LMFDB - Embedded newform 430.2.q.d.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			101.4
Character	$\chi$	$=$	430.101
Dual form			430.2.q.d.281.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.623490 + 0.781831i) q^{2} +(0.272539 - 0.694419i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(-0.0747301 - 0.997204i) q^{5} +(0.372993 + 0.646043i) q^{6} +(0.186100 - 0.322335i) q^{7} +(0.900969 + 0.433884i) q^{8} +(1.79122 + 1.66201i) q^{9} +O(q^{10})$	\(q+(-0.623490 + 0.781831i) q^{2} +(0.272539 - 0.694419i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(-0.0747301 - 0.997204i) q^{5} +(0.372993 + 0.646043i) q^{6} +(0.186100 - 0.322335i) q^{7} +(0.900969 + 0.433884i) q^{8} +(1.79122 + 1.66201i) q^{9} +(0.826239 + 0.563320i) q^{10} +(-0.208252 + 0.912410i) q^{11} +(-0.737654 - 0.111183i) q^{12} +(-0.289952 + 0.197686i) q^{13} +(0.135980 + 0.346472i) q^{14} +(-0.712844 - 0.219883i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(0.552955 - 7.37867i) q^{17} +(-2.41621 + 0.364186i) q^{18} +(3.70188 - 3.43484i) q^{19} +(-0.955573 + 0.294755i) q^{20} +(-0.173116 - 0.217081i) q^{21} +(-0.583508 - 0.731696i) q^{22} +(6.69665 - 2.06564i) q^{23} +(0.546846 - 0.507399i) q^{24} +(-0.988831 + 0.149042i) q^{25} +(0.0262251 - 0.349949i) q^{26} +(3.65863 - 1.76191i) q^{27} +(-0.355665 - 0.109708i) q^{28} +(-1.38912 - 3.53941i) q^{29} +(0.616362 - 0.420229i) q^{30} +(0.466552 + 0.0703215i) q^{31} +(0.222521 - 0.974928i) q^{32} +(0.576838 + 0.393281i) q^{33} +(5.42411 + 5.03284i) q^{34} +(-0.335341 - 0.161492i) q^{35} +(1.22175 - 2.11614i) q^{36} +(-0.201603 - 0.349187i) q^{37} +(0.377384 + 5.03583i) q^{38} +(0.0582535 + 0.255225i) q^{39} +(0.365341 - 0.930874i) q^{40} +(-7.52567 + 9.43689i) q^{41} +0.277656 q^{42} +(4.76405 + 4.50598i) q^{43} +0.935875 q^{44} +(1.52350 - 1.91041i) q^{45} +(-2.56031 + 6.52356i) q^{46} +(-2.25903 - 9.89747i) q^{47} +(0.0557476 + 0.743900i) q^{48} +(3.43073 + 5.94220i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-4.97318 - 2.39496i) q^{51} +(0.257250 + 0.238693i) q^{52} +(-2.53763 - 1.73013i) q^{53} +(-0.903608 + 3.95897i) q^{54} +(0.925422 + 0.139485i) q^{55} +(0.307527 - 0.209668i) q^{56} +(-1.37631 - 3.50678i) q^{57} +(3.63332 + 1.12073i) q^{58} +(-1.97135 + 0.949353i) q^{59} +(-0.0557476 + 0.743900i) q^{60} +(7.53048 - 1.13504i) q^{61} +(-0.345870 + 0.320921i) q^{62} +(0.869069 - 0.268072i) q^{63} +(0.623490 + 0.781831i) q^{64} +(0.218802 + 0.274368i) q^{65} +(-0.667132 + 0.205783i) q^{66} +(-8.63716 + 8.01411i) q^{67} +(-7.31671 + 1.10282i) q^{68} +(0.390679 - 5.21325i) q^{69} +(0.335341 - 0.161492i) q^{70} +(11.0889 + 3.42047i) q^{71} +(0.892713 + 2.27459i) q^{72} +(-3.23396 + 2.20488i) q^{73} +(0.398703 + 0.0600948i) q^{74} +(-0.165997 + 0.727282i) q^{75} +(-4.17247 - 2.84474i) q^{76} +(0.255346 + 0.236927i) q^{77} +(-0.235864 - 0.113586i) q^{78} +(-3.79542 + 6.57385i) q^{79} +(0.500000 + 0.866025i) q^{80} +(0.321432 + 4.28921i) q^{81} +(-2.68588 - 11.7676i) q^{82} +(3.15213 - 8.03151i) q^{83} +(-0.173116 + 0.217081i) q^{84} -7.39936 q^{85} +(-6.49325 + 0.915251i) q^{86} -2.83642 q^{87} +(-0.583508 + 0.731696i) q^{88} +(-2.47198 + 6.29850i) q^{89} +(0.543731 + 2.38224i) q^{90} +(0.00976099 + 0.130251i) q^{91} +(-3.50400 - 6.06910i) q^{92} +(0.175986 - 0.304817i) q^{93} +(9.14664 + 4.40479i) q^{94} +(-3.70188 - 3.43484i) q^{95} +(-0.616362 - 0.420229i) q^{96} +(2.64937 - 11.6077i) q^{97} +(-6.78483 - 1.02265i) q^{98} +(-1.88945 + 1.28821i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) $ 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9	\( 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9} + 5 q^{10} + 3 q^{11} - q^{12} + 13 q^{13} - 15 q^{14} + q^{15} - 10 q^{16} + 38 q^{17} + 6 q^{18} + 17 q^{19} - 5 q^{20} + 4 q^{21} + 11 q^{22} - 8 q^{23} + q^{24} + 5 q^{25} + 29 q^{26} - 16 q^{27} - 6 q^{28} - 41 q^{29} - q^{30} + 15 q^{31} + 10 q^{32} + 63 q^{33} - 10 q^{34} + 2 q^{35} - 48 q^{36} + 7 q^{37} + 25 q^{38} - 64 q^{39} + 5 q^{40} - 22 q^{41} - 60 q^{42} + 6 q^{43} - 4 q^{44} + 30 q^{45} - 20 q^{46} - 13 q^{47} - q^{48} - 93 q^{49} + 30 q^{50} + 18 q^{51} - 15 q^{52} + 71 q^{53} - 5 q^{54} - 16 q^{55} - q^{56} - 94 q^{57} - 22 q^{58} + 20 q^{59} + q^{60} + 91 q^{61} + 69 q^{62} - 50 q^{63} - 10 q^{64} + 5 q^{65} + 14 q^{66} - 26 q^{67} - 18 q^{68} - 94 q^{69} - 2 q^{70} + 20 q^{71} - 36 q^{72} - 56 q^{73} - 7 q^{74} + 2 q^{75} + 38 q^{76} + 41 q^{77} - 13 q^{78} - 46 q^{79} + 30 q^{80} + 39 q^{81} + 8 q^{82} - 115 q^{83} + 4 q^{84} + 6 q^{85} + 29 q^{86} + 20 q^{87} + 11 q^{88} + 30 q^{89} - 16 q^{90} - 53 q^{91} - 8 q^{92} + 16 q^{93} + 41 q^{94} - 17 q^{95} + q^{96} + 113 q^{97} + 2 q^{98} + 139 q^{99}+O(q^{100}) \) 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9 + 5 * q^10 + 3 * q^11 - q^12 + 13 * q^13 - 15 * q^14 + q^15 - 10 * q^16 + 38 * q^17 + 6 * q^18 + 17 * q^19 - 5 * q^20 + 4 * q^21 + 11 * q^22 - 8 * q^23 + q^24 + 5 * q^25 + 29 * q^26 - 16 * q^27 - 6 * q^28 - 41 * q^29 - q^30 + 15 * q^31 + 10 * q^32 + 63 * q^33 - 10 * q^34 + 2 * q^35 - 48 * q^36 + 7 * q^37 + 25 * q^38 - 64 * q^39 + 5 * q^40 - 22 * q^41 - 60 * q^42 + 6 * q^43 - 4 * q^44 + 30 * q^45 - 20 * q^46 - 13 * q^47 - q^48 - 93 * q^49 + 30 * q^50 + 18 * q^51 - 15 * q^52 + 71 * q^53 - 5 * q^54 - 16 * q^55 - q^56 - 94 * q^57 - 22 * q^58 + 20 * q^59 + q^60 + 91 * q^61 + 69 * q^62 - 50 * q^63 - 10 * q^64 + 5 * q^65 + 14 * q^66 - 26 * q^67 - 18 * q^68 - 94 * q^69 - 2 * q^70 + 20 * q^71 - 36 * q^72 - 56 * q^73 - 7 * q^74 + 2 * q^75 + 38 * q^76 + 41 * q^77 - 13 * q^78 - 46 * q^79 + 30 * q^80 + 39 * q^81 + 8 * q^82 - 115 * q^83 + 4 * q^84 + 6 * q^85 + 29 * q^86 + 20 * q^87 + 11 * q^88 + 30 * q^89 - 16 * q^90 - 53 * q^91 - 8 * q^92 + 16 * q^93 + 41 * q^94 - 17 * q^95 + q^96 + 113 * q^97 + 2 * q^98 + 139 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{13}{21}\right)$

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 $

$2$	−0.623490	+	0.781831i	−0.440874	+	0.552838i
$2$	−0.623490	+	0.781831i	−0.440874	+	0.552838i
$3$	0.272539	−	0.694419i	0.157351	−	0.400923i	−0.830358	−	0.557231i	$-0.811864\pi$
$3$	0.272539	−	0.694419i	0.157351	−	0.400923i	0.987708	+	0.156308i	$0.0499592\pi$
$4$	−0.222521	−	0.974928i	−0.111260	−	0.487464i
$5$	−0.0747301	−	0.997204i	−0.0334203	−	0.445963i
$5$	−0.0747301	−	0.997204i	−0.0334203	−	0.445963i
$6$	0.372993	+	0.646043i	0.152274	+	0.263746i
$7$	0.186100	−	0.322335i	0.0703393	−	0.121831i	−0.828711	−	0.559677i	$-0.810925\pi$
$7$	0.186100	−	0.322335i	0.0703393	−	0.121831i	0.899050	+	0.437846i	$0.144258\pi$
$8$	0.900969	+	0.433884i	0.318541	+	0.153401i
$9$	1.79122	+	1.66201i	0.597072	+	0.554002i
$10$	0.826239	+	0.563320i	0.261280	+	0.178137i
$11$	−0.208252	+	0.912410i	−0.0627902	+	0.275102i	−0.996571	−	0.0827440i	$-0.973632\pi$
$11$	−0.208252	+	0.912410i	−0.0627902	+	0.275102i	0.933781	+	0.357846i	$0.116489\pi$
$12$	−0.737654	−	0.111183i	−0.212942	−	0.0320959i
$13$	−0.289952	+	0.197686i	−0.0804183	+	0.0548283i	−0.602862	−	0.797846i	$-0.705973\pi$
$13$	−0.289952	+	0.197686i	−0.0804183	+	0.0548283i	0.522443	+	0.852674i	$0.325021\pi$
$14$	0.135980	+	0.346472i	0.0363422	+	0.0925985i
$15$	−0.712844	−	0.219883i	−0.184055	−	0.0567736i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	0.552955	−	7.37867i	0.134111	−	1.78959i	−0.373124	−	0.927782i	$-0.621713\pi$
$17$	0.552955	−	7.37867i	0.134111	−	1.78959i	0.507235	−	0.861808i	$-0.330668\pi$
$18$	−2.41621	+	0.364186i	−0.569507	+	0.0858394i
$19$	3.70188	−	3.43484i	0.849269	−	0.788007i	−0.129799	−	0.991540i	$-0.541433\pi$
$19$	3.70188	−	3.43484i	0.849269	−	0.788007i	0.979068	+	0.203534i	$0.0652426\pi$
$20$	−0.955573	+	0.294755i	−0.213673	+	0.0659093i
$21$	−0.173116	−	0.217081i	−0.0377770	−	0.0473709i
$22$	−0.583508	−	0.731696i	−0.124404	−	0.155998i
$23$	6.69665	−	2.06564i	1.39635	−	0.430716i	0.496924	−	0.867794i	$-0.334463\pi$
$23$	6.69665	−	2.06564i	1.39635	−	0.430716i	0.899424	+	0.437078i	$0.143986\pi$
$24$	0.546846	−	0.507399i	0.111625	−	0.103572i
$25$	−0.988831	+	0.149042i	−0.197766	+	0.0298085i
$26$	0.0262251	−	0.349949i	0.00514316	−	0.0686307i
$27$	3.65863	−	1.76191i	0.704104	−	0.339079i
$28$	−0.355665	−	0.109708i	−0.0672143	−	0.0207329i
$29$	−1.38912	−	3.53941i	−0.257952	−	0.657252i	0.741961	−	0.670444i	$-0.233896\pi$
$29$	−1.38912	−	3.53941i	−0.257952	−	0.657252i	−0.999913	+	0.0131914i	$0.995801\pi$
$30$	0.616362	−	0.420229i	0.112532	−	0.0767229i
$31$	0.466552	+	0.0703215i	0.0837953	+	0.0126301i	0.190806	−	0.981628i	$-0.438890\pi$
$31$	0.466552	+	0.0703215i	0.0837953	+	0.0126301i	−0.107011	+	0.994258i	$0.534128\pi$
$32$	0.222521	−	0.974928i	0.0393365	−	0.172345i
$33$	0.576838	+	0.393281i	0.100415	+	0.0684615i
$34$	5.42411	+	5.03284i	0.930228	+	0.863125i
$35$	−0.335341	−	0.161492i	−0.0566830	−	0.0272971i
$36$	1.22175	−	2.11614i	0.203625	−	0.352690i
$37$	−0.201603	−	0.349187i	−0.0331434	−	0.0574060i	0.848978	−	0.528428i	$-0.177218\pi$
$37$	−0.201603	−	0.349187i	−0.0331434	−	0.0574060i	−0.882121	+	0.471022i	$0.843885\pi$
$38$	0.377384	+	5.03583i	0.0612197	+	0.816920i
$39$	0.0582535	+	0.255225i	0.00932803	+	0.0408688i
$40$	0.365341	−	0.930874i	0.0577655	−	0.147184i
$41$	−7.52567	+	9.43689i	−1.17531	+	1.47380i	−0.326424	+	0.945223i	$0.605844\pi$
$41$	−7.52567	+	9.43689i	−1.17531	+	1.47380i	−0.848889	+	0.528572i	$0.822728\pi$
$42$	0.277656			0.0428433
$43$	4.76405	+	4.50598i	0.726511	+	0.687155i
$43$	4.76405	+	4.50598i	0.726511	+	0.687155i
$44$	0.935875			0.141088
$45$	1.52350	−	1.91041i	0.227110	−	0.284787i
$46$	−2.56031	+	6.52356i	−0.377497	+	0.961846i
$47$	−2.25903	−	9.89747i	−0.329514	−	1.44369i	−0.820059	−	0.572279i	$-0.806060\pi$
$47$	−2.25903	−	9.89747i	−0.329514	−	1.44369i	0.490545	−	0.871416i	$-0.336798\pi$
$48$	0.0557476	+	0.743900i	0.00804647	+	0.107373i
$49$	3.43073	+	5.94220i	0.490105	+	0.848886i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−4.97318	−	2.39496i	−0.696385	−	0.335361i
$52$	0.257250	+	0.238693i	0.0356742	+	0.0331008i
