LMFDB - Embedded newform 228.3.b.e.227.72

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,3,Mod(227,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("228.227");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	228.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:	$6.21255002741$
Analytic rank:	$0$
Dimension:	$72$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			227.72
Character	$\chi$	$=$	228.227
Dual form			228.3.b.e.227.70

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.99370 + 0.158675i) q^{2} +(1.15371 - 2.76929i) q^{3} +(3.94964 + 0.632700i) q^{4} -8.12041i q^{5} +(2.73957 - 5.33805i) q^{6} +8.99393i q^{7} +(7.77400 + 1.88812i) q^{8} +(-6.33790 - 6.38992i) q^{9} +O(q^{10})$	\(q+(1.99370 + 0.158675i) q^{2} +(1.15371 - 2.76929i) q^{3} +(3.94964 + 0.632700i) q^{4} -8.12041i q^{5} +(2.73957 - 5.33805i) q^{6} +8.99393i q^{7} +(7.77400 + 1.88812i) q^{8} +(-6.33790 - 6.38992i) q^{9} +(1.28851 - 16.1896i) q^{10} -0.680370 q^{11} +(6.30888 - 10.2077i) q^{12} -4.64238i q^{13} +(-1.42711 + 17.9312i) q^{14} +(-22.4877 - 9.36861i) q^{15} +(15.1994 + 4.99788i) q^{16} +21.2842i q^{17} +(-11.6219 - 13.7452i) q^{18} +(10.8345 - 15.6081i) q^{19} +(5.13778 - 32.0727i) q^{20} +(24.9068 + 10.3764i) q^{21} +(-1.35645 - 0.107958i) q^{22} -34.5295 q^{23} +(14.1977 - 19.3501i) q^{24} -40.9411 q^{25} +(0.736630 - 9.25549i) q^{26} +(-25.0076 + 10.1793i) q^{27} +(-5.69046 + 35.5228i) q^{28} +28.9611 q^{29} +(-43.3472 - 22.2464i) q^{30} +38.0395 q^{31} +(29.5099 + 12.3760i) q^{32} +(-0.784951 + 1.88414i) q^{33} +(-3.37727 + 42.4341i) q^{34} +73.0344 q^{35} +(-20.9895 - 29.2479i) q^{36} +50.9685i q^{37} +(24.0773 - 29.3987i) q^{38} +(-12.8561 - 5.35597i) q^{39} +(15.3323 - 63.1280i) q^{40} +41.0318 q^{41} +(48.0100 + 24.6395i) q^{42} +47.4246i q^{43} +(-2.68722 - 0.430470i) q^{44} +(-51.8887 + 51.4663i) q^{45} +(-68.8414 - 5.47898i) q^{46} -15.0004 q^{47} +(31.3763 - 36.3253i) q^{48} -31.8908 q^{49} +(-81.6240 - 6.49633i) q^{50} +(58.9419 + 24.5558i) q^{51} +(2.93723 - 18.3357i) q^{52} -52.3819 q^{53} +(-51.4728 + 16.3264i) q^{54} +5.52489i q^{55} +(-16.9816 + 69.9188i) q^{56} +(-30.7236 - 48.0111i) q^{57} +(57.7396 + 4.59540i) q^{58} -52.0870i q^{59} +(-82.8911 - 51.2307i) q^{60} -28.5427 q^{61} +(75.8391 + 6.03592i) q^{62} +(57.4705 - 57.0026i) q^{63} +(56.8700 + 29.3565i) q^{64} -37.6980 q^{65} +(-1.86392 + 3.63185i) q^{66} +53.2338 q^{67} +(-13.4665 + 84.0649i) q^{68} +(-39.8371 + 95.6222i) q^{69} +(145.608 + 11.5887i) q^{70} +29.3024i q^{71} +(-37.2059 - 61.6419i) q^{72} +0.749301 q^{73} +(-8.08743 + 101.616i) q^{74} +(-47.2342 + 113.378i) q^{75} +(52.6676 - 54.7917i) q^{76} -6.11920i q^{77} +(-24.7812 - 12.7181i) q^{78} -138.146 q^{79} +(40.5848 - 123.425i) q^{80} +(-0.662080 + 80.9973i) q^{81} +(81.8050 + 6.51073i) q^{82} -92.3122 q^{83} +(91.8078 + 56.7416i) q^{84} +172.836 q^{85} +(-7.52510 + 94.5502i) q^{86} +(33.4128 - 80.2016i) q^{87} +(-5.28920 - 1.28462i) q^{88} -15.2070 q^{89} +(-111.617 + 94.3748i) q^{90} +41.7532 q^{91} +(-136.379 - 21.8468i) q^{92} +(43.8866 - 105.342i) q^{93} +(-29.9062 - 2.38018i) q^{94} +(-126.745 - 87.9804i) q^{95} +(68.3186 - 67.4430i) q^{96} +28.9978i q^{97} +(-63.5805 - 5.06027i) q^{98} +(4.31212 + 4.34751i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 16 q^{4} + 6 q^{6} - 48 q^{9}+O(q^{10}) $ 72 * q - 16 * q^4 + 6 * q^6 - 48 * q^9	$ 72 q - 16 q^{4} + 6 q^{6} - 48 q^{9} - 40 q^{16} + 94 q^{24} - 408 q^{25} + 60 q^{28} + 176 q^{30} - 214 q^{36} + 2 q^{42} + 96 q^{45} - 616 q^{49} + 72 q^{54} + 320 q^{57} + 564 q^{58} + 592 q^{61} - 424 q^{64} + 608 q^{66} + 128 q^{73} - 292 q^{76} - 208 q^{81} + 472 q^{82} - 160 q^{85} + 128 q^{93} + 166 q^{96}+O(q^{100}) $ 72 * q - 16 * q^4 + 6 * q^6 - 48 * q^9 - 40 * q^16 + 94 * q^24 - 408 * q^25 + 60 * q^28 + 176 * q^30 - 214 * q^36 + 2 * q^42 + 96 * q^45 - 616 * q^49 + 72 * q^54 + 320 * q^57 + 564 * q^58 + 592 * q^61 - 424 * q^64 + 608 * q^66 + 128 * q^73 - 292 * q^76 - 208 * q^81 + 472 * q^82 - 160 * q^85 + 128 * q^93 + 166 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.99370	+	0.158675i	0.996848	+	0.0793375i
$2$	1.99370	+	0.158675i	0.996848	+	0.0793375i
$3$	1.15371	−	2.76929i	0.384571	−	0.923096i
$3$	1.15371	−	2.76929i	0.384571	−	0.923096i
$4$	3.94964	+	0.632700i	0.987411	+	0.158175i
$5$		−	8.12041i		−	1.62408i	−0.583600	−	0.812041i	$-0.698357\pi$
$5$		−	8.12041i		−	1.62408i	0.583600	−	0.812041i	$-0.301643\pi$
$6$	2.73957	−	5.33805i	0.456594	−	0.889675i
$7$			8.99393i			1.28485i	0.766350	+	0.642424i	$0.222071\pi$
$7$			8.99393i			1.28485i	−0.766350	+	0.642424i	$0.777929\pi$
$8$	7.77400	+	1.88812i	0.971749	+	0.236015i
$9$	−6.33790	−	6.38992i	−0.704211	−	0.709991i
$10$	1.28851	−	16.1896i	0.128851	−	1.61896i
$11$	−0.680370			−0.0618519			−0.0309259	−	0.999522i	$-0.509846\pi$
$11$	−0.680370			−0.0618519			−0.0309259	+	0.999522i	$0.509846\pi$
$12$	6.30888	−	10.2077i	0.525740	−	0.850645i
$13$		−	4.64238i		−	0.357106i	−0.983930	−	0.178553i	$-0.942858\pi$
$13$		−	4.64238i		−	0.357106i	0.983930	−	0.178553i	$-0.0571416\pi$
$14$	−1.42711	+	17.9312i	−0.101937	+	1.28080i
$15$	−22.4877	−	9.36861i	−1.49918	−	0.624574i
$16$	15.1994	+	4.99788i	0.949961	+	0.312367i
$17$			21.2842i			1.25201i	0.779819	+	0.626005i	$0.215311\pi$
$17$			21.2842i			1.25201i	−0.779819	+	0.626005i	$0.784689\pi$
$18$	−11.6219	−	13.7452i	−0.645662	−	0.763623i
$19$	10.8345	−	15.6081i	0.570235	−	0.821481i
$19$	10.8345	−	15.6081i	0.570235	−	0.821481i
$20$	5.13778	−	32.0727i	0.256889	−	1.60364i
$21$	24.9068	+	10.3764i	1.18604	+	0.494114i
$22$	−1.35645	−	0.107958i	−0.0616569	−	0.00490717i
$23$	−34.5295			−1.50128			−0.750642	−	0.660709i	$-0.770256\pi$
$23$	−34.5295			−1.50128			−0.750642	+	0.660709i	$0.770256\pi$
$24$	14.1977	−	19.3501i	0.591571	−	0.806253i
$25$	−40.9411			−1.63764
$26$	0.736630	−	9.25549i	0.0283319	−	0.355980i
$27$	−25.0076	+	10.1793i	−0.926208	+	0.377012i
$28$	−5.69046	+	35.5228i	−0.203231	+	1.26867i
$29$	28.9611			0.998659			0.499329	−	0.866412i	$-0.333580\pi$
$29$	28.9611			0.998659			0.499329	+	0.866412i	$0.333580\pi$
$30$	−43.3472	−	22.2464i	−1.44491	−	0.741547i
$31$	38.0395			1.22708			0.613540	−	0.789664i	$-0.289745\pi$
$31$	38.0395			1.22708			0.613540	+	0.789664i	$0.289745\pi$
$32$	29.5099	+	12.3760i	0.922185	+	0.386750i
$33$	−0.784951	+	1.88414i	−0.0237864	+	0.0570952i
$34$	−3.37727	+	42.4341i	−0.0993313	+	1.24806i
$35$	73.0344			2.08670
$36$	−20.9895	−	29.2479i	−0.583043	−	0.812441i
$37$			50.9685i			1.37753i	0.724986	+	0.688764i	$0.241846\pi$
$37$			50.9685i			1.37753i	−0.724986	+	0.688764i	$0.758154\pi$
$38$	24.0773	−	29.3987i	0.633612	−	0.773651i
$39$	−12.8561	−	5.35597i	−0.329643	−	0.137332i
$40$	15.3323	−	63.1280i	0.383308	−	1.57820i
$41$	41.0318			1.00078			0.500388	−	0.865801i	$-0.333191\pi$
$41$	41.0318			1.00078			0.500388	+	0.865801i	$0.333191\pi$
$42$	48.0100	+	24.6395i	1.14310	+	0.586654i
$43$			47.4246i			1.10290i	0.834209	+	0.551449i	$0.185925\pi$
$43$			47.4246i			1.10290i	−0.834209	+	0.551449i	$0.814075\pi$
$44$	−2.68722	−	0.430470i	−0.0610732	−	0.00978341i
$45$	−51.8887	+	51.4663i	−1.15308	+	1.14370i
$46$	−68.8414	−	5.47898i	−1.49655	−	0.119108i
$47$	−15.0004			−0.319157			−0.159578	−	0.987185i	$-0.551013\pi$
$47$	−15.0004			−0.319157			−0.159578	+	0.987185i	$0.551013\pi$
$48$	31.3763	−	36.3253i	0.653672	−	0.756778i
$49$	−31.8908			−0.650832
$50$	−81.6240	−	6.49633i	−1.63248	−	0.129927i
$51$	58.9419	+	24.5558i	1.15572	+	0.481486i
$52$	2.93723	−	18.3357i	0.0564852	−	0.352611i
$53$	−52.3819			−0.988338			−0.494169	−	0.869366i	$-0.664528\pi$
$53$	−52.3819			−0.988338			−0.494169	+	0.869366i	$0.664528\pi$
$54$	−51.4728	+	16.3264i	−0.953200	+	0.302341i
$55$			5.52489i			0.100452i
$56$	−16.9816	+	69.9188i	−0.303243	+	1.24855i
$57$	−30.7236	−	48.0111i	−0.539010	−	0.842299i
$58$	57.7396	+	4.59540i	0.995511	+	0.0792311i
$59$		−	52.0870i		−	0.882830i	−0.897303	−	0.441415i	$-0.854477\pi$
$59$		−	52.0870i		−	0.882830i	0.897303	−	0.441415i	$-0.145523\pi$
$60$	−82.8911	−	51.2307i	−1.38152	−	0.853845i
$61$	−28.5427			−0.467913			−0.233957	−	0.972247i	$-0.575167\pi$
$61$	−28.5427			−0.467913			−0.233957	+	0.972247i	$0.575167\pi$
$62$	75.8391	+	6.03592i	1.22321	+	0.0973535i
$63$	57.4705	−	57.0026i	0.912230	−	0.904803i
$64$	56.8700	+	29.3565i	0.888594	+	0.458695i
$65$	−37.6980			−0.579970
$66$	−1.86392	+	3.63185i	−0.0282412	+	0.0550280i
