LMFDB - Embedded newform 1155.2.c.d.694.3

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:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			694.3
Root			$-0.854638 + 0.854638i$ of defining polynomial
Character	$\chi$	$=$	1155.694
Dual form			1155.2.c.d.694.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.539189i q^{2} +1.00000i q^{3} +1.70928 q^{4} +(2.17009 + 0.539189i) q^{5} +0.539189 q^{6} -1.00000i q^{7} -2.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-0.539189i q^{2} +1.00000i q^{3} +1.70928 q^{4} +(2.17009 + 0.539189i) q^{5} +0.539189 q^{6} -1.00000i q^{7} -2.00000i q^{8} -1.00000 q^{9} +(0.290725 - 1.17009i) q^{10} +1.00000 q^{11} +1.70928i q^{12} -0.829914i q^{13} -0.539189 q^{14} +(-0.539189 + 2.17009i) q^{15} +2.34017 q^{16} -1.63090i q^{17} +0.539189i q^{18} +1.92162 q^{19} +(3.70928 + 0.921622i) q^{20} +1.00000 q^{21} -0.539189i q^{22} -4.70928i q^{23} +2.00000 q^{24} +(4.41855 + 2.34017i) q^{25} -0.447480 q^{26} -1.00000i q^{27} -1.70928i q^{28} +5.82991 q^{29} +(1.17009 + 0.290725i) q^{30} -3.95774 q^{31} -5.26180i q^{32} +1.00000i q^{33} -0.879362 q^{34} +(0.539189 - 2.17009i) q^{35} -1.70928 q^{36} +1.51026i q^{37} -1.03612i q^{38} +0.829914 q^{39} +(1.07838 - 4.34017i) q^{40} -8.24846 q^{41} -0.539189i q^{42} +5.43188i q^{43} +1.70928 q^{44} +(-2.17009 - 0.539189i) q^{45} -2.53919 q^{46} +6.72261i q^{47} +2.34017i q^{48} -1.00000 q^{49} +(1.26180 - 2.38243i) q^{50} +1.63090 q^{51} -1.41855i q^{52} +2.26180i q^{53} -0.539189 q^{54} +(2.17009 + 0.539189i) q^{55} -2.00000 q^{56} +1.92162i q^{57} -3.14342i q^{58} -8.21953 q^{59} +(-0.921622 + 3.70928i) q^{60} +9.38962 q^{61} +2.13397i q^{62} +1.00000i q^{63} +1.84324 q^{64} +(0.447480 - 1.80098i) q^{65} +0.539189 q^{66} +13.5174i q^{67} -2.78765i q^{68} +4.70928 q^{69} +(-1.17009 - 0.290725i) q^{70} +0.248464 q^{71} +2.00000i q^{72} -2.92162i q^{73} +0.814315 q^{74} +(-2.34017 + 4.41855i) q^{75} +3.28458 q^{76} -1.00000i q^{77} -0.447480i q^{78} +0.0422604 q^{79} +(5.07838 + 1.26180i) q^{80} +1.00000 q^{81} +4.44748i q^{82} -6.70928i q^{83} +1.70928 q^{84} +(0.879362 - 3.53919i) q^{85} +2.92881 q^{86} +5.82991i q^{87} -2.00000i q^{88} -8.08557 q^{89} +(-0.290725 + 1.17009i) q^{90} -0.829914 q^{91} -8.04945i q^{92} -3.95774i q^{93} +3.62475 q^{94} +(4.17009 + 1.03612i) q^{95} +5.26180 q^{96} +14.0856i q^{97} +0.539189i q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{4} + 2 q^{5} - 6 q^{9}+O(q^{10}) $ 6 * q - 4 * q^4 + 2 * q^5 - 6 * q^9	$ 6 q - 4 q^{4} + 2 q^{5} - 6 q^{9} + 16 q^{10} + 6 q^{11} - 8 q^{16} + 18 q^{19} + 8 q^{20} + 6 q^{21} + 12 q^{24} - 2 q^{25} - 4 q^{26} + 46 q^{29} - 4 q^{30} + 8 q^{31} + 20 q^{34} + 4 q^{36} + 16 q^{39} - 32 q^{41} - 4 q^{44} - 2 q^{45} - 12 q^{46} - 6 q^{49} - 8 q^{50} + 2 q^{51} + 2 q^{55} - 12 q^{56} - 2 q^{59} - 12 q^{60} - 2 q^{61} + 24 q^{64} + 4 q^{65} + 14 q^{69} + 4 q^{70} - 16 q^{71} - 12 q^{74} + 8 q^{75} - 36 q^{76} + 32 q^{79} + 24 q^{80} + 6 q^{81} - 4 q^{84} - 20 q^{85} - 44 q^{86} + 26 q^{89} - 16 q^{90} - 16 q^{91} - 56 q^{94} + 14 q^{95} + 16 q^{96} - 6 q^{99}+O(q^{100}) $ 6 * q - 4 * q^4 + 2 * q^5 - 6 * q^9 + 16 * q^10 + 6 * q^11 - 8 * q^16 + 18 * q^19 + 8 * q^20 + 6 * q^21 + 12 * q^24 - 2 * q^25 - 4 * q^26 + 46 * q^29 - 4 * q^30 + 8 * q^31 + 20 * q^34 + 4 * q^36 + 16 * q^39 - 32 * q^41 - 4 * q^44 - 2 * q^45 - 12 * q^46 - 6 * q^49 - 8 * q^50 + 2 * q^51 + 2 * q^55 - 12 * q^56 - 2 * q^59 - 12 * q^60 - 2 * q^61 + 24 * q^64 + 4 * q^65 + 14 * q^69 + 4 * q^70 - 16 * q^71 - 12 * q^74 + 8 * q^75 - 36 * q^76 + 32 * q^79 + 24 * q^80 + 6 * q^81 - 4 * q^84 - 20 * q^85 - 44 * q^86 + 26 * q^89 - 16 * q^90 - 16 * q^91 - 56 * q^94 + 14 * q^95 + 16 * q^96 - 6 * 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 $

$2$		−	0.539189i		−	0.381264i	−0.981662	−	0.190632i	$-0.938946\pi$
$2$		−	0.539189i		−	0.381264i	0.981662	−	0.190632i	$-0.0610537\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.70928			0.854638
$5$	2.17009	+	0.539189i	0.970492	+	0.241133i
$5$	2.17009	+	0.539189i	0.970492	+	0.241133i
$6$	0.539189			0.220123
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	2.00000i		−	0.707107i
$9$	−1.00000			−0.333333
$10$	0.290725	−	1.17009i	0.0919352	−	0.370014i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$			1.70928i			0.493425i
$13$		−	0.829914i		−	0.230177i	−0.993355	−	0.115088i	$-0.963285\pi$
$13$		−	0.829914i		−	0.230177i	0.993355	−	0.115088i	$-0.0367151\pi$
$14$	−0.539189			−0.144104
$15$	−0.539189	+	2.17009i	−0.139218	+	0.560314i
$16$	2.34017			0.585043
$17$		−	1.63090i		−	0.395551i	−0.980247	−	0.197775i	$-0.936628\pi$
$17$		−	1.63090i		−	0.395551i	0.980247	−	0.197775i	$-0.0633717\pi$
$18$			0.539189i			0.127088i
$19$	1.92162			0.440850			0.220425	−	0.975404i	$-0.429256\pi$
$19$	1.92162			0.440850			0.220425	+	0.975404i	$0.429256\pi$
$20$	3.70928	+	0.921622i	0.829419	+	0.206081i
$21$	1.00000			0.218218
$22$		−	0.539189i		−	0.114955i
$23$		−	4.70928i		−	0.981952i	−0.871173	−	0.490976i	$-0.836640\pi$
$23$		−	4.70928i		−	0.981952i	0.871173	−	0.490976i	$-0.163360\pi$
$24$	2.00000			0.408248
$25$	4.41855	+	2.34017i	0.883710	+	0.468035i
$26$	−0.447480			−0.0877581
$27$		−	1.00000i		−	0.192450i
$28$		−	1.70928i		−	0.323023i
$29$	5.82991			1.08259			0.541294	−	0.840833i	$-0.317935\pi$
$29$	5.82991			1.08259			0.541294	+	0.840833i	$0.317935\pi$
$30$	1.17009	+	0.290725i	0.213628	+	0.0530788i
$31$	−3.95774			−0.710831			−0.355416	−	0.934708i	$-0.615661\pi$
$31$	−3.95774			−0.710831			−0.355416	+	0.934708i	$0.615661\pi$
$32$		−	5.26180i		−	0.930163i
$33$			1.00000i			0.174078i
$34$	−0.879362			−0.150809
$35$	0.539189	−	2.17009i	0.0911396	−	0.366812i
$36$	−1.70928			−0.284879
$37$			1.51026i			0.248285i	0.992264	+	0.124143i	$0.0396180\pi$
$37$			1.51026i			0.248285i	−0.992264	+	0.124143i	$0.960382\pi$
$38$		−	1.03612i		−	0.168080i
$39$	0.829914			0.132893
$40$	1.07838	−	4.34017i	0.170506	−	0.686242i
$41$	−8.24846			−1.28819			−0.644097	−	0.764944i	$-0.722767\pi$
$41$	−8.24846			−1.28819			−0.644097	+	0.764944i	$0.722767\pi$
$42$		−	0.539189i		−	0.0831986i
$43$			5.43188i			0.828354i	0.910196	+	0.414177i	$0.135931\pi$
$43$			5.43188i			0.828354i	−0.910196	+	0.414177i	$0.864069\pi$
$44$	1.70928			0.257683
$45$	−2.17009	−	0.539189i	−0.323497	−	0.0803775i
$46$	−2.53919			−0.374383
$47$			6.72261i			0.980593i	0.871556	+	0.490296i	$0.163111\pi$
$47$			6.72261i			0.980593i	−0.871556	+	0.490296i	$0.836889\pi$
$48$			2.34017i			0.337775i
$49$	−1.00000			−0.142857
$50$	1.26180	−	2.38243i	0.178445	−	0.336927i
$51$	1.63090			0.228371
$52$		−	1.41855i		−	0.196718i
$53$			2.26180i			0.310681i	0.987861	+	0.155341i	$0.0496475\pi$
$53$			2.26180i			0.310681i	−0.987861	+	0.155341i	$0.950352\pi$
$54$	−0.539189			−0.0733743
$55$	2.17009	+	0.539189i	0.292614	+	0.0727042i
$56$	−2.00000			−0.267261
$57$			1.92162i			0.254525i
$58$		−	3.14342i		−	0.412752i
$59$	−8.21953			−1.07009			−0.535046	−	0.844823i	$-0.679706\pi$
$59$	−8.21953			−1.07009			−0.535046	+	0.844823i	$0.679706\pi$
$60$	−0.921622	+	3.70928i	−0.118981	+	0.478865i
$61$	9.38962			1.20222			0.601109	−	0.799167i	$-0.294726\pi$
