LMFDB - Embedded newform 700.2.t.d.199.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(199,700)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [32,0,0,2,0,0,0,0,16,0,0,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.10
Character	$\chi$	$=$	700.199
Dual form			700.2.t.d.299.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.620297 + 1.27092i) q^{2} +(-0.573616 - 0.331177i) q^{3} +(-1.23046 + 1.57669i) q^{4} +(0.0650866 - 0.934447i) q^{6} +(2.03775 - 1.68748i) q^{7} +(-2.76710 - 0.585797i) q^{8} +(-1.28064 - 2.21814i) q^{9} +(-3.12892 - 1.80648i) q^{11} +(1.22798 - 0.496915i) q^{12} -5.83027 q^{13} +(3.40866 + 1.54307i) q^{14} +(-0.971925 - 3.88012i) q^{16} +(-0.684063 + 1.18483i) q^{17} +(2.02469 - 3.00350i) q^{18} +(-2.04788 - 3.54704i) q^{19} +(-1.72774 + 0.293111i) q^{21} +(0.355029 - 5.09715i) q^{22} +(1.62259 + 2.81042i) q^{23} +(1.39325 + 1.25242i) q^{24} +(-3.61650 - 7.40979i) q^{26} +3.68354i q^{27} +(0.153273 + 5.28928i) q^{28} -5.19327 q^{29} +(4.43405 - 7.67999i) q^{31} +(4.32843 - 3.64207i) q^{32} +(1.19653 + 2.07245i) q^{33} +(-1.93014 - 0.134439i) q^{34} +(5.07311 + 0.710155i) q^{36} +(-9.34942 + 5.39789i) q^{37} +(3.23770 - 4.80291i) q^{38} +(3.34434 + 1.93085i) q^{39} -0.832730i q^{41} +(-1.44423 - 2.01400i) q^{42} +3.10642 q^{43} +(6.69828 - 2.71054i) q^{44} +(-2.56532 + 3.80548i) q^{46} +(5.97212 - 3.44801i) q^{47} +(-0.727497 + 2.54758i) q^{48} +(1.30481 - 6.87732i) q^{49} +(0.784778 - 0.453092i) q^{51} +(7.17393 - 9.19255i) q^{52} +(6.42376 + 3.70876i) q^{53} +(-4.68148 + 2.28489i) q^{54} +(-6.62717 + 3.47572i) q^{56} +2.71285i q^{57} +(-3.22137 - 6.60021i) q^{58} +(3.73928 - 6.47663i) q^{59} +(1.28652 - 0.742772i) q^{61} +(12.5111 + 0.871427i) q^{62} +(-6.35269 - 2.35894i) q^{63} +(7.31368 + 3.24192i) q^{64} +(-1.89171 + 2.80623i) q^{66} +(-1.26880 + 2.19763i) q^{67} +(-1.02640 - 2.53645i) q^{68} -2.14947i q^{69} +3.52502i q^{71} +(2.24429 + 6.88801i) q^{72} +(2.58492 - 4.47721i) q^{73} +(-12.6597 - 8.53405i) q^{74} +(8.11244 + 1.13561i) q^{76} +(-9.42434 + 1.59884i) q^{77} +(-0.379472 + 5.44808i) q^{78} +(-9.82082 + 5.67005i) q^{79} +(-2.62202 + 4.54148i) q^{81} +(1.05833 - 0.516540i) q^{82} -6.49145i q^{83} +(1.66377 - 3.08478i) q^{84} +(1.92690 + 3.94800i) q^{86} +(2.97894 + 1.71989i) q^{87} +(7.59979 + 6.83162i) q^{88} +(-8.13303 + 4.69560i) q^{89} +(-11.8806 + 9.83847i) q^{91} +(-6.42771 - 0.899777i) q^{92} +(-5.08688 + 2.93691i) q^{93} +(8.08662 + 5.45128i) q^{94} +(-3.68903 + 0.655668i) q^{96} -0.343189 q^{97} +(9.54987 - 2.60767i) q^{98} +9.25383i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{4} + 16 q^{9} + 14 q^{12} + 8 q^{13} - 2 q^{14} - 14 q^{16} - 54 q^{18} - 12 q^{21} - 36 q^{24} + 30 q^{26} - 32 q^{28} + 40 q^{29} - 60 q^{32} + 24 q^{33} + 60 q^{36} + 60 q^{37} + 46 q^{38}+ \cdots + 124 q^{98}+O(q^{100}) $ 32 * q + 2 * q^4 + 16 * q^9 + 14 * q^12 + 8 * q^13 - 2 * q^14 - 14 * q^16 - 54 * q^18 - 12 * q^21 - 36 * q^24 + 30 * q^26 - 32 * q^28 + 40 * q^29 - 60 * q^32 + 24 * q^33 + 60 * q^36 + 60 * q^37 + 46 * q^38 - 78 * q^42 + 18 * q^44 + 2 * q^46 + 28 * q^48 + 16 * q^49 + 46 * q^52 + 12 * q^53 - 12 * q^54 - 4 * q^56 - 42 * q^58 + 24 * q^61 - 8 * q^62 - 4 * q^64 + 24 * q^66 + 4 * q^68 - 90 * q^72 + 24 * q^73 - 38 * q^74 - 20 * q^77 - 36 * q^81 - 8 * q^82 + 20 * q^84 + 28 * q^86 + 78 * q^88 + 60 * q^89 - 72 * q^93 - 18 * q^94 - 60 * q^96 + 48 * q^97 + 124 * q^98

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 $

$2$	0.620297	+	1.27092i	0.438616	+	0.898674i
$2$	0.620297	+	1.27092i	0.438616	+	0.898674i
$3$	−0.573616	−	0.331177i	−0.331177	−	0.191205i	0.325186	−	0.945650i	$-0.394573\pi$
$3$	−0.573616	−	0.331177i	−0.331177	−	0.191205i	−0.656364	+	0.754445i	$0.727906\pi$
$4$	−1.23046	+	1.57669i	−0.615231	+	0.788347i
$5$		0			0
$5$		0			0
$6$	0.0650866	−	0.934447i	0.0265715	−	0.381486i
$7$	2.03775	−	1.68748i	0.770195	−	0.637808i
$7$	2.03775	−	1.68748i	0.770195	−	0.637808i
$8$	−2.76710	−	0.585797i	−0.978318	−	0.207111i
$9$	−1.28064	−	2.21814i	−0.426881	−	0.739380i
$10$		0			0
$11$	−3.12892	−	1.80648i	−0.943404	−	0.544674i	−0.0523781	−	0.998627i	$-0.516680\pi$
$11$	−3.12892	−	1.80648i	−0.943404	−	0.544674i	−0.891026	+	0.453953i	$0.850013\pi$
$12$	1.22798	−	0.496915i	0.354487	−	0.143447i
$13$	−5.83027			−1.61703			−0.808513	−	0.588478i	$-0.799727\pi$
$13$	−5.83027			−1.61703			−0.808513	+	0.588478i	$0.799727\pi$
$14$	3.40866	+	1.54307i	0.911002	+	0.412402i
$15$		0			0
$16$	−0.971925	−	3.88012i	−0.242981	−	0.970031i
$17$	−0.684063	+	1.18483i	−0.165910	+	0.287364i	−0.936978	−	0.349389i	$-0.886389\pi$
$17$	−0.684063	+	1.18483i	−0.165910	+	0.287364i	0.771068	+	0.636752i	$0.219723\pi$
$18$	2.02469	−	3.00350i	0.477224	−	0.707931i
$19$	−2.04788	−	3.54704i	−0.469817	−	0.813747i	0.529588	−	0.848255i	$-0.322347\pi$
$19$	−2.04788	−	3.54704i	−0.469817	−	0.813747i	−0.999404	+	0.0345086i	$0.989013\pi$
$20$		0			0
$21$	−1.72774	+	0.293111i	−0.377024	+	0.0639622i
$22$	0.355029	−	5.09715i	0.0756925	−	1.08672i
$23$	1.62259	+	2.81042i	0.338334	+	0.586012i	0.984120	−	0.177507i	$-0.0568032\pi$
$23$	1.62259	+	2.81042i	0.338334	+	0.586012i	−0.645785	+	0.763519i	$0.723470\pi$
$24$	1.39325	+	1.25242i	0.284396	+	0.255650i
$25$		0			0
$26$	−3.61650	−	7.40979i	−0.709254	−	1.45318i
$27$			3.68354i			0.708898i
$28$	0.153273	+	5.28928i	0.0289658	+	0.999580i
$29$	−5.19327			−0.964365			−0.482183	−	0.876071i	$-0.660156\pi$
$29$	−5.19327			−0.964365			−0.482183	+	0.876071i	$0.660156\pi$
$30$		0			0
$31$	4.43405	−	7.67999i	0.796378	−	1.37937i	−0.125582	−	0.992083i	$-0.540080\pi$
$31$	4.43405	−	7.67999i	0.796378	−	1.37937i	0.921960	−	0.387284i	$-0.126587\pi$
$32$	4.32843	−	3.64207i	0.765166	−	0.643833i
$33$	1.19653	+	2.07245i	0.208289	+	0.360768i
$34$	−1.93014	−	0.134439i	−0.331017	−	0.0230562i
$35$		0			0
$36$	5.07311	+	0.710155i	0.845518	+	0.118359i
$37$	−9.34942	+	5.39789i	−1.53704	+	0.887408i	−0.538026	+	0.842928i	$0.680830\pi$
$37$	−9.34942	+	5.39789i	−1.53704	+	0.887408i	−0.999010	+	0.0444796i	$0.985837\pi$
$38$	3.23770	−	4.80291i	0.525224	−	0.779135i
$39$	3.34434	+	1.93085i	0.535522	+	0.309184i
$40$		0			0
$41$		−	0.832730i		−	0.130051i	−0.997884	−	0.0650253i	$-0.979287\pi$
$41$		−	0.832730i		−	0.130051i	0.997884	−	0.0650253i	$-0.0207128\pi$
$42$	−1.44423	−	2.01400i	−0.222850	−	0.310767i
$43$	3.10642			0.473725			0.236862	−	0.971543i	$-0.423881\pi$
$43$	3.10642			0.473725			0.236862	+	0.971543i	$0.423881\pi$
$44$	6.69828	−	2.71054i	1.00980	−	0.408629i
$45$		0			0
$46$	−2.56532	+	3.80548i	−0.378235	+	0.561087i
$47$	5.97212	−	3.44801i	0.871124	−	0.502943i	0.00340208	−	0.999994i	$-0.498917\pi$
$47$	5.97212	−	3.44801i	0.871124	−	0.502943i	0.867721	+	0.497051i	$0.165584\pi$
$48$	−0.727497	+	2.54758i	−0.105005	+	0.367712i
$49$	1.30481	−	6.87732i	0.186402	−	0.982474i
$50$		0			0
$51$	0.784778	−	0.453092i	0.109891	−	0.0634456i
$52$	7.17393	−	9.19255i	0.994845	−	1.27478i
$53$	6.42376	+	3.70876i	0.882371	+	0.509437i	0.871440	−	0.490503i	$-0.163187\pi$
$53$	6.42376	+	3.70876i	0.882371	+	0.509437i	0.0109318	+	0.999940i	$0.496520\pi$
$54$	−4.68148	+	2.28489i	−0.637069	+	0.310934i
$55$		0			0
$56$	−6.62717	+	3.47572i	−0.885592	+	0.464463i
$57$			2.71285i			0.359326i
$58$	−3.22137	−	6.60021i	−0.422986	−	0.866650i
$59$	3.73928	−	6.47663i	0.486813	−	0.843185i	−0.513072	−	0.858346i	$-0.671493\pi$
$59$	3.73928	−	6.47663i	0.486813	−	0.843185i	0.999885	+	0.0151606i	$0.00482595\pi$
$60$		0			0
$61$	1.28652	−	0.742772i	0.164722	−	0.0951022i	−0.415373	−	0.909651i	$-0.636349\pi$
$61$	1.28652	−	0.742772i	0.164722	−	0.0951022i	0.580095	+	0.814549i	$0.303016\pi$
$62$	12.5111	+	0.871427i	1.58891	+	0.110671i
$63$	−6.35269	−	2.35894i	−0.800364	−	0.297199i
$64$	7.31368	+	3.24192i	0.914210	+	0.405240i
$65$		0			0
$66$	−1.89171	+	2.80623i	−0.232854	+	0.345423i
$67$	−1.26880	+	2.19763i	−0.155009	+	0.268484i	−0.933062	−	0.359715i	$-0.882874\pi$
$67$	−1.26880	+	2.19763i	−0.155009	+	0.268484i	0.778053	+	0.628198i	$0.216207\pi$
$68$	−1.02640	−	2.53645i	−0.124470	−	0.307589i
$69$		−	2.14947i		−	0.258765i
$70$		0			0
$71$			3.52502i			0.418342i	0.977879	+	0.209171i	$0.0670766\pi$
$71$			3.52502i			0.418342i	−0.977879	+	0.209171i	$0.932923\pi$
$72$	2.24429	+	6.88801i	0.264492	+	0.811760i
$73$	2.58492	−	4.47721i	0.302542	−	0.524018i	−0.674169	−	0.738577i	$-0.735498\pi$
