LMFDB - Embedded newform 429.2.i.f.133.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(100,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("429.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.42558224671$
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} + 7x^{8} + 4x^{7} + 32x^{6} + 3x^{5} + 30x^{4} - 7x^{3} + 26x^{2} - 5x + 1 $ x^10 - x^9 + 7x^8 + 4x^7 + 32x^6 + 3x^5 + 30x^4 - 7x^3 + 26x^2 - 5x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.5
Root			$-0.863288 - 1.49526i$ of defining polynomial
Character	$\chi$	$=$	429.133
Dual form			429.2.i.f.100.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36329 + 2.36128i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.71711 + 4.70617i) q^{4} -2.20286 q^{5} +(1.36329 - 2.36128i) q^{6} +(-0.0642304 + 0.111250i) q^{7} -9.36366 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.36329 + 2.36128i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.71711 + 4.70617i) q^{4} -2.20286 q^{5} +(1.36329 - 2.36128i) q^{6} +(-0.0642304 + 0.111250i) q^{7} -9.36366 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-3.00314 - 5.20159i) q^{10} +(-0.500000 - 0.866025i) q^{11} +5.43422 q^{12} +(-2.97611 + 2.03538i) q^{13} -0.350258 q^{14} +(1.10143 + 1.90774i) q^{15} +(-7.33114 - 12.6979i) q^{16} +(-1.15166 + 1.99474i) q^{17} -2.72658 q^{18} +(-0.427519 + 0.740484i) q^{19} +(5.98542 - 10.3670i) q^{20} +0.128461 q^{21} +(1.36329 - 2.36128i) q^{22} +(1.17869 + 2.04155i) q^{23} +(4.68183 + 8.10916i) q^{24} -0.147395 q^{25} +(-8.86341 - 4.25262i) q^{26} +1.00000 q^{27} +(-0.349042 - 0.604558i) q^{28} +(1.59318 + 2.75947i) q^{29} +(-3.00314 + 5.20159i) q^{30} +10.2116 q^{31} +(10.6253 - 18.4035i) q^{32} +(-0.500000 + 0.866025i) q^{33} -6.28019 q^{34} +(0.141491 - 0.245069i) q^{35} +(-2.71711 - 4.70617i) q^{36} +(3.53842 + 6.12872i) q^{37} -2.33132 q^{38} +(3.25075 + 1.55969i) q^{39} +20.6269 q^{40} +(-1.31376 - 2.27550i) q^{41} +(0.175129 + 0.303332i) q^{42} +(-3.54651 + 6.14274i) q^{43} +5.43422 q^{44} +(1.10143 - 1.90774i) q^{45} +(-3.21379 + 5.56645i) q^{46} -12.5936 q^{47} +(-7.33114 + 12.6979i) q^{48} +(3.49175 + 6.04789i) q^{49} +(-0.200942 - 0.348042i) q^{50} +2.30332 q^{51} +(-1.49245 - 19.5364i) q^{52} -11.6206 q^{53} +(1.36329 + 2.36128i) q^{54} +(1.10143 + 1.90774i) q^{55} +(0.601431 - 1.04171i) q^{56} +0.855037 q^{57} +(-4.34393 + 7.52390i) q^{58} +(2.83157 - 4.90442i) q^{59} -11.9708 q^{60} +(3.74606 - 6.48836i) q^{61} +(13.9213 + 24.1124i) q^{62} +(-0.0642304 - 0.111250i) q^{63} +28.6166 q^{64} +(6.55596 - 4.48367i) q^{65} -2.72658 q^{66} +(2.74389 + 4.75256i) q^{67} +(-6.25838 - 10.8398i) q^{68} +(1.17869 - 2.04155i) q^{69} +0.771571 q^{70} +(-7.80517 + 13.5190i) q^{71} +(4.68183 - 8.10916i) q^{72} +7.77876 q^{73} +(-9.64776 + 16.7104i) q^{74} +(0.0736977 + 0.127648i) q^{75} +(-2.32323 - 4.02395i) q^{76} +0.128461 q^{77} +(0.748827 + 9.80225i) q^{78} +5.70485 q^{79} +(16.1495 + 27.9718i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.58207 - 6.20433i) q^{82} +15.3729 q^{83} +(-0.349042 + 0.604558i) q^{84} +(2.53695 - 4.39413i) q^{85} -19.3397 q^{86} +(1.59318 - 2.75947i) q^{87} +(4.68183 + 8.10916i) q^{88} +(3.32940 + 5.76670i) q^{89} +6.00627 q^{90} +(-0.0352805 - 0.461826i) q^{91} -12.8105 q^{92} +(-5.10578 - 8.84348i) q^{93} +(-17.1687 - 29.7371i) q^{94} +(0.941765 - 1.63118i) q^{95} -21.2505 q^{96} +(0.842163 - 1.45867i) q^{97} +(-9.52052 + 16.4900i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} - 5 q^{3} - 6 q^{4} - 8 q^{5} + 4 q^{6} + 3 q^{7} - 18 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 - 5 * q^3 - 6 * q^4 - 8 * q^5 + 4 * q^6 + 3 * q^7 - 18 * q^8 - 5 * q^9	\( 10 q + 4 q^{2} - 5 q^{3} - 6 q^{4} - 8 q^{5} + 4 q^{6} + 3 q^{7} - 18 q^{8} - 5 q^{9} + 5 q^{10} - 5 q^{11} + 12 q^{12} + 5 q^{13} + 14 q^{14} + 4 q^{15} - 12 q^{16} - 9 q^{17} - 8 q^{18} + 9 q^{19} + 6 q^{20} - 6 q^{21} + 4 q^{22} + 9 q^{23} + 9 q^{24} + 2 q^{25} - 12 q^{26} + 10 q^{27} - q^{28} - 8 q^{29} + 5 q^{30} - 12 q^{31} + 27 q^{32} - 5 q^{33} - 14 q^{34} + 2 q^{35} - 6 q^{36} + 17 q^{37} - 2 q^{38} + 2 q^{39} + 46 q^{40} + 6 q^{41} - 7 q^{42} - 13 q^{43} + 12 q^{44} + 4 q^{45} - 6 q^{46} - 32 q^{47} - 12 q^{48} + 18 q^{49} - 8 q^{50} + 18 q^{51} + 7 q^{52} - 26 q^{53} + 4 q^{54} + 4 q^{55} - q^{56} - 18 q^{57} + 11 q^{58} + 8 q^{59} - 12 q^{60} - 4 q^{61} + 22 q^{62} + 3 q^{63} + 22 q^{64} + 26 q^{65} - 8 q^{66} + 5 q^{67} - 34 q^{68} + 9 q^{69} + 8 q^{70} + 19 q^{71} + 9 q^{72} - 4 q^{73} - 27 q^{74} - q^{75} - 6 q^{76} - 6 q^{77} - 3 q^{78} - 16 q^{79} + 32 q^{80} - 5 q^{81} - 16 q^{82} - 20 q^{83} - q^{84} + 21 q^{85} + 8 q^{86} - 8 q^{87} + 9 q^{88} + 32 q^{89} - 10 q^{90} - 17 q^{91} - 84 q^{92} + 6 q^{93} - 66 q^{94} - 11 q^{95} - 54 q^{96} - 5 q^{97} - 18 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - 5 * q^3 - 6 * q^4 - 8 * q^5 + 4 * q^6 + 3 * q^7 - 18 * q^8 - 5 * q^9 + 5 * q^10 - 5 * q^11 + 12 * q^12 + 5 * q^13 + 14 * q^14 + 4 * q^15 - 12 * q^16 - 9 * q^17 - 8 * q^18 + 9 * q^19 + 6 * q^20 - 6 * q^21 + 4 * q^22 + 9 * q^23 + 9 * q^24 + 2 * q^25 - 12 * q^26 + 10 * q^27 - q^28 - 8 * q^29 + 5 * q^30 - 12 * q^31 + 27 * q^32 - 5 * q^33 - 14 * q^34 + 2 * q^35 - 6 * q^36 + 17 * q^37 - 2 * q^38 + 2 * q^39 + 46 * q^40 + 6 * q^41 - 7 * q^42 - 13 * q^43 + 12 * q^44 + 4 * q^45 - 6 * q^46 - 32 * q^47 - 12 * q^48 + 18 * q^49 - 8 * q^50 + 18 * q^51 + 7 * q^52 - 26 * q^53 + 4 * q^54 + 4 * q^55 - q^56 - 18 * q^57 + 11 * q^58 + 8 * q^59 - 12 * q^60 - 4 * q^61 + 22 * q^62 + 3 * q^63 + 22 * q^64 + 26 * q^65 - 8 * q^66 + 5 * q^67 - 34 * q^68 + 9 * q^69 + 8 * q^70 + 19 * q^71 + 9 * q^72 - 4 * q^73 - 27 * q^74 - q^75 - 6 * q^76 - 6 * q^77 - 3 * q^78 - 16 * q^79 + 32 * q^80 - 5 * q^81 - 16 * q^82 - 20 * q^83 - q^84 + 21 * q^85 + 8 * q^86 - 8 * q^87 + 9 * q^88 + 32 * q^89 - 10 * q^90 - 17 * q^91 - 84 * q^92 + 6 * q^93 - 66 * q^94 - 11 * q^95 - 54 * q^96 - 5 * q^97 - 18 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	1.36329	+	2.36128i	0.963990	+	1.66968i	0.712304	+	0.701871i	$0.247652\pi$
$2$	1.36329	+	2.36128i	0.963990	+	1.66968i	0.251686	+	0.967809i	$0.419015\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−2.71711	+	4.70617i	−1.35855	+	2.35309i
$5$	−2.20286			−0.985150			−0.492575	−	0.870270i	$-0.663944\pi$
$5$	−2.20286			−0.985150			−0.492575	+	0.870270i	$0.663944\pi$
$6$	1.36329	−	2.36128i	0.556560	−	0.963990i
$7$	−0.0642304	+	0.111250i	−0.0242768	+	0.0420487i	−0.877909	−	0.478828i	$-0.841062\pi$
$7$	−0.0642304	+	0.111250i	−0.0242768	+	0.0420487i	0.853632	+	0.520877i	$0.174395\pi$
$8$	−9.36366			−3.31055
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−3.00314	−	5.20159i	−0.949675	−	1.64489i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	5.43422			1.56872
$13$	−2.97611	+	2.03538i	−0.825424	+	0.564514i
$13$	−2.97611	+	2.03538i	−0.825424	+	0.564514i
$14$	−0.350258			−0.0936104
$15$	1.10143	+	1.90774i	0.284388	+	0.492575i
$16$	−7.33114	−	12.6979i	−1.83279	−	3.17448i
$17$	−1.15166	+	1.99474i	−0.279319	+	0.483795i	−0.971216	−	0.238202i	$-0.923442\pi$
$17$	−1.15166	+	1.99474i	−0.279319	+	0.483795i	0.691897	+	0.721997i	$0.256775\pi$
$18$	−2.72658			−0.642660
$19$	−0.427519	+	0.740484i	−0.0980795	+	0.169879i	−0.910890	−	0.412650i	$-0.864603\pi$
$19$	−0.427519	+	0.740484i	−0.0980795	+	0.169879i	0.812810	+	0.582529i	$0.197937\pi$
$20$	5.98542	−	10.3670i	1.33838	−	2.31814i
$21$	0.128461			0.0280324
$22$	1.36329	−	2.36128i	0.290654	−	0.503428i
$23$	1.17869	+	2.04155i	0.245774	+	0.425693i	0.962349	−	0.271817i	$-0.0876245\pi$
$23$	1.17869	+	2.04155i	0.245774	+	0.425693i	−0.716575	+	0.697510i	$0.754291\pi$
$24$	4.68183	+	8.10916i	0.955674	+	1.65528i
$25$	−0.147395			−0.0294791
$26$	−8.86341	−	4.25262i	−1.73826	−	0.834008i
$27$	1.00000			0.192450
$28$	−0.349042	−	0.604558i	−0.0659627	−	0.114251i
$29$	1.59318	+	2.75947i	0.295846	+	0.512421i	0.975181	−	0.221408i	$-0.0710651\pi$
$29$	1.59318	+	2.75947i	0.295846	+	0.512421i	−0.679335	+	0.733828i	$0.737732\pi$
$30$	−3.00314	+	5.20159i	−0.548295	+	0.949675i
$31$	10.2116			1.83405			0.917026	−	0.398828i	$-0.130583\pi$
$31$	10.2116			1.83405			0.917026	+	0.398828i	$0.130583\pi$
$32$	10.6253	−	18.4035i	1.87830	−	3.25331i
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$	−6.28019			−1.07704
$35$	0.141491	−	0.245069i	0.0239163	−	0.0414243i
$36$	−2.71711	−	4.70617i	−0.452851	−	0.784362i
$37$	3.53842	+	6.12872i	0.581712	+	1.00756i	0.995277	+	0.0970802i	$0.0309503\pi$
$37$	3.53842	+	6.12872i	0.581712	+	1.00756i	−0.413564	+	0.910475i	$0.635716\pi$
$38$	−2.33132			−0.378191
$39$	3.25075	+	1.55969i	0.520536	+	0.249751i
$40$	20.6269			3.26139
$41$	−1.31376	−	2.27550i	−0.205175	−	0.355374i	0.745013	−	0.667049i	$-0.232443\pi$
$41$	−1.31376	−	2.27550i	−0.205175	−	0.355374i	−0.950189	+	0.311676i	$0.899110\pi$
$42$	0.175129	+	0.303332i	0.0270230	+	0.0468052i
$43$	−3.54651	+	6.14274i	−0.540838	+	0.936759i	0.458018	+	0.888943i	$0.348559\pi$
$43$	−3.54651	+	6.14274i	−0.540838	+	0.936759i	−0.998856	+	0.0478161i	$0.984774\pi$
