LMFDB - Embedded newform 85.2.j.c.64.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [85,2,Mod(4,85)] 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("85.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(85, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.678728417181$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 24x^{10} + 188x^{8} + 572x^{6} + 776x^{4} + 464x^{2} + 100 $ x^12 + 24x^10 + 188x^8 + 572x^6 + 776x^4 + 464*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			64.3
Root			$-0.767611i$ of defining polynomial
Character	$\chi$	$=$	85.64
Dual form			85.2.j.c.4.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.232389 q^{2} +(1.69306 - 1.69306i) q^{3} -1.94600 q^{4} +(2.04770 + 0.898299i) q^{5} +(-0.393449 + 0.393449i) q^{6} +(-1.46067 - 1.46067i) q^{7} +0.917007 q^{8} -2.73289i q^{9} +(-0.475863 - 0.208755i) q^{10} +(-0.339444 + 0.339444i) q^{11} +(-3.29468 + 3.29468i) q^{12} +4.07073i q^{13} +(0.339444 + 0.339444i) q^{14} +(4.98774 - 1.94600i) q^{15} +3.67889 q^{16} +(-3.75946 + 1.69306i) q^{17} +0.635095i q^{18} +4.00000i q^{19} +(-3.98481 - 1.74809i) q^{20} -4.94600 q^{21} +(0.0788831 - 0.0788831i) q^{22} +(-5.76379 - 5.76379i) q^{23} +(1.55255 - 1.55255i) q^{24} +(3.38612 + 3.67889i) q^{25} -0.945995i q^{26} +(0.452229 + 0.452229i) q^{27} +(2.84245 + 2.84245i) q^{28} +(0.732893 + 0.732893i) q^{29} +(-1.15910 + 0.452229i) q^{30} +(-4.28544 - 4.28544i) q^{31} -2.68895 q^{32} +1.14940i q^{33} +(0.873659 - 0.393449i) q^{34} +(-1.67889 - 4.30312i) q^{35} +5.31820i q^{36} +(0.917007 - 0.917007i) q^{37} -0.929557i q^{38} +(6.89199 + 6.89199i) q^{39} +(1.87775 + 0.823747i) q^{40} +(7.62488 - 7.62488i) q^{41} +1.14940 q^{42} +7.45685 q^{43} +(0.660556 - 0.660556i) q^{44} +(2.45496 - 5.59613i) q^{45} +(1.33944 + 1.33944i) q^{46} -3.60596i q^{47} +(6.22857 - 6.22857i) q^{48} -2.73289i q^{49} +(-0.786897 - 0.854934i) q^{50} +(-3.49854 + 9.23143i) q^{51} -7.92163i q^{52} -6.14969 q^{53} +(-0.105093 - 0.105093i) q^{54} +(-1.00000 + 0.390156i) q^{55} +(-1.33944 - 1.33944i) q^{56} +(6.77223 + 6.77223i) q^{57} +(-0.170316 - 0.170316i) q^{58} -6.00000i q^{59} +(-9.70612 + 3.78690i) q^{60} +(-4.00000 + 4.00000i) q^{61} +(0.995890 + 0.995890i) q^{62} +(-3.99185 + 3.99185i) q^{63} -6.73289 q^{64} +(-3.65674 + 8.33563i) q^{65} -0.267107i q^{66} +3.14118i q^{67} +(7.31589 - 3.29468i) q^{68} -19.5169 q^{69} +(0.390156 + 1.00000i) q^{70} +(1.28544 + 1.28544i) q^{71} -2.50608i q^{72} +(-8.60625 + 8.60625i) q^{73} +(-0.213103 + 0.213103i) q^{74} +(11.9615 + 0.495679i) q^{75} -7.78398i q^{76} +0.991630 q^{77} +(-1.60162 - 1.60162i) q^{78} +(7.23143 - 7.23143i) q^{79} +(7.53324 + 3.30474i) q^{80} +9.72998 q^{81} +(-1.77194 + 1.77194i) q^{82} -2.23672 q^{83} +9.62488 q^{84} +(-9.21911 + 0.0897461i) q^{85} -1.73289 q^{86} +2.48166 q^{87} +(-0.311272 + 0.311272i) q^{88} -9.37220 q^{89} +(-0.570505 + 1.30048i) q^{90} +(5.94600 - 5.94600i) q^{91} +(11.2163 + 11.2163i) q^{92} -14.5110 q^{93} +0.837986i q^{94} +(-3.59320 + 8.19078i) q^{95} +(-4.55255 + 4.55255i) q^{96} +(11.8220 - 11.8220i) q^{97} +0.635095i q^{98} +(0.927664 + 0.927664i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{4} - 20 q^{6} - 4 q^{10} + 16 q^{11} - 16 q^{14} + 4 q^{16} - 32 q^{20} - 24 q^{21} - 32 q^{24} + 4 q^{29} + 52 q^{30} + 4 q^{31} + 20 q^{35} + 12 q^{39} + 24 q^{40} + 16 q^{41} + 28 q^{44}+ \cdots + 36 q^{99}+O(q^{100}) $ 12 * q + 12 * q^4 - 20 * q^6 - 4 * q^10 + 16 * q^11 - 16 * q^14 + 4 * q^16 - 32 * q^20 - 24 * q^21 - 32 * q^24 + 4 * q^29 + 52 * q^30 + 4 * q^31 + 20 * q^35 + 12 * q^39 + 24 * q^40 + 16 * q^41 + 28 * q^44 - 20 * q^45 - 4 * q^46 - 40 * q^50 + 44 * q^51 + 100 * q^54 - 12 * q^55 + 4 * q^56 - 48 * q^61 - 76 * q^64 + 8 * q^65 - 88 * q^69 - 40 * q^71 + 28 * q^74 + 64 * q^75 - 4 * q^79 + 12 * q^80 - 60 * q^81 + 40 * q^84 - 52 * q^85 - 16 * q^86 - 16 * q^89 - 84 * q^90 + 36 * q^91 - 4 * q^96 + 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.232389			−0.164324			−0.0821620	−	0.996619i	$-0.526183\pi$
$2$	−0.232389			−0.164324			−0.0821620	+	0.996619i	$0.526183\pi$
$3$	1.69306	−	1.69306i	0.977488	−	0.977488i	−0.0222645	−	0.999752i	$-0.507088\pi$
$3$	1.69306	−	1.69306i	0.977488	−	0.977488i	0.999752	+	0.0222645i	$0.00708759\pi$
$4$	−1.94600			−0.972998
$5$	2.04770	+	0.898299i	0.915757	+	0.401732i
$5$	2.04770	+	0.898299i	0.915757	+	0.401732i
$6$	−0.393449	+	0.393449i	−0.160625	+	0.160625i
$7$	−1.46067	−	1.46067i	−0.552081	−	0.552081i	0.374960	−	0.927041i	$-0.377656\pi$
$7$	−1.46067	−	1.46067i	−0.552081	−	0.552081i	−0.927041	+	0.374960i	$0.877656\pi$
$8$	0.917007			0.324211
$9$		−	2.73289i		−	0.910964i
$10$	−0.475863	−	0.208755i	−0.150481	−	0.0660142i
$11$	−0.339444	+	0.339444i	−0.102346	+	0.102346i	−0.756426	−	0.654080i	$-0.773056\pi$
$11$	−0.339444	+	0.339444i	−0.102346	+	0.102346i	0.654080	+	0.756426i	$0.273056\pi$
$12$	−3.29468	+	3.29468i	−0.951093	+	0.951093i
$13$			4.07073i			1.12902i	0.825427	+	0.564509i	$0.190935\pi$
$13$			4.07073i			1.12902i	−0.825427	+	0.564509i	$0.809065\pi$
$14$	0.339444	+	0.339444i	0.0907202	+	0.0907202i
$15$	4.98774	−	1.94600i	1.28783	−	0.502454i
$16$	3.67889			0.919722
$17$	−3.75946	+	1.69306i	−0.911803	+	0.410627i
$17$	−3.75946	+	1.69306i	−0.911803	+	0.410627i
$18$			0.635095i			0.149693i
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$	−3.98481	−	1.74809i	−0.891030	−	0.390884i
$21$	−4.94600			−1.07930
$22$	0.0788831	−	0.0788831i	0.0168179	−	0.0168179i
$23$	−5.76379	−	5.76379i	−1.20183	−	1.20183i	−0.973608	−	0.228226i	$-0.926708\pi$
$23$	−5.76379	−	5.76379i	−1.20183	−	1.20183i	−0.228226	−	0.973608i	$-0.573292\pi$
$24$	1.55255	−	1.55255i	0.316912	−	0.316912i
$25$	3.38612	+	3.67889i	0.677223	+	0.735778i
$26$		−	0.945995i		−	0.185525i
$27$	0.452229	+	0.452229i	0.0870314	+	0.0870314i
$28$	2.84245	+	2.84245i	0.537173	+	0.537173i
$29$	0.732893	+	0.732893i	0.136095	+	0.136095i	0.771872	−	0.635778i	$-0.219320\pi$
$29$	0.732893	+	0.732893i	0.136095	+	0.136095i	−0.635778	+	0.771872i	$0.719320\pi$
$30$	−1.15910	+	0.452229i	−0.211621	+	0.0825653i
$31$	−4.28544	−	4.28544i	−0.769688	−	0.769688i	0.208364	−	0.978051i	$-0.433186\pi$
$31$	−4.28544	−	4.28544i	−0.769688	−	0.769688i	−0.978051	+	0.208364i	$0.933186\pi$
$32$	−2.68895			−0.475343
$33$			1.14940i			0.200084i
$34$	0.873659	−	0.393449i	0.149831	−	0.0674759i
$35$	−1.67889	−	4.30312i	−0.283784	−	0.727361i
$36$			5.31820i			0.886366i
$37$	0.917007	−	0.917007i	0.150755	−	0.150755i	−0.627700	−	0.778455i	$-0.716004\pi$
$37$	0.917007	−	0.917007i	0.150755	−	0.150755i	0.778455	+	0.627700i	$0.216004\pi$
$38$		−	0.929557i		−	0.150794i
$39$	6.89199	+	6.89199i	1.10360	+	1.10360i
$40$	1.87775	+	0.823747i	0.296899	+	0.130246i
$41$	7.62488	−	7.62488i	1.19081	−	1.19081i	0.213965	−	0.976841i	$-0.431362\pi$
$41$	7.62488	−	7.62488i	1.19081	−	1.19081i	0.976841	−	0.213965i	$-0.0686380\pi$
$42$	1.14940			0.177356
$43$	7.45685			1.13716			0.568580	−	0.822628i	$-0.307493\pi$
$43$	7.45685			1.13716			0.568580	+	0.822628i	$0.307493\pi$
$44$	0.660556	−	0.660556i	0.0995826	−	0.0995826i
$45$	2.45496	−	5.59613i	0.365963	−	0.834222i
$46$	1.33944	+	1.33944i	0.197490	+	0.197490i
$47$		−	3.60596i		−	0.525983i	−0.964798	−	0.262991i	$-0.915291\pi$
$47$		−	3.60596i		−	0.525983i	0.964798	−	0.262991i	$-0.0847091\pi$
$48$	6.22857	−	6.22857i	0.899017	−	0.899017i
$49$		−	2.73289i		−	0.390413i
$50$	−0.786897	−	0.854934i	−0.111284	−	0.120906i
$51$	−3.49854	+	9.23143i	−0.489894	+	1.29266i
$52$		−	7.92163i		−	1.09853i
$53$	−6.14969			−0.844725			−0.422362	−	0.906427i	$-0.638799\pi$
$53$	−6.14969			−0.844725			−0.422362	+	0.906427i	$0.638799\pi$
$54$	−0.105093	−	0.105093i	−0.0143014	−	0.0143014i
$55$	−1.00000	+	0.390156i	−0.134840	+	0.0526086i
$56$	−1.33944	−	1.33944i	−0.178991	−	0.178991i
$57$	6.77223	+	6.77223i	0.897004	+	0.897004i
$58$	−0.170316	−	0.170316i	−0.0223636	−	0.0223636i
$59$		−	6.00000i		−	0.781133i	−0.920575	−	0.390567i	$-0.872279\pi$
$59$		−	6.00000i		−	0.781133i	0.920575	−	0.390567i	$-0.127721\pi$
$60$	−9.70612	+	3.78690i	−1.25305	+	0.488886i
$61$	−4.00000	+	4.00000i	−0.512148	+	0.512148i	−0.915184	−	0.403036i	$-0.867955\pi$
$61$	−4.00000	+	4.00000i	−0.512148	+	0.512148i	0.403036	+	0.915184i	$0.367955\pi$
$62$	0.995890	+	0.995890i	0.126478	+	0.126478i
$63$	−3.99185	+	3.99185i	−0.502926	+	0.502926i
$64$	−6.73289			−0.841612
$65$	−3.65674	+	8.33563i	−0.453563	+	1.03391i
$66$		−	0.267107i		−	0.0328787i
$67$			3.14118i			0.383756i	0.981419	+	0.191878i	$0.0614578\pi$
$67$			3.14118i			0.383756i	−0.981419	+	0.191878i	$0.938542\pi$
