LMFDB - Embedded newform 740.2.u.a.31.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(31,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 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("740.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.u (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$76$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.4
Character	$\chi$	$=$	740.31
Dual form			740.2.u.a.191.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40327 - 0.175606i) q^{2} -0.390097 q^{3} +(1.93833 + 0.492844i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.547410 + 0.0685032i) q^{6} +0.0448530i q^{7} +(-2.63344 - 1.03197i) q^{8} -2.84782 q^{9} +(1.11643 - 0.868089i) q^{10} -2.85638 q^{11} +(-0.756134 - 0.192257i) q^{12} +(3.09774 - 3.09774i) q^{13} +(0.00787644 - 0.0629408i) q^{14} +(0.275840 - 0.275840i) q^{15} +(3.51421 + 1.91058i) q^{16} +(3.53399 - 3.53399i) q^{17} +(3.99626 + 0.500094i) q^{18} +(4.46281 + 4.46281i) q^{19} +(-1.71910 + 1.02211i) q^{20} -0.0174970i q^{21} +(4.00827 + 0.501597i) q^{22} +(3.31647 + 3.31647i) q^{23} +(1.02730 + 0.402569i) q^{24} -1.00000i q^{25} +(-4.89094 + 3.80298i) q^{26} +2.28122 q^{27} +(-0.0221055 + 0.0869397i) q^{28} +(-2.45713 - 2.45713i) q^{29} +(-0.435517 + 0.338638i) q^{30} +(-2.73590 + 2.73590i) q^{31} +(-4.59587 - 3.29818i) q^{32} +1.11427 q^{33} +(-5.57972 + 4.33855i) q^{34} +(-0.0317159 - 0.0317159i) q^{35} +(-5.52001 - 1.40353i) q^{36} +(2.89955 + 5.34720i) q^{37} +(-5.47882 - 7.04621i) q^{38} +(-1.20842 + 1.20842i) q^{39} +(2.59184 - 1.13241i) q^{40} +1.06401i q^{41} +(-0.00307257 + 0.0245530i) q^{42} +(5.19486 + 5.19486i) q^{43} +(-5.53660 - 1.40775i) q^{44} +(2.01372 - 2.01372i) q^{45} +(-4.07150 - 5.23629i) q^{46} +3.71007i q^{47} +(-1.37088 - 0.745312i) q^{48} +6.99799 q^{49} +(-0.175606 + 1.40327i) q^{50} +(-1.37860 + 1.37860i) q^{51} +(7.53113 - 4.47773i) q^{52} +10.8130 q^{53} +(-3.20116 - 0.400595i) q^{54} +(2.01977 - 2.01977i) q^{55} +(0.0462871 - 0.118118i) q^{56} +(-1.74093 - 1.74093i) q^{57} +(3.01653 + 3.87950i) q^{58} +(0.734461 + 0.734461i) q^{59} +(0.670614 - 0.398721i) q^{60} +(-2.01043 - 2.01043i) q^{61} +(4.31964 - 3.35876i) q^{62} -0.127734i q^{63} +(5.87006 + 5.43529i) q^{64} +4.38087i q^{65} +(-1.56361 - 0.195671i) q^{66} +3.33602 q^{67} +(8.59172 - 5.10831i) q^{68} +(-1.29374 - 1.29374i) q^{69} +(0.0389364 + 0.0500754i) q^{70} +14.2248i q^{71} +(7.49959 + 2.93888i) q^{72} -2.47925i q^{73} +(-3.12985 - 8.01274i) q^{74} +0.390097i q^{75} +(6.45090 + 10.8498i) q^{76} -0.128117i q^{77} +(1.90794 - 1.48353i) q^{78} +(1.48130 + 1.48130i) q^{79} +(-3.83591 + 1.13393i) q^{80} +7.65358 q^{81} +(0.186846 - 1.49309i) q^{82} -13.2274i q^{83} +(0.00862329 - 0.0339149i) q^{84} +4.99781i q^{85} +(-6.37754 - 8.20204i) q^{86} +(0.958518 + 0.958518i) q^{87} +(7.52213 + 2.94771i) q^{88} +(2.68197 + 2.68197i) q^{89} +(-3.17940 + 2.47216i) q^{90} +(0.138943 + 0.138943i) q^{91} +(4.79389 + 8.06289i) q^{92} +(1.06727 - 1.06727i) q^{93} +(0.651509 - 5.20622i) q^{94} -6.31136 q^{95} +(1.79283 + 1.28661i) q^{96} +(-4.05678 + 4.05678i) q^{97} +(-9.82006 - 1.22889i) q^{98} +8.13448 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q - 4 q^{2} - 4 q^{8} + 152 q^{9} - 16 q^{13} + 24 q^{14} + 40 q^{16} + 16 q^{22} - 36 q^{24} + 32 q^{29} - 4 q^{32} - 16 q^{37} - 40 q^{38} - 20 q^{42} - 72 q^{44} + 8 q^{46} - 248 q^{49} - 4 q^{50}+ \cdots + 24 q^{98}+O(q^{100}) $ 152 * q - 4 * q^2 - 4 * q^8 + 152 * q^9 - 16 * q^13 + 24 * q^14 + 40 * q^16 + 16 * q^22 - 36 * q^24 + 32 * q^29 - 4 * q^32 - 16 * q^37 - 40 * q^38 - 20 * q^42 - 72 * q^44 + 8 * q^46 - 248 * q^49 - 4 * q^50 - 20 * q^52 + 8 * q^54 - 4 * q^56 + 48 * q^57 + 28 * q^60 + 16 * q^61 + 16 * q^66 - 28 * q^68 - 128 * q^72 - 80 * q^74 + 76 * q^76 + 152 * q^81 + 16 * q^82 - 56 * q^84 - 96 * q^86 - 72 * q^88 + 8 * q^89 - 152 * q^92 + 16 * q^93 + 28 * q^94 + 48 * q^96 - 48 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.40327	−	0.175606i	−0.992261	−	0.124172i
$2$	−1.40327	−	0.175606i	−0.992261	−	0.124172i
$3$	−0.390097			−0.225222			−0.112611	−	0.993639i	$-0.535921\pi$
$3$	−0.390097			−0.225222			−0.112611	+	0.993639i	$0.535921\pi$
$4$	1.93833	+	0.492844i	0.969163	+	0.246422i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	0.547410	+	0.0685032i	0.223479	+	0.0279663i
$7$			0.0448530i			0.0169528i	0.999964	+	0.00847642i	$0.00269816\pi$
$7$			0.0448530i			0.0169528i	−0.999964	+	0.00847642i	$0.997302\pi$
$8$	−2.63344	−	1.03197i	−0.931063	−	0.364858i
$9$	−2.84782			−0.949275
$10$	1.11643	−	0.868089i	0.353047	−	0.274514i
$11$	−2.85638			−0.861232			−0.430616	−	0.902535i	$-0.641704\pi$
$11$	−2.85638			−0.861232			−0.430616	+	0.902535i	$0.641704\pi$
$12$	−0.756134	−	0.192257i	−0.218277	−	0.0554997i
$13$	3.09774	−	3.09774i	0.859159	−	0.859159i	−0.132080	−	0.991239i	$-0.542166\pi$
$13$	3.09774	−	3.09774i	0.859159	−	0.859159i	0.991239	+	0.132080i	$0.0421656\pi$
$14$	0.00787644	−	0.0629408i	0.00210507	−	0.0168216i
$15$	0.275840	−	0.275840i	0.0712216	−	0.0712216i
$16$	3.51421	+	1.91058i	0.878552	+	0.477646i
$17$	3.53399	−	3.53399i	0.857118	−	0.857118i	−0.133879	−	0.990998i	$-0.542743\pi$
$17$	3.53399	−	3.53399i	0.857118	−	0.857118i	0.990998	+	0.133879i	$0.0427435\pi$
$18$	3.99626	+	0.500094i	0.941928	+	0.117873i
$19$	4.46281	+	4.46281i	1.02384	+	1.02384i	0.999709	+	0.0241290i	$0.00768126\pi$
$19$	4.46281	+	4.46281i	1.02384	+	1.02384i	0.0241290	+	0.999709i	$0.492319\pi$
$20$	−1.71910	+	1.02211i	−0.384402	+	0.228551i
$21$		−	0.0174970i		−	0.00381816i
$22$	4.00827	+	0.501597i	0.854566	+	0.106941i
$23$	3.31647	+	3.31647i	0.691531	+	0.691531i	0.962569	−	0.271037i	$-0.0873667\pi$
$23$	3.31647	+	3.31647i	0.691531	+	0.691531i	−0.271037	+	0.962569i	$0.587367\pi$
$24$	1.02730	+	0.402569i	0.209696	+	0.0821741i
$25$		−	1.00000i		−	0.200000i
$26$	−4.89094	+	3.80298i	−0.959193	+	0.745826i
$27$	2.28122			0.439020
$28$	−0.0221055	+	0.0869397i	−0.00417755	+	0.0164301i
$29$	−2.45713	−	2.45713i	−0.456277	−	0.456277i	0.441154	−	0.897431i	$-0.354569\pi$
$29$	−2.45713	−	2.45713i	−0.456277	−	0.456277i	−0.897431	+	0.441154i	$0.854569\pi$
$30$	−0.435517	+	0.338638i	−0.0795141	+	0.0618266i
$31$	−2.73590	+	2.73590i	−0.491382	+	0.491382i	−0.908742	−	0.417359i	$-0.862956\pi$
$31$	−2.73590	+	2.73590i	−0.491382	+	0.491382i	0.417359	+	0.908742i	$0.362956\pi$
$32$	−4.59587	−	3.29818i	−0.812443	−	0.583041i
$33$	1.11427			0.193969
$34$	−5.57972	+	4.33855i	−0.956915	+	0.744055i
$35$	−0.0317159	−	0.0317159i	−0.00536096	−	0.00536096i
$36$	−5.52001	−	1.40353i	−0.920002	−	0.233922i
$37$	2.89955	+	5.34720i	0.476684	+	0.879075i
$37$	2.89955	+	5.34720i	0.476684	+	0.879075i
$38$	−5.47882	−	7.04621i	−0.888782	−	1.14305i
$39$	−1.20842	+	1.20842i	−0.193502	+	0.193502i
$40$	2.59184	−	1.13241i	0.409806	−	0.179050i
$41$			1.06401i			0.166170i	0.996542	+	0.0830850i	$0.0264773\pi$
$41$			1.06401i			0.166170i	−0.996542	+	0.0830850i	$0.973523\pi$
$42$	−0.00307257	+	0.0245530i	−0.000474108	+	0.00378861i
$43$	5.19486	+	5.19486i	0.792209	+	0.792209i	0.981853	−	0.189644i	$-0.0607333\pi$
$43$	5.19486	+	5.19486i	0.792209	+	0.792209i	−0.189644	+	0.981853i	$0.560733\pi$
$44$	−5.53660	−	1.40775i	−0.834674	−	0.212226i
$45$	2.01372	−	2.01372i	0.300187	−	0.300187i
$46$	−4.07150	−	5.23629i	−0.600311	−	0.772048i
$47$			3.71007i			0.541169i	0.962696	+	0.270584i	$0.0872169\pi$
$47$			3.71007i			0.541169i	−0.962696	+	0.270584i	$0.912783\pi$
$48$	−1.37088	−	0.745312i	−0.197870	−	0.107577i
$49$	6.99799			0.999713
$50$	−0.175606	+	1.40327i	−0.0248344	+	0.198452i
$51$	−1.37860	+	1.37860i	−0.193042	+	0.193042i
$52$	7.53113	−	4.47773i	1.04438	−	0.620949i
$53$	10.8130			1.48528			0.742638	−	0.669693i	$-0.233574\pi$
$53$	10.8130			1.48528			0.742638	+	0.669693i	$0.233574\pi$
$54$	−3.20116	−	0.400595i	−0.435623	−	0.0545140i
$55$	2.01977	−	2.01977i	0.272345	−	0.272345i
$56$	0.0462871	−	0.118118i	0.00618538	−	0.0157842i
$57$	−1.74093	−	1.74093i	−0.230591	−	0.230591i
$58$	3.01653	+	3.87950i	0.396089	+	0.509403i
$59$	0.734461	+	0.734461i	0.0956187	+	0.0956187i	0.753298	−	0.657679i	$-0.228462\pi$
$59$	0.734461	+	0.734461i	0.0956187	+	0.0956187i	−0.657679	+	0.753298i	$0.728462\pi$
$60$	0.670614	−	0.398721i	0.0865758	−	0.0514747i
$61$	−2.01043	−	2.01043i	−0.257410	−	0.257410i	0.566590	−	0.824000i	$-0.308262\pi$
$61$	−2.01043	−	2.01043i	−0.257410	−	0.257410i	−0.824000	+	0.566590i	$0.808262\pi$
$62$	4.31964	−	3.35876i	0.548595	−	0.426563i
$63$		−	0.127734i		−	0.0160929i
$64$	5.87006	+	5.43529i	0.733758	+	0.679411i
$65$			4.38087i			0.543380i
$66$	−1.56361	−	0.195671i	−0.192467	−	0.0240855i
$67$	3.33602			0.407560			0.203780	−	0.979017i	$-0.434677\pi$
$67$	3.33602			0.407560			0.203780	+	0.979017i	$0.434677\pi$
$68$	8.59172	−	5.10831i	1.04190	−	0.619474i
$69$	−1.29374	−	1.29374i	−0.155748	−	0.155748i
