LMFDB - Embedded newform 880.2.w.a.221.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(221,880)] 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("880.221"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.w (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			221.18
Character	$\chi$	$=$	880.221
Dual form			880.2.w.a.661.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0549372 - 1.41315i) q^{2} +(-1.66048 - 1.66048i) q^{3} +(-1.99396 + 0.155268i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-2.25527 + 2.43772i) q^{6} +1.68953i q^{7} +(0.328960 + 2.80923i) q^{8} +2.51436i q^{9} +(-1.03809 - 0.960399i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(3.56875 + 3.05311i) q^{12} +(3.39375 + 3.39375i) q^{13} +(2.38755 - 0.0928179i) q^{14} -2.34827 q^{15} +(3.95178 - 0.619199i) q^{16} +0.675956 q^{17} +(3.55315 - 0.138132i) q^{18} +(1.94870 + 1.94870i) q^{19} +(-1.30015 + 1.51974i) q^{20} +(2.80542 - 2.80542i) q^{21} +(1.03809 + 0.960399i) q^{22} +1.68037i q^{23} +(4.11843 - 5.21089i) q^{24} -1.00000i q^{25} +(4.60943 - 4.98231i) q^{26} +(-0.806401 + 0.806401i) q^{27} +(-0.262331 - 3.36886i) q^{28} +(6.92603 + 6.92603i) q^{29} +(0.129007 + 3.31844i) q^{30} -0.0481311 q^{31} +(-1.09212 - 5.55043i) q^{32} +2.34827 q^{33} +(-0.0371351 - 0.955224i) q^{34} +(1.19468 + 1.19468i) q^{35} +(-0.390400 - 5.01353i) q^{36} +(-2.65562 + 2.65562i) q^{37} +(2.64674 - 2.86085i) q^{38} -11.2705i q^{39} +(2.21904 + 1.75382i) q^{40} -10.6774i q^{41} +(-4.11859 - 3.81035i) q^{42} +(-3.53666 + 3.53666i) q^{43} +(1.30015 - 1.51974i) q^{44} +(1.77792 + 1.77792i) q^{45} +(2.37461 - 0.0923147i) q^{46} +0.257353 q^{47} +(-7.59000 - 5.53367i) q^{48} +4.14549 q^{49} +(-1.41315 + 0.0549372i) q^{50} +(-1.12241 - 1.12241i) q^{51} +(-7.29397 - 6.24008i) q^{52} +(-2.73111 + 2.73111i) q^{53} +(1.18386 + 1.09526i) q^{54} +1.00000i q^{55} +(-4.74628 + 0.555787i) q^{56} -6.47153i q^{57} +(9.40700 - 10.1680i) q^{58} +(-5.31352 + 5.31352i) q^{59} +(4.68236 - 0.364612i) q^{60} +(0.469577 + 0.469577i) q^{61} +(0.00264418 + 0.0680162i) q^{62} -4.24808 q^{63} +(-7.78357 + 1.84825i) q^{64} +4.79949 q^{65} +(-0.129007 - 3.31844i) q^{66} +(-2.55331 - 2.55331i) q^{67} +(-1.34783 + 0.104955i) q^{68} +(2.79021 - 2.79021i) q^{69} +(1.62262 - 1.75389i) q^{70} -5.41449i q^{71} +(-7.06341 + 0.827121i) q^{72} +4.44466i q^{73} +(3.89867 + 3.60688i) q^{74} +(-1.66048 + 1.66048i) q^{75} +(-4.18820 - 3.58306i) q^{76} +(-1.19468 - 1.19468i) q^{77} +(-15.9268 + 0.619169i) q^{78} +15.2127 q^{79} +(2.35649 - 3.23217i) q^{80} +10.2211 q^{81} +(-15.0888 + 0.586587i) q^{82} +(-7.93224 - 7.93224i) q^{83} +(-5.15832 + 6.02950i) q^{84} +(0.477973 - 0.477973i) q^{85} +(5.19211 + 4.80352i) q^{86} -23.0010i q^{87} +(-2.21904 - 1.75382i) q^{88} +4.40246i q^{89} +(2.41478 - 2.61013i) q^{90} +(-5.73385 + 5.73385i) q^{91} +(-0.260908 - 3.35060i) q^{92} +(0.0799204 + 0.0799204i) q^{93} +(-0.0141383 - 0.363678i) q^{94} +2.75587 q^{95} +(-7.40292 + 11.0298i) q^{96} +1.04568 q^{97} +(-0.227741 - 5.85818i) q^{98} +(-1.77792 - 1.77792i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 12 q^{6} - 4 q^{10} + 12 q^{12} - 8 q^{14} + 8 q^{15} + 4 q^{16} + 56 q^{17} + 20 q^{18} + 8 q^{19} - 8 q^{20} + 4 q^{22} - 24 q^{24} - 24 q^{27} + 20 q^{28} - 20 q^{30} + 20 q^{32} - 8 q^{33} + 4 q^{34}+ \cdots - 60 q^{98}+O(q^{100}) $ 72 * q + 12 * q^6 - 4 * q^10 + 12 * q^12 - 8 * q^14 + 8 * q^15 + 4 * q^16 + 56 * q^17 + 20 * q^18 + 8 * q^19 - 8 * q^20 + 4 * q^22 - 24 * q^24 - 24 * q^27 + 20 * q^28 - 20 * q^30 + 20 * q^32 - 8 * q^33 + 4 * q^34 - 60 * q^36 + 12 * q^38 - 40 * q^42 + 8 * q^44 - 20 * q^46 + 40 * q^47 + 20 * q^48 - 24 * q^49 + 32 * q^51 - 84 * q^52 + 72 * q^54 + 8 * q^56 - 8 * q^58 + 32 * q^60 - 16 * q^61 - 96 * q^62 + 36 * q^64 - 40 * q^65 + 20 * q^66 - 76 * q^68 - 16 * q^69 + 24 * q^70 + 20 * q^72 + 56 * q^74 + 56 * q^76 - 132 * q^78 - 16 * q^79 + 56 * q^81 + 36 * q^82 - 40 * q^83 - 152 * q^84 + 16 * q^85 + 56 * q^86 - 36 * q^90 + 88 * q^91 + 80 * q^92 + 48 * q^93 - 76 * q^94 - 32 * q^96 - 64 * q^97 - 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.0549372	−	1.41315i	−0.0388464	−	0.999245i
$2$	−0.0549372	−	1.41315i	−0.0388464	−	0.999245i
$3$	−1.66048	−	1.66048i	−0.958676	−	0.958676i	0.0405036	−	0.999179i	$-0.487104\pi$
$3$	−1.66048	−	1.66048i	−0.958676	−	0.958676i	−0.999179	+	0.0405036i	$0.987104\pi$
$4$	−1.99396	+	0.155268i	−0.996982	+	0.0776342i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	−2.25527	+	2.43772i	−0.920711	+	0.995193i
$7$			1.68953i			0.638582i	0.947657	+	0.319291i	$0.103445\pi$
$7$			1.68953i			0.638582i	−0.947657	+	0.319291i	$0.896555\pi$
$8$	0.328960	+	2.80923i	0.116305	+	0.993214i
$9$			2.51436i			0.838118i
$10$	−1.03809	−	0.960399i	−0.328273	−	0.303705i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$12$	3.56875	+	3.05311i	1.03021	+	0.881356i
$13$	3.39375	+	3.39375i	0.941258	+	0.941258i	0.998368	−	0.0571098i	$-0.0181885\pi$
$13$	3.39375	+	3.39375i	0.941258	+	0.941258i	−0.0571098	+	0.998368i	$0.518189\pi$
$14$	2.38755	−	0.0928179i	0.638100	−	0.0248066i
$15$	−2.34827			−0.606320
$16$	3.95178	−	0.619199i	0.987946	−	0.154800i
$17$	0.675956			0.163943			0.0819717	−	0.996635i	$-0.473878\pi$
$17$	0.675956			0.163943			0.0819717	+	0.996635i	$0.473878\pi$
$18$	3.55315	−	0.138132i	0.837486	−	0.0325579i
$19$	1.94870	+	1.94870i	0.447062	+	0.447062i	0.894377	−	0.447315i	$-0.147620\pi$
$19$	1.94870	+	1.94870i	0.447062	+	0.447062i	−0.447315	+	0.894377i	$0.647620\pi$
$20$	−1.30015	+	1.51974i	−0.290723	+	0.339823i
$21$	2.80542	−	2.80542i	0.612193	−	0.612193i
$22$	1.03809	+	0.960399i	0.221322	+	0.204758i
$23$			1.68037i			0.350381i	0.984535	+	0.175191i	$0.0560542\pi$
$23$			1.68037i			0.350381i	−0.984535	+	0.175191i	$0.943946\pi$
$24$	4.11843	−	5.21089i	0.840671	−	1.06367i
$25$		−	1.00000i		−	0.200000i
$26$	4.60943	−	4.98231i	0.903983	−	0.977112i
$27$	−0.806401	+	0.806401i	−0.155192	+	0.155192i
$28$	−0.262331	−	3.36886i	−0.0495758	−	0.636655i
$29$	6.92603	+	6.92603i	1.28613	+	1.28613i	0.937117	+	0.349015i	$0.113484\pi$
$29$	6.92603	+	6.92603i	1.28613	+	1.28613i	0.349015	+	0.937117i	$0.386516\pi$
$30$	0.129007	+	3.31844i	0.0235534	+	0.605862i
$31$	−0.0481311			−0.00864459			−0.00432230	−	0.999991i	$-0.501376\pi$
$31$	−0.0481311			−0.00864459			−0.00432230	+	0.999991i	$0.501376\pi$
$32$	−1.09212	−	5.55043i	−0.193061	−	0.981187i
$33$	2.34827			0.408781
$34$	−0.0371351	−	0.955224i	−0.00636861	−	0.163820i
$35$	1.19468	+	1.19468i	0.201937	+	0.201937i
$36$	−0.390400	−	5.01353i	−0.0650667	−	0.835589i
$37$	−2.65562	+	2.65562i	−0.436581	+	0.436581i	−0.890860	−	0.454279i	$-0.849897\pi$
$37$	−2.65562	+	2.65562i	−0.436581	+	0.436581i	0.454279	+	0.890860i	$0.349897\pi$
$38$	2.64674	−	2.86085i	0.429358	−	0.464091i
$39$		−	11.2705i		−	1.80472i
$40$	2.21904	+	1.75382i	0.350861	+	0.277303i
$41$		−	10.6774i		−	1.66753i	−0.552116	−	0.833767i	$-0.686180\pi$
$41$		−	10.6774i		−	1.66753i	0.552116	−	0.833767i	$-0.313820\pi$
$42$	−4.11859	−	3.81035i	−0.635513	−	0.587950i
$43$	−3.53666	+	3.53666i	−0.539335	+	0.539335i	−0.923334	−	0.383999i	$-0.874547\pi$
$43$	−3.53666	+	3.53666i	−0.539335	+	0.539335i	0.383999	+	0.923334i	$0.374547\pi$
$44$	1.30015	−	1.51974i	0.196006	−	0.229109i
$45$	1.77792	+	1.77792i	0.265036	+	0.265036i
$46$	2.37461	−	0.0923147i	0.350117	−	0.0136111i
$47$	0.257353			0.0375388			0.0187694	−	0.999824i	$-0.494025\pi$
$47$	0.257353			0.0375388			0.0187694	+	0.999824i	$0.494025\pi$
$48$	−7.59000	−	5.53367i	−1.09552	−	0.798717i
$49$	4.14549			0.592213
$50$	−1.41315	+	0.0549372i	−0.199849	+	0.00776929i
$51$	−1.12241	−	1.12241i	−0.157169	−	0.157169i
$52$	−7.29397	−	6.24008i	−1.01149	−	0.865343i
$53$	−2.73111	+	2.73111i	−0.375147	+	0.375147i	−0.869348	−	0.494201i	$-0.835461\pi$
$53$	−2.73111	+	2.73111i	−0.375147	+	0.375147i	0.494201	+	0.869348i	$0.335461\pi$
$54$	1.18386	+	1.09526i	0.161104	+	0.149046i
$55$			1.00000i			0.134840i
$56$	−4.74628	+	0.555787i	−0.634248	+	0.0742702i
$57$		−	6.47153i		−	0.857175i
$58$	9.40700	−	10.1680i	1.23520	−	1.33512i
$59$	−5.31352	+	5.31352i	−0.691762	+	0.691762i	−0.962619	−	0.270858i	$-0.912693\pi$
$59$	−5.31352	+	5.31352i	−0.691762	+	0.691762i	0.270858	+	0.962619i	$0.412693\pi$
$60$	4.68236	−	0.364612i	0.604490	−	0.0470712i
$61$	0.469577	+	0.469577i	0.0601231	+	0.0601231i	0.736529	−	0.676406i	$-0.236463\pi$
$61$	0.469577	+	0.469577i	0.0601231	+	0.0601231i	−0.676406	+	0.736529i	$0.736463\pi$
$62$	0.00264418	+	0.0680162i	0.000335812	+	0.00863807i
$63$	−4.24808			−0.535207
$64$	−7.78357	+	1.84825i	−0.972946	+	0.231031i
$65$	4.79949			0.595304
$66$	−0.129007	−	3.31844i	−0.0158797	−	0.408472i
$67$	−2.55331	−	2.55331i	−0.311937	−	0.311937i	0.533723	−	0.845660i	$-0.320793\pi$
