LMFDB - Embedded newform 950.2.l.c.251.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			251.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	950.251
Dual form			950.2.l.c.651.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(-0.326352 - 1.85083i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.326352 - 1.85083i) q^{6} +(-1.53209 + 2.65366i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.500000 + 0.181985i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(-0.326352 - 1.85083i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.326352 - 1.85083i) q^{6} +(-1.53209 + 2.65366i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.500000 + 0.181985i) q^{9} +(2.17365 + 3.76487i) q^{11} +(0.939693 - 1.62760i) q^{12} +(1.00000 - 5.67128i) q^{13} +(-2.34730 + 1.96962i) q^{14} +(0.173648 + 0.984808i) q^{16} +(1.93969 + 0.705990i) q^{17} -0.532089 q^{18} +(4.34002 - 0.405223i) q^{19} +(5.41147 + 1.96962i) q^{21} +(0.754900 + 4.28125i) q^{22} +(5.94356 + 4.98724i) q^{23} +(1.43969 - 1.20805i) q^{24} +(2.87939 - 4.98724i) q^{26} +(-2.31908 - 4.01676i) q^{27} +(-2.87939 + 1.04801i) q^{28} +(-3.87939 + 1.41198i) q^{29} +(4.22668 - 7.32083i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(6.25877 - 5.25173i) q^{33} +(1.58125 + 1.32683i) q^{34} +(-0.500000 - 0.181985i) q^{36} +4.00000 q^{37} +(4.21688 + 1.10359i) q^{38} -10.8229 q^{39} +(-0.0248149 - 0.140732i) q^{41} +(4.41147 + 3.70167i) q^{42} +(-8.34002 + 6.99811i) q^{43} +(-0.754900 + 4.28125i) q^{44} +(3.87939 + 6.71929i) q^{46} +(5.53209 - 2.01352i) q^{47} +(1.76604 - 0.642788i) q^{48} +(-1.19459 - 2.06910i) q^{49} +(0.673648 - 3.82045i) q^{51} +(4.41147 - 3.70167i) q^{52} +(3.87939 + 3.25519i) q^{53} +(-0.805407 - 4.56769i) q^{54} -3.06418 q^{56} +(-2.16637 - 7.90041i) q^{57} -4.12836 q^{58} +(-7.19119 - 2.61738i) q^{59} +(-6.94356 - 5.82634i) q^{61} +(6.47565 - 5.43372i) q^{62} +(0.283119 - 1.60565i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(7.67752 - 2.79439i) q^{66} +(5.92989 - 2.15830i) q^{67} +(1.03209 + 1.78763i) q^{68} +(7.29086 - 12.6281i) q^{69} +(4.34730 - 3.64781i) q^{71} +(-0.407604 - 0.342020i) q^{72} +(-0.365715 - 2.07407i) q^{73} +(3.75877 + 1.36808i) q^{74} +(3.58512 + 2.47929i) q^{76} -13.3209 q^{77} +(-10.1702 - 3.70167i) q^{78} +(-0.0641778 - 0.363970i) q^{79} +(-7.90033 + 6.62916i) q^{81} +(0.0248149 - 0.140732i) q^{82} +(-0.376859 + 0.652739i) q^{83} +(2.87939 + 4.98724i) q^{84} +(-10.2306 + 3.72362i) q^{86} +(3.87939 + 6.71929i) q^{87} +(-2.17365 + 3.76487i) q^{88} +(0.308811 - 1.75135i) q^{89} +(13.5175 + 11.3426i) q^{91} +(1.34730 + 7.64090i) q^{92} +(-14.9290 - 5.43372i) q^{93} +5.88713 q^{94} +1.87939 q^{96} +(-10.0360 - 3.65279i) q^{97} +(-0.414878 - 2.35289i) q^{98} +(-1.77197 - 1.48686i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} + 3 q^{6} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 + 3 * q^6 + 3 * q^8 - 3 * q^9	$ 6 q - 3 q^{3} + 3 q^{6} + 3 q^{8} - 3 q^{9} + 12 q^{11} + 6 q^{13} - 12 q^{14} + 6 q^{17} + 6 q^{18} + 6 q^{19} + 12 q^{21} + 6 q^{22} + 6 q^{23} + 3 q^{24} + 6 q^{26} + 3 q^{27} - 6 q^{28} - 12 q^{29} + 12 q^{31} + 15 q^{33} + 12 q^{34} - 3 q^{36} + 24 q^{37} + 9 q^{38} - 24 q^{39} + 27 q^{41} + 6 q^{42} - 30 q^{43} - 6 q^{44} + 12 q^{46} + 24 q^{47} + 6 q^{48} - 3 q^{49} + 3 q^{51} + 6 q^{52} + 12 q^{53} - 9 q^{54} + 6 q^{57} + 12 q^{58} + 3 q^{59} - 12 q^{61} + 18 q^{63} - 3 q^{64} + 21 q^{66} + 27 q^{67} - 3 q^{68} + 12 q^{69} + 24 q^{71} - 6 q^{72} - 12 q^{73} + 12 q^{77} - 18 q^{78} + 18 q^{79} - 33 q^{81} - 27 q^{82} - 6 q^{83} + 6 q^{84} - 24 q^{86} + 12 q^{87} - 12 q^{88} + 48 q^{89} + 36 q^{91} + 6 q^{92} - 24 q^{93} - 24 q^{94} - 27 q^{97} - 24 q^{98} - 33 q^{99}+O(q^{100}) $ 6 * q - 3 * q^3 + 3 * q^6 + 3 * q^8 - 3 * q^9 + 12 * q^11 + 6 * q^13 - 12 * q^14 + 6 * q^17 + 6 * q^18 + 6 * q^19 + 12 * q^21 + 6 * q^22 + 6 * q^23 + 3 * q^24 + 6 * q^26 + 3 * q^27 - 6 * q^28 - 12 * q^29 + 12 * q^31 + 15 * q^33 + 12 * q^34 - 3 * q^36 + 24 * q^37 + 9 * q^38 - 24 * q^39 + 27 * q^41 + 6 * q^42 - 30 * q^43 - 6 * q^44 + 12 * q^46 + 24 * q^47 + 6 * q^48 - 3 * q^49 + 3 * q^51 + 6 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^57 + 12 * q^58 + 3 * q^59 - 12 * q^61 + 18 * q^63 - 3 * q^64 + 21 * q^66 + 27 * q^67 - 3 * q^68 + 12 * q^69 + 24 * q^71 - 6 * q^72 - 12 * q^73 + 12 * q^77 - 18 * q^78 + 18 * q^79 - 33 * q^81 - 27 * q^82 - 6 * q^83 + 6 * q^84 - 24 * q^86 + 12 * q^87 - 12 * q^88 + 48 * q^89 + 36 * q^91 + 6 * q^92 - 24 * q^93 - 24 * q^94 - 27 * q^97 - 24 * q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	−0.326352	−	1.85083i	−0.188419	−	1.06858i	−0.921483	−	0.388419i	$-0.873021\pi$
$3$	−0.326352	−	1.85083i	−0.188419	−	1.06858i	0.733064	−	0.680160i	$-0.238090\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$		0			0
$5$		0			0
$6$	0.326352	−	1.85083i	0.133233	−	0.755599i
$7$	−1.53209	+	2.65366i	−0.579075	+	1.00299i	0.416511	+	0.909131i	$0.363253\pi$
$7$	−1.53209	+	2.65366i	−0.579075	+	1.00299i	−0.995586	+	0.0938567i	$0.970080\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−0.500000	+	0.181985i	−0.166667	+	0.0606617i
$10$		0			0
$11$	2.17365	+	3.76487i	0.655380	+	1.13515i	0.981798	+	0.189926i	$0.0608247\pi$
$11$	2.17365	+	3.76487i	0.655380	+	1.13515i	−0.326419	+	0.945225i	$0.605842\pi$
$12$	0.939693	−	1.62760i	0.271266	−	0.469846i
$13$	1.00000	−	5.67128i	0.277350	−	1.57293i	−0.454046	−	0.890978i	$-0.650020\pi$
$13$	1.00000	−	5.67128i	0.277350	−	1.57293i	0.731396	−	0.681953i	$-0.238869\pi$
$14$	−2.34730	+	1.96962i	−0.627341	+	0.526402i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	1.93969	+	0.705990i	0.470445	+	0.171228i	0.566354	−	0.824162i	$-0.308354\pi$
$17$	1.93969	+	0.705990i	0.470445	+	0.171228i	−0.0959092	+	0.995390i	$0.530576\pi$
$18$	−0.532089			−0.125415
$19$	4.34002	−	0.405223i	0.995669	−	0.0929645i
$19$	4.34002	−	0.405223i	0.995669	−	0.0929645i
$20$		0			0
$21$	5.41147	+	1.96962i	1.18088	+	0.429805i
$22$	0.754900	+	4.28125i	0.160945	+	0.912766i
$23$	5.94356	+	4.98724i	1.23932	+	1.03991i	0.997577	+	0.0695711i	$0.0221631\pi$
$23$	5.94356	+	4.98724i	1.23932	+	1.03991i	0.241742	+	0.970341i	$0.422281\pi$
$24$	1.43969	−	1.20805i	0.293876	−	0.246591i
$25$		0			0
$26$	2.87939	−	4.98724i	0.564694	−	0.978079i
$27$	−2.31908	−	4.01676i	−0.446307	−	0.773026i
$28$	−2.87939	+	1.04801i	−0.544153	+	0.198055i
$29$	−3.87939	+	1.41198i	−0.720384	+	0.262198i	−0.676089	−	0.736820i	$-0.736326\pi$
$29$	−3.87939	+	1.41198i	−0.720384	+	0.262198i	−0.0442951	+	0.999018i	$0.514104\pi$
$30$		0			0
$31$	4.22668	−	7.32083i	0.759134	−	1.31486i	−0.184158	−	0.982897i	$-0.558956\pi$
$31$	4.22668	−	7.32083i	0.759134	−	1.31486i	0.943292	−	0.331963i	$-0.107711\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	6.25877	−	5.25173i	1.08951	−	0.914209i
$34$	1.58125	+	1.32683i	0.271182	+	0.227549i
$35$		0			0
$36$	−0.500000	−	0.181985i	−0.0833333	−	0.0303309i
$37$	4.00000			0.657596			0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000			0.657596			0.328798	+	0.944400i	$0.393356\pi$
$38$	4.21688	+	1.10359i	0.684068	+	0.179026i
$39$	−10.8229			−1.73306
$40$		0			0
$41$	−0.0248149	−	0.140732i	−0.00387544	−	0.0219787i	0.982809	−	0.184627i	$-0.0591076\pi$
$41$	−0.0248149	−	0.140732i	−0.00387544	−	0.0219787i	−0.986684	+	0.162648i	$0.947997\pi$
$42$	4.41147	+	3.70167i	0.680705	+	0.571180i
$43$	−8.34002	+	6.99811i	−1.27184	+	1.06720i	−0.277527	+	0.960718i	$0.589515\pi$
$43$	−8.34002	+	6.99811i	−1.27184	+	1.06720i	−0.994314	+	0.106484i	$0.966041\pi$
$44$	−0.754900	+	4.28125i	−0.113805	+	0.645423i
$45$		0			0
$46$	3.87939	+	6.71929i	0.571984	+	0.990706i
$47$	5.53209	−	2.01352i	0.806938	−	0.293701i	0.0945797	−	0.995517i	$-0.469849\pi$
$47$	5.53209	−	2.01352i	0.806938	−	0.293701i	0.712358	+	0.701816i	$0.247627\pi$
$48$	1.76604	−	0.642788i	0.254907	−	0.0927784i
$49$	−1.19459	−	2.06910i	−0.170656	−	0.295585i
$50$		0			0
$51$	0.673648	−	3.82045i	0.0943296	−	0.534970i
$52$	4.41147	−	3.70167i	0.611761	−	0.513329i
$53$	3.87939	+	3.25519i	0.532875	+	0.447135i	0.869093	−	0.494649i	$-0.164703\pi$
$53$	3.87939	+	3.25519i	0.532875	+	0.447135i	−0.336218	+	0.941784i	$0.609148\pi$
$54$	−0.805407	−	4.56769i	−0.109602	−	0.621584i
$55$		0			0
$56$	−3.06418			−0.409468
$57$	−2.16637	−	7.90041i	−0.286943	−	1.04644i
$58$	−4.12836			−0.542080
$59$	−7.19119	−	2.61738i	−0.936213	−	0.340754i	−0.171544	−	0.985177i	$-0.554875\pi$
$59$	−7.19119	−	2.61738i	−0.936213	−	0.340754i	−0.764669	+	0.644423i	$0.777098\pi$
$60$		0			0
$61$	−6.94356	−	5.82634i	−0.889032	−	0.745987i	0.0789836	−	0.996876i	$-0.474833\pi$
