LMFDB - Embedded newform 930.2.h.c.371.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(371,930)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("930.371");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.h (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} + 10x^{12} - 42x^{10} + 82x^{8} - 378x^{6} + 810x^{4} - 1458x^{2} + 6561 $ x^16 - 2x^14 + 10x^12 - 42x^10 + 82x^8 - 378x^6 + 810x^4 - 1458*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			371.5
Root			$1.71746 - 0.224352i$ of defining polynomial
Character	$\chi$	$=$	930.371
Dual form			930.2.h.c.371.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.224352 + 1.71746i) q^{3} -1.00000 q^{4} -1.00000i q^{5} +(1.71746 - 0.224352i) q^{6} -2.17181 q^{7} +1.00000i q^{8} +(-2.89933 + 0.770630i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.224352 + 1.71746i) q^{3} -1.00000 q^{4} -1.00000i q^{5} +(1.71746 - 0.224352i) q^{6} -2.17181 q^{7} +1.00000i q^{8} +(-2.89933 + 0.770630i) q^{9} -1.00000 q^{10} +3.24275 q^{11} +(-0.224352 - 1.71746i) q^{12} -4.02509i q^{13} +2.17181i q^{14} +(1.71746 - 0.224352i) q^{15} +1.00000 q^{16} -1.33949 q^{17} +(0.770630 + 2.89933i) q^{18} +5.97048 q^{19} +1.00000i q^{20} +(-0.487251 - 3.73000i) q^{21} -3.24275i q^{22} +6.67767 q^{23} +(-1.71746 + 0.224352i) q^{24} -1.00000 q^{25} -4.02509 q^{26} +(-1.97400 - 4.80659i) q^{27} +2.17181 q^{28} +4.69731 q^{29} +(-0.224352 - 1.71746i) q^{30} +(4.16811 - 3.69146i) q^{31} -1.00000i q^{32} +(0.727518 + 5.56930i) q^{33} +1.33949i q^{34} +2.17181i q^{35} +(2.89933 - 0.770630i) q^{36} -3.43492i q^{37} -5.97048i q^{38} +(6.91292 - 0.903036i) q^{39} +1.00000 q^{40} +5.45504i q^{41} +(-3.73000 + 0.487251i) q^{42} +7.95279i q^{43} -3.24275 q^{44} +(0.770630 + 2.89933i) q^{45} -6.67767i q^{46} -11.1386i q^{47} +(0.224352 + 1.71746i) q^{48} -2.28322 q^{49} +1.00000i q^{50} +(-0.300517 - 2.30052i) q^{51} +4.02509i q^{52} +11.9652 q^{53} +(-4.80659 + 1.97400i) q^{54} -3.24275i q^{55} -2.17181i q^{56} +(1.33949 + 10.2541i) q^{57} -4.69731i q^{58} +12.6010i q^{59} +(-1.71746 + 0.224352i) q^{60} +3.87700i q^{61} +(-3.69146 - 4.16811i) q^{62} +(6.29681 - 1.67367i) q^{63} -1.00000 q^{64} -4.02509 q^{65} +(5.56930 - 0.727518i) q^{66} -3.59733 q^{67} +1.33949 q^{68} +(1.49815 + 11.4686i) q^{69} +2.17181 q^{70} -8.31411i q^{71} +(-0.770630 - 2.89933i) q^{72} -14.2148i q^{73} -3.43492 q^{74} +(-0.224352 - 1.71746i) q^{75} -5.97048 q^{76} -7.04266 q^{77} +(-0.903036 - 6.91292i) q^{78} -12.4910i q^{79} -1.00000i q^{80} +(7.81226 - 4.46863i) q^{81} +5.45504 q^{82} +0.448704 q^{83} +(0.487251 + 3.73000i) q^{84} +1.33949i q^{85} +7.95279 q^{86} +(1.05385 + 8.06744i) q^{87} +3.24275i q^{88} +5.85126 q^{89} +(2.89933 - 0.770630i) q^{90} +8.74175i q^{91} -6.67767 q^{92} +(7.27505 + 6.33038i) q^{93} -11.1386 q^{94} -5.97048i q^{95} +(1.71746 - 0.224352i) q^{96} +14.7433 q^{97} +2.28322i q^{98} +(-9.40182 + 2.49896i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 20 q^{7} - 4 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 - 20 * q^7 - 4 * q^9	$ 16 q - 16 q^{4} - 20 q^{7} - 4 q^{9} - 16 q^{10} + 16 q^{16} + 12 q^{18} - 4 q^{19} - 16 q^{25} + 20 q^{28} - 4 q^{31} - 16 q^{33} + 4 q^{36} - 4 q^{39} + 16 q^{40} + 12 q^{45} + 4 q^{49} + 52 q^{51} - 12 q^{63} - 16 q^{64} + 4 q^{66} + 112 q^{67} - 4 q^{69} + 20 q^{70} - 12 q^{72} + 4 q^{76} - 28 q^{78} - 32 q^{81} + 32 q^{82} - 24 q^{87} + 4 q^{90} + 16 q^{93} - 8 q^{94} + 8 q^{97}+O(q^{100}) $ 16 * q - 16 * q^4 - 20 * q^7 - 4 * q^9 - 16 * q^10 + 16 * q^16 + 12 * q^18 - 4 * q^19 - 16 * q^25 + 20 * q^28 - 4 * q^31 - 16 * q^33 + 4 * q^36 - 4 * q^39 + 16 * q^40 + 12 * q^45 + 4 * q^49 + 52 * q^51 - 12 * q^63 - 16 * q^64 + 4 * q^66 + 112 * q^67 - 4 * q^69 + 20 * q^70 - 12 * q^72 + 4 * q^76 - 28 * q^78 - 32 * q^81 + 32 * q^82 - 24 * q^87 + 4 * q^90 + 16 * q^93 - 8 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.224352	+	1.71746i	0.129530	+	0.991576i
$3$	0.224352	+	1.71746i	0.129530	+	0.991576i
$4$	−1.00000			−0.500000
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	1.71746	−	0.224352i	0.701150	−	0.0915913i
$7$	−2.17181			−0.820869			−0.410434	−	0.911890i	$-0.634623\pi$
$7$	−2.17181			−0.820869			−0.410434	+	0.911890i	$0.634623\pi$
$8$			1.00000i			0.353553i
$9$	−2.89933	+	0.770630i	−0.966444	+	0.256877i
$10$	−1.00000			−0.316228
$11$	3.24275			0.977727			0.488863	−	0.872360i	$-0.337412\pi$
$11$	3.24275			0.977727			0.488863	+	0.872360i	$0.337412\pi$
$12$	−0.224352	−	1.71746i	−0.0647648	−	0.495788i
$13$		−	4.02509i		−	1.11636i	−0.829720	−	0.558179i	$-0.811500\pi$
$13$		−	4.02509i		−	1.11636i	0.829720	−	0.558179i	$-0.188500\pi$
$14$			2.17181i			0.580442i
$15$	1.71746	−	0.224352i	0.443446	−	0.0579274i
$16$	1.00000			0.250000
$17$	−1.33949			−0.324874			−0.162437	−	0.986719i	$-0.551935\pi$
$17$	−1.33949			−0.324874			−0.162437	+	0.986719i	$0.551935\pi$
$18$	0.770630	+	2.89933i	0.181639	+	0.683379i
$19$	5.97048			1.36972			0.684861	−	0.728674i	$-0.259863\pi$
$19$	5.97048			1.36972			0.684861	+	0.728674i	$0.259863\pi$
$20$			1.00000i			0.223607i
$21$	−0.487251	−	3.73000i	−0.106327	−	0.813953i
$22$		−	3.24275i		−	0.691357i
$23$	6.67767			1.39239			0.696195	−	0.717852i	$-0.254875\pi$
$23$	6.67767			1.39239			0.696195	+	0.717852i	$0.254875\pi$
$24$	−1.71746	+	0.224352i	−0.350575	+	0.0457956i
$25$	−1.00000			−0.200000
$26$	−4.02509			−0.789385
$27$	−1.97400	−	4.80659i	−0.379896	−	0.925029i
$28$	2.17181			0.410434
$29$	4.69731			0.872269			0.436135	−	0.899881i	$-0.356347\pi$
$29$	4.69731			0.872269			0.436135	+	0.899881i	$0.356347\pi$
$30$	−0.224352	−	1.71746i	−0.0409609	−	0.313564i
$31$	4.16811	−	3.69146i	0.748615	−	0.663005i
$31$	4.16811	−	3.69146i	0.748615	−	0.663005i
$32$		−	1.00000i		−	0.176777i
$33$	0.727518	+	5.56930i	0.126645	+	0.969490i
$34$			1.33949i			0.229720i
$35$			2.17181i			0.367104i
$36$	2.89933	−	0.770630i	0.483222	−	0.128438i
$37$		−	3.43492i		−	0.564697i	−0.959312	−	0.282349i	$-0.908887\pi$
$37$		−	3.43492i		−	0.564697i	0.959312	−	0.282349i	$-0.0911135\pi$
$38$		−	5.97048i		−	0.968540i
$39$	6.91292	−	0.903036i	1.10695	−	0.144602i
$40$	1.00000			0.158114
$41$			5.45504i			0.851933i	0.904739	+	0.425967i	$0.140066\pi$
$41$			5.45504i			0.851933i	−0.904739	+	0.425967i	$0.859934\pi$
$42$	−3.73000	+	0.487251i	−0.575552	+	0.0751844i
$43$			7.95279i			1.21279i	0.795164	+	0.606394i	$0.207385\pi$
$43$			7.95279i			1.21279i	−0.795164	+	0.606394i	$0.792615\pi$
$44$	−3.24275			−0.488863
$45$	0.770630	+	2.89933i	0.114879	+	0.432207i
$46$		−	6.67767i		−	0.984569i
$47$		−	11.1386i		−	1.62473i	−0.583149	−	0.812365i	$-0.698180\pi$
$47$		−	11.1386i		−	1.62473i	0.583149	−	0.812365i	$-0.301820\pi$
$48$	0.224352	+	1.71746i	0.0323824	+	0.247894i
$49$	−2.28322			−0.326174
$50$			1.00000i			0.141421i
$51$	−0.300517	−	2.30052i	−0.0420808	−	0.322137i
$52$			4.02509i			0.558179i
$53$	11.9652			1.64354			0.821770	−	0.569819i	$-0.192987\pi$
$53$	11.9652			1.64354			0.821770	+	0.569819i	$0.192987\pi$
$54$	−4.80659	+	1.97400i	−0.654094	+	0.268627i
$55$		−	3.24275i		−	0.437253i
$56$		−	2.17181i		−	0.290221i
$57$	1.33949	+	10.2541i	0.177420	+	1.35818i
$58$		−	4.69731i		−	0.616787i
$59$			12.6010i			1.64051i	0.571995	+	0.820257i	$0.306170\pi$
$59$			12.6010i			1.64051i	−0.571995	+	0.820257i	$0.693830\pi$
$60$	−1.71746	+	0.224352i	−0.221723	+	0.0289637i
$61$			3.87700i			0.496399i	0.968709	+	0.248199i	$0.0798388\pi$
$61$			3.87700i			0.496399i	−0.968709	+	0.248199i	$0.920161\pi$
$62$	−3.69146	−	4.16811i	−0.468815	−	0.529351i
