LMFDB - Embedded newform 950.2.l.h.301.1

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:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 12x^{10} + 105x^{8} + 394x^{6} + 1077x^{4} + 1443x^{2} + 1369 $ x^12 + 12x^10 + 105x^8 + 394x^6 + 1077x^4 + 1443*x^2 + 1369
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			301.1
Root			$1.36120 - 2.35767i$ of defining polynomial
Character	$\chi$	$=$	950.301
Dual form			950.2.l.h.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(-2.55822 + 0.931116i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-2.55822 - 0.931116i) q^{6} +(-2.33394 - 4.04250i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(3.37939 - 2.83564i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(-2.55822 + 0.931116i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-2.55822 - 0.931116i) q^{6} +(-2.33394 - 4.04250i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(3.37939 - 2.83564i) q^{9} +(0.0690243 - 0.119554i) q^{11} +(-1.36120 - 2.35767i) q^{12} +(3.59307 + 1.30777i) q^{13} +(0.810569 - 4.59697i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(4.53081 + 3.80180i) q^{17} +4.41147 q^{18} +(-3.96789 - 1.80439i) q^{19} +(9.73478 + 8.16845i) q^{21} +(0.129723 - 0.0472154i) q^{22} +(1.04580 + 5.93104i) q^{23} +(0.472740 - 2.68104i) q^{24} +(1.91183 + 3.31139i) q^{26} +(-1.92130 + 3.32779i) q^{27} +(3.57581 - 3.00046i) q^{28} +(4.90120 - 4.11259i) q^{29} +(2.80760 + 4.86291i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-0.0652611 + 0.370114i) q^{33} +(1.02705 + 5.82470i) q^{34} +(3.37939 + 2.83564i) q^{36} -2.34850 q^{37} +(-1.87974 - 3.93276i) q^{38} -10.4096 q^{39} +(-1.71002 + 0.622395i) q^{41} +(2.20670 + 12.5148i) q^{42} +(-1.14606 + 6.49960i) q^{43} +(0.129723 + 0.0472154i) q^{44} +(-3.01127 + 5.21567i) q^{46} +(5.39812 - 4.52956i) q^{47} +(2.08548 - 1.74993i) q^{48} +(-7.39456 + 12.8078i) q^{49} +(-15.1307 - 5.50714i) q^{51} +(-0.663973 + 3.76558i) q^{52} +(-0.642011 - 3.64102i) q^{53} +(-3.61086 + 1.31425i) q^{54} +4.66788 q^{56} +(11.8308 + 0.921455i) q^{57} +6.39806 q^{58} +(6.81662 + 5.71983i) q^{59} +(1.58755 + 9.00344i) q^{61} +(-0.975069 + 5.52989i) q^{62} +(-19.3504 - 7.04296i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.287898 + 0.241575i) q^{66} +(-3.35029 + 2.81122i) q^{67} +(-2.95728 + 5.12215i) q^{68} +(-8.19789 - 14.1992i) q^{69} +(0.856537 - 4.85766i) q^{71} +(0.766044 + 4.34445i) q^{72} +(9.44311 - 3.43701i) q^{73} +(-1.79905 - 1.50958i) q^{74} +(1.08796 - 4.22094i) q^{76} -0.644394 q^{77} +(-7.97418 - 6.69113i) q^{78} +(13.0782 - 4.76006i) q^{79} +(-0.481582 + 2.73119i) q^{81} +(-1.71002 - 0.622395i) q^{82} +(5.98005 + 10.3577i) q^{83} +(-6.35393 + 11.0053i) q^{84} +(-5.05579 + 4.24231i) q^{86} +(-8.70905 + 15.0845i) q^{87} +(0.0690243 + 0.119554i) q^{88} +(11.7821 + 4.28835i) q^{89} +(-3.09935 - 17.5773i) q^{91} +(-5.65933 + 2.05983i) q^{92} +(-11.7104 - 9.82619i) q^{93} +7.04674 q^{94} +2.72240 q^{96} +(-5.18524 - 4.35093i) q^{97} +(-13.8972 + 5.05818i) q^{98} +(-0.105751 - 0.599745i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{7} - 6 q^{8} + 18 q^{9}+O(q^{10}) $ 12 * q - 6 * q^7 - 6 * q^8 + 18 * q^9	$ 12 q - 6 q^{7} - 6 q^{8} + 18 q^{9} + 6 q^{11} - 6 q^{13} + 18 q^{17} + 12 q^{18} + 12 q^{21} + 6 q^{22} + 30 q^{23} - 6 q^{29} + 6 q^{31} + 24 q^{33} + 18 q^{36} - 36 q^{37} - 18 q^{38} - 36 q^{39} - 6 q^{41} + 30 q^{42} + 6 q^{44} - 12 q^{46} + 6 q^{47} - 18 q^{49} + 12 q^{52} + 12 q^{53} + 12 q^{56} + 18 q^{57} + 36 q^{58} - 24 q^{59} - 30 q^{61} + 6 q^{62} - 18 q^{63} - 6 q^{64} + 24 q^{66} - 12 q^{67} - 12 q^{68} + 6 q^{69} - 42 q^{71} - 6 q^{73} + 6 q^{74} + 18 q^{76} + 24 q^{77} - 48 q^{78} + 60 q^{79} + 18 q^{81} - 6 q^{82} - 24 q^{83} - 24 q^{84} - 36 q^{86} - 54 q^{87} + 6 q^{88} - 12 q^{89} + 24 q^{91} - 24 q^{92} - 6 q^{93} + 60 q^{94} - 30 q^{97} - 36 q^{98} - 12 q^{99}+O(q^{100}) $ 12 * q - 6 * q^7 - 6 * q^8 + 18 * q^9 + 6 * q^11 - 6 * q^13 + 18 * q^17 + 12 * q^18 + 12 * q^21 + 6 * q^22 + 30 * q^23 - 6 * q^29 + 6 * q^31 + 24 * q^33 + 18 * q^36 - 36 * q^37 - 18 * q^38 - 36 * q^39 - 6 * q^41 + 30 * q^42 + 6 * q^44 - 12 * q^46 + 6 * q^47 - 18 * q^49 + 12 * q^52 + 12 * q^53 + 12 * q^56 + 18 * q^57 + 36 * q^58 - 24 * q^59 - 30 * q^61 + 6 * q^62 - 18 * q^63 - 6 * q^64 + 24 * q^66 - 12 * q^67 - 12 * q^68 + 6 * q^69 - 42 * q^71 - 6 * q^73 + 6 * q^74 + 18 * q^76 + 24 * q^77 - 48 * q^78 + 60 * q^79 + 18 * q^81 - 6 * q^82 - 24 * q^83 - 24 * q^84 - 36 * q^86 - 54 * q^87 + 6 * q^88 - 12 * q^89 + 24 * q^91 - 24 * q^92 - 6 * q^93 + 60 * q^94 - 30 * q^97 - 36 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	−2.55822	+	0.931116i	−1.47699	+	0.537580i	−0.949989	−	0.312284i	$-0.898906\pi$
$3$	−2.55822	+	0.931116i	−1.47699	+	0.537580i	−0.527001	+	0.849865i	$0.676684\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$		0			0
$5$		0			0
$6$	−2.55822	−	0.931116i	−1.04439	−	0.380127i
$7$	−2.33394	−	4.04250i	−0.882147	−	1.52792i	−0.848949	−	0.528474i	$-0.822764\pi$
$7$	−2.33394	−	4.04250i	−0.882147	−	1.52792i	−0.0331977	−	0.999449i	$-0.510569\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	3.37939	−	2.83564i	1.12646	−	0.945214i
$10$		0			0
$11$	0.0690243	−	0.119554i	0.0208116	−	0.0360467i	−0.855432	−	0.517915i	$-0.826708\pi$
$11$	0.0690243	−	0.119554i	0.0208116	−	0.0360467i	0.876244	+	0.481868i	$0.160042\pi$
$12$	−1.36120	−	2.35767i	−0.392945	−	0.680601i
$13$	3.59307	+	1.30777i	0.996538	+	0.362710i	0.788249	−	0.615357i	$-0.210988\pi$
$13$	3.59307	+	1.30777i	0.996538	+	0.362710i	0.208290	+	0.978067i	$0.433210\pi$
$14$	0.810569	−	4.59697i	0.216634	−	1.22859i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	4.53081	+	3.80180i	1.09888	+	0.922072i	0.997349	−	0.0727597i	$-0.0231806\pi$
$17$	4.53081	+	3.80180i	1.09888	+	0.922072i	0.101534	+	0.994832i	$0.467625\pi$
$18$	4.41147			1.03979
$19$	−3.96789	−	1.80439i	−0.910297	−	0.413955i
$19$	−3.96789	−	1.80439i	−0.910297	−	0.413955i
$20$		0			0
$21$	9.73478	+	8.16845i	2.12430	+	1.78250i
$22$	0.129723	−	0.0472154i	0.0276571	−	0.0100664i
$23$	1.04580	+	5.93104i	0.218065	+	1.23671i	0.875508	+	0.483204i	$0.160527\pi$
$23$	1.04580	+	5.93104i	0.218065	+	1.23671i	−0.657443	+	0.753504i	$0.728362\pi$
$24$	0.472740	−	2.68104i	0.0964977	−	0.547266i
$25$		0			0
$26$	1.91183	+	3.31139i	0.374941	+	0.649417i
$27$	−1.92130	+	3.32779i	−0.369754	+	0.640433i
$28$	3.57581	−	3.00046i	0.675764	−	0.567033i
$29$	4.90120	−	4.11259i	0.910130	−	0.763690i	−0.0620139	−	0.998075i	$-0.519752\pi$
$29$	4.90120	−	4.11259i	0.910130	−	0.763690i	0.972144	+	0.234386i	$0.0753079\pi$
$30$		0			0
$31$	2.80760	+	4.86291i	0.504260	+	0.873404i	0.999988	+	0.00492597i	$0.00156799\pi$
$31$	2.80760	+	4.86291i	0.504260	+	0.873404i	−0.495728	+	0.868478i	$0.665099\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	−0.0652611	+	0.370114i	−0.0113605	+	0.0644286i
$34$	1.02705	+	5.82470i	0.176138	+	0.998928i
$35$		0			0
$36$	3.37939	+	2.83564i	0.563231	+	0.472607i
$37$	−2.34850			−0.386090			−0.193045	−	0.981190i	$-0.561836\pi$
$37$	−2.34850			−0.386090			−0.193045	+	0.981190i	$0.561836\pi$
$38$	−1.87974	−	3.93276i	−0.304935	−	0.637977i
$39$	−10.4096			−1.66686
$40$		0			0
$41$	−1.71002	+	0.622395i	−0.267060	+	0.0972018i	−0.472079	−	0.881556i	$-0.656496\pi$
$41$	−1.71002	+	0.622395i	−0.267060	+	0.0972018i	0.205020	+	0.978758i	$0.434274\pi$
$42$	2.20670	+	12.5148i	0.340501	+	1.93107i
$43$	−1.14606	+	6.49960i	−0.174772	+	0.991180i	0.763635	+	0.645648i	$0.223413\pi$
$43$	−1.14606	+	6.49960i	−0.174772	+	0.991180i	−0.938407	+	0.345532i	$0.887698\pi$
$44$	0.129723	+	0.0472154i	0.0195565	+	0.00711798i
$45$		0			0
$46$	−3.01127	+	5.21567i	−0.443987	+	0.769009i
$47$	5.39812	−	4.52956i	0.787397	−	0.660704i	−0.157703	−	0.987487i	$-0.550409\pi$
$47$	5.39812	−	4.52956i	0.787397	−	0.660704i	0.945100	+	0.326782i	$0.105964\pi$
$48$	2.08548	−	1.74993i	0.301013	−	0.252580i
$49$	−7.39456	+	12.8078i	−1.05637	+	1.82968i
$50$		0			0
$51$	−15.1307	−	5.50714i	−2.11873	−	0.771154i
$52$	−0.663973	+	3.76558i	−0.0920764	+	0.522191i
$53$	−0.642011	−	3.64102i	−0.0881870	−	0.500133i	−0.996623	−	0.0821099i	$-0.973834\pi$
$53$	−0.642011	−	3.64102i	−0.0881870	−	0.500133i	0.908436	−	0.418023i	$-0.137277\pi$
$54$	−3.61086	+	1.31425i	−0.491376	+	0.178846i
$55$		0			0
$56$	4.66788			0.623772
$57$	11.8308	+	0.921455i	1.56703	+	0.122050i
$58$	6.39806			0.840107
$59$	6.81662	+	5.71983i	0.887449	+	0.744658i	0.967697	−	0.252117i	$-0.0811268\pi$
$59$	6.81662	+	5.71983i	0.887449	+	0.744658i	−0.0802481	+	0.996775i	$0.525571\pi$
$60$		0			0