$68$	7.31589	−	3.29468i	0.887183	−	0.399539i
$69$	−19.5169			−2.34956
$70$	0.390156	+	1.00000i	0.0466325	+	0.119523i
$71$	1.28544	+	1.28544i	0.152554	+	0.152554i	0.779257	−	0.626704i	$-0.215596\pi$
$71$	1.28544	+	1.28544i	0.152554	+	0.152554i	−0.626704	+	0.779257i	$0.715596\pi$
$72$		−	2.50608i		−	0.295345i
$73$	−8.60625	+	8.60625i	−1.00729	+	1.00729i	−0.00731179	+	0.999973i	$0.502327\pi$
$73$	−8.60625	+	8.60625i	−1.00729	+	1.00729i	−0.999973	+	0.00731179i	$0.997673\pi$
$74$	−0.213103	+	0.213103i	−0.0247727	+	0.0247727i
$75$	11.9615	+	0.495679i	1.38119	+	0.0572360i
$76$		−	7.78398i		−	0.892884i
$77$	0.991630			0.113007
$78$	−1.60162	−	1.60162i	−0.181348	−	0.181348i
$79$	7.23143	−	7.23143i	0.813600	−	0.813600i	−0.171572	−	0.985172i	$-0.554885\pi$
$79$	7.23143	−	7.23143i	0.813600	−	0.813600i	0.985172	+	0.171572i	$0.0548845\pi$
$80$	7.53324	+	3.30474i	0.842242	+	0.369481i
$81$	9.72998			1.08111
$82$	−1.77194	+	1.77194i	−0.195678	+	0.195678i
$83$	−2.23672			−0.245512			−0.122756	−	0.992437i	$-0.539173\pi$
$83$	−2.23672			−0.245512			−0.122756	+	0.992437i	$0.539173\pi$
$84$	9.62488			1.05016
$85$	−9.21911	+	0.0897461i	−0.999953	+	0.00973434i
$86$	−1.73289			−0.186863
$87$	2.48166			0.266062
$88$	−0.311272	+	0.311272i	−0.0331818	+	0.0331818i
$89$	−9.37220			−0.993451			−0.496726	−	0.867908i	$-0.665464\pi$
$89$	−9.37220			−0.993451			−0.496726	+	0.867908i	$0.665464\pi$
$90$	−0.570505	+	1.30048i	−0.0601366	+	0.137083i
$91$	5.94600	−	5.94600i	0.623310	−	0.623310i
$92$	11.2163	+	11.2163i	1.16938	+	1.16938i
$93$	−14.5110			−1.50472
$94$			0.837986i			0.0864316i
$95$	−3.59320	+	8.19078i	−0.368654	+	0.840357i
$96$	−4.55255	+	4.55255i	−0.464642	+	0.464642i
$97$	11.8220	−	11.8220i	1.20035	−	1.20035i	0.226286	−	0.974061i	$-0.427342\pi$
$97$	11.8220	−	11.8220i	1.20035	−	1.20035i	0.974061	−	0.226286i	$-0.0726585\pi$
$98$			0.635095i			0.0641543i
$99$	0.927664	+	0.927664i	0.0932337	+	0.0932337i
$100$	−6.58937	−	7.15910i	−0.658937	−	0.715910i
$101$	−4.41178			−0.438989			−0.219494	−	0.975614i	$-0.570441\pi$
$101$	−4.41178			−0.438989			−0.219494	+	0.975614i	$0.570441\pi$
$102$	0.813024	−	2.14529i	0.0805013	−	0.212415i
$103$			17.4323i			1.71766i	0.512262	+	0.858829i	$0.328808\pi$
$103$			17.4323i			1.71766i	−0.512262	+	0.858829i	$0.671192\pi$
$104$			3.73289i			0.366040i
$105$	−10.1279	−	4.44298i	−0.988381	−	0.433591i
$106$	1.42912			0.138809
$107$	3.68484	−	3.68484i	0.356227	−	0.356227i	−0.506193	−	0.862420i	$-0.668948\pi$
$107$	3.68484	−	3.68484i	0.356227	−	0.356227i	0.862420	+	0.506193i	$0.168948\pi$
$108$	−0.880035	−	0.880035i	−0.0846814	−	0.0846814i
$109$	−5.73289	+	5.73289i	−0.549112	+	0.549112i	−0.926184	−	0.377072i	$-0.876931\pi$
$109$	−5.73289	+	5.73289i	−0.549112	+	0.549112i	0.377072	+	0.926184i	$0.376931\pi$
$110$	0.232389	−	0.0906680i	0.0221575	−	0.00864485i
$111$		−	3.10509i		−	0.294722i
$112$	−5.37364	−	5.37364i	−0.507761	−	0.507761i
$113$	−2.45656	−	2.45656i	−0.231094	−	0.231094i	0.582055	−	0.813149i	$-0.302249\pi$
$113$	−2.45656	−	2.45656i	−0.231094	−	0.231094i	−0.813149	+	0.582055i	$0.802249\pi$
$114$	−1.57379	−	1.57379i	−0.147399	−	0.147399i
$115$	−6.62488	−	16.9801i	−0.617774	−	1.58340i
$116$	−1.42621	−	1.42621i	−0.132420	−	0.132420i
$117$	11.1249			1.02850
$118$			1.39434i			0.128359i
$119$	7.96433	+	3.01833i	0.730089	+	0.276690i
$120$	4.57379	−	1.78449i	0.417528	−	0.162901i
$121$			10.7696i			0.979051i
$122$	0.929557	−	0.929557i	0.0841582	−	0.0841582i
$123$		−	25.8187i		−	2.32800i
$124$	8.33944	+	8.33944i	0.748904	+	0.748904i
$125$	3.62899	+	10.5750i	0.324587	+	0.945856i
$126$	0.927664	−	0.927664i	0.0826428	−	0.0826428i
$127$	−2.98341			−0.264735			−0.132367	−	0.991201i	$-0.542258\pi$
$127$	−2.98341			−0.264735			−0.132367	+	0.991201i	$0.542258\pi$
$128$	6.94255			0.613640
$129$	12.6249	−	12.6249i	1.11156	−	1.11156i
$130$	0.849787	−	1.93711i	0.0745312	−	0.169896i
$131$	5.08676	+	5.08676i	0.444432	+	0.444432i	0.893499	−	0.449066i	$-0.148243\pi$
$131$	5.08676	+	5.08676i	0.444432	+	0.444432i	−0.449066	+	0.893499i	$0.648243\pi$
$132$		−	2.23672i		−	0.194681i
$133$	5.84268	−	5.84268i	0.506624	−	0.506624i
$134$		−	0.729976i		−	0.0630603i
$135$	0.519790	+	1.33226i	0.0447364	+	0.114663i
$136$	−3.44745	+	1.55255i	−0.295617	+	0.133130i
$137$		−	0.526852i		−	0.0450120i	−0.999747	−	0.0225060i	$-0.992836\pi$
$137$		−	0.526852i		−	0.0450120i	0.999747	−	0.0225060i	$-0.00716448\pi$
$138$	4.53551			0.386089
$139$	12.4985	+	12.4985i	1.06011	+	1.06011i	0.998074	+	0.0620387i	$0.0197602\pi$
$139$	12.4985	+	12.4985i	1.06011	+	1.06011i	0.0620387	+	0.998074i	$0.480240\pi$
$140$	3.26711	+	8.37386i	0.276121	+	0.707720i
$141$	−6.10509	−	6.10509i	−0.514142	−	0.514142i
$142$	−0.298722	−	0.298722i	−0.0250682	−	0.0250682i
$143$	−1.38179	−	1.38179i	−0.115551	−	0.115551i
$144$		−	10.0540i		−	0.837834i
$145$	0.842384	+	2.15910i	0.0699562	+	0.179303i
$146$	2.00000	−	2.00000i	0.165521	−	0.165521i
$147$	−4.62695	−	4.62695i	−0.381624	−	0.381624i
$148$	−1.78449	+	1.78449i	−0.146684	+	0.146684i
$149$	7.32111			0.599769			0.299884	−	0.953976i	$-0.403052\pi$
$149$	7.32111			0.599769			0.299884	+	0.953976i	$0.403052\pi$
$150$	−2.77972	−	0.115190i	−0.226963	−	0.00940526i
$151$		−	7.46579i		−	0.607557i	−0.952743	−	0.303778i	$-0.901752\pi$
$151$		−	7.46579i		−	0.607557i	0.952743	−	0.303778i	$-0.0982483\pi$
$152$			3.66803i			0.297516i
$153$	4.62695	+	10.2742i	0.374066	+	0.830620i
$154$	−0.230444			−0.0185697
$155$	−4.92567	−	12.6249i	−0.395639	−	1.01405i
$156$	−13.4118	−	13.4118i	−1.07380	−	1.07380i
$157$			12.4571i			0.994188i	0.867697	+	0.497094i	$0.165600\pi$
$157$			12.4571i			0.994188i	−0.867697	+	0.497094i	$0.834400\pi$
$158$	−1.68051	+	1.68051i	−0.133694	+	0.133694i
$159$	−10.4118	+	10.4118i	−0.825708	+	0.825708i
$160$	−5.50615	−	2.41548i	−0.435299	−	0.190961i
$161$			16.8380i			1.32702i
$162$	−2.26114			−0.177652
$163$	6.05825	+	6.05825i	0.474519	+	0.474519i	0.903374	−	0.428854i	$-0.141083\pi$
$163$	6.05825	+	6.05825i	0.474519	+	0.474519i	−0.428854	+	0.903374i	$0.641083\pi$
$164$	−14.8380	+	14.8380i	−1.15865	+	1.15865i
$165$	−1.03250	+	2.35361i	−0.0803802	+	0.183229i
$166$	0.519790			0.0403435
$167$	−6.68080	+	6.68080i	−0.516976	+	0.516976i	−0.916655	−	0.399679i	$-0.869122\pi$
$167$	−6.68080	+	6.68080i	−0.516976	+	0.516976i	0.399679	+	0.916655i	$0.369122\pi$
$168$	−4.53551			−0.349922
$169$	−3.57088			−0.274683
$170$	2.14242	−	0.0208560i	0.164316	−	0.00159959i
$171$	10.9316			0.835958
$172$	−14.5110			−1.10645
$173$	11.6979	−	11.6979i	0.889375	−	0.889375i	−0.105088	−	0.994463i	$-0.533512\pi$
$173$	11.6979	−	11.6979i	0.889375	−	0.889375i	0.994463	+	0.105088i	$0.0335124\pi$
$174$	−0.576711			−0.0437204
$175$	0.427642	−	10.3196i	0.0323267	−	0.780091i
$176$	−1.24878	+	1.24878i	−0.0941300	+	0.0941300i
$177$	−10.1583	−	10.1583i	−0.763548	−	0.763548i
$178$	2.17800			0.163248
$179$		−	19.5313i		−	1.45984i	−0.683534	−	0.729919i	$-0.739558\pi$
$179$		−	19.5313i		−	1.45984i	0.683534	−	0.729919i	$-0.260442\pi$
$180$	−4.77733	+	10.8900i	−0.356081	+	0.811696i
$181$	7.41178	−	7.41178i	0.550913	−	0.550913i	−0.375791	−	0.926704i	$-0.622629\pi$
$181$	7.41178	−	7.41178i	0.550913	−	0.550913i	0.926704	+	0.375791i	$0.122629\pi$
$182$	−1.38179	+	1.38179i	−0.102425	+	0.102425i
$183$			13.5445i			1.00124i
$184$	−5.28544	−	5.28544i	−0.389648	−	0.389648i
$185$	2.70150	−	1.05400i	0.198618	−	0.0774920i
$186$	3.37220			0.247262
$187$	0.701428	−	1.85082i	0.0512935	−	0.135346i
$188$			7.01717i			0.511780i
$189$		−	1.32111i		−	0.0960968i
$190$	0.835021	−	1.90345i	0.0605788	−	0.138091i
$191$	−5.32111			−0.385022			−0.192511	−	0.981295i	$-0.561663\pi$
$191$	−5.32111			−0.385022			−0.192511	+	0.981295i	$0.561663\pi$
$192$	−11.3992	+	11.3992i	−0.822665	+	0.822665i
$193$	−8.82609	−	8.82609i	−0.635316	−	0.635316i	0.314081	−	0.949396i	$-0.398304\pi$
$193$	−8.82609	−	8.82609i	−0.635316	−	0.635316i	−0.949396	+	0.314081i	$0.898304\pi$
$194$	−2.74732	+	2.74732i	−0.197246	+	0.197246i
$195$	7.92163	+	20.3038i	0.567280	+	1.45398i
$196$			5.31820i			0.379871i
$197$	0.390156	+	0.390156i	0.0277974	+	0.0277974i	0.720869	−	0.693071i	$-0.243743\pi$
$197$	0.390156	+	0.390156i	0.0277974	+	0.0277974i	−0.693071	+	0.720869i	$0.743743\pi$
$198$	−0.215579	−	0.215579i	−0.0153205	−	0.0153205i
$199$	−12.4445	−	12.4445i	−0.882170	−	0.882170i	0.111585	−	0.993755i	$-0.464407\pi$
$199$	−12.4445	−	12.4445i	−0.882170	−	0.882170i	−0.993755	+	0.111585i	$0.964407\pi$
$200$	3.10509	+	3.37357i	0.219563	+	0.238547i
$201$	5.31820	+	5.31820i	0.375117	+	0.375117i
