LMFDB - Embedded newform 91.2.e.c.53.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(53,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("91.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.e (of order $3$, degree $2$, 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:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 $ x^10 - x^9 + 8x^8 + 7x^7 + 41x^6 + 18x^5 + 58x^4 + 28x^3 + 64x^2 + 16x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			53.2
Root			$-0.606661 - 1.05077i$ of defining polynomial
Character	$\chi$	$=$	91.53
Dual form			91.2.e.c.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10666 - 1.91679i) q^{2} +(-1.23721 + 2.14292i) q^{3} +(-1.44940 + 2.51043i) q^{4} +(1.06140 + 1.83839i) q^{5} +5.47671 q^{6} +(2.63169 + 0.272389i) q^{7} +1.98932 q^{8} +(-1.56140 - 2.70442i) q^{9} +O(q^{10})$	\(q+(-1.10666 - 1.91679i) q^{2} +(-1.23721 + 2.14292i) q^{3} +(-1.44940 + 2.51043i) q^{4} +(1.06140 + 1.83839i) q^{5} +5.47671 q^{6} +(2.63169 + 0.272389i) q^{7} +1.98932 q^{8} +(-1.56140 - 2.70442i) q^{9} +(2.34921 - 4.06896i) q^{10} +(-2.39448 + 4.14736i) q^{11} +(-3.58643 - 6.21188i) q^{12} +1.00000 q^{13} +(-2.39028 - 5.34585i) q^{14} -5.25271 q^{15} +(0.697291 + 1.20774i) q^{16} +(1.88914 - 3.27208i) q^{17} +(-3.45588 + 5.98575i) q^{18} +(1.78362 + 3.08931i) q^{19} -6.15355 q^{20} +(-3.83967 + 5.30250i) q^{21} +10.5995 q^{22} +(-2.23721 - 3.87497i) q^{23} +(-2.46122 + 4.26295i) q^{24} +(0.246870 - 0.427591i) q^{25} +(-1.10666 - 1.91679i) q^{26} +0.303848 q^{27} +(-4.49818 + 6.21188i) q^{28} -5.90107 q^{29} +(5.81296 + 10.0683i) q^{30} +(1.88558 - 3.26592i) q^{31} +(3.53265 - 6.11873i) q^{32} +(-5.92496 - 10.2623i) q^{33} -8.36254 q^{34} +(2.29251 + 5.12720i) q^{35} +9.05234 q^{36} +(-2.81285 - 4.87200i) q^{37} +(3.94772 - 6.83765i) q^{38} +(-1.23721 + 2.14292i) q^{39} +(2.11146 + 3.65716i) q^{40} +10.3948 q^{41} +(14.4130 + 1.49180i) q^{42} +3.40733 q^{43} +(-6.94110 - 12.0223i) q^{44} +(3.31453 - 5.74093i) q^{45} +(-4.95168 + 8.57655i) q^{46} +(3.55438 + 6.15636i) q^{47} -3.45079 q^{48} +(6.85161 + 1.43369i) q^{49} -1.09280 q^{50} +(4.67454 + 8.09654i) q^{51} +(-1.44940 + 2.51043i) q^{52} +(6.19003 - 10.7214i) q^{53} +(-0.336257 - 0.582415i) q^{54} -10.1660 q^{55} +(5.23528 + 0.541869i) q^{56} -8.82686 q^{57} +(6.53049 + 11.3111i) q^{58} +(-2.39448 + 4.14736i) q^{59} +(7.61326 - 13.1865i) q^{60} +(-1.60348 - 2.77732i) q^{61} -8.34680 q^{62} +(-3.37246 - 7.54251i) q^{63} -12.8486 q^{64} +(1.06140 + 1.83839i) q^{65} +(-13.1139 + 22.7139i) q^{66} +(1.44978 - 2.51109i) q^{67} +(5.47622 + 9.48510i) q^{68} +11.0717 q^{69} +(7.29075 - 10.0683i) q^{70} -2.53876 q^{71} +(-3.10612 - 5.37996i) q^{72} +(-3.85035 + 6.66901i) q^{73} +(-6.22574 + 10.7833i) q^{74} +(0.610862 + 1.05804i) q^{75} -10.3407 q^{76} +(-7.43122 + 10.2623i) q^{77} +5.47671 q^{78} +(2.58925 + 4.48471i) q^{79} +(-1.48021 + 2.56379i) q^{80} +(4.30827 - 7.46214i) q^{81} +(-11.5035 - 19.9247i) q^{82} +3.46731 q^{83} +(-7.74633 - 17.3247i) q^{84} +8.02051 q^{85} +(-3.77076 - 6.53115i) q^{86} +(7.30089 - 12.6455i) q^{87} +(-4.76338 + 8.25042i) q^{88} +(-1.83216 - 3.17339i) q^{89} -14.6722 q^{90} +(2.63169 + 0.272389i) q^{91} +12.9704 q^{92} +(4.66574 + 8.08129i) q^{93} +(7.86698 - 13.6260i) q^{94} +(-3.78625 + 6.55798i) q^{95} +(8.74129 + 15.1404i) q^{96} -5.40733 q^{97} +(-4.83432 - 14.7197i) q^{98} +14.9549 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} - 8 q^{4} - 2 q^{5} - 10 q^{6} + q^{7} + 18 q^{8} - 3 q^{9}+O(q^{10}) $ 10 * q - 4 * q^2 - 8 * q^4 - 2 * q^5 - 10 * q^6 + q^7 + 18 * q^8 - 3 * q^9	\( 10 q - 4 q^{2} - 8 q^{4} - 2 q^{5} - 10 q^{6} + q^{7} + 18 q^{8} - 3 q^{9} + 5 q^{10} - 11 q^{11} - 5 q^{12} + 10 q^{13} + 10 q^{14} - 10 q^{16} + 5 q^{17} - 9 q^{18} - 9 q^{19} + 2 q^{20} + 2 q^{21} + 16 q^{22} - 10 q^{23} - 9 q^{25} - 4 q^{26} + 37 q^{28} - 6 q^{29} + 13 q^{30} + 6 q^{31} - 22 q^{32} - 8 q^{33} - 44 q^{34} - 4 q^{35} + 14 q^{36} - 4 q^{37} + 10 q^{38} - 28 q^{40} + 28 q^{41} + 52 q^{42} + 4 q^{43} + 32 q^{45} - 3 q^{46} - q^{47} - 46 q^{48} - 11 q^{49} + 18 q^{50} + 8 q^{51} - 8 q^{52} - 17 q^{53} - 23 q^{54} - 21 q^{56} - 32 q^{57} + 27 q^{58} - 11 q^{59} + 29 q^{60} + 11 q^{61} - 46 q^{62} + 5 q^{63} + 18 q^{64} - 2 q^{65} - 21 q^{66} - 13 q^{67} + 32 q^{68} + 36 q^{69} + 49 q^{70} + 30 q^{71} + 19 q^{72} + 33 q^{74} + 20 q^{75} + 16 q^{76} - 46 q^{77} - 10 q^{78} - 2 q^{79} - 55 q^{80} + 19 q^{81} - 34 q^{82} + 12 q^{83} - 23 q^{84} - 44 q^{85} - 28 q^{86} + 8 q^{87} + 3 q^{88} + 4 q^{89} - 68 q^{90} + q^{91} + 42 q^{92} - 18 q^{93} - 20 q^{94} + 12 q^{95} + 37 q^{96} - 24 q^{97} - 7 q^{98} + 22 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 - 8 * q^4 - 2 * q^5 - 10 * q^6 + q^7 + 18 * q^8 - 3 * q^9 + 5 * q^10 - 11 * q^11 - 5 * q^12 + 10 * q^13 + 10 * q^14 - 10 * q^16 + 5 * q^17 - 9 * q^18 - 9 * q^19 + 2 * q^20 + 2 * q^21 + 16 * q^22 - 10 * q^23 - 9 * q^25 - 4 * q^26 + 37 * q^28 - 6 * q^29 + 13 * q^30 + 6 * q^31 - 22 * q^32 - 8 * q^33 - 44 * q^34 - 4 * q^35 + 14 * q^36 - 4 * q^37 + 10 * q^38 - 28 * q^40 + 28 * q^41 + 52 * q^42 + 4 * q^43 + 32 * q^45 - 3 * q^46 - q^47 - 46 * q^48 - 11 * q^49 + 18 * q^50 + 8 * q^51 - 8 * q^52 - 17 * q^53 - 23 * q^54 - 21 * q^56 - 32 * q^57 + 27 * q^58 - 11 * q^59 + 29 * q^60 + 11 * q^61 - 46 * q^62 + 5 * q^63 + 18 * q^64 - 2 * q^65 - 21 * q^66 - 13 * q^67 + 32 * q^68 + 36 * q^69 + 49 * q^70 + 30 * q^71 + 19 * q^72 + 33 * q^74 + 20 * q^75 + 16 * q^76 - 46 * q^77 - 10 * q^78 - 2 * q^79 - 55 * q^80 + 19 * q^81 - 34 * q^82 + 12 * q^83 - 23 * q^84 - 44 * q^85 - 28 * q^86 + 8 * q^87 + 3 * q^88 + 4 * q^89 - 68 * q^90 + q^91 + 42 * q^92 - 18 * q^93 - 20 * q^94 + 12 * q^95 + 37 * q^96 - 24 * q^97 - 7 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.10666	−	1.91679i	−0.782527	−	1.35538i	−0.930465	−	0.366381i	$-0.880597\pi$
$2$	−1.10666	−	1.91679i	−0.782527	−	1.35538i	0.147938	−	0.988997i	$-0.452737\pi$
$3$	−1.23721	+	2.14292i	−0.714306	+	1.23721i	0.248921	+	0.968524i	$0.419924\pi$
$3$	−1.23721	+	2.14292i	−0.714306	+	1.23721i	−0.963227	+	0.268690i	$0.913409\pi$
$4$	−1.44940	+	2.51043i	−0.724699	+	1.25521i
$5$	1.06140	+	1.83839i	0.474671	+	0.822155i	0.999579	−	0.0290040i	$-0.00923354\pi$
$5$	1.06140	+	1.83839i	0.474671	+	0.822155i	−0.524908	+	0.851159i	$0.675900\pi$
$6$	5.47671			2.23586
$7$	2.63169	+	0.272389i	0.994686	+	0.102953i
$7$	2.63169	+	0.272389i	0.994686	+	0.102953i
$8$	1.98932			0.703331
$9$	−1.56140	−	2.70442i	−0.520466	−	0.901473i
$10$	2.34921	−	4.06896i	0.742887	−	1.28672i
$11$	−2.39448	+	4.14736i	−0.721962	+	1.25048i	0.238250	+	0.971204i	$0.423426\pi$
$11$	−2.39448	+	4.14736i	−0.721962	+	1.25048i	−0.960212	+	0.279272i	$0.909907\pi$
$12$	−3.58643	−	6.21188i	−1.03531	−	1.79321i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−2.39028	−	5.34585i	−0.638829	−	1.42874i
$15$	−5.25271			−1.35624
$16$	0.697291	+	1.20774i	0.174323	+	0.301936i
$17$	1.88914	−	3.27208i	0.458183	−	0.793597i	−0.540682	−	0.841227i	$-0.681834\pi$
$17$	1.88914	−	3.27208i	0.458183	−	0.793597i	0.998865	+	0.0476304i	$0.0151670\pi$
$18$	−3.45588	+	5.98575i	−0.814558	+	1.41086i
$19$	1.78362	+	3.08931i	0.409190	+	0.708737i	0.994799	−	0.101856i	$-0.0324781\pi$
$19$	1.78362	+	3.08931i	0.409190	+	0.708737i	−0.585609	+	0.810593i	$0.699145\pi$
$20$	−6.15355			−1.37597
$21$	−3.83967	+	5.30250i	−0.837886	+	1.15710i
$22$	10.5995			2.25982
$23$	−2.23721	−	3.87497i	−0.466491	−	0.807987i	0.532776	−	0.846256i	$-0.321149\pi$
$23$	−2.23721	−	3.87497i	−0.466491	−	0.807987i	−0.999267	+	0.0382695i	$0.987815\pi$
$24$	−2.46122	+	4.26295i	−0.502394	+	0.870171i
$25$	0.246870	−	0.427591i	0.0493740	−	0.0855182i
$26$	−1.10666	−	1.91679i	−0.217034	−	0.375914i
$27$	0.303848			0.0584757
$28$	−4.49818	+	6.21188i	−0.850076	+	1.17393i
$29$	−5.90107			−1.09580			−0.547901	−	0.836543i	$-0.684573\pi$
$29$	−5.90107			−1.09580			−0.547901	+	0.836543i	$0.684573\pi$
$30$	5.81296	+	10.0683i	1.06130	+	1.83822i
$31$	1.88558	−	3.26592i	0.338660	−	0.586577i	−0.645521	−	0.763743i	$-0.723360\pi$
$31$	1.88558	−	3.26592i	0.338660	−	0.586577i	0.984181	+	0.177166i	$0.0566929\pi$
$32$	3.53265	−	6.11873i	0.624490	−	1.08165i
$33$	−5.92496	−	10.2623i	−1.03140	−	1.78644i
$34$	−8.36254			−1.43416
$35$	2.29251	+	5.12720i	0.387505	+	0.866655i
$36$	9.05234			1.50872
$37$	−2.81285	−	4.87200i	−0.462429	−	0.800951i	0.536652	−	0.843804i	$-0.319689\pi$
$37$	−2.81285	−	4.87200i	−0.462429	−	0.800951i	−0.999081	+	0.0428524i	$0.986355\pi$
$38$	3.94772	−	6.83765i	0.640404	−	1.10921i
$39$	−1.23721	+	2.14292i	−0.198113	+	0.343141i
$40$	2.11146	+	3.65716i	0.333851	+	0.578247i
$41$	10.3948			1.62340			0.811698	−	0.584077i	$-0.198543\pi$
$41$	10.3948			1.62340			0.811698	+	0.584077i	$0.198543\pi$
$42$	14.4130	+	1.49180i	2.22398	+	0.230189i
$43$	3.40733			0.519613			0.259807	−	0.965661i	$-0.416341\pi$
$43$	3.40733			0.519613			0.259807	+	0.965661i	$0.416341\pi$
$44$	−6.94110	−	12.0223i	−1.04641	−	1.81244i
$45$	3.31453	−	5.74093i	0.494101	−	0.855807i
$46$	−4.95168	+	8.57655i	−0.730085	+	1.26454i
