LMFDB - Embedded newform 1805.2.b.m.1084.9

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:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1084.9
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.m.1084.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.74138i q^{2} -0.766290i q^{3} -1.03240 q^{4} +(2.19703 - 0.415991i) q^{5} -1.33440 q^{6} +2.32579i q^{7} -1.68496i q^{8} +2.41280 q^{9} +O(q^{10})$	\(q-1.74138i q^{2} -0.766290i q^{3} -1.03240 q^{4} +(2.19703 - 0.415991i) q^{5} -1.33440 q^{6} +2.32579i q^{7} -1.68496i q^{8} +2.41280 q^{9} +(-0.724398 - 3.82586i) q^{10} -4.04273 q^{11} +0.791116i q^{12} -3.88017i q^{13} +4.05007 q^{14} +(-0.318770 - 1.68356i) q^{15} -4.99895 q^{16} +4.16444i q^{17} -4.20160i q^{18} +(-2.26821 + 0.429468i) q^{20} +1.78223 q^{21} +7.03992i q^{22} -7.90748i q^{23} -1.29117 q^{24} +(4.65390 - 1.82789i) q^{25} -6.75684 q^{26} -4.14777i q^{27} -2.40113i q^{28} -7.12927 q^{29} +(-2.93172 + 0.555099i) q^{30} +2.72162 q^{31} +5.33514i q^{32} +3.09790i q^{33} +7.25187 q^{34} +(0.967506 + 5.10983i) q^{35} -2.49097 q^{36} -3.70141i q^{37} -2.97334 q^{39} +(-0.700929 - 3.70192i) q^{40} +3.50888 q^{41} -3.10353i q^{42} -9.37966i q^{43} +4.17370 q^{44} +(5.30100 - 1.00370i) q^{45} -13.7699 q^{46} -0.333679i q^{47} +3.83065i q^{48} +1.59072 q^{49} +(-3.18305 - 8.10420i) q^{50} +3.19117 q^{51} +4.00588i q^{52} -6.90990i q^{53} -7.22284 q^{54} +(-8.88201 + 1.68174i) q^{55} +3.91886 q^{56} +12.4148i q^{58} +7.15190 q^{59} +(0.329097 + 1.73811i) q^{60} -1.35027 q^{61} -4.73938i q^{62} +5.61165i q^{63} -0.707410 q^{64} +(-1.61412 - 8.52486i) q^{65} +5.39462 q^{66} -7.79425i q^{67} -4.29936i q^{68} -6.05942 q^{69} +(8.89814 - 1.68479i) q^{70} +0.0586372 q^{71} -4.06548i q^{72} -9.15027i q^{73} -6.44556 q^{74} +(-1.40070 - 3.56624i) q^{75} -9.40252i q^{77} +5.17770i q^{78} -11.6317 q^{79} +(-10.9829 + 2.07952i) q^{80} +4.06000 q^{81} -6.11029i q^{82} +11.5689i q^{83} -1.83997 q^{84} +(1.73237 + 9.14942i) q^{85} -16.3335 q^{86} +5.46309i q^{87} +6.81185i q^{88} +17.4767 q^{89} +(-1.74783 - 9.23104i) q^{90} +9.02444 q^{91} +8.16366i q^{92} -2.08555i q^{93} -0.581061 q^{94} +4.08826 q^{96} -3.84357i q^{97} -2.77005i q^{98} -9.75430 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 48 q^{4} + 6 q^{5} + 20 q^{6} - 52 q^{9}+O(q^{10}) $ 40 * q - 48 * q^4 + 6 * q^5 + 20 * q^6 - 52 * q^9	$ 40 q - 48 q^{4} + 6 q^{5} + 20 q^{6} - 52 q^{9} + 20 q^{11} + 40 q^{16} - 18 q^{20} - 92 q^{24} - 26 q^{25} + 76 q^{26} + 40 q^{30} + 4 q^{35} + 156 q^{36} - 80 q^{39} - 48 q^{44} - 22 q^{45} - 72 q^{49} - 32 q^{54} - 40 q^{55} + 80 q^{61} - 72 q^{64} + 16 q^{66} - 100 q^{74} - 66 q^{80} + 40 q^{81} + 44 q^{85} + 380 q^{96} - 128 q^{99}+O(q^{100}) $ 40 * q - 48 * q^4 + 6 * q^5 + 20 * q^6 - 52 * q^9 + 20 * q^11 + 40 * q^16 - 18 * q^20 - 92 * q^24 - 26 * q^25 + 76 * q^26 + 40 * q^30 + 4 * q^35 + 156 * q^36 - 80 * q^39 - 48 * q^44 - 22 * q^45 - 72 * q^49 - 32 * q^54 - 40 * q^55 + 80 * q^61 - 72 * q^64 + 16 * q^66 - 100 * q^74 - 66 * q^80 + 40 * q^81 + 44 * q^85 + 380 * q^96 - 128 * q^99

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 $

$2$		−	1.74138i		−	1.23134i	−0.788004	−	0.615670i	$-0.788885\pi$
$2$		−	1.74138i		−	1.23134i	0.788004	−	0.615670i	$-0.211115\pi$
$3$		−	0.766290i		−	0.442418i	−0.975226	−	0.221209i	$-0.929000\pi$
$3$		−	0.766290i		−	0.442418i	0.975226	−	0.221209i	$-0.0710003\pi$
$4$	−1.03240			−0.516199
$5$	2.19703	−	0.415991i	0.982543	−	0.186037i
$5$	2.19703	−	0.415991i	0.982543	−	0.186037i
$6$	−1.33440			−0.544767
$7$			2.32579i			0.879064i	0.898227	+	0.439532i	$0.144856\pi$
$7$			2.32579i			0.879064i	−0.898227	+	0.439532i	$0.855144\pi$
$8$		−	1.68496i		−	0.595724i
$9$	2.41280			0.804266
$10$	−0.724398	−	3.82586i	−0.229075	−	1.20984i
$11$	−4.04273			−1.21893			−0.609464	−	0.792813i	$-0.708615\pi$
$11$	−4.04273			−1.21893			−0.609464	+	0.792813i	$0.708615\pi$
$12$			0.791116i			0.228375i
$13$		−	3.88017i		−	1.07617i	−0.842892	−	0.538083i	$-0.819149\pi$
$13$		−	3.88017i		−	1.07617i	0.842892	−	0.538083i	$-0.180851\pi$
$14$	4.05007			1.08243
$15$	−0.318770	−	1.68356i	−0.0823060	−	0.434694i
$16$	−4.99895			−1.24974
$17$			4.16444i			1.01003i	0.863112	+	0.505013i	$0.168512\pi$
$17$			4.16444i			1.01003i	−0.863112	+	0.505013i	$0.831488\pi$
$18$		−	4.20160i		−	0.990326i
$19$		0			0
$19$		0			0
$20$	−2.26821	+	0.429468i	−0.507187	+	0.0960320i
$21$	1.78223			0.388914
$22$			7.03992i			1.50092i
$23$		−	7.90748i		−	1.64882i	−0.565991	−	0.824412i	$-0.691506\pi$
$23$		−	7.90748i		−	1.64882i	0.565991	−	0.824412i	$-0.308494\pi$
$24$	−1.29117			−0.263559
$25$	4.65390	−	1.82789i	0.930781	−	0.365578i
$26$	−6.75684			−1.32513
$27$		−	4.14777i		−	0.798240i
$28$		−	2.40113i		−	0.453772i
$29$	−7.12927			−1.32387			−0.661936	−	0.749560i	$-0.730265\pi$
$29$	−7.12927			−1.32387			−0.661936	+	0.749560i	$0.730265\pi$
$30$	−2.93172	+	0.555099i	−0.535257	+	0.101347i
$31$	2.72162			0.488818			0.244409	−	0.969672i	$-0.421406\pi$
$31$	2.72162			0.488818			0.244409	+	0.969672i	$0.421406\pi$
$32$			5.33514i			0.943128i
$33$			3.09790i			0.539276i
$34$	7.25187			1.24369
$35$	0.967506	+	5.10983i	0.163538	+	0.863718i
$36$	−2.49097			−0.415161
$37$		−	3.70141i		−	0.608509i	−0.952591	−	0.304254i	$-0.901593\pi$
$37$		−	3.70141i		−	0.608509i	0.952591	−	0.304254i	$-0.0984073\pi$
$38$		0			0
$39$	−2.97334			−0.476115
$40$	−0.700929	−	3.70192i	−0.110827	−	0.585324i
$41$	3.50888			0.547995			0.273998	−	0.961730i	$-0.411654\pi$
$41$	3.50888			0.547995			0.273998	+	0.961730i	$0.411654\pi$
$42$		−	3.10353i		−	0.478885i
$43$		−	9.37966i		−	1.43038i	−0.698928	−	0.715192i	$-0.746339\pi$
$43$		−	9.37966i		−	1.43038i	0.698928	−	0.715192i	$-0.253661\pi$
$44$	4.17370			0.629209
$45$	5.30100	−	1.00370i	0.790226	−	0.149623i
$46$	−13.7699			−2.03026
$47$		−	0.333679i		−	0.0486721i	−0.999704	−	0.0243360i	$-0.992253\pi$
$47$		−	0.333679i		−	0.0486721i	0.999704	−	0.0243360i	$-0.00774717\pi$
$48$			3.83065i			0.552906i
$49$	1.59072			0.227246
$50$	−3.18305	−	8.10420i	−0.450151	−	1.14611i
$51$	3.19117			0.446853
$52$			4.00588i			0.555515i
$53$		−	6.90990i		−	0.949147i	−0.880216	−	0.474574i	$-0.842602\pi$
$53$		−	6.90990i		−	0.949147i	0.880216	−	0.474574i	$-0.157398\pi$
$54$	−7.22284			−0.982905
$55$	−8.88201	+	1.68174i	−1.19765	+	0.226766i
$56$	3.91886			0.523680
$57$		0			0
$58$			12.4148i			1.63014i
$59$	7.15190			0.931098			0.465549	−	0.885022i	$-0.345857\pi$
$59$	7.15190			0.931098			0.465549	+	0.885022i	$0.345857\pi$
$60$	0.329097	+	1.73811i	0.0424863	+	0.224389i
$61$	−1.35027			−0.172885			−0.0864424	−	0.996257i	$-0.527550\pi$
$61$	−1.35027			−0.172885			−0.0864424	+	0.996257i	$0.527550\pi$
$62$		−	4.73938i		−	0.601901i
$63$			5.61165i			0.707002i
$64$	−0.707410			−0.0884263
$65$	−1.61412	−	8.52486i	−0.200206	−	1.05738i
$66$	5.39462			0.664032
$67$		−	7.79425i		−	0.952220i	−0.879386	−	0.476110i	$-0.842046\pi$