$61$	9.38962			1.20222			0.601109	+	0.799167i	$0.294726\pi$
$62$			2.13397i			0.271014i
$63$			1.00000i			0.125988i
$64$	1.84324			0.230406
$65$	0.447480	−	1.80098i	0.0555031	−	0.223385i
$66$	0.539189			0.0663696
$67$			13.5174i			1.65142i	0.564096	+	0.825710i	$0.309225\pi$
$67$			13.5174i			1.65142i	−0.564096	+	0.825710i	$0.690775\pi$
$68$		−	2.78765i		−	0.338053i
$69$	4.70928			0.566930
$70$	−1.17009	−	0.290725i	−0.139852	−	0.0347482i
$71$	0.248464			0.0294873			0.0147436	−	0.999891i	$-0.495307\pi$
$71$	0.248464			0.0294873			0.0147436	+	0.999891i	$0.495307\pi$
$72$			2.00000i			0.235702i
$73$		−	2.92162i		−	0.341950i	−0.985275	−	0.170975i	$-0.945308\pi$
$73$		−	2.92162i		−	0.341950i	0.985275	−	0.170975i	$-0.0546917\pi$
$74$	0.814315			0.0946622
$75$	−2.34017	+	4.41855i	−0.270220	+	0.510210i
$76$	3.28458			0.376767
$77$		−	1.00000i		−	0.113961i
$78$		−	0.447480i		−	0.0506671i
$79$	0.0422604			0.00475467			0.00237733	−	0.999997i	$-0.499243\pi$
$79$	0.0422604			0.00475467			0.00237733	+	0.999997i	$0.499243\pi$
$80$	5.07838	+	1.26180i	0.567780	+	0.141073i
$81$	1.00000			0.111111
$82$			4.44748i			0.491142i
$83$		−	6.70928i		−	0.736439i	−0.929739	−	0.368219i	$-0.879968\pi$
$83$		−	6.70928i		−	0.736439i	0.929739	−	0.368219i	$-0.120032\pi$
$84$	1.70928			0.186497
$85$	0.879362	−	3.53919i	0.0953802	−	0.383879i
$86$	2.92881			0.315822
$87$			5.82991i			0.625032i
$88$		−	2.00000i		−	0.213201i
$89$	−8.08557			−0.857068			−0.428534	−	0.903526i	$-0.640970\pi$
$89$	−8.08557			−0.857068			−0.428534	+	0.903526i	$0.640970\pi$
$90$	−0.290725	+	1.17009i	−0.0306451	+	0.123338i
$91$	−0.829914			−0.0869986
$92$		−	8.04945i		−	0.839213i
$93$		−	3.95774i		−	0.410398i
$94$	3.62475			0.373865
$95$	4.17009	+	1.03612i	0.427842	+	0.106303i
$96$	5.26180			0.537030
$97$			14.0856i			1.43017i	0.699036	+	0.715086i	$0.253613\pi$
$97$			14.0856i			1.43017i	−0.699036	+	0.715086i	$0.746387\pi$
$98$			0.539189i			0.0544663i
$99$	−1.00000			−0.100504
$100$	7.55252	+	4.00000i	0.755252	+	0.400000i
$101$	−4.52359			−0.450114			−0.225057	−	0.974346i	$-0.572257\pi$
$101$	−4.52359			−0.450114			−0.225057	+	0.974346i	$0.572257\pi$
$102$		−	0.879362i		−	0.0870698i
$103$			7.58864i			0.747731i	0.927483	+	0.373865i	$0.121968\pi$
$103$			7.58864i			0.747731i	−0.927483	+	0.373865i	$0.878032\pi$
$104$	−1.65983			−0.162759
$105$	2.17009	+	0.539189i	0.211779	+	0.0526194i
$106$	1.21953			0.118452
$107$		−	14.3968i		−	1.39179i	−0.718143	−	0.695896i	$-0.755007\pi$
$107$		−	14.3968i		−	1.39179i	0.718143	−	0.695896i	$-0.244993\pi$
$108$		−	1.70928i		−	0.164475i
$109$	−0.963883			−0.0923232			−0.0461616	−	0.998934i	$-0.514699\pi$
$109$	−0.963883			−0.0923232			−0.0461616	+	0.998934i	$0.514699\pi$
$110$	0.290725	−	1.17009i	0.0277195	−	0.111563i
$111$	−1.51026			−0.143347
$112$		−	2.34017i		−	0.221126i
$113$		−	6.89269i		−	0.648410i	−0.945987	−	0.324205i	$-0.894903\pi$
$113$		−	6.89269i		−	0.648410i	0.945987	−	0.324205i	$-0.105097\pi$
$114$	1.03612			0.0970413
$115$	2.53919	−	10.2195i	0.236781	−	0.952977i
$116$	9.96493			0.925220
$117$			0.829914i			0.0767255i
$118$			4.43188i			0.407988i
$119$	−1.63090			−0.149504
$120$	4.34017	+	1.07838i	0.396202	+	0.0984420i
$121$	1.00000			0.0909091
$122$		−	5.06278i		−	0.458363i
$123$		−	8.24846i		−	0.743739i
$124$	−6.76487			−0.607503
$125$	8.32684	+	7.46081i	0.744775	+	0.667315i
$126$	0.539189			0.0480348
$127$		−	10.6442i		−	0.944523i	−0.881459	−	0.472261i	$-0.843438\pi$
$127$		−	10.6442i		−	0.944523i	0.881459	−	0.472261i	$-0.156562\pi$
$128$		−	11.5174i		−	1.01801i
$129$	−5.43188			−0.478251
$130$	−0.971071	−	0.241276i	−0.0851685	−	0.0211613i
$131$	−15.6670			−1.36883			−0.684417	−	0.729091i	$-0.739943\pi$
$131$	−15.6670			−1.36883			−0.684417	+	0.729091i	$0.739943\pi$
$132$			1.70928i			0.148773i
$133$		−	1.92162i		−	0.166626i
$134$	7.28846			0.629627
$135$	0.539189	−	2.17009i	0.0464060	−	0.186771i
$136$	−3.26180			−0.279697
$137$			1.70928i			0.146033i	0.997331	+	0.0730166i	$0.0232626\pi$
$137$			1.70928i			0.146033i	−0.997331	+	0.0730166i	$0.976737\pi$
$138$		−	2.53919i		−	0.216150i
$139$	14.9444			1.26757			0.633784	−	0.773510i	$-0.281501\pi$
$139$	14.9444			1.26757			0.633784	+	0.773510i	$0.281501\pi$
$140$	0.921622	−	3.70928i	0.0778913	−	0.313491i
$141$	−6.72261			−0.566146
$142$		−	0.133969i		−	0.0112424i
$143$		−	0.829914i		−	0.0694009i
$144$	−2.34017			−0.195014
$145$	12.6514	+	3.14342i	1.05064	+	0.261047i
$146$	−1.57531			−0.130373
$147$		−	1.00000i		−	0.0824786i
$148$			2.58145i			0.212194i
$149$	12.5236			1.02597			0.512986	−	0.858397i	$-0.328539\pi$
$149$	12.5236			1.02597			0.512986	+	0.858397i	$0.328539\pi$
$150$	2.38243	+	1.26180i	0.194525	+	0.103025i
$151$	−15.2618			−1.24199			−0.620994	−	0.783816i	$-0.713271\pi$
$151$	−15.2618			−1.24199			−0.620994	+	0.783816i	$0.713271\pi$
$152$		−	3.84324i		−	0.311728i
$153$			1.63090i			0.131850i
$154$	−0.539189			−0.0434491
$155$	−8.58864	−	2.13397i	−0.689856	−	0.171405i
$156$	1.41855			0.113575
$157$			14.9844i			1.19589i	0.801539	+	0.597943i	$0.204015\pi$
$157$			14.9844i			1.19589i	−0.801539	+	0.597943i	$0.795985\pi$
$158$		−	0.0227863i		−	0.00181278i
$159$	−2.26180			−0.179372
$160$	2.83710	−	11.4186i	0.224293	−	0.902716i
$161$	−4.70928			−0.371143
$162$		−	0.539189i		−	0.0423627i
$163$		−	5.69368i		−	0.445963i	−0.974823	−	0.222982i	$-0.928421\pi$
$163$		−	5.69368i		−	0.445963i	0.974823	−	0.222982i	$-0.0715790\pi$
$164$	−14.0989			−1.10094
$165$	−0.539189	+	2.17009i	−0.0419758	+	0.168941i
$166$	−3.61757			−0.280778
$167$			6.04945i			0.468120i	0.972222	+	0.234060i	$0.0752013\pi$
$167$			6.04945i			0.468120i	−0.972222	+	0.234060i	$0.924799\pi$
$168$		−	2.00000i		−	0.154303i
$169$	12.3112			0.947019
$170$	−1.90829	−	0.474142i	−0.146359	−	0.0363650i
$171$	−1.92162			−0.146950
$172$			9.28458i			0.707943i
$173$		−	14.4885i		−	1.10154i	−0.834657	−	0.550771i	$-0.814334\pi$
$173$		−	14.4885i		−	1.10154i	0.834657	−	0.550771i	$-0.185666\pi$
$174$	3.14342			0.238302
$175$	2.34017	−	4.41855i	0.176900	−	0.334011i
$176$	2.34017			0.176397
$177$		−	8.21953i		−	0.617818i
$178$			4.35965i			0.326769i
$179$	6.95547			0.519876			0.259938	−	0.965625i	$-0.416298\pi$
$179$	6.95547			0.519876			0.259938	+	0.965625i	$0.416298\pi$
$180$	−3.70928	−	0.921622i	−0.276473	−	0.0686937i
$181$	0.183417			0.0136333			0.00681666	−	0.999977i	$-0.497830\pi$
$181$	0.183417			0.0136333			0.00681666	+	0.999977i	$0.497830\pi$
$182$			0.447480i			0.0331694i
$183$			9.38962i			0.694101i
$184$	−9.41855			−0.694345
$185$	−0.814315	+	3.27739i	−0.0598696	+	0.240959i
$186$	−2.13397			−0.156470
$187$		−	1.63090i		−	0.119263i
$188$			11.4908i			0.838052i
$189$	−1.00000			−0.0727393
$190$	0.558663	−	2.24846i	0.0405297	−	0.163121i
$191$	−26.9360			−1.94902			−0.974510	−	0.224343i	$-0.927976\pi$
$191$	−26.9360			−1.94902			−0.974510	+	0.224343i	$0.927976\pi$
$192$			1.84324i			0.133025i
$193$			7.26180i			0.522715i	0.965242	+	0.261358i	$0.0841702\pi$
$193$			7.26180i			0.522715i	−0.965242	+	0.261358i	$0.915830\pi$
$194$	7.59478			0.545273
$195$	1.80098	+	0.447480i	0.128971	+	0.0320447i
$196$	−1.70928			−0.122091
$197$			0.0578588i			0.00412227i	0.999998	+	0.00206114i	$0.000656080\pi$