$67$	53.2338			0.794535			0.397267	−	0.917703i	$-0.369959\pi$
$67$	53.2338			0.794535			0.397267	+	0.917703i	$0.369959\pi$
$68$	−13.4665	+	84.0649i	−0.198036	+	1.23625i
$69$	−39.8371	+	95.6222i	−0.577350	+	1.38583i
$70$	145.608	+	11.5887i	2.08012	+	0.165553i
$71$			29.3024i			0.412710i	0.978477	+	0.206355i	$0.0661601\pi$
$71$			29.3024i			0.412710i	−0.978477	+	0.206355i	$0.933840\pi$
$72$	−37.2059	−	61.6419i	−0.516748	−	0.856138i
$73$	0.749301			0.0102644			0.00513220	−	0.999987i	$-0.498366\pi$
$73$	0.749301			0.0102644			0.00513220	+	0.999987i	$0.498366\pi$
$74$	−8.08743	+	101.616i	−0.109290	+	1.37319i
$75$	−47.2342	+	113.378i	−0.629789	+	1.51170i
$76$	52.6676	−	54.7917i	0.692994	−	0.720943i
$77$		−	6.11920i		−	0.0794702i
$78$	−24.7812	−	12.7181i	−0.317708	−	0.163053i
$79$	−138.146			−1.74869			−0.874343	−	0.485309i	$-0.838707\pi$
$79$	−138.146			−1.74869			−0.874343	+	0.485309i	$0.838707\pi$
$80$	40.5848	−	123.425i	0.507310	−	1.54282i
$81$	−0.662080	+	80.9973i	−0.00817383	+	0.999967i
$82$	81.8050	+	6.51073i	0.997622	+	0.0793991i
$83$	−92.3122			−1.11220			−0.556098	−	0.831117i	$-0.687702\pi$
$83$	−92.3122			−1.11220			−0.556098	+	0.831117i	$0.687702\pi$
$84$	91.8078	+	56.7416i	1.09295	+	0.675495i
$85$	172.836			2.03337
$86$	−7.52510	+	94.5502i	−0.0875012	+	1.09942i
$87$	33.4128	−	80.2016i	0.384055	−	0.921857i
$88$	−5.28920	−	1.28462i	−0.0601045	−	0.0145980i
$89$	−15.2070			−0.170866			−0.0854328	−	0.996344i	$-0.527227\pi$
$89$	−15.2070			−0.170866			−0.0854328	+	0.996344i	$0.527227\pi$
$90$	−111.617	+	94.3748i	−1.24019	+	1.04861i
$91$	41.7532			0.458827
$92$	−136.379	−	21.8468i	−1.48238	−	0.237465i
$93$	43.8866	−	105.342i	0.471899	−	1.13271i
$94$	−29.9062	−	2.38018i	−0.318151	−	0.0253211i
$95$	−126.745	−	87.9804i	−1.33415	−	0.926109i
$96$	68.3186	−	67.4430i	0.711652	−	0.702532i
$97$			28.9978i			0.298947i	0.988766	+	0.149473i	$0.0477578\pi$
$97$			28.9978i			0.298947i	−0.988766	+	0.149473i	$0.952242\pi$
$98$	−63.5805	−	5.06027i	−0.648781	−	0.0516354i
$99$	4.31212	+	4.34751i	0.0435568	+	0.0439142i
$100$	−161.703	−	25.9034i	−1.61703	−	0.259034i
$101$			76.1094i			0.753558i	0.926303	+	0.376779i	$0.122968\pi$
$101$			76.1094i			0.753558i	−0.926303	+	0.376779i	$0.877032\pi$
$102$	113.616	+	58.3094i	1.11388	+	0.571661i
$103$	−38.0358			−0.369280			−0.184640	−	0.982806i	$-0.559112\pi$
$103$	−38.0358			−0.369280			−0.184640	+	0.982806i	$0.559112\pi$
$104$	8.76537	−	36.0898i	0.0842824	−	0.347018i
$105$	84.2606	−	202.253i	0.802482	−	1.92622i
$106$	−104.434	−	8.31170i	−0.985222	−	0.0784123i
$107$		−	182.234i		−	1.70312i	−0.524260	−	0.851558i	$-0.675658\pi$
$107$		−	182.234i		−	1.70312i	0.524260	−	0.851558i	$-0.324342\pi$
$108$	−105.212	+	24.3825i	−0.974182	+	0.225763i
$109$		−	106.882i		−	0.980568i	−0.871563	−	0.490284i	$-0.836893\pi$
$109$		−	106.882i		−	0.980568i	0.871563	−	0.490284i	$-0.163107\pi$
$110$	−0.876662	+	11.0149i	−0.00796965	+	0.100136i
$111$	141.146	+	58.8030i	1.27159	+	0.529756i
$112$	−44.9506	+	136.702i	−0.401344	+	1.22056i
$113$	−18.0796			−0.159996			−0.0799981	−	0.996795i	$-0.525491\pi$
$113$	−18.0796			−0.159996			−0.0799981	+	0.996795i	$0.525491\pi$
$114$	−53.6353	−	100.595i	−0.470485	−	0.882408i
$115$			280.394i			2.43821i
$116$	114.386	+	18.3237i	0.986087	+	0.157963i
$117$	−29.6644	+	29.4229i	−0.253542	+	0.251478i
$118$	8.26490	−	103.846i	0.0700416	−	0.880047i
$119$	−191.428			−1.60864
$120$	−157.131	−	115.291i	−1.30942	−	0.960759i
$121$	−120.537			−0.996174
$122$	−56.9055	−	4.52902i	−0.466438	−	0.0371231i
$123$	47.3389	−	113.629i	0.384869	−	0.923813i
$124$	150.242	+	24.0676i	1.21163	+	0.194093i
$125$			129.448i			1.03558i
$126$	123.624	−	104.527i	0.981139	−	0.829577i
$127$	−3.71414			−0.0292452			−0.0146226	−	0.999893i	$-0.504655\pi$
$127$	−3.71414			−0.0292452			−0.0146226	+	0.999893i	$0.504655\pi$
$128$	108.723	+	67.5517i	0.849401	+	0.527748i
$129$	131.332	+	54.7143i	1.01808	+	0.424142i
$130$	−75.1584	−	5.98174i	−0.578141	−	0.0460134i
$131$	212.845			1.62477			0.812384	−	0.583123i	$-0.198169\pi$
$131$	212.845			1.62477			0.812384	+	0.583123i	$0.198169\pi$
$132$	−4.29237	+	6.94505i	−0.0325180	+	0.0526140i
$133$	140.379	+	97.4445i	1.05548	+	0.732665i
$134$	106.132	+	8.44688i	0.792030	+	0.0630364i
$135$	82.6604	+	203.072i	0.612299	+	1.50424i
$136$	−40.1871	+	165.463i	−0.295493	+	1.21664i
$137$		−	48.0117i		−	0.350450i	−0.984528	−	0.175225i	$-0.943935\pi$
$137$		−	48.0117i		−	0.350450i	0.984528	−	0.175225i	$-0.0560654\pi$
$138$	−94.5959	+	184.320i	−0.685478	+	1.33565i
$139$		−	69.8921i		−	0.502821i	−0.967881	−	0.251410i	$-0.919106\pi$
$139$		−	69.8921i		−	0.502821i	0.967881	−	0.251410i	$-0.0808943\pi$
$140$	288.460	+	46.2088i	2.06043	+	0.330063i
$141$	−17.3061	+	41.5403i	−0.122738	+	0.294612i
$142$	−4.64956	+	58.4201i	−0.0327434	+	0.411409i
$143$			3.15854i			0.0220877i
$144$	−64.3961	−	128.799i	−0.447195	−	0.894436i
$145$		−	235.176i		−	1.62190i
$146$	1.49388	+	0.118895i	0.0102320	+	0.000814352i
$147$	−36.7928	+	88.3147i	−0.250291	+	0.600780i
$148$	−32.2478	+	201.308i	−0.217890	+	1.36019i
$149$		−	175.499i		−	1.17785i	−0.808189	−	0.588923i	$-0.799552\pi$
$149$		−	175.499i		−	1.17785i	0.808189	−	0.588923i	$-0.200448\pi$
$150$	−112.161	+	218.545i	−0.747738	+	1.45697i
$151$	82.5476			0.546673			0.273336	−	0.961919i	$-0.411873\pi$
$151$	82.5476			0.546673			0.273336	+	0.961919i	$0.411873\pi$
$152$	113.697	−	100.881i	0.748008	−	0.663690i
$153$	136.004	−	134.897i	0.888915	−	0.881679i
$154$	0.970965	−	12.1998i	0.00630497	−	0.0792197i
$155$		−	308.896i		−	1.99288i
$156$	−47.3882	−	29.2882i	−0.303771	−	0.187745i
$157$	−19.7480			−0.125784			−0.0628919	−	0.998020i	$-0.520032\pi$
$157$	−19.7480			−0.125784			−0.0628919	+	0.998020i	$0.520032\pi$
$158$	−275.421	−	21.9203i	−1.74317	−	0.138736i
$159$	−60.4336	+	145.061i	−0.380086	+	0.912330i
$160$	100.498	−	239.633i	0.628114	−	1.49770i
$161$		−	310.556i		−	1.92892i
$162$	−14.1722	+	161.379i	−0.0874829	+	0.996166i
$163$		−	206.915i		−	1.26941i	−0.772753	−	0.634707i	$-0.781121\pi$
$163$		−	206.915i		−	1.26941i	0.772753	−	0.634707i	$-0.218879\pi$
$164$	162.061	+	25.9608i	0.988178	+	0.158298i
$165$	15.3000	+	6.37413i	0.0927272	+	0.0386311i
$166$	−184.042	−	14.6476i	−1.10869	−	0.0882388i
$167$			173.787i			1.04064i	0.853971	+	0.520321i	$0.174188\pi$
$167$			173.787i			1.04064i	−0.853971	+	0.520321i	$0.825812\pi$
$168$	174.033	+	127.693i	1.03591	+	0.760078i
$169$	147.448			0.872475
$170$	344.583	+	27.4248i	2.02696	+	0.161322i
$171$	−168.403	+	29.6915i	−0.984810	+	0.173634i
$172$	−30.0055	+	187.310i	−0.174451	+	1.08901i
$173$	−333.994			−1.93060			−0.965301	−	0.261139i	$-0.915902\pi$
$173$	−333.994			−1.93060			−0.965301	+	0.261139i	$0.915902\pi$
$174$	79.3409	−	154.596i	0.455982	−	0.888481i
$175$		−	368.221i		−	2.10412i
$176$	−10.3412	−	3.40041i	−0.0587569	−	0.0193205i
$177$	−144.244	−	60.0934i	−0.814937	−	0.339510i
$178$	−30.3182	−	2.41298i	−0.170327	−	0.0135561i
$179$			49.2676i			0.275238i	0.990485	+	0.137619i	$0.0439449\pi$
$179$			49.2676i			0.275238i	−0.990485	+	0.137619i	$0.956055\pi$
$180$	−237.505	+	170.444i	−1.31947	+	0.946910i
$181$			146.281i			0.808180i	0.914719	+	0.404090i	$0.132412\pi$
$181$			146.281i			0.808180i	−0.914719	+	0.404090i	$0.867588\pi$
$182$	83.2432	+	6.62520i	0.457380	+	0.0364022i
$183$	−32.9301	+	79.0429i	−0.179946	+	0.431929i
$184$	−268.432	−	65.1959i	−1.45887	−	0.354326i
$185$	413.885			2.23722
$186$	104.212	−	203.057i	0.560278	−	1.09170i
$187$		−	14.4811i		−	0.0774391i
$188$	−59.2461	−	9.49073i	−0.315139	−	0.0504826i
$189$	−91.5522	−	224.917i	−0.484403	−	1.19004i
$190$	−238.730	−	195.517i	−1.25647	−	1.02904i
$191$	−189.757			−0.993491			−0.496745	−	0.867896i	$-0.665472\pi$
$191$	−189.757			−0.993491			−0.496745	+	0.867896i	$0.665472\pi$
$192$	146.908	−	123.620i	0.765146	−	0.643856i
$193$		−	276.362i		−	1.43193i	−0.698139	−	0.715963i	$-0.745988\pi$
$193$		−	276.362i		−	1.43193i	0.698139	−	0.715963i	$-0.254012\pi$
$194$	−4.60123	+	57.8129i	−0.0237177	+	0.298004i
$195$	−43.4926	+	104.397i	−0.223039	+	0.535367i
$196$	−125.957	−	20.1773i	−0.642639	−	0.102945i
$197$			172.398i			0.875117i	0.899190	+	0.437558i	$0.144157\pi$
$197$			172.398i			0.875117i	−0.899190	+	0.437558i	$0.855843\pi$
$198$	7.90721	+	9.35184i	0.0399354	+	0.0472315i
$199$		−	140.619i		−	0.706630i	−0.935504	−	0.353315i	$-0.885054\pi$
$199$		−	140.619i		−	0.706630i	0.935504	−	0.353315i	$-0.114946\pi$