$67$		−	7.79425i		−	0.952220i	0.879386	−	0.476110i	$-0.157954\pi$
$68$		−	4.29936i		−	0.521374i
$69$	−6.05942			−0.729469
$70$	8.89814	−	1.68479i	1.06353	−	0.201371i
$71$	0.0586372			0.00695895			0.00347947	−	0.999994i	$-0.498892\pi$
$71$	0.0586372			0.00695895			0.00347947	+	0.999994i	$0.498892\pi$
$72$		−	4.06548i		−	0.479121i
$73$		−	9.15027i		−	1.07096i	−0.844548	−	0.535479i	$-0.820131\pi$
$73$		−	9.15027i		−	1.07096i	0.844548	−	0.535479i	$-0.179869\pi$
$74$	−6.44556			−0.749281
$75$	−1.40070	−	3.56624i	−0.161738	−	0.411794i
$76$		0			0
$77$		−	9.40252i		−	1.07152i
$78$			5.17770i			0.586259i
$79$	−11.6317			−1.30867			−0.654337	−	0.756203i	$-0.727052\pi$
$79$	−11.6317			−1.30867			−0.654337	+	0.756203i	$0.727052\pi$
$80$	−10.9829	+	2.07952i	−1.22792	+	0.232497i
$81$	4.06000			0.451111
$82$		−	6.11029i		−	0.674768i
$83$			11.5689i			1.26985i	0.772573	+	0.634927i	$0.218970\pi$
$83$			11.5689i			1.26985i	−0.772573	+	0.634927i	$0.781030\pi$
$84$	−1.83997			−0.200757
$85$	1.73237	+	9.14942i	0.187902	+	0.992393i
$86$	−16.3335			−1.76129
$87$			5.46309i			0.585705i
$88$			6.81185i			0.726145i
$89$	17.4767			1.85253			0.926264	−	0.376874i	$-0.123001\pi$
$89$	17.4767			1.85253			0.926264	+	0.376874i	$0.123001\pi$
$90$	−1.74783	−	9.23104i	−0.184237	−	0.973037i
$91$	9.02444			0.946019
$92$			8.16366i			0.851120i
$93$		−	2.08555i		−	0.216262i
$94$	−0.581061			−0.0599319
$95$		0			0
$96$	4.08826			0.417257
$97$		−	3.84357i		−	0.390256i	−0.980778	−	0.195128i	$-0.937488\pi$
$97$		−	3.84357i		−	0.390256i	0.980778	−	0.195128i	$-0.0625122\pi$
$98$		−	2.77005i		−	0.279817i
$99$	−9.75430			−0.980344
$100$	−4.80468	+	1.88711i	−0.480468	+	0.188711i
$101$	9.32583			0.927955			0.463977	−	0.885847i	$-0.346422\pi$
$101$	9.32583			0.927955			0.463977	+	0.885847i	$0.346422\pi$
$102$		−	5.55704i		−	0.550228i
$103$			2.54848i			0.251109i	0.992087	+	0.125555i	$0.0400710\pi$
$103$			2.54848i			0.251109i	−0.992087	+	0.125555i	$0.959929\pi$
$104$	−6.53794			−0.641098
$105$	3.91561	−	0.741390i	0.382124	−	0.0723523i
$106$	−12.0327			−1.16872
$107$			4.38721i			0.424128i	0.977256	+	0.212064i	$0.0680185\pi$
$107$			4.38721i			0.424128i	−0.977256	+	0.212064i	$0.931982\pi$
$108$			4.28215i			0.412050i
$109$	4.92361			0.471596			0.235798	−	0.971802i	$-0.424230\pi$
$109$	4.92361			0.471596			0.235798	+	0.971802i	$0.424230\pi$
$110$	2.92854	+	15.4669i	0.279226	+	1.47471i
$111$	−2.83636			−0.269215
$112$		−	11.6265i		−	1.09860i
$113$			17.6256i			1.65808i	0.559189	+	0.829040i	$0.311113\pi$
$113$			17.6256i			1.65808i	−0.559189	+	0.829040i	$0.688887\pi$
$114$		0			0
$115$	−3.28944	−	17.3730i	−0.306742	−	1.62004i
$116$	7.36024			0.683381
$117$		−	9.36207i		−	0.865524i
$118$		−	12.4542i		−	1.14650i
$119$	−9.68560			−0.887877
$120$	−2.83674	+	0.537115i	−0.258958	+	0.0490317i
$121$	5.34366			0.485788
$122$			2.35134i			0.212880i
$123$		−	2.68882i		−	0.242443i
$124$	−2.80980			−0.252327
$125$	9.46439	−	5.95192i	0.846521	−	0.532356i
$126$	9.77201			0.870560
$127$			0.634620i			0.0563134i	0.999604	+	0.0281567i	$0.00896374\pi$
$127$			0.634620i			0.0563134i	−0.999604	+	0.0281567i	$0.991036\pi$
$128$			11.9021i			1.05201i
$129$	−7.18754			−0.632828
$130$	−14.8450	+	2.81079i	−1.30199	+	0.246522i
$131$	2.08649			0.182297			0.0911487	−	0.995837i	$-0.470946\pi$
$131$	2.08649			0.182297			0.0911487	+	0.995837i	$0.470946\pi$
$132$		−	3.19827i		−	0.278373i
$133$		0			0
$134$	−13.5727			−1.17251
$135$	−1.72544	−	9.11280i	−0.148502	−	0.784305i
$136$	7.01693			0.601697
$137$			21.6457i			1.84931i	0.380802	+	0.924657i	$0.375648\pi$
$137$			21.6457i			1.84931i	−0.380802	+	0.924657i	$0.624352\pi$
$138$			10.5517i			0.898224i
$139$	4.11480			0.349013			0.174506	−	0.984656i	$-0.444167\pi$
$139$	4.11480			0.349013			0.174506	+	0.984656i	$0.444167\pi$
$140$	−0.998851	−	5.27537i	−0.0844183	−	0.445850i
$141$	−0.255695			−0.0215334
$142$		−	0.102109i		−	0.00856883i
$143$			15.6865i			1.31177i
$144$	−12.0615			−1.00512
$145$	−15.6632	+	2.96571i	−1.30076	+	0.246289i
$146$	−15.9341			−1.31871
$147$		−	1.21895i		−	0.100538i
$148$			3.82133i			0.314111i
$149$	3.80062			0.311359			0.155679	−	0.987808i	$-0.450243\pi$
$149$	3.80062			0.311359			0.155679	+	0.987808i	$0.450243\pi$
$150$	−6.21017	+	2.43914i	−0.507058	+	0.199155i
$151$	−22.5773			−1.83731			−0.918656	−	0.395058i	$-0.870725\pi$
$151$	−22.5773			−1.83731			−0.918656	+	0.395058i	$0.870725\pi$
$152$		0			0
$153$			10.0480i			0.812330i
$154$	−16.3733			−1.31940
$155$	5.97950	−	1.13217i	0.480285	−	0.0909382i
$156$	3.06966			0.245770
$157$			20.7361i			1.65492i	0.561523	+	0.827461i	$0.310216\pi$
$157$			20.7361i			1.65492i	−0.561523	+	0.827461i	$0.689784\pi$
$158$			20.2553i			1.61142i
$159$	−5.29499			−0.419920
$160$	2.21937	+	11.7215i	0.175457	+	0.926664i
$161$	18.3911			1.44942
$162$		−	7.06999i		−	0.555471i
$163$			6.63865i			0.519979i	0.965611	+	0.259990i	$0.0837191\pi$
$163$			6.63865i			0.519979i	−0.965611	+	0.259990i	$0.916281\pi$
$164$	−3.62256			−0.282874
$165$	1.28870	+	6.80620i	0.100325	+	0.529862i
$166$	20.1458			1.56362
$167$			16.1480i			1.24957i	0.780798	+	0.624784i	$0.214813\pi$
$167$			16.1480i			1.24957i	−0.780798	+	0.624784i	$0.785187\pi$
$168$		−	3.00298i		−	0.231685i
$169$	−2.05571			−0.158132
$170$	15.9326	−	3.01671i	1.22197	−	0.231371i
$171$		0			0
$172$			9.68353i			0.738362i
$173$			26.1105i			1.98514i	0.121666	+	0.992571i	$0.461176\pi$
$173$			26.1105i			1.98514i	−0.121666	+	0.992571i	$0.538824\pi$
$174$	9.51330			0.721202
$175$	4.25128	+	10.8240i	0.321367	+	0.818216i
$176$	20.2094			1.52334
$177$		−	5.48043i		−	0.411934i
$178$		−	30.4336i		−	2.28109i
$179$	−12.4803			−0.932824			−0.466412	−	0.884568i	$-0.654453\pi$
$179$	−12.4803			−0.932824			−0.466412	+	0.884568i	$0.654453\pi$
$180$	−5.47274	+	1.03622i	−0.407914	+	0.0772353i
$181$	2.22650			0.165495			0.0827473	−	0.996571i	$-0.473631\pi$
$181$	2.22650			0.165495			0.0827473	+	0.996571i	$0.473631\pi$
$182$		−	15.7150i		−	1.16487i
$183$			1.03470i			0.0764873i
$184$	−13.3238			−0.982244
$185$	−1.53976	−	8.13213i	−0.113205	−	0.597886i
$186$	−3.63174			−0.266292
$187$		−	16.8357i		−	1.23115i
$188$			0.344489i			0.0251245i
$189$	9.64683			0.701704
$190$		0			0
$191$	11.0417			0.798946			0.399473	−	0.916745i	$-0.369193\pi$
$191$	11.0417			0.798946			0.399473	+	0.916745i	$0.369193\pi$
$192$			0.542082i			0.0391214i
$193$		−	5.53517i		−	0.398430i	−0.979956	−	0.199215i	$-0.936161\pi$
$193$		−	5.53517i		−	0.398430i	0.979956	−	0.199215i	$-0.0638392\pi$
$194$	−6.69312			−0.480538
$195$	−6.53251	+	1.23688i	−0.467803	+	0.0885749i
$196$	−1.64226			−0.117304
$197$			13.5611i			0.966188i	0.875569	+	0.483094i	$0.160487\pi$
$197$			13.5611i			0.966188i	−0.875569	+	0.483094i	$0.839513\pi$
$198$			16.9859i			1.20714i
$199$	−12.0521			−0.854348			−0.427174	−	0.904169i	$-0.640491\pi$
$199$	−12.0521			−0.854348			−0.427174	+	0.904169i	$0.640491\pi$
