LMFDB - Embedded newform 91.2.e.c.79.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [91,2,Mod(53,91)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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			79.1
Root			$-0.862625 + 1.49411i$ of defining polynomial
Character	$\chi$	$=$	91.79
Dual form			91.2.e.c.53.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36263 + 2.36014i) q^{2} +(0.673208 + 1.16603i) q^{3} +(-2.71349 - 4.69991i) q^{4} +(-1.09358 + 1.89414i) q^{5} -3.66932 q^{6} +(-2.19729 + 1.47375i) q^{7} +9.33940 q^{8} +(0.593582 - 1.02811i) q^{9} +(-2.98028 - 5.16200i) q^{10} +(0.524077 + 0.907729i) q^{11} +(3.65349 - 6.32803i) q^{12} +1.00000 q^{13} +(-0.484172 - 7.19406i) q^{14} -2.94483 q^{15} +(-7.29912 + 12.6424i) q^{16} +(2.64562 + 4.58236i) q^{17} +(1.61766 + 2.80187i) q^{18} +(-0.378453 + 0.655500i) q^{19} +11.8697 q^{20} +(-3.19767 - 1.56996i) q^{21} -2.85648 q^{22} +(-0.326792 + 0.566020i) q^{23} +(6.28736 + 10.8900i) q^{24} +(0.108157 + 0.187333i) q^{25} +(-1.36263 + 2.36014i) q^{26} +5.63766 q^{27} +(12.8888 + 6.32803i) q^{28} -3.10408 q^{29} +(4.01270 - 6.95021i) q^{30} +(-0.513956 - 0.890198i) q^{31} +(-10.5525 - 18.2775i) q^{32} +(-0.705626 + 1.22218i) q^{33} -14.4200 q^{34} +(-0.388575 - 5.77363i) q^{35} -6.44273 q^{36} +(5.44661 - 9.43381i) q^{37} +(-1.03138 - 1.78640i) q^{38} +(0.673208 + 1.16603i) q^{39} +(-10.2134 + 17.6901i) q^{40} +7.32040 q^{41} +(8.06254 - 5.40766i) q^{42} +0.887771 q^{43} +(2.84416 - 4.92623i) q^{44} +(1.29826 + 2.24865i) q^{45} +(-0.890590 - 1.54255i) q^{46} +(-1.16875 + 2.02434i) q^{47} -19.6553 q^{48} +(2.65613 - 6.47650i) q^{49} -0.589510 q^{50} +(-3.56211 + 6.16976i) q^{51} +(-2.71349 - 4.69991i) q^{52} +(-2.44407 - 4.23325i) q^{53} +(-7.68202 + 13.3057i) q^{54} -2.29249 q^{55} +(-20.5213 + 13.7639i) q^{56} -1.01911 q^{57} +(4.22970 - 7.32606i) q^{58} +(0.524077 + 0.907729i) q^{59} +(7.99079 + 13.8404i) q^{60} +(6.24989 - 10.8251i) q^{61} +2.80132 q^{62} +(0.210913 + 3.13385i) q^{63} +28.3200 q^{64} +(-1.09358 + 1.89414i) q^{65} +(-1.92301 - 3.33075i) q^{66} +(-2.23944 - 3.87883i) q^{67} +(14.3578 - 24.8684i) q^{68} -0.879996 q^{69} +(14.1560 + 6.95021i) q^{70} -6.60274 q^{71} +(5.54370 - 9.60197i) q^{72} +(4.14174 + 7.17370i) q^{73} +(14.8434 + 25.7095i) q^{74} +(-0.145624 + 0.252229i) q^{75} +4.10772 q^{76} +(-2.48931 - 1.22218i) q^{77} -3.66932 q^{78} +(-1.07007 + 1.85342i) q^{79} +(-15.9644 - 27.6511i) q^{80} +(2.01457 + 3.48935i) q^{81} +(-9.97496 + 17.2771i) q^{82} -6.66558 q^{83} +(1.29817 + 19.2888i) q^{84} -11.5728 q^{85} +(-1.20970 + 2.09526i) q^{86} +(-2.08969 - 3.61946i) q^{87} +(4.89457 + 8.47765i) q^{88} +(2.88388 - 4.99503i) q^{89} -7.07617 q^{90} +(-2.19729 + 1.47375i) q^{91} +3.54699 q^{92} +(0.691998 - 1.19858i) q^{93} +(-3.18515 - 5.51684i) q^{94} +(-0.827739 - 1.43369i) q^{95} +(14.2081 - 24.6091i) q^{96} -2.88777 q^{97} +(11.6661 + 15.0939i) q^{98} +1.24433 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} + 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}+ \cdots + 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

Character values

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

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

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 $

$2$	−1.36263	+	2.36014i	−0.963521	+	1.66887i	−0.249986	+	0.968250i	$0.580426\pi$
$2$	−1.36263	+	2.36014i	−0.963521	+	1.66887i	−0.713536	+	0.700619i	$0.752907\pi$
$3$	0.673208	+	1.16603i	0.388677	+	0.673208i	0.992272	−	0.124083i	$-0.0395989\pi$
$3$	0.673208	+	1.16603i	0.388677	+	0.673208i	−0.603595	+	0.797291i	$0.706266\pi$
$4$	−2.71349	−	4.69991i	−1.35675	−	2.34996i
$5$	−1.09358	+	1.89414i	−0.489065	+	0.847085i	−0.999921	−	0.0125813i	$-0.995995\pi$
$5$	−1.09358	+	1.89414i	−0.489065	+	0.847085i	0.510856	+	0.859666i	$0.329328\pi$
$6$	−3.66932			−1.49799
$7$	−2.19729	+	1.47375i	−0.830496	+	0.557025i
$7$	−2.19729	+	1.47375i	−0.830496	+	0.557025i
$8$	9.33940			3.30198
$9$	0.593582	−	1.02811i	0.197861	−	0.342705i
$10$	−2.98028	−	5.16200i	−0.942449	−	1.63237i
$11$	0.524077	+	0.907729i	0.158015	+	0.273691i	0.934153	−	0.356873i	$-0.116157\pi$
$11$	0.524077	+	0.907729i	0.158015	+	0.273691i	−0.776138	+	0.630564i	$0.782824\pi$
$12$	3.65349	−	6.32803i	1.05467	−	1.82675i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−0.484172	−	7.19406i	−0.129400	−	1.92269i
$15$	−2.94483			−0.760352
$16$	−7.29912	+	12.6424i	−1.82478	+	3.16061i
$17$	2.64562	+	4.58236i	0.641658	+	1.11138i	0.985063	+	0.172197i	$0.0550865\pi$
$17$	2.64562	+	4.58236i	0.641658	+	1.11138i	−0.343404	+	0.939188i	$0.611580\pi$
$18$	1.61766	+	2.80187i	0.381286	+	0.660407i
$19$	−0.378453	+	0.655500i	−0.0868231	+	0.150382i	−0.906167	−	0.422921i	$-0.861005\pi$
$19$	−0.378453	+	0.655500i	−0.0868231	+	0.150382i	0.819344	+	0.573303i	$0.194338\pi$
$20$	11.8697			2.65415
$21$	−3.19767	−	1.56996i	−0.697788	−	0.342594i
$22$	−2.85648			−0.609005
$23$	−0.326792	+	0.566020i	−0.0681408	+	0.118023i	−0.898083	−	0.439826i	$-0.855040\pi$
$23$	−0.326792	+	0.566020i	−0.0681408	+	0.118023i	0.829942	+	0.557850i	$0.188373\pi$
$24$	6.28736	+	10.8900i	1.28340	+	2.22292i
$25$	0.108157	+	0.187333i	0.0216314	+	0.0374667i
$26$	−1.36263	+	2.36014i	−0.267233	+	0.462861i
$27$	5.63766			1.08497
$28$	12.8888	+	6.32803i	2.43576	+	1.19589i
$29$	−3.10408			−0.576414			−0.288207	−	0.957568i	$-0.593059\pi$
$29$	−3.10408			−0.576414			−0.288207	+	0.957568i	$0.593059\pi$
$30$	4.01270	−	6.95021i	0.732616	−	1.26893i
$31$	−0.513956	−	0.890198i	−0.0923092	−	0.159884i	0.816173	−	0.577807i	$-0.196091\pi$
$31$	−0.513956	−	0.890198i	−0.0923092	−	0.159884i	−0.908482	+	0.417923i	$0.862758\pi$
$32$	−10.5525	−	18.2775i	−1.86544	−	3.23104i
$33$	−0.705626	+	1.22218i	−0.122834	+	0.212754i
$34$	−14.4200			−2.47301
$35$	−0.388575	−	5.77363i	−0.0656811	−	0.975922i
$36$	−6.44273			−1.07379
$37$	5.44661	−	9.43381i	0.895418	−	1.55091i	0.0621309	−	0.998068i	$-0.480210\pi$
$37$	5.44661	−	9.43381i	0.895418	−	1.55091i	0.833287	−	0.552841i	$-0.186456\pi$
$38$	−1.03138	−	1.78640i	−0.167312	−	0.289793i
$39$	0.673208	+	1.16603i	0.107800	+	0.186714i
$40$	−10.2134	+	17.6901i	−1.61488	+	2.79706i
$41$	7.32040			1.14325			0.571627	−	0.820514i	$-0.306312\pi$
$41$	7.32040			1.14325			0.571627	+	0.820514i	$0.306312\pi$
$42$	8.06254	−	5.40766i	1.24408	−	0.834420i
$43$	0.887771			0.135384			0.0676919	−	0.997706i	$-0.478437\pi$
$43$	0.887771			0.135384			0.0676919	+	0.997706i	$0.478437\pi$
$44$	2.84416	−	4.92623i	0.428774	−	0.742658i
$45$	1.29826	+	2.24865i	0.193533	+	0.335210i
$46$	−0.890590	−	1.54255i	−0.131310	−	0.227436i
$47$	−1.16875	+	2.02434i	−0.170480	+	0.295281i	−0.938588	−	0.345040i	$-0.887865\pi$
$47$	−1.16875	+	2.02434i	−0.170480	+	0.295281i	0.768108	+	0.640321i	$0.221199\pi$
$48$	−19.6553			−2.83700
$49$	2.65613	−	6.47650i	0.379447	−	0.925214i
$50$	−0.589510			−0.0833692
$51$	−3.56211	+	6.16976i	−0.498795	+	0.863939i
$52$	−2.71349	−	4.69991i	−0.376294	−	0.651760i
$53$	−2.44407	−	4.23325i	−0.335719	−	0.581482i	0.647904	−	0.761722i	$-0.275646\pi$
$53$	−2.44407	−	4.23325i	−0.335719	−	0.581482i	−0.983623	+	0.180240i	$0.942313\pi$
$54$	−7.68202	+	13.3057i	−1.04539	+	1.81067i
$55$	−2.29249			−0.309119
$56$	−20.5213	+	13.7639i	−2.74228	+	1.83928i
$57$	−1.01911			−0.134985
$58$	4.22970	−	7.32606i	0.555387	−	0.961959i
$59$	0.524077	+	0.907729i	0.0682291	+	0.118176i	0.898122	−	0.439747i	$-0.144932\pi$
$59$	0.524077	+	0.907729i	0.0682291	+	0.118176i	−0.829893	+	0.557923i	$0.811598\pi$
$60$	7.99079	+	13.8404i	1.03161	+	1.78679i
$61$	6.24989	−	10.8251i	0.800217	−	1.38602i	−0.119256	−	0.992864i	$-0.538051\pi$
$61$	6.24989	−	10.8251i	0.800217	−	1.38602i	0.919473	−	0.393153i	$-0.128616\pi$
$62$	2.80132			0.355768
$63$	0.210913	+	3.13385i	0.0265726	+	0.394828i
$64$	28.3200			3.54000
$65$	−1.09358	+	1.89414i	−0.135642	+	0.234939i
$66$	−1.92301	−	3.33075i	−0.236706	−	0.409987i
$67$	−2.23944	−	3.87883i	−0.273592	−	0.473875i	0.696187	−	0.717860i	$-0.254878\pi$
$67$	−2.23944	−	3.87883i	−0.273592	−	0.473875i	−0.969779	+	0.243986i	$0.921545\pi$
$68$	14.3578	−	24.8684i	1.74114	−	3.01574i
$69$	−0.879996			−0.105939
$70$	14.1560	+	6.95021i	1.69197	+	0.830708i
$71$	−6.60274			−0.783601			−0.391801	−	0.920050i	$-0.628148\pi$
$71$	−6.60274			−0.783601			−0.391801	+	0.920050i	$0.628148\pi$
$72$	5.54370	−	9.60197i	0.653331	−	1.13160i
$73$	4.14174	+	7.17370i	0.484754	+	0.839618i	0.999847	−	0.0175164i	$-0.00557593\pi$
$73$	4.14174	+	7.17370i	0.484754	+	0.839618i	−0.515093	+	0.857134i	$0.672243\pi$