$200$	−318.276	−	77.3017i	−1.59138	−	0.386508i
$201$	61.4165	−	147.420i	0.305555	−	0.733432i
$202$	−12.0767	+	151.739i	−0.0597854	+	0.751183i
$203$			260.474i			1.28312i
$204$	217.263	+	134.279i	1.06502	+	0.658231i
$205$		−	333.195i		−	1.62534i
$206$	−75.8319	−	6.03534i	−0.368116	−	0.0292978i
$207$	218.845	+	220.641i	1.05722	+	1.06590i
$208$	23.2020	−	70.5613i	0.111548	−	0.339237i
$209$	−7.37145	+	10.6193i	−0.0352701	+	0.0508101i
$210$	200.083	−	389.861i	0.952774	−	1.85648i
$211$	31.3874			0.148755			0.0743777	−	0.997230i	$-0.476303\pi$
$211$	31.3874			0.148755			0.0743777	+	0.997230i	$0.476303\pi$
$212$	−206.890	−	33.1420i	−0.975896	−	0.156330i
$213$	81.1467	+	33.8065i	0.380971	+	0.158716i
$214$	28.9159	−	363.318i	0.135121	−	1.69775i
$215$	385.107			1.79120
$216$	−213.629	+	31.9167i	−0.989023	+	0.147763i
$217$			342.124i			1.57661i
$218$	16.9595	−	213.090i	0.0777959	−	0.977477i
$219$	0.864477	−	2.07503i	0.00394738	−	0.00947502i
$220$	−3.49559	+	21.8213i	−0.0158891	+	0.0991879i
$221$	98.8091			0.447100
$222$	272.072	+	139.632i	1.22555	+	0.628971i
$223$	127.248			0.570617			0.285309	−	0.958436i	$-0.407904\pi$
$223$	127.248			0.570617			0.285309	+	0.958436i	$0.407904\pi$
$224$	−111.309	+	265.410i	−0.496915	+	1.18487i
$225$	259.480	+	261.610i	1.15325	+	1.16271i
$226$	−36.0451	−	2.86878i	−0.159492	−	0.0126937i
$227$		−	242.362i		−	1.06767i	−0.845587	−	0.533837i	$-0.820750\pi$
$227$		−	242.362i		−	1.06767i	0.845587	−	0.533837i	$-0.179250\pi$
$228$	−90.9706	−	209.065i	−0.398994	−	0.916954i
$229$	12.8227			0.0559942			0.0279971	−	0.999608i	$-0.491087\pi$
$229$	12.8227			0.0559942			0.0279971	+	0.999608i	$0.491087\pi$
$230$	−44.4915	+	559.020i	−0.193441	+	2.43052i
$231$	−16.9458	−	7.05980i	−0.0733586	−	0.0305619i
$232$	225.143	+	54.6820i	0.970446	+	0.235698i
$233$		−	38.3668i		−	0.164664i	−0.996605	−	0.0823321i	$-0.973763\pi$
$233$		−	38.3668i		−	0.164664i	0.996605	−	0.0823321i	$-0.0262368\pi$
$234$	−63.8105	+	53.9534i	−0.272694	+	0.230570i
$235$			121.809i			0.518337i
$236$	32.9554	−	205.725i	0.139642	−	0.871716i
$237$	−159.381	+	382.566i	−0.672493	+	1.61420i
$238$	−381.650	−	30.3749i	−1.60357	−	0.127626i
$239$	−220.694			−0.923405			−0.461703	−	0.887035i	$-0.652761\pi$
$239$	−220.694			−0.923405			−0.461703	+	0.887035i	$0.652761\pi$
$240$	−294.977	−	254.788i	−1.22907	−	1.06162i
$241$			210.725i			0.874379i	0.899369	+	0.437189i	$0.144026\pi$
$241$			210.725i			0.874379i	−0.899369	+	0.437189i	$0.855974\pi$
$242$	−240.314	−	19.1262i	−0.993034	−	0.0790340i
$243$	223.541	+	95.2810i	0.919921	+	0.392103i
$244$	−112.734	−	18.0590i	−0.462023	−	0.0740121i
$245$			258.966i			1.05701i
$246$	112.409	−	219.030i	0.456949	−	0.890366i
$247$	−72.4589	−	50.2977i	−0.293356	−	0.203635i
$248$	295.719	+	71.8231i	1.19241	+	0.289609i
$249$	−106.502	+	255.639i	−0.427718	+	1.02666i
$250$	−20.5402	+	258.080i	−0.0821607	+	1.03232i
$251$	−279.661			−1.11419			−0.557094	−	0.830449i	$-0.688084\pi$
$251$	−279.661			−1.11419			−0.557094	+	0.830449i	$0.688084\pi$
$252$	263.053	−	188.779i	1.04386	−	0.749121i
$253$	23.4929			0.0928572
$254$	−7.40487	−	0.589342i	−0.0291530	−	0.00232024i
$255$	199.403	−	478.633i	0.781973	−	1.87699i
$256$	206.042	+	151.929i	0.804853	+	0.593474i
$257$	−57.9259			−0.225392			−0.112696	−	0.993629i	$-0.535949\pi$
$257$	−57.9259			−0.225392			−0.112696	+	0.993629i	$0.535949\pi$
$258$	253.155	+	129.923i	0.981220	+	0.503577i
$259$	−458.407			−1.76991
$260$	−148.894	−	23.8515i	−0.572668	−	0.0917366i
$261$	−183.553	−	185.059i	−0.703266	−	0.709038i
$262$	424.347	+	33.7731i	1.61965	+	0.128905i
$263$	168.294			0.639901			0.319951	−	0.947434i	$-0.396334\pi$
$263$	168.294			0.639901			0.319951	+	0.947434i	$0.396334\pi$
$264$	−9.65969	+	13.1652i	−0.0365897	+	0.0498683i
$265$			425.363i			1.60514i
$266$	264.410	+	216.549i	0.994023	+	0.814095i
$267$	−17.5445	+	42.1126i	−0.0657099	+	0.157725i
$268$	210.255	+	33.6810i	0.784533	+	0.125675i
$269$	−218.898			−0.813747			−0.406873	−	0.913485i	$-0.633381\pi$
$269$	−218.898			−0.813747			−0.406873	+	0.913485i	$0.633381\pi$
$270$	132.577	+	417.980i	0.491027	+	1.54807i
$271$			248.836i			0.918214i	0.888381	+	0.459107i	$0.151831\pi$
$271$			248.836i			0.918214i	−0.888381	+	0.459107i	$0.848169\pi$
$272$	−106.376	+	323.506i	−0.391087	+	1.18936i
$273$	48.1712	−	115.627i	0.176451	−	0.423541i
$274$	7.61826	−	95.7207i	0.0278039	−	0.349346i
$275$	27.8551			0.101291
$276$	−217.843	+	352.469i	−0.789285	+	1.27706i
$277$	−329.910			−1.19101			−0.595505	−	0.803351i	$-0.703048\pi$
$277$	−329.910			−1.19101			−0.595505	+	0.803351i	$0.703048\pi$
$278$	11.0901	−	139.344i	0.0398925	−	0.501236i
$279$	−241.090	−	243.069i	−0.864123	−	0.871215i
$280$	567.769	+	137.898i	2.02775	+	0.492492i
$281$	424.452			1.51050			0.755252	−	0.655434i	$-0.227514\pi$
$281$	424.452			1.51050			0.755252	+	0.655434i	$0.227514\pi$
$282$	−41.0945	+	80.0727i	−0.145725	+	0.283946i
$283$			26.3488i			0.0931052i	0.998916	+	0.0465526i	$0.0148235\pi$
$283$			26.3488i			0.0931052i	−0.998916	+	0.0465526i	$0.985176\pi$
$284$	−18.5396	+	115.734i	−0.0652803	+	0.407514i
$285$	−389.870	+	249.488i	−1.36796	+	0.875397i
$286$	−0.501181	+	6.29716i	−0.00175238	+	0.0220180i
$287$			369.038i			1.28585i
$288$	−107.949	−	267.004i	−0.374823	−	0.927096i
$289$	−164.016			−0.567528
$290$	37.3166	−	468.869i	0.128678	−	1.61679i
$291$	80.3033	+	33.4551i	0.275956	+	0.114966i
$292$	2.95947	+	0.474082i	0.0101352	+	0.00162357i
$293$	−337.650			−1.15239			−0.576194	−	0.817313i	$-0.695463\pi$
$293$	−337.650			−1.15239			−0.576194	+	0.817313i	$0.695463\pi$
$294$	−87.3669	+	170.235i	−0.297166	+	0.579029i
$295$	−422.968			−1.43379
$296$	−96.2347	+	396.229i	−0.325117	+	1.33861i
$297$	17.0144	−	6.92572i	0.0572877	−	0.0233189i
$298$	27.8473	−	349.892i	0.0934474	−	1.17413i
$299$			160.299i			0.536118i
$300$	−258.292	+	417.916i	−0.860974	+	1.39305i
$301$	−426.533			−1.41705
$302$	164.575	+	13.0982i	0.544949	+	0.0433717i
$303$	210.769	+	87.8083i	0.695606	+	0.289796i
$304$	242.685	−	183.085i	0.798305	−	0.602253i
$305$			231.778i			0.759929i
$306$	292.555	−	247.363i	0.956063	−	0.808375i
$307$	408.402			1.33030			0.665149	−	0.746711i	$-0.268368\pi$
$307$	408.402			1.33030			0.665149	+	0.746711i	$0.268368\pi$
$308$	3.87162	−	24.1687i	0.0125702	−	0.0784697i
$309$	−43.8824	+	105.332i	−0.142014	+	0.340881i
$310$	49.0141	−	615.845i	0.158110	−	1.98660i
$311$	123.463			0.396987			0.198494	−	0.980102i	$-0.436395\pi$
$311$	123.463			0.396987			0.198494	+	0.980102i	$0.436395\pi$
$312$	−89.8304	−	65.9111i	−0.287918	−	0.211253i
$313$	−62.2650			−0.198930			−0.0994649	−	0.995041i	$-0.531713\pi$
$313$	−62.2650			−0.198930			−0.0994649	+	0.995041i	$0.531713\pi$
$314$	−39.3716	−	3.13352i	−0.125387	−	0.00997937i
$315$	−462.885	−	466.684i	−1.46948	−	1.48154i
$316$	−545.628	−	87.4050i	−1.72667	−	0.276598i
$317$	−149.638			−0.472045			−0.236023	−	0.971748i	$-0.575844\pi$
$317$	−149.638			−0.472045			−0.236023	+	0.971748i	$0.575844\pi$
$318$	−143.504	+	279.617i	−0.451270	+	0.879299i
$319$	−19.7043			−0.0617689
$320$	238.387	−	461.808i	0.744958	−	1.44315i
$321$	−504.657	−	210.245i	−1.57214	−	0.654969i
$322$	49.2775	−	619.155i	0.153036	−	1.92284i
$323$	332.206	+	230.603i	1.02850	+	0.713940i
$324$	−53.8619	+	319.492i	−0.166241	+	0.986085i
$325$			190.064i			0.584812i
$326$	32.8322	−	412.525i	0.100712	−	1.26541i
$327$	−295.987	−	123.311i	−0.905158	−	0.377098i
$328$	318.981	+	77.4731i	0.972504	+	0.236198i
$329$		−	134.912i		−	0.410068i
$330$	29.4921	+	15.1358i	0.0893701	+	0.0458660i
$331$	−24.6170			−0.0743716			−0.0371858	−	0.999308i	$-0.511839\pi$
$331$	−24.6170			−0.0743716			−0.0371858	+	0.999308i	$0.511839\pi$
$332$	−364.600	−	58.4059i	−1.09819	−	0.175921i
$333$	325.685	−	323.033i	0.978032	−	0.970070i
$334$	−27.5757	+	346.479i	−0.0825619	+	1.03736i
$335$		−	432.281i		−	1.29039i
$336$	326.708	+	282.196i	0.972344	+	0.839869i
$337$		−	68.9147i		−	0.204495i	−0.994759	−	0.102247i	$-0.967397\pi$
$337$		−	68.9147i		−	0.204495i	0.994759	−	0.102247i	$-0.0326033\pi$
$338$	293.967	+	23.3964i	0.869725	+	0.0692200i
$339$	−20.8586	+	50.0675i	−0.0615298	+	0.147692i
$340$	682.641	+	109.353i	2.00777	+	0.321627i
$341$	−25.8809			−0.0758972
$342$	−340.455	+	32.4745i	−0.995482	+	0.0949546i
$343$			153.879i			0.448627i
$344$	−89.5433	+	368.679i	−0.260300	+	1.07174i
$345$	776.491	+	323.494i	2.25070	+	0.937663i