$61$	−6.94356	−	5.82634i	−0.889032	−	0.745987i	−0.968016	+	0.250889i	$0.919277\pi$
$62$	6.47565	−	5.43372i	0.822409	−	0.690083i
$63$	0.283119	−	1.60565i	0.0356696	−	0.202292i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	7.67752	−	2.79439i	0.945037	−	0.343965i
$67$	5.92989	−	2.15830i	0.724452	−	0.263679i	0.0466373	−	0.998912i	$-0.485150\pi$
$67$	5.92989	−	2.15830i	0.724452	−	0.263679i	0.677814	+	0.735233i	$0.262927\pi$
$68$	1.03209	+	1.78763i	0.125159	+	0.216782i
$69$	7.29086	−	12.6281i	0.877716	−	1.52025i
$70$		0			0
$71$	4.34730	−	3.64781i	0.515929	−	0.432916i	−0.347281	−	0.937761i	$-0.612895\pi$
$71$	4.34730	−	3.64781i	0.515929	−	0.432916i	0.863210	+	0.504845i	$0.168450\pi$
$72$	−0.407604	−	0.342020i	−0.0480366	−	0.0403075i
$73$	−0.365715	−	2.07407i	−0.0428037	−	0.242752i	0.955898	−	0.293700i	$-0.0948867\pi$
$73$	−0.365715	−	2.07407i	−0.0428037	−	0.242752i	−0.998701	+	0.0509484i	$0.983776\pi$
$74$	3.75877	+	1.36808i	0.436948	+	0.159036i
$75$		0			0
$76$	3.58512	+	2.47929i	0.411242	+	0.284395i
$77$	−13.3209			−1.51806
$78$	−10.1702	−	3.70167i	−1.15155	−	0.419131i
$79$	−0.0641778	−	0.363970i	−0.00722056	−	0.0409499i	0.980985	−	0.194086i	$-0.0621739\pi$
$79$	−0.0641778	−	0.363970i	−0.00722056	−	0.0409499i	−0.988205	+	0.153136i	$0.951063\pi$
$80$		0			0
$81$	−7.90033	+	6.62916i	−0.877814	+	0.736574i
$82$	0.0248149	−	0.140732i	0.00274035	−	0.0155413i
$83$	−0.376859	+	0.652739i	−0.0413657	+	0.0716474i	−0.885967	−	0.463748i	$-0.846504\pi$
$83$	−0.376859	+	0.652739i	−0.0413657	+	0.0716474i	0.844601	+	0.535396i	$0.179838\pi$
$84$	2.87939	+	4.98724i	0.314167	+	0.544153i
$85$		0			0
$86$	−10.2306	+	3.72362i	−1.10319	+	0.401528i
$87$	3.87939	+	6.71929i	0.415914	+	0.720384i
$88$	−2.17365	+	3.76487i	−0.231712	+	0.401336i
$89$	0.308811	−	1.75135i	0.0327339	−	0.185643i	−0.964057	−	0.265697i	$-0.914398\pi$
$89$	0.308811	−	1.75135i	0.0327339	−	0.185643i	0.996791	+	0.0800536i	$0.0255091\pi$
$90$		0			0
$91$	13.5175	+	11.3426i	1.41702	+	1.18902i
$92$	1.34730	+	7.64090i	0.140465	+	0.796619i
$93$	−14.9290	−	5.43372i	−1.54807	−	0.563450i
$94$	5.88713			0.607211
$95$		0			0
$96$	1.87939			0.191814
$97$	−10.0360	−	3.65279i	−1.01900	−	0.370885i	−0.222116	−	0.975020i	$-0.571296\pi$
$97$	−10.0360	−	3.65279i	−1.01900	−	0.370885i	−0.796882	+	0.604136i	$0.793519\pi$
$98$	−0.414878	−	2.35289i	−0.0419090	−	0.237678i
$99$	−1.77197	−	1.48686i	−0.178090	−	0.149435i
$100$		0			0
$101$	−0.898986	+	5.09840i	−0.0894524	+	0.507310i	0.906854	+	0.421444i	$0.138477\pi$
$101$	−0.898986	+	5.09840i	−0.0894524	+	0.507310i	−0.996307	+	0.0858656i	$0.972634\pi$
$102$	1.93969	−	3.35965i	0.192058	−	0.332655i
$103$	8.90167	+	15.4182i	0.877108	+	1.51920i	0.854500	+	0.519451i	$0.173864\pi$
$103$	8.90167	+	15.4182i	0.877108	+	1.51920i	0.0226079	+	0.999744i	$0.492803\pi$
$104$	5.41147	−	1.96962i	0.530639	−	0.193137i
$105$		0			0
$106$	2.53209	+	4.38571i	0.245938	+	0.425977i
$107$	−2.37939	+	4.12122i	−0.230024	+	0.398413i	−0.957815	−	0.287386i	$-0.907214\pi$
$107$	−2.37939	+	4.12122i	−0.230024	+	0.398413i	0.727791	+	0.685799i	$0.240547\pi$
$108$	0.805407	−	4.56769i	0.0775004	−	0.439526i
$109$	−14.1480	+	11.8715i	−1.35513	+	1.13709i	−0.377675	+	0.925938i	$0.623276\pi$
$109$	−14.1480	+	11.8715i	−1.35513	+	1.13709i	−0.977454	+	0.211149i	$0.932279\pi$
$110$		0			0
$111$	−1.30541	−	7.40333i	−0.123904	−	0.702693i
$112$	−2.87939	−	1.04801i	−0.272076	−	0.0990277i
$113$	−2.58853			−0.243508			−0.121754	−	0.992560i	$-0.538852\pi$
$113$	−2.58853			−0.243508			−0.121754	+	0.992560i	$0.538852\pi$
$114$	0.666374	−	8.16490i	0.0624117	−	0.764713i
$115$		0			0
$116$	−3.87939	−	1.41198i	−0.360192	−	0.131099i
$117$	0.532089	+	3.01763i	0.0491916	+	0.278980i
$118$	−5.86231	−	4.91906i	−0.539669	−	0.452836i
$119$	−4.84524	+	4.06564i	−0.444162	+	0.372696i
$120$		0			0
$121$	−3.94949	+	6.84072i	−0.359045	+	0.621884i
$122$	−4.53209	−	7.84981i	−0.410316	−	0.710688i
$123$	−0.252374	+	0.0918566i	−0.0227558	+	0.00828243i
$124$	7.94356	−	2.89122i	0.713353	−	0.259639i
$125$		0			0
$126$	0.815207	−	1.41198i	0.0726245	−	0.125789i
$127$	1.87939	−	10.6585i	0.166768	−	0.945791i	−0.780454	−	0.625213i	$-0.785012\pi$
$127$	1.87939	−	10.6585i	0.166768	−	0.945791i	0.947222	−	0.320578i	$-0.103877\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	15.6741	+	13.1521i	1.38003	+	1.15798i
$130$		0			0
$131$	−6.95084	−	2.52990i	−0.607297	−	0.221038i	0.0200229	−	0.999800i	$-0.493626\pi$
$131$	−6.95084	−	2.52990i	−0.607297	−	0.221038i	−0.627320	+	0.778761i	$0.715848\pi$
$132$	8.17024			0.711129
$133$	−5.57398	+	12.1378i	−0.483325	+	1.05248i
$134$	6.31046			0.545141
$135$		0			0
$136$	0.358441	+	2.03282i	0.0307360	+	0.174313i
$137$	6.22075	+	5.21983i	0.531475	+	0.445960i	0.868610	−	0.495496i	$-0.165014\pi$
$137$	6.22075	+	5.21983i	0.531475	+	0.445960i	−0.337136	+	0.941456i	$0.609458\pi$
$138$	11.1702	−	9.37295i	0.950874	−	0.797878i
$139$	−2.57145	+	14.5834i	−0.218108	+	1.23695i	0.657324	+	0.753608i	$0.271688\pi$
$139$	−2.57145	+	14.5834i	−0.218108	+	1.23695i	−0.875432	+	0.483342i	$0.839423\pi$
$140$		0			0
$141$	−5.53209	−	9.58186i	−0.465886	−	0.806938i
$142$	5.33275	−	1.94096i	0.447514	−	0.162882i
$143$	23.5253	−	8.56250i	1.96728	−	0.716032i
$144$	−0.266044	−	0.460802i	−0.0221704	−	0.0384002i
$145$		0			0
$146$	0.365715	−	2.07407i	0.0302668	−	0.171651i
$147$	−3.43969	+	2.88624i	−0.283701	+	0.238053i
$148$	3.06418	+	2.57115i	0.251874	+	0.211347i
$149$	−0.822948	−	4.66717i	−0.0674185	−	0.382350i	−0.999783	−	0.0208299i	$-0.993369\pi$
$149$	−0.822948	−	4.66717i	−0.0674185	−	0.382350i	0.932364	−	0.361520i	$-0.117742\pi$
$150$		0			0
$151$	0.453363			0.0368942			0.0184471	−	0.999830i	$-0.494128\pi$
$151$	0.453363			0.0368942			0.0184471	+	0.999830i	$0.494128\pi$
$152$	2.52094	+	3.55596i	0.204476	+	0.288426i
$153$	−1.09833			−0.0887944
$154$	−12.5175	−	4.55601i	−1.00869	−	0.367134i
$155$		0			0
$156$	−8.29086	−	6.95686i	−0.663800	−	0.556994i
$157$	−10.0077	+	8.39749i	−0.798705	+	0.670193i	−0.947883	−	0.318617i	$-0.896781\pi$
$157$	−10.0077	+	8.39749i	−0.798705	+	0.670193i	0.149179	+	0.988810i	$0.452337\pi$
$158$	0.0641778	−	0.363970i	0.00510571	−	0.0289559i
$159$	4.75877	−	8.24243i	0.377395	−	0.653667i
$160$		0			0
$161$	−22.3405	+	8.13127i	−1.76068	+	0.640834i
$162$	−9.69119	+	3.52730i	−0.761412	+	0.277131i
$163$	2.93969	+	5.09170i	0.230254	+	0.398812i	0.957883	−	0.287159i	$-0.0927108\pi$
$163$	2.93969	+	5.09170i	0.230254	+	0.398812i	−0.727628	+	0.685971i	$0.759377\pi$
$164$	0.0714517	−	0.123758i	0.00557944	−	0.00966388i
$165$		0			0
$166$	−0.577382	+	0.484481i	−0.0448135	+	0.0376030i
$167$	−17.0273	−	14.2876i	−1.31762	−	1.10561i	−0.986805	−	0.161913i	$-0.948234\pi$
$167$	−17.0273	−	14.2876i	−1.31762	−	1.10561i	−0.330810	−	0.943697i	$-0.607322\pi$
$168$	1.00000	+	5.67128i	0.0771517	+	0.437549i
$169$	−18.9474	−	6.89630i	−1.45749	−	0.530485i
$170$		0			0
$171$	−2.09627	+	0.992431i	−0.160306	+	0.0758931i
$172$	−10.8871			−0.830136
$173$	−19.9145	−	7.24827i	−1.51407	−	0.551076i	−0.554410	−	0.832244i	$-0.687056\pi$
$173$	−19.9145	−	7.24827i	−1.51407	−	0.551076i	−0.959659	+	0.281168i	$0.909278\pi$
$174$	1.34730	+	7.64090i	0.102138	+	0.579255i
$175$		0			0
$176$	−3.33022	+	2.79439i	−0.251025	+	0.210635i
$177$	−2.49747	+	14.1639i	−0.187722	+	1.06462i
$178$	0.889185	−	1.54011i	0.0666473	−	0.115436i
$179$	−1.88666	−	3.26779i	−0.141016	−	0.244246i	0.786864	−	0.617127i	$-0.211703\pi$
$179$	−1.88666	−	3.26779i	−0.141016	−	0.244246i	−0.927879	+	0.372881i	$0.878370\pi$
$180$		0			0
$181$	−8.79561	+	3.20134i	−0.653772	+	0.237954i	−0.647545	−	0.762027i	$-0.724204\pi$
$181$	−8.79561	+	3.20134i	−0.653772	+	0.237954i	−0.00622701	+	0.999981i	$0.501982\pi$
$182$	8.82295	+	15.2818i	0.654000	+	1.13276i
$183$	−8.51754	+	14.7528i	−0.629635	+	1.09056i
$184$	−1.34730	+	7.64090i	−0.0993240	+	0.563294i
$185$		0			0
$186$	−12.1702	−	10.2120i	−0.892366	−	0.748784i
$187$	1.55825	+	8.83726i	0.113950	+	0.646245i
$188$	5.53209	+	2.01352i	0.403469	+	0.146851i
$189$	14.2121			1.03378
$190$		0			0
$191$	18.7101			1.35381			0.676907	−	0.736069i	$-0.263320\pi$
$191$	18.7101			1.35381			0.676907	+	0.736069i	$0.263320\pi$
$192$	1.76604	+	0.642788i	0.127453	+	0.0463892i
$193$	−2.07263	−	11.7545i	−0.149191	−	0.846107i	−0.963906	−	0.266244i	$-0.914217\pi$
$193$	−2.07263	−	11.7545i	−0.149191	−	0.846107i	0.814714	−	0.579863i	$-0.196894\pi$
$194$	−8.18139	−	6.86500i	−0.587389	−	0.492878i
$195$		0			0
$196$	0.414878	−	2.35289i	0.0296341	−	0.168063i
$197$	1.49020	−	2.58110i	0.106172	−	0.183896i	−0.808044	−	0.589122i	$-0.799474\pi$
