LMFDB - Embedded newform 845.2.d.c.844.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(844,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("845.844");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.d (of order $2$, degree $1$, not 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.49787136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			844.4
Root			$-1.09445 + 0.895644i$ of defining polynomial
Character	$\chi$	$=$	845.844
Dual form			845.2.d.c.844.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.456850 q^{2} +1.00000i q^{3} -1.79129 q^{4} +(-2.18890 + 0.456850i) q^{5} -0.456850i q^{6} +1.73205 q^{7} +1.73205 q^{8} +2.00000 q^{9} +(1.00000 - 0.208712i) q^{10} -2.64575i q^{11} -1.79129i q^{12} -0.791288 q^{14} +(-0.456850 - 2.18890i) q^{15} +2.79129 q^{16} +4.58258i q^{17} -0.913701 q^{18} +1.73205i q^{19} +(3.92095 - 0.818350i) q^{20} +1.73205i q^{21} +1.20871i q^{22} +4.58258i q^{23} +1.73205i q^{24} +(4.58258 - 2.00000i) q^{25} +5.00000i q^{27} -3.10260 q^{28} -4.58258 q^{29} +(0.208712 + 1.00000i) q^{30} -6.20520i q^{31} -4.73930 q^{32} +2.64575 q^{33} -2.09355i q^{34} +(-3.79129 + 0.791288i) q^{35} -3.58258 q^{36} -7.93725 q^{37} -0.791288i q^{38} +(-3.79129 + 0.791288i) q^{40} +2.64575i q^{41} -0.791288i q^{42} +10.5826i q^{43} +4.73930i q^{44} +(-4.37780 + 0.913701i) q^{45} -2.09355i q^{46} +1.82740 q^{47} +2.79129i q^{48} -4.00000 q^{49} +(-2.09355 + 0.913701i) q^{50} -4.58258 q^{51} +7.58258i q^{53} -2.28425i q^{54} +(1.20871 + 5.79129i) q^{55} +3.00000 q^{56} -1.73205 q^{57} +2.09355 q^{58} +13.9518i q^{59} +(0.818350 + 3.92095i) q^{60} -1.41742 q^{61} +2.83485i q^{62} +3.46410 q^{63} -3.41742 q^{64} -1.20871 q^{66} +1.00905 q^{67} -8.20871i q^{68} -4.58258 q^{69} +(1.73205 - 0.361500i) q^{70} -7.02355i q^{71} +3.46410 q^{72} +3.62614 q^{74} +(2.00000 + 4.58258i) q^{75} -3.10260i q^{76} -4.58258i q^{77} +6.00000 q^{79} +(-6.10985 + 1.27520i) q^{80} +1.00000 q^{81} -1.20871i q^{82} -6.01450 q^{83} -3.10260i q^{84} +(-2.09355 - 10.0308i) q^{85} -4.83465i q^{86} -4.58258i q^{87} -4.58258i q^{88} +9.57395i q^{89} +(2.00000 - 0.417424i) q^{90} -8.20871i q^{92} +6.20520 q^{93} -0.834849 q^{94} +(-0.791288 - 3.79129i) q^{95} -4.73930i q^{96} +11.4014 q^{97} +1.82740 q^{98} -5.29150i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 16 q^{9} + 8 q^{10} + 12 q^{14} + 4 q^{16} + 20 q^{30} - 12 q^{35} + 8 q^{36} - 12 q^{40} - 32 q^{49} + 28 q^{55} + 24 q^{56} - 48 q^{61} - 64 q^{64} - 28 q^{66} + 84 q^{74} + 16 q^{75}+ \cdots + 12 q^{95}+O(q^{100}) $ 8 * q + 4 * q^4 + 16 * q^9 + 8 * q^10 + 12 * q^14 + 4 * q^16 + 20 * q^30 - 12 * q^35 + 8 * q^36 - 12 * q^40 - 32 * q^49 + 28 * q^55 + 24 * q^56 - 48 * q^61 - 64 * q^64 - 28 * q^66 + 84 * q^74 + 16 * q^75 + 48 * q^79 + 8 * q^81 + 16 * q^90 - 80 * q^94 + 12 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−0.456850			−0.323042			−0.161521	−	0.986869i	$-0.551640\pi$
$2$	−0.456850			−0.323042			−0.161521	+	0.986869i	$0.551640\pi$
$3$			1.00000i			0.577350i	0.957427	+	0.288675i	$0.0932147\pi$
$3$			1.00000i			0.577350i	−0.957427	+	0.288675i	$0.906785\pi$
$4$	−1.79129			−0.895644
$5$	−2.18890	+	0.456850i	−0.978906	+	0.204310i
$5$	−2.18890	+	0.456850i	−0.978906	+	0.204310i
$6$		−	0.456850i		−	0.186508i
$7$	1.73205			0.654654			0.327327	−	0.944911i	$-0.393852\pi$
$7$	1.73205			0.654654			0.327327	+	0.944911i	$0.393852\pi$
$8$	1.73205			0.612372
$9$	2.00000			0.666667
$10$	1.00000	−	0.208712i	0.316228	−	0.0660006i
$11$		−	2.64575i		−	0.797724i	−0.917011	−	0.398862i	$-0.869405\pi$
$11$		−	2.64575i		−	0.797724i	0.917011	−	0.398862i	$-0.130595\pi$
$12$		−	1.79129i		−	0.517100i
$13$		0			0
$13$		0			0
$14$	−0.791288			−0.211481
$15$	−0.456850	−	2.18890i	−0.117958	−	0.565172i
$16$	2.79129			0.697822
$17$			4.58258i			1.11144i	0.831370	+	0.555719i	$0.187557\pi$
$17$			4.58258i			1.11144i	−0.831370	+	0.555719i	$0.812443\pi$
$18$	−0.913701			−0.215361
$19$			1.73205i			0.397360i	0.980064	+	0.198680i	$0.0636654\pi$
$19$			1.73205i			0.397360i	−0.980064	+	0.198680i	$0.936335\pi$
$20$	3.92095	−	0.818350i	0.876751	−	0.182989i
$21$			1.73205i			0.377964i
$22$			1.20871i			0.257698i
$23$			4.58258i			0.955533i	0.878487	+	0.477767i	$0.158554\pi$
$23$			4.58258i			0.955533i	−0.878487	+	0.477767i	$0.841446\pi$
$24$			1.73205i			0.353553i
$25$	4.58258	−	2.00000i	0.916515	−	0.400000i
$26$		0			0
$27$			5.00000i			0.962250i
$28$	−3.10260			−0.586337
$29$	−4.58258			−0.850963			−0.425481	−	0.904967i	$-0.639895\pi$
$29$	−4.58258			−0.850963			−0.425481	+	0.904967i	$0.639895\pi$
$30$	0.208712	+	1.00000i	0.0381055	+	0.182574i
$31$		−	6.20520i		−	1.11449i	−0.830349	−	0.557244i	$-0.811859\pi$
$31$		−	6.20520i		−	1.11449i	0.830349	−	0.557244i	$-0.188141\pi$
$32$	−4.73930			−0.837798
$33$	2.64575			0.460566
$34$		−	2.09355i		−	0.359041i
$35$	−3.79129	+	0.791288i	−0.640845	+	0.133752i
$36$	−3.58258			−0.597096
$37$	−7.93725			−1.30488			−0.652438	−	0.757842i	$-0.726254\pi$
$37$	−7.93725			−1.30488			−0.652438	+	0.757842i	$0.726254\pi$
$38$		−	0.791288i		−	0.128364i
$39$		0			0
$40$	−3.79129	+	0.791288i	−0.599455	+	0.125114i
$41$			2.64575i			0.413197i	0.978426	+	0.206598i	$0.0662394\pi$
$41$			2.64575i			0.413197i	−0.978426	+	0.206598i	$0.933761\pi$
$42$		−	0.791288i		−	0.122098i
$43$			10.5826i			1.61383i	0.590669	+	0.806914i	$0.298864\pi$
$43$			10.5826i			1.61383i	−0.590669	+	0.806914i	$0.701136\pi$
$44$			4.73930i			0.714477i
$45$	−4.37780	+	0.913701i	−0.652604	+	0.136206i
$46$		−	2.09355i		−	0.308677i
$47$	1.82740			0.266554			0.133277	−	0.991079i	$-0.457450\pi$
$47$	1.82740			0.266554			0.133277	+	0.991079i	$0.457450\pi$
$48$			2.79129i			0.402888i
$49$	−4.00000			−0.571429
$50$	−2.09355	+	0.913701i	−0.296073	+	0.129217i
$51$	−4.58258			−0.641689
$52$		0			0
$53$			7.58258i			1.04155i	0.853695	+	0.520773i	$0.174356\pi$
$53$			7.58258i			1.04155i	−0.853695	+	0.520773i	$0.825644\pi$
$54$		−	2.28425i		−	0.310847i
$55$	1.20871	+	5.79129i	0.162983	+	0.780897i
$56$	3.00000			0.400892
$57$	−1.73205			−0.229416
$58$	2.09355			0.274897
$59$			13.9518i			1.81636i	0.418576	+	0.908182i	$0.362530\pi$
$59$			13.9518i			1.81636i	−0.418576	+	0.908182i	$0.637470\pi$
$60$	0.818350	+	3.92095i	0.105649	+	0.506193i
$61$	−1.41742			−0.181483			−0.0907413	−	0.995874i	$-0.528924\pi$
$61$	−1.41742			−0.181483			−0.0907413	+	0.995874i	$0.528924\pi$
$62$			2.83485i			0.360026i
$63$	3.46410			0.436436
$64$	−3.41742			−0.427178
$65$		0			0
$66$	−1.20871			−0.148782
$67$	1.00905			0.123275			0.0616376	−	0.998099i	$-0.480368\pi$
$67$	1.00905			0.123275			0.0616376	+	0.998099i	$0.480368\pi$
$68$		−	8.20871i		−	0.995453i
$69$	−4.58258			−0.551677
$70$	1.73205	−	0.361500i	0.207020	−	0.0432075i
$71$		−	7.02355i		−	0.833542i	−0.909011	−	0.416771i	$-0.863162\pi$
$71$		−	7.02355i		−	0.833542i	0.909011	−	0.416771i	$-0.136838\pi$
$72$	3.46410			0.408248
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$	3.62614			0.421530