$47$	3.55438	+	6.15636i	0.518459	+	0.897998i	0.999770	+	0.0214479i	$0.00682759\pi$
$47$	3.55438	+	6.15636i	0.518459	+	0.897998i	−0.481311	+	0.876550i	$0.659839\pi$
$48$	−3.45079			−0.498079
$49$	6.85161	+	1.43369i	0.978801	+	0.204813i
$50$	−1.09280			−0.154546
$51$	4.67454	+	8.09654i	0.654566	+	1.13374i
$52$	−1.44940	+	2.51043i	−0.200995	+	0.348134i
$53$	6.19003	−	10.7214i	0.850266	−	1.47270i	−0.0307027	−	0.999529i	$-0.509774\pi$
$53$	6.19003	−	10.7214i	0.850266	−	1.47270i	0.880968	−	0.473175i	$-0.156892\pi$
$54$	−0.336257	−	0.582415i	−0.0457588	−	0.0792566i
$55$	−10.1660			−1.37078
$56$	5.23528	+	0.541869i	0.699594	+	0.0724103i
$57$	−8.82686			−1.16915
$58$	6.53049	+	11.3111i	0.857495	+	1.48522i
$59$	−2.39448	+	4.14736i	−0.311734	+	0.539940i	−0.978738	−	0.205115i	$-0.934243\pi$
$59$	−2.39448	+	4.14736i	−0.311734	+	0.539940i	0.667003	+	0.745055i	$0.267577\pi$
$60$	7.61326	−	13.1865i	0.982867	−	1.70238i
$61$	−1.60348	−	2.77732i	−0.205305	−	0.355599i	0.744925	−	0.667148i	$-0.232485\pi$
$61$	−1.60348	−	2.77732i	−0.205305	−	0.355599i	−0.950230	+	0.311550i	$0.899152\pi$
$62$	−8.34680			−1.06004
$63$	−3.37246	−	7.54251i	−0.424890	−	0.950267i
$64$	−12.8486			−1.60608
$65$	1.06140	+	1.83839i	0.131650	+	0.228025i
$66$	−13.1139	+	22.7139i	−1.61420	+	2.79588i
$67$	1.44978	−	2.51109i	0.177118	−	0.306778i	−0.763774	−	0.645484i	$-0.776656\pi$
$67$	1.44978	−	2.51109i	0.177118	−	0.306778i	0.940892	+	0.338706i	$0.109989\pi$
$68$	5.47622	+	9.48510i	0.664090	+	1.15024i
$69$	11.0717			1.33287
$70$	7.29075	−	10.0683i	0.871411	−	1.20340i
$71$	−2.53876			−0.301295			−0.150648	−	0.988588i	$-0.548136\pi$
$71$	−2.53876			−0.301295			−0.150648	+	0.988588i	$0.548136\pi$
$72$	−3.10612	−	5.37996i	−0.366060	−	0.634034i
$73$	−3.85035	+	6.66901i	−0.450650	+	0.780548i	−0.998426	−	0.0560762i	$-0.982141\pi$
$73$	−3.85035	+	6.66901i	−0.450650	+	0.780548i	0.547777	+	0.836625i	$0.315474\pi$
$74$	−6.22574	+	10.7833i	−0.723727	+	1.25353i
$75$	0.610862	+	1.05804i	0.0705362	+	0.122172i
$76$	−10.3407			−1.18616
$77$	−7.43122	+	10.2623i	−0.846867	+	1.16950i
$78$	5.47671			0.620115
$79$	2.58925	+	4.48471i	0.291313	+	0.504569i	0.974120	−	0.226029i	$-0.0725745\pi$
$79$	2.58925	+	4.48471i	0.291313	+	0.504569i	−0.682807	+	0.730598i	$0.739241\pi$
$80$	−1.48021	+	2.56379i	−0.165492	+	0.286641i
$81$	4.30827	−	7.46214i	0.478696	−	0.829126i
$82$	−11.5035	−	19.9247i	−1.27035	−	2.20032i
$83$	3.46731			0.380587			0.190294	−	0.981727i	$-0.439056\pi$
$83$	3.46731			0.380587			0.190294	+	0.981727i	$0.439056\pi$
$84$	−7.74633	−	17.3247i	−0.845194	−	1.89027i
$85$	8.02051			0.869946
$86$	−3.77076	−	6.53115i	−0.406612	−	0.704272i
$87$	7.30089	−	12.6455i	0.782738	−	1.35574i
$88$	−4.76338	+	8.25042i	−0.507778	+	0.879498i
$89$	−1.83216	−	3.17339i	−0.194209	−	0.336379i	0.752432	−	0.658670i	$-0.228881\pi$
$89$	−1.83216	−	3.17339i	−0.194209	−	0.336379i	−0.946641	+	0.322291i	$0.895547\pi$
$90$	−14.6722			−1.54659
$91$	2.63169	+	0.272389i	0.275876	+	0.0285541i
$92$	12.9704			1.35226
$93$	4.66574	+	8.08129i	0.483814	+	0.837991i
$94$	7.86698	−	13.6260i	0.811417	−	1.40542i
$95$	−3.78625	+	6.55798i	−0.388461	+	0.672835i
$96$	8.74129	+	15.1404i	0.892154	+	1.54526i
$97$	−5.40733			−0.549031			−0.274516	−	0.961583i	$-0.588518\pi$
$97$	−5.40733			−0.549031			−0.274516	+	0.961583i	$0.588518\pi$
$98$	−4.83432	−	14.7197i	−0.488340	−	1.48692i
$99$	14.9549			1.50303
$100$	0.715625	+	1.23950i	0.0715625	+	0.123950i
$101$	−4.65862	+	8.06897i	−0.463550	+	0.802892i	−0.999135	−	0.0415891i	$-0.986758\pi$
$101$	−4.65862	+	8.06897i	−0.463550	+	0.802892i	0.535585	+	0.844482i	$0.320091\pi$
$102$	10.3463	−	17.9202i	1.02443	−	1.77437i
$103$	−3.65318	−	6.32749i	−0.359958	−	0.623466i	0.627995	−	0.778217i	$-0.283876\pi$
$103$	−3.65318	−	6.32749i	−0.359958	−	0.623466i	−0.987953	+	0.154751i	$0.950542\pi$
$104$	1.98932			0.195069
$105$	−13.8235	−	1.43078i	−1.34904	−	0.139630i
$106$	−27.4011			−2.66143
$107$	−3.37365	−	5.84333i	−0.326143	−	0.564896i	0.655600	−	0.755108i	$-0.272416\pi$
$107$	−3.37365	−	5.84333i	−0.326143	−	0.564896i	−0.981743	+	0.190212i	$0.939082\pi$
$108$	−0.440397	+	0.762790i	−0.0423772	+	0.0733995i
$109$	−2.08822	+	3.61691i	−0.200016	+	0.346437i	−0.948533	−	0.316678i	$-0.897433\pi$
$109$	−2.08822	+	3.61691i	−0.200016	+	0.346437i	0.748518	+	0.663115i	$0.230766\pi$
$110$	11.2503	+	19.4861i	1.07267	+	1.85792i
$111$	13.9204			1.32126
$112$	1.50608	+	3.36834i	0.142311	+	0.318278i
$113$	5.90107			0.555126			0.277563	−	0.960707i	$-0.410473\pi$
$113$	5.90107			0.555126			0.277563	+	0.960707i	$0.410473\pi$
$114$	9.76834	+	16.9193i	0.914889	+	1.58463i
$115$	4.74915	−	8.22577i	0.442860	−	0.767057i
$116$	8.55300	−	14.8142i	0.794126	−	1.37547i
$117$	−1.56140	−	2.70442i	−0.144351	−	0.250024i
$118$	10.5995			0.975763
$119$	5.86291	−	8.09654i	0.537452	−	0.742208i
$120$	−10.4493			−0.953888
$121$	−5.96705	−	10.3352i	−0.542459	−	0.939567i
$122$	−3.54903	+	6.14709i	−0.321314	+	0.556532i
$123$	−12.8606	+	22.2752i	−1.15960	+	2.00849i
$124$	5.46591	+	9.46724i	0.490853	+	0.850183i
$125$	11.6621			1.04309
$126$	−10.7253	+	14.8113i	−0.955482	+	1.31950i
$127$	−10.5268			−0.934100			−0.467050	−	0.884231i	$-0.654683\pi$
$127$	−10.5268			−0.934100			−0.467050	+	0.884231i	$0.654683\pi$
$128$	7.15377	+	12.3907i	0.632309	+	1.09519i
$129$	−4.21560	+	7.30163i	−0.371163	+	0.642873i
$130$	2.34921	−	4.06896i	0.206040	−	0.356871i
$131$	−2.71204	−	4.69740i	−0.236952	−	0.410413i	0.722886	−	0.690967i	$-0.242815\pi$
$131$	−2.71204	−	4.69740i	−0.236952	−	0.410413i	−0.959838	+	0.280554i	$0.909482\pi$
$132$	34.3505			2.98983
$133$	3.85243	+	8.61596i	0.334048	+	0.747099i
$134$	−6.41765			−0.554400
$135$	0.322504	+	0.558593i	0.0277567	+	0.0480761i
$136$	3.75810	−	6.50922i	0.322255	−	0.558161i
$137$	−11.1224	+	19.2645i	−0.950248	+	1.64588i	−0.205363	+	0.978686i	$0.565837\pi$
$137$	−11.1224	+	19.2645i	−0.950248	+	1.64588i	−0.744886	+	0.667192i	$0.767496\pi$
$138$	−12.2526	−	21.2221i	−1.04301	−	1.80654i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	−16.1942	−	1.67616i	−1.36866	−	0.141661i
$141$	−17.5901			−1.48135
$142$	2.80955	+	4.86628i	0.235772	+	0.408369i
$143$	−2.39448	+	4.14736i	−0.200236	+	0.346819i
$144$	2.17750	−	3.77153i	0.181458	−	0.314294i
$145$	−6.26338	−	10.8485i	−0.520146	−	0.900919i
$146$	17.0441			1.41058
$147$	−11.5492	+	12.9087i	−0.952561	+	1.06469i
$148$	16.3077			1.34049
$149$	−1.47736	−	2.55887i	−0.121030	−	0.209630i	0.799144	−	0.601140i	$-0.205286\pi$
$149$	−1.47736	−	2.55887i	−0.121030	−	0.209630i	−0.920174	+	0.391509i	$0.871953\pi$
$150$	1.35203	−	2.34179i	0.110393	−	0.191206i
$151$	9.27736	−	16.0689i	0.754981	−	1.30766i	−0.190403	−	0.981706i	$-0.560980\pi$
$151$	9.27736	−	16.0689i	0.754981	−	1.30766i	0.945384	−	0.325959i	$-0.105687\pi$
$152$	3.54818	+	6.14564i	0.287796	+	0.498477i
$153$	−11.7988			−0.953875
$154$	27.8946	+	2.88719i	2.24781	+	0.232656i
$155$	8.00541			0.643010
$156$	−3.58643	−	6.21188i	−0.287144	−	0.497348i
$157$	4.89982	−	8.48673i	0.391048	−	0.677315i	−0.601540	−	0.798843i	$-0.705446\pi$
$157$	4.89982	−	8.48673i	0.391048	−	0.677315i	0.992588	+	0.121528i	$0.0387793\pi$
$158$	5.73084	−	9.92610i	0.455921	−	0.789678i
$159$	15.3168	+	26.5294i	1.21470	+	2.10392i
$160$	14.9982			1.18571
$161$	−4.83216	−	10.8071i	−0.380828	−	0.851720i
$162$	−19.0712			−1.49837
$163$	−6.91709	−	11.9808i	−0.541788	−	0.938405i	−0.998801	−	0.0489451i	$-0.984414\pi$
$163$	−6.91709	−	11.9808i	−0.541788	−	0.938405i	0.457013	−	0.889460i	$-0.348919\pi$
$164$	−15.0662	+	26.0954i	−1.17647	+	2.03771i
$165$	12.5775	−	21.7848i	0.979156	−	1.69595i
$166$	−3.83714	−	6.64612i	−0.297820	−	0.515839i
$167$	17.3534			1.34285			0.671424	−	0.741073i	$-0.265683\pi$
$167$	17.3534			1.34285			0.671424	+	0.741073i	$0.265683\pi$
$168$	−7.63834	+	10.5484i	−0.589311	+	0.813824i
$169$	1.00000			0.0769231
$170$	−8.87598	−	15.3737i	−0.680757	−	1.17911i
$171$	5.56987	−	9.64730i	0.425939	−	0.737747i
$172$	−4.93858	+	8.55387i	−0.376563	+	0.652226i
$173$	1.48069	+	2.56463i	0.112575	+	0.194985i	0.916808	−	0.399329i	$-0.130757\pi$
$173$	1.48069	+	2.56463i	0.112575	+	0.194985i	−0.804233	+	0.594314i	$0.797424\pi$
$174$	−32.3184			−2.45005
$175$	0.766156	−	1.05804i	0.0579160	−	0.0799806i
$176$	−6.67859			−0.503418
$177$	−5.92496	−	10.2623i	−0.445348	−	0.771365i
$178$	−4.05516	+	7.02374i	−0.303947	+	0.526452i
$179$	2.83444	−	4.90939i	0.211856	−	0.366945i	−0.740440	−	0.672123i	$-0.765383\pi$
$179$	2.83444	−	4.90939i	0.211856	−	0.366945i	0.952295	+	0.305178i	$0.0987159\pi$
$180$	9.60813	+	16.6418i	0.716148	+	1.24040i
$181$	7.17645			0.533421			0.266711	−	0.963777i	$-0.414063\pi$
$181$	7.17645			0.533421			0.266711	+	0.963777i	$0.414063\pi$
$182$	−2.39028	−	5.34585i	−0.177179	−	0.396261i
$183$	7.93541			0.586603
$184$	−4.45054	−	7.70855i	−0.328098	−	0.568282i
$185$	5.97110	−	10.3423i	0.439004	−	0.760377i
$186$	10.3268	−	17.8865i	0.757196	−	1.31150i
$187$	9.04700	+	15.6699i	0.661582	+	1.14589i
$188$	−20.6068			−1.50291
$189$	0.799636	+	0.0827650i	0.0581649	+	0.00602027i
$190$	16.7604			1.21593