$73$	2.58492	−	4.47721i	0.302542	−	0.524018i	0.976711	+	0.214559i	$0.0688314\pi$
$74$	−12.6597	−	8.53405i	−1.47166	−	0.992063i
$75$		0			0
$76$	8.11244	+	1.13561i	0.930561	+	0.130264i
$77$	−9.42434	+	1.59884i	−1.07400	+	0.182205i
$78$	−0.379472	+	5.44808i	−0.0429668	+	0.616873i
$79$	−9.82082	+	5.67005i	−1.10493	+	0.637931i	−0.937511	−	0.347955i	$-0.886876\pi$
$79$	−9.82082	+	5.67005i	−1.10493	+	0.637931i	−0.167417	+	0.985886i	$0.553543\pi$
$80$		0			0
$81$	−2.62202	+	4.54148i	−0.291336	+	0.504609i
$82$	1.05833	−	0.516540i	0.116873	−	0.0570423i
$83$		−	6.49145i		−	0.712529i	−0.934385	−	0.356264i	$-0.884050\pi$
$83$		−	6.49145i		−	0.712529i	0.934385	−	0.356264i	$-0.115950\pi$
$84$	1.66377	−	3.08478i	0.181532	−	0.336577i
$85$		0			0
$86$	1.92690	+	3.94800i	0.207783	+	0.425724i
$87$	2.97894	+	1.71989i	0.319376	+	0.184392i
$88$	7.59979	+	6.83162i	0.810141	+	0.728253i
$89$	−8.13303	+	4.69560i	−0.862099	+	0.497733i	−0.864715	−	0.502264i	$-0.832501\pi$
$89$	−8.13303	+	4.69560i	−0.862099	+	0.497733i	0.00261566	+	0.999997i	$0.499167\pi$
$90$		0			0
$91$	−11.8806	+	9.83847i	−1.24543	+	1.03135i
$92$	−6.42771	−	0.899777i	−0.670135	−	0.0938083i
$93$	−5.08688	+	2.93691i	−0.527485	+	0.304544i
$94$	8.08662	+	5.45128i	0.834071	+	0.562257i
$95$		0			0
$96$	−3.68903	+	0.655668i	−0.376510	+	0.0669189i
$97$	−0.343189			−0.0348455			−0.0174228	−	0.999848i	$-0.505546\pi$
$97$	−0.343189			−0.0348455			−0.0174228	+	0.999848i	$0.505546\pi$
$98$	9.54987	−	2.60767i	0.964683	−	0.263415i
$99$			9.25383i			0.930045i
$100$		0			0
$101$	3.92859	+	2.26817i	0.390910	+	0.225692i	0.682554	−	0.730835i	$-0.260869\pi$
$101$	3.92859	+	2.26817i	0.390910	+	0.225692i	−0.291645	+	0.956527i	$0.594202\pi$
$102$	1.06264	+	0.716337i	0.105217	+	0.0709279i
$103$	−5.31577	+	3.06906i	−0.523778	+	0.302404i	−0.738479	−	0.674276i	$-0.764456\pi$
$103$	−5.31577	+	3.06906i	−0.523778	+	0.302404i	0.214701	+	0.976680i	$0.431122\pi$
$104$	16.1329	+	3.41536i	1.58196	+	0.334903i
$105$		0			0
$106$	−0.728886	+	10.4646i	−0.0707957	+	1.01641i
$107$	−3.83398	−	6.64066i	−0.370645	−	0.641976i	0.619020	−	0.785375i	$-0.287530\pi$
$107$	−3.83398	−	6.64066i	−0.370645	−	0.641976i	−0.989665	+	0.143399i	$0.954197\pi$
$108$	−5.80782	−	4.53246i	−0.558858	−	0.436136i
$109$	0.647616	−	1.12170i	0.0620304	−	0.107440i	−0.833342	−	0.552757i	$-0.813576\pi$
$109$	0.647616	−	1.12170i	0.0620304	−	0.107440i	0.895373	+	0.445317i	$0.146909\pi$
$110$		0			0
$111$	7.15064			0.678709
$112$	−8.52817	−	6.26660i	−0.805837	−	0.592138i
$113$			7.10591i			0.668468i	0.942490	+	0.334234i	$0.108478\pi$
$113$			7.10591i			0.668468i	−0.942490	+	0.334234i	$0.891522\pi$
$114$	−3.44781	+	1.68277i	−0.322917	+	0.157606i
$115$		0			0
$116$	6.39012	−	8.18819i	0.593308	−	0.760254i
$117$	7.46649	+	12.9323i	0.690278	+	1.19560i
$118$	10.5507	+	0.734884i	0.971273	+	0.0676516i
$119$	0.605436	+	3.56873i	0.0555002	+	0.327145i
$120$		0			0
$121$	1.02675	+	1.77837i	0.0933405	+	0.161670i
$122$	1.74203	+	1.17432i	0.157716	+	0.106318i
$123$	−0.275781	+	0.477667i	−0.0248664	+	0.0430698i
$124$	6.65307	+	16.4411i	0.597463	+	1.47645i
$125$		0			0
$126$	−0.942541	−	9.53699i	−0.0839682	−	0.849623i
$127$	−17.0178			−1.51008			−0.755041	−	0.655677i	$-0.772383\pi$
$127$	−17.0178			−1.51008			−0.755041	+	0.655677i	$0.772383\pi$
$128$	0.416448	+	11.3060i	0.0368091	+	0.999322i
$129$	−1.78189	−	1.02878i	−0.156887	−	0.0905787i
$130$		0			0
$131$	0.603066	+	1.04454i	0.0526901	+	0.0912619i	0.891167	−	0.453674i	$-0.149887\pi$
$131$	0.603066	+	1.04454i	0.0526901	+	0.0912619i	−0.838477	+	0.544936i	$0.816554\pi$
$132$	−4.73991	−	0.663512i	−0.412556	−	0.0577513i
$133$	−10.1586	−	3.77220i	−0.880865	−	0.327091i
$134$	−3.58005	−	0.249359i	−0.309269	−	0.0215414i
$135$		0			0
$136$	2.58694	−	2.87782i	0.221828	−	0.246771i
$137$	1.85754	+	1.07245i	0.158701	+	0.0916258i	0.577247	−	0.816570i	$-0.304127\pi$
$137$	1.85754	+	1.07245i	0.158701	+	0.0916258i	−0.418547	+	0.908195i	$0.637460\pi$
$138$	2.73179	−	1.33331i	0.232546	−	0.113499i
$139$	−3.39555			−0.288007			−0.144004	−	0.989577i	$-0.545998\pi$
$139$	−3.39555			−0.288007			−0.144004	+	0.989577i	$0.545998\pi$
$140$		0			0
$141$	−4.56761			−0.384662
$142$	−4.48000	+	2.18656i	−0.375954	+	0.183492i
$143$	18.2424	+	10.5323i	1.52551	+	0.880753i
$144$	−7.36197	+	7.12492i	−0.613497	+	0.593743i
$145$		0			0
$146$	7.29359	+	0.508017i	0.603622	+	0.0420438i
$147$	−3.02607	+	3.51281i	−0.249586	+	0.289732i
$148$	2.99329	−	21.3831i	0.246047	−	1.75768i
$149$	−9.54319	−	16.5293i	−0.781808	−	1.35413i	−0.930887	−	0.365307i	$-0.880964\pi$
$149$	−9.54319	−	16.5293i	−0.781808	−	1.35413i	0.149079	−	0.988825i	$-0.452369\pi$
$150$		0			0
$151$	8.31900	+	4.80298i	0.676990	+	0.390861i	0.798720	−	0.601703i	$-0.205511\pi$
$151$	8.31900	+	4.80298i	0.676990	+	0.390861i	−0.121730	+	0.992563i	$0.538844\pi$
$152$	3.58885	+	11.0147i	0.291095	+	0.893407i
$153$	3.50416			0.283295
$154$	−7.87789	−	10.9858i	−0.634818	−	0.885261i
$155$		0			0
$156$	−7.15944	+	2.89715i	−0.573214	+	0.231958i
$157$	8.23118	−	14.2568i	0.656919	−	1.13782i	−0.324490	−	0.945889i	$-0.605193\pi$
$157$	8.23118	−	14.2568i	0.656919	−	1.13782i	0.981409	−	0.191928i	$-0.0614742\pi$
$158$	−13.2980	−	8.96433i	−1.05793	−	0.713164i
$159$	−2.45651	−	4.25481i	−0.194814	−	0.337428i
$160$		0			0
$161$	8.04896	+	2.98881i	0.634347	+	0.235552i
$162$	−7.39828	−	0.515309i	−0.581264	−	0.0404865i
$163$	−3.57806	−	6.19738i	−0.280255	−	0.485416i	0.691192	−	0.722671i	$-0.257086\pi$
$163$	−3.57806	−	6.19738i	−0.280255	−	0.485416i	−0.971447	+	0.237255i	$0.923752\pi$
$164$	1.31296	+	1.02464i	0.102525	+	0.0800112i
$165$		0			0
$166$	8.25009	−	4.02663i	0.640331	−	0.312527i
$167$			13.7127i			1.06112i	0.847646	+	0.530562i	$0.178019\pi$
$167$			13.7127i			1.06112i	−0.847646	+	0.530562i	$0.821981\pi$
$168$	4.95253	+	0.201036i	0.382096	+	0.0155103i
$169$	20.9920			1.61477
$170$		0			0
$171$	−5.24522	+	9.08498i	−0.401112	+	0.694746i
$172$	−3.82233	+	4.89787i	−0.291450	+	0.373459i
$173$	1.96219	+	3.39862i	0.149183	+	0.258392i	0.930926	−	0.365209i	$-0.119002\pi$
$173$	1.96219	+	3.39862i	0.149183	+	0.258392i	−0.781743	+	0.623601i	$0.785669\pi$
$174$	−0.338012	+	4.85283i	−0.0256246	+	0.367892i
$175$		0			0
$176$	−3.96830	+	13.8963i	−0.299122	+	1.04748i
$177$	−4.28982	+	2.47673i	−0.322443	+	0.186162i
$178$	−11.0126	−	7.42373i	−0.825431	−	0.556432i
$179$	17.8002	+	10.2769i	1.33045	+	0.768134i	0.985368	−	0.170440i	$-0.0545188\pi$
$179$	17.8002	+	10.2769i	1.33045	+	0.768134i	0.345079	+	0.938574i	$0.387852\pi$
$180$		0			0
$181$		−	13.0603i		−	0.970762i	−0.874303	−	0.485381i	$-0.838681\pi$
$181$		−	13.0603i		−	0.970762i	0.874303	−	0.485381i	$-0.161319\pi$
$182$	−19.8734	−	8.99649i	−1.47311	−	0.666864i
$183$	−0.983957			−0.0727362
$184$	−2.84355	−	8.72722i	−0.209629	−	0.643379i
$185$		0			0
$186$	−6.88795	−	4.64325i	−0.505049	−	0.340459i
$187$	4.28075	−	2.47149i	0.313039	−	0.180733i
$188$	−1.91202	+	13.6588i	−0.139449	+	0.996174i
$189$	6.21591	+	7.50612i	0.452141	+	0.545990i
$190$		0			0
$191$	10.8038	−	6.23755i	0.781733	−	0.451334i	−0.0553113	−	0.998469i	$-0.517615\pi$
$191$	10.8038	−	6.23755i	0.781733	−	0.451334i	0.837044	+	0.547136i	$0.184282\pi$
$192$	−3.12160	−	4.28174i	−0.225282	−	0.309008i
$193$	−16.5103	−	9.53225i	−1.18844	−	0.686147i	−0.230489	−	0.973075i	$-0.574033\pi$
$193$	−16.5103	−	9.53225i	−1.18844	−	0.686147i	−0.957952	+	0.286928i	$0.907366\pi$
$194$	−0.212879	−	0.436165i	−0.0152838	−	0.0313148i
$195$		0			0
$196$	9.23790	+	10.5196i	0.659850	+	0.751397i
$197$		−	1.93188i		−	0.137641i	−0.997629	−	0.0688203i	$-0.978076\pi$
$197$		−	1.93188i		−	0.137641i	0.997629	−	0.0688203i	$-0.0219235\pi$
$198$	−11.7609	+	5.74013i	−0.835807	+	0.407933i
$199$	10.2823	−	17.8094i	0.728892	−	1.26248i	−0.228460	−	0.973553i	$-0.573369\pi$
$199$	10.2823	−	17.8094i	0.728892	−	1.26248i	0.957352	−	0.288924i	$-0.0932976\pi$
$200$		0			0
$201$	1.45561	−	0.840398i	0.102671	−	0.0592771i
$202$	−0.445766	+	6.39986i	−0.0313640	+	0.450293i
$203$	−10.5826	+	8.76354i	−0.742750	+	0.615080i
$204$	−0.251253	+	1.79487i	−0.0175912	+	0.125666i
$205$		0			0
$206$	−7.19788	−	4.85217i	−0.501500	−	0.338067i
$207$	4.15593	−	7.19828i	0.288857	−	0.500315i
$208$	5.66658	+	22.6222i	0.392907	+	1.56857i
$209$			14.7979i			1.02359i
$210$		0			0