$197$			0.0578588i			0.00412227i	−0.999998	+	0.00206114i	$0.999344\pi$
$198$			0.539189i			0.0383185i
$199$	−18.5958			−1.31822			−0.659112	−	0.752045i	$-0.729067\pi$
$199$	−18.5958			−1.31822			−0.659112	+	0.752045i	$0.729067\pi$
$200$	4.68035	−	8.83710i	0.330950	−	0.624877i
$201$	−13.5174			−0.953447
$202$			2.43907i			0.171612i
$203$		−	5.82991i		−	0.409180i
$204$	2.78765			0.195175
$205$	−17.8999	−	4.44748i	−1.25018	−	0.310625i
$206$	4.09171			0.285083
$207$			4.70928i			0.327317i
$208$		−	1.94214i		−	0.134663i
$209$	1.92162			0.132921
$210$	0.290725	−	1.17009i	0.0200619	−	0.0807436i
$211$	3.41855			0.235343			0.117671	−	0.993053i	$-0.462457\pi$
$211$	3.41855			0.235343			0.117671	+	0.993053i	$0.462457\pi$
$212$			3.86603i			0.265520i
$213$			0.248464i			0.0170245i
$214$	−7.76260			−0.530640
$215$	−2.92881	+	11.7877i	−0.199743	+	0.803911i
$216$	−2.00000			−0.136083
$217$			3.95774i			0.268669i
$218$			0.519715i			0.0351995i
$219$	2.92162			0.197425
$220$	3.70928	+	0.921622i	0.250079	+	0.0621358i
$221$	−1.35350			−0.0910465
$222$			0.814315i			0.0546533i
$223$			9.77205i			0.654385i	0.944958	+	0.327193i	$0.106103\pi$
$223$			9.77205i			0.654385i	−0.944958	+	0.327193i	$0.893897\pi$
$224$	−5.26180			−0.351568
$225$	−4.41855	−	2.34017i	−0.294570	−	0.156012i
$226$	−3.71646			−0.247215
$227$			14.8166i			0.983411i	0.870762	+	0.491706i	$0.163626\pi$
$227$			14.8166i			0.983411i	−0.870762	+	0.491706i	$0.836374\pi$
$228$			3.28458i			0.217527i
$229$	−3.64423			−0.240817			−0.120409	−	0.992724i	$-0.538421\pi$
$229$	−3.64423			−0.240817			−0.120409	+	0.992724i	$0.538421\pi$
$230$	−5.51026	−	1.36910i	−0.363336	−	0.0902759i
$231$	1.00000			0.0657952
$232$		−	11.6598i		−	0.765505i
$233$			1.64423i			0.107717i	0.998549	+	0.0538585i	$0.0171520\pi$
$233$			1.64423i			0.107717i	−0.998549	+	0.0538585i	$0.982848\pi$
$234$	0.447480			0.0292527
$235$	−3.62475	+	14.5886i	−0.236453	+	0.951658i
$236$	−14.0494			−0.914541
$237$			0.0422604i			0.00274511i
$238$			0.879362i			0.0570006i
$239$	−14.7431			−0.953653			−0.476827	−	0.878997i	$-0.658213\pi$
$239$	−14.7431			−0.953653			−0.476827	+	0.878997i	$0.658213\pi$
$240$	−1.26180	+	5.07838i	−0.0814485	+	0.327808i
$241$	−20.2329			−1.30331			−0.651657	−	0.758514i	$-0.725926\pi$
$241$	−20.2329			−1.30331			−0.651657	+	0.758514i	$0.725926\pi$
$242$		−	0.539189i		−	0.0346604i
$243$			1.00000i			0.0641500i
$244$	16.0494			1.02746
$245$	−2.17009	−	0.539189i	−0.138642	−	0.0344475i
$246$	−4.44748			−0.283561
$247$		−	1.59478i		−	0.101473i
$248$			7.91548i			0.502633i
$249$	6.70928			0.425183
$250$	4.02279	−	4.48974i	0.254423	−	0.283956i
$251$	−10.8371			−0.684032			−0.342016	−	0.939694i	$-0.611110\pi$
$251$	−10.8371			−0.684032			−0.342016	+	0.939694i	$0.611110\pi$
$252$			1.70928i			0.107674i
$253$		−	4.70928i		−	0.296070i
$254$	−5.73925			−0.360113
$255$	3.53919	+	0.879362i	0.221633	+	0.0550678i
$256$	−2.52359			−0.157724
$257$		−	6.51253i		−	0.406240i	−0.979154	−	0.203120i	$-0.934892\pi$
$257$		−	6.51253i		−	0.406240i	0.979154	−	0.203120i	$-0.0651082\pi$
$258$			2.92881i			0.182340i
$259$	1.51026			0.0938430
$260$	0.764867	−	3.07838i	0.0474350	−	0.190913i
$261$	−5.82991			−0.360863
$262$			8.44748i			0.521887i
$263$		−	20.8371i		−	1.28487i	−0.766340	−	0.642435i	$-0.777924\pi$
$263$		−	20.8371i		−	1.28487i	0.766340	−	0.642435i	$-0.222076\pi$
$264$	2.00000			0.123091
$265$	−1.21953	+	4.90829i	−0.0749154	+	0.301514i
$266$	−1.03612			−0.0635284
$267$		−	8.08557i		−	0.494829i
$268$			23.1050i			1.41136i
$269$	−3.93722			−0.240057			−0.120028	−	0.992770i	$-0.538299\pi$
$269$	−3.93722			−0.240057			−0.120028	+	0.992770i	$0.538299\pi$
$270$	−1.17009	−	0.290725i	−0.0712092	−	0.0176929i
$271$	−18.8348			−1.14413			−0.572067	−	0.820207i	$-0.693858\pi$
$271$	−18.8348			−1.14413			−0.572067	+	0.820207i	$0.693858\pi$
$272$		−	3.81658i		−	0.231414i
$273$		−	0.829914i		−	0.0502287i
$274$	0.921622			0.0556772
$275$	4.41855	+	2.34017i	0.266449	+	0.141118i
$276$	8.04945			0.484520
$277$		−	1.45362i		−	0.0873398i	−0.999046	−	0.0436699i	$-0.986095\pi$
$277$		−	1.45362i		−	0.0873398i	0.999046	−	0.0436699i	$-0.0139050\pi$
$278$		−	8.05786i		−	0.483278i
$279$	3.95774			0.236944
$280$	−4.34017	−	1.07838i	−0.259375	−	0.0644454i
$281$	−18.8143			−1.12237			−0.561184	−	0.827691i	$-0.689654\pi$
$281$	−18.8143			−1.12237			−0.561184	+	0.827691i	$0.689654\pi$
$282$			3.62475i			0.215851i
$283$			13.0589i			0.776271i	0.921602	+	0.388136i	$0.126881\pi$
$283$			13.0589i			0.776271i	−0.921602	+	0.388136i	$0.873119\pi$
$284$	0.424694			0.0252009
$285$	−1.03612	+	4.17009i	−0.0613743	+	0.247015i
$286$	−0.447480			−0.0264601
$287$			8.24846i			0.486891i
$288$			5.26180i			0.310054i
$289$	14.3402			0.843540
$290$	1.69490	−	6.82150i	0.0995279	−	0.400572i
$291$	−14.0856			−0.825710
$292$		−	4.99386i		−	0.292243i
$293$			23.7792i			1.38920i	0.719397	+	0.694599i	$0.244418\pi$
$293$			23.7792i			1.38920i	−0.719397	+	0.694599i	$0.755582\pi$
$294$	−0.539189			−0.0314461
$295$	−17.8371	−	4.43188i	−1.03852	−	0.258034i
$296$	3.02052			0.175564
$297$		−	1.00000i		−	0.0580259i
$298$		−	6.75258i		−	0.391166i
$299$	−3.90829			−0.226022
$300$	−4.00000	+	7.55252i	−0.230940	+	0.436045i
$301$	5.43188			0.313088
$302$			8.22899i			0.473525i
$303$		−	4.52359i		−	0.259873i
$304$	4.49693			0.257917
$305$	20.3763	+	5.06278i	1.16674	+	0.289894i
$306$	0.879362			0.0502698
$307$		−	6.81044i		−	0.388692i	−0.980933	−	0.194346i	$-0.937741\pi$
$307$		−	6.81044i		−	0.388692i	0.980933	−	0.194346i	$-0.0622585\pi$
$308$		−	1.70928i		−	0.0973950i
$309$	−7.58864			−0.431702
$310$	−1.15061	+	4.63090i	−0.0653504	+	0.263017i
$311$	26.0410			1.47665			0.738326	−	0.674444i	$-0.235617\pi$
$311$	26.0410			1.47665			0.738326	+	0.674444i	$0.235617\pi$
$312$		−	1.65983i		−	0.0939692i
$313$		−	27.8359i		−	1.57338i	−0.617350	−	0.786688i	$-0.711794\pi$
$313$		−	27.8359i		−	1.57338i	0.617350	−	0.786688i	$-0.288206\pi$
$314$	8.07942			0.455948
$315$	−0.539189	+	2.17009i	−0.0303799	+	0.122271i
$316$	0.0722347			0.00406352
$317$		−	30.1217i		−	1.69180i	−0.533340	−	0.845901i	$-0.679063\pi$
$317$		−	30.1217i		−	1.69180i	0.533340	−	0.845901i	$-0.320937\pi$
$318$			1.21953i			0.0683881i
$319$	5.82991			0.326412
$320$	4.00000	+	0.993857i	0.223607	+	0.0555583i
$321$	14.3968			0.803552
$322$			2.53919i			0.141503i
$323$		−	3.13397i		−	0.174379i
$324$	1.70928			0.0949597
$325$	1.94214	−	3.66701i	0.107731	−	0.203409i
$326$	−3.06997			−0.170030
$327$		−	0.963883i		−	0.0533028i
$328$			16.4969i			0.910890i
$329$	6.72261			0.370629
$330$	1.17009	+	0.290725i	0.0644111	+	0.0160039i
$331$	−33.4534			−1.83877			−0.919384	−	0.393362i	$-0.871312\pi$
$331$	−33.4534			−1.83877			−0.919384	+	0.393362i	$0.871312\pi$
$332$		−	11.4680i		−	0.629388i
$333$		−	1.51026i		−	0.0827617i
$334$	3.26180			0.178477
$335$	−7.28846	+	29.3340i	−0.398211	+	1.60269i
$336$	2.34017			0.127667
$337$		−	8.48360i		−	0.462131i	−0.972938	−	0.231066i	$-0.925779\pi$
$337$		−	8.48360i		−	0.462131i	0.972938	−	0.231066i	$-0.0742212\pi$
$338$		−	6.63809i		−	0.361064i
$339$	6.89269			0.374360
$340$	1.50307	−	6.04945i	0.0815155	−	0.328077i
