LMFDB - Embedded newform 1805.2.b.l.1084.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1084,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1805.1084");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.b (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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1084.3
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.l.1084.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.32462i q^{2} +1.14858i q^{3} -3.40387 q^{4} +(-2.01201 + 0.975617i) q^{5} +2.67001 q^{6} -0.143302i q^{7} +3.26348i q^{8} +1.68077 q^{9} +O(q^{10})$	\(q-2.32462i q^{2} +1.14858i q^{3} -3.40387 q^{4} +(-2.01201 + 0.975617i) q^{5} +2.67001 q^{6} -0.143302i q^{7} +3.26348i q^{8} +1.68077 q^{9} +(2.26794 + 4.67716i) q^{10} -2.81557 q^{11} -3.90962i q^{12} +1.70854i q^{13} -0.333123 q^{14} +(-1.12057 - 2.31095i) q^{15} +0.778610 q^{16} +3.55886i q^{17} -3.90715i q^{18} +(6.84862 - 3.32088i) q^{20} +0.164594 q^{21} +6.54515i q^{22} -7.19394i q^{23} -3.74836 q^{24} +(3.09634 - 3.92590i) q^{25} +3.97171 q^{26} +5.37623i q^{27} +0.487782i q^{28} +7.57154 q^{29} +(-5.37209 + 2.60491i) q^{30} -4.84686 q^{31} +4.71698i q^{32} -3.23391i q^{33} +8.27302 q^{34} +(0.139808 + 0.288325i) q^{35} -5.72111 q^{36} -9.49127i q^{37} -1.96239 q^{39} +(-3.18390 - 6.56614i) q^{40} +0.187320 q^{41} -0.382619i q^{42} -10.9943i q^{43} +9.58385 q^{44} +(-3.38171 + 1.63978i) q^{45} -16.7232 q^{46} -3.67032i q^{47} +0.894296i q^{48} +6.97946 q^{49} +(-9.12623 - 7.19783i) q^{50} -4.08764 q^{51} -5.81566i q^{52} +1.64322i q^{53} +12.4977 q^{54} +(5.66495 - 2.74692i) q^{55} +0.467663 q^{56} -17.6010i q^{58} -5.36637 q^{59} +(3.81429 + 7.86618i) q^{60} +10.1127 q^{61} +11.2671i q^{62} -0.240857i q^{63} +12.5224 q^{64} +(-1.66688 - 3.43760i) q^{65} -7.51762 q^{66} -6.00805i q^{67} -12.1139i q^{68} +8.26281 q^{69} +(0.670247 - 0.325001i) q^{70} -0.540979 q^{71} +5.48514i q^{72} -10.4674i q^{73} -22.0636 q^{74} +(4.50920 + 3.55640i) q^{75} +0.403477i q^{77} +4.56183i q^{78} -11.6088 q^{79} +(-1.56657 + 0.759625i) q^{80} -1.13273 q^{81} -0.435449i q^{82} -7.59579i q^{83} -0.560257 q^{84} +(-3.47209 - 7.16046i) q^{85} -25.5576 q^{86} +8.69652i q^{87} -9.18856i q^{88} +1.44684 q^{89} +(3.81188 + 7.86121i) q^{90} +0.244837 q^{91} +24.4873i q^{92} -5.56701i q^{93} -8.53210 q^{94} -5.41783 q^{96} -8.80212i q^{97} -16.2246i q^{98} -4.73232 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9}+O(q^{10}) $ 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9	$ 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} + 6 q^{10} + 12 q^{11} + 24 q^{14} + 9 q^{15} + 6 q^{16} + 21 q^{20} - 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} + 36 q^{29} - 18 q^{30} - 42 q^{31} + 6 q^{34} + 27 q^{35} - 6 q^{36} - 24 q^{39} - 12 q^{40} - 60 q^{41} + 30 q^{44} + 9 q^{45} - 6 q^{46} - 12 q^{49} - 18 q^{50} - 30 q^{51} + 24 q^{54} + 33 q^{55} - 18 q^{56} + 60 q^{59} + 42 q^{60} + 30 q^{61} - 18 q^{65} + 36 q^{66} + 66 q^{69} - 9 q^{70} - 96 q^{71} - 24 q^{74} - 36 q^{75} + 72 q^{79} - 42 q^{80} - 96 q^{81} - 54 q^{84} - 27 q^{85} - 108 q^{86} + 84 q^{89} + 93 q^{90} - 96 q^{91} + 36 q^{94} - 120 q^{96}+O(q^{100}) $ 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9 + 6 * q^10 + 12 * q^11 + 24 * q^14 + 9 * q^15 + 6 * q^16 + 21 * q^20 - 6 * q^21 + 42 * q^24 - 3 * q^25 - 12 * q^26 + 36 * q^29 - 18 * q^30 - 42 * q^31 + 6 * q^34 + 27 * q^35 - 6 * q^36 - 24 * q^39 - 12 * q^40 - 60 * q^41 + 30 * q^44 + 9 * q^45 - 6 * q^46 - 12 * q^49 - 18 * q^50 - 30 * q^51 + 24 * q^54 + 33 * q^55 - 18 * q^56 + 60 * q^59 + 42 * q^60 + 30 * q^61 - 18 * q^65 + 36 * q^66 + 66 * q^69 - 9 * q^70 - 96 * q^71 - 24 * q^74 - 36 * q^75 + 72 * q^79 - 42 * q^80 - 96 * q^81 - 54 * q^84 - 27 * q^85 - 108 * q^86 + 84 * q^89 + 93 * q^90 - 96 * q^91 + 36 * q^94 - 120 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times$.

$n$	$362$	$1446$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	2.32462i		−	1.64376i	−0.569663	−	0.821878i	$-0.692926\pi$
$2$		−	2.32462i		−	1.64376i	0.569663	−	0.821878i	$-0.307074\pi$
$3$			1.14858i			0.663133i	0.943432	+	0.331566i	$0.107577\pi$
$3$			1.14858i			0.663133i	−0.943432	+	0.331566i	$0.892423\pi$
$4$	−3.40387			−1.70194
$5$	−2.01201	+	0.975617i	−0.899797	+	0.436309i
$5$	−2.01201	+	0.975617i	−0.899797	+	0.436309i
$6$	2.67001			1.09003
$7$		−	0.143302i		−	0.0541631i	−0.999633	−	0.0270816i	$-0.991379\pi$
$7$		−	0.143302i		−	0.0541631i	0.999633	−	0.0270816i	$-0.00862138\pi$
$8$			3.26348i			1.15381i
$9$	1.68077			0.560255
$10$	2.26794	+	4.67716i	0.717186	+	1.47905i
$11$	−2.81557			−0.848927			−0.424463	−	0.905445i	$-0.639537\pi$
$11$	−2.81557			−0.848927			−0.424463	+	0.905445i	$0.639537\pi$
$12$		−	3.90962i		−	1.12861i
$13$			1.70854i			0.473864i	0.971526	+	0.236932i	$0.0761418\pi$
$13$			1.70854i			0.473864i	−0.971526	+	0.236932i	$0.923858\pi$
$14$	−0.333123			−0.0890310
$15$	−1.12057	−	2.31095i	−0.289331	−	0.596685i
$16$	0.778610			0.194653
$17$			3.55886i			0.863151i	0.902077	+	0.431576i	$0.142042\pi$
$17$			3.55886i			0.863151i	−0.902077	+	0.431576i	$0.857958\pi$
$18$		−	3.90715i		−	0.920923i
$19$		0			0
$19$		0			0
$20$	6.84862	−	3.32088i	1.53140	−	0.742571i
$21$	0.164594			0.0359173
$22$			6.54515i			1.39543i
$23$		−	7.19394i		−	1.50004i	−0.661415	−	0.750020i	$-0.730044\pi$
$23$		−	7.19394i		−	1.50004i	0.661415	−	0.750020i	$-0.269956\pi$
$24$	−3.74836			−0.765132
$25$	3.09634	−	3.92590i	0.619269	−	0.785179i
$26$	3.97171			0.778917
$27$			5.37623i			1.03466i
$28$			0.487782i			0.0921822i
$29$	7.57154			1.40600			0.703000	−	0.711190i	$-0.251843\pi$
$29$	7.57154			1.40600			0.703000	+	0.711190i	$0.251843\pi$
$30$	−5.37209	+	2.60491i	−0.980805	+	0.475589i
$31$	−4.84686			−0.870522			−0.435261	−	0.900304i	$-0.643344\pi$
$31$	−4.84686			−0.870522			−0.435261	+	0.900304i	$0.643344\pi$
$32$			4.71698i			0.833852i
$33$		−	3.23391i		−	0.562951i
$34$	8.27302			1.41881
$35$	0.139808	+	0.288325i	0.0236319	+	0.0487358i
$36$	−5.72111			−0.953519
$37$		−	9.49127i		−	1.56035i	−0.625559	−	0.780177i	$-0.715129\pi$
$37$		−	9.49127i		−	1.56035i	0.625559	−	0.780177i	$-0.284871\pi$
$38$		0			0
$39$	−1.96239			−0.314235
$40$	−3.18390	−	6.56614i	−0.503419	−	1.03820i
$41$	0.187320			0.0292545			0.0146272	−	0.999893i	$-0.495344\pi$
$41$	0.187320			0.0292545			0.0146272	+	0.999893i	$0.495344\pi$
$42$		−	0.382619i		−	0.0590393i
$43$		−	10.9943i		−	1.67662i	−0.545196	−	0.838309i	$-0.683545\pi$
$43$		−	10.9943i		−	1.67662i	0.545196	−	0.838309i	$-0.316455\pi$
$44$	9.58385			1.44482
$45$	−3.38171	+	1.63978i	−0.504116	+	0.244444i
$46$	−16.7232			−2.46570
$47$		−	3.67032i		−	0.535371i	−0.963506	−	0.267685i	$-0.913741\pi$
$47$		−	3.67032i		−	0.535371i	0.963506	−	0.267685i	$-0.0862587\pi$
$48$			0.894296i			0.129080i
$49$	6.97946			0.997066
$50$	−9.12623	−	7.19783i	−1.29064	−	1.01793i
$51$	−4.08764			−0.572384
$52$		−	5.81566i		−	0.806486i
$53$			1.64322i			0.225714i	0.993611	+	0.112857i	$0.0360002\pi$
$53$			1.64322i			0.225714i	−0.993611	+	0.112857i	$0.964000\pi$
$54$	12.4977			1.70072
$55$	5.66495	−	2.74692i	0.763862	−	0.370395i
$56$	0.467663			0.0624941
$57$		0			0