$74$	14.8434	+	25.7095i	1.72551	+	2.98867i
$75$	−0.145624	+	0.252229i	−0.0168152	+	0.0291249i
$76$	4.10772			0.471188
$77$	−2.48931	−	1.22218i	−0.283683	−	0.139280i
$78$	−3.66932			−0.415469
$79$	−1.07007	+	1.85342i	−0.120392	+	0.208526i	−0.919922	−	0.392100i	$-0.871749\pi$
$79$	−1.07007	+	1.85342i	−0.120392	+	0.208526i	0.799530	+	0.600626i	$0.205082\pi$
$80$	−15.9644	−	27.6511i	−1.78487	−	3.09149i
$81$	2.01457	+	3.48935i	0.223842	+	0.387705i
$82$	−9.97496	+	17.2771i	−1.10155	+	1.90794i
$83$	−6.66558			−0.731642			−0.365821	−	0.930685i	$-0.619212\pi$
$83$	−6.66558			−0.731642			−0.365821	+	0.930685i	$0.619212\pi$
$84$	1.29817	+	19.2888i	0.141642	+	2.10458i
$85$	−11.5728			−1.25525
$86$	−1.20970	+	2.09526i	−0.130445	+	0.225938i
$87$	−2.08969	−	3.61946i	−0.224039	−	0.388047i
$88$	4.89457	+	8.47765i	0.521763	+	0.903720i
$89$	2.88388	−	4.99503i	0.305691	−	0.529472i	−0.671724	−	0.740802i	$-0.734446\pi$
$89$	2.88388	−	4.99503i	0.305691	−	0.529472i	0.977415	+	0.211329i	$0.0677792\pi$
$90$	−7.07617			−0.745894
$91$	−2.19729	+	1.47375i	−0.230338	+	0.154491i
$92$	3.54699			0.369800
$93$	0.691998	−	1.19858i	0.0717569	−	0.124287i
$94$	−3.18515	−	5.51684i	−0.328523	−	0.569019i
$95$	−0.827739	−	1.43369i	−0.0849242	−	0.147093i
$96$	14.2081	−	24.6091i	1.45011	−	2.51166i
$97$	−2.88777			−0.293209			−0.146604	−	0.989195i	$-0.546834\pi$
$97$	−2.88777			−0.293209			−0.146604	+	0.989195i	$0.546834\pi$
$98$	11.6661	+	15.0939i	1.17845	+	1.52471i
$99$	1.24433			0.125060
$100$	0.586967	−	1.01666i	0.0586967	−	0.101666i
$101$	5.62716	+	9.74653i	0.559924	+	0.969816i	0.997502	+	0.0706359i	$0.0225028\pi$
$101$	5.62716	+	9.74653i	0.559924	+	0.969816i	−0.437579	+	0.899180i	$0.644164\pi$
$102$	−9.70764	−	16.8141i	−0.961200	−	1.66485i
$103$	−10.1167	+	17.5226i	−0.996828	+	1.72656i	−0.429487	+	0.903073i	$0.641306\pi$
$103$	−10.1167	+	17.5226i	−0.996828	+	1.72656i	−0.567341	+	0.823483i	$0.692028\pi$
$104$	9.33940			0.915804
$105$	6.47064	−	4.33994i	0.631470	−	0.423535i
$106$	13.3214			1.29389
$107$	−4.52758	+	7.84201i	−0.437698	+	0.758115i	−0.997512	−	0.0705034i	$-0.977539\pi$
$107$	−4.52758	+	7.84201i	−0.437698	+	0.758115i	0.559813	+	0.828619i	$0.310873\pi$
$108$	−15.2978	−	26.4965i	−1.47203	−	2.54963i
$109$	−7.55070	−	13.0782i	−0.723226	−	1.25266i	−0.959700	−	0.281026i	$-0.909325\pi$
$109$	−7.55070	−	13.0782i	−0.723226	−	1.25266i	0.236474	−	0.971638i	$-0.424008\pi$
$110$	3.12380	−	5.41058i	0.297843	−	0.515879i
$111$	14.6668			1.39211
$112$	−2.59354	−	38.5361i	−0.245067	−	3.64132i
$113$	3.10408			0.292008			0.146004	−	0.989284i	$-0.453359\pi$
$113$	3.10408			0.292008			0.146004	+	0.989284i	$0.453359\pi$
$114$	1.38867	−	2.40524i	0.130061	−	0.225271i
$115$	−0.714748	−	1.23798i	−0.0666506	−	0.115442i
$116$	8.42292	+	14.5889i	0.782048	+	1.35455i
$117$	0.593582	−	1.02811i	0.0548767	−	0.0950492i
$118$	−2.85648			−0.262961
$119$	−12.5664	−	6.16976i	−1.15196	−	0.565581i
$120$	−27.5030			−2.51067
$121$	4.95069	−	8.57484i	0.450062	−	0.779531i
$122$	17.0325	+	29.5012i	1.54205	+	2.67091i
$123$	4.92815	+	8.53581i	0.444356	+	0.769648i
$124$	−2.78923	+	4.83109i	−0.250481	+	0.433845i
$125$	−11.4089			−1.02045
$126$	−7.68371	−	3.77248i	−0.684519	−	0.336079i
$127$	8.78914			0.779910			0.389955	−	0.920834i	$-0.372491\pi$
$127$	8.78914			0.779910			0.389955	+	0.920834i	$0.372491\pi$
$128$	−17.4846	+	30.2841i	−1.54543	+	2.67676i
$129$	0.597654	+	1.03517i	0.0526205	+	0.0911414i
$130$	−2.98028	−	5.16200i	−0.261388	−	0.452738i
$131$	5.25723	−	9.10580i	0.459327	−	0.795577i	−0.539599	−	0.841922i	$-0.681424\pi$
$131$	5.25723	−	9.10580i	0.459327	−	0.795577i	0.998925	+	0.0463451i	$0.0147574\pi$
$132$	7.65885			0.666618
$133$	−0.134473	−	1.99807i	−0.0116603	−	0.173254i
$134$	12.2061			1.05445
$135$	−6.16525	+	10.6785i	−0.530620	+	0.919061i
$136$	24.7086	+	42.7965i	2.11874	+	3.66977i
$137$	−4.36583	−	7.56183i	−0.372998	−	0.646051i	0.617028	−	0.786942i	$-0.288337\pi$
$137$	−4.36583	−	7.56183i	−0.372998	−	0.646051i	−0.990025	+	0.140891i	$0.955003\pi$
$138$	1.19910	−	2.07691i	0.102075	−	0.176798i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	−26.0812	+	17.4930i	−2.20426	+	1.47843i
$141$	−3.14726			−0.265047
$142$	8.99706	−	15.5834i	0.755016	−	1.30773i
$143$	0.524077	+	0.907729i	0.0438256	+	0.0759081i
$144$	8.66525	+	15.0087i	0.722104	+	1.25072i
$145$	3.39457	−	5.87957i	0.281904	−	0.488272i
$146$	−22.5745			−1.86828
$147$	9.33992	−	1.26290i	0.770343	−	0.104163i
$148$	−59.1174			−4.85942
$149$	−7.69632	+	13.3304i	−0.630507	+	1.09207i	0.356941	+	0.934127i	$0.383820\pi$
$149$	−7.69632	+	13.3304i	−0.630507	+	1.09207i	−0.987448	+	0.157944i	$0.949514\pi$
$150$	−0.396863	−	0.687386i	−0.0324037	−	0.0561248i
$151$	6.83786	+	11.8435i	0.556457	+	0.963812i	0.997789	+	0.0664680i	$0.0211730\pi$
$151$	6.83786	+	11.8435i	0.556457	+	0.963812i	−0.441331	+	0.897344i	$0.645494\pi$
$152$	−3.53453	+	6.12198i	−0.286688	+	0.496558i
$153$	6.28158			0.507836
$154$	6.27651	−	4.20974i	0.505776	−	0.339231i
$155$	2.24821			0.180581
$156$	3.65349	−	6.32803i	0.292514	−	0.506648i
$157$	−1.69378	−	2.93371i	−0.135178	−	0.234136i	0.790487	−	0.612478i	$-0.209827\pi$
$157$	−1.69378	−	2.93371i	−0.135178	−	0.234136i	−0.925666	+	0.378343i	$0.876494\pi$
$158$	−2.91621	−	5.05102i	−0.232001	−	0.401838i
$159$	3.29074	−	5.69972i	0.260972	−	0.452017i
$160$	46.1602			3.64928
$161$	−0.116117	−	1.72532i	−0.00915128	−	0.135974i
$162$	−10.9804			−0.862705
$163$	6.90502	−	11.9598i	0.540843	−	0.936767i	−0.458013	−	0.888946i	$-0.651439\pi$
$163$	6.90502	−	11.9598i	0.540843	−	0.936767i	0.998856	−	0.0478219i	$-0.0152280\pi$
$164$	−19.8639	−	34.4052i	−1.55111	−	2.68660i
$165$	−1.54332	−	2.67311i	−0.120147	−	0.208101i
$166$	9.08268	−	15.7317i	0.704953	−	1.22101i
$167$	16.3783			1.26739			0.633695	−	0.773583i	$-0.281538\pi$
$167$	16.3783			1.26739			0.633695	+	0.773583i	$0.281538\pi$
$168$	−29.8643	−	14.6625i	−2.30408	−	1.13124i
$169$	1.00000			0.0769231
$170$	15.7694	−	27.3134i	1.20946	−	2.09485i
$171$	0.449286	+	0.778186i	0.0343578	+	0.0595094i
$172$	−2.40896	−	4.17244i	−0.183682	−	0.318146i
$173$	−2.06273	+	3.57275i	−0.156826	+	0.271631i	−0.933723	−	0.357997i	$-0.883460\pi$
$173$	−2.06273	+	3.57275i	−0.156826	+	0.271631i	0.776896	+	0.629629i	$0.216793\pi$
$174$	11.3899			0.863465
$175$	−0.513734	−	0.252229i	−0.0388346	−	0.0190667i
$176$	−15.3012			−1.15337
$177$	−0.705626	+	1.22218i	−0.0530381	+	0.0918647i
$178$	7.85930	+	13.6127i	0.589080	+	1.02032i
$179$	−7.20679	−	12.4825i	−0.538661	−	0.932988i	−0.998976	−	0.0452324i	$-0.985597\pi$
$179$	−7.20679	−	12.4825i	−0.538661	−	0.932988i	0.460316	−	0.887755i	$-0.347736\pi$
$180$	7.04565	−	12.2034i	0.525152	−	0.909589i
$181$	18.1014			1.34547			0.672733	−	0.739885i	$-0.265120\pi$
$181$	18.1014			1.34547			0.672733	+	0.739885i	$0.265120\pi$
$182$	−0.484172	−	7.19406i	−0.0358892	−	0.533259i
$183$	16.8299			1.24410
$184$	−3.05204	+	5.28629i	−0.225000	+	0.389711i
$185$	11.9126	+	20.6333i	0.875834	+	1.51699i
$186$	1.88587	+	3.26642i	0.138279	+	0.239506i
$187$	−2.77302	+	4.80302i	−0.202784	+	0.351232i
$188$	12.6856			0.925195
$189$	−12.3876	+	8.30850i	−0.901062	+	0.604355i
$190$	4.51159			0.327305
$191$	−2.77068	+	4.79895i	−0.200479	+	0.347240i	−0.948683	−	0.316229i	$-0.897583\pi$
$191$	−2.77068	+	4.79895i	−0.200479	+	0.347240i	0.748204	+	0.663469i	$0.230917\pi$
$192$	19.0653	+	33.0220i	1.37592	+	2.38316i
$193$	4.37044	+	7.56983i	0.314591	+	0.544888i	0.979351	−	0.202170i	$-0.0647992\pi$
$193$	4.37044	+	7.56983i	0.314591	+	0.544888i	−0.664759	+	0.747058i	$0.731466\pi$
$194$	3.93495	−	6.81553i	0.282513	−	0.489327i
$195$	−2.94483			−0.210884
$196$	−37.6463	+	5.09038i	−2.68902	+	0.363598i
$197$	−5.46874			−0.389632			−0.194816	−	0.980840i	$-0.562411\pi$
$197$	−5.46874			−0.389632			−0.194816	+	0.980840i	$0.562411\pi$
$198$	−1.69556	+	2.93679i	−0.120498	+	0.208709i
$199$	−9.76839	−	16.9193i	−0.692463	−	1.19938i	−0.971029	−	0.238963i	$-0.923192\pi$
$199$	−9.76839	−	16.9193i	−0.692463	−	1.19938i	0.278566	−	0.960417i	$-0.410141\pi$
$200$	1.01012	+	1.74958i	0.0714264	+	0.123714i
$201$	3.01522	−	5.22252i	0.212677	−	0.368368i
$202$	−30.6708			−2.15799
$203$	6.82056	−	4.57464i	0.478709	−	0.321077i
$204$	38.6631			2.70696
$205$	−8.00546	+	13.8659i	−0.559125	+	0.968433i
$206$	−27.5705	−	47.7536i	−1.92093	−	3.32715i
$207$	0.387956	+	0.671959i	0.0269648	+	0.0467044i
$208$	−7.29912	+	12.6424i	−0.506103	+	0.876596i
$209$	−0.793355			−0.0548775
$210$	1.42581	+	21.1853i	0.0983899	+	1.46192i
