LMFDB - Embedded newform 527.2.h.c.35.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [527,2,Mod(35,527)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(527, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("527.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 527 = 17 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	527.h (of order $5$, degree $4$, 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:	$4.20811618652$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			35.5
Character	$\chi$	$=$	527.35
Dual form			527.2.h.c.256.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.630601 - 1.94079i) q^{2} +(0.0988673 - 0.304282i) q^{3} +(-1.75098 + 1.27216i) q^{4} +1.33965 q^{5} -0.652894 q^{6} +(-3.74126 + 2.71818i) q^{7} +(0.271294 + 0.197106i) q^{8} +(2.34424 + 1.70319i) q^{9} +O(q^{10})$	\(q+(-0.630601 - 1.94079i) q^{2} +(0.0988673 - 0.304282i) q^{3} +(-1.75098 + 1.27216i) q^{4} +1.33965 q^{5} -0.652894 q^{6} +(-3.74126 + 2.71818i) q^{7} +(0.271294 + 0.197106i) q^{8} +(2.34424 + 1.70319i) q^{9} +(-0.844788 - 2.59999i) q^{10} +(-4.35268 + 3.16241i) q^{11} +(0.213981 + 0.658567i) q^{12} +(0.259604 - 0.798979i) q^{13} +(7.63467 + 5.54691i) q^{14} +(0.132448 - 0.407633i) q^{15} +(-1.12616 + 3.46598i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(1.82725 - 5.62371i) q^{18} +(2.12491 + 6.53979i) q^{19} +(-2.34571 + 1.70425i) q^{20} +(0.457207 + 1.40714i) q^{21} +(8.88238 + 6.45343i) q^{22} +(-5.76709 - 4.19004i) q^{23} +(0.0867981 - 0.0630625i) q^{24} -3.20533 q^{25} -1.71436 q^{26} +(1.52653 - 1.10909i) q^{27} +(3.09290 - 9.51896i) q^{28} +(1.86081 + 5.72697i) q^{29} -0.874653 q^{30} +(-5.20791 + 1.96918i) q^{31} +8.10757 q^{32} +(0.531927 + 1.63710i) q^{33} +(-0.630601 + 1.94079i) q^{34} +(-5.01200 + 3.64143i) q^{35} -6.27144 q^{36} +2.18292 q^{37} +(11.3524 - 8.24800i) q^{38} +(-0.217449 - 0.157986i) q^{39} +(0.363440 + 0.264055i) q^{40} +(-1.88238 - 5.79338i) q^{41} +(2.44265 - 1.77469i) q^{42} +(1.99125 + 6.12843i) q^{43} +(3.59836 - 11.0746i) q^{44} +(3.14047 + 2.28168i) q^{45} +(-4.49525 + 13.8350i) q^{46} +(3.93144 - 12.0997i) q^{47} +(0.943294 + 0.685343i) q^{48} +(4.44538 - 13.6815i) q^{49} +(2.02128 + 6.22087i) q^{50} +(-0.258838 + 0.188057i) q^{51} +(0.561868 + 1.72925i) q^{52} +(6.60462 + 4.79853i) q^{53} +(-3.11515 - 2.26329i) q^{54} +(-5.83109 + 4.23654i) q^{55} -1.55075 q^{56} +2.20003 q^{57} +(9.94143 - 7.22287i) q^{58} +(1.11360 - 3.42729i) q^{59} +(0.286661 + 0.882252i) q^{60} -3.08496 q^{61} +(7.10588 + 8.86570i) q^{62} -13.4000 q^{63} +(-2.86031 - 8.80314i) q^{64} +(0.347780 - 1.07036i) q^{65} +(2.84184 - 2.06472i) q^{66} -5.48147 q^{67} +2.16433 q^{68} +(-1.84513 + 1.34057i) q^{69} +(10.2278 + 7.43095i) q^{70} +(-2.25993 - 1.64194i) q^{71} +(0.300268 + 0.924129i) q^{72} +(3.59861 - 2.61454i) q^{73} +(-1.37655 - 4.23659i) q^{74} +(-0.316902 + 0.975324i) q^{75} +(-12.0403 - 8.74781i) q^{76} +(7.68851 - 23.6628i) q^{77} +(-0.169494 + 0.521649i) q^{78} +(-4.14559 - 3.01194i) q^{79} +(-1.50867 + 4.64321i) q^{80} +(2.49971 + 7.69330i) q^{81} +(-10.0567 + 7.30662i) q^{82} +(2.11909 + 6.52188i) q^{83} +(-2.59067 - 1.88223i) q^{84} +(-1.08380 - 0.787429i) q^{85} +(10.6383 - 7.72919i) q^{86} +1.92659 q^{87} -1.80419 q^{88} +(-9.75515 + 7.08753i) q^{89} +(2.44789 - 7.53383i) q^{90} +(1.20053 + 3.69484i) q^{91} +15.4284 q^{92} +(0.0842946 + 1.77936i) q^{93} -25.9622 q^{94} +(2.84664 + 8.76107i) q^{95} +(0.801574 - 2.46699i) q^{96} +(-2.86572 + 2.08207i) q^{97} -29.3562 q^{98} -15.5899 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9}+O(q^{10}) $ 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9	\( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9} - 13 q^{10} - 4 q^{11} - 14 q^{12} - 14 q^{13} + 17 q^{14} - 9 q^{15} - 58 q^{16} - 24 q^{17} - 24 q^{18} - 6 q^{19} + 43 q^{20} + 26 q^{21} + 42 q^{22} - 11 q^{23} - 38 q^{24} + 126 q^{25} - 44 q^{26} - q^{27} + 31 q^{28} - 10 q^{29} - 70 q^{30} + 21 q^{31} + 28 q^{32} - 36 q^{33} - 2 q^{34} + 2 q^{35} + 160 q^{36} + 54 q^{37} + 15 q^{38} - 10 q^{39} - 29 q^{40} - 14 q^{41} - 3 q^{42} + 6 q^{43} - 5 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 93 q^{48} - 72 q^{49} + 108 q^{50} + q^{51} + 13 q^{52} - 30 q^{53} - 63 q^{54} - 12 q^{55} + 66 q^{56} - 62 q^{57} + 29 q^{58} + 8 q^{59} - 86 q^{60} - 14 q^{61} - 34 q^{62} + 86 q^{63} - 122 q^{64} + 13 q^{65} - 40 q^{66} + 126 q^{67} + 120 q^{68} - 34 q^{69} - 38 q^{70} - 39 q^{71} - 51 q^{72} - 60 q^{73} - 111 q^{74} - 41 q^{75} + 64 q^{76} - 26 q^{77} - 99 q^{78} - 33 q^{79} - 91 q^{80} + 81 q^{81} - 88 q^{82} + 22 q^{83} + 160 q^{84} - 4 q^{85} + 35 q^{86} + 70 q^{87} - 120 q^{88} + 101 q^{89} + 125 q^{90} - 13 q^{91} - 98 q^{92} + 47 q^{93} - 8 q^{94} - 64 q^{95} + 208 q^{96} + 16 q^{97} + 8 q^{98} + 280 q^{99}+O(q^{100}) \) 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9 - 13 * q^10 - 4 * q^11 - 14 * q^12 - 14 * q^13 + 17 * q^14 - 9 * q^15 - 58 * q^16 - 24 * q^17 - 24 * q^18 - 6 * q^19 + 43 * q^20 + 26 * q^21 + 42 * q^22 - 11 * q^23 - 38 * q^24 + 126 * q^25 - 44 * q^26 - q^27 + 31 * q^28 - 10 * q^29 - 70 * q^30 + 21 * q^31 + 28 * q^32 - 36 * q^33 - 2 * q^34 + 2 * q^35 + 160 * q^36 + 54 * q^37 + 15 * q^38 - 10 * q^39 - 29 * q^40 - 14 * q^41 - 3 * q^42 + 6 * q^43 - 5 * q^44 - q^45 - 17 * q^46 - 14 * q^47 - 93 * q^48 - 72 * q^49 + 108 * q^50 + q^51 + 13 * q^52 - 30 * q^53 - 63 * q^54 - 12 * q^55 + 66 * q^56 - 62 * q^57 + 29 * q^58 + 8 * q^59 - 86 * q^60 - 14 * q^61 - 34 * q^62 + 86 * q^63 - 122 * q^64 + 13 * q^65 - 40 * q^66 + 126 * q^67 + 120 * q^68 - 34 * q^69 - 38 * q^70 - 39 * q^71 - 51 * q^72 - 60 * q^73 - 111 * q^74 - 41 * q^75 + 64 * q^76 - 26 * q^77 - 99 * q^78 - 33 * q^79 - 91 * q^80 + 81 * q^81 - 88 * q^82 + 22 * q^83 + 160 * q^84 - 4 * q^85 + 35 * q^86 + 70 * q^87 - 120 * q^88 + 101 * q^89 + 125 * q^90 - 13 * q^91 - 98 * q^92 + 47 * q^93 - 8 * q^94 - 64 * q^95 + 208 * q^96 + 16 * q^97 + 8 * q^98 + 280 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/527\mathbb{Z}\right)^\times$.

$n$	$156$	$375$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.630601	−	1.94079i	−0.445902	−	1.37235i	−0.881491	−	0.472201i	$-0.843460\pi$
$2$	−0.630601	−	1.94079i	−0.445902	−	1.37235i	0.435589	−	0.900146i	$-0.356540\pi$
$3$	0.0988673	−	0.304282i	0.0570811	−	0.175677i	−0.918451	−	0.395535i	$-0.870559\pi$
$3$	0.0988673	−	0.304282i	0.0570811	−	0.175677i	0.975532	+	0.219857i	$0.0705592\pi$
$4$	−1.75098	+	1.27216i	−0.875489	+	0.636080i
$5$	1.33965			0.599112			0.299556	−	0.954079i	$-0.403161\pi$
$5$	1.33965			0.599112			0.299556	+	0.954079i	$0.403161\pi$
$6$	−0.652894			−0.266543
$7$	−3.74126	+	2.71818i	−1.41406	+	1.02738i	−0.421348	+	0.906899i	$0.638443\pi$
$7$	−3.74126	+	2.71818i	−1.41406	+	1.02738i	−0.992716	+	0.120478i	$0.961557\pi$
$8$	0.271294	+	0.197106i	0.0959168	+	0.0696876i
$9$	2.34424	+	1.70319i	0.781413	+	0.567730i
$10$	−0.844788	−	2.59999i	−0.267145	−	0.822189i
$11$	−4.35268	+	3.16241i	−1.31238	+	0.953502i	−0.312389	+	0.949954i	$0.601129\pi$
$11$	−4.35268	+	3.16241i	−1.31238	+	0.953502i	−0.999994	+	0.00354779i	$0.998871\pi$
$12$	0.213981	+	0.658567i	0.0617711	+	0.190112i
$13$	0.259604	−	0.798979i	0.0720012	−	0.221597i	−0.908580	−	0.417711i	$-0.862832\pi$
$13$	0.259604	−	0.798979i	0.0720012	−	0.221597i	0.980581	+	0.196114i	$0.0628324\pi$
$14$	7.63467	+	5.54691i	2.04045	+	1.48248i
$15$	0.132448	−	0.407633i	0.0341979	−	0.105250i
$16$	−1.12616	+	3.46598i	−0.281541	+	0.866494i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$18$	1.82725	−	5.62371i	0.430688	−	1.32552i
$19$	2.12491	+	6.53979i	0.487487	+	1.50033i	0.828346	+	0.560217i	$0.189282\pi$
$19$	2.12491	+	6.53979i	0.487487	+	1.50033i	−0.340858	+	0.940115i	$0.610718\pi$
$20$	−2.34571	+	1.70425i	−0.524516	+	0.381083i
$21$	0.457207	+	1.40714i	0.0997708	+	0.307063i
$22$	8.88238	+	6.45343i	1.89373	+	1.37588i
$23$	−5.76709	−	4.19004i	−1.20252	−	0.873683i	−0.207991	−	0.978131i	$-0.566693\pi$
$23$	−5.76709	−	4.19004i	−1.20252	−	0.873683i	−0.994530	+	0.104448i	$0.966693\pi$
$24$	0.0867981	−	0.0630625i	0.0177176	−	0.0128726i
$25$	−3.20533			−0.641065
$26$	−1.71436			−0.336213
$27$	1.52653	−	1.10909i	0.293781	−	0.213445i
$28$	3.09290	−	9.51896i	0.584503	−	1.79891i
$29$	1.86081	+	5.72697i	0.345543	+	1.06347i	0.961293	+	0.275530i	$0.0888533\pi$
$29$	1.86081	+	5.72697i	0.345543	+	1.06347i	−0.615750	+	0.787942i	$0.711147\pi$
$30$	−0.874653			−0.159689
$31$	−5.20791	+	1.96918i	−0.935368	+	0.353675i
$31$	−5.20791	+	1.96918i	−0.935368	+	0.353675i
$32$	8.10757			1.43323
$33$	0.531927	+	1.63710i	0.0925966	+	0.284983i
$34$	−0.630601	+	1.94079i	−0.108147	+	0.332843i
$35$	−5.01200	+	3.64143i	−0.847182	+	0.615514i
$36$	−6.27144			−1.04524
$37$	2.18292			0.358870			0.179435	−	0.983770i	$-0.442573\pi$
$37$	2.18292			0.358870			0.179435	+	0.983770i	$0.442573\pi$
$38$	11.3524	−	8.24800i	1.84160	−	1.33800i
$39$	−0.217449	−	0.157986i	−0.0348197	−	0.0252980i
$40$	0.363440	+	0.264055i	0.0574649	+	0.0417507i
$41$	−1.88238	−	5.79338i	−0.293979	−	0.904774i	−0.983563	−	0.180568i	$-0.942206\pi$
$41$	−1.88238	−	5.79338i	−0.293979	−	0.904774i	0.689584	−	0.724206i	$-0.257794\pi$
$42$	2.44265	−	1.77469i	0.376909	−	0.273840i
$43$	1.99125	+	6.12843i	0.303662	+	0.934577i	0.980173	+	0.198144i	$0.0634913\pi$
$43$	1.99125	+	6.12843i	0.303662	+	0.934577i	−0.676511	+	0.736433i	$0.736509\pi$
$44$	3.59836	−	11.0746i	0.542473	−	1.66956i
