LMFDB - Embedded newform 253.2.i.b.133.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [253,2,Mod(12,253)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(253, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 20])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("253.12"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 253 = 11 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	253.i (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [120] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.02021517114$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			133.9
Character	$\chi$	$=$	253.133
Dual form			253.2.i.b.78.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.31635 + 0.386515i) q^{2} +(2.12429 - 2.45157i) q^{3} +(-0.0991254 - 0.0637040i) q^{4} +(-0.175069 + 1.21763i) q^{5} +(3.74388 - 2.40605i) q^{6} +(1.65863 + 3.63189i) q^{7} +(-1.90270 - 2.19583i) q^{8} +(-1.07061 - 7.44623i) q^{9} +(-0.701085 + 1.53516i) q^{10} +(-0.959493 + 0.281733i) q^{11} +(-0.366746 + 0.107686i) q^{12} +(-0.977112 + 2.13958i) q^{13} +(0.779555 + 5.42193i) q^{14} +(2.61321 + 3.01580i) q^{15} +(-1.55800 - 3.41153i) q^{16} +(-4.03158 + 2.59094i) q^{17} +(1.46879 - 10.2156i) q^{18} +(0.159142 + 0.102275i) q^{19} +(0.0949218 - 0.109546i) q^{20} +(12.4272 + 3.64897i) q^{21} -1.37192 q^{22} +(-4.29400 - 2.13579i) q^{23} -9.42511 q^{24} +(3.34549 + 0.982323i) q^{25} +(-2.11320 + 2.43876i) q^{26} +(-12.3424 - 7.93198i) q^{27} +(0.0669539 - 0.465674i) q^{28} +(8.24996 - 5.30193i) q^{29} +(2.27424 + 4.97989i) q^{30} +(-0.726311 - 0.838207i) q^{31} +(0.0947340 + 0.658890i) q^{32} +(-1.34756 + 2.95074i) q^{33} +(-6.30840 + 1.85231i) q^{34} +(-4.71269 + 1.38377i) q^{35} +(-0.368230 + 0.806312i) q^{36} +(0.798010 + 5.55028i) q^{37} +(0.169956 + 0.196140i) q^{38} +(3.16964 + 6.94054i) q^{39} +(3.00681 - 1.93236i) q^{40} +(-1.49113 + 10.3710i) q^{41} +(14.9482 + 9.60663i) q^{42} +(0.167519 - 0.193327i) q^{43} +(0.113058 + 0.0331967i) q^{44} +9.25420 q^{45} +(-4.82688 - 4.47114i) q^{46} +3.04112 q^{47} +(-11.6732 - 3.42757i) q^{48} +(-5.85557 + 6.75769i) q^{49} +(4.02415 + 2.58616i) q^{50} +(-2.21240 + 15.3876i) q^{51} +(0.233156 - 0.149840i) q^{52} +(-5.40690 - 11.8395i) q^{53} +(-13.1811 - 15.2118i) q^{54} +(-0.175069 - 1.21763i) q^{55} +(4.81915 - 10.5525i) q^{56} +(0.588798 - 0.172887i) q^{57} +(12.9091 - 3.79046i) q^{58} +(2.43390 - 5.32951i) q^{59} +(-0.0669165 - 0.465414i) q^{60} +(-1.66044 - 1.91624i) q^{61} +(-0.632099 - 1.38410i) q^{62} +(25.2682 - 16.2389i) q^{63} +(-1.19746 + 8.32851i) q^{64} +(-2.43415 - 1.56434i) q^{65} +(-2.91437 + 3.36336i) q^{66} +(-5.95619 - 1.74889i) q^{67} +0.564685 q^{68} +(-14.3577 + 5.98997i) q^{69} -6.73839 q^{70} +(8.45222 + 2.48179i) q^{71} +(-14.3136 + 16.5188i) q^{72} +(-3.98150 - 2.55876i) q^{73} +(-1.09481 + 7.61455i) q^{74} +(9.51503 - 6.11494i) q^{75} +(-0.00925975 - 0.0202760i) q^{76} +(-2.61467 - 3.01749i) q^{77} +(1.48973 + 10.3613i) q^{78} +(0.603024 - 1.32044i) q^{79} +(4.42675 - 1.29981i) q^{80} +(-24.0105 + 7.05011i) q^{81} +(-5.97140 + 13.0756i) q^{82} +(-0.819137 - 5.69722i) q^{83} +(-0.999402 - 1.15337i) q^{84} +(-2.44900 - 5.36257i) q^{85} +(0.295237 - 0.189737i) q^{86} +(4.52732 - 31.4882i) q^{87} +(2.44426 + 1.57083i) q^{88} +(6.49063 - 7.49058i) q^{89} +(12.1818 + 3.57689i) q^{90} -9.39138 q^{91} +(0.289586 + 0.485256i) q^{92} -3.59782 q^{93} +(4.00318 + 1.17544i) q^{94} +(-0.152394 + 0.175872i) q^{95} +(1.81655 + 1.16743i) q^{96} +(-0.806090 + 5.60648i) q^{97} +(-10.3199 + 6.63222i) q^{98} +(3.12508 + 6.84298i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - q^{2} - 4 q^{3} - 19 q^{4} - 6 q^{5} - 25 q^{6} - 6 q^{8} - 26 q^{9} + 41 q^{10} - 12 q^{11} - 17 q^{12} - 18 q^{13} - 12 q^{14} + 19 q^{15} - 33 q^{16} - 10 q^{17} + 28 q^{18} + 28 q^{19} - 34 q^{20}+ \cdots - 26 q^{99}+O(q^{100}) $ 120 * q - q^2 - 4 * q^3 - 19 * q^4 - 6 * q^5 - 25 * q^6 - 6 * q^8 - 26 * q^9 + 41 * q^10 - 12 * q^11 - 17 * q^12 - 18 * q^13 - 12 * q^14 + 19 * q^15 - 33 * q^16 - 10 * q^17 + 28 * q^18 + 28 * q^19 - 34 * q^20 - 26 * q^21 + 10 * q^22 + 3 * q^23 + 108 * q^24 - 6 * q^25 - 26 * q^26 - 46 * q^27 - 3 * q^28 + 18 * q^29 + 16 * q^30 - 34 * q^31 - 63 * q^32 + 7 * q^33 - 24 * q^34 - 48 * q^35 - 122 * q^36 - 32 * q^37 + 143 * q^38 - 42 * q^39 + 8 * q^40 - 8 * q^41 + 174 * q^42 + 51 * q^43 - 19 * q^44 - 2 * q^45 - 67 * q^46 - 2 * q^47 - 111 * q^48 + 12 * q^49 - 113 * q^50 + 34 * q^51 + 127 * q^52 - 22 * q^53 - 27 * q^54 - 6 * q^55 + 191 * q^56 + 32 * q^57 - 71 * q^58 - 40 * q^59 + 12 * q^60 - 19 * q^61 + q^62 - 82 * q^63 - 6 * q^64 + 171 * q^65 - 3 * q^66 - 30 * q^67 - 152 * q^68 - 48 * q^69 + 86 * q^70 - 22 * q^71 - 130 * q^72 - 70 * q^73 - 27 * q^74 + 200 * q^75 + 4 * q^76 - 94 * q^78 - 6 * q^79 + 197 * q^80 + 4 * q^81 - 47 * q^82 + 50 * q^83 + 411 * q^84 - 98 * q^85 - 9 * q^86 - 72 * q^87 - 6 * q^88 - 41 * q^89 - 260 * q^90 + 30 * q^92 + 130 * q^93 + 33 * q^94 - 28 * q^95 - 265 * q^96 + 84 * q^97 - 117 * q^98 - 26 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/253\mathbb{Z}\right)^\times$.

$n$	$24$	$166$
$\chi(n)$	$1$	$e\left(\frac{6}{11}\right)$

Coefficient data

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

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

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

$2$	1.31635	+	0.386515i	0.930800	+	0.273307i	0.711771	−	0.702411i	$-0.247893\pi$
$2$	1.31635	+	0.386515i	0.930800	+	0.273307i	0.219028	+	0.975719i	$0.429711\pi$
$3$	2.12429	−	2.45157i	1.22646	−	1.41541i	0.348071	−	0.937468i	$-0.386837\pi$
$3$	2.12429	−	2.45157i	1.22646	−	1.41541i	0.878390	−	0.477944i	$-0.158618\pi$
$4$	−0.0991254	−	0.0637040i	−0.0495627	−	0.0318520i
$5$	−0.175069	+	1.21763i	−0.0782933	+	0.544542i	0.912491	+	0.409096i	$0.134156\pi$
$5$	−0.175069	+	1.21763i	−0.0782933	+	0.544542i	−0.990785	+	0.135446i	$0.956753\pi$
$6$	3.74388	−	2.40605i	1.52843	−	0.982264i
$7$	1.65863	+	3.63189i	0.626903	+	1.37273i	0.910390	+	0.413751i	$0.135782\pi$
$7$	1.65863	+	3.63189i	0.626903	+	1.37273i	−0.283487	+	0.958976i	$0.591491\pi$
$8$	−1.90270	−	2.19583i	−0.672705	−	0.776343i
$9$	−1.07061	−	7.44623i	−0.356869	−	2.48208i
$10$	−0.701085	+	1.53516i	−0.221703	+	0.485461i
$11$	−0.959493	+	0.281733i	−0.289298	+	0.0849456i
$11$	−0.959493	+	0.281733i	−0.289298	+	0.0849456i
$12$	−0.366746	+	0.107686i	−0.105870	+	0.0310864i
$13$	−0.977112	+	2.13958i	−0.271002	+	0.593412i	−0.995382	−	0.0959888i	$-0.969399\pi$
$13$	−0.977112	+	2.13958i	−0.271002	+	0.593412i	0.724380	+	0.689401i	$0.242126\pi$
$14$	0.779555	+	5.42193i	0.208345	+	1.44907i
$15$	2.61321	+	3.01580i	0.674727	+	0.778677i
$16$	−1.55800	−	3.41153i	−0.389499	−	0.852883i
$17$	−4.03158	+	2.59094i	−0.977801	+	0.628394i	−0.928869	−	0.370408i	$-0.879218\pi$
$17$	−4.03158	+	2.59094i	−0.977801	+	0.628394i	−0.0489315	+	0.998802i	$0.515582\pi$
$18$	1.46879	−	10.2156i	0.346197	−	2.40785i
$19$	0.159142	+	0.102275i	0.0365098	+	0.0234634i	0.558768	−	0.829324i	$-0.311274\pi$
$19$	0.159142	+	0.102275i	0.0365098	+	0.0234634i	−0.522259	+	0.852787i	$0.674910\pi$
$20$	0.0949218	−	0.109546i	0.0212252	−	0.0244952i
$21$	12.4272	+	3.64897i	2.71185	+	0.796270i
$22$	−1.37192			−0.292495
$23$	−4.29400	−	2.13579i	−0.895360	−	0.445343i
$23$	−4.29400	−	2.13579i	−0.895360	−	0.445343i
$24$	−9.42511			−1.92389
$25$	3.34549	+	0.982323i	0.669097	+	0.196465i
$26$	−2.11320	+	2.43876i	−0.414432	+	0.478281i
$27$	−12.3424	−	7.93198i	−2.37530	−	1.52651i
$28$	0.0669539	−	0.465674i	0.0126531	−	0.0880042i
$29$	8.24996	−	5.30193i	1.53198	−	0.984544i	0.542470	−	0.840075i	$-0.317489\pi$
$29$	8.24996	−	5.30193i	1.53198	−	0.984544i	0.989509	−	0.144469i	$-0.0461473\pi$
$30$	2.27424	+	4.97989i	0.415218	+	0.909200i
$31$	−0.726311	−	0.838207i	−0.130449	−	0.150546i	0.686767	−	0.726878i	$-0.259029\pi$
$31$	−0.726311	−	0.838207i	−0.130449	−	0.150546i	−0.817216	+	0.576331i	$0.804484\pi$
$32$	0.0947340	+	0.658890i	0.0167468	+	0.116476i
$33$	−1.34756	+	2.95074i	−0.234580	+	0.513658i
$34$	−6.30840	+	1.85231i	−1.08188	+	0.317669i
$35$	−4.71269	+	1.38377i	−0.796589	+	0.233900i
$36$	−0.368230	+	0.806312i	−0.0613717	+	0.134385i
$37$	0.798010	+	5.55028i	0.131192	+	0.912460i	0.944004	+	0.329934i	$0.107027\pi$
$37$	0.798010	+	5.55028i	0.131192	+	0.912460i	−0.812812	+	0.582526i	$0.802064\pi$
$38$	0.169956	+	0.196140i	0.0275705	+	0.0318181i
$39$	3.16964	+	6.94054i	0.507549	+	1.11138i
$40$	3.00681	−	1.93236i	0.475419	−	0.305533i
$41$	−1.49113	+	10.3710i	−0.232875	+	1.61968i	0.452688	+	0.891669i	$0.350465\pi$
$41$	−1.49113	+	10.3710i	−0.232875	+	1.61968i	−0.685563	+	0.728013i	$0.740444\pi$
$42$	14.9482	+	9.60663i	2.30656	+	1.48234i
$43$	0.167519	−	0.193327i	0.0255464	−	0.0294821i	−0.742833	−	0.669477i	$-0.766518\pi$
$43$	0.167519	−	0.193327i	0.0255464	−	0.0294821i	0.768379	+	0.639995i	$0.221064\pi$
$44$	0.113058	+	0.0331967i	0.0170441	+	0.00500459i
$45$	9.25420			1.37953
$46$	−4.82688	−	4.47114i	−0.711685	−	0.659233i
$47$	3.04112			0.443594			0.221797	−	0.975093i	$-0.428808\pi$
$47$	3.04112			0.443594			0.221797	+	0.975093i	$0.428808\pi$
$48$	−11.6732	−	3.42757i	−1.68489	−	0.494727i
$49$	−5.85557	+	6.75769i	−0.836511	+	0.965385i
$50$	4.02415	+	2.58616i	0.569100	+	0.365738i
$51$	−2.21240	+	15.3876i	−0.309798	+	2.15469i
$52$	0.233156	−	0.149840i	0.0323329	−	0.0207791i
$53$	−5.40690	−	11.8395i	−0.742695	−	1.62628i	−0.779070	−	0.626937i	$-0.784308\pi$
$53$	−5.40690	−	11.8395i	−0.742695	−	1.62628i	0.0363749	−	0.999338i	$-0.488419\pi$
$54$	−13.1811	−	15.2118i	−1.79372	−	2.07006i
$55$	−0.175069	−	1.21763i	−0.0236063	−	0.164185i
