LMFDB - Embedded newform 85.2.j.c.64.4

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			64.4
Root			$-1.23239i$ of defining polynomial
Character	$\chi$	$=$	85.64
Dual form			85.2.j.c.4.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.232389 q^{2} +(-1.69306 + 1.69306i) q^{3} -1.94600 q^{4} +(0.898299 + 2.04770i) q^{5} +(-0.393449 + 0.393449i) q^{6} +(1.46067 + 1.46067i) q^{7} -0.917007 q^{8} -2.73289i q^{9} +(0.208755 + 0.475863i) 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} +(-1.74809 - 3.98481i) 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} +(-0.823747 - 1.87775i) q^{40} +(7.62488 - 7.62488i) q^{41} -1.14940 q^{42} -7.45685 q^{43} +(0.660556 - 0.660556i) q^{44} +(5.59613 - 2.45496i) 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} +(8.33563 - 3.65674i) 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} +(-0.495679 - 11.9615i) q^{75} -7.78398i q^{76} -0.991630 q^{77} +(1.60162 + 1.60162i) q^{78} +(7.23143 - 7.23143i) q^{79} +(3.30474 + 7.53324i) q^{80} +9.72998 q^{81} +(1.77194 - 1.77194i) q^{82} +2.23672 q^{83} +9.62488 q^{84} +(6.84399 + 6.17736i) q^{85} -1.73289 q^{86} -2.48166 q^{87} +(0.311272 - 0.311272i) q^{88} -9.37220 q^{89} +(1.30048 - 0.570505i) q^{90} +(5.94600 - 5.94600i) q^{91} +(-11.2163 - 11.2163i) q^{92} +14.5110 q^{93} +0.837986i q^{94} +(-8.19078 + 3.59320i) 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	$-0.473817\pi$
$2$	0.232389			0.164324			0.0821620	+	0.996619i	$0.473817\pi$
$3$	−1.69306	+	1.69306i	−0.977488	+	0.977488i	−0.999752	−	0.0222645i	$-0.992912\pi$
$3$	−1.69306	+	1.69306i	−0.977488	+	0.977488i	0.0222645	+	0.999752i	$0.492912\pi$
$4$	−1.94600			−0.972998
$5$	0.898299	+	2.04770i	0.401732	+	0.915757i
$5$	0.898299	+	2.04770i	0.401732	+	0.915757i
$6$	−0.393449	+	0.393449i	−0.160625	+	0.160625i
$7$	1.46067	+	1.46067i	0.552081	+	0.552081i	0.927041	−	0.374960i	$-0.122344\pi$
$7$	1.46067	+	1.46067i	0.552081	+	0.552081i	−0.374960	+	0.927041i	$0.622344\pi$
$8$	−0.917007			−0.324211
$9$		−	2.73289i		−	0.910964i
$10$	0.208755	+	0.475863i	0.0660142	+	0.150481i
$11$	−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	$-0.809065\pi$
$13$		−	4.07073i		−	1.12902i	0.825427	−	0.564509i	$-0.190935\pi$
$14$	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	$0.848268\pi$
$20$	−1.74809	−	3.98481i	−0.390884	−	0.891030i
$21$	−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	$0.0732924\pi$
$23$	5.76379	+	5.76379i	1.20183	+	1.20183i	0.228226	+	0.973608i	$0.426708\pi$
$24$	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	−0.778455	−	0.627700i	$-0.783996\pi$
$37$	−0.917007	+	0.917007i	−0.150755	+	0.150755i	0.627700	+	0.778455i	$0.283996\pi$
$38$			0.929557i			0.150794i
$39$	6.89199	+	6.89199i	1.10360	+	1.10360i
$40$	−0.823747	−	1.87775i	−0.130246	−	0.296899i
$41$	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	$-0.692507\pi$
$43$	−7.45685			−1.13716			−0.568580	+	0.822628i	$0.692507\pi$
$44$	0.660556	−	0.660556i	0.0995826	−	0.0995826i
$45$	5.59613	−	2.45496i	0.834222	−	0.365963i
$46$	1.33944	+	1.33944i	0.197490	+	0.197490i
$47$			3.60596i			0.525983i	0.964798	+	0.262991i	$0.0847091\pi$
$47$			3.60596i			0.525983i	−0.964798	+	0.262991i	$0.915291\pi$
$48$	−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	$-0.361201\pi$
$53$	6.14969			0.844725			0.422362	+	0.906427i	$0.361201\pi$
$54$	−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
$65$	8.33563	−	3.65674i	1.03391	−	0.453563i
$66$		−	0.267107i		−	0.0328787i
$67$		−	3.14118i		−	0.383756i	−0.981419	−	0.191878i	$-0.938542\pi$
$67$		−	3.14118i		−	0.383756i	0.981419	−	0.191878i	$-0.0614578\pi$
$68$	−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	$-0.497673\pi$
$73$	8.60625	−	8.60625i	1.00729	−	1.00729i	0.999973	−	0.00731179i	$-0.00232744\pi$
$74$	−0.213103	+	0.213103i	−0.0247727	+	0.0247727i
$75$	−0.495679	−	11.9615i	−0.0572360	−	1.38119i