$341$	−3.95774			−0.214324
$342$			1.03612i			0.0560268i
$343$			1.00000i			0.0539949i
$344$	10.8638			0.585735
$345$	10.2195	+	2.53919i	0.550201	+	0.136705i
$346$	−7.81205			−0.419978
$347$			17.8310i			0.957216i	0.878029	+	0.478608i	$0.158858\pi$
$347$			17.8310i			0.957216i	−0.878029	+	0.478608i	$0.841142\pi$
$348$			9.96493i			0.534176i
$349$	19.5814			1.04817			0.524085	−	0.851666i	$-0.324407\pi$
$349$	19.5814			1.04817			0.524085	+	0.851666i	$0.324407\pi$
$350$	−2.38243	−	1.26180i	−0.127346	−	0.0674458i
$351$	−0.829914			−0.0442975
$352$		−	5.26180i		−	0.280455i
$353$			21.7009i			1.15502i	0.816383	+	0.577510i	$0.195976\pi$
$353$			21.7009i			1.15502i	−0.816383	+	0.577510i	$0.804024\pi$
$354$	−4.43188			−0.235552
$355$	0.539189	+	0.133969i	0.0286172	+	0.00711034i
$356$	−13.8205			−0.732483
$357$		−	1.63090i		−	0.0863163i
$358$		−	3.75031i		−	0.198210i
$359$	−17.4319			−0.920020			−0.460010	−	0.887914i	$-0.652154\pi$
$359$	−17.4319			−0.920020			−0.460010	+	0.887914i	$0.652154\pi$
$360$	−1.07838	+	4.34017i	−0.0568355	+	0.228747i
$361$	−15.3074			−0.805651
$362$		−	0.0988967i		−	0.00519789i
$363$			1.00000i			0.0524864i
$364$	−1.41855			−0.0743523
$365$	1.57531	−	6.34017i	0.0824553	−	0.331860i
$366$	5.06278			0.264636
$367$		−	11.3246i		−	0.591138i	−0.955321	−	0.295569i	$-0.904491\pi$
$367$		−	11.3246i		−	0.591138i	0.955321	−	0.295569i	$-0.0955092\pi$
$368$		−	11.0205i		−	0.574484i
$369$	8.24846			0.429398
$370$	1.76713	+	0.439070i	0.0918689	+	0.0228261i
$371$	2.26180			0.117427
$372$		−	6.76487i		−	0.350742i
$373$			14.6898i			0.760609i	0.924861	+	0.380305i	$0.124181\pi$
$373$			14.6898i			0.760609i	−0.924861	+	0.380305i	$0.875819\pi$
$374$	−0.879362			−0.0454707
$375$	−7.46081	+	8.32684i	−0.385275	+	0.429996i
$376$	13.4452			0.693384
$377$		−	4.83832i		−	0.249186i
$378$			0.539189i			0.0277329i
$379$	−28.4101			−1.45933			−0.729665	−	0.683804i	$-0.760324\pi$
$379$	−28.4101			−1.45933			−0.729665	+	0.683804i	$0.760324\pi$
$380$	7.12783	+	1.77101i	0.365650	+	0.0908509i
$381$	10.6442			0.545320
$382$			14.5236i			0.743092i
$383$		−	4.75380i		−	0.242908i	−0.992597	−	0.121454i	$-0.961244\pi$
$383$		−	4.75380i		−	0.242908i	0.992597	−	0.121454i	$-0.0387557\pi$
$384$	11.5174			0.587747
$385$	0.539189	−	2.17009i	0.0274796	−	0.110598i
$386$	3.91548			0.199293
$387$		−	5.43188i		−	0.276118i
$388$			24.0761i			1.22228i
$389$	30.9744			1.57046			0.785232	−	0.619202i	$-0.212544\pi$
$389$	30.9744			1.57046			0.785232	+	0.619202i	$0.212544\pi$
$390$	0.241276	−	0.971071i	0.0122175	−	0.0491721i
$391$	−7.68035			−0.388412
$392$			2.00000i			0.101015i
$393$		−	15.6670i		−	0.790296i
$394$	0.0311968			0.00157167
$395$	0.0917087	+	0.0227863i	0.00461437	+	0.00114651i
$396$	−1.70928			−0.0858943
$397$		−	12.7565i		−	0.640228i	−0.947379	−	0.320114i	$-0.896279\pi$
$397$		−	12.7565i		−	0.640228i	0.947379	−	0.320114i	$-0.103721\pi$
$398$			10.0267i			0.502591i
$399$	1.92162			0.0962014
$400$	10.3402	+	5.47641i	0.517009	+	0.273820i
$401$	8.71420			0.435166			0.217583	−	0.976042i	$-0.430183\pi$
$401$	8.71420			0.435166			0.217583	+	0.976042i	$0.430183\pi$
$402$			7.28846i			0.363515i
$403$			3.28458i			0.163617i
$404$	−7.73206			−0.384684
$405$	2.17009	+	0.539189i	0.107832	+	0.0267925i
$406$	−3.14342			−0.156006
$407$			1.51026i			0.0748608i
$408$		−	3.26180i		−	0.161483i
$409$	5.49466			0.271694			0.135847	−	0.990730i	$-0.456625\pi$
$409$	5.49466			0.271694			0.135847	+	0.990730i	$0.456625\pi$
$410$	−2.39803	+	9.65142i	−0.118430	+	0.476649i
$411$	−1.70928			−0.0843123
$412$			12.9711i			0.639039i
$413$			8.21953i			0.404457i
$414$	2.53919			0.124794
$415$	3.61757	−	14.5597i	0.177579	−	0.714708i
$416$	−4.36683			−0.214102
$417$			14.9444i			0.731831i
$418$		−	1.03612i		−	0.0506782i
$419$	−22.0544			−1.07743			−0.538713	−	0.842489i	$-0.681089\pi$
$419$	−22.0544			−1.07743			−0.538713	+	0.842489i	$0.681089\pi$
$420$	3.70928	+	0.921622i	0.180994	+	0.0449706i
$421$	12.2351			0.596304			0.298152	−	0.954518i	$-0.403630\pi$
$421$	12.2351			0.596304			0.298152	+	0.954518i	$0.403630\pi$
$422$		−	1.84324i		−	0.0897277i
$423$		−	6.72261i		−	0.326864i
$424$	4.52359			0.219685
$425$	3.81658	−	7.20620i	0.185131	−	0.349552i
$426$	0.133969			0.00649083
$427$		−	9.38962i		−	0.454396i
$428$		−	24.6081i		−	1.18948i
$429$	0.829914			0.0400686
$430$	6.35577	+	1.57918i	0.306503	+	0.0761549i
$431$	18.0722			0.870509			0.435254	−	0.900307i	$-0.356658\pi$
$431$	18.0722			0.870509			0.435254	+	0.900307i	$0.356658\pi$
$432$		−	2.34017i		−	0.112592i
$433$			32.1399i			1.54455i	0.635290	+	0.772273i	$0.280880\pi$
$433$			32.1399i			1.54455i	−0.635290	+	0.772273i	$0.719120\pi$
$434$	2.13397			0.102434
$435$	−3.14342	+	12.6514i	−0.150716	+	0.606589i
$436$	−1.64754			−0.0789029
$437$		−	9.04945i		−	0.432894i
$438$		−	1.57531i		−	0.0752710i
$439$	−7.89043			−0.376589			−0.188295	−	0.982113i	$-0.560296\pi$
$439$	−7.89043			−0.376589			−0.188295	+	0.982113i	$0.560296\pi$
$440$	1.07838	−	4.34017i	0.0514096	−	0.206910i
$441$	1.00000			0.0476190
$442$			0.729794i			0.0347128i
$443$		−	24.6719i		−	1.17220i	−0.810239	−	0.586100i	$-0.800663\pi$
$443$		−	24.6719i		−	1.17220i	0.810239	−	0.586100i	$-0.199337\pi$
$444$	−2.58145			−0.122510
$445$	−17.5464	−	4.35965i	−0.831778	−	0.206667i
$446$	5.26898			0.249494
$447$			12.5236i			0.592346i
$448$		−	1.84324i		−	0.0870851i
$449$	19.1845			0.905371			0.452685	−	0.891670i	$-0.350466\pi$
$449$	19.1845			0.905371			0.452685	+	0.891670i	$0.350466\pi$
$450$	−1.26180	+	2.38243i	−0.0594816	+	0.112309i
$451$	−8.24846			−0.388405
$452$		−	11.7815i		−	0.554156i
$453$		−	15.2618i		−	0.717062i
$454$	7.98894			0.374939
$455$	−1.80098	−	0.447480i	−0.0844314	−	0.0209782i
$456$	3.84324			0.179976
$457$		−	36.8960i		−	1.72592i	−0.505270	−	0.862961i	$-0.668607\pi$
$457$		−	36.8960i		−	1.72592i	0.505270	−	0.862961i	$-0.331393\pi$
$458$			1.96493i			0.0918150i
$459$	−1.63090			−0.0761238
$460$	4.34017	−	17.4680i	0.202362	−	0.814450i
$461$	−11.8699			−0.552837			−0.276418	−	0.961037i	$-0.589148\pi$
$461$	−11.8699			−0.552837			−0.276418	+	0.961037i	$0.589148\pi$
$462$		−	0.539189i		−	0.0250853i
$463$			26.6537i			1.23870i	0.785114	+	0.619351i	$0.212604\pi$
$463$			26.6537i			1.23870i	−0.785114	+	0.619351i	$0.787396\pi$
$464$	13.6430			0.633361
$465$	2.13397	−	8.58864i	0.0989604	−	0.398289i
$466$	0.886550			0.0410686
$467$			0.325797i			0.0150761i	0.999972	+	0.00753805i	$0.00239946\pi$
$467$			0.325797i			0.0150761i	−0.999972	+	0.00753805i	$0.997601\pi$
$468$			1.41855i			0.0655725i
$469$	13.5174			0.624178
$470$	7.86603	+	1.95443i	0.362833	+	0.0901510i
$471$	−14.9844			−0.690445
$472$			16.4391i			0.756670i
$473$			5.43188i			0.249758i
$474$	0.0227863			0.00104661
$475$	8.49079	+	4.49693i	0.389584	+	0.206333i
$476$	−2.78765			−0.127772
$477$		−	2.26180i		−	0.103560i
$478$			7.94933i			0.363594i
$479$	−9.32684			−0.426154			−0.213077	−	0.977035i	$-0.568349\pi$
$479$	−9.32684			−0.426154			−0.213077	+	0.977035i	$0.568349\pi$
$480$	11.4186	+	2.83710i	0.521183	+	0.129495i
$481$	1.25338			0.0571494
$482$			10.9093i			0.496907i
$483$		−	4.70928i		−	0.214279i
