	0.187402i
$136$	−16.1359			−1.38364
$137$			18.6392i			1.59245i	0.605000	+	0.796226i	$0.293173\pi$
$137$			18.6392i			1.59245i	−0.605000	+	0.796226i	$0.706827\pi$
$138$			10.0288i			0.853709i
$139$	−7.27340			−0.616922			−0.308461	−	0.951237i	$-0.599814\pi$
$139$	−7.27340			−0.616922			−0.308461	+	0.951237i	$0.599814\pi$
$140$	2.20936	−	9.45516i	0.186725	−	0.799107i
$141$	−3.41906			−0.287937
$142$			14.0481i			1.17889i
$143$			1.93158i			0.161527i
$144$	−6.17150			−0.514291
$145$	−1.95382	−	0.456544i	−0.162256	−	0.0379139i
$146$	−23.8232			−1.97162
$147$		−	1.00000i		−	0.0824786i
$148$		−	13.4468i		−	1.10532i
$149$	5.55113			0.454767			0.227383	−	0.973805i	$-0.426983\pi$
$149$	5.55113			0.454767			0.227383	+	0.973805i	$0.426983\pi$
$150$	11.2882	+	5.58002i	0.921676	+	0.455607i
$151$	−4.91722			−0.400158			−0.200079	−	0.979780i	$-0.564120\pi$
$151$	−4.91722			−0.400158			−0.200079	+	0.979780i	$0.564120\pi$
$152$		−	33.9157i		−	2.75093i
$153$		−	2.73533i		−	0.221138i
$154$	2.51841			0.202939
$155$	−22.4234	−	5.23960i	−1.80109	−	0.420855i
$156$	−8.38767			−0.671551
$157$			10.7928i			0.861360i	0.902505	+	0.430680i	$0.141726\pi$
$157$			10.7928i			0.861360i	−0.902505	+	0.430680i	$0.858274\pi$
$158$		−	33.7757i		−	2.68705i
$159$	−9.17420			−0.727561
$160$	−1.90502	+	8.15270i	−0.150605	+	0.644528i
$161$	3.98220			0.313841
$162$		−	2.51841i		−	0.197865i
$163$			5.23865i			0.410322i	0.978728	+	0.205161i	$0.0657719\pi$
$163$			5.23865i			0.410322i	−0.978728	+	0.205161i	$0.934228\pi$
$164$	−34.0386			−2.65796
$165$	−0.508790	+	2.17741i	−0.0396092	+	0.169511i
$166$	20.7523			1.61069
$167$		−	16.7794i		−	1.29843i	−0.760604	−	0.649216i	$-0.775097\pi$
$167$		−	16.7794i		−	1.29843i	0.760604	−	0.649216i	$-0.224903\pi$
$168$			5.89907i			0.455123i
$169$	9.26898			0.712999
$170$	−14.9995	−	3.50489i	−1.15041	−	0.268813i
$171$	5.74934			0.439663
$172$		−	17.4192i		−	1.32820i
$173$			1.79619i			0.136562i	0.997666	+	0.0682808i	$0.0217514\pi$
$173$			1.79619i			0.136562i	−0.997666	+	0.0682808i	$0.978249\pi$
$174$	2.25980			0.171315
$175$	2.21569	−	4.48227i	0.167491	−	0.338827i
$176$	−6.17150			−0.465194
$177$		−	9.82410i		−	0.738424i
$178$			23.2030i			1.73914i
$179$	−8.35101			−0.624184			−0.312092	−	0.950052i	$-0.601030\pi$
$179$	−8.35101			−0.624184			−0.312092	+	0.950052i	$0.601030\pi$
$180$	−9.45516	−	2.20936i	−0.704746	−	0.164676i
$181$	−13.7909			−1.02507			−0.512536	−	0.858666i	$-0.671294\pi$
$181$	−13.7909			−1.02507			−0.512536	+	0.858666i	$0.671294\pi$
$182$			4.86452i			0.360582i
$183$			1.57645i			0.116534i
$184$	−23.4913			−1.73180
$185$	1.57554	−	6.74267i	0.115836	−	0.495731i
$186$	25.9350			1.90165
$187$		−	2.73533i		−	0.200027i
$188$		−	14.8468i		−	1.08282i
$189$	−1.00000			−0.0727393
$190$	7.36686	−	31.5272i	0.534449	−	2.28722i
$191$	−17.3693			−1.25680			−0.628399	−	0.777891i	$-0.716290\pi$
$191$	−17.3693			−1.25680			−0.628399	+	0.777891i	$0.716290\pi$
$192$			2.91353i			0.210266i
$193$		−	19.1698i		−	1.37987i	−0.723869	−	0.689937i	$-0.757638\pi$
$193$		−	19.1698i		−	1.37987i	0.723869	−	0.689937i	$-0.242362\pi$
$194$	39.9537			2.86851
$195$	−4.20586	−	0.982771i	−0.301188	−	0.0703777i
$196$	4.34238			0.310170
$197$			13.2602i			0.944752i	0.881397	+	0.472376i	$0.156604\pi$
$197$			13.2602i			0.944752i	−0.881397	+	0.472376i	$0.843396\pi$
$198$		−	2.51841i		−	0.178975i
$199$	−11.6731			−0.827486			−0.413743	−	0.910394i	$-0.635779\pi$
$199$	−11.6731			−0.827486			−0.413743	+	0.910394i	$0.635779\pi$
$200$	−13.0705	+	26.4412i	−0.924225	+	1.86967i
$201$	5.66006			0.399230
$202$			44.5593i			3.13518i
$203$		−	0.897314i		−	0.0629791i
$204$	11.8778			0.831616
$205$	−17.0681	−	3.98825i	−1.19209	−	0.278551i
$206$	−26.9374			−1.87682
$207$		−	3.98220i		−	0.276782i
$208$		−	11.9208i		−	0.826556i
$209$	5.74934			0.397690
$210$	−1.28134	+	5.48362i	−0.0884209	+	0.378406i
$211$	−6.24626			−0.430010			−0.215005	−	0.976613i	$-0.568977\pi$
$211$	−6.24626			−0.430010			−0.215005	+	0.976613i	$0.568977\pi$
$212$		−	39.8378i		−	2.73607i
$213$		−	5.57815i		−	0.382209i
$214$	14.5930			0.997554
$215$	2.04098	−	8.73458i	0.139194	−	0.595693i
$216$	5.89907			0.401381
$217$		−	10.2982i		−	0.699085i
$218$		−	25.1024i		−	1.70015i
$219$	9.45961			0.639221
$220$	−9.45516	−	2.20936i	−0.637467	−	0.148955i
$221$	5.28352			0.355408
$222$			7.79861i			0.523408i
$223$			15.6620i			1.04880i	0.851471	+	0.524402i	$0.175711\pi$
$223$			15.6620i			1.04880i	−0.851471	+	0.524402i	$0.824289\pi$
$224$	−3.74421			−0.250171
$225$	−4.48227	−	2.21569i	−0.298818	−	0.147713i
$226$	20.3001			1.35035
$227$		−	12.5488i		−	0.832895i	−0.909160	−	0.416448i	$-0.863275\pi$
$227$		−	12.5488i		−	0.832895i	0.909160	−	0.416448i	$-0.136725\pi$
$228$			24.9658i			1.65340i
$229$	−27.4136			−1.81154			−0.905772	−	0.423765i	$-0.860708\pi$
$229$	−27.4136			−1.81154			−0.905772	+	0.423765i	$0.860708\pi$
$230$	−21.8369	−	5.10256i	−1.43988	−	0.336453i
$231$	−1.00000			−0.0657952
$232$			5.29331i			0.347523i
$233$			13.8607i			0.908047i	0.890990	+	0.454023i	$0.150012\pi$
$233$			13.8607i			0.908047i	−0.890990	+	0.454023i	$0.849988\pi$
$234$	4.86452			0.318003
$235$	1.73958	−	7.44470i	0.113478	−	0.485639i
$236$	42.6600			2.77693
$237$			13.4115i			0.871173i
$238$		−	6.88868i		−	0.446527i
$239$	20.8546			1.34897			0.674486	−	0.738288i	$-0.264365\pi$
$239$	20.8546			1.34897			0.674486	+	0.738288i	$0.264365\pi$
$240$	3.13999	−	13.4379i	0.202686	−	0.867413i
$241$	−16.6597			−1.07315			−0.536574	−	0.843853i	$-0.680282\pi$
$241$	−16.6597			−1.07315			−0.536574	+	0.843853i	$0.680282\pi$
$242$		−	2.51841i		−	0.161889i
$243$			1.00000i			0.0641500i
$244$	−6.84553			−0.438240
$245$	2.17741	+	0.508790i	0.139110	+	0.0325054i