$63$	6.29681	−	1.67367i	0.793324	−	0.210862i
$64$	−1.00000			−0.125000
$65$	−4.02509			−0.499251
$66$	5.56930	−	0.727518i	0.685533	−	0.0895512i
$67$	−3.59733			−0.439484			−0.219742	−	0.975558i	$-0.570522\pi$
$67$	−3.59733			−0.439484			−0.219742	+	0.975558i	$0.570522\pi$
$68$	1.33949			0.162437
$69$	1.49815	+	11.4686i	0.180356	+	1.38066i
$70$	2.17181			0.259582
$71$		−	8.31411i		−	0.986703i	−0.869830	−	0.493352i	$-0.835772\pi$
$71$		−	8.31411i		−	0.986703i	0.869830	−	0.493352i	$-0.164228\pi$
$72$	−0.770630	−	2.89933i	−0.0908197	−	0.341690i
$73$		−	14.2148i		−	1.66371i	−0.554991	−	0.831857i	$-0.687278\pi$
$73$		−	14.2148i		−	1.66371i	0.554991	−	0.831857i	$-0.312722\pi$
$74$	−3.43492			−0.399301
$75$	−0.224352	−	1.71746i	−0.0259059	−	0.198315i
$76$	−5.97048			−0.684861
$77$	−7.04266			−0.802585
$78$	−0.903036	−	6.91292i	−0.102249	−	0.782735i
$79$		−	12.4910i		−	1.40534i	−0.711515	−	0.702671i	$-0.751991\pi$
$79$		−	12.4910i		−	1.40534i	0.711515	−	0.702671i	$-0.248009\pi$
$80$		−	1.00000i		−	0.111803i
$81$	7.81226	−	4.46863i	0.868029	−	0.496514i
$82$	5.45504			0.602408
$83$	0.448704			0.0492516			0.0246258	−	0.999697i	$-0.492161\pi$
$83$	0.448704			0.0492516			0.0246258	+	0.999697i	$0.492161\pi$
$84$	0.487251	+	3.73000i	0.0531634	+	0.406977i
$85$			1.33949i			0.145288i
$86$	7.95279			0.857571
$87$	1.05385	+	8.06744i	0.112985	+	0.864921i
$88$			3.24275i			0.345679i
$89$	5.85126			0.620232			0.310116	−	0.950699i	$-0.399632\pi$
$89$	5.85126			0.620232			0.310116	+	0.950699i	$0.399632\pi$
$90$	2.89933	−	0.770630i	0.305616	−	0.0812316i
$91$			8.74175i			0.916384i
$92$	−6.67767			−0.696195
$93$	7.27505	+	6.33038i	0.754387	+	0.656429i
$94$	−11.1386			−1.14886
$95$		−	5.97048i		−	0.612558i
$96$	1.71746	−	0.224352i	0.175287	−	0.0228978i
$97$	14.7433			1.49696			0.748479	−	0.663158i	$-0.230784\pi$
$97$	14.7433			1.49696			0.748479	+	0.663158i	$0.230784\pi$
$98$			2.28322i			0.230640i
$99$	−9.40182	+	2.49896i	−0.944918	+	0.251155i
$100$	1.00000			0.100000
$101$			15.6540i			1.55763i	0.627251	+	0.778817i	$0.284180\pi$
$101$			15.6540i			1.55763i	−0.627251	+	0.778817i	$0.715820\pi$
$102$	−2.30052	+	0.300517i	−0.227785	+	0.0297556i
$103$	−16.0198			−1.57848			−0.789238	−	0.614088i	$-0.789524\pi$
$103$	−16.0198			−1.57848			−0.789238	+	0.614088i	$0.789524\pi$
$104$	4.02509			0.394692
$105$	−3.73000	+	0.487251i	−0.364011	+	0.0475508i
$106$		−	11.9652i		−	1.16216i
$107$		−	12.0493i		−	1.16485i	−0.812885	−	0.582425i	$-0.802104\pi$
$107$		−	12.0493i		−	1.16485i	0.812885	−	0.582425i	$-0.197896\pi$
$108$	1.97400	+	4.80659i	0.189948	+	0.462515i
$109$	−4.99630			−0.478558			−0.239279	−	0.970951i	$-0.576911\pi$
$109$	−4.99630			−0.478558			−0.239279	+	0.970951i	$0.576911\pi$
$110$	−3.24275			−0.309184
$111$	5.89933	−	0.770630i	0.559940	−	0.0731450i
$112$	−2.17181			−0.205217
$113$		−	0.745663i		−	0.0701461i	−0.999385	−	0.0350731i	$-0.988834\pi$
$113$		−	0.745663i		−	0.0701461i	0.999385	−	0.0350731i	$-0.0111664\pi$
$114$	10.2541	−	1.33949i	0.960380	−	0.125455i
$115$		−	6.67767i		−	0.622696i
$116$	−4.69731			−0.436135
$117$	3.10186	+	11.6701i	0.286767	+	1.07890i
$118$	12.6010			1.16002
$119$	2.90912			0.266679
$120$	0.224352	+	1.71746i	0.0204804	+	0.156782i
$121$	−0.484556			−0.0440505
$122$	3.87700			0.351007
$123$	−9.36880	+	1.22385i	−0.844756	+	0.110351i
$124$	−4.16811	+	3.69146i	−0.374307	+	0.331503i
$125$			1.00000i			0.0894427i
$126$	−1.67367	−	6.29681i	−0.149102	−	0.560965i
$127$			10.2871i			0.912830i	0.889767	+	0.456415i	$0.150867\pi$
$127$			10.2871i			0.912830i	−0.889767	+	0.456415i	$0.849133\pi$
$128$			1.00000i			0.0883883i
$129$	−13.6586	+	1.78422i	−1.20257	+	0.157092i
$130$			4.02509i			0.353024i
$131$		−	0.402670i		−	0.0351815i	−0.999845	−	0.0175907i	$-0.994400\pi$
$131$		−	0.402670i		−	0.0351815i	0.999845	−	0.0175907i	$-0.00559959\pi$
$132$	−0.727518	−	5.56930i	−0.0633223	−	0.484745i
$133$	−12.9668			−1.12436
$134$			3.59733i			0.310762i
$135$	−4.80659	+	1.97400i	−0.413686	+	0.169895i
$136$		−	1.33949i		−	0.114860i
$137$	−1.95396			−0.166938			−0.0834692	−	0.996510i	$-0.526600\pi$
$137$	−1.95396			−0.166938			−0.0834692	+	0.996510i	$0.526600\pi$
$138$	11.4686	−	1.49815i	0.976274	−	0.127531i
$139$		−	12.5417i		−	1.06377i	−0.846817	−	0.531884i	$-0.821484\pi$
$139$		−	12.5417i		−	1.06377i	0.846817	−	0.531884i	$-0.178516\pi$
$140$		−	2.17181i		−	0.183552i
$141$	19.1301	−	2.49896i	1.61104	−	0.210451i
$142$	−8.31411			−0.697705
$143$		−	13.0524i		−	1.09149i
$144$	−2.89933	+	0.770630i	−0.241611	+	0.0642192i
$145$		−	4.69731i		−	0.390091i
$146$	−14.2148			−1.17642
$147$	−0.512245	−	3.92134i	−0.0422492	−	0.323427i
$148$			3.43492i			0.282349i
$149$		−	0.200699i		−	0.0164419i	−0.999966	−	0.00822094i	$-0.997383\pi$
$149$		−	0.200699i		−	0.0164419i	0.999966	−	0.00822094i	$-0.00261684\pi$
$150$	−1.71746	+	0.224352i	−0.140230	+	0.0183183i
$151$		−	3.96072i		−	0.322319i	−0.986928	−	0.161159i	$-0.948477\pi$
$151$		−	3.96072i		−	0.322319i	0.986928	−	0.161159i	$-0.0515233\pi$
$152$			5.97048i			0.484270i
$153$	3.88362	−	1.03225i	0.313972	−	0.0834525i
$154$			7.04266i			0.567514i
$155$	−3.69146	−	4.16811i	−0.296505	−	0.334791i
$156$	−6.91292	+	0.903036i	−0.553477	+	0.0723008i
$157$	−21.9903			−1.75501			−0.877507	−	0.479564i	$-0.840795\pi$
$157$	−21.9903			−1.75501			−0.877507	+	0.479564i	$0.840795\pi$
$158$	−12.4910			−0.993727
$159$	2.68440	+	20.5497i	0.212887	+	1.62969i
$160$	−1.00000			−0.0790569
$161$	−14.5027			−1.14297
$162$	−4.46863	−	7.81226i	−0.351089	−	0.613789i
$163$	−16.2846			−1.27551			−0.637754	−	0.770240i	$-0.720136\pi$
$163$	−16.2846			−1.27551			−0.637754	+	0.770240i	$0.720136\pi$
$164$		−	5.45504i		−	0.425967i
$165$	5.56930	−	0.727518i	0.433569	−	0.0566372i
$166$		−	0.448704i		−	0.0348262i
$167$	−8.85682			−0.685361			−0.342681	−	0.939452i	$-0.611335\pi$
$167$	−8.85682			−0.685361			−0.342681	+	0.939452i	$0.611335\pi$
$168$	3.73000	−	0.487251i	0.287776	−	0.0375922i
$169$	−3.20134			−0.246257
$170$	1.33949			0.102734
$171$	−17.3104	+	4.60103i	−1.32376	+	0.351850i
$172$		−	7.95279i		−	0.606394i
$173$			3.60474i			0.274063i	0.990567	+	0.137032i	$0.0437562\pi$
$173$			3.60474i			0.274063i	−0.990567	+	0.137032i	$0.956244\pi$
$174$	8.06744	−	1.05385i	0.611591	−	0.0798922i
$175$	2.17181			0.164174
$176$	3.24275			0.244432
$177$	−21.6418	+	2.82707i	−1.62669	+	0.212495i
$178$		−	5.85126i		−	0.438570i
$179$	20.0017			1.49499			0.747497	−	0.664265i	$-0.231255\pi$
$179$	20.0017			1.49499			0.747497	+	0.664265i	$0.231255\pi$
$180$	−0.770630	−	2.89933i	−0.0574394	−	0.216103i
$181$			13.0988i			0.973626i	0.873506	+	0.486813i	$0.161841\pi$
$181$			13.0988i			0.973626i	−0.873506	+	0.486813i	$0.838159\pi$
$182$	8.74175			0.647981
$183$	−6.65859	+	0.869812i	−0.492217	+	0.0642984i
$184$			6.67767i			0.492284i
$185$	−3.43492			−0.252540
$186$	6.33038	−	7.27505i	0.464166	−	0.533433i
$187$	−4.34363			−0.317638
$188$			11.1386i			0.812365i
$189$	4.28716	+	10.4390i	0.311845	+	0.759328i
$190$	−5.97048			−0.433144
$191$			0.201335i			0.0145681i	0.999973	+	0.00728405i	$0.00231860\pi$
$191$			0.201335i			0.0145681i	−0.999973	+	0.00728405i	$0.997681\pi$
$192$	−0.224352	−	1.71746i	−0.0161912	−	0.123947i
$193$	−21.6761			−1.56028			−0.780142	−	0.625603i	$-0.784853\pi$
$193$	−21.6761			−1.56028			−0.780142	+	0.625603i	$0.784853\pi$
$194$		−	14.7433i		−	1.05851i
$195$	−0.903036	−	6.91292i	−0.0646678	−	0.495045i
$196$	2.28322			0.163087
$197$	10.8949			0.776231			0.388116	−	0.921611i	$-0.373126\pi$