$191$	−5.94088	−	10.2899i	−0.429867	−	0.744552i	0.566994	−	0.823722i	$-0.308106\pi$
$191$	−5.94088	−	10.2899i	−0.429867	−	0.744552i	−0.996861	+	0.0791703i	$0.974773\pi$
$192$	15.8965	−	27.5335i	1.14723	−	1.98706i
$193$	−11.4851	+	19.8927i	−0.826714	+	1.43191i	0.0738876	+	0.997267i	$0.476459\pi$
$193$	−11.4851	+	19.8927i	−0.826714	+	1.43191i	−0.900602	+	0.434645i	$0.856874\pi$
$194$	5.98408	+	10.3647i	0.429632	+	0.744145i
$195$	−5.25271			−0.376154
$196$	−13.5299	+	15.1225i	−0.966420	+	1.08018i
$197$	16.9216			1.20561			0.602806	−	0.797888i	$-0.294049\pi$
$197$	16.9216			1.20561			0.602806	+	0.797888i	$0.294049\pi$
$198$	−16.5500	−	28.6655i	−1.17616	−	2.03717i
$199$	−5.02953	+	8.71140i	−0.356534	+	0.617535i	−0.987379	−	0.158374i	$-0.949375\pi$
$199$	−5.02953	+	8.71140i	−0.356534	+	0.617535i	0.630845	+	0.775909i	$0.282708\pi$
$200$	0.491103	−	0.850616i	0.0347262	−	0.0601476i
$201$	3.58737	+	6.21351i	0.253034	+	0.438267i
$202$	20.6221			1.45096
$203$	−15.5298	−	1.60739i	−1.08998	−	0.112817i
$204$	−27.1010			−1.89745
$205$	11.0330	+	19.1098i	0.770580	+	1.33468i
$206$	−8.08566	+	14.0048i	−0.563355	+	0.975759i
$207$	−6.98636	+	12.1007i	−0.485586	+	0.841059i
$208$	0.697291	+	1.20774i	0.0483484	+	0.0837419i
$209$	−17.0833			−1.18168
$210$	12.5554	+	28.0802i	0.866406	+	1.93772i
$211$	−24.4609			−1.68396			−0.841978	−	0.539512i	$-0.818609\pi$
$211$	−24.4609			−1.68396			−0.841978	+	0.539512i	$0.818609\pi$
$212$	17.9436	+	31.0793i	1.23237	+	2.13453i
$213$	3.14099	−	5.44035i	0.215217	−	0.372767i
$214$	−7.46697	+	12.9332i	−0.510431	+	0.884093i
$215$	3.61654	+	6.26402i	0.246646	+	0.427203i
$216$	0.604452			0.0411277
$217$	5.85187	−	8.08129i	0.397251	−	0.548594i
$218$	9.24382			0.626071
$219$	−9.52742	−	16.5020i	−0.643804	−	1.11510i
$220$	14.7345	−	25.5210i	0.993402	−	1.72062i
$221$	1.88914	−	3.27208i	0.127077	−	0.220104i
$222$	−15.4051	−	26.6825i	−1.03393	−	1.79081i
$223$	−29.2625			−1.95956			−0.979780	−	0.200076i	$-0.935881\pi$
$223$	−29.2625			−1.95956			−0.979780	+	0.200076i	$0.935881\pi$
$224$	10.9635	−	15.1404i	0.732531	−	1.01161i
$225$	−1.54185			−0.102790
$226$	−6.53049	−	11.3111i	−0.434401	−	0.752405i
$227$	5.03685	−	8.72408i	0.334307	−	0.579038i	−0.649044	−	0.760751i	$-0.724831\pi$
$227$	5.03685	−	8.72408i	0.334307	−	0.579038i	0.983352	+	0.181713i	$0.0581643\pi$
$228$	12.7936	−	22.1592i	0.847279	−	1.46753i
$229$	5.56997	+	9.64748i	0.368074	+	0.637523i	0.989264	−	0.146137i	$-0.0466839\pi$
$229$	5.56997	+	9.64748i	0.368074	+	0.637523i	−0.621190	+	0.783660i	$0.713351\pi$
$230$	−21.0228			−1.38620
$231$	−12.7973	−	28.6212i	−0.842003	−	1.88314i
$232$	−11.7391			−0.770711
$233$	8.54166	+	14.7946i	0.559583	+	0.969226i	0.997531	+	0.0702257i	$0.0223720\pi$
$233$	8.54166	+	14.7946i	0.559583	+	0.969226i	−0.437948	+	0.899000i	$0.644295\pi$
$234$	−3.45588	+	5.98575i	−0.225918	+	0.391301i
$235$	−7.54522	+	13.0687i	−0.492196	+	0.852508i
$236$	−6.94110	−	12.0223i	−0.451827	−	0.782587i
$237$	−12.8138			−0.832347
$238$	−22.0076	−	2.27787i	−1.42654	−	0.147652i
$239$	6.92142			0.447710			0.223855	−	0.974622i	$-0.428136\pi$
$239$	6.92142			0.447710			0.223855	+	0.974622i	$0.428136\pi$
$240$	−3.66266	−	6.34392i	−0.236424	−	0.409498i
$241$	−3.24812	+	5.62592i	−0.209230	+	0.362397i	−0.951472	−	0.307735i	$-0.900429\pi$
$241$	−3.24812	+	5.62592i	−0.209230	+	0.362397i	0.742242	+	0.670132i	$0.233762\pi$
$242$	−13.2070	+	22.8752i	−0.848978	+	1.47047i
$243$	11.1163	+	19.2539i	0.713109	+	1.23514i
$244$	9.29634			0.595137
$245$	4.63660	+	14.1177i	0.296221	+	0.901945i
$246$	56.9293			3.62968
$247$	1.78362	+	3.08931i	0.113489	+	0.196568i
$248$	3.75103	−	6.49697i	0.238190	−	0.412558i
$249$	−4.28981	+	7.43017i	−0.271856	+	0.470868i
$250$	−12.9060	−	22.3538i	−0.816246	−	1.41378i
$251$	−9.86804			−0.622865			−0.311433	−	0.950268i	$-0.600809\pi$
$251$	−9.86804			−0.622865			−0.311433	+	0.950268i	$0.600809\pi$
$252$	23.8230	+	2.46576i	1.50071	+	0.155328i
$253$	21.4278			1.34716
$254$	11.6496	+	20.1776i	0.730959	+	1.26606i
$255$	−9.92309	+	17.1873i	−0.621408	+	1.07631i
$256$	2.98497	−	5.17012i	0.186560	−	0.323132i
$257$	−3.43234	−	5.94499i	−0.214104	−	0.370838i	0.738891	−	0.673825i	$-0.235350\pi$
$257$	−3.43234	−	5.94499i	−0.214104	−	0.370838i	−0.952995	+	0.302986i	$0.902016\pi$
$258$	18.6610			1.16178
$259$	−6.07547	−	13.5878i	−0.377511	−	0.844304i
$260$	−6.15355			−0.381627
$261$	9.21392	+	15.9590i	0.570327	+	0.987836i
$262$	−6.00262	+	10.3969i	−0.370843	+	0.642320i
$263$	0.0632753	−	0.109596i	0.00390172	−	0.00675798i	−0.864068	−	0.503375i	$-0.832091\pi$
$263$	0.0632753	−	0.109596i	0.00390172	−	0.00675798i	0.867970	+	0.496617i	$0.165425\pi$
$264$	−11.7867	−	20.4151i	−0.725418	−	1.25646i
$265$	26.2803			1.61439
$266$	12.2517	−	16.9193i	0.751199	−	1.03739i
$267$	9.06710			0.554897
$268$	4.20261	+	7.27913i	0.256715	+	0.444643i
$269$	2.12154	−	3.67462i	0.129353	−	0.224045i	−0.794073	−	0.607822i	$-0.792043\pi$
$269$	2.12154	−	3.67462i	0.129353	−	0.224045i	0.923426	+	0.383777i	$0.125377\pi$
$270$	0.713805	−	1.23635i	0.0434408	−	0.0752417i
$271$	−0.783616	−	1.35726i	−0.0476013	−	0.0824479i	0.841243	−	0.540657i	$-0.181824\pi$
$271$	−0.783616	−	1.35726i	−0.0476013	−	0.0824479i	−0.888844	+	0.458209i	$0.848491\pi$
$272$	5.26911			0.319487
$273$	−3.83967	+	5.30250i	−0.232388	+	0.320922i
$274$	49.2348			2.97438
$275$	1.18225	+	2.04771i	0.0712923	+	0.123482i
$276$	−16.0472	+	27.7946i	−0.965929	+	1.67304i
$277$	6.37260	−	11.0377i	0.382892	−	0.663189i	−0.608582	−	0.793491i	$-0.708261\pi$
$277$	6.37260	−	11.0377i	0.382892	−	0.663189i	0.991474	+	0.130302i	$0.0415947\pi$
$278$	4.42664	+	7.66717i	0.265492	+	0.459846i
$279$	−11.7766			−0.705045
$280$	4.56054	+	10.1996i	0.272545	+	0.609546i
$281$	4.62986			0.276194			0.138097	−	0.990419i	$-0.455901\pi$
$281$	4.62986			0.276194			0.138097	+	0.990419i	$0.455901\pi$
$282$	19.4663	+	33.7166i	1.15920	+	2.00779i
$283$	−1.82416	+	3.15954i	−0.108435	+	0.187815i	−0.915136	−	0.403144i	$-0.867917\pi$
$283$	−1.82416	+	3.15954i	−0.108435	+	0.187815i	0.806701	+	0.590959i	$0.201251\pi$
$284$	3.67967	−	6.37338i	0.218348	−	0.378190i
$285$	−9.36881	−	16.2273i	−0.554960	−	0.961220i
$286$	10.5995			0.626762
$287$	27.3559	+	2.83143i	1.61477	+	0.167134i
$288$	−22.0635			−1.30010
$289$	1.36231	+	2.35959i	0.0801360	+	0.138800i
$290$	−13.8629	+	24.0112i	−0.814057	+	1.40999i
$291$	6.69003	−	11.5875i	0.392176	−	0.679269i
$292$	−11.1614	−	19.3321i	−0.653171	−	1.13132i
$293$	−21.0415			−1.22926			−0.614630	−	0.788816i	$-0.710695\pi$
$293$	−21.0415			−1.22926			−0.614630	+	0.788816i	$0.710695\pi$
$294$	37.5242	+	7.85189i	2.18846	+	0.457932i
$295$	−10.1660			−0.591886
$296$	−5.59566	−	9.69196i	−0.325241	−	0.563334i
$297$	−0.727559	+	1.26017i	−0.0422172	+	0.0731224i
$298$	−3.26988	+	5.66359i	−0.189419	+	0.328083i
$299$	−2.23721	−	3.87497i	−0.129381	−	0.224095i
$300$	−3.54152			−0.204470
$301$	8.96705	+	0.928120i	0.516852	+	0.0534960i
$302$	−41.0676			−2.36317
$303$	−11.5274	−	19.9661i	−0.662233	−	1.14702i
$304$	−2.48740	+	4.30830i	−0.142662	+	0.247098i
$305$	3.40387	−	5.89567i	0.194905	−	0.337585i
$306$	13.0573	+	22.6158i	0.746434	+	1.29286i
$307$	−4.95861			−0.283003			−0.141502	−	0.989938i	$-0.545193\pi$
$307$	−4.95861			−0.283003			−0.141502	+	0.989938i	$0.545193\pi$
$308$	−14.9921	−	33.5298i	−0.854253	−	1.91054i
$309$	18.0791			1.02848
$310$	−8.85927	−	15.3447i	−0.503173	−	0.871521i
$311$	1.21079	−	2.09715i	0.0686575	−	0.118918i	−0.829653	−	0.558279i	$-0.811462\pi$
$311$	1.21079	−	2.09715i	0.0686575	−	0.118918i	0.898311	+	0.439361i	$0.144795\pi$
$312$	−2.46122	+	4.26295i	−0.139339	+	0.241342i
$313$	−6.98026	−	12.0902i	−0.394548	−	0.683377i	0.598496	−	0.801126i	$-0.295765\pi$
$313$	−6.98026	−	12.0902i	−0.394548	−	0.683377i	−0.993043	+	0.117749i	$0.962432\pi$
$314$	−21.6897			−1.22402
$315$	10.2866	−	14.2055i	0.579583	−	0.800390i
$316$	−15.0114			−0.844457
$317$	−1.53431	−	2.65750i	−0.0861753	−	0.149260i	0.819716	−	0.572770i	$-0.194131\pi$
$317$	−1.53431	−	2.65750i	−0.0861753	−	0.149260i	−0.905891	+	0.423510i	$0.860798\pi$
$318$	33.9010	−	58.7182i	1.90107	−	3.29275i
$319$	14.1300	−	24.4739i	0.791127	−	1.37027i
$320$	−13.6375	−	23.6208i	−0.762359	−	1.32044i
$321$	16.6957			0.931863
$322$	−15.3674	+	21.2221i	−0.856394	+	1.18266i
$323$	13.4780			0.749936
$324$	12.4888	+	21.6312i	0.693821	+	1.20173i
$325$	0.246870	−	0.427591i	0.0136939	−	0.0237185i
$326$	−15.3098	+	26.5173i	−0.847929	+	1.46866i
$327$	−5.16716	−	8.94978i	−0.285745	−	0.494924i
$328$	20.6786			1.14179
$329$	7.67710	+	17.1698i	0.423252	+	0.946603i
$330$	−55.6761			−3.06487
$331$	−6.80261	−	11.7825i	−0.373905	−	0.647623i	0.616257	−	0.787545i	$-0.288648\pi$
$331$	−6.80261	−	11.7825i	−0.373905	−	0.647623i	−0.990162	+	0.139922i	$0.955315\pi$
$332$	−5.02551	+	8.70445i	−0.275811	+	0.477719i
$333$	−8.78395	+	15.2142i	−0.481358	+	0.833736i
$334$	−19.2044	−	33.2629i	−1.05082	−	1.82007i
$335$	6.15516			0.336292
$336$	−9.08142	−	0.939958i	−0.495432	−	0.0512789i
$337$	−35.1646			−1.91554			−0.957769	−	0.287538i	$-0.907163\pi$