$346$	−665.883	−	52.9965i	−1.92452	−	0.153169i
$347$	239.321			0.689685			0.344842	−	0.938661i	$-0.387932\pi$
$347$	239.321			0.689685			0.344842	+	0.938661i	$0.387932\pi$
$348$	182.712	−	295.628i	0.525035	−	0.849504i
$349$	503.363			1.44230			0.721150	−	0.692779i	$-0.243614\pi$
$349$	503.363			1.44230			0.721150	+	0.692779i	$0.243614\pi$
$350$	58.4275	−	734.121i	0.166936	−	2.09749i
$351$	47.2563	+	116.095i	0.134633	+	0.330755i
$352$	−20.0777	−	8.42027i	−0.0570388	−	0.0239212i
$353$			208.927i			0.591860i	0.955210	+	0.295930i	$0.0956296\pi$
$353$			208.927i			0.591860i	−0.955210	+	0.295930i	$0.904370\pi$
$354$	−278.043	−	142.696i	−0.785432	−	0.403095i
$355$	237.947			0.670275
$356$	−60.0624	−	9.62149i	−0.168715	−	0.0270266i
$357$	−220.853	+	530.120i	−0.618636	+	1.48493i
$358$	−7.81754	+	98.2246i	−0.0218367	+	0.274370i
$359$	−222.794			−0.620595			−0.310298	−	0.950639i	$-0.600429\pi$
$359$	−222.794			−0.620595			−0.310298	+	0.950639i	$0.600429\pi$
$360$	−500.558	+	302.127i	−1.39044	+	0.839241i
$361$	−126.228	−	338.212i	−0.349663	−	0.936875i
$362$	−23.2111	+	291.639i	−0.0641190	+	0.805633i
$363$	−139.065	+	333.802i	−0.383099	+	0.919564i
$364$	164.910	+	26.4173i	0.453051	+	0.0725749i
$365$		−	6.08463i		−	0.0166702i
$366$	−78.1947	+	152.362i	−0.213647	+	0.416291i
$367$			537.119i			1.46354i	0.681551	+	0.731770i	$0.261306\pi$
$367$			537.119i			1.46354i	−0.681551	+	0.731770i	$0.738694\pi$
$368$	−524.828	−	172.574i	−1.42616	−	0.468952i
$369$	−260.056	−	262.190i	−0.704758	−	0.710542i
$370$	825.161	+	65.6733i	2.23017	+	0.177495i
$371$		−	471.119i		−	1.26986i
$372$	239.986	−	388.297i	0.645125	−	1.04381i
$373$			547.260i			1.46719i	0.679589	+	0.733593i	$0.262158\pi$
$373$			547.260i			1.46719i	−0.679589	+	0.733593i	$0.737842\pi$
$374$	2.29779	−	28.8709i	0.00614383	−	0.0771950i
$375$	358.479	+	149.346i	0.955943	+	0.398255i
$376$	−116.613	−	28.3225i	−0.310140	−	0.0753258i
$377$		−	134.448i		−	0.356627i
$378$	−146.839	−	462.943i	−0.388462	−	1.22472i
$379$	−107.913			−0.284730			−0.142365	−	0.989814i	$-0.545471\pi$
$379$	−107.913			−0.284730			−0.142365	+	0.989814i	$0.545471\pi$
$380$	−444.931	−	427.682i	−1.17087	−	1.12548i
$381$	−4.28505	+	10.2855i	−0.0112469	+	0.0269961i
$382$	−378.317	−	30.1097i	−0.990359	−	0.0788211i
$383$		−	273.050i		−	0.712925i	−0.934310	−	0.356463i	$-0.883983\pi$
$383$		−	273.050i		−	0.712925i	0.934310	−	0.356463i	$-0.116017\pi$
$384$	312.506	−	223.151i	0.813816	−	0.581122i
$385$	−49.6904			−0.129066
$386$	43.8517	−	550.981i	0.113605	−	1.42741i
$387$	303.039	−	300.572i	0.783047	−	0.776673i
$388$	−18.3469	+	114.531i	−0.0472859	+	0.295183i
$389$			264.532i			0.680032i	0.940420	+	0.340016i	$0.110432\pi$
$389$			264.532i			0.680032i	−0.940420	+	0.340016i	$0.889568\pi$
$390$	−103.276	+	201.234i	−0.264811	+	0.515984i
$391$		−	734.932i		−	1.87962i
$392$	−247.919	−	60.2136i	−0.632446	−	0.153606i
$393$	245.561	−	589.428i	0.624838	−	1.49982i
$394$	−27.3553	+	343.709i	−0.0694296	+	0.872358i
$395$			1121.80i			2.84001i
$396$	14.2807	+	19.8994i	0.0360623	+	0.0502510i
$397$	107.465			0.270691			0.135346	−	0.990798i	$-0.456785\pi$
$397$	107.465			0.270691			0.135346	+	0.990798i	$0.456785\pi$
$398$	22.3128	−	280.352i	0.0560623	−	0.704403i
$399$	431.808	−	276.326i	1.08223	−	0.692546i
$400$	−622.279	−	204.618i	−1.55570	−	0.511546i
$401$	506.614			1.26338			0.631688	−	0.775223i	$-0.282362\pi$
$401$	506.614			1.26338			0.631688	+	0.775223i	$0.282362\pi$
$402$	145.838	−	284.165i	0.362780	−	0.706878i
$403$		−	176.594i		−	0.438198i
$404$	−48.1544	+	300.605i	−0.119194	+	0.744072i
$405$	657.731	+	5.37636i	1.62403	+	0.0132750i
$406$	−41.3307	+	519.306i	−0.101800	+	1.27908i
$407$		−	34.6775i		−	0.0852026i
$408$	411.850	+	302.186i	1.00944	+	0.740652i
$409$		−	98.7589i		−	0.241464i	−0.992685	−	0.120732i	$-0.961476\pi$
$409$		−	98.7589i		−	0.241464i	0.992685	−	0.120732i	$-0.0385242\pi$
$410$	52.8698	−	664.290i	0.128951	−	1.62022i
$411$	−132.958	−	55.3917i	−0.323499	−	0.134773i
$412$	−150.228	−	24.0653i	−0.364631	−	0.0584108i
$413$	468.467			1.13430
$414$	401.299	+	474.616i	0.969322	+	1.14642i
$415$			749.613i			1.80630i
$416$	57.4541	−	136.996i	0.138111	−	0.329318i
$417$	−193.551	−	80.6353i	−0.464151	−	0.193370i
$418$	−16.3815	+	20.0020i	−0.0391901	+	0.0478517i
$419$	572.504			1.36636			0.683180	−	0.730250i	$-0.260597\pi$
$419$	572.504			1.36636			0.683180	+	0.730250i	$0.260597\pi$
$420$	460.765	−	745.517i	1.09706	−	1.77504i
$421$		−	580.868i		−	1.37973i	−0.723936	−	0.689867i	$-0.757669\pi$
$421$		−	580.868i		−	1.37973i	0.723936	−	0.689867i	$-0.242331\pi$
$422$	62.5769	+	4.98040i	0.148286	+	0.0118019i
$423$	95.0708	+	95.8511i	0.224754	+	0.226598i
$424$	−407.217	−	98.9033i	−0.960417	−	0.233263i
$425$		−	871.396i		−	2.05034i
$426$	156.418	+	80.2759i	0.367178	+	0.188441i
$427$		−	256.711i		−	0.601197i
$428$	115.299	−	719.758i	0.269390	−	1.68168i
$429$	8.74689	+	3.64404i	0.0203890	+	0.00849427i
$430$	767.786	+	61.1069i	1.78555	+	0.142109i
$431$			578.264i			1.34168i	0.741603	+	0.670839i	$0.234066\pi$
$431$			578.264i			1.34168i	−0.741603	+	0.670839i	$0.765934\pi$
$432$	−430.975	+	29.7346i	−0.997628	+	0.0688302i
$433$		−	799.529i		−	1.84649i	−0.384214	−	0.923244i	$-0.625528\pi$
$433$		−	799.529i		−	1.84649i	0.384214	−	0.923244i	$-0.374472\pi$
$434$	−54.2866	+	682.092i	−0.125084	+	1.57164i
$435$	−651.270	−	271.325i	−1.49717	−	0.623736i
$436$	67.6241	−	422.146i	0.155101	−	0.968224i
$437$	−374.109	+	538.942i	−0.856085	+	1.23328i
$438$	2.05276	−	3.99980i	0.00468666	−	0.00913197i
$439$	695.464			1.58420			0.792100	−	0.610391i	$-0.208988\pi$
$439$	695.464			1.58420			0.792100	+	0.610391i	$0.208988\pi$
$440$	−10.4317	+	42.9504i	−0.0237083	+	0.0976146i
$441$	202.121	+	203.779i	0.458323	+	0.462085i
$442$	196.995	+	15.6785i	0.445691	+	0.0354718i
$443$	−438.140			−0.989029			−0.494514	−	0.869169i	$-0.664654\pi$
$443$	−438.140			−0.989029			−0.494514	+	0.869169i	$0.664654\pi$
$444$	520.274	+	321.554i	1.17179	+	0.724221i
$445$			123.487i			0.277500i
$446$	253.693	+	20.1910i	0.568819	+	0.0452714i
$447$	−486.007	−	202.475i	−1.08726	−	0.452965i
$448$	−264.030	+	511.485i	−0.589353	+	1.14171i
$449$	163.984			0.365221			0.182611	−	0.983185i	$-0.441545\pi$
$449$	163.984			0.365221			0.182611	+	0.983185i	$0.441545\pi$
$450$	475.814	+	562.744i	1.05736	+	1.25054i
$451$	−27.9168			−0.0618999
$452$	−71.4078	−	11.4389i	−0.157982	−	0.0253074i
$453$	95.2361	−	228.598i	0.210234	−	0.504631i
$454$	38.4568	−	483.196i	0.0847066	−	1.06431i
$455$		−	339.053i		−	0.745172i
$456$	−148.194	−	431.248i	−0.324987	−	0.945718i
$457$	−502.783			−1.10018			−0.550091	−	0.835105i	$-0.685407\pi$
$457$	−502.783			−1.10018			−0.550091	+	0.835105i	$0.685407\pi$
$458$	25.5645	+	2.03464i	0.0558177	+	0.00444244i
$459$	−216.659	−	532.266i	−0.472023	−	1.15962i
$460$	−177.405	+	1107.46i	−0.385663	+	2.40751i
$461$		−	528.229i		−	1.14583i	−0.819614	−	0.572917i	$-0.805812\pi$
$461$		−	528.229i		−	1.14583i	0.819614	−	0.572917i	$-0.194188\pi$
$462$	−32.6646	−	16.7640i	−0.0707026	−	0.0362856i
$463$		−	765.064i		−	1.65241i	−0.563373	−	0.826203i	$-0.690496\pi$
$463$		−	765.064i		−	1.65241i	0.563373	−	0.826203i	$-0.309504\pi$
$464$	440.191	+	144.744i	0.948687	+	0.311948i
$465$	−855.422	−	356.377i	−1.83962	−	0.766402i
$466$	6.08785	−	76.4916i	0.0130640	−	0.164145i
$467$	−32.3426			−0.0692560			−0.0346280	−	0.999400i	$-0.511025\pi$
$467$	−32.3426			−0.0692560			−0.0346280	+	0.999400i	$0.511025\pi$
$468$	−135.780	+	97.4414i	−0.290128	+	0.208208i
$469$			478.781i			1.02086i
$470$	−19.3281	+	242.850i	−0.0411236	+	0.516703i
$471$	−22.7835	+	54.6880i	−0.0483727	+	0.116110i
$472$	98.3465	−	404.924i	0.208361	−	0.857890i
$473$		−	32.2663i		−	0.0682163i
$474$	−378.461	+	737.431i	−0.798440	+	1.55576i
$475$	−443.575	+	639.014i	−0.933842	+	1.34529i
$476$	−756.074	−	121.117i	−1.58839	−	0.254447i
$477$	331.991	+	334.716i	0.695998	+	0.701711i
$478$	−439.996	−	35.0186i	−0.920494	−	0.0732607i
$479$	363.197			0.758240			0.379120	−	0.925347i	$-0.376227\pi$
$479$	363.197			0.758240			0.379120	+	0.925347i	$0.376227\pi$
$480$	−547.665	−	554.775i	−1.14097	−	1.15578i
$481$	236.615			0.491923
$482$	−33.4369	+	420.122i	−0.0693711	+	0.871623i
$483$	−860.019	−	358.292i	−1.78058	−	0.741806i
$484$	−476.079	−	76.2638i	−0.983634	−	0.157570i
$485$	235.474			0.485514
$486$	430.554	+	225.432i	0.885913	+	0.463851i
$487$	538.760			1.10628			0.553142	−	0.833087i	$-0.313429\pi$
