LMFDB - Embedded newform 930.2.z.c.469.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(109,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 2]))

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

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

chi := DirichletCharacter("930.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.z (of order $10$, degree $4$, 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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			469.3
Character	$\chi$	$=$	930.469
Dual form			930.2.z.c.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.618034 + 2.14896i) q^{5} -1.00000 q^{6} +(-1.53347 - 2.11064i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.618034 + 2.14896i) q^{5} -1.00000 q^{6} +(-1.53347 - 2.11064i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-1.25185 - 1.85280i) q^{10} +(-1.18111 + 0.858129i) q^{11} +(0.951057 - 0.309017i) q^{12} +(-4.52499 - 1.47026i) q^{13} +(2.11064 + 1.53347i) q^{14} +(-0.0762803 + 2.23477i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.98439 + 4.10766i) q^{17} +(-0.951057 - 0.309017i) q^{18} +(0.574481 + 1.76807i) q^{19} +(1.76313 + 1.37527i) q^{20} +(-0.806193 - 2.48121i) q^{21} +(0.858129 - 1.18111i) q^{22} +(-2.59484 + 3.57150i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(-4.23607 + 2.65626i) q^{25} +4.75786 q^{26} +(0.587785 + 0.809017i) q^{27} +(-2.48121 - 0.806193i) q^{28} +(0.334189 + 1.02853i) q^{29} +(-0.618034 - 2.14896i) q^{30} +(-1.69375 + 5.30389i) q^{31} +1.00000i q^{32} +(-1.38848 + 0.451145i) q^{33} +(1.56899 - 4.82884i) q^{34} +(3.58795 - 4.59982i) q^{35} +1.00000 q^{36} +4.67804i q^{37} +(-1.09273 - 1.50401i) q^{38} +(-3.84919 - 2.79660i) q^{39} +(-2.10182 - 0.763128i) q^{40} +(-2.57073 - 7.91189i) q^{41} +(1.53347 + 2.11064i) q^{42} +(-4.48308 + 1.45664i) q^{43} +(-0.451145 + 1.38848i) q^{44} +(-0.763128 + 2.10182i) q^{45} +(1.36419 - 4.19855i) q^{46} +(9.18597 + 2.98470i) q^{47} +(0.587785 - 0.809017i) q^{48} +(0.0598438 - 0.184180i) q^{49} +(3.20791 - 3.83527i) q^{50} +(-4.10766 + 2.98439i) q^{51} +(-4.52499 + 1.47026i) q^{52} +(0.866223 - 1.19225i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(-2.57405 - 2.00781i) q^{55} +2.60890 q^{56} +1.85906i q^{57} +(-0.635666 - 0.874919i) q^{58} +(-1.33847 + 4.11940i) q^{59} +(1.25185 + 1.85280i) q^{60} -0.894288 q^{61} +(-0.0281347 - 5.56769i) q^{62} -2.60890i q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.362931 - 10.6327i) q^{65} +(1.18111 - 0.858129i) q^{66} +2.19683i q^{67} +5.07734i q^{68} +(-3.57150 + 2.59484i) q^{69} +(-1.99092 + 5.48342i) q^{70} +(9.22722 + 6.70397i) q^{71} +(-0.951057 + 0.309017i) q^{72} +(-7.37431 - 10.1499i) q^{73} +(-1.44559 - 4.44908i) q^{74} +(-4.84957 + 1.21724i) q^{75} +(1.50401 + 1.09273i) q^{76} +(3.62240 + 1.17699i) q^{77} +(4.52499 + 1.47026i) q^{78} +(-2.95125 - 2.14421i) q^{79} +(2.23477 + 0.0762803i) q^{80} +(0.309017 + 0.951057i) q^{81} +(4.88982 + 6.73026i) q^{82} +(-1.39630 + 0.453685i) q^{83} +(-2.11064 - 1.53347i) q^{84} +(-10.6716 - 3.87466i) q^{85} +(3.81353 - 2.77069i) q^{86} +1.08146i q^{87} -1.45994i q^{88} +(-1.40650 + 1.02188i) q^{89} +(0.0762803 - 2.23477i) q^{90} +(3.83575 + 11.8052i) q^{91} +4.41461i q^{92} +(-3.24985 + 4.52090i) q^{93} -9.65870 q^{94} +(-3.44446 + 2.32726i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(1.18626 + 1.63274i) q^{97} +0.193659i q^{98} -1.45994 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} - 16 q^{5} - 32 q^{6} + 8 q^{9}+O(q^{10}) $ 32 * q + 8 * q^4 - 16 * q^5 - 32 * q^6 + 8 * q^9	$ 32 q + 8 q^{4} - 16 q^{5} - 32 q^{6} + 8 q^{9} - 4 q^{11} - 4 q^{14} - 8 q^{16} - 16 q^{19} + 16 q^{20} - 4 q^{21} - 8 q^{24} - 64 q^{25} - 16 q^{26} + 4 q^{29} + 16 q^{30} - 24 q^{31} - 12 q^{34} + 32 q^{36} + 4 q^{39} - 48 q^{41} + 4 q^{44} + 16 q^{45} + 8 q^{46} - 28 q^{49} + 8 q^{51} - 8 q^{54} - 8 q^{55} - 16 q^{56} - 8 q^{59} + 32 q^{61} + 8 q^{64} - 8 q^{65} + 4 q^{66} - 12 q^{69} - 8 q^{70} + 32 q^{71} + 4 q^{74} - 24 q^{76} + 64 q^{79} + 24 q^{80} - 8 q^{81} + 4 q^{84} + 28 q^{85} + 84 q^{86} - 128 q^{89} - 28 q^{91} + 40 q^{94} + 8 q^{95} + 8 q^{96} - 16 q^{99}+O(q^{100}) $ 32 * q + 8 * q^4 - 16 * q^5 - 32 * q^6 + 8 * q^9 - 4 * q^11 - 4 * q^14 - 8 * q^16 - 16 * q^19 + 16 * q^20 - 4 * q^21 - 8 * q^24 - 64 * q^25 - 16 * q^26 + 4 * q^29 + 16 * q^30 - 24 * q^31 - 12 * q^34 + 32 * q^36 + 4 * q^39 - 48 * q^41 + 4 * q^44 + 16 * q^45 + 8 * q^46 - 28 * q^49 + 8 * q^51 - 8 * q^54 - 8 * q^55 - 16 * q^56 - 8 * q^59 + 32 * q^61 + 8 * q^64 - 8 * q^65 + 4 * q^66 - 12 * q^69 - 8 * q^70 + 32 * q^71 + 4 * q^74 - 24 * q^76 + 64 * q^79 + 24 * q^80 - 8 * q^81 + 4 * q^84 + 28 * q^85 + 84 * q^86 - 128 * q^89 - 28 * q^91 + 40 * q^94 + 8 * q^95 + 8 * q^96 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	0.618034	+	2.14896i	0.276393	+	0.961045i
$5$	0.618034	+	2.14896i	0.276393	+	0.961045i
$6$	−1.00000			−0.408248
$7$	−1.53347	−	2.11064i	−0.579598	−	0.797748i	0.414054	−	0.910252i	$-0.364113\pi$
$7$	−1.53347	−	2.11064i	−0.579598	−	0.797748i	−0.993651	+	0.112505i	$0.964113\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	−1.25185	−	1.85280i	−0.395870	−	0.585907i
$11$	−1.18111	+	0.858129i	−0.356119	+	0.258735i	−0.751431	−	0.659811i	$-0.770636\pi$
$11$	−1.18111	+	0.858129i	−0.356119	+	0.258735i	0.395313	+	0.918547i	$0.370636\pi$
$12$	0.951057	−	0.309017i	0.274546	−	0.0892055i
$13$	−4.52499	−	1.47026i	−1.25501	−	0.407776i	−0.395294	−	0.918555i	$-0.629357\pi$
$13$	−4.52499	−	1.47026i	−1.25501	−	0.407776i	−0.859713	+	0.510778i	$0.829357\pi$
$14$	2.11064	+	1.53347i	0.564093	+	0.409837i
$15$	−0.0762803	+	2.23477i	−0.0196955	+	0.577014i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−2.98439	+	4.10766i	−0.723820	+	0.996253i	0.275568	+	0.961282i	$0.411134\pi$
$17$	−2.98439	+	4.10766i	−0.723820	+	0.996253i	−0.999388	+	0.0349716i	$0.988866\pi$
$18$	−0.951057	−	0.309017i	−0.224166	−	0.0728360i
$19$	0.574481	+	1.76807i	0.131795	+	0.405623i	0.995078	−	0.0990975i	$-0.0315956\pi$
$19$	0.574481	+	1.76807i	0.131795	+	0.405623i	−0.863283	+	0.504720i	$0.831596\pi$
$20$	1.76313	+	1.37527i	0.394247	+	0.307521i
$21$	−0.806193	−	2.48121i	−0.175926	−	0.541444i
$22$	0.858129	−	1.18111i	0.182954	−	0.251814i
$23$	−2.59484	+	3.57150i	−0.541062	+	0.744708i	−0.988766	−	0.149474i	$-0.952242\pi$
$23$	−2.59484	+	3.57150i	−0.541062	+	0.744708i	0.447703	+	0.894182i	$0.352242\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	−4.23607	+	2.65626i	−0.847214	+	0.531252i
$26$	4.75786			0.933093
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	−2.48121	−	0.806193i	−0.468904	−	0.152356i
$29$	0.334189	+	1.02853i	0.0620574	+	0.190993i	0.977279	−	0.211959i	$-0.0679842\pi$
$29$	0.334189	+	1.02853i	0.0620574	+	0.190993i	−0.915221	+	0.402952i	$0.867984\pi$
$30$	−0.618034	−	2.14896i	−0.112837	−	0.392345i
$31$	−1.69375	+	5.30389i	−0.304207	+	0.952606i
$31$	−1.69375	+	5.30389i	−0.304207	+	0.952606i
$32$			1.00000i			0.176777i
$33$	−1.38848	+	0.451145i	−0.241704	+	0.0785342i
$34$	1.56899	−	4.82884i	0.269079	−	0.828139i
$35$	3.58795	−	4.59982i	0.606474	−	0.777511i
$36$	1.00000			0.166667
$37$			4.67804i			0.769064i	0.923112	+	0.384532i	$0.125637\pi$
$37$			4.67804i			0.769064i	−0.923112	+	0.384532i	$0.874363\pi$
$38$	−1.09273	−	1.50401i	−0.177264	−	0.243983i
$39$	−3.84919	−	2.79660i	−0.616363	−	0.447814i
$40$	−2.10182	−	0.763128i	−0.332327	−	0.120661i
$41$	−2.57073	−	7.91189i	−0.401481	−	1.23563i	−0.923798	−	0.382879i	$-0.874932\pi$
$41$	−2.57073	−	7.91189i	−0.401481	−	1.23563i	0.522318	−	0.852751i	$-0.325068\pi$
$42$	1.53347	+	2.11064i	0.236620	+	0.325679i
$43$	−4.48308	+	1.45664i	−0.683663	+	0.222136i	−0.630198	−	0.776434i	$-0.717026\pi$
$43$	−4.48308	+	1.45664i	−0.683663	+	0.222136i	−0.0534646	+	0.998570i	$0.517026\pi$
$44$	−0.451145	+	1.38848i	−0.0680126	+	0.209321i
$45$	−0.763128	+	2.10182i	−0.113760	+	0.313320i
$46$	1.36419	−	4.19855i	0.201139	−	0.619042i
$47$	9.18597	+	2.98470i	1.33991	+	0.435364i	0.889287	−	0.457350i	$-0.151201\pi$
$47$	9.18597	+	2.98470i	1.33991	+	0.435364i	0.450624	+	0.892714i	$0.351201\pi$
$48$	0.587785	−	0.809017i	0.0848395	−	0.116772i
$49$	0.0598438	−	0.184180i	0.00854912	−	0.0263115i
$50$	3.20791	−	3.83527i	0.453667	−	0.542389i
$51$	−4.10766	+	2.98439i	−0.575187	+	0.417898i
$52$	−4.52499	+	1.47026i	−0.627503	+	0.203888i
$53$	0.866223	−	1.19225i	0.118985	−	0.163769i	−0.745370	−	0.666651i	$-0.767727\pi$
$53$	0.866223	−	1.19225i	0.118985	−	0.163769i	0.864355	+	0.502882i	$0.167727\pi$
$54$	−0.809017	−	0.587785i	−0.110093	−	0.0799874i
$55$	−2.57405	−	2.00781i	−0.347085	−	0.270733i
$56$	2.60890			0.348628
$57$			1.85906i			0.246238i
$58$	−0.635666	−	0.874919i	−0.0834670	−	0.114883i
$59$	−1.33847	+	4.11940i	−0.174254	+	0.536300i	−0.999599	−	0.0283300i	$-0.990981\pi$
$59$	−1.33847	+	4.11940i	−0.174254	+	0.536300i	0.825344	+	0.564630i	$0.190981\pi$
$60$	1.25185	+	1.85280i	0.161613	+	0.239196i
$61$	−0.894288			−0.114502			−0.0572509	−	0.998360i	$-0.518234\pi$
$61$	−0.894288			−0.114502			−0.0572509	+	0.998360i	$0.518234\pi$
$62$	−0.0281347	−	5.56769i	−0.00357311	−	0.707098i
$63$		−	2.60890i		−	0.328690i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	0.362931	−	10.6327i	0.0450160	−	1.31882i