$67$	−2.55331	−	2.55331i	−0.311937	−	0.311937i	−0.845660	+	0.533723i	$0.820793\pi$
$68$	−1.34783	+	0.104955i	−0.163449	+	0.0127276i
$69$	2.79021	−	2.79021i	0.335902	−	0.335902i
$70$	1.62262	−	1.75389i	0.193940	−	0.209630i
$71$		−	5.41449i		−	0.642582i	−0.946981	−	0.321291i	$-0.895883\pi$
$71$		−	5.41449i		−	0.642582i	0.946981	−	0.321291i	$-0.104117\pi$
$72$	−7.06341	+	0.827121i	−0.832431	+	0.0974772i
$73$			4.44466i			0.520208i	0.965581	+	0.260104i	$0.0837568\pi$
$73$			4.44466i			0.520208i	−0.965581	+	0.260104i	$0.916243\pi$
$74$	3.89867	+	3.60688i	0.453211	+	0.419292i
$75$	−1.66048	+	1.66048i	−0.191735	+	0.191735i
$76$	−4.18820	−	3.58306i	−0.480420	−	0.411005i
$77$	−1.19468	−	1.19468i	−0.136146	−	0.136146i
$78$	−15.9268	+	0.619169i	−1.80336	+	0.0701070i
$79$	15.2127			1.71156			0.855781	−	0.517339i	$-0.173077\pi$
$79$	15.2127			1.71156			0.855781	+	0.517339i	$0.173077\pi$
$80$	2.35649	−	3.23217i	0.263464	−	0.361368i
$81$	10.2211			1.13568
$82$	−15.0888	+	0.586587i	−1.66628	+	0.0647778i
$83$	−7.93224	−	7.93224i	−0.870676	−	0.870676i	0.121870	−	0.992546i	$-0.461111\pi$
$83$	−7.93224	−	7.93224i	−0.870676	−	0.870676i	−0.992546	+	0.121870i	$0.961111\pi$
$84$	−5.15832	+	6.02950i	−0.562818	+	0.657873i
$85$	0.477973	−	0.477973i	0.0518434	−	0.0518434i
$86$	5.19211	+	4.80352i	0.559879	+	0.517977i
$87$		−	23.0010i		−	2.46597i
$88$	−2.21904	−	1.75382i	−0.236550	−	0.186958i
$89$			4.40246i			0.466660i	0.972398	+	0.233330i	$0.0749623\pi$
$89$			4.40246i			0.466660i	−0.972398	+	0.233330i	$0.925038\pi$
$90$	2.41478	−	2.61013i	0.254541	−	0.275132i
$91$	−5.73385	+	5.73385i	−0.601071	+	0.601071i
$92$	−0.260908	−	3.35060i	−0.0272016	−	0.349324i
$93$	0.0799204	+	0.0799204i	0.00828736	+	0.00828736i
$94$	−0.0141383	−	0.363678i	−0.00145825	−	0.0375105i
$95$	2.75587			0.282747
$96$	−7.40292	+	11.0298i	−0.755557	+	1.12572i
$97$	1.04568			0.106172			0.0530862	−	0.998590i	$-0.483094\pi$
$97$	1.04568			0.106172			0.0530862	+	0.998590i	$0.483094\pi$
$98$	−0.227741	−	5.85818i	−0.0230054	−	0.591766i
$99$	−1.77792	−	1.77792i	−0.178687	−	0.178687i
$100$	0.155268	+	1.99396i	0.0155268	+	0.199396i
$101$	7.91671	−	7.91671i	0.787743	−	0.787743i	−0.193381	−	0.981124i	$-0.561945\pi$
$101$	7.91671	−	7.91671i	0.787743	−	0.787743i	0.981124	+	0.193381i	$0.0619454\pi$
$102$	−1.52446	+	1.64779i	−0.150944	+	0.163155i
$103$			14.0940i			1.38873i	0.719624	+	0.694364i	$0.244314\pi$
$103$			14.0940i			1.38873i	−0.719624	+	0.694364i	$0.755686\pi$
$104$	−8.41744	+	10.6503i	−0.825397	+	1.04434i
$105$		−	3.96746i		−	0.387185i
$106$	4.00950	+	3.70942i	0.389437	+	0.360291i
$107$	11.5533	−	11.5533i	1.11690	−	1.11690i	0.124701	−	0.992194i	$-0.460203\pi$
$107$	11.5533	−	11.5533i	1.11690	−	1.11690i	0.992194	−	0.124701i	$-0.0397970\pi$
$108$	1.48273	−	1.73314i	0.142675	−	0.166772i
$109$	14.0368	+	14.0368i	1.34448	+	1.34448i	0.891545	+	0.452932i	$0.149622\pi$
$109$	14.0368	+	14.0368i	1.34448	+	1.34448i	0.452932	+	0.891545i	$0.350378\pi$
$110$	1.41315	−	0.0549372i	0.134738	−	0.00523805i
$111$	8.81917			0.837079
$112$	1.04616	+	6.67665i	0.0988524	+	0.630885i
$113$	6.58501			0.619466			0.309733	−	0.950824i	$-0.399760\pi$
$113$	6.58501			0.619466			0.309733	+	0.950824i	$0.399760\pi$
$114$	−9.14521	+	0.355527i	−0.856528	+	0.0332982i
$115$	1.18820	+	1.18820i	0.110800	+	0.110800i
$116$	−14.8857	−	12.7349i	−1.38210	−	1.18240i
$117$	−8.53310	+	8.53310i	−0.788886	+	0.788886i
$118$	7.80069	+	7.21687i	0.718112	+	0.664367i
$119$			1.14205i			0.104691i
$120$	−0.772485	−	6.59683i	−0.0705179	−	0.602205i
$121$		−	1.00000i		−	0.0909091i
$122$	0.637783	−	0.689378i	0.0577422	−	0.0624133i
$123$	−17.7296	+	17.7296i	−1.59862	+	1.59862i
$124$	0.0959716	−	0.00747323i	0.00861850	−	0.000671116i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	0.233377	+	6.00315i	0.0207909	+	0.534803i
$127$	−7.77791			−0.690178			−0.345089	−	0.938570i	$-0.612151\pi$
$127$	−7.77791			−0.690178			−0.345089	+	0.938570i	$0.612151\pi$
$128$	3.03945	+	10.8978i	0.268652	+	0.963237i
$129$	11.7451			1.03410
$130$	−0.263671	−	6.78239i	−0.0231254	−	0.594855i
$131$	8.47391	+	8.47391i	0.740369	+	0.740369i	0.972649	−	0.232280i	$-0.0746186\pi$
$131$	8.47391	+	8.47391i	0.740369	+	0.740369i	−0.232280	+	0.972649i	$0.574619\pi$
$132$	−4.68236	+	0.364612i	−0.407547	+	0.0317354i
$133$	−3.29238	+	3.29238i	−0.285486	+	0.285486i
$134$	−3.46793	+	3.74848i	−0.299584	+	0.323819i
$135$			1.14042i			0.0981520i
$136$	0.222362	+	1.89892i	0.0190674	+	0.162831i
$137$		−	3.01638i		−	0.257707i	−0.991664	−	0.128854i	$-0.958870\pi$
$137$		−	3.01638i		−	0.257707i	0.991664	−	0.128854i	$-0.0411297\pi$
$138$	−4.09626	−	3.78969i	−0.348697	−	0.322600i
$139$	−11.4183	+	11.4183i	−0.968492	+	0.968492i	−0.999519	−	0.0310270i	$-0.990122\pi$
$139$	−11.4183	+	11.4183i	−0.968492	+	0.968492i	0.0310270	+	0.999519i	$0.490122\pi$
$140$	−2.56764	−	2.19665i	−0.217005	−	0.185651i
$141$	−0.427329	−	0.427329i	−0.0359876	−	0.0359876i
$142$	−7.65146	+	0.297457i	−0.642097	+	0.0249620i
$143$	−4.79949			−0.401354
$144$	1.55689	+	9.93619i	0.129741	+	0.828016i
$145$	9.79489			0.813421
$146$	6.28095	−	0.244177i	0.519815	−	0.0202082i
$147$	−6.88348	−	6.88348i	−0.567740	−	0.567740i
$148$	4.88287	−	5.70754i	0.401370	−	0.469157i
$149$	−0.865438	+	0.865438i	−0.0708994	+	0.0708994i	−0.741667	−	0.670768i	$-0.765965\pi$
$149$	−0.865438	+	0.865438i	−0.0708994	+	0.0708994i	0.670768	+	0.741667i	$0.265965\pi$
$150$	2.43772	+	2.25527i	0.199039	+	0.184142i
$151$		−	0.777348i		−	0.0632597i	−0.999500	−	0.0316298i	$-0.989930\pi$
$151$		−	0.777348i		−	0.0632597i	0.999500	−	0.0316298i	$-0.0100698\pi$
$152$	−4.83330	+	6.11539i	−0.392032	+	0.496023i
$153$			1.69959i			0.137404i
$154$	−1.62262	+	1.75389i	−0.130755	+	0.141332i
$155$	−0.0340338	+	0.0340338i	−0.00273366	+	0.00273366i
$156$	1.74995	+	22.4729i	0.140108	+	1.79928i
$157$	1.94995	+	1.94995i	0.155623	+	0.155623i	0.780624	−	0.625001i	$-0.214902\pi$
$157$	1.94995	+	1.94995i	0.155623	+	0.155623i	−0.625001	+	0.780624i	$0.714902\pi$
$158$	−0.835742	−	21.4978i	−0.0664881	−	1.71027i
$159$	9.06988			0.719289
$160$	−4.69699	−	3.15250i	−0.371330	−	0.249227i
$161$	−2.83903			−0.223747
$162$	−0.561517	−	14.4439i	−0.0441170	−	1.13482i
$163$	13.6060	+	13.6060i	1.06570	+	1.06570i	0.997684	+	0.0680185i	$0.0216677\pi$
$163$	13.6060	+	13.6060i	1.06570	+	1.06570i	0.0680185	+	0.997684i	$0.478332\pi$
$164$	1.65787	+	21.2904i	0.129458	+	1.66250i
$165$	1.66048	−	1.66048i	0.129268	−	0.129268i
$166$	−10.7736	+	11.6452i	−0.836196	+	0.903842i
$167$		−	0.200763i		−	0.0155355i	−0.999970	−	0.00776774i	$-0.997527\pi$
$167$		−	0.200763i		−	0.0155355i	0.999970	−	0.00776774i	$-0.00247257\pi$
$168$	8.80395	+	6.95821i	0.679240	+	0.536838i
$169$			10.0351i			0.771934i
$170$	−0.701704	−	0.649187i	−0.0538182	−	0.0497904i
$171$	−4.89972	+	4.89972i	−0.374691	+	0.374691i
$172$	6.50284	−	7.60110i	0.495837	−	0.579578i
$173$	8.26463	+	8.26463i	0.628348	+	0.628348i	0.947652	−	0.319304i	$-0.103449\pi$
$173$	8.26463	+	8.26463i	0.628348	+	0.628348i	−0.319304	+	0.947652i	$0.603449\pi$
$174$	−32.5038	+	1.26361i	−2.46411	+	0.0957940i
$175$	1.68953			0.127716
$176$	−2.35649	+	3.23217i	−0.177627	+	0.243634i
$177$	17.6459			1.32635
$178$	6.22133	−	0.241859i	0.466308	−	0.0181281i
$179$	0.189806	+	0.189806i	0.0141868	+	0.0141868i	0.714165	−	0.699978i	$-0.246807\pi$
$179$	0.189806	+	0.189806i	0.0141868	+	0.0141868i	−0.699978	+	0.714165i	$0.746807\pi$
$180$	−3.82116	−	3.26905i	−0.284812	−	0.243661i
$181$	15.7398	−	15.7398i	1.16993	−	1.16993i	0.187703	−	0.982226i	$-0.439896\pi$
$181$	15.7398	−	15.7398i	1.16993	−	1.16993i	0.982226	−	0.187703i	$-0.0601041\pi$
$182$	8.41777	+	7.78776i	0.623966	+	0.577267i
$183$		−	1.55944i		−	0.115277i
$184$	−4.72055	+	0.552774i	−0.348003	+	0.0407510i
$185$			3.75561i			0.276118i
$186$	0.108549	−	0.117330i	0.00795917	−	0.00860304i
$187$	−0.477973	+	0.477973i	−0.0349528	+	0.0349528i
$188$	−0.513153	+	0.0399589i	−0.0374255	+	0.00291430i
$189$	−1.36244	−	1.36244i	−0.0991028	−	0.0991028i
$190$	−0.151400	−	3.89445i	−0.0109837	−	0.282533i
$191$	−1.62672			−0.117705			−0.0588527	−	0.998267i	$-0.518744\pi$
$191$	−1.62672			−0.117705			−0.0588527	+	0.998267i	$0.518744\pi$
$192$	15.9934	+	9.85546i	1.15422	+	0.711256i
$193$	−22.9626			−1.65288			−0.826442	−	0.563022i	$-0.809639\pi$
$193$	−22.9626			−1.65288			−0.826442	+	0.563022i	$0.809639\pi$
$194$	−0.0574465	−	1.47769i	−0.00412442	−	0.106092i
$195$	−7.96944	−	7.96944i	−0.570703	−	0.570703i
$196$	−8.26596	+	0.643664i	−0.590426	+	0.0459760i
$197$	−9.46596	+	9.46596i	−0.674422	+	0.674422i	−0.958732	−	0.284311i	$-0.908235\pi$
$197$	−9.46596	+	9.46596i	−0.674422	+	0.674422i	0.284311	+	0.958732i	$0.408235\pi$
$198$	−2.41478	+	2.61013i	−0.171611	+	0.185494i
$199$		−	19.8428i		−	1.40662i	−0.710884	−	0.703309i	$-0.751705\pi$
