LMFDB - Embedded newform 430.2.q.d.111.5

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			111.5
Character	$\chi$	$=$	430.111
Dual form			430.2.q.d.31.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900969 + 0.433884i) q^{2} +(1.82153 + 1.24190i) q^{3} +(0.623490 + 0.781831i) q^{4} +(0.733052 - 0.680173i) q^{5} +(1.10230 + 1.90924i) q^{6} +(1.71615 - 2.97246i) q^{7} +(0.222521 + 0.974928i) q^{8} +(0.679638 + 1.73169i) q^{9} +O(q^{10})$	\(q+(0.900969 + 0.433884i) q^{2} +(1.82153 + 1.24190i) q^{3} +(0.623490 + 0.781831i) q^{4} +(0.733052 - 0.680173i) q^{5} +(1.10230 + 1.90924i) q^{6} +(1.71615 - 2.97246i) q^{7} +(0.222521 + 0.974928i) q^{8} +(0.679638 + 1.73169i) q^{9} +(0.955573 - 0.294755i) q^{10} +(-2.77306 + 3.47730i) q^{11} +(0.164750 + 2.19844i) q^{12} +(-0.0256818 - 0.00792179i) q^{13} +(2.83590 - 1.93348i) q^{14} +(2.17998 - 0.328579i) q^{15} +(-0.222521 + 0.974928i) q^{16} +(-1.78193 - 1.65339i) q^{17} +(-0.139019 + 1.85508i) q^{18} +(1.11445 - 2.83957i) q^{19} +(0.988831 + 0.149042i) q^{20} +(6.81750 - 3.28314i) q^{21} +(-4.00718 + 1.92976i) q^{22} +(-6.55509 - 0.988021i) q^{23} +(-0.805433 + 2.05221i) q^{24} +(0.0747301 - 0.997204i) q^{25} +(-0.0197014 - 0.0182802i) q^{26} +(0.559111 - 2.44963i) q^{27} +(3.39396 - 0.511557i) q^{28} +(-5.55798 + 3.78937i) q^{29} +(2.10666 + 0.649819i) q^{30} +(0.548899 + 7.32454i) q^{31} +(-0.623490 + 0.781831i) q^{32} +(-9.36966 + 2.89016i) q^{33} +(-0.888086 - 2.26281i) q^{34} +(-0.763758 - 3.34624i) q^{35} +(-0.930142 + 1.61105i) q^{36} +(4.05805 + 7.02874i) q^{37} +(2.23613 - 2.07482i) q^{38} +(-0.0369422 - 0.0463240i) q^{39} +(0.826239 + 0.563320i) q^{40} +(-1.20402 - 0.579827i) q^{41} +7.56686 q^{42} +(-6.15062 - 2.27375i) q^{43} -4.44764 q^{44} +(1.67606 + 0.807147i) q^{45} +(-5.47724 - 3.73432i) q^{46} +(3.09660 + 3.88301i) q^{47} +(-1.61609 + 1.49951i) q^{48} +(-2.39033 - 4.14017i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-1.19250 - 5.22468i) q^{51} +(-0.00981885 - 0.0250180i) q^{52} +(0.182273 - 0.0562237i) q^{53} +(1.56660 - 1.96445i) q^{54} +(0.332372 + 4.43520i) q^{55} +(3.27981 + 1.01169i) q^{56} +(5.55646 - 3.78833i) q^{57} +(-6.65172 + 1.00259i) q^{58} +(1.90422 - 8.34293i) q^{59} +(1.61609 + 1.49951i) q^{60} +(0.944147 - 12.5988i) q^{61} +(-2.68346 + 6.83734i) q^{62} +(6.31373 + 0.951642i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(-0.0242143 + 0.0116610i) q^{65} +(-9.69576 - 1.46140i) q^{66} +(2.52053 - 6.42219i) q^{67} +(0.181657 - 2.42405i) q^{68} +(-10.7133 - 9.94046i) q^{69} +(0.763758 - 3.34624i) q^{70} +(0.383425 - 0.0577920i) q^{71} +(-1.53704 + 1.04794i) q^{72} +(10.8306 + 