$44$	5.43422			0.819239
$45$	1.10143	−	1.90774i	0.164192	−	0.284388i
$46$	−3.21379	+	5.56645i	−0.473848	+	0.820729i
$47$	−12.5936			−1.83697			−0.918483	−	0.395461i	$-0.870585\pi$
$47$	−12.5936			−1.83697			−0.918483	+	0.395461i	$0.870585\pi$
$48$	−7.33114	+	12.6979i	−1.05816	+	1.83279i
$49$	3.49175	+	6.04789i	0.498821	+	0.863984i
$50$	−0.200942	−	0.348042i	−0.0284175	−	0.0492206i
$51$	2.30332			0.322530
$52$	−1.49245	−	19.5364i	−0.206966	−	2.70922i
$53$	−11.6206			−1.59621			−0.798105	−	0.602519i	$-0.794164\pi$
$53$	−11.6206			−1.59621			−0.798105	+	0.602519i	$0.794164\pi$
$54$	1.36329	+	2.36128i	0.185520	+	0.321330i
$55$	1.10143	+	1.90774i	0.148517	+	0.257239i
$56$	0.601431	−	1.04171i	0.0803697	−	0.139204i
$57$	0.855037			0.113252
$58$	−4.34393	+	7.52390i	−0.570386	+	0.987937i
$59$	2.83157	−	4.90442i	0.368639	−	0.638502i	−0.620714	−	0.784037i	$-0.713157\pi$
$59$	2.83157	−	4.90442i	0.368639	−	0.638502i	0.989353	+	0.145536i	$0.0464905\pi$
$60$	−11.9708			−1.54543
$61$	3.74606	−	6.48836i	0.479634	−	0.830750i	−0.520093	−	0.854109i	$-0.674103\pi$
$61$	3.74606	−	6.48836i	0.479634	−	0.830750i	0.999727	+	0.0233594i	$0.00743622\pi$
$62$	13.9213	+	24.1124i	1.76801	+	3.06228i
$63$	−0.0642304	−	0.111250i	−0.00809227	−	0.0140162i
$64$	28.6166			3.57708
$65$	6.55596	−	4.48367i	0.813166	−	0.556131i
$66$	−2.72658			−0.335618
$67$	2.74389	+	4.75256i	0.335220	+	0.580618i	0.983527	−	0.180761i	$-0.0578561\pi$
$67$	2.74389	+	4.75256i	0.335220	+	0.580618i	−0.648307	+	0.761379i	$0.724523\pi$
$68$	−6.25838	−	10.8398i	−0.758941	−	1.31452i
$69$	1.17869	−	2.04155i	0.141898	−	0.245774i
$70$	0.771571			0.0922203
$71$	−7.80517	+	13.5190i	−0.926304	+	1.60441i	−0.136853	+	0.990591i	$0.543699\pi$
$71$	−7.80517	+	13.5190i	−0.926304	+	1.60441i	−0.789451	+	0.613814i	$0.789634\pi$
$72$	4.68183	−	8.10916i	0.551759	−	0.955674i
$73$	7.77876			0.910435			0.455217	−	0.890380i	$-0.349562\pi$
$73$	7.77876			0.910435			0.455217	+	0.890380i	$0.349562\pi$
$74$	−9.64776	+	16.7104i	−1.12153	+	1.94255i
$75$	0.0736977	+	0.127648i	0.00850987	+	0.0147395i
$76$	−2.32323	−	4.02395i	−0.266493	−	0.461579i
$77$	0.128461			0.0146395
$78$	0.748827	+	9.80225i	0.0847879	+	1.10989i
$79$	5.70485			0.641846			0.320923	−	0.947105i	$-0.396007\pi$
$79$	5.70485			0.641846			0.320923	+	0.947105i	$0.396007\pi$
$80$	16.1495	+	27.9718i	1.80557	+	3.12734i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.58207	−	6.20433i	0.395574	−	0.685154i
$83$	15.3729			1.68739			0.843695	−	0.536823i	$-0.180376\pi$
$83$	15.3729			1.68739			0.843695	+	0.536823i	$0.180376\pi$
$84$	−0.349042	+	0.604558i	−0.0380836	+	0.0659627i
$85$	2.53695	−	4.39413i	0.275171	−	0.476611i
$86$	−19.3397			−2.08545
$87$	1.59318	−	2.75947i	0.170807	−	0.295846i
$88$	4.68183	+	8.10916i	0.499085	+	0.864440i
$89$	3.32940	+	5.76670i	0.352916	+	0.611268i	0.986759	−	0.162193i	$-0.0518568\pi$
$89$	3.32940	+	5.76670i	0.352916	+	0.611268i	−0.633843	+	0.773462i	$0.718523\pi$
$90$	6.00627			0.633117
$91$	−0.0352805	−	0.461826i	−0.00369840	−	0.0484126i
$92$	−12.8105			−1.33559
$93$	−5.10578	−	8.84348i	−0.529445	−	0.917026i
$94$	−17.1687	−	29.7371i	−1.77082	−	3.06715i
$95$	0.941765	−	1.63118i	0.0966230	−	0.167356i
$96$	−21.2505			−2.16887
$97$	0.842163	−	1.45867i	0.0855087	−	0.148105i	−0.820099	−	0.572221i	$-0.806082\pi$
$97$	0.842163	−	1.45867i	0.0855087	−	0.148105i	0.905608	+	0.424116i	$0.139415\pi$
$98$	−9.52052	+	16.4900i	−0.961718	+	1.66574i
$99$	1.00000			0.100504
$100$	0.400489	−	0.693668i	0.0400489	−	0.0693668i
$101$	−5.58615	−	9.67549i	−0.555842	−	0.962747i	−0.997837	−	0.0657296i	$-0.979063\pi$
$101$	−5.58615	−	9.67549i	−0.555842	−	0.962747i	0.441995	−	0.897017i	$-0.354271\pi$
$102$	3.14010	+	5.43880i	0.310916	+	0.538522i
$103$	2.06869			0.203834			0.101917	−	0.994793i	$-0.467502\pi$
$103$	2.06869			0.203834			0.101917	+	0.994793i	$0.467502\pi$
$104$	27.8672	−	19.0586i	2.73261	−	1.86885i
$105$	−0.282982			−0.0276162
$106$	−15.8422	−	27.4395i	−1.53873	−	2.66516i
$107$	−6.69251	−	11.5918i	−0.646990	−	1.12062i	−0.983838	−	0.179060i	$-0.942694\pi$
$107$	−6.69251	−	11.5918i	−0.646990	−	1.12062i	0.336849	−	0.941559i	$-0.390639\pi$
$108$	−2.71711	+	4.70617i	−0.261454	+	0.452851i
$109$	−13.6667			−1.30903			−0.654515	−	0.756049i	$-0.727127\pi$
$109$	−13.6667			−1.30903			−0.654515	+	0.756049i	$0.727127\pi$
$110$	−3.00314	+	5.20159i	−0.286338	+	0.495952i
$111$	3.53842	−	6.12872i	0.335852	−	0.581712i
$112$	1.88353			0.177977
$113$	3.30697	−	5.72785i	0.311094	−	0.538830i	−0.667506	−	0.744605i	$-0.732638\pi$
$113$	3.30697	−	5.72785i	0.311094	−	0.538830i	0.978599	+	0.205774i	$0.0659713\pi$
$114$	1.16566	+	2.01899i	0.109174	+	0.189095i
$115$	−2.59650	−	4.49726i	−0.242125	−	0.419372i
$116$	−17.3154			−1.60769
$117$	−0.274640	−	3.59508i	−0.0253905	−	0.332365i
$118$	15.4410			1.42146
$119$	−0.147943	−	0.256246i	−0.0135620	−	0.0234900i
$120$	−10.3134	−	17.8634i	−0.941483	−	1.63070i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	20.4278			1.84945
$123$	−1.31376	+	2.27550i	−0.118458	+	0.205175i
$124$	−27.7459	+	48.0574i	−2.49166	+	4.31568i
$125$	11.3390			1.01419
$126$	0.175129	−	0.303332i	0.0156017	−	0.0270230i
$127$	2.00137	+	3.46648i	0.177593	+	0.307600i	0.941056	−	0.338252i	$-0.109836\pi$
$127$	2.00137	+	3.46648i	0.177593	+	0.307600i	−0.763463	+	0.645852i	$0.776502\pi$
$128$	17.7622	+	30.7650i	1.56997	+	2.71927i
$129$	7.09302			0.624506
$130$	19.5249	+	9.36794i	1.71245	+	0.821623i
$131$	−16.7087			−1.45985			−0.729923	−	0.683530i	$-0.760444\pi$
$131$	−16.7087			−1.45985			−0.729923	+	0.683530i	$0.760444\pi$
$132$	−2.71711	−	4.70617i	−0.236494	−	0.409620i
$133$	−0.0549194	−	0.0951231i	−0.00476211	−	0.00824822i
$134$	−7.48143	+	12.9582i	−0.646297	+	1.11942i
$135$	−2.20286			−0.189592
$136$	10.7838	−	18.6780i	0.924701	−	1.60163i
$137$	6.37660	−	11.0446i	0.544789	−	0.943603i	−0.453831	−	0.891088i	$-0.649943\pi$
$137$	6.37660	−	11.0446i	0.544789	−	0.943603i	0.998620	−	0.0525150i	$-0.0167237\pi$
$138$	6.42759			0.547152
$139$	0.674461	−	1.16820i	0.0572070	−	0.0990855i	−0.836004	−	0.548724i	$-0.815114\pi$
$139$	0.674461	−	1.16820i	0.0572070	−	0.0990855i	0.893211	+	0.449638i	$0.148447\pi$
$140$	0.768892	+	1.33176i	0.0649832	+	0.112554i
$141$	6.29680	+	10.9064i	0.530286	+	0.918483i
$142$	−42.5628			−3.57179
$143$	3.25075	+	1.55969i	0.271841	+	0.130428i
$144$	14.6623			1.22186
$145$	−3.50956	−	6.07873i	−0.291453	−	0.504811i
$146$	10.6047	+	18.3679i	0.877650	+	1.52014i
$147$	3.49175	−	6.04789i	0.287995	−	0.498821i
$148$	−38.4571			−3.16115
$149$	−2.09559	+	3.62968i	−0.171678	+	0.297355i	−0.939007	−	0.343899i	$-0.888252\pi$
$149$	−2.09559	+	3.62968i	−0.171678	+	0.297355i	0.767329	+	0.641254i	$0.221585\pi$
$150$	−0.200942	+	0.348042i	−0.0164069	+	0.0284175i
$151$	16.1966			1.31806			0.659030	−	0.752117i	$-0.270967\pi$
$151$	16.1966			1.31806			0.659030	+	0.752117i	$0.270967\pi$
$152$	4.00314	−	6.93364i	0.324697	−	0.562392i
$153$	−1.15166	−	1.99474i	−0.0931064	−	0.161265i
$154$	0.175129	+	0.303332i	0.0141123	+	0.0244432i
$155$	−22.4947			−1.80682
$156$	−16.1728	+	11.0607i	−1.29486	+	0.885566i
$157$	−2.09175			−0.166940			−0.0834698	−	0.996510i	$-0.526600\pi$
$157$	−2.09175			−0.166940			−0.0834698	+	0.996510i	$0.526600\pi$
$158$	7.77736	+	13.4708i	0.618733	+	1.07168i
$159$	5.81029	+	10.0637i	0.460786	+	0.798105i
$160$	−23.4060	+	40.5404i	−1.85041	+	3.20500i
$161$	−0.302831			−0.0238665
$162$	1.36329	−	2.36128i	0.107110	−	0.185520i
$163$	−6.03193	+	10.4476i	−0.472457	+	0.818320i	−0.999503	−	0.0315168i	$-0.989966\pi$
$163$	−6.03193	+	10.4476i	−0.472457	+	0.818320i	0.527046	+	0.849837i	$0.323300\pi$
$164$	14.2785			1.11497
$165$	1.10143	−	1.90774i	0.0857463	−	0.148517i
$166$	20.9576	+	36.2997i	1.62663	+	2.81740i
$167$	8.61718	+	14.9254i	0.666817	+	1.15496i	0.978789	+	0.204870i	$0.0656771\pi$
$167$	8.61718	+	14.9254i	0.666817	+	1.15496i	−0.311972	+	0.950091i	$0.600990\pi$
$168$	−1.20286			−0.0928029
$169$	4.71443	−	12.1150i	0.362648	−	0.931926i
$170$	13.8344			1.06105
$171$	−0.427519	−	0.740484i	−0.0326932	−	0.0566262i
$172$	−19.2725	−	33.3810i	−1.46952	−	2.54528i
$173$	8.42336	−	14.5897i	0.640416	−	1.10923i	−0.344924	−	0.938631i	$-0.612095\pi$
$173$	8.42336	−	14.5897i	0.640416	−	1.10923i	0.985340	−	0.170602i	$-0.0545713\pi$
$174$	8.68786			0.658625
$175$	0.00946726	−	0.0163978i	0.000715658	−	0.00123956i
$176$	−7.33114	+	12.6979i	−0.552606	+	0.957141i
$177$	−5.66314			−0.425668
$178$	−9.07787	+	15.7233i	−0.680415	+	1.17851i
$179$	−1.31611	−	2.27957i	−0.0983705	−	0.170383i	0.812640	−	0.582766i	$-0.198030\pi$
$179$	−1.31611	−	2.27957i	−0.0983705	−	0.170383i	−0.911010	+	0.412384i	$0.864696\pi$
$180$	5.98542	+	10.3670i	0.446127	+	0.772714i
$181$	−3.31040			−0.246060			−0.123030	−	0.992403i	$-0.539261\pi$
$181$	−3.31040			−0.246060			−0.123030	+	0.992403i	$0.539261\pi$
$182$	1.04241	−	0.712910i	0.0772683	−	0.0528444i
$183$	−7.49212			−0.553833
$184$	−11.0369	−	19.1164i	−0.813649	−	1.40928i
$185$	−7.79465	−	13.5007i	−0.573074	−	0.992593i