$53$	−2.53763	−	1.73013i	−0.348571	−	0.237651i	0.376360	−	0.926474i	$-0.377176\pi$
$53$	−2.53763	−	1.73013i	−0.348571	−	0.237651i	−0.724930	+	0.688822i	$0.758128\pi$
$54$	−0.903608	+	3.95897i	−0.122965	+	0.538747i
$55$	0.925422	+	0.139485i	0.124784	+	0.0188081i
$56$	0.307527	−	0.209668i	0.0410950	−	0.0280181i
$57$	−1.37631	−	3.50678i	−0.182297	−	0.464485i
$58$	3.63332	+	1.12073i	0.477079	+	0.147159i
$59$	−1.97135	+	0.949353i	−0.256648	+	0.123595i	−0.557784	−	0.829986i	$-0.688348\pi$
$59$	−1.97135	+	0.949353i	−0.256648	+	0.123595i	0.301136	+	0.953581i	$0.402634\pi$
$60$	−0.0557476	+	0.743900i	−0.00719698	+	0.0960371i
$61$	7.53048	−	1.13504i	0.964179	−	0.145327i	0.351960	−	0.936015i	$-0.385515\pi$
$61$	7.53048	−	1.13504i	0.964179	−	0.145327i	0.612219	+	0.790688i	$0.290277\pi$
$62$	−0.345870	+	0.320921i	−0.0439256	+	0.0407570i
$63$	0.869069	−	0.268072i	0.109492	−	0.0337739i
$64$	0.623490	+	0.781831i	0.0779362	+	0.0977289i
$65$	0.218802	+	0.274368i	0.0271390	+	0.0340312i
$66$	−0.667132	+	0.205783i	−0.0821183	+	0.0253301i
$67$	−8.63716	+	8.01411i	−1.05520	+	0.979079i	−0.999812	−	0.0193859i	$-0.993829\pi$
$67$	−8.63716	+	8.01411i	−1.05520	+	0.979079i	−0.0553844	+	0.998465i	$0.517638\pi$
$68$	−7.31671	+	1.10282i	−0.887282	+	0.133736i
$69$	0.390679	−	5.21325i	0.0470322	−	0.627601i
$70$	0.335341	−	0.161492i	0.0400809	−	0.0193020i
$71$	11.0889	+	3.42047i	1.31601	+	0.405935i	0.871745	−	0.489961i	$-0.162989\pi$
$71$	11.0889	+	3.42047i	1.31601	+	0.405935i	0.444265	+	0.895896i	$0.353465\pi$
$72$	0.892713	+	2.27459i	0.105207	+	0.268064i
$73$	−3.23396	+	2.20488i	−0.378506	+	0.258061i	−0.737597	−	0.675241i	$-0.764039\pi$
$73$	−3.23396	+	2.20488i	−0.378506	+	0.258061i	0.359090	+	0.933303i	$0.383087\pi$
$74$	0.398703	+	0.0600948i	0.0463483	+	0.00698588i
$75$	−0.165997	+	0.727282i	−0.0191677	+	0.0839793i
$76$	−4.17247	−	2.84474i	−0.478615	−	0.326314i
$77$	0.255346	+	0.236927i	0.0290994	+	0.0270003i
$78$	−0.235864	−	0.113586i	−0.0267063	−	0.0128611i
$79$	−3.79542	+	6.57385i	−0.427018	+	0.739616i	−0.996606	−	0.0823135i	$-0.973769\pi$
$79$	−3.79542	+	6.57385i	−0.427018	+	0.739616i	0.569589	+	0.821930i	$0.307102\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	0.321432	+	4.28921i	0.0357146	+	0.476579i
$82$	−2.68588	−	11.7676i	−0.296606	−	1.29952i
$83$	3.15213	−	8.03151i	0.345992	−	0.881572i	−0.646903	−	0.762573i	$-0.723936\pi$
$83$	3.15213	−	8.03151i	0.345992	−	0.881572i	0.992894	−	0.119000i	$-0.0379688\pi$
$84$	−0.173116	+	0.217081i	−0.0188885	+	0.0236854i
$85$	−7.39936			−0.802573
$86$	−6.49325	+	0.915251i	−0.700185	+	0.0986940i
$87$	−2.83642			−0.304096
$88$	−0.583508	+	0.731696i	−0.0622022	+	0.0779991i
$89$	−2.47198	+	6.29850i	−0.262029	+	0.667640i	−0.999974	−	0.00722152i	$-0.997701\pi$
$89$	−2.47198	+	6.29850i	−0.262029	+	0.667640i	0.737945	+	0.674861i	$0.235797\pi$
$90$	0.543731	+	2.38224i	0.0573143	+	0.251110i
$91$	0.00976099	+	0.130251i	0.00102323	+	0.0136540i
$92$	−3.50400	−	6.06910i	−0.365317	−	0.632748i
$93$	0.175986	−	0.304817i	0.0182489	−	0.0316081i
$94$	9.14664	+	4.40479i	0.943404	+	0.454319i
$95$	−3.70188	−	3.43484i	−0.379805	−	0.352407i
$96$	−0.616362	−	0.420229i	−0.0629072	−	0.0428894i
$97$	2.64937	−	11.6077i	0.269003	−	1.17858i	−0.642173	−	0.766560i	$-0.721967\pi$
$97$	2.64937	−	11.6077i	0.269003	−	1.17858i	0.911175	−	0.412019i	$-0.135176\pi$
$98$	−6.78483	−	1.02265i	−0.685371	−	0.103303i
$99$	−1.88945	+	1.28821i	−0.189897	+	0.129470i
$100$	0.365341	+	0.930874i	0.0365341	+	0.0930874i
$101$	−11.6416	−	3.59094i	−1.15838	−	0.357312i	−0.344748	−	0.938695i	$-0.612036\pi$
$101$	−11.6416	−	3.59094i	−1.15838	−	0.357312i	−0.813630	+	0.581383i	$0.802512\pi$
$102$	4.97318	−	2.39496i	0.492418	−	0.237136i
$103$	−0.786453	+	10.4945i	−0.0774915	+	1.03405i	0.813956	+	0.580927i	$0.197310\pi$
$103$	−0.786453	+	10.4945i	−0.0774915	+	1.03405i	−0.891447	+	0.453125i	$0.850309\pi$
$104$	−0.347011	+	0.0523035i	−0.0340272	+	0.00512878i
$105$	−0.203537	+	0.188854i	−0.0198631	+	0.0184303i
$106$	2.93486	−	0.905283i	0.285058	−	0.0879289i
$107$	−3.01646	−	3.78252i	−0.291612	−	0.365670i	0.614347	−	0.789036i	$-0.289420\pi$
$107$	−3.01646	−	3.78252i	−0.291612	−	0.365670i	−0.905958	+	0.423367i	$0.860848\pi$
$108$	−2.53185	−	3.17484i	−0.243628	−	0.305499i
$109$	−14.1317	+	4.35906i	−1.35357	+	0.417522i	−0.884872	−	0.465834i	$-0.845754\pi$
$109$	−14.1317	+	4.35906i	−1.35357	+	0.417522i	−0.468702	+	0.883356i	$0.655278\pi$
$110$	−0.686045	+	0.636556i	−0.0654118	+	0.0606933i
$111$	−0.297427	+	0.0448299i	−0.0282305	+	0.00425506i
$112$	−0.0278146	+	0.371160i	−0.00262823	+	0.0350713i
$113$	−15.5559	+	7.49132i	−1.46337	+	0.704724i	−0.984859	−	0.173356i	$-0.944539\pi$
$113$	−15.5559	+	7.49132i	−1.46337	+	0.704724i	−0.478515	+	0.878080i	$0.658825\pi$
$114$	3.59983	+	1.11040i	0.337155	+	0.103998i
$115$	−2.56031	−	6.52356i	−0.238750	−	0.608325i
$116$	−3.14156	+	2.14188i	−0.291687	+	0.198869i
$117$	−0.847923	−	0.127804i	−0.0783905	−	0.0118155i
$118$	0.486884	−	2.13318i	0.0448213	−	0.196375i
$119$	−2.27550	−	1.55141i	−0.208595	−	0.142217i
$120$	−0.546846	−	0.507399i	−0.0499200	−	0.0463190i
$121$	9.12153	+	4.39270i	0.829230	+	0.399336i
$122$	−3.80777	+	6.59525i	−0.344739	+	0.597106i
$123$	4.50211	+	7.79789i	0.405942	+	0.703112i
$124$	−0.0352593	−	0.470503i	−0.00316638	−	0.0422524i
$125$	0.222521	+	0.974928i	0.0199029	+	0.0872002i
$126$	−0.332268	+	0.846606i	−0.0296008	+	0.0754216i
$127$	3.18508	−	3.99396i	0.282630	−	0.354407i	−0.620170	−	0.784467i	$-0.712936\pi$
$127$	3.18508	−	3.99396i	0.282630	−	0.354407i	0.902800	+	0.430061i	$0.141508\pi$
$128$	−1.00000			−0.0883883
$129$	4.42743	−	2.08019i	0.389813	−	0.183150i
$130$	−0.350930			−0.0307786
$131$	2.45464	−	3.07803i	0.214463	−	0.268928i	−0.662950	−	0.748664i	$-0.730696\pi$
$131$	2.45464	−	3.07803i	0.214463	−	0.268928i	0.877413	+	0.479735i	$0.159267\pi$
$132$	0.255063	−	0.649889i	0.0222003	−	0.0565655i
$133$	−0.418250	−	1.83247i	−0.0362668	−	0.158895i
$134$	−0.880504	−	11.7495i	−0.0760640	−	1.01500i
$135$	−2.03039	−	3.51674i	−0.174748	−	0.302672i
$136$	3.69968	−	6.40803i	0.317245	−	0.549484i
$137$	−5.15369	−	2.48189i	−0.440309	−	0.212042i	0.200576	−	0.979678i	$-0.435718\pi$
$137$	−5.15369	−	2.48189i	−0.440309	−	0.212042i	−0.640886	+	0.767636i	$0.721433\pi$
$138$	3.83230	+	3.55585i	0.326227	+	0.302694i
$139$	10.0281	+	6.83703i	0.850571	+	0.579910i	0.908251	−	0.418426i	$-0.137418\pi$
$139$	10.0281	+	6.83703i	0.850571	+	0.579910i	−0.0576799	+	0.998335i	$0.518370\pi$
$140$	−0.0828224	+	0.362869i	−0.00699977	+	0.0306680i
$141$	−7.48866	−	1.12873i	−0.630659	−	0.0950566i
$142$	−9.58804	+	6.53702i	−0.804611	+	0.548574i
$143$	−0.119988	−	0.305724i	−0.0100339	−	0.0255659i
$144$	−2.33495	−	0.720236i	−0.194579	−	0.0600197i
$145$	−3.42571	+	1.64973i	−0.284489	+	0.137003i
$146$	0.292499	−	3.90313i	0.0242074	−	0.323025i
$147$	5.06139	−	0.762881i	0.417456	−	0.0629214i
$148$	−0.295571	+	0.274250i	−0.0242958	+	0.0225432i
$149$	−12.0312	+	3.71114i	−0.985636	+	0.304029i	−0.745350	−	0.666674i	$-0.767718\pi$
$149$	−12.0312	+	3.71114i	−0.985636	+	0.304029i	−0.240286	+	0.970702i	$0.577241\pi$
$150$	−0.465114	−	0.583235i	−0.0379764	−	0.0476209i
$151$	6.01612	+	7.54397i	0.489585	+	0.613920i	0.963845	−	0.266465i	$-0.0858557\pi$
$151$	6.01612	+	7.54397i	0.489585	+	0.613920i	−0.474260	+	0.880385i	$0.657284\pi$
$152$	4.82560	−	1.48850i	0.391408	−	0.120733i
$153$	13.2538	−	12.2978i	1.07151	−	0.994216i
$154$	−0.344443	+	0.0519164i	−0.0277560	+	0.00418354i
$155$	0.0352593	−	0.470503i	0.00283210	−	0.0377917i
$156$	0.235864	−	0.113586i	0.0188842	−	0.00909416i
$157$	−5.19517	−	1.60250i	−0.414620	−	0.127893i	0.0804252	−	0.996761i	$-0.474372\pi$
$157$	−5.19517	−	1.60250i	−0.414620	−	0.127893i	−0.495045	+	0.868867i	$0.664848\pi$
$158$	−2.77324	−	7.06611i	−0.220627	−	0.562149i
$159$	−1.89304	+	1.29065i	−0.150128	+	0.102355i
$160$	−0.988831	−	0.149042i	−0.0781739	−	0.0117828i
$161$	0.580419	−	2.54298i	0.0457435	−	0.200415i
$162$	−3.55385	−	2.42297i	−0.279217	−	0.190367i
$163$	9.42916	+	8.74898i	0.738549	+	0.685273i	0.956841	−	0.290610i	$-0.0938583\pi$
$163$	9.42916	+	8.74898i	0.738549	+	0.685273i	−0.218293	+	0.975883i	$0.570049\pi$
$164$	10.8749	+	5.23708i	0.849188	+	0.408947i
$165$	0.349075	−	0.604615i	0.0271754	−	0.0470692i
$166$	4.31396	+	7.47200i	0.334828	+	0.579940i
$167$	0.798805	+	10.6593i	0.0618134	+	0.824842i	0.938830	+	0.344382i	$0.111911\pi$
$167$	0.798805	+	10.6593i	0.0618134	+	0.824842i	−0.877016	+	0.480461i	$0.840470\pi$
$168$	−0.0617844	−	0.270695i	−0.00476677	−	0.0208846i
$169$	−4.70444	+	11.9867i	−0.361880	+	0.922055i
$170$	4.61342	−	5.78505i	0.353833	−	0.443693i
$171$	12.3396			0.943632
$172$	3.33290	−	5.64728i	0.254132	−	0.430601i
$173$	1.03189			0.0784529			0.0392264	−	0.999230i	$-0.487511\pi$
$173$	1.03189			0.0784529			0.0392264	+	0.999230i	$0.487511\pi$
$174$	1.76848	−	2.21760i	0.134068	−	0.168116i
$175$	−0.135980	+	0.346472i	−0.0102791	+	0.0261908i
$176$	−0.208252	−	0.912410i	−0.0156976	−	0.0687755i
$177$	0.121978	+	1.62768i	0.00916841	+	0.122344i
$178$	−3.38311	−	5.85972i	−0.253575	−	0.439205i
$179$	−4.16226	+	7.20925i	−0.311102	+	0.538844i	−0.978601	−	0.205766i	$-0.934031\pi$
$179$	−4.16226	+	7.20925i	−0.311102	+	0.538844i	0.667499	+	0.744610i	$0.267365\pi$
$180$	−2.20152	−	1.06020i	−0.164092	−	0.0790224i
$181$	−1.59384	−	1.47887i	−0.118469	−	0.109923i	0.618714	−	0.785616i	$-0.287654\pi$
$181$	−1.59384	−	1.47887i	−0.118469	−	0.109923i	−0.737183	+	0.675693i	$0.763844\pi$
$182$	−0.107920	−	0.0735789i	−0.00799960	−	0.00545403i
$183$	1.26416	−	5.53865i	0.0934494	−	0.409428i
$184$	6.92972	+	1.04449i	0.510866	+	0.0770006i
$185$	−0.333145	+	0.227134i	−0.0244933	+	0.0166992i
$186$	0.128590	+	0.327642i	0.00942868	+	0.0240239i
$187$	6.61722	+	2.04114i	0.483899	+	0.149263i
$188$	−9.14664	+	4.40479i	−0.667087	+	0.321252i
$189$	0.112949	−	1.50720i	0.00821582	−	0.109633i
$190$	4.99355	−	0.752657i	0.362270	−	0.0546035i
$191$	17.7187	−	16.4406i	1.28208	−	1.18960i	0.311118	−	0.950371i	$-0.399297\pi$
$191$	17.7187	−	16.4406i	1.28208	−	1.18960i	0.970964	−	0.239227i	$-0.0768939\pi$
