LMFDB - Embedded newform 1155.2.l.e.1121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(1121,1155)]

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([1, 0, 0, 1]))

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

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

chi := DirichletCharacter("1155.1121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.l (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:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1121.3
Character	$\chi$	$=$	1155.1121
Dual form			1155.2.l.e.1121.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55898 q^{2} +(-0.371837 - 1.69167i) q^{3} +4.54836 q^{4} -1.00000i q^{5} +(0.951521 + 4.32893i) q^{6} +1.00000i q^{7} -6.52118 q^{8} +(-2.72347 + 1.25805i) q^{9} +O(q^{10})$	\(q-2.55898 q^{2} +(-0.371837 - 1.69167i) q^{3} +4.54836 q^{4} -1.00000i q^{5} +(0.951521 + 4.32893i) q^{6} +1.00000i q^{7} -6.52118 q^{8} +(-2.72347 + 1.25805i) q^{9} +2.55898i q^{10} +(3.20087 - 0.868568i) q^{11} +(-1.69125 - 7.69430i) q^{12} +4.12555i q^{13} -2.55898i q^{14} +(-1.69167 + 0.371837i) q^{15} +7.59082 q^{16} -4.41559 q^{17} +(6.96930 - 3.21931i) q^{18} -1.90905i q^{19} -4.54836i q^{20} +(1.69167 - 0.371837i) q^{21} +(-8.19096 + 2.22264i) q^{22} -0.792469i q^{23} +(2.42481 + 11.0317i) q^{24} -1.00000 q^{25} -10.5572i q^{26} +(3.14089 + 4.13942i) q^{27} +4.54836i q^{28} +2.29702 q^{29} +(4.32893 - 0.951521i) q^{30} +10.5297 q^{31} -6.38238 q^{32} +(-2.65953 - 5.09185i) q^{33} +11.2994 q^{34} +1.00000 q^{35} +(-12.3873 + 5.72205i) q^{36} +3.49950 q^{37} +4.88522i q^{38} +(6.97906 - 1.53403i) q^{39} +6.52118i q^{40} +0.636941 q^{41} +(-4.32893 + 0.951521i) q^{42} -9.10331i q^{43} +(14.5587 - 3.95056i) q^{44} +(1.25805 + 2.72347i) q^{45} +2.02791i q^{46} -0.336540i q^{47} +(-2.82255 - 12.8411i) q^{48} -1.00000 q^{49} +2.55898 q^{50} +(1.64188 + 7.46971i) q^{51} +18.7645i q^{52} +11.0786i q^{53} +(-8.03745 - 10.5927i) q^{54} +(-0.868568 - 3.20087i) q^{55} -6.52118i q^{56} +(-3.22948 + 0.709856i) q^{57} -5.87801 q^{58} -1.83800i q^{59} +(-7.69430 + 1.69125i) q^{60} +11.3716i q^{61} -26.9452 q^{62} +(-1.25805 - 2.72347i) q^{63} +1.15070 q^{64} +4.12555 q^{65} +(6.80567 + 13.0299i) q^{66} +9.49889 q^{67} -20.0837 q^{68} +(-1.34059 + 0.294669i) q^{69} -2.55898 q^{70} +5.28271i q^{71} +(17.7603 - 8.20396i) q^{72} -10.2542i q^{73} -8.95514 q^{74} +(0.371837 + 1.69167i) q^{75} -8.68304i q^{76} +(0.868568 + 3.20087i) q^{77} +(-17.8592 + 3.92555i) q^{78} -4.50128i q^{79} -7.59082i q^{80} +(5.83463 - 6.85253i) q^{81} -1.62992 q^{82} +2.03873 q^{83} +(7.69430 - 1.69125i) q^{84} +4.41559i q^{85} +23.2952i q^{86} +(-0.854116 - 3.88579i) q^{87} +(-20.8735 + 5.66409i) q^{88} -6.21466i q^{89} +(-3.21931 - 6.96930i) q^{90} -4.12555 q^{91} -3.60443i q^{92} +(-3.91533 - 17.8127i) q^{93} +0.861197i q^{94} -1.90905 q^{95} +(2.37320 + 10.7969i) q^{96} +8.07652 q^{97} +2.55898 q^{98} +(-7.62480 + 6.39238i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9	$ 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9} - 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} + 40 q^{18} - 2 q^{21} - 4 q^{22} - 12 q^{24} - 40 q^{25} + 32 q^{27} - 24 q^{29} - 8 q^{31} + 52 q^{32} - 16 q^{33} + 32 q^{34} + 40 q^{35} - 48 q^{37} + 66 q^{39} - 16 q^{41} + 32 q^{44} + 32 q^{48} - 40 q^{49} + 4 q^{50} - 14 q^{51} - 72 q^{54} + 8 q^{55} - 24 q^{57} - 80 q^{58} + 24 q^{60} + 48 q^{62} + 76 q^{64} + 4 q^{65} - 76 q^{66} - 48 q^{67} - 32 q^{68} - 20 q^{69} - 4 q^{70} + 128 q^{72} + 4 q^{75} - 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} - 24 q^{83} - 24 q^{84} - 32 q^{87} - 16 q^{88} + 8 q^{90} - 4 q^{91} - 20 q^{93} - 12 q^{95} + 12 q^{96} + 100 q^{97} + 4 q^{98} - 54 q^{99}+O(q^{100}) $ 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9 - 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 + 40 * q^18 - 2 * q^21 - 4 * q^22 - 12 * q^24 - 40 * q^25 + 32 * q^27 - 24 * q^29 - 8 * q^31 + 52 * q^32 - 16 * q^33 + 32 * q^34 + 40 * q^35 - 48 * q^37 + 66 * q^39 - 16 * q^41 + 32 * q^44 + 32 * q^48 - 40 * q^49 + 4 * q^50 - 14 * q^51 - 72 * q^54 + 8 * q^55 - 24 * q^57 - 80 * q^58 + 24 * q^60 + 48 * q^62 + 76 * q^64 + 4 * q^65 - 76 * q^66 - 48 * q^67 - 32 * q^68 - 20 * q^69 - 4 * q^70 + 128 * q^72 + 4 * q^75 - 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 - 24 * q^83 - 24 * q^84 - 32 * q^87 - 16 * q^88 + 8 * q^90 - 4 * q^91 - 20 * q^93 - 12 * q^95 + 12 * q^96 + 100 * q^97 + 4 * q^98 - 54 * 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 $

$2$	−2.55898			−1.80947			−0.904734	−	0.425976i	$-0.859931\pi$
$2$	−2.55898			−1.80947			−0.904734	+	0.425976i	$0.859931\pi$
$3$	−0.371837	−	1.69167i	−0.214680	−	0.976684i
$3$	−0.371837	−	1.69167i	−0.214680	−	0.976684i
$4$	4.54836			2.27418
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	0.951521	+	4.32893i	0.388457	+	1.76728i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−6.52118			−2.30558
$9$	−2.72347	+	1.25805i	−0.907825	+	0.419349i
$10$			2.55898i			0.809219i
$11$	3.20087	−	0.868568i	0.965100	−	0.261883i
$11$	3.20087	−	0.868568i	0.965100	−	0.261883i
$12$	−1.69125	−	7.69430i	−0.488221	−	2.22115i
$13$			4.12555i			1.14422i	0.820176	+	0.572111i	$0.193875\pi$
$13$			4.12555i			1.14422i	−0.820176	+	0.572111i	$0.806125\pi$
$14$		−	2.55898i		−	0.683915i
$15$	−1.69167	+	0.371837i	−0.436787	+	0.0960079i
$16$	7.59082			1.89771
$17$	−4.41559			−1.07094			−0.535469	−	0.844555i	$-0.679865\pi$
$17$	−4.41559			−1.07094			−0.535469	+	0.844555i	$0.679865\pi$
$18$	6.96930	−	3.21931i	1.64268	−	0.758800i
$19$		−	1.90905i		−	0.437966i	−0.975729	−	0.218983i	$-0.929726\pi$
$19$		−	1.90905i		−	0.437966i	0.975729	−	0.218983i	$-0.0702740\pi$
$20$		−	4.54836i		−	1.01704i
$21$	1.69167	−	0.371837i	0.369152	−	0.0811414i
$22$	−8.19096	+	2.22264i	−1.74632	+	0.473870i
$23$		−	0.792469i		−	0.165241i	−0.996581	−	0.0826206i	$-0.973671\pi$
$23$		−	0.792469i		−	0.165241i	0.996581	−	0.0826206i	$-0.0263290\pi$
$24$	2.42481	+	11.0317i	0.494963	+	2.25183i
$25$	−1.00000			−0.200000
$26$		−	10.5572i		−	2.07043i
$27$	3.14089	+	4.13942i	0.604464	+	0.796632i
$28$			4.54836i			0.859558i
$29$	2.29702			0.426546			0.213273	−	0.976993i	$-0.431588\pi$
$29$	2.29702			0.426546			0.213273	+	0.976993i	$0.431588\pi$
$30$	4.32893	−	0.951521i	0.790352	−	0.173723i
$31$	10.5297			1.89119			0.945595	−	0.325346i	$-0.105481\pi$
$31$	10.5297			1.89119			0.945595	+	0.325346i	$0.105481\pi$
$32$	−6.38238			−1.12826
$33$	−2.65953	−	5.09185i	−0.462965	−	0.886377i
$34$	11.2994			1.93783
$35$	1.00000			0.169031
$36$	−12.3873	+	5.72205i	−2.06456	+	0.953675i
$37$	3.49950			0.575315			0.287657	−	0.957733i	$-0.407124\pi$
$37$	3.49950			0.575315			0.287657	+	0.957733i	$0.407124\pi$
$38$			4.88522i			0.792487i
$39$	6.97906	−	1.53403i	1.11754	−	0.245642i
$40$			6.52118i			1.03109i
$41$	0.636941			0.0994734			0.0497367	−	0.998762i	$-0.484162\pi$
$41$	0.636941			0.0994734			0.0497367	+	0.998762i	$0.484162\pi$
$42$	−4.32893	+	0.951521i	−0.667969	+	0.146823i
$43$		−	9.10331i		−	1.38824i	−0.719858	−	0.694121i	$-0.755793\pi$
$43$		−	9.10331i		−	1.38824i	0.719858	−	0.694121i	$-0.244207\pi$
$44$	14.5587	−	3.95056i	2.19481	−	0.595569i
$45$	1.25805	+	2.72347i	0.187539	+	0.405992i
$46$			2.02791i			0.298999i
$47$		−	0.336540i		−	0.0490894i	−0.999699	−	0.0245447i	$-0.992186\pi$
$47$		−	0.336540i		−	0.0490894i	0.999699	−	0.0245447i	$-0.00781360\pi$
$48$	−2.82255	−	12.8411i	−0.407400	−	1.85346i
$49$	−1.00000			−0.142857
$50$	2.55898			0.361894
$51$	1.64188	+	7.46971i	0.229909	+	1.04597i
$52$			18.7645i			2.60216i
$53$			11.0786i			1.52176i	0.648893	+	0.760879i	$0.275232\pi$
$53$			11.0786i			1.52176i	−0.648893	+	0.760879i	$0.724768\pi$