$186$	13.9213	−	24.1124i	1.02076	−	1.76801i
$187$	2.30332			0.168436
$188$	34.2182	−	59.2676i	2.49562	−	4.32254i
$189$	−0.0642304	+	0.111250i	−0.00467207	+	0.00809227i
$190$	5.13559			0.372575
$191$	−3.37753	+	5.85006i	−0.244390	+	0.423296i	−0.961960	−	0.273191i	$-0.911921\pi$
$191$	−3.37753	+	5.85006i	−0.244390	+	0.423296i	0.717570	+	0.696486i	$0.245254\pi$
$192$	−14.3083	−	24.7827i	−1.03261	−	1.78854i
$193$	−3.05078	−	5.28410i	−0.219600	−	0.380358i	0.735086	−	0.677974i	$-0.237142\pi$
$193$	−3.05078	−	5.28410i	−0.219600	−	0.380358i	−0.954686	+	0.297616i	$0.903809\pi$
$194$	4.59244			0.329718
$195$	−7.16095	−	3.43579i	−0.512806	−	0.246042i
$196$	−37.9498			−2.71070
$197$	11.6180	+	20.1229i	0.827745	+	1.43370i	0.899803	+	0.436296i	$0.143710\pi$
$197$	11.6180	+	20.1229i	0.827745	+	1.43370i	−0.0720583	+	0.997400i	$0.522957\pi$
$198$	1.36329	+	2.36128i	0.0968847	+	0.167809i
$199$	3.31212	−	5.73677i	0.234790	−	0.406669i	−0.724421	−	0.689357i	$-0.757893\pi$
$199$	3.31212	−	5.73677i	0.234790	−	0.406669i	0.959212	+	0.282689i	$0.0912263\pi$
$200$	1.38016			0.0975920
$201$	2.74389	−	4.75256i	0.193539	−	0.335220i
$202$	15.2311	−	26.3810i	1.07165	−	1.85616i
$203$	−0.409322			−0.0287288
$204$	−6.25838	+	10.8398i	−0.438175	+	0.758941i
$205$	2.89404	+	5.01262i	0.202128	+	0.350096i
$206$	2.82021	+	4.88475i	0.196494	+	0.340337i
$207$	−2.35738			−0.163849
$208$	47.6634	+	22.8687i	3.30486	+	1.58566i
$209$	0.855037			0.0591441
$210$	−0.385785	−	0.668200i	−0.0266217	−	0.0461102i
$211$	−7.97516	−	13.8134i	−0.549032	−	0.950952i	−0.998341	−	0.0575755i	$-0.981663\pi$
$211$	−7.97516	−	13.8134i	−0.549032	−	0.950952i	0.449309	−	0.893377i	$-0.351670\pi$
$212$	31.5744	−	54.6884i	2.16854	−	3.75602i
$213$	15.6103			1.06960
$214$	18.2476	−	31.6058i	1.24738	−	2.16053i
$215$	7.81248	−	13.5316i	0.532807	−	0.922848i
$216$	−9.36366			−0.637116
$217$	−0.655893	+	1.13604i	−0.0445249	+	0.0771194i
$218$	−18.6316	−	32.2709i	−1.26189	−	2.18566i
$219$	−3.88938	−	6.73660i	−0.262820	−	0.455217i
$220$	−11.9708			−0.807074
$221$	−0.632585	−	8.28063i	−0.0425523	−	0.557015i
$222$	19.2955			1.29503
$223$	11.2992	+	19.5708i	0.756650	+	1.31056i	0.944550	+	0.328368i	$0.106499\pi$
$223$	11.2992	+	19.5708i	0.756650	+	1.31056i	−0.187900	+	0.982188i	$0.560168\pi$
$224$	1.36493	+	2.36413i	0.0911982	+	0.157960i
$225$	0.0736977	−	0.127648i	0.00491318	−	0.00850987i
$226$	18.0334			1.19957
$227$	−8.45867	+	14.6508i	−0.561421	+	0.972411i	0.435951	+	0.899970i	$0.356412\pi$
$227$	−8.45867	+	14.6508i	−0.561421	+	0.972411i	−0.997373	+	0.0724403i	$0.976921\pi$
$228$	−2.32323	+	4.02395i	−0.153860	+	0.266493i
$229$	−7.48358			−0.494529			−0.247265	−	0.968948i	$-0.579532\pi$
$229$	−7.48358			−0.494529			−0.247265	+	0.968948i	$0.579532\pi$
$230$	7.07955	−	12.2621i	0.466811	−	0.808541i
$231$	−0.0642304	−	0.111250i	−0.00422605	−	0.00731973i
$232$	−14.9180	−	25.8387i	−0.979414	−	1.69640i
$233$	−21.1610			−1.38631			−0.693153	−	0.720791i	$-0.743779\pi$
$233$	−21.1610			−1.38631			−0.693153	+	0.720791i	$0.743779\pi$
$234$	8.11458	−	5.54963i	0.530467	−	0.362791i
$235$	27.7420			1.80969
$236$	15.3874	+	26.6517i	1.00163	+	1.73488i
$237$	−2.85243	−	4.94055i	−0.185285	−	0.320923i
$238$	0.403379	−	0.698673i	0.0261472	−	0.0452883i
$239$	−14.9404			−0.966414			−0.483207	−	0.875506i	$-0.660528\pi$
$239$	−14.9404			−0.966414			−0.483207	+	0.875506i	$0.660528\pi$
$240$	16.1495	−	27.9718i	1.04245	−	1.80557i
$241$	13.4457	−	23.2886i	0.866113	−	1.50015i	0.000175483	−	1.00000i	$-0.499944\pi$
$241$	13.4457	−	23.2886i	0.866113	−	1.50015i	0.865938	−	0.500152i	$-0.166723\pi$
$242$	−2.72658			−0.175271
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	20.3569	+	35.2592i	1.30322	+	2.25724i
$245$	−7.69184	−	13.3227i	−0.491414	−	0.851154i
$246$	−7.16414			−0.456769
$247$	−0.234827	−	3.07392i	−0.0149417	−	0.195589i
$248$	−95.6176			−6.07173
$249$	−7.68643	−	13.3133i	−0.487108	−	0.843695i
$250$	15.4583	+	26.7746i	0.977671	+	1.69338i
$251$	−11.2870	+	19.5497i	−0.712430	+	1.23396i	0.251513	+	0.967854i	$0.419072\pi$
$251$	−11.2870	+	19.5497i	−0.712430	+	1.23396i	−0.963942	+	0.266111i	$0.914261\pi$
$252$	0.698084			0.0439752
$253$	1.17869	−	2.04155i	0.0741037	−	0.128351i
$254$	−5.45689	+	9.45162i	−0.342396	+	0.593047i
$255$	−5.07391			−0.317740
$256$	−19.8133	+	34.3176i	−1.23833	+	2.14485i
$257$	1.61683	+	2.80043i	0.100855	+	0.174686i	0.912037	−	0.410108i	$-0.134509\pi$
$257$	1.61683	+	2.80043i	0.100855	+	0.174686i	−0.811182	+	0.584793i	$0.801176\pi$
$258$	9.66984	+	16.7486i	0.602018	+	1.04273i
$259$	−0.909096			−0.0564885
$260$	3.28767	+	43.0361i	0.203893	+	2.66898i
$261$	−3.18636			−0.197231
$262$	−22.7788	−	39.4540i	−1.40728	−	2.43747i
$263$	7.13392	+	12.3563i	0.439896	+	0.761923i	0.997681	−	0.0680628i	$-0.0216818\pi$
$263$	7.13392	+	12.3563i	0.439896	+	0.761923i	−0.557785	+	0.829986i	$0.688348\pi$
$264$	4.68183	−	8.10916i	0.288147	−	0.499085i
$265$	25.5985			1.57251
$266$	0.149742	−	0.259360i	0.00918126	−	0.0159024i
$267$	3.32940	−	5.76670i	0.203756	−	0.352916i
$268$	−29.8218			−1.82166
$269$	−0.704595	+	1.22040i	−0.0429599	+	0.0744088i	−0.886706	−	0.462334i	$-0.847012\pi$
$269$	−0.704595	+	1.22040i	−0.0429599	+	0.0744088i	0.843746	+	0.536743i	$0.180345\pi$
$270$	−3.00314	−	5.20159i	−0.182765	−	0.316558i
$271$	12.3433	+	21.3793i	0.749803	+	1.29870i	0.947917	+	0.318519i	$0.103185\pi$
$271$	12.3433	+	21.3793i	0.749803	+	1.29870i	−0.198113	+	0.980179i	$0.563481\pi$
$272$	33.7720			2.04773
$273$	−0.382313	+	0.261467i	−0.0231386	+	0.0158247i
$274$	34.7726			2.10069
$275$	0.0736977	+	0.127648i	0.00444414	+	0.00769747i
$276$	6.40527	+	11.0942i	0.385552	+	0.667795i
$277$	−6.06948	+	10.5126i	−0.364680	+	0.631644i	−0.988725	−	0.149745i	$-0.952155\pi$
$277$	−6.06948	+	10.5126i	−0.364680	+	0.631644i	0.624045	+	0.781388i	$0.285488\pi$
$278$	3.67794			0.220588
$279$	−5.10578	+	8.84348i	−0.305675	+	0.529445i
$280$	−1.32487	+	2.29474i	−0.0791762	+	0.137137i
$281$	29.1014			1.73604			0.868021	−	0.496527i	$-0.165392\pi$
$281$	29.1014			1.73604			0.868021	+	0.496527i	$0.165392\pi$
$282$	−17.1687	+	29.7371i	−1.02238	+	1.77082i
$283$	−7.07269	−	12.2503i	−0.420428	−	0.728203i	0.575553	−	0.817764i	$-0.304787\pi$
$283$	−7.07269	−	12.2503i	−0.420428	−	0.728203i	−0.995981	+	0.0895616i	$0.971453\pi$
$284$	−42.4150	−	73.4650i	−2.51687	−	4.35934i
$285$	−1.88353			−0.111571
$286$	0.748827	+	9.80225i	0.0442791	+	0.579619i
$287$	0.337534			0.0199240
$288$	10.6253	+	18.4035i	0.626100	+	1.08444i
$289$	5.84735	+	10.1279i	0.343962	+	0.595759i
$290$	9.56908	−	16.5741i	0.561916	−	0.973266i
$291$	−1.68433			−0.0987370
$292$	−21.1357	+	36.6082i	−1.23688	+	2.14233i
$293$	1.68736	−	2.92260i	0.0985769	−	0.170740i	−0.812519	−	0.582935i	$-0.801904\pi$
$293$	1.68736	−	2.92260i	0.0985769	−	0.170740i	0.911096	+	0.412195i	$0.135238\pi$
$294$	19.0410			1.11050
$295$	−6.23756	+	10.8038i	−0.363165	+	0.629020i
$296$	−33.1325	−	57.3872i	−1.92579	−	3.33556i
$297$	−0.500000	−	0.866025i	−0.0290129	−	0.0502519i
$298$	−11.4276			−0.661983
$299$	−7.66326	−	3.67679i	−0.443178	−	0.212635i
$300$	−0.800978			−0.0462445
$301$	−0.455588	−	0.789101i	−0.0262596	−	0.0454830i
$302$	22.0806	+	38.2447i	1.27060	+	2.20074i
$303$	−5.58615	+	9.67549i	−0.320916	+	0.555842i
$304$	12.5368			0.719035
$305$	−8.25205	+	14.2930i	−0.472511	+	0.818413i
$306$	3.14010	−	5.43880i	0.179507	−	0.310916i
$307$	−10.8835			−0.621155			−0.310578	−	0.950548i	$-0.600522\pi$
$307$	−10.8835			−0.621155			−0.310578	+	0.950548i	$0.600522\pi$
$308$	−0.349042	+	0.604558i	−0.0198885	+	0.0344479i
$309$	−1.03434	−	1.79153i	−0.0588417	−	0.101917i
$310$	−30.6667	−	53.1163i	−1.74175	−	3.01681i
$311$	18.6179			1.05572			0.527862	−	0.849330i	$-0.322994\pi$
$311$	18.6179			1.05572			0.527862	+	0.849330i	$0.322994\pi$
$312$	−30.4389	−	14.6044i	−1.72326	−	0.826813i
$313$	−23.5845			−1.33307			−0.666536	−	0.745472i	$-0.732224\pi$
$313$	−23.5845			−1.33307			−0.666536	+	0.745472i	$0.732224\pi$
$314$	−2.85165	−	4.93921i	−0.160928	−	0.278736i
$315$	0.141491	+	0.245069i	0.00797210	+	0.0138081i
$316$	−15.5007	+	26.8480i	−0.871983	+	1.51032i
$317$	21.9654			1.23370			0.616851	−	0.787080i	$-0.288408\pi$
$317$	21.9654			1.23370			0.616851	+	0.787080i	$0.288408\pi$
$318$	−15.8422	+	27.4395i	−0.888386	+	1.53873i
$319$	1.59318	−	2.75947i	0.0892010	−	0.154501i
$320$	−63.0385			−3.52396
$321$	−6.69251	+	11.5918i	−0.373540	+	0.646990i
$322$	−0.412846	−	0.715071i	−0.0230070	−	0.0398493i
$323$	−0.984714	−	1.70557i	−0.0547910	−	0.0949007i
$324$	5.43422			0.301901
$325$	0.438664	−	0.300006i	0.0243327	−	0.0166413i
$326$	−32.8930			−1.82178
$327$	6.83333	+	11.8357i	0.377884	+	0.654515i
$328$	12.3016	+	21.3070i	0.679243	+	1.17648i
$329$	0.808892	−	1.40104i	0.0445957	−	0.0772420i
$330$	6.00627			0.330634
$331$	1.86024	−	3.22203i	0.102248	−	0.177099i	−0.810363	−	0.585929i	$-0.800730\pi$
$331$	1.86024	−	3.22203i	0.102248	−	0.177099i	0.912610	+	0.408830i	$0.134063\pi$
$332$	−41.7697	+	72.3473i	−2.29241	+	3.97057i
$333$	−7.07683			−0.387808