$56$	4.81915	−	10.5525i	0.643986	−	1.41013i
$57$	0.588798	−	0.172887i	0.0779882	−	0.0228994i
$58$	12.9091	−	3.79046i	1.69505	−	0.497711i
$59$	2.43390	−	5.32951i	0.316867	−	0.693843i	−0.682444	−	0.730937i	$-0.739083\pi$
$59$	2.43390	−	5.32951i	0.316867	−	0.693843i	0.999312	+	0.0370948i	$0.0118104\pi$
$60$	−0.0669165	−	0.465414i	−0.00863888	−	0.0600847i
$61$	−1.66044	−	1.91624i	−0.212597	−	0.245350i	0.639428	−	0.768851i	$-0.279171\pi$
$61$	−1.66044	−	1.91624i	−0.212597	−	0.245350i	−0.852025	+	0.523501i	$0.824626\pi$
$62$	−0.632099	−	1.38410i	−0.0802766	−	0.175781i
$63$	25.2682	−	16.2389i	3.18349	−	2.04591i
$64$	−1.19746	+	8.32851i	−0.149682	+	1.04106i
$65$	−2.43415	−	1.56434i	−0.301920	−	0.194032i
$66$	−2.91437	+	3.36336i	−0.358734	+	0.414001i
$67$	−5.95619	−	1.74889i	−0.727664	−	0.213661i	−0.103140	−	0.994667i	$-0.532889\pi$
$67$	−5.95619	−	1.74889i	−0.727664	−	0.213661i	−0.624524	+	0.781006i	$0.714707\pi$
$68$	0.564685			0.0684781
$69$	−14.3577	+	5.98997i	−1.72847	+	0.721108i
$70$	−6.73839			−0.805391
$71$	8.45222	+	2.48179i	1.00309	+	0.294535i	0.741725	−	0.670704i	$-0.234008\pi$
$71$	8.45222	+	2.48179i	1.00309	+	0.294535i	0.261369	+	0.965239i	$0.415826\pi$
$72$	−14.3136	+	16.5188i	−1.68687	+	1.94676i
$73$	−3.98150	−	2.55876i	−0.466000	−	0.299480i	0.286491	−	0.958083i	$-0.407511\pi$
$73$	−3.98150	−	2.55876i	−0.466000	−	0.299480i	−0.752490	+	0.658603i	$0.771148\pi$
$74$	−1.09481	+	7.61455i	−0.127269	+	0.885174i
$75$	9.51503	−	6.11494i	1.09870	−	0.706092i
$76$	−0.00925975	−	0.0202760i	−0.00106217	−	0.00232582i
$77$	−2.61467	−	3.01749i	−0.297969	−	0.343875i
$78$	1.48973	+	10.3613i	0.168679	+	1.17319i
$79$	0.603024	−	1.32044i	0.0678455	−	0.148561i	−0.872671	−	0.488308i	$-0.837614\pi$
$79$	0.603024	−	1.32044i	0.0678455	−	0.148561i	0.940517	+	0.339747i	$0.110341\pi$
$80$	4.42675	−	1.29981i	0.494926	−	0.145323i
$81$	−24.0105	+	7.05011i	−2.66783	+	0.783345i
$82$	−5.97140	+	13.0756i	−0.659431	+	1.44395i
$83$	−0.819137	−	5.69722i	−0.0899119	−	0.625351i	−0.984094	−	0.177648i	$-0.943151\pi$
$83$	−0.819137	−	5.69722i	−0.0899119	−	0.625351i	0.894182	−	0.447703i	$-0.147758\pi$
$84$	−0.999402	−	1.15337i	−0.109044	−	0.125843i
$85$	−2.44900	−	5.36257i	−0.265632	−	0.581652i
$86$	0.295237	−	0.189737i	0.0318362	−	0.0204599i
$87$	4.52732	−	31.4882i	0.485379	−	3.37589i
$88$	2.44426	+	1.57083i	0.260559	+	0.167451i
$89$	6.49063	−	7.49058i	0.688005	−	0.794000i	−0.299075	−	0.954230i	$-0.596678\pi$
$89$	6.49063	−	7.49058i	0.688005	−	0.794000i	0.987080	+	0.160230i	$0.0512235\pi$
$90$	12.1818	+	3.57689i	1.28407	+	0.377037i
$91$	−9.39138			−0.984484
$92$	0.289586	+	0.485256i	0.0301914	+	0.0505914i
$93$	−3.59782			−0.373076
$94$	4.00318	+	1.17544i	0.412897	+	0.121237i
$95$	−0.152394	+	0.175872i	−0.0156353	+	0.0180441i
$96$	1.81655	+	1.16743i	0.185401	+	0.119150i
$97$	−0.806090	+	5.60648i	−0.0818461	+	0.569252i	0.907093	+	0.420930i	$0.138296\pi$
$97$	−0.806090	+	5.60648i	−0.0818461	+	0.569252i	−0.988939	+	0.148322i	$0.952613\pi$
$98$	−10.3199	+	6.63222i	−1.04247	+	0.669955i
$99$	3.12508	+	6.84298i	0.314083	+	0.687745i
$100$	−0.269045	−	0.310494i	−0.0269045	−	0.0310494i
$101$	−1.18047	−	8.21034i	−0.117461	−	0.816959i	−0.960335	−	0.278849i	$-0.910047\pi$
$101$	−1.18047	−	8.21034i	−0.117461	−	0.816959i	0.842874	−	0.538111i	$-0.180862\pi$
$102$	−8.85982	+	19.4003i	−0.877253	+	1.92092i
$103$	−1.34747	+	0.395653i	−0.132770	+	0.0389849i	−0.347443	−	0.937701i	$-0.612950\pi$
$103$	−1.34747	+	0.395653i	−0.132770	+	0.0389849i	0.214672	+	0.976686i	$0.431132\pi$
$104$	6.55729	−	1.92539i	0.642995	−	0.188800i
$105$	−6.61873	+	14.4930i	−0.645922	+	1.41437i
$106$	−2.54124	−	17.6747i	−0.246827	−	1.71672i
$107$	−2.49917	−	2.88419i	−0.241604	−	0.278825i	0.621978	−	0.783035i	$-0.286329\pi$
$107$	−2.49917	−	2.88419i	−0.241604	−	0.278825i	−0.863581	+	0.504209i	$0.831784\pi$
$108$	0.718147	+	1.57252i	0.0691037	+	0.151316i
$109$	8.05061	−	5.17381i	0.771108	−	0.495561i	−0.0949635	−	0.995481i	$-0.530273\pi$
$109$	8.05061	−	5.17381i	0.771108	−	0.495561i	0.866072	+	0.499920i	$0.166637\pi$
$110$	0.240181	−	1.67050i	0.0229004	−	0.159276i
$111$	15.3021	+	9.83405i	1.45241	+	0.933407i
$112$	9.80619	−	11.3169i	0.926598	−	1.06935i
$113$	−10.5011	−	3.08339i	−0.987857	−	0.290061i	−0.252393	−	0.967625i	$-0.581218\pi$
$113$	−10.5011	−	3.08339i	−0.987857	−	0.290061i	−0.735464	+	0.677564i	$0.763036\pi$
$114$	0.841887			0.0788500
$115$	3.35235	−	4.85460i	0.312608	−	0.452694i
$116$	−1.15554			−0.107289
$117$	16.9779	+	4.98515i	1.56961	+	0.460878i
$118$	5.26380	−	6.07475i	0.484572	−	0.559226i
$119$	−16.0969	−	10.3449i	−1.47560	−	0.948311i
$120$	1.65004	−	11.4763i	0.150628	−	1.04764i
$121$	0.841254	−	0.540641i	0.0764776	−	0.0491492i
$122$	−1.44506	−	3.16423i	−0.130829	−	0.286476i
$123$	22.2577	+	25.6867i	2.00691	+	2.31609i
$124$	0.0185987	+	0.129356i	0.00167021	+	0.0116166i
$125$	−4.33692	+	9.49653i	−0.387906	+	0.849396i
$126$	39.5383	−	11.6095i	3.52235	−	1.03426i
$127$	16.5558	−	4.86121i	1.46909	−	0.431363i	0.553285	−	0.832992i	$-0.313374\pi$
$127$	16.5558	−	4.86121i	1.46909	−	0.431363i	0.915802	+	0.401630i	$0.131556\pi$
$128$	−4.24231	+	9.28937i	−0.374971	+	0.821072i
$129$	−0.118095	−	0.821367i	−0.0103977	−	0.0723173i
$130$	−2.59956	−	3.00005i	−0.227996	−	0.263122i
$131$	3.05258	+	6.68422i	0.266705	+	0.584003i	0.994843	−	0.101428i	$-0.0323411\pi$
$131$	3.05258	+	6.68422i	0.266705	+	0.584003i	−0.728138	+	0.685431i	$0.759614\pi$
$132$	0.321551	−	0.206649i	0.0279875	−	0.0179865i
$133$	−0.107492	+	0.747624i	−0.00932075	+	0.0648272i
$134$	−7.16445	−	4.60431i	−0.618914	−	0.397752i
$135$	11.8190	−	13.6399i	1.01722	−	1.17393i
$136$	13.3601	+	3.92288i	1.14562	+	0.336385i
$137$	−1.34457			−0.114874			−0.0574372	−	0.998349i	$-0.518293\pi$
$137$	−1.34457			−0.114874			−0.0574372	+	0.998349i	$0.518293\pi$
$138$	−21.2150	+	2.33541i	−1.80594	+	0.198804i
$139$	−8.53553			−0.723974			−0.361987	−	0.932183i	$-0.617902\pi$
$139$	−8.53553			−0.723974			−0.361987	+	0.932183i	$0.617902\pi$
$140$	0.555298	+	0.163050i	0.0469313	+	0.0137803i
$141$	6.46024	−	7.45552i	0.544050	−	0.627868i
$142$	10.1668	+	6.53382i	0.853180	+	0.548306i
$143$	0.334744	−	2.32819i	0.0279927	−	0.194693i
$144$	−23.7351	+	15.2536i	−1.97792	+	1.27113i
$145$	5.01149	+	10.9736i	0.416181	+	0.911310i
$146$	−4.25205	−	4.90713i	−0.351902	−	0.406117i
$147$	4.12797	+	28.7107i	0.340469	+	2.36801i
$148$	0.274472	−	0.601010i	0.0225615	−	0.0494027i
$149$	−4.33397	+	1.27257i	−0.355053	+	0.104253i	−0.454395	−	0.890800i	$-0.650144\pi$
$149$	−4.33397	+	1.27257i	−0.355053	+	0.104253i	0.0993418	+	0.995053i	$0.468326\pi$
$150$	14.8886	−	4.37169i	1.21565	−	0.356947i
$151$	1.12258	−	2.45810i	0.0913540	−	0.200037i	−0.858439	−	0.512915i	$-0.828566\pi$
$151$	1.12258	−	2.45810i	0.0913540	−	0.200037i	0.949793	+	0.312877i	$0.101293\pi$
$152$	−0.0782221	−	0.544047i	−0.00634465	−	0.0441280i
$153$	23.6089	+	27.2462i	1.90867	+	2.20272i
$154$	−2.27551	−	4.98267i	−0.183366	−	0.401515i
$155$	1.14778	−	0.737635i	0.0921921	−	0.0592483i
$156$	0.127949	−	0.889903i	0.0102441	−	0.0712492i
$157$	14.4011	+	9.25503i	1.14933	+	0.738632i	0.969506	−	0.245067i	$-0.0788099\pi$
$157$	14.4011	+	9.25503i	1.14933	+	0.738632i	0.179827	+	0.983698i	$0.442446\pi$
$158$	1.30416	−	1.50508i	0.103753	−	0.119738i
$159$	−40.5111	−	11.8951i	−3.21274	−	0.943345i
$160$	−0.818870			−0.0647374
$161$	0.634806	−	19.1378i	0.0500297	−	1.50827i
$162$	−34.3311			−2.69731
$163$	−8.49074	−	2.49311i	−0.665046	−	0.195275i	−0.0682500	−	0.997668i	$-0.521742\pi$
$163$	−8.49074	−	2.49311i	−0.665046	−	0.195275i	−0.596796	+	0.802393i	$0.703560\pi$
$164$	0.808485	−	0.933041i	0.0631321	−	0.0728583i
$165$	−3.35700	−	2.15742i	−0.261342	−	0.167955i
$166$	1.12379	−	7.81614i	0.0872231	−	0.606650i
$167$	4.96713	−	3.19218i	0.384368	−	0.247018i	−0.334160	−	0.942516i	$-0.608453\pi$
$167$	4.96713	−	3.19218i	0.384368	−	0.247018i	0.718528	+	0.695498i	$0.244816\pi$
$168$	−15.6328	−	34.2310i	−1.20609	−	2.64098i
$169$	4.89015	+	5.64353i	0.376165	+	0.434118i
$170$	−1.15103	−	8.00559i	−0.0882800	−	0.614001i
$171$	0.591181	−	1.29451i	0.0452087	−	0.0989934i
$172$	−0.0289211	+	0.00849199i	−0.00220521	+	0.000647509i
$173$	−17.0933	+	5.01904i	−1.29958	+	0.381590i	−0.857082	−	0.515180i	$-0.827725\pi$
$173$	−17.0933	+	5.01904i	−1.29958	+	0.381590i	−0.442496	+	0.896771i	$0.645907\pi$
$174$	18.1302	−	39.6996i	1.37445	−	3.00962i
$175$	1.98123	+	13.7798i	0.149767	+	1.04165i
$176$	2.45603	+	2.83440i	0.185130	+	0.213651i
$177$	−7.89531	−	17.2883i	−0.593448	−	1.29947i
$178$	11.4392	−	7.35150i	0.857401	−	0.551018i
$179$	−0.700699	+	4.87347i	−0.0523727	+	0.364260i	0.946735	+	0.322015i	$0.104360\pi$
$179$	−0.700699	+	4.87347i	−0.0523727	+	0.364260i	−0.999107	+	0.0422451i	$0.986549\pi$
$180$	−0.917326	−	0.589529i	−0.0683734	−	0.0439409i
$181$	−8.79855	+	10.1541i	−0.653991	+	0.754746i	−0.981783	−	0.190004i	$-0.939150\pi$
$181$	−8.79855	+	10.1541i	−0.653991	+	0.754746i	0.327792	+	0.944750i	$0.393695\pi$
$182$	−12.3623	−	3.62991i	−0.916358	−	0.269067i
$183$	−8.22505			−0.608013
$184$	3.48034	+	13.4926i	0.256574	+	0.994691i
$185$	−6.89791			−0.507144
$186$	−4.73598	−	1.39061i	−0.347259	−	0.101964i
$187$	3.13832	−	3.62181i	0.229497	−	0.264853i
$188$	−0.301453	−	0.193732i	−0.0219857	−	0.0141293i
$189$	8.33663	−	57.9825i	0.606401	−	4.21761i
$190$	−0.268580	+	0.172606i	−0.0194849	+	0.0125222i
$191$	−5.41992	−	11.8680i	−0.392172	−	0.858737i	−0.998004	−	0.0631444i	$-0.979887\pi$
$191$	−5.41992	−	11.8680i	−0.392172	−	0.858737i	0.605833	−	0.795592i	$-0.292840\pi$
$192$	17.8741	+	20.6278i	1.28995	+	1.48869i