$200$	−3.07993	−	7.84165i	−0.217784	−	0.554488i
$201$	−5.97266			−0.421279
$202$		−	16.2398i		−	1.14263i
$203$		−	16.5811i		−	1.16377i
$204$	−3.29456			−0.230665
$205$	7.70912	−	1.45966i	0.538429	−	0.101947i
$206$	4.43787			0.309201
$207$		−	19.0792i		−	1.32609i
$208$			19.3968i			1.34492i
$209$		0			0
$210$	−1.29104	−	6.81856i	−0.0890903	−	0.470525i
$211$	19.5049			1.34277			0.671386	−	0.741108i	$-0.265699\pi$
$211$	19.5049			1.34277			0.671386	+	0.741108i	$0.265699\pi$
$212$			7.13376i			0.489948i
$213$		−	0.0449331i		−	0.00307876i
$214$	7.63979			0.522245
$215$	−3.90185	−	20.6074i	−0.266104	−	1.40541i
$216$	−6.98884			−0.475531
$217$			6.32991i			0.429703i
$218$		−	8.57386i		−	0.580695i
$219$	−7.01176			−0.473811
$220$	9.16976	−	1.73622i	0.618225	−	0.117056i
$221$	16.1587			1.08695
$222$			4.93917i			0.331495i
$223$			0.0751415i			0.00503184i	0.999997	+	0.00251592i	$0.000800844\pi$
$223$			0.0751415i			0.00503184i	−0.999997	+	0.00251592i	$0.999199\pi$
$224$	−12.4084			−0.829070
$225$	11.2289	−	4.41034i	0.748596	−	0.294022i
$226$	30.6929			2.04166
$227$			22.4805i			1.49208i	0.665900	+	0.746041i	$0.268048\pi$
$227$			22.4805i			1.49208i	−0.665900	+	0.746041i	$0.731952\pi$
$228$		0			0
$229$	4.66105			0.308011			0.154006	−	0.988070i	$-0.450783\pi$
$229$	4.66105			0.308011			0.154006	+	0.988070i	$0.450783\pi$
$230$	−30.2529	+	5.72816i	−1.99482	+	0.377704i
$231$	−7.20506			−0.474058
$232$			12.0125i			0.788663i
$233$		−	3.67529i		−	0.240776i	−0.992727	−	0.120388i	$-0.961586\pi$
$233$		−	3.67529i		−	0.240776i	0.992727	−	0.120388i	$-0.0384139\pi$
$234$	−16.3029			−1.06575
$235$	−0.138808	−	0.733104i	−0.00905480	−	0.0478224i
$236$	−7.38360			−0.480631
$237$			8.91329i			0.578981i
$238$			16.8663i			1.09328i
$239$	8.22852			0.532259			0.266129	−	0.963937i	$-0.414255\pi$
$239$	8.22852			0.532259			0.266129	+	0.963937i	$0.414255\pi$
$240$	1.59351	+	8.41605i	0.102861	+	0.543254i
$241$	−2.83862			−0.182852			−0.0914259	−	0.995812i	$-0.529142\pi$
$241$	−2.83862			−0.182852			−0.0914259	+	0.995812i	$0.529142\pi$
$242$		−	9.30534i		−	0.598170i
$243$		−	15.5545i		−	0.997819i
$244$	1.39402			0.0892429
$245$	3.49487	−	0.661726i	0.223279	−	0.0422761i
$246$	−4.68225			−0.298530
$247$		0			0
$248$		−	4.58583i		−	0.291201i
$249$	8.86514			0.561806
$250$	−10.3645	−	16.4811i	−0.655511	−	1.04235i
$251$	27.4254			1.73108			0.865539	−	0.500842i	$-0.166976\pi$
$251$	27.4254			1.73108			0.865539	+	0.500842i	$0.166976\pi$
$252$		−	5.79346i		−	0.364953i
$253$			31.9678i			2.00980i
$254$	1.10511			0.0693410
$255$	7.01111	−	1.32750i	0.439053	−	0.0831312i
$256$	19.3113			1.20696
$257$			11.1290i			0.694210i	0.937826	+	0.347105i	$0.112835\pi$
$257$			11.1290i			0.694210i	−0.937826	+	0.347105i	$0.887165\pi$
$258$			12.5162i			0.779226i
$259$	8.60869			0.534918
$260$	1.66641	+	8.80104i	0.103346	+	0.545817i
$261$	−17.2015			−1.06475
$262$		−	3.63337i		−	0.224470i
$263$		−	20.3716i		−	1.25617i	−0.778146	−	0.628084i	$-0.783839\pi$
$263$		−	20.3716i		−	1.25617i	0.778146	−	0.628084i	$-0.216161\pi$
$264$	5.21985			0.321260
$265$	−2.87446	−	15.1813i	−0.176576	−	0.932578i
$266$		0			0
$267$		−	13.3922i		−	0.819592i
$268$			8.04677i			0.491534i
$269$	4.31804			0.263275			0.131638	−	0.991298i	$-0.457976\pi$
$269$	4.31804			0.263275			0.131638	+	0.991298i	$0.457976\pi$
$270$	−15.8688	+	3.00464i	−0.965746	+	0.182857i
$271$	−28.0845			−1.70601			−0.853007	−	0.521899i	$-0.825224\pi$
$271$	−28.0845			−1.70601			−0.853007	+	0.521899i	$0.825224\pi$
$272$		−	20.8178i		−	1.26227i
$273$		−	6.91534i		−	0.418535i
$274$	37.6933			2.27713
$275$	−18.8145	+	7.38967i	−1.13456	+	0.445614i
$276$	6.25573			0.376551
$277$		−	0.807334i		−	0.0485080i	−0.999706	−	0.0242540i	$-0.992279\pi$
$277$		−	0.807334i		−	0.0485080i	0.999706	−	0.0242540i	$-0.00772104\pi$
$278$		−	7.16542i		−	0.429753i
$279$	6.56673			0.393140
$280$	8.60986	−	1.63021i	0.514538	−	0.0974238i
$281$	−23.8805			−1.42459			−0.712296	−	0.701879i	$-0.752345\pi$
$281$	−23.8805			−1.42459			−0.712296	+	0.701879i	$0.752345\pi$
$282$			0.445262i			0.0265149i
$283$			1.68201i			0.0999850i	0.998750	+	0.0499925i	$0.0159197\pi$
$283$			1.68201i			0.0999850i	−0.998750	+	0.0499925i	$0.984080\pi$
$284$	−0.0605368			−0.00359220
$285$		0			0
$286$	27.3161			1.61523
$287$			8.16090i			0.481723i
$288$			12.8726i			0.758526i
$289$	−0.342582			−0.0201519
$290$	5.16443	+	27.2756i	0.303266	+	1.60168i
$291$	−2.94529			−0.172656
$292$			9.44671i			0.552827i
$293$		−	19.3023i		−	1.12765i	−0.825894	−	0.563825i	$-0.809329\pi$
$293$		−	19.3023i		−	1.12765i	0.825894	−	0.563825i	$-0.190671\pi$
$294$	−2.12266			−0.123796
$295$	15.7129	−	2.97513i	0.914843	−	0.173219i
$296$	−6.23674			−0.362503
$297$			16.7683i			0.972997i
$298$		−	6.61831i		−	0.383388i
$299$	−30.6824			−1.77441
$300$	1.44607	+	3.68178i	0.0834891	+	0.212567i
$301$	21.8151			1.25740
$302$			39.3156i			2.26236i
$303$		−	7.14629i		−	0.410544i
$304$		0			0
$305$	−2.96659	+	0.561702i	−0.169867	+	0.0321630i
$306$	17.4973			1.00025
$307$		−	12.3938i		−	0.707354i	−0.935368	−	0.353677i	$-0.884931\pi$
$307$		−	12.3938i		−	0.707354i	0.935368	−	0.353677i	$-0.115069\pi$
$308$			9.70714i			0.553115i
$309$	1.95288			0.111095
$310$	−1.97154	−	10.4126i	−0.111976	−	0.591394i
$311$	−0.571645			−0.0324150			−0.0162075	−	0.999869i	$-0.505159\pi$
$311$	−0.571645			−0.0324150			−0.0162075	+	0.999869i	$0.505159\pi$
$312$			5.00996i			0.283633i
$313$		−	12.9902i		−	0.734252i	−0.930171	−	0.367126i	$-0.880342\pi$
$313$		−	12.9902i		−	0.734252i	0.930171	−	0.367126i	$-0.119658\pi$
$314$	36.1094			2.03777
$315$	2.33440	+	12.3290i	0.131528	+	0.694660i
$316$	12.0086			0.675536
$317$		−	0.179990i		−	0.0101092i	−0.999987	−	0.00505462i	$-0.998391\pi$
$317$		−	0.179990i		−	0.0101092i	0.999987	−	0.00505462i	$-0.00160894\pi$
$318$			9.22057i			0.517064i
$319$	28.8217			1.61371
$320$	−1.55420	+	0.294276i	−0.0868826	+	0.0164506i
$321$	3.36188			0.187642
$322$		−	32.0259i		−	1.78473i
$323$		0			0
$324$	−4.19153			−0.232863
$325$	−7.09253	−	18.0579i	−0.393423	−	1.00167i
$326$	11.5604			0.640271
$327$		−	3.77291i		−	0.208643i
$328$		−	5.91233i		−	0.326454i
$329$	0.776066			0.0427859
$330$	11.8522	−	2.24411i	0.652440	−	0.123534i
$331$	−20.7379			−1.13986			−0.569928	−	0.821695i	$-0.693029\pi$
$331$	−20.7379			−1.13986			−0.569928	+	0.821695i	$0.693029\pi$
$332$		−	11.9437i		−	0.655496i
$333$		−	8.93077i		−	0.489403i
$334$	28.1197			1.53864
$335$	−3.24234	−	17.1242i	−0.177148	−	0.935597i
$336$	−8.90926			−0.486040
$337$		−	24.5019i		−	1.33470i	−0.744743	−	0.667352i	$-0.767428\pi$
$337$		−	24.5019i		−	1.33470i	0.744743	−	0.667352i	$-0.232572\pi$
$338$			3.57978i			0.194714i
$339$	13.5064			0.733564
$340$	−1.78850	−	9.44583i	−0.0969948	−	0.512272i
$341$	−11.0028			−0.595835
$342$		0			0
$343$			19.9802i			1.07883i
$344$	−15.8044			−0.852115
$345$	−13.3128	+	2.52067i	−0.716734	+	0.135708i