$45$	3.14047	+	2.28168i	0.468154	+	0.340133i
$46$	−4.49525	+	13.8350i	−0.662789	+	2.03985i
$47$	3.93144	−	12.0997i	0.573459	−	1.76492i	−0.0679091	−	0.997692i	$-0.521633\pi$
$47$	3.93144	−	12.0997i	0.573459	−	1.76492i	0.641368	−	0.767233i	$-0.278367\pi$
$48$	0.943294	+	0.685343i	0.136153	+	0.0989208i
$49$	4.44538	−	13.6815i	0.635055	−	1.95450i
$50$	2.02128	+	6.22087i	0.285852	+	0.879763i
$51$	−0.258838	+	0.188057i	−0.0362446	+	0.0263332i
$52$	0.561868	+	1.72925i	0.0779171	+	0.239804i
$53$	6.60462	+	4.79853i	0.907214	+	0.659129i	0.940309	−	0.340323i	$-0.110536\pi$
$53$	6.60462	+	4.79853i	0.907214	+	0.659129i	−0.0330948	+	0.999452i	$0.510536\pi$
$54$	−3.11515	−	2.26329i	−0.423918	−	0.307994i
$55$	−5.83109	+	4.23654i	−0.786264	+	0.571254i
$56$	−1.55075			−0.207228
$57$	2.20003			0.291401
$58$	9.94143	−	7.22287i	1.30537	−	0.948409i
$59$	1.11360	−	3.42729i	0.144978	−	0.446196i	−0.852030	−	0.523492i	$-0.824629\pi$
$59$	1.11360	−	3.42729i	0.144978	−	0.446196i	0.997008	+	0.0772967i	$0.0246289\pi$
$60$	0.286661	+	0.882252i	0.0370078	+	0.113898i
$61$	−3.08496			−0.394989			−0.197494	−	0.980304i	$-0.563280\pi$
$61$	−3.08496			−0.394989			−0.197494	+	0.980304i	$0.563280\pi$
$62$	7.10588	+	8.86570i	0.902448	+	1.12594i
$63$	−13.4000			−1.68824
$64$	−2.86031	−	8.80314i	−0.357539	−	1.10039i
$65$	0.347780	−	1.07036i	0.0431368	−	0.132761i
$66$	2.84184	−	2.06472i	0.349806	−	0.254149i
$67$	−5.48147			−0.669668			−0.334834	−	0.942277i	$-0.608680\pi$
$67$	−5.48147			−0.669668			−0.334834	+	0.942277i	$0.608680\pi$
$68$	2.16433			0.262463
$69$	−1.84513	+	1.34057i	−0.222128	+	0.161385i
$70$	10.2278	+	7.43095i	1.22246	+	0.888168i
$71$	−2.25993	−	1.64194i	−0.268205	−	0.194862i	0.445552	−	0.895256i	$-0.353008\pi$
$71$	−2.25993	−	1.64194i	−0.268205	−	0.194862i	−0.713756	+	0.700394i	$0.753008\pi$
$72$	0.300268	+	0.924129i	0.0353869	+	0.108910i
$73$	3.59861	−	2.61454i	0.421185	−	0.306009i	−0.356929	−	0.934131i	$-0.616176\pi$
$73$	3.59861	−	2.61454i	0.421185	−	0.306009i	0.778115	+	0.628122i	$0.216176\pi$
$74$	−1.37655	−	4.23659i	−0.160021	−	0.492494i
$75$	−0.316902	+	0.975324i	−0.0365927	+	0.112621i
$76$	−12.0403	−	8.74781i	−1.38112	−	1.00344i
$77$	7.68851	−	23.6628i	0.876187	−	2.69662i
$78$	−0.169494	+	0.521649i	−0.0191914	+	0.0590651i
$79$	−4.14559	−	3.01194i	−0.466415	−	0.338870i	0.329628	−	0.944111i	$-0.393077\pi$
$79$	−4.14559	−	3.01194i	−0.466415	−	0.338870i	−0.796042	+	0.605241i	$0.793077\pi$
$80$	−1.50867	+	4.64321i	−0.168674	+	0.519127i
$81$	2.49971	+	7.69330i	0.277745	+	0.854811i
$82$	−10.0567	+	7.30662i	−1.11058	+	0.806881i
$83$	2.11909	+	6.52188i	0.232600	+	0.715870i	0.997431	+	0.0716382i	$0.0228227\pi$
$83$	2.11909	+	6.52188i	0.232600	+	0.715870i	−0.764831	+	0.644232i	$0.777177\pi$
$84$	−2.59067	−	1.88223i	−0.282665	−	0.205368i
$85$	−1.08380	−	0.787429i	−0.117555	−	0.0854087i
$86$	10.6383	−	7.72919i	1.14716	−	0.833460i
$87$	1.92659			0.206552
$88$	−1.80419			−0.192327
$89$	−9.75515	+	7.08753i	−1.03404	+	0.751277i	−0.969114	−	0.246613i	$-0.920682\pi$
$89$	−9.75515	+	7.08753i	−1.03404	+	0.751277i	−0.0649299	+	0.997890i	$0.520682\pi$
$90$	2.44789	−	7.53383i	0.258030	−	0.794135i
$91$	1.20053	+	3.69484i	0.125849	+	0.387324i
$92$	15.4284			1.60853
$93$	0.0842946	+	1.77936i	0.00874094	+	0.184511i
$94$	−25.9622			−2.67780
$95$	2.84664	+	8.76107i	0.292059	+	0.898867i
$96$	0.801574	−	2.46699i	0.0818103	−	0.251786i
$97$	−2.86572	+	2.08207i	−0.290970	+	0.211402i	−0.723688	−	0.690127i	$-0.757555\pi$
$97$	−2.86572	+	2.08207i	−0.290970	+	0.211402i	0.432718	+	0.901529i	$0.357555\pi$
$98$	−29.3562			−2.96542
$99$	−15.5899			−1.56684
$100$	5.61245	−	4.07769i	0.561245	−	0.407769i
$101$	13.9959	+	10.1686i	1.39265	+	1.01182i	0.995569	+	0.0940330i	$0.0299759\pi$
$101$	13.9959	+	10.1686i	1.39265	+	1.01182i	0.397078	+	0.917785i	$0.370024\pi$
$102$	0.528203	+	0.383762i	0.0522998	+	0.0379981i
$103$	−0.470588	−	1.44832i	−0.0463684	−	0.142707i	0.925192	−	0.379500i	$-0.123904\pi$
$103$	−0.470588	−	1.44832i	−0.0463684	−	0.142707i	−0.971560	+	0.236792i	$0.923904\pi$
$104$	0.227913	−	0.165588i	0.0223487	−	0.0162373i
$105$	0.612500	+	1.88508i	0.0597739	+	0.183965i
$106$	5.14807	−	15.8441i	0.500025	−	1.53892i
$107$	8.27123	+	6.00940i	0.799610	+	0.580951i	0.910800	−	0.412849i	$-0.135466\pi$
$107$	8.27123	+	6.00940i	0.799610	+	0.580951i	−0.111190	+	0.993799i	$0.535466\pi$
$108$	−1.26198	+	3.88399i	−0.121434	+	0.373737i
$109$	0.959375	−	2.95265i	0.0918915	−	0.282813i	−0.894540	−	0.446989i	$-0.852496\pi$
$109$	0.959375	−	2.95265i	0.0918915	−	0.282813i	0.986431	+	0.164176i	$0.0524964\pi$
$110$	11.8993	+	8.64536i	1.13456	+	0.824303i
$111$	0.215820	−	0.664224i	0.0204847	−	0.0630454i
$112$	−5.20789	−	16.0282i	−0.492099	−	1.51453i
$113$	−11.7139	+	8.51062i	−1.10195	+	0.800612i	−0.981377	−	0.192092i	$-0.938473\pi$
$113$	−11.7139	+	8.51062i	−1.10195	+	0.800612i	−0.120571	+	0.992705i	$0.538473\pi$
$114$	−1.38734	−	4.26979i	−0.129936	−	0.399903i
$115$	−7.72591	−	5.61320i	−0.720445	−	0.523434i
$116$	−10.5438	−	7.66055i	−0.978972	−	0.711265i
$117$	1.96939	−	1.43084i	0.182070	−	0.132281i
$118$	−7.35390			−0.676981
$119$	4.62445			0.423923
$120$	0.116279	−	0.0844820i	0.0106148	−	0.00771211i
$121$	5.54582	−	17.0683i	0.504166	−	1.55166i
$122$	1.94538	+	5.98726i	0.176126	+	0.542061i
$123$	−1.94893			−0.175729
$124$	6.61382	−	10.0733i	0.593939	−	0.904608i
$125$	−10.9923			−0.983181
$126$	8.45005	+	26.0066i	0.752790	+	2.31685i
$127$	−4.57480	+	14.0798i	−0.405948	+	1.24938i	0.514153	+	0.857698i	$0.328106\pi$
$127$	−4.57480	+	14.0798i	−0.405948	+	1.24938i	−0.920101	+	0.391681i	$0.871894\pi$
$128$	−2.16302	+	1.57153i	−0.191186	+	0.138905i
$129$	2.06164			0.181517
$130$	−2.29665			−0.201429
$131$	6.77349	−	4.92123i	0.591802	−	0.429969i	−0.251157	−	0.967946i	$-0.580811\pi$
$131$	6.77349	−	4.92123i	0.591802	−	0.429969i	0.842960	+	0.537977i	$0.180811\pi$
$132$	−3.01405	−	2.18983i	−0.262339	−	0.190601i
$133$	−25.7262	−	18.6912i	−2.23075	−	1.62073i
$134$	3.45662	+	10.6384i	0.298606	+	0.919016i
$135$	2.04503	−	1.48580i	0.176008	−	0.127877i
$136$	−0.103625	−	0.318925i	−0.00888577	−	0.0273476i
$137$	−4.54958	+	14.0022i	−0.388697	+	1.19629i	0.545065	+	0.838394i	$0.316505\pi$
$137$	−4.54958	+	14.0022i	−0.388697	+	1.19629i	−0.933762	+	0.357893i	$0.883495\pi$
$138$	3.76530	+	2.73565i	0.320524	+	0.232874i
$139$	−1.52011	+	4.67843i	−0.128934	+	0.396819i	−0.994597	−	0.103808i	$-0.966897\pi$
$139$	−1.52011	+	4.67843i	−0.128934	+	0.396819i	0.865663	+	0.500627i	$0.166897\pi$
$140$	4.14342	−	12.7521i	0.350183	−	1.07775i
$141$	−3.29304	−	2.39253i	−0.277324	−	0.201488i
$142$	−1.76154	+	5.42146i	−0.147825	+	0.454959i
$143$	1.39672	+	4.29867i	0.116800	+	0.359473i
$144$	−8.54321	+	6.20700i	−0.711934	+	0.517250i
$145$	2.49284	+	7.67216i	0.207019	+	0.637138i
$146$	−7.34356	−	5.33541i	−0.607758	−	0.441562i
$147$	−3.72353	−	2.70530i	−0.307112	−	0.223130i
$148$	−3.82224	+	2.77702i	−0.314187	+	0.228270i
$149$	−16.8716			−1.38218			−0.691089	−	0.722770i	$-0.742869\pi$
$149$	−16.8716			−1.38218			−0.691089	+	0.722770i	$0.742869\pi$
$150$	2.09274			0.170871
$151$	−11.2018	+	8.13861i	−0.911593	+	0.662311i	−0.941417	−	0.337244i	$-0.890505\pi$
$151$	−11.2018	+	8.13861i	−0.911593	+	0.662311i	0.0298244	+	0.999555i	$0.490505\pi$
$152$	−0.712561	+	2.19304i	−0.0577963	+	0.177879i
$153$	−0.895419	−	2.75582i	−0.0723904	−	0.222795i
$154$	−50.7729			−4.09140
$155$	−6.97680	+	2.63802i	−0.560390	+	0.211891i
$156$	0.581731			0.0465758
$157$	0.156881	+	0.482829i	0.0125204	+	0.0385339i	0.957122	−	0.289687i	$-0.0935511\pi$
$157$	0.156881	+	0.482829i	0.0125204	+	0.0385339i	−0.944601	+	0.328221i	$0.893551\pi$
$158$	−3.23134	+	9.94505i	−0.257072	+	0.791186i
$159$	2.11309	−	1.53525i	0.167579	−	0.121753i
$160$	10.8613			0.858665
$161$	32.9655			2.59804
$162$	13.3548	−	9.70281i	1.04925	−	0.762325i
$163$	−0.940247	−	0.683129i	−0.0736458	−	0.0535068i	0.550353	−	0.834932i	$-0.314493\pi$
$163$	−0.940247	−	0.683129i	−0.0736458	−	0.0535068i	−0.623999	+	0.781425i	$0.714493\pi$
$164$	10.6661	+	7.74938i	0.832883	+	0.605125i
$165$	0.712599	+	2.19315i	0.0554757	+	0.170737i
$166$	11.3213	−	8.22541i	0.878704	−	0.638416i
$167$	1.98472	+	6.10833i	0.153582	+	0.472677i	0.998014	−	0.0629851i	$-0.0200621\pi$
$167$	1.98472	+	6.10833i	0.153582	+	0.472677i	−0.844432	+	0.535662i	$0.820062\pi$
$168$	−0.153319	+	0.471866i	−0.0118288	+	0.0364053i
$169$	9.94625	+	7.22637i	0.765096	+	0.555875i
$170$	−0.844788	+	2.59999i	−0.0647923	+	0.199410i
$171$	−6.15721	+	18.9500i	−0.470854	+	1.44914i
$172$	−11.2830	−	8.19756i	−0.860318	−	0.625058i
$173$	3.58507	−	11.0337i	0.272568	−	0.838878i	−0.717285	−	0.696780i	$-0.754615\pi$
$173$	3.58507	−	11.0337i	0.272568	−	0.838878i	0.989853	−	0.142098i	$-0.0453848\pi$
$174$	−1.21491	−	3.73911i	−0.0921020	−	0.283461i
$175$	11.9920	−	8.71267i	0.906507	−	0.658616i
$176$	−6.05900	−	18.6477i	−0.456714	−	1.40562i
$177$	−0.932767	−	0.677695i	−0.0701111	−	0.0509387i
$178$	19.9070	+	14.4633i	1.49209	+	1.08407i
$179$	11.7783	−	8.55741i	0.880349	−	0.639611i	−0.0529948	−	0.998595i	$-0.516877\pi$
$179$	11.7783	−	8.55741i	0.880349	−	0.639611i	0.933344	+	0.358984i	$0.116877\pi$
$180$	−8.40156			−0.626215
$181$	−15.1790			−1.12825			−0.564125	−	0.825690i	$-0.690786\pi$
$181$	−15.1790			−1.12825			−0.564125	+	0.825690i	$0.690786\pi$
$182$	6.41386	−	4.65994i	0.475427	−	0.345418i
$183$	−0.305002	+	0.938699i	−0.0225464	+	0.0693906i
