LMFDB - Embedded newform 304.2.m.a.227.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(75,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("304.75");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.m (of order $4$, degree $2$, 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:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			227.20
Character	$\chi$	$=$	304.227
Dual form			304.2.m.a.75.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0324855 + 1.41384i) q^{2} +(-0.549728 - 0.549728i) q^{3} +(-1.99789 + 0.0918587i) q^{4} +(1.49999 - 1.49999i) q^{5} +(0.759369 - 0.795085i) q^{6} -3.48044 q^{7} +(-0.194776 - 2.82171i) q^{8} -2.39560i q^{9} +(2.16948 + 2.07202i) q^{10} +(-3.68459 - 3.68459i) q^{11} +(1.14879 + 1.04780i) q^{12} +(-3.73303 + 3.73303i) q^{13} +(-0.113064 - 4.92078i) q^{14} -1.64918 q^{15} +(3.98312 - 0.367047i) q^{16} +1.51477 q^{17} +(3.38699 - 0.0778223i) q^{18} +(1.27937 - 4.16692i) q^{19} +(-2.85904 + 3.13461i) q^{20} +(1.91329 + 1.91329i) q^{21} +(5.08972 - 5.32911i) q^{22} -0.482269 q^{23} +(-1.44410 + 1.65825i) q^{24} +0.500032i q^{25} +(-5.39918 - 5.15664i) q^{26} +(-2.96611 + 2.96611i) q^{27} +(6.95353 - 0.319708i) q^{28} +(7.26730 - 7.26730i) q^{29} +(-0.0535744 - 2.33167i) q^{30} +2.39300 q^{31} +(0.648339 + 5.61958i) q^{32} +4.05104i q^{33} +(0.0492080 + 2.14164i) q^{34} +(-5.22064 + 5.22064i) q^{35} +(0.220057 + 4.78614i) q^{36} +(-3.14537 - 3.14537i) q^{37} +(5.93292 + 1.67346i) q^{38} +4.10430 q^{39} +(-4.52472 - 3.94039i) q^{40} -7.94060 q^{41} +(-2.64294 + 2.76724i) q^{42} +(3.02093 + 3.02093i) q^{43} +(7.69986 + 7.02293i) q^{44} +(-3.59339 - 3.59339i) q^{45} +(-0.0156667 - 0.681851i) q^{46} +3.58534i q^{47} +(-2.39141 - 1.98786i) q^{48} +5.11344 q^{49} +(-0.706966 + 0.0162438i) q^{50} +(-0.832709 - 0.832709i) q^{51} +(7.11527 - 7.80109i) q^{52} +(3.55950 + 3.55950i) q^{53} +(-4.28996 - 4.09725i) q^{54} -11.0537 q^{55} +(0.677905 + 9.82079i) q^{56} +(-2.99397 + 1.58737i) q^{57} +(10.5109 + 10.0387i) q^{58} +(-0.408827 + 0.408827i) q^{59} +(3.29487 - 0.151491i) q^{60} +(2.47804 + 2.47804i) q^{61} +(0.0777377 + 3.38332i) q^{62} +8.33773i q^{63} +(-7.92412 + 1.09920i) q^{64} +11.1991i q^{65} +(-5.72752 + 0.131600i) q^{66} +(-10.6691 - 10.6691i) q^{67} +(-3.02634 + 0.139144i) q^{68} +(0.265116 + 0.265116i) q^{69} +(-7.55074 - 7.21155i) q^{70} +5.59302i q^{71} +(-6.75969 + 0.466605i) q^{72} -13.6019i q^{73} +(4.34487 - 4.54923i) q^{74} +(0.274881 - 0.274881i) q^{75} +(-2.17327 + 8.44256i) q^{76} +(12.8240 + 12.8240i) q^{77} +(0.133330 + 5.80283i) q^{78} -5.02027 q^{79} +(5.42410 - 6.52523i) q^{80} -3.92569 q^{81} +(-0.257955 - 11.2267i) q^{82} +(10.3497 - 10.3497i) q^{83} +(-3.99830 - 3.64679i) q^{84} +(2.27214 - 2.27214i) q^{85} +(-4.17297 + 4.36925i) q^{86} -7.99007 q^{87} +(-9.67917 + 11.1145i) q^{88} -7.42593 q^{89} +(4.96374 - 5.19721i) q^{90} +(12.9926 - 12.9926i) q^{91} +(0.963519 - 0.0443005i) q^{92} +(-1.31550 - 1.31550i) q^{93} +(-5.06909 + 0.116471i) q^{94} +(-4.33131 - 8.16940i) q^{95} +(2.73283 - 3.44565i) q^{96} -3.70124i q^{97} +(0.166113 + 7.22959i) q^{98} +(-8.82679 + 8.82679i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 4 q^{4} - 4 q^{5} - 4 q^{6} - 8 q^{7} - 4 q^{11} + 4 q^{16} - 8 q^{17} + 6 q^{19} - 32 q^{20} - 8 q^{23} - 12 q^{24} - 8 q^{26} - 40 q^{30} + 44 q^{36} - 12 q^{38} - 8 q^{39} + 12 q^{42} - 4 q^{43}+ \cdots + 76 q^{99}+O(q^{100}) $ 76 * q - 4 * q^4 - 4 * q^5 - 4 * q^6 - 8 * q^7 - 4 * q^11 + 4 * q^16 - 8 * q^17 + 6 * q^19 - 32 * q^20 - 8 * q^23 - 12 * q^24 - 8 * q^26 - 40 * q^30 + 44 * q^36 - 12 * q^38 - 8 * q^39 + 12 * q^42 - 4 * q^43 - 76 * q^44 + 4 * q^45 + 44 * q^49 + 96 * q^54 - 8 * q^55 + 24 * q^58 + 28 * q^61 + 20 * q^62 - 64 * q^64 + 12 * q^66 - 80 * q^74 + 12 * q^76 - 32 * q^77 - 16 * q^80 - 52 * q^81 + 68 * q^82 + 36 * q^83 - 56 * q^85 - 120 * q^87 - 8 * q^92 - 16 * q^93 + 48 * q^96 + 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.0324855	+	1.41384i	0.0229707	+	0.999736i
$2$	0.0324855	+	1.41384i	0.0229707	+	0.999736i
$3$	−0.549728	−	0.549728i	−0.317385	−	0.317385i	0.530377	−	0.847762i	$-0.322050\pi$
$3$	−0.549728	−	0.549728i	−0.317385	−	0.317385i	−0.847762	+	0.530377i	$0.822050\pi$
$4$	−1.99789	+	0.0918587i	−0.998945	+	0.0459293i
$5$	1.49999	−	1.49999i	0.670818	−	0.670818i	−0.287087	−	0.957905i	$-0.592687\pi$
$5$	1.49999	−	1.49999i	0.670818	−	0.670818i	0.957905	+	0.287087i	$0.0926868\pi$
$6$	0.759369	−	0.795085i	0.310011	−	0.324592i
$7$	−3.48044			−1.31548			−0.657741	−	0.753244i	$-0.728488\pi$
$7$	−3.48044			−1.31548			−0.657741	+	0.753244i	$0.728488\pi$
$8$	−0.194776	−	2.82171i	−0.0688637	−	0.997626i
$9$		−	2.39560i		−	0.798533i
$10$	2.16948	+	2.07202i	0.686050	+	0.655232i
$11$	−3.68459	−	3.68459i	−1.11094	−	1.11094i	−0.993023	−	0.117921i	$-0.962377\pi$
$11$	−3.68459	−	3.68459i	−1.11094	−	1.11094i	−0.117921	−	0.993023i	$-0.537623\pi$
$12$	1.14879	+	1.04780i	0.331628	+	0.302473i
$13$	−3.73303	+	3.73303i	−1.03536	+	1.03536i	−0.0360050	+	0.999352i	$0.511463\pi$
$13$	−3.73303	+	3.73303i	−1.03536	+	1.03536i	−0.999352	+	0.0360050i	$0.988537\pi$
$14$	−0.113064	−	4.92078i	−0.0302176	−	1.31513i
$15$	−1.64918			−0.425816
$16$	3.98312	−	0.367047i	0.995781	−	0.0917617i
$17$	1.51477			0.367385			0.183693	−	0.982984i	$-0.441195\pi$
$17$	1.51477			0.367385			0.183693	+	0.982984i	$0.441195\pi$
$18$	3.38699	−	0.0778223i	0.798322	−	0.0183429i
$19$	1.27937	−	4.16692i	0.293507	−	0.955957i
$19$	1.27937	−	4.16692i	0.293507	−	0.955957i
$20$	−2.85904	+	3.13461i	−0.639300	+	0.700920i
$21$	1.91329	+	1.91329i	0.417515	+	0.417515i
$22$	5.08972	−	5.32911i	1.08513	−	1.13617i
$23$	−0.482269			−0.100560			−0.0502800	−	0.998735i	$-0.516011\pi$
$23$	−0.482269			−0.100560			−0.0502800	+	0.998735i	$0.516011\pi$
$24$	−1.44410	+	1.65825i	−0.294776	+	0.338488i
$25$			0.500032i			0.100006i
$26$	−5.39918	−	5.15664i	−1.05887	−	1.01130i
$27$	−2.96611	+	2.96611i	−0.570828	+	0.570828i
$28$	6.95353	−	0.319708i	1.31409	−	0.0604192i
$29$	7.26730	−	7.26730i	1.34950	−	1.34950i	0.463303	−	0.886200i	$-0.346664\pi$
$29$	7.26730	−	7.26730i	1.34950	−	1.34950i	0.886200	−	0.463303i	$-0.153336\pi$
$30$	−0.0535744	−	2.33167i	−0.00978129	−	0.425703i
$31$	2.39300			0.429795			0.214897	−	0.976637i	$-0.431058\pi$
$31$	2.39300			0.429795			0.214897	+	0.976637i	$0.431058\pi$
$32$	0.648339	+	5.61958i	0.114611	+	0.993410i
$33$			4.05104i			0.705195i
$34$	0.0492080	+	2.14164i	0.00843910	+	0.367288i
$35$	−5.22064	+	5.22064i	−0.882449	+	0.882449i
$36$	0.220057	+	4.78614i	0.0366761	+	0.797690i
$37$	−3.14537	−	3.14537i	−0.517096	−	0.517096i	0.399596	−	0.916691i	$-0.369150\pi$
$37$	−3.14537	−	3.14537i	−0.517096	−	0.517096i	−0.916691	+	0.399596i	$0.869150\pi$
$38$	5.93292	+	1.67346i	0.962447	+	0.271471i
$39$	4.10430			0.657214
$40$	−4.52472	−	3.94039i	−0.715421	−	0.623031i
$41$	−7.94060			−1.24011			−0.620057	−	0.784557i	$-0.712890\pi$
$41$	−7.94060			−1.24011			−0.620057	+	0.784557i	$0.712890\pi$
$42$	−2.64294	+	2.76724i	−0.407814	+	0.426995i
$43$	3.02093	+	3.02093i	0.460687	+	0.460687i	0.898881	−	0.438193i	$-0.144382\pi$
$43$	3.02093	+	3.02093i	0.460687	+	0.460687i	−0.438193	+	0.898881i	$0.644382\pi$
$44$	7.69986	+	7.02293i	1.16080	+	1.05875i
$45$	−3.59339	−	3.59339i	−0.535670	−	0.535670i
$46$	−0.0156667	−	0.681851i	−0.00230993	−	0.100533i
$47$			3.58534i			0.522975i	0.965207	+	0.261488i	$0.0842130\pi$
$47$			3.58534i			0.522975i	−0.965207	+	0.261488i	$0.915787\pi$
$48$	−2.39141	−	1.98786i	−0.345170	−	0.286922i
$49$	5.11344			0.730492
$50$	−0.706966	+	0.0162438i	−0.0999800	+	0.00229722i
$51$	−0.832709	−	0.832709i	−0.116603	−	0.116603i
$52$	7.11527	−	7.80109i	0.986711	−	1.08182i
$53$	3.55950	+	3.55950i	0.488935	+	0.488935i	0.907970	−	0.419035i	$-0.137631\pi$
$53$	3.55950	+	3.55950i	0.488935	+	0.488935i	−0.419035	+	0.907970i	$0.637631\pi$
$54$	−4.28996	−	4.09725i	−0.583790	−	0.557565i
$55$	−11.0537			−1.49048
$56$	0.677905	+	9.82079i	0.0905889	+	1.31236i
$57$	−2.99397	+	1.58737i	−0.396562	+	0.210252i
$58$	10.5109	+	10.0387i	1.38015	+	1.31815i
$59$	−0.408827	+	0.408827i	−0.0532248	+	0.0532248i	−0.733218	−	0.679993i	$-0.761983\pi$
$59$	−0.408827	+	0.408827i	−0.0532248	+	0.0532248i	0.679993	+	0.733218i	$0.261983\pi$
$60$	3.29487	−	0.151491i	0.425366	−	0.0195574i
$61$	2.47804	+	2.47804i	0.317281	+	0.317281i	0.847722	−	0.530441i	$-0.177974\pi$
$61$	2.47804	+	2.47804i	0.317281	+	0.317281i	−0.530441	+	0.847722i	$0.677974\pi$
$62$	0.0777377	+	3.38332i	0.00987270	+	0.429682i
$63$			8.33773i			1.05046i
$64$	−7.92412	+	1.09920i	−0.990516	+	0.137400i
$65$			11.1991i			1.38907i
$66$	−5.72752	+	0.131600i	−0.705009	+	0.0161988i
$67$	−10.6691	−	10.6691i	−1.30344	−	1.30344i	−0.926056	−	0.377387i	$-0.876823\pi$
$67$	−10.6691	−	10.6691i	−1.30344	−	1.30344i	−0.377387	−	0.926056i	$-0.623177\pi$