$211$	16.6905			1.14902			0.574511	−	0.818497i	$-0.305192\pi$
$211$	16.6905			1.14902			0.574511	+	0.818497i	$0.305192\pi$
$212$	−13.2639	+	22.9738i	−0.910971	+	1.57785i
$213$	−4.44502	−	7.69900i	−0.304568	−	0.527527i
$214$	−12.3388	−	21.3714i	−0.843463	−	1.46092i
$215$	−0.970850	+	1.68156i	−0.0662114	+	0.114682i
$216$	52.6524			3.58254
$217$	2.44124	+	1.19858i	0.165722	+	0.0813647i
$218$	41.1551			2.78737
$219$	−5.57650	+	9.65878i	−0.376825	+	0.652680i
$220$	6.22065	+	10.7745i	0.419396	+	0.726415i
$221$	2.64562	+	4.58236i	0.177964	+	0.308243i
$222$	−19.9854	+	34.6157i	−1.34133	+	2.32325i
$223$	−5.34217			−0.357738			−0.178869	−	0.983873i	$-0.557244\pi$
$223$	−5.34217			−0.357738			−0.178869	+	0.983873i	$0.557244\pi$
$224$	50.1233	+	24.6091i	3.34901	+	1.64427i
$225$	0.256800			0.0171200
$226$	−4.22970	+	7.32606i	−0.281356	+	0.487322i
$227$	−10.0608	−	17.4258i	−0.667757	−	1.15659i	−0.978530	−	0.206104i	$-0.933921\pi$
$227$	−10.0608	−	17.4258i	−0.667757	−	1.15659i	0.310774	−	0.950484i	$-0.399412\pi$
$228$	2.76535	+	4.78973i	0.183140	+	0.317208i
$229$	−12.6249	+	21.8669i	−0.834275	+	1.44501i	0.0603445	+	0.998178i	$0.480780\pi$
$229$	−12.6249	+	21.8669i	−0.834275	+	1.44501i	−0.894619	+	0.446829i	$0.852553\pi$
$230$	3.89573			0.256877
$231$	−0.250725	−	3.72540i	−0.0164965	−	0.245113i
$232$	−28.9903			−1.90331
$233$	0.396678	−	0.687066i	0.0259872	−	0.0450112i	−0.852739	−	0.522337i	$-0.825060\pi$
$233$	0.396678	−	0.687066i	0.0259872	−	0.0450112i	0.878727	+	0.477326i	$0.158394\pi$
$234$	1.61766	+	2.80187i	0.105750	+	0.183164i
$235$	−2.55626	−	4.42757i	−0.166752	−	0.288823i
$236$	2.84416	−	4.92623i	0.185139	−	0.320671i
$237$	−2.88152			−0.187175
$238$	31.6848	−	21.2514i	2.05382	−	1.37753i
$239$	20.0488			1.29685			0.648425	−	0.761279i	$-0.275428\pi$
$239$	20.0488			1.29685			0.648425	+	0.761279i	$0.275428\pi$
$240$	21.4947	−	37.2299i	1.38748	−	2.40318i
$241$	−6.90602	−	11.9616i	−0.444856	−	0.770513i	0.553186	−	0.833058i	$-0.313412\pi$
$241$	−6.90602	−	11.9616i	−0.444856	−	0.770513i	−0.998042	+	0.0625446i	$0.980078\pi$
$242$	13.4919	+	23.3686i	0.867289	+	1.50219i
$243$	5.74404	−	9.94897i	0.368480	−	0.638227i
$244$	−67.8362			−4.34277
$245$	9.36269	+	12.1137i	0.598161	+	0.773913i
$246$	−26.8609			−1.71259
$247$	−0.378453	+	0.655500i	−0.0240804	+	0.0417085i
$248$	−4.80004	−	8.31392i	−0.304803	−	0.527934i
$249$	−4.48732	−	7.77227i	−0.284372	−	0.492547i
$250$	15.5461	−	26.9266i	0.983222	−	1.70299i
$251$	−26.1095			−1.64802			−0.824010	−	0.566576i	$-0.808268\pi$
$251$	−26.1095			−1.64802			−0.824010	+	0.566576i	$0.808268\pi$
$252$	14.1565	−	9.49496i	0.891776	−	0.598126i
$253$	−0.685057			−0.0430692
$254$	−11.9763	+	20.7436i	−0.751460	+	1.30157i
$255$	−7.79092	−	13.4943i	−0.487886	−	0.845044i
$256$	−19.3298	−	33.4801i	−1.20811	−	2.09251i
$257$	−5.30990	+	9.19701i	−0.331222	+	0.573694i	−0.982752	−	0.184930i	$-0.940794\pi$
$257$	−5.30990	+	9.19701i	−0.331222	+	0.573694i	0.651530	+	0.758623i	$0.274128\pi$
$258$	−3.25752			−0.202804
$259$	1.93531	+	28.7557i	0.120254	+	1.78679i
$260$	11.8697			0.736128
$261$	−1.84253	+	3.19135i	−0.114050	+	0.197540i
$262$	14.3273	+	24.8156i	0.885142	+	1.53311i
$263$	−5.17888	−	8.97008i	−0.319343	−	0.553119i	0.661008	−	0.750379i	$-0.270129\pi$
$263$	−5.17888	−	8.97008i	−0.319343	−	0.553119i	−0.980351	+	0.197260i	$0.936796\pi$
$264$	−6.59013	+	11.4144i	−0.405594	+	0.702510i
$265$	10.6912			0.656753
$266$	4.89894	+	2.40524i	0.300374	+	0.147475i
$267$	7.76581			0.475260
$268$	−12.1534	+	21.0504i	−0.742389	+	1.28586i
$269$	−5.98503	−	10.3664i	−0.364914	−	0.632049i	0.623849	−	0.781545i	$-0.285568\pi$
$269$	−5.98503	−	10.3664i	−0.364914	−	0.632049i	−0.988762	+	0.149496i	$0.952235\pi$
$270$	−16.8018	−	29.1016i	−1.02253	−	1.77107i
$271$	1.37845	−	2.38755i	0.0837351	−	0.145033i	−0.821116	−	0.570761i	$-0.806648\pi$
$271$	1.37845	−	2.38755i	0.0837351	−	0.145033i	0.904852	+	0.425727i	$0.139982\pi$
$272$	−77.2429			−4.68354
$273$	−3.19767	−	1.56996i	−0.193532	−	0.0950184i
$274$	23.7959			1.43757
$275$	−0.113365	+	0.196354i	−0.00683618	+	0.0118406i
$276$	2.38786	+	4.13590i	0.143733	+	0.248952i
$277$	11.9637	+	20.7218i	0.718831	+	1.24505i	0.961463	+	0.274933i	$0.0886558\pi$
$277$	11.9637	+	20.7218i	0.718831	+	1.24505i	−0.242632	+	0.970118i	$0.578011\pi$
$278$	5.45050	−	9.44054i	0.326899	−	0.566206i
$279$	−1.22030			−0.0730574
$280$	−3.62906	−	53.9223i	−0.216878	−	3.22247i
$281$	−3.87870			−0.231384			−0.115692	−	0.993285i	$-0.536909\pi$
$281$	−3.87870			−0.231384			−0.115692	+	0.993285i	$0.536909\pi$
$282$	4.28854	−	7.42796i	0.255379	−	0.442329i
$283$	3.10499	+	5.37801i	0.184573	+	0.319689i	0.943432	−	0.331565i	$-0.107577\pi$
$283$	3.10499	+	5.37801i	0.184573	+	0.319689i	−0.758860	+	0.651254i	$0.774243\pi$
$284$	17.9165	+	31.0323i	1.06315	+	1.84143i
$285$	1.11448	−	1.93034i	0.0660162	−	0.114343i
$286$	−2.85648			−0.168907
$287$	−16.0850	+	10.7884i	−0.949468	+	0.636821i
$288$	−25.0551			−1.47639
$289$	−5.49866	+	9.52395i	−0.323450	+	0.560232i
$290$	9.25106	+	16.0233i	0.543241	+	0.940920i
$291$	−1.94407	−	3.36723i	−0.113963	−	0.197390i
$292$	22.4772	−	38.9316i	1.31538	−	2.27830i
$293$	16.5754			0.968347			0.484174	−	0.874972i	$-0.339120\pi$
$293$	16.5754			0.968347			0.484174	+	0.874972i	$0.339120\pi$
$294$	−9.74618	+	23.7643i	−0.568409	+	1.38596i
$295$	−2.29249			−0.133474
$296$	50.8681	−	88.1062i	2.95665	−	5.12107i
$297$	2.95457	+	5.11747i	0.171442	+	0.296946i
$298$	−20.9744	−	36.3287i	−1.21501	−	2.10447i
$299$	−0.326792	+	0.566020i	−0.0188989	+	0.0327338i
$300$	1.58060			0.0912561
$301$	−1.95069	+	1.30835i	−0.112436	+	0.0754121i
$302$	−37.2698			−2.14463
$303$	−7.57650	+	13.1229i	−0.435259	+	0.753890i
$304$	−5.52475	−	9.56914i	−0.316866	−	0.548828i
$305$	13.6695	+	23.6763i	0.782716	+	1.35570i
$306$	−8.55944	+	14.8254i	−0.489311	+	0.847511i
$307$	−7.05788			−0.402815			−0.201407	−	0.979508i	$-0.564551\pi$
$307$	−7.05788			−0.402815			−0.201407	+	0.979508i	$0.564551\pi$
$308$	1.01060	+	15.0159i	0.0575841	+	0.855612i
$309$	−27.2426			−1.54978
$310$	−3.06347	+	5.30609i	−0.173993	+	0.301365i
$311$	−10.5551	−	18.2820i	−0.598525	−	1.03668i	−0.993039	−	0.117785i	$-0.962420\pi$
$311$	−10.5551	−	18.2820i	−0.598525	−	1.03668i	0.394514	−	0.918890i	$-0.370913\pi$
$312$	6.28736	+	10.8900i	0.355952	+	0.616526i
$313$	−0.990260	+	1.71518i	−0.0559728	+	0.0969477i	−0.892654	−	0.450742i	$-0.851159\pi$
$313$	−0.990260	+	1.71518i	−0.0559728	+	0.0969477i	0.836681	+	0.547690i	$0.184493\pi$
$314$	9.23194			0.520989
$315$	−6.16660	−	3.02762i	−0.347449	−	0.170587i
$316$	11.6145			0.653368
$317$	9.02297	−	15.6282i	0.506781	−	0.877770i	−0.493189	−	0.869922i	$-0.664169\pi$
$317$	9.02297	−	15.6282i	0.506781	−	0.877770i	0.999969	−	0.00784727i	$-0.00249789\pi$
$318$	8.96808	+	15.5332i	0.502905	+	0.871057i
$319$	−1.62678	−	2.81767i	−0.0910822	−	0.157759i
$320$	−30.9703	+	53.6421i	−1.73129	+	2.99868i
$321$	−12.1920			−0.680492
$322$	4.23021	+	2.07691i	0.235740	+	0.115742i
$323$	−4.00498			−0.222843
$324$	10.9331	−	18.9366i	0.607393	−	1.05204i
$325$	0.108157	+	0.187333i	0.00599947	+	0.0103914i
$326$	18.8179	+	32.5936i	1.04223	+	1.80519i
$327$	10.1664	−	17.6087i	0.562202	−	0.973763i
$328$	68.3682			3.77500
$329$	−0.415285	−	6.17051i	−0.0228954	−	0.340191i
$330$	8.41187			0.463058
$331$	7.33689	−	12.7079i	0.403272	−	0.698488i	−0.590847	−	0.806784i	$-0.701206\pi$
$331$	7.33689	−	12.7079i	0.403272	−	0.698488i	0.994119	+	0.108296i	$0.0345395\pi$
$332$	18.0870	+	31.3276i	0.992653	+	1.71933i
$333$	−6.46602	−	11.1995i	−0.354336	−	0.613728i
$334$	−22.3175	+	38.6550i	−1.22116	+	2.11511i
$335$	9.79606			0.535216
$336$	43.1883	−	28.9670i	2.35611	−	1.58028i
$337$	12.8080			0.697698			0.348849	−	0.937179i	$-0.386573\pi$
$337$	12.8080			0.697698			0.348849	+	0.937179i	$0.386573\pi$
$338$	−1.36263	+	2.36014i	−0.0741170	+	0.128374i
$339$	2.08969	+	3.61946i	0.113497	+	0.196582i
$340$	31.4028	+	54.3913i	1.70306	+	2.94978i
$341$	0.538705	−	0.933065i	0.0291725	−	0.0505283i
$342$	−2.44883			−0.132418
$343$	3.70846	+	18.1452i	0.200238	+	0.979747i
$344$	8.29125			0.447034
$345$	0.962348	−	1.66684i	0.0518111	−	0.0897394i
$346$	−5.62146	−	9.73665i	−0.302211	−	0.523445i
$347$	−10.1027	−	17.4984i	−0.542342	−	0.939363i	−0.998769	−	0.0496025i	$-0.984205\pi$
$347$	−10.1027	−	17.4984i	−0.542342	−	0.939363i	0.456428	−	0.889761i	$-0.349129\pi$
$348$	−11.3408	+	19.6428i	−0.607928	+	1.05296i
$349$	−18.4434			−0.987252			−0.493626	−	0.869674i	$-0.664329\pi$