$484$	1.70928			0.0776943
$485$	−7.59478	+	30.5669i	−0.344861	+	1.38797i
$486$	0.539189			0.0244581
$487$		−	21.8576i		−	0.990463i	−0.868761	−	0.495232i	$-0.835083\pi$
$487$		−	21.8576i		−	0.990463i	0.868761	−	0.495232i	$-0.164917\pi$
$488$		−	18.7792i		−	0.850096i
$489$	5.69368			0.257477
$490$	−0.290725	+	1.17009i	−0.0131336	+	0.0528591i
$491$	−0.899881			−0.0406111			−0.0203055	−	0.999794i	$-0.506464\pi$
$491$	−0.899881			−0.0406111			−0.0203055	+	0.999794i	$0.506464\pi$
$492$		−	14.0989i		−	0.635627i
$493$		−	9.50799i		−	0.428218i
$494$	−0.859888			−0.0386882
$495$	−2.17009	−	0.539189i	−0.0975381	−	0.0242347i
$496$	−9.26180			−0.415867
$497$		−	0.248464i		−	0.0111451i
$498$		−	3.61757i		−	0.162107i
$499$	19.1483			0.857198			0.428599	−	0.903495i	$-0.359007\pi$
$499$	19.1483			0.857198			0.428599	+	0.903495i	$0.359007\pi$
$500$	14.2329	+	12.7526i	0.636513	+	0.570313i
$501$	−6.04945			−0.270269
$502$			5.84324i			0.260797i
$503$			31.0456i			1.38425i	0.721776	+	0.692127i	$0.243326\pi$
$503$			31.0456i			1.38425i	−0.721776	+	0.692127i	$0.756674\pi$
$504$	2.00000			0.0890871
$505$	−9.81658	−	2.43907i	−0.436832	−	0.108537i
$506$	−2.53919			−0.112881
$507$			12.3112i			0.546762i
$508$		−	18.1939i		−	0.807225i
$509$	38.2255			1.69432			0.847158	−	0.531341i	$-0.178312\pi$
$509$	38.2255			1.69432			0.847158	+	0.531341i	$0.178312\pi$
$510$	0.474142	−	1.90829i	0.0209954	−	0.0845006i
$511$	−2.92162			−0.129245
$512$		−	21.6742i		−	0.957873i
$513$		−	1.92162i		−	0.0848417i
$514$	−3.51148			−0.154885
$515$	−4.09171	+	16.4680i	−0.180302	+	0.725667i
$516$	−9.28458			−0.408731
$517$			6.72261i			0.295660i
$518$		−	0.814315i		−	0.0357790i
$519$	14.4885			0.635975
$520$	−3.60197	−	0.894960i	−0.157957	−	0.0392466i
$521$	−8.71646			−0.381875			−0.190938	−	0.981602i	$-0.561153\pi$
$521$	−8.71646			−0.381875			−0.190938	+	0.981602i	$0.561153\pi$
$522$			3.14342i			0.137584i
$523$		−	41.7998i		−	1.82778i	−0.405966	−	0.913888i	$-0.633065\pi$
$523$		−	41.7998i		−	1.82778i	0.405966	−	0.913888i	$-0.366935\pi$
$524$	−26.7792			−1.16986
$525$	4.41855	+	2.34017i	0.192841	+	0.102134i
$526$	−11.2351			−0.489875
$527$			6.45467i			0.281170i
$528$			2.34017i			0.101843i
$529$	0.822726			0.0357707
$530$	2.64650	+	0.657560i	0.114956	+	0.0285626i
$531$	8.21953			0.356697
$532$		−	3.28458i		−	0.142405i
$533$			6.84551i			0.296512i
$534$	−4.35965			−0.188660
$535$	7.76260	−	31.2423i	0.335606	−	1.35072i
$536$	27.0349			1.16773
$537$			6.95547i			0.300151i
$538$			2.12291i			0.0915250i
$539$	−1.00000			−0.0430730
$540$	0.921622	−	3.70928i	0.0396603	−	0.159622i
$541$	13.1883			0.567011			0.283505	−	0.958971i	$-0.408503\pi$
$541$	13.1883			0.567011			0.283505	+	0.958971i	$0.408503\pi$
$542$			10.1555i			0.436217i
$543$			0.183417i			0.00787120i
$544$	−8.58145			−0.367927
$545$	−2.09171	−	0.519715i	−0.0895990	−	0.0222621i
$546$	−0.447480			−0.0191504
$547$			4.48747i			0.191870i	0.995388	+	0.0959352i	$0.0305842\pi$
$547$			4.48747i			0.191870i	−0.995388	+	0.0959352i	$0.969416\pi$
$548$			2.92162i			0.124806i
$549$	−9.38962			−0.400739
$550$	1.26180	−	2.38243i	0.0538031	−	0.101587i
$551$	11.2029			0.477259
$552$		−	9.41855i		−	0.400880i
$553$		−	0.0422604i		−	0.00179710i
$554$	−0.783777			−0.0332995
$555$	−3.27739	−	0.814315i	−0.139118	−	0.0345658i
$556$	25.5441			1.08331
$557$			30.7480i			1.30284i	0.758719	+	0.651418i	$0.225826\pi$
$557$			30.7480i			1.30284i	−0.758719	+	0.651418i	$0.774174\pi$
$558$		−	2.13397i		−	0.0903381i
$559$	4.50799			0.190668
$560$	1.26180	−	5.07838i	0.0533206	−	0.214601i
$561$	1.63090			0.0688566
$562$			10.1445i			0.427919i
$563$		−	40.9854i		−	1.72733i	−0.504066	−	0.863665i	$-0.668163\pi$
$563$		−	40.9854i		−	1.72733i	0.504066	−	0.863665i	$-0.331837\pi$
$564$	−11.4908			−0.483849
$565$	3.71646	−	14.9577i	0.156353	−	0.629277i
$566$	7.04122			0.295964
$567$		−	1.00000i		−	0.0419961i
$568$		−	0.496928i		−	0.0208507i
$569$	−24.8420			−1.04143			−0.520716	−	0.853730i	$-0.674335\pi$
$569$	−24.8420			−1.04143			−0.520716	+	0.853730i	$0.674335\pi$
$570$	2.24846	+	0.558663i	0.0941778	+	0.0233998i
$571$	−10.2835			−0.430353			−0.215176	−	0.976575i	$-0.569033\pi$
$571$	−10.2835			−0.430353			−0.215176	+	0.976575i	$0.569033\pi$
$572$		−	1.41855i		−	0.0593126i
$573$		−	26.9360i		−	1.12527i
$574$	4.44748			0.185634
$575$	11.0205	−	20.8082i	0.459587	−	0.867761i
$576$	−1.84324			−0.0768019
$577$		−	15.9733i		−	0.664979i	−0.943107	−	0.332489i	$-0.892111\pi$
$577$		−	15.9733i		−	0.664979i	0.943107	−	0.332489i	$-0.107889\pi$
$578$		−	7.73206i		−	0.321611i
$579$	−7.26180			−0.301790
$580$	21.6248	+	5.37298i	0.897919	+	0.223101i
$581$	−6.70928			−0.278348
$582$			7.59478i			0.314814i
$583$			2.26180i			0.0936740i
$584$	−5.84324			−0.241795
$585$	−0.447480	+	1.80098i	−0.0185010	+	0.0744615i
$586$	12.8215			0.529651
$587$		−	30.3390i		−	1.25222i	−0.779734	−	0.626111i	$-0.784646\pi$
$587$		−	30.3390i		−	1.25222i	0.779734	−	0.626111i	$-0.215354\pi$
$588$		−	1.70928i		−	0.0704893i
$589$	−7.60528			−0.313370
$590$	−2.38962	+	9.61757i	−0.0983792	+	0.395949i
$591$	−0.0578588			−0.00237999
$592$			3.53427i			0.145258i
$593$			20.7298i			0.851271i	0.904895	+	0.425635i	$0.139949\pi$
$593$			20.7298i			0.851271i	−0.904895	+	0.425635i	$0.860051\pi$
$594$	−0.539189			−0.0221232
$595$	−3.53919	−	0.879362i	−0.145093	−	0.0360503i
$596$	21.4063			0.876835
$597$		−	18.5958i		−	0.761076i
$598$			2.10731i			0.0861742i
$599$	6.76487			0.276405			0.138202	−	0.990404i	$-0.455868\pi$
$599$	6.76487			0.276405			0.138202	+	0.990404i	$0.455868\pi$
$600$	8.83710	+	4.68035i	0.360773	+	0.191074i
$601$	−29.2907			−1.19479			−0.597397	−	0.801946i	$-0.703798\pi$
$601$	−29.2907			−1.19479			−0.597397	+	0.801946i	$0.703798\pi$
$602$		−	2.92881i		−	0.119369i
$603$		−	13.5174i		−	0.550473i
$604$	−26.0866			−1.06145
$605$	2.17009	+	0.539189i	0.0882266	+	0.0219211i
$606$	−2.43907			−0.0990804
$607$		−	26.8515i		−	1.08987i	−0.838479	−	0.544934i	$-0.816555\pi$
$607$		−	26.8515i		−	1.08987i	0.838479	−	0.544934i	$-0.183445\pi$
$608$		−	10.1112i		−	0.410063i
$609$	5.82991			0.236240
$610$	2.72979	−	10.9867i	0.110526	−	0.444837i
$611$	5.57918			0.225710
$612$			2.78765i			0.112684i
$613$			35.0784i			1.41680i	0.705810	+	0.708401i	$0.250583\pi$
$613$			35.0784i			1.41680i	−0.705810	+	0.708401i	$0.749417\pi$
$614$	−3.67211			−0.148194
$615$	4.44748	−	17.8999i	0.179340	−	0.721793i
$616$	−2.00000			−0.0805823
$617$		−	4.08065i		−	0.164281i	−0.996621	−	0.0821403i	$-0.973824\pi$
$617$		−	4.08065i		−	0.164281i	0.996621	−	0.0821403i	$-0.0261756\pi$
$618$			4.09171i			0.164593i
$619$	34.8781			1.40187			0.700935	−	0.713225i	$-0.252766\pi$
$619$	34.8781			1.40187			0.700935	+	0.713225i	$0.252766\pi$
$620$	−14.6803	−	3.64754i	−0.589577	−	0.146489i
$621$	−4.70928			−0.188977
$622$		−	14.0410i		−	0.562994i
$623$			8.08557i			0.323941i
$624$	1.94214			0.0777479
$625$	14.0472	+	20.6803i	0.561887	+	0.827214i
$626$	−15.0088			−0.599872
$627$			1.92162i			0.0767422i
$628$			25.6125i			1.02205i
$629$	2.46308			0.0982094
$630$	1.17009	+	0.290725i	0.0466174	+	0.0115827i
$631$	36.4413			1.45071			0.725353	−	0.688377i	$-0.241676\pi$