$54$	−8.03745	−	10.5927i	−1.09376	−	1.44148i
$55$	−0.868568	−	3.20087i	−0.117118	−	0.431606i
$56$		−	6.52118i		−	0.871429i
$57$	−3.22948	+	0.709856i	−0.427755	+	0.0940227i
$58$	−5.87801			−0.771821
$59$		−	1.83800i		−	0.239287i	−0.992817	−	0.119643i	$-0.961825\pi$
$59$		−	1.83800i		−	0.239287i	0.992817	−	0.119643i	$-0.0381751\pi$
$60$	−7.69430	+	1.69125i	−0.993330	+	0.218339i
$61$			11.3716i			1.45598i	0.685586	+	0.727992i	$0.259546\pi$
$61$			11.3716i			1.45598i	−0.685586	+	0.727992i	$0.740454\pi$
$62$	−26.9452			−3.42205
$63$	−1.25805	−	2.72347i	−0.158499	−	0.343126i
$64$	1.15070			0.143837
$65$	4.12555			0.511711
$66$	6.80567	+	13.0299i	0.837721	+	1.60387i
$67$	9.49889			1.16047			0.580237	−	0.814448i	$-0.302960\pi$
$67$	9.49889			1.16047			0.580237	+	0.814448i	$0.302960\pi$
$68$	−20.0837			−2.43550
$69$	−1.34059	+	0.294669i	−0.161389	+	0.0354740i
$70$	−2.55898			−0.305856
$71$			5.28271i			0.626943i	0.949598	+	0.313471i	$0.101492\pi$
$71$			5.28271i			0.626943i	−0.949598	+	0.313471i	$0.898508\pi$
$72$	17.7603	−	8.20396i	2.09307	−	0.966846i
$73$		−	10.2542i		−	1.20016i	−0.799938	−	0.600082i	$-0.795134\pi$
$73$		−	10.2542i		−	1.20016i	0.799938	−	0.600082i	$-0.204866\pi$
$74$	−8.95514			−1.04101
$75$	0.371837	+	1.69167i	0.0429360	+	0.195337i
$76$		−	8.68304i		−	0.996014i
$77$	0.868568	+	3.20087i	0.0989825	+	0.364773i
$78$	−17.8592	+	3.92555i	−2.02216	+	0.444481i
$79$		−	4.50128i		−	0.506434i	−0.967410	−	0.253217i	$-0.918511\pi$
$79$		−	4.50128i		−	0.506434i	0.967410	−	0.253217i	$-0.0814887\pi$
$80$		−	7.59082i		−	0.848680i
$81$	5.83463	−	6.85253i	0.648292	−	0.761392i
$82$	−1.62992			−0.179994
$83$	2.03873			0.223779			0.111890	−	0.993721i	$-0.464310\pi$
$83$	2.03873			0.223779			0.111890	+	0.993721i	$0.464310\pi$
$84$	7.69430	−	1.69125i	0.839517	−	0.184530i
$85$			4.41559i			0.478938i
$86$			23.2952i			2.51198i
$87$	−0.854116	−	3.88579i	−0.0915709	−	0.416600i
$88$	−20.8735	+	5.66409i	−2.22512	+	0.603794i
$89$		−	6.21466i		−	0.658753i	−0.944199	−	0.329376i	$-0.893161\pi$
$89$		−	6.21466i		−	0.658753i	0.944199	−	0.329376i	$-0.106839\pi$
$90$	−3.21931	−	6.96930i	−0.339346	−	0.734629i
$91$	−4.12555			−0.432475
$92$		−	3.60443i		−	0.375788i
$93$	−3.91533	−	17.8127i	−0.406001	−	1.84710i
$94$			0.861197i			0.0888257i
$95$	−1.90905			−0.195865
$96$	2.37320	+	10.7969i	0.242214	+	1.10195i
$97$	8.07652			0.820047			0.410023	−	0.912075i	$-0.365521\pi$
$97$	8.07652			0.820047			0.410023	+	0.912075i	$0.365521\pi$
$98$	2.55898			0.258496
$99$	−7.62480	+	6.39238i	−0.766321	+	0.642458i
$100$	−4.54836			−0.454836
$101$	18.9862			1.88920			0.944601	−	0.328222i	$-0.106449\pi$
$101$	18.9862			1.88920			0.944601	+	0.328222i	$0.106449\pi$
$102$	−4.20153	−	19.1148i	−0.416014	−	1.89265i
$103$	−3.86411			−0.380742			−0.190371	−	0.981712i	$-0.560969\pi$
$103$	−3.86411			−0.380742			−0.190371	+	0.981712i	$0.560969\pi$
$104$		−	26.9034i		−	2.63810i
$105$	−0.371837	−	1.69167i	−0.0362876	−	0.165090i
$106$		−	28.3498i		−	2.75357i
$107$	6.64791			0.642678			0.321339	−	0.946964i	$-0.395867\pi$
$107$	6.64791			0.642678			0.321339	+	0.946964i	$0.395867\pi$
$108$	14.2859	+	18.8276i	1.37466	+	1.81168i
$109$		−	7.70444i		−	0.737952i	−0.929439	−	0.368976i	$-0.879709\pi$
$109$		−	7.70444i		−	0.737952i	0.929439	−	0.368976i	$-0.120291\pi$
$110$	2.22264	+	8.19096i	0.211921	+	0.780977i
$111$	−1.30124	−	5.91999i	−0.123509	−	0.561901i
$112$			7.59082i			0.717266i
$113$		−	16.8738i		−	1.58736i	−0.608338	−	0.793678i	$-0.708163\pi$
$113$		−	16.8738i		−	1.58736i	0.608338	−	0.793678i	$-0.291837\pi$
$114$	8.26416	−	1.81650i	0.774009	−	0.170131i
$115$	−0.792469			−0.0738981
$116$	10.4477			0.970040
$117$	−5.19014	−	11.2358i	−0.479829	−	1.03875i
$118$			4.70339i			0.432982i
$119$		−	4.41559i		−	0.404777i
$120$	11.0317	−	2.42481i	1.00705	−	0.221354i
$121$	9.49118	−	5.56035i	0.862834	−	0.505487i
$122$		−	29.0996i		−	2.63456i
$123$	−0.236838	−	1.07749i	−0.0213550	−	0.0971541i
$124$	47.8928			4.30090
$125$			1.00000i			0.0894427i
$126$	3.21931	+	6.96930i	0.286799	+	0.620875i
$127$		−	8.00679i		−	0.710488i	−0.934774	−	0.355244i	$-0.884398\pi$
$127$		−	8.00679i		−	0.710488i	0.934774	−	0.355244i	$-0.115602\pi$
$128$	9.82015			0.867987
$129$	−15.3998	+	3.38495i	−1.35587	+	0.298028i
$130$	−10.5572			−0.925926
$131$	−6.90004			−0.602859			−0.301430	−	0.953488i	$-0.597464\pi$
$131$	−6.90004			−0.602859			−0.301430	+	0.953488i	$0.597464\pi$
$132$	−12.0965	−	23.1595i	−1.05286	−	2.01578i
$133$	1.90905			0.165536
$134$	−24.3074			−2.09984
$135$	4.13942	−	3.14089i	0.356265	−	0.270325i
$136$	28.7949			2.46914
$137$		−	5.33519i		−	0.455816i	−0.973683	−	0.227908i	$-0.926811\pi$
$137$		−	5.33519i		−	0.455816i	0.973683	−	0.227908i	$-0.0731886\pi$
$138$	3.43055	−	0.754051i	0.292028	−	0.0641891i
$139$		−	11.8486i		−	1.00498i	−0.864582	−	0.502492i	$-0.832417\pi$
$139$		−	11.8486i		−	1.00498i	0.864582	−	0.502492i	$-0.167583\pi$
$140$	4.54836			0.384406
$141$	−0.569313	+	0.125138i	−0.0479448	+	0.0105385i
$142$		−	13.5183i		−	1.13443i
$143$	3.58332	+	13.2054i	0.299652	+	1.10429i
$144$	−20.6734	+	9.54962i	−1.72278	+	0.795802i
$145$		−	2.29702i		−	0.190757i
$146$			26.2403i			2.17166i
$147$	0.371837	+	1.69167i	0.0306686	+	0.139526i
$148$	15.9170			1.30837
$149$	−17.3474			−1.42115			−0.710577	−	0.703620i	$-0.751566\pi$
$149$	−17.3474			−1.42115			−0.710577	+	0.703620i	$0.751566\pi$
$150$	−0.951521	−	4.32893i	−0.0776914	−	0.353456i
$151$			12.5544i			1.02166i	0.859682	+	0.510830i	$0.170662\pi$
$151$			12.5544i			1.02166i	−0.859682	+	0.510830i	$0.829338\pi$
$152$			12.4493i			1.00977i
$153$	12.0258	−	5.55503i	0.972225	−	0.449097i
$154$	−2.22264	−	8.19096i	−0.179106	−	0.660046i
$155$		−	10.5297i		−	0.845766i
$156$	31.7432	−	6.97732i	2.54149	−	0.558633i
$157$	−6.91993			−0.552270			−0.276135	−	0.961119i	$-0.589054\pi$
$157$	−6.91993			−0.552270			−0.276135	+	0.961119i	$0.589054\pi$
$158$			11.5187i			0.916377i
$159$	18.7413	−	4.11942i	1.48628	−	0.326691i
$160$			6.38238i			0.504571i
$161$	0.792469			0.0624553
$162$	−14.9307	+	17.5354i	−1.17306	+	1.37771i
$163$	21.6705			1.69737			0.848684	−	0.528900i	$-0.177395\pi$
$163$	21.6705			1.69737			0.848684	+	0.528900i	$0.177395\pi$
$164$	2.89703			0.226220
$165$	−5.09185	+	2.65953i	−0.396400	+	0.207044i
$166$	−5.21705			−0.404921
$167$	−5.35232			−0.414175			−0.207088	−	0.978322i	$-0.566399\pi$
$167$	−5.35232			−0.414175			−0.207088	+	0.978322i	$0.566399\pi$
$168$	−11.0317	+	2.42481i	−0.851111	+	0.187078i
$169$	−4.02015			−0.309243
$170$		−	11.2994i		−	0.866624i
$171$	2.40168	+	5.19925i	0.183661	+	0.397597i
$172$		−	41.4051i		−	3.15711i
$173$	9.76385			0.742332			0.371166	−	0.928567i	$-0.378958\pi$
$173$	9.76385			0.742332			0.371166	+	0.928567i	$0.378958\pi$
$174$	2.18566	+	9.94364i	0.165695	+	0.753826i
$175$		−	1.00000i		−	0.0755929i
$176$	24.2973	−	6.59315i	1.83148	−	0.496977i
$177$	−3.10928	+	0.683435i	−0.233708	+	0.0513701i
$178$			15.9032i			1.19199i
$179$		−	14.0774i		−	1.05220i	−0.850424	−	0.526098i	$-0.823655\pi$
$179$		−	14.0774i		−	1.05220i	0.850424	−	0.526098i	$-0.176345\pi$
$180$	5.72205	+	12.3873i	0.426496	+	0.923297i
$181$	−23.8155			−1.77019			−0.885097	−	0.465406i	$-0.845908\pi$
$181$	−23.8155			−1.77019			−0.885097	+	0.465406i	$0.845908\pi$
$182$	10.5572			0.782550
$183$	19.2370	−	4.22838i	1.42204	−	0.312571i
$184$			5.16783i			0.380978i
$185$		−	3.49950i		−	0.257289i
$186$	10.0192	+	45.5824i	0.734646	+	3.34226i
$187$	−14.1338	+	3.83524i	−1.03356	+	0.280461i
$188$		−	1.53070i		−	0.111638i
$189$	−4.13942	+	3.14089i	−0.301099	+	0.228466i
$190$	4.88522			0.354411
$191$			24.8781i			1.80012i	0.435769	+	0.900058i	$0.356476\pi$
$191$			24.8781i			1.80012i	−0.435769	+	0.900058i	$0.643524\pi$