$334$	−23.4954	+	40.6952i	−1.28561	+	2.22674i
$335$	−6.04442	−	10.4692i	−0.330242	−	0.571996i
$336$	−0.941765	−	1.63118i	−0.0513775	−	0.0889884i
$337$	−23.2932			−1.26886			−0.634430	−	0.772981i	$-0.718765\pi$
$337$	−23.2932			−1.26886			−0.634430	+	0.772981i	$0.718765\pi$
$338$	35.0342	−	5.38418i	1.90561	−	0.292861i
$339$	−6.61395			−0.359220
$340$	13.7864	+	23.8787i	0.747670	+	1.29500i
$341$	−5.10578	−	8.84348i	−0.276494	−	0.478901i
$342$	1.16566	−	2.01899i	0.0630318	−	0.109174i
$343$	−1.79633			−0.0969928
$344$	33.2083	−	57.5185i	1.79047	−	3.10119i
$345$	−2.59650	+	4.49726i	−0.139791	+	0.242125i
$346$	45.9338			2.46942
$347$	−6.38305	+	11.0558i	−0.342660	+	0.593505i	−0.984926	−	0.172977i	$-0.944661\pi$
$347$	−6.38305	+	11.0558i	−0.342660	+	0.593505i	0.642266	+	0.766482i	$0.277995\pi$
$348$	8.65769	+	14.9956i	0.464101	+	0.803846i
$349$	−10.1452	−	17.5720i	−0.543060	−	0.940608i	−0.998726	−	0.0504574i	$-0.983932\pi$
$349$	−10.1452	−	17.5720i	−0.543060	−	0.940608i	0.455666	−	0.890151i	$-0.349401\pi$
$350$	0.0516264			0.00275955
$351$	−2.97611	+	2.03538i	−0.158853	+	0.108641i
$352$	−21.2505			−1.13266
$353$	−7.74097	−	13.4077i	−0.412010	−	0.713622i	0.583099	−	0.812401i	$-0.301840\pi$
$353$	−7.74097	−	13.4077i	−0.412010	−	0.713622i	−0.995109	+	0.0987784i	$0.968507\pi$
$354$	−7.72049	−	13.3723i	−0.410340	−	0.710729i
$355$	17.1937	−	29.7804i	0.912548	−	1.58058i
$356$	−36.1854			−1.91782
$357$	−0.147943	+	0.256246i	−0.00783000	+	0.0135620i
$358$	3.58847	−	6.21541i	0.189656	−	0.328495i
$359$	−15.7322			−0.830313			−0.415156	−	0.909750i	$-0.636273\pi$
$359$	−15.7322			−0.830313			−0.415156	+	0.909750i	$0.636273\pi$
$360$	−10.3134	+	17.8634i	−0.543565	+	0.941483i
$361$	9.13446	+	15.8213i	0.480761	+	0.832702i
$362$	−4.51303	−	7.81681i	−0.237200	−	0.410842i
$363$	1.00000			0.0524864
$364$	2.26929	+	1.08880i	0.118943	+	0.0570684i
$365$	−17.1355			−0.896915
$366$	−10.2139	−	17.6910i	−0.533890	−	0.924724i
$367$	15.8573	+	27.4657i	0.827745	+	1.43370i	0.899804	+	0.436295i	$0.143710\pi$
$367$	15.8573	+	27.4657i	0.827745	+	1.43370i	−0.0720591	+	0.997400i	$0.522957\pi$
$368$	17.2823	−	29.9339i	0.900903	−	1.56041i
$369$	2.62752			0.136783
$370$	21.2527	−	36.8108i	1.10488	−	1.91370i
$371$	0.746394	−	1.29279i	0.0387509	−	0.0671185i
$372$	55.4919			2.87712
$373$	−5.31230	+	9.20117i	−0.275060	+	0.476419i	−0.970150	−	0.242504i	$-0.922031\pi$
$373$	−5.31230	+	9.20117i	−0.275060	+	0.476419i	0.695090	+	0.718923i	$0.255365\pi$
$374$	3.14010	+	5.43880i	0.162370	+	0.281234i
$375$	−5.66950	−	9.81987i	−0.292772	−	0.507096i
$376$	117.922			6.08137
$377$	−10.3581	−	4.96974i	−0.533467	−	0.255955i
$378$	−0.350258			−0.0180153
$379$	18.0654	+	31.2902i	0.927957	+	1.60727i	0.786735	+	0.617291i	$0.211770\pi$
$379$	18.0654	+	31.2902i	0.927957	+	1.60727i	0.141222	+	0.989978i	$0.454897\pi$
$380$	5.11775	+	8.86421i	0.262535	+	0.454724i
$381$	2.00137	−	3.46648i	0.102533	−	0.177593i
$382$	−18.4182			−0.942358
$383$	−8.67703	+	15.0291i	−0.443375	+	0.767949i	−0.997937	−	0.0641937i	$-0.979552\pi$
$383$	−8.67703	+	15.0291i	−0.443375	+	0.767949i	0.554562	+	0.832142i	$0.312886\pi$
$384$	17.7622	−	30.7650i	0.906422	−	1.56997i
$385$	−0.282982			−0.0144221
$386$	8.31818	−	14.4075i	0.423384	−	0.733323i
$387$	−3.54651	−	6.14274i	−0.180279	−	0.312253i
$388$	4.57650	+	7.92673i	0.232337	+	0.402419i
$389$	15.9550			0.808952			0.404476	−	0.914549i	$-0.367454\pi$
$389$	15.9550			0.808952			0.404476	+	0.914549i	$0.367454\pi$
$390$	−1.64956	−	21.5930i	−0.0835288	−	1.09340i
$391$	−5.42982			−0.274598
$392$	−32.6955	−	56.6303i	−1.65137	−	2.86026i
$393$	8.35435	+	14.4702i	0.421421	+	0.729923i
$394$	−31.6772	+	54.8666i	−1.59588	+	2.76414i
$395$	−12.5670			−0.632315
$396$	−2.71711	+	4.70617i	−0.136540	+	0.236494i
$397$	−7.60210	+	13.1672i	−0.381539	+	0.660844i	−0.991282	−	0.131754i	$-0.957939\pi$
$397$	−7.60210	+	13.1672i	−0.381539	+	0.660844i	0.609744	+	0.792599i	$0.291272\pi$
$398$	18.0615			0.905342
$399$	−0.0549194	+	0.0951231i	−0.00274941	+	0.00476211i
$400$	1.08058	+	1.87161i	0.0540288	+	0.0935807i
$401$	3.22827	+	5.59153i	0.161212	+	0.279228i	0.935304	−	0.353846i	$-0.115126\pi$
$401$	3.22827	+	5.59153i	0.161212	+	0.279228i	−0.774091	+	0.633074i	$0.781793\pi$
$402$	14.9629			0.746280
$403$	−30.3907	+	20.7845i	−1.51387	+	1.03535i
$404$	60.7127			3.02057
$405$	1.10143	+	1.90774i	0.0547306	+	0.0947961i
$406$	−0.558024	−	0.966527i	−0.0276943	−	0.0479679i
$407$	3.53842	−	6.12872i	0.175393	−	0.303789i
$408$	−21.5675			−1.06775
$409$	−4.53924	+	7.86220i	−0.224451	+	0.388761i	−0.956155	−	0.292862i	$-0.905392\pi$
$409$	−4.53924	+	7.86220i	−0.224451	+	0.388761i	0.731704	+	0.681623i	$0.238726\pi$
$410$	−7.89081	+	13.6673i	−0.389699	+	0.674979i
$411$	−12.7532			−0.629069
$412$	−5.62084	+	9.73559i	−0.276919	+	0.479638i
$413$	0.363746	+	0.630026i	0.0178988	+	0.0310016i
$414$	−3.21379	−	5.56645i	−0.157949	−	0.273576i
$415$	−33.8643			−1.66233
$416$	5.83625	+	76.3973i	0.286145	+	3.74569i
$417$	−1.34892			−0.0660570
$418$	1.16566	+	2.01899i	0.0570144	+	0.0987518i
$419$	9.04831	+	15.6721i	0.442039	+	0.765634i	0.997841	−	0.0656812i	$-0.0209220\pi$
$419$	9.04831	+	15.6721i	0.442039	+	0.765634i	−0.555802	+	0.831315i	$0.687589\pi$
$420$	0.768892	−	1.33176i	0.0375181	−	0.0649832i
$421$	−11.6614			−0.568344			−0.284172	−	0.958773i	$-0.591719\pi$
$421$	−11.6614			−0.568344			−0.284172	+	0.958773i	$0.591719\pi$
$422$	21.7449	−	37.6632i	1.05852	−	1.83342i
$423$	6.29680	−	10.9064i	0.306161	−	0.530286i
$424$	108.811			5.28433
$425$	0.169750	−	0.294015i	0.00823407	−	0.0142618i
$426$	21.2814	+	36.8605i	1.03109	+	1.78590i
$427$	0.481222	+	0.833500i	0.0232880	+	0.0403359i
$428$	72.7371			3.51588
$429$	−0.274640	−	3.59508i	−0.0132597	−	0.173572i
$430$	42.6026			2.05448
$431$	0.227580	+	0.394180i	0.0109621	+	0.0189870i	0.871454	−	0.490476i	$-0.163177\pi$
$431$	0.227580	+	0.394180i	0.0109621	+	0.0189870i	−0.860492	+	0.509463i	$0.829844\pi$
$432$	−7.33114	−	12.6979i	−0.352720	−	0.610929i
$433$	14.2959	−	24.7612i	0.687015	−	1.18995i	−0.285783	−	0.958294i	$-0.592254\pi$
$433$	14.2959	−	24.7612i	0.687015	−	1.18995i	0.972799	−	0.231651i	$-0.0744129\pi$
$434$	−3.57669			−0.171686
$435$	−3.50956	+	6.07873i	−0.168270	+	0.291453i
$436$	37.1338	−	64.3177i	1.77839	−	3.08026i
$437$	−2.01565			−0.0964216
$438$	10.6047	−	18.3679i	0.506712	−	0.877650i
$439$	−0.932723	−	1.61552i	−0.0445165	−	0.0771048i	0.842909	−	0.538057i	$-0.180841\pi$
$439$	−0.932723	−	1.61552i	−0.0445165	−	0.0771048i	−0.887425	+	0.460952i	$0.847508\pi$
$440$	−10.3134	−	17.8634i	−0.491673	−	0.851603i
$441$	−6.98350			−0.332548
$442$	18.6905	−	12.7826i	0.889017	−	0.608006i
$443$	−8.19846			−0.389521			−0.194760	−	0.980851i	$-0.562393\pi$
$443$	−8.19846			−0.389521			−0.194760	+	0.980851i	$0.562393\pi$
$444$	19.2285	+	33.3048i	0.912546	+	1.58058i
$445$	−7.33422	−	12.7032i	−0.347675	−	0.602191i
$446$	−30.8081	+	53.3612i	−1.45881	+	2.52673i
$447$	4.19119			0.198236
$448$	−1.83806	+	3.18361i	−0.0868400	+	0.150411i
$449$	10.4679	−	18.1310i	0.494011	−	0.855653i	−0.505965	−	0.862554i	$-0.668863\pi$
$449$	10.4679	−	18.1310i	0.494011	−	0.855653i	0.999976	+	0.00690148i	$0.00219683\pi$
$450$	0.401885			0.0189450
$451$	−1.31376	+	2.27550i	−0.0618626	+	0.107149i
$452$	17.9708	+	31.1264i	0.845276	+	1.46406i
$453$	−8.09829	−	14.0267i	−0.380491	−	0.659030i
$454$	−46.1264			−2.16482
$455$	0.0777180	+	1.01734i	0.00364348	+	0.0476936i
$456$	−8.00627			−0.374928
$457$	5.54850	+	9.61028i	0.259548	+	0.449550i	0.966121	−	0.258090i	$-0.0830931\pi$
$457$	5.54850	+	9.61028i	0.259548	+	0.449550i	−0.706573	+	0.707640i	$0.749760\pi$
$458$	−10.2023	−	17.6709i	−0.476721	−	0.825705i
$459$	−1.15166	+	1.99474i	−0.0537550	+	0.0931064i
$460$	28.2199			1.31576
$461$	13.5540	−	23.4762i	0.631273	−	1.09340i	−0.356018	−	0.934479i	$-0.615866\pi$
$461$	13.5540	−	23.4762i	0.631273	−	1.09340i	0.987292	−	0.158919i	$-0.0508008\pi$
$462$	0.175129	−	0.303332i	0.00814774	−	0.0141123i
$463$	−17.6750			−0.821425			−0.410712	−	0.911765i	$-0.634720\pi$
$463$	−17.6750			−0.821425			−0.410712	+	0.911765i	$0.634720\pi$
$464$	23.3597	−	40.4601i	1.08445	−	1.87831i
$465$	11.2473	+	19.4810i	0.521583	+	0.903408i
$466$	−28.8486	−	49.9672i	−1.33639	−	2.31469i
$467$	−7.78739			−0.360358			−0.180179	−	0.983634i	$-0.557668\pi$
$467$	−7.78739			−0.360358			−0.180179	+	0.983634i	$0.557668\pi$
$468$	17.6653	+	8.47571i	0.816577	+	0.391790i
$469$	−0.704965			−0.0325523
$470$	37.8203	+	65.5067i	1.74452	+	3.02160i
$471$	1.04587	+	1.81151i	0.0481913	+	0.0834698i
$472$	−26.5139	+	45.9233i	−1.22040	+	2.11379i
$473$	7.09302			0.326138
$474$	7.77736	−	13.4708i	0.357226	−	0.618733i
$475$	0.0630142	−	0.109144i	0.00289129	−	0.00500786i
$476$	1.60791			0.0736986
$477$	5.81029	−	10.0637i	0.266035	−	0.460786i
$478$	−20.3681	−	35.2785i	−0.931614	−	1.61360i
$479$	6.20031	+	10.7392i	0.283299	+	0.490689i	0.972195	−	0.234171i	$-0.0752377\pi$
$479$	6.20031	+	10.7392i	0.283299	+	0.490689i	−0.688896	+	0.724860i	$0.741904\pi$
$480$	46.8120			2.13667