$349$	−18.4434			−0.987252			−0.493626	+	0.869674i	$0.664329\pi$
$350$	1.29532	−	0.868789i	0.0692378	−	0.0464387i
$351$	5.63766			0.300916
$352$	11.0607	−	19.1576i	0.589536	−	1.02111i
$353$	4.07218	+	7.05322i	0.216740	+	0.375405i	0.953810	−	0.300412i	$-0.0971242\pi$
$353$	4.07218	+	7.05322i	0.216740	+	0.375405i	−0.737069	+	0.675817i	$0.763791\pi$
$354$	−1.92301	−	3.33075i	−0.102207	−	0.177027i
$355$	7.22064	−	12.5065i	0.383232	−	0.663777i
$356$	−31.3016			−1.65898
$357$	−1.26570	−	18.8064i	−0.0669879	−	0.995339i
$358$	39.2806			2.07604
$359$	16.3050	−	28.2411i	0.860545	−	1.49051i	−0.0108595	−	0.999941i	$-0.503457\pi$
$359$	16.3050	−	28.2411i	0.860545	−	1.49051i	0.871404	−	0.490566i	$-0.163210\pi$
$360$	12.1250	+	21.0011i	0.639043	+	1.10685i
$361$	9.21355	+	15.9583i	0.484923	+	0.839912i
$362$	−24.6654	+	42.7218i	−1.29639	+	2.24541i
$363$	13.3314			0.699715
$364$	12.8888	+	6.32803i	0.675557	+	0.331679i
$365$	−18.1173			−0.948304
$366$	−22.9329	+	39.7209i	−1.19872	+	2.07624i
$367$	1.58006	+	2.73675i	0.0824786	+	0.142857i	0.904314	−	0.426868i	$-0.140383\pi$
$367$	1.58006	+	2.73675i	0.0824786	+	0.142857i	−0.821835	+	0.569725i	$0.807050\pi$
$368$	−4.77059	−	8.26290i	−0.248684	−	0.430733i
$369$	4.34526	−	7.52621i	0.226205	−	0.391799i
$370$	−64.9298			−3.37554
$371$	11.6091	+	5.69972i	0.602713	+	0.295915i
$372$	−7.51094			−0.389424
$373$	0.738849	−	1.27972i	0.0382561	−	0.0662616i	−0.846263	−	0.532765i	$-0.821153\pi$
$373$	0.738849	−	1.27972i	0.0382561	−	0.0662616i	0.884520	+	0.466503i	$0.154486\pi$
$374$	−7.55718	−	13.0894i	−0.390773	−	0.676838i
$375$	−7.68059	−	13.3032i	−0.396624	−	0.686972i
$376$	−10.9155	+	18.9061i	−0.562922	+	0.975010i
$377$	−3.10408			−0.159868
$378$	−2.72960	−	40.5577i	−0.140395	−	2.08606i
$379$	10.7254			0.550927			0.275463	−	0.961312i	$-0.411169\pi$
$379$	10.7254			0.550927			0.275463	+	0.961312i	$0.411169\pi$
$380$	−4.49213	+	7.78060i	−0.230441	+	0.399136i
$381$	5.91692	+	10.2484i	0.303133	+	0.525042i
$382$	−7.55079	−	13.0784i	−0.386332	−	0.669147i
$383$	10.7054	−	18.5424i	0.547023	−	0.947471i	−0.451454	−	0.892294i	$-0.649094\pi$
$383$	10.7054	−	18.5424i	0.547023	−	0.947471i	0.998477	−	0.0551766i	$-0.0175722\pi$
$384$	−47.0830			−2.40269
$385$	5.03725	−	3.37855i	0.256722	−	0.172187i
$386$	−23.8211			−1.21246
$387$	0.526965	−	0.912730i	0.0267871	−	0.0463967i
$388$	7.83595	+	13.5723i	0.397810	+	0.689027i
$389$	−17.3909	−	30.1220i	−0.881755	−	1.52725i	−0.849388	−	0.527769i	$-0.823029\pi$
$389$	−17.3909	−	30.1220i	−0.881755	−	1.52725i	−0.0323675	−	0.999476i	$-0.510305\pi$
$390$	4.01270	−	6.95021i	0.203191	−	0.351937i
$391$	−3.45828			−0.174893
$392$	24.8066	−	60.4866i	1.25292	−	3.05503i
$393$	14.1568			0.714119
$394$	7.45185	−	12.9070i	0.375419	−	0.650244i
$395$	−2.34042	−	4.05373i	−0.117759	−	0.203965i
$396$	−3.37649	−	5.84825i	−0.169675	−	0.293886i
$397$	−2.22605	+	3.85564i	−0.111722	+	0.193509i	−0.916465	−	0.400115i	$-0.868970\pi$
$397$	−2.22605	+	3.85564i	−0.111722	+	0.193509i	0.804742	+	0.593624i	$0.202303\pi$
$398$	53.2426			2.66881
$399$	2.23928	−	1.50191i	0.112104	−	0.0751897i
$400$	−3.15780			−0.157890
$401$	6.87687	−	11.9111i	0.343415	−	0.594811i	−0.641650	−	0.766998i	$-0.721750\pi$
$401$	6.87687	−	11.9111i	0.343415	−	0.594811i	0.985064	+	0.172186i	$0.0550831\pi$
$402$	8.21724	+	14.2327i	0.409839	+	0.709861i
$403$	−0.513956	−	0.890198i	−0.0256020	−	0.0443439i
$404$	30.5385	−	52.8943i	1.51935	−	2.63159i
$405$	−8.81241			−0.437892
$406$	1.50291	+	22.3310i	0.0745882	+	1.10827i
$407$	11.4178			0.565959
$408$	−33.2680	+	57.6219i	−1.64701	+	2.85271i
$409$	1.74603	+	3.02422i	0.0863358	+	0.149538i	0.905960	−	0.423364i	$-0.139151\pi$
$409$	1.74603	+	3.02422i	0.0863358	+	0.149538i	−0.819624	+	0.572902i	$0.805818\pi$
$410$	−21.8169	−	37.7879i	−1.07746	−	1.86621i
$411$	5.87822	−	10.1814i	0.289951	−	0.502210i
$412$	109.806			5.40977
$413$	−2.48931	−	1.22218i	−0.122491	−	0.0601396i
$414$	−2.11455			−0.103925
$415$	7.28935	−	12.6255i	0.357820	−	0.619763i
$416$	−10.5525	−	18.2775i	−0.517380	−	0.896128i
$417$	−2.69283	−	4.66412i	−0.131869	−	0.228403i
$418$	1.08105	−	1.87243i	0.0528757	−	0.0915834i
$419$	−3.56737			−0.174278			−0.0871388	−	0.996196i	$-0.527772\pi$
$419$	−3.56737			−0.174278			−0.0871388	+	0.996196i	$0.527772\pi$
$420$	−37.9554	−	18.6350i	−1.85203	−	0.909295i
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	−22.7429	+	39.3919i	−1.10711	+	1.91757i
$423$	1.38750	+	2.40323i	0.0674627	+	0.116849i
$424$	−22.8262	−	39.5361i	−1.10854	−	1.92004i
$425$	−0.572285	+	0.991227i	−0.0277599	+	0.0480816i
$426$	24.2276			1.17383
$427$	2.22073	+	32.9967i	0.107469	+	1.59682i
$428$	49.1423			2.37538
$429$	−0.705626	+	1.22218i	−0.0340680	+	0.0590074i
$430$	−2.64581	−	4.58268i	−0.127592	−	0.220996i
$431$	5.68211	+	9.84171i	0.273698	+	0.474059i	0.969806	−	0.243879i	$-0.0784198\pi$
$431$	5.68211	+	9.84171i	0.273698	+	0.474059i	−0.696108	+	0.717937i	$0.745087\pi$
$432$	−41.1500	+	71.2738i	−1.97983	+	3.42916i
$433$	−21.2136			−1.01946			−0.509731	−	0.860334i	$-0.670255\pi$
$433$	−21.2136			−1.01946			−0.509731	+	0.860334i	$0.670255\pi$
$434$	−6.15529	+	4.12844i	−0.295464	+	0.198171i
$435$	9.14101			0.438278
$436$	−40.9776	+	70.9752i	−1.96247	+	3.39910i
$437$	−0.247351	−	0.428424i	−0.0118324	−	0.0204943i
$438$	−15.1974	−	26.3226i	−0.726158	−	1.25774i
$439$	12.2503	−	21.2182i	0.584676	−	1.01269i	−0.410239	−	0.911978i	$-0.634555\pi$
$439$	12.2503	−	21.2182i	0.584676	−	1.01269i	0.994916	−	0.100711i	$-0.0321118\pi$
$440$	−21.4105			−1.02070
$441$	−5.08195	−	6.57513i	−0.241997	−	0.313102i
$442$	−14.4200			−0.685888
$443$	−20.2344	+	35.0470i	−0.961366	+	1.66513i	−0.242288	+	0.970204i	$0.577898\pi$
$443$	−20.2344	+	35.0470i	−0.961366	+	1.66513i	−0.719077	+	0.694930i	$0.755435\pi$
$444$	−39.7983	−	68.9327i	−1.88874	−	3.27140i
$445$	6.30753	+	10.9250i	0.299005	+	0.517893i
$446$	7.27937	−	12.6082i	0.344688	−	0.597017i
$447$	−20.7249			−0.980254
$448$	−62.2272	+	41.7366i	−2.93996	+	1.97187i
$449$	−27.7638			−1.31025			−0.655127	−	0.755519i	$-0.727385\pi$
$449$	−27.7638			−1.31025			−0.655127	+	0.755519i	$0.727385\pi$
$450$	−0.349922	+	0.606083i	−0.0164955	+	0.0285710i
$451$	3.83646	+	6.64494i	0.180652	+	0.312898i
$452$	−8.42292	−	14.5889i	−0.396181	−	0.686205i
$453$	−9.20661	+	15.9463i	−0.432564	+	0.749223i
$454$	54.8362			2.57359
$455$	−0.388575	−	5.77363i	−0.0182167	−	0.270672i
$456$	−9.51789			−0.445716
$457$	5.59696	−	9.69422i	0.261815	−	0.453476i	−0.704910	−	0.709297i	$-0.749012\pi$
$457$	5.59696	−	9.69422i	0.261815	−	0.453476i	0.966724	+	0.255821i	$0.0823457\pi$
$458$	−34.4059	−	59.5928i	−1.60768	−	2.78459i
$459$	14.9151	+	25.8338i	0.696179	+	1.20582i
$460$	−3.87893	+	6.71850i	−0.180856	+	0.313252i
$461$	−9.29773			−0.433038			−0.216519	−	0.976278i	$-0.569470\pi$
$461$	−9.29773			−0.433038			−0.216519	+	0.976278i	$0.569470\pi$
$462$	9.13409	+	4.48457i	0.424956	+	0.208641i
$463$	28.2439			1.31260			0.656302	−	0.754499i	$-0.272120\pi$
$463$	28.2439			1.31260			0.656302	+	0.754499i	$0.272120\pi$
$464$	22.6571	−	39.2432i	1.05183	−	1.82182i
$465$	1.51351	+	2.62148i	0.0701875	+	0.121568i
$466$	1.08105	+	1.87243i	0.0500785	+	0.0867385i
$467$	−11.1303	+	19.2783i	−0.515050	+	0.892093i	0.484797	+	0.874626i	$0.338893\pi$
$467$	−11.1303	+	19.2783i	−0.515050	+	0.892093i	−0.999847	+	0.0174663i	$0.994440\pi$
$468$	−6.44273			−0.297815
$469$	10.6371	+	5.22252i	0.491177	+	0.241154i
$470$	13.9329			0.642676
$471$	2.28053	−	3.95000i	0.105081	−	0.182006i
$472$	4.89457	+	8.47765i	0.225291	+	0.390215i
$473$	0.465261	+	0.805855i	0.0213927	+	0.0370533i
$474$	3.92643	−	6.80078i	0.180347	−	0.312370i
$475$	−0.163729			−0.00751242
$476$	5.10165	+	75.8027i	0.233834	+	3.47441i
$477$	−5.80302			−0.265702
$478$	−27.3190	+	47.3179i	−1.24954	+	2.16427i
$479$	16.4382	+	28.4718i	0.751081	+	1.30091i	0.947299	+	0.320350i	$0.103800\pi$
$479$	16.4382	+	28.4718i	0.751081	+	1.30091i	−0.196219	+	0.980560i	$0.562866\pi$
$480$	31.0754	+	53.8242i	1.41839	+	2.45673i
$481$	5.44661	−	9.43381i	0.248344	−	0.430145i
$482$	37.6413			1.71451
$483$	1.93360	−	1.29689i	0.0879820	−	0.0590107i
$484$	−53.7346			−2.44248
$485$	3.15801	−	5.46984i	0.143398	−	0.248373i
$486$	15.6539	+	27.1134i	0.710078	+	1.22989i
$487$	13.9462	+	24.1555i	0.631962	+	1.09459i	0.987150	+	0.159796i	$0.0510836\pi$
$487$	13.9462	+	24.1555i	0.631962	+	1.09459i	−0.355188	+	0.934795i	$0.615583\pi$
$488$	58.3703	−	101.100i	2.64230	−	4.57660i
$489$	18.5941			0.840852
$490$	−41.3477	+	5.59086i	−1.86790	+	0.252569i