$192$	−0.427871	−	1.94660i	−0.0308790	−	0.140483i
$193$		−	5.80284i		−	0.417697i	−0.977948	−	0.208849i	$-0.933028\pi$
$193$		−	5.80284i		−	0.417697i	0.977948	−	0.208849i	$-0.0669716\pi$
$194$	−20.6676			−1.48385
$195$	−1.53403	−	6.97906i	−0.109854	−	0.499781i
$196$	−4.54836			−0.324883
$197$	24.7371			1.76244			0.881222	−	0.472703i	$-0.156722\pi$
$197$	24.7371			1.76244			0.881222	+	0.472703i	$0.156722\pi$
$198$	19.5117	−	16.3579i	1.38663	−	1.16251i
$199$	25.0595			1.77642			0.888212	−	0.459434i	$-0.151948\pi$
$199$	25.0595			1.77642			0.888212	+	0.459434i	$0.151948\pi$
$200$	6.52118			0.461117
$201$	−3.53204	−	16.0690i	−0.249131	−	1.13342i
$202$	−48.5853			−3.41845
$203$			2.29702i			0.161219i
$204$	7.46785	+	33.9749i	0.522854	+	2.37872i
$205$		−	0.636941i		−	0.0444859i
$206$	9.88816			0.688941
$207$	0.996965	+	2.15827i	0.0692938	+	0.150010i
$208$			31.3163i			2.17140i
$209$	−1.65814	−	6.11063i	−0.114696	−	0.422681i
$210$	0.951521	+	4.32893i	0.0656612	+	0.298725i
$211$		−	22.4060i		−	1.54249i	−0.636537	−	0.771246i	$-0.719634\pi$
$211$		−	22.4060i		−	1.54249i	0.636537	−	0.771246i	$-0.280366\pi$
$212$			50.3893i			3.46075i
$213$	8.93659	−	1.96431i	0.612325	−	0.134592i
$214$	−17.0118			−1.16291
$215$	−9.10331			−0.620841
$216$	−20.4823	−	26.9939i	−1.39364	−	1.83670i
$217$			10.5297i			0.714803i
$218$			19.7155i			1.33530i
$219$	−17.3467	+	3.81289i	−1.17218	+	0.257651i
$220$	−3.95056	−	14.5587i	−0.266347	−	0.981548i
$221$		−	18.2167i		−	1.22539i
$222$	3.32985	+	15.1491i	0.223485	+	1.01674i
$223$	−25.4543			−1.70454			−0.852272	−	0.523099i	$-0.824776\pi$
$223$	−25.4543			−1.70454			−0.852272	+	0.523099i	$0.824776\pi$
$224$		−	6.38238i		−	0.426441i
$225$	2.72347	−	1.25805i	0.181565	−	0.0838699i
$226$			43.1797i			2.87227i
$227$	−23.4749			−1.55808			−0.779041	−	0.626973i	$-0.784293\pi$
$227$	−23.4749			−1.55808			−0.779041	+	0.626973i	$0.784293\pi$
$228$	−14.6888	+	3.22868i	−0.972791	+	0.213824i
$229$	−21.3696			−1.41215			−0.706073	−	0.708139i	$-0.749535\pi$
$229$	−21.3696			−1.41215			−0.706073	+	0.708139i	$0.749535\pi$
$230$	2.02791			0.133716
$231$	5.09185	−	2.65953i	0.335019	−	0.174984i
$232$	−14.9793			−0.983437
$233$	8.44754			0.553417			0.276708	−	0.960954i	$-0.410756\pi$
$233$	8.44754			0.553417			0.276708	+	0.960954i	$0.410756\pi$
$234$	13.2814	+	28.7522i	0.868235	+	1.87959i
$235$	−0.336540			−0.0219534
$236$		−	8.35986i		−	0.544181i
$237$	−7.61467	+	1.67374i	−0.494626	+	0.108721i
$238$			11.2994i			0.732431i
$239$	−2.43920			−0.157779			−0.0788895	−	0.996883i	$-0.525137\pi$
$239$	−2.43920			−0.157779			−0.0788895	+	0.996883i	$0.525137\pi$
$240$	−12.8411	+	2.82255i	−0.828893	+	0.182195i
$241$		−	17.1869i		−	1.10710i	−0.832814	−	0.553552i	$-0.813272\pi$
$241$		−	17.1869i		−	1.10710i	0.832814	−	0.553552i	$-0.186728\pi$
$242$	−24.2877	+	14.2288i	−1.56127	+	0.914663i
$243$	−13.7617	−	7.32223i	−0.882815	−	0.469721i
$244$			51.7221i			3.31117i
$245$			1.00000i			0.0638877i
$246$	0.606063	+	2.75727i	0.0386411	+	0.175797i
$247$	7.87589			0.501131
$248$	−68.6660			−4.36030
$249$	−0.758073	−	3.44884i	−0.0480409	−	0.218562i
$250$		−	2.55898i		−	0.161844i
$251$			11.0401i			0.696842i	0.937338	+	0.348421i	$0.113282\pi$
$251$			11.0401i			0.696842i	−0.937338	+	0.348421i	$0.886718\pi$
$252$	−5.72205	−	12.3873i	−0.360455	−	0.780328i
$253$	−0.688314	−	2.53659i	−0.0432739	−	0.159474i
$254$			20.4892i			1.28561i
$255$	7.46971	−	1.64188i	0.467772	−	0.102819i
$256$	−27.4309			−1.71443
$257$			10.0091i			0.624352i	0.950024	+	0.312176i	$0.101058\pi$
$257$			10.0091i			0.624352i	−0.950024	+	0.312176i	$0.898942\pi$
$258$	39.4076	−	8.66200i	2.45341	−	0.539272i
$259$			3.49950i			0.217449i
$260$	18.7645			1.16372
$261$	−6.25587	+	2.88976i	−0.387229	+	0.178872i
$262$	17.6570			1.09085
$263$	11.0320			0.680263			0.340131	−	0.940378i	$-0.389528\pi$
$263$	11.0320			0.680263			0.340131	+	0.940378i	$0.389528\pi$
$264$	17.3433	+	33.2048i	1.06740	+	2.04362i
$265$	11.0786			0.680551
$266$	−4.88522			−0.299532
$267$	−10.5131	+	2.31084i	−0.643394	+	0.141421i
$268$	43.2043			2.63912
$269$		−	5.39984i		−	0.329234i	−0.986358	−	0.164617i	$-0.947361\pi$
$269$		−	5.39984i		−	0.329234i	0.986358	−	0.164617i	$-0.0526388\pi$
$270$	−10.5927	+	8.03745i	−0.644650	+	0.489144i
$271$			24.1117i			1.46468i	0.680939	+	0.732340i	$0.261572\pi$
$271$			24.1117i			1.46468i	−0.680939	+	0.732340i	$0.738428\pi$
$272$	−33.5180			−2.03233
$273$	1.53403	+	6.97906i	0.0928438	+	0.422392i
$274$			13.6526i			0.824785i
$275$	−3.20087	+	0.868568i	−0.193020	+	0.0523766i
$276$	−6.09750	+	1.34026i	−0.367026	+	0.0806742i
$277$		−	13.5369i		−	0.813351i	−0.913573	−	0.406675i	$-0.866688\pi$
$277$		−	13.5369i		−	0.813351i	0.913573	−	0.406675i	$-0.133312\pi$
$278$			30.3202i			1.81849i
$279$	−28.6774	+	13.2469i	−1.71687	+	0.793069i
$280$	−6.52118			−0.389715
$281$	15.9123			0.949249			0.474624	−	0.880188i	$-0.342584\pi$
$281$	15.9123			0.949249			0.474624	+	0.880188i	$0.342584\pi$
$282$	1.45686	−	0.320225i	0.0867547	−	0.0190691i
$283$			22.5091i			1.33803i	0.743251	+	0.669013i	$0.233283\pi$
$283$			22.5091i			1.33803i	−0.743251	+	0.669013i	$0.766717\pi$
$284$			24.0277i			1.42578i
$285$	0.709856	+	3.22948i	0.0420482	+	0.191298i
$286$	−9.16963	−	33.7922i	−0.542212	−	1.99817i
$287$			0.636941i			0.0375974i
$288$	17.3822	−	8.02934i	1.02426	−	0.473133i
$289$	2.49746			0.146909
$290$			5.87801i			0.345169i
$291$	−3.00315	−	13.6628i	−0.176048	−	0.800927i
$292$		−	46.6398i		−	2.72939i
$293$	9.27014			0.541567			0.270784	−	0.962640i	$-0.412717\pi$
$293$	9.27014			0.541567			0.270784	+	0.962640i	$0.412717\pi$
$294$	−0.951521	−	4.32893i	−0.0554939	−	0.252469i
$295$	−1.83800			−0.107012
$296$	−22.8209			−1.32644
$297$	13.6490	+	10.5217i	0.791993	+	0.610531i
$298$	44.3916			2.57153
$299$	3.26937			0.189073
$300$	1.69125	+	7.69430i	0.0976441	+	0.444231i
$301$	9.10331			0.524706
$302$		−	32.1263i		−	1.84866i
$303$	−7.05978	−	32.1184i	−0.405574	−	1.84515i
$304$		−	14.4913i		−	0.831132i
$305$	11.3716			0.651136
$306$	−30.7736	+	14.2152i	−1.75921	+	0.812628i
$307$			15.9859i			0.912364i	0.889886	+	0.456182i	$0.150783\pi$
$307$			15.9859i			0.912364i	−0.889886	+	0.456182i	$0.849217\pi$
$308$	3.95056	+	14.5587i	0.225104	+	0.829559i
$309$	1.43682	+	6.53679i	0.0817377	+	0.371865i
$310$			26.9452i			1.53039i
$311$		−	21.7034i		−	1.23069i	−0.788259	−	0.615343i	$-0.789017\pi$
$311$		−	21.7034i		−	1.23069i	0.788259	−	0.615343i	$-0.210983\pi$
$312$	−45.5117	+	10.0037i	−2.57659	+	0.566347i
$313$	1.26146			0.0713017			0.0356508	−	0.999364i	$-0.488650\pi$
$313$	1.26146			0.0713017			0.0356508	+	0.999364i	$0.488650\pi$
$314$	17.7079			0.999316
$315$	−2.72347	+	1.25805i	−0.153450	+	0.0708830i
$316$		−	20.4734i		−	1.15172i
$317$		−	11.7176i		−	0.658125i	−0.944308	−	0.329063i	$-0.893267\pi$
$317$		−	11.7176i		−	0.658125i	0.944308	−	0.329063i	$-0.106733\pi$
$318$	−47.9584	+	10.5415i	−2.68937	+	0.591138i
$319$	7.35246	−	1.99512i	0.411659	−	0.111705i
$320$		−	1.15070i		−	0.0643259i
$321$	−2.47194	−	11.2461i	−0.137970	−	0.627693i
$322$	−2.02791			−0.113011
$323$			8.42959i			0.469035i
$324$	26.5380	−	31.1677i	1.47433	−	1.73154i
$325$		−	4.12555i		−	0.228844i
$326$	−55.4544			−3.07133
$327$	−13.0333	+	2.86479i	−0.720746	+	0.158424i
$328$	−4.15360			−0.229344
$329$	0.336540			0.0185540
$330$	13.0299	−	6.80567i	0.717273	−	0.374640i
$331$	15.1588			0.833202			0.416601	−	0.909090i	$-0.363221\pi$
$331$	15.1588			0.833202			0.416601	+	0.909090i	$0.363221\pi$
$332$	9.27285			0.508914
$333$	−9.53081	+	4.40254i	−0.522285	+	0.241258i
$334$	13.6965			0.749437
$335$		−	9.49889i		−	0.518980i
$336$	12.8411	−	2.82255i	0.700542	−	0.153983i
$337$			6.79520i			0.370158i	0.982724	+	0.185079i	$0.0592541\pi$