$193$	0.122080	+	0.849087i	0.00878753	+	0.0611186i	0.993743	−	0.111688i	$-0.0356256\pi$
$193$	0.122080	+	0.849087i	0.00878753	+	0.0611186i	−0.984956	+	0.172806i	$0.944717\pi$
$194$	−3.22809	+	7.06852i	−0.231763	+	0.507490i
$195$	−9.00593	+	2.64438i	−0.644928	+	0.189368i
$196$	1.01093	−	0.296835i	0.0722092	−	0.0212025i
$197$	−2.34968	+	5.14507i	−0.167408	+	0.366571i	−0.974679	−	0.223609i	$-0.928216\pi$
$197$	−2.34968	+	5.14507i	−0.167408	+	0.366571i	0.807271	+	0.590180i	$0.200943\pi$
$198$	1.46879	+	10.2156i	0.104382	+	0.725994i
$199$	15.5675	+	17.9658i	1.10355	+	1.27356i	0.958796	+	0.284095i	$0.0916932\pi$
$199$	15.5675	+	17.9658i	1.10355	+	1.27356i	0.144753	+	0.989468i	$0.453761\pi$
$200$	−4.20843	−	9.21518i	−0.297581	−	0.651612i
$201$	−16.9402	+	10.8868i	−1.19487	+	0.767897i
$202$	1.61951	−	11.2639i	0.113948	−	0.792528i
$203$	32.9397	+	21.1691i	2.31191	+	1.48578i
$204$	1.19956	−	1.38436i	0.0839857	−	0.0969247i
$205$	−12.3670	−	3.63129i	−0.863752	−	0.253620i
$206$	−1.92667			−0.134237
$207$	−11.3064	+	34.2607i	−0.785849	+	2.38128i
$208$	8.82157			0.611666
$209$	−0.181510	−	0.0532962i	−0.0125553	−	0.00368657i
$210$	−14.3143	+	16.5196i	−0.987782	+	1.13996i
$211$	6.56344	+	4.21807i	0.451846	+	0.290384i	0.746703	−	0.665158i	$-0.231636\pi$
$211$	6.56344	+	4.21807i	0.451846	+	0.290384i	−0.294857	+	0.955541i	$0.595272\pi$
$212$	−0.218260	+	1.51803i	−0.0149902	+	0.104259i
$213$	24.0393	−	15.4491i	1.64714	−	1.05856i
$214$	−2.17499	−	4.76257i	−0.148679	−	0.325563i
$215$	0.206074	+	0.237822i	0.0140541	+	0.0162193i
$216$	6.06658	+	42.1940i	0.412778	+	2.87094i
$217$	1.83960	−	4.02816i	0.124880	−	0.273449i
$218$	12.5972	−	3.69886i	0.853188	−	0.250519i
$219$	−14.7308	+	4.32536i	−0.995418	+	0.292281i
$220$	−0.0602143	+	0.131851i	−0.00405964	+	0.00888938i
$221$	−1.60421	−	11.1575i	−0.107911	−	0.750535i
$222$	16.3419	+	18.8595i	1.09680	+	1.26577i
$223$	7.59817	+	16.6377i	0.508811	+	1.11414i	0.973504	+	0.228669i	$0.0734374\pi$
$223$	7.59817	+	16.6377i	0.508811	+	1.11414i	−0.464693	+	0.885472i	$0.653835\pi$
$224$	−2.23589	+	1.43692i	−0.149392	+	0.0960081i
$225$	3.73291	−	25.9629i	0.248860	−	1.73086i
$226$	−12.6313	−	8.11764i	−0.840221	−	0.539977i
$227$	15.8196	−	18.2568i	1.04999	−	1.21175i	0.0732485	−	0.997314i	$-0.476663\pi$
$227$	15.8196	−	18.2568i	1.04999	−	1.21175i	0.976738	−	0.214435i	$-0.0687912\pi$
$228$	−0.0693784	−	0.0203713i	−0.00459470	−	0.00134912i
$229$	12.6252			0.834299			0.417150	−	0.908838i	$-0.363029\pi$
$229$	12.6252			0.834299			0.417150	+	0.908838i	$0.363029\pi$
$230$	6.28924	−	5.09461i	0.414700	−	0.335929i
$231$	−12.9519			−0.852172
$232$	−27.3393	−	8.02755i	−1.79491	−	0.527034i
$233$	−7.40352	+	8.54411i	−0.485020	+	0.559743i	−0.944528	−	0.328430i	$-0.893480\pi$
$233$	−7.40352	+	8.54411i	−0.485020	+	0.559743i	0.459508	+	0.888174i	$0.348026\pi$
$234$	20.4220	+	13.1244i	1.33503	+	0.857969i
$235$	−0.532407	+	3.70297i	−0.0347304	+	0.241555i
$236$	−0.580773	+	0.373240i	−0.0378051	+	0.0242958i
$237$	−1.95614	−	4.28335i	−0.127065	−	0.278234i
$238$	−17.1907	−	19.8391i	−1.11431	−	1.28598i
$239$	2.75479	+	19.1600i	0.178193	+	1.23936i	0.860942	+	0.508703i	$0.169875\pi$
$239$	2.75479	+	19.1600i	0.178193	+	1.23936i	−0.682749	+	0.730653i	$0.739216\pi$
$240$	6.21714	−	13.6136i	0.401315	−	0.878757i
$241$	−26.6600	+	7.82809i	−1.71732	+	0.504252i	−0.984383	−	0.176041i	$-0.943671\pi$
$241$	−26.6600	+	7.82809i	−1.71732	+	0.504252i	−0.732941	+	0.680292i	$0.761853\pi$
$242$	1.31635	−	0.386515i	0.0846181	−	0.0248461i
$243$	−15.4373	+	33.8029i	−0.990300	+	2.16846i
$244$	0.0425188	+	0.295725i	0.00272199	+	0.0189318i
$245$	−7.20325	−	8.31300i	−0.460199	−	0.531098i
$246$	19.3706	+	42.4156i	1.23502	+	2.70432i
$247$	−0.374324	+	0.240564i	−0.0238177	+	0.0153067i
$248$	−0.458611	+	3.18971i	−0.0291218	+	0.202547i
$249$	−15.7072	−	10.0944i	−0.995403	−	0.639707i
$250$	−9.37945	+	10.8245i	−0.593209	+	0.684599i
$251$	16.0654	+	4.71723i	1.01404	+	0.297749i	0.746205	−	0.665716i	$-0.231874\pi$
$251$	16.0654	+	4.71723i	1.01404	+	0.297749i	0.267835	+	0.963465i	$0.413692\pi$
$252$	−3.53920			−0.222949
$253$	4.72178	+	0.839516i	0.296856	+	0.0527799i
$254$	23.6721			1.48532
$255$	−18.3491	−	5.38778i	−1.14906	−	0.337396i
$256$	1.84535	−	2.12965i	0.115334	−	0.133103i
$257$	−23.7087	−	15.2367i	−1.47891	−	0.950437i	−0.997252	−	0.0740776i	$-0.976399\pi$
$257$	−23.7087	−	15.2367i	−1.47891	−	0.950437i	−0.481657	−	0.876360i	$-0.659965\pi$
$258$	0.162017	−	1.12685i	0.0100867	−	0.0701547i
$259$	−18.8344	+	12.1042i	−1.17031	+	0.752115i
$260$	0.141632	+	0.310131i	0.00878365	+	0.0192335i
$261$	−48.3118	−	55.7548i	−2.99043	−	3.45114i
$262$	1.43471	+	9.97864i	0.0886368	+	0.616482i
$263$	5.28063	−	11.5630i	0.325617	−	0.713003i	−0.674053	−	0.738683i	$-0.735448\pi$
$263$	5.28063	−	11.5630i	0.325617	−	0.713003i	0.999670	+	0.0256806i	$0.00817527\pi$
$264$	9.04332	−	2.65536i	0.556578	−	0.163426i
$265$	15.3627	−	4.51089i	0.943723	−	0.277102i
$266$	−0.430465	+	0.942587i	−0.0263935	+	0.0577937i
$267$	−4.57566	−	31.8244i	−0.280026	−	1.94762i
$268$	0.478998	+	0.552793i	0.0292594	+	0.0337672i
$269$	−2.40389	−	5.26378i	−0.146568	−	0.320938i	0.822082	−	0.569369i	$-0.192812\pi$
$269$	−2.40389	−	5.26378i	−0.146568	−	0.320938i	−0.968650	+	0.248431i	$0.920085\pi$
$270$	20.8300	−	13.3866i	1.26767	−	0.814683i
$271$	−1.42191	+	9.88959i	−0.0863748	+	0.600750i	0.899957	+	0.435979i	$0.143598\pi$
$271$	−1.42191	+	9.88959i	−0.0863748	+	0.600750i	−0.986332	+	0.164771i	$0.947311\pi$
$272$	15.1202	+	9.71719i	0.916799	+	0.589191i
$273$	−19.9501	+	23.0236i	−1.20743	+	1.39345i
$274$	−1.76993	−	0.519697i	−0.106925	−	0.0313960i
$275$	−3.48672			−0.210257
$276$	1.80480	+	0.320887i	0.108636	+	0.0193151i
$277$	7.79230			0.468194			0.234097	−	0.972213i	$-0.424787\pi$
$277$	7.79230			0.468194			0.234097	+	0.972213i	$0.424787\pi$
$278$	−11.2357	−	3.29911i	−0.673875	−	0.197867i
$279$	−5.46389	+	6.30566i	−0.327114	+	0.377510i
$280$	12.0053	+	7.71536i	0.717456	+	0.461081i
$281$	−0.691452	+	4.80915i	−0.0412485	+	0.286890i	0.958748	+	0.284257i	$0.0917470\pi$
$281$	−0.691452	+	4.80915i	−0.0412485	+	0.286890i	−0.999997	+	0.00263250i	$0.999162\pi$
$282$	11.3856	−	7.31708i	0.678003	−	0.435726i
$283$	6.36696	+	13.9417i	0.378476	+	0.828747i	0.999006	+	0.0445649i	$0.0141902\pi$
$283$	6.36696	+	13.9417i	0.378476	+	0.828747i	−0.620530	+	0.784183i	$0.713083\pi$
$284$	−0.679729	−	0.784449i	−0.0403345	−	0.0465485i
$285$	0.107432	+	0.747206i	0.00636373	+	0.0442607i
$286$	1.34052	−	2.93533i	0.0792667	−	0.173570i
$287$	−40.1397	+	11.7861i	−2.36937	+	0.695710i
$288$	4.80482	−	1.41082i	0.283127	−	0.0831335i
$289$	2.47860	−	5.42737i	0.145800	−	0.319257i
$290$	2.35540	+	16.3821i	0.138314	+	0.961992i
$291$	12.0323	+	13.8860i	0.705345	+	0.814012i
$292$	0.231665	+	0.507275i	0.0135572	+	0.0296860i
$293$	1.16323	−	0.747564i	0.0679568	−	0.0436732i	−0.506221	−	0.862404i	$-0.668958\pi$
$293$	1.16323	−	0.747564i	0.0679568	−	0.0436732i	0.574178	+	0.818730i	$0.305322\pi$
$294$	−5.66325	+	39.3888i	−0.330287	+	2.29720i
$295$	6.06328	+	3.89663i	0.353018	+	0.226871i
$296$	10.6691	−	12.3128i	0.620129	−	0.715667i
$297$	14.0772	+	4.13342i	0.816839	+	0.239846i
$298$	−6.19689			−0.358976
$299$	8.76540	−	7.10043i	0.506916	−	0.410628i
$300$	−1.33273			−0.0769450
$301$	0.979995	+	0.287753i	0.0564860	+	0.0165858i
$302$	2.42780	−	2.80183i	0.139704	−	0.161227i
$303$	−22.6359	−	14.5472i	−1.30040	−	0.835714i
$304$	0.100970	−	0.702263i	0.00579104	−	0.0402775i
$305$	2.62397	−	1.68632i	0.150248	−	0.0965586i
$306$	20.5466	+	44.9907i	1.17457	+	2.57195i
$307$	−0.477376	−	0.550921i	−0.0272453	−	0.0314427i	0.741963	−	0.670440i	$-0.233895\pi$
$307$	−0.477376	−	0.550921i	−0.0272453	−	0.0314427i	−0.769209	+	0.638998i	$0.779349\pi$
$308$	0.0669539	+	0.465674i	0.00381505	+	0.0265343i
$309$	−1.89245	+	4.14390i	−0.107658	+	0.235738i
$310$	1.79599	−	0.527350i	0.102005	−	0.0299515i
$311$	10.8356	−	3.18162i	0.614430	−	0.180413i	0.0403141	−	0.999187i	$-0.487164\pi$
$311$	10.8356	−	3.18162i	0.614430	−	0.180413i	0.574116	+	0.818774i	$0.305346\pi$
$312$	9.20938	−	20.1657i	0.521379	−	1.14166i
$313$	2.11385	+	14.7021i	0.119482	+	0.831013i	0.958129	+	0.286338i	$0.0924380\pi$
$313$	2.11385	+	14.7021i	0.119482	+	0.831013i	−0.838647	+	0.544675i	$0.816653\pi$
$314$	15.3797	+	17.7491i	0.867925	+	1.00164i
$315$	15.3493	+	33.6103i	0.864835	+	1.89372i
$316$	−0.143892	+	0.0924739i	−0.00809457	+	0.00520207i
$317$	−1.16606	+	8.11010i	−0.0654923	+	0.455509i	0.930516	+	0.366251i	$0.119359\pi$
$317$	−1.16606	+	8.11010i	−0.0654923	+	0.455509i	−0.996009	+	0.0892582i	$0.971550\pi$
$318$	−48.7291	−	31.3163i	−2.73259	−	1.75613i
$319$	−6.42206	+	7.41145i	−0.359566	+	0.414961i
$320$	−9.93142	−	2.91613i	−0.555183	−	0.163016i
$321$	−12.3798			−0.690970
$322$	8.23268	−	24.9467i	0.458790	−	1.39023i
$323$	−0.906581			−0.0504435
$324$	2.82917	+	0.830718i	0.157176	+	0.0461510i
$325$	−5.37067	+	6.19808i	−0.297911	+	0.343808i
$326$	−10.2132	−	6.56359i	−0.565654	−	0.363524i
$327$	4.41792	−	30.7273i	0.244311	−	1.69922i
$328$	25.6102	−	16.4587i	1.41409	−	0.908777i
$329$	5.04410	+	11.0450i	0.278090	+	0.608933i
$330$	−3.58512	−	4.13744i	−0.197354	−	0.227759i
$331$	−3.21803	−	22.3819i	−0.176879	−	1.23022i	−0.863931	−	0.503610i	$-0.832005\pi$
$331$	−3.21803	−	22.3819i	−0.176879	−	1.23022i	0.687052	−	0.726608i	$-0.258904\pi$
$332$	−0.281739	+	0.616921i	−0.0154624	+	0.0338580i
$333$	40.4743	−	11.8843i	2.21798	−	0.651257i
$334$	7.77230	−	2.28215i	0.425281	−	0.124874i
$335$	3.17225	−	6.94626i	0.173319	−	0.379515i
$336$	−6.91301	−	48.0810i	−0.377136	−	2.62304i
