LMFDB - Embedded newform 700.2.t.c.199.7

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)

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")

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);

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			199.7
Character	$\chi$	$=$	700.199
Dual form			700.2.t.c.299.7

$q$ -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	0.656364	−	0.754445i	$-0.272094\pi$
$3$	0.573616	+	0.331177i	0.331177	+	0.191205i	−0.325186	+	0.945650i	$0.605427\pi$
$4$	−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	$-0.200273\pi$
$13$	5.83027			1.61703			0.808513	+	0.588478i	$0.200273\pi$
$14$	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	−0.771068	−	0.636752i	$-0.780277\pi$
$17$	0.684063	−	1.18483i	0.165910	−	0.287364i	0.936978	+	0.349389i	$0.113611\pi$
$18$	−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	0.645785	−	0.763519i	$-0.276530\pi$
$23$	−1.62259	−	2.81042i	−0.338334	−	0.586012i	−0.984120	+	0.177507i	$0.943197\pi$
$24$	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	$-0.319170\pi$
$37$	9.34942	−	5.39789i	1.53704	−	0.887408i	0.999010	−	0.0444796i	$-0.0141630\pi$
$38$	−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	$-0.576119\pi$
$43$	−3.10642			−0.473725			−0.236862	+	0.971543i	$0.576119\pi$
$44$	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	−0.867721	−	0.497051i	$-0.834416\pi$
$47$	−5.97212	+	3.44801i	−0.871124	+	0.502943i	−0.00340208	+	0.999994i	$0.501083\pi$
$48$	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	−0.0109318	−	0.999940i	$-0.503480\pi$
$53$	−6.42376	−	3.70876i	−0.882371	−	0.509437i	−0.871440	+	0.490503i	$0.836813\pi$
$54$	−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	−0.778053	−	0.628198i	$-0.783793\pi$
$67$	1.26880	−	2.19763i	0.155009	−	0.268484i	0.933062	+	0.359715i	$0.117126\pi$
$68$	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	−0.976711	−	0.214559i	$-0.931169\pi$
$73$	−2.58492	+	4.47721i	−0.302542	+	0.524018i	0.674169	+	0.738577i	$0.264502\pi$
$74$	−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	$0.115950\pi$
$83$			6.49145i			0.712529i	−0.934385	+	0.356264i	$0.884050\pi$
$84$	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	$-0.494454\pi$
$97$	0.343189			0.0348455			0.0174228	+	0.999848i	$0.494454\pi$
$98$	−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	−0.214701	−	0.976680i	$-0.568878\pi$
$103$	5.31577	−	3.06906i	0.523778	−	0.302404i	0.738479	+	0.674276i	$0.235544\pi$
$104$	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	0.989665	−	0.143399i	$-0.0458032\pi$
$107$	3.83398	+	6.64066i	0.370645	+	0.641976i	−0.619020	+	0.785375i	$0.712470\pi$
$108$	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	$-0.891522\pi$
$113$		−	7.10591i		−	0.668468i	0.942490	−	0.334234i	$-0.108478\pi$
$114$	−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	$-0.227617\pi$
$127$	17.0178			1.51008			0.755041	+	0.655677i	$0.227617\pi$
$128$	−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	0.418547	−	0.908195i	$-0.362540\pi$
$137$	−1.85754	−	1.07245i	−0.158701	−	0.0916258i	−0.577247	+	0.816570i	$0.695873\pi$
$138$	−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	$0.394807\pi$
$157$	−8.23118	+	14.2568i	−0.656919	+	1.13782i	−0.981409	+	0.191928i	$0.938526\pi$
$158$	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	0.971447	−	0.237255i	$-0.0762476\pi$
$163$	3.57806	+	6.19738i	0.280255	+	0.485416i	−0.691192	+	0.722671i	$0.742914\pi$
$164$	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	$-0.821981\pi$
$167$		−	13.7127i		−	1.06112i	0.847646	−	0.530562i	$-0.178019\pi$
$168$	−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	0.781743	−	0.623601i	$-0.214331\pi$
$173$	−1.96219	−	3.39862i	−0.149183	−	0.258392i	−0.930926	+	0.365209i	$0.880998\pi$
$174$	−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	0.957952	−	0.286928i	$-0.0926341\pi$
$193$	16.5103	+	9.53225i	1.18844	+	0.686147i	0.230489	+	0.973075i	$0.425967\pi$
$194$	−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	$0.0219235\pi$
$197$			1.93188i			0.137641i	−0.997629	+	0.0688203i	$0.978076\pi$
$198$	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	$0.190394\pi$
$223$			16.8179i			1.12621i	−0.826384	+	0.563106i	$0.809606\pi$
$224$	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	0.946443	−	0.322870i	$-0.104648\pi$
$227$	17.1766	+	9.91692i	1.14005	+	0.658209i	0.193608	+	0.981079i	$0.437981\pi$
$228$	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	−0.761195	−	0.648523i	$-0.775387\pi$
$233$	−8.85568	+	5.11283i	−0.580155	+	0.334953i	0.181040	+	0.983476i	$0.442054\pi$
$234$	−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	0.753098	−	0.657908i	$-0.228559\pi$
$257$	−3.09749	−	5.36502i	−0.193216	−	0.334660i	−0.946314	+	0.323248i	$0.895225\pi$
$258$	−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	$-0.607182\pi$
$263$	10.5768	−	18.3196i	0.652194	−	1.12963i	0.982589	−	0.185790i	$-0.0594844\pi$