$61$	1.58755	+	9.00344i	0.203265	+	1.15277i	0.900147	+	0.435587i	$0.143459\pi$
$61$	1.58755	+	9.00344i	0.203265	+	1.15277i	−0.696882	+	0.717186i	$0.745430\pi$
$62$	−0.975069	+	5.52989i	−0.123834	+	0.702297i
$63$	−19.3504	−	7.04296i	−2.43792	−	0.887330i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$		0			0
$66$	−0.287898	+	0.241575i	−0.0354377	+	0.0297358i
$67$	−3.35029	+	2.81122i	−0.409303	+	0.343446i	−0.824076	−	0.566479i	$-0.808305\pi$
$67$	−3.35029	+	2.81122i	−0.409303	+	0.343446i	0.414773	+	0.909925i	$0.363861\pi$
$68$	−2.95728	+	5.12215i	−0.358622	+	0.621152i
$69$	−8.19789	−	14.1992i	−0.986909	−	1.70938i
$70$		0			0
$71$	0.856537	−	4.85766i	0.101652	−	0.576499i	−0.890853	−	0.454293i	$-0.849892\pi$
$71$	0.856537	−	4.85766i	0.101652	−	0.576499i	0.992505	−	0.122206i	$-0.0389968\pi$
$72$	0.766044	+	4.34445i	0.0902792	+	0.511999i
$73$	9.44311	−	3.43701i	1.10523	−	0.402272i	0.275990	−	0.961161i	$-0.410994\pi$
$73$	9.44311	−	3.43701i	1.10523	−	0.402272i	0.829243	+	0.558889i	$0.188772\pi$
$74$	−1.79905	−	1.50958i	−0.209136	−	0.175486i
$75$		0			0
$76$	1.08796	−	4.22094i	0.124797	−	0.484175i
$77$	−0.644394			−0.0734355
$78$	−7.97418	−	6.69113i	−0.902898	−	0.757622i
$79$	13.0782	−	4.76006i	1.47141	−	0.535549i	0.522925	−	0.852379i	$-0.324841\pi$
$79$	13.0782	−	4.76006i	1.47141	−	0.535549i	0.948482	+	0.316830i	$0.102618\pi$
$80$		0			0
$81$	−0.481582	+	2.73119i	−0.0535091	+	0.303465i
$82$	−1.71002	−	0.622395i	−0.188840	−	0.0687320i
$83$	5.98005	+	10.3577i	0.656395	+	1.13691i	0.981542	+	0.191246i	$0.0612529\pi$
$83$	5.98005	+	10.3577i	0.656395	+	1.13691i	−0.325147	+	0.945664i	$0.605414\pi$
$84$	−6.35393	+	11.0053i	−0.693270	+	1.20078i
$85$		0			0
$86$	−5.05579	+	4.24231i	−0.545180	+	0.457461i
$87$	−8.70905	+	15.0845i	−0.933708	+	1.61723i
$88$	0.0690243	+	0.119554i	0.00735801	+	0.0127444i
$89$	11.7821	+	4.28835i	1.24890	+	0.454564i	0.880031	−	0.474916i	$-0.157521\pi$
$89$	11.7821	+	4.28835i	1.24890	+	0.454564i	0.368873	+	0.929480i	$0.379744\pi$
$90$		0			0
$91$	−3.09935	−	17.5773i	−0.324900	−	1.84260i
$92$	−5.65933	+	2.05983i	−0.590026	+	0.214752i
$93$	−11.7104	−	9.82619i	−1.21431	−	1.01893i
$94$	7.04674			0.726816
$95$		0			0
$96$	2.72240			0.277854
$97$	−5.18524	−	4.35093i	−0.526481	−	0.441770i	0.340403	−	0.940280i	$-0.389436\pi$
$97$	−5.18524	−	4.35093i	−0.526481	−	0.441770i	−0.866884	+	0.498510i	$0.833881\pi$
$98$	−13.8972	+	5.05818i	−1.40383	+	0.510953i
$99$	−0.105751	−	0.599745i	−0.0106284	−	0.0602767i
$100$		0			0
$101$	−2.79977	−	1.01903i	−0.278587	−	0.101397i	0.198948	−	0.980010i	$-0.436247\pi$
$101$	−2.79977	−	1.01903i	−0.278587	−	0.101397i	−0.477535	+	0.878613i	$0.658470\pi$
$102$	−8.05090	−	13.9446i	−0.797158	−	1.38072i
$103$	7.36822	−	12.7621i	0.726013	−	1.25749i	−0.232543	−	0.972586i	$-0.574705\pi$
$103$	7.36822	−	12.7621i	0.726013	−	1.25749i	0.958556	−	0.284905i	$-0.0919620\pi$
$104$	−2.92910	+	2.45781i	−0.287222	+	0.241008i
$105$		0			0
$106$	1.84860	−	3.20186i	0.179552	−	0.310992i
$107$	−0.261163	−	0.452348i	−0.0252476	−	0.0437301i	0.853126	−	0.521706i	$-0.174704\pi$
$107$	−0.261163	−	0.452348i	−0.0252476	−	0.0437301i	−0.878373	+	0.477976i	$0.841371\pi$
$108$	−3.61086	−	1.31425i	−0.347455	−	0.126463i
$109$	−1.04403	+	5.92097i	−0.0999996	+	0.567126i	0.893101	+	0.449857i	$0.148525\pi$
$109$	−1.04403	+	5.92097i	−0.0999996	+	0.567126i	−0.993100	+	0.117269i	$0.962586\pi$
$110$		0			0
$111$	6.00797	−	2.18672i	0.570252	−	0.207555i
$112$	3.57581	+	3.00046i	0.337882	+	0.283517i
$113$	5.96326			0.560976			0.280488	−	0.959857i	$-0.409504\pi$
$113$	5.96326			0.560976			0.280488	+	0.959857i	$0.409504\pi$
$114$	8.47065	+	8.31060i	0.793349	+	0.778359i
$115$		0			0
$116$	4.90120	+	4.11259i	0.455065	+	0.381845i
$117$	15.8507	−	5.76920i	1.46540	−	0.533362i
$118$	1.54520	+	8.76328i	0.142247	+	0.806725i
$119$	4.79416	−	27.1890i	0.439480	−	2.49241i
$120$		0			0
$121$	5.49047	+	9.50978i	0.499134	+	0.864525i
$122$	−4.57117	+	7.91749i	−0.413854	+	0.716816i
$123$	3.79508	−	3.18445i	0.342191	−	0.287132i
$124$	−4.30149	+	3.60938i	−0.386286	+	0.324132i
$125$		0			0
$126$	−10.2961	−	17.8334i	−0.917251	−	1.58873i
$127$	7.79994	+	2.83894i	0.692132	+	0.251916i	0.664048	−	0.747690i	$-0.268837\pi$
$127$	7.79994	+	2.83894i	0.692132	+	0.251916i	0.0280844	+	0.999606i	$0.491059\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	−3.12002	−	17.6945i	−0.274703	−	1.55792i
$130$		0			0
$131$	−1.70845	−	1.43356i	−0.149268	−	0.125251i	0.565096	−	0.825025i	$-0.308839\pi$
$131$	−1.70845	−	1.43356i	−0.149268	−	0.125251i	−0.714363	+	0.699775i	$0.753284\pi$
$132$	−0.375824			−0.0327112
$133$	1.96658	+	20.2516i	0.170524	+	1.75603i
$134$	−4.37349			−0.377812
$135$		0			0
$136$	−5.55786	+	2.02290i	−0.476583	+	0.173462i
$137$	0.612341	+	3.47276i	0.0523158	+	0.296698i	0.999728	−	0.0233178i	$-0.00742297\pi$
$137$	0.612341	+	3.47276i	0.0523158	+	0.296698i	−0.947412	+	0.320016i	$0.896312\pi$
$138$	2.84710	−	16.1467i	0.242361	−	1.37450i
$139$	4.63579	+	1.68729i	0.393203	+	0.143114i	0.531052	−	0.847339i	$-0.321797\pi$
$139$	4.63579	+	1.68729i	0.393203	+	0.143114i	−0.137850	+	0.990453i	$0.544019\pi$
$140$		0			0
$141$	−9.59204	+	16.6139i	−0.807795	+	1.39914i
$142$	3.77859	−	3.17061i	0.317092	−	0.266072i
$143$	0.404358	−	0.339296i	0.0338141	−	0.0283734i
$144$	−2.20574	+	3.82045i	−0.183811	+	0.318371i
$145$		0			0
$146$	9.44311	+	3.43701i	0.781517	+	0.284449i
$147$	6.99142	−	39.6503i	0.576642	−	3.27030i
$148$	−0.407812	−	2.31282i	−0.0335219	−	0.190112i
$149$	−9.24760	+	3.36585i	−0.757593	+	0.275741i	−0.691797	−	0.722092i	$-0.743181\pi$
$149$	−9.24760	+	3.36585i	−0.757593	+	0.275741i	−0.0657958	+	0.997833i	$0.520959\pi$
$150$		0			0
$151$	−0.804582			−0.0654760			−0.0327380	−	0.999464i	$-0.510423\pi$
$151$	−0.804582			−0.0654760			−0.0327380	+	0.999464i	$0.510423\pi$
$152$	3.54659	−	2.53410i	0.287667	−	0.205543i
$153$	26.0919			2.10941
$154$	−0.493635	−	0.414209i	−0.0397782	−	0.0333779i
$155$		0			0
$156$	−1.80760	−	10.2514i	−0.144724	−	0.820770i
$157$	0.528676	−	2.99827i	0.0421929	−	0.239288i	−0.956417	−	0.292006i	$-0.905677\pi$
$157$	0.528676	−	2.99827i	0.0421929	−	0.239288i	0.998609	+	0.0527179i	$0.0167884\pi$
$158$	13.0782	+	4.76006i	1.04044	+	0.378690i
$159$	5.03262	+	8.71676i	0.399113	+	0.691284i
$160$		0			0
$161$	21.5354	−	18.0704i	1.69723	−	1.42414i
$162$	−2.12449	+	1.78265i	−0.166915	+	0.140059i
$163$	−8.30962	+	14.3927i	−0.650860	+	1.12732i	0.332055	+	0.943260i	$0.392258\pi$
$163$	−8.30962	+	14.3927i	−0.650860	+	1.12732i	−0.982915	+	0.184062i	$0.941075\pi$
$164$	−0.909881	−	1.57596i	−0.0710497	−	0.123062i
$165$		0			0
$166$	−2.07685	+	11.7784i	−0.161195	+	0.914180i
$167$	−1.96202	−	11.1272i	−0.151826	−	0.861048i	−0.961630	−	0.274348i	$-0.911538\pi$
$167$	−1.96202	−	11.1272i	−0.151826	−	0.861048i	0.809804	−	0.586700i	$-0.199573\pi$
$168$	−11.9415	+	4.34634i	−0.921305	+	0.335328i
$169$	1.24131	+	1.04159i	0.0954857	+	0.0801220i
$170$		0			0
$171$	−18.5256	+	5.15380i	−1.41669	+	0.394121i
$172$	−6.59987			−0.503235
$173$	−1.43032	−	1.20018i	−0.108746	−	0.0912484i	0.586794	−	0.809737i	$-0.300390\pi$
$173$	−1.43032	−	1.20018i	−0.108746	−	0.0912484i	−0.695539	+	0.718488i	$0.744834\pi$
$174$	−16.3677	+	5.95734i	−1.24083	+	0.451625i
$175$		0			0
$176$	−0.0239719	+	0.135951i	−0.00180695	+	0.0102477i
$177$	−22.7643	−	8.28551i	−1.71107	−	0.622777i
$178$	6.26915	+	10.8585i	0.469892	+	0.813877i
$179$	−2.23944	+	3.87882i	−0.167383	+	0.289916i	−0.937499	−	0.347988i	$-0.886865\pi$
$179$	−2.23944	+	3.87882i	−0.167383	+	0.289916i	0.770116	+	0.637904i	$0.220198\pi$
$180$		0			0
$181$	16.7448	−	14.0506i	1.24463	−	1.04437i	0.247487	−	0.968891i	$-0.420395\pi$
$181$	16.7448	−	14.0506i	1.24463	−	1.04437i	0.997147	−	0.0754805i	$-0.0240491\pi$
$182$	8.92421	−	15.4572i	0.661507	−	1.14576i
$183$	−12.4446	−	21.5546i	−0.919928	−	1.59336i
$184$	−5.65933	−	2.05983i	−0.417212	−	0.151853i
$185$		0			0
$186$	−2.65453	−	15.0546i	−0.194640	−	1.10386i
$187$	0.767255	−	0.279258i	0.0561072	−	0.0204214i
$188$	5.39812	+	4.52956i	0.393698	+	0.330352i
$189$	17.9368			1.30471
$190$		0			0
$191$	−20.7005			−1.49783			−0.748917	−	0.662664i	$-0.769426\pi$
$191$	−20.7005			−1.49783			−0.748917	+	0.662664i	$0.769426\pi$
$192$	2.08548	+	1.74993i	0.150507	+	0.126290i
$193$	−8.37342	+	3.04767i	−0.602732	+	0.219376i	−0.625320	−	0.780368i	$-0.715032\pi$
$193$	−8.37342	+	3.04767i	−0.602732	+	0.219376i	0.0225883	+	0.999745i	$0.492809\pi$
$194$	−1.17540	−	6.66601i	−0.0843886	−	0.478592i
$195$		0			0
$196$	−13.8972	−	5.05818i	−0.992660	−	0.361299i