$337$	−18.5061	−	21.3572i	−1.00809	−	1.16340i	−0.986521	−	0.163635i	$-0.947678\pi$
$337$	−18.5061	−	21.3572i	−1.00809	−	1.16340i	−0.0215730	−	0.999767i	$-0.506867\pi$
$338$	4.25583	+	9.31898i	0.231487	+	0.506886i
$339$	−29.8665	+	19.1940i	−1.62212	+	1.04248i
$340$	−0.0988588	+	0.687578i	−0.00536137	+	0.0372892i
$341$	0.933040	+	0.599628i	0.0505270	+	0.0324717i
$342$	1.27855	−	1.47552i	0.0691359	−	0.0797871i
$343$	−7.43864	−	2.18418i	−0.401649	−	0.117935i
$344$	−0.743251			−0.0400734
$345$	−4.77999	−	18.5311i	−0.257346	−	0.997681i
$346$	−24.4406			−1.31394
$347$	−9.85669	−	2.89419i	−0.529135	−	0.155368i	0.00624314	−	0.999981i	$-0.498013\pi$
$347$	−9.85669	−	2.89419i	−0.529135	−	0.155368i	−0.535378	+	0.844612i	$0.679831\pi$
$348$	−2.45470	+	2.83287i	−0.131586	+	0.151858i
$349$	26.3622	+	16.9420i	1.41114	+	0.906882i	0.999989	−	0.00468739i	$-0.00149205\pi$
$349$	26.3622	+	16.9420i	1.41114	+	0.906882i	0.411147	+	0.911569i	$0.365128\pi$
$350$	−2.71809	+	18.9048i	−0.145288	+	1.01050i
$351$	29.0310	−	18.6571i	1.54956	−	0.995842i
$352$	−0.276527	−	0.605510i	−0.0147390	−	0.0322738i
$353$	4.66465	+	5.38329i	0.248274	+	0.286524i	0.866184	−	0.499725i	$-0.166566\pi$
$353$	4.66465	+	5.38329i	0.248274	+	0.286524i	−0.617910	+	0.786249i	$0.712020\pi$
$354$	−3.71079	−	25.8091i	−0.197226	−	1.37174i
$355$	−4.50163	+	9.85720i	−0.238922	+	0.523166i
$356$	−1.12057	+	0.329028i	−0.0593899	+	0.0174384i
$357$	−59.5556	+	17.4871i	−3.15202	+	0.925516i
$358$	−2.80603	+	6.14436i	−0.148303	+	0.324739i
$359$	4.71835	+	32.8168i	0.249025	+	1.73201i	0.603872	+	0.797081i	$0.293624\pi$
$359$	4.71835	+	32.8168i	0.249025	+	1.73201i	−0.354847	+	0.934924i	$0.615467\pi$
$360$	−17.6079	−	20.3206i	−0.928019	−	1.07099i
$361$	−7.87802	−	17.2505i	−0.414633	−	0.907919i
$362$	−15.5067	+	9.96553i	−0.815012	+	0.523776i
$363$	0.461653	−	3.21087i	0.0242305	−	0.168527i
$364$	0.930924	+	0.598269i	0.0487937	+	0.0313578i
$365$	3.81266	−	4.40005i	0.199564	−	0.230309i
$366$	−10.8270	−	3.17911i	−0.565938	−	0.166175i
$367$	−25.5793			−1.33523			−0.667613	−	0.744508i	$-0.732684\pi$
$367$	−25.5793			−1.33523			−0.667613	+	0.744508i	$0.732684\pi$
$368$	−0.596290	+	17.9767i	−0.0310838	+	0.937098i
$369$	78.8215			4.10328
$370$	−9.08005	−	2.66614i	−0.472050	−	0.138606i
$371$	34.0316	−	39.2746i	1.76683	−	2.03903i
$372$	0.356635	+	0.229195i	0.0184907	+	0.0118832i
$373$	−1.42691	+	9.92435i	−0.0738824	+	0.513864i	0.918952	+	0.394369i	$0.129037\pi$
$373$	−1.42691	+	9.92435i	−0.0738824	+	0.513864i	−0.992835	+	0.119495i	$0.961872\pi$
$374$	5.53101	−	3.55456i	0.286002	−	0.183802i
$375$	14.0685	+	30.8057i	0.726493	+	1.59080i
$376$	−5.78634	−	6.67779i	−0.298407	−	0.344381i
$377$	3.28275	+	22.8320i	0.169070	+	1.17591i
$378$	33.3850	−	73.1031i	1.71714	−	3.76002i
$379$	17.6260	−	5.17547i	0.905388	−	0.265846i	0.204290	−	0.978911i	$-0.434512\pi$
$379$	17.6260	−	5.17547i	0.905388	−	0.265846i	0.701098	+	0.713065i	$0.252693\pi$
$380$	0.0263098	−	0.00772526i	0.00134967	−	0.000396297i
$381$	23.2517	−	50.9142i	1.19122	−	2.60841i
$382$	−2.54736	−	17.7173i	−0.130334	−	0.906495i
$383$	−18.0552	−	20.8368i	−0.922576	−	1.06471i	−0.997717	−	0.0675363i	$-0.978486\pi$
$383$	−18.0552	−	20.8368i	−0.922576	−	1.06471i	0.0751411	−	0.997173i	$-0.476059\pi$
$384$	13.7616	+	30.1337i	0.702268	+	1.53775i
$385$	4.13194	−	2.65543i	0.210583	−	0.135333i
$386$	−0.167485	+	1.16488i	−0.00852474	+	0.0592908i
$387$	−1.61890	−	1.04041i	−0.0822935	−	0.0528868i
$388$	0.437059	−	0.504393i	0.0221883	−	0.0256067i
$389$	−3.87891	−	1.13895i	−0.196669	−	0.0577471i	0.181915	−	0.983314i	$-0.441770\pi$
$389$	−3.87891	−	1.13895i	−0.196669	−	0.0577471i	−0.378583	+	0.925567i	$0.623589\pi$
$390$	−12.8770			−0.652055
$391$	22.8453	−	2.51488i	1.15533	−	0.127183i
$392$	25.9801			1.31219
$393$	22.8714	+	6.71564i	1.15371	+	0.338759i
$394$	−5.08164	+	5.86453i	−0.256010	+	0.295451i
$395$	1.50224	+	0.965430i	0.0755858	+	0.0485760i
$396$	0.126150	−	0.877393i	0.00633928	−	0.0440907i
$397$	1.95183	−	1.25437i	0.0979598	−	0.0629549i	−0.490744	−	0.871304i	$-0.663275\pi$
$397$	1.95183	−	1.25437i	0.0979598	−	0.0629549i	0.588704	+	0.808349i	$0.299639\pi$
$398$	13.5482	+	29.6664i	0.679108	+	1.48704i
$399$	1.60450	+	1.85170i	0.0803257	+	0.0927008i
$400$	−1.86102	−	12.9437i	−0.0930511	−	0.647185i
$401$	5.24169	−	11.4777i	0.261758	−	0.573169i	−0.732429	−	0.680844i	$-0.761613\pi$
$401$	5.24169	−	11.4777i	0.261758	−	0.573169i	0.994186	+	0.107675i	$0.0343405\pi$
$402$	−26.5072	+	7.78320i	−1.32206	+	0.388191i
$403$	2.50309	−	0.734975i	0.124688	−	0.0366117i
$404$	−0.406017	+	0.889054i	−0.0202001	+	0.0442321i
$405$	−4.38095	−	30.4702i	−0.217691	−	1.51407i
$406$	35.1780	+	40.5976i	1.74585	+	2.01482i
$407$	−2.32938	−	5.10063i	−0.115463	−	0.252829i
$408$	37.9980	−	24.4198i	1.88118	−	1.20896i
$409$	1.08857	−	7.57120i	0.0538266	−	0.374372i	−0.945048	−	0.326933i	$-0.893985\pi$
$409$	1.08857	−	7.57120i	0.0538266	−	0.374372i	0.998874	−	0.0474391i	$-0.0151060\pi$
$410$	−14.8758	−	9.56010i	−0.734664	−	0.472140i
$411$	−2.85626	+	3.29630i	−0.140889	+	0.162595i
$412$	0.158773	+	0.0466200i	0.00782220	+	0.00229680i
$413$	23.3932			1.15110
$414$	−28.1254	+	40.7289i	−1.38229	+	2.00172i
$415$	7.08052			0.347569
$416$	−1.50231	−	0.441118i	−0.0736568	−	0.0216276i
$417$	−18.1320	+	20.9254i	−0.887926	+	1.02472i
$418$	−0.218331	−	0.140313i	−0.0106789	−	0.00686292i
$419$	2.91581	−	20.2799i	0.142447	−	0.990737i	−0.785723	−	0.618579i	$-0.787709\pi$
$419$	2.91581	−	20.2799i	0.142447	−	0.990737i	0.928169	−	0.372158i	$-0.121382\pi$
$420$	1.57935	−	1.01498i	0.0770642	−	0.0495261i
$421$	12.0886	+	26.4704i	0.589163	+	1.29009i	0.935947	+	0.352142i	$0.114546\pi$
$421$	12.0886	+	26.4704i	0.589163	+	1.29009i	−0.346784	+	0.937945i	$0.612726\pi$
$422$	7.00944	+	8.08932i	0.341214	+	0.393782i
$423$	−3.25585	−	22.6449i	−0.158305	−	1.10103i
$424$	−15.7097	+	34.3995i	−0.762932	+	1.67059i
$425$	−16.0327	+	4.70763i	−0.777701	+	0.228354i
$426$	37.6154	−	11.0449i	1.82247	−	0.535126i
$427$	4.20555	−	9.20887i	0.203521	−	0.445648i
$428$	0.0639962	+	0.445104i	0.00309338	+	0.0215149i
$429$	−4.99662	−	5.76641i	−0.241239	−	0.278405i
$430$	0.179343	+	0.392707i	0.00864871	+	0.0189380i
$431$	−27.0779	+	17.4019i	−1.30430	+	0.838221i	−0.993673	−	0.112312i	$-0.964175\pi$
$431$	−27.0779	+	17.4019i	−1.30430	+	0.838221i	−0.310624	+	0.950533i	$0.600538\pi$
$432$	−7.83082	+	54.4645i	−0.376760	+	2.62043i
$433$	−13.5842	−	8.73002i	−0.652814	−	0.419538i	0.171879	−	0.985118i	$-0.445016\pi$
$433$	−13.5842	−	8.73002i	−0.652814	−	0.419538i	−0.824694	+	0.565580i	$0.808652\pi$
$434$	3.97850	−	4.59143i	0.190974	−	0.220396i
$435$	37.5484	+	11.0252i	1.80031	+	0.528619i
$436$	−1.12761			−0.0540028
$437$	−0.464920	−	0.779061i	−0.0222401	−	0.0372675i
$438$	−21.0627			−1.00642
$439$	−14.0072	−	4.11287i	−0.668525	−	0.196297i	−0.0701790	−	0.997534i	$-0.522357\pi$
$439$	−14.0072	−	4.11287i	−0.668525	−	0.196297i	−0.598346	+	0.801238i	$0.704175\pi$
$440$	−2.34061	+	2.70121i	−0.111584	+	0.128775i
$441$	56.5883	+	36.3671i	2.69468	+	1.73177i
$442$	2.20085	−	15.3072i	0.104684	−	0.728090i
$443$	19.6912	−	12.6548i	0.935558	−	0.601247i	0.0184262	−	0.999830i	$-0.494134\pi$
$443$	19.6912	−	12.6548i	0.935558	−	0.601247i	0.917132	+	0.398583i	$0.130498\pi$
$444$	−0.890356	−	1.94961i	−0.0422544	−	0.0925243i
$445$	7.98446	+	9.21456i	0.378500	+	0.436812i
$446$	3.57114	+	24.8378i	0.169098	+	1.17610i
$447$	−6.08685	+	13.3283i	−0.287898	+	0.630409i
$448$	−32.2344	+	9.46487i	−1.52293	+	0.447173i
$449$	−27.4960	+	8.07354i	−1.29761	+	0.381014i	−0.856365	−	0.516371i	$-0.827283\pi$
$449$	−27.4960	+	8.07354i	−1.29761	+	0.381014i	−0.441249	+	0.897385i	$0.645465\pi$
$450$	14.9489	−	32.7335i	0.704697	−	1.54307i
$451$	−1.49113	−	10.3710i	−0.0702145	−	0.488353i
$452$	0.844497	+	0.974602i	0.0397218	+	0.0458414i
$453$	−3.64151	−	7.97380i	−0.171093	−	0.374642i
$454$	27.8807	−	17.9179i	1.30851	−	0.840926i
$455$	1.64414	−	11.4352i	0.0770785	−	0.536093i
$456$	−1.49993	−	0.963949i	−0.0702408	−	0.0451410i
$457$	9.11340	−	10.5174i	0.426307	−	0.491985i	−0.501441	−	0.865192i	$-0.667197\pi$
$457$	9.11340	−	10.5174i	0.426307	−	0.491985i	0.927748	+	0.373207i	$0.121742\pi$
$458$	16.6192	+	4.87985i	0.776565	+	0.228020i
$459$	70.3106			3.28182
$460$	−0.641560	+	0.267656i	−0.0299129	+	0.0124795i
$461$	8.00154			0.372669			0.186334	−	0.982486i	$-0.440339\pi$
$461$	8.00154			0.372669			0.186334	+	0.982486i	$0.440339\pi$
$462$	−17.0492	−	5.00610i	−0.793201	−	0.232905i
$463$	25.4574	−	29.3794i	1.18310	−	1.36537i	0.267367	−	0.963595i	$-0.413846\pi$
$463$	25.4574	−	29.3794i	1.18310	−	1.36537i	0.915736	−	0.401780i	$-0.131608\pi$
$464$	−30.9411	−	19.8846i	−1.43641	−	0.923122i
$465$	0.629866	−	4.38082i	0.0292094	−	0.203156i
$466$	−13.0480	+	8.38547i	−0.604439	+	0.388449i
$467$	9.01744	+	19.7454i	0.417277	+	0.913710i	0.995222	+	0.0976342i	$0.0311275\pi$
$467$	9.01744	+	19.7454i	0.417277	+	0.913710i	−0.577945	+	0.816076i	$0.696145\pi$
$468$	−1.36536	−	1.57571i	−0.0631140	−	0.0728374i
$469$	−3.52731	−	24.5330i	−0.162876	−	1.13283i
$470$	−2.13209	+	4.66862i	−0.0983458	+	0.215347i
$471$	53.2815	−	15.6449i	2.45508	−	0.720877i
$472$	−16.3337	+	4.79600i	−0.751818	+	0.220754i
$473$	−0.106267	+	0.232691i	−0.00488614	+	0.0106992i
$474$	−0.919386	−	6.39447i	−0.0422288	−	0.293708i
$475$	0.431942	+	0.498487i	0.0198189	+	0.0228722i
$476$	0.936603	+	2.05087i	0.0429291	+	0.0940017i
$477$	−82.3707	+	52.9364i	−3.77149	+	2.42379i
$478$	−3.77936	+	26.2860i	−0.172864	+	1.20229i
$479$	11.4234	+	7.34139i	0.521949	+	0.335437i	0.774943	−	0.632032i	$-0.217779\pi$