$211$			9.98398i			0.687326i	0.939093	+	0.343663i	$0.111668\pi$
$211$			9.98398i			0.687326i	−0.939093	+	0.343663i	$0.888332\pi$
$212$	−13.7518	+	5.56481i	−0.944476	+	0.382193i
$213$	1.16741	−	2.02200i	0.0799893	−	0.138545i
$214$	6.06151	−	8.99186i	0.414357	−	0.614671i
$215$		0			0
$216$	2.15781	−	10.1927i	0.146820	−	0.693528i
$217$	−3.92439	−	23.1322i	−0.266405	−	1.57032i
$218$	1.82731	+	0.127277i	0.123761	+	0.00862026i
$219$	−2.96550	+	1.71213i	−0.200390	+	0.115695i
$220$		0			0
$221$	3.98827	−	6.90789i	0.268280	−	0.464675i
$222$	4.43552	+	9.08787i	0.297693	+	0.609938i
$223$		−	16.8179i		−	1.12621i	−0.826384	−	0.563106i	$-0.809606\pi$
$223$		−	16.8179i		−	1.12621i	0.826384	−	0.563106i	$-0.190394\pi$
$224$	2.67433	−	14.7258i	0.178686	−	0.983906i
$225$		0			0
$226$	−9.03103	+	4.40778i	−0.600735	+	0.293201i
$227$	−17.1766	−	9.91692i	−1.14005	−	0.658209i	−0.193608	−	0.981079i	$-0.562019\pi$
$227$	−17.1766	−	9.91692i	−1.14005	−	0.658209i	−0.946443	+	0.322870i	$0.895352\pi$
$228$	−4.27733	−	3.33806i	−0.283273	−	0.221069i
$229$	−12.0664	+	6.96655i	−0.797371	+	0.460363i	−0.842551	−	0.538616i	$-0.818947\pi$
$229$	−12.0664	+	6.96655i	−0.797371	+	0.460363i	0.0451798	+	0.998979i	$0.485614\pi$
$230$		0			0
$231$	5.93545	+	2.20401i	0.390524	+	0.145013i
$232$	14.3703	+	3.04220i	0.943455	+	0.199730i
$233$	8.85568	−	5.11283i	0.580155	−	0.334953i	−0.181040	−	0.983476i	$-0.557946\pi$
$233$	8.85568	−	5.11283i	0.580155	−	0.334953i	0.761195	+	0.648523i	$0.224613\pi$
$234$	−11.8045	+	17.5112i	−0.771684	+	1.14474i
$235$		0			0
$236$	5.61061	+	13.8649i	0.365220	+	0.902531i
$237$	7.51117			0.487903
$238$	−4.16001	+	2.98313i	−0.269653	+	0.193368i
$239$		−	17.0835i		−	1.10504i	−0.833501	−	0.552518i	$-0.813667\pi$
$239$		−	17.0835i		−	1.10504i	0.833501	−	0.552518i	$-0.186333\pi$
$240$		0			0
$241$	−16.0074	−	9.24185i	−1.03112	−	0.595320i	−0.113818	−	0.993502i	$-0.536308\pi$
$241$	−16.0074	−	9.24185i	−1.03112	−	0.595320i	−0.917307	+	0.398182i	$0.869641\pi$
$242$	−1.62328	+	2.40803i	−0.104348	+	0.154794i
$243$	12.5782	−	7.26203i	0.806892	−	0.465859i
$244$	−0.411889	+	2.94240i	−0.0263685	+	0.188368i
$245$		0			0
$246$	−0.778142	−	0.0541995i	−0.0496125	−	0.00345564i
$247$	11.9397	+	20.6802i	0.759706	+	1.31585i
$248$	−16.7684	+	18.6539i	−1.06479	+	1.18452i
$249$	−2.14982	+	3.72360i	−0.136239	+	0.235973i
$250$		0			0
$251$	−16.5313			−1.04344			−0.521722	−	0.853116i	$-0.674710\pi$
$251$	−16.5313			−1.04344			−0.521722	+	0.853116i	$0.674710\pi$
$252$	11.5361	−	7.11366i	0.726704	−	0.448119i
$253$		−	11.7247i		−	0.737128i
$254$	−10.5561	−	21.6282i	−0.662347	−	1.35707i
$255$		0			0
$256$	−14.1107	+	7.54238i	−0.881920	+	0.471399i
$257$	3.09749	+	5.36502i	0.193216	+	0.334660i	0.946314	−	0.323248i	$-0.104775\pi$
$257$	3.09749	+	5.36502i	0.193216	+	0.334660i	−0.753098	+	0.657908i	$0.771441\pi$
$258$	0.202186	−	2.90279i	0.0125876	−	0.180720i
$259$	−9.94290	+	26.7765i	−0.617822	+	1.66381i
$260$		0			0
$261$	6.65072	+	11.5194i	0.411669	+	0.713032i
$262$	−0.953445	+	1.41437i	−0.0589040	+	0.0873802i
$263$	−10.5768	+	18.3196i	−0.652194	+	1.12963i	0.330396	+	0.943842i	$0.392818\pi$
$263$	−10.5768	+	18.3196i	−0.652194	+	1.12963i	−0.982589	+	0.185790i	$0.940516\pi$
$264$	−2.09688	−	6.43561i	−0.129054	−	0.396084i
$265$		0			0
$266$	−1.50722	−	15.2507i	−0.0924137	−	0.935078i
$267$	6.22031			0.380677
$268$	−1.90378	−	4.70462i	−0.116292	−	0.287380i
$269$	26.8352	+	15.4933i	1.63617	+	0.944642i	0.982135	+	0.188177i	$0.0602578\pi$
$269$	26.8352	+	15.4933i	1.63617	+	0.944642i	0.654033	+	0.756466i	$0.273076\pi$
$270$		0			0
$271$	−11.5190	−	19.9516i	−0.699732	−	1.21197i	−0.968559	−	0.248783i	$-0.919969\pi$
$271$	−11.5190	−	19.9516i	−0.699732	−	1.21197i	0.268827	−	0.963188i	$-0.413364\pi$
$272$	5.26215	+	1.50268i	0.319065	+	0.0911134i
$273$	10.0732	−	1.70892i	0.609657	−	0.103428i
$274$	−0.210770	+	3.02602i	−0.0127331	+	0.182809i
$275$		0			0
$276$	3.38905	+	2.64484i	0.203997	+	0.159201i
$277$	6.01508	+	3.47281i	0.361411	+	0.208661i	0.669700	−	0.742632i	$-0.266423\pi$
$277$	6.01508	+	3.47281i	0.361411	+	0.208661i	−0.308288	+	0.951293i	$0.599756\pi$
$278$	−2.10625	−	4.31547i	−0.126325	−	0.258825i
$279$	−22.7137			−1.35984
$280$		0			0
$281$	−4.24391			−0.253170			−0.126585	−	0.991956i	$-0.540402\pi$
$281$	−4.24391			−0.253170			−0.126585	+	0.991956i	$0.540402\pi$
$282$	−2.83327	−	5.80505i	−0.168719	−	0.345686i
$283$	7.38891	+	4.26599i	0.439225	+	0.253587i	0.703269	−	0.710924i	$-0.251723\pi$
$283$	7.38891	+	4.26599i	0.439225	+	0.253587i	−0.264044	+	0.964511i	$0.585056\pi$
$284$	−5.55787	−	4.33740i	−0.329799	−	0.257377i
$285$		0			0
$286$	−2.06992	+	29.7178i	−0.122397	+	1.75725i
$287$	−1.40522	−	1.69689i	−0.0829473	−	0.100164i
$288$	−13.6218	−	4.93688i	−0.802672	−	0.290909i
$289$	7.56412	+	13.1014i	0.444948	+	0.770673i
$290$		0			0
$291$	0.196859	+	0.113656i	0.0115401	+	0.00666265i
$292$	3.87855	+	9.58467i	0.226975	+	0.560900i
$293$	25.2319			1.47406			0.737032	−	0.675857i	$-0.236227\pi$
$293$	25.2319			1.47406			0.737032	+	0.675857i	$0.236227\pi$
$294$	−6.34156	−	1.66690i	−0.369847	−	0.0972154i
$295$		0			0
$296$	29.0329	−	9.45964i	1.68750	−	0.549831i
$297$	6.65425	−	11.5255i	0.386119	−	0.668777i
$298$	15.0877	−	22.3817i	0.874010	−	1.29654i
$299$	−9.46017	−	16.3855i	−0.547096	−	0.947597i
$300$		0			0
$301$	6.33009	−	5.24203i	0.364861	−	0.302145i
$302$	−0.943933	+	13.5520i	−0.0543172	+	0.779832i
$303$	−1.50234	−	2.60212i	−0.0863070	−	0.149488i
$304$	−11.7726	+	11.3935i	−0.675203	+	0.653462i
$305$		0			0
$306$	2.17362	+	4.45350i	0.124258	+	0.254590i
$307$		−	29.2635i		−	1.67016i	−0.550132	−	0.835078i	$-0.685423\pi$
$307$		−	29.2635i		−	1.67016i	0.550132	−	0.835078i	$-0.314577\pi$
$308$	9.07541	−	16.8266i	0.517119	−	0.958785i
$309$	4.06561			0.231285
$310$		0			0
$311$	11.3730	−	19.6987i	0.644906	−	1.11701i	−0.339417	−	0.940636i	$-0.610230\pi$
$311$	11.3730	−	19.6987i	0.644906	−	1.11701i	0.984323	−	0.176374i	$-0.0564369\pi$
$312$	−8.12302	−	7.30197i	−0.459876	−	0.413392i
$313$	3.29240	+	5.70261i	0.186098	+	0.322331i	0.943946	−	0.330100i	$-0.107083\pi$
$313$	3.29240	+	5.70261i	0.186098	+	0.322331i	−0.757848	+	0.652431i	$0.773749\pi$
$314$	23.2250	+	1.61768i	1.31066	+	0.0912910i
$315$		0			0
$316$	3.14421	−	22.4612i	0.176876	−	1.26354i
$317$	12.2298	−	7.06086i	0.686892	−	0.396577i	−0.115555	−	0.993301i	$-0.536865\pi$
$317$	12.2298	−	7.06086i	0.686892	−	0.396577i	0.802447	+	0.596724i	$0.203531\pi$
$318$	3.88374	−	5.76127i	0.217789	−	0.323076i
$319$	16.2493	+	9.38153i	0.909786	+	0.525265i
$320$		0			0
$321$			5.07891i			0.283477i
$322$	1.19421	+	12.0835i	0.0665509	+	0.673388i
$323$	5.60352			0.311788
$324$	−3.93422	−	9.72224i	−0.218568	−	0.540125i
$325$		0			0
$326$	5.65690	−	8.39163i	0.313306	−	0.464770i
$327$	−0.742966	+	0.428952i	−0.0410861	+	0.0237211i
$328$	−0.487811	+	2.30425i	−0.0269349	+	0.127231i
$329$	6.35122	−	17.1040i	0.350154	−	0.942974i
$330$		0			0
$331$	−17.5997	+	10.1612i	−0.967368	+	0.558510i	−0.898433	−	0.439111i	$-0.855293\pi$
$331$	−17.5997	+	10.1612i	−0.967368	+	0.558510i	−0.0689349	+	0.997621i	$0.521960\pi$
$332$	10.2350	+	7.98748i	0.561720	+	0.438370i
$333$	23.9466	+	13.8255i	1.31226	+	0.757635i
$334$	−17.4278	+	8.50598i	−0.953605	+	0.465426i
$335$		0			0
$336$	2.81654	+	6.41896i	0.153655	+	0.350183i
$337$		−	15.7704i		−	0.859067i	−0.903051	−	0.429533i	$-0.858678\pi$
$337$		−	15.7704i		−	0.859067i	0.903051	−	0.429533i	$-0.141322\pi$
$338$	13.0213	+	26.6792i	0.708266	+	1.45115i
$339$	2.35332	−	4.07607i	0.127815	−	0.221381i
$340$		0			0
$341$	−27.7475	+	16.0200i	−1.50261	+	0.867534i
$342$	−14.7999	−	1.03085i	−0.800285	−	0.0557418i
$343$	−8.94647	−	16.2161i	−0.483064	−	0.875585i
$344$	−8.59578	−	1.81973i	−0.463453	−	0.0981134i
$345$		0			0
$346$	−3.10222	+	4.60194i	−0.166776	+	0.247402i
$347$	1.52392	−	2.63950i	0.0818082	−	0.141696i	−0.822218	−	0.569172i	$-0.807264\pi$
$347$	1.52392	−	2.63950i	0.0818082	−	0.141696i	0.904027	+	0.427476i	$0.140597\pi$
$348$	−6.37722	+	2.58061i	−0.341855	+	0.138335i
$349$			8.40462i			0.449889i	0.974372	+	0.224944i	$0.0722201\pi$
$349$			8.40462i			0.449889i	−0.974372	+	0.224944i	$0.927780\pi$
$350$		0			0
$351$		−	21.4761i		−	1.14631i
$352$	−20.1226	+	3.57649i	−1.07254	+	0.190628i
$353$	−0.216411	+	0.374834i	−0.0115184	+	0.0199504i	−0.871727	−	0.489992i	$-0.837000\pi$