$58$		−	17.6010i		−	2.31112i
$59$	−5.36637			−0.698642			−0.349321	−	0.937003i	$-0.613588\pi$
$59$	−5.36637			−0.698642			−0.349321	+	0.937003i	$0.613588\pi$
$60$	3.81429	+	7.86618i	0.492423	+	1.01552i
$61$	10.1127			1.29480			0.647402	−	0.762148i	$-0.275855\pi$
$61$	10.1127			1.29480			0.647402	+	0.762148i	$0.275855\pi$
$62$			11.2671i			1.43093i
$63$		−	0.240857i		−	0.0303452i
$64$	12.5224			1.56530
$65$	−1.66688	−	3.43760i	−0.206751	−	0.426381i
$66$	−7.51762			−0.925355
$67$		−	6.00805i		−	0.734001i	−0.930221	−	0.367000i	$-0.880385\pi$
$67$		−	6.00805i		−	0.734001i	0.930221	−	0.367000i	$-0.119615\pi$
$68$		−	12.1139i		−	1.46903i
$69$	8.26281			0.994725
$70$	0.670247	−	0.325001i	0.0801098	−	0.0388450i
$71$	−0.540979			−0.0642024			−0.0321012	−	0.999485i	$-0.510220\pi$
$71$	−0.540979			−0.0642024			−0.0321012	+	0.999485i	$0.510220\pi$
$72$			5.48514i			0.646430i
$73$		−	10.4674i		−	1.22512i	−0.790425	−	0.612559i	$-0.790140\pi$
$73$		−	10.4674i		−	1.22512i	0.790425	−	0.612559i	$-0.209860\pi$
$74$	−22.0636			−2.56484
$75$	4.50920	+	3.55640i	0.520678	+	0.410657i
$76$		0			0
$77$			0.403477i			0.0459805i
$78$			4.56183i			0.516525i
$79$	−11.6088			−1.30610			−0.653048	−	0.757317i	$-0.726510\pi$
$79$	−11.6088			−1.30610			−0.653048	+	0.757317i	$0.726510\pi$
$80$	−1.56657	+	0.759625i	−0.175148	+	0.0849287i
$81$	−1.13273			−0.125859
$82$		−	0.435449i		−	0.0480873i
$83$		−	7.59579i		−	0.833746i	−0.908965	−	0.416873i	$-0.863126\pi$
$83$		−	7.59579i		−	0.833746i	0.908965	−	0.416873i	$-0.136874\pi$
$84$	−0.560257			−0.0611290
$85$	−3.47209	−	7.16046i	−0.376601	−	0.776661i
$86$	−25.5576			−2.75595
$87$			8.69652i			0.932365i
$88$		−	9.18856i		−	0.979504i
$89$	1.44684			0.153365			0.0766823	−	0.997056i	$-0.475567\pi$
$89$	1.44684			0.153365			0.0766823	+	0.997056i	$0.475567\pi$
$90$	3.81188	+	7.86121i	0.401807	+	0.828644i
$91$	0.244837			0.0256659
$92$			24.4873i			2.55297i
$93$		−	5.56701i		−	0.577272i
$94$	−8.53210			−0.880019
$95$		0			0
$96$	−5.41783			−0.552955
$97$		−	8.80212i		−	0.893720i	−0.894604	−	0.446860i	$-0.852542\pi$
$97$		−	8.80212i		−	0.893720i	0.894604	−	0.446860i	$-0.147458\pi$
$98$		−	16.2246i		−	1.63893i
$99$	−4.73232			−0.475616
$100$	−10.5396	+	13.3633i	−1.05396	+	1.33633i
$101$	−2.87795			−0.286367			−0.143183	−	0.989696i	$-0.545734\pi$
$101$	−2.87795			−0.286367			−0.143183	+	0.989696i	$0.545734\pi$
$102$			9.50222i			0.940860i
$103$			1.19966i			0.118206i	0.998252	+	0.0591032i	$0.0188241\pi$
$103$			1.19966i			0.118206i	−0.998252	+	0.0591032i	$0.981176\pi$
$104$	−5.57578			−0.546751
$105$	−0.331164	+	0.160581i	−0.0323183	+	0.0156711i
$106$	3.81987			0.371019
$107$			4.09536i			0.395913i	0.980211	+	0.197957i	$0.0634305\pi$
$107$			4.09536i			0.395913i	−0.980211	+	0.197957i	$0.936570\pi$
$108$		−	18.3000i		−	1.76092i
$109$	−16.1941			−1.55111			−0.775555	−	0.631280i	$-0.782530\pi$
$109$	−16.1941			−1.55111			−0.775555	+	0.631280i	$0.782530\pi$
$110$	−6.38555	−	13.1689i	−0.608839	−	1.25560i
$111$	10.9015			1.03472
$112$		−	0.111576i		−	0.0105430i
$113$			3.11845i			0.293359i	0.989184	+	0.146680i	$0.0468586\pi$
$113$			3.11845i			0.293359i	−0.989184	+	0.146680i	$0.953141\pi$
$114$		0			0
$115$	7.01853	+	14.4743i	0.654481	+	1.34973i
$116$	−25.7726			−2.39292
$117$			2.87166i			0.265485i
$118$			12.4748i			1.14840i
$119$	0.509993			0.0467509
$120$	7.54173	−	3.65697i	0.688463	−	0.333834i
$121$	−3.07255			−0.279323
$122$		−	23.5083i		−	2.12834i
$123$			0.215152i			0.0193996i
$124$	16.4981			1.48157
$125$	−2.39970	+	10.9198i	−0.214635	+	0.976694i
$126$	−0.559902			−0.0498801
$127$			8.16019i			0.724100i	0.932159	+	0.362050i	$0.117923\pi$
$127$			8.16019i			0.724100i	−0.932159	+	0.362050i	$0.882077\pi$
$128$		−	19.6760i		−	1.73913i
$129$	12.6278			1.11182
$130$	−7.99111	+	3.87487i	−0.700867	+	0.339849i
$131$	2.61996			0.228907			0.114453	−	0.993429i	$-0.463488\pi$
$131$	2.61996			0.228907			0.114453	+	0.993429i	$0.463488\pi$
$132$			11.0078i			0.958108i
$133$		0			0
$134$	−13.9665			−1.20652
$135$	−5.24514	−	10.8170i	−0.451430	−	0.930980i
$136$	−11.6143			−0.995916
$137$		−	12.3205i		−	1.05261i	−0.850296	−	0.526305i	$-0.823577\pi$
$137$		−	12.3205i		−	1.05261i	0.850296	−	0.526305i	$-0.176423\pi$
$138$		−	19.2079i		−	1.63509i
$139$	−7.95376			−0.674629			−0.337314	−	0.941392i	$-0.609519\pi$
$139$	−7.95376			−0.674629			−0.337314	+	0.941392i	$0.609519\pi$
$140$	−0.475889	−	0.981421i	−0.0402199	−	0.0829452i
$141$	4.21565			0.355022
$142$			1.25757i			0.105533i
$143$		−	4.81052i		−	0.402276i
$144$	1.30866			0.109055
$145$	−15.2340	+	7.38692i	−1.26511	+	0.613451i
$146$	−24.3328			−2.01380
$147$			8.01647i			0.661187i
$148$			32.3071i			2.65562i
$149$	4.19620			0.343766			0.171883	−	0.985117i	$-0.445015\pi$
$149$	4.19620			0.343766			0.171883	+	0.985117i	$0.445015\pi$
$150$	8.26728	−	10.4822i	0.675021	−	0.855868i
$151$	2.86140			0.232857			0.116429	−	0.993199i	$-0.462855\pi$
$151$	2.86140			0.232857			0.116429	+	0.993199i	$0.462855\pi$
$152$		0			0
$153$			5.98161i			0.483585i
$154$	0.937933			0.0755808
$155$	9.75192	−	4.72868i	0.783293	−	0.379817i
$156$	6.67974			0.534807
$157$		−	11.5244i		−	0.919744i	−0.887985	−	0.459872i	$-0.847895\pi$
$157$		−	11.5244i		−	0.919744i	0.887985	−	0.459872i	$-0.152105\pi$
$158$			26.9862i			2.14690i
$159$	−1.88737			−0.149678
$160$	−4.60197	−	9.49060i	−0.363817	−	0.750298i
$161$	−1.03091			−0.0812468
$162$			2.63318i			0.206882i
$163$		−	18.9195i		−	1.48189i	−0.671567	−	0.740944i	$-0.734379\pi$
$163$		−	18.9195i		−	1.48189i	0.671567	−	0.740944i	$-0.265621\pi$
$164$	−0.637614			−0.0497893
$165$	3.15506	+	6.50665i	0.245621	+	0.506542i
$166$	−17.6573			−1.37048
$167$		−	15.0690i		−	1.16607i	−0.812447	−	0.583036i	$-0.801865\pi$
$167$		−	15.0690i		−	1.16607i	0.812447	−	0.583036i	$-0.198135\pi$
$168$			0.537148i			0.0414419i
$169$	10.0809			0.775453
$170$	−16.6454	+	8.07129i	−1.27664	+	0.619040i
$171$		0			0
$172$			37.4233i			2.85350i
$173$			21.6950i			1.64944i	0.565542	+	0.824719i	$0.308667\pi$
$173$			21.6950i			1.64944i	−0.565542	+	0.824719i	$0.691333\pi$
$174$	20.2161			1.53258
$175$	−0.562589	−	0.443713i	−0.0425277	−	0.0335415i
$176$	−2.19223			−0.165246
$177$		−	6.16370i		−	0.463292i
$178$		−	3.36336i		−	0.252094i
$179$	22.8790			1.71006			0.855028	−	0.518581i	$-0.173540\pi$
$179$	22.8790			1.71006			0.855028	+	0.518581i	$0.173540\pi$
$180$	11.5109	−	5.58161i	0.857973	−	0.416029i
$181$	11.5660			0.859693			0.429847	−	0.902902i	$-0.358568\pi$
$181$	11.5660			0.859693			0.429847	+	0.902902i	$0.358568\pi$
$182$		−	0.569155i		−	0.0421886i
$183$			11.6153i			0.858627i
$184$	23.4773			1.73077
$185$	9.25984	+	19.0965i	0.680797	+	1.40400i
$186$	−12.9412			−0.948894
$187$		−	10.0202i		−	0.732752i
$188$			12.4933i			0.911167i
$189$	0.770425			0.0560402
$190$		0			0
$191$	7.28958			0.527455			0.263728	−	0.964597i	$-0.415048\pi$
$191$	7.28958			0.527455			0.263728	+	0.964597i	$0.415048\pi$
$192$			14.3830i			1.03800i
$193$		−	26.1862i		−	1.88493i	−0.334308	−	0.942464i	$-0.608503\pi$
$193$		−	26.1862i		−	1.88493i	0.334308	−	0.942464i	$-0.391497\pi$
$194$	−20.4616			−1.46906
$195$	3.94835	−	1.91454i	0.282747	−	0.137103i