$197$	−8.74406	−	15.1452i	−0.622988	−	1.07905i	−0.988926	−	0.148408i	$-0.952585\pi$
$197$	−8.74406	−	15.1452i	−0.622988	−	1.07905i	0.365938	−	0.930639i	$-0.380748\pi$
$198$	0.304499	−	0.527407i	0.0216398	−	0.0374812i
$199$	12.7454	−	10.6947i	0.903498	−	0.758125i	−0.0673728	−	0.997728i	$-0.521462\pi$
$199$	12.7454	−	10.6947i	0.903498	−	0.758125i	0.970871	+	0.239603i	$0.0770172\pi$
$200$		0			0
$201$	5.95320	−	10.3112i	0.419906	−	0.727299i
$202$	−1.48972	−	2.58028i	−0.104817	−	0.181548i
$203$	−28.0643	−	10.2146i	−1.96973	−	0.716922i
$204$	2.79605	−	15.8572i	0.195762	−	1.11022i
$205$		0			0
$206$	13.8477	−	5.04016i	0.964817	−	0.351165i
$207$	20.3525	+	17.0778i	1.41459	+	1.18699i
$208$	−3.82367			−0.265124
$209$	−0.489602	+	0.349829i	−0.0338665	+	0.0241982i
$210$		0			0
$211$	−20.8315	−	17.4797i	−1.43410	−	1.20335i	−0.943241	−	0.332110i	$-0.892239\pi$
$211$	−20.8315	−	17.4797i	−1.43410	−	1.20335i	−0.490857	−	0.871240i	$-0.663316\pi$
$212$	3.47422	−	1.26451i	0.238611	−	0.0868472i
$213$	2.33184	+	13.2245i	0.159775	+	0.906129i
$214$	0.0907010	−	0.514391i	0.00620019	−	0.0351630i
$215$		0			0
$216$	−1.92130	−	3.32779i	−0.130728	−	0.226427i
$217$	13.1055	−	22.6995i	0.889663	−	1.54094i
$218$	−4.60570	+	3.86464i	−0.311937	+	0.261746i
$219$	−20.9573	+	17.5853i	−1.41616	+	1.18830i
$220$		0			0
$221$	11.3076	+	19.5854i	0.760634	+	1.31746i
$222$	6.00797	+	2.18672i	0.403229	+	0.146763i
$223$	−2.00303	+	11.3597i	−0.134133	+	0.760704i	0.841327	+	0.540526i	$0.181775\pi$
$223$	−2.00303	+	11.3597i	−0.134133	+	0.760704i	−0.975460	+	0.220178i	$0.929336\pi$
$224$	0.810569	+	4.59697i	0.0541584	+	0.307148i
$225$		0			0
$226$	4.56812	+	3.83311i	0.303867	+	0.254975i
$227$	5.99286			0.397760			0.198880	−	0.980024i	$-0.436270\pi$
$227$	5.99286			0.397760			0.198880	+	0.980024i	$0.436270\pi$
$228$	1.14695	+	11.8111i	0.0759585	+	0.782210i
$229$	9.75689			0.644753			0.322377	−	0.946611i	$-0.395518\pi$
$229$	9.75689			0.644753			0.322377	+	0.946611i	$0.395518\pi$
$230$		0			0
$231$	1.64850	−	0.600006i	0.108464	−	0.0394775i
$232$	1.11101	+	6.30086i	0.0729415	+	0.413672i
$233$	4.63213	−	26.2701i	0.303461	−	1.72101i	−0.327202	−	0.944955i	$-0.606106\pi$
$233$	4.63213	−	26.2701i	0.303461	−	1.72101i	0.630662	−	0.776057i	$-0.282783\pi$
$234$	15.8507	+	5.76920i	1.03620	+	0.377144i
$235$		0			0
$236$	−4.44923	+	7.70630i	−0.289620	+	0.501637i
$237$	−29.0247	+	24.3546i	−1.88535	+	1.58200i
$238$	21.1493	−	17.7464i	1.37091	−	1.15033i
$239$	−8.67237	+	15.0210i	−0.560969	+	0.971627i	0.436443	+	0.899732i	$0.356238\pi$
$239$	−8.67237	+	15.0210i	−0.560969	+	0.971627i	−0.997412	+	0.0718952i	$0.977095\pi$
$240$		0			0
$241$	−14.1477	−	5.14934i	−0.911333	−	0.331698i	−0.156548	−	0.987670i	$-0.550037\pi$
$241$	−14.1477	−	5.14934i	−0.911333	−	0.331698i	−0.754785	+	0.655972i	$0.772259\pi$
$242$	−1.90682	+	10.8141i	−0.122575	+	0.695158i
$243$	−3.31284	−	18.7881i	−0.212519	−	1.20525i
$244$	−8.59098	+	3.12686i	−0.549981	+	0.200177i
$245$		0			0
$246$	4.95412			0.315863
$247$	−11.8972	−	11.6724i	−0.757000	−	0.742697i
$248$	−5.61520			−0.356566
$249$	−24.9425	−	20.9293i	−1.58067	−	1.32634i
$250$		0			0
$251$	−0.426358	−	2.41799i	−0.0269115	−	0.152622i	0.968391	−	0.249437i	$-0.0802456\pi$
$251$	−0.426358	−	2.41799i	−0.0269115	−	0.152622i	−0.995302	+	0.0968148i	$0.969135\pi$
$252$	3.57581	−	20.2794i	0.225255	−	1.27748i
$253$	0.781263	+	0.284356i	0.0491176	+	0.0178773i
$254$	4.15026	+	7.18846i	0.260410	+	0.451044i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	6.92779	−	5.81310i	0.432143	−	0.362611i	−0.400616	−	0.916246i	$-0.631204\pi$
$257$	6.92779	−	5.81310i	0.432143	−	0.362611i	0.832760	+	0.553635i	$0.186760\pi$
$258$	8.98375	−	15.5603i	0.559304	−	0.968743i
$259$	5.48125	+	9.49381i	0.340588	+	0.589916i
$260$		0			0
$261$	4.90120	−	27.7961i	0.303377	−	1.72053i
$262$	−0.387274	−	2.19634i	−0.0239258	−	0.135690i
$263$	16.0702	−	5.84907i	0.990929	−	0.360669i	0.204849	−	0.978794i	$-0.434330\pi$
$263$	16.0702	−	5.84907i	0.990929	−	0.360669i	0.786080	+	0.618125i	$0.212107\pi$
$264$	−0.287898	−	0.241575i	−0.0177189	−	0.0148679i
$265$		0			0
$266$	−11.5110	+	16.7777i	−0.705783	+	1.02871i
$267$	−34.1343			−2.08898
$268$	−3.35029	−	2.81122i	−0.204651	−	0.171723i
$269$	−0.911523	+	0.331767i	−0.0555765	+	0.0202282i	−0.369659	−	0.929168i	$-0.620525\pi$
$269$	−0.911523	+	0.331767i	−0.0555765	+	0.0202282i	0.314082	+	0.949396i	$0.398303\pi$
$270$		0			0
$271$	−0.883972	+	5.01325i	−0.0536975	+	0.304533i	−0.999814	−	0.0192933i	$-0.993858\pi$
$271$	−0.883972	+	5.01325i	−0.0536975	+	0.304533i	0.946116	+	0.323827i	$0.104969\pi$
$272$	−5.55786	−	2.02290i	−0.336995	−	0.122656i
$273$	24.2953	+	42.0807i	1.47042	+	2.54684i
$274$	−1.76317	+	3.05389i	−0.106517	+	0.184492i
$275$		0			0
$276$	12.5599	−	10.5390i	0.756016	−	0.634373i
$277$	−10.1369	+	17.5576i	−0.609068	+	1.05494i	0.382327	+	0.924027i	$0.375123\pi$
$277$	−10.1369	+	17.5576i	−0.609068	+	1.05494i	−0.991394	+	0.130909i	$0.958211\pi$
$278$	2.46665	+	4.27237i	0.147940	+	0.256240i
$279$	23.2774	+	8.47229i	1.39358	+	0.507223i
$280$		0			0
$281$	−0.973949	−	5.52354i	−0.0581009	−	0.329507i	0.941878	−	0.335954i	$-0.109059\pi$
$281$	−0.973949	−	5.52354i	−0.0581009	−	0.329507i	−0.999979	+	0.00644756i	$0.997948\pi$
$282$	−18.0271	+	6.56134i	−1.07350	+	0.390722i
$283$	12.0180	+	10.0843i	0.714399	+	0.599452i	0.925830	−	0.377941i	$-0.123368\pi$
$283$	12.0180	+	10.0843i	0.714399	+	0.599452i	−0.211431	+	0.977393i	$0.567812\pi$
$284$	4.93260			0.292696
$285$		0			0
$286$	0.527851			0.0312125
$287$	6.50711	+	5.46012i	0.384103	+	0.322300i
$288$	−4.14543	+	1.50881i	−0.244272	+	0.0889077i
$289$	3.12253	+	17.7088i	0.183678	+	1.04169i
$290$		0			0
$291$	17.3162	+	6.30258i	1.01509	+	0.369464i
$292$	5.02457	+	8.70282i	0.294041	+	0.509294i
$293$	−9.97548	+	17.2780i	−0.582774	+	1.00939i	0.412375	+	0.911014i	$0.364699\pi$
$293$	−9.97548	+	17.2780i	−0.582774	+	1.00939i	−0.995149	+	0.0983794i	$0.968634\pi$
$294$	30.8424	−	25.8799i	1.79877	−	1.50935i
$295$		0			0
$296$	1.17425	−	2.03386i	0.0682518	−	0.118216i
$297$	0.265233	+	0.459396i	0.0153904	+	0.0266569i
$298$	−9.24760	−	3.36585i	−0.535699	−	0.194979i
$299$	−3.99880	+	22.6783i	−0.231257	+	1.31152i
$300$		0			0
$301$	28.9495	−	10.5368i	1.66862	−	0.607329i
$302$	−0.616346	−	0.517176i	−0.0354667	−	0.0297601i
$303$	8.11126			0.465980
$304$	4.34574	+	0.338471i	0.249245	+	0.0194127i
$305$		0			0
$306$	19.9876	+	16.7716i	1.14261	+	0.958766i
$307$	−14.4144	+	5.24643i	−0.822675	+	0.299429i	−0.718849	−	0.695166i	$-0.755331\pi$
$307$	−14.4144	+	5.24643i	−0.822675	+	0.299429i	−0.103826	+	0.994595i	$0.533109\pi$
$308$	−0.111898	−	0.634604i	−0.00637597	−	0.0361599i
$309$	−6.96651	+	39.5090i	−0.396311	+	2.24759i
$310$		0			0
$311$	11.2342	+	19.4582i	0.637032	+	1.10337i	0.986081	+	0.166267i	$0.0531715\pi$
$311$	11.2342	+	19.4582i	0.637032	+	1.10337i	−0.349049	+	0.937105i	$0.613495\pi$
$312$	5.20478	−	9.01494i	0.294663	−	0.510371i
$313$	−0.526455	+	0.441748i	−0.0297570	+	0.0249691i	−0.657545	−	0.753415i	$-0.728405\pi$
$313$	−0.526455	+	0.441748i	−0.0297570	+	0.0249691i	0.627788	+	0.778384i	$0.283961\pi$
$314$	2.33224	−	1.95698i	0.131616	−	0.110439i
$315$		0			0
$316$	6.95874	+	12.0529i	0.391460	+	0.678028i
$317$	9.32931	+	3.39559i	0.523986	+	0.190715i	0.590451	−	0.807073i	$-0.298950\pi$
$317$	9.32931	+	3.39559i	0.523986	+	0.190715i	−0.0664648	+	0.997789i	$0.521172\pi$
$318$	−1.74781	+	9.91233i	−0.0980124	+	0.555856i
$319$	−0.153373	−	0.869824i	−0.00858727	−	0.0487008i
$320$		0			0
$321$	1.08930	+	0.914032i	0.0607989	+	0.0510163i
$322$	28.1125			1.56665
$323$	−11.1178	−	23.2605i	−0.618614	−	1.29425i
$324$	−2.77332			−0.154073
$325$		0			0
$326$	−15.6170	+	5.68411i	−0.864944	+	0.314814i
$327$	−2.84226	−	16.1193i	−0.157177	−	0.891397i
$328$	0.315998	−	1.79212i	0.0174481	−	0.0989530i
$329$	−30.9097	−	11.2502i	−1.70410	−	0.620243i
$330$		0			0
$331$	9.22736	−	15.9822i	0.507181	−	0.878464i	−0.492784	−	0.870152i	$-0.664021\pi$
$331$	9.22736	−	15.9822i	0.507181	−	0.878464i	0.999965	−	0.00831226i	$-0.00264590\pi$
$332$	−9.16196	+	7.68780i	−0.502828	+	0.421923i
$333$	−7.93647	+	6.65949i	−0.434916	+	0.364938i
$334$	5.64942	−	9.78509i	0.309123	−	0.535416i
$335$		0			0
$336$	−11.9415	−	4.34634i	−0.651461	−	0.237112i
$337$	−2.32120	+	13.1642i	−0.126444	+	0.717098i	0.853996	+	0.520279i	$0.174172\pi$
$337$	−2.32120	+	13.1642i	−0.126444	+	0.717098i	−0.980440	+	0.196819i	$0.936939\pi$
$338$	0.281383	+	1.59580i	0.0153052	+	0.0868002i
$339$	−15.2553	+	5.55249i	−0.828556	+	0.301570i
$340$		0			0
$341$	0.775170			0.0419778
$342$	−17.5043	−	7.96002i	−0.946522	−	0.430428i