$70$	0.0389364	+	0.0500754i	0.00465379	+	0.00598515i
$71$			14.2248i			1.68817i	0.536207	+	0.844086i	$0.319857\pi$
$71$			14.2248i			1.68817i	−0.536207	+	0.844086i	$0.680143\pi$
$72$	7.49959	+	2.93888i	0.883835	+	0.346350i
$73$		−	2.47925i		−	0.290174i	−0.989419	−	0.145087i	$-0.953654\pi$
$73$		−	2.47925i		−	0.290174i	0.989419	−	0.145087i	$-0.0463462\pi$
$74$	−3.12985	−	8.01274i	−0.363838	−	0.931462i
$75$			0.390097i			0.0450445i
$76$	6.45090	+	10.8498i	0.739969	+	1.24456i
$77$		−	0.128117i		−	0.0146003i
$78$	1.90794	−	1.48353i	0.216032	−	0.167977i
$79$	1.48130	+	1.48130i	0.166659	+	0.166659i	0.785509	−	0.618850i	$-0.212401\pi$
$79$	1.48130	+	1.48130i	0.166659	+	0.166659i	−0.618850	+	0.785509i	$0.712401\pi$
$80$	−3.83591	+	1.13393i	−0.428868	+	0.126778i
$81$	7.65358			0.850398
$82$	0.186846	−	1.49309i	0.0206337	−	0.164884i
$83$		−	13.2274i		−	1.45190i	−0.687747	−	0.725950i	$-0.741400\pi$
$83$		−	13.2274i		−	1.45190i	0.687747	−	0.725950i	$-0.258600\pi$
$84$	0.00862329	−	0.0339149i	0.000940878	−	0.00370042i
$85$			4.99781i			0.542089i
$86$	−6.37754	−	8.20204i	−0.687708	−	0.884448i
$87$	0.958518	+	0.958518i	0.102764	+	0.102764i
$88$	7.52213	+	2.94771i	0.801861	+	0.314227i
$89$	2.68197	+	2.68197i	0.284289	+	0.284289i	0.834817	−	0.550528i	$-0.185574\pi$
$89$	2.68197	+	2.68197i	0.284289	+	0.284289i	−0.550528	+	0.834817i	$0.685574\pi$
$90$	−3.17940	+	2.47216i	−0.335139	+	0.260589i
$91$	0.138943	+	0.138943i	0.0145652	+	0.0145652i
$92$	4.79389	+	8.06289i	0.499798	+	0.840615i
$93$	1.06727	−	1.06727i	0.110670	−	0.110670i
$94$	0.651509	−	5.20622i	0.0671980	−	0.536981i
$95$	−6.31136			−0.647532
$96$	1.79283	+	1.28661i	0.182980	+	0.131314i
$97$	−4.05678	+	4.05678i	−0.411904	+	0.411904i	−0.882401	−	0.470497i	$-0.844075\pi$
$97$	−4.05678	+	4.05678i	−0.411904	+	0.411904i	0.470497	+	0.882401i	$0.344075\pi$
$98$	−9.82006	−	1.22889i	−0.991976	−	0.124136i
$99$	8.13448			0.817546
$100$	0.492844	−	1.93833i	0.0492844	−	0.193833i
$101$			2.51377i			0.250129i	0.992149	+	0.125065i	$0.0399138\pi$
$101$			2.51377i			0.250129i	−0.992149	+	0.125065i	$0.960086\pi$
$102$	2.17663	−	1.69245i	0.215519	−	0.167578i
$103$	12.6477	−	12.6477i	1.24621	−	1.24621i	0.288835	−	0.957379i	$-0.406732\pi$
$103$	12.6477	−	12.6477i	1.24621	−	1.24621i	0.957379	−	0.288835i	$-0.0932679\pi$
$104$	−11.3545	+	4.96094i	−1.11340	+	0.486461i
$105$	0.0123723	+	0.0123723i	0.00120741	+	0.00120741i
$106$	−15.1735	−	1.89882i	−1.47378	−	0.184430i
$107$		−	6.19838i		−	0.599220i	−0.954062	−	0.299610i	$-0.903143\pi$
$107$		−	6.19838i		−	0.599220i	0.954062	−	0.299610i	$-0.0968565\pi$
$108$	4.42174	+	1.12428i	0.425482	+	0.108184i
$109$	10.1251	−	10.1251i	0.969813	−	0.969813i	−0.0297449	−	0.999558i	$-0.509469\pi$
$109$	10.1251	−	10.1251i	0.969813	−	0.969813i	0.999558	+	0.0297449i	$0.00946949\pi$
$110$	−3.18896	+	2.47959i	−0.304055	+	0.236420i
$111$	−1.13111	−	2.08593i	−0.107360	−	0.197987i
$112$	−0.0856954	+	0.157623i	−0.00809746	+	0.0148940i
$113$	1.32235	+	1.32235i	0.124397	+	0.124397i	0.766564	−	0.642168i	$-0.221965\pi$
$113$	1.32235	+	1.32235i	0.124397	+	0.124397i	−0.642168	+	0.766564i	$0.721965\pi$
$114$	2.13727	+	2.74870i	0.200174	+	0.257440i
$115$	−4.69019			−0.437363
$116$	−3.55173	−	5.97370i	−0.329770	−	0.554644i
$117$	−8.82183	+	8.82183i	−0.815578	+	0.815578i
$118$	−0.901671	−	1.15962i	−0.0830055	−	0.106752i
$119$	0.158510	+	0.158510i	0.0145306	+	0.0145306i
$120$	−1.01107	+	0.441750i	−0.0922975	+	0.0403261i
$121$	−2.84108			−0.258280
$122$	2.46814	+	3.17422i	0.223454	+	0.287381i
$123$		−	0.415066i		−	0.0374252i
$124$	−6.65144	+	3.95469i	−0.597317	+	0.355142i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−0.0224307	+	0.179244i	−0.00199829	+	0.0159684i
$127$		−	4.08301i		−	0.362309i	−0.983455	−	0.181154i	$-0.942017\pi$
$127$		−	4.08301i		−	0.362309i	0.983455	−	0.181154i	$-0.0579834\pi$
$128$	−7.28281	−	8.65799i	−0.643715	−	0.765265i
$129$	−2.02650	−	2.02650i	−0.178423	−	0.178423i
$130$	0.769305	−	6.14753i	0.0674726	−	0.539174i
$131$	−12.7419	+	12.7419i	−1.11327	+	1.11327i	−0.120563	+	0.992706i	$0.538470\pi$
$131$	−12.7419	+	12.7419i	−1.11327	+	1.11327i	−0.992706	+	0.120563i	$0.961530\pi$
$132$	2.15981	+	0.549159i	0.187987	+	0.0477981i
$133$	−0.200170	+	0.200170i	−0.0173570	+	0.0173570i
$134$	−4.68133	−	0.585824i	−0.404405	−	0.0506075i
$135$	−1.61306	+	1.61306i	−0.138830	+	0.138830i
$136$	−12.9535	+	5.65958i	−1.11076	+	0.485305i
$137$	−0.754756			−0.0644832			−0.0322416	−	0.999480i	$-0.510265\pi$
$137$	−0.754756			−0.0644832			−0.0322416	+	0.999480i	$0.510265\pi$
$138$	1.58828	+	2.04266i	0.135203	+	0.173883i
$139$	16.5182			1.40105			0.700526	−	0.713627i	$-0.252949\pi$
$139$	16.5182			1.40105			0.700526	+	0.713627i	$0.252949\pi$
$140$	−0.0458447	−	0.0771066i	−0.00387458	−	0.00651670i
$141$		−	1.44728i		−	0.121883i
$142$	2.49796	−	19.9612i	0.209624	−	1.67511i
$143$	−8.84834	+	8.84834i	−0.739935	+	0.739935i
$144$	−10.0079	−	5.44101i	−0.833988	−	0.453417i
$145$	3.47491			0.288575
$146$	−0.435370	+	3.47905i	−0.0360315	+	0.287928i
$147$	−2.72989			−0.225158
$148$	2.98494	+	11.7936i	0.245361	+	0.969432i
$149$	19.8516			1.62630			0.813151	−	0.582052i	$-0.197750\pi$
$149$	19.8516			1.62630			0.813151	+	0.582052i	$0.197750\pi$
$150$	0.0685032	−	0.547410i	0.00559326	−	0.0446959i
$151$	−14.0203			−1.14096			−0.570478	−	0.821313i	$-0.693242\pi$
$151$	−14.0203			−1.14096			−0.570478	+	0.821313i	$0.693242\pi$
$152$	−7.14706	−	16.3580i	−0.579703	−	1.32681i
$153$	−10.0642	+	10.0642i	−0.813641	+	0.813641i
$154$	−0.0224981	+	0.179783i	−0.00181295	+	0.0144873i
$155$		−	3.86915i		−	0.310777i
$156$	−2.93787	+	1.74675i	−0.235218	+	0.139852i
$157$	−16.9849			−1.35554			−0.677772	−	0.735272i	$-0.737054\pi$
$157$	−16.9849			−1.35554			−0.677772	+	0.735272i	$0.737054\pi$
$158$	−1.81854	−	2.33879i	−0.144675	−	0.186064i
$159$	−4.21811			−0.334518
$160$	5.58193	−	0.917608i	0.441291	−	0.0725433i
$161$	−0.148754	+	0.148754i	−0.0117234	+	0.0117234i
$162$	−10.7400	−	1.34401i	−0.843816	−	0.105596i
$163$	−4.27466	+	4.27466i	−0.334818	+	0.334818i	−0.854413	−	0.519595i	$-0.826083\pi$
$163$	−4.27466	+	4.27466i	−0.334818	+	0.334818i	0.519595	+	0.854413i	$0.326083\pi$
$164$	−0.524390	+	2.06239i	−0.0409480	+	0.161046i
$165$	−0.787904	+	0.787904i	−0.0613383	+	0.0613383i
$166$	−2.32281	+	18.5616i	−0.180285	+	1.44066i
$167$	−1.70243	−	1.70243i	−0.131738	−	0.131738i	0.638163	−	0.769901i	$-0.279694\pi$
$167$	−1.70243	−	1.70243i	−0.131738	−	0.131738i	−0.769901	+	0.638163i	$0.779694\pi$
$168$	−0.0180564	+	0.0460774i	−0.00139308	+	0.00355495i
$169$		−	6.19201i		−	0.476308i
$170$	0.877645	−	7.01328i	0.0673123	−	0.537894i
$171$	−12.7093	−	12.7093i	−0.971904	−	0.971904i
$172$	7.50908	+	12.6296i	0.572562	+	0.962997i
$173$		−	23.5732i		−	1.79224i	−0.443815	−	0.896119i	$-0.646375\pi$
$173$		−	23.5732i		−	1.79224i	0.443815	−	0.896119i	$-0.353625\pi$
$174$	−1.17674	−	1.51338i	−0.0892082	−	0.114729i
$175$	0.0448530			0.00339057
$176$	−10.0379	−	5.45736i	−0.756637	−	0.411364i
$177$	−0.286511	−	0.286511i	−0.0215355	−	0.0215355i
$178$	−3.29256	−	4.23450i	−0.246788	−	0.317389i
$179$	−7.85864	+	7.85864i	−0.587382	+	0.587382i	−0.936922	−	0.349540i	$-0.886338\pi$
$179$	−7.85864	+	7.85864i	−0.587382	+	0.587382i	0.349540	+	0.936922i	$0.386338\pi$
$180$	4.89568	−	2.91079i	0.364903	−	0.216957i
$181$	3.18365			0.236639			0.118319	−	0.992976i	$-0.462249\pi$
$181$	3.18365			0.236639			0.118319	+	0.992976i	$0.462249\pi$
$182$	−0.170575	−	0.219374i	−0.0126439	−	0.0162611i
$183$	0.784263	+	0.784263i	0.0579744	+	0.0579744i
$184$	−5.31123	−	12.1562i	−0.391549	−	0.896170i
$185$	−5.83134	−	1.73075i	−0.428729	−	0.127247i
$186$	−1.68508	+	1.31024i	−0.123556	+	0.0960716i
$187$	−10.0944	+	10.0944i	−0.738177	+	0.738177i
$188$	−1.82848	+	7.19132i	−0.133356	+	0.524481i
$189$			0.102319i			0.00744264i
$190$	8.85653	+	1.10831i	0.642521	+	0.0804053i
$191$	6.07979	+	6.07979i	0.439918	+	0.439918i	0.891984	−	0.452066i	$-0.149313\pi$
$191$	6.07979	+	6.07979i	0.439918	+	0.439918i	−0.452066	+	0.891984i	$0.649313\pi$
$192$	−2.28989	−	2.12029i	−0.165259	−	0.153019i
$193$	−16.5447	+	16.5447i	−1.19091	+	1.19091i	−0.214100	+	0.976812i	$0.568682\pi$
$193$	−16.5447	+	16.5447i	−1.19091	+	1.19091i	−0.976812	+	0.214100i	$0.931318\pi$
$194$	6.40515	−	4.98036i	0.459863	−	0.357569i
$195$		−	1.70896i		−	0.122381i
$196$	13.5644	+	3.44892i	0.968884	+	0.246351i
$197$	10.4641			0.745539			0.372769	−	0.927924i	$-0.378408\pi$
$197$	10.4641			0.745539			0.372769	+	0.927924i	$0.378408\pi$
$198$	−11.4149	−	1.42846i	−0.811218	−	0.101516i
$199$	12.3289	−	12.3289i	0.873973	−	0.873973i	−0.118930	−	0.992903i	$-0.537946\pi$
$199$	12.3289	−	12.3289i	0.873973	−	0.873973i	0.992903	+	0.118930i	$0.0379464\pi$
$200$	−1.03197	+	2.63344i	−0.0729715	+	0.186213i
$201$	−1.30137			−0.0917915