$246$	19.7410			1.25864
$247$			11.1053i			0.706616i
$248$			60.7496i			3.85760i
$249$	−8.24025			−0.522205
$250$	−17.8933	+	21.7400i	−1.13167	+	1.37496i
$251$	5.04024			0.318137			0.159068	−	0.987268i	$-0.449151\pi$
$251$	5.04024			0.318137			0.159068	+	0.987268i	$0.449151\pi$
$252$		−	4.34238i		−	0.273544i
$253$		−	3.98220i		−	0.250359i
$254$	46.0769			2.89112
$255$	5.95595	+	1.39171i	0.372976	+	0.0871522i
$256$	−31.5106			−1.96941
$257$			22.8836i			1.42744i	0.700430	+	0.713721i	$0.252991\pi$
$257$			22.8836i			1.42744i	−0.700430	+	0.713721i	$0.747009\pi$
$258$			10.1025i			0.628952i
$259$	3.09664			0.192416
$260$	4.26756	−	18.2634i	0.264663	−	1.13265i
$261$	−0.897314			−0.0555423
$262$		−	5.85150i		−	0.361507i
$263$			1.94233i			0.119769i	0.998205	+	0.0598845i	$0.0190733\pi$
$263$			1.94233i			0.119769i	−0.998205	+	0.0598845i	$0.980927\pi$
$264$	5.89907			0.363062
$265$	4.66774	−	19.9760i	0.286737	−	1.22712i
$266$	14.4792			0.887776
$267$		−	9.21337i		−	0.563849i
$268$			24.5781i			1.50135i
$269$	18.0770			1.10217			0.551086	−	0.834448i	$-0.314214\pi$
$269$	18.0770			1.10217			0.551086	+	0.834448i	$0.314214\pi$
$270$	5.48362	+	1.28134i	0.333722	+	0.0779799i
$271$	−0.990072			−0.0601426			−0.0300713	−	0.999548i	$-0.509573\pi$
$271$	−0.990072			−0.0601426			−0.0300713	+	0.999548i	$0.509573\pi$
$272$			16.8811i			1.02357i
$273$		−	1.93158i		−	0.116905i
$274$	46.9410			2.83581
$275$	−4.48227	−	2.21569i	−0.270291	−	0.133611i
$276$	17.2922			1.04087
$277$			21.6115i			1.29851i	0.760571	+	0.649255i	$0.224919\pi$
$277$			21.6115i			1.29851i	−0.760571	+	0.649255i	$0.775081\pi$
$278$			18.3174i			1.09860i
$279$	−10.2982			−0.616535
$280$	−12.8447	−	3.00139i	−0.767618	−	0.179367i
$281$	−1.05458			−0.0629112			−0.0314556	−	0.999505i	$-0.510014\pi$
$281$	−1.05458			−0.0629112			−0.0314556	+	0.999505i	$0.510014\pi$
$282$			8.61058i			0.512753i
$283$			15.5919i			0.926844i	0.886138	+	0.463422i	$0.153379\pi$
$283$			15.5919i			0.926844i	−0.886138	+	0.463422i	$0.846621\pi$
$284$	24.2224			1.43734
$285$	−2.92521	+	12.5187i	−0.173274	+	0.741544i
$286$	4.86452			0.287645
$287$		−	7.83869i		−	0.462703i
$288$			3.74421i			0.220630i
$289$	9.51796			0.559880
$290$	−1.14976	+	4.92053i	−0.0675165	+	0.288943i
$291$	−15.8647			−0.930003
$292$			41.0772i			2.40386i
$293$			28.2397i			1.64978i	0.565292	+	0.824891i	$0.308764\pi$
$293$			28.2397i			1.64978i	−0.565292	+	0.824891i	$0.691236\pi$
$294$	−2.51841			−0.146877
$295$	21.3911	+	4.99840i	1.24544	+	0.291018i
$296$	−18.2673			−1.06176
$297$			1.00000i			0.0580259i
$298$		−	13.9800i		−	0.809841i
$299$	7.69196			0.444837
$300$	9.62138	−	19.4637i	0.555490	−	1.12374i
$301$	4.01145			0.231216
$302$			12.3836i			0.712595i
$303$		−	17.6934i		−	1.01646i
$304$	−35.4820			−2.03503
$305$	−3.43258	−	0.802081i	−0.196549	−	0.0459270i
$306$	−6.88868			−0.393800
$307$		−	7.96272i		−	0.454456i	−0.973842	−	0.227228i	$-0.927034\pi$
$307$		−	7.96272i		−	0.454456i	0.973842	−	0.227228i	$-0.0729663\pi$
$308$		−	4.34238i		−	0.247430i
$309$	10.6962			0.608486
$310$	−13.1955	+	56.4712i	−0.749452	+	3.20735i
$311$	−7.18130			−0.407214			−0.203607	−	0.979053i	$-0.565266\pi$
$311$	−7.18130			−0.407214			−0.203607	+	0.979053i	$0.565266\pi$
$312$			11.3945i			0.645089i
$313$		−	22.5430i		−	1.27421i	−0.770779	−	0.637103i	$-0.780133\pi$
$313$		−	22.5430i		−	1.27421i	0.770779	−	0.637103i	$-0.219867\pi$
$314$	27.1807			1.53389
$315$	0.508790	−	2.17741i	0.0286671	−	0.122683i
$316$	−58.2380			−3.27614
$317$		−	19.7730i		−	1.11056i	−0.831663	−	0.555281i	$-0.812611\pi$
$317$		−	19.7730i		−	1.11056i	0.831663	−	0.555281i	$-0.187389\pi$
$318$			23.1044i			1.29563i
$319$	−0.897314			−0.0502399
$320$	−6.34397	−	1.48238i	−0.354639	−	0.0828674i
$321$	−5.79452			−0.323418
$322$		−	10.0288i		−	0.558884i
$323$		−	15.7264i		−	0.875038i
$324$	−4.34238			−0.241243
$325$	4.27980	−	8.65787i	0.237400	−	0.480252i
$326$	13.1930			0.730695
$327$			9.96757i			0.551208i
$328$			46.2409i			2.55323i
$329$	3.41906			0.188499
$330$	5.48362	+	1.28134i	0.301863	+	0.0705355i
$331$	29.2958			1.61024			0.805121	−	0.593110i	$-0.202100\pi$
$331$	29.2958			1.61024			0.805121	+	0.593110i	$0.202100\pi$
$332$		−	35.7823i		−	1.96381i
$333$		−	3.09664i		−	0.169695i
$334$	−42.2575			−2.31223
$335$	−2.87978	+	12.3243i	−0.157339	+	0.673348i
$336$	6.17150			0.336683
$337$		−	14.7637i		−	0.804230i	−0.915589	−	0.402115i	$-0.868275\pi$
$337$		−	14.7637i		−	0.804230i	0.915589	−	0.402115i	$-0.131725\pi$
$338$		−	23.3431i		−	1.26970i
$339$	−8.06070			−0.437797
$340$	−6.04333	+	25.8630i	−0.327746	+	1.40262i
$341$	−10.2982			−0.557677
$342$		−	14.4792i		−	0.782945i
$343$			1.00000i			0.0539949i
$344$	−23.6638			−1.27587
$345$	8.67090	+	2.02610i	0.466826	+	0.109082i
$346$	4.52353			0.243187
$347$		−	8.14373i		−	0.437179i	−0.975817	−	0.218589i	$-0.929855\pi$
$347$		−	8.14373i		−	0.437179i	0.975817	−	0.218589i	$-0.0701455\pi$
$348$		−	3.89648i		−	0.208873i
$349$	31.6394			1.69362			0.846809	−	0.531897i	$-0.178521\pi$
$349$	31.6394			1.69362			0.846809	+	0.531897i	$0.178521\pi$
$350$	−11.2882	−	5.58002i	−0.603378	−	0.298265i
$351$	−1.93158			−0.103100
$352$			3.74421i			0.199567i
$353$		−	17.5983i		−	0.936665i	−0.883552	−	0.468332i	$-0.844855\pi$
$353$		−	17.5983i		−	0.936665i	0.883552	−	0.468332i	$-0.155145\pi$
$354$	−24.7411			−1.31497
$355$	12.1459	+	2.83811i	0.644640	+	0.150631i
$356$	40.0079			2.12042
$357$			2.73533i			0.144769i
$358$			21.0312i			1.11154i
$359$	−21.7549			−1.14818			−0.574091	−	0.818791i	$-0.694644\pi$
$359$	−21.7549			−1.14818			−0.574091	+	0.818791i	$0.694644\pi$
$360$	−3.00139	+	12.8447i	−0.158187	+	0.676976i
$361$	14.0549			0.739733
$362$			34.7312i			1.82543i
$363$			1.00000i			0.0524864i