$75$	2.00000	+	4.58258i	0.230940	+	0.529150i
$76$		−	3.10260i		−	0.355893i
$77$		−	4.58258i		−	0.522233i
$78$		0			0
$79$	6.00000			0.675053			0.337526	−	0.941316i	$-0.390410\pi$
$79$	6.00000			0.675053			0.337526	+	0.941316i	$0.390410\pi$
$80$	−6.10985	+	1.27520i	−0.683102	+	0.142572i
$81$	1.00000			0.111111
$82$		−	1.20871i		−	0.133480i
$83$	−6.01450			−0.660177			−0.330089	−	0.943950i	$-0.607079\pi$
$83$	−6.01450			−0.660177			−0.330089	+	0.943950i	$0.607079\pi$
$84$		−	3.10260i		−	0.338522i
$85$	−2.09355	−	10.0308i	−0.227077	−	1.08799i
$86$		−	4.83465i		−	0.521334i
$87$		−	4.58258i		−	0.491304i
$88$		−	4.58258i		−	0.488504i
$89$			9.57395i			1.01484i	0.861700	+	0.507419i	$0.169400\pi$
$89$			9.57395i			1.01484i	−0.861700	+	0.507419i	$0.830600\pi$
$90$	2.00000	−	0.417424i	0.210819	−	0.0440004i
$91$		0			0
$92$		−	8.20871i		−	0.855817i
$93$	6.20520			0.643450
$94$	−0.834849			−0.0861081
$95$	−0.791288	−	3.79129i	−0.0811844	−	0.388978i
$96$		−	4.73930i		−	0.483703i
$97$	11.4014			1.15763			0.578816	−	0.815458i	$-0.303515\pi$
$97$	11.4014			1.15763			0.578816	+	0.815458i	$0.303515\pi$
$98$	1.82740			0.184595
$99$		−	5.29150i		−	0.531816i
$100$	−8.20871	+	3.58258i	−0.820871	+	0.358258i
$101$	9.00000			0.895533			0.447767	−	0.894150i	$-0.352219\pi$
$101$	9.00000			0.895533			0.447767	+	0.894150i	$0.352219\pi$
$102$	2.09355			0.207292
$103$			3.16515i			0.311872i	0.987767	+	0.155936i	$0.0498393\pi$
$103$			3.16515i			0.311872i	−0.987767	+	0.155936i	$0.950161\pi$
$104$		0			0
$105$	−0.791288	−	3.79129i	−0.0772218	−	0.369992i
$106$		−	3.46410i		−	0.336463i
$107$			10.5826i			1.02306i	0.859267	+	0.511528i	$0.170920\pi$
$107$			10.5826i			1.02306i	−0.859267	+	0.511528i	$0.829080\pi$
$108$		−	8.95644i		−	0.861834i
$109$			13.1334i			1.25795i	0.777425	+	0.628976i	$0.216526\pi$
$109$			13.1334i			1.25795i	−0.777425	+	0.628976i	$0.783474\pi$
$110$	−0.552200	−	2.64575i	−0.0526502	−	0.252262i
$111$		−	7.93725i		−	0.753371i
$112$	4.83465			0.456832
$113$		−	7.41742i		−	0.697773i	−0.937165	−	0.348886i	$-0.886560\pi$
$113$		−	7.41742i		−	0.697773i	0.937165	−	0.348886i	$-0.113440\pi$
$114$	0.791288			0.0741109
$115$	−2.09355	−	10.0308i	−0.195225	−	0.935377i
$116$	8.20871			0.762160
$117$		0			0
$118$		−	6.37386i		−	0.586762i
$119$			7.93725i			0.727607i
$120$	−0.791288	−	3.79129i	−0.0722344	−	0.346096i
$121$	4.00000			0.363636
$122$	0.647551			0.0586265
$123$	−2.64575			−0.238559
$124$			11.1153i			0.998184i
$125$	−9.11710	+	6.47135i	−0.815459	+	0.578815i
$126$	−1.58258			−0.140987
$127$		−	17.7477i		−	1.57486i	−0.616407	−	0.787428i	$-0.711412\pi$
$127$		−	17.7477i		−	1.57486i	0.616407	−	0.787428i	$-0.288588\pi$
$128$	11.0399			0.975795
$129$	−10.5826			−0.931744
$130$		0			0
$131$	−7.58258			−0.662493			−0.331246	−	0.943544i	$-0.607469\pi$
$131$	−7.58258			−0.662493			−0.331246	+	0.943544i	$0.607469\pi$
$132$	−4.73930			−0.412503
$133$			3.00000i			0.260133i
$134$	−0.460985			−0.0398230
$135$	−2.28425	−	10.9445i	−0.196597	−	0.941953i
$136$			7.93725i			0.680614i
$137$	−10.4877			−0.896021			−0.448010	−	0.894028i	$-0.647867\pi$
$137$	−10.4877			−0.896021			−0.448010	+	0.894028i	$0.647867\pi$
$138$	2.09355			0.178215
$139$	21.7477			1.84462			0.922309	−	0.386453i	$-0.126300\pi$
$139$	21.7477			1.84462			0.922309	+	0.386453i	$0.126300\pi$
$140$	6.79129	−	1.41742i	0.573969	−	0.119794i
$141$			1.82740i			0.153895i
$142$			3.20871i			0.269269i
$143$		0			0
$144$	5.58258			0.465215
$145$	10.0308	−	2.09355i	0.833013	−	0.173860i
$146$		0			0
$147$		−	4.00000i		−	0.329914i
$148$	14.2179			1.16870
$149$			16.6929i			1.36753i	0.729701	+	0.683766i	$0.239659\pi$
$149$			16.6929i			1.36753i	−0.729701	+	0.683766i	$0.760341\pi$
$150$	−0.913701	−	2.09355i	−0.0746033	−	0.170938i
$151$			9.66930i			0.786877i	0.919351	+	0.393438i	$0.128715\pi$
$151$			9.66930i			0.786877i	−0.919351	+	0.393438i	$0.871285\pi$
$152$			3.00000i			0.243332i
$153$			9.16515i			0.740959i
$154$			2.09355i			0.168703i
$155$	2.83485	+	13.5826i	0.227701	+	1.09098i
$156$		0			0
$157$		−	9.16515i		−	0.731459i	−0.930721	−	0.365729i	$-0.880820\pi$
$157$		−	9.16515i		−	0.731459i	0.930721	−	0.365729i	$-0.119180\pi$
$158$	−2.74110			−0.218070
$159$	−7.58258			−0.601337
$160$	10.3739	−	2.16515i	0.820126	−	0.171170i
$161$			7.93725i			0.625543i
$162$	−0.456850			−0.0358935
$163$	−21.0707			−1.65038			−0.825191	−	0.564854i	$-0.808932\pi$
$163$	−21.0707			−1.65038			−0.825191	+	0.564854i	$0.808932\pi$
$164$		−	4.73930i		−	0.370077i
$165$	−5.79129	+	1.20871i	−0.450851	+	0.0940981i
$166$	2.74773			0.213265
$167$	9.57395			0.740855			0.370427	−	0.928861i	$-0.379211\pi$
$167$	9.57395			0.740855			0.370427	+	0.928861i	$0.379211\pi$
$168$			3.00000i			0.231455i
$169$		0			0
$170$	0.956439	+	4.58258i	0.0733555	+	0.351468i
$171$			3.46410i			0.264906i
$172$		−	18.9564i		−	1.44541i
$173$		−	16.5826i		−	1.26075i	−0.776291	−	0.630375i	$-0.782901\pi$
$173$		−	16.5826i		−	1.26075i	0.776291	−	0.630375i	$-0.217099\pi$
$174$			2.09355i			0.158712i
$175$	7.93725	−	3.46410i	0.600000	−	0.261861i
$176$		−	7.38505i		−	0.556669i
$177$	−13.9518			−1.04868
$178$		−	4.37386i		−	0.327835i
$179$	−18.1652			−1.35773			−0.678864	−	0.734264i	$-0.737527\pi$
$179$	−18.1652			−1.35773			−0.678864	+	0.734264i	$0.737527\pi$
$180$	7.84190	−	1.63670i	0.584501	−	0.121992i
$181$	8.74773			0.650213			0.325107	−	0.945677i	$-0.394600\pi$
$181$	8.74773			0.650213			0.325107	+	0.945677i	$0.394600\pi$
$182$		0			0
$183$		−	1.41742i		−	0.104779i
$184$			7.93725i			0.585142i
$185$	17.3739	−	3.62614i	1.27735	−	0.266599i
$186$	−2.83485			−0.207861
$187$	12.1244			0.886621
$188$	−3.27340			−0.238737
$189$			8.66025i			0.629941i
$190$	0.361500	+	1.73205i	0.0262260	+	0.125656i
$191$	−16.5826			−1.19987			−0.599937	−	0.800048i	$-0.704808\pi$
$191$	−16.5826			−1.19987			−0.599937	+	0.800048i	$0.704808\pi$
$192$		−	3.41742i		−	0.246631i
$193$	−14.8655			−1.07004			−0.535020	−	0.844840i	$-0.679696\pi$
$193$	−14.8655			−1.07004			−0.535020	+	0.844840i	$0.679696\pi$
$194$	−5.20871			−0.373964
$195$		0			0
$196$	7.16515			0.511797
$197$	14.6748			1.04553			0.522767	−	0.852476i	$-0.324900\pi$
$197$	14.6748			1.04553			0.522767	+	0.852476i	$0.324900\pi$
$198$			2.41742i			0.171799i
$199$	−10.5826			−0.750179			−0.375089	−	0.926989i	$-0.622388\pi$
$199$	−10.5826			−0.750179			−0.375089	+	0.926989i	$0.622388\pi$
$200$	7.93725	−	3.46410i	0.561249	−	0.244949i
$201$			1.00905i			0.0711729i
$202$	−4.11165			−0.289295
$203$	−7.93725			−0.557086
$204$	8.20871			0.574725
$205$	−1.20871	−	5.79129i	−0.0844201	−	0.404481i
$206$		−	1.44600i		−	0.100748i
$207$			9.16515i			0.637022i
$208$		0			0
$209$	4.58258			0.316983
$210$	0.361500	+	1.73205i	0.0249459	+	0.119523i
$211$	−0.165151			−0.0113695			−0.00568475	−	0.999984i	$-0.501810\pi$
$211$	−0.165151			−0.0113695			−0.00568475	+	0.999984i	$0.501810\pi$
$212$		−	13.5826i		−	0.932855i
$213$	7.02355			0.481246
$214$		−	4.83465i		−	0.330490i
$215$	−4.83465	−	23.1642i	−0.329721	−	1.57979i