$184$	−0.738692	−	2.27346i	−0.0544571	−	0.167602i
$185$	2.92436			0.215003
$186$	3.40021	−	1.28567i	0.249316	−	0.0942696i
$187$	5.38021			0.393440
$188$	8.50891	+	26.1877i	0.620576	+	1.90994i
$189$	−2.69644	+	8.29880i	−0.196137	+	0.603649i
$190$	15.2083	−	11.0495i	1.10333	−	0.801613i
$191$	25.7848			1.86572			0.932860	−	0.360240i	$-0.117305\pi$
$191$	25.7848			1.86572			0.932860	+	0.360240i	$0.117305\pi$
$192$	−2.96143			−0.213723
$193$	0.482974	−	0.350901i	0.0347652	−	0.0252584i	−0.570267	−	0.821459i	$-0.693160\pi$
$193$	0.482974	−	0.350901i	0.0347652	−	0.0252584i	0.605032	+	0.796201i	$0.293160\pi$
$194$	5.84799	+	4.24881i	0.419861	+	0.305047i
$195$	−0.291306	−	0.211646i	−0.0208609	−	0.0151563i
$196$	9.62126	+	29.6112i	0.687233	+	2.11509i
$197$	−3.58540	+	2.60495i	−0.255449	+	0.185595i	−0.708138	−	0.706074i	$-0.750465\pi$
$197$	−3.58540	+	2.60495i	−0.255449	+	0.185595i	0.452689	+	0.891668i	$0.350465\pi$
$198$	9.83101	+	30.2567i	0.698659	+	2.15025i
$199$	2.91962	−	8.98567i	0.206967	−	0.636978i	−0.792660	−	0.609663i	$-0.791305\pi$
$199$	2.91962	−	8.98567i	0.206967	−	0.636978i	0.999627	−	0.0273141i	$-0.00869542\pi$
$200$	−0.869584	−	0.631790i	−0.0614889	−	0.0446743i
$201$	−0.541938	+	1.66791i	−0.0382254	+	0.117646i
$202$	10.9094	−	33.5755i	0.767580	−	2.36237i
$203$	−22.5287	−	16.3681i	−1.58121	−	1.14881i
$204$	0.213981	−	0.658567i	0.0149817	−	0.0461089i
$205$	−2.52174	−	7.76113i	−0.176126	−	0.542061i
$206$	−2.51413	+	1.82662i	−0.175168	+	0.127267i
$207$	−6.38301	−	19.6449i	−0.443650	−	1.36541i
$208$	2.47688	+	1.79956i	0.171741	+	0.124777i
$209$	−29.9306	−	21.7458i	−2.07034	−	1.50419i
$210$	3.27230	−	2.37747i	0.225810	−	0.164061i
$211$	18.8987			1.30104			0.650520	−	0.759490i	$-0.274551\pi$
$211$	18.8987			1.30104			0.650520	+	0.759490i	$0.274551\pi$
$212$	−17.6690			−1.21351
$213$	−0.723046	+	0.525324i	−0.0495423	+	0.0359946i
$214$	6.44714	−	19.8423i	0.440718	−	1.35639i
$215$	2.66758	+	8.20998i	0.181928	+	0.559916i
$216$	0.632748			0.0430530
$217$	14.1316	−	21.5233i	0.959312	−	1.46110i
$218$	−6.33547			−0.429092
$219$	−0.439774	−	1.35349i	−0.0297172	−	0.0914601i
$220$	4.82056	−	14.8362i	0.325002	−	1.00025i
$221$	−0.679652	+	0.493796i	−0.0457183	+	0.0332163i
$222$	−1.42522			−0.0956542
$223$	−3.18222			−0.213097			−0.106549	−	0.994307i	$-0.533980\pi$
$223$	−3.18222			−0.213097			−0.106549	+	0.994307i	$0.533980\pi$
$224$	−30.3325	+	22.0379i	−2.02668	+	1.47247i
$225$	−7.51404	−	5.45927i	−0.500936	−	0.363952i
$226$	23.9041	+	17.3674i	1.59008	+	1.15526i
$227$	−4.85617	−	14.9457i	−0.322315	−	0.991984i	−0.972638	−	0.232326i	$-0.925366\pi$
$227$	−4.85617	−	14.9457i	−0.322315	−	0.991984i	0.650323	−	0.759658i	$-0.274634\pi$
$228$	−3.85220	+	2.79879i	−0.255118	+	0.185354i
$229$	−5.13193	−	15.7945i	−0.339128	−	1.04373i	−0.964653	−	0.263524i	$-0.915115\pi$
$229$	−5.13193	−	15.7945i	−0.339128	−	1.04373i	0.625525	−	0.780204i	$-0.284885\pi$
$230$	−6.02208	+	18.5341i	−0.397084	+	1.22210i
$231$	−6.44003	−	4.67895i	−0.423723	−	0.307852i
$232$	−0.623998	+	1.92047i	−0.0409675	+	0.126085i
$233$	0.0880054	−	0.270853i	0.00576543	−	0.0177442i	−0.948132	−	0.317876i	$-0.897031\pi$
$233$	0.0880054	−	0.270853i	0.00576543	−	0.0177442i	0.953898	+	0.300131i	$0.0970306\pi$
$234$	−4.01886	−	2.91987i	−0.262721	−	0.190878i
$235$	5.26677	−	16.2094i	0.343566	−	1.05739i
$236$	2.41018	+	7.41779i	0.156890	+	0.482857i
$237$	−1.32634	+	0.963646i	−0.0861553	+	0.0625955i
$238$	−2.91619	−	8.97510i	−0.189028	−	0.581769i
$239$	14.5540	+	10.5741i	0.941418	+	0.683980i	0.948762	−	0.315993i	$-0.102338\pi$
$239$	14.5540	+	10.5741i	0.941418	+	0.683980i	−0.00734349	+	0.999973i	$0.502338\pi$
$240$	1.26369	+	0.918124i	0.0815707	+	0.0592646i
$241$	−0.959307	+	0.696978i	−0.0617944	+	0.0448963i	−0.618254	−	0.785979i	$-0.712160\pi$
$241$	−0.959307	+	0.696978i	−0.0617944	+	0.0448963i	0.556459	+	0.830875i	$0.312160\pi$
$242$	−36.6232			−2.35423
$243$	8.24877			0.529159
$244$	5.40169	−	3.92456i	0.345808	−	0.251244i
$245$	5.95528	−	18.3285i	0.380469	−	1.17096i
$246$	1.22900	+	3.78246i	0.0783580	+	0.241161i
$247$	5.77679			0.367569
$248$	−1.80101	−	0.492286i	−0.114364	−	0.0312602i
$249$	2.19400			0.139039
$250$	6.93176	+	21.3338i	0.438403	+	1.34927i
$251$	−3.81270	+	11.7343i	−0.240655	+	0.740661i	0.755665	+	0.654958i	$0.227314\pi$
$251$	−3.81270	+	11.7343i	−0.240655	+	0.740661i	−0.996321	+	0.0857030i	$0.972686\pi$
$252$	23.4631	−	17.0469i	1.47803	−	1.07386i
$253$	38.3529			2.41123
$254$	30.2108			1.89559
$255$	−0.346754	+	0.251931i	−0.0217146	+	0.0157765i
$256$	−10.5628	−	7.67432i	−0.660174	−	0.479645i
$257$	6.23332	+	4.52877i	0.388824	+	0.282497i	0.764973	−	0.644062i	$-0.222752\pi$
$257$	6.23332	+	4.52877i	0.388824	+	0.282497i	−0.376150	+	0.926559i	$0.622752\pi$
$258$	−1.30007	−	4.00122i	−0.0809391	−	0.249105i
$259$	−8.16687	+	5.93358i	−0.507465	+	0.368695i
$260$	0.752709	+	2.31660i	0.0466810	+	0.143669i
$261$	−5.39194	+	16.5947i	−0.333753	+	1.02719i
$262$	−13.8224	−	10.0426i	−0.853953	−	0.620433i
$263$	8.68662	−	26.7347i	0.535640	−	1.64853i	−0.206623	−	0.978421i	$-0.566247\pi$
$263$	8.68662	−	26.7347i	0.535640	−	1.64853i	0.742263	−	0.670109i	$-0.233753\pi$
$264$	−0.178375	+	0.548982i	−0.0109782	+	0.0337875i
$265$	8.84791	+	6.42838i	0.543523	+	0.394892i
$266$	−20.0527	+	61.7159i	−1.22951	+	3.78404i
$267$	1.19215	+	3.66905i	0.0729581	+	0.224542i
$268$	9.59793	−	6.97330i	0.586287	−	0.425962i
$269$	−3.28045	−	10.0962i	−0.200013	−	0.615575i	−0.999881	−	0.0154006i	$-0.995098\pi$
$269$	−3.28045	−	10.0962i	−0.200013	−	0.615575i	0.799869	−	0.600175i	$-0.204902\pi$
$270$	−4.17322	−	3.03202i	−0.253974	−	0.184523i
$271$	9.84095	+	7.14987i	0.597795	+	0.434324i	0.845096	−	0.534615i	$-0.179543\pi$
$271$	9.84095	+	7.14987i	0.597795	+	0.434324i	−0.247300	+	0.968939i	$0.579543\pi$
$272$	2.94833	−	2.14209i	0.178769	−	0.129883i
$273$	1.24297			0.0752278
$274$	30.0443			1.81504
$275$	13.9518	−	10.1365i	0.841323	−	0.611257i
$276$	1.52537	−	4.69460i	0.0918164	−	0.282582i
$277$	2.90445	+	8.93899i	0.174512	+	0.537092i	0.999611	−	0.0278963i	$-0.00888080\pi$
$277$	2.90445	+	8.93899i	0.174512	+	0.537092i	−0.825099	+	0.564988i	$0.808881\pi$
$278$	10.0384			0.602066
$279$	−15.5625	−	4.25383i	−0.931700	−	0.254670i
$280$	−2.07747			−0.124153
$281$	7.73994	+	23.8211i	0.461726	+	1.42105i	0.863054	+	0.505112i	$0.168549\pi$
$281$	7.73994	+	23.8211i	0.461726	+	1.42105i	−0.401328	+	0.915934i	$0.631451\pi$
$282$	−2.56681	+	7.89983i	−0.152851	+	0.470428i
$283$	5.74007	−	4.17040i	0.341212	−	0.247905i	−0.403961	−	0.914776i	$-0.632367\pi$
$283$	5.74007	−	4.17040i	0.341212	−	0.247905i	0.745173	+	0.666871i	$0.232367\pi$
$284$	6.04590			0.358758
$285$	2.94728			0.174582
$286$	7.46205	−	5.42150i	0.441240	−	0.320580i
$287$	22.7900	+	16.5579i	1.34525	+	0.977380i
$288$	19.0061	+	13.8087i	1.11994	+	0.813687i
$289$	0.309017	+	0.951057i	0.0181775	+	0.0559445i
$290$	13.3181	−	9.67615i	0.782064	−	0.568203i
$291$	0.350211	+	1.07784i	0.0205297	+	0.0631840i
$292$	−2.97497	+	9.15601i	−0.174097	+	0.535815i
$293$	12.2610	+	8.90812i	0.716294	+	0.520418i	0.885198	−	0.465215i	$-0.154023\pi$
$293$	12.2610	+	8.90812i	0.716294	+	0.520418i	−0.168904	+	0.985632i	$0.554023\pi$
$294$	−2.90236	+	8.93256i	−0.169269	+	0.520957i
$295$	1.49183	−	4.59139i	0.0868579	−	0.267321i
$296$	0.592213	+	0.430268i	0.0344217	+	0.0250088i
$297$	−3.13711	+	9.65504i	−0.182034	+	0.560242i
$298$	10.6393	+	32.7443i	0.616316	+	1.89683i
$299$	−4.84491	+	3.52003i	−0.280188	+	0.203569i
$300$	−0.685879	−	2.11092i	−0.0395993	−	0.121874i
$301$	−24.1080	−	17.5155i	−1.38956	−	1.00957i
$302$	22.8592	+	16.6082i	1.31540	+	0.955695i
$303$	4.47788	−	3.25337i	0.257247	−	0.186901i
$304$	−25.0598			−1.43728
$305$	−4.13278			−0.236642
$306$	−4.78381	+	3.47564i	−0.273472	+	0.198689i
$307$	−4.48122	+	13.7918i	−0.255757	+	0.787138i	0.737923	+	0.674885i	$0.235807\pi$
$307$	−4.48122	+	13.7918i	−0.255757	+	0.787138i	−0.993680	+	0.112253i	$0.964193\pi$
$308$	16.6404	+	51.2140i	0.948177	+	2.91819i
$309$	−0.487224			−0.0277172
$310$	9.51943	+	11.8770i	0.540667	+	0.674567i
$311$	20.1995			1.14541			0.572704	−	0.819762i	$-0.305894\pi$
$311$	20.1995			1.14541			0.572704	+	0.819762i	$0.305894\pi$
$312$	−0.0278525	−	0.0857211i	−0.00157684	−	0.00485300i
$313$	−10.6585	+	32.8035i	−0.602454	+	1.85416i	−0.0890251	+	0.996029i	$0.528375\pi$
$313$	−10.6585	+	32.8035i	−0.602454	+	1.85416i	−0.513429	+	0.858132i	$0.671625\pi$
$314$	0.838141	−	0.608945i	0.0472990	−	0.0343647i
$315$	−17.9514			−1.01144
$316$	11.0905			0.623890
$317$	11.2608	−	8.18142i	0.632468	−	0.459515i	−0.224787	−	0.974408i	$-0.572169\pi$
$317$	11.2608	−	8.18142i	0.632468	−	0.459515i	0.857254	+	0.514893i	$0.172169\pi$
$318$	−4.31212	−	3.13294i	−0.241811	−	0.175686i
$319$	−26.2105	−	19.0431i	−1.46751	−	1.06621i
$320$	−3.83183	−	11.7932i	−0.214206	−	0.659258i
$321$	2.64631	−	1.92266i	0.147703	−	0.107312i
$322$	−20.7881	−	63.9791i	−1.15847	−	3.56542i
$323$	2.12491	−	6.53979i	0.118233	−	0.363884i
$324$	−14.1640	−	10.2908i	−0.786891	−	0.571710i
$325$	−0.832115	+	2.56099i	−0.0461574	+	0.142058i
$326$	−0.732890	+	2.25560i	−0.0405910	+	0.124926i
$327$	−0.803589	−	0.583842i	−0.0444386	−	0.0322865i
$328$	0.631233	−	1.94274i	0.0348540	−	0.107270i
$329$	18.1807	+	55.9546i	1.00234	+	3.08487i
$330$	3.80709	−	2.76601i	0.209573	−	0.152264i
$331$	−4.69934	−	14.4631i	−0.258299	−	0.794963i	−0.993162	−	0.116747i	$-0.962753\pi$