$631$	36.4413			1.45071			0.725353	+	0.688377i	$0.241676\pi$
$632$		−	0.0845208i		−	0.00336206i
$633$			3.41855i			0.135875i
$634$	−16.2413			−0.645023
$635$	5.73925	−	23.0989i	0.227755	−	0.916652i
$636$	−3.86603			−0.153298
$637$			0.829914i			0.0328824i
$638$		−	3.14342i		−	0.124449i
$639$	−0.248464			−0.00982909
$640$	6.21008	−	24.9939i	0.245475	−	0.987969i
$641$	37.1338			1.46670			0.733348	−	0.679853i	$-0.237956\pi$
$641$	37.1338			1.46670			0.733348	+	0.679853i	$0.237956\pi$
$642$		−	7.76260i		−	0.306365i
$643$			34.6274i			1.36557i	0.730619	+	0.682786i	$0.239232\pi$
$643$			34.6274i			1.36557i	−0.730619	+	0.682786i	$0.760768\pi$
$644$	−8.04945			−0.317193
$645$	−11.7877	−	2.92881i	−0.464138	−	0.115322i
$646$	−1.68980			−0.0664843
$647$			31.6020i			1.24240i	0.783651	+	0.621201i	$0.213355\pi$
$647$			31.6020i			1.24240i	−0.783651	+	0.621201i	$0.786645\pi$
$648$		−	2.00000i		−	0.0785674i
$649$	−8.21953			−0.322645
$650$	−1.97721	−	1.04718i	−0.0775527	−	0.0410738i
$651$	−3.95774			−0.155116
$652$		−	9.73206i		−	0.381137i
$653$		−	26.9565i		−	1.05489i	−0.849589	−	0.527445i	$-0.823150\pi$
$653$		−	26.9565i		−	1.05489i	0.849589	−	0.527445i	$-0.176850\pi$
$654$	−0.519715			−0.0203225
$655$	−33.9988	−	8.44748i	−1.32844	−	0.330070i
$656$	−19.3028			−0.753649
$657$			2.92162i			0.113983i
$658$		−	3.62475i		−	0.141308i
$659$	−3.29791			−0.128468			−0.0642342	−	0.997935i	$-0.520460\pi$
$659$	−3.29791			−0.128468			−0.0642342	+	0.997935i	$0.520460\pi$
$660$	−0.921622	+	3.70928i	−0.0358741	+	0.144383i
$661$	31.4219			1.22217			0.611084	−	0.791565i	$-0.290734\pi$
$661$	31.4219			1.22217			0.611084	+	0.791565i	$0.290734\pi$
$662$			18.0377i			0.701056i
$663$		−	1.35350i		−	0.0525657i
$664$	−13.4186			−0.520741
$665$	1.03612	−	4.17009i	0.0401789	−	0.161709i
$666$	−0.814315			−0.0315541
$667$		−	27.4547i		−	1.06305i
$668$			10.3402i			0.400073i
$669$	−9.77205			−0.377809
$670$	15.8166	+	3.92986i	0.611048	+	0.151824i
$671$	9.38962			0.362482
$672$		−	5.26180i		−	0.202978i
$673$			18.1038i			0.697851i	0.937150	+	0.348925i	$0.113453\pi$
$673$			18.1038i			0.697851i	−0.937150	+	0.348925i	$0.886547\pi$
$674$	−4.57426			−0.176194
$675$	2.34017	−	4.41855i	0.0900733	−	0.170070i
$676$	21.0433			0.809358
$677$			19.2017i			0.737980i	0.929433	+	0.368990i	$0.120296\pi$
$677$			19.2017i			0.737980i	−0.929433	+	0.368990i	$0.879704\pi$
$678$		−	3.71646i		−	0.142730i
$679$	14.0856			0.540554
$680$	−7.07838	−	1.75872i	−0.271443	−	0.0674440i
$681$	−14.8166			−0.567773
$682$			2.13397i			0.0817139i
$683$			1.30737i			0.0500250i	0.999687	+	0.0250125i	$0.00796256\pi$
$683$			1.30737i			0.0500250i	−0.999687	+	0.0250125i	$0.992037\pi$
$684$	−3.28458			−0.125589
$685$	−0.921622	+	3.70928i	−0.0352134	+	0.141724i
$686$	0.539189			0.0205863
$687$		−	3.64423i		−	0.139036i
$688$			12.7115i			0.484623i
$689$	1.87709			0.0715116
$690$	1.36910	−	5.51026i	0.0521208	−	0.209772i
$691$	−2.52813			−0.0961744			−0.0480872	−	0.998843i	$-0.515313\pi$
$691$	−2.52813			−0.0961744			−0.0480872	+	0.998843i	$0.515313\pi$
$692$		−	24.7649i		−	0.941419i
$693$			1.00000i			0.0379869i
$694$	9.61425			0.364952
$695$	32.4307	+	8.05786i	1.23017	+	0.305652i
$696$	11.6598			0.441965
$697$			13.4524i			0.509546i
$698$		−	10.5581i		−	0.399630i
$699$	−1.64423			−0.0621904
$700$	4.00000	−	7.55252i	0.151186	−	0.285458i
$701$	−31.4996			−1.18972			−0.594861	−	0.803828i	$-0.702793\pi$
$701$	−31.4996			−1.18972			−0.594861	+	0.803828i	$0.702793\pi$
$702$			0.447480i			0.0168890i
$703$			2.90215i			0.109457i
$704$	1.84324			0.0694699
$705$	−14.5886	−	3.62475i	−0.549440	−	0.136516i
$706$	11.7009			0.440368
$707$			4.52359i			0.170127i
$708$		−	14.0494i		−	0.528011i
$709$	28.8804			1.08463			0.542313	−	0.840176i	$-0.317549\pi$
$709$	28.8804			1.08463			0.542313	+	0.840176i	$0.317549\pi$
$710$	0.0722347	−	0.290725i	0.00271092	−	0.0109107i
$711$	−0.0422604			−0.00158489
$712$			16.1711i			0.606039i
$713$			18.6381i			0.698002i
$714$	−0.879362			−0.0329093
$715$	0.447480	−	1.80098i	0.0167348	−	0.0673530i
$716$	11.8888			0.444306
$717$		−	14.7431i		−	0.550592i
$718$			9.39908i			0.350770i
$719$	17.9516			0.669482			0.334741	−	0.942310i	$-0.391351\pi$
$719$	17.9516			0.669482			0.334741	+	0.942310i	$0.391351\pi$
$720$	−5.07838	−	1.26180i	−0.189260	−	0.0470243i
$721$	7.58864			0.282616
$722$			8.25356i			0.307166i
$723$		−	20.2329i		−	0.752468i
$724$	0.313511			0.0116515
$725$	25.7598	+	13.6430i	0.956694	+	0.506689i
$726$	0.539189			0.0200112
$727$		−	24.8732i		−	0.922497i	−0.887271	−	0.461248i	$-0.847402\pi$
$727$		−	24.8732i		−	0.922497i	0.887271	−	0.461248i	$-0.152598\pi$
$728$			1.65983i			0.0615173i
$729$	−1.00000			−0.0370370
$730$	−3.41855	−	0.849388i	−0.126526	−	0.0314372i
$731$	8.85884			0.327656
$732$			16.0494i			0.593205i
$733$			8.29914i			0.306536i	0.988185	+	0.153268i	$0.0489797\pi$
$733$			8.29914i			0.306536i	−0.988185	+	0.153268i	$0.951020\pi$
$734$	−6.10608			−0.225380
$735$	0.539189	−	2.17009i	0.0198883	−	0.0800448i
$736$	−24.7792			−0.913375
$737$			13.5174i			0.497922i
$738$		−	4.44748i		−	0.163714i
$739$	23.1240			0.850628			0.425314	−	0.905046i	$-0.360164\pi$
$739$	23.1240			0.850628			0.425314	+	0.905046i	$0.360164\pi$
$740$	−1.39189	+	5.60197i	−0.0511668	+	0.205932i
$741$	1.59478			0.0585857
$742$		−	1.21953i		−	0.0447705i
$743$			52.5113i			1.92645i	0.268691	+	0.963226i	$0.413409\pi$
$743$			52.5113i			1.92645i	−0.268691	+	0.963226i	$0.586591\pi$
$744$	−7.91548			−0.290196
$745$	27.1773	+	6.75258i	0.995698	+	0.247395i
$746$	7.92058			0.289993
$747$			6.70928i			0.245480i
$748$		−	2.78765i		−	0.101927i
$749$	−14.3968			−0.526048
$750$	4.48974	+	4.02279i	0.163942	+	0.146891i
$751$	23.4703			0.856442			0.428221	−	0.903674i	$-0.359140\pi$
$751$	23.4703			0.856442			0.428221	+	0.903674i	$0.359140\pi$
$752$			15.7321i			0.573689i
$753$		−	10.8371i		−	0.394926i
$754$	−2.60877			−0.0950058
$755$	−33.1194	−	8.22899i	−1.20534	−	0.299484i
$756$	−1.70928			−0.0621657
$757$		−	49.5897i		−	1.80237i	−0.433437	−	0.901184i	$-0.642699\pi$
$757$		−	49.5897i		−	1.80237i	0.433437	−	0.901184i	$-0.357301\pi$
$758$			15.3184i			0.556390i
$759$	4.70928			0.170936
$760$	2.07223	−	8.34017i	0.0751679	−	0.302530i
$761$	45.8264			1.66121			0.830603	−	0.556865i	$-0.187996\pi$
$761$	45.8264			1.66121			0.830603	+	0.556865i	$0.187996\pi$
$762$		−	5.73925i		−	0.207911i
$763$			0.963883i			0.0348949i
$764$	−46.0410			−1.66571
$765$	−0.879362	+	3.53919i	−0.0317934	+	0.127960i
$766$	−2.56320			−0.0926121
$767$			6.82150i			0.246310i
$768$		−	2.52359i		−	0.0910622i
$769$	5.47027			0.197263			0.0986314	−	0.995124i	$-0.468554\pi$
$769$	5.47027			0.197263			0.0986314	+	0.995124i	$0.468554\pi$
$770$	−1.17009	−	0.290725i	−0.0421670	−	0.0104770i
$771$	6.51253			0.234543
$772$			12.4124i			0.446732i
$773$			21.7998i			0.784083i	0.919948	+	0.392041i	$0.128231\pi$
$773$			21.7998i			0.784083i	−0.919948	+	0.392041i	$0.871769\pi$
$774$	−2.92881			−0.105274
$775$	−17.4875	−	9.26180i	−0.628169	−	0.332694i
$776$	28.1711			1.01128
$777$			1.51026i			0.0541803i
$778$		−	16.7010i		−	0.598761i
$779$	−15.8504			−0.567901