$479$	11.4234	+	7.34139i	0.521949	+	0.335437i	−0.252993	+	0.967468i	$0.581415\pi$
$480$	−1.73952	+	2.00751i	−0.0793979	+	0.0916301i
$481$	−12.6550	−	3.71584i	−0.577018	−	0.169428i
$482$	−38.1196			−1.73630
$483$	−45.5691	−	42.2106i	−2.07347	−	1.92065i
$484$	−0.117831			−0.00535593
$485$	−6.68551	−	1.96304i	−0.303573	−	0.0891372i
$486$	−33.3861	+	38.5297i	−1.51443	+	1.74774i
$487$	−32.0598	−	20.6036i	−1.45277	−	0.933636i	−0.999098	−	0.0424656i	$-0.986479\pi$
$487$	−32.0598	−	20.6036i	−1.45277	−	0.933636i	−0.453668	−	0.891171i	$-0.649885\pi$
$488$	−1.04844	+	7.29206i	−0.0474607	+	0.330096i
$489$	−24.1488	+	15.5195i	−1.09205	+	0.701817i
$490$	−6.26890	−	13.7270i	−0.283200	−	0.620122i
$491$	19.2645	+	22.2324i	0.869393	+	1.00333i	0.999929	+	0.0118892i	$0.00378453\pi$
$491$	19.2645	+	22.2324i	0.869393	+	1.00333i	−0.130537	+	0.991443i	$0.541670\pi$
$492$	−0.569953	−	3.96411i	−0.0256954	−	0.178716i
$493$	−19.5234	+	42.7503i	−0.879289	+	1.92538i
$494$	−0.585723	+	0.171984i	−0.0263529	+	0.00773791i
$495$	−8.87934	+	2.60721i	−0.399096	+	0.117185i
$496$	−1.72798	+	3.78376i	−0.0775887	+	0.169896i
$497$	5.00549	+	34.8139i	0.224527	+	1.56162i
$498$	−16.7745	−	19.3588i	−0.751684	−	0.867490i
$499$	−0.0664124	−	0.145423i	−0.00297303	−	0.00651002i	0.908140	−	0.418667i	$-0.137503\pi$
$499$	−0.0664124	−	0.145423i	−0.00297303	−	0.00651002i	−0.911113	+	0.412157i	$0.864775\pi$
$500$	1.03487	−	0.665068i	0.0462806	−	0.0297427i
$501$	2.72580	−	18.9584i	0.121780	−	0.846997i
$502$	19.3244	+	12.4190i	0.862491	+	0.554289i
$503$	−13.2150	+	15.2509i	−0.589226	+	0.680003i	−0.969562	−	0.244845i	$-0.921263\pi$
$503$	−13.2150	+	15.2509i	−0.589226	+	0.680003i	0.380336	+	0.924848i	$0.375808\pi$
$504$	−83.7354	−	24.5869i	−3.72987	−	1.09519i
$505$	10.2038			0.454065
$506$	5.89103	+	2.93014i	0.261888	+	0.130260i
$507$	24.2236			1.07581
$508$	−1.95078	−	0.572799i	−0.0865517	−	0.0254139i
$509$	−12.1218	+	13.9893i	−0.537287	+	0.620063i	−0.957874	−	0.287190i	$-0.907279\pi$
$509$	−12.1218	+	13.9893i	−0.537287	+	0.620063i	0.420586	+	0.907253i	$0.361824\pi$
$510$	−22.0714	−	14.1844i	−0.977336	−	0.628096i
$511$	2.68929	−	18.7044i	0.118967	−	0.827435i
$512$	20.4344	−	13.1324i	0.903082	−	0.580375i
$513$	−1.15296	−	2.52463i	−0.0509044	−	0.111465i
$514$	−25.3198	−	29.2206i	−1.11681	−	1.28886i
$515$	−0.245860	−	1.70999i	−0.0108339	−	0.0753512i
$516$	−0.0406182	+	0.0889414i	−0.00178812	+	0.00391543i
$517$	−2.91794	+	0.856784i	−0.128331	+	0.0376813i
$518$	−29.4711	+	8.65350i	−1.29489	+	0.380213i
$519$	−24.0066	+	52.5672i	−1.05377	+	2.30744i
$520$	1.19644	+	8.32144i	0.0524675	+	0.364919i
$521$	13.8486	+	15.9822i	0.606719	+	0.700191i	0.973128	−	0.230263i	$-0.0739586\pi$
$521$	13.8486	+	15.9822i	0.606719	+	0.700191i	−0.366410	+	0.930454i	$0.619413\pi$
$522$	−42.0452	−	92.0661i	−1.84027	−	4.02962i
$523$	4.99899	−	3.21266i	0.218591	−	0.140480i	−0.426763	−	0.904363i	$-0.640346\pi$
$523$	4.99899	−	3.21266i	0.218591	−	0.140480i	0.645354	+	0.763884i	$0.276710\pi$
$524$	0.123223	−	0.857038i	0.00538304	−	0.0374399i
$525$	37.9907	+	24.4151i	1.65805	+	1.06556i
$526$	11.4204	−	13.1799i	0.497953	−	0.574669i
$527$	5.09992	+	1.49747i	0.222156	+	0.0652309i
$528$	12.1660			0.529459
$529$	13.8768	+	18.3421i	0.603340	+	0.797484i
$530$	21.9662			0.954151
$531$	−42.2905	−	12.4176i	−1.83525	−	0.538878i
$532$	0.0582818	−	0.0672608i	0.00252684	−	0.00291613i
$533$	−20.7326	−	13.3240i	−0.898029	−	0.577128i
$534$	6.27744	−	43.6606i	0.271652	−	1.88938i
$535$	3.94941	−	2.53813i	0.170748	−	0.109733i
$536$	7.49254	+	16.4064i	0.323628	+	0.708648i
$537$	10.4591	+	12.0705i	0.451345	+	0.520880i
$538$	−1.12983	−	7.85811i	−0.0487103	−	0.338787i
$539$	3.71452	−	8.13367i	0.159996	−	0.350342i
$540$	−2.04048	+	0.599138i	−0.0878082	+	0.0257828i
$541$	−24.3591	+	7.15248i	−1.04728	+	0.307509i	−0.759718	−	0.650253i	$-0.774663\pi$
$541$	−24.3591	+	7.15248i	−1.04728	+	0.307509i	−0.287562	+	0.957762i	$0.592845\pi$
$542$	−5.69421	+	12.4686i	−0.244587	+	0.535571i
$543$	6.20266	+	43.1404i	0.266182	+	1.85133i
$544$	−2.08907	−	2.41091i	−0.0895681	−	0.103367i
$545$	4.89039	+	10.7085i	0.209481	+	0.458700i
$546$	−35.1602	+	22.5961i	−1.50472	+	0.967024i
$547$	−2.79217	+	19.4200i	−0.119385	+	0.830338i	0.838852	+	0.544360i	$0.183228\pi$
$547$	−2.79217	+	19.4200i	−0.119385	+	0.830338i	−0.958236	+	0.285978i	$0.907682\pi$
$548$	0.133281	+	0.0856546i	0.00569349	+	0.00365898i
$549$	−12.4911	+	14.4155i	−0.533108	+	0.615239i
$550$	−4.58975	−	1.34767i	−0.195707	−	0.0574649i
$551$	1.85517			0.0790330
$552$	40.4714	+	20.1300i	1.72258	+	0.856791i
$553$	5.79589			0.246466
$554$	10.2574	+	3.01184i	0.435795	+	0.127961i
$555$	−14.6532	+	16.9107i	−0.621993	+	0.717818i
$556$	0.846088	+	0.543747i	0.0358821	+	0.0230600i
$557$	0.903808	−	6.28612i	0.0382956	−	0.266352i	−0.961674	−	0.274197i	$-0.911588\pi$
$557$	0.903808	−	6.28612i	0.0382956	−	0.266352i	0.999969	+	0.00784505i	$0.00249718\pi$
$558$	−9.62962	+	6.18858i	−0.407654	+	0.261984i
$559$	0.249953	+	0.547321i	0.0105719	+	0.0231492i
$560$	12.0631	+	13.9216i	0.509760	+	0.588294i
$561$	−2.21240	−	15.3876i	−0.0934076	−	0.649664i
$562$	−2.76900	+	6.06327i	−0.116803	+	0.255763i
$563$	13.8993	−	4.08120i	0.585785	−	0.172002i	0.0246072	−	0.999697i	$-0.492167\pi$
$563$	13.8993	−	4.08120i	0.585785	−	0.172002i	0.561178	+	0.827695i	$0.310348\pi$
$564$	−1.11532	+	0.327488i	−0.0469634	+	0.0137897i
$565$	5.59284	−	12.2466i	0.235293	−	0.515219i
$566$	2.99247	+	20.8131i	0.125783	+	0.874838i
$567$	−65.4297	−	75.5099i	−2.74779	−	3.17112i
$568$	−10.6324	−	23.2817i	−0.446126	−	0.976879i
$569$	23.1626	−	14.8857i	0.971027	−	0.624041i	0.0439980	−	0.999032i	$-0.485990\pi$
$569$	23.1626	−	14.8857i	0.971027	−	0.624041i	0.927029	+	0.374991i	$0.122354\pi$
$570$	−0.147388	+	1.02511i	−0.00617342	+	0.0429371i
$571$	20.0257	+	12.8697i	0.838050	+	0.538582i	0.887827	−	0.460178i	$-0.152214\pi$
$571$	20.0257	+	12.8697i	0.838050	+	0.538582i	−0.0497763	+	0.998760i	$0.515851\pi$
$572$	−0.181497	+	0.209458i	−0.00758876	+	0.00875790i
$573$	−40.6086	−	11.9238i	−1.69645	−	0.498123i
$574$	−57.3934			−2.39555
$575$	−12.2675	−	11.3633i	−0.511589	−	0.473884i
$576$	63.2980			2.63742
$577$	−40.3672	−	11.8529i	−1.68051	−	0.493441i	−0.704231	−	0.709971i	$-0.748708\pi$
$577$	−40.3672	−	11.8529i	−1.68051	−	0.493441i	−0.976276	+	0.216530i	$0.930526\pi$
$578$	5.36046	−	6.18630i	0.222966	−	0.257316i
$579$	2.34093	+	1.50442i	0.0972856	+	0.0625216i
$580$	0.202298	−	1.40702i	0.00839999	−	0.0584232i
$581$	19.3331	−	12.4246i	0.802070	−	0.515459i
$582$	10.4715	+	22.9295i	0.434060	+	0.950458i
$583$	8.52345	+	9.83658i	0.353005	+	0.407390i
$584$	1.95700	+	13.6112i	0.0809812	+	0.563237i
$585$	−9.04238	+	19.8001i	−0.373857	+	0.818632i
$586$	1.82017	−	0.534449i	0.0751903	−	0.0220779i
$587$	25.0912	−	7.36744i	1.03562	−	0.304087i	0.280628	−	0.959817i	$-0.409457\pi$
$587$	25.0912	−	7.36744i	1.03562	−	0.304087i	0.754996	+	0.655730i	$0.227639\pi$
$588$	1.41980	−	3.10892i	0.0585515	−	0.128210i
$589$	−0.0298595	−	0.207677i	−0.00123034	−	0.00855720i
$590$	6.47528	+	7.47288i	0.266583	+	0.307653i
$591$	7.62209	+	16.6900i	0.313531	+	0.686536i
$592$	17.6917	−	11.3697i	0.727123	−	0.467294i
$593$	−4.36268	+	30.3431i	−0.179154	+	1.24604i	0.679573	+	0.733608i	$0.262165\pi$
$593$	−4.36268	+	30.3431i	−0.179154	+	1.24604i	−0.858727	+	0.512434i	$0.828744\pi$
$594$	16.9328	+	10.8821i	0.694762	+	0.446496i
$595$	15.4143	−	17.7890i	0.631924	−	0.729280i
$596$	0.510675	+	0.149948i	0.0209180	+	0.00614209i
$597$	77.1143			3.15608
$598$	14.2827	−	5.95869i	0.584065	−	0.243669i
$599$	22.2683			0.909860			0.454930	−	0.890527i	$-0.349664\pi$
$599$	22.2683			0.909860			0.454930	+	0.890527i	$0.349664\pi$
$600$	−31.5316	−	9.25850i	−1.28727	−	0.377977i
$601$	−5.47264	+	6.31577i	−0.223234	+	0.257626i	−0.856308	−	0.516466i	$-0.827247\pi$
$601$	−5.47264	+	6.31577i	−0.223234	+	0.257626i	0.633074	+	0.774091i	$0.281793\pi$
$602$	1.17880	+	0.757566i	0.0480441	+	0.0308761i
$603$	−6.64593	+	46.2235i	−0.270643	+	1.88237i
$604$	−0.267867	+	0.172147i	−0.0108993	+	0.00700458i
$605$	0.511024	+	1.11899i	0.0207761	+	0.0454933i
$606$	−24.1740	−	27.8983i	−0.982001	−	1.13329i
$607$	0.291674	+	2.02864i	0.0118387	+	0.0823400i	0.994884	−	0.101022i	$-0.0322112\pi$
$607$	0.291674	+	2.02864i	0.0118387	+	0.0823400i	−0.983046	+	0.183362i	$0.941302\pi$
$608$	−0.0523115	+	0.114546i	−0.00212151	+	0.00464546i
$609$	121.871	−	35.7845i	4.93846	−	1.45006i
$610$	4.10585	−	1.20559i	0.166241	−	0.0488128i
$611$	−2.97152	+	6.50672i	−0.120215	+	0.263234i
$612$	−0.604555	−	4.20477i	−0.0244377	−	0.169968i
$613$	−15.0204	−	17.3345i	−0.606669	−	0.700133i	0.366450	−	0.930438i	$-0.380573\pi$
$613$	−15.0204	−	17.3345i	−0.606669	−	0.700133i	−0.973119	+	0.230305i	$0.926028\pi$
$614$	−0.415454	−	0.909718i	−0.0167664	−	0.0367132i
$615$	−35.1736	+	22.6047i	−1.41834	+	0.911509i
$616$	−1.65097	+	11.4827i	−0.0665193	+	0.462652i
$617$	−40.6999	−	26.1562i	−1.63852	−	1.05301i	−0.942078	−	0.335394i	$-0.891130\pi$
$617$	−40.6999	−	26.1562i	−1.63852	−	1.05301i	−0.696439	−	0.717616i	$-0.745233\pi$
$618$	−4.09281	+	4.72335i	−0.164637	+	0.190001i
$619$	28.8242	+	8.46355i	1.15854	+	0.340179i	0.803866	−	0.594811i	$-0.202773\pi$
$619$	28.8242	+	8.46355i	1.15854	+	0.340179i	0.354676	+	0.934989i	$0.384591\pi$
$620$	−0.160765			−0.00645646
$621$	36.0572	+	60.4207i	1.44693	+	2.42460i
$622$	15.4932			0.621219
$623$	37.9705	+	11.1492i	1.52126	+	0.446682i
$624$	18.7396	−	21.6267i	0.750185	−	0.865760i
$625$	3.86207	+	2.48200i	0.154483	+	0.0992801i
$626$	−2.90003	+	20.1702i	−0.115909	+	0.806162i
$627$	−0.516240	+	0.331767i	−0.0206166	+	0.0132495i