$76$		−	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	$0.0548845\pi$
$80$	3.30474	+	7.53324i	0.369481	+	0.842242i
$81$	9.72998			1.08111
$82$	1.77194	−	1.77194i	0.195678	−	0.195678i
$83$	2.23672			0.245512			0.122756	−	0.992437i	$-0.460827\pi$
$83$	2.23672			0.245512			0.122756	+	0.992437i	$0.460827\pi$
$84$	9.62488			1.05016
$85$	6.84399	+	6.17736i	0.742335	+	0.670029i
$86$	−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	$0.665464\pi$
$90$	1.30048	−	0.570505i	0.137083	−	0.0601366i
$91$	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
$95$	−8.19078	+	3.59320i	−0.840357	+	0.368654i
$96$	−4.55255	+	4.55255i	−0.464642	+	0.464642i
$97$	−11.8220	+	11.8220i	−1.20035	+	1.20035i	−0.226286	+	0.974061i	$0.572658\pi$
$97$	−11.8220	+	11.8220i	−1.20035	+	1.20035i	−0.974061	+	0.226286i	$0.927342\pi$
$98$		−	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	$-0.671192\pi$
$103$		−	17.4323i		−	1.71766i	0.512262	−	0.858829i	$-0.328808\pi$
$104$			3.73289i			0.366040i
$105$	−4.44298	−	10.1279i	−0.433591	−	0.988381i
$106$	1.42912			0.138809
$107$	−3.68484	+	3.68484i	−0.356227	+	0.356227i	−0.862420	−	0.506193i	$-0.831052\pi$
$107$	−3.68484	+	3.68484i	−0.356227	+	0.356227i	0.506193	+	0.862420i	$0.331052\pi$
$108$	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	0.813149	−	0.582055i	$-0.197751\pi$
$113$	2.45656	+	2.45656i	0.231094	+	0.231094i	−0.582055	+	0.813149i	$0.697751\pi$
$114$	−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
$125$	−10.5750	−	3.62899i	−0.945856	−	0.324587i
$126$	0.927664	−	0.927664i	0.0826428	−	0.0826428i
$127$	2.98341			0.264735			0.132367	−	0.991201i	$-0.457742\pi$
$127$	2.98341			0.264735			0.132367	+	0.991201i	$0.457742\pi$
$128$	−6.94255			−0.613640
$129$	12.6249	−	12.6249i	1.11156	−	1.11156i
$130$	1.93711	−	0.849787i	0.169896	−	0.0745312i
$131$	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	$0.00716448\pi$
$137$			0.526852i			0.0450120i	−0.999747	+	0.0225060i	$0.992836\pi$
$138$	−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	$0.403052\pi$
$150$	−0.115190	−	2.77972i	−0.00940526	−	0.226963i
$151$		−	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	$-0.834400\pi$
$157$		−	12.4571i		−	0.994188i	0.867697	−	0.497094i	$-0.165600\pi$
$158$	1.68051	−	1.68051i	0.133694	−	0.133694i
$159$	−10.4118	+	10.4118i	−0.825708	+	0.825708i
$160$	2.41548	+	5.50615i	0.190961	+	0.435299i
$161$			16.8380i			1.32702i
$162$	2.26114			0.177652
$163$	−6.05825	−	6.05825i	−0.474519	−	0.474519i	0.428854	−	0.903374i	$-0.358917\pi$
$163$	−6.05825	−	6.05825i	−0.474519	−	0.474519i	−0.903374	+	0.428854i	$0.858917\pi$
$164$	−14.8380	+	14.8380i	−1.15865	+	1.15865i
$165$	2.35361	−	1.03250i	0.183229	−	0.0803802i
$166$	0.519790			0.0403435
$167$	6.68080	−	6.68080i	0.516976	−	0.516976i	−0.399679	−	0.916655i	$-0.630878\pi$
$167$	6.68080	−	6.68080i	0.516976	−	0.516976i	0.916655	+	0.399679i	$0.130878\pi$
$168$	4.53551			0.349922
$169$	−3.57088			−0.274683
$170$	1.59047	+	1.43555i	0.121984	+	0.110102i
$171$	10.9316			0.835958
$172$	14.5110			1.10645
$173$	−11.6979	+	11.6979i	−0.889375	+	0.889375i	−0.994463	−	0.105088i	$-0.966488\pi$
$173$	−11.6979	+	11.6979i	−0.889375	+	0.889375i	0.105088	+	0.994463i	$0.466488\pi$
$174$	−0.576711			−0.0437204
$175$	−10.3196	+	0.427642i	−0.780091	+	0.0323267i
$176$	−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	$-0.260442\pi$
$180$	−10.8900	+	4.77733i	−0.811696	+	0.356081i
$181$	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
$190$	−1.90345	+	0.835021i	−0.138091	+	0.0605788i
$191$	−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	0.949396	−	0.314081i	$-0.101696\pi$
$193$	8.82609	+	8.82609i	0.635316	+	0.635316i	−0.314081	+	0.949396i	$0.601696\pi$
$194$	−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	0.693071	−	0.720869i	$-0.256257\pi$