$196$	−23.7572			−1.69694
$197$		−	2.28820i		−	0.163027i	−0.996672	−	0.0815136i	$-0.974025\pi$
$197$		−	2.28820i		−	0.163027i	0.996672	−	0.0815136i	$-0.0259754\pi$
$198$			11.0009i			0.781797i
$199$	12.2469			0.868159			0.434079	−	0.900875i	$-0.357074\pi$
$199$	12.2469			0.868159			0.434079	+	0.900875i	$0.357074\pi$
$200$	12.8121	+	10.1049i	0.905950	+	0.714521i
$201$	6.90073			0.486740
$202$			6.69015i			0.470717i
$203$		−	1.08502i		−	0.0761533i
$204$	13.9138			0.974161
$205$	−0.376889	+	0.182753i	−0.0263231	+	0.0127640i
$206$	2.78877			0.194302
$207$		−	12.0913i		−	0.840405i
$208$			1.33029i			0.0922388i
$209$		0			0
$210$	0.373289	+	0.769832i	0.0257594	+	0.0531234i
$211$	−3.00309			−0.206741			−0.103371	−	0.994643i	$-0.532963\pi$
$211$	−3.00309			−0.206741			−0.103371	+	0.994643i	$0.532963\pi$
$212$		−	5.59332i		−	0.384151i
$213$		−	0.621357i		−	0.0425747i
$214$	9.52016			0.650785
$215$	10.7262	+	22.1206i	0.731523	+	1.50861i
$216$	−17.5452			−1.19380
$217$			0.694565i			0.0471502i
$218$			37.6451i			2.54965i
$219$	12.0227			0.812416
$220$	−19.2828	+	9.35017i	−1.30004	+	0.630388i
$221$	−6.08046			−0.409016
$222$		−	25.3418i		−	1.70083i
$223$			2.19363i			0.146897i	0.997299	+	0.0734483i	$0.0234004\pi$
$223$			2.19363i			0.146897i	−0.997299	+	0.0734483i	$0.976600\pi$
$224$	0.675953			0.0451640
$225$	5.20423	−	6.59851i	0.346948	−	0.439901i
$226$	7.24922			0.482211
$227$			6.44357i			0.427675i	0.976869	+	0.213838i	$0.0685963\pi$
$227$			6.44357i			0.427675i	−0.976869	+	0.213838i	$0.931404\pi$
$228$		0			0
$229$	1.54321			0.101978			0.0509892	−	0.998699i	$-0.483763\pi$
$229$	1.54321			0.101978			0.0509892	+	0.998699i	$0.483763\pi$
$230$	33.6472	−	16.3154i	2.21863	−	1.07581i
$231$	−0.463426			−0.0304912
$232$			24.7096i			1.62226i
$233$		−	20.4612i		−	1.34046i	−0.742155	−	0.670228i	$-0.766196\pi$
$233$		−	20.4612i		−	1.34046i	0.742155	−	0.670228i	$-0.233804\pi$
$234$	6.67552			0.436392
$235$	3.58082	+	7.38470i	0.233587	+	0.481725i
$236$	18.2665			1.18904
$237$		−	13.3337i		−	0.866115i
$238$		−	1.18554i		−	0.0768472i
$239$	−6.24066			−0.403675			−0.201837	−	0.979419i	$-0.564691\pi$
$239$	−6.24066			−0.403675			−0.201837	+	0.979419i	$0.564691\pi$
$240$	−0.872490	−	1.79933i	−0.0563190	−	0.116146i
$241$	26.3148			1.69508			0.847542	−	0.530728i	$-0.178081\pi$
$241$	26.3148			1.69508			0.847542	+	0.530728i	$0.178081\pi$
$242$			7.14253i			0.459139i
$243$			14.8277i			0.951195i
$244$	−34.4225			−2.20368
$245$	−14.0427	+	6.80928i	−0.897157	+	0.435029i
$246$	0.500147			0.0318882
$247$		0			0
$248$		−	15.8176i		−	1.00442i
$249$	8.72437			0.552884
$250$	25.3844	+	5.57839i	1.60545	+	0.352808i
$251$	−10.7064			−0.675779			−0.337889	−	0.941186i	$-0.609713\pi$
$251$	−10.7064			−0.675779			−0.337889	+	0.941186i	$0.609713\pi$
$252$			0.819847i			0.0516455i
$253$			20.2551i			1.27342i
$254$	18.9694			1.19024
$255$	8.22436	−	3.98797i	0.515029	−	0.249736i
$256$	−20.6943			−1.29340
$257$			13.5240i			0.843603i	0.906688	+	0.421802i	$0.138602\pi$
$257$			13.5240i			0.843603i	−0.906688	+	0.421802i	$0.861398\pi$
$258$		−	29.3550i		−	1.82756i
$259$	−1.36012			−0.0845136
$260$	5.67385	+	11.7011i	0.351877	+	0.725674i
$261$	12.7260			0.787719
$262$		−	6.09042i		−	0.376267i
$263$			6.54056i			0.403308i	0.979457	+	0.201654i	$0.0646317\pi$
$263$			6.54056i			0.403308i	−0.979457	+	0.201654i	$0.935368\pi$
$264$	10.5538			0.649541
$265$	−1.60315	−	3.30617i	−0.0984810	−	0.203097i
$266$		0			0
$267$			1.66181i			0.101701i
$268$			20.4507i			1.24922i
$269$	14.4220			0.879327			0.439663	−	0.898163i	$-0.355098\pi$
$269$	14.4220			0.879327			0.439663	+	0.898163i	$0.355098\pi$
$270$	−25.1455	+	12.1930i	−1.53031	+	0.742041i
$271$	−2.18429			−0.132686			−0.0663431	−	0.997797i	$-0.521133\pi$
$271$	−2.18429			−0.132686			−0.0663431	+	0.997797i	$0.521133\pi$
$272$			2.77097i			0.168015i
$273$			0.281215i			0.0170199i
$274$	−28.6405			−1.73024
$275$	−8.71798	+	11.0536i	−0.525714	+	0.666560i
$276$	−28.1256			−1.69296
$277$			15.9746i			0.959823i	0.877317	+	0.479911i	$0.159331\pi$
$277$			15.9746i			0.959823i	−0.877317	+	0.479911i	$0.840669\pi$
$278$			18.4895i			1.10893i
$279$	−8.14644			−0.487714
$280$	−0.940942	+	0.456260i	−0.0562320	+	0.0272668i
$281$	14.2569			0.850496			0.425248	−	0.905077i	$-0.360187\pi$
$281$	14.2569			0.850496			0.425248	+	0.905077i	$0.360187\pi$
$282$		−	9.79980i		−	0.583569i
$283$		−	7.06732i		−	0.420108i	−0.977690	−	0.210054i	$-0.932636\pi$
$283$		−	7.06732i		−	0.420108i	0.977690	−	0.210054i	$-0.0673640\pi$
$284$	1.84142			0.109268
$285$		0			0
$286$	−11.1826			−0.661244
$287$		−	0.0268434i		−	0.00158451i
$288$			7.92814i			0.467170i
$289$	4.33449			0.254970
$290$	17.1718	+	35.4133i	1.00836	+	2.07954i
$291$	10.1099			0.592655
$292$			35.6298i			2.08507i
$293$		−	0.976745i		−	0.0570621i	−0.999593	−	0.0285310i	$-0.990917\pi$
$293$		−	0.976745i		−	0.0570621i	0.999593	−	0.0285310i	$-0.00908294\pi$
$294$	18.6353			1.08683
$295$	10.7972	−	5.23552i	0.628636	−	0.304824i
$296$	30.9745			1.80036
$297$		−	15.1372i		−	0.878347i
$298$		−	9.75458i		−	0.565068i
$299$	12.2911			0.710815
$300$	−15.3488	−	12.1055i	−0.886161	−	0.698913i
$301$	−1.57551			−0.0908108
$302$		−	6.65167i		−	0.382760i
$303$		−	3.30555i		−	0.189899i
$304$		0			0
$305$	−20.3469	+	9.86617i	−1.16506	+	0.564935i
$306$	13.9050			0.794896
$307$			28.4670i			1.62470i	0.583171	+	0.812350i	$0.301812\pi$
$307$			28.4670i			1.62470i	−0.583171	+	0.812350i	$0.698188\pi$
$308$		−	1.37339i		−	0.0782559i
$309$	−1.37791			−0.0783865
$310$	−10.9924	−	22.6695i	−0.624326	−	1.28754i
$311$	−25.5461			−1.44858			−0.724292	−	0.689493i	$-0.757833\pi$
$311$	−25.5461			−1.44858			−0.724292	+	0.689493i	$0.757833\pi$
$312$		−	6.40423i		−	0.362568i
$313$		−	14.9513i		−	0.845098i	−0.906340	−	0.422549i	$-0.861135\pi$
$313$		−	14.9513i		−	0.845098i	0.906340	−	0.422549i	$-0.138865\pi$
$314$	−26.7898			−1.51184
$315$	0.234984	+	0.484606i	0.0132399	+	0.0273045i
$316$	39.5150			2.22289
$317$			22.5401i			1.26598i	0.774160	+	0.632990i	$0.218173\pi$
$317$			22.5401i			1.26598i	−0.774160	+	0.632990i	$0.781827\pi$
$318$			4.38743i			0.246035i
$319$	−21.3182			−1.19359
$320$	−25.1952	+	12.2171i	−1.40845	+	0.682956i
$321$	−4.70384			−0.262543
$322$			2.39647i			0.133550i
$323$		0			0
$324$	3.85568			0.214204
$325$	6.70755	+	5.29023i	0.372068	+	0.293449i
$326$	−43.9806			−2.43586
$327$		−	18.6002i		−	1.02859i
$328$			0.611315i			0.0337542i
$329$	−0.525964			−0.0289973
$330$	15.1255	−	7.33432i	0.832632	−	0.403741i
$331$	10.8681			0.597365			0.298682	−	0.954353i	$-0.403453\pi$
$331$	10.8681			0.597365			0.298682	+	0.954353i	$0.403453\pi$
$332$			25.8551i			1.41898i
$333$		−	15.9526i		−	0.874196i
$334$	−35.0297			−1.91674
$335$	5.86156	+	12.0882i	0.320251	+	0.660451i
$336$	0.128154			0.00699140
$337$		−	7.70906i		−	0.419939i	−0.977708	−	0.209970i	$-0.932663\pi$
$337$		−	7.70906i		−	0.419939i	0.977708	−	0.209970i	$-0.0673365\pi$
$338$		−	23.4343i		−	1.27466i
$339$	−3.58179			−0.194536
$340$	11.8185	+	24.3733i	0.640951	+	1.32183i
$341$	13.6467			0.739010
$342$		0			0
$343$		−	2.00329i		−	0.108167i
$344$	35.8797			1.93450
$345$	−16.6248	+	8.06134i	−0.895051	+	0.434008i