$197$	1.49020	−	2.58110i	0.106172	−	0.183896i	0.914217	+	0.405226i	$0.132807\pi$
$198$	−1.15657	−	2.00324i	−0.0821941	−	0.142364i
$199$	22.7246	−	8.27109i	1.61091	−	0.586322i	0.629287	−	0.777173i	$-0.283347\pi$
$199$	22.7246	−	8.27109i	1.61091	−	0.586322i	0.981619	+	0.190851i	$0.0611249\pi$
$200$		0			0
$201$	−5.92989	−	10.2709i	−0.418262	−	0.724452i
$202$	−2.58853	+	4.48346i	−0.182128	+	0.315455i
$203$	2.19665	−	12.4578i	0.154175	−	0.874368i
$204$	2.97178	−	2.49362i	0.208066	−	0.174588i
$205$		0			0
$206$	3.09152	+	17.5329i	0.215396	+	1.22157i
$207$	−3.87939	−	1.41198i	−0.269636	−	0.0981394i
$208$	5.75877			0.399299
$209$	10.9593	+	15.4588i	0.758070	+	1.06931i
$210$		0			0
$211$	−12.2947	−	4.47492i	−0.846404	−	0.308066i	−0.117831	−	0.993034i	$-0.537594\pi$
$211$	−12.2947	−	4.47492i	−0.846404	−	0.308066i	−0.728573	+	0.684968i	$0.759816\pi$
$212$	0.879385	+	4.98724i	0.0603964	+	0.342525i
$213$	−8.17024	−	6.85565i	−0.559816	−	0.469741i
$214$	−3.64543	+	3.05888i	−0.249196	+	0.209101i
$215$		0			0
$216$	2.31908	−	4.01676i	0.157793	−	0.273306i
$217$	12.9513	+	22.4323i	0.879192	+	1.52280i
$218$	−17.3550	+	6.31672i	−1.17543	+	0.427822i
$219$	−3.71941	+	1.35375i	−0.251334	+	0.0914782i
$220$		0			0
$221$	5.94356	−	10.2946i	0.399807	−	0.692487i
$222$	1.30541	−	7.40333i	0.0876132	−	0.496879i
$223$	2.09833	−	1.76070i	0.140514	−	0.117906i	−0.569821	−	0.821769i	$-0.692988\pi$
$223$	2.09833	−	1.76070i	0.140514	−	0.117906i	0.710336	+	0.703863i	$0.248543\pi$
$224$	−2.34730	−	1.96962i	−0.156835	−	0.131600i
$225$		0			0
$226$	−2.43242	−	0.885328i	−0.161802	−	0.0588911i
$227$	−24.2422			−1.60901			−0.804504	−	0.593947i	$-0.797569\pi$
$227$	−24.2422			−1.60901			−0.804504	+	0.593947i	$0.797569\pi$
$228$	3.41875	−	7.44459i	0.226412	−	0.493030i
$229$	−15.6750			−1.03583			−0.517916	−	0.855431i	$-0.673292\pi$
$229$	−15.6750			−1.03583			−0.517916	+	0.855431i	$0.673292\pi$
$230$		0			0
$231$	4.34730	+	24.6547i	0.286031	+	1.62216i
$232$	−3.16250	−	2.65366i	−0.207629	−	0.174221i
$233$	20.2481	−	16.9902i	1.32650	−	1.11306i	0.341614	−	0.939840i	$-0.389026\pi$
$233$	20.2481	−	16.9902i	1.32650	−	1.11306i	0.984883	−	0.173223i	$-0.0554180\pi$
$234$	−0.532089	+	3.01763i	−0.0347837	+	0.197268i
$235$		0			0
$236$	−3.82635	−	6.62744i	−0.249074	−	0.431409i
$237$	−0.652704	+	0.237565i	−0.0423977	+	0.0154315i
$238$	−5.94356	+	2.16328i	−0.385264	+	0.140225i
$239$	6.87939	+	11.9154i	0.444990	+	0.770746i	0.998052	−	0.0623946i	$-0.0198737\pi$
$239$	6.87939	+	11.9154i	0.444990	+	0.770746i	−0.553061	+	0.833141i	$0.686540\pi$
$240$		0			0
$241$	2.24257	−	12.7183i	0.144457	−	0.819256i	−0.823345	−	0.567542i	$-0.807895\pi$
$241$	2.24257	−	12.7183i	0.144457	−	0.819256i	0.967802	−	0.251714i	$-0.0809943\pi$
$242$	−6.05097	+	5.07737i	−0.388971	+	0.326386i
$243$	4.18866	+	3.51471i	0.268703	+	0.225468i
$244$	−1.57398	−	8.92647i	−0.100764	−	0.571459i
$245$		0			0
$246$	−0.268571			−0.0171234
$247$	2.04189	−	25.0187i	0.129922	−	1.59190i
$248$	8.45336			0.536789
$249$	1.33110	+	0.484481i	0.0843550	+	0.0307027i
$250$		0			0
$251$	13.9231	+	11.6829i	0.878817	+	0.737415i	0.965936	−	0.258783i	$-0.0833213\pi$
$251$	13.9231	+	11.6829i	0.878817	+	0.737415i	−0.0871182	+	0.996198i	$0.527766\pi$
$252$	1.24897	−	1.04801i	0.0786777	−	0.0660185i
$253$	−5.85710	+	33.2172i	−0.368233	+	2.08835i
$254$	5.41147	−	9.37295i	0.339546	−	0.588111i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−6.55216	+	2.38479i	−0.408712	+	0.148759i	−0.538191	−	0.842823i	$-0.680892\pi$
$257$	−6.55216	+	2.38479i	−0.408712	+	0.148759i	0.129478	+	0.991582i	$0.458670\pi$
$258$	10.2306	+	17.7198i	0.636926	+	1.10319i
$259$	−6.12836	+	10.6146i	−0.380797	+	0.659561i
$260$		0			0
$261$	1.68273	−	1.41198i	0.104159	−	0.0873994i
$262$	−5.66637	−	4.75465i	−0.350070	−	0.293743i
$263$	−1.79561	−	10.1834i	−0.110722	−	0.627935i	−0.988780	−	0.149381i	$-0.952272\pi$
$263$	−1.79561	−	10.1834i	−0.110722	−	0.627935i	0.878058	−	0.478554i	$-0.158839\pi$
$264$	7.67752	+	2.79439i	0.472519	+	0.171983i
$265$		0			0
$266$	−9.38919	+	9.49935i	−0.575688	+	0.582443i
$267$	−3.34224			−0.204542
$268$	5.92989	+	2.15830i	0.362226	+	0.131839i
$269$	−1.81521	−	10.2946i	−0.110675	−	0.627670i	−0.988801	−	0.149240i	$-0.952317\pi$
$269$	−1.81521	−	10.2946i	−0.110675	−	0.627670i	0.878126	−	0.478430i	$-0.158794\pi$
$270$		0			0
$271$	−14.7023	+	12.3367i	−0.893103	+	0.749403i	−0.968830	−	0.247726i	$-0.920317\pi$
$271$	−14.7023	+	12.3367i	−0.893103	+	0.749403i	0.0757270	+	0.997129i	$0.475872\pi$
$272$	−0.358441	+	2.03282i	−0.0217337	+	0.123258i
$273$	16.5817	−	28.7204i	1.00357	−	1.73824i
$274$	4.06031	+	7.03266i	0.245292	+	0.424858i
$275$		0			0
$276$	13.7023	−	4.98724i	0.824784	−	0.300197i
$277$	−14.8229	−	25.6741i	−0.890625	−	1.54261i	−0.839128	−	0.543934i	$-0.816934\pi$
$277$	−14.8229	−	25.6741i	−0.890625	−	1.54261i	−0.0514966	−	0.998673i	$-0.516399\pi$
$278$	−7.40420	+	12.8245i	−0.444074	+	0.769159i
$279$	−0.781059	+	4.42961i	−0.0467608	+	0.265194i
$280$		0			0
$281$	−13.4552	−	11.2902i	−0.802668	−	0.673519i	0.146177	−	0.989258i	$-0.453303\pi$
$281$	−13.4552	−	11.2902i	−0.802668	−	0.673519i	−0.948846	+	0.315740i	$0.897747\pi$
$282$	−1.92127	−	10.8961i	−0.114410	−	0.648853i
$283$	−5.24257	−	1.90814i	−0.311639	−	0.113427i	0.181466	−	0.983397i	$-0.441916\pi$
$283$	−5.24257	−	1.90814i	−0.311639	−	0.113427i	−0.493105	+	0.869970i	$0.664138\pi$
$284$	5.67499			0.336749
$285$		0			0
$286$	25.0351			1.48036
$287$	0.411474	+	0.149764i	0.0242885	+	0.00884031i
$288$	−0.0923963	−	0.524005i	−0.00544450	−	0.0308773i
$289$	−9.75877	−	8.18858i	−0.574045	−	0.481681i
$290$		0			0
$291$	−3.48545	+	19.7670i	−0.204321	+	1.15876i
$292$	1.05303	−	1.82391i	0.0616241	−	0.106736i
$293$	10.2713	+	17.7903i	0.600053	+	1.03932i	0.992812	+	0.119681i	$0.0381873\pi$
$293$	10.2713	+	17.7903i	0.600053	+	1.03932i	−0.392759	+	0.919641i	$0.628479\pi$
$294$	−4.21941	+	1.53574i	−0.246081	+	0.0895661i
$295$		0			0
$296$	2.00000	+	3.46410i	0.116248	+	0.201347i
$297$	10.0817	−	17.4620i	0.585001	−	1.01325i
$298$	0.822948	−	4.66717i	0.0476721	−	0.270362i
$299$	34.2276	−	28.7204i	1.97943	−	1.66094i
$300$		0			0
$301$	−5.79292	−	32.8533i	−0.333898	−	1.89363i
$302$	0.426022	+	0.155059i	0.0245148	+	0.00892266i
$303$	9.72967			0.558955
$304$	1.15270	+	4.20372i	0.0661121	+	0.241100i
$305$		0			0
$306$	−1.03209	−	0.375650i	−0.0590006	−	0.0214745i
$307$	0.245100	+	1.39003i	0.0139886	+	0.0793332i	0.991003	−	0.133841i	$-0.0427310\pi$
$307$	0.245100	+	1.39003i	0.0139886	+	0.0793332i	−0.977014	+	0.213174i	$0.931620\pi$
$308$	−10.2044	−	8.56250i	−0.581449	−	0.487894i
$309$	25.6313	−	21.5073i	1.45812	−	1.22350i
$310$		0			0
$311$	5.22668	−	9.05288i	0.296378	−	0.513342i	−0.678927	−	0.734206i	$-0.737555\pi$
$311$	5.22668	−	9.05288i	0.296378	−	0.513342i	0.975304	+	0.220865i	$0.0708879\pi$
$312$	−5.41147	−	9.37295i	−0.306364	−	0.530639i
$313$	−31.4342	+	11.4411i	−1.77677	+	0.646691i	−0.776914	+	0.629607i	$0.783216\pi$
$313$	−31.4342	+	11.4411i	−1.77677	+	0.646691i	−0.999854	+	0.0170834i	$0.994562\pi$
$314$	−12.2763	+	4.46821i	−0.692792	+	0.252156i
$315$		0			0
$316$	0.184793	−	0.320070i	0.0103954	−	0.0180053i
$317$	0.650015	−	3.68642i	0.0365085	−	0.207050i	−0.961097	−	0.276211i	$-0.910921\pi$
$317$	0.650015	−	3.68642i	0.0365085	−	0.207050i	0.997606	+	0.0691611i	$0.0220322\pi$
$318$	7.29086	−	6.11776i	0.408851	−	0.343067i
$319$	−13.7483	−	11.5362i	−0.769759	−	0.645905i
$320$		0			0
$321$	8.40420	+	3.05888i	0.469077	+	0.170730i
$322$	−23.7743			−1.32489
$323$	8.70439	+	2.27801i	0.484325	+	0.126752i
$324$	−10.3131			−0.572953
$325$		0			0
$326$	1.02094	+	5.79006i	0.0565449	+	0.320682i
$327$	26.5895	+	22.3112i	1.47040	+	1.23381i
$328$	0.109470	−	0.0918566i	0.00604449	−	0.00507193i
$329$	−3.13247	+	17.7651i	−0.172699	+	0.979424i
$330$		0			0
$331$	2.52094	+	4.36640i	0.138564	+	0.239999i	0.926953	−	0.375177i	$-0.122418\pi$
$331$	2.52094	+	4.36640i	0.138564	+	0.239999i	−0.788389	+	0.615176i	$0.789085\pi$
$332$	−0.708263	+	0.257787i	−0.0388710	+	0.0141479i
$333$	−2.00000	+	0.727940i	−0.109599	+	0.0398909i
$334$	−11.1138	−	19.2497i	−0.608120	−	1.05330i
$335$		0			0
$336$	−1.00000	+	5.67128i	−0.0545545	+	0.309394i
$337$	2.08054	−	1.74578i	0.113334	−	0.0950986i	−0.584359	−	0.811495i	$-0.698654\pi$
$337$	2.08054	−	1.74578i	0.113334	−	0.0950986i	0.697694	+	0.716396i	$0.254210\pi$
$338$	−15.4461	−	12.9608i	−0.840156	−	0.704975i
$339$	0.844770	+	4.79093i	0.0458816	+	0.260208i
$340$		0			0
$341$	36.7493			1.99008
$342$	−2.30928	+	0.215615i	−0.124871	+	0.0116591i
$343$	−14.1284			−0.762859
$344$	−10.2306	−	3.72362i	−0.551594	−	0.200764i
$345$		0			0
