LMFDB - Embedded newform 700.2.t.e.199.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(199,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("700.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.26
Character	$\chi$	$=$	700.199
Dual form			700.2.t.e.299.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15273 + 0.819270i) q^{2} +(-1.52103 - 0.878165i) q^{3} +(0.657592 + 1.88880i) q^{4} +(-1.03388 - 2.25842i) q^{6} +(1.72616 + 2.00509i) q^{7} +(-0.789410 + 2.71603i) q^{8} +(0.0423472 + 0.0733475i) q^{9} +O(q^{10})$	\(q+(1.15273 + 0.819270i) q^{2} +(-1.52103 - 0.878165i) q^{3} +(0.657592 + 1.88880i) q^{4} +(-1.03388 - 2.25842i) q^{6} +(1.72616 + 2.00509i) q^{7} +(-0.789410 + 2.71603i) q^{8} +(0.0423472 + 0.0733475i) q^{9} +(3.59956 + 2.07821i) q^{11} +(0.658464 - 3.45039i) q^{12} -4.90376 q^{13} +(0.347088 + 3.72552i) q^{14} +(-3.13514 + 2.48412i) q^{16} +(-0.113880 + 0.197246i) q^{17} +(-0.0112764 + 0.119244i) q^{18} +(0.396093 + 0.686053i) q^{19} +(-0.864729 - 4.56564i) q^{21} +(2.44673 + 5.34464i) q^{22} +(2.72379 + 4.71775i) q^{23} +(3.58584 - 3.43792i) q^{24} +(-5.65273 - 4.01750i) q^{26} +5.12024i q^{27} +(-2.65211 + 4.57890i) q^{28} +8.17136 q^{29} +(-2.11825 + 3.66891i) q^{31} +(-5.64916 + 0.295003i) q^{32} +(-3.65002 - 6.32202i) q^{33} +(-0.292871 + 0.134074i) q^{34} +(-0.110692 + 0.128218i) q^{36} +(-4.47631 + 2.58440i) q^{37} +(-0.105473 + 1.11534i) q^{38} +(7.45874 + 4.30631i) q^{39} +5.46577i q^{41} +(2.74369 - 5.97142i) q^{42} +4.95932 q^{43} +(-1.55828 + 8.16548i) q^{44} +(-0.725302 + 7.66984i) q^{46} +(-5.01175 + 2.89353i) q^{47} +(6.95011 - 1.02524i) q^{48} +(-1.04077 + 6.92220i) q^{49} +(0.346429 - 0.200011i) q^{51} +(-3.22467 - 9.26222i) q^{52} +(-9.38050 - 5.41584i) q^{53} +(-4.19486 + 5.90227i) q^{54} +(-6.80853 + 3.10546i) q^{56} -1.39134i q^{57} +(9.41941 + 6.69456i) q^{58} +(3.93063 - 6.80806i) q^{59} +(11.5731 - 6.68172i) q^{61} +(-5.44760 + 2.49386i) q^{62} +(-0.0739705 + 0.211519i) q^{63} +(-6.75366 - 4.28813i) q^{64} +(0.971941 - 10.2780i) q^{66} +(3.24881 - 5.62711i) q^{67} +(-0.447445 - 0.0853894i) q^{68} -9.56776i q^{69} -2.03817i q^{71} +(-0.232644 + 0.0571151i) q^{72} +(2.68098 - 4.64359i) q^{73} +(-7.27732 - 0.688183i) q^{74} +(-1.03535 + 1.19928i) q^{76} +(2.04641 + 10.8048i) q^{77} +(5.06992 + 11.0748i) q^{78} +(-4.42687 + 2.55585i) q^{79} +(4.62346 - 8.00806i) q^{81} +(-4.47794 + 6.30058i) q^{82} -9.52133i q^{83} +(8.05496 - 4.63563i) q^{84} +(5.71677 + 4.06302i) q^{86} +(-12.4289 - 7.17580i) q^{87} +(-8.48602 + 8.13597i) q^{88} +(2.01542 - 1.16361i) q^{89} +(-8.46465 - 9.83247i) q^{91} +(-7.11975 + 8.24706i) q^{92} +(6.44381 - 3.72034i) q^{93} +(-8.14780 - 0.770500i) q^{94} +(8.85158 + 4.51218i) q^{96} +17.7211 q^{97} +(-6.87088 + 7.12678i) q^{98} +0.352025i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 2 q^{4} + 32 q^{9}+O(q^{10}) $ 64 * q - 2 * q^4 + 32 * q^9	$ 64 q - 2 q^{4} + 32 q^{9} + 26 q^{14} + 2 q^{16} + 24 q^{21} + 36 q^{24} - 30 q^{26} - 16 q^{29} - 60 q^{36} - 24 q^{44} + 4 q^{46} - 40 q^{49} - 114 q^{54} - 62 q^{56} - 24 q^{61} - 80 q^{64} - 132 q^{66} + 2 q^{74} - 72 q^{81} - 134 q^{84} + 8 q^{86} + 120 q^{89} - 90 q^{94} + 186 q^{96}+O(q^{100}) $ 64 * q - 2 * q^4 + 32 * q^9 + 26 * q^14 + 2 * q^16 + 24 * q^21 + 36 * q^24 - 30 * q^26 - 16 * q^29 - 60 * q^36 - 24 * q^44 + 4 * q^46 - 40 * q^49 - 114 * q^54 - 62 * q^56 - 24 * q^61 - 80 * q^64 - 132 * q^66 + 2 * q^74 - 72 * q^81 - 134 * q^84 + 8 * q^86 + 120 * q^89 - 90 * q^94 + 186 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.15273	+	0.819270i	0.815106	+	0.579312i
$2$	1.15273	+	0.819270i	0.815106	+	0.579312i
$3$	−1.52103	−	0.878165i	−0.878165	−	0.507009i	−0.00811200	−	0.999967i	$-0.502582\pi$
$3$	−1.52103	−	0.878165i	−0.878165	−	0.507009i	−0.870053	+	0.492958i	$0.835915\pi$
$4$	0.657592	+	1.88880i	0.328796	+	0.944401i
$5$		0			0
$5$		0			0
$6$	−1.03388	−	2.25842i	−0.422082	−	0.921997i
$7$	1.72616	+	2.00509i	0.652426	+	0.757853i
$7$	1.72616	+	2.00509i	0.652426	+	0.757853i
$8$	−0.789410	+	2.71603i	−0.279099	+	0.960262i
$9$	0.0423472	+	0.0733475i	0.0141157	+	0.0244492i
$10$		0			0
$11$	3.59956	+	2.07821i	1.08531	+	0.626604i	0.932324	−	0.361625i	$-0.117778\pi$
$11$	3.59956	+	2.07821i	1.08531	+	0.626604i	0.152986	+	0.988228i	$0.451111\pi$
$12$	0.658464	−	3.45039i	0.190082	−	0.996042i
$13$	−4.90376			−1.36006			−0.680029	−	0.733186i	$-0.738033\pi$
$13$	−4.90376			−1.36006			−0.680029	+	0.733186i	$0.738033\pi$
$14$	0.347088	+	3.72552i	0.0927633	+	0.995688i
$15$		0			0
$16$	−3.13514	+	2.48412i	−0.783786	+	0.621031i
$17$	−0.113880	+	0.197246i	−0.0276200	+	0.0478392i	−0.879505	−	0.475890i	$-0.842126\pi$
$17$	−0.113880	+	0.197246i	−0.0276200	+	0.0478392i	0.851885	+	0.523729i	$0.175459\pi$
$18$	−0.0112764	+	0.119244i	−0.00265786	+	0.0281061i
$19$	0.396093	+	0.686053i	0.0908700	+	0.157391i	0.907877	−	0.419236i	$-0.137702\pi$
$19$	0.396093	+	0.686053i	0.0908700	+	0.157391i	−0.817007	+	0.576627i	$0.804369\pi$
$20$		0			0
$21$	−0.864729	−	4.56564i	−0.188699	−	0.996305i
$22$	2.44673	+	5.34464i	0.521644	+	1.13948i
$23$	2.72379	+	4.71775i	0.567950	+	0.983719i	0.996768	+	0.0803281i	$0.0255968\pi$
$23$	2.72379	+	4.71775i	0.567950	+	0.983719i	−0.428818	+	0.903391i	$0.641070\pi$
$24$	3.58584	−	3.43792i	0.731956	−	0.701763i
$25$		0			0
$26$	−5.65273	−	4.01750i	−1.10859	−	0.787897i
$27$			5.12024i			0.985390i
$28$	−2.65211	+	4.57890i	−0.501202	+	0.865330i
$29$	8.17136			1.51738			0.758692	−	0.651449i	$-0.225839\pi$
$29$	8.17136			1.51738			0.758692	+	0.651449i	$0.225839\pi$
$30$		0			0
$31$	−2.11825	+	3.66891i	−0.380448	+	0.658956i	−0.991126	−	0.132923i	$-0.957564\pi$
$31$	−2.11825	+	3.66891i	−0.380448	+	0.658956i	0.610678	+	0.791879i	$0.290897\pi$
$32$	−5.64916	+	0.295003i	−0.998639	+	0.0521496i
$33$	−3.65002	−	6.32202i	−0.635387	−	1.10052i
$34$	−0.292871	+	0.134074i	−0.0502270	+	0.0229934i
$35$		0			0
$36$	−0.110692	+	0.128218i	−0.0184486	+	0.0213697i
$37$	−4.47631	+	2.58440i	−0.735901	+	0.424873i	−0.820577	−	0.571536i	$-0.806348\pi$
$37$	−4.47631	+	2.58440i	−0.735901	+	0.424873i	0.0846759	+	0.996409i	$0.473014\pi$
$38$	−0.105473	+	1.11534i	−0.0171100	+	0.180933i
$39$	7.45874	+	4.30631i	1.19435	+	0.689561i
$40$		0			0
$41$			5.46577i			0.853610i	0.904344	+	0.426805i	$0.140361\pi$
$41$			5.46577i			0.853610i	−0.904344	+	0.426805i	$0.859639\pi$
$42$	2.74369	−	5.97142i	0.423361	−	0.921410i
$43$	4.95932			0.756289			0.378144	−	0.925747i	$-0.376562\pi$
$43$	4.95932			0.756289			0.378144	+	0.925747i	$0.376562\pi$
$44$	−1.55828	+	8.16548i	−0.234920	+	1.23099i
$45$		0			0
$46$	−0.725302	+	7.66984i	−0.106940	+	1.13086i
$47$	−5.01175	+	2.89353i	−0.731038	+	0.422065i	−0.818802	−	0.574076i	$-0.805361\pi$
$47$	−5.01175	+	2.89353i	−0.731038	+	0.422065i	0.0877636	+	0.996141i	$0.472028\pi$
$48$	6.95011	−	1.02524i	1.00316	−	0.147981i
$49$	−1.04077	+	6.92220i	−0.148682	+	0.988885i
$50$		0			0
$51$	0.346429	−	0.200011i	0.0485098	−	0.0280071i
$52$	−3.22467	−	9.26222i	−0.447182	−	1.28444i
$53$	−9.38050	−	5.41584i	−1.28851	−	0.743922i	−0.310123	−	0.950697i	$-0.600370\pi$
$53$	−9.38050	−	5.41584i	−1.28851	−	0.743922i	−0.978389	+	0.206774i	$0.933703\pi$
$54$	−4.19486	+	5.90227i	−0.570848	+	0.803198i
$55$		0			0
$56$	−6.80853	+	3.10546i	−0.909829	+	0.414984i
$57$		−	1.39134i		−	0.184287i
$58$	9.41941	+	6.69456i	1.23683	+	0.879038i
$59$	3.93063	−	6.80806i	0.511725	−	0.886334i	−0.488183	−	0.872741i	$-0.662340\pi$
$59$	3.93063	−	6.80806i	0.511725	−	0.886334i	0.999908	−	0.0135921i	$-0.00432665\pi$
$60$		0			0
$61$	11.5731	−	6.68172i	1.48178	−	0.855507i	0.481995	−	0.876174i	$-0.339912\pi$
$61$	11.5731	−	6.68172i	1.48178	−	0.855507i	0.999786	+	0.0206676i	$0.00657915\pi$
$62$	−5.44760	+	2.49386i	−0.691846	+	0.316721i
$63$	−0.0739705	+	0.211519i	−0.00931940	+	0.0266489i
$64$	−6.75366	−	4.28813i	−0.844208	−	0.536016i
$65$		0			0
$66$	0.971941	−	10.2780i	0.119638	−	1.26513i
$67$	3.24881	−	5.62711i	0.396906	−	0.687461i	−0.596437	−	0.802660i	$-0.703417\pi$
$67$	3.24881	−	5.62711i	0.396906	−	0.687461i	0.993342	+	0.115199i	$0.0367506\pi$
$68$	−0.447445	−	0.0853894i	−0.0542607	−	0.0103550i
$69$		−	9.56776i		−	1.15182i
$70$		0			0
$71$		−	2.03817i		−	0.241886i	−0.992659	−	0.120943i	$-0.961408\pi$
$71$		−	2.03817i		−	0.241886i	0.992659	−	0.120943i	$-0.0385919\pi$