$216$			8.66025i			0.589256i
$217$		−	10.7477i		−	0.729603i
$218$		−	6.00000i		−	0.406371i
$219$		0			0
$220$	−2.16515	−	10.3739i	−0.145974	−	0.699406i
$221$		0			0
$222$			3.62614i			0.243370i
$223$	8.66025			0.579934			0.289967	−	0.957037i	$-0.406356\pi$
$223$	8.66025			0.579934			0.289967	+	0.957037i	$0.406356\pi$
$224$	−8.20871			−0.548468
$225$	9.16515	−	4.00000i	0.611010	−	0.266667i
$226$			3.38865i			0.225410i
$227$	−0.818350			−0.0543158			−0.0271579	−	0.999631i	$-0.508646\pi$
$227$	−0.818350			−0.0543158			−0.0271579	+	0.999631i	$0.508646\pi$
$228$	3.10260			0.205475
$229$		−	26.2668i		−	1.73576i	−0.496774	−	0.867880i	$-0.665482\pi$
$229$		−	26.2668i		−	1.73576i	0.496774	−	0.867880i	$-0.334518\pi$
$230$	0.956439	+	4.58258i	0.0630657	+	0.302166i
$231$	4.58258			0.301511
$232$	−7.93725			−0.521106
$233$			2.83485i			0.185717i	0.995679	+	0.0928586i	$0.0296004\pi$
$233$			2.83485i			0.185717i	−0.995679	+	0.0928586i	$0.970400\pi$
$234$		0			0
$235$	−4.00000	+	0.834849i	−0.260931	+	0.0544595i
$236$		−	24.9916i		−	1.62682i
$237$			6.00000i			0.389742i
$238$		−	3.62614i		−	0.235048i
$239$		−	0.190700i		−	0.0123354i	−0.999981	−	0.00616769i	$-0.998037\pi$
$239$		−	0.190700i		−	0.0123354i	0.999981	−	0.00616769i	$-0.00196325\pi$
$240$	−1.27520	−	6.10985i	−0.0823138	−	0.394389i
$241$			1.73205i			0.111571i	0.998443	+	0.0557856i	$0.0177663\pi$
$241$			1.73205i			0.111571i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	−1.82740			−0.117470
$243$			16.0000i			1.02640i
$244$	2.53901			0.162544
$245$	8.75560	−	1.82740i	0.559375	−	0.116748i
$246$	1.20871			0.0770647
$247$		0			0
$248$		−	10.7477i		−	0.682481i
$249$		−	6.01450i		−	0.381154i
$250$	4.16515	−	2.95644i	0.263427	−	0.186982i
$251$	−0.165151			−0.0104243			−0.00521213	−	0.999986i	$-0.501659\pi$
$251$	−0.165151			−0.0104243			−0.00521213	+	0.999986i	$0.501659\pi$
$252$	−6.20520			−0.390891
$253$	12.1244			0.762252
$254$			8.10805i			0.508745i
$255$	10.0308	−	2.09355i	0.628153	−	0.131103i
$256$	1.79129			0.111955
$257$			18.1652i			1.13311i	0.824024	+	0.566556i	$0.191724\pi$
$257$			18.1652i			1.13311i	−0.824024	+	0.566556i	$0.808276\pi$
$258$	4.83465			0.300992
$259$	−13.7477			−0.854242
$260$		0			0
$261$	−9.16515			−0.567309
$262$	3.46410			0.214013
$263$			9.00000i			0.554964i	0.960731	+	0.277482i	$0.0894999\pi$
$263$			9.00000i			0.554964i	−0.960731	+	0.277482i	$0.910500\pi$
$264$	4.58258			0.282038
$265$	−3.46410	−	16.5975i	−0.212798	−	1.01958i
$266$		−	1.37055i		−	0.0840339i
$267$	−9.57395			−0.585917
$268$	−1.80750			−0.110411
$269$	15.0000			0.914566			0.457283	−	0.889321i	$-0.348823\pi$
$269$	15.0000			0.914566			0.457283	+	0.889321i	$0.348823\pi$
$270$	1.04356	+	5.00000i	0.0635091	+	0.304290i
$271$			8.66025i			0.526073i	0.964786	+	0.263036i	$0.0847240\pi$
$271$			8.66025i			0.526073i	−0.964786	+	0.263036i	$0.915276\pi$
$272$			12.7913i			0.775586i
$273$		0			0
$274$	4.79129			0.289452
$275$	−5.29150	−	12.1244i	−0.319090	−	0.731126i
$276$	8.20871			0.494106
$277$			7.41742i			0.445670i	0.974856	+	0.222835i	$0.0715311\pi$
$277$			7.41742i			0.445670i	−0.974856	+	0.222835i	$0.928469\pi$
$278$	−9.93545			−0.595889
$279$		−	12.4104i		−	0.742992i
$280$	−6.56670	+	1.37055i	−0.392436	+	0.0819061i
$281$		−	3.65480i		−	0.218027i	−0.994040	−	0.109014i	$-0.965231\pi$
$281$		−	3.65480i		−	0.218027i	0.994040	−	0.109014i	$-0.0347692\pi$
$282$		−	0.834849i		−	0.0497145i
$283$		−	27.7477i		−	1.64943i	−0.565548	−	0.824716i	$-0.691335\pi$
$283$		−	27.7477i		−	1.64943i	0.565548	−	0.824716i	$-0.308665\pi$
$284$			12.5812i			0.746557i
$285$	3.79129	−	0.791288i	0.224577	−	0.0468718i
$286$		0			0
$287$			4.58258i			0.270501i
$288$	−9.47860			−0.558532
$289$	−4.00000			−0.235294
$290$	−4.58258	+	0.956439i	−0.269098	+	0.0561640i
$291$			11.4014i			0.668359i
$292$		0			0
$293$	18.1389			1.05968			0.529842	−	0.848097i	$-0.322251\pi$
$293$	18.1389			1.05968			0.529842	+	0.848097i	$0.322251\pi$
$294$			1.82740i			0.106576i
$295$	−6.37386	−	30.5390i	−0.371101	−	1.77805i
$296$	−13.7477			−0.799070
$297$	13.2288			0.767610
$298$		−	7.62614i		−	0.441770i
$299$		0			0
$300$	−3.58258	−	8.20871i	−0.206840	−	0.473930i
$301$			18.3296i			1.05650i
$302$		−	4.41742i		−	0.254194i
$303$			9.00000i			0.517036i
$304$			4.83465i			0.277286i
$305$	3.10260	−	0.647551i	0.177654	−	0.0370786i
$306$		−	4.18710i		−	0.239361i
$307$	24.2487			1.38395			0.691974	−	0.721923i	$-0.256741\pi$
$307$	24.2487			1.38395			0.691974	+	0.721923i	$0.256741\pi$
$308$			8.20871i			0.467735i
$309$	−3.16515			−0.180059
$310$	−1.29510	−	6.20520i	−0.0735568	−	0.352432i
$311$	7.58258			0.429968			0.214984	−	0.976618i	$-0.431030\pi$
$311$	7.58258			0.429968			0.214984	+	0.976618i	$0.431030\pi$
$312$		0			0
$313$		−	3.25227i		−	0.183829i	−0.995767	−	0.0919147i	$-0.970701\pi$
$313$		−	3.25227i		−	0.183829i	0.995767	−	0.0919147i	$-0.0292987\pi$
$314$			4.18710i			0.236292i
$315$	−7.58258	+	1.58258i	−0.427230	+	0.0891680i
$316$	−10.7477			−0.604607
$317$	−0.190700			−0.0107108			−0.00535540	−	0.999986i	$-0.501705\pi$
$317$	−0.190700			−0.0107108			−0.00535540	+	0.999986i	$0.501705\pi$
$318$	3.46410			0.194257
$319$			12.1244i			0.678834i
$320$	7.48040	−	1.56125i	0.418167	−	0.0872766i
$321$	−10.5826			−0.590662
$322$		−	3.62614i		−	0.202077i
$323$	−7.93725			−0.441641
$324$	−1.79129			−0.0995160
$325$		0			0
$326$	9.62614			0.533142
$327$	−13.1334			−0.726279
$328$			4.58258i			0.253030i
$329$	3.16515			0.174500
$330$	2.64575	−	0.552200i	0.145644	−	0.0303976i
$331$			4.47315i			0.245867i	0.992415	+	0.122933i	$0.0392301\pi$
$331$			4.47315i			0.245867i	−0.992415	+	0.122933i	$0.960770\pi$
$332$	10.7737			0.591284
$333$	−15.8745			−0.869918
$334$	−4.37386			−0.239327
$335$	−2.20871	+	0.460985i	−0.120675	+	0.0251863i
$336$			4.83465i			0.263752i
$337$		−	30.7477i		−	1.67494i	−0.546487	−	0.837468i	$-0.684035\pi$
$337$		−	30.7477i		−	1.67494i	0.546487	−	0.837468i	$-0.315965\pi$
$338$		0			0
$339$	7.41742			0.402859
$340$	3.75015	+	17.9681i	0.203381	+	0.974455i
$341$	−16.4174			−0.889053
$342$		−	1.58258i		−	0.0855759i
$343$	−19.0526			−1.02874
$344$			18.3296i			0.988264i
$345$	10.0308	−	2.09355i	0.540040	−	0.112713i
$346$			7.57575i			0.407275i
$347$			21.3303i			1.14507i	0.819880	+	0.572535i	$0.194040\pi$
$347$			21.3303i			1.14507i	−0.819880	+	0.572535i	$0.805960\pi$
$348$			8.20871i			0.440033i
$349$			2.45505i			0.131416i	0.997839	+	0.0657079i	$0.0209306\pi$
$349$			2.45505i			0.131416i	−0.997839	+	0.0657079i	$0.979069\pi$
$350$	−3.62614	+	1.58258i	−0.193825	+	0.0845922i
$351$		0			0
$352$			12.5390i			0.668332i
$353$	−6.83285			−0.363676			−0.181838	−	0.983328i	$-0.558205\pi$
$353$	−6.83285			−0.363676			−0.181838	+	0.983328i	$0.558205\pi$
$354$	6.37386			0.338767
$355$	3.20871	+	15.3739i	0.170301	+	0.815960i
$356$		−	17.1497i		−	0.908933i
$357$	−7.93725			−0.420084
$358$	8.29875			0.438603
$359$			19.5293i			1.03072i	0.856975	+	0.515359i	$0.172341\pi$