$487$	538.760			1.10628			0.553142	+	0.833087i	$0.313429\pi$
$488$	−221.891	−	53.8921i	−0.454694	−	0.110435i
$489$	−573.006	−	238.720i	−1.17179	−	0.488179i
$490$	−41.0915	+	516.300i	−0.0838602	+	1.05367i
$491$	−499.978			−1.01828			−0.509142	−	0.860682i	$-0.670037\pi$
$491$	−499.978			−1.01828			−0.509142	+	0.860682i	$0.670037\pi$
$492$	258.865	−	418.843i	0.526148	−	0.851306i
$493$			616.413i			1.25033i
$494$	−136.480	−	111.776i	−0.276275	−	0.226267i
$495$	35.3036	−	35.0162i	0.0713203	−	0.0707397i
$496$	578.177	+	190.117i	1.16568	+	0.383300i
$497$	−263.544			−0.530269
$498$	−252.895	+	492.767i	−0.507822	+	0.989492i
$499$			471.587i			0.945065i	0.881313	+	0.472532i	$0.156660\pi$
$499$			471.587i			0.945065i	−0.881313	+	0.472532i	$0.843340\pi$
$500$	−81.9017	+	511.273i	−0.163803	+	1.02255i
$501$	481.266	+	200.500i	0.960611	+	0.400200i
$502$	−557.559	−	44.3753i	−1.11068	−	0.0883969i
$503$	−348.496			−0.692835			−0.346418	−	0.938080i	$-0.612602\pi$
$503$	−348.496			−0.692835			−0.346418	+	0.938080i	$0.612602\pi$
$504$	554.403	−	334.627i	1.10001	−	0.663942i
$505$	618.039			1.22384
$506$	46.8376	+	3.72773i	0.0925645	+	0.00736706i
$507$	170.113	−	408.327i	0.335528	−	0.805378i
$508$	−14.6695	−	2.34994i	−0.0288771	−	0.00462586i
$509$	−306.802			−0.602755			−0.301378	−	0.953505i	$-0.597446\pi$
$509$	−306.802			−0.602755			−0.301378	+	0.953505i	$0.597446\pi$
$510$	473.496	−	922.608i	0.928424	−	1.80903i
$511$			6.73916i			0.0131882i
$512$	386.679	+	335.595i	0.755232	+	0.655458i
$513$	−112.064	+	500.610i	−0.218448	+	0.975849i
$514$	−115.487	−	9.19139i	−0.224682	−	0.0178821i
$515$			308.867i			0.599741i
$516$	484.098	+	299.196i	0.938175	+	0.579837i
$517$	10.2058			0.0197404
$518$	−913.925	−	72.7378i	−1.76433	−	0.140420i
$519$	−385.333	+	924.926i	−0.742453	+	1.78213i
$520$	−293.064	−	71.1784i	−0.563585	−	0.136882i
$521$	469.207			0.900589			0.450295	−	0.892880i	$-0.351319\pi$
$521$	469.207			0.900589			0.450295	+	0.892880i	$0.351319\pi$
$522$	−336.584	−	398.077i	−0.644796	−	0.762599i
$523$	961.414			1.83827			0.919134	−	0.393945i	$-0.128890\pi$
$523$	961.414			1.83827			0.919134	+	0.393945i	$0.128890\pi$
$524$	840.660	+	134.667i	1.60431	+	0.256997i
$525$	−1019.71	−	424.821i	−1.94230	−	0.809183i
$526$	335.527	+	26.7041i	0.637884	+	0.0507682i
$527$			809.638i			1.53632i
$528$	−21.3475	+	24.7147i	−0.0404308	+	0.0468081i
$529$	663.288			1.25385
$530$	−67.4944	+	848.043i	−0.127348	+	1.60008i
$531$	−332.831	+	330.122i	−0.626801	+	0.621699i
$532$	492.792	+	473.689i	0.926301	+	0.890392i
$533$		−	190.485i		−	0.357383i
$534$	−41.6607	+	81.1759i	−0.0780163	+	0.152015i
$535$	−1479.81			−2.76600
$536$	413.840	+	100.512i	0.772089	+	0.187522i
$537$	136.436	+	56.8406i	0.254071	+	0.105848i
$538$	−436.416	−	34.7336i	−0.811182	−	0.0645607i
$539$	21.6975			0.0402552
$540$	197.996	+	854.362i	0.366658	+	1.58215i
$541$	248.736			0.459771			0.229885	−	0.973218i	$-0.426165\pi$
$541$	248.736			0.459771			0.229885	+	0.973218i	$0.426165\pi$
$542$	−39.4841	+	496.103i	−0.0728489	+	0.915320i
$543$	405.093	+	168.766i	0.746028	+	0.310802i
$544$	−263.413	+	628.094i	−0.484215	+	1.15458i
$545$	−867.925			−1.59252
$546$	114.386	−	222.881i	0.209498	−	0.408207i
$547$	843.146			1.54140			0.770700	−	0.637198i	$-0.219907\pi$
$547$	843.146			1.54140			0.770700	+	0.637198i	$0.219907\pi$
$548$	30.3770	−	189.629i	0.0554324	−	0.346039i
$549$	180.901	+	182.386i	0.329510	+	0.332214i
$550$	55.5346	+	4.41991i	0.100972	+	0.00803620i
$551$	313.778	−	452.029i	0.569470	−	0.820379i
$552$	−490.240	+	668.149i	−0.888116	+	1.21041i
$553$		−	1242.48i		−	2.24679i
$554$	−657.740	−	52.3485i	−1.18726	−	0.0944919i
$555$	477.504	−	1146.17i	0.860368	−	2.06517i
$556$	44.2207	−	276.049i	0.0795336	−	0.496491i
$557$		−	20.5199i		−	0.0368400i	−0.999830	−	0.0184200i	$-0.994136\pi$
$557$		−	20.5199i		−	0.0368400i	0.999830	−	0.0184200i	$-0.00586360\pi$
$558$	−442.092	−	522.861i	−0.792279	−	0.937027i
$559$	220.163			0.393851
$560$	1110.08	+	365.017i	1.98228	+	0.651816i
$561$	−40.1024	−	16.7070i	−0.0714837	−	0.0297808i
$562$	846.228	+	67.3499i	1.50574	+	0.119840i
$563$		−	540.888i		−	0.960724i	−0.877070	−	0.480362i	$-0.840505\pi$
$563$		−	540.888i		−	0.960724i	0.877070	−	0.480362i	$-0.159495\pi$
$564$	−94.6355	+	153.120i	−0.167793	+	0.271489i
$565$			146.813i			0.259847i
$566$	−4.18089	+	52.5314i	−0.00738674	+	0.0928117i
$567$	−728.484	−	5.95470i	−1.28480	−	0.0105021i
$568$	−55.3265	+	227.797i	−0.0974057	+	0.401050i
$569$	−352.384			−0.619305			−0.309652	−	0.950850i	$-0.600213\pi$
$569$	−352.384			−0.619305			−0.309652	+	0.950850i	$0.600213\pi$
$570$	−816.869	+	435.541i	−1.43310	+	0.764106i
$571$		−	727.290i		−	1.27371i	−0.770982	−	0.636857i	$-0.780234\pi$
$571$		−	727.290i		−	1.27371i	0.770982	−	0.636857i	$-0.219766\pi$
$572$	−1.99840	+	12.4751i	−0.00349371	+	0.0218096i
$573$	−218.925	+	525.491i	−0.382067	+	0.917087i
$574$	−58.5571	+	735.749i	−0.102016	+	1.28179i
$575$	1413.68			2.45857
$576$	−172.851	−	549.453i	−0.300088	−	0.953911i
$577$	−366.980			−0.636014			−0.318007	−	0.948088i	$-0.603014\pi$
$577$	−366.980			−0.636014			−0.318007	+	0.948088i	$0.603014\pi$
$578$	−326.997	−	26.0252i	−0.565739	−	0.0450263i
$579$	−765.324	−	318.842i	−1.32180	−	0.550676i
$580$	148.796	−	928.862i	0.256544	−	1.60149i
$581$		−	830.250i		−	1.42900i
$582$	154.792	+	79.4415i	0.265965	+	0.136497i
$583$	35.6391			0.0611305
$584$	5.82506	+	1.41477i	0.00997442	+	0.00242255i
$585$	238.926	+	240.887i	0.408421	+	0.411773i
$586$	−673.171	−	53.5766i	−1.14876	−	0.0914276i
$587$	−118.215			−0.201388			−0.100694	−	0.994917i	$-0.532106\pi$
$587$	−118.215			−0.201388			−0.100694	+	0.994917i	$0.532106\pi$
$588$	−201.195	+	325.533i	−0.342168	+	0.553628i
$589$	412.138	−	593.726i	0.699724	−	1.00802i
$590$	−843.269	−	67.1144i	−1.42927	−	0.113753i
$591$	477.420	+	198.898i	0.807817	+	0.336544i
$592$	−254.734	+	774.690i	−0.430294	+	1.30860i
$593$			133.760i			0.225565i	0.993620	+	0.112783i	$0.0359764\pi$
$593$			133.760i			0.225565i	−0.993620	+	0.112783i	$0.964024\pi$
$594$	35.0206	−	11.1080i	0.0589572	−	0.0187004i
$595$			1554.48i			2.61256i
$596$	111.038	−	693.159i	0.186306	−	1.16302i
$597$	−389.416	−	162.234i	−0.652287	−	0.271749i
$598$	−25.4355	+	319.588i	−0.0425342	+	0.534428i
$599$			658.901i			1.10000i	0.835164	+	0.550001i	$0.185373\pi$
$599$			658.901i			1.10000i	−0.835164	+	0.550001i	$0.814627\pi$
$600$	−581.269	+	792.213i	−0.968781	+	1.32035i
$601$		−	167.405i		−	0.278543i	−0.990254	−	0.139272i	$-0.955524\pi$
$601$		−	167.405i		−	0.278543i	0.990254	−	0.139272i	$-0.0444761\pi$
$602$	−850.378	−	67.6802i	−1.41259	−	0.112426i
$603$	−337.391	−	340.160i	−0.559520	−	0.564113i
$604$	326.034	+	52.2278i	0.539791	+	0.0864699i
$605$			978.811i			1.61787i
$606$	406.276	+	208.507i	0.670422	+	0.344070i
$607$	−355.550			−0.585750			−0.292875	−	0.956151i	$-0.594612\pi$
$607$	−355.550			−0.585750			−0.292875	+	0.956151i	$0.594612\pi$
$608$	512.891	−	326.507i	0.843570	−	0.537019i
$609$	721.327	+	300.512i	1.18445	+	0.493452i
$610$	−36.7775	+	462.096i	−0.0602909	+	0.757534i
$611$			69.6374i			0.113973i
$612$	622.517	−	446.745i	1.01718	−	0.729975i
$613$	990.431			1.61571			0.807856	−	0.589380i	$-0.200628\pi$
$613$	990.431			1.61571			0.807856	+	0.589380i	$0.200628\pi$
$614$	814.228	+	64.8031i	1.32610	+	0.105543i
$615$	−922.714	−	384.411i	−1.50035	−	0.625059i
$616$	11.5538	−	47.5707i	0.0187562	−	0.0772251i
$617$			834.131i			1.35191i	0.736941	+	0.675957i	$0.236270\pi$
$617$			834.131i			1.35191i	−0.736941	+	0.675957i	$0.763730\pi$
$618$	−104.202	+	203.037i	−0.168611	+	0.328539i
$619$			17.8849i			0.0288932i	0.999896	+	0.0144466i	$0.00459866\pi$
$619$			17.8849i			0.0288932i	−0.999896	+	0.0144466i	$0.995401\pi$
$620$	195.438	−	1220.03i	0.315223	−	1.96779i
$621$	863.501	−	351.488i	1.39050	−	0.566003i
$622$	246.148	+	19.5905i	0.395736	+	0.0314960i
$623$		−	136.771i		−	0.219536i
$624$	−168.636	−	145.660i	−0.270250	−	0.233430i
$625$	27.6440			0.0442304
$626$	−124.138	−	9.87991i	−0.198303	−	0.0157826i
$627$	20.9034	+	32.6653i	0.0333388	+	0.0520978i
$628$	−77.9977	−	12.4946i	−0.124200	−	0.0198958i
$629$	−1084.82			−1.72468
$630$	−848.800	−	1003.87i	−1.34730	−	1.59345i
$631$		−	377.774i		−	0.598691i	−0.954145	−	0.299345i	$-0.903232\pi$
$631$		−	377.774i		−	0.598691i	0.954145	−	0.299345i	$-0.0967683\pi$
$632$	−1073.95	−	260.837i	−1.69928	−	0.412716i
$633$	36.2120	−	86.9207i	0.0572069	−	0.137315i