$197$	10.8949			0.776231			0.388116	+	0.921611i	$0.373126\pi$
$198$	2.49896	+	9.40182i	0.177594	+	0.668158i
$199$			18.1804i			1.28878i	0.764698	+	0.644389i	$0.222888\pi$
$199$			18.1804i			1.28878i	−0.764698	+	0.644389i	$0.777112\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	−0.807068	−	6.17827i	−0.0569262	−	0.435781i
$202$	15.6540			1.10141
$203$	−10.2017			−0.716019
$204$	0.300517	+	2.30052i	0.0210404	+	0.161068i
$205$	5.45504			0.380996
$206$			16.0198i			1.11615i
$207$	−19.3608	+	5.14602i	−1.34567	+	0.357673i
$208$		−	4.02509i		−	0.279090i
$209$	19.3608			1.33921
$210$	0.487251	+	3.73000i	0.0336235	+	0.257395i
$211$	18.4853			1.27258			0.636290	−	0.771450i	$-0.280468\pi$
$211$	18.4853			1.27258			0.636290	+	0.771450i	$0.280468\pi$
$212$	−11.9652			−0.821770
$213$	14.2791	−	1.86529i	0.978391	−	0.127807i
$214$	−12.0493			−0.823673
$215$	7.95279			0.542376
$216$	4.80659	−	1.97400i	0.327047	−	0.134313i
$217$	−9.05237	+	8.01716i	−0.614515	+	0.544240i
$218$			4.99630i			0.338392i
$219$	24.4133	−	3.18911i	1.64970	−	0.215500i
$220$			3.24275i			0.218626i
$221$			5.39156i			0.362676i
$222$	−0.770630	−	5.89933i	−0.0517213	−	0.395937i
$223$			16.9895i			1.13770i	0.822441	+	0.568850i	$0.192611\pi$
$223$			16.9895i			1.13770i	−0.822441	+	0.568850i	$0.807389\pi$
$224$			2.17181i			0.145110i
$225$	2.89933	−	0.770630i	0.193289	−	0.0513754i
$226$	−0.745663			−0.0496008
$227$		−	15.7057i		−	1.04242i	−0.853428	−	0.521211i	$-0.825480\pi$
$227$		−	15.7057i		−	1.04242i	0.853428	−	0.521211i	$-0.174520\pi$
$228$	−1.33949	−	10.2541i	−0.0887098	−	0.679091i
$229$		−	2.41138i		−	0.159348i	−0.996821	−	0.0796742i	$-0.974612\pi$
$229$		−	2.41138i		−	0.159348i	0.996821	−	0.0796742i	$-0.0253880\pi$
$230$	−6.67767			−0.440313
$231$	−1.58003	−	12.0955i	−0.103959	−	0.795824i
$232$			4.69731i			0.308394i
$233$			28.3974i			1.86037i	0.367087	+	0.930187i	$0.380355\pi$
$233$			28.3974i			1.86037i	−0.367087	+	0.930187i	$0.619645\pi$
$234$	11.6701	−	3.10186i	0.762896	−	0.202775i
$235$	−11.1386			−0.726602
$236$		−	12.6010i		−	0.820257i
$237$	21.4527	−	2.80237i	1.39350	−	0.182033i
$238$		−	2.90912i		−	0.188570i
$239$	7.89599			0.510749			0.255375	−	0.966842i	$-0.417801\pi$
$239$	7.89599			0.510749			0.255375	+	0.966842i	$0.417801\pi$
$240$	1.71746	−	0.224352i	0.110862	−	0.0144819i
$241$		−	1.05160i		−	0.0677392i	−0.999426	−	0.0338696i	$-0.989217\pi$
$241$		−	1.05160i		−	0.0677392i	0.999426	−	0.0338696i	$-0.0107831\pi$
$242$			0.484556i			0.0311484i
$243$	9.42738	+	12.4147i	0.604767	+	0.796403i
$244$		−	3.87700i		−	0.248199i
$245$			2.28322i			0.145870i
$246$	1.22385	+	9.36880i	0.0780297	+	0.597333i
$247$		−	24.0317i		−	1.52910i
$248$	3.69146	+	4.16811i	0.234408	+	0.264675i
$249$	0.100668	+	0.770630i	0.00637955	+	0.0488367i
$250$	1.00000			0.0632456
$251$	0.199215			0.0125743			0.00628717	−	0.999980i	$-0.497999\pi$
$251$	0.199215			0.0125743			0.00628717	+	0.999980i	$0.497999\pi$
$252$	−6.29681	+	1.67367i	−0.396662	+	0.105431i
$253$	21.6540			1.36138
$254$	10.2871			0.645468
$255$	−2.30052	+	0.300517i	−0.144064	+	0.0188191i
$256$	1.00000			0.0625000
$257$			10.4853i			0.654054i	0.945015	+	0.327027i	$0.106047\pi$
$257$			10.4853i			0.654054i	−0.945015	+	0.327027i	$0.893953\pi$
$258$	1.78422	+	13.6586i	0.111081	+	0.850347i
$259$			7.46001i			0.463542i
$260$	4.02509			0.249625
$261$	−13.6191	+	3.61989i	−0.842999	+	0.224066i
$262$	−0.402670			−0.0248770
$263$	29.2305			1.80243			0.901215	−	0.433372i	$-0.142676\pi$
$263$	29.2305			1.80243			0.901215	+	0.433372i	$0.142676\pi$
$264$	−5.56930	+	0.727518i	−0.342766	+	0.0447756i
$265$		−	11.9652i		−	0.735014i
$266$			12.9668i			0.795044i
$267$	1.31274	+	10.0493i	0.0803384	+	0.615007i
$268$	3.59733			0.219742
$269$	−10.9010			−0.664647			−0.332324	−	0.943165i	$-0.607833\pi$
$269$	−10.9010			−0.664647			−0.332324	+	0.943165i	$0.607833\pi$
$270$	1.97400	+	4.80659i	0.120134	+	0.292520i
$271$		−	1.17277i		−	0.0712405i	−0.999365	−	0.0356202i	$-0.988659\pi$
$271$		−	1.17277i		−	0.0712405i	0.999365	−	0.0356202i	$-0.0113407\pi$
$272$	−1.33949			−0.0812184
$273$	−15.0136	+	1.96123i	−0.908664	+	0.118699i
$274$			1.95396i			0.118043i
$275$	−3.24275			−0.195545
$276$	−1.49815	−	11.4686i	−0.0901779	−	0.690330i
$277$			20.4570i			1.22914i	0.788862	+	0.614571i	$0.210671\pi$
$277$			20.4570i			1.22914i	−0.788862	+	0.614571i	$0.789329\pi$
$278$	−12.5417			−0.752198
$279$	−9.23999	+	13.9148i	−0.553184	+	0.833059i
$280$	−2.17181			−0.129791
$281$			16.6799i			0.995037i	0.867454	+	0.497518i	$0.165755\pi$
$281$			16.6799i			0.995037i	−0.867454	+	0.497518i	$0.834245\pi$
$282$	−2.49896	−	19.1301i	−0.148811	−	1.13918i
$283$	−1.64896			−0.0980207			−0.0490103	−	0.998798i	$-0.515607\pi$
$283$	−1.64896			−0.0980207			−0.0490103	+	0.998798i	$0.515607\pi$
$284$			8.31411i			0.493352i
$285$	10.2541	−	1.33949i	0.607398	−	0.0793444i
$286$	−13.0524			−0.771803
$287$		−	11.8473i		−	0.699326i
$288$	0.770630	+	2.89933i	0.0454098	+	0.170845i
$289$	−15.2058			−0.894457
$290$	−4.69731			−0.275836
$291$	3.30769	+	25.3211i	0.193900	+	1.48435i
$292$			14.2148i			0.831857i
$293$		−	12.2920i		−	0.718106i	−0.933317	−	0.359053i	$-0.883100\pi$
$293$		−	12.2920i		−	0.718106i	0.933317	−	0.359053i	$-0.116900\pi$
$294$	−3.92134	+	0.512245i	−0.228697	+	0.0298747i
$295$	12.6010			0.733661
$296$	3.43492			0.199651
$297$	−6.40118	−	15.5866i	−0.371434	−	0.904426i
$298$	−0.200699			−0.0116262
$299$		−	26.8782i		−	1.55441i
$300$	0.224352	+	1.71746i	0.0129530	+	0.0991576i
$301$		−	17.2720i		−	0.995540i
$302$	−3.96072			−0.227914
$303$	−26.8852	+	3.51201i	−1.54451	+	0.201760i
$304$	5.97048			0.342430
$305$	3.87700			0.221996
$306$	−1.03225	−	3.88362i	−0.0590098	−	0.222012i
$307$	2.56644			0.146475			0.0732373	−	0.997315i	$-0.476667\pi$
$307$	2.56644			0.146475			0.0732373	+	0.997315i	$0.476667\pi$
$308$	7.04266			0.401293
$309$	−3.59407	−	27.5133i	−0.204459	−	1.56518i
$310$	−4.16811	+	3.69146i	−0.236733	+	0.209661i
$311$			3.68356i			0.208875i	0.994531	+	0.104438i	$0.0333043\pi$
$311$			3.68356i			0.208875i	−0.994531	+	0.104438i	$0.966696\pi$
$312$	0.903036	+	6.91292i	0.0511244	+	0.391367i
$313$			3.51864i			0.198885i	0.995043	+	0.0994425i	$0.0317059\pi$
$313$			3.51864i			0.198885i	−0.995043	+	0.0994425i	$0.968294\pi$
$314$			21.9903i			1.24098i
$315$	−1.67367	−	6.29681i	−0.0943004	−	0.354785i
$316$			12.4910i			0.702671i
$317$		−	20.4496i		−	1.14857i	−0.818657	−	0.574283i	$-0.805281\pi$
$317$		−	20.4496i		−	1.14857i	0.818657	−	0.574283i	$-0.194719\pi$
$318$	20.5497	−	2.68440i	1.15237	−	0.150534i
$319$	15.2322			0.852841
$320$			1.00000i			0.0559017i
$321$	20.6942	−	2.70328i	1.15504	−	0.150883i
$322$			14.5027i			0.808202i
$323$	−7.99739			−0.444987
$324$	−7.81226	+	4.46863i	−0.434014	+	0.248257i
$325$			4.02509i			0.223272i
$326$			16.2846i			0.901920i
$327$	−1.12093	−	8.58094i	−0.0619875	−	0.474527i
$328$	−5.45504			−0.301204
$329$			24.1910i			1.33369i
$330$	−0.727518	−	5.56930i	−0.0400485	−	0.306580i
$331$			10.0442i			0.552080i	0.961146	+	0.276040i	$0.0890221\pi$
$331$			10.0442i			0.552080i	−0.961146	+	0.276040i	$0.910978\pi$
$332$	−0.448704			−0.0246258
$333$	2.64705	+	9.95897i	0.145058	+	0.545748i
$334$			8.85682i			0.484624i
$335$			3.59733i			0.196543i
$336$	−0.487251	−	3.73000i	−0.0265817	−	0.203488i
$337$			8.27536i			0.450788i	0.974268	+	0.225394i	$0.0723669\pi$
$337$			8.27536i			0.450788i	−0.974268	+	0.225394i	$0.927633\pi$
$338$			3.20134i			0.174130i
$339$	1.28065	−	0.167291i	0.0695552	−	0.00908600i