$359$			19.5293i			1.03072i	−0.856975	+	0.515359i	$0.827659\pi$
$360$	−7.58258	+	1.58258i	−0.399637	+	0.0834091i
$361$	16.0000			0.842105
$362$	−3.99640			−0.210046
$363$			4.00000i			0.209946i
$364$		0			0
$365$		0			0
$366$			0.647551i			0.0338480i
$367$			1.74773i			0.0912306i	0.998959	+	0.0456153i	$0.0145248\pi$
$367$			1.74773i			0.0912306i	−0.998959	+	0.0456153i	$0.985475\pi$
$368$			12.7913i			0.666792i
$369$			5.29150i			0.275465i
$370$	−7.93725	+	1.65660i	−0.412638	+	0.0861226i
$371$			13.1334i			0.681852i
$372$	−11.1153			−0.576302
$373$		−	13.0000i		−	0.673114i	−0.941663	−	0.336557i	$-0.890737\pi$
$373$		−	13.0000i		−	0.673114i	0.941663	−	0.336557i	$-0.109263\pi$
$374$	−5.53901			−0.286416
$375$	−6.47135	−	9.11710i	−0.334179	−	0.470805i
$376$	3.16515			0.163230
$377$		0			0
$378$		−	3.95644i		−	0.203497i
$379$		−	10.6784i		−	0.548510i	−0.961657	−	0.274255i	$-0.911569\pi$
$379$		−	10.6784i		−	0.548510i	0.961657	−	0.274255i	$-0.0884313\pi$
$380$	1.41742	+	6.79129i	0.0727123	+	0.348386i
$381$	17.7477			0.909244
$382$	7.57575			0.387609
$383$	−23.6211			−1.20698			−0.603490	−	0.797371i	$-0.706224\pi$
$383$	−23.6211			−1.20698			−0.603490	+	0.797371i	$0.706224\pi$
$384$			11.0399i			0.563375i
$385$	2.09355	+	10.0308i	0.106697	+	0.511217i
$386$	6.79129			0.345667
$387$			21.1652i			1.07589i
$388$	−20.4231			−1.03683
$389$	3.16515			0.160480			0.0802398	−	0.996776i	$-0.474431\pi$
$389$	3.16515			0.160480			0.0802398	+	0.996776i	$0.474431\pi$
$390$		0			0
$391$	−21.0000			−1.06202
$392$	−6.92820			−0.349927
$393$		−	7.58258i		−	0.382490i
$394$	−6.70417			−0.337751
$395$	−13.1334	+	2.74110i	−0.660813	+	0.137920i
$396$			9.47860i			0.476318i
$397$	20.3477			1.02122			0.510610	−	0.859812i	$-0.329420\pi$
$397$	20.3477			1.02122			0.510610	+	0.859812i	$0.329420\pi$
$398$	4.83465			0.242339
$399$	−3.00000			−0.150188
$400$	12.7913	−	5.58258i	0.639564	−	0.279129i
$401$		−	29.8263i		−	1.48945i	−0.667370	−	0.744726i	$-0.732580\pi$
$401$		−	29.8263i		−	1.48945i	0.667370	−	0.744726i	$-0.267420\pi$
$402$		−	0.460985i		−	0.0229918i
$403$		0			0
$404$	−16.1216			−0.802079
$405$	−2.18890	+	0.456850i	−0.108767	+	0.0227011i
$406$	3.62614			0.179962
$407$			21.0000i			1.04093i
$408$	−7.93725			−0.392953
$409$		−	8.66025i		−	0.428222i	−0.976809	−	0.214111i	$-0.931315\pi$
$409$		−	8.66025i		−	0.428222i	0.976809	−	0.214111i	$-0.0686854\pi$
$410$	0.552200	+	2.64575i	0.0272712	+	0.130664i
$411$		−	10.4877i		−	0.517318i
$412$		−	5.66970i		−	0.279326i
$413$			24.1652i			1.18909i
$414$		−	4.18710i		−	0.205785i
$415$	13.1652	−	2.74773i	0.646252	−	0.134881i
$416$		0			0
$417$			21.7477i			1.06499i
$418$	−2.09355			−0.102399
$419$	5.83485			0.285051			0.142526	−	0.989791i	$-0.454478\pi$
$419$	5.83485			0.285051			0.142526	+	0.989791i	$0.454478\pi$
$420$	1.41742	+	6.79129i	0.0691632	+	0.331381i
$421$		−	5.48220i		−	0.267186i	−0.991036	−	0.133593i	$-0.957348\pi$
$421$		−	5.48220i		−	0.267186i	0.991036	−	0.133593i	$-0.0426515\pi$
$422$	0.0754495			0.00367282
$423$	3.65480			0.177703
$424$			13.1334i			0.637815i
$425$	9.16515	+	21.0000i	0.444575	+	1.01865i
$426$	−3.20871			−0.155463
$427$	−2.45505			−0.118808
$428$		−	18.9564i		−	0.916294i
$429$		0			0
$430$	2.20871	+	10.5826i	0.106514	+	0.510337i
$431$			8.46955i			0.407964i	0.978975	+	0.203982i	$0.0653884\pi$
$431$			8.46955i			0.407964i	−0.978975	+	0.203982i	$0.934612\pi$
$432$			13.9564i			0.671479i
$433$			9.74773i			0.468446i	0.972183	+	0.234223i	$0.0752546\pi$
$433$			9.74773i			0.468446i	−0.972183	+	0.234223i	$0.924745\pi$
$434$			4.91010i			0.235692i
$435$	2.09355	+	10.0308i	0.100378	+	0.480940i
$436$		−	23.5257i		−	1.12668i
$437$	−7.93725			−0.379690
$438$		0			0
$439$	14.4955			0.691830			0.345915	−	0.938266i	$-0.387569\pi$
$439$	14.4955			0.691830			0.345915	+	0.938266i	$0.387569\pi$
$440$	2.09355	+	10.0308i	0.0998061	+	0.478200i
$441$	−8.00000			−0.380952
$442$		0			0
$443$			19.9129i			0.946089i	0.881038	+	0.473045i	$0.156845\pi$
$443$			19.9129i			0.946089i	−0.881038	+	0.473045i	$0.843155\pi$
$444$			14.2179i			0.674752i
$445$	−4.37386	−	20.9564i	−0.207341	−	0.993430i
$446$	−3.95644			−0.187343
$447$	−16.6929			−0.789545
$448$	−5.91915			−0.279654
$449$		−	11.0200i		−	0.520064i	−0.965600	−	0.260032i	$-0.916267\pi$
$449$		−	11.0200i		−	0.520064i	0.965600	−	0.260032i	$-0.0837331\pi$
$450$	−4.18710	+	1.82740i	−0.197382	+	0.0861445i
$451$	7.00000			0.329617
$452$			13.2867i			0.624956i
$453$	−9.66930			−0.454304
$454$	0.373864			0.0175463
$455$		0			0
$456$	−3.00000			−0.140488
$457$	−1.73205			−0.0810219			−0.0405110	−	0.999179i	$-0.512899\pi$
$457$	−1.73205			−0.0810219			−0.0405110	+	0.999179i	$0.512899\pi$
$458$			12.0000i			0.560723i
$459$	−22.9129			−1.06948
$460$	3.75015	+	17.9681i	0.174852	+	0.837765i
$461$		−	35.8408i		−	1.66927i	−0.550803	−	0.834635i	$-0.685678\pi$
$461$		−	35.8408i		−	1.66927i	0.550803	−	0.834635i	$-0.314322\pi$
$462$	−2.09355			−0.0974008
$463$	39.4002			1.83108			0.915542	−	0.402223i	$-0.131762\pi$
$463$	39.4002			1.83108			0.915542	+	0.402223i	$0.131762\pi$
$464$	−12.7913			−0.593821
$465$	−13.5826	+	2.83485i	−0.629877	+	0.131463i
$466$		−	1.29510i		−	0.0599944i
$467$			24.3303i			1.12587i	0.826500	+	0.562936i	$0.190328\pi$
$467$			24.3303i			1.12587i	−0.826500	+	0.562936i	$0.809672\pi$
$468$		0			0
$469$	1.74773			0.0807025
$470$	1.82740	−	0.381401i	0.0842917	−	0.0175927i
$471$	9.16515			0.422308
$472$			24.1652i			1.11229i
$473$	27.9989			1.28739
$474$		−	2.74110i		−	0.125903i
$475$	3.46410	+	7.93725i	0.158944	+	0.364186i
$476$		−	14.2179i		−	0.651677i
$477$			15.1652i			0.694365i
$478$			0.0871215i			0.00398485i
$479$			4.66385i			0.213097i	0.994308	+	0.106548i	$0.0339799\pi$
$479$			4.66385i			0.213097i	−0.994308	+	0.106548i	$0.966020\pi$
$480$	2.16515	+	10.3739i	0.0988252	+	0.473500i
$481$		0			0
$482$		−	0.791288i		−	0.0360422i
$483$	−7.93725			−0.361158
$484$	−7.16515			−0.325689
$485$	−24.9564	+	5.20871i	−1.13321	+	0.236515i
$486$		−	7.30960i		−	0.331570i
$487$	−10.6784			−0.483882			−0.241941	−	0.970291i	$-0.577784\pi$
$487$	−10.6784			−0.483882			−0.241941	+	0.970291i	$0.577784\pi$
$488$	−2.45505			−0.111135
$489$		−	21.0707i		−	0.952848i
$490$	−4.00000	+	0.834849i	−0.180702	+	0.0377146i
$491$	19.4174			0.876296			0.438148	−	0.898903i	$-0.355635\pi$
$491$	19.4174			0.876296			0.438148	+	0.898903i	$0.355635\pi$
$492$	4.73930			0.213664
$493$		−	21.0000i		−	0.945792i
$494$		0			0
$495$	2.41742	+	11.5826i	0.108655	+	0.520598i
$496$		−	17.3205i		−	0.777714i
$497$		−	12.1652i		−	0.545682i
$498$			2.74773i			0.123129i
$499$		−	0.723000i		−	0.0323659i	−0.999869	−	0.0161830i	$-0.994849\pi$
$499$		−	0.723000i		−	0.0323659i	0.999869	−	0.0161830i	$-0.00515142\pi$
$500$	16.3314	−	11.5921i	0.730361	−	0.518413i
$501$			9.57395i			0.427733i
$502$	0.0754495			0.00336747
$503$			0.165151i			0.00736374i	0.999993	+	0.00368187i	$0.00117198\pi$
$503$			0.165151i			0.00736374i	−0.999993	+	0.00368187i	$0.998828\pi$