$66$	1.18111	−	0.858129i	0.145385	−	0.105628i
$67$			2.19683i			0.268385i	0.990955	+	0.134193i	$0.0428441\pi$
$67$			2.19683i			0.268385i	−0.990955	+	0.134193i	$0.957156\pi$
$68$			5.07734i			0.615718i
$69$	−3.57150	+	2.59484i	−0.429958	+	0.312382i
$70$	−1.99092	+	5.48342i	−0.237961	+	0.655395i
$71$	9.22722	+	6.70397i	1.09507	+	0.795615i	0.980248	−	0.197771i	$-0.0633703\pi$
$71$	9.22722	+	6.70397i	1.09507	+	0.795615i	0.114822	+	0.993386i	$0.463370\pi$
$72$	−0.951057	+	0.309017i	−0.112083	+	0.0364180i
$73$	−7.37431	−	10.1499i	−0.863098	−	1.18795i	−0.980822	−	0.194906i	$-0.937560\pi$
$73$	−7.37431	−	10.1499i	−0.863098	−	1.18795i	0.117724	−	0.993046i	$-0.462440\pi$
$74$	−1.44559	−	4.44908i	−0.168047	−	0.517195i
$75$	−4.84957	+	1.21724i	−0.559980	+	0.140555i
$76$	1.50401	+	1.09273i	0.172522	+	0.125344i
$77$	3.62240	+	1.17699i	0.412811	+	0.134130i
$78$	4.52499	+	1.47026i	0.512354	+	0.166474i
$79$	−2.95125	−	2.14421i	−0.332042	−	0.241242i	0.409255	−	0.912420i	$-0.365789\pi$
$79$	−2.95125	−	2.14421i	−0.332042	−	0.241242i	−0.741296	+	0.671178i	$0.765789\pi$
$80$	2.23477	+	0.0762803i	0.249854	+	0.00852839i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	4.88982	+	6.73026i	0.539990	+	0.743233i
$83$	−1.39630	+	0.453685i	−0.153264	+	0.0497984i	−0.384644	−	0.923065i	$-0.625676\pi$
$83$	−1.39630	+	0.453685i	−0.153264	+	0.0497984i	0.231380	+	0.972863i	$0.425676\pi$
$84$	−2.11064	−	1.53347i	−0.230290	−	0.167315i
$85$	−10.6716	−	3.87466i	−1.15750	−	0.420266i
$86$	3.81353	−	2.77069i	0.411224	−	0.298772i
$87$			1.08146i			0.115945i
$88$		−	1.45994i		−	0.155630i
$89$	−1.40650	+	1.02188i	−0.149089	+	0.108319i	−0.659829	−	0.751416i	$-0.729371\pi$
$89$	−1.40650	+	1.02188i	−0.149089	+	0.108319i	0.510740	+	0.859735i	$0.329371\pi$
$90$	0.0762803	−	2.23477i	0.00804065	−	0.235565i
$91$	3.83575	+	11.8052i	0.402096	+	1.23752i
$92$			4.41461i			0.460255i
$93$	−3.24985	+	4.52090i	−0.336993	+	0.468795i
$94$	−9.65870			−0.996219
$95$	−3.44446	+	2.32726i	−0.353395	+	0.238772i
$96$	−0.309017	+	0.951057i	−0.0315389	+	0.0970668i
$97$	1.18626	+	1.63274i	0.120446	+	0.165780i	0.864983	−	0.501802i	$-0.167329\pi$
$97$	1.18626	+	1.63274i	0.120446	+	0.165780i	−0.744536	+	0.667582i	$0.767329\pi$
$98$			0.193659i			0.0195625i
$99$	−1.45994			−0.146729
$100$	−1.86574	+	4.63886i	−0.186574	+	0.463886i
$101$	5.04616	+	3.66625i	0.502112	+	0.364806i	0.809823	−	0.586674i	$-0.199563\pi$
$101$	5.04616	+	3.66625i	0.502112	+	0.364806i	−0.307711	+	0.951480i	$0.599563\pi$
$102$	2.98439	−	4.10766i	0.295498	−	0.406719i
$103$	2.87221	−	0.933237i	0.283007	−	0.0919546i	−0.164074	−	0.986448i	$-0.552464\pi$
$103$	2.87221	−	0.933237i	0.283007	−	0.0919546i	0.447081	+	0.894493i	$0.352464\pi$
$104$	3.84919	−	2.79660i	0.377444	−	0.274229i
$105$	4.83376	−	3.26595i	0.471727	−	0.318724i
$106$	−0.455400	+	1.40158i	−0.0442324	+	0.136133i
$107$	−1.39348	+	1.91797i	−0.134713	+	0.185417i	−0.871044	−	0.491205i	$-0.836557\pi$
$107$	−1.39348	+	1.91797i	−0.134713	+	0.185417i	0.736331	+	0.676622i	$0.236557\pi$
$108$	0.951057	+	0.309017i	0.0915155	+	0.0297352i
$109$	−0.533694	+	1.64254i	−0.0511186	+	0.157327i	−0.973357	−	0.229295i	$-0.926358\pi$
$109$	−0.533694	+	1.64254i	−0.0511186	+	0.157327i	0.922238	+	0.386622i	$0.126358\pi$
$110$	3.06852	+	1.11412i	0.292572	+	0.106227i
$111$	−1.44559	+	4.44908i	−0.137210	+	0.422288i
$112$	−2.48121	+	0.806193i	−0.234452	+	0.0761781i
$113$	−9.36957	−	12.8961i	−0.881415	−	1.21316i	−0.976027	−	0.217650i	$-0.930161\pi$
$113$	−9.36957	−	12.8961i	−0.881415	−	1.21316i	0.0946114	−	0.995514i	$-0.469839\pi$
$114$	−0.574481	−	1.76807i	−0.0538050	−	0.165595i
$115$	−9.27871	−	3.36891i	−0.865244	−	0.314153i
$116$	0.874919	+	0.635666i	0.0812342	+	0.0590201i
$117$	−2.79660	−	3.84919i	−0.258546	−	0.355858i
$118$		−	4.33139i		−	0.398737i
$119$	13.2463			1.21428
$120$	−1.76313	−	1.37527i	−0.160951	−	0.125545i
$121$	−2.74054	+	8.43453i	−0.249140	+	0.766775i
$122$	0.850518	−	0.276350i	0.0770023	−	0.0250196i
$123$		−	8.31906i		−	0.750104i
$124$	1.74727	+	5.28650i	0.156909	+	0.474741i
$125$	−8.32624	−	7.46149i	−0.744721	−	0.667376i
$126$	0.806193	+	2.48121i	0.0718214	+	0.221044i
$127$	2.33670	+	0.759239i	0.207348	+	0.0673716i	0.410850	−	0.911703i	$-0.365232\pi$
$127$	2.33670	+	0.759239i	0.207348	+	0.0673716i	−0.203501	+	0.979075i	$0.565232\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$	−4.71379			−0.415026
$130$	2.94052	+	10.2245i	0.257900	+	0.896744i
$131$	−12.2671	+	8.91259i	−1.07178	+	0.778697i	−0.976232	−	0.216728i	$-0.930462\pi$
$131$	−12.2671	+	8.91259i	−1.07178	+	0.778697i	−0.0955522	+	0.995424i	$0.530462\pi$
$132$	−0.858129	+	1.18111i	−0.0746905	+	0.102803i
$133$	2.85081	−	3.92381i	0.247197	−	0.340237i
$134$	−0.678857	−	2.08931i	−0.0586443	−	0.180489i
$135$	−1.37527	+	1.76313i	−0.118365	+	0.151746i
$136$	−1.56899	−	4.82884i	−0.134539	−	0.414070i
$137$	−0.913334	−	0.296760i	−0.0780314	−	0.0253539i	0.269741	−	0.962933i	$-0.413062\pi$
$137$	−0.913334	−	0.296760i	−0.0780314	−	0.0253539i	−0.347773	+	0.937579i	$0.613062\pi$
$138$	2.59484	−	3.57150i	0.220888	−	0.304026i
$139$	1.59641	−	4.91325i	0.135406	−	0.416736i	−0.860247	−	0.509877i	$-0.829691\pi$
$139$	1.59641	−	4.91325i	0.135406	−	0.416736i	0.995653	+	0.0931411i	$0.0296908\pi$
$140$	0.199007	−	5.83027i	0.0168192	−	0.492748i
$141$	7.81405	+	5.67724i	0.658062	+	0.478110i
$142$	−10.8473	−	3.52449i	−0.910281	−	0.295768i
$143$	6.60620	−	2.14648i	0.552438	−	0.179498i
$144$	0.809017	−	0.587785i	0.0674181	−	0.0489821i
$145$	−2.00373	+	1.35383i	−0.166401	+	0.112429i
$146$	10.1499	+	7.37431i	0.840009	+	0.610302i
$147$	0.113830	−	0.156673i	0.00938852	−	0.0129222i
$148$	2.74968	+	3.78461i	0.226022	+	0.311093i
$149$	−8.79127			−0.720209			−0.360104	−	0.932912i	$-0.617259\pi$
$149$	−8.79127			−0.720209			−0.360104	+	0.932912i	$0.617259\pi$
$150$	4.23607	−	2.65626i	0.345874	−	0.216883i
$151$	−15.2240	+	11.0609i	−1.23891	+	0.900124i	−0.997526	−	0.0703048i	$-0.977603\pi$
$151$	−15.2240	+	11.0609i	−1.23891	+	0.900124i	−0.241389	+	0.970429i	$0.577603\pi$
$152$	−1.76807	−	0.574481i	−0.143409	−	0.0465965i
$153$	−4.82884	+	1.56899i	−0.390389	+	0.126845i
$154$	−3.80882			−0.306924
$155$	−12.4446	−	0.361831i	−0.999578	−	0.0290629i
$156$	−4.75786			−0.380933
$157$	21.8225	−	7.09056i	1.74163	−	0.565888i	0.746578	−	0.665297i	$-0.231695\pi$
$157$	21.8225	−	7.09056i	1.74163	−	0.565888i	0.995047	+	0.0994091i	$0.0316953\pi$
$158$	3.46940	+	1.12728i	0.276011	+	0.0896814i
$159$	1.19225	−	0.866223i	0.0945519	−	0.0686960i
$160$	−2.14896	+	0.618034i	−0.169890	+	0.0488599i
$161$	11.5173			0.907688
$162$	−0.587785	−	0.809017i	−0.0461808	−	0.0635624i
$163$	12.9023	−	17.7584i	1.01058	−	1.39095i	0.0919830	−	0.995761i	$-0.470679\pi$
$163$	12.9023	−	17.7584i	1.01058	−	1.39095i	0.918600	−	0.395188i	$-0.129321\pi$
$164$	−6.73026	−	4.88982i	−0.525545	−	0.381831i
$165$	−1.82762	−	2.70497i	−0.142280	−	0.210582i
$166$	1.18776	−	0.862961i	0.0921883	−	0.0669787i
$167$	−11.5829	+	3.76350i	−0.896308	+	0.291228i	−0.720712	−	0.693234i	$-0.756185\pi$
$167$	−11.5829	+	3.76350i	−0.896308	+	0.291228i	−0.175596	+	0.984462i	$0.556185\pi$
$168$	2.48121	+	0.806193i	0.191429	+	0.0621992i
$169$	7.79667	+	5.66461i	0.599744	+	0.435739i
$170$	11.3467	+	0.387301i	0.870250	+	0.0297046i
$171$	−0.574481	+	1.76807i	−0.0439316	+	0.135208i
$172$	−2.77069	+	3.81353i	−0.211263	+	0.290779i
$173$	22.8869	+	7.43640i	1.74006	+	0.565379i	0.994841	−	0.101443i	$-0.0323459\pi$
$173$	22.8869	+	7.43640i	1.74006	+	0.565379i	0.745217	+	0.666822i	$0.232346\pi$
$174$	−0.334189	−	1.02853i	−0.0253348	−	0.0779726i
$175$	12.1023	+	4.86752i	0.914848	+	0.367950i
$176$	0.451145	+	1.38848i	0.0340063	+	0.104661i
$177$	−2.54593	+	3.50417i	−0.191364	+	0.263389i
$178$	1.02188	−	1.40650i	0.0765933	−	0.105422i
$179$	8.82509	−	6.41180i	0.659618	−	0.479241i	−0.206916	−	0.978359i	$-0.566343\pi$
$179$	8.82509	−	6.41180i	0.659618	−	0.479241i	0.866534	+	0.499118i	$0.166343\pi$
$180$	0.618034	+	2.14896i	0.0460655	+	0.160174i
$181$	4.16517			0.309595			0.154797	−	0.987946i	$-0.450528\pi$
$181$	4.16517			0.309595			0.154797	+	0.987946i	$0.450528\pi$
$182$	−7.29604	−	10.0421i	−0.540818	−	0.744372i
$183$	−0.850518	−	0.276350i	−0.0628721	−	0.0204284i
$184$	−1.36419	−	4.19855i	−0.100569	−	0.309521i
$185$	−10.0529	+	2.89118i	−0.739105	+	0.212564i
$186$	1.69375	−	5.30389i	0.124192	−	0.388900i
$187$		−	7.41259i		−	0.542063i
$188$	9.18597	−	2.98470i	0.669956	−	0.217682i
$189$	0.806193	−	2.48121i	0.0586419	−	0.180481i
$190$	2.55672	−	3.27776i	0.185484	−	0.237793i
$191$	13.8431			1.00165			0.500826	−	0.865548i	$-0.333030\pi$
$191$	13.8431			1.00165			0.500826	+	0.865548i	$0.333030\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	−7.50660	−	10.3319i	−0.540337	−	0.743710i	0.448325	−	0.893871i	$-0.352021\pi$
$193$	−7.50660	−	10.3319i	−0.540337	−	0.743710i	−0.988662	+	0.150161i	$0.952021\pi$
$194$	−1.63274	−	1.18626i	−0.117224	−	0.0851684i
$195$	3.63085	−	10.0001i	0.260011	−	0.716125i
$196$	−0.0598438	−	0.184180i	−0.00427456	−	0.0131557i
$197$	9.40690	+	12.9475i	0.670214	+	0.922470i	0.999765	−	0.0216673i	$-0.00689744\pi$
$197$	9.40690	+	12.9475i	0.670214	+	0.922470i	−0.329551	+	0.944138i	$0.606897\pi$
$198$	1.38848	−	0.451145i	0.0986751	−	0.0320615i