$331$	−4.69934	−	14.4631i	−0.258299	−	0.794963i	0.734863	−	0.678216i	$-0.237247\pi$
$332$	−12.0074	−	8.72385i	−0.658989	−	0.478784i
$333$	5.11729	+	3.71793i	0.280426	+	0.203741i
$334$	10.6034	−	7.70384i	0.580194	−	0.421536i
$335$	−7.34327			−0.401206
$336$	−5.39200			−0.294158
$337$	−6.76939	+	4.91825i	−0.368752	+	0.267914i	−0.756693	−	0.653770i	$-0.773186\pi$
$337$	−6.76939	+	4.91825i	−0.368752	+	0.267914i	0.387941	+	0.921684i	$0.373186\pi$
$338$	7.75276	−	23.8605i	0.421695	−	1.29784i
$339$	1.43151	+	4.40575i	0.0777492	+	0.239287i
$340$	2.89945			0.157245
$341$	16.4410	−	25.0408i	0.890331	−	1.35603i
$342$	40.6606			2.19868
$343$	10.5542	+	32.4825i	0.569874	+	1.75389i
$344$	−0.667740	+	2.05509i	−0.0360021	+	0.110803i
$345$	−2.47184	+	1.79590i	−0.133079	+	0.0966878i
$346$	−23.6749			−1.27277
$347$	3.20789			0.172208			0.0861042	−	0.996286i	$-0.472558\pi$
$347$	3.20789			0.172208			0.0861042	+	0.996286i	$0.472558\pi$
$348$	−3.37341	+	2.45093i	−0.180834	+	0.131384i
$349$	−12.5190	−	9.09558i	−0.670126	−	0.486875i	0.199941	−	0.979808i	$-0.435925\pi$
$349$	−12.5190	−	9.09558i	−0.670126	−	0.486875i	−0.870067	+	0.492933i	$0.835925\pi$
$350$	−24.4716	−	17.7797i	−1.30806	−	0.950363i
$351$	−0.489846	−	1.50759i	−0.0261461	−	0.0804693i
$352$	−35.2897	+	25.6394i	−1.88095	+	1.36659i
$353$	−8.86044	−	27.2696i	−0.471594	−	1.45142i	−0.850497	−	0.525980i	$-0.823699\pi$
$353$	−8.86044	−	27.2696i	−0.471594	−	1.45142i	0.378903	−	0.925436i	$-0.376301\pi$
$354$	−0.727060	+	2.23766i	−0.0386428	+	0.118930i
$355$	−3.02753	−	2.19963i	−0.160685	−	0.116744i
$356$	8.06458	−	24.8202i	0.427422	−	1.31547i
$357$	0.457207	−	1.40714i	0.0241980	−	0.0744737i
$358$	−24.0355	−	17.4628i	−1.27032	−	0.922940i
$359$	−1.40020	+	4.30939i	−0.0739000	+	0.227441i	−0.981183	−	0.193080i	$-0.938152\pi$
$359$	−1.40020	+	4.30939i	−0.0739000	+	0.227441i	0.907283	+	0.420520i	$0.138152\pi$
$360$	0.402255	+	1.23801i	0.0212007	+	0.0652490i
$361$	−22.8824	+	16.6250i	−1.20433	+	0.875000i
$362$	9.57192	+	29.4593i	0.503089	+	1.54835i
$363$	−4.64528	−	3.37499i	−0.243814	−	0.177141i
$364$	−6.80252	−	4.94232i	−0.356549	−	0.259048i
$365$	4.82089	−	3.50258i	0.252337	−	0.183334i
$366$	2.01415			0.105281
$367$	−12.0186			−0.627367			−0.313684	−	0.949528i	$-0.601563\pi$
$367$	−12.0186			−0.627367			−0.313684	+	0.949528i	$0.601563\pi$
$368$	21.0173	−	15.2699i	1.09560	−	0.796000i
$369$	5.45446	−	16.7871i	0.283948	−	0.873902i
$370$	−1.84410	−	5.67557i	−0.0958704	−	0.295059i
$371$	−37.7529			−1.96003
$372$	−2.41123	−	3.00839i	−0.125017	−	0.155978i
$373$	17.4220			0.902078			0.451039	−	0.892504i	$-0.351054\pi$
$373$	17.4220			0.902078			0.451039	+	0.892504i	$0.351054\pi$
$374$	−3.39277	−	10.4419i	−0.175436	−	0.539936i
$375$	−1.08678	+	3.34476i	−0.0561211	+	0.172723i
$376$	3.45151	−	2.50767i	0.177998	−	0.129323i
$377$	5.05880			0.260542
$378$	17.8066			0.915873
$379$	−26.5257	+	19.2720i	−1.36253	+	0.989937i	−0.364252	+	0.931300i	$0.618675\pi$
$379$	−26.5257	+	19.2720i	−1.36253	+	0.989937i	−0.998279	+	0.0586366i	$0.981325\pi$
$380$	−16.1299	−	11.7190i	−0.827446	−	0.601174i
$381$	3.83193	+	2.78406i	0.196316	+	0.142632i
$382$	−16.2599	−	50.0428i	−0.831929	−	2.56041i
$383$	−10.4657	+	7.60374i	−0.534770	+	0.388533i	−0.822139	−	0.569287i	$-0.807219\pi$
$383$	−10.4657	+	7.60374i	−0.534770	+	0.388533i	0.287369	+	0.957820i	$0.407219\pi$
$384$	0.264336	+	0.813543i	0.0134893	+	0.0415159i
$385$	10.2999	−	31.7000i	0.524934	−	1.61558i
$386$	−0.985589	−	0.716072i	−0.0501652	−	0.0364471i
$387$	−5.76991	+	17.7580i	−0.293301	+	0.902688i
$388$	2.36909	−	7.29131i	0.120272	−	0.370160i
$389$	2.43789	+	1.77123i	0.123606	+	0.0898050i	0.647871	−	0.761750i	$-0.275660\pi$
$389$	2.43789	+	1.77123i	0.123606	+	0.0898050i	−0.524265	+	0.851555i	$0.675660\pi$
$390$	−0.227063	+	0.698829i	−0.0114978	+	0.0353866i
$391$	2.20283	+	6.77962i	0.111402	+	0.342860i
$392$	3.90271	−	2.83549i	0.197117	−	0.143214i
$393$	−0.827766	−	2.54760i	−0.0417552	−	0.128509i
$394$	7.31661	+	5.31583i	0.368606	+	0.267808i
$395$	−5.55365	−	4.03497i	−0.279435	−	0.203021i
$396$	27.2976	−	19.8328i	1.37175	−	0.996638i
$397$	30.5886			1.53520			0.767599	−	0.640931i	$-0.221452\pi$
$397$	30.5886			1.53520			0.767599	+	0.640931i	$0.221452\pi$
$398$	−19.2804			−0.966441
$399$	−8.23088	+	5.98008i	−0.412059	+	0.299379i
$400$	3.60972	−	11.1096i	0.180486	−	0.555479i
$401$	−7.83205	−	24.1046i	−0.391114	−	1.20372i	−0.931947	−	0.362595i	$-0.881891\pi$
$401$	−7.83205	−	24.1046i	−0.391114	−	1.20372i	0.540833	−	0.841130i	$-0.318109\pi$
$402$	3.57882			0.178495
$403$	0.221339	+	4.67222i	0.0110257	+	0.232740i
$404$	−37.4427			−1.86284
$405$	3.34874	+	10.3064i	0.166400	+	0.512128i
$406$	−17.5604	+	54.0453i	−0.871507	+	2.68222i
$407$	−9.50156	+	6.90329i	−0.470975	+	0.342183i
$408$	−0.107288			−0.00531156
$409$	−9.44409			−0.466980			−0.233490	−	0.972359i	$-0.575015\pi$
$409$	−9.44409			−0.466980			−0.233490	+	0.972359i	$0.575015\pi$
$410$	−13.4725	+	9.78835i	−0.665360	+	0.483412i
$411$	3.81081	+	2.76872i	0.187973	+	0.136571i
$412$	2.66648	+	1.93731i	0.131368	+	0.0954446i
$413$	5.14977	+	15.8494i	0.253404	+	0.779896i
$414$	−34.1015	+	24.7762i	−1.67600	+	1.21768i
$415$	2.83885	+	8.73707i	0.139354	+	0.428886i
$416$	2.10476	−	6.47778i	0.103194	−	0.317599i
$417$	1.27327	+	0.925088i	0.0623525	+	0.0453018i
$418$	−23.3298	+	71.8019i	−1.14110	+	3.51194i
$419$	−5.69727	+	17.5344i	−0.278330	+	0.856611i	0.709989	+	0.704212i	$0.248700\pi$
$419$	−5.69727	+	17.5344i	−0.278330	+	0.856611i	−0.988319	+	0.152398i	$0.951300\pi$
$420$	−3.47060	−	2.52154i	−0.169348	−	0.123038i
$421$	−0.292455	+	0.900085i	−0.0142534	+	0.0438674i	−0.957930	−	0.287001i	$-0.907342\pi$
$421$	−0.292455	+	0.900085i	−0.0142534	+	0.0438674i	0.943677	+	0.330869i	$0.107342\pi$
$422$	−11.9175	−	36.6784i	−0.580136	−	1.78548i
$423$	29.8243	−	21.6686i	1.45011	−	1.05357i
$424$	0.845969	+	2.60362i	0.0410839	+	0.126443i
$425$	2.59316	+	1.88404i	0.125787	+	0.0913895i
$426$	1.47550	+	1.07201i	0.0714881	+	0.0519391i
$427$	11.5416	−	8.38549i	0.558539	−	0.405802i
$428$	−22.1277			−1.06958
$429$	1.44610			0.0698184
$430$	14.2517	−	10.3544i	0.687277	−	0.499336i
$431$	−5.15989	+	15.8805i	−0.248543	+	0.764937i	0.746491	+	0.665396i	$0.231737\pi$
$431$	−5.15989	+	15.8805i	−0.248543	+	0.764937i	−0.995034	+	0.0995405i	$0.968263\pi$
$432$	2.12496	+	6.53994i	0.102237	+	0.314653i
$433$	−13.5492			−0.651132			−0.325566	−	0.945519i	$-0.605555\pi$
$433$	−13.5492			−0.651132			−0.325566	+	0.945519i	$0.605555\pi$
$434$	−50.6836	−	13.8538i	−2.43289	−	0.665003i
$435$	2.58096			0.123748
$436$	2.07640	+	6.39051i	0.0994416	+	0.306050i
$437$	15.1474	−	46.6190i	0.724600	−	2.23009i
$438$	−2.34951	+	1.70702i	−0.112264	+	0.0815645i
$439$	20.2946			0.968609			0.484304	−	0.874900i	$-0.339073\pi$
$439$	20.2946			0.968609			0.484304	+	0.874900i	$0.339073\pi$
$440$	−2.41699			−0.115225
$441$	33.7232	−	24.5013i	1.60587	−	1.16673i
$442$	1.38694	+	1.00767i	0.0659702	+	0.0479302i
$443$	3.87358	+	2.81432i	0.184039	+	0.133712i	0.675990	−	0.736911i	$-0.263716\pi$
$443$	3.87358	+	2.81432i	0.184039	+	0.133712i	−0.491951	+	0.870623i	$0.663716\pi$
$444$	0.467104	+	1.43760i	0.0221678	+	0.0682254i
$445$	−13.0685	+	9.49485i	−0.619508	+	0.450099i
$446$	2.00671	+	6.17603i	0.0950206	+	0.292443i
$447$	−1.66805	+	5.13374i	−0.0788962	+	0.242817i
$448$	34.6298	+	25.1600i	1.63610	+	1.18870i
$449$	7.95287	−	24.4764i	0.375319	−	1.15511i	−0.567944	−	0.823067i	$-0.692261\pi$
$449$	7.95287	−	24.4764i	0.375319	−	1.15511i	0.943263	−	0.332047i	$-0.107739\pi$
$450$	−5.85694	+	18.0258i	−0.276099	+	0.849745i
$451$	26.5144	+	19.2639i	1.24852	+	0.907100i
$452$	9.68385	−	29.8038i	0.455490	−	1.40185i
$453$	1.36894	+	4.21316i	0.0643184	+	0.197952i
$454$	−25.9443	+	18.8496i	−1.21762	+	0.884656i
$455$	1.60829	+	4.94981i	0.0753978	+	0.232051i
$456$	0.596854	+	0.433640i	0.0279502	+	0.0203070i
$457$	−20.6035	−	14.9693i	−0.963792	−	0.700236i	−0.00976341	−	0.999952i	$-0.503108\pi$
$457$	−20.6035	−	14.9693i	−0.963792	−	0.700236i	−0.954028	+	0.299717i	$0.903108\pi$
$458$	−27.4176	+	19.9200i	−1.28114	+	0.930801i
$459$	−1.88690			−0.0880729
$460$	20.6688			0.963687
$461$	16.0445	−	11.6570i	0.747265	−	0.542920i	−0.147713	−	0.989030i	$-0.547191\pi$
$461$	16.0445	−	11.6570i	0.747265	−	0.542920i	0.894978	+	0.446110i	$0.147191\pi$
$462$	−5.01978	+	15.4493i	−0.233541	+	0.718766i
$463$	−8.81051	−	27.1160i	−0.409459	−	1.26019i	−0.917114	−	0.398625i	$-0.869487\pi$
$463$	−8.81051	−	27.1160i	−0.409459	−	1.26019i	0.507655	−	0.861561i	$-0.330513\pi$
$464$	−21.9451			−1.01878
$465$	0.112926	+	2.38373i	0.00523680	+	0.110543i
$466$	−0.581165			−0.0269220
$467$	−6.05697	−	18.6414i	−0.280283	−	0.862623i	−0.987773	−	0.155899i	$-0.950172\pi$
$467$	−6.05697	−	18.6414i	−0.280283	−	0.862623i	0.707490	−	0.706723i	$-0.249828\pi$
$468$	−1.62809	+	5.01075i	−0.0752585	+	0.231622i
$469$	20.5076	−	14.8996i	0.946953	−	0.688002i
$470$	−34.7804			−1.60430
$471$	0.162427			0.00748422
$472$	0.977653	−	0.710307i	0.0450001	−	0.0326945i
$473$	−28.0479	−	20.3780i	−1.28964	−	0.936980i
$474$	2.70663	+	1.96648i	0.124320	+	0.0903235i
$475$	−6.81102	−	20.9622i	−0.312511	−	0.961810i
$476$	−8.09731	+	5.88304i	−0.371140	+	0.269649i
$477$	7.30998	+	22.4978i	0.334701	+	1.03010i
$478$	11.3443	−	34.9142i	0.518877	−	1.59694i
$479$	19.4449	+	14.1275i	0.888459	+	0.645503i	0.935476	−	0.353391i	$-0.114971\pi$