$353$	−0.216411	+	0.374834i	−0.0115184	+	0.0199504i	0.860209	+	0.509942i	$0.170333\pi$
$354$	−5.80869	−	3.91570i	−0.308728	−	0.208117i
$355$		0			0
$356$	2.60385	−	18.6011i	0.138004	−	0.985854i
$357$	0.834594	−	2.24759i	0.0441714	−	0.118955i
$358$	−2.01973	+	28.9973i	−0.106746	+	1.53255i
$359$	23.3662	−	13.4905i	1.23322	−	0.712002i	0.265522	−	0.964105i	$-0.414456\pi$
$359$	23.3662	−	13.4905i	1.23322	−	0.712002i	0.967700	+	0.252103i	$0.0811222\pi$
$360$		0			0
$361$	1.11234	−	1.92663i	0.0585442	−	0.101402i
$362$	16.5985	−	8.10125i	0.872399	−	0.425792i
$363$		−	1.36014i		−	0.0713888i
$364$	−0.893621	−	30.8379i	−0.0468385	−	1.61635i
$365$		0			0
$366$	−0.610346	−	1.25053i	−0.0319033	−	0.0653661i
$367$	18.0317	+	10.4106i	0.941248	+	0.543430i	0.890351	−	0.455274i	$-0.150459\pi$
$367$	18.0317	+	10.4106i	0.941248	+	0.543430i	0.0508965	+	0.998704i	$0.483792\pi$
$368$	9.32773	−	9.02738i	0.486241	−	0.470585i
$369$	−1.84711	+	1.06643i	−0.0961568	+	0.0555161i
$370$		0			0
$371$	19.3485	−	3.28247i	1.00452	−	0.170417i
$372$	1.62860	−	11.6342i	0.0844392	−	0.603206i
$373$	−15.2953	+	8.83072i	−0.791958	+	0.457237i	−0.840652	−	0.541576i	$-0.817828\pi$
$373$	−15.2953	+	8.83072i	−0.791958	+	0.457237i	0.0486931	+	0.998814i	$0.484494\pi$
$374$	5.79640	+	3.90742i	0.299725	+	0.202048i
$375$		0			0
$376$	−18.5453	+	6.04253i	−0.956400	+	0.311619i
$377$	30.2781			1.55940
$378$	−5.68395	+	12.5559i	−0.292351	+	0.645808i
$379$		−	15.0551i		−	0.773331i	−0.922220	−	0.386665i	$-0.873627\pi$
$379$		−	15.0551i		−	0.773331i	0.922220	−	0.386665i	$-0.126373\pi$
$380$		0			0
$381$	9.76166	+	5.63590i	0.500105	+	0.288736i
$382$	14.6290	+	9.86155i	0.748483	+	0.504561i
$383$	26.2843	−	15.1753i	1.34307	−	0.775420i	0.355811	−	0.934558i	$-0.384205\pi$
$383$	26.2843	−	15.1753i	1.34307	−	0.775420i	0.987256	+	0.159138i	$0.0508714\pi$
$384$	3.50542	−	6.62324i	0.178885	−	0.337991i
$385$		0			0
$386$	1.87338	−	26.8961i	0.0953527	−	1.36898i
$387$	−3.97822	−	6.89047i	−0.202224	−	0.350262i
$388$	0.422281	−	0.541104i	0.0214381	−	0.0274704i
$389$	−3.13909	+	5.43706i	−0.159158	+	0.275670i	−0.934565	−	0.355792i	$-0.884211\pi$
$389$	−3.13909	+	5.43706i	−0.159158	+	0.275670i	0.775407	+	0.631462i	$0.217545\pi$
$390$		0			0
$391$	−4.43983			−0.224532
$392$	−7.63925	+	18.2659i	−0.385841	+	0.922565i
$393$		−	0.798887i		−	0.0402985i
$394$	2.45526	−	1.19834i	0.123694	−	0.0603715i
$395$		0			0
$396$	−14.5905	−	11.3865i	−0.733198	−	0.572193i
$397$	4.86104	+	8.41956i	0.243968	+	0.422566i	0.961841	−	0.273609i	$-0.0882173\pi$
$397$	4.86104	+	8.41956i	0.243968	+	0.422566i	−0.717873	+	0.696174i	$0.754884\pi$
$398$	29.0124	+	2.02079i	1.45426	+	0.101293i
$399$	4.57789	+	5.52810i	0.229181	+	0.276751i
$400$		0			0
$401$	−3.49372	−	6.05130i	−0.174468	−	0.302188i	0.765509	−	0.643425i	$-0.222487\pi$
$401$	−3.49372	−	6.05130i	−0.174468	−	0.302188i	−0.939977	+	0.341238i	$0.889154\pi$
$402$	1.97099	+	1.32867i	0.0983040	+	0.0662679i
$403$	−25.8517	+	44.7764i	−1.28776	+	2.23047i
$404$	−8.41020	+	3.40329i	−0.418423	+	0.169320i
$405$		0			0
$406$	−17.7021	−	8.01355i	−0.878539	−	0.397706i
$407$	39.0048			1.93339
$408$	−2.43698	+	0.794030i	−0.120649	+	0.0393103i
$409$	−1.94474	−	1.12280i	−0.0961611	−	0.0555186i	0.451148	−	0.892449i	$-0.351015\pi$
$409$	−1.94474	−	1.12280i	−0.0961611	−	0.0555186i	−0.547309	+	0.836930i	$0.684348\pi$
$410$		0			0
$411$	−0.710344	−	1.23035i	−0.0350387	−	0.0606888i
$412$	1.70189	−	12.1577i	0.0838459	−	0.598967i
$413$	−3.30948	−	19.5077i	−0.162849	−	0.959910i
$414$	11.7263	+	0.816769i	0.576318	+	0.0401420i
$415$		0			0
$416$	−25.2359	+	21.2342i	−1.23729	+	1.04109i
$417$	1.94774	+	1.12453i	0.0953814	+	0.0550685i
$418$	−18.8069	+	9.17907i	−0.919873	+	0.448963i
$419$	−18.3565			−0.896775			−0.448388	−	0.893839i	$-0.648002\pi$
$419$	−18.3565			−0.896775			−0.448388	+	0.893839i	$0.648002\pi$
$420$		0			0
$421$	2.27310			0.110784			0.0553921	−	0.998465i	$-0.482359\pi$
$421$	2.27310			0.110784			0.0553921	+	0.998465i	$0.482359\pi$
$422$	−12.6888	+	6.19304i	−0.617682	+	0.301472i
$423$	−15.2963	−	8.83133i	−0.743732	−	0.429394i
$424$	−15.6026	−	14.0255i	−0.757730	−	0.681140i
$425$		0			0
$426$	3.29394	+	0.229431i	0.159592	+	0.0111160i
$427$	1.36818	−	3.68456i	0.0662110	−	0.178308i
$428$	15.1879	+	2.12606i	0.734133	+	0.102767i
$429$	−6.97610	−	12.0830i	−0.336809	−	0.583371i
$430$		0			0
$431$	11.1379	+	6.43048i	0.536494	+	0.309745i	0.743657	−	0.668561i	$-0.233090\pi$
$431$	11.1379	+	6.43048i	0.536494	+	0.309745i	−0.207163	+	0.978307i	$0.566423\pi$
$432$	14.2926	−	3.58013i	0.687653	−	0.172249i
$433$	−33.6307			−1.61619			−0.808094	−	0.589054i	$-0.799501\pi$
$433$	−33.6307			−1.61619			−0.808094	+	0.589054i	$0.799501\pi$
$434$	26.9649	−	19.3364i	1.29436	−	0.928179i
$435$		0			0
$436$	0.971716	+	2.40131i	0.0465368	+	0.115002i
$437$	6.64577	−	11.5108i	0.317910	−	0.550637i
$438$	−4.01547	−	2.70688i	−0.191867	−	0.129340i
$439$	12.4435	+	21.5528i	0.593896	+	1.02866i	0.993702	+	0.112058i	$0.0357442\pi$
$439$	12.4435	+	21.5528i	0.593896	+	1.02866i	−0.399806	+	0.916600i	$0.630922\pi$
$440$		0			0
$441$	−16.9258	+	5.91313i	−0.805992	+	0.281578i
$442$	11.2533	+	0.783818i	0.535263	+	0.0372824i
$443$	−3.97386	−	6.88293i	−0.188804	−	0.327018i	0.756048	−	0.654516i	$-0.227128\pi$
$443$	−3.97386	−	6.88293i	−0.188804	−	0.327018i	−0.944852	+	0.327498i	$0.893794\pi$
$444$	−8.79859	+	11.2744i	−0.417563	+	0.535058i
$445$		0			0
$446$	21.3742	−	10.4321i	1.01210	−	0.493976i
$447$			12.6420i			0.597944i
$448$	20.3741	−	5.73550i	0.962586	−	0.270977i
$449$	−14.3027			−0.674988			−0.337494	−	0.941328i	$-0.609579\pi$
$449$	−14.3027			−0.674988			−0.337494	+	0.941328i	$0.609579\pi$
$450$		0			0
$451$	−1.50431	+	2.60554i	−0.0708352	+	0.122690i
$452$	−11.2038	−	8.74356i	−0.526985	−	0.411262i
$453$	−3.18127	−	5.51013i	−0.149469	−	0.258888i
$454$	1.94898	−	27.9815i	0.0914702	−	1.31324i
$455$		0			0
$456$	1.58918	−	7.50673i	0.0744202	−	0.351535i
$457$	−19.2073	+	11.0893i	−0.898478	+	0.518737i	−0.876706	−	0.481026i	$-0.840264\pi$
$457$	−19.2073	+	11.0893i	−0.898478	+	0.518737i	−0.0217719	+	0.999763i	$0.506931\pi$
$458$	−16.3387	−	11.0141i	−0.763456	−	0.514655i
$459$	−4.36438	−	2.51977i	−0.203712	−	0.117613i
$460$		0			0
$461$			32.8587i			1.53038i	0.643803	+	0.765192i	$0.277356\pi$
$461$			32.8587i			1.53038i	−0.643803	+	0.765192i	$0.722644\pi$
$462$	0.880635	+	8.91061i	0.0409708	+	0.414559i
$463$	3.31392			0.154011			0.0770055	−	0.997031i	$-0.475464\pi$
$463$	3.31392			0.154011			0.0770055	+	0.997031i	$0.475464\pi$
$464$	5.04746	+	20.1505i	0.234323	+	0.935464i
$465$		0			0
$466$	11.9911	+	8.08337i	0.555479	+	0.374455i
$467$	−30.4264	+	17.5667i	−1.40797	+	0.812890i	−0.995192	−	0.0979429i	$-0.968774\pi$
$467$	−30.4264	+	17.5667i	−1.40797	+	0.812890i	−0.412775	+	0.910833i	$0.635440\pi$
$468$	−29.5776	−	4.14039i	−1.36722	−	0.191390i
$469$	1.12297	+	6.61930i	0.0518538	+	0.305651i
$470$		0			0
$471$	−9.44307	+	5.45196i	−0.435114	+	0.251213i
$472$	−14.1410	+	15.7310i	−0.650890	+	0.724079i
$473$	−9.71973	−	5.61169i	−0.446914	−	0.258026i
$474$	4.65916	+	9.54608i	0.214002	+	0.438466i
$475$		0			0
$476$	−6.37176	−	3.43660i	−0.292049	−	0.157516i
$477$		−	18.9984i		−	0.869877i
$478$	21.7117	−	10.5968i	0.993068	−	0.484687i
$479$	11.1633	−	19.3354i	0.510065	−	0.883459i	−0.489867	−	0.871797i	$-0.662955\pi$
$479$	11.1633	−	19.3354i	0.510065	−	0.883459i	0.999932	−	0.0116615i	$-0.00371206\pi$
$480$		0			0
$481$	54.5097	−	31.4712i	2.48543	−	1.43496i
$482$	1.81631	−	26.0767i	0.0827306	−	1.18776i
$483$	−3.62719	−	4.38007i	−0.165043	−	0.199300i
$484$	−4.06732	−	0.569361i	−0.184878	−	0.0258800i
$485$		0			0
$486$	17.0317	+	11.4812i	0.772572	+	0.520799i
$487$	3.59259	−	6.22255i	0.162796	−	0.281971i	−0.773074	−	0.634315i	$-0.781282\pi$
$487$	3.59259	−	6.22255i	0.162796	−	0.281971i	0.935870	+	0.352344i	$0.114615\pi$
$488$	−3.99504	+	1.30168i	−0.180847	+	0.0589245i
$489$			4.73989i			0.214345i
$490$		0			0
$491$		−	5.80059i		−	0.261777i	−0.991397	−	0.130889i	$-0.958217\pi$
$491$		−	5.80059i		−	0.261777i	0.991397	−	0.130889i	$-0.0417830\pi$
$492$	−0.413796	−	1.02257i	−0.0186554	−	0.0461012i
$493$	3.55252	−	6.15314i	0.159997	−	0.277124i
$494$	−18.8766	+	28.0023i	−0.849301	+	1.25988i
$495$		0			0
$496$	−34.1089	−	9.74027i	−1.53153	−	0.437351i