$72$	−0.232644	+	0.0571151i	−0.0274173	+	0.00673108i
$73$	2.68098	−	4.64359i	0.313785	−	0.543491i	−0.665394	−	0.746493i	$-0.731736\pi$
$73$	2.68098	−	4.64359i	0.313785	−	0.543491i	0.979178	+	0.203002i	$0.0650696\pi$
$74$	−7.27732	−	0.688183i	−0.845971	−	0.0799997i
$75$		0			0
$76$	−1.03535	+	1.19928i	−0.118763	+	0.137567i
$77$	2.04641	+	10.8048i	0.233210	+	1.23132i
$78$	5.06992	+	11.0748i	0.574055	+	1.25397i
$79$	−4.42687	+	2.55585i	−0.498062	+	0.287556i	−0.727913	−	0.685670i	$-0.759509\pi$
$79$	−4.42687	+	2.55585i	−0.498062	+	0.287556i	0.229851	+	0.973226i	$0.426176\pi$
$80$		0			0
$81$	4.62346	−	8.00806i	0.513717	−	0.889784i
$82$	−4.47794	+	6.30058i	−0.494506	+	0.695783i
$83$		−	9.52133i		−	1.04510i	−0.852608	−	0.522551i	$-0.824980\pi$
$83$		−	9.52133i		−	1.04510i	0.852608	−	0.522551i	$-0.175020\pi$
$84$	8.05496	−	4.63563i	0.878868	−	0.505789i
$85$		0			0
$86$	5.71677	+	4.06302i	0.616456	+	0.438127i
$87$	−12.4289	−	7.17580i	−1.33251	−	0.769327i
$88$	−8.48602	+	8.13597i	−0.904612	+	0.867298i
$89$	2.01542	−	1.16361i	0.213634	−	0.123342i	−0.389365	−	0.921084i	$-0.627305\pi$
$89$	2.01542	−	1.16361i	0.213634	−	0.123342i	0.602999	+	0.797742i	$0.293972\pi$
$90$		0			0
$91$	−8.46465	−	9.83247i	−0.887336	−	1.03072i
$92$	−7.11975	+	8.24706i	−0.742285	+	0.859816i
$93$	6.44381	−	3.72034i	0.668192	−	0.385781i
$94$	−8.14780	−	0.770500i	−0.840381	−	0.0794710i
$95$		0			0
$96$	8.85158	+	4.51218i	0.903410	+	0.460523i
$97$	17.7211			1.79931			0.899654	−	0.436603i	$-0.143819\pi$
$97$	17.7211			1.79931			0.899654	+	0.436603i	$0.143819\pi$
$98$	−6.87088	+	7.12678i	−0.694064	+	0.719913i
$99$			0.352025i			0.0353799i
$100$		0			0
$101$	−13.3283	−	7.69509i	−1.32621	−	0.765690i	−0.341502	−	0.939881i	$-0.610936\pi$
$101$	−13.3283	−	7.69509i	−1.32621	−	0.765690i	−0.984712	+	0.174191i	$0.944269\pi$
$102$	0.563204	+	0.0532596i	0.0557655	+	0.00527349i
$103$	9.47127	−	5.46824i	0.933231	−	0.538801i	0.0453993	−	0.998969i	$-0.485544\pi$
$103$	9.47127	−	5.46824i	0.933231	−	0.538801i	0.887832	+	0.460167i	$0.152211\pi$
$104$	3.87107	−	13.3188i	0.379590	−	1.30601i
$105$		0			0
$106$	−6.37619	−	13.9282i	−0.619311	−	1.35283i
$107$	−2.36075	−	4.08895i	−0.228223	−	0.395293i	0.729059	−	0.684451i	$-0.239958\pi$
$107$	−2.36075	−	4.08895i	−0.228223	−	0.395293i	−0.957281	+	0.289158i	$0.906625\pi$
$108$	−9.67112	+	3.36703i	−0.930603	+	0.323993i
$109$	4.06945	−	7.04850i	0.389783	−	0.675124i	−0.602637	−	0.798015i	$-0.705883\pi$
$109$	4.06945	−	7.04850i	0.389783	−	0.675124i	0.992420	+	0.122891i	$0.0392167\pi$
$110$		0			0
$111$	9.07812			0.861657
$112$	−10.3926	−	1.99826i	−0.982012	−	0.188818i
$113$			9.50633i			0.894280i	0.894464	+	0.447140i	$0.147557\pi$
$113$			9.50633i			0.894280i	−0.894464	+	0.447140i	$0.852443\pi$
$114$	1.13988	−	1.60385i	0.106760	−	0.150214i
$115$		0			0
$116$	5.37343	+	15.4341i	0.498910	+	1.43302i
$117$	−0.207660	−	0.359678i	−0.0191982	−	0.0332523i
$118$	10.1086	−	4.62763i	0.930574	−	0.426008i
$119$	−0.592071	+	0.112138i	−0.0542750	+	0.0102796i
$120$		0			0
$121$	3.13791	+	5.43502i	0.285265	+	0.494093i
$122$	18.8148	+	1.77923i	1.70341	+	0.161084i
$123$	4.79985	−	8.31358i	0.432788	−	0.749610i
$124$	−8.32278	−	1.58830i	−0.747408	−	0.142634i
$125$		0			0
$126$	−0.258560	+	0.183224i	−0.0230343	+	0.0163229i
$127$	12.3200			1.09322			0.546612	−	0.837386i	$-0.315917\pi$
$127$	12.3200			1.09322			0.546612	+	0.837386i	$0.315917\pi$
$128$	−4.27204	−	10.4761i	−0.377599	−	0.925969i
$129$	−7.54325	−	4.35510i	−0.664146	−	0.383445i
$130$		0			0
$131$	8.32817	+	14.4248i	0.727635	+	1.26030i	0.957880	+	0.287169i	$0.0927140\pi$
$131$	8.32817	+	14.4248i	0.727635	+	1.26030i	−0.230245	+	0.973133i	$0.573953\pi$
$132$	9.54082	−	11.0515i	0.830422	−	0.961908i
$133$	−0.691880	+	1.97844i	−0.0599936	+	0.171552i
$134$	8.35514	−	3.82491i	0.721774	−	0.330422i
$135$		0			0
$136$	−0.445829	−	0.465010i	−0.0382295	−	0.0398743i
$137$	−3.81315	−	2.20153i	−0.325780	−	0.188089i	0.328186	−	0.944613i	$-0.393563\pi$
$137$	−3.81315	−	2.20153i	−0.325780	−	0.188089i	−0.653966	+	0.756524i	$0.726896\pi$
$138$	7.83858	−	11.0291i	0.667265	−	0.938858i
$139$	−13.2240			−1.12164			−0.560822	−	0.827936i	$-0.689515\pi$
$139$	−13.2240			−1.12164			−0.560822	+	0.827936i	$0.689515\pi$
$140$		0			0
$141$	10.1640			0.855963
$142$	1.66981	−	2.34947i	0.140128	−	0.197163i
$143$	−17.6514	−	10.1910i	−1.47608	−	0.852217i
$144$	−0.314969	−	0.124759i	−0.0262474	−	0.0103966i
$145$		0			0
$146$	6.89481	−	3.15638i	0.570619	−	0.261224i
$147$	7.66187	−	9.61487i	0.631940	−	0.793021i
$148$	−7.82501	−	6.75538i	−0.643212	−	0.555289i
$149$	−5.77374	−	10.0004i	−0.473003	−	0.819265i	0.526520	−	0.850163i	$-0.323497\pi$
$149$	−5.77374	−	10.0004i	−0.473003	−	0.819265i	−0.999523	+	0.0308978i	$0.990163\pi$
$150$		0			0
$151$	−14.9095	−	8.60802i	−1.21332	−	0.700511i	−0.249839	−	0.968287i	$-0.580378\pi$
$151$	−14.9095	−	8.60802i	−1.21332	−	0.700511i	−0.963481	+	0.267776i	$0.913711\pi$
$152$	−2.17602	+	0.534224i	−0.176499	+	0.0433313i
$153$	−0.0192900			−0.00155950
$154$	−6.49305	+	14.1316i	−0.523225	+	1.13876i
$155$		0			0
$156$	−3.22895	+	16.9199i	−0.258523	+	1.35467i
$157$	10.4421	−	18.0862i	0.833369	−	1.44344i	−0.0619833	−	0.998077i	$-0.519743\pi$
$157$	10.4421	−	18.0862i	0.833369	−	1.44344i	0.895352	−	0.445359i	$-0.146924\pi$
$158$	−7.19694	−	0.680582i	−0.572558	−	0.0541442i
$159$	9.51200	+	16.4753i	0.754350	+	1.30657i
$160$		0			0
$161$	−4.75782	+	13.6050i	−0.374969	+	1.07223i
$162$	11.8904	−	5.44330i	0.934196	−	0.427666i
$163$	3.60798	+	6.24921i	0.282599	+	0.489476i	0.972024	−	0.234881i	$-0.0754701\pi$
$163$	3.60798	+	6.24921i	0.282599	+	0.489476i	−0.689425	+	0.724357i	$0.742137\pi$
$164$	−10.3238	+	3.59425i	−0.806150	+	0.280664i
$165$		0			0
$166$	7.80055	−	10.9756i	0.605440	−	0.851869i
$167$			14.7801i			1.14372i	0.820351	+	0.571860i	$0.193778\pi$
$167$			14.7801i			1.14372i	−0.820351	+	0.571860i	$0.806222\pi$
$168$	13.0831	+	1.25553i	1.00938	+	0.0968665i
$169$	11.0468			0.849756
$170$		0			0
$171$	−0.0335469	+	0.0581049i	−0.00256539	+	0.00444339i
$172$	3.26121	+	9.36717i	0.248665	+	0.714240i
$173$	−9.38545	−	16.2561i	−0.713563	−	1.23593i	−0.963511	−	0.267667i	$-0.913747\pi$
$173$	−9.38545	−	16.2561i	−0.713563	−	1.23593i	0.249949	−	0.968259i	$-0.419586\pi$
$174$	−8.44825	−	18.4544i	−0.640460	−	1.39902i
$175$		0			0
$176$	−16.4477	+	2.42627i	−1.23979	+	0.182887i
$177$	−11.9572	+	6.90349i	−0.898758	+	0.518898i
$178$	3.27655	+	0.309849i	0.245588	+	0.0232242i
$179$	−11.1064	−	6.41230i	−0.830134	−	0.479278i	0.0237648	−	0.999718i	$-0.492435\pi$
$179$	−11.1064	−	6.41230i	−0.830134	−	0.479278i	−0.853898	+	0.520440i	$0.825768\pi$
$180$		0			0
$181$			8.55295i			0.635736i	0.948135	+	0.317868i	$0.102967\pi$
$181$			8.55295i			0.635736i	−0.948135	+	0.317868i	$0.897033\pi$
$182$	−1.70204	−	18.2691i	−0.126163	−	1.35419i
$183$	−23.4706			−1.73500
$184$	−14.9638	+	3.67367i	−1.10314	+	0.270827i
$185$		0			0
$186$	10.4760	+	0.990665i	0.768135	+	0.0726391i
$187$	−0.819837	+	0.473333i	−0.0599524	+	0.0346135i
$188$	−8.76100	−	7.56343i	−0.638961	−	0.551620i
$189$	−10.2665	+	8.83833i	−0.746781	+	0.642894i
$190$		0			0
$191$	0.426822	−	0.246426i	0.0308837	−	0.0178307i	−0.484479	−	0.874803i	$-0.660991\pi$
$191$	0.426822	−	0.246426i	0.0308837	−	0.0178307i	0.515362	+	0.856972i	$0.327657\pi$
$192$	6.50682	+	12.4532i	0.469589	+	0.898731i
$193$	23.3615	+	13.4878i	1.68160	+	0.970870i	0.960602	+	0.277928i	$0.0896478\pi$
$193$	23.3615	+	13.4878i	1.68160	+	0.970870i	0.720994	+	0.692941i	$0.243686\pi$
$194$	20.4278	+	14.5184i	1.46663	+	1.04236i
$195$		0			0
$196$	−13.7591	+	2.58617i	−0.982790	+	0.184727i
$197$		−	2.48025i		−	0.176710i	−0.996089	−	0.0883552i	$-0.971839\pi$
$197$		−	2.48025i		−	0.176710i	0.996089	−	0.0883552i	$-0.0281611\pi$
$198$	−0.288404	+	0.405792i	−0.0204960	+	0.0288384i
$199$	2.76798	−	4.79428i	0.196217	−	0.339858i	−0.751082	−	0.660209i	$-0.770468\pi$
$199$	2.76798	−	4.79428i	0.196217	−	0.339858i	0.947299	+	0.320351i	$0.103801\pi$
$200$		0			0
$201$	−9.88306	+	5.70599i	−0.697097	+	0.402469i
$202$	−9.05961	−	19.7899i	−0.637432	−	1.39241i
$203$	14.1050	+	16.3843i	0.989980	+	1.14995i
$204$	0.605590	+	0.522810i	0.0423998	+	0.0366040i
$205$		0			0
$206$	15.3978	+	1.45610i	1.07282	+	0.101451i
