LMFDB - Embedded newform 300.2.w.a.223.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(67,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 13]))

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

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

chi := DirichletCharacter("300.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			223.3
Character	$\chi$	$=$	300.223
Dual form			300.2.w.a.187.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.35338 + 0.410309i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(1.66329 - 1.11061i) q^{4} +(2.17065 + 0.536923i) q^{5} +(0.980011 + 1.01960i) q^{6} +(0.403183 + 0.403183i) q^{7} +(-1.79538 + 2.18554i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(-3.15802 + 0.163973i) q^{10} +(2.68322 + 3.69314i) q^{11} +(-1.74468 - 0.977799i) q^{12} +(-0.669605 - 4.22772i) q^{13} +(-0.711090 - 0.380232i) q^{14} +(-0.507052 - 2.17782i) q^{15} +(1.53309 - 3.69454i) q^{16} +(1.13184 + 0.576699i) q^{17} +(0.463552 - 1.33608i) q^{18} +(0.214045 + 0.658762i) q^{19} +(4.20674 - 1.51768i) q^{20} +(0.176197 - 0.542280i) q^{21} +(-5.14676 - 3.89729i) q^{22} +(0.103651 - 0.654427i) q^{23} +(2.76242 + 0.607480i) q^{24} +(4.42343 + 2.33094i) q^{25} +(2.64090 + 5.44698i) q^{26} +(0.987688 + 0.156434i) q^{27} +(1.11839 + 0.222833i) q^{28} +(5.48448 + 1.78201i) q^{29} +(1.57981 + 2.73938i) q^{30} +(7.87705 - 2.55941i) q^{31} +(-0.558959 + 5.62917i) q^{32} +(2.07245 - 4.06742i) q^{33} +(-1.76843 - 0.316093i) q^{34} +(0.658690 + 1.09165i) q^{35} +(-0.0791572 + 1.99843i) q^{36} +(-0.551102 + 0.0872860i) q^{37} +(-0.559981 - 0.803734i) q^{38} +(-3.46293 + 2.51597i) q^{39} +(-5.07061 + 3.78007i) q^{40} +(-3.58374 - 2.60374i) q^{41} +(-0.0159605 + 0.806208i) q^{42} +(2.72923 - 2.72923i) q^{43} +(8.56463 + 3.16276i) q^{44} +(-1.71026 + 1.44050i) q^{45} +(0.128237 + 0.928219i) q^{46} +(-9.06571 + 4.61921i) q^{47} +(-3.98787 + 0.311292i) q^{48} -6.67489i q^{49} +(-6.94300 - 1.33969i) q^{50} -1.27029i q^{51} +(-5.80910 - 6.28827i) q^{52} +(7.66275 - 3.90436i) q^{53} +(-1.40091 + 0.193541i) q^{54} +(3.84140 + 9.45719i) q^{55} +(-1.60504 + 0.157307i) q^{56} +(0.489787 - 0.489787i) q^{57} +(-8.15378 - 0.161421i) q^{58} +(-5.72938 - 4.16264i) q^{59} +(-3.26208 - 3.05922i) q^{60} +(-10.7384 + 7.80192i) q^{61} +(-9.61052 + 6.69588i) q^{62} +(-0.563167 + 0.0891968i) q^{63} +(-1.55321 - 7.84777i) q^{64} +(0.816485 - 9.53642i) q^{65} +(-1.13593 + 6.35513i) q^{66} +(-4.20759 + 8.25787i) q^{67} +(2.52306 - 0.297808i) q^{68} +(-0.630155 + 0.204750i) q^{69} +(-1.33937 - 1.20715i) q^{70} +(1.71079 + 0.555870i) q^{71} +(-0.712844 - 2.73712i) q^{72} +(-6.95389 - 1.10139i) q^{73} +(0.710038 - 0.344253i) q^{74} +(0.0686916 - 4.99953i) q^{75} +(1.08765 + 0.857995i) q^{76} +(-0.407181 + 2.57084i) q^{77} +(3.65435 - 4.82594i) q^{78} +(2.36601 - 7.28182i) q^{79} +(5.31149 - 7.19640i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(5.91851 + 2.05342i) q^{82} +(-7.97834 - 4.06517i) q^{83} +(-0.309193 - 1.09766i) q^{84} +(2.14717 + 1.85952i) q^{85} +(-2.57387 + 4.81352i) q^{86} +(-0.902114 - 5.69572i) q^{87} +(-12.8889 - 0.766290i) q^{88} +(3.05003 + 4.19801i) q^{89} +(1.72358 - 2.65128i) q^{90} +(1.43457 - 1.97452i) q^{91} +(-0.554411 - 1.20362i) q^{92} +(-5.85655 - 5.85655i) q^{93} +(10.3741 - 9.97131i) q^{94} +(0.110911 + 1.54487i) q^{95} +(5.26939 - 2.05755i) q^{96} +(5.74169 + 11.2687i) q^{97} +(2.73876 + 9.03368i) q^{98} -4.56497 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44}+ \cdots + 256 q^{98}+O(q^{100}) $ 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

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 $

$2$	−1.35338	+	0.410309i	−0.956987	+	0.290132i
$2$	−1.35338	+	0.410309i	−0.956987	+	0.290132i
$3$	−0.453990	−	0.891007i	−0.262112	−	0.514423i
$3$	−0.453990	−	0.891007i	−0.262112	−	0.514423i
$4$	1.66329	−	1.11061i	0.831647	−	0.555305i
$5$	2.17065	+	0.536923i	0.970743	+	0.240119i
$5$	2.17065	+	0.536923i	0.970743	+	0.240119i
$6$	0.980011	+	1.01960i	0.400088	+	0.416249i
$7$	0.403183	+	0.403183i	0.152389	+	0.152389i	0.779184	−	0.626795i	$-0.215634\pi$
$7$	0.403183	+	0.403183i	0.152389	+	0.152389i	−0.626795	+	0.779184i	$0.715634\pi$
$8$	−1.79538	+	2.18554i	−0.634763	+	0.772707i
$9$	−0.587785	+	0.809017i	−0.195928	+	0.269672i
$10$	−3.15802	+	0.163973i	−0.998655	+	0.0518527i
$11$	2.68322	+	3.69314i	0.809022	+	1.11352i	0.991473	+	0.130309i	$0.0415969\pi$
$11$	2.68322	+	3.69314i	0.809022	+	1.11352i	−0.182451	+	0.983215i	$0.558403\pi$
$12$	−1.74468	−	0.977799i	−0.503646	−	0.282266i
$13$	−0.669605	−	4.22772i	−0.185715	−	1.17256i	−0.887719	−	0.460386i	$-0.847711\pi$
$13$	−0.669605	−	4.22772i	−0.185715	−	1.17256i	0.702004	−	0.712173i	$-0.252289\pi$
$14$	−0.711090	−	0.380232i	−0.190047	−	0.101621i
$15$	−0.507052	−	2.17782i	−0.130920	−	0.562311i
$16$	1.53309	−	3.69454i	0.383273	−	0.923635i
$17$	1.13184	+	0.576699i	0.274511	+	0.139870i	0.585827	−	0.810436i	$-0.300770\pi$
$17$	1.13184	+	0.576699i	0.274511	+	0.139870i	−0.311316	+	0.950306i	$0.600770\pi$
$18$	0.463552	−	1.33608i	0.109260	−	0.314918i
$19$	0.214045	+	0.658762i	0.0491053	+	0.151130i	0.972602	−	0.232475i	$-0.0746823\pi$
$19$	0.214045	+	0.658762i	0.0491053	+	0.151130i	−0.923497	+	0.383605i	$0.874682\pi$
$20$	4.20674	−	1.51768i	0.940655	−	0.339364i
$21$	0.176197	−	0.542280i	0.0384494	−	0.118335i
$22$	−5.14676	−	3.89729i	−1.09729	−	0.830904i
$23$	0.103651	−	0.654427i	0.0216127	−	0.136457i	−0.974523	−	0.224289i	$-0.927994\pi$
$23$	0.103651	−	0.654427i	0.0216127	−	0.136457i	0.996135	+	0.0878321i	$0.0279939\pi$
$24$	2.76242	+	0.607480i	0.563877	+	0.124001i
$25$	4.42343	+	2.33094i	0.884685	+	0.466189i
$26$	2.64090	+	5.44698i	0.517924	+	1.06824i
$27$	0.987688	+	0.156434i	0.190081	+	0.0301058i
$28$	1.11839	+	0.222833i	0.211356	+	0.0421114i
$29$	5.48448	+	1.78201i	1.01844	+	0.330912i	0.770211	−	0.637789i	$-0.220151\pi$
$29$	5.48448	+	1.78201i	1.01844	+	0.330912i	0.248231	+	0.968701i	$0.420151\pi$
$30$	1.57981	+	2.73938i	0.288433	+	0.500140i
$31$	7.87705	−	2.55941i	1.41476	−	0.459683i	0.500826	−	0.865548i	$-0.333030\pi$
$31$	7.87705	−	2.55941i	1.41476	−	0.459683i	0.913933	+	0.405865i	$0.133030\pi$
$32$	−0.558959	+	5.62917i	−0.0988109	+	0.995106i
$33$	2.07245	−	4.06742i	0.360768	−	0.708047i
$34$	−1.76843	−	0.316093i	−0.303284	−	0.0542095i
$35$	0.658690	+	1.09165i	0.111339	+	0.184522i
$36$	−0.0791572	+	1.99843i	−0.0131929	+	0.333072i
$37$	−0.551102	+	0.0872860i	−0.0906006	+	0.0143497i	−0.201570	−	0.979474i	$-0.564604\pi$
$37$	−0.551102	+	0.0872860i	−0.0906006	+	0.0143497i	0.110970	+	0.993824i	$0.464604\pi$
$38$	−0.559981	−	0.803734i	−0.0908409	−	0.130383i
$39$	−3.46293	+	2.51597i	−0.554513	+	0.402877i
$40$	−5.07061	+	3.78007i	−0.801734	+	0.597681i
$41$	−3.58374	−	2.60374i	−0.559686	−	0.406636i	0.271658	−	0.962394i	$-0.412428\pi$
$41$	−3.58374	−	2.60374i	−0.559686	−	0.406636i	−0.831344	+	0.555758i	$0.812428\pi$
$42$	−0.0159605	+	0.806208i	−0.00246277	+	0.124401i
$43$	2.72923	−	2.72923i	0.416204	−	0.416204i	−0.467689	−	0.883893i	$-0.654913\pi$
$43$	2.72923	−	2.72923i	0.416204	−	0.416204i	0.883893	+	0.467689i	$0.154913\pi$
$44$	8.56463	+	3.16276i	1.29117	+	0.476804i
$45$	−1.71026	+	1.44050i	−0.254950	+	0.214736i
$46$	0.128237	+	0.928219i	0.0189076	+	0.136858i
$47$	−9.06571	+	4.61921i	−1.32237	+	0.673781i	−0.965507	−	0.260375i	$-0.916154\pi$
$47$	−9.06571	+	4.61921i	−1.32237	+	0.673781i	−0.356863	+	0.934157i	$0.616154\pi$
$48$	−3.98787	+	0.311292i	−0.575599	+	0.0449311i
$49$		−	6.67489i		−	0.953555i
$50$	−6.94300	−	1.33969i	−0.981888	−	0.189461i
$51$		−	1.27029i		−	0.177876i
$52$	−5.80910	−	6.28827i	−0.805577	−	0.872027i
$53$	7.66275	−	3.90436i	1.05256	−	0.536306i	0.159944	−	0.987126i	$-0.448868\pi$
$53$	7.66275	−	3.90436i	1.05256	−	0.536306i	0.892615	+	0.450820i	$0.148868\pi$
$54$	−1.40091	+	0.193541i	−0.190639	+	0.0263376i
$55$	3.84140	+	9.45719i	0.517974	+	1.27521i
$56$	−1.60504	+	0.157307i	−0.214483	+	0.0210211i
$57$	0.489787	−	0.489787i	0.0648739	−	0.0648739i
$58$	−8.15378	−	0.161421i	−1.07064	−	0.0211956i
$59$	−5.72938	−	4.16264i	−0.745902	−	0.541929i	0.148652	−	0.988890i	$-0.452507\pi$
$59$	−5.72938	−	4.16264i	−0.745902	−	0.541929i	−0.894554	+	0.446960i	$0.852507\pi$
$60$	−3.26208	−	3.05922i	−0.421133	−	0.394943i
$61$	−10.7384	+	7.80192i	−1.37491	+	0.998934i	−0.377579	+	0.925977i	$0.623243\pi$
$61$	−10.7384	+	7.80192i	−1.37491	+	0.998934i	−0.997335	+	0.0729561i	$0.976757\pi$
$62$	−9.61052	+	6.69588i	−1.22054	+	0.850378i
$63$	−0.563167	+	0.0891968i	−0.0709523	+	0.0112377i
$64$	−1.55321	−	7.84777i	−0.194151	−	0.980972i
$65$	0.816485	−	9.53642i	0.101272	−	1.18285i
$66$	−1.13593	+	6.35513i	−0.139823	+	0.782262i
$67$	−4.20759	+	8.25787i	−0.514039	+	1.00886i	0.477448	+	0.878660i	$0.341562\pi$
$67$	−4.20759	+	8.25787i	−0.514039	+	1.00886i	−0.991488	+	0.130199i	$0.958438\pi$
$68$	2.52306	−	0.297808i	0.305966	−	0.0361145i
$69$	−0.630155	+	0.204750i	−0.0758618	+	0.0246490i
$70$	−1.33937	−	1.20715i	−0.160086	−	0.144282i
$71$	1.71079	+	0.555870i	0.203034	+	0.0659696i	0.408768	−	0.912638i	$-0.365958\pi$
$71$	1.71079	+	0.555870i	0.203034	+	0.0659696i	−0.205735	+	0.978608i	$0.565958\pi$
$72$	−0.712844	−	2.73712i	−0.0840095	−	0.322573i
$73$	−6.95389	−	1.10139i	−0.813892	−	0.128908i	−0.264407	−	0.964411i	$-0.585176\pi$
$73$	−6.95389	−	1.10139i	−0.813892	−	0.128908i	−0.549485	+	0.835504i	$0.685176\pi$