$343$	36.3587			1.96319
$344$	−5.05579	−	4.24231i	−0.272590	−	0.228730i
$345$		0			0
$346$	−0.324228	−	1.83879i	−0.0174306	−	0.0988539i
$347$	−5.05144	+	28.6482i	−0.271176	+	1.53791i	0.479678	+	0.877445i	$0.340754\pi$
$347$	−5.05144	+	28.6482i	−0.271176	+	1.53791i	−0.750854	+	0.660469i	$0.770358\pi$
$348$	−16.3677	−	5.95734i	−0.877398	−	0.319347i
$349$	13.2993	+	23.0350i	0.711893	+	1.23303i	0.964146	+	0.265373i	$0.0854950\pi$
$349$	13.2993	+	23.0350i	0.711893	+	1.23303i	−0.252253	+	0.967661i	$0.581172\pi$
$350$		0			0
$351$	−11.2554	+	9.44436i	−0.600766	+	0.504103i
$352$	−0.105751	+	0.0887359i	−0.00563656	+	0.00472964i
$353$	−5.74340	+	9.94786i	−0.305690	+	0.529471i	−0.977415	−	0.211330i	$-0.932221\pi$
$353$	−5.74340	+	9.94786i	−0.305690	+	0.529471i	0.671724	+	0.740801i	$0.265554\pi$
$354$	−12.1126	−	20.9796i	−0.643778	−	1.11506i
$355$		0			0
$356$	−2.17725	+	12.3478i	−0.115394	+	0.654433i
$357$	13.0516	+	74.0194i	0.690765	+	3.91752i
$358$	−4.20876	+	1.53186i	−0.222440	+	0.0809616i
$359$	−12.3172	−	10.3354i	−0.650077	−	0.545480i	0.257017	−	0.966407i	$-0.417260\pi$
$359$	−12.3172	−	10.3354i	−0.650077	−	0.545480i	−0.907094	+	0.420927i	$0.861705\pi$
$360$		0			0
$361$	12.4884	+	14.3192i	0.657282	+	0.753645i
$362$	21.8588			1.14887
$363$	−22.9005	−	19.2158i	−1.20197	−	1.00857i
$364$	16.7720	−	6.10452i	0.879093	−	0.319964i
$365$		0			0
$366$	4.32195	−	24.5110i	0.225912	−	1.28121i
$367$	27.8208	+	10.1259i	1.45223	+	0.528569i	0.943214	−	0.332187i	$-0.107786\pi$
$367$	27.8208	+	10.1259i	1.45223	+	0.528569i	0.509018	+	0.860756i	$0.330009\pi$
$368$	−3.01127	−	5.21567i	−0.156973	−	0.271886i
$369$	−4.01392	+	6.95231i	−0.208956	+	0.361923i
$370$		0			0
$371$	−13.2204	+	11.0933i	−0.686371	+	0.575934i
$372$	7.64342	−	13.2388i	0.396293	−	0.686399i
$373$	−10.8325	−	18.7624i	−0.560883	−	0.971479i	−0.997420	−	0.0717919i	$-0.977128\pi$
$373$	−10.8325	−	18.7624i	−0.560883	−	0.971479i	0.436536	−	0.899687i	$-0.356205\pi$
$374$	0.767255	+	0.279258i	0.0396738	+	0.0144401i
$375$		0			0
$376$	1.22365	+	6.93969i	0.0631052	+	0.357887i
$377$	22.9887	−	8.36720i	1.18398	−	0.430933i
$378$	13.7404	+	11.5296i	0.706729	+	0.593016i
$379$	19.4023			0.996628			0.498314	−	0.866997i	$-0.333953\pi$
$379$	19.4023			0.996628			0.498314	+	0.866997i	$0.333953\pi$
$380$		0			0
$381$	−22.5973			−1.15770
$382$	−15.8575	−	13.3060i	−0.811339	−	0.680794i
$383$	−21.2251	+	7.72532i	−1.08455	+	0.394745i	−0.821601	−	0.570063i	$-0.806919\pi$
$383$	−21.2251	+	7.72532i	−1.08455	+	0.394745i	−0.262953	+	0.964809i	$0.584696\pi$
$384$	0.472740	+	2.68104i	0.0241244	+	0.136816i
$385$		0			0
$386$	−8.37342	−	3.04767i	−0.426196	−	0.155123i
$387$	14.5576	+	25.2145i	0.740003	+	1.28172i
$388$	3.38442	−	5.86199i	0.171818	−	0.297598i
$389$	2.24531	−	1.88404i	0.113842	−	0.0955246i	−0.584090	−	0.811689i	$-0.698548\pi$
$389$	2.24531	−	1.88404i	0.113842	−	0.0955246i	0.697932	+	0.716164i	$0.254104\pi$
$390$		0			0
$391$	−17.8103	+	30.8484i	−0.900706	+	1.56007i
$392$	−7.39456	−	12.8078i	−0.373482	−	0.646890i
$393$	5.70540	+	2.07659i	0.287799	+	0.104750i
$394$	3.03678	−	17.2224i	0.152991	−	0.867654i
$395$		0			0
$396$	0.572270	−	0.208289i	0.0287577	−	0.0104669i
$397$	−19.7607	−	16.5812i	−0.991762	−	0.832187i	−0.00593989	−	0.999982i	$-0.501891\pi$
$397$	−19.7607	−	16.5812i	−0.991762	−	0.832187i	−0.985822	+	0.167795i	$0.946335\pi$
$398$	16.6380			0.833985
$399$	−23.8875	−	49.9769i	−1.19587	−	2.50197i
$400$		0			0
$401$	−27.0133	−	22.6669i	−1.34898	−	1.13193i	−0.979220	−	0.202803i	$-0.934995\pi$
$401$	−27.0133	−	22.6669i	−1.34898	−	1.13193i	−0.369761	−	0.929127i	$-0.620561\pi$
$402$	11.1884	−	4.07223i	0.558024	−	0.203104i
$403$	3.72834	+	21.1445i	0.185722	+	1.05328i
$404$	0.517376	−	2.93418i	0.0257404	−	0.145981i
$405$		0			0
$406$	−14.9327	−	25.8642i	−0.741097	−	1.28362i
$407$	−0.162103	+	0.280771i	−0.00803516	+	0.0139173i
$408$	12.3347	−	10.3500i	0.610658	−	0.512403i
$409$	10.6334	−	8.92250i	0.525789	−	0.441189i	−0.340855	−	0.940116i	$-0.610717\pi$
$409$	10.6334	−	8.92250i	0.525789	−	0.441189i	0.866644	+	0.498926i	$0.166272\pi$
$410$		0			0
$411$	−4.80005	−	8.31392i	−0.236769	−	0.410096i
$412$	13.8477	+	5.04016i	0.682229	+	0.248311i
$413$	7.21283	−	40.9060i	0.354920	−	2.01285i
$414$	4.61353	+	26.1646i	0.226743	+	1.28592i
$415$		0			0
$416$	−2.92910	−	2.45781i	−0.143611	−	0.120504i
$417$	−13.4304			−0.657691
$418$	−0.599923	−	0.0467255i	−0.0293432	−	0.00228542i
$419$	−3.07400			−0.150175			−0.0750874	−	0.997177i	$-0.523924\pi$
$419$	−3.07400			−0.150175			−0.0750874	+	0.997177i	$0.523924\pi$
$420$		0			0
$421$	−19.2422	+	7.00360i	−0.937808	+	0.341334i	−0.765300	−	0.643674i	$-0.777409\pi$
$421$	−19.2422	+	7.00360i	−0.937808	+	0.341334i	−0.172508	+	0.985008i	$0.555187\pi$
$422$	−4.72211	−	26.7804i	−0.229869	−	1.30365i
$423$	5.39812	−	30.6143i	0.262466	−	1.48852i
$424$	3.47422	+	1.26451i	0.168723	+	0.0614103i
$425$		0			0
$426$	−6.71426	+	11.6294i	−0.325307	+	0.563448i
$427$	32.6912	−	27.4312i	1.58204	−	1.32749i
$428$	0.400125	−	0.335745i	0.0193408	−	0.0162288i
$429$	−0.718512	+	1.24450i	−0.0346901	+	0.0600850i
$430$		0			0
$431$	15.7213	+	5.72210i	0.757270	+	0.275624i	0.691662	−	0.722222i	$-0.256879\pi$
$431$	15.7213	+	5.72210i	0.757270	+	0.275624i	0.0656084	+	0.997845i	$0.479101\pi$
$432$	0.667261	−	3.78422i	0.0321036	−	0.182068i
$433$	4.56412	+	25.8844i	0.219338	+	1.24393i	0.873219	+	0.487329i	$0.162029\pi$
$433$	4.56412	+	25.8844i	0.219338	+	1.24393i	−0.653881	+	0.756597i	$0.726860\pi$
$434$	24.6304	−	8.96472i	1.18230	−	0.430321i
$435$		0			0
$436$	−6.01231			−0.287937
$437$	6.55227	−	25.4208i	0.313438	−	1.21604i
$438$	−27.3578			−1.30721
$439$	−14.7598	−	12.3849i	−0.704446	−	0.591100i	0.218589	−	0.975817i	$-0.429855\pi$
$439$	−14.7598	−	12.3849i	−0.704446	−	0.591100i	−0.923035	+	0.384717i	$0.874299\pi$
$440$		0			0
$441$	11.3291	+	64.2507i	0.539482	+	3.05956i
$442$	−3.92710	+	22.2717i	−0.186793	+	1.05936i
$443$	−25.7029	−	9.35508i	−1.22118	−	0.444473i	−0.350612	−	0.936521i	$-0.614026\pi$
$443$	−25.7029	−	9.35508i	−1.22118	−	0.444473i	−0.870568	+	0.492047i	$0.836249\pi$
$444$	3.19678	+	5.53698i	0.151712	+	0.262773i
$445$		0			0
$446$	−8.83631	+	7.41454i	−0.418411	+	0.351089i
$447$	20.5234	−	17.2212i	0.970724	−	0.814534i
$448$	−2.33394	+	4.04250i	−0.110268	+	0.190990i
$449$	−13.6608	−	23.6613i	−0.644695	−	1.11664i	−0.984372	−	0.176103i	$-0.943651\pi$
$449$	−13.6608	−	23.6613i	−0.644695	−	1.11664i	0.339677	−	0.940542i	$-0.389682\pi$
$450$		0			0
$451$	−0.0436231	+	0.247399i	−0.00205413	+	0.0116496i
$452$	1.03551	+	5.87266i	0.0487063	+	0.276227i
$453$	2.05830	−	0.749160i	0.0967074	−	0.0351986i
$454$	4.59080	+	3.85214i	0.215457	+	0.180790i
$455$		0			0
$456$	−6.71343	+	9.78509i	−0.314385	+	0.458229i
$457$	−20.4504			−0.956628			−0.478314	−	0.878189i	$-0.658752\pi$
$457$	−20.4504			−0.956628			−0.478314	+	0.878189i	$0.658752\pi$
$458$	7.47421	+	6.27161i	0.349247	+	0.293053i
$459$	−21.3566	+	7.77318i	−0.996843	+	0.362821i
$460$		0			0
$461$	3.97777	−	22.5590i	0.185263	−	1.05068i	−0.740354	−	0.672217i	$-0.765342\pi$
$461$	3.97777	−	22.5590i	0.185263	−	1.05068i	0.925617	−	0.378462i	$-0.123547\pi$
$462$	1.64850	+	0.600006i	0.0766953	+	0.0279148i
$463$	−2.06259	−	3.57250i	−0.0958565	−	0.166028i	0.814109	−	0.580712i	$-0.197226\pi$
$463$	−2.06259	−	3.57250i	−0.0958565	−	0.166028i	−0.909966	+	0.414683i	$0.863892\pi$
$464$	−3.19903	+	5.54088i	−0.148511	+	0.257229i
$465$		0			0
$466$	20.4345	−	17.1466i	0.946611	−	0.794301i
$467$	−10.9696	+	18.9998i	−0.507610	+	0.879207i	0.492351	+	0.870397i	$0.336138\pi$
$467$	−10.9696	+	18.9998i	−0.507610	+	0.879207i	−0.999961	+	0.00881016i	$0.997196\pi$
$468$	8.43400	+	14.6081i	0.389862	+	0.675261i
$469$	19.1838	+	6.98232i	0.885824	+	0.322414i
$470$		0			0
$471$	1.43927	+	8.16250i	0.0663180	+	0.376108i
$472$	−8.36183	+	3.04346i	−0.384884	+	0.140086i
$473$	0.697945	+	0.585645i	0.0320915	+	0.0269280i
$474$	−37.8890			−1.74030
$475$		0			0
$476$	27.6084			1.26543
$477$	−12.4942	−	10.4839i	−0.572072	−	0.480025i
$478$	−16.2987	+	5.93225i	−0.745487	+	0.271335i
$479$	−1.90321	−	10.7937i	−0.0869600	−	0.493174i	−0.996916	−	0.0784707i	$-0.974996\pi$
$479$	−1.90321	−	10.7937i	−0.0869600	−	0.493174i	0.909956	−	0.414704i	$-0.136115\pi$
$480$		0			0
$481$	−8.43831	−	3.07129i	−0.384754	−	0.140039i
$482$	−7.52783	−	13.0386i	−0.342883	−	0.593891i
$483$	−38.2668	+	66.2800i	−1.74120	+	3.01584i
$484$	−8.41189	+	7.05841i	−0.382359	+	0.320837i
$485$		0			0
$486$	9.53894	−	16.5219i	0.432695	−	0.749450i
$487$	7.05884	+	12.2263i	0.319866	+	0.554025i	0.980460	−	0.196719i	$-0.0630286\pi$