$68$	−3.02634	+	0.139144i	−0.366997	+	0.0168737i
$69$	0.265116	+	0.265116i	0.0319163	+	0.0319163i
$70$	−7.55074	−	7.21155i	−0.902486	−	0.861945i
$71$			5.59302i			0.663769i	0.943320	+	0.331885i	$0.107684\pi$
$71$			5.59302i			0.663769i	−0.943320	+	0.331885i	$0.892316\pi$
$72$	−6.75969	+	0.466605i	−0.796637	+	0.0549899i
$73$		−	13.6019i		−	1.59198i	−0.605311	−	0.795989i	$-0.706951\pi$
$73$		−	13.6019i		−	1.59198i	0.605311	−	0.795989i	$-0.293049\pi$
$74$	4.34487	−	4.54923i	0.505081	−	0.528837i
$75$	0.274881	−	0.274881i	0.0317406	−	0.0317406i
$76$	−2.17327	+	8.44256i	−0.249291	+	0.968429i
$77$	12.8240	+	12.8240i	1.46143	+	1.46143i
$78$	0.133330	+	5.80283i	0.0150967	+	0.657041i
$79$	−5.02027			−0.564825			−0.282412	−	0.959293i	$-0.591135\pi$
$79$	−5.02027			−0.564825			−0.282412	+	0.959293i	$0.591135\pi$
$80$	5.42410	−	6.52523i	0.606432	−	0.729543i
$81$	−3.92569			−0.436188
$82$	−0.257955	−	11.2267i	−0.0284863	−	1.23979i
$83$	10.3497	−	10.3497i	1.13603	−	1.13603i	0.146870	−	0.989156i	$-0.453080\pi$
$83$	10.3497	−	10.3497i	1.13603	−	1.13603i	0.989156	−	0.146870i	$-0.0469198\pi$
$84$	−3.99830	−	3.64679i	−0.436250	−	0.397898i
$85$	2.27214	−	2.27214i	0.246448	−	0.246448i
$86$	−4.17297	+	4.36925i	−0.449983	+	0.471148i
$87$	−7.99007			−0.856625
$88$	−9.67917	+	11.1145i	−1.03180	+	1.18481i
$89$	−7.42593			−0.787147			−0.393573	−	0.919293i	$-0.628761\pi$
$89$	−7.42593			−0.787147			−0.393573	+	0.919293i	$0.628761\pi$
$90$	4.96374	−	5.19721i	0.523224	−	0.547834i
$91$	12.9926	−	12.9926i	1.36199	−	1.36199i
$92$	0.963519	−	0.0443005i	0.100454	−	0.00461865i
$93$	−1.31550	−	1.31550i	−0.136411	−	0.136411i
$94$	−5.06909	+	0.116471i	−0.522837	+	0.0120131i
$95$	−4.33131	−	8.16940i	−0.444383	−	0.838163i
$96$	2.73283	−	3.44565i	0.278918	−	0.351670i
$97$		−	3.70124i		−	0.375804i	−0.982188	−	0.187902i	$-0.939831\pi$
$97$		−	3.70124i		−	0.375804i	0.982188	−	0.187902i	$-0.0601688\pi$
$98$	0.166113	+	7.22959i	0.0167799	+	0.730299i
$99$	−8.82679	+	8.82679i	−0.887126	+	0.887126i
$100$	−0.0459323	−	0.999009i	−0.00459323	−	0.0999009i
$101$	4.78718	−	4.78718i	0.476342	−	0.476342i	−0.427618	−	0.903960i	$-0.640647\pi$
$101$	4.78718	−	4.78718i	0.476342	−	0.476342i	0.903960	+	0.427618i	$0.140647\pi$
$102$	1.15027	−	1.20437i	0.113893	−	0.119250i
$103$			11.4253i			1.12577i	0.826536	+	0.562885i	$0.190308\pi$
$103$			11.4253i			1.12577i	−0.826536	+	0.562885i	$0.809692\pi$
$104$	11.2606	+	9.80644i	1.10420	+	0.961600i
$105$	5.73986			0.560153
$106$	−4.91694	+	5.14820i	−0.477575	+	0.500037i
$107$	11.7874	−	11.7874i	1.13953	−	1.13953i	0.150999	−	0.988534i	$-0.451751\pi$
$107$	11.7874	−	11.7874i	1.13953	−	1.13953i	0.988534	−	0.150999i	$-0.0482490\pi$
$108$	5.65350	−	6.19842i	0.544008	−	0.596443i
$109$	10.3205	−	10.3205i	0.988523	−	0.988523i	−0.0114120	−	0.999935i	$-0.503633\pi$
$109$	10.3205	−	10.3205i	0.988523	−	0.988523i	0.999935	+	0.0114120i	$0.00363264\pi$
$110$	−0.359086	−	15.6282i	−0.0342375	−	1.49009i
$111$			3.45819i			0.328237i
$112$	−13.8630	+	1.27748i	−1.30993	+	0.120711i
$113$			14.0443i			1.32118i	0.750747	+	0.660590i	$0.229694\pi$
$113$			14.0443i			1.32118i	−0.750747	+	0.660590i	$0.770306\pi$
$114$	−2.34154	−	4.18144i	−0.219306	−	0.391627i
$115$	−0.723400	+	0.723400i	−0.0674574	+	0.0674574i
$116$	−13.8517	+	15.1868i	−1.28610	+	1.41006i
$117$	8.94285	+	8.94285i	0.826766	+	0.826766i
$118$	−0.591297	−	0.564735i	−0.0544333	−	0.0519881i
$119$	−5.27205			−0.483288
$120$	0.321220	+	4.65350i	0.0293232	+	0.424805i
$121$			16.1523i			1.46839i
$122$	−3.42306	+	3.58406i	−0.309909	+	0.324485i
$123$	4.36517	+	4.36517i	0.393594	+	0.393594i
$124$	−4.78094	+	0.219817i	−0.429341	+	0.0197402i
$125$	8.25002	+	8.25002i	0.737904	+	0.737904i
$126$	−11.7882	+	0.270856i	−1.05018	+	0.0241297i
$127$	5.68283			0.504269			0.252135	−	0.967692i	$-0.418867\pi$
$127$	5.68283			0.504269			0.252135	+	0.967692i	$0.418867\pi$
$128$	−1.81152	−	11.1677i	−0.160117	−	0.987098i
$129$		−	3.32138i		−	0.292431i
$130$	−15.8337	+	0.363807i	−1.38871	+	0.0319080i
$131$	0.994673	−	0.994673i	0.0869050	−	0.0869050i	−0.662318	−	0.749223i	$-0.730427\pi$
$131$	0.994673	−	0.994673i	0.0869050	−	0.0869050i	0.749223	+	0.662318i	$0.230427\pi$
$132$	−0.372123	−	8.09352i	−0.0323891	−	0.704451i
$133$	−4.45276	+	14.5027i	−0.386104	+	1.25754i
$134$	14.7379	−	15.4311i	1.27316	−	1.33304i
$135$			8.89830i			0.765844i
$136$	−0.295040	−	4.27424i	−0.0252995	−	0.366513i
$137$		−	10.6023i		−	0.905817i	−0.891557	−	0.452909i	$-0.850386\pi$
$137$		−	10.6023i		−	0.905817i	0.891557	−	0.452909i	$-0.149614\pi$
$138$	−0.366220	+	0.383445i	−0.0311747	+	0.0326410i
$139$	9.25182	+	9.25182i	0.784729	+	0.784729i	0.980625	−	0.195895i	$-0.0627613\pi$
$139$	9.25182	+	9.25182i	0.784729	+	0.784729i	−0.195895	+	0.980625i	$0.562761\pi$
$140$	9.95070	−	10.9098i	0.840987	−	0.922048i
$141$	1.97096	−	1.97096i	0.165985	−	0.165985i
$142$	−7.90764	+	0.181692i	−0.663594	+	0.0152473i
$143$	27.5093			2.30045
$144$	−0.879297	−	9.54197i	−0.0732748	−	0.795164i
$145$		−	21.8018i		−	1.81054i
$146$	19.2309	−	0.441864i	1.59156	−	0.0365689i
$147$	−2.81100	−	2.81100i	−0.231847	−	0.231847i
$148$	6.57303	+	5.99517i	0.540300	+	0.492800i
$149$	0.265791	−	0.265791i	0.0217745	−	0.0217745i	−0.696136	−	0.717910i	$-0.745099\pi$
$149$	0.265791	−	0.265791i	0.0217745	−	0.0217745i	0.717910	+	0.696136i	$0.245099\pi$
$150$	0.397568	+	0.379709i	0.0324613	+	0.0310031i
$151$		−	8.26373i		−	0.672493i	−0.941774	−	0.336246i	$-0.890843\pi$
$151$		−	8.26373i		−	0.672493i	0.941774	−	0.336246i	$-0.109157\pi$
$152$	−12.0070	−	2.79840i	−0.973899	−	0.226980i
$153$		−	3.62878i		−	0.293369i
$154$	−17.7145	+	18.5476i	−1.42747	+	1.49461i
$155$	3.58948	−	3.58948i	0.288314	−	0.288314i
$156$	−8.19994	+	0.377016i	−0.656521	+	0.0301854i
$157$	−11.1943	−	11.1943i	−0.893405	−	0.893405i	0.101437	−	0.994842i	$-0.467656\pi$
$157$	−11.1943	−	11.1943i	−0.893405	−	0.893405i	−0.994842	+	0.101437i	$0.967656\pi$
$158$	−0.163086	−	7.09786i	−0.0129744	−	0.564676i
$159$		−	3.91351i		−	0.310362i
$160$	9.40184	+	7.45683i	0.743281	+	0.589514i
$161$	1.67851			0.132285
$162$	−0.127528	−	5.55030i	−0.0100196	−	0.436073i
$163$	5.31053	−	5.31053i	0.415953	−	0.415953i	−0.467853	−	0.883806i	$-0.654972\pi$
$163$	5.31053	−	5.31053i	0.415953	−	0.415953i	0.883806	+	0.467853i	$0.154972\pi$
$164$	15.8644	−	0.729413i	1.23881	−	0.0569576i
$165$	6.07653	+	6.07653i	0.473058	+	0.473058i
$166$	14.9690	+	14.2966i	1.16182	+	1.10963i
$167$			9.02701i			0.698531i	0.937024	+	0.349266i	$0.113569\pi$
$167$			9.02701i			0.698531i	−0.937024	+	0.349266i	$0.886431\pi$
$168$	5.02610	−	5.77142i	0.387772	−	0.445275i
$169$		−	14.8710i		−	1.14393i
$170$	3.28626	+	3.13864i	0.252045	+	0.240722i
$171$	−9.98227	−	3.06486i	−0.763363	−	0.234375i
$172$	−6.31298	−	5.75798i	−0.481360	−	0.439042i
$173$	7.82463	−	7.82463i	0.594895	−	0.594895i	−0.344054	−	0.938950i	$-0.611800\pi$
$173$	7.82463	−	7.82463i	0.594895	−	0.594895i	0.938950	+	0.344054i	$0.111800\pi$
$174$	−0.259561	−	11.2967i	−0.0196773	−	0.856399i
$175$		−	1.74033i		−	0.131557i
$176$	−16.0286	−	13.3237i	−1.20820	−	1.00432i
$177$	0.449487			0.0337855
$178$	−0.241235	−	10.4991i	−0.0180813	−	0.786939i
$179$	2.95338	+	2.95338i	0.220746	+	0.220746i	0.808813	−	0.588067i	$-0.200111\pi$
$179$	2.95338	+	2.95338i	0.220746	+	0.220746i	−0.588067	+	0.808813i	$0.700111\pi$
$180$	7.50927	+	6.84910i	0.559708	+	0.510502i
$181$	−6.95777	−	6.95777i	−0.517167	−	0.517167i	0.399546	−	0.916713i	$-0.369168\pi$
$181$	−6.95777	−	6.95777i	−0.517167	−	0.517167i	−0.916713	+	0.399546i	$0.869168\pi$
$182$	18.7915	+	17.9474i	1.39292	+	1.33035i
$183$		−	2.72450i		−	0.201401i
$184$	0.0939343	+	1.36082i	0.00692493	+	0.100321i
$185$	−9.43607			−0.693754
$186$	1.81717	−	1.90264i	0.133241	−	0.139508i
$187$	−5.58129	−	5.58129i	−0.408144	−	0.408144i
$188$	−0.329344	−	7.16311i	−0.0240199	−	0.522423i
$189$	10.3234	−	10.3234i	0.750914	−	0.750914i
$190$	11.4095	−	6.38917i	0.827734	−	0.463519i
$191$		−	3.91455i		−	0.283247i	−0.989921	−	0.141624i	$-0.954768\pi$
$191$		−	3.91455i		−	0.283247i	0.989921	−	0.141624i	$-0.0452322\pi$
$192$	4.96037	+	3.75185i	0.357984	+	0.270766i
$193$		−	17.5680i		−	1.26457i	−0.774736	−	0.632285i	$-0.782117\pi$
$193$		−	17.5680i		−	1.26457i	0.774736	−	0.632285i	$-0.217883\pi$
$194$	5.23297	−	0.120237i	0.375705	−	0.00863249i
$195$	6.15643	−	6.15643i	0.440871	−	0.440871i
$196$	−10.2161	+	0.469714i	−0.729721	+	0.0335510i
$197$	−16.2889	+	16.2889i	−1.16053	+	1.16053i	−0.176176	+	0.984359i	$0.556373\pi$
$197$	−16.2889	+	16.2889i	−1.16053	+	1.16053i	−0.984359	+	0.176176i	$0.943627\pi$
$198$	−12.7664	−	12.1929i	−0.907270	−	0.866514i
$199$	21.6100			1.53189			0.765945	−	0.642906i	$-0.222272\pi$
$199$	21.6100			1.53189			0.765945	+	0.642906i	$0.222272\pi$
$200$	1.41095	−	0.0973942i	0.0997690	−	0.00688681i