$199$	−4.33373	+	13.3378i	−0.307210	+	0.945495i	0.671633	+	0.740884i	$0.265593\pi$
$199$	−4.33373	+	13.3378i	−0.307210	+	0.945495i	−0.978843	+	0.204611i	$0.934407\pi$
$200$	0.340937	−	4.98836i	0.0241079	−	0.352731i
$201$	−0.678857	+	2.08931i	−0.0478829	+	0.147368i
$202$	−5.93212	−	1.92746i	−0.417382	−	0.135616i
$203$	1.65839	−	2.28257i	0.116396	−	0.160205i
$204$	−1.56899	+	4.82884i	−0.109851	+	0.338086i
$205$	15.4136	−	10.4142i	1.07653	−	0.727361i
$206$	−2.44325	+	1.77512i	−0.170229	+	0.123679i
$207$	−4.19855	+	1.36419i	−0.291819	+	0.0948178i
$208$	−2.79660	+	3.84919i	−0.193909	+	0.266893i
$209$	−2.19576	−	1.59531i	−0.151884	−	0.110350i
$210$	−3.58795	+	4.59982i	−0.247592	+	0.317418i
$211$	−0.562969			−0.0387564			−0.0193782	−	0.999812i	$-0.506169\pi$
$211$	−0.562969			−0.0387564			−0.0193782	+	0.999812i	$0.506169\pi$
$212$		−	1.47371i		−	0.101215i
$213$	6.70397	+	9.22722i	0.459348	+	0.632239i
$214$	0.732598	−	2.25470i	0.0500794	−	0.154128i
$215$	−5.90096	−	8.73371i	−0.402442	−	0.595634i
$216$	−1.00000			−0.0680414
$217$	13.7919	−	4.55845i	0.936257	−	0.309447i
$218$		−	1.72707i		−	0.116972i
$219$	−3.87690	−	11.9319i	−0.261977	−	0.806282i
$220$	−3.26261	−	0.111364i	−0.219965	−	0.00750818i
$221$	19.5436	−	14.1993i	1.31465	−	0.955148i
$222$		−	4.67804i		−	0.313969i
$223$		−	2.28518i		−	0.153027i	−0.997069	−	0.0765136i	$-0.975621\pi$
$223$		−	2.28518i		−	0.153027i	0.997069	−	0.0765136i	$-0.0243789\pi$
$224$	2.11064	−	1.53347i	0.141023	−	0.102459i
$225$	−4.98836	−	0.340937i	−0.332558	−	0.0227291i
$226$	12.8961	+	9.36957i	0.857837	+	0.623255i
$227$	26.2931	−	8.54313i	1.74513	−	0.567028i	0.749637	−	0.661849i	$-0.230228\pi$
$227$	26.2931	−	8.54313i	1.74513	−	0.567028i	0.995494	+	0.0948217i	$0.0302281\pi$
$228$	1.09273	+	1.50401i	0.0723676	+	0.0996055i
$229$	−5.72909	−	17.6323i	−0.378589	−	1.16518i	−0.941025	−	0.338337i	$-0.890136\pi$
$229$	−5.72909	−	17.6323i	−0.378589	−	1.16518i	0.562436	−	0.826841i	$-0.309864\pi$
$230$	9.86563	+	0.336748i	0.650520	+	0.0222045i
$231$	3.08140	+	2.23877i	0.202741	+	0.147300i
$232$	−1.02853	−	0.334189i	−0.0675263	−	0.0219406i
$233$	22.2747	+	7.23747i	1.45926	+	0.474143i	0.927844	−	0.372968i	$-0.121660\pi$
$233$	22.2747	+	7.23747i	1.45926	+	0.474143i	0.531417	+	0.847110i	$0.321660\pi$
$234$	3.84919	+	2.79660i	0.251629	+	0.182819i
$235$	−0.736768	+	21.5849i	−0.0480614	+	1.40805i
$236$	1.33847	+	4.11940i	0.0871272	+	0.268150i
$237$	−2.14421	−	2.95125i	−0.139281	−	0.191704i
$238$	−12.5979	+	4.09332i	−0.816603	+	0.265331i
$239$	9.55003	+	6.93850i	0.617740	+	0.448814i	0.852131	−	0.523328i	$-0.175310\pi$
$239$	9.55003	+	6.93850i	0.617740	+	0.448814i	−0.234392	+	0.972142i	$0.575310\pi$
$240$	2.10182	+	0.763128i	0.135672	+	0.0492597i
$241$	16.8369	−	12.2327i	1.08456	−	0.787979i	0.106088	−	0.994357i	$-0.466167\pi$
$241$	16.8369	−	12.2327i	1.08456	−	0.787979i	0.978472	+	0.206377i	$0.0661675\pi$
$242$		−	8.86859i		−	0.570094i
$243$			1.00000i			0.0641500i
$244$	−0.723494	+	0.525649i	−0.0463170	+	0.0336512i
$245$	0.432782	+	0.0147723i	0.0276494	+	0.000943770i
$246$	2.57073	+	7.91189i	0.163904	+	0.504444i
$247$		−	8.84513i		−	0.562802i
$248$	−3.29537	−	4.48782i	−0.209256	−	0.284977i
$249$	−1.46816			−0.0930406
$250$	10.2244	+	4.52335i	0.646651	+	0.286081i
$251$	−1.44571	+	4.44945i	−0.0912527	+	0.280847i	−0.986259	−	0.165207i	$-0.947171\pi$
$251$	−1.44571	+	4.44945i	−0.0912527	+	0.280847i	0.895006	+	0.446054i	$0.147171\pi$
$252$	−1.53347	−	2.11064i	−0.0965996	−	0.132958i
$253$		−	6.44505i		−	0.405197i
$254$	−2.45695			−0.154163
$255$	−8.95200	−	6.98274i	−0.560596	−	0.437276i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−11.6077	+	15.9767i	−0.724071	+	0.996598i	0.275308	+	0.961356i	$0.411220\pi$
$257$	−11.6077	+	15.9767i	−0.724071	+	0.996598i	−0.999379	+	0.0352422i	$0.988780\pi$
$258$	4.48308	−	1.45664i	0.279104	−	0.0906865i
$259$	9.87366	−	7.17363i	0.613519	−	0.445748i
$260$	−5.95613	−	8.81536i	−0.369383	−	0.546705i
$261$	−0.334189	+	1.02853i	−0.0206858	+	0.0636644i
$262$	8.91259	−	12.2671i	0.550622	−	0.757866i
$263$	−23.7210	−	7.70742i	−1.46270	−	0.475260i	−0.533807	−	0.845607i	$-0.679239\pi$
$263$	−23.7210	−	7.70742i	−1.46270	−	0.475260i	−0.928894	+	0.370347i	$0.879239\pi$
$264$	0.451145	−	1.38848i	0.0277660	−	0.0854551i
$265$	3.09746	+	1.12463i	0.190276	+	0.0690853i
$266$	−1.49876	+	4.61271i	−0.0918949	+	0.282823i
$267$	−1.65344	+	0.537236i	−0.101189	+	0.0328783i
$268$	1.29126	+	1.77727i	0.0788764	+	0.108564i
$269$	5.83891	+	17.9703i	0.356004	+	1.09567i	0.955425	+	0.295235i	$0.0953978\pi$
$269$	5.83891	+	17.9703i	0.356004	+	1.09567i	−0.599420	+	0.800434i	$0.704602\pi$
$270$	0.763128	−	2.10182i	0.0464425	−	0.127913i
$271$	21.3250	+	15.4935i	1.29540	+	0.941162i	0.999899	−	0.0141810i	$-0.00451409\pi$
$271$	21.3250	+	15.4935i	1.29540	+	0.941162i	0.295499	+	0.955343i	$0.404514\pi$
$272$	2.98439	+	4.10766i	0.180955	+	0.249063i
$273$			12.4128i			0.751254i
$274$	0.960337			0.0580161
$275$	2.72386	−	6.77244i	0.164255	−	0.408393i
$276$	−1.36419	+	4.19855i	−0.0821146	+	0.252723i
$277$	20.9454	−	6.80557i	1.25849	−	0.408907i	0.397532	−	0.917589i	$-0.369867\pi$
$277$	20.9454	−	6.80557i	1.25849	−	0.408907i	0.860955	+	0.508682i	$0.169867\pi$
$278$			5.16610i			0.309842i
$279$	−4.48782	+	3.29537i	−0.268679	+	0.197289i
$280$	1.61239	+	5.60642i	0.0963585	+	0.335048i
$281$	2.45248	+	7.54795i	0.146303	+	0.450273i	0.997176	−	0.0750973i	$-0.0239267\pi$
$281$	2.45248	+	7.54795i	0.146303	+	0.450273i	−0.850874	+	0.525370i	$0.823927\pi$
$282$	−9.18597	−	2.98470i	−0.547016	−	0.177736i
$283$	4.03165	+	5.54909i	0.239657	+	0.329859i	0.911855	−	0.410512i	$-0.134650\pi$
$283$	4.03165	+	5.54909i	0.239657	+	0.329859i	−0.672199	+	0.740371i	$0.734650\pi$
$284$	11.4055			0.676790
$285$	−3.99504	+	1.14896i	−0.236646	+	0.0680586i
$286$	−5.61957	+	4.08285i	−0.332292	+	0.241424i
$287$	−12.7570	+	17.5586i	−0.753024	+	1.03645i
$288$	−0.587785	+	0.809017i	−0.0346356	+	0.0476718i
$289$	−2.71299	−	8.34972i	−0.159588	−	0.491160i
$290$	1.48730	−	1.90675i	0.0873375	−	0.111968i
$291$	0.623653	+	1.91941i	0.0365592	+	0.112518i
$292$	−11.9319	−	3.87690i	−0.698261	−	0.226879i
$293$	−19.1762	+	26.3937i	−1.12028	+	1.54194i	−0.314957	+	0.949106i	$0.601990\pi$
$293$	−19.1762	+	26.3937i	−1.12028	+	1.54194i	−0.805327	+	0.592831i	$0.798010\pi$
$294$	−0.0598438	+	0.184180i	−0.00349016	+	0.0107416i
$295$	−9.67965	−	0.330400i	−0.563571	−	0.0192366i
$296$	−3.78461	−	2.74968i	−0.219976	−	0.159822i
$297$	−1.38848	−	0.451145i	−0.0805678	−	0.0261781i
$298$	8.36099	−	2.71665i	0.484339	−	0.157371i
$299$	16.9927	−	12.3459i	0.982711	−	0.713982i
$300$	−3.20791	+	3.83527i	−0.185209	+	0.221430i
$301$	9.94911	+	7.22845i	0.573457	+	0.416641i
$302$	11.0609	−	15.2240i	0.636484	−	0.876045i
$303$	3.66625	+	5.04616i	0.210621	+	0.289894i
$304$	1.85906			0.106624
$305$	−0.552700	−	1.92179i	−0.0316475	−	0.110041i
$306$	4.10766	−	2.98439i	0.234819	−	0.170606i
$307$	−3.05911	−	0.993966i	−0.174593	−	0.0567286i	0.220416	−	0.975406i	$-0.429258\pi$
$307$	−3.05911	−	0.993966i	−0.174593	−	0.0567286i	−0.395009	+	0.918677i	$0.629258\pi$
$308$	3.62240	−	1.17699i	0.206406	−	0.0670652i
$309$	3.02002			0.171803
$310$	11.9474	−	3.50148i	0.678565	−	0.198871i
$311$	−4.19986			−0.238152			−0.119076	−	0.992885i	$-0.537993\pi$
$311$	−4.19986			−0.238152			−0.119076	+	0.992885i	$0.537993\pi$
$312$	4.52499	−	1.47026i	0.256177	−	0.0832370i
$313$	2.87211	+	0.933206i	0.162341	+	0.0527479i	0.389060	−	0.921212i	$-0.372800\pi$
$313$	2.87211	+	0.933206i	0.162341	+	0.0527479i	−0.226719	+	0.973960i	$0.572800\pi$
$314$	−18.5633	+	13.4870i	−1.04759	+	0.761118i
$315$	5.60642	−	1.61239i	0.315886	−	0.0908477i
$316$	−3.64795			−0.205213
$317$	−7.38243	−	10.1610i	−0.414639	−	0.570701i	0.549703	−	0.835360i	$-0.314741\pi$
$317$	−7.38243	−	10.1610i	−0.414639	−	0.570701i	−0.964342	+	0.264659i	$0.914741\pi$
$318$	−0.866223	+	1.19225i	−0.0485754	+	0.0668583i
$319$	−1.27733	−	0.928031i	−0.0715165	−	0.0519598i
$320$	1.85280	−	1.25185i	0.103575	−	0.0699806i
$321$	−1.91797	+	1.39348i	−0.107050	+	0.0777767i
$322$	−10.9536	+	3.55903i	−0.610419	+	0.198337i
$323$	−8.97710	−	2.91684i	−0.499499	−	0.162297i
$324$	0.809017	+	0.587785i	0.0449454	+	0.0326547i
$325$	23.0736	−	5.79145i	1.27989	−	0.321252i
$326$	−6.78312	+	20.8763i	−0.375682	+	1.15623i
$327$	−1.01515	+	1.39723i	−0.0561377	+	0.0772670i
$328$	7.91189	+	2.57073i	0.436861	+	0.141945i
$329$	−7.78678	−	23.9652i	−0.429299	−	1.32125i
$330$	2.57405	+	2.00781i	0.141697	+	0.110526i
$331$	0.117391	+	0.361292i	0.00645238	+	0.0198584i	0.954231	−	0.299071i	$-0.0966767\pi$
$331$	0.117391	+	0.361292i	0.00645238	+	0.0198584i	−0.947778	+	0.318929i	$0.896677\pi$
$332$	−0.862961	+	1.18776i	−0.0473611	+	0.0651870i
$333$	−2.74968	+	3.78461i	−0.150682	+	0.207395i
$334$	9.85296	−	7.15860i	0.539130	−	0.391701i
$335$	−4.72090	+	1.35771i	−0.257930	+	0.0741798i
$336$	−2.60890			−0.142327
$337$	12.7064	+	17.4889i	0.692162	+	0.952679i	0.999999	+	0.00123971i	$0.000394612\pi$
$337$	12.7064	+	17.4889i	0.692162	+	0.952679i	−0.307838	+	0.951439i	$0.599605\pi$
$338$	−9.16553	−	2.97806i	−0.498539	−	0.161985i
$339$	−4.92588	−	15.1603i	−0.267537	−	0.823394i
$340$	−10.9110	+	3.13797i	−0.591733	+	0.170180i
$341$	−2.55090	−	7.71794i	−0.138139	−	0.417950i