3.34079i) q^{73} +(0.606517 + 8.09340i) q^{74} +(1.37455 - 1.72363i) q^{75} +(2.91491 - 0.899132i) q^{76} +(5.57715 + 14.2103i) q^{77} +(-0.0131845 - 0.0577651i) q^{78} +(-4.00950 + 6.94466i) q^{79} +(0.500000 + 0.866025i) q^{80} +(8.15168 - 7.56365i) q^{81} +(-0.833209 - 1.04481i) q^{82} +(-4.78821 - 3.26455i) q^{83} +(6.81750 + 3.28314i) q^{84} -2.43084 q^{85} +(-4.55497 - 4.71723i) q^{86} -14.8300 q^{87} +(-4.00718 - 1.92976i) q^{88} +(7.49483 + 5.10989i) q^{89} +(1.15987 + 1.45443i) q^{90} +(-0.0676210 + 0.0627431i) q^{91} +(-3.31457 - 5.74100i) q^{92} +(-8.09650 + 14.0236i) q^{93} +(1.10516 + 4.84203i) q^{94} +(-1.11445 - 2.83957i) q^{95} +(-2.10666 + 0.649819i) q^{96} +(5.34232 - 6.69906i) q^{97} +(-0.357259 - 4.76729i) q^{98} +(-7.90628 - 2.43876i) 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 $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{4}{21}\right)$

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 $

$2$	0.900969	+	0.433884i	0.637081	+	0.306802i
$2$	0.900969	+	0.433884i	0.637081	+	0.306802i
$3$	1.82153	+	1.24190i	1.05166	+	0.717010i	0.960346	−	0.278812i	$-0.0899405\pi$
$3$	1.82153	+	1.24190i	1.05166	+	0.717010i	0.0913152	+	0.995822i	$0.470893\pi$
$4$	0.623490	+	0.781831i	0.311745	+	0.390916i
$5$	0.733052	−	0.680173i	0.327831	−	0.304182i
$5$	0.733052	−	0.680173i	0.327831	−	0.304182i
$6$	1.10230	+	1.90924i	0.450013	+	0.779446i
$7$	1.71615	−	2.97246i	0.648643	−	1.12348i	−0.334804	−	0.942288i	$-0.608670\pi$
$7$	1.71615	−	2.97246i	0.648643	−	1.12348i	0.983447	−	0.181195i	$-0.0579965\pi$
$8$	0.222521	+	0.974928i	0.0786730	+	0.344689i
$9$	0.679638	+	1.73169i	0.226546	+	0.577230i
$10$	0.955573	−	0.294755i	0.302179	−	0.0932098i
$11$	−2.77306	+	3.47730i	−0.836108	+	1.04845i	0.161990	+	0.986792i	$0.448209\pi$
$11$	−2.77306	+	3.47730i	−0.836108	+	1.04845i	−0.998098	+	0.0616534i	$0.980363\pi$
$12$	0.164750	+	2.19844i	0.0475593	+	0.634635i
$13$	−0.0256818	−	0.00792179i	−0.00712286	−	0.00219711i	0.291192	−	0.956665i	$-0.405948\pi$
$13$	−0.0256818	−	0.00792179i	−0.00712286	−	0.00219711i	−0.298315	+	0.954468i	$0.596424\pi$
$14$	2.83590	−	1.93348i	0.757925	−	0.516745i
$15$	2.17998	−	0.328579i	0.562869	−	0.0848388i
$16$	−0.222521	+	0.974928i	−0.0556302	+	0.243732i
$17$	−1.78193	−	1.65339i	−0.432182	−	0.401007i	0.433858	−	0.900981i	$-0.357152\pi$
$17$	−1.78193	−	1.65339i	−0.432182	−	0.401007i	−0.866040	+	0.499975i	$0.833343\pi$
$18$	−0.139019	+	1.85508i	−0.0327671	+	0.437247i
$19$	1.11445	−	2.83957i	0.255672	−	0.651442i	−0.744191	−	0.667967i	$-0.767165\pi$
$19$	1.11445	−	2.83957i	0.255672	−	0.651442i	0.999863	+	0.0165242i	$0.00526007\pi$
$20$	0.988831	+	0.149042i	0.221109	+	0.0333269i