$337$			6.79520i			0.370158i	−0.982724	+	0.185079i	$0.940746\pi$
$338$	10.2875			0.559565
$339$	−28.5449	+	6.27431i	−1.55035	+	0.340774i
$340$			20.0837i			1.08919i
$341$	33.7042	−	9.14576i	1.82519	−	0.495271i
$342$	−6.14584	−	13.3048i	−0.332329	−	0.719439i
$343$		−	1.00000i		−	0.0539949i
$344$			59.3643i			3.20071i
$345$	0.294669	+	1.34059i	0.0158645	+	0.0721752i
$346$	−24.9854			−1.34323
$347$	23.7883			1.27702			0.638511	−	0.769613i	$-0.279551\pi$
$347$	23.7883			1.27702			0.638511	+	0.769613i	$0.279551\pi$
$348$	−3.88482	−	17.6740i	−0.208248	−	0.947423i
$349$			22.0561i			1.18064i	0.807170	+	0.590319i	$0.200998\pi$
$349$			22.0561i			1.18064i	−0.807170	+	0.590319i	$0.799002\pi$
$350$			2.55898i			0.136783i
$351$	−17.0774	+	12.9579i	−0.911524	+	0.691641i
$352$	−20.4292	+	5.54353i	−1.08888	+	0.295471i
$353$			12.0179i			0.639648i	0.947477	+	0.319824i	$0.103624\pi$
$353$			12.0179i			0.639648i	−0.947477	+	0.319824i	$0.896376\pi$
$354$	7.95657	−	1.74889i	0.422887	−	0.0929526i
$355$	5.28271			0.280377
$356$		−	28.2665i		−	1.49812i
$357$	−7.46971	+	1.64188i	−0.395339	+	0.0868975i
$358$			36.0238i			1.90391i
$359$	13.6012			0.717844			0.358922	−	0.933368i	$-0.383144\pi$
$359$	13.6012			0.717844			0.358922	+	0.933368i	$0.383144\pi$
$360$	−8.20396	−	17.7603i	−0.432386	−	0.936048i
$361$	15.3555			0.808185
$362$	60.9434			3.20311
$363$	−12.9354	−	13.9884i	−0.678934	−	0.734199i
$364$	−18.7645			−0.983525
$365$	−10.2542			−0.536730
$366$	−49.2269	+	10.8203i	−2.57313	+	0.565587i
$367$	21.6869			1.13205			0.566023	−	0.824390i	$-0.308481\pi$
$367$	21.6869			1.13205			0.566023	+	0.824390i	$0.308481\pi$
$368$		−	6.01549i		−	0.313579i
$369$	−1.73469	+	0.801302i	−0.0903045	+	0.0417141i
$370$			8.95514i			0.465556i
$371$	−11.0786			−0.575171
$372$	−17.8083	−	81.0187i	−0.923318	−	4.20062i
$373$			12.9717i			0.671648i	0.941925	+	0.335824i	$0.109015\pi$
$373$			12.9717i			0.671648i	−0.941925	+	0.335824i	$0.890985\pi$
$374$	36.1679	−	9.81430i	1.87020	−	0.507485i
$375$	1.69167	−	0.371837i	0.0873573	−	0.0192016i
$376$			2.19464i			0.113180i
$377$			9.47646i			0.488063i
$378$	10.5927	−	8.03745i	0.544829	−	0.413402i
$379$	−9.57687			−0.491931			−0.245965	−	0.969279i	$-0.579105\pi$
$379$	−9.57687			−0.491931			−0.245965	+	0.969279i	$0.579105\pi$
$380$	−8.68304			−0.445431
$381$	−13.5448	+	2.97722i	−0.693923	+	0.152528i
$382$		−	63.6625i		−	3.25726i
$383$		−	0.168275i		−	0.00859844i	−0.999991	−	0.00429922i	$-0.998632\pi$
$383$		−	0.168275i		−	0.00859844i	0.999991	−	0.00429922i	$-0.00136849\pi$
$384$	−3.65149	−	16.6124i	−0.186339	−	0.847749i
$385$	3.20087	−	0.868568i	0.163132	−	0.0442663i
$386$			14.8493i			0.755810i
$387$	11.4524	+	24.7926i	0.582159	+	1.26028i
$388$	36.7349			1.86493
$389$		−	28.3042i		−	1.43508i	−0.696517	−	0.717540i	$-0.745268\pi$
$389$		−	28.3042i		−	1.43508i	0.696517	−	0.717540i	$-0.254732\pi$
$390$	3.92555	+	17.8592i	0.198778	+	0.904337i
$391$			3.49922i			0.176963i
$392$	6.52118			0.329369
$393$	2.56569	+	11.6726i	0.129422	+	0.588803i
$394$	−63.3016			−3.18909
$395$	−4.50128			−0.226484
$396$	−34.6803	+	29.0748i	−1.74275	+	1.46106i
$397$	−13.2260			−0.663796			−0.331898	−	0.943315i	$-0.607689\pi$
$397$	−13.2260			−0.663796			−0.331898	+	0.943315i	$0.607689\pi$
$398$	−64.1268			−3.21438
$399$	−0.709856	−	3.22948i	−0.0355372	−	0.161676i
$400$	−7.59082			−0.379541
$401$		−	19.3310i		−	0.965342i	−0.875802	−	0.482671i	$-0.839667\pi$
$401$		−	19.3310i		−	0.965342i	0.875802	−	0.482671i	$-0.160333\pi$
$402$	9.03839	+	41.1201i	0.450794	+	2.05088i
$403$			43.4408i			2.16394i
$404$	86.3562			4.29638
$405$	−6.85253	−	5.83463i	−0.340505	−	0.289925i
$406$		−	5.87801i		−	0.291721i
$407$	11.2015	−	3.03956i	0.555236	−	0.150665i
$408$	−10.7070	−	48.7113i	−0.530075	−	2.41157i
$409$			19.0008i			0.939527i	0.882792	+	0.469763i	$0.155661\pi$
$409$			19.0008i			0.939527i	−0.882792	+	0.469763i	$0.844339\pi$
$410$			1.62992i			0.0804958i
$411$	−9.02537	+	1.98382i	−0.445189	+	0.0978547i
$412$	−17.5753			−0.865875
$413$	1.83800			0.0904419
$414$	−2.55121	−	5.52296i	−0.125385	−	0.271439i
$415$		−	2.03873i		−	0.100077i
$416$		−	26.3308i		−	1.29097i
$417$	−20.0439	+	4.40574i	−0.981552	+	0.215750i
$418$	4.24314	+	15.6370i	0.207539	+	0.764829i
$419$			26.0672i			1.27347i	0.771084	+	0.636733i	$0.219715\pi$
$419$			26.0672i			1.27347i	−0.771084	+	0.636733i	$0.780285\pi$
$420$	−1.69125	−	7.69430i	−0.0825244	−	0.375444i
$421$	−0.329380			−0.0160530			−0.00802650	−	0.999968i	$-0.502555\pi$
$421$	−0.329380			−0.0160530			−0.00802650	+	0.999968i	$0.502555\pi$
$422$			57.3364i			2.79109i
$423$	0.423383	+	0.916557i	0.0205856	+	0.0445645i
$424$		−	72.2453i		−	3.50854i
$425$	4.41559			0.214188
$426$	−22.8685	+	5.02662i	−1.10798	+	0.243540i
$427$	−11.3716			−0.550310
$428$	30.2371			1.46156
$429$	21.0067	−	10.9720i	1.01421	−	0.529734i
$430$	23.2952			1.12339
$431$	−2.98340			−0.143705			−0.0718527	−	0.997415i	$-0.522891\pi$
$431$	−2.98340			−0.143705			−0.0718527	+	0.997415i	$0.522891\pi$
$432$	23.8419	+	31.4216i	1.14710	+	1.51177i
$433$	5.34476			0.256853			0.128427	−	0.991719i	$-0.459007\pi$
$433$	5.34476			0.256853			0.128427	+	0.991719i	$0.459007\pi$
$434$		−	26.9452i		−	1.29341i
$435$	−3.88579	+	0.854116i	−0.186309	+	0.0409517i
$436$		−	35.0425i		−	1.67823i
$437$	−1.51286			−0.0723701
$438$	44.3898	−	9.75710i	2.12103	−	0.466212i
$439$			15.6498i			0.746924i	0.927645	+	0.373462i	$0.121829\pi$
$439$			15.6498i			0.746924i	−0.927645	+	0.373462i	$0.878171\pi$
$440$	5.66409	+	20.8735i	0.270025	+	0.995103i
$441$	2.72347	−	1.25805i	0.129689	−	0.0599071i
$442$			46.6162i			2.21731i
$443$			24.8246i			1.17945i	0.807604	+	0.589725i	$0.200764\pi$
$443$			24.8246i			1.17945i	−0.807604	+	0.589725i	$0.799236\pi$
$444$	−5.91852	−	26.9262i	−0.280881	−	1.27786i
$445$	−6.21466			−0.294603
$446$	65.1368			3.08432
$447$	6.45040	+	29.3460i	0.305093	+	1.38802i
$448$			1.15070i			0.0543653i
$449$			22.4702i			1.06043i	0.847862	+	0.530217i	$0.177890\pi$
$449$			22.4702i			1.06043i	−0.847862	+	0.530217i	$0.822110\pi$
$450$	−6.96930	+	3.21931i	−0.328536	+	0.151760i
$451$	2.03877	−	0.553227i	0.0960018	−	0.0260504i
$452$		−	76.7482i		−	3.60993i
$453$	21.2378	−	4.66817i	0.997839	−	0.219330i
$454$	60.0716			2.81930
$455$			4.12555i			0.193409i
$456$	21.0600	−	4.62910i	0.986225	−	0.216777i
$457$		−	1.46651i		−	0.0686004i	−0.999412	−	0.0343002i	$-0.989080\pi$
$457$		−	1.46651i		−	0.0686004i	0.999412	−	0.0343002i	$-0.0109202\pi$
$458$	54.6844			2.55523
$459$	−13.8689	−	18.2780i	−0.647344	−	0.853144i
$460$	−3.60443			−0.168057
$461$	−0.929994			−0.0433141			−0.0216571	−	0.999765i	$-0.506894\pi$
$461$	−0.929994			−0.0433141			−0.0216571	+	0.999765i	$0.506894\pi$
$462$	−13.0299	+	6.80567i	−0.606206	+	0.316629i
$463$	−40.7326			−1.89301			−0.946503	−	0.322694i	$-0.895412\pi$
$463$	−40.7326			−1.89301			−0.946503	+	0.322694i	$0.895412\pi$
$464$	17.4363			0.809458
$465$	−17.8127	+	3.91533i	−0.826046	+	0.181569i
$466$	−21.6170			−1.00139
$467$		−	3.09122i		−	0.143045i	−0.997439	−	0.0715223i	$-0.977214\pi$
$467$		−	3.09122i		−	0.143045i	0.997439	−	0.0715223i	$-0.0227857\pi$
$468$	−23.6066	−	51.1045i	−1.09122	−	2.36231i
$469$			9.49889i			0.438618i
$470$	0.861197			0.0397240
$471$	2.57308	+	11.7062i	0.118561	+	0.539394i
$472$			11.9859i			0.551696i
$473$	−7.90685	−	29.1385i	−0.363557	−	1.33979i
$474$	19.4858	−	4.28307i	0.895011	−	0.196728i
$475$			1.90905i			0.0875933i
$476$		−	20.0837i		−	0.920534i
$477$	−13.9374	−	30.1722i	−0.638149	−	1.38149i
$478$	6.24186			0.285496
$479$	−22.0835			−1.00902			−0.504511	−	0.863405i	$-0.668327\pi$
$479$	−22.0835			−1.00902			−0.504511	+	0.863405i	$0.668327\pi$
$480$	10.7969	−	2.37320i	0.492807	−	0.108321i
$481$			14.4374i			0.658288i