$346$	−16.2344	−	13.6223i	−0.872768	−	0.732339i
$347$	9.15910	−	7.68540i	0.491686	−	0.412574i	−0.362944	−	0.931811i	$-0.618228\pi$
$347$	9.15910	−	7.68540i	0.491686	−	0.412574i	0.854630	+	0.519237i	$0.173784\pi$
$348$	−1.34730	+	7.64090i	−0.0722227	+	0.409595i
$349$	8.53714	−	14.7868i	0.456983	−	0.791517i	−0.541817	−	0.840496i	$-0.682263\pi$
$349$	8.53714	−	14.7868i	0.456983	−	0.791517i	0.998800	+	0.0489792i	$0.0155968\pi$
$350$		0			0
$351$	−25.0993	+	9.13538i	−1.33970	+	0.487611i
$352$	−4.08512	+	1.48686i	−0.217738	+	0.0792501i
$353$	−1.93629	−	3.35375i	−0.103058	−	0.178502i	0.809885	−	0.586589i	$-0.199529\pi$
$353$	−1.93629	−	3.35375i	−0.103058	−	0.178502i	−0.912943	+	0.408087i	$0.866196\pi$
$354$	−7.19119	+	12.4555i	−0.382207	+	0.662003i
$355$		0			0
$356$	1.36231	−	1.14311i	0.0722023	−	0.0605850i
$357$	9.10607	+	7.64090i	0.481944	+	0.404399i
$358$	−0.655230	−	3.71599i	−0.0346300	−	0.196396i
$359$	22.1780	+	8.07213i	1.17051	+	0.426031i	0.852841	−	0.522171i	$-0.174878\pi$
$359$	22.1780	+	8.07213i	1.17051	+	0.426031i	0.317669	+	0.948202i	$0.397100\pi$
$360$		0			0
$361$	18.6716	−	3.51735i	0.982715	−	0.185124i
$362$	−9.36009			−0.491955
$363$	13.9500	+	5.07737i	0.732183	+	0.266493i
$364$	3.06418	+	17.3778i	0.160607	+	0.910845i
$365$		0			0
$366$	−13.0496	+	10.9499i	−0.682115	+	0.572363i
$367$	1.77332	−	10.0570i	0.0925665	−	0.524971i	−0.902899	−	0.429852i	$-0.858566\pi$
$367$	1.77332	−	10.0570i	0.0925665	−	0.524971i	0.995466	−	0.0951187i	$-0.0303231\pi$
$368$	−3.87939	+	6.71929i	−0.202227	+	0.350267i
$369$	0.0380187	+	0.0658503i	0.00197917	+	0.00342803i
$370$		0			0
$371$	−14.5817	+	5.30731i	−0.757045	+	0.275542i
$372$	−7.94356	−	13.7587i	−0.411855	−	0.713353i
$373$	11.1848	−	19.3726i	0.579127	−	1.00308i	−0.416453	−	0.909157i	$-0.636727\pi$
$373$	11.1848	−	19.3726i	0.579127	−	1.00308i	0.995580	−	0.0939195i	$-0.0299396\pi$
$374$	−1.55825	+	8.83726i	−0.0805751	+	0.456964i
$375$		0			0
$376$	4.50980	+	3.78417i	0.232575	+	0.195154i
$377$	4.12836	+	23.4131i	0.212621	+	1.20583i
$378$	13.3550	+	4.86084i	0.686909	+	0.250014i
$379$	−25.4783			−1.30873			−0.654367	−	0.756177i	$-0.727065\pi$
$379$	−25.4783			−1.30873			−0.654367	+	0.756177i	$0.727065\pi$
$380$		0			0
$381$	−20.3405			−1.04207
$382$	17.5817	+	6.39922i	0.899559	+	0.327413i
$383$	2.54933	+	14.4579i	0.130264	+	0.738766i	0.978041	+	0.208413i	$0.0668297\pi$
$383$	2.54933	+	14.4579i	0.130264	+	0.738766i	−0.847777	+	0.530354i	$0.822059\pi$
$384$	1.43969	+	1.20805i	0.0734690	+	0.0616478i
$385$		0			0
$386$	2.07263	−	11.7545i	0.105494	−	0.598288i
$387$	2.89646	−	5.01681i	0.147235	−	0.255019i
$388$	−5.34002	−	9.24919i	−0.271099	−	0.469556i
$389$	27.0060	−	9.82938i	1.36926	−	0.498369i	0.450354	−	0.892850i	$-0.351298\pi$
$389$	27.0060	−	9.82938i	1.36926	−	0.498369i	0.918904	+	0.394481i	$0.129076\pi$
$390$		0			0
$391$	8.00774	+	13.8698i	0.404969	+	0.701427i
$392$	1.19459	−	2.06910i	0.0603360	−	0.104505i
$393$	−2.41400	+	13.6905i	−0.121770	+	0.690593i
$394$	2.28312	−	1.91576i	0.115022	−	0.0965148i
$395$		0			0
$396$	−0.401674	−	2.27801i	−0.0201849	−	0.114474i
$397$	19.5672	+	7.12187i	0.982048	+	0.357436i	0.782636	−	0.622479i	$-0.213875\pi$
$397$	19.5672	+	7.12187i	0.982048	+	0.357436i	0.199412	+	0.979916i	$0.436097\pi$
$398$	24.1830			1.21219
$399$	24.2841	+	6.35532i	1.21572	+	0.318164i
$400$		0			0
$401$	−6.97906	−	2.54017i	−0.348517	−	0.126850i	0.161829	−	0.986819i	$-0.448261\pi$
$401$	−6.97906	−	2.54017i	−0.348517	−	0.126850i	−0.510347	+	0.859969i	$0.670483\pi$
$402$	−2.05943	−	11.6796i	−0.102715	−	0.582526i
$403$	−37.2918	−	31.2915i	−1.85764	−	1.55874i
$404$	−3.96585	+	3.32774i	−0.197308	+	0.165561i
$405$		0			0
$406$	6.32501	−	10.9552i	0.313905	−	0.543699i
$407$	8.69459	+	15.0595i	0.430975	+	0.746471i
$408$	3.64543	−	1.32683i	0.180476	−	0.0656878i
$409$	−19.7729	+	7.19675i	−0.977707	+	0.355856i	−0.780948	−	0.624596i	$-0.785264\pi$
$409$	−19.7729	+	7.19675i	−0.977707	+	0.355856i	−0.196759	+	0.980452i	$0.563042\pi$
$410$		0			0
$411$	7.63088	−	13.2171i	0.376404	−	0.651950i
$412$	−3.09152	+	17.5329i	−0.152308	+	0.863783i
$413$	17.9632	−	15.0729i	0.883909	−	0.741688i
$414$	−3.16250	−	2.65366i	−0.155429	−	0.130420i
$415$		0			0
$416$	5.41147	+	1.96962i	0.265319	+	0.0965683i
$417$	27.8307			1.36287
$418$	5.01114	+	18.2748i	0.245103	+	0.893851i
$419$	−18.9162			−0.924118			−0.462059	−	0.886849i	$-0.652889\pi$
$419$	−18.9162			−0.924118			−0.462059	+	0.886849i	$0.652889\pi$
$420$		0			0
$421$	1.26352	+	7.16577i	0.0615801	+	0.349238i	0.999993	+	0.00372244i	$0.00118489\pi$
$421$	1.26352	+	7.16577i	0.0615801	+	0.349238i	−0.938413	+	0.345516i	$0.887704\pi$
$422$	−10.0228	−	8.41009i	−0.487900	−	0.409397i
$423$	−2.39961	+	2.01352i	−0.116673	+	0.0979005i
$424$	−0.879385	+	4.98724i	−0.0427067	+	0.242202i
$425$		0			0
$426$	−5.33275	−	9.23659i	−0.258373	−	0.447514i
$427$	26.0993	−	9.49935i	1.26303	−	0.459706i
$428$	−4.47178	+	1.62760i	−0.216152	+	0.0786728i
$429$	−23.5253	−	40.7470i	−1.13581	−	1.96728i
$430$		0			0
$431$	2.47565	−	14.0401i	0.119248	−	0.676289i	−0.865311	−	0.501235i	$-0.832879\pi$
$431$	2.47565	−	14.0401i	0.119248	−	0.676289i	0.984559	−	0.175053i	$-0.0560098\pi$
$432$	3.55303	−	2.98135i	0.170945	−	0.143440i
$433$	5.78880	+	4.85738i	0.278192	+	0.233431i	0.771198	−	0.636595i	$-0.219658\pi$
$433$	5.78880	+	4.85738i	0.278192	+	0.233431i	−0.493006	+	0.870026i	$0.664102\pi$
$434$	4.49794	+	25.5091i	0.215908	+	1.22448i
$435$		0			0
$436$	−18.4688			−0.884497
$437$	27.8161	+	19.2363i	1.33063	+	0.920196i
$438$	−3.95811			−0.189126
$439$	−5.72193	−	2.08261i	−0.273093	−	0.0993977i	0.201844	−	0.979418i	$-0.435307\pi$
$439$	−5.72193	−	2.08261i	−0.273093	−	0.0993977i	−0.474937	+	0.880020i	$0.657529\pi$
$440$		0			0
$441$	0.973841	+	0.817150i	0.0463734	+	0.0389119i
$442$	9.10607	−	7.64090i	0.433131	−	0.363440i
$443$	−4.73514	+	26.8543i	−0.224973	+	1.27589i	0.637763	+	0.770232i	$0.279860\pi$
$443$	−4.73514	+	26.8543i	−0.224973	+	1.27589i	−0.862736	+	0.505654i	$0.831251\pi$
$444$	3.75877	−	6.51038i	0.178383	−	0.308969i
$445$		0			0
$446$	2.57398	−	0.936851i	0.121881	−	0.0443612i
$447$	−8.36959	+	3.04628i	−0.395868	+	0.144084i
$448$	−1.53209	−	2.65366i	−0.0723844	−	0.125373i
$449$	−19.8464	+	34.3750i	−0.936610	+	1.62226i	−0.164874	+	0.986315i	$0.552722\pi$
$449$	−19.8464	+	34.3750i	−0.936610	+	1.62226i	−0.771737	+	0.635942i	$0.780612\pi$
$450$		0			0
$451$	0.475900	−	0.399328i	0.0224093	−	0.0188036i
$452$	−1.98293	−	1.66387i	−0.0932690	−	0.0782620i
$453$	−0.147956	−	0.839100i	−0.00695157	−	0.0394243i
$454$	−22.7802	−	8.29131i	−1.06913	−	0.389130i
$455$		0			0
$456$	5.75877	−	5.82634i	0.269679	−	0.272843i
$457$	6.93676			0.324488			0.162244	−	0.986751i	$-0.448127\pi$
$457$	6.93676			0.324488			0.162244	+	0.986751i	$0.448127\pi$
$458$	−14.7297	−	5.36116i	−0.688272	−	0.250511i
$459$	−1.66250	−	9.42853i	−0.0775990	−	0.440086i
$460$		0			0
$461$	20.5817	−	17.2701i	0.958586	−	0.804349i	−0.0221363	−	0.999755i	$-0.507047\pi$
$461$	20.5817	−	17.2701i	0.958586	−	0.804349i	0.980723	+	0.195406i	$0.0626023\pi$
$462$	−4.34730	+	24.6547i	−0.202255	+	1.14704i
$463$	7.53714	−	13.0547i	0.350281	−	0.606704i	−0.636018	−	0.771674i	$-0.719420\pi$
$463$	7.53714	−	13.0547i	0.350281	−	0.606704i	0.986299	+	0.164970i	$0.0527529\pi$
$464$	−2.06418	−	3.57526i	−0.0958270	−	0.165977i
$465$		0			0
$466$	24.8380	−	9.04028i	1.15060	−	0.418783i
$467$	−10.6873	−	18.5110i	−0.494550	−	0.856586i	0.505430	−	0.862868i	$-0.331334\pi$
$467$	−10.6873	−	18.5110i	−0.494550	−	0.856586i	−0.999980	+	0.00628157i	$0.998000\pi$
$468$	−1.53209	+	2.65366i	−0.0708208	+	0.122665i
$469$	−3.35773	+	19.0426i	−0.155045	+	0.879306i
$470$		0			0
$471$	18.8084	+	15.7821i	0.866645	+	0.727202i
$472$	−1.32888	−	7.53644i	−0.0611666	−	0.346893i
$473$	−44.4752	−	16.1877i	−2.04497	−	0.744310i
$474$	−0.694593			−0.0319037
$475$		0			0
$476$	−6.32501			−0.289906
$477$	−2.53209	−	0.921605i	−0.115936	−	0.0421974i
$478$	2.38919	+	13.5497i	0.109279	+	0.619751i
$479$	−5.00774	−	4.20199i	−0.228810	−	0.191994i	0.521174	−	0.853450i	$-0.325494\pi$
$479$	−5.00774	−	4.20199i	−0.228810	−	0.191994i	−0.749984	+	0.661456i	$0.769939\pi$
$480$		0			0
$481$	4.00000	−	22.6851i	0.182384	−	1.03435i
$482$	6.45723	−	11.1843i	0.294119	−	0.509429i
$483$	22.3405	+	38.6949i	1.01653	+	1.76068i
$484$	−7.42262	+	2.70161i	−0.337392	+	0.122801i
$485$		0			0
$486$	2.73396	+	4.73535i	0.124015	+	0.214800i
$487$	−8.82295	+	15.2818i	−0.399806	+	0.692484i	−0.993702	−	0.112058i	$-0.964256\pi$
$487$	−8.82295	+	15.2818i	−0.399806	+	0.692484i	0.593896	+	0.804542i	$0.297589\pi$