$342$		−	1.85906i		−	0.100526i
$343$	−17.8490	+	5.79948i	−0.963753	+	0.313142i
$344$	1.45664	−	4.48308i	0.0785368	−	0.241711i
$345$	−7.78352	−	6.07130i	−0.419051	−	0.326868i
$346$	−24.0647			−1.29373
$347$		−	12.7424i		−	0.684047i	−0.939691	−	0.342023i	$-0.888888\pi$
$347$		−	12.7424i		−	0.684047i	0.939691	−	0.342023i	$-0.111112\pi$
$348$	0.635666	+	0.874919i	0.0340753	+	0.0469006i
$349$	−28.5687	−	20.7564i	−1.52925	−	1.11106i	−0.956656	−	0.291222i	$-0.905938\pi$
$349$	−28.5687	−	20.7564i	−1.52925	−	1.11106i	−0.572591	−	0.819841i	$-0.694062\pi$
$350$	−13.0141	−	0.889470i	−0.695634	−	0.0475442i
$351$	−1.47026	−	4.52499i	−0.0784766	−	0.241526i
$352$	−0.858129	−	1.18111i	−0.0457384	−	0.0629535i
$353$	−21.2468	+	6.90352i	−1.13086	+	0.367437i	−0.813901	−	0.581004i	$-0.802660\pi$
$353$	−21.2468	+	6.90352i	−1.13086	+	0.367437i	−0.316954	+	0.948441i	$0.602660\pi$
$354$	1.33847	−	4.11940i	0.0711390	−	0.218943i
$355$	−8.70383	+	23.9722i	−0.461951	+	1.27231i
$356$	−0.537236	+	1.65344i	−0.0284734	+	0.0876322i
$357$	12.5979	+	4.09332i	0.666754	+	0.216641i
$358$	−6.41180	+	8.82509i	−0.338874	+	0.466420i
$359$	−8.69462	+	26.7593i	−0.458884	+	1.41230i	0.407629	+	0.913148i	$0.366356\pi$
$359$	−8.69462	+	26.7593i	−0.458884	+	1.41230i	−0.866514	+	0.499153i	$0.833644\pi$
$360$	−1.25185	−	1.85280i	−0.0659783	−	0.0976512i
$361$	12.5753	−	9.13648i	0.661857	−	0.480867i
$362$	−3.96132	+	1.28711i	−0.208202	+	0.0676490i
$363$	−5.21283	+	7.17484i	−0.273602	+	0.376581i
$364$	10.0421	+	7.29604i	0.526351	+	0.382416i
$365$	17.2541	−	22.1201i	0.903121	−	1.15782i
$366$	0.894288			0.0467452
$367$			17.4128i			0.908943i	0.890761	+	0.454471i	$0.150172\pi$
$367$			17.4128i			0.908943i	−0.890761	+	0.454471i	$0.849828\pi$
$368$	2.59484	+	3.57150i	0.135266	+	0.186177i
$369$	2.57073	−	7.91189i	0.133827	−	0.411877i
$370$	8.66747	−	5.85620i	0.450600	−	0.304449i
$371$	−3.84475			−0.199609
$372$	0.0281347	+	5.56769i	0.00145872	+	0.288671i
$373$		−	33.9694i		−	1.75887i	−0.476020	−	0.879435i	$-0.657921\pi$
$373$		−	33.9694i		−	1.75887i	0.476020	−	0.879435i	$-0.342079\pi$
$374$	2.29062	+	7.04980i	0.118445	+	0.364536i
$375$	−5.61300	−	9.66924i	−0.289854	−	0.499318i
$376$	−7.81405	+	5.67724i	−0.402979	+	0.292781i
$377$		−	5.14543i		−	0.265003i
$378$			2.60890i			0.134187i
$379$	5.35456	−	3.89031i	0.275045	−	0.199832i	−0.441708	−	0.897159i	$-0.645627\pi$
$379$	5.35456	−	3.89031i	0.275045	−	0.199832i	0.716753	+	0.697327i	$0.245627\pi$
$380$	−1.41870	+	3.90740i	−0.0727777	+	0.200445i
$381$	1.98771	+	1.44416i	0.101834	+	0.0739865i
$382$	−13.1656	+	4.27776i	−0.673610	+	0.218869i
$383$	8.33438	+	11.4713i	0.425867	+	0.586156i	0.966998	−	0.254782i	$-0.0820038\pi$
$383$	8.33438	+	11.4713i	0.425867	+	0.586156i	−0.541131	+	0.840938i	$0.682004\pi$
$384$	0.309017	+	0.951057i	0.0157695	+	0.0485334i
$385$	−0.290538	+	8.51182i	−0.0148072	+	0.433803i
$386$	10.3319	+	7.50660i	0.525882	+	0.382076i
$387$	−4.48308	−	1.45664i	−0.227888	−	0.0740452i
$388$	1.91941	+	0.623653i	0.0974431	+	0.0316612i
$389$	−9.25458	−	6.72385i	−0.469226	−	0.340913i	0.327914	−	0.944708i	$-0.393654\pi$
$389$	−9.25458	−	6.72385i	−0.469226	−	0.340913i	−0.797140	+	0.603795i	$0.793654\pi$
$390$	−0.362931	+	10.6327i	−0.0183777	+	0.538408i
$391$	−6.92646	−	21.3175i	−0.350286	−	1.07807i
$392$	0.113830	+	0.156673i	0.00574927	+	0.00791319i
$393$	−14.4209	+	4.68563i	−0.727437	+	0.236359i
$394$	−12.9475	−	9.40690i	−0.652285	−	0.473913i
$395$	2.78385	−	7.66732i	0.140071	−	0.385785i
$396$	−1.18111	+	0.858129i	−0.0593531	+	0.0431226i
$397$			6.08289i			0.305291i	0.988281	+	0.152646i	$0.0487793\pi$
$397$			6.08289i			0.305291i	−0.988281	+	0.152646i	$0.951221\pi$
$398$		−	14.0242i		−	0.702972i
$399$	3.92381	−	2.85081i	0.196436	−	0.142719i
$400$	1.21724	+	4.84957i	0.0608619	+	0.242479i
$401$	−10.6744	−	32.8524i	−0.533054	−	1.64057i	−0.747817	−	0.663905i	$-0.768898\pi$
$401$	−10.6744	−	32.8524i	−0.533054	−	1.64057i	0.214764	−	0.976666i	$-0.431102\pi$
$402$		−	2.19683i		−	0.109568i
$403$	15.4623	−	21.5098i	0.770232	−	1.07148i
$404$	6.23740			0.310322
$405$	−1.85280	+	1.25185i	−0.0920664	+	0.0622050i
$406$	−0.871866	+	2.68333i	−0.0432700	+	0.133171i
$407$	−4.01436	−	5.52529i	−0.198984	−	0.273878i
$408$		−	5.07734i		−	0.251366i
$409$	5.99496			0.296432			0.148216	−	0.988955i	$-0.452647\pi$
$409$	5.99496			0.296432			0.148216	+	0.988955i	$0.452647\pi$
$410$	−11.4410	+	14.6676i	−0.565030	+	0.724379i
$411$	−0.776929	−	0.564472i	−0.0383231	−	0.0278433i
$412$	1.77512	−	2.44325i	0.0874540	−	0.120370i
$413$	10.7471	−	3.49194i	0.528829	−	0.171827i
$414$	3.57150	−	2.59484i	0.175529	−	0.127530i
$415$	−1.83791	−	2.72020i	−0.0902196	−	0.133529i
$416$	1.47026	−	4.52499i	0.0720854	−	0.221856i
$417$	3.03655	−	4.17946i	0.148701	−	0.204669i
$418$	2.58127	+	0.838705i	0.126254	+	0.0410224i
$419$	−8.78260	+	27.0301i	−0.429058	+	1.32051i	0.469996	+	0.882669i	$0.344255\pi$
$419$	−8.78260	+	27.0301i	−0.429058	+	1.32051i	−0.899054	+	0.437837i	$0.855745\pi$
$420$	1.99092	−	5.48342i	0.0971470	−	0.267564i
$421$	−7.38365	+	22.7245i	−0.359857	+	1.10753i	0.593282	+	0.804994i	$0.297832\pi$
$421$	−7.38365	+	22.7245i	−0.359857	+	1.10753i	−0.953139	+	0.302531i	$0.902168\pi$
$422$	0.535415	−	0.173967i	0.0260636	−	0.00846858i
$423$	5.67724	+	7.81405i	0.276037	+	0.379932i
$424$	0.455400	+	1.40158i	0.0221162	+	0.0680667i
$425$	1.73105	−	25.3276i	0.0839685	−	1.22857i
$426$	−9.22722	−	6.70397i	−0.447060	−	0.324808i
$427$	1.37136	+	1.88752i	0.0663650	+	0.0913436i
$428$			2.37074i			0.114594i
$429$	6.94617			0.335364
$430$	8.31101	+	6.48275i	0.400792	+	0.312626i
$431$	2.00824	−	6.18073i	0.0967335	−	0.297715i	−0.890968	−	0.454066i	$-0.849973\pi$
$431$	2.00824	−	6.18073i	0.0967335	−	0.297715i	0.987702	+	0.156351i	$0.0499731\pi$
$432$	0.951057	−	0.309017i	0.0457577	−	0.0148676i
$433$		−	19.6221i		−	0.942979i	−0.881872	−	0.471490i	$-0.843716\pi$
$433$		−	19.6221i		−	0.942979i	0.881872	−	0.471490i	$-0.156284\pi$
$434$	−11.7083	+	8.59728i	−0.562015	+	0.412683i
$435$	−2.32401	+	0.668379i	−0.111428	+	0.0320463i
$436$	0.533694	+	1.64254i	0.0255593	+	0.0786635i
$437$	−7.80534	−	2.53611i	−0.373380	−	0.121319i
$438$	7.37431	+	10.1499i	0.352358	+	0.484979i
$439$	−20.2699			−0.967428			−0.483714	−	0.875226i	$-0.660713\pi$
$439$	−20.2699			−0.967428			−0.483714	+	0.875226i	$0.660713\pi$
$440$	3.13734	−	0.902290i	0.149567	−	0.0430150i
$441$	0.156673	−	0.113830i	0.00746063	−	0.00542046i
$442$	−14.1993	+	19.5436i	−0.675391	+	0.929597i
$443$	0.392196	−	0.539812i	0.0186338	−	0.0256472i	−0.799598	−	0.600535i	$-0.794954\pi$
$443$	0.392196	−	0.539812i	0.0186338	−	0.0256472i	0.818232	+	0.574888i	$0.194954\pi$
$444$	1.44559	+	4.44908i	0.0686048	+	0.211144i
$445$	−3.06525	−	2.39096i	−0.145307	−	0.113342i
$446$	0.706161	+	2.17334i	0.0334377	+	0.102911i
$447$	−8.36099	−	2.71665i	−0.395461	−	0.128493i
$448$	−1.53347	+	2.11064i	−0.0724497	+	0.0997184i
$449$	−6.52879	+	20.0936i	−0.308113	+	0.948274i	0.670384	+	0.742014i	$0.266129\pi$
$449$	−6.52879	+	20.0936i	−0.308113	+	0.948274i	−0.978497	+	0.206260i	$0.933871\pi$
$450$	4.84957	−	1.21724i	0.228611	−	0.0573812i
$451$	9.82574	+	7.13882i	0.462676	+	0.336154i
$452$	−15.1603	−	4.92588i	−0.713080	−	0.231694i
$453$	−17.8969	+	5.81506i	−0.840871	+	0.273215i
$454$	−22.3662	+	16.2500i	−1.04970	+	0.762650i
$455$	−22.9984	+	15.5389i	−1.07818	+	0.728476i
$456$	−1.50401	−	1.09273i	−0.0704317	−	0.0511716i
$457$	7.42348	−	10.2175i	0.347256	−	0.477957i	−0.599287	−	0.800534i	$-0.704549\pi$
$457$	7.42348	−	10.2175i	0.347256	−	0.477957i	0.946543	+	0.322577i	$0.104549\pi$
$458$	10.8974	+	14.9990i	0.509201	+	0.700855i
$459$	−5.07734			−0.236990
$460$	−9.48683	+	2.72838i	−0.442326	+	0.127211i
$461$	−11.0161	+	8.00364i	−0.513069	+	0.372767i	−0.813987	−	0.580884i	$-0.802707\pi$
$461$	−11.0161	+	8.00364i	−0.513069	+	0.372767i	0.300917	+	0.953650i	$0.402707\pi$
$462$	−3.62240	−	1.17699i	−0.168529	−	0.0547585i
$463$	−22.4421	+	7.29188i	−1.04297	+	0.338883i	−0.779907	−	0.625895i	$-0.784734\pi$
$463$	−22.4421	+	7.29188i	−1.04297	+	0.338883i	−0.263066	+	0.964778i	$0.584734\pi$
$464$	1.08146			0.0502055
$465$	−11.7237	−	4.18973i	−0.543676	−	0.194294i
$466$	−23.4210			−1.08495
$467$	2.13216	−	0.692779i	0.0986644	−	0.0320580i	−0.259269	−	0.965805i	$-0.583482\pi$
$467$	2.13216	−	0.692779i	0.0986644	−	0.0320580i	0.357933	+	0.933747i	$0.383482\pi$
$468$	−4.52499	−	1.47026i	−0.209168	−	0.0679627i
$469$	4.63671	−	3.36877i	0.214104	−	0.155555i
$470$	−5.96940	−	20.7562i	−0.275348	−	0.957411i
$471$	22.9455			1.05727
$472$	−2.54593	−	3.50417i	−0.117186	−	0.161292i
$473$	4.04503	−	5.56751i	0.185991	−	0.255994i
$474$	2.95125	+	2.14421i	0.135555	+	0.0984868i
$475$	−7.12999	−	5.96369i	−0.327147	−	0.273633i
$476$	10.7165	−	7.78596i	0.491188	−	0.356869i
$477$	1.40158	−	0.455400i	0.0641739	−	0.0208514i
$478$	−11.2267	−	3.64779i	−0.513499	−	0.166846i
$479$	−22.0284	−	16.0046i	−1.00650	−	0.731268i	−0.0430312	−	0.999074i	$-0.513701\pi$
$479$	−22.0284	−	16.0046i	−1.00650	−	0.731268i	−0.963473	+	0.267806i	$0.913701\pi$
$480$	−2.23477	−	0.0762803i	−0.102003	−	0.00348170i
$481$	6.87792	−	21.1681i	0.313606	−	0.965181i
$482$	−12.2327	+	16.8369i	−0.557186	+	0.766900i
$483$	10.9536	+	3.55903i	0.498405	+	0.161942i