$202$	0.441432	−	3.52749i	0.0310590	−	0.248193i
$203$	0.110210	−	0.110210i	0.00773520	−	0.00773520i
$204$	−3.35160	+	1.99274i	−0.234659	+	0.139519i
$205$	−0.752367	−	0.752367i	−0.0525476	−	0.0525476i
$206$	−19.9691	+	15.5271i	−1.39131	+	1.08182i
$207$	−9.44472	−	9.44472i	−0.656453	−	0.656453i
$208$	16.8046	−	4.96762i	1.16519	−	0.344442i
$209$	−12.7475	−	12.7475i	−0.881762	−	0.881762i
$210$	−0.0151890	−	0.0195342i	−0.00104814	−	0.00134799i
$211$		−	14.8319i		−	1.02107i	−0.859857	−	0.510534i	$-0.829448\pi$
$211$		−	14.8319i		−	1.02107i	0.859857	−	0.510534i	$-0.170552\pi$
$212$	20.9591	+	5.32911i	1.43947	+	0.366005i
$213$		−	5.54904i		−	0.380214i
$214$	−1.08847	+	8.69799i	−0.0744063	+	0.594582i
$215$	−7.34665			−0.501037
$216$	−6.00746	−	2.35415i	−0.408756	−	0.160180i
$217$	−0.122713	−	0.122713i	−0.00833033	−	0.00833033i
$218$	−15.9863	+	12.4303i	−1.08273	+	0.841883i
$219$			0.967147i			0.0653537i
$220$	4.91040	−	2.91954i	0.331059	−	0.196835i
$221$		−	21.8948i		−	1.47280i
$222$	1.22095	+	3.12574i	0.0819445	+	0.209786i
$223$			5.93949i			0.397738i	0.980026	+	0.198869i	$0.0637268\pi$
$223$			5.93949i			0.397738i	−0.980026	+	0.198869i	$0.936273\pi$
$224$	0.147933	−	0.206139i	0.00988420	−	0.0137732i
$225$			2.84782i			0.189855i
$226$	−1.62340	−	2.08783i	−0.107987	−	0.138880i
$227$	−16.4797	−	16.4797i	−1.09380	−	1.09380i	−0.995120	−	0.0986761i	$-0.968539\pi$
$227$	−16.4797	−	16.4797i	−1.09380	−	1.09380i	−0.0986761	−	0.995120i	$-0.531461\pi$
$228$	−2.51648	−	4.23248i	−0.166658	−	0.280303i
$229$	11.5013			0.760027			0.380013	−	0.924981i	$-0.375919\pi$
$229$	11.5013			0.760027			0.380013	+	0.924981i	$0.375919\pi$
$230$	6.58160	+	0.823625i	0.433978	+	0.0543082i
$231$			0.0499781i			0.00328832i
$232$	3.93502	+	9.00641i	0.258347	+	0.591300i
$233$			22.4796i			1.47269i	0.676609	+	0.736343i	$0.263449\pi$
$233$			22.4796i			1.47269i	−0.676609	+	0.736343i	$0.736551\pi$
$234$	13.9286	−	10.8302i	0.910538	−	0.707994i
$235$	−2.62341	−	2.62341i	−0.171133	−	0.171133i
$236$	1.06165	+	1.78560i	0.0691075	+	0.116233i
$237$	−0.577851	−	0.577851i	−0.0375354	−	0.0375354i
$238$	−0.194597	−	0.250267i	−0.0126138	−	0.0162224i
$239$	−10.6494	−	10.6494i	−0.688855	−	0.688855i	0.273124	−	0.961979i	$-0.411943\pi$
$239$	−10.6494	−	10.6494i	−0.688855	−	0.688855i	−0.961979	+	0.273124i	$0.911943\pi$
$240$	1.49637	−	0.442344i	0.0965906	−	0.0285532i
$241$	−10.4557	+	10.4557i	−0.673510	+	0.673510i	−0.958523	−	0.285014i	$-0.908002\pi$
$241$	−10.4557	+	10.4557i	−0.673510	+	0.673510i	0.285014	+	0.958523i	$0.408002\pi$
$242$	3.98680	+	0.498910i	0.256281	+	0.0320711i
$243$	−9.82928			−0.630549
$244$	−2.90604	−	4.88771i	−0.186040	−	0.312903i
$245$	−4.94832	+	4.94832i	−0.316137	+	0.316137i
$246$	−0.0728879	+	0.582449i	−0.00464716	+	0.0371356i
$247$	27.6492			1.75928
$248$	10.0282	−	4.38147i	0.636793	−	0.278223i
$249$			5.15998i			0.327000i
$250$	−0.868089	−	1.11643i	−0.0549028	−	0.0706094i
$251$	3.91868	−	3.91868i	0.247345	−	0.247345i	−0.572535	−	0.819880i	$-0.694040\pi$
$251$	3.91868	−	3.91868i	0.247345	−	0.247345i	0.819880	+	0.572535i	$0.194040\pi$
$252$	0.0629527	−	0.247589i	0.00396565	−	0.0155966i
$253$	−9.47310	−	9.47310i	−0.595569	−	0.595569i
$254$	−0.717000	+	5.72956i	−0.0449886	+	0.359505i
$255$		−	1.94963i		−	0.122091i
$256$	8.69934	+	13.4284i	0.543709	+	0.839274i
$257$	−9.93499	+	9.93499i	−0.619728	+	0.619728i	−0.945461	−	0.325734i	$-0.894389\pi$
$257$	−9.93499	+	9.93499i	−0.619728	+	0.619728i	0.325734	+	0.945461i	$0.394389\pi$
$258$	2.48786	+	3.19959i	0.154887	+	0.199198i
$259$	−0.239838	+	0.130054i	−0.0149028	+	0.00808115i
$260$	−2.15908	+	8.49155i	−0.133901	+	0.526623i
$261$	6.99747	+	6.99747i	0.433133	+	0.433133i
$262$	20.1179	−	15.6428i	1.24289	−	0.966416i
$263$	−1.15262			−0.0710735			−0.0355367	−	0.999368i	$-0.511314\pi$
$263$	−1.15262			−0.0710735			−0.0355367	+	0.999368i	$0.511314\pi$
$264$	−2.93436	−	1.14989i	−0.180597	−	0.0707709i
$265$	−7.64593	+	7.64593i	−0.469686	+	0.469686i
$266$	0.316044	−	0.245742i	0.0193779	−	0.0150674i
$267$	−1.04623	−	1.04623i	−0.0640282	−	0.0640282i
$268$	6.46629	+	1.64414i	0.394992	+	0.100432i
$269$	−1.39067			−0.0847908			−0.0423954	−	0.999101i	$-0.513499\pi$
$269$	−1.39067			−0.0847908			−0.0423954	+	0.999101i	$0.513499\pi$
$270$	2.54682	−	1.98030i	0.154995	−	0.120517i
$271$		−	15.6495i		−	0.950642i	−0.879813	−	0.475321i	$-0.842332\pi$
$271$		−	15.6495i		−	0.950642i	0.879813	−	0.475321i	$-0.157668\pi$
$272$	19.1712	−	5.66720i	1.16242	−	0.343624i
$273$	−0.0542012	−	0.0542012i	−0.00328041	−	0.00328041i
$274$	1.05913	+	0.132540i	0.0639841	+	0.00800701i
$275$			2.85638i			0.172246i
$276$	−1.87008	−	3.14531i	−0.112566	−	0.189325i
$277$	−0.262093	−	0.262093i	−0.0157477	−	0.0157477i	0.699189	−	0.714937i	$-0.253545\pi$
$277$	−0.262093	−	0.262093i	−0.0157477	−	0.0157477i	−0.714937	+	0.699189i	$0.753545\pi$
$278$	−23.1794	−	2.90068i	−1.39021	−	0.173971i
$279$	7.79137	−	7.79137i	0.466457	−	0.466457i
$280$	0.0507921	+	0.116252i	0.00303541	+	0.00694738i
$281$	−12.8644	+	12.8644i	−0.767424	+	0.767424i	−0.977652	−	0.210228i	$-0.932579\pi$
$281$	−12.8644	+	12.8644i	−0.767424	+	0.767424i	0.210228	+	0.977652i	$0.432579\pi$
$282$	−0.254151	+	2.03093i	−0.0151345	+	0.120940i
$283$	−11.3230	+	11.3230i	−0.673082	+	0.673082i	−0.958425	−	0.285343i	$-0.907892\pi$
$283$	−11.3230	+	11.3230i	−0.673082	+	0.673082i	0.285343	+	0.958425i	$0.407892\pi$
$284$	−7.01060	+	27.5723i	−0.416003	+	1.63611i
$285$	2.46204			0.145839
$286$	13.9704	−	10.8628i	0.826088	−	0.642329i
$287$	−0.0477239			−0.00281706
$288$	13.0882	+	9.39263i	0.771232	+	0.553466i
$289$		−	7.97815i		−	0.469303i
$290$	−4.87623	−	0.610213i	−0.286342	−	0.0358330i
$291$	1.58254	−	1.58254i	0.0927700	−	0.0927700i
$292$	1.22188	−	4.80559i	0.0715053	−	0.281226i
$293$	19.9728			1.16683			0.583413	−	0.812176i	$-0.301717\pi$
$293$	19.9728			1.16683			0.583413	+	0.812176i	$0.301717\pi$
$294$	3.83077	+	0.479384i	0.223415	+	0.0279583i
$295$	−1.03868			−0.0604746
$296$	−2.11765	−	17.0738i	−0.123086	−	0.992396i
$297$	−6.51603			−0.378098
$298$	−27.8571	−	3.48605i	−1.61372	−	0.201941i
$299$	20.5471			1.18827
$300$	−0.192257	+	0.756134i	−0.0110999	+	0.0436554i
$301$	−0.233005	+	0.233005i	−0.0134302	+	0.0134302i
$302$	19.6742	+	2.46204i	1.13213	+	0.141675i
$303$		−	0.980612i		−	0.0563347i
$304$	7.15667	+	24.2098i	0.410463	+	1.38853i
$305$	2.84318			0.162800
$306$	15.8901	−	12.3554i	0.908375	−	0.706312i
$307$	29.9086			1.70698			0.853488	−	0.521113i	$-0.174483\pi$
$307$	29.9086			1.70698			0.853488	+	0.521113i	$0.174483\pi$
$308$	0.0631419	−	0.248333i	0.00359784	−	0.0141501i
$309$	−4.93382	+	4.93382i	−0.280675	+	0.280675i
$310$	−0.679445	+	5.42945i	−0.0385899	+	0.308372i
$311$	−21.3067	+	21.3067i	−1.20819	+	1.20819i	−0.236580	+	0.971612i	$0.576027\pi$
$311$	−21.3067	+	21.3067i	−1.20819	+	1.20819i	−0.971612	+	0.236580i	$0.923973\pi$
$312$	4.42936	−	1.93525i	0.250763	−	0.109562i
$313$	9.41081	−	9.41081i	0.531930	−	0.531930i	−0.389216	−	0.921146i	$-0.627254\pi$
$313$	9.41081	−	9.41081i	0.531930	−	0.531930i	0.921146	+	0.389216i	$0.127254\pi$
$314$	23.8344	+	2.98265i	1.34505	+	0.168321i
$315$	0.0903212	+	0.0903212i	0.00508902	+	0.00508902i
$316$	2.14119	+	3.60129i	0.120452	+	0.202589i
$317$			0.923768i			0.0518840i	0.999663	+	0.0259420i	$0.00825852\pi$
$317$			0.923768i			0.0518840i	−0.999663	+	0.0259420i	$0.991741\pi$
$318$	5.91914	+	0.740723i	0.331929	+	0.0415377i
$319$	7.01850	+	7.01850i	0.392961	+	0.392961i
$320$	−7.99409	+	0.307431i	−0.446883	+	0.0171859i
$321$			2.41797i			0.134958i
$322$	0.234863	−	0.182619i	0.0130884	−	0.0101770i
$323$	31.5430			1.75510
$324$	14.8351	+	3.77202i	0.824174	+	0.209557i
$325$	−3.09774	−	3.09774i	−0.171832	−	0.171832i
$326$	6.74916	−	5.24785i	0.373801	−	0.290651i
$327$	−3.94978	+	3.94978i	−0.218423	+	0.218423i
$328$	1.09803	−	2.80201i	0.0606284	−	0.154715i
$329$	−0.166408			−0.00917435
$330$	1.24400	−	0.967281i	0.0684801	−	0.0532471i
$331$	14.1087	+	14.1087i	0.775487	+	0.775487i	0.979060	−	0.203573i	$-0.0652554\pi$
$331$	14.1087	+	14.1087i	0.775487	+	0.775487i	−0.203573	+	0.979060i	$0.565255\pi$
$332$	6.51906	−	25.6391i	0.357780	−	1.40713i
$333$	−8.25742	−	15.2279i	−0.452504	−	0.834484i
$334$	2.09001	+	2.68792i	0.114360	+	0.147076i
$335$	−2.35892	+	2.35892i	−0.128882	+	0.128882i
$336$	0.0334295	−	0.0614882i	0.00182373	−	0.00335445i
$337$			18.5088i			1.00824i	0.863633	+	0.504120i	$0.168183\pi$
$337$			18.5088i			1.00824i	−0.863633	+	0.504120i	$0.831817\pi$
$338$	−1.08735	+	8.68905i	−0.0591441	+	0.472622i
$339$	−0.515845	−	0.515845i	−0.0280169	−	0.0280169i
$340$	−2.46314	+	9.68739i	−0.133583	+	0.525373i
$341$	7.81478	−	7.81478i	0.423194	−	0.423194i
$342$	15.6027	+	20.0664i	0.843699	+	1.08506i
$343$			0.627852i			0.0339008i
$344$	−8.31943	−	19.0413i	−0.448553	−	1.02664i
$345$	1.82963			0.0985039