$201$			11.7302i			0.827387i
$202$	6.92382	+	6.61279i	0.487158	+	0.465274i
$203$	−25.2934	+	25.2934i	−1.77525	+	1.77525i
$204$	1.74015	+	1.58717i	0.121835	+	0.111124i
$205$	−11.9109	+	11.9109i	−0.831891	+	0.831891i
$206$	−16.1536	+	0.371157i	−1.12547	+	0.0258597i
$207$			1.15532i			0.0803004i
$208$	−13.4989	+	16.2393i	−0.935982	+	1.12599i
$209$	−20.0673	+	10.6394i	−1.38809	+	0.735944i
$210$	0.186462	+	8.11524i	0.0128671	+	0.560005i
$211$	−16.6981	−	16.6981i	−1.14954	−	1.14954i	−0.986642	−	0.162901i	$-0.947915\pi$
$211$	−16.6981	−	16.6981i	−1.14954	−	1.14954i	−0.162901	−	0.986642i	$-0.552085\pi$
$212$	−7.43846	−	6.78452i	−0.510876	−	0.465963i
$213$	3.07464	−	3.07464i	0.210671	−	0.210671i
$214$	17.0485	+	16.2826i	1.16541	+	1.11306i
$215$	9.06275			0.618075
$216$	8.94724	+	7.79178i	0.608782	+	0.530164i
$217$	−8.32868			−0.565387
$218$	14.9268	+	14.2562i	1.01097	+	0.965555i
$219$	−7.47732	+	7.47732i	−0.505271	+	0.505271i
$220$	22.0841	−	1.01538i	1.48891	−	0.0684569i
$221$	−5.65467	+	5.65467i	−0.380374	+	0.380374i
$222$	−4.88933	+	0.112341i	−0.328151	+	0.00753984i
$223$	−1.63480			−0.109474			−0.0547372	−	0.998501i	$-0.517432\pi$
$223$	−1.63480			−0.109474			−0.0547372	+	0.998501i	$0.517432\pi$
$224$	−2.25650	−	19.5586i	−0.150769	−	1.30681i
$225$	1.19788			0.0798584
$226$	−19.8565	+	0.456238i	−1.32083	+	0.0303485i
$227$	0.463368	+	0.463368i	0.0307548	+	0.0307548i	0.722317	−	0.691562i	$-0.243077\pi$
$227$	0.463368	+	0.463368i	0.0307548	+	0.0307548i	−0.691562	+	0.722317i	$0.743077\pi$
$228$	5.83582	−	3.44640i	0.386486	−	0.228244i
$229$	−8.36381	+	8.36381i	−0.552696	+	0.552696i	−0.927218	−	0.374522i	$-0.877807\pi$
$229$	−8.36381	+	8.36381i	−0.552696	+	0.552696i	0.374522	+	0.927218i	$0.377807\pi$
$230$	−1.04627	−	0.999273i	−0.0689892	−	0.0658901i
$231$		−	14.0994i		−	0.927671i
$232$	−21.9217	−	19.0907i	−1.43923	−	1.25337i
$233$			9.02414i			0.591191i	0.955313	+	0.295596i	$0.0955181\pi$
$233$			9.02414i			0.591191i	−0.955313	+	0.295596i	$0.904482\pi$
$234$	−12.3532	+	12.9343i	−0.807557	+	0.845540i
$235$	5.37799	+	5.37799i	0.350821	+	0.350821i
$236$	0.779237	−	0.854346i	0.0507240	−	0.0556132i
$237$	2.75978	+	2.75978i	0.179267	+	0.179267i
$238$	−0.171265	−	7.45384i	−0.0111015	−	0.483161i
$239$			0.575236i			0.0372089i	0.999827	+	0.0186045i	$0.00592233\pi$
$239$			0.575236i			0.0372089i	−0.999827	+	0.0186045i	$0.994078\pi$
$240$	−6.56888	+	0.605325i	−0.424019	+	0.0390736i
$241$		−	10.2254i		−	0.658678i	−0.944212	−	0.329339i	$-0.893174\pi$
$241$		−	10.2254i		−	0.658678i	0.944212	−	0.329339i	$-0.106826\pi$
$242$	−22.8368	+	0.524717i	−1.46801	+	0.0337301i
$243$	11.0564	+	11.0564i	0.709268	+	0.709268i
$244$	−5.17849	−	4.72323i	−0.331519	−	0.302374i
$245$	7.67014	−	7.67014i	0.490027	−	0.490027i
$246$	−6.02985	+	6.31346i	−0.384449	+	0.402531i
$247$	10.7793	+	20.3312i	0.685871	+	1.29364i
$248$	−0.466098	−	6.75235i	−0.0295973	−	0.428775i
$249$	−11.3790			−0.721116
$250$	−11.3962	+	11.9322i	−0.720759	+	0.754660i
$251$	−9.67088	−	9.67088i	−0.610421	−	0.610421i	0.332635	−	0.943056i	$-0.392062\pi$
$251$	−9.67088	−	9.67088i	−0.610421	−	0.610421i	−0.943056	+	0.332635i	$0.892062\pi$
$252$	−0.765893	−	16.6579i	−0.0482467	−	1.04935i
$253$	1.77696	+	1.77696i	0.111717	+	0.111717i
$254$	0.184610	+	8.03461i	0.0115834	+	0.504136i
$255$	−2.49812			−0.156438
$256$	15.7306	−	2.92399i	0.983160	−	0.182749i
$257$			18.8850i			1.17802i	0.808127	+	0.589008i	$0.200481\pi$
$257$			18.8850i			1.17802i	−0.808127	+	0.589008i	$0.799519\pi$
$258$	4.69589	−	0.107897i	0.292354	−	0.00671735i
$259$	10.9473	+	10.9473i	0.680230	+	0.680230i
$260$	−1.02873	−	22.3745i	−0.0637991	−	1.38761i
$261$	−17.4095	−	17.4095i	−1.07762	−	1.07762i
$262$	1.43862	+	1.37400i	0.0888783	+	0.0848858i
$263$	−12.0775			−0.744732			−0.372366	−	0.928086i	$-0.621453\pi$
$263$	−12.0775			−0.744732			−0.372366	+	0.928086i	$0.621453\pi$
$264$	11.4309	−	0.789045i	0.703521	−	0.0485623i
$265$	10.6785			0.655973
$266$	−20.6492	−	5.82437i	−1.26608	−	0.357115i
$267$	4.08224	+	4.08224i	0.249829	+	0.249829i
$268$	22.2958	+	20.3357i	1.36193	+	1.24220i
$269$	8.54359	−	8.54359i	0.520912	−	0.520912i	−0.396935	−	0.917847i	$-0.629926\pi$
$269$	8.54359	−	8.54359i	0.520912	−	0.520912i	0.917847	+	0.396935i	$0.129926\pi$
$270$	−12.5808	+	0.289066i	−0.765641	+	0.0175920i
$271$			8.30882i			0.504725i	0.967633	+	0.252362i	$0.0812075\pi$
$271$			8.30882i			0.504725i	−0.967633	+	0.252362i	$0.918793\pi$
$272$	6.03351	−	0.555991i	0.365835	−	0.0337119i
$273$	−14.2848			−0.864553
$274$	14.9900	−	0.344422i	0.905578	−	0.0208073i
$275$	1.84241	−	1.84241i	0.111102	−	0.111102i
$276$	−0.554026	−	0.505320i	−0.0333485	−	0.0304167i
$277$	9.55608	−	9.55608i	0.574169	−	0.574169i	−0.359122	−	0.933291i	$-0.616924\pi$
$277$	9.55608	−	9.55608i	0.574169	−	0.574169i	0.933291	+	0.359122i	$0.116924\pi$
$278$	−12.7801	+	13.3812i	−0.766497	+	0.802548i
$279$		−	5.73266i		−	0.343205i
$280$	15.7480	+	13.7143i	0.941123	+	0.819585i
$281$	9.32142			0.556069			0.278035	−	0.960571i	$-0.410317\pi$
$281$	9.32142			0.556069			0.278035	+	0.960571i	$0.410317\pi$
$282$	2.85065	+	2.72259i	0.169754	+	0.162128i
$283$	4.19436	+	4.19436i	0.249329	+	0.249329i	0.820695	−	0.571366i	$-0.193586\pi$
$283$	4.19436	+	4.19436i	0.249329	+	0.249329i	−0.571366	+	0.820695i	$0.693586\pi$
$284$	−0.513767	−	11.1742i	−0.0304865	−	0.663069i
$285$	−2.10991	+	6.87199i	−0.124980	+	0.407061i
$286$	0.893655	+	38.8938i	0.0528429	+	2.29984i
$287$	27.6368			1.63135
$288$	13.4623	−	1.55316i	0.793271	−	0.0915209i
$289$	−14.7055			−0.865028
$290$	30.8243	−	0.708243i	1.81006	−	0.0415895i
$291$	−2.03467	+	2.03467i	−0.119275	+	0.119275i
$292$	1.24945	+	27.1750i	0.0731185	+	1.59030i
$293$	−13.7219	−	13.7219i	−0.801640	−	0.801640i	0.181712	−	0.983352i	$-0.441836\pi$
$293$	−13.7219	−	13.7219i	−0.801640	−	0.801640i	−0.983352	+	0.181712i	$0.941836\pi$
$294$	3.88299	−	4.06562i	0.226461	−	0.237112i
$295$			1.22648i			0.0714083i
$296$	−8.26269	+	9.48797i	−0.480259	+	0.551477i
$297$	21.8578			1.26832
$298$	0.384421	+	0.367152i	0.0222689	+	0.0212686i
$299$	1.80032	−	1.80032i	0.104115	−	0.104115i
$300$	−0.523932	+	0.574433i	−0.0302493	+	0.0331649i
$301$	−10.5142	−	10.5142i	−0.606026	−	0.606026i
$302$	11.6836	−	0.268451i	0.672315	−	0.0154476i
$303$	−5.26329			−0.302368
$304$	3.56643	−	17.0669i	0.204549	−	0.978856i
$305$	7.43410			0.425675
$306$	5.13051	−	0.117883i	0.293292	−	0.00673890i
$307$	9.90107	+	9.90107i	0.565084	+	0.565084i	0.930747	−	0.365663i	$-0.119158\pi$
$307$	9.90107	+	9.90107i	0.565084	+	0.565084i	−0.365663	+	0.930747i	$0.619158\pi$
$308$	−26.7989	−	24.4429i	−1.52701	−	1.39276i
$309$	6.28081	−	6.28081i	0.357303	−	0.357303i
$310$	5.19156	+	4.95835i	0.294861	+	0.281615i
$311$	17.4462			0.989283			0.494642	−	0.869097i	$-0.335299\pi$
$311$	17.4462			0.989283			0.494642	+	0.869097i	$0.335299\pi$
$312$	−0.799419	−	11.5812i	−0.0452582	−	0.655654i
$313$			9.14849i			0.517103i	0.965997	+	0.258552i	$0.0832452\pi$
$313$			9.14849i			0.517103i	−0.965997	+	0.258552i	$0.916755\pi$
$314$	15.4633	−	16.1906i	0.872647	−	0.913691i
$315$	12.5066	+	12.5066i	0.704665	+	0.704665i
$316$	10.0299	−	0.461155i	0.564229	−	0.0259420i
$317$	−19.0979	+	19.0979i	−1.07264	+	1.07264i	−0.0754990	+	0.997146i	$0.524055\pi$
$317$	−19.0979	+	19.0979i	−1.07264	+	1.07264i	−0.997146	+	0.0754990i	$0.975945\pi$
$318$	5.53308	−	0.127132i	0.310280	−	0.00712924i
$319$	−53.5539			−2.99845
$320$	−10.2373	+	13.5349i	−0.572285	+	0.756626i
$321$	−12.9597			−0.723342
$322$	0.0545271	+	2.37314i	0.00303868	+	0.132250i
$323$	1.93795	−	6.31191i	0.107830	−	0.351204i
$324$	7.84310	−	0.360609i	0.435728	−	0.0200338i
$325$	−1.86664	−	1.86664i	−0.103542	−	0.103542i
$326$	7.68076	+	7.33573i	0.425398	+	0.406289i
$327$	−11.3469			−0.627485
$328$	1.54664	+	22.4061i	0.0853988	+	1.23717i
$329$		−	12.4785i		−	0.687964i
$330$	−8.39385	+	8.78865i	−0.462066	+	0.483799i
$331$	−3.09582	+	3.09582i	−0.170162	+	0.170162i	−0.787050	−	0.616889i	$-0.788393\pi$
$331$	−3.09582	+	3.09582i	−0.170162	+	0.170162i	0.616889	+	0.787050i	$0.288393\pi$
$332$	−19.7268	+	21.6282i	−1.08265	+	1.18700i
$333$	−7.53504	+	7.53504i	−0.412918	+	0.412918i
$334$	−12.7628	+	0.293247i	−0.698347	+	0.0160458i
$335$	−32.0073			−1.74875
$336$	8.32315	+	6.91861i	0.454065	+	0.377441i
$337$			12.1693i			0.662903i	0.943472	+	0.331452i	$0.107538\pi$
$337$			12.1693i			0.662903i	−0.943472	+	0.331452i	$0.892462\pi$
$338$	21.0253	−	0.483093i	1.14362	−	0.0262768i
$339$	7.72056	−	7.72056i	0.419323	−	0.419323i
$340$	−4.33077	+	4.74821i	−0.234869	+	0.257508i
$341$	−8.81720	−	8.81720i	−0.477478	−	0.477478i
$342$	4.00894	−	14.2129i	0.216779	−	0.768545i
$343$	6.56604			0.354533
$344$	7.93579	−	9.11260i	0.427869	−	0.491318i
$345$	0.795346			0.0428200
$346$	11.3170	+	10.8086i	0.608403	+	0.581073i