$74$	0.710038	−	0.344253i	0.0825402	−	0.0400186i
$75$	0.0686916	−	4.99953i	0.00793183	−	0.577296i
$76$	1.08765	+	0.857995i	0.124762	+	0.0984188i
$77$	−0.407181	+	2.57084i	−0.0464026	+	0.292974i
$78$	3.65435	−	4.82594i	0.413774	−	0.546430i
$79$	2.36601	−	7.28182i	0.266197	−	0.819269i	−0.725219	−	0.688518i	$-0.758261\pi$
$79$	2.36601	−	7.28182i	0.266197	−	0.819269i	0.991415	−	0.130750i	$-0.0417386\pi$
$80$	5.31149	−	7.19640i	0.593842	−	0.804581i
$81$	−0.309017	−	0.951057i	−0.0343352	−	0.105673i
$82$	5.91851	+	2.05342i	0.653590	+	0.226762i
$83$	−7.97834	−	4.06517i	−0.875737	−	0.446210i	−0.0424806	−	0.999097i	$-0.513526\pi$
$83$	−7.97834	−	4.06517i	−0.875737	−	0.446210i	−0.833256	+	0.552887i	$0.813526\pi$
$84$	−0.309193	−	1.09766i	−0.0337357	−	0.119764i
$85$	2.14717	+	1.85952i	0.232894	+	0.201693i
$86$	−2.57387	+	4.81352i	−0.277547	+	0.519055i
$87$	−0.902114	−	5.69572i	−0.0967168	−	0.610646i
$88$	−12.8889	−	0.766290i	−1.37397	−	0.0816868i
$89$	3.05003	+	4.19801i	0.323303	+	0.444988i	0.939472	−	0.342626i	$-0.111316\pi$
$89$	3.05003	+	4.19801i	0.323303	+	0.444988i	−0.616169	+	0.787614i	$0.711316\pi$
$90$	1.72358	−	2.65128i	0.181682	−	0.279469i
$91$	1.43457	−	1.97452i	0.150384	−	0.206986i
$92$	−0.554411	−	1.20362i	−0.0578013	−	0.125486i
$93$	−5.85655	−	5.85655i	−0.607296	−	0.607296i
$94$	10.3741	−	9.97131i	1.07001	−	1.02846i
$95$	0.110911	+	1.54487i	0.0113793	+	0.158500i
$96$	5.26939	−	2.05755i	0.537805	−	0.209998i
$97$	5.74169	+	11.2687i	0.582981	+	1.14416i	0.974582	+	0.224029i	$0.0719210\pi$
$97$	5.74169	+	11.2687i	0.582981	+	1.14416i	−0.391602	+	0.920135i	$0.628079\pi$
$98$	2.73876	+	9.03368i	0.276657	+	0.912540i
$99$	−4.56497			−0.458797
$100$	9.94623	−	1.03566i	0.994623	−	0.103566i
$101$	−18.5684			−1.84763			−0.923813	−	0.382845i	$-0.874945\pi$
$101$	−18.5684			−1.84763			−0.923813	+	0.382845i	$0.874945\pi$
$102$	0.521211	+	1.71919i	0.0516075	+	0.170225i
$103$	3.40490	+	6.68249i	0.335495	+	0.658445i	0.995700	−	0.0926401i	$-0.0295306\pi$
$103$	3.40490	+	6.68249i	0.335495	+	0.658445i	−0.660205	+	0.751085i	$0.729531\pi$
$104$	10.4421	+	6.12692i	1.02393	+	0.600794i
$105$	0.673625	−	1.08249i	0.0657391	−	0.105641i
$106$	−8.76864	+	8.42819i	−0.851686	+	0.818618i
$107$	−0.808322	−	0.808322i	−0.0781434	−	0.0781434i	0.666955	−	0.745098i	$-0.267597\pi$
$107$	−0.808322	−	0.808322i	−0.0781434	−	0.0781434i	−0.745098	+	0.666955i	$0.767597\pi$
$108$	1.81655	−	0.836740i	0.174798	−	0.0805153i
$109$	−10.5714	+	14.5503i	−1.01256	+	1.39367i	−0.0952690	+	0.995452i	$0.530371\pi$
$109$	−10.5714	+	14.5503i	−1.01256	+	1.39367i	−0.917291	+	0.398218i	$0.869629\pi$
$110$	−9.07926	−	11.2231i	−0.865673	−	1.07008i
$111$	0.327967	+	0.451408i	0.0311293	+	0.0428458i
$112$	2.10769	−	0.871459i	0.199158	−	0.0823451i
$113$	−1.84765	−	11.6656i	−0.173813	−	1.09741i	−0.908156	−	0.418632i	$-0.862510\pi$
$113$	−1.84765	−	11.6656i	−0.173813	−	1.09741i	0.734343	−	0.678778i	$-0.237490\pi$
$114$	−0.461906	+	0.863834i	−0.0432615	+	0.0809055i
$115$	0.576367	−	1.36488i	0.0537465	−	0.127276i
$116$	11.1014	−	3.12710i	1.03074	−	0.290344i
$117$	3.81388	+	1.94327i	0.352594	+	0.179655i
$118$	9.46201	+	3.28283i	0.871049	+	0.302209i
$119$	0.223822	+	0.688852i	0.0205177	+	0.0631469i
$120$	5.67007	+	2.80183i	0.517605	+	0.255771i
$121$	−3.04041	+	9.35742i	−0.276401	+	0.850675i
$122$	11.3320	−	14.9651i	1.02595	−	1.35487i
$123$	−0.692965	+	4.37521i	−0.0624825	+	0.394499i
$124$	10.2593	−	13.0054i	0.921316	−	1.16792i
$125$	8.35017	+	7.43470i	0.746862	+	0.664980i
$126$	0.725582	−	0.351790i	0.0646400	−	0.0313399i
$127$	19.6106	+	3.10602i	1.74016	+	0.275614i	0.944113	−	0.329621i	$-0.106921\pi$
$127$	19.6106	+	3.10602i	1.74016	+	0.275614i	0.796047	+	0.605235i	$0.206921\pi$
$128$	5.32210	+	9.98375i	0.470412	+	0.882447i
$129$	−3.67081	−	1.19272i	−0.323196	−	0.105013i
$130$	2.80786	+	13.2415i	0.246266	+	1.16135i
$131$	−21.6599	+	7.03773i	−1.89243	+	0.614889i	−0.915083	+	0.403264i	$0.867875\pi$
$131$	−21.6599	+	7.03773i	−1.89243	+	0.614889i	−0.977351	+	0.211625i	$0.932125\pi$
$132$	−1.07022	−	9.06700i	−0.0931505	−	0.789181i
$133$	−0.179302	+	0.351901i	−0.0155475	+	0.0305137i
$134$	2.30621	−	12.9025i	0.199227	−	1.11460i
$135$	2.05993	+	0.869877i	0.177291	+	0.0748671i
$136$	−3.29248	+	1.43828i	−0.282328	+	0.123332i
$137$	−16.5163	+	2.61593i	−1.41109	+	0.223494i	−0.815016	−	0.579438i	$-0.803272\pi$
$137$	−16.5163	+	2.61593i	−1.41109	+	0.223494i	−0.596070	+	0.802932i	$0.703272\pi$
$138$	0.768831	−	0.535663i	0.0654472	−	0.0455987i
$139$	−0.991605	+	0.720443i	−0.0841068	+	0.0611072i	−0.629044	−	0.777370i	$-0.716553\pi$
$139$	−0.991605	+	0.720443i	−0.0841068	+	0.0611072i	0.544937	+	0.838477i	$0.316553\pi$
$140$	2.30799	+	1.08418i	0.195061	+	0.0916300i
$141$	8.23150	+	5.98053i	0.693217	+	0.503652i
$142$	−2.54343	−	0.0503525i	−0.213440	−	0.00422549i
$143$	13.8169	−	13.8169i	1.15542	−	1.15542i
$144$	2.08782	+	3.41189i	0.173985	+	0.284324i
$145$	10.9481	+	6.81287i	0.909187	+	0.565778i
$146$	9.86319	−	1.36264i	0.816284	−	0.112773i
$147$	−5.94737	+	3.03034i	−0.490531	+	0.249938i
$148$	−0.819704	+	0.757241i	−0.0673792	+	0.0622449i
$149$			13.9644i			1.14401i	0.820251	+	0.572003i	$0.193834\pi$
$149$			13.9644i			1.14401i	−0.820251	+	0.572003i	$0.806166\pi$
$150$	1.95838	+	6.79446i	0.159901	+	0.554766i
$151$		−	19.3040i		−	1.57094i	−0.618901	−	0.785469i	$-0.712422\pi$
$151$		−	19.3040i		−	1.57094i	0.618901	−	0.785469i	$-0.287578\pi$
$152$	−1.82405	−	0.714925i	−0.147950	−	0.0579881i
$153$	−1.13184	+	0.576699i	−0.0915035	+	0.0466234i
$154$	−0.503766	−	3.64640i	−0.0405946	−	0.293836i
$155$	18.4725	−	1.32620i	1.48375	−	0.106523i
$156$	−2.96562	+	8.03076i	−0.237439	+	0.642976i
$157$	11.6248	−	11.6248i	0.927763	−	0.927763i	−0.0697978	−	0.997561i	$-0.522235\pi$
$157$	11.6248	−	11.6248i	0.927763	−	0.927763i	0.997561	+	0.0697978i	$0.0222354\pi$
$158$	−0.214321	+	10.8259i	−0.0170504	+	0.861261i
$159$	−6.95763	−	5.05501i	−0.551776	−	0.400889i
$160$	−4.23574	+	11.9188i	−0.334864	+	0.942266i
$161$	0.305644	−	0.222063i	0.0240881	−	0.0175010i
$162$	0.808445	+	1.16035i	0.0635175	+	0.0911658i
$163$	−17.3839	+	2.75333i	−1.36161	+	0.215658i	−0.794139	−	0.607736i	$-0.792078\pi$
$163$	−17.3839	+	2.75333i	−1.36161	+	0.215658i	−0.567470	+	0.823394i	$0.692078\pi$
$164$	−8.85255	−	0.350646i	−0.691268	−	0.0273809i
$165$	6.68246	−	7.71619i	0.520229	−	0.600705i
$166$	12.4657	+	2.22815i	0.967528	+	0.172938i
$167$	3.04644	−	5.97897i	0.235741	−	0.462667i	−0.742582	−	0.669756i	$-0.766399\pi$
$167$	3.04644	−	5.97897i	0.235741	−	0.462667i	0.978322	+	0.207089i	$0.0663989\pi$
$168$	0.868835	+	1.35869i	0.0670321	+	0.104825i
$169$	−5.06153	+	1.64459i	−0.389349	+	0.126507i
$170$	−3.66893	−	1.63564i	−0.281394	−	0.125448i
$171$	−0.658762	−	0.214045i	−0.0503768	−	0.0163684i
$172$	1.50840	−	7.57062i	0.115015	−	0.577254i
$173$	−0.974029	−	0.154271i	−0.0740540	−	0.0117290i	0.119297	−	0.992859i	$-0.461936\pi$
$173$	−0.974029	−	0.154271i	−0.0740540	−	0.0117290i	−0.193352	+	0.981130i	$0.561936\pi$
$174$	3.55791	+	7.33835i	0.269725	+	0.556319i
$175$	0.843653	+	2.72325i	0.0637742	+	0.205858i
$176$	17.7581	−	4.25136i	1.33857	−	0.320458i
$177$	−1.10785	+	6.99471i	−0.0832714	+	0.525755i
$178$	−5.85034	−	4.43006i	−0.438502	−	0.332047i
$179$	5.08238	−	15.6420i	0.379875	−	1.16914i	−0.560255	−	0.828320i	$-0.689297\pi$
$179$	5.08238	−	15.6420i	0.379875	−	1.16914i	0.940130	−	0.340815i	$-0.110703\pi$
$180$	−1.24483	+	4.29539i	−0.0927840	+	0.320160i
$181$	−7.05393	−	21.7098i	−0.524314	−	1.61367i	−0.765668	−	0.643236i	$-0.777591\pi$
$181$	−7.05393	−	21.7098i	−0.524314	−	1.61367i	0.241353	−	0.970437i	$-0.422409\pi$
$182$	−1.13136	+	3.26090i	−0.0838622	+	0.241714i
$183$	11.8267	+	6.02601i	0.874255	+	0.445455i
$184$	1.24419	+	1.40148i	0.0917226	+	0.103318i
$185$	−1.24311	−	0.106432i	−0.0913956	−	0.00782506i
$186$	10.3292	+	5.52317i	0.757370	+	0.404978i
$187$	0.907138	+	5.72744i	0.0663365	+	0.418832i
$188$	−9.94880	+	17.7516i	−0.725591	+	1.29467i
$189$	0.335147	+	0.461291i	0.0243784	+	0.0335540i
$190$	−0.783978	−	2.04529i	−0.0568757	−	0.148381i
$191$	5.09993	−	7.01945i	0.369018	−	0.507910i	−0.583616	−	0.812030i	$-0.698362\pi$
$191$	5.09993	−	7.01945i	0.369018	−	0.507910i	0.952634	+	0.304120i	$0.0983625\pi$
$192$	−6.28727	+	4.94674i	−0.453745	+	0.357000i
$193$	3.60845	+	3.60845i	0.259742	+	0.259742i	0.824949	−	0.565207i	$-0.191204\pi$
$193$	3.60845	+	3.60845i	0.259742	+	0.259742i	−0.565207	+	0.824949i	$0.691204\pi$
$194$	−12.3944	−	12.8950i	−0.889863	−	0.925808i
$195$	−8.86769	+	3.60195i	−0.635029	+	0.257941i
$196$	−7.41320	−	11.1023i	−0.529514	−	0.793021i
$197$	5.27204	+	10.3470i	0.375617	+	0.737190i	0.998999	−	0.0447274i	$-0.0142419\pi$
$197$	5.27204	+	10.3470i	0.375617	+	0.737190i	−0.623382	+	0.781917i	$0.714242\pi$
$198$	6.17816	−	1.87305i	0.439063	−	0.133112i
$199$	−1.27147			−0.0901321			−0.0450661	−	0.998984i	$-0.514350\pi$
$199$	−1.27147			−0.0901321			−0.0450661	+	0.998984i	$0.514350\pi$
$200$	−13.0361	+	5.48267i	−0.921793	+	0.387683i
$201$	9.26802			0.653716
$202$	25.1302	−	7.61878i	1.76815	−	0.536055i
$203$	1.49277	+	2.92972i	0.104772	+	0.205626i
$204$	−1.41080	−	2.11286i	−0.0987754	−	0.147930i
$205$	−6.38103	−	7.57599i	−0.445670	−	0.529130i
$206$	−7.35002	−	7.64691i	−0.512100	−	0.532786i
$207$	0.468518	+	0.468518i	0.0325642	+	0.0325642i
$208$	−16.6461	−	4.00760i	−1.15420	−	0.277877i
$209$	−1.85857	+	2.55811i	−0.128560	+	0.176948i