$197$	−0.390156	−	0.390156i	−0.0277974	−	0.0277974i	−0.720869	+	0.693071i	$0.756257\pi$
$198$	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
$210$	−1.03250	−	2.35361i	−0.0712494	−	0.162415i
$211$	−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
$215$	−6.69848	−	15.2694i	−0.456833	−	1.04136i
$216$	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	$-0.456479\pi$
$223$	4.07073			0.272597			0.136298	+	0.990668i	$0.456479\pi$
$224$	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	0.972642	−	0.232309i	$-0.0746281\pi$
$227$	11.1542	+	11.1542i	0.740333	+	0.740333i	−0.232309	+	0.972642i	$0.574628\pi$
$228$	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	−0.723753	−	0.690060i	$-0.757584\pi$
$233$	−0.514301	+	0.514301i	−0.0336930	+	0.0336930i	0.690060	+	0.723753i	$0.257584\pi$
$234$	−2.58530			−0.169007
$235$	−7.38390	+	3.23923i	−0.481673	+	0.211304i
$236$			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
$245$	5.59613	−	2.45496i	0.357524	−	0.156841i
$246$			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
$250$	−2.45751	−	0.843340i	−0.155427	−	0.0533375i
$251$	−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
$255$	−22.0459	+	1.12864i	−1.38057	+	0.0706783i
$256$	11.8524			0.740776
$257$	−27.2752			−1.70138			−0.850689	−	0.525670i	$-0.823815\pi$
$257$	−27.2752			−1.70138			−0.850689	+	0.525670i	$0.823815\pi$
$258$	2.93389	−	2.93389i	0.182656	−	0.182656i
$259$	−2.67889			−0.166458
$260$	−16.2211	+	7.11599i	−1.00599	+	0.441315i
$261$	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	$-0.624552\pi$
$263$	−12.3700			−0.762765			−0.381382	+	0.924417i	$0.624552\pi$
$264$			1.05400i			0.0648695i
$265$	5.52426	+	12.5927i	0.339353	+	0.773563i
$266$	−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
$275$	−0.0993794	−	2.39817i	−0.00599280	−	0.144615i
$276$	37.9797			2.28611
$277$	−4.78045	+	4.78045i	−0.287230	+	0.287230i	−0.835984	−	0.548754i	$-0.815102\pi$
$277$	−4.78045	+	4.78045i	−0.287230	+	0.287230i	0.548754	+	0.835984i	$0.315102\pi$
$278$	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	$-0.980302\pi$
$283$	−17.8308	−	17.8308i	−1.05993	−	1.05993i	−0.0618440	−	0.998086i	$-0.519698\pi$
$284$	−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	$-0.721740\pi$
$293$		−	26.2584i		−	1.53403i	0.641627	−	0.767017i	$-0.278260\pi$
$294$	1.07525	+	1.07525i	0.0627100	+	0.0627100i
$295$	12.2862	−	5.38980i	0.715329	−	0.313806i
$296$	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
$300$	0.964588	+	23.2770i	0.0556905	+	1.34390i
$301$	−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	$-0.870036\pi$
$307$		−	13.9136i		−	0.794088i	0.917800	−	0.397044i	$-0.129964\pi$
$308$	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	0.554487	−	0.832193i	$-0.312915\pi$
$313$	−4.91312	−	4.91312i	−0.277706	−	0.277706i	−0.832193	+	0.554487i	$0.812915\pi$
$314$		−	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	0.785908	−	0.618343i	$-0.212196\pi$
$317$	2.98341	+	2.98341i	0.167565	+	0.167565i	−0.618343	+	0.785908i	$0.712196\pi$
$318$	−2.41959	+	2.41959i	−0.135684	+	0.135684i
$319$	−0.497552			−0.0278575
$320$	−6.04815	−	13.7869i	−0.338102	−	0.770712i
$321$		−	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
$330$	0.546955	−	0.239942i	0.0301089	−	0.0132084i
$331$			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
$335$	6.43218	−	2.82172i	0.351427	−	0.154167i
$336$	−18.1958			−0.992660
$337$	−4.58504	+	4.58504i	−0.249763	+	0.249763i	−0.820873	−	0.571110i	$-0.806513\pi$
$337$	−4.58504	+	4.58504i	−0.249763	+	0.249763i	0.571110	+	0.820873i	$0.306513\pi$
$338$	−0.829834			−0.0451370
$339$	−8.31820			−0.451782
$340$	−13.3184	−	12.0211i	−0.722290	−	0.651937i
$341$	2.90933			0.157549
$342$	2.54038			0.137368
$343$	14.2165	−	14.2165i	0.767621	−	0.767621i
$344$	6.83799			0.368679
$345$	−17.5320	−	39.9646i	−0.943891	−	2.15162i
$346$	−2.71847	+	2.71847i	−0.146146	+	0.146146i