$347$	−8.14038	−	8.14038i	−0.436999	−	0.436999i	0.454002	−	0.891001i	$-0.349996\pi$
$347$	−8.14038	−	8.14038i	−0.436999	−	0.436999i	−0.891001	+	0.454002i	$0.849996\pi$
$348$	15.9633	−	0.733957i	0.855721	−	0.0393442i
$349$	11.7882	+	11.7882i	0.631010	+	0.631010i	0.948321	−	0.317311i	$-0.102780\pi$
$349$	11.7882	+	11.7882i	0.631010	+	0.631010i	−0.317311	+	0.948321i	$0.602780\pi$
$350$	2.46055	−	0.0565355i	0.131522	−	0.00302195i
$351$		−	22.1452i		−	1.18202i
$352$	18.3170	−	23.0947i	0.976297	−	1.23095i
$353$	4.06776			0.216505			0.108253	−	0.994123i	$-0.465474\pi$
$353$	4.06776			0.216505			0.108253	+	0.994123i	$0.465474\pi$
$354$	0.0146018	+	0.635503i	0.000776078	+	0.0337766i
$355$	8.38950	+	8.38950i	0.445268	+	0.445268i
$356$	14.8362	−	0.682136i	0.786316	−	0.0361531i
$357$	2.89819	+	2.89819i	0.153389	+	0.153389i
$358$	−4.07966	+	4.27155i	−0.215617	+	0.225758i
$359$	−7.30143			−0.385355			−0.192677	−	0.981262i	$-0.561717\pi$
$359$	−7.30143			−0.385355			−0.192677	+	0.981262i	$0.561717\pi$
$360$	−9.43960	+	10.8394i	−0.497510	+	0.571287i
$361$	−15.7264	−	10.6621i	−0.827707	−	0.561161i
$362$	9.61114	−	10.0632i	0.505150	−	0.528910i
$363$	8.87939	−	8.87939i	0.466047	−	0.466047i
$364$	−24.7643	+	27.1512i	−1.29800	+	1.42311i
$365$	−20.4027	−	20.4027i	−1.06793	−	1.06793i
$366$	3.85200	−	0.0885067i	0.201347	−	0.00462632i
$367$			8.15940i			0.425917i	0.977061	+	0.212959i	$0.0683100\pi$
$367$			8.15940i			0.425917i	−0.977061	+	0.212959i	$0.931690\pi$
$368$	−1.92094	+	0.177015i	−0.100136	+	0.00922755i
$369$			19.0225i			0.990272i
$370$	−0.306536	−	13.3411i	−0.0159360	−	0.693571i
$371$	−12.3886	−	12.3886i	−0.643185	−	0.643185i
$372$	2.74906	+	2.50738i	0.142532	+	0.130001i
$373$	−7.35016	−	7.35016i	−0.380577	−	0.380577i	0.490733	−	0.871310i	$-0.336729\pi$
$373$	−7.35016	−	7.35016i	−0.380577	−	0.380577i	−0.871310	+	0.490733i	$0.836729\pi$
$374$	7.70974	−	8.07236i	0.398661	−	0.417412i
$375$		−	9.07053i		−	0.468400i
$376$	10.1168	−	0.698337i	0.521734	−	0.0360140i
$377$			54.2581i			2.79443i
$378$	14.9309	+	14.2602i	0.767965	+	0.733467i
$379$	20.2426	−	20.2426i	1.03979	−	1.03979i	0.0406169	−	0.999175i	$-0.487068\pi$
$379$	20.2426	−	20.2426i	1.03979	−	1.03979i	0.999175	−	0.0406169i	$-0.0129323\pi$
$380$	9.40391	+	15.9237i	0.482410	+	0.816868i
$381$	−3.12401	−	3.12401i	−0.160048	−	0.160048i
$382$	5.53455	−	0.127166i	0.283172	−	0.00650639i
$383$	18.4669			0.943615			0.471807	−	0.881702i	$-0.343602\pi$
$383$	18.4669			0.943615			0.471807	+	0.881702i	$0.343602\pi$
$384$	−5.14337	+	7.13506i	−0.262472	+	0.364109i
$385$	38.4718			1.96070
$386$	24.8383	−	0.570704i	1.26424	−	0.0290481i
$387$	7.23693	−	7.23693i	0.367874	−	0.367874i
$388$	0.339991	+	7.39467i	0.0172604	+	0.375408i
$389$	−16.3368	+	16.3368i	−0.828309	+	0.828309i	−0.987283	−	0.158974i	$-0.949181\pi$
$389$	−16.3368	+	16.3368i	−0.828309	+	0.828309i	0.158974	+	0.987283i	$0.449181\pi$
$390$	8.90420	+	8.50421i	0.450882	+	0.430628i
$391$	−0.730525			−0.0369442
$392$	−0.995976	−	14.4287i	−0.0503044	−	0.728758i
$393$	−1.09360			−0.0551648
$394$	−23.5590	−	22.5007i	−1.18689	−	1.13357i
$395$	−7.53038	+	7.53038i	−0.378895	+	0.378895i
$396$	16.8241	−	18.4458i	0.845445	−	0.926935i
$397$	−13.0533	−	13.0533i	−0.655126	−	0.655126i	0.299097	−	0.954223i	$-0.403315\pi$
$397$	−13.0533	−	13.0533i	−0.655126	−	0.655126i	−0.954223	+	0.299097i	$0.903315\pi$
$398$	0.702011	+	30.5530i	0.0351886	+	1.53149i
$399$	10.4203	−	5.52473i	0.521670	−	0.276582i
$400$	0.183535	+	1.99169i	0.00917676	+	0.0995845i
$401$		−	26.3416i		−	1.31544i	−0.753263	−	0.657719i	$-0.771521\pi$
$401$		−	26.3416i		−	1.31544i	0.753263	−	0.657719i	$-0.228479\pi$
$402$	−16.5847	+	0.381063i	−0.827169	+	0.0190057i
$403$	−8.93313	+	8.93313i	−0.444991	+	0.444991i
$404$	−9.12451	+	10.0040i	−0.453961	+	0.497717i
$405$	−5.88852	+	5.88852i	−0.292603	+	0.292603i
$406$	−36.5825	−	34.9391i	−1.81556	−	1.73400i
$407$			23.1788i			1.14893i
$408$	−2.18747	+	2.51186i	−0.108296	+	0.124356i
$409$	−0.821310			−0.0406112			−0.0203056	−	0.999794i	$-0.506464\pi$
$409$	−0.821310			−0.0406112			−0.0203056	+	0.999794i	$0.506464\pi$
$410$	−17.2270	−	16.4531i	−0.850780	−	0.812562i
$411$	−5.82839	+	5.82839i	−0.287493	+	0.287493i
$412$	−1.04951	−	22.8265i	−0.0517058	−	1.12458i
$413$	1.42290	−	1.42290i	0.0700162	−	0.0700162i
$414$	−1.63344	+	0.0375312i	−0.0802793	+	0.00184456i
$415$		−	31.0489i		−	1.52413i
$416$	−23.3983	−	18.5578i	−1.14720	−	0.909870i
$417$		−	10.1720i		−	0.498123i
$418$	−15.6943	−	28.0264i	−0.767636	−	1.37081i
$419$	2.51426	−	2.51426i	0.122830	−	0.122830i	−0.643020	−	0.765849i	$-0.722319\pi$
$419$	2.51426	−	2.51426i	0.122830	−	0.122830i	0.765849	+	0.643020i	$0.222319\pi$
$420$	−11.4676	+	0.527256i	−0.559562	+	0.0257274i
$421$	9.64923	+	9.64923i	0.470275	+	0.470275i	0.902003	−	0.431729i	$-0.142096\pi$
$421$	9.64923	+	9.64923i	0.470275	+	0.470275i	−0.431729	+	0.902003i	$0.642096\pi$
$422$	23.0660	−	24.1509i	1.12283	−	1.17565i
$423$	8.58903			0.417613
$424$	9.35059	−	10.7372i	0.454105	−	0.521444i
$425$			0.757432i			0.0367409i
$426$	4.44693	+	4.24717i	0.215454	+	0.205776i
$427$	−8.62467	−	8.62467i	−0.417377	−	0.417377i
$428$	−22.4672	+	24.6327i	−1.08599	+	1.19067i
$429$	−15.1226	−	15.1226i	−0.730128	−	0.730128i
$430$	0.294408	+	12.8133i	0.0141976	+	0.617911i
$431$	5.87725			0.283097			0.141549	−	0.989931i	$-0.454792\pi$
$431$	5.87725			0.283097			0.141549	+	0.989931i	$0.454792\pi$
$432$	−10.7257	+	12.9031i	−0.516040	+	0.620800i
$433$		−	2.62302i		−	0.126054i	−0.998012	−	0.0630271i	$-0.979925\pi$
$433$		−	2.62302i		−	0.126054i	0.998012	−	0.0630271i	$-0.0200754\pi$
$434$	−0.270561	−	11.7754i	−0.0129874	−	0.565238i
$435$	−11.9851	+	11.9851i	−0.574639	+	0.574639i
$436$	−19.6712	+	21.5672i	−0.942077	+	1.03288i
$437$	−0.617000	+	2.00957i	−0.0295151	+	0.0961310i
$438$	−10.8146	−	10.3288i	−0.516744	−	0.493531i
$439$		−	34.6282i		−	1.65272i	−0.563146	−	0.826358i	$-0.690409\pi$
$439$		−	34.6282i		−	1.65272i	0.563146	−	0.826358i	$-0.309591\pi$
$440$	2.15300	+	31.1904i	0.102640	+	1.48694i
$441$		−	12.2498i		−	0.583322i
$442$	−8.17850	−	7.81111i	−0.389012	−	0.371537i
$443$	3.58478	+	3.58478i	0.170318	+	0.170318i	0.787119	−	0.616801i	$-0.211572\pi$
$443$	3.58478	+	3.58478i	0.170318	+	0.170318i	−0.616801	+	0.787119i	$0.711572\pi$
$444$	−0.317665	−	6.90909i	−0.0150757	−	0.327891i
$445$	−11.1389	+	11.1389i	−0.528032	+	0.528032i
$446$	−0.0531074	−	2.31135i	−0.00251471	−	0.109446i
$447$	−0.292226			−0.0138218
$448$	27.5794	−	3.82571i	1.30301	−	0.180748i
$449$		−	6.98073i		−	0.329441i	−0.986340	−	0.164721i	$-0.947328\pi$
$449$		−	6.98073i		−	0.329441i	0.986340	−	0.164721i	$-0.0526722\pi$
$450$	0.0389136	+	1.69361i	0.00183441	+	0.0798374i
$451$	29.2578	+	29.2578i	1.37770	+	1.37770i
$452$	−1.29009	−	28.0590i	−0.0606809	−	1.31979i
$453$	−4.54280	+	4.54280i	−0.213439	+	0.213439i
$454$	−0.640076	+	0.670181i	−0.0300402	+	0.0314532i
$455$		−	38.9776i		−	1.82730i
$456$	5.06224	+	8.13896i	0.237061	+	0.381142i
$457$		−	1.61947i		−	0.0757556i	−0.999282	−	0.0378778i	$-0.987940\pi$
$457$		−	1.61947i		−	0.0757556i	0.999282	−	0.0378778i	$-0.0120598\pi$
$458$	−12.0968	−	11.5534i	−0.565246	−	0.539854i
$459$	−4.49297	+	4.49297i	−0.209714	+	0.209714i
$460$	1.37882	−	1.51172i	0.0642880	−	0.0704845i
$461$	11.2678	+	11.2678i	0.524792	+	0.524792i	0.919015	−	0.394223i	$-0.128986\pi$
$461$	11.2678	+	11.2678i	0.524792	+	0.524792i	−0.394223	+	0.919015i	$0.628986\pi$
$462$	19.9343	−	0.458026i	0.927426	−	0.0213093i
$463$		−	26.2153i		−	1.21833i	−0.793043	−	0.609165i	$-0.791505\pi$
$463$		−	26.2153i		−	1.21833i	0.793043	−	0.609165i	$-0.208495\pi$
$464$	26.2791	−	31.6140i	1.21998	−	1.46764i
$465$	−3.94648			−0.183013
$466$	−12.7587	+	0.293154i	−0.591035	+	0.0135801i
$467$	7.45814	−	7.45814i	0.345121	−	0.345121i	−0.513167	−	0.858289i	$-0.671528\pi$
$467$	7.45814	−	7.45814i	0.345121	−	0.345121i	0.858289	+	0.513167i	$0.171528\pi$
$468$	−18.6883	−	17.0453i	−0.863867	−	0.787921i
$469$	37.1333	+	37.1333i	1.71465	+	1.71465i
$470$	−7.42891	+	7.77832i	−0.342670	+	0.358787i
$471$			12.3077i			0.567107i
$472$	1.23322	+	1.07396i	0.0567637	+	0.0494332i
$473$		−	22.2617i		−	1.02360i
$474$	−3.81224	+	3.99154i	−0.175102	+	0.183338i
$475$	2.08359	+	0.639726i	0.0956018	+	0.0293526i
$476$	10.5330	−	0.484284i	0.482778	−	0.0221971i
$477$	8.52714	−	8.52714i	0.390431	−	0.390431i
$478$	−0.813292	+	0.0186868i	−0.0371991	+	0.000854716i
$479$			22.0408i			1.00707i	0.863975	+	0.503534i	$0.167967\pi$
$479$			22.0408i			1.00707i	−0.863975	+	0.503534i	$0.832033\pi$
$480$	−1.06923	−	9.26768i	−0.0488033	−	0.423010i
$481$	23.4835			1.07076
$482$	14.4571	−	0.332178i	0.658504	−	0.0151303i
$483$	−0.922721	−	0.922721i	−0.0419853	−	0.0419853i
$484$	−1.48373	−	32.2706i	−0.0674424	−	1.46685i
$485$	−5.55184	−	5.55184i	−0.252096	−	0.252096i