$497$	5.94840	+	7.18308i	0.266822	+	0.322205i
$498$	−6.06591	−	0.422506i	−0.271820	−	0.0189329i
$499$	−34.3466	+	19.8300i	−1.53757	+	0.887715i	−0.538587	+	0.842570i	$0.681042\pi$
$499$	−34.3466	+	19.8300i	−1.53757	+	0.887715i	−0.998980	+	0.0451448i	$0.985625\pi$
$500$		0			0
$501$	4.54135	−	7.86585i	0.202892	−	0.351420i
$502$	−10.2543	−	21.0099i	−0.457672	−	0.937716i
$503$		−	8.22384i		−	0.366683i	−0.983049	−	0.183341i	$-0.941309\pi$
$503$		−	8.22384i		−	0.366683i	0.983049	−	0.183341i	$-0.0586914\pi$
$504$	16.1967	+	10.2488i	0.721457	+	0.456518i
$505$		0			0
$506$	14.9012	−	7.27283i	0.662438	−	0.323317i
$507$	−12.0414	−	6.95209i	−0.534776	−	0.308753i
$508$	20.9397	−	26.8318i	0.929050	−	1.19047i
$509$	28.2081	−	16.2860i	1.25030	−	0.721863i	0.279134	−	0.960252i	$-0.409953\pi$
$509$	28.2081	−	16.2860i	1.25030	−	0.721863i	0.971170	+	0.238389i	$0.0766194\pi$
$510$		0			0
$511$	−2.28781	−	13.4854i	−0.101207	−	0.596560i
$512$	−18.3386	−	13.2550i	−0.810459	−	0.585796i
$513$	13.0657	−	7.54347i	0.576864	−	0.333052i
$514$	−4.89712	+	7.26456i	−0.216003	+	0.320426i
$515$		0			0
$516$	3.81462	−	1.54363i	0.167929	−	0.0679544i
$517$	−24.9150			−1.09576
$518$	−40.1983	+	3.97280i	−1.76621	+	0.174555i
$519$		−	2.59934i		−	0.114098i
$520$		0			0
$521$	−4.88783	−	2.82199i	−0.214140	−	0.123634i	0.389094	−	0.921198i	$-0.372788\pi$
$521$	−4.88783	−	2.82199i	−0.214140	−	0.123634i	−0.603234	+	0.797564i	$0.706121\pi$
$522$	−10.5148	+	15.5980i	−0.460219	+	0.682704i
$523$	2.36780	−	1.36705i	0.103537	−	0.0597770i	−0.447338	−	0.894365i	$-0.647628\pi$
$523$	2.36780	−	1.36705i	0.103537	−	0.0597770i	0.550874	+	0.834588i	$0.314294\pi$
$524$	−2.38897	−	0.334418i	−0.104363	−	0.0146091i
$525$		0			0
$526$	−29.8434	−	2.07867i	−1.30123	−	0.0906342i
$527$	6.06633	+	10.5072i	0.264254	+	0.457701i
$528$	6.87843	−	6.65696i	0.299345	−	0.289707i
$529$	6.23437	−	10.7982i	0.271060	−	0.469489i
$530$		0			0
$531$	−19.1547			−0.831245
$532$	18.4474	−	11.3755i	0.799797	−	0.493191i
$533$			4.85504i			0.210295i
$534$	3.85844	+	7.90550i	0.166971	+	0.342104i
$535$		0			0
$536$	4.79828	−	5.33781i	0.207254	−	0.230558i
$537$	−6.80697	−	11.7900i	−0.293743	−	0.508777i
$538$	−3.04491	+	43.7157i	−0.131275	+	1.88472i
$539$	−16.5064	+	19.1614i	−0.710980	+	0.825341i
$540$		0			0
$541$	−14.1500	−	24.5085i	−0.608355	−	1.05370i	−0.991512	−	0.130018i	$-0.958497\pi$
$541$	−14.1500	−	24.5085i	−0.608355	−	1.05370i	0.383157	−	0.923683i	$-0.374837\pi$
$542$	18.2116	−	27.0157i	0.782254	−	1.16042i
$543$	−4.32526	+	7.49157i	−0.185615	+	0.321494i
$544$	1.35431	+	7.61987i	0.0580657	+	0.326699i
$545$		0			0
$546$	8.42026	+	11.7421i	0.360354	+	0.502517i
$547$	−20.7596			−0.887616			−0.443808	−	0.896122i	$-0.646373\pi$
$547$	−20.7596			−0.887616			−0.443808	+	0.896122i	$0.646373\pi$
$548$	−3.97656	+	1.60916i	−0.169870	+	0.0687400i
$549$	−3.29514	−	1.90245i	−0.140633	−	0.0811946i
$550$		0			0
$551$	10.6352	+	18.4207i	0.453075	+	0.784749i
$552$	−1.25915	+	5.94779i	−0.0535930	+	0.253155i
$553$	−10.4442	+	28.1266i	−0.444133	+	1.19606i
$554$	−0.682514	+	9.79885i	−0.0289973	+	0.416313i
$555$		0			0
$556$	4.17810	−	5.35375i	0.177191	−	0.227049i
$557$	−16.2445	−	9.37876i	−0.688301	−	0.397391i	0.114674	−	0.993403i	$-0.463418\pi$
$557$	−16.2445	−	9.37876i	−0.688301	−	0.397391i	−0.802975	+	0.596012i	$0.796751\pi$
$558$	−14.0893	−	28.8673i	−0.596446	−	1.22205i
$559$	−18.1113			−0.766025
$560$		0			0
$561$	−3.27401			−0.138229
$562$	−2.63248	−	5.39365i	−0.111045	−	0.227518i
$563$	28.9028	+	16.6870i	1.21811	+	0.703274i	0.964513	−	0.264037i	$-0.0850540\pi$
$563$	28.9028	+	16.6870i	1.21811	+	0.703274i	0.253594	+	0.967311i	$0.418387\pi$
$564$	5.62027	−	7.20171i	0.236656	−	0.303247i
$565$		0			0
$566$	−0.838399	+	12.0369i	−0.0352405	+	0.505948i
$567$	2.32064	+	13.6790i	0.0974579	+	0.574464i
$568$	2.06494	−	9.75407i	0.0866431	−	0.409272i
$569$	6.51501	+	11.2843i	0.273124	+	0.473064i	0.969660	−	0.244457i	$-0.0786099\pi$
$569$	6.51501	+	11.2843i	0.273124	+	0.473064i	−0.696536	+	0.717521i	$0.745277\pi$
$570$		0			0
$571$	28.5406	+	16.4779i	1.19439	+	0.689579i	0.959298	−	0.282395i	$-0.0911290\pi$
$571$	28.5406	+	16.4779i	1.19439	+	0.689579i	0.235088	+	0.971974i	$0.424462\pi$
$572$	−39.0528	+	15.8032i	−1.63288	+	0.660763i
$573$	−8.26295			−0.345190
$574$	1.28496	−	2.83849i	0.0536331	−	0.118476i
$575$		0			0
$576$	−2.17519	−	20.3745i	−0.0906330	−	0.848938i
$577$	−18.1937	+	31.5124i	−0.757414	+	1.31188i	0.186751	+	0.982407i	$0.440204\pi$
$577$	−18.1937	+	31.5124i	−0.757414	+	1.31188i	−0.944165	+	0.329473i	$0.893129\pi$
$578$	−11.9588	+	17.7402i	−0.497422	+	0.737893i
$579$	6.31373	+	10.9357i	0.262390	+	0.454472i
$580$		0			0
$581$	−10.9542	−	13.2279i	−0.454457	−	0.548786i
$582$	−0.0223370	+	0.320692i	−0.000925898	+	0.0132931i
$583$	−13.3996	−	23.2088i	−0.554955	−	0.961210i
$584$	−9.77547	+	10.8747i	−0.404512	+	0.449997i
$585$		0			0
$586$	15.6513	+	32.0677i	0.646549	+	1.32470i
$587$		−	28.4245i		−	1.17321i	−0.809875	−	0.586603i	$-0.800465\pi$
$587$		−	28.4245i		−	1.17321i	0.809875	−	0.586603i	$-0.199535\pi$
$588$	−1.81516	−	9.09357i	−0.0748561	−	0.375013i
$589$	−36.3217			−1.49661
$590$		0			0
$591$	−0.639794	+	1.10816i	−0.0263176	+	0.0455835i
$592$	30.0314	+	31.0306i	1.23428	+	1.27535i
$593$	3.78574	+	6.55710i	0.155462	+	0.269268i	0.933227	−	0.359287i	$-0.116980\pi$
$593$	3.78574	+	6.55710i	0.155462	+	0.269268i	−0.777765	+	0.628555i	$0.783647\pi$
$594$	18.7756	+	1.30777i	0.770371	+	0.0536583i
$595$		0			0
$596$	37.8042	+	5.29198i	1.54852	+	0.216768i
$597$	−11.7962	+	6.81052i	−0.482785	+	0.278736i
$598$	14.9565	−	22.1870i	0.611616	−	0.907292i
$599$	41.0937	+	23.7255i	1.67904	+	0.969397i	0.962272	+	0.272090i	$0.0877147\pi$
$599$	41.0937	+	23.7255i	1.67904	+	0.969397i	0.716772	+	0.697307i	$0.245619\pi$
$600$		0			0
$601$		−	13.3242i		−	0.543506i	−0.962367	−	0.271753i	$-0.912397\pi$
$601$		−	13.3242i		−	0.543506i	0.962367	−	0.271753i	$-0.0876034\pi$
$602$	10.5887	+	4.79341i	0.431564	+	0.195365i
$603$	6.49954			0.264682
$604$	−17.8090	+	7.20663i	−0.724639	+	0.293234i
$605$		0			0
$606$	2.37519	−	3.52344i	0.0964854	−	0.143130i
$607$	−13.0610	+	7.54080i	−0.530132	+	0.306072i	−0.741070	−	0.671428i	$-0.765681\pi$
$607$	−13.0610	+	7.54080i	−0.530132	+	0.306072i	0.210938	+	0.977499i	$0.432348\pi$
$608$	−21.7827	−	7.89460i	−0.883405	−	0.320168i
$609$	8.97261	−	1.52221i	0.363588	−	0.0616829i
$610$		0			0
$611$	−34.8191	+	20.1028i	−1.40863	+	0.813272i
$612$	−4.31174	+	5.52499i	−0.174292	+	0.223334i
$613$	4.50739	+	2.60234i	0.182052	+	0.105108i	0.588256	−	0.808675i	$-0.299815\pi$
$613$	4.50739	+	2.60234i	0.182052	+	0.105108i	−0.406205	+	0.913782i	$0.633148\pi$
$614$	37.1915	−	18.1521i	1.50093	−	0.732558i
$615$		0			0
$616$	27.0147	+	1.09660i	1.08845	+	0.0441831i
$617$			35.7404i			1.43885i	0.694569	+	0.719426i	$0.255595\pi$
$617$			35.7404i			1.43885i	−0.694569	+	0.719426i	$0.744405\pi$
$618$	2.52189	+	5.16706i	0.101445	+	0.207850i
$619$	19.1219	−	33.1200i	0.768573	−	1.33121i	−0.169764	−	0.985485i	$-0.554301\pi$
$619$	19.1219	−	33.1200i	0.768573	−	1.33121i	0.938337	−	0.345722i	$-0.112366\pi$
$620$		0			0
$621$	−10.3523	+	5.97690i	−0.415423	+	0.239845i
$622$	32.0901	+	2.23515i	1.28670	+	0.0896215i
$623$	−8.64929	+	23.2928i	−0.346526	+	0.933205i
$624$	4.24151	−	14.8531i	0.169796	−	0.594599i
$625$		0			0
$626$	−5.20528	+	7.72169i	−0.208045	+	0.308621i
$627$	4.90071	−	8.48828i	0.195716	−	0.338989i
$628$	12.3505	+	30.5205i	0.492838	+	1.21790i
$629$		−	14.7700i		−	0.588918i
$630$		0			0
$631$		−	12.0334i		−	0.479042i	−0.970891	−	0.239521i	$-0.923010\pi$
$631$		−	12.0334i		−	0.479042i	0.970891	−	0.239521i	$-0.0769904\pi$
$632$	30.4967	−	9.93659i	1.21309	−	0.395256i
$633$	3.30647	−	5.72697i	0.131420	−	0.227627i
$634$	16.5599	+	11.1632i	0.657676	+	0.443347i
$635$		0			0
$636$	9.73118	+	1.36221i	0.385866	+	0.0540152i
$637$	−7.60740	+	40.0966i	−0.301416	+	1.58869i
$638$	−1.84376	+	26.4709i	−0.0729952	+	1.04799i
$639$	7.81897	−	4.51429i	0.309314	−	0.178582i
$640$		0			0
$641$	−11.4676	+	19.8625i	−0.452944	+	0.784522i	−0.998567	−	0.0535086i	$-0.982960\pi$
$641$	−11.4676	+	19.8625i	−0.452944	+	0.784522i	0.545624	+	0.838030i	$0.316293\pi$
$642$	−6.45488	+	3.15044i	−0.254754	+	0.124338i
$643$			1.23955i			0.0488833i	0.999701	+	0.0244416i	$0.00778079\pi$