$628$	−0.837932	−	1.83482i	−0.0334371	−	0.0732171i
$629$	−17.5977	−	20.3088i	−0.701665	−	0.809764i
$630$	7.21416	+	50.1756i	0.287419	+	1.99904i
$631$	14.7289	−	32.2518i	0.586348	−	1.28392i	−0.351275	−	0.936272i	$-0.614252\pi$
$631$	14.7289	−	32.2518i	0.586348	−	1.28392i	0.937624	−	0.347652i	$-0.113021\pi$
$632$	−4.04683	+	1.18826i	−0.160974	+	0.0472663i
$633$	24.2836	−	7.13030i	0.965185	−	0.283404i
$634$	−4.66962	+	10.2250i	−0.185454	+	0.406088i
$635$	3.02076	+	21.0099i	0.119875	+	0.833752i
$636$	3.25791	+	3.75983i	0.129184	+	0.149087i
$637$	−8.73705	−	19.1315i	−0.346175	−	0.758017i
$638$	−11.3183	+	7.27383i	−0.448096	+	0.287974i
$639$	9.43102	−	65.5942i	0.373085	−	2.59486i
$640$	−10.5683	−	6.79186i	−0.417750	−	0.268472i
$641$	0.152498	−	0.175992i	0.00602329	−	0.00695125i	−0.752730	−	0.658329i	$-0.771263\pi$
$641$	0.152498	−	0.175992i	0.00602329	−	0.00695125i	0.758753	+	0.651378i	$0.225809\pi$
$642$	−16.2961	−	4.78496i	−0.643155	−	0.188847i
$643$	−33.0573			−1.30365			−0.651827	−	0.758368i	$-0.725997\pi$
$643$	−33.0573			−1.30365			−0.651827	+	0.758368i	$0.725997\pi$
$644$	−1.28208	+	1.85660i	−0.0505211	+	0.0731605i
$645$	1.02080			0.0401939
$646$	−1.19338	−	0.350407i	−0.0469528	−	0.0137866i
$647$	17.5393	−	20.2415i	0.689542	−	0.795774i	−0.297758	−	0.954641i	$-0.596239\pi$
$647$	17.5393	−	20.2415i	0.689542	−	0.795774i	0.987300	+	0.158867i	$0.0507843\pi$
$648$	61.1654	+	39.3086i	2.40281	+	1.54419i
$649$	−0.833818	+	5.79933i	−0.0327302	+	0.227644i
$650$	−9.46533	+	6.08300i	−0.371261	+	0.238595i
$651$	−5.96745	−	13.0669i	−0.233883	−	0.512132i
$652$	0.682827	+	0.788024i	0.0267416	+	0.0308614i
$653$	2.54001	+	17.6662i	0.0993984	+	0.691331i	0.977202	+	0.212311i	$0.0680989\pi$
$653$	2.54001	+	17.6662i	0.0993984	+	0.691331i	−0.877804	+	0.479020i	$0.840992\pi$
$654$	17.6921	−	38.7403i	0.691815	−	1.51486i
$655$	−8.67333	+	2.54672i	−0.338895	+	0.0995086i
$656$	37.7043	−	11.0710i	1.47211	−	0.432249i
$657$	−14.7905	+	32.3866i	−0.577031	+	1.26352i
$658$	2.37072	+	16.4888i	0.0924205	+	0.642798i
$659$	−32.0485	−	36.9859i	−1.24843	−	1.44077i	−0.852699	−	0.522402i	$-0.825036\pi$
$659$	−32.0485	−	36.9859i	−1.24843	−	1.44077i	−0.395733	−	0.918366i	$-0.629509\pi$
$660$	0.195328	+	0.427709i	0.00760314	+	0.0166486i
$661$	4.71648	−	3.03109i	0.183450	−	0.117896i	−0.445693	−	0.895186i	$-0.647043\pi$
$661$	4.71648	−	3.03109i	0.183450	−	0.117896i	0.629142	+	0.777290i	$0.283406\pi$
$662$	4.41488	−	30.7062i	0.171589	−	1.19343i
$663$	−30.7611	−	19.7690i	−1.19466	−	0.767764i
$664$	−10.9516	+	12.6388i	−0.425003	+	0.490479i
$665$	−0.891512	−	0.261772i	−0.0345714	−	0.0101511i
$666$	57.8718			2.24249
$667$	−46.7491	+	5.14629i	−1.81013	+	0.199265i
$668$	−0.695723			−0.0269183
$669$	56.9291	+	16.7159i	2.20101	+	0.646274i
$670$	6.86063	−	7.91759i	0.265049	−	0.305883i
$671$	2.13304	+	1.37082i	0.0823453	+	0.0529201i
$672$	−1.22698	+	8.53386i	−0.0473320	+	0.329201i
$673$	−38.8695	+	24.9799i	−1.49831	+	0.962906i	−0.503197	+	0.864172i	$0.667843\pi$
$673$	−38.8695	+	24.9799i	−1.49831	+	0.962906i	−0.995114	+	0.0987336i	$0.968521\pi$
$674$	−16.1057	−	35.2665i	−0.620367	−	1.35841i
$675$	−33.4996	−	38.6606i	−1.28940	−	1.48805i
$676$	−0.125222	−	0.870940i	−0.00481624	−	0.0334977i
$677$	0.541327	−	1.18534i	0.0208049	−	0.0455563i	−0.898944	−	0.438063i	$-0.855665\pi$
$677$	0.541327	−	1.18534i	0.0208049	−	0.0455563i	0.919749	+	0.392507i	$0.128392\pi$
$678$	−46.7335	+	13.7222i	−1.79479	+	0.526997i
$679$	−21.6992	+	6.37145i	−0.832737	+	0.244514i
$680$	−7.11557	+	15.5809i	−0.272870	+	0.597501i
$681$	−11.1523	−	77.5658i	−0.427356	−	2.97233i
$682$	0.996441	+	1.14995i	0.0381557	+	0.0440340i
$683$	−19.8952	−	43.5645i	−0.761270	−	1.66695i	−0.744985	−	0.667081i	$-0.767543\pi$
$683$	−19.8952	−	43.5645i	−0.761270	−	1.66695i	−0.0162847	−	0.999867i	$-0.505184\pi$
$684$	−0.141066	+	0.0906578i	−0.00539380	+	0.00346639i
$685$	0.235393	−	1.63719i	0.00899390	−	0.0625539i
$686$	−8.94763	−	5.75029i	−0.341622	−	0.219547i
$687$	26.8197	−	30.9516i	1.02324	−	1.18088i
$688$	−0.920535	−	0.270294i	−0.0350951	−	0.0103048i
$689$	30.6146			1.16632
$690$	0.870418	−	26.2409i	0.0331363	−	0.998975i
$691$	34.9666			1.33019			0.665096	−	0.746757i	$-0.268390\pi$
$691$	34.9666			1.33019			0.665096	+	0.746757i	$0.268390\pi$
$692$	2.01411	+	0.591396i	0.0765650	+	0.0224815i
$693$	−19.6696	+	22.6999i	−0.747187	+	0.862300i
$694$	−11.8562	−	7.61952i	−0.450055	−	0.289233i
$695$	1.49431	−	10.3931i	0.0566823	−	0.394234i
$696$	−77.7568	+	49.9712i	−2.94736	+	1.89416i
$697$	−20.8591	−	45.6750i	−0.790094	−	1.73006i
$698$	28.1535	+	32.4909i	1.06563	+	1.22980i
$699$	5.21921	+	36.3004i	0.197409	+	1.37301i
$700$	0.681436	−	1.49214i	0.0257559	−	0.0563975i
$701$	−4.32101	+	1.26876i	−0.163202	+	0.0479205i	−0.362313	−	0.932056i	$-0.618013\pi$
$701$	−4.32101	+	1.26876i	−0.163202	+	0.0479205i	0.199111	+	0.979977i	$0.436195\pi$
$702$	45.4262	−	13.3383i	1.71450	−	0.503423i
$703$	−0.440655	+	0.964901i	−0.0166196	+	0.0363919i
$704$	−1.19746	−	8.32851i	−0.0451309	−	0.313892i
$705$	7.94709	+	9.17143i	0.299305	+	0.345416i
$706$	4.05958	+	8.88925i	0.152784	+	0.334551i
$707$	27.8611	−	17.9053i	1.04783	−	0.673397i
$708$	−0.318710	+	2.21667i	−0.0119778	+	0.0833077i
$709$	−7.82098	−	5.02624i	−0.293723	−	0.188764i	0.385477	−	0.922717i	$-0.374037\pi$
$709$	−7.82098	−	5.02624i	−0.293723	−	0.188764i	−0.679200	+	0.733953i	$0.737673\pi$
$710$	−9.73568	+	11.2356i	−0.365374	+	0.421664i
$711$	−10.4779	−	3.07659i	−0.392952	−	0.115381i
$712$	−28.7977			−1.07924
$713$	1.32854	+	5.15050i	0.0497543	+	0.192888i
$714$	−85.1550			−3.18685
$715$	2.77628	+	0.815189i	0.103827	+	0.0304863i
$716$	0.379917	−	0.438447i	0.0141981	−	0.0163855i
$717$	52.8239	+	33.9479i	1.97275	+	1.26781i
$718$	−6.47320	+	45.0221i	−0.241578	+	1.68021i
$719$	28.3283	−	18.2055i	1.05647	−	0.678950i	0.107461	−	0.994209i	$-0.465728\pi$
$719$	28.3283	−	18.2055i	1.05647	−	0.678950i	0.949006	+	0.315259i	$0.102091\pi$
$720$	−14.4180	−	31.5710i	−0.537327	−	1.17658i
$721$	−3.67193	−	4.23763i	−0.136750	−	0.157818i
$722$	−3.70266	−	25.7526i	−0.137799	−	0.958412i
$723$	−37.4427	+	81.9880i	−1.39251	+	3.04917i
$724$	1.51901	−	0.446023i	0.0564537	−	0.0165763i
$725$	32.8084	−	9.63340i	1.21847	−	0.357776i
$726$	1.84875	−	4.04819i	0.0686134	−	0.150242i
$727$	−4.28065	−	29.7725i	−0.158760	−	1.10420i	−0.900922	−	0.433981i	$-0.857108\pi$
$727$	−4.28065	−	29.7725i	−0.158760	−	1.10420i	0.742161	−	0.670221i	$-0.233801\pi$
$728$	17.8690	+	20.6219i	0.662267	+	0.764297i
$729$	18.8905	+	41.3645i	0.699649	+	1.53202i
$730$	6.71948	−	4.31835i	0.248699	−	0.159829i
$731$	−0.174467	+	1.21344i	−0.00645289	+	0.0448808i
$732$	0.815311	+	0.523969i	0.0301348	+	0.0193664i
$733$	12.2796	−	14.1714i	0.453558	−	0.523434i	−0.482207	−	0.876057i	$-0.660165\pi$
$733$	12.2796	−	14.1714i	0.453558	−	0.523434i	0.935765	+	0.352623i	$0.114710\pi$
$734$	−33.6712	−	9.88677i	−1.24283	−	0.364927i
$735$	−35.6817			−1.31614
$736$	1.00046	−	3.03160i	0.0368775	−	0.111746i
$737$	6.20764			0.228661
$738$	103.757	+	30.4657i	3.81933	+	1.12146i
$739$	−16.5992	+	19.1565i	−0.610613	+	0.704685i	−0.973896	−	0.226994i	$-0.927110\pi$
$739$	−16.5992	+	19.1565i	−0.610613	+	0.704685i	0.363283	+	0.931679i	$0.381656\pi$
$740$	0.683758	+	0.439424i	0.0251354	+	0.0161536i
$741$	−0.205417	+	1.42871i	−0.00754619	+	0.0524849i
$742$	59.9777	−	38.5453i	2.20185	−	1.41504i
$743$	−2.05256	−	4.49448i	−0.0753011	−	0.164886i	0.868238	−	0.496148i	$-0.165253\pi$
$743$	−2.05256	−	4.49448i	−0.0753011	−	0.164886i	−0.943539	+	0.331262i	$0.892526\pi$
$744$	6.84555	+	7.90019i	0.250970	+	0.289635i
$745$	−0.790777	−	5.49997i	−0.0289718	−	0.201503i
$746$	−5.71422	+	12.5124i	−0.209212	+	0.458111i
$747$	−41.5458	+	12.1990i	−1.52008	+	0.446336i
$748$	−0.541811	+	0.159090i	−0.0198106	+	0.00581691i
$749$	6.32989	−	13.8605i	0.231289	−	0.506452i
$750$	6.61218	+	45.9887i	0.241443	+	1.67927i
$751$	−13.6658	−	15.7711i	−0.498670	−	0.575496i	0.449491	−	0.893285i	$-0.351605\pi$
$751$	−13.6658	−	15.7711i	−0.498670	−	0.575496i	−0.948162	+	0.317788i	$0.897060\pi$
$752$	−4.73806	−	10.3749i	−0.172779	−	0.378334i
$753$	45.6923	−	29.3646i	1.66512	−	1.07011i
$754$	−4.50367	+	31.3237i	−0.164014	+	1.14074i
$755$	2.79653	+	1.79722i	0.101776	+	0.0654076i
$756$	−4.52009	+	5.21647i	−0.164394	+	0.189721i
$757$	18.9096	+	5.55236i	0.687281	+	0.201804i	0.606684	−	0.794943i	$-0.292499\pi$
$757$	18.9096	+	5.55236i	0.687281	+	0.201804i	0.0805968	+	0.996747i	$0.474317\pi$
$758$	25.2024			0.915392
$759$	12.0886	−	9.79238i	0.438788	−	0.355441i
$760$	0.676143			0.0245263
$761$	−29.5737	−	8.68361i	−1.07204	−	0.314781i	−0.302352	−	0.953196i	$-0.597772\pi$
$761$	−29.5737	−	8.68361i	−1.07204	−	0.314781i	−0.769692	+	0.638416i	$0.779590\pi$
$762$	50.2865	−	58.0337i	1.82169	−	2.10234i
$763$	32.1437	+	20.6575i	1.16368	+	0.747852i
$764$	−0.218786	+	1.52169i	−0.00791539	+	0.0550528i
$765$	−37.3090	+	23.9770i	−1.34891	+	0.866892i
$766$	−15.7132	−	34.4071i	−0.567740	−	1.24318i
$767$	9.02469	+	10.4150i	0.325863	+	0.376066i
$768$	−1.30090	−	9.04799i	−0.0469423	−	0.326491i
$769$	12.7067	−	27.8239i	0.458217	−	1.00336i	−0.529673	−	0.848202i	$-0.677685\pi$
$769$	12.7067	−	27.8239i	0.458217	−	1.00336i	0.987890	−	0.155154i	$-0.0495873\pi$
$770$	6.46544	−	1.89842i	0.232998	−	0.0684144i
$771$	−87.7180	+	25.7563i	−3.15909	+	0.927591i
$772$	0.0419890	−	0.0919430i	0.00151122	−	0.00330910i
$773$	−0.243220	−	1.69164i	−0.00874803	−	0.0608439i	0.984980	−	0.172670i	$-0.0552393\pi$
$773$	−0.243220	−	1.69164i	−0.00874803	−	0.0608439i	−0.993728	+	0.111826i	$0.964330\pi$