$192$	0.712844	−	0.219883i	0.0514451	−	0.0158687i
$193$	13.5493	+	16.9903i	0.975303	+	1.22299i	0.974821	+	0.222991i	$0.0715820\pi$
$193$	13.5493	+	16.9903i	0.975303	+	1.22299i	0.000482095		1.00000i	$0.499847\pi$
$194$	7.42337	+	9.30862i	0.532967	+	0.668320i
$195$	0.250159	−	0.0771637i	0.0179142	−	0.00552581i
$196$	5.02981	−	4.66698i	0.359272	−	0.333356i
$197$	−24.2473	+	3.65469i	−1.72755	+	0.260386i	−0.936323	−	0.351139i	$-0.885794\pi$
$197$	−24.2473	+	3.65469i	−1.72755	+	0.260386i	−0.791225	+	0.611525i	$0.790556\pi$
$198$	0.170894	−	2.28042i	0.0121449	−	0.162062i
$199$	−1.20141	+	0.578569i	−0.0851658	+	0.0410137i	−0.475982	−	0.879455i	$-0.657907\pi$
$199$	−1.20141	+	0.578569i	−0.0851658	+	0.0410137i	0.390816	+	0.920469i	$0.372193\pi$
$200$	−0.955573	−	0.294755i	−0.0675692	−	0.0208423i
$201$	3.21118	+	8.18196i	0.226499	+	0.577111i
$202$	10.0659	−	6.86282i	0.708235	−	0.482866i
$203$	−1.39939	−	0.210924i	−0.0982181	−	0.0148040i
$204$	−1.22827	+	5.38142i	−0.0859964	+	0.376775i
$205$	9.97290	+	6.79941i	0.696538	+	0.474891i
$206$	−7.71457	−	7.15808i	−0.537500	−	0.498727i
$207$	15.4283	+	7.42986i	1.07234	+	0.516411i
$208$	0.175465	−	0.303915i	0.0121663	−	0.0210727i
$209$	2.36306	+	4.09294i	0.163456	+	0.283115i
$210$	−0.0207493	−	0.276880i	−0.00143184	−	0.0191065i
$211$	−4.82535	−	21.1412i	−0.332191	−	1.45542i	−0.814879	−	0.579631i	$-0.803197\pi$
$211$	−4.82535	−	21.1412i	−0.332191	−	1.45542i	0.482689	−	0.875792i	$-0.339660\pi$
$212$	−1.12207	+	2.85900i	−0.0770644	+	0.196357i
$213$	5.39740	−	6.76812i	0.369823	−	0.463744i
$214$	4.83802			0.330720
$215$	4.13736	−	5.08746i	0.282166	−	0.346962i
$216$	4.06078			0.276301
$217$	0.109493	−	0.137299i	0.00743284	−	0.00932049i
$218$	5.40294	−	13.7665i	0.365933	−	0.932382i
$219$	0.649727	+	2.84664i	0.0439044	+	0.192358i
$220$	−0.0699380	−	0.933258i	−0.00471522	−	0.0629202i
$221$	1.29833	+	2.24877i	0.0873351	+	0.151269i
$222$	0.150393	−	0.260489i	0.0100937	−	0.0174828i
$223$	−5.31176	−	2.55801i	−0.355702	−	0.171297i	0.247495	−	0.968889i	$-0.420393\pi$
$223$	−5.31176	−	2.55801i	−0.355702	−	0.171297i	−0.603197	+	0.797592i	$0.706107\pi$
$224$	−0.272842	−	0.253161i	−0.0182301	−	0.0169150i
$225$	−2.01892	−	1.37648i	−0.134595	−	0.0917650i
$226$	3.84198	−	16.8328i	0.255565	−	1.11970i
$227$	−4.54180	−	0.684566i	−0.301450	−	0.0454362i	−0.00342418	−	0.999994i	$-0.501090\pi$
$227$	−4.54180	−	0.684566i	−0.301450	−	0.0454362i	−0.298026	+	0.954558i	$0.596328\pi$
$228$	−3.11260	+	2.12214i	−0.206137	+	0.140542i
$229$	−0.688759	−	1.75493i	−0.0455145	−	0.115969i	0.906309	−	0.422616i	$-0.138888\pi$
$229$	−0.688759	−	1.75493i	−0.0455145	−	0.115969i	−0.951823	+	0.306647i	$0.900793\pi$
$230$	6.69665	+	2.06564i	0.441564	+	0.136204i
$231$	0.234118	−	0.112745i	0.0154038	−	0.00741810i
$232$	0.284142	−	3.79161i	0.0186549	−	0.248932i
$233$	25.2170	−	3.80084i	1.65202	−	0.249002i	0.744075	−	0.668096i	$-0.232890\pi$
$233$	25.2170	−	3.80084i	1.65202	−	0.249002i	0.907943	+	0.419094i	$0.137652\pi$
$234$	0.628592	−	0.583248i	0.0410924	−	0.0381281i
$235$	−9.70098	+	2.99235i	−0.632822	+	0.195200i
$236$	1.36422	+	1.71068i	0.0888030	+	0.111356i
$237$	3.53061	+	4.42724i	0.229338	+	0.287580i
$238$	2.63169	−	0.811769i	0.170587	−	0.0526192i
$239$	18.0959	−	16.7905i	1.17052	−	1.08609i	0.175704	−	0.984443i	$-0.443780\pi$
$239$	18.0959	−	16.7905i	1.17052	−	1.08609i	0.994821	−	0.101645i	$-0.0324106\pi$
$240$	0.737654	−	0.111183i	0.0476153	−	0.00717686i
$241$	−0.252878	+	3.37443i	−0.0162893	+	0.217366i	0.983119	+	0.182968i	$0.0585704\pi$
$241$	−0.252878	+	3.37443i	−0.0162893	+	0.217366i	−0.999408	+	0.0343981i	$0.989049\pi$
$242$	−9.12153	+	4.39270i	−0.586354	+	0.282373i
$243$	14.7072	+	4.53657i	0.943468	+	0.291021i
$244$	−2.78227	−	7.08910i	−0.178116	−	0.453833i
$245$	5.66921	−	3.86520i	0.362193	−	0.246939i
$246$	−8.90366	−	1.34201i	−0.567676	−	0.0855635i
$247$	−0.394348	+	1.72775i	−0.0250917	+	0.109934i
$248$	0.389838	+	0.265787i	0.0247547	+	0.0168775i
$249$	−4.71815	−	4.37780i	−0.299000	−	0.277432i
$250$	−0.900969	−	0.433884i	−0.0569823	−	0.0274412i
$251$	−9.71347	+	16.8242i	−0.613109	+	1.06194i	0.377605	+	0.925967i	$0.376748\pi$
$251$	−9.71347	+	16.8242i	−0.613109	+	1.06194i	−0.990713	+	0.135968i	$0.956585\pi$
$252$	−0.454737	−	0.787628i	−0.0286458	−	0.0496159i
$253$	0.490125	+	6.54027i	0.0308139	+	0.411183i
$254$	1.13674	+	4.98039i	0.0713255	+	0.312497i
$255$	−2.01661	+	5.13825i	−0.126285	+	0.321770i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	3.34321			0.208544			0.104272	−	0.994549i	$-0.466749\pi$
$257$	3.34321			0.208544			0.104272	+	0.994549i	$0.466749\pi$
$258$	−1.13410	+	4.75848i	−0.0706059	+	0.296250i
$259$	−0.150074			−0.00932513
$260$	0.218802	−	0.274368i	0.0135695	−	0.0170156i
$261$	3.39431	−	8.64857i	0.210103	−	0.535333i
$262$	0.876052	+	3.83824i	0.0541227	+	0.237127i
$263$	0.946207	+	12.6263i	0.0583456	+	0.778568i	0.947254	+	0.320483i	$0.103845\pi$
$263$	0.946207	+	12.6263i	0.0583456	+	0.778568i	−0.888908	+	0.458085i	$0.848536\pi$
$264$	0.349075	+	0.604615i	0.0214841	+	0.0372115i
$265$	−1.53565	+	2.65983i	−0.0943344	+	0.163392i
$266$	1.69346	+	0.815527i	0.103833	+	0.0500031i
$267$	3.70008	+	3.43318i	0.226441	+	0.210107i
$268$	9.73513	+	6.63730i	0.594667	+	0.405437i
$269$	3.89865	−	17.0811i	0.237705	−	1.04145i	−0.705361	−	0.708848i	$-0.749215\pi$
$269$	3.89865	−	17.0811i	0.237705	−	1.04145i	0.943066	−	0.332605i	$-0.107928\pi$
$270$	4.01542	+	0.605227i	0.244371	+	0.0368330i
$271$	3.74348	−	2.55226i	0.227400	−	0.155039i	−0.444261	−	0.895898i	$-0.646534\pi$
$271$	3.74348	−	2.55226i	0.227400	−	0.155039i	0.671661	+	0.740859i	$0.265581\pi$
$272$	2.70329	+	6.88787i	0.163911	+	0.417638i
$273$	0.0931092	+	0.0287204i	0.00563522	+	0.00173824i
$274$	5.15369	−	2.48189i	0.311346	−	0.149936i
$275$	0.0699380	−	0.933258i	0.00421742	−	0.0562776i
$276$	−5.16947	+	0.779173i	−0.311166	+	0.0469007i
$277$	4.70244	−	4.36322i	0.282542	−	0.262161i	−0.526152	−	0.850391i	$-0.676366\pi$
$277$	4.70244	−	4.36322i	0.282542	−	0.262161i	0.808694	+	0.588230i	$0.200175\pi$
$278$	−11.5978	+	3.57745i	−0.695591	+	0.214561i
$279$	0.718821	+	0.901374i	0.0430347	+	0.0539638i
$280$	−0.232063	−	0.290998i	−0.0138684	−	0.0173905i
$281$	−15.0624	+	4.64613i	−0.898547	+	0.277165i	−0.709419	−	0.704787i	$-0.751042\pi$
$281$	−15.0624	+	4.64613i	−0.898547	+	0.277165i	−0.189128	+	0.981952i	$0.560566\pi$
$282$	5.55158	−	5.15112i	0.330592	−	0.306745i
$283$	−2.75917	+	0.415878i	−0.164016	+	0.0247214i	−0.230537	−	0.973064i	$-0.574048\pi$
$283$	−2.75917	+	0.415878i	−0.164016	+	0.0247214i	0.0665209	+	0.997785i	$0.478810\pi$
$284$	0.867201	−	11.5720i	0.0514589	−	0.686672i
$285$	−3.39413	+	1.63452i	−0.201051	+	0.0968209i
$286$	0.313836	+	0.0968055i	0.0185575	+	0.00572423i
$287$	1.64131	+	4.18200i	0.0968837	+	0.246856i
$288$	2.01892	−	1.37648i	0.118966	−	0.0811096i
$289$	−37.3288	−	5.62642i	−2.19581	−	0.330966i
$290$	0.846079	−	3.70692i	0.0496835	−	0.217678i
$291$	−7.33851	−	5.00331i	−0.430191	−	0.293299i
$292$	2.86922	+	2.66225i	0.167908	+	0.155796i
$293$	−25.6314	−	12.3434i	−1.49740	−	0.721112i	−0.507343	−	0.861744i	$-0.669372\pi$
$293$	−25.6314	−	12.3434i	−1.49740	−	0.721112i	−0.990062	+	0.140633i	$0.955086\pi$
$294$	−2.55928	+	4.43280i	−0.149260	+	0.258526i
$295$	1.09402	+	1.89490i	0.0636962	+	0.110325i
$296$	−0.0301317	−	0.402079i	−0.00175137	−	0.0233704i
$297$	0.845664	+	3.70509i	0.0490704	+	0.214991i
$298$	4.59986	−	11.7202i	0.266463	−	0.678936i
$299$	−1.53336	+	1.92277i	−0.0886765	+	0.111197i
$300$	0.745986			0.0430695
$301$	2.33903	−	0.697056i	0.134819	−	0.0401777i
$302$	−9.64910			−0.555243
$303$	−5.66640	+	7.10544i	−0.325526	+	0.408197i
$304$	−1.84496	+	4.70087i	−0.105815	+	0.269613i
$305$	−1.69462	−	7.42460i	−0.0970335	−	0.425131i
$306$	1.35115	+	18.0298i	0.0772400	+	1.03070i
$307$	−0.809848	−	1.40270i	−0.0462205	−	0.0800562i	0.841990	−	0.539494i	$-0.181384\pi$
$307$	−0.809848	−	1.40270i	−0.0462205	−	0.0800562i	−0.888210	+	0.459438i	$0.848051\pi$
$308$	0.174167	−	0.301665i	0.00992406	−	0.0171890i
$309$	7.07322	+	3.40628i	0.402382	+	0.193777i
$310$	0.345870	+	0.320921i	0.0196441	+	0.0182271i
$311$	−0.0953784	−	0.0650279i	−0.00540841	−	0.00368739i	0.560613	−	0.828078i	$-0.310566\pi$
$311$	−0.0953784	−	0.0650279i	−0.00540841	−	0.00368739i	−0.566021	+	0.824391i	$0.691518\pi$
$312$	−0.0582535	+	0.255225i	−0.00329796	+	0.0144493i
$313$	0.343439	+	0.0517651i	0.0194123	+	0.00292594i	0.158741	−	0.987320i	$-0.449256\pi$
$313$	0.343439	+	0.0517651i	0.0194123	+	0.00292594i	−0.139329	+	0.990246i	$0.544495\pi$
$314$	4.49202	−	3.06261i	0.253499	−	0.172833i
$315$	−0.332268	−	0.846606i	−0.0187212	−	0.0477008i
$316$	7.25359	+	2.23744i	0.408046	+	0.125866i
$317$	14.5174	−	6.99121i	0.815378	−	0.392666i	0.0207673	−	0.999784i	$-0.493389\pi$
$317$	14.5174	−	6.99121i	0.815378	−	0.392666i	0.794611	+	0.607119i	$0.207675\pi$
$318$	0.171218	−	2.28474i	0.00960142	−	0.128122i
$319$	3.51868	−	0.530356i	0.197008	−	0.0296942i
$320$	0.733052	−	0.680173i	0.0409788	−	0.0380228i
$321$	−3.44875	+	1.06380i	−0.192491	+	0.0593755i
$322$	1.62630	+	2.03931i	0.0906301	+	0.113647i
$323$	−23.2976	−	29.2142i	−1.29631	−	1.62552i
$324$	4.11014	−	1.26781i	0.228341	−	0.0704339i
$325$	0.257250	−	0.238693i	0.0142697	−	0.0132403i
$326$	−12.7192	+	1.91711i	−0.704452	+	0.106179i
$327$	−0.824437	+	11.0013i	−0.0455915	+	0.608376i
$328$	−10.8749	+	5.23708i	−0.600467	+	0.289169i
$329$	−3.61071	−	1.11376i	−0.199065	−	0.0614034i
$330$	0.255063	+	0.649889i	0.0140407	+	0.0357752i
$331$	5.77491	−	3.93727i	0.317418	−	0.216412i	−0.394121	−	0.919058i	$-0.628951\pi$
$331$	5.77491	−	3.93727i	0.317418	−	0.216412i	0.711539	+	0.702647i	$0.247999\pi$
$332$	−8.53156	−	1.28593i	−0.468230	−	0.0705743i
$333$	0.219236	−	0.960535i	0.0120141	−	0.0526370i
$334$	−8.83183	−	6.02144i	−0.483256	−	0.329479i
$335$	8.63716	+	8.01411i	0.471898	+	0.437858i
$336$	0.250160	+	0.120471i	0.0136473	+	0.00657221i
$337$	3.32235	−	5.75449i	0.180980	−	0.313467i	−0.761234	−	0.648477i	$-0.775406\pi$