$210$	−0.467516	+	1.74142i	−0.0322617	+	0.120170i
$211$	−2.56831	−	3.53497i	−0.176810	−	0.243358i	0.711409	−	0.702778i	$-0.248057\pi$
$211$	−2.56831	−	3.53497i	−0.176810	−	0.243358i	−0.888219	+	0.459420i	$0.848057\pi$
$212$	8.40917	−	15.0044i	0.577544	−	1.03051i
$213$	−0.281399	−	1.77669i	−0.0192812	−	0.121736i
$214$	1.42563	+	0.762308i	0.0974541	+	0.0521103i
$215$	7.38958	−	4.45881i	0.503965	−	0.304088i
$216$	−2.11517	+	1.87778i	−0.143919	+	0.127767i
$217$	4.20780	+	2.14398i	0.285644	+	0.145543i
$218$	8.33708	−	24.0297i	0.564658	−	1.62750i
$219$	2.17566	+	6.69598i	0.147017	+	0.452473i
$220$	16.8926	+	11.4638i	1.13890	+	0.772889i
$221$	1.68024	−	5.17125i	0.113025	−	0.347856i
$222$	−0.629082	−	0.476361i	−0.0422212	−	0.0319712i
$223$	−1.79466	+	11.3311i	−0.120180	+	0.758784i	0.851826	+	0.523825i	$0.175496\pi$
$223$	−1.79466	+	11.3311i	−0.120180	+	0.758784i	−0.972005	+	0.234959i	$0.924504\pi$
$224$	−2.49495	+	2.04422i	−0.166701	+	0.136585i
$225$	−4.48580	+	2.20853i	−0.299053	+	0.147236i
$226$	7.28709	+	15.0300i	0.484730	+	0.999778i
$227$	−29.6086	−	4.68955i	−1.96519	−	0.311256i	−0.998460	−	0.0554697i	$-0.982334\pi$
$227$	−29.6086	−	4.68955i	−1.96519	−	0.311256i	−0.966733	−	0.255786i	$-0.917666\pi$
$228$	0.270698	−	1.35862i	0.0179274	−	0.0899770i
$229$	0.824628	+	0.267938i	0.0544929	+	0.0177058i	0.336137	−	0.941813i	$-0.390880\pi$
$229$	0.824628	+	0.267938i	0.0544929	+	0.0177058i	−0.281644	+	0.959519i	$0.590880\pi$
$230$	−0.220024	+	2.08369i	−0.0145080	+	0.137395i
$231$	2.47549	−	0.804336i	0.162875	−	0.0529214i
$232$	−13.7414	+	8.78718i	−0.902167	+	0.576906i
$233$	−4.29817	+	8.43563i	−0.281582	+	0.552637i	−0.987869	−	0.155289i	$-0.950369\pi$
$233$	−4.29817	+	8.43563i	−0.281582	+	0.552637i	0.706287	+	0.707926i	$0.250369\pi$
$234$	−5.95899	−	1.06512i	−0.389551	−	0.0696291i
$235$	−22.1586	+	5.15909i	−1.44547	+	0.336542i
$236$	−14.1527	−	0.560584i	−0.921263	−	0.0364909i
$237$	−7.56229	+	1.19775i	−0.491224	+	0.0778022i
$238$	−0.585558	−	0.840445i	−0.0379561	−	0.0544779i
$239$	8.95405	−	6.50550i	0.579190	−	0.420806i	−0.259242	−	0.965812i	$-0.583473\pi$
$239$	8.95405	−	6.50550i	0.579190	−	0.420806i	0.838432	+	0.545006i	$0.183473\pi$
$240$	−8.82340	−	1.46547i	−0.569548	−	0.0945960i
$241$	−0.593499	−	0.431202i	−0.0382306	−	0.0277762i	0.568506	−	0.822679i	$-0.307522\pi$
$241$	−0.593499	−	0.431202i	−0.0382306	−	0.0277762i	−0.606736	+	0.794903i	$0.707522\pi$
$242$	0.275411	−	13.9117i	0.0177041	−	0.894277i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−9.19626	+	24.9031i	−0.588730	+	1.59426i
$245$	3.58390	−	14.4888i	0.228967	−	0.925658i
$246$	−0.857338	−	6.20566i	−0.0546619	−	0.395659i
$247$	2.64174	−	1.34603i	0.168090	−	0.0856461i
$248$	−8.54860	+	21.8107i	−0.542837	+	1.38498i
$249$			8.95430i			0.567456i
$250$	−14.3515	−	6.63585i	−0.907668	−	0.419688i
$251$			13.1418i			0.829505i	0.909934	+	0.414753i	$0.136132\pi$
$251$			13.1418i			0.829505i	−0.909934	+	0.414753i	$0.863868\pi$
$252$	−0.837649	+	0.773819i	−0.0527669	+	0.0487460i
$253$	2.69501	−	1.37318i	0.169434	−	0.0863308i
$254$	−27.8151	+	3.84277i	−1.74527	+	0.241117i
$255$	0.682048	−	2.75735i	0.0427115	−	0.172672i
$256$	−11.2993	−	11.3281i	−0.706204	−	0.708009i
$257$	11.0515	−	11.0515i	0.689375	−	0.689375i	−0.272719	−	0.962094i	$-0.587923\pi$
$257$	11.0515	−	11.0515i	0.689375	−	0.689375i	0.962094	+	0.272719i	$0.0879230\pi$
$258$	5.45739	+	0.108040i	0.339762	+	0.00672630i
$259$	−0.257387	−	0.187003i	−0.0159932	−	0.0116198i
$260$	−9.23319	−	16.7687i	−0.572618	−	1.03995i
$261$	−4.66538	+	3.38959i	−0.288779	+	0.209811i
$262$	26.4265	−	18.4120i	1.63264	−	1.13750i
$263$	13.8057	−	2.18660i	0.851294	−	0.134832i	0.284485	−	0.958681i	$-0.408178\pi$
$263$	13.8057	−	2.18660i	0.851294	−	0.134832i	0.566810	+	0.823849i	$0.308178\pi$
$264$	5.16868	+	11.8320i	0.318111	+	0.728210i
$265$	18.7295	−	4.36069i	1.15054	−	0.267875i
$266$	0.0982770	−	0.549826i	0.00602575	−	0.0337120i
$267$	2.35577	−	4.62346i	0.144171	−	0.282951i
$268$	2.17281	+	18.4083i	0.132725	+	1.12446i
$269$	−5.95656	+	1.93540i	−0.363178	+	0.118004i	−0.484921	−	0.874558i	$-0.661152\pi$
$269$	−5.95656	+	1.93540i	−0.363178	+	0.118004i	0.121743	+	0.992562i	$0.461152\pi$
$270$	−3.14479	−	0.332070i	−0.191386	−	0.0202091i
$271$	−19.0797	−	6.19936i	−1.15901	−	0.376584i	−0.334478	−	0.942404i	$-0.608560\pi$
$271$	−19.0797	−	6.19936i	−1.15901	−	0.376584i	−0.824529	+	0.565820i	$0.808560\pi$
$272$	3.86585	−	3.29748i	0.234401	−	0.199939i
$273$	−2.41059	−	0.381800i	−0.145896	−	0.0231076i
$274$	21.2796	−	10.3172i	1.28555	−	0.623282i
$275$	3.26054	+	22.5908i	0.196618	+	1.36228i
$276$	−0.820736	+	1.04042i	−0.0494025	+	0.0626257i
$277$	1.56268	−	9.86635i	0.0938922	−	0.592812i	−0.895217	−	0.445630i	$-0.852980\pi$
$277$	1.56268	−	9.86635i	0.0938922	−	0.592812i	0.989109	−	0.147182i	$-0.0470203\pi$
$278$	1.04642	−	1.38190i	0.0627600	−	0.0828809i
$279$	−2.55941	+	7.87705i	−0.153228	+	0.471586i
$280$	−3.56844	−	0.520325i	−0.213255	−	0.0310954i
$281$	−8.65459	−	26.6361i	−0.516290	−	1.58898i	−0.780923	−	0.624627i	$-0.785251\pi$
$281$	−8.65459	−	26.6361i	−0.516290	−	1.58898i	0.264633	−	0.964349i	$-0.414749\pi$
$282$	−13.5942	−	4.71650i	−0.809525	−	0.280863i
$283$	8.54906	+	4.35596i	0.508189	+	0.258935i	0.689233	−	0.724540i	$-0.257948\pi$
$283$	8.54906	+	4.35596i	0.508189	+	0.258935i	−0.181044	+	0.983475i	$0.557948\pi$
$284$	3.46290	−	0.975447i	0.205485	−	0.0578821i
$285$	1.32613	−	0.800178i	0.0785534	−	0.0473984i
$286$	−13.0303	+	24.3687i	−0.770500	+	1.44095i
$287$	−0.395119	−	2.49468i	−0.0233232	−	0.147257i
$288$	−4.22555	−	3.76095i	−0.248993	−	0.221616i
$289$	−9.04388	−	12.4478i	−0.531993	−	0.732225i
$290$	−17.6123	−	4.72834i	−1.03423	−	0.277658i
$291$	7.43382	−	10.2318i	0.435778	−	0.599797i
$292$	−12.7896	+	5.89113i	−0.748454	+	0.344752i
$293$	−0.365499	−	0.365499i	−0.0213527	−	0.0213527i	0.696350	−	0.717703i	$-0.254806\pi$
$293$	−0.365499	−	0.365499i	−0.0213527	−	0.0213527i	−0.717703	+	0.696350i	$0.754806\pi$
$294$	6.80570	−	6.54146i	0.396916	−	0.381506i
$295$	−10.2014	−	12.1119i	−0.593951	−	0.705180i
$296$	0.798671	−	1.36117i	0.0464218	−	0.0791164i
$297$	2.07245	+	4.06742i	0.120256	+	0.236016i
$298$	−5.72970	−	18.8992i	−0.331913	−	1.09480i
$299$	−2.83614			−0.164018
$300$	−5.43827	−	8.39197i	−0.313979	−	0.484511i
$301$	2.20076			0.126850
$302$	7.92060	+	26.1257i	0.455780	+	1.50337i
$303$	8.42988	+	16.5446i	0.484284	+	0.950461i
$304$	2.76198	+	0.219146i	0.158410	+	0.0125689i
$305$	−27.4984	+	11.1695i	−1.57455	+	0.639565i
$306$	1.29518	−	1.24490i	0.0740407	−	0.0711660i
$307$	7.86266	+	7.86266i	0.448745	+	0.448745i	0.894937	−	0.446192i	$-0.147220\pi$
$307$	7.86266	+	7.86266i	0.448745	+	0.448745i	−0.446192	+	0.894937i	$0.647220\pi$
$308$	2.17794	+	4.72828i	0.124100	+	0.269419i
$309$	4.40835	−	6.06757i	0.250782	−	0.345172i
$310$	−24.4562	+	9.37429i	−1.38902	+	0.532424i
$311$	11.2964	+	15.5482i	0.640562	+	0.881658i	0.998645	−	0.0520319i	$-0.0165698\pi$
$311$	11.2964	+	15.5482i	0.640562	+	0.881658i	−0.358084	+	0.933689i	$0.616570\pi$
$312$	0.718525	−	12.0855i	0.0406784	−	0.684208i
$313$	1.18066	+	7.45438i	0.0667347	+	0.421346i	0.998326	+	0.0578387i	$0.0184209\pi$
$313$	1.18066	+	7.45438i	0.0667347	+	0.421346i	−0.931591	+	0.363508i	$0.881579\pi$
$314$	−10.9631	+	20.5026i	−0.618683	+	1.15703i
$315$	−1.27033	−	0.108762i	−0.0715749	−	0.00612806i
$316$	−4.15190	−	14.7395i	−0.233562	−	0.829162i
$317$	10.8062	+	5.50604i	0.606937	+	0.309250i	0.730316	−	0.683110i	$-0.239373\pi$
$317$	10.8062	+	5.50604i	0.606937	+	0.309250i	−0.123379	+	0.992360i	$0.539373\pi$
$318$	11.4905	+	3.98660i	0.644353	+	0.223557i
$319$	8.13485	+	25.0365i	0.455464	+	1.40177i
$320$	0.842175	−	17.8687i	0.0470790	−	0.998891i
$321$	−0.353250	+	1.08719i	−0.0197165	+	0.0606811i
$322$	−0.322539	+	0.425945i	−0.0179744	+	0.0237370i
$323$	−0.137644	+	0.869050i	−0.00765872	+	0.0483553i
$324$	−1.57024	−	1.23869i	−0.0872355	−	0.0688161i
$325$	6.89263	−	20.2618i	0.382334	−	1.12392i
$326$	22.3973	−	10.8591i	1.24047	−	0.601428i
$327$	17.7638	+	2.81351i	0.982339	+	0.155587i
$328$	12.1248	−	3.15772i	0.669478	−	0.174356i
$329$	−5.51753	−	1.79275i	−0.304191	−	0.0988377i
$330$	−5.87791	+	13.1848i	−0.323569	+	0.725801i
$331$	−1.45790	+	0.473702i	−0.0801336	+	0.0260370i	−0.348809	−	0.937194i	$-0.613414\pi$
$331$	−1.45790	+	0.473702i	−0.0801336	+	0.0260370i	0.268676	+	0.963231i	$0.413414\pi$
$332$	−17.7851	+	2.09926i	−0.976086	+	0.115212i
$333$	0.253314	−	0.497156i	0.0138815	−	0.0272440i
$334$	−1.66978	+	9.34182i	−0.0913661	+	0.511162i
$335$	−13.5670	+	15.6658i	−0.741247	+	0.855913i
$336$	−1.73335	−	1.48233i	−0.0945619	−	0.0808679i
$337$	1.08031	−	0.171104i	0.0588481	−	0.00932062i	−0.126941	−	0.991910i	$-0.540516\pi$
$337$	1.08031	−	0.171104i	0.0588481	−	0.00932062i	0.185789	+	0.982590i	$0.440516\pi$
$338$	6.17540	−	4.30255i	0.335898	−	0.234028i
$339$	−9.55533	+	6.94235i	−0.518974	+	0.377057i
$340$	5.63658	+	0.708255i	0.305687	+	0.0384105i
$341$	30.5881	+	22.2236i	1.65644	+	1.20347i
$342$	0.979383	+	0.0193889i	0.0529590	+	0.00104843i
$343$	5.51348	−	5.51348i	0.297700	−	0.297700i
$344$	1.06485	+	10.8649i	0.0574126	+	0.585794i
$345$	−1.47778	+	0.106095i	−0.0795610	+	0.00571196i
$346$	1.38153	−	0.190865i	0.0742717	−	0.0102609i
$347$	−20.4311	+	10.4102i	−1.09680	+	0.558846i	−0.906212	−	0.422824i	$-0.861039\pi$
$347$	−20.4311	+	10.4102i	−1.09680	+	0.558846i	−0.190586	+	0.981670i	$0.561039\pi$