$199$		−	19.8428i		−	1.40662i	0.710884	−	0.703309i	$-0.248295\pi$
$200$	2.80923	−	0.328960i	0.198643	−	0.0232610i
$201$			8.47942i			0.598092i
$202$	−11.6224	−	10.7526i	−0.817749	−	0.756547i
$203$	−11.7017	+	11.7017i	−0.821301	+	0.821301i
$204$	2.41231	+	2.06377i	0.168896	+	0.144493i
$205$	−7.55008	−	7.55008i	−0.527321	−	0.527321i
$206$	19.9169	−	0.774287i	1.38768	−	0.0539471i
$207$	−4.22504			−0.293661
$208$	15.5128	+	11.3100i	1.07562	+	0.784205i
$209$	−2.75587			−0.190628
$210$	−5.60661	+	0.217961i	−0.386893	+	0.0150408i
$211$	−2.12671	−	2.12671i	−0.146409	−	0.146409i	0.630103	−	0.776512i	$-0.283013\pi$
$211$	−2.12671	−	2.12671i	−0.146409	−	0.146409i	−0.776512	+	0.630103i	$0.783013\pi$
$212$	5.02168	−	5.86979i	0.344891	−	0.403139i
$213$	−8.99062	+	8.99062i	−0.616027	+	0.616027i
$214$	−16.9611	−	15.6917i	−1.15944	−	1.07266i
$215$			5.00159i			0.341106i
$216$	−2.53064	−	2.00009i	−0.172188	−	0.136089i
$217$		−	0.0813188i		−	0.00552028i
$218$	19.0648	−	20.6071i	1.29123	−	1.39569i
$219$	7.38024	−	7.38024i	0.498711	−	0.498711i
$220$	−0.155268	−	1.99396i	−0.0104682	−	0.134433i
$221$	2.29403	+	2.29403i	0.154313	+	0.154313i
$222$	−0.484500	−	12.4628i	−0.0325175	−	0.836447i
$223$	−4.80697			−0.321899			−0.160949	−	0.986963i	$-0.551456\pi$
$223$	−4.80697			−0.321899			−0.160949	+	0.986963i	$0.551456\pi$
$224$	9.37761	−	1.84517i	0.626568	−	0.123285i
$225$	2.51436			0.167624
$226$	−0.361762	−	9.30558i	−0.0240640	−	0.618998i
$227$	15.5347	+	15.5347i	1.03107	+	1.03107i	0.999502	+	0.0315699i	$0.0100507\pi$
$227$	15.5347	+	15.5347i	1.03107	+	1.03107i	0.0315699	+	0.999502i	$0.489949\pi$
$228$	1.00482	+	12.9040i	0.0665461	+	0.854588i
$229$	−10.4084	+	10.4084i	−0.687806	+	0.687806i	−0.961747	−	0.273940i	$-0.911673\pi$
$229$	−10.4084	+	10.4084i	−0.687806	+	0.687806i	0.273940	+	0.961747i	$0.411673\pi$
$230$	1.61382	−	1.74438i	0.106412	−	0.115021i
$231$			3.96746i			0.261040i
$232$	−17.1785	+	21.7352i	−1.12782	+	1.42699i
$233$			11.2408i			0.736411i	0.929744	+	0.368206i	$0.120028\pi$
$233$			11.2408i			0.736411i	−0.929744	+	0.368206i	$0.879972\pi$
$234$	12.5273	+	11.5897i	0.818936	+	0.757645i
$235$	0.181976	−	0.181976i	0.0118708	−	0.0118708i
$236$	9.76995	−	11.4200i	0.635969	−	0.743378i
$237$	−25.2603	−	25.2603i	−1.64083	−	1.64083i
$238$	1.61388	−	0.0627408i	0.104612	−	0.00406688i
$239$	27.2900			1.76524			0.882621	−	0.470086i	$-0.155777\pi$
$239$	27.2900			1.76524			0.882621	+	0.470086i	$0.155777\pi$
$240$	−9.27984	+	1.45404i	−0.599011	+	0.0938582i
$241$	−6.99069			−0.450310			−0.225155	−	0.974323i	$-0.572289\pi$
$241$	−6.99069			−0.450310			−0.225155	+	0.974323i	$0.572289\pi$
$242$	−1.41315	+	0.0549372i	−0.0908405	+	0.00353149i
$243$	−14.5527	−	14.5527i	−0.933553	−	0.933553i
$244$	−1.00923	−	0.863409i	−0.0646093	−	0.0552741i
$245$	2.93130	−	2.93130i	0.187274	−	0.187274i
$246$	26.0285	+	24.0805i	1.65952	+	1.53532i
$247$			13.2268i			0.841601i
$248$	−0.0158332	−	0.135211i	−0.00100541	−	0.00858593i
$249$			26.3426i			1.66939i
$250$	−0.960399	+	1.03809i	−0.0607410	+	0.0656547i
$251$	4.51783	−	4.51783i	0.285163	−	0.285163i	−0.550001	−	0.835164i	$-0.685373\pi$
$251$	4.51783	−	4.51783i	0.285163	−	0.285163i	0.835164	+	0.550001i	$0.185373\pi$
$252$	8.47051	−	0.659592i	0.533592	−	0.0415504i
$253$	−1.18820	−	1.18820i	−0.0747015	−	0.0747015i
$254$	0.427296	+	10.9913i	0.0268110	+	0.689657i
$255$	−1.58732			−0.0994021
$256$	15.2332	−	4.89388i	0.952074	−	0.305868i
$257$	19.1893			1.19700			0.598499	−	0.801124i	$-0.295764\pi$
$257$	19.1893			1.19700			0.598499	+	0.801124i	$0.295764\pi$
$258$	−0.645240	−	16.5975i	−0.0401709	−	1.03331i
$259$	−4.48674	−	4.48674i	−0.278793	−	0.278793i
$260$	−9.57002	+	0.745210i	−0.593507	+	0.0462160i
$261$	−17.4145	+	17.4145i	−1.07793	+	1.07793i
$262$	11.5093	−	12.4404i	0.711049	−	0.768571i
$263$		−	31.4982i		−	1.94227i	−0.238541	−	0.971133i	$-0.576669\pi$
$263$		−	31.4982i		−	1.94227i	0.238541	−	0.971133i	$-0.423331\pi$
$264$	0.772485	+	6.59683i	0.0475432	+	0.406007i
$265$			3.86237i			0.237264i
$266$	4.83349	+	4.47174i	0.296360	+	0.274180i
$267$	7.31018	−	7.31018i	0.447376	−	0.447376i
$268$	5.48766	+	4.69476i	0.335212	+	0.286778i
$269$	−17.1197	−	17.1197i	−1.04381	−	1.04381i	−0.998996	−	0.0448096i	$-0.985732\pi$
$269$	−17.1197	−	17.1197i	−1.04381	−	1.04381i	−0.0448096	−	0.998996i	$-0.514268\pi$
$270$	1.61159	−	0.0626516i	0.0980779	−	0.00381286i
$271$	4.61153			0.280131			0.140065	−	0.990142i	$-0.455269\pi$
$271$	4.61153			0.280131			0.140065	+	0.990142i	$0.455269\pi$
$272$	2.67123	−	0.418551i	0.161967	−	0.0253784i
$273$	19.0418			1.15246
$274$	−4.26259	+	0.165712i	−0.257513	+	0.0100110i
$275$	0.707107	+	0.707107i	0.0426401	+	0.0426401i
$276$	−5.13035	+	5.99681i	−0.308811	+	0.360966i
$277$	−12.5166	+	12.5166i	−0.752048	+	0.752048i	−0.974861	−	0.222813i	$-0.928476\pi$
$277$	−12.5166	+	12.5166i	−0.752048	+	0.752048i	0.222813	+	0.974861i	$0.428476\pi$
$278$	16.7631	+	15.5085i	1.00538	+	0.930138i
$279$		−	0.121019i		−	0.00724519i
$280$	−2.96313	+	3.74913i	−0.177081	+	0.224053i
$281$			20.2443i			1.20767i	0.797109	+	0.603836i	$0.206362\pi$
$281$			20.2443i			1.20767i	−0.797109	+	0.603836i	$0.793638\pi$
$282$	−0.580402	+	0.627354i	−0.0345624	+	0.0373584i
$283$	7.42377	−	7.42377i	0.441297	−	0.441297i	−0.451151	−	0.892448i	$-0.648986\pi$
$283$	7.42377	−	7.42377i	0.441297	−	0.441297i	0.892448	+	0.451151i	$0.148986\pi$
$284$	0.840699	+	10.7963i	0.0498863	+	0.640642i
$285$	−4.57606	−	4.57606i	−0.271062	−	0.271062i
$286$	0.263671	+	6.78239i	0.0155912	+	0.401051i
$287$	18.0398			1.06486
$288$	13.9558	−	2.74597i	0.822351	−	0.161808i
$289$	−16.5431			−0.973123
$290$	−0.538103	−	13.8416i	−0.0315985	−	0.812807i
$291$	−1.73632	−	1.73632i	−0.101785	−	0.101785i
$292$	−0.690115	−	8.86249i	−0.0403859	−	0.518638i
$293$	−3.79964	+	3.79964i	−0.221977	+	0.221977i	−0.809331	−	0.587353i	$-0.800170\pi$
$293$	−3.79964	+	3.79964i	−0.221977	+	0.221977i	0.587353	+	0.809331i	$0.300170\pi$
$294$	−9.34921	+	10.1055i	−0.545257	+	0.589366i
$295$			7.51445i			0.437508i
$296$	−8.33384	−	6.58666i	−0.484395	−	0.382842i
$297$		−	1.14042i		−	0.0661741i
$298$	1.27053	+	1.17545i	0.0736001	+	0.0680917i
$299$	−5.70276	+	5.70276i	−0.329799	+	0.329799i
$300$	3.05311	−	3.56875i	0.176271	−	0.206042i
$301$	−5.97529	−	5.97529i	−0.344410	−	0.344410i
$302$	−1.09851	+	0.0427053i	−0.0632120	+	0.00245741i
$303$	−26.2910			−1.51038
$304$	8.90746	+	6.49420i	0.510878	+	0.372468i
$305$	0.664082			0.0380252
$306$	2.40177	−	0.0933708i	0.137300	−	0.00533765i
$307$	−9.48929	−	9.48929i	−0.541582	−	0.541582i	0.382410	−	0.923993i	$-0.375094\pi$
$307$	−9.48929	−	9.48929i	−0.541582	−	0.541582i	−0.923993	+	0.382410i	$0.875094\pi$
$308$	2.56764	+	2.19665i	0.146305	+	0.125166i
$309$	23.4028	−	23.4028i	1.33134	−	1.33134i
$310$	0.0499644	+	0.0462250i	0.00283779	+	0.00262540i
$311$			6.88988i			0.390689i	0.980735	+	0.195345i	$0.0625825\pi$
$311$			6.88988i			0.390689i	−0.980735	+	0.195345i	$0.937417\pi$
$312$	31.6614	−	3.70754i	1.79248	−	0.209898i
$313$		−	13.4710i		−	0.761423i	−0.924694	−	0.380712i	$-0.875679\pi$
$313$		−	13.4710i		−	0.761423i	0.924694	−	0.380712i	$-0.124321\pi$
$314$	2.64843	−	2.86268i	0.149460	−	0.161551i
$315$	−3.00384	+	3.00384i	−0.169247	+	0.169247i
$316$	−30.3336	+	2.36205i	−1.70640	+	0.132876i
$317$	−7.67139	−	7.67139i	−0.430868	−	0.430868i	0.458056	−	0.888924i	$-0.348546\pi$
$317$	−7.67139	−	7.67139i	−0.430868	−	0.430868i	−0.888924	+	0.458056i	$0.848546\pi$
$318$	−0.498274	−	12.8171i	−0.0279418	−	0.718746i
$319$	−9.79489			−0.548409
$320$	−4.19691	+	6.81072i	−0.234614	+	0.380731i
$321$	−38.3678			−2.14148
$322$	0.155968	+	4.01197i	0.00869178	+	0.223578i
$323$	1.31723	+	1.31723i	0.0732928	+	0.0732928i
$324$	−20.3805	+	1.58701i	−1.13225	+	0.0881673i
$325$	3.39375	−	3.39375i	0.188252	−	0.188252i
$326$	18.4798	−	19.9747i	1.02350	−	1.10630i
$327$		−	46.6154i		−	2.57784i
$328$	29.9954	−	3.51244i	1.65622	−	0.193942i
$329$			0.434806i			0.0239716i
$330$	−2.43772	−	2.25527i	−0.134192	−	0.124149i
$331$	−8.16687	+	8.16687i	−0.448892	+	0.448892i	−0.894986	−	0.446094i	$-0.852815\pi$
$331$	−8.16687	+	8.16687i	−0.448892	+	0.448892i	0.446094	+	0.894986i	$0.352815\pi$
$332$	17.0482	+	14.5850i	0.935643	+	0.800454i
$333$	−6.67717	−	6.67717i	−0.365906	−	0.365906i
$334$	−0.283707	+	0.0110293i	−0.0155237	+	0.000603498i
$335$	−3.61093			−0.197286
$336$	9.34930	−	12.8235i	0.510046	−	0.699581i
$337$	−26.6027			−1.44914			−0.724572	−	0.689199i	$-0.757962\pi$
$337$	−26.6027			−1.44914			−0.724572	+	0.689199i	$0.757962\pi$
$338$	14.1811	−	0.551302i	0.771351	−	0.0299869i
$339$	−10.9342	−	10.9342i	−0.593867	−	0.593867i
$340$	−0.878847	+	1.02727i	−0.0476621	+	0.0557118i
$341$	0.0340338	−	0.0340338i	0.00184303	−	0.00184303i
$342$	7.19319	+	6.65484i	0.388963	+	0.359852i
$343$			18.8306i			1.01676i