$346$	50.4327			2.71128
$347$			20.2699i			1.08814i	0.839039	+	0.544072i	$0.183118\pi$
$347$			20.2699i			1.08814i	−0.839039	+	0.544072i	$0.816882\pi$
$348$		−	29.6019i		−	1.58683i
$349$	−19.0503			−1.01974			−0.509870	−	0.860252i	$-0.670306\pi$
$349$	−19.0503			−1.01974			−0.509870	+	0.860252i	$0.670306\pi$
$350$	−1.03146	+	1.30781i	−0.0551341	+	0.0699053i
$351$	−9.18551			−0.490286
$352$		−	13.2810i		−	0.707880i
$353$			18.1667i			0.966917i	0.875367	+	0.483459i	$0.160620\pi$
$353$			18.1667i			0.966917i	−0.875367	+	0.483459i	$0.839380\pi$
$354$	−14.3283			−0.761540
$355$	1.08845	−	0.527788i	0.0577691	−	0.0280121i
$356$	−4.92486			−0.261017
$357$			0.585767i			0.0310021i
$358$		−	53.1851i		−	2.81092i
$359$	16.1318			0.851406			0.425703	−	0.904863i	$-0.360027\pi$
$359$	16.1318			0.851406			0.425703	+	0.904863i	$0.360027\pi$
$360$	−5.35139	−	11.0361i	−0.282043	−	0.581656i
$361$		0			0
$362$		−	26.8866i		−	1.41313i
$363$		−	3.52907i		−	0.185228i
$364$	−0.833396			−0.0436818
$365$	10.2122	+	21.0605i	0.534530	+	1.10236i
$366$	27.0012			1.41137
$367$		−	32.2616i		−	1.68404i	−0.539445	−	0.842021i	$-0.681366\pi$
$367$		−	32.2616i		−	1.68404i	0.539445	−	0.842021i	$-0.318634\pi$
$368$		−	5.60127i		−	0.291987i
$369$	0.314841			0.0163900
$370$	44.3922	−	21.5256i	2.30784	−	1.11906i
$371$	0.235477			0.0122254
$372$			18.9494i			0.982480i
$373$		−	2.38037i		−	0.123251i	−0.998099	−	0.0616253i	$-0.980372\pi$
$373$		−	2.38037i		−	0.123251i	0.998099	−	0.0616253i	$-0.0196284\pi$
$374$	−23.2933			−1.20447
$375$	−12.5422	−	2.75624i	−0.647678	−	0.142332i
$376$	11.9780			0.617718
$377$			12.9363i			0.666253i
$378$		−	1.79095i		−	0.0921164i
$379$	17.7215			0.910291			0.455145	−	0.890417i	$-0.349587\pi$
$379$	17.7215			0.910291			0.455145	+	0.890417i	$0.349587\pi$
$380$		0			0
$381$	−9.37263			−0.480174
$382$		−	16.9455i		−	0.867009i
$383$		−	10.6646i		−	0.544934i	−0.962165	−	0.272467i	$-0.912160\pi$
$383$		−	10.6646i		−	0.544934i	0.962165	−	0.272467i	$-0.0878395\pi$
$384$	22.5994			1.15327
$385$	−0.393639	−	0.811799i	−0.0200617	−	0.0413731i
$386$	−60.8732			−3.09836
$387$		−	18.4789i		−	0.939333i
$388$			29.9613i			1.52105i
$389$	−22.7313			−1.15252			−0.576262	−	0.817265i	$-0.695489\pi$
$389$	−22.7313			−1.15252			−0.576262	+	0.817265i	$0.695489\pi$
$390$	−4.45060	−	9.17843i	−0.225365	−	0.464768i
$391$	25.6022			1.29476
$392$			22.7773i			1.15043i
$393$			3.00923i			0.151796i
$394$	−5.31919			−0.267977
$395$	23.3570	−	11.3258i	1.17522	−	0.569861i
$396$	16.1082			0.809468
$397$			20.4405i			1.02588i	0.858425	+	0.512939i	$0.171443\pi$
$397$			20.4405i			1.02588i	−0.858425	+	0.512939i	$0.828557\pi$
$398$		−	28.4694i		−	1.42704i
$399$		0			0
$400$	2.41084	−	3.05674i	0.120542	−	0.152837i
$401$	−16.6972			−0.833817			−0.416908	−	0.908949i	$-0.636886\pi$
$401$	−16.6972			−0.833817			−0.416908	+	0.908949i	$0.636886\pi$
$402$		−	16.0416i		−	0.800082i
$403$		−	8.28106i		−	0.412509i
$404$	9.79618			0.487378
$405$	2.27907	−	1.10511i	0.113248	−	0.0549135i
$406$	−2.52226			−0.125178
$407$			26.7233i			1.32463i
$408$		−	13.3399i		−	0.660424i
$409$	−17.6846			−0.874447			−0.437224	−	0.899353i	$-0.644038\pi$
$409$	−17.6846			−0.874447			−0.437224	+	0.899353i	$0.644038\pi$
$410$	0.424831	+	0.876126i	0.0209809	+	0.0432688i
$411$	14.1511			0.698021
$412$		−	4.08350i		−	0.201180i
$413$			0.769012i			0.0378406i
$414$	−28.1078			−1.38142
$415$	7.41058	+	15.2828i	0.363771	+	0.750202i
$416$	−8.05915			−0.395133
$417$		−	9.13552i		−	0.447369i
$418$		0			0
$419$	37.9339			1.85319			0.926596	−	0.376059i	$-0.122721\pi$
$419$	37.9339			1.85319			0.926596	+	0.376059i	$0.122721\pi$
$420$	1.12724	−	0.546596i	0.0550037	−	0.0266711i
$421$	−11.5822			−0.564481			−0.282241	−	0.959344i	$-0.591078\pi$
$421$	−11.5822			−0.564481			−0.282241	+	0.959344i	$0.591078\pi$
$422$			6.98106i			0.339833i
$423$		−	6.16894i		−	0.299944i
$424$	−5.36262			−0.260432
$425$	13.9717	+	11.0195i	0.677728	+	0.534523i
$426$	−1.44442			−0.0699825
$427$		−	1.44918i		−	0.0701306i
$428$		−	13.9401i		−	0.673819i
$429$	5.52526			0.266762
$430$	51.4221	−	24.9345i	2.47980	−	1.20245i
$431$	−31.7898			−1.53126			−0.765629	−	0.643282i	$-0.777572\pi$
$431$	−31.7898			−1.53126			−0.765629	+	0.643282i	$0.777572\pi$
$432$			4.18599i			0.201398i
$433$			4.08848i			0.196480i	0.995163	+	0.0982399i	$0.0313212\pi$
$433$			4.08848i			0.196480i	−0.995163	+	0.0982399i	$0.968679\pi$
$434$	1.61460			0.0775034
$435$	−8.48447	−	17.4975i	−0.406799	−	0.838939i
$436$	55.1226			2.63989
$437$		0			0
$438$		−	27.9481i		−	1.33541i
$439$	−11.7557			−0.561070			−0.280535	−	0.959844i	$-0.590512\pi$
$439$	−11.7557			−0.561070			−0.280535	+	0.959844i	$0.590512\pi$
$440$	8.96451	+	18.4874i	0.427366	+	0.881354i
$441$	11.7308			0.558611
$442$			14.1348i			0.672323i
$443$		−	7.88658i		−	0.374703i	−0.982293	−	0.187351i	$-0.940010\pi$
$443$		−	7.88658i		−	0.374703i	0.982293	−	0.187351i	$-0.0599903\pi$
$444$	−37.1072			−1.76103
$445$	−2.91105	+	1.41156i	−0.137997	+	0.0669144i
$446$	5.09937			0.241462
$447$			4.81967i			0.227962i
$448$		−	1.79449i		−	0.0847817i
$449$	−1.16079			−0.0547812			−0.0273906	−	0.999625i	$-0.508720\pi$
$449$	−1.16079			−0.0547812			−0.0273906	+	0.999625i	$0.508720\pi$
$450$	−15.3390	−	12.0979i	−0.723090	−	0.570299i
$451$	−0.527413			−0.0248349
$452$		−	10.6148i		−	0.499279i
$453$			3.28654i			0.154415i
$454$	14.9789			0.702994
$455$	−0.492615	+	0.238867i	−0.0230941	+	0.0111983i
$456$		0			0
$457$		−	38.6888i		−	1.80978i	−0.425641	−	0.904892i	$-0.639951\pi$
$457$		−	38.6888i		−	1.80978i	0.425641	−	0.904892i	$-0.360049\pi$
$458$		−	3.58739i		−	0.167628i
$459$	−19.1333			−0.893065
$460$	−23.8902	−	49.2685i	−1.11389	−	2.29716i
$461$	−24.4994			−1.14105			−0.570525	−	0.821280i	$-0.693260\pi$
$461$	−24.4994			−1.14105			−0.570525	+	0.821280i	$0.693260\pi$
$462$			1.07729i			0.0501201i
$463$		−	32.4849i		−	1.50970i	−0.655895	−	0.754852i	$-0.727709\pi$
$463$		−	32.4849i		−	1.50970i	0.655895	−	0.754852i	$-0.272291\pi$
$464$	5.89528			0.273681
$465$	5.43126	+	11.2009i	0.251869	+	0.519427i
$466$	−47.5645			−2.20338
$467$		−	14.7020i		−	0.680327i	−0.940366	−	0.340163i	$-0.889518\pi$
$467$		−	14.7020i		−	0.680327i	0.940366	−	0.340163i	$-0.110482\pi$
$468$		−	9.77475i		−	0.451838i
$469$	−0.860967			−0.0397558
$470$	17.1666	−	8.32406i	0.791838	−	0.383960i
$471$	13.2366			0.609912
$472$		−	17.5130i		−	0.806103i
$473$			30.9553i			1.42333i
$474$	−30.9957			−1.42368
$475$		0			0
$476$	−1.73595			−0.0795672
$477$			2.76187i			0.126457i
$478$			14.5072i			0.663543i
$479$	13.2196			0.604020			0.302010	−	0.953305i	$-0.402342\pi$
$479$	13.2196			0.604020			0.302010	+	0.953305i	$0.402342\pi$
$480$	10.9007	−	5.28572i	0.497547	−	0.241259i
$481$	16.2162			0.739396
$482$		−	61.1720i		−	2.78631i
$483$		−	1.18408i		−	0.0538774i
$484$	10.4586			0.475390
$485$	8.58749	+	17.7099i	0.389938	+	0.804166i
$486$	34.4687			1.56353
$487$		−	9.66071i		−	0.437769i	−0.975751	−	0.218884i	$-0.929758\pi$
$487$		−	9.66071i		−	0.437769i	0.975751	−	0.218884i	$-0.0702417\pi$
$488$			33.0027i			1.49396i
$489$	21.7305			0.982688
$490$	15.8290	+	32.6441i	0.715082	+	1.47471i