$487$	7.05884	+	12.2263i	0.319866	+	0.554025i	−0.660593	+	0.750744i	$0.729695\pi$
$488$	−8.59098	−	3.12686i	−0.388896	−	0.141546i
$489$	7.85658	−	44.5569i	0.355287	−	2.01493i
$490$		0			0
$491$	28.2855	−	10.2951i	1.27651	−	0.464611i	0.387232	−	0.921982i	$-0.373431\pi$
$491$	28.2855	−	10.2951i	1.27651	−	0.464611i	0.889276	+	0.457372i	$0.151209\pi$
$492$	3.79508	+	3.18445i	0.171095	+	0.143566i
$493$	37.8417			1.70430
$494$	−1.61091	−	16.5889i	−0.0724783	−	0.746372i
$495$		0			0
$496$	−4.30149	−	3.60938i	−0.193143	−	0.162066i
$497$	−21.6362	+	7.87495i	−0.970518	+	0.353240i
$498$	−5.65402	−	32.0655i	−0.253362	−	1.43689i
$499$	−1.91957	+	10.8864i	−0.0859319	+	0.487344i	0.911220	+	0.411921i	$0.135142\pi$
$499$	−1.91957	+	10.8864i	−0.0859319	+	0.487344i	−0.997152	+	0.0754233i	$0.975969\pi$
$500$		0			0
$501$	15.3800	+	26.6390i	0.687128	+	1.19014i
$502$	1.22765	−	2.12635i	0.0547926	−	0.0949036i
$503$	26.3760	−	22.1321i	1.17605	−	0.986821i	0.176051	−	0.984381i	$-0.443668\pi$
$503$	26.3760	−	22.1321i	1.17605	−	0.986821i	0.999997	−	0.00244044i	$-0.000776817\pi$
$504$	15.7746	−	13.2364i	0.702655	−	0.589598i
$505$		0			0
$506$	0.415701	+	0.720016i	0.0184802	+	0.0320086i
$507$	−4.14540	−	1.50880i	−0.184103	−	0.0670082i
$508$	−1.44137	+	8.17441i	−0.0639504	+	0.362681i
$509$	4.74042	+	26.8842i	0.210115	+	1.19162i	0.889185	+	0.457549i	$0.151272\pi$
$509$	4.74042	+	26.8842i	0.210115	+	1.19162i	−0.679069	+	0.734074i	$0.737616\pi$
$510$		0			0
$511$	−35.9338	−	30.1520i	−1.58962	−	1.33385i
$512$	1.00000			0.0441942
$513$	13.6281	−	9.73754i	0.601697	−	0.429923i
$514$	9.04358			0.398895
$515$		0			0
$516$	16.8839	−	6.14525i	0.743274	−	0.270529i
$517$	−0.168924	−	0.958014i	−0.00742925	−	0.0421334i
$518$	−1.90362	+	10.7960i	−0.0836402	+	0.474347i
$519$	4.77660	+	1.73854i	0.209669	+	0.0763134i
$520$		0			0
$521$	−0.487781	+	0.844861i	−0.0213701	+	0.0370140i	−0.876513	−	0.481379i	$-0.840136\pi$
$521$	−0.487781	+	0.844861i	−0.0213701	+	0.0370140i	0.855143	+	0.518393i	$0.173469\pi$
$522$	21.6215	−	18.1426i	0.946348	−	0.794080i
$523$	−6.46328	+	5.42333i	−0.282619	+	0.237146i	−0.773066	−	0.634325i	$-0.781278\pi$
$523$	−6.46328	+	5.42333i	−0.282619	+	0.237146i	0.490447	+	0.871471i	$0.336834\pi$
$524$	1.11511	−	1.93143i	0.0487138	−	0.0843748i
$525$		0			0
$526$	16.0702	+	5.84907i	0.700693	+	0.255031i
$527$	−5.76710	+	32.7069i	−0.251219	+	1.42473i
$528$	−0.0652611	−	0.370114i	−0.00284012	−	0.0161071i
$529$	−12.4706	+	4.53894i	−0.542201	+	0.197345i
$530$		0			0
$531$	39.2554			1.70354
$532$	−19.6024	+	5.45335i	−0.849872	+	0.236433i
$533$	−6.95816			−0.301391
$534$	−26.1484	−	21.9411i	−1.13155	−	0.949484i
$535$		0			0
$536$	−0.759448	−	4.30705i	−0.0328032	−	0.186036i
$537$	2.11734	−	12.0081i	0.0913701	−	0.518186i
$538$	−0.911523	−	0.331767i	−0.0392985	−	0.0143035i
$539$	1.02081	+	1.76809i	0.0439693	+	0.0761571i
$540$		0			0
$541$	−18.4531	+	15.4840i	−0.793361	+	0.665709i	−0.946575	−	0.322484i	$-0.895482\pi$
$541$	−18.4531	+	15.4840i	−0.793361	+	0.665709i	0.153214	+	0.988193i	$0.451038\pi$
$542$	−3.89962	+	3.27217i	−0.167503	+	0.140552i
$543$	−29.7543	+	51.5359i	−1.27688	+	2.21162i
$544$	−2.95728	−	5.12215i	−0.126792	−	0.219611i
$545$		0			0
$546$	−8.43767	+	47.8524i	−0.361099	+	2.04789i
$547$	3.90328	+	22.1366i	0.166892	+	0.946494i	0.947092	+	0.320963i	$0.104006\pi$
$547$	3.90328	+	22.1366i	0.166892	+	0.946494i	−0.780199	+	0.625531i	$0.784882\pi$
$548$	−3.31367	+	1.20608i	−0.141553	+	0.0515210i
$549$	30.8955	+	25.9244i	1.31859	+	1.10643i
$550$		0			0
$551$	−26.8682	+	7.47467i	−1.14462	+	0.318432i
$552$	16.3958			0.697850
$553$	−49.7662	−	41.7588i	−2.11627	−	1.77577i
$554$	−19.0511	+	6.93405i	−0.809406	+	0.294600i
$555$		0			0
$556$	−0.856659	+	4.85836i	−0.0363304	+	0.206040i
$557$	−2.67101	−	0.972169i	−0.113174	−	0.0411921i	0.284812	−	0.958583i	$-0.408069\pi$
$557$	−2.67101	−	0.972169i	−0.113174	−	0.0411921i	−0.397987	+	0.917391i	$0.630291\pi$
$558$	12.3857	+	21.4526i	0.524327	+	0.908160i
$559$	−12.6178	+	21.8548i	−0.533678	+	0.924358i
$560$		0			0
$561$	−1.70279	+	1.42881i	−0.0718917	+	0.0603243i
$562$	2.80437	−	4.85732i	0.118295	−	0.204894i
$563$	7.22552	+	12.5150i	0.304519	+	0.527443i	0.977154	−	0.212532i	$-0.0681708\pi$
$563$	7.22552	+	12.5150i	0.304519	+	0.527443i	−0.672635	+	0.739975i	$0.734837\pi$
$564$	−18.0271	−	6.56134i	−0.759079	−	0.276282i
$565$		0			0
$566$	2.72427	+	15.4501i	0.114510	+	0.649416i
$567$	12.1648	−	4.42763i	0.510874	−	0.185943i
$568$	3.77859	+	3.17061i	0.158546	+	0.133036i
$569$	17.5025			0.733745			0.366872	−	0.930271i	$-0.380429\pi$
$569$	17.5025			0.733745			0.366872	+	0.930271i	$0.380429\pi$
$570$		0			0
$571$	15.5450			0.650537			0.325268	−	0.945622i	$-0.394545\pi$
$571$	15.5450			0.650537			0.325268	+	0.945622i	$0.394545\pi$
$572$	0.404358	+	0.339296i	0.0169070	+	0.0141867i
$573$	52.9564	−	19.2745i	2.21228	−	0.805206i
$574$	1.47504	+	8.36538i	0.0615671	+	0.349164i
$575$		0			0
$576$	−4.14543	−	1.50881i	−0.172726	−	0.0628672i
$577$	6.79752	+	11.7737i	0.282984	+	0.490143i	0.972118	−	0.234491i	$-0.0753422\pi$
$577$	6.79752	+	11.7737i	0.282984	+	0.490143i	−0.689134	+	0.724634i	$0.742009\pi$
$578$	−8.99097	+	15.5728i	−0.373975	+	0.647744i
$579$	18.5833	−	15.5932i	0.772296	−	0.648033i
$580$		0			0
$581$	27.9142	−	48.3487i	1.15807	−	2.00584i
$582$	9.21376	+	15.9587i	0.381923	+	0.661509i
$583$	−0.479612	−	0.174564i	−0.0198635	−	0.00722972i
$584$	−1.74502	+	9.89648i	−0.0722093	+	0.409519i
$585$		0			0
$586$	−18.7478	+	6.82363i	−0.774463	+	0.281881i
$587$	−21.9897	−	18.4515i	−0.907611	−	0.761576i	0.0640521	−	0.997947i	$-0.479598\pi$
$587$	−21.9897	−	18.4515i	−0.907611	−	0.761576i	−0.971663	+	0.236371i	$0.924042\pi$
$588$	40.2620			1.66038
$589$	−2.36569	−	24.3615i	−0.0974764	−	1.00380i
$590$		0			0
$591$	36.4711	+	30.6029i	1.50022	+	1.25884i
$592$	2.20686	−	0.803233i	0.0907016	−	0.0330127i
$593$	−5.74871	−	32.6026i	−0.236071	−	1.33883i	−0.840346	−	0.542051i	$-0.817648\pi$
$593$	−5.74871	−	32.6026i	−0.236071	−	1.33883i	0.604275	−	0.796776i	$-0.293463\pi$
$594$	−0.0921143	+	0.522406i	−0.00377950	+	0.0214346i
$595$		0			0
$596$	−4.92055	−	8.52264i	−0.201553	−	0.349101i
$597$	−22.6476	+	39.2268i	−0.926904	+	1.60545i
$598$	−17.6406	+	14.8022i	−0.721378	+	0.605308i
$599$	3.20093	−	2.68590i	0.130787	−	0.109743i	−0.575048	−	0.818120i	$-0.695017\pi$
$599$	3.20093	−	2.68590i	0.130787	−	0.109743i	0.705835	+	0.708377i	$0.250572\pi$
$600$		0			0
$601$	6.71590	+	11.6323i	0.273947	+	0.474490i	0.969869	−	0.243627i	$-0.0783373\pi$
$601$	6.71590	+	11.6323i	0.273947	+	0.474490i	−0.695922	+	0.718118i	$0.745004\pi$
$602$	28.9495	+	10.5368i	1.17989	+	0.429446i
$603$	−3.35029	+	19.0004i	−0.136434	+	0.773757i
$604$	−0.139714	−	0.792359i	−0.00568489	−	0.0322406i
$605$		0			0
$606$	6.21359	+	5.21382i	0.252410	+	0.211797i
$607$	−25.1952			−1.02264			−0.511321	−	0.859390i	$-0.670844\pi$
$607$	−25.1952			−1.02264			−0.511321	+	0.859390i	$0.670844\pi$
$608$	3.11146	+	3.05267i	0.126186	+	0.123802i
$609$	81.3056			3.29467
$610$		0			0
$611$	25.3194	−	9.21553i	1.02432	−	0.372820i
$612$	4.53081	+	25.6955i	0.183147	+	1.03868i
$613$	−3.88819	+	22.0510i	−0.157042	+	0.890632i	0.799852	+	0.600197i	$0.204911\pi$
$613$	−3.88819	+	22.0510i	−0.157042	+	0.890632i	−0.956895	+	0.290435i	$0.906200\pi$
$614$	−14.4144	−	5.24643i	−0.581719	−	0.211728i
$615$		0			0
$616$	0.322197	−	0.558062i	0.0129817	−	0.0224849i
$617$	28.2380	−	23.6945i	1.13682	−	0.953904i	0.137489	−	0.990503i	$-0.456097\pi$
$617$	28.2380	−	23.6945i	1.13682	−	0.953904i	0.999330	+	0.0365990i	$0.0116524\pi$
$618$	−30.7326	+	25.7877i	−1.23625	+	1.03733i
$619$	5.56491	−	9.63870i	0.223673	−	0.387412i	−0.732248	−	0.681038i	$-0.761529\pi$
$619$	5.56491	−	9.63870i	0.223673	−	0.387412i	0.955920	+	0.293626i	$0.0948620\pi$
$620$		0			0
$621$	−21.7466	−	7.91510i	−0.872659	−	0.317622i
$622$	−3.90159	+	22.1270i	−0.156440	+	0.887213i
$623$	−10.1632	−	57.6381i	−0.407178	−	2.30922i
$624$	9.78178	−	3.56028i	0.391585	−	0.142525i
$625$		0			0
$626$	−0.687238			−0.0274676
$627$	0.926779	−	1.35082i	0.0370120	−	0.0539464i
$628$	3.04452			0.121490
$629$	−10.6406	−	8.92852i	−0.424268	−	0.356003i
$630$		0			0
$631$	1.51355	+	8.58377i	0.0602535	+	0.341715i	1.00000		0.000157520i	$-5.01402e-5\pi$
$631$	1.51355	+	8.58377i	0.0602535	+	0.341715i	−0.939746	+	0.341872i	$0.888939\pi$
$632$	−2.41675	+	13.7060i	−0.0961330	+	0.545197i
$633$	69.5671	+	25.3204i	2.76504	+	1.00639i
$634$	4.96402	+	8.59794i	0.197147	+	0.341468i
$635$		0			0
$636$	−7.71043	+	6.46982i	−0.305738	+	0.256545i