$484$	2.74054	+	8.43453i	0.124570	+	0.383388i
$485$	−2.77556	+	3.55831i	−0.126032	+	0.161575i
$486$	−0.309017	−	0.951057i	−0.0140173	−	0.0431408i
$487$	−24.2935	+	33.4372i	−1.10084	+	1.51518i	−0.266584	+	0.963812i	$0.585895\pi$
$487$	−24.2935	+	33.4372i	−1.10084	+	1.51518i	−0.834261	+	0.551370i	$0.814105\pi$
$488$	0.525649	−	0.723494i	0.0237950	−	0.0327510i
$489$	17.7584	−	12.9023i	0.803065	−	0.583461i
$490$	−0.416165	+	0.119688i	−0.0188004	+	0.00540694i
$491$	−17.4627			−0.788080			−0.394040	−	0.919093i	$-0.628923\pi$
$491$	−17.4627			−0.788080			−0.394040	+	0.919093i	$0.628923\pi$
$492$	−4.88982	−	6.73026i	−0.220450	−	0.303424i
$493$	−5.22220	−	1.69679i	−0.235196	−	0.0764198i
$494$	2.73330	+	8.41222i	0.122977	+	0.378484i
$495$	−0.902290	−	3.13734i	−0.0405549	−	0.141013i
$496$	4.52090	+	3.24985i	0.202994	+	0.145922i
$497$		−	29.7557i		−	1.33473i
$498$	1.39630	−	0.453685i	0.0625697	−	0.0203301i
$499$	0.869270	−	2.67534i	0.0389139	−	0.119765i	−0.929713	−	0.368286i	$-0.879945\pi$
$499$	0.869270	−	2.67534i	0.0389139	−	0.119765i	0.968626	+	0.248522i	$0.0799447\pi$
$500$	−11.1218	−	1.14243i	−0.497383	−	0.0510910i
$501$	−12.1789			−0.544115
$502$		−	4.67843i		−	0.208809i
$503$	23.6481	+	32.5488i	1.05441	+	1.45128i	0.884918	+	0.465747i	$0.154214\pi$
$503$	23.6481	+	32.5488i	1.05441	+	1.45128i	0.169497	+	0.985531i	$0.445786\pi$
$504$	2.11064	+	1.53347i	0.0940155	+	0.0683062i
$505$	−4.75993	+	13.1099i	−0.211814	+	0.583382i
$506$	1.99163	+	6.12960i	0.0885387	+	0.272494i
$507$	5.66461	+	7.79667i	0.251574	+	0.346262i
$508$	2.33670	−	0.759239i	0.103674	−	0.0336858i
$509$	−2.53618	+	7.80555i	−0.112414	+	0.345975i	−0.991399	−	0.130875i	$-0.958221\pi$
$509$	−2.53618	+	7.80555i	−0.112414	+	0.345975i	0.878985	+	0.476850i	$0.158221\pi$
$510$	10.6716	+	3.87466i	0.472549	+	0.171573i
$511$	−10.1144	+	31.1290i	−0.447437	+	1.37707i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	−1.09273	+	1.50401i	−0.0482451	+	0.0664036i
$514$	6.10255	−	18.7817i	0.269172	−	0.828426i
$515$	3.78061	+	5.59549i	0.166594	+	0.246567i
$516$	−3.81353	+	2.77069i	−0.167881	+	0.121973i
$517$	−13.4109	+	4.35747i	−0.589812	+	0.191641i
$518$	−7.17363	+	9.87366i	−0.315191	+	0.433824i
$519$	19.4688	+	14.1449i	0.854583	+	0.620891i
$520$	8.38871	+	6.54336i	0.367869	+	0.286945i
$521$	−21.1992			−0.928755			−0.464377	−	0.885637i	$-0.653722\pi$
$521$	−21.1992			−0.928755			−0.464377	+	0.885637i	$0.653722\pi$
$522$		−	1.08146i		−	0.0473342i
$523$	24.9394	+	34.3261i	1.09052	+	1.50098i	0.847380	+	0.530988i	$0.178179\pi$
$523$	24.9394	+	34.3261i	1.09052	+	1.50098i	0.243144	+	0.969990i	$0.421821\pi$
$524$	−4.68563	+	14.4209i	−0.204693	+	0.629979i
$525$	10.0058	+	8.36911i	0.436690	+	0.365258i
$526$	24.9417			1.08751
$527$	−16.7317	−	22.7862i	−0.728845	−	0.992583i
$528$			1.45994i			0.0635355i
$529$	1.08502	+	3.33935i	0.0471749	+	0.145189i
$530$	−3.29339	−	0.112415i	−0.143056	−	0.00488298i
$531$	−3.50417	+	2.54593i	−0.152068	+	0.110484i
$532$		−	4.85009i		−	0.210278i
$533$			39.5809i			1.71444i
$534$	1.40650	−	1.02188i	0.0608652	−	0.0442212i
$535$	−4.98285	−	1.80917i	−0.215428	−	0.0782174i
$536$	−1.77727	−	1.29126i	−0.0767664	−	0.0557740i
$537$	10.3745	−	3.37088i	0.447693	−	0.145464i
$538$	−11.1063	−	15.2865i	−0.478825	−	0.659046i
$539$	0.0873681	+	0.268891i	0.00376321	+	0.0115820i
$540$	−0.0762803	+	2.23477i	−0.00328258	+	0.0961690i
$541$	29.0823	+	21.1295i	1.25035	+	0.908429i	0.998242	−	0.0592708i	$-0.0188776\pi$
$541$	29.0823	+	21.1295i	1.25035	+	0.908429i	0.252104	+	0.967700i	$0.418878\pi$
$542$	−25.0690	−	8.14541i	−1.07680	−	0.349875i
$543$	3.96132	+	1.28711i	0.169996	+	0.0552351i
$544$	−4.10766	−	2.98439i	−0.176114	−	0.127955i
$545$	−3.85960	−	0.131741i	−0.165327	−	0.00564318i
$546$	−3.83575	−	11.8052i	−0.164155	−	0.505217i
$547$	14.9307	+	20.5503i	0.638389	+	0.878668i	0.998528	−	0.0542310i	$-0.0172707\pi$
$547$	14.9307	+	20.5503i	0.638389	+	0.878668i	−0.360139	+	0.932899i	$0.617271\pi$
$548$	−0.913334	+	0.296760i	−0.0390157	+	0.0126770i
$549$	−0.723494	−	0.525649i	−0.0308780	−	0.0224342i
$550$	−0.497746	+	7.28269i	−0.0212240	+	0.310535i
$551$	−1.62653	+	1.18174i	−0.0692923	+	0.0503438i
$552$		−	4.41461i		−	0.187898i
$553$			9.51712i			0.404709i
$554$	−17.8172	+	12.9450i	−0.756981	+	0.549979i
$555$	−10.4543	−	0.356842i	−0.443761	−	0.0151471i
$556$	−1.59641	−	4.91325i	−0.0677029	−	0.208368i
$557$			12.1202i			0.513548i	0.966471	+	0.256774i	$0.0826596\pi$
$557$			12.1202i			0.513548i	−0.966471	+	0.256774i	$0.917340\pi$
$558$	3.24985	−	4.52090i	0.137577	−	0.191385i
$559$	22.4275			0.948583
$560$	−3.26595	−	4.83376i	−0.138012	−	0.204264i
$561$	2.29062	−	7.04980i	0.0967099	−	0.297643i
$562$	−4.66489	−	6.42067i	−0.196777	−	0.270840i
$563$			23.6343i			0.996068i	0.867157	+	0.498034i	$0.165945\pi$
$563$			23.6343i			0.996068i	−0.867157	+	0.498034i	$0.834055\pi$
$564$	9.65870			0.406705
$565$	21.9225	−	28.1051i	0.922288	−	1.18239i
$566$	−5.54909	−	4.03165i	−0.233245	−	0.169463i
$567$	1.53347	−	2.11064i	0.0643997	−	0.0886386i
$568$	−10.8473	+	3.52449i	−0.455141	+	0.147884i
$569$	14.7873	−	10.7436i	0.619915	−	0.450395i	−0.232977	−	0.972482i	$-0.574847\pi$
$569$	14.7873	−	10.7436i	0.619915	−	0.450395i	0.852892	+	0.522087i	$0.174847\pi$
$570$	3.44446	−	2.32726i	0.144273	−	0.0974783i
$571$	−2.63673	+	8.11503i	−0.110344	+	0.339603i	−0.990947	−	0.134250i	$-0.957137\pi$
$571$	−2.63673	+	8.11503i	−0.110344	+	0.339603i	0.880604	+	0.473854i	$0.157137\pi$
$572$	4.08285	−	5.61957i	0.170713	−	0.234966i
$573$	13.1656	+	4.27776i	0.550000	+	0.178706i
$574$	6.70677	−	20.6413i	0.279935	−	0.861552i
$575$	1.50511	−	22.0217i	0.0627672	−	0.918368i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	−32.2896	+	10.4915i	−1.34423	+	0.436768i	−0.890749	−	0.454496i	$-0.849819\pi$
$577$	−32.2896	+	10.4915i	−1.34423	+	0.436768i	−0.453484	+	0.891264i	$0.649819\pi$
$578$	5.16041	+	7.10270i	0.214645	+	0.295433i
$579$	−3.94645	−	12.1459i	−0.164009	−	0.504768i
$580$	−0.825292	+	2.27303i	−0.0342684	+	0.0943825i
$581$	3.09875	+	2.25138i	0.128558	+	0.0934028i
$582$	−1.18626	−	1.63274i	−0.0491720	−	0.0676794i
$583$			2.15152i			0.0891067i
$584$	12.5459			0.519154
$585$	6.54336	−	8.38871i	0.270535	−	0.346830i
$586$	10.0815	−	31.0277i	0.416463	−	1.28174i
$587$	23.2577	−	7.55690i	0.959950	−	0.311907i	0.213198	−	0.977009i	$-0.431612\pi$
$587$	23.2577	−	7.55690i	0.959950	−	0.311907i	0.746752	+	0.665103i	$0.231612\pi$
$588$		−	0.193659i		−	0.00798635i
$589$	−10.3507	+	0.0523040i	−0.426492	+	0.00215515i
$590$	9.30799	−	2.67695i	0.383204	−	0.110208i
$591$	4.94550	+	15.2207i	0.203431	+	0.626095i
$592$	4.44908	+	1.44559i	0.182856	+	0.0594135i
$593$	−7.65636	−	10.5381i	−0.314409	−	0.432747i	0.622341	−	0.782746i	$-0.286182\pi$
$593$	−7.65636	−	10.5381i	−0.314409	−	0.432747i	−0.936750	+	0.350000i	$0.886182\pi$
$594$	1.45994			0.0599019
$595$	8.18664	+	28.4657i	0.335620	+	1.16698i
$596$	−7.11228	+	5.16738i	−0.291330	+	0.211664i
$597$	−8.24324	+	11.3459i	−0.337373	+	0.464355i
$598$	−12.3459	+	16.9927i	−0.504861	+	0.694882i
$599$	11.0471	+	33.9993i	0.451370	+	1.38918i	0.875344	+	0.483501i	$0.160635\pi$
$599$	11.0471	+	33.9993i	0.451370	+	1.38918i	−0.423974	+	0.905675i	$0.639365\pi$
$600$	1.86574	−	4.63886i	0.0761685	−	0.189381i
$601$	3.47202	+	10.6858i	0.141627	+	0.435882i	0.996562	−	0.0828529i	$-0.0264032\pi$
$601$	3.47202	+	10.6858i	0.141627	+	0.435882i	−0.854935	+	0.518735i	$0.826403\pi$
$602$	−11.6959	−	3.80022i	−0.476689	−	0.154886i
$603$	−1.29126	+	1.77727i	−0.0525843	+	0.0723760i
$604$	−5.81506	+	17.8969i	−0.236612	+	0.728215i
$605$	−19.8192	−	0.676498i	−0.805766	−	0.0275036i
$606$	−5.04616	−	3.66625i	−0.204986	−	0.148931i
$607$	31.7362	+	10.3117i	1.28813	+	0.418540i	0.871438	−	0.490505i	$-0.163188\pi$
$607$	31.7362	+	10.3117i	1.28813	+	0.418540i	0.416696	+	0.909046i	$0.363188\pi$
$608$	−1.76807	+	0.574481i	−0.0717047	+	0.0232983i
$609$	2.28257	−	1.65839i	0.0924946	−	0.0672012i
$610$	1.11952	+	1.65694i	0.0453278	+	0.0670874i
$611$	−37.1781	−	27.0115i	−1.50407	−	1.09277i
$612$	−2.98439	+	4.10766i	−0.120637	+	0.166042i
$613$	−19.3732	−	26.6650i	−0.782477	−	1.07699i	−0.995004	−	0.0998322i	$-0.968169\pi$
$613$	−19.3732	−	26.6650i	−0.782477	−	1.07699i	0.212527	−	0.977155i	$-0.431831\pi$
$614$	3.21654			0.129809
$615$	17.8773	−	5.14146i	0.720884	−	0.207324i
$616$	−3.08140	+	2.23877i	−0.124153	+	0.0902026i
$617$	−25.3159	−	8.22563i	−1.01918	−	0.331152i	−0.248676	−	0.968587i	$-0.579995\pi$
$617$	−25.3159	−	8.22563i	−1.01918	−	0.331152i	−0.770504	+	0.637435i	$0.779995\pi$
$618$	−2.87221	+	0.933237i	−0.115537	+	0.0375403i
$619$	−22.4470			−0.902219			−0.451110	−	0.892469i	$-0.648972\pi$
$619$	−22.4470			−0.902219			−0.451110	+	0.892469i	$0.648972\pi$
$620$	−10.2806	+	7.02205i	−0.412879	+	0.282012i
$621$	−4.41461			−0.177152
$622$	3.99431	−	1.29783i	0.160157	−	0.0520382i
$623$	4.31366	+	1.40159i	0.172823	+	0.0561536i
$624$	−3.84919	+	2.79660i	−0.154091	+	0.111954i
$625$	10.8885	−	22.5042i	0.435542	−	0.900169i
$626$	−3.01992			−0.120700
$627$	−1.59531	−	2.19576i	−0.0637106	−	0.0876901i
$628$	13.4870	−	18.5633i	0.538192	−	0.740757i
$629$	−19.2158	−	13.9611i	−0.766183	−	0.556664i
$630$	−4.83376	+	3.26595i	−0.192582	+	0.130119i
$631$	20.3171	−	14.7612i	0.808811	−	0.587636i	−0.104675	−	0.994507i	$-0.533380\pi$