$337$	−35.1646			−1.91554			−0.957769	+	0.287538i	$0.907163\pi$
$338$	−1.10666	−	1.91679i	−0.0601944	−	0.104260i
$339$	−7.30089	+	12.6455i	−0.396530	+	0.686810i
$340$	−11.6249	+	20.1349i	−0.630449	+	1.09197i
$341$	9.02997	+	15.6404i	0.489000	+	0.846973i
$342$	−24.6558			−1.33323
$343$	17.6408	+	5.63933i	0.952514	+	0.304495i
$344$	6.77828			0.365460
$345$	11.7514	+	20.3541i	0.632676	+	1.09583i
$346$	3.27724	−	5.67635i	0.176186	−	0.305162i
$347$	2.73551	−	4.73804i	0.146850	−	0.254351i	−0.783212	−	0.621755i	$-0.786420\pi$
$347$	2.73551	−	4.73804i	0.146850	−	0.254351i	0.930062	+	0.367404i	$0.119753\pi$
$348$	21.1638	+	36.6567i	1.13450	+	1.96501i
$349$	4.34196			0.232420			0.116210	−	0.993225i	$-0.462925\pi$
$349$	4.34196			0.232420			0.116210	+	0.993225i	$0.462925\pi$
$350$	−2.87593	−	0.297668i	−0.153725	−	0.0159110i
$351$	0.303848			0.0162182
$352$	16.9177	+	29.3023i	0.901717	+	1.56182i
$353$	−13.7996	+	23.9016i	−0.734479	+	1.27216i	0.220472	+	0.975393i	$0.429240\pi$
$353$	−13.7996	+	23.9016i	−0.734479	+	1.27216i	−0.954951	+	0.296762i	$0.904093\pi$
$354$	−13.1139	+	22.7139i	−0.696993	+	1.20723i
$355$	−2.69463	−	4.66724i	−0.143016	−	0.247712i
$356$	10.6221			0.562971
$357$	10.0965	+	22.5809i	0.534365	+	1.19511i
$358$	−12.5470			−0.663132
$359$	−3.31427	−	5.74049i	−0.174921	−	0.302971i	0.765213	−	0.643777i	$-0.222634\pi$
$359$	−3.31427	−	5.74049i	−0.174921	−	0.302971i	−0.940134	+	0.340806i	$0.889300\pi$
$360$	6.59366	−	11.4206i	0.347516	−	0.601916i
$361$	3.13742	−	5.43418i	0.165128	−	0.286009i
$362$	−7.94189	−	13.7558i	−0.417417	−	0.722987i
$363$	29.5301			1.54993
$364$	−4.49818	+	6.21188i	−0.235769	+	0.325591i
$365$	−16.3470			−0.855643
$366$	−8.78181	−	15.2105i	−0.459033	−	0.795068i
$367$	−15.6037	+	27.0264i	−0.814506	+	1.41077i	0.0951768	+	0.995460i	$0.469658\pi$
$367$	−15.6037	+	27.0264i	−0.814506	+	1.41077i	−0.909682	+	0.415305i	$0.863675\pi$
$368$	3.11998	−	5.40396i	0.162640	−	0.281701i
$369$	−16.2304	−	28.1119i	−0.844923	−	1.46345i
$370$	−26.4319			−1.37413
$371$	19.2107	−	26.5294i	0.997368	−	1.37734i
$372$	−27.0500			−1.40248
$373$	7.88730	+	13.6612i	0.408389	+	0.707350i	0.994709	−	0.102729i	$-0.0327574\pi$
$373$	7.88730	+	13.6612i	0.408389	+	0.707350i	−0.586321	+	0.810079i	$0.699424\pi$
$374$	20.0239	−	34.6825i	1.03541	−	1.79339i
$375$	−14.4285	+	24.9909i	−0.745084	+	1.29052i
$376$	7.07080	+	12.2470i	0.364649	+	0.631590i
$377$	−5.90107			−0.303921
$378$	−0.726282	−	1.62433i	−0.0373559	−	0.0835465i
$379$	31.6512			1.62581			0.812907	−	0.582393i	$-0.197884\pi$
$379$	31.6512			1.62581			0.812907	+	0.582393i	$0.197884\pi$
$380$	−10.9756	−	19.0102i	−0.563035	−	0.975205i
$381$	13.0239	−	22.5580i	0.667233	−	1.15568i
$382$	−13.1491	+	22.7749i	−0.672766	+	1.16526i
$383$	−6.19675	−	10.7331i	−0.316639	−	0.548435i	0.663145	−	0.748491i	$-0.269221\pi$
$383$	−6.19675	−	10.7331i	−0.316639	−	0.548435i	−0.979785	+	0.200055i	$0.935888\pi$
$384$	−35.4030			−1.80665
$385$	−26.7537	−	2.76910i	−1.36350	−	0.141126i
$386$	50.8404			2.58771
$387$	−5.32020	−	9.21486i	−0.270441	−	0.468418i
$388$	7.83737	−	13.5747i	0.397882	−	0.689152i
$389$	7.03705	−	12.1885i	0.356792	−	0.617983i	−0.630631	−	0.776083i	$-0.717204\pi$
$389$	7.03705	−	12.1885i	0.356792	−	0.617983i	0.987423	+	0.158100i	$0.0505370\pi$
$390$	5.81296	+	10.0683i	0.294351	+	0.509831i
$391$	−16.9056			−0.854954
$392$	13.6300	+	2.85207i	0.688421	+	0.144051i
$393$	13.4215			0.677026
$394$	−18.7265	−	32.4352i	−0.943425	−	1.63406i
$395$	−5.49644	+	9.52012i	−0.276556	+	0.479009i
$396$	−21.6756	+	37.5433i	−1.08924	+	1.88662i
$397$	3.48652	+	6.03884i	0.174984	+	0.303081i	0.940156	−	0.340745i	$-0.110679\pi$
$397$	3.48652	+	6.03884i	0.174984	+	0.303081i	−0.765172	+	0.643826i	$0.777346\pi$
$398$	22.2639			1.11599
$399$	−23.2296	−	2.40434i	−1.16293	−	0.120368i
$400$	0.688560			0.0344280
$401$	−1.36841	−	2.37016i	−0.0683352	−	0.118360i	0.829833	−	0.558011i	$-0.188435\pi$
$401$	−1.36841	−	2.37016i	−0.0683352	−	0.118360i	−0.898169	+	0.439651i	$0.855102\pi$
$402$	7.94000	−	13.7525i	0.396011	−	0.685912i
$403$	1.88558	−	3.26592i	0.0939275	−	0.162687i
$404$	−13.5044	−	23.3903i	−0.671868	−	1.16371i
$405$	18.2911			0.908894
$406$	14.1052	+	31.5463i	0.700029	+	1.56561i
$407$	26.9412			1.33543
$408$	9.29915	+	16.1066i	0.460377	+	0.797396i
$409$	12.2577	−	21.2309i	0.606104	−	1.04980i	−0.385772	−	0.922594i	$-0.626065\pi$
$409$	12.2577	−	21.2309i	0.606104	−	1.04980i	0.991876	−	0.127208i	$-0.0406017\pi$
$410$	24.4196	−	42.2961i	1.20600	−	2.08885i
$411$	−27.5215	−	47.6686i	−1.35754	−	2.35132i
$412$	21.1796			1.04345
$413$	−7.43122	+	10.2623i	−0.365667	+	0.504977i
$414$	30.9261			1.51994
$415$	3.68020	+	6.37429i	0.180654	+	0.312902i
$416$	3.53265	−	6.11873i	0.173202	−	0.299995i
$417$	4.94886	−	8.57167i	0.242347	−	0.419757i
$418$	18.9054	+	32.7452i	0.924696	+	1.60162i
$419$	−3.01252			−0.147171			−0.0735856	−	0.997289i	$-0.523444\pi$
$419$	−3.01252			−0.147171			−0.0735856	+	0.997289i	$0.523444\pi$
$420$	23.6276	−	32.6292i	1.15291	−	1.59214i
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	27.0699	+	46.8864i	1.31774	+	2.28240i
$423$	11.0996	−	19.2251i	0.539681	−	0.934755i
$424$	12.3140	−	21.3284i	0.598018	−	1.03580i
$425$	−0.932742	−	1.61556i	−0.0452447	−	0.0783660i
$426$	−13.9040			−0.673653
$427$	−3.46337	−	7.74581i	−0.167604	−	0.374846i
$428$	19.5590			0.945421
$429$	−5.92496	−	10.2623i	−0.286060	−	0.495470i
$430$	8.00456	−	13.8643i	0.386014	−	0.668596i
$431$	9.39711	−	16.2763i	0.452643	−	0.784001i	−0.545906	−	0.837846i	$-0.683815\pi$
$431$	9.39711	−	16.2763i	0.452643	−	0.784001i	0.998549	+	0.0538455i	$0.0171478\pi$
$432$	0.211871	+	0.366971i	0.0101936	+	0.0176559i
$433$	−7.76911			−0.373360			−0.186680	−	0.982421i	$-0.559773\pi$
$433$	−7.76911			−0.373360			−0.186680	+	0.982421i	$0.559773\pi$
$434$	−21.9662	−	2.27358i	−1.05441	−	0.109135i
$435$	30.9966			1.48617
$436$	−6.05333	−	10.4847i	−0.289902	−	0.502125i
$437$	7.98066	−	13.8229i	0.381767	−	0.661240i
$438$	−21.0873	+	36.5242i	−1.00759	+	1.74519i
$439$	18.9841	+	32.8814i	0.906060	+	1.56934i	0.819488	+	0.573096i	$0.194258\pi$
$439$	18.9841	+	32.8814i	0.906060	+	1.56934i	0.0865713	+	0.996246i	$0.472409\pi$
$440$	−20.2234			−0.964112
$441$	−6.82079	−	20.7682i	−0.324799	−	0.988961i
$442$	−8.36254			−0.397766
$443$	−17.8135	−	30.8539i	−0.846344	−	1.46591i	−0.884449	−	0.466637i	$-0.845465\pi$
$443$	−17.8135	−	30.8539i	−0.846344	−	1.46591i	0.0381050	−	0.999274i	$-0.487868\pi$
$444$	−20.1762	+	34.9461i	−0.957518	+	1.65847i
$445$	3.88930	−	6.73647i	0.184371	−	0.319339i
$446$	32.3837	+	56.0901i	1.53341	+	2.65594i
$447$	7.31125			0.345810
$448$	−33.8136	−	3.49982i	−1.59754	−	0.165351i
$449$	−8.05285			−0.380038			−0.190019	−	0.981780i	$-0.560855\pi$
$449$	−8.05285			−0.380038			−0.190019	+	0.981780i	$0.560855\pi$
$450$	1.70630	+	2.95540i	0.0804359	+	0.139319i
$451$	−24.8901	+	43.1110i	−1.17203	+	2.03002i
$452$	−8.55300	+	14.8142i	−0.402299	+	0.696803i
$453$	22.9562	+	39.7612i	1.07857	+	1.86815i
$454$	−22.2963			−1.04642
$455$	2.29251	+	5.12720i	0.107475	+	0.240367i
$456$	−17.5595			−0.822297
$457$	−7.79881	−	13.5079i	−0.364813	−	0.631875i	0.623933	−	0.781478i	$-0.285534\pi$
$457$	−7.79881	−	13.5079i	−0.364813	−	0.631875i	−0.988746	+	0.149603i	$0.952200\pi$
$458$	12.3281	−	21.3530i	0.576056	−	0.997759i
$459$	0.574012	−	0.994218i	0.0267926	−	0.0464061i
$460$	13.7668	+	23.8448i	0.641880	+	1.11177i
$461$	−25.6991			−1.19692			−0.598462	−	0.801151i	$-0.704221\pi$
$461$	−25.6991			−1.19692			−0.598462	+	0.801151i	$0.704221\pi$
$462$	−40.6986	+	56.2038i	−1.89347	+	2.61484i
$463$	−20.5209			−0.953685			−0.476842	−	0.878989i	$-0.658219\pi$
$463$	−20.5209			−0.953685			−0.476842	+	0.878989i	$0.658219\pi$
$464$	−4.11476	−	7.12698i	−0.191023	−	0.330862i
$465$	−9.90440	+	17.1549i	−0.459306	+	0.795541i
$466$	18.9054	−	32.7452i	0.875778	−	1.51689i
$467$	−5.91241	−	10.2406i	−0.273594	−	0.473878i	0.696186	−	0.717862i	$-0.254879\pi$
$467$	−5.91241	−	10.2406i	−0.273594	−	0.473878i	−0.969779	+	0.243984i	$0.921546\pi$
$468$	9.05234			0.418445
$469$	4.49936	−	6.21351i	0.207761	−	0.286913i
$470$	33.4000			1.54063
$471$	12.1242	+	20.9998i	0.558656	+	0.967620i
$472$	−4.76338	+	8.25042i	−0.219253	+	0.379757i
$473$	−8.15878	+	14.1314i	−0.375141	+	0.649764i
$474$	14.1805	+	24.5614i	0.651334	+	1.12814i
$475$	1.76128			0.0808133
$476$	11.8281	+	26.4535i	0.542140	+	1.21250i
$477$	−38.6604			−1.77014
$478$	−7.65967	−	13.2669i	−0.350345	−	0.606816i
$479$	−11.3276	+	19.6200i	−0.517571	+	0.896459i	0.482221	+	0.876050i	$0.339830\pi$
$479$	−11.3276	+	19.6200i	−0.517571	+	0.896459i	−0.999792	+	0.0204092i	$0.993503\pi$
$480$	−18.5560	+	32.1399i	−0.846960	+	1.46698i
$481$	−2.81285	−	4.87200i	−0.128255	−	0.222144i
$482$	14.3783			0.654913
$483$	29.1372	+	3.01580i	1.32579	+	0.137224i
$484$	34.5945			1.57248
$485$	−5.73933	−	9.94081i	−0.260610	−	0.451389i
$486$	24.6039	−	42.6152i	1.11606	−	1.93306i
$487$	16.3584	−	28.3335i	0.741268	−	1.28391i	−0.210650	−	0.977562i	$-0.567558\pi$
$487$	16.3584	−	28.3335i	0.741268	−	1.28391i	0.951918	−	0.306353i	$-0.0991087\pi$