$364$	8.38767			0.439633
$365$	−4.81296	+	20.5975i	−0.251922	+	1.07812i
$366$	3.97014			0.207522
$367$		−	4.67786i		−	0.244182i	−0.992519	−	0.122091i	$-0.961040\pi$
$367$		−	4.67786i		−	0.244182i	0.992519	−	0.122091i	$-0.0389600\pi$
$368$			24.5761i			1.28112i
$369$	−7.83869			−0.408066
$370$	−16.9808	−	3.96785i	−0.882790	−	0.206279i
$371$	9.17420			0.476301
$372$		−	44.7185i		−	2.31855i
$373$		−	3.00329i		−	0.155504i	−0.996973	−	0.0777522i	$-0.975226\pi$
$373$		−	3.00329i		−	0.155504i	0.996973	−	0.0777522i	$-0.0247743\pi$
$374$	−6.88868			−0.356205
$375$	7.10501	−	8.63243i	0.366901	−	0.445777i
$376$	−20.1692			−1.04015
$377$		−	1.73324i		−	0.0892663i
$378$			2.51841i			0.129533i
$379$	−14.0793			−0.723204			−0.361602	−	0.932333i	$-0.617770\pi$
$379$	−14.0793			−0.723204			−0.361602	+	0.932333i	$0.617770\pi$
$380$	−54.3609	−	12.7024i	−2.78866	−	0.651617i
$381$	−18.2960			−0.937334
$382$			43.7430i			2.23809i
$383$			3.12889i			0.159879i	0.996800	+	0.0799395i	$0.0254727\pi$
$383$			3.12889i			0.159879i	−0.996800	+	0.0799395i	$0.974527\pi$
$384$	14.8259			0.756581
$385$	0.508790	−	2.17741i	0.0259303	−	0.110971i
$386$	−48.2774			−2.45726
$387$		−	4.01145i		−	0.203913i
$388$		−	68.8904i		−	3.49738i
$389$	6.46694			0.327887			0.163943	−	0.986470i	$-0.447579\pi$
$389$	6.46694			0.327887			0.163943	+	0.986470i	$0.447579\pi$
$390$	−2.47502	+	10.5921i	−0.125327	+	0.536350i
$391$	−10.8926			−0.550865
$392$		−	5.89907i		−	0.297948i
$393$			2.32349i			0.117205i
$394$	33.3947			1.68240
$395$	−29.2025	−	6.82366i	−1.46934	−	0.343335i
$396$	−4.34238			−0.218213
$397$			14.6224i			0.733877i	0.930245	+	0.366938i	$0.119594\pi$
$397$			14.6224i			0.733877i	−0.930245	+	0.366938i	$0.880406\pi$
$398$			29.3977i			1.47357i
$399$	−5.74934			−0.287827
$400$	27.6623	+	13.6741i	1.38311	+	0.683707i
$401$	25.7387			1.28533			0.642665	−	0.766147i	$-0.277829\pi$
$401$	25.7387			1.28533			0.642665	+	0.766147i	$0.277829\pi$
$402$		−	14.2543i		−	0.710942i
$403$		−	19.8918i		−	0.990880i
$404$	76.8316			3.82251
$405$	−2.17741	−	0.508790i	−0.108197	−	0.0252820i
$406$	−2.25980			−0.112152
$407$		−	3.09664i		−	0.153495i
$408$		−	16.1359i		−	0.798846i
$409$	10.0472			0.496803			0.248401	−	0.968657i	$-0.420095\pi$
$409$	10.0472			0.496803			0.248401	+	0.968657i	$0.420095\pi$
$410$	−10.0440	+	42.9844i	−0.496039	+	2.12285i
$411$	−18.6392			−0.919402
$412$			46.4470i			2.28828i
$413$			9.82410i			0.483412i
$414$	−10.0288			−0.492889
$415$	4.19256	−	17.9424i	0.205805	−	0.880760i
$416$	−7.23226			−0.354591
$417$		−	7.27340i		−	0.356180i
$418$		−	14.4792i		−	0.708200i
$419$	6.75857			0.330178			0.165089	−	0.986279i	$-0.447209\pi$
$419$	6.75857			0.330178			0.165089	+	0.986279i	$0.447209\pi$
$420$	9.45516	+	2.20936i	0.461364	+	0.107806i
$421$	2.33958			0.114024			0.0570121	−	0.998373i	$-0.481843\pi$
$421$	2.33958			0.114024			0.0570121	+	0.998373i	$0.481843\pi$
$422$			15.7306i			0.765755i
$423$		−	3.41906i		−	0.166240i
$424$	−54.1192			−2.62826
$425$	−6.06066	+	12.2605i	−0.293985	+	0.594721i
$426$	−14.0481			−0.680631
$427$		−	1.57645i		−	0.0762897i
$428$		−	25.1620i		−	1.21625i
$429$	−1.93158			−0.0932578
$430$	−21.9972	−	5.14003i	−1.06080	−	0.247874i
$431$	13.1471			0.633273			0.316636	−	0.948547i	$-0.397447\pi$
$431$	13.1471			0.633273			0.316636	+	0.948547i	$0.397447\pi$
$432$		−	6.17150i		−	0.296926i
$433$		−	27.4941i		−	1.32128i	−0.750702	−	0.660641i	$-0.770285\pi$
$433$		−	27.4941i		−	1.32128i	0.750702	−	0.660641i	$-0.229715\pi$
$434$	−25.9350			−1.24492
$435$	0.456544	−	1.95382i	0.0218896	−	0.0936787i
$436$	−43.2830			−2.07288
$437$		−	22.8950i		−	1.09522i
$438$		−	23.8232i		−	1.13831i
$439$	−32.6151			−1.55663			−0.778317	−	0.627872i	$-0.783926\pi$
$439$	−32.6151			−1.55663			−0.778317	+	0.627872i	$0.783926\pi$
$440$	−3.00139	+	12.8447i	−0.143085	+	0.612347i
$441$	1.00000			0.0476190
$442$		−	13.3061i		−	0.632905i
$443$		−	21.4514i		−	1.01919i	−0.860415	−	0.509595i	$-0.829795\pi$
$443$		−	21.4514i		−	1.01919i	0.860415	−	0.509595i	$-0.170205\pi$
$444$	13.4468			0.638156
$445$	20.0613	+	4.68767i	0.950998	+	0.222217i
$446$	39.4432			1.86769
$447$			5.55113i			0.262560i
$448$		−	2.91353i		−	0.137652i
$449$	−36.2417			−1.71035			−0.855176	−	0.518338i	$-0.826551\pi$
$449$	−36.2417			−1.71035			−0.855176	+	0.518338i	$0.826551\pi$
$450$	−5.58002	+	11.2882i	−0.263045	+	0.532130i
$451$	−7.83869			−0.369109
$452$		−	35.0026i		−	1.64639i
$453$		−	4.91722i		−	0.231031i
$454$	−31.6031			−1.48321
$455$	4.20586	+	0.982771i	0.197174	+	0.0460730i
$456$	33.9157			1.58825
$457$			15.9313i			0.745233i	0.927986	+	0.372616i	$0.121539\pi$
$457$			15.9313i			0.745233i	−0.927986	+	0.372616i	$0.878461\pi$
$458$			69.0387i			3.22597i
$459$	2.73533			0.127674
$460$	−8.79811	+	37.6523i	−0.410214	+	1.75555i
$461$	35.7258			1.66391			0.831957	−	0.554839i	$-0.187220\pi$
$461$	35.7258			1.66391			0.831957	+	0.554839i	$0.187220\pi$
$462$			2.51841i			0.117167i
$463$			29.5009i			1.37102i	0.728061	+	0.685512i	$0.240422\pi$
$463$			29.5009i			1.37102i	−0.728061	+	0.685512i	$0.759578\pi$
$464$	5.53777			0.257084
$465$	5.23960	−	22.4234i	0.242981	−	1.03986i
$466$	34.9070			1.61703
$467$			18.9759i			0.878099i	0.898463	+	0.439050i	$0.144685\pi$
$467$			18.9759i			0.878099i	−0.898463	+	0.439050i	$0.855315\pi$
$468$		−	8.38767i		−	0.387720i
$469$	−5.66006			−0.261357
$470$	−18.7488	−	4.38098i	−0.864818	−	0.202079i
$471$	−10.7928			−0.497306
$472$		−	57.9530i		−	2.66750i
$473$		−	4.01145i		−	0.184447i
$474$	33.7757			1.55137
$475$	−25.7701	−	12.7388i	−1.18241	−	0.584495i
$476$	−11.8778			−0.544420
$477$		−	9.17420i		−	0.420058i
$478$		−	52.5204i		−	2.40223i
$479$	−11.2070			−0.512061			−0.256031	−	0.966669i	$-0.582415\pi$