$347$	3.53962	+	3.53962i	0.190017	+	0.190017i	0.795703	−	0.605686i	$-0.207101\pi$
$347$	3.53962	+	3.53962i	0.190017	+	0.190017i	−0.605686	+	0.795703i	$0.707101\pi$
$348$	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	$0.920692\pi$
$350$	−2.39817	+	0.0993794i	−0.128188	+	0.00531205i
$351$	−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	$0.120247\pi$
$353$			13.8600i			0.737693i	−0.929490	+	0.368847i	$0.879753\pi$
$354$	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	$-0.0981679\pi$
$360$	−5.13169	+	2.25121i	−0.270464	+	0.118649i
$361$	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	0.251023	−	0.967981i	$-0.419233\pi$
$367$	−13.7349	−	13.7349i	−0.716958	−	0.716958i	−0.967981	+	0.251023i	$0.919233\pi$
$368$	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	$0.0462215\pi$
$373$			5.58922i			0.289399i	−0.989476	+	0.144699i	$0.953779\pi$
$374$	−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	$0.754549\pi$
$380$	15.9392	−	6.99234i	0.817665	−	0.358700i
$381$	−5.05109	+	5.05109i	−0.258775	+	0.258775i
$382$	−1.23657			−0.0632684
$383$	24.8020			1.26732			0.633662	−	0.773610i	$-0.281551\pi$
$383$	24.8020			1.26732			0.633662	+	0.773610i	$0.281551\pi$
$384$	11.7541	−	11.7541i	0.599826	−	0.599826i
$385$	−0.890781	−	2.03056i	−0.0453984	−	0.103487i
$386$	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	0.571149	−	0.820847i	$-0.306498\pi$
$397$	−4.97519	−	4.97519i	−0.249698	−	0.249698i	−0.820847	+	0.571149i	$0.806498\pi$
$398$	−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
$405$	8.74043	+	19.9240i	0.434316	+	0.990033i
$406$			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
$415$	2.00924	+	4.58012i	0.0986299	+	0.224829i
$416$		−	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	$0.472692\pi$
$420$	8.64603	+	19.7088i	0.421883	+	0.961693i
$421$	−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
$425$	−6.50140	+	19.5635i	−0.315364	+	0.948971i
$426$	−1.01151			−0.0490078
$427$	−11.6854			−0.565494
$428$	7.17068	−	7.17068i	0.346608	−	0.346608i
$429$	−4.67889			−0.225899
$430$	−1.55666	−	3.54844i	−0.0750686	−	0.171121i
$431$	−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	$-0.547949\pi$
$433$	−6.24538			−0.300134			−0.150067	+	0.988676i	$0.547949\pi$
$434$		−	2.90933i		−	0.139652i
$435$	−2.22927	−	5.08168i	−0.106885	−	0.243648i
$436$	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	$0.244709\pi$
$443$			29.2669i			1.39051i	−0.718761	+	0.695257i	$0.755291\pi$
$444$			6.04250i			0.286764i
$445$	−8.41904	−	19.1914i	−0.399101	−	0.909760i
$446$	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	$-0.236631\pi$
$457$	31.4752			1.47235			0.736174	+	0.676792i	$0.236631\pi$
$458$		−	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	$0.107068\pi$
$463$			14.2040i			0.660115i	−0.943961	+	0.330058i	$0.892932\pi$
$464$	2.69623	+	2.69623i	0.125169	+	0.125169i
$465$	13.0352	+	29.7141i	0.604494	+	1.37796i
$466$	−0.119518	+	0.119518i	−0.00553657	+	0.00553657i
$467$	29.1177			1.34741			0.673703	−	0.739002i	$-0.264703\pi$
$467$	29.1177			1.34741			0.673703	+	0.739002i	$0.264703\pi$
$468$	21.6490			1.00072
$469$	4.58822	−	4.58822i	0.211864	−	0.211864i
$470$	−1.71594	+	0.752762i	−0.0791504	+	0.0347223i
$471$	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	0.625390	−	0.780312i	$-0.284940\pi$
$487$	−3.41883	−	3.41883i	−0.154922	−	0.154922i	−0.780312	+	0.625390i	$0.784940\pi$
$488$	3.66803	−	3.66803i	0.166044	−	0.166044i
$489$	20.5140			0.927673
$490$	1.30048	−	0.570505i	0.0587498	−	0.0257728i
$491$		−	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	$0.218994\pi$
$500$	20.5789	+	7.06201i	0.920315	+	0.315822i
$501$			22.6220i			1.01067i
$502$	−1.40286			−0.0626125
$503$	−8.13721	−	8.13721i	−0.362820	−	0.362820i	0.502030	−	0.864850i	$-0.332587\pi$
$503$	−8.13721	−	8.13721i	−0.362820	−	0.362820i	−0.864850	+	0.502030i	$0.832587\pi$