$488$	1.57398	−	8.92647i	0.0712506	−	0.404082i
$489$	8.46451	−	7.10257i	0.382778	−	0.321189i
$490$		0			0
$491$	2.53549	+	14.3795i	0.114425	+	0.648937i	0.987033	+	0.160516i	$0.0513159\pi$
$491$	2.53549	+	14.3795i	0.114425	+	0.648937i	−0.872608	+	0.488421i	$0.837573\pi$
$492$	−0.252374	−	0.0918566i	−0.0113779	−	0.00414121i
$493$	−8.52166			−0.383796
$494$	10.4757	−	22.8115i	0.471322	−	1.02634i
$495$		0			0
$496$	7.94356	+	2.89122i	0.356677	+	0.129820i
$497$	3.01960	+	17.1250i	0.135448	+	0.768161i
$498$	1.08512	+	0.910526i	0.0486255	+	0.0408016i
$499$	−10.0248	+	8.41182i	−0.448772	+	0.376565i	−0.838980	−	0.544162i	$-0.816848\pi$
$499$	−10.0248	+	8.41182i	−0.448772	+	0.376565i	0.390208	+	0.920727i	$0.372403\pi$
$500$		0			0
$501$	−20.8871	+	36.1776i	−0.933168	+	1.61629i
$502$	9.08765	+	15.7403i	0.405602	+	0.702523i
$503$	26.9368	−	9.80418i	1.20105	−	0.437147i	0.337460	−	0.941340i	$-0.390432\pi$
$503$	26.9368	−	9.80418i	1.20105	−	0.437147i	0.863591	+	0.504193i	$0.168210\pi$
$504$	1.53209	−	0.557635i	0.0682447	−	0.0248390i
$505$		0			0
$506$	−16.8648	+	29.2108i	−0.749733	+	1.29858i
$507$	−6.58037	+	37.3192i	−0.292245	+	1.65740i
$508$	8.29086	−	6.95686i	0.367847	−	0.308661i
$509$	18.1361	+	15.2180i	0.803868	+	0.674526i	0.949136	−	0.314867i	$-0.101960\pi$
$509$	18.1361	+	15.2180i	0.803868	+	0.674526i	−0.145268	+	0.989392i	$0.546404\pi$
$510$		0			0
$511$	6.06418	+	2.20718i	0.268263	+	0.0976399i
$512$	−1.00000			−0.0441942
$513$	−11.6925	−	16.4931i	−0.516238	−	0.728188i
$514$	−6.97266			−0.307551
$515$		0			0
$516$	3.55303	+	20.1503i	0.156414	+	0.887065i
$517$	19.6054	+	16.4509i	0.862246	+	0.723510i
$518$	−9.38919	+	7.87846i	−0.412537	+	0.346160i
$519$	−6.91622	+	39.2238i	−0.303588	+	1.72174i
$520$		0			0
$521$	20.3812	+	35.3013i	0.892916	+	1.54658i	0.836362	+	0.548177i	$0.184678\pi$
$521$	20.3812	+	35.3013i	0.892916	+	1.54658i	0.0565541	+	0.998400i	$0.481989\pi$
$522$	2.06418	−	0.751299i	0.0903466	−	0.0328835i
$523$	−32.7101	+	11.9055i	−1.43031	+	0.520591i	−0.937021	−	0.349274i	$-0.886428\pi$
$523$	−32.7101	+	11.9055i	−1.43031	+	0.520591i	−0.493291	+	0.869864i	$0.664206\pi$
$524$	−3.69846	−	6.40593i	−0.161568	−	0.279844i
$525$		0			0
$526$	1.79561	−	10.1834i	0.0782922	−	0.444017i
$527$	13.3669	−	11.2162i	0.582271	−	0.488584i
$528$	6.25877	+	5.25173i	0.272378	+	0.228552i
$529$	6.45946	+	36.6334i	0.280846	+	1.59276i
$530$		0			0
$531$	4.07192			0.176706
$532$	−12.0719	+	5.71518i	−0.523384	+	0.247785i
$533$	−0.822948			−0.0356458
$534$	−3.14068	−	1.14311i	−0.135911	−	0.0494674i
$535$		0			0
$536$	4.83409	+	4.05629i	0.208801	+	0.175205i
$537$	−5.43242	+	4.55834i	−0.234426	+	0.196707i
$538$	1.81521	−	10.2946i	0.0782592	−	0.443830i
$539$	5.19325	−	8.99497i	0.223689	−	0.387441i
$540$		0			0
$541$	19.1138	−	6.95686i	0.821767	−	0.299099i	0.103291	−	0.994651i	$-0.467063\pi$
$541$	19.1138	−	6.95686i	0.821767	−	0.299099i	0.718475	+	0.695552i	$0.244840\pi$
$542$	−18.0351	+	6.56423i	−0.774673	+	0.281958i
$543$	8.79561	+	15.2344i	0.377456	+	0.653772i
$544$	−1.03209	+	1.78763i	−0.0442504	+	0.0766440i
$545$		0			0
$546$	25.4047	−	21.3170i	1.08722	−	0.912285i
$547$	12.0688	+	10.1269i	0.516023	+	0.432995i	0.863243	−	0.504789i	$-0.168430\pi$
$547$	12.0688	+	10.1269i	0.516023	+	0.432995i	−0.347220	+	0.937784i	$0.612874\pi$
$548$	1.41013	+	7.99724i	0.0602378	+	0.341625i
$549$	4.53209	+	1.64955i	0.193425	+	0.0704009i
$550$		0			0
$551$	−16.2645	+	7.70004i	−0.692889	+	0.328033i
$552$	14.5817			0.620639
$553$	1.06418	+	0.387329i	0.0452534	+	0.0164709i
$554$	−5.14796	−	29.1955i	−0.218716	−	1.24040i
$555$		0			0
$556$	−11.3439	+	9.51866i	−0.481088	+	0.403681i
$557$	5.58172	−	31.6555i	0.236505	−	1.34129i	−0.602916	−	0.797805i	$-0.705995\pi$
$557$	5.58172	−	31.6555i	0.236505	−	1.34129i	0.839421	−	0.543482i	$-0.182894\pi$
$558$	−2.24897	+	3.89533i	−0.0952065	+	0.164903i
$559$	31.3482	+	54.2967i	1.32589	+	2.29651i
$560$		0			0
$561$	15.8478	−	5.76811i	0.669093	−	0.243530i
$562$	−8.78224	−	15.2113i	−0.370456	−	0.641649i
$563$	1.51320	−	2.62095i	0.0637739	−	0.110460i	−0.832376	−	0.554212i	$-0.813020\pi$
$563$	1.51320	−	2.62095i	0.0637739	−	0.110460i	0.896149	+	0.443752i	$0.146353\pi$
$564$	1.92127	−	10.8961i	0.0809002	−	0.458808i
$565$		0			0
$566$	−4.27379	−	3.58613i	−0.179641	−	0.150736i
$567$	−5.48751	−	31.1212i	−0.230454	−	1.30697i
$568$	5.33275	+	1.94096i	0.223757	+	0.0814409i
$569$	−0.132474			−0.00555361			−0.00277681	−	0.999996i	$-0.500884\pi$
$569$	−0.132474			−0.00555361			−0.00277681	+	0.999996i	$0.500884\pi$
$570$		0			0
$571$	27.3969			1.14653			0.573263	−	0.819372i	$-0.305677\pi$
$571$	27.3969			1.14653			0.573263	+	0.819372i	$0.305677\pi$
$572$	23.5253	+	8.56250i	0.983641	+	0.358016i
$573$	−6.10607	−	34.6292i	−0.255085	−	1.44666i
$574$	0.335437	+	0.281465i	0.0140009	+	0.0117481i
$575$		0			0
$576$	0.0923963	−	0.524005i	0.00384984	−	0.0218336i
$577$	9.74763	−	16.8834i	0.405799	−	0.702864i	−0.588615	−	0.808413i	$-0.700327\pi$
$577$	9.74763	−	16.8834i	0.405799	−	0.702864i	0.994414	+	0.105549i	$0.0336600\pi$
$578$	−6.36959	−	11.0324i	−0.264940	−	0.458889i
$579$	−21.0792	+	7.67220i	−0.876021	+	0.318846i
$580$		0			0
$581$	−1.15476	−	2.00011i	−0.0479076	−	0.0829785i
$582$	−10.0360	+	17.3828i	−0.416004	+	0.720540i
$583$	−3.82295	+	21.6810i	−0.158330	+	0.897936i
$584$	1.61334	−	1.35375i	0.0667605	−	0.0560187i
$585$		0			0
$586$	3.56717	+	20.2304i	0.147358	+	0.835711i
$587$	−35.1450	−	12.7917i	−1.45059	−	0.527972i	−0.507834	−	0.861455i	$-0.669554\pi$
$587$	−35.1450	−	12.7917i	−1.45059	−	0.527972i	−0.942756	+	0.333483i	$0.891776\pi$
$588$	−4.49020			−0.185173
$589$	15.3773	−	33.4853i	0.633612	−	1.37974i
$590$		0			0
$591$	−5.26352	−	1.91576i	−0.216512	−	0.0788040i
$592$	0.694593	+	3.93923i	0.0285476	+	0.161901i
$593$	−11.0025	−	9.23222i	−0.451820	−	0.379122i	0.388291	−	0.921537i	$-0.373066\pi$
$593$	−11.0025	−	9.23222i	−0.451820	−	0.379122i	−0.840111	+	0.542415i	$0.817510\pi$
$594$	15.4461	−	12.9608i	0.633761	−	0.531788i
$595$		0			0
$596$	2.36959	−	4.10424i	0.0970620	−	0.168116i
$597$	−22.7246	−	39.3602i	−0.930057	−	1.61091i
$598$	41.9864	−	15.2818i	1.71695	−	0.624919i
$599$	−5.40198	+	1.96616i	−0.220719	+	0.0803351i	−0.450013	−	0.893022i	$-0.648581\pi$
$599$	−5.40198	+	1.96616i	−0.220719	+	0.0803351i	0.229294	+	0.973357i	$0.426358\pi$
$600$		0			0
$601$	18.0385	−	31.2436i	0.735805	−	1.27445i	−0.218564	−	0.975823i	$-0.570137\pi$
$601$	18.0385	−	31.2436i	0.735805	−	1.27445i	0.954369	−	0.298629i	$-0.0965294\pi$
$602$	5.79292	−	32.8533i	0.236102	−	1.33900i
$603$	−2.57217	+	2.15830i	−0.104747	+	0.0878929i
$604$	0.347296	+	0.291416i	0.0141313	+	0.0118576i
$605$		0			0
$606$	9.14290	+	3.32774i	0.371405	+	0.135180i
$607$	−6.49256			−0.263525			−0.131763	−	0.991281i	$-0.542064\pi$
$607$	−6.49256			−0.263525			−0.131763	+	0.991281i	$0.542064\pi$
$608$	−0.354570	+	4.34445i	−0.0143797	+	0.176191i
$609$	−23.7743			−0.963381
$610$		0			0
$611$	−5.88713	−	33.3876i	−0.238168	−	1.35072i
$612$	−0.841367	−	0.705990i	−0.0340102	−	0.0285380i
$613$	−0.825637	+	0.692791i	−0.0333471	+	0.0279816i	−0.659309	−	0.751872i	$-0.729151\pi$
$613$	−0.825637	+	0.692791i	−0.0333471	+	0.0279816i	0.625962	+	0.779854i	$0.284707\pi$
$614$	−0.245100	+	1.39003i	−0.00989143	+	0.0560971i
$615$		0			0
$616$	−6.66044	−	11.5362i	−0.268357	−	0.464808i
$617$	−16.2040	+	5.89777i	−0.652348	+	0.237435i	−0.646929	−	0.762550i	$-0.723947\pi$
$617$	−16.2040	+	5.89777i	−0.652348	+	0.237435i	−0.00541866	+	0.999985i	$0.501725\pi$
$618$	31.4415	−	11.4438i	1.26476	−	0.460336i
$619$	12.5865	+	21.8004i	0.505893	+	0.876232i	0.999977	+	0.00681784i	$0.00217020\pi$
$619$	12.5865	+	21.8004i	0.505893	+	0.876232i	−0.494084	+	0.869414i	$0.664496\pi$
$620$		0			0
$621$	6.24897	−	35.4397i	0.250763	−	1.42215i
$622$	8.00774	−	6.71929i	0.321081	−	0.269419i
$623$	4.17436	+	3.50271i	0.167242	+	0.140333i
$624$	−1.87939	−	10.6585i	−0.0752356	−	0.426682i
$625$		0			0
$626$	−33.4516			−1.33700
$627$	25.0351	−	25.3288i	0.999805	−	1.01154i
$628$	−13.0642			−0.521317
$629$	7.75877	+	2.82396i	0.309362	+	0.112599i
$630$		0			0
$631$	19.0838	+	16.0132i	0.759713	+	0.637475i	0.938052	−	0.346494i	$-0.112628\pi$
$631$	19.0838	+	16.0132i	0.759713	+	0.637475i	−0.178339	+	0.983969i	$0.557072\pi$
$632$	0.283119	−	0.237565i	0.0112619	−	0.00944982i
$633$	−4.26991	+	24.2159i	−0.169714	+	0.962495i
$634$	1.87164	−	3.24178i	0.0743325	−	0.128748i
$635$		0			0
$636$	8.94356	−	3.25519i	0.354635	−	0.129077i
$637$	−12.9290	+	4.70578i	−0.512266	+	0.186450i
$638$	−8.97359	−	15.5427i	−0.355268	−	0.615342i
$639$	−1.50980	+	2.61505i	−0.0597268	+	0.103450i
$640$		0			0