$631$	20.3171	−	14.7612i	0.808811	−	0.587636i	0.913486	+	0.406871i	$0.133380\pi$
$632$	3.46940	−	1.12728i	0.138005	−	0.0448407i
$633$	−0.535415	−	0.173967i	−0.0212809	−	0.00691457i
$634$	10.1610	+	7.38243i	0.403547	+	0.293194i
$635$	−0.187417	+	5.49071i	−0.00743741	+	0.217892i
$636$	0.455400	−	1.40158i	0.0180578	−	0.0555762i
$637$	−0.541586	+	0.745429i	−0.0214584	+	0.0295350i
$638$	1.50159	+	0.487895i	0.0594484	+	0.0193159i
$639$	3.52449	+	10.8473i	0.139426	+	0.429111i
$640$	−1.37527	+	1.76313i	−0.0543625	+	0.0696937i
$641$	−7.24021	−	22.2831i	−0.285971	−	0.880129i	−0.986106	−	0.166118i	$-0.946877\pi$
$641$	−7.24021	−	22.2831i	−0.285971	−	0.880129i	0.700135	−	0.714011i	$-0.253123\pi$
$642$	1.39348	−	1.91797i	0.0549964	−	0.0756961i
$643$	12.2372	−	16.8430i	0.482587	−	0.664225i	−0.496412	−	0.868087i	$-0.665350\pi$
$643$	12.2372	−	16.8430i	0.482587	−	0.664225i	0.979000	+	0.203862i	$0.0653495\pi$
$644$	9.31766	−	6.76968i	0.367167	−	0.266763i
$645$	−2.91328	−	10.1297i	−0.114710	−	0.398858i
$646$	9.43908			0.371375
$647$	17.4051	+	23.9560i	0.684264	+	0.941809i	0.999975	−	0.00704651i	$-0.00224299\pi$
$647$	17.4051	+	23.9560i	0.684264	+	0.941809i	−0.315711	+	0.948855i	$0.602243\pi$
$648$	−0.951057	−	0.309017i	−0.0373610	−	0.0121393i
$649$	−1.95408	−	6.01405i	−0.0767045	−	0.236072i
$650$	−20.1546	+	12.6381i	−0.790529	+	0.495708i
$651$	14.5255	−	0.0734005i	0.569301	−	0.00287679i
$652$		−	21.9506i		−	0.859654i
$653$	11.1471	−	3.62191i	0.436219	−	0.141736i	−0.0826716	−	0.996577i	$-0.526345\pi$
$653$	11.1471	−	3.62191i	0.436219	−	0.141736i	0.518890	+	0.854841i	$0.326345\pi$
$654$	0.533694	−	1.64254i	0.0208691	−	0.0642285i
$655$	−26.7343	−	20.8533i	−1.04460	−	0.814806i
$656$	−8.31906			−0.324805
$657$		−	12.5459i		−	0.489463i
$658$	14.8113	+	20.3861i	0.577406	+	0.794731i
$659$	−1.47672	−	1.07290i	−0.0575247	−	0.0417941i	0.558651	−	0.829403i	$-0.311319\pi$
$659$	−1.47672	−	1.07290i	−0.0575247	−	0.0417941i	−0.616176	+	0.787608i	$0.711319\pi$
$660$	−3.06852	−	1.11412i	−0.119442	−	0.0433669i
$661$	−8.71960	−	26.8362i	−0.339153	−	1.04381i	−0.964640	−	0.263571i	$-0.915100\pi$
$661$	−8.71960	−	26.8362i	−0.339153	−	1.04381i	0.625487	−	0.780235i	$-0.284900\pi$
$662$	−0.223291	−	0.307333i	−0.00867844	−	0.0119448i
$663$	22.9749	−	7.46501i	0.892273	−	0.289917i
$664$	0.453685	−	1.39630i	0.0176064	−	0.0541869i
$665$	10.1940	+	3.70124i	0.395307	+	0.143528i
$666$	1.44559	−	4.44908i	0.0560156	−	0.172398i
$667$	−4.54056	−	1.47532i	−0.175811	−	0.0571245i
$668$	−7.15860	+	9.85296i	−0.276974	+	0.381223i
$669$	0.706161	−	2.17334i	0.0273017	−	0.0840261i
$670$	4.07028	−	2.75010i	0.157249	−	0.106246i
$671$	1.05625	−	0.767414i	0.0407763	−	0.0296257i
$672$	2.48121	−	0.806193i	0.0957147	−	0.0310996i
$673$	−14.1205	+	19.4353i	−0.544307	+	0.749174i	−0.989226	−	0.146397i	$-0.953232\pi$
$673$	−14.1205	+	19.4353i	−0.544307	+	0.749174i	0.444919	+	0.895571i	$0.353232\pi$
$674$	−17.4889	−	12.7064i	−0.673645	−	0.489432i
$675$	−4.63886	−	1.86574i	−0.178550	−	0.0718123i
$676$	9.63721			0.370662
$677$			35.4285i			1.36163i	0.732457	+	0.680813i	$0.238373\pi$
$677$			35.4285i			1.36163i	−0.732457	+	0.680813i	$0.761627\pi$
$678$	9.36957	+	12.8961i	0.359836	+	0.495272i
$679$	1.62705	−	5.00753i	0.0624403	−	0.192171i
$680$	9.40730	−	6.35608i	0.360754	−	0.243744i
$681$	27.6462			1.05940
$682$	4.81103	+	6.55193i	0.184224	+	0.250886i
$683$			12.5875i			0.481645i	0.970569	+	0.240823i	$0.0774172\pi$
$683$			12.5875i			0.481645i	−0.970569	+	0.240823i	$0.922583\pi$
$684$	0.574481	+	1.76807i	0.0219658	+	0.0676038i
$685$	0.0732547	−	2.14613i	0.00279892	−	0.0819993i
$686$	15.1832	−	11.0313i	0.579699	−	0.421176i
$687$		−	18.5397i		−	0.707335i
$688$			4.71379i			0.179711i
$689$	−5.67257	+	4.12137i	−0.216108	+	0.157012i
$690$	9.27871	+	3.36891i	0.353234	+	0.128252i
$691$	−26.9201	−	19.5586i	−1.02409	−	0.744043i	−0.0569709	−	0.998376i	$-0.518144\pi$
$691$	−26.9201	−	19.5586i	−1.02409	−	0.744043i	−0.967117	+	0.254333i	$0.918144\pi$
$692$	22.8869	−	7.43640i	0.870029	−	0.282690i
$693$	2.23877	+	3.08140i	0.0850438	+	0.117053i
$694$	3.93761	+	12.1187i	0.149470	+	0.460020i
$695$	11.5450	+	0.394071i	0.437927	+	0.0149480i
$696$	−0.874919	−	0.635666i	−0.0331637	−	0.0240949i
$697$	40.1714	+	13.0525i	1.52160	+	0.494398i
$698$	33.5845	+	10.9123i	1.27119	+	0.413035i
$699$	18.9480	+	13.7665i	0.716677	+	0.520697i
$700$	12.6520	−	3.17565i	0.478202	−	0.120028i
$701$	−7.61791	−	23.4455i	−0.287725	−	0.885525i	−0.985569	−	0.169276i	$-0.945857\pi$
$701$	−7.61791	−	23.4455i	−0.287725	−	0.885525i	0.697844	−	0.716250i	$-0.254143\pi$
$702$	2.79660	+	3.84919i	0.105551	+	0.145278i
$703$	−8.27109	+	2.68744i	−0.311950	+	0.101359i
$704$	1.18111	+	0.858129i	0.0445149	+	0.0323419i
$705$	−7.37082	+	20.3008i	−0.277601	+	0.764573i
$706$	18.0736	−	13.1313i	0.680211	−	0.494202i
$707$		−	16.2727i		−	0.611999i
$708$			4.33139i			0.162784i
$709$	7.27724	−	5.28722i	0.273302	−	0.198566i	−0.442688	−	0.896676i	$-0.645975\pi$
$709$	7.27724	−	5.28722i	0.273302	−	0.198566i	0.715991	+	0.698110i	$0.245975\pi$
$710$	0.870013	−	25.4886i	0.0326510	−	0.956569i
$711$	−1.12728	−	3.46940i	−0.0422762	−	0.130113i
$712$		−	1.73853i		−	0.0651542i
$713$	−14.5478	−	19.8120i	−0.544819	−	0.741965i
$714$	−13.2463			−0.495729
$715$	8.69556	+	12.8699i	0.325196	+	0.481305i
$716$	3.37088	−	10.3745i	0.125976	−	0.387714i
$717$	6.93850	+	9.55003i	0.259123	+	0.356652i
$718$		−	28.1364i		−	1.05004i
$719$	8.11160			0.302512			0.151256	−	0.988495i	$-0.451668\pi$
$719$	8.11160			0.302512			0.151256	+	0.988495i	$0.451668\pi$
$720$	1.76313	+	1.37527i	0.0657079	+	0.0512535i
$721$	−6.37418	−	4.63111i	−0.237387	−	0.172472i
$722$	−9.13648	+	12.5753i	−0.340024	+	0.468004i
$723$	19.7930	−	6.43113i	0.736109	−	0.239176i
$724$	3.36970	−	2.44823i	0.125234	−	0.0909877i
$725$	−4.14769	−	3.46922i	−0.154041	−	0.128844i
$726$	2.74054	−	8.43453i	0.101711	−	0.313035i
$727$	−5.62794	+	7.74619i	−0.208729	+	0.287290i	−0.900527	−	0.434801i	$-0.856819\pi$
$727$	−5.62794	+	7.74619i	−0.208729	+	0.287290i	0.691798	+	0.722091i	$0.256819\pi$
$728$	−11.8052	−	3.83575i	−0.437531	−	0.142162i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	−9.57414	+	26.3692i	−0.354355	+	0.975969i
$731$	7.39586	−	22.7621i	0.273546	−	0.841887i
$732$	−0.850518	+	0.276350i	−0.0314361	+	0.0102142i
$733$	−27.7464	−	38.1897i	−1.02484	−	1.41057i	−0.908755	−	0.417330i	$-0.862966\pi$
$733$	−27.7464	−	38.1897i	−1.02484	−	1.41057i	−0.116083	−	0.993239i	$-0.537034\pi$
$734$	−5.38086	−	16.5606i	−0.198611	−	0.611263i
$735$	0.407035	+	0.147786i	0.0150137	+	0.00545118i
$736$	−3.57150	−	2.59484i	−0.131647	−	0.0956472i
$737$	−1.88516	−	2.59470i	−0.0694407	−	0.0955770i
$738$			8.31906i			0.306229i
$739$	45.0761			1.65815			0.829075	−	0.559137i	$-0.188868\pi$
$739$	45.0761			1.65815			0.829075	+	0.559137i	$0.188868\pi$
$740$	−6.43358	+	8.24797i	−0.236503	+	0.303202i
$741$	2.73330	−	8.41222i	0.100410	−	0.309031i
$742$	3.65657	−	1.18809i	0.134237	−	0.0436163i
$743$		−	52.2621i		−	1.91731i	−0.284569	−	0.958656i	$-0.591851\pi$
$743$		−	52.2621i		−	1.91731i	0.284569	−	0.958656i	$-0.408149\pi$
$744$	−1.74727	−	5.28650i	−0.0640580	−	0.193812i
$745$	−5.43330	−	18.8921i	−0.199061	−	0.692153i
$746$	10.4971	+	32.3068i	0.384327	+	1.18284i
$747$	−1.39630	−	0.453685i	−0.0510879	−	0.0165995i
$748$	−4.35701	−	5.99691i	−0.159308	−	0.219269i
$749$	6.18501			0.225995
$750$	8.32624	+	7.46149i	0.304031	+	0.272455i
$751$	17.7962	−	12.9297i	0.649392	−	0.471811i	−0.213672	−	0.976905i	$-0.568542\pi$
$751$	17.7962	−	12.9297i	0.649392	−	0.471811i	0.863064	+	0.505095i	$0.168542\pi$
$752$	5.67724	−	7.81405i	0.207028	−	0.284949i
$753$	−2.74991	+	3.78493i	−0.100212	+	0.137931i
$754$	1.59003	+	4.89360i	0.0579053	+	0.178214i
$755$	−33.1784	−	25.8798i	−1.20749	−	0.941864i
$756$	−0.806193	−	2.48121i	−0.0293210	−	0.0902407i
$757$	21.1136	+	6.86021i	0.767385	+	0.249339i	0.666445	−	0.745554i	$-0.267815\pi$
$757$	21.1136	+	6.86021i	0.767385	+	0.249339i	0.100940	+	0.994893i	$0.467815\pi$
$758$	−3.89031	+	5.35456i	−0.141303	+	0.194486i
$759$	1.99163	−	6.12960i	0.0722916	−	0.222491i
$760$	0.141809	−	4.15456i	0.00514397	−	0.150702i
$761$	−28.0817	−	20.4025i	−1.01796	−	0.739591i	−0.0520960	−	0.998642i	$-0.516590\pi$
$761$	−28.0817	−	20.4025i	−1.01796	−	0.739591i	−0.965864	+	0.259051i	$0.916590\pi$
$762$	−2.33670	−	0.759239i	−0.0846497	−	0.0275043i
$763$	4.28522	−	1.39235i	0.155135	−	0.0504066i
$764$	11.1993	−	8.13678i	0.405177	−	0.294378i
$765$	−6.35608	−	9.40730i	−0.229804	−	0.340122i
$766$	−11.4713	−	8.33438i	−0.414475	−	0.301134i
$767$	12.1132	−	16.6723i	0.437381	−	0.602003i
$768$	−0.587785	−	0.809017i	−0.0212099	−	0.0291929i
$769$	38.9753			1.40549			0.702743	−	0.711443i	$-0.251958\pi$
$769$	38.9753			1.40549			0.702743	+	0.711443i	$0.251958\pi$
$770$	−2.35398	−	8.18501i	−0.0848316	−	0.294967i
$771$	−15.9767	+	11.6077i	−0.575386	+	0.418043i
$772$	−12.1459	−	3.94645i	−0.437142	−	0.142036i
$773$	6.82707	−	2.21825i	0.245553	−	0.0797849i	−0.183655	−	0.982991i	$-0.558793\pi$
$773$	6.82707	−	2.21825i	0.245553	−	0.0797849i	0.429208	+	0.903206i	$0.358793\pi$
$774$	4.71379			0.169434
$775$	−6.91365	−	26.9667i	−0.248346	−	0.968671i
$776$	−2.01818			−0.0724486