$344$	−11.0987	−	8.77187i	−0.598402	−	0.472948i
$345$		−	3.94595i		−	0.212443i
$346$	11.2251	−	12.1332i	0.603465	−	0.652283i
$347$	−2.09877	+	2.09877i	−0.112668	+	0.112668i	−0.761193	−	0.648525i	$-0.775386\pi$
$347$	−2.09877	+	2.09877i	−0.112668	+	0.112668i	0.648525	+	0.761193i	$0.275386\pi$
$348$	3.57133	+	45.8632i	0.191443	+	2.45852i
$349$	−13.2961	−	13.2961i	−0.711722	−	0.711722i	0.255173	−	0.966895i	$-0.417868\pi$
$349$	−13.2961	−	13.2961i	−0.711722	−	0.711722i	−0.966895	+	0.255173i	$0.917868\pi$
$350$	−0.0928179	−	2.38755i	−0.00496133	−	0.127620i
$351$	−5.47346			−0.292151
$352$	4.69699	+	3.15250i	0.250350	+	0.168029i
$353$	18.8437			1.00295			0.501473	−	0.865173i	$-0.332792\pi$
$353$	18.8437			1.00295			0.501473	+	0.865173i	$0.332792\pi$
$354$	−0.969418	−	24.9363i	−0.0515240	−	1.32535i
$355$	−3.82862	−	3.82862i	−0.203202	−	0.203202i
$356$	−0.683564	−	8.77836i	−0.0362288	−	0.465252i
$357$	1.89634	−	1.89634i	0.100365	−	0.100365i
$358$	0.257797	−	0.278652i	0.0136250	−	0.0147272i
$359$		−	30.1007i		−	1.58866i	−0.607489	−	0.794328i	$-0.707823\pi$
$359$		−	30.1007i		−	1.58866i	0.607489	−	0.794328i	$-0.292177\pi$
$360$	−4.40972	+	5.57945i	−0.232413	+	0.294063i
$361$		−	11.4052i		−	0.600271i
$362$	−23.1073	−	21.3779i	−1.21449	−	1.12360i
$363$	−1.66048	+	1.66048i	−0.0871523	+	0.0871523i
$364$	10.5428	−	12.3234i	0.552593	−	0.645920i
$365$	3.14285	+	3.14285i	0.164504	+	0.164504i
$366$	−2.20372	+	0.0856713i	−0.115190	+	0.00447811i
$367$	−26.5869			−1.38783			−0.693913	−	0.720058i	$-0.744115\pi$
$367$	−26.5869			−1.38783			−0.693913	+	0.720058i	$0.744115\pi$
$368$	1.04048	+	6.64046i	0.0542390	+	0.346158i
$369$	26.8468			1.39759
$370$	5.30723	−	0.206323i	0.275910	−	0.0107262i
$371$	−4.61429	−	4.61429i	−0.239562	−	0.239562i
$372$	−0.171768	−	0.146949i	−0.00890573	−	0.00761897i
$373$	−4.53500	+	4.53500i	−0.234813	+	0.234813i	−0.814698	−	0.579885i	$-0.803097\pi$
$373$	−4.53500	+	4.53500i	−0.234813	+	0.234813i	0.579885	+	0.814698i	$0.303097\pi$
$374$	0.701704	+	0.649187i	0.0362843	+	0.0335687i
$375$			2.34827i			0.121264i
$376$	0.0846589	+	0.722965i	0.00436595	+	0.0372841i
$377$			47.0105i			2.42116i
$378$	−1.85048	+	2.00017i	−0.0951782	+	0.102878i
$379$	−6.35631	+	6.35631i	−0.326502	+	0.326502i	−0.851255	−	0.524753i	$-0.824158\pi$
$379$	−6.35631	+	6.35631i	−0.326502	+	0.326502i	0.524753	+	0.851255i	$0.324158\pi$
$380$	−5.49511	+	0.427900i	−0.281893	+	0.0219508i
$381$	12.9150	+	12.9150i	0.661657	+	0.661657i
$382$	0.0893674	+	2.29879i	0.00457243	+	0.117616i
$383$	5.96901			0.305002			0.152501	−	0.988303i	$-0.451267\pi$
$383$	5.96901			0.305002			0.152501	+	0.988303i	$0.451267\pi$
$384$	13.0486	−	23.1424i	0.665882	−	1.18098i
$385$	−1.68953			−0.0861064
$386$	1.26150	+	32.4495i	0.0642086	+	1.65164i
$387$	−8.89241	−	8.89241i	−0.452027	−	0.452027i
$388$	−2.08504	+	0.162361i	−0.105852	+	0.00824261i
$389$	−8.21974	+	8.21974i	−0.416758	+	0.416758i	−0.884085	−	0.467327i	$-0.845217\pi$
$389$	−8.21974	+	8.21974i	−0.416758	+	0.416758i	0.467327	+	0.884085i	$0.345217\pi$
$390$	−10.8242	+	11.6998i	−0.548103	+	0.592442i
$391$			1.13586i			0.0574427i
$392$	1.36370	+	11.6456i	0.0688772	+	0.588194i
$393$		−	28.1414i		−	1.41955i
$394$	13.8968	+	12.8568i	0.700112	+	0.647714i
$395$	10.7570	−	10.7570i	0.541243	−	0.541243i
$396$	3.82116	+	3.26905i	0.192020	+	0.164276i
$397$	−9.15096	−	9.15096i	−0.459274	−	0.459274i	0.439143	−	0.898417i	$-0.355282\pi$
$397$	−9.15096	−	9.15096i	−0.459274	−	0.459274i	−0.898417	+	0.439143i	$0.855282\pi$
$398$	−28.0408	+	1.09011i	−1.40556	+	0.0546421i
$399$	10.9338			0.547376
$400$	−0.619199	−	3.95178i	−0.0309600	−	0.197589i
$401$	−2.97282			−0.148455			−0.0742277	−	0.997241i	$-0.523649\pi$
$401$	−2.97282			−0.148455			−0.0742277	+	0.997241i	$0.523649\pi$
$402$	11.9827	−	0.465835i	0.597641	−	0.0232338i
$403$	−0.163345	−	0.163345i	−0.00813679	−	0.00813679i
$404$	−14.5564	+	17.0149i	−0.724209	+	0.846521i
$405$	7.22740	−	7.22740i	0.359132	−	0.359132i
$406$	17.1791	+	15.8934i	0.852586	+	0.788776i
$407$		−	3.75561i		−	0.186159i
$408$	2.78388	−	3.52233i	0.137822	−	0.174381i
$409$		−	31.0774i		−	1.53668i	−0.640042	−	0.768340i	$-0.721083\pi$
$409$		−	31.0774i		−	1.53668i	0.640042	−	0.768340i	$-0.278917\pi$
$410$	−10.2546	+	11.0841i	−0.506438	+	0.547407i
$411$	−5.00863	+	5.00863i	−0.247058	+	0.247058i
$412$	−2.18836	−	28.1030i	−0.107813	−	1.38454i
$413$	−8.97735	−	8.97735i	−0.441747	−	0.441747i
$414$	0.232112	+	5.97061i	0.0114077	+	0.293439i
$415$	−11.2179			−0.550664
$416$	15.1304	−	22.5432i	0.741830	−	1.10527i
$417$	37.9198			1.85694
$418$	0.151400	+	3.89445i	0.00740521	+	0.190484i
$419$	27.0603	+	27.0603i	1.32198	+	1.32198i	0.912172	+	0.409808i	$0.134404\pi$
$419$	27.0603	+	27.0603i	1.32198	+	1.32198i	0.409808	+	0.912172i	$0.365596\pi$
$420$	0.616022	+	7.91098i	0.0300588	+	0.386016i
$421$	−11.0008	+	11.0008i	−0.536145	+	0.536145i	−0.922394	−	0.386250i	$-0.873770\pi$
$421$	−11.0008	+	11.0008i	−0.536145	+	0.536145i	0.386250	+	0.922394i	$0.373770\pi$
$422$	−2.88852	+	3.12219i	−0.140611	+	0.151986i
$423$			0.647078i			0.0314620i
$424$	−8.57075	−	6.77390i	−0.416232	−	0.328970i
$425$		−	0.675956i		−	0.0327887i
$426$	13.1990	+	12.2111i	0.639493	+	0.591632i
$427$	−0.793364	+	0.793364i	−0.0383936	+	0.0383936i
$428$	−21.2429	+	24.8306i	−1.02681	+	1.20023i
$429$	7.96944	+	7.96944i	0.384768	+	0.384768i
$430$	7.06798	−	0.274773i	0.340848	−	0.0132507i
$431$	−21.1953			−1.02094			−0.510471	−	0.859895i	$-0.670529\pi$
$431$	−21.1953			−1.02094			−0.510471	+	0.859895i	$0.670529\pi$
$432$	−2.68740	+	3.68605i	−0.129298	+	0.177345i
$433$	23.7544			1.14156			0.570782	−	0.821101i	$-0.306640\pi$
$433$	23.7544			1.14156			0.570782	+	0.821101i	$0.306640\pi$
$434$	−0.114915	+	0.00446742i	−0.00551611	+	0.000214443i
$435$	−16.2642	−	16.2642i	−0.779807	−	0.779807i
$436$	−30.1682	−	25.8093i	−1.44480	−	1.23604i
$437$	−3.27453	+	3.27453i	−0.156642	+	0.156642i
$438$	−10.8348	−	10.0239i	−0.517707	−	0.478961i
$439$		−	10.5031i		−	0.501285i	−0.968080	−	0.250643i	$-0.919358\pi$
$439$		−	10.5031i		−	0.501285i	0.968080	−	0.250643i	$-0.0806419\pi$
$440$	−2.80923	+	0.328960i	−0.133925	+	0.0156825i
$441$			10.4232i			0.496345i
$442$	3.11577	−	3.36782i	0.148202	−	0.160191i
$443$	−20.3271	+	20.3271i	−0.965769	+	0.965769i	−0.999433	−	0.0336638i	$-0.989282\pi$
$443$	−20.3271	+	20.3271i	−0.965769	+	0.965769i	0.0336638	+	0.999433i	$0.489282\pi$
$444$	−17.5851	+	1.36934i	−0.834553	+	0.0649860i
$445$	3.11301	+	3.11301i	0.147571	+	0.147571i
$446$	0.264081	+	6.79296i	0.0125046	+	0.321656i
$447$	2.87408			0.135939
$448$	−3.12267	−	13.1506i	−0.147532	−	0.621306i
$449$	−19.3438			−0.912889			−0.456444	−	0.889752i	$-0.650877\pi$
$449$	−19.3438			−0.912889			−0.456444	+	0.889752i	$0.650877\pi$
$450$	−0.138132	−	3.55315i	−0.00651158	−	0.167497i
$451$	7.55008	+	7.55008i	0.355519	+	0.355519i
$452$	−13.1303	+	1.02244i	−0.617596	+	0.0480917i
$453$	−1.29077	+	1.29077i	−0.0606455	+	0.0606455i
$454$	21.0993	−	22.8062i	0.990240	−	1.07035i
$455$			8.10889i			0.380150i
$456$	18.1800	−	2.12887i	0.851357	−	0.0996935i
$457$			39.0477i			1.82657i	0.407318	+	0.913286i	$0.366464\pi$
$457$			39.0477i			1.82657i	−0.407318	+	0.913286i	$0.633536\pi$
$458$	15.2804	+	14.1368i	0.714006	+	0.660568i
$459$	−0.545092	+	0.545092i	−0.0254427	+	0.0254427i
$460$	−2.55372	−	2.18474i	−0.119068	−	0.101864i
$461$	−23.1460	−	23.1460i	−1.07802	−	1.07802i	−0.996687	−	0.0813286i	$-0.974084\pi$
$461$	−23.1460	−	23.1460i	−1.07802	−	1.07802i	−0.0813286	−	0.996687i	$-0.525916\pi$
$462$	5.60661	−	0.217961i	0.260843	−	0.0101405i
$463$	27.1043			1.25964			0.629822	−	0.776739i	$-0.283128\pi$
$463$	27.1043			1.25964			0.629822	+	0.776739i	$0.283128\pi$
$464$	31.6588	+	23.0816i	1.46972	+	1.07154i
$465$	0.113025			0.00524139
$466$	15.8849	−	0.617539i	0.735855	−	0.0286069i
$467$	16.2077	+	16.2077i	0.750003	+	0.750003i	0.974480	−	0.224476i	$-0.0720671\pi$
$467$	16.2077	+	16.2077i	0.750003	+	0.750003i	−0.224476	+	0.974480i	$0.572067\pi$
$468$	15.6898	−	18.3396i	0.725260	−	0.847749i
$469$	4.31390	−	4.31390i	0.199197	−	0.199197i
$470$	−0.267156	−	0.247162i	−0.0123230	−	0.0114007i
$471$		−	6.47567i		−	0.298383i
$472$	−16.6748	−	13.1790i	−0.767522	−	0.606612i
$473$		−	5.00159i		−	0.229973i
$474$	−34.3088	+	37.0842i	−1.57585	+	1.70333i
$475$	1.94870	−	1.94870i	0.0894124	−	0.0894124i
$476$	−0.177324	−	2.27720i	−0.00812763	−	0.104375i
$477$	−6.86698	−	6.86698i	−0.314418	−	0.314418i
$478$	−1.49923	−	38.5647i	−0.0685733	−	1.76391i
$479$	4.07691			0.186279			0.0931394	−	0.995653i	$-0.470310\pi$
$479$	4.07691			0.186279			0.0931394	+	0.995653i	$0.470310\pi$
$480$	2.56459	+	13.0339i	0.117057	+	0.594913i
$481$	−18.0250			−0.821871
$482$	0.384048	+	9.87886i	0.0174929	+	0.449970i
$483$	4.71414	+	4.71414i	0.214501	+	0.214501i