$479$	19.4449	+	14.1275i	0.888459	+	0.645503i	−0.0470167	+	0.998894i	$0.514971\pi$
$480$	1.07383	−	3.30491i	0.0490135	−	0.150848i
$481$	0.566695	−	1.74411i	0.0258391	−	0.0795245i
$482$	1.95763	+	1.42230i	0.0891675	+	0.0647840i
$483$	3.25921	−	10.0308i	0.148299	−	0.456418i
$484$	12.0030	+	36.9414i	0.545590	+	1.67915i
$485$	−3.83908	+	2.78925i	−0.174324	+	0.126654i
$486$	−5.20168	−	16.0091i	−0.235953	−	0.726189i
$487$	26.5064	+	19.2580i	1.20112	+	0.872664i	0.994394	−	0.105736i	$-0.0337198\pi$
$487$	26.5064	+	19.2580i	1.20112	+	0.872664i	0.206724	+	0.978399i	$0.433720\pi$
$488$	−0.836930	−	0.608065i	−0.0378860	−	0.0275258i
$489$	−0.300824	+	0.218561i	−0.0136037	+	0.00988368i
$490$	−39.3271			−1.77662
$491$	−31.6193			−1.42696			−0.713480	−	0.700675i	$-0.752882\pi$
$491$	−31.6193			−1.42696			−0.713480	+	0.700675i	$0.752882\pi$
$492$	3.41253	−	2.47935i	0.153849	−	0.111778i
$493$	1.86081	−	5.72697i	0.0838065	−	0.257930i
$494$	−3.64285	−	11.2115i	−0.163900	−	0.504431i
$495$	−20.8851			−0.938715
$496$	−0.960170	−	20.2681i	−0.0431129	−	0.910065i
$497$	12.9181			0.579455
$498$	−1.38354	−	4.25810i	−0.0619979	−	0.190810i
$499$	2.39923	−	7.38409i	0.107405	−	0.330557i	−0.882883	−	0.469593i	$-0.844400\pi$
$499$	2.39923	−	7.38409i	0.107405	−	0.330557i	0.990287	+	0.139036i	$0.0444005\pi$
$500$	19.2473	−	13.9840i	0.860764	−	0.625382i
$501$	2.05488			0.0918053
$502$	25.1781			1.12375
$503$	−0.356255	+	0.258835i	−0.0158846	+	0.0115409i	−0.595699	−	0.803208i	$-0.703125\pi$
$503$	−0.356255	+	0.258835i	−0.0158846	+	0.0115409i	0.579815	+	0.814748i	$0.303125\pi$
$504$	−3.63533	−	2.64122i	−0.161931	−	0.117649i
$505$	18.7497	+	13.6225i	0.834352	+	0.606192i
$506$	−24.1854	−	74.4350i	−1.07517	−	3.30904i
$507$	3.18222	−	2.31202i	0.141327	−	0.102680i
$508$	−9.90137	−	30.4733i	−0.439302	−	1.35203i
$509$	−7.58282	+	23.3375i	−0.336102	+	1.03442i	0.630074	+	0.776535i	$0.283025\pi$
$509$	−7.58282	+	23.3375i	−0.336102	+	1.03442i	−0.966176	+	0.257882i	$0.916975\pi$
$510$	0.707609	+	0.514108i	0.0313335	+	0.0227651i
$511$	−6.35652	+	19.5634i	−0.281196	+	0.865432i
$512$	−9.88574	+	30.4252i	−0.436892	+	1.34462i
$513$	10.4970	+	7.62649i	0.463453	+	0.336718i
$514$	4.85866	−	14.9534i	0.214306	−	0.659567i
$515$	−0.630425	−	1.94025i	−0.0277799	−	0.0854976i
$516$	−3.60989	+	2.62274i	−0.158916	+	0.115460i
$517$	21.1520	+	65.0990i	0.930262	+	2.86305i
$518$	16.6659	+	12.1085i	0.732257	+	0.532016i
$519$	−3.00292	−	2.18175i	−0.131814	−	0.0957681i
$520$	0.305324	−	0.221831i	0.0133894	−	0.00972794i
$521$	20.2305			0.886313			0.443156	−	0.896444i	$-0.353859\pi$
$521$	20.2305			0.886313			0.443156	+	0.896444i	$0.353859\pi$
$522$	35.6070			1.55847
$523$	−8.35276	+	6.06864i	−0.365241	+	0.265363i	−0.755235	−	0.655454i	$-0.772477\pi$
$523$	−8.35276	+	6.06864i	−0.365241	+	0.265363i	0.389994	+	0.920817i	$0.372477\pi$
$524$	−5.59964	+	17.2339i	−0.244621	+	0.752867i
$525$	−1.46550	−	4.51034i	−0.0639596	−	0.196847i
$526$	−57.3642			−2.50120
$527$	5.37074	+	1.46803i	0.233953	+	0.0639485i
$528$	−6.27320			−0.273006
$529$	8.59554	+	26.4543i	0.373719	+	1.15019i
$530$	6.89664	−	21.2257i	0.299571	−	0.921985i
$531$	8.44786	−	6.13773i	0.366606	−	0.266355i
$532$	68.8242			2.98391
$533$	−5.11746			−0.221662
$534$	6.36908	−	4.62741i	0.275617	−	0.200248i
$535$	11.0806	+	8.05052i	0.479056	+	0.348054i
$536$	−1.48709	−	1.08043i	−0.0642324	−	0.0466676i
$537$	−1.43938	−	4.42997i	−0.0621140	−	0.191167i
$538$	−17.5259	+	12.7333i	−0.755597	+	0.548973i
$539$	23.9171	+	73.6092i	1.03018	+	3.17057i
$540$	−1.69062	+	5.20320i	−0.0727528	+	0.223910i
$541$	18.1732	+	13.2036i	0.781325	+	0.567666i	0.905376	−	0.424610i	$-0.139589\pi$
$541$	18.1732	+	13.2036i	0.781325	+	0.567666i	−0.124051	+	0.992276i	$0.539589\pi$
$542$	7.67069	−	23.6079i	0.329484	−	1.01405i
$543$	−1.50071	+	4.61871i	−0.0644017	+	0.198208i
$544$	−6.55916	−	4.76551i	−0.281222	−	0.204320i
$545$	1.28523	−	3.95554i	0.0550533	−	0.169437i
$546$	−0.783817	−	2.41234i	−0.0335443	−	0.103239i
$547$	13.1618	−	9.56261i	0.562758	−	0.408868i	−0.269709	−	0.962942i	$-0.586928\pi$
$547$	13.1618	−	9.56261i	0.562758	−	0.408868i	0.832467	+	0.554074i	$0.186928\pi$
$548$	−9.84679	−	30.3053i	−0.420634	−	1.29458i
$549$	−7.23188	−	5.25427i	−0.308649	−	0.224247i
$550$	−28.4709	−	20.6853i	−1.21400	−	0.882025i
$551$	−33.4992	+	24.3386i	−1.42711	+	1.03686i
$552$	−0.764807			−0.0325523
$553$	23.6967			1.00769
$554$	15.5172	−	11.2739i	0.659261	−	0.478981i
$555$	0.289124	−	0.889831i	0.0122726	−	0.0377712i
$556$	−3.29003	−	10.1257i	−0.139528	−	0.429423i
$557$	−1.97379			−0.0836321			−0.0418161	−	0.999125i	$-0.513314\pi$
$557$	−1.97379			−0.0836321			−0.0418161	+	0.999125i	$0.513314\pi$
$558$	1.55792	+	32.8860i	0.0659521	+	1.39217i
$559$	5.41342			0.228963
$560$	−6.97677	−	21.4723i	−0.294823	−	0.907370i
$561$	0.531927	−	1.63710i	0.0224580	−	0.0691185i
$562$	41.3509	−	30.0432i	1.74428	−	1.26730i
$563$	−38.2696			−1.61287			−0.806436	−	0.591321i	$-0.798606\pi$
$563$	−38.2696			−1.61287			−0.806436	+	0.591321i	$0.798606\pi$
$564$	8.80972			0.370956
$565$	−15.6925	+	11.4013i	−0.660190	+	0.479656i
$566$	−11.7136	−	8.51041i	−0.492358	−	0.357719i
$567$	−30.2639	−	21.9880i	−1.27096	−	0.923409i
$568$	−0.289469	−	0.890894i	−0.0121459	−	0.0373811i
$569$	3.93507	−	2.85899i	0.164967	−	0.119855i	−0.502239	−	0.864729i	$-0.667490\pi$
$569$	3.93507	−	2.85899i	0.164967	−	0.119855i	0.667206	+	0.744874i	$0.267490\pi$
$570$	−1.85856	−	5.72005i	−0.0778464	−	0.239587i
$571$	−11.4050	+	35.1010i	−0.477285	+	1.46893i	0.365566	+	0.930785i	$0.380875\pi$
$571$	−11.4050	+	35.1010i	−0.477285	+	1.46893i	−0.842851	+	0.538147i	$0.819125\pi$
$572$	−7.91423	−	5.75003i	−0.330911	−	0.240421i
$573$	2.54927	−	7.84584i	0.106497	−	0.327765i
$574$	17.7640	−	54.6720i	0.741455	−	2.28196i
$575$	18.4854	+	13.4304i	0.770895	+	0.560088i
$576$	8.28816	−	25.5083i	0.345340	−	1.06285i
$577$	−5.18275	−	15.9509i	−0.215761	−	0.664043i	−0.999099	−	0.0424469i	$-0.986485\pi$
$577$	−5.18275	−	15.9509i	−0.215761	−	0.664043i	0.783338	−	0.621596i	$-0.213515\pi$
$578$	1.65094	−	1.19947i	0.0686699	−	0.0498916i
$579$	−0.0590226	−	0.181653i	−0.00245290	−	0.00754924i
$580$	−14.1251	−	10.2625i	−0.586514	−	0.426127i
$581$	−25.6557	−	18.6400i	−1.06438	−	0.773317i
$582$	1.87101	−	1.35937i	0.0775560	−	0.0563477i
$583$	−43.9227			−1.81909
$584$	1.49162			0.0617238
$585$	2.63830	−	1.91683i	0.109080	−	0.0792514i
$586$	9.55701	−	29.4134i	0.394796	−	1.21506i
$587$	−5.82214	−	17.9187i	−0.240305	−	0.739584i	−0.996373	−	0.0850908i	$-0.972882\pi$
$587$	−5.82214	−	17.9187i	−0.240305	−	0.739584i	0.756068	−	0.654493i	$-0.227118\pi$
$588$	9.96139			0.410801
$589$	−23.9444	−	29.8743i	−0.986610	−	1.23095i
$590$	−9.85168			−0.405587
$591$	0.438160	+	1.34852i	0.0180235	+	0.0554706i
$592$	−2.45833	+	7.56595i	−0.101037	+	0.310959i
$593$	1.83572	−	1.33373i	0.0753842	−	0.0547698i	−0.549455	−	0.835523i	$-0.685165\pi$
$593$	1.83572	−	1.33373i	0.0753842	−	0.0547698i	0.624839	+	0.780754i	$0.285165\pi$
$594$	20.7167			0.850016
$595$	6.19517			0.253977
$596$	29.5418	−	21.4634i	1.21008	−	0.879175i
$597$	−2.44553	−	1.77678i	−0.100089	−	0.0727187i
$598$	9.88686	+	7.18322i	0.404304	+	0.293744i
$599$	−8.92838	−	27.4787i	−0.364804	−	1.12275i	−0.950104	−	0.311934i	$-0.899023\pi$
$599$	−8.92838	−	27.4787i	−0.364804	−	1.12275i	0.585300	−	0.810817i	$-0.300977\pi$
$600$	−0.278216	+	0.202136i	−0.0113581	+	0.00825216i
$601$	11.0972	+	34.1536i	0.452663	+	1.39315i	0.873857	+	0.486183i	$0.161611\pi$
$601$	11.0972	+	34.1536i	0.452663	+	1.39315i	−0.421194	+	0.906971i	$0.638389\pi$
$602$	−18.7913	+	57.8338i	−0.765878	+	2.35713i
$603$	−12.8499	−	9.33597i	−0.523287	−	0.380190i
$604$	9.26055	−	28.5011i	0.376807	−	1.15969i
$605$	7.42949	−	22.8656i	0.302052	−	0.929620i
$606$	−9.13786	−	6.63905i	−0.371200	−	0.269693i
$607$	−4.21404	+	12.9695i	−0.171043	+	0.526415i	−0.999431	−	0.0337396i	$-0.989258\pi$
$607$	−4.21404	+	12.9695i	−0.171043	+	0.526415i	0.828388	+	0.560155i	$0.189258\pi$
$608$	17.2278	+	53.0218i	0.698681	+	2.15032i
$609$	−7.20787	+	5.23682i	−0.292078	+	0.212207i
$610$	2.60614	+	8.02086i	0.105519	+	0.324755i
$611$	−8.64680	−	6.28227i	−0.349812	−	0.254153i
$612$	5.07370	+	3.68626i	0.205092	+	0.149008i
$613$	29.2823	−	21.2749i	1.18270	−	0.859284i	0.190229	−	0.981740i	$-0.439077\pi$
$613$	29.2823	−	21.2749i	1.18270	−	0.859284i	0.992474	+	0.122456i	$0.0390771\pi$
$614$	29.5928			1.19427
$615$	−2.61089			−0.105281
$616$	6.74993	−	4.90411i	0.271962	−	0.197592i
$617$	−8.59681	+	26.4583i	−0.346094	+	1.06517i	0.614901	+	0.788604i	$0.289196\pi$
$617$	−8.59681	+	26.4583i	−0.346094	+	1.06517i	−0.960995	+	0.276565i	$0.910804\pi$
$618$	0.307244	+	0.945600i	0.0123592	+	0.0380376i
$619$	31.1811			1.25327			0.626637	−	0.779311i	$-0.284431\pi$
$619$	31.1811			1.25327			0.626637	+	0.779311i	$0.284431\pi$
$620$	8.86024	−	13.4947i	0.355836	−	0.541961i
$621$	−13.4508			−0.539761
$622$	−12.7378	−	39.2030i	−0.510741	−	1.57190i
$623$	17.2313	−	53.0326i	0.690359	−	2.12471i
$624$	0.792458	−	0.575754i	0.0317237	−	0.0230486i
$625$	1.30073			0.0520294
$626$	70.3859			2.81319
$627$	−9.57602	+	6.95739i	−0.382429	+	0.277851i
$628$	−0.888930	−	0.645845i	−0.0354722	−	0.0257720i
$629$	−1.76602	−	1.28309i	−0.0704158	−	0.0511601i
$630$	11.3201	+	34.8398i	0.451005	+	1.38805i
$631$	−23.5996	+	17.1461i	−0.939486	+	0.682576i	−0.948297	−	0.317385i	$-0.897195\pi$
$631$	−23.5996	+	17.1461i	−0.939486	+	0.682576i	0.00881114	+	0.999961i	$0.497195\pi$