$348$	−7.82621	−	8.47176i	−0.419529	−	0.454134i
$349$		−	20.7955i		−	1.11316i	−0.830795	−	0.556578i	$-0.812114\pi$
$349$		−	20.7955i		−	1.11316i	0.830795	−	0.556578i	$-0.187886\pi$
$350$	−2.25916	−	3.33944i	−0.120757	−	0.178500i
$351$		−	4.28042i		−	0.228472i
$352$	−22.2891	+	13.0400i	−1.18801	+	0.695035i
$353$	20.9677	−	10.6836i	1.11600	−	0.568628i	0.204059	−	0.978959i	$-0.434587\pi$
$353$	20.9677	−	10.6836i	1.11600	−	0.568628i	0.911937	+	0.410330i	$0.134587\pi$
$354$	−1.37064	−	9.92109i	−0.0728487	−	0.527300i
$355$	3.41507	+	2.12516i	0.181253	+	0.112792i
$356$	9.73545	+	3.59513i	0.515978	+	0.190541i
$357$	0.512159	−	0.512159i	0.0271063	−	0.0271063i
$358$	−0.460379	+	23.2549i	−0.0243318	+	1.22906i
$359$	28.2460	+	20.5219i	1.49077	+	1.08311i	0.973883	+	0.227051i	$0.0729084\pi$
$359$	28.2460	+	20.5219i	1.49077	+	1.08311i	0.516885	+	0.856055i	$0.327092\pi$
$360$	−0.0777078	−	6.32408i	−0.00409556	−	0.333308i
$361$	14.9832	−	10.8859i	0.788588	−	0.572943i
$362$	18.4544	+	26.4873i	0.969940	+	1.39214i
$363$	9.71784	−	1.53916i	0.510055	−	0.0807847i
$364$	0.193194	−	4.87745i	0.0101261	−	0.255648i
$365$	−14.5031	−	6.12443i	−0.759127	−	0.320568i
$366$	−18.4786	−	3.30290i	−0.965891	−	0.172645i
$367$	7.31720	−	14.3608i	0.381955	−	0.749628i	−0.617359	−	0.786682i	$-0.711797\pi$
$367$	7.31720	−	14.3608i	0.381955	−	0.749628i	0.999313	+	0.0370536i	$0.0117972\pi$
$368$	−2.25890	−	1.38624i	−0.117753	−	0.0722627i
$369$	4.21294	−	1.36887i	0.219317	−	0.0712604i
$370$	1.72608	−	0.366017i	0.0897346	−	0.0190283i
$371$	4.66366	+	1.51531i	0.242125	+	0.0786712i
$372$	−16.2455	−	3.23682i	−0.842291	−	0.167821i
$373$	−11.3634	−	1.79978i	−0.588373	−	0.0931891i	−0.144852	−	0.989453i	$-0.546271\pi$
$373$	−11.3634	−	1.79978i	−0.588373	−	0.0931891i	−0.443520	+	0.896264i	$0.646271\pi$
$374$	−3.57772	−	7.37922i	−0.185000	−	0.381570i
$375$	2.83347	−	10.8153i	0.146320	−	0.558501i
$376$	6.18092	−	28.1068i	0.318757	−	1.44950i
$377$	3.86143	−	24.3801i	0.198874	−	1.25564i
$378$	−0.642854	−	0.486789i	−0.0330649	−	0.0250377i
$379$	3.02441	−	9.30816i	0.155353	−	0.478128i	−0.842843	−	0.538159i	$-0.819120\pi$
$379$	3.02441	−	9.30816i	0.155353	−	0.478128i	0.998197	+	0.0600309i	$0.0191199\pi$
$380$	1.90022	+	2.44639i	0.0974794	+	0.125497i
$381$	−6.13555	−	18.8833i	−0.314334	−	0.967420i
$382$	−4.02202	+	11.5926i	−0.205784	+	0.593127i
$383$	−14.8289	−	7.55569i	−0.757720	−	0.386078i	0.0320454	−	0.999486i	$-0.489798\pi$
$383$	−14.8289	−	7.55569i	−0.757720	−	0.386078i	−0.789766	+	0.613409i	$0.789798\pi$
$384$	6.47940	−	9.27455i	0.330651	−	0.473290i
$385$	−2.26419	+	5.36176i	−0.115394	+	0.273261i
$386$	−6.36419	−	3.40304i	−0.323929	−	0.173210i
$387$	0.603792	+	3.81219i	0.0306925	+	0.193785i
$388$	22.0653	+	12.3664i	1.12019	+	0.627808i
$389$	8.71062	+	11.9891i	0.441646	+	0.607873i	0.970577	−	0.240792i	$-0.0774070\pi$
$389$	8.71062	+	11.9891i	0.441646	+	0.607873i	−0.528931	+	0.848665i	$0.677407\pi$
$390$	10.5235	−	8.51331i	0.532877	−	0.431088i
$391$	0.494723	−	0.680928i	0.0250192	−	0.0344360i
$392$	14.5883	+	11.9840i	0.736819	+	0.605282i
$393$	16.1041	+	16.1041i	0.812342	+	0.812342i
$394$	−11.3805	−	11.8402i	−0.573343	−	0.596502i
$395$	9.04555	−	14.5359i	0.455131	−	0.731381i
$396$	−7.59289	+	5.06990i	−0.381557	+	0.254772i
$397$	16.9966	+	33.3577i	0.853034	+	1.67417i	0.731768	+	0.681554i	$0.238696\pi$
$397$	16.9966	+	33.3577i	0.853034	+	1.67417i	0.121267	+	0.992620i	$0.461304\pi$
$398$	1.72079	−	0.521695i	0.0862552	−	0.0261502i
$399$	0.394948			0.0197721
$400$	15.3933	−	12.7690i	0.769664	−	0.638449i
$401$	6.38092			0.318648			0.159324	−	0.987226i	$-0.449069\pi$
$401$	6.38092			0.318648			0.159324	+	0.987226i	$0.449069\pi$
$402$	−12.5432	+	3.80275i	−0.625597	+	0.189664i
$403$	−16.0950	−	31.5882i	−0.801748	−	1.57352i
$404$	−30.8847	+	20.6223i	−1.53657	+	1.02600i
$405$	−0.160123	−	2.23033i	−0.00795657	−	0.110826i
$406$	−3.22238	−	3.35254i	−0.159924	−	0.166384i
$407$	−1.80109	−	1.80109i	−0.0892767	−	0.0892767i
$408$	2.77627	+	2.28065i	0.137446	+	0.112909i
$409$	7.75145	−	10.6690i	0.383285	−	0.527546i	−0.573166	−	0.819439i	$-0.694285\pi$
$409$	7.75145	−	10.6690i	0.383285	−	0.527546i	0.956451	+	0.291893i	$0.0942851\pi$
$410$	11.7445	+	7.63503i	0.580018	+	0.377067i
$411$	9.82907	+	13.5286i	0.484832	+	0.667315i
$412$	13.0850	+	7.33343i	0.644651	+	0.361292i
$413$	−0.631683	−	3.98829i	−0.0310831	−	0.196251i
$414$	−0.826321	−	0.441847i	−0.0406115	−	0.0217156i
$415$	−15.1355	−	13.1078i	−0.742972	−	0.643437i
$416$	24.1729	−	1.40620i	1.18517	−	0.0689447i
$417$	1.09210	+	0.556452i	0.0534803	+	0.0272496i
$418$	1.46575	−	4.22469i	0.0716921	−	0.206636i
$419$	−1.32767	−	4.08615i	−0.0648610	−	0.199622i	0.913374	−	0.407121i	$-0.133467\pi$
$419$	−1.32767	−	4.08615i	−0.0648610	−	0.199622i	−0.978235	+	0.207500i	$0.933467\pi$
$420$	−0.0817922	−	2.54864i	−0.00399105	−	0.124361i
$421$	−1.80550	+	5.55676i	−0.0879948	+	0.270820i	−0.985365	−	0.170459i	$-0.945475\pi$
$421$	−1.80550	+	5.55676i	−0.0879948	+	0.270820i	0.897370	+	0.441279i	$0.145475\pi$
$422$	4.92634	+	3.73038i	0.239810	+	0.181592i
$423$	1.59167	−	10.0494i	0.0773897	−	0.488620i
$424$	−5.22439	+	23.7571i	−0.253719	+	1.15375i
$425$	3.66234	+	5.18923i	0.177650	+	0.251715i
$426$	1.10983	+	2.28908i	0.0537715	+	0.110906i
$427$	−7.47515	−	1.18395i	−0.361748	−	0.0572952i
$428$	−2.24221	−	0.446746i	−0.108381	−	0.0215943i
$429$	−18.5837	−	6.03819i	−0.897227	−	0.291527i
$430$	−8.17145	+	9.06649i	−0.394062	+	0.437225i
$431$	−2.92353	+	0.949912i	−0.140821	+	0.0457556i	−0.378580	−	0.925569i	$-0.623587\pi$
$431$	−2.92353	+	0.949912i	−0.140821	+	0.0457556i	0.237758	+	0.971324i	$0.423587\pi$
$432$	2.09217	−	3.40923i	0.100660	−	0.164026i
$433$	−12.4138	+	24.3634i	−0.596568	+	1.17083i	0.373416	+	0.927664i	$0.378186\pi$
$433$	−12.4138	+	24.3634i	−0.596568	+	1.17083i	−0.969984	+	0.243167i	$0.921814\pi$
$434$	−6.57446	−	1.17513i	−0.315584	−	0.0564081i
$435$	1.09999	−	12.8478i	0.0527407	−	0.616004i
$436$	−1.42366	+	35.9422i	−0.0681809	+	1.72132i
$437$	0.453298	−	0.0717953i	0.0216842	−	0.00343444i
$438$	−5.69192	−	8.16954i	−0.271970	−	0.390356i
$439$	−19.5015	+	14.1687i	−0.930757	+	0.676235i	−0.946178	−	0.323646i	$-0.895091\pi$
$439$	−19.5015	+	14.1687i	−0.930757	+	0.676235i	0.0154210	+	0.999881i	$0.495091\pi$
$440$	−27.5659	−	8.58372i	−1.31415	−	0.409213i
$441$	5.40010	+	3.92340i	0.257147	+	0.186829i
$442$	−0.152202	+	7.68810i	−0.00723950	+	0.365686i
$443$	17.8280	−	17.8280i	0.847032	−	0.847032i	−0.142730	−	0.989762i	$-0.545588\pi$
$443$	17.8280	−	17.8280i	0.847032	−	0.847032i	0.989762	+	0.142730i	$0.0455881\pi$
$444$	1.04684	+	0.386581i	0.0496810	+	0.0183463i
$445$	4.36654	+	10.7500i	0.206994	+	0.509601i
$446$	−2.22036	−	16.0716i	−0.105137	−	0.761014i
$447$	12.4424	−	6.33969i	0.588503	−	0.299857i
$448$	2.53786	−	3.79031i	0.119903	−	0.179076i
$449$			10.8433i			0.511725i	0.966713	+	0.255862i	$0.0823594\pi$
$449$			10.8433i			0.511725i	−0.966713	+	0.255862i	$0.917641\pi$
$450$	5.16482	−	4.82955i	0.243472	−	0.227667i
$451$		−	20.2217i		−	0.952201i
$452$	−16.0291	−	17.3513i	−0.753948	−	0.816138i
$453$	−17.2000	+	8.76384i	−0.808127	+	0.411761i
$454$	41.9960	−	5.80192i	1.97097	−	0.272298i
$455$	4.17411	−	3.51573i	0.195686	−	0.164820i
$456$	0.191097	+	1.94981i	0.00894894	+	0.0913081i
$457$	−10.7529	+	10.7529i	−0.502999	+	0.502999i	−0.912369	−	0.409369i	$-0.865749\pi$
$457$	−10.7529	+	10.7529i	−0.502999	+	0.502999i	0.409369	+	0.912369i	$0.365749\pi$
$458$	−1.22597	−	0.0242707i	−0.0572860	−	0.00113410i
$459$	1.02769	+	0.746657i	0.0479682	+	0.0348510i
$460$	−0.557179	−	2.91031i	−0.0259786	−	0.135694i
$461$	−6.99954	+	5.08547i	−0.326001	+	0.236854i	−0.738732	−	0.673999i	$-0.764575\pi$
$461$	−6.99954	+	5.08547i	−0.326001	+	0.236854i	0.412731	+	0.910853i	$0.364575\pi$
$462$	−3.02026	+	2.10429i	−0.140515	+	0.0979005i
$463$	−6.98414	+	1.10618i	−0.324581	+	0.0514085i	−0.316599	−	0.948560i	$-0.602541\pi$
$463$	−6.98414	+	1.10618i	−0.324581	+	0.0514085i	−0.00798209	+	0.999968i	$0.502541\pi$
$464$	14.9919	−	17.5306i	0.695983	−	0.813839i
$465$	−9.56800	−	15.8570i	−0.443705	−	0.735352i
$466$	2.35586	−	13.1802i	0.109133	−	0.610562i
$467$	8.40547	−	16.4967i	0.388959	−	0.763374i	−0.610634	−	0.791913i	$-0.709085\pi$
$467$	8.40547	−	16.4967i	0.388959	−	0.763374i	0.999593	+	0.0285385i	$0.00908532\pi$
$468$	8.50182	−	1.00351i	0.392997	−	0.0463871i
$469$	−5.02586	+	1.63300i	−0.232073	+	0.0754050i
$470$	27.8723	−	16.0741i	1.28565	−	0.741443i
$471$	−15.6354	−	5.08024i	−0.720440	−	0.234085i
$472$	19.3841	−	5.04829i	0.892223	−	0.232367i
$473$	17.4026	+	2.75630i	0.800171	+	0.126735i
$474$	9.74324	−	4.72389i	0.447522	−	0.216975i
$475$	−0.588726	+	3.41291i	−0.0270126	+	0.156595i
$476$	1.13733	+	0.897185i	0.0521293	+	0.0411224i
$477$	−1.34535	+	8.49422i	−0.0615994	+	0.388924i
$478$	−9.44901	+	12.4784i	−0.432187	+	0.570747i
$479$	−7.81425	+	24.0498i	−0.357042	+	1.09886i	0.597774	+	0.801665i	$0.296052\pi$
$479$	−7.81425	+	24.0498i	−0.357042	+	1.09886i	−0.954816	+	0.297198i	$0.903948\pi$
$480$	12.5427	−	1.63697i	0.572495	−	0.0747170i
$481$	0.738042	+	2.27146i	0.0336518	+	0.103570i
$482$	0.980158	+	0.340064i	0.0446450	+	0.0154895i
$483$	−0.336619	−	0.171516i	−0.0153167	−	0.00780425i
$484$	5.33535	+	18.9409i	0.242516	+	0.860948i
$485$	6.41276	+	27.5432i	0.291189	+	1.25067i
$486$	0.666855	−	1.24712i	0.0302491	−	0.0565705i