$643$			1.23955i			0.0488833i	−0.999701	+	0.0244416i	$0.992219\pi$
$644$	−14.6164	+	9.01312i	−0.575966	+	0.355167i
$645$		0			0
$646$	3.47585	+	7.12162i	0.136756	+	0.280196i
$647$	−12.2469	−	7.07077i	−0.481477	−	0.277981i	0.239555	−	0.970883i	$-0.422998\pi$
$647$	−12.2469	−	7.07077i	−0.481477	−	0.277981i	−0.721032	+	0.692902i	$0.756332\pi$
$648$	9.91579	−	11.0307i	0.389529	−	0.433329i
$649$	−23.3998	+	13.5099i	−0.918523	+	0.530309i
$650$		0			0
$651$	−5.40978	+	14.5687i	−0.212026	+	0.570992i
$652$	14.1740	+	1.98414i	0.555098	+	0.0777049i
$653$	−14.8017	+	8.54579i	−0.579237	+	0.334423i	−0.760830	−	0.648951i	$-0.775208\pi$
$653$	−14.8017	+	8.54579i	−0.579237	+	0.334423i	0.181593	+	0.983374i	$0.441875\pi$
$654$	−1.00602	−	0.678171i	−0.0393386	−	0.0265186i
$655$		0			0
$656$	−3.23110	+	0.809351i	−0.126153	+	0.0315999i
$657$	−13.2414			−0.516598
$658$	25.6774	−	2.53770i	1.00101	−	0.0989298i
$659$		−	3.45765i		−	0.134691i	−0.997730	−	0.0673455i	$-0.978547\pi$
$659$		−	3.45765i		−	0.134691i	0.997730	−	0.0673455i	$-0.0214530\pi$
$660$		0			0
$661$	13.1317	+	7.58160i	0.510765	+	0.294890i	0.733148	−	0.680069i	$-0.238050\pi$
$661$	13.1317	+	7.58160i	0.510765	+	0.294890i	−0.222383	+	0.974959i	$0.571384\pi$
$662$	−23.8311	−	16.0648i	−0.926222	−	0.624377i
$663$	−4.57547	+	2.64165i	−0.177697	+	0.102593i
$664$	−3.80267	+	17.9625i	−0.147572	+	0.697079i
$665$		0			0
$666$	−2.71715	+	39.0100i	−0.105287	+	1.51161i
$667$	−8.42657	−	14.5952i	−0.326278	−	0.565130i
$668$	−21.6208	−	16.8730i	−0.836533	−	0.652836i
$669$	−5.56972	+	9.64704i	−0.215338	+	0.372976i
$670$		0			0
$671$	−5.36721			−0.207199
$672$	−6.41087	+	7.56125i	−0.247305	+	0.291682i
$673$		−	11.2116i		−	0.432175i	−0.976374	−	0.216087i	$-0.930670\pi$
$673$		−	11.2116i		−	0.432175i	0.976374	−	0.216087i	$-0.0693296\pi$
$674$	20.0428	−	9.78232i	0.772021	−	0.376801i
$675$		0			0
$676$	−25.8299	+	33.0980i	−0.993458	+	1.27300i
$677$	−1.83818	−	3.18383i	−0.0706471	−	0.122364i	0.828538	−	0.559933i	$-0.189173\pi$
$677$	−1.83818	−	3.18383i	−0.0706471	−	0.122364i	−0.899185	+	0.437568i	$0.855840\pi$
$678$	6.64010	+	0.462500i	0.255011	+	0.0177622i
$679$	−0.699331	+	0.579125i	−0.0268379	+	0.0222248i
$680$		0			0
$681$	6.56852	+	11.3770i	0.251706	+	0.435968i
$682$	−37.5719	−	25.3276i	−1.43870	−	0.969845i
$683$	21.0938	−	36.5356i	0.807133	−	1.39800i	−0.107708	−	0.994183i	$-0.534351\pi$
$683$	21.0938	−	36.5356i	0.807133	−	1.39800i	0.914841	−	0.403814i	$-0.132316\pi$
$684$	−7.87019	−	19.4488i	−0.300924	−	0.743645i
$685$		0			0
$686$	15.0598	−	21.4290i	0.574986	−	0.818163i
$687$	9.22865			0.352095
$688$	−3.01921	−	12.0533i	−0.115106	−	0.459528i
$689$	−37.4523	−	21.6231i	−1.42682	−	0.823773i
$690$		0			0
$691$	11.5615	+	20.0251i	0.439820	+	0.761790i	0.997675	−	0.0681478i	$-0.0217089\pi$
$691$	11.5615	+	20.0251i	0.439820	+	0.761790i	−0.557855	+	0.829938i	$0.688376\pi$
$692$	−7.77298	−	1.08809i	−0.295485	−	0.0413631i
$693$	15.6157	+	18.8569i	0.593190	+	0.716316i
$694$	4.29987	+	0.299497i	0.163221	+	0.0113688i
$695$		0			0
$696$	−7.23552	−	6.50417i	−0.274262	−	0.246540i
$697$	0.986645	+	0.569640i	0.0373718	+	0.0215766i
$698$	−10.6816	+	5.21336i	−0.404304	+	0.197329i
$699$	−6.77301			−0.256179
$700$		0			0
$701$	29.3192			1.10737			0.553686	−	0.832725i	$-0.313221\pi$
$701$	29.3192			1.10737			0.553686	+	0.832725i	$0.313221\pi$
$702$	27.2943	−	13.3215i	1.03016	−	0.502789i
$703$	38.2931	+	22.1085i	1.44425	+	0.833839i
$704$	−17.0274	−	23.3557i	−0.641746	−	0.880252i
$705$		0			0
$706$	−0.610622	−	0.0425314i	−0.0229811	−	0.00160069i
$707$	11.8330	−	2.00747i	0.445025	−	0.0754986i
$708$	1.37342	−	9.81126i	0.0516163	−	0.368730i
$709$	1.67720	+	2.90499i	0.0629884	+	0.109099i	0.895800	−	0.444458i	$-0.146604\pi$
$709$	1.67720	+	2.90499i	0.0629884	+	0.109099i	−0.832811	+	0.553557i	$0.813270\pi$
$710$		0			0
$711$	25.1539	+	14.5226i	0.943346	+	0.544641i
$712$	25.2556	−	8.22890i	0.946492	−	0.308391i
$713$	28.7786			1.07777
$714$	3.37419	−	0.333471i	0.126276	−	0.0124798i
$715$		0			0
$716$	−38.1060	+	15.4200i	−1.42409	+	0.576274i
$717$	−5.65765	+	9.79934i	−0.211289	+	0.365963i
$718$	31.6393	+	21.3284i	1.18077	+	0.795970i
$719$	−15.5142	−	26.8714i	−0.578583	−	1.00213i	−0.995642	−	0.0932556i	$-0.970273\pi$
$719$	−15.5142	−	26.8714i	−0.578583	−	1.00213i	0.417059	−	0.908879i	$-0.363061\pi$
$720$		0			0
$721$	−5.65320	+	15.2242i	−0.210536	+	0.566980i
$722$	3.13857	+	0.218609i	0.116805	+	0.00813579i
$723$	6.12138	+	10.6025i	0.227657	+	0.394313i
$724$	20.5920	+	16.0702i	0.765297	+	0.597243i
$725$		0			0
$726$	1.72862	−	0.843691i	0.0641553	−	0.0313123i
$727$			37.9906i			1.40899i	0.709707	+	0.704497i	$0.248827\pi$
$727$			37.9906i			1.40899i	−0.709707	+	0.704497i	$0.751173\pi$
$728$	38.6382	−	20.2644i	1.43203	−	0.751049i
$729$	6.11207			0.226373
$730$		0			0
$731$	−2.12499	+	3.68058i	−0.0785955	+	0.136131i
$732$	1.21072	−	1.55140i	0.0447496	−	0.0573413i
$733$	−15.4876	−	26.8252i	−0.572046	−	0.990813i	−0.996356	−	0.0852956i	$-0.972817\pi$
$733$	−15.4876	−	26.8252i	−0.572046	−	0.990813i	0.424310	−	0.905517i	$-0.360517\pi$
$734$	−2.04601	+	29.3745i	−0.0755195	+	1.08423i
$735$		0			0
$736$	17.2590	+	6.25511i	0.636176	+	0.230566i
$737$	7.93996	−	4.58414i	0.292472	−	0.168859i
$738$	−2.50110	−	1.68602i	−0.0920669	−	0.0620633i
$739$	2.53077	+	1.46114i	0.0930957	+	0.0537488i	0.545825	−	0.837899i	$-0.316216\pi$
$739$	2.53077	+	1.46114i	0.0930957	+	0.0537488i	−0.452729	+	0.891648i	$0.649550\pi$
$740$		0			0
$741$		−	15.8167i		−	0.581039i
$742$	16.1735	+	22.5542i	0.593749	+	0.827990i
$743$	−36.6505			−1.34457			−0.672287	−	0.740290i	$-0.734688\pi$
$743$	−36.6505			−1.34457			−0.672287	+	0.740290i	$0.734688\pi$
$744$	15.7963	−	5.14685i	0.579122	−	0.188693i
$745$		0			0
$746$	−20.7107	−	13.9613i	−0.758274	−	0.511161i
$747$	−14.3989	+	8.31323i	−0.526829	+	0.304165i
$748$	−1.37052	+	9.79051i	−0.0501110	+	0.357976i
$749$	−19.0187	−	7.06219i	−0.694927	−	0.258047i
$750$		0			0
$751$	31.3355	−	18.0915i	1.14345	−	0.660170i	0.196166	−	0.980571i	$-0.437151\pi$
$751$	31.3355	−	18.0915i	1.14345	−	0.660170i	0.947282	+	0.320401i	$0.103818\pi$
$752$	−19.1831	−	19.8214i	−0.699537	−	0.722811i
$753$	9.48259	+	5.47478i	0.345565	+	0.199512i
$754$	18.7814	+	38.4810i	0.683980	+	1.40140i
$755$		0			0
$756$	−19.4833	+	0.564587i	−0.708601	+	0.0205338i
$757$			1.44394i			0.0524807i	0.999656	+	0.0262404i	$0.00835352\pi$
$757$			1.44394i			0.0524807i	−0.999656	+	0.0262404i	$0.991646\pi$
$758$	19.1338	−	9.33867i	0.694973	−	0.339196i
$759$	−3.88297	+	6.72550i	−0.140943	+	0.244120i
$760$		0			0
$761$	−24.4509	+	14.1167i	−0.886343	+	0.511730i	−0.872744	−	0.488177i	$-0.837662\pi$
$761$	−24.4509	+	14.1167i	−0.886343	+	0.511730i	−0.0135983	+	0.999908i	$0.504329\pi$
$762$	−1.10763	+	15.9022i	−0.0401251	+	0.576076i
$763$	−0.573178	−	3.37859i	−0.0207505	−	0.122313i
$764$	−3.45891	+	24.7093i	−0.125139	+	0.893951i
$765$		0			0
$766$	35.5906	+	23.9920i	1.28594	+	0.866868i
$767$	−21.8010	+	37.7605i	−0.787189	+	1.36345i
$768$	10.5920	+	0.346723i	0.382206	+	0.0125113i
$769$		−	38.3866i		−	1.38426i	−0.721774	−	0.692129i	$-0.756673\pi$
$769$		−	38.3866i		−	1.38426i	0.721774	−	0.692129i	$-0.243327\pi$
$770$		0			0
$771$		−	4.10328i		−	0.147776i
$772$	35.3448	−	14.3027i	1.27209	−	0.514765i
$773$	−9.54086	+	16.5252i	−0.343161	+	0.594372i	−0.985018	−	0.172452i	$-0.944831\pi$
$773$	−9.54086	+	16.5252i	−0.343161	+	0.594372i	0.641857	+	0.766824i	$0.278164\pi$
$774$	6.28955	−	9.33013i	0.226073	−	0.335364i
$775$		0			0
$776$	0.949638	+	0.201039i	0.0340900	+	0.00721688i
$777$	14.5712	−	12.0666i	0.522738	−	0.432886i
$778$	−8.85722	−	0.616928i	−0.317547	−	0.0221179i
$779$	−2.95373	+	1.70533i	−0.105828	+	0.0611000i
$780$		0			0
$781$	6.36787	−	11.0295i	0.227860	−	0.394666i
$782$	−2.75401	−	5.64265i	−0.0984833	−	0.201781i
$783$		−	19.1296i		−	0.683637i
$784$	−27.9530	+	1.62141i	−0.998322	+	0.0579073i
$785$		0			0
$786$	1.01532	−	0.495547i	0.0362152	−	0.0176756i
$787$	4.41858	+	2.55107i	0.157505	+	0.0909358i	0.576681	−	0.816969i	$-0.304348\pi$
$787$	4.41858	+	2.55107i	0.157505	+	0.0909358i	−0.419176	+	0.907905i	$0.637681\pi$
$788$	3.04598	+	2.37710i	0.108509	+	0.0846808i
$789$	12.1340	−	7.00559i	0.431983	−	0.249406i
$790$		0			0
$791$	11.9911	+	14.4800i	0.426354	+	0.514851i
$792$	5.42087	−	25.6063i	0.192622	−	0.909879i