$207$	−0.230690	+	0.399567i	−0.0160341	+	0.0277718i
$208$	15.3740	−	12.1815i	1.06599	−	0.844637i
$209$			3.29266i			0.227758i
$210$		0			0
$211$			21.7260i			1.49568i	0.663879	+	0.747840i	$0.268909\pi$
$211$			21.7260i			1.49568i	−0.663879	+	0.747840i	$0.731091\pi$
$212$	4.06089	−	21.2793i	0.278903	−	1.46147i
$213$	−1.78985	+	3.10011i	−0.122638	+	0.212416i
$214$	0.628630	−	6.64756i	0.0429723	−	0.454418i
$215$		0			0
$216$	−13.9067	−	4.04197i	−0.946233	−	0.275021i
$217$	−11.0129	+	2.08584i	−0.747605	+	0.141596i
$218$	10.4656	−	4.79106i	0.708822	−	0.324492i
$219$	−8.15568	+	4.70868i	−0.551110	+	0.318183i
$220$		0			0
$221$	0.558440	−	0.967246i	0.0375647	−	0.0650640i
$222$	10.4647	+	7.43743i	0.702342	+	0.499168i
$223$			24.6124i			1.64817i	0.566467	+	0.824084i	$0.308310\pi$
$223$			24.6124i			1.64817i	−0.566467	+	0.824084i	$0.691690\pi$
$224$	−10.3428	−	10.8178i	−0.691060	−	0.722798i
$225$		0			0
$226$	−7.78825	+	10.9583i	−0.518067	+	0.728933i
$227$	7.10120	+	4.09988i	0.471323	+	0.272119i	0.716793	−	0.697286i	$-0.245609\pi$
$227$	7.10120	+	4.09988i	0.471323	+	0.272119i	−0.245470	+	0.969404i	$0.578942\pi$
$228$	2.62797	−	0.914934i	0.174041	−	0.0605930i
$229$	4.20964	−	2.43044i	0.278181	−	0.160608i	−0.354419	−	0.935087i	$-0.615321\pi$
$229$	4.20964	−	2.43044i	0.278181	−	0.160608i	0.632600	+	0.774479i	$0.281988\pi$
$230$		0			0
$231$	6.37572	−	18.2314i	0.419491	−	1.19954i
$232$	−6.45056	+	22.1937i	−0.423500	+	1.45709i
$233$	18.3238	−	10.5793i	1.20043	−	0.693071i	0.239783	−	0.970827i	$-0.422924\pi$
$233$	18.3238	−	10.5793i	1.20043	−	0.693071i	0.960652	+	0.277755i	$0.0895904\pi$
$234$	0.0552965	−	0.584743i	0.00361485	−	0.0382259i
$235$		0			0
$236$	15.4438	+	2.94726i	1.00531	+	0.191850i
$237$	8.97784			0.583174
$238$	−0.774371	−	0.355801i	−0.0501950	−	0.0230632i
$239$		−	2.45963i		−	0.159100i	−0.996831	−	0.0795500i	$-0.974652\pi$
$239$		−	2.45963i		−	0.159100i	0.996831	−	0.0795500i	$-0.0253483\pi$
$240$		0			0
$241$	−1.36901	−	0.790395i	−0.0881854	−	0.0509138i	0.455259	−	0.890359i	$-0.349547\pi$
$241$	−1.36901	−	0.790395i	−0.0881854	−	0.0509138i	−0.543444	+	0.839445i	$0.682880\pi$
$242$	−0.835574	+	8.83593i	−0.0537127	+	0.567995i
$243$	−0.762024	+	0.439955i	−0.0488839	+	0.0282231i
$244$	20.2308	+	17.4654i	1.29515	+	1.11811i
$245$		0			0
$246$	12.3440	−	5.65098i	0.787026	−	0.360293i
$247$	−1.94234	−	3.36424i	−0.123588	−	0.214061i
$248$	−8.29271	−	8.64950i	−0.526588	−	0.549244i
$249$	−8.36130	+	14.4822i	−0.529876	+	0.917772i
$250$		0			0
$251$	26.3036			1.66027			0.830135	−	0.557562i	$-0.188263\pi$
$251$	26.3036			1.66027			0.830135	+	0.557562i	$0.188263\pi$
$252$	−0.448160		0.000622162i	−0.0282314		3.91925e-5i
$253$			22.6425i			1.42352i
$254$	14.2017	+	10.0934i	0.891093	+	0.633317i
$255$		0			0
$256$	3.65826	−	15.5762i	0.228642	−	0.973511i
$257$	−5.99938	−	10.3912i	−0.374231	−	0.648187i	0.615981	−	0.787761i	$-0.288760\pi$
$257$	−5.99938	−	10.3912i	−0.374231	−	0.648187i	−0.990212	+	0.139574i	$0.955427\pi$
$258$	−5.12736	−	11.2002i	−0.319216	−	0.697296i
$259$	−12.9088	−	4.51433i	−0.802112	−	0.280507i
$260$		0			0
$261$	0.346034	+	0.599349i	0.0214190	+	0.0370988i
$262$	−2.21765	+	23.4510i	−0.137007	+	1.44881i
$263$	4.85628	−	8.41133i	0.299451	−	0.518665i	−0.676559	−	0.736388i	$-0.736530\pi$
$263$	4.85628	−	8.41133i	0.299451	−	0.518665i	0.976011	+	0.217723i	$0.0698631\pi$
$264$	20.0522	−	4.92291i	1.23413	−	0.302984i
$265$		0			0
$266$	−2.41843	+	1.71378i	−0.148283	+	0.105078i
$267$	−4.08735			−0.250142
$268$	12.7649	+	2.43602i	0.779740	+	0.148804i
$269$	−2.91623	−	1.68369i	−0.177806	−	0.102656i	0.408456	−	0.912778i	$-0.366067\pi$
$269$	−2.91623	−	1.68369i	−0.177806	−	0.102656i	−0.586261	+	0.810122i	$0.699401\pi$
$270$		0			0
$271$	4.96774	+	8.60437i	0.301768	+	0.522678i	0.976537	−	0.215352i	$-0.0690897\pi$
$271$	4.96774	+	8.60437i	0.301768	+	0.522678i	−0.674768	+	0.738030i	$0.735756\pi$
$272$	−0.132953	−	0.901287i	−0.00806146	−	0.0546485i
$273$	4.24042	+	22.3888i	0.256642	+	1.35503i
$274$	−2.59191	−	5.66178i	−0.156583	−	0.342041i
$275$		0			0
$276$	18.0716	−	6.29169i	1.08778	−	0.378715i
$277$	−0.347087	−	0.200391i	−0.0208544	−	0.0120403i	0.489537	−	0.871983i	$-0.337166\pi$
$277$	−0.347087	−	0.200391i	−0.0208544	−	0.0120403i	−0.510391	+	0.859942i	$0.670499\pi$
$278$	−15.2438	−	10.8340i	−0.914260	−	0.649782i
$279$	−0.358807			−0.0214812
$280$		0			0
$281$	−21.4548			−1.27988			−0.639942	−	0.768423i	$-0.721042\pi$
$281$	−21.4548			−1.27988			−0.639942	+	0.768423i	$0.721042\pi$
$282$	11.7164	+	8.32706i	0.697701	+	0.495869i
$283$	−17.6896	−	10.2131i	−1.05154	−	0.607106i	−0.128459	−	0.991715i	$-0.541003\pi$
$283$	−17.6896	−	10.2131i	−1.05154	−	0.607106i	−0.923080	+	0.384609i	$0.874336\pi$
$284$	3.84970	−	1.34029i	0.228438	−	0.0795313i
$285$		0			0
$286$	−11.9981	−	26.2088i	−0.709465	−	1.54976i
$287$	−10.9594	+	9.43477i	−0.646911	+	0.556917i
$288$	−0.260864	−	0.401859i	−0.0153715	−	0.0236798i
$289$	8.47406	+	14.6775i	0.498474	+	0.863383i
$290$		0			0
$291$	−26.9543	−	15.5621i	−1.58009	−	0.912265i
$292$	10.5338	+	2.01025i	0.616445	+	0.117641i
$293$	−4.64138			−0.271152			−0.135576	−	0.990767i	$-0.543289\pi$
$293$	−4.64138			−0.271152			−0.135576	+	0.990767i	$0.543289\pi$
$294$	16.7093	−	4.80625i	0.974505	−	0.280306i
$295$		0			0
$296$	−3.48567	−	14.1980i	−0.202600	−	0.825240i
$297$	−10.6409	+	18.4306i	−0.617449	+	1.06945i
$298$	1.53745	−	16.2581i	0.0890622	−	0.941804i
$299$	−13.3568	−	23.1347i	−0.772445	−	1.33791i
$300$		0			0
$301$	8.56055	+	9.94388i	0.493422	+	0.573155i
$302$	−10.1344	−	22.1377i	−0.583171	−	1.27388i
$303$	13.5151	+	23.4089i	0.776423	+	1.34480i
$304$	−2.94605	−	1.16693i	−0.168968	−	0.0669282i
$305$		0			0
$306$	−0.0222362	−	0.0158037i	−0.00127116	−	0.000903439i
$307$		−	6.02430i		−	0.343825i	−0.985112	−	0.171912i	$-0.945005\pi$
$307$		−	6.02430i		−	0.343825i	0.985112	−	0.171912i	$-0.0549946\pi$
$308$	−19.0624	+	10.9704i	−1.08618	+	0.625096i
$309$	−19.2081			−1.09271
$310$		0			0
$311$	−11.5074	+	19.9313i	−0.652522	+	1.13020i	0.329987	+	0.943986i	$0.392956\pi$
$311$	−11.5074	+	19.9313i	−0.652522	+	1.13020i	−0.982509	+	0.186216i	$0.940378\pi$
$312$	−17.5841	+	16.8587i	−0.995502	+	0.954438i
$313$	4.26073	+	7.37980i	0.240831	+	0.417131i	0.960951	−	0.276718i	$-0.0892468\pi$
$313$	4.26073	+	7.37980i	0.240831	+	0.417131i	−0.720120	+	0.693849i	$0.755913\pi$
$314$	26.8544	−	12.2937i	1.51548	−	0.693774i
$315$		0			0
$316$	−7.73857	−	6.68077i	−0.435329	−	0.375822i
$317$	−3.63973	+	2.10140i	−0.204428	+	0.118026i	−0.598719	−	0.800959i	$-0.704323\pi$
$317$	−3.63973	+	2.10140i	−0.204428	+	0.118026i	0.394291	+	0.918985i	$0.370990\pi$
$318$	−2.53289	+	26.7845i	−0.142037	+	1.50200i
$319$	29.4133	+	16.9818i	1.64683	+	0.950799i
$320$		0			0
$321$			8.29252i			0.462844i
$322$	−16.6307	+	11.7850i	−0.926792	+	0.656755i
$323$	−0.180428			−0.0100393
$324$	18.1660	+	3.46675i	1.00922	+	0.192597i
$325$		0			0
$326$	−0.960746	+	10.1596i	−0.0532108	+	0.562687i
$327$	−12.3795	+	7.14730i	−0.684587	+	0.395247i
$328$	−14.8452	−	4.31474i	−0.819690	−	0.238241i
$329$	−14.4528	−	5.05431i	−0.796811	−	0.278653i
$330$		0			0
$331$	9.27412	−	5.35442i	0.509752	−	0.294305i	−0.222980	−	0.974823i	$-0.571578\pi$
$331$	9.27412	−	5.35442i	0.509752	−	0.294305i	0.732732	+	0.680518i	$0.238245\pi$
$332$	17.9839	−	6.26116i	0.986995	−	0.343626i
$333$	−0.379119	−	0.218884i	−0.0207756	−	0.0119948i
$334$	−12.1089	+	17.0376i	−0.662570	+	0.932253i
$335$		0			0
$336$	14.0527	+	12.1659i	0.766636	+	0.663702i
$337$		−	28.6850i		−	1.56257i	−0.624173	−	0.781286i	$-0.714564\pi$
$337$		−	28.6850i		−	1.56257i	0.624173	−	0.781286i	$-0.285436\pi$
$338$	12.7341	+	9.05034i	0.692641	+	0.492273i
$339$	8.34812	−	14.4594i	0.453408	−	0.785326i
$340$		0			0
$341$	−15.2495	+	8.80432i	−0.825808	+	0.476780i
$342$	−0.0862742	+	0.0394955i	−0.00466517	+	0.00213567i
$343$	−15.6762	+	9.86195i	−0.846433	+	0.532495i
$344$	−3.91493	+	13.4697i	−0.211079	+	0.726236i
$345$		0			0
$346$	2.49919	−	26.4282i	0.134357	−	1.42079i
$347$	11.7072	−	20.2775i	0.628475	−	1.08855i	−0.359383	−	0.933190i	$-0.617013\pi$
$347$	11.7072	−	20.2775i	0.628475	−	1.08855i	0.987858	−	0.155361i	$-0.0496540\pi$
$348$	5.38055	−	28.1944i	0.288428	−	1.51138i
$349$			19.7474i			1.05706i	0.848916	+	0.528528i	$0.177256\pi$