$479$	−11.2070			−0.512061			−0.256031	+	0.966669i	$0.582415\pi$
$480$	−8.15270	−	1.90502i	−0.372118	−	0.0869518i
$481$	5.98142			0.272729
$482$			41.9560i			1.91104i
$483$			3.98220i			0.181196i
$484$	−4.34238			−0.197381
$485$	8.07178	−	34.5439i	0.366521	−	1.56856i
$486$	2.51841			0.114237
$487$		−	12.8184i		−	0.580859i	−0.956896	−	0.290429i	$-0.906202\pi$
$487$		−	12.8184i		−	0.580859i	0.956896	−	0.290429i	$-0.0937981\pi$
$488$			9.29957i			0.420972i
$489$	−5.23865			−0.236900
$490$	1.28134	−	5.48362i	0.0578851	−	0.247725i
$491$	−17.5676			−0.792817			−0.396408	−	0.918074i	$-0.629744\pi$
$491$	−17.5676			−0.792817			−0.396408	+	0.918074i	$0.629744\pi$
$492$		−	34.0386i		−	1.53458i
$493$			2.45445i			0.110543i
$494$	27.9678			1.25833
$495$	−2.17741	−	0.508790i	−0.0978675	−	0.0228684i
$496$	63.5551			2.85371
$497$			5.57815i			0.250214i
$498$			20.7523i			0.929933i
$499$	−29.7751			−1.33292			−0.666458	−	0.745543i	$-0.732190\pi$
$499$	−29.7751			−1.33292			−0.666458	+	0.745543i	$0.732190\pi$
$500$	37.4853	+	30.8527i	1.67639	+	1.37977i
$501$	16.7794			0.749650
$502$		−	12.6934i		−	0.566533i
$503$			23.6396i			1.05404i	0.849853	+	0.527019i	$0.176690\pi$
$503$			23.6396i			1.05404i	−0.849853	+	0.527019i	$0.823310\pi$
$504$	−5.89907			−0.262765
$505$	38.5259	+	9.00224i	1.71438	+	0.400594i
$506$	−10.0288			−0.445835
$507$			9.26898i			0.411650i
$508$		−	79.4483i		−	3.52495i
$509$	−26.7267			−1.18464			−0.592321	−	0.805702i	$-0.701788\pi$
$509$	−26.7267			−1.18464			−0.592321	+	0.805702i	$0.701788\pi$
$510$	3.50489	−	14.9995i	0.155199	−	0.664190i
$511$	−9.45961			−0.418469
$512$			49.7047i			2.19666i
$513$			5.74934i			0.253840i
$514$	57.6303			2.54196
$515$	−5.44212	+	23.2901i	−0.239808	+	1.02628i
$516$	17.4192			0.766838
$517$		−	3.41906i		−	0.150370i
$518$		−	7.79861i		−	0.342651i
$519$	−1.79619			−0.0788439
$520$	−24.8106	−	5.79743i	−1.08802	−	0.254234i
$521$	40.2358			1.76276			0.881381	−	0.472407i	$-0.156615\pi$
$521$	40.2358			1.76276			0.881381	+	0.472407i	$0.156615\pi$
$522$			2.25980i			0.0989089i
$523$			1.59645i			0.0698079i	0.999391	+	0.0349040i	$0.0111125\pi$
$523$			1.59645i			0.0698079i	−0.999391	+	0.0349040i	$0.988887\pi$
$524$	−10.0895			−0.440761
$525$	4.48227	+	2.21569i	0.195622	+	0.0967008i
$526$	4.89157			0.213283
$527$			28.1689i			1.22706i
$528$		−	6.17150i		−	0.268580i
$529$	7.14207			0.310525
$530$	−50.3078	−	11.7553i	−2.18523	−	0.510616i
$531$	9.82410			0.426330
$532$		−	24.9658i		−	1.08241i
$533$		−	15.1411i		−	0.655833i
$534$	−23.2030			−1.00409
$535$	2.94819	−	12.6171i	0.127461	−	0.545483i
$536$	33.3891			1.44219
$537$		−	8.35101i		−	0.360373i
$538$		−	45.5252i		−	1.96273i
$539$	1.00000			0.0430730
$540$	2.20936	−	9.45516i	0.0950757	−	0.406885i
$541$	−9.91477			−0.426269			−0.213135	−	0.977023i	$-0.568367\pi$
$541$	−9.91477			−0.426269			−0.213135	+	0.977023i	$0.568367\pi$
$542$			2.49341i			0.107101i
$543$		−	13.7909i		−	0.591826i
$544$	10.2417			0.439108
$545$	−21.7035	−	5.07140i	−0.929677	−	0.217235i
$546$	−4.86452			−0.208182
$547$		−	11.1725i		−	0.477704i	−0.971056	−	0.238852i	$-0.923229\pi$
$547$		−	11.1725i		−	0.477704i	0.971056	−	0.238852i	$-0.0767710\pi$
$548$		−	80.9383i		−	3.45751i
$549$	−1.57645			−0.0672812
$550$	−5.58002	+	11.2882i	−0.237933	+	0.481329i
$551$	−5.15896			−0.219779
$552$		−	23.4913i		−	0.999855i
$553$		−	13.4115i		−	0.570317i
$554$	54.4266			2.31236
$555$	6.74267	+	1.57554i	0.286210	+	0.0668780i
$556$	31.5839			1.33945
$557$			25.0884i			1.06303i	0.847048	+	0.531516i	$0.178377\pi$
$557$			25.0884i			1.06303i	−0.847048	+	0.531516i	$0.821623\pi$
$558$			25.9350i			1.09792i
$559$	7.74845			0.327724
$560$	−3.13999	+	13.4379i	−0.132689	+	0.567855i
$561$	2.73533			0.115486
$562$			2.65587i			0.112031i
$563$		−	26.3424i		−	1.11020i	−0.831784	−	0.555099i	$-0.812680\pi$
$563$		−	26.3424i		−	1.11020i	0.831784	−	0.555099i	$-0.187320\pi$
$564$	14.8468			0.625165
$565$	4.10121	−	17.5515i	0.172539	−	0.738397i
$566$	39.2668			1.65051
$567$		−	1.00000i		−	0.0419961i
$568$		−	32.9059i		−	1.38070i
$569$	26.1376			1.09574			0.547872	−	0.836562i	$-0.315438\pi$
$569$	26.1376			1.09574			0.547872	+	0.836562i	$0.315438\pi$
$570$	31.5272	+	7.36686i	1.32053	+	0.308564i
$571$	−5.02585			−0.210325			−0.105163	−	0.994455i	$-0.533536\pi$
$571$	−5.02585			−0.210325			−0.105163	+	0.994455i	$0.533536\pi$
$572$		−	8.38767i		−	0.350706i
$573$		−	17.3693i		−	0.725613i
$574$	−19.7410			−0.823974
$575$	−8.82333	+	17.8493i	−0.367959	+	0.744367i
$576$	−2.91353			−0.121397
$577$		−	30.4481i		−	1.26757i	−0.773508	−	0.633786i	$-0.781500\pi$
$577$		−	30.4481i		−	1.26757i	0.773508	−	0.633786i	$-0.218500\pi$
$578$		−	23.9701i		−	0.997025i
$579$	19.1698			0.796671
$580$	8.48424	+	1.98249i	0.352289	+	0.0823183i
$581$	8.24025			0.341863
$582$			39.9537i			1.65613i
$583$		−	9.17420i		−	0.379957i
$584$	55.8029			2.30914
$585$	0.982771	−	4.20586i	0.0406326	−	0.173891i
$586$	71.1192			2.93791
$587$		−	30.4031i		−	1.25487i	−0.778669	−	0.627435i	$-0.784105\pi$
$587$		−	30.4031i		−	1.25487i	0.778669	−	0.627435i	$-0.215895\pi$
$588$			4.34238i			0.179077i
$589$	−59.2077			−2.43961
$590$	12.5880	−	53.8716i	0.518240	−	2.21786i
$591$	−13.2602			−0.545453
$592$			19.1109i			0.785454i
$593$		−	10.7140i		−	0.439972i	−0.975503	−	0.219986i	$-0.929399\pi$
$593$		−	10.7140i		−	0.439972i	0.975503	−	0.219986i	$-0.0706012\pi$
$594$	2.51841			0.103332
$595$	−5.95595	−	1.39171i	−0.244170	−	0.0570545i
$596$	−24.1051			−0.987384
$597$		−	11.6731i		−	0.477749i
$598$		−	19.3715i		−	0.792159i
$599$	−27.1016			−1.10734			−0.553670	−	0.832736i	$-0.686773\pi$
$599$	−27.1016			−1.10734			−0.553670	+	0.832736i	$0.686773\pi$
$600$	−26.4412	−	13.0705i	−1.07946	−	0.533602i