$21$	6.81750	−	3.28314i	1.48770	−	0.716439i
$22$	−4.00718	+	1.92976i	−0.854334	+	0.411426i
$23$	−6.55509	−	0.988021i	−1.36683	−	0.206017i	−0.575698	−	0.817662i	$-0.695270\pi$
$23$	−6.55509	−	0.988021i	−1.36683	−	0.206017i	−0.791132	+	0.611646i	$0.790508\pi$
$24$	−0.805433	+	2.05221i	−0.164408	+	0.418905i
$25$	0.0747301	−	0.997204i	0.0149460	−	0.199441i
$26$	−0.0197014	−	0.0182802i	−0.00386376	−	0.00358504i
$27$	0.559111	−	2.44963i	0.107601	−	0.471431i
$28$	3.39396	−	0.511557i	0.641398	−	0.0966752i
$29$	−5.55798	+	3.78937i	−1.03209	+	0.703668i	−0.955980	−	0.293431i	$-0.905203\pi$
$29$	−5.55798	+	3.78937i	−1.03209	+	0.703668i	−0.0761116	+	0.997099i	$0.524251\pi$
$30$	2.10666	+	0.649819i	0.384622	+	0.118640i
$31$	0.548899	+	7.32454i	0.0985851	+	1.31553i	0.798801	+	0.601595i	$0.205468\pi$
$31$	0.548899	+	7.32454i	0.0985851	+	1.31553i	−0.700216	+	0.713931i	$0.746913\pi$
$32$	−0.623490	+	0.781831i	−0.110218	+	0.138210i
$33$	−9.36966	+	2.89016i	−1.63105	+	0.503112i
$34$	−0.888086	−	2.26281i	−0.152306	−	0.388068i
$35$	−0.763758	−	3.34624i	−0.129099	−	0.565618i
$36$	−0.930142	+	1.61105i	−0.155024	+	0.268509i
$37$	4.05805	+	7.02874i	0.667139	+	1.15552i	0.978701	+	0.205293i	$0.0658146\pi$
$37$	4.05805	+	7.02874i	0.667139	+	1.15552i	−0.311562	+	0.950226i	$0.600852\pi$
$38$	2.23613	−	2.07482i	0.362748	−	0.336581i
$39$	−0.0369422	−	0.0463240i	−0.00591548	−	0.00741778i
$40$	0.826239	+	0.563320i	0.130640	+	0.0890687i
$41$	−1.20402	−	0.579827i	−0.188037	−	0.0905537i	0.337497	−	0.941327i	$-0.390420\pi$
$41$	−1.20402	−	0.579827i	−0.188037	−	0.0905537i	−0.525533	+	0.850773i	$0.676134\pi$
$42$	7.56686			1.16759
$43$	−6.15062	−	2.27375i	−0.937960	−	0.346743i
$43$	−6.15062	−	2.27375i	−0.937960	−	0.346743i
$44$	−4.44764			−0.670506
$45$	1.67606	+	0.807147i	0.249852	+	0.120322i
$46$	−5.47724	−	3.73432i	−0.807576	−	0.550596i
$47$	3.09660	+	3.88301i	0.451685	+	0.566395i	0.954581	−	0.297952i	$-0.0963035\pi$
$47$	3.09660	+	3.88301i	0.451685	+	0.566395i	−0.502896	+	0.864347i	$0.667732\pi$
$48$	−1.61609	+	1.49951i	−0.233262	+	0.216436i
$49$	−2.39033	−	4.14017i	−0.341476	−	0.591453i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−1.19250	−	5.22468i	−0.166983	−	0.731602i
$52$	−0.00981885	−	0.0250180i	−0.00136163	−	0.00346937i
$53$	0.182273	−	0.0562237i	0.0250371	−	0.00772292i	−0.282211	−	0.959352i	$-0.591068\pi$
$53$	0.182273	−	0.0562237i	0.0250371	−	0.00772292i	0.307248	+	0.951629i	$0.400592\pi$
$54$	1.56660	−	1.96445i	0.213187	−	0.267328i
$55$	0.332372	+	4.43520i	0.0448171	+	0.598042i
$56$	3.27981	+	1.01169i	0.438283	+	0.135192i
$57$	5.55646	−	3.78833i	0.735972	−	0.501777i