$632$	−0.530998	−	1.63424i	−0.0211220	−	0.0650067i
$633$	1.86846	−	5.75054i	0.0742647	−	0.228563i
$634$	−22.9795	−	16.6956i	−0.912632	−	0.663066i
$635$	−6.12865	+	18.8621i	−0.243208	+	0.748518i
$636$	−1.74689	+	5.37638i	−0.0692687	+	0.213187i
$637$	−9.77718	−	7.10353i	−0.387386	−	0.281452i
$638$	−20.4302	+	62.8777i	−0.808839	+	2.48935i
$639$	−2.50129	−	7.69818i	−0.0989495	−	0.304535i
$640$	−2.89770	+	2.10531i	−0.114542	+	0.0832195i
$641$	8.13155	+	25.0263i	0.321177	+	0.988481i	0.973137	+	0.230228i	$0.0739471\pi$
$641$	8.13155	+	25.0263i	0.321177	+	0.988481i	−0.651960	+	0.758254i	$0.726053\pi$
$642$	−5.40024	−	3.92350i	−0.213130	−	0.154848i
$643$	31.5026	+	22.8880i	1.24234	+	0.902613i	0.997752	−	0.0670144i	$-0.0213474\pi$
$643$	31.5026	+	22.8880i	1.24234	+	0.902613i	0.244588	+	0.969627i	$0.421347\pi$
$644$	−57.7218	+	41.9374i	−2.27456	+	1.65256i
$645$	2.76189			0.108749
$646$	−14.0323			−0.552095
$647$	33.6005	−	24.4122i	1.32097	−	0.959741i	0.321051	−	0.947062i	$-0.395964\pi$
$647$	33.6005	−	24.4122i	1.32097	−	0.959741i	0.999920	−	0.0126791i	$-0.00403600\pi$
$648$	−0.838245	+	2.57985i	−0.0329294	+	0.101346i
$649$	5.99138	+	18.4396i	0.235182	+	0.723816i
$650$	5.49507			0.215535
$651$	−5.15200	−	6.42793i	−0.201923	−	0.251930i
$652$	2.51540			0.0985107
$653$	2.42167	+	7.45313i	0.0947672	+	0.291664i	0.987193	−	0.159531i	$-0.0509981\pi$
$653$	2.42167	+	7.45313i	0.0947672	+	0.291664i	−0.892426	+	0.451194i	$0.850998\pi$
$654$	−0.626371	+	1.92777i	−0.0244930	+	0.0753818i
$655$	9.07413	−	6.59274i	0.354556	−	0.257600i
$656$	22.1996			0.866748
$657$	12.8891			0.502850
$658$	97.1313	−	70.5700i	3.78657	−	2.75111i
$659$	−14.7866	−	10.7431i	−0.576004	−	0.418491i	0.261277	−	0.965264i	$-0.415856\pi$
$659$	−14.7866	−	10.7431i	−0.576004	−	0.418491i	−0.837281	+	0.546772i	$0.815856\pi$
$660$	−4.03778	−	2.93362i	−0.157171	−	0.114191i
$661$	9.08020	+	27.9460i	0.353179	+	1.08697i	0.957058	+	0.289897i	$0.0936210\pi$
$661$	9.08020	+	27.9460i	0.353179	+	1.08697i	−0.603879	+	0.797076i	$0.706379\pi$
$662$	−25.1064	+	18.2409i	−0.975789	+	0.708952i
$663$	0.0830581	+	0.255626i	0.00322571	+	0.00992771i
$664$	−0.710610	+	2.18703i	−0.0275770	+	0.0848733i
$665$	−34.4642	−	25.0397i	−1.33647	−	0.970999i
$666$	3.98875	−	12.2761i	0.154561	−	0.475690i
$667$	13.2648	−	40.8248i	0.513614	−	1.58074i
$668$	−11.2460	−	8.17068i	−0.435120	−	0.316133i
$669$	−0.314618	+	0.968294i	−0.0121638	+	0.0374364i
$670$	4.63068	+	14.2518i	0.178899	+	0.550594i
$671$	13.4278	−	9.75590i	0.518376	−	0.376622i
$672$	3.70684	+	11.4085i	0.142994	+	0.440092i
$673$	−2.68508	−	1.95083i	−0.103502	−	0.0751988i	0.534830	−	0.844960i	$-0.320376\pi$
$673$	−2.68508	−	1.95083i	−0.103502	−	0.0751988i	−0.638333	+	0.769761i	$0.720376\pi$
$674$	13.8141	+	10.0365i	0.532098	+	0.386592i
$675$	−4.89303	+	3.55500i	−0.188333	+	0.136832i
$676$	−26.6088			−1.02341
$677$	−16.0723			−0.617707			−0.308854	−	0.951110i	$-0.599945\pi$
$677$	−16.0723			−0.617707			−0.308854	+	0.951110i	$0.599945\pi$
$678$	7.64792	−	5.55654i	0.293717	−	0.213398i
$679$	5.06197	−	15.5791i	0.194260	−	0.597872i
$680$	−0.138822	−	0.427249i	−0.00532357	−	0.0163843i
$681$	−5.02784			−0.192667
$682$	−58.9666	−	16.1179i	−2.25795	−	0.617185i
$683$	−43.1126			−1.64966			−0.824828	−	0.565384i	$-0.808728\pi$
$683$	−43.1126			−1.64966			−0.824828	+	0.565384i	$0.808728\pi$
$684$	−13.3262	−	41.0139i	−0.509541	−	1.56821i
$685$	−6.09487	+	18.7581i	−0.232873	+	0.716710i
$686$	56.3863	−	40.9671i	2.15284	−	1.56413i
$687$	−5.31336			−0.202717
$688$	−23.4835			−0.895298
$689$	5.54851	−	4.03123i	0.211382	−	0.153578i
$690$	5.04420	+	3.66483i	0.192030	+	0.139518i
$691$	21.2397	+	15.4315i	0.807996	+	0.587044i	0.913249	−	0.407402i	$-0.133565\pi$
$691$	21.2397	+	15.4315i	0.807996	+	0.587044i	−0.105253	+	0.994445i	$0.533565\pi$
$692$	7.75927	+	23.8806i	0.294963	+	0.907803i
$693$	58.3259	−	42.3762i	2.21562	−	1.60974i
$694$	−2.02290	−	6.22584i	−0.0767882	−	0.236330i
$695$	−2.03643	+	6.26748i	−0.0772461	+	0.237739i
$696$	0.522671	+	0.379743i	0.0198118	+	0.0143941i
$697$	−1.88238	+	5.79338i	−0.0713003	+	0.219440i
$698$	−9.75813	+	30.0324i	−0.369350	+	1.13674i
$699$	−0.0737149	−	0.0535570i	−0.00278815	−	0.00202571i
$700$	−9.91374	+	30.5114i	−0.374704	+	1.15322i
$701$	−2.64481	−	8.13988i	−0.0998930	−	0.307439i	0.888605	−	0.458673i	$-0.151675\pi$
$701$	−2.64481	−	8.13988i	−0.0998930	−	0.307439i	−0.988498	+	0.151234i	$0.951675\pi$
$702$	−2.61702	+	1.90138i	−0.0987732	+	0.0717629i
$703$	4.63851	+	14.2759i	0.174945	+	0.538424i
$704$	40.2892	+	29.2718i	1.51846	+	1.10322i
$705$	−4.41154	−	3.20517i	−0.166148	−	0.120714i
$706$	−47.3372	+	34.3925i	−1.78156	+	1.29438i
$707$	−80.0027			−3.00881
$708$	2.49539			0.0937825
$709$	−10.5125	+	7.63775i	−0.394804	+	0.286842i	−0.767421	−	0.641143i	$-0.778460\pi$
$709$	−10.5125	+	7.63775i	−0.394804	+	0.286842i	0.372617	+	0.927985i	$0.378460\pi$
$710$	−2.35986	+	7.26289i	−0.0885638	+	0.272571i
$711$	−4.58833	−	14.1214i	−0.172076	−	0.529595i
$712$	−4.04351			−0.151537
$713$	38.2854	+	10.4649i	1.43380	+	0.391913i
$714$	−3.01928			−0.112994
$715$	1.87113	+	5.75874i	0.0699762	+	0.215365i
$716$	−9.73709	+	29.9677i	−0.363892	+	1.11994i
$717$	4.65642	−	3.38309i	0.173897	−	0.126344i
$718$	9.24659			0.345080
$719$	12.7951			0.477178			0.238589	−	0.971121i	$-0.423315\pi$
$719$	12.7951			0.477178			0.238589	+	0.971121i	$0.423315\pi$
$720$	−11.4449	+	8.31524i	−0.426528	+	0.309891i
$721$	5.69739	+	4.13940i	0.212182	+	0.154159i
$722$	46.6953	+	33.9261i	1.73782	+	1.26260i
$723$	0.117234	+	0.360809i	0.00435997	+	0.0134186i
$724$	26.5782	−	19.3102i	0.987769	−	0.717656i
$725$	−5.96449	−	18.3568i	−0.221515	−	0.681754i
$726$	−3.62084	+	11.1438i	−0.134382	+	0.413585i
$727$	23.0190	+	16.7243i	0.853729	+	0.620271i	0.926172	−	0.377102i	$-0.123079\pi$
$727$	23.0190	+	16.7243i	0.853729	+	0.620271i	−0.0724425	+	0.997373i	$0.523079\pi$
$728$	−0.402581	+	1.23902i	−0.0149207	+	0.0459211i
$729$	−6.68358	+	20.5699i	−0.247540	+	0.761850i
$730$	−9.83784	−	7.14761i	−0.364115	−	0.264545i
$731$	1.99125	−	6.12843i	0.0736489	−	0.226668i
$732$	−0.660123	−	2.03165i	−0.0243989	−	0.0750920i
$733$	1.01401	−	0.736720i	0.0374532	−	0.0272114i	−0.568901	−	0.822406i	$-0.692631\pi$
$733$	1.01401	−	0.736720i	0.0374532	−	0.0272114i	0.606354	+	0.795195i	$0.292631\pi$
$734$	7.57896	+	23.3256i	0.279744	+	0.860965i
$735$	−4.98824	−	3.62417i	−0.183994	−	0.133680i
$736$	−46.7571	−	33.9710i	−1.72349	−	1.25219i
$737$	23.8591	−	17.3346i	0.878861	−	0.638530i
$738$	−36.0199			−1.32591
$739$	−37.5386			−1.38088			−0.690440	−	0.723389i	$-0.742583\pi$
$739$	−37.5386			−1.38088			−0.690440	+	0.723389i	$0.742583\pi$
$740$	−5.12049	+	3.72025i	−0.188233	+	0.136759i
$741$	0.571136	−	1.75778i	0.0209812	−	0.0645735i
$742$	23.8070	+	73.2705i	0.873983	+	2.68984i
$743$	−49.4414			−1.81383			−0.906914	−	0.421315i	$-0.861569\pi$
$743$	−49.4414			−1.81383			−0.906914	+	0.421315i	$0.861569\pi$
$744$	−0.327855	+	0.499345i	−0.0120198	+	0.0183069i
$745$	−22.6022			−0.828079
$746$	−10.9863	−	33.8125i	−0.402239	−	1.23796i
$747$	−6.14035	+	18.8981i	−0.224664	+	0.691444i
$748$	−9.42063	+	6.84449i	−0.344452	+	0.250259i
$749$	−47.2795			−1.72755
$750$	7.17681			0.262060
$751$	15.4919	−	11.2555i	0.565308	−	0.410720i	−0.268090	−	0.963394i	$-0.586392\pi$
$751$	15.4919	−	11.2555i	0.565308	−	0.410720i	0.833398	+	0.552674i	$0.186392\pi$
$752$	37.5099	+	27.2525i	1.36784	+	0.993797i
$753$	3.19358	+	2.32027i	0.116381	+	0.0845554i
$754$	−3.19009	−	9.81807i	−0.116176	−	0.357553i
$755$	−15.0066	+	10.9029i	−0.546146	+	0.396798i
$756$	−5.83598	−	17.9613i	−0.212253	−	0.653247i
$757$	−0.915072	+	2.81630i	−0.0332589	+	0.102360i	−0.966308	−	0.257389i	$-0.917138\pi$
$757$	−0.915072	+	2.81630i	−0.0332589	+	0.102360i	0.933049	+	0.359749i	$0.117138\pi$
$758$	54.1301	+	39.3278i	1.96609	+	1.42845i
$759$	3.79185	−	11.6701i	0.137635	−	0.423598i
$760$	−0.954586	+	2.93791i	−0.0346265	+	0.106569i
$761$	37.8684	+	27.5130i	1.37273	+	0.997346i	0.997518	+	0.0704060i	$0.0224295\pi$
$761$	37.8684	+	27.5130i	1.37273	+	0.997346i	0.375210	+	0.926940i	$0.377571\pi$
$762$	2.98686	−	9.19261i	0.108203	−	0.333013i
$763$	4.43659	+	13.6544i	0.160615	+	0.494323i
$764$	−45.1485	+	32.8023i	−1.63342	+	1.18675i
$765$	−1.19955	−	3.69184i	−0.0433699	−	0.133479i
$766$	21.3569	+	15.5167i	0.771657	+	0.560642i
$767$	−2.44924	−	1.77948i	−0.0884370	−	0.0642532i
$768$	−3.37947	+	2.45533i	−0.121946	+	0.0885991i
$769$	4.52783			0.163278			0.0816389	−	0.996662i	$-0.473985\pi$
$769$	4.52783			0.163278			0.0816389	+	0.996662i	$0.473985\pi$
$770$	−68.0182			−2.45120
$771$	1.99430	−	1.44894i	0.0718228	−	0.0521823i
$772$	−0.399274	+	1.22884i	−0.0143702	+	0.0442269i
$773$	−1.18577	−	3.64941i	−0.0426491	−	0.131260i	0.927465	−	0.373910i	$-0.121983\pi$
$773$	−1.18577	−	3.64941i	−0.0426491	−	0.131260i	−0.970114	+	0.242650i	$0.921983\pi$
$774$	38.1030			1.36958
$775$	16.6930	−	6.31186i	0.599632	−	0.226729i
$776$	−1.18784			−0.0426410
$777$	0.998047	+	3.07167i	0.0358047	+	0.110196i
$778$	1.90025	−	5.84837i	0.0681273	−	0.209674i
$779$	33.8876	−	24.6208i	1.21415	−	0.882131i
$780$	0.779319			0.0279041
$781$	15.0292			0.537789
$782$	11.7687	−	8.55048i	0.420849	−	0.305764i
$783$	9.19231	+	6.67860i	0.328506	+	0.238674i
$784$	42.4134	+	30.8152i	1.51477	+	1.10054i
$785$	0.210166	+	0.646824i	0.00750114	+	0.0230861i
$786$	−4.42237	+	3.21304i	−0.157741	+	0.114605i