$601$	38.3834			1.56569			0.782845	−	0.622217i	$-0.213768\pi$
$601$	38.3834			1.56569			0.782845	+	0.622217i	$0.213768\pi$
$602$		−	10.1025i		−	0.411745i
$603$			5.66006i			0.230495i
$604$	21.3524			0.868819
$605$	−2.17741	−	0.508790i	−0.0885245	−	0.0206853i
$606$	−44.5593			−1.81010
$607$			31.6429i			1.28435i	0.766560	+	0.642173i	$0.221967\pi$
$607$			31.6429i			1.28435i	−0.766560	+	0.642173i	$0.778033\pi$
$608$			21.5268i			0.873025i
$609$	0.897314			0.0363610
$610$	−2.01997	+	8.64464i	−0.0817861	+	0.350011i
$611$	6.60420			0.267177
$612$			11.8778i			0.480134i
$613$		−	16.1066i		−	0.650538i	−0.945622	−	0.325269i	$-0.894545\pi$
$613$		−	16.1066i		−	0.650538i	0.945622	−	0.325269i	$-0.105455\pi$
$614$	−20.0534			−0.809288
$615$	3.98825	−	17.0681i	0.160822	−	0.688251i
$616$	−5.89907			−0.237680
$617$			35.3185i			1.42187i	0.703258	+	0.710935i	$0.251728\pi$
$617$			35.3185i			1.42187i	−0.703258	+	0.710935i	$0.748272\pi$
$618$		−	26.9374i		−	1.08358i
$619$	37.8224			1.52021			0.760105	−	0.649800i	$-0.225147\pi$
$619$	37.8224			1.52021			0.760105	+	0.649800i	$0.225147\pi$
$620$	97.3708	+	22.7523i	3.91051	+	0.913756i
$621$	3.98220			0.159800
$622$			18.0854i			0.725160i
$623$			9.21337i			0.369126i
$624$	11.9208			0.477212
$625$	15.1814	+	19.8626i	0.607256	+	0.794506i
$626$	−56.7725			−2.26908
$627$			5.74934i			0.229607i
$628$		−	46.8664i		−	1.87017i
$629$	−8.47034			−0.337735
$630$	−5.48362	−	1.28134i	−0.218473	−	0.0510498i
$631$	−37.3162			−1.48554			−0.742768	−	0.669549i	$-0.766487\pi$
$631$	−37.3162			−1.48554			−0.742768	+	0.669549i	$0.766487\pi$
$632$			79.1156i			3.14705i
$633$		−	6.24626i		−	0.248267i
$634$	−49.7965			−1.97767
$635$	9.30884	−	39.8380i	0.369410	−	1.58092i
$636$	39.8378			1.57967
$637$			1.93158i			0.0765322i
$638$			2.25980i			0.0894664i
$639$	5.57815			0.220668
$640$	−7.54327	+	32.2821i	−0.298174	+	1.27606i
$641$	33.5681			1.32586			0.662930	−	0.748682i	$-0.269313\pi$
$641$	33.5681			1.32586			0.662930	+	0.748682i	$0.269313\pi$
$642$			14.5930i			0.575938i
$643$			19.3063i			0.761366i	0.924706	+	0.380683i	$0.124311\pi$
$643$			19.3063i			0.761366i	−0.924706	+	0.380683i	$0.875689\pi$
$644$	−17.2922			−0.681409
$645$	8.73458	+	2.04098i	0.343924	+	0.0803636i
$646$	−39.6054			−1.55825
$647$			6.02907i			0.237027i	0.992952	+	0.118514i	$0.0378129\pi$
$647$			6.02907i			0.237027i	−0.992952	+	0.118514i	$0.962187\pi$
$648$			5.89907i			0.231737i
$649$	9.82410			0.385630
$650$	−21.8041	−	10.7783i	−0.855226	−	0.422759i
$651$	10.2982			0.403617
$652$		−	22.7482i		−	0.890888i
$653$		−	37.2726i		−	1.45859i	−0.684199	−	0.729295i	$-0.739848\pi$
$653$		−	37.2726i		−	1.45859i	0.684199	−	0.729295i	$-0.260152\pi$
$654$	25.1024			0.981582
$655$	−5.05920	−	1.18217i	−0.197679	−	0.0461911i
$656$	48.3764			1.88878
$657$			9.45961i			0.369055i
$658$		−	8.61058i		−	0.335675i
$659$	−5.54093			−0.215844			−0.107922	−	0.994159i	$-0.534420\pi$
$659$	−5.54093			−0.215844			−0.107922	+	0.994159i	$0.534420\pi$
$660$	2.20936	−	9.45516i	0.0859992	−	0.368042i
$661$	34.7511			1.35166			0.675831	−	0.737057i	$-0.263785\pi$
$661$	34.7511			1.35166			0.675831	+	0.737057i	$0.263785\pi$
$662$		−	73.7788i		−	2.86749i
$663$			5.28352i			0.205195i
$664$	−48.6098			−1.88643
$665$	2.92521	−	12.5187i	0.113435	−	0.485454i
$666$	−7.79861			−0.302190
$667$			3.57328i			0.138358i
$668$			72.8627i			2.81914i
$669$	−15.6620			−0.605527
$670$	31.0376	+	7.25246i	1.19909	+	0.280187i
$671$	−1.57645			−0.0608581
$672$		−	3.74421i		−	0.144436i
$673$			23.0302i			0.887751i	0.896089	+	0.443875i	$0.146397\pi$
$673$			23.0302i			0.887751i	−0.896089	+	0.443875i	$0.853603\pi$
$674$	−37.1810			−1.43216
$675$	2.21569	−	4.48227i	0.0852821	−	0.172522i
$676$	−40.2494			−1.54806
$677$		−	13.6076i		−	0.522982i	−0.965206	−	0.261491i	$-0.915786\pi$
$677$		−	13.6076i		−	0.522982i	0.965206	−	0.261491i	$-0.0842141\pi$
$678$			20.3001i			0.779622i
$679$	15.8647			0.608830
$680$	35.1345	+	8.20978i	1.34735	+	0.314831i
$681$	12.5488			0.480872
$682$			25.9350i			0.993102i
$683$		−	26.8635i		−	1.02790i	−0.857819	−	0.513951i	$-0.828181\pi$
$683$		−	26.8635i		−	1.02790i	0.857819	−	0.513951i	$-0.171819\pi$
$684$	−24.9658			−0.954592
$685$	9.48342	−	40.5852i	0.362343	−	1.55068i
$686$	2.51841			0.0961533
$687$		−	27.4136i		−	1.04590i
$688$			24.7566i			0.943837i
$689$	17.7207			0.675106
$690$	5.10256	−	21.8369i	0.194251	−	0.831315i
$691$	−40.9306			−1.55707			−0.778537	−	0.627598i	$-0.784038\pi$
$691$	−40.9306			−1.55707			−0.778537	+	0.627598i	$0.784038\pi$
$692$		−	7.79973i		−	0.296501i
$693$		−	1.00000i		−	0.0379869i
$694$	−20.5092			−0.778520
$695$	15.8372	+	3.70063i	0.600740	+	0.140373i
$696$	−5.29331			−0.200643
$697$			21.4414i			0.812151i
$698$		−	79.6809i		−	3.01597i
$699$	−13.8607			−0.524261
$700$	−9.62138	+	19.4637i	−0.363654	+	0.735659i
$701$	−16.4709			−0.622096			−0.311048	−	0.950394i	$-0.600680\pi$
$701$	−16.4709			−0.622096			−0.311048	+	0.950394i	$0.600680\pi$
$702$			4.86452i			0.183599i
$703$		−	17.8037i		−	0.671477i
$704$	−2.91353			−0.109808
$705$	7.44470	+	1.73958i	0.280384	+	0.0655164i
$706$	−44.3198			−1.66800
$707$			17.6934i			0.665430i
$708$			42.6600i			1.60326i
$709$	26.5439			0.996878			0.498439	−	0.866925i	$-0.333907\pi$
$709$	26.5439			0.996878			0.498439	+	0.866925i	$0.333907\pi$
$710$	7.14751	−	30.5884i	0.268241	−	1.14796i
$711$	−13.4115			−0.502972
$712$		−	54.3502i		−	2.03686i
$713$			41.0094i			1.53581i
$714$	6.88868			0.257802
$715$	0.982771	−	4.20586i	0.0367535	−	0.157290i
$716$	36.2632			1.35522
$717$			20.8546i			0.778829i
$718$			54.7878i			2.04466i
$719$	−29.5195			−1.10089			−0.550446	−	0.834871i	$-0.685542\pi$
$719$	−29.5195			−1.10089			−0.550446	+	0.834871i	$0.685542\pi$