$346$	45.4682			2.44439
$347$		−	8.41377i		−	0.451675i	−0.974165	−	0.225837i	$-0.927488\pi$
$347$		−	8.41377i		−	0.451675i	0.974165	−	0.225837i	$-0.0725118\pi$
$348$		−	5.64008i		−	0.302340i
$349$	27.3303			1.46296			0.731479	−	0.681864i	$-0.238830\pi$
$349$	27.3303			1.46296			0.731479	+	0.681864i	$0.238830\pi$
$350$	18.8486	−	7.40309i	1.00750	−	0.395712i
$351$	−16.0941			−0.859038
$352$		−	21.5685i		−	1.14961i
$353$			9.68021i			0.515226i	0.966248	+	0.257613i	$0.0829359\pi$
$353$			9.68021i			0.515226i	−0.966248	+	0.257613i	$0.917064\pi$
$354$	−9.54350			−0.507231
$355$	0.128828	−	0.0243925i	0.00683747	−	0.00129462i
$356$	−18.0429			−0.956273
$357$			7.42198i			0.392813i
$358$			21.7330i			1.14862i
$359$	−26.8328			−1.41618			−0.708092	−	0.706121i	$-0.750444\pi$
$359$	−26.8328			−1.41618			−0.708092	+	0.706121i	$0.750444\pi$
$360$	−1.69120	−	8.93198i	−0.0891342	−	0.470757i
$361$		0			0
$362$		−	3.87718i		−	0.203780i
$363$		−	4.09480i		−	0.214921i
$364$	−9.31681			−0.488333
$365$	−3.80643	−	20.1034i	−0.199238	−	1.05226i
$366$	1.80181			0.0941819
$367$			20.5444i			1.07241i	0.844089	+	0.536204i	$0.180142\pi$
$367$			20.5444i			1.07241i	−0.844089	+	0.536204i	$0.819858\pi$
$368$			39.5291i			2.06060i
$369$	8.46622			0.440734
$370$	−14.1611	+	2.68130i	−0.736201	+	0.139394i
$371$	16.0709			0.834361
$372$			2.15312i			0.111634i
$373$			0.337866i			0.0174940i	0.999962	+	0.00874702i	$0.00278430\pi$
$373$			0.337866i			0.0174940i	−0.999962	+	0.00874702i	$0.997216\pi$
$374$	−29.3173			−1.51596
$375$	−4.56090	−	7.25247i	−0.235524	−	0.374516i
$376$	−0.562237			−0.0289951
$377$			27.6628i			1.42471i
$378$		−	16.7988i		−	0.864036i
$379$	6.76387			0.347437			0.173718	−	0.984795i	$-0.444422\pi$
$379$	6.76387			0.347437			0.173718	+	0.984795i	$0.444422\pi$
$380$		0			0
$381$	0.486303			0.0249141
$382$		−	19.2277i		−	0.983774i
$383$			19.0257i			0.972166i	0.873913	+	0.486083i	$0.161575\pi$
$383$			19.0257i			0.972166i	−0.873913	+	0.486083i	$0.838425\pi$
$384$	9.12050			0.465428
$385$	−3.91137	−	20.6576i	−0.199342	−	1.05281i
$386$	−9.63882			−0.490603
$387$		−	22.6312i		−	1.15041i
$388$			3.96810i			0.201450i
$389$	9.47260			0.480280			0.240140	−	0.970738i	$-0.422807\pi$
$389$	9.47260			0.480280			0.240140	+	0.970738i	$0.422807\pi$
$390$	2.15388	+	11.3756i	0.109066	+	0.576025i
$391$	32.9302			1.66535
$392$		−	2.68031i		−	0.135376i
$393$		−	1.59886i		−	0.0806517i
$394$	23.6150			1.18971
$395$	−25.5553	+	4.83870i	−1.28583	+	0.243462i
$396$	10.0703			0.506052
$397$			3.16382i			0.158787i	0.996843	+	0.0793937i	$0.0252984\pi$
$397$			3.16382i			0.158787i	−0.996843	+	0.0793937i	$0.974702\pi$
$398$			20.9872i			1.05199i
$399$		0			0
$400$	−23.2646	+	9.13754i	−1.16323	+	0.456877i
$401$	28.1675			1.40662			0.703309	−	0.710884i	$-0.251705\pi$
$401$	28.1675			1.40662			0.703309	+	0.710884i	$0.251705\pi$
$402$			10.4007i			0.518738i
$403$		−	10.5604i		−	0.526049i
$404$	−9.62796			−0.479009
$405$	8.91995	−	1.68892i	0.443236	−	0.0839233i
$406$	−28.8740			−1.43299
$407$			14.9638i			0.741729i
$408$		−	5.37700i		−	0.266201i
$409$	13.7523			0.680006			0.340003	−	0.940424i	$-0.389572\pi$
$409$	13.7523			0.680006			0.340003	+	0.940424i	$0.389572\pi$
$410$	−2.54183	−	13.4245i	−0.125532	−	0.662989i
$411$	16.5869			0.818169
$412$		−	2.63105i		−	0.129622i
$413$			16.6338i			0.818495i
$414$	−33.2240			−1.63287
$415$	4.81256	+	25.4173i	0.236240	+	1.24768i
$416$	20.7012			1.01496
$417$		−	3.15313i		−	0.154409i
$418$		0			0
$419$	0.643795			0.0314514			0.0157257	−	0.999876i	$-0.494994\pi$
$419$	0.643795			0.0314514			0.0157257	+	0.999876i	$0.494994\pi$
$420$	−4.04246	+	0.765409i	−0.197252	+	0.0373482i
$421$	−17.8741			−0.871130			−0.435565	−	0.900157i	$-0.643451\pi$
$421$	−17.8741			−0.871130			−0.435565	+	0.900157i	$0.643451\pi$
$422$		−	33.9654i		−	1.65341i
$423$		−	0.805101i		−	0.0391453i
$424$	−11.6429			−0.565430
$425$	7.61215	+	19.3809i	0.369244	+	0.940112i
$426$	−0.0782455			−0.00379100
$427$		−	3.14045i		−	0.151977i
$428$		−	4.52934i		−	0.218934i
$429$	12.0204			0.580350
$430$	−35.8853	+	6.79460i	−1.73054	+	0.327665i
$431$	0.386981			0.0186402			0.00932011	−	0.999957i	$-0.497033\pi$
$431$	0.386981			0.0186402			0.00932011	+	0.999957i	$0.497033\pi$
$432$			20.7345i			0.997590i
$433$		−	28.7457i		−	1.38143i	−0.723128	−	0.690714i	$-0.757296\pi$
$433$		−	28.7457i		−	1.38143i	0.723128	−	0.690714i	$-0.242704\pi$
$434$	11.0228			0.529110
$435$	2.27260	+	12.0026i	0.108963	+	0.575480i
$436$	−5.08312			−0.243437
$437$		0			0
$438$			12.2101i			0.583423i
$439$	−27.3604			−1.30584			−0.652921	−	0.757426i	$-0.726456\pi$
$439$	−27.3604			−1.30584			−0.652921	+	0.757426i	$0.726456\pi$
$440$	2.83367	+	14.9658i	0.135090	+	0.713469i
$441$	3.83809			0.182766
$442$		−	28.1385i		−	1.33841i
$443$		−	24.5657i		−	1.16715i	−0.812059	−	0.583576i	$-0.801653\pi$
$443$		−	24.5657i		−	1.16715i	0.812059	−	0.583576i	$-0.198347\pi$
$444$	2.92825			0.138968
$445$	38.3969	−	7.27016i	1.82019	−	0.344639i
$446$	0.130850			0.00619591
$447$		−	2.91237i		−	0.137751i
$448$		−	1.64528i		−	0.0777324i
$449$	−21.2925			−1.00486			−0.502428	−	0.864619i	$-0.667560\pi$
$449$	−21.2925			−1.00486			−0.502428	+	0.864619i	$0.667560\pi$
$450$	−7.68006	−	19.5538i	−0.362042	−	0.921776i
$451$	−14.1855			−0.667967
$452$		−	18.1967i		−	0.855899i
$453$			17.3007i			0.812860i
$454$	39.1470			1.83726
$455$	19.8270	−	3.75409i	0.929504	−	0.175994i
$456$		0			0
$457$			2.77590i			0.129851i	0.997890	+	0.0649257i	$0.0206810\pi$
$457$			2.77590i			0.129851i	−0.997890	+	0.0649257i	$0.979319\pi$
$458$		−	8.11665i		−	0.379266i
$459$	17.2732			0.806243
$460$	3.39601	+	17.9358i	0.158340	+	0.836262i
$461$	28.4961			1.32720			0.663599	−	0.748089i	$-0.269028\pi$
$461$	28.4961			1.32720			0.663599	+	0.748089i	$0.269028\pi$
$462$			12.5467i			0.583727i
$463$			5.14894i			0.239291i	0.992817	+	0.119646i	$0.0381759\pi$
$463$			5.14894i			0.239291i	−0.992817	+	0.119646i	$0.961824\pi$
$464$	35.6389			1.65449
$465$	−0.867572	−	4.58203i	−0.0402327	−	0.212487i
$466$	−6.40006			−0.296477
$467$		−	2.47435i		−	0.114499i	−0.998360	−	0.0572496i	$-0.981767\pi$
$467$		−	2.47435i		−	0.114499i	0.998360	−	0.0572496i	$-0.0182331\pi$
$468$			9.66537i			0.446782i
$469$	18.1278			0.837062
$470$	−1.27661	+	0.241716i	−0.0588857	+	0.0111495i
$471$	15.8899			0.732167
$472$		−	12.0507i		−	0.554677i
$473$			37.9194i			1.74354i
$474$	15.5214			0.712922
$475$		0			0
$476$	9.99939			0.458321
$477$		−	16.6722i		−	0.763367i
$478$		−	14.3290i		−	0.655392i
$479$	3.35535			0.153310			0.0766550	−	0.997058i	$-0.475576\pi$
$479$	3.35535			0.153310			0.0766550	+	0.997058i	$0.475576\pi$
$480$	8.98205	−	1.70068i	0.409972	−	0.0776251i
$481$	−14.3621			−0.654856
$482$			4.94312i			0.225153i
$483$		−	14.0929i		−	0.641250i
$484$	−5.51678			−0.250763
$485$	−1.59889	−	8.44446i	−0.0726020	−	0.383443i
$486$	−27.0862			−1.22865