$787$	10.6443	+	32.7597i	0.379428	+	1.16776i	0.940442	+	0.339953i	$0.110411\pi$
$787$	10.6443	+	32.7597i	0.379428	+	1.16776i	−0.561015	+	0.827806i	$0.689589\pi$
$788$	2.96405	−	9.12240i	0.105590	−	0.324972i
$789$	−7.27606	−	5.28637i	−0.259035	−	0.188200i
$790$	−4.32888	+	13.3229i	−0.154015	+	0.474009i
$791$	20.6912	−	63.6809i	0.735694	−	2.26423i
$792$	−4.22944	−	3.07287i	−0.150287	−	0.109190i
$793$	−0.800868	+	2.46482i	−0.0284396	+	0.0875282i
$794$	−19.2892	−	59.3660i	−0.684548	−	2.10682i
$795$	2.83081	−	2.05670i	0.100399	−	0.0729438i
$796$	6.31902	+	19.4479i	0.223972	+	0.689314i
$797$	−33.4116	−	24.2750i	−1.18350	−	0.859864i	−0.190939	−	0.981602i	$-0.561153\pi$
$797$	−33.4116	−	24.2750i	−1.18350	−	0.859864i	−0.992562	+	0.121738i	$0.961153\pi$
$798$	16.7965	+	12.2034i	0.594589	+	0.431994i
$799$	−10.2926	+	7.47804i	−0.364127	+	0.264554i
$800$	−25.9874			−0.918793
$801$	−34.9398			−1.23454
$802$	−41.8430	+	30.4007i	−1.47753	+	1.07349i
$803$	−7.39535	+	22.7605i	−0.260976	+	0.803202i
$804$	−1.17293	−	3.60991i	−0.0413661	−	0.127312i
$805$	44.1624			1.55652
$806$	8.92822	−	3.37588i	0.314483	−	0.118910i
$807$	−3.39642			−0.119560
$808$	1.79270	+	5.51738i	0.0630671	+	0.194101i
$809$	−5.23438	+	16.1098i	−0.184031	+	0.566390i	−0.999930	−	0.0118045i	$-0.996242\pi$
$809$	−5.23438	+	16.1098i	−0.184031	+	0.566390i	0.815899	+	0.578194i	$0.196242\pi$
$810$	17.8908	−	12.9984i	0.628618	−	0.456718i
$811$	7.19459			0.252636			0.126318	−	0.991990i	$-0.459684\pi$
$811$	7.19459			0.252636			0.126318	+	0.991990i	$0.459684\pi$
$812$	60.2701			2.11507
$813$	3.14853	−	2.28754i	0.110424	−	0.0802275i
$814$	19.3895	+	14.0873i	0.679603	+	0.493760i
$815$	−1.25961	−	0.915157i	−0.0441221	−	0.0320566i
$816$	−0.360306	−	1.10891i	−0.0126132	−	0.0388196i
$817$	−35.8474	+	26.0447i	−1.25414	+	0.911189i
$818$	5.95546	+	18.3290i	0.208228	+	0.640859i
$819$	−3.47869	+	10.7063i	−0.121555	+	0.374109i
$820$	14.2889	+	10.3815i	0.498990	+	0.362538i
$821$	−3.88731	+	11.9639i	−0.135668	+	0.417543i	−0.995693	−	0.0927084i	$-0.970448\pi$
$821$	−3.88731	+	11.9639i	−0.135668	+	0.417543i	0.860025	+	0.510251i	$0.170448\pi$
$822$	2.97040	−	9.14194i	0.103605	−	0.318862i
$823$	−31.9686	−	23.2265i	−1.11435	−	0.809626i	−0.131010	−	0.991381i	$-0.541822\pi$
$823$	−31.9686	−	23.2265i	−1.11435	−	0.809626i	−0.983344	+	0.181755i	$0.941822\pi$
$824$	0.157806	−	0.485676i	0.00549742	−	0.0169193i
$825$	−1.70500	−	5.24745i	−0.0593604	−	0.182693i
$826$	27.5128	−	19.9893i	0.957294	−	0.695515i
$827$	9.67579	+	29.7790i	0.336460	+	1.03552i	0.965998	+	0.258549i	$0.0832442\pi$
$827$	9.67579	+	29.7790i	0.336460	+	1.03552i	−0.629538	+	0.776970i	$0.716756\pi$
$828$	36.1679	+	26.2775i	1.25692	+	0.913208i
$829$	28.5675	+	20.7555i	0.992191	+	0.720869i	0.960400	−	0.278626i	$-0.0898788\pi$
$829$	28.5675	+	20.7555i	0.992191	+	0.720869i	0.0317912	+	0.999495i	$0.489879\pi$
$830$	15.1666	−	11.0192i	0.526442	−	0.382483i
$831$	3.00713			0.104316
$832$	−7.77608			−0.269587
$833$	−11.6382	+	8.45562i	−0.403238	+	0.292970i
$834$	0.992474	−	3.05452i	0.0343666	−	0.105769i
$835$	2.65884	+	8.18306i	0.0920128	+	0.283186i
$836$	80.0719			2.76934
$837$	−5.76605	+	8.78206i	−0.199304	+	0.303553i
$838$	37.6233			1.29967
$839$	2.30156	+	7.08346i	0.0794586	+	0.244548i	0.982893	−	0.184178i	$-0.0589624\pi$
$839$	2.30156	+	7.08346i	0.0794586	+	0.244548i	−0.903434	+	0.428727i	$0.858962\pi$
$840$	−0.205394	+	0.632138i	−0.00708677	+	0.0218108i
$841$	−5.87409	+	4.26778i	−0.202555	+	0.147165i
$842$	1.93130			0.0665570
$843$	8.01356			0.276002
$844$	−33.0912	+	24.0421i	−1.13905	+	0.827565i
$845$	13.3245	+	9.68084i	0.458378	+	0.333031i
$846$	−60.8615	−	44.2185i	−2.09246	−	1.52026i
$847$	25.6464	+	78.9315i	0.881221	+	2.71212i
$848$	−24.0695	+	17.4875i	−0.826549	+	0.600523i
$849$	−0.701475	−	2.15892i	−0.0240745	−	0.0740938i
$850$	2.02128	−	6.22087i	0.0693294	−	0.213374i
$851$	−12.5891	−	9.14652i	−0.431549	−	0.313539i
$852$	0.597742	−	1.83966i	0.0204783	−	0.0630257i
$853$	1.08078	−	3.32630i	0.0370052	−	0.113890i	−0.930848	−	0.365408i	$-0.880930\pi$
$853$	1.08078	−	3.32630i	0.0370052	−	0.113890i	0.967853	+	0.251517i	$0.0809296\pi$
$854$	−23.5527	−	17.1120i	−0.805955	−	0.585561i
$855$	−8.24854	+	25.3864i	−0.282094	+	0.868196i
$856$	1.05944	+	3.26062i	0.0362110	+	0.111446i
$857$	−22.2526	+	16.1675i	−0.760135	+	0.552270i	−0.898952	−	0.438048i	$-0.855670\pi$
$857$	−22.2526	+	16.1675i	−0.760135	+	0.552270i	0.138817	+	0.990318i	$0.455670\pi$
$858$	−0.911913	−	2.80658i	−0.0311322	−	0.0958151i
$859$	7.84999	+	5.70335i	0.267838	+	0.194596i	0.713595	−	0.700558i	$-0.247066\pi$
$859$	7.84999	+	5.70335i	0.267838	+	0.194596i	−0.445757	+	0.895154i	$0.647066\pi$
$860$	−15.1153	−	10.9819i	−0.515427	−	0.374480i
$861$	7.29145	−	5.29755i	0.248492	−	0.180540i
$862$	34.0746			1.16058
$863$	−21.3153			−0.725580			−0.362790	−	0.931871i	$-0.618176\pi$
$863$	−21.3153			−0.725580			−0.362790	+	0.931871i	$0.618176\pi$
$864$	12.3765	−	8.99203i	0.421056	−	0.305915i
$865$	4.80276	−	14.7814i	0.163299	−	0.502582i
$866$	8.54413	+	26.2961i	0.290341	+	0.893579i
$867$	0.319941			0.0108658
$868$	2.63701	+	55.6644i	0.0895061	+	1.88937i
$869$	27.5694			0.935228
$870$	−1.62756	−	5.00911i	−0.0551794	−	0.169825i
$871$	−1.42301	+	4.37958i	−0.0482169	+	0.148396i
$872$	0.842259	−	0.611937i	0.0285225	−	0.0207228i
$873$	−10.2641			−0.347387
$874$	−100.030			−3.38356
$875$	41.1251	−	29.8791i	1.39028	−	1.01010i
$876$	2.49188	+	1.81046i	0.0841930	+	0.0611698i
$877$	−19.9772	−	14.5143i	−0.674582	−	0.490113i	0.196974	−	0.980409i	$-0.436889\pi$
$877$	−19.9772	−	14.5143i	−0.674582	−	0.490113i	−0.871556	+	0.490296i	$0.836889\pi$
$878$	−12.7978	−	39.3876i	−0.431905	−	1.32927i
$879$	3.92279	−	2.85008i	0.132312	−	0.0961306i
$880$	−8.11696	−	24.9814i	−0.273623	−	0.842124i
$881$	−2.22105	+	6.83568i	−0.0748290	+	0.230300i	−0.981474	−	0.191594i	$-0.938634\pi$
$881$	−2.22105	+	6.83568i	−0.0748290	+	0.230300i	0.906645	+	0.421894i	$0.138634\pi$
$882$	−68.8178	−	49.9991i	−2.31722	−	1.68356i
$883$	0.899402	−	2.76807i	0.0302673	−	0.0931531i	−0.934782	−	0.355223i	$-0.884405\pi$
$883$	0.899402	−	2.76807i	0.0302673	−	0.0931531i	0.965049	+	0.262070i	$0.0844050\pi$
$884$	0.561868	−	1.72925i	0.0188977	−	0.0581610i
$885$	−1.24959	−	0.907877i	−0.0420044	−	0.0305180i
$886$	3.01932	−	9.29252i	0.101436	−	0.312188i
$887$	−0.472482	−	1.45415i	−0.0158644	−	0.0488255i	0.942811	−	0.333328i	$-0.108172\pi$
$887$	−0.472482	−	1.45415i	−0.0158644	−	0.0488255i	−0.958675	+	0.284502i	$0.908172\pi$
$888$	0.189473	−	0.137660i	0.00635831	−	0.00461958i
$889$	−21.1559	−	65.1113i	−0.709548	−	2.18376i
$890$	26.6685	+	19.3758i	0.893932	+	0.649479i
$891$	−35.2098	−	25.5814i	−1.17957	−	0.857009i
$892$	5.57200	−	4.04830i	0.186564	−	0.135547i
$893$	87.4836			2.92753
$894$	11.0154			0.368410
$895$	15.7788	−	11.4640i	0.527428	−	0.383199i
$896$	3.82073	−	11.7590i	0.127642	−	0.392840i
$897$	0.592081	+	1.82224i	0.0197690	+	0.0608427i
$898$	−52.5187			−1.75257
$899$	−20.9683	−	26.1613i	−0.699333	−	0.872528i
$900$	20.1020			0.670066
$901$	−2.52274	−	7.76419i	−0.0840446	−	0.258663i
$902$	20.6671	−	63.6068i	0.688139	−	2.11787i
$903$	−7.71314	+	5.60392i	−0.256677	+	0.186487i
$904$	−4.85540			−0.161488
$905$	−20.3347			−0.675947
$906$	7.31362	−	5.31365i	0.242979	−	0.176534i
$907$	18.3103	+	13.3032i	0.607983	+	0.441725i	0.848703	−	0.528869i	$-0.177384\pi$
$907$	18.3103	+	13.3032i	0.607983	+	0.441725i	−0.240721	+	0.970594i	$0.577384\pi$
$908$	27.5164	+	19.9918i	0.913164	+	0.663452i
$909$	15.4907	+	47.6754i	0.513794	+	1.58129i
$910$	8.59236	−	6.24271i	0.284834	−	0.206944i
$911$	−12.4824	−	38.4169i	−0.413561	−	1.27281i	−0.913532	−	0.406767i	$-0.866656\pi$
$911$	−12.4824	−	38.4169i	−0.413561	−	1.27281i	0.499971	−	0.866042i	$-0.333344\pi$
$912$	−2.47759	+	7.62524i	−0.0820412	+	0.252497i
$913$	−29.8486	−	21.6863i	−0.987844	−	0.717710i
$914$	−16.0597	+	49.4268i	−0.531209	+	1.63489i
$915$	−0.408597	+	1.25753i	−0.0135078	+	0.0415727i
$916$	29.0790	+	21.1271i	0.960797	+	0.698060i
$917$	−11.9646	+	36.8232i	−0.395105	+	1.21601i
$918$	1.18988	+	3.66207i	0.0392719	+	0.120866i
$919$	−5.85365	+	4.25293i	−0.193094	+	0.140291i	−0.680132	−	0.733090i	$-0.738077\pi$
$919$	−5.85365	+	4.25293i	−0.193094	+	0.140291i	0.487038	+	0.873381i	$0.338077\pi$
$920$	−0.989593	−	3.04565i	−0.0326259	−	0.100412i
$921$	3.75354	+	2.72711i	0.123683	+	0.0898613i
$922$	−32.7414	−	23.7880i	−1.07828	−	0.783417i
$923$	−1.89856	+	1.37939i	−0.0624919	+	0.0454030i
$924$	17.2287			0.566783
$925$	−6.99697			−0.230059
$926$	−47.0705	+	34.1987i	−1.54683	+	1.12384i
$927$	1.36359	−	4.19671i	0.0447863	−	0.137838i
$928$	15.0866	+	46.4318i	0.495242	+	1.52420i
$929$	−5.00421			−0.164183			−0.0820913	−	0.996625i	$-0.526160\pi$
$929$	−5.00421			−0.164183			−0.0820913	+	0.996625i	$0.526160\pi$
$930$	4.55511	−	1.72235i	0.149368	−	0.0564780i
$931$	98.9201			3.24198
$932$	0.190473	+	0.586214i	0.00623914	+	0.0192021i
$933$	1.99707	−	6.14635i	0.0653812	−	0.201223i
$934$	−32.3596	+	23.5106i	−1.05884	+	0.769291i
$935$	7.20762			0.235715
$936$	0.816310			0.0266819
$937$	−10.6968	+	7.77171i	−0.349450	+	0.253891i	−0.748638	−	0.662979i	$-0.769292\pi$
$937$	−10.6968	+	7.77171i	−0.349450	+	0.253891i	0.399188	+	0.916869i	$0.369292\pi$
$938$	−41.8492	−	30.4052i	−1.36643	−	0.992766i
$939$	8.92774	+	6.48638i	0.291346	+	0.211675i
$940$	11.3990	+	35.0825i	0.371795	+	1.14427i
$941$	20.7375	−	15.0667i	0.676023	−	0.491159i	−0.196013	−	0.980601i	$-0.562800\pi$