$793$	−7.50075	+	4.33056i	−0.266359	+	0.153783i
$794$	−7.68528	+	11.4006i	−0.272740	+	0.404592i
$795$		0			0
$796$	15.4281	+	38.1259i	0.546833	+	1.35134i
$797$	−25.6101			−0.907155			−0.453578	−	0.891217i	$-0.649852\pi$
$797$	−25.6101			−0.907155			−0.453578	+	0.891217i	$0.649852\pi$
$798$	−4.18611	+	9.24718i	−0.148187	+	0.327347i
$799$			9.43461i			0.333772i
$800$		0			0
$801$	20.8310	+	12.0268i	0.736027	+	0.424946i
$802$	5.52356	−	8.19384i	0.195044	−	0.289335i
$803$	−16.1760	+	9.33922i	−0.570839	+	0.329574i
$804$	−0.466026	+	3.32913i	−0.0164355	+	0.117409i
$805$		0			0
$806$	−72.9429	−	5.08065i	−2.56930	−	0.178958i
$807$	−10.2621	−	17.7744i	−0.361241	−	0.625688i
$808$	−9.54212	−	8.57763i	−0.335691	−	0.301760i
$809$	25.2381	−	43.7136i	0.887323	−	1.53689i	0.0442955	−	0.999018i	$-0.485896\pi$
$809$	25.2381	−	43.7136i	0.887323	−	1.53689i	0.843028	−	0.537870i	$-0.180771\pi$
$810$		0			0
$811$	3.15050			0.110629			0.0553145	−	0.998469i	$-0.482384\pi$
$811$	3.15050			0.110629			0.0553145	+	0.998469i	$0.482384\pi$
$812$	−0.795986	−	27.4686i	−0.0279336	−	0.963961i
$813$			15.2594i			0.535170i
$814$	24.1945	+	49.5718i	0.848018	+	1.73749i
$815$		0			0
$816$	−2.52080	−	2.60467i	−0.0882456	−	0.0911816i
$817$	−6.36159	−	11.0186i	−0.222564	−	0.385492i
$818$	0.220664	−	3.16807i	0.00771533	−	0.110769i
$819$	37.0379	+	13.7533i	1.29421	+	0.480578i
$820$		0			0
$821$	17.7416	+	30.7294i	0.619187	+	1.07246i	0.989634	+	0.143609i	$0.0458709\pi$
$821$	17.7416	+	30.7294i	0.619187	+	1.07246i	−0.370448	+	0.928853i	$0.620796\pi$
$822$	1.12305	−	1.66597i	0.0391709	−	0.0581074i
$823$	4.20565	−	7.28440i	0.146600	−	0.253918i	−0.783369	−	0.621557i	$-0.786500\pi$
$823$	4.20565	−	7.28440i	0.146600	−	0.253918i	0.929969	+	0.367639i	$0.119834\pi$
$824$	16.5071	−	5.37843i	0.575052	−	0.187367i
$825$		0			0
$826$	22.7398	−	16.3066i	0.791219	−	0.567381i
$827$	−4.33435			−0.150720			−0.0753601	−	0.997156i	$-0.524011\pi$
$827$	−4.33435			−0.150720			−0.0753601	+	0.997156i	$0.524011\pi$
$828$	6.23577	+	15.4098i	0.216708	+	0.535529i
$829$	−20.9404	−	12.0899i	−0.727289	−	0.419900i	0.0901408	−	0.995929i	$-0.471268\pi$
$829$	−20.9404	−	12.0899i	−0.727289	−	0.419900i	−0.817429	+	0.576029i	$0.804602\pi$
$830$		0			0
$831$	−2.30023	−	3.98412i	−0.0797942	−	0.138208i
$832$	−42.6407	−	18.9013i	−1.47830	−	0.655283i
$833$	7.25589	+	6.25050i	0.251402	+	0.216567i
$834$	−0.221005	+	3.17296i	−0.00765277	+	0.109871i
$835$		0			0
$836$	−23.3317	−	18.2082i	−0.806943	−	0.629744i
$837$	28.2896	+	16.3330i	0.977831	+	0.564551i
$838$	−11.3865	−	23.3296i	−0.393340	−	0.805909i
$839$	−18.3056			−0.631979			−0.315989	−	0.948763i	$-0.602336\pi$
$839$	−18.3056			−0.631979			−0.315989	+	0.948763i	$0.602336\pi$
$840$		0			0
$841$	−2.02999			−0.0699998
$842$	1.41000	+	2.88892i	0.0485917	+	0.0995588i
$843$	2.43437	+	1.40549i	0.0838442	+	0.0484075i
$844$	−15.7417	−	12.2849i	−0.541851	−	0.422864i
$845$		0			0
$846$	1.73563	−	24.9184i	0.0596722	−	0.856712i
$847$	5.09322	+	1.89126i	0.175005	+	0.0649845i
$848$	8.14704	−	28.5296i	0.279770	−	0.979711i
$849$	−2.82560	−	4.89408i	−0.0969743	−	0.167964i
$850$		0			0
$851$	−30.3407	−	17.5172i	−1.04006	−	0.600481i
$852$	1.75163	+	4.32864i	0.0600100	+	0.148297i
$853$	−16.9533			−0.580469			−0.290234	−	0.956956i	$-0.593733\pi$
$853$	−16.9533			−0.580469			−0.290234	+	0.956956i	$0.593733\pi$
$854$	5.53145	−	0.546673i	0.189282	−	0.0187068i
$855$		0			0
$856$	6.71894	+	20.6213i	0.229649	+	0.704821i
$857$	−25.2872	+	43.7988i	−0.863795	+	1.49614i	0.00444284	+	0.999990i	$0.498586\pi$
$857$	−25.2872	+	43.7988i	−0.863795	+	1.49614i	−0.868238	+	0.496147i	$0.834748\pi$
$858$	11.0292	−	16.3611i	0.376530	−	0.558558i
$859$	−2.51925	−	4.36346i	−0.0859555	−	0.148879i	0.819842	−	0.572589i	$-0.194061\pi$
$859$	−2.51925	−	4.36346i	−0.0859555	−	0.148879i	−0.905798	+	0.423710i	$0.860728\pi$
$860$		0			0
$861$	0.244083	+	1.43874i	0.00831832	+	0.0490321i
$862$	−1.26379	+	18.1442i	−0.0430448	+	0.617993i
$863$	5.87084	+	10.1686i	0.199846	+	0.346143i	0.948478	−	0.316842i	$-0.102623\pi$
$863$	5.87084	+	10.1686i	0.199846	+	0.346143i	−0.748633	+	0.662985i	$0.769289\pi$
$864$	13.4157	+	15.9440i	0.456412	+	0.542425i
$865$		0			0
$866$	−20.8610	−	42.7418i	−0.708887	−	1.45243i
$867$		−	10.0203i		−	0.340306i
$868$	41.3013	+	22.2758i	1.40186	+	0.756090i
$869$	40.9714			1.38986
$870$		0			0
$871$	7.39747	−	12.8128i	0.250654	−	0.434145i
$872$	−2.44911	+	2.72450i	−0.0829373	+	0.0922631i
$873$	0.439502	+	0.761240i	0.0148749	+	0.0257641i
$874$	18.7517	+	1.30610i	0.634284	+	0.0441795i
$875$		0			0
$876$	0.949429	−	6.78241i	0.0320782	−	0.229156i
$877$	20.9426	−	12.0912i	0.707180	−	0.408290i	−0.102836	−	0.994698i	$-0.532792\pi$
$877$	20.9426	−	12.0912i	0.707180	−	0.408290i	0.810016	+	0.586408i	$0.199458\pi$
$878$	−19.6731	+	29.1838i	−0.663936	+	0.984905i
$879$	−14.4734	−	8.35624i	−0.488177	−	0.281849i
$880$		0			0
$881$			19.6285i			0.661301i	0.943753	+	0.330651i	$0.107268\pi$
$881$			19.6285i			0.661301i	−0.943753	+	0.330651i	$0.892732\pi$
$882$	−18.0142	−	17.8434i	−0.606568	−	0.600820i
$883$	11.2418			0.378315			0.189158	−	0.981947i	$-0.439424\pi$
$883$	11.2418			0.378315			0.189158	+	0.981947i	$0.439424\pi$
$884$	5.98420	+	14.7882i	0.201271	+	0.497380i
$885$		0			0
$886$	6.28266	−	9.31991i	0.211070	−	0.313109i
$887$	36.2085	−	20.9050i	1.21576	−	0.701920i	0.251753	−	0.967792i	$-0.418993\pi$
$887$	36.2085	−	20.9050i	1.21576	−	0.701920i	0.964009	+	0.265871i	$0.0856596\pi$
$888$	−19.7865	−	4.18882i	−0.663993	−	0.140568i
$889$	−34.6779	+	28.7172i	−1.16306	+	0.963143i
$890$		0			0
$891$	16.4082	−	9.47327i	0.549695	−	0.317366i
$892$	26.5167	+	20.6938i	0.887846	+	0.692881i
$893$	−24.4604	−	14.1222i	−0.818537	−	0.472583i
$894$	−16.0669	+	7.84177i	−0.537357	+	0.262268i
$895$		0			0
$896$	19.9274	+	22.3361i	0.665726	+	0.746196i
$897$			12.5320i			0.418430i
$898$	−8.87195	−	18.1776i	−0.296061	−	0.606594i
$899$	−23.0272	+	39.8842i	−0.768000	+	1.33021i
$900$		0			0
$901$	−8.78851	+	5.07405i	−0.292788	+	0.169041i
$902$	−4.24455	−	0.295644i	−0.141328	−	0.00984385i
$903$	−5.36708	+	0.910527i	−0.178605	+	0.0303005i
$904$	4.16262	−	19.6628i	0.138447	−	0.653974i
$905$		0			0
$906$	5.02958	−	7.46105i	0.167097	−	0.247877i
$907$	10.9044	−	18.8870i	0.362076	−	0.627133i	−0.626227	−	0.779641i	$-0.715402\pi$
$907$	10.9044	−	18.8870i	0.362076	−	0.627133i	0.988302	+	0.152508i	$0.0487349\pi$
$908$	36.7711	−	14.8798i	1.22029	−	0.493805i
$909$		−	11.6189i		−	0.385374i
$910$		0			0
$911$			2.40991i			0.0798440i	0.999203	+	0.0399220i	$0.0127109\pi$
$911$			2.40991i			0.0798440i	−0.999203	+	0.0399220i	$0.987289\pi$
$912$	10.5262	−	2.63669i	0.348557	−	0.0873095i
$913$	−11.7267	+	20.3112i	−0.388096	+	0.672202i
$914$	−26.0078	−	17.5322i	−0.860262	−	0.579913i
$915$		0			0
$916$	3.86316	−	27.5971i	0.127642	−	0.911835i
$917$	2.99154	+	1.11085i	0.0987893	+	0.0366833i
$918$	0.495214	−	7.10977i	0.0163445	−	0.234657i
$919$	−13.1661	+	7.60145i	−0.434310	+	0.250749i	−0.701181	−	0.712983i	$-0.747343\pi$
$919$	−13.1661	+	7.60145i	−0.434310	+	0.250749i	0.266871	+	0.963732i	$0.414010\pi$
$920$		0			0
$921$	−9.69140	+	16.7860i	−0.319343	+	0.553118i
$922$	−41.7607	+	20.3822i	−1.37532	+	0.671251i
$923$		−	20.5518i		−	0.676470i
$924$	−10.7784	+	6.64644i	−0.354583	+	0.218652i
$925$		0			0
$926$	2.05562	+	4.21172i	0.0675517	+	0.138406i
$927$	13.6152	+	7.86074i	0.447182	+	0.258181i
$928$	−22.4787	+	18.9142i	−0.737900	+	0.620890i
$929$	−18.0735	+	10.4347i	−0.592971	+	0.342352i	−0.766272	−	0.642517i	$-0.777890\pi$
$929$	−18.0735	+	10.4347i	−0.592971	+	0.342352i	0.173300	+	0.984869i	$0.444557\pi$
$930$		0			0
$931$	−27.0662	+	9.45573i	−0.887059	+	0.309899i
$932$	−2.83522	+	20.2538i	−0.0928706	+	0.663437i
$933$	−13.0475	+	7.53299i	−0.427157	+	0.246619i
$934$	−41.1993	−	27.7729i	−1.34808	−	0.908757i
$935$		0			0
$936$	−13.0848	−	40.1590i	−0.427690	−	1.31264i
$937$	−10.9083			−0.356358			−0.178179	−	0.983998i	$-0.557021\pi$
$937$	−10.9083			−0.356358			−0.178179	+	0.983998i	$0.557021\pi$
$938$	−7.71601	+	5.53313i	−0.251937	+	0.180663i
$939$		−	4.36148i		−	0.142331i
$940$		0			0
$941$	−42.7569	−	24.6857i	−1.39383	−	0.804730i	−0.400097	−	0.916473i	$-0.631023\pi$
$941$	−42.7569	−	24.6857i	−1.39383	−	0.804730i	−0.993737	+	0.111743i	$0.964357\pi$