$491$	2.68634			0.121233			0.0606165	−	0.998161i	$-0.480693\pi$
$491$	2.68634			0.121233			0.0606165	+	0.998161i	$0.480693\pi$
$492$		−	0.732350i		−	0.0330169i
$493$			26.9461i			1.21359i
$494$		0			0
$495$	9.52145	−	4.61693i	0.427957	−	0.207515i
$496$	−3.77382			−0.169449
$497$			0.0775234i			0.00347740i
$498$		−	20.2809i		−	0.908807i
$499$	−2.35546			−0.105445			−0.0527224	−	0.998609i	$-0.516790\pi$
$499$	−2.35546			−0.105445			−0.0527224	+	0.998609i	$0.516790\pi$
$500$	8.16827	−	37.1695i	0.365296	−	1.66227i
$501$	17.3079			0.773260
$502$			24.8882i			1.11082i
$503$			13.7390i			0.612590i	0.951937	+	0.306295i	$0.0990894\pi$
$503$			13.7390i			0.612590i	−0.951937	+	0.306295i	$0.900911\pi$
$504$	0.786032			0.0350127
$505$	5.79045	−	2.80778i	0.257672	−	0.124944i
$506$	47.0854			2.09320
$507$			11.5787i			0.514228i
$508$		−	27.7763i		−	1.23237i
$509$	−36.3796			−1.61250			−0.806249	−	0.591577i	$-0.798506\pi$
$509$	−36.3796			−1.61250			−0.806249	+	0.591577i	$0.798506\pi$
$510$	−9.27052	−	19.1185i	−0.410506	−	0.846583i
$511$	−1.50000			−0.0663562
$512$			8.75464i			0.386904i
$513$		0			0
$514$	31.4382			1.38668
$515$	−1.17041	−	2.41373i	−0.0515745	−	0.106362i
$516$	−42.9836			−1.89225
$517$			10.3340i			0.454491i
$518$			3.16176i			0.138920i
$519$	−24.9184			−1.09380
$520$	11.2185	−	5.43983i	0.491965	−	0.238552i
$521$	−0.580423			−0.0254288			−0.0127144	−	0.999919i	$-0.504047\pi$
$521$	−0.580423			−0.0254288			−0.0127144	+	0.999919i	$0.504047\pi$
$522$		−	29.5831i		−	1.29482i
$523$			19.2463i			0.841582i	0.907158	+	0.420791i	$0.138247\pi$
$523$			19.2463i			0.841582i	−0.907158	+	0.420791i	$0.861753\pi$
$524$	−8.91801			−0.389585
$525$	0.509639	−	0.646178i	0.0222425	−	0.0282015i
$526$	15.2043			0.662941
$527$		−	17.2493i		−	0.751392i
$528$		−	2.51795i		−	0.109580i
$529$	−28.7528			−1.25012
$530$	−7.68561	+	3.72673i	−0.333841	+	0.161879i
$531$	−9.01961			−0.391418
$532$		0			0
$533$			0.320044i			0.0138626i
$534$	3.86308			0.167172
$535$	−3.99550	−	8.23989i	−0.172740	−	0.356241i
$536$	19.6072			0.846900
$537$			26.2783i			1.13399i
$538$		−	33.5258i		−	1.44540i
$539$	−19.6512			−0.846437
$540$	17.8538	+	36.8198i	0.768305	+	1.58447i
$541$	−31.9066			−1.37177			−0.685886	−	0.727709i	$-0.740585\pi$
$541$	−31.9066			−1.37177			−0.685886	+	0.727709i	$0.740585\pi$
$542$			5.07765i			0.218104i
$543$			13.2845i			0.570091i
$544$	−16.7871			−0.719741
$545$	32.5826	−	15.7992i	1.39568	−	0.676763i
$546$	0.653720			0.0279766
$547$			3.43452i			0.146849i	0.997301	+	0.0734246i	$0.0233928\pi$
$547$			3.43452i			0.146849i	−0.997301	+	0.0734246i	$0.976607\pi$
$548$			41.9374i			1.79148i
$549$	16.9972			0.725421
$550$	25.6956	+	20.2660i	1.09566	+	0.864146i
$551$		0			0
$552$			26.9655i			1.14773i
$553$			1.66357i			0.0707422i
$554$	37.1350			1.57772
$555$	−21.9338	+	10.6357i	−0.931040	+	0.451459i
$556$	27.0736			1.14818
$557$			6.83010i			0.289401i	0.989476	+	0.144700i	$0.0462218\pi$
$557$			6.83010i			0.289401i	−0.989476	+	0.144700i	$0.953778\pi$
$558$			18.9374i			0.801684i
$559$	18.7842			0.794488
$560$	0.108856	+	0.224493i	0.00460000	+	0.00948654i
$561$	11.5090			0.485912
$562$		−	33.1419i		−	1.39801i
$563$		−	12.5628i		−	0.529460i	−0.964323	−	0.264730i	$-0.914717\pi$
$563$		−	12.5628i		−	0.529460i	0.964323	−	0.264730i	$-0.0852828\pi$
$564$	−14.3495			−0.604225
$565$	−3.04241	−	6.27434i	−0.127995	−	0.263964i
$566$	−16.4289			−0.690556
$567$			0.162323i			0.00681692i
$568$		−	1.76547i		−	0.0740776i
$569$	3.47978			0.145880			0.0729400	−	0.997336i	$-0.476762\pi$
$569$	3.47978			0.145880			0.0729400	+	0.997336i	$0.476762\pi$
$570$		0			0
$571$	−0.621524			−0.0260100			−0.0130050	−	0.999915i	$-0.504140\pi$
$571$	−0.621524			−0.0260100			−0.0130050	+	0.999915i	$0.504140\pi$
$572$			16.3744i			0.684648i
$573$			8.37266i			0.349773i
$574$	−0.0624007			−0.00260456
$575$	−28.2426	−	22.2749i	−1.17780	−	0.928928i
$576$	21.0473			0.876969
$577$			3.85170i			0.160348i	0.996781	+	0.0801742i	$0.0255477\pi$
$577$			3.85170i			0.160348i	−0.996781	+	0.0801742i	$0.974452\pi$
$578$		−	10.0761i		−	0.419109i
$579$	30.0770			1.24996
$580$	51.8546	−	25.1442i	2.15315	−	1.04405i
$581$	−1.08849			−0.0451583
$582$		−	23.5018i		−	0.974180i
$583$		−	4.62661i		−	0.191615i
$584$	34.1602			1.41356
$585$	−2.80163	−	5.77779i	−0.115833	−	0.238882i
$586$	−2.27056			−0.0937961
$587$			40.4333i			1.66886i	0.551113	+	0.834431i	$0.314203\pi$
$587$			40.4333i			1.66886i	−0.551113	+	0.834431i	$0.685797\pi$
$588$		−	27.2871i		−	1.12530i
$589$		0			0
$590$	−12.1706	−	25.0994i	−0.501056	−	1.03332i
$591$	2.62817			0.108109
$592$		−	7.38999i		−	0.303727i
$593$			5.87362i			0.241201i	0.992701	+	0.120600i	$0.0384820\pi$
$593$			5.87362i			0.241201i	−0.992701	+	0.120600i	$0.961518\pi$
$594$	−35.1882			−1.44379
$595$	−1.02611	+	0.497557i	−0.0420664	+	0.0203979i
$596$	−14.2833			−0.585068
$597$			14.0665i			0.575704i
$598$		−	28.5723i		−	1.16841i
$599$	−13.3107			−0.543862			−0.271931	−	0.962317i	$-0.587662\pi$
$599$	−13.3107			−0.543862			−0.271931	+	0.962317i	$0.587662\pi$
$600$	−11.6062	+	14.7157i	−0.473822	+	0.600765i
$601$	−5.16016			−0.210487			−0.105244	−	0.994446i	$-0.533562\pi$
$601$	−5.16016			−0.210487			−0.105244	+	0.994446i	$0.533562\pi$
$602$			3.66246i			0.149271i
$603$		−	10.0981i		−	0.411228i
$604$	−9.73983			−0.396308
$605$	6.18200	−	2.99763i	0.251334	−	0.121871i
$606$	−7.68417			−0.312148
$607$		−	30.5069i		−	1.23824i	−0.785297	−	0.619119i	$-0.787490\pi$
$607$		−	30.5069i		−	1.23824i	0.785297	−	0.619119i	$-0.212510\pi$
$608$		0			0
$609$	1.24623			0.0504998
$610$	22.9351	+	47.2989i	0.928616	+	1.91508i
$611$	6.27088			0.253693
$612$		−	20.3607i		−	0.823031i
$613$			45.5007i			1.83776i	0.394540	+	0.918879i	$0.370904\pi$
$613$			45.5007i			1.83776i	−0.394540	+	0.918879i	$0.629096\pi$
$614$	66.1751			2.67061
$615$	−0.209906	−	0.432887i	−0.00846422	−	0.0174557i
$616$	−1.31674			−0.0530530
$617$			2.48247i			0.0999403i	0.998751	+	0.0499701i	$0.0159126\pi$
$617$			2.48247i			0.0999403i	−0.998751	+	0.0499701i	$0.984087\pi$
$618$			3.20312i			0.128848i
$619$	−23.4945			−0.944325			−0.472162	−	0.881512i	$-0.656526\pi$
$619$	−23.4945			−0.944325			−0.472162	+	0.881512i	$0.656526\pi$
$620$	−33.1943	+	16.0958i	−1.33312	+	0.646424i
$621$	38.6763			1.55203
$622$			59.3850i			2.38112i
$623$		−	0.207335i		−	0.00830670i
$624$	−1.52794			−0.0611666
$625$	−5.82531	−	24.3118i	−0.233012	−	0.972474i
$626$	−34.7562			−1.38914
$627$		0			0
$628$			39.2275i			1.56535i
$629$	33.7781			1.34682
$630$	1.12653	−	0.546250i	0.0448819	−	0.0217631i
$631$	−17.8197			−0.709392			−0.354696	−	0.934982i	$-0.615416\pi$
$631$	−17.8197			−0.709392			−0.354696	+	0.934982i	$0.615416\pi$
$632$		−	37.8852i		−	1.50699i
$633$		−	3.44929i		−	0.137097i
$634$	52.3974			2.08096
$635$	−7.96122	−	16.4184i	−0.315931	−	0.651543i
$636$	6.42437			0.254743
$637$			11.9247i			0.472474i
$638$			49.5568i			1.96197i
$639$	−0.909259			−0.0359697
$640$	19.1962	+	39.5882i	0.758796	+	1.56486i
$641$	−37.4631			−1.47970			−0.739852	−	0.672770i	$-0.765104\pi$
$641$	−37.4631			−1.47970			−0.739852	+	0.672770i	$0.765104\pi$
$642$			10.9347i			0.431557i