$264$	−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	0.308288	−	0.951293i	$-0.400244\pi$
$277$	−6.01508	−	3.47281i	−0.361411	−	0.208661i	−0.669700	+	0.742632i	$0.733577\pi$
$278$	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	0.264044	−	0.964511i	$-0.414944\pi$
$283$	−7.38891	−	4.26599i	−0.439225	−	0.253587i	−0.703269	+	0.710924i	$0.748277\pi$
$284$	−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	$-0.763773\pi$
$293$	−25.2319			−1.47406			−0.737032	+	0.675857i	$0.763773\pi$
$294$	−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	$0.314577\pi$
$307$			29.2635i			1.67016i	−0.550132	+	0.835078i	$0.685423\pi$
$308$	−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	0.757848	−	0.652431i	$-0.226251\pi$
$313$	−3.29240	−	5.70261i	−0.186098	−	0.322331i	−0.943946	+	0.330100i	$0.892917\pi$
$314$	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	−0.802447	−	0.596724i	$-0.796469\pi$
$317$	−12.2298	+	7.06086i	−0.686892	+	0.396577i	0.115555	+	0.993301i	$0.463135\pi$
$318$	−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	$0.141322\pi$
$337$			15.7704i			0.859067i	−0.903051	+	0.429533i	$0.858678\pi$
$338$	−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	−0.904027	−	0.427476i	$-0.859403\pi$
$347$	−1.52392	+	2.63950i	−0.0818082	+	0.141696i	0.822218	+	0.569172i	$0.192736\pi$
$348$	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	−0.860209	−	0.509942i	$-0.829667\pi$
$353$	0.216411	−	0.374834i	0.0115184	−	0.0199504i	0.871727	+	0.489992i	$0.163000\pi$
$354$	−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	−0.0508965	−	0.998704i	$-0.516208\pi$
$367$	−18.0317	−	10.4106i	−0.941248	−	0.543430i	−0.890351	+	0.455274i	$0.849541\pi$
$368$	−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	−0.0486931	−	0.998814i	$-0.515506\pi$
$373$	15.2953	−	8.83072i	0.791958	−	0.457237i	0.840652	+	0.541576i	$0.182172\pi$
$374$	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	−0.987256	−	0.159138i	$-0.949129\pi$
$383$	−26.2843	+	15.1753i	−1.34307	+	0.775420i	−0.355811	+	0.934558i	$0.615795\pi$
$384$	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	0.717873	−	0.696174i	$-0.245116\pi$
$397$	−4.86104	−	8.41956i	−0.243968	−	0.422566i	−0.961841	+	0.273609i	$0.911783\pi$
$398$	−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	$-0.200499\pi$
$433$	33.6307			1.61619			0.808094	+	0.589054i	$0.200499\pi$
$434$	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	0.944852	−	0.327498i	$-0.106206\pi$
$443$	3.97386	+	6.88293i	0.188804	+	0.327018i	−0.756048	+	0.654516i	$0.772872\pi$
$444$	−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	0.0217719	−	0.999763i	$-0.493069\pi$
$457$	19.2073	−	11.0893i	0.898478	−	0.518737i	0.876706	+	0.481026i	$0.159736\pi$
$458$	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	$-0.524536\pi$
$463$	−3.31392			−0.154011			−0.0770055	+	0.997031i	$0.524536\pi$
$464$	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	0.412775	−	0.910833i	$-0.364560\pi$
$467$	30.4264	−	17.5667i	1.40797	−	0.812890i	0.995192	+	0.0979429i	$0.0312263\pi$
$468$	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	−0.935870	−	0.352344i	$-0.885385\pi$
$487$	−3.59259	+	6.22255i	−0.162796	+	0.281971i	0.773074	+	0.634315i	$0.218718\pi$
$488$	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	$0.0586914\pi$
$503$			8.22384i			0.366683i	−0.983049	+	0.183341i	$0.941309\pi$
$504$	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	−0.550874	−	0.834588i	$-0.685706\pi$
$523$	−2.36780	+	1.36705i	−0.103537	+	0.0597770i	0.447338	+	0.894365i	$0.352372\pi$
$524$	−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	$-0.353627\pi$
$547$	20.7596			0.887616			0.443808	+	0.896122i	$0.353627\pi$
$548$	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	0.802975	−	0.596012i	$-0.203249\pi$
$557$	16.2445	+	9.37876i	0.688301	+	0.397391i	−0.114674	+	0.993403i	$0.536582\pi$
$558$	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	−0.253594	−	0.967311i	$-0.581613\pi$
$563$	−28.9028	−	16.6870i	−1.21811	−	0.703274i	−0.964513	+	0.264037i	$0.914946\pi$
$564$	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	$-0.559796\pi$
$577$	18.1937	−	31.5124i	0.757414	−	1.31188i	0.944165	−	0.329473i	$-0.106871\pi$
$578$	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	$0.199535\pi$
$587$			28.4245i			1.17321i	−0.809875	+	0.586603i	$0.800465\pi$
$588$	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	0.777765	−	0.628555i	$-0.216353\pi$
$593$	−3.78574	−	6.55710i	−0.155462	−	0.269268i	−0.933227	+	0.359287i	$0.883020\pi$
$594$	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	−0.210938	−	0.977499i	$-0.567652\pi$
$607$	13.0610	−	7.54080i	0.530132	−	0.306072i	0.741070	+	0.671428i	$0.234319\pi$
$608$	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	0.406205	−	0.913782i	$-0.366852\pi$
$613$	−4.50739	−	2.60234i	−0.182052	−	0.105108i	−0.588256	+	0.808675i	$0.700185\pi$