$487$	−3.69540	−	23.3318i	−0.167455	−	1.05727i	−0.918038	−	0.396491i	$-0.870228\pi$
$487$	−3.69540	−	23.3318i	−0.167455	−	1.05727i	0.750584	−	0.660775i	$-0.229772\pi$
$488$	2.22812	−	37.4767i	0.100862	−	1.69649i
$489$	10.3453	+	14.2391i	0.467833	+	0.643917i
$490$	1.09450	+	21.0795i	0.0494444	+	0.952273i
$491$	−14.0618	+	19.3544i	−0.634599	+	0.873451i	−0.998313	−	0.0580598i	$-0.981509\pi$
$491$	−14.0618	+	19.3544i	−0.634599	+	0.873451i	0.363714	+	0.931511i	$0.381509\pi$
$492$	3.70654	+	8.04687i	0.167104	+	0.362781i
$493$	5.17984	+	5.17984i	0.233288	+	0.233288i
$494$	−3.02300	+	2.90563i	−0.136011	+	0.130730i
$495$	−9.90895	−	2.45104i	−0.445374	−	0.110166i
$496$	2.62040	−	33.0259i	0.117659	−	1.48291i
$497$	0.465644	+	0.913879i	0.0208870	+	0.0409931i
$498$	−3.67403	−	12.1186i	−0.164637	−	0.543048i
$499$	−3.20194			−0.143339			−0.0716693	−	0.997428i	$-0.522833\pi$
$499$	−3.20194			−0.143339			−0.0716693	+	0.997428i	$0.522833\pi$
$500$	22.1458	+	3.09231i	0.990391	+	0.138292i
$501$	−6.71036			−0.299797
$502$	−5.39221	−	17.7859i	−0.240666	−	0.793825i
$503$	−5.20750	−	10.2203i	−0.232191	−	0.455701i	0.745285	−	0.666746i	$-0.232313\pi$
$503$	−5.20750	−	10.2203i	−0.232191	−	0.455701i	−0.977476	+	0.211045i	$0.932313\pi$
$504$	0.816155	−	1.39097i	0.0363544	−	0.0619586i
$505$	−40.3055	−	9.96981i	−1.79357	−	0.443651i
$506$	−3.08396	+	2.96422i	−0.137099	+	0.131776i
$507$	3.76323	+	3.76323i	0.167131	+	0.167131i
$508$	36.0678	−	16.6135i	1.60025	−	0.737106i
$509$	13.6267	−	18.7556i	0.603994	−	0.831327i	−0.392072	−	0.919934i	$-0.628242\pi$
$509$	13.6267	−	18.7556i	0.603994	−	0.831327i	0.996067	+	0.0886075i	$0.0282417\pi$
$510$	0.208293	+	4.01160i	0.00922335	+	0.177637i
$511$	−2.35963	−	3.24775i	−0.104384	−	0.143672i
$512$	19.9403	+	10.6951i	0.881244	+	0.472662i
$513$	0.108357	+	0.684136i	0.00478406	+	0.0302053i
$514$	−10.4224	+	19.4915i	−0.459713	+	0.859732i
$515$	3.80285	+	16.3335i	0.167574	+	0.719740i
$516$	−7.43027	+	2.09299i	−0.327099	+	0.0921389i
$517$	−41.3847	−	21.0866i	−1.82010	−	0.927387i
$518$	0.425072	+	0.147478i	0.0186766	+	0.00647982i
$519$	0.304743	+	0.937904i	0.0133767	+	0.0411694i
$520$	19.3764	+	18.9060i	0.849711	+	0.829082i
$521$	−4.78400	+	14.7236i	−0.209591	+	0.645054i	0.789903	+	0.613232i	$0.210131\pi$
$521$	−4.78400	+	14.7236i	−0.209591	+	0.645054i	−0.999494	+	0.0318218i	$0.989869\pi$
$522$	4.92326	−	6.50166i	0.215485	−	0.284570i
$523$	−1.35911	+	8.58111i	−0.0594299	+	0.375226i	0.939991	+	0.341199i	$0.110833\pi$
$523$	−1.35911	+	8.58111i	−0.0594299	+	0.375226i	−0.999421	+	0.0340265i	$0.989167\pi$
$524$	−28.2106	+	35.7615i	−1.23239	+	1.56225i
$525$	2.04342	−	1.98803i	0.0891821	−	0.0867647i
$526$	−17.7872	+	8.62390i	−0.775558	+	0.376020i
$527$	10.3915	+	1.64586i	0.452662	+	0.0716946i
$528$	−11.8500	−	13.8925i	−0.515705	−	0.604593i
$529$	21.4568	+	6.97173i	0.932903	+	0.303119i
$530$	−23.5589	+	13.5866i	−1.02333	+	0.590162i
$531$	6.73529	−	2.18843i	0.292287	−	0.0949697i
$532$	0.0925920	+	0.784450i	0.00401437	+	0.0340102i
$533$	−8.60819	+	16.8945i	−0.372862	+	0.731783i
$534$	−1.29121	+	7.22390i	−0.0558763	+	0.312609i
$535$	−1.32058	−	2.18859i	−0.0570935	−	0.0946210i
$536$	−10.4937	−	24.0219i	−0.453259	−	1.03759i
$537$	−16.2445	+	2.57287i	−0.701000	+	0.111027i
$538$	7.26739	−	5.06337i	0.313319	−	0.218297i
$539$	24.6513	−	17.9102i	1.06181	−	0.771448i
$540$	4.39236	−	0.840918i	0.189017	−	0.0361874i
$541$	30.7034	+	22.3073i	1.32004	+	0.959067i	0.999932	+	0.0116875i	$0.00372033\pi$
$541$	30.7034	+	22.3073i	1.32004	+	0.959067i	0.320111	+	0.947380i	$0.396280\pi$
$542$	28.3657	+	0.561559i	1.21841	+	0.0241210i
$543$	−16.1411	+	16.1411i	−0.692682	+	0.692682i
$544$	−3.87899	+	6.04895i	−0.166310	+	0.259346i
$545$	−30.7593	+	25.9076i	−1.31758	+	1.10976i
$546$	3.41911	−	0.472364i	0.146324	−	0.0202153i
$547$	−12.8211	+	6.53267i	−0.548190	+	0.279317i	−0.706071	−	0.708141i	$-0.749534\pi$
$547$	−12.8211	+	6.53267i	−0.548190	+	0.279317i	0.157881	+	0.987458i	$0.449534\pi$
$548$	−24.5662	+	22.6943i	−1.04942	+	0.969451i
$549$		−	13.2734i		−	0.566496i
$550$	−13.6820	−	29.2362i	−0.583401	−	1.24663i
$551$			3.99440i			0.170167i
$552$	0.683879	−	1.74484i	0.0291078	−	0.0742652i
$553$	3.88984	−	1.98197i	0.165413	−	0.0842820i
$554$	1.93335	+	13.9941i	0.0821401	+	0.594554i
$555$	0.469530	+	1.15594i	0.0199304	+	0.0490670i
$556$	−0.849199	+	2.29960i	−0.0360141	+	0.0975246i
$557$	22.6217	−	22.6217i	0.958513	−	0.958513i	−0.0406596	−	0.999173i	$-0.512946\pi$
$557$	22.6217	−	22.6217i	0.958513	−	0.958513i	0.999173	+	0.0406596i	$0.0129459\pi$
$558$	0.231840	−	11.7108i	0.00981456	−	0.495758i
$559$	−13.3659	−	9.71092i	−0.565319	−	0.410728i
$560$	5.04296	−	0.759962i	0.213104	−	0.0321143i
$561$	4.69136	−	3.40847i	0.198069	−	0.143906i
$562$	22.6420	+	32.4978i	0.955095	+	1.37084i
$563$	−33.9090	+	5.37066i	−1.42909	+	0.226346i	−0.822545	−	0.568700i	$-0.807447\pi$
$563$	−33.9090	+	5.37066i	−1.42909	+	0.226346i	−0.606549	+	0.795046i	$0.707447\pi$
$564$	20.3334	+	0.805400i	0.856192	+	0.0339135i
$565$	2.25294	−	26.3140i	0.0947819	−	1.10704i
$566$	−13.3574	−	2.38754i	−0.561455	−	0.100356i
$567$	0.258859	−	0.508040i	0.0108711	−	0.0213357i
$568$	−4.28640	+	2.74101i	−0.179853	+	0.115010i
$569$	−13.8272	+	4.49274i	−0.579667	+	0.188345i	−0.584151	−	0.811645i	$-0.698573\pi$
$569$	−13.8272	+	4.49274i	−0.579667	+	0.188345i	0.00448435	+	0.999990i	$0.498573\pi$
$570$	−1.46645	+	1.62707i	−0.0614228	+	0.0681505i
$571$	32.5728	+	10.5835i	1.36313	+	0.442908i	0.897087	−	0.441854i	$-0.145679\pi$
$571$	32.5728	+	10.5835i	1.36313	+	0.442908i	0.466043	+	0.884762i	$0.345679\pi$
$572$	7.63636	−	38.3267i	0.319292	−	1.60252i
$573$	−8.56970	−	1.35731i	−0.358004	−	0.0567023i
$574$	1.55834	+	3.21414i	0.0650438	+	0.134156i
$575$	1.98392	−	2.65320i	0.0827354	−	0.110646i
$576$	7.26194	+	3.35623i	0.302581	+	0.139843i
$577$	4.65814	−	29.4103i	0.193921	−	1.22437i	−0.678126	−	0.734945i	$-0.737208\pi$
$577$	4.65814	−	29.4103i	0.193921	−	1.22437i	0.872047	−	0.489422i	$-0.162792\pi$
$578$	17.3473	+	13.1359i	0.721552	+	0.546382i
$579$	1.57695	−	4.85335i	0.0655358	−	0.201698i
$580$	25.7763	−	0.827225i	1.07030	−	0.0343487i
$581$	−1.57772	−	4.85574i	−0.0654550	−	0.201450i
$582$	−5.86262	+	16.8977i	−0.243013	+	0.700431i
$583$	34.9802	+	17.8233i	1.44873	+	0.738166i
$584$	14.8920	−	13.2206i	0.616236	−	0.547074i
$585$	7.23521	+	6.26592i	0.299139	+	0.259064i
$586$	0.644627	+	0.344693i	0.0266293	+	0.0142391i
$587$	0.417161	+	2.63385i	0.0172181	+	0.108711i	0.994801	−	0.101842i	$-0.0324736\pi$
$587$	0.417161	+	2.63385i	0.0172181	+	0.108711i	−0.977583	+	0.210553i	$0.932474\pi$
$588$	−6.52670	+	11.6455i	−0.269157	+	0.480254i
$589$	3.37208	+	4.64127i	0.138944	+	0.191240i
$590$	18.7761	+	12.2062i	0.772999	+	0.502523i
$591$	6.82575	−	9.39484i	0.280774	−	0.386452i
$592$	−0.522408	+	2.16989i	−0.0214708	+	0.0891817i
$593$	−4.29407	−	4.29407i	−0.176336	−	0.176336i	0.613420	−	0.789757i	$-0.289793\pi$
$593$	−4.29407	−	4.29407i	−0.176336	−	0.176336i	−0.789757	+	0.613420i	$0.789793\pi$
$594$	−4.47372	−	4.65443i	−0.183559	−	0.190974i
$595$	0.115977	+	1.61543i	0.00475460	+	0.0662262i
$596$	15.5090	+	23.2269i	0.635272	+	0.951409i
$597$	0.577235	+	1.13289i	0.0236247	+	0.0463660i
$598$	3.83839	−	1.16369i	0.156963	−	0.0475869i
$599$	−1.90922			−0.0780086			−0.0390043	−	0.999239i	$-0.512419\pi$
$599$	−1.90922			−0.0780086			−0.0390043	+	0.999239i	$0.512419\pi$
$600$	10.8034	+	9.12619i	0.441046	+	0.372575i
$601$	−19.9000			−0.811739			−0.405869	−	0.913931i	$-0.633031\pi$
$601$	−19.9000			−0.811739			−0.405869	+	0.913931i	$0.633031\pi$
$602$	−2.97847	+	0.902990i	−0.121393	+	0.0368031i
$603$	−4.20759	−	8.25787i	−0.171346	−	0.336286i
$604$	−21.4392	−	32.1082i	−0.872350	−	1.30647i
$605$	−11.6239	+	18.6792i	−0.472578	+	0.759418i
$606$	−18.1972	−	18.9323i	−0.739212	−	0.769072i
$607$	6.68008	+	6.68008i	0.271136	+	0.271136i	0.829557	−	0.558421i	$-0.188593\pi$
$607$	6.68008	+	6.68008i	0.271136	+	0.271136i	−0.558421	+	0.829557i	$0.688593\pi$
$608$	−3.82793	+	0.836674i	−0.155243	+	0.0339316i
$609$	1.93270	−	2.66013i	0.0783170	−	0.107794i
$610$	32.6329	−	26.3995i	1.32127	−	1.06888i
$611$	25.5992	+	35.2343i	1.03563	+	1.42543i
$612$	−1.24209	+	2.21625i	−0.0502084	+	0.0895865i
$613$	1.64882	+	10.4102i	0.0665950	+	0.420465i	0.998352	+	0.0573826i	$0.0182755\pi$
$613$	1.64882	+	10.4102i	0.0665950	+	0.420465i	−0.931757	+	0.363082i	$0.881725\pi$
$614$	−13.8673	−	7.41507i	−0.559639	−	0.299248i
$615$	−3.85333	+	9.12497i	−0.155381	+	0.367954i
$616$	−4.88764	−	5.50555i	−0.196929	−	0.221825i
$617$	−33.5664	−	17.1029i	−1.35133	−	0.688538i	−0.379717	−	0.925103i	$-0.623979\pi$
$617$	−33.5664	−	17.1029i	−1.35133	−	0.688538i	−0.971616	+	0.236564i	$0.923979\pi$
$618$	−3.47661	+	10.0205i	−0.139850	+	0.403085i
$619$	−11.4354	−	35.1945i	−0.459627	−	1.41459i	−0.865616	−	0.500708i	$-0.833073\pi$
$619$	−11.4354	−	35.1945i	−0.459627	−	1.41459i	0.405989	−	0.913878i	$-0.366927\pi$
$620$	29.2523	−	22.7216i	1.17480	−	0.912522i
$621$	0.204750	−	0.630155i	0.00821633	−	0.0252873i
$622$	−21.6680	−	16.4077i	−0.868806	−	0.657887i
$623$	−0.462845	+	2.92229i	−0.0185435	+	0.117079i
$624$	3.98635	+	16.6512i	0.159582	+	0.666580i
$625$	14.1334	+	20.6215i	0.565336	+	0.824860i
$626$	−4.65648	−	9.60420i	−0.186110	−	0.383861i
$627$	3.12306	+	0.494644i	0.124723	+	0.0197542i
$628$	6.42486	−	32.2462i	0.256380	−	1.28676i
$629$	−0.674095	−	0.219027i	−0.0268779	−	0.00873316i