$337$	3.32235	−	5.75449i	0.180980	−	0.313467i	0.942215	+	0.335010i	$0.108740\pi$
$338$	−6.43842	−	11.1517i	−0.350204	−	0.606571i
$339$	0.962522	+	12.8440i	0.0522770	+	0.697589i
$340$	1.64651	+	7.21384i	0.0892946	+	0.391225i
$341$	−0.161322	+	0.411043i	−0.00873609	+	0.0222592i
$342$	−7.69361	+	9.64748i	−0.416023	+	0.521676i
$343$	5.15925			0.278573
$344$	2.33719	+	6.12679i	0.126013	+	0.330334i
$345$	−5.22787			−0.281459
$346$	−0.643371	+	0.806761i	−0.0345878	+	0.0433718i
$347$	−8.09584	+	20.6279i	−0.434607	+	1.10736i	0.531003	+	0.847370i	$0.321815\pi$
$347$	−8.09584	+	20.6279i	−0.434607	+	1.10736i	−0.965611	+	0.259992i	$0.916280\pi$
$348$	0.631163	+	2.76531i	0.0338339	+	0.148236i
$349$	−2.28373	−	30.4743i	−0.122245	−	1.63125i	−0.634856	−	0.772630i	$-0.718941\pi$
$349$	−2.28373	−	30.4743i	−0.122245	−	1.63125i	0.512611	−	0.858621i	$-0.328678\pi$
$350$	−0.186100	−	0.322335i	−0.00994748	−	0.0172295i
$351$	−0.712525	+	1.23413i	−0.0380318	+	0.0658730i
$352$	0.843194	+	0.406061i	0.0449424	+	0.0216431i
$353$	1.75545	+	1.62882i	0.0934330	+	0.0866932i	0.725507	−	0.688215i	$-0.241606\pi$
$353$	1.75545	+	1.62882i	0.0934330	+	0.0866932i	−0.632074	+	0.774908i	$0.717796\pi$
$354$	−1.34862	−	0.919476i	−0.0716785	−	0.0488696i
$355$	2.58223	−	11.3135i	0.137051	−	0.600458i
$356$	6.69065	+	1.00845i	0.354604	+	0.0534479i
$357$	−1.69749	+	1.15733i	−0.0898407	+	0.0612524i
$358$	−3.04129	−	7.74908i	−0.160737	−	0.409551i
$359$	−4.43110	−	1.36681i	−0.233864	−	0.0721376i	0.175608	−	0.984460i	$-0.443811\pi$
$359$	−4.43110	−	1.36681i	−0.233864	−	0.0721376i	−0.409472	+	0.912323i	$0.634287\pi$
$360$	2.20152	−	1.06020i	0.116030	−	0.0558773i
$361$	0.485899	−	6.48387i	0.0255736	−	0.341256i
$362$	2.14997	−	0.324055i	0.113000	−	0.0170320i
$363$	5.53635	−	5.13698i	0.290583	−	0.269621i
$364$	0.124814	−	0.0384999i	0.00654201	−	0.00201794i
$365$	2.44039	+	3.06015i	0.127736	+	0.160175i
$366$	3.54210	+	4.44165i	0.185148	+	0.232169i
$367$	−25.3814	+	7.82912i	−1.32490	+	0.408677i	−0.874879	−	0.484342i	$-0.839059\pi$
$367$	−25.3814	+	7.82912i	−1.32490	+	0.408677i	−0.450019	+	0.893019i	$0.648583\pi$
$368$	−5.13722	+	4.76665i	−0.267796	+	0.248479i
$369$	−29.1643	+	4.39581i	−1.51823	+	0.228837i
$370$	0.0301317	−	0.402079i	0.00156647	−	0.0209031i
$371$	−1.02994	+	0.495991i	−0.0534716	+	0.0257506i
$372$	−0.336335	−	0.103746i	−0.0174382	−	0.00537897i
$373$	−2.32104	−	5.91390i	−0.120179	−	0.306210i	0.858107	−	0.513471i	$-0.171641\pi$
$373$	−2.32104	−	5.91390i	−0.120179	−	0.306210i	−0.978286	+	0.207260i	$0.933545\pi$
$374$	−5.72160	+	3.90092i	−0.295857	+	0.201712i
$375$	0.737654	+	0.111183i	0.0380923	+	0.00574149i
$376$	2.25903	−	9.89747i	0.116501	−	0.510423i
$377$	1.10247	+	0.751651i	0.0567801	+	0.0387120i
$378$	1.10795	+	1.02803i	0.0569869	+	0.0528761i
$379$	−7.95655	−	3.83167i	−0.408700	−	0.196820i	0.218226	−	0.975898i	$-0.429973\pi$
$379$	−7.95655	−	3.83167i	−0.408700	−	0.196820i	−0.626926	+	0.779079i	$0.715687\pi$
$380$	−2.52498	+	4.37339i	−0.129529	+	0.224350i
$381$	−1.90542	−	3.30029i	−0.0976177	−	0.169079i
$382$	1.80631	+	24.1036i	0.0924190	+	1.23325i
$383$	5.68200	+	24.8945i	0.290336	+	1.27205i	0.884058	+	0.467377i	$0.154801\pi$
$383$	5.68200	+	24.8945i	0.290336	+	1.27205i	−0.593722	+	0.804670i	$0.702342\pi$
$384$	−0.272539	+	0.694419i	−0.0139080	+	0.0354369i
$385$	0.217182	−	0.272338i	0.0110686	−	0.0138796i
$386$	−21.7314			−1.10610
$387$	1.04448	+	15.9891i	0.0530937	+	0.812769i
$388$	−11.9062			−0.604444
$389$	8.89715	−	11.1567i	0.451103	−	0.565666i	−0.503328	−	0.864095i	$-0.667891\pi$
$389$	8.89715	−	11.1567i	0.451103	−	0.565666i	0.954432	+	0.298430i	$0.0964628\pi$
$390$	−0.0956423	+	0.243693i	−0.00484304	+	0.0123399i
$391$	−11.5387	−	50.5546i	−0.583540	−	2.55665i
$392$	0.512758	+	6.84228i	0.0258982	+	0.345587i
$393$	−1.46845	−	2.54343i	−0.0740736	−	0.128299i
$394$	12.2606	−	21.2360i	0.617680	−	1.06985i
$395$	6.83910	+	3.29354i	0.344113	+	0.165716i
$396$	1.67635	+	1.55543i	0.0842399	+	0.0781632i
$397$	11.9372	+	8.13865i	0.599112	+	0.408467i	0.824549	−	0.565790i	$-0.191429\pi$
$397$	11.9372	+	8.13865i	0.599112	+	0.408467i	−0.225438	+	0.974258i	$0.572381\pi$
$398$	0.296724	−	1.30003i	0.0148734	−	0.0651647i
$399$	−1.38649	−	0.208980i	−0.0694114	−	0.0104621i
$400$	0.826239	−	0.563320i	0.0413119	−	0.0281660i
$401$	10.5327	+	26.8369i	0.525979	+	1.34017i	0.909140	+	0.416490i	$0.136740\pi$
$401$	10.5327	+	26.8369i	0.525979	+	1.34017i	−0.383162	+	0.923681i	$0.625165\pi$
$402$	−8.39905	−	2.59076i	−0.418907	−	0.129216i
$403$	−0.149179	+	0.0718411i	−0.00743116	+	0.00357866i
$404$	−0.910422	+	12.1487i	−0.0452952	+	0.604422i
$405$	4.25319	−	0.641066i	0.211343	−	0.0318548i
$406$	1.03741	−	0.962580i	0.0514860	−	0.0477720i
$407$	0.360586	−	0.111226i	0.0178736	−	0.00551327i
$408$	−3.44155	−	4.31556i	−0.170382	−	0.213652i
$409$	−2.85651	−	3.58195i	−0.141245	−	0.177116i	0.706177	−	0.708035i	$-0.250418\pi$
$409$	−2.85651	−	3.58195i	−0.141245	−	0.177116i	−0.847423	+	0.530919i	$0.821847\pi$
$410$	−11.5340	+	3.55777i	−0.569623	+	0.175706i
$411$	−3.12805	+	2.90241i	−0.154295	+	0.143165i
$412$	10.4064	−	1.56851i	0.512685	−	0.0772748i
$413$	−0.0608593	+	0.812111i	−0.00299469	+	0.0399614i
$414$	−15.4283	+	7.42986i	−0.758258	+	0.365158i
$415$	−8.24461	−	2.54312i	−0.404712	−	0.124837i
$416$	0.128209	+	0.326672i	0.00628598	+	0.0160164i
$417$	7.48081	−	5.10033i	0.366337	−	0.249764i
$418$	−4.67334	−	0.704392i	−0.228580	−	0.0344530i
$419$	−0.181521	+	0.795294i	−0.00886786	+	0.0388527i	−0.979168	−	0.203050i	$-0.934914\pi$
$419$	−0.181521	+	0.795294i	−0.00886786	+	0.0388527i	0.970300	+	0.241903i	$0.0777716\pi$
$420$	0.229410	+	0.156409i	0.0111941	+	0.00763200i
$421$	13.3465	+	12.3838i	0.650471	+	0.603549i	0.934798	−	0.355179i	$-0.115580\pi$
$421$	13.3465	+	12.3838i	0.650471	+	0.603549i	−0.284328	+	0.958727i	$0.591770\pi$
$422$	19.5374	+	9.40873i	0.951068	+	0.458010i
$423$	12.4032	−	21.4830i	0.603066	−	1.04454i
$424$	−1.53565	−	2.65983i	−0.0745779	−	0.129173i
$425$	0.552955	+	7.37867i	0.0268222	+	0.357918i
$426$	1.92631	+	8.43971i	0.0933299	+	0.408905i
$427$	1.03556	−	2.63857i	0.0501144	−	0.127689i
$428$	−3.01646	+	3.78252i	−0.145806	+	0.182835i
$429$	−0.245002			−0.0118288
$430$	1.39793	+	6.40670i	0.0674143	+	0.308958i
$431$	−12.8634			−0.619609			−0.309804	−	0.950800i	$-0.600264\pi$
$431$	−12.8634			−0.619609			−0.309804	+	0.950800i	$0.600264\pi$
$432$	−2.53185	+	3.17484i	−0.121814	+	0.152750i
$433$	−14.1918	+	36.1601i	−0.682014	+	1.73774i	−0.00695791	+	0.999976i	$0.502215\pi$
$433$	−14.1918	+	36.1601i	−0.682014	+	1.73774i	−0.675056	+	0.737767i	$0.735880\pi$
$434$	0.0390775	+	0.171210i	0.00187578	+	0.00821832i
$435$	0.211966	+	2.82849i	0.0101630	+	0.135616i
$436$	7.39437	+	12.8074i	0.354126	+	0.613365i
$437$	17.6950	−	30.6487i	0.846468	−	1.46613i
$438$	−2.63069	−	1.26687i	−0.125699	−	0.0605335i
$439$	3.16147	+	2.93341i	0.150889	+	0.140004i	0.752005	−	0.659157i	$-0.229087\pi$
$439$	3.16147	+	2.93341i	0.150889	+	0.140004i	−0.601117	+	0.799161i	$0.705277\pi$
$440$	0.773256	+	0.527197i	0.0368635	+	0.0251331i
$441$	−3.73079	+	16.3457i	−0.177657	+	0.778365i
$442$	−2.56766	−	0.387012i	−0.122131	−	0.0184083i
$443$	−27.9260	+	19.0396i	−1.32680	+	0.904598i	−0.999191	−	0.0402143i	$-0.987196\pi$
$443$	−27.9260	+	19.0396i	−1.32680	+	0.904598i	−0.327611	+	0.944813i	$0.606244\pi$
$444$	0.109890	+	0.279994i	0.00521513	+	0.0132879i
$445$	6.46562	+	1.99438i	0.306500	+	0.0945427i
$446$	5.31176	−	2.55801i	0.251519	−	0.121125i
$447$	−0.701895	+	9.36614i	−0.0331985	+	0.443003i
$448$	0.368044	−	0.0554736i	0.0173884	−	0.00262088i
$449$	10.9067	−	10.1199i	0.514717	−	0.477588i	−0.379518	−	0.925184i	$-0.623910\pi$
$449$	10.9067	−	10.1199i	0.514717	−	0.477588i	0.894236	+	0.447596i	$0.147720\pi$
$450$	2.33495	−	0.720236i	0.110070	−	0.0339522i
$451$	−7.04309	−	8.83175i	−0.331646	−	0.415871i
$452$	10.7650	+	13.4989i	0.506343	+	0.634934i
$453$	6.87830	−	2.12167i	0.323171	−	0.0996850i
$454$	3.36698	−	3.12410i	0.158020	−	0.146621i
$455$	0.129158	−	0.0194674i	0.00605500	−	0.000912645i
$456$	0.281523	−	3.75666i	0.0131835	−	0.175922i
$457$	−2.72544	+	1.31250i	−0.127491	+	0.0613963i	−0.496542	−	0.868013i	$-0.665397\pi$
$457$	−2.72544	+	1.31250i	−0.127491	+	0.0613963i	0.369051	+	0.929409i	$0.379683\pi$
$458$	1.80149	+	0.555687i	0.0841782	+	0.0259655i
$459$	−10.9775	−	27.9701i	−0.512384	−	1.30553i
$460$	−5.79028	+	3.94774i	−0.269973	+	0.184065i
$461$	13.0814	+	1.97170i	0.609261	+	0.0918313i	0.446424	−	0.894822i	$-0.352697\pi$
$461$	13.0814	+	1.97170i	0.609261	+	0.0918313i	0.162837	+	0.986653i	$0.447935\pi$
$462$	−0.0578224	+	0.253337i	−0.00269014	+	0.0117863i
$463$	−2.49282	−	1.69957i	−0.115851	−	0.0789859i	0.504008	−	0.863699i	$-0.331858\pi$
$463$	−2.49282	−	1.69957i	−0.115851	−	0.0789859i	−0.619859	+	0.784713i	$0.712810\pi$
$464$	2.78724	+	2.58618i	0.129395	+	0.120061i
$465$	−0.317116	−	0.152715i	−0.0147059	−	0.00708200i
$466$	−12.7509	+	22.0852i	−0.590674	+	1.02308i
$467$	15.0961	+	26.1472i	0.698563	+	1.20995i	0.968965	+	0.247199i	$0.0795100\pi$
$467$	15.0961	+	26.1472i	0.698563	+	1.20995i	−0.270402	+	0.962747i	$0.587157\pi$
$468$	0.0640811	+	0.855103i	0.00296215	+	0.0395271i
$469$	0.975852	+	4.27549i	0.0450607	+	0.197424i
$470$	3.70894	−	9.45023i	0.171081	−	0.435907i
$471$	−2.52869	+	3.17088i	−0.116516	+	0.146106i
$472$	−2.18804			−0.100713
$473$	−5.10342	+	3.40839i	−0.234656	+	0.156718i
$474$	−5.66265			−0.260094
$475$	−3.14860	+	3.94821i	−0.144467	+	0.181156i
$476$	−1.00617	+	2.56367i	−0.0461175	+	0.117506i
$477$	−1.66996	−	7.31659i	−0.0764624	−	0.335004i
$478$	1.84476	+	24.6166i	0.0843774	+	1.12594i
$479$	−15.8627	−	27.4749i	−0.724783	−	1.25536i	−0.959063	−	0.283192i	$-0.908607\pi$
$479$	−15.8627	−	27.4749i	−0.724783	−	1.25536i	0.234280	−	0.972169i	$-0.424727\pi$
$480$	−0.372993	+	0.646043i	−0.0170247	+	0.0294877i
$481$	0.127485	+	0.0613934i	0.00581281	+	0.00279930i
$482$	−2.48057	−	2.30163i	−0.112987	−	0.104836i
$483$	−1.60771	−	1.09612i	−0.0731532	−	0.0498750i
$484$	2.25283	−	9.87031i	0.102401	−	0.448650i