$486$	−15.2728	+	15.9911i	−0.692788	+	0.725373i
$487$			21.9766i			0.995856i	0.867218	+	0.497928i	$0.165906\pi$
$487$			21.9766i			0.995856i	−0.867218	+	0.497928i	$0.834094\pi$
$488$	6.50966	−	7.47499i	0.294679	−	0.338377i
$489$	−5.83869			−0.264035
$490$	11.0935	+	10.5952i	0.501154	+	0.478642i
$491$	−17.7224	−	17.7224i	−0.799803	−	0.799803i	0.183261	−	0.983064i	$-0.441335\pi$
$491$	−17.7224	−	17.7224i	−0.799803	−	0.799803i	−0.983064	+	0.183261i	$0.941335\pi$
$492$	−9.12210	−	8.32014i	−0.411256	−	0.375101i
$493$	11.0083	−	11.0083i	0.495787	−	0.495787i
$494$	−28.3948	+	15.9007i	−1.27754	+	0.715406i
$495$			26.4803i			1.19020i
$496$	9.53160	−	0.878342i	0.427982	−	0.0394387i
$497$		−	19.4662i		−	0.873176i
$498$	−0.369653	−	16.0881i	−0.0165646	−	0.720925i
$499$	−30.3549	+	30.3549i	−1.35887	+	1.35887i	−0.483562	+	0.875310i	$0.660657\pi$
$499$	−30.3549	+	30.3549i	−1.35887	+	1.35887i	−0.875310	+	0.483562i	$0.839343\pi$
$500$	−17.2405	−	15.7248i	−0.771017	−	0.703234i
$501$	4.96240	−	4.96240i	0.221704	−	0.221704i
$502$	13.3589	−	13.9872i	0.596238	−	0.624281i
$503$	7.49320			0.334105			0.167053	−	0.985948i	$-0.446575\pi$
$503$	7.49320			0.334105			0.167053	+	0.985948i	$0.446575\pi$
$504$	23.5267	−	1.62399i	1.04796	−	0.0723382i
$505$		−	14.3615i		−	0.639077i
$506$	−2.45461	+	2.57006i	−0.109121	+	0.114253i
$507$	−8.17502	+	8.17502i	−0.363066	+	0.363066i
$508$	−11.3537	+	0.522017i	−0.503737	+	0.0231608i
$509$	−21.4192	+	21.4192i	−0.949391	+	0.949391i	−0.998780	−	0.0493888i	$-0.984273\pi$
$509$	−21.4192	+	21.4192i	−0.949391	+	0.949391i	0.0493888	+	0.998780i	$0.484273\pi$
$510$	−0.0811527	−	3.53194i	−0.00359350	−	0.156397i
$511$			47.3405i			2.09422i
$512$	4.64507	+	22.1455i	0.205285	+	0.978702i
$513$	8.56479	+	16.1543i	0.378145	+	0.713229i
$514$	−26.7004	+	0.613490i	−1.17771	+	0.0270599i
$515$	17.1379	+	17.1379i	0.755186	+	0.755186i
$516$	0.305097	+	6.63574i	0.0134311	+	0.292122i
$517$	13.2105	−	13.2105i	0.580996	−	0.580996i
$518$	−15.1221	+	15.8333i	−0.664425	+	0.695676i
$519$	−8.60283			−0.377622
$520$	31.6005	−	2.18131i	1.38577	−	0.0956566i
$521$	28.5238			1.24965			0.624824	−	0.780765i	$-0.285171\pi$
$521$	28.5238			1.24965			0.624824	+	0.780765i	$0.285171\pi$
$522$	24.0487	−	25.1798i	1.05258	−	1.10209i
$523$	2.87573	−	2.87573i	0.125747	−	0.125747i	−0.641433	−	0.767179i	$-0.721660\pi$
$523$	2.87573	−	2.87573i	0.125747	−	0.125747i	0.767179	+	0.641433i	$0.221660\pi$
$524$	−1.89588	+	2.07862i	−0.0828218	+	0.0908048i
$525$	−0.956708	+	0.956708i	−0.0417541	+	0.0417541i
$526$	−0.392344	−	17.0757i	−0.0171070	−	0.744535i
$527$	3.62483			0.157900
$528$	1.48692	+	16.1358i	0.0647099	+	0.702220i
$529$	−22.7674			−0.989888
$530$	0.346896	+	15.0977i	0.0150682	+	0.655800i
$531$	0.979386	+	0.979386i	0.0425017	+	0.0425017i
$532$	7.56393	−	29.3838i	0.327938	−	1.27395i
$533$	29.6425	−	29.6425i	1.28396	−	1.28396i
$534$	−5.63902	+	5.90425i	−0.244024	+	0.255502i
$535$		−	35.3621i		−	1.52884i
$536$	−28.0271	+	32.1833i	−1.21059	+	1.39011i
$537$		−	3.24711i		−	0.140123i
$538$	12.3568	+	11.8017i	0.532740	+	0.508809i
$539$	−18.8409	−	18.8409i	−0.811536	−	0.811536i
$540$	−0.817386	−	17.7778i	−0.0351747	−	0.765035i
$541$	1.13344	+	1.13344i	0.0487304	+	0.0487304i	0.731052	−	0.682322i	$-0.239030\pi$
$541$	1.13344	+	1.13344i	0.0487304	+	0.0487304i	−0.682322	+	0.731052i	$0.739030\pi$
$542$	−11.7473	+	0.269916i	−0.504591	+	0.0115939i
$543$			7.64975i			0.328282i
$544$	0.982083	+	8.51235i	0.0421065	+	0.364964i
$545$		−	30.9613i		−	1.32624i
$546$	−0.464048	−	20.1964i	−0.0198594	−	0.864325i
$547$	−13.4249	−	13.4249i	−0.574008	−	0.574008i	0.359238	−	0.933246i	$-0.383037\pi$
$547$	−13.4249	−	13.4249i	−0.574008	−	0.574008i	−0.933246	+	0.359238i	$0.883037\pi$
$548$	0.973915	+	21.1823i	0.0416036	+	0.904861i
$549$	5.93640	−	5.93640i	0.253359	−	0.253359i
$550$	2.66473	+	2.54502i	0.113624	+	0.108520i
$551$	−20.9847	−	39.5798i	−0.893977	−	1.68616i
$552$	0.696444	−	0.799720i	0.0296426	−	0.0340384i
$553$	17.4727			0.743017
$554$	13.8212	+	13.2003i	0.587207	+	0.560828i
$555$	5.18727	+	5.18727i	0.220187	+	0.220187i
$556$	−19.3340	−	17.6343i	−0.819943	−	0.747859i
$557$	7.79578	+	7.79578i	0.330318	+	0.330318i	0.852707	−	0.522389i	$-0.174959\pi$
$557$	7.79578	+	7.79578i	0.330318	+	0.330318i	−0.522389	+	0.852707i	$0.674959\pi$
$558$	8.10507	−	0.186228i	0.343115	−	0.00788368i
$559$	−22.5544			−0.953951
$560$	−18.8782	+	22.7107i	−0.797751	+	0.959701i
$561$			6.13638i			0.259078i
$562$	0.302811	+	13.1790i	0.0127733	+	0.555922i
$563$	−4.84245	−	4.84245i	−0.204085	−	0.204085i	0.597663	−	0.801748i	$-0.296096\pi$
$563$	−4.84245	−	4.84245i	−0.204085	−	0.204085i	−0.801748	+	0.597663i	$0.796096\pi$
$564$	−3.75671	+	4.11881i	−0.158186	+	0.173433i
$565$	21.0664	+	21.0664i	0.886272	+	0.886272i
$566$	−5.79390	+	6.06641i	−0.243536	+	0.254990i
$567$	13.6631			0.573797
$568$	15.7819	−	1.08939i	0.662194	−	0.0457096i
$569$	20.2563			0.849190			0.424595	−	0.905383i	$-0.360417\pi$
$569$	20.2563			0.849190			0.424595	+	0.905383i	$0.360417\pi$
$570$	−9.78443	−	2.75983i	−0.409825	−	0.115597i
$571$	18.3379	+	18.3379i	0.767419	+	0.767419i	0.977651	−	0.210233i	$-0.0674222\pi$
$571$	18.3379	+	18.3379i	0.767419	+	0.767419i	−0.210233	+	0.977651i	$0.567422\pi$
$572$	−54.9606	+	2.52697i	−2.29802	+	0.105658i
$573$	−2.15194	+	2.15194i	−0.0898985	+	0.0898985i
$574$	0.897795	+	39.0740i	0.0374732	+	1.63092i
$575$		−	0.241150i		−	0.0100566i
$576$	2.63325	+	18.9830i	0.109719	+	0.790959i
$577$	−5.18354			−0.215793			−0.107897	−	0.994162i	$-0.534412\pi$
$577$	−5.18354			−0.215793			−0.107897	+	0.994162i	$0.534412\pi$
$578$	−0.477715	−	20.7912i	−0.0198703	−	0.864800i
$579$	−9.65759	+	9.65759i	−0.401356	+	0.401356i
$580$	2.00268	+	43.5576i	0.0831570	+	1.80863i
$581$	−36.0214	+	36.0214i	−1.49442	+	1.49442i
$582$	−2.94280	−	2.81061i	−0.121983	−	0.116503i
$583$		−	26.2306i		−	1.08636i
$584$	−38.3806	+	2.64932i	−1.58820	+	0.109630i
$585$	26.8284			1.10922
$586$	18.9548	−	19.8463i	0.783014	−	0.819842i
$587$	−1.88371	−	1.88371i	−0.0777491	−	0.0777491i	0.667163	−	0.744912i	$-0.267509\pi$
$587$	−1.88371	−	1.88371i	−0.0777491	−	0.0777491i	−0.744912	+	0.667163i	$0.767509\pi$
$588$	5.87428	+	5.35785i	0.242251	+	0.220954i
$589$	3.06153	−	9.97142i	0.126148	−	0.410865i
$590$	−1.73404	+	0.0398427i	−0.0713894	+	0.00164030i
$591$	17.9089			0.736673
$592$	−13.6829	−	11.3739i	−0.562363	−	0.467464i
$593$	44.2304			1.81632			0.908162	−	0.418619i	$-0.137486\pi$
$593$	44.2304			1.81632			0.908162	+	0.418619i	$0.137486\pi$
$594$	0.710061	+	30.9034i	0.0291342	+	1.26798i
$595$	−7.90805	+	7.90805i	−0.324198	+	0.324198i
$596$	−0.506607	+	0.555437i	−0.0207514	+	0.0227516i
$597$	−11.8796	−	11.8796i	−0.486199	−	0.486199i
$598$	2.60385	+	2.48689i	0.106480	+	0.101696i
$599$			25.1207i			1.02640i	0.858268	+	0.513202i	$0.171541\pi$
$599$			25.1207i			1.02640i	−0.858268	+	0.513202i	$0.828459\pi$
$600$	−0.829177	−	0.722096i	−0.0338510	−	0.0294795i
$601$	21.0826			0.859976			0.429988	−	0.902835i	$-0.358518\pi$
$601$	21.0826			0.859976			0.429988	+	0.902835i	$0.358518\pi$
$602$	14.5238	−	15.2069i	0.591945	−	0.619787i
$603$	−25.5590	+	25.5590i	−1.04084	+	1.04084i
$604$	0.759095	+	16.5100i	0.0308871	+	0.671783i
$605$	24.2284	+	24.2284i	0.985026	+	0.985026i
$606$	−0.170981	−	7.44145i	−0.00694561	−	0.302288i
$607$	−15.2446			−0.618759			−0.309379	−	0.950939i	$-0.600121\pi$
$607$	−15.2446			−0.618759			−0.309379	+	0.950939i	$0.600121\pi$
$608$	24.2458	+	4.48794i	0.983297	+	0.182010i
$609$	27.8089			1.12687
$610$	0.241501	+	10.5106i	0.00977807	+	0.425563i
$611$	−13.3842	−	13.3842i	−0.541466	−	0.541466i
$612$	0.333334	+	7.24989i	0.0134742	+	0.293059i
$613$	21.4123	−	21.4123i	0.864833	−	0.864833i	−0.127062	−	0.991895i	$-0.540555\pi$
$613$	21.4123	−	21.4123i	0.864833	−	0.864833i	0.991895	+	0.127062i	$0.0405546\pi$
$614$	−13.6769	+	14.3202i	−0.551954	+	0.577915i
$615$	13.0955			0.528060
$616$	33.6878	−	38.6834i	1.35732	−	1.55860i
$617$			47.5231i			1.91321i	0.291390	+	0.956604i	$0.405882\pi$
$617$			47.5231i			1.91321i	−0.291390	+	0.956604i	$0.594118\pi$
$618$	9.08409	+	8.67602i	0.365416	+	0.349001i
$619$	−1.43559	−	1.43559i	−0.0577014	−	0.0577014i	0.677667	−	0.735369i	$-0.262991\pi$
$619$	−1.43559	−	1.43559i	−0.0577014	−	0.0577014i	−0.735369	+	0.677667i	$0.762991\pi$
$620$	−6.84166	+	7.50111i	−0.274768	+	0.301252i
$621$	1.43046	−	1.43046i	0.0574024	−	0.0574024i
$622$	0.566749	+	24.6661i	0.0227246	+	0.989022i
$623$	25.8455			1.03548
$624$	16.3479	−	1.50647i	0.654441	−	0.0603071i
$625$	22.2498			0.889992
$626$	−12.9345	+	0.297193i	−0.516967	+	0.0118782i
$627$	16.8803	+	5.18277i	0.674136	+	0.206980i
$628$	23.3933	+	21.3367i	0.933495	+	0.851428i
$629$	−4.76450	−	4.76450i	−0.189973	−	0.189973i
$630$	−17.2760	+	18.0886i	−0.688292	+	0.720665i