$634$	−298.333	−	23.7439i	−0.470557	−	0.0374509i
$635$			30.1604i			0.0474966i
$636$	−330.471	+	534.701i	−0.519609	+	0.840725i
$637$			148.049i			0.232416i
$638$	−39.2843	−	3.12658i	−0.0615742	−	0.00490059i
$639$	187.240	−	185.716i	0.293020	−	0.290635i
$640$	548.548	−	882.878i	0.857106	−	1.37950i
$641$	554.614			0.865232			0.432616	−	0.901578i	$-0.357591\pi$
$641$	554.614			0.865232			0.432616	+	0.901578i	$0.357591\pi$
$642$	−972.772	−	499.241i	−1.51522	−	0.777634i
$643$			774.247i			1.20412i	0.798452	+	0.602058i	$0.205652\pi$
$643$			774.247i			1.20412i	−0.798452	+	0.602058i	$0.794348\pi$
$644$	196.489	−	1226.59i	0.305107	−	1.90464i
$645$	444.303	−	1066.47i	0.688841	−	1.65345i
$646$	625.727	+	512.464i	0.968618	+	0.793288i
$647$	780.259			1.20596			0.602982	−	0.797755i	$-0.293979\pi$
$647$	780.259			1.20596			0.602982	+	0.797755i	$0.293979\pi$
$648$	−158.080	+	628.422i	−0.243950	+	0.969788i
$649$			35.4384i			0.0546047i
$650$	−30.1584	+	378.930i	−0.0463975	+	0.582969i
$651$	947.441	+	394.713i	1.45536	+	0.606318i
$652$	130.915	−	817.239i	0.200789	−	1.25343i
$653$			710.610i			1.08822i	0.839013	+	0.544112i	$0.183133\pi$
$653$			710.610i			1.08822i	−0.839013	+	0.544112i	$0.816867\pi$
$654$	−570.541	−	292.810i	−0.872387	−	0.447722i
$655$		−	1728.39i		−	2.63876i
$656$	623.659	+	205.072i	0.950699	+	0.312610i
$657$	−4.74899	−	4.78797i	−0.00722830	−	0.00728762i
$658$	21.4072	−	268.974i	0.0325338	−	0.408775i
$659$			288.511i			0.437801i	0.975747	+	0.218901i	$0.0702470\pi$
$659$			288.511i			0.437801i	−0.975747	+	0.218901i	$0.929753\pi$
$660$	56.3966	+	34.8558i	0.0854494	+	0.0528119i
$661$			511.393i			0.773666i	0.922150	+	0.386833i	$0.126431\pi$
$661$			511.393i			0.773666i	−0.922150	+	0.386833i	$0.873569\pi$
$662$	−49.0788	−	3.90610i	−0.0741371	−	0.00590046i
$663$	113.997	−	273.631i	0.171942	−	0.412716i
$664$	−717.635	−	174.297i	−1.08078	−	0.262495i
$665$	791.289	−	1139.93i	1.18991	−	1.71418i
$666$	700.573	−	592.352i	1.05191	−	0.889417i
$667$	−1000.01			−1.49927
$668$	−109.955	+	686.397i	−0.164603	+	1.02754i
$669$	146.807	−	352.385i	0.219443	−	0.526734i
$670$	68.5922	−	861.836i	0.102376	−	1.28632i
$671$	19.4196			0.0289413
$672$	606.578	+	614.453i	0.902646	+	0.914365i
$673$			382.837i			0.568852i	0.958698	+	0.284426i	$0.0918029\pi$
$673$			382.837i			0.568852i	−0.958698	+	0.284426i	$0.908197\pi$
$674$	10.9350	−	137.395i	0.0162241	−	0.203850i
$675$	1023.84	−	416.753i	1.51680	−	0.617412i
$676$	582.368	+	93.2905i	0.861492	+	0.138004i
$677$	816.986			1.20677			0.603387	−	0.797448i	$-0.293817\pi$
$677$	816.986			1.20677			0.603387	+	0.797448i	$0.293817\pi$
$678$	−49.5302	+	96.5096i	−0.0730533	+	0.142345i
$679$	−260.805			−0.384101
$680$	1343.63	+	326.335i	1.97592	+	0.479905i
$681$	−671.170	−	279.616i	−0.985565	−	0.410596i
$682$	−51.5987	−	4.10666i	−0.0756579	−	0.00602149i
$683$			1079.12i			1.57997i	0.613125	+	0.789986i	$0.289912\pi$
$683$			1079.12i			1.57997i	−0.613125	+	0.789986i	$0.710088\pi$
$684$	−683.916	+	10.7225i	−0.999877	+	0.0156762i
$685$	−389.875			−0.569160
$686$	−24.4168	+	306.788i	−0.0355930	+	0.447213i
$687$	14.7937	−	35.5097i	0.0215337	−	0.0516880i
$688$	−237.022	+	720.825i	−0.344509	+	1.04771i
$689$			243.177i			0.352941i
$690$	1496.76	+	768.158i	2.16921	+	1.11327i
$691$		−	443.085i		−	0.641223i	−0.947211	−	0.320611i	$-0.896112\pi$
$691$		−	443.085i		−	0.641223i	0.947211	−	0.320611i	$-0.103888\pi$
$692$	−1319.16	−	211.318i	−1.90630	−	0.305373i
$693$	−39.1012	+	38.7829i	−0.0564231	+	0.0559638i
$694$	477.132	+	37.9742i	0.687511	+	0.0547179i
$695$	−567.552			−0.816622
$696$	411.181	−	560.399i	0.590777	−	0.805172i
$697$			873.328i			1.25298i
$698$	1003.55	+	79.8711i	1.43775	+	0.114429i
$699$	−106.249	−	44.2642i	−0.152001	−	0.0633250i
$700$	232.973	−	1454.34i	0.332819	−	2.07763i
$701$		−	746.646i		−	1.06512i	−0.846393	−	0.532558i	$-0.821231\pi$
$701$		−	746.646i		−	1.06512i	0.846393	−	0.532558i	$-0.178769\pi$
$702$	75.7934	+	238.956i	0.107968	+	0.340393i
$703$	795.524	+	552.217i	1.13161	+	0.785515i
$704$	−38.6927	−	19.9733i	−0.0549612	−	0.0283711i
$705$	337.325	+	140.533i	0.478474	+	0.199337i
$706$	−33.1515	+	416.536i	−0.0469567	+	0.589995i
$707$	−684.522			−0.968207
$708$	−531.691	−	328.610i	−0.750975	−	0.464139i
$709$	−1010.20			−1.42482			−0.712408	−	0.701765i	$-0.752396\pi$
$709$	−1010.20			−1.42482			−0.712408	+	0.701765i	$0.752396\pi$
$710$	474.395	+	37.7563i	0.668162	+	0.0531779i
$711$	875.556	+	882.742i	1.23144	+	1.24155i
$712$	−118.219	−	28.7127i	−0.166039	−	0.0403269i
$713$	−1313.49			−1.84220
$714$	−524.431	+	1021.85i	−0.734497	+	1.43117i
$715$	25.6486			0.0358722
$716$	−31.1716	+	194.590i	−0.0435357	+	0.271773i
$717$	−254.617	+	611.164i	−0.355114	+	0.852391i
$718$	−444.183	−	35.3518i	−0.618639	−	0.0492365i
$719$	348.387			0.484544			0.242272	−	0.970208i	$-0.422107\pi$
$719$	348.387			0.484544			0.242272	+	0.970208i	$0.422107\pi$
$720$	−1045.90	+	522.923i	−1.45264	+	0.726282i
$721$		−	342.092i		−	0.474468i
$722$	−197.995	−	694.321i	−0.274232	−	0.961664i
$723$	583.559	+	243.116i	0.807135	+	0.336260i
$724$	−92.5517	+	577.756i	−0.127834	+	0.798006i
$725$	−1185.70			−1.63545
$726$	−330.219	+	643.433i	−0.454848	+	0.886271i
$727$			234.334i			0.322330i	0.986927	+	0.161165i	$0.0515251\pi$
$727$			234.334i			0.322330i	−0.986927	+	0.161165i	$0.948475\pi$
$728$	324.589	+	78.8351i	0.445865	+	0.108290i
$729$	521.762	−	509.122i	0.715723	−	0.698384i
$730$	0.965479	−	12.1309i	0.00132257	−	0.0166177i
$731$	−1009.39			−1.38084
$732$	−180.072	+	291.357i	−0.246001	+	0.398028i
$733$	−288.845			−0.394059			−0.197029	−	0.980398i	$-0.563129\pi$
$733$	−288.845			−0.394059			−0.197029	+	0.980398i	$0.563129\pi$
$734$	−85.2274	+	1070.85i	−0.116114	+	1.45893i
$735$	717.152	+	298.772i	0.975717	+	0.406493i
$736$	−1018.96	−	427.338i	−1.38446	−	0.580622i
$737$	−36.2187			−0.0491435
$738$	−476.869	−	563.992i	−0.646164	−	0.764216i
$739$		−	372.008i		−	0.503394i	−0.967806	−	0.251697i	$-0.919011\pi$
$739$		−	372.008i		−	0.503394i	0.967806	−	0.251697i	$-0.0809886\pi$
$740$	1634.70	+	261.865i	2.20905	+	0.353872i
$741$	−222.886	+	142.630i	−0.300790	+	0.192484i
$742$	74.7549	−	939.268i	0.100748	−	1.26586i
$743$		−	827.448i		−	1.11366i	−0.830627	−	0.556829i	$-0.812018\pi$
$743$		−	827.448i		−	1.11366i	0.830627	−	0.556829i	$-0.187982\pi$
$744$	540.073	−	736.067i	0.725905	−	0.989337i
$745$	−1425.12			−1.91292
$746$	−86.8365	+	1091.07i	−0.116403	+	1.46256i
$747$	585.066	+	589.867i	0.783220	+	0.789649i
$748$	9.16219	−	57.1952i	0.0122489	−	0.0764642i
$749$	1639.00			2.18824
$750$	691.000	+	354.631i	0.921333	+	0.472842i
$751$	−808.513			−1.07658			−0.538291	−	0.842759i	$-0.680930\pi$
$751$	−808.513			−1.07658			−0.538291	+	0.842759i	$0.680930\pi$
$752$	−227.996	−	74.9700i	−0.303187	−	0.0996941i
$753$	−322.648	+	774.462i	−0.428484	+	1.02850i
$754$	21.3336	−	268.049i	0.0282939	−	0.355503i
$755$		−	670.320i		−	0.887841i
$756$	−219.294	−	946.266i	−0.290072	−	1.25168i
$757$	−746.276			−0.985834			−0.492917	−	0.870076i	$-0.664069\pi$
$757$	−746.276			−0.985834			−0.492917	+	0.870076i	$0.664069\pi$
$758$	−215.145	−	17.1230i	−0.283832	−	0.0225898i
$759$	27.1040	−	65.0585i	0.0357101	−	0.0857161i
$760$	−819.194	−	923.268i	−1.07789	−	1.21483i
$761$			121.237i			0.159313i	0.996822	+	0.0796565i	$0.0253824\pi$
$761$			121.237i			0.159313i	−0.996822	+	0.0796565i	$0.974618\pi$
$762$	−10.1751	+	19.8263i	−0.0133532	+	0.0260187i
$763$	961.289			1.25988
$764$	−749.472	−	120.059i	−0.980984	−	0.157145i
$765$	−1095.42	−	1104.41i	−1.43192	−	1.44367i
$766$	43.3263	−	544.379i	0.0565617	−	0.710678i
$767$	−241.807			−0.315264
$768$	658.449	−	395.308i	0.857356	−	0.514724i
$769$	1085.12			1.41108			0.705539	−	0.708671i	$-0.250705\pi$
$769$	1085.12			1.41108			0.705539	+	0.708671i	$0.250705\pi$
$770$	−99.0676	−	7.88463i	−0.128659	−	0.0102398i
$771$	−66.8297	+	160.413i	−0.0866793	+	0.208059i
$772$	174.854	−	1091.53i	0.226495	−	1.41390i
$773$	322.155			0.416760			0.208380	−	0.978048i	$-0.433181\pi$
$773$	322.155			0.416760			0.208380	+	0.978048i	$0.433181\pi$
$774$	651.861	−	551.165i	0.842198	−	0.712099i
$775$	−1557.38			−2.00952
$776$	−54.7514	+	225.429i	−0.0705559	+	0.290501i
$777$	−528.870	+	1269.46i	−0.680656	+	1.63380i
$778$	−41.9747	+	527.397i	−0.0539521	+	0.677888i
$779$	444.558	−	640.431i	0.570678	−	0.822119i
$780$	−237.832	+	384.812i	−0.304913	+	0.493348i