$484$	0.155268	+	1.99396i	0.00705766	+	0.0906347i
$485$	0.739405	−	0.739405i	0.0335747	−	0.0335747i
$486$	−19.7655	+	21.3645i	−0.896583	+	0.969114i
$487$			10.3937i			0.470983i	0.971876	+	0.235492i	$0.0756700\pi$
$487$			10.3937i			0.470983i	−0.971876	+	0.235492i	$0.924330\pi$
$488$	−1.16468	+	1.47362i	−0.0527225	+	0.0667077i
$489$		−	45.1848i		−	2.04333i
$490$	−4.30340	−	3.98132i	−0.194408	−	0.179858i
$491$	26.4396	−	26.4396i	1.19320	−	1.19320i	0.217041	−	0.976162i	$-0.430359\pi$
$491$	26.4396	−	26.4396i	1.19320	−	1.19320i	0.976162	−	0.217041i	$-0.0696407\pi$
$492$	32.5993	−	38.1050i	1.46969	−	1.71791i
$493$	4.68169	+	4.68169i	0.210853	+	0.210853i
$494$	18.6914	−	0.726643i	0.840966	−	0.0326932i
$495$	−2.51436			−0.113012
$496$	−0.190203	+	0.0298027i	−0.00854039	+	0.00133818i
$497$	9.14794			0.410341
$498$	37.2259	−	1.44719i	1.66813	−	0.0648499i
$499$	25.1452	+	25.1452i	1.12565	+	1.12565i	0.990876	+	0.134777i	$0.0430318\pi$
$499$	25.1452	+	25.1452i	1.12565	+	1.12565i	0.134777	+	0.990876i	$0.456968\pi$
$500$	1.51974	+	1.30015i	0.0679647	+	0.0581447i
$501$	−0.333361	+	0.333361i	−0.0148935	+	0.0148935i
$502$	−6.63254	−	6.13615i	−0.296025	−	0.273870i
$503$		−	21.5528i		−	0.960992i	−0.876997	−	0.480496i	$-0.840457\pi$
$503$		−	21.5528i		−	0.960992i	0.876997	−	0.480496i	$-0.159543\pi$
$504$	−1.39745	−	11.9338i	−0.0622472	−	0.531575i
$505$		−	11.1959i		−	0.498212i
$506$	−1.61382	+	1.74438i	−0.0717432	+	0.0775470i
$507$	16.6631	−	16.6631i	0.740034	−	0.740034i
$508$	15.5089	−	1.20766i	0.688095	−	0.0535814i
$509$	10.0728	+	10.0728i	0.446470	+	0.446470i	0.894179	−	0.447709i	$-0.147760\pi$
$509$	10.0728	+	10.0728i	0.446470	+	0.446470i	−0.447709	+	0.894179i	$0.647760\pi$
$510$	0.0872031	+	2.24312i	0.00386142	+	0.0993271i
$511$	−7.50938			−0.332195
$512$	−7.75264	−	21.2579i	−0.342622	−	0.939474i
$513$	−3.14286			−0.138761
$514$	−1.05421	−	27.1173i	−0.0464991	−	1.19609i
$515$	9.96599	+	9.96599i	0.439154	+	0.439154i
$516$	−23.4192	+	1.82364i	−1.03097	+	0.0802812i
$517$	−0.181976	+	0.181976i	−0.00800331	+	0.00800331i
$518$	−6.09394	+	6.58691i	−0.267752	+	0.289412i
$519$		−	27.4464i		−	1.20476i
$520$	1.57884	+	13.4829i	0.0692367	+	0.591264i
$521$		−	25.5528i		−	1.11949i	−0.828665	−	0.559745i	$-0.810899\pi$
$521$		−	25.5528i		−	1.11949i	0.828665	−	0.559745i	$-0.189101\pi$
$522$	25.5659	+	23.6525i	1.11899	+	1.03524i
$523$	−9.79402	+	9.79402i	−0.428262	+	0.428262i	−0.888036	−	0.459774i	$-0.847931\pi$
$523$	−9.79402	+	9.79402i	−0.428262	+	0.428262i	0.459774	+	0.888036i	$0.347931\pi$
$524$	−18.2124	−	15.5809i	−0.795612	−	0.680656i
$525$	−2.80542	−	2.80542i	−0.122439	−	0.122439i
$526$	−44.5116	+	1.73042i	−1.94080	+	0.0754501i
$527$	−0.0325345			−0.00141722
$528$	9.27984	−	1.45404i	0.403853	−	0.0632792i
$529$	20.1764			0.877233
$530$	5.45810	−	0.212188i	0.237085	−	0.00921685i
$531$	−13.3601	−	13.3601i	−0.579778	−	0.579778i
$532$	6.05369	−	7.07609i	0.262461	−	0.306787i
$533$	36.2366	−	36.2366i	1.56958	−	1.56958i
$534$	−10.7320	−	9.92876i	−0.464417	−	0.429659i
$535$		−	16.3388i		−	0.706386i
$536$	6.33291	−	8.01278i	0.273540	−	0.346100i
$537$		−	0.630338i		−	0.0272011i
$538$	−23.2521	+	25.1331i	−1.00247	+	1.08357i
$539$	−2.93130	+	2.93130i	−0.126260	+	0.126260i
$540$	−0.177072	−	2.27396i	−0.00761996	−	0.0978558i
$541$	−31.7729	−	31.7729i	−1.36602	−	1.36602i	−0.866027	−	0.499997i	$-0.833334\pi$
$541$	−31.7729	−	31.7729i	−1.36602	−	1.36602i	−0.499997	−	0.866027i	$-0.666666\pi$
$542$	−0.253345	−	6.51677i	−0.0108821	−	0.279919i
$543$	−52.2710			−2.24316
$544$	−0.738224	−	3.75185i	−0.0316511	−	0.160859i
$545$	19.8510			0.850322
$546$	−1.04610	−	26.9089i	−0.0447691	−	1.15159i
$547$	−2.43139	−	2.43139i	−0.103959	−	0.103959i	0.653214	−	0.757173i	$-0.273420\pi$
$547$	−2.43139	−	2.43139i	−0.103959	−	0.103959i	−0.757173	+	0.653214i	$0.773420\pi$
$548$	0.468349	+	6.01456i	0.0200069	+	0.256929i
$549$	−1.18068	+	1.18068i	−0.0503903	+	0.0503903i
$550$	0.960399	−	1.03809i	0.0409515	−	0.0442644i
$551$			26.9935i			1.14996i
$552$	8.75622	+	6.92048i	0.372689	+	0.294555i
$553$			25.7023i			1.09297i
$554$	18.3754	+	17.0001i	0.780695	+	0.722266i
$555$	6.23610	−	6.23610i	0.264708	−	0.264708i
$556$	20.9949	−	24.5407i	0.890380	−	1.04076i
$557$	−32.4602	−	32.4602i	−1.37538	−	1.37538i	−0.852252	−	0.523131i	$-0.824764\pi$
$557$	−32.4602	−	32.4602i	−1.37538	−	1.37538i	−0.523131	−	0.852252i	$-0.675236\pi$
$558$	−0.171017	+	0.00664841i	−0.00723972	+	0.000281450i
$559$	−24.0051			−1.01531
$560$	5.46085	+	3.98136i	0.230763	+	0.168243i
$561$	1.58732			0.0670169
$562$	28.6081	−	1.11216i	1.20676	−	0.0469137i
$563$	2.93158	+	2.93158i	0.123551	+	0.123551i	0.766179	−	0.642627i	$-0.222156\pi$
$563$	2.93158	+	2.93158i	0.123551	+	0.123551i	−0.642627	+	0.766179i	$0.722156\pi$
$564$	0.918429	+	0.785727i	0.0386728	+	0.0330851i
$565$	4.65631	−	4.65631i	0.195892	−	0.195892i
$566$	−10.8987	−	10.0830i	−0.458107	−	0.423821i
$567$			17.2688i			0.725222i
$568$	15.2106	−	1.78115i	0.638221	−	0.0747353i
$569$		−	8.45104i		−	0.354286i	−0.984185	−	0.177143i	$-0.943314\pi$
$569$		−	8.45104i		−	0.354286i	0.984185	−	0.177143i	$-0.0566855\pi$
$570$	−6.21525	+	6.71804i	−0.260328	+	0.281388i
$571$	−18.3768	+	18.3768i	−0.769045	+	0.769045i	−0.977938	−	0.208894i	$-0.933014\pi$
$571$	−18.3768	+	18.3768i	−0.769045	+	0.769045i	0.208894	+	0.977938i	$0.433014\pi$
$572$	9.57002	−	0.745210i	0.400142	−	0.0311588i
$573$	2.70113	+	2.70113i	0.112841	+	0.112841i
$574$	−0.991057	−	25.4929i	−0.0413659	−	1.06405i
$575$	1.68037			0.0700762
$576$	−4.64715	−	19.5707i	−0.193631	−	0.815444i
$577$	32.5491			1.35504			0.677519	−	0.735505i	$-0.263055\pi$
$577$	32.5491			1.35504			0.677519	+	0.735505i	$0.263055\pi$
$578$	0.908830	+	23.3778i	0.0378023	+	0.972388i
$579$	38.1288	+	38.1288i	1.58458	+	1.58458i
$580$	−19.5307	+	1.52084i	−0.810966	+	0.0631493i
$581$	13.4017	−	13.4017i	0.555998	−	0.555998i
$582$	−2.35829	+	2.54906i	−0.0977541	+	0.105662i
$583$		−	3.86237i		−	0.159963i
$584$	−12.4861	+	1.46211i	−0.516678	+	0.0605027i
$585$			12.0676i			0.498935i
$586$	5.57819	+	5.16071i	0.230433	+	0.213187i
$587$	24.9569	−	24.9569i	1.03008	−	1.03008i	0.0305492	−	0.999533i	$-0.490274\pi$
$587$	24.9569	−	24.9569i	1.03008	−	1.03008i	0.999533	−	0.0305492i	$-0.00972563\pi$
$588$	14.7942	+	12.6566i	0.610103	+	0.521951i
$589$	−0.0937928	−	0.0937928i	−0.00386467	−	0.00386467i
$590$	10.6190	−	0.412823i	0.437178	−	0.0169956i
$591$	31.4360			1.29310
$592$	−8.85007	+	12.1388i	−0.363736	+	0.498901i
$593$	8.35122			0.342944			0.171472	−	0.985189i	$-0.445148\pi$
$593$	8.35122			0.342944			0.171472	+	0.985189i	$0.445148\pi$
$594$	−1.61159	+	0.0626516i	−0.0661241	+	0.00257063i
$595$	0.807549	+	0.807549i	0.0331063	+	0.0331063i
$596$	1.59128	−	1.86003i	0.0651812	−	0.0761896i
$597$	−32.9485	+	32.9485i	−1.34849	+	1.34849i
$598$	8.37213	+	7.74554i	0.342362	+	0.316739i
$599$			14.8595i			0.607143i	0.952809	+	0.303572i	$0.0981792\pi$
$599$			14.8595i			0.607143i	−0.952809	+	0.303572i	$0.901821\pi$
$600$	−5.21089	−	4.11843i	−0.212734	−	0.168134i
$601$			41.6661i			1.69960i	0.527108	+	0.849798i	$0.323276\pi$
$601$			41.6661i			1.69960i	−0.527108	+	0.849798i	$0.676724\pi$
$602$	−8.11569	+	8.77222i	−0.330771	+	0.357529i
$603$	6.41993	−	6.41993i	0.261440	−	0.261440i
$604$	0.120698	+	1.55000i	0.00491112	+	0.0630688i
$605$	−0.707107	−	0.707107i	−0.0287480	−	0.0287480i
$606$	1.44435	+	37.1530i	0.0586728	+	1.50924i
$607$	23.3376			0.947246			0.473623	−	0.880728i	$-0.342946\pi$
$607$	23.3376			0.947246			0.473623	+	0.880728i	$0.342946\pi$
$608$	8.68790	−	12.9443i	0.352341	−	0.524961i
$609$	38.8609			1.57472
$610$	−0.0364828	−	0.938445i	−0.00147714	−	0.0379965i
$611$	0.873394	+	0.873394i	0.0353337	+	0.0353337i
$612$	−0.263893	−	3.38893i	−0.0106672	−	0.136989i
$613$	17.1012	−	17.1012i	0.690711	−	0.690711i	−0.271677	−	0.962388i	$-0.587578\pi$
$613$	17.1012	−	17.1012i	0.690711	−	0.690711i	0.962388	+	0.271677i	$0.0875783\pi$
$614$	−12.8884	+	13.9311i	−0.520135	+	0.562212i
$615$			25.0734i			1.01106i
$616$	2.96313	−	3.74913i	0.119388	−	0.151057i
$617$		−	2.38811i		−	0.0961415i	−0.998844	−	0.0480708i	$-0.984693\pi$
$617$		−	2.38811i		−	0.0961415i	0.998844	−	0.0480708i	$-0.0153073\pi$
$618$	−34.3573	−	31.7859i	−1.38205	−	1.27862i
$619$	−2.82704	+	2.82704i	−0.113628	+	0.113628i	−0.761635	−	0.648006i	$-0.775603\pi$
$619$	−2.82704	+	2.82704i	−0.113628	+	0.113628i	0.648006	+	0.761635i	$0.275603\pi$
$620$	0.0625778	−	0.0731465i	0.00251318	−	0.00293764i
$621$	−1.35505	−	1.35505i	−0.0543764	−	0.0543764i
$622$	9.73640	−	0.378510i	0.390394	−	0.0151769i
$623$	−7.43809			−0.298001
$624$	−6.97868	−	44.5385i	−0.279371	−	1.78297i
$625$	−1.00000			−0.0400000
$626$	−19.0364	+	0.740056i	−0.760849	+	0.0295786i
$627$	4.57606	+	4.57606i	0.182750	+	0.182750i
$628$	−4.19089	−	3.58536i	−0.167235	−	0.143071i