$643$			19.8886i			0.784331i	0.919895	+	0.392165i	$0.128274\pi$
$643$			19.8886i			0.784331i	−0.919895	+	0.392165i	$0.871726\pi$
$644$	3.50908			0.138277
$645$	−25.4073	+	12.3199i	−1.00041	+	0.485097i
$646$		0			0
$647$		−	23.0645i		−	0.906759i	−0.891318	−	0.453380i	$-0.850218\pi$
$647$		−	23.0645i		−	0.906759i	0.891318	−	0.453380i	$-0.149782\pi$
$648$		−	3.69665i		−	0.145218i
$649$	15.1094			0.593096
$650$	12.2978	−	15.5925i	0.482359	−	0.611589i
$651$	−0.797764			−0.0312668
$652$			64.3995i			2.52208i
$653$			26.9839i			1.05596i	0.849256	+	0.527981i	$0.177051\pi$
$653$			26.9839i			1.05596i	−0.849256	+	0.527981i	$0.822949\pi$
$654$	−43.2384			−1.69075
$655$	−5.27138	+	2.55608i	−0.205970	+	0.0998742i
$656$	0.145849			0.00569446
$657$		−	17.5933i		−	0.686379i
$658$			1.22267i			0.0476646i
$659$	13.4880			0.525418			0.262709	−	0.964875i	$-0.415384\pi$
$659$	13.4880			0.525418			0.262709	+	0.964875i	$0.415384\pi$
$660$	−10.7394	−	22.1478i	−0.418031	−	0.862102i
$661$	21.9777			0.854835			0.427417	−	0.904054i	$-0.359423\pi$
$661$	21.9777			0.854835			0.427417	+	0.904054i	$0.359423\pi$
$662$		−	25.2642i		−	0.981922i
$663$		−	6.98389i		−	0.271232i
$664$	24.7887			0.961988
$665$		0			0
$666$	−37.0838			−1.43697
$667$		−	54.4692i		−	2.10906i
$668$			51.2928i			1.98458i
$669$	−2.51956			−0.0974119
$670$	28.1006	−	13.6259i	1.08562	−	0.526415i
$671$	−28.4732			−1.09919
$672$			0.776386i			0.0299497i
$673$		−	23.1998i		−	0.894286i	−0.894462	−	0.447143i	$-0.852441\pi$
$673$		−	23.1998i		−	0.894286i	0.894462	−	0.447143i	$-0.147559\pi$
$674$	−17.9207			−0.690278
$675$	21.1065	+	16.6467i	0.812390	+	0.640730i
$676$	−34.3141			−1.31977
$677$		−	28.7294i		−	1.10416i	−0.833791	−	0.552081i	$-0.813834\pi$
$677$		−	28.7294i		−	1.10416i	0.833791	−	0.552081i	$-0.186166\pi$
$678$			8.32631i			0.319770i
$679$	−1.26136			−0.0484066
$680$	23.3680	−	11.3311i	0.896122	−	0.434527i
$681$	−7.40096			−0.283605
$682$		−	31.7234i		−	1.21475i
$683$			24.0010i			0.918374i	0.888340	+	0.459187i	$0.151859\pi$
$683$			24.0010i			0.918374i	−0.888340	+	0.459187i	$0.848141\pi$
$684$		0			0
$685$	12.0201	+	24.7889i	0.459264	+	0.947136i
$686$	−4.65689			−0.177801
$687$			1.77250i			0.0676252i
$688$		−	8.56028i		−	0.326358i
$689$	−2.80751			−0.106958
$690$	18.7396	+	38.6465i	0.713403	+	1.47125i
$691$	37.3866			1.42226			0.711128	−	0.703063i	$-0.248185\pi$
$691$	37.3866			1.42226			0.711128	+	0.703063i	$0.248185\pi$
$692$		−	73.8470i		−	2.80724i
$693$			0.678151i			0.0257608i
$694$	47.1198			1.78864
$695$	16.0030	−	7.75982i	0.607029	−	0.294347i
$696$	−28.3809			−1.07578
$697$			0.666647i			0.0252510i
$698$			44.2848i			1.67620i
$699$	23.5013			0.888900
$700$	1.91498	+	1.51034i	0.0723795	+	0.0570856i
$701$	−2.32624			−0.0878609			−0.0439304	−	0.999035i	$-0.513988\pi$
$701$	−2.32624			−0.0878609			−0.0439304	+	0.999035i	$0.513988\pi$
$702$			21.3528i			0.805911i
$703$		0			0
$704$	−35.2578			−1.32883
$705$	−8.48192	+	4.11286i	−0.319447	+	0.154899i
$706$	42.2308			1.58938
$707$			0.412416i			0.0155105i
$708$			20.9805i			0.788494i
$709$	24.3523			0.914568			0.457284	−	0.889321i	$-0.348822\pi$
$709$	24.3523			0.914568			0.457284	+	0.889321i	$0.348822\pi$
$710$	−1.22691	−	2.53024i	−0.0460451	−	0.0949584i
$711$	−19.5117			−0.731747
$712$			4.72173i			0.176954i
$713$			34.8680i			1.30582i
$714$	1.36169			0.0509599
$715$	4.69322	+	9.67880i	0.175517	+	0.361967i
$716$	−77.8772			−2.91041
$717$		−	7.16789i		−	0.267690i
$718$		−	37.5004i		−	1.39950i
$719$	−17.0622			−0.636311			−0.318155	−	0.948039i	$-0.603063\pi$
$719$	−17.0622			−0.636311			−0.318155	+	0.948039i	$0.603063\pi$
$720$	−2.63303	+	1.27675i	−0.0981274	+	0.0475817i
$721$	0.171914			0.00640242
$722$		0			0
$723$			30.2246i			1.12407i
$724$	−39.3692			−1.46314
$725$	23.4441	−	29.7251i	0.870692	−	1.10396i
$726$	−8.20376			−0.304470
$727$		−	14.6251i		−	0.542415i	−0.962521	−	0.271207i	$-0.912577\pi$
$727$		−	14.6251i		−	0.542415i	0.962521	−	0.271207i	$-0.0874229\pi$
$728$			0.799022i			0.0296137i
$729$	−20.4289			−0.756628
$730$	48.9577	−	23.7395i	1.81201	−	0.878638i
$731$	39.1273			1.44717
$732$		−	39.5370i		−	1.46133i
$733$		−	33.5260i		−	1.23831i	−0.785268	−	0.619156i	$-0.787475\pi$
$733$		−	33.5260i		−	1.23831i	0.785268	−	0.619156i	$-0.212525\pi$
$734$	−74.9961			−2.76816
$735$	−7.82100	−	16.1292i	−0.288482	−	0.594934i
$736$	33.9337			1.25081
$737$			16.9161i			0.623113i
$738$		−	0.731887i		−	0.0269411i
$739$	15.2098			0.559501			0.279751	−	0.960073i	$-0.409748\pi$
$739$	15.2098			0.559501			0.279751	+	0.960073i	$0.409748\pi$
$740$	−31.5193	−	65.0021i	−1.15867	−	2.38952i
$741$		0			0
$742$		−	0.547396i		−	0.0200955i
$743$			6.65799i			0.244258i	0.992514	+	0.122129i	$0.0389722\pi$
$743$			6.65799i			0.244258i	−0.992514	+	0.122129i	$0.961028\pi$
$744$	18.1678			0.666064
$745$	−8.44278	+	4.09388i	−0.309319	+	0.149988i
$746$	−5.53345			−0.202594
$747$		−	12.7667i		−	0.467110i
$748$			34.1076i			1.24710i
$749$	0.586873			0.0214439
$750$	−6.40723	+	29.1560i	−0.233959	+	1.06462i
$751$	−7.81110			−0.285031			−0.142516	−	0.989793i	$-0.545519\pi$
$751$	−7.81110			−0.285031			−0.142516	+	0.989793i	$0.545519\pi$
$752$		−	2.85774i		−	0.104211i
$753$		−	12.2971i		−	0.448131i
$754$	30.0720			1.09516
$755$	−5.75715	+	2.79163i	−0.209524	+	0.101598i
$756$	−2.62243			−0.0953769
$757$		−	18.3846i		−	0.668201i	−0.942537	−	0.334100i	$-0.891568\pi$
$757$		−	18.3846i		−	0.668201i	0.942537	−	0.334100i	$-0.108432\pi$
$758$		−	41.1958i		−	1.49630i
$759$	−23.2645			−0.844449
$760$		0			0
$761$	22.4779			0.814822			0.407411	−	0.913245i	$-0.366432\pi$
$761$	22.4779			0.814822			0.407411	+	0.913245i	$0.366432\pi$
$762$			21.7878i			0.789290i
$763$			2.32064i			0.0840129i
$764$	−24.8128			−0.897696
$765$	−5.83576	−	12.0350i	−0.210992	−	0.435128i
$766$	−24.7911			−0.895739
$767$		−	9.16866i		−	0.331061i
$768$		−	23.7691i		−	0.857694i
$769$	−5.51880			−0.199013			−0.0995065	−	0.995037i	$-0.531726\pi$
$769$	−5.51880			−0.199013			−0.0995065	+	0.995037i	$0.531726\pi$
$770$	−1.88713	+	0.915063i	−0.0680074	+	0.0329766i
$771$	−15.5334			−0.559421
$772$			89.1347i			3.20803i
$773$		−	33.1881i		−	1.19369i	−0.802356	−	0.596846i	$-0.796420\pi$
$773$		−	33.1881i		−	1.19369i	0.802356	−	0.596846i	$-0.203580\pi$
$774$	−42.9564			−1.54404
$775$	−15.0076	+	19.0283i	−0.539087	+	0.683516i
$776$	28.7255			1.03119
$777$		−	1.56220i		−	0.0560438i
$778$			52.8418i			1.89447i
$779$		0			0
$780$	−13.4397	+	6.51687i	−0.481218	+	0.233341i
$781$	1.52317			0.0545031
$782$		−	59.5156i		−	2.12827i
$783$			40.7064i			1.45473i
$784$	5.43428			0.194081
$785$	11.2434	+	23.1871i	0.401293	+	0.827583i
$786$	6.99533			0.249515
$787$			48.6451i			1.73401i	0.498300	+	0.867005i	$0.333958\pi$
$787$			48.6451i			1.73401i	−0.498300	+	0.867005i	$0.666042\pi$
$788$			7.78873i			0.277462i
$789$	−7.51235			−0.267447
$790$	−26.3281	−	54.2963i	−0.936713	−	1.93178i
$791$	0.446881			0.0158892
$792$		−	15.4438i		−	0.548772i
$793$			17.2780i			0.613561i
$794$	47.5164			1.68630
$795$	3.79740	−	1.84135i	0.134680	−	0.0653060i
$796$	−41.6869			−1.47755
$797$			1.06027i			0.0375567i	0.999824	+	0.0187784i	$0.00597769\pi$