$488$	−3.18984	−	5.52497i	−0.144397	−	0.250104i
$489$	34.2317			1.54801
$490$	21.9295	−	24.5109i	0.990675	−	1.10729i
$491$	6.17281			0.278575			0.139288	−	0.990252i	$-0.455519\pi$
$491$	6.17281			0.278575			0.139288	+	0.990252i	$0.455519\pi$
$492$	−37.2803	−	64.5713i	−1.68072	−	2.91110i
$493$	−11.1479	+	19.3088i	−0.502078	+	0.869625i
$494$	3.94772	−	6.83765i	0.177616	−	0.307640i
$495$	15.8731	+	27.4931i	0.713444	+	1.23572i
$496$	5.25919			0.236145
$497$	−6.68123	−	0.691531i	−0.299694	−	0.0310194i
$498$	18.9895			0.850938
$499$	7.31934	+	12.6775i	0.327659	+	0.567521i	0.982047	−	0.188637i	$-0.0604071\pi$
$499$	7.31934	+	12.6775i	0.327659	+	0.567521i	−0.654388	+	0.756159i	$0.727074\pi$
$500$	−16.9030	+	29.2768i	−0.755925	+	1.30930i
$501$	−21.4699	+	37.1870i	−0.959205	+	1.66139i
$502$	10.9206	+	18.9150i	0.487409	+	0.844218i
$503$	12.7787			0.569774			0.284887	−	0.958561i	$-0.408044\pi$
$503$	12.7787			0.569774			0.284887	+	0.958561i	$0.408044\pi$
$504$	−6.70891	−	15.0045i	−0.298839	−	0.668352i
$505$	−19.7786			−0.880136
$506$	−23.7134	−	41.0727i	−1.05419	−	1.82591i
$507$	−1.23721	+	2.14292i	−0.0549466	+	0.0951703i
$508$	15.2575	−	26.4267i	0.676941	−	1.17250i
$509$	−5.84263	−	10.1197i	−0.258970	−	0.448549i	0.706996	−	0.707217i	$-0.250050\pi$
$509$	−5.84263	−	10.1197i	−0.258970	−	0.448549i	−0.965966	+	0.258668i	$0.916716\pi$
$510$	43.9260			1.94507
$511$	−11.9495	+	16.5020i	−0.528615	+	0.730005i
$512$	15.4017			0.680664
$513$	0.541949	+	0.938683i	0.0239276	+	0.0414439i
$514$	−7.59688	+	13.1582i	−0.335084	+	0.580382i
$515$	7.75495	−	13.4320i	0.341724	−	0.591883i
$516$	−12.2202	−	21.1659i	−0.537962	−	0.931778i
$517$	−34.0435			−1.49723
$518$	−19.3215	+	26.6825i	−0.848937	+	1.17236i
$519$	−7.32772			−0.321651
$520$	2.11146	+	3.65716i	0.0925937	+	0.160377i
$521$	−4.23838	+	7.34108i	−0.185687	+	0.321619i	−0.943808	−	0.330495i	$-0.892784\pi$
$521$	−4.23838	+	7.34108i	−0.185687	+	0.321619i	0.758121	+	0.652114i	$0.226118\pi$
$522$	20.3934	−	35.3224i	0.892594	−	1.54602i
$523$	−16.3554	−	28.3284i	−0.715172	−	1.23871i	−0.962893	−	0.269883i	$-0.913015\pi$
$523$	−16.3554	−	28.3284i	−0.715172	−	1.23871i	0.247721	−	0.968831i	$-0.420318\pi$
$524$	15.7233			0.686876
$525$	1.31940	+	2.95084i	0.0575833	+	0.128785i
$526$	−0.280097			−0.0122128
$527$	−7.12425	−	12.3396i	−0.310337	−	0.537520i
$528$	8.26284	−	14.3117i	0.359594	−	0.622835i
$529$	1.48975	−	2.58032i	0.0647716	−	0.112188i
$530$	−29.0834	−	50.3739i	−1.26330	−	2.18810i
$531$	14.9549			0.648989
$532$	−27.2135	−	2.81669i	−1.17985	−	0.122119i
$533$	10.3948			0.450249
$534$	−10.0342	−	17.3797i	−0.434222	−	0.752095i
$535$	7.16156	−	12.4042i	0.309621	−	0.536280i
$536$	2.88407	−	4.99536i	0.124573	−	0.215767i
$537$	7.01361	+	12.1479i	0.302660	+	0.524222i
$538$	−9.39131			−0.404888
$539$	−22.3520	+	24.9831i	−0.962771	+	1.07610i
$540$	−1.86975			−0.0804610
$541$	14.0853	+	24.3964i	0.605573	+	1.04888i	0.991961	+	0.126547i	$0.0403893\pi$
$541$	14.0853	+	24.3964i	0.605573	+	1.04888i	−0.386388	+	0.922336i	$0.626277\pi$
$542$	−1.73440	+	3.00406i	−0.0744987	+	0.129035i
$543$	−8.87880	+	15.3785i	−0.381026	+	0.659956i
$544$	−13.3473	−	23.1182i	−0.572262	−	0.991187i
$545$	−8.86574			−0.379767
$546$	14.4130	+	1.49180i	0.616820	+	0.0638430i
$547$	−18.5377			−0.792615			−0.396307	−	0.918118i	$-0.629709\pi$
$547$	−18.5377			−0.792615			−0.396307	+	0.918118i	$0.629709\pi$
$548$	−32.2415	−	55.8438i	−1.37729	−	2.38553i
$549$	−5.00735	+	8.67299i	−0.213709	+	0.370154i
$550$	2.61670	−	4.53225i	0.111576	−	0.193256i
$551$	−10.5252	−	18.2303i	−0.448391	−	0.776635i
$552$	22.0251			0.937449
$553$	5.59252	+	12.5077i	0.237818	+	0.531880i
$554$	−28.2092			−1.19850
$555$	14.7751	+	25.5912i	0.627167	+	1.08628i
$556$	5.79759	−	10.0417i	0.245873	−	0.425864i
$557$	−2.00142	+	3.46655i	−0.0848027	+	0.146883i	−0.905307	−	0.424758i	$-0.860359\pi$
$557$	−2.00142	+	3.46655i	−0.0848027	+	0.146883i	0.820504	+	0.571640i	$0.193693\pi$
$558$	13.0327	+	22.5732i	0.551717	+	0.955602i
$559$	3.40733			0.144115
$560$	−4.59379	+	6.34392i	−0.194123	+	0.268079i
$561$	−44.7723			−1.89029
$562$	−5.12368	−	8.87448i	−0.216129	−	0.374347i
$563$	8.93100	−	15.4689i	0.376397	−	0.651938i	−0.614138	−	0.789199i	$-0.710496\pi$
$563$	8.93100	−	15.4689i	0.376397	−	0.651938i	0.990535	+	0.137260i	$0.0438296\pi$
$564$	25.4951	−	44.1587i	1.07354	−	1.85942i
$565$	6.26338	+	10.8485i	0.263503	+	0.456400i
$566$	8.07490			0.339413
$567$	13.3706	−	18.4645i	0.561514	−	0.775437i
$568$	−5.05041			−0.211910
$569$	18.7336	+	32.4475i	0.785353	+	1.36027i	0.928788	+	0.370612i	$0.120852\pi$
$569$	18.7336	+	32.4475i	0.785353	+	1.36027i	−0.143434	+	0.989660i	$0.545815\pi$
$570$	−20.7362	+	35.9161i	−0.868544	+	1.50436i
$571$	−8.78514	+	15.2163i	−0.367646	+	0.636782i	−0.989197	−	0.146592i	$-0.953170\pi$
$571$	−8.78514	+	15.2163i	−0.367646	+	0.636782i	0.621551	+	0.783374i	$0.286503\pi$
$572$	−6.94110	−	12.0223i	−0.290222	−	0.502679i
$573$	29.4006			1.22823
$574$	−24.8465	−	55.5691i	−1.03707	−	2.31941i
$575$	−2.20920			−0.0921301
$576$	20.0618	+	34.7481i	0.835908	+	1.44784i
$577$	17.1247	−	29.6608i	0.712910	−	1.23480i	−0.250850	−	0.968026i	$-0.580710\pi$
$577$	17.1247	−	29.6608i	0.712910	−	1.23480i	0.963760	−	0.266770i	$-0.0859565\pi$
$578$	3.01524	−	5.22254i	0.125417	−	0.217229i
$579$	−28.4190	−	49.2232i	−1.18105	−	2.04565i
$580$	36.3125			1.50780
$581$	9.12490	+	0.944459i	0.378565	+	0.0391828i
$582$	−29.6144			−1.22756
$583$	29.6438	+	51.3445i	1.22772	+	2.12647i
$584$	−7.65959	+	13.2668i	−0.316956	+	0.548984i
$585$	3.31453	−	5.74093i	0.137039	−	0.237358i
$586$	23.2859	+	40.3323i	0.961930	+	1.66611i
$587$	−29.4494			−1.21551			−0.607754	−	0.794126i	$-0.707929\pi$
$587$	−29.4494			−1.21551			−0.607754	+	0.794126i	$0.707929\pi$
$588$	−15.6669	−	47.7032i	−0.646092	−	1.96725i
$589$	13.4526			0.554305
$590$	11.2503	+	19.4861i	0.463167	+	0.802229i
$591$	−20.9356	+	36.2616i	−0.861176	+	1.49160i
$592$	3.92275	−	6.79439i	0.161224	−	0.279248i
$593$	17.0001	+	29.4450i	0.698109	+	1.20916i	0.969121	+	0.246584i	$0.0793081\pi$
$593$	17.0001	+	29.4450i	0.698109	+	1.20916i	−0.271013	+	0.962576i	$0.587359\pi$
$594$	3.22064			0.132145
$595$	21.1075	+	2.18470i	0.865324	+	0.0895640i
$596$	8.56514			0.350842
$597$	−12.4452	−	21.5557i	−0.509349	−	0.882218i
$598$	−4.95168	+	8.57655i	−0.202489	+	0.350721i
$599$	−10.7209	+	18.5691i	−0.438043	+	0.758713i	−0.997539	−	0.0701203i	$-0.977662\pi$
$599$	−10.7209	+	18.5691i	−0.438043	+	0.758713i	0.559495	+	0.828834i	$0.310995\pi$
$600$	1.21520	+	2.10479i	0.0496103	+	0.0859276i
$601$	40.4039			1.64811			0.824054	−	0.566511i	$-0.191707\pi$
$601$	40.4039			1.64811			0.824054	+	0.566511i	$0.191707\pi$
$602$	−8.14447	−	18.2151i	−0.331944	−	0.742392i
$603$	−9.05472			−0.368737
$604$	26.8931	+	46.5803i	1.09427	+	1.89533i
$605$	12.6668	−	21.9396i	0.514980	−	0.891971i
$606$	−25.5139	+	44.1914i	−1.03643	+	1.79515i
$607$	21.9456	+	38.0110i	0.890746	+	1.54282i	0.838983	+	0.544158i	$0.183151\pi$
$607$	21.9456	+	38.0110i	0.890746	+	1.54282i	0.0517636	+	0.998659i	$0.483516\pi$
$608$	25.2036			1.02214
$609$	22.6582	−	31.2904i	0.918156	−	1.26795i
$610$	−15.0677			−0.610074
$611$	3.55438	+	6.15636i	0.143795	+	0.249060i
$612$	17.1011	−	29.6200i	0.691272	−	1.19732i
$613$	7.15777	−	12.3976i	0.289100	−	0.500735i	−0.684496	−	0.729017i	$-0.739977\pi$
$613$	7.15777	−	12.3976i	0.289100	−	0.500735i	0.973595	+	0.228282i	$0.0733108\pi$
$614$	5.48750	+	9.50464i	0.221458	+	0.383576i
$615$	−54.6009			−2.20172
$616$	−14.7831	+	20.4151i	−0.595628	+	0.822547i
$617$	−36.9097			−1.48593			−0.742965	−	0.669330i	$-0.766581\pi$
$617$	−36.9097			−1.48593			−0.742965	+	0.669330i	$0.766581\pi$
$618$	−20.0074	−	34.6538i	−0.804815	−	1.39398i
$619$	−7.14646	+	12.3780i	−0.287240	+	0.497515i	−0.973150	−	0.230172i	$-0.926071\pi$
$619$	−7.14646	+	12.3780i	−0.287240	+	0.497515i	0.685910	+	0.727687i	$0.259405\pi$
$620$	−11.6030	+	20.0970i	−0.465988	+	0.807115i
$621$	−0.679774	−	1.17740i	−0.0272784	−	0.0472476i
$622$	−5.35973			−0.214906
$623$	−3.95728	−	8.85046i	−0.158545	−	0.354586i
$624$	−3.45079			−0.138142
$625$	11.1438	+	19.3016i	0.445750	+	0.772062i
$626$	−15.4496	+	26.7594i	−0.617489	+	1.06952i
$627$	21.1357	−	36.6082i	0.844080	−	1.46199i
$628$	14.2036	+	24.6013i	0.566784	+	0.981698i
$629$	−21.2554			−0.847510
$630$	−38.6128	−	3.99656i	−1.53837	−	0.159227i
$631$	−0.0431064			−0.00171604			−0.000858019	−	1.00000i	$-0.500273\pi$
$631$	−0.0431064			−0.00171604			−0.000858019		1.00000i	$0.500273\pi$
$632$	5.15084	+	8.92152i	0.204890	+	0.354879i
$633$	30.2633	−	52.4176i	1.20286	−	2.08341i
$634$	−3.39592	+	5.88190i	−0.134869	+	0.233600i
$635$	−11.1731	−	19.3524i	−0.443390	−	0.767975i
$636$	−88.8004			−3.52116
$637$	6.85161	+	1.43369i	0.271471	+	0.0568048i
$638$	−62.5484			−2.47632
$639$	3.96401	+	6.86587i	0.156814	+	0.271610i
$640$	−15.1860	+	26.3029i	−0.600279	+	1.03971i
$641$	−21.3328	+	36.9494i	−0.842594	+	1.45942i	0.0451008	+	0.998982i	$0.485639\pi$
$641$	−21.3328	+	36.9494i	−0.842594	+	1.45942i	−0.887695	+	0.460433i	$0.847694\pi$