$346$	−4.13959	+	33.0795i	−0.222546	+	1.77837i
$347$	2.22890	−	2.22890i	0.119654	−	0.119654i	−0.644744	−	0.764398i	$-0.723036\pi$
$347$	2.22890	−	2.22890i	0.119654	−	0.119654i	0.764398	+	0.644744i	$0.223036\pi$
$348$	1.38552	+	2.33032i	0.0742716	+	0.124918i
$349$	−11.8860			−0.636242			−0.318121	−	0.948050i	$-0.603052\pi$
$349$	−11.8860			−0.636242			−0.318121	+	0.948050i	$0.603052\pi$
$350$	−0.0629408	−	0.00787644i	−0.00336433	−	0.000421014i
$351$	7.06662	−	7.06662i	0.377188	−	0.377188i
$352$	13.1276	+	9.42086i	0.699702	+	0.502133i
$353$	−3.54921	−	3.54921i	−0.188906	−	0.188906i	0.606317	−	0.795223i	$-0.292646\pi$
$353$	−3.54921	−	3.54921i	−0.188906	−	0.188906i	−0.795223	+	0.606317i	$0.792646\pi$
$354$	0.351739	+	0.452365i	0.0186947	+	0.0240429i
$355$	−10.0585	−	10.0585i	−0.533847	−	0.533847i
$356$	3.87674	+	6.52033i	0.205467	+	0.345577i
$357$	−0.0618342	−	0.0618342i	−0.00327261	−	0.00327261i
$358$	12.4078	−	9.64776i	0.655773	−	0.509900i
$359$		−	12.7312i		−	0.671930i	−0.941875	−	0.335965i	$-0.890938\pi$
$359$		−	12.7312i		−	0.671930i	0.941875	−	0.335965i	$-0.109062\pi$
$360$	−7.38111	+	3.22491i	−0.389019	+	0.169968i
$361$			20.8333i			1.09649i
$362$	−4.46752	−	0.559067i	−0.234807	−	0.0293839i
$363$	1.10830			0.0581704
$364$	0.200840	+	0.337794i	0.0105269	+	0.0177052i
$365$	1.75309	+	1.75309i	0.0917612	+	0.0917612i
$366$	−0.962811	−	1.23825i	−0.0503269	−	0.0647245i
$367$		−	19.1752i		−	1.00094i	−0.865755	−	0.500468i	$-0.833161\pi$
$367$		−	19.1752i		−	1.00094i	0.865755	−	0.500468i	$-0.166839\pi$
$368$	5.31837	+	17.9912i	0.277239	+	0.937854i
$369$		−	3.03011i		−	0.157741i
$370$	7.87900	+	3.45272i	0.409610	+	0.179498i
$371$			0.484995i			0.0251797i
$372$	2.59470	−	1.54271i	0.134529	−	0.0799859i
$373$		−	18.6570i		−	0.966022i	−0.875614	−	0.483011i	$-0.839543\pi$
$373$		−	18.6570i		−	0.966022i	0.875614	−	0.483011i	$-0.160457\pi$
$374$	15.9378	−	12.3925i	0.824125	−	0.640803i
$375$	−0.275840	−	0.275840i	−0.0142443	−	0.0142443i
$376$	3.82869	−	9.77026i	0.197450	−	0.503863i
$377$	−15.2231			−0.784030
$378$	0.0179679	−	0.143582i	0.000924168	−	0.00738504i
$379$			26.7146i			1.37224i	0.727490	+	0.686119i	$0.240687\pi$
$379$			26.7146i			1.37224i	−0.727490	+	0.686119i	$0.759313\pi$
$380$	−12.2335	−	3.11052i	−0.627564	−	0.159566i
$381$			1.59277i			0.0816001i
$382$	−7.46393	−	9.59922i	−0.381888	−	0.491139i
$383$	10.1266	+	10.1266i	0.517443	+	0.517443i	0.916797	−	0.399354i	$-0.130766\pi$
$383$	10.1266	+	10.1266i	0.517443	+	0.517443i	−0.399354	+	0.916797i	$0.630766\pi$
$384$	2.84100	+	3.37745i	0.144979	+	0.172355i
$385$	0.0905927	+	0.0905927i	0.00461703	+	0.00461703i
$386$	26.1220	−	20.3113i	1.32957	−	1.03382i
$387$	−14.7941	−	14.7941i	−0.752024	−	0.752024i
$388$	−9.86273	+	5.86401i	−0.500704	+	0.297700i
$389$	17.4802	−	17.4802i	0.886279	−	0.886279i	−0.107885	−	0.994163i	$-0.534408\pi$
$389$	17.4802	−	17.4802i	0.886279	−	0.886279i	0.994163	+	0.107885i	$0.0344077\pi$
$390$	−0.300103	+	2.39813i	−0.0151963	+	0.121434i
$391$	23.4407			1.18545
$392$	−18.4288	−	7.22174i	−0.930796	−	0.364753i
$393$	4.97059	−	4.97059i	0.250733	−	0.250733i
$394$	−14.6840	−	1.83756i	−0.739769	−	0.0925750i
$395$	−2.09488			−0.105405
$396$	15.7673	+	4.00903i	0.792335	+	0.201461i
$397$			20.4858i			1.02815i	0.857744	+	0.514077i	$0.171865\pi$
$397$			20.4858i			1.02815i	−0.857744	+	0.514077i	$0.828135\pi$
$398$	−19.4658	+	15.1357i	−0.975732	+	0.758686i
$399$	0.0780857	−	0.0780857i	0.00390918	−	0.00390918i
$400$	1.91058	−	3.51421i	0.0955292	−	0.175710i
$401$	11.0005	+	11.0005i	0.549340	+	0.549340i	0.926250	−	0.376910i	$-0.123013\pi$
$401$	11.0005	+	11.0005i	0.549340	+	0.549340i	−0.376910	+	0.926250i	$0.623013\pi$
$402$	1.82617	+	0.228528i	0.0910811	+	0.0113979i
$403$			16.9502i			0.844351i
$404$	−1.23889	+	4.87250i	−0.0616373	+	0.242416i
$405$	−5.41190	+	5.41190i	−0.268919	+	0.268919i
$406$	−0.174007	+	0.135300i	−0.00863583	+	0.00671484i
$407$	−8.28224	−	15.2737i	−0.410535	−	0.757087i
$408$	5.05313	−	2.20778i	0.250167	−	0.109302i
$409$	−21.4158	−	21.4158i	−1.05894	−	1.05894i	−0.998150	−	0.0607934i	$-0.980637\pi$
$409$	−21.4158	−	21.4158i	−1.05894	−	1.05894i	−0.0607934	−	0.998150i	$-0.519363\pi$
$410$	0.923653	+	1.18789i	0.0456160	+	0.0586658i
$411$	0.294428			0.0145231
$412$	30.7487	−	18.2820i	1.51488	−	0.900690i
$413$	−0.0329428	+	0.0329428i	−0.00162101	+	0.00162101i
$414$	11.5949	+	14.9120i	0.569860	+	0.732886i
$415$	9.35321	+	9.35321i	0.459131	+	0.459131i
$416$	−24.4537	+	4.01992i	−1.19894	+	0.197093i
$417$	−6.44368			−0.315548
$418$	15.6496	+	20.1267i	0.765447	+	0.984428i
$419$		−	4.93672i		−	0.241175i	−0.992703	−	0.120587i	$-0.961522\pi$
$419$		−	4.93672i		−	0.241175i	0.992703	−	0.120587i	$-0.0384778\pi$
$420$	0.0178839	+	0.0300790i	0.000872643	+	0.00146771i
$421$	−23.7076	−	23.7076i	−1.15544	−	1.15544i	−0.985445	−	0.169993i	$-0.945626\pi$
$421$	−23.7076	−	23.7076i	−1.15544	−	1.15544i	−0.169993	−	0.985445i	$-0.554374\pi$
$422$	−2.60456	+	20.8131i	−0.126788	+	1.01317i
$423$		−	10.5656i		−	0.513718i
$424$	−28.4754	−	11.1587i	−1.38289	−	0.541915i
$425$	−3.53399	−	3.53399i	−0.171424	−	0.171424i
$426$	−0.974444	+	7.78680i	−0.0472120	+	0.377272i
$427$	0.0901740	−	0.0901740i	0.00436383	−	0.00436383i
$428$	3.05483	−	12.0145i	0.147661	−	0.580741i
$429$	3.45171	−	3.45171i	0.166650	−	0.166650i
$430$	10.3093	+	1.29011i	0.497160	+	0.0622148i
$431$	14.8073	−	14.8073i	0.713243	−	0.713243i	−0.253969	−	0.967212i	$-0.581736\pi$
$431$	14.8073	−	14.8073i	0.713243	−	0.713243i	0.967212	+	0.253969i	$0.0817362\pi$
$432$	8.01667	+	4.35845i	0.385702	+	0.209696i
$433$	13.6325			0.655135			0.327567	−	0.944828i	$-0.393771\pi$
$433$	13.6325			0.655135			0.327567	+	0.944828i	$0.393771\pi$
$434$	0.150651	+	0.193749i	0.00723146	+	0.00930025i
$435$	−1.35555			−0.0649936
$436$	24.6159	−	14.6357i	1.17889	−	0.700923i
$437$			29.6015i			1.41603i
$438$	0.169836	−	1.35717i	0.00811510	−	0.0648479i
$439$	−27.7048	+	27.7048i	−1.32228	+	1.32228i	−0.410352	+	0.911927i	$0.634594\pi$
$439$	−27.7048	+	27.7048i	−1.32228	+	1.32228i	−0.911927	+	0.410352i	$0.865406\pi$
$440$	−7.40329	+	3.23460i	−0.352938	+	0.154203i
$441$	−19.9290			−0.949002
$442$	−3.84485	+	30.7242i	−0.182881	+	1.46140i
$443$	16.2841			0.773680			0.386840	−	0.922147i	$-0.373567\pi$
$443$	16.2841			0.773680			0.386840	+	0.922147i	$0.373567\pi$
$444$	−1.16442	−	4.60066i	−0.0552608	−	0.218338i
$445$	−3.79289			−0.179800
$446$	1.04301	−	8.33470i	0.0493879	−	0.394659i
$447$	−7.74402			−0.366280
$448$	−0.243789	+	0.263290i	−0.0115180	+	0.0124393i
$449$	−12.2797	+	12.2797i	−0.579516	+	0.579516i	−0.934770	−	0.355254i	$-0.884394\pi$
$449$	−12.2797	+	12.2797i	−0.579516	+	0.579516i	0.355254	+	0.934770i	$0.384394\pi$
$450$	0.500094	−	3.99626i	0.0235747	−	0.188386i
$451$		−	3.03921i		−	0.143111i
$452$	1.91144	+	3.21486i	0.0899064	+	0.151214i
$453$	5.46927			0.256969
$454$	20.2315	+	26.0194i	0.949512	+	1.22115i
$455$	−0.196495			−0.00921183
$456$	2.78804	+	6.38122i	0.130562	+	0.298828i
$457$	−10.9937	+	10.9937i	−0.514262	+	0.514262i	−0.915830	−	0.401567i	$-0.868466\pi$
$457$	−10.9937	+	10.9937i	−0.514262	+	0.514262i	0.401567	+	0.915830i	$0.368466\pi$
$458$	−16.1394	−	2.01969i	−0.754144	−	0.0943740i
$459$	8.06179	−	8.06179i	0.376292	−	0.376292i
$460$	−9.09112	−	2.31153i	−0.423876	−	0.107776i
$461$	18.2870	−	18.2870i	0.851710	−	0.851710i	−0.138633	−	0.990344i	$-0.544271\pi$
$461$	18.2870	−	18.2870i	0.851710	−	0.851710i	0.990344	+	0.138633i	$0.0442710\pi$
$462$	0.00877645	−	0.0701328i	0.000408317	−	0.00326287i
$463$	−0.440137	−	0.440137i	−0.0204549	−	0.0204549i	0.696805	−	0.717260i	$-0.254604\pi$
$463$	−0.440137	−	0.440137i	−0.0204549	−	0.0204549i	−0.717260	+	0.696805i	$0.754604\pi$
$464$	−3.94032	−	13.3294i	−0.182925	−	0.618803i
$465$			1.50934i			0.0699940i
$466$	3.94754	−	31.5449i	0.182866	−	1.46129i
$467$	−0.949274	−	0.949274i	−0.0439272	−	0.0439272i	0.684802	−	0.728729i	$-0.259889\pi$
$467$	−0.949274	−	0.949274i	−0.0439272	−	0.0439272i	−0.728729	+	0.684802i	$0.759889\pi$
$468$	−21.4473	+	12.7518i	−0.991404	+	0.589451i
$469$			0.149631i			0.00690930i
$470$	3.22067	+	4.14204i	0.148558	+	0.191058i
$471$	6.62576			0.305299
$472$	−1.17622	−	2.69211i	−0.0541399	−	0.123914i
$473$	−14.8385	−	14.8385i	−0.682276	−	0.682276i
$474$	0.709406	+	0.912354i	0.0325841	+	0.0419058i
$475$	4.46281	−	4.46281i	0.204768	−	0.204768i
$476$	0.229123	+	0.385365i	0.0105018	+	0.0176632i
$477$	−30.7935			−1.40994
$478$	13.0739	+	16.8141i	0.597987	+	0.769060i
$479$	28.1930	+	28.1930i	1.28817	+	1.28817i	0.935897	+	0.352274i	$0.114592\pi$
$479$	28.1930	+	28.1930i	1.28817	+	1.28817i	0.352274	+	0.935897i	$0.385408\pi$
$480$	−2.17749	+	0.357956i	−0.0993885	+	0.0163384i
$481$	25.5463	+	7.58218i	1.16481	+	0.345718i
$482$	16.5082	−	12.8361i	0.751928	−	0.584666i
$483$	0.0580283	−	0.0580283i	0.00264038	−	0.00264038i