$485$	−11.7732	−	1.77452i	−0.534593	−	0.0805769i
$486$	−12.7166	+	8.67005i	−0.576838	+	0.393282i
$487$	−3.40554	−	8.67719i	−0.154320	−	0.393201i	0.832716	−	0.553700i	$-0.186785\pi$
$487$	−3.40554	−	8.67719i	−0.154320	−	0.393201i	−0.987036	+	0.160500i	$0.948689\pi$
$488$	7.27720	+	2.24472i	0.329423	+	0.101614i
$489$	8.64527	−	4.16334i	0.390953	−	0.188273i
$490$	−0.512758	+	6.84228i	−0.0231640	+	0.309103i
$491$	31.8353	−	4.79840i	1.43671	−	0.216549i	0.615931	−	0.787800i	$-0.288780\pi$
$491$	31.8353	−	4.79840i	1.43671	−	0.216549i	0.820775	+	0.571252i	$0.193542\pi$
$492$	6.60057	−	6.12443i	0.297576	−	0.276111i
$493$	−26.8843	+	8.29269i	−1.21081	+	0.373484i
$494$	−1.10494	−	1.38555i	−0.0497135	−	0.0623388i
$495$	1.42581	+	1.78790i	0.0640852	+	0.0803603i
$496$	−0.450860	+	0.139072i	−0.0202442	+	0.00624452i
$497$	3.16618	−	2.93779i	0.142023	−	0.131778i
$498$	6.36442	−	0.959282i	0.285196	−	0.0429864i
$499$	−1.84980	+	24.6838i	−0.0828084	+	1.10500i	0.788752	+	0.614712i	$0.210728\pi$
$499$	−1.84980	+	24.6838i	−0.0828084	+	1.10500i	−0.871560	+	0.490289i	$0.836891\pi$
$500$	0.900969	−	0.433884i	0.0402926	−	0.0194039i
$501$	7.61973	+	2.35038i	0.340424	+	0.105007i
$502$	−7.09746	−	18.0840i	−0.316775	−	0.807129i
$503$	28.9513	−	19.7386i	1.29087	−	0.880102i	0.293749	−	0.955883i	$-0.405097\pi$
$503$	28.9513	−	19.7386i	1.29087	−	0.880102i	0.997125	+	0.0757802i	$0.0241447\pi$
$504$	0.899316	+	0.135550i	0.0400587	+	0.00603788i
$505$	−2.71093	+	11.8774i	−0.120635	+	0.528535i
$506$	−5.41897	−	3.69459i	−0.240903	−	0.164245i
$507$	7.04166	+	6.53370i	0.312731	+	0.290172i
$508$	−4.60257	−	2.21648i	−0.204206	−	0.0983405i
$509$	16.7825	−	29.0681i	0.743871	−	1.28842i	−0.206850	−	0.978373i	$-0.566321\pi$
$509$	16.7825	−	29.0681i	0.743871	−	1.28842i	0.950720	−	0.310049i	$-0.100346\pi$
$510$	−2.75991	−	4.78030i	−0.122211	−	0.211675i
$511$	0.108868	+	1.45275i	0.00481606	+	0.0642658i
$512$	0.222521	+	0.974928i	0.00983413	+	0.0430861i
$513$	7.49195	−	19.0892i	0.330778	−	0.842808i
$514$	−2.08446	+	2.61382i	−0.0919414	+	0.115291i
$515$	10.5239			0.463739
$516$	−3.01323	−	3.85354i	−0.132650	−	0.169642i
$517$	9.50100			0.417854
$518$	0.0935695	−	0.117332i	0.00411121	−	0.00515529i
$519$	0.281229	−	0.716561i	0.0123446	−	0.0314535i
$520$	0.0780894	+	0.342132i	0.00342444	+	0.0150035i
$521$	1.61959	+	21.6120i	0.0709556	+	0.946837i	0.913140	+	0.407647i	$0.133651\pi$
$521$	1.61959	+	21.6120i	0.0709556	+	0.946837i	−0.842184	+	0.539190i	$0.818730\pi$
$522$	4.64540	+	8.04608i	0.203324	+	0.352167i
$523$	20.6765	−	35.8128i	0.904121	−	1.56598i	0.0820280	−	0.996630i	$-0.473860\pi$
$523$	20.6765	−	35.8128i	0.904121	−	1.56598i	0.822093	−	0.569353i	$-0.192806\pi$
$524$	−3.54706	−	1.70818i	−0.154954	−	0.0746220i
$525$	0.203537	+	0.188854i	0.00888306	+	0.00824228i
$526$	−10.4616	−	7.13257i	−0.456146	−	0.310995i
$527$	0.776861	−	3.40365i	0.0338406	−	0.148265i
$528$	−0.690351	−	0.104054i	−0.0300437	−	0.00452836i
$529$	21.5748	−	14.7094i	0.938033	−	0.639540i
$530$	−1.12207	−	2.85900i	−0.0487398	−	0.124187i
$531$	−5.10895	−	1.57590i	−0.221710	−	0.0683883i
$532$	−1.69346	+	0.815527i	−0.0734207	+	0.0353576i
$533$	0.316543	−	4.22397i	0.0137110	−	0.182960i
$534$	−4.99113	+	0.752292i	−0.215987	+	0.0325549i
$535$	−3.54652	+	3.29069i	−0.153329	+	0.142269i
$536$	−11.2590	+	3.47294i	−0.486315	+	0.150008i
$537$	3.87185	+	4.85515i	0.167083	+	0.209515i
$538$	10.9238	+	13.6980i	0.470957	+	0.590562i
$539$	−6.13618	+	1.89276i	−0.264304	+	0.0815270i
$540$	−2.97676	+	2.76203i	−0.128099	+	0.118859i
$541$	−33.8946	+	5.10878i	−1.45724	+	0.219644i	−0.829381	−	0.558683i	$-0.811307\pi$
$541$	−33.8946	+	5.10878i	−1.45724	+	0.219644i	−0.627860	+	0.778327i	$0.716069\pi$
$542$	−0.338584	+	4.51808i	−0.0145434	+	0.194068i
$543$	−1.46134	+	0.703742i	−0.0627119	+	0.0302005i
$544$	−7.07062	−	2.18100i	−0.303151	−	0.0935096i
$545$	5.40294	+	13.7665i	0.231436	+	0.589690i
$546$	−0.0805071	+	0.0548888i	−0.00344539	+	0.00234902i
$547$	−21.6575	−	3.26434i	−0.926006	−	0.139573i	−0.331309	−	0.943522i	$-0.607490\pi$
$547$	−21.6575	−	3.26434i	−0.926006	−	0.139573i	−0.594698	+	0.803949i	$0.702728\pi$
$548$	−1.27286	+	5.57675i	−0.0543737	+	0.238227i
$549$	15.3752	+	10.4826i	0.656196	+	0.447387i
$550$	0.686045	+	0.636556i	0.0292530	+	0.0271429i
$551$	−17.2997	−	8.33108i	−0.736990	−	0.354916i
$552$	2.61393	−	4.52746i	0.111256	−	0.192702i
$553$	1.41266	+	2.44679i	0.0600723	+	0.104048i
$554$	0.479384	+	6.39694i	0.0203671	+	0.271780i
$555$	0.0669313	+	0.293245i	0.00284107	+	0.0124476i
$556$	4.43416	−	11.2980i	0.188050	−	0.479144i
$557$	−11.8181	+	14.8195i	−0.500751	+	0.627921i	−0.966398	−	0.257049i	$-0.917250\pi$
$557$	−11.8181	+	14.8195i	−0.500751	+	0.627921i	0.465648	+	0.884970i	$0.345821\pi$
$558$	−1.15290			−0.0488062
$559$	−2.27212	−	0.364733i	−0.0961003	−	0.0154266i
$560$	0.372201			0.0157284
$561$	3.22086	−	4.03883i	0.135985	−	0.170519i
$562$	5.75876	−	14.6731i	0.242918	−	0.618946i
$563$	−5.25554	−	23.0260i	−0.221494	−	0.970431i	−0.956354	−	0.292211i	$-0.905609\pi$
$563$	−5.25554	−	23.0260i	−0.221494	−	0.970431i	0.734859	−	0.678219i	$-0.237248\pi$
$564$	0.565950	+	7.55207i	0.0238308	+	0.318000i
$565$	8.63286	+	14.9526i	0.363187	+	0.629059i
$566$	1.39517	−	2.41650i	0.0586433	−	0.101573i
$567$	1.44238	+	0.694614i	0.0605743	+	0.0291711i
$568$	8.50666	+	7.89303i	0.356932	+	0.331184i
$569$	−5.69001	−	3.87938i	−0.238538	−	0.162632i	0.438151	−	0.898901i	$-0.355633\pi$
$569$	−5.69001	−	3.87938i	−0.238538	−	0.162632i	−0.676689	+	0.736269i	$0.736586\pi$
$570$	0.838280	−	3.67274i	0.0351117	−	0.153834i
$571$	−16.9861	−	2.56025i	−0.710848	−	0.107143i	−0.216342	−	0.976318i	$-0.569413\pi$
$571$	−16.9861	−	2.56025i	−0.710848	−	0.107143i	−0.494506	+	0.869174i	$0.664651\pi$
$572$	−0.271359	+	0.185009i	−0.0113461	+	0.00773563i
$573$	−6.58759	−	16.7849i	−0.275201	−	0.701200i
$574$	−4.29296	−	1.32420i	−0.179185	−	0.0552712i
$575$	−6.31399	+	3.04066i	−0.263311	+	0.126804i
$576$	−0.182603	+	2.43667i	−0.00760847	+	0.101528i
$577$	−11.4980	+	1.73304i	−0.478668	+	0.0721476i	−0.383945	−	0.923356i	$-0.625435\pi$
$577$	−11.4980	+	1.73304i	−0.478668	+	0.0721476i	−0.0947231	+	0.995504i	$0.530197\pi$
$578$	27.6731	−	25.6769i	1.15105	−	1.06802i
$579$	15.4911	−	4.77838i	0.643789	−	0.198583i
$580$	2.37066	+	2.97272i	0.0984364	+	0.123435i
$581$	−2.00222	−	2.51071i	−0.0830663	−	0.104162i
$582$	8.48724	−	2.61797i	0.351807	−	0.108518i
$583$	2.10705	−	1.95506i	0.0872652	−	0.0809703i
$584$	−3.87036	+	0.583363i	−0.160157	+	0.0241397i
$585$	−0.0640811	+	0.855103i	−0.00264943	+	0.0353541i
$586$	25.6314	−	12.3434i	1.05882	−	0.509903i
$587$	40.0845	+	12.3644i	1.65447	+	0.510335i	0.974780	−	0.223168i	$-0.0716398\pi$
$587$	40.0845	+	12.3644i	1.65447	+	0.510335i	0.679686	+	0.733503i	$0.262116\pi$
$588$	−1.87002	−	4.76473i	−0.0771183	−	0.196494i
$589$	1.96866	−	1.34221i	0.0811174	−	0.0553049i
$590$	−2.16360	−	0.326110i	−0.0890739	−	0.0134257i
$591$	−4.07045	+	17.8338i	−0.167436	+	0.733585i
$592$	0.333145	+	0.227134i	0.0136922	+	0.00933516i
$593$	−6.18070	−	5.73485i	−0.253811	−	0.235502i	0.542997	−	0.839734i	$-0.317289\pi$
$593$	−6.18070	−	5.73485i	−0.253811	−	0.235502i	−0.796808	+	0.604232i	$0.793480\pi$
$594$	−3.42402	−	1.64892i	−0.140489	−	0.0676561i
$595$	−1.37702	+	2.38507i	−0.0564524	+	0.0977785i
$596$	6.29529	+	10.9038i	0.257865	+	0.446636i
$597$	0.0743375	+	0.991965i	0.00304243	+	0.0405984i
$598$	−0.547250	−	2.39766i	−0.0223787	−	0.0980475i
$599$	−10.0964	+	25.7253i	−0.412529	+	1.05111i	0.562057	+	0.827098i	$0.310010\pi$
$599$	−10.0964	+	25.7253i	−0.412529	+	1.05111i	−0.974587	+	0.224010i	$0.928085\pi$
$600$	−0.465114	+	0.583235i	−0.0189882	+	0.0238105i
$601$	34.6449			1.41320			0.706598	−	0.707615i	$-0.250229\pi$
$601$	34.6449			1.41320			0.706598	+	0.707615i	$0.250229\pi$
$602$	−0.913379	+	2.26333i	−0.0372265	+	0.0922465i
$603$	−28.7905			−1.17244
$604$	6.01612	−	7.54397i	0.244792	−	0.306960i
$605$	3.69876	−	9.42429i	0.150376	−	0.383152i
$606$	−2.02231	−	8.86034i	−0.0821509	−	0.359927i
$607$	0.116875	+	1.55959i	0.00474382	+	0.0633018i	0.999073	−	0.0430415i	$-0.0137048\pi$
$607$	0.116875	+	1.55959i	0.00474382	+	0.0633018i	−0.994329	+	0.106343i	$0.966086\pi$
$608$	−2.52498	−	4.37339i	−0.102401	−	0.177364i
$609$	−0.527859	+	0.914279i	−0.0213899	+	0.0370484i
$610$	6.86136	+	3.30426i	0.277808	+	0.133785i
$611$	2.61160	+	2.42321i	0.105654	+	0.0980328i
$612$	−14.9387	−	10.1850i	−0.603861	−	0.411706i
$613$	6.10893	−	26.7650i	0.246737	−	1.08103i	−0.688007	−	0.725705i	$-0.741514\pi$
$613$	6.10893	−	26.7650i	0.246737	−	1.08103i	0.934744	−	0.355322i	$-0.115629\pi$
$614$	1.60161	+	0.241403i	0.0646356	+	0.00974224i
$615$	7.43964	−	5.07226i	0.299995	−	0.204533i
$616$	0.127260	+	0.324254i	0.00512747	+	0.0130646i
$617$	14.1548	+	4.36618i	0.569851	+	0.175776i	0.566273	−	0.824218i	$-0.308385\pi$
$617$	14.1548	+	4.36618i	0.569851	+	0.175776i	0.00357793	+	0.999994i	$0.498861\pi$
$618$	−7.07322	+	3.40628i	−0.284527	+	0.137021i
$619$	1.12711	−	15.0403i	0.0453025	−	0.604519i	−0.927641	−	0.373474i	$-0.878166\pi$
$619$	1.12711	−	15.0403i	0.0453025	−	0.604519i	0.972943	−	0.231045i	$-0.0742145\pi$
$620$	−0.466552	+	0.0703215i	−0.0187372	+	0.00282418i
$621$	20.8611	−	19.3563i	0.837128	−	0.776741i
$622$	0.110308	−	0.0340256i	0.00442296	−	0.00136430i
$623$	1.57019	+	1.96896i	0.0629084	+	0.0788847i
$624$	−0.163223	−	0.204675i	−0.00653414	−	0.00819355i
$625$	0.955573	−	0.294755i	0.0382229	−	0.0117902i
$626$	−0.254602	+	0.236236i	−0.0101760	+	0.00944190i
$627$	3.48624	−	0.525467i	0.139227	−	0.0209851i
$628$	−0.406286	+	5.42150i	−0.0162126	+	0.216342i
$629$	−2.68801	+	1.29448i	−0.107178	+	0.0516142i
$630$	0.869069	+	0.268072i	0.0346245	+	0.0106803i
$631$	−15.8868	−	40.4790i	−0.632445	−	1.61144i	−0.782418	−	0.622753i	$-0.786014\pi$
$631$	−15.8868	−	40.4790i	−0.632445	−	1.61144i	0.149973	−	0.988690i	$-0.452081\pi$
$632$	−6.27184	+	4.27607i	−0.249480	+	0.170093i
$633$	−15.9960	−	2.41100i	−0.635782	−	0.0958288i
$634$	−3.58550	+	15.7091i	−0.142398	+	0.623888i