$642$	−18.4765	−	32.0022i	−0.729208	−	1.26303i
$643$	−5.49737			−0.216795			−0.108398	−	0.994108i	$-0.534572\pi$
$643$	−5.49737			−0.216795			−0.108398	+	0.994108i	$0.534572\pi$
$644$	34.1342	+	3.53301i	1.34508	+	0.139220i
$645$	−17.8977			−0.704722
$646$	−14.9156	−	25.8345i	−0.586845	−	1.01645i
$647$	19.0933	−	33.0706i	0.750637	−	1.30014i	−0.196877	−	0.980428i	$-0.563080\pi$
$647$	19.0933	−	33.0706i	0.750637	−	1.30014i	0.947514	−	0.319713i	$-0.103587\pi$
$648$	8.57053	−	14.8446i	0.336682	−	0.583150i
$649$	−11.4671	−	19.8615i	−0.450121	−	0.779633i
$650$	−1.09280			−0.0428633
$651$	10.0775	+	22.5384i	0.394969	+	0.883348i
$652$	40.1024			1.57053
$653$	−19.2510	−	33.3437i	−0.753349	−	1.30484i	−0.946191	−	0.323608i	$-0.895104\pi$
$653$	−19.2510	−	33.3437i	−0.753349	−	1.30484i	0.192843	−	0.981230i	$-0.438229\pi$
$654$	−11.4366	+	19.8088i	−0.447206	+	0.774584i
$655$	5.75711	−	9.97161i	0.224949	−	0.389623i
$656$	7.24820	+	12.5543i	0.282995	+	0.490161i
$657$	24.0477			0.938192
$658$	24.4151	−	33.7166i	0.951798	−	1.31441i
$659$	19.4843			0.759002			0.379501	−	0.925191i	$-0.376096\pi$
$659$	19.4843			0.759002			0.379501	+	0.925191i	$0.376096\pi$
$660$	36.4595	+	63.1498i	1.41919	+	2.45810i
$661$	20.8334	−	36.0844i	0.810324	−	1.40352i	−0.102314	−	0.994752i	$-0.532625\pi$
$661$	20.8334	−	36.0844i	0.810324	−	1.40352i	0.912638	−	0.408770i	$-0.134042\pi$
$662$	−15.0564	+	26.0784i	−0.585182	+	1.01356i
$663$	4.67454	+	8.09654i	0.181544	+	0.314443i
$664$	6.89760			0.267679
$665$	−11.7506	+	16.2273i	−0.455668	+	0.629266i
$666$	38.8834			1.50670
$667$	13.2020	+	22.8665i	0.511182	+	0.885393i
$668$	−25.1520	+	43.5645i	−0.973160	+	1.68556i
$669$	36.2040	−	62.7071i	1.39973	−	2.42440i
$670$	−6.81168	−	11.7982i	−0.263158	−	0.455803i
$671$	15.3580			0.592890
$672$	18.8803	+	42.2258i	0.728324	+	1.62889i
$673$	−14.3157			−0.551830			−0.275915	−	0.961182i	$-0.588981\pi$
$673$	−14.3157			−0.551830			−0.275915	+	0.961182i	$0.588981\pi$
$674$	38.9153	+	67.4033i	1.49896	+	2.59628i
$675$	0.0750110	−	0.129923i	0.00288718	−	0.00500073i
$676$	−1.44940	+	2.51043i	−0.0557460	+	0.0965550i
$677$	14.7641	+	25.5721i	0.567429	+	0.982815i	0.996819	+	0.0796963i	$0.0253950\pi$
$677$	14.7641	+	25.5721i	0.567429	+	0.982815i	−0.429391	+	0.903119i	$0.641272\pi$
$678$	32.3184			1.24118
$679$	−14.2304	−	1.47290i	−0.546114	−	0.0565247i
$680$	15.9554			0.611860
$681$	12.4633	+	21.5871i	0.477596	+	0.827220i
$682$	19.9862	−	34.6172i	0.765312	−	1.32556i
$683$	−23.5349	+	40.7637i	−0.900539	+	1.55978i	−0.0737441	+	0.997277i	$0.523495\pi$
$683$	−23.5349	+	40.7637i	−0.900539	+	1.55978i	−0.826795	+	0.562503i	$0.809839\pi$
$684$	16.1459	+	27.9655i	0.617354	+	1.06929i
$685$	−47.2210			−1.80422
$686$	−8.71296	−	40.0546i	−0.332662	−	1.52929i
$687$	−27.5650			−1.05167
$688$	2.37590	+	4.11518i	0.0905804	+	0.156890i
$689$	6.19003	−	10.7214i	0.235821	−	0.408454i
$690$	26.0097	−	45.0501i	0.990172	−	1.71503i
$691$	15.4334	+	26.7314i	0.587113	+	1.01691i	0.994608	+	0.103703i	$0.0330690\pi$
$691$	15.4334	+	26.7314i	0.587113	+	1.01691i	−0.407495	+	0.913207i	$0.633598\pi$
$692$	−8.58442			−0.326331
$693$	39.3568	+	4.07356i	1.49504	+	0.154742i
$694$	−12.1091			−0.459656
$695$	−4.24559	−	7.35358i	−0.161044	−	0.278937i
$696$	14.5238	−	25.1560i	0.550524	−	0.953535i
$697$	19.6372	−	34.0127i	0.743813	−	1.28832i
$698$	−4.80508	−	8.32264i	−0.181875	−	0.315017i
$699$	−42.2715			−1.59885
$700$	1.54568	+	3.45691i	0.0584211	+	0.130659i
$701$	6.48958			0.245108			0.122554	−	0.992462i	$-0.460892\pi$
$701$	6.48958			0.245108			0.122554	+	0.992462i	$0.460892\pi$
$702$	−0.336257	−	0.582415i	−0.0126912	−	0.0219818i
$703$	10.0341	−	17.3795i	0.378443	−	0.655482i
$704$	30.7657	−	53.2878i	1.15953	−	2.00836i
$705$	−18.6701	−	32.3376i	−0.703157	−	1.21790i
$706$	61.0860			2.29900
$707$	−14.4580	+	19.9661i	−0.543747	+	0.750902i
$708$	34.3505			1.29097
$709$	6.68689	+	11.5820i	0.251131	+	0.434972i	0.963838	−	0.266490i	$-0.0858641\pi$
$709$	6.68689	+	11.5820i	0.251131	+	0.434972i	−0.712706	+	0.701463i	$0.752531\pi$
$710$	−5.96409	+	10.3301i	−0.223828	+	0.387682i
$711$	8.08569	−	14.0048i	0.303237	−	0.525222i
$712$	−3.64475	−	6.31290i	−0.136593	−	0.236586i
$713$	−16.8738			−0.631929
$714$	32.1094	−	44.3424i	1.20167	−	1.65947i
$715$	−10.1660			−0.380186
$716$	8.21645	+	14.2313i	0.307063	+	0.531849i
$717$	−8.56328	+	14.8320i	−0.319802	+	0.553913i
$718$	−7.33555	+	12.7055i	−0.273760	+	0.474167i
$719$	8.37048	+	14.4981i	0.312166	+	0.540688i	0.978831	−	0.204670i	$-0.0656120\pi$
$719$	8.37048	+	14.4981i	0.312166	+	0.540688i	−0.666665	+	0.745358i	$0.732279\pi$
$720$	9.24476			0.344532
$721$	−7.89050	−	17.6471i	−0.293858	−	0.657212i
$722$	−13.8883			−0.516868
$723$	−8.03725	−	13.9209i	−0.298909	−	0.517725i
$724$	−10.4015	+	18.0160i	−0.386570	+	0.669558i
$725$	−1.45680	+	2.52325i	−0.0541041	+	0.0937110i
$726$	−32.6798	−	56.6030i	−1.21286	−	2.10074i
$727$	38.8138			1.43952			0.719761	−	0.694221i	$-0.244251\pi$
$727$	38.8138			1.43952			0.719761	+	0.694221i	$0.244251\pi$
$728$	5.23528	+	0.541869i	0.194032	+	0.0200830i
$729$	−29.1632			−1.08012
$730$	18.0906	+	31.3339i	0.669564	+	1.15972i
$731$	6.43692	−	11.1491i	0.238078	−	0.412364i
$732$	−11.5016	+	19.9213i	−0.425110	+	0.736312i
$733$	−18.8639	−	32.6733i	−0.696756	−	1.20682i	−0.969585	−	0.244754i	$-0.921293\pi$
$733$	−18.8639	−	32.6733i	−0.696756	−	1.20682i	0.272830	−	0.962062i	$-0.412040\pi$
$734$	69.0719			2.54949
$735$	−35.9895	−	7.53074i	−1.32749	−	0.277776i
$736$	−31.6132			−1.16528
$737$	6.94292	+	12.0255i	0.255746	+	0.442965i
$738$	−35.9232	+	62.2208i	−1.32235	+	2.29038i
$739$	4.61476	−	7.99300i	0.169757	−	0.294027i	−0.768578	−	0.639757i	$-0.779035\pi$
$739$	4.61476	−	7.99300i	0.169757	−	0.294027i	0.938334	+	0.345729i	$0.112368\pi$
$740$	17.3090	+	29.9801i	0.636291	+	1.10209i
$741$	−8.82686			−0.324263
$742$	−72.1111	−	7.46375i	−2.64728	−	0.274003i
$743$	−3.56327			−0.130724			−0.0653619	−	0.997862i	$-0.520820\pi$
$743$	−3.56327			−0.130724			−0.0653619	+	0.997862i	$0.520820\pi$
$744$	9.28164	+	16.0763i	0.340282	+	0.589385i
$745$	3.13614	−	5.43195i	0.114899	−	0.199011i
$746$	17.4571	−	30.2366i	0.639151	−	1.10704i
$747$	−5.41386	−	9.37707i	−0.198083	−	0.343089i
$748$	−52.4508			−1.91779
$749$	−7.28674	−	16.2968i	−0.266252	−	0.595472i
$750$	63.8698			2.33220
$751$	−25.6053	−	44.3496i	−0.934350	−	1.61834i	−0.775789	−	0.630992i	$-0.782648\pi$
$751$	−25.6053	−	44.3496i	−0.934350	−	1.61834i	−0.158561	−	0.987349i	$-0.550685\pi$
$752$	−4.95687	+	8.58555i	−0.180758	+	0.313083i
$753$	12.2089	−	21.1464i	0.444916	−	0.770618i
$754$	6.53049	+	11.3111i	0.237826	+	0.411927i
$755$	39.3879			1.43347
$756$	−1.36677	+	1.88747i	−0.0497088	+	0.0686466i
$757$	25.2305			0.917019			0.458509	−	0.888690i	$-0.348384\pi$
$757$	25.2305			0.917019			0.458509	+	0.888690i	$0.348384\pi$
$758$	−35.0272	−	60.6688i	−1.27224	−	2.20359i
$759$	−26.5108	+	45.9181i	−0.962282	+	1.66672i
$760$	−7.53207	+	13.0459i	−0.273217	+	0.473226i
$761$	−1.82372	−	3.15878i	−0.0661099	−	0.114506i	0.831076	−	0.556159i	$-0.187725\pi$
$761$	−1.82372	−	3.15878i	−0.0661099	−	0.114506i	−0.897186	+	0.441653i	$0.854392\pi$
$762$	−57.6520			−2.08851
$763$	−6.48077	+	8.94978i	−0.234620	+	0.324004i
$764$	34.4428			1.24610
$765$	−12.5232	−	21.6908i	−0.452777	−	0.784233i
$766$	−13.7154	+	23.7558i	−0.495558	+	0.858331i
$767$	−2.39448	+	4.14736i	−0.0864596	+	0.149752i
$768$	7.38609	+	12.7931i	0.266523	+	0.461631i
$769$	21.9882			0.792914			0.396457	−	0.918053i	$-0.370240\pi$
$769$	21.9882			0.792914			0.396457	+	0.918053i	$0.370240\pi$
$770$	24.2995	+	54.3458i	0.875693	+	1.95849i
$771$	16.9862			0.611742
$772$	−33.2929	−	57.6650i	−1.19824	−	2.07541i
$773$	−10.9295	+	18.9305i	−0.393108	+	0.680882i	−0.992858	−	0.119305i	$-0.961933\pi$
$773$	−10.9295	+	18.9305i	−0.393108	+	0.680882i	0.599750	+	0.800187i	$0.295267\pi$
$774$	−11.7753	+	20.3954i	−0.423255	+	0.733099i
$775$	−0.930986	−	1.61252i	−0.0334420	−	0.0579233i
$776$	−10.7569			−0.386151
$777$	36.6342	+	3.79176i	1.31424	+	0.136029i
$778$	−31.1505			−1.11680
$779$	18.5404	+	32.1128i	0.664277	+	1.15056i
$780$	7.61326	−	13.1865i	0.272598	−	0.472154i
$781$	6.07900	−	10.5291i	0.217524	−	0.376762i
$782$	18.7088	+	32.4046i	0.669025	+	1.15879i
$783$	−1.79303			−0.0640777
$784$	3.04603	+	9.27468i	0.108787	+	0.331239i
$785$	20.8026			0.742477
$786$	−14.8531	−	25.7263i	−0.529791	−	0.917625i
$787$	−19.9336	+	34.5261i	−0.710557	+	1.23072i	0.254091	+	0.967180i	$0.418224\pi$
$787$	−19.9336	+	34.5261i	−0.710557	+	1.23072i	−0.964648	+	0.263541i	$0.915109\pi$
$788$	−24.5261	+	42.4804i	−0.873706	+	1.51330i
$789$	0.156570	+	0.271188i	0.00557405	+	0.00965454i
$790$	24.3308			0.865651
$791$	15.5298	+	1.60739i	0.552176	+	0.0571521i
$792$	29.7502			1.05713
$793$	−1.60348	−	2.77732i	−0.0569414	−	0.0986254i
$794$	7.71680	−	13.3659i	0.273859	−	0.474338i
$795$	−32.5144	+	56.3166i	−1.15317	+	1.99734i
$796$	−14.5796	−	25.2526i	−0.516759	−	0.895053i
$797$	−40.1971			−1.42385			−0.711927	−	0.702253i	$-0.752178\pi$