$720$	13.4379	+	3.13999i	0.500801	+	0.117021i
$721$	−10.6962			−0.398347
$722$		−	35.3960i		−	1.31730i
$723$		−	16.6597i		−	0.619582i
$724$	59.8855			2.22563
$725$	4.02200	+	1.98817i	0.149373	+	0.0738389i
$726$	2.51841			0.0934669
$727$		−	15.4557i		−	0.573222i	−0.958047	−	0.286611i	$-0.907471\pi$
$727$		−	15.4557i		−	0.573222i	0.958047	−	0.286611i	$-0.0925287\pi$
$728$		−	11.3945i		−	0.422310i
$729$	−1.00000			−0.0370370
$730$	51.8729	+	12.1210i	1.91990	+	0.448618i
$731$	−10.9726			−0.405838
$732$		−	6.84553i		−	0.253018i
$733$		−	27.1612i		−	1.00322i	−0.865093	−	0.501611i	$-0.832741\pi$
$733$		−	27.1612i		−	1.00322i	0.865093	−	0.501611i	$-0.167259\pi$
$734$	−11.7808			−0.434836
$735$	−0.508790	+	2.17741i	−0.0187670	+	0.0803151i
$736$	14.9102			0.549598
$737$			5.66006i			0.208491i
$738$			19.7410i			0.726677i
$739$	28.6245			1.05297			0.526485	−	0.850185i	$-0.323510\pi$
$739$	28.6245			1.05297			0.526485	+	0.850185i	$0.323510\pi$
$740$	−6.84159	+	29.2792i	−0.251502	+	1.07633i
$741$	−11.1053			−0.407965
$742$		−	23.1044i		−	0.848188i
$743$			0.730764i			0.0268091i	0.999910	+	0.0134046i	$0.00426693\pi$
$743$			0.730764i			0.0268091i	−0.999910	+	0.0134046i	$0.995733\pi$
$744$	−60.7496			−2.22719
$745$	−12.0871	−	2.82436i	−0.442838	−	0.103477i
$746$	−7.56351			−0.276920
$747$		−	8.24025i		−	0.301495i
$748$			11.8778i			0.434297i
$749$	5.79452			0.211727
$750$	−21.7400	−	17.8933i	−0.793832	−	0.653372i
$751$	29.3236			1.07003			0.535016	−	0.844842i	$-0.320306\pi$
$751$	29.3236			1.07003			0.535016	+	0.844842i	$0.320306\pi$
$752$			21.1007i			0.769463i
$753$			5.04024i			0.183676i
$754$	−4.36500			−0.158964
$755$	10.7068	+	2.50183i	0.389661	+	0.0910510i
$756$	4.34238			0.157931
$757$			40.9665i			1.48895i	0.667649	+	0.744476i	$0.267301\pi$
$757$			40.9665i			1.48895i	−0.667649	+	0.744476i	$0.732699\pi$
$758$			35.4574i			1.28787i
$759$	3.98220			0.144545
$760$	−17.2560	+	73.8486i	−0.625940	+	2.67877i
$761$	19.2534			0.697935			0.348967	−	0.937135i	$-0.386532\pi$
$761$	19.2534			0.697935			0.348967	+	0.937135i	$0.386532\pi$
$762$			46.0769i			1.66919i
$763$		−	9.96757i		−	0.360850i
$764$	75.4241			2.72875
$765$	−1.39171	+	5.95595i	−0.0503174	+	0.215338i
$766$	7.87983			0.284710
$767$			18.9761i			0.685186i
$768$		−	31.5106i		−	1.13704i
$769$	−18.8886			−0.681140			−0.340570	−	0.940219i	$-0.610620\pi$
$769$	−18.8886			−0.681140			−0.340570	+	0.940219i	$0.610620\pi$
$770$	−5.48362	−	1.28134i	−0.197616	−	0.0461763i
$771$	−22.8836			−0.824134
$772$			83.2426i			2.99597i
$773$			39.2200i			1.41065i	0.708886	+	0.705323i	$0.249198\pi$
$773$			39.2200i			1.41065i	−0.708886	+	0.705323i	$0.750802\pi$
$774$	−10.1025			−0.363125
$775$	46.1591	+	22.8176i	1.65808	+	0.819632i
$776$	−93.5867			−3.35957
$777$			3.09664i			0.111091i
$778$		−	16.2864i		−	0.583895i
$779$	−45.0673			−1.61470
$780$	18.2634	+	4.26756i	0.653936	+	0.152803i
$781$	5.57815			0.199602
$782$			27.4321i			0.980970i
$783$		−	0.897314i		−	0.0320674i
$784$	−6.17150			−0.220411
$785$	5.49127	−	23.5004i	0.195992	−	0.838766i
$786$	5.85150			0.208716
$787$		−	6.02795i		−	0.214873i	−0.994212	−	0.107437i	$-0.965736\pi$
$787$		−	6.02795i		−	0.214873i	0.994212	−	0.107437i	$-0.0342643\pi$
$788$		−	57.5809i		−	2.05124i
$789$	−1.94233			−0.0691487
$790$	−17.1848	+	73.5438i	−0.611406	+	2.61657i
$791$	8.06070			0.286606
$792$			5.89907i			0.209614i
$793$		−	3.04504i		−	0.108133i
$794$	36.8252			1.30688
$795$	19.9760	+	4.66774i	0.708477	+	0.165548i
$796$	50.6891			1.79663
$797$			39.3052i			1.39226i	0.717916	+	0.696130i	$0.245096\pi$
$797$			39.3052i			1.39226i	−0.717916	+	0.696130i	$0.754904\pi$
$798$			14.4792i			0.512558i
$799$	−9.35226			−0.330859
$800$	8.29603	−	16.7826i	0.293309	−	0.593353i
$801$	9.21337			0.325538
$802$		−	64.8206i		−	2.28889i
$803$			9.45961i			0.333822i
$804$	−24.5781			−0.866803
$805$	−8.67090	−	2.02610i	−0.305609	−	0.0714108i
$806$	−50.0956			−1.76454
$807$			18.0770i			0.636340i
$808$		−	104.375i		−	3.67189i
$809$	−3.75113			−0.131883			−0.0659414	−	0.997823i	$-0.521005\pi$
$809$	−3.75113			−0.131883			−0.0659414	+	0.997823i	$0.521005\pi$
$810$	−1.28134	+	5.48362i	−0.0450217	+	0.192675i
$811$	19.3790			0.680490			0.340245	−	0.940337i	$-0.389490\pi$
$811$	19.3790			0.680490			0.340245	+	0.940337i	$0.389490\pi$
$812$			3.89648i			0.136740i
$813$		−	0.990072i		−	0.0347234i
$814$	−7.79861			−0.273341
$815$	2.66537	−	11.4067i	0.0933639	−	0.399559i
$816$	−16.8811			−0.590956
$817$		−	23.0632i		−	0.806878i
$818$		−	25.3030i		−	0.884698i
$819$	1.93158			0.0674950
$820$	74.1160	+	17.3185i	2.58824	+	0.604787i
$821$	36.8702			1.28678			0.643390	−	0.765539i	$-0.277528\pi$
$821$	36.8702			1.28678			0.643390	+	0.765539i	$0.277528\pi$
$822$			46.9410i			1.63726i
$823$			44.2773i			1.54341i	0.635981	+	0.771705i	$0.280596\pi$
$823$			44.2773i			1.54341i	−0.635981	+	0.771705i	$0.719404\pi$
$824$	63.0976			2.19811
$825$	2.21569	−	4.48227i	0.0771405	−	0.156052i
$826$	24.7411			0.860852
$827$			44.5865i			1.55042i	0.631701	+	0.775212i	$0.282357\pi$
$827$			44.5865i			1.55042i	−0.631701	+	0.775212i	$0.717643\pi$
$828$			17.2922i			0.600946i
$829$	−45.3494			−1.57505			−0.787525	−	0.616283i	$-0.788638\pi$
$829$	−45.3494			−1.57505			−0.787525	+	0.616283i	$0.788638\pi$
$830$	−45.1864	−	10.5586i	−1.56844	−	0.366493i
$831$	−21.6115			−0.749695
$832$		−	5.62774i		−	0.195107i
$833$		−	2.73533i		−	0.0947736i
$834$	−18.3174			−0.634280
$835$	−8.53721	+	36.5358i	−0.295442	+	1.26437i
$836$	−24.9658			−0.863461
$837$		−	10.2982i		−	0.355957i
$838$		−	17.0208i		−	0.587975i
$839$	−45.3592			−1.56597			−0.782987	−	0.622038i	$-0.786305\pi$
$839$	−45.3592			−1.56597			−0.782987	+	0.622038i	$0.786305\pi$