$481$	−23.0050	−	11.0377i	−1.04894	−	0.503275i
$482$	73.3214			3.33970
$483$	0.151416	+	0.262260i	0.00688965	+	0.0119332i
$484$	−2.71711	−	4.70617i	−0.123505	−	0.213917i
$485$	−1.85517	+	3.21325i	−0.0842389	+	0.145906i
$486$	−2.72658			−0.123680
$487$	−16.9442	+	29.3482i	−0.767813	+	1.32989i	0.170933	+	0.985283i	$0.445322\pi$
$487$	−16.9442	+	29.3482i	−0.767813	+	1.32989i	−0.938746	+	0.344609i	$0.888011\pi$
$488$	−35.0768	+	60.7548i	−1.58785	+	2.75024i
$489$	12.0639			0.545547
$490$	20.9724	−	36.3253i	0.947436	−	1.64101i
$491$	−8.75875	−	15.1706i	−0.395277	−	0.684639i	0.597860	−	0.801601i	$-0.296018\pi$
$491$	−8.75875	−	15.1706i	−0.395277	−	0.684639i	−0.993136	+	0.116961i	$0.962685\pi$
$492$	−7.13927	−	12.3656i	−0.321863	−	0.557483i
$493$	−7.33922			−0.330542
$494$	6.93827	−	4.74514i	0.312167	−	0.213494i
$495$	−2.20286			−0.0990113
$496$	−74.8625	−	129.666i	−3.36142	−	5.82216i
$497$	−1.00266	−	1.73666i	−0.0449754	−	0.0778997i
$498$	20.9576	−	36.2997i	0.939134	−	1.62663i
$499$	3.93223			0.176031			0.0880154	−	0.996119i	$-0.471948\pi$
$499$	3.93223			0.176031			0.0880154	+	0.996119i	$0.471948\pi$
$500$	−30.8093	+	53.3633i	−1.37783	+	2.38648i
$501$	8.61718	−	14.9254i	0.384987	−	0.666817i
$502$	−61.5498			−2.74710
$503$	6.33261	−	10.9684i	0.282357	−	0.489057i	−0.689608	−	0.724183i	$-0.742217\pi$
$503$	6.33261	−	10.9684i	0.282357	−	0.489057i	0.971965	+	0.235126i	$0.0755504\pi$
$504$	0.601431	+	1.04171i	0.0267899	+	0.0464014i
$505$	12.3055	+	21.3138i	0.547588	+	0.948450i
$506$	6.42759			0.285741
$507$	−12.8491	+	1.97470i	−0.570651	+	0.0876996i
$508$	−21.7518			−0.965080
$509$	10.6168	+	18.3888i	0.470580	+	0.815068i	0.999434	−	0.0336444i	$-0.0107114\pi$
$509$	10.6168	+	18.3888i	0.470580	+	0.815068i	−0.528854	+	0.848713i	$0.677378\pi$
$510$	−6.91720	−	11.9809i	−0.306299	−	0.530525i
$511$	−0.499633	+	0.865389i	−0.0221025	+	0.0382826i
$512$	−36.9962			−1.63502
$513$	−0.427519	+	0.740484i	−0.0188754	+	0.0326932i
$514$	−4.40840	+	7.63557i	−0.194446	+	0.336791i
$515$	−4.55703			−0.200807
$516$	−19.2725	+	33.3810i	−0.848425	+	1.46952i
$517$	6.29680	+	10.9064i	0.276933	+	0.479662i
$518$	−1.23936	−	2.14663i	−0.0544543	−	0.0943177i
$519$	−16.8467			−0.739489
$520$	−61.3877	+	41.9835i	−2.69203	+	1.84110i
$521$	10.3365			0.452849			0.226424	−	0.974029i	$-0.427296\pi$
$521$	10.3365			0.452849			0.226424	+	0.974029i	$0.427296\pi$
$522$	−4.34393	−	7.52390i	−0.190129	−	0.329312i
$523$	−15.0445	−	26.0578i	−0.657850	−	1.13943i	−0.981171	−	0.193140i	$-0.938133\pi$
$523$	−15.0445	−	26.0578i	−0.657850	−	1.13943i	0.323321	−	0.946289i	$-0.395200\pi$
$524$	45.3993	−	78.6340i	1.98328	−	3.43514i
$525$	−0.0189345			−0.000826370
$526$	−19.4512	+	33.6904i	−0.848112	+	1.46897i
$527$	−11.7603	+	20.3694i	−0.512286	+	0.887305i
$528$	14.6623			0.638094
$529$	8.72137	−	15.1059i	0.379190	−	0.656776i
$530$	34.8982	+	60.4454i	1.51588	+	2.62558i
$531$	2.83157	+	4.90442i	0.122880	+	0.212834i
$532$	0.596888			0.0258784
$533$	8.54141	+	4.09813i	0.369970	+	0.177510i
$534$	18.1557			0.785676
$535$	14.7427	+	25.5351i	0.637382	+	1.10398i
$536$	−25.6929	−	44.5013i	−1.10976	−	1.92217i
$537$	−1.31611	+	2.27957i	−0.0567943	+	0.0983705i
$538$	−3.84227			−0.165652
$539$	3.49175	−	6.04789i	0.150400	−	0.260501i
$540$	5.98542	−	10.3670i	0.257571	−	0.446127i
$541$	−28.1919			−1.21206			−0.606031	−	0.795441i	$-0.707239\pi$
$541$	−28.1919			−1.21206			−0.606031	+	0.795441i	$0.707239\pi$
$542$	−33.6550	+	58.2922i	−1.44561	+	2.50386i
$543$	1.65520	+	2.86689i	0.0710315	+	0.123030i
$544$	24.4734	+	42.3892i	1.04929	+	1.81742i
$545$	30.1058			1.28959
$546$	−1.13860	−	0.546295i	−0.0487276	−	0.0233793i
$547$	7.90177			0.337855			0.168928	−	0.985628i	$-0.445970\pi$
$547$	7.90177			0.337855			0.168928	+	0.985628i	$0.445970\pi$
$548$	34.6518	+	60.0187i	1.48025	+	2.56387i
$549$	3.74606	+	6.48836i	0.159878	+	0.276917i
$550$	−0.200942	+	0.348042i	−0.00856821	+	0.0148406i
$551$	−2.72446			−0.116066
$552$	−11.0369	+	19.1164i	−0.469760	+	0.813649i
$553$	−0.366425	+	0.634666i	−0.0155820	+	0.0269888i
$554$	−33.0978			−1.40619
$555$	−7.79465	+	13.5007i	−0.330864	+	0.573074i
$556$	3.66517	+	6.34826i	0.155438	+	0.269226i
$557$	1.10466	+	1.91333i	0.0468060	+	0.0810704i	0.888479	−	0.458917i	$-0.151762\pi$
$557$	1.10466	+	1.91333i	0.0468060	+	0.0810704i	−0.841673	+	0.539987i	$0.818429\pi$
$558$	−27.8426			−1.17867
$559$	−1.94803	−	25.5000i	−0.0823928	−	1.07853i
$560$	−4.14916			−0.175334
$561$	−1.15166	−	1.99474i	−0.0486232	−	0.0842179i
$562$	39.6736	+	68.7166i	1.67353	+	2.89864i
$563$	9.18103	−	15.9020i	0.386934	−	0.670190i	−0.605101	−	0.796149i	$-0.706867\pi$
$563$	9.18103	−	15.9020i	0.386934	−	0.670190i	0.992036	+	0.125959i	$0.0402006\pi$
$564$	−68.4364			−2.88169
$565$	−7.28481	+	12.6177i	−0.306474	+	0.530829i
$566$	19.2842	−	33.4013i	0.810577	−	1.40396i
$567$	0.128461			0.00539485
$568$	73.0850	−	126.587i	3.06658	−	5.31147i
$569$	−1.08978	−	1.88755i	−0.0456858	−	0.0791301i	0.842278	−	0.539043i	$-0.181214\pi$
$569$	−1.08978	−	1.88755i	−0.0456858	−	0.0791301i	−0.887964	+	0.459913i	$0.847881\pi$
$570$	−2.56779	−	4.44755i	−0.107553	−	0.186287i
$571$	−1.71370			−0.0717160			−0.0358580	−	0.999357i	$-0.511416\pi$
$571$	−1.71370			−0.0717160			−0.0358580	+	0.999357i	$0.511416\pi$
$572$	−16.1728	+	11.0607i	−0.676219	+	0.462472i
$573$	6.75507			0.282197
$574$	0.460156	+	0.797013i	0.0192065	+	0.0332667i
$575$	−0.173734	−	0.300916i	−0.00724519	−	0.0125490i
$576$	−14.3083	+	24.7827i	−0.596180	+	1.03261i
$577$	−27.5202			−1.14568			−0.572841	−	0.819667i	$-0.694159\pi$
$577$	−27.5202			−1.14568			−0.572841	+	0.819667i	$0.694159\pi$
$578$	−15.9432	+	27.6145i	−0.663151	+	1.14861i
$579$	−3.05078	+	5.28410i	−0.126786	+	0.219600i
$580$	38.1434			1.58382
$581$	−0.987405	+	1.71024i	−0.0409644	+	0.0709525i
$582$	−2.29622	−	3.97717i	−0.0951815	−	0.164859i
$583$	5.81029	+	10.0637i	0.240638	+	0.416797i
$584$	−72.8376			−3.01404
$585$	0.604994	+	7.91946i	0.0250134	+	0.327429i
$586$	9.20145			0.380109
$587$	5.86145	+	10.1523i	0.241928	+	0.419032i	0.961263	−	0.275631i	$-0.0888869\pi$
$587$	5.86145	+	10.1523i	0.241928	+	0.419032i	−0.719335	+	0.694663i	$0.755554\pi$
$588$	18.9749	+	32.8655i	0.782513	+	1.35535i
$589$	−4.36563	+	7.56150i	−0.179883	+	0.311566i
$590$	−34.0144			−1.40035
$591$	11.6180	−	20.1229i	0.477899	−	0.827745i
$592$	51.8813	−	89.8610i	2.13231	−	3.69327i
$593$	11.9940			0.492534			0.246267	−	0.969202i	$-0.420796\pi$
$593$	11.9940			0.492534			0.246267	+	0.969202i	$0.420796\pi$
$594$	1.36329	−	2.36128i	0.0559364	−	0.0968847i
$595$	0.325899	+	0.564474i	0.0133606	+	0.0231412i
$596$	−11.3879	−	19.7244i	−0.466467	−	0.807945i
$597$	−6.62425			−0.271112
$598$	−1.76527	−	23.1077i	−0.0721873	−	0.944943i
$599$	11.1692			0.456362			0.228181	−	0.973619i	$-0.426722\pi$
$599$	11.1692			0.456362			0.228181	+	0.973619i	$0.426722\pi$
$600$	−0.690080	−	1.19525i	−0.0281724	−	0.0487960i
$601$	3.70840	+	6.42314i	0.151269	+	0.262005i	0.931694	−	0.363244i	$-0.118331\pi$
$601$	3.70840	+	6.42314i	0.151269	+	0.262005i	−0.780425	+	0.625249i	$0.784997\pi$
$602$	1.24219	−	2.15154i	0.0506281	−	0.0876904i
$603$	−5.48778			−0.223480
$604$	−44.0079	+	76.2239i	−1.79066	+	3.10151i
$605$	1.10143	−	1.90774i	0.0447796	−	0.0775605i
$606$	−30.4621			−1.23744
$607$	1.94104	−	3.36197i	0.0787842	−	0.136458i	−0.823941	−	0.566675i	$-0.808230\pi$
$607$	1.94104	−	3.36197i	0.0787842	−	0.136458i	0.902726	+	0.430217i	$0.141563\pi$
$608$	9.08500	+	15.7357i	0.368445	+	0.638166i
$609$	0.204661	+	0.354484i	0.00829329	+	0.0143644i
$610$	−44.9997			−1.82198
$611$	37.4799	−	25.6328i	1.51628	−	1.03699i
$612$	12.5168			0.505960
$613$	10.0364	+	17.3835i	0.405365	+	0.702112i	0.994364	−	0.106022i	$-0.0338112\pi$
$613$	10.0364	+	17.3835i	0.405365	+	0.702112i	−0.588999	+	0.808134i	$0.700478\pi$
$614$	−14.8374	−	25.6991i	−0.598788	−	1.03713i
$615$	2.89404	−	5.01262i	0.116699	−	0.202128i
$616$	−1.20286			−0.0484647
$617$	−2.96555	+	5.13648i	−0.119388	+	0.206787i	−0.919525	−	0.393030i	$-0.871427\pi$
$617$	−2.96555	+	5.13648i	−0.119388	+	0.206787i	0.800137	+	0.599817i	$0.204760\pi$
$618$	2.82021	−	4.88475i	0.113446	−	0.196494i
$619$	15.4410			0.620628			0.310314	−	0.950634i	$-0.399566\pi$
$619$	15.4410			0.620628			0.310314	+	0.950634i	$0.399566\pi$
$620$	61.1205	−	105.864i	2.45466	−	4.25159i
$621$	1.17869	+	2.04155i	0.0472993	+	0.0819247i
$622$	25.3816	+	43.9621i	1.01771	+	1.76272i
$623$	−0.855396			−0.0342707
$624$	−4.02685	−	52.7120i	−0.161203	−	2.11017i
$625$	−24.2413			−0.969652
$626$	−32.1524	−	55.6896i	−1.28507	−	2.22581i
$627$	−0.427519	−	0.740484i	−0.0170734	−	0.0295721i
$628$	5.68350	−	9.84412i	0.226797	−	0.392823i
$629$	−16.3002			−0.649933
$630$	−0.385785	+	0.668200i	−0.0153701	+	0.0266217i
$631$	14.2472	−	24.6769i	0.567173	−	0.982372i	−0.429671	−	0.902985i	$-0.641370\pi$
$631$	14.2472	−	24.6769i	0.567173	−	0.982372i	0.996844	−	0.0793866i	$-0.0252962\pi$
$632$	−53.4183			−2.12486
$633$	−7.97516	+	13.8134i	−0.316984	+	0.549032i
$634$	29.9452	+	51.8666i	1.18928	+	2.05989i