$797$	−40.1971			−1.42385			−0.711927	+	0.702253i	$0.752178\pi$
$798$	21.0986	+	47.1871i	0.746884	+	1.67041i
$799$	26.8589			0.950198
$800$	−1.74421	−	3.02106i	−0.0616671	−	0.106811i
$801$	−5.72146	+	9.90986i	−0.202158	+	0.350148i
$802$	−3.02873	+	5.24592i	−0.106948	+	0.185240i
$803$	−18.4392	−	31.9376i	−0.650704	−	1.12705i
$804$	−20.7981			−0.733492
$805$	14.7389	−	20.3541i	0.519478	−	0.717387i
$806$	−8.34680			−0.294003
$807$	5.24960	+	9.09258i	0.184795	+	0.320074i
$808$	−9.26749	+	16.0518i	−0.326029	+	0.564699i
$809$	−1.26924	+	2.19840i	−0.0446243	+	0.0772915i	−0.887475	−	0.460856i	$-0.847542\pi$
$809$	−1.26924	+	2.19840i	−0.0446243	+	0.0772915i	0.842851	+	0.538148i	$0.180876\pi$
$810$	−20.2421	−	35.0603i	−0.711235	−	1.23189i
$811$	−41.7062			−1.46450			−0.732251	−	0.681035i	$-0.761530\pi$
$811$	−41.7062			−1.46450			−0.732251	+	0.681035i	$0.761530\pi$
$812$	26.5441	−	36.6567i	0.931515	−	1.28640i
$813$	3.87801			0.136008
$814$	−29.8148	−	51.6407i	−1.04501	−	1.81001i
$815$	14.6836	−	25.4327i	0.514343	−	0.890868i
$816$	−6.51902	+	11.2913i	−0.228211	+	0.395274i
$817$	6.07737	+	10.5263i	0.212620	+	0.368269i
$818$	−54.2604			−1.89717
$819$	−3.37246	−	7.54251i	−0.117843	−	0.263557i
$820$	−63.9650			−2.23375
$821$	−15.9652	−	27.6525i	−0.557189	−	0.965079i	−0.997730	−	0.0673467i	$-0.978547\pi$
$821$	−15.9652	−	27.6525i	−0.557189	−	0.965079i	0.440541	−	0.897733i	$-0.354787\pi$
$822$	−60.9140	+	105.506i	−2.12462	+	3.67995i
$823$	17.1266	−	29.6641i	0.596995	−	1.03402i	−0.396267	−	0.918135i	$-0.629695\pi$
$823$	17.1266	−	29.6641i	0.596995	−	1.03402i	0.993262	−	0.115890i	$-0.0369720\pi$
$824$	−7.26734	−	12.5874i	−0.253170	−	0.438503i
$825$	−5.85078			−0.203698
$826$	27.8946	+	2.88719i	0.970578	+	0.100458i
$827$	36.9755			1.28576			0.642882	−	0.765965i	$-0.277739\pi$
$827$	36.9755			1.28576			0.642882	+	0.765965i	$0.277739\pi$
$828$	−20.2520	−	35.0775i	−0.703807	−	1.21903i
$829$	9.99473	−	17.3114i	0.347131	−	0.601249i	−0.638607	−	0.769533i	$-0.720489\pi$
$829$	9.99473	−	17.3114i	0.347131	−	0.601249i	0.985739	+	0.168284i	$0.0538225\pi$
$830$	8.14547	−	14.1084i	0.282733	−	0.489708i
$831$	15.7685	+	27.3119i	0.547005	+	0.947440i
$832$	−12.8486			−0.445446
$833$	17.6348	−	19.7106i	0.611009	−	0.682932i
$834$	−21.9068			−0.758571
$835$	18.4189	+	31.9024i	0.637412	+	1.10403i
$836$	24.7605	−	42.8865i	0.856360	−	1.48326i
$837$	0.572931	−	0.992346i	0.0198034	−	0.0343005i
$838$	3.33384	+	5.77438i	0.115166	+	0.199473i
$839$	12.8147			0.442411			0.221206	−	0.975227i	$-0.429001\pi$
$839$	12.8147			0.442411			0.221206	+	0.975227i	$0.429001\pi$
$840$	−27.4994	−	2.84628i	−0.948819	−	0.0982060i
$841$	5.82265			0.200781
$842$	11.0666	+	19.1679i	0.381381	+	0.660571i
$843$	−5.72812	+	9.92140i	−0.197287	+	0.341711i
$844$	35.4535	−	61.4073i	1.22036	−	2.11373i
$845$	1.06140	+	1.83839i	0.0365132	+	0.0632427i
$846$	−49.1340			−1.68926
$847$	−12.8882	−	28.8245i	−0.442845	−	0.990422i
$848$	17.2650			0.592882
$849$	−4.51375	−	7.81805i	−0.154912	−	0.268315i
$850$	−2.06446	+	3.57575i	−0.0708104	+	0.122647i
$851$	−12.5859	+	21.7994i	−0.431439	+	0.747274i
$852$	9.10508	+	15.7705i	0.311935	+	0.540287i
$853$	−30.1839			−1.03348			−0.516739	−	0.856143i	$-0.672854\pi$
$853$	−30.1839			−1.03348			−0.516739	+	0.856143i	$0.672854\pi$
$854$	−11.0143	+	15.2105i	−0.376903	+	0.520494i
$855$	23.6474			0.808724
$856$	−6.71127	−	11.6243i	−0.229386	−	0.397309i
$857$	26.6164	−	46.1009i	0.909197	−	1.57478i	0.0940154	−	0.995571i	$-0.470030\pi$
$857$	26.6164	−	46.1009i	0.909197	−	1.57478i	0.815182	−	0.579205i	$-0.196637\pi$
$858$	−13.1139	+	22.7139i	−0.447700	+	0.775438i
$859$	6.13597	+	10.6278i	0.209357	+	0.362616i	0.951512	−	0.307611i	$-0.0995297\pi$
$859$	6.13597	+	10.6278i	0.209357	+	0.362616i	−0.742155	+	0.670228i	$0.766196\pi$
$860$	−20.9672			−0.714975
$861$	−39.9127	+	55.1185i	−1.36022	+	1.87843i
$862$	−41.5977			−1.41682
$863$	−12.2226	−	21.1702i	−0.416064	−	0.720643i	0.579476	−	0.814989i	$-0.303257\pi$
$863$	−12.2226	−	21.1702i	−0.416064	−	0.720643i	−0.995539	+	0.0943460i	$0.969924\pi$
$864$	1.07339	−	1.85917i	0.0365175	−	0.0632501i
$865$	−3.14320	+	5.44418i	−0.106872	+	0.185108i
$866$	8.59778	+	14.8918i	0.292164	+	0.506043i
$867$	−6.74189			−0.228967
$868$	11.8058	+	26.4037i	0.400716	+	0.896200i
$869$	−24.7996			−0.841268
$870$	−34.3027	−	59.4141i	−1.16297	−	2.01432i
$871$	1.44978	−	2.51109i	0.0491238	−	0.0850850i
$872$	−4.15415	+	7.19519i	−0.140677	+	0.243660i
$873$	8.44300	+	14.6237i	0.285752	+	0.494937i
$874$	−35.3276			−1.19497
$875$	30.6910	+	3.17663i	1.03755	+	0.107390i
$876$	55.2361			1.86625
$877$	26.4376	+	45.7913i	0.892736	+	1.54626i	0.836582	+	0.547842i	$0.184550\pi$
$877$	26.4376	+	45.7913i	0.892736	+	1.54626i	0.0561539	+	0.998422i	$0.482116\pi$
$878$	42.0178	−	72.7770i	1.41803	−	2.45611i
$879$	26.0329	−	45.0903i	0.878068	−	1.52086i
$880$	−7.08864	−	12.2779i	−0.238958	−	0.413887i
$881$	55.0118			1.85339			0.926697	−	0.375809i	$-0.122635\pi$
$881$	55.0118			1.85339			0.926697	+	0.375809i	$0.122635\pi$
$882$	−32.2600	+	36.0574i	−1.08625	+	1.21412i
$883$	44.1730			1.48654			0.743269	−	0.668992i	$-0.233274\pi$
$883$	44.1730			1.48654			0.743269	+	0.668992i	$0.233274\pi$
$884$	5.47622	+	9.48510i	0.184185	+	0.319018i
$885$	12.5775	−	21.7848i	0.422788	−	0.732290i
$886$	−39.4270	+	68.2895i	−1.32457	+	2.29423i
$887$	2.54330	+	4.40512i	0.0853955	+	0.147909i	0.905560	−	0.424219i	$-0.139451\pi$
$887$	2.54330	+	4.40512i	0.0853955	+	0.147909i	−0.820164	+	0.572128i	$0.806118\pi$
$888$	27.6921			0.929286
$889$	−27.7032	−	2.86738i	−0.929136	−	0.0961688i
$890$	−17.2165			−0.577100
$891$	20.6321	+	35.7359i	0.691202	+	1.19720i
$892$	42.4130	−	73.4614i	1.42009	−	2.45967i
$893$	−12.6793	+	21.9612i	−0.424296	+	0.734903i
$894$	−8.09108	−	14.0142i	−0.270606	−	0.468704i
$895$	12.0339			0.402248
$896$	15.4514	+	34.5571i	0.516196	+	1.15447i
$897$	11.0717			0.369672
$898$	8.91178	+	15.4356i	0.297390	+	0.515094i
$899$	−11.1270	+	19.2724i	−0.371105	+	0.642772i
$900$	2.23475	−	3.87070i	0.0744917	−	0.129023i
$901$	−23.3876	−	40.5086i	−0.779155	−	1.34954i
$902$	110.180			3.66859
$903$	−13.0830	+	18.0674i	−0.435377	+	0.601244i
$904$	11.7391			0.390437
$905$	7.61706	+	13.1931i	0.253200	+	0.438555i
$906$	50.8094	−	88.0044i	1.68803	−	2.92375i
$907$	9.06264	−	15.6969i	0.300920	−	0.521209i	−0.675425	−	0.737429i	$-0.736040\pi$
$907$	9.06264	−	15.6969i	0.300920	−	0.521209i	0.976345	+	0.216220i	$0.0693730\pi$
$908$	14.6008	+	25.2893i	0.484544	+	0.839255i
$909$	29.0958			0.965048
$910$	7.29075	−	10.0683i	0.241686	−	0.333763i
$911$	−9.65804			−0.319985			−0.159993	−	0.987118i	$-0.551147\pi$
$911$	−9.65804			−0.319985			−0.159993	+	0.987118i	$0.551147\pi$
$912$	−6.15489	−	10.6606i	−0.203809	−	0.353007i
$913$	−8.30241	+	14.3802i	−0.274770	+	0.475915i
$914$	−17.2613	+	29.8974i	−0.570952	+	0.988918i
$915$	8.42263	+	14.5884i	0.278444	+	0.482278i
$916$	−32.2924			−1.06697
$917$	−5.85774	−	13.1008i	−0.193440	−	0.432628i
$918$	−2.54095			−0.0838637
$919$	−23.8801	−	41.3616i	−0.787733	−	1.36439i	−0.927353	−	0.374188i	$-0.877922\pi$
$919$	−23.8801	−	41.3616i	−0.787733	−	1.36439i	0.139620	−	0.990205i	$-0.455412\pi$
$920$	9.44758	−	16.3637i	0.311477	−	0.539495i
$921$	6.13487	−	10.6259i	0.202151	−	0.350135i
$922$	28.4401	+	49.2598i	0.936626	+	1.62228i
$923$	−2.53876			−0.0835643
$924$	90.4000	+	9.35670i	2.97394	+	0.307813i
$925$	−2.77763			−0.0913279
$926$	22.7096	+	39.3342i	0.746285	+	1.29260i
$927$	−11.4081	+	19.7595i	−0.374692	+	0.648986i
$928$	−20.8464	+	36.1071i	−0.684317	+	1.18527i
$929$	−16.9905	−	29.4285i	−0.557442	−	0.965517i	−0.997709	−	0.0676505i	$-0.978450\pi$
$929$	−16.9905	−	29.4285i	−0.557442	−	0.965517i	0.440267	−	0.897867i	$-0.354884\pi$
$930$	43.8433			1.43768
$931$	7.79153	+	23.7239i	0.255357	+	0.777520i
$932$	−49.5210			−1.62212
$933$	2.99601	+	5.18924i	0.0980850	+	0.169888i
$934$	−13.0861	+	22.6657i	−0.428189	+	0.741645i
$935$	−19.2049	+	33.2639i	−0.628068	+	1.08785i
$936$	−3.10612	−	5.37996i	−0.101527	−	0.175849i
$937$	−24.7948			−0.810012			−0.405006	−	0.914314i	$-0.632731\pi$
$937$	−24.7948			−0.810012			−0.405006	+	0.914314i	$0.632731\pi$
$938$	−16.8893	−	1.74810i	−0.551454	−	0.0570774i
$939$	34.5443			1.12731
$940$	−21.8720	−	37.8835i	−0.713387	−	1.23562i
$941$	4.12098	−	7.13774i	0.134340	−	0.232684i	−0.791005	−	0.611810i	$-0.790442\pi$
$941$	4.12098	−	7.13774i	0.134340	−	0.232684i	0.925345	+	0.379126i	$0.123775\pi$
$942$	26.8349	−	46.4793i	0.874327	−	1.51438i
$943$	−23.2554	−	40.2796i	−0.757301	−	1.31168i
$944$	−6.67859			−0.217370
$945$	0.696577	+	1.55789i	0.0226596	+	0.0506783i
$946$	36.1160			1.17423
$947$	−9.98643	−	17.2970i	−0.324515	−	0.562077i	0.656899	−	0.753979i	$-0.271868\pi$
$947$	−9.98643	−	17.2970i	−0.324515	−	0.562077i	−0.981414	+	0.191902i	$0.938535\pi$
$948$	18.5723	−	32.1682i	0.603200	−	1.04477i
$949$	−3.85035	+	6.66901i	−0.124988	+	0.216485i
$950$	−1.94914	−	3.37602i	−0.0632386	−	0.109532i
$951$	7.59307			0.246222
$952$	11.6632	−	16.1066i	0.378007	−	0.522018i
$953$	−21.5341			−0.697557			−0.348778	−	0.937205i	$-0.613403\pi$