$340$		−	1.33949i		−	0.0726440i
$341$	13.5162	−	11.9705i	0.731941	−	0.648238i
$342$	4.60103	+	17.3104i	0.248795	+	0.936040i
$343$	20.1614			1.08862
$344$	−7.95279			−0.428786
$345$	11.4686	−	1.49815i	0.617450	−	0.0806576i
$346$	3.60474			0.193792
$347$	−29.5201			−1.58472			−0.792360	−	0.610054i	$-0.791148\pi$
$347$	−29.5201			−1.58472			−0.792360	+	0.610054i	$0.791148\pi$
$348$	−1.05385	−	8.06744i	−0.0564923	−	0.432460i
$349$	28.5074			1.52597			0.762983	−	0.646418i	$-0.223734\pi$
$349$	28.5074			1.52597			0.762983	+	0.646418i	$0.223734\pi$
$350$		−	2.17181i		−	0.116088i
$351$	−19.3470	+	7.94551i	−1.03266	+	0.424100i
$352$		−	3.24275i		−	0.172839i
$353$	−30.5123			−1.62400			−0.812002	−	0.583655i	$-0.801622\pi$
$353$	−30.5123			−1.62400			−0.812002	+	0.583655i	$0.801622\pi$
$354$	2.82707	+	21.6418i	0.150257	+	1.15025i
$355$	−8.31411			−0.441267
$356$	−5.85126			−0.310116
$357$	0.652667	+	4.99630i	0.0345428	+	0.264432i
$358$		−	20.0017i		−	1.05712i
$359$		−	12.2778i		−	0.647998i	−0.946057	−	0.323999i	$-0.894972\pi$
$359$		−	12.2778i		−	0.647998i	0.946057	−	0.323999i	$-0.105028\pi$
$360$	−2.89933	+	0.770630i	−0.152808	+	0.0406158i
$361$	16.6466			0.876138
$362$	13.0988			0.688458
$363$	−0.108711	−	0.832205i	−0.00570585	−	0.0436794i
$364$		−	8.74175i		−	0.458192i
$365$	−14.2148			−0.744035
$366$	0.869812	+	6.65859i	0.0454658	+	0.348050i
$367$		−	25.2698i		−	1.31907i	−0.751673	−	0.659536i	$-0.770753\pi$
$367$		−	25.2698i		−	1.31907i	0.751673	−	0.659536i	$-0.229247\pi$
$368$	6.67767			0.348098
$369$	−4.20382	−	15.8160i	−0.218842	−	0.823346i
$370$			3.43492i			0.178573i
$371$	−25.9861			−1.34913
$372$	−7.27505	−	6.33038i	−0.377194	−	0.328215i
$373$	6.57892			0.340644			0.170322	−	0.985388i	$-0.445519\pi$
$373$	6.57892			0.340644			0.170322	+	0.985388i	$0.445519\pi$
$374$			4.34363i			0.224604i
$375$	−1.71746	+	0.224352i	−0.0886892	+	0.0115855i
$376$	11.1386			0.574429
$377$		−	18.9071i		−	0.973765i
$378$	10.4390	−	4.28716i	0.536926	−	0.220508i
$379$	6.44456			0.331035			0.165517	−	0.986207i	$-0.447071\pi$
$379$	6.44456			0.331035			0.165517	+	0.986207i	$0.447071\pi$
$380$			5.97048i			0.306279i
$381$	−17.6676	+	2.30792i	−0.905140	+	0.118239i
$382$	0.201335			0.0103012
$383$	−30.1147			−1.53879			−0.769394	−	0.638775i	$-0.779442\pi$
$383$	−30.1147			−1.53879			−0.769394	+	0.638775i	$0.779442\pi$
$384$	−1.71746	+	0.224352i	−0.0876437	+	0.0114489i
$385$			7.04266i			0.358927i
$386$			21.6761i			1.10329i
$387$	−6.12866	−	23.0578i	−0.311537	−	1.17209i
$388$	−14.7433			−0.748479
$389$	13.0547			0.661901			0.330950	−	0.943648i	$-0.392631\pi$
$389$	13.0547			0.661901			0.330950	+	0.943648i	$0.392631\pi$
$390$	−6.91292	+	0.903036i	−0.350050	+	0.0457270i
$391$	−8.94466			−0.452351
$392$		−	2.28322i		−	0.115320i
$393$	0.691570	−	0.0903398i	0.0348851	−	0.00455704i
$394$		−	10.8949i		−	0.548878i
$395$	−12.4910			−0.628488
$396$	9.40182	−	2.49896i	0.472459	−	0.125578i
$397$	10.4520			0.524569			0.262285	−	0.964991i	$-0.415524\pi$
$397$	10.4520			0.524569			0.262285	+	0.964991i	$0.415524\pi$
$398$	18.1804			0.911304
$399$	−2.90912	−	22.2699i	−0.145638	−	1.11489i
$400$	−1.00000			−0.0500000
$401$	10.4000			0.519349			0.259675	−	0.965696i	$-0.416385\pi$
$401$	10.4000			0.519349			0.259675	+	0.965696i	$0.416385\pi$
$402$	−6.17827	+	0.807068i	−0.308144	+	0.0402529i
$403$	−14.8584	−	16.7770i	−0.740151	−	0.835723i
$404$		−	15.6540i		−	0.778817i
$405$	−4.46863	−	7.81226i	−0.222048	−	0.388194i
$406$			10.2017i			0.506302i
$407$		−	11.1386i		−	0.552119i
$408$	2.30052	−	0.300517i	0.113893	−	0.0148778i
$409$			5.45935i			0.269948i	0.990849	+	0.134974i	$0.0430950\pi$
$409$			5.45935i			0.269948i	−0.990849	+	0.134974i	$0.956905\pi$
$410$		−	5.45504i		−	0.269405i
$411$	−0.438376	−	3.35585i	−0.0216235	−	0.165532i
$412$	16.0198			0.789238
$413$		−	27.3671i		−	1.34665i
$414$	5.14602	+	19.3608i	0.252913	+	0.951531i
$415$		−	0.448704i		−	0.0220260i
$416$	−4.02509			−0.197346
$417$	21.5398	−	2.81374i	1.05481	−	0.137790i
$418$		−	19.3608i		−	0.946967i
$419$		−	27.7379i		−	1.35509i	−0.735483	−	0.677543i	$-0.763045\pi$
$419$		−	27.7379i		−	1.35509i	0.735483	−	0.677543i	$-0.236955\pi$
$420$	3.73000	−	0.487251i	0.182006	−	0.0237754i
$421$	−26.7994			−1.30612			−0.653061	−	0.757305i	$-0.726516\pi$
$421$	−26.7994			−1.30612			−0.653061	+	0.757305i	$0.726516\pi$
$422$		−	18.4853i		−	0.899850i
$423$	8.58374	+	32.2945i	0.417356	+	1.57021i
$424$			11.9652i			0.581079i
$425$	1.33949			0.0649747
$426$	−1.86529	−	14.2791i	−0.0903734	−	0.691827i
$427$		−	8.42012i		−	0.407478i
$428$			12.0493i			0.582425i
$429$	22.4169	−	2.92832i	1.08230	−	0.141381i
$430$		−	7.95279i		−	0.383517i
$431$			3.88489i			0.187129i	0.995613	+	0.0935643i	$0.0298261\pi$
$431$			3.88489i			0.187129i	−0.995613	+	0.0935643i	$0.970174\pi$
$432$	−1.97400	−	4.80659i	−0.0949740	−	0.231257i
$433$		−	11.2529i		−	0.540778i	−0.962751	−	0.270389i	$-0.912848\pi$
$433$		−	11.2529i		−	0.540778i	0.962751	−	0.270389i	$-0.0871523\pi$
$434$	8.01716	+	9.05237i	0.384836	+	0.434527i
$435$	8.06744	−	1.05385i	0.386804	−	0.0505283i
$436$	4.99630			0.239279
$437$	39.8689			1.90719
$438$	−3.18911	−	24.4133i	−0.152382	−	1.16651i
$439$	16.6164			0.793056			0.396528	−	0.918023i	$-0.370215\pi$
$439$	16.6164			0.793056			0.396528	+	0.918023i	$0.370215\pi$
$440$	3.24275			0.154592
$441$	6.61982	−	1.75952i	0.315229	−	0.0837866i
$442$	5.39156			0.256450
$443$		−	3.36204i		−	0.159735i	−0.996805	−	0.0798676i	$-0.974550\pi$
$443$		−	3.36204i		−	0.159735i	0.996805	−	0.0798676i	$-0.0254498\pi$
$444$	−5.89933	+	0.770630i	−0.279970	+	0.0365725i
$445$		−	5.85126i		−	0.277376i
$446$	16.9895			0.804475
$447$	0.344692	−	0.0450271i	0.0163034	−	0.00212971i
$448$	2.17181			0.102609
$449$	8.98295			0.423932			0.211966	−	0.977277i	$-0.432013\pi$
$449$	8.98295			0.423932			0.211966	+	0.977277i	$0.432013\pi$
$450$	−0.770630	−	2.89933i	−0.0363279	−	0.136676i
$451$			17.6893i			0.832958i
$452$			0.745663i			0.0350731i
$453$	6.80237	−	0.888594i	0.319603	−	0.0417498i
$454$	−15.7057			−0.737104
$455$	8.74175			0.409819
$456$	−10.2541	+	1.33949i	−0.480190	+	0.0627273i
$457$		−	21.8476i		−	1.02199i	−0.859584	−	0.510994i	$-0.829278\pi$
$457$		−	21.8476i		−	1.02199i	0.859584	−	0.510994i	$-0.170722\pi$
$458$	−2.41138			−0.112676
$459$	2.64415	+	6.43838i	0.123418	+	0.300518i
$460$			6.67767i			0.311348i
$461$	−16.0166			−0.745969			−0.372985	−	0.927838i	$-0.621666\pi$
$461$	−16.0166			−0.745969			−0.372985	+	0.927838i	$0.621666\pi$
$462$	−12.0955	+	1.58003i	−0.562733	+	0.0735098i
$463$			16.3609i			0.760356i	0.924913	+	0.380178i	$0.124137\pi$
$463$			16.3609i			0.760356i	−0.924913	+	0.380178i	$0.875863\pi$
$464$	4.69731			0.218067
$465$	6.33038	−	7.27505i	0.293564	−	0.337372i
$466$	28.3974			1.31548
$467$		−	8.38786i		−	0.388144i	−0.980987	−	0.194072i	$-0.937831\pi$
$467$		−	8.38786i		−	0.388144i	0.980987	−	0.194072i	$-0.0621695\pi$
$468$	−3.10186	−	11.6701i	−0.143383	−	0.539449i
$469$	7.81273			0.360759
$470$			11.1386i			0.513785i
$471$	−4.93356	−	37.7674i	−0.227326	−	1.74023i
$472$	−12.6010			−0.580010
$473$			25.7889i			1.18578i
$474$	−2.80237	−	21.4527i	−0.128717	−	0.985355i
$475$	−5.97048			−0.273944
$476$	−2.90912			−0.133339
$477$	−34.6910	+	9.22071i	−1.58839	+	0.422187i
$478$		−	7.89599i		−	0.361154i
$479$			2.14293i			0.0979130i	0.998801	+	0.0489565i	$0.0155896\pi$
$479$			2.14293i			0.0979130i	−0.998801	+	0.0489565i	$0.984410\pi$
$480$	−0.224352	−	1.71746i	−0.0102402	−	0.0783909i