$482$			43.9808i			2.00327i
$483$	−0.294669	−	1.34059i	−0.0134079	−	0.0609991i
$484$	43.1692	−	25.2905i	1.96224	−	1.14957i
$485$		−	8.07652i		−	0.366736i
$486$	35.2159	+	18.7374i	1.59743	+	0.849946i
$487$	40.9224			1.85437			0.927186	−	0.374602i	$-0.122221\pi$
$487$	40.9224			1.85437			0.927186	+	0.374602i	$0.122221\pi$
$488$		−	74.1562i		−	3.35689i
$489$	−8.05791	−	36.6593i	−0.364391	−	1.65779i
$490$		−	2.55898i		−	0.115603i
$491$	4.77855			0.215653			0.107826	−	0.994170i	$-0.465611\pi$
$491$	4.77855			0.215653			0.107826	+	0.994170i	$0.465611\pi$
$492$	−1.07722	−	4.90081i	−0.0485650	−	0.220946i
$493$	−10.1427			−0.456804
$494$	−20.1542			−0.906780
$495$	6.39238	+	7.62480i	0.287316	+	0.342709i
$496$	79.9291			3.58892
$497$	−5.28271			−0.236962
$498$	1.93989	+	8.82551i	0.0869286	+	0.395480i
$499$	−21.4538			−0.960406			−0.480203	−	0.877158i	$-0.659437\pi$
$499$	−21.4538			−0.960406			−0.480203	+	0.877158i	$0.659437\pi$
$500$			4.54836i			0.203409i
$501$	1.99019	+	9.05435i	0.0889152	+	0.404519i
$502$		−	28.2512i		−	1.26091i
$503$	40.4938			1.80553			0.902766	−	0.430133i	$-0.141533\pi$
$503$	40.4938			1.80553			0.902766	+	0.430133i	$0.141533\pi$
$504$	8.20396	+	17.7603i	0.365433	+	0.791105i
$505$		−	18.9862i		−	0.844877i
$506$	1.76138	+	6.49108i	0.0783028	+	0.288564i
$507$	1.49484	+	6.80076i	0.0663882	+	0.302032i
$508$		−	36.4177i		−	1.61578i
$509$		−	11.9679i		−	0.530468i	−0.964184	−	0.265234i	$-0.914551\pi$
$509$		−	11.9679i		−	0.530468i	0.964184	−	0.265234i	$-0.0854493\pi$
$510$	−19.1148	+	4.20153i	−0.846418	+	0.186047i
$511$	10.2542			0.453620
$512$	50.5547			2.23422
$513$	7.90237	−	5.99612i	0.348898	−	0.264735i
$514$		−	25.6131i		−	1.12974i
$515$			3.86411i			0.170273i
$516$	−70.0436	+	15.3959i	−3.08350	+	0.677769i
$517$	−0.292308	−	1.07722i	−0.0128557	−	0.0473761i
$518$		−	8.95514i		−	0.393466i
$519$	−3.63056	−	16.5172i	−0.159364	−	0.725024i
$520$	−26.9034			−1.17979
$521$		−	7.99723i		−	0.350365i	−0.984536	−	0.175182i	$-0.943948\pi$
$521$		−	7.99723i		−	0.350365i	0.984536	−	0.175182i	$-0.0560515\pi$
$522$	16.0086	−	7.39482i	0.700678	−	0.323663i
$523$		−	16.5727i		−	0.724673i	−0.932047	−	0.362336i	$-0.881979\pi$
$523$		−	16.5727i		−	0.724673i	0.932047	−	0.362336i	$-0.118021\pi$
$524$	−31.3838			−1.37101
$525$	−1.69167	+	0.371837i	−0.0738304	+	0.0162283i
$526$	−28.2306			−1.23091
$527$	−46.4949			−2.02535
$528$	−20.1880	−	38.6513i	−0.878571	−	1.68208i
$529$	22.3720			0.972695
$530$	−28.3498			−1.23144
$531$	2.31229	+	5.00574i	0.100345	+	0.217230i
$532$	8.68304			0.376458
$533$			2.62773i			0.113820i
$534$	26.9029	−	5.91338i	1.16420	−	0.255897i
$535$		−	6.64791i		−	0.287414i
$536$	−61.9439			−2.67557
$537$	−23.8143	+	5.23450i	−1.02766	+	0.225885i
$538$			13.8181i			0.595739i
$539$	−3.20087	+	0.868568i	−0.137871	+	0.0374119i
$540$	18.8276	−	14.2859i	0.810210	−	0.614766i
$541$			10.6523i			0.457977i	0.973429	+	0.228989i	$0.0735419\pi$
$541$			10.6523i			0.457977i	−0.973429	+	0.228989i	$0.926458\pi$
$542$		−	61.7012i		−	2.65029i
$543$	8.85549	+	40.2880i	0.380026	+	1.72892i
$544$	28.1820			1.20829
$545$	−7.70444			−0.330022
$546$	−3.92555	−	17.8592i	−0.167998	−	0.764305i
$547$		−	39.9870i		−	1.70972i	−0.518857	−	0.854861i	$-0.673642\pi$
$547$		−	39.9870i		−	1.70972i	0.518857	−	0.854861i	$-0.326358\pi$
$548$		−	24.2663i		−	1.03661i
$549$	−14.3060	−	30.9703i	−0.610566	−	1.32178i
$550$	8.19096	−	2.22264i	0.349264	−	0.0947739i
$551$		−	4.38513i		−	0.186813i
$552$	8.74225	−	1.92159i	0.372095	−	0.0817883i
$553$	4.50128			0.191414
$554$			34.6405i			1.47173i
$555$	−5.91999	+	1.30124i	−0.251290	+	0.0552347i
$556$		−	53.8916i		−	2.28551i
$557$	43.3992			1.83888			0.919441	−	0.393228i	$-0.128642\pi$
$557$	43.3992			1.83888			0.919441	+	0.393228i	$0.128642\pi$
$558$	73.3847	−	33.8984i	3.10662	−	1.43503i
$559$	37.5562			1.58846
$560$	7.59082			0.320771
$561$	11.7434	+	22.4835i	0.495807	+	0.949255i
$562$	−40.7192			−1.71764
$563$	26.1808			1.10339			0.551695	−	0.834046i	$-0.313981\pi$
$563$	26.1808			1.10339			0.551695	+	0.834046i	$0.313981\pi$
$564$	−2.58944	+	0.569171i	−0.109035	+	0.0239664i
$565$	−16.8738			−0.709887
$566$		−	57.6002i		−	2.42112i
$567$	6.85253	+	5.83463i	0.287779	+	0.245031i
$568$		−	34.4495i		−	1.44547i
$569$	−16.1198			−0.675778			−0.337889	−	0.941186i	$-0.609713\pi$
$569$	−16.1198			−0.675778			−0.337889	+	0.941186i	$0.609713\pi$
$570$	−1.81650	−	8.26416i	−0.0760849	−	0.346148i
$571$			30.5396i			1.27804i	0.769189	+	0.639021i	$0.220660\pi$
$571$			30.5396i			1.27804i	−0.769189	+	0.639021i	$0.779340\pi$
$572$	16.2982	+	60.0627i	0.681463	+	2.51135i
$573$	42.0855	−	9.25060i	1.75815	−	0.386449i
$574$		−	1.62992i		−	0.0680314i
$575$			0.792469i			0.0330483i
$576$	−3.13389	+	1.44763i	−0.130579	+	0.0603180i
$577$	−4.69062			−0.195273			−0.0976366	−	0.995222i	$-0.531128\pi$
$577$	−4.69062			−0.195273			−0.0976366	+	0.995222i	$0.531128\pi$
$578$	−6.39094			−0.265828
$579$	−9.81647	+	2.15771i	−0.407958	+	0.0896713i
$580$		−	10.4477i		−	0.433815i
$581$			2.03873i			0.0845806i
$582$	7.68498	+	34.9627i	0.318553	+	1.44925i
$583$	9.62249	+	35.4611i	0.398523	+	1.46865i
$584$			66.8695i			2.76708i
$585$	−11.2358	+	5.19014i	−0.464544	+	0.214586i
$586$	−23.7221			−0.979949
$587$			31.9490i			1.31868i	0.751847	+	0.659338i	$0.229163\pi$
$587$			31.9490i			1.31868i	−0.751847	+	0.659338i	$0.770837\pi$
$588$	1.69125	+	7.69430i	0.0697458	+	0.317308i
$589$		−	20.1017i		−	0.828278i
$590$	4.70339			0.193635
$591$	−9.19815	−	41.8469i	−0.378362	−	1.72135i
$592$	26.5641			1.09178
$593$	−6.44694			−0.264744			−0.132372	−	0.991200i	$-0.542259\pi$
$593$	−6.44694			−0.264744			−0.132372	+	0.991200i	$0.542259\pi$
$594$	−34.9273	−	26.9248i	−1.43309	−	1.10474i
$595$	−4.41559			−0.181022
$596$	−78.9021			−3.23196
$597$	−9.31806	−	42.3924i	−0.381363	−	1.73501i
$598$	−8.36624			−0.342121
$599$			36.0240i			1.47190i	0.677036	+	0.735950i	$0.263264\pi$
$599$			36.0240i			1.47190i	−0.677036	+	0.735950i	$0.736736\pi$
$600$	−2.42481	−	11.0317i	−0.0989926	−	0.450366i
$601$		−	35.4307i		−	1.44525i	−0.691240	−	0.722625i	$-0.742935\pi$
$601$		−	35.4307i		−	1.44525i	0.691240	−	0.722625i	$-0.257065\pi$
$602$	−23.2952			−0.949440
$603$	−25.8700	+	11.9501i	−1.05351	+	0.486644i
$604$			57.1017i			2.32344i
$605$	−5.56035	−	9.49118i	−0.226061	−	0.385871i
$606$	18.0658	+	82.1902i	0.733873	+	3.33875i
$607$		−	39.5684i		−	1.60603i	−0.595958	−	0.803016i	$-0.703227\pi$
$607$		−	39.5684i		−	1.60603i	0.595958	−	0.803016i	$-0.296773\pi$
$608$			12.1843i			0.494138i
$609$	3.88579	−	0.854116i	0.157460	−	0.0346105i
$610$	−29.0996			−1.17821
$611$	1.38841			0.0561691
$612$	54.6974	−	25.2662i	2.21101	−	1.02133i
$613$		−	10.8324i		−	0.437516i	−0.975779	−	0.218758i	$-0.929799\pi$
$613$		−	10.8324i		−	0.437516i	0.975779	−	0.218758i	$-0.0702005\pi$
$614$		−	40.9076i		−	1.65090i
$615$	−1.07749	+	0.236838i	−0.0434487	+	0.00955023i
$616$	−5.66409	−	20.8735i	−0.228213	−	0.841016i
$617$		−	26.0725i		−	1.04964i	−0.851213	−	0.524820i	$-0.824133\pi$
$617$		−	26.0725i		−	1.04964i	0.851213	−	0.524820i	$-0.175867\pi$
$618$	−3.67678	−	16.7275i	−0.147902	−	0.672878i
$619$	13.9488			0.560650			0.280325	−	0.959905i	$-0.409558\pi$
$619$	13.9488			0.560650			0.280325	+	0.959905i	$0.409558\pi$
$620$		−	47.8928i		−	1.92342i
$621$	3.28037	−	2.48906i	0.131637	−	0.0998824i
$622$			55.5385i			2.22689i
$623$	6.21466			0.248985
$624$	52.9768	−	11.6446i	2.12077	−	0.466156i
$625$	1.00000			0.0400000
$626$	−3.22803			−0.129018
$627$	−9.72060	+	5.07718i	−0.388203	+	0.202763i
$628$	−31.4743			−1.25596
$629$	−15.4524			−0.616127
$630$	6.96930	−	3.21931i	0.277664	−	0.128261i
$631$	36.8300			1.46618			0.733089	−	0.680133i	$-0.238078\pi$