$797$			1.06027i			0.0375567i	−0.999824	+	0.0187784i	$0.994022\pi$
$798$		0			0
$799$	13.0622			0.462106
$800$	18.5184	+	14.6054i	0.654723	+	0.516379i
$801$	2.43180			0.0859233
$802$			38.8146i			1.37059i
$803$			29.4718i			1.04004i
$804$	−23.4892			−0.828400
$805$	2.07419	−	1.00577i	0.0731056	−	0.0354487i
$806$	−19.2503			−0.678064
$807$			16.5648i			0.583110i
$808$		−	9.39213i		−	0.330414i
$809$	13.6192			0.478826			0.239413	−	0.970918i	$-0.423045\pi$
$809$	13.6192			0.478826			0.239413	+	0.970918i	$0.423045\pi$
$810$	−2.56897	−	5.29797i	−0.0902645	−	0.186152i
$811$	−22.3947			−0.786385			−0.393192	−	0.919456i	$-0.628629\pi$
$811$	−22.3947			−0.786385			−0.393192	+	0.919456i	$0.628629\pi$
$812$			3.69326i			0.129608i
$813$		−	2.50883i		−	0.0879886i
$814$	62.1217			2.17736
$815$	18.4582	+	38.0661i	0.646561	+	1.33340i
$816$	−3.18268			−0.111416
$817$		0			0
$818$			41.1100i			1.43738i
$819$	0.411514			0.0143795
$820$	1.28288	−	0.622067i	0.0448002	−	0.0217235i
$821$	−5.51937			−0.192627			−0.0963137	−	0.995351i	$-0.530705\pi$
$821$	−5.51937			−0.192627			−0.0963137	+	0.995351i	$0.530705\pi$
$822$		−	32.8959i		−	1.14738i
$823$			22.3523i			0.779154i	0.920994	+	0.389577i	$0.127379\pi$
$823$			22.3523i			0.779154i	−0.920994	+	0.389577i	$0.872621\pi$
$824$	−3.91508			−0.136388
$825$	−12.6960	−	10.0133i	−0.442017	−	0.348618i
$826$	1.78766			0.0622008
$827$			4.48687i			0.156024i	0.996952	+	0.0780118i	$0.0248572\pi$
$827$			4.48687i			0.156024i	−0.996952	+	0.0780118i	$0.975143\pi$
$828$			41.1573i			1.43032i
$829$	27.0312			0.938832			0.469416	−	0.882977i	$-0.344465\pi$
$829$	27.0312			0.938832			0.469416	+	0.882977i	$0.344465\pi$
$830$	35.5267	−	17.2268i	1.23315	−	0.597951i
$831$	−18.3481			−0.636490
$832$			21.3951i			0.741741i
$833$			24.8390i			0.860619i
$834$	−21.2367			−0.735365
$835$	14.7015	+	30.3188i	0.508767	+	1.04923i
$836$		0			0
$837$		−	26.0578i		−	0.900691i
$838$		−	88.1820i		−	3.04620i
$839$	−10.1152			−0.349214			−0.174607	−	0.984638i	$-0.555865\pi$
$839$	−10.1152			−0.349214			−0.174607	+	0.984638i	$0.555865\pi$
$840$	−0.524051	−	1.08075i	−0.0180815	−	0.0372893i
$841$	28.3283			0.976837
$842$			26.9242i			0.927870i
$843$			16.3752i			0.563991i
$844$	10.2221			0.351861
$845$	−20.2828	+	9.83508i	−0.697750	+	0.338337i
$846$	−14.3405			−0.493035
$847$			0.440303i			0.0151290i
$848$			1.27943i			0.0439358i
$849$	8.11738			0.278588
$850$	25.6161	−	32.4790i	0.878625	−	1.11402i
$851$	−68.2796			−2.34059
$852$			2.11502i			0.0724595i
$853$		−	27.6102i		−	0.945356i	−0.881235	−	0.472678i	$-0.843287\pi$
$853$		−	27.6102i		−	0.945356i	0.881235	−	0.472678i	$-0.156713\pi$
$854$	−3.36879			−0.115278
$855$		0			0
$856$	−13.3651			−0.456810
$857$			38.6174i			1.31915i	0.751640	+	0.659573i	$0.229263\pi$
$857$			38.6174i			1.31915i	−0.751640	+	0.659573i	$0.770737\pi$
$858$		−	12.8442i		−	0.438492i
$859$	−57.1723			−1.95069			−0.975346	−	0.220681i	$-0.929172\pi$
$859$	−57.1723			−1.95069			−0.975346	+	0.220681i	$0.929172\pi$
$860$	−36.5108	−	75.2959i	−1.24501	−	2.56757i
$861$	0.0308317			0.00105074
$862$			73.8992i			2.51702i
$863$		−	28.4419i		−	0.968173i	−0.875020	−	0.484087i	$-0.839152\pi$
$863$		−	28.4419i		−	0.968173i	0.875020	−	0.484087i	$-0.160848\pi$
$864$	−25.3596			−0.862750
$865$	−21.1660	−	43.6505i	−0.719665	−	1.48416i
$866$	9.50417			0.322965
$867$			4.97851i			0.169079i
$868$		−	2.36421i		−	0.0802466i
$869$	32.6855			1.10878
$870$	−40.6750	+	19.7232i	−1.37901	+	0.668679i
$871$	10.2650			0.347816
$872$		−	52.8490i		−	1.78969i
$873$		−	14.7943i		−	0.500711i
$874$		0			0
$875$	1.56483	+	0.343882i	0.0529008	+	0.0116253i
$876$	−40.9236			−1.38268
$877$			13.3300i			0.450121i	0.974345	+	0.225060i	$0.0722579\pi$
$877$			13.3300i			0.450121i	−0.974345	+	0.225060i	$0.927742\pi$
$878$			27.3276i			0.922263i
$879$	1.12187			0.0378397
$880$	4.41079	−	2.13878i	0.148688	−	0.0720982i
$881$	−28.1384			−0.948007			−0.474004	−	0.880523i	$-0.657192\pi$
$881$	−28.1384			−0.948007			−0.474004	+	0.880523i	$0.657192\pi$
$882$		−	27.2698i		−	0.918222i
$883$			35.6238i			1.19884i	0.800436	+	0.599418i	$0.204601\pi$
$883$			35.6238i			1.19884i	−0.800436	+	0.599418i	$0.795399\pi$
$884$	20.6971			0.696120
$885$	6.01341	+	12.4014i	0.202139	+	0.416869i
$886$	−18.3333			−0.615920
$887$		−	59.1722i		−	1.98681i	−0.114672	−	0.993403i	$-0.536582\pi$
$887$		−	59.1722i		−	1.98681i	0.114672	−	0.993403i	$-0.463418\pi$
$888$			35.5767i			1.19388i
$889$	1.16937			0.0392195
$890$	3.28135	+	6.76710i	0.109991	+	0.226834i
$891$	3.18929			0.106845
$892$		−	7.46685i		−	0.250009i
$893$		0			0
$894$	11.2039			0.374715
$895$	−46.0327	+	22.3211i	−1.53870	+	0.746113i
$896$	−2.81961			−0.0941964
$897$			14.1173i			0.471364i
$898$			2.69841i			0.0900470i
$899$	−36.6982			−1.22395
$900$	−17.7145	+	22.4605i	−0.590484	+	0.748683i
$901$	−5.84800			−0.194825
$902$			1.22604i			0.0408226i
$903$		−	1.80960i		−	0.0602196i
$904$	−10.1770			−0.338482
$905$	−23.2709	+	11.2840i	−0.773549	+	0.375092i
$906$	7.63997			0.253821
$907$		−	46.2445i		−	1.53552i	−0.640735	−	0.767762i	$-0.721370\pi$
$907$		−	46.2445i		−	1.53552i	0.640735	−	0.767762i	$-0.278630\pi$
$908$		−	21.9331i		−	0.727876i
$909$	−4.83716			−0.160438
$910$	0.555277	+	1.14514i	0.0184073	+	0.0379611i
$911$	−48.8276			−1.61773			−0.808866	−	0.587994i	$-0.799918\pi$
$911$	−48.8276			−1.61773			−0.808866	+	0.587994i	$0.799918\pi$
$912$		0			0
$913$			21.3865i			0.707790i
$914$	−89.9368			−2.97485
$915$	−11.3321	−	23.3701i	−0.374627	−	0.772590i
$916$	−5.25291			−0.173561
$917$		−	0.375446i		−	0.0123983i
$918$			44.4777i			1.46798i
$919$	9.60929			0.316981			0.158491	−	0.987360i	$-0.449337\pi$
$919$	9.60929			0.316981			0.158491	+	0.987360i	$0.449337\pi$
$920$	−47.2364	+	22.9048i	−1.55734	+	0.755149i
$921$	−32.6967			−1.07739
$922$			56.9519i			1.87561i
$923$		−	0.924285i		−	0.0304232i
$924$	1.57744			0.0518941
$925$	−37.2617	−	29.3882i	−1.22516	−	0.966279i
$926$	−75.5153			−2.48159
$927$			2.01635i			0.0662257i
$928$			35.7148i			1.17240i
$929$	−51.7174			−1.69679			−0.848396	−	0.529362i	$-0.822431\pi$
$929$	−51.7174			−1.69679			−0.848396	+	0.529362i	$0.822431\pi$
$930$	26.0378	−	12.6256i	0.853812	−	0.414011i
$931$		0			0
$932$			69.6473i			2.28137i
$933$		−	29.3417i		−	0.960604i
$934$	−34.1766			−1.11829
$935$	9.77591	+	20.1608i	0.319706	+	0.659328i
$936$	−9.37158			−0.306320
$937$		−	11.4894i		−	0.375341i	−0.982232	−	0.187671i	$-0.939906\pi$
$937$		−	11.4894i		−	0.375341i	0.982232	−	0.187671i	$-0.0600938\pi$
$938$			2.00142i			0.0653488i
$939$	17.1728			0.560412
$940$	−12.1887	−	25.1366i	−0.397550	−	0.819865i
$941$	−26.4897			−0.863540			−0.431770	−	0.901984i	$-0.642111\pi$
$941$	−26.4897			−0.863540			−0.431770	+	0.901984i	$0.642111\pi$
$942$		−	30.7702i		−	1.00255i
$943$		−	1.34757i		−	0.0438829i
$944$	−4.17831			−0.135992
$945$	−1.55010	+	0.751640i	−0.0504248	+	0.0244508i
$946$	71.9594			2.33960
$947$			14.7018i			0.477745i	0.971051	+	0.238873i	$0.0767778\pi$
$947$			14.7018i			0.477745i	−0.971051	+	0.238873i	$0.923222\pi$
$948$			45.3861i			1.47407i
$949$	17.8840			0.580539
$950$		0			0
$951$	−25.8892			−0.839513
$952$			1.66435i			0.0539419i