$504$	−3.66056	+	3.66056i	−0.163054	+	0.163054i
$505$	−3.96310	−	9.03398i	−0.176356	−	0.402007i
$506$	−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	$0.219440\pi$
$510$	−5.12323	+	0.262284i	−0.226861	+	0.0116141i
$511$	25.1418			1.11221
$512$	16.6395			0.735368
$513$	1.80891	−	1.80891i	0.0798655	−	0.0798655i
$514$	−6.33845			−0.279577
$515$	35.6961	−	15.6595i	1.57296	−	0.690038i
$516$	−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
$520$	−7.64383	+	3.35325i	−0.335204	+	0.147050i
$521$	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	$0.117435\pi$
$523$			16.4943i			0.721243i	−0.932712	+	0.360622i	$0.882565\pi$
$524$	−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
$530$	1.28378	+	2.92641i	0.0557638	+	0.127115i
$531$	−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	−0.870415	−	0.492320i	$-0.836149\pi$
$547$	−8.84290	+	8.84290i	−0.378095	+	0.378095i	0.492320	+	0.870415i	$0.336149\pi$
$548$		−	1.02525i		−	0.0437965i
$549$	10.9316	+	10.9316i	0.466548	+	0.466548i
$550$	−0.0230947	−	0.557310i	−0.000984762	−	0.0237638i
$551$	−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
$555$	6.35829	−	2.78930i	0.269894	−	0.118399i
$556$	−24.3221	−	24.3221i	−1.03149	−	1.03149i
$557$		−	38.9354i		−	1.64975i	−0.565318	−	0.824873i	$-0.691247\pi$
$557$		−	38.9354i		−	1.64975i	0.565318	−	0.824873i	$-0.308753\pi$
$558$	−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	$-0.555133\pi$
$563$	−8.17844			−0.344680			−0.172340	+	0.985038i	$0.555133\pi$
$564$	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
$575$	−40.7212	+	1.68747i	−1.69819	+	0.0703725i
$576$			18.4003i			0.766678i
$577$			6.58601i			0.274179i	0.990559	+	0.137090i	$0.0437749\pi$
$577$			6.58601i			0.274179i	−0.990559	+	0.137090i	$0.956225\pi$
$578$	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
$585$	−9.99347	−	22.7804i	−0.413179	−	0.941852i
$586$		−	6.10218i		−	0.252079i
$587$	22.3369			0.921944			0.460972	−	0.887415i	$-0.347501\pi$
$587$	22.3369			0.921944			0.460972	+	0.887415i	$0.347501\pi$
$588$	−9.00402	−	9.00402i	−0.371319	−	0.371319i
$589$	17.1418	−	17.1418i	0.706314	−	0.706314i
$590$	2.85518	−	1.25253i	0.117546	−	0.0515659i
$591$	1.32111			0.0543433
$592$	−3.37357	+	3.37357i	−0.138653	+	0.138653i
$593$	−30.1344			−1.23747			−0.618736	−	0.785599i	$-0.712355\pi$
$593$	−30.1344			−1.23747			−0.618736	+	0.785599i	$0.712355\pi$
$594$	0.0713464			0.00292738
$595$	0.973725	+	19.0199i	0.0399188	+	0.779739i
$596$	−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	$0.558127\pi$
$600$	0.454541	+	10.9687i	0.0185566	+	0.447797i
$601$	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
$605$	−22.0528	+	9.67429i	−0.896573	+	0.393316i
$606$	1.73581	−	1.73581i	0.0705124	−	0.0705124i
$607$	10.5442	−	10.5442i	0.427978	−	0.427978i	−0.459961	−	0.887939i	$-0.652137\pi$
$607$	10.5442	−	10.5442i	0.427978	−	0.427978i	0.887939	+	0.459961i	$0.152137\pi$
$608$			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	$0.218187\pi$
$613$			31.3459i			1.26605i	−0.774132	+	0.633024i	$0.781813\pi$
$614$		−	3.23336i		−	0.130488i
$615$	−52.8689	+	23.1930i	−2.13188	+	0.935230i
$616$	0.909332			0.0366380
$617$	−10.9050	+	10.9050i	−0.439020	+	0.439020i	−0.891682	−	0.452662i	$-0.850474\pi$
$617$	−10.9050	+	10.9050i	−0.439020	+	0.439020i	0.452662	+	0.891682i	$0.350474\pi$
$618$	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
$635$	2.68000	+	6.10912i	0.106352	+	0.242433i
$636$	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
$640$	−6.23649	−	14.2162i	−0.246519	−	0.561946i
$641$	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	−0.804871	−	0.593450i	$-0.797765\pi$
$643$	−5.36109	+	5.36109i	−0.211421	+	0.211421i	0.593450	+	0.804871i	$0.297765\pi$
$644$		−	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	$0.0646024\pi$