$630$	1.76387	−	0.374030i	0.0702742	−	0.0149017i
$631$	11.9182	−	3.87246i	0.474456	−	0.154160i	−0.0620213	−	0.998075i	$-0.519755\pi$
$631$	11.9182	−	3.87246i	0.474456	−	0.154160i	0.536477	+	0.843915i	$0.319755\pi$
$632$	11.6669	+	18.2447i	0.464083	+	0.725733i
$633$	−1.98370	+	3.89322i	−0.0788449	+	0.154742i
$634$	−16.8841	−	3.01790i	−0.670554	−	0.119856i
$635$	40.9000	+	17.2715i	1.62307	+	0.685397i
$636$	−17.1867	−	0.680760i	−0.681498	−	0.0269939i
$637$	−28.2196	+	4.46954i	−1.11810	+	0.177090i
$638$	−21.2823	−	30.5462i	−0.842573	−	1.20933i
$639$	−1.45529	+	1.05733i	−0.0575702	+	0.0418272i
$640$	6.19190	+	24.5288i	0.244756	+	0.969585i
$641$	12.9136	+	9.38230i	0.510058	+	0.370579i	0.812845	−	0.582479i	$-0.197917\pi$
$641$	12.9136	+	9.38230i	0.510058	+	0.370579i	−0.302788	+	0.953058i	$0.597917\pi$
$642$	0.0319985	−	1.61633i	0.00126288	−	0.0637913i
$643$	−18.8472	+	18.8472i	−0.743260	+	0.743260i	−0.973204	−	0.229944i	$-0.926146\pi$
$643$	−18.8472	+	18.8472i	−0.743260	+	0.743260i	0.229944	+	0.973204i	$0.426146\pi$
$644$	0.261750	−	0.708808i	0.0103144	−	0.0279309i
$645$	−7.32763	−	4.55991i	−0.288525	−	0.179546i
$646$	−0.170294	−	1.23264i	−0.00670012	−	0.0484974i
$647$	9.13665	−	4.65536i	0.359199	−	0.183021i	−0.265073	−	0.964228i	$-0.585396\pi$
$647$	9.13665	−	4.65536i	0.359199	−	0.183021i	0.624271	+	0.781207i	$0.285396\pi$
$648$	2.63338	+	1.03214i	0.103449	+	0.0405462i
$649$		−	32.3287i		−	1.26901i
$650$	−1.01477	+	30.2501i	−0.0398024	+	1.18651i
$651$		−	4.72252i		−	0.185090i
$652$	−25.8566	+	23.8863i	−1.01262	+	0.935459i
$653$	−16.6573	+	8.48730i	−0.651849	+	0.332134i	−0.748452	−	0.663189i	$-0.769202\pi$
$653$	−16.6573	+	8.48730i	−0.651849	+	0.332134i	0.0966028	+	0.995323i	$0.469202\pi$
$654$	−25.1956	+	3.48088i	−0.985226	+	0.136113i
$655$	−50.7947	+	3.64673i	−1.98472	+	0.142489i
$656$	−15.1138	+	9.24850i	−0.590096	+	0.361093i
$657$	4.97844	−	4.97844i	0.194227	−	0.194227i
$658$	8.20291	+	0.162394i	0.319783	+	0.00633076i
$659$	2.98224	+	2.16672i	0.116171	+	0.0844035i	0.644354	−	0.764727i	$-0.277126\pi$
$659$	2.98224	+	2.16672i	0.116171	+	0.0844035i	−0.528183	+	0.849131i	$0.677126\pi$
$660$	2.54522	−	20.2559i	0.0990725	−	0.788460i
$661$	19.7563	−	14.3538i	0.768432	−	0.558299i	−0.133053	−	0.991109i	$-0.542478\pi$
$661$	19.7563	−	14.3538i	0.768432	−	0.558299i	0.901485	+	0.432810i	$0.142478\pi$
$662$	1.77874	−	1.23929i	0.0691327	−	0.0481664i
$663$	−5.37043	+	0.850592i	−0.208570	+	0.0330343i
$664$	23.2088	−	10.1385i	0.900675	−	0.393450i
$665$	−0.578146	+	0.667581i	−0.0224196	+	0.0258877i
$666$	−0.138843	+	0.776780i	−0.00538006	+	0.0300996i
$667$	1.73467	−	3.40448i	0.0671667	−	0.131822i
$668$	−1.57318	−	13.3282i	−0.0608683	−	0.515683i
$669$	10.9108	−	3.54514i	0.421836	−	0.137063i
$670$	11.9336	−	26.7685i	0.461036	−	1.03416i
$671$	−57.6272	−	18.7242i	−2.22467	−	0.722840i
$672$	2.95410	+	1.29496i	0.113957	+	0.0499540i
$673$	−23.5644	−	3.73224i	−0.908342	−	0.143867i	−0.315256	−	0.949007i	$-0.602090\pi$
$673$	−23.5644	−	3.73224i	−0.908342	−	0.143867i	−0.593086	+	0.805139i	$0.702090\pi$
$674$	−1.39186	+	0.674828i	−0.0536126	+	0.0259934i
$675$	4.00433	+	2.99422i	0.154127	+	0.115248i
$676$	−6.59231	+	8.35682i	−0.253550	+	0.321416i
$677$	1.26062	−	7.95924i	0.0484495	−	0.305898i	−0.951549	−	0.307497i	$-0.900509\pi$
$677$	1.26062	−	7.95924i	0.0484495	−	0.305898i	0.999999	+	0.00159823i	$0.000508732\pi$
$678$	10.0835	−	13.3163i	0.387255	−	0.511410i
$679$	−2.22840	+	6.85830i	−0.0855180	+	0.263197i
$680$	−7.91906	+	1.35420i	−0.303682	+	0.0519311i
$681$	9.26362	+	28.5105i	0.354983	+	1.09252i
$682$	−50.5160	−	17.5264i	−1.93436	−	0.671122i
$683$	−35.5849	−	18.1314i	−1.36162	−	0.693780i	−0.387937	−	0.921686i	$-0.626812\pi$
$683$	−35.5849	−	18.1314i	−1.36162	−	0.693780i	−0.973683	+	0.227906i	$0.926812\pi$
$684$	−1.33344	+	0.375609i	−0.0509852	+	0.0143618i
$685$	−37.2557	−	3.18974i	−1.42347	−	0.121874i
$686$	−5.19962	+	9.72408i	−0.198523	+	0.371267i
$687$	−0.135639	−	0.856390i	−0.00517494	−	0.0326733i
$688$	−5.89909	−	14.2674i	−0.224901	−	0.543940i
$689$	−21.6376	−	29.7816i	−0.824326	−	1.13459i
$690$	1.95647	−	0.749933i	0.0744816	−	0.0285495i
$691$	−28.5593	+	39.3084i	−1.08645	+	1.49536i	−0.234223	+	0.972183i	$0.575255\pi$
$691$	−28.5593	+	39.3084i	−1.08645	+	1.49536i	−0.852222	+	0.523181i	$0.824745\pi$
$692$	−1.79143	+	0.825168i	−0.0681000	+	0.0313682i
$693$	−1.84052	−	1.84052i	−0.0699155	−	0.0699155i
$694$	23.3797	−	22.4720i	0.887482	−	0.853025i
$695$	−2.53925	+	1.03141i	−0.0963192	+	0.0391237i
$696$	14.0679	+	8.25438i	0.533242	+	0.312882i
$697$	−2.55463	−	5.01374i	−0.0967635	−	0.189909i
$698$	8.53257	+	28.1443i	0.322962	+	1.06528i
$699$	9.46753			0.358095
$700$	4.42771	+	3.59259i	0.167352	+	0.135787i
$701$	−0.239240			−0.00903597			−0.00451799	−	0.999990i	$-0.501438\pi$
$701$	−0.239240			−0.00903597			−0.00451799	+	0.999990i	$0.501438\pi$
$702$	1.75629	+	5.79305i	0.0662870	+	0.218645i
$703$	−0.175461	−	0.344362i	−0.00661765	−	0.0129879i
$704$	24.8153	−	26.7936i	0.935262	−	1.00982i
$705$	14.6566	+	17.4013i	0.551999	+	0.655371i
$706$	−23.9937	+	23.0622i	−0.903016	+	0.867956i
$707$	−7.48646	−	7.48646i	−0.281557	−	0.281557i
$708$	5.92571	+	12.8647i	0.222702	+	0.483483i
$709$	−8.43241	+	11.6062i	−0.316686	+	0.435881i	−0.937452	−	0.348115i	$-0.886822\pi$
$709$	−8.43241	+	11.6062i	−0.316686	+	0.435881i	0.620766	+	0.783996i	$0.286822\pi$
$710$	−5.49387	−	1.47493i	−0.206181	−	0.0553530i
$711$	4.50041	+	6.19429i	0.168779	+	0.232304i
$712$	−14.6509	−	0.871046i	−0.549066	−	0.0326438i
$713$	−0.858481	−	5.42024i	−0.0321504	−	0.202989i
$714$	−0.483004	+	0.903290i	−0.0180760	+	0.0338048i
$715$	37.4102	−	22.5730i	1.39906	−	0.844181i
$716$	−8.91863	−	31.6617i	−0.333305	−	1.18325i
$717$	−9.86150	−	5.02469i	−0.368284	−	0.187650i
$718$	−46.6480	−	16.1845i	−1.74089	−	0.603999i
$719$	−9.40688	−	28.9514i	−0.350818	−	1.07971i	−0.958395	−	0.285445i	$-0.907859\pi$
$719$	−9.40688	−	28.9514i	−0.350818	−	1.07971i	0.607578	−	0.794260i	$-0.292141\pi$
$720$	2.69999	+	8.52702i	0.100623	+	0.317783i
$721$	−1.32147	+	4.06706i	−0.0492141	+	0.151465i
$722$	−15.8114	+	20.8805i	−0.588439	+	0.777093i
$723$	−0.114761	+	0.724573i	−0.00426801	+	0.0269472i
$724$	−35.8438	−	28.2755i	−1.33213	−	1.05085i
$725$	20.1064	+	20.6666i	0.746733	+	0.767539i
$726$	−12.5204	+	6.07038i	−0.464677	+	0.225293i
$727$	21.2294	+	3.36240i	0.787354	+	0.124705i	0.537148	−	0.843488i	$-0.319502\pi$
$727$	21.2294	+	3.36240i	0.787354	+	0.124705i	0.250206	+	0.968193i	$0.419502\pi$
$728$	1.73980	+	6.68033i	0.0644811	+	0.247590i
$729$	0.951057	+	0.309017i	0.0352243	+	0.0114451i
$730$	22.1412	+	2.33796i	0.819481	+	0.0865319i
$731$	4.66298	−	1.51510i	0.172467	−	0.0560378i
$732$	26.3638	−	3.11184i	0.974435	−	0.115017i
$733$	14.4461	−	28.3522i	0.533581	−	1.04721i	−0.454133	−	0.890934i	$-0.650051\pi$
$733$	14.4461	−	28.3522i	0.533581	−	1.04721i	0.987713	−	0.156277i	$-0.0499492\pi$
$734$	−4.01061	+	22.4380i	−0.148034	+	0.828201i
$735$	−14.5367	+	3.38451i	−0.536194	+	0.124840i
$736$	3.62594	+	0.949267i	0.133654	+	0.0349904i
$737$	−41.7874	+	6.61847i	−1.53926	+	0.243795i
$738$	−5.14006	+	3.58121i	−0.189208	+	0.131826i
$739$	9.06553	−	6.58650i	0.333481	−	0.242288i	−0.408425	−	0.912792i	$-0.633922\pi$
$739$	9.06553	−	6.58650i	0.333481	−	0.242288i	0.741906	+	0.670504i	$0.233922\pi$
$740$	−2.18587	+	1.20359i	−0.0803541	+	0.0442447i
$741$	−2.39865	−	1.74272i	−0.0881166	−	0.0640204i
$742$	−6.93347	−	0.137262i	−0.254536	−	0.00503906i
$743$	−22.0818	+	22.0818i	−0.810104	+	0.810104i	−0.984649	−	0.174545i	$-0.944154\pi$
$743$	−22.0818	+	22.0818i	−0.810104	+	0.810104i	0.174545	+	0.984649i	$0.444154\pi$
$744$	23.3145	−	2.28501i	0.854751	−	0.0837726i
$745$	−7.49780	+	30.3118i	−0.274698	+	1.11054i
$746$	16.1175	−	2.22669i	0.590102	−	0.0815250i
$747$	7.97834	−	4.06517i	0.291912	−	0.148737i
$748$	7.86979	+	8.51894i	0.287748	+	0.311483i
$749$		−	0.651803i		−	0.0238164i
$750$	0.602856	+	15.7999i	0.0220132	+	0.576930i
$751$		−	3.26645i		−	0.119194i	−0.998223	−	0.0595972i	$-0.981018\pi$
$751$		−	3.26645i		−	0.119194i	0.998223	−	0.0595972i	$-0.0189816\pi$
$752$	3.16730	+	40.5753i	0.115499	+	1.47963i
$753$	11.7095	−	5.96627i	0.426716	−	0.217423i
$754$	4.77737	+	34.5800i	0.173982	+	1.25933i
$755$	10.3648	−	41.9022i	0.377213	−	1.52498i
$756$	1.06976	+	0.395044i	0.0389069	+	0.0143676i
$757$	−1.58095	+	1.58095i	−0.0574608	+	0.0574608i	−0.735253	−	0.677792i	$-0.762937\pi$
$757$	−1.58095	+	1.58095i	−0.0574608	+	0.0574608i	0.677792	+	0.735253i	$0.262937\pi$
$758$	−0.273961	+	13.8385i	−0.00995070	+	0.502635i
$759$	−2.44702	−	1.77786i	−0.0888211	−	0.0645323i
$760$	−3.57550	−	2.53122i	−0.129697	−	0.0918172i
$761$	−0.114145	+	0.0829313i	−0.00413776	+	0.00300626i	−0.589852	−	0.807511i	$-0.700814\pi$
$761$	−0.114145	+	0.0829313i	−0.00413776	+	0.00300626i	0.585714	+	0.810517i	$0.300814\pi$
$762$	16.0517	+	23.0389i	0.581493	+	0.834610i
$763$	−10.1287	+	1.60422i	−0.366682	+	0.0580768i
$764$	0.686809	−	17.3394i	0.0248479	−	0.627319i
$765$	−2.76646	+	0.644102i	−0.100022	+	0.0232876i
$766$	23.1693	+	4.14133i	0.837142	+	0.149632i
$767$	−13.7621	+	27.0096i	−0.496919	+	0.975258i
$768$	−4.96369	+	15.2106i	−0.179112	+	0.548865i
$769$	30.9057	−	10.0419i	1.11449	−	0.362120i	0.306828	−	0.951765i	$-0.400733\pi$
$769$	30.9057	−	10.0419i	1.11449	−	0.362120i	0.807662	+	0.589645i	$0.200733\pi$
$770$	0.864340	−	8.18554i	0.0311487	−	0.294986i