$491$	10.6571			0.480948			0.240474	−	0.970656i	$-0.422697\pi$
$491$	10.6571			0.480948			0.240474	+	0.970656i	$0.422697\pi$
$492$	26.7450	−	46.3237i	1.20576	−	2.08844i
$493$	−8.21224	−	14.2240i	−0.369861	−	0.640618i
$494$	−1.03138	−	1.78640i	−0.0464040	−	0.0803740i
$495$	−1.36078	+	2.35694i	−0.0611625	+	0.105936i
$496$	15.0057			0.673776
$497$	14.5081	−	9.73078i	0.650777	−	0.436485i
$498$	24.4581			1.09600
$499$	12.2557	−	21.2275i	0.548641	−	0.950274i	−0.449727	−	0.893166i	$-0.648479\pi$
$499$	12.2557	−	21.2275i	0.548641	−	0.950274i	0.998368	−	0.0571077i	$-0.0181878\pi$
$500$	30.9581	+	53.6210i	1.38449	+	2.39800i
$501$	11.0260	+	19.0976i	0.492605	+	0.853217i
$502$	35.5775	−	61.6221i	1.58790	−	2.75033i
$503$	−38.0054			−1.69458			−0.847288	−	0.531134i	$-0.821766\pi$
$503$	−38.0054			−1.69458			−0.847288	+	0.531134i	$0.821766\pi$
$504$	1.96980	+	29.2683i	0.0877421	+	1.30371i
$505$	−24.6151			−1.09536
$506$	0.933476	−	1.61683i	0.0414981	−	0.0718768i
$507$	0.673208	+	1.16603i	0.0298982	+	0.0517852i
$508$	−23.8493	−	41.3082i	−1.05814	−	1.83275i
$509$	−19.9250	+	34.5112i	−0.883161	+	1.52968i	−0.0353545	+	0.999375i	$0.511256\pi$
$509$	−19.9250	+	34.5112i	−0.883161	+	1.52968i	−0.847807	+	0.530305i	$0.822077\pi$
$510$	42.4644			1.88036
$511$	−19.6728	−	9.65878i	−0.870274	−	0.427279i
$512$	35.4186			1.56530
$513$	−2.13359	+	3.69549i	−0.0942004	+	0.163160i
$514$	−14.4708	−	25.0642i	−0.638279	−	1.10553i
$515$	−22.1269	−	38.3249i	−0.975027	−	1.68880i
$516$	3.24346	−	5.61784i	0.142786	−	0.247312i
$517$	−2.45007			−0.107754
$518$	−70.5045	−	34.6157i	−3.09779	−	1.52093i
$519$	−5.55459			−0.243819
$520$	−10.2134	+	17.6901i	−0.447887	+	0.775764i
$521$	9.81670	+	17.0030i	0.430077	+	0.744916i	0.996880	−	0.0789382i	$-0.0251530\pi$
$521$	9.81670	+	17.0030i	0.430077	+	0.744916i	−0.566802	+	0.823854i	$0.691820\pi$
$522$	−5.02135	−	8.69724i	−0.219779	−	0.380668i
$523$	−11.4162	+	19.7734i	−0.499195	+	0.864632i	−1.00000		0.000928862i	$-0.999704\pi$
$523$	−11.4162	+	19.7734i	−0.499195	+	0.864632i	0.500804	+	0.865561i	$0.333038\pi$
$524$	−57.0619			−2.49276
$525$	−0.0517436	−	0.768832i	−0.00225828	−	0.0335546i
$526$	28.2275			1.23078
$527$	2.71947	−	4.71026i	0.118462	−	0.205182i
$528$	−10.3009	−	17.8417i	−0.448289	−	0.776459i
$529$	11.2864	+	19.5486i	0.490714	+	0.849941i
$530$	−14.5681	+	25.2326i	−0.632796	+	1.09603i
$531$	1.24433			0.0539994
$532$	−9.02584	+	6.05375i	−0.391320	+	0.262463i
$533$	7.32040			0.317082
$534$	−10.5819	+	18.3284i	−0.457923	+	0.793146i
$535$	−9.90257	−	17.1518i	−0.428125	−	0.741535i
$536$	−20.9151	−	36.2260i	−0.903394	−	1.56472i
$537$	9.70333	−	16.8067i	0.418730	−	0.725261i
$538$	32.6214			1.40641
$539$	7.27092	−	0.983142i	0.313181	−	0.0423469i
$540$	66.9175			2.87967
$541$	4.82334	−	8.35427i	0.207372	−	0.359178i	−0.743514	−	0.668720i	$-0.766842\pi$
$541$	4.82334	−	8.35427i	0.207372	−	0.359178i	0.950886	+	0.309542i	$0.100176\pi$
$542$	3.75663	+	6.50667i	0.161361	+	0.279486i
$543$	12.1860	+	21.1068i	0.522952	+	0.905779i
$544$	55.8360	−	96.7108i	2.39395	−	4.14644i
$545$	33.0292			1.41482
$546$	8.06254	−	5.40766i	0.345045	−	0.231426i
$547$	−43.8570			−1.87519			−0.937596	−	0.347728i	$-0.886953\pi$
$547$	−43.8570			−1.87519			−0.937596	+	0.347728i	$0.886953\pi$
$548$	−23.6933	+	41.0380i	−1.01213	+	1.75306i
$549$	−7.41965	−	12.8512i	−0.316663	−	0.548476i
$550$	−0.308949	−	0.535115i	−0.0131736	−	0.0228174i
$551$	1.17475	−	2.03473i	0.0500461	−	0.0866823i
$552$	−8.21864			−0.349808
$553$	−0.380221	−	5.64950i	−0.0161686	−	0.240241i
$554$	−65.2083			−2.77044
$555$	−16.0394	+	27.7810i	−0.680833	+	1.17924i
$556$	10.8540	+	18.7996i	0.460311	+	0.797282i
$557$	−7.45977	−	12.9207i	−0.316080	−	0.547467i	0.663586	−	0.748100i	$-0.269034\pi$
$557$	−7.45977	−	12.9207i	−0.316080	−	0.547467i	−0.979667	+	0.200633i	$0.935700\pi$
$558$	1.66281	−	2.88007i	0.0703924	−	0.121923i
$559$	0.887771			0.0375487
$560$	75.8290	+	37.2299i	3.20436	+	1.57325i
$561$	−7.46729			−0.315269
$562$	5.28521	−	9.15426i	0.222943	−	0.386149i
$563$	8.63486	+	14.9560i	0.363916	+	0.630321i	0.988602	−	0.150555i	$-0.0481062\pi$
$563$	8.63486	+	14.9560i	0.363916	+	0.630321i	−0.624686	+	0.780876i	$0.714773\pi$
$564$	8.54007	+	14.7918i	0.359602	+	0.622849i
$565$	−3.39457	+	5.87957i	−0.142811	+	0.247355i
$566$	−16.9238			−0.711359
$567$	−9.56902	−	4.69811i	−0.401861	−	0.197302i
$568$	−61.6657			−2.58743
$569$	−13.2662	+	22.9777i	−0.556148	+	0.963277i	0.441665	+	0.897180i	$0.354388\pi$
$569$	−13.2662	+	22.9777i	−0.556148	+	0.963277i	−0.997813	+	0.0660972i	$0.978945\pi$
$570$	3.03724	+	5.26065i	0.127216	+	0.220345i
$571$	0.992844	+	1.71966i	0.0415492	+	0.0719654i	0.886052	−	0.463586i	$-0.153437\pi$
$571$	0.992844	+	1.71966i	0.0415492	+	0.0719654i	−0.844503	+	0.535551i	$0.820104\pi$
$572$	2.84416	−	4.92623i	0.118920	−	0.205976i
$573$	−7.46097			−0.311686
$574$	−3.54433	−	52.6634i	−0.147938	−	2.19813i
$575$	−0.141379			−0.00589593
$576$	16.8103	−	29.1162i	0.700428	−	1.21318i
$577$	−5.94915	−	10.3042i	−0.247666	−	0.428971i	0.715212	−	0.698908i	$-0.246330\pi$
$577$	−5.94915	−	10.3042i	−0.247666	−	0.428971i	−0.962878	+	0.269937i	$0.912997\pi$
$578$	−14.9852	−	25.9551i	−0.623303	−	1.07959i
$579$	−5.88443	+	10.1921i	−0.244549	+	0.423571i
$580$	−36.8446			−1.52989
$581$	14.6462	−	9.82339i	0.607626	−	0.407543i
$582$	10.5962			0.439225
$583$	2.56176	−	4.43711i	0.106097	−	0.183766i
$584$	38.6814	+	66.9981i	1.60065	+	2.77240i
$585$	1.29826	+	2.24865i	0.0536765	+	0.0929704i
$586$	−22.5861	+	39.1203i	−0.933024	+	1.61604i
$587$	33.5122			1.38320			0.691598	−	0.722283i	$-0.256907\pi$
$587$	33.5122			1.38320			0.691598	+	0.722283i	$0.256907\pi$
$588$	−31.2793	−	40.4699i	−1.28994	−	1.66895i
$589$	0.778033			0.0320583
$590$	3.12380	−	5.41058i	0.128605	−	0.222750i
$591$	−3.68160	−	6.37672i	−0.151441	−	0.262303i
$592$	79.5109	+	137.717i	3.26788	+	5.66013i
$593$	−17.6408	+	30.5547i	−0.724419	+	1.25473i	0.234793	+	0.972045i	$0.424559\pi$
$593$	−17.6408	+	30.5547i	−0.724419	+	1.25473i	−0.959213	+	0.282686i	$0.908775\pi$
$594$	−16.1039			−0.660751
$595$	25.4288	−	17.0554i	1.04248	−	0.699205i
$596$	83.5357			3.42176
$597$	13.1523	−	22.7805i	0.538288	−	0.932343i
$598$	−0.890590	−	1.54255i	−0.0364189	−	0.0630794i
$599$	12.5034	+	21.6565i	0.510876	+	0.884863i	0.999921	+	0.0126040i	$0.00401207\pi$
$599$	12.5034	+	21.6565i	0.510876	+	0.884863i	−0.489045	+	0.872259i	$0.662655\pi$
$600$	−1.36004	+	2.35566i	−0.0555236	+	0.0961696i
$601$	−28.4688			−1.16127			−0.580634	−	0.814165i	$-0.697195\pi$
$601$	−28.4688			−1.16127			−0.580634	+	0.814165i	$0.697195\pi$
$602$	−0.429834	−	6.38668i	−0.0175187	−	0.260301i
$603$	−5.31717			−0.216532
$604$	37.1090	−	64.2747i	1.50994	−	2.61530i
$605$	10.8280	+	18.7546i	0.440219	+	0.762482i
$606$	−20.6479	−	35.7631i	−0.838762	−	1.45278i
$607$	−18.0234	+	31.2175i	−0.731549	+	1.26708i	0.224672	+	0.974434i	$0.427869\pi$
$607$	−18.0234	+	31.2175i	−0.731549	+	1.26708i	−0.956221	+	0.292646i	$0.905464\pi$
$608$	15.9745			0.647853
$609$	9.92583	+	4.87330i	0.402215	+	0.197476i
$610$	−74.5058			−3.01665
$611$	−1.16875	+	2.02434i	−0.0472827	+	0.0818961i
$612$	−17.0450	−	29.5229i	−0.689005	−	1.19339i
$613$	−9.16264	−	15.8702i	−0.370075	−	0.640989i	0.619501	−	0.784996i	$-0.287335\pi$
$613$	−9.16264	−	15.8702i	−0.370075	−	0.640989i	−0.989577	+	0.144006i	$0.954001\pi$
$614$	9.61725	−	16.6576i	0.388121	−	0.672245i
$615$	−21.5573			−0.869276
$616$	−23.2487	−	11.4144i	−0.936717	−	0.459901i
$617$	44.3782			1.78660			0.893299	−	0.449463i	$-0.148385\pi$
$617$	44.3782			1.78660			0.893299	+	0.449463i	$0.148385\pi$
$618$	37.1214	−	64.2962i	1.49324	−	2.58637i
$619$	12.5043	+	21.6580i	0.502588	+	0.870509i	0.999996	+	0.00299144i	$0.000952205\pi$
$619$	12.5043	+	21.6580i	0.502588	+	0.870509i	−0.497407	+	0.867517i	$0.665714\pi$
$620$	−6.10051	−	10.5664i	−0.245002	−	0.424357i
$621$	−1.84234	+	3.19103i	−0.0739307	+	0.128052i
$622$	57.5306			2.30677
$623$	1.02471	+	15.2256i	0.0410541	+	0.610002i
$624$	−19.6553			−0.786842
$625$	11.9358	−	20.6734i	0.477433	−	0.826938i
$626$	−2.69871	−	4.67429i	−0.107862	−	0.186822i
$627$	−0.534093	−	0.925076i	−0.0213296	−	0.0369440i
$628$	−9.19212	+	15.9212i	−0.366806	+	0.635326i
$629$	57.6388			2.29821
$630$	15.5484	−	10.4285i	0.619462	−	0.415482i
$631$	−18.4638			−0.735032			−0.367516	−	0.930017i	$-0.619792\pi$
$631$	−18.4638			−0.735032			−0.367516	+	0.930017i	$0.619792\pi$
$632$	−9.99382	+	17.3098i	−0.397533	+	0.688547i
$633$	11.2362	+	19.4616i	0.446598	+	0.773531i