$631$	−0.490988			−0.0195459			−0.00977296	−	0.999952i	$-0.503111\pi$
$631$	−0.490988			−0.0195459			−0.00977296	+	0.999952i	$0.503111\pi$
$632$	0.977828	+	14.1658i	0.0388959	+	0.563484i
$633$			18.3588i			0.729696i
$634$	−27.6218	−	26.3810i	−1.09700	−	1.04772i
$635$	8.52421	−	8.52421i	0.338273	−	0.338273i
$636$	0.359490	+	7.81877i	0.0142547	+	0.310034i
$637$	−19.0886	+	19.0886i	−0.756320	+	0.756320i
$638$	−1.73973	−	75.7167i	−0.0688765	−	2.99765i
$639$	13.3986			0.530042
$640$	−19.4688	−	14.0343i	−0.769573	−	0.554754i
$641$			16.9893i			0.671039i	0.942033	+	0.335519i	$0.108912\pi$
$641$			16.9893i			0.671039i	−0.942033	+	0.335519i	$0.891088\pi$
$642$	−0.421004	−	18.3230i	−0.0166157	−	0.723151i
$643$	12.5699	−	12.5699i	0.495709	−	0.495709i	−0.414390	−	0.910099i	$-0.636005\pi$
$643$	12.5699	−	12.5699i	0.495709	−	0.495709i	0.910099	+	0.414390i	$0.136005\pi$
$644$	−3.35347	+	0.154185i	−0.132145	+	0.00607575i
$645$	−4.98204	−	4.98204i	−0.196168	−	0.196168i
$646$	8.98699	+	2.53490i	0.353588	+	0.0997344i
$647$	−37.3005			−1.46643			−0.733217	−	0.679995i	$-0.761982\pi$
$647$	−37.3005			−1.46643			−0.733217	+	0.679995i	$0.761982\pi$
$648$	0.764630	+	11.0772i	0.0300375	+	0.435153i
$649$	3.01272			0.118260
$650$	2.57849	−	2.69976i	0.101137	−	0.105893i
$651$	4.57850	+	4.57850i	0.179446	+	0.179446i
$652$	−10.1220	+	11.0977i	−0.396410	+	0.434619i
$653$	−19.3569	−	19.3569i	−0.757496	−	0.757496i	0.218370	−	0.975866i	$-0.429926\pi$
$653$	−19.3569	−	19.3569i	−0.757496	−	0.757496i	−0.975866	+	0.218370i	$0.929926\pi$
$654$	−0.368610	−	16.0427i	−0.0144138	−	0.627320i
$655$		−	2.98401i		−	0.116595i
$656$	−31.6284	+	2.91457i	−1.23488	+	0.113795i
$657$	−32.5846			−1.27125
$658$	17.6427	−	0.405372i	0.687783	−	0.0158030i
$659$	27.9807	+	27.9807i	1.08997	+	1.08997i	0.995530	+	0.0944429i	$0.0301070\pi$
$659$	27.9807	+	27.9807i	1.08997	+	1.08997i	0.0944429	+	0.995530i	$0.469893\pi$
$660$	−12.6984	−	11.5821i	−0.494286	−	0.450831i
$661$	−27.6554	−	27.6554i	−1.07567	−	1.07567i	−0.996892	−	0.0787770i	$-0.974898\pi$
$661$	−27.6554	−	27.6554i	−1.07567	−	1.07567i	−0.0787770	−	0.996892i	$-0.525102\pi$
$662$	−4.47756	−	4.27642i	−0.174025	−	0.166208i
$663$	6.21706			0.241451
$664$	−31.2197	−	27.1880i	−1.21156	−	1.05510i
$665$	15.0749	+	28.4331i	0.584578	+	1.10259i
$666$	−10.8981	−	10.4086i	−0.422294	−	0.403324i
$667$	−3.50479	+	3.50479i	−0.135706	+	0.135706i
$668$	−0.829209	−	18.0350i	−0.0320831	−	0.697794i
$669$	0.898696	+	0.898696i	0.0347456	+	0.0347456i
$670$	−1.03977	−	45.2532i	−0.0401700	−	1.74828i
$671$		−	18.2611i		−	0.704963i
$672$	−9.51143	+	11.9924i	−0.366911	+	0.462615i
$673$			10.1211i			0.390141i	0.980789	+	0.195070i	$0.0624935\pi$
$673$			10.1211i			0.390141i	−0.980789	+	0.195070i	$0.937506\pi$
$674$	−17.2054	+	0.395326i	−0.662728	+	0.0152274i
$675$	−1.48315	−	1.48315i	−0.0570865	−	0.0570865i
$676$	1.36603	+	29.7107i	0.0525398	+	1.14272i
$677$	−22.3139	−	22.3139i	−0.857593	−	0.857593i	0.133461	−	0.991054i	$-0.457391\pi$
$677$	−22.3139	−	22.3139i	−0.857593	−	0.857593i	−0.991054	+	0.133461i	$0.957391\pi$
$678$	11.1664	+	10.6648i	0.428845	+	0.409581i
$679$			12.8819i			0.494363i
$680$	−6.85389	−	5.96878i	−0.262835	−	0.228892i
$681$		−	0.509452i		−	0.0195223i
$682$	12.1797	−	12.7525i	0.466384	−	0.488320i
$683$	14.4876	−	14.4876i	0.554354	−	0.554354i	−0.373340	−	0.927695i	$-0.621788\pi$
$683$	14.4876	−	14.4876i	0.554354	−	0.554354i	0.927695	+	0.373340i	$0.121788\pi$
$684$	20.2250	+	5.20628i	0.773322	+	0.199067i
$685$	−15.9034	−	15.9034i	−0.607638	−	0.607638i
$686$	0.213301	+	9.28333i	0.00814388	+	0.354439i
$687$	9.19563			0.350835
$688$	13.1416	+	10.9239i	0.501017	+	0.416470i
$689$	−26.5755			−1.01244
$690$	0.0258372	+	1.12449i	0.000983606	+	0.0428087i
$691$	−24.4373	+	24.4373i	−0.929638	+	0.929638i	−0.997682	−	0.0680444i	$-0.978324\pi$
$691$	−24.4373	+	24.4373i	−0.929638	+	0.929638i	0.0680444	+	0.997682i	$0.478324\pi$
$692$	−14.9140	+	16.3515i	−0.566944	+	0.621591i
$693$	30.7211	−	30.7211i	1.16700	−	1.16700i
$694$	11.2448	−	11.7736i	0.426845	−	0.446922i
$695$	27.7554			1.05282
$696$	1.55627	+	22.5457i	0.0589904	+	0.854591i
$697$	−12.0282			−0.455599
$698$	−16.2838	+	17.0496i	−0.616349	+	0.645339i
$699$	4.96082	−	4.96082i	0.187635	−	0.187635i
$700$	0.159864	+	3.47699i	0.00604231	+	0.131418i
$701$	16.1800	+	16.1800i	0.611110	+	0.611110i	0.943235	−	0.332125i	$-0.107766\pi$
$701$	16.1800	+	16.1800i	0.611110	+	0.611110i	−0.332125	+	0.943235i	$0.607766\pi$
$702$	31.3097	−	0.719397i	1.18171	−	0.0271519i
$703$	−17.1306	+	9.08241i	−0.646092	+	0.342550i
$704$	33.2472	+	25.1470i	1.25305	+	0.947764i
$705$		−	5.91285i		−	0.222691i
$706$	0.132143	+	5.75117i	0.00497328	+	0.216448i
$707$	−16.6615	+	16.6615i	−0.626619	+	0.626619i
$708$	−0.898026	+	0.0412893i	−0.0337499	+	0.00155175i
$709$	11.6536	−	11.6536i	0.437660	−	0.437660i	−0.453563	−	0.891224i	$-0.649847\pi$
$709$	11.6536	−	11.6536i	0.437660	−	0.437660i	0.891224	+	0.453563i	$0.149847\pi$
$710$	−11.5889	+	12.1340i	−0.434923	+	0.455379i
$711$			12.0266i			0.451031i
$712$	1.44639	+	20.9538i	0.0542058	+	0.785278i
$713$	−1.15407			−0.0432202
$714$	−4.00343	+	4.19173i	−0.149825	+	0.156872i
$715$	41.2639	−	41.2639i	1.54318	−	1.54318i
$716$	−6.17182	−	5.62923i	−0.230652	−	0.210374i
$717$	0.316223	−	0.316223i	0.0118096	−	0.0118096i
$718$	−0.237191	−	10.3231i	−0.00885188	−	0.385253i
$719$		−	49.0662i		−	1.82986i	−0.403611	−	0.914931i	$-0.632245\pi$
$719$		−	49.0662i		−	1.82986i	0.403611	−	0.914931i	$-0.367755\pi$
$720$	−15.6318	−	12.9940i	−0.582564	−	0.484256i
$721$		−	39.7651i		−	1.48093i
$722$	14.5636	−	22.5810i	0.542000	−	0.840379i
$723$	−5.62120	+	5.62120i	−0.209055	+	0.209055i
$724$	14.5400	+	13.2617i	0.540374	+	0.492868i
$725$	3.63388	+	3.63388i	0.134959	+	0.134959i
$726$	12.8425	+	12.2656i	0.476630	+	0.455219i
$727$	−10.6283			−0.394182			−0.197091	−	0.980385i	$-0.563149\pi$
$727$	−10.6283			−0.394182			−0.197091	+	0.980385i	$0.563149\pi$
$728$	−39.1920	−	34.1307i	−1.45255	−	1.26497i
$729$		−	0.378928i		−	0.0140344i
$730$	28.1834	−	29.5090i	1.04311	−	1.09218i
$731$	4.57600	+	4.57600i	0.169250	+	0.169250i
$732$	0.250269	+	5.44324i	0.00925020	+	0.201188i
$733$	36.3785	+	36.3785i	1.34367	+	1.34367i	0.892375	+	0.451295i	$0.149038\pi$
$733$	36.3785	+	36.3785i	1.34367	+	1.34367i	0.451295	+	0.892375i	$0.350962\pi$
$734$	−11.5361	+	0.265062i	−0.425805	+	0.00978363i
$735$	−8.43297			−0.311055
$736$	−0.312674	−	2.71015i	−0.0115253	−	0.0998973i
$737$			78.6227i			2.89610i
$738$	−26.8948	+	0.617956i	−0.990010	+	0.0227473i
$739$	−9.52584	+	9.52584i	−0.350414	+	0.350414i	−0.860263	−	0.509850i	$-0.829701\pi$
$739$	−9.52584	+	9.52584i	−0.350414	+	0.350414i	0.509850	+	0.860263i	$0.329701\pi$
$740$	18.8522	−	0.866785i	0.693022	−	0.0318637i
$741$	5.25092	−	17.1023i	0.192897	−	0.628268i
$742$	17.1131	−	17.9180i	0.628241	−	0.657790i
$743$		−	15.1555i		−	0.556001i	−0.960581	−	0.278000i	$-0.910328\pi$
$743$		−	15.1555i		−	0.556001i	0.960581	−	0.278000i	$-0.0896716\pi$
$744$	−3.45573	+	3.96818i	−0.126693	+	0.145481i
$745$		−	0.797372i		−	0.0292134i
$746$	10.1532	−	10.6307i	0.371734	−	0.389219i
$747$	−24.7937	−	24.7937i	−0.907154	−	0.907154i
$748$	11.6635	+	10.6381i	0.426459	+	0.388968i
$749$	−41.0254	+	41.0254i	−1.49903	+	1.49903i
$750$	12.8243	−	0.294661i	0.468276	−	0.0107595i
$751$	−40.2293			−1.46799			−0.733994	−	0.679156i	$-0.762346\pi$
$751$	−40.2293			−1.46799			−0.733994	+	0.679156i	$0.762346\pi$
$752$	1.31599	+	14.2808i	0.0479891	+	0.520769i
$753$			10.6327i			0.387477i
$754$	−76.7123	+	1.76260i	−2.79370	+	0.0641902i
$755$	−12.3955	−	12.3955i	−0.451120	−	0.451120i
$756$	−19.6766	+	21.5732i	−0.715632	+	0.784610i
$757$	−35.3310	+	35.3310i	−1.28413	+	1.28413i	−0.345827	+	0.938298i	$0.612402\pi$
$757$	−35.3310	+	35.3310i	−1.28413	+	1.28413i	−0.938298	+	0.345827i	$0.887598\pi$
$758$	29.2774	+	27.9622i	1.06340	+	1.01563i
$759$		−	1.95369i		−	0.0709144i
$760$	−22.2081	+	13.8129i	−0.805572	+	0.501047i
$761$			5.10254i			0.184967i	0.995714	+	0.0924834i	$0.0294805\pi$
$761$			5.10254i			0.184967i	−0.995714	+	0.0924834i	$0.970519\pi$
$762$	4.31536	−	4.51833i	0.156329	−	0.163682i
$763$	−35.9198	+	35.9198i	−1.30038	+	1.30038i
$764$	0.359585	+	7.82084i	0.0130093	+	0.282948i
$765$	−5.44314	−	5.44314i	−0.196797	−	0.196797i
$766$	0.599907	+	26.1093i	0.0216755	+	0.943366i
$767$		−	3.05233i		−	0.110213i
$768$	−10.2549	−	7.04012i	−0.370042	−	0.254039i
$769$	35.3943			1.27635			0.638175	−	0.769891i	$-0.279690\pi$
$769$	35.3943			1.27635			0.638175	+	0.769891i	$0.279690\pi$
$770$	1.24978	+	54.3929i	0.0450388	+	1.96019i
$771$	10.3816	−	10.3816i	0.373885	−	0.373885i
$772$	1.61377	+	35.0988i	0.0580808	+	1.26323i
$773$	12.5110	+	12.5110i	0.449991	+	0.449991i	0.895351	−	0.445360i	$-0.146924\pi$
$773$	12.5110	+	12.5110i	0.449991	+	0.449991i	−0.445360	+	0.895351i	$0.646924\pi$