$504$	6.00000			0.267261
$505$	−19.7001	+	4.11165i	−0.876643	+	0.182966i
$506$	−5.53901			−0.246239
$507$		0			0
$508$			31.7913i			1.41051i
$509$		−	8.46955i		−	0.375406i	−0.982226	−	0.187703i	$-0.939896\pi$
$509$		−	8.46955i		−	0.375406i	0.982226	−	0.187703i	$-0.0601043\pi$
$510$	−4.58258	+	0.956439i	−0.202920	+	0.0423518i
$511$		0			0
$512$	−22.8981			−1.01196
$513$	−8.66025			−0.382360
$514$		−	8.29875i		−	0.366042i
$515$	−1.44600	−	6.92820i	−0.0637184	−	0.305293i
$516$	18.9564			0.834511
$517$		−	4.83485i		−	0.212636i
$518$	6.28065			0.275956
$519$	16.5826			0.727894
$520$		0			0
$521$	27.4955			1.20460			0.602299	−	0.798271i	$-0.294252\pi$
$521$	27.4955			1.20460			0.602299	+	0.798271i	$0.294252\pi$
$522$	4.18710			0.183264
$523$			0.165151i			0.00722157i	0.999993	+	0.00361078i	$0.00114935\pi$
$523$			0.165151i			0.00722157i	−0.999993	+	0.00361078i	$0.998851\pi$
$524$	13.5826			0.593358
$525$	3.46410	+	7.93725i	0.151186	+	0.346410i
$526$		−	4.11165i		−	0.179277i
$527$	28.4358			1.23868
$528$	7.38505			0.321393
$529$	2.00000			0.0869565
$530$	1.58258	+	7.58258i	0.0687427	+	0.329366i
$531$			27.9035i			1.21091i
$532$		−	5.37386i		−	0.232987i
$533$		0			0
$534$	4.37386			0.189276
$535$	−4.83465	−	23.1642i	−0.209020	−	1.00148i
$536$	1.74773			0.0754903
$537$		−	18.1652i		−	0.783884i
$538$	−6.85275			−0.295443
$539$			10.5830i			0.455842i
$540$	4.09175	+	19.6048i	0.176081	+	0.843655i
$541$			10.3923i			0.446800i	0.974727	+	0.223400i	$0.0717156\pi$
$541$			10.3923i			0.446800i	−0.974727	+	0.223400i	$0.928284\pi$
$542$		−	3.95644i		−	0.169944i
$543$			8.74773i			0.375401i
$544$		−	21.7182i		−	0.931161i
$545$	−6.00000	−	28.7477i	−0.257012	−	1.23142i
$546$		0			0
$547$		−	28.7477i		−	1.22916i	−0.788853	−	0.614582i	$-0.789325\pi$
$547$		−	28.7477i		−	1.22916i	0.788853	−	0.614582i	$-0.210675\pi$
$548$	18.7864			0.802516
$549$	−2.83485			−0.120988
$550$	2.41742	+	5.53901i	0.103079	+	0.236184i
$551$		−	7.93725i		−	0.338138i
$552$	−7.93725			−0.337832
$553$	10.3923			0.441926
$554$		−	3.38865i		−	0.143970i
$555$	3.62614	+	17.3739i	0.153921	+	0.737479i
$556$	−38.9564			−1.65212
$557$	−7.74655			−0.328232			−0.164116	−	0.986441i	$-0.552477\pi$
$557$	−7.74655			−0.328232			−0.164116	+	0.986441i	$0.552477\pi$
$558$			5.66970i			0.240017i
$559$		0			0
$560$	−10.5826	+	2.20871i	−0.447195	+	0.0933351i
$561$			12.1244i			0.511891i
$562$			1.66970i			0.0704319i
$563$		−	9.00000i		−	0.379305i	−0.981851	−	0.189652i	$-0.939264\pi$
$563$		−	9.00000i		−	0.379305i	0.981851	−	0.189652i	$-0.0607361\pi$
$564$		−	3.27340i		−	0.137835i
$565$	3.38865	+	16.2360i	0.142562	+	0.683054i
$566$			12.6766i			0.532835i
$567$	1.73205			0.0727393
$568$		−	12.1652i		−	0.510438i
$569$	−7.74773			−0.324802			−0.162401	−	0.986725i	$-0.551924\pi$
$569$	−7.74773			−0.324802			−0.162401	+	0.986725i	$0.551924\pi$
$570$	−1.73205	+	0.361500i	−0.0725476	+	0.0151416i
$571$	−35.0780			−1.46797			−0.733985	−	0.679166i	$-0.762342\pi$
$571$	−35.0780			−1.46797			−0.733985	+	0.679166i	$0.762342\pi$
$572$		0			0
$573$		−	16.5826i		−	0.692747i
$574$		−	2.09355i		−	0.0873831i
$575$	9.16515	+	21.0000i	0.382213	+	0.875761i
$576$	−6.83485			−0.284785
$577$	−6.92820			−0.288425			−0.144212	−	0.989547i	$-0.546065\pi$
$577$	−6.92820			−0.288425			−0.144212	+	0.989547i	$0.546065\pi$
$578$	1.82740			0.0760099
$579$		−	14.8655i		−	0.617787i
$580$	−17.9681	+	3.75015i	−0.746083	+	0.155717i
$581$	−10.4174			−0.432188
$582$		−	5.20871i		−	0.215908i
$583$	20.0616			0.830867
$584$		0			0
$585$		0			0
$586$	−8.28674			−0.342322
$587$	−39.4956			−1.63016			−0.815078	−	0.579351i	$-0.803306\pi$
$587$	−39.4956			−1.63016			−0.815078	+	0.579351i	$0.803306\pi$
$588$			7.16515i			0.295486i
$589$	10.7477			0.442852
$590$	2.91190	+	13.9518i	0.119881	+	0.574385i
$591$			14.6748i			0.603639i
$592$	−22.1552			−0.910571
$593$	−21.1660			−0.869184			−0.434592	−	0.900627i	$-0.643107\pi$
$593$	−21.1660			−0.869184			−0.434592	+	0.900627i	$0.643107\pi$
$594$	−6.04356			−0.247970
$595$	−3.62614	−	17.3739i	−0.148657	−	0.712259i
$596$		−	29.9017i		−	1.22482i
$597$		−	10.5826i		−	0.433116i
$598$		0			0
$599$	−15.4955			−0.633127			−0.316564	−	0.948571i	$-0.602529\pi$
$599$	−15.4955			−0.633127			−0.316564	+	0.948571i	$0.602529\pi$
$600$	3.46410	+	7.93725i	0.141421	+	0.324037i
$601$	16.9129			0.689891			0.344945	−	0.938623i	$-0.387897\pi$
$601$	16.9129			0.689891			0.344945	+	0.938623i	$0.387897\pi$
$602$		−	8.37386i		−	0.341293i
$603$	2.01810			0.0821834
$604$		−	17.3205i		−	0.704761i
$605$	−8.75560	+	1.82740i	−0.355966	+	0.0742944i
$606$		−	4.11165i		−	0.167024i
$607$		−	7.74773i		−	0.314471i	−0.987561	−	0.157235i	$-0.949742\pi$
$607$		−	7.74773i		−	0.314471i	0.987561	−	0.157235i	$-0.0502581\pi$
$608$		−	8.20871i		−	0.332907i
$609$		−	7.93725i		−	0.321634i
$610$	−1.41742	+	0.295834i	−0.0573898	+	0.0119780i
$611$		0			0
$612$		−	16.4174i		−	0.663635i
$613$	5.91915			0.239072			0.119536	−	0.992830i	$-0.461859\pi$
$613$	5.91915			0.239072			0.119536	+	0.992830i	$0.461859\pi$
$614$	−11.0780			−0.447073
$615$	5.79129	−	1.20871i	0.233527	−	0.0487400i
$616$		−	7.93725i		−	0.319801i
$617$	13.9518			0.561677			0.280838	−	0.959755i	$-0.409388\pi$
$617$	13.9518			0.561677			0.280838	+	0.959755i	$0.409388\pi$
$618$	1.44600			0.0581667
$619$			29.7309i			1.19499i	0.801874	+	0.597493i	$0.203836\pi$
$619$			29.7309i			1.19499i	−0.801874	+	0.597493i	$0.796164\pi$
$620$	−5.07803	−	24.3303i	−0.203939	−	0.977128i
$621$	−22.9129			−0.919462
$622$	−3.46410			−0.138898
$623$			16.5826i			0.664367i
$624$		0			0
$625$	17.0000	−	18.3303i	0.680000	−	0.733212i
$626$			1.48580i			0.0593846i
$627$			4.58258i			0.183010i
$628$			16.4174i			0.655127i
$629$		−	36.3731i		−	1.45029i
$630$	3.46410	−	0.723000i	0.138013	−	0.0288050i
$631$			5.91915i			0.235638i	0.993035	+	0.117819i	$0.0375902\pi$
$631$			5.91915i			0.235638i	−0.993035	+	0.117819i	$0.962410\pi$
$632$	10.3923			0.413384
$633$		−	0.165151i		−	0.00656418i
$634$	0.0871215			0.00346004
$635$	8.10805	+	38.8480i	0.321758	+	1.54164i
$636$	13.5826			0.538584
$637$		0			0
$638$		−	5.53901i		−	0.219292i
$639$		−	14.0471i		−	0.555695i
$640$	−24.1652	+	5.04356i	−0.955211	+	0.199364i
$641$	18.1652			0.717480			0.358740	−	0.933437i	$-0.383206\pi$
$641$	18.1652			0.717480			0.358740	+	0.933437i	$0.383206\pi$
$642$	4.83465			0.190809
$643$	21.7937			0.859458			0.429729	−	0.902958i	$-0.358609\pi$
$643$	21.7937			0.859458			0.429729	+	0.902958i	$0.358609\pi$
$644$		−	14.2179i		−	0.560264i
$645$	23.1642	−	4.83465i	0.912090	−	0.190364i
$646$	3.62614			0.142668
$647$		−	27.0000i		−	1.06148i	−0.847535	−	0.530740i	$-0.821914\pi$
$647$		−	27.0000i		−	1.06148i	0.847535	−	0.530740i	$-0.178086\pi$
$648$	1.73205			0.0680414
$649$	36.9129			1.44896
$650$		0			0
$651$	10.7477			0.421237
$652$	37.7436			1.47815
$653$		−	42.8258i		−	1.67590i	−0.545746	−	0.837951i	$-0.683754\pi$
$653$		−	42.8258i		−	1.67590i	0.545746	−	0.837951i	$-0.316246\pi$