$634$	24.5899	+	42.5909i	0.976588	+	1.69150i
$635$	−9.61165	+	16.6479i	−0.381427	+	0.660650i
$636$	−35.7176			−1.41629
$637$	2.65613	−	6.47650i	0.105240	−	0.256608i
$638$	8.86677			0.351039
$639$	−3.91927	+	6.78837i	−0.155044	+	0.268544i
$640$	−38.2416	−	66.2364i	−1.51163	−	2.61822i
$641$	10.6284	+	18.4088i	0.419795	+	0.727106i	0.995919	−	0.0902567i	$-0.0287687\pi$
$641$	10.6284	+	18.4088i	0.419795	+	0.727106i	−0.576124	+	0.817362i	$0.695435\pi$
$642$	16.6132	−	28.7748i	0.655669	−	1.13565i
$643$	−36.0554			−1.42188			−0.710942	−	0.703251i	$-0.751731\pi$
$643$	−36.0554			−1.42188			−0.710942	+	0.703251i	$0.751731\pi$
$644$	−7.79376	+	5.22738i	−0.307117	+	0.205988i
$645$	−2.61434			−0.102939
$646$	5.45729	−	9.45230i	0.214714	−	0.371896i
$647$	−19.9117	−	34.4881i	−0.782809	−	1.35587i	−0.930299	−	0.366802i	$-0.880453\pi$
$647$	−19.9117	−	34.4881i	−0.782809	−	1.35587i	0.147490	−	0.989064i	$-0.452881\pi$
$648$	18.8149	+	32.5884i	0.739120	+	1.28019i
$649$	−0.549314	+	0.951440i	−0.0215625	+	0.0373473i
$650$	−0.589510			−0.0231225
$651$	0.245883	+	3.65345i	0.00963691	+	0.143190i
$652$	−74.9469			−2.93515
$653$	16.2335	−	28.1172i	0.635265	−	1.10031i	−0.351195	−	0.936303i	$-0.614224\pi$
$653$	16.2335	−	28.1172i	0.635265	−	1.10031i	0.986459	−	0.164008i	$-0.0524423\pi$
$654$	27.7059	+	47.9881i	1.08339	+	1.87648i
$655$	11.4984	+	19.9159i	0.449281	+	0.778177i
$656$	−53.4324	+	92.5477i	−2.08619	+	3.61338i
$657$	9.83384			0.383655
$658$	15.1291	+	7.42796i	0.589794	+	0.289572i
$659$	23.5230			0.916327			0.458164	−	0.888868i	$-0.348507\pi$
$659$	23.5230			0.916327			0.458164	+	0.888868i	$0.348507\pi$
$660$	−8.37558	+	14.5069i	−0.326019	+	0.564682i
$661$	−7.01944	−	12.1580i	−0.273025	−	0.472893i	0.696610	−	0.717450i	$-0.254691\pi$
$661$	−7.01944	−	12.1580i	−0.273025	−	0.472893i	−0.969635	+	0.244557i	$0.921357\pi$
$662$	19.9949	+	34.6321i	0.777122	+	1.34602i
$663$	−3.56211	+	6.16976i	−0.138341	+	0.239614i
$664$	−62.2525			−2.41587
$665$	3.93167	+	1.93034i	0.152464	+	0.0748553i
$666$	35.2431			1.36564
$667$	1.01439	−	1.75698i	0.0392773	−	0.0680303i
$668$	−44.4424	−	76.9765i	−1.71953	−	2.97831i
$669$	−3.59639	−	6.22913i	−0.139044	−	0.240832i
$670$	−13.3484	+	23.1200i	−0.515692	+	0.893205i
$671$	13.1017			0.505786
$672$	5.04846	+	75.0124i	0.194748	+	2.89367i
$673$	−47.1937			−1.81918			−0.909592	−	0.415502i	$-0.863606\pi$
$673$	−47.1937			−1.81918			−0.909592	+	0.415502i	$0.863606\pi$
$674$	−17.4526	+	30.2287i	−0.672247	+	1.16437i
$675$	0.609753	+	1.05612i	0.0234694	+	0.0406502i
$676$	−2.71349	−	4.69991i	−0.104365	−	0.180766i
$677$	4.79438	−	8.30411i	0.184263	−	0.319153i	−0.759065	−	0.651015i	$-0.774344\pi$
$677$	4.79438	−	8.30411i	0.184263	−	0.319153i	0.943328	+	0.331862i	$0.107677\pi$
$678$	−11.3899			−0.437426
$679$	6.34526	−	4.25585i	0.243509	−	0.163325i
$680$	−108.083			−4.14481
$681$	13.5460	−	23.4623i	0.519083	−	0.899078i
$682$	1.46811	+	2.54284i	0.0562167	+	0.0973702i
$683$	−23.6581	−	40.9769i	−0.905250	−	1.56794i	−0.820581	−	0.571530i	$-0.806350\pi$
$683$	−23.6581	−	40.9769i	−0.905250	−	1.56794i	−0.0846691	−	0.996409i	$-0.526983\pi$
$684$	2.43827	−	4.22321i	0.0932296	−	0.161478i
$685$	19.0976			0.729680
$686$	−47.8783	−	15.9726i	−1.82800	−	0.609837i
$687$	−33.9967			−1.29705
$688$	−6.47994	+	11.2236i	−0.247045	+	0.427895i
$689$	−2.44407	−	4.23325i	−0.0931117	−	0.161274i
$690$	2.62264	+	4.54254i	0.0998421	+	0.172932i
$691$	13.5559	−	23.4796i	0.515692	−	0.893205i	−0.484142	−	0.874990i	$-0.660868\pi$
$691$	13.5559	−	23.4796i	0.515692	−	0.893205i	0.999834	−	0.0182158i	$-0.00579859\pi$
$692$	22.3888			0.851095
$693$	−2.73415	+	1.83383i	−0.103862	+	0.0696615i
$694$	55.0648			2.09023
$695$	4.37433	−	7.57656i	0.165928	−	0.287395i
$696$	−19.5165	−	33.8036i	−0.739771	−	1.28132i
$697$	19.3670	+	33.5447i	0.733578	+	1.27059i
$698$	25.1314	−	43.5289i	0.951238	−	1.64759i
$699$	1.06819			0.0404025
$700$	0.208563	+	3.09893i	0.00788293	+	0.117128i
$701$	−1.79821			−0.0679176			−0.0339588	−	0.999423i	$-0.510811\pi$
$701$	−1.79821			−0.0679176			−0.0339588	+	0.999423i	$0.510811\pi$
$702$	−7.68202	+	13.3057i	−0.289939	+	0.502190i
$703$	4.12258	+	7.14051i	0.155486	+	0.269310i
$704$	14.8419	+	25.7069i	0.559375	+	0.968866i
$705$	3.44179	−	5.96135i	0.129625	−	0.224517i
$706$	−22.1954			−0.835336
$707$	−26.7284	−	13.1229i	−1.00523	−	0.493537i
$708$	7.65885			0.287837
$709$	14.1615	−	24.5284i	0.531846	−	0.921185i	−0.467462	−	0.884013i	$-0.654832\pi$
$709$	14.1615	−	24.5284i	0.531846	−	0.921185i	0.999309	−	0.0371721i	$-0.0118350\pi$
$710$	19.6780	+	34.0834i	0.738504	+	1.27913i
$711$	1.27035	+	2.20031i	0.0476418	+	0.0825180i
$712$	26.9337	−	46.6506i	1.00938	−	1.74831i
$713$	0.671827			0.0251601
$714$	46.1103	+	22.6388i	1.72563	+	0.847236i
$715$	−2.29249			−0.0857341
$716$	−39.1112	+	67.7425i	−1.46165	+	2.53166i
$717$	13.4970	+	23.3775i	0.504055	+	0.873050i
$718$	44.4352	+	76.9640i	1.65831	+	2.87227i
$719$	20.9485	−	36.2839i	0.781249	−	1.35316i	−0.149966	−	0.988691i	$-0.547916\pi$
$719$	20.9485	−	36.2839i	0.781249	−	1.35316i	0.931215	−	0.364471i	$-0.118750\pi$
$720$	−37.9046			−1.41262
$721$	−3.59469	−	53.4117i	−0.133873	−	1.98916i
$722$	−50.2184			−1.86894
$723$	9.29838	−	16.1053i	0.345810	−	0.598961i
$724$	−49.1180	−	85.0749i	−1.82546	−	3.16179i
$725$	−0.335728	−	0.581499i	−0.0124686	−	0.0215963i
$726$	−18.1657	+	31.4638i	−0.674191	+	1.16773i
$727$	19.5123			0.723670			0.361835	−	0.932242i	$-0.382150\pi$
$727$	19.5123			0.723670			0.361835	+	0.932242i	$0.382150\pi$
$728$	−20.5213	+	13.7639i	−0.760571	+	0.510125i
$729$	27.5552			1.02056
$730$	24.6871	−	42.7593i	0.913711	−	1.58259i
$731$	2.34871	+	4.06808i	0.0868701	+	0.150463i
$732$	−45.6679	−	79.0991i	−1.68793	−	2.92359i
$733$	−8.87698	+	15.3754i	−0.327879	+	0.567902i	−0.982091	−	0.188409i	$-0.939667\pi$
$733$	−8.87698	+	15.3754i	−0.327879	+	0.567902i	0.654212	+	0.756311i	$0.273000\pi$
$734$	−8.61213			−0.317880
$735$	−7.82185	+	19.0722i	−0.288513	+	0.703488i
$736$	13.7939			0.508450
$737$	2.34728	−	4.06562i	0.0864633	−	0.149759i
$738$	11.8419	+	20.5108i	0.435907	+	0.755013i
$739$	−22.1571	−	38.3772i	−0.815061	−	1.41173i	−0.909284	−	0.416176i	$-0.863370\pi$
$739$	−22.1571	−	38.3772i	−0.815061	−	1.41173i	0.0942227	−	0.995551i	$-0.469963\pi$
$740$	64.6497	−	111.977i	2.37657	−	4.11634i
$741$	−1.01911			−0.0374380
$742$	−29.2709	+	19.6324i	−1.07457	+	0.720729i
$743$	−7.16727			−0.262941			−0.131471	−	0.991320i	$-0.541970\pi$
$743$	−7.16727			−0.262941			−0.131471	+	0.991320i	$0.541970\pi$
$744$	6.46285	−	11.1940i	0.236940	−	0.410392i
$745$	−16.8331	−	29.1558i	−0.616718	−	1.06819i
$746$	2.01355	+	3.48757i	0.0737212	+	0.127689i
$747$	−3.95657	+	6.85297i	−0.144763	+	0.250737i
$748$	30.0983			1.10050
$749$	−1.60875	−	23.9036i	−0.0587826	−	0.873420i
$750$	41.8630			1.52862
$751$	16.9532	−	29.3639i	0.618632	−	1.07150i	−0.371103	−	0.928592i	$-0.621020\pi$
$751$	16.9532	−	29.3639i	0.618632	−	1.07150i	0.989736	−	0.142911i	$-0.0456462\pi$
$752$	−17.0618	−	29.5518i	−0.622178	−	1.07764i
$753$	−17.5772	−	30.4445i	−0.640547	−	1.10946i
$754$	4.22970	−	7.32606i	0.154037	−	0.266799i
$755$	−29.9110			−1.08857
$756$	72.6628	+	35.6753i	2.64272	+	1.29750i
$757$	−0.906670			−0.0329535			−0.0164767	−	0.999864i	$-0.505245\pi$
$757$	−0.906670			−0.0329535			−0.0164767	+	0.999864i	$0.505245\pi$
$758$	−14.6147	+	25.3134i	−0.530830	+	0.919424i
$759$	−0.461186	−	0.798798i	−0.0167400	−	0.0289945i
$760$	−7.73059	−	13.3898i	−0.280418	−	0.485698i
$761$	−10.1247	+	17.5365i	−0.367020	+	0.635697i	−0.989098	−	0.147258i	$-0.952955\pi$
$761$	−10.1247	+	17.5365i	−0.367020	+	0.635697i	0.622079	+	0.782955i	$0.286288\pi$
$762$	−32.2502			−1.16830
$763$	35.8650	+	17.6087i	1.29840	+	0.637477i
$764$	30.0729			1.08800
$765$	−6.86942	+	11.8982i	−0.248364	+	0.430180i
$766$	29.1750	+	50.5326i	1.05414	+	1.82582i
$767$	0.524077	+	0.907729i	0.0189233	+	0.0327762i
$768$	26.0259	−	45.0782i	0.939129	−	1.62662i
$769$	−36.9094			−1.33099			−0.665494	−	0.746403i	$-0.731779\pi$
$769$	−36.9094			−1.33099			−0.665494	+	0.746403i	$0.731779\pi$
$770$	1.10996	+	16.4923i	0.0400001	+	0.594341i
$771$	−14.2987			−0.514954
$772$	23.7183	−	41.0814i	0.853642	−	1.47855i
$773$	4.94018	+	8.55665i	0.177686	+	0.307761i	0.941088	−	0.338163i	$-0.109806\pi$
$773$	4.94018	+	8.55665i	0.177686	+	0.307761i	−0.763402	+	0.645924i	$0.776472\pi$
$774$	1.43611	+	2.48742i	0.0516199	+	0.0894083i
$775$	0.111176	−	0.192562i	0.00399355	−	0.00691704i
$776$	−26.9701			−0.968169
$777$	−32.2272	+	21.6152i	−1.15614	+	0.775441i