$781$		−	19.9365i		−	0.0255269i
$782$	116.615	−	1465.23i	0.149125	−	1.87370i
$783$	−724.248	+	294.805i	−0.924966	+	0.376507i
$784$	−484.720	−	159.386i	−0.618266	−	0.203299i
$785$			160.362i			0.204283i
$786$	583.102	−	1136.17i	0.741860	−	1.44552i
$787$	−1440.14			−1.82992			−0.914958	−	0.403548i	$-0.867777\pi$
$787$	−1440.14			−1.82992			−0.914958	+	0.403548i	$0.867777\pi$
$788$	−109.076	+	680.911i	−0.138422	+	0.864100i
$789$	194.163	−	466.055i	0.246087	−	0.590690i
$790$	−178.002	+	2236.53i	−0.225319	+	2.83106i
$791$		−	162.606i		−	0.205571i
$792$	25.3138	+	41.9393i	0.0319618	+	0.0529537i
$793$			132.506i			0.167095i
$794$	214.252	+	17.0519i	0.269838	+	0.0214760i
$795$	1177.95	+	490.746i	1.48170	+	0.617290i
$796$	88.9699	−	555.397i	0.111771	−	0.697735i
$797$	1378.60			1.72974			0.864870	−	0.501996i	$-0.167401\pi$
$797$	1378.60			1.72974			0.864870	+	0.501996i	$0.167401\pi$
$798$	904.740	−	482.392i	1.13376	−	0.604501i
$799$		−	319.270i		−	0.399587i
$800$	−1208.17	−	506.687i	−1.51021	−	0.633359i
$801$	96.3807	+	97.1717i	0.120325	+	0.121313i
$802$	1010.03	+	80.3870i	1.25939	+	0.100233i
$803$	−0.509802			−0.000634872
$804$	335.846	−	543.398i	0.417719	−	0.675868i
$805$	−2521.84			−3.13272
$806$	28.0210	−	352.074i	0.0347655	−	0.436816i
$807$	−252.545	+	606.191i	−0.312943	+	0.751166i
$808$	−143.704	+	591.674i	−0.177851	+	0.732270i
$809$			537.748i			0.664707i	0.943155	+	0.332353i	$0.107843\pi$
$809$			537.748i			0.664707i	−0.943155	+	0.332353i	$0.892157\pi$
$810$	1310.46	+	115.084i	1.61786	+	0.142079i
$811$	−236.597			−0.291735			−0.145868	−	0.989304i	$-0.546597\pi$
$811$	−236.597			−0.291735			−0.145868	+	0.989304i	$0.546597\pi$
$812$	−164.802	+	1028.78i	−0.202958	+	1.26697i
$813$	689.098	+	287.085i	0.847600	+	0.353118i
$814$	5.50245	−	69.1363i	0.00675977	−	0.0849340i
$815$	−1680.23			−2.06163
$816$	773.154	+	667.817i	0.947493	+	0.818404i
$817$	740.210	+	513.820i	0.906010	+	0.628911i
$818$	15.6706	−	196.895i	0.0191572	−	0.240703i
$819$	−264.628	−	266.800i	−0.323111	−	0.325763i
$820$	210.813	−	1316.00i	0.257089	−	1.60488i
$821$			120.128i			0.146320i	0.997320	+	0.0731598i	$0.0233083\pi$
$821$			120.128i			0.146320i	−0.997320	+	0.0731598i	$0.976692\pi$
$822$	−256.289	−	131.531i	−0.311787	−	0.160014i
$823$			682.105i			0.828803i	0.910094	+	0.414402i	$0.136009\pi$
$823$			682.105i			0.828803i	−0.910094	+	0.414402i	$0.863991\pi$
$824$	−295.690	−	71.8162i	−0.358847	−	0.0871556i
$825$	32.1367	−	77.1387i	0.0389536	−	0.0935015i
$826$	933.980	+	74.3340i	1.13073	+	0.0899927i
$827$			143.383i			0.173377i	0.996235	+	0.0866886i	$0.0276285\pi$
$827$			143.383i			0.173377i	−0.996235	+	0.0866886i	$0.972371\pi$
$828$	724.759	+	1009.92i	0.875313	+	1.21971i
$829$		−	1290.28i		−	1.55644i	−0.627995	−	0.778218i	$-0.716124\pi$
$829$		−	1290.28i		−	1.55644i	0.627995	−	0.778218i	$-0.283876\pi$
$830$	−118.945	+	1494.50i	−0.143307	+	1.80060i
$831$	−380.621	+	913.616i	−0.458028	+	1.09942i
$832$	136.284	−	264.012i	0.163803	−	0.317322i
$833$		−	678.769i		−	0.814848i
$834$	−373.087	−	191.474i	−0.447347	−	0.229585i
$835$	1411.22			1.69009
$836$	−35.8335	+	37.2786i	−0.0428630	+	0.0445917i
$837$	−951.277	+	387.217i	−1.13653	+	0.462624i
$838$	1141.40	+	90.8422i	1.36205	+	0.108404i
$839$		−	144.176i		−	0.171843i	−0.996302	−	0.0859213i	$-0.972617\pi$
$839$		−	144.176i		−	0.171843i	0.996302	−	0.0859213i	$-0.0273834\pi$
$840$	1036.92	−	1413.22i	1.23443	−	1.68241i
$841$	−2.25485			−0.00268115
$842$	92.1693	−	1158.07i	0.109465	−	1.37538i
$843$	489.695	−	1175.43i	0.580896	−	1.39434i
$844$	123.969	+	19.8588i	0.146883	+	0.0235294i
$845$		−	1197.34i		−	1.41697i
$846$	174.333	+	206.183i	0.206068	+	0.243716i
$847$		−	1084.10i		−	1.27993i
$848$	−796.173	−	261.798i	−0.938883	−	0.308724i
$849$	72.9673	+	30.3989i	0.0859450	+	0.0358055i
$850$	138.269	−	1737.30i	0.162669	−	2.04388i
$851$		−	1759.92i		−	2.06806i
$852$	299.111	+	184.865i	0.351070	+	0.216978i
$853$	1259.97			1.47711			0.738554	−	0.674194i	$-0.235509\pi$
$853$	1259.97			1.47711			0.738554	+	0.674194i	$0.235509\pi$
$854$	40.7337	−	511.804i	0.0476975	−	0.599302i
$855$	241.107	+	1367.50i	0.281996	+	1.59941i
$856$	344.079	−	1416.68i	0.401961	−	1.65500i
$857$	478.927			0.558841			0.279421	−	0.960169i	$-0.409858\pi$
$857$	478.927			0.558841			0.279421	+	0.960169i	$0.409858\pi$
$858$	16.8604	+	8.65302i	0.0196508	+	0.0100851i
$859$		−	337.966i		−	0.393441i	−0.980460	−	0.196720i	$-0.936971\pi$
$859$		−	337.966i		−	0.393441i	0.980460	−	0.196720i	$-0.0630292\pi$
$860$	1521.04	+	243.657i	1.76865	+	0.283322i
$861$	1021.97	+	425.763i	1.18696	+	0.494498i
$862$	−91.7560	+	1152.88i	−0.106445	+	1.33745i
$863$		−	580.522i		−	0.672679i	−0.941741	−	0.336339i	$-0.890811\pi$
$863$		−	580.522i		−	0.672679i	0.941741	−	0.336339i	$-0.109189\pi$
$864$	−863.952	−	9.10324i	−0.999944	−	0.0105362i
$865$			2712.17i			3.13546i
$866$	126.865	−	1594.02i	0.146496	−	1.84067i
$867$	−189.227	+	454.206i	−0.218254	+	0.523882i
$868$	−216.462	+	1351.27i	−0.249380	+	1.55676i
$869$	93.9905			0.108159
$870$	−1255.38	−	644.280i	−1.44297	−	0.740552i
$871$		−	247.132i		−	0.283733i
$872$	201.806	−	830.900i	0.231429	−	0.952866i
$873$	185.294	−	183.785i	0.212249	−	0.210522i
$874$	−831.377	+	1015.12i	−0.951232	+	1.16147i
$875$	−1164.25			−1.33057
$876$	4.72725	−	7.64867i	0.00539640	−	0.00873136i
$877$			1027.14i			1.17120i	0.810601	+	0.585599i	$0.199141\pi$
$877$			1027.14i			1.17120i	−0.810601	+	0.585599i	$0.800859\pi$
$878$	1386.54	+	110.353i	1.57921	+	0.125687i
$879$	−389.550	+	935.049i	−0.443175	+	1.06376i
$880$	−27.6127	+	83.9749i	−0.0313781	+	0.0954260i
$881$			1582.74i			1.79653i	0.439458	+	0.898263i	$0.355170\pi$
$881$			1582.74i			1.79653i	−0.439458	+	0.898263i	$0.644830\pi$
$882$	370.632	+	438.346i	0.420218	+	0.496991i
$883$		−	30.2748i		−	0.0342863i	−0.999853	−	0.0171431i	$-0.994543\pi$
$883$		−	30.2748i		−	0.0342863i	0.999853	−	0.0171431i	$-0.00545710\pi$
$884$	390.261	+	62.5165i	0.441472	+	0.0707200i
$885$	−487.983	+	1171.32i	−0.551393	+	1.32352i
$886$	−873.517	−	69.5219i	−0.985911	−	0.0784671i
$887$		−	758.267i		−	0.854866i	−0.904047	−	0.427433i	$-0.859418\pi$
$887$		−	758.267i		−	0.854866i	0.904047	−	0.427433i	$-0.140582\pi$
$888$	986.245	+	723.635i	1.11064	+	0.814905i
$889$		−	33.4048i		−	0.0375756i
$890$	−19.5944	+	246.196i	−0.0220161	+	0.276625i
$891$	0.450460	−	55.1082i	0.000505566	−	0.0618498i
$892$	502.583	+	80.5096i	0.563434	+	0.0902573i
$893$	−162.521	+	234.128i	−0.181995	+	0.262181i
$894$	−936.822	−	480.791i	−1.04790	−	0.537798i
$895$	400.073			0.447009
$896$	−607.556	+	977.850i	−0.678075	+	1.09135i
$897$	443.914	+	184.939i	0.494888	+	0.206175i
$898$	326.935	+	26.0202i	0.364070	+	0.0289758i
$899$	1101.67			1.22543
$900$	859.334	+	1197.44i	0.954816	+	1.33049i
$901$		−	1114.90i		−	1.23741i
$902$	−55.6577	−	4.42971i	−0.0617048	−	0.00491098i
$903$	−492.097	+	1181.19i	−0.544958	+	1.30808i
$904$	−140.550	−	34.1364i	−0.155476	−	0.0377615i
$905$	1187.86			1.31255
$906$	226.145	−	440.643i	0.249608	−	0.486361i
$907$	1688.70			1.86185			0.930927	−	0.365206i	$-0.119002\pi$
$907$	1688.70			1.86185			0.930927	+	0.365206i	$0.119002\pi$
$908$	153.342	−	957.244i	0.168879	−	1.05423i
$909$	486.332	−	482.373i	0.535019	−	0.530664i
$910$	53.7993	−	675.969i	0.0591201	−	0.742823i
$911$		−	1141.68i		−	1.25321i	−0.779335	−	0.626607i	$-0.784443\pi$
$911$		−	1141.68i		−	1.25321i	0.779335	−	0.626607i	$-0.215557\pi$
$912$	−227.026	−	883.291i	−0.248932	−	0.968521i
$913$	62.8065			0.0687913
$914$	−1002.40	−	79.7792i	−1.09671	−	0.0872857i
$915$	641.861	+	267.406i	0.701488	+	0.292247i
$916$	50.6450	+	8.11290i	0.0552893	+	0.00885688i
$917$			1914.31i			2.08758i
$918$	−347.494	−	1095.56i	−0.378534	−	1.19342i
$919$		−	612.125i		−	0.666077i	−0.942913	−	0.333039i	$-0.891926\pi$
$919$		−	612.125i		−	0.666077i	0.942913	−	0.333039i	$-0.108074\pi$
$920$	−529.418	+	2179.78i	−0.575454	+	2.36933i
$921$	471.178	−	1130.98i	0.511594	−	1.22799i
$922$	83.8168	−	1053.13i	0.0909076	−	1.14222i
$923$	136.033			0.147381
$924$	−62.4633	−	38.6053i	−0.0676009	−	0.0417806i
$925$		−	2086.71i		−	2.25590i
$926$	121.397	−	1525.30i	0.131098	−	1.64720i
$927$	241.067	+	243.046i	0.260051	+	0.262185i
$928$	854.639	+	358.423i	0.920947	+	0.386231i
$929$		−	633.806i		−	0.682246i	−0.940019	−	0.341123i	$-0.889193\pi$
$929$		−	633.806i		−	0.682246i	0.940019	−	0.341123i	$-0.110807\pi$
$930$	−1648.90	−	846.242i	−1.77301	−	0.909937i