$840$	3.00139	−	12.8447i	0.103558	−	0.443185i
$841$	−28.1948			−0.972235
$842$		−	5.89202i		−	0.203052i
$843$		−	1.05458i		−	0.0363218i
$844$	27.1236			0.933634
$845$	−20.1824	−	4.71596i	−0.694296	−	0.162234i
$846$	−8.61058			−0.296038
$847$		−	1.00000i		−	0.0343604i
$848$			56.6185i			1.94429i
$849$	−15.5919			−0.535113
$850$	30.8769	+	15.2632i	1.05907	+	0.523524i
$851$	−12.3315			−0.422717
$852$			24.2224i			0.829847i
$853$		−	29.1110i		−	0.996740i	−0.866964	−	0.498370i	$-0.833932\pi$
$853$		−	29.1110i		−	0.996740i	0.866964	−	0.498370i	$-0.166068\pi$
$854$	−3.97014			−0.135855
$855$	−12.5187	−	2.92521i	−0.428130	−	0.100040i
$856$	−34.1822			−1.16832
$857$		−	0.199601i		−	0.00681824i	−0.999994	−	0.00340912i	$-0.998915\pi$
$857$		−	0.199601i		−	0.00681824i	0.999994	−	0.00340912i	$-0.00108516\pi$
$858$			4.86452i			0.166072i
$859$	−4.79202			−0.163502			−0.0817509	−	0.996653i	$-0.526051\pi$
$859$	−4.79202			−0.163502			−0.0817509	+	0.996653i	$0.526051\pi$
$860$	−8.86272	+	37.9289i	−0.302216	+	1.29336i
$861$	7.83869			0.267142
$862$		−	33.1097i		−	1.12772i
$863$		−	34.8190i		−	1.18525i	−0.805478	−	0.592626i	$-0.798091\pi$
$863$		−	34.8190i		−	1.18525i	0.805478	−	0.592626i	$-0.201909\pi$
$864$	−3.74421			−0.127381
$865$	0.913882	−	3.91104i	0.0310729	−	0.132979i
$866$	−69.2413			−2.35292
$867$			9.51796i			0.323247i
$868$			44.7185i			1.51785i
$869$	−13.4115			−0.454955
$870$	−4.92053	−	1.14976i	−0.166821	−	0.0389807i
$871$	−10.9329			−0.370446
$872$			58.7994i			1.99120i
$873$		−	15.8647i		−	0.536937i
$874$	−57.6590			−1.95035
$875$	−7.10501	+	8.63243i	−0.240193	+	0.291829i
$876$	−41.0772			−1.38787
$877$		−	21.1956i		−	0.715725i	−0.933774	−	0.357863i	$-0.883506\pi$
$877$		−	21.1956i		−	0.715725i	0.933774	−	0.357863i	$-0.116494\pi$
$878$			82.1381i			2.77203i
$879$	−28.2397			−0.952502
$880$	13.4379	+	3.13999i	0.452992	+	0.105849i
$881$	−46.8565			−1.57864			−0.789318	−	0.613984i	$-0.789566\pi$
$881$	−46.8565			−1.57864			−0.789318	+	0.613984i	$0.789566\pi$
$882$		−	2.51841i		−	0.0847992i
$883$		−	5.15615i		−	0.173518i	−0.996229	−	0.0867591i	$-0.972349\pi$
$883$		−	5.15615i		−	0.173518i	0.996229	−	0.0867591i	$-0.0276511\pi$
$884$	−22.9431			−0.771659
$885$	−4.99840	+	21.3911i	−0.168019	+	0.719055i
$886$	−54.0235			−1.81495
$887$			32.1671i			1.08007i	0.841644	+	0.540033i	$0.181588\pi$
$887$			32.1671i			1.08007i	−0.841644	+	0.540033i	$0.818412\pi$
$888$		−	18.2673i		−	0.613010i
$889$	18.2960			0.613629
$890$	11.8055	−	50.5226i	0.395720	−	1.69352i
$891$	−1.00000			−0.0335013
$892$		−	68.0102i		−	2.27715i
$893$		−	19.6573i		−	0.657807i
$894$	13.9800			0.467562
$895$	18.1836	+	4.24891i	0.607811	+	0.142025i
$896$	−14.8259			−0.495298
$897$			7.69196i			0.256827i
$898$			91.2714i			3.04577i
$899$	9.24069			0.308194
$900$	19.4637	+	9.62138i	0.648790	+	0.320713i
$901$	−25.0945			−0.836018
$902$			19.7410i			0.657304i
$903$			4.01145i			0.133493i
$904$	−47.5506			−1.58151
$905$	30.0286	+	7.01669i	0.998184	+	0.233243i
$906$	−12.3836			−0.411417
$907$			1.43291i			0.0475791i	0.999717	+	0.0237896i	$0.00757317\pi$
$907$			1.43291i			0.0475791i	−0.999717	+	0.0237896i	$0.992427\pi$
$908$			54.4918i			1.80837i
$909$	17.6934			0.586854
$910$	2.47502	−	10.5921i	0.0820460	−	0.351124i
$911$	−32.8612			−1.08874			−0.544371	−	0.838845i	$-0.683231\pi$
$911$	−32.8612			−1.08874			−0.544371	+	0.838845i	$0.683231\pi$
$912$		−	35.4820i		−	1.17493i
$913$		−	8.24025i		−	0.272713i
$914$	40.1214			1.32710
$915$	0.802081	−	3.43258i	0.0265160	−	0.113478i
$916$	119.040			3.93321
$917$		−	2.32349i		−	0.0767284i
$918$		−	6.88868i		−	0.227360i
$919$	8.11060			0.267544			0.133772	−	0.991012i	$-0.457291\pi$
$919$	8.11060			0.267544			0.133772	+	0.991012i	$0.457291\pi$
$920$	51.1502	+	11.9521i	1.68637	+	0.394050i
$921$	7.96272			0.262380
$922$		−	89.9721i		−	2.96307i
$923$			10.7747i			0.354653i
$924$	4.34238			0.142854
$925$	−6.86121	+	13.8800i	−0.225595	+	0.456371i
$926$	74.2954			2.44150
$927$			10.6962i			0.351309i
$928$		−	3.35973i		−	0.110289i
$929$	32.0625			1.05194			0.525968	−	0.850505i	$-0.323703\pi$
$929$	32.0625			1.05194			0.525968	+	0.850505i	$0.323703\pi$
$930$	−56.4712	−	13.1955i	−1.85176	−	0.432696i
$931$	5.74934			0.188427
$932$		−	60.1885i		−	1.97154i
$933$		−	7.18130i		−	0.235105i
$934$	47.7890			1.56370
$935$	−1.39171	+	5.95595i	−0.0455138	+	0.194780i
$936$	−11.3945			−0.372442
$937$			10.5934i			0.346072i	0.984915	+	0.173036i	$0.0553578\pi$
$937$			10.5934i			0.346072i	−0.984915	+	0.173036i	$0.944642\pi$
$938$			14.2543i			0.465421i
$939$	22.5430			0.735663
$940$	−7.55392	+	32.3277i	−0.246382	+	1.05441i
$941$	30.9354			1.00846			0.504232	−	0.863568i	$-0.331776\pi$
$941$	30.9354			1.00846			0.504232	+	0.863568i	$0.331776\pi$
$942$			27.1807i			0.885595i
$943$			31.2152i			1.01651i
$944$	−60.6294			−1.97332
$945$	2.17741	+	0.508790i	0.0708313	+	0.0165509i
$946$	−10.1025			−0.328459
$947$			57.8119i			1.87863i	0.343051	+	0.939317i	$0.388540\pi$
$947$			57.8119i			1.87863i	−0.343051	+	0.939317i	$0.611460\pi$
$948$		−	58.2380i		−	1.89148i
$949$	−18.2720			−0.593135
$950$	−32.0814	+	64.8996i	−1.04086	+	2.10562i
$951$	19.7730			0.641184
$952$			16.1359i			0.522968i
$953$			8.67683i			0.281070i	0.990076	+	0.140535i	$0.0448823\pi$
$953$			8.67683i			0.281070i	−0.990076	+	0.140535i	$0.955118\pi$
$954$	−23.1044			−0.748032
$955$	37.8202	+	8.83732i	1.22383	+	0.285969i
$956$	−90.5585			−2.92887
$957$		−	0.897314i		−	0.0290060i
$958$			28.2238i			0.911870i
$959$	18.6392			0.601890
$960$	1.48238	−	6.34397i	0.0478435	−	0.204751i
$961$	75.0522			2.42104
$962$		−	15.0637i		−	0.485672i
$963$		−	5.79452i		−	0.186726i
$964$	72.3429			2.33001
$965$	−9.75341	+	41.7407i	−0.313974	+	1.34368i