$487$		−	2.94178i		−	0.133305i	−0.997776	−	0.0666524i	$-0.978768\pi$
$487$		−	2.94178i		−	0.133305i	0.997776	−	0.0666524i	$-0.0212319\pi$
$488$			2.27516i			0.102992i
$489$	5.08713			0.230048
$490$	−1.15232	−	6.08589i	−0.0520563	−	0.274932i
$491$	23.1381			1.04421			0.522105	−	0.852881i	$-0.325147\pi$
$491$	23.1381			1.04421			0.522105	+	0.852881i	$0.325147\pi$
$492$			2.77593i			0.125149i
$493$		−	29.6894i		−	1.33714i
$494$		0			0
$495$	−21.4305	+	4.05770i	−0.963230	+	0.182380i
$496$	−13.6053			−0.610894
$497$			0.136377i			0.00611736i
$498$		−	15.4376i		−	0.691774i
$499$	7.90214			0.353748			0.176874	−	0.984233i	$-0.443401\pi$
$499$	7.90214			0.353748			0.176874	+	0.984233i	$0.443401\pi$
$500$	−9.77101	+	6.14475i	−0.436973	+	0.274801i
$501$	12.3740			0.552831
$502$		−	47.7580i		−	2.13155i
$503$			0.354301i			0.0157975i	0.999969	+	0.00789875i	$0.00251427\pi$
$503$			0.354301i			0.0157975i	−0.999969	+	0.00789875i	$0.997486\pi$
$504$	9.45543			0.421178
$505$	20.4892	−	3.87946i	0.911755	−	0.172634i
$506$	55.6680			2.47475
$507$			1.57527i			0.0699604i
$508$		−	0.655180i		−	0.0290689i
$509$	1.56126			0.0692016			0.0346008	−	0.999401i	$-0.488984\pi$
$509$	1.56126			0.0692016			0.0346008	+	0.999401i	$0.488984\pi$
$510$	−2.31168	−	12.2090i	−0.102363	−	0.540623i
$511$	21.2816			0.941441
$512$		−	9.82400i		−	0.434164i
$513$		0			0
$514$	19.3799			0.854809
$515$	1.06015	+	5.59910i	0.0467156	+	0.246726i
$516$	7.42040			0.326665
$517$			1.34897i			0.0593278i
$518$		−	14.9910i		−	0.658666i
$519$	20.0082			0.878262
$520$	−14.3641	+	2.71972i	−0.629906	+	0.119268i
$521$	20.6501			0.904695			0.452348	−	0.891842i	$-0.350587\pi$
$521$	20.6501			0.904695			0.452348	+	0.891842i	$0.350587\pi$
$522$			29.9543i			1.31106i
$523$			3.02628i			0.132330i	0.997809	+	0.0661650i	$0.0210764\pi$
$523$			3.02628i			0.132330i	−0.997809	+	0.0661650i	$0.978924\pi$
$524$	−2.15409			−0.0941017
$525$	8.29431	−	3.25772i	0.361993	−	0.142178i
$526$	−35.4747			−1.54677
$527$			11.3340i			0.493719i
$528$		−	15.4863i		−	0.673953i
$529$	−39.5282			−1.71862
$530$	−26.4363	+	5.00551i	−1.14832	+	0.217426i
$531$	17.2561			0.748851
$532$		0			0
$533$		−	13.6151i		−	0.589733i
$534$	−23.3210			−1.00920
$535$	1.82504	+	9.63884i	0.0789034	+	0.416724i
$536$	−13.1330			−0.567260
$537$			9.56355i			0.412698i
$538$		−	7.51934i		−	0.324182i
$539$	−6.43086			−0.276997
$540$	1.78134	+	9.40802i	0.0766565	+	0.404857i
$541$	5.76862			0.248013			0.124006	−	0.992281i	$-0.460426\pi$
$541$	5.76862			0.248013			0.124006	+	0.992281i	$0.460426\pi$
$542$			48.9058i			2.10068i
$543$		−	1.70615i		−	0.0732178i
$544$	−22.2179			−0.952583
$545$	10.8173	−	2.04818i	0.463363	−	0.0877343i
$546$	−12.0422			−0.515360
$547$		−	8.33319i		−	0.356301i	−0.984003	−	0.178151i	$-0.942989\pi$
$547$		−	8.33319i		−	0.356301i	0.984003	−	0.178151i	$-0.0570114\pi$
$548$		−	22.3469i		−	0.954613i
$549$	−3.25794			−0.139045
$550$	12.8682	+	32.7631i	0.548703	+	1.39702i
$551$		0			0
$552$			10.2099i			0.434562i
$553$		−	27.0530i		−	1.15041i
$554$	−1.40587			−0.0597298
$555$	−6.23157	+	1.17990i	−0.264515	+	0.0500839i
$556$	−4.24810			−0.180160
$557$		−	20.2069i		−	0.856195i	−0.903733	−	0.428097i	$-0.859184\pi$
$557$		−	20.2069i		−	0.856195i	0.903733	−	0.428097i	$-0.140816\pi$
$558$		−	11.4352i		−	0.484089i
$559$	−36.3947			−1.53933
$560$	−4.83652	−	25.5438i	−0.204380	−	1.07942i
$561$	−12.9010			−0.544682
$562$			41.5850i			1.75416i
$563$			7.27888i			0.306768i	0.988167	+	0.153384i	$0.0490172\pi$
$563$			7.27888i			0.306768i	−0.988167	+	0.153384i	$0.950983\pi$
$564$	0.263979			0.0111155
$565$	7.33211	+	38.7241i	0.308464	+	1.62913i
$566$	2.92901			0.123116
$567$			9.44269i			0.396556i
$568$		−	0.0988014i		−	0.00414561i
$569$	−40.7572			−1.70863			−0.854315	−	0.519756i	$-0.826023\pi$
$569$	−40.7572			−1.70863			−0.854315	+	0.519756i	$0.826023\pi$
$570$		0			0
$571$	40.5222			1.69580			0.847900	−	0.530156i	$-0.177867\pi$
$571$	40.5222			1.69580			0.847900	+	0.530156i	$0.177867\pi$
$572$		−	16.1947i		−	0.677133i
$573$		−	8.46111i		−	0.353468i
$574$	14.2112			0.593165
$575$	−14.4540	−	36.8006i	−0.602774	−	1.53469i
$576$	−1.70684			−0.0711183
$577$		−	11.0408i		−	0.459634i	−0.973234	−	0.229817i	$-0.926187\pi$
$577$		−	11.0408i		−	0.459634i	0.973234	−	0.229817i	$-0.0738127\pi$
$578$			0.596564i			0.0248138i
$579$	−4.24154			−0.176273
$580$	16.1707	−	3.06179i	0.671451	−	0.127134i
$581$	−26.9068			−1.11628
$582$			5.12887i			0.212598i
$583$			27.9348i			1.15694i
$584$	−15.4179			−0.637996
$585$	−3.89454	−	20.5688i	−0.161019	−	0.850414i
$586$	−33.6125			−1.38852
$587$		−	29.6241i		−	1.22272i	−0.791353	−	0.611360i	$-0.790623\pi$
$587$		−	29.6241i		−	1.22272i	0.791353	−	0.611360i	$-0.209377\pi$
$588$			1.25845i			0.0518974i
$589$		0			0
$590$	−5.18082	−	27.3622i	−0.213291	−	1.12648i
$591$	10.3917			0.427459
$592$			18.5032i			0.760476i
$593$		−	19.3436i		−	0.794347i	−0.917744	−	0.397173i	$-0.869991\pi$
$593$		−	19.3436i		−	0.794347i	0.917744	−	0.397173i	$-0.130009\pi$
$594$	29.2000			1.19809
$595$	−21.2796	+	4.02912i	−0.872378	+	0.165178i
$596$	−3.92374			−0.160723
$597$			9.23537i			0.377979i
$598$			53.4296i			2.18490i
$599$	14.4175			0.589082			0.294541	−	0.955639i	$-0.404833\pi$
$599$	14.4175			0.589082			0.294541	+	0.955639i	$0.404833\pi$
$600$	−6.00898	+	2.36012i	−0.245316	+	0.0963515i
$601$	3.21193			0.131017			0.0655087	−	0.997852i	$-0.479133\pi$
$601$	3.21193			0.131017			0.0655087	+	0.997852i	$0.479133\pi$
$602$		−	37.9883i		−	1.54829i
$603$		−	18.8060i		−	0.765838i
$604$	23.3087			0.948418
$605$	11.7402	−	2.22292i	0.477307	−	0.0903744i
$606$	−12.4444			−0.505519
$607$		−	0.236307i		−	0.00959142i	−0.999989	−	0.00479571i	$-0.998473\pi$
$607$		−	0.236307i		−	0.00959142i	0.999989	−	0.00479571i	$-0.00152653\pi$
$608$		0			0
$609$	−12.7060			−0.514872
$610$	0.978135	+	5.16596i	0.0396035	+	0.209164i
$611$	−1.29473			−0.0523792
$612$		−	10.3735i		−	0.419323i
$613$		−	10.3793i		−	0.419215i	−0.977786	−	0.209608i	$-0.932781\pi$
$613$		−	10.3793i		−	0.419215i	0.977786	−	0.209608i	$-0.0672187\pi$
$614$	−21.5824			−0.870993
$615$	−1.11853	−	5.90743i	−0.0451033	−	0.238210i
$616$	−15.8429			−0.638328
$617$			3.39868i			0.136826i	0.997657	+	0.0684128i	$0.0217935\pi$
$617$			3.39868i			0.136826i	−0.997657	+	0.0684128i	$0.978206\pi$
$618$		−	3.40070i		−	0.136796i
$619$	−8.50122			−0.341693			−0.170847	−	0.985298i	$-0.554650\pi$
$619$	−8.50122			−0.341693			−0.170847	+	0.985298i	$0.554650\pi$
$620$	−6.17322	+	1.16885i	−0.247922	+	0.0469422i
$621$	−32.7984			−1.31616
$622$			0.995451i			0.0399139i
$623$			40.6471i			1.62849i
$624$	14.8636			0.595018
$625$	18.3176	−	17.0137i	0.732705	−	0.680547i
$626$	−22.6209			−0.904114
$627$		0			0
$628$		−	21.4079i		−	0.854269i
$629$	15.4143			0.614609
$630$	21.4694	−	4.06507i	0.855362	−	0.161956i
$631$	26.5738			1.05789			0.528943	−	0.848658i	$-0.322589\pi$
$631$	26.5738			1.05789			0.528943	+	0.848658i	$0.322589\pi$