$647$			10.2540i			0.403128i	−0.979475	+	0.201564i	$0.935398\pi$
$648$	−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	0.876839	−	0.480785i	$-0.159648\pi$
$653$	10.1207	+	10.1207i	0.396054	+	0.396054i	−0.480785	+	0.876839i	$0.659648\pi$
$654$		−	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	$0.827257\pi$
$660$	−4.58012	+	2.00924i	−0.178281	+	0.0782097i
$661$		−	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
$670$	1.49477	−	0.655737i	0.0577480	−	0.0253333i
$671$		−	2.71555i		−	0.104833i
$672$	−13.2995			−0.513040
$673$	32.7151	+	32.7151i	1.26108	+	1.26108i	0.950572	+	0.310503i	$0.100497\pi$
$673$	32.7151	+	32.7151i	1.26108	+	1.26108i	0.310503	+	0.950572i	$0.399503\pi$
$674$	−1.06551	+	1.06551i	−0.0410420	+	0.0410420i
$675$	3.19500	−	0.132399i	0.122975	−	0.00509606i
$676$	6.94891			0.267266
$677$	−1.24509	+	1.24509i	−0.0478527	+	0.0478527i	−0.730628	−	0.682776i	$-0.760773\pi$
$677$	−1.24509	+	1.24509i	−0.0478527	+	0.0478527i	0.682776	+	0.730628i	$0.260773\pi$
$678$	−1.93306			−0.0742387
$679$	−34.5362			−1.32538
$680$	−6.27599	−	5.66468i	−0.240673	−	0.217231i
$681$	−37.7696			−1.44733
$682$	0.676098			0.0258891
$683$	16.2377	−	16.2377i	0.621317	−	0.621317i	−0.324551	−	0.945868i	$-0.605213\pi$
$683$	16.2377	−	16.2377i	0.621317	−	0.621317i	0.945868	+	0.324551i	$0.105213\pi$
$684$	−21.2728			−0.813385
$685$	−1.07883	+	0.473270i	−0.0412200	+	0.0180827i
$686$	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
$690$	−4.07425	−	9.28735i	−0.155104	−	0.353563i
$691$	−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
$700$	20.0820	−	0.832189i	0.759027	−	0.0314538i
$701$	−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	$0.466519\pi$
$720$	20.5875	−	9.03151i	0.767252	−	0.336584i
$721$	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
$725$	−5.17789	+	0.214570i	−0.192302	+	0.00796892i
$726$	−4.23727	−	4.23727i	−0.157260	−	0.157260i
$727$		−	12.2458i		−	0.454172i	−0.973875	−	0.227086i	$-0.927080\pi$
$727$		−	12.2458i		−	0.454172i	0.973875	−	0.227086i	$-0.0729199\pi$
$728$	−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	$-0.292584\pi$
$733$	32.8393			1.21295			0.606473	+	0.795104i	$0.292584\pi$
$734$	−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	−0.345268	−	0.938504i	$-0.612212\pi$
$743$	16.1704	−	16.1704i	0.593236	−	0.593236i	0.938504	+	0.345268i	$0.112212\pi$
$744$	−13.3067			−0.487847
$745$	6.57655	+	14.9914i	0.240946	+	0.549243i
$746$			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
$755$	15.2877	−	6.70651i	0.556375	−	0.244075i
$756$			2.57088i			0.0935019i
$757$	36.2220			1.31651			0.658256	−	0.752794i	$-0.271294\pi$
$757$	36.2220			1.31651			0.658256	+	0.752794i	$0.271294\pi$
$758$	−0.0914333	−	0.0914333i	−0.00332101	−	0.00332101i
$759$	6.62488	−	6.62488i	0.240468	−	0.240468i
$760$	7.51101	−	3.29499i	0.272453	−	0.119522i
$761$	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
$765$	16.8821	−	18.7039i	0.610372	−	0.676241i
$766$	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	$0.531960\pi$
$770$	−0.207008	−	0.471880i	−0.00746005	−	0.0170054i
$771$	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	$-0.728210\pi$
$773$	−36.5376			−1.31416			−0.657082	+	0.753819i	$0.728210\pi$
$774$			4.73581i			0.170225i
$775$	30.2766	−	1.25465i	1.08757	−	0.0450685i
$776$	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
$785$	25.5084	−	11.1902i	0.910435	−	0.399397i
$786$	−4.00276			−0.142774
$787$	11.3490	−	11.3490i	0.404547	−	0.404547i	−0.475285	−	0.879832i	$-0.657655\pi$
$787$	11.3490	−	11.3490i	0.404547	−	0.404547i	0.879832	+	0.475285i	$0.157655\pi$
$788$	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	$-0.711319\pi$
$797$	−34.7907			−1.23235			−0.616175	+	0.787609i	$0.711319\pi$
$798$		−	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
$805$	−34.4791	+	15.1256i	−1.21523	+	0.533106i
$806$	−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	$0.357726\pi$