$953$	−21.5341			−0.697557			−0.348778	+	0.937205i	$0.613403\pi$
$954$	42.7839	+	74.1040i	1.38518	+	2.39920i
$955$	12.6113	−	21.8434i	0.408091	−	0.706835i
$956$	−10.0319	+	17.3757i	−0.324455	+	0.561972i
$957$	34.9636	+	60.5588i	1.13021	+	1.95759i
$958$	50.1432			1.62005
$959$	−34.5181	+	47.6686i	−1.11465	+	1.53930i
$960$	67.4900			2.17823
$961$	8.38917	+	14.5305i	0.270618	+	0.468725i
$962$	−6.22574	+	10.7833i	−0.200726	+	0.347667i
$963$	−10.5352	+	18.2475i	−0.339492	+	0.588018i
$964$	−9.41564	−	16.3084i	−0.303257	−	0.525257i
$965$	−48.7610			−1.56967
$966$	−26.4643	−	59.1874i	−0.851476	−	1.90432i
$967$	43.2887			1.39207			0.696036	−	0.718007i	$-0.254945\pi$
$967$	43.2887			1.39207			0.696036	+	0.718007i	$0.254945\pi$
$968$	−11.8704	−	20.5601i	−0.381528	−	0.660827i
$969$	−16.6752	+	28.8822i	−0.535683	+	0.927831i
$970$	−12.7030	+	22.0022i	−0.407868	+	0.706449i
$971$	26.3356	+	45.6147i	0.845151	+	1.46384i	0.885490	+	0.464658i	$0.153823\pi$
$971$	26.3356	+	45.6147i	0.845151	+	1.46384i	−0.0403390	+	0.999186i	$0.512844\pi$
$972$	−64.4476			−2.06716
$973$	−10.5268	−	1.08956i	−0.337473	−	0.0349296i
$974$	−72.4127			−2.32025
$975$	0.610862	+	1.05804i	0.0195632	+	0.0338845i
$976$	2.23619	−	3.87319i	0.0715787	−	0.123978i
$977$	−7.70305	+	13.3421i	−0.246442	+	0.426851i	−0.962536	−	0.271153i	$-0.912595\pi$
$977$	−7.70305	+	13.3421i	−0.246442	+	0.426851i	0.716094	+	0.698004i	$0.245928\pi$
$978$	−37.8829	−	65.6151i	−1.21136	−	2.09814i
$979$	17.5483			0.560845
$980$	−42.1617	−	8.82227i	−1.34681	−	0.281817i
$981$	13.0422			0.416405
$982$	−6.83121	−	11.8320i	−0.217993	−	0.377575i
$983$	−3.79073	+	6.56574i	−0.120906	+	0.209415i	−0.920125	−	0.391625i	$-0.871913\pi$
$983$	−3.79073	+	6.56574i	−0.120906	+	0.209415i	0.799219	+	0.601039i	$0.205246\pi$
$984$	−25.5839	+	44.3126i	−0.815584	+	1.41263i
$985$	17.9605	+	31.1085i	0.572270	+	0.991201i
$986$	49.3480			1.57156
$987$	−46.2918	−	4.79136i	−1.47348	−	0.152511i
$988$	−10.3407			−0.328981
$989$	−7.62293	−	13.2033i	−0.242395	−	0.419841i
$990$	35.1323	−	60.8510i	1.11658	−	1.93397i
$991$	9.50923	−	16.4705i	0.302071	−	0.523202i	−0.674534	−	0.738244i	$-0.735655\pi$
$991$	9.50923	−	16.4705i	0.302071	−	0.523202i	0.976605	+	0.215042i	$0.0689888\pi$
$992$	−13.3222	−	23.0747i	−0.422980	−	0.732623i
$993$	33.6651			1.06833
$994$	6.06834	+	13.5718i	0.192476	+	0.430472i
$995$	−21.3533			−0.676946
$996$	−12.4353	−	21.5385i	−0.394027	−	0.682474i
$997$	−23.0499	+	39.9236i	−0.729998	+	1.26439i	0.226885	+	0.973922i	$0.427146\pi$
$997$	−23.0499	+	39.9236i	−0.729998	+	1.26439i	−0.956883	+	0.290473i	$0.906187\pi$
$998$	16.2001	−	28.0593i	0.512804	−	0.888202i
$999$	−0.854680	−	1.48035i	−0.0270409	−	0.0468362i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.e.c.53.2	✓	10
3.2	odd	2		819.2.j.h.235.4		10
4.3	odd	2		1456.2.r.p.417.5		10
7.2	even	3	inner	91.2.e.c.79.2	yes	10
7.3	odd	6		637.2.a.k.1.4		5
7.4	even	3		637.2.a.l.1.4		5
7.5	odd	6		637.2.e.m.79.2		10
7.6	odd	2		637.2.e.m.508.2		10
13.12	even	2		1183.2.e.f.508.4		10
21.2	odd	6		819.2.j.h.352.4		10
21.11	odd	6		5733.2.a.bl.1.2		5
21.17	even	6		5733.2.a.bm.1.2		5
28.23	odd	6		1456.2.r.p.625.5		10
91.25	even	6		8281.2.a.bw.1.2		5
91.38	odd	6		8281.2.a.bx.1.2		5
91.51	even	6		1183.2.e.f.170.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.2	✓	10	1.1	even	1	trivial
91.2.e.c.79.2	yes	10	7.2	even	3	inner
637.2.a.k.1.4		5	7.3	odd	6
637.2.a.l.1.4		5	7.4	even	3
637.2.e.m.79.2		10	7.5	odd	6
637.2.e.m.508.2		10	7.6	odd	2
819.2.j.h.235.4		10	3.2	odd	2
819.2.j.h.352.4		10	21.2	odd	6
1183.2.e.f.170.4		10	91.51	even	6
1183.2.e.f.508.4		10	13.12	even	2
1456.2.r.p.417.5		10	4.3	odd	2
1456.2.r.p.625.5		10	28.23	odd	6
5733.2.a.bl.1.2		5	21.11	odd	6
5733.2.a.bm.1.2		5	21.17	even	6
8281.2.a.bw.1.2		5	91.25	even	6
8281.2.a.bx.1.2		5	91.38	odd	6

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.10666 - 1.91679i) q^{2} +(-1.23721 + 2.14292i) q^{3} +(-1.44940 + 2.51043i) q^{4} +(1.06140 + 1.83839i) q^{5} +5.47671 q^{6} +(2.63169 + 0.272389i) q^{7} +1.98932 q^{8} +(-1.56140 - 2.70442i) q^{9} +O(q^{10})\)	\(q+(-1.10666 - 1.91679i) q^{2} +(-1.23721 + 2.14292i) q^{3} +(-1.44940 + 2.51043i) q^{4} +(1.06140 + 1.83839i) q^{5} +5.47671 q^{6} +(2.63169 + 0.272389i) q^{7} +1.98932 q^{8} +(-1.56140 - 2.70442i) q^{9} +(2.34921 - 4.06896i) q^{10} +(-2.39448 + 4.14736i) q^{11} +(-3.58643 - 6.21188i) q^{12} +1.00000 q^{13} +(-2.39028 - 5.34585i) q^{14} -5.25271 q^{15} +(0.697291 + 1.20774i) q^{16} +(1.88914 - 3.27208i) q^{17} +(-3.45588 + 5.98575i) q^{18} +(1.78362 + 3.08931i) q^{19} -6.15355 q^{20} +(-3.83967 + 5.30250i) q^{21} +10.5995 q^{22} +(-2.23721 - 3.87497i) q^{23} +(-2.46122 + 4.26295i) q^{24} +(0.246870 - 0.427591i) q^{25} +(-1.10666 - 1.91679i) q^{26} +0.303848 q^{27} +(-4.49818 + 6.21188i) q^{28} -5.90107 q^{29} +(5.81296 + 10.0683i) q^{30} +(1.88558 - 3.26592i) q^{31} +(3.53265 - 6.11873i) q^{32} +(-5.92496 - 10.2623i) q^{33} -8.36254 q^{34} +(2.29251 + 5.12720i) q^{35} +9.05234 q^{36} +(-2.81285 - 4.87200i) q^{37} +(3.94772 - 6.83765i) q^{38} +(-1.23721 + 2.14292i) q^{39} +(2.11146 + 3.65716i) q^{40} +10.3948 q^{41} +(14.4130 + 1.49180i) q^{42} +3.40733 q^{43} +(-6.94110 - 12.0223i) q^{44} +(3.31453 - 5.74093i) q^{45} +(-4.95168 + 8.57655i) q^{46} +(3.55438 + 6.15636i) q^{47} -3.45079 q^{48} +(6.85161 + 1.43369i) q^{49} -1.09280 q^{50} +(4.67454 + 8.09654i) q^{51} +(-1.44940 + 2.51043i) q^{52} +(6.19003 - 10.7214i) q^{53} +(-0.336257 - 0.582415i) q^{54} -10.1660 q^{55} +(5.23528 + 0.541869i) q^{56} -8.82686 q^{57} +(6.53049 + 11.3111i) q^{58} +(-2.39448 + 4.14736i) q^{59} +(7.61326 - 13.1865i) q^{60} +(-1.60348 - 2.77732i) q^{61} -8.34680 q^{62} +(-3.37246 - 7.54251i) q^{63} -12.8486 q^{64} +(1.06140 + 1.83839i) q^{65} +(-13.1139 + 22.7139i) q^{66} +(1.44978 - 2.51109i) q^{67} +(5.47622 + 9.48510i) q^{68} +11.0717 q^{69} +(7.29075 - 10.0683i) q^{70} -2.53876 q^{71} +(-3.10612 - 5.37996i) q^{72} +(-3.85035 + 6.66901i) q^{73} +(-6.22574 + 10.7833i) q^{74} +(0.610862 + 1.05804i) q^{75} -10.3407 q^{76} +(-7.43122 + 10.2623i) q^{77} +5.47671 q^{78} +(2.58925 + 4.48471i) q^{79} +(-1.48021 + 2.56379i) q^{80} +(4.30827 - 7.46214i) q^{81} +(-11.5035 - 19.9247i) q^{82} +3.46731 q^{83} +(-7.74633 - 17.3247i) q^{84} +8.02051 q^{85} +(-3.77076 - 6.53115i) q^{86} +(7.30089 - 12.6455i) q^{87} +(-4.76338 + 8.25042i) q^{88} +(-1.83216 - 3.17339i) q^{89} -14.6722 q^{90} +(2.63169 + 0.272389i) q^{91} +12.9704 q^{92} +(4.66574 + 8.08129i) q^{93} +(7.86698 - 13.6260i) q^{94} +(-3.78625 + 6.55798i) q^{95} +(8.74129 + 15.1404i) q^{96} -5.40733 q^{97} +(-4.83432 - 14.7197i) q^{98} +14.9549 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 8 q^{4} - 2 q^{5} - 10 q^{6} + q^{7} + 18 q^{8} - 3 q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 - 8 * q^4 - 2 * q^5 - 10 * q^6 + q^7 + 18 * q^8 - 3 * q^9	\( 10 q - 4 q^{2} - 8 q^{4} - 2 q^{5} - 10 q^{6} + q^{7} + 18 q^{8} - 3 q^{9} + 5 q^{10} - 11 q^{11} - 5 q^{12} + 10 q^{13} + 10 q^{14} - 10 q^{16} + 5 q^{17} - 9 q^{18} - 9 q^{19} + 2 q^{20} + 2 q^{21} + 16 q^{22} - 10 q^{23} - 9 q^{25} - 4 q^{26} + 37 q^{28} - 6 q^{29} + 13 q^{30} + 6 q^{31} - 22 q^{32} - 8 q^{33} - 44 q^{34} - 4 q^{35} + 14 q^{36} - 4 q^{37} + 10 q^{38} - 28 q^{40} + 28 q^{41} + 52 q^{42} + 4 q^{43} + 32 q^{45} - 3 q^{46} - q^{47} - 46 q^{48} - 11 q^{49} + 18 q^{50} + 8 q^{51} - 8 q^{52} - 17 q^{53} - 23 q^{54} - 21 q^{56} - 32 q^{57} + 27 q^{58} - 11 q^{59} + 29 q^{60} + 11 q^{61} - 46 q^{62} + 5 q^{63} + 18 q^{64} - 2 q^{65} - 21 q^{66} - 13 q^{67} + 32 q^{68} + 36 q^{69} + 49 q^{70} + 30 q^{71} + 19 q^{72} + 33 q^{74} + 20 q^{75} + 16 q^{76} - 46 q^{77} - 10 q^{78} - 2 q^{79} - 55 q^{80} + 19 q^{81} - 34 q^{82} + 12 q^{83} - 23 q^{84} - 44 q^{85} - 28 q^{86} + 8 q^{87} + 3 q^{88} + 4 q^{89} - 68 q^{90} + q^{91} + 42 q^{92} - 18 q^{93} - 20 q^{94} + 12 q^{95} + 37 q^{96} - 24 q^{97} - 7 q^{98} + 22 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 - 8 * q^4 - 2 * q^5 - 10 * q^6 + q^7 + 18 * q^8 - 3 * q^9 + 5 * q^10 - 11 * q^11 - 5 * q^12 + 10 * q^13 + 10 * q^14 - 10 * q^16 + 5 * q^17 - 9 * q^18 - 9 * q^19 + 2 * q^20 + 2 * q^21 + 16 * q^22 - 10 * q^23 - 9 * q^25 - 4 * q^26 + 37 * q^28 - 6 * q^29 + 13 * q^30 + 6 * q^31 - 22 * q^32 - 8 * q^33 - 44 * q^34 - 4 * q^35 + 14 * q^36 - 4 * q^37 + 10 * q^38 - 28 * q^40 + 28 * q^41 + 52 * q^42 + 4 * q^43 + 32 * q^45 - 3 * q^46 - q^47 - 46 * q^48 - 11 * q^49 + 18 * q^50 + 8 * q^51 - 8 * q^52 - 17 * q^53 - 23 * q^54 - 21 * q^56 - 32 * q^57 + 27 * q^58 - 11 * q^59 + 29 * q^60 + 11 * q^61 - 46 * q^62 + 5 * q^63 + 18 * q^64 - 2 * q^65 - 21 * q^66 - 13 * q^67 + 32 * q^68 + 36 * q^69 + 49 * q^70 + 30 * q^71 + 19 * q^72 + 33 * q^74 + 20 * q^75 + 16 * q^76 - 46 * q^77 - 10 * q^78 - 2 * q^79 - 55 * q^80 + 19 * q^81 - 34 * q^82 + 12 * q^83 - 23 * q^84 - 44 * q^85 - 28 * q^86 + 8 * q^87 + 3 * q^88 + 4 * q^89 - 68 * q^90 + q^91 + 42 * q^92 - 18 * q^93 - 20 * q^94 + 12 * q^95 + 37 * q^96 - 24 * q^97 - 7 * q^98 + 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more