$629$	−1.79508	+	1.79508i	−0.0715745	+	0.0715745i
$630$	4.40989	+	4.07985i	0.175694	+	0.162545i
$631$			4.66539i			0.185726i	0.995679	+	0.0928632i	$0.0296019\pi$
$631$			4.66539i			0.185726i	−0.995679	+	0.0928632i	$0.970398\pi$
$632$	5.00436	+	42.7360i	0.199063	+	1.69995i
$633$			7.06270i			0.280717i
$634$	−10.4193	+	11.2622i	−0.413805	+	0.447280i
$635$	−5.49981	+	5.49981i	−0.218253	+	0.218253i
$636$	−18.0850	+	1.40827i	−0.717118	+	0.0558414i
$637$	14.0688	+	14.0688i	0.557425	+	0.557425i
$638$	0.538103	+	13.8416i	0.0213037	+	0.547995i
$639$	13.6139			0.538559
$640$	9.85512	+	5.55668i	0.389558	+	0.219647i
$641$	−32.4635			−1.28223			−0.641115	−	0.767445i	$-0.721528\pi$
$641$	−32.4635			−1.28223			−0.641115	+	0.767445i	$0.721528\pi$
$642$	2.10782	+	54.2193i	0.0831889	+	2.13986i
$643$	−20.1741	−	20.1741i	−0.795588	−	0.795588i	0.186808	−	0.982396i	$-0.440186\pi$
$643$	−20.1741	−	20.1741i	−0.795588	−	0.795588i	−0.982396	+	0.186808i	$0.940186\pi$
$644$	5.66093	−	0.440812i	0.223072	−	0.0173704i
$645$	8.30501	−	8.30501i	0.327010	−	0.327010i
$646$	1.78908	−	1.93381i	0.0703903	−	0.0760847i
$647$		−	32.8105i		−	1.28991i	−0.764219	−	0.644957i	$-0.776875\pi$
$647$		−	32.8105i		−	1.28991i	0.764219	−	0.644957i	$-0.223125\pi$
$648$	3.36232	+	28.7134i	0.132085	+	1.12797i
$649$		−	7.51445i		−	0.294968i
$650$	−4.98231	−	4.60943i	−0.195422	−	0.180797i
$651$	−0.135028	+	0.135028i	−0.00529216	+	0.00529216i
$652$	−29.2424	−	25.0173i	−1.14522	−	0.979751i
$653$	−3.84271	−	3.84271i	−0.150377	−	0.150377i	0.627910	−	0.778286i	$-0.283911\pi$
$653$	−3.84271	−	3.84271i	−0.150377	−	0.150377i	−0.778286	+	0.627910i	$0.783911\pi$
$654$	−65.8743	+	2.56092i	−2.57589	+	0.100140i
$655$	11.9839			0.468250
$656$	−6.61146	−	42.1949i	−0.258134	−	1.64743i
$657$	−11.1754			−0.435996
$658$	0.614444	−	0.0238870i	0.0239535	−	0.000931212i
$659$	28.4996	+	28.4996i	1.11019	+	1.11019i	0.993124	+	0.117063i	$0.0373479\pi$
$659$	28.4996	+	28.4996i	1.11019	+	1.11019i	0.117063	+	0.993124i	$0.462652\pi$
$660$	−3.05311	+	3.56875i	−0.118842	+	0.138913i
$661$	1.90927	−	1.90927i	0.0742620	−	0.0742620i	−0.669000	−	0.743262i	$-0.733277\pi$
$661$	1.90927	−	1.90927i	0.0742620	−	0.0742620i	0.743262	+	0.669000i	$0.233277\pi$
$662$	11.9896	+	11.0923i	0.465991	+	0.431115i
$663$		−	7.61835i		−	0.295872i
$664$	19.6741	−	24.8929i	0.763504	−	0.966031i
$665$			4.65613i			0.180557i
$666$	−9.06899	+	9.80264i	−0.351416	+	0.379844i
$667$	−11.6383	+	11.6383i	−0.450637	+	0.450637i
$668$	0.0311721	+	0.400313i	0.00120608	+	0.0154886i
$669$	7.98186	+	7.98186i	0.308597	+	0.308597i
$670$	0.198374	+	5.10277i	0.00766386	+	0.197137i
$671$	−0.664082			−0.0256366
$672$	−18.6351	−	12.5074i	−0.718866	−	0.482485i
$673$	−27.5533			−1.06210			−0.531051	−	0.847340i	$-0.678203\pi$
$673$	−27.5533			−1.06210			−0.531051	+	0.847340i	$0.678203\pi$
$674$	1.46148	+	37.5936i	0.0562941	+	1.44805i
$675$	0.806401	+	0.806401i	0.0310384	+	0.0310384i
$676$	−1.55814	−	20.0097i	−0.0599285	−	0.769604i
$677$	15.0923	−	15.0923i	0.580046	−	0.580046i	−0.354870	−	0.934916i	$-0.615475\pi$
$677$	15.0923	−	15.0923i	0.580046	−	0.580046i	0.934916	+	0.354870i	$0.115475\pi$
$678$	−14.8510	+	16.0524i	−0.570349	+	0.616488i
$679$			1.76670i			0.0677998i
$680$	1.49997	+	1.18550i	0.0575213	+	0.0454620i
$681$		−	51.5898i		−	1.97693i
$682$	−0.0499644	−	0.0462250i	−0.00191324	−	0.00177005i
$683$	−31.1216	+	31.1216i	−1.19083	+	1.19083i	−0.213999	+	0.976834i	$0.568649\pi$
$683$	−31.1216	+	31.1216i	−1.19083	+	1.19083i	−0.976834	+	0.213999i	$0.931351\pi$
$684$	9.00909	−	10.5306i	0.344471	−	0.402649i
$685$	−2.13291	−	2.13291i	−0.0814941	−	0.0814941i
$686$	26.6104	−	1.03450i	1.01599	−	0.0394974i
$687$	34.5658			1.31877
$688$	−11.7862	+	16.1660i	−0.449345	+	0.616323i
$689$	−18.5374			−0.706220
$690$	−5.57621	+	0.216780i	−0.212283	+	0.00825265i
$691$	1.91674	+	1.91674i	0.0729163	+	0.0729163i	0.742624	−	0.669708i	$-0.233581\pi$
$691$	1.91674	+	1.91674i	0.0729163	+	0.0729163i	−0.669708	+	0.742624i	$0.733581\pi$
$692$	−17.7626	−	15.1961i	−0.675233	−	0.577670i
$693$	3.00384	−	3.00384i	0.114107	−	0.114107i
$694$	3.08117	+	2.85057i	0.116960	+	0.108206i
$695$			16.1480i			0.612528i
$696$	64.6152	−	7.56641i	2.44923	−	0.286804i
$697$		−	7.21747i		−	0.273381i
$698$	−18.0588	+	19.5197i	−0.683537	+	0.738833i
$699$	18.6651	−	18.6651i	0.705979	−	0.705979i
$700$	−3.36886	+	0.262331i	−0.127331	+	0.00991516i
$701$	33.5126	+	33.5126i	1.26576	+	1.26576i	0.948260	+	0.317495i	$0.102842\pi$
$701$	33.5126	+	33.5126i	1.26576	+	1.26576i	0.317495	+	0.948260i	$0.397158\pi$
$702$	0.300696	+	7.73479i	0.0113490	+	0.291931i
$703$	−10.3500			−0.390357
$704$	4.19691	−	6.81072i	0.158177	−	0.256689i
$705$	−0.604334			−0.0227605
$706$	−1.03522	−	26.6288i	−0.0389609	−	1.00219i
$707$	13.3755	+	13.3755i	0.503038	+	0.503038i
$708$	−35.1854	+	2.73986i	−1.32235	+	0.102970i
$709$	25.1649	−	25.1649i	0.945088	−	0.945088i	−0.0534805	−	0.998569i	$-0.517032\pi$
$709$	25.1649	−	25.1649i	0.945088	−	0.945088i	0.998569	+	0.0534805i	$0.0170315\pi$
$710$	−5.20007	+	5.62074i	−0.195155	+	0.210942i
$711$			38.2501i			1.43449i
$712$	−12.3675	+	1.44823i	−0.463493	+	0.0542748i
$713$		−	0.0808779i		−	0.00302890i
$714$	−2.78399	−	2.57563i	−0.104188	−	0.0963904i
$715$	−3.39375	+	3.39375i	−0.126919	+	0.126919i
$716$	−0.407938	−	0.348996i	−0.0152454	−	0.0130426i
$717$	−45.3143	−	45.3143i	−1.69229	−	1.69229i
$718$	−42.5367	+	1.65365i	−1.58746	+	0.0617136i
$719$	−20.6861			−0.771462			−0.385731	−	0.922611i	$-0.626051\pi$
$719$	−20.6861			−0.771462			−0.385731	+	0.922611i	$0.626051\pi$
$720$	8.12683	+	5.92506i	0.302869	+	0.220814i
$721$	−23.8123			−0.886816
$722$	−16.1172	+	0.626567i	−0.599818	+	0.0233184i
$723$	11.6079	+	11.6079i	0.431701	+	0.431701i
$724$	−28.9407	+	33.8284i	−1.07557	+	1.25722i
$725$	6.92603	−	6.92603i	0.257226	−	0.257226i
$726$	2.43772	+	2.25527i	0.0904721	+	0.0837010i
$727$			39.7783i			1.47530i	0.675186	+	0.737648i	$0.264063\pi$
$727$			39.7783i			1.47530i	−0.675186	+	0.737648i	$0.735937\pi$
$728$	−17.9939	−	14.2215i	−0.666899	−	0.527084i
$729$			17.6654i			0.654273i
$730$	4.26864	−	4.61396i	0.157990	−	0.170770i
$731$	−2.39062	+	2.39062i	−0.0884204	+	0.0884204i
$732$	0.242132	+	3.10947i	0.00894946	+	0.114929i
$733$	3.21055	+	3.21055i	0.118584	+	0.118584i	0.763909	−	0.645324i	$-0.223278\pi$
$733$	3.21055	+	3.21055i	0.118584	+	0.118584i	−0.645324	+	0.763909i	$0.723278\pi$
$734$	1.46061	+	37.5712i	0.0539121	+	1.38678i
$735$	−9.73472			−0.359070
$736$	9.32677	−	1.83516i	0.343789	−	0.0676450i
$737$	3.61093			0.133010
$738$	−1.47489	−	37.9385i	−0.0542914	−	1.39654i
$739$	−0.0875188	−	0.0875188i	−0.00321943	−	0.00321943i	0.705495	−	0.708715i	$-0.250725\pi$
$739$	−0.0875188	−	0.0875188i	−0.00321943	−	0.00321943i	−0.708715	+	0.705495i	$0.750725\pi$
$740$	−0.583128	−	7.48855i	−0.0214362	−	0.275285i
$741$	21.9628	−	21.9628i	0.806823	−	0.806823i
$742$	−6.26717	+	6.77417i	−0.230075	+	0.248687i
$743$		−	36.0864i		−	1.32388i	−0.749556	−	0.661941i	$-0.769733\pi$
$743$		−	36.0864i		−	1.32388i	0.749556	−	0.661941i	$-0.230267\pi$
$744$	−0.198224	+	0.250806i	−0.00726726	+	0.00919498i
$745$			1.22391i			0.0448407i
$746$	6.65776	+	6.15948i	0.243758	+	0.225515i
$747$	19.9445	−	19.9445i	0.729730	−	0.729730i
$748$	0.878847	−	1.02727i	0.0321338	−	0.0375609i
$749$	19.5196	+	19.5196i	0.713229	+	0.713229i
$750$	3.31844	−	0.129007i	0.121172	−	0.00471067i
$751$	22.2566			0.812155			0.406077	−	0.913839i	$-0.366896\pi$
$751$	22.2566			0.812155			0.406077	+	0.913839i	$0.366896\pi$
$752$	1.01700	−	0.159353i	0.0370863	−	0.00581101i
$753$	−15.0035			−0.546757
$754$	66.4327	−	2.58262i	2.41934	−	0.0940536i
$755$	−0.549668	−	0.549668i	−0.0200045	−	0.0200045i
$756$	2.92820	+	2.50511i	0.106497	+	0.0911099i
$757$	−6.54688	+	6.54688i	−0.237950	+	0.237950i	−0.816001	−	0.578051i	$-0.803814\pi$
$757$	−6.54688	+	6.54688i	−0.237950	+	0.237950i	0.578051	+	0.816001i	$0.303814\pi$
$758$	9.33159	+	8.63320i	0.338939	+	0.313572i
$759$			3.94595i			0.143229i
$760$	0.906571	+	7.74189i	0.0328848	+	0.280828i
$761$			34.6771i			1.25704i	0.777792	+	0.628522i	$0.216340\pi$
$761$			34.6771i			1.25704i	−0.777792	+	0.628522i	$0.783660\pi$
$762$	17.5413	−	18.9603i	0.635455	−	0.686861i
$763$	−23.7155	+	23.7155i	−0.858559	+	0.858559i
$764$	3.24362	−	0.252578i	0.117350	−	0.00913796i
$765$	1.20179	+	1.20179i	0.0434509	+	0.0434509i
$766$	−0.327920	−	8.43508i	−0.0118482	−	0.304772i
$767$	−36.0656			−1.30225
$768$	−33.4205	−	17.1682i	−1.20596	−	0.619502i
$769$	−14.6484			−0.528233			−0.264117	−	0.964491i	$-0.585080\pi$
$769$	−14.6484			−0.528233			−0.264117	+	0.964491i	$0.585080\pi$
$770$	0.0928179	+	2.38755i	0.00334493	+	0.0860414i
$771$	−31.8634	−	31.8634i	−1.14753	−	1.14753i
$772$	45.7866	−	3.56537i	1.64790	−	0.128320i