$810$	2.03118	+	4.63013i	0.0713685	+	0.162686i
$811$	−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	0.999963	−	0.00855996i	$-0.00272475\pi$
$823$	28.4414	+	28.4414i	0.991403	+	0.991403i	−0.00855996	+	0.999963i	$0.502725\pi$
$824$			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	0.988027	−	0.154284i	$-0.0493071\pi$
$827$	23.9764	+	23.9764i	0.833742	+	0.833742i	−0.154284	+	0.988027i	$0.549307\pi$
$828$	−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	$0.545377\pi$
$830$	0.466927	+	1.06437i	0.0162073	+	0.0369449i
$831$		−	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	$0.126159\pi$
$840$	4.07425	+	9.28735i	0.140575	+	0.320444i
$841$		−	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
$845$	−3.20772	−	7.31207i	−0.110349	−	0.251543i
$846$	2.29012			0.0787361
$847$	−15.7308	+	15.7308i	−0.540515	+	0.540515i
$848$	22.6240			0.776912
$849$	60.3771			2.07214
$850$	−1.51086	+	4.54636i	−0.0518220	+	0.155939i
$851$	−10.5709			−0.362365
$852$	8.47023			0.290185
$853$	−26.1383	+	26.1383i	−0.894959	+	0.894959i	−0.994985	−	0.100026i	$-0.968107\pi$
$853$	−26.1383	+	26.1383i	−0.894959	+	0.894959i	0.100026	+	0.994985i	$0.468107\pi$
$854$	−2.71555			−0.0929242
$855$	9.81982	+	22.3845i	0.335831	+	0.765535i
$856$	3.37902	−	3.37902i	0.115493	−	0.115493i
$857$	−10.6231	−	10.6231i	−0.362879	−	0.362879i	0.501993	−	0.864872i	$-0.332600\pi$
$857$	−10.6231	−	10.6231i	−0.362879	−	0.362879i	−0.864872	+	0.501993i	$0.832600\pi$
$858$	−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	$0.759317\pi$
$860$	13.0352	+	29.7141i	0.444497	+	1.01324i
$861$	−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	$-0.932386\pi$
$863$		−	12.3865i		−	0.421643i	0.977525	−	0.210822i	$-0.0676139\pi$
$864$	−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
$870$	−0.518059	−	1.18093i	−0.0175639	−	0.0400372i
$871$	−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	$-0.973863\pi$
$877$	−31.9433	−	31.9433i	−1.07865	−	1.07865i	−0.0820188	−	0.996631i	$-0.526137\pi$
$878$	−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	$0.0721164\pi$
$883$			13.3497i			0.449254i	−0.974445	+	0.224627i	$0.927884\pi$
$884$	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	$0.518780\pi$
$887$	−31.4868	+	31.4868i	−1.05722	+	1.05722i	−0.998260	+	0.0589646i	$0.981220\pi$
$888$			2.84739i			0.0955522i
$889$	4.35778	+	4.35778i	0.146155	+	0.146155i
$890$	−1.95650	−	4.45988i	−0.0655819	−	0.149496i
$891$	−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
$895$	39.9942	−	17.5450i	1.33686	−	0.586463i
$896$	−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	0.205195	−	0.978721i	$-0.434217\pi$
$907$	−23.2958	−	23.2958i	−0.773526	−	0.773526i	−0.978721	+	0.205195i	$0.934217\pi$
$908$	−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
$915$	27.7349	−	12.1670i	0.916889	−	0.402228i
$916$			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
$925$	−0.268473	−	6.47866i	−0.00882735	−	0.213017i
$926$			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	$0.316823\pi$
$930$	3.02925	+	6.90524i	0.0993329	+	0.226432i
$931$	10.9316			0.358268
$932$	1.00083	−	1.00083i	0.0327832	−	0.0327832i
$933$	20.9274			0.685131
$934$	6.76664			0.221411
$935$	−4.42002	+	0.226283i	−0.144550	+	0.00740025i
$936$	10.2016			0.333450
$937$	−30.7655			−1.00506			−0.502532	−	0.864558i	$-0.667598\pi$
$937$	−30.7655			−1.00506			−0.502532	+	0.864558i	$0.667598\pi$
$938$	1.06625	−	1.06625i	0.0348144	−	0.0348144i
$939$	16.6364			0.542908
$940$	14.3690	−	6.30352i	0.468666	−	0.205598i
$941$	−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
$945$	2.70524	−	1.18675i	0.0880013	−	0.0386051i
$946$	0.588220	−	0.588220i	0.0191247	−	0.0191247i
$947$	−2.52289	+	2.52289i	−0.0819830	+	0.0819830i	−0.746909	−	0.664926i	$-0.768463\pi$
$947$	−2.52289	+	2.52289i	−0.0819830	+	0.0819830i	0.664926	+	0.746909i	$0.268463\pi$