$771$	−14.8643	−	4.82969i	−0.535323	−	0.173937i
$772$	10.0095	+	1.99433i	0.360249	+	0.0717776i
$773$	35.2942	+	5.59005i	1.26944	+	0.201060i	0.754578	−	0.656210i	$-0.227842\pi$
$773$	35.2942	+	5.59005i	1.26944	+	0.201060i	0.514866	+	0.857271i	$0.327842\pi$
$774$	−2.38134	−	4.91162i	−0.0855955	−	0.176545i
$775$	40.8094	+	7.03959i	1.46592	+	0.252870i
$776$	−34.9368	−	7.68290i	−1.25416	−	0.275800i
$777$	−0.0497693	+	0.314231i	−0.00178546	+	0.0112730i
$778$	−16.7080	−	12.6519i	−0.599013	−	0.453591i
$779$	0.948164	−	2.91815i	0.0339715	−	0.104554i
$780$	−10.7492	+	15.8397i	−0.384884	+	0.567151i
$781$	2.53753	+	7.80972i	0.0908000	+	0.279454i
$782$	−0.390160	+	1.12455i	−0.0139521	+	0.0402137i
$783$	5.13819	+	2.61804i	0.183624	+	0.0935610i
$784$	−24.6606	−	10.2332i	−0.880737	−	0.365472i
$785$	31.4751	−	18.9918i	1.12339	−	0.677846i
$786$	−28.4026	−	15.1873i	−1.01309	−	0.541714i
$787$	−2.87851	−	18.1742i	−0.102608	−	0.647841i	−0.984365	−	0.176138i	$-0.943639\pi$
$787$	−2.87851	−	18.1742i	−0.102608	−	0.647841i	0.881758	−	0.471703i	$-0.156361\pi$
$788$	20.2604	+	11.3548i	0.721746	+	0.404500i
$789$	−8.21592	−	11.3082i	−0.292495	−	0.402584i
$790$	−6.27789	+	23.3841i	−0.223357	+	0.831970i
$791$	3.95844	−	5.44832i	0.140746	−	0.193720i
$792$	8.19587	−	9.97695i	0.291227	−	0.354516i
$793$	40.1749	+	40.1749i	1.42665	+	1.42665i
$794$	−36.6898	−	38.1719i	−1.30207	−	1.35467i
$795$	−12.3884	−	14.7084i	−0.439372	−	0.521652i
$796$	−2.11483	+	1.41211i	−0.0749581	+	0.0500508i
$797$	−0.180269	−	0.353797i	−0.00638545	−	0.0125322i	0.887792	−	0.460245i	$-0.152239\pi$
$797$	−0.180269	−	0.353797i	−0.00638545	−	0.0125322i	−0.894177	+	0.447713i	$0.852239\pi$
$798$	−0.534516	+	0.162050i	−0.0189216	+	0.00573652i
$799$	−12.9248			−0.457246
$800$	−15.5938	+	23.5973i	−0.551324	+	0.834291i
$801$	−5.18903			−0.183345
$802$	−8.63583	+	2.61815i	−0.304942	+	0.0924500i
$803$	−14.5913	−	28.6370i	−0.514915	−	1.01058i
$804$	15.4154	−	10.2932i	0.543661	−	0.363012i
$805$	0.782676	−	0.317914i	0.0275857	−	0.0112050i
$806$	34.7436	+	36.1470i	1.22379	+	1.27322i
$807$	4.42868	+	4.42868i	0.155897	+	0.155897i
$808$	33.3374	−	40.5821i	1.17280	−	1.42767i
$809$	27.2343	−	37.4848i	0.957506	−	1.31789i	0.00939488	−	0.999956i	$-0.497009\pi$
$809$	27.2343	−	37.4848i	0.957506	−	1.31789i	0.948111	−	0.317938i	$-0.102991\pi$
$810$	1.13183	+	2.95279i	0.0397685	+	0.103750i
$811$	10.0855	+	13.8814i	0.354148	+	0.487443i	0.948507	−	0.316757i	$-0.102594\pi$
$811$	10.0855	+	13.8814i	0.354148	+	0.487443i	−0.594358	+	0.804200i	$0.702594\pi$
$812$	5.73669	+	3.21511i	0.201319	+	0.112828i
$813$	3.13832	+	19.8146i	0.110066	+	0.694927i
$814$	3.17657	+	1.69856i	0.111339	+	0.0595346i
$815$	−39.2126	−	3.35728i	−1.37356	−	0.117600i
$816$	−4.69313	−	1.94747i	−0.164293	−	0.0681751i
$817$	2.38209	+	1.21374i	0.0833388	+	0.0424633i
$818$	−6.11312	+	17.6197i	−0.213740	+	0.616058i
$819$	0.754199	+	2.32119i	0.0263538	+	0.0811088i
$820$	−19.0275	−	5.51427i	−0.664469	−	0.192567i
$821$	−7.99259	+	24.5987i	−0.278943	+	0.858499i	0.709206	+	0.705002i	$0.249054\pi$
$821$	−7.99259	+	24.5987i	−0.278943	+	0.858499i	−0.988149	+	0.153498i	$0.950946\pi$
$822$	−18.8534	−	14.2764i	−0.657587	−	0.497946i
$823$	−4.34747	+	27.4488i	−0.151543	+	0.956806i	0.788323	+	0.615262i	$0.210950\pi$
$823$	−4.34747	+	27.4488i	−0.151543	+	0.956806i	−0.939866	+	0.341544i	$0.889050\pi$
$824$	−20.7180	−	4.55606i	−0.721745	−	0.158718i
$825$	18.6483	−	13.1612i	0.649250	−	0.458213i
$826$	2.49134	+	5.13850i	0.0866848	+	0.178791i
$827$	27.6226	+	4.37499i	0.960533	+	0.152133i	0.616962	−	0.786993i	$-0.288363\pi$
$827$	27.6226	+	4.37499i	0.960533	+	0.152133i	0.343571	+	0.939127i	$0.388363\pi$
$828$	1.29962	+	0.258942i	0.0451650	+	0.00899887i
$829$	26.8128	+	8.71201i	0.931248	+	0.302581i	0.735073	−	0.677988i	$-0.237148\pi$
$829$	26.8128	+	8.71201i	0.931248	+	0.302581i	0.196175	+	0.980569i	$0.437148\pi$
$830$	25.8624	+	11.5297i	0.897696	+	0.400201i
$831$	−9.50043	+	3.08688i	−0.329566	+	0.107083i
$832$	−32.1382	+	11.8215i	−1.11419	+	0.409835i
$833$	3.84940	−	7.55488i	0.133374	−	0.261761i
$834$	−1.70635	−	0.304996i	−0.0590859	−	0.0105611i
$835$	9.82300	−	11.3425i	0.339939	−	0.392525i
$836$	−0.250295	+	6.31903i	−0.00865662	+	0.218548i
$837$	8.18045	−	1.29566i	0.282758	−	0.0447844i
$838$	3.47343	+	4.98538i	0.119988	+	0.172217i
$839$	26.1157	−	18.9742i	0.901615	−	0.655062i	−0.0372654	−	0.999305i	$-0.511865\pi$
$839$	26.1157	−	18.9742i	0.901615	−	0.655062i	0.938880	+	0.344244i	$0.111865\pi$
$840$	1.15643	+	3.41573i	0.0399005	+	0.117854i
$841$	3.44243	+	2.50107i	0.118704	+	0.0862438i
$842$	0.163548	−	8.26125i	0.00563625	−	0.284701i
$843$	−19.8038	+	19.8038i	−0.682080	+	0.682080i
$844$	−8.19783	−	3.02731i	−0.282181	−	0.104204i
$845$	−11.8698	+	0.852175i	−0.408334	+	0.0293157i
$846$	1.96922	+	14.2538i	0.0677032	+	0.490056i
$847$	−4.99859	+	2.54691i	−0.171754	+	0.0875129i
$848$	−2.67714	−	34.2961i	−0.0919334	−	1.17773i
$849$		−	9.59484i		−	0.329294i
$850$	−7.08574	−	5.52033i	−0.243039	−	0.189346i
$851$			0.369703i			0.0126733i
$852$	−2.44125	−	2.64263i	−0.0836360	−	0.0905348i
$853$	11.7252	−	5.97427i	0.401462	−	0.204555i	−0.241589	−	0.970379i	$-0.577668\pi$
$853$	11.7252	−	5.97427i	0.401462	−	0.204555i	0.643051	+	0.765824i	$0.277668\pi$
$854$	10.6025	−	1.46478i	0.362811	−	0.0501238i
$855$	−1.31502	−	0.818321i	−0.0449726	−	0.0279860i
$856$	3.21787	−	0.315378i	0.109985	−	0.0107794i
$857$	17.3368	−	17.3368i	0.592213	−	0.592213i	−0.346015	−	0.938229i	$-0.612466\pi$
$857$	17.3368	−	17.3368i	0.592213	−	0.592213i	0.938229	+	0.346015i	$0.112466\pi$
$858$	27.6283	+	0.546960i	0.943216	+	0.0186729i
$859$	26.4354	+	19.2065i	0.901966	+	0.655317i	0.938970	−	0.343999i	$-0.111782\pi$
$859$	26.4354	+	19.2065i	0.901966	+	0.655317i	−0.0370044	+	0.999315i	$0.511782\pi$
$860$	7.33905	−	15.6233i	0.250260	−	0.532749i
$861$	−2.04340	+	1.48462i	−0.0696389	+	0.0505956i
$862$	3.56690	−	2.48514i	0.121489	−	0.0846443i
$863$	25.5766	−	4.05093i	0.870637	−	0.137895i	0.294898	−	0.955529i	$-0.404714\pi$
$863$	25.5766	−	4.05093i	0.870637	−	0.137895i	0.575739	+	0.817634i	$0.304714\pi$
$864$	−1.43267	+	5.47243i	−0.0487405	+	0.186176i
$865$	−2.03144	−	0.857847i	−0.0690711	−	0.0291677i
$866$	6.80408	−	38.0665i	0.231212	−	1.29355i
$867$	−6.98526	+	13.7094i	−0.237232	+	0.465594i
$868$	9.37993	−	1.10715i	0.318376	−	0.0375792i
$869$	33.2413	−	10.8008i	1.12763	−	0.366391i
$870$	3.78284	+	17.8393i	0.128250	+	0.604809i
$871$	37.7294	+	12.2590i	1.27841	+	0.415381i
$872$	−12.8206	−	49.2277i	−0.434162	−	1.66706i
$873$	−12.4915	−	1.97845i	−0.422772	−	0.0669605i
$874$	−0.584028	+	0.283159i	−0.0197550	+	0.00957798i
$875$	0.369101	+	6.36419i	0.0124779	+	0.215149i
$876$	11.0554	+	8.72108i	0.373527	+	0.294658i
$877$	−2.40885	+	15.2089i	−0.0813410	+	0.513567i	0.913054	+	0.407839i	$0.133717\pi$
$877$	−2.40885	+	15.2089i	−0.0813410	+	0.513567i	−0.994395	+	0.105728i	$0.966283\pi$
$878$	20.5795	−	27.1773i	0.694525	−	0.917190i
$879$	−0.159729	+	0.491595i	−0.00538752	+	0.0165811i
$880$	40.8292	+	0.306531i	1.37635	+	0.0103331i
$881$	−6.30400	−	19.4017i	−0.212387	−	0.653660i	−0.999329	−	0.0366329i	$-0.988337\pi$
$881$	−6.30400	−	19.4017i	−0.212387	−	0.653660i	0.786942	−	0.617027i	$-0.211663\pi$
$882$	−8.91821	−	3.09416i	−0.300292	−	0.104186i
$883$	42.2974	+	21.5516i	1.42342	+	0.725270i	0.984847	−	0.173424i	$-0.0554833\pi$
$883$	42.2974	+	21.5516i	1.42342	+	0.725270i	0.438575	+	0.898694i	$0.355483\pi$
$884$	−2.94851	−	10.4674i	−0.0991690	−	0.352057i
$885$	−6.16038	+	14.5882i	−0.207079	+	0.490378i
$886$	−16.8131	+	31.4430i	−0.564847	+	1.05635i
$887$	−5.53478	−	34.9452i	−0.185840	−	1.17335i	−0.887491	−	0.460825i	$-0.847553\pi$
$887$	−5.53478	−	34.9452i	−0.185840	−	1.17335i	0.701651	−	0.712521i	$-0.252447\pi$
$888$	−1.57540	−	0.0936628i	−0.0528670	−	0.00314312i
$889$	6.65437	+	9.15895i	0.223180	+	0.307181i
$890$	−10.3204	−	12.7573i	−0.345942	−	0.427625i
$891$	2.68322	−	3.69314i	0.0898914	−	0.123725i
$892$	9.59934	+	20.8401i	0.321410	+	0.697777i
$893$	−4.98343	−	4.98343i	−0.166764	−	0.166764i
$894$	−14.2380	+	13.6852i	−0.476191	+	0.457703i
$895$	19.4306	−	31.2244i	0.649493	−	1.04372i
$896$	−1.87950	+	6.17105i	−0.0627896	+	0.206160i
$897$	1.28758	+	2.52702i	0.0429911	+	0.0843747i
$898$	−4.44908	−	14.6751i	−0.148468	−	0.489714i
$899$	47.7624			1.59296
$900$	−5.00838	+	8.65541i	−0.166946	+	0.288514i
$901$	10.9246			0.363952
$902$	8.29713	+	27.3677i	0.276264	+	0.911244i
$903$	−0.999123	−	1.96089i	−0.0332487	−	0.0652543i
$904$	28.8130	+	16.9061i	0.958306	+	0.562289i
$905$	−3.65512	−	50.9117i	−0.121500	−	1.69236i
$906$	19.6823	−	18.9181i	0.653901	−	0.628513i
$907$	25.9955	+	25.9955i	0.863166	+	0.863166i	0.991705	−	0.128538i	$-0.0410286\pi$
$907$	25.9955	+	25.9955i	0.863166	+	0.863166i	−0.128538	+	0.991705i	$0.541029\pi$
$908$	−54.4561	+	25.0835i	−1.80719	+	0.832427i
$909$	10.9142	−	15.0222i	0.362002	−	0.498254i
$910$	−4.20664	+	6.47081i	−0.139449	+	0.214505i
$911$	−4.91355	−	6.76292i	−0.162793	−	0.224065i	0.719826	−	0.694155i	$-0.244222\pi$
$911$	−4.91355	−	6.76292i	−0.162793	−	0.224065i	−0.882619	+	0.470089i	$0.844222\pi$
$912$	−1.05865	−	2.56043i	−0.0350554	−	0.0847842i
$913$	−6.39444	−	40.3729i	−0.211625	−	1.33615i
$914$	10.1408	−	18.9648i	0.335427	−	0.627300i
$915$	22.4361	+	19.4304i	0.741715	+	0.642348i
$916$	1.66917	−	0.470180i	0.0551510	−	0.0155352i