$635$	−4.40875	−	7.63618i	−0.174956	−	0.303032i
$636$	−63.1488			−2.50401
$637$	−22.7016	−	10.8921i	−0.899470	−	0.431561i
$638$	8.68786			0.343955
$639$	−7.80517	−	13.5190i	−0.308768	−	0.534802i
$640$	−39.1276	−	67.7710i	−1.54666	−	2.67889i
$641$	−6.95517	+	12.0467i	−0.274713	+	0.475817i	−0.970063	−	0.242855i	$-0.921916\pi$
$641$	−6.95517	+	12.0467i	−0.274713	+	0.475817i	0.695350	+	0.718671i	$0.255249\pi$
$642$	−36.4953			−1.44035
$643$	13.6910	−	23.7135i	0.539920	−	0.935169i	−0.458988	−	0.888443i	$-0.651788\pi$
$643$	13.6910	−	23.7135i	0.539920	−	0.935169i	0.998908	−	0.0467263i	$-0.0148789\pi$
$644$	0.822826	−	1.42518i	0.0324239	−	0.0561598i
$645$	−15.6250			−0.615232
$646$	2.68490	−	4.65038i	0.105636	−	0.182967i
$647$	1.25252	+	2.16944i	0.0492418	+	0.0852894i	0.889596	−	0.456749i	$-0.150986\pi$
$647$	1.25252	+	2.16944i	0.0492418	+	0.0852894i	−0.840354	+	0.542038i	$0.817653\pi$
$648$	4.68183	+	8.10916i	0.183920	+	0.318558i
$649$	−5.66314			−0.222298
$650$	1.30643	+	0.626817i	0.0512422	+	0.0245858i
$651$	1.31179			0.0514130
$652$	−32.7788	−	56.7746i	−1.28372	−	2.22346i
$653$	24.5717	+	42.5595i	0.961566	+	1.66548i	0.718571	+	0.695454i	$0.244797\pi$
$653$	24.5717	+	42.5595i	0.961566	+	1.66548i	0.242995	+	0.970027i	$0.421870\pi$
$654$	−18.6316	+	32.2709i	−0.728554	+	1.26189i
$655$	36.8070			1.43817
$656$	−19.2628	+	33.3641i	−0.752084	+	1.30265i
$657$	−3.88938	+	6.73660i	−0.151739	+	0.262820i
$658$	4.41101			0.171959
$659$	−7.80449	+	13.5178i	−0.304020	+	0.526577i	−0.977043	−	0.213044i	$-0.931662\pi$
$659$	−7.80449	+	13.5178i	−0.304020	+	0.526577i	0.673023	+	0.739622i	$0.264996\pi$
$660$	5.98542	+	10.3670i	0.232982	+	0.403537i
$661$	−2.79725	−	4.84499i	−0.108801	−	0.188448i	0.806484	−	0.591256i	$-0.201368\pi$
$661$	−2.79725	−	4.84499i	−0.108801	−	0.188448i	−0.915285	+	0.402808i	$0.868034\pi$
$662$	10.1442			0.394264
$663$	−6.85494	+	4.68815i	−0.266224	+	0.182073i
$664$	−143.946			−5.58619
$665$	0.120980	+	0.209543i	0.00469140	+	0.00812574i
$666$	−9.64776	−	16.7104i	−0.373843	−	0.647516i
$667$	−3.75574	+	6.50513i	−0.145423	+	0.251880i
$668$	−93.6552			−3.62363
$669$	11.2992	−	19.5708i	0.436852	−	0.756650i
$670$	16.4806	−	28.5452i	0.636700	−	1.10280i
$671$	−7.49212			−0.289230
$672$	1.36493	−	2.36413i	0.0526533	−	0.0911982i
$673$	−1.31161	−	2.27177i	−0.0505588	−	0.0875703i	0.839638	−	0.543146i	$-0.182767\pi$
$673$	−1.31161	−	2.27177i	−0.0505588	−	0.0875703i	−0.890197	+	0.455575i	$0.849434\pi$
$674$	−31.7553	−	55.0018i	−1.22317	−	2.11859i
$675$	−0.147395			−0.00567325
$676$	44.2058	+	55.1048i	1.70022	+	2.11942i
$677$	−23.4345			−0.900660			−0.450330	−	0.892862i	$-0.648694\pi$
$677$	−23.4345			−0.900660			−0.450330	+	0.892862i	$0.648694\pi$
$678$	−9.01671	−	15.6174i	−0.346285	−	0.599783i
$679$	0.108185	+	0.187382i	0.00415176	+	0.00719106i
$680$	−23.7552	+	41.1452i	−0.910969	+	1.57784i
$681$	16.9173			0.648274
$682$	13.9213	−	24.1124i	0.533075	−	0.923312i
$683$	17.4365	−	30.2009i	0.667189	−	1.15561i	−0.311498	−	0.950247i	$-0.600831\pi$
$683$	17.4365	−	30.2009i	0.667189	−	1.15561i	0.978687	−	0.205359i	$-0.0658361\pi$
$684$	4.64646			0.177662
$685$	−14.0468	+	24.3297i	−0.536699	+	0.929591i
$686$	−2.44892	−	4.24165i	−0.0935001	−	0.161947i
$687$	3.74179	+	6.48097i	0.142758	+	0.247265i
$688$	104.000			3.96496
$689$	34.5841	−	23.6523i	1.31755	−	0.901082i
$690$	−14.1591			−0.539027
$691$	−18.9287	−	32.7855i	−0.720083	−	1.24722i	−0.960966	−	0.276666i	$-0.910771\pi$
$691$	−18.9287	−	32.7855i	−0.720083	−	1.24722i	0.240884	−	0.970554i	$-0.422563\pi$
$692$	45.7743	+	79.2835i	1.74008	+	3.01391i
$693$	−0.0642304	+	0.111250i	−0.00243991	+	0.00422605i
$694$	−34.8077			−1.32128
$695$	−1.48575	+	2.57339i	−0.0563575	+	0.0976141i
$696$	−14.9180	+	25.8387i	−0.565465	+	0.979414i
$697$	6.05204			0.229237
$698$	27.6617	−	47.9114i	1.04701	−	1.81347i
$699$	10.5805	+	18.3260i	0.400192	+	0.693153i
$700$	0.0514472	+	0.0891091i	0.00194452	+	0.00336801i
$701$	−0.238661			−0.00901412			−0.00450706	−	0.999990i	$-0.501435\pi$
$701$	−0.238661			−0.00901412			−0.00450706	+	0.999990i	$0.501435\pi$
$702$	−8.86341	−	4.25262i	−0.334528	−	0.160505i
$703$	−6.05096			−0.228216
$704$	−14.3083	−	24.7827i	−0.539265	−	0.934034i
$705$	−13.8710	−	24.0253i	−0.522412	−	0.904844i
$706$	21.1063	−	36.5573i	0.794348	−	1.37585i
$707$	1.43520			0.0539763
$708$	15.3874	−	26.6517i	0.578293	−	1.00163i
$709$	17.7385	−	30.7239i	0.666183	−	1.15386i	−0.312781	−	0.949825i	$-0.601261\pi$
$709$	17.7385	−	30.7239i	0.666183	−	1.15386i	0.978963	−	0.204037i	$-0.0654062\pi$
$710$	93.7600			3.51875
$711$	−2.85243	+	4.94055i	−0.106974	+	0.185285i
$712$	−31.1754	−	53.9974i	−1.16835	−	2.02364i
$713$	12.0363	+	20.8475i	0.450763	+	0.780744i
$714$	−0.806758			−0.0301922
$715$	−7.16095	−	3.43579i	−0.267804	−	0.128491i
$716$	14.3040			0.534567
$717$	7.47020	+	12.9388i	0.278980	+	0.483207i
$718$	−21.4475	−	37.1482i	−0.800414	−	1.38636i
$719$	12.8797	−	22.3084i	0.480333	−	0.831961i	−0.519412	−	0.854524i	$-0.673849\pi$
$719$	12.8797	−	22.3084i	0.480333	−	0.831961i	0.999745	+	0.0225623i	$0.00718242\pi$
$720$	−32.2990			−1.20371
$721$	−0.132872	+	0.230142i	−0.00494843	+	0.00857093i
$722$	−24.9058	+	43.1381i	−0.926898	+	1.60543i
$723$	−26.8914			−1.00010
$724$	8.99473	−	15.5793i	0.334286	−	0.579001i
$725$	−0.234827	−	0.406733i	−0.00872127	−	0.0151057i
$726$	1.36329	+	2.36128i	0.0505964	+	0.0876355i
$727$	38.2460			1.41846			0.709232	−	0.704975i	$-0.249042\pi$
$727$	38.2460			1.41846			0.709232	+	0.704975i	$0.249042\pi$
$728$	0.330354	+	4.32438i	0.0122437	+	0.160272i
$729$	1.00000			0.0370370
$730$	−23.3607	−	40.4619i	−0.864617	−	1.49756i
$731$	−8.16877	−	14.1487i	−0.302133	−	0.523309i
$732$	20.3569	−	35.2592i	0.752413	−	1.30322i
$733$	52.2468			1.92978			0.964890	−	0.262654i	$-0.0845976\pi$
$733$	52.2468			1.92978			0.964890	+	0.262654i	$0.0845976\pi$
$734$	−43.2361	+	74.8872i	−1.59588	+	2.76414i
$735$	−7.69184	+	13.3227i	−0.283718	+	0.491414i
$736$	50.0957			1.84655
$737$	2.74389	−	4.75256i	0.101073	−	0.175063i
$738$	3.58207	+	6.20433i	0.131858	+	0.228385i
$739$	−2.22528	−	3.85430i	−0.0818584	−	0.141783i	0.822190	−	0.569213i	$-0.192752\pi$
$739$	−2.22528	−	3.85430i	−0.0818584	−	0.141783i	−0.904048	+	0.427431i	$0.859419\pi$
$740$	84.7156			3.11421
$741$	−2.54468	+	1.74033i	−0.0934812	+	0.0639325i
$742$	4.07020			0.149422
$743$	16.4901	+	28.5617i	0.604963	+	1.04783i	0.992057	+	0.125787i	$0.0401456\pi$
$743$	16.4901	+	28.5617i	0.604963	+	1.04783i	−0.387094	+	0.922040i	$0.626521\pi$
$744$	47.8088	+	82.8073i	1.75276	+	3.03586i
$745$	4.61631	−	7.99568i	0.169128	−	0.292939i
$746$	−28.9688			−1.06062
$747$	−7.68643	+	13.3133i	−0.281232	+	0.487108i
$748$	−6.25838	+	10.8398i	−0.228829	+	0.396344i
$749$	1.71945			0.0628274
$750$	15.4583	−	26.7746i	0.564458	−	0.977671i
$751$	19.3072	+	33.4410i	0.704528	+	1.22028i	0.966861	+	0.255302i	$0.0821748\pi$
$751$	19.3072	+	33.4410i	0.704528	+	1.22028i	−0.262333	+	0.964977i	$0.584492\pi$
$752$	92.3255	+	159.912i	3.36677	+	5.83141i
$753$	22.5740			0.822643
$754$	−2.38603	−	31.2335i	−0.0868942	−	1.13746i
$755$	−35.6789			−1.29849
$756$	−0.349042	−	0.604558i	−0.0126945	−	0.0219876i
$757$	14.2799	+	24.7335i	0.519011	+	0.898953i	0.999756	+	0.0220925i	$0.00703284\pi$
$757$	14.2799	+	24.7335i	0.519011	+	0.898953i	−0.480745	+	0.876860i	$0.659634\pi$
$758$	−49.2567	+	85.3151i	−1.78908	+	3.09878i
$759$	−2.35738			−0.0855676
$760$	−8.81836	+	15.2738i	−0.319876	+	0.554041i
$761$	21.1256	−	36.5906i	0.765802	−	1.32641i	−0.174020	−	0.984742i	$-0.555676\pi$
$761$	21.1256	−	36.5906i	0.765802	−	1.32641i	0.939822	−	0.341665i	$-0.110991\pi$
$762$	10.9138			0.395365
$763$	0.877816	−	1.52042i	0.0317791	−	0.0550429i
$764$	−18.3543	−	31.7905i	−0.664034	−	1.15014i
$765$	2.53695	+	4.39413i	0.0917238	+	0.158870i
$766$	−47.3171			−1.70964
$767$	1.55532	+	20.3594i	0.0561595	+	0.735136i
$768$	39.6266			1.42990
$769$	−6.84841	−	11.8618i	−0.246960	−	0.427747i	0.715721	−	0.698386i	$-0.246098\pi$
$769$	−6.84841	−	11.8618i	−0.246960	−	0.427747i	−0.962681	+	0.270639i	$0.912765\pi$
$770$	−0.385785	−	0.668200i	−0.0139027	−	0.0240802i
$771$	1.61683	−	2.80043i	0.0582286	−	0.100855i
$772$	33.1572			1.19335
$773$	−4.79111	+	8.29845i	−0.172324	+	0.298475i	−0.939232	−	0.343283i	$-0.888461\pi$
$773$	−4.79111	+	8.29845i	−0.172324	+	0.298475i	0.766908	+	0.641757i	$0.221794\pi$
$774$	9.66984	−	16.7486i	0.347575	−	0.602018i
$775$	−1.50514			−0.0540661
$776$	−7.88573	+	13.6585i	−0.283081	+	0.490311i
$777$	0.454548	+	0.787300i	0.0163068	+	0.0282442i
$778$	21.7513	+	37.6743i	0.779822	+	1.35069i
$779$	2.24663			0.0804939
$780$	35.6265	−	24.3652i	1.27563	−	0.872416i
$781$	15.6103			0.558582
$782$	−7.40241	−	12.8213i	−0.264710	−	0.458490i
$783$	1.59318	+	2.75947i	0.0569356	+	0.0986154i
$784$	51.1970	−	88.6759i	1.82847	−	3.16699i
$785$	4.60783			0.164461
$786$	−22.7788	+	39.4540i	−0.812492	+	1.40728i
$787$	0.421770	−	0.730527i	0.0150345	−	0.0260405i	−0.858410	−	0.512964i	$-0.828548\pi$
$787$	0.421770	−	0.730527i	0.0150345	−	0.0260405i	0.873445	+	0.486923i	$0.161881\pi$