$481$	−13.8258			−0.630404
$482$	−1.05160			−0.0478989
$483$	−3.25370	−	24.9077i	−0.148048	−	1.13334i
$484$	0.484556			0.0220253
$485$		−	14.7433i		−	0.669460i
$486$	12.4147	−	9.42738i	0.563142	−	0.427635i
$487$		−	4.04496i		−	0.183294i	−0.995792	−	0.0916472i	$-0.970787\pi$
$487$		−	4.04496i		−	0.183294i	0.995792	−	0.0916472i	$-0.0292132\pi$
$488$	−3.87700			−0.175504
$489$	−3.65348	−	27.9681i	−0.165216	−	1.26476i
$490$	2.28322			0.103145
$491$	−29.2751			−1.32117			−0.660584	−	0.750752i	$-0.729691\pi$
$491$	−29.2751			−1.32117			−0.660584	+	0.750752i	$0.729691\pi$
$492$	9.36880	−	1.22385i	0.422378	−	0.0551753i
$493$	−6.29200			−0.283377
$494$	−24.0317			−1.08124
$495$	2.49896	+	9.40182i	0.112320	+	0.422580i
$496$	4.16811	−	3.69146i	0.187154	−	0.165751i
$497$			18.0567i			0.809954i
$498$	0.770630	−	0.100668i	0.0345328	−	0.00451102i
$499$		−	24.7683i		−	1.10878i	−0.832256	−	0.554391i	$-0.812951\pi$
$499$		−	24.7683i		−	1.10878i	0.832256	−	0.554391i	$-0.187049\pi$
$500$		−	1.00000i		−	0.0447214i
$501$	−1.98704	−	15.2112i	−0.0887746	−	0.679587i
$502$		−	0.199215i		−	0.00889140i
$503$			30.3695i			1.35411i	0.735932	+	0.677055i	$0.236744\pi$
$503$			30.3695i			1.35411i	−0.735932	+	0.677055i	$0.763256\pi$
$504$	1.67367	+	6.29681i	0.0745510	+	0.280482i
$505$	15.6540			0.696595
$506$		−	21.6540i		−	0.962639i
$507$	−0.718226	−	5.49816i	−0.0318975	−	0.244182i
$508$		−	10.2871i		−	0.456415i
$509$	−3.28902			−0.145783			−0.0728915	−	0.997340i	$-0.523223\pi$
$509$	−3.28902			−0.145783			−0.0728915	+	0.997340i	$0.523223\pi$
$510$	0.300517	+	2.30052i	0.0133071	+	0.101869i
$511$			30.8719i			1.36569i
$512$		−	1.00000i		−	0.0441942i
$513$	−11.7857	−	28.6977i	−0.520352	−	1.26703i
$514$	10.4853			0.462486
$515$			16.0198i			0.705916i
$516$	13.6586	−	1.78422i	0.601286	−	0.0785460i
$517$		−	36.1197i		−	1.58854i
$518$	7.46001			0.327774
$519$	−6.19099	+	0.808730i	−0.271754	+	0.0354993i
$520$		−	4.02509i		−	0.176512i
$521$			11.3597i			0.497678i	0.968545	+	0.248839i	$0.0800489\pi$
$521$			11.3597i			0.497678i	−0.968545	+	0.248839i	$0.919951\pi$
$522$	3.61989	+	13.6191i	0.158438	+	0.596091i
$523$			7.82594i			0.342205i	0.985253	+	0.171102i	$0.0547329\pi$
$523$			7.82594i			0.342205i	−0.985253	+	0.171102i	$0.945267\pi$
$524$			0.402670i			0.0175907i
$525$	0.487251	+	3.73000i	0.0212654	+	0.162791i
$526$		−	29.2305i		−	1.27451i
$527$	−5.58314	+	4.94466i	−0.243205	+	0.215393i
$528$	0.727518	+	5.56930i	0.0316611	+	0.242372i
$529$	21.5913			0.938752
$530$	−11.9652			−0.519733
$531$	−9.71074	−	36.5346i	−0.421410	−	1.58547i
$532$	12.9668			0.562181
$533$	21.9570			0.951063
$534$	10.0493	−	1.31274i	0.434876	−	0.0568079i
$535$	−12.0493			−0.520937
$536$		−	3.59733i		−	0.155381i
$537$	4.48741	+	34.3520i	0.193646	+	1.48240i
$538$			10.9010i			0.469977i
$539$	−7.40392			−0.318909
$540$	4.80659	−	1.97400i	0.206843	−	0.0849473i
$541$	−0.264811			−0.0113851			−0.00569257	−	0.999984i	$-0.501812\pi$
$541$	−0.264811			−0.0113851			−0.00569257	+	0.999984i	$0.501812\pi$
$542$	−1.17277			−0.0503746
$543$	−22.4967	+	2.93874i	−0.965424	+	0.126113i
$544$			1.33949i			0.0574301i
$545$			4.99630i			0.214018i
$546$	1.96123	+	15.0136i	0.0839328	+	0.642522i
$547$	33.4718			1.43115			0.715576	−	0.698535i	$-0.246164\pi$
$547$	33.4718			1.43115			0.715576	+	0.698535i	$0.246164\pi$
$548$	1.95396			0.0834692
$549$	−2.98773	−	11.2407i	−0.127513	−	0.479742i
$550$			3.24275i			0.138271i
$551$	28.0452			1.19477
$552$	−11.4686	+	1.49815i	−0.488137	+	0.0637654i
$553$			27.1280i			1.15360i
$554$	20.4570			0.869134
$555$	−0.770630	−	5.89933i	−0.0327114	−	0.250413i
$556$			12.5417i			0.531884i
$557$	3.68702			0.156224			0.0781120	−	0.996945i	$-0.475111\pi$
$557$	3.68702			0.156224			0.0781120	+	0.996945i	$0.475111\pi$
$558$	13.9148	+	9.23999i	0.589062	+	0.391160i
$559$	32.0107			1.35391
$560$			2.17181i			0.0917759i
$561$	−0.974502	−	7.46001i	−0.0411435	−	0.314962i
$562$	16.6799			0.703597
$563$		−	31.6517i		−	1.33396i	−0.745076	−	0.666980i	$-0.767587\pi$
$563$		−	31.6517i		−	1.33396i	0.745076	−	0.666980i	$-0.232413\pi$
$564$	−19.1301	+	2.49896i	−0.805521	+	0.105225i
$565$	−0.745663			−0.0313703
$566$			1.64896i			0.0693111i
$567$	−16.9668	+	9.70503i	−0.712538	+	0.407573i
$568$	8.31411			0.348852
$569$	5.81067			0.243596			0.121798	−	0.992555i	$-0.461134\pi$
$569$	5.81067			0.243596			0.121798	+	0.992555i	$0.461134\pi$
$570$	−1.33949	−	10.2541i	−0.0561050	−	0.429495i
$571$			41.7528i			1.74730i	0.486554	+	0.873651i	$0.338254\pi$
$571$			41.7528i			1.74730i	−0.486554	+	0.873651i	$0.661746\pi$
$572$			13.0524i			0.545747i
$573$	−0.345785	+	0.0451699i	−0.0144454	+	0.00188700i
$574$	−11.8473			−0.494498
$575$	−6.67767			−0.278478
$576$	2.89933	−	0.770630i	0.120806	−	0.0321096i
$577$	7.66081			0.318924			0.159462	−	0.987204i	$-0.449024\pi$
$577$	7.66081			0.318924			0.159462	+	0.987204i	$0.449024\pi$
$578$			15.2058i			0.632477i
$579$	−4.86308	−	37.2279i	−0.202103	−	1.54714i
$580$			4.69731i			0.195045i
$581$	−0.974502			−0.0404291
$582$	25.3211	−	3.30769i	1.04959	−	0.137108i
$583$	38.8000			1.60693
$584$	14.2148			0.588211
$585$	11.6701	−	3.10186i	0.482498	−	0.128246i
$586$	−12.2920			−0.507778
$587$	10.8532			0.447959			0.223980	−	0.974594i	$-0.428095\pi$
$587$	10.8532			0.447959			0.223980	+	0.974594i	$0.428095\pi$
$588$	0.512245	+	3.92134i	0.0211246	+	0.161713i
$589$	24.8856	−	22.0398i	1.02539	−	0.908133i
$590$		−	12.6010i		−	0.518776i
$591$	2.44430	+	18.7116i	0.100545	+	0.769692i
$592$		−	3.43492i		−	0.141174i
$593$		−	9.99703i		−	0.410529i	−0.978707	−	0.205264i	$-0.934195\pi$
$593$		−	9.99703i		−	0.410529i	0.978707	−	0.205264i	$-0.0658054\pi$
$594$	−15.5866	+	6.40118i	−0.639526	+	0.262644i
$595$		−	2.90912i		−	0.119262i
$596$			0.200699i			0.00822094i
$597$	−31.2242	+	4.07882i	−1.27792	+	0.166935i
$598$	−26.8782			−1.09913
$599$			16.6350i			0.679687i	0.940482	+	0.339844i	$0.110374\pi$
$599$			16.6350i			0.679687i	−0.940482	+	0.339844i	$0.889626\pi$
$600$	1.71746	−	0.224352i	0.0701150	−	0.00915913i
$601$			20.2506i			0.826040i	0.910722	+	0.413020i	$0.135526\pi$
$601$			20.2506i			0.826040i	−0.910722	+	0.413020i	$0.864474\pi$
$602$	−17.2720			−0.703953
$603$	10.4299	−	2.77221i	0.424737	−	0.112893i
$604$			3.96072i			0.161159i
$605$			0.484556i			0.0197000i
$606$	3.51201	+	26.8852i	0.142666	+	1.09214i
$607$	−12.9668			−0.526305			−0.263153	−	0.964754i	$-0.584762\pi$
$607$	−12.9668			−0.526305			−0.263153	+	0.964754i	$0.584762\pi$
$608$		−	5.97048i		−	0.242135i
$609$	−2.28877	−	17.5210i	−0.0927456	−	0.709986i
$610$		−	3.87700i		−	0.156975i
$611$	−44.8338			−1.81378
$612$	−3.88362	+	1.03225i	−0.156986	+	0.0417263i
$613$			36.3482i			1.46809i	0.679101	+	0.734044i	$0.262370\pi$
$613$			36.3482i			1.46809i	−0.679101	+	0.734044i	$0.737630\pi$
$614$		−	2.56644i		−	0.103573i
$615$	1.22385	+	9.36880i	0.0493503	+	0.377787i
$616$		−	7.04266i		−	0.283757i
$617$			6.91241i			0.278283i	0.990273	+	0.139141i	$0.0444343\pi$
$617$			6.91241i			0.278283i	−0.990273	+	0.139141i	$0.955566\pi$
$618$	−27.5133	+	3.59407i	−1.10675	+	0.144575i
$619$		−	15.6293i		−	0.628193i	−0.949391	−	0.314097i	$-0.898298\pi$
$619$		−	15.6293i		−	0.628193i	0.949391	−	0.314097i	$-0.101702\pi$
$620$	3.69146	+	4.16811i	0.148252	+	0.167395i
$621$	−13.1817	−	32.0968i	−0.528964	−	1.28800i
$622$	3.68356			0.147697
$623$	−12.7078			−0.509129
$624$	6.91292	−	0.903036i	0.276738	−	0.0361504i
$625$	1.00000			0.0400000
$626$	3.51864			0.140633
$627$	4.34363	+	33.2514i	0.173468	+	1.32793i