$774$	−1.72891	−	1.99527i	−0.0621444	−	0.0717185i
$775$	−1.60647	−	3.51768i	−0.0577062	−	0.126359i
$776$	13.8446	−	8.89740i	0.496993	−	0.319398i
$777$	−10.3357	+	71.8866i	−0.370792	+	2.57892i
$778$	−4.66578	−	2.99852i	−0.167276	−	0.107502i
$779$	−1.29799	+	1.49797i	−0.0465055	+	0.0536702i
$780$	1.06117	+	0.311589i	0.0379961	+	0.0111567i
$781$	−8.80904			−0.315212
$782$	31.0444	+	5.51958i	1.11015	+	0.197380i
$783$	−143.879			−5.14182
$784$	32.1771	+	9.44804i	1.14918	+	0.337430i
$785$	−13.7904	+	15.9150i	−0.492201	+	0.568030i
$786$	27.5110	+	17.6803i	0.981286	+	0.630634i
$787$	−3.04719	+	21.1937i	−0.108621	+	0.755473i	0.860600	+	0.509281i	$0.170089\pi$
$787$	−3.04719	+	21.1937i	−0.108621	+	0.755473i	−0.969221	+	0.246192i	$0.920820\pi$
$788$	0.560675	−	0.360324i	0.0199732	−	0.0128360i
$789$	−17.1298	−	37.5089i	−0.609835	−	1.33535i
$790$	1.60432	+	1.85148i	0.0570790	+	0.0658727i
$791$	−6.21883	−	43.2529i	−0.221116	−	1.53790i
$792$	9.07992	−	19.8823i	0.322641	−	0.706485i
$793$	5.72238	−	1.68024i	0.203208	−	0.0596672i
$794$	3.05413	−	0.896773i	0.108387	−	0.0318253i
$795$	21.5761	−	47.2451i	0.765226	−	1.67561i
$796$	−0.398637	−	2.77258i	−0.0141293	−	0.0982715i
$797$	17.5479	+	20.2513i	0.621577	+	0.717338i	0.976006	−	0.217745i	$-0.0698702\pi$
$797$	17.5479	+	20.2513i	0.621577	+	0.717338i	−0.354429	+	0.935083i	$0.615325\pi$
$798$	1.39638	+	3.05764i	0.0494313	+	0.108239i
$799$	−12.2605	+	7.87936i	−0.433746	+	0.278752i
$800$	−0.330311	+	2.29737i	−0.0116783	+	0.0812241i
$801$	−62.7255	−	40.3112i	−2.21630	−	1.42433i
$802$	11.3362	−	13.0827i	0.400295	−	0.461965i
$803$	4.54111	+	1.33339i	0.160252	+	0.0470543i
$804$	2.37274			0.0836801
$805$	23.1917	+	4.12340i	0.817400	+	0.145331i
$806$	3.57903			0.126066
$807$	−18.0111	−	5.28853i	−0.634020	−	0.186165i
$808$	−15.7824	+	18.2139i	−0.555224	+	0.640763i
$809$	−19.1052	−	12.2782i	−0.671703	−	0.431677i	0.159836	−	0.987144i	$-0.448903\pi$
$809$	−19.1052	−	12.2782i	−0.671703	−	0.431677i	−0.831539	+	0.555467i	$0.812540\pi$
$810$	6.01032	−	41.8027i	0.211181	−	1.46880i
$811$	9.26177	−	5.95218i	0.325225	−	0.209009i	−0.367832	−	0.929892i	$-0.619900\pi$
$811$	9.26177	−	5.95218i	0.325225	−	0.209009i	0.693057	+	0.720883i	$0.256264\pi$
$812$	−1.91661	−	4.19678i	−0.0672597	−	0.147278i
$813$	21.2244	+	24.4943i	0.744374	+	0.859053i
$814$	−1.09481	−	7.61455i	−0.0383730	−	0.266890i
$815$	4.52215	−	9.90213i	0.158404	−	0.346856i
$816$	55.9422	−	16.4261i	1.95837	−	0.575029i
$817$	0.0464318	−	0.0136336i	0.00162444	−	0.000476979i
$818$	4.35933	−	9.54560i	0.152420	−	0.333754i
$819$	10.0545	+	69.9304i	0.351332	+	2.44357i
$820$	0.994560	+	1.14778i	0.0347316	+	0.0400823i
$821$	11.2301	+	24.5904i	0.391932	+	0.858210i	0.998025	+	0.0628170i	$0.0200084\pi$
$821$	11.2301	+	24.5904i	0.391932	+	0.858210i	−0.606093	+	0.795393i	$0.707264\pi$
$822$	−5.03391	+	3.23510i	−0.175578	+	0.112837i
$823$	1.99767	−	13.8941i	0.0696344	−	0.484318i	−0.924925	−	0.380149i	$-0.875873\pi$
$823$	1.99767	−	13.8941i	0.0696344	−	0.484318i	0.994560	−	0.104169i	$-0.0332182\pi$
$824$	3.43262	+	2.20601i	0.119581	+	0.0768499i
$825$	−7.40682	+	8.54793i	−0.257873	+	0.297601i
$826$	30.7936	+	9.04180i	1.07144	+	0.314605i
$827$	9.76163			0.339445			0.169723	−	0.985492i	$-0.445713\pi$
$827$	9.76163			0.339445			0.169723	+	0.985492i	$0.445713\pi$
$828$	3.30329	−	2.67584i	0.114797	−	0.0929918i
$829$	−40.4957			−1.40647			−0.703237	−	0.710955i	$-0.748263\pi$
$829$	−40.4957			−1.40647			−0.703237	+	0.710955i	$0.748263\pi$
$830$	9.32044	+	2.73673i	0.323517	+	0.0949932i
$831$	16.5531	−	19.1033i	0.574222	−	0.662688i
$832$	−16.6494	−	10.6999i	−0.577215	−	0.370954i
$833$	6.09844	−	42.4156i	0.211298	−	1.46961i
$834$	−31.9560	+	20.5369i	−1.10655	+	0.711134i
$835$	3.01731	+	6.60698i	0.104418	+	0.228644i
$836$	0.0145971	+	0.0168459i	0.000504850	+	0.000582628i
$837$	2.31578	+	16.1066i	0.0800449	+	0.556725i
$838$	11.6767	−	25.5684i	0.403365	−	0.883246i
$839$	−35.2897	+	10.3620i	−1.21833	+	0.357735i	−0.826836	−	0.562443i	$-0.809862\pi$
$839$	−35.2897	+	10.3620i	−1.21833	+	0.357735i	−0.391499	+	0.920179i	$0.628043\pi$
$840$	44.4176	−	13.0422i	1.53255	−	0.449998i
$841$	27.9044	−	61.1021i	0.962221	−	2.10697i
$842$	5.68164	+	39.5167i	0.195802	+	1.36183i
$843$	10.3211	+	11.9112i	0.355478	+	0.410243i
$844$	−0.381896	−	0.836236i	−0.0131454	−	0.0287844i
$845$	−7.72786	+	4.96639i	−0.265847	+	0.170849i
$846$	4.46677	−	31.0670i	0.153571	−	1.06811i
$847$	3.35888	+	2.15862i	0.115412	+	0.0741711i
$848$	−31.9668	+	36.8917i	−1.09774	+	1.26686i
$849$	47.7043	+	14.0072i	1.63721	+	0.480727i
$850$	−22.9242			−0.786295
$851$	8.42758	−	25.5373i	0.288894	−	0.875406i
$852$	−3.36707			−0.115354
$853$	5.52630	+	1.62267i	0.189217	+	0.0555591i	0.374968	−	0.927038i	$-0.377654\pi$
$853$	5.52630	+	1.62267i	0.189217	+	0.0555591i	−0.185751	+	0.982597i	$0.559472\pi$
$854$	9.09534	−	10.4966i	0.311236	−	0.359185i
$855$	1.47273	+	0.946469i	0.0503665	+	0.0323686i
$856$	−1.57804	+	10.9755i	−0.0539362	+	0.375134i
$857$	−9.47264	+	6.08770i	−0.323579	+	0.207952i	−0.692338	−	0.721573i	$-0.743419\pi$
$857$	−9.47264	+	6.08770i	−0.323579	+	0.207952i	0.368759	+	0.929525i	$0.379783\pi$
$858$	−4.34850	−	9.52188i	−0.148455	−	0.325072i
$859$	−13.4184	−	15.4857i	−0.457831	−	0.528365i	0.479156	−	0.877730i	$-0.340943\pi$
$859$	−13.4184	−	15.4857i	−0.457831	−	0.528365i	−0.936987	+	0.349365i	$0.886397\pi$
$860$	−0.00527694	−	0.0367019i	−0.000179942	−	0.00125152i
$861$	−56.3742	+	123.442i	−1.92123	+	4.20690i
$862$	−42.3701	+	12.4410i	−1.44313	+	0.423742i
$863$	−33.2838	+	9.77300i	−1.13299	+	0.332677i	−0.793883	−	0.608070i	$-0.791944\pi$
$863$	−33.2838	+	9.77300i	−1.13299	+	0.332677i	−0.339110	+	0.940747i	$0.610126\pi$
$864$	4.05706	−	8.88371i	0.138024	−	0.302230i
$865$	−3.11884	−	21.6920i	−0.106044	−	0.737550i
$866$	−14.5072	−	16.7423i	−0.492976	−	0.568925i
$867$	−8.04029	−	17.6058i	−0.273062	−	0.597923i
$868$	−0.438961	+	0.282103i	−0.0148993	+	0.00957520i
$869$	−0.206587	+	1.43684i	−0.00700798	+	0.0487416i
$870$	45.1654	+	29.0261i	1.53125	+	0.984076i
$871$	9.56175	−	11.0348i	0.323988	−	0.373902i
$872$	−26.6787	−	7.83356i	−0.903454	−	0.265278i
$873$	42.6102			1.44214
$874$	−0.310878	−	1.20522i	−0.0105156	−	0.0407670i
$875$	−41.6837			−1.40917
$876$	1.73574	+	0.509660i	0.0586453	+	0.0172198i
$877$	−8.35460	+	9.64173i	−0.282115	+	0.325578i	−0.879066	−	0.476699i	$-0.841833\pi$
$877$	−8.35460	+	9.64173i	−0.282115	+	0.325578i	0.596951	+	0.802277i	$0.296378\pi$
$878$	−16.8486	−	10.8280i	−0.568614	−	0.365426i
$879$	0.638345	−	4.43979i	0.0215308	−	0.149750i
$880$	−3.88124	+	2.49432i	−0.130836	+	0.0840835i
$881$	8.14678	+	17.8390i	0.274472	+	0.601010i	0.995797	−	0.0915868i	$-0.0291939\pi$
$881$	8.14678	+	17.8390i	0.274472	+	0.601010i	−0.721325	+	0.692597i	$0.756467\pi$
$882$	60.4336	+	69.7441i	2.03490	+	2.34841i
$883$	−0.387880	−	2.69776i	−0.0130532	−	0.0907869i	0.982253	−	0.187559i	$-0.0600574\pi$
$883$	−0.387880	−	2.69776i	−0.0130532	−	0.0907869i	−0.995307	+	0.0967716i	$0.969148\pi$
$884$	−0.551760	+	1.20819i	−0.0185577	+	0.0406357i
$885$	22.4330	−	6.58693i	0.754078	−	0.221417i
$886$	30.8118	−	9.04716i	1.03514	−	0.303945i
$887$	6.18445	−	13.5421i	0.207654	−	0.454698i	−0.776936	−	0.629580i	$-0.783227\pi$
$887$	6.18445	−	13.5421i	0.207654	−	0.454698i	0.984589	+	0.174882i	$0.0559543\pi$
$888$	−7.52133	−	52.3120i	−0.252399	−	1.75548i
$889$	45.1153	+	52.0658i	1.51312	+	1.74623i
$890$	6.94878	+	15.2157i	0.232924	+	0.510031i
$891$	21.0516	−	13.5291i	0.705256	−	0.453240i
$892$	0.306715	−	2.13325i	0.0102696	−	0.0714265i
$893$	0.483972	+	0.311030i	0.0161955	+	0.0104082i
$894$	−13.1640	+	15.1921i	−0.440271	+	0.508099i
$895$	−5.81142	−	1.70639i	−0.194254	−	0.0570382i
$896$	−40.7744			−1.36218
$897$	1.21311	−	36.5723i	0.0405047	−	1.22112i
$898$	−39.3148			−1.31195
$899$	−10.4362	−	3.06433i	−0.348065	−	0.102201i
$900$	−2.02397	+	2.33578i	−0.0674656	+	0.0778595i
$901$	52.4736	+	33.7228i	1.74815	+	1.12347i
$902$	2.04571	−	14.2282i	0.0681148	−	0.473749i
$903$	2.78724	−	1.79125i	0.0927536	−	0.0596091i
$904$	13.2097	+	28.9253i	0.439349	+	0.962041i
$905$	−10.8236	−	12.4911i	−0.359787	−	0.415217i
$906$	−1.71151	−	11.9038i	−0.0568611	−	0.395477i
$907$	4.25360	−	9.31408i	0.141238	−	0.309269i	−0.825773	−	0.564003i	$-0.809261\pi$
$907$	4.25360	−	9.31408i	0.141238	−	0.309269i	0.967011	+	0.254734i	$0.0819879\pi$
$908$	−2.73116	+	0.801942i	−0.0906368	+	0.0266134i
$909$	−59.8723	+	17.5801i	−1.98584	+	0.583094i
$910$	6.58416	−	14.4173i	0.218263	−	0.477929i
$911$	2.08856	+	14.5262i	0.0691969	+	0.481275i	0.994723	+	0.102593i	$0.0327138\pi$
$911$	2.08856	+	14.5262i	0.0691969	+	0.481275i	−0.925527	+	0.378683i	$0.876377\pi$
$912$	−1.50715	−	1.73935i	−0.0499068	−	0.0575956i
$913$	2.39105	+	5.23567i	0.0791322	+	0.173275i
$914$	16.0616	−	10.3221i	0.531269	−	0.341426i
$915$	1.43995	−	10.0151i	0.0476033	−	0.331089i
$916$	−1.25148	−	0.804279i	−0.0413501	−	0.0265741i
$917$	−19.2133	+	22.1733i	−0.634478	+	0.732227i
$918$	92.5533	+	27.1761i	3.05472	+	0.896945i
$919$	25.7121			0.848164			0.424082	−	0.905624i	$-0.360597\pi$
$919$	25.7121			0.848164			0.424082	+	0.905624i	$0.360597\pi$
$920$	−17.0384	+	1.87564i	−0.561738	+	0.0618379i
$921$	−2.36471			−0.0779197
$922$	10.5328	+	3.09271i	0.346880	+	0.101853i
$923$	−13.5687	+	15.6592i	−0.446621	+	0.515428i
$924$	1.28386	+	0.825087i	0.0422359	+	0.0271434i
$925$	−2.78244	+	19.3523i	−0.0914860	+	0.636299i
$926$	44.8663	−	28.8338i	1.47440	−	0.947539i
$927$	4.38873	+	9.60999i	0.144145	+	0.315633i
$928$	4.27494	+	4.93354i	0.140332	+	0.161951i