$788$	−126.269			−4.49815
$789$	7.13392	−	12.3563i	0.253974	−	0.439896i
$790$	−17.1324	−	29.6743i	−0.609545	−	1.05576i
$791$	0.424816	+	0.735804i	0.0151047	+	0.0261622i
$792$	−9.36366			−0.332723
$793$	2.05763	+	26.9347i	0.0730688	+	0.956480i
$794$	−41.4554			−1.47120
$795$	−12.7993	−	22.1690i	−0.453943	−	0.786253i
$796$	17.9988	+	31.1748i	0.637951	+	1.10496i
$797$	−5.76818	+	9.99079i	−0.204320	+	0.353892i	−0.949916	−	0.312506i	$-0.898832\pi$
$797$	−5.76818	+	9.99079i	−0.204320	+	0.353892i	0.745596	+	0.666398i	$0.232165\pi$
$798$	−0.299484			−0.0106016
$799$	14.5036	−	25.1209i	0.513100	−	0.888715i
$800$	−1.56611	+	2.71259i	−0.0553705	+	0.0959045i
$801$	−6.65881			−0.235277
$802$	−8.80213	+	15.2457i	−0.310814	+	0.538346i
$803$	−3.88938	−	6.73660i	−0.137253	−	0.237730i
$804$	14.9109	+	25.8264i	0.525867	+	0.910828i
$805$	0.667096			0.0235120
$806$	−90.5093	−	43.4259i	−3.18805	−	1.52961i
$807$	1.40919			0.0496059
$808$	52.3067	+	90.5979i	1.84015	+	3.18722i
$809$	−16.4006	−	28.4067i	−0.576614	−	0.998725i	−0.995864	−	0.0908541i	$-0.971040\pi$
$809$	−16.4006	−	28.4067i	−0.576614	−	0.998725i	0.419250	−	0.907871i	$-0.362293\pi$
$810$	−3.00314	+	5.20159i	−0.105519	+	0.182765i
$811$	−9.14559			−0.321145			−0.160572	−	0.987024i	$-0.551334\pi$
$811$	−9.14559			−0.321145			−0.160572	+	0.987024i	$0.551334\pi$
$812$	1.11217	−	1.92634i	0.0390296	−	0.0676013i
$813$	12.3433	−	21.3793i	0.432899	−	0.749803i
$814$	19.2955			0.676308
$815$	13.2875	−	23.0147i	0.465441	−	0.806168i
$816$	−16.8860	−	29.2474i	−0.591128	−	1.02386i
$817$	−3.03240	−	5.25227i	−0.106090	−	0.183754i
$818$	−24.7532			−0.865474
$819$	0.417594	+	0.200359i	0.0145919	+	0.00700112i
$820$	−31.4536			−1.09841
$821$	−12.8883	−	22.3232i	−0.449804	−	0.779083i	0.548569	−	0.836105i	$-0.315173\pi$
$821$	−12.8883	−	22.3232i	−0.449804	−	0.779083i	−0.998373	+	0.0570219i	$0.981840\pi$
$822$	−17.3863	−	30.1139i	−0.606416	−	1.05034i
$823$	24.7787	−	42.9180i	0.863732	−	1.49603i	−0.00456894	−	0.999990i	$-0.501454\pi$
$823$	24.7787	−	42.9180i	0.863732	−	1.49603i	0.868301	−	0.496038i	$-0.165212\pi$
$824$	−19.3705			−0.674802
$825$	0.0736977	−	0.127648i	0.00256582	−	0.00444414i
$826$	−0.991781	+	1.71781i	−0.0345085	+	0.0597704i
$827$	35.0003			1.21708			0.608541	−	0.793523i	$-0.291755\pi$
$827$	35.0003			1.21708			0.608541	+	0.793523i	$0.291755\pi$
$828$	6.40527	−	11.0942i	0.222598	−	0.385552i
$829$	12.6053	+	21.8331i	0.437801	+	0.758293i	0.997520	−	0.0703894i	$-0.0224242\pi$
$829$	12.6053	+	21.8331i	0.437801	+	0.758293i	−0.559719	+	0.828683i	$0.689091\pi$
$830$	−46.1668	−	79.9632i	−1.60247	−	2.77556i
$831$	12.1390			0.421096
$832$	−85.1661	+	58.2458i	−2.95260	+	2.01931i
$833$	−16.0853			−0.557321
$834$	−1.83897	−	3.18519i	−0.0636783	−	0.110294i
$835$	−18.9825	−	32.8786i	−0.656915	−	1.13781i
$836$	−2.32323	+	4.02395i	−0.0803505	+	0.139171i
$837$	10.2116			0.352963
$838$	−24.6709	+	42.7313i	−0.852242	+	1.47613i
$839$	25.1966	−	43.6417i	0.869882	−	1.50668i	0.00776452	−	0.999970i	$-0.497528\pi$
$839$	25.1966	−	43.6417i	0.869882	−	1.50668i	0.862117	−	0.506709i	$-0.169138\pi$
$840$	2.64974			0.0914248
$841$	9.42355	−	16.3221i	0.324950	−	0.562830i
$842$	−15.8979	−	27.5360i	−0.547878	−	0.948952i
$843$	−14.5507	−	25.2025i	−0.501152	−	0.868021i
$844$	86.6775			2.98356
$845$	−10.3852	+	26.6878i	−0.357263	+	0.918087i
$846$	34.3374			1.18054
$847$	−0.0642304	−	0.111250i	−0.00220698	−	0.00382261i
$848$	85.1921	+	147.557i	2.92551	+	5.06713i
$849$	−7.07269	+	12.2503i	−0.242734	+	0.420428i
$850$	0.925671			0.0317502
$851$	−8.34141	+	14.4477i	−0.285940	+	0.495262i
$852$	−42.4150	+	73.4650i	−1.45311	+	2.51687i
$853$	−51.8324			−1.77471			−0.887354	−	0.461089i	$-0.847459\pi$
$853$	−51.8324			−1.77471			−0.887354	+	0.461089i	$0.847459\pi$
$854$	−1.31209	+	2.27260i	−0.0448987	+	0.0777669i
$855$	0.941765	+	1.63118i	0.0322077	+	0.0557853i
$856$	62.6664	+	108.541i	2.14189	+	3.70987i
$857$	−14.7019			−0.502207			−0.251104	−	0.967960i	$-0.580793\pi$
$857$	−14.7019			−0.502207			−0.251104	+	0.967960i	$0.580793\pi$
$858$	8.11458	−	5.54963i	0.277027	−	0.189461i
$859$	−11.7519			−0.400969			−0.200485	−	0.979697i	$-0.564252\pi$
$859$	−11.7519			−0.400969			−0.200485	+	0.979697i	$0.564252\pi$
$860$	42.4547	+	73.5337i	1.44769	+	2.50748i
$861$	−0.168767	−	0.292313i	−0.00575156	−	0.00996199i
$862$	−0.620514	+	1.07476i	−0.0211348	+	0.0366065i
$863$	16.4289			0.559246			0.279623	−	0.960110i	$-0.409791\pi$
$863$	16.4289			0.559246			0.279623	+	0.960110i	$0.409791\pi$
$864$	10.6253	−	18.4035i	0.361479	−	0.626100i
$865$	−18.5555	+	32.1391i	−0.630906	+	1.09276i
$866$	77.9575			2.64910
$867$	5.84735	−	10.1279i	0.198586	−	0.343962i
$868$	−3.56427	−	6.17349i	−0.120979	−	0.209542i
$869$	−2.85243	−	4.94055i	−0.0967619	−	0.167597i
$870$	−19.1382			−0.648844
$871$	−17.8394	−	8.55926i	−0.604465	−	0.290019i
$872$	127.970			4.33361
$873$	0.842163	+	1.45867i	0.0285029	+	0.0493685i
$874$	−2.74791	−	4.75952i	−0.0929495	−	0.160993i
$875$	−0.728309	+	1.26147i	−0.0246213	+	0.0426454i
$876$	42.2715			1.42822
$877$	24.2841	−	42.0614i	0.820017	−	1.42031i	−0.0856515	−	0.996325i	$-0.527297\pi$
$877$	24.2841	−	42.0614i	0.820017	−	1.42031i	0.905669	−	0.423986i	$-0.139370\pi$
$878$	2.54314	−	4.40485i	0.0858269	−	0.148656i
$879$	−3.37473			−0.113827
$880$	16.1495	−	27.9718i	0.544400	−	0.942928i
$881$	−2.12316	−	3.67741i	−0.0715309	−	0.123895i	0.828042	−	0.560667i	$-0.189455\pi$
$881$	−2.12316	−	3.67741i	−0.0715309	−	0.123895i	−0.899572	+	0.436772i	$0.856122\pi$
$882$	−9.52052	−	16.4900i	−0.320573	−	0.555248i
$883$	26.8673			0.904156			0.452078	−	0.891978i	$-0.350683\pi$
$883$	26.8673			0.904156			0.452078	+	0.891978i	$0.350683\pi$
$884$	40.6889	+	19.5223i	1.36851	+	0.656607i
$885$	12.4751			0.419347
$886$	−11.1769	−	19.3589i	−0.375494	−	0.650375i
$887$	4.48910	+	7.77534i	0.150729	+	0.261070i	0.931496	−	0.363752i	$-0.118505\pi$
$887$	4.48910	+	7.77534i	0.150729	+	0.261070i	−0.780767	+	0.624823i	$0.785171\pi$
$888$	−33.1325	+	57.3872i	−1.11185	+	1.92579i
$889$	−0.514196			−0.0172456
$890$	19.9973	−	34.6363i	0.670311	−	1.16101i
$891$	−0.500000	+	0.866025i	−0.0167506	+	0.0290129i
$892$	−122.805			−4.11180
$893$	5.38400	−	9.32536i	0.180169	−	0.312061i
$894$	5.71380	+	9.89659i	0.191098	+	0.330991i
$895$	2.89921	+	5.02157i	0.0969098	+	0.167853i
$896$	−4.56348			−0.152455
$897$	0.647432	+	8.47497i	0.0216171	+	0.282971i
$898$	57.0831			1.90489
$899$	16.2689	+	28.1785i	0.542597	+	0.939806i
$900$	0.400489	+	0.693668i	0.0133496	+	0.0231223i
$901$	13.3830	−	23.1800i	0.445852	−	0.772238i
$902$	−7.16414			−0.238540
$903$	−0.455588	+	0.789101i	−0.0151610	+	0.0262596i
$904$	−30.9654	+	53.6336i	−1.02989	+	1.78383i
$905$	7.29237			0.242406
$906$	22.0806	−	38.2447i	0.733579	−	1.27060i
$907$	−2.36356	−	4.09380i	−0.0784807	−	0.135932i	0.824114	−	0.566424i	$-0.191674\pi$
$907$	−2.36356	−	4.09380i	−0.0784807	−	0.135932i	−0.902595	+	0.430492i	$0.858340\pi$
$908$	−45.9662	−	79.6159i	−1.52544	−	2.64215i
$909$	11.1723			0.370561
$910$	−2.29628	+	1.57044i	−0.0761208	+	0.0520596i
$911$	30.5855			1.01334			0.506671	−	0.862139i	$-0.330876\pi$
$911$	30.5855			1.01334			0.506671	+	0.862139i	$0.330876\pi$
$912$	−6.26840	−	10.8572i	−0.207567	−	0.359517i
$913$	−7.68643	−	13.3133i	−0.254384	−	0.440605i
$914$	−15.1284	+	26.2032i	−0.500403	+	0.866724i
$915$	16.5041			0.545609
$916$	20.3337	−	35.2190i	0.671845	−	1.16367i
$917$	1.07321	−	1.85885i	0.0354404	−	0.0613845i
$918$	−6.28019			−0.207277
$919$	−5.14900	+	8.91834i	−0.169850	+	0.294189i	−0.938367	−	0.345641i	$-0.887662\pi$
$919$	−5.14900	+	8.91834i	−0.169850	+	0.294189i	0.768517	+	0.639829i	$0.220995\pi$
$920$	24.3127	+	42.1108i	0.801566	+	1.38835i
$921$	5.44176	+	9.42540i	0.179312	+	0.310578i
$922$	73.9121			2.43417
$923$	−4.28723	−	56.1204i	−0.141116	−	1.84723i
$924$	0.698084			0.0229653
$925$	−0.521546	−	0.903344i	−0.0171483	−	0.0297018i
$926$	−24.0961	−	41.7356i	−0.791845	−	1.37152i
$927$	−1.03434	+	1.79153i	−0.0339723	+	0.0588417i
$928$	67.7119			2.22275
$929$	−5.36066	+	9.28493i	−0.175877	+	0.304629i	−0.940465	−	0.339892i	$-0.889610\pi$
$929$	−5.36066	+	9.28493i	−0.175877	+	0.304629i	0.764587	+	0.644520i	$0.222943\pi$
$930$	−30.6667	+	53.1163i	−1.00560	+	1.74175i
$931$	−5.97115			−0.195697
$932$	57.4968	−	99.5875i	1.88337	−	3.26210i
$933$	−9.30895	−	16.1236i	−0.304761	−	0.527862i
$934$	−10.6165	−	18.3882i	−0.347381	−	0.601682i
$935$	−5.07391			−0.165935
$936$	2.57163	+	33.6631i	0.0840565	+	1.10031i
$937$	−53.2056			−1.73815			−0.869075	−	0.494680i	$-0.835285\pi$
$937$	−53.2056			−1.73815			−0.869075	+	0.494680i	$0.835285\pi$
$938$	−0.961070	−	1.66462i	−0.0313801	−	0.0543519i
$939$	11.7922	+	20.4247i	0.384825	+	0.666536i
$940$	−75.3780	+	130.558i	−2.45856	+	4.25835i
$941$	7.51750			0.245063			0.122532	−	0.992465i	$-0.460899\pi$
$941$	7.51750			0.245063			0.122532	+	0.992465i	$0.460899\pi$
$942$	−2.85165	+	4.93921i	−0.0929119	+	0.160928i
$943$	3.09704	−	5.36423i	0.100853	−	0.174683i