$941$	20.7375	−	15.0667i	0.676023	−	0.491159i	0.872036	+	0.489442i	$0.162800\pi$
$942$	−0.102426	−	0.315236i	−0.00333723	−	0.0102709i
$943$	−13.4186	+	41.2982i	−0.436970	+	1.34485i
$944$	10.6248	+	7.71939i	0.345809	+	0.251245i
$945$	−3.61230	+	11.1175i	−0.117508	+	0.361653i
$946$	−21.8623	+	67.2854i	−0.710806	+	2.18764i
$947$	4.43402	+	3.22150i	0.144086	+	0.104685i	0.657493	−	0.753460i	$-0.271617\pi$
$947$	4.43402	+	3.22150i	0.144086	+	0.104685i	−0.513407	+	0.858145i	$0.671617\pi$
$948$	1.09649	−	3.37464i	0.0356123	−	0.109603i
$949$	−1.15475	−	3.55396i	−0.0374848	−	0.115366i
$950$	−36.3881	+	26.4375i	−1.18059	+	0.857747i
$951$	−1.37614	−	4.23533i	−0.0446244	−	0.137340i
$952$	1.25458	+	0.911509i	0.0406613	+	0.0295422i
$953$	7.22457	+	5.24896i	0.234027	+	0.170030i	0.698618	−	0.715495i	$-0.253799\pi$
$953$	7.22457	+	5.24896i	0.234027	+	0.170030i	−0.464591	+	0.885525i	$0.653799\pi$
$954$	39.0539	−	28.3743i	1.26442	−	0.918652i
$955$	34.5427			1.11777
$956$	−38.9356			−1.25927
$957$	−8.38583	+	6.09266i	−0.271075	+	0.196948i
$958$	15.1566	−	46.6473i	0.489688	−	1.50711i
$959$	−21.0393	−	64.7524i	−0.679396	−	2.09096i
$960$	−3.96730			−0.128044
$961$	23.2447	−	20.5106i	0.749828	−	0.661633i
$962$	−3.74231			−0.120657
$963$	9.15459	+	28.1749i	0.295003	+	0.907924i
$964$	0.793059	−	2.44078i	0.0255427	−	0.0786124i
$965$	0.647018	−	0.470086i	0.0208282	−	0.0151326i
$966$	−21.5230			−0.692490
$967$	3.85716			0.124038			0.0620190	−	0.998075i	$-0.480246\pi$
$967$	3.85716			0.124038			0.0620190	+	0.998075i	$0.480246\pi$
$968$	4.86882	−	3.53740i	0.156490	−	0.113696i
$969$	−1.77986	−	1.29314i	−0.0571773	−	0.0415418i
$970$	7.83429	+	5.69194i	0.251544	+	0.182757i
$971$	−4.28022	−	13.1732i	−0.137359	−	0.422747i	0.858591	−	0.512662i	$-0.171340\pi$
$971$	−4.28022	−	13.1732i	−0.137359	−	0.422747i	−0.995949	+	0.0899149i	$0.971340\pi$
$972$	−14.4434	+	10.4938i	−0.463273	+	0.336587i
$973$	−7.02970	−	21.6352i	−0.225362	−	0.693592i
$974$	20.6608	−	63.5874i	0.662015	−	2.03747i
$975$	0.696994	+	0.506396i	0.0223217	+	0.0162176i
$976$	3.47417	−	10.6924i	0.111205	−	0.342255i
$977$	10.2105	−	31.4248i	0.326664	−	1.00537i	−0.644020	−	0.765009i	$-0.722735\pi$
$977$	10.2105	−	31.4248i	0.326664	−	1.00537i	0.970684	−	0.240360i	$-0.0772653\pi$
$978$	0.613882	+	0.446011i	0.0196298	+	0.0142619i
$979$	20.0474	−	61.6995i	0.640718	−	1.97193i
$980$	12.8892	+	39.6688i	0.411729	+	1.26717i
$981$	7.27793	−	5.28773i	0.232366	−	0.168824i
$982$	19.9392	+	61.3665i	0.636285	+	1.95828i
$983$	7.06658	+	5.13417i	0.225389	+	0.163755i	0.694749	−	0.719252i	$-0.255515\pi$
$983$	7.06658	+	5.13417i	0.225389	+	0.163755i	−0.469360	+	0.883007i	$0.655515\pi$
$984$	−0.528732	−	0.384146i	−0.0168554	−	0.0122461i
$985$	−4.80320	+	3.48973i	−0.153043	+	0.111192i
$986$	−12.2883			−0.391338
$987$	18.8235			0.599157
$988$	−10.1150	+	7.34900i	−0.321802	+	0.233803i
$989$	14.1946	−	43.6866i	0.451363	−	1.38915i
$990$	13.1702	+	40.5336i	0.418575	+	1.28824i
$991$	31.0222			0.985453			0.492727	−	0.870184i	$-0.336000\pi$
$991$	31.0222			0.985453			0.492727	+	0.870184i	$0.336000\pi$
$992$	−42.2235	+	15.9653i	−1.34060	+	0.506898i
$993$	−4.86547			−0.154401
$994$	−8.14616	−	25.0713i	−0.258380	−	0.795213i
$995$	3.91129	−	12.0377i	0.123996	−	0.381621i
$996$	−3.84165	+	2.79112i	−0.121727	+	0.0884401i
$997$	−46.0843			−1.45951			−0.729753	−	0.683711i	$-0.760365\pi$
$997$	−46.0843			−1.45951			−0.729753	+	0.683711i	$0.760365\pi$
$998$	−15.8439			−0.501531
$999$	3.33230	−	2.42106i	0.105429	−	0.0765989i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	527.2.h.c.35.5	✓	96
31.8	even	5	inner	527.2.h.c.256.5	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
527.2.h.c.35.5	✓	96	1.1	even	1	trivial
527.2.h.c.256.5	yes	96	31.8	even	5	inner

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:	\( N \)	\(=\)	\( 527 = 17 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	527.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.630601 - 1.94079i) q^{2} +(0.0988673 - 0.304282i) q^{3} +(-1.75098 + 1.27216i) q^{4} +1.33965 q^{5} -0.652894 q^{6} +(-3.74126 + 2.71818i) q^{7} +(0.271294 + 0.197106i) q^{8} +(2.34424 + 1.70319i) q^{9} +O(q^{10})\)	\(q+(-0.630601 - 1.94079i) q^{2} +(0.0988673 - 0.304282i) q^{3} +(-1.75098 + 1.27216i) q^{4} +1.33965 q^{5} -0.652894 q^{6} +(-3.74126 + 2.71818i) q^{7} +(0.271294 + 0.197106i) q^{8} +(2.34424 + 1.70319i) q^{9} +(-0.844788 - 2.59999i) q^{10} +(-4.35268 + 3.16241i) q^{11} +(0.213981 + 0.658567i) q^{12} +(0.259604 - 0.798979i) q^{13} +(7.63467 + 5.54691i) q^{14} +(0.132448 - 0.407633i) q^{15} +(-1.12616 + 3.46598i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(1.82725 - 5.62371i) q^{18} +(2.12491 + 6.53979i) q^{19} +(-2.34571 + 1.70425i) q^{20} +(0.457207 + 1.40714i) q^{21} +(8.88238 + 6.45343i) q^{22} +(-5.76709 - 4.19004i) q^{23} +(0.0867981 - 0.0630625i) q^{24} -3.20533 q^{25} -1.71436 q^{26} +(1.52653 - 1.10909i) q^{27} +(3.09290 - 9.51896i) q^{28} +(1.86081 + 5.72697i) q^{29} -0.874653 q^{30} +(-5.20791 + 1.96918i) q^{31} +8.10757 q^{32} +(0.531927 + 1.63710i) q^{33} +(-0.630601 + 1.94079i) q^{34} +(-5.01200 + 3.64143i) q^{35} -6.27144 q^{36} +2.18292 q^{37} +(11.3524 - 8.24800i) q^{38} +(-0.217449 - 0.157986i) q^{39} +(0.363440 + 0.264055i) q^{40} +(-1.88238 - 5.79338i) q^{41} +(2.44265 - 1.77469i) q^{42} +(1.99125 + 6.12843i) q^{43} +(3.59836 - 11.0746i) q^{44} +(3.14047 + 2.28168i) q^{45} +(-4.49525 + 13.8350i) q^{46} +(3.93144 - 12.0997i) q^{47} +(0.943294 + 0.685343i) q^{48} +(4.44538 - 13.6815i) q^{49} +(2.02128 + 6.22087i) q^{50} +(-0.258838 + 0.188057i) q^{51} +(0.561868 + 1.72925i) q^{52} +(6.60462 + 4.79853i) q^{53} +(-3.11515 - 2.26329i) q^{54} +(-5.83109 + 4.23654i) q^{55} -1.55075 q^{56} +2.20003 q^{57} +(9.94143 - 7.22287i) q^{58} +(1.11360 - 3.42729i) q^{59} +(0.286661 + 0.882252i) q^{60} -3.08496 q^{61} +(7.10588 + 8.86570i) q^{62} -13.4000 q^{63} +(-2.86031 - 8.80314i) q^{64} +(0.347780 - 1.07036i) q^{65} +(2.84184 - 2.06472i) q^{66} -5.48147 q^{67} +2.16433 q^{68} +(-1.84513 + 1.34057i) q^{69} +(10.2278 + 7.43095i) q^{70} +(-2.25993 - 1.64194i) q^{71} +(0.300268 + 0.924129i) q^{72} +(3.59861 - 2.61454i) q^{73} +(-1.37655 - 4.23659i) q^{74} +(-0.316902 + 0.975324i) q^{75} +(-12.0403 - 8.74781i) q^{76} +(7.68851 - 23.6628i) q^{77} +(-0.169494 + 0.521649i) q^{78} +(-4.14559 - 3.01194i) q^{79} +(-1.50867 + 4.64321i) q^{80} +(2.49971 + 7.69330i) q^{81} +(-10.0567 + 7.30662i) q^{82} +(2.11909 + 6.52188i) q^{83} +(-2.59067 - 1.88223i) q^{84} +(-1.08380 - 0.787429i) q^{85} +(10.6383 - 7.72919i) q^{86} +1.92659 q^{87} -1.80419 q^{88} +(-9.75515 + 7.08753i) q^{89} +(2.44789 - 7.53383i) q^{90} +(1.20053 + 3.69484i) q^{91} +15.4284 q^{92} +(0.0842946 + 1.77936i) q^{93} -25.9622 q^{94} +(2.84664 + 8.76107i) q^{95} +(0.801574 - 2.46699i) q^{96} +(-2.86572 + 2.08207i) q^{97} -29.3562 q^{98} -15.5899 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9}+O(q^{10}) \) 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9	\( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9} - 13 q^{10} - 4 q^{11} - 14 q^{12} - 14 q^{13} + 17 q^{14} - 9 q^{15} - 58 q^{16} - 24 q^{17} - 24 q^{18} - 6 q^{19} + 43 q^{20} + 26 q^{21} + 42 q^{22} - 11 q^{23} - 38 q^{24} + 126 q^{25} - 44 q^{26} - q^{27} + 31 q^{28} - 10 q^{29} - 70 q^{30} + 21 q^{31} + 28 q^{32} - 36 q^{33} - 2 q^{34} + 2 q^{35} + 160 q^{36} + 54 q^{37} + 15 q^{38} - 10 q^{39} - 29 q^{40} - 14 q^{41} - 3 q^{42} + 6 q^{43} - 5 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 93 q^{48} - 72 q^{49} + 108 q^{50} + q^{51} + 13 q^{52} - 30 q^{53} - 63 q^{54} - 12 q^{55} + 66 q^{56} - 62 q^{57} + 29 q^{58} + 8 q^{59} - 86 q^{60} - 14 q^{61} - 34 q^{62} + 86 q^{63} - 122 q^{64} + 13 q^{65} - 40 q^{66} + 126 q^{67} + 120 q^{68} - 34 q^{69} - 38 q^{70} - 39 q^{71} - 51 q^{72} - 60 q^{73} - 111 q^{74} - 41 q^{75} + 64 q^{76} - 26 q^{77} - 99 q^{78} - 33 q^{79} - 91 q^{80} + 81 q^{81} - 88 q^{82} + 22 q^{83} + 160 q^{84} - 4 q^{85} + 35 q^{86} + 70 q^{87} - 120 q^{88} + 101 q^{89} + 125 q^{90} - 13 q^{91} - 98 q^{92} + 47 q^{93} - 8 q^{94} - 64 q^{95} + 208 q^{96} + 16 q^{97} + 8 q^{98} + 280 q^{99}+O(q^{100}) \) 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9 - 13 * q^10 - 4 * q^11 - 14 * q^12 - 14 * q^13 + 17 * q^14 - 9 * q^15 - 58 * q^16 - 24 * q^17 - 24 * q^18 - 6 * q^19 + 43 * q^20 + 26 * q^21 + 42 * q^22 - 11 * q^23 - 38 * q^24 + 126 * q^25 - 44 * q^26 - q^27 + 31 * q^28 - 10 * q^29 - 70 * q^30 + 21 * q^31 + 28 * q^32 - 36 * q^33 - 2 * q^34 + 2 * q^35 + 160 * q^36 + 54 * q^37 + 15 * q^38 - 10 * q^39 - 29 * q^40 - 14 * q^41 - 3 * q^42 + 6 * q^43 - 5 * q^44 - q^45 - 17 * q^46 - 14 * q^47 - 93 * q^48 - 72 * q^49 + 108 * q^50 + q^51 + 13 * q^52 - 30 * q^53 - 63 * q^54 - 12 * q^55 + 66 * q^56 - 62 * q^57 + 29 * q^58 + 8 * q^59 - 86 * q^60 - 14 * q^61 - 34 * q^62 + 86 * q^63 - 122 * q^64 + 13 * q^65 - 40 * q^66 + 126 * q^67 + 120 * q^68 - 34 * q^69 - 38 * q^70 - 39 * q^71 - 51 * q^72 - 60 * q^73 - 111 * q^74 - 41 * q^75 + 64 * q^76 - 26 * q^77 - 99 * q^78 - 33 * q^79 - 91 * q^80 + 81 * q^81 - 88 * q^82 + 22 * q^83 + 160 * q^84 - 4 * q^85 + 35 * q^86 + 70 * q^87 - 120 * q^88 + 101 * q^89 + 125 * q^90 - 13 * q^91 - 98 * q^92 + 47 * q^93 - 8 * q^94 - 64 * q^95 + 208 * q^96 + 16 * q^97 + 8 * q^98 + 280 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more