$349$			19.7474i			1.05706i	−0.848916	+	0.528528i	$0.822744\pi$
$350$		0			0
$351$		−	25.1084i		−	1.34019i
$352$	−20.9476	−	10.6782i	−1.11651	−	0.569153i
$353$	−10.7803	+	18.6720i	−0.573776	+	0.993809i	0.422398	+	0.906411i	$0.361189\pi$
$353$	−10.7803	+	18.6720i	−0.573776	+	0.993809i	−0.996173	+	0.0873982i	$0.972145\pi$
$354$	−19.4393	−	1.83829i	−1.03319	−	0.0977038i
$355$		0			0
$356$	3.52315	+	3.04156i	0.186726	+	0.161202i
$357$	0.999030	+	0.349371i	0.0528743	+	0.0184907i
$358$	−7.54936	−	16.4908i	−0.398996	−	0.871568i
$359$	6.74629	−	3.89497i	0.356056	−	0.205569i	−0.311294	−	0.950314i	$-0.600762\pi$
$359$	6.74629	−	3.89497i	0.356056	−	0.205569i	0.667349	+	0.744745i	$0.267429\pi$
$360$		0			0
$361$	9.18622	−	15.9110i	0.483485	−	0.837421i
$362$	−7.00718	+	9.85928i	−0.368289	+	0.518192i
$363$		−	11.0224i		−	0.578526i
$364$	13.0053	−	22.4538i	0.681663	−	1.17690i
$365$		0			0
$366$	−27.0554	−	19.2288i	−1.41421	−	1.00510i
$367$	4.79223	+	2.76679i	0.250152	+	0.144425i	0.619834	−	0.784733i	$-0.287200\pi$
$367$	4.79223	+	2.76679i	0.250152	+	0.144425i	−0.369682	+	0.929158i	$0.620533\pi$
$368$	−20.2590	−	8.02459i	−1.05607	−	0.418311i
$369$	−0.400901	+	0.231460i	−0.0208701	+	0.0120493i
$370$		0			0
$371$	−5.33297	−	28.1573i	−0.276874	−	1.46186i
$372$	11.2644	+	9.72462i	0.584031	+	0.504198i
$373$	−8.20453	+	4.73689i	−0.424814	+	0.245267i	−0.697135	−	0.716940i	$-0.745542\pi$
$373$	−8.20453	+	4.73689i	−0.424814	+	0.245267i	0.272321	+	0.962207i	$0.412209\pi$
$374$	−1.33284	−	0.126041i	−0.0689196	−	0.00651742i
$375$		0			0
$376$	−3.90261	−	15.8962i	−0.201262	−	0.819786i
$377$	−40.0704			−2.06373
$378$	−19.0756	+	1.77718i	−0.981141	+	0.0914080i
$379$		−	23.6212i		−	1.21334i	−0.794954	−	0.606670i	$-0.792505\pi$
$379$		−	23.6212i		−	1.21334i	0.794954	−	0.606670i	$-0.207495\pi$
$380$		0			0
$381$	−18.7390	−	10.8190i	−0.960030	−	0.554274i
$382$	0.693901	+	0.0656191i	0.0355031	+	0.00335737i
$383$	−14.6082	+	8.43407i	−0.746446	+	0.430961i	−0.824408	−	0.565996i	$-0.808492\pi$
$383$	−14.6082	+	8.43407i	−0.746446	+	0.430961i	0.0779625	+	0.996956i	$0.475159\pi$
$384$	−2.70189	+	19.6861i	−0.137880	+	1.00460i
$385$		0			0
$386$	15.8795	+	34.6872i	0.808243	+	1.76553i
$387$	0.210013	+	0.363754i	0.0106756	+	0.0184906i
$388$	11.6533	+	33.4717i	0.591606	+	1.69927i
$389$	−5.17328	+	8.96039i	−0.262296	+	0.454310i	−0.966852	−	0.255339i	$-0.917813\pi$
$389$	−5.17328	+	8.96039i	−0.262296	+	0.454310i	0.704556	+	0.709649i	$0.251146\pi$
$390$		0			0
$391$	−1.24074			−0.0627471
$392$	−17.9793	−	8.29122i	−0.908092	−	0.418770i
$393$		−	29.2540i		−	1.47567i
$394$	2.03199	−	2.85907i	0.102370	−	0.144038i
$395$		0			0
$396$	−0.664906	+	0.231489i	−0.0334128	+	0.0116328i
$397$	1.29257	+	2.23880i	0.0648724	+	0.112362i	0.896637	−	0.442766i	$-0.146003\pi$
$397$	1.29257	+	2.23880i	0.0648724	+	0.112362i	−0.831765	+	0.555128i	$0.812669\pi$
$398$	7.11856	−	3.25881i	0.356821	−	0.163349i
$399$	2.78976	−	2.40167i	0.139663	−	0.120234i
$400$		0			0
$401$	−3.98844	−	6.90819i	−0.199173	−	0.344978i	0.749087	−	0.662471i	$-0.230492\pi$
$401$	−3.98844	−	6.90819i	−0.199173	−	0.344978i	−0.948261	+	0.317493i	$0.897159\pi$
$402$	−16.0673	−	1.51941i	−0.801364	−	0.0757813i
$403$	10.3874	−	17.9914i	0.517431	−	0.896217i
$404$	5.76992	−	30.2347i	0.287064	−	1.50423i
$405$		0			0
$406$	2.83619	+	30.4426i	0.140758	+	1.51084i
$407$	−21.4837			−1.06491
$408$	0.269762	+	1.09880i	0.0133552	+	0.0543989i
$409$	5.63217	+	3.25173i	0.278493	+	0.160788i	0.632741	−	0.774364i	$-0.281930\pi$
$409$	5.63217	+	3.25173i	0.278493	+	0.160788i	−0.354248	+	0.935151i	$0.615263\pi$
$410$		0			0
$411$	3.86661	+	6.69716i	0.190726	+	0.330346i
$412$	16.5566	+	14.2935i	0.815688	+	0.704189i
$413$	20.4357	−	3.87049i	1.00557	−	0.190455i
$414$	−0.593278	+	0.271597i	−0.0291580	+	0.0133483i
$415$		0			0
$416$	27.7021	−	1.44662i	1.35821	−	0.0709265i
$417$	20.1140	+	11.6128i	0.984989	+	0.568684i
$418$	−2.69758	+	3.79556i	−0.131943	+	0.185647i
$419$	29.4385			1.43817			0.719083	−	0.694924i	$-0.244562\pi$
$419$	29.4385			1.43817			0.719083	+	0.694924i	$0.244562\pi$
$420$		0			0
$421$	−11.3233			−0.551863			−0.275932	−	0.961177i	$-0.588986\pi$
$421$	−11.3233			−0.551863			−0.275932	+	0.961177i	$0.588986\pi$
$422$	−17.7995	+	25.0443i	−0.866465	+	1.21914i
$423$	−0.424467	−	0.245066i	−0.0206383	−	0.0119155i
$424$	22.1147	−	21.2024i	1.07398	−	1.02968i
$425$		0			0
$426$	−4.60305	+	2.10723i	−0.223018	+	0.102096i
$427$	33.3744	+	11.6714i	1.61510	+	0.564817i
$428$	6.17079	−	7.14785i	0.298277	−	0.345505i
$429$	17.8988	+	31.0017i	0.864163	+	1.49677i
$430$		0			0
$431$	−28.5918	−	16.5075i	−1.37722	−	0.795136i	−0.385393	−	0.922753i	$-0.625934\pi$
$431$	−28.5918	−	16.5075i	−1.37722	−	0.795136i	−0.991824	+	0.127616i	$0.959267\pi$
$432$	−12.7193	−	16.0527i	−0.611958	−	0.772335i
$433$	−18.9367			−0.910041			−0.455021	−	0.890481i	$-0.650368\pi$
$433$	−18.9367			−0.910041			−0.455021	+	0.890481i	$0.650368\pi$
$434$	−14.4038	−	6.61814i	−0.691406	−	0.317681i
$435$		0			0
$436$	15.9893	+	3.05135i	0.765747	+	0.146133i
$437$	−2.15775	+	3.73734i	−0.103219	+	0.178781i
$438$	−13.2590	−	1.25384i	−0.633540	−	0.0599110i
$439$	12.1486	+	21.0420i	0.579820	+	1.00428i	0.995500	+	0.0947665i	$0.0302104\pi$
$439$	12.1486	+	21.0420i	0.579820	+	1.00428i	−0.415680	+	0.909511i	$0.636456\pi$
$440$		0			0
$441$	−0.551800	+	0.216798i	−0.0262762	+	0.0103237i
$442$	1.43617	−	0.657465i	0.0683116	−	0.0312724i
$443$	7.50299	+	12.9956i	0.356478	+	0.617438i	0.987370	−	0.158433i	$-0.0506442\pi$
$443$	7.50299	+	12.9956i	0.356478	+	0.617438i	−0.630892	+	0.775871i	$0.717311\pi$
$444$	5.96970	+	17.1468i	0.283309	+	0.813749i
$445$		0			0
$446$	−20.1642	+	28.3716i	−0.954803	+	1.34343i
$447$			20.2812i			0.959267i
$448$	−3.05980	−	20.9437i	−0.144562	−	0.989496i
$449$	−10.9965			−0.518957			−0.259479	−	0.965749i	$-0.583551\pi$
$449$	−10.9965			−0.518957			−0.259479	+	0.965749i	$0.583551\pi$
$450$		0			0
$451$	−11.3590	+	19.6744i	−0.534875	+	0.926431i
$452$	−17.9556	+	6.25129i	−0.844559	+	0.294036i
$453$	15.1185	+	26.1861i	0.710330	+	1.23033i
$454$	4.82689	+	10.5439i	0.226537	+	0.494848i
$455$		0			0
$456$	3.77892	+	1.09834i	0.176964	+	0.0514344i
$457$	14.3732	−	8.29835i	0.672348	−	0.388180i	−0.124618	−	0.992205i	$-0.539770\pi$
$457$	14.3732	−	8.29835i	0.672348	−	0.388180i	0.796966	+	0.604024i	$0.206437\pi$
$458$	6.84379	+	0.647186i	0.319789	+	0.0302410i
$459$	−1.00995	−	0.583093i	−0.0471403	−	0.0272164i
$460$		0			0
$461$			6.62872i			0.308730i	0.988014	+	0.154365i	$0.0493332\pi$
$461$			6.62872i			0.308730i	−0.988014	+	0.154365i	$0.950667\pi$
$462$	22.2860	−	15.7925i	1.03684	−	0.734736i
$463$	2.10944			0.0980341			0.0490170	−	0.998798i	$-0.484391\pi$
$463$	2.10944			0.0980341			0.0490170	+	0.998798i	$0.484391\pi$
$464$	−25.6184	+	20.2987i	−1.18930	+	0.942342i
$465$		0			0
$466$	29.7898	+	2.81709i	1.37999	+	0.130499i
$467$	9.85173	−	5.68790i	0.455883	−	0.263204i	−0.254428	−	0.967092i	$-0.581887\pi$
$467$	9.85173	−	5.68790i	0.455883	−	0.263204i	0.710312	+	0.703887i	$0.248554\pi$
$468$	0.542805	−	0.628751i	0.0250912	−	0.0290640i
$469$	16.8908	−	3.19911i	0.779946	−	0.147721i
$470$		0			0
$471$	−31.7653	+	18.3397i	−1.46367	+	0.845050i
$472$	15.3880	+	16.0501i	0.708291	+	0.738765i
$473$	17.8514	+	10.3065i	0.820807	+	0.473893i
$474$	10.3491	+	7.35528i	0.475348	+	0.337839i
$475$		0			0
$476$	−0.601147	−	1.04456i	−0.0275535	−	0.0478775i
$477$		−	0.917382i		−	0.0420040i
$478$	2.01510	−	2.83530i	0.0921685	−	0.129683i
$479$	−5.01824	+	8.69185i	−0.229289	+	0.397141i	−0.957598	−	0.288109i	$-0.906974\pi$
$479$	−5.01824	+	8.69185i	−0.229289	+	0.397141i	0.728308	+	0.685250i	$0.240307\pi$
$480$		0			0
$481$	21.9507	−	12.6733i	1.00087	−	0.577851i
$482$	−0.930551	−	2.03270i	−0.0423855	−	0.0925870i
$483$	19.1842	−	16.5155i	0.872913	−	0.751479i
$484$	−8.20221	+	9.50092i	−0.372828	+	0.431860i
$485$		0			0
$486$	−1.23885	−	0.117153i	−0.0561955	−	0.00531416i
$487$	13.0973	−	22.6852i	0.593495	−	1.02796i	−0.400262	−	0.916401i	$-0.631081\pi$
$487$	13.0973	−	22.6852i	0.593495	−	1.02796i	0.993757	−	0.111563i	$-0.0355856\pi$
$488$	9.01186	+	36.7075i	0.407948	+	1.66167i
$489$		−	12.6736i		−	0.573120i
$490$		0			0
$491$			26.0472i			1.17549i	0.809045	+	0.587747i	$0.199985\pi$