$654$	6.00000			0.234619
$655$	16.5975	−	3.46410i	0.648518	−	0.135354i
$656$			7.38505i			0.288338i
$657$		0			0
$658$	−1.44600			−0.0563710
$659$	−30.4955			−1.18793			−0.593967	−	0.804489i	$-0.702439\pi$
$659$	−30.4955			−1.18793			−0.593967	+	0.804489i	$0.702439\pi$
$660$	10.3739	−	2.16515i	0.403802	−	0.0842784i
$661$			18.3296i			0.712937i	0.934307	+	0.356469i	$0.116019\pi$
$661$			18.3296i			0.712937i	−0.934307	+	0.356469i	$0.883981\pi$
$662$		−	2.04356i		−	0.0794252i
$663$		0			0
$664$	−10.4174			−0.404274
$665$	−1.37055	−	6.56670i	−0.0531477	−	0.254646i
$666$	7.25227			0.281020
$667$		−	21.0000i		−	0.813123i
$668$	−17.1497			−0.663542
$669$			8.66025i			0.334825i
$670$	1.00905	−	0.210601i	0.0389830	−	0.00813623i
$671$			3.75015i			0.144773i
$672$		−	8.20871i		−	0.316658i
$673$		−	24.1652i		−	0.931498i	−0.884917	−	0.465749i	$-0.845785\pi$
$673$		−	24.1652i		−	0.931498i	0.884917	−	0.465749i	$-0.154215\pi$
$674$			14.0471i			0.541074i
$675$	10.0000	+	22.9129i	0.384900	+	0.881917i
$676$		0			0
$677$			2.83485i			0.108952i	0.998515	+	0.0544760i	$0.0173489\pi$
$677$			2.83485i			0.108952i	−0.998515	+	0.0544760i	$0.982651\pi$
$678$	−3.38865			−0.130140
$679$	19.7477			0.757848
$680$	−3.62614	−	17.3739i	−0.139056	−	0.666257i
$681$		−	0.818350i		−	0.0313593i
$682$	7.50030			0.287202
$683$	−33.0997			−1.26652			−0.633262	−	0.773938i	$-0.718284\pi$
$683$	−33.0997			−1.26652			−0.633262	+	0.773938i	$0.718284\pi$
$684$		−	6.20520i		−	0.237262i
$685$	22.9564	−	4.79129i	0.877120	−	0.183066i
$686$	8.70417			0.332327
$687$	26.2668			1.00214
$688$			29.5390i			1.12616i
$689$		0			0
$690$	−4.58258	+	0.956439i	−0.174456	+	0.0364110i
$691$			19.7756i			0.752298i	0.926559	+	0.376149i	$0.122752\pi$
$691$			19.7756i			0.752298i	−0.926559	+	0.376149i	$0.877248\pi$
$692$			29.7042i			1.12918i
$693$		−	9.16515i		−	0.348155i
$694$		−	9.74475i		−	0.369906i
$695$	−47.6036	+	9.93545i	−1.80571	+	0.376873i
$696$		−	7.93725i		−	0.300861i
$697$	−12.1244			−0.459243
$698$		−	1.12159i		−	0.0424528i
$699$	−2.83485			−0.107224
$700$	−14.2179	+	6.20520i	−0.537386	+	0.234535i
$701$	−21.1652			−0.799397			−0.399698	−	0.916647i	$-0.630885\pi$
$701$	−21.1652			−0.799397			−0.399698	+	0.916647i	$0.630885\pi$
$702$		0			0
$703$		−	13.7477i		−	0.518505i
$704$			9.04165i			0.340770i
$705$	−0.834849	−	4.00000i	−0.0314422	−	0.150649i
$706$	3.12159			0.117483
$707$	15.5885			0.586264
$708$	24.9916			0.939242
$709$		−	36.3731i		−	1.36602i	−0.730409	−	0.683010i	$-0.760671\pi$
$709$		−	36.3731i		−	1.36602i	0.730409	−	0.683010i	$-0.239329\pi$
$710$	−1.46590	−	7.02355i	−0.0550143	−	0.263589i
$711$	12.0000			0.450035
$712$			16.5826i			0.621458i
$713$	28.4358			1.06493
$714$	3.62614			0.135705
$715$		0			0
$716$	32.5390			1.21604
$717$	0.190700			0.00712184
$718$		−	8.92197i		−	0.332965i
$719$	24.4955			0.913526			0.456763	−	0.889588i	$-0.349009\pi$
$719$	24.4955			0.913526			0.456763	+	0.889588i	$0.349009\pi$
$720$	−12.2197	+	2.55040i	−0.455402	+	0.0950478i
$721$			5.48220i			0.204168i
$722$	−7.30960			−0.272035
$723$	−1.73205			−0.0644157
$724$	−15.6697			−0.582360
$725$	−21.0000	+	9.16515i	−0.779920	+	0.340385i
$726$		−	1.82740i		−	0.0678212i
$727$			15.2523i			0.565675i	0.959168	+	0.282838i	$0.0912758\pi$
$727$			15.2523i			0.565675i	−0.959168	+	0.282838i	$0.908724\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$		0			0
$731$	−48.4955			−1.79367
$732$			2.53901i			0.0938447i
$733$	22.8027			0.842237			0.421119	−	0.907006i	$-0.361638\pi$
$733$	22.8027			0.842237			0.421119	+	0.907006i	$0.361638\pi$
$734$		−	0.798450i		−	0.0294713i
$735$	1.82740	+	8.75560i	0.0674047	+	0.322955i
$736$		−	21.7182i		−	0.800544i
$737$		−	2.66970i		−	0.0983396i
$738$		−	2.41742i		−	0.0889866i
$739$		−	17.0345i		−	0.626623i	−0.949650	−	0.313311i	$-0.898562\pi$
$739$		−	17.0345i		−	0.626623i	0.949650	−	0.313311i	$-0.101438\pi$
$740$	−31.1216	+	6.49545i	−1.14405	+	0.238778i
$741$		0			0
$742$		−	6.00000i		−	0.220267i
$743$	−5.72845			−0.210157			−0.105078	−	0.994464i	$-0.533509\pi$
$743$	−5.72845			−0.210157			−0.105078	+	0.994464i	$0.533509\pi$
$744$	10.7477			0.394031
$745$	−7.62614	−	36.5390i	−0.279400	−	1.33869i
$746$			5.93905i			0.217444i
$747$	−12.0290			−0.440118
$748$	−21.7182			−0.794096
$749$			18.3296i			0.669748i
$750$	2.95644	+	4.16515i	0.107954	+	0.152090i
$751$	11.7477			0.428681			0.214340	−	0.976759i	$-0.431240\pi$
$751$	11.7477			0.428681			0.214340	+	0.976759i	$0.431240\pi$
$752$	5.10080			0.186007
$753$		−	0.165151i		−	0.00601845i
$754$		0			0
$755$	−4.41742	−	21.1652i	−0.160767	−	0.770279i
$756$		−	15.5130i		−	0.564203i
$757$		−	9.74773i		−	0.354287i	−0.984185	−	0.177144i	$-0.943314\pi$
$757$		−	9.74773i		−	0.354287i	0.984185	−	0.177144i	$-0.0566857\pi$
$758$			4.87841i			0.177192i
$759$			12.1244i			0.440086i
$760$	−1.37055	−	6.56670i	−0.0497151	−	0.238199i
$761$			35.4594i			1.28540i	0.766118	+	0.642701i	$0.222186\pi$
$761$			35.4594i			1.28540i	−0.766118	+	0.642701i	$0.777814\pi$
$762$	−8.10805			−0.293724
$763$			22.7477i			0.823523i
$764$	29.7042			1.07466
$765$	−4.18710	−	20.0616i	−0.151385	−	0.725329i
$766$	10.7913			0.389905
$767$		0			0
$768$			1.79129i			0.0646375i
$769$		−	15.5885i		−	0.562134i	−0.959688	−	0.281067i	$-0.909312\pi$
$769$		−	15.5885i		−	0.562134i	0.959688	−	0.281067i	$-0.0906883\pi$
$770$	−0.956439	−	4.58258i	−0.0344677	−	0.165145i
$771$	−18.1652			−0.654202
$772$	26.6283			0.958374
$773$	24.1534			0.868736			0.434368	−	0.900735i	$-0.356972\pi$
$773$	24.1534			0.868736			0.434368	+	0.900735i	$0.356972\pi$
$774$		−	9.66930i		−	0.347556i
$775$	−12.4104	−	28.4358i	−0.445795	−	1.02144i
$776$	19.7477			0.708902
$777$		−	13.7477i		−	0.493197i
$778$	−1.44600			−0.0518416
$779$	−4.58258			−0.164188
$780$		0			0
$781$	−18.5826			−0.664937
$782$	9.59386			0.343076
$783$		−	22.9129i		−	0.818839i
$784$	−11.1652			−0.398755
$785$	4.18710	+	20.0616i	0.149444	+	0.716030i
$786$			3.46410i			0.123560i
$787$	−16.3115			−0.581441			−0.290720	−	0.956808i	$-0.593895\pi$
$787$	−16.3115			−0.581441			−0.290720	+	0.956808i	$0.593895\pi$
$788$	−26.2867			−0.936425
$789$	−9.00000			−0.320408
$790$	6.00000	−	1.25227i	0.213470	−	0.0445539i
$791$		−	12.8474i		−	0.456799i
$792$		−	9.16515i		−	0.325669i
$793$		0			0
$794$	−9.29583			−0.329897
$795$	16.5975	−	3.46410i	0.588653	−	0.122859i
$796$	18.9564			0.671893
$797$		−	44.0780i		−	1.56132i	−0.624954	−	0.780662i	$-0.714882\pi$
$797$		−	44.0780i		−	1.56132i	0.624954	−	0.780662i	$-0.285118\pi$
$798$	1.37055			0.0485170
$799$			8.37420i			0.296258i
$800$	−21.7182	+	9.47860i	−0.767855	+	0.335119i
$801$			19.1479i			0.676558i
$802$			13.6261i			0.481156i
$803$		0			0
$804$		−	1.80750i		−	0.0637456i
$805$	−3.62614	−	17.3739i	−0.127805	−	0.612348i
$806$		0			0
$807$			15.0000i			0.528025i
$808$	15.5885			0.548400
$809$	54.8258			1.92757			0.963785	−	0.266679i	$-0.0859263\pi$
$809$	54.8258			1.92757			0.963785	+	0.266679i	$0.0859263\pi$