$635$	−4.22081	−	2.87770i	−0.167498	−	0.114198i
$636$	1.67953	+	1.55838i	0.0665978	+	0.0617937i
$637$	−2.16944	−	1.04475i	−0.0859564	−	0.0413944i
$638$	−1.77921	+	3.08169i	−0.0704397	+	0.122005i
$639$	14.1778	+	24.5566i	0.560864	+	0.971444i
$640$	0.0747301	+	0.997204i	0.00295397	+	0.0394179i
$641$	5.65165	+	24.7615i	0.223227	+	0.978021i	0.955031	+	0.296506i	$0.0958215\pi$
$641$	5.65165	+	24.7615i	0.223227	+	0.978021i	−0.731804	+	0.681515i	$0.761321\pi$
$642$	1.31855	−	3.35961i	0.0520390	−	0.132593i
$643$	−17.6283	+	22.1052i	−0.695193	+	0.871745i	−0.996654	−	0.0817338i	$-0.973954\pi$
$643$	−17.6283	+	22.1052i	−0.695193	+	0.871745i	0.301461	+	0.953479i	$0.402526\pi$
$644$	−2.60838			−0.102785
$645$	−2.40523	−	4.25959i	−0.0947059	−	0.167721i
$646$	37.3664			1.47016
$647$	−3.34602	+	4.19577i	−0.131545	+	0.164953i	−0.843242	−	0.537534i	$-0.819356\pi$
$647$	−3.34602	+	4.19577i	−0.131545	+	0.164953i	0.711696	+	0.702487i	$0.247927\pi$
$648$	−1.57142	+	4.00391i	−0.0617311	+	0.157288i
$649$	−0.455662	−	1.99639i	−0.0178863	−	0.0783650i
$650$	0.0262251	+	0.349949i	0.00102863	+	0.0137261i
$651$	−0.0655022	−	0.113453i	−0.00256723	−	0.00444658i
$652$	6.43144	−	11.1396i	0.251875	−	0.436260i
$653$	32.1936	+	15.5036i	1.25983	+	0.606704i	0.940131	−	0.340814i	$-0.110703\pi$
$653$	32.1936	+	15.5036i	1.25983	+	0.606704i	0.319703	+	0.947518i	$0.396417\pi$
$654$	−8.08717	−	7.50380i	−0.316233	−	0.293422i
$655$	−3.25286	−	2.21776i	−0.127100	−	0.0866550i
$656$	2.68588	−	11.7676i	0.104866	−	0.459448i
$657$	−9.45724	−	1.42545i	−0.368962	−	0.0556121i
$658$	3.12201	−	2.12855i	0.121709	−	0.0829796i
$659$	−13.7564	−	35.0506i	−0.535872	−	1.36538i	−0.900756	−	0.434326i	$-0.856987\pi$
$659$	−13.7564	−	35.0506i	−0.535872	−	1.36538i	0.364884	−	0.931053i	$-0.381109\pi$
$660$	−0.667132	−	0.205783i	−0.0259681	−	0.00801009i
$661$	1.82761	−	0.880133i	0.0710859	−	0.0342332i	−0.398003	−	0.917384i	$-0.630297\pi$
$661$	1.82761	−	0.880133i	0.0710859	−	0.0342332i	0.469089	+	0.883151i	$0.344582\pi$
$662$	−0.522318	+	6.96985i	−0.0203005	+	0.270891i
$663$	1.91544	−	0.288705i	0.0743893	−	0.0112124i
$664$	6.32471	−	5.86848i	0.245447	−	0.227741i
$665$	−1.79609	+	0.554021i	−0.0696495	+	0.0214840i
$666$	0.614285	+	0.770290i	0.0238031	+	0.0298481i
$667$	−16.6136	−	20.8328i	−0.643281	−	0.806648i
$668$	10.2143	−	3.15070i	0.395204	−	0.121904i
$669$	−3.22399	+	2.99143i	−0.124647	+	0.115655i
$670$	−11.6509	+	1.75608i	−0.450112	+	0.0678435i
$671$	−0.532615	+	7.10726i	−0.0205614	+	0.274373i
$672$	−0.250160	+	0.120471i	−0.00965012	+	0.00464725i
$673$	0.00824501	+	0.00254325i	0.000317822	+	9.80350e-5i	0.294914	−	0.955524i	$-0.404709\pi$
$673$	0.00824501	+	0.00254325i	0.000317822	+	9.80350e-5i	−0.294596	+	0.955622i	$0.595185\pi$
$674$	2.42758	+	6.18539i	0.0935071	+	0.238252i
$675$	−3.35517	+	2.28752i	−0.129141	+	0.0880466i
$676$	12.7330	+	1.91919i	0.489732	+	0.0738152i
$677$	8.06042	−	35.3150i	0.309787	−	1.35727i	−0.545065	−	0.838394i	$-0.683495\pi$
$677$	8.06042	−	35.3150i	0.309787	−	1.35727i	0.854852	−	0.518872i	$-0.173648\pi$
$678$	−10.6419	−	7.25555i	−0.408701	−	0.278648i
$679$	−3.24851	−	3.01417i	−0.124666	−	0.115673i
$680$	−6.66659	−	3.21046i	−0.255652	−	0.123116i
$681$	−1.71319	+	2.96734i	−0.0656497	+	0.113709i
$682$	−0.220783	−	0.382408i	−0.00845423	−	0.0146431i
$683$	−0.632543	−	8.44070i	−0.0242036	−	0.322974i	−0.996143	−	0.0877434i	$-0.972034\pi$
$683$	−0.632543	−	8.44070i	−0.0242036	−	0.322974i	0.971940	−	0.235231i	$-0.0755846\pi$
$684$	−2.74582	−	12.0302i	−0.104989	−	0.459987i
$685$	−2.08981	+	5.32475i	−0.0798475	+	0.203448i
$686$	−3.21674	+	4.03366i	−0.122816	+	0.154006i
$687$	−1.40637			−0.0536563
$688$	−6.24733	−	1.99270i	−0.238177	−	0.0759711i
$689$	1.07781			0.0410615
$690$	3.25952	−	4.08731i	0.124088	−	0.155601i
$691$	−9.83120	+	25.0495i	−0.373996	+	0.952928i	0.612694	+	0.790320i	$0.290086\pi$
$691$	−9.83120	+	25.0495i	−0.373996	+	0.952928i	−0.986691	+	0.162608i	$0.948010\pi$
$692$	−0.229616	−	1.00601i	−0.00872870	−	0.0382429i
$693$	0.0636068	+	0.848774i	0.00241622	+	0.0322423i
$694$	−11.0798	−	19.1908i	−0.420585	−	0.728474i
$695$	6.06852	−	10.5110i	0.230192	−	0.398704i
$696$	−2.55553	−	1.23068i	−0.0968670	−	0.0466487i
$697$	65.4703	+	60.7476i	2.47987	+	2.30098i
$698$	25.2496	+	17.2149i	0.955713	+	0.651594i
$699$	4.23323	−	18.5470i	0.160116	−	0.701512i
$700$	0.368044	+	0.0554736i	0.0139107	+	0.00209671i
$701$	−8.95819	+	6.10759i	−0.338346	+	0.230680i	−0.720559	−	0.693394i	$-0.756115\pi$
$701$	−8.95819	+	6.10759i	−0.338346	+	0.230680i	0.382213	+	0.924074i	$0.375162\pi$
$702$	−0.520629	−	1.32654i	−0.0196499	−	0.0500671i
$703$	−1.94571	−	0.600173i	−0.0733840	−	0.0226360i
$704$	−0.843194	+	0.406061i	−0.0317791	+	0.0153040i
$705$	−0.565950	+	7.55207i	−0.0213149	+	0.284427i
$706$	−2.36796	+	0.356913i	−0.0891195	+	0.0134326i
$707$	−3.32399	+	3.08421i	−0.125011	+	0.115994i
$708$	1.55973	−	0.481112i	0.0586182	−	0.0180813i
$709$	1.06724	+	1.33828i	0.0400810	+	0.0502600i	0.801468	−	0.598038i	$-0.204053\pi$
$709$	1.06724	+	1.33828i	0.0400810	+	0.0502600i	−0.761387	+	0.648298i	$0.775481\pi$
$710$	7.23525	+	9.07272i	0.271534	+	0.340493i
$711$	−17.7242	+	5.46719i	−0.664709	+	0.205036i
$712$	−4.95999	+	4.60220i	−0.185884	+	0.172475i
$713$	3.26960	−	0.492812i	0.122447	−	0.0184560i
$714$	0.153531	−	2.04873i	0.00574577	−	0.0766720i
$715$	−0.295902	+	0.142499i	−0.0110661	+	0.00532916i
$716$	7.95468	+	2.45370i	0.297281	+	0.0916989i
$717$	−6.72781	−	17.1422i	−0.251255	−	0.640187i
$718$	3.83136	−	2.61218i	0.142985	−	0.0974856i
$719$	35.5112	+	5.35245i	1.32434	+	0.199613i	0.772862	−	0.634575i	$-0.218825\pi$
$719$	35.5112	+	5.35245i	1.32434	+	0.199613i	0.551481	+	0.834187i	$0.314063\pi$
$720$	−0.543731	+	2.38224i	−0.0202637	+	0.0887809i
$721$	3.23638	+	2.20653i	0.120529	+	0.0821754i
$722$	4.76634	+	4.42252i	0.177385	+	0.164589i
$723$	2.27435	+	1.09527i	0.0845838	+	0.0407334i
$724$	−1.08713	+	1.88296i	−0.0404027	+	0.0699795i
$725$	1.90112	+	3.29284i	0.0706059	+	0.122293i
$726$	0.564396	+	7.53134i	0.0209467	+	0.279514i
$727$	0.177963	+	0.779705i	0.00660027	+	0.0289177i	0.978121	−	0.208038i	$-0.0667077\pi$
$727$	0.177963	+	0.779705i	0.00660027	+	0.0289177i	−0.971521	+	0.236955i	$0.923851\pi$
$728$	−0.0477196	+	0.121588i	−0.00176861	+	0.00450633i
$729$	−0.886754	+	1.11195i	−0.0328427	+	0.0411835i
$730$	−3.91408			−0.144866
$731$	35.8824	−	32.6607i	1.32716	−	1.20800i
$732$	−5.68108			−0.209979
$733$	−12.1318	+	15.2129i	−0.448100	+	0.561900i	−0.953658	−	0.300893i	$-0.902715\pi$
$733$	−12.1318	+	15.2129i	−0.448100	+	0.561900i	0.505558	+	0.862793i	$0.331287\pi$
$734$	9.70398	−	24.7253i	0.358180	−	0.912629i
$735$	−1.13899	−	4.99022i	−0.0420121	−	0.184067i
$736$	−0.523708	−	6.98840i	−0.0193041	−	0.257596i
$737$	−5.51345	−	9.54958i	−0.203091	−	0.351763i
$738$	14.7468	−	25.5423i	0.542839	−	0.940225i
$739$	−0.567491	−	0.273289i	−0.0208755	−	0.0100531i	0.423417	−	0.905935i	$-0.360831\pi$
$739$	−0.567491	−	0.273289i	−0.0208755	−	0.0100531i	−0.444292	+	0.895882i	$0.646545\pi$
$740$	0.295571	+	0.274250i	0.0108654	+	0.0100816i
$741$	1.09231	+	0.744722i	0.0401269	+	0.0273581i
$742$	0.254373	−	1.11448i	0.00933833	−	0.0409139i
$743$	−6.06098	−	0.913546i	−0.222356	−	0.0335147i	0.0369193	−	0.999318i	$-0.488246\pi$
$743$	−6.06098	−	0.913546i	−0.222356	−	0.0335147i	−0.259275	+	0.965804i	$0.583484\pi$
$744$	0.290813	−	0.198273i	0.0106617	−	0.00726905i
$745$	4.59986	+	11.7202i	0.168526	+	0.429397i
$746$	6.07082	+	1.87260i	0.222268	+	0.0685607i
$747$	18.9946	−	9.14730i	0.694975	−	0.334682i
$748$	0.517496	−	6.90551i	0.0189215	−	0.252490i
$749$	−1.78060	+	0.268383i	−0.0650618	+	0.00980649i
$750$	−0.546846	+	0.507399i	−0.0199680	+	0.0185276i
$751$	−36.4290	+	11.2369i	−1.32931	+	0.410039i	−0.876429	−	0.481531i	$-0.840081\pi$
$751$	−36.4290	+	11.2369i	−1.32931	+	0.410039i	−0.452883	+	0.891570i	$0.649605\pi$
$752$	6.32967	+	7.93715i	0.230819	+	0.289438i
$753$	9.03575	+	11.3305i	0.329281	+	0.412905i
$754$	−1.27504	+	0.393299i	−0.0464343	+	0.0143231i
$755$	7.07329	−	6.56306i	0.257423	−	0.238854i
$756$	−1.49454	+	0.225266i	−0.0543560	+	0.00819285i
$757$	2.86032	−	38.1683i	0.103960	−	1.38725i	−0.664468	−	0.747316i	$-0.731342\pi$
$757$	2.86032	−	38.1683i	0.103960	−	1.38725i	0.768429	−	0.639935i	$-0.221039\pi$
$758$	7.95655	−	3.83167i	0.288995	−	0.139173i
$759$	4.67526	+	1.44213i	0.169701	+	0.0523459i
$760$	−1.84496	−	4.70087i	−0.0669236	−	0.170519i
$761$	−19.6292	+	13.3830i	−0.711559	+	0.485133i	−0.864200	−	0.503149i	$-0.832175\pi$
$761$	−19.6292	+	13.3830i	−0.711559	+	0.485133i	0.152641	+	0.988282i	$0.451222\pi$
$762$	3.76828	+	0.567977i	0.136510	+	0.0205756i
$763$	−1.22484	+	5.36638i	−0.0443422	+	0.194276i
$764$	−19.9712	−	13.6161i	−0.722531	−	0.492613i
$765$	−13.2538	−	12.2978i	−0.479194	−	0.444627i
$766$	−23.0059	−	11.0791i	−0.831238	−	0.400303i
$767$	0.383924	−	0.664976i	0.0138627	−	0.0240109i
$768$	−0.372993	−	0.646043i	−0.0134592	−	0.0233121i
$769$	2.30034	+	30.6959i	0.0829524	+	1.10692i	0.870991	+	0.491298i	$0.163477\pi$
$769$	2.30034	+	30.6959i	0.0829524	+	1.10692i	−0.788039	+	0.615625i	$0.788904\pi$
$770$	0.0775114	+	0.339600i	0.00279332	+	0.0122383i
$771$	0.911155	−	2.32159i	0.0328144	−	0.0836098i
$772$	13.5493	−	16.9903i	0.487651	−	0.611495i
$773$	9.64732			0.346990			0.173495	−	0.984835i	$-0.444494\pi$
$773$	9.64732			0.346990			0.173495	+	0.984835i	$0.444494\pi$
$774$	−13.1520	−	9.15241i	−0.472738	−	0.328977i
$775$	−0.471822			−0.0169484
$776$	7.42337	−	9.30862i	0.266484	−	0.334160i
$777$	−0.0409010	+	0.104214i	−0.00146731	+	0.00373866i
$778$	3.17536	+	13.9121i	0.113842	+	0.498774i
$779$	4.55511	+	60.7837i	0.163204	+	2.17780i
$780$	−0.130895	−	0.226716i	−0.00468678	−	0.00811773i
$781$	−5.43015	+	9.40530i	−0.194306	+	0.336548i
$782$	46.7194	+	22.4989i	1.67068	+	0.804559i
$783$	−11.3184	−	10.5019i	−0.404486	−	0.375308i
$784$	−5.66921	−	3.86520i	−0.202472	−	0.138043i
$785$	−1.20978	+	5.30040i	−0.0431789	+	0.189179i
$786$	2.90410	+	0.437723i	0.103586	+	0.0156131i