$953$			5.85051i			0.189517i	0.995500	+	0.0947583i	$0.0302078\pi$
$953$			5.85051i			0.189517i	−0.995500	+	0.0947583i	$0.969792\pi$
$954$	6.42031			0.207865
$955$	−14.6667	+	7.11184i	−0.474603	+	0.230134i
$956$	21.2424			0.687029
$957$		−	24.4857i		−	0.791510i
$958$		−	30.7306i		−	0.992862i
$959$	−1.76555			−0.0570127
$960$	−14.0323	−	28.9387i	−0.452890	−	0.933992i
$961$	−7.50793			−0.242191
$962$		−	37.6966i		−	1.21539i
$963$			6.88333i			0.221812i
$964$	−89.5722			−2.88493
$965$	25.5477	+	52.6869i	0.822411	+	1.69605i
$966$	−2.75254			−0.0885614
$967$		−	24.0705i		−	0.774054i	−0.922068	−	0.387027i	$-0.873502\pi$
$967$		−	24.0705i		−	0.774054i	0.922068	−	0.387027i	$-0.126498\pi$
$968$		−	10.0272i		−	0.322287i
$969$		0			0
$970$	41.1689	−	19.9627i	1.32185	−	0.640963i
$971$	−52.6618			−1.69000			−0.844999	−	0.534768i	$-0.820399\pi$
$971$	−52.6618			−1.69000			−0.844999	+	0.534768i	$0.820399\pi$
$972$		−	50.4715i		−	1.61887i
$973$			1.13979i			0.0365400i
$974$	−22.4575			−0.719585
$975$	−6.07625	+	7.70416i	−0.194596	+	0.246730i
$976$	7.87389			0.252037
$977$			6.50872i			0.208232i	0.994565	+	0.104116i	$0.0332014\pi$
$977$			6.50872i			0.208232i	−0.994565	+	0.104116i	$0.966799\pi$
$978$		−	50.5153i		−	1.61530i
$979$	−4.07368			−0.130195
$980$	47.7997	−	23.1779i	1.52691	−	0.740392i
$981$	−27.2184			−0.869017
$982$		−	6.24474i		−	0.199278i
$983$		−	1.24935i		−	0.0398480i	−0.999801	−	0.0199240i	$-0.993658\pi$
$983$		−	1.24935i		−	0.0398480i	0.999801	−	0.0199240i	$-0.00634243\pi$
$984$	−0.702144			−0.0223835
$985$	2.23240	+	4.60387i	0.0711302	+	0.146691i
$986$	62.6395			1.99485
$987$		−	0.604111i		−	0.0192291i
$988$		0			0
$989$	−79.0924			−2.51499
$990$	−10.7326	−	22.1338i	−0.341105	−	0.703458i
$991$	−37.5958			−1.19427			−0.597134	−	0.802141i	$-0.703694\pi$
$991$	−37.5958			−1.19427			−0.597134	+	0.802141i	$0.703694\pi$
$992$		−	22.8626i		−	0.725887i
$993$			12.4829i			0.396132i
$994$	0.180213			0.00571600
$995$	−24.6408	+	11.9483i	−0.781166	+	0.378785i
$996$	−29.6966			−0.940974
$997$			29.9308i			0.947918i	0.880547	+	0.473959i	$0.157175\pi$
$997$			29.9308i			0.947918i	−0.880547	+	0.473959i	$0.842825\pi$
$998$			5.47555i			0.173325i
$999$	51.0272			1.61443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.l.1084.3		24
5.2	odd	4		9025.2.a.ct.1.22		24
5.3	odd	4		9025.2.a.ct.1.3		24
5.4	even	2	inner	1805.2.b.l.1084.22		24
19.2	odd	18		95.2.p.a.4.7	yes	48
19.10	odd	18		95.2.p.a.24.2	yes	48
19.18	odd	2		1805.2.b.k.1084.22		24
57.2	even	18		855.2.da.b.289.2		48
57.29	even	18		855.2.da.b.784.7		48
95.2	even	36		475.2.l.f.251.7		48
95.18	even	4		9025.2.a.cu.1.22		24
95.29	odd	18		95.2.p.a.24.7	yes	48
95.37	even	4		9025.2.a.cu.1.3		24
95.48	even	36		475.2.l.f.176.2		48
95.59	odd	18		95.2.p.a.4.2	✓	48
95.67	even	36		475.2.l.f.176.7		48
95.78	even	36		475.2.l.f.251.2		48
95.94	odd	2		1805.2.b.k.1084.3		24
285.29	even	18		855.2.da.b.784.2		48
285.59	even	18		855.2.da.b.289.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.4.2	✓	48	95.59	odd	18
95.2.p.a.4.7	yes	48	19.2	odd	18
95.2.p.a.24.2	yes	48	19.10	odd	18
95.2.p.a.24.7	yes	48	95.29	odd	18
475.2.l.f.176.2		48	95.48	even	36
475.2.l.f.176.7		48	95.67	even	36
475.2.l.f.251.2		48	95.78	even	36
475.2.l.f.251.7		48	95.2	even	36
855.2.da.b.289.2		48	57.2	even	18
855.2.da.b.289.7		48	285.59	even	18
855.2.da.b.784.2		48	285.29	even	18
855.2.da.b.784.7		48	57.29	even	18
1805.2.b.k.1084.3		24	95.94	odd	2
1805.2.b.k.1084.22		24	19.18	odd	2
1805.2.b.l.1084.3		24	1.1	even	1	trivial
1805.2.b.l.1084.22		24	5.4	even	2	inner
9025.2.a.ct.1.3		24	5.3	odd	4
9025.2.a.ct.1.22		24	5.2	odd	4
9025.2.a.cu.1.3		24	95.37	even	4
9025.2.a.cu.1.22		24	95.18	even	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.32462i q^{2} +1.14858i q^{3} -3.40387 q^{4} +(-2.01201 + 0.975617i) q^{5} +2.67001 q^{6} -0.143302i q^{7} +3.26348i q^{8} +1.68077 q^{9} +O(q^{10})\)	\(q-2.32462i q^{2} +1.14858i q^{3} -3.40387 q^{4} +(-2.01201 + 0.975617i) q^{5} +2.67001 q^{6} -0.143302i q^{7} +3.26348i q^{8} +1.68077 q^{9} +(2.26794 + 4.67716i) q^{10} -2.81557 q^{11} -3.90962i q^{12} +1.70854i q^{13} -0.333123 q^{14} +(-1.12057 - 2.31095i) q^{15} +0.778610 q^{16} +3.55886i q^{17} -3.90715i q^{18} +(6.84862 - 3.32088i) q^{20} +0.164594 q^{21} +6.54515i q^{22} -7.19394i q^{23} -3.74836 q^{24} +(3.09634 - 3.92590i) q^{25} +3.97171 q^{26} +5.37623i q^{27} +0.487782i q^{28} +7.57154 q^{29} +(-5.37209 + 2.60491i) q^{30} -4.84686 q^{31} +4.71698i q^{32} -3.23391i q^{33} +8.27302 q^{34} +(0.139808 + 0.288325i) q^{35} -5.72111 q^{36} -9.49127i q^{37} -1.96239 q^{39} +(-3.18390 - 6.56614i) q^{40} +0.187320 q^{41} -0.382619i q^{42} -10.9943i q^{43} +9.58385 q^{44} +(-3.38171 + 1.63978i) q^{45} -16.7232 q^{46} -3.67032i q^{47} +0.894296i q^{48} +6.97946 q^{49} +(-9.12623 - 7.19783i) q^{50} -4.08764 q^{51} -5.81566i q^{52} +1.64322i q^{53} +12.4977 q^{54} +(5.66495 - 2.74692i) q^{55} +0.467663 q^{56} -17.6010i q^{58} -5.36637 q^{59} +(3.81429 + 7.86618i) q^{60} +10.1127 q^{61} +11.2671i q^{62} -0.240857i q^{63} +12.5224 q^{64} +(-1.66688 - 3.43760i) q^{65} -7.51762 q^{66} -6.00805i q^{67} -12.1139i q^{68} +8.26281 q^{69} +(0.670247 - 0.325001i) q^{70} -0.540979 q^{71} +5.48514i q^{72} -10.4674i q^{73} -22.0636 q^{74} +(4.50920 + 3.55640i) q^{75} +0.403477i q^{77} +4.56183i q^{78} -11.6088 q^{79} +(-1.56657 + 0.759625i) q^{80} -1.13273 q^{81} -0.435449i q^{82} -7.59579i q^{83} -0.560257 q^{84} +(-3.47209 - 7.16046i) q^{85} -25.5576 q^{86} +8.69652i q^{87} -9.18856i q^{88} +1.44684 q^{89} +(3.81188 + 7.86121i) q^{90} +0.244837 q^{91} +24.4873i q^{92} -5.56701i q^{93} -8.53210 q^{94} -5.41783 q^{96} -8.80212i q^{97} -16.2246i q^{98} -4.73232 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9}+O(q^{10}) \) 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9	\( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} + 6 q^{10} + 12 q^{11} + 24 q^{14} + 9 q^{15} + 6 q^{16} + 21 q^{20} - 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} + 36 q^{29} - 18 q^{30} - 42 q^{31} + 6 q^{34} + 27 q^{35} - 6 q^{36} - 24 q^{39} - 12 q^{40} - 60 q^{41} + 30 q^{44} + 9 q^{45} - 6 q^{46} - 12 q^{49} - 18 q^{50} - 30 q^{51} + 24 q^{54} + 33 q^{55} - 18 q^{56} + 60 q^{59} + 42 q^{60} + 30 q^{61} - 18 q^{65} + 36 q^{66} + 66 q^{69} - 9 q^{70} - 96 q^{71} - 24 q^{74} - 36 q^{75} + 72 q^{79} - 42 q^{80} - 96 q^{81} - 54 q^{84} - 27 q^{85} - 108 q^{86} + 84 q^{89} + 93 q^{90} - 96 q^{91} + 36 q^{94} - 120 q^{96}+O(q^{100}) \) 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9 + 6 * q^10 + 12 * q^11 + 24 * q^14 + 9 * q^15 + 6 * q^16 + 21 * q^20 - 6 * q^21 + 42 * q^24 - 3 * q^25 - 12 * q^26 + 36 * q^29 - 18 * q^30 - 42 * q^31 + 6 * q^34 + 27 * q^35 - 6 * q^36 - 24 * q^39 - 12 * q^40 - 60 * q^41 + 30 * q^44 + 9 * q^45 - 6 * q^46 - 12 * q^49 - 18 * q^50 - 30 * q^51 + 24 * q^54 + 33 * q^55 - 18 * q^56 + 60 * q^59 + 42 * q^60 + 30 * q^61 - 18 * q^65 + 36 * q^66 + 66 * q^69 - 9 * q^70 - 96 * q^71 - 24 * q^74 - 36 * q^75 + 72 * q^79 - 42 * q^80 - 96 * q^81 - 54 * q^84 - 27 * q^85 - 108 * q^86 + 84 * q^89 + 93 * q^90 - 96 * q^91 + 36 * q^94 - 120 * q^96

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