$491$			26.0472i			1.17549i	−0.809045	+	0.587747i	$0.800015\pi$
$492$	18.8591	+	3.59902i	0.850232	+	0.162256i
$493$	−0.930555	+	1.61177i	−0.0419101	+	0.0725904i
$494$	0.517214	−	5.46938i	0.0232706	−	0.246079i
$495$		0			0
$496$	−2.47302	−	16.7645i	−0.111042	−	0.752750i
$497$	4.08671	−	3.51820i	0.183314	−	0.157813i
$498$	−21.5032	+	9.84396i	−0.963581	+	0.441118i
$499$	−15.0374	+	8.68187i	−0.673169	+	0.388654i	−0.797276	−	0.603615i	$-0.793727\pi$
$499$	−15.0374	+	8.68187i	−0.673169	+	0.388654i	0.124108	+	0.992269i	$0.460393\pi$
$500$		0			0
$501$	12.9794	−	22.4810i	0.579876	−	1.00437i
$502$	30.3211	+	21.5498i	1.35330	+	0.961814i
$503$			31.7491i			1.41562i	0.706403	+	0.707810i	$0.250317\pi$
$503$			31.7491i			1.41562i	−0.706403	+	0.707810i	$0.749683\pi$
$504$	−0.516100	−	0.367882i	−0.0229889	−	0.0163867i
$505$		0			0
$506$	−18.5503	+	26.1007i	−0.824661	+	1.16032i
$507$	−16.8025	−	9.70093i	−0.746226	−	0.430834i
$508$	8.10154	+	23.2700i	0.359448	+	1.03244i
$509$	8.90601	−	5.14189i	0.394752	−	0.227910i	−0.289465	−	0.957189i	$-0.593477\pi$
$509$	8.90601	−	5.14189i	0.394752	−	0.227910i	0.684217	+	0.729278i	$0.260144\pi$
$510$		0			0
$511$	13.9386	−	2.63996i	0.616607	−	0.116785i
$512$	16.9781	−	14.9581i	0.750333	−	0.661060i
$513$	−3.51276	+	2.02809i	−0.155092	+	0.0895424i
$514$	1.59754	−	16.8934i	0.0704643	−	0.745138i
$515$		0			0
$516$	3.26553	−	17.1116i	0.143757	−	0.753296i
$517$	−24.0535			−1.05787
$518$	−11.1819	−	15.7796i	−0.491305	−	0.693316i
$519$			32.9679i			1.44713i
$520$		0			0
$521$	13.7812	+	7.95657i	0.603764	+	0.348584i	0.770521	−	0.637415i	$-0.219996\pi$
$521$	13.7812	+	7.95657i	0.603764	+	0.348584i	−0.166757	+	0.985998i	$0.553329\pi$
$522$	−0.0921433	+	0.974386i	−0.00403300	+	0.0426477i
$523$	2.03784	−	1.17655i	0.0891087	−	0.0514470i	−0.454783	−	0.890602i	$-0.650283\pi$
$523$	2.03784	−	1.17655i	0.0891087	−	0.0514470i	0.543892	+	0.839155i	$0.316950\pi$
$524$	−21.7691	+	25.2159i	−0.950986	+	1.10156i
$525$		0			0
$526$	12.4892	−	5.71742i	0.544553	−	0.249291i
$527$	−0.482452	−	0.835631i	−0.0210159	−	0.0364007i
$528$	27.1480	+	10.7534i	1.18147	+	0.467980i
$529$	−3.33811	+	5.78178i	−0.145135	+	0.251382i
$530$		0			0
$531$	0.665805			0.0288935
$532$	−4.19185	−	0.00581937i	−0.181740	−	0.000252302i
$533$		−	26.8028i		−	1.16096i
$534$	−4.71163	−	3.34864i	−0.203892	−	0.144910i
$535$		0			0
$536$	12.7188	+	13.2660i	0.549367	+	0.573003i
$537$	11.2621	+	19.5066i	0.485996	+	0.841770i
$538$	−1.98225	−	4.33003i	−0.0854607	−	0.186681i
$539$	−18.1321	+	22.7539i	−0.781005	+	0.980082i
$540$		0			0
$541$	23.1217	+	40.0480i	0.994081	+	1.72180i	0.591126	+	0.806579i	$0.298683\pi$
$541$	23.1217	+	40.0480i	0.994081	+	1.72180i	0.402955	+	0.915220i	$0.367983\pi$
$542$	−1.32283	+	13.9885i	−0.0568203	+	0.600856i
$543$	7.51090	−	13.0093i	0.322324	−	0.558281i
$544$	0.585138	−	1.14787i	0.0250876	−	0.0492145i
$545$		0			0
$546$	−13.4544	+	29.2824i	−0.575795	+	1.25317i
$547$	0.635487			0.0271715			0.0135857	−	0.999908i	$-0.495675\pi$
$547$	0.635487			0.0271715			0.0135857	+	0.999908i	$0.495675\pi$
$548$	1.65074	−	8.65000i	0.0705163	−	0.369510i
$549$	0.980175	+	0.565904i	0.0418329	+	0.0241522i
$550$		0			0
$551$	3.23662	+	5.60599i	0.137885	+	0.238823i
$552$	25.9864	+	7.55289i	1.10605	+	0.321472i
$553$	−12.7662	−	4.46447i	−0.542873	−	0.189848i
$554$	−0.235925	−	0.515355i	−0.0100235	−	0.0218953i
$555$		0			0
$556$	−8.69600	−	24.9775i	−0.368792	−	1.05928i
$557$	26.4995	+	15.2995i	1.12282	+	0.648260i	0.942119	−	0.335279i	$-0.108830\pi$
$557$	26.4995	+	15.2995i	1.12282	+	0.648260i	0.180700	+	0.983538i	$0.442164\pi$
$558$	−0.413609	−	0.293960i	−0.0175095	−	0.0124443i
$559$	−24.3193			−1.02860
$560$		0			0
$561$	1.66266			0.0701975
$562$	−24.7317	−	17.5773i	−1.04324	−	0.741452i
$563$	−8.81511	−	5.08940i	−0.371512	−	0.214493i	0.302607	−	0.953116i	$-0.402143\pi$
$563$	−8.81511	−	5.08940i	−0.371512	−	0.214493i	−0.674119	+	0.738623i	$0.735477\pi$
$564$	6.68377	+	19.1978i	0.281437	+	0.808372i
$565$		0			0
$566$	−12.0241	−	26.2656i	−0.505412	−	1.10402i
$567$	24.0377	−	4.55272i	1.00949	−	0.191196i
$568$	5.53574	+	1.60895i	0.232274	+	0.0675101i
$569$	−19.6151	−	33.9744i	−0.822308	−	1.42428i	−0.903959	−	0.427618i	$-0.859353\pi$
$569$	−19.6151	−	33.9744i	−0.822308	−	1.42428i	0.0816516	−	0.996661i	$-0.473981\pi$
$570$		0			0
$571$	19.0886	+	11.0208i	0.798833	+	0.461206i	0.843063	−	0.537815i	$-0.180750\pi$
$571$	19.0886	+	11.0208i	0.798833	+	0.461206i	−0.0442302	+	0.999021i	$0.514083\pi$
$572$	7.64142	−	40.0415i	0.319504	−	1.67422i
$573$	−0.865610			−0.0361614
$574$	−20.3629	+	1.89711i	−0.849930	+	0.0791837i
$575$		0			0
$576$	0.0285246	−	0.676955i	0.00118853	−	0.0282064i
$577$	20.6789	−	35.8168i	0.860872	−	1.49107i	−0.0102160	−	0.999948i	$-0.503252\pi$
$577$	20.6789	−	35.8168i	0.860872	−	1.49107i	0.871088	−	0.491127i	$-0.163415\pi$
$578$	−2.25650	+	23.8618i	−0.0938582	+	0.992521i
$579$	−23.6889	−	41.0305i	−0.984479	−	1.70517i
$580$		0			0
$581$	19.0911	−	16.4353i	0.792033	−	0.681851i
$582$	−18.3216	−	40.0218i	−0.759455	−	1.65896i
$583$	−22.5105	−	38.9893i	−0.932289	−	1.61477i
$584$	10.4958	+	10.9473i	0.434317	+	0.453003i
$585$		0			0
$586$	−5.35028	−	3.80254i	−0.221018	−	0.157082i
$587$		−	0.600496i		−	0.0247851i	−0.999923	−	0.0123926i	$-0.996055\pi$
$587$		−	0.600496i		−	0.0247851i	0.999923	−	0.0123926i	$-0.00394478\pi$
$588$	23.1990	+	8.14909i	0.956710	+	0.336063i
$589$	−3.35609			−0.138285
$590$		0			0
$591$	−2.17807	+	3.77252i	−0.0895938	+	0.155181i
$592$	7.61392	−	19.2222i	0.312930	−	0.790027i
$593$	−18.0379	−	31.2425i	−0.740727	−	1.28298i	−0.952165	−	0.305586i	$-0.901148\pi$
$593$	−18.0379	−	31.2425i	−0.740727	−	1.28298i	0.211437	−	0.977392i	$-0.432186\pi$
$594$	−27.3658	+	12.5278i	−1.12283	+	0.514023i
$595$		0			0
$596$	15.0920	−	17.4816i	0.618193	−	0.716076i
$597$	−8.42034	+	4.86149i	−0.344622	+	0.198967i
$598$	3.55670	−	37.6110i	0.145444	−	1.53803i
$599$	4.57779	+	2.64299i	0.187043	+	0.107989i	0.590598	−	0.806966i	$-0.298892\pi$
$599$	4.57779	+	2.64299i	0.187043	+	0.107989i	−0.403554	+	0.914956i	$0.632225\pi$
$600$		0			0
$601$		−	34.2340i		−	1.39643i	−0.715886	−	0.698217i	$-0.753977\pi$
$601$		−	34.2340i		−	1.39643i	0.715886	−	0.698217i	$-0.246023\pi$
$602$	1.72132	+	18.4761i	0.0701558	+	0.753028i
$603$	0.550313			0.0224105
$604$	6.45445	−	33.8217i	0.262628	−	1.37619i
$605$		0			0
$606$	−3.59885	+	38.0567i	−0.146193	+	1.54595i
$607$	−26.3130	+	15.1918i	−1.06801	+	0.616618i	−0.927638	−	0.373481i	$-0.878164\pi$
$607$	−26.3130	+	15.1918i	−1.06801	+	0.616618i	−0.140375	+	0.990098i	$0.544831\pi$
$608$	−2.43998	−	3.75877i	−0.0989542	−	0.152438i
$609$	−7.06601	−	37.3075i	−0.286329	−	1.51178i
$610$		0			0
$611$	24.5764	−	14.1892i	0.994254	−	0.574033i
$612$	−0.0126850	−	0.0364350i	−0.000512759	−	0.00147280i
$613$	−2.20790	−	1.27473i	−0.0891763	−	0.0514859i	0.454749	−	0.890620i	$-0.349729\pi$
$613$	−2.20790	−	1.27473i	−0.0891763	−	0.0514859i	−0.543925	+	0.839134i	$0.683062\pi$
$614$	4.93553	−	6.94442i	0.199182	−	0.280254i
$615$		0			0
$616$	−30.9615	−	2.97127i	−1.24748	−	0.119716i
$617$			30.0546i			1.20995i	0.796243	+	0.604976i	$0.206817\pi$
$617$			30.0546i			1.20995i	−0.796243	+	0.604976i	$0.793183\pi$
$618$	−22.1418	−	15.7366i	−0.890673	−	0.633019i
$619$	5.95465	−	10.3137i	0.239337	−	0.414545i	−0.721187	−	0.692741i	$-0.756403\pi$
$619$	5.95465	−	10.3137i	0.239337	−	0.414545i	0.960524	+	0.278196i	$0.0897365\pi$
$620$		0			0
$621$	−24.1560	+	13.9465i	−0.969347	+	0.559653i
$622$	−29.5941	+	13.5479i	−1.18661	+	0.543220i
$623$	5.81207	+	2.03254i	0.232856	+	0.0814320i
$624$	−34.0816	+	5.02754i	−1.36436	+	0.201263i
$625$		0			0
$626$	−1.13456	+	11.9976i	−0.0453462	+	0.479522i
$627$	2.89150	−	5.00822i	0.115475	−	0.200009i
$628$	41.0279	+	7.82966i	1.63719	+	0.312438i
$629$		−	1.17725i		−	0.0469399i
$630$		0			0
$631$		−	25.8722i		−	1.02996i	−0.857203	−	0.514979i	$-0.827800\pi$
$631$		−	25.8722i		−	1.02996i	0.857203	−	0.514979i	$-0.172200\pi$
$632$	−3.44717	−	14.0411i	−0.137121	−	0.558526i
$633$	19.0790	−	33.0458i	0.758323	−	1.31345i
$634$	−5.91726	−	0.559568i	−0.235004	−	0.0222233i
$635$		0			0
$636$	−24.8635	+	28.8003i	−0.985901	+	1.14201i
$637$	5.10369	−	33.9448i	0.202215	−	1.34494i
$638$	19.9931	+	43.6730i	0.791534	+	1.72903i
$639$	0.149495	−	0.0863108i	0.00591392	−	0.00341440i