$637$	−43.3188	+	36.3488i	−1.71635	+	1.44019i
$638$	0.441621	−	0.764911i	0.0174840	−	0.0302831i
$639$	−10.8800	−	18.8447i	−0.430407	−	0.745487i
$640$		0			0
$641$	1.39698	−	7.92265i	0.0551773	−	0.312926i	−0.944711	−	0.327906i	$-0.893657\pi$
$641$	1.39698	−	7.92265i	0.0551773	−	0.312926i	0.999888	+	0.0149796i	$0.00476834\pi$
$642$	0.246925	+	1.40038i	0.00974534	+	0.0552685i
$643$	34.3548	−	12.5041i	1.35482	−	0.493114i	0.440372	−	0.897816i	$-0.354847\pi$
$643$	34.3548	−	12.5041i	1.35482	−	0.493114i	0.914449	+	0.404701i	$0.132624\pi$
$644$	21.5354	+	18.0704i	0.848615	+	0.712072i
$645$		0			0
$646$	6.43479	−	24.9650i	0.253173	−	0.982234i
$647$	9.46927			0.372276			0.186138	−	0.982524i	$-0.440403\pi$
$647$	9.46927			0.372276			0.186138	+	0.982524i	$0.440403\pi$
$648$	−2.12449	−	1.78265i	−0.0834577	−	0.0700293i
$649$	1.15434	−	0.420144i	0.0453117	−	0.0164921i
$650$		0			0
$651$	−12.3910	+	70.2731i	−0.485643	+	2.75422i
$652$	−15.6170	−	5.68411i	−0.611608	−	0.222607i
$653$	−3.84213	−	6.65476i	−0.150354	−	0.260421i	0.781004	−	0.624527i	$-0.214708\pi$
$653$	−3.84213	−	6.65476i	−0.150354	−	0.260421i	−0.931358	+	0.364106i	$0.881375\pi$
$654$	8.18396	−	14.1750i	0.320018	−	0.554288i
$655$		0			0
$656$	1.39402	−	1.16972i	0.0544273	−	0.0456699i
$657$	22.1658	−	38.3923i	0.864769	−	1.49782i
$658$	−16.4467	−	28.4865i	−0.641159	−	1.11052i
$659$	−45.6152	−	16.6026i	−1.77692	−	0.646745i	−0.999850	−	0.0173281i	$-0.994484\pi$
$659$	−45.6152	−	16.6026i	−1.77692	−	0.646745i	−0.777068	−	0.629417i	$-0.783294\pi$
$660$		0			0
$661$	4.76812	+	27.0413i	0.185458	+	1.05179i	0.925365	+	0.379077i	$0.123758\pi$
$661$	4.76812	+	27.0413i	0.185458	+	1.05179i	−0.739907	+	0.672709i	$0.765131\pi$
$662$	17.3418	−	6.31188i	0.674007	−	0.245318i
$663$	−47.1637	−	39.5751i	−1.83169	−	1.53697i
$664$	−11.9601			−0.464142
$665$		0			0
$666$	−10.3603			−0.401455
$667$	29.5177	+	24.7683i	1.14293	+	0.959031i
$668$	10.6174	−	3.86443i	0.410801	−	0.149519i
$669$	−5.45305	−	30.9258i	−0.210827	−	1.19566i
$670$		0			0
$671$	1.18597	+	0.431659i	0.0457840	+	0.0166640i
$672$	−6.35393	−	11.0053i	−0.245108	−	0.424540i
$673$	5.96010	−	10.3232i	0.229745	−	0.397930i	−0.727988	−	0.685590i	$-0.759544\pi$
$673$	5.96010	−	10.3232i	0.229745	−	0.397930i	0.957732	+	0.287661i	$0.0928775\pi$
$674$	−10.2399	+	8.59230i	−0.394426	+	0.330963i
$675$		0			0
$676$	−0.810210	+	1.40333i	−0.0311619	+	0.0539741i
$677$	−6.46935	−	11.2052i	−0.248637	−	0.430652i	0.714511	−	0.699625i	$-0.246649\pi$
$677$	−6.46935	−	11.2052i	−0.248637	−	0.430652i	−0.963148	+	0.268972i	$0.913316\pi$
$678$	−15.2553	−	5.55249i	−0.585878	−	0.213242i
$679$	−5.48662	+	31.1162i	−0.210557	+	1.19413i
$680$		0			0
$681$	−15.3311	+	5.58005i	−0.587488	+	0.213828i
$682$	0.593815	+	0.498270i	0.0227383	+	0.0190797i
$683$	−28.7224			−1.09903			−0.549516	−	0.835483i	$-0.685188\pi$
$683$	−28.7224			−1.09903			−0.549516	+	0.835483i	$0.685188\pi$
$684$	−8.29244	−	17.3492i	−0.317069	−	0.663365i
$685$		0			0
$686$	27.8524	+	23.3709i	1.06341	+	0.892307i
$687$	−24.9603	+	9.08480i	−0.952294	+	0.346607i
$688$	−1.14606	−	6.49960i	−0.0436930	−	0.247795i
$689$	2.45483	−	13.9221i	0.0935218	−	0.530388i
$690$		0			0
$691$	−10.1778	−	17.6284i	−0.387181	−	0.670617i	0.604888	−	0.796310i	$-0.293218\pi$
$691$	−10.1778	−	17.6284i	−0.387181	−	0.670617i	−0.992069	+	0.125693i	$0.959884\pi$
$692$	0.933578	−	1.61700i	0.0354893	−	0.0614693i
$693$	−2.17766	+	1.82727i	−0.0827223	+	0.0694123i
$694$	−22.2843	+	18.6988i	−0.845901	+	0.709795i
$695$		0			0
$696$	−8.70905	−	15.0845i	−0.330116	−	0.571777i
$697$	−10.1140	−	3.68119i	−0.383094	−	0.139435i
$698$	−4.61878	+	26.1944i	−0.174823	+	0.991473i
$699$	12.6105	+	71.5178i	0.476974	+	2.70505i
$700$		0			0
$701$	−23.4983	−	19.7174i	−0.887520	−	0.744717i	0.0801914	−	0.996779i	$-0.474447\pi$
$701$	−23.4983	−	19.7174i	−0.887520	−	0.744717i	−0.967711	+	0.252062i	$0.918891\pi$
$702$	−14.6928			−0.554545
$703$	9.31858	+	4.23760i	0.351457	+	0.159824i
$704$	−0.138049			−0.00520290
$705$		0			0
$706$	−10.7941	+	3.92872i	−0.406240	+	0.147859i
$707$	2.41505	+	13.6964i	0.0908273	+	0.515107i
$708$	4.20666	−	23.8572i	0.158096	−	0.896608i
$709$	−19.8690	−	7.23173i	−0.746197	−	0.271593i	−0.0591922	−	0.998247i	$-0.518852\pi$
$709$	−19.8690	−	7.23173i	−0.746197	−	0.271593i	−0.687004	+	0.726653i	$0.741075\pi$
$710$		0			0
$711$	30.6983	−	53.1710i	1.15128	−	1.99407i
$712$	−9.60489	+	8.05946i	−0.359958	+	0.302041i
$713$	−25.9059	+	21.7376i	−0.970184	+	0.814081i
$714$	−37.5806	+	65.0916i	−1.40642	+	2.43599i
$715$		0			0
$716$	−4.20876	−	1.53186i	−0.157289	−	0.0572485i
$717$	8.19956	−	46.5020i	0.306218	−	1.73665i
$718$	−2.79208	−	15.8347i	−0.104200	−	0.590946i
$719$	5.78051	−	2.10393i	0.215577	−	0.0784635i	−0.231974	−	0.972722i	$-0.574519\pi$
$719$	5.78051	−	2.10393i	0.215577	−	0.0784635i	0.447551	+	0.894258i	$0.352296\pi$
$720$		0			0
$721$	−68.7880			−2.56180
$722$	0.362405	+	18.9965i	0.0134873	+	0.706978i
$723$	40.9876			1.52434
$724$	16.7448	+	14.0506i	0.622317	+	0.522186i
$725$		0			0
$726$	−5.19113	−	29.4404i	−0.192661	−	1.09263i
$727$	−2.25435	+	12.7851i	−0.0836094	+	0.474172i	0.914039	+	0.405627i	$0.132947\pi$
$727$	−2.25435	+	12.7851i	−0.0836094	+	0.474172i	−0.997648	+	0.0685453i	$0.978164\pi$
$728$	16.7720	+	6.10452i	0.621613	+	0.226249i
$729$	21.8089	+	37.7741i	0.807736	+	1.39904i
$730$		0			0
$731$	−29.9028	+	25.0914i	−1.10599	+	0.928039i
$732$	19.0662	−	15.9984i	0.704706	−	0.591318i
$733$	16.1718	−	28.0103i	0.597318	−	1.03459i	−0.395897	−	0.918295i	$-0.629566\pi$
$733$	16.1718	−	28.0103i	0.597318	−	1.03459i	0.993215	−	0.116290i	$-0.0371003\pi$
$734$	14.8031	+	25.6398i	0.546393	+	0.946381i
$735$		0			0
$736$	1.04580	−	5.93104i	0.0385488	−	0.218621i
$737$	0.104841	+	0.594581i	0.00386186	+	0.0219017i
$738$	−7.54369	+	2.74568i	−0.277687	+	0.101070i
$739$	9.49026	+	7.96327i	0.349105	+	0.292934i	0.800430	−	0.599426i	$-0.204604\pi$
$739$	9.49026	+	7.96327i	0.349105	+	0.292934i	−0.451326	+	0.892359i	$0.649049\pi$
$740$		0			0
$741$	41.3040	+	18.7829i	1.51734	+	0.690007i
$742$	−17.2581			−0.633563
$743$	37.4163	+	31.3960i	1.37267	+	1.15181i	0.971836	+	0.235659i	$0.0757249\pi$
$743$	37.4163	+	31.3960i	1.37267	+	1.15181i	0.400837	+	0.916150i	$0.368720\pi$
$744$	14.3649	−	5.22841i	0.526644	−	0.191683i
$745$		0			0
$746$	3.76207	−	21.3358i	0.137739	−	0.781158i
$747$	49.5797	+	18.0455i	1.81403	+	0.660252i
$748$	0.408248	+	0.707106i	0.0149270	+	0.0258543i
$749$	−1.21908	+	2.11151i	−0.0445442	+	0.0771528i
$750$		0			0
$751$	15.8455	−	13.2959i	0.578210	−	0.485176i	−0.306149	−	0.951984i	$-0.599040\pi$
$751$	15.8455	−	13.2959i	0.578210	−	0.485176i	0.884359	+	0.466808i	$0.154596\pi$
$752$	−3.52337	+	6.10266i	−0.128484	+	0.222541i
$753$	3.34215	+	5.78878i	0.121795	+	0.210955i
$754$	22.9887	+	8.36720i	0.837198	+	0.304715i
$755$		0			0
$756$	3.11469	+	17.6643i	0.113280	+	0.642445i
$757$	22.2249	−	8.08920i	0.807778	−	0.294007i	0.0950722	−	0.995470i	$-0.469692\pi$
$757$	22.2249	−	8.08920i	0.807778	−	0.294007i	0.712706	+	0.701463i	$0.247470\pi$
$758$	14.8630	+	12.4715i	0.539848	+	0.452987i
$759$	−2.26341			−0.0821566
$760$		0			0
$761$	−21.8364			−0.791570			−0.395785	−	0.918343i	$-0.629527\pi$
$761$	−21.8364			−0.791570			−0.395785	+	0.918343i	$0.629527\pi$
$762$	−17.3106	−	14.5253i	−0.627096	−	0.526196i
$763$	26.3723	−	9.59871i	0.954740	−	0.347497i
$764$	−3.59460	−	20.3860i	−0.130048	−	0.737539i
$765$		0			0
$766$	−21.2251	−	7.72532i	−0.766895	−	0.279127i
$767$	17.0124	+	29.4663i	0.614282	+	1.06397i
$768$	−1.36120	+	2.35767i	−0.0491181	+	0.0850751i
$769$	−30.1867	+	25.3297i	−1.08856	+	0.913411i	−0.996603	−	0.0823524i	$-0.973757\pi$
$769$	−30.1867	+	25.3297i	−1.08856	+	0.913411i	−0.0919571	+	0.995763i	$0.529312\pi$
$770$		0			0
$771$	−12.3101	+	21.3218i	−0.443339	+	0.767885i
$772$	−4.45540	−	7.71698i	−0.160353	−	0.277740i
$773$	22.5116	+	8.19356i	0.809687	+	0.294702i	0.713494	−	0.700661i	$-0.247111\pi$
$773$	22.5116	+	8.19356i	0.809687	+	0.294702i	0.0961923	+	0.995363i	$0.469334\pi$
$774$	−5.05579	+	28.6728i	−0.181727	+	1.03062i
$775$		0			0
$776$	6.36063	−	2.31508i	0.228333	−	0.0831066i
$777$	−22.8621	−	19.1836i	−0.820173	−	0.688207i
$778$	2.93104			0.105083
$779$	7.90821	+	0.615937i	0.283341	+	0.0220682i
$780$		0			0
$781$	−0.521629	−	0.437699i	−0.0186653	−	0.0156621i
$782$	−33.4724	+	12.1830i	−1.19697	+	0.435662i
$783$	4.26917	+	24.2117i	0.152568	+	0.865255i
$784$	2.56811	−	14.5644i	0.0917180	−	0.520159i
$785$		0			0
$786$	3.03578	+	5.25812i	0.108283	+	0.187551i
$787$	6.42750	−	11.1328i	0.229116	−	0.396840i	−0.728431	−	0.685120i	$-0.759750\pi$