$202$	1.02525			0.0721364
$203$		−	2.14103i		−	0.150271i
$204$	6.80815	−	17.9643i	0.476666	−	1.25775i
$205$	22.4629	−	8.76401i	1.56887	−	0.612105i
$206$		−	4.05109i		−	0.282253i
$207$	−15.7518	+	15.7518i	−1.09483	+	1.09483i
$208$			14.9758i			1.03838i
$209$	−1.35778	−	1.35778i	−0.0939193	−	0.0939193i
$210$	2.35361	+	1.03250i	0.162415	+	0.0712494i
$211$	−9.07234	+	9.07234i	−0.624565	+	0.624565i	−0.946695	−	0.322130i	$-0.895601\pi$
$211$	−9.07234	+	9.07234i	−0.624565	+	0.624565i	0.322130	+	0.946695i	$0.395601\pi$
$212$	11.9673			0.821915
$213$	4.35265			0.298238
$214$	−0.856317	+	0.856317i	−0.0585366	+	0.0585366i
$215$	15.2694	+	6.69848i	1.04136	+	0.456833i
$216$	0.414697	+	0.414697i	0.0282165	+	0.0282165i
$217$			12.5192i			0.849860i
$218$	1.33226	−	1.33226i	0.0902322	−	0.0902322i
$219$			29.1418i			1.96922i
$220$	1.94600	−	0.759241i	0.131199	−	0.0511880i
$221$	−6.89199	−	15.3038i	−0.463605	−	1.02944i
$222$			0.721590i			0.0484300i
$223$	−4.07073			−0.272597			−0.136298	−	0.990668i	$-0.543521\pi$
$223$	−4.07073			−0.272597			−0.136298	+	0.990668i	$0.543521\pi$
$224$	3.92766	+	3.92766i	0.262428	+	0.262428i
$225$	10.0540	−	9.25389i	0.670267	−	0.616926i
$226$	0.570878	+	0.570878i	0.0379742	+	0.0379742i
$227$	−11.1542	−	11.1542i	−0.740333	−	0.740333i	0.232309	−	0.972642i	$-0.425372\pi$
$227$	−11.1542	−	11.1542i	−0.740333	−	0.740333i	−0.972642	+	0.232309i	$0.925372\pi$
$228$	−13.1787	−	13.1787i	−0.872783	−	0.872783i
$229$		−	14.9460i		−	0.987659i	−0.869559	−	0.493830i	$-0.835597\pi$
$229$		−	14.9460i		−	0.987659i	0.869559	−	0.493830i	$-0.164403\pi$
$230$	1.53955	+	3.94600i	0.101515	+	0.260191i
$231$	1.67889	−	1.67889i	0.110463	−	0.110463i
$232$	0.672068	+	0.672068i	0.0441234	+	0.0441234i
$233$	0.514301	−	0.514301i	0.0336930	−	0.0336930i	−0.690060	−	0.723753i	$-0.742416\pi$
$233$	0.514301	−	0.514301i	0.0336930	−	0.0336930i	0.723753	+	0.690060i	$0.242416\pi$
$234$	−2.58530			−0.169007
$235$	3.23923	−	7.38390i	0.211304	−	0.481673i
$236$			11.6760i			0.760041i
$237$		−	24.4865i		−	1.59057i
$238$	−1.85082	−	0.701428i	−0.119971	−	0.0454668i
$239$	−9.57379			−0.619277			−0.309639	−	0.950854i	$-0.600208\pi$
$239$	−9.57379			−0.619277			−0.309639	+	0.950854i	$0.600208\pi$
$240$	18.3493	−	7.15910i	1.18444	−	0.462118i
$241$	6.00000	+	6.00000i	0.386494	+	0.386494i	0.873435	−	0.486941i	$-0.161887\pi$
$241$	6.00000	+	6.00000i	0.386494	+	0.386494i	−0.486941	+	0.873435i	$0.661887\pi$
$242$		−	2.50273i		−	0.160882i
$243$	15.1167	−	15.1167i	0.969739	−	0.969739i
$244$	7.78398	−	7.78398i	0.498318	−	0.498318i
$245$	2.45496	−	5.59613i	0.156841	−	0.357524i
$246$			6.00000i			0.382546i
$247$	−16.2829			−1.03606
$248$	−3.92978	−	3.92978i	−0.249541	−	0.249541i
$249$	−3.78690	+	3.78690i	−0.239985	+	0.239985i
$250$	−0.843340	−	2.45751i	−0.0533375	−	0.155427i
$251$	−6.03666			−0.381031			−0.190515	−	0.981684i	$-0.561016\pi$
$251$	−6.03666			−0.381031			−0.190515	+	0.981684i	$0.561016\pi$
$252$	7.76812	−	7.76812i	0.489346	−	0.489346i
$253$	3.91297			0.246006
$254$	0.693313			0.0435023
$255$	−15.4565	+	15.7604i	−0.967926	+	0.986957i
$256$	11.8524			0.740776
$257$	27.2752			1.70138			0.850689	−	0.525670i	$-0.176185\pi$
$257$	27.2752			1.70138			0.850689	+	0.525670i	$0.176185\pi$
$258$	−2.93389	+	2.93389i	−0.182656	+	0.182656i
$259$	−2.67889			−0.166458
$260$	7.11599	−	16.2211i	0.441315	−	1.00599i
$261$	2.00292	−	2.00292i	0.123977	−	0.123977i
$262$	−1.18211	−	1.18211i	−0.0730309	−	0.0730309i
$263$	12.3700			0.762765			0.381382	−	0.924417i	$-0.375448\pi$
$263$	12.3700			0.762765			0.381382	+	0.924417i	$0.375448\pi$
$264$			1.05400i			0.0648695i
$265$	−12.5927	−	5.52426i	−0.773563	−	0.339353i
$266$	−1.35778	+	1.35778i	−0.0832506	+	0.0832506i
$267$	−15.8677	+	15.8677i	−0.971086	+	0.971086i
$268$		−	6.11272i		−	0.373394i
$269$	14.1958	+	14.1958i	0.865531	+	0.865531i	0.991974	−	0.126443i	$-0.0403561\pi$
$269$	14.1958	+	14.1958i	0.865531	+	0.865531i	−0.126443	+	0.991974i	$0.540356\pi$
$270$	−0.120794	−	0.309604i	−0.00735127	−	0.0188419i
$271$	−24.2102			−1.47066			−0.735332	−	0.677707i	$-0.762974\pi$
$271$	−24.2102			−1.47066			−0.735332	+	0.677707i	$0.762974\pi$
$272$	−13.8306	+	6.22857i	−0.838606	+	0.377663i
$273$		−	20.1338i		−	1.21855i
$274$			0.122435i			0.00739655i
$275$	−2.39817	−	0.0993794i	−0.144615	−	0.00599280i
$276$	37.9797			2.28611
$277$	4.78045	−	4.78045i	0.287230	−	0.287230i	−0.548754	−	0.835984i	$-0.684898\pi$
$277$	4.78045	−	4.78045i	0.287230	−	0.287230i	0.835984	+	0.548754i	$0.184898\pi$
$278$	−2.90453	−	2.90453i	−0.174202	−	0.174202i
$279$	−11.7116	+	11.7116i	−0.701158	+	0.701158i
$280$	−1.53955	−	3.94600i	−0.0920058	−	0.235818i
$281$			18.0367i			1.07598i	0.842952	+	0.537989i	$0.180816\pi$
$281$			18.0367i			1.07598i	−0.842952	+	0.537989i	$0.819184\pi$
$282$	1.41876	+	1.41876i	0.0844858	+	0.0844858i
$283$	17.8308	+	17.8308i	1.05993	+	1.05993i	0.998086	+	0.0618440i	$0.0196981\pi$
$283$	17.8308	+	17.8308i	1.05993	+	1.05993i	0.0618440	+	0.998086i	$0.480302\pi$
$284$	−2.50146	−	2.50146i	−0.148434	−	0.148434i
$285$	7.78398	+	19.9510i	0.461083	+	1.18179i
$286$	0.321112	+	0.321112i	0.0189878	+	0.0189878i
$287$	−22.2749			−1.31484
$288$			7.34861i			0.433021i
$289$	11.2671	−	12.7300i	0.662771	−	0.748822i
$290$	−0.195761	−	0.501751i	−0.0114955	−	0.0294639i
$291$		−	40.0308i		−	2.34665i
$292$	16.7477	−	16.7477i	0.980086	−	0.980086i
$293$			26.2584i			1.53403i	0.641627	+	0.767017i	$0.278260\pi$
$293$			26.2584i			1.53403i	−0.641627	+	0.767017i	$0.721740\pi$
$294$	1.07525	+	1.07525i	0.0627100	+	0.0627100i
$295$	5.38980	−	12.2862i	0.313806	−	0.715329i
$296$	0.840902	−	0.840902i	0.0488764	−	0.0488764i
$297$	−0.307012			−0.0178147
$298$	−1.70135			−0.0985565
$299$	23.4629	−	23.4629i	1.35689	−	1.35689i
$300$	−23.2770	−	0.964588i	−1.34390	−	0.0556905i
$301$	−10.8920	−	10.8920i	−0.627804	−	0.627804i
$302$			1.73497i			0.0998362i
$303$	−7.46940	+	7.46940i	−0.429106	+	0.429106i
$304$			14.7156i			0.843995i
$305$	−11.7840	+	4.59759i	−0.674749	+	0.263257i
$306$	−1.07525	−	2.38762i	−0.0614681	−	0.136491i
$307$			13.9136i			0.794088i	0.917800	+	0.397044i	$0.129964\pi$
$307$			13.9136i			0.794088i	−0.917800	+	0.397044i	$0.870036\pi$
$308$	−1.92971			−0.109955
$309$	29.5140	+	29.5140i	1.67899	+	1.67899i
$310$	1.14467	+	2.93389i	0.0650130	+	0.166634i
$311$	−6.18035	−	6.18035i	−0.350455	−	0.350455i	0.509824	−	0.860279i	$-0.329711\pi$
$311$	−6.18035	−	6.18035i	−0.350455	−	0.350455i	−0.860279	+	0.509824i	$0.829711\pi$
$312$	6.32000	+	6.32000i	0.357800	+	0.357800i
$313$	4.91312	+	4.91312i	0.277706	+	0.277706i	0.832193	−	0.554487i	$-0.187085\pi$
$313$	4.91312	+	4.91312i	0.277706	+	0.277706i	−0.554487	+	0.832193i	$0.687085\pi$
$314$		−	2.89491i		−	0.163369i
$315$	−11.7600	+	4.58822i	−0.662600	+	0.258517i
$316$	−14.0723	+	14.0723i	−0.791631	+	0.791631i
$317$	−2.98341	−	2.98341i	−0.167565	−	0.167565i	0.618343	−	0.785908i	$-0.287804\pi$
$317$	−2.98341	−	2.98341i	−0.167565	−	0.167565i	−0.785908	+	0.618343i	$0.787804\pi$
$318$	2.41959	−	2.41959i	0.135684	−	0.135684i
$319$	−0.497552			−0.0278575
$320$	−13.7869	−	6.04815i	−0.770712	−	0.338102i
$321$		−	12.4773i		−	0.696415i
$322$		−	3.91297i		−	0.218061i
$323$	−6.77223	−	15.0378i	−0.376817	−	0.836728i
$324$	−18.9345			−1.05192
$325$	−14.9758	+	13.7840i	−0.830707	+	0.764598i
$326$	−1.40787	−	1.40787i	−0.0779749	−	0.0779749i
$327$			19.4122i			1.07350i
$328$	6.99207	−	6.99207i	0.386073	−	0.386073i
$329$	−5.26711	+	5.26711i	−0.290385	+	0.290385i
$330$	0.239942	−	0.546955i	0.0132084	−	0.0301089i
$331$			13.6760i			0.751699i	0.926681	+	0.375850i	$0.122649\pi$
$331$			13.6760i			0.751699i	−0.926681	+	0.375850i	$0.877351\pi$
$332$	4.35265			0.238883
$333$	−2.50608	−	2.50608i	−0.137332	−	0.137332i
$334$	1.55255	−	1.55255i	0.0849516	−	0.0849516i
$335$	−2.82172	+	6.43218i	−0.154167	+	0.351427i
$336$	−18.1958			−0.992660
$337$	4.58504	−	4.58504i	0.249763	−	0.249763i	−0.571110	−	0.820873i	$-0.693487\pi$
$337$	4.58504	−	4.58504i	0.249763	−	0.249763i	0.820873	+	0.571110i	$0.193487\pi$
$338$	0.829834			0.0451370
$339$	−8.31820			−0.451782
$340$	17.9403	−	0.174646i	0.972952	−	0.00947148i
$341$	2.90933			0.157549
$342$	−2.54038			−0.137368
$343$	−14.2165	+	14.2165i	−0.767621	+	0.767621i
$344$	6.83799			0.368679
$345$	−39.9646	−	17.5320i	−2.15162	−	0.943891i
$346$	−2.71847	+	2.71847i	−0.146146	+	0.146146i
$347$	−3.53962	−	3.53962i	−0.190017	−	0.190017i	0.605686	−	0.795703i	$-0.292899\pi$
$347$	−3.53962	−	3.53962i	−0.190017	−	0.190017i	−0.795703	+	0.605686i	$0.792899\pi$