$484$	−5.50694	−	1.40021i	−0.250315	−	0.0636458i
$485$		−	5.73716i		−	0.260511i
$486$	13.7931	+	1.72608i	0.625669	+	0.0782965i
$487$	−28.7916	−	28.7916i	−1.30467	−	1.30467i	−0.925205	−	0.379468i	$-0.876107\pi$
$487$	−28.7916	−	28.7916i	−1.30467	−	1.30467i	−0.379468	−	0.925205i	$-0.623893\pi$
$488$	3.21965	+	7.36908i	0.145747	+	0.333583i
$489$	1.66753	−	1.66753i	0.0754084	−	0.0754084i
$490$	7.81278	−	6.07487i	0.352946	−	0.274435i
$491$		−	29.4826i		−	1.33053i	−0.746607	−	0.665265i	$-0.768318\pi$
$491$		−	29.4826i		−	1.33053i	0.746607	−	0.665265i	$-0.231682\pi$
$492$	0.204563	−	0.804532i	0.00922240	−	0.0362711i
$493$	−17.3669			−0.782167
$494$	−38.7993	−	4.85536i	−1.74566	−	0.218453i
$495$	−5.75194	+	5.75194i	−0.258531	+	0.258531i
$496$	−14.8417	+	4.38736i	−0.666412	+	0.196998i
$497$	−0.638025			−0.0286193
$498$	0.906122	−	7.24084i	0.0406043	−	0.324470i
$499$	3.26061	−	3.26061i	0.145965	−	0.145965i	−0.630348	−	0.776313i	$-0.717088\pi$
$499$	3.26061	−	3.26061i	0.145965	−	0.145965i	0.776313	+	0.630348i	$0.217088\pi$
$500$	1.02211	+	1.71910i	0.0457101	+	0.0768803i
$501$	0.664111	+	0.664111i	0.0296703	+	0.0296703i
$502$	−6.18711	+	4.81082i	−0.276144	+	0.214718i
$503$	−2.06453	−	2.06453i	−0.0920528	−	0.0920528i	0.659581	−	0.751634i	$-0.270734\pi$
$503$	−2.06453	−	2.06453i	−0.0920528	−	0.0920528i	−0.751634	+	0.659581i	$0.770734\pi$
$504$	−0.131818	+	0.336379i	−0.00587162	+	0.0149835i
$505$	−1.77750	−	1.77750i	−0.0790978	−	0.0790978i
$506$	11.6298	+	14.9568i	0.517006	+	0.664912i
$507$			2.41548i			0.107275i
$508$	2.01229	−	7.91421i	0.0892809	−	0.351136i
$509$		−	18.5829i		−	0.823672i	−0.911258	−	0.411836i	$-0.864888\pi$
$509$		−	18.5829i		−	0.823672i	0.911258	−	0.411836i	$-0.135112\pi$
$510$	−0.342366	+	2.73586i	−0.0151602	+	0.121146i
$511$	0.111202			0.00491928
$512$	−9.84941	−	20.3713i	−0.435287	−	0.900292i
$513$	10.1806	+	10.1806i	0.449486	+	0.449486i
$514$	15.6861	−	12.1968i	0.691884	−	0.537979i
$515$			17.8865i			0.788175i
$516$	−2.92927	−	4.92676i	−0.128954	−	0.216889i
$517$		−	10.5974i		−	0.466072i
$518$	0.359396	−	0.140383i	0.0157909	−	0.00616809i
$519$			9.19582i			0.403652i
$520$	4.52094	−	11.5368i	0.198256	−	0.505921i
$521$			9.48681i			0.415625i	0.978169	+	0.207812i	$0.0666344\pi$
$521$			9.48681i			0.415625i	−0.978169	+	0.207812i	$0.933366\pi$
$522$	−8.59054	−	11.0481i	−0.375998	−	0.483564i
$523$	−27.5831	−	27.5831i	−1.20612	−	1.20612i	−0.972272	−	0.233852i	$-0.924867\pi$
$523$	−27.5831	−	27.5831i	−1.20612	−	1.20612i	−0.233852	−	0.972272i	$-0.575133\pi$
$524$	−30.9778	+	18.4182i	−1.35327	+	0.804604i
$525$	−0.0174970			−0.000763632
$526$	1.61743	+	0.202406i	0.0705234	+	0.00882533i
$527$			19.3373i			0.842345i
$528$	3.91576	+	2.12890i	0.170412	+	0.0926483i
$529$		−	1.00208i		−	0.0435689i
$530$	12.0720	−	9.38662i	0.524373	−	0.407729i
$531$	−2.09162	−	2.09162i	−0.0907684	−	0.0907684i
$532$	−0.486648	+	0.289342i	−0.0210989	+	0.0125446i
$533$	3.29602	+	3.29602i	0.142767	+	0.142767i
$534$	1.28442	+	1.65186i	0.0555822	+	0.0714832i
$535$	4.38291	+	4.38291i	0.189490	+	0.189490i
$536$	−8.78522	−	3.44268i	−0.379464	−	0.148701i
$537$	3.06563	−	3.06563i	0.132292	−	0.132292i
$538$	1.95149	+	0.244210i	0.0841346	+	0.0105286i
$539$	−19.9889			−0.860984
$540$	−3.92163	+	2.33165i	−0.168760	+	0.100338i
$541$	8.46670	−	8.46670i	0.364012	−	0.364012i	−0.501276	−	0.865288i	$-0.667136\pi$
$541$	8.46670	−	8.46670i	0.364012	−	0.364012i	0.865288	+	0.501276i	$0.167136\pi$
$542$	−2.74815	+	21.9605i	−0.118043	+	0.943284i
$543$	−1.24193			−0.0532964
$544$	−27.8975	+	4.58603i	−1.19609	+	0.196625i
$545$			14.3191i			0.613363i
$546$	0.0665408	+	0.0855769i	0.00284768	+	0.00366235i
$547$	4.03020	−	4.03020i	0.172319	−	0.172319i	−0.615679	−	0.787997i	$-0.711118\pi$
$547$	4.03020	−	4.03020i	0.172319	−	0.172319i	0.787997	+	0.615679i	$0.211118\pi$
$548$	−1.46296	−	0.371977i	−0.0624947	−	0.0158901i
$549$	5.72536	+	5.72536i	0.244353	+	0.244353i
$550$	0.501597	−	4.00827i	0.0213882	−	0.170913i
$551$		−	21.9314i		−	0.934308i
$552$	2.07189	+	4.74211i	0.0881856	+	0.201838i
$553$	−0.0664408	+	0.0664408i	−0.00282535	+	0.00282535i
$554$	0.321762	+	0.413812i	0.0136704	+	0.0175812i
$555$	2.27479	+	0.675159i	0.0965593	+	0.0286589i
$556$	32.0176	+	8.14088i	1.35785	+	0.345250i
$557$	28.1667	+	28.1667i	1.19346	+	1.19346i	0.976088	+	0.217374i	$0.0697493\pi$
$557$	28.1667	+	28.1667i	1.19346	+	1.19346i	0.217374	+	0.976088i	$0.430251\pi$
$558$	−12.3016	+	9.56517i	−0.520768	+	0.404926i
$559$	32.1847			1.36127
$560$	−0.0508604	−	0.172052i	−0.00214924	−	0.00727053i
$561$	3.93780	−	3.93780i	0.166254	−	0.166254i
$562$	20.3112	−	15.7931i	0.856778	−	0.666193i
$563$	27.1010	+	27.1010i	1.14217	+	1.14217i	0.988052	+	0.154119i	$0.0492538\pi$
$563$	27.1010	+	27.1010i	1.14217	+	1.14217i	0.154119	+	0.988052i	$0.450746\pi$
$564$	0.713285	−	2.80531i	0.0300347	−	0.118125i
$565$	−1.87009			−0.0786753
$566$	17.8776	−	13.9008i	0.751451	−	0.584295i
$567$			0.343286i			0.0144167i
$568$	14.6796	−	37.4602i	0.615943	−	1.57180i
$569$	29.8584	+	29.8584i	1.25173	+	1.25173i	0.954945	+	0.296783i	$0.0959140\pi$
$569$	29.8584	+	29.8584i	1.25173	+	1.25173i	0.296783	+	0.954945i	$0.404086\pi$
$570$	−3.45490	−	0.432348i	−0.144710	−	0.0181091i
$571$		−	13.1669i		−	0.551019i	−0.961298	−	0.275510i	$-0.911153\pi$
$571$		−	13.1669i		−	0.551019i	0.961298	−	0.275510i	$-0.0888466\pi$
$572$	−21.5118	+	12.7901i	−0.899454	+	0.534781i
$573$	−2.37170	−	2.37170i	−0.0990794	−	0.0990794i
$574$	0.0669695	+	0.00838060i	0.00279525	+	0.000349799i
$575$	3.31647	−	3.31647i	0.138306	−	0.138306i
$576$	−16.7169	−	15.4788i	−0.696538	−	0.644948i
$577$	17.7276	−	17.7276i	0.738010	−	0.738010i	−0.234182	−	0.972193i	$-0.575241\pi$
$577$	17.7276	−	17.7276i	0.738010	−	0.738010i	0.972193	+	0.234182i	$0.0752413\pi$
$578$	−1.40101	+	11.1955i	−0.0582743	+	0.465671i
$579$	6.45402	−	6.45402i	0.268220	−	0.268220i
$580$	6.73550	+	1.71259i	0.279676	+	0.0711113i
$581$	0.593290			0.0246138
$582$	−2.49863	+	1.94282i	−0.103571	+	0.0805326i
$583$	−30.8860			−1.27917
$584$	−2.55852	+	6.52897i	−0.105872	+	0.270171i
$585$		−	12.4759i		−	0.515817i
$586$	−28.0273	−	3.50734i	−1.15780	−	0.144887i
$587$	−30.1006	+	30.1006i	−1.24239	+	1.24239i	−0.283376	+	0.959009i	$0.591455\pi$
$587$	−30.1006	+	30.1006i	−1.24239	+	1.24239i	−0.959009	+	0.283376i	$0.908545\pi$
$588$	−5.29142	−	1.34541i	−0.218214	−	0.0554838i
$589$	−24.4196			−1.00619
$590$	1.45755	+	0.182399i	0.0600065	+	0.00750925i
$591$	−4.08202			−0.167912
$592$	−0.0266354	+	24.3310i	−0.00109471	+	0.999999i
$593$	48.0202			1.97195			0.985976	−	0.166886i	$-0.0533710\pi$
$593$	48.0202			1.97195			0.985976	+	0.166886i	$0.0533710\pi$
$594$	9.14374	+	1.14425i	0.375172	+	0.0469492i
$595$	−0.224167			−0.00918995
$596$	38.4788	+	9.78372i	1.57615	+	0.400757i
$597$	−4.80946	+	4.80946i	−0.196838	+	0.196838i
$598$	−28.8331	−	3.60819i	−1.17907	−	0.147550i
$599$			29.9803i			1.22496i	0.790486	+	0.612480i	$0.209828\pi$
$599$			29.9803i			1.22496i	−0.790486	+	0.612480i	$0.790172\pi$
$600$	0.402569	−	1.02730i	0.0164348	−	0.0419393i
$601$	43.6441			1.78028			0.890141	−	0.455685i	$-0.150606\pi$
$601$	43.6441			1.78028			0.890141	+	0.455685i	$0.150606\pi$
$602$	0.367886	−	0.286052i	0.0149939	−	0.0116586i
$603$	−9.50040			−0.386886
$604$	−27.1759	−	6.90982i	−1.10577	−	0.281157i
$605$	2.00895	−	2.00895i	0.0816753	−	0.0816753i
$606$	−0.172201	+	1.37606i	−0.00699519	+	0.0558987i
$607$	−14.6973	+	14.6973i	−0.596547	+	0.596547i	−0.939392	−	0.342845i	$-0.888609\pi$
$607$	−14.6973	+	14.6973i	−0.596547	+	0.596547i	0.342845	+	0.939392i	$0.388609\pi$
$608$	−5.79135	−	35.2296i	−0.234870	−	1.42875i
$609$	−0.0429924	+	0.0429924i	−0.00174214	+	0.00174214i
$610$	−3.98975	−	0.499279i	−0.161540	−	0.0202152i
$611$	11.4928	+	11.4928i	0.464950	+	0.464950i
$612$	−24.4677	+	14.5476i	−0.989049	+	0.588051i
$613$			21.8594i			0.882894i	0.897287	+	0.441447i	$0.145535\pi$
$613$			21.8594i			0.882894i	−0.897287	+	0.441447i	$0.854465\pi$
$614$	−41.9698	−	5.25212i	−1.69376	−	0.211958i
$615$	0.293496	+	0.293496i	0.0118349	+	0.0118349i
$616$	−0.132214	+	0.337390i	−0.00532704	+	0.0135938i
$617$		−	10.2679i		−	0.413369i	−0.978408	−	0.206684i	$-0.933733\pi$
$617$		−	10.2679i		−	0.413369i	0.978408	−	0.206684i	$-0.0662674\pi$
$618$	7.78988	−	6.05707i	0.313355	−	0.243651i
$619$	−13.9257			−0.559721			−0.279860	−	0.960041i	$-0.590288\pi$
$619$	−13.9257			−0.559721			−0.279860	+	0.960041i	$0.590288\pi$
$620$	1.90689	−	7.49967i	0.0765824	−	0.301194i
$621$	7.56558	+	7.56558i	0.303596	+	0.303596i
$622$	33.6406	−	26.1574i	1.34887	−	1.04882i
$623$	−0.120295	+	0.120295i	−0.00481950	+	0.00481950i
$624$	−6.55542	+	1.93785i	−0.262427	+	0.0775761i
$625$	−1.00000			−0.0400000
$626$	−14.8585	+	11.5533i	−0.593864	+	0.461763i
$627$	4.97275	+	4.97275i	0.198592	+	0.198592i
$628$	−32.9223	−	8.37091i	−1.31374	−	0.334036i