$787$	−11.9100	+	8.12012i	−0.424546	+	0.289451i	−0.756685	−	0.653780i	$-0.773182\pi$
$787$	−11.9100	+	8.12012i	−0.424546	+	0.289451i	0.332138	+	0.943231i	$0.392230\pi$
$788$	8.95859	+	22.8261i	0.319137	+	0.813147i
$789$	9.02579	+	2.78409i	0.321326	+	0.0991161i
$790$	−6.83910	+	3.29354i	−0.243324	+	0.117179i
$791$	−0.480239	+	6.40834i	−0.0170753	+	0.227855i
$792$	−2.26127	+	0.340832i	−0.0803508	+	0.0121109i
$793$	−1.95910	+	1.81778i	−0.0695696	+	0.0645512i
$794$	−13.8058	+	4.25852i	−0.489949	+	0.151129i
$795$	1.42851	+	1.79129i	0.0506640	+	0.0635306i
$796$	0.831402	+	1.04255i	0.0294683	+	0.0369520i
$797$	−45.5946	+	14.0641i	−1.61504	+	0.498175i	−0.965116	−	0.261822i	$-0.915677\pi$
$797$	−45.5946	+	14.0641i	−1.61504	+	0.498175i	−0.649926	+	0.759997i	$0.725200\pi$
$798$	1.02785	−	0.953706i	0.0363855	−	0.0337608i
$799$	−74.2793	+	11.1958i	−2.62781	+	0.396079i
$800$	−0.0747301	+	0.997204i	−0.00264211	+	0.0352565i
$801$	−14.8960	+	7.17353i	−0.526324	+	0.253464i
$802$	−27.5490	−	8.49774i	−0.972788	−	0.300065i
$803$	−1.33827	−	3.40987i	−0.0472267	−	0.120332i
$804$	7.26227	−	4.95133i	0.256120	−	0.174620i
$805$	−2.57925	−	0.388759i	−0.0909065	−	0.0137020i
$806$	0.0368443	−	0.161425i	0.00129778	−	0.00568597i
$807$	−10.7989	−	7.36256i	−0.380139	−	0.259175i
$808$	−8.93063	−	8.28641i	−0.314178	−	0.291515i
$809$	33.4121	+	16.0904i	1.17471	+	0.565709i	0.916365	−	0.400345i	$-0.131110\pi$
$809$	33.4121	+	16.0904i	1.17471	+	0.565709i	0.258342	+	0.966054i	$0.416824\pi$
$810$	−2.15062	+	3.72498i	−0.0755650	+	0.130882i
$811$	−4.15983	−	7.20503i	−0.146071	−	0.253003i	0.783701	−	0.621138i	$-0.213330\pi$
$811$	−4.15983	−	7.20503i	−0.146071	−	0.253003i	−0.929772	+	0.368136i	$0.879996\pi$
$812$	0.105758	+	1.41124i	0.00371138	+	0.0495249i
$813$	−0.752093	−	3.29514i	−0.0263771	−	0.115565i
$814$	−0.137862	+	0.351266i	−0.00483205	+	0.0123119i
$815$	8.01987	−	10.0566i	0.280924	−	0.352267i
$816$	5.51981			0.193232
$817$	33.1133	+	0.316838i	1.15849	+	0.0110848i
$818$	4.58149			0.160188
$819$	−0.198994	+	0.249531i	−0.00695343	+	0.00871932i
$820$	4.40975	−	11.2359i	0.153995	−	0.392374i
$821$	5.99679	+	26.2736i	0.209289	+	0.916956i	0.965041	+	0.262098i	$0.0844144\pi$
$821$	5.99679	+	26.2736i	0.209289	+	0.916956i	−0.755752	+	0.654858i	$0.772728\pi$
$822$	−0.318885	−	4.25523i	−0.0111224	−	0.148418i
$823$	7.19120	+	12.4555i	0.250670	+	0.434172i	0.963710	−	0.266950i	$-0.0860159\pi$
$823$	7.19120	+	12.4555i	0.250670	+	0.434172i	−0.713041	+	0.701123i	$0.752683\pi$
$824$	−5.26195	+	9.11397i	−0.183309	+	0.317500i
$825$	−0.629011	−	0.302916i	−0.0218993	−	0.0105462i
$826$	−0.596989	−	0.553925i	−0.0207719	−	0.0192735i
$827$	−12.0975	−	8.24795i	−0.420672	−	0.286809i	0.334425	−	0.942422i	$-0.391458\pi$
$827$	−12.0975	−	8.24795i	−0.420672	−	0.286809i	−0.755097	+	0.655613i	$0.772410\pi$
$828$	3.81047	−	16.6947i	0.132423	−	0.580182i
$829$	39.9889	+	6.02736i	1.38887	+	0.209339i	0.800539	−	0.599280i	$-0.204546\pi$
$829$	39.9889	+	6.02736i	1.38887	+	0.209339i	0.588333	+	0.808619i	$0.299784\pi$
$830$	7.12872	−	4.86028i	0.247442	−	0.168703i
$831$	−1.74831	−	4.45461i	−0.0606480	−	0.154529i
$832$	−0.335340	−	0.103439i	−0.0116258	−	0.00358609i
$833$	45.7426	−	22.0285i	1.58489	−	0.763241i
$834$	−0.676610	+	9.02874i	−0.0234291	+	0.312640i
$835$	10.5698	−	1.59314i	0.365783	−	0.0551330i
$836$	3.46449	−	3.21458i	0.119822	−	0.111179i
$837$	1.83084	−	0.564741i	0.0632832	−	0.0195203i
$838$	−0.508610	−	0.637776i	−0.0175696	−	0.0220316i
$839$	31.9774	+	40.0984i	1.10398	+	1.38435i	0.915520	+	0.402272i	$0.131779\pi$
$839$	31.9774	+	40.0984i	1.10398	+	1.38435i	0.188463	+	0.982080i	$0.439649\pi$
$840$	−0.265321	+	0.0818407i	−0.00915444	+	0.00282377i
$841$	10.6607	−	9.89170i	0.367611	−	0.341093i
$842$	−18.0035	+	2.71359i	−0.620440	+	0.0935163i
$843$	−0.878732	+	11.7259i	−0.0302651	+	0.403860i
$844$	−19.5374	+	9.40873i	−0.672506	+	0.323862i
$845$	12.3048	+	3.79552i	0.423297	+	0.130570i
$846$	9.06282	+	23.0917i	0.311586	+	0.793909i
$847$	3.11344	−	2.12271i	0.106979	−	0.0729372i
$848$	3.03700	+	0.457754i	0.104291	+	0.0157194i
$849$	−0.463189	+	2.02936i	−0.0158966	+	0.0696476i
$850$	−6.11364	−	4.16821i	−0.209696	−	0.142968i
$851$	−2.07136	−	1.92194i	−0.0710054	−	0.0658834i
$852$	−7.79946	−	3.75602i	−0.267205	−	0.128679i
$853$	−4.81599	+	8.34154i	−0.164896	+	0.285609i	−0.936618	−	0.350351i	$-0.886062\pi$
$853$	−4.81599	+	8.34154i	−0.164896	+	0.285609i	0.771722	+	0.635960i	$0.219396\pi$
$854$	1.41725	+	2.45476i	0.0484974	+	0.0840000i
$855$	−0.922139	−	12.3051i	−0.0315365	−	0.420825i
$856$	−1.07656	−	4.71672i	−0.0367961	−	0.161214i
$857$	−3.12346	+	7.95845i	−0.106695	+	0.271855i	−0.974244	−	0.225497i	$-0.927599\pi$
$857$	−3.12346	+	7.95845i	−0.106695	+	0.271855i	0.867548	+	0.497353i	$0.165695\pi$
$858$	0.152756	−	0.191550i	0.00521501	−	0.00653941i
$859$	−2.09248			−0.0713945			−0.0356972	−	0.999363i	$-0.511365\pi$
$859$	−2.09248			−0.0713945			−0.0356972	+	0.999363i	$0.511365\pi$
$860$	−5.88056	−	2.90156i	−0.200525	−	0.0989425i
$861$	3.35138			0.114215
$862$	8.02021	−	10.0570i	0.273169	−	0.342544i
$863$	−4.96497	+	12.6505i	−0.169009	+	0.430629i	−0.990135	−	0.140119i	$-0.955251\pi$
$863$	−4.96497	+	12.6505i	−0.169009	+	0.430629i	0.821125	+	0.570748i	$0.193347\pi$
$864$	−0.903608	−	3.95897i	−0.0307414	−	0.134687i
$865$	−0.0771130	−	1.02900i	−0.00262192	−	0.0349871i
$866$	−19.4227	−	33.6410i	−0.660009	−	1.14317i
$867$	−14.0807	+	24.3884i	−0.478204	+	0.828274i
$868$	−0.158221	−	0.0761954i	−0.00537039	−	0.00258624i
$869$	−5.20765	−	4.83199i	−0.176657	−	0.163914i
$870$	−2.34356	−	1.59781i	−0.0794542	−	0.0541709i
$871$	0.920085	−	4.03116i	0.0311759	−	0.136590i
$872$	−14.6236	−	2.20415i	−0.495217	−	0.0746419i
$873$	24.0376	−	16.3885i	0.813549	−	0.554668i
$874$	12.9294	+	32.9437i	0.437345	+	1.11434i
$875$	0.355665	+	0.109708i	0.0120237	+	0.00370881i
$876$	2.63069	−	1.26687i	0.0888827	−	0.0428037i
$877$	−0.141846	+	1.89280i	−0.00478980	+	0.0639154i	−0.999086	−	0.0427340i	$-0.986393\pi$
$877$	−0.141846	+	1.89280i	−0.00478980	+	0.0639154i	0.994297	+	0.106649i	$0.0340123\pi$
$878$	−4.26458	+	0.642782i	−0.143923	+	0.0216928i
$879$	−15.5571	+	14.4349i	−0.524728	+	0.486876i
$880$	−0.894296	+	0.275854i	−0.0301467	+	0.00929903i
$881$	21.2831	+	26.6882i	0.717047	+	0.899149i	0.998167	−	0.0605241i	$-0.0192772\pi$
$881$	21.2831	+	26.6882i	0.717047	+	0.899149i	−0.281120	+	0.959673i	$0.590706\pi$
$882$	−10.4534	−	13.1082i	−0.351986	−	0.441376i
$883$	−55.1959	+	17.0257i	−1.85749	+	0.572960i	−0.859392	+	0.511317i	$0.829158\pi$
$883$	−55.1959	+	17.0257i	−1.85749	+	0.572960i	−0.998098	+	0.0616425i	$0.980366\pi$
$884$	1.90349	−	1.76618i	0.0640212	−	0.0594030i
$885$	1.61401	−	0.243273i	0.0542545	−	0.00817754i
$886$	2.52579	−	33.7044i	0.0848557	−	1.13232i
$887$	−33.8567	+	16.3045i	−1.13680	+	0.547452i	−0.905042	−	0.425323i	$-0.860161\pi$
$887$	−33.8567	+	16.3045i	−1.13680	+	0.547452i	−0.231753	+	0.972775i	$0.574446\pi$
$888$	−0.287423	−	0.0886583i	−0.00964529	−	0.00297518i
$889$	−0.694651	−	1.76994i	−0.0232978	−	0.0593619i
$890$	−5.59052	+	3.81155i	−0.187395	+	0.127763i
$891$	−3.98046	−	0.599957i	−0.133350	−	0.0200993i
$892$	−1.31190	+	5.74780i	−0.0439256	+	0.192450i
$893$	−42.3589	−	28.8798i	−1.41749	−	0.966426i
$894$	−6.88512	−	6.38845i	−0.230273	−	0.213662i
$895$	7.50013	+	3.61187i	0.250702	+	0.120732i
$896$	−0.186100	+	0.322335i	−0.00621718	+	0.0107685i
$897$	0.917308	+	1.58882i	0.0306280	+	0.0530493i
$898$	1.11187	+	14.8368i	0.0371035	+	0.495111i
$899$	−0.399199	−	1.74901i	−0.0133140	−	0.0583326i
$900$	−0.892713	+	2.27459i	−0.0297571	+	0.0758198i
$901$	−14.1692	+	17.7677i	−0.472046	+	0.591927i
$902$	11.2962			0.376123
$903$	0.153428	−	1.81424i	0.00510575	−	0.0603741i
$904$	−17.2657			−0.574249
$905$	−1.35562	+	1.69990i	−0.0450624	+	0.0565065i
$906$	−2.62976	+	6.70052i	−0.0873679	+	0.222610i
$907$	−2.04980	−	8.98076i	−0.0680625	−	0.298201i	0.929428	−	0.369004i	$-0.120301\pi$
$907$	−2.04980	−	8.98076i	−0.0680625	−	0.298201i	−0.997490	+	0.0708027i	$0.977444\pi$
$908$	0.343243	+	4.58026i	0.0113909	+	0.152001i
$909$	−14.8844	−	25.7805i	−0.493683	−	0.855085i
$910$	−0.0653083	+	0.113117i	−0.00216495	+	0.00374980i
$911$	−27.3211	−	13.1572i	−0.905190	−	0.435916i	−0.0774291	−	0.996998i	$-0.524671\pi$
$911$	−27.3211	−	13.1572i	−0.905190	−	0.435916i	−0.827761	+	0.561081i	$0.810385\pi$
$912$	2.76155	+	2.56234i	0.0914440	+	0.0848477i
$913$	6.67159	+	4.54861i	0.220797	+	0.150537i
$914$	0.673129	−	2.94917i	0.0222651	−	0.0975498i
$915$	−5.61763	−	0.846721i	−0.185713	−	0.0279917i
$916$	−1.55767	+	1.06200i	−0.0514667	+	0.0350894i
$917$	−0.535346	−	1.36404i	−0.0176787	−	0.0450446i
$918$	28.7122	+	8.85655i	0.947645	+	0.292310i
$919$	35.2057	−	16.9542i	1.16133	−	0.559267i	0.248912	−	0.968526i	$-0.419927\pi$
$919$	35.2057	−	16.9542i	1.16133	−	0.559267i	0.912418	+	0.409259i	$0.134213\pi$
$920$	0.523708	−	6.98840i	0.0172661	−	0.230401i
$921$	−1.19478	+	0.180083i	−0.0393692	+	0.00593395i
$922$	−9.69765	+	8.99811i	−0.319375	+	0.296337i
$923$	−3.89143	+	1.20035i	−0.128088	+	0.0395099i
$924$	−0.162015	−	0.203160i	−0.00532990	−	0.00668348i
$925$	0.251395	+	0.315240i	0.00826582	+	0.0103650i
$926$	2.88303	−	0.889296i	0.0947421	−	0.0292241i
$927$	−18.8506	+	17.4908i	−0.619135	+	0.574473i
$928$	−3.75978	+	0.566695i	−0.123421	+	0.0186027i
$929$	−0.582811	+	7.77707i	−0.0191214	+	0.255157i	0.979448	+	0.201695i	$0.0646449\pi$
$929$	−0.582811	+	7.77707i	−0.0191214	+	0.255157i	−0.998570	+	0.0534627i	$0.982974\pi$
$930$	0.317116	−	0.152715i	0.0103987	−	0.00500773i
$931$	33.1107	+	10.2133i	1.08516	+	0.334727i
$932$	−9.31685	−	23.7389i	−0.305184	−	0.777595i
$933$	−0.0711509	+	0.0485099i	−0.00232938	+	0.00158814i
$934$	−29.8549	−	4.49990i	−0.976883	−	0.147241i
$935$	1.54093	−	6.75125i	0.0503938	−	0.220789i
$936$	−0.708500	−	0.483047i	−0.0231580	−	0.0157889i
$937$	−16.3630	−	15.1826i	−0.534556	−	0.495995i	0.366072	−	0.930586i	$-0.380702\pi$
$937$	−16.3630	−	15.1826i	−0.534556	−	0.495995i	−0.900628	+	0.434591i	$0.856893\pi$
$938$	−3.95115	−	1.90277i	−0.129009	−	0.0621277i