$942$	−12.7865	−	8.61952i	−0.416607	−	0.280839i
$943$	2.34032	−	1.35118i	0.0762113	−	0.0440006i
$944$	−28.7644	−	8.21408i	−0.936202	−	0.267346i
$945$		0			0
$946$	1.10287	−	15.8339i	0.0358574	−	0.514804i
$947$	7.27929	+	12.6081i	0.236545	+	0.409708i	0.959721	−	0.280956i	$-0.0906515\pi$
$947$	7.27929	+	12.6081i	0.236545	+	0.409708i	−0.723175	+	0.690664i	$0.757318\pi$
$948$	−9.24221	+	11.8428i	−0.300173	+	0.384637i
$949$	−15.0708	+	26.1034i	−0.489218	+	0.847351i
$950$		0			0
$951$	−9.35358			−0.303311
$952$	0.415250	−	10.2297i	0.0134583	−	0.331546i
$953$		−	9.87954i		−	0.320030i	−0.987115	−	0.160015i	$-0.948846\pi$
$953$		−	9.87954i		−	0.320030i	0.987115	−	0.160015i	$-0.0511542\pi$
$954$	24.1454	−	11.7847i	0.781736	−	0.381542i
$955$		0			0
$956$	26.9354	+	21.0205i	0.871152	+	0.679853i
$957$	−6.21390	−	10.7628i	−0.200867	−	0.347912i
$958$	31.4983	+	2.19394i	1.01766	+	0.0708829i
$959$	5.59494	−	0.949183i	0.180670	−	0.0306507i
$960$		0			0
$961$	−23.8215	−	41.2601i	−0.768437	−	1.33097i
$962$	73.8095	+	49.7558i	2.37971	+	1.60419i
$963$	−9.81993	+	17.0086i	−0.316443	+	0.548095i
$964$	34.2680	−	13.8669i	1.10370	−	0.446624i
$965$		0			0
$966$	3.31677	−	7.32680i	0.106715	−	0.235736i
$967$	−15.5047			−0.498597			−0.249298	−	0.968427i	$-0.580200\pi$
$967$	−15.5047			−0.498597			−0.249298	+	0.968427i	$0.580200\pi$
$968$	−1.79934	−	5.52240i	−0.0578330	−	0.177497i
$969$	−3.21427	−	1.85576i	−0.103257	−	0.0596156i
$970$		0			0
$971$	−16.5173	−	28.6089i	−0.530067	−	0.918102i	−0.999385	−	0.0350732i	$-0.988834\pi$
$971$	−16.5173	−	28.6089i	−0.530067	−	0.918102i	0.469318	−	0.883029i	$-0.344500\pi$
$972$	−4.02701	+	28.7676i	−0.129166	+	0.922721i
$973$	−6.91927	+	5.72993i	−0.221822	+	0.183693i
$974$	10.1368	+	0.706056i	0.324805	+	0.0226235i
$975$		0			0
$976$	−4.13245	−	4.26993i	−0.132276	−	0.136677i
$977$	−44.1430	−	25.4860i	−1.41226	−	0.815369i	−0.416660	−	0.909062i	$-0.636799\pi$
$977$	−44.1430	−	25.4860i	−1.41226	−	0.815369i	−0.995601	+	0.0936930i	$0.970133\pi$
$978$	−6.02400	+	2.94014i	−0.192626	+	0.0940153i
$979$	33.9301			1.08441
$980$		0			0
$981$	−3.31746			−0.105918
$982$	7.37207	−	3.59809i	0.235252	−	0.114820i
$983$	−21.2423	−	12.2642i	−0.677523	−	0.391168i	0.121398	−	0.992604i	$-0.461262\pi$
$983$	−21.2423	−	12.2642i	−0.677523	−	0.391168i	−0.798921	+	0.601436i	$0.794596\pi$
$984$	1.04293	−	1.16020i	0.0332474	−	0.0369859i
$985$		0			0
$986$	10.0238	+	0.698180i	0.319221	+	0.0222346i
$987$	−9.30762	+	7.70775i	−0.296265	+	0.245340i
$988$	−47.2977	−	6.62093i	−1.50474	−	0.210640i
$989$	5.04046	+	8.73034i	0.160277	+	0.277609i
$990$		0			0
$991$	−45.8274	−	26.4585i	−1.45576	−	0.840481i	−0.456957	−	0.889489i	$-0.651061\pi$
$991$	−45.8274	−	26.4585i	−1.45576	−	0.840481i	−0.998798	+	0.0490078i	$0.984394\pi$
$992$	−8.77857	−	49.3915i	−0.278720	−	1.56818i
$993$	13.4606			0.427160
$994$	−5.43933	+	12.0156i	−0.172525	+	0.381111i
$995$		0			0
$996$	−3.22570	−	7.97135i	−0.102210	−	0.252582i
$997$	8.51148	−	14.7423i	0.269561	−	0.466894i	−0.699187	−	0.714939i	$-0.746455\pi$
$997$	8.51148	−	14.7423i	0.269561	−	0.466894i	0.968749	+	0.248045i	$0.0797880\pi$
$998$	−46.5075	−	31.3512i	−1.47217	−	0.992406i
$999$	−19.8834	−	34.4390i	−0.629082	−	1.08960i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.t.d.199.10		32
4.3	odd	2	inner	700.2.t.d.199.5		32
5.2	odd	4		140.2.o.a.31.2	✓	32
5.3	odd	4		700.2.p.c.451.15		32
5.4	even	2		700.2.t.c.199.7		32
7.5	odd	6		700.2.t.c.299.12		32
20.3	even	4		700.2.p.c.451.3		32
20.7	even	4		140.2.o.a.31.14	yes	32
20.19	odd	2		700.2.t.c.199.12		32
28.19	even	6		700.2.t.c.299.7		32
35.2	odd	12		980.2.o.f.411.14		32
35.12	even	12		140.2.o.a.131.14	yes	32
35.17	even	12		980.2.g.a.391.17		32
35.19	odd	6	inner	700.2.t.d.299.5		32
35.27	even	4		980.2.o.f.31.2		32
35.32	odd	12		980.2.g.a.391.18		32
35.33	even	12		700.2.p.c.551.3		32
140.19	even	6	inner	700.2.t.d.299.10		32
140.27	odd	4		980.2.o.f.31.14		32
140.47	odd	12		140.2.o.a.131.2	yes	32
140.67	even	12		980.2.g.a.391.19		32
140.87	odd	12		980.2.g.a.391.20		32
140.103	odd	12		700.2.p.c.551.15		32
140.107	even	12		980.2.o.f.411.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.2	✓	32	5.2	odd	4
140.2.o.a.31.14	yes	32	20.7	even	4
140.2.o.a.131.2	yes	32	140.47	odd	12
140.2.o.a.131.14	yes	32	35.12	even	12
700.2.p.c.451.3		32	20.3	even	4
700.2.p.c.451.15		32	5.3	odd	4
700.2.p.c.551.3		32	35.33	even	12
700.2.p.c.551.15		32	140.103	odd	12
700.2.t.c.199.7		32	5.4	even	2
700.2.t.c.199.12		32	20.19	odd	2
700.2.t.c.299.7		32	28.19	even	6
700.2.t.c.299.12		32	7.5	odd	6
700.2.t.d.199.5		32	4.3	odd	2	inner
700.2.t.d.199.10		32	1.1	even	1	trivial
700.2.t.d.299.5		32	35.19	odd	6	inner
700.2.t.d.299.10		32	140.19	even	6	inner
980.2.g.a.391.17		32	35.17	even	12
980.2.g.a.391.18		32	35.32	odd	12
980.2.g.a.391.19		32	140.67	even	12
980.2.g.a.391.20		32	140.87	odd	12
980.2.o.f.31.2		32	35.27	even	4
980.2.o.f.31.14		32	140.27	odd	4
980.2.o.f.411.2		32	140.107	even	12
980.2.o.f.411.14		32	35.2	odd	12

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 $\F_{q}$
Belyi maps

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+(0.620297 + 1.27092i) q^{2} +(-0.573616 - 0.331177i) q^{3} +(-1.23046 + 1.57669i) q^{4} +(0.0650866 - 0.934447i) q^{6} +(2.03775 - 1.68748i) q^{7} +(-2.76710 - 0.585797i) q^{8} +(-1.28064 - 2.21814i) q^{9} +(-3.12892 - 1.80648i) q^{11} +(1.22798 - 0.496915i) q^{12} -5.83027 q^{13} +(3.40866 + 1.54307i) q^{14} +(-0.971925 - 3.88012i) q^{16} +(-0.684063 + 1.18483i) q^{17} +(2.02469 - 3.00350i) q^{18} +(-2.04788 - 3.54704i) q^{19} +(-1.72774 + 0.293111i) q^{21} +(0.355029 - 5.09715i) q^{22} +(1.62259 + 2.81042i) q^{23} +(1.39325 + 1.25242i) q^{24} +(-3.61650 - 7.40979i) q^{26} +3.68354i q^{27} +(0.153273 + 5.28928i) q^{28} -5.19327 q^{29} +(4.43405 - 7.67999i) q^{31} +(4.32843 - 3.64207i) q^{32} +(1.19653 + 2.07245i) q^{33} +(-1.93014 - 0.134439i) q^{34} +(5.07311 + 0.710155i) q^{36} +(-9.34942 + 5.39789i) q^{37} +(3.23770 - 4.80291i) q^{38} +(3.34434 + 1.93085i) q^{39} -0.832730i q^{41} +(-1.44423 - 2.01400i) q^{42} +3.10642 q^{43} +(6.69828 - 2.71054i) q^{44} +(-2.56532 + 3.80548i) q^{46} +(5.97212 - 3.44801i) q^{47} +(-0.727497 + 2.54758i) q^{48} +(1.30481 - 6.87732i) q^{49} +(0.784778 - 0.453092i) q^{51} +(7.17393 - 9.19255i) q^{52} +(6.42376 + 3.70876i) q^{53} +(-4.68148 + 2.28489i) q^{54} +(-6.62717 + 3.47572i) q^{56} +2.71285i q^{57} +(-3.22137 - 6.60021i) q^{58} +(3.73928 - 6.47663i) q^{59} +(1.28652 - 0.742772i) q^{61} +(12.5111 + 0.871427i) q^{62} +(-6.35269 - 2.35894i) q^{63} +(7.31368 + 3.24192i) q^{64} +(-1.89171 + 2.80623i) q^{66} +(-1.26880 + 2.19763i) q^{67} +(-1.02640 - 2.53645i) q^{68} -2.14947i q^{69} +3.52502i q^{71} +(2.24429 + 6.88801i) q^{72} +(2.58492 - 4.47721i) q^{73} +(-12.6597 - 8.53405i) q^{74} +(8.11244 + 1.13561i) q^{76} +(-9.42434 + 1.59884i) q^{77} +(-0.379472 + 5.44808i) q^{78} +(-9.82082 + 5.67005i) q^{79} +(-2.62202 + 4.54148i) q^{81} +(1.05833 - 0.516540i) q^{82} -6.49145i q^{83} +(1.66377 - 3.08478i) q^{84} +(1.92690 + 3.94800i) q^{86} +(2.97894 + 1.71989i) q^{87} +(7.59979 + 6.83162i) q^{88} +(-8.13303 + 4.69560i) q^{89} +(-11.8806 + 9.83847i) q^{91} +(-6.42771 - 0.899777i) q^{92} +(-5.08688 + 2.93691i) q^{93} +(8.08662 + 5.45128i) q^{94} +(-3.68903 + 0.655668i) q^{96} -0.343189 q^{97} +(9.54987 - 2.60767i) q^{98} +9.25383i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{4} + 16 q^{9} + 14 q^{12} + 8 q^{13} - 2 q^{14} - 14 q^{16} - 54 q^{18} - 12 q^{21} - 36 q^{24} + 30 q^{26} - 32 q^{28} + 40 q^{29} - 60 q^{32} + 24 q^{33} + 60 q^{36} + 60 q^{37} + 46 q^{38}+ \cdots + 124 q^{98}+O(q^{100}) \) 32 * q + 2 * q^4 + 16 * q^9 + 14 * q^12 + 8 * q^13 - 2 * q^14 - 14 * q^16 - 54 * q^18 - 12 * q^21 - 36 * q^24 + 30 * q^26 - 32 * q^28 + 40 * q^29 - 60 * q^32 + 24 * q^33 + 60 * q^36 + 60 * q^37 + 46 * q^38 - 78 * q^42 + 18 * q^44 + 2 * q^46 + 28 * q^48 + 16 * q^49 + 46 * q^52 + 12 * q^53 - 12 * q^54 - 4 * q^56 - 42 * q^58 + 24 * q^61 - 8 * q^62 - 4 * q^64 + 24 * q^66 + 4 * q^68 - 90 * q^72 + 24 * q^73 - 38 * q^74 - 20 * q^77 - 36 * q^81 - 8 * q^82 + 20 * q^84 + 28 * q^86 + 78 * q^88 + 60 * q^89 - 72 * q^93 - 18 * q^94 - 60 * q^96 + 48 * q^97 + 124 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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