$632$			19.5991i			0.779609i
$633$		−	14.9464i		−	0.594066i
$634$	−0.313430			−0.0124479
$635$	0.263996	+	1.39428i	0.0104764	+	0.0553303i
$636$	5.46653			0.216762
$637$		−	6.17227i		−	0.244554i
$638$		−	50.1895i		−	1.98702i
$639$	0.141480			0.00559685
$640$	4.95119	+	26.1494i	0.195713	+	1.03365i
$641$	31.0995			1.22836			0.614178	−	0.789167i	$-0.289488\pi$
$641$	31.0995			1.22836			0.614178	+	0.789167i	$0.289488\pi$
$642$		−	5.85430i		−	0.231051i
$643$			25.1196i			0.990621i	0.868716	+	0.495310i	$0.164946\pi$
$643$			25.1196i			0.990621i	−0.868716	+	0.495310i	$0.835054\pi$
$644$	−18.9869			−0.748189
$645$	−15.7913	+	2.98995i	−0.621780	+	0.117729i
$646$		0			0
$647$			18.9775i			0.746082i	0.927815	+	0.373041i	$0.121685\pi$
$647$			18.9775i			0.746082i	−0.927815	+	0.373041i	$0.878315\pi$
$648$		−	6.84095i		−	0.268738i
$649$	−28.9132			−1.13494
$650$	−31.4457	+	12.3508i	−1.23340	+	0.484437i
$651$	4.85055			0.190108
$652$		−	6.85372i		−	0.268413i
$653$		−	11.5113i		−	0.450473i	−0.974304	−	0.225237i	$-0.927684\pi$
$653$		−	11.5113i		−	0.450473i	0.974304	−	0.225237i	$-0.0723155\pi$
$654$	−6.57007			−0.256910
$655$	4.58409	−	0.867961i	0.179115	−	0.0339141i
$656$	−17.5407			−0.684850
$657$		−	22.0778i		−	0.861336i
$658$		−	1.35142i		−	0.0526840i
$659$	2.91294			0.113472			0.0567360	−	0.998389i	$-0.481931\pi$
$659$	2.91294			0.113472			0.0567360	+	0.998389i	$0.481931\pi$
$660$	−1.33045	−	7.02670i	−0.0517877	−	0.273514i
$661$	−10.8013			−0.420122			−0.210061	−	0.977688i	$-0.567366\pi$
$661$	−10.8013			−0.420122			−0.210061	+	0.977688i	$0.567366\pi$
$662$			36.1124i			1.40355i
$663$		−	12.3823i		−	0.480888i
$664$	19.4932			0.756482
$665$		0			0
$666$	−15.5518			−0.602622
$667$			56.3746i			2.18283i
$668$		−	16.6711i		−	0.645025i
$669$	0.0575802			0.00222618
$670$	−29.8198	+	5.64614i	−1.15204	+	0.218129i
$671$	5.45879			0.210734
$672$			9.50842i			0.366795i
$673$			42.4780i			1.63741i	0.574217	+	0.818703i	$0.305307\pi$
$673$			42.4780i			1.63741i	−0.574217	+	0.818703i	$0.694693\pi$
$674$	−42.6671			−1.64347
$675$	−7.58168	−	19.3033i	−0.291819	−	0.742986i
$676$	2.12231			0.0816275
$677$		−	28.3053i		−	1.08786i	−0.839130	−	0.543931i	$-0.816935\pi$
$677$		−	28.3053i		−	1.08786i	0.839130	−	0.543931i	$-0.183065\pi$
$678$		−	23.5197i		−	0.903267i
$679$	8.93933			0.343060
$680$	15.4164	−	2.91898i	0.591193	−	0.111938i
$681$	17.2266			0.660124
$682$			19.1600i			0.733675i
$683$		−	34.0091i		−	1.30132i	−0.759369	−	0.650660i	$-0.774492\pi$
$683$		−	34.0091i		−	1.30132i	0.759369	−	0.650660i	$-0.225508\pi$
$684$		0			0
$685$	9.00440	+	47.5562i	0.344040	+	1.81703i
$686$	34.7930			1.32840
$687$		−	3.57172i		−	0.136270i
$688$			46.8884i			1.78761i
$689$	−26.8116			−1.02144
$690$	4.38943	+	23.1825i	0.167103	+	0.882544i
$691$	−16.7147			−0.635859			−0.317929	−	0.948114i	$-0.602988\pi$
$691$	−16.7147			−0.635859			−0.317929	+	0.948114i	$0.602988\pi$
$692$		−	26.9564i		−	1.02473i
$693$		−	22.6864i		−	0.861785i
$694$	−14.6515			−0.556165
$695$	9.04034	−	1.71172i	0.342920	−	0.0649292i
$696$	9.20510			0.348918
$697$			14.6125i			0.553489i
$698$		−	47.5924i		−	1.80140i
$699$	−2.81634			−0.106524
$700$	−4.38901	−	11.1746i	−0.165889	−	0.422362i
$701$	15.7626			0.595346			0.297673	−	0.954668i	$-0.403789\pi$
$701$	15.7626			0.595346			0.297673	+	0.954668i	$0.403789\pi$
$702$			28.0259i			1.05777i
$703$		0			0
$704$	2.85987			0.107785
$705$	−0.561770	+	0.106367i	−0.0211575	+	0.00400601i
$706$	16.8569			0.634418
$707$			21.6899i			0.815732i
$708$			5.65798i			0.212640i
$709$	37.2598			1.39932			0.699660	−	0.714476i	$-0.253335\pi$
$709$	37.2598			1.39932			0.699660	+	0.714476i	$0.253335\pi$
$710$	−0.0424766	−	0.224338i	−0.00159412	−	0.00841925i
$711$	−28.0651			−1.05252
$712$		−	29.4476i		−	1.10360i
$713$		−	21.5212i		−	0.805975i
$714$	12.9245			0.483686
$715$	6.52544	+	34.4637i	0.244037	+	1.28887i
$716$	12.8847			0.481522
$717$		−	6.30544i		−	0.235481i
$718$			46.7261i			1.74380i
$719$	−27.0703			−1.00955			−0.504777	−	0.863250i	$-0.668425\pi$
$719$	−27.0703			−1.00955			−0.504777	+	0.863250i	$0.668425\pi$
$720$	−26.4994	+	5.01746i	−0.987575	+	0.186990i
$721$	−5.92722			−0.220741
$722$		0			0
$723$			2.17521i			0.0808969i
$724$	−2.29864			−0.0854281
$725$	−33.1789	+	13.0315i	−1.23223	+	0.483979i
$726$	−7.13059			−0.264641
$727$			45.9733i			1.70506i	0.522682	+	0.852528i	$0.324932\pi$
$727$			45.9733i			1.70506i	−0.522682	+	0.852528i	$0.675068\pi$
$728$		−	15.2058i		−	0.563566i
$729$	0.260767			0.00965803
$730$	−35.0077	+	6.62844i	−1.29569	+	0.245329i
$731$	39.0610			1.44473
$732$		−	1.06822i		−	0.0394826i
$733$		−	4.85724i		−	0.179406i	−0.995969	−	0.0897031i	$-0.971408\pi$
$733$		−	4.85724i		−	0.179406i	0.995969	−	0.0897031i	$-0.0285918\pi$
$734$	35.7755			1.32050
$735$	−0.507074	−	2.67808i	−0.0187037	−	0.0987826i
$736$	42.1875			1.55505
$737$			31.5101i			1.16069i
$738$		−	14.7429i		−	0.542694i
$739$	−16.1356			−0.593557			−0.296778	−	0.954946i	$-0.595912\pi$
$739$	−16.1356			−0.593557			−0.296778	+	0.954946i	$0.595912\pi$
$740$	1.58964	+	8.39558i	0.0584363	+	0.308628i
$741$		0			0
$742$		−	27.9856i		−	1.02738i
$743$		−	2.05600i		−	0.0754273i	−0.999289	−	0.0377136i	$-0.987993\pi$
$743$		−	2.05600i		−	0.0754273i	0.999289	−	0.0377136i	$-0.0120075\pi$
$744$	−3.51408			−0.128832
$745$	8.35008	−	1.58102i	0.305923	−	0.0579242i
$746$	0.588353			0.0215411
$747$			27.9135i			1.02130i
$748$			17.3811i			0.635518i
$749$	−10.2037			−0.372835
$750$	−12.6293	+	7.94225i	−0.461156	+	0.290010i
$751$	−13.1607			−0.480242			−0.240121	−	0.970743i	$-0.577187\pi$
$751$	−13.1607			−0.480242			−0.240121	+	0.970743i	$0.577187\pi$
$752$			1.66805i			0.0608273i
$753$		−	21.0158i		−	0.765860i
$754$	48.1713			1.75430
$755$	−49.6030	+	9.39195i	−1.80524	+	0.341808i
$756$	−9.95936			−0.362219
$757$		−	51.8621i		−	1.88496i	−0.334263	−	0.942480i	$-0.608487\pi$
$757$		−	51.8621i		−	1.88496i	0.334263	−	0.942480i	$-0.391513\pi$
$758$		−	11.7784i		−	0.427813i
$759$	24.4966			0.889171
$760$		0			0
$761$	−32.4340			−1.17573			−0.587866	−	0.808958i	$-0.700032\pi$
$761$	−32.4340			−1.17573			−0.587866	+	0.808958i	$0.700032\pi$
$762$		−	0.846837i		−	0.0306777i
$763$			11.4513i			0.414563i
$764$	−11.3994			−0.412415
$765$	4.17986	+	22.0757i	0.151123	+	0.798149i
$766$	33.1309			1.19707
$767$		−	27.7506i		−	1.00202i
$768$		−	14.7981i		−	0.533979i
$769$	52.7350			1.90167			0.950837	−	0.309693i	$-0.100226\pi$
$769$	52.7350			1.90167			0.950837	+	0.309693i	$0.100226\pi$
$770$	−35.9728	+	6.81117i	−1.29637	+	0.245457i
$771$	8.52807			0.307131
$772$			5.71449i			0.205669i
$773$			37.1753i			1.33710i	0.743666	+	0.668552i	$0.233085\pi$
$773$			37.1753i			1.33710i	−0.743666	+	0.668552i	$0.766915\pi$
$774$	−39.4095			−1.41655
$775$	12.6662	−	4.97484i	0.454982	−	0.178701i
$776$	−6.47628			−0.232485
$777$		−	6.59676i		−	0.236657i
$778$		−	16.4954i		−	0.591388i