$628$	21.9903			0.877507
$629$			4.60103i			0.183455i
$630$	−6.29681	+	1.67367i	−0.250871	+	0.0666805i
$631$		−	41.1628i		−	1.63867i	−0.573317	−	0.819333i	$-0.694344\pi$
$631$		−	41.1628i		−	1.63867i	0.573317	−	0.819333i	$-0.305656\pi$
$632$	12.4910			0.496863
$633$	4.14721	+	31.7477i	0.164837	+	1.26186i
$634$	−20.4496			−0.812159
$635$	10.2871			0.408230
$636$	−2.68440	−	20.5497i	−0.106444	−	0.814847i
$637$			9.19016i			0.364128i
$638$		−	15.2322i		−	0.603050i
$639$	6.40711	+	24.1054i	0.253461	+	0.953594i
$640$	1.00000			0.0395285
$641$	−24.6329			−0.972943			−0.486471	−	0.873697i	$-0.661716\pi$
$641$	−24.6329			−0.972943			−0.486471	+	0.873697i	$0.661716\pi$
$642$	−2.70328	−	20.6942i	−0.106690	−	0.816734i
$643$		−	27.5624i		−	1.08695i	−0.839424	−	0.543477i	$-0.817108\pi$
$643$		−	27.5624i		−	1.08695i	0.839424	−	0.543477i	$-0.182892\pi$
$644$	14.5027			0.571485
$645$	1.78422	+	13.6586i	0.0702537	+	0.537806i
$646$			7.99739i			0.314653i
$647$	44.9621			1.76764			0.883822	−	0.467824i	$-0.154962\pi$
$647$	44.9621			1.76764			0.883822	+	0.467824i	$0.154962\pi$
$648$	4.46863	+	7.81226i	0.175544	+	0.306894i
$649$			40.8620i			1.60398i
$650$	4.02509			0.157877
$651$	−15.8001	−	13.7484i	−0.619253	−	0.538842i
$652$	16.2846			0.637754
$653$			32.3906i			1.26754i	0.773521	+	0.633771i	$0.218494\pi$
$653$			32.3906i			1.26754i	−0.773521	+	0.633771i	$0.781506\pi$
$654$	−8.58094	+	1.12093i	−0.335541	+	0.0438318i
$655$	−0.402670			−0.0157336
$656$			5.45504i			0.212983i
$657$	10.9543	+	41.2133i	0.427369	+	1.60789i
$658$	24.1910			0.943062
$659$			19.3127i			0.752318i	0.926555	+	0.376159i	$0.122755\pi$
$659$			19.3127i			0.752318i	−0.926555	+	0.376159i	$0.877245\pi$
$660$	−5.56930	+	0.727518i	−0.216785	+	0.0283186i
$661$	3.34733			0.130196			0.0650981	−	0.997879i	$-0.479264\pi$
$661$	3.34733			0.130196			0.0650981	+	0.997879i	$0.479264\pi$
$662$	10.0442			0.390379
$663$	−9.25978	+	1.20961i	−0.359620	+	0.0469772i
$664$			0.448704i			0.0174131i
$665$			12.9668i			0.502830i
$666$	9.95897	−	2.64705i	0.385902	−	0.102571i
$667$	31.3671			1.21454
$668$	8.85682			0.342681
$669$	−29.1787	+	3.81162i	−1.12811	+	0.147366i
$670$	3.59733			0.138977
$671$			12.5721i			0.485342i
$672$	−3.73000	+	0.487251i	−0.143888	+	0.0187961i
$673$			10.2088i			0.393522i	0.980451	+	0.196761i	$0.0630423\pi$
$673$			10.2088i			0.393522i	−0.980451	+	0.196761i	$0.936958\pi$
$674$	8.27536			0.318755
$675$	1.97400	+	4.80659i	0.0759792	+	0.185006i
$676$	3.20134			0.123128
$677$	10.0195			0.385080			0.192540	−	0.981289i	$-0.438328\pi$
$677$	10.0195			0.385080			0.192540	+	0.981289i	$0.438328\pi$
$678$	−0.167291	−	1.28065i	−0.00642477	−	0.0491829i
$679$	−32.0198			−1.22881
$680$	−1.33949			−0.0513670
$681$	26.9738	−	3.52360i	1.03364	−	0.135025i
$682$	−11.9705	−	13.5162i	−0.458373	−	0.517560i
$683$			23.8326i			0.911930i	0.889998	+	0.455965i	$0.150706\pi$
$683$			23.8326i			0.911930i	−0.889998	+	0.455965i	$0.849294\pi$
$684$	17.3104	−	4.60103i	0.661880	−	0.175925i
$685$			1.95396i			0.0746571i
$686$		−	20.1614i		−	0.769767i
$687$	4.14144	−	0.540997i	0.158006	−	0.0206403i
$688$			7.95279i			0.303197i
$689$		−	48.1608i		−	1.83478i
$690$	−1.49815	−	11.4686i	−0.0570335	−	0.436603i
$691$	−29.0802			−1.10626			−0.553131	−	0.833094i	$-0.686567\pi$
$691$	−29.0802			−1.10626			−0.553131	+	0.833094i	$0.686567\pi$
$692$		−	3.60474i		−	0.137032i
$693$	20.4190	−	5.42729i	0.775654	−	0.206166i
$694$			29.5201i			1.12057i
$695$	−12.5417			−0.475732
$696$	−8.06744	+	1.05385i	−0.305796	+	0.0399461i
$697$		−	7.30696i		−	0.276771i
$698$		−	28.5074i		−	1.07902i
$699$	−48.7713	+	6.37100i	−1.84470	+	0.240973i
$700$	−2.17181			−0.0820869
$701$		−	5.63426i		−	0.212803i	−0.994323	−	0.106401i	$-0.966067\pi$
$701$		−	5.63426i		−	0.212803i	0.994323	−	0.106401i	$-0.0339329\pi$
$702$	7.94551	+	19.3470i	0.299884	+	0.730204i
$703$		−	20.5081i		−	0.773478i
$704$	−3.24275			−0.122216
$705$	−2.49896	−	19.1301i	−0.0941164	−	0.720480i
$706$			30.5123i			1.14834i
$707$		−	33.9977i		−	1.27861i
$708$	21.6418	−	2.82707i	0.813347	−	0.106248i
$709$			2.80677i			0.105410i	0.998610	+	0.0527052i	$0.0167844\pi$
$709$			2.80677i			0.105410i	−0.998610	+	0.0527052i	$0.983216\pi$
$710$			8.31411i			0.312023i
$711$	9.62591	+	36.2154i	0.361000	+	1.35818i
$712$			5.85126i			0.219285i
$713$	27.8333	−	24.6503i	1.04236	−	0.923162i
$714$	4.99630	−	0.652667i	0.186982	−	0.0244254i
$715$	−13.0524			−0.488131
$716$	−20.0017			−0.747497
$717$	1.77148	+	13.5610i	0.0661571	+	0.506446i
$718$	−12.2778			−0.458204
$719$	−51.7313			−1.92925			−0.964626	−	0.263624i	$-0.915082\pi$
$719$	−51.7313			−1.92925			−0.964626	+	0.263624i	$0.915082\pi$
$720$	0.770630	+	2.89933i	0.0287197	+	0.108052i
$721$	34.7920			1.29572
$722$		−	16.6466i		−	0.619523i
$723$	1.80607	−	0.235927i	0.0671686	−	0.00877424i
$724$		−	13.0988i		−	0.486813i
$725$	−4.69731			−0.174454
$726$	−0.832205	+	0.108711i	−0.0308860	+	0.00403464i
$727$	−49.9374			−1.85207			−0.926037	−	0.377433i	$-0.876807\pi$
$727$	−49.9374			−1.85207			−0.926037	+	0.377433i	$0.876807\pi$
$728$	−8.74175			−0.323991
$729$	−19.2067	+	18.9764i	−0.711358	+	0.702830i
$730$			14.2148i			0.526112i
$731$		−	10.6527i		−	0.394003i
$732$	6.65859	−	0.869812i	0.246109	−	0.0321492i
$733$	−29.6517			−1.09521			−0.547605	−	0.836737i	$-0.684460\pi$
$733$	−29.6517			−1.09521			−0.547605	+	0.836737i	$0.684460\pi$
$734$	−25.2698			−0.932725
$735$	−3.92134	+	0.512245i	−0.144641	+	0.0188944i
$736$		−	6.67767i		−	0.246142i
$737$	−11.6653			−0.429695
$738$	−15.8160	+	4.20382i	−0.582194	+	0.154745i
$739$			32.2670i			1.18696i	0.804848	+	0.593480i	$0.202247\pi$
$739$			32.2670i			1.18696i	−0.804848	+	0.593480i	$0.797753\pi$
$740$	3.43492			0.126270
$741$	41.2735	−	5.39156i	1.51622	−	0.198064i
$742$			25.9861i			0.953980i
$743$	31.2498			1.14644			0.573222	−	0.819400i	$-0.305693\pi$
$743$	31.2498			1.14644			0.573222	+	0.819400i	$0.305693\pi$
$744$	−6.33038	+	7.27505i	−0.232083	+	0.266716i
$745$	−0.200699			−0.00735303
$746$		−	6.57892i		−	0.240871i
$747$	−1.30094	+	0.345785i	−0.0475990	+	0.0126516i
$748$	4.34363			0.158819
$749$			26.1688i			0.956189i
$750$	0.224352	+	1.71746i	0.00819217	+	0.0627127i
$751$	−7.11268			−0.259545			−0.129773	−	0.991544i	$-0.541425\pi$
$751$	−7.11268			−0.259545			−0.129773	+	0.991544i	$0.541425\pi$
$752$		−	11.1386i		−	0.406183i
$753$	0.0446943	+	0.342144i	0.00162875	+	0.0124684i
$754$	−18.9071			−0.688556
$755$	−3.96072			−0.144145
$756$	−4.28716	−	10.4390i	−0.155922	−	0.379664i
$757$			47.0500i			1.71006i	0.518578	+	0.855030i	$0.326462\pi$
$757$			47.0500i			1.71006i	−0.518578	+	0.855030i	$0.673538\pi$
$758$		−	6.44456i		−	0.234077i
$759$	4.85812	+	37.1899i	0.176339	+	1.34991i
$760$	5.97048			0.216572
$761$	24.6173			0.892378			0.446189	−	0.894939i	$-0.352781\pi$
$761$	24.6173			0.892378			0.446189	+	0.894939i	$0.352781\pi$
$762$	2.30792	+	17.6676i	0.0836073	+	0.640031i
$763$	10.8510			0.392834
$764$		−	0.201335i		−	0.00728405i
$765$	−1.03225	−	3.88362i	−0.0373211	−	0.140413i
$766$			30.1147i			1.08809i
$767$	50.7203			1.83140
$768$	0.224352	+	1.71746i	0.00809560	+	0.0619735i
$769$	18.5671			0.669546			0.334773	−	0.942299i	$-0.391340\pi$
$769$	18.5671			0.669546			0.334773	+	0.942299i	$0.391340\pi$
$770$	7.04266			0.253800
$771$	−18.0081	+	2.35239i	−0.648544	+	0.0847194i
$772$	21.6761			0.780142
$773$	26.6805			0.959630			0.479815	−	0.877370i	$-0.340704\pi$
$773$	26.6805			0.959630			0.479815	+	0.877370i	$0.340704\pi$