$777$	11.6072	−	3.77140i	0.416405	−	0.135298i
$778$	10.8794	+	3.53494i	0.390046	+	0.126734i
$779$	12.5119	−	9.09046i	0.448287	−	0.325700i
$780$	−2.94052	−	10.2245i	−0.105287	−	0.366094i
$781$	−16.6513			−0.595829
$782$	13.1749	+	18.1337i	0.471134	+	0.648460i
$783$	−0.635666	+	0.874919i	−0.0227168	+	0.0312671i
$784$	−0.156673	−	0.113830i	−0.00559547	−	0.00406535i
$785$	28.7244	+	42.5135i	1.02522	+	1.51737i
$786$	12.2671	−	8.91259i	0.437554	−	0.317902i
$787$	−34.2730	+	11.1360i	−1.22170	+	0.396954i	−0.847700	−	0.530475i	$-0.822013\pi$
$787$	−34.2730	+	11.1360i	−1.22170	+	0.396954i	−0.373999	+	0.927429i	$0.622013\pi$
$788$	15.2207	+	4.94550i	0.542215	+	0.176176i
$789$	−20.1783	−	14.6604i	−0.718366	−	0.521924i
$790$	−0.278266	+	8.15231i	−0.00990027	+	0.290046i
$791$	−12.8511	+	39.5516i	−0.456933	+	1.40629i
$792$	0.858129	−	1.18111i	0.0304923	−	0.0419690i
$793$	4.04665	+	1.31483i	0.143701	+	0.0466912i
$794$	−1.87972	−	5.78517i	−0.0667086	−	0.205308i
$795$	2.59833	+	2.02675i	0.0921534	+	0.0718815i
$796$	4.33373	+	13.3378i	0.153605	+	0.472747i
$797$	24.3472	−	33.5111i	0.862424	−	1.18702i	−0.118563	−	0.992947i	$-0.537829\pi$
$797$	24.3472	−	33.5111i	0.862424	−	1.18702i	0.980986	−	0.194078i	$-0.0621714\pi$
$798$	−2.85081	+	3.92381i	−0.100918	+	0.138901i
$799$	−39.6746	+	28.8253i	−1.40359	+	1.01977i
$800$	−2.65626	−	4.23607i	−0.0939130	−	0.149768i
$801$	−1.73853			−0.0614280
$802$	20.3039	+	27.9459i	0.716956	+	0.986805i
$803$	17.4198	+	5.66003i	0.614731	+	0.199738i
$804$	0.678857	+	2.08931i	0.0239414	+	0.0736842i
$805$	7.11806	+	24.7502i	0.250879	+	0.872328i
$806$	−8.05864	+	25.2351i	−0.283854	+	0.888870i
$807$			18.8951i			0.665139i
$808$	−5.93212	+	1.92746i	−0.208691	+	0.0678079i
$809$	−10.2628	+	31.5858i	−0.360822	+	1.11050i	0.591734	+	0.806133i	$0.298443\pi$
$809$	−10.2628	+	31.5858i	−0.360822	+	1.11050i	−0.952556	+	0.304363i	$0.901557\pi$
$810$	1.37527	−	1.76313i	0.0483222	−	0.0619500i
$811$	−23.4552			−0.823623			−0.411811	−	0.911269i	$-0.635104\pi$
$811$	−23.4552			−0.823623			−0.411811	+	0.911269i	$0.635104\pi$
$812$		−	2.82142i		−	0.0990123i
$813$	15.4935	+	21.3250i	0.543380	+	0.747899i
$814$	5.52529	+	4.01436i	0.193661	+	0.140703i
$815$	46.1362	+	16.7511i	1.61608	+	0.586767i
$816$	1.56899	+	4.82884i	0.0549255	+	0.169043i
$817$	−5.15088	−	7.08958i	−0.180207	−	0.248033i
$818$	−5.70155	+	1.85255i	−0.199350	+	0.0647728i
$819$	−3.83575	+	11.8052i	−0.134032	+	0.412508i
$820$	6.34850	−	17.4851i	0.221699	−	0.610608i
$821$	−9.64494	+	29.6841i	−0.336611	+	1.03598i	0.629313	+	0.777152i	$0.283337\pi$
$821$	−9.64494	+	29.6841i	−0.336611	+	1.03598i	−0.965923	+	0.258829i	$0.916663\pi$
$822$	0.913334	+	0.296760i	0.0318562	+	0.0103507i
$823$	26.4718	−	36.4353i	0.922749	−	1.27006i	−0.0398723	−	0.999205i	$-0.512695\pi$
$823$	26.4718	−	36.4353i	0.922749	−	1.27006i	0.962621	−	0.270850i	$-0.0873049\pi$
$824$	−0.933237	+	2.87221i	−0.0325108	+	0.100058i
$825$	4.68334	−	5.59925i	0.163053	−	0.194941i
$826$	−9.14201	+	6.64206i	−0.318091	+	0.231107i
$827$	28.2092	−	9.16573i	0.980930	−	0.318723i	0.225710	−	0.974195i	$-0.427530\pi$
$827$	28.2092	−	9.16573i	0.980930	−	0.318723i	0.755220	+	0.655471i	$0.227530\pi$
$828$	−2.59484	+	3.57150i	−0.0901771	+	0.124118i
$829$	35.9303	+	26.1049i	1.24791	+	0.906660i	0.998099	−	0.0616345i	$-0.0196313\pi$
$829$	35.9303	+	26.1049i	1.24791	+	0.906660i	0.249812	+	0.968294i	$0.419631\pi$
$830$	2.58855	+	2.01912i	0.0898498	+	0.0700846i
$831$	22.0233			0.763979
$832$			4.75786i			0.164949i
$833$	0.577953	+	0.795484i	0.0200249	+	0.0275619i
$834$	−1.59641	+	4.91325i	−0.0552792	+	0.170132i
$835$	−15.2462	−	22.5651i	−0.527617	−	0.780899i
$836$	−2.71410			−0.0938693
$837$	−5.28650	+	1.74727i	−0.182728	+	0.0603945i
$838$		−	28.4211i		−	0.981791i
$839$	5.30216	+	16.3184i	0.183051	+	0.563372i	0.999909	−	0.0134657i	$-0.00428641\pi$
$839$	5.30216	+	16.3184i	0.183051	+	0.563372i	−0.816859	+	0.576838i	$0.804286\pi$
$840$	−0.199007	+	5.83027i	−0.00686640	+	0.201164i
$841$	22.5153	−	16.3583i	0.776390	−	0.564080i
$842$		−	23.8940i		−	0.823441i
$843$			7.93639i			0.273344i
$844$	−0.455452	+	0.330905i	−0.0156773	+	0.0113902i
$845$	−7.35442	+	20.2557i	−0.253000	+	0.696816i
$846$	−7.81405	−	5.67724i	−0.268653	−	0.195188i
$847$	22.0048	−	7.14980i	0.756094	−	0.245670i
$848$	−0.866223	−	1.19225i	−0.0297462	−	0.0409422i
$849$	2.11956	+	6.52334i	0.0727432	+	0.223880i
$850$	6.18034	+	24.6229i	0.211984	+	0.844560i
$851$	−16.7076	−	12.1388i	−0.572729	−	0.416112i
$852$	10.8473	+	3.52449i	0.371621	+	0.120747i
$853$	−40.3181	−	13.1002i	−1.38047	−	0.448541i	−0.477644	−	0.878554i	$-0.658509\pi$
$853$	−40.3181	−	13.1002i	−1.38047	−	0.448541i	−0.902823	+	0.430013i	$0.858509\pi$
$854$	−1.88752	−	1.37136i	−0.0645897	−	0.0469271i
$855$	−4.15456	−	0.141809i	−0.142083	−	0.00484978i
$856$	−0.732598	−	2.25470i	−0.0250397	−	0.0770642i
$857$	22.2137	+	30.5745i	0.758804	+	1.04440i	0.997313	+	0.0732637i	$0.0233415\pi$
$857$	22.2137	+	30.5745i	0.758804	+	1.04440i	−0.238509	+	0.971140i	$0.576659\pi$
$858$	−6.60620	+	2.14648i	−0.225532	+	0.0732797i
$859$	−31.9424	−	23.2075i	−1.08986	−	0.791830i	−0.110485	−	0.993878i	$-0.535240\pi$
$859$	−31.9424	−	23.2075i	−1.08986	−	0.791830i	−0.979376	+	0.202048i	$0.935240\pi$
$860$	−9.90752	−	3.59722i	−0.337844	−	0.122664i
$861$	−17.5586	+	12.7570i	−0.598394	+	0.434759i
$862$			6.49880i			0.221350i
$863$		−	37.2565i		−	1.26823i	−0.773241	−	0.634113i	$-0.781366\pi$
$863$		−	37.2565i		−	1.26823i	0.773241	−	0.634113i	$-0.218634\pi$
$864$	−0.809017	+	0.587785i	−0.0275233	+	0.0199969i
$865$	−1.83566	+	53.7790i	−0.0624144	+	1.82854i
$866$	6.06357	+	18.6618i	0.206049	+	0.634152i
$867$		−	8.77941i		−	0.298165i
$868$	8.47851	−	11.7945i	0.287780	−	0.400333i
$869$	5.32577			0.180664
$870$	2.00373	−	1.35383i	0.0679328	−	0.0458990i
$871$	3.22990	−	9.94062i	0.109441	−	0.336825i
$872$	−1.01515	−	1.39723i	−0.0343772	−	0.0473162i
$873$			2.01818i			0.0683052i
$874$	8.20702			0.277607
$875$	−2.98048	+	29.0157i	−0.100759	+	0.980909i
$876$	−10.1499	−	7.37431i	−0.342932	−	0.249155i
$877$	4.29984	−	5.91822i	0.145195	−	0.199844i	−0.730225	−	0.683207i	$-0.760585\pi$
$877$	4.29984	−	5.91822i	0.145195	−	0.199844i	0.875420	+	0.483363i	$0.160585\pi$
$878$	19.2778	−	6.26373i	0.650594	−	0.211391i
$879$	−26.3937	+	19.1762i	−0.890238	+	0.646796i
$880$	−2.70497	+	1.82762i	−0.0911845	+	0.0616091i
$881$	−14.7602	+	45.4272i	−0.497283	+	1.53048i	0.316085	+	0.948731i	$0.397632\pi$
$881$	−14.7602	+	45.4272i	−0.497283	+	1.53048i	−0.813368	+	0.581749i	$0.802368\pi$
$882$	−0.113830	+	0.156673i	−0.00383285	+	0.00527546i
$883$	−43.9748	−	14.2883i	−1.47987	−	0.480839i	−0.545795	−	0.837918i	$-0.683772\pi$
$883$	−43.9748	−	14.2883i	−1.47987	−	0.480839i	−0.934074	+	0.357080i	$0.883772\pi$
$884$	7.46501	−	22.9749i	0.251075	−	0.772731i
$885$	−9.10379	−	3.30540i	−0.306021	−	0.111110i
$886$	−0.206190	+	0.634587i	−0.00692708	+	0.0213194i
$887$	−17.5663	+	5.70763i	−0.589818	+	0.191643i	−0.588694	−	0.808356i	$-0.700358\pi$
$887$	−17.5663	+	5.70763i	−0.589818	+	0.191643i	−0.00112363	+	0.999999i	$0.500358\pi$
$888$	−2.74968	−	3.78461i	−0.0922732	−	0.127003i
$889$	−1.98078	−	6.09620i	−0.0664331	−	0.204460i
$890$	3.65407	+	1.32672i	0.122485	+	0.0444718i
$891$	−1.18111	−	0.858129i	−0.0395688	−	0.0287484i
$892$	−1.34320	−	1.84875i	−0.0449736	−	0.0619008i
$893$			17.9561i			0.600877i
$894$	8.79127			0.294024
$895$	19.2329	+	15.0021i	0.642885	+	0.501464i
$896$	0.806193	−	2.48121i	0.0269330	−	0.0828913i
$897$	19.9761	−	6.49062i	0.666982	−	0.216716i
$898$		−	21.1276i		−	0.705038i
$899$	−6.02124	+	0.0304265i	−0.200819	+	0.00101478i
$900$	−4.23607	+	2.65626i	−0.141202	+	0.0885421i
$901$	2.31222	+	7.11630i	0.0770314	+	0.237078i
$902$	−11.5509	−	3.75310i	−0.384601	−	0.124965i
$903$	7.22845	+	9.94911i	0.240548	+	0.331086i
$904$	15.9405			0.530172
$905$	2.57422	+	8.95080i	0.0855699	+	0.297535i
$906$	15.2240	−	11.0609i	0.505785	−	0.367474i
$907$	−27.9282	+	38.4399i	−0.927341	+	1.27638i	0.0335465	+	0.999437i	$0.489320\pi$
$907$	−27.9282	+	38.4399i	−0.927341	+	1.27638i	−0.960888	+	0.276938i	$0.910680\pi$
$908$	16.2500	−	22.3662i	0.539275	−	0.742249i
$909$	1.92746	+	5.93212i	0.0639299	+	0.196756i
$910$	17.0710	−	21.8853i	0.565897	−	0.725490i
$911$	18.2126	+	56.0526i	0.603410	+	1.85710i	0.507373	+	0.861726i	$0.330616\pi$
$911$	18.2126	+	56.0526i	0.603410	+	1.85710i	0.0960362	+	0.995378i	$0.469384\pi$
$912$	1.76807	+	0.574481i	0.0585466	+	0.0190230i
$913$	1.25987	−	1.73406i	0.0416955	−	0.0573889i
$914$	−3.90276	+	12.0114i	−0.129092	+	0.397303i
$915$	0.0682165	−	1.99852i	0.00225517	−	0.0660692i
$916$	−14.9990	−	10.8974i	−0.495580	−	0.360060i
$917$	37.6226	+	12.2243i	1.24241	+	0.403683i
$918$	4.82884	−	1.56899i	0.159375	−	0.0517842i
$919$	13.0684	−	9.49472i	0.431085	−	0.313202i	−0.350997	−	0.936376i	$-0.614157\pi$
$919$	13.0684	−	9.49472i	0.431085	−	0.313202i	0.782083	+	0.623175i	$0.214157\pi$
$920$	8.17939	−	5.52644i	0.269667	−	0.182201i
$921$	−2.60224	−	1.89064i	−0.0857466	−	0.0622986i
$922$	8.00364	−	11.0161i	0.263586	−	0.362795i
$923$	−31.8965	−	43.9018i	−1.04989	−	1.44505i
$924$	3.80882			0.125301
$925$	−12.4261	−	19.8165i	−0.408567	−	0.651562i
$926$	19.0904	−	13.8700i	0.627349	−	0.455796i
$927$	2.87221	+	0.933237i	0.0943357	+	0.0306515i