$640$		0			0
$641$	−17.7104	+	30.6754i	−0.699520	+	1.21160i	0.269113	+	0.963109i	$0.413270\pi$
$641$	−17.7104	+	30.6754i	−0.699520	+	1.21160i	−0.968633	+	0.248496i	$0.920064\pi$
$642$	−6.79382	+	9.55908i	−0.268131	+	0.377267i
$643$		−	23.1771i		−	0.914017i	−0.889462	−	0.457008i	$-0.848921\pi$
$643$		−	23.1771i		−	0.914017i	0.889462	−	0.457008i	$-0.151079\pi$
$644$	−28.8259	−	0.0400178i	−1.13590	−	0.00157692i
$645$		0			0
$646$	−0.207986	−	0.147820i	−0.00818310	−	0.00581588i
$647$	−28.8793	−	16.6735i	−1.13536	−	0.655501i	−0.190083	−	0.981768i	$-0.560876\pi$
$647$	−28.8793	−	16.6735i	−1.13536	−	0.655501i	−0.945278	+	0.326267i	$0.894209\pi$
$648$	18.1003	+	18.8791i	0.711049	+	0.741641i
$649$	28.2971	−	16.3374i	1.11076	−	0.641298i
$650$		0			0
$651$	18.5826	+	6.49854i	0.728311	+	0.254698i
$652$	−9.43093	+	10.9242i	−0.369344	+	0.427824i
$653$	−9.86500	+	5.69556i	−0.386047	+	0.222884i	−0.680446	−	0.732798i	$-0.738214\pi$
$653$	−9.86500	+	5.69556i	−0.386047	+	0.222884i	0.294399	+	0.955683i	$0.404881\pi$
$654$	−20.1258	−	1.90321i	−0.786982	−	0.0744214i
$655$		0			0
$656$	−13.5777	−	17.1360i	−0.530118	−	0.669048i
$657$	0.454128			0.0177172
$658$	−12.5194	−	17.6671i	−0.488059	−	0.688734i
$659$		−	9.33865i		−	0.363782i	−0.983319	−	0.181891i	$-0.941778\pi$
$659$		−	9.33865i		−	0.363782i	0.983319	−	0.181891i	$-0.0582218\pi$
$660$		0			0
$661$	−8.88871	−	5.13190i	−0.345731	−	0.199608i	0.317072	−	0.948401i	$-0.397300\pi$
$661$	−8.88871	−	5.13190i	−0.345731	−	0.199608i	−0.662803	+	0.748793i	$0.730633\pi$
$662$	15.0773	+	1.42579i	0.585996	+	0.0554150i
$663$	−1.69880	+	0.980805i	−0.0659761	+	0.0380913i
$664$	25.8602	+	7.51624i	1.00357	+	0.291687i
$665$		0			0
$666$	−0.257698	−	0.562916i	−0.00998558	−	0.0218125i
$667$	22.2571	+	38.5505i	0.861799	+	1.49268i
$668$	−27.9167	+	9.71929i	−1.08013	+	0.376051i
$669$	21.6137	−	37.4361i	0.835636	−	1.44736i
$670$		0			0
$671$	55.5441			2.14425
$672$	6.23187	+	25.5369i	0.240400	+	0.985109i
$673$		−	14.1636i		−	0.545967i	−0.962019	−	0.272983i	$-0.911990\pi$
$673$		−	14.1636i		−	0.545967i	0.962019	−	0.272983i	$-0.0880104\pi$
$674$	23.5008	−	33.0662i	0.905216	−	1.27366i
$675$		0			0
$676$	7.26431	+	20.8653i	0.279396	+	0.802510i
$677$	7.78573	+	13.4853i	0.299230	+	0.518281i	0.975960	−	0.217950i	$-0.0699370\pi$
$677$	7.78573	+	13.4853i	0.299230	+	0.518281i	−0.676730	+	0.736231i	$0.736604\pi$
$678$	21.4693	−	9.82845i	0.824524	−	0.377459i
$679$	30.5894	+	35.5325i	1.17392	+	1.36361i
$680$		0			0
$681$	−7.20074	−	12.4720i	−0.275933	−	0.477930i
$682$	−24.7918	−	2.34445i	−0.949326	−	0.0897734i
$683$	0.0471556	−	0.0816759i	0.00180436	−	0.00312524i	−0.865122	−	0.501562i	$-0.832759\pi$
$683$	0.0471556	−	0.0816759i	0.00180436	−	0.00312524i	0.866926	+	0.498437i	$0.166092\pi$
$684$	−0.131809	−	0.0251541i	−0.00503983	−	0.000961789i
$685$		0			0
$686$	−26.1500	−	1.47480i	−0.998413	−	0.0563083i
$687$	−8.53730			−0.325718
$688$	−15.5482	+	12.3196i	−0.592769	+	0.469679i
$689$	45.9997	+	26.5579i	1.75245	+	1.01178i
$690$		0			0
$691$	3.68824	+	6.38822i	0.140307	+	0.243019i	0.927612	−	0.373544i	$-0.121858\pi$
$691$	3.68824	+	6.38822i	0.140307	+	0.243019i	−0.787305	+	0.616564i	$0.788524\pi$
$692$	24.5327	−	28.4171i	0.932594	−	1.08026i
$693$	−0.705843	+	0.607651i	−0.0268127	+	0.0230827i
$694$	30.1080	−	13.7832i	1.14288	−	0.523202i
$695$		0			0
$696$	29.3012	−	28.0925i	1.11066	−	1.06484i
$697$	−1.07810	−	0.622442i	−0.0408360	−	0.0235767i
$698$	−16.1785	+	22.7636i	−0.612365	+	0.861613i
$699$	−37.1614			−1.40557
$700$		0			0
$701$	3.40837			0.128732			0.0643661	−	0.997926i	$-0.479497\pi$
$701$	3.40837			0.128732			0.0643661	+	0.997926i	$0.479497\pi$
$702$	20.5706	−	28.9433i	0.776386	−	1.09239i
$703$	−3.54607	−	2.04733i	−0.133743	−	0.0772163i
$704$	−15.3986	−	29.4709i	−0.580357	−	1.11073i
$705$		0			0
$706$	−27.7242	+	12.6919i	−1.04341	+	0.477665i
$707$	−7.57735	−	40.0073i	−0.284976	−	1.50463i
$708$	−20.9023	−	18.0451i	−0.785556	−	0.678176i
$709$	−13.4643	−	23.3209i	−0.505663	−	0.875834i	−0.999979	−	0.00655175i	$-0.997914\pi$
$709$	−13.4643	−	23.3209i	−0.505663	−	0.875834i	0.494315	−	0.869283i	$-0.335419\pi$
$710$		0			0
$711$	−0.374931	−	0.216466i	−0.0140610	−	0.00811813i
$712$	1.56939	+	6.39252i	0.0588155	+	0.239570i
$713$	−23.0787			−0.864303
$714$	0.865387	+	1.22121i	0.0323863	+	0.0457026i
$715$		0			0
$716$	4.80806	−	25.1945i	0.179686	−	0.941564i
$717$	−2.15996	+	3.74116i	−0.0806651	+	0.139716i
$718$	10.9677	+	1.03717i	0.409311	+	0.0387067i
$719$	0.995916	+	1.72498i	0.0371414	+	0.0643308i	0.883999	−	0.467490i	$-0.154841\pi$
$719$	0.995916	+	1.72498i	0.0371414	+	0.0643308i	−0.846857	+	0.531820i	$0.821508\pi$
$720$		0			0
$721$	27.3132	+	9.55171i	1.01720	+	0.355724i
$722$	23.6247	−	10.8152i	0.879220	−	0.402498i
$723$	1.38820	+	2.40442i	0.0516275	+	0.0894215i
$724$	−16.1548	+	5.62436i	−0.600390	+	0.209028i
$725$		0			0
$726$	9.03033	−	12.7059i	0.335147	−	0.471560i
$727$			26.2307i			0.972843i	0.873724	+	0.486422i	$0.161698\pi$
$727$			26.2307i			0.972843i	−0.873724	+	0.486422i	$0.838302\pi$
$728$	33.3874	−	15.2284i	1.23742	−	0.564402i
$729$	−26.1953			−0.970197
$730$		0			0
$731$	−0.564767	+	0.978205i	−0.0208887	+	0.0361802i
$732$	−15.4341	−	44.3313i	−0.570460	−	1.63853i
$733$	−1.54402	−	2.67432i	−0.0570296	−	0.0987782i	0.836101	−	0.548575i	$-0.184830\pi$
$733$	−1.54402	−	2.67432i	−0.0570296	−	0.0987782i	−0.893131	+	0.449797i	$0.851496\pi$
$734$	3.25741	+	7.11551i	0.120233	+	0.262638i
$735$		0			0
$736$	−16.7789	−	25.8478i	−0.618478	−	0.952762i
$737$	23.3886	−	13.5034i	0.861531	−	0.497405i
$738$	−0.651760	−	0.0616340i	−0.0239916	−	0.00226878i
$739$	−10.1238	−	5.84500i	−0.372411	−	0.215012i	0.302100	−	0.953276i	$-0.402312\pi$
$739$	−10.1238	−	5.84500i	−0.372411	−	0.215012i	−0.674511	+	0.738264i	$0.735646\pi$
$740$		0			0
$741$			6.82279i			0.250642i
$742$	16.9210	−	36.8271i	0.621188	−	1.35196i
$743$	12.3264			0.452214			0.226107	−	0.974103i	$-0.427400\pi$
$743$	12.3264			0.452214			0.226107	+	0.974103i	$0.427400\pi$
$744$	5.01775	+	20.4385i	0.183960	+	0.749311i
$745$		0			0
$746$	−13.3384	−	1.26136i	−0.488355	−	0.0461815i
$747$	0.698366	−	0.403202i	0.0255519	−	0.0147524i
$748$	−1.43315	−	1.23725i	−0.0524012	−	0.0452383i
$749$	4.12367	−	11.7917i	0.150676	−	0.430859i
$750$		0			0
$751$	23.8338	−	13.7605i	0.869709	−	0.502127i	0.00245756	−	0.999997i	$-0.499218\pi$
$751$	23.8338	−	13.7605i	0.869709	−	0.502127i	0.867252	+	0.497870i	$0.165884\pi$
$752$	8.52466	−	21.5214i	0.310862	−	0.784806i
$753$	−40.0085	−	23.0989i	−1.45799	−	0.841772i
$754$	−46.1905	−	32.8285i	−1.68216	−	1.19554i
$755$		0			0
$756$	−23.4450	−	13.5794i	−0.852688	−	0.493879i
$757$			20.5776i			0.747904i	0.927448	+	0.373952i	$0.121998\pi$
$757$			20.5776i			0.747904i	−0.927448	+	0.373952i	$0.878002\pi$
$758$	19.3521	−	27.2290i	0.702902	−	0.989001i
$759$	19.8838	−	34.4398i	0.721737	−	1.25008i
$760$		0			0
$761$	2.16571	−	1.25037i	0.0785069	−	0.0453260i	−0.460233	−	0.887798i	$-0.652234\pi$
$761$	2.16571	−	1.25037i	0.0785069	−	0.0453260i	0.538740	+	0.842472i	$0.318901\pi$
$762$	−12.7375	−	27.8238i	−0.461429	−	1.00795i
$763$	21.1574	−	4.00719i	0.765949	−	0.145070i
$764$	0.746124	+	0.644134i	0.0269938	+	0.0233040i
$765$		0			0
$766$	−23.7492	−	2.24585i	−0.858093	−	0.0811460i
$767$	−19.2749	+	33.3851i	−0.695975	+	1.20546i
$768$	−19.2428	+	20.4792i	−0.694363	+	0.738980i
$769$		−	36.2043i		−	1.30556i	−0.757548	−	0.652779i	$-0.773603\pi$
$769$		−	36.2043i		−	1.30556i	0.757548	−	0.652779i	$-0.226397\pi$
$770$		0			0
$771$			21.0738i			0.758953i
$772$	−10.1134	+	52.9946i	−0.363988	+	1.90732i
$773$	5.61812	−	9.73087i	0.202070	−	0.349995i	−0.747125	−	0.664683i	$-0.768567\pi$
$773$	5.61812	−	9.73087i	0.202070	−	0.349995i	0.949195	+	0.314688i	$0.101900\pi$
$774$	−0.0559231	+	0.591369i	−0.00201011	+	0.0212563i
$775$		0			0
$776$	−13.9892	+	48.1312i	−0.502185	+	1.72781i
$777$	15.6702	+	18.2024i	0.562167	+	0.653009i
$778$	−13.3044	+	6.09063i	−0.476986	+	0.218360i
$779$	−3.74981	+	2.16495i	−0.134351	+	0.0775675i
$780$		0			0
$781$	4.23574	−	7.33653i	0.151567	−	0.262522i
$782$	−1.43025	−	1.01650i	−0.0511455	−	0.0363501i
$783$			41.8393i			1.49522i
$784$	−13.9326	−	24.2875i	−0.497594	−	0.867410i
$785$		0			0
$786$	23.9669	−	33.7221i	0.854873	−	1.20283i