$614$	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	$-0.744405\pi$
$617$		−	35.7404i		−	1.43885i	0.694569	−	0.719426i	$-0.255595\pi$
$618$	−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	$-0.992219\pi$
$643$		−	1.23955i		−	0.0488833i	0.999701	−	0.0244416i	$-0.00778079\pi$
$644$	−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	0.721032	−	0.692902i	$-0.243668\pi$
$647$	12.2469	+	7.07077i	0.481477	+	0.277981i	−0.239555	+	0.970883i	$0.577002\pi$
$648$	−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	−0.181593	−	0.983374i	$-0.558125\pi$
$653$	14.8017	−	8.54579i	0.579237	−	0.334423i	0.760830	+	0.648951i	$0.224792\pi$
$654$	−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	$0.0693296\pi$
$673$			11.2116i			0.432175i	−0.976374	+	0.216087i	$0.930670\pi$
$674$	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	0.899185	−	0.437568i	$-0.144160\pi$
$677$	1.83818	+	3.18383i	0.0706471	+	0.122364i	−0.828538	+	0.559933i	$0.810827\pi$
$678$	−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	$0.465649\pi$
$683$	−21.0938	+	36.5356i	−0.807133	+	1.39800i	−0.914841	+	0.403814i	$0.867684\pi$
$684$	−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	$-0.751173\pi$
$727$		−	37.9906i		−	1.40899i	0.709707	−	0.704497i	$-0.248827\pi$
$728$	−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	$0.0271835\pi$
$733$	15.4876	+	26.8252i	0.572046	+	0.990813i	−0.424310	+	0.905517i	$0.639483\pi$
$734$	−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	$-0.265312\pi$
$743$	36.6505			1.34457			0.672287	+	0.740290i	$0.265312\pi$
$744$	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	$-0.991646\pi$
$757$		−	1.44394i		−	0.0524807i	0.999656	−	0.0262404i	$-0.00835352\pi$
$758$	−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	−0.641857	−	0.766824i	$-0.721836\pi$
$773$	9.54086	−	16.5252i	0.343161	−	0.594372i	0.985018	+	0.172452i	$0.0551691\pi$
$774$	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	0.419176	−	0.907905i	$-0.362319\pi$
$787$	−4.41858	−	2.55107i	−0.157505	−	0.0909358i	−0.576681	+	0.816969i	$0.695652\pi$
$788$	−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	$-0.350148\pi$
$797$	25.6101			0.907155			0.453578	+	0.891217i	$0.350148\pi$
$798$	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	−0.929969	−	0.367639i	$-0.880166\pi$
$823$	−4.20565	+	7.28440i	−0.146600	+	0.253918i	0.783369	+	0.621557i	$0.213500\pi$
$824$	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	$-0.475989\pi$
$827$	4.33435			0.150720			0.0753601	+	0.997156i	$0.475989\pi$
$828$	−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	$-0.406267\pi$
$853$	16.9533			0.580469			0.290234	+	0.956956i	$0.406267\pi$
$854$	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	$-0.501414\pi$
$857$	25.2872	−	43.7988i	0.863795	−	1.49614i	0.868238	−	0.496147i	$-0.165252\pi$
$858$	−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	0.748633	−	0.662985i	$-0.230711\pi$
$863$	−5.87084	−	10.1686i	−0.199846	−	0.346143i	−0.948478	+	0.316842i	$0.897377\pi$
$864$	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	−0.810016	−	0.586408i	$-0.800542\pi$
$877$	−20.9426	+	12.0912i	−0.707180	+	0.408290i	0.102836	+	0.994698i	$0.467208\pi$
$878$	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	$-0.560576\pi$
$883$	−11.2418			−0.378315			−0.189158	+	0.981947i	$0.560576\pi$
$884$	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	−0.964009	−	0.265871i	$-0.914340\pi$
$887$	−36.2085	+	20.9050i	−1.21576	+	0.701920i	−0.251753	+	0.967792i	$0.581007\pi$
$888$	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	−0.988302	−	0.152508i	$-0.951265\pi$
$907$	−10.9044	+	18.8870i	−0.362076	+	0.627133i	0.626227	+	0.779641i	$0.284598\pi$
$908$	−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	$-0.442979\pi$
$937$	10.9083			0.356358			0.178179	+	0.983998i	$0.442979\pi$
$938$	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	0.723175	−	0.690664i	$-0.242682\pi$
$947$	−7.27929	−	12.6081i	−0.236545	−	0.409708i	−0.959721	+	0.280956i	$0.909349\pi$
$948$	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	$0.0511542\pi$
$953$			9.87954i			0.320030i	−0.987115	+	0.160015i	$0.948846\pi$
$954$	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	$-0.419800\pi$
$967$	15.5047			0.498597			0.249298	+	0.968427i	$0.419800\pi$
$968$	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	0.995601	−	0.0936930i	$-0.0298672\pi$
$977$	44.1430	+	25.4860i	1.41226	+	0.815369i	0.416660	+	0.909062i	$0.363201\pi$
$978$	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	0.798921	−	0.601436i	$-0.205404\pi$
$983$	21.2423	+	12.2642i	0.677523	+	0.391168i	−0.121398	+	0.992604i	$0.538738\pi$
$984$	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	−0.968749	−	0.248045i	$-0.920212\pi$
$997$	−8.51148	+	14.7423i	−0.269561	+	0.466894i	0.699187	+	0.714939i	$0.253545\pi$
$998$	46.5075	+	31.3512i	1.47217	+	0.992406i
$999$	−19.8834	−	34.4390i	−0.629082	−	1.08960i