$928$	−1.02853	+	0.334189i	−0.0337631	+	0.0109703i
$929$	−51.6821			−1.69564			−0.847818	−	0.530288i	$-0.822084\pi$
$929$	−51.6821			−1.69564			−0.847818	+	0.530288i	$0.822084\pi$
$930$	12.4446	+	0.361831i	0.408076	+	0.0118649i
$931$	0.360023			0.0117993
$932$	22.2747	−	7.23747i	0.729631	−	0.237071i
$933$	−3.99431	−	1.29783i	−0.130768	−	0.0424890i
$934$	−1.81372	+	1.31774i	−0.0593467	+	0.0431179i
$935$	15.9294	−	4.58123i	0.520946	−	0.149822i
$936$	4.75786			0.155515
$937$	−29.7872	−	40.9985i	−0.973104	−	1.33936i	−0.940463	−	0.339895i	$-0.889608\pi$
$937$	−29.7872	−	40.9985i	−0.973104	−	1.33936i	−0.0326407	−	0.999467i	$-0.510392\pi$
$938$	−3.36877	+	4.63671i	−0.109994	+	0.151394i
$939$	2.44316	+	1.77506i	0.0797297	+	0.0579270i
$940$	12.0912	+	17.8956i	0.394373	+	0.583691i
$941$	22.9923	−	16.7049i	0.749529	−	0.544565i	−0.146152	−	0.989262i	$-0.546689\pi$
$941$	22.9923	−	16.7049i	0.749529	−	0.544565i	0.895681	+	0.444698i	$0.146689\pi$
$942$	−21.8225	+	7.09056i	−0.711015	+	0.231023i
$943$	34.9279	+	11.3488i	1.13741	+	0.369567i
$944$	3.50417	+	2.54593i	0.114051	+	0.0828629i
$945$	5.83027	+	0.199007i	0.189659	+	0.00647371i
$946$	−2.12660	+	6.54500i	−0.0691417	+	0.212796i
$947$	17.4818	−	24.0616i	0.568082	−	0.781898i	−0.424244	−	0.905548i	$-0.639460\pi$
$947$	17.4818	−	24.0616i	0.568082	−	0.781898i	0.992326	+	0.123650i	$0.0394601\pi$
$948$	−3.46940	−	1.12728i	−0.112681	−	0.0366123i
$949$	18.4458	+	56.7702i	0.598775	+	1.84284i
$950$	8.62391	+	3.46852i	0.279797	+	0.112534i
$951$	−3.88118	−	11.9450i	−0.125856	−	0.387344i
$952$	−7.78596	+	10.7165i	−0.252344	+	0.347322i
$953$	−4.97527	+	6.84787i	−0.161165	+	0.221824i	−0.881961	−	0.471323i	$-0.843777\pi$
$953$	−4.97527	+	6.84787i	−0.161165	+	0.221824i	0.720796	+	0.693147i	$0.243777\pi$
$954$	−1.19225	+	0.866223i	−0.0386006	+	0.0280450i
$955$	8.55551	+	29.7483i	0.276850	+	0.962633i
$956$	11.8045			0.381784
$957$	−0.928031	−	1.27733i	−0.0299990	−	0.0412901i
$958$	25.8960	+	8.41411i	0.836660	+	0.271847i
$959$	0.774217	+	2.38279i	0.0250008	+	0.0769445i
$960$	2.14896	−	0.618034i	0.0693574	−	0.0199470i
$961$	−25.2624	−	17.9670i	−0.814916	−	0.579579i
$962$			22.2574i			0.717608i
$963$	−2.25470	+	0.732598i	−0.0726568	+	0.0236076i
$964$	6.43113	−	19.7930i	0.207133	−	0.637489i
$965$	17.5636	−	22.5169i	0.565393	−	0.724844i
$966$	−11.5173			−0.370562
$967$			32.1088i			1.03255i	0.856423	+	0.516274i	$0.172681\pi$
$967$			32.1088i			1.03255i	−0.856423	+	0.516274i	$0.827319\pi$
$968$	−5.21283	−	7.17484i	−0.167547	−	0.230608i
$969$	−7.63637	−	5.54815i	−0.245316	−	0.178232i
$970$	1.54013	−	4.24185i	0.0494506	−	0.136198i
$971$	−12.4203	−	38.2256i	−0.398585	−	1.22672i	−0.926134	−	0.377195i	$-0.876889\pi$
$971$	−12.4203	−	38.2256i	−0.398585	−	1.22672i	0.527549	−	0.849525i	$-0.323111\pi$
$972$	0.587785	+	0.809017i	0.0188532	+	0.0259492i
$973$	−12.8182	+	4.16487i	−0.410931	+	0.133520i
$974$	12.7719	−	39.3077i	0.409237	−	1.25950i
$975$	23.7339	+	1.62213i	0.760094	+	0.0519497i
$976$	−0.276350	+	0.850518i	−0.00884575	+	0.0272244i
$977$	20.3479	+	6.61144i	0.650987	+	0.211519i	0.615849	−	0.787864i	$-0.288813\pi$
$977$	20.3479	+	6.61144i	0.650987	+	0.211519i	0.0351378	+	0.999382i	$0.488813\pi$
$978$	−12.9023	+	17.7584i	−0.412569	+	0.567852i
$979$	0.784329	−	2.41392i	0.0250673	−	0.0771491i
$980$	0.358811	−	0.242432i	0.0114618	−	0.00774420i
$981$	−1.39723	+	1.01515i	−0.0446101	+	0.0324111i
$982$	16.6080	−	5.39627i	0.529983	−	0.172202i
$983$	−21.5434	+	29.6520i	−0.687129	+	0.945752i	−0.999992	−	0.00404612i	$-0.998712\pi$
$983$	−21.5434	+	29.6520i	−0.687129	+	0.945752i	0.312863	+	0.949798i	$0.398712\pi$
$984$	6.73026	+	4.88982i	0.214553	+	0.155882i
$985$	−22.0099	+	28.2171i	−0.701293	+	0.899070i
$986$	5.49094			0.174867
$987$		−	25.1985i		−	0.802079i
$988$	−5.19904	−	7.15586i	−0.165403	−	0.227658i
$989$	6.43050	−	19.7910i	0.204478	−	0.629319i
$990$	1.82762	+	2.70497i	0.0580856	+	0.0859696i
$991$	−24.3097			−0.772224			−0.386112	−	0.922452i	$-0.626182\pi$
$991$	−24.3097			−0.772224			−0.386112	+	0.922452i	$0.626182\pi$
$992$	−5.30389	−	1.69375i	−0.168399	−	0.0537767i
$993$			0.379885i			0.0120553i
$994$	9.19502	+	28.2994i	0.291648	+	0.897601i
$995$	−31.3409	−	1.06977i	−0.993574	−	0.0339141i
$996$	−1.18776	+	0.862961i	−0.0376357	+	0.0273440i
$997$		−	56.2831i		−	1.78250i	−0.453510	−	0.891251i	$-0.649828\pi$
$997$		−	56.2831i		−	1.78250i	0.453510	−	0.891251i	$-0.350172\pi$
$998$			2.81302i			0.0890445i
$999$	−3.78461	+	2.74968i	−0.119740	+	0.0869960i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.z.c.469.3	yes	32
5.4	even	2	inner	930.2.z.c.469.6	yes	32
31.8	even	5	inner	930.2.z.c.349.8	yes	32
155.39	even	10	inner	930.2.z.c.349.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.c.349.1	✓	32	155.39	even	10	inner
930.2.z.c.349.8	yes	32	31.8	even	5	inner
930.2.z.c.469.3	yes	32	1.1	even	1	trivial
930.2.z.c.469.6	yes	32	5.4	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.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.618034 + 2.14896i) q^{5} -1.00000 q^{6} +(-1.53347 - 2.11064i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.618034 + 2.14896i) q^{5} -1.00000 q^{6} +(-1.53347 - 2.11064i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-1.25185 - 1.85280i) q^{10} +(-1.18111 + 0.858129i) q^{11} +(0.951057 - 0.309017i) q^{12} +(-4.52499 - 1.47026i) q^{13} +(2.11064 + 1.53347i) q^{14} +(-0.0762803 + 2.23477i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.98439 + 4.10766i) q^{17} +(-0.951057 - 0.309017i) q^{18} +(0.574481 + 1.76807i) q^{19} +(1.76313 + 1.37527i) q^{20} +(-0.806193 - 2.48121i) q^{21} +(0.858129 - 1.18111i) q^{22} +(-2.59484 + 3.57150i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(-4.23607 + 2.65626i) q^{25} +4.75786 q^{26} +(0.587785 + 0.809017i) q^{27} +(-2.48121 - 0.806193i) q^{28} +(0.334189 + 1.02853i) q^{29} +(-0.618034 - 2.14896i) q^{30} +(-1.69375 + 5.30389i) q^{31} +1.00000i q^{32} +(-1.38848 + 0.451145i) q^{33} +(1.56899 - 4.82884i) q^{34} +(3.58795 - 4.59982i) q^{35} +1.00000 q^{36} +4.67804i q^{37} +(-1.09273 - 1.50401i) q^{38} +(-3.84919 - 2.79660i) q^{39} +(-2.10182 - 0.763128i) q^{40} +(-2.57073 - 7.91189i) q^{41} +(1.53347 + 2.11064i) q^{42} +(-4.48308 + 1.45664i) q^{43} +(-0.451145 + 1.38848i) q^{44} +(-0.763128 + 2.10182i) q^{45} +(1.36419 - 4.19855i) q^{46} +(9.18597 + 2.98470i) q^{47} +(0.587785 - 0.809017i) q^{48} +(0.0598438 - 0.184180i) q^{49} +(3.20791 - 3.83527i) q^{50} +(-4.10766 + 2.98439i) q^{51} +(-4.52499 + 1.47026i) q^{52} +(0.866223 - 1.19225i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(-2.57405 - 2.00781i) q^{55} +2.60890 q^{56} +1.85906i q^{57} +(-0.635666 - 0.874919i) q^{58} +(-1.33847 + 4.11940i) q^{59} +(1.25185 + 1.85280i) q^{60} -0.894288 q^{61} +(-0.0281347 - 5.56769i) q^{62} -2.60890i q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.362931 - 10.6327i) q^{65} +(1.18111 - 0.858129i) q^{66} +2.19683i q^{67} +5.07734i q^{68} +(-3.57150 + 2.59484i) q^{69} +(-1.99092 + 5.48342i) q^{70} +(9.22722 + 6.70397i) q^{71} +(-0.951057 + 0.309017i) q^{72} +(-7.37431 - 10.1499i) q^{73} +(-1.44559 - 4.44908i) q^{74} +(-4.84957 + 1.21724i) q^{75} +(1.50401 + 1.09273i) q^{76} +(3.62240 + 1.17699i) q^{77} +(4.52499 + 1.47026i) q^{78} +(-2.95125 - 2.14421i) q^{79} +(2.23477 + 0.0762803i) q^{80} +(0.309017 + 0.951057i) q^{81} +(4.88982 + 6.73026i) q^{82} +(-1.39630 + 0.453685i) q^{83} +(-2.11064 - 1.53347i) q^{84} +(-10.6716 - 3.87466i) q^{85} +(3.81353 - 2.77069i) q^{86} +1.08146i q^{87} -1.45994i q^{88} +(-1.40650 + 1.02188i) q^{89} +(0.0762803 - 2.23477i) q^{90} +(3.83575 + 11.8052i) q^{91} +4.41461i q^{92} +(-3.24985 + 4.52090i) q^{93} -9.65870 q^{94} +(-3.44446 + 2.32726i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(1.18626 + 1.63274i) q^{97} +0.193659i q^{98} -1.45994 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} - 16 q^{5} - 32 q^{6} + 8 q^{9}+O(q^{10}) \) 32 * q + 8 * q^4 - 16 * q^5 - 32 * q^6 + 8 * q^9	\( 32 q + 8 q^{4} - 16 q^{5} - 32 q^{6} + 8 q^{9} - 4 q^{11} - 4 q^{14} - 8 q^{16} - 16 q^{19} + 16 q^{20} - 4 q^{21} - 8 q^{24} - 64 q^{25} - 16 q^{26} + 4 q^{29} + 16 q^{30} - 24 q^{31} - 12 q^{34} + 32 q^{36} + 4 q^{39} - 48 q^{41} + 4 q^{44} + 16 q^{45} + 8 q^{46} - 28 q^{49} + 8 q^{51} - 8 q^{54} - 8 q^{55} - 16 q^{56} - 8 q^{59} + 32 q^{61} + 8 q^{64} - 8 q^{65} + 4 q^{66} - 12 q^{69} - 8 q^{70} + 32 q^{71} + 4 q^{74} - 24 q^{76} + 64 q^{79} + 24 q^{80} - 8 q^{81} + 4 q^{84} + 28 q^{85} + 84 q^{86} - 128 q^{89} - 28 q^{91} + 40 q^{94} + 8 q^{95} + 8 q^{96} - 16 q^{99}+O(q^{100}) \) 32 * q + 8 * q^4 - 16 * q^5 - 32 * q^6 + 8 * q^9 - 4 * q^11 - 4 * q^14 - 8 * q^16 - 16 * q^19 + 16 * q^20 - 4 * q^21 - 8 * q^24 - 64 * q^25 - 16 * q^26 + 4 * q^29 + 16 * q^30 - 24 * q^31 - 12 * q^34 + 32 * q^36 + 4 * q^39 - 48 * q^41 + 4 * q^44 + 16 * q^45 + 8 * q^46 - 28 * q^49 + 8 * q^51 - 8 * q^54 - 8 * q^55 - 16 * q^56 - 8 * q^59 + 32 * q^61 + 8 * q^64 - 8 * q^65 + 4 * q^66 - 12 * q^69 - 8 * q^70 + 32 * q^71 + 4 * q^74 - 24 * q^76 + 64 * q^79 + 24 * q^80 - 8 * q^81 + 4 * q^84 + 28 * q^85 + 84 * q^86 - 128 * q^89 - 28 * q^91 + 40 * q^94 + 8 * q^95 + 8 * q^96 - 16 * q^99

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