$774$	10.4670	+	9.99677i	0.376227	+	0.359327i
$775$			1.19658i			0.0429823i
$776$	−10.4438	+	0.720913i	−0.374912	+	0.0258793i
$777$		−	12.0360i		−	0.431790i
$778$	−23.6283	−	22.5669i	−0.847117	−	0.809063i
$779$	−10.1590	+	33.0878i	−0.363983	+	1.18550i
$780$	−11.7343	+	12.8654i	−0.420157	+	0.460655i
$781$	20.6080	−	20.6080i	0.737411	−	0.737411i
$782$	−0.0237315	−	1.03285i	−0.000848635	−	0.0369345i
$783$			43.1112i			1.54067i
$784$	20.3675	−	1.87687i	0.727410	−	0.0670312i
$785$	−33.5829			−1.19862
$786$	−0.0355261	−	1.54617i	−0.00126717	−	0.0551502i
$787$	0.304154	+	0.304154i	0.0108419	+	0.0108419i	0.712507	−	0.701665i	$-0.247560\pi$
$787$	0.304154	+	0.304154i	0.0108419	+	0.0108419i	−0.701665	+	0.712507i	$0.747560\pi$
$788$	31.0471	−	34.0397i	1.10601	−	1.21261i
$789$	6.63935	+	6.63935i	0.236367	+	0.236367i
$790$	−10.8914	−	10.4021i	−0.387498	−	0.370091i
$791$		−	48.8805i		−	1.73799i
$792$	26.6259	+	23.1874i	0.946111	+	0.823929i
$793$	−18.5012			−0.656998
$794$	18.0312	−	18.8793i	0.639905	−	0.670002i
$795$	−5.87025	−	5.87025i	−0.208196	−	0.208196i
$796$	−43.1743	+	1.98506i	−1.53027	+	0.0703587i
$797$	−10.6768	+	10.6768i	−0.378190	+	0.378190i	−0.870449	−	0.492259i	$-0.836171\pi$
$797$	−10.6768	+	10.6768i	−0.378190	+	0.378190i	0.492259	+	0.870449i	$0.336171\pi$
$798$	8.14959	+	14.5532i	0.288492	+	0.515179i
$799$			5.43095i			0.192133i
$800$	−2.80997	+	0.324191i	−0.0993474	+	0.0114619i
$801$			17.7895i			0.628563i
$802$	37.2429	−	0.855721i	1.31509	−	0.0302166i
$803$	−50.1173	+	50.1173i	−1.76860	+	1.76860i
$804$	−1.07752	−	23.4357i	−0.0380013	−	0.826514i
$805$	2.51775	−	2.51775i	0.0887390	−	0.0887390i
$806$	−12.9202	−	12.3398i	−0.455095	−	0.434652i
$807$	−9.39329			−0.330660
$808$	−14.4405	−	12.5756i	−0.508014	−	0.442408i
$809$		−	9.58027i		−	0.336824i	−0.985717	−	0.168412i	$-0.946136\pi$
$809$		−	9.58027i		−	0.336824i	0.985717	−	0.168412i	$-0.0538640\pi$
$810$	−8.51672	−	8.13413i	−0.299247	−	0.285804i
$811$	−22.4309	+	22.4309i	−0.787654	+	0.787654i	−0.981109	−	0.193455i	$-0.938031\pi$
$811$	−22.4309	+	22.4309i	−0.787654	+	0.787654i	0.193455	+	0.981109i	$0.438031\pi$
$812$	48.2099	−	52.8568i	1.69184	−	1.85491i
$813$	4.56759	−	4.56759i	0.160192	−	0.160192i
$814$	−32.7711	+	0.752974i	−1.14863	+	0.0263917i
$815$		−	15.9315i		−	0.558058i
$816$	−3.62243	−	3.01114i	−0.126810	−	0.105411i
$817$	16.4528	−	8.72308i	0.575612	−	0.305182i
$818$	−0.0266807	−	1.16120i	−0.000932868	−	0.0406005i
$819$	−31.1250	−	31.1250i	−1.08760	−	1.08760i
$820$	22.7025	−	24.8907i	0.792805	−	0.869221i
$821$	24.5153	−	24.5153i	0.855590	−	0.855590i	−0.135225	−	0.990815i	$-0.543176\pi$
$821$	24.5153	−	24.5153i	0.855590	−	0.855590i	0.990815	+	0.135225i	$0.0431756\pi$
$822$	−8.42975	−	8.05107i	−0.294021	−	0.280813i
$823$	−23.3599			−0.814274			−0.407137	−	0.913367i	$-0.633473\pi$
$823$	−23.3599			−0.814274			−0.407137	+	0.913367i	$0.633473\pi$
$824$	32.2389	−	2.22538i	1.12310	−	0.0775246i
$825$	−2.02565			−0.0705240
$826$	2.05797	+	1.96553i	0.0716061	+	0.0683894i
$827$	24.9222	−	24.9222i	0.866631	−	0.866631i	−0.125467	−	0.992098i	$-0.540043\pi$
$827$	24.9222	−	24.9222i	0.866631	−	0.866631i	0.992098	+	0.125467i	$0.0400428\pi$
$828$	−0.106126	−	2.30821i	−0.00368815	−	0.0802157i
$829$	8.85684	−	8.85684i	0.307611	−	0.307611i	−0.536371	−	0.843982i	$-0.680205\pi$
$829$	8.85684	−	8.85684i	0.307611	−	0.307611i	0.843982	+	0.536371i	$0.180205\pi$
$830$	43.8983	−	1.00864i	1.52373	−	0.0350104i
$831$	−10.5065			−0.364466
$832$	25.4776	−	33.6844i	0.883278	−	1.16780i
$833$	7.74568			0.268372
$834$	14.3815	−	0.330441i	0.497992	−	0.0114423i
$835$	13.5405	+	13.5405i	0.468587	+	0.468587i
$836$	39.1150	−	23.0998i	1.35282	−	0.798922i
$837$	−7.09789	+	7.09789i	−0.245339	+	0.245339i
$838$	3.63644	+	3.47309i	0.125619	+	0.119976i
$839$			23.5109i			0.811686i	0.913943	+	0.405843i	$0.133022\pi$
$839$			23.5109i			0.811686i	−0.913943	+	0.405843i	$0.866978\pi$
$840$	−1.11799	−	16.1962i	−0.0385742	−	0.558823i
$841$		−	76.6272i		−	2.64232i
$842$	−13.3290	+	13.9559i	−0.459348	+	0.480953i
$843$	−5.12424	−	5.12424i	−0.176488	−	0.176488i
$844$	34.8948	+	31.8271i	1.20113	+	1.09553i
$845$	−22.3065	−	22.3065i	−0.767366	−	0.767366i
$846$	0.279019	+	12.1435i	0.00959287	+	0.417503i
$847$		−	56.2172i		−	1.93165i
$848$	15.4844	+	12.8714i	0.531738	+	0.442007i
$849$		−	4.61151i		−	0.158267i
$850$	−1.07089	+	0.0246056i	−0.0367312	+	0.000843964i
$851$	1.51691	+	1.51691i	0.0519991	+	0.0519991i
$852$	−5.86035	+	6.42522i	−0.200772	+	0.220124i
$853$	−2.97132	+	2.97132i	−0.101736	+	0.101736i	−0.756143	−	0.654407i	$-0.772918\pi$
$853$	−2.97132	+	2.97132i	−0.101736	+	0.101736i	0.654407	+	0.756143i	$0.272918\pi$
$854$	11.9137	−	12.4741i	0.407680	−	0.426855i
$855$	−19.5706	+	10.3761i	−0.669301	+	0.354854i
$856$	−35.5566	−	30.9648i	−1.21530	−	1.05836i
$857$	35.1401			1.20036			0.600181	−	0.799864i	$-0.295095\pi$
$857$	35.1401			1.20036			0.600181	+	0.799864i	$0.295095\pi$
$858$	20.8897	−	21.8723i	0.713164	−	0.746707i
$859$	34.6341	+	34.6341i	1.18170	+	1.18170i	0.979304	+	0.202395i	$0.0648725\pi$
$859$	34.6341	+	34.6341i	1.18170	+	1.18170i	0.202395	+	0.979304i	$0.435128\pi$
$860$	−18.1064	+	0.832492i	−0.617422	+	0.0283877i
$861$	−15.1927	−	15.1927i	−0.517766	−	0.517766i
$862$	0.190926	+	8.30950i	0.00650295	+	0.283023i
$863$	−22.4122			−0.762921			−0.381461	−	0.924385i	$-0.624579\pi$
$863$	−22.4122			−0.762921			−0.381461	+	0.924385i	$0.624579\pi$
$864$	−18.5913	−	14.7452i	−0.632490	−	0.501643i
$865$		−	23.4738i		−	0.798133i
$866$	3.70853	−	0.0852100i	0.126021	−	0.00289555i
$867$	8.08401	+	8.08401i	0.274547	+	0.274547i
$868$	16.6398	−	0.765061i	0.564791	−	0.0259679i
$869$	18.4976	+	18.4976i	0.627489	+	0.627489i
$870$	−17.3343	−	16.5556i	−0.587688	−	0.561288i
$871$	79.6564			2.69906
$872$	−31.1316	−	27.1113i	−1.05425	−	0.918103i
$873$	−8.86669			−0.300092
$874$	−2.86126	−	0.807057i	−0.0967836	−	0.0272991i
$875$	−28.7137	−	28.7137i	−0.970699	−	0.970699i
$876$	14.2520	−	15.6257i	0.481531	−	0.527944i
$877$	−19.6785	+	19.6785i	−0.664496	+	0.664496i	−0.956437	−	0.291940i	$-0.905699\pi$
$877$	−19.6785	+	19.6785i	−0.664496	+	0.664496i	0.291940	+	0.956437i	$0.405699\pi$
$878$	48.9588	−	1.12492i	1.65228	−	0.0379641i
$879$			15.0866i			0.508857i
$880$	−44.0283	+	4.05723i	−1.48419	+	0.136769i
$881$	6.88025			0.231801			0.115901	−	0.993261i	$-0.463025\pi$
$881$	6.88025			0.231801			0.115901	+	0.993261i	$0.463025\pi$
$882$	17.3192	−	0.397940i	0.583168	−	0.0133993i
$883$	32.4715	−	32.4715i	1.09275	−	1.09275i	0.0975191	−	0.995234i	$-0.468909\pi$
$883$	32.4715	−	32.4715i	1.09275	−	1.09275i	0.995234	−	0.0975191i	$-0.0310907\pi$
$884$	10.7780	−	11.8168i	0.362503	−	0.397443i
$885$	0.674228	−	0.674228i	0.0226639	−	0.0226639i
$886$	−4.95185	+	5.18476i	−0.166361	+	0.174185i
$887$		−	11.4832i		−	0.385567i	−0.981241	−	0.192783i	$-0.938249\pi$
$887$		−	11.4832i		−	0.385567i	0.981241	−	0.192783i	$-0.0617515\pi$
$888$	9.75803	−	0.673573i	0.327458	−	0.0226036i
$889$	−19.7787			−0.663357
$890$	−16.1104	−	15.3867i	−0.540022	−	0.515764i
$891$	14.4646	+	14.4646i	0.484581	+	0.484581i
$892$	3.26615	−	0.150171i	0.109359	−	0.00502809i
$893$	14.9398	+	4.58697i	0.499942	+	0.153497i
$894$	−0.00949310	−	0.413161i	−0.000317497	−	0.0138182i
$895$	8.86010			0.296161
$896$	6.30487	+	38.8686i	0.210631	+	1.29851i
$897$	−1.97938			−0.0660894
$898$	9.86964	−	0.226773i	0.329354	−	0.00756750i
$899$	17.3906	−	17.3906i	0.580010	−	0.580010i
$900$	−2.39322	+	0.110035i	−0.0797742	+	0.00366784i
$901$	5.39182	+	5.39182i	0.179627	+	0.179627i
$902$	−40.4154	+	42.3164i	−1.34569	+	1.40898i
$903$			11.5598i			0.384687i
$904$	39.6291	−	2.73550i	1.31804	−	0.0909814i
$905$	−20.8732			−0.693849
$906$	−6.57037	−	6.27522i	−0.218286	−	0.208480i
$907$	1.11054	−	1.11054i	0.0368750	−	0.0368750i	−0.688429	−	0.725304i	$-0.741699\pi$
$907$	1.11054	−	1.11054i	0.0368750	−	0.0368750i	0.725304	+	0.688429i	$0.241699\pi$
$908$	−0.968323	−	0.883194i	−0.0321349	−	0.0293098i
$909$	−11.4682	−	11.4682i	−0.380375	−	0.380375i
$910$	55.1081	−	1.26621i	1.82682	−	0.0419744i
$911$	4.52560			0.149940			0.0749699	−	0.997186i	$-0.476114\pi$
$911$	4.52560			0.149940			0.0749699	+	0.997186i	$0.476114\pi$
$912$	−11.3427	+	7.42160i	−0.375596	+	0.245754i
$913$	−76.2686			−2.52412
$914$	2.28967	−	0.0526093i	0.0757357	−	0.00174016i
$915$	−4.08673	−	4.08673i	−0.135103	−	0.135103i
$916$	15.9417	−	17.4783i	0.526728	−	0.577498i
$917$	−3.46190	+	3.46190i	−0.114322	+	0.114322i
$918$	−6.49829	−	6.20638i	−0.214476	−	0.204841i
$919$	−34.2586			−1.13009			−0.565043	−	0.825062i	$-0.691140\pi$
$919$	−34.2586			−1.13009			−0.565043	+	0.825062i	$0.691140\pi$
$920$	2.18213	+	1.90033i	0.0719427	+	0.0626519i
$921$		−	10.8858i		−	0.358699i
$922$	−15.5648	+	16.2969i	−0.512599	+	0.536709i
$923$	−20.8789	−	20.8789i	−0.687238	−	0.687238i