$780$	3.07838	+	0.764867i	0.110224	+	0.0273866i
$781$	0.248464			0.00889075
$782$			4.14116i			0.148087i
$783$		−	5.82991i		−	0.208344i
$784$	−2.34017			−0.0835776
$785$	−8.07942	+	32.5174i	−0.288367	+	1.16060i
$786$	−8.44748			−0.301312
$787$		−	7.05172i		−	0.251367i	−0.992070	−	0.125683i	$-0.959888\pi$
$787$		−	7.05172i		−	0.251367i	0.992070	−	0.125683i	$-0.0401123\pi$
$788$			0.0988967i			0.00352305i
$789$	20.8371			0.741820
$790$	0.0122861	−	0.0494483i	0.000437121	−	0.00175929i
$791$	−6.89269			−0.245076
$792$			2.00000i			0.0710669i
$793$		−	7.79257i		−	0.276722i
$794$	−6.87814			−0.244096
$795$	−4.90829	−	1.21953i	−0.174079	−	0.0432524i
$796$	−31.7854			−1.12660
$797$			18.8104i			0.666300i	0.942874	+	0.333150i	$0.108112\pi$
$797$			18.8104i			0.666300i	−0.942874	+	0.333150i	$0.891888\pi$
$798$		−	1.03612i		−	0.0366782i
$799$	10.9639			0.387874
$800$	12.3135	−	23.2495i	0.435348	−	0.821994i
$801$	8.08557			0.285689
$802$		−	4.69860i		−	0.165913i
$803$		−	2.92162i		−	0.103102i
$804$	−23.1050			−0.814852
$805$	−10.2195	−	2.53919i	−0.360191	−	0.0894946i
$806$	1.77101			0.0623812
$807$		−	3.93722i		−	0.138597i
$808$			9.04718i			0.318279i
$809$	38.5814			1.35645			0.678226	−	0.734854i	$-0.262749\pi$
$809$	38.5814			1.35645			0.678226	+	0.734854i	$0.262749\pi$
$810$	0.290725	−	1.17009i	0.0102150	−	0.0411126i
$811$	24.5503			0.862076			0.431038	−	0.902334i	$-0.358147\pi$
$811$	24.5503			0.862076			0.431038	+	0.902334i	$0.358147\pi$
$812$		−	9.96493i		−	0.349700i
$813$		−	18.8348i		−	0.660566i
$814$	0.814315			0.0285417
$815$	3.06997	−	12.3558i	0.107536	−	0.432804i
$816$	3.81658			0.133607
$817$			10.4380i			0.365180i
$818$		−	2.96266i		−	0.103587i
$819$	0.829914			0.0289995
$820$	−30.5958	−	7.60197i	−1.06845	−	0.265472i
$821$	21.2667			0.742213			0.371107	−	0.928590i	$-0.378978\pi$
$821$	21.2667			0.742213			0.371107	+	0.928590i	$0.378978\pi$
$822$			0.921622i			0.0321453i
$823$			10.3908i			0.362202i	0.983464	+	0.181101i	$0.0579661\pi$
$823$			10.3908i			0.362202i	−0.983464	+	0.181101i	$0.942034\pi$
$824$	15.1773			0.528725
$825$	−2.34017	+	4.41855i	−0.0814744	+	0.153834i
$826$	4.43188			0.154205
$827$			24.4703i			0.850915i	0.904979	+	0.425457i	$0.139887\pi$
$827$			24.4703i			0.850915i	−0.904979	+	0.425457i	$0.860113\pi$
$828$			8.04945i			0.279738i
$829$	12.3668			0.429518			0.214759	−	0.976667i	$-0.431103\pi$
$829$	12.3668			0.429518			0.214759	+	0.976667i	$0.431103\pi$
$830$	−7.85043	−	1.95055i	−0.272492	−	0.0677046i
$831$	1.45362			0.0504256
$832$		−	1.52973i		−	0.0530340i
$833$			1.63090i			0.0565073i
$834$	8.05786			0.279021
$835$	−3.26180	+	13.1278i	−0.112879	+	0.454307i
$836$	3.28458			0.113600
$837$			3.95774i			0.136799i
$838$			11.8915i			0.410784i
$839$	8.41136			0.290392			0.145196	−	0.989403i	$-0.453619\pi$
$839$	8.41136			0.290392			0.145196	+	0.989403i	$0.453619\pi$
$840$	1.07838	−	4.34017i	0.0372076	−	0.149750i
$841$	4.98789			0.171996
$842$		−	6.59705i		−	0.227349i
$843$		−	18.8143i		−	0.647999i
$844$	5.84324			0.201133
$845$	26.7165	+	6.63809i	0.919074	+	0.228357i
$846$	−3.62475			−0.124622
$847$		−	1.00000i		−	0.0343604i
$848$			5.29299i			0.181762i
$849$	−13.0589			−0.448180
$850$	−3.88550	−	2.05786i	−0.133272	−	0.0705840i
$851$	7.11223			0.243804
$852$			0.424694i			0.0145498i
$853$			4.21727i			0.144396i	0.997390	+	0.0721982i	$0.0230014\pi$
$853$			4.21727i			0.144396i	−0.997390	+	0.0721982i	$0.976999\pi$
$854$	−5.06278			−0.173245
$855$	−4.17009	−	1.03612i	−0.142614	−	0.0354345i
$856$	−28.7936			−0.984146
$857$			52.9192i			1.80768i	0.427866	+	0.903842i	$0.359266\pi$
$857$			52.9192i			1.80768i	−0.427866	+	0.903842i	$0.640734\pi$
$858$		−	0.447480i		−	0.0152767i
$859$	−40.8092			−1.39239			−0.696196	−	0.717851i	$-0.745126\pi$
$859$	−40.8092			−1.39239			−0.696196	+	0.717851i	$0.745126\pi$
$860$	−5.00614	+	20.1483i	−0.170708	+	0.687053i
$861$	−8.24846			−0.281107
$862$		−	9.74435i		−	0.331894i
$863$			27.2122i			0.926313i	0.886277	+	0.463157i	$0.153283\pi$
$863$			27.2122i			0.926313i	−0.886277	+	0.463157i	$0.846717\pi$
$864$	−5.26180			−0.179010
$865$	7.81205	−	31.4413i	0.265618	−	1.06904i
$866$	17.3295			0.588880
$867$			14.3402i			0.487018i
$868$			6.76487i			0.229615i
$869$	0.0422604			0.00143359
$870$	6.82150	+	1.69490i	0.231271	+	0.0574625i
$871$	11.2183			0.380118
$872$			1.92777i			0.0652824i
$873$		−	14.0856i		−	0.476724i
$874$	−4.87936			−0.165047
$875$	7.46081	−	8.32684i	0.252221	−	0.281499i
$876$	4.99386			0.168727
$877$		−	47.7454i		−	1.61225i	−0.591747	−	0.806124i	$-0.701562\pi$
$877$		−	47.7454i		−	1.61225i	0.591747	−	0.806124i	$-0.298438\pi$
$878$			4.25443i			0.143580i
$879$	−23.7792			−0.802054
$880$	5.07838	+	1.26180i	0.171192	+	0.0425351i
$881$	12.2157			0.411556			0.205778	−	0.978599i	$-0.434028\pi$
$881$	12.2157			0.411556			0.205778	+	0.978599i	$0.434028\pi$
$882$		−	0.539189i		−	0.0181554i
$883$			0.769402i			0.0258924i	0.999916	+	0.0129462i	$0.00412102\pi$
$883$			0.769402i			0.0258924i	−0.999916	+	0.0129462i	$0.995879\pi$
$884$	−2.31351			−0.0778118
$885$	4.43188	−	17.8371i	0.148976	−	0.599588i
$886$	−13.3028			−0.446917
$887$			45.7382i			1.53574i	0.640607	+	0.767869i	$0.278683\pi$
$887$			45.7382i			1.53574i	−0.640607	+	0.767869i	$0.721317\pi$
$888$			3.02052i			0.101362i
$889$	−10.6442			−0.356996
$890$	−2.35067	+	9.46081i	−0.0787947	+	0.317127i
$891$	1.00000			0.0335013
$892$			16.7031i			0.559262i
$893$			12.9183i			0.432295i
$894$	6.75258			0.225840
$895$	15.0940	+	3.75031i	0.504536	+	0.125359i
$896$	−11.5174			−0.384771
$897$		−	3.90829i		−	0.130494i
$898$		−	10.3440i		−	0.345185i
$899$	−23.0733			−0.769537
$900$	−7.55252	−	4.00000i	−0.251751	−	0.133333i
$901$	3.68876			0.122890
$902$			4.44748i			0.148085i
$903$			5.43188i			0.180762i
$904$	−13.7854			−0.458495
$905$	0.398032	+	0.0988967i	0.0132310	+	0.00328744i
$906$	−8.22899			−0.273390
$907$			22.7910i			0.756762i	0.925650	+	0.378381i	$0.123519\pi$
$907$			22.7910i			0.756762i	−0.925650	+	0.378381i	$0.876481\pi$
$908$			25.3256i			0.840460i
$909$	4.52359			0.150038
$910$	−0.241276	+	0.971071i	−0.00799823	+	0.0321907i
$911$	−20.9171			−0.693014			−0.346507	−	0.938047i	$-0.612632\pi$
$911$	−20.9171			−0.693014			−0.346507	+	0.938047i	$0.612632\pi$
$912$			4.49693i			0.148908i
$913$		−	6.70928i		−	0.222045i
$914$	−19.8939			−0.658032
$915$	−5.06278	+	20.3763i	−0.167370	+	0.673619i
$916$	−6.22899			−0.205812
$917$			15.6670i			0.517370i
$918$			0.879362i			0.0290233i
$919$	−32.8104			−1.08232			−0.541158	−	0.840921i	$-0.682014\pi$
$919$	−32.8104			−1.08232			−0.541158	+	0.840921i	$0.682014\pi$
$920$	−20.4391	−	5.07838i	−0.673856	−	0.167429i
$921$	6.81044			0.224412
$922$			6.40012i			0.210777i
$923$		−	0.206204i		−	0.00678728i
$924$	1.70928			0.0562310
$925$	−3.53427	+	6.67316i	−0.116206	+	0.219412i
$926$	14.3714			0.472273
$927$		−	7.58864i		−	0.249244i
$928$		−	30.6758i		−	1.00698i
$929$	−5.48237			−0.179871			−0.0899354	−	0.995948i	$-0.528666\pi$
$929$	−5.48237			−0.179871			−0.0899354	+	0.995948i	$0.528666\pi$
$930$	−4.63090	−	1.15061i	−0.151853	−	0.0377301i
$931$	−1.92162			−0.0629786
$932$			2.81044i			0.0920590i
$933$			26.0410i			0.852545i