$948$		−	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	$-0.662711\pi$
$953$		−	53.8491i		−	1.74434i	0.489200	−	0.872172i	$-0.337289\pi$
$954$		−	3.90564i		−	0.126450i
$955$	−4.77995	−	10.8960i	−0.154676	−	0.352587i
$956$	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	$-0.575790\pi$
$967$	−14.6688			−0.471716			−0.235858	+	0.971788i	$0.575790\pi$
$968$		−	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
$975$	−48.6919	+	2.01778i	−1.55939	+	0.0646206i
$976$	−14.7156	+	14.7156i	−0.471033	+	0.471033i
$977$	20.9141			0.669103			0.334551	−	0.942378i	$-0.391415\pi$
$977$	20.9141			0.669103			0.334551	+	0.942378i	$0.391415\pi$
$978$	4.76722			0.152439
$979$	3.18134	−	3.18134i	0.101676	−	0.101676i
$980$	−10.8900	+	4.77733i	−0.347870	+	0.152606i
$981$	15.6674	+	15.6674i	0.500221	+	0.500221i
$982$		−	3.92620i		−	0.125290i
$983$	−12.3036	+	12.3036i	−0.392425	+	0.392425i	−0.875551	−	0.483126i	$-0.839501\pi$
$983$	−12.3036	+	12.3036i	−0.392425	+	0.392425i	0.483126	+	0.875551i	$0.339501\pi$
$984$		−	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	0.933290	−	0.359123i	$-0.116924\pi$
$997$	18.1295	+	18.1295i	0.574167	+	0.574167i	−0.359123	+	0.933290i	$0.616924\pi$
$998$	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.64.4	yes	12
3.2	odd	2		765.2.t.e.64.3		12
5.2	odd	4		425.2.e.d.251.4		12
5.3	odd	4		425.2.e.d.251.3		12
5.4	even	2	inner	85.2.j.c.64.3	yes	12
15.14	odd	2		765.2.t.e.64.4		12
17.2	even	8		1445.2.b.f.579.8		12
17.4	even	4	inner	85.2.j.c.4.3	✓	12
17.15	even	8		1445.2.b.f.579.7		12
51.38	odd	4		765.2.t.e.514.4		12
85.2	odd	8		7225.2.a.bp.1.6		12
85.4	even	4	inner	85.2.j.c.4.4	yes	12
85.19	even	8		1445.2.b.f.579.5		12
85.32	odd	8		7225.2.a.bp.1.5		12
85.38	odd	4		425.2.e.d.276.4		12
85.49	even	8		1445.2.b.f.579.6		12
85.53	odd	8		7225.2.a.bp.1.7		12
85.72	odd	4		425.2.e.d.276.3		12
85.83	odd	8		7225.2.a.bp.1.8		12
255.89	odd	4		765.2.t.e.514.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.j.c.4.3	✓	12	17.4	even	4	inner
85.2.j.c.4.4	yes	12	85.4	even	4	inner
85.2.j.c.64.3	yes	12	5.4	even	2	inner
85.2.j.c.64.4	yes	12	1.1	even	1	trivial
425.2.e.d.251.3		12	5.3	odd	4
425.2.e.d.251.4		12	5.2	odd	4
425.2.e.d.276.3		12	85.72	odd	4
425.2.e.d.276.4		12	85.38	odd	4
765.2.t.e.64.3		12	3.2	odd	2
765.2.t.e.64.4		12	15.14	odd	2
765.2.t.e.514.3		12	255.89	odd	4
765.2.t.e.514.4		12	51.38	odd	4
1445.2.b.f.579.5		12	85.19	even	8
1445.2.b.f.579.6		12	85.49	even	8
1445.2.b.f.579.7		12	17.15	even	8
1445.2.b.f.579.8		12	17.2	even	8
7225.2.a.bp.1.5		12	85.32	odd	8
7225.2.a.bp.1.6		12	85.2	odd	8
7225.2.a.bp.1.7		12	85.53	odd	8
7225.2.a.bp.1.8		12	85.83	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} +(0.898299 + 2.04770i) q^{5} +(-0.393449 + 0.393449i) q^{6} +(1.46067 + 1.46067i) q^{7} -0.917007 q^{8} -2.73289i q^{9} +(0.208755 + 0.475863i) 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} +(-1.74809 - 3.98481i) 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} +(-0.823747 - 1.87775i) q^{40} +(7.62488 - 7.62488i) q^{41} -1.14940 q^{42} -7.45685 q^{43} +(0.660556 - 0.660556i) q^{44} +(5.59613 - 2.45496i) 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} +(8.33563 - 3.65674i) 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} +(-0.495679 - 11.9615i) q^{75} -7.78398i q^{76} -0.991630 q^{77} +(1.60162 + 1.60162i) q^{78} +(7.23143 - 7.23143i) q^{79} +(3.30474 + 7.53324i) q^{80} +9.72998 q^{81} +(1.77194 - 1.77194i) q^{82} +2.23672 q^{83} +9.62488 q^{84} +(6.84399 + 6.17736i) q^{85} -1.73289 q^{86} -2.48166 q^{87} +(0.311272 - 0.311272i) q^{88} -9.37220 q^{89} +(1.30048 - 0.570505i) q^{90} +(5.94600 - 5.94600i) q^{91} +(-11.2163 - 11.2163i) q^{92} +14.5110 q^{93} +0.837986i q^{94} +(-8.19078 + 3.59320i) 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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