$641$	−11.5587	+	9.69891i	−0.456542	+	0.383084i	−0.841857	−	0.539701i	$-0.818537\pi$
$641$	−11.5587	+	9.69891i	−0.456542	+	0.383084i	0.385315	+	0.922785i	$0.374093\pi$
$642$	6.85117	+	5.74881i	0.270394	+	0.226887i
$643$	2.18520	+	12.3929i	0.0861760	+	0.488728i	0.997097	+	0.0761467i	$0.0242617\pi$
$643$	2.18520	+	12.3929i	0.0861760	+	0.488728i	−0.910921	+	0.412582i	$0.864627\pi$
$644$	−22.3405	−	8.13127i	−0.880339	−	0.320417i
$645$		0			0
$646$	7.40033	+	5.11770i	0.291162	+	0.201353i
$647$	27.7161			1.08963			0.544815	−	0.838556i	$-0.316600\pi$
$647$	27.7161			1.08963			0.544815	+	0.838556i	$0.316600\pi$
$648$	−9.69119	−	3.52730i	−0.380706	−	0.138566i
$649$	−5.77703	−	32.7631i	−0.226768	−	1.28607i
$650$		0			0
$651$	37.2918	−	31.2915i	1.46158	−	1.22641i
$652$	−1.02094	+	5.79006i	−0.0399833	+	0.226756i
$653$	−6.01960	+	10.4263i	−0.235565	+	0.408011i	−0.959437	−	0.281924i	$-0.909027\pi$
$653$	−6.01960	+	10.4263i	−0.235565	+	0.408011i	0.723872	+	0.689935i	$0.242361\pi$
$654$	17.3550	+	30.0598i	0.678636	+	1.17543i
$655$		0			0
$656$	0.134285	−	0.0488759i	0.00524296	−	0.00190828i
$657$	0.560307	+	0.970481i	0.0218597	+	0.0378621i
$658$	−9.01960	+	15.6224i	−0.351621	+	0.609025i
$659$	6.09223	−	34.5508i	0.237320	−	1.34591i	−0.600353	−	0.799735i	$-0.704973\pi$
$659$	6.09223	−	34.5508i	0.237320	−	1.34591i	0.837673	−	0.546172i	$-0.183916\pi$
$660$		0			0
$661$	−16.3746	−	13.7400i	−0.636900	−	0.534422i	0.266165	−	0.963928i	$-0.414243\pi$
$661$	−16.3746	−	13.7400i	−0.636900	−	0.534422i	−0.903064	+	0.429505i	$0.858688\pi$
$662$	0.875515	+	4.96529i	0.0340279	+	0.192982i
$663$	−20.9932	−	7.64090i	−0.815308	−	0.296748i
$664$	−0.753718			−0.0292499
$665$		0			0
$666$	−2.12836			−0.0824721
$667$	−30.0993	−	10.9552i	−1.16545	−	0.424188i
$668$	−3.85978	−	21.8899i	−0.149340	−	0.846947i
$669$	−3.94356	−	3.30904i	−0.152467	−	0.127935i
$670$		0			0
$671$	6.84255	−	38.8060i	0.264154	−	1.49809i
$672$	−2.87939	+	4.98724i	−0.111075	+	0.192387i
$673$	−1.25372	−	2.17150i	−0.0483273	−	0.0837053i	0.840850	−	0.541268i	$-0.182056\pi$
$673$	−1.25372	−	2.17150i	−0.0483273	−	0.0837053i	−0.889177	+	0.457563i	$0.848722\pi$
$674$	2.55216	−	0.928909i	0.0983054	−	0.0357802i
$675$		0			0
$676$	−10.0817	−	17.4620i	−0.387758	−	0.671617i
$677$	8.15064	−	14.1173i	0.313255	−	0.542573i	−0.665810	−	0.746121i	$-0.731914\pi$
$677$	8.15064	−	14.1173i	0.313255	−	0.542573i	0.979065	+	0.203548i	$0.0652473\pi$
$678$	−0.844770	+	4.79093i	−0.0324432	+	0.183995i
$679$	25.0692	−	21.0356i	0.962069	−	0.807272i
$680$		0			0
$681$	7.91147	+	44.8682i	0.303168	+	1.71935i
$682$	34.5330	+	12.5690i	1.32234	+	0.481292i
$683$	42.2181			1.61543			0.807716	−	0.589572i	$-0.200704\pi$
$683$	42.2181			1.61543			0.807716	+	0.589572i	$0.200704\pi$
$684$	−2.24376	−	0.587208i	−0.0857921	−	0.0224525i
$685$		0			0
$686$	−13.2763	−	4.83218i	−0.506892	−	0.184494i
$687$	5.11556	+	29.0118i	0.195171	+	1.10687i
$688$	−8.34002	−	6.99811i	−0.317960	−	0.266800i
$689$	22.3405	−	18.7459i	0.851105	−	0.714162i
$690$		0			0
$691$	−9.44862	+	16.3655i	−0.359442	+	0.622572i	−0.987868	−	0.155298i	$-0.950366\pi$
$691$	−9.44862	+	16.3655i	−0.359442	+	0.622572i	0.628425	+	0.777870i	$0.283700\pi$
$692$	−10.5963	−	18.3533i	−0.402810	−	0.697687i
$693$	6.66044	−	2.42420i	0.253009	−	0.0920879i
$694$	11.2353	−	4.08931i	0.426486	−	0.155228i
$695$		0			0
$696$	−3.87939	+	6.71929i	−0.147048	+	0.254694i
$697$	0.0512224	−	0.290497i	0.00194019	−	0.0110033i
$698$	13.0797	−	10.9751i	0.495072	−	0.415415i
$699$	−38.0540	−	31.9311i	−1.43933	−	1.20774i
$700$		0			0
$701$	−18.0300	−	6.56239i	−0.680985	−	0.247858i	−0.0217145	−	0.999764i	$-0.506912\pi$
$701$	−18.0300	−	6.56239i	−0.680985	−	0.247858i	−0.659270	+	0.751906i	$0.729135\pi$
$702$	−26.7101			−1.00811
$703$	17.3601	−	1.62089i	0.654748	−	0.0611331i
$704$	−4.34730			−0.163845
$705$		0			0
$706$	−0.672466	−	3.81374i	−0.0253086	−	0.143532i
$707$	−12.1521	−	10.1968i	−0.457026	−	0.383490i
$708$	−11.0175	+	9.24481i	−0.414065	+	0.347441i
$709$	−3.48246	+	19.7500i	−0.130786	+	0.741727i	0.846915	+	0.531728i	$0.178457\pi$
$709$	−3.48246	+	19.7500i	−0.130786	+	0.741727i	−0.977702	+	0.209999i	$0.932654\pi$
$710$		0			0
$711$	0.0983261	+	0.170306i	0.00368752	+	0.00638696i
$712$	1.67112	−	0.608239i	0.0626279	−	0.0227947i
$713$	61.6323	−	22.4323i	2.30815	−	0.840097i
$714$	5.94356	+	10.2946i	0.222432	+	0.385264i
$715$		0			0
$716$	0.655230	−	3.71599i	0.0244871	−	0.138873i
$717$	19.8084	−	16.6212i	0.739758	−	0.620731i
$718$	18.0797	+	15.1706i	0.674727	+	0.566163i
$719$	−4.88444	−	27.7010i	−0.182159	−	1.03307i	−0.929552	−	0.368692i	$-0.879806\pi$
$719$	−4.88444	−	27.7010i	−0.182159	−	1.03307i	0.747393	−	0.664382i	$-0.231305\pi$
$720$		0			0
$721$	−54.5526			−2.03165
$722$	18.7486	+	3.08083i	0.697749	+	0.114657i
$723$	−24.2713			−0.902658
$724$	−8.79561	−	3.20134i	−0.326886	−	0.118977i
$725$		0			0
$726$	11.3721	+	9.54233i	0.422059	+	0.354149i
$727$	−23.6236	+	19.8226i	−0.876151	+	0.735178i	−0.965384	−	0.260833i	$-0.916003\pi$
$727$	−23.6236	+	19.8226i	−0.876151	+	0.735178i	0.0892329	+	0.996011i	$0.471558\pi$
$728$	−3.06418	+	17.3778i	−0.113566	+	0.644065i
$729$	−10.3316	+	17.8948i	−0.382651	+	0.662770i
$730$		0			0
$731$	−21.1177	+	7.68621i	−0.781066	+	0.284285i
$732$	−16.0077	+	5.82634i	−0.591663	+	0.215348i
$733$	−15.5790	−	26.9837i	−0.575425	−	0.996665i	−0.995995	−	0.0894049i	$-0.971503\pi$
$733$	−15.5790	−	26.9837i	−0.575425	−	0.996665i	0.420571	−	0.907260i	$-0.361830\pi$
$734$	5.10607	−	8.84397i	0.188468	−	0.326437i
$735$		0			0
$736$	−5.94356	+	4.98724i	−0.219083	+	0.183832i
$737$	21.0152	+	17.6339i	0.774106	+	0.649552i
$738$	0.0132037	+	0.0748822i	0.000486037	+	0.00275645i
$739$	−39.6724	−	14.4396i	−1.45937	−	0.531168i	−0.514179	−	0.857683i	$-0.671903\pi$
$739$	−39.6724	−	14.4396i	−1.45937	−	0.531168i	−0.945192	+	0.326515i	$0.894126\pi$
$740$		0			0
$741$	−46.9718	+	4.38571i	−1.72555	+	0.161113i
$742$	−15.5175			−0.569667
$743$	35.3996	+	12.8844i	1.29869	+	0.472683i	0.896568	−	0.442905i	$-0.146052\pi$
$743$	35.3996	+	12.8844i	1.29869	+	0.472683i	0.402117	+	0.915588i	$0.368274\pi$
$744$	−2.75877	−	15.6458i	−0.101141	−	0.573602i
$745$		0			0
$746$	17.1361	−	14.3789i	0.627397	−	0.526449i
$747$	0.0696407	−	0.394952i	0.00254802	−	0.0144505i
$748$	−4.48680	+	7.77136i	−0.164054	+	0.284149i
$749$	−7.29086	−	12.6281i	−0.266402	−	0.461422i
$750$		0			0
$751$	−24.6186	+	8.96042i	−0.898344	+	0.326970i	−0.749589	−	0.661904i	$-0.769749\pi$
$751$	−24.6186	+	8.96042i	−0.898344	+	0.326970i	−0.148755	+	0.988874i	$0.547527\pi$
$752$	2.94356	+	5.09840i	0.107341	+	0.185920i
$753$	17.0792	−	29.5820i	0.622400	−	1.07803i
$754$	−4.12836	+	23.4131i	−0.150346	+	0.852654i
$755$		0			0
$756$	10.8871	+	9.13538i	0.395961	+	0.332251i
$757$	−0.894867	−	5.07504i	−0.0325245	−	0.184456i	0.964217	−	0.265113i	$-0.0854092\pi$
$757$	−0.894867	−	5.07504i	−0.0325245	−	0.184456i	−0.996742	+	0.0806572i	$0.974298\pi$
$758$	−23.9418	−	8.71411i	−0.869606	−	0.316511i
$759$	63.3911			2.30095
$760$		0			0
$761$	3.84018			0.139207			0.0696033	−	0.997575i	$-0.477827\pi$
$761$	3.84018			0.139207			0.0696033	+	0.997575i	$0.477827\pi$
$762$	−19.1138	−	6.95686i	−0.692420	−	0.252020i
$763$	−9.82707	−	55.7321i	−0.355764	−	2.01764i
$764$	14.3327	+	12.0266i	0.518541	+	0.435107i
$765$		0			0
$766$	−2.54933	+	14.4579i	−0.0921109	+	0.522387i
$767$	−22.0351	+	38.1659i	−0.795641	+	1.37809i
$768$	0.939693	+	1.62760i	0.0339082	+	0.0587308i
$769$	−20.8268	+	7.58034i	−0.751034	+	0.273354i	−0.689041	−	0.724722i	$-0.741968\pi$
$769$	−20.8268	+	7.58034i	−0.751034	+	0.273354i	−0.0619934	+	0.998077i	$0.519746\pi$
$770$		0			0
$771$	6.55216	+	11.3487i	0.235970	+	0.408712i
$772$	5.96791	−	10.3367i	0.214790	−	0.372027i
$773$	−7.41416	+	42.0478i	−0.266669	+	1.51235i	0.497572	+	0.867423i	$0.334225\pi$
$773$	−7.41416	+	42.0478i	−0.266669	+	1.51235i	−0.764240	+	0.644931i	$0.776886\pi$
$774$	4.43763	−	3.72362i	0.159507	−	0.133843i
$775$		0			0
$776$	−1.85457	−	10.5178i	−0.0665752	−	0.377567i
$777$	21.6459	+	7.87846i	0.776542	+	0.282638i
$778$	28.7392			1.03035
$779$	−0.164725	−	0.600726i	−0.00590190	−	0.0215233i
$780$		0			0
$781$	23.1830	+	8.43794i	0.829554	+	0.301933i
$782$	2.78106	+	15.7722i	0.0994505	+	0.564012i
$783$	14.6682	+	12.3081i	0.524198	+	0.439854i
$784$	1.83022	−	1.53574i	0.0653651	−	0.0548478i
$785$		0			0
$786$	−6.95084	+	12.0392i	−0.247928	+	0.429424i
$787$	11.6193	+	20.1252i	0.414182	+	0.717385i	0.995342	−	0.0964046i	$-0.0307343\pi$
$787$	11.6193	+	20.1252i	0.414182	+	0.717385i	−0.581160	+	0.813789i	$0.697401\pi$
$788$	2.80066	−	1.01936i	0.0997694	−	0.0363131i