$810$	1.00000	−	0.208712i	0.0351364	−	0.00733340i
$811$			50.5155i			1.77384i	0.461923	+	0.886920i	$0.347160\pi$
$811$			50.5155i			1.77384i	−0.461923	+	0.886920i	$0.652840\pi$
$812$	14.2179			0.498951
$813$	−8.66025			−0.303728
$814$		−	9.59386i		−	0.336264i
$815$	46.1216	−	9.62614i	1.61557	−	0.337189i
$816$	−12.7913			−0.447785
$817$	−18.3296			−0.641270
$818$			3.95644i			0.138334i
$819$		0			0
$820$	2.16515	+	10.3739i	0.0756104	+	0.362271i
$821$			18.1389i			0.633051i	0.948584	+	0.316525i	$0.102516\pi$
$821$			18.1389i			0.633051i	−0.948584	+	0.316525i	$0.897484\pi$
$822$			4.79129i			0.167115i
$823$		−	31.4174i		−	1.09514i	−0.836759	−	0.547571i	$-0.815552\pi$
$823$		−	31.4174i		−	1.09514i	0.836759	−	0.547571i	$-0.184448\pi$
$824$			5.48220i			0.190982i
$825$	12.1244	−	5.29150i	0.422116	−	0.184226i
$826$		−	11.0399i		−	0.384126i
$827$	10.7737			0.374638			0.187319	−	0.982299i	$-0.440020\pi$
$827$	10.7737			0.374638			0.187319	+	0.982299i	$0.440020\pi$
$828$		−	16.4174i		−	0.570545i
$829$	33.3303			1.15761			0.578805	−	0.815466i	$-0.303519\pi$
$829$	33.3303			1.15761			0.578805	+	0.815466i	$0.303519\pi$
$830$	−6.01450	+	1.25530i	−0.208766	+	0.0435721i
$831$	−7.41742			−0.257308
$832$		0			0
$833$		−	18.3303i		−	0.635107i
$834$		−	9.93545i		−	0.344037i
$835$	−20.9564	+	4.37386i	−0.725227	+	0.151364i
$836$	−8.20871			−0.283904
$837$	31.0260			1.07242
$838$	−2.66565			−0.0920834
$839$		−	43.6827i		−	1.50809i	−0.656821	−	0.754047i	$-0.728099\pi$
$839$		−	43.6827i		−	1.50809i	0.656821	−	0.754047i	$-0.271901\pi$
$840$	−1.37055	−	6.56670i	−0.0472885	−	0.226573i
$841$	−8.00000			−0.275862
$842$			2.50455i			0.0863123i
$843$	3.65480			0.125878
$844$	0.295834			0.0101830
$845$		0			0
$846$	−1.66970			−0.0574054
$847$	6.92820			0.238056
$848$			21.1652i			0.726814i
$849$	27.7477			0.952300
$850$	−4.18710	−	9.59386i	−0.143616	−	0.329067i
$851$		−	36.3731i		−	1.24685i
$852$	−12.5812			−0.431025
$853$	−5.63310			−0.192874			−0.0964369	−	0.995339i	$-0.530745\pi$
$853$	−5.63310			−0.192874			−0.0964369	+	0.995339i	$0.530745\pi$
$854$	1.12159			0.0383800
$855$	−1.58258	−	7.58258i	−0.0541229	−	0.259319i
$856$			18.3296i			0.626491i
$857$			4.74773i			0.162179i	0.996707	+	0.0810896i	$0.0258400\pi$
$857$			4.74773i			0.162179i	−0.996707	+	0.0810896i	$0.974160\pi$
$858$		0			0
$859$	44.2432			1.50956			0.754779	−	0.655979i	$-0.227744\pi$
$859$	44.2432			1.50956			0.754779	+	0.655979i	$0.227744\pi$
$860$	8.66025	+	41.4938i	0.295312	+	1.41493i
$861$	−4.58258			−0.156174
$862$		−	3.86932i		−	0.131789i
$863$	13.6657			0.465186			0.232593	−	0.972574i	$-0.425279\pi$
$863$	13.6657			0.465186			0.232593	+	0.972574i	$0.425279\pi$
$864$		−	23.6965i		−	0.806172i
$865$	7.57575	+	36.2976i	0.257583	+	1.23416i
$866$		−	4.45325i		−	0.151328i
$867$		−	4.00000i		−	0.135847i
$868$			19.2523i			0.653465i
$869$		−	15.8745i		−	0.538506i
$870$	−0.956439	−	4.58258i	−0.0324263	−	0.155364i
$871$		0			0
$872$			22.7477i			0.770335i
$873$	22.8027			0.771755
$874$	3.62614			0.122656
$875$	−15.7913	+	11.2087i	−0.533843	+	0.378924i
$876$		0			0
$877$	7.93725			0.268022			0.134011	−	0.990980i	$-0.457214\pi$
$877$	7.93725			0.268022			0.134011	+	0.990980i	$0.457214\pi$
$878$	−6.62225			−0.223490
$879$			18.1389i			0.611809i
$880$	3.37386	+	16.1652i	0.113733	+	0.544927i
$881$	36.4955			1.22956			0.614782	−	0.788697i	$-0.289244\pi$
$881$	36.4955			1.22956			0.614782	+	0.788697i	$0.289244\pi$
$882$	3.65480			0.123064
$883$			36.2432i			1.21968i	0.792524	+	0.609840i	$0.208766\pi$
$883$			36.2432i			1.21968i	−0.792524	+	0.609840i	$0.791234\pi$
$884$		0			0
$885$	30.5390	−	6.37386i	1.02656	−	0.214255i
$886$		−	9.09720i		−	0.305627i
$887$		−	54.4955i		−	1.82978i	−0.403705	−	0.914889i	$-0.632278\pi$
$887$		−	54.4955i		−	1.82978i	0.403705	−	0.914889i	$-0.367722\pi$
$888$		−	13.7477i		−	0.461344i
$889$		−	30.7400i		−	1.03099i
$890$	1.99820	+	9.57395i	0.0669798	+	0.320920i
$891$		−	2.64575i		−	0.0886360i
$892$	−15.5130			−0.519414
$893$			3.16515i			0.105918i
$894$	7.62614			0.255056
$895$	39.7617	−	8.29875i	1.32909	−	0.277397i
$896$	19.1216			0.638808
$897$		0			0
$898$			5.03447i			0.168002i
$899$			28.4358i			0.948387i
$900$	−16.4174	+	7.16515i	−0.547247	+	0.238838i
$901$	−34.7477			−1.15761
$902$	−3.19795			−0.106480
$903$	−18.3296			−0.609970
$904$		−	12.8474i		−	0.427297i
$905$	−19.1479	+	3.99640i	−0.636498	+	0.132845i
$906$	4.41742			0.146759
$907$			6.25227i			0.207603i	0.994598	+	0.103802i	$0.0331007\pi$
$907$			6.25227i			0.207603i	−0.994598	+	0.103802i	$0.966899\pi$
$908$	1.46590			0.0486476
$909$	18.0000			0.597022
$910$		0			0
$911$	−7.91288			−0.262165			−0.131083	−	0.991371i	$-0.541845\pi$
$911$	−7.91288			−0.262165			−0.131083	+	0.991371i	$0.541845\pi$
$912$	−4.83465			−0.160091
$913$			15.9129i			0.526639i
$914$	0.791288			0.0261735
$915$	0.647551	+	3.10260i	0.0214074	+	0.102569i
$916$			47.0514i			1.55462i
$917$	−13.1334			−0.433703
$918$	10.4678			0.345487
$919$	−54.1652			−1.78674			−0.893372	−	0.449318i	$-0.851667\pi$
$919$	−54.1652			−1.78674			−0.893372	+	0.449318i	$0.851667\pi$
$920$	−3.62614	−	17.3739i	−0.119550	−	0.572799i
$921$			24.2487i			0.799022i
$922$			16.3739i			0.539244i
$923$		0			0
$924$	−8.20871			−0.270047
$925$	−36.3731	+	15.8745i	−1.19594	+	0.521951i
$926$	−18.0000			−0.591517
$927$			6.33030i			0.207914i
$928$	21.7182			0.712935
$929$		−	26.3622i		−	0.864915i	−0.901654	−	0.432457i	$-0.857647\pi$
$929$		−	26.3622i		−	0.864915i	0.901654	−	0.432457i	$-0.142353\pi$
$930$	6.20520	−	1.29510i	0.203477	−	0.0424680i
$931$		−	6.92820i		−	0.227063i
$932$		−	5.07803i		−	0.166336i
$933$			7.58258i			0.248242i
$934$		−	11.1153i		−	0.363704i
$935$	−26.5390	+	5.53901i	−0.867919	+	0.181145i
$936$		0			0
$937$		−	31.4955i		−	1.02891i	−0.857517	−	0.514456i	$-0.827994\pi$
$937$		−	31.4955i		−	1.02891i	0.857517	−	0.514456i	$-0.172006\pi$
$938$	−0.798450			−0.0260703
$939$	3.25227			0.106134
$940$	7.16515	−	1.49545i	0.233701	−	0.0487763i
$941$			26.4575i			0.862490i	0.902235	+	0.431245i	$0.141926\pi$
$941$			26.4575i			0.862490i	−0.902235	+	0.431245i	$0.858074\pi$
$942$	−4.18710			−0.136423
$943$	−12.1244			−0.394823
$944$			38.9434i			1.26750i
$945$	−3.95644	−	18.9564i	−0.128703	−	0.616653i
$946$	−12.7913			−0.415881
$947$	−14.3332			−0.465765			−0.232883	−	0.972505i	$-0.574816\pi$
$947$	−14.3332			−0.465765			−0.232883	+	0.972505i	$0.574816\pi$
$948$		−	10.7477i		−	0.349070i
$949$		0			0
$950$	−1.58258	−	3.62614i	−0.0513455	−	0.117647i
$951$		−	0.190700i		−	0.00618388i
$952$			13.7477i			0.445566i
$953$		−	8.07803i		−	0.261673i	−0.991404	−	0.130837i	$-0.958234\pi$
$953$		−	8.07803i		−	0.261673i	0.991404	−	0.130837i	$-0.0417663\pi$
$954$		−	6.92820i		−	0.224309i
$955$	36.2976	−	7.57575i	1.17456	−	0.245146i
$956$			0.341599i			0.0110481i
$957$	−12.1244			−0.391925
$958$		−	2.13068i		−	0.0688392i
$959$	−18.1652			−0.586583
$960$	1.56125	+	7.48040i	0.0503892	+	0.241429i
$961$	−7.50455			−0.242082
$962$		0			0