$787$	−33.2271	−	19.1837i	−1.18442	−	0.683825i	−0.227387	−	0.973805i	$-0.573018\pi$
$787$	−33.2271	−	19.1837i	−1.18442	−	0.683825i	−0.957033	+	0.289980i	$0.906351\pi$
$788$	4.68470	−	1.63099i	0.166886	−	0.0581017i
$789$	−14.7731	+	8.52923i	−0.525935	+	0.303649i
$790$		0			0
$791$	−19.0610	+	16.4094i	−0.677733	+	0.583451i
$792$	−0.956112	−	0.277892i	−0.0339740	−	0.00987448i
$793$	−56.7516	+	32.7655i	−2.01531	+	1.16354i
$794$	−0.344191	+	3.63971i	−0.0122149	+	0.129168i
$795$		0			0
$796$	10.8757	+	2.07548i	0.385477	+	0.0735636i
$797$	−35.5238			−1.25832			−0.629159	−	0.777276i	$-0.716601\pi$
$797$	−35.5238			−1.25832			−0.629159	+	0.777276i	$0.716601\pi$
$798$	5.18347	−	0.482918i	0.183493	−	0.0170951i
$799$		−	1.31806i		−	0.0466297i
$800$		0			0
$801$	0.170695	+	0.0985508i	0.00603121	+	0.00348212i
$802$	1.06206	−	11.2309i	0.0375025	−	0.396577i
$803$	19.3007	−	11.1433i	0.681107	−	0.393237i
$804$	−17.2765	−	14.9149i	−0.609295	−	0.526009i
$805$		0			0
$806$	26.7137	−	12.2293i	0.940951	−	0.430758i
$807$	2.95711	+	5.12186i	0.104095	+	0.180298i
$808$	31.4216	−	30.1255i	1.10541	−	1.05981i
$809$	−1.74646	+	3.02495i	−0.0614022	+	0.106352i	−0.895092	−	0.445881i	$-0.852891\pi$
$809$	−1.74646	+	3.02495i	−0.0614022	+	0.106352i	0.833690	+	0.552232i	$0.186224\pi$
$810$		0			0
$811$	−16.6986			−0.586367			−0.293184	−	0.956056i	$-0.594715\pi$
$811$	−16.6986			−0.586367			−0.293184	+	0.956056i	$0.594715\pi$
$812$	−21.6714	+	37.4158i	−0.760516	+	1.31304i
$813$		−	17.4500i		−	0.611997i
$814$	−24.7650	−	17.6010i	−0.868013	−	0.616913i
$815$		0			0
$816$	−0.589253	+	1.48764i	−0.0206280	+	0.0520777i
$817$	1.96435	+	3.40235i	0.0687239	+	0.119033i
$818$	3.82834	+	8.36265i	0.133855	+	0.292393i
$819$	0.362733	−	1.03724i	0.0126749	−	0.0362440i
$820$		0			0
$821$	−14.5330	−	25.1719i	−0.507206	−	0.878506i	−0.999965	−	0.00834036i	$-0.997345\pi$
$821$	−14.5330	−	25.1719i	−0.507206	−	0.878506i	0.492760	−	0.870165i	$-0.335988\pi$
$822$	−1.02961	+	10.8878i	−0.0359119	+	0.379757i
$823$	−1.47377	+	2.55264i	−0.0513724	+	0.0889796i	−0.890568	−	0.454850i	$-0.849693\pi$
$823$	−1.47377	+	2.55264i	−0.0513724	+	0.0889796i	0.839196	+	0.543830i	$0.183026\pi$
$824$	7.37520	+	30.0409i	0.256927	+	1.04653i
$825$		0			0
$826$	26.7279	+	12.2807i	0.929981	+	0.427299i
$827$	−17.2803			−0.600896			−0.300448	−	0.953798i	$-0.597136\pi$
$827$	−17.2803			−0.600896			−0.300448	+	0.953798i	$0.597136\pi$
$828$	−0.906403	−	0.172976i	−0.0314997	−	0.00601132i
$829$	1.71627	+	0.990889i	0.0596085	+	0.0344150i	0.529508	−	0.848305i	$-0.322377\pi$
$829$	1.71627	+	0.990889i	0.0596085	+	0.0344150i	−0.469900	+	0.882720i	$0.655710\pi$
$830$		0			0
$831$	0.351952	+	0.609599i	0.0122091	+	0.0211468i
$832$	33.1183	+	21.0279i	1.14817	+	0.729012i
$833$	−1.24685	−	0.993588i	−0.0432009	−	0.0344258i
$834$	13.6721	+	29.8654i	0.473426	+	1.03415i
$835$		0			0
$836$	−6.21918	+	2.16523i	−0.215095	+	0.0748859i
$837$	−18.7857	−	10.8459i	−0.649328	−	0.374890i
$838$	33.9348	+	24.1181i	1.17226	+	0.833146i
$839$	28.7538			0.992693			0.496346	−	0.868125i	$-0.334675\pi$
$839$	28.7538			0.992693			0.496346	+	0.868125i	$0.334675\pi$
$840$		0			0
$841$	37.7712			1.30245
$842$	−13.0527	−	9.27683i	−0.449827	−	0.319701i
$843$	32.6333	+	18.8408i	1.12395	+	0.648913i
$844$	−41.0361	+	14.2869i	−1.41252	+	0.491774i
$845$		0			0
$846$	−0.288522	−	0.630249i	−0.00991959	−	0.0216684i
$847$	−5.48118	+	15.6735i	−0.188336	+	0.538547i
$848$	42.8628	−	6.32290i	1.47192	−	0.217129i
$849$	17.9376	+	31.0688i	0.615616	+	1.06628i
$850$		0			0
$851$	−24.3851	−	14.0788i	−0.835911	−	0.482613i
$852$	−7.03249	−	1.34206i	−0.240929	−	0.0459783i
$853$	54.2406			1.85716			0.928582	−	0.371127i	$-0.121028\pi$
$853$	54.2406			1.85716			0.928582	+	0.371127i	$0.121028\pi$
$854$	28.9098	+	40.7966i	0.989273	+	1.39603i
$855$		0			0
$856$	12.9693	−	3.18403i	0.443282	−	0.108828i
$857$	2.48284	−	4.30041i	0.0848123	−	0.146899i	−0.820499	−	0.571648i	$-0.806304\pi$
$857$	2.48284	−	4.30041i	0.0848123	−	0.146899i	0.905311	+	0.424749i	$0.139638\pi$
$858$	−4.76616	+	50.4006i	−0.162714	+	1.72065i
$859$	17.3837	+	30.1095i	0.593125	+	1.02732i	0.993809	+	0.111106i	$0.0354392\pi$
$859$	17.3837	+	30.1095i	0.593125	+	1.02732i	−0.400684	+	0.916216i	$0.631228\pi$
$860$		0			0
$861$	24.9548	−	4.72641i	0.850456	−	0.161076i
$862$	−19.4346	−	42.4531i	−0.661946	−	1.44596i
$863$	−16.4912	−	28.5637i	−0.561369	−	0.972319i	−0.997377	−	0.0723765i	$-0.976942\pi$
$863$	−16.4912	−	28.5637i	−0.561369	−	0.972319i	0.436009	−	0.899942i	$-0.356392\pi$
$864$	−1.51048	−	28.9250i	−0.0513877	−	0.984049i
$865$		0			0
$866$	−21.8290	−	15.5143i	−0.741780	−	0.527197i
$867$		−	29.7665i		−	1.01092i
$868$	−11.1817	−	19.4296i	−0.379533	−	0.659483i
$869$	−21.2464			−0.720735
$870$		0			0
$871$	−15.9314	+	27.5940i	−0.539815	+	0.934986i
$872$	15.9315	+	16.6169i	0.539508	+	0.562720i
$873$	0.750440	+	1.29980i	0.0253986	+	0.0439916i
$874$	−5.54920	+	2.54037i	−0.187705	+	0.0859294i
$875$		0			0
$876$	−14.2569	−	12.3081i	−0.481695	−	0.415851i
$877$	27.3489	−	15.7899i	0.923507	−	0.533187i	0.0387545	−	0.999249i	$-0.487661\pi$
$877$	27.3489	−	15.7899i	0.923507	−	0.533187i	0.884752	+	0.466062i	$0.154328\pi$
$878$	−3.23497	+	34.2087i	−0.109175	+	1.15449i
$879$	7.05966	+	4.07590i	0.238116	+	0.137477i
$880$		0			0
$881$		−	31.0031i		−	1.04452i	−0.852786	−	0.522261i	$-0.825089\pi$
$881$		−	31.0031i		−	1.04452i	0.852786	−	0.522261i	$-0.174911\pi$
$882$	−0.813694	−	0.202163i	−0.0273985	−	0.00680718i
$883$	−1.05418			−0.0354759			−0.0177380	−	0.999843i	$-0.505646\pi$
$883$	−1.05418			−0.0354759			−0.0177380	+	0.999843i	$0.505646\pi$
$884$	2.19416	+	0.418729i	0.0737977	+	0.0140834i
$885$		0			0
$886$	−1.99792	+	21.1274i	−0.0671215	+	0.709789i
$887$	17.0213	−	9.82722i	0.571518	−	0.329966i	−0.186238	−	0.982505i	$-0.559629\pi$
$887$	17.0213	−	9.82722i	0.571518	−	0.329966i	0.757755	+	0.652539i	$0.226296\pi$
$888$	−7.16636	+	24.6565i	−0.240487	+	0.827417i
$889$	21.2662	+	24.7027i	0.713247	+	0.828502i
$890$		0			0
$891$	33.2848	−	19.2170i	1.11508	−	0.643794i
$892$	−46.4879	+	16.1849i	−1.55653	+	0.541911i
$893$	−3.97023	−	2.29222i	−0.132859	−	0.0767061i
$894$	−16.6158	+	23.3788i	−0.555714	+	0.781904i
$895$		0			0
$896$	13.6314	−	26.6493i	0.455393	−	0.890290i
$897$			46.9180i			1.56655i
$898$	−12.6761	−	9.00911i	−0.423005	−	0.300638i
$899$	−17.3090	+	29.9800i	−0.577286	+	0.999889i
$900$		0			0
$901$	2.13650	−	1.23351i	0.0711773	−	0.0410942i
$902$	−29.2126	+	13.3732i	−0.972673	+	0.445280i
$903$	−4.28846	−	22.6425i	−0.142711	−	0.753494i
$904$	−25.8195	−	7.50439i	−0.858744	−	0.249592i
$905$		0			0
$906$	−4.02582	+	42.5717i	−0.133749	+	1.41435i
$907$	6.43706	−	11.1493i	0.213739	−	0.370207i	−0.739143	−	0.673549i	$-0.764769\pi$
$907$	6.43706	−	11.1493i	0.213739	−	0.370207i	0.952882	+	0.303342i	$0.0981025\pi$
$908$	−3.07417	+	16.1088i	−0.102020	+	0.534590i
$909$		−	1.30346i		−	0.0432331i
$910$		0			0
$911$		−	15.4628i		−	0.512306i	−0.966636	−	0.256153i	$-0.917545\pi$
$911$		−	15.4628i		−	0.512306i	0.966636	−	0.256153i	$-0.0824551\pi$
$912$	3.45626	+	4.36205i	0.114448	+	0.144442i
$913$	19.7873	−	34.2727i	0.654865	−	1.13426i
$914$	23.3670	+	2.20971i	0.772913	+	0.0730909i
$915$		0			0
$916$	7.35885	+	6.35294i	0.243143	+	0.209907i
$917$	−14.5473	+	41.5982i	−0.480395	+	1.37369i
$918$	−0.686489	−	1.49957i	−0.0226575	−	0.0494932i
$919$	13.7399	−	7.93272i	0.453236	−	0.261676i	−0.255960	−	0.966687i	$-0.582391\pi$
$919$	13.7399	−	7.93272i	0.453236	−	0.261676i	0.709196	+	0.705011i	$0.249058\pi$
$920$		0			0
$921$	−5.29033	+	9.16312i	−0.174322	+	0.301935i
$922$	−5.43071	+	7.64115i	−0.178851	+	0.251648i
$923$			9.99469i			0.328979i
$924$	38.6282	+	0.0536258i	1.27077	+	0.00176416i
$925$		0			0
$926$	2.43163	+	1.72820i	0.0799082	+	0.0567923i
$927$	0.802163	+	0.463129i	0.0263465	+	0.0152112i
$928$	−46.1613	+	2.41058i	−1.51532	+	0.0791310i
$929$	−0.835215	+	0.482212i	−0.0274025	+	0.0158209i	−0.513639	−	0.858007i	$-0.671703\pi$
$929$	−0.835215	+	0.482212i	−0.0274025	+	0.0158209i	0.486236	+	0.873827i	$0.338369\pi$
$930$		0			0
$931$	−5.16124	+	2.02781i	−0.169153	+	0.0664588i
$932$	32.0318	+	27.6533i	1.04924	+	0.905813i
$933$	35.0060	−	20.2107i	1.14604	−	0.661669i
$934$	16.0163	+	1.51459i	0.524071	+	0.0495590i
$935$		0			0