$789$	−18.2618	+	6.64674i	−0.650136	+	0.236630i
$790$		0			0
$791$	3.96585	−	6.86906i	0.141009	−	0.244236i
$792$	0.401674	−	2.27801i	0.0142729	−	0.0809454i
$793$	−39.9864	+	33.5526i	−1.41996	+	1.19149i
$794$	15.9513	+	13.3847i	0.566091	+	0.475006i
$795$		0			0
$796$	22.7246	+	8.27109i	0.805453	+	0.293161i
$797$	26.8331			0.950476			0.475238	−	0.879857i	$-0.342362\pi$
$797$	26.8331			0.950476			0.475238	+	0.879857i	$0.342362\pi$
$798$	20.6459	+	14.2777i	0.730857	+	0.505425i
$799$	12.1521			0.429909
$800$		0			0
$801$	0.164315	+	0.931876i	0.00580578	+	0.0329262i
$802$	−5.68938	−	4.77396i	−0.200899	−	0.168574i
$803$	7.01367	−	5.88517i	0.247507	−	0.207683i
$804$	2.05943	−	11.6796i	0.0726305	−	0.411908i
$805$		0			0
$806$	−24.3405	−	42.1590i	−0.857357	−	1.48499i
$807$	−18.4611	+	6.71929i	−0.649862	+	0.236530i
$808$	−4.86484	+	1.77066i	−0.171144	+	0.0622915i
$809$	−1.99391	−	3.45355i	−0.0701021	−	0.121420i	0.828844	−	0.559480i	$-0.188999\pi$
$809$	−1.99391	−	3.45355i	−0.0701021	−	0.121420i	−0.898946	+	0.438060i	$0.855666\pi$
$810$		0			0
$811$	−1.41828	+	8.04347i	−0.0498026	+	0.282445i	−0.999531	−	0.0306312i	$-0.990248\pi$
$811$	−1.41828	+	8.04347i	−0.0498026	+	0.282445i	0.949728	+	0.313076i	$0.101359\pi$
$812$	9.69047	−	8.13127i	0.340069	−	0.285352i
$813$	27.6313	+	23.1855i	0.969074	+	0.813149i
$814$	3.01960	+	17.1250i	0.105837	+	0.600231i
$815$		0			0
$816$	3.87939			0.135806
$817$	−33.3601	+	33.7515i	−1.16712	+	1.18082i
$818$	−21.0419			−0.735712
$819$	−8.82295	−	3.21129i	−0.308299	−	0.112212i
$820$		0			0
$821$	40.4466	+	33.9387i	1.41159	+	1.18447i	0.955666	+	0.294452i	$0.0951371\pi$
$821$	40.4466	+	33.9387i	1.41159	+	1.18447i	0.455928	+	0.890017i	$0.349307\pi$
$822$	11.6912	−	9.81007i	0.407777	−	0.342166i
$823$	−0.137527	+	0.779953i	−0.00479388	+	0.0271875i	−0.987111	−	0.160038i	$-0.948838\pi$
$823$	−0.137527	+	0.779953i	−0.00479388	+	0.0271875i	0.982317	+	0.187225i	$0.0599495\pi$
$824$	−8.90167	+	15.4182i	−0.310105	+	0.537117i
$825$		0			0
$826$	22.0351	−	8.02011i	0.766699	−	0.279055i
$827$	−15.4547	+	5.62505i	−0.537413	+	0.195602i	−0.596445	−	0.802654i	$-0.703421\pi$
$827$	−15.4547	+	5.62505i	−0.537413	+	0.195602i	0.0590324	+	0.998256i	$0.481198\pi$
$828$	−2.06418	−	3.57526i	−0.0717351	−	0.124249i
$829$	−10.9855	+	19.0274i	−0.381541	+	0.660848i	−0.991283	−	0.131752i	$-0.957940\pi$
$829$	−10.9855	+	19.0274i	−0.381541	+	0.660848i	0.609742	+	0.792600i	$0.291273\pi$
$830$		0			0
$831$	−42.6810	+	35.8136i	−1.48059	+	1.24236i
$832$	4.41147	+	3.70167i	0.152940	+	0.128332i
$833$	−0.856381	−	4.85678i	−0.0296719	−	0.168277i
$834$	26.1523	+	9.51866i	0.905580	+	0.329604i
$835$		0			0
$836$	−1.54142	+	18.8866i	−0.0533112	+	0.653208i
$837$	−39.2080			−1.35523
$838$	−17.7754	−	6.46973i	−0.614042	−	0.223493i
$839$	−5.38919	−	30.5636i	−0.186055	−	1.05517i	−0.924592	−	0.380959i	$-0.875594\pi$
$839$	−5.38919	−	30.5636i	−0.186055	−	1.05517i	0.738537	−	0.674213i	$-0.235517\pi$
$840$		0			0
$841$	−9.15935	+	7.68561i	−0.315840	+	0.265021i
$842$	−1.26352	+	7.16577i	−0.0435437	+	0.246949i
$843$	−16.5052	+	28.5879i	−0.568470	+	0.984619i
$844$	−6.54189	−	11.3309i	−0.225181	−	0.390025i
$845$		0			0
$846$	−2.94356	+	1.07137i	−0.101202	+	0.0368344i
$847$	−12.1019	−	20.9612i	−0.415828	−	0.720235i
$848$	−2.53209	+	4.38571i	−0.0869523	+	0.150606i
$849$	−1.82073	+	10.3259i	−0.0624872	+	0.354382i
$850$		0			0
$851$	23.7743	+	19.9490i	0.814971	+	0.683842i
$852$	−1.85204	−	10.5035i	−0.0634500	−	0.359843i
$853$	40.9350	+	14.8991i	1.40159	+	0.510136i	0.928649	−	0.370959i	$-0.120971\pi$
$853$	40.9350	+	14.8991i	1.40159	+	0.510136i	0.472939	+	0.881095i	$0.343193\pi$
$854$	27.7743			0.950415
$855$		0			0
$856$	−4.75877			−0.162651
$857$	−29.5727	−	10.7636i	−1.01018	−	0.367677i	−0.216680	−	0.976243i	$-0.569523\pi$
$857$	−29.5727	−	10.7636i	−1.01018	−	0.367677i	−0.793503	+	0.608566i	$0.791745\pi$
$858$	−8.17024	−	46.3358i	−0.278928	−	1.58188i
$859$	−13.2069	−	11.0819i	−0.450614	−	0.378110i	0.389049	−	0.921217i	$-0.372804\pi$
$859$	−13.2069	−	11.0819i	−0.450614	−	0.378110i	−0.839664	+	0.543107i	$0.817248\pi$
$860$		0			0
$861$	0.142903	−	0.810446i	0.00487014	−	0.0276199i
$862$	7.12836	−	12.3467i	0.242793	−	0.420529i
$863$	2.38919	+	4.13819i	0.0813288	+	0.140866i	0.903821	−	0.427911i	$-0.140750\pi$
$863$	2.38919	+	4.13819i	0.0813288	+	0.140866i	−0.822492	+	0.568776i	$0.807417\pi$
$864$	4.35844	−	1.58634i	0.148277	−	0.0539685i
$865$		0			0
$866$	3.77837	+	6.54433i	0.128394	+	0.222385i
$867$	−11.9709	+	20.7342i	−0.406553	+	0.704171i
$868$	−4.49794	+	25.5091i	−0.152670	+	0.865835i
$869$	1.23080	−	1.03276i	0.0417520	−	0.0350341i
$870$		0			0
$871$	−6.31046	−	35.7884i	−0.213822	−	1.21264i
$872$	−17.3550	−	6.31672i	−0.587716	−	0.213911i
$873$	5.68273			0.192331
$874$	19.5594	+	27.5899i	0.661608	+	0.933241i
$875$		0			0
$876$	−3.71941	−	1.35375i	−0.125667	−	0.0457391i
$877$	−9.59390	−	54.4097i	−0.323963	−	1.83729i	−0.516864	−	0.856068i	$-0.672901\pi$
$877$	−9.59390	−	54.4097i	−0.323963	−	1.83729i	0.192901	−	0.981218i	$-0.438210\pi$
$878$	−4.66456	−	3.91403i	−0.157421	−	0.132092i
$879$	29.5749	−	24.8163i	0.997537	−	0.837033i
$880$		0			0
$881$	23.3778	−	40.4915i	0.787618	−	1.36419i	−0.139805	−	0.990179i	$-0.544648\pi$
$881$	23.3778	−	40.4915i	0.787618	−	1.36419i	0.927423	−	0.374015i	$-0.122019\pi$
$882$	0.635630	+	1.10094i	0.0214028	+	0.0370707i
$883$	2.62449	−	0.955234i	0.0883210	−	0.0321462i	−0.297482	−	0.954727i	$-0.596147\pi$
$883$	2.62449	−	0.955234i	0.0883210	−	0.0321462i	0.385803	+	0.922581i	$0.373925\pi$
$884$	11.1702	−	4.06564i	0.375696	−	0.136742i
$885$		0			0
$886$	−13.6343	+	23.6153i	−0.458053	+	0.793371i
$887$	−5.17705	+	29.3605i	−0.173828	+	0.985830i	0.765659	+	0.643247i	$0.222413\pi$
$887$	−5.17705	+	29.3605i	−0.173828	+	0.985830i	−0.939487	+	0.342583i	$0.888698\pi$
$888$	5.75877	−	4.83218i	0.193252	−	0.162157i
$889$	25.4047	+	21.3170i	0.852045	+	0.714951i
$890$		0			0
$891$	−42.1305	−	15.3342i	−1.41142	−	0.513716i
$892$	2.73917			0.0917142
$893$	23.1935	−	10.9804i	0.776140	−	0.367446i
$894$	−8.90673			−0.297885
$895$		0			0
$896$	−0.532089	−	3.01763i	−0.0177758	−	0.100812i
$897$	−64.3269	−	53.9767i	−2.14781	−	1.80223i
$898$	−30.4065	+	25.5141i	−1.01468	+	0.851415i
$899$	−6.06006	+	34.3683i	−0.202114	+	1.14625i
$900$		0			0
$901$	5.22668	+	9.05288i	0.174126	+	0.301595i
$902$	0.583778	−	0.212478i	0.0194377	−	0.00707474i
$903$	−58.9154	+	21.4435i	−1.96058	+	0.713593i
$904$	−1.29426	−	2.24173i	−0.0430465	−	0.0745588i
$905$		0			0
$906$	0.147956	−	0.839100i	0.00491551	−	0.0278772i
$907$	−24.7167	+	20.7398i	−0.820705	+	0.688653i	−0.953137	−	0.302539i	$-0.902166\pi$
$907$	−24.7167	+	20.7398i	−0.820705	+	0.688653i	0.132432	+	0.991192i	$0.457721\pi$
$908$	−18.5706	−	15.5826i	−0.616286	−	0.517125i
$909$	−0.478340	−	2.71280i	−0.0158655	−	0.0899780i
$910$		0			0
$911$	−55.2336			−1.82997			−0.914985	−	0.403487i	$-0.867798\pi$
$911$	−55.2336			−1.82997			−0.914985	+	0.403487i	$0.867798\pi$
$912$	7.40420	−	3.50535i	0.245178	−	0.116074i
$913$	−3.27664			−0.108441
$914$	6.51842	+	2.37251i	0.215610	+	0.0784757i
$915$		0			0
$916$	−12.0077	−	10.0757i	−0.396747	−	0.332910i
$917$	17.3628	−	14.5691i	0.573369	−	0.481114i
$918$	1.66250	−	9.42853i	0.0548708	−	0.311188i
$919$	2.04963	−	3.55006i	0.0676111	−	0.117106i	−0.830238	−	0.557409i	$-0.811796\pi$
$919$	2.04963	−	3.55006i	0.0676111	−	0.117106i	0.897849	+	0.440303i	$0.145129\pi$
$920$		0			0
$921$	2.49273	−	0.907278i	0.0821381	−	0.0298958i
$922$	25.2472	−	9.18923i	0.831473	−	0.302631i
$923$	−16.3405	−	28.3026i	−0.537854	−	0.931590i
$924$	−12.5175	+	21.6810i	−0.411797	+	0.713253i
$925$		0			0
$926$	11.5476	−	9.68956i	0.379477	−	0.318419i
$927$	−7.25671	−	6.08910i	−0.238342	−	0.199992i
$928$	−0.716881	−	4.06564i	−0.0235328	−	0.133461i
$929$	5.84389	+	2.12700i	0.191732	+	0.0697847i	0.436102	−	0.899897i	$-0.356359\pi$
$929$	5.84389	+	2.12700i	0.191732	+	0.0697847i	−0.244370	+	0.969682i	$0.578581\pi$
$930$		0			0
$931$	−6.02300	−	8.49584i	−0.197396	−	0.278440i
$932$	26.4320			0.865809
$933$	−18.4611	−	6.71929i	−0.604389	−	0.219980i
$934$	−3.71167	−	21.0499i	−0.121449	−	0.688774i
$935$		0			0
$936$	−2.34730	+	1.96962i	−0.0767238	+	0.0643789i
$937$	−7.25268	+	41.1320i	−0.236935	+	1.34372i	0.601566	+	0.798823i	$0.294544\pi$
$937$	−7.25268	+	41.1320i	−0.236935	+	1.34372i	−0.838501	+	0.544900i	$0.816567\pi$
$938$	−9.66819	+	16.7458i	−0.315677	+	0.546769i
$939$	31.4342	+	54.4457i	1.02582	+	1.77677i
$940$		0			0
$941$	−0.610815	+	0.222318i	−0.0199120	+	0.00724737i	−0.351957	−	0.936016i	$-0.614484\pi$