$963$			21.1652i			0.682037i
$964$		−	3.10260i		−	0.0999281i
$965$	32.5390	−	6.79129i	1.04747	−	0.218619i
$966$	3.62614			0.116669
$967$	−37.3821			−1.20213			−0.601064	−	0.799201i	$-0.705256\pi$
$967$	−37.3821			−1.20213			−0.601064	+	0.799201i	$0.705256\pi$
$968$	6.92820			0.222681
$969$		−	7.93725i		−	0.254981i
$970$	11.4014	−	2.37960i	0.366075	−	0.0764044i
$971$	−18.4955			−0.593547			−0.296774	−	0.954948i	$-0.595911\pi$
$971$	−18.4955			−0.593547			−0.296774	+	0.954948i	$0.595911\pi$
$972$		−	28.6606i		−	0.919289i
$973$	37.6682			1.20759
$974$	4.87841			0.156314
$975$		0			0
$976$	−3.95644			−0.126643
$977$	35.3085			1.12962			0.564809	−	0.825222i	$-0.308950\pi$
$977$	35.3085			1.12962			0.564809	+	0.825222i	$0.308950\pi$
$978$			9.62614i			0.307810i
$979$	25.3303			0.809560
$980$	−15.6838	+	3.27340i	−0.501001	+	0.104565i
$981$			26.2668i			0.838635i
$982$	−8.87086			−0.283080
$983$	55.0840			1.75691			0.878454	−	0.477827i	$-0.158576\pi$
$983$	55.0840			1.75691			0.878454	+	0.477827i	$0.158576\pi$
$984$	−4.58258			−0.146087
$985$	−32.1216	+	6.70417i	−1.02348	+	0.213613i
$986$			9.59386i			0.305531i
$987$			3.16515i			0.100748i
$988$		0			0
$989$	−48.4955			−1.54207
$990$	−1.10440	−	5.29150i	−0.0351002	−	0.168175i
$991$	−13.0000			−0.412959			−0.206479	−	0.978451i	$-0.566201\pi$
$991$	−13.0000			−0.412959			−0.206479	+	0.978451i	$0.566201\pi$
$992$			29.4083i			0.933715i
$993$	−4.47315			−0.141951
$994$			5.55765i			0.176278i
$995$	23.1642	−	4.83465i	0.734355	−	0.153269i
$996$			10.7737i			0.341378i
$997$		−	0.165151i		−	0.00523040i	−0.999997	−	0.00261520i	$-0.999168\pi$
$997$		−	0.165151i		−	0.00523040i	0.999997	−	0.00261520i	$-0.000832444\pi$
$998$			0.330303i			0.0104556i
$999$		−	39.6863i		−	1.25562i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.d.c.844.4		8
5.4	even	2	inner	845.2.d.c.844.5		8
13.2	odd	12		845.2.n.d.529.1		8
13.3	even	3		845.2.l.c.654.3		8
13.4	even	6		845.2.l.c.699.2		8
13.5	odd	4		845.2.b.f.339.6		8
13.6	odd	12		845.2.n.c.484.4		8
13.7	odd	12		845.2.n.d.484.2		8
13.8	odd	4		845.2.b.f.339.4		8
13.9	even	3		65.2.l.a.49.3	yes	8
13.10	even	6		65.2.l.a.4.2	✓	8
13.11	odd	12		845.2.n.c.529.3		8
13.12	even	2	inner	845.2.d.c.844.6		8
39.23	odd	6		585.2.bf.a.199.3		8
39.35	odd	6		585.2.bf.a.244.2		8
52.23	odd	6		1040.2.df.b.849.4		8
52.35	odd	6		1040.2.df.b.49.1		8
65.4	even	6		845.2.l.c.699.3		8
65.8	even	4		4225.2.a.bj.1.2		4
65.9	even	6		65.2.l.a.49.2	yes	8
65.18	even	4		4225.2.a.bj.1.3		4
65.19	odd	12		845.2.n.d.484.1		8
65.22	odd	12		325.2.n.c.101.1		4
65.23	odd	12		325.2.n.b.251.2		4
65.24	odd	12		845.2.n.d.529.2		8
65.29	even	6		845.2.l.c.654.2		8
65.34	odd	4		845.2.b.f.339.5		8
65.44	odd	4		845.2.b.f.339.3		8
65.47	even	4		4225.2.a.bk.1.3		4
65.48	odd	12		325.2.n.b.101.2		4
65.49	even	6		65.2.l.a.4.3	yes	8
65.54	odd	12		845.2.n.c.529.4		8
65.57	even	4		4225.2.a.bk.1.2		4
65.59	odd	12		845.2.n.c.484.3		8
65.62	odd	12		325.2.n.c.251.1		4
65.64	even	2	inner	845.2.d.c.844.3		8
195.74	odd	6		585.2.bf.a.244.3		8
195.179	odd	6		585.2.bf.a.199.2		8
260.139	odd	6		1040.2.df.b.49.4		8
260.179	odd	6		1040.2.df.b.849.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.l.a.4.2	✓	8	13.10	even	6
65.2.l.a.4.3	yes	8	65.49	even	6
65.2.l.a.49.2	yes	8	65.9	even	6
65.2.l.a.49.3	yes	8	13.9	even	3
325.2.n.b.101.2		4	65.48	odd	12
325.2.n.b.251.2		4	65.23	odd	12
325.2.n.c.101.1		4	65.22	odd	12
325.2.n.c.251.1		4	65.62	odd	12
585.2.bf.a.199.2		8	195.179	odd	6
585.2.bf.a.199.3		8	39.23	odd	6
585.2.bf.a.244.2		8	39.35	odd	6
585.2.bf.a.244.3		8	195.74	odd	6
845.2.b.f.339.3		8	65.44	odd	4
845.2.b.f.339.4		8	13.8	odd	4
845.2.b.f.339.5		8	65.34	odd	4
845.2.b.f.339.6		8	13.5	odd	4
845.2.d.c.844.3		8	65.64	even	2	inner
845.2.d.c.844.4		8	1.1	even	1	trivial
845.2.d.c.844.5		8	5.4	even	2	inner
845.2.d.c.844.6		8	13.12	even	2	inner
845.2.l.c.654.2		8	65.29	even	6
845.2.l.c.654.3		8	13.3	even	3
845.2.l.c.699.2		8	13.4	even	6
845.2.l.c.699.3		8	65.4	even	6
845.2.n.c.484.3		8	65.59	odd	12
845.2.n.c.484.4		8	13.6	odd	12
845.2.n.c.529.3		8	13.11	odd	12
845.2.n.c.529.4		8	65.54	odd	12
845.2.n.d.484.1		8	65.19	odd	12
845.2.n.d.484.2		8	13.7	odd	12
845.2.n.d.529.1		8	13.2	odd	12
845.2.n.d.529.2		8	65.24	odd	12
1040.2.df.b.49.1		8	52.35	odd	6
1040.2.df.b.49.4		8	260.139	odd	6
1040.2.df.b.849.1		8	260.179	odd	6
1040.2.df.b.849.4		8	52.23	odd	6
4225.2.a.bj.1.2		4	65.8	even	4
4225.2.a.bj.1.3		4	65.18	even	4
4225.2.a.bk.1.2		4	65.57	even	4
4225.2.a.bk.1.3		4	65.47	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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-0.456850 q^{2} +1.00000i q^{3} -1.79129 q^{4} +(-2.18890 + 0.456850i) q^{5} -0.456850i q^{6} +1.73205 q^{7} +1.73205 q^{8} +2.00000 q^{9} +(1.00000 - 0.208712i) q^{10} -2.64575i q^{11} -1.79129i q^{12} -0.791288 q^{14} +(-0.456850 - 2.18890i) q^{15} +2.79129 q^{16} +4.58258i q^{17} -0.913701 q^{18} +1.73205i q^{19} +(3.92095 - 0.818350i) q^{20} +1.73205i q^{21} +1.20871i q^{22} +4.58258i q^{23} +1.73205i q^{24} +(4.58258 - 2.00000i) q^{25} +5.00000i q^{27} -3.10260 q^{28} -4.58258 q^{29} +(0.208712 + 1.00000i) q^{30} -6.20520i q^{31} -4.73930 q^{32} +2.64575 q^{33} -2.09355i q^{34} +(-3.79129 + 0.791288i) q^{35} -3.58258 q^{36} -7.93725 q^{37} -0.791288i q^{38} +(-3.79129 + 0.791288i) q^{40} +2.64575i q^{41} -0.791288i q^{42} +10.5826i q^{43} +4.73930i q^{44} +(-4.37780 + 0.913701i) q^{45} -2.09355i q^{46} +1.82740 q^{47} +2.79129i q^{48} -4.00000 q^{49} +(-2.09355 + 0.913701i) q^{50} -4.58258 q^{51} +7.58258i q^{53} -2.28425i q^{54} +(1.20871 + 5.79129i) q^{55} +3.00000 q^{56} -1.73205 q^{57} +2.09355 q^{58} +13.9518i q^{59} +(0.818350 + 3.92095i) q^{60} -1.41742 q^{61} +2.83485i q^{62} +3.46410 q^{63} -3.41742 q^{64} -1.20871 q^{66} +1.00905 q^{67} -8.20871i q^{68} -4.58258 q^{69} +(1.73205 - 0.361500i) q^{70} -7.02355i q^{71} +3.46410 q^{72} +3.62614 q^{74} +(2.00000 + 4.58258i) q^{75} -3.10260i q^{76} -4.58258i q^{77} +6.00000 q^{79} +(-6.10985 + 1.27520i) q^{80} +1.00000 q^{81} -1.20871i q^{82} -6.01450 q^{83} -3.10260i q^{84} +(-2.09355 - 10.0308i) q^{85} -4.83465i q^{86} -4.58258i q^{87} -4.58258i q^{88} +9.57395i q^{89} +(2.00000 - 0.417424i) q^{90} -8.20871i q^{92} +6.20520 q^{93} -0.834849 q^{94} +(-0.791288 - 3.79129i) q^{95} -4.73930i q^{96} +11.4014 q^{97} +1.82740 q^{98} -5.29150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 16 q^{9} + 8 q^{10} + 12 q^{14} + 4 q^{16} + 20 q^{30} - 12 q^{35} + 8 q^{36} - 12 q^{40} - 32 q^{49} + 28 q^{55} + 24 q^{56} - 48 q^{61} - 64 q^{64} - 28 q^{66} + 84 q^{74} + 16 q^{75}+ \cdots + 12 q^{95}+O(q^{100}) \) 8 * q + 4 * q^4 + 16 * q^9 + 8 * q^10 + 12 * q^14 + 4 * q^16 + 20 * q^30 - 12 * q^35 + 8 * q^36 - 12 * q^40 - 32 * q^49 + 28 * q^55 + 24 * q^56 - 48 * q^61 - 64 * q^64 - 28 * q^66 + 84 * q^74 + 16 * q^75 + 48 * q^79 + 8 * q^81 + 16 * q^90 - 80 * q^94 + 12 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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