$931$	−345.520	+	497.756i	−0.371128	+	0.534647i
$932$	24.2746	−	151.535i	0.0260457	−	0.162591i
$933$	142.441	−	341.904i	0.152670	−	0.366457i
$934$	−64.4812	−	5.13196i	−0.0690377	−	0.00549460i
$935$	−117.593			−0.125767
$936$	−286.165	+	172.724i	−0.305732	+	0.184534i
$937$	−1617.58			−1.72634			−0.863169	−	0.504915i	$-0.831524\pi$
$937$	−1617.58			−1.72634			−0.863169	+	0.504915i	$0.831524\pi$
$938$	−75.9707	+	954.545i	−0.0809922	+	1.01764i
$939$	−71.8359	+	172.430i	−0.0765026	+	0.183631i
$940$	−77.0686	+	481.103i	−0.0819879	+	0.511812i
$941$	−678.176			−0.720697			−0.360349	−	0.932818i	$-0.617342\pi$
$941$	−678.176			−0.720697			−0.360349	+	0.932818i	$0.617342\pi$
$942$	−54.1011	+	105.416i	−0.0574321	+	0.111907i
$943$	−1416.81			−1.50245
$944$	260.324	−	791.690i	0.275767	−	0.838655i
$945$	−1826.42	+	743.442i	−1.93272	+	0.786711i
$946$	5.11986	−	64.3292i	0.00541211	−	0.0680012i
$947$	474.722			0.501290			0.250645	−	0.968079i	$-0.419357\pi$
$947$	474.722			0.501290			0.250645	+	0.968079i	$0.419357\pi$
$948$	−871.547	+	1410.16i	−0.919353	+	1.48751i
$949$		−	3.47854i		−	0.00366548i
$950$	−985.749	+	1203.62i	−1.03763	+	1.26696i
$951$	−172.639	+	414.391i	−0.181535	+	0.435743i
$952$	−1488.16	−	361.440i	−1.56320	−	0.379663i
$953$	−37.5573			−0.0394095			−0.0197048	−	0.999806i	$-0.506273\pi$
$953$	−37.5573			−0.0394095			−0.0197048	+	0.999806i	$0.506273\pi$
$954$	608.778	+	720.001i	0.638132	+	0.754718i
$955$			1540.90i			1.61351i
$956$	−871.662	−	139.633i	−0.911780	−	0.146059i
$957$	−22.7330	+	54.5668i	−0.0237545	+	0.0570186i
$958$	724.104	+	57.6303i	0.755850	+	0.0601569i
$959$	431.814			0.450275
$960$	−1003.85	−	1192.95i	−1.04568	−	1.24266i
$961$	486.002			0.505725
$962$	471.739	+	37.5449i	0.490373	+	0.0390280i
$963$	−1164.46	+	1154.98i	−1.20920	+	1.19935i
$964$	−133.326	+	832.290i	−0.138305	+	0.863372i
$965$	−2244.17			−2.32556
$966$	−1657.76	−	850.789i	−1.71611	−	0.880734i
$967$		−	1816.25i		−	1.87823i	−0.343599	−	0.939116i	$-0.611646\pi$
$967$		−	1816.25i		−	1.87823i	0.343599	−	0.939116i	$-0.388354\pi$
$968$	−937.055	−	227.589i	−0.968032	−	0.235112i
$969$	1021.88	−	653.926i	1.05457	−	0.674846i
$970$	469.464	+	37.3639i	0.483984	+	0.0385195i
$971$			949.066i			0.977411i	0.872449	+	0.488706i	$0.162531\pi$
$971$			949.066i			0.977411i	−0.872449	+	0.488706i	$0.837469\pi$
$972$	822.623	+	517.760i	0.846320	+	0.532675i
$973$	628.604			0.646048
$974$	1074.12	+	85.4878i	1.10280	+	0.0877698i
$975$	526.342	+	219.279i	0.539837	+	0.224902i
$976$	−433.832	−	142.653i	−0.444500	−	0.146161i
$977$	−1420.39			−1.45383			−0.726915	−	0.686727i	$-0.759047\pi$
$977$	−1420.39			−1.45383			−0.726915	+	0.686727i	$0.759047\pi$
$978$	−1104.52	−	566.856i	−1.12937	−	0.579608i
$979$	10.3464			0.0105684
$980$	−163.848	+	1022.82i	−0.167192	+	1.04370i
$981$	−682.967	+	677.407i	−0.696194	+	0.690527i
$982$	−996.803	−	79.3340i	−1.01507	−	0.0807882i
$983$		−	580.731i		−	0.590774i	−0.955378	−	0.295387i	$-0.904551\pi$
$983$		−	580.731i		−	0.590774i	0.955378	−	0.295387i	$-0.0954485\pi$
$984$	582.558	−	793.969i	0.592030	−	0.806879i
$985$	1399.94			1.42126
$986$	−97.8093	+	1228.94i	−0.0991981	+	1.24639i
$987$	−373.611	−	155.650i	−0.378532	−	0.157700i
$988$	−254.364	−	244.503i	−0.257453	−	0.247473i
$989$		−	1637.55i		−	1.65576i
$990$	75.9408	−	64.2098i	0.0767078	−	0.0648584i
$991$	64.8116			0.0654002			0.0327001	−	0.999465i	$-0.489589\pi$
$991$	64.8116			0.0654002			0.0327001	+	0.999465i	$0.489589\pi$
$992$	1122.54	+	470.777i	1.13159	+	0.474573i
$993$	−28.4009	+	68.1715i	−0.0286011	+	0.0686521i
$994$	−525.426	−	41.8178i	−0.528598	−	0.0420702i
$995$	−1141.89			−1.14763
$996$	−582.387	+	942.300i	−0.584725	+	0.946084i
$997$	144.120			0.144553			0.0722766	−	0.997385i	$-0.476974\pi$
$997$	144.120			0.144553			0.0722766	+	0.997385i	$0.476974\pi$
$998$	−74.8292	+	940.202i	−0.0749791	+	0.942086i
$999$	−518.826	−	1274.60i	−0.519345	−	1.27588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.3.b.e.227.72	yes	72
3.2	odd	2	inner	228.3.b.e.227.2	yes	72
4.3	odd	2	inner	228.3.b.e.227.69	yes	72
12.11	even	2	inner	228.3.b.e.227.3	yes	72
19.18	odd	2	inner	228.3.b.e.227.1	✓	72
57.56	even	2	inner	228.3.b.e.227.71	yes	72
76.75	even	2	inner	228.3.b.e.227.4	yes	72
228.227	odd	2	inner	228.3.b.e.227.70	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.3.b.e.227.1	✓	72	19.18	odd	2	inner
228.3.b.e.227.2	yes	72	3.2	odd	2	inner
228.3.b.e.227.3	yes	72	12.11	even	2	inner
228.3.b.e.227.4	yes	72	76.75	even	2	inner
228.3.b.e.227.69	yes	72	4.3	odd	2	inner
228.3.b.e.227.70	yes	72	228.227	odd	2	inner
228.3.b.e.227.71	yes	72	57.56	even	2	inner
228.3.b.e.227.72	yes	72	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	228.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.99370 + 0.158675i) q^{2} +(1.15371 - 2.76929i) q^{3} +(3.94964 + 0.632700i) q^{4} -8.12041i q^{5} +(2.73957 - 5.33805i) q^{6} +8.99393i q^{7} +(7.77400 + 1.88812i) q^{8} +(-6.33790 - 6.38992i) q^{9} +O(q^{10})\)	\(q+(1.99370 + 0.158675i) q^{2} +(1.15371 - 2.76929i) q^{3} +(3.94964 + 0.632700i) q^{4} -8.12041i q^{5} +(2.73957 - 5.33805i) q^{6} +8.99393i q^{7} +(7.77400 + 1.88812i) q^{8} +(-6.33790 - 6.38992i) q^{9} +(1.28851 - 16.1896i) q^{10} -0.680370 q^{11} +(6.30888 - 10.2077i) q^{12} -4.64238i q^{13} +(-1.42711 + 17.9312i) q^{14} +(-22.4877 - 9.36861i) q^{15} +(15.1994 + 4.99788i) q^{16} +21.2842i q^{17} +(-11.6219 - 13.7452i) q^{18} +(10.8345 - 15.6081i) q^{19} +(5.13778 - 32.0727i) q^{20} +(24.9068 + 10.3764i) q^{21} +(-1.35645 - 0.107958i) q^{22} -34.5295 q^{23} +(14.1977 - 19.3501i) q^{24} -40.9411 q^{25} +(0.736630 - 9.25549i) q^{26} +(-25.0076 + 10.1793i) q^{27} +(-5.69046 + 35.5228i) q^{28} +28.9611 q^{29} +(-43.3472 - 22.2464i) q^{30} +38.0395 q^{31} +(29.5099 + 12.3760i) q^{32} +(-0.784951 + 1.88414i) q^{33} +(-3.37727 + 42.4341i) q^{34} +73.0344 q^{35} +(-20.9895 - 29.2479i) q^{36} +50.9685i q^{37} +(24.0773 - 29.3987i) q^{38} +(-12.8561 - 5.35597i) q^{39} +(15.3323 - 63.1280i) q^{40} +41.0318 q^{41} +(48.0100 + 24.6395i) q^{42} +47.4246i q^{43} +(-2.68722 - 0.430470i) q^{44} +(-51.8887 + 51.4663i) q^{45} +(-68.8414 - 5.47898i) q^{46} -15.0004 q^{47} +(31.3763 - 36.3253i) q^{48} -31.8908 q^{49} +(-81.6240 - 6.49633i) q^{50} +(58.9419 + 24.5558i) q^{51} +(2.93723 - 18.3357i) q^{52} -52.3819 q^{53} +(-51.4728 + 16.3264i) q^{54} +5.52489i q^{55} +(-16.9816 + 69.9188i) q^{56} +(-30.7236 - 48.0111i) q^{57} +(57.7396 + 4.59540i) q^{58} -52.0870i q^{59} +(-82.8911 - 51.2307i) q^{60} -28.5427 q^{61} +(75.8391 + 6.03592i) q^{62} +(57.4705 - 57.0026i) q^{63} +(56.8700 + 29.3565i) q^{64} -37.6980 q^{65} +(-1.86392 + 3.63185i) q^{66} +53.2338 q^{67} +(-13.4665 + 84.0649i) q^{68} +(-39.8371 + 95.6222i) q^{69} +(145.608 + 11.5887i) q^{70} +29.3024i q^{71} +(-37.2059 - 61.6419i) q^{72} +0.749301 q^{73} +(-8.08743 + 101.616i) q^{74} +(-47.2342 + 113.378i) q^{75} +(52.6676 - 54.7917i) q^{76} -6.11920i q^{77} +(-24.7812 - 12.7181i) q^{78} -138.146 q^{79} +(40.5848 - 123.425i) q^{80} +(-0.662080 + 80.9973i) q^{81} +(81.8050 + 6.51073i) q^{82} -92.3122 q^{83} +(91.8078 + 56.7416i) q^{84} +172.836 q^{85} +(-7.52510 + 94.5502i) q^{86} +(33.4128 - 80.2016i) q^{87} +(-5.28920 - 1.28462i) q^{88} -15.2070 q^{89} +(-111.617 + 94.3748i) q^{90} +41.7532 q^{91} +(-136.379 - 21.8468i) q^{92} +(43.8866 - 105.342i) q^{93} +(-29.9062 - 2.38018i) q^{94} +(-126.745 - 87.9804i) q^{95} +(68.3186 - 67.4430i) q^{96} +28.9978i q^{97} +(-63.5805 - 5.06027i) q^{98} +(4.31212 + 4.34751i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 16 q^{4} + 6 q^{6} - 48 q^{9}+O(q^{10}) \) 72 * q - 16 * q^4 + 6 * q^6 - 48 * q^9	\( 72 q - 16 q^{4} + 6 q^{6} - 48 q^{9} - 40 q^{16} + 94 q^{24} - 408 q^{25} + 60 q^{28} + 176 q^{30} - 214 q^{36} + 2 q^{42} + 96 q^{45} - 616 q^{49} + 72 q^{54} + 320 q^{57} + 564 q^{58} + 592 q^{61} - 424 q^{64} + 608 q^{66} + 128 q^{73} - 292 q^{76} - 208 q^{81} + 472 q^{82} - 160 q^{85} + 128 q^{93} + 166 q^{96}+O(q^{100}) \) 72 * q - 16 * q^4 + 6 * q^6 - 48 * q^9 - 40 * q^16 + 94 * q^24 - 408 * q^25 + 60 * q^28 + 176 * q^30 - 214 * q^36 + 2 * q^42 + 96 * q^45 - 616 * q^49 + 72 * q^54 + 320 * q^57 + 564 * q^58 + 592 * q^61 - 424 * q^64 + 608 * q^66 + 128 * q^73 - 292 * q^76 - 208 * q^81 + 472 * q^82 - 160 * q^85 + 128 * q^93 + 166 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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