$58$	−6.65172	+	1.00259i	−0.873413	+	0.131646i
$59$	1.90422	−	8.34293i	0.247908	−	1.08616i	−0.685707	−	0.727878i	$-0.740507\pi$
$59$	1.90422	−	8.34293i	0.247908	−	1.08616i	0.933615	−	0.358278i	$-0.116636\pi$
$60$	1.61609	+	1.49951i	0.208636	+	0.193586i
$61$	0.944147	−	12.5988i	0.120886	−	1.61311i	−0.525976	−	0.850500i	$-0.676300\pi$
$61$	0.944147	−	12.5988i	0.120886	−	1.61311i	0.646861	−	0.762608i	$-0.276081\pi$
$62$	−2.68346	+	6.83734i	−0.340800	+	0.868343i
$63$	6.31373	+	0.951642i	0.795455	+	0.119896i
$64$	−0.900969	+	0.433884i	−0.112621	+	0.0542355i
$65$	−0.0242143	+	0.0116610i	−0.00300341	+	0.00144637i
$66$	−9.69576	−	1.46140i	−1.19347	−	0.179886i
$67$	2.52053	−	6.42219i	0.307931	−	0.784596i	−0.690208	−	0.723611i	$-0.742481\pi$
$67$	2.52053	−	6.42219i	0.307931	−	0.784596i	0.998139	−	0.0609843i	$-0.0194240\pi$
$68$	0.181657	−	2.42405i	0.0220292	−	0.293959i
$69$	−10.7133	−	9.94046i	−1.28973	−	1.19669i
$70$	0.763758	−	3.34624i	0.0912865	−	0.399952i
$71$	0.383425	−	0.0577920i	0.0455041	−	0.00685864i	−0.126251	−	0.991998i	$-0.540294\pi$
$71$	0.383425	−	0.0577920i	0.0455041	−	0.00685864i	0.171755	+	0.985140i	$0.445056\pi$
$72$	−1.53704	+	1.04794i	−0.181142	+	0.123500i
$73$	10.8306	+	3.34079i	1.26762	+	0.391010i	0.854398	−	0.519619i	$-0.173926\pi$
$73$	10.8306	+	3.34079i	1.26762	+	0.391010i	0.413225	+	0.910629i	$0.364402\pi$
$74$	0.606517	+	8.09340i	0.0705061	+	0.940839i
$75$	1.37455	−	1.72363i	0.158719	−	0.199028i
$76$	2.91491	−	0.899132i	0.334364	−	0.103138i
$77$	5.57715	+	14.2103i	0.635575	+	1.61942i
$78$	−0.0131845	−	0.0577651i	−0.00149285	−	0.00654061i
$79$	−4.00950	+	6.94466i	−0.451104	+	0.781336i	−0.998455	−	0.0555677i	$-0.982303\pi$
$79$	−4.00950	+	6.94466i	−0.451104	+	0.781336i	0.547350	+	0.836903i	$0.315636\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	8.15168	−	7.56365i	0.905742	−	0.840406i
$82$	−0.833209	−	1.04481i	−0.0920126	−	0.115380i
$83$	−4.78821	−	3.26455i	−0.525574	−	0.358330i	0.271282	−	0.962500i	$-0.412553\pi$
$83$	−4.78821	−	3.26455i	−0.525574	−	0.358330i	−0.796856	+	0.604170i	$0.793505\pi$
$84$	6.81750	+	3.28314i	0.743851	+	0.358220i
$85$	−2.43084			−0.263662
$86$	−4.55497	−	4.71723i	−0.491175	−	0.508672i
$87$	−14.8300			−1.58995
$88$	−4.00718	−	1.92976i	−0.427167	−	0.205713i
$89$	7.49483	+	5.10989i	0.794451	+	0.541647i	0.891173	−	0.453664i	$-0.149883\pi$
$89$	7.49483	+	5.10989i	0.794451	+	0.541647i	−0.0967219	+	0.995311i	$0.530836\pi$
$90$	1.15987	+	1.45443i	0.122261	+	0.153310i
$91$	−0.0676210	+	0.0627431i	−0.00708861	+	0.00657727i
$92$	−3.31457	−	5.74100i	−0.345567	−	0.598540i
$93$	−8.09650	+	14.0236i	−0.839568	+	1.45417i
$94$	1.10516	+	4.84203i	0.113989	+	0.499417i