$779$		0			0
$780$	6.74415	−	1.27695i	0.241479	−	0.0457222i
$781$	−0.237054			−0.00848246
$782$		−	57.3440i		−	2.05062i
$783$			29.5706i			1.05677i
$784$	−7.95194			−0.283998
$785$	8.62604	+	45.5579i	0.307877	+	1.62603i
$786$	−2.78421			−0.0993096
$787$			35.6252i			1.26990i	0.772553	+	0.634950i	$0.218979\pi$
$787$			35.6252i			1.26990i	−0.772553	+	0.634950i	$0.781021\pi$
$788$		−	14.0004i		−	0.498745i
$789$	−15.6106			−0.555751
$790$	8.42601	+	44.5015i	0.299784	+	1.58329i
$791$	−40.9934			−1.45756
$792$			16.4356i			0.584014i
$793$			5.23929i			0.186053i
$794$	5.50940			0.195521
$795$	−11.6333	+	2.20267i	−0.412589	+	0.0781206i
$796$	12.4425			0.441013
$797$			38.2899i			1.35630i	0.734924	+	0.678150i	$0.237218\pi$
$797$			38.2899i			1.35630i	−0.734924	+	0.678150i	$0.762782\pi$
$798$		0			0
$799$	1.38959			0.0491601
$800$	9.75206	+	24.8292i	0.344787	+	0.877845i
$801$	42.1678			1.48993
$802$		−	49.0503i		−	1.73203i
$803$			36.9921i			1.30542i
$804$	6.16616			0.217464
$805$	40.4058	−	7.65054i	1.42412	−	0.269646i
$806$	−18.3896			−0.647745
$807$		−	3.30887i		−	0.116478i
$808$		−	15.7137i		−	0.552805i
$809$	−44.4492			−1.56275			−0.781375	−	0.624061i	$-0.785482\pi$
$809$	−44.4492			−1.56275			−0.781375	+	0.624061i	$0.785482\pi$
$810$	−2.94105	−	15.5330i	−0.103338	−	0.545774i
$811$	35.0033			1.22913			0.614566	−	0.788865i	$-0.289331\pi$
$811$	35.0033			1.22913			0.614566	+	0.788865i	$0.289331\pi$
$812$			17.1183i			0.600736i
$813$			21.5209i			0.754771i
$814$	26.0577			0.913321
$815$	2.76162	+	14.5853i	0.0967353	+	0.510902i
$816$	−15.9525			−0.558449
$817$		0			0
$818$		−	23.9479i		−	0.837318i
$819$	21.7742			0.760851
$820$	−7.95888	+	1.50695i	−0.277936	+	0.0526250i
$821$	−14.3150			−0.499596			−0.249798	−	0.968298i	$-0.580364\pi$
$821$	−14.3150			−0.499596			−0.249798	+	0.968298i	$0.580364\pi$
$822$		−	28.8840i		−	1.00744i
$823$		−	17.4214i		−	0.607270i	−0.952788	−	0.303635i	$-0.901800\pi$
$823$		−	17.4214i		−	0.607270i	0.952788	−	0.303635i	$-0.0982004\pi$
$824$	4.29410			0.149592
$825$	5.66263	+	14.4173i	0.197148	+	0.501947i
$826$	28.9657			1.00785
$827$			24.7778i			0.861607i	0.902446	+	0.430803i	$0.141770\pi$
$827$			24.7778i			0.861607i	−0.902446	+	0.430803i	$0.858230\pi$
$828$			19.6973i			0.684528i
$829$	−26.4870			−0.919931			−0.459966	−	0.887937i	$-0.652138\pi$
$829$	−26.4870			−0.919931			−0.459966	+	0.887937i	$0.652138\pi$
$830$	44.2611	−	8.38049i	1.53632	−	0.290891i
$831$	−0.618652			−0.0214608
$832$			2.74487i			0.0951613i
$833$			6.62447i			0.229524i
$834$	−5.49079			−0.190130
$835$	6.71741	+	35.4776i	0.232466	+	1.22775i
$836$		0			0
$837$		−	11.2887i		−	0.390194i
$838$		−	1.12109i		−	0.0387274i
$839$	31.9369			1.10259			0.551293	−	0.834312i	$-0.314135\pi$
$839$	31.9369			1.10259			0.551293	+	0.834312i	$0.314135\pi$
$840$	−1.24921	−	6.59765i	−0.0431020	−	0.227641i
$841$	21.8265			0.752637
$842$			31.1256i			1.07266i
$843$			18.2994i			0.630265i
$844$	−20.1368			−0.693137
$845$	−4.51647	+	0.855159i	−0.155371	+	0.0294184i
$846$	−1.40198			−0.0482012
$847$			12.4282i			0.427039i
$848$			34.5422i			1.18619i
$849$	1.28891			0.0442351
$850$	33.7495	−	13.2556i	1.15760	−	0.454664i
$851$	−29.2689			−1.00332
$852$			0.0463888i			0.00158925i
$853$		−	40.4950i		−	1.38652i	−0.720686	−	0.693262i	$-0.756173\pi$
$853$		−	40.4950i		−	1.38652i	0.720686	−	0.693262i	$-0.243827\pi$
$854$	−5.46870			−0.187135
$855$		0			0
$856$	7.39228			0.252663
$857$			47.7479i			1.63104i	0.578732	+	0.815518i	$0.303548\pi$
$857$			47.7479i			1.63104i	−0.578732	+	0.815518i	$0.696452\pi$
$858$		−	20.9320i		−	0.714608i
$859$	−51.3803			−1.75307			−0.876537	−	0.481334i	$-0.840153\pi$
$859$	−51.3803			−1.75307			−0.876537	+	0.481334i	$0.840153\pi$
$860$	4.02826	+	21.2750i	0.137363	+	0.725473i
$861$	6.25362			0.213123
$862$		−	0.673881i		−	0.0229525i
$863$			4.82884i			0.164376i	0.996617	+	0.0821878i	$0.0261907\pi$
$863$			4.82884i			0.164376i	−0.996617	+	0.0821878i	$0.973809\pi$
$864$	22.1289			0.752842
$865$	10.8617	+	57.3655i	0.369310	+	1.95049i
$866$	−50.0570			−1.70101
$867$			0.262517i			0.00891555i
$868$		−	6.53499i		−	0.221812i
$869$	47.0240			1.59518
$870$	20.9010	−	3.95745i	0.708611	−	0.134170i
$871$	−30.2430			−1.02475
$872$		−	8.29610i		−	0.280941i
$873$		−	9.27377i		−	0.313870i
$874$		0			0
$875$	13.8429	+	22.0121i	0.467975	+	0.744146i
$876$	7.23892			0.244581
$877$		−	11.8051i		−	0.398631i	−0.979935	−	0.199315i	$-0.936128\pi$
$877$		−	11.8051i		−	0.398631i	0.979935	−	0.199315i	$-0.0638718\pi$
$878$			47.6448i			1.60793i
$879$	−14.7911			−0.498892
$880$	44.4007	−	8.40693i	1.49675	−	0.283398i
$881$	2.35229			0.0792508			0.0396254	−	0.999215i	$-0.487384\pi$
$881$	2.35229			0.0792508			0.0396254	+	0.999215i	$0.487384\pi$
$882$		−	6.68357i		−	0.225048i
$883$			27.9076i			0.939166i	0.882888	+	0.469583i	$0.155596\pi$
$883$			27.9076i			0.939166i	−0.882888	+	0.469583i	$0.844404\pi$
$884$	−16.6822			−0.561084
$885$	−2.27981	−	12.0407i	−0.0766350	−	0.404743i
$886$	−42.7782			−1.43716
$887$		−	7.08061i		−	0.237744i	−0.992910	−	0.118872i	$-0.962072\pi$
$887$		−	7.08061i		−	0.237744i	0.992910	−	0.118872i	$-0.0379277\pi$
$888$			4.77915i			0.160378i
$889$	−1.47599			−0.0495031
$890$	−12.6601	−	66.8636i	−0.424367	−	2.24127i
$891$	−16.4135			−0.549872
$892$		−	0.0775758i		−	0.00259743i
$893$		0			0
$894$	−5.07154			−0.169618
$895$	−27.4197	+	5.19171i	−0.916539	+	0.173540i
$896$	−27.6818			−0.924785
$897$			23.5116i			0.785029i
$898$			37.0783i			1.23732i
$899$	−19.4032			−0.647133
$900$	−11.5927	+	4.55322i	−0.386424	+	0.151774i
$901$	28.7759			0.958663
$902$			24.7022i			0.822495i
$903$		−	16.7167i		−	0.556296i
$904$	29.6985			0.987759
$905$	4.89170	−	0.926206i	0.162606	−	0.0307881i
$906$	30.1271			1.00091
$907$		−	21.3883i		−	0.710187i	−0.934831	−	0.355094i	$-0.884449\pi$
$907$		−	21.3883i		−	0.710187i	0.934831	−	0.355094i	$-0.115551\pi$
$908$		−	23.2088i		−	0.770211i
$909$	22.5014			0.746323
$910$	−6.53729	−	34.5263i	−0.216709	−	1.14454i
$911$	−0.0308998			−0.00102375			−0.000511877	−	1.00000i	$-0.500163\pi$
$911$	−0.0308998			−0.00102375			−0.000511877		1.00000i	$0.500163\pi$
$912$		0			0
$913$		−	46.7700i		−	1.54786i
$914$	4.83390			0.159891
$915$	0.430427	+	2.27327i	0.0142295	+	0.0751521i
$916$	−4.81206			−0.158995
$917$			4.85273i			0.160251i
$918$		−	30.0791i		−	0.992759i
$919$	10.9750			0.362033			0.181016	−	0.983480i	$-0.442061\pi$
$919$	10.9750			0.362033			0.181016	+	0.983480i	$0.442061\pi$
$920$	−29.2728	+	5.54259i	−0.965097	+	0.182734i
$921$	−9.49727			−0.312946
$922$		−	49.6225i		−	1.63423i
$923$		−	0.227522i		−	0.00748898i
$924$	7.43848			0.244708
$925$	−6.76579	−	17.2260i	−0.222458	−	0.566388i
$926$	8.96625			0.294649
$927$			6.14898i			0.201959i
$928$		−	38.0356i		−	1.24858i
$929$	−44.0615			−1.44561			−0.722806	−	0.691051i	$-0.757148\pi$
$929$	−44.0615			−1.44561			−0.722806	+	0.691051i	$0.757148\pi$