$631$	36.8300			1.46618			0.733089	+	0.680133i	$0.238078\pi$
$632$			29.3537i			1.16763i
$633$	−37.9035	+	8.33137i	−1.50653	+	0.331142i
$634$			29.9850i			1.19086i
$635$	−8.00679			−0.317740
$636$	85.2419	−	18.7366i	3.38006	−	0.742954i
$637$		−	4.12555i		−	0.163460i
$638$	−18.8148	+	5.10546i	−0.744884	+	0.202127i
$639$	−6.64591	−	14.3873i	−0.262908	−	0.569154i
$640$		−	9.82015i		−	0.388175i
$641$		−	22.9376i		−	0.905982i	−0.891515	−	0.452991i	$-0.850357\pi$
$641$		−	22.9376i		−	0.905982i	0.891515	−	0.452991i	$-0.149643\pi$
$642$	6.32563	+	28.7784i	0.249653	+	1.13579i
$643$	−36.5524			−1.44149			−0.720743	−	0.693202i	$-0.756199\pi$
$643$	−36.5524			−1.44149			−0.720743	+	0.693202i	$0.756199\pi$
$644$	3.60443			0.142035
$645$	3.38495	+	15.3998i	0.133282	+	0.606366i
$646$		−	21.5711i		−	0.848705i
$647$			42.6396i			1.67634i	0.545412	+	0.838168i	$0.316373\pi$
$647$			42.6396i			1.67634i	−0.545412	+	0.838168i	$0.683627\pi$
$648$	−38.0487	+	44.6865i	−1.49469	+	1.75545i
$649$	−1.59643	−	5.88319i	−0.0626652	−	0.230936i
$650$			10.5572i			0.414087i
$651$	17.8127	−	3.91533i	0.698137	−	0.153454i
$652$	98.5653			3.86012
$653$			18.0040i			0.704551i	0.935896	+	0.352276i	$0.114592\pi$
$653$			18.0040i			0.704551i	−0.935896	+	0.352276i	$0.885408\pi$
$654$	33.3520	−	7.33094i	1.30417	−	0.286662i
$655$			6.90004i			0.269607i
$656$	4.83491			0.188771
$657$	12.9003	+	27.9271i	0.503288	+	1.08954i
$658$	−0.861197			−0.0335729
$659$	22.0916			0.860568			0.430284	−	0.902694i	$-0.358413\pi$
$659$	22.0916			0.860568			0.430284	+	0.902694i	$0.358413\pi$
$660$	−23.1595	+	12.0965i	−0.901483	+	0.470855i
$661$	31.2299			1.21470			0.607351	−	0.794433i	$-0.292232\pi$
$661$	31.2299			1.21470			0.607351	+	0.794433i	$0.292232\pi$
$662$	−38.7909			−1.50765
$663$	−30.8167	+	6.77366i	−1.19682	+	0.263067i
$664$	−13.2949			−0.515942
$665$		−	1.90905i		−	0.0740298i
$666$	24.3891	−	11.2660i	0.945059	−	0.436549i
$667$		−	1.82032i		−	0.0704829i
$668$	−24.3443			−0.941908
$669$	9.46483	+	43.0601i	0.365932	+	1.66480i
$670$			24.3074i			0.939077i
$671$	9.87701	+	36.3990i	0.381298	+	1.40517i
$672$	−10.7969	+	2.37320i	−0.416498	+	0.0915483i
$673$			38.2911i			1.47601i	0.674794	+	0.738006i	$0.264233\pi$
$673$			38.2911i			1.47601i	−0.674794	+	0.738006i	$0.735767\pi$
$674$		−	17.3887i		−	0.669790i
$675$	−3.14089	−	4.13942i	−0.120893	−	0.159326i
$676$	−18.2851			−0.703273
$677$	−10.5666			−0.406107			−0.203054	−	0.979168i	$-0.565087\pi$
$677$	−10.5666			−0.406107			−0.203054	+	0.979168i	$0.565087\pi$
$678$	73.0457	−	16.0558i	2.80530	−	0.616620i
$679$			8.07652i			0.309948i
$680$		−	28.7949i		−	1.10423i
$681$	8.72882	+	39.7116i	0.334489	+	1.52175i
$682$	−86.2483	+	23.4038i	−3.30262	+	0.896177i
$683$			17.1453i			0.656047i	0.944670	+	0.328024i	$0.106383\pi$
$683$			17.1453i			0.656047i	−0.944670	+	0.328024i	$0.893617\pi$
$684$	10.9237	+	23.6481i	0.417678	+	0.904206i
$685$	−5.33519			−0.203847
$686$			2.55898i			0.0977021i
$687$	7.94602	+	36.1503i	0.303159	+	1.37922i
$688$		−	69.1017i		−	2.63448i
$689$	−45.7052			−1.74123
$690$	−0.754051	−	3.43055i	−0.0287062	−	0.130599i
$691$	−23.6567			−0.899942			−0.449971	−	0.893043i	$-0.648566\pi$
$691$	−23.6567			−0.899942			−0.449971	+	0.893043i	$0.648566\pi$
$692$	44.4094			1.68819
$693$	−6.39238	−	7.62480i	−0.242826	−	0.289642i
$694$	−60.8736			−2.31073
$695$	−11.8486			−0.449442
$696$	5.56984	+	25.3399i	0.211124	+	0.960508i
$697$	−2.81247			−0.106530
$698$		−	56.4411i		−	2.13633i
$699$	−3.14111	−	14.2904i	−0.118808	−	0.540514i
$700$		−	4.54836i		−	0.171912i
$701$	9.06142			0.342245			0.171122	−	0.985250i	$-0.445261\pi$
$701$	9.06142			0.342245			0.171122	+	0.985250i	$0.445261\pi$
$702$	43.7006	−	33.1589i	1.64937	−	1.25150i
$703$		−	6.68073i		−	0.251969i
$704$	3.68323	−	0.999459i	0.138817	−	0.0376685i
$705$	0.125138	+	0.569313i	0.00471296	+	0.0214416i
$706$		−	30.7535i		−	1.15742i
$707$			18.9862i			0.714051i
$708$	−14.1421	+	3.10850i	−0.531493	+	0.116825i
$709$	13.4825			0.506347			0.253173	−	0.967421i	$-0.418526\pi$
$709$	13.4825			0.506347			0.253173	+	0.967421i	$0.418526\pi$
$710$	−13.5183			−0.507334
$711$	5.66283	+	12.2591i	0.212373	+	0.459753i
$712$			40.5269i			1.51881i
$713$		−	8.34446i		−	0.312503i
$714$	19.1148	−	4.20153i	0.715354	−	0.157238i
$715$	13.2054	−	3.58332i	0.493852	−	0.134009i
$716$		−	64.0291i		−	2.39288i
$717$	0.906985	+	4.12632i	0.0338720	+	0.154100i
$718$	−34.8052			−1.29892
$719$		−	35.4461i		−	1.32192i	−0.750423	−	0.660958i	$-0.770150\pi$
$719$		−	35.4461i		−	1.32192i	0.750423	−	0.660958i	$-0.229850\pi$
$720$	9.54962	+	20.6734i	0.355893	+	0.770453i
$721$		−	3.86411i		−	0.143907i
$722$	−39.2944			−1.46239
$723$	−29.0745	+	6.39072i	−1.08129	+	0.237673i
$724$	−108.322			−4.02574
$725$	−2.29702			−0.0853091
$726$	33.1015	+	35.7959i	1.22851	+	1.32851i
$727$	46.4312			1.72204			0.861020	−	0.508572i	$-0.169826\pi$
$727$	46.4312			1.72204			0.861020	+	0.508572i	$0.169826\pi$
$728$	26.9034			0.997108
$729$	−7.26966	+	26.0029i	−0.269247	+	0.963071i
$730$	26.2403			0.971196
$731$			40.1965i			1.48672i
$732$	87.4965	−	19.2322i	3.23396	−	0.710841i
$733$			38.0111i			1.40397i	0.712191	+	0.701985i	$0.247703\pi$
$733$			38.0111i			1.40397i	−0.712191	+	0.701985i	$0.752297\pi$
$734$	−55.4962			−2.04840
$735$	1.69167	−	0.371837i	0.0623981	−	0.0137154i
$736$			5.05784i			0.186434i
$737$	30.4047	−	8.25043i	1.11997	−	0.303909i
$738$	4.43903	−	2.05051i	0.163403	−	0.0754804i
$739$			3.91110i			0.143872i	0.997409	+	0.0719361i	$0.0229178\pi$
$739$			3.91110i			0.143872i	−0.997409	+	0.0719361i	$0.977082\pi$
$740$		−	15.9170i		−	0.585120i
$741$	−2.92854	−	13.3234i	−0.107583	−	0.489446i
$742$	28.3498			1.04075
$743$	−1.52807			−0.0560596			−0.0280298	−	0.999607i	$-0.508923\pi$
$743$	−1.52807			−0.0560596			−0.0280298	+	0.999607i	$0.508923\pi$
$744$	25.5326	+	116.160i	0.936069	+	4.25864i
$745$			17.3474i			0.635559i
$746$		−	33.1942i		−	1.21533i
$747$	−5.55242	+	2.56481i	−0.203152	+	0.0938417i
$748$	−64.2853	+	17.4441i	−2.35050	+	0.637818i
$749$			6.64791i			0.242909i
$750$	−4.32893	+	0.951521i	−0.158070	+	0.0347446i
$751$	25.7596			0.939982			0.469991	−	0.882671i	$-0.344257\pi$
$751$	25.7596			0.939982			0.469991	+	0.882671i	$0.344257\pi$
$752$		−	2.55461i		−	0.0931572i
$753$	18.6761	−	4.10510i	0.680595	−	0.149598i
$754$		−	24.2500i		−	0.883134i
$755$	12.5544			0.456900
$756$	−18.8276	+	14.2859i	−0.684752	+	0.519572i
$757$	−13.9743			−0.507903			−0.253951	−	0.967217i	$-0.581730\pi$
$757$	−13.9743			−0.507903			−0.253951	+	0.967217i	$0.581730\pi$
$758$	24.5070			0.890133
$759$	−4.03513	+	2.10760i	−0.146466	+	0.0765009i
$760$	12.4493			0.451582
$761$	−22.2794			−0.807628			−0.403814	−	0.914841i	$-0.632316\pi$
$761$	−22.2794			−0.807628			−0.403814	+	0.914841i	$0.632316\pi$
$762$	34.6609	−	7.61863i	1.25563	−	0.275994i
$763$	7.70444			0.278919
$764$			113.154i			4.09379i
$765$	−5.55503	−	12.0258i	−0.200842	−	0.434792i
$766$			0.430611i			0.0155586i
$767$	7.58274			0.273797
$768$	10.1998	+	46.4040i	0.368054	+	1.67446i
$769$			52.0944i			1.87857i	0.343136	+	0.939286i	$0.388511\pi$
$769$			52.0944i			1.87857i	−0.343136	+	0.939286i	$0.611489\pi$
$770$	−8.19096	+	2.22264i	−0.295182	+	0.0800986i
$771$	16.9321	−	3.72176i	0.609794	−	0.134036i
$772$		−	26.3934i		−	0.949918i
$773$		−	46.4183i		−	1.66955i	−0.550591	−	0.834775i	$-0.685598\pi$
$773$		−	46.4183i		−	1.66955i	0.550591	−	0.834775i	$-0.314402\pi$
$774$	−29.3064	−	63.4438i	−1.05340	−	2.28044i
$775$	−10.5297			−0.378238
$776$	−52.6684			−1.89069
$777$	5.91999	−	1.30124i	0.212379	−	0.0466819i
$778$			72.4298i			2.59673i
$779$		−	1.21595i		−	0.0435660i
$780$	−6.97732	−	31.7432i	−0.249828	−	1.13659i
$781$	4.58840	+	16.9093i	0.164186	+	0.605062i
$782$		−	8.95442i		−	0.320209i