$773$	−14.0408	+	14.0408i	−0.505014	+	0.505014i	−0.912992	−	0.407978i	$-0.866234\pi$
$773$	−14.0408	+	14.0408i	−0.505014	+	0.505014i	0.407978	+	0.912992i	$0.366234\pi$
$774$	−12.0778	+	13.0548i	−0.434126	+	0.469245i
$775$			0.0481311i			0.00172892i
$776$	0.343985	+	2.93755i	0.0123484	+	0.105452i
$777$			14.9003i			0.534544i
$778$	12.0673	+	11.1641i	0.432633	+	0.400253i
$779$	20.8071	−	20.8071i	0.745491	−	0.745491i
$780$	17.1282	+	14.6534i	0.613287	+	0.524675i
$781$	3.82862	+	3.82862i	0.136999	+	0.136999i
$782$	1.60513	−	0.0624007i	0.0573993	−	0.00223144i
$783$	−11.1703			−0.399195
$784$	16.3821	−	2.56689i	0.585074	−	0.0916745i
$785$	2.75764			0.0984244
$786$	−39.7679	+	1.54601i	−1.41848	+	0.0551443i
$787$	−18.0714	−	18.0714i	−0.644175	−	0.644175i	0.307404	−	0.951579i	$-0.400540\pi$
$787$	−18.0714	−	18.0714i	−0.644175	−	0.644175i	−0.951579	+	0.307404i	$0.900540\pi$
$788$	17.4050	−	20.3445i	0.620028	−	0.724744i
$789$	−52.3021	+	52.3021i	−1.86200	+	1.86200i
$790$	−15.7922	−	14.6102i	−0.561860	−	0.519809i
$791$			11.1256i			0.395580i
$792$	4.40972	−	5.57945i	0.156693	−	0.198257i
$793$			3.18726i			0.113183i
$794$	−12.4289	+	13.4344i	−0.441086	+	0.476768i
$795$	6.41338	−	6.41338i	0.227459	−	0.227459i
$796$	3.08096	+	39.5658i	0.109202	+	1.40237i
$797$	15.9741	+	15.9741i	0.565831	+	0.565831i	0.930958	−	0.365127i	$-0.118974\pi$
$797$	15.9741	+	15.9741i	0.565831	+	0.565831i	−0.365127	+	0.930958i	$0.618974\pi$
$798$	−0.600674	−	15.4511i	−0.0212636	−	0.546963i
$799$	0.173959			0.00615424
$800$	−5.55043	+	1.09212i	−0.196237	+	0.0386122i
$801$	−11.0694			−0.391117
$802$	0.163318	+	4.20103i	0.00576696	+	0.148343i
$803$	−3.14285	−	3.14285i	−0.110909	−	0.110909i
$804$	−1.31659	−	16.9077i	−0.0464324	−	0.596287i
$805$	−2.00750	+	2.00750i	−0.0707551	+	0.0707551i
$806$	−0.221857	+	0.239804i	−0.00781457	+	0.00844674i
$807$			56.8536i			2.00134i
$808$	24.8442	+	19.6356i	0.874015	+	0.690778i
$809$		−	10.4457i		−	0.367251i	−0.982996	−	0.183625i	$-0.941217\pi$
$809$		−	10.4457i		−	0.367251i	0.982996	−	0.183625i	$-0.0587833\pi$
$810$	−10.6104	−	9.81632i	−0.372812	−	0.344910i
$811$	5.27025	−	5.27025i	0.185064	−	0.185064i	−0.608495	−	0.793558i	$-0.708226\pi$
$811$	5.27025	−	5.27025i	0.185064	−	0.185064i	0.793558	+	0.608495i	$0.208226\pi$
$812$	21.5159	−	25.1497i	0.755061	−	0.882583i
$813$	−7.65734	−	7.65734i	−0.268555	−	0.268555i
$814$	−5.30723	+	0.206323i	−0.186018	+	0.00723160i
$815$	19.2418			0.674009
$816$	−5.13051	−	3.74052i	−0.179604	−	0.130944i
$817$	−13.7837			−0.482232
$818$	−43.9170	+	1.70731i	−1.53552	+	0.0596945i
$819$	−14.4169	−	14.4169i	−0.503768	−	0.503768i
$820$	16.2269	+	13.8823i	0.566667	+	0.484791i
$821$	−25.4438	+	25.4438i	−0.887995	+	0.887995i	−0.994330	−	0.106336i	$-0.966088\pi$
$821$	−25.4438	+	25.4438i	−0.887995	+	0.887995i	0.106336	+	0.994330i	$0.466088\pi$
$822$	7.35309	+	6.80277i	0.256468	+	0.237274i
$823$			46.3808i			1.61673i	0.588679	+	0.808367i	$0.299648\pi$
$823$			46.3808i			1.61673i	−0.588679	+	0.808367i	$0.700352\pi$
$824$	−39.5934	+	4.63637i	−1.37930	+	0.161516i
$825$		−	2.34827i		−	0.0817561i
$826$	−12.1931	+	13.1795i	−0.424253	+	0.458573i
$827$	−4.49220	+	4.49220i	−0.156209	+	0.156209i	−0.780885	−	0.624675i	$-0.785231\pi$
$827$	−4.49220	+	4.49220i	−0.156209	+	0.156209i	0.624675	+	0.780885i	$0.285231\pi$
$828$	8.42459	−	0.656016i	0.292775	−	0.0227981i
$829$	0.650733	+	0.650733i	0.0226009	+	0.0226009i	0.718317	−	0.695716i	$-0.244913\pi$
$829$	0.650733	+	0.650733i	0.0226009	+	0.0226009i	−0.695716	+	0.718317i	$0.744913\pi$
$830$	0.616278	+	15.8525i	0.0213913	+	0.550248i
$831$	41.5669			1.44194
$832$	−32.6880	−	20.1430i	−1.13325	−	0.698334i
$833$	2.80217			0.0970894
$834$	−2.08320	−	53.5862i	−0.0721354	−	1.85554i
$835$	−0.141961	−	0.141961i	−0.00491275	−	0.00491275i
$836$	5.49511	−	0.427900i	0.190052	−	0.0147992i
$837$	0.0388129	−	0.0388129i	0.00134157	−	0.00134157i
$838$	36.7535	−	39.7267i	1.26963	−	1.37234i
$839$		−	14.5792i		−	0.503330i	−0.967814	−	0.251665i	$-0.919022\pi$
$839$		−	14.5792i		−	0.503330i	0.967814	−	0.251665i	$-0.0809782\pi$
$840$	11.1455	−	1.30514i	0.384557	−	0.0450315i
$841$			66.9399i			2.30827i
$842$	16.1500	+	14.9413i	0.556567	+	0.514913i
$843$	33.6151	−	33.6151i	1.15776	−	1.15776i
$844$	4.57079	+	3.91037i	0.157333	+	0.134601i
$845$	7.09591	+	7.09591i	0.244107	+	0.244107i
$846$	0.914415	−	0.0355486i	0.0314382	−	0.00122219i
$847$	1.68953			0.0580529
$848$	−9.10166	+	12.4839i	−0.312552	+	0.428698i
$849$	−24.6540			−0.846122
$850$	−0.955224	+	0.0371351i	−0.0327639	+	0.00127372i
$851$	−4.46242	−	4.46242i	−0.152970	−	0.152970i
$852$	16.5310	−	19.3229i	0.566343	−	0.661993i
$853$	26.5918	−	26.5918i	0.910485	−	0.910485i	−0.0858248	−	0.996310i	$-0.527353\pi$
$853$	26.5918	−	26.5918i	0.910485	−	0.910485i	0.996310	+	0.0858248i	$0.0273525\pi$
$854$	1.16472	+	1.07755i	0.0398560	+	0.0368731i
$855$			6.92925i			0.236975i
$856$	36.2563	+	28.6552i	1.23922	+	0.979415i
$857$		−	0.614156i		−	0.0209792i	−0.999945	−	0.0104896i	$-0.996661\pi$
$857$		−	0.614156i		−	0.0209792i	0.999945	−	0.0104896i	$-0.00333900\pi$
$858$	10.8242	−	11.6998i	0.369531	−	0.399425i
$859$	−1.72103	+	1.72103i	−0.0587207	+	0.0587207i	−0.735857	−	0.677137i	$-0.763221\pi$
$859$	−1.72103	+	1.72103i	−0.0587207	+	0.0587207i	0.677137	+	0.735857i	$0.263221\pi$
$860$	−0.776589	−	9.97299i	−0.0264815	−	0.340076i
$861$	−29.9547	−	29.9547i	−1.02085	−	1.02085i
$862$	1.16441	+	29.9520i	0.0396599	+	1.02017i
$863$	22.9222			0.780280			0.390140	−	0.920756i	$-0.372427\pi$
$863$	22.9222			0.780280			0.390140	+	0.920756i	$0.372427\pi$
$864$	5.35656	+	3.59519i	0.182234	+	0.122311i
$865$	11.6879			0.397402
$866$	−1.30500	−	33.5685i	−0.0443457	−	1.14070i
$867$	27.4694	+	27.4694i	0.932909	+	0.932909i
$868$	0.0126262	+	0.162147i	0.000428563	+	0.00550362i
$869$	−10.7570	+	10.7570i	−0.364906	+	0.364906i
$870$	−22.0901	+	23.8772i	−0.748926	+	0.809511i
$871$		−	17.3306i		−	0.587226i
$872$	−34.8150	+	44.0500i	−1.17898	+	1.49172i
$873$			2.62920i			0.0889850i
$874$	4.80728	+	4.44750i	0.162609	+	0.150439i
$875$	1.19468	−	1.19468i	0.0403875	−	0.0403875i
$876$	−13.5700	+	15.8619i	−0.458489	+	0.535923i
$877$	6.88089	+	6.88089i	0.232351	+	0.232351i	0.813673	−	0.581322i	$-0.197464\pi$
$877$	6.88089	+	6.88089i	0.232351	+	0.232351i	−0.581322	+	0.813673i	$0.697464\pi$
$878$	−14.8424	+	0.577010i	−0.500907	+	0.0194731i
$879$	12.6184			0.425609
$880$	0.619199	+	3.95178i	0.0208732	+	0.133215i
$881$	−13.5399			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$881$	−13.5399			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$882$	14.7296	−	0.572623i	0.495970	−	0.0192812i
$883$	−25.2132	−	25.2132i	−0.848492	−	0.848492i	0.141453	−	0.989945i	$-0.454823\pi$
$883$	−25.2132	−	25.2132i	−0.848492	−	0.848492i	−0.989945	+	0.141453i	$0.954823\pi$
$884$	−4.93040	−	4.21802i	−0.165827	−	0.141867i
$885$	12.4776	−	12.4776i	0.419429	−	0.419429i
$886$	29.8419	+	27.6084i	1.00256	+	0.927524i
$887$			3.71272i			0.124661i	0.998056	+	0.0623304i	$0.0198533\pi$
$887$			3.71272i			0.124661i	−0.998056	+	0.0623304i	$0.980147\pi$
$888$	2.90115	+	24.7751i	0.0973563	+	0.831398i
$889$		−	13.1410i		−	0.440735i
$890$	4.22812	−	4.57016i	0.141727	−	0.153192i
$891$	−7.22740	+	7.22740i	−0.242127	+	0.242127i
$892$	9.58493	−	0.746371i	0.320927	−	0.0249904i
$893$	0.501504	+	0.501504i	0.0167822	+	0.0167822i
$894$	−0.157893	−	4.06149i	−0.00528075	−	0.135836i
$895$	0.268427			0.00897252
$896$	−18.4121	+	5.13524i	−0.615106	+	0.171556i
$897$	18.9386			0.632341
$898$	1.06269	+	27.3356i	0.0354625	+	0.912199i
$899$	−0.333357	−	0.333357i	−0.0111181	−	0.0111181i
$900$	−5.01353	+	0.390400i	−0.167118	+	0.0130133i
$901$	−1.84611	+	1.84611i	−0.0615029	+	0.0615029i
$902$	10.2546	−	11.0841i	0.341440	−	0.369062i
$903$			19.8436i			0.660355i
$904$	2.16620	+	18.4988i	0.0720468	+	0.615262i
$905$		−	22.2594i		−	0.739928i
$906$	1.89495	+	1.75313i	0.0629556	+	0.0582439i
$907$	−31.6995	+	31.6995i	−1.05256	+	1.05256i	−0.0540236	+	0.998540i	$0.517205\pi$
$907$	−31.6995	+	31.6995i	−1.05256	+	1.05256i	−0.998540	+	0.0540236i	$0.982795\pi$
$908$	−33.3876	−	28.5635i	−1.10801	−	0.947913i
$909$	19.9054	+	19.9054i	0.660221	+	0.660221i
$910$	11.4590	−	0.445479i	0.379863	−	0.0147675i
$911$	34.3610			1.13843			0.569215	−	0.822189i	$-0.307247\pi$
$911$	34.3610			1.13843			0.569215	+	0.822189i	$0.307247\pi$
$912$	−4.00716	−	25.5741i	−0.132690	−	0.846842i
$913$	11.2179			0.371258
$914$	55.1801	−	2.14517i	1.82519	−	0.0709558i
$915$	−1.10269	−	1.10269i	−0.0364539	−	0.0364539i
$916$	19.1379	−	22.3701i	0.632333	−	0.739128i
$917$	−14.3169	+	14.3169i	−0.472786	+	0.472786i
$918$	0.800240	+	0.740348i	0.0264118	+	0.0244351i
$919$			15.4640i			0.510111i	0.966926	+	0.255056i	$0.0820938\pi$
$919$			15.4640i			0.510111i	−0.966926	+	0.255056i	$0.917906\pi$