$629$	29.1440	+	8.64996i	1.16205	+	0.344897i
$630$	−0.110884	−	0.142606i	−0.00441773	−	0.00568155i
$631$	−25.2297	+	25.2297i	−1.00438	+	1.00438i	−0.00438888	+	0.999990i	$0.501397\pi$
$631$	−25.2297	+	25.2297i	−1.00438	+	1.00438i	−0.999990	+	0.00438888i	$0.998603\pi$
$632$	−2.37226	−	5.42959i	−0.0943635	−	0.215977i
$633$			5.78587i			0.229968i
$634$	0.162219	−	1.29630i	0.00644254	−	0.0514825i
$635$	2.88713	+	2.88713i	0.114572	+	0.114572i
$636$	−8.17606	−	2.07887i	−0.324202	−	0.0824325i
$637$	21.6780	−	21.6780i	0.858912	−	0.858912i
$638$	−8.61635	−	11.0813i	−0.341125	−	0.438714i
$639$		−	40.5097i		−	1.60254i
$640$	11.2718	+	0.972400i	0.445559	+	0.0384375i
$641$	−41.0266			−1.62046			−0.810228	−	0.586115i	$-0.800657\pi$
$641$	−41.0266			−1.62046			−0.810228	+	0.586115i	$0.800657\pi$
$642$	0.424609	−	3.39306i	0.0167580	−	0.133913i
$643$	−6.83209	+	6.83209i	−0.269431	+	0.269431i	−0.828871	−	0.559440i	$-0.811016\pi$
$643$	−6.83209	+	6.83209i	−0.269431	+	0.269431i	0.559440	+	0.828871i	$0.311016\pi$
$644$	−0.361645	+	0.215020i	−0.0142508	+	0.00847299i
$645$	2.86590			0.112845
$646$	−44.2633	−	5.53913i	−1.74152	−	0.217934i
$647$	−16.1837	+	16.1837i	−0.636245	+	0.636245i	−0.949627	−	0.313382i	$-0.898538\pi$
$647$	−16.1837	+	16.1837i	−0.636245	+	0.636245i	0.313382	+	0.949627i	$0.398538\pi$
$648$	−20.1553	−	7.89829i	−0.791774	−	0.310274i
$649$	−2.09790	−	2.09790i	−0.0823499	−	0.0823499i
$650$	3.80298	+	4.89094i	0.149165	+	0.191839i
$651$	0.0478701	+	0.0478701i	0.00187618	+	0.00187618i
$652$	−10.3924	+	6.17895i	−0.406999	+	0.241986i
$653$	−13.0370	−	13.0370i	−0.510176	−	0.510176i	0.404404	−	0.914580i	$-0.367479\pi$
$653$	−13.0370	−	13.0370i	−0.510176	−	0.510176i	−0.914580	+	0.404404i	$0.867479\pi$
$654$	6.23621	−	4.84900i	0.243855	−	0.189611i
$655$		−	18.0198i		−	0.704093i
$656$	−2.03288	+	3.73915i	−0.0793705	+	0.145989i
$657$			7.06047i			0.275455i
$658$	0.233515	+	0.0292221i	0.00910335	+	0.00113920i
$659$	−39.7647			−1.54901			−0.774506	−	0.632567i	$-0.782001\pi$
$659$	−39.7647			−1.54901			−0.774506	+	0.632567i	$0.782001\pi$
$660$	−1.91553	+	1.13890i	−0.0745619	+	0.0443317i
$661$	−24.6743	−	24.6743i	−0.959719	−	0.959719i	0.0395007	−	0.999220i	$-0.487423\pi$
$661$	−24.6743	−	24.6743i	−0.959719	−	0.959719i	−0.999220	+	0.0395007i	$0.987423\pi$
$662$	−17.3208	−	22.2759i	−0.673192	−	0.865779i
$663$			8.54107i			0.331708i
$664$	−13.6504	+	34.8337i	−0.529737	+	1.35181i
$665$		−	0.283084i		−	0.0109775i
$666$	8.91328	+	22.8189i	0.345382	+	0.884214i
$667$		−	16.2980i		−	0.631060i
$668$	−2.46083	−	4.13889i	−0.0952122	−	0.160138i
$669$		−	2.31697i		−	0.0895794i
$670$	3.72444	−	2.89596i	0.143888	−	0.111881i
$671$	5.74257	+	5.74257i	0.221689	+	0.221689i
$672$	−0.0577082	+	0.0804140i	−0.00222614	+	0.00310204i
$673$	−30.4234			−1.17274			−0.586369	−	0.810044i	$-0.699443\pi$
$673$	−30.4234			−1.17274			−0.586369	+	0.810044i	$0.699443\pi$
$674$	3.25026	−	25.9729i	0.125195	−	1.00044i
$675$		−	2.28122i		−	0.0878041i
$676$	3.05169	−	12.0021i	0.117373	−	0.461620i
$677$		−	32.8142i		−	1.26115i	−0.776127	−	0.630576i	$-0.782819\pi$
$677$		−	32.8142i		−	1.26115i	0.776127	−	0.630576i	$-0.217181\pi$
$678$	0.633284	+	0.814455i	0.0243211	+	0.0312790i
$679$	−0.181959	−	0.181959i	−0.00698294	−	0.00698294i
$680$	5.15761	−	13.1615i	0.197785	−	0.504719i
$681$	6.42867	+	6.42867i	0.246347	+	0.246347i
$682$	−12.3386	+	9.59392i	−0.472468	+	0.367370i
$683$	−29.7384	−	29.7384i	−1.13791	−	1.13791i	−0.988824	−	0.149085i	$-0.952367\pi$
$683$	−29.7384	−	29.7384i	−1.13791	−	1.13791i	−0.149085	−	0.988824i	$-0.547633\pi$
$684$	−18.3710	−	30.8984i	−0.702434	−	1.18143i
$685$	0.533693	−	0.533693i	0.0203914	−	0.0203914i
$686$	0.110254	−	0.881045i	0.00420953	−	0.0336384i
$687$	−4.48661			−0.171175
$688$	8.33062	+	28.1811i	0.317602	+	1.07439i
$689$	33.4958	−	33.4958i	1.27609	−	1.27609i
$690$	−2.56746	−	0.321293i	−0.0977415	−	0.0122314i
$691$	30.1381			1.14651			0.573254	−	0.819378i	$-0.305681\pi$
$691$	30.1381			1.14651			0.573254	+	0.819378i	$0.305681\pi$
$692$	11.6179	−	45.6925i	0.441647	−	1.73697i
$693$			0.364856i			0.0138597i
$694$	−3.51916	+	2.73634i	−0.133585	+	0.103870i
$695$	−11.6801	+	11.6801i	−0.443052	+	0.443052i
$696$	−1.53504	−	3.51337i	−0.0581855	−	0.133174i
$697$	3.76019	+	3.76019i	0.142427	+	0.142427i
$698$	16.6792	+	2.08725i	0.631318	+	0.0790035i
$699$		−	8.76920i		−	0.331682i
$700$	0.0869397	+	0.0221055i	0.00328601	+	0.000835511i
$701$	−0.329081	+	0.329081i	−0.0124292	+	0.0124292i	−0.713294	−	0.700865i	$-0.752798\pi$
$701$	−0.329081	+	0.329081i	−0.0124292	+	0.0124292i	0.700865	+	0.713294i	$0.252798\pi$
$702$	−11.1573	+	8.67543i	−0.421105	+	0.327433i
$703$	−10.9234	+	36.8037i	−0.411983	+	1.38808i
$704$	−16.7671	−	15.5253i	−0.631935	−	0.585130i
$705$	1.02338	+	1.02338i	0.0385429	+	0.0385429i
$706$	4.35724	+	5.60376i	0.163987	+	0.210900i
$707$	−0.112750			−0.00424040
$708$	−0.414146	−	0.696556i	−0.0155646	−	0.0261782i
$709$	−7.40763	+	7.40763i	−0.278200	+	0.278200i	−0.832390	−	0.554190i	$-0.813028\pi$
$709$	−7.40763	+	7.40763i	−0.278200	+	0.278200i	0.554190	+	0.832390i	$0.313028\pi$
$710$	12.3484	+	15.8810i	0.463427	+	0.596004i
$711$	−4.21849	−	4.21849i	−0.158206	−	0.158206i
$712$	−4.29511	−	9.83056i	−0.160966	−	0.368416i
$713$	−18.1471			−0.679613
$714$	0.0759116	+	0.0976285i	0.00284092	+	0.00365365i
$715$		−	12.5134i		−	0.467976i
$716$	−19.1057	+	11.3595i	−0.714013	+	0.424525i
$717$	4.15431	+	4.15431i	0.155146	+	0.155146i
$718$	−2.23568	+	17.8654i	−0.0834348	+	0.666729i
$719$		−	8.83988i		−	0.329672i	−0.986321	−	0.164836i	$-0.947291\pi$
$719$		−	8.83988i		−	0.329672i	0.986321	−	0.164836i	$-0.0527095\pi$
$720$	10.9240	−	3.22925i	0.407113	−	0.120347i
$721$	0.567287	+	0.567287i	0.0211269	+	0.0211269i
$722$	3.65844	−	29.2347i	0.136153	−	1.08800i
$723$	4.07873	−	4.07873i	0.151689	−	0.151689i
$724$	6.17095	+	1.56904i	0.229342	+	0.0583130i
$725$	−2.45713	+	2.45713i	−0.0912555	+	0.0912555i
$726$	−1.55524	−	0.194623i	−0.0577202	−	0.00722314i
$727$	−4.11691	+	4.11691i	−0.152688	+	0.152688i	−0.779317	−	0.626630i	$-0.784434\pi$
$727$	−4.11691	+	4.11691i	−0.152688	+	0.152688i	0.626630	+	0.779317i	$0.284434\pi$
$728$	−0.222513	−	0.509284i	−0.00824689	−	0.0188753i
$729$	−19.1264			−0.708384
$730$	−2.15221	−	2.76792i	−0.0796568	−	0.102445i
$731$	36.7172			1.35803
$732$	1.13364	+	1.90668i	0.0419005	+	0.0704728i
$733$			24.2209i			0.894619i	0.894379	+	0.447310i	$0.147618\pi$
$733$			24.2209i			0.894619i	−0.894379	+	0.447310i	$0.852382\pi$
$734$	−3.36727	+	26.9079i	−0.124288	+	0.993189i
$735$	1.93032	−	1.93032i	0.0712011	−	0.0712011i
$736$	−4.30376	−	26.1804i	−0.158639	−	0.965021i
$737$	−9.52895			−0.351003
$738$	−0.532104	+	4.25205i	−0.0195870	+	0.156520i
$739$	−28.8331			−1.06064			−0.530322	−	0.847796i	$-0.677929\pi$
$739$	−28.8331			−1.06064			−0.530322	+	0.847796i	$0.677929\pi$
$740$	−10.4500	−	6.22869i	−0.384151	−	0.228971i
$741$	−10.7859			−0.396229
$742$	0.0851678	−	0.680578i	0.00312661	−	0.0249848i
$743$	48.0010			1.76098			0.880492	−	0.474061i	$-0.157212\pi$
$743$	48.0010			1.76098			0.880492	+	0.474061i	$0.157212\pi$
$744$	−3.91197	+	1.70920i	−0.143420	+	0.0626621i
$745$	−14.0372	+	14.0372i	−0.514282	+	0.514282i
$746$	−3.27627	+	26.1807i	−0.119953	+	0.958545i
$747$			37.6694i			1.37825i
$748$	−24.5413	+	14.5913i	−0.897317	+	0.533511i
$749$	0.278016			0.0101585
$750$	0.338638	+	0.435517i	0.0123653	+	0.0159028i
$751$	14.8213			0.540838			0.270419	−	0.962743i	$-0.412838\pi$
$751$	14.8213			0.540838			0.270419	+	0.962743i	$0.412838\pi$
$752$	−7.08839	+	13.0380i	−0.258487	+	0.475445i
$753$	−1.52867	+	1.52867i	−0.0557077	+	0.0557077i
$754$	21.3621	+	2.67326i	0.777962	+	0.0973545i
$755$	9.91385	−	9.91385i	0.360802	−	0.360802i
$756$	−0.0504275	+	0.198328i	−0.00183403	+	0.00721313i
$757$	14.7533	−	14.7533i	0.536218	−	0.536218i	−0.386198	−	0.922416i	$-0.626212\pi$
$757$	14.7533	−	14.7533i	0.536218	−	0.536218i	0.922416	+	0.386198i	$0.126212\pi$
$758$	4.69124	−	37.4878i	0.170393	−	1.36162i
$759$	3.69542	+	3.69542i	0.134135	+	0.134135i
$760$	16.6206	+	6.51316i	0.602893	+	0.236257i
$761$			30.7305i			1.11398i	0.830519	+	0.556991i	$0.188044\pi$
$761$			30.7305i			1.11398i	−0.830519	+	0.556991i	$0.811956\pi$
$762$	0.279699	−	2.23508i	0.0101324	−	0.0809685i
$763$	0.454143	+	0.454143i	0.0164411	+	0.0164411i
$764$	8.78822	+	14.7810i	0.317947	+	0.534757i
$765$		−	14.2329i		−	0.514592i
$766$	−12.4320	−	15.9886i	−0.449186	−	0.577690i
$767$	4.55034			0.164303
$768$	−3.39358	−	5.23837i	−0.122455	−	0.189023i
$769$	3.05169	+	3.05169i	0.110047	+	0.110047i	0.759986	−	0.649939i	$-0.225206\pi$
$769$	3.05169	+	3.05169i	0.110047	+	0.110047i	−0.649939	+	0.759986i	$0.725206\pi$
$770$	−0.111217	−	0.143034i	−0.00400799	−	0.00515460i
$771$	3.87561	−	3.87561i	0.139577	−	0.139577i
$772$	−40.2229	+	23.9150i	−1.44765	+	0.860720i