$917$	−11.5704	−	5.89541i	−0.382088	−	0.194684i
$918$	−1.69721	−	0.588845i	−0.0560164	−	0.0194348i
$919$	12.4509	+	38.3200i	0.410718	+	1.26406i	0.916025	+	0.401121i	$0.131379\pi$
$919$	12.4509	+	38.3200i	0.410718	+	1.26406i	−0.505307	+	0.862940i	$0.668621\pi$
$920$	1.94820	+	3.71015i	0.0642304	+	0.122320i
$921$	3.43611	−	10.5752i	0.113224	−	0.348466i
$922$	7.38646	−	9.75456i	0.243260	−	0.321249i
$923$	1.20451	−	7.60496i	0.0396469	−	0.250320i
$924$	3.22417	−	4.08715i	0.106067	−	0.134457i
$925$	−2.64122	−	0.898484i	−0.0868427	−	0.0295420i
$926$	8.99835	−	4.36274i	0.295704	−	0.143369i
$927$	−7.40760	−	1.17325i	−0.243297	−	0.0385345i
$928$	−13.0969	+	29.8770i	−0.429926	+	0.980760i
$929$	15.1027	+	4.90715i	0.495502	+	0.160998i	0.546099	−	0.837721i	$-0.316112\pi$
$929$	15.1027	+	4.90715i	0.495502	+	0.160998i	−0.0505966	+	0.998719i	$0.516112\pi$
$930$	19.4554	+	17.5348i	0.637969	+	0.574989i
$931$	4.39717	−	1.42873i	0.144111	−	0.0468246i
$932$	2.21958	+	18.8045i	0.0727047	+	0.615962i
$933$	8.72508	−	17.1239i	0.285646	−	0.560612i
$934$	−4.60710	+	25.7751i	−0.150749	+	0.843389i
$935$	−1.10612	+	12.9193i	−0.0361740	+	0.422507i
$936$	−11.0945	+	4.84650i	−0.362634	+	0.158413i
$937$	−2.53917	+	0.402165i	−0.0829512	+	0.0131382i	−0.197772	−	0.980248i	$-0.563371\pi$
$937$	−2.53917	+	0.402165i	−0.0829512	+	0.0131382i	0.114821	+	0.993386i	$0.463371\pi$
$938$	6.13188	−	4.27223i	0.200213	−	0.139493i
$939$	6.10589	−	4.43619i	0.199258	−	0.144770i
$940$	−31.1266	+	33.1907i	−1.01524	+	1.08256i
$941$	−13.7615	−	9.99831i	−0.448612	−	0.325935i	0.340436	−	0.940268i	$-0.389425\pi$
$941$	−13.7615	−	9.99831i	−0.448612	−	0.325935i	−0.789047	+	0.614332i	$0.789425\pi$
$942$	23.2451	+	0.460185i	0.757367	+	0.0149936i
$943$	−2.07541	+	2.07541i	−0.0675848	+	0.0675848i
$944$	−24.1627	+	14.7857i	−0.786429	+	0.481234i
$945$	0.479809	+	1.18125i	0.0156082	+	0.0384260i
$946$	−24.6833	+	3.41010i	−0.802522	+	0.110872i
$947$	−25.4121	+	12.9481i	−0.825782	+	0.420757i	−0.815195	−	0.579187i	$-0.803370\pi$
$947$	−25.4121	+	12.9481i	−0.825782	+	0.420757i	−0.0105872	+	0.999944i	$0.503370\pi$
$948$	−11.2481	+	10.3910i	−0.365321	+	0.337483i
$949$			30.1366i			0.978276i
$950$	−0.603576	−	4.86054i	−0.0195826	−	0.157697i
$951$		−	12.1281i		−	0.393280i
$952$	−1.90736	−	0.747580i	−0.0618179	−	0.0242292i
$953$	−13.9573	+	7.11160i	−0.452121	+	0.230367i	−0.665196	−	0.746669i	$-0.731652\pi$
$953$	−13.9573	+	7.11160i	−0.452121	+	0.230367i	0.213075	+	0.977036i	$0.431652\pi$
$954$	−1.66447	−	12.0479i	−0.0538893	−	0.390067i
$955$	14.8391	−	12.4985i	0.480181	−	0.404442i
$956$	7.66815	−	20.7650i	0.248006	−	0.671589i
$957$	18.6145	−	18.6145i	0.601722	−	0.601722i
$958$	0.707841	−	35.7548i	0.0228693	−	1.15519i
$959$	−7.71380	−	5.60441i	−0.249092	−	0.180976i
$960$	−16.3035	+	7.36184i	−0.526192	+	0.237602i
$961$	30.4178	−	22.0998i	0.981218	−	0.712897i
$962$	−1.93085	−	2.77133i	−0.0622532	−	0.0893513i
$963$	1.12907	−	0.178826i	0.0363836	−	0.00576260i
$964$	−1.46606	−	0.0580702i	−0.0472186	−	0.00187031i
$965$	5.89521	+	9.77013i	0.189774	+	0.314512i
$966$	0.525950	+	0.0940093i	0.0169221	+	0.00302470i
$967$	1.53584	−	3.01425i	0.0493891	−	0.0969316i	−0.864993	−	0.501784i	$-0.832677\pi$
$967$	1.53584	−	3.01425i	0.0493891	−	0.0969316i	0.914382	+	0.404853i	$0.132677\pi$
$968$	−14.9924	−	23.4451i	−0.481873	−	0.753554i
$969$	0.836819	−	0.271899i	0.0268825	−	0.00873465i
$970$	−19.9802	−	34.6454i	−0.641524	−	1.11240i
$971$	0.924449	+	0.300372i	0.0296670	+	0.00963939i	0.323813	−	0.946121i	$-0.395035\pi$
$971$	0.924449	+	0.300372i	0.0296670	+	0.00963939i	−0.294146	+	0.955761i	$0.595035\pi$
$972$	−0.390806	+	1.96145i	−0.0125351	+	0.0629134i
$973$	−0.690268	−	0.109328i	−0.0221290	−	0.00350489i
$974$	14.5746	+	30.0607i	0.466999	+	0.963206i
$975$	−21.1826	+	3.05730i	−0.678387	+	0.0979120i
$976$	12.3615	+	51.6346i	0.395683	+	1.65278i
$977$	−1.61466	+	10.1946i	−0.0516576	+	0.326153i	0.948304	+	0.317364i	$0.102798\pi$
$977$	−1.61466	+	10.1946i	−0.0516576	+	0.326153i	−0.999961	+	0.00878920i	$0.997202\pi$
$978$	−19.8437	−	15.0262i	−0.634531	−	0.480486i
$979$	−7.31992	+	22.5284i	−0.233946	+	0.720011i
$980$	−10.1304	−	28.0795i	−0.323602	−	0.896967i
$981$	−5.55773	−	17.1049i	−0.177445	−	0.546119i
$982$	11.0897	−	31.9636i	0.353887	−	1.02000i
$983$	−2.23630	−	1.13945i	−0.0713268	−	0.0363428i	0.417963	−	0.908464i	$-0.362744\pi$
$983$	−2.23630	−	1.13945i	−0.0713268	−	0.0363428i	−0.489290	+	0.872121i	$0.662744\pi$
$984$	−8.31808	−	9.36967i	−0.265171	−	0.298694i
$985$	5.88821	+	25.2903i	0.187614	+	0.805815i
$986$	−9.13565	−	4.88498i	−0.290938	−	0.155569i
$987$	0.907550	+	5.73005i	0.0288876	+	0.182389i
$988$	2.89907	−	5.17279i	0.0922317	−	0.164568i
$989$	−1.50319	−	2.06897i	−0.0477988	−	0.0657894i
$990$	14.4163	−	0.748531i	0.458180	−	0.0237899i
$991$	−22.1826	+	30.5317i	−0.704653	+	0.969871i	0.295243	+	0.955422i	$0.404599\pi$
$991$	−22.1826	+	30.5317i	−0.704653	+	0.969871i	−0.999896	+	0.0144492i	$0.995401\pi$
$992$	10.0044	+	45.7718i	0.317640	+	1.45326i
$993$	1.08395	+	1.08395i	0.0343980	+	0.0343980i
$994$	−1.00517	−	1.04577i	−0.0318820	−	0.0331698i
$995$	−2.75991	−	0.682682i	−0.0874952	−	0.0216425i
$996$	9.94474	+	14.8936i	0.315111	+	0.471923i
$997$	3.03505	+	5.95663i	0.0961211	+	0.188648i	0.934060	−	0.357115i	$-0.116240\pi$
$997$	3.03505	+	5.95663i	0.0961211	+	0.188648i	−0.837939	+	0.545764i	$0.816240\pi$
$998$	4.33345	−	1.31378i	0.137173	−	0.0415871i
$999$	−0.557971			−0.0176534

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.223.3	yes	240
3.2	odd	2		900.2.bj.f.523.28		240
4.3	odd	2	inner	300.2.w.a.223.25	yes	240
12.11	even	2		900.2.bj.f.523.6		240
25.12	odd	20	inner	300.2.w.a.187.25	yes	240
75.62	even	20		900.2.bj.f.487.6		240
100.87	even	20	inner	300.2.w.a.187.3	✓	240
300.287	odd	20		900.2.bj.f.487.28		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.187.3	✓	240	100.87	even	20	inner
300.2.w.a.187.25	yes	240	25.12	odd	20	inner
300.2.w.a.223.3	yes	240	1.1	even	1	trivial
300.2.w.a.223.25	yes	240	4.3	odd	2	inner
900.2.bj.f.487.6		240	75.62	even	20
900.2.bj.f.487.28		240	300.287	odd	20
900.2.bj.f.523.6		240	12.11	even	2
900.2.bj.f.523.28		240	3.2	odd	2

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35338 + 0.410309i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(1.66329 - 1.11061i) q^{4} +(2.17065 + 0.536923i) q^{5} +(0.980011 + 1.01960i) q^{6} +(0.403183 + 0.403183i) q^{7} +(-1.79538 + 2.18554i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(-3.15802 + 0.163973i) q^{10} +(2.68322 + 3.69314i) q^{11} +(-1.74468 - 0.977799i) q^{12} +(-0.669605 - 4.22772i) q^{13} +(-0.711090 - 0.380232i) q^{14} +(-0.507052 - 2.17782i) q^{15} +(1.53309 - 3.69454i) q^{16} +(1.13184 + 0.576699i) q^{17} +(0.463552 - 1.33608i) q^{18} +(0.214045 + 0.658762i) q^{19} +(4.20674 - 1.51768i) q^{20} +(0.176197 - 0.542280i) q^{21} +(-5.14676 - 3.89729i) q^{22} +(0.103651 - 0.654427i) q^{23} +(2.76242 + 0.607480i) q^{24} +(4.42343 + 2.33094i) q^{25} +(2.64090 + 5.44698i) q^{26} +(0.987688 + 0.156434i) q^{27} +(1.11839 + 0.222833i) q^{28} +(5.48448 + 1.78201i) q^{29} +(1.57981 + 2.73938i) q^{30} +(7.87705 - 2.55941i) q^{31} +(-0.558959 + 5.62917i) q^{32} +(2.07245 - 4.06742i) q^{33} +(-1.76843 - 0.316093i) q^{34} +(0.658690 + 1.09165i) q^{35} +(-0.0791572 + 1.99843i) q^{36} +(-0.551102 + 0.0872860i) q^{37} +(-0.559981 - 0.803734i) q^{38} +(-3.46293 + 2.51597i) q^{39} +(-5.07061 + 3.78007i) q^{40} +(-3.58374 - 2.60374i) q^{41} +(-0.0159605 + 0.806208i) q^{42} +(2.72923 - 2.72923i) q^{43} +(8.56463 + 3.16276i) q^{44} +(-1.71026 + 1.44050i) q^{45} +(0.128237 + 0.928219i) q^{46} +(-9.06571 + 4.61921i) q^{47} +(-3.98787 + 0.311292i) q^{48} -6.67489i q^{49} +(-6.94300 - 1.33969i) q^{50} -1.27029i q^{51} +(-5.80910 - 6.28827i) q^{52} +(7.66275 - 3.90436i) q^{53} +(-1.40091 + 0.193541i) q^{54} +(3.84140 + 9.45719i) q^{55} +(-1.60504 + 0.157307i) q^{56} +(0.489787 - 0.489787i) q^{57} +(-8.15378 - 0.161421i) q^{58} +(-5.72938 - 4.16264i) q^{59} +(-3.26208 - 3.05922i) q^{60} +(-10.7384 + 7.80192i) q^{61} +(-9.61052 + 6.69588i) q^{62} +(-0.563167 + 0.0891968i) q^{63} +(-1.55321 - 7.84777i) q^{64} +(0.816485 - 9.53642i) q^{65} +(-1.13593 + 6.35513i) q^{66} +(-4.20759 + 8.25787i) q^{67} +(2.52306 - 0.297808i) q^{68} +(-0.630155 + 0.204750i) q^{69} +(-1.33937 - 1.20715i) q^{70} +(1.71079 + 0.555870i) q^{71} +(-0.712844 - 2.73712i) q^{72} +(-6.95389 - 1.10139i) q^{73} +(0.710038 - 0.344253i) q^{74} +(0.0686916 - 4.99953i) q^{75} +(1.08765 + 0.857995i) q^{76} +(-0.407181 + 2.57084i) q^{77} +(3.65435 - 4.82594i) q^{78} +(2.36601 - 7.28182i) q^{79} +(5.31149 - 7.19640i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(5.91851 + 2.05342i) q^{82} +(-7.97834 - 4.06517i) q^{83} +(-0.309193 - 1.09766i) q^{84} +(2.14717 + 1.85952i) q^{85} +(-2.57387 + 4.81352i) q^{86} +(-0.902114 - 5.69572i) q^{87} +(-12.8889 - 0.766290i) q^{88} +(3.05003 + 4.19801i) q^{89} +(1.72358 - 2.65128i) q^{90} +(1.43457 - 1.97452i) q^{91} +(-0.554411 - 1.20362i) q^{92} +(-5.85655 - 5.85655i) q^{93} +(10.3741 - 9.97131i) q^{94} +(0.110911 + 1.54487i) q^{95} +(5.26939 - 2.05755i) q^{96} +(5.74169 + 11.2687i) q^{97} +(2.73876 + 9.03368i) q^{98} -4.56497 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44}+ \cdots + 256 q^{98}+O(q^{100}) \) 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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