$920$	−2.94706	+	3.72880i	−0.0971617	+	0.122935i
$921$			31.5135i			1.03840i
$922$	−31.4371	+	33.9802i	−1.03533	+	1.11908i
$923$	18.3754	−	18.3754i	0.604835	−	0.604835i
$924$	−0.616022	−	7.91098i	−0.0202656	−	0.260252i
$925$	2.65562	+	2.65562i	0.0873162	+	0.0873162i
$926$	−1.48903	−	38.3024i	−0.0489327	−	1.25869i
$927$	−35.4374			−1.16392
$928$	30.8784	−	46.0065i	1.01363	−	1.51024i
$929$	−25.7314			−0.844220			−0.422110	−	0.906545i	$-0.638710\pi$
$929$	−25.7314			−0.844220			−0.422110	+	0.906545i	$0.638710\pi$
$930$	−0.00620925	−	0.159720i	−0.000203609	−	0.00523743i
$931$	8.07831	+	8.07831i	0.264756	+	0.264756i
$932$	−1.74535	−	22.4138i	−0.0571707	−	0.734188i
$933$	11.4405	−	11.4405i	0.374544	−	0.374544i
$934$	22.0135	−	23.7943i	0.720302	−	0.778572i
$935$			0.675956i			0.0221061i
$936$	−26.7785	−	21.1644i	−0.875283	−	0.691781i
$937$		−	34.6673i		−	1.13253i	−0.824223	−	0.566266i	$-0.808387\pi$
$937$		−	34.6673i		−	1.13253i	0.824223	−	0.566266i	$-0.191613\pi$
$938$	−6.33316	−	5.85917i	−0.206785	−	0.191309i
$939$	−22.3682	+	22.3682i	−0.729958	+	0.729958i
$940$	−0.334599	+	0.391109i	−0.0109134	+	0.0127566i
$941$	23.5656	+	23.5656i	0.768218	+	0.768218i	0.977793	−	0.209575i	$-0.0672080\pi$
$941$	23.5656	+	23.5656i	0.768218	+	0.768218i	−0.209575	+	0.977793i	$0.567208\pi$
$942$	−9.15107	+	0.355755i	−0.298158	+	0.0115911i
$943$	17.9420			0.584273
$944$	−17.7078	+	24.2880i	−0.576338	+	0.790508i
$945$	−1.92678			−0.0626781
$946$	−7.06798	+	0.274773i	−0.229800	+	0.00893364i
$947$	1.69197	+	1.69197i	0.0549816	+	0.0549816i	0.734063	−	0.679081i	$-0.237622\pi$
$947$	1.69197	+	1.69197i	0.0549816	+	0.0549816i	−0.679081	+	0.734063i	$0.737622\pi$
$948$	54.2902	+	46.4460i	1.76327	+	1.50850i
$949$	−15.0841	+	15.0841i	−0.489650	+	0.489650i
$950$	−2.86085	−	2.64674i	−0.0928182	−	0.0858715i
$951$			25.4763i			0.826125i
$952$	−3.20828	+	0.375687i	−0.103981	+	0.0121761i
$953$		−	48.7521i		−	1.57924i	−0.613598	−	0.789619i	$-0.710278\pi$
$953$		−	48.7521i		−	1.57924i	0.613598	−	0.789619i	$-0.289722\pi$
$954$	−9.32680	+	10.0813i	−0.301966	+	0.326394i
$955$	−1.15026	+	1.15026i	−0.0372217	+	0.0372217i
$956$	−54.4152	+	4.23727i	−1.75991	+	0.137043i
$957$	16.2642	+	16.2642i	0.525746	+	0.525746i
$958$	−0.223974	−	5.76127i	−0.00723627	−	0.186138i
$959$	5.09627			0.164567
$960$	18.2779	−	4.34018i	0.589917	−	0.140079i
$961$	−30.9977			−0.999925
$962$	0.990244	+	25.4720i	0.0319267	+	0.821250i
$963$	29.0490	+	29.0490i	0.936090	+	0.936090i
$964$	13.9392	−	1.08543i	0.448951	−	0.0349594i
$965$	−16.2370	+	16.2370i	−0.522688	+	0.522688i
$966$	6.40279	−	6.92076i	0.206006	−	0.222672i
$967$			3.03730i			0.0976730i	0.998807	+	0.0488365i	$0.0155513\pi$
$967$			3.03730i			0.0976730i	−0.998807	+	0.0488365i	$0.984449\pi$
$968$	2.80923	−	0.328960i	0.0902921	−	0.0105732i
$969$		−	4.37447i		−	0.140528i
$970$	−1.08551	−	1.00427i	−0.0348536	−	0.0322451i
$971$	34.8583	−	34.8583i	1.11866	−	1.11866i	0.126716	−	0.991939i	$-0.459556\pi$
$971$	34.8583	−	34.8583i	1.11866	−	1.11866i	0.991939	−	0.126716i	$-0.0404438\pi$
$972$	31.2770	+	26.7579i	1.00321	+	0.858260i
$973$	−19.2916	−	19.2916i	−0.618461	−	0.618461i
$974$	14.6878	−	0.571000i	0.470628	−	0.0182960i
$975$	−11.2705			−0.360945
$976$	2.14643	+	1.56490i	0.0687055	+	0.0500914i
$977$	−13.6205			−0.435759			−0.217880	−	0.975976i	$-0.569914\pi$
$977$	−13.6205			−0.435759			−0.217880	+	0.975976i	$0.569914\pi$
$978$	−63.8527	+	2.48232i	−2.04178	+	0.0793759i
$979$	−3.11301	−	3.11301i	−0.0994923	−	0.0994923i
$980$	−5.38978	+	6.30005i	−0.172170	+	0.201248i
$981$	−35.2934	+	35.2934i	−1.12683	+	1.12683i
$982$	−38.8156	−	35.9105i	−1.23865	−	1.14595i
$983$		−	41.1883i		−	1.31370i	−0.754020	−	0.656852i	$-0.771888\pi$
$983$		−	41.1883i		−	1.31370i	0.754020	−	0.656852i	$-0.228112\pi$
$984$	−55.6389	−	43.9742i	−1.77370	−	1.40185i
$985$			13.3869i			0.426542i
$986$	6.35872	−	6.87311i	0.202503	−	0.218885i
$987$	0.721985	−	0.721985i	0.0229810	−	0.0229810i
$988$	−2.05370	−	26.3738i	−0.0653370	−	0.839061i
$989$	−5.94289	−	5.94289i	−0.188973	−	0.188973i
$990$	0.138132	+	3.55315i	0.00439011	+	0.112927i
$991$	21.2759			0.675851			0.337926	−	0.941173i	$-0.390275\pi$
$991$	21.2759			0.675851			0.337926	+	0.941173i	$0.390275\pi$
$992$	0.0525648	+	0.267148i	0.00166893	+	0.00848196i
$993$	27.1218			0.860683
$994$	−0.502562	−	12.9274i	−0.0159403	−	0.410031i
$995$	−14.0310	−	14.0310i	−0.444812	−	0.444812i
$996$	−4.09017	−	52.5261i	−0.129602	−	1.66435i
$997$	−16.0966	+	16.0966i	−0.509786	+	0.509786i	−0.914461	−	0.404675i	$-0.867385\pi$
$997$	−16.0966	+	16.0966i	−0.509786	+	0.509786i	0.404675	+	0.914461i	$0.367385\pi$
$998$	34.1524	−	36.9152i	1.08108	−	1.16853i
$999$		−	4.28299i		−	0.135508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.w.a.221.18	✓	72
16.5	even	4	inner	880.2.w.a.661.18	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
880.2.w.a.221.18	✓	72	1.1	even	1	trivial
880.2.w.a.661.18	yes	72	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0549372 - 1.41315i) q^{2} +(-1.66048 - 1.66048i) q^{3} +(-1.99396 + 0.155268i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-2.25527 + 2.43772i) q^{6} +1.68953i q^{7} +(0.328960 + 2.80923i) q^{8} +2.51436i q^{9} +(-1.03809 - 0.960399i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(3.56875 + 3.05311i) q^{12} +(3.39375 + 3.39375i) q^{13} +(2.38755 - 0.0928179i) q^{14} -2.34827 q^{15} +(3.95178 - 0.619199i) q^{16} +0.675956 q^{17} +(3.55315 - 0.138132i) q^{18} +(1.94870 + 1.94870i) q^{19} +(-1.30015 + 1.51974i) q^{20} +(2.80542 - 2.80542i) q^{21} +(1.03809 + 0.960399i) q^{22} +1.68037i q^{23} +(4.11843 - 5.21089i) q^{24} -1.00000i q^{25} +(4.60943 - 4.98231i) q^{26} +(-0.806401 + 0.806401i) q^{27} +(-0.262331 - 3.36886i) q^{28} +(6.92603 + 6.92603i) q^{29} +(0.129007 + 3.31844i) q^{30} -0.0481311 q^{31} +(-1.09212 - 5.55043i) q^{32} +2.34827 q^{33} +(-0.0371351 - 0.955224i) q^{34} +(1.19468 + 1.19468i) q^{35} +(-0.390400 - 5.01353i) q^{36} +(-2.65562 + 2.65562i) q^{37} +(2.64674 - 2.86085i) q^{38} -11.2705i q^{39} +(2.21904 + 1.75382i) q^{40} -10.6774i q^{41} +(-4.11859 - 3.81035i) q^{42} +(-3.53666 + 3.53666i) q^{43} +(1.30015 - 1.51974i) q^{44} +(1.77792 + 1.77792i) q^{45} +(2.37461 - 0.0923147i) q^{46} +0.257353 q^{47} +(-7.59000 - 5.53367i) q^{48} +4.14549 q^{49} +(-1.41315 + 0.0549372i) q^{50} +(-1.12241 - 1.12241i) q^{51} +(-7.29397 - 6.24008i) q^{52} +(-2.73111 + 2.73111i) q^{53} +(1.18386 + 1.09526i) q^{54} +1.00000i q^{55} +(-4.74628 + 0.555787i) q^{56} -6.47153i q^{57} +(9.40700 - 10.1680i) q^{58} +(-5.31352 + 5.31352i) q^{59} +(4.68236 - 0.364612i) q^{60} +(0.469577 + 0.469577i) q^{61} +(0.00264418 + 0.0680162i) q^{62} -4.24808 q^{63} +(-7.78357 + 1.84825i) q^{64} +4.79949 q^{65} +(-0.129007 - 3.31844i) q^{66} +(-2.55331 - 2.55331i) q^{67} +(-1.34783 + 0.104955i) q^{68} +(2.79021 - 2.79021i) q^{69} +(1.62262 - 1.75389i) q^{70} -5.41449i q^{71} +(-7.06341 + 0.827121i) q^{72} +4.44466i q^{73} +(3.89867 + 3.60688i) q^{74} +(-1.66048 + 1.66048i) q^{75} +(-4.18820 - 3.58306i) q^{76} +(-1.19468 - 1.19468i) q^{77} +(-15.9268 + 0.619169i) q^{78} +15.2127 q^{79} +(2.35649 - 3.23217i) q^{80} +10.2211 q^{81} +(-15.0888 + 0.586587i) q^{82} +(-7.93224 - 7.93224i) q^{83} +(-5.15832 + 6.02950i) q^{84} +(0.477973 - 0.477973i) q^{85} +(5.19211 + 4.80352i) q^{86} -23.0010i q^{87} +(-2.21904 - 1.75382i) q^{88} +4.40246i q^{89} +(2.41478 - 2.61013i) q^{90} +(-5.73385 + 5.73385i) q^{91} +(-0.260908 - 3.35060i) q^{92} +(0.0799204 + 0.0799204i) q^{93} +(-0.0141383 - 0.363678i) q^{94} +2.75587 q^{95} +(-7.40292 + 11.0298i) q^{96} +1.04568 q^{97} +(-0.227741 - 5.85818i) q^{98} +(-1.77792 - 1.77792i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 12 q^{6} - 4 q^{10} + 12 q^{12} - 8 q^{14} + 8 q^{15} + 4 q^{16} + 56 q^{17} + 20 q^{18} + 8 q^{19} - 8 q^{20} + 4 q^{22} - 24 q^{24} - 24 q^{27} + 20 q^{28} - 20 q^{30} + 20 q^{32} - 8 q^{33} + 4 q^{34}+ \cdots - 60 q^{98}+O(q^{100}) \) 72 * q + 12 * q^6 - 4 * q^10 + 12 * q^12 - 8 * q^14 + 8 * q^15 + 4 * q^16 + 56 * q^17 + 20 * q^18 + 8 * q^19 - 8 * q^20 + 4 * q^22 - 24 * q^24 - 24 * q^27 + 20 * q^28 - 20 * q^30 + 20 * q^32 - 8 * q^33 + 4 * q^34 - 60 * q^36 + 12 * q^38 - 40 * q^42 + 8 * q^44 - 20 * q^46 + 40 * q^47 + 20 * q^48 - 24 * q^49 + 32 * q^51 - 84 * q^52 + 72 * q^54 + 8 * q^56 - 8 * q^58 + 32 * q^60 - 16 * q^61 - 96 * q^62 + 36 * q^64 - 40 * q^65 + 20 * q^66 - 76 * q^68 - 16 * q^69 + 24 * q^70 + 20 * q^72 + 56 * q^74 + 56 * q^76 - 132 * q^78 - 16 * q^79 + 56 * q^81 + 36 * q^82 - 40 * q^83 - 152 * q^84 + 16 * q^85 + 56 * q^86 - 36 * q^90 + 88 * q^91 + 80 * q^92 + 48 * q^93 - 76 * q^94 - 32 * q^96 - 64 * q^97 - 60 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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