$939$	0.129547	−	0.224382i	0.00422761	−	0.00732244i
$940$	5.07600	+	8.79189i	0.165561	+	0.286760i
$941$	0.769997	+	10.2749i	0.0251012	+	0.334952i	0.995590	+	0.0938074i	$0.0299038\pi$
$941$	0.769997	+	10.2749i	0.0251012	+	0.334952i	−0.970489	+	0.241145i	$0.922477\pi$
$942$	−0.902479	−	3.95402i	−0.0294044	−	0.128829i
$943$	−30.9035	+	78.7409i	−1.00636	+	2.56416i
$944$	1.36422	−	1.71068i	0.0444015	−	0.0556778i
$945$	−1.51142			−0.0491666
$946$	0.517146	−	6.11511i	0.0168139	−	0.198819i
$947$	−26.8043			−0.871022			−0.435511	−	0.900183i	$-0.643432\pi$
$947$	−26.8043			−0.871022			−0.435511	+	0.900183i	$0.643432\pi$
$948$	3.53061	−	4.42724i	0.114669	−	0.143790i
$949$	0.501821	−	1.27862i	0.0162898	−	0.0415057i
$950$	−1.12372	−	4.92334i	−0.0364583	−	0.159734i
$951$	−0.898266	−	11.9865i	−0.0291283	−	0.388690i
$952$	−1.37702	−	2.38507i	−0.0446296	−	0.0773007i
$953$	5.97815	−	10.3545i	0.193651	−	0.335414i	−0.752806	−	0.658242i	$-0.771300\pi$
$953$	5.97815	−	10.3545i	0.193651	−	0.335414i	0.946458	+	0.322828i	$0.104634\pi$
$954$	6.76155	+	3.25619i	0.218913	+	0.105423i
$955$	−17.7187	−	16.4406i	−0.573364	−	0.532004i
$956$	−20.3963	−	13.9059i	−0.659662	−	0.449750i
$957$	0.590690	−	2.58798i	0.0190943	−	0.0836575i
$958$	31.3710	+	4.72841i	1.01355	+	0.152768i
$959$	−1.75910	+	1.19934i	−0.0568044	+	0.0387286i
$960$	−0.272539	−	0.694419i	−0.00879616	−	0.0224123i
$961$	−29.4100	−	9.07179i	−0.948711	−	0.292638i
$962$	−0.127485	+	0.0613934i	−0.00411027	+	0.00197940i
$963$	0.883439	−	11.7887i	0.0284684	−	0.379885i
$964$	3.34609	−	0.504343i	0.107770	−	0.0162438i
$965$	15.9303	−	14.7811i	0.512814	−	0.475822i
$966$	1.85937	−	0.573539i	0.0598242	−	0.0184533i
$967$	28.8391	+	36.1631i	0.927402	+	1.16293i	0.986350	+	0.164664i	$0.0526541\pi$
$967$	28.8391	+	36.1631i	0.927402	+	1.16293i	−0.0589475	+	0.998261i	$0.518774\pi$
$968$	6.31230	+	7.91537i	0.202885	+	0.254410i
$969$	−26.6364	+	8.21625i	−0.855685	+	0.263944i
$970$	8.72784	−	8.09825i	0.280234	−	0.260019i
$971$	41.9462	−	6.32237i	1.34612	−	0.202895i	0.563871	−	0.825863i	$-0.309312\pi$
$971$	41.9462	−	6.32237i	1.34612	−	0.202895i	0.782247	+	0.622968i	$0.214074\pi$
$972$	1.15017	−	15.3480i	0.0368917	−	0.492286i
$973$	4.07005	−	1.96003i	0.130480	−	0.0628357i
$974$	8.90742	+	2.74758i	0.285412	+	0.0880380i
$975$	−0.0956423	−	0.243693i	−0.00306300	−	0.00780441i
$976$	−6.29225	+	4.28999i	−0.201410	+	0.137319i
$977$	−21.8563	−	3.29430i	−0.699244	−	0.105394i	−0.210207	−	0.977657i	$-0.567414\pi$
$977$	−21.8563	−	3.29430i	−0.699244	−	0.105394i	−0.489037	+	0.872263i	$0.662652\pi$
$978$	−2.13520	+	9.35494i	−0.0682763	+	0.299138i
$979$	−5.23202	−	3.56713i	−0.167216	−	0.114006i
$980$	−5.02981	−	4.66698i	−0.160671	−	0.149081i
$981$	−32.5578	−	15.6790i	−1.03949	−	0.500592i
$982$	−16.0974	+	27.8816i	−0.513690	+	0.889737i
$983$	5.78370	+	10.0177i	0.184471	+	0.319514i	0.943398	−	0.331662i	$-0.107609\pi$
$983$	5.78370	+	10.0177i	0.184471	+	0.319514i	−0.758927	+	0.651176i	$0.774276\pi$
$984$	0.672887	+	8.97905i	0.0214508	+	0.286242i
$985$	5.45648	+	23.9064i	0.173858	+	0.761721i
$986$	10.2786	−	26.1894i	0.327336	−	0.834039i
$987$	−1.75747	+	2.20380i	−0.0559410	+	0.0701478i
$988$	1.77218			0.0563806
$989$	41.2109	+	20.3341i	1.31043	+	0.646588i
$990$	−2.28681			−0.0726797
$991$	35.4788	−	44.4891i	1.12702	−	1.41324i	0.228926	−	0.973444i	$-0.426479\pi$
$991$	35.4788	−	44.4891i	1.12702	−	1.41324i	0.898097	−	0.439798i	$-0.144950\pi$
$992$	0.172376	−	0.439207i	0.00547294	−	0.0139448i
$993$	−1.16022	−	5.08326i	−0.0368185	−	0.161312i
$994$	0.322773	+	4.30711i	0.0102377	+	0.136613i
$995$	0.666733	+	1.15481i	0.0211368	+	0.0366101i
$996$	−3.21815	+	5.57401i	−0.101971	+	0.176619i
$997$	−52.6422	−	25.3512i	−1.66720	−	0.802880i	−0.998223	−	0.0595936i	$-0.981020\pi$
$997$	−52.6422	−	25.3512i	−1.66720	−	0.802880i	−0.668974	−	0.743286i	$-0.733266\pi$
$998$	−18.1453	−	16.8364i	−0.574379	−	0.532946i
$999$	−1.35283	−	0.922342i	−0.0428016	−	0.0291816i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.d.101.4	✓	60
43.23	even	21	inner	430.2.q.d.281.4	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.d.101.4	✓	60	1.1	even	1	trivial
430.2.q.d.281.4	yes	60	43.23	even	21	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.623490 + 0.781831i) q^{2} +(0.272539 - 0.694419i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(-0.0747301 - 0.997204i) q^{5} +(0.372993 + 0.646043i) q^{6} +(0.186100 - 0.322335i) q^{7} +(0.900969 + 0.433884i) q^{8} +(1.79122 + 1.66201i) q^{9} +O(q^{10})\)	\(q+(-0.623490 + 0.781831i) q^{2} +(0.272539 - 0.694419i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(-0.0747301 - 0.997204i) q^{5} +(0.372993 + 0.646043i) q^{6} +(0.186100 - 0.322335i) q^{7} +(0.900969 + 0.433884i) q^{8} +(1.79122 + 1.66201i) q^{9} +(0.826239 + 0.563320i) q^{10} +(-0.208252 + 0.912410i) q^{11} +(-0.737654 - 0.111183i) q^{12} +(-0.289952 + 0.197686i) q^{13} +(0.135980 + 0.346472i) q^{14} +(-0.712844 - 0.219883i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(0.552955 - 7.37867i) q^{17} +(-2.41621 + 0.364186i) q^{18} +(3.70188 - 3.43484i) q^{19} +(-0.955573 + 0.294755i) q^{20} +(-0.173116 - 0.217081i) q^{21} +(-0.583508 - 0.731696i) q^{22} +(6.69665 - 2.06564i) q^{23} +(0.546846 - 0.507399i) q^{24} +(-0.988831 + 0.149042i) q^{25} +(0.0262251 - 0.349949i) q^{26} +(3.65863 - 1.76191i) q^{27} +(-0.355665 - 0.109708i) q^{28} +(-1.38912 - 3.53941i) q^{29} +(0.616362 - 0.420229i) q^{30} +(0.466552 + 0.0703215i) q^{31} +(0.222521 - 0.974928i) q^{32} +(0.576838 + 0.393281i) q^{33} +(5.42411 + 5.03284i) q^{34} +(-0.335341 - 0.161492i) q^{35} +(1.22175 - 2.11614i) q^{36} +(-0.201603 - 0.349187i) q^{37} +(0.377384 + 5.03583i) q^{38} +(0.0582535 + 0.255225i) q^{39} +(0.365341 - 0.930874i) q^{40} +(-7.52567 + 9.43689i) q^{41} +0.277656 q^{42} +(4.76405 + 4.50598i) q^{43} +0.935875 q^{44} +(1.52350 - 1.91041i) q^{45} +(-2.56031 + 6.52356i) q^{46} +(-2.25903 - 9.89747i) q^{47} +(0.0557476 + 0.743900i) q^{48} +(3.43073 + 5.94220i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-4.97318 - 2.39496i) q^{51} +(0.257250 + 0.238693i) q^{52} +(-2.53763 - 1.73013i) q^{53} +(-0.903608 + 3.95897i) q^{54} +(0.925422 + 0.139485i) q^{55} +(0.307527 - 0.209668i) q^{56} +(-1.37631 - 3.50678i) q^{57} +(3.63332 + 1.12073i) q^{58} +(-1.97135 + 0.949353i) q^{59} +(-0.0557476 + 0.743900i) q^{60} +(7.53048 - 1.13504i) q^{61} +(-0.345870 + 0.320921i) q^{62} +(0.869069 - 0.268072i) q^{63} +(0.623490 + 0.781831i) q^{64} +(0.218802 + 0.274368i) q^{65} +(-0.667132 + 0.205783i) q^{66} +(-8.63716 + 8.01411i) q^{67} +(-7.31671 + 1.10282i) q^{68} +(0.390679 - 5.21325i) q^{69} +(0.335341 - 0.161492i) q^{70} +(11.0889 + 3.42047i) q^{71} +(0.892713 + 2.27459i) q^{72} +(-3.23396 + 2.20488i) q^{73} +(0.398703 + 0.0600948i) q^{74} +(-0.165997 + 0.727282i) q^{75} +(-4.17247 - 2.84474i) q^{76} +(0.255346 + 0.236927i) q^{77} +(-0.235864 - 0.113586i) q^{78} +(-3.79542 + 6.57385i) q^{79} +(0.500000 + 0.866025i) q^{80} +(0.321432 + 4.28921i) q^{81} +(-2.68588 - 11.7676i) q^{82} +(3.15213 - 8.03151i) q^{83} +(-0.173116 + 0.217081i) q^{84} -7.39936 q^{85} +(-6.49325 + 0.915251i) q^{86} -2.83642 q^{87} +(-0.583508 + 0.731696i) q^{88} +(-2.47198 + 6.29850i) q^{89} +(0.543731 + 2.38224i) q^{90} +(0.00976099 + 0.130251i) q^{91} +(-3.50400 - 6.06910i) q^{92} +(0.175986 - 0.304817i) q^{93} +(9.14664 + 4.40479i) q^{94} +(-3.70188 - 3.43484i) q^{95} +(-0.616362 - 0.420229i) q^{96} +(2.64937 - 11.6077i) q^{97} +(-6.78483 - 1.02265i) q^{98} +(-1.88945 + 1.28821i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) \) 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9	\( 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9} + 5 q^{10} + 3 q^{11} - q^{12} + 13 q^{13} - 15 q^{14} + q^{15} - 10 q^{16} + 38 q^{17} + 6 q^{18} + 17 q^{19} - 5 q^{20} + 4 q^{21} + 11 q^{22} - 8 q^{23} + q^{24} + 5 q^{25} + 29 q^{26} - 16 q^{27} - 6 q^{28} - 41 q^{29} - q^{30} + 15 q^{31} + 10 q^{32} + 63 q^{33} - 10 q^{34} + 2 q^{35} - 48 q^{36} + 7 q^{37} + 25 q^{38} - 64 q^{39} + 5 q^{40} - 22 q^{41} - 60 q^{42} + 6 q^{43} - 4 q^{44} + 30 q^{45} - 20 q^{46} - 13 q^{47} - q^{48} - 93 q^{49} + 30 q^{50} + 18 q^{51} - 15 q^{52} + 71 q^{53} - 5 q^{54} - 16 q^{55} - q^{56} - 94 q^{57} - 22 q^{58} + 20 q^{59} + q^{60} + 91 q^{61} + 69 q^{62} - 50 q^{63} - 10 q^{64} + 5 q^{65} + 14 q^{66} - 26 q^{67} - 18 q^{68} - 94 q^{69} - 2 q^{70} + 20 q^{71} - 36 q^{72} - 56 q^{73} - 7 q^{74} + 2 q^{75} + 38 q^{76} + 41 q^{77} - 13 q^{78} - 46 q^{79} + 30 q^{80} + 39 q^{81} + 8 q^{82} - 115 q^{83} + 4 q^{84} + 6 q^{85} + 29 q^{86} + 20 q^{87} + 11 q^{88} + 30 q^{89} - 16 q^{90} - 53 q^{91} - 8 q^{92} + 16 q^{93} + 41 q^{94} - 17 q^{95} + q^{96} + 113 q^{97} + 2 q^{98} + 139 q^{99}+O(q^{100}) \) 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9 + 5 * q^10 + 3 * q^11 - q^12 + 13 * q^13 - 15 * q^14 + q^15 - 10 * q^16 + 38 * q^17 + 6 * q^18 + 17 * q^19 - 5 * q^20 + 4 * q^21 + 11 * q^22 - 8 * q^23 + q^24 + 5 * q^25 + 29 * q^26 - 16 * q^27 - 6 * q^28 - 41 * q^29 - q^30 + 15 * q^31 + 10 * q^32 + 63 * q^33 - 10 * q^34 + 2 * q^35 - 48 * q^36 + 7 * q^37 + 25 * q^38 - 64 * q^39 + 5 * q^40 - 22 * q^41 - 60 * q^42 + 6 * q^43 - 4 * q^44 + 30 * q^45 - 20 * q^46 - 13 * q^47 - q^48 - 93 * q^49 + 30 * q^50 + 18 * q^51 - 15 * q^52 + 71 * q^53 - 5 * q^54 - 16 * q^55 - q^56 - 94 * q^57 - 22 * q^58 + 20 * q^59 + q^60 + 91 * q^61 + 69 * q^62 - 50 * q^63 - 10 * q^64 + 5 * q^65 + 14 * q^66 - 26 * q^67 - 18 * q^68 - 94 * q^69 - 2 * q^70 + 20 * q^71 - 36 * q^72 - 56 * q^73 - 7 * q^74 + 2 * q^75 + 38 * q^76 + 41 * q^77 - 13 * q^78 - 46 * q^79 + 30 * q^80 + 39 * q^81 + 8 * q^82 - 115 * q^83 + 4 * q^84 + 6 * q^85 + 29 * q^86 + 20 * q^87 + 11 * q^88 + 30 * q^89 - 16 * q^90 - 53 * q^91 - 8 * q^92 + 16 * q^93 + 41 * q^94 - 17 * q^95 + q^96 + 113 * q^97 + 2 * q^98 + 139 * q^99

Introduction

L-functions

Modular forms

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Database

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