$774$	−23.0578	+	6.12866i	−0.828795	+	0.220290i
$775$	−4.16811	+	3.69146i	−0.149723	+	0.132601i
$776$			14.7433i			0.529255i
$777$	−12.8123	+	1.67367i	−0.459637	+	0.0600425i
$778$		−	13.0547i		−	0.468035i
$779$			32.5692i			1.16691i
$780$	0.903036	+	6.91292i	0.0323339	+	0.247522i
$781$		−	26.9606i		−	0.964726i
$782$			8.94466i			0.319860i
$783$	−9.27248	−	22.5781i	−0.331371	−	0.806874i
$784$	−2.28322			−0.0815436
$785$			21.9903i			0.784866i
$786$	−0.0903398	−	0.691570i	−0.00322231	−	0.0246675i
$787$			13.7821i			0.491278i	0.969361	+	0.245639i	$0.0789978\pi$
$787$			13.7821i			0.491278i	−0.969361	+	0.245639i	$0.921002\pi$
$788$	−10.8949			−0.388116
$789$	6.55792	+	50.2022i	0.233468	+	1.78725i
$790$			12.4910i			0.444408i
$791$			1.61944i			0.0575808i
$792$	−2.49896	−	9.40182i	−0.0887968	−	0.334079i
$793$	15.6053			0.554159
$794$		−	10.4520i		−	0.370926i
$795$	20.5497	−	2.68440i	0.728821	−	0.0952060i
$796$		−	18.1804i		−	0.644389i
$797$	−29.5554			−1.04691			−0.523454	−	0.852054i	$-0.675357\pi$
$797$	−29.5554			−1.04691			−0.523454	+	0.852054i	$0.675357\pi$
$798$	−22.2699	+	2.90912i	−0.788346	+	0.102982i
$799$			14.9200i			0.527832i
$800$			1.00000i			0.0353553i
$801$	−16.9647	+	4.50916i	−0.599420	+	0.159323i
$802$		−	10.4000i		−	0.367235i
$803$		−	46.0950i		−	1.62666i
$804$	0.807068	+	6.17827i	0.0284631	+	0.217891i
$805$			14.5027i			0.511152i
$806$	−16.7770	+	14.8584i	−0.590945	+	0.523366i
$807$	−2.44567	−	18.7221i	−0.0860915	−	0.659048i
$808$	−15.6540			−0.550707
$809$	−15.3340			−0.539116			−0.269558	−	0.962984i	$-0.586878\pi$
$809$	−15.3340			−0.539116			−0.269558	+	0.962984i	$0.586878\pi$
$810$	−7.81226	+	4.46863i	−0.274495	+	0.157012i
$811$	19.3769			0.680413			0.340207	−	0.940351i	$-0.389503\pi$
$811$	19.3769			0.680413			0.340207	+	0.940351i	$0.389503\pi$
$812$	10.2017			0.358009
$813$	2.01418	−	0.263112i	0.0706403	−	0.00922775i
$814$	−11.1386			−0.390407
$815$			16.2846i			0.570424i
$816$	−0.300517	−	2.30052i	−0.0105202	−	0.0805342i
$817$			47.4820i			1.66118i
$818$	5.45935			0.190882
$819$	−6.73666	−	25.3452i	−0.235398	−	0.885634i
$820$	−5.45504			−0.190498
$821$	53.0163			1.85028			0.925141	−	0.379623i	$-0.123946\pi$
$821$	53.0163			1.85028			0.925141	+	0.379623i	$0.123946\pi$
$822$	−3.35585	+	0.438376i	−0.117049	+	0.0152901i
$823$		−	8.51875i		−	0.296945i	−0.988917	−	0.148472i	$-0.952564\pi$
$823$		−	8.51875i		−	0.296945i	0.988917	−	0.148472i	$-0.0474356\pi$
$824$		−	16.0198i		−	0.558075i
$825$	−0.727518	−	5.56930i	−0.0253289	−	0.193898i
$826$	−27.3671			−0.952224
$827$	54.2961			1.88806			0.944031	−	0.329857i	$-0.107001\pi$
$827$	54.2961			1.88806			0.944031	+	0.329857i	$0.107001\pi$
$828$	19.3608	−	5.14602i	0.672834	−	0.178836i
$829$		−	39.2832i		−	1.36436i	−0.731184	−	0.682180i	$-0.761032\pi$
$829$		−	39.2832i		−	1.36436i	0.731184	−	0.682180i	$-0.238968\pi$
$830$	−0.448704			−0.0155747
$831$	−35.1340	+	4.58956i	−1.21879	+	0.159210i
$832$			4.02509i			0.139545i
$833$	3.05835			0.105965
$834$	−2.81374	−	21.5398i	−0.0974320	−	0.745861i
$835$			8.85682i			0.306503i
$836$	−19.3608			−0.669607
$837$	−25.9712	−	12.7475i	−0.897695	−	0.440618i
$838$	−27.7379			−0.958191
$839$		−	46.9122i		−	1.61959i	−0.586714	−	0.809794i	$-0.699579\pi$
$839$		−	46.9122i		−	1.61959i	0.586714	−	0.809794i	$-0.300421\pi$
$840$	−0.487251	−	3.73000i	−0.0168117	−	0.128697i
$841$	−6.93525			−0.239147
$842$			26.7994i			0.923568i
$843$	−28.6470	+	3.74216i	−0.986654	+	0.128887i
$844$	−18.4853			−0.636290
$845$			3.20134i			0.110129i
$846$	32.2945	−	8.58374i	1.11031	−	0.295115i
$847$	1.05237			0.0361597
$848$	11.9652			0.410885
$849$	−0.369948	−	2.83203i	−0.0126966	−	0.0971949i
$850$		−	1.33949i		−	0.0459441i
$851$		−	22.9373i		−	0.786279i
$852$	−14.2791	+	1.86529i	−0.489195	+	0.0639037i
$853$	−4.45810			−0.152643			−0.0763213	−	0.997083i	$-0.524317\pi$
$853$	−4.45810			−0.152643			−0.0763213	+	0.997083i	$0.524317\pi$
$854$	−8.42012			−0.288131
$855$	4.60103	+	17.3104i	0.157352	+	0.592003i
$856$	12.0493			0.411837
$857$			15.3597i			0.524677i	0.964976	+	0.262339i	$0.0844938\pi$
$857$			15.3597i			0.524677i	−0.964976	+	0.262339i	$0.915506\pi$
$858$	−2.92832	−	22.4169i	−0.0999713	−	0.765301i
$859$		−	25.4709i		−	0.869057i	−0.900658	−	0.434529i	$-0.856915\pi$
$859$		−	25.4709i		−	0.869057i	0.900658	−	0.434529i	$-0.143085\pi$
$860$	−7.95279			−0.271188
$861$	20.3473	−	2.65797i	0.693434	−	0.0905834i
$862$	3.88489			0.132320
$863$	44.4358			1.51261			0.756306	−	0.654218i	$-0.227002\pi$
$863$	44.4358			1.51261			0.756306	+	0.654218i	$0.227002\pi$
$864$	−4.80659	+	1.97400i	−0.163524	+	0.0671567i
$865$	3.60474			0.122565
$866$	−11.2529			−0.382388
$867$	−3.41144	−	26.1153i	−0.115859	−	0.886922i
$868$	9.05237	−	8.01716i	0.307257	−	0.272120i
$869$		−	40.5051i		−	1.37404i
$870$	−1.05385	−	8.06744i	−0.0357289	−	0.273512i
$871$			14.4796i			0.490622i
$872$		−	4.99630i		−	0.169196i
$873$	−42.7458	+	11.3617i	−1.44673	+	0.384534i
$874$		−	39.8689i		−	1.34859i
$875$		−	2.17181i		−	0.0734207i
$876$	−24.4133	+	3.18911i	−0.824849	+	0.107750i
$877$	−15.0751			−0.509050			−0.254525	−	0.967066i	$-0.581919\pi$
$877$	−15.0751			−0.509050			−0.254525	+	0.967066i	$0.581919\pi$
$878$		−	16.6164i		−	0.560776i
$879$	21.1110	−	2.75773i	0.712056	−	0.0930160i
$880$		−	3.24275i		−	0.109313i
$881$	−43.1072			−1.45232			−0.726159	−	0.687526i	$-0.758697\pi$
$881$	−43.1072			−1.45232			−0.726159	+	0.687526i	$0.758697\pi$
$882$	−1.75952	−	6.61982i	−0.0592461	−	0.222901i
$883$			42.7785i			1.43961i	0.694175	+	0.719806i	$0.255769\pi$
$883$			42.7785i			1.43961i	−0.694175	+	0.719806i	$0.744231\pi$
$884$		−	5.39156i		−	0.181338i
$885$	2.82707	+	21.6418i	0.0950308	+	0.727480i
$886$	−3.36204			−0.112950
$887$			51.1930i			1.71889i	0.511227	+	0.859446i	$0.329191\pi$
$887$			51.1930i			1.71889i	−0.511227	+	0.859446i	$0.670809\pi$
$888$	0.770630	+	5.89933i	0.0258607	+	0.197969i
$889$		−	22.3416i		−	0.749314i
$890$	−5.85126			−0.196135
$891$	25.3332	−	14.4907i	0.848695	−	0.485455i
$892$		−	16.9895i		−	0.568850i
$893$		−	66.5027i		−	2.22543i
$894$	−0.0450271	−	0.344692i	−0.00150593	−	0.0115282i
$895$		−	20.0017i		−	0.668582i
$896$		−	2.17181i		−	0.0725552i
$897$	46.1622	−	6.03018i	1.54131	−	0.201342i
$898$		−	8.98295i		−	0.299765i
$899$	19.5789	−	17.3399i	0.652994	−	0.578319i
$900$	−2.89933	+	0.770630i	−0.0966444	+	0.0256877i
$901$	−16.0272			−0.533943
$902$	17.6893			0.588990
$903$	29.6639	−	3.87500i	0.987154	−	0.128952i
$904$	0.745663			0.0248004
$905$	13.0988			0.435419
$906$	−0.888594	−	6.80237i	−0.0295216	−	0.225994i
$907$	26.1786			0.869246			0.434623	−	0.900613i	$-0.356882\pi$
$907$	26.1786			0.869246			0.434623	+	0.900613i	$0.356882\pi$
$908$			15.7057i			0.521211i
$909$	−12.0635	−	45.3863i	−0.400120	−	1.50537i
$910$		−	8.74175i		−	0.289786i
$911$	11.3304			0.375392			0.187696	−	0.982227i	$-0.439898\pi$
$911$	11.3304			0.375392			0.187696	+	0.982227i	$0.439898\pi$
$912$	1.33949	+	10.2541i	0.0443549	+	0.339546i
$913$	1.45504			0.0481546
$914$	−21.8476			−0.722654
$915$	0.869812	+	6.65859i	0.0287551	+	0.220126i
$916$			2.41138i			0.0796742i
$917$			0.874525i			0.0288794i
$918$	6.43838	−	2.64415i	0.212498	−	0.0872698i
$919$	−19.4669			−0.642153			−0.321077	−	0.947053i	$-0.604045\pi$
$919$	−19.4669			−0.642153			−0.321077	+	0.947053i	$0.604045\pi$
$920$	6.67767			0.220156
$921$	0.575786	+	4.40776i	0.0189728	+	0.145241i
$922$			16.0166i			0.527480i
$923$	−33.4650			−1.10151
$924$	1.58003	+	12.0955i	0.0519793	+	0.397912i
$925$			3.43492i			0.112939i