$348$	−4.82930			−0.258878
$349$			9.21310i			0.493166i	0.969122	+	0.246583i	$0.0793078\pi$
$349$			9.21310i			0.493166i	−0.969122	+	0.246583i	$0.920692\pi$
$350$	−0.0993794	+	2.39817i	−0.00531205	+	0.128188i
$351$	−1.84090	+	1.84090i	−0.0982601	+	0.0982601i
$352$	0.912747	−	0.912747i	0.0486496	−	0.0486496i
$353$		−	13.8600i		−	0.737693i	−0.929490	−	0.368847i	$-0.879753\pi$
$353$		−	13.8600i		−	0.737693i	0.929490	−	0.368847i	$-0.120247\pi$
$354$	2.36069	+	2.36069i	0.125469	+	0.125469i
$355$	1.47748	+	3.78690i	0.0784165	+	0.200988i
$356$	18.2383			0.966626
$357$	18.5943	−	8.37386i	0.984114	−	0.443192i
$358$			4.53887i			0.239886i
$359$		−	11.5024i		−	0.607076i	−0.952819	−	0.303538i	$-0.901832\pi$
$359$		−	11.5024i		−	0.607076i	0.952819	−	0.303538i	$-0.0981679\pi$
$360$	2.25121	−	5.13169i	0.118649	−	0.270464i
$361$	3.00000			0.157895
$362$	−1.72242	+	1.72242i	−0.0905283	+	0.0905283i
$363$	18.2335	+	18.2335i	0.957010	+	0.957010i
$364$	−11.5709	+	11.5709i	−0.606479	+	0.606479i
$365$	−25.3540	+	9.89199i	−1.32709	+	0.517770i
$366$		−	3.14759i		−	0.164527i
$367$	13.7349	+	13.7349i	0.716958	+	0.716958i	0.967981	−	0.251023i	$-0.0807669\pi$
$367$	13.7349	+	13.7349i	0.716958	+	0.716958i	−0.251023	+	0.967981i	$0.580767\pi$
$368$	−21.2043	−	21.2043i	−1.10535	−	1.10535i
$369$	−20.8380	−	20.8380i	−1.08478	−	1.08478i
$370$	−0.627799	+	0.244939i	−0.0326377	+	0.0127338i
$371$	8.98266	+	8.98266i	0.466356	+	0.466356i
$372$	28.2383			1.46409
$373$		−	5.58922i		−	0.289399i	−0.989476	−	0.144699i	$-0.953779\pi$
$373$		−	5.58922i		−	0.289399i	0.989476	−	0.144699i	$-0.0462215\pi$
$374$	−0.163004	+	0.430112i	−0.00842876	+	0.0222406i
$375$	24.0482	+	11.7600i	1.24184	+	0.607282i
$376$		−	3.30669i		−	0.170529i
$377$	−2.98341	+	2.98341i	−0.153653	+	0.153653i
$378$			0.307012i			0.0157910i
$379$	−0.393449	−	0.393449i	−0.0202101	−	0.0202101i	0.696930	−	0.717140i	$-0.254549\pi$
$379$	−0.393449	−	0.393449i	−0.0202101	−	0.0202101i	−0.717140	+	0.696930i	$0.754549\pi$
$380$	6.99234	−	15.9392i	0.358700	−	0.817665i
$381$	−5.05109	+	5.05109i	−0.258775	+	0.258775i
$382$	1.23657			0.0632684
$383$	−24.8020			−1.26732			−0.633662	−	0.773610i	$-0.718449\pi$
$383$	−24.8020			−1.26732			−0.633662	+	0.773610i	$0.718449\pi$
$384$	11.7541	−	11.7541i	0.599826	−	0.599826i
$385$	2.03056	+	0.890781i	0.103487	+	0.0453984i
$386$	2.05109	+	2.05109i	0.104398	+	0.104398i
$387$		−	20.3788i		−	1.03591i
$388$	−23.0056	+	23.0056i	−1.16793	+	1.16793i
$389$		−	8.76664i		−	0.444486i	−0.974991	−	0.222243i	$-0.928662\pi$
$389$		−	8.76664i		−	0.444486i	0.974991	−	0.222243i	$-0.0713379\pi$
$390$	−1.84090	−	4.71838i	−0.0932177	−	0.238924i
$391$	31.4272	+	11.9103i	1.58934	+	0.602331i
$392$		−	2.50608i		−	0.126576i
$393$	17.2244			0.868854
$394$	−0.0906680	−	0.0906680i	−0.00456779	−	0.00456779i
$395$	21.3038	−	8.31179i	1.07191	−	0.418211i
$396$	−1.80523	−	1.80523i	−0.0907162	−	0.0907162i
$397$	4.97519	+	4.97519i	0.249698	+	0.249698i	0.820847	−	0.571149i	$-0.193502\pi$
$397$	4.97519	+	4.97519i	0.249698	+	0.249698i	−0.571149	+	0.820847i	$0.693502\pi$
$398$	2.89198	+	2.89198i	0.144962	+	0.144962i
$399$		−	19.7840i		−	0.990438i
$400$	12.4571	+	13.5342i	0.622857	+	0.676711i
$401$	−7.51979	+	7.51979i	−0.375520	+	0.375520i	−0.869483	−	0.493963i	$-0.835548\pi$
$401$	−7.51979	+	7.51979i	−0.375520	+	0.375520i	0.493963	+	0.869483i	$0.335548\pi$
$402$	−1.23589	−	1.23589i	−0.0616407	−	0.0616407i
$403$	17.4449	−	17.4449i	0.868992	−	0.868992i
$404$	8.58530			0.427135
$405$	19.9240	+	8.74043i	0.990033	+	0.434316i
$406$			0.497552i			0.0246931i
$407$			0.622545i			0.0308584i
$408$	−3.20819	+	8.46529i	−0.158829	+	0.419094i
$409$	−2.53421			−0.125309			−0.0626544	−	0.998035i	$-0.519957\pi$
$409$	−2.53421			−0.125309			−0.0626544	+	0.998035i	$0.519957\pi$
$410$	−5.22013	+	2.03666i	−0.257804	+	0.100584i
$411$	−0.891990	−	0.891990i	−0.0439986	−	0.0439986i
$412$		−	33.9232i		−	1.67128i
$413$	−8.76401	+	8.76401i	−0.431249	+	0.431249i
$414$	3.66056	−	3.66056i	0.179907	−	0.179907i
$415$	−4.58012	−	2.00924i	−0.224829	−	0.0986299i
$416$		−	10.9460i		−	0.536672i
$417$	42.3215			2.07249
$418$	0.315533	+	0.315533i	0.0154332	+	0.0154332i
$419$	−18.6403	+	18.6403i	−0.910638	+	0.910638i	−0.996322	−	0.0856842i	$-0.972692\pi$
$419$	−18.6403	+	18.6403i	−0.910638	+	0.910638i	0.0856842	+	0.996322i	$0.472692\pi$
$420$	19.7088	+	8.64603i	0.961693	+	0.421883i
$421$	−7.94308			−0.387122			−0.193561	−	0.981088i	$-0.562004\pi$
$421$	−7.94308			−0.387122			−0.193561	+	0.981088i	$0.562004\pi$
$422$	2.10831	−	2.10831i	0.102631	−	0.102631i
$423$	−9.85469			−0.479151
$424$	−5.63931			−0.273869
$425$	−18.9585	−	8.09775i	−0.919625	−	0.392798i
$426$	−1.01151			−0.0490078
$427$	11.6854			0.565494
$428$	−7.17068	+	7.17068i	−0.346608	+	0.346608i
$429$	−4.67889			−0.225899
$430$	−3.54844	−	1.55666i	−0.171121	−	0.0750686i
$431$	−8.01833	+	8.01833i	−0.386229	+	0.386229i	−0.873340	−	0.487111i	$-0.838051\pi$
$431$	−8.01833	+	8.01833i	−0.386229	+	0.386229i	0.487111	+	0.873340i	$0.338051\pi$
$432$	1.66370	+	1.66370i	0.0800447	+	0.0800447i
$433$	6.24538			0.300134			0.150067	−	0.988676i	$-0.452051\pi$
$433$	6.24538			0.300134			0.150067	+	0.988676i	$0.452051\pi$
$434$		−	2.90933i		−	0.139652i
$435$	5.08168	+	2.22927i	0.243648	+	0.106885i
$436$	11.1562	−	11.1562i	0.534284	−	0.534284i
$437$	23.0552	−	23.0552i	1.10288	−	1.10288i
$438$		−	6.77223i		−	0.323590i
$439$	−7.44454	−	7.44454i	−0.355308	−	0.355308i	0.506772	−	0.862080i	$-0.330839\pi$
$439$	−7.44454	−	7.44454i	−0.355308	−	0.355308i	−0.862080	+	0.506772i	$0.830839\pi$
$440$	−0.917007	+	0.357775i	−0.0437166	+	0.0170563i
$441$	−7.46870			−0.355652
$442$	1.60162	+	3.55643i	0.0761815	+	0.169162i
$443$		−	29.2669i		−	1.39051i	−0.718761	−	0.695257i	$-0.755291\pi$
$443$		−	29.2669i		−	1.39051i	0.718761	−	0.695257i	$-0.244709\pi$
$444$			6.04250i			0.286764i
$445$	−19.1914	−	8.41904i	−0.909760	−	0.399101i
$446$	0.945995			0.0447942
$447$	12.3951	−	12.3951i	0.586267	−	0.586267i
$448$	9.83453	+	9.83453i	0.464638	+	0.464638i
$449$	−23.1418	+	23.1418i	−1.09213	+	1.09213i	−0.0968256	+	0.995301i	$0.530869\pi$
$449$	−23.1418	+	23.1418i	−1.09213	+	1.09213i	−0.995301	+	0.0968256i	$0.969131\pi$
$450$	−2.33644	+	2.15051i	−0.110141	+	0.101376i
$451$			5.17644i			0.243749i
$452$	4.78045	+	4.78045i	0.224854	+	0.224854i
$453$	−12.6400	−	12.6400i	−0.593879	−	0.593879i
$454$	2.59213	+	2.59213i	0.121655	+	0.121655i
$455$	17.5169	−	6.83431i	0.821204	−	0.320397i
$456$	6.21019	+	6.21019i	0.290819	+	0.290819i
$457$	−31.4752			−1.47235			−0.736174	−	0.676792i	$-0.763369\pi$
$457$	−31.4752			−1.47235			−0.736174	+	0.676792i	$0.763369\pi$
$458$			3.47329i			0.162296i
$459$	−2.46579	−	0.934487i	−0.115093	−	0.0436181i
$460$	12.8920	+	33.0432i	0.601092	+	1.54065i
$461$		−	26.6442i		−	1.24094i	−0.784228	−	0.620472i	$-0.786941\pi$
$461$		−	26.6442i		−	1.24094i	0.784228	−	0.620472i	$-0.213059\pi$
$462$	−0.390156	+	0.390156i	−0.0181517	+	0.0181517i
$463$		−	14.2040i		−	0.660115i	−0.943961	−	0.330058i	$-0.892932\pi$
$463$		−	14.2040i		−	0.660115i	0.943961	−	0.330058i	$-0.107068\pi$
$464$	2.69623	+	2.69623i	0.125169	+	0.125169i
$465$	−29.7141	−	13.0352i	−1.37796	−	0.604494i
$466$	−0.119518	+	0.119518i	−0.00553657	+	0.00553657i
$467$	−29.1177			−1.34741			−0.673703	−	0.739002i	$-0.735297\pi$
$467$	−29.1177			−1.34741			−0.673703	+	0.739002i	$0.735297\pi$
$468$	−21.6490			−1.00072
$469$	4.58822	−	4.58822i	0.211864	−	0.211864i
$470$	−0.752762	+	1.71594i	−0.0347223	+	0.0791504i
$471$	21.0907	+	21.0907i	0.971807	+	0.971807i
$472$		−	5.50204i		−	0.253252i
$473$	−2.53118	+	2.53118i	−0.116384	+	0.116384i
$474$			5.69040i			0.261369i
$475$	−14.7156	+	13.5445i	−0.675196	+	0.621463i
$476$	−15.4985	−	5.87366i	−0.710374	−	0.269219i
$477$			16.8064i			0.769514i
$478$	2.22485			0.101762
$479$	−1.39053	−	1.39053i	−0.0635350	−	0.0635350i	0.674625	−	0.738160i	$-0.264305\pi$
$479$	−1.39053	−	1.39053i	−0.0635350	−	0.0635350i	−0.738160	+	0.674625i	$0.764305\pi$
$480$	−13.4118	+	5.23268i	−0.612161	+	0.238838i
$481$	3.73289	+	3.73289i	0.170205	+	0.170205i
$482$	−1.39434	−	1.39434i	−0.0635103	−	0.0635103i
$483$	28.5077	+	28.5077i	1.29714	+	1.29714i
$484$		−	20.9575i		−	0.952614i
$485$	34.8277	−	13.5882i	1.58144	−	0.617009i
$486$	−3.51297	+	3.51297i	−0.159351	+	0.159351i
$487$	3.41883	+	3.41883i	0.154922	+	0.154922i	0.780312	−	0.625390i	$-0.215060\pi$
$487$	3.41883	+	3.41883i	0.154922	+	0.154922i	−0.625390	+	0.780312i	$0.715060\pi$
$488$	−3.66803	+	3.66803i	−0.166044	+	0.166044i
$489$	20.5140			0.927673