$778$	94.7893			3.39836
$779$	−2.77043	+	4.79852i	−0.0992609	+	0.171925i
$780$	7.99079	+	13.8404i	0.286116	+	0.495568i
$781$	−3.46035	−	5.99350i	−0.123821	−	0.214464i
$782$	4.71233	−	8.16200i	0.168513	−	0.291873i
$783$	−17.4998			−0.625391
$784$	62.4913	+	80.8526i	2.23183	+	2.88759i
$785$	7.40915			0.264444
$786$	−19.2905	+	33.4121i	−0.688069	+	1.19177i
$787$	−18.8411	−	32.6337i	−0.671611	−	1.16326i	−0.977447	−	0.211180i	$-0.932269\pi$
$787$	−18.8411	−	32.6337i	−0.671611	−	1.16326i	0.305836	−	0.952084i	$-0.401064\pi$
$788$	14.8394	+	25.7026i	0.528632	+	0.915617i
$789$	6.97292	−	12.0775i	0.248243	−	0.429969i
$790$	12.7565			0.453854
$791$	−6.82056	+	4.57464i	−0.242511	+	0.162656i
$792$	11.6213			0.412945
$793$	6.24989	−	10.8251i	0.221940	−	0.384412i
$794$	−6.06656	−	10.5076i	−0.215294	−	0.372900i
$795$	7.19738	+	12.4662i	0.255265	+	0.442131i
$796$	−53.0129	+	91.8211i	−1.87899	+	3.25451i
$797$	28.3837			1.00540			0.502701	−	0.864460i	$-0.332340\pi$
$797$	28.3837			1.00540			0.502701	+	0.864460i	$0.332340\pi$
$798$	0.493425	+	7.33155i	0.0174671	+	0.259534i
$799$	−12.3683			−0.437560
$800$	2.28266	−	3.95368i	0.0807041	−	0.139784i
$801$	−3.42364	−	5.92992i	−0.120968	−	0.209524i
$802$	18.7412	+	32.4607i	0.661775	+	1.14623i
$803$	−4.34118	+	7.51915i	−0.153197	+	0.265345i
$804$	−32.7272			−1.15420
$805$	3.39498	+	1.66684i	0.119657	+	0.0587482i
$806$	2.80132			0.0986722
$807$	8.05834	−	13.9574i	0.283667	−	0.491325i
$808$	52.5543	+	91.0268i	1.84886	+	3.20231i
$809$	5.87327	+	10.1728i	0.206493	+	0.357657i	0.950607	−	0.310396i	$-0.100461\pi$
$809$	5.87327	+	10.1728i	0.206493	+	0.357657i	−0.744114	+	0.668052i	$0.767128\pi$
$810$	12.0080	−	20.7985i	0.421919	−	0.730784i
$811$	2.01940			0.0709108			0.0354554	−	0.999371i	$-0.488712\pi$
$811$	2.01940			0.0709108			0.0354554	+	0.999371i	$0.488712\pi$
$812$	−40.0080	−	19.6428i	−1.40400	−	0.689326i
$813$	3.71194			0.130184
$814$	−15.5582	+	26.9475i	−0.545313	+	0.944511i
$815$	15.1024	+	26.1581i	0.529014	+	0.916280i
$816$	−52.0005	−	90.0676i	−1.82038	−	3.15300i
$817$	−0.335980	+	0.581934i	−0.0117544	+	0.0203593i
$818$	−9.51676			−0.332746
$819$	0.210913	+	3.13385i	0.00736991	+	0.109506i
$820$	86.8910			3.03437
$821$	7.54208	−	13.0633i	0.263220	−	0.455911i	−0.703875	−	0.710323i	$-0.748549\pi$
$821$	7.54208	−	13.0633i	0.263220	−	0.455911i	0.967096	+	0.254412i	$0.0818820\pi$
$822$	16.0196	+	27.7468i	0.558748	+	0.967780i
$823$	7.38828	+	12.7969i	0.257539	+	0.446071i	0.965582	−	0.260098i	$-0.0837550\pi$
$823$	7.38828	+	12.7969i	0.257539	+	0.446071i	−0.708043	+	0.706170i	$0.750422\pi$
$824$	−94.4839	+	163.651i	−3.29150	+	5.70105i
$825$	−0.305274			−0.0106283
$826$	6.27651	−	4.20974i	0.218388	−	0.146476i
$827$	13.0407			0.453471			0.226736	−	0.973956i	$-0.427195\pi$
$827$	13.0407			0.453471			0.226736	+	0.973956i	$0.427195\pi$
$828$	2.10543	−	3.64671i	0.0731688	−	0.126732i
$829$	12.7291	+	22.0474i	0.442099	+	0.765738i	0.997845	−	0.0656144i	$-0.0209007\pi$
$829$	12.7291	+	22.0474i	0.442099	+	0.765738i	−0.555746	+	0.831352i	$0.687567\pi$
$830$	19.8653	+	34.4077i	0.689535	+	1.19431i
$831$	−16.1082	+	27.9002i	−0.558786	+	0.967845i
$832$	28.3200			0.981820
$833$	36.7047	−	4.96305i	1.27174	−	0.171960i
$834$	14.6773			0.508233
$835$	−17.9110	+	31.0228i	−0.619835	+	1.07359i
$836$	2.15277	+	3.72870i	0.0744549	+	0.128960i
$837$	−2.89751	−	5.01864i	−0.100153	−	0.173469i
$838$	4.86099	−	8.41948i	0.167920	−	0.290846i
$839$	32.1703			1.11064			0.555321	−	0.831636i	$-0.312596\pi$
$839$	32.1703			1.11064			0.555321	+	0.831636i	$0.312596\pi$
$840$	60.4319	−	40.5325i	2.08510	−	1.39850i
$841$	−19.3647			−0.667747
$842$	13.6263	−	23.6014i	0.469592	−	0.813357i
$843$	−2.61117	−	4.52268i	−0.0899335	−	0.155769i
$844$	−45.2896	−	78.4439i	−1.55893	−	2.70015i
$845$	−1.09358	+	1.89414i	−0.0376204	+	0.0651604i
$846$	−7.56259			−0.260007
$847$	1.75909	+	26.1374i	0.0604431	+	0.898093i
$848$	71.3582			2.45045
$849$	−4.18061	+	7.24104i	−0.143478	+	0.248512i
$850$	−1.55962	−	2.70134i	−0.0534946	−	0.0926553i
$851$	3.55982	+	6.16579i	0.122029	+	0.211360i
$852$	−24.1231	+	41.7824i	−0.826442	+	1.43144i
$853$	−19.3910			−0.663934			−0.331967	−	0.943291i	$-0.607712\pi$
$853$	−19.3910			−0.663934			−0.331967	+	0.943291i	$0.607712\pi$
$854$	−80.9027	−	39.7209i	−2.76843	−	1.35922i
$855$	−1.96532			−0.0672127
$856$	−42.2849	+	73.2396i	−1.44527	+	2.50328i
$857$	−8.71210	−	15.0898i	−0.297600	−	0.515458i	0.677987	−	0.735074i	$-0.262853\pi$
$857$	−8.71210	−	15.0898i	−0.297600	−	0.515458i	−0.975586	+	0.219616i	$0.929519\pi$
$858$	−1.92301	−	3.33075i	−0.0656504	−	0.113710i
$859$	17.7459	−	30.7367i	0.605481	−	1.04872i	−0.386495	−	0.922292i	$-0.626314\pi$
$859$	17.7459	−	30.7367i	0.605481	−	1.04872i	0.991975	−	0.126432i	$-0.0403524\pi$
$860$	10.5376			0.359329
$861$	−23.4082	−	11.4927i	−0.797749	−	0.391672i
$862$	−30.9704			−1.05486
$863$	−28.0010	+	48.4991i	−0.953164	+	1.65093i	−0.214648	+	0.976691i	$0.568860\pi$
$863$	−28.0010	+	48.4991i	−0.953164	+	1.65093i	−0.738516	+	0.674236i	$0.764473\pi$
$864$	−59.4916	−	103.042i	−2.02394	−	3.50557i
$865$	−4.51153	−	7.81420i	−0.153397	−	0.265691i
$866$	28.9062	−	50.0670i	0.982273	−	1.70135i
$867$	−14.8070			−0.502871
$868$	−0.991079	−	14.7259i	−0.0336394	−	0.499830i
$869$	−2.24320			−0.0760953
$870$	−12.4558	+	21.5740i	−0.422290	+	0.731428i
$871$	−2.23944	−	3.87883i	−0.0758807	−	0.131429i
$872$	−70.5190	−	122.143i	−2.38808	−	4.13627i
$873$	−1.71413	+	2.96896i	−0.0580145	+	0.100484i
$874$	1.34819			0.0456031
$875$	25.0687	−	16.8139i	0.847476	−	0.568414i
$876$	60.5272			2.04503
$877$	−12.6031	+	21.8292i	−0.425577	+	0.737120i	−0.996474	−	0.0839011i	$-0.973262\pi$
$877$	−12.6031	+	21.8292i	−0.425577	+	0.737120i	0.570898	+	0.821021i	$0.306595\pi$
$878$	33.3852	+	57.8249i	1.12670	+	1.95150i
$879$	11.1587	+	19.3275i	0.376374	+	0.651899i
$880$	16.7331	−	28.9826i	0.564074	−	0.977004i
$881$	−18.6082			−0.626925			−0.313463	−	0.949601i	$-0.601489\pi$
$881$	−18.6082			−0.626925			−0.313463	+	0.949601i	$0.601489\pi$
$882$	22.4430	−	3.03465i	0.755695	−	0.102182i
$883$	−11.2552			−0.378768			−0.189384	−	0.981903i	$-0.560649\pi$
$883$	−11.2552			−0.378768			−0.189384	+	0.981903i	$0.560649\pi$
$884$	14.3578	−	24.8684i	0.482904	−	0.836415i
$885$	−1.54332	−	2.67311i	−0.0518781	−	0.0898556i
$886$	−55.1438	−	95.5119i	−1.85259	−	3.20879i
$887$	19.6056	−	33.9579i	0.658292	−	1.14020i	−0.322765	−	0.946479i	$-0.604612\pi$
$887$	19.6056	−	33.9579i	0.658292	−	1.14020i	0.981057	−	0.193717i	$-0.0620543\pi$
$888$	136.979			4.59672
$889$	−19.3123	+	12.9530i	−0.647712	+	0.434429i
$890$	−34.3792			−1.15239
$891$	−2.11159	+	3.65738i	−0.0707408	+	0.122527i
$892$	14.4959	+	25.1077i	0.485360	+	0.840668i
$893$	−0.884638	−	1.53224i	−0.0296033	−	0.0512744i
$894$	28.2403	−	48.9136i	0.944496	−	1.63592i
$895$	31.5249			1.05376
$896$	−6.21266	−	92.3107i	−0.207551	−	3.08389i
$897$	−0.879996			−0.0293822
$898$	37.8316	−	65.5263i	1.26246	−	2.18664i
$899$	1.59536	+	2.76325i	0.0532083	+	0.0921595i
$900$	−0.696826	−	1.20694i	−0.0232275	−	0.0402312i
$901$	12.9322	−	22.3992i	0.430834	−	0.746226i
$902$	−20.9106			−0.696247
$903$	−2.83879	−	1.39377i	−0.0944692	−	0.0463816i
$904$	28.9903			0.964203
$905$	−19.7954	+	34.2866i	−0.658020	+	1.13972i
$906$	−25.0903	−	43.4577i	−0.833570	−	1.44378i
$907$	−10.7985	−	18.7035i	−0.358558	−	0.621040i	0.629162	−	0.777274i	$-0.283398\pi$
$907$	−10.7985	−	18.7035i	−0.358558	−	0.621040i	−0.987720	+	0.156234i	$0.950065\pi$
$908$	−54.5997	+	94.5694i	−1.81195	+	3.13840i
$909$	13.3607			0.443147
$910$	14.1560	+	6.95021i	0.469268	+	0.230397i
$911$	−32.4434			−1.07490			−0.537449	−	0.843297i	$-0.680612\pi$
$911$	−32.4434			−1.07490			−0.537449	+	0.843297i	$0.680612\pi$
$912$	7.43861	−	12.8840i	0.246317	−	0.426634i
$913$	−3.49328	−	6.05054i	−0.115611	−	0.200244i
$914$	15.2531	+	26.4192i	0.504528	+	0.873868i
$915$	−18.4049	+	31.8782i	−0.608447	+	1.05386i
$916$	137.030			4.52760
$917$	1.86802	+	27.7559i	0.0616873	+	0.916580i
$918$	−81.2950			−2.68313
$919$	−17.8686	+	30.9493i	−0.589430	+	1.02092i	0.404877	+	0.914371i	$0.367314\pi$
$919$	−17.8686	+	30.9493i	−0.589430	+	1.02092i	−0.994307	+	0.106552i	$0.966019\pi$
$920$	−6.67532	−	11.5620i	−0.220079	−	0.381187i
$921$	−4.75142	−	8.22971i	−0.156565	−	0.271178i
$922$	12.6693	−	21.9439i	0.417242	−	0.722684i
$923$	−6.60274			−0.217332
$924$	−16.8287	+	11.2872i	−0.553623	+	0.371323i
$925$	2.35636			0.0774765
$926$	−38.4858	+	66.6594i	−1.26472	+	2.19056i
$927$	12.0102	+	20.8022i	0.394466	+	0.683235i