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

)

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.2	✓	32	5.3	odd	4
140.2.o.a.31.14	yes	32	20.3	even	4
140.2.o.a.131.2	yes	32	140.103	odd	12
140.2.o.a.131.14	yes	32	35.33	even	12
700.2.p.c.451.3		32	20.7	even	4
700.2.p.c.451.15		32	5.2	odd	4
700.2.p.c.551.3		32	35.12	even	12
700.2.p.c.551.15		32	140.47	odd	12
700.2.t.c.199.7		32	1.1	even	1	trivial
700.2.t.c.199.12		32	4.3	odd	2	inner
700.2.t.c.299.7		32	140.19	even	6	inner
700.2.t.c.299.12		32	35.19	odd	6	inner
700.2.t.d.199.5		32	20.19	odd	2
700.2.t.d.199.10		32	5.4	even	2
700.2.t.d.299.5		32	7.5	odd	6
700.2.t.d.299.10		32	28.19	even	6
980.2.g.a.391.17		32	35.3	even	12
980.2.g.a.391.18		32	35.18	odd	12
980.2.g.a.391.19		32	140.123	even	12
980.2.g.a.391.20		32	140.3	odd	12
980.2.o.f.31.2		32	35.13	even	4
980.2.o.f.31.14		32	140.83	odd	4
980.2.o.f.411.2		32	140.23	even	12
980.2.o.f.411.14		32	35.23	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	700.2.t.c.199.7

Level	$700$
Weight	$2$
Character	700.199
Analytic conductor	$5.590$
Analytic rank	$0$
Dimension	$32$
Inner twists	$4$