$930$	−7.97905	+	1.51077i	−0.261643	+	0.0495401i
$931$		0			0
$932$			3.79436i			0.124288i
$933$			0.438046i			0.0143410i
$934$	−4.30878			−0.140988
$935$	−7.00351	−	36.9886i	−0.229039	−	1.20966i
$936$	−15.7747			−0.515613
$937$			21.2417i			0.693935i	0.937877	+	0.346968i	$0.112789\pi$
$937$			21.2417i			0.693935i	−0.937877	+	0.346968i	$0.887211\pi$
$938$		−	31.5673i		−	1.03071i
$939$	−9.95429			−0.324846
$940$	0.143304	+	0.756854i	0.00467408	+	0.0246859i
$941$	−16.7371			−0.545613			−0.272807	−	0.962069i	$-0.587952\pi$
$941$	−16.7371			−0.545613			−0.272807	+	0.962069i	$0.587952\pi$
$942$		−	27.6703i		−	0.901547i
$943$		−	27.7464i		−	0.903547i
$944$	−35.7520			−1.16363
$945$	21.1944	−	4.01300i	0.689454	−	0.130543i
$946$	66.0320			2.14689
$947$		−	28.6132i		−	0.929805i	−0.885362	−	0.464903i	$-0.846089\pi$
$947$		−	28.6132i		−	0.929805i	0.885362	−	0.464903i	$-0.153911\pi$
$948$		−	9.20206i		−	0.298869i
$949$	−35.5046			−1.15253
$950$		0			0
$951$	−0.137925			−0.00447251
$952$			16.3199i			0.528930i
$953$			29.4375i			0.953575i	0.879019	+	0.476788i	$0.158199\pi$
$953$			29.4375i			0.953575i	−0.879019	+	0.476788i	$0.841801\pi$
$954$	−29.0326			−0.939965
$955$	24.2589	−	4.59323i	0.784999	−	0.148633i
$956$	−8.49510			−0.274751
$957$		−	22.0858i		−	0.713932i
$958$		−	5.84294i		−	0.188777i
$959$	−50.3431			−1.62567
$960$	0.225501	+	1.19097i	0.00727802	+	0.0384384i
$961$	−23.5928			−0.761057
$962$			25.0099i			0.806351i
$963$			10.5855i			0.341112i
$964$	2.93059			0.0943878
$965$	−2.30258	−	12.1609i	−0.0741227	−	0.391475i
$966$	−24.5411			−0.789597
$967$			54.7395i			1.76030i	0.474691	+	0.880152i	$0.342560\pi$
$967$			54.7395i			1.76030i	−0.474691	+	0.880152i	$0.657440\pi$
$968$		−	9.00387i		−	0.289395i
$969$		0			0
$970$	−14.7050	+	2.78428i	−0.472149	+	0.0893977i
$971$	−40.9402			−1.31383			−0.656916	−	0.753964i	$-0.728139\pi$
$971$	−40.9402			−1.31383			−0.656916	+	0.753964i	$0.728139\pi$
$972$			16.0584i			0.515073i
$973$			9.57014i			0.306804i
$974$	−5.12275			−0.164144
$975$	−13.8376	+	5.43494i	−0.443158	+	0.174057i
$976$	6.74995			0.216061
$977$			30.8153i			0.985868i	0.870067	+	0.492934i	$0.164076\pi$
$977$			30.8153i			0.985868i	−0.870067	+	0.492934i	$0.835924\pi$
$978$		−	8.85862i		−	0.283267i
$979$	−70.6537			−2.25810
$980$	−3.60809	+	0.683164i	−0.115256	+	0.0218229i
$981$	11.8797			0.379289
$982$		−	40.2923i		−	1.28578i
$983$		−	35.6988i		−	1.13862i	−0.822125	−	0.569308i	$-0.807211\pi$
$983$		−	35.6988i		−	1.13862i	0.822125	−	0.569308i	$-0.192789\pi$
$984$	−4.53056			−0.144429
$985$	5.64129	+	29.7942i	0.179747	+	0.949321i
$986$	−51.7005			−1.64648
$987$		−	0.594692i		−	0.0189292i
$988$		0			0
$989$	−74.1695			−2.35845
$990$	7.06599	+	37.3186i	0.224572	+	1.18606i
$991$	−35.1472			−1.11649			−0.558245	−	0.829676i	$-0.688525\pi$
$991$	−35.1472			−1.11649			−0.558245	+	0.829676i	$0.688525\pi$
$992$			14.5202i			0.461018i
$993$			15.8912i			0.504292i
$994$	0.237485			0.00753256
$995$	−26.4788	+	5.01355i	−0.839433	+	0.158940i
$996$	−9.15235			−0.290003
$997$		−	31.3541i		−	0.992995i	−0.868038	−	0.496498i	$-0.834619\pi$
$997$		−	31.3541i		−	0.992995i	0.868038	−	0.496498i	$-0.165381\pi$
$998$		−	13.7606i		−	0.435585i
$999$	−15.3526			−0.485736

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.m.1084.9	✓	40
5.2	odd	4		9025.2.a.cv.1.31		40
5.3	odd	4		9025.2.a.cv.1.10		40
5.4	even	2	inner	1805.2.b.m.1084.32	yes	40
19.18	odd	2	inner	1805.2.b.m.1084.31	yes	40
95.18	even	4		9025.2.a.cv.1.32		40
95.37	even	4		9025.2.a.cv.1.9		40
95.94	odd	2	inner	1805.2.b.m.1084.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.b.m.1084.9	✓	40	1.1	even	1	trivial
1805.2.b.m.1084.10	yes	40	95.94	odd	2	inner
1805.2.b.m.1084.31	yes	40	19.18	odd	2	inner
1805.2.b.m.1084.32	yes	40	5.4	even	2	inner
9025.2.a.cv.1.9		40	95.37	even	4
9025.2.a.cv.1.10		40	5.3	odd	4
9025.2.a.cv.1.31		40	5.2	odd	4
9025.2.a.cv.1.32		40	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)

\(f(q)\)	\(=\)	\(q-1.74138i q^{2} -0.766290i q^{3} -1.03240 q^{4} +(2.19703 - 0.415991i) q^{5} -1.33440 q^{6} +2.32579i q^{7} -1.68496i q^{8} +2.41280 q^{9} +O(q^{10})\)	\(q-1.74138i q^{2} -0.766290i q^{3} -1.03240 q^{4} +(2.19703 - 0.415991i) q^{5} -1.33440 q^{6} +2.32579i q^{7} -1.68496i q^{8} +2.41280 q^{9} +(-0.724398 - 3.82586i) q^{10} -4.04273 q^{11} +0.791116i q^{12} -3.88017i q^{13} +4.05007 q^{14} +(-0.318770 - 1.68356i) q^{15} -4.99895 q^{16} +4.16444i q^{17} -4.20160i q^{18} +(-2.26821 + 0.429468i) q^{20} +1.78223 q^{21} +7.03992i q^{22} -7.90748i q^{23} -1.29117 q^{24} +(4.65390 - 1.82789i) q^{25} -6.75684 q^{26} -4.14777i q^{27} -2.40113i q^{28} -7.12927 q^{29} +(-2.93172 + 0.555099i) q^{30} +2.72162 q^{31} +5.33514i q^{32} +3.09790i q^{33} +7.25187 q^{34} +(0.967506 + 5.10983i) q^{35} -2.49097 q^{36} -3.70141i q^{37} -2.97334 q^{39} +(-0.700929 - 3.70192i) q^{40} +3.50888 q^{41} -3.10353i q^{42} -9.37966i q^{43} +4.17370 q^{44} +(5.30100 - 1.00370i) q^{45} -13.7699 q^{46} -0.333679i q^{47} +3.83065i q^{48} +1.59072 q^{49} +(-3.18305 - 8.10420i) q^{50} +3.19117 q^{51} +4.00588i q^{52} -6.90990i q^{53} -7.22284 q^{54} +(-8.88201 + 1.68174i) q^{55} +3.91886 q^{56} +12.4148i q^{58} +7.15190 q^{59} +(0.329097 + 1.73811i) q^{60} -1.35027 q^{61} -4.73938i q^{62} +5.61165i q^{63} -0.707410 q^{64} +(-1.61412 - 8.52486i) q^{65} +5.39462 q^{66} -7.79425i q^{67} -4.29936i q^{68} -6.05942 q^{69} +(8.89814 - 1.68479i) q^{70} +0.0586372 q^{71} -4.06548i q^{72} -9.15027i q^{73} -6.44556 q^{74} +(-1.40070 - 3.56624i) q^{75} -9.40252i q^{77} +5.17770i q^{78} -11.6317 q^{79} +(-10.9829 + 2.07952i) q^{80} +4.06000 q^{81} -6.11029i q^{82} +11.5689i q^{83} -1.83997 q^{84} +(1.73237 + 9.14942i) q^{85} -16.3335 q^{86} +5.46309i q^{87} +6.81185i q^{88} +17.4767 q^{89} +(-1.74783 - 9.23104i) q^{90} +9.02444 q^{91} +8.16366i q^{92} -2.08555i q^{93} -0.581061 q^{94} +4.08826 q^{96} -3.84357i q^{97} -2.77005i q^{98} -9.75430 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 48 q^{4} + 6 q^{5} + 20 q^{6} - 52 q^{9}+O(q^{10}) \) 40 * q - 48 * q^4 + 6 * q^5 + 20 * q^6 - 52 * q^9	\( 40 q - 48 q^{4} + 6 q^{5} + 20 q^{6} - 52 q^{9} + 20 q^{11} + 40 q^{16} - 18 q^{20} - 92 q^{24} - 26 q^{25} + 76 q^{26} + 40 q^{30} + 4 q^{35} + 156 q^{36} - 80 q^{39} - 48 q^{44} - 22 q^{45} - 72 q^{49} - 32 q^{54} - 40 q^{55} + 80 q^{61} - 72 q^{64} + 16 q^{66} - 100 q^{74} - 66 q^{80} + 40 q^{81} + 44 q^{85} + 380 q^{96} - 128 q^{99}+O(q^{100}) \) 40 * q - 48 * q^4 + 6 * q^5 + 20 * q^6 - 52 * q^9 + 20 * q^11 + 40 * q^16 - 18 * q^20 - 92 * q^24 - 26 * q^25 + 76 * q^26 + 40 * q^30 + 4 * q^35 + 156 * q^36 - 80 * q^39 - 48 * q^44 - 22 * q^45 - 72 * q^49 - 32 * q^54 - 40 * q^55 + 80 * q^61 - 72 * q^64 + 16 * q^66 - 100 * q^74 - 66 * q^80 + 40 * q^81 + 44 * q^85 + 380 * q^96 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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