$928$	32.7559	+	56.7349i	1.07527	+	1.86241i
$929$	−5.88847	+	10.1991i	−0.193194	+	0.334622i	−0.946307	−	0.323269i	$-0.895218\pi$
$929$	−5.88847	+	10.1991i	−0.193194	+	0.334622i	0.753113	+	0.657891i	$0.228551\pi$
$930$	−8.24941			−0.270509
$931$	3.24012	+	4.19214i	0.106191	+	0.137392i
$932$	−4.30553			−0.141032
$933$	14.2116	−	24.6151i	0.465265	−	0.805863i
$934$	−30.3329	−	52.5382i	−0.992523	−	1.71910i
$935$	−6.06506	−	10.5050i	−0.198349	−	0.343550i
$936$	5.54370	−	9.60197i	0.181202	−	0.313850i
$937$	18.9937			0.620497			0.310248	−	0.950655i	$-0.399588\pi$
$937$	18.9937			0.620497			0.310248	+	0.950655i	$0.399588\pi$
$938$	−26.8203	+	17.9887i	−0.875713	+	0.587352i
$939$	−2.66660			−0.0870213
$940$	−13.8728	+	24.0284i	−0.452480	+	0.783719i
$941$	−3.40932	−	5.90511i	−0.111141	−	0.192501i	0.805090	−	0.593153i	$-0.202117\pi$
$941$	−3.40932	−	5.90511i	−0.111141	−	0.192501i	−0.916230	+	0.400652i	$0.868784\pi$
$942$	6.21502	+	10.7647i	0.202496	+	0.350734i
$943$	−2.39225	+	4.14349i	−0.0779023	+	0.134931i
$944$	−15.3012			−0.498012
$945$	−2.19065	−	32.5498i	−0.0712620	−	1.05884i
$946$	−2.53590			−0.0824493
$947$	−0.529958	+	0.917914i	−0.0172213	+	0.0298282i	−0.874508	−	0.485012i	$-0.838815\pi$
$947$	−0.529958	+	0.917914i	−0.0172213	+	0.0298282i	0.857286	+	0.514840i	$0.172149\pi$
$948$	7.81899	+	13.5429i	0.253949	+	0.439853i
$949$	4.14174	+	7.17370i	0.134446	+	0.232868i
$950$	0.223102	−	0.386424i	0.00723838	−	0.0125372i
$951$	24.2973			0.787895
$952$	−117.363	−	57.6219i	−3.80376	−	1.86753i
$953$	−40.4127			−1.30910			−0.654548	−	0.756020i	$-0.727141\pi$
$953$	−40.4127			−1.30910			−0.654548	+	0.756020i	$0.727141\pi$
$954$	7.90735	−	13.6959i	0.256010	−	0.443422i
$955$	−6.05993	−	10.4961i	−0.196095	−	0.339646i
$956$	−54.4023	−	94.2276i	−1.75950	−	3.04754i
$957$	2.19032	−	3.79375i	0.0708031	−	0.122635i
$958$	−89.5964			−2.89473
$959$	20.7372	+	10.1814i	0.669639	+	0.328774i
$960$	−83.3978			−2.69165
$961$	14.9717	−	25.9317i	0.482958	−	0.836508i
$962$	14.8434	+	25.7095i	0.478570	+	0.828907i
$963$	5.37498	+	9.30975i	0.173206	+	0.300002i
$964$	−37.4789	+	64.9154i	−1.20711	+	2.09078i
$965$	−19.1177			−0.615422
$966$	0.426069	+	6.33074i	0.0137086	+	0.203688i
$967$	−36.2949			−1.16717			−0.583583	−	0.812053i	$-0.698350\pi$
$967$	−36.2949			−1.16717			−0.583583	+	0.812053i	$0.698350\pi$
$968$	46.2365	−	80.0839i	1.48610	−	2.57399i
$969$	−2.69618	−	4.66993i	−0.0866139	−	0.150020i
$970$	8.60638	+	14.9067i	0.276334	+	0.478625i
$971$	10.7218	−	18.5708i	0.344080	−	0.595964i	−0.641106	−	0.767452i	$-0.721524\pi$
$971$	10.7218	−	18.5708i	0.344080	−	0.595964i	0.985186	+	0.171488i	$0.0548575\pi$
$972$	−62.3457			−1.99974
$973$	8.78914	−	5.89500i	0.281767	−	0.188985i
$974$	−76.0137			−2.43564
$975$	−0.145624	+	0.252229i	−0.00466371	+	0.00807778i
$976$	91.2374	+	158.028i	2.92044	+	5.05835i
$977$	19.9138	+	34.4918i	0.637100	+	1.10349i	0.986066	+	0.166354i	$0.0531994\pi$
$977$	19.9138	+	34.4918i	0.637100	+	1.10349i	−0.348966	+	0.937135i	$0.613467\pi$
$978$	−25.3367	+	43.8845i	−0.810179	+	1.40327i
$979$	6.04551			0.193215
$980$	31.5275	−	76.8742i	1.00711	−	2.45565i
$981$	−17.9278			−0.572392
$982$	−14.5216	+	25.1522i	−0.463403	+	0.802638i
$983$	−7.94071	−	13.7537i	−0.253269	−	0.438675i	0.711155	−	0.703036i	$-0.248173\pi$
$983$	−7.94071	−	13.7537i	−0.253269	−	0.438675i	−0.964424	+	0.264360i	$0.914839\pi$
$984$	46.0260	+	79.7194i	1.46725	+	2.54136i
$985$	5.98052	−	10.3586i	0.190555	−	0.330051i
$986$	44.7608			1.42548
$987$	6.91543	−	4.63827i	0.220120	−	0.147638i
$988$	4.10772			0.130684
$989$	−0.290116	+	0.502496i	−0.00922516	+	0.0159785i
$990$	−3.70846	−	6.42325i	−0.117863	−	0.204144i
$991$	8.83435	+	15.3016i	0.280633	+	0.486070i	0.971541	−	0.236873i	$-0.0761225\pi$
$991$	8.83435	+	15.3016i	0.280633	+	0.486070i	−0.690908	+	0.722943i	$0.742789\pi$
$992$	−10.8471	+	18.7877i	−0.344394	+	0.596509i
$993$	19.7570			0.626970
$994$	3.19686	+	47.5005i	0.101398	+	1.50662i
$995$	42.7301			1.35464
$996$	−24.3526	+	42.1800i	−0.771643	+	1.33652i
$997$	12.4304	+	21.5301i	0.393675	+	0.681865i	0.992931	−	0.118692i	$-0.0378701\pi$
$997$	12.4304	+	21.5301i	0.393675	+	0.681865i	−0.599256	+	0.800558i	$0.704537\pi$
$998$	33.3999	+	57.8503i	1.05725	+	1.83122i
$999$	30.7062	−	53.1847i	0.971500	−	1.68269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.e.c.79.1	yes	10
3.2	odd	2		819.2.j.h.352.5		10
4.3	odd	2		1456.2.r.p.625.2		10
7.2	even	3		637.2.a.l.1.5		5
7.3	odd	6		637.2.e.m.508.1		10
7.4	even	3	inner	91.2.e.c.53.1	✓	10
7.5	odd	6		637.2.a.k.1.5		5
7.6	odd	2		637.2.e.m.79.1		10
13.12	even	2		1183.2.e.f.170.5		10
21.2	odd	6		5733.2.a.bl.1.1		5
21.5	even	6		5733.2.a.bm.1.1		5
21.11	odd	6		819.2.j.h.235.5		10
28.11	odd	6		1456.2.r.p.417.2		10
91.12	odd	6		8281.2.a.bx.1.1		5
91.25	even	6		1183.2.e.f.508.5		10
91.51	even	6		8281.2.a.bw.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.1	✓	10	7.4	even	3	inner
91.2.e.c.79.1	yes	10	1.1	even	1	trivial
637.2.a.k.1.5		5	7.5	odd	6
637.2.a.l.1.5		5	7.2	even	3
637.2.e.m.79.1		10	7.6	odd	2
637.2.e.m.508.1		10	7.3	odd	6
819.2.j.h.235.5		10	21.11	odd	6
819.2.j.h.352.5		10	3.2	odd	2
1183.2.e.f.170.5		10	13.12	even	2
1183.2.e.f.508.5		10	91.25	even	6
1456.2.r.p.417.2		10	28.11	odd	6
1456.2.r.p.625.2		10	4.3	odd	2
5733.2.a.bl.1.1		5	21.2	odd	6
5733.2.a.bm.1.1		5	21.5	even	6
8281.2.a.bw.1.1		5	91.51	even	6
8281.2.a.bx.1.1		5	91.12	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.36263 + 2.36014i) q^{2} +(0.673208 + 1.16603i) q^{3} +(-2.71349 - 4.69991i) q^{4} +(-1.09358 + 1.89414i) q^{5} -3.66932 q^{6} +(-2.19729 + 1.47375i) q^{7} +9.33940 q^{8} +(0.593582 - 1.02811i) q^{9} +(-2.98028 - 5.16200i) q^{10} +(0.524077 + 0.907729i) q^{11} +(3.65349 - 6.32803i) q^{12} +1.00000 q^{13} +(-0.484172 - 7.19406i) q^{14} -2.94483 q^{15} +(-7.29912 + 12.6424i) q^{16} +(2.64562 + 4.58236i) q^{17} +(1.61766 + 2.80187i) q^{18} +(-0.378453 + 0.655500i) q^{19} +11.8697 q^{20} +(-3.19767 - 1.56996i) q^{21} -2.85648 q^{22} +(-0.326792 + 0.566020i) q^{23} +(6.28736 + 10.8900i) q^{24} +(0.108157 + 0.187333i) q^{25} +(-1.36263 + 2.36014i) q^{26} +5.63766 q^{27} +(12.8888 + 6.32803i) q^{28} -3.10408 q^{29} +(4.01270 - 6.95021i) q^{30} +(-0.513956 - 0.890198i) q^{31} +(-10.5525 - 18.2775i) q^{32} +(-0.705626 + 1.22218i) q^{33} -14.4200 q^{34} +(-0.388575 - 5.77363i) q^{35} -6.44273 q^{36} +(5.44661 - 9.43381i) q^{37} +(-1.03138 - 1.78640i) q^{38} +(0.673208 + 1.16603i) q^{39} +(-10.2134 + 17.6901i) q^{40} +7.32040 q^{41} +(8.06254 - 5.40766i) q^{42} +0.887771 q^{43} +(2.84416 - 4.92623i) q^{44} +(1.29826 + 2.24865i) q^{45} +(-0.890590 - 1.54255i) q^{46} +(-1.16875 + 2.02434i) q^{47} -19.6553 q^{48} +(2.65613 - 6.47650i) q^{49} -0.589510 q^{50} +(-3.56211 + 6.16976i) q^{51} +(-2.71349 - 4.69991i) q^{52} +(-2.44407 - 4.23325i) q^{53} +(-7.68202 + 13.3057i) q^{54} -2.29249 q^{55} +(-20.5213 + 13.7639i) q^{56} -1.01911 q^{57} +(4.22970 - 7.32606i) q^{58} +(0.524077 + 0.907729i) q^{59} +(7.99079 + 13.8404i) q^{60} +(6.24989 - 10.8251i) q^{61} +2.80132 q^{62} +(0.210913 + 3.13385i) q^{63} +28.3200 q^{64} +(-1.09358 + 1.89414i) q^{65} +(-1.92301 - 3.33075i) q^{66} +(-2.23944 - 3.87883i) q^{67} +(14.3578 - 24.8684i) q^{68} -0.879996 q^{69} +(14.1560 + 6.95021i) q^{70} -6.60274 q^{71} +(5.54370 - 9.60197i) q^{72} +(4.14174 + 7.17370i) q^{73} +(14.8434 + 25.7095i) q^{74} +(-0.145624 + 0.252229i) q^{75} +4.10772 q^{76} +(-2.48931 - 1.22218i) q^{77} -3.66932 q^{78} +(-1.07007 + 1.85342i) q^{79} +(-15.9644 - 27.6511i) q^{80} +(2.01457 + 3.48935i) q^{81} +(-9.97496 + 17.2771i) q^{82} -6.66558 q^{83} +(1.29817 + 19.2888i) q^{84} -11.5728 q^{85} +(-1.20970 + 2.09526i) q^{86} +(-2.08969 - 3.61946i) q^{87} +(4.89457 + 8.47765i) q^{88} +(2.88388 - 4.99503i) q^{89} -7.07617 q^{90} +(-2.19729 + 1.47375i) q^{91} +3.54699 q^{92} +(0.691998 - 1.19858i) q^{93} +(-3.18515 - 5.51684i) q^{94} +(-0.827739 - 1.43369i) q^{95} +(14.2081 - 24.6091i) q^{96} -2.88777 q^{97} +(11.6661 + 15.0939i) q^{98} +1.24433 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 8 q^{4} - 2 q^{5} - 10 q^{6} + q^{7} + 18 q^{8} - 3 q^{9} + 5 q^{10} - 11 q^{11} - 5 q^{12} + 10 q^{13} + 10 q^{14} - 10 q^{16} + 5 q^{17} - 9 q^{18} - 9 q^{19} + 2 q^{20} + 2 q^{21} + 16 q^{22}+ \cdots + 22 q^{99}+O(q^{100}) \) 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

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Representations

Groups

Database

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