$966$	10.0288			0.322672
$967$			45.1612i			1.45229i	0.687544	+	0.726143i	$0.258689\pi$
$967$			45.1612i			1.45229i	−0.687544	+	0.726143i	$0.741311\pi$
$968$			5.89907i			0.189603i
$969$	15.7264			0.505203
$970$	−86.9957	−	20.3280i	−2.79326	−	0.652694i
$971$	−2.33588			−0.0749619			−0.0374809	−	0.999297i	$-0.511933\pi$
$971$	−2.33588			−0.0749619			−0.0374809	+	0.999297i	$0.511933\pi$
$972$		−	4.34238i		−	0.139282i
$973$			7.27340i			0.233175i
$974$	−32.2821			−1.03438
$975$	8.65787	+	4.27980i	0.277274	+	0.137063i
$976$	9.72904			0.311419
$977$		−	17.7364i		−	0.567437i	−0.958908	−	0.283719i	$-0.908432\pi$
$977$		−	17.7364i		−	0.567437i	0.958908	−	0.283719i	$-0.0915681\pi$
$978$			13.1930i			0.421867i
$979$	9.21337			0.294460
$980$	−9.45516	−	2.20936i	−0.302034	−	0.0705754i
$981$	−9.96757			−0.318240
$982$			44.2425i			1.41183i
$983$		−	23.0645i		−	0.735642i	−0.929897	−	0.367821i	$-0.880104\pi$
$983$		−	23.0645i		−	0.735642i	0.929897	−	0.367821i	$-0.119896\pi$
$984$	−46.2409			−1.47411
$985$	6.74667	−	28.8730i	0.214967	−	0.919971i
$986$	6.18131			0.196853
$987$			3.41906i			0.108830i
$988$		−	48.2236i		−	1.53420i
$989$	−15.9744			−0.507956
$990$	−1.28134	+	5.48362i	−0.0407237	+	0.174281i
$991$	0.575473			0.0182805			0.00914025	−	0.999958i	$-0.497091\pi$
$991$	0.575473			0.0182805			0.00914025	+	0.999958i	$0.497091\pi$
$992$		−	38.5585i		−	1.22423i
$993$			29.2958i			0.929674i
$994$	14.0481			0.445577
$995$	25.4172	+	5.93917i	0.805780	+	0.188284i
$996$	35.7823			1.13381
$997$			52.5486i			1.66423i	0.554602	+	0.832116i	$0.312871\pi$
$997$			52.5486i			1.66423i	−0.554602	+	0.832116i	$0.687129\pi$
$998$			74.9858i			2.37363i
$999$	3.09664			0.0979734

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.c.e.694.2	✓	20
5.2	odd	4		5775.2.a.cp.1.9		10
5.3	odd	4		5775.2.a.cm.1.2		10
5.4	even	2	inner	1155.2.c.e.694.19	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.c.e.694.2	✓	20	1.1	even	1	trivial
1155.2.c.e.694.19	yes	20	5.4	even	2	inner
5775.2.a.cm.1.2		10	5.3	odd	4
5775.2.a.cp.1.9		10	5.2	odd	4

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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.51841i q^{2} +1.00000i q^{3} -4.34238 q^{4} +(-2.17741 - 0.508790i) q^{5} +2.51841 q^{6} -1.00000i q^{7} +5.89907i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.51841i q^{2} +1.00000i q^{3} -4.34238 q^{4} +(-2.17741 - 0.508790i) q^{5} +2.51841 q^{6} -1.00000i q^{7} +5.89907i q^{8} -1.00000 q^{9} +(-1.28134 + 5.48362i) q^{10} -1.00000 q^{11} -4.34238i q^{12} -1.93158i q^{13} -2.51841 q^{14} +(0.508790 - 2.17741i) q^{15} +6.17150 q^{16} +2.73533i q^{17} +2.51841i q^{18} -5.74934 q^{19} +(9.45516 + 2.20936i) q^{20} +1.00000 q^{21} +2.51841i q^{22} +3.98220i q^{23} -5.89907 q^{24} +(4.48227 + 2.21569i) q^{25} -4.86452 q^{26} -1.00000i q^{27} +4.34238i q^{28} +0.897314 q^{29} +(-5.48362 - 1.28134i) q^{30} +10.2982 q^{31} -3.74421i q^{32} -1.00000i q^{33} +6.88868 q^{34} +(-0.508790 + 2.17741i) q^{35} +4.34238 q^{36} +3.09664i q^{37} +14.4792i q^{38} +1.93158 q^{39} +(3.00139 - 12.8447i) q^{40} +7.83869 q^{41} -2.51841i q^{42} +4.01145i q^{43} +4.34238 q^{44} +(2.17741 + 0.508790i) q^{45} +10.0288 q^{46} +3.41906i q^{47} +6.17150i q^{48} -1.00000 q^{49} +(5.58002 - 11.2882i) q^{50} -2.73533 q^{51} +8.38767i q^{52} +9.17420i q^{53} -2.51841 q^{54} +(2.17741 + 0.508790i) q^{55} +5.89907 q^{56} -5.74934i q^{57} -2.25980i q^{58} -9.82410 q^{59} +(-2.20936 + 9.45516i) q^{60} +1.57645 q^{61} -25.9350i q^{62} +1.00000i q^{63} +2.91353 q^{64} +(-0.982771 + 4.20586i) q^{65} -2.51841 q^{66} -5.66006i q^{67} -11.8778i q^{68} -3.98220 q^{69} +(5.48362 + 1.28134i) q^{70} -5.57815 q^{71} -5.89907i q^{72} -9.45961i q^{73} +7.79861 q^{74} +(-2.21569 + 4.48227i) q^{75} +24.9658 q^{76} +1.00000i q^{77} -4.86452i q^{78} +13.4115 q^{79} +(-13.4379 - 3.13999i) q^{80} +1.00000 q^{81} -19.7410i q^{82} +8.24025i q^{83} -4.34238 q^{84} +(1.39171 - 5.95595i) q^{85} +10.1025 q^{86} +0.897314i q^{87} -5.89907i q^{88} -9.21337 q^{89} +(1.28134 - 5.48362i) q^{90} -1.93158 q^{91} -17.2922i q^{92} +10.2982i q^{93} +8.61058 q^{94} +(12.5187 + 2.92521i) q^{95} +3.74421 q^{96} +15.8647i q^{97} +2.51841i q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} - 2 q^{10} - 20 q^{11} - 6 q^{14} + 2 q^{15} + 38 q^{16} + 2 q^{19} + 4 q^{20} + 20 q^{21} - 18 q^{24} + 12 q^{25} + 20 q^{26} - 38 q^{29} + 6 q^{30} + 20 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} + 2 q^{40} + 12 q^{41} + 26 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{49} - 6 q^{50} + 26 q^{51} - 6 q^{54} + 2 q^{55} + 18 q^{56} - 22 q^{59} + 16 q^{60} + 34 q^{61} - 26 q^{64} - 28 q^{65} - 6 q^{66} - 26 q^{69} - 6 q^{70} + 72 q^{71} - 72 q^{74} - 8 q^{75} + 44 q^{76} + 4 q^{79} - 8 q^{80} + 20 q^{81} - 26 q^{84} - 16 q^{85} + 52 q^{86} + 6 q^{89} + 2 q^{90} + 16 q^{94} + 14 q^{95} + 62 q^{96} + 20 q^{99}+O(q^{100}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9 - 2 * q^10 - 20 * q^11 - 6 * q^14 + 2 * q^15 + 38 * q^16 + 2 * q^19 + 4 * q^20 + 20 * q^21 - 18 * q^24 + 12 * q^25 + 20 * q^26 - 38 * q^29 + 6 * q^30 + 20 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 + 2 * q^40 + 12 * q^41 + 26 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^49 - 6 * q^50 + 26 * q^51 - 6 * q^54 + 2 * q^55 + 18 * q^56 - 22 * q^59 + 16 * q^60 + 34 * q^61 - 26 * q^64 - 28 * q^65 - 6 * q^66 - 26 * q^69 - 6 * q^70 + 72 * q^71 - 72 * q^74 - 8 * q^75 + 44 * q^76 + 4 * q^79 - 8 * q^80 + 20 * q^81 - 26 * q^84 - 16 * q^85 + 52 * q^86 + 6 * q^89 + 2 * q^90 + 16 * q^94 + 14 * q^95 + 62 * q^96 + 20 * q^99

Introduction

L-functions

Modular forms

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