$936$	1.14083	−	0.280079i	0.0372891	−	0.00915465i
$937$	24.0110			0.784404			0.392202	−	0.919879i	$-0.371713\pi$
$937$	24.0110			0.784404			0.392202	+	0.919879i	$0.371713\pi$
$938$	22.0916	+	10.1504i	0.721315	+	0.331423i
$939$		−	14.9665i		−	0.488413i
$940$		0			0
$941$	2.18480	+	1.26140i	0.0712225	+	0.0411203i	0.535188	−	0.844733i	$-0.320241\pi$
$941$	2.18480	+	1.26140i	0.0712225	+	0.0411203i	−0.463966	+	0.885853i	$0.653574\pi$
$942$	−51.6422	−	4.88357i	−1.68259	−	0.159115i
$943$	−25.7861	+	14.8876i	−0.839713	+	0.484808i
$944$	4.58895	+	31.1084i	0.149358	+	1.01249i
$945$		0			0
$946$	12.1341	+	26.5058i	0.394513	+	0.861777i
$947$	9.84254	+	17.0478i	0.319840	+	0.553978i	0.980454	−	0.196747i	$-0.0630377\pi$
$947$	9.84254	+	17.0478i	0.319840	+	0.553978i	−0.660615	+	0.750725i	$0.729704\pi$
$948$	5.90376	+	16.9574i	0.191745	+	0.550750i
$949$	−13.1469	+	22.7710i	−0.426765	+	0.739179i
$950$		0			0
$951$	7.38150			0.239362
$952$	0.162817	−	1.69661i	0.00527693	−	0.0549873i
$953$			26.9765i			0.873856i	0.899496	+	0.436928i	$0.143934\pi$
$953$			26.9765i			0.873856i	−0.899496	+	0.436928i	$0.856066\pi$
$954$	0.751584	−	1.05750i	0.0243334	−	0.0342378i
$955$		0			0
$956$	4.64575	−	1.61743i	0.150254	−	0.0523115i
$957$	−29.8257	−	51.6595i	−0.964126	−	1.66992i
$958$	−12.9057	+	5.90810i	−0.416963	+	0.190882i
$959$	−2.16784	−	11.4459i	−0.0700033	−	0.369607i
$960$		0			0
$961$	6.52607	+	11.3035i	0.210518	+	0.364629i
$962$	35.6862	+	3.37468i	1.15057	+	0.108804i
$963$	0.199943	−	0.346311i	0.00644306	−	0.0111597i
$964$	0.592653	−	3.10554i	0.0190881	−	0.100023i
$965$		0			0
$966$	35.6449	−	3.32086i	1.14686	−	0.106847i
$967$	22.8186			0.733797			0.366898	−	0.930261i	$-0.380420\pi$
$967$	22.8186			0.733797			0.366898	+	0.930261i	$0.380420\pi$
$968$	−17.2388	+	4.23221i	−0.554076	+	0.136028i
$969$	0.274436	+	0.158446i	0.00881616	+	0.00509001i
$970$		0			0
$971$	−12.7360	−	22.0594i	−0.408718	−	0.707921i	0.586028	−	0.810291i	$-0.300691\pi$
$971$	−12.7360	−	22.0594i	−0.408718	−	0.707921i	−0.994746	+	0.102370i	$0.967357\pi$
$972$	−1.33209	−	1.15000i	−0.0427268	−	0.0368863i
$973$	−22.8267	−	26.5153i	−0.731790	−	0.850042i
$974$	33.6830	−	15.4198i	1.07927	−	0.494081i
$975$		0			0
$976$	−19.6851	+	49.6971i	−0.630103	+	1.59077i
$977$	10.5694	+	6.10223i	0.338144	+	0.195228i	0.659451	−	0.751748i	$-0.270789\pi$
$977$	10.5694	+	6.10223i	0.338144	+	0.195228i	−0.321307	+	0.946975i	$0.604122\pi$
$978$	10.3831	−	14.6093i	0.332015	−	0.467154i
$979$	9.67286			0.309146
$980$		0			0
$981$	0.689320			0.0220083
$982$	−21.3397	+	30.0255i	−0.680977	+	0.958152i
$983$	−6.42315	−	3.70841i	−0.204867	−	0.118280i	0.394057	−	0.919086i	$-0.371071\pi$
$983$	−6.42315	−	3.70841i	−0.204867	−	0.118280i	−0.598923	+	0.800806i	$0.704405\pi$
$984$	18.7909	+	19.5994i	0.599032	+	0.624805i
$985$		0			0
$986$	−2.39316	+	1.09556i	−0.0762137	+	0.0348899i
$987$	17.5446	+	20.3797i	0.558452	+	0.648694i
$988$	5.07711	−	5.88100i	0.161524	−	0.187099i
$989$	13.5082	+	23.3968i	0.429535	+	0.743976i
$990$		0			0
$991$	−22.8598	−	13.1981i	−0.726164	−	0.419251i	0.0908531	−	0.995864i	$-0.471041\pi$
$991$	−22.8598	−	13.1981i	−0.726164	−	0.419251i	−0.817017	+	0.576613i	$0.804374\pi$
$992$	10.8840	−	21.3511i	0.345566	−	0.677899i
$993$	−18.8082			−0.596862
$994$	7.59325	−	0.707425i	0.240843	−	0.0224382i
$995$		0			0
$996$	−32.8523	−	6.26946i	−1.04097	−	0.198655i
$997$	4.15834	−	7.20245i	0.131696	−	0.228104i	−0.792635	−	0.609697i	$-0.791291\pi$
$997$	4.15834	−	7.20245i	0.131696	−	0.228104i	0.924330	+	0.381593i	$0.124624\pi$
$998$	−24.4470	−	2.31184i	−0.773856	−	0.0731800i
$999$	−13.2327	−	22.9198i	−0.418665	−	0.725150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.t.e.199.26		64
4.3	odd	2	inner	700.2.t.e.199.15		64
5.2	odd	4		700.2.p.d.451.6	✓	32
5.3	odd	4		700.2.p.f.451.11	yes	32
5.4	even	2	inner	700.2.t.e.199.7		64
7.5	odd	6	inner	700.2.t.e.299.18		64
20.3	even	4		700.2.p.f.451.1	yes	32
20.7	even	4		700.2.p.d.451.16	yes	32
20.19	odd	2	inner	700.2.t.e.199.18		64
28.19	even	6	inner	700.2.t.e.299.7		64
35.12	even	12		700.2.p.d.551.16	yes	32
35.19	odd	6	inner	700.2.t.e.299.15		64
35.33	even	12		700.2.p.f.551.1	yes	32
140.19	even	6	inner	700.2.t.e.299.26		64
140.47	odd	12		700.2.p.d.551.6	yes	32
140.103	odd	12		700.2.p.f.551.11	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.p.d.451.6	✓	32	5.2	odd	4
700.2.p.d.451.16	yes	32	20.7	even	4
700.2.p.d.551.6	yes	32	140.47	odd	12
700.2.p.d.551.16	yes	32	35.12	even	12
700.2.p.f.451.1	yes	32	20.3	even	4
700.2.p.f.451.11	yes	32	5.3	odd	4
700.2.p.f.551.1	yes	32	35.33	even	12
700.2.p.f.551.11	yes	32	140.103	odd	12
700.2.t.e.199.7		64	5.4	even	2	inner
700.2.t.e.199.15		64	4.3	odd	2	inner
700.2.t.e.199.18		64	20.19	odd	2	inner
700.2.t.e.199.26		64	1.1	even	1	trivial
700.2.t.e.299.7		64	28.19	even	6	inner
700.2.t.e.299.15		64	35.19	odd	6	inner
700.2.t.e.299.18		64	7.5	odd	6	inner
700.2.t.e.299.26		64	140.19	even	6	inner

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.15273 + 0.819270i) q^{2} +(-1.52103 - 0.878165i) q^{3} +(0.657592 + 1.88880i) q^{4} +(-1.03388 - 2.25842i) q^{6} +(1.72616 + 2.00509i) q^{7} +(-0.789410 + 2.71603i) q^{8} +(0.0423472 + 0.0733475i) q^{9} +O(q^{10})\)	\(q+(1.15273 + 0.819270i) q^{2} +(-1.52103 - 0.878165i) q^{3} +(0.657592 + 1.88880i) q^{4} +(-1.03388 - 2.25842i) q^{6} +(1.72616 + 2.00509i) q^{7} +(-0.789410 + 2.71603i) q^{8} +(0.0423472 + 0.0733475i) q^{9} +(3.59956 + 2.07821i) q^{11} +(0.658464 - 3.45039i) q^{12} -4.90376 q^{13} +(0.347088 + 3.72552i) q^{14} +(-3.13514 + 2.48412i) q^{16} +(-0.113880 + 0.197246i) q^{17} +(-0.0112764 + 0.119244i) q^{18} +(0.396093 + 0.686053i) q^{19} +(-0.864729 - 4.56564i) q^{21} +(2.44673 + 5.34464i) q^{22} +(2.72379 + 4.71775i) q^{23} +(3.58584 - 3.43792i) q^{24} +(-5.65273 - 4.01750i) q^{26} +5.12024i q^{27} +(-2.65211 + 4.57890i) q^{28} +8.17136 q^{29} +(-2.11825 + 3.66891i) q^{31} +(-5.64916 + 0.295003i) q^{32} +(-3.65002 - 6.32202i) q^{33} +(-0.292871 + 0.134074i) q^{34} +(-0.110692 + 0.128218i) q^{36} +(-4.47631 + 2.58440i) q^{37} +(-0.105473 + 1.11534i) q^{38} +(7.45874 + 4.30631i) q^{39} +5.46577i q^{41} +(2.74369 - 5.97142i) q^{42} +4.95932 q^{43} +(-1.55828 + 8.16548i) q^{44} +(-0.725302 + 7.66984i) q^{46} +(-5.01175 + 2.89353i) q^{47} +(6.95011 - 1.02524i) q^{48} +(-1.04077 + 6.92220i) q^{49} +(0.346429 - 0.200011i) q^{51} +(-3.22467 - 9.26222i) q^{52} +(-9.38050 - 5.41584i) q^{53} +(-4.19486 + 5.90227i) q^{54} +(-6.80853 + 3.10546i) q^{56} -1.39134i q^{57} +(9.41941 + 6.69456i) q^{58} +(3.93063 - 6.80806i) q^{59} +(11.5731 - 6.68172i) q^{61} +(-5.44760 + 2.49386i) q^{62} +(-0.0739705 + 0.211519i) q^{63} +(-6.75366 - 4.28813i) q^{64} +(0.971941 - 10.2780i) q^{66} +(3.24881 - 5.62711i) q^{67} +(-0.447445 - 0.0853894i) q^{68} -9.56776i q^{69} -2.03817i q^{71} +(-0.232644 + 0.0571151i) q^{72} +(2.68098 - 4.64359i) q^{73} +(-7.27732 - 0.688183i) q^{74} +(-1.03535 + 1.19928i) q^{76} +(2.04641 + 10.8048i) q^{77} +(5.06992 + 11.0748i) q^{78} +(-4.42687 + 2.55585i) q^{79} +(4.62346 - 8.00806i) q^{81} +(-4.47794 + 6.30058i) q^{82} -9.52133i q^{83} +(8.05496 - 4.63563i) q^{84} +(5.71677 + 4.06302i) q^{86} +(-12.4289 - 7.17580i) q^{87} +(-8.48602 + 8.13597i) q^{88} +(2.01542 - 1.16361i) q^{89} +(-8.46465 - 9.83247i) q^{91} +(-7.11975 + 8.24706i) q^{92} +(6.44381 - 3.72034i) q^{93} +(-8.14780 - 0.770500i) q^{94} +(8.85158 + 4.51218i) q^{96} +17.7211 q^{97} +(-6.87088 + 7.12678i) q^{98} +0.352025i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 2 q^{4} + 32 q^{9}+O(q^{10}) \) 64 * q - 2 * q^4 + 32 * q^9	\( 64 q - 2 q^{4} + 32 q^{9} + 26 q^{14} + 2 q^{16} + 24 q^{21} + 36 q^{24} - 30 q^{26} - 16 q^{29} - 60 q^{36} - 24 q^{44} + 4 q^{46} - 40 q^{49} - 114 q^{54} - 62 q^{56} - 24 q^{61} - 80 q^{64} - 132 q^{66} + 2 q^{74} - 72 q^{81} - 134 q^{84} + 8 q^{86} + 120 q^{89} - 90 q^{94} + 186 q^{96}+O(q^{100}) \) 64 * q - 2 * q^4 + 32 * q^9 + 26 * q^14 + 2 * q^16 + 24 * q^21 + 36 * q^24 - 30 * q^26 - 16 * q^29 - 60 * q^36 - 24 * q^44 + 4 * q^46 - 40 * q^49 - 114 * q^54 - 62 * q^56 - 24 * q^61 - 80 * q^64 - 132 * q^66 + 2 * q^74 - 72 * q^81 - 134 * q^84 + 8 * q^86 + 120 * q^89 - 90 * q^94 + 186 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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