$783$	7.21468	+	9.50833i	0.257831	+	0.339800i
$784$	−7.59082			−0.271101
$785$			6.91993i			0.246983i
$786$	−6.56553	−	29.8698i	−0.234185	−	1.06542i
$787$		−	19.6598i		−	0.700796i	−0.936601	−	0.350398i	$-0.886046\pi$
$787$		−	19.6598i		−	0.700796i	0.936601	−	0.350398i	$-0.113954\pi$
$788$	112.513			4.00811
$789$	−4.10211	−	18.6625i	−0.146039	−	0.664402i
$790$	11.5187			0.409816
$791$	16.8738			0.599964
$792$	49.7227	−	41.6858i	1.76682	−	1.48124i
$793$	−46.9141			−1.66597
$794$	33.8451			1.20112
$795$	−4.11942	−	18.7413i	−0.146101	−	0.664684i
$796$	113.980			4.03990
$797$			22.8636i			0.809870i	0.914345	+	0.404935i	$0.132706\pi$
$797$			22.8636i			0.809870i	−0.914345	+	0.404935i	$0.867294\pi$
$798$	1.81650	+	8.26416i	0.0643035	+	0.292548i
$799$			1.48602i			0.0525717i
$800$	6.38238			0.225651
$801$	7.81834	+	16.9255i	0.276248	+	0.598032i
$802$			49.4675i			1.74676i
$803$	−8.90648	−	32.8224i	−0.314303	−	1.15828i
$804$	−16.0650	−	73.0873i	−0.566567	−	2.57759i
$805$		−	0.792469i		−	0.0279309i
$806$		−	111.164i		−	3.91558i
$807$	−9.13474	+	2.00786i	−0.321558	+	0.0706800i
$808$	−123.813			−4.35571
$809$	1.26221			0.0443769			0.0221884	−	0.999754i	$-0.492937\pi$
$809$	1.26221			0.0443769			0.0221884	+	0.999754i	$0.492937\pi$
$810$	17.5354	+	14.9307i	0.616133	+	0.524610i
$811$			10.8242i			0.380089i	0.981775	+	0.190045i	$0.0608633\pi$
$811$			10.8242i			0.380089i	−0.981775	+	0.190045i	$0.939137\pi$
$812$			10.4477i			0.366641i
$813$	40.7890	−	8.96562i	1.43053	−	0.314438i
$814$	−28.6643	+	7.77815i	−1.00468	+	0.272624i
$815$		−	21.6705i		−	0.759086i
$816$	12.4632	+	56.7013i	0.436300	+	1.98494i
$817$	−17.3787			−0.608004
$818$		−	48.6225i		−	1.70004i
$819$	11.2358	−	5.19014i	0.392612	−	0.181358i
$820$		−	2.89703i		−	0.101169i
$821$	−51.7295			−1.80537			−0.902686	−	0.430300i	$-0.858408\pi$
$821$	−51.7295			−1.80537			−0.902686	+	0.430300i	$0.858408\pi$
$822$	23.0957	−	5.07655i	0.805555	−	0.177065i
$823$	−35.2859			−1.22999			−0.614995	−	0.788531i	$-0.710842\pi$
$823$	−35.2859			−1.22999			−0.614995	+	0.788531i	$0.710842\pi$
$824$	25.1985			0.877833
$825$	2.65953	+	5.09185i	0.0925930	+	0.177275i
$826$	−4.70339			−0.163652
$827$	−21.8184			−0.758701			−0.379350	−	0.925253i	$-0.623853\pi$
$827$	−21.8184			−0.758701			−0.379350	+	0.925253i	$0.623853\pi$
$828$	4.53455	+	9.81658i	0.157586	+	0.341150i
$829$	−20.2423			−0.703044			−0.351522	−	0.936180i	$-0.614336\pi$
$829$	−20.2423			−0.703044			−0.351522	+	0.936180i	$0.614336\pi$
$830$			5.21705i			0.181086i
$831$	−22.8998	+	5.03350i	−0.794387	+	0.174610i
$832$			4.74726i			0.164581i
$833$	4.41559			0.152991
$834$	51.2917	−	11.2742i	1.77609	−	0.390393i
$835$			5.35232i			0.185225i
$836$	−7.54182	−	27.7933i	−0.260839	−	0.961252i
$837$	33.0726	+	43.5869i	1.14316	+	1.50658i
$838$		−	66.7053i		−	2.30430i
$839$		−	32.0192i		−	1.10543i	−0.833371	−	0.552713i	$-0.813592\pi$
$839$		−	32.0192i		−	1.10543i	0.833371	−	0.552713i	$-0.186408\pi$
$840$	2.42481	+	11.0317i	0.0836640	+	0.380629i
$841$	−23.7237			−0.818059
$842$	0.842876			0.0290474
$843$	−5.91678	−	26.9183i	−0.203785	−	0.927116i
$844$		−	101.910i		−	3.50790i
$845$			4.02015i			0.138298i
$846$	−1.08343	−	2.34545i	−0.0372490	−	0.0806382i
$847$	5.56035	+	9.49118i	0.191056	+	0.326121i
$848$			84.0955i			2.88785i
$849$	38.0779	−	8.36970i	1.30683	−	0.287248i
$850$	−11.2994			−0.387566
$851$		−	2.77325i		−	0.0950657i
$852$	40.6468	−	8.93437i	1.39254	−	0.306086i
$853$		−	28.5458i		−	0.977389i	−0.872455	−	0.488695i	$-0.837473\pi$
$853$		−	28.5458i		−	0.977389i	0.872455	−	0.488695i	$-0.162527\pi$
$854$	29.0996			0.995769
$855$	5.19925	−	2.40168i	0.177811	−	0.0821357i
$856$	−43.3522			−1.48175
$857$	−14.0455			−0.479786			−0.239893	−	0.970799i	$-0.577112\pi$
$857$	−14.0455			−0.479786			−0.239893	+	0.970799i	$0.577112\pi$
$858$	−53.7555	+	28.0771i	−1.83518	+	0.958538i
$859$	−32.9270			−1.12346			−0.561728	−	0.827322i	$-0.689863\pi$
$859$	−32.9270			−1.12346			−0.561728	+	0.827322i	$0.689863\pi$
$860$	−41.4051			−1.41190
$861$	1.07749	−	0.236838i	0.0367208	−	0.00807142i
$862$	7.63445			0.260030
$863$			28.3845i			0.966219i	0.875560	+	0.483110i	$0.160493\pi$
$863$			28.3845i			0.966219i	−0.875560	+	0.483110i	$0.839507\pi$
$864$	−20.0463	−	26.4194i	−0.681990	−	0.898805i
$865$		−	9.76385i		−	0.331981i
$866$	−13.6771			−0.464768
$867$	−0.928648	−	4.22487i	−0.0315385	−	0.143484i
$868$			47.8928i			1.62559i
$869$	−3.90967	−	14.4080i	−0.132627	−	0.488759i
$870$	9.94364	−	2.18566i	0.337121	−	0.0741009i
$871$			39.1881i			1.32784i
$872$			50.2420i			1.70141i
$873$	−21.9962	+	10.1607i	−0.744459	+	0.343886i
$874$	3.87138			0.130951
$875$	−1.00000			−0.0338062
$876$	−78.8990	+	17.3424i	−2.66575	+	0.585945i
$877$		−	48.0391i		−	1.62216i	−0.584932	−	0.811082i	$-0.698879\pi$
$877$		−	48.0391i		−	1.62216i	0.584932	−	0.811082i	$-0.301121\pi$
$878$		−	40.0475i		−	1.35154i
$879$	−3.44698	−	15.6820i	−0.116264	−	0.528940i
$880$	−6.59315	−	24.2973i	−0.222255	−	0.819061i
$881$		−	5.72169i		−	0.192768i	−0.995344	−	0.0963842i	$-0.969272\pi$
$881$		−	5.72169i		−	0.192768i	0.995344	−	0.0963842i	$-0.0307278\pi$
$882$	−6.96930	+	3.21931i	−0.234669	+	0.108400i
$883$	−9.10238			−0.306319			−0.153160	−	0.988201i	$-0.548945\pi$
$883$	−9.10238			−0.306319			−0.153160	+	0.988201i	$0.548945\pi$
$884$		−	82.8562i		−	2.78676i
$885$	0.683435	+	3.10928i	0.0229734	+	0.104517i
$886$		−	63.5254i		−	2.13418i
$887$	−42.5047			−1.42717			−0.713584	−	0.700569i	$-0.752929\pi$
$887$	−42.5047			−1.42717			−0.713584	+	0.700569i	$0.752929\pi$
$888$	8.48565	+	38.6053i	0.284760	+	1.29551i
$889$	8.00679			0.268539
$890$	15.9032			0.533075
$891$	12.7240	−	27.0018i	0.426271	−	0.904596i
$892$	−115.775			−3.87644
$893$	−0.642472			−0.0214995
$894$	−16.5064	−	75.0957i	−0.552057	−	2.51158i
$895$	−14.0774			−0.470556
$896$			9.82015i			0.328068i
$897$	−1.21567	−	5.53069i	−0.0405901	−	0.184664i
$898$		−	57.5007i		−	1.91882i
$899$	24.1869			0.806679
$900$	12.3873	−	5.72205i	0.412911	−	0.190735i
$901$		−	48.9185i		−	1.62971i
$902$	−5.21715	+	1.41569i	−0.173712	+	0.0471374i
$903$	−3.38495	−	15.3998i	−0.112644	−	0.512472i
$904$			110.037i			3.65978i
$905$			23.8155i			0.791655i
$906$	−54.3470	+	11.9457i	−1.80556	+	0.396871i
$907$	27.5600			0.915114			0.457557	−	0.889180i	$-0.348725\pi$
$907$	27.5600			0.915114			0.457557	+	0.889180i	$0.348725\pi$
$908$	−106.772			−3.54335
$909$	−51.7085	+	23.8856i	−1.71506	+	0.792235i
$910$		−	10.5572i		−	0.349967i
$911$			47.7356i			1.58155i	0.612107	+	0.790775i	$0.290322\pi$
$911$			47.7356i			1.58155i	−0.612107	+	0.790775i	$0.709678\pi$
$912$	−24.5144	+	5.38839i	−0.811753	+	0.178427i
$913$	6.52570	−	1.77077i	0.215969	−	0.0586040i
$914$			3.75276i			0.124130i
$915$	−4.22838	−	19.2370i	−0.139786	−	0.635954i
$916$	−97.1967			−3.21147
$917$		−	6.90004i		−	0.227859i
$918$	35.4901	+	46.7730i	1.17135	+	1.54374i
$919$			11.7309i			0.386967i	0.981104	+	0.193484i	$0.0619786\pi$
$919$			11.7309i			0.386967i	−0.981104	+	0.193484i	$0.938021\pi$
$920$	5.16783			0.170378
$921$	27.0428	−	5.94415i	0.891092	−	0.195866i
$922$	2.37983			0.0783755
$923$	−21.7941			−0.717361
$924$	23.1595	−	12.0965i	0.761892	−	0.397945i
$925$	−3.49950			−0.115063
$926$	104.234			3.42534
$927$	10.5238	−	4.86124i	0.345647	−	0.159664i
$928$	−14.6604			−0.481252
$929$			27.4069i			0.899190i	0.893233	+	0.449595i	$0.148432\pi$
$929$			27.4069i			0.899190i	−0.893233	+	0.449595i	$0.851568\pi$
$930$	45.5824	−	10.0192i	1.49471	−	0.328544i
$931$			1.90905i			0.0625666i
$932$	38.4224			1.25857
$933$	−36.7149	+	8.07012i	−1.20199	+	0.264204i
$934$			7.91036i			0.258835i
$935$	3.83524	+	14.1338i	0.125426	+	0.462223i
$936$	33.8458	+	73.2708i	1.10629	+	2.39493i