$490$	−0.570505	+	1.30048i	−0.0257728	+	0.0587498i
$491$		−	16.8949i		−	0.762456i	−0.924481	−	0.381228i	$-0.875501\pi$
$491$		−	16.8949i		−	0.762456i	0.924481	−	0.381228i	$-0.124499\pi$
$492$			50.2431i			2.26514i
$493$	−3.99611	−	1.51445i	−0.179976	−	0.0682075i
$494$	3.78398			0.170249
$495$	1.06625	+	2.73289i	0.0479245	+	0.122834i
$496$	−15.7656	−	15.7656i	−0.707899	−	0.707899i
$497$		−	3.75520i		−	0.168444i
$498$	0.880035	−	0.880035i	0.0394353	−	0.0394353i
$499$	3.07234	−	3.07234i	0.137537	−	0.137537i	−0.634987	−	0.772523i	$-0.718994\pi$
$499$	3.07234	−	3.07234i	0.137537	−	0.137537i	0.772523	+	0.634987i	$0.218994\pi$
$500$	−7.06201	−	20.5789i	−0.315822	−	0.920315i
$501$			22.6220i			1.01067i
$502$	1.40286			0.0626125
$503$	8.13721	+	8.13721i	0.362820	+	0.362820i	0.864850	−	0.502030i	$-0.167413\pi$
$503$	8.13721	+	8.13721i	0.362820	+	0.362820i	−0.502030	+	0.864850i	$0.667413\pi$
$504$	−3.66056	+	3.66056i	−0.163054	+	0.163054i
$505$	−9.03398	−	3.96310i	−0.402007	−	0.176356i
$506$	−0.909332			−0.0404247
$507$	−6.04570	+	6.04570i	−0.268499	+	0.268499i
$508$	5.80570			0.257586
$509$	34.8177			1.54327			0.771634	−	0.636066i	$-0.219440\pi$
$509$	34.8177			1.54327			0.771634	+	0.636066i	$0.219440\pi$
$510$	3.59194	−	3.66256i	0.159054	−	0.162181i
$511$	25.1418			1.11221
$512$	−16.6395			−0.735368
$513$	−1.80891	+	1.80891i	−0.0798655	+	0.0798655i
$514$	−6.33845			−0.279577
$515$	−15.6595	+	35.6961i	−0.690038	+	1.57296i
$516$	−24.5680	+	24.5680i	−1.08154	+	1.08154i
$517$	1.22402	+	1.22402i	0.0538323	+	0.0538323i
$518$	0.622545			0.0273531
$519$		−	39.6105i		−	1.73871i
$520$	−3.35325	+	7.64383i	−0.147050	+	0.335204i
$521$	15.8746	−	15.8746i	0.695481	−	0.695481i	−0.267951	−	0.963432i	$-0.586347\pi$
$521$	15.8746	−	15.8746i	0.695481	−	0.695481i	0.963432	+	0.267951i	$0.0863467\pi$
$522$	−0.465456	+	0.465456i	−0.0203725	+	0.0203725i
$523$		−	16.4943i		−	0.721243i	−0.932712	−	0.360622i	$-0.882565\pi$
$523$		−	16.4943i		−	0.721243i	0.932712	−	0.360622i	$-0.117435\pi$
$524$	−9.89881	−	9.89881i	−0.432432	−	0.432432i
$525$	−16.7477	−	18.1958i	−0.730930	−	0.794128i
$526$	−2.87465			−0.125341
$527$	23.3664	+	8.85545i	1.01786	+	0.385749i
$528$			4.22850i			0.184022i
$529$			43.4426i			1.88881i
$530$	2.92641	+	1.28378i	0.127115	+	0.0557638i
$531$	−16.3974			−0.711585
$532$	−11.3698	+	11.3698i	−0.492944	+	0.492944i
$533$	31.0389	+	31.0389i	1.34444	+	1.34444i
$534$	3.68748	−	3.68748i	0.159573	−	0.159573i
$535$	10.8555	−	4.23534i	0.469325	−	0.183110i
$536$			2.88048i			0.124418i
$537$	−33.0676	−	33.0676i	−1.42697	−	1.42697i
$538$	−3.29894	−	3.29894i	−0.142228	−	0.142228i
$539$	0.927664	+	0.927664i	0.0399573	+	0.0399573i
$540$	−1.01151	−	2.59258i	−0.0435284	−	0.111567i
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	0.486654	−	0.873595i	$-0.338217\pi$
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	−0.873595	+	0.486654i	$0.838217\pi$
$542$	5.62619			0.241666
$543$		−	25.0972i		−	1.07702i
$544$	10.1090	−	4.55255i	0.433420	−	0.195189i
$545$	−16.8891	+	6.58937i	−0.723448	+	0.282257i
$546$			4.67889i			0.200238i
$547$	8.84290	−	8.84290i	0.378095	−	0.378095i	−0.492320	−	0.870415i	$-0.663851\pi$
$547$	8.84290	−	8.84290i	0.378095	−	0.378095i	0.870415	+	0.492320i	$0.163851\pi$
$548$			1.02525i			0.0437965i
$549$	10.9316	+	10.9316i	0.466548	+	0.466548i
$550$	0.557310	+	0.0230947i	0.0237638	+	0.000984762i
$551$	−2.93157	+	2.93157i	−0.124889	+	0.124889i
$552$	−17.8971			−0.761752
$553$	−21.1255			−0.898346
$554$	−1.11093	+	1.11093i	−0.0471987	+	0.0471987i
$555$	2.78930	−	6.35829i	0.118399	−	0.269894i
$556$	−24.3221	−	24.3221i	−1.03149	−	1.03149i
$557$			38.9354i			1.64975i	0.565318	+	0.824873i	$0.308753\pi$
$557$			38.9354i			1.64975i	−0.565318	+	0.824873i	$0.691247\pi$
$558$	2.72166	−	2.72166i	0.115217	−	0.115217i
$559$			30.3549i			1.28387i
$560$	−6.17644	−	15.8307i	−0.261002	−	0.668970i
$561$	−1.94600	−	4.32111i	−0.0821600	−	0.182438i
$562$		−	4.19153i		−	0.176809i
$563$	8.17844			0.344680			0.172340	−	0.985038i	$-0.444867\pi$
$563$	8.17844			0.344680			0.172340	+	0.985038i	$0.444867\pi$
$564$	11.8805	+	11.8805i	0.500259	+	0.500259i
$565$	−2.82356	−	7.23701i	−0.118788	−	0.304463i
$566$	−4.14368	−	4.14368i	−0.174172	−	0.174172i
$567$	−14.2123	−	14.2123i	−0.596859	−	0.596859i
$568$	1.17876	+	1.17876i	0.0494595	+	0.0494595i
$569$			11.8920i			0.498538i	0.968434	+	0.249269i	$0.0801904\pi$
$569$			11.8920i			0.498538i	−0.968434	+	0.249269i	$0.919810\pi$
$570$	−1.80891	−	4.63639i	−0.0757671	−	0.194197i
$571$	−2.80523	+	2.80523i	−0.117395	+	0.117395i	−0.763364	−	0.645969i	$-0.776454\pi$
$571$	−2.80523	+	2.80523i	−0.117395	+	0.117395i	0.645969	+	0.763364i	$0.276454\pi$
$572$	2.68895	+	2.68895i	0.112431	+	0.112431i
$573$	−9.00895	+	9.00895i	−0.376354	+	0.376354i
$574$	5.17644			0.216060
$575$	1.68747	−	40.7212i	0.0703725	−	1.69819i
$576$			18.4003i			0.766678i
$577$		−	6.58601i		−	0.274179i	−0.990559	−	0.137090i	$-0.956225\pi$
$577$		−	6.58601i		−	0.274179i	0.990559	−	0.137090i	$-0.0437749\pi$
$578$	−2.61836	+	2.95831i	−0.108909	+	0.123049i
$579$	−29.8862			−1.24203
$580$	−1.63928	−	4.20159i	−0.0680672	−	0.174462i
$581$	3.26711	+	3.26711i	0.135542	+	0.135542i
$582$			9.30274i			0.385611i
$583$	2.08747	−	2.08747i	0.0864543	−	0.0864543i
$584$	−7.89199	+	7.89199i	−0.326573	+	0.326573i
$585$	22.7804	+	9.99347i	0.941852	+	0.413179i
$586$		−	6.10218i		−	0.252079i
$587$	−22.3369			−0.921944			−0.460972	−	0.887415i	$-0.652499\pi$
$587$	−22.3369			−0.921944			−0.460972	+	0.887415i	$0.652499\pi$
$588$	9.00402	+	9.00402i	0.371319	+	0.371319i
$589$	17.1418	−	17.1418i	0.706314	−	0.706314i
$590$	−1.25253	+	2.85518i	−0.0515659	+	0.117546i
$591$	1.32111			0.0543433
$592$	3.37357	−	3.37357i	0.138653	−	0.138653i
$593$	30.1344			1.23747			0.618736	−	0.785599i	$-0.287645\pi$
$593$	30.1344			1.23747			0.618736	+	0.785599i	$0.287645\pi$
$594$	0.0713464			0.00292738
$595$	13.5972	+	13.3350i	0.557429	+	0.546681i
$596$	−14.2468			−0.583574
$597$	−42.1387			−1.72462
$598$	−5.45252	+	5.45252i	−0.222970	+	0.222970i
$599$	−8.88907			−0.363198			−0.181599	−	0.983373i	$-0.558127\pi$
$599$	−8.88907			−0.363198			−0.181599	+	0.983373i	$0.558127\pi$
$600$	10.9687	+	0.454541i	0.447797	+	0.0185566i
$601$	17.1418	−	17.1418i	0.699227	−	0.699227i	−0.265017	−	0.964244i	$-0.585378\pi$
$601$	17.1418	−	17.1418i	0.699227	−	0.699227i	0.964244	+	0.265017i	$0.0853776\pi$
$602$	2.53118	+	2.53118i	0.103163	+	0.103163i
$603$	8.58450			0.349588
$604$			14.5284i			0.591151i
$605$	−9.67429	+	22.0528i	−0.393316	+	0.896573i
$606$	1.73581	−	1.73581i	0.0705124	−	0.0705124i
$607$	−10.5442	+	10.5442i	−0.427978	+	0.427978i	−0.887939	−	0.459961i	$-0.847863\pi$
$607$	−10.5442	+	10.5442i	−0.427978	+	0.427978i	0.459961	+	0.887939i	$0.347863\pi$
$608$		−	10.7558i		−	0.436205i
$609$	−3.62488	−	3.62488i	−0.146888	−	0.146888i
$610$	2.73847	−	1.06843i	0.110877	−	0.0432595i
$611$	14.6789			0.593844
$612$	−9.00402	−	19.9936i	−0.363966	−	0.808192i
$613$		−	31.3459i		−	1.26605i	−0.774132	−	0.633024i	$-0.781813\pi$
$613$		−	31.3459i		−	1.26605i	0.774132	−	0.633024i	$-0.218187\pi$
$614$		−	3.23336i		−	0.130488i
$615$	23.1930	−	52.8689i	0.935230	−	2.13188i
$616$	0.909332			0.0366380
$617$	10.9050	−	10.9050i	0.439020	−	0.439020i	−0.452662	−	0.891682i	$-0.649526\pi$
$617$	10.9050	−	10.9050i	0.439020	−	0.439020i	0.891682	+	0.452662i	$0.149526\pi$
$618$	−6.85873	−	6.85873i	−0.275899	−	0.275899i
$619$	31.8930	−	31.8930i	1.28189	−	1.28189i	0.342294	−	0.939593i	$-0.388796\pi$
$619$	31.8930	−	31.8930i	1.28189	−	1.28189i	0.939593	−	0.342294i	$-0.111204\pi$
$620$	9.58533	+	24.5680i	0.384956	+	0.986673i
$621$		−	5.21310i		−	0.209195i
$622$	1.43625	+	1.43625i	0.0575882	+	0.0575882i
$623$	13.6897	+	13.6897i	0.548466	+	0.548466i
$624$	25.3549	+	25.3549i	1.01501	+	1.01501i
$625$	−2.06843	+	24.9143i	−0.0827372	+	0.996571i
$626$	−1.14176	−	1.14176i	−0.0456338	−	0.0456338i
$627$	−4.59759			−0.183610
$628$		−	24.2415i		−	0.967343i
$629$	−1.89491	+	5.00000i	−0.0755549	+	0.199363i
$630$	2.73289	−	1.06625i	0.108881	−	0.0424805i
$631$			29.7493i			1.18430i	0.805827	+	0.592150i	$0.201721\pi$
$631$			29.7493i			1.18430i	−0.805827	+	0.592150i	$0.798279\pi$
$632$	6.63128	−	6.63128i	0.263778	−	0.263778i
$633$			30.7200i			1.22101i
$634$	0.693313	+	0.693313i	0.0275350	+	0.0275350i
$635$	−6.10912	−	2.68000i	−0.242433	−	0.106352i
$636$	20.2613	−	20.2613i	0.803412	−	0.803412i
$637$	11.1249			0.440784
$638$	0.115626			0.00457767
$639$	3.51297	−	3.51297i	0.138971	−	0.138971i
$640$	14.2162	+	6.23649i	0.561946	+	0.246519i