$773$	30.4811			1.09633			0.548164	−	0.836371i	$-0.315327\pi$
$773$	30.4811			1.09633			0.548164	+	0.836371i	$0.315327\pi$
$774$	18.1621	+	23.3580i	0.652824	+	0.839585i
$775$	2.73590	+	2.73590i	0.0982765	+	0.0982765i
$776$	14.8698	−	6.49682i	0.533795	−	0.233222i
$777$	0.0935600	−	0.0507335i	0.00335645	−	0.00182006i
$778$	−27.5990	+	21.4597i	−0.989471	+	0.769369i
$779$	−4.74846	+	4.74846i	−0.170131	+	0.170131i
$780$	0.842251	−	3.31252i	0.0301574	−	0.118607i
$781$		−	40.6315i		−	1.45391i
$782$	−32.8936	−	4.11632i	−1.17627	−	0.147199i
$783$	−5.60524	−	5.60524i	−0.200315	−	0.200315i
$784$	24.5924	+	13.3702i	0.878300	+	0.477509i
$785$	12.0101	−	12.0101i	0.428661	−	0.428661i
$786$	−7.84793	+	6.10221i	−0.279926	+	0.217658i
$787$		−	17.2527i		−	0.614992i	−0.951549	−	0.307496i	$-0.900509\pi$
$787$		−	17.2527i		−	0.614992i	0.951549	−	0.307496i	$-0.0994910\pi$
$788$	20.2829	+	5.15719i	0.722548	+	0.183717i
$789$	0.449632			0.0160073
$790$	2.93967	+	0.367872i	0.104589	+	0.0130883i
$791$	−0.0593115	+	0.0593115i	−0.00210887	+	0.00210887i
$792$	−21.4217	−	8.39456i	−0.761187	−	0.298288i
$793$	−12.4556			−0.442312
$794$	3.59743	−	28.7471i	0.127668	−	1.02020i
$795$	2.98265	−	2.98265i	0.105784	−	0.105784i
$796$	29.9736	−	17.8212i	1.06239	−	0.631656i
$797$	15.9135	+	15.9135i	0.563686	+	0.563686i	0.930353	−	0.366666i	$-0.119501\pi$
$797$	15.9135	+	15.9135i	0.563686	+	0.563686i	−0.366666	+	0.930353i	$0.619501\pi$
$798$	−0.123288	+	0.0958630i	−0.00436433	+	0.00339351i
$799$	13.1113	+	13.1113i	0.463846	+	0.463846i
$800$	−3.29818	+	4.59587i	−0.116608	+	0.162489i
$801$	−7.63779	−	7.63779i	−0.269868	−	0.269868i
$802$	−13.5049	−	17.3685i	−0.476876	−	0.613302i
$803$			7.08169i			0.249907i
$804$	−2.52248	−	0.641372i	−0.0889609	−	0.0226195i
$805$		−	0.210369i		−	0.00741454i
$806$	2.97656	−	23.7857i	0.104845	−	0.837816i
$807$	0.542497			0.0190968
$808$	2.59414	−	6.61986i	0.0912615	−	0.232886i
$809$	3.37621	+	3.37621i	0.118701	+	0.118701i	0.763962	−	0.645261i	$-0.223251\pi$
$809$	3.37621	+	3.37621i	0.118701	+	0.118701i	−0.645261	+	0.763962i	$0.723251\pi$
$810$	8.54471	−	6.64399i	0.300230	−	0.233446i
$811$			47.2500i			1.65917i	0.558379	+	0.829586i	$0.311424\pi$
$811$			47.2500i			1.65917i	−0.558379	+	0.829586i	$0.688576\pi$
$812$	0.267938	−	0.159306i	0.00940279	−	0.00559054i
$813$			6.10483i			0.214106i
$814$	8.94006	+	22.8875i	0.313349	+	0.802205i
$815$		−	6.04529i		−	0.211757i
$816$	−7.47860	+	2.21075i	−0.261803	+	0.0773919i
$817$			46.3673i			1.62219i
$818$	26.2914	+	33.8129i	0.919257	+	1.18224i
$819$	−0.395685	−	0.395685i	−0.0138264	−	0.0138264i
$820$	−1.08753	−	1.82913i	−0.0379783	−	0.0638760i
$821$	−2.14692			−0.0749279			−0.0374640	−	0.999298i	$-0.511928\pi$
$821$	−2.14692			−0.0749279			−0.0374640	+	0.999298i	$0.511928\pi$
$822$	−0.413161	−	0.0517032i	−0.0144107	−	0.00180336i
$823$		−	35.9498i		−	1.25313i	−0.779368	−	0.626566i	$-0.784460\pi$
$823$		−	35.9498i		−	1.25313i	0.779368	−	0.626566i	$-0.215540\pi$
$824$	−46.3591	+	20.2549i	−1.61499	+	0.705613i
$825$		−	1.11427i		−	0.0387937i
$826$	0.0520125	−	0.0404426i	0.00180975	−	0.00140718i
$827$	−10.2670	−	10.2670i	−0.357019	−	0.357019i	0.505694	−	0.862713i	$-0.331236\pi$
$827$	−10.2670	−	10.2670i	−0.357019	−	0.357019i	−0.862713	+	0.505694i	$0.831236\pi$
$828$	−13.6522	−	22.9617i	−0.474446	−	0.797975i
$829$	16.8252	+	16.8252i	0.584364	+	0.584364i	0.936099	−	0.351735i	$-0.114408\pi$
$829$	16.8252	+	16.8252i	0.584364	+	0.584364i	−0.351735	+	0.936099i	$0.614408\pi$
$830$	−11.4826	−	14.7675i	−0.398567	−	0.512589i
$831$	0.102242	+	0.102242i	0.00354673	+	0.00354673i
$832$	35.0211	−	1.34681i	1.21414	−	0.0466924i
$833$	24.7308	−	24.7308i	0.856872	−	0.856872i
$834$	9.04221	+	1.13155i	0.313106	+	0.0391823i
$835$	2.40759			0.0833183
$836$	−18.4262	−	30.9913i	−0.637285	−	1.07186i
$837$	−6.24118	+	6.24118i	−0.215727	+	0.215727i
$838$	−0.866916	+	6.92754i	−0.0299471	+	0.239308i
$839$	−9.86632			−0.340623			−0.170312	−	0.985390i	$-0.554477\pi$
$839$	−9.86632			−0.340623			−0.170312	+	0.985390i	$0.554477\pi$
$840$	−0.0198138	−	0.0453495i	−0.000683641	−	0.00156471i
$841$		−	16.9250i		−	0.583622i
$842$	29.1050	+	37.4313i	1.00302	+	1.28997i
$843$	5.01835	−	5.01835i	0.172841	−	0.172841i
$844$	7.30980	−	28.7490i	0.251614	−	0.989582i
$845$	4.37841	+	4.37841i	0.150622	+	0.150622i
$846$	−1.85538	+	14.8264i	−0.0637894	+	0.509742i
$847$		−	0.127431i		−	0.00437858i
$848$	37.9991	+	20.6591i	1.30489	+	0.709436i
$849$	4.41706	−	4.41706i	0.151593	−	0.151593i
$850$	4.33855	+	5.57972i	0.148811	+	0.191383i
$851$	−8.11755	+	27.3501i	−0.278266	+	0.937550i
$852$	2.73481	−	10.7559i	0.0936931	−	0.368489i
$853$	34.6973	+	34.6973i	1.18801	+	1.18801i	0.977616	+	0.210398i	$0.0674760\pi$
$853$	34.6973	+	34.6973i	1.18801	+	1.18801i	0.210398	+	0.977616i	$0.432524\pi$
$854$	−0.142373	+	0.110703i	−0.00487192	+	0.00378819i
$855$	17.9736			0.614686
$856$	−6.39656	+	16.3231i	−0.218630	+	0.557912i
$857$	13.5965	−	13.5965i	0.464448	−	0.464448i	−0.435663	−	0.900110i	$-0.643486\pi$
$857$	13.5965	−	13.5965i	0.464448	−	0.464448i	0.900110	+	0.435663i	$0.143486\pi$
$858$	−5.44981	+	4.23753i	−0.186053	+	0.144667i
$859$	3.26638	+	3.26638i	0.111447	+	0.111447i	0.760631	−	0.649184i	$-0.224889\pi$
$859$	3.26638	+	3.26638i	0.111447	+	0.111447i	−0.649184	+	0.760631i	$0.724889\pi$
$860$	−14.2402	−	3.62075i	−0.485587	−	0.123467i
$861$	0.0186169			0.000634464
$862$	−23.3789	+	18.1784i	−0.796288	+	0.619158i
$863$		−	49.5936i		−	1.68818i	−0.536198	−	0.844092i	$-0.680140\pi$
$863$		−	49.5936i		−	1.68818i	0.536198	−	0.844092i	$-0.319860\pi$
$864$	−10.4842	−	7.52386i	−0.356679	−	0.255967i
$865$	16.6688	+	16.6688i	0.566755	+	0.566755i
$866$	−19.1300	−	2.39394i	−0.650064	−	0.0813494i
$867$			3.11225i			0.105698i
$868$	−0.177380	−	0.298337i	−0.00602067	−	0.0101262i
$869$	−4.23116	−	4.23116i	−0.143532	−	0.143532i
$870$	1.90220	+	0.238042i	0.0644906	+	0.00807038i
$871$	10.3341	−	10.3341i	0.350159	−	0.350159i
$872$	−37.1129	+	16.2151i	−1.25680	+	0.549113i
$873$	11.5530	−	11.5530i	0.391010	−	0.391010i
$874$	5.19819	−	41.5389i	0.175831	−	1.40507i
$875$	−0.0317159	+	0.0317159i	−0.00107219	+	0.00107219i
$876$	−0.476652	+	1.87465i	−0.0161046	+	0.0633384i
$877$	14.2684			0.481810			0.240905	−	0.970549i	$-0.422556\pi$
$877$	14.2684			0.481810			0.240905	+	0.970549i	$0.422556\pi$
$878$	43.7424	−	34.0122i	1.47624	−	1.14786i
$879$	−7.79133			−0.262795
$880$	10.9568	−	3.23895i	0.369354	−	0.109185i
$881$			17.9480i			0.604683i	0.953200	+	0.302341i	$0.0977682\pi$
$881$			17.9480i			0.604683i	−0.953200	+	0.302341i	$0.902232\pi$
$882$	27.9658	+	3.49965i	0.941657	+	0.117839i
$883$	8.76864	−	8.76864i	0.295088	−	0.295088i	−0.543998	−	0.839086i	$-0.683090\pi$
$883$	8.76864	−	8.76864i	0.295088	−	0.295088i	0.839086	+	0.543998i	$0.183090\pi$
$884$	10.7907	−	42.4392i	0.362931	−	1.42738i
$885$	0.405187			0.0136202
$886$	−22.8509	−	2.85958i	−0.767692	−	0.0960694i
$887$	0.573958			0.0192716			0.00963582	−	0.999954i	$-0.496933\pi$
$887$	0.573958			0.0192716			0.00963582	+	0.999954i	$0.496933\pi$
$888$	0.826086	+	6.66044i	0.0277216	+	0.223510i
$889$	0.183135			0.00614217
$890$	5.32244	+	0.666052i	0.178408	+	0.0223261i
$891$	−21.8615			−0.732389
$892$	−2.92724	+	11.5127i	−0.0980113	+	0.385472i
$893$	−16.5573	+	16.5573i	−0.554069	+	0.554069i
$894$	10.8669	+	1.35989i	0.363445	+	0.0454817i
$895$		−	11.1138i		−	0.371493i
$896$	0.388337	−	0.326656i	0.0129734	−	0.0109128i
$897$	−8.01536			−0.267625
$898$	19.3881	−	15.0754i	0.646991	−	0.503071i
$899$	13.4449			0.448413
$900$	−1.40353	+	5.52001i	−0.0467844	+	0.184000i
$901$	38.2129	−	38.2129i	1.27306	−	1.27306i
$902$	−0.533703	+	4.26483i	−0.0177704	+	0.142003i
$903$	0.0908946	−	0.0908946i	0.00302478	−	0.00302478i
$904$	−2.11771	−	4.84698i	−0.0704340	−	0.161208i
$905$	−2.25118	+	2.25118i	−0.0748318	+	0.0748318i
$906$	−7.67486	−	0.960435i	−0.254980	−	0.0319083i
$907$	−29.0488	−	29.0488i	−0.964549	−	0.964549i	0.0348439	−	0.999393i	$-0.488907\pi$
$907$	−29.0488	−	29.0488i	−0.964549	−	0.964549i	−0.999393	+	0.0348439i	$0.988907\pi$
$908$	−23.8211	−	40.0649i	−0.790531	−	1.32960i
$909$		−	7.15877i		−	0.237441i
$910$	0.275735	+	0.0345057i	0.00914054	+	0.00114385i
$911$	15.6841	+	15.6841i	0.519638	+	0.519638i	0.917462	−	0.397824i	$-0.130235\pi$
$911$	15.6841	+	15.6841i	0.519638	+	0.519638i	−0.397824	+	0.917462i	$0.630235\pi$
$912$	−2.79179	−	9.44416i	−0.0924455	−	0.312727i
$913$			37.7826i			1.25042i
$914$	17.3576	−	13.4965i	0.574139	−	0.446425i
$915$	−1.10912			−0.0366662
$916$	22.2932	+	5.66834i	0.736589	+	0.187287i
$917$	−0.571514	−	0.571514i	−0.0188731	−	0.0188731i
$918$	−12.7286	+	9.89716i	−0.420105	+	0.326655i
$919$	7.45919	−	7.45919i	0.246056	−	0.246056i	−0.573294	−	0.819350i	$-0.694335\pi$
$919$	7.45919	−	7.45919i	0.246056	−	0.246056i	0.819350	+	0.573294i	$0.194335\pi$