$937$		−	14.0906i		−	0.460320i	−0.973153	−	0.230160i	$-0.926075\pi$
$937$		−	14.0906i		−	0.460320i	0.973153	−	0.230160i	$-0.0739250\pi$
$938$		−	24.3074i		−	0.793665i
$939$	−0.469056	−	2.13396i	−0.0153071	−	0.0696393i
$940$	−1.53070			−0.0499260
$941$	−0.151091			−0.00492544			−0.00246272	−	0.999997i	$-0.500784\pi$
$941$	−0.151091			−0.00492544			−0.00246272	+	0.999997i	$0.500784\pi$
$942$	−6.58446	−	29.9559i	−0.214533	−	0.976016i
$943$		−	0.504756i		−	0.0164371i
$944$		−	13.9519i		−	0.454096i
$945$	3.14089	+	4.13942i	0.102173	+	0.134655i
$946$	20.2334	+	74.5648i	0.657846	+	2.42431i
$947$		−	11.6819i		−	0.379609i	−0.981822	−	0.189805i	$-0.939215\pi$
$947$		−	11.6819i		−	0.379609i	0.981822	−	0.189805i	$-0.0607855\pi$
$948$	−34.6342	+	7.61278i	−1.12487	+	0.247252i
$949$	42.3042			1.37325
$950$		−	4.88522i		−	0.158497i
$951$	−19.8223	+	4.35703i	−0.642781	+	0.141286i
$952$			28.7949i			0.933247i
$953$	0.945931			0.0306417			0.0153208	−	0.999883i	$-0.495123\pi$
$953$	0.945931			0.0306417			0.0153208	+	0.999883i	$0.495123\pi$
$954$	35.6654	+	77.2099i	1.15471	+	2.49976i
$955$	24.8781			0.805037
$956$	−11.0944			−0.358817
$957$	−6.10899	−	11.6961i	−0.197476	−	0.378080i
$958$	56.5112			1.82579
$959$	5.33519			0.172282
$960$	−1.94660	+	0.427871i	−0.0628261	+	0.0138095i
$961$	79.8746			2.57660
$962$		−	36.9449i		−	1.19115i
$963$	−18.1054	+	8.36339i	−0.583439	+	0.269507i
$964$		−	78.1721i		−	2.51775i
$965$	−5.80284			−0.186800
$966$	0.754051	+	3.43055i	0.0242612	+	0.110376i
$967$			15.4856i			0.497983i	0.968506	+	0.248992i	$0.0800992\pi$
$967$			15.4856i			0.497983i	−0.968506	+	0.248992i	$0.919901\pi$
$968$	−61.8937	+	36.2601i	−1.98934	+	1.16544i
$969$	14.2601	−	3.13443i	0.458099	−	0.100693i
$970$			20.6676i			0.663597i
$971$			0.644382i			0.0206792i	0.999947	+	0.0103396i	$0.00329126\pi$
$971$			0.644382i			0.0206792i	−0.999947	+	0.0103396i	$0.996709\pi$
$972$	−62.5932	−	33.3041i	−2.00768	−	1.06823i
$973$	11.8486			0.379848
$974$	−104.719			−3.35543
$975$	−6.97906	+	1.53403i	−0.223509	+	0.0491283i
$976$			86.3198i			2.76303i
$977$			22.6353i			0.724169i	0.932145	+	0.362084i	$0.117935\pi$
$977$			22.6353i			0.724169i	−0.932145	+	0.362084i	$0.882065\pi$
$978$	20.6200	+	93.8104i	0.659354	+	2.99972i
$979$	−5.39786	−	19.8923i	−0.172516	−	0.635762i
$980$			4.54836i			0.145292i
$981$	9.69256	+	20.9829i	0.309460	+	0.669931i
$982$	−12.2282			−0.390217
$983$		−	0.797624i		−	0.0254403i	−0.999919	−	0.0127201i	$-0.995951\pi$
$983$		−	0.797624i		−	0.0254403i	0.999919	−	0.0127201i	$-0.00404905\pi$
$984$	1.54446	+	7.02652i	0.0492357	+	0.223997i
$985$		−	24.7371i		−	0.788189i
$986$	25.9549			0.826573
$987$	−0.125138	−	0.569313i	−0.00398318	−	0.0181214i
$988$	35.8223			1.13966
$989$	−7.21410			−0.229395
$990$	−16.3579	−	19.5117i	−0.519889	−	0.620121i
$991$	−27.2323			−0.865061			−0.432530	−	0.901619i	$-0.642379\pi$
$991$	−27.2323			−0.865061			−0.432530	+	0.901619i	$0.642379\pi$
$992$	−67.2045			−2.13375
$993$	−5.63659	−	25.6436i	−0.178872	−	0.813775i
$994$	13.5183			0.428776
$995$		−	25.0595i		−	0.794441i
$996$	−3.44799	−	15.6866i	−0.109254	−	0.497048i
$997$			35.1209i			1.11229i	0.831085	+	0.556145i	$0.187720\pi$
$997$			35.1209i			1.11229i	−0.831085	+	0.556145i	$0.812280\pi$
$998$	54.8998			1.73782
$999$	10.9915	+	14.4859i	0.347757	+	0.458314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.l.e.1121.3	✓	40
3.2	odd	2		1155.2.l.f.1121.38	yes	40
11.10	odd	2		1155.2.l.f.1121.37	yes	40
33.32	even	2	inner	1155.2.l.e.1121.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.l.e.1121.3	✓	40	1.1	even	1	trivial
1155.2.l.e.1121.4	yes	40	33.32	even	2	inner
1155.2.l.f.1121.37	yes	40	11.10	odd	2
1155.2.l.f.1121.38	yes	40	3.2	odd	2

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.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.55898 q^{2} +(-0.371837 - 1.69167i) q^{3} +4.54836 q^{4} -1.00000i q^{5} +(0.951521 + 4.32893i) q^{6} +1.00000i q^{7} -6.52118 q^{8} +(-2.72347 + 1.25805i) q^{9} +O(q^{10})\)	\(q-2.55898 q^{2} +(-0.371837 - 1.69167i) q^{3} +4.54836 q^{4} -1.00000i q^{5} +(0.951521 + 4.32893i) q^{6} +1.00000i q^{7} -6.52118 q^{8} +(-2.72347 + 1.25805i) q^{9} +2.55898i q^{10} +(3.20087 - 0.868568i) q^{11} +(-1.69125 - 7.69430i) q^{12} +4.12555i q^{13} -2.55898i q^{14} +(-1.69167 + 0.371837i) q^{15} +7.59082 q^{16} -4.41559 q^{17} +(6.96930 - 3.21931i) q^{18} -1.90905i q^{19} -4.54836i q^{20} +(1.69167 - 0.371837i) q^{21} +(-8.19096 + 2.22264i) q^{22} -0.792469i q^{23} +(2.42481 + 11.0317i) q^{24} -1.00000 q^{25} -10.5572i q^{26} +(3.14089 + 4.13942i) q^{27} +4.54836i q^{28} +2.29702 q^{29} +(4.32893 - 0.951521i) q^{30} +10.5297 q^{31} -6.38238 q^{32} +(-2.65953 - 5.09185i) q^{33} +11.2994 q^{34} +1.00000 q^{35} +(-12.3873 + 5.72205i) q^{36} +3.49950 q^{37} +4.88522i q^{38} +(6.97906 - 1.53403i) q^{39} +6.52118i q^{40} +0.636941 q^{41} +(-4.32893 + 0.951521i) q^{42} -9.10331i q^{43} +(14.5587 - 3.95056i) q^{44} +(1.25805 + 2.72347i) q^{45} +2.02791i q^{46} -0.336540i q^{47} +(-2.82255 - 12.8411i) q^{48} -1.00000 q^{49} +2.55898 q^{50} +(1.64188 + 7.46971i) q^{51} +18.7645i q^{52} +11.0786i q^{53} +(-8.03745 - 10.5927i) q^{54} +(-0.868568 - 3.20087i) q^{55} -6.52118i q^{56} +(-3.22948 + 0.709856i) q^{57} -5.87801 q^{58} -1.83800i q^{59} +(-7.69430 + 1.69125i) q^{60} +11.3716i q^{61} -26.9452 q^{62} +(-1.25805 - 2.72347i) q^{63} +1.15070 q^{64} +4.12555 q^{65} +(6.80567 + 13.0299i) q^{66} +9.49889 q^{67} -20.0837 q^{68} +(-1.34059 + 0.294669i) q^{69} -2.55898 q^{70} +5.28271i q^{71} +(17.7603 - 8.20396i) q^{72} -10.2542i q^{73} -8.95514 q^{74} +(0.371837 + 1.69167i) q^{75} -8.68304i q^{76} +(0.868568 + 3.20087i) q^{77} +(-17.8592 + 3.92555i) q^{78} -4.50128i q^{79} -7.59082i q^{80} +(5.83463 - 6.85253i) q^{81} -1.62992 q^{82} +2.03873 q^{83} +(7.69430 - 1.69125i) q^{84} +4.41559i q^{85} +23.2952i q^{86} +(-0.854116 - 3.88579i) q^{87} +(-20.8735 + 5.66409i) q^{88} -6.21466i q^{89} +(-3.21931 - 6.96930i) q^{90} -4.12555 q^{91} -3.60443i q^{92} +(-3.91533 - 17.8127i) q^{93} +0.861197i q^{94} -1.90905 q^{95} +(2.37320 + 10.7969i) q^{96} +8.07652 q^{97} +2.55898 q^{98} +(-7.62480 + 6.39238i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9	\( 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9} - 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} + 40 q^{18} - 2 q^{21} - 4 q^{22} - 12 q^{24} - 40 q^{25} + 32 q^{27} - 24 q^{29} - 8 q^{31} + 52 q^{32} - 16 q^{33} + 32 q^{34} + 40 q^{35} - 48 q^{37} + 66 q^{39} - 16 q^{41} + 32 q^{44} + 32 q^{48} - 40 q^{49} + 4 q^{50} - 14 q^{51} - 72 q^{54} + 8 q^{55} - 24 q^{57} - 80 q^{58} + 24 q^{60} + 48 q^{62} + 76 q^{64} + 4 q^{65} - 76 q^{66} - 48 q^{67} - 32 q^{68} - 20 q^{69} - 4 q^{70} + 128 q^{72} + 4 q^{75} - 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} - 24 q^{83} - 24 q^{84} - 32 q^{87} - 16 q^{88} + 8 q^{90} - 4 q^{91} - 20 q^{93} - 12 q^{95} + 12 q^{96} + 100 q^{97} + 4 q^{98} - 54 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9 - 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 + 40 * q^18 - 2 * q^21 - 4 * q^22 - 12 * q^24 - 40 * q^25 + 32 * q^27 - 24 * q^29 - 8 * q^31 + 52 * q^32 - 16 * q^33 + 32 * q^34 + 40 * q^35 - 48 * q^37 + 66 * q^39 - 16 * q^41 + 32 * q^44 + 32 * q^48 - 40 * q^49 + 4 * q^50 - 14 * q^51 - 72 * q^54 + 8 * q^55 - 24 * q^57 - 80 * q^58 + 24 * q^60 + 48 * q^62 + 76 * q^64 + 4 * q^65 - 76 * q^66 - 48 * q^67 - 32 * q^68 - 20 * q^69 - 4 * q^70 + 128 * q^72 + 4 * q^75 - 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 - 24 * q^83 - 24 * q^84 - 32 * q^87 - 16 * q^88 + 8 * q^90 - 4 * q^91 - 20 * q^93 - 12 * q^95 + 12 * q^96 + 100 * q^97 + 4 * q^98 - 54 * q^99

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