$641$	31.2131	+	31.2131i	1.23284	+	1.23284i	0.962867	+	0.269977i	$0.0870159\pi$
$641$	31.2131	+	31.2131i	1.23284	+	1.23284i	0.269977	+	0.962867i	$0.412984\pi$
$642$			2.89959i			0.114438i
$643$	5.36109	−	5.36109i	0.211421	−	0.211421i	−0.593450	−	0.804871i	$-0.702235\pi$
$643$	5.36109	−	5.36109i	0.211421	−	0.211421i	0.804871	+	0.593450i	$0.202235\pi$
$644$		−	32.7666i		−	1.29119i
$645$	37.1928	−	14.5110i	1.46447	−	0.571370i
$646$	1.57379	+	3.49464i	0.0619201	+	0.137495i
$647$		−	10.2540i		−	0.403128i	−0.979475	−	0.201564i	$-0.935398\pi$
$647$		−	10.2540i		−	0.403128i	0.979475	−	0.201564i	$-0.0646024\pi$
$648$	8.92246			0.350507
$649$	2.03666	+	2.03666i	0.0799460	+	0.0799460i
$650$	3.48021	−	3.20325i	0.136505	−	0.125642i
$651$	21.1958	+	21.1958i	0.830727	+	0.830727i
$652$	−11.7893	−	11.7893i	−0.461706	−	0.461706i
$653$	−10.1207	−	10.1207i	−0.396054	−	0.396054i	0.480785	−	0.876839i	$-0.340352\pi$
$653$	−10.1207	−	10.1207i	−0.396054	−	0.396054i	−0.876839	+	0.480785i	$0.840352\pi$
$654$		−	4.51120i		−	0.176402i
$655$	5.84671	+	14.9856i	0.228450	+	0.585535i
$656$	28.0511	−	28.0511i	1.09521	−	1.09521i
$657$	23.5199	+	23.5199i	0.917601	+	0.917601i
$658$	1.22402	−	1.22402i	0.0477172	−	0.0477172i
$659$	−43.9653			−1.71265			−0.856323	−	0.516441i	$-0.827257\pi$
$659$	−43.9653			−1.71265			−0.856323	+	0.516441i	$0.827257\pi$
$660$	2.00924	−	4.58012i	0.0782097	−	0.178281i
$661$		−	20.7077i		−	0.805438i	−0.915324	−	0.402719i	$-0.868065\pi$
$661$		−	20.7077i		−	0.805438i	0.915324	−	0.402719i	$-0.131935\pi$
$662$		−	3.17815i		−	0.123522i
$663$	−37.5787	−	14.2416i	−1.45944	−	0.553099i
$664$	−2.05109			−0.0795977
$665$	17.2125	−	6.71555i	0.667472	−	0.260418i
$666$	0.582387	+	0.582387i	0.0225670	+	0.0225670i
$667$		−	8.44848i		−	0.327126i
$668$	13.0008	−	13.0008i	0.503016	−	0.503016i
$669$	−6.89199	+	6.89199i	−0.266460	+	0.266460i
$670$	0.655737	−	1.49477i	0.0253333	−	0.0577480i
$671$		−	2.71555i		−	0.104833i
$672$	13.2995			0.513040
$673$	−32.7151	−	32.7151i	−1.26108	−	1.26108i	−0.950572	−	0.310503i	$-0.899503\pi$
$673$	−32.7151	−	32.7151i	−1.26108	−	1.26108i	−0.310503	−	0.950572i	$-0.600497\pi$
$674$	−1.06551	+	1.06551i	−0.0410420	+	0.0410420i
$675$	−0.132399	+	3.19500i	−0.00509606	+	0.122975i
$676$	6.94891			0.267266
$677$	1.24509	−	1.24509i	0.0478527	−	0.0478527i	−0.682776	−	0.730628i	$-0.739227\pi$
$677$	1.24509	−	1.24509i	0.0478527	−	0.0478527i	0.730628	+	0.682776i	$0.239227\pi$
$678$	1.93306			0.0742387
$679$	−34.5362			−1.32538
$680$	−8.45399	+	0.0822978i	−0.324196	+	0.00315598i
$681$	−37.7696			−1.44733
$682$	−0.676098			−0.0258891
$683$	−16.2377	+	16.2377i	−0.621317	+	0.621317i	−0.945868	−	0.324551i	$-0.894787\pi$
$683$	−16.2377	+	16.2377i	−0.621317	+	0.621317i	0.324551	+	0.945868i	$0.394787\pi$
$684$	−21.2728			−0.813385
$685$	0.473270	−	1.07883i	0.0180827	−	0.0412200i
$686$	3.30377	−	3.30377i	0.126139	−	0.126139i
$687$	−25.3044	−	25.3044i	−0.965425	−	0.965425i
$688$	27.4329			1.04587
$689$		−	25.0337i		−	0.953710i
$690$	9.28735	+	4.07425i	0.353563	+	0.155104i
$691$	−18.2314	+	18.2314i	−0.693556	+	0.693556i	−0.963013	−	0.269456i	$-0.913156\pi$
$691$	−18.2314	+	18.2314i	−0.693556	+	0.693556i	0.269456	+	0.963013i	$0.413156\pi$
$692$	−22.7641	+	22.7641i	−0.865360	+	0.865360i
$693$		−	2.71002i		−	0.102945i
$694$	0.822571	+	0.822571i	0.0312244	+	0.0312244i
$695$	14.3658	+	36.8206i	0.544925	+	1.39669i
$696$	2.27570			0.0862602
$697$	−15.7561	+	41.5748i	−0.596804	+	1.57476i
$698$		−	2.14103i		−	0.0810391i
$699$		−	1.74148i		−	0.0658690i
$700$	−0.832189	+	20.0820i	−0.0314538	+	0.759027i
$701$	−25.1195			−0.948751			−0.474376	−	0.880323i	$-0.657326\pi$
$701$	−25.1195			−0.948751			−0.474376	+	0.880323i	$0.657326\pi$
$702$	0.427806	−	0.427806i	0.0161465	−	0.0161465i
$703$	3.66803	+	3.66803i	0.138342	+	0.138342i
$704$	2.28544	−	2.28544i	0.0861357	−	0.0861357i
$705$	−7.01717	−	17.9856i	−0.264282	−	0.677376i
$706$			3.22092i			0.121221i
$707$	6.44415	+	6.44415i	0.242357	+	0.242357i
$708$	19.7681	+	19.7681i	0.742931	+	0.742931i
$709$	−23.7156	−	23.7156i	−0.890656	−	0.890656i	0.103929	−	0.994585i	$-0.466859\pi$
$709$	−23.7156	−	23.7156i	−0.890656	−	0.890656i	−0.994585	+	0.103929i	$0.966859\pi$
$710$	−0.343350	−	0.880035i	−0.0128857	−	0.0330271i
$711$	−19.7627	−	19.7627i	−0.741160	−	0.741160i
$712$	−8.59437			−0.322088
$713$			49.4008i			1.85007i
$714$	−4.32111	+	1.94600i	−0.161714	+	0.0728270i
$715$	−1.58822	−	4.07073i	−0.0593961	−	0.152237i
$716$			38.0078i			1.42042i
$717$	−16.2090	+	16.2090i	−0.605336	+	0.605336i
$718$			2.67305i			0.0997572i
$719$	29.4812	+	29.4812i	1.09946	+	1.09946i	0.994473	+	0.104990i	$0.0334810\pi$
$719$	29.4812	+	29.4812i	1.09946	+	1.09946i	0.104990	+	0.994473i	$0.466519\pi$
$720$	9.03151	−	20.5875i	0.336584	−	0.767252i
$721$	25.4629	−	25.4629i	0.948287	−	0.948287i
$722$	−0.697168			−0.0259459
$723$	20.3167			0.755586
$724$	−14.4233	+	14.4233i	−0.536037	+	0.536037i
$725$	−0.214570	+	5.17789i	−0.00796892	+	0.192302i
$726$	−4.23727	−	4.23727i	−0.157260	−	0.157260i
$727$			12.2458i			0.454172i	0.973875	+	0.227086i	$0.0729199\pi$
$727$			12.2458i			0.454172i	−0.973875	+	0.227086i	$0.927080\pi$
$728$	5.45252	−	5.45252i	0.202084	−	0.202084i
$729$		−	21.9971i		−	0.814707i
$730$	5.89199	−	2.29879i	0.218072	−	0.0850821i
$731$	−28.0337	+	12.6249i	−1.03687	+	0.466948i
$732$		−	26.3575i		−	0.974200i
$733$	−32.8393			−1.21295			−0.606473	−	0.795104i	$-0.707416\pi$
$733$	−32.8393			−1.21295			−0.606473	+	0.795104i	$0.707416\pi$
$734$	−3.19185	−	3.19185i	−0.117814	−	0.117814i
$735$	−5.31820	−	13.6310i	−0.196165	−	0.502786i
$736$	15.4985	+	15.4985i	0.571284	+	0.571284i
$737$	−1.06625	−	1.06625i	−0.0392759	−	0.0392759i
$738$	4.84253	+	4.84253i	0.178256	+	0.178256i
$739$		−	6.00000i		−	0.220714i	−0.993892	−	0.110357i	$-0.964801\pi$
$739$		−	6.00000i		−	0.220714i	0.993892	−	0.110357i	$-0.0351994\pi$
$740$	−5.25710	+	2.05109i	−0.193255	+	0.0753995i
$741$	−27.5680	+	27.5680i	−1.01273	+	1.01273i
$742$	−2.08747	−	2.08747i	−0.0766336	−	0.0766336i
$743$	−16.1704	+	16.1704i	−0.593236	+	0.593236i	−0.938504	−	0.345268i	$-0.887788\pi$
$743$	−16.1704	+	16.1704i	−0.593236	+	0.593236i	0.345268	+	0.938504i	$0.387788\pi$
$744$	−13.3067			−0.487847
$745$	14.9914	+	6.57655i	0.549243	+	0.240946i
$746$			1.29887i			0.0475552i
$747$			6.11272i			0.223653i
$748$	−1.36498	+	3.60170i	−0.0499085	+	0.131691i
$749$	−10.7647			−0.393332
$750$	−5.58854	−	2.73289i	−0.204065	−	0.0997911i
$751$	−22.6799	−	22.6799i	−0.827600	−	0.827600i	0.159584	−	0.987184i	$-0.448985\pi$
$751$	−22.6799	−	22.6799i	−0.827600	−	0.827600i	−0.987184	+	0.159584i	$0.948985\pi$
$752$		−	13.2659i		−	0.483758i
$753$	−10.2204	+	10.2204i	−0.372453	+	0.372453i
$754$	0.693313	−	0.693313i	0.0252490	−	0.0252490i
$755$	6.70651	−	15.2877i	0.244075	−	0.556375i
$756$			2.57088i			0.0935019i
$757$	−36.2220			−1.31651			−0.658256	−	0.752794i	$-0.728706\pi$
$757$	−36.2220			−1.31651			−0.658256	+	0.752794i	$0.728706\pi$
$758$	0.0914333	+	0.0914333i	0.00332101	+	0.00332101i
$759$	6.62488	−	6.62488i	0.240468	−	0.240468i
$760$	−3.29499	+	7.51101i	−0.119522	+	0.272453i
$761$	24.4851			0.887584			0.443792	−	0.896130i	$-0.353633\pi$
$761$	24.4851			0.887584			0.443792	+	0.896130i	$0.353633\pi$
$762$	1.17382	−	1.17382i	0.0425230	−	0.0425230i
$763$	16.7477			0.606308
$764$	10.3549			0.374626
$765$	0.245267	+	25.1948i	0.00886763	+	0.910921i
$766$	5.76372			0.208252
$767$	24.4244			0.881914
$768$	20.0668	−	20.0668i	0.724099	−	0.724099i
$769$	−5.55937			−0.200476			−0.100238	−	0.994963i	$-0.531960\pi$
$769$	−5.55937			−0.200476			−0.100238	+	0.994963i	$0.531960\pi$
$770$	−0.471880	−	0.207008i	−0.0170054	−	0.00746005i
$771$	46.1784	−	46.1784i	1.66308	−	1.66308i
$772$	17.1755	+	17.1755i	0.618161	+	0.618161i
$773$	36.5376			1.31416			0.657082	−	0.753819i	$-0.271790\pi$
$773$	36.5376			1.31416			0.657082	+	0.753819i	$0.271790\pi$
$774$			4.73581i			0.170225i
$775$	1.25465	−	30.2766i	0.0450685	−	1.08757i
$776$	10.8409	−	10.8409i	0.389166	−	0.389166i
$777$	−4.53551	+	4.53551i	−0.162711	+	0.162711i
$778$			2.03727i			0.0730398i
$779$	30.4995	+	30.4995i	1.09276	+	1.09276i
$780$	−15.4155	−	39.5110i	−0.551962	−	1.41472i
$781$	−0.872669			−0.0312265
$782$	−7.30334	−	2.76783i	−0.261167	−	0.0989775i
$783$			0.662870i			0.0236890i
$784$		−	10.0540i		−	0.359072i
$785$	−11.1902	+	25.5084i	−0.399397	+	0.910435i
$786$	−4.00276			−0.142774
$787$	−11.3490	+	11.3490i	−0.404547	+	0.404547i	−0.879832	−	0.475285i	$-0.842345\pi$