$944$	−83.0346			−2.70255
$945$	0.141491	−	0.245069i	0.00460269	−	0.00797210i
$946$	9.66984	+	16.7486i	0.314393	+	0.544545i
$947$	−4.85245	−	8.40469i	−0.157683	−	0.273116i	0.776349	−	0.630303i	$-0.217069\pi$
$947$	−4.85245	−	8.40469i	−0.157683	−	0.273116i	−0.934033	+	0.357187i	$0.883736\pi$
$948$	31.0014			1.00688
$949$	−23.1504	+	15.8328i	−0.751495	+	0.513953i
$950$	0.343626			0.0111487
$951$	−10.9827	−	19.0226i	−0.356139	−	0.616851i
$952$	1.38529	+	2.39940i	0.0448976	+	0.0777649i
$953$	5.67618	−	9.83142i	0.183869	−	0.318471i	−0.759326	−	0.650711i	$-0.774471\pi$
$953$	5.67618	−	9.83142i	0.183869	−	0.318471i	0.943195	+	0.332240i	$0.107804\pi$
$954$	31.6844			1.02582
$955$	7.44024	−	12.8869i	0.240761	−	0.417010i
$956$	40.5947	−	70.3121i	1.31293	−	2.27406i
$957$	−3.18636			−0.103000
$958$	−16.9056	+	29.2814i	−0.546195	+	0.946038i
$959$	0.819143	+	1.41880i	0.0264515	+	0.0458153i
$960$	31.5192	+	54.5929i	1.01728	+	1.76198i
$961$	73.2761			2.36375
$962$	−5.29932	−	69.3689i	−0.170857	−	2.23654i
$963$	13.3850			0.431326
$964$	73.0668	+	126.555i	2.35332	+	4.07608i
$965$	6.72045	+	11.6402i	0.216339	+	0.374710i
$966$	−0.412846	+	0.715071i	−0.0132831	+	0.0230070i
$967$	−53.1136			−1.70802			−0.854010	−	0.520257i	$-0.825836\pi$
$967$	−53.1136			−1.70802			−0.854010	+	0.520257i	$0.825836\pi$
$968$	4.68183	−	8.10916i	0.150480	−	0.260638i
$969$	−0.984714	+	1.70557i	−0.0316336	+	0.0547910i
$970$	−10.1165			−0.324822
$971$	−1.19222	+	2.06499i	−0.0382603	+	0.0662688i	−0.884521	−	0.466499i	$-0.845515\pi$
$971$	−1.19222	+	2.06499i	−0.0382603	+	0.0662688i	0.846261	+	0.532768i	$0.178848\pi$
$972$	−2.71711	−	4.70617i	−0.0871513	−	0.150950i
$973$	0.0866418	+	0.150068i	0.00277761	+	0.00481096i
$974$	−92.3991			−2.96066
$975$	−0.479145	−	0.229891i	−0.0153449	−	0.00736242i
$976$	−109.852			−3.51626
$977$	11.9525	+	20.7023i	0.382394	+	0.662327i	0.991404	−	0.130836i	$-0.0417662\pi$
$977$	11.9525	+	20.7023i	0.382394	+	0.662327i	−0.609010	+	0.793163i	$0.708433\pi$
$978$	16.4465	+	28.4862i	0.525902	+	0.910888i
$979$	3.32940	−	5.76670i	0.106408	−	0.184304i
$980$	83.5983			2.67045
$981$	6.83333	−	11.8357i	0.218172	−	0.377884i
$982$	23.8814	−	41.3638i	0.762086	−	1.31997i
$983$	24.3252			0.775853			0.387926	−	0.921690i	$-0.373191\pi$
$983$	24.3252			0.775853			0.387926	+	0.921690i	$0.373191\pi$
$984$	12.3016	−	21.3070i	0.392161	−	0.679243i
$985$	−25.5928	−	44.3280i	−0.815453	−	1.41241i
$986$	−10.0055	−	17.3300i	−0.318639	−	0.551899i
$987$	−1.61778			−0.0514946
$988$	15.1045	+	7.24705i	0.480537	+	0.230559i
$989$	−16.7210			−0.531696
$990$	−3.00314	−	5.20159i	−0.0954460	−	0.165317i
$991$	−1.64711	−	2.85288i	−0.0523221	−	0.0906246i	0.838678	−	0.544627i	$-0.183329\pi$
$991$	−1.64711	−	2.85288i	−0.0523221	−	0.0906246i	−0.891000	+	0.454003i	$0.849996\pi$
$992$	108.501	−	187.929i	3.44490	−	5.96674i
$993$	−3.72047			−0.118066
$994$	2.73383	−	4.73513i	0.0867117	−	0.150189i
$995$	−7.29615	+	12.6373i	−0.231304	+	0.400630i
$996$	83.5395			2.64705
$997$	−16.6359	+	28.8143i	−0.526866	+	0.912558i	0.472644	+	0.881253i	$0.343300\pi$
$997$	−16.6359	+	28.8143i	−0.526866	+	0.912558i	−0.999510	+	0.0313049i	$0.990034\pi$
$998$	5.36076	+	9.28511i	0.169692	+	0.293915i
$999$	3.53842	+	6.12872i	0.111951	+	0.193904i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.i.f.133.5	yes	10
13.3	even	3		5577.2.a.n.1.1		5
13.9	even	3	inner	429.2.i.f.100.5	✓	10
13.10	even	6		5577.2.a.w.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.i.f.100.5	✓	10	13.9	even	3	inner
429.2.i.f.133.5	yes	10	1.1	even	1	trivial
5577.2.a.n.1.1		5	13.3	even	3
5577.2.a.w.1.5		5	13.10	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36329 + 2.36128i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.71711 + 4.70617i) q^{4} -2.20286 q^{5} +(1.36329 - 2.36128i) q^{6} +(-0.0642304 + 0.111250i) q^{7} -9.36366 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.36329 + 2.36128i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.71711 + 4.70617i) q^{4} -2.20286 q^{5} +(1.36329 - 2.36128i) q^{6} +(-0.0642304 + 0.111250i) q^{7} -9.36366 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-3.00314 - 5.20159i) q^{10} +(-0.500000 - 0.866025i) q^{11} +5.43422 q^{12} +(-2.97611 + 2.03538i) q^{13} -0.350258 q^{14} +(1.10143 + 1.90774i) q^{15} +(-7.33114 - 12.6979i) q^{16} +(-1.15166 + 1.99474i) q^{17} -2.72658 q^{18} +(-0.427519 + 0.740484i) q^{19} +(5.98542 - 10.3670i) q^{20} +0.128461 q^{21} +(1.36329 - 2.36128i) q^{22} +(1.17869 + 2.04155i) q^{23} +(4.68183 + 8.10916i) q^{24} -0.147395 q^{25} +(-8.86341 - 4.25262i) q^{26} +1.00000 q^{27} +(-0.349042 - 0.604558i) q^{28} +(1.59318 + 2.75947i) q^{29} +(-3.00314 + 5.20159i) q^{30} +10.2116 q^{31} +(10.6253 - 18.4035i) q^{32} +(-0.500000 + 0.866025i) q^{33} -6.28019 q^{34} +(0.141491 - 0.245069i) q^{35} +(-2.71711 - 4.70617i) q^{36} +(3.53842 + 6.12872i) q^{37} -2.33132 q^{38} +(3.25075 + 1.55969i) q^{39} +20.6269 q^{40} +(-1.31376 - 2.27550i) q^{41} +(0.175129 + 0.303332i) q^{42} +(-3.54651 + 6.14274i) q^{43} +5.43422 q^{44} +(1.10143 - 1.90774i) q^{45} +(-3.21379 + 5.56645i) q^{46} -12.5936 q^{47} +(-7.33114 + 12.6979i) q^{48} +(3.49175 + 6.04789i) q^{49} +(-0.200942 - 0.348042i) q^{50} +2.30332 q^{51} +(-1.49245 - 19.5364i) q^{52} -11.6206 q^{53} +(1.36329 + 2.36128i) q^{54} +(1.10143 + 1.90774i) q^{55} +(0.601431 - 1.04171i) q^{56} +0.855037 q^{57} +(-4.34393 + 7.52390i) q^{58} +(2.83157 - 4.90442i) q^{59} -11.9708 q^{60} +(3.74606 - 6.48836i) q^{61} +(13.9213 + 24.1124i) q^{62} +(-0.0642304 - 0.111250i) q^{63} +28.6166 q^{64} +(6.55596 - 4.48367i) q^{65} -2.72658 q^{66} +(2.74389 + 4.75256i) q^{67} +(-6.25838 - 10.8398i) q^{68} +(1.17869 - 2.04155i) q^{69} +0.771571 q^{70} +(-7.80517 + 13.5190i) q^{71} +(4.68183 - 8.10916i) q^{72} +7.77876 q^{73} +(-9.64776 + 16.7104i) q^{74} +(0.0736977 + 0.127648i) q^{75} +(-2.32323 - 4.02395i) q^{76} +0.128461 q^{77} +(0.748827 + 9.80225i) q^{78} +5.70485 q^{79} +(16.1495 + 27.9718i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.58207 - 6.20433i) q^{82} +15.3729 q^{83} +(-0.349042 + 0.604558i) q^{84} +(2.53695 - 4.39413i) q^{85} -19.3397 q^{86} +(1.59318 - 2.75947i) q^{87} +(4.68183 + 8.10916i) q^{88} +(3.32940 + 5.76670i) q^{89} +6.00627 q^{90} +(-0.0352805 - 0.461826i) q^{91} -12.8105 q^{92} +(-5.10578 - 8.84348i) q^{93} +(-17.1687 - 29.7371i) q^{94} +(0.941765 - 1.63118i) q^{95} -21.2505 q^{96} +(0.842163 - 1.45867i) q^{97} +(-9.52052 + 16.4900i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} - 5 q^{3} - 6 q^{4} - 8 q^{5} + 4 q^{6} + 3 q^{7} - 18 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 - 5 * q^3 - 6 * q^4 - 8 * q^5 + 4 * q^6 + 3 * q^7 - 18 * q^8 - 5 * q^9	\( 10 q + 4 q^{2} - 5 q^{3} - 6 q^{4} - 8 q^{5} + 4 q^{6} + 3 q^{7} - 18 q^{8} - 5 q^{9} + 5 q^{10} - 5 q^{11} + 12 q^{12} + 5 q^{13} + 14 q^{14} + 4 q^{15} - 12 q^{16} - 9 q^{17} - 8 q^{18} + 9 q^{19} + 6 q^{20} - 6 q^{21} + 4 q^{22} + 9 q^{23} + 9 q^{24} + 2 q^{25} - 12 q^{26} + 10 q^{27} - q^{28} - 8 q^{29} + 5 q^{30} - 12 q^{31} + 27 q^{32} - 5 q^{33} - 14 q^{34} + 2 q^{35} - 6 q^{36} + 17 q^{37} - 2 q^{38} + 2 q^{39} + 46 q^{40} + 6 q^{41} - 7 q^{42} - 13 q^{43} + 12 q^{44} + 4 q^{45} - 6 q^{46} - 32 q^{47} - 12 q^{48} + 18 q^{49} - 8 q^{50} + 18 q^{51} + 7 q^{52} - 26 q^{53} + 4 q^{54} + 4 q^{55} - q^{56} - 18 q^{57} + 11 q^{58} + 8 q^{59} - 12 q^{60} - 4 q^{61} + 22 q^{62} + 3 q^{63} + 22 q^{64} + 26 q^{65} - 8 q^{66} + 5 q^{67} - 34 q^{68} + 9 q^{69} + 8 q^{70} + 19 q^{71} + 9 q^{72} - 4 q^{73} - 27 q^{74} - q^{75} - 6 q^{76} - 6 q^{77} - 3 q^{78} - 16 q^{79} + 32 q^{80} - 5 q^{81} - 16 q^{82} - 20 q^{83} - q^{84} + 21 q^{85} + 8 q^{86} - 8 q^{87} + 9 q^{88} + 32 q^{89} - 10 q^{90} - 17 q^{91} - 84 q^{92} + 6 q^{93} - 66 q^{94} - 11 q^{95} - 54 q^{96} - 5 q^{97} - 18 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - 5 * q^3 - 6 * q^4 - 8 * q^5 + 4 * q^6 + 3 * q^7 - 18 * q^8 - 5 * q^9 + 5 * q^10 - 5 * q^11 + 12 * q^12 + 5 * q^13 + 14 * q^14 + 4 * q^15 - 12 * q^16 - 9 * q^17 - 8 * q^18 + 9 * q^19 + 6 * q^20 - 6 * q^21 + 4 * q^22 + 9 * q^23 + 9 * q^24 + 2 * q^25 - 12 * q^26 + 10 * q^27 - q^28 - 8 * q^29 + 5 * q^30 - 12 * q^31 + 27 * q^32 - 5 * q^33 - 14 * q^34 + 2 * q^35 - 6 * q^36 + 17 * q^37 - 2 * q^38 + 2 * q^39 + 46 * q^40 + 6 * q^41 - 7 * q^42 - 13 * q^43 + 12 * q^44 + 4 * q^45 - 6 * q^46 - 32 * q^47 - 12 * q^48 + 18 * q^49 - 8 * q^50 + 18 * q^51 + 7 * q^52 - 26 * q^53 + 4 * q^54 + 4 * q^55 - q^56 - 18 * q^57 + 11 * q^58 + 8 * q^59 - 12 * q^60 - 4 * q^61 + 22 * q^62 + 3 * q^63 + 22 * q^64 + 26 * q^65 - 8 * q^66 + 5 * q^67 - 34 * q^68 + 9 * q^69 + 8 * q^70 + 19 * q^71 + 9 * q^72 - 4 * q^73 - 27 * q^74 - q^75 - 6 * q^76 - 6 * q^77 - 3 * q^78 - 16 * q^79 + 32 * q^80 - 5 * q^81 - 16 * q^82 - 20 * q^83 - q^84 + 21 * q^85 + 8 * q^86 - 8 * q^87 + 9 * q^88 + 32 * q^89 - 10 * q^90 - 17 * q^91 - 84 * q^92 + 6 * q^93 - 66 * q^94 - 11 * q^95 - 54 * q^96 - 5 * q^97 - 18 * q^98 + 10 * q^99

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