$787$	6.42750	−	11.1328i	0.229116	−	0.396840i	0.957546	+	0.288280i	$0.0930833\pi$
$788$	13.3967	−	11.2411i	0.477237	−	0.400449i
$789$	−35.6649	+	29.9264i	−1.26970	+	1.06541i
$790$		0			0
$791$	−13.9179	−	24.1065i	−0.494863	−	0.857129i
$792$	0.572270	+	0.208289i	0.0203347	+	0.00740124i
$793$	−6.07026	+	34.4262i	−0.215561	+	1.22251i
$794$	−4.47939	−	25.4039i	−0.158968	−	0.901550i
$795$		0			0
$796$	12.7454	+	10.6947i	0.451749	+	0.379062i
$797$	−12.3873			−0.438782			−0.219391	−	0.975637i	$-0.570407\pi$
$797$	−12.3873			−0.438782			−0.219391	+	0.975637i	$0.570407\pi$
$798$	13.8256	−	53.6391i	0.489422	−	1.89880i
$799$	41.6783			1.47447
$800$		0			0
$801$	51.9766	−	18.9179i	1.83650	−	0.668433i
$802$	−6.12342	−	34.7277i	−0.216226	−	1.22628i
$803$	0.240897	−	1.36619i	0.00850107	−	0.0482119i
$804$	11.1884	+	4.07223i	0.394583	+	0.143616i
$805$		0			0
$806$	−10.7353	+	18.5941i	−0.378136	+	0.654950i
$807$	2.02296	−	1.69747i	0.0712117	−	0.0597537i
$808$	2.28239	−	1.91515i	0.0802942	−	0.0673748i
$809$	−1.36313	+	2.36101i	−0.0479251	+	0.0830088i	−0.888993	−	0.457921i	$-0.848594\pi$
$809$	−1.36313	+	2.36101i	−0.0479251	+	0.0830088i	0.841068	+	0.540930i	$0.181928\pi$
$810$		0			0
$811$	0.421513	+	0.153418i	0.0148013	+	0.00538724i	0.349410	−	0.936970i	$-0.386382\pi$
$811$	0.421513	+	0.153418i	0.0148013	+	0.00538724i	−0.334609	+	0.942357i	$0.608604\pi$
$812$	5.18607	−	29.4117i	0.181995	−	1.03215i
$813$	−2.40653	−	13.6481i	−0.0844006	−	0.478660i
$814$	−0.304654	+	0.110885i	−0.0106781	+	0.00388652i
$815$		0			0
$816$	16.1018			0.563676
$817$	16.2752	−	23.7218i	0.569399	−	0.829921i
$818$	13.8810			0.485336
$819$	−60.3167	−	50.6117i	−2.10764	−	1.76852i
$820$		0			0
$821$	−0.873894	−	4.95610i	−0.0304991	−	0.172969i	0.965753	−	0.259462i	$-0.0835452\pi$
$821$	−0.873894	−	4.95610i	−0.0304991	−	0.172969i	−0.996252	+	0.0864927i	$0.972434\pi$
$822$	1.66704	−	9.45424i	0.0581446	−	0.329755i
$823$	8.60047	+	3.13031i	0.299793	+	0.109116i	0.487537	−	0.873102i	$-0.337895\pi$
$823$	8.60047	+	3.13031i	0.299793	+	0.109116i	−0.187744	+	0.982218i	$0.560118\pi$
$824$	7.36822	+	12.7621i	0.256684	+	0.444590i
$825$		0			0
$826$	31.8192	−	26.6995i	1.10713	−	0.928994i
$827$	−2.10252	+	1.76423i	−0.0731119	+	0.0613482i	−0.678611	−	0.734498i	$-0.737418\pi$
$827$	−2.10252	+	1.76423i	−0.0731119	+	0.0613482i	0.605499	+	0.795846i	$0.292973\pi$
$828$	−13.2841	+	23.0088i	−0.461656	+	0.799611i
$829$	2.51643	+	4.35858i	0.0873991	+	0.151380i	0.906411	−	0.422397i	$-0.138811\pi$
$829$	2.51643	+	4.35858i	0.0873991	+	0.151380i	−0.819012	+	0.573777i	$0.805478\pi$
$830$		0			0
$831$	9.58424	−	54.3549i	0.332474	−	1.88555i
$832$	−0.663973	−	3.76558i	−0.0230191	−	0.130548i
$833$	−82.1959	+	29.9169i	−2.84792	+	1.03656i
$834$	−10.2883	−	8.63292i	−0.356255	−	0.298934i
$835$		0			0
$836$	−0.429533	−	0.421417i	−0.0148557	−	0.0145750i
$837$	−21.5770			−0.745809
$838$	−2.35482	−	1.97593i	−0.0813460	−	0.0682574i
$839$	35.7096	−	12.9972i	1.23283	−	0.448715i	0.358267	−	0.933619i	$-0.383368\pi$
$839$	35.7096	−	12.9972i	1.23283	−	0.448715i	0.874567	+	0.484904i	$0.161146\pi$
$840$		0			0
$841$	2.07252	−	11.7539i	0.0714663	−	0.405305i
$842$	−19.2422	−	7.00360i	−0.663131	−	0.241360i
$843$	7.63464	+	13.2236i	0.262951	+	0.455444i
$844$	13.5968	−	23.5503i	0.468020	−	0.810635i
$845$		0			0
$846$	23.8137	−	19.9820i	0.818731	−	0.686997i
$847$	25.6289	−	44.3905i	0.880619	−	1.52528i
$848$	1.84860	+	3.20186i	0.0634811	+	0.109952i
$849$	−40.1345	−	14.6078i	−1.37741	−	0.501337i
$850$		0			0
$851$	−2.45606	−	13.9290i	−0.0841928	−	0.477481i
$852$	−12.6187	+	4.59283i	−0.432309	+	0.157348i
$853$	33.6835	+	28.2638i	1.15330	+	0.967735i	0.999792	−	0.0204116i	$-0.00649768\pi$
$853$	33.6835	+	28.2638i	1.15330	+	0.967735i	0.153510	+	0.988147i	$0.450942\pi$
$854$	42.6753			1.46032
$855$		0			0
$856$	0.522326			0.0178527
$857$	13.4206	+	11.2612i	0.458438	+	0.384675i	0.842556	−	0.538609i	$-0.181050\pi$
$857$	13.4206	+	11.2612i	0.458438	+	0.384675i	−0.384118	+	0.923284i	$0.625494\pi$
$858$	−1.35036	+	0.491491i	−0.0461006	+	0.0167792i
$859$	5.08692	+	28.8494i	0.173563	+	0.984327i	0.939789	+	0.341755i	$0.111021\pi$
$859$	5.08692	+	28.8494i	0.173563	+	0.984327i	−0.766225	+	0.642572i	$0.777867\pi$
$860$		0			0
$861$	−21.7306	−	7.90931i	−0.740578	−	0.269548i
$862$	8.36515	+	14.4889i	0.284918	+	0.493493i
$863$	21.3043	−	36.9001i	0.725206	−	1.25609i	−0.233683	−	0.972313i	$-0.575078\pi$
$863$	21.3043	−	36.9001i	0.725206	−	1.25609i	0.958889	−	0.283781i	$-0.0915888\pi$
$864$	2.94360	−	2.46998i	0.100143	−	0.0840303i
$865$		0			0
$866$	−13.1419	+	22.7624i	−0.446579	+	0.773497i
$867$	−24.4770	−	42.3955i	−0.831284	−	1.43983i
$868$	24.6304	+	8.96472i	0.836009	+	0.304283i
$869$	0.333628	−	1.89210i	0.0113176	−	0.0641851i
$870$		0			0
$871$	−15.7143	+	5.71952i	−0.532457	+	0.193799i
$872$	−4.60570	−	3.86464i	−0.155969	−	0.130873i
$873$	−29.8606			−1.01063
$874$	21.3595	−	15.2617i	0.722496	−	0.516236i
$875$		0			0
$876$	−20.9573	−	17.5853i	−0.708082	−	0.594151i
$877$	40.5395	−	14.7552i	1.36892	−	0.498247i	0.450121	−	0.892967i	$-0.351381\pi$
$877$	40.5395	−	14.7552i	1.36892	−	0.498247i	0.918801	+	0.394720i	$0.129158\pi$
$878$	−3.34577	−	18.9748i	−0.112914	−	0.640369i
$879$	9.43162	−	53.4894i	0.318121	−	1.80415i
$880$		0			0
$881$	3.73599	+	6.47092i	0.125869	+	0.218011i	0.922072	−	0.387018i	$-0.126495\pi$
$881$	3.73599	+	6.47092i	0.125869	+	0.218011i	−0.796204	+	0.605029i	$0.793162\pi$
$882$	−32.6209	+	56.5011i	−1.09840	+	1.90249i
$883$	−14.4078	+	12.0896i	−0.484862	+	0.406848i	−0.852181	−	0.523247i	$-0.824720\pi$
$883$	−14.4078	+	12.0896i	−0.484862	+	0.406848i	0.367318	+	0.930095i	$0.380276\pi$
$884$	−17.3243	+	14.5368i	−0.582680	+	0.488926i
$885$		0			0
$886$	−13.6762	−	23.6879i	−0.459461	−	0.795811i
$887$	−43.9058	−	15.9804i	−1.47421	−	0.536570i	−0.524972	−	0.851119i	$-0.675924\pi$
$887$	−43.9058	−	15.9804i	−1.47421	−	0.536570i	−0.949241	+	0.314550i	$0.898146\pi$
$888$	−1.11023	+	6.29642i	−0.0372568	+	0.211294i
$889$	−6.72814	−	38.1572i	−0.225655	−	1.27975i
$890$		0			0
$891$	0.293282	+	0.246093i	0.00982532	+	0.00824442i
$892$	−11.5350			−0.386220
$893$	−29.5923	+	8.23251i	−0.990267	+	0.275490i
$894$	26.7914			0.896039
$895$		0			0
$896$	−4.38637	+	1.59651i	−0.146539	+	0.0533357i
$897$	−10.8863	−	61.7395i	−0.363484	−	2.06142i
$898$	4.74436	−	26.9066i	0.158321	−	0.897885i
$899$	33.7598	+	12.2876i	1.12595	+	0.409813i
$900$		0			0
$901$	10.9336	−	18.9376i	0.364252	−	0.630903i
$902$	−0.192442	+	0.161478i	−0.00640762	+	0.00537663i
$903$	−64.2483	+	53.9107i	−2.13805	+	1.79404i
$904$	−2.98163	+	5.16433i	−0.0991675	+	0.171763i
$905$		0			0
$906$	2.05830	+	0.749160i	0.0683824	+	0.0248892i
$907$	2.16514	−	12.2791i	0.0718923	−	0.407722i	−0.927530	−	0.373748i	$-0.878073\pi$
$907$	2.16514	−	12.2791i	0.0718923	−	0.407722i	0.999423	−	0.0339740i	$-0.0108163\pi$
$908$	1.04065	+	5.90182i	0.0345352	+	0.195859i
$909$	−12.3511	+	4.49543i	−0.409660	+	0.149104i
$910$		0			0
$911$	−19.0731			−0.631920			−0.315960	−	0.948773i	$-0.602327\pi$
$911$	−19.0731			−0.631920			−0.315960	+	0.948773i	$0.602327\pi$
$912$	−11.4325	+	3.18050i	−0.378568	+	0.105317i
$913$	1.65107			0.0546425
$914$	−15.6659	−	13.1452i	−0.518182	−	0.434806i
$915$		0			0
$916$	1.69427	+	9.60866i	0.0559801	+	0.317479i
$917$	−1.80775	+	10.2522i	−0.0596971	+	0.338559i
$918$	−21.3566	−	7.77318i	−0.704874	−	0.256553i
$919$	−18.1413	−	31.4217i	−0.598427	−	1.03651i	−0.993053	−	0.117664i	$-0.962459\pi$
$919$	−18.1413	−	31.4217i	−0.598427	−	1.03651i	0.394626	−	0.918842i	$-0.370874\pi$
$920$		0			0
$921$	31.9903	−	26.8430i	1.05412	−	0.884508i
$922$	17.5478	−	14.7244i	0.577907	−	0.484921i
$923$	9.43031	−	16.3338i	0.310402	−	0.537633i
$924$	0.877150	+	1.51927i	0.0288561	+	0.0499803i
$925$		0			0
$926$	0.716329	−	4.06250i	0.0235400	−	0.133502i
$927$	−11.2888	−	64.0218i	−0.370772	−	2.10275i
$928$	−6.01221	+	2.18827i	−0.197360	+	0.0718333i
$929$	−2.39685	−	2.01119i	−0.0786380	−	0.0659851i	0.602621	−	0.798027i	$-0.294123\pi$
$929$	−2.39685	−	2.01119i	−0.0786380	−	0.0659851i	−0.681259	+	0.732042i	$0.738567\pi$
$930$		0			0
$931$	52.4510	−	37.4772i	1.71901	−	1.22826i
$932$	26.6754			0.873781
$933$	−46.8574	−	39.3180i	−1.53404	−	1.28721i
$934$	−20.6160	+	7.50362i	−0.674577	+	0.245526i
$935$		0			0
$936$	−2.92910	+	16.6117i	−0.0957406	+	0.542972i
$937$	−10.8419	−	3.94612i	−0.354188	−	0.128914i	0.158797	−	0.987311i	$-0.449238\pi$
$937$	−10.8419	−	3.94612i	−0.354188	−	0.128914i	−0.512986	+	0.858397i	$0.671461\pi$
$938$	10.2075	+	17.6799i	0.333286	+	0.577268i