$787$	−11.3490	+	11.3490i	−0.404547	+	0.404547i	0.475285	+	0.879832i	$0.342345\pi$
$788$	−0.759241	−	0.759241i	−0.0270468	−	0.0270468i
$789$	20.9431	−	20.9431i	0.745593	−	0.745593i
$790$	−4.95077	+	1.93157i	−0.176140	+	0.0687222i
$791$			7.17644i			0.255165i
$792$	0.850674	+	0.850674i	0.0302274	+	0.0302274i
$793$	−16.2829	−	16.2829i	−0.578224	−	0.578224i
$794$	−1.15618	−	1.15618i	−0.0410313	−	0.0410313i
$795$	−30.6731	+	11.9673i	−1.08786	+	0.424435i
$796$	24.2170	+	24.2170i	0.858349	+	0.858349i
$797$	34.7907			1.23235			0.616175	−	0.787609i	$-0.288681\pi$
$797$	34.7907			1.23235			0.616175	+	0.787609i	$0.288681\pi$
$798$			4.59759i			0.162753i
$799$	6.10509	+	13.5565i	0.215983	+	0.479593i
$800$	−9.10509	−	9.89234i	−0.321914	−	0.349747i
$801$			25.6132i			0.904999i
$802$	1.74752	−	1.74752i	0.0617070	−	0.0617070i
$803$		−	5.84268i		−	0.206184i
$804$	−10.3492	−	10.3492i	−0.364988	−	0.364988i
$805$	−15.1256	+	34.4791i	−0.533106	+	1.21523i
$806$	−4.05400	+	4.05400i	−0.142796	+	0.142796i
$807$	48.0685			1.69209
$808$	−4.04563			−0.142325
$809$	−13.3549	+	13.3549i	−0.469532	+	0.469532i	−0.901763	−	0.432231i	$-0.857726\pi$
$809$	−13.3549	+	13.3549i	−0.469532	+	0.469532i	0.432231	+	0.901763i	$0.357726\pi$
$810$	−4.63013	−	2.03118i	−0.162686	−	0.0713685i
$811$	−9.28544	−	9.28544i	−0.326056	−	0.326056i	0.525029	−	0.851085i	$-0.324055\pi$
$811$	−9.28544	−	9.28544i	−0.326056	−	0.326056i	−0.851085	+	0.525029i	$0.824055\pi$
$812$			4.16643i			0.146213i
$813$	−40.9893	+	40.9893i	−1.43756	+	1.43756i
$814$		−	0.144673i		−	0.00507078i
$815$	6.96334	+	17.8476i	0.243915	+	0.625174i
$816$	−12.8707	+	33.9614i	−0.450566	+	1.18889i
$817$			29.8274i			1.04353i
$818$	0.588924			0.0205913
$819$	−16.2498	−	16.2498i	−0.567813	−	0.567813i
$820$	−43.7126	+	17.0547i	−1.52651	+	0.595577i
$821$	−27.8206	−	27.8206i	−0.970947	−	0.970947i	0.0286425	−	0.999590i	$-0.490882\pi$
$821$	−27.8206	−	27.8206i	−0.970947	−	0.970947i	−0.999590	+	0.0286425i	$0.990882\pi$
$822$	0.207289	+	0.207289i	0.00723004	+	0.00723004i
$823$	−28.4414	−	28.4414i	−0.991403	−	0.991403i	0.00855996	−	0.999963i	$-0.497275\pi$
$823$	−28.4414	−	28.4414i	−0.991403	−	0.991403i	−0.999963	+	0.00855996i	$0.997275\pi$
$824$			15.9856i			0.556884i
$825$	−4.22850	+	3.89199i	−0.147217	+	0.135502i
$826$	2.03666	−	2.03666i	0.0708646	−	0.0708646i
$827$	−23.9764	−	23.9764i	−0.833742	−	0.833742i	0.154284	−	0.988027i	$-0.450693\pi$
$827$	−23.9764	−	23.9764i	−0.833742	−	0.833742i	−0.988027	+	0.154284i	$0.950693\pi$
$828$	30.6530	−	30.6530i	1.06526	−	1.06526i
$829$	−8.18134			−0.284150			−0.142075	−	0.989856i	$-0.545377\pi$
$829$	−8.18134			−0.284150			−0.142075	+	0.989856i	$0.545377\pi$
$830$	1.06437	+	0.466927i	0.0369449	+	0.0162073i
$831$		−	16.1872i		−	0.561527i
$832$		−	27.4078i		−	0.950195i
$833$	4.62695	+	10.2742i	0.160314	+	0.355980i
$834$	−9.83507			−0.340561
$835$	−19.6816	+	7.67889i	−0.681110	+	0.265739i
$836$	2.64222	+	2.64222i	0.0913832	+	0.0913832i
$837$		−	3.87600i		−	0.133974i
$838$	4.33181	−	4.33181i	0.149640	−	0.149640i
$839$	15.5381	−	15.5381i	0.536436	−	0.536436i	−0.386045	−	0.922480i	$-0.626159\pi$
$839$	15.5381	−	15.5381i	0.536436	−	0.536436i	0.922480	+	0.386045i	$0.126159\pi$
$840$	−9.28735	−	4.07425i	−0.320444	−	0.140575i
$841$		−	27.9257i		−	0.962956i
$842$	1.84589			0.0636135
$843$	30.5371	+	30.5371i	1.05175	+	1.05175i
$844$	17.6547	−	17.6547i	0.607701	−	0.607701i
$845$	−7.31207	−	3.20772i	−0.251543	−	0.110349i
$846$	2.29012			0.0787361
$847$	15.7308	−	15.7308i	0.540515	−	0.540515i
$848$	−22.6240			−0.776912
$849$	60.3771			2.07214
$850$	4.40576	+	1.88183i	0.151116	+	0.0645462i
$851$	−10.5709			−0.362365
$852$	−8.47023			−0.290185
$853$	26.1383	−	26.1383i	0.894959	−	0.894959i	−0.100026	−	0.994985i	$-0.531893\pi$
$853$	26.1383	−	26.1383i	0.894959	−	0.894959i	0.994985	+	0.100026i	$0.0318927\pi$
$854$	−2.71555			−0.0929242
$855$	22.3845	+	9.81982i	0.765535	+	0.335831i
$856$	3.37902	−	3.37902i	0.115493	−	0.115493i
$857$	10.6231	+	10.6231i	0.362879	+	0.362879i	0.864872	−	0.501993i	$-0.167400\pi$
$857$	10.6231	+	10.6231i	0.362879	+	0.362879i	−0.501993	+	0.864872i	$0.667400\pi$
$858$	1.08732			0.0371206
$859$			40.2180i			1.37222i	0.727498	+	0.686110i	$0.240683\pi$
$859$			40.2180i			1.37222i	−0.727498	+	0.686110i	$0.759317\pi$
$860$	−29.7141	−	13.0352i	−1.01324	−	0.444497i
$861$	−37.7126	+	37.7126i	−1.28524	+	1.28524i
$862$	1.86337	−	1.86337i	0.0634668	−	0.0634668i
$863$			12.3865i			0.421643i	0.977525	+	0.210822i	$0.0676139\pi$
$863$			12.3865i			0.421643i	−0.977525	+	0.210822i	$0.932386\pi$
$864$	−1.21602	−	1.21602i	−0.0413698	−	0.0413698i
$865$	34.4620	−	13.4455i	1.17174	−	0.457162i
$866$	−1.45136			−0.0493192
$867$	−2.47672	−	40.6285i	−0.0841139	−	1.37981i
$868$		−	24.3623i		−	0.826911i
$869$			4.90933i			0.166538i
$870$	−1.18093	−	0.518059i	−0.0400372	−	0.0175639i
$871$	−12.7869			−0.433267
$872$	−5.25710	+	5.25710i	−0.178028	+	0.178028i
$873$	−32.3084	−	32.3084i	−1.09347	−	1.09347i
$874$	−5.35778	+	5.35778i	−0.181229	+	0.181229i
$875$	10.1458	−	20.7473i	0.342991	−	0.701387i
$876$		−	56.7097i		−	1.91604i
$877$	31.9433	+	31.9433i	1.07865	+	1.07865i	0.996631	+	0.0820188i	$0.0261368\pi$
$877$	31.9433	+	31.9433i	1.07865	+	1.07865i	0.0820188	+	0.996631i	$0.473863\pi$
$878$	1.73003	+	1.73003i	0.0583857	+	0.0583857i
$879$	44.4570	+	44.4570i	1.49950	+	1.49950i
$880$	−3.67889	+	1.43534i	−0.124015	+	0.0483853i
$881$	−12.0367	−	12.0367i	−0.405525	−	0.405525i	0.474649	−	0.880175i	$-0.342575\pi$
$881$	−12.0367	−	12.0367i	−0.405525	−	0.405525i	−0.880175	+	0.474649i	$0.842575\pi$
$882$	1.73565			0.0584423
$883$		−	13.3497i		−	0.449254i	−0.974445	−	0.224627i	$-0.927884\pi$
$883$		−	13.3497i		−	0.449254i	0.974445	−	0.224627i	$-0.0721164\pi$
$884$	13.4118	+	29.7811i	0.451087	+	1.00165i
$885$	−11.6760	−	29.9264i	−0.392483	−	1.00597i
$886$			6.80132i			0.228495i
$887$	31.4868	−	31.4868i	1.05722	−	1.05722i	0.0589646	−	0.998260i	$-0.481220\pi$
$887$	31.4868	−	31.4868i	1.05722	−	1.05722i	0.998260	−	0.0589646i	$-0.0187799\pi$
$888$		−	2.84739i		−	0.0955522i
$889$	4.35778	+	4.35778i	0.146155	+	0.146155i
$890$	4.45988	+	1.95650i	0.149496	+	0.0655819i
$891$	−3.30278	+	3.30278i	−0.110647	+	0.110647i
$892$	7.92163			0.265236
$893$	14.4238			0.482675
$894$	−2.88048	+	2.88048i	−0.0963377	+	0.0963377i
$895$	17.5450	−	39.9942i	0.586463	−	1.33686i
$896$	−10.1408	−	10.1408i	−0.338779	−	0.338779i
$897$		−	79.4480i		−	2.65269i
$898$	5.37790	−	5.37790i	0.179463	−	0.179463i
$899$		−	6.28153i		−	0.209501i
$900$	−19.5650	+	18.0080i	−0.652168	+	0.600268i
$901$	23.1195	−	10.4118i	0.770223	−	0.346867i
$902$		−	1.20295i		−	0.0400538i
$903$	−36.8815			−1.22734
$904$	−2.25268	−	2.25268i	−0.0749231	−	0.0749231i
$905$	21.8351	−	8.51907i	0.725822	−	0.283184i
$906$	2.93740	+	2.93740i	0.0975887	+	0.0975887i
$907$	23.2958	+	23.2958i	0.773526	+	0.773526i	0.978721	−	0.205195i	$-0.0657829\pi$
$907$	23.2958	+	23.2958i	0.773526	+	0.773526i	−0.205195	+	0.978721i	$0.565783\pi$
$908$	21.7061	+	21.7061i	0.720342	+	0.720342i
$909$			12.0569i			0.399903i
$910$	−4.07073	+	1.58822i	−0.134944	+	0.0526490i
$911$	25.1630	−	25.1630i	0.833688	−	0.833688i	−0.154332	−	0.988019i	$-0.549322\pi$
$911$	25.1630	−	25.1630i	0.833688	−	0.833688i	0.988019	+	0.154332i	$0.0493224\pi$
$912$	24.9143	+	24.9143i	0.824994	+	0.824994i
$913$	0.759241	−	0.759241i	0.0251272	−	0.0251272i
$914$	7.31450			0.241942
$915$	−12.1670	+	27.7349i	−0.402228	+	0.916889i
$916$			29.0848i			0.960990i
$917$		−	14.8601i		−	0.490725i
$918$	0.573022	+	0.217165i	0.0189125	+	0.00716750i
$919$	28.5997			0.943418			0.471709	−	0.881754i	$-0.343637\pi$
$919$	28.5997			0.943418			0.471709	+	0.881754i	$0.343637\pi$
$920$	−6.07507	−	15.5709i	−0.200289	−	0.513357i
$921$	23.5565	+	23.5565i	0.776212	+	0.776212i
$922$			6.19183i			0.203917i
$923$	−5.23268	+	5.23268i	−0.172236	+	0.172236i
$924$	−3.26711	+	3.26711i	−0.107480	+	0.107480i
$925$	6.47866	+	0.268473i	0.213017	+	0.00882735i
$926$			3.30085i			0.108473i
$927$	47.6407			1.56473
$928$	−1.97071	−	1.97071i	−0.0646917	−	0.0646917i
$929$	−8.98266	+	8.98266i	−0.294711	+	0.294711i	−0.838938	−	0.544227i	$-0.816823\pi$
$929$	−8.98266	+	8.98266i	−0.294711	+	0.294711i	0.544227	+	0.838938i	$0.316823\pi$
$930$	6.90524	+	3.02925i	0.226432	+	0.0993329i
$931$	10.9316			0.358268
$932$	−1.00083	+	1.00083i	−0.0327832	+	0.0327832i
$933$	−20.9274			−0.685131
$934$	6.76664			0.221411
$935$	3.09891	−	3.15983i	0.101345	−	0.103338i
$936$	10.2016			0.333450
$937$	30.7655			1.00506			0.502532	−	0.864558i	$-0.332402\pi$
$937$	30.7655			1.00506			0.502532	+	0.864558i	$0.332402\pi$