$926$	16.3609			0.537653
$927$	46.4467	−	12.3453i	1.52551	−	0.405474i
$928$		−	4.69731i		−	0.154197i
$929$	−59.1834			−1.94175			−0.970873	−	0.239596i	$-0.922985\pi$
$929$	−59.1834			−1.94175			−0.970873	+	0.239596i	$0.922985\pi$
$930$	−7.27505	−	6.33038i	−0.238558	−	0.207581i
$931$	−13.6319			−0.446768
$932$		−	28.3974i		−	0.930187i
$933$	−6.32636	+	0.826413i	−0.207116	+	0.0270555i
$934$	−8.38786			−0.274459
$935$			4.34363i			0.142052i
$936$	−11.6701	+	3.10186i	−0.381448	+	0.101387i
$937$	−46.3486			−1.51414			−0.757071	−	0.653332i	$-0.773370\pi$
$937$	−46.3486			−1.51414			−0.757071	+	0.653332i	$0.773370\pi$
$938$		−	7.81273i		−	0.255095i
$939$	−6.04311	+	0.789413i	−0.197210	+	0.0257615i
$940$	11.1386			0.363301
$941$	8.46544			0.275965			0.137983	−	0.990435i	$-0.455938\pi$
$941$	8.46544			0.275965			0.137983	+	0.990435i	$0.455938\pi$
$942$	−37.7674	+	4.93356i	−1.23053	+	0.160744i
$943$			36.4269i			1.18622i
$944$			12.6010i			0.410129i
$945$	10.4390	−	4.28716i	0.339582	−	0.139461i
$946$	25.7889			0.838470
$947$	−59.0894			−1.92015			−0.960073	−	0.279749i	$-0.909749\pi$
$947$	−59.0894			−1.92015			−0.960073	+	0.279749i	$0.909749\pi$
$948$	−21.4527	+	2.80237i	−0.696751	+	0.0910167i
$949$	−57.2157			−1.85730
$950$			5.97048i			0.193708i
$951$	35.1214	−	4.58791i	1.13889	−	0.148773i
$952$			2.90912i			0.0942851i
$953$	−44.3542			−1.43677			−0.718386	−	0.695644i	$-0.755119\pi$
$953$	−44.3542			−1.43677			−0.718386	+	0.695644i	$0.755119\pi$
$954$	9.22071	+	34.6910i	0.298532	+	1.12316i
$955$	0.201335			0.00651505
$956$	−7.89599			−0.255375
$957$	3.41738	+	26.1607i	0.110468	+	0.845656i
$958$	2.14293			0.0692350
$959$	4.24365			0.137035
$960$	−1.71746	+	0.224352i	−0.0554308	+	0.00724093i
$961$	3.74630	−	30.7728i	0.120848	−	0.992671i
$962$			13.8258i			0.445763i
$963$	9.28556	+	34.9349i	0.299223	+	1.12576i
$964$			1.05160i			0.0338696i
$965$			21.6761i			0.697780i
$966$	−24.9077	+	3.25370i	−0.801393	+	0.104686i
$967$		−	8.23999i		−	0.264980i	−0.991184	−	0.132490i	$-0.957703\pi$
$967$		−	8.23999i		−	0.264980i	0.991184	−	0.132490i	$-0.0422973\pi$
$968$		−	0.484556i		−	0.0155742i
$969$	−1.79423	−	13.7352i	−0.0576389	−	0.441238i
$970$	−14.7433			−0.473380
$971$			7.28089i			0.233655i	0.993152	+	0.116827i	$0.0372724\pi$
$971$			7.28089i			0.233655i	−0.993152	+	0.116827i	$0.962728\pi$
$972$	−9.42738	−	12.4147i	−0.302383	−	0.398201i
$973$			27.2381i			0.873215i
$974$	−4.04496			−0.129609
$975$	−6.91292	+	0.903036i	−0.221391	+	0.0289203i
$976$			3.87700i			0.124100i
$977$			30.2896i			0.969049i	0.874778	+	0.484524i	$0.161007\pi$
$977$			30.2896i			0.969049i	−0.874778	+	0.484524i	$0.838993\pi$
$978$	−27.9681	+	3.65348i	−0.894322	+	0.116825i
$979$	18.9742			0.606418
$980$		−	2.28322i		−	0.0729348i
$981$	14.4859	−	3.85030i	0.462500	−	0.122931i
$982$			29.2751i			0.934206i
$983$	29.9992			0.956825			0.478413	−	0.878135i	$-0.341212\pi$
$983$	29.9992			0.956825			0.478413	+	0.878135i	$0.341212\pi$
$984$	−1.22385	−	9.36880i	−0.0390148	−	0.298666i
$985$		−	10.8949i		−	0.347141i
$986$			6.29200i			0.200378i
$987$	−41.5470	+	5.42729i	−1.32245	+	0.172752i
$988$			24.0317i			0.764550i
$989$			53.1061i			1.68868i
$990$	9.40182	−	2.49896i	0.298809	−	0.0794223i
$991$		−	3.32647i		−	0.105669i	−0.998603	−	0.0528344i	$-0.983174\pi$
$991$		−	3.32647i		−	0.105669i	0.998603	−	0.0528344i	$-0.0168255\pi$
$992$	−3.69146	−	4.16811i	−0.117204	−	0.132338i
$993$	−17.2505	+	2.25344i	−0.547429	+	0.0715107i
$994$	18.0567			0.572724
$995$	18.1804			0.576359
$996$	−0.100668	−	0.770630i	−0.00318977	−	0.0244184i
$997$	9.82755			0.311242			0.155621	−	0.987817i	$-0.450262\pi$
$997$	9.82755			0.311242			0.155621	+	0.987817i	$0.450262\pi$
$998$	−24.7683			−0.784027
$999$	−16.5103	+	6.78052i	−0.522361	+	0.214526i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.h.c.371.5	yes	16
3.2	odd	2	inner	930.2.h.c.371.12	yes	16
31.30	odd	2	inner	930.2.h.c.371.4	✓	16
93.92	even	2	inner	930.2.h.c.371.13	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.h.c.371.4	✓	16	31.30	odd	2	inner
930.2.h.c.371.5	yes	16	1.1	even	1	trivial
930.2.h.c.371.12	yes	16	3.2	odd	2	inner
930.2.h.c.371.13	yes	16	93.92	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.224352 + 1.71746i) q^{3} -1.00000 q^{4} -1.00000i q^{5} +(1.71746 - 0.224352i) q^{6} -2.17181 q^{7} +1.00000i q^{8} +(-2.89933 + 0.770630i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.224352 + 1.71746i) q^{3} -1.00000 q^{4} -1.00000i q^{5} +(1.71746 - 0.224352i) q^{6} -2.17181 q^{7} +1.00000i q^{8} +(-2.89933 + 0.770630i) q^{9} -1.00000 q^{10} +3.24275 q^{11} +(-0.224352 - 1.71746i) q^{12} -4.02509i q^{13} +2.17181i q^{14} +(1.71746 - 0.224352i) q^{15} +1.00000 q^{16} -1.33949 q^{17} +(0.770630 + 2.89933i) q^{18} +5.97048 q^{19} +1.00000i q^{20} +(-0.487251 - 3.73000i) q^{21} -3.24275i q^{22} +6.67767 q^{23} +(-1.71746 + 0.224352i) q^{24} -1.00000 q^{25} -4.02509 q^{26} +(-1.97400 - 4.80659i) q^{27} +2.17181 q^{28} +4.69731 q^{29} +(-0.224352 - 1.71746i) q^{30} +(4.16811 - 3.69146i) q^{31} -1.00000i q^{32} +(0.727518 + 5.56930i) q^{33} +1.33949i q^{34} +2.17181i q^{35} +(2.89933 - 0.770630i) q^{36} -3.43492i q^{37} -5.97048i q^{38} +(6.91292 - 0.903036i) q^{39} +1.00000 q^{40} +5.45504i q^{41} +(-3.73000 + 0.487251i) q^{42} +7.95279i q^{43} -3.24275 q^{44} +(0.770630 + 2.89933i) q^{45} -6.67767i q^{46} -11.1386i q^{47} +(0.224352 + 1.71746i) q^{48} -2.28322 q^{49} +1.00000i q^{50} +(-0.300517 - 2.30052i) q^{51} +4.02509i q^{52} +11.9652 q^{53} +(-4.80659 + 1.97400i) q^{54} -3.24275i q^{55} -2.17181i q^{56} +(1.33949 + 10.2541i) q^{57} -4.69731i q^{58} +12.6010i q^{59} +(-1.71746 + 0.224352i) q^{60} +3.87700i q^{61} +(-3.69146 - 4.16811i) q^{62} +(6.29681 - 1.67367i) q^{63} -1.00000 q^{64} -4.02509 q^{65} +(5.56930 - 0.727518i) q^{66} -3.59733 q^{67} +1.33949 q^{68} +(1.49815 + 11.4686i) q^{69} +2.17181 q^{70} -8.31411i q^{71} +(-0.770630 - 2.89933i) q^{72} -14.2148i q^{73} -3.43492 q^{74} +(-0.224352 - 1.71746i) q^{75} -5.97048 q^{76} -7.04266 q^{77} +(-0.903036 - 6.91292i) q^{78} -12.4910i q^{79} -1.00000i q^{80} +(7.81226 - 4.46863i) q^{81} +5.45504 q^{82} +0.448704 q^{83} +(0.487251 + 3.73000i) q^{84} +1.33949i q^{85} +7.95279 q^{86} +(1.05385 + 8.06744i) q^{87} +3.24275i q^{88} +5.85126 q^{89} +(2.89933 - 0.770630i) q^{90} +8.74175i q^{91} -6.67767 q^{92} +(7.27505 + 6.33038i) q^{93} -11.1386 q^{94} -5.97048i q^{95} +(1.71746 - 0.224352i) q^{96} +14.7433 q^{97} +2.28322i q^{98} +(-9.40182 + 2.49896i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 20 q^{7} - 4 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 - 20 * q^7 - 4 * q^9	\( 16 q - 16 q^{4} - 20 q^{7} - 4 q^{9} - 16 q^{10} + 16 q^{16} + 12 q^{18} - 4 q^{19} - 16 q^{25} + 20 q^{28} - 4 q^{31} - 16 q^{33} + 4 q^{36} - 4 q^{39} + 16 q^{40} + 12 q^{45} + 4 q^{49} + 52 q^{51} - 12 q^{63} - 16 q^{64} + 4 q^{66} + 112 q^{67} - 4 q^{69} + 20 q^{70} - 12 q^{72} + 4 q^{76} - 28 q^{78} - 32 q^{81} + 32 q^{82} - 24 q^{87} + 4 q^{90} + 16 q^{93} - 8 q^{94} + 8 q^{97}+O(q^{100}) \) 16 * q - 16 * q^4 - 20 * q^7 - 4 * q^9 - 16 * q^10 + 16 * q^16 + 12 * q^18 - 4 * q^19 - 16 * q^25 + 20 * q^28 - 4 * q^31 - 16 * q^33 + 4 * q^36 - 4 * q^39 + 16 * q^40 + 12 * q^45 + 4 * q^49 + 52 * q^51 - 12 * q^63 - 16 * q^64 + 4 * q^66 + 112 * q^67 - 4 * q^69 + 20 * q^70 - 12 * q^72 + 4 * q^76 - 28 * q^78 - 32 * q^81 + 32 * q^82 - 24 * q^87 + 4 * q^90 + 16 * q^93 - 8 * q^94 + 8 * q^97

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