$934$	0.175666			0.00574797
$935$	0.879362	−	3.53919i	0.0287582	−	0.115744i
$936$	1.65983			0.0542531
$937$		−	26.8176i		−	0.876094i	−0.898952	−	0.438047i	$-0.855670\pi$
$937$		−	26.8176i		−	0.876094i	0.898952	−	0.438047i	$-0.144330\pi$
$938$		−	7.28846i		−	0.237977i
$939$	27.8359			0.908390
$940$	−6.19570	+	24.9360i	−0.202082	+	0.813323i
$941$	6.64650			0.216670			0.108335	−	0.994114i	$-0.465448\pi$
$941$	6.64650			0.216670			0.108335	+	0.994114i	$0.465448\pi$
$942$			8.07942i			0.263242i
$943$			38.8443i			1.26494i
$944$	−19.2351			−0.626050
$945$	−2.17009	−	0.539189i	−0.0705929	−	0.0175398i
$946$	2.92881			0.0952238
$947$			19.6765i			0.639399i	0.947519	+	0.319700i	$0.103582\pi$
$947$			19.6765i			0.639399i	−0.947519	+	0.319700i	$0.896418\pi$
$948$			0.0722347i			0.00234607i
$949$	−2.42469			−0.0787089
$950$	2.42469	−	4.57814i	0.0786675	−	0.148534i
$951$	30.1217			0.976762
$952$			3.26180i			0.105715i
$953$		−	10.8781i		−	0.352377i	−0.984356	−	0.176189i	$-0.943623\pi$
$953$		−	10.8781i		−	0.352377i	0.984356	−	0.176189i	$-0.0563769\pi$
$954$	−1.21953			−0.0394839
$955$	−58.4534	−	14.5236i	−1.89151	−	0.469972i
$956$	−25.2001			−0.815028
$957$			5.82991i			0.188454i
$958$			5.02893i			0.162477i
$959$	1.70928			0.0551954
$960$	−0.993857	+	4.00000i	−0.0320766	+	0.129099i
$961$	−15.3363			−0.494719
$962$		−	0.675811i		−	0.0217890i
$963$			14.3968i			0.463931i
$964$	−34.5835			−1.11386
$965$	−3.91548	+	15.7587i	−0.126044	+	0.507291i
$966$	−2.53919			−0.0816971
$967$			31.0794i			0.999447i	0.866185	+	0.499723i	$0.166565\pi$
$967$			31.0794i			0.999447i	−0.866185	+	0.499723i	$0.833435\pi$
$968$		−	2.00000i		−	0.0642824i
$969$	3.13397			0.100678
$970$	16.4813	+	4.09502i	0.529184	+	0.131483i
$971$	28.0856			0.901309			0.450654	−	0.892699i	$-0.351191\pi$
$971$	28.0856			0.901309			0.450654	+	0.892699i	$0.351191\pi$
$972$			1.70928i			0.0548250i
$973$		−	14.9444i		−	0.479096i
$974$	−11.7854			−0.377628
$975$	3.66701	+	1.94214i	0.117438	+	0.0621983i
$976$	21.9733			0.703349
$977$		−	2.88882i		−	0.0924215i	−0.998932	−	0.0462107i	$-0.985285\pi$
$977$		−	2.88882i		−	0.0924215i	0.998932	−	0.0462107i	$-0.0147146\pi$
$978$		−	3.06997i		−	0.0981667i
$979$	−8.08557			−0.258416
$980$	−3.70928	−	0.921622i	−0.118488	−	0.0294401i
$981$	0.963883			0.0307744
$982$			0.485206i			0.0154835i
$983$		−	39.7776i		−	1.26871i	−0.773042	−	0.634355i	$-0.781266\pi$
$983$		−	39.7776i		−	1.26871i	0.773042	−	0.634355i	$-0.218734\pi$
$984$	−16.4969			−0.525903
$985$	−0.0311968	+	0.125559i	−0.000994014	+	0.00400063i
$986$	−5.12660			−0.163264
$987$			6.72261i			0.213983i
$988$		−	2.72592i		−	0.0867230i
$989$	25.5802			0.813404
$990$	−0.290725	+	1.17009i	−0.00923984	+	0.0371878i
$991$	−36.3028			−1.15320			−0.576599	−	0.817027i	$-0.695620\pi$
$991$	−36.3028			−1.15320			−0.576599	+	0.817027i	$0.695620\pi$
$992$			20.8248i			0.661189i
$993$		−	33.4534i		−	1.06161i
$994$	−0.133969			−0.00424924
$995$	−40.3545	−	10.0267i	−1.27933	−	0.317867i
$996$	11.4680			0.363377
$997$		−	56.1933i		−	1.77966i	−0.456294	−	0.889829i	$-0.650823\pi$
$997$		−	56.1933i		−	1.77966i	0.456294	−	0.889829i	$-0.349177\pi$
$998$		−	10.3246i		−	0.326819i
$999$	1.51026			0.0477825

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.c.d.694.3	✓	6
5.2	odd	4		5775.2.a.bv.1.2		3
5.3	odd	4		5775.2.a.bs.1.2		3
5.4	even	2	inner	1155.2.c.d.694.4	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.c.d.694.3	✓	6	1.1	even	1	trivial
1155.2.c.d.694.4	yes	6	5.4	even	2	inner
5775.2.a.bs.1.2		3	5.3	odd	4
5775.2.a.bv.1.2		3	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)

\(f(q)\)	\(=\)	\(q-0.539189i q^{2} +1.00000i q^{3} +1.70928 q^{4} +(2.17009 + 0.539189i) q^{5} +0.539189 q^{6} -1.00000i q^{7} -2.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-0.539189i q^{2} +1.00000i q^{3} +1.70928 q^{4} +(2.17009 + 0.539189i) q^{5} +0.539189 q^{6} -1.00000i q^{7} -2.00000i q^{8} -1.00000 q^{9} +(0.290725 - 1.17009i) q^{10} +1.00000 q^{11} +1.70928i q^{12} -0.829914i q^{13} -0.539189 q^{14} +(-0.539189 + 2.17009i) q^{15} +2.34017 q^{16} -1.63090i q^{17} +0.539189i q^{18} +1.92162 q^{19} +(3.70928 + 0.921622i) q^{20} +1.00000 q^{21} -0.539189i q^{22} -4.70928i q^{23} +2.00000 q^{24} +(4.41855 + 2.34017i) q^{25} -0.447480 q^{26} -1.00000i q^{27} -1.70928i q^{28} +5.82991 q^{29} +(1.17009 + 0.290725i) q^{30} -3.95774 q^{31} -5.26180i q^{32} +1.00000i q^{33} -0.879362 q^{34} +(0.539189 - 2.17009i) q^{35} -1.70928 q^{36} +1.51026i q^{37} -1.03612i q^{38} +0.829914 q^{39} +(1.07838 - 4.34017i) q^{40} -8.24846 q^{41} -0.539189i q^{42} +5.43188i q^{43} +1.70928 q^{44} +(-2.17009 - 0.539189i) q^{45} -2.53919 q^{46} +6.72261i q^{47} +2.34017i q^{48} -1.00000 q^{49} +(1.26180 - 2.38243i) q^{50} +1.63090 q^{51} -1.41855i q^{52} +2.26180i q^{53} -0.539189 q^{54} +(2.17009 + 0.539189i) q^{55} -2.00000 q^{56} +1.92162i q^{57} -3.14342i q^{58} -8.21953 q^{59} +(-0.921622 + 3.70928i) q^{60} +9.38962 q^{61} +2.13397i q^{62} +1.00000i q^{63} +1.84324 q^{64} +(0.447480 - 1.80098i) q^{65} +0.539189 q^{66} +13.5174i q^{67} -2.78765i q^{68} +4.70928 q^{69} +(-1.17009 - 0.290725i) q^{70} +0.248464 q^{71} +2.00000i q^{72} -2.92162i q^{73} +0.814315 q^{74} +(-2.34017 + 4.41855i) q^{75} +3.28458 q^{76} -1.00000i q^{77} -0.447480i q^{78} +0.0422604 q^{79} +(5.07838 + 1.26180i) q^{80} +1.00000 q^{81} +4.44748i q^{82} -6.70928i q^{83} +1.70928 q^{84} +(0.879362 - 3.53919i) q^{85} +2.92881 q^{86} +5.82991i q^{87} -2.00000i q^{88} -8.08557 q^{89} +(-0.290725 + 1.17009i) q^{90} -0.829914 q^{91} -8.04945i q^{92} -3.95774i q^{93} +3.62475 q^{94} +(4.17009 + 1.03612i) q^{95} +5.26180 q^{96} +14.0856i q^{97} +0.539189i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{4} + 2 q^{5} - 6 q^{9}+O(q^{10}) \) 6 * q - 4 * q^4 + 2 * q^5 - 6 * q^9	\( 6 q - 4 q^{4} + 2 q^{5} - 6 q^{9} + 16 q^{10} + 6 q^{11} - 8 q^{16} + 18 q^{19} + 8 q^{20} + 6 q^{21} + 12 q^{24} - 2 q^{25} - 4 q^{26} + 46 q^{29} - 4 q^{30} + 8 q^{31} + 20 q^{34} + 4 q^{36} + 16 q^{39} - 32 q^{41} - 4 q^{44} - 2 q^{45} - 12 q^{46} - 6 q^{49} - 8 q^{50} + 2 q^{51} + 2 q^{55} - 12 q^{56} - 2 q^{59} - 12 q^{60} - 2 q^{61} + 24 q^{64} + 4 q^{65} + 14 q^{69} + 4 q^{70} - 16 q^{71} - 12 q^{74} + 8 q^{75} - 36 q^{76} + 32 q^{79} + 24 q^{80} + 6 q^{81} - 4 q^{84} - 20 q^{85} - 44 q^{86} + 26 q^{89} - 16 q^{90} - 16 q^{91} - 56 q^{94} + 14 q^{95} + 16 q^{96} - 6 q^{99}+O(q^{100}) \) 6 * q - 4 * q^4 + 2 * q^5 - 6 * q^9 + 16 * q^10 + 6 * q^11 - 8 * q^16 + 18 * q^19 + 8 * q^20 + 6 * q^21 + 12 * q^24 - 2 * q^25 - 4 * q^26 + 46 * q^29 - 4 * q^30 + 8 * q^31 + 20 * q^34 + 4 * q^36 + 16 * q^39 - 32 * q^41 - 4 * q^44 - 2 * q^45 - 12 * q^46 - 6 * q^49 - 8 * q^50 + 2 * q^51 + 2 * q^55 - 12 * q^56 - 2 * q^59 - 12 * q^60 - 2 * q^61 + 24 * q^64 + 4 * q^65 + 14 * q^69 + 4 * q^70 - 16 * q^71 - 12 * q^74 + 8 * q^75 - 36 * q^76 + 32 * q^79 + 24 * q^80 + 6 * q^81 - 4 * q^84 - 20 * q^85 - 44 * q^86 + 26 * q^89 - 16 * q^90 - 16 * q^91 - 56 * q^94 + 14 * q^95 + 16 * q^96 - 6 * q^99

Introduction

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Database

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