$938$	−1.06625	+	1.06625i	−0.0348144	+	0.0348144i
$939$	16.6364			0.542908
$940$	−6.30352	+	14.3690i	−0.205598	+	0.468666i
$941$	−27.7522	+	27.7522i	−0.904696	+	0.904696i	−0.995838	−	0.0911416i	$-0.970948\pi$
$941$	−27.7522	+	27.7522i	−0.904696	+	0.904696i	0.0911416	+	0.995838i	$0.470948\pi$
$942$	−4.90125	−	4.90125i	−0.159691	−	0.159691i
$943$	−87.8965			−2.86230
$944$		−	22.0733i		−	0.718426i
$945$	1.18675	−	2.70524i	0.0386051	−	0.0880013i
$946$	0.588220	−	0.588220i	0.0191247	−	0.0191247i
$947$	2.52289	−	2.52289i	0.0819830	−	0.0819830i	−0.664926	−	0.746909i	$-0.731537\pi$
$947$	2.52289	−	2.52289i	0.0819830	−	0.0819830i	0.746909	+	0.664926i	$0.231537\pi$
$948$			47.6506i			1.54762i
$949$	−35.0337	−	35.0337i	−1.13724	−	1.13724i
$950$	3.41974	−	3.14759i	0.110951	−	0.102121i
$951$	−10.1022			−0.327586
$952$	7.30334	+	2.76783i	0.236703	+	0.0897059i
$953$			53.8491i			1.74434i	0.489200	+	0.872172i	$0.337289\pi$
$953$			53.8491i			1.74434i	−0.489200	+	0.872172i	$0.662711\pi$
$954$		−	3.90564i		−	0.126450i
$955$	−10.8960	−	4.77995i	−0.352587	−	0.154676i
$956$	18.6306			0.602555
$957$	−0.842384	+	0.842384i	−0.0272304	+	0.0272304i
$958$	0.323145	+	0.323145i	0.0104403	+	0.0104403i
$959$	−0.769556	+	0.769556i	−0.0248503	+	0.0248503i
$960$	−33.5819	+	13.1022i	−1.08385	+	0.422871i
$961$			5.72998i			0.184838i
$962$	−0.867484	−	0.867484i	−0.0279688	−	0.0279688i
$963$	−10.0703	−	10.0703i	−0.324510	−	0.324510i
$964$	−11.6760	−	11.6760i	−0.376058	−	0.376058i
$965$	−10.1447	−	26.0016i	−0.326569	−	0.837021i
$966$	−6.62488	−	6.62488i	−0.213152	−	0.213152i
$967$	14.6688			0.471716			0.235858	−	0.971788i	$-0.424210\pi$
$967$	14.6688			0.471716			0.235858	+	0.971788i	$0.424210\pi$
$968$			9.87576i			0.317419i
$969$	−36.9257	−	13.9942i	−1.18623	−	0.449557i
$970$	−8.09358	+	3.15776i	−0.259869	+	0.101389i
$971$			14.2468i			0.457203i	0.973520	+	0.228602i	$0.0734153\pi$
$971$			14.2468i			0.457203i	−0.973520	+	0.228602i	$0.926585\pi$
$972$	−29.4171	+	29.4171i	−0.943553	+	0.943553i
$973$		−	36.5125i		−	1.17054i
$974$	−0.794499	−	0.794499i	−0.0254574	−	0.0254574i
$975$	−2.01778	+	48.6919i	−0.0646206	+	1.55939i
$976$	−14.7156	+	14.7156i	−0.471033	+	0.471033i
$977$	−20.9141			−0.669103			−0.334551	−	0.942378i	$-0.608585\pi$
$977$	−20.9141			−0.669103			−0.334551	+	0.942378i	$0.608585\pi$
$978$	−4.76722			−0.152439
$979$	3.18134	−	3.18134i	0.101676	−	0.101676i
$980$	−4.77733	+	10.8900i	−0.152606	+	0.347870i
$981$	15.6674	+	15.6674i	0.500221	+	0.500221i
$982$			3.92620i			0.125290i
$983$	12.3036	−	12.3036i	0.392425	−	0.392425i	−0.483126	−	0.875551i	$-0.660499\pi$
$983$	12.3036	−	12.3036i	0.392425	−	0.392425i	0.875551	+	0.483126i	$0.160499\pi$
$984$		−	23.6760i		−	0.754762i
$985$	0.448443	+	1.14940i	0.0142886	+	0.0366228i
$986$	0.928654	+	0.351942i	0.0295744	+	0.0112081i
$987$			17.8350i			0.567696i
$988$	31.6865			1.00808
$989$	−42.9797	−	42.9797i	−1.36668	−	1.36668i
$990$	−0.247786	−	0.635095i	−0.00787515	−	0.0201846i
$991$	3.73190	+	3.73190i	0.118548	+	0.118548i	0.763892	−	0.645344i	$-0.223286\pi$
$991$	3.73190	+	3.73190i	0.118548	+	0.118548i	−0.645344	+	0.763892i	$0.723286\pi$
$992$	11.5233	+	11.5233i	0.365866	+	0.365866i
$993$	23.1542	+	23.1542i	0.734777	+	0.734777i
$994$			0.872669i			0.0276794i
$995$	−14.3037	−	36.6615i	−0.453458	−	1.16225i
$996$	7.36928	−	7.36928i	0.233505	−	0.233505i
$997$	−18.1295	−	18.1295i	−0.574167	−	0.574167i	0.359123	−	0.933290i	$-0.383076\pi$
$997$	−18.1295	−	18.1295i	−0.574167	−	0.574167i	−0.933290	+	0.359123i	$0.883076\pi$
$998$	−0.713978	+	0.713978i	−0.0226006	+	0.0226006i
$999$	0.829394			0.0262409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.j.c.64.3	yes	12
3.2	odd	2		765.2.t.e.64.4		12
5.2	odd	4		425.2.e.d.251.3		12
5.3	odd	4		425.2.e.d.251.4		12
5.4	even	2	inner	85.2.j.c.64.4	yes	12
15.14	odd	2		765.2.t.e.64.3		12
17.2	even	8		1445.2.b.f.579.5		12
17.4	even	4	inner	85.2.j.c.4.4	yes	12
17.15	even	8		1445.2.b.f.579.6		12
51.38	odd	4		765.2.t.e.514.3		12
85.2	odd	8		7225.2.a.bp.1.7		12
85.4	even	4	inner	85.2.j.c.4.3	✓	12
85.19	even	8		1445.2.b.f.579.8		12
85.32	odd	8		7225.2.a.bp.1.8		12
85.38	odd	4		425.2.e.d.276.3		12
85.49	even	8		1445.2.b.f.579.7		12
85.53	odd	8		7225.2.a.bp.1.6		12
85.72	odd	4		425.2.e.d.276.4		12
85.83	odd	8		7225.2.a.bp.1.5		12
255.89	odd	4		765.2.t.e.514.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.j.c.4.3	✓	12	85.4	even	4	inner
85.2.j.c.4.4	yes	12	17.4	even	4	inner
85.2.j.c.64.3	yes	12	1.1	even	1	trivial
85.2.j.c.64.4	yes	12	5.4	even	2	inner
425.2.e.d.251.3		12	5.2	odd	4
425.2.e.d.251.4		12	5.3	odd	4
425.2.e.d.276.3		12	85.38	odd	4
425.2.e.d.276.4		12	85.72	odd	4
765.2.t.e.64.3		12	15.14	odd	2
765.2.t.e.64.4		12	3.2	odd	2
765.2.t.e.514.3		12	51.38	odd	4
765.2.t.e.514.4		12	255.89	odd	4
1445.2.b.f.579.5		12	17.2	even	8
1445.2.b.f.579.6		12	17.15	even	8
1445.2.b.f.579.7		12	85.49	even	8
1445.2.b.f.579.8		12	85.19	even	8
7225.2.a.bp.1.5		12	85.83	odd	8
7225.2.a.bp.1.6		12	85.53	odd	8
7225.2.a.bp.1.7		12	85.2	odd	8
7225.2.a.bp.1.8		12	85.32	odd	8

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:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.232389 q^{2} +(1.69306 - 1.69306i) q^{3} -1.94600 q^{4} +(2.04770 + 0.898299i) q^{5} +(-0.393449 + 0.393449i) q^{6} +(-1.46067 - 1.46067i) q^{7} +0.917007 q^{8} -2.73289i q^{9} +(-0.475863 - 0.208755i) q^{10} +(-0.339444 + 0.339444i) q^{11} +(-3.29468 + 3.29468i) q^{12} +4.07073i q^{13} +(0.339444 + 0.339444i) q^{14} +(4.98774 - 1.94600i) q^{15} +3.67889 q^{16} +(-3.75946 + 1.69306i) q^{17} +0.635095i q^{18} +4.00000i q^{19} +(-3.98481 - 1.74809i) q^{20} -4.94600 q^{21} +(0.0788831 - 0.0788831i) q^{22} +(-5.76379 - 5.76379i) q^{23} +(1.55255 - 1.55255i) q^{24} +(3.38612 + 3.67889i) q^{25} -0.945995i q^{26} +(0.452229 + 0.452229i) q^{27} +(2.84245 + 2.84245i) q^{28} +(0.732893 + 0.732893i) q^{29} +(-1.15910 + 0.452229i) q^{30} +(-4.28544 - 4.28544i) q^{31} -2.68895 q^{32} +1.14940i q^{33} +(0.873659 - 0.393449i) q^{34} +(-1.67889 - 4.30312i) q^{35} +5.31820i q^{36} +(0.917007 - 0.917007i) q^{37} -0.929557i q^{38} +(6.89199 + 6.89199i) q^{39} +(1.87775 + 0.823747i) q^{40} +(7.62488 - 7.62488i) q^{41} +1.14940 q^{42} +7.45685 q^{43} +(0.660556 - 0.660556i) q^{44} +(2.45496 - 5.59613i) q^{45} +(1.33944 + 1.33944i) q^{46} -3.60596i q^{47} +(6.22857 - 6.22857i) q^{48} -2.73289i q^{49} +(-0.786897 - 0.854934i) q^{50} +(-3.49854 + 9.23143i) q^{51} -7.92163i q^{52} -6.14969 q^{53} +(-0.105093 - 0.105093i) q^{54} +(-1.00000 + 0.390156i) q^{55} +(-1.33944 - 1.33944i) q^{56} +(6.77223 + 6.77223i) q^{57} +(-0.170316 - 0.170316i) q^{58} -6.00000i q^{59} +(-9.70612 + 3.78690i) q^{60} +(-4.00000 + 4.00000i) q^{61} +(0.995890 + 0.995890i) q^{62} +(-3.99185 + 3.99185i) q^{63} -6.73289 q^{64} +(-3.65674 + 8.33563i) q^{65} -0.267107i q^{66} +3.14118i q^{67} +(7.31589 - 3.29468i) q^{68} -19.5169 q^{69} +(0.390156 + 1.00000i) q^{70} +(1.28544 + 1.28544i) q^{71} -2.50608i q^{72} +(-8.60625 + 8.60625i) q^{73} +(-0.213103 + 0.213103i) q^{74} +(11.9615 + 0.495679i) q^{75} -7.78398i q^{76} +0.991630 q^{77} +(-1.60162 - 1.60162i) q^{78} +(7.23143 - 7.23143i) q^{79} +(7.53324 + 3.30474i) q^{80} +9.72998 q^{81} +(-1.77194 + 1.77194i) q^{82} -2.23672 q^{83} +9.62488 q^{84} +(-9.21911 + 0.0897461i) q^{85} -1.73289 q^{86} +2.48166 q^{87} +(-0.311272 + 0.311272i) q^{88} -9.37220 q^{89} +(-0.570505 + 1.30048i) q^{90} +(5.94600 - 5.94600i) q^{91} +(11.2163 + 11.2163i) q^{92} -14.5110 q^{93} +0.837986i q^{94} +(-3.59320 + 8.19078i) q^{95} +(-4.55255 + 4.55255i) q^{96} +(11.8220 - 11.8220i) q^{97} +0.635095i q^{98} +(0.927664 + 0.927664i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{4} - 20 q^{6} - 4 q^{10} + 16 q^{11} - 16 q^{14} + 4 q^{16} - 32 q^{20} - 24 q^{21} - 32 q^{24} + 4 q^{29} + 52 q^{30} + 4 q^{31} + 20 q^{35} + 12 q^{39} + 24 q^{40} + 16 q^{41} + 28 q^{44}+ \cdots + 36 q^{99}+O(q^{100}) \) 12 * q + 12 * q^4 - 20 * q^6 - 4 * q^10 + 16 * q^11 - 16 * q^14 + 4 * q^16 - 32 * q^20 - 24 * q^21 - 32 * q^24 + 4 * q^29 + 52 * q^30 + 4 * q^31 + 20 * q^35 + 12 * q^39 + 24 * q^40 + 16 * q^41 + 28 * q^44 - 20 * q^45 - 4 * q^46 - 40 * q^50 + 44 * q^51 + 100 * q^54 - 12 * q^55 + 4 * q^56 - 48 * q^61 - 76 * q^64 + 8 * q^65 - 88 * q^69 - 40 * q^71 + 28 * q^74 + 64 * q^75 - 4 * q^79 + 12 * q^80 - 60 * q^81 + 40 * q^84 - 52 * q^85 - 16 * q^86 - 16 * q^89 - 84 * q^90 + 36 * q^91 - 4 * q^96 + 36 * q^99

Introduction

L-functions

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