$924$	1.29515	+	28.1690i	0.0426073	+	0.926692i
$925$	1.57279	−	1.57279i	0.0517129	−	0.0517129i
$926$	37.0643	−	0.851619i	1.21801	−	0.0279859i
$927$	27.3705			0.898964
$928$	45.5508	+	36.1275i	1.49528	+	1.18594i
$929$	13.5486			0.444516			0.222258	−	0.974988i	$-0.428657\pi$
$929$	13.5486			0.444516			0.222258	+	0.974988i	$0.428657\pi$
$930$	−0.128203	−	5.57969i	−0.00420395	−	0.182965i
$931$	6.54198	−	21.3073i	0.214405	−	0.698319i
$932$	−0.828946	−	18.0292i	−0.0271530	−	0.590567i
$933$	−9.59066	−	9.59066i	−0.313984	−	0.313984i
$934$	10.7869	+	10.3023i	0.352958	+	0.337103i
$935$	−16.7438			−0.547581
$936$	23.4923	−	26.9760i	0.767870	−	0.881738i
$937$		−	32.7572i		−	1.07013i	−0.844811	−	0.535065i	$-0.820287\pi$
$937$		−	32.7572i		−	1.07013i	0.844811	−	0.535065i	$-0.179713\pi$
$938$	−51.2942	+	53.7068i	−1.67482	+	1.75359i
$939$	5.02918	−	5.02918i	0.164121	−	0.164121i
$940$	−11.2386	−	10.2506i	−0.366564	−	0.334338i
$941$	24.7542	−	24.7542i	0.806965	−	0.806965i	−0.177208	−	0.984173i	$-0.556707\pi$
$941$	24.7542	−	24.7542i	0.806965	−	0.806965i	0.984173	+	0.177208i	$0.0567066\pi$
$942$	−17.4011	+	0.399821i	−0.566957	+	0.0130269i
$943$	3.82950			0.124706
$944$	−1.47835	+	1.77847i	−0.0481162	+	0.0578842i
$945$		−	30.9700i		−	1.00745i
$946$	31.4745	−	0.723184i	1.02333	−	0.0235127i
$947$	27.4034	−	27.4034i	0.890491	−	0.890491i	−0.104078	−	0.994569i	$-0.533189\pi$
$947$	27.4034	−	27.4034i	0.890491	−	0.890491i	0.994569	+	0.104078i	$0.0331893\pi$
$948$	−5.76725	−	5.26023i	−0.187312	−	0.170844i
$949$	50.7762	+	50.7762i	1.64827	+	1.64827i
$950$	−0.836783	+	2.96665i	−0.0271488	+	0.0962508i
$951$	20.9973			0.680884
$952$	1.02687	+	14.8762i	0.0332810	+	0.482141i
$953$	−35.9912			−1.16587			−0.582935	−	0.812519i	$-0.698096\pi$
$953$	−35.9912			−1.16587			−0.582935	+	0.812519i	$0.698096\pi$
$954$	12.3330	+	11.7790i	0.399296	+	0.381359i
$955$	−5.87181	−	5.87181i	−0.190007	−	0.190007i
$956$	−0.0528404	−	1.14926i	−0.00170898	−	0.0371697i
$957$	29.4401	+	29.4401i	0.951663	+	0.951663i
$958$	−31.1621	+	0.716006i	−1.00680	+	0.0231331i
$959$			36.9007i			1.19159i
$960$	13.0683	−	1.81278i	0.421777	−	0.0585073i
$961$	−25.2736			−0.815276
$962$	0.762874	+	33.2020i	0.0245961	+	1.07047i
$963$	−28.2379	−	28.2379i	−0.909955	−	0.909955i
$964$	0.939294	+	20.4293i	0.0302526	+	0.657983i
$965$	−26.3518	−	26.3518i	−0.848296	−	0.848296i
$966$	1.27460	−	1.33456i	0.0410097	−	0.0429386i
$967$	−20.6822			−0.665093			−0.332547	−	0.943087i	$-0.607908\pi$
$967$	−20.6822			−0.665093			−0.332547	+	0.943087i	$0.607908\pi$
$968$	45.5773	−	3.14609i	1.46491	−	0.101119i
$969$	−4.53518	+	2.40449i	−0.145691	+	0.0772433i
$970$	7.66907	−	8.02977i	0.246239	−	0.257821i
$971$	5.17002	−	5.17002i	0.165914	−	0.165914i	−0.619267	−	0.785181i	$-0.712570\pi$
$971$	5.17002	−	5.17002i	0.165914	−	0.165914i	0.785181	+	0.619267i	$0.212570\pi$
$972$	−23.1051	−	21.0738i	−0.741095	−	0.675943i
$973$	−32.2004	−	32.2004i	−1.03230	−	1.03230i
$974$	−31.0714	+	0.713922i	−0.995593	+	0.0228755i
$975$			2.05228i			0.0657256i
$976$	10.7799	+	8.96079i	0.345057	+	0.286828i
$977$		−	25.5684i		−	0.818006i	−0.912533	−	0.409003i	$-0.865877\pi$
$977$		−	25.5684i		−	0.818006i	0.912533	−	0.409003i	$-0.134123\pi$
$978$	−0.189673	−	8.25498i	−0.00606507	−	0.263965i
$979$	27.3615	+	27.3615i	0.874476	+	0.874476i
$980$	−14.6195	+	16.0287i	−0.467003	+	0.512017i
$981$	−24.7237	−	24.7237i	−0.789368	−	0.789368i
$982$	24.4810	−	25.6324i	0.781220	−	0.817964i
$983$		−	20.9464i		−	0.668085i	−0.942558	−	0.334042i	$-0.891587\pi$
$983$		−	20.9464i		−	0.668085i	0.942558	−	0.334042i	$-0.108413\pi$
$984$	11.4670	−	13.1675i	0.365555	−	0.419764i
$985$			48.8665i			1.55702i
$986$	15.9215	+	15.2063i	0.507045	+	0.484268i
$987$	−6.85980	+	6.85980i	−0.218350	+	0.218350i
$988$	−23.4035	−	39.6292i	−0.744564	−	1.26077i
$989$	−1.45690	−	1.45690i	−0.0463267	−	0.0463267i
$990$	−37.4389	+	0.860225i	−1.18989	+	0.0273398i
$991$	35.4955			1.12755			0.563776	−	0.825928i	$-0.309348\pi$
$991$	35.4955			1.12755			0.563776	+	0.825928i	$0.309348\pi$
$992$	1.55147	+	13.4476i	0.0492594	+	0.426963i
$993$	3.40371			0.108014
$994$	27.5220	−	0.632368i	0.872946	−	0.0200575i
$995$	32.4148	−	32.4148i	1.02762	−	1.02762i
$996$	22.7340	−	1.04526i	0.720355	−	0.0331204i
$997$	−33.0690	+	33.0690i	−1.04731	+	1.04731i	−0.0484820	+	0.998824i	$0.515438\pi$
$997$	−33.0690	+	33.0690i	−1.04731	+	1.04731i	−0.998824	+	0.0484820i	$0.984562\pi$
$998$	−43.9031	−	41.9309i	−1.38973	−	1.32730i
$999$	18.6590			0.590345

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.m.a.227.20	yes	76
4.3	odd	2		1216.2.m.a.303.23		76
16.5	even	4		1216.2.m.a.911.16		76
16.11	odd	4	inner	304.2.m.a.75.19	✓	76
19.18	odd	2	inner	304.2.m.a.227.19	yes	76
76.75	even	2		1216.2.m.a.303.16		76
304.37	odd	4		1216.2.m.a.911.23		76
304.75	even	4	inner	304.2.m.a.75.20	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.m.a.75.19	✓	76	16.11	odd	4	inner
304.2.m.a.75.20	yes	76	304.75	even	4	inner
304.2.m.a.227.19	yes	76	19.18	odd	2	inner
304.2.m.a.227.20	yes	76	1.1	even	1	trivial
1216.2.m.a.303.16		76	76.75	even	2
1216.2.m.a.303.23		76	4.3	odd	2
1216.2.m.a.911.16		76	16.5	even	4
1216.2.m.a.911.23		76	304.37	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0324855 + 1.41384i) q^{2} +(-0.549728 - 0.549728i) q^{3} +(-1.99789 + 0.0918587i) q^{4} +(1.49999 - 1.49999i) q^{5} +(0.759369 - 0.795085i) q^{6} -3.48044 q^{7} +(-0.194776 - 2.82171i) q^{8} -2.39560i q^{9} +(2.16948 + 2.07202i) q^{10} +(-3.68459 - 3.68459i) q^{11} +(1.14879 + 1.04780i) q^{12} +(-3.73303 + 3.73303i) q^{13} +(-0.113064 - 4.92078i) q^{14} -1.64918 q^{15} +(3.98312 - 0.367047i) q^{16} +1.51477 q^{17} +(3.38699 - 0.0778223i) q^{18} +(1.27937 - 4.16692i) q^{19} +(-2.85904 + 3.13461i) q^{20} +(1.91329 + 1.91329i) q^{21} +(5.08972 - 5.32911i) q^{22} -0.482269 q^{23} +(-1.44410 + 1.65825i) q^{24} +0.500032i q^{25} +(-5.39918 - 5.15664i) q^{26} +(-2.96611 + 2.96611i) q^{27} +(6.95353 - 0.319708i) q^{28} +(7.26730 - 7.26730i) q^{29} +(-0.0535744 - 2.33167i) q^{30} +2.39300 q^{31} +(0.648339 + 5.61958i) q^{32} +4.05104i q^{33} +(0.0492080 + 2.14164i) q^{34} +(-5.22064 + 5.22064i) q^{35} +(0.220057 + 4.78614i) q^{36} +(-3.14537 - 3.14537i) q^{37} +(5.93292 + 1.67346i) q^{38} +4.10430 q^{39} +(-4.52472 - 3.94039i) q^{40} -7.94060 q^{41} +(-2.64294 + 2.76724i) q^{42} +(3.02093 + 3.02093i) q^{43} +(7.69986 + 7.02293i) q^{44} +(-3.59339 - 3.59339i) q^{45} +(-0.0156667 - 0.681851i) q^{46} +3.58534i q^{47} +(-2.39141 - 1.98786i) q^{48} +5.11344 q^{49} +(-0.706966 + 0.0162438i) q^{50} +(-0.832709 - 0.832709i) q^{51} +(7.11527 - 7.80109i) q^{52} +(3.55950 + 3.55950i) q^{53} +(-4.28996 - 4.09725i) q^{54} -11.0537 q^{55} +(0.677905 + 9.82079i) q^{56} +(-2.99397 + 1.58737i) q^{57} +(10.5109 + 10.0387i) q^{58} +(-0.408827 + 0.408827i) q^{59} +(3.29487 - 0.151491i) q^{60} +(2.47804 + 2.47804i) q^{61} +(0.0777377 + 3.38332i) q^{62} +8.33773i q^{63} +(-7.92412 + 1.09920i) q^{64} +11.1991i q^{65} +(-5.72752 + 0.131600i) q^{66} +(-10.6691 - 10.6691i) q^{67} +(-3.02634 + 0.139144i) q^{68} +(0.265116 + 0.265116i) q^{69} +(-7.55074 - 7.21155i) q^{70} +5.59302i q^{71} +(-6.75969 + 0.466605i) q^{72} -13.6019i q^{73} +(4.34487 - 4.54923i) q^{74} +(0.274881 - 0.274881i) q^{75} +(-2.17327 + 8.44256i) q^{76} +(12.8240 + 12.8240i) q^{77} +(0.133330 + 5.80283i) q^{78} -5.02027 q^{79} +(5.42410 - 6.52523i) q^{80} -3.92569 q^{81} +(-0.257955 - 11.2267i) q^{82} +(10.3497 - 10.3497i) q^{83} +(-3.99830 - 3.64679i) q^{84} +(2.27214 - 2.27214i) q^{85} +(-4.17297 + 4.36925i) q^{86} -7.99007 q^{87} +(-9.67917 + 11.1145i) q^{88} -7.42593 q^{89} +(4.96374 - 5.19721i) q^{90} +(12.9926 - 12.9926i) q^{91} +(0.963519 - 0.0443005i) q^{92} +(-1.31550 - 1.31550i) q^{93} +(-5.06909 + 0.116471i) q^{94} +(-4.33131 - 8.16940i) q^{95} +(2.73283 - 3.44565i) q^{96} -3.70124i q^{97} +(0.166113 + 7.22959i) q^{98} +(-8.82679 + 8.82679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 4 q^{4} - 4 q^{5} - 4 q^{6} - 8 q^{7} - 4 q^{11} + 4 q^{16} - 8 q^{17} + 6 q^{19} - 32 q^{20} - 8 q^{23} - 12 q^{24} - 8 q^{26} - 40 q^{30} + 44 q^{36} - 12 q^{38} - 8 q^{39} + 12 q^{42} - 4 q^{43}+ \cdots + 76 q^{99}+O(q^{100}) \) 76 * q - 4 * q^4 - 4 * q^5 - 4 * q^6 - 8 * q^7 - 4 * q^11 + 4 * q^16 - 8 * q^17 + 6 * q^19 - 32 * q^20 - 8 * q^23 - 12 * q^24 - 8 * q^26 - 40 * q^30 + 44 * q^36 - 12 * q^38 - 8 * q^39 + 12 * q^42 - 4 * q^43 - 76 * q^44 + 4 * q^45 + 44 * q^49 + 96 * q^54 - 8 * q^55 + 24 * q^58 + 28 * q^61 + 20 * q^62 - 64 * q^64 + 12 * q^66 - 80 * q^74 + 12 * q^76 - 32 * q^77 - 16 * q^80 - 52 * q^81 + 68 * q^82 + 36 * q^83 - 56 * q^85 - 120 * q^87 - 8 * q^92 - 16 * q^93 + 48 * q^96 + 76 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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