$929$	−1.29394	−	8.99954i	−0.0424528	−	0.295265i	−0.999976	−	0.00690977i	$-0.997801\pi$
$929$	−1.29394	−	8.99954i	−0.0424528	−	0.295265i	0.957523	−	0.288356i	$-0.0931086\pi$
$930$	2.52238	−	5.52323i	0.0827120	−	0.181114i
$931$	−1.62301	+	0.476559i	−0.0531920	+	0.0156186i
$932$	1.27817	−	0.375305i	0.0418679	−	0.0122935i
$933$	15.2180	−	33.3228i	0.498216	−	1.09094i
$934$	4.23819	+	29.4773i	0.138678	+	0.964526i
$935$	3.86061	+	4.45538i	0.126255	+	0.145707i
$936$	−21.3572	−	46.7657i	−0.698082	−	1.52859i
$937$	10.6623	−	6.85227i	0.348323	−	0.223854i	−0.354766	−	0.934955i	$-0.615440\pi$
$937$	10.6623	−	6.85227i	0.348323	−	0.223854i	0.703090	+	0.711101i	$0.251803\pi$
$938$	4.83920	−	33.6574i	0.158005	−	1.09895i
$939$	40.5337	+	26.0494i	1.32277	+	0.850090i
$940$	0.288669	−	0.333142i	0.00941535	−	0.0108659i
$941$	−41.0123	−	12.0423i	−1.33696	−	0.392568i	−0.466378	−	0.884586i	$-0.654441\pi$
$941$	−41.0123	−	12.0423i	−1.33696	−	0.392568i	−0.870585	+	0.492018i	$0.836259\pi$
$942$	76.1840			2.48221
$943$	28.5532	−	41.3484i	0.929821	−	1.34649i
$944$	−21.9738			−0.715186
$945$	69.1419	+	20.3019i	2.24919	+	0.660421i
$946$	−0.229823	+	0.265230i	−0.00747218	+	0.00862336i
$947$	7.02666	+	4.51576i	0.228336	+	0.146743i	0.649807	−	0.760099i	$-0.274850\pi$
$947$	7.02666	+	4.51576i	0.228336	+	0.146743i	−0.421471	+	0.906842i	$0.638486\pi$
$948$	−0.0789635	+	0.549203i	−0.00256462	+	0.0178373i
$949$	9.36503	−	6.01854i	0.304002	−	0.195370i
$950$	0.375913	+	0.823136i	0.0121962	+	0.0267060i
$951$	17.4054	+	20.0869i	0.564409	+	0.651363i
$952$	7.91200	+	55.0292i	0.256429	+	1.78351i
$953$	−4.16749	+	9.12552i	−0.134998	+	0.295605i	−0.965043	−	0.262092i	$-0.915588\pi$
$953$	−4.16749	+	9.12552i	−0.134998	+	0.295605i	0.830045	+	0.557697i	$0.188315\pi$
$954$	−128.889	+	37.8453i	−4.17295	+	1.22529i
$955$	15.3997	−	4.52176i	0.498322	−	0.146321i
$956$	0.947498	−	2.07473i	0.0306443	−	0.0671016i
$957$	4.52732	+	31.4882i	0.146347	+	1.01787i
$958$	12.1997	+	14.0792i	0.394153	+	0.454877i
$959$	−2.23015	−	4.88334i	−0.0720152	−	0.157691i
$960$	−28.2463	+	18.1528i	−0.911646	+	0.585880i
$961$	4.23670	−	29.4669i	0.136668	−	0.950544i
$962$	−15.2222	−	9.78269i	−0.490782	−	0.315407i
$963$	−18.8007	+	21.6972i	−0.605845	+	0.699183i
$964$	3.14137	+	0.922389i	0.101177	+	0.0297081i
$965$	−1.05525			−0.0339696
$966$	−43.6698	−	73.1771i	−1.40505	−	2.35443i
$967$	30.1635			0.969992			0.484996	−	0.874516i	$-0.338821\pi$
$967$	30.1635			0.969992			0.484996	+	0.874516i	$0.338821\pi$
$968$	−2.78780	−	0.818573i	−0.0896034	−	0.0263099i
$969$	−1.92585	+	2.22254i	−0.0618671	+	0.0713984i
$970$	−8.04172	−	5.16810i	−0.258204	−	0.165938i
$971$	3.49207	−	24.2879i	0.112066	−	0.779434i	−0.853839	−	0.520537i	$-0.825732\pi$
$971$	3.49207	−	24.2879i	0.112066	−	0.779434i	0.965905	−	0.258897i	$-0.0833591\pi$
$972$	3.68360	−	2.36731i	0.118152	−	0.0759314i
$973$	−14.1573	−	31.0001i	−0.453862	−	0.993819i
$974$	−34.2383	−	39.5131i	−1.09706	−	1.26608i
$975$	3.78613	+	26.3331i	0.121253	+	0.843334i
$976$	−3.95038	+	8.65013i	−0.126449	+	0.276884i
$977$	−50.9412	+	14.9577i	−1.62975	+	0.478539i	−0.963616	−	0.267289i	$-0.913872\pi$
$977$	−50.9412	+	14.9577i	−1.62975	+	0.478539i	−0.666138	+	0.745828i	$0.732054\pi$
$978$	−37.7868	+	11.0952i	−1.20829	+	0.354786i
$979$	−4.11737	+	9.01578i	−0.131592	+	0.288146i
$980$	0.184454	+	1.28291i	0.00589217	+	0.0409809i
$981$	−47.1444	−	54.4075i	−1.50521	−	1.73710i
$982$	16.7656	+	36.7116i	0.535012	+	1.17151i
$983$	40.1003	−	25.7709i	1.27900	−	0.821965i	0.288238	−	0.957559i	$-0.406931\pi$
$983$	40.1003	−	25.7709i	1.27900	−	0.821965i	0.990765	+	0.135594i	$0.0432942\pi$
$984$	14.0540	−	97.7480i	0.448027	−	3.11609i
$985$	−5.85345	−	3.76179i	−0.186507	−	0.119860i
$986$	−42.2232	+	48.7282i	−1.34466	+	1.55182i
$987$	37.7928	+	11.0970i	1.20296	+	0.353220i
$988$	0.0524299			0.00166802
$989$	−1.13223	+	0.472361i	−0.0360029	+	0.0150202i
$990$	−12.6960			−0.403506
$991$	−13.5412	−	3.97606i	−0.430150	−	0.126304i	0.0594882	−	0.998229i	$-0.481053\pi$
$991$	−13.5412	−	3.97606i	−0.430150	−	0.126304i	−0.489639	+	0.871925i	$0.662871\pi$
$992$	0.483480	−	0.557965i	0.0153505	−	0.0177154i
$993$	−61.7066	−	39.6565i	−1.95820	−	1.25846i
$994$	−6.86714	+	47.7620i	−0.217812	+	1.51492i
$995$	−24.6011	+	15.8102i	−0.779909	+	0.501217i
$996$	0.913928	+	2.00122i	0.0289589	+	0.0634112i
$997$	−0.792176	−	0.914220i	−0.0250885	−	0.0289536i	0.743067	−	0.669217i	$-0.233371\pi$
$997$	−0.792176	−	0.914220i	−0.0250885	−	0.0289536i	−0.768155	+	0.640264i	$0.778825\pi$
$998$	−0.0312138	−	0.217097i	−0.000988055	−	0.00687207i
$999$	34.1754	−	74.8336i	1.08126	−	2.36763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	253.2.i.b.133.9	yes	120
23.3	even	11		5819.2.a.u.1.18		60
23.9	even	11	inner	253.2.i.b.78.9	✓	120
23.20	odd	22		5819.2.a.t.1.18		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.2.i.b.78.9	✓	120	23.9	even	11	inner
253.2.i.b.133.9	yes	120	1.1	even	1	trivial
5819.2.a.t.1.18		60	23.20	odd	22
5819.2.a.u.1.18		60	23.3	even	11

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 253 = 11 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	253.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.31635 + 0.386515i) q^{2} +(2.12429 - 2.45157i) q^{3} +(-0.0991254 - 0.0637040i) q^{4} +(-0.175069 + 1.21763i) q^{5} +(3.74388 - 2.40605i) q^{6} +(1.65863 + 3.63189i) q^{7} +(-1.90270 - 2.19583i) q^{8} +(-1.07061 - 7.44623i) q^{9} +(-0.701085 + 1.53516i) q^{10} +(-0.959493 + 0.281733i) q^{11} +(-0.366746 + 0.107686i) q^{12} +(-0.977112 + 2.13958i) q^{13} +(0.779555 + 5.42193i) q^{14} +(2.61321 + 3.01580i) q^{15} +(-1.55800 - 3.41153i) q^{16} +(-4.03158 + 2.59094i) q^{17} +(1.46879 - 10.2156i) q^{18} +(0.159142 + 0.102275i) q^{19} +(0.0949218 - 0.109546i) q^{20} +(12.4272 + 3.64897i) q^{21} -1.37192 q^{22} +(-4.29400 - 2.13579i) q^{23} -9.42511 q^{24} +(3.34549 + 0.982323i) q^{25} +(-2.11320 + 2.43876i) q^{26} +(-12.3424 - 7.93198i) q^{27} +(0.0669539 - 0.465674i) q^{28} +(8.24996 - 5.30193i) q^{29} +(2.27424 + 4.97989i) q^{30} +(-0.726311 - 0.838207i) q^{31} +(0.0947340 + 0.658890i) q^{32} +(-1.34756 + 2.95074i) q^{33} +(-6.30840 + 1.85231i) q^{34} +(-4.71269 + 1.38377i) q^{35} +(-0.368230 + 0.806312i) q^{36} +(0.798010 + 5.55028i) q^{37} +(0.169956 + 0.196140i) q^{38} +(3.16964 + 6.94054i) q^{39} +(3.00681 - 1.93236i) q^{40} +(-1.49113 + 10.3710i) q^{41} +(14.9482 + 9.60663i) q^{42} +(0.167519 - 0.193327i) q^{43} +(0.113058 + 0.0331967i) q^{44} +9.25420 q^{45} +(-4.82688 - 4.47114i) q^{46} +3.04112 q^{47} +(-11.6732 - 3.42757i) q^{48} +(-5.85557 + 6.75769i) q^{49} +(4.02415 + 2.58616i) q^{50} +(-2.21240 + 15.3876i) q^{51} +(0.233156 - 0.149840i) q^{52} +(-5.40690 - 11.8395i) q^{53} +(-13.1811 - 15.2118i) q^{54} +(-0.175069 - 1.21763i) q^{55} +(4.81915 - 10.5525i) q^{56} +(0.588798 - 0.172887i) q^{57} +(12.9091 - 3.79046i) q^{58} +(2.43390 - 5.32951i) q^{59} +(-0.0669165 - 0.465414i) q^{60} +(-1.66044 - 1.91624i) q^{61} +(-0.632099 - 1.38410i) q^{62} +(25.2682 - 16.2389i) q^{63} +(-1.19746 + 8.32851i) q^{64} +(-2.43415 - 1.56434i) q^{65} +(-2.91437 + 3.36336i) q^{66} +(-5.95619 - 1.74889i) q^{67} +0.564685 q^{68} +(-14.3577 + 5.98997i) q^{69} -6.73839 q^{70} +(8.45222 + 2.48179i) q^{71} +(-14.3136 + 16.5188i) q^{72} +(-3.98150 - 2.55876i) q^{73} +(-1.09481 + 7.61455i) q^{74} +(9.51503 - 6.11494i) q^{75} +(-0.00925975 - 0.0202760i) q^{76} +(-2.61467 - 3.01749i) q^{77} +(1.48973 + 10.3613i) q^{78} +(0.603024 - 1.32044i) q^{79} +(4.42675 - 1.29981i) q^{80} +(-24.0105 + 7.05011i) q^{81} +(-5.97140 + 13.0756i) q^{82} +(-0.819137 - 5.69722i) q^{83} +(-0.999402 - 1.15337i) q^{84} +(-2.44900 - 5.36257i) q^{85} +(0.295237 - 0.189737i) q^{86} +(4.52732 - 31.4882i) q^{87} +(2.44426 + 1.57083i) q^{88} +(6.49063 - 7.49058i) q^{89} +(12.1818 + 3.57689i) q^{90} -9.39138 q^{91} +(0.289586 + 0.485256i) q^{92} -3.59782 q^{93} +(4.00318 + 1.17544i) q^{94} +(-0.152394 + 0.175872i) q^{95} +(1.81655 + 1.16743i) q^{96} +(-0.806090 + 5.60648i) q^{97} +(-10.3199 + 6.63222i) q^{98} +(3.12508 + 6.84298i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - q^{2} - 4 q^{3} - 19 q^{4} - 6 q^{5} - 25 q^{6} - 6 q^{8} - 26 q^{9} + 41 q^{10} - 12 q^{11} - 17 q^{12} - 18 q^{13} - 12 q^{14} + 19 q^{15} - 33 q^{16} - 10 q^{17} + 28 q^{18} + 28 q^{19} - 34 q^{20}+ \cdots - 26 q^{99}+O(q^{100}) \) 120 * q - q^2 - 4 * q^3 - 19 * q^4 - 6 * q^5 - 25 * q^6 - 6 * q^8 - 26 * q^9 + 41 * q^10 - 12 * q^11 - 17 * q^12 - 18 * q^13 - 12 * q^14 + 19 * q^15 - 33 * q^16 - 10 * q^17 + 28 * q^18 + 28 * q^19 - 34 * q^20 - 26 * q^21 + 10 * q^22 + 3 * q^23 + 108 * q^24 - 6 * q^25 - 26 * q^26 - 46 * q^27 - 3 * q^28 + 18 * q^29 + 16 * q^30 - 34 * q^31 - 63 * q^32 + 7 * q^33 - 24 * q^34 - 48 * q^35 - 122 * q^36 - 32 * q^37 + 143 * q^38 - 42 * q^39 + 8 * q^40 - 8 * q^41 + 174 * q^42 + 51 * q^43 - 19 * q^44 - 2 * q^45 - 67 * q^46 - 2 * q^47 - 111 * q^48 + 12 * q^49 - 113 * q^50 + 34 * q^51 + 127 * q^52 - 22 * q^53 - 27 * q^54 - 6 * q^55 + 191 * q^56 + 32 * q^57 - 71 * q^58 - 40 * q^59 + 12 * q^60 - 19 * q^61 + q^62 - 82 * q^63 - 6 * q^64 + 171 * q^65 - 3 * q^66 - 30 * q^67 - 152 * q^68 - 48 * q^69 + 86 * q^70 - 22 * q^71 - 130 * q^72 - 70 * q^73 - 27 * q^74 + 200 * q^75 + 4 * q^76 - 94 * q^78 - 6 * q^79 + 197 * q^80 + 4 * q^81 - 47 * q^82 + 50 * q^83 + 411 * q^84 - 98 * q^85 - 9 * q^86 - 72 * q^87 - 6 * q^88 - 41 * q^89 - 260 * q^90 + 30 * q^92 + 130 * q^93 + 33 * q^94 - 28 * q^95 - 265 * q^96 + 84 * q^97 - 117 * q^98 - 26 * q^99

Introduction

L-functions

Modular forms

Varieties

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