$941$	−0.610815	+	0.222318i	−0.0199120	+	0.00724737i	0.332045	+	0.943264i	$0.392261\pi$
$942$	12.2763	+	21.2632i	0.399984	+	0.692792i
$943$	0.554378	−	0.960210i	0.0180530	−	0.0312687i
$944$	1.32888	−	7.53644i	0.0432513	−	0.245290i
$945$		0			0
$946$	−36.2565	−	30.4229i	−1.17880	−	0.989132i
$947$	−3.87702	−	21.9877i	−0.125986	−	0.714504i	−0.980717	−	0.195432i	$-0.937389\pi$
$947$	−3.87702	−	21.9877i	−0.125986	−	0.714504i	0.854731	−	0.519071i	$-0.173722\pi$
$948$	−0.652704	−	0.237565i	−0.0211988	−	0.00771574i
$949$	−12.1284			−0.393703
$950$		0			0
$951$	−7.03508			−0.228128
$952$	−5.94356	−	2.16328i	−0.192632	−	0.0701123i
$953$	0.0644262	+	0.365379i	0.00208697	+	0.0118358i	0.985833	−	0.167727i	$-0.0536428\pi$
$953$	0.0644262	+	0.365379i	0.00208697	+	0.0118358i	−0.983746	+	0.179563i	$0.942532\pi$
$954$	−2.06418	−	1.73205i	−0.0668302	−	0.0560772i
$955$		0			0
$956$	−2.38919	+	13.5497i	−0.0772718	+	0.438230i
$957$	−16.8648	+	29.2108i	−0.545163	+	0.944250i
$958$	−3.26857	−	5.66133i	−0.105603	−	0.182909i
$959$	−23.3824	+	8.51049i	−0.755056	+	0.274818i
$960$		0			0
$961$	−20.2297	−	35.0388i	−0.652570	−	1.13028i
$962$	11.5175	−	19.9490i	0.371340	−	0.643180i
$963$	0.439693	−	2.49362i	0.0141689	−	0.0803558i
$964$	9.89306	−	8.30126i	0.318634	−	0.267366i
$965$		0			0
$966$	7.75877	+	44.0022i	0.249634	+	1.41575i
$967$	1.36184	+	0.495671i	0.0437940	+	0.0159397i	0.363824	−	0.931468i	$-0.381471\pi$
$967$	1.36184	+	0.495671i	0.0437940	+	0.0159397i	−0.320030	+	0.947407i	$0.603693\pi$
$968$	−7.89899			−0.253883
$969$	1.37551	−	16.8538i	0.0441879	−	0.541422i
$970$		0			0
$971$	4.86262	+	1.76985i	0.156049	+	0.0567971i	0.418863	−	0.908049i	$-0.362429\pi$
$971$	4.86262	+	1.76985i	0.156049	+	0.0567971i	−0.262815	+	0.964846i	$0.584651\pi$
$972$	0.949493	+	5.38484i	0.0304550	+	0.172719i
$973$	−34.7597	−	29.1669i	−1.11434	−	0.935046i
$974$	−13.5175	+	11.3426i	−0.433130	+	0.363439i
$975$		0			0
$976$	4.53209	−	7.84981i	0.145069	−	0.251266i
$977$	15.9106	+	27.5580i	0.509025	+	0.881657i	0.999945	+	0.0104528i	$0.00332730\pi$
$977$	15.9106	+	27.5580i	0.509025	+	0.881657i	−0.490920	+	0.871204i	$0.663339\pi$
$978$	10.3833	−	3.77920i	0.332020	−	0.120845i
$979$	7.26486	−	2.64419i	0.232186	−	0.0845088i
$980$		0			0
$981$	4.91353	−	8.51049i	0.156877	−	0.271719i
$982$	−2.53549	+	14.3795i	−0.0809108	+	0.458868i
$983$	−17.5253	+	14.7055i	−0.558970	+	0.469031i	−0.877965	−	0.478725i	$-0.841099\pi$
$983$	−17.5253	+	14.7055i	−0.558970	+	0.469031i	0.318995	+	0.947756i	$0.396655\pi$
$984$	−0.205737	−	0.172634i	−0.00655866	−	0.00550337i
$985$		0			0
$986$	−8.00774	−	2.91458i	−0.255018	−	0.0928191i
$987$	33.9026			1.07913
$988$	17.6459	−	17.8529i	0.561391	−	0.567978i
$989$	−84.4707			−2.68601
$990$		0			0
$991$	−3.24030	−	18.3766i	−0.102931	−	0.583753i	−0.992026	−	0.126030i	$-0.959776\pi$
$991$	−3.24030	−	18.3766i	−0.102931	−	0.583753i	0.889095	−	0.457723i	$-0.151335\pi$
$992$	6.47565	+	5.43372i	0.205602	+	0.172521i
$993$	7.25877	−	6.09083i	0.230350	−	0.193287i
$994$	−3.01960	+	17.1250i	−0.0957759	+	0.543172i
$995$		0			0
$996$	0.708263	+	1.22675i	0.0224422	+	0.0388710i
$997$	−13.1575	+	4.78892i	−0.416701	+	0.151667i	−0.541858	−	0.840470i	$-0.682279\pi$
$997$	−13.1575	+	4.78892i	−0.416701	+	0.151667i	0.125157	+	0.992137i	$0.460057\pi$
$998$	−12.2973	+	4.47584i	−0.389263	+	0.141680i
$999$	−9.27631	−	16.0670i	−0.293490	−	0.508339i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.c.251.1		6
5.2	odd	4		950.2.u.c.99.1		12
5.3	odd	4		950.2.u.c.99.2		12
5.4	even	2		190.2.k.a.61.1	✓	6
19.5	even	9	inner	950.2.l.c.651.1		6
95.9	even	18		3610.2.a.x.1.3		3
95.24	even	18		190.2.k.a.81.1	yes	6
95.29	odd	18		3610.2.a.w.1.1		3
95.43	odd	36		950.2.u.c.499.1		12
95.62	odd	36		950.2.u.c.499.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.a.61.1	✓	6	5.4	even	2
190.2.k.a.81.1	yes	6	95.24	even	18
950.2.l.c.251.1		6	1.1	even	1	trivial
950.2.l.c.651.1		6	19.5	even	9	inner
950.2.u.c.99.1		12	5.2	odd	4
950.2.u.c.99.2		12	5.3	odd	4
950.2.u.c.499.1		12	95.43	odd	36
950.2.u.c.499.2		12	95.62	odd	36
3610.2.a.w.1.1		3	95.29	odd	18
3610.2.a.x.1.3		3	95.9	even	18

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.326352 - 1.85083i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.326352 - 1.85083i) q^{6} +(-1.53209 + 2.65366i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.500000 + 0.181985i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.326352 - 1.85083i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.326352 - 1.85083i) q^{6} +(-1.53209 + 2.65366i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.500000 + 0.181985i) q^{9} +(2.17365 + 3.76487i) q^{11} +(0.939693 - 1.62760i) q^{12} +(1.00000 - 5.67128i) q^{13} +(-2.34730 + 1.96962i) q^{14} +(0.173648 + 0.984808i) q^{16} +(1.93969 + 0.705990i) q^{17} -0.532089 q^{18} +(4.34002 - 0.405223i) q^{19} +(5.41147 + 1.96962i) q^{21} +(0.754900 + 4.28125i) q^{22} +(5.94356 + 4.98724i) q^{23} +(1.43969 - 1.20805i) q^{24} +(2.87939 - 4.98724i) q^{26} +(-2.31908 - 4.01676i) q^{27} +(-2.87939 + 1.04801i) q^{28} +(-3.87939 + 1.41198i) q^{29} +(4.22668 - 7.32083i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(6.25877 - 5.25173i) q^{33} +(1.58125 + 1.32683i) q^{34} +(-0.500000 - 0.181985i) q^{36} +4.00000 q^{37} +(4.21688 + 1.10359i) q^{38} -10.8229 q^{39} +(-0.0248149 - 0.140732i) q^{41} +(4.41147 + 3.70167i) q^{42} +(-8.34002 + 6.99811i) q^{43} +(-0.754900 + 4.28125i) q^{44} +(3.87939 + 6.71929i) q^{46} +(5.53209 - 2.01352i) q^{47} +(1.76604 - 0.642788i) q^{48} +(-1.19459 - 2.06910i) q^{49} +(0.673648 - 3.82045i) q^{51} +(4.41147 - 3.70167i) q^{52} +(3.87939 + 3.25519i) q^{53} +(-0.805407 - 4.56769i) q^{54} -3.06418 q^{56} +(-2.16637 - 7.90041i) q^{57} -4.12836 q^{58} +(-7.19119 - 2.61738i) q^{59} +(-6.94356 - 5.82634i) q^{61} +(6.47565 - 5.43372i) q^{62} +(0.283119 - 1.60565i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(7.67752 - 2.79439i) q^{66} +(5.92989 - 2.15830i) q^{67} +(1.03209 + 1.78763i) q^{68} +(7.29086 - 12.6281i) q^{69} +(4.34730 - 3.64781i) q^{71} +(-0.407604 - 0.342020i) q^{72} +(-0.365715 - 2.07407i) q^{73} +(3.75877 + 1.36808i) q^{74} +(3.58512 + 2.47929i) q^{76} -13.3209 q^{77} +(-10.1702 - 3.70167i) q^{78} +(-0.0641778 - 0.363970i) q^{79} +(-7.90033 + 6.62916i) q^{81} +(0.0248149 - 0.140732i) q^{82} +(-0.376859 + 0.652739i) q^{83} +(2.87939 + 4.98724i) q^{84} +(-10.2306 + 3.72362i) q^{86} +(3.87939 + 6.71929i) q^{87} +(-2.17365 + 3.76487i) q^{88} +(0.308811 - 1.75135i) q^{89} +(13.5175 + 11.3426i) q^{91} +(1.34730 + 7.64090i) q^{92} +(-14.9290 - 5.43372i) q^{93} +5.88713 q^{94} +1.87939 q^{96} +(-10.0360 - 3.65279i) q^{97} +(-0.414878 - 2.35289i) q^{98} +(-1.77197 - 1.48686i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} + 3 q^{6} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 + 3 * q^6 + 3 * q^8 - 3 * q^9	\( 6 q - 3 q^{3} + 3 q^{6} + 3 q^{8} - 3 q^{9} + 12 q^{11} + 6 q^{13} - 12 q^{14} + 6 q^{17} + 6 q^{18} + 6 q^{19} + 12 q^{21} + 6 q^{22} + 6 q^{23} + 3 q^{24} + 6 q^{26} + 3 q^{27} - 6 q^{28} - 12 q^{29} + 12 q^{31} + 15 q^{33} + 12 q^{34} - 3 q^{36} + 24 q^{37} + 9 q^{38} - 24 q^{39} + 27 q^{41} + 6 q^{42} - 30 q^{43} - 6 q^{44} + 12 q^{46} + 24 q^{47} + 6 q^{48} - 3 q^{49} + 3 q^{51} + 6 q^{52} + 12 q^{53} - 9 q^{54} + 6 q^{57} + 12 q^{58} + 3 q^{59} - 12 q^{61} + 18 q^{63} - 3 q^{64} + 21 q^{66} + 27 q^{67} - 3 q^{68} + 12 q^{69} + 24 q^{71} - 6 q^{72} - 12 q^{73} + 12 q^{77} - 18 q^{78} + 18 q^{79} - 33 q^{81} - 27 q^{82} - 6 q^{83} + 6 q^{84} - 24 q^{86} + 12 q^{87} - 12 q^{88} + 48 q^{89} + 36 q^{91} + 6 q^{92} - 24 q^{93} - 24 q^{94} - 27 q^{97} - 24 q^{98} - 33 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 + 3 * q^6 + 3 * q^8 - 3 * q^9 + 12 * q^11 + 6 * q^13 - 12 * q^14 + 6 * q^17 + 6 * q^18 + 6 * q^19 + 12 * q^21 + 6 * q^22 + 6 * q^23 + 3 * q^24 + 6 * q^26 + 3 * q^27 - 6 * q^28 - 12 * q^29 + 12 * q^31 + 15 * q^33 + 12 * q^34 - 3 * q^36 + 24 * q^37 + 9 * q^38 - 24 * q^39 + 27 * q^41 + 6 * q^42 - 30 * q^43 - 6 * q^44 + 12 * q^46 + 24 * q^47 + 6 * q^48 - 3 * q^49 + 3 * q^51 + 6 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^57 + 12 * q^58 + 3 * q^59 - 12 * q^61 + 18 * q^63 - 3 * q^64 + 21 * q^66 + 27 * q^67 - 3 * q^68 + 12 * q^69 + 24 * q^71 - 6 * q^72 - 12 * q^73 + 12 * q^77 - 18 * q^78 + 18 * q^79 - 33 * q^81 - 27 * q^82 - 6 * q^83 + 6 * q^84 - 24 * q^86 + 12 * q^87 - 12 * q^88 + 48 * q^89 + 36 * q^91 + 6 * q^92 - 24 * q^93 - 24 * q^94 - 27 * q^97 - 24 * q^98 - 33 * q^99

Introduction

L-functions

Modular forms

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