$939$	0.935469	−	1.62028i	0.0305279	−	0.0528759i
$940$		0			0
$941$	14.2183	−	11.9306i	0.463503	−	0.388925i	−0.380915	−	0.924610i	$-0.624391\pi$
$941$	14.2183	−	11.9306i	0.463503	−	0.388925i	0.844418	+	0.535685i	$0.179946\pi$
$942$	−4.14421	+	7.17798i	−0.135026	+	0.233871i
$943$	−5.47979	−	9.49128i	−0.178447	−	0.309078i
$944$	−8.36183	−	3.04346i	−0.272154	−	0.0990560i
$945$		0			0
$946$	0.158211	+	0.897261i	0.00514389	+	0.0291725i
$947$	−47.8593	+	17.4193i	−1.55522	+	0.566053i	−0.969634	−	0.244560i	$-0.921357\pi$
$947$	−47.8593	+	17.4193i	−1.55522	+	0.566053i	−0.585583	+	0.810612i	$0.699134\pi$
$948$	−29.0247	−	24.3546i	−0.942677	−	0.791000i
$949$	38.4246			1.24731
$950$		0			0
$951$	−27.0281			−0.876448
$952$	21.1493	+	17.7464i	0.685453	+	0.575163i
$953$	−10.7930	+	3.92833i	−0.349620	+	0.127251i	−0.510860	−	0.859664i	$-0.670673\pi$
$953$	−10.7930	+	3.92833i	−0.349620	+	0.127251i	0.161240	+	0.986915i	$0.448451\pi$
$954$	−2.83221	−	16.0623i	−0.0916963	−	0.520036i
$955$		0			0
$956$	−16.2987	−	5.93225i	−0.527139	−	0.191863i
$957$	1.20227	+	2.08239i	0.0388639	+	0.0673143i
$958$	5.48008	−	9.49178i	0.177053	−	0.306665i
$959$	12.6095	−	10.5806i	0.407181	−	0.341666i
$960$		0			0
$961$	−0.265242	+	0.459412i	−0.00855619	+	0.0148198i
$962$	−4.48993	−	7.77679i	−0.144761	−	0.250734i
$963$	−2.16527	−	0.788093i	−0.0697747	−	0.0253959i
$964$	2.61439	−	14.8269i	0.0842038	−	0.477543i
$965$		0			0
$966$	−71.9180	+	26.1760i	−2.31392	+	0.842199i
$967$	−8.10743	−	6.80294i	−0.260717	−	0.218768i	0.503054	−	0.864255i	$-0.332210\pi$
$967$	−8.10743	−	6.80294i	−0.260717	−	0.218768i	−0.763771	+	0.645487i	$0.776654\pi$
$968$	−10.9809			−0.352941
$969$	50.1001	+	49.1535i	1.60945	+	1.57904i
$970$		0			0
$971$	14.1027	+	11.8335i	0.452576	+	0.379757i	0.840391	−	0.541981i	$-0.182325\pi$
$971$	14.1027	+	11.8335i	0.452576	+	0.379757i	−0.387815	+	0.921737i	$0.626770\pi$
$972$	17.9274	−	6.52502i	0.575020	−	0.209290i
$973$	−3.99879	−	22.6782i	−0.128195	−	0.727031i
$974$	−2.45151	+	13.9032i	−0.0785514	+	0.445487i
$975$		0			0
$976$	−4.57117	−	7.91749i	−0.146320	−	0.253433i
$977$	2.73143	−	4.73098i	0.0873863	−	0.151358i	−0.819019	−	0.573766i	$-0.805482\pi$
$977$	2.73143	−	4.73098i	0.0873863	−	0.151358i	0.906406	+	0.422408i	$0.138815\pi$
$978$	34.6591	−	29.0824i	1.10828	−	0.929954i
$979$	1.32594	−	1.11260i	0.0423772	−	0.0355587i
$980$		0			0
$981$	13.2616	+	22.9697i	0.423410	+	0.733367i
$982$	28.2855	+	10.2951i	0.902627	+	0.328529i
$983$	9.51326	−	53.9524i	0.303426	−	1.72081i	−0.327397	−	0.944887i	$-0.606171\pi$
$983$	9.51326	−	53.9524i	0.303426	−	1.72081i	0.630823	−	0.775927i	$-0.282718\pi$
$984$	0.860274	+	4.87886i	0.0274245	+	0.155532i
$985$		0			0
$986$	28.9884	+	24.3242i	0.923179	+	0.774639i
$987$	89.5490			2.85038
$988$	9.42914	−	13.7433i	0.299981	−	0.437234i
$989$	−39.7480			−1.26391
$990$		0			0
$991$	−29.1365	+	10.6048i	−0.925551	+	0.336873i	−0.760445	−	0.649403i	$-0.775019\pi$
$991$	−29.1365	+	10.6048i	−0.925551	+	0.336873i	−0.165106	+	0.986276i	$0.552797\pi$
$992$	−0.975069	−	5.52989i	−0.0309585	−	0.175574i
$993$	−8.72428	+	49.4779i	−0.276857	+	1.57013i
$994$	−21.6362	−	7.87495i	−0.686260	−	0.249778i
$995$		0			0
$996$	16.2801	−	28.1979i	0.515854	−	0.893486i
$997$	10.8099	−	9.07058i	0.342353	−	0.287268i	−0.455358	−	0.890308i	$-0.650489\pi$
$997$	10.8099	−	9.07058i	0.342353	−	0.287268i	0.797711	+	0.603040i	$0.206044\pi$
$998$	−8.46815	+	7.10562i	−0.268055	+	0.224924i
$999$	4.51217	−	7.81530i	0.142759	−	0.247265i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.h.301.1		12
5.2	odd	4		950.2.u.e.149.2		24
5.3	odd	4		950.2.u.e.149.3		24
5.4	even	2		190.2.k.b.111.2	yes	12
19.6	even	9	inner	950.2.l.h.101.1		12
95.14	odd	18		3610.2.a.be.1.6		6
95.24	even	18		3610.2.a.bc.1.1		6
95.44	even	18		190.2.k.b.101.2	✓	12
95.63	odd	36		950.2.u.e.899.2		24
95.82	odd	36		950.2.u.e.899.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.b.101.2	✓	12	95.44	even	18
190.2.k.b.111.2	yes	12	5.4	even	2
950.2.l.h.101.1		12	19.6	even	9	inner
950.2.l.h.301.1		12	1.1	even	1	trivial
950.2.u.e.149.2		24	5.2	odd	4
950.2.u.e.149.3		24	5.3	odd	4
950.2.u.e.899.2		24	95.63	odd	36
950.2.u.e.899.3		24	95.82	odd	36
3610.2.a.bc.1.1		6	95.24	even	18
3610.2.a.be.1.6		6	95.14	odd	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)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(-2.55822 + 0.931116i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-2.55822 - 0.931116i) q^{6} +(-2.33394 - 4.04250i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(3.37939 - 2.83564i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(-2.55822 + 0.931116i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-2.55822 - 0.931116i) q^{6} +(-2.33394 - 4.04250i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(3.37939 - 2.83564i) q^{9} +(0.0690243 - 0.119554i) q^{11} +(-1.36120 - 2.35767i) q^{12} +(3.59307 + 1.30777i) q^{13} +(0.810569 - 4.59697i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(4.53081 + 3.80180i) q^{17} +4.41147 q^{18} +(-3.96789 - 1.80439i) q^{19} +(9.73478 + 8.16845i) q^{21} +(0.129723 - 0.0472154i) q^{22} +(1.04580 + 5.93104i) q^{23} +(0.472740 - 2.68104i) q^{24} +(1.91183 + 3.31139i) q^{26} +(-1.92130 + 3.32779i) q^{27} +(3.57581 - 3.00046i) q^{28} +(4.90120 - 4.11259i) q^{29} +(2.80760 + 4.86291i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-0.0652611 + 0.370114i) q^{33} +(1.02705 + 5.82470i) q^{34} +(3.37939 + 2.83564i) q^{36} -2.34850 q^{37} +(-1.87974 - 3.93276i) q^{38} -10.4096 q^{39} +(-1.71002 + 0.622395i) q^{41} +(2.20670 + 12.5148i) q^{42} +(-1.14606 + 6.49960i) q^{43} +(0.129723 + 0.0472154i) q^{44} +(-3.01127 + 5.21567i) q^{46} +(5.39812 - 4.52956i) q^{47} +(2.08548 - 1.74993i) q^{48} +(-7.39456 + 12.8078i) q^{49} +(-15.1307 - 5.50714i) q^{51} +(-0.663973 + 3.76558i) q^{52} +(-0.642011 - 3.64102i) q^{53} +(-3.61086 + 1.31425i) q^{54} +4.66788 q^{56} +(11.8308 + 0.921455i) q^{57} +6.39806 q^{58} +(6.81662 + 5.71983i) q^{59} +(1.58755 + 9.00344i) q^{61} +(-0.975069 + 5.52989i) q^{62} +(-19.3504 - 7.04296i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.287898 + 0.241575i) q^{66} +(-3.35029 + 2.81122i) q^{67} +(-2.95728 + 5.12215i) q^{68} +(-8.19789 - 14.1992i) q^{69} +(0.856537 - 4.85766i) q^{71} +(0.766044 + 4.34445i) q^{72} +(9.44311 - 3.43701i) q^{73} +(-1.79905 - 1.50958i) q^{74} +(1.08796 - 4.22094i) q^{76} -0.644394 q^{77} +(-7.97418 - 6.69113i) q^{78} +(13.0782 - 4.76006i) q^{79} +(-0.481582 + 2.73119i) q^{81} +(-1.71002 - 0.622395i) q^{82} +(5.98005 + 10.3577i) q^{83} +(-6.35393 + 11.0053i) q^{84} +(-5.05579 + 4.24231i) q^{86} +(-8.70905 + 15.0845i) q^{87} +(0.0690243 + 0.119554i) q^{88} +(11.7821 + 4.28835i) q^{89} +(-3.09935 - 17.5773i) q^{91} +(-5.65933 + 2.05983i) q^{92} +(-11.7104 - 9.82619i) q^{93} +7.04674 q^{94} +2.72240 q^{96} +(-5.18524 - 4.35093i) q^{97} +(-13.8972 + 5.05818i) q^{98} +(-0.105751 - 0.599745i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{7} - 6 q^{8} + 18 q^{9}+O(q^{10}) \) 12 * q - 6 * q^7 - 6 * q^8 + 18 * q^9	\( 12 q - 6 q^{7} - 6 q^{8} + 18 q^{9} + 6 q^{11} - 6 q^{13} + 18 q^{17} + 12 q^{18} + 12 q^{21} + 6 q^{22} + 30 q^{23} - 6 q^{29} + 6 q^{31} + 24 q^{33} + 18 q^{36} - 36 q^{37} - 18 q^{38} - 36 q^{39} - 6 q^{41} + 30 q^{42} + 6 q^{44} - 12 q^{46} + 6 q^{47} - 18 q^{49} + 12 q^{52} + 12 q^{53} + 12 q^{56} + 18 q^{57} + 36 q^{58} - 24 q^{59} - 30 q^{61} + 6 q^{62} - 18 q^{63} - 6 q^{64} + 24 q^{66} - 12 q^{67} - 12 q^{68} + 6 q^{69} - 42 q^{71} - 6 q^{73} + 6 q^{74} + 18 q^{76} + 24 q^{77} - 48 q^{78} + 60 q^{79} + 18 q^{81} - 6 q^{82} - 24 q^{83} - 24 q^{84} - 36 q^{86} - 54 q^{87} + 6 q^{88} - 12 q^{89} + 24 q^{91} - 24 q^{92} - 6 q^{93} + 60 q^{94} - 30 q^{97} - 36 q^{98} - 12 q^{99}+O(q^{100}) \) 12 * q - 6 * q^7 - 6 * q^8 + 18 * q^9 + 6 * q^11 - 6 * q^13 + 18 * q^17 + 12 * q^18 + 12 * q^21 + 6 * q^22 + 30 * q^23 - 6 * q^29 + 6 * q^31 + 24 * q^33 + 18 * q^36 - 36 * q^37 - 18 * q^38 - 36 * q^39 - 6 * q^41 + 30 * q^42 + 6 * q^44 - 12 * q^46 + 6 * q^47 - 18 * q^49 + 12 * q^52 + 12 * q^53 + 12 * q^56 + 18 * q^57 + 36 * q^58 - 24 * q^59 - 30 * q^61 + 6 * q^62 - 18 * q^63 - 6 * q^64 + 24 * q^66 - 12 * q^67 - 12 * q^68 + 6 * q^69 - 42 * q^71 - 6 * q^73 + 6 * q^74 + 18 * q^76 + 24 * q^77 - 48 * q^78 + 60 * q^79 + 18 * q^81 - 6 * q^82 - 24 * q^83 - 24 * q^84 - 36 * q^86 - 54 * q^87 + 6 * q^88 - 12 * q^89 + 24 * q^91 - 24 * q^92 - 6 * q^93 + 60 * q^94 - 30 * q^97 - 36 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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