$920$	12.3514	+	4.84015i	0.407212	+	0.159575i
$921$	−11.6673			−0.384449
$922$	−28.8729	+	22.4503i	−0.950877	+	0.739360i
$923$	44.0647	+	44.0647i	1.45041	+	1.45041i
$924$	−0.0246314	+	0.0968739i	−0.000810314	+	0.00318692i
$925$	5.34720	−	2.89955i	0.175815	−	0.0953368i
$926$	0.540340	+	0.694921i	0.0177567	+	0.0228365i
$927$	−36.0184	+	36.0184i	−1.18300	+	1.18300i
$928$	3.18860	+	19.3967i	0.104671	+	0.636728i
$929$			17.7470i			0.582260i	0.956684	+	0.291130i	$0.0940312\pi$
$929$			17.7470i			0.582260i	−0.956684	+	0.291130i	$0.905969\pi$
$930$	0.265049	−	2.11801i	0.00869130	−	0.0694523i
$931$	31.2307	+	31.2307i	1.02354	+	1.02354i
$932$	−11.0789	+	43.5727i	−0.362902	+	1.42727i
$933$	8.31167	−	8.31167i	0.272112	−	0.272112i
$934$	1.16539	+	1.49878i	0.0381327	+	0.0490417i
$935$		−	14.2757i		−	0.466864i
$936$	32.3357	−	14.1279i	1.05692	−	0.461785i
$937$	−31.3905			−1.02548			−0.512741	−	0.858544i	$-0.671370\pi$
$937$	−31.3905			−1.02548			−0.512741	+	0.858544i	$0.671370\pi$
$938$	0.0262760	−	0.209972i	0.000857941	−	0.00685582i
$939$	−3.67112	+	3.67112i	−0.119803	+	0.119803i
$940$	−3.79210	−	6.37796i	−0.123685	−	0.208026i
$941$	25.3048			0.824913			0.412457	−	0.910977i	$-0.364671\pi$
$941$	25.3048			0.824913			0.412457	+	0.910977i	$0.364671\pi$
$942$	−9.29772	−	1.16352i	−0.302936	−	0.0379096i
$943$	−3.52875	+	3.52875i	−0.114912	+	0.114912i
$944$	1.17780	+	3.98430i	0.0383342	+	0.129678i
$945$	−0.0723508	−	0.0723508i	−0.00235357	−	0.00235357i
$946$	18.2167	+	23.4282i	0.592276	+	0.761715i
$947$	26.8948	+	26.8948i	0.873963	+	0.873963i	0.992902	−	0.118939i	$-0.0379493\pi$
$947$	26.8948	+	26.8948i	0.873963	+	0.873963i	−0.118939	+	0.992902i	$0.537949\pi$
$948$	−0.835272	−	1.40485i	−0.0271284	−	0.0456275i
$949$	−7.68008	−	7.68008i	−0.249306	−	0.249306i
$950$	−7.04621	+	5.47882i	−0.228609	+	0.177756i
$951$		−	0.360359i		−	0.0116854i
$952$	−0.253849	−	0.581006i	−0.00822730	−	0.0188305i
$953$		−	49.9057i		−	1.61660i	−0.588767	−	0.808302i	$-0.700387\pi$
$953$		−	49.9057i		−	1.61660i	0.588767	−	0.808302i	$-0.299613\pi$
$954$	43.2115	+	5.40751i	1.39902	+	0.175075i
$955$	−8.59812			−0.278229
$956$	−15.3936	−	25.8906i	−0.497863	−	0.837361i
$957$	−2.73789	−	2.73789i	−0.0885035	−	0.0885035i
$958$	−34.6115	−	44.5132i	−1.11825	−	1.43816i
$959$		−	0.0338531i		−	0.00109317i
$960$	3.11847	−	0.119928i	0.100648	−	0.00387065i
$961$			16.0297i			0.517087i
$962$	−34.5169	−	15.1259i	−1.11287	−	0.487679i
$963$			17.6519i			0.568824i
$964$	−25.4195	+	15.1135i	−0.818708	+	0.486773i
$965$		−	23.3977i		−	0.753199i
$966$	−0.0916193	+	0.0712391i	−0.00294780	+	0.00229208i
$967$	−22.1255	−	22.1255i	−0.711507	−	0.711507i	0.255343	−	0.966851i	$-0.417812\pi$
$967$	−22.1255	−	22.1255i	−0.711507	−	0.711507i	−0.966851	+	0.255343i	$0.917812\pi$
$968$	7.48182	+	2.93192i	0.240475	+	0.0942354i
$969$	−12.3048			−0.395288
$970$	−1.00748	+	8.05077i	−0.0323482	+	0.258495i
$971$		−	1.32080i		−	0.0423864i	−0.999775	−	0.0211932i	$-0.993253\pi$
$971$		−	1.32080i		−	0.0423864i	0.999775	−	0.0211932i	$-0.00674651\pi$
$972$	−19.0524	−	4.84430i	−0.611104	−	0.155381i
$973$			0.740889i			0.0237518i
$974$	35.3464	+	45.4584i	1.13257	+	1.45658i
$975$	1.20842	+	1.20842i	0.0387004	+	0.0387004i
$976$	−3.22398	−	10.9062i	−0.103197	−	0.349099i
$977$	−14.7716	−	14.7716i	−0.472585	−	0.472585i	0.430165	−	0.902750i	$-0.358455\pi$
$977$	−14.7716	−	14.7716i	−0.472585	−	0.472585i	−0.902750	+	0.430165i	$0.858455\pi$
$978$	−2.63282	+	2.04717i	−0.0841884	+	0.0654612i
$979$	−7.66075	−	7.66075i	−0.244839	−	0.244839i
$980$	−12.0302	+	7.15271i	−0.384291	+	0.228485i
$981$	−28.8346	+	28.8346i	−0.920619	+	0.920619i
$982$	−5.17731	+	41.3720i	−0.165215	+	1.32023i
$983$	7.82437			0.249559			0.124779	−	0.992185i	$-0.460178\pi$
$983$	7.82437			0.249559			0.124779	+	0.992185i	$0.460178\pi$
$984$	−0.428337	+	1.09305i	−0.0136549	+	0.0348452i
$985$	−7.39926	+	7.39926i	−0.235760	+	0.235760i
$986$	24.3705	+	3.04973i	0.776114	+	0.0971233i
$987$	0.0649151			0.00206627
$988$	53.5932	+	13.6268i	1.70503	+	0.433525i
$989$			34.4572i			1.09568i
$990$	9.08160	−	7.06145i	0.288632	−	0.224428i
$991$	4.54915	−	4.54915i	0.144508	−	0.144508i	−0.631151	−	0.775660i	$-0.717417\pi$
$991$	4.54915	−	4.54915i	0.144508	−	0.144508i	0.775660	+	0.631151i	$0.217417\pi$
$992$	21.5973	−	3.55036i	0.685716	−	0.112724i
$993$	−5.50377	−	5.50377i	−0.174657	−	0.174657i
$994$	0.895320	+	0.112041i	0.0283978	+	0.00355372i
$995$			17.4357i			0.552749i
$996$	−2.54306	+	10.0017i	−0.0805801	+	0.316917i
$997$	30.2135	−	30.2135i	0.956873	−	0.956873i	−0.0422350	−	0.999108i	$-0.513448\pi$
$997$	30.2135	−	30.2135i	0.956873	−	0.956873i	0.999108	+	0.0422350i	$0.0134478\pi$
$998$	−5.14809	+	4.00293i	−0.162960	+	0.126710i
$999$	6.61451	+	12.1981i	0.209274	+	0.385932i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.u.a.31.4	✓	152
4.3	odd	2	inner	740.2.u.a.31.37	yes	152
37.6	odd	4	inner	740.2.u.a.191.37	yes	152
148.43	even	4	inner	740.2.u.a.191.4	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.u.a.31.4	✓	152	1.1	even	1	trivial
740.2.u.a.31.37	yes	152	4.3	odd	2	inner
740.2.u.a.191.4	yes	152	148.43	even	4	inner
740.2.u.a.191.37	yes	152	37.6	odd	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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40327 - 0.175606i) q^{2} -0.390097 q^{3} +(1.93833 + 0.492844i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.547410 + 0.0685032i) q^{6} +0.0448530i q^{7} +(-2.63344 - 1.03197i) q^{8} -2.84782 q^{9} +(1.11643 - 0.868089i) q^{10} -2.85638 q^{11} +(-0.756134 - 0.192257i) q^{12} +(3.09774 - 3.09774i) q^{13} +(0.00787644 - 0.0629408i) q^{14} +(0.275840 - 0.275840i) q^{15} +(3.51421 + 1.91058i) q^{16} +(3.53399 - 3.53399i) q^{17} +(3.99626 + 0.500094i) q^{18} +(4.46281 + 4.46281i) q^{19} +(-1.71910 + 1.02211i) q^{20} -0.0174970i q^{21} +(4.00827 + 0.501597i) q^{22} +(3.31647 + 3.31647i) q^{23} +(1.02730 + 0.402569i) q^{24} -1.00000i q^{25} +(-4.89094 + 3.80298i) q^{26} +2.28122 q^{27} +(-0.0221055 + 0.0869397i) q^{28} +(-2.45713 - 2.45713i) q^{29} +(-0.435517 + 0.338638i) q^{30} +(-2.73590 + 2.73590i) q^{31} +(-4.59587 - 3.29818i) q^{32} +1.11427 q^{33} +(-5.57972 + 4.33855i) q^{34} +(-0.0317159 - 0.0317159i) q^{35} +(-5.52001 - 1.40353i) q^{36} +(2.89955 + 5.34720i) q^{37} +(-5.47882 - 7.04621i) q^{38} +(-1.20842 + 1.20842i) q^{39} +(2.59184 - 1.13241i) q^{40} +1.06401i q^{41} +(-0.00307257 + 0.0245530i) q^{42} +(5.19486 + 5.19486i) q^{43} +(-5.53660 - 1.40775i) q^{44} +(2.01372 - 2.01372i) q^{45} +(-4.07150 - 5.23629i) q^{46} +3.71007i q^{47} +(-1.37088 - 0.745312i) q^{48} +6.99799 q^{49} +(-0.175606 + 1.40327i) q^{50} +(-1.37860 + 1.37860i) q^{51} +(7.53113 - 4.47773i) q^{52} +10.8130 q^{53} +(-3.20116 - 0.400595i) q^{54} +(2.01977 - 2.01977i) q^{55} +(0.0462871 - 0.118118i) q^{56} +(-1.74093 - 1.74093i) q^{57} +(3.01653 + 3.87950i) q^{58} +(0.734461 + 0.734461i) q^{59} +(0.670614 - 0.398721i) q^{60} +(-2.01043 - 2.01043i) q^{61} +(4.31964 - 3.35876i) q^{62} -0.127734i q^{63} +(5.87006 + 5.43529i) q^{64} +4.38087i q^{65} +(-1.56361 - 0.195671i) q^{66} +3.33602 q^{67} +(8.59172 - 5.10831i) q^{68} +(-1.29374 - 1.29374i) q^{69} +(0.0389364 + 0.0500754i) q^{70} +14.2248i q^{71} +(7.49959 + 2.93888i) q^{72} -2.47925i q^{73} +(-3.12985 - 8.01274i) q^{74} +0.390097i q^{75} +(6.45090 + 10.8498i) q^{76} -0.128117i q^{77} +(1.90794 - 1.48353i) q^{78} +(1.48130 + 1.48130i) q^{79} +(-3.83591 + 1.13393i) q^{80} +7.65358 q^{81} +(0.186846 - 1.49309i) q^{82} -13.2274i q^{83} +(0.00862329 - 0.0339149i) q^{84} +4.99781i q^{85} +(-6.37754 - 8.20204i) q^{86} +(0.958518 + 0.958518i) q^{87} +(7.52213 + 2.94771i) q^{88} +(2.68197 + 2.68197i) q^{89} +(-3.17940 + 2.47216i) q^{90} +(0.138943 + 0.138943i) q^{91} +(4.79389 + 8.06289i) q^{92} +(1.06727 - 1.06727i) q^{93} +(0.651509 - 5.20622i) q^{94} -6.31136 q^{95} +(1.79283 + 1.28661i) q^{96} +(-4.05678 + 4.05678i) q^{97} +(-9.82006 - 1.22889i) q^{98} +8.13448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 4 q^{2} - 4 q^{8} + 152 q^{9} - 16 q^{13} + 24 q^{14} + 40 q^{16} + 16 q^{22} - 36 q^{24} + 32 q^{29} - 4 q^{32} - 16 q^{37} - 40 q^{38} - 20 q^{42} - 72 q^{44} + 8 q^{46} - 248 q^{49} - 4 q^{50}+ \cdots + 24 q^{98}+O(q^{100}) \) 152 * q - 4 * q^2 - 4 * q^8 + 152 * q^9 - 16 * q^13 + 24 * q^14 + 40 * q^16 + 16 * q^22 - 36 * q^24 + 32 * q^29 - 4 * q^32 - 16 * q^37 - 40 * q^38 - 20 * q^42 - 72 * q^44 + 8 * q^46 - 248 * q^49 - 4 * q^50 - 20 * q^52 + 8 * q^54 - 4 * q^56 + 48 * q^57 + 28 * q^60 + 16 * q^61 + 16 * q^66 - 28 * q^68 - 128 * q^72 - 80 * q^74 + 76 * q^76 + 152 * q^81 + 16 * q^82 - 56 * q^84 - 96 * q^86 - 72 * q^88 + 8 * q^89 - 152 * q^92 + 16 * q^93 + 28 * q^94 + 48 * q^96 - 48 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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