$95$	−1.11445	−	2.83957i	−0.114340	−	0.291334i
$96$	−2.10666	+	0.649819i	−0.215010	+	0.0663219i
$97$	5.34232	−	6.69906i	0.542431	−	0.680186i	−0.432771	−	0.901504i	$-0.642464\pi$
$97$	5.34232	−	6.69906i	0.542431	−	0.680186i	0.975202	+	0.221317i	$0.0710357\pi$
$98$	−0.357259	−	4.76729i	−0.0360886	−	0.481569i
$99$	−7.90628	−	2.43876i	−0.794611	−	0.245105i
$100$	0.826239	−	0.563320i	0.0826239	−	0.0563320i
$101$	12.2177	−	1.84153i	1.21571	−	0.183239i	0.490298	−	0.871555i	$-0.336888\pi$
$101$	12.2177	−	1.84153i	1.21571	−	0.183239i	0.725411	+	0.688316i	$0.241650\pi$
$102$	1.19250	−	5.22468i	0.118075	−	0.517321i
$103$	2.68683	+	2.49302i	0.264742	+	0.245644i	0.801362	−	0.598179i	$-0.204109\pi$
$103$	2.68683	+	2.49302i	0.264742	+	0.245644i	−0.536621	+	0.843824i	$0.680299\pi$
$104$	0.00200843	−	0.0268007i	0.000196943	−	0.00262802i
$105$	2.76448	−	7.04379i	0.269786	−	0.687404i
$106$	0.188617	+	0.0284294i	0.0183201	+	0.00276131i
$107$	3.60851	−	1.73777i	0.348848	−	0.167996i	−0.251251	−	0.967922i	$-0.580842\pi$
$107$	3.60851	−	1.73777i	0.348848	−	0.167996i	0.600099	+	0.799926i	$0.295128\pi$
$108$	2.26380	−	1.09019i	0.217834	−	0.104903i
$109$	−14.6857	−	2.21351i	−1.40664	−	0.212016i	−0.598552	−	0.801084i	$-0.704257\pi$
$109$	−14.6857	−	2.21351i	−1.40664	−	0.212016i	−0.808084	+	0.589068i	$0.799495\pi$
$110$	−1.62490	+	4.14019i	−0.154928	+	0.394751i
$111$	−1.33713	+	17.8428i	−0.126915	+	1.69356i
$112$	2.51605	+	2.33455i	0.237745	+	0.220595i
$113$	1.79236	−	7.85285i	0.168611	−	0.738734i	−0.817943	−	0.575299i	$-0.804886\pi$
$113$	1.79236	−	7.85285i	0.168611	−	0.738734i	0.986554	−	0.163435i	$-0.0522573\pi$
$114$	6.64990	−	1.00231i	0.622820	−	0.0938750i
$115$	−5.47724	+	3.73432i	−0.510756	+	0.348227i
$116$	−6.42800	−	1.98277i	−0.596824	−	0.184096i
$117$	−0.00373626	−	0.0498569i	−0.000345417	−	0.00460927i
$118$	5.33550	−	6.69051i	0.491173	−	0.615911i
$119$	−7.97270	+	2.45925i	−0.730856	+	0.225439i
$120$	0.805433	+	2.05221i	0.0735256	+	0.187340i
$121$	−1.95406	−	8.56129i	−0.177642	−	0.778299i
$122$	6.31705	−	10.9414i	0.571919	−	0.990592i
$123$	−1.47308	−	2.55144i	−0.132823	−	0.230056i
$124$	−5.38433	+	4.99592i	−0.483527	+	0.448647i
$125$	−0.623490	−	0.781831i	−0.0557666	−	0.0699291i
$126$	5.27557	+	3.59682i	0.469985	+	0.320431i
$127$	7.42039	+	3.57347i	0.658453	+	0.317094i	0.733105	−	0.680115i	$-0.238070\pi$
$127$	7.42039	+	3.57347i	0.658453	+	0.317094i	−0.0746521	+	0.997210i	$0.523785\pi$
$128$	−1.00000			−0.0883883
$129$	−8.37977	−	11.7801i	−0.737797	−	1.03718i
$130$	−0.0268758			−0.00235717
$131$	−6.82030	−	3.28448i	−0.595892	−	0.286967i	0.111526	−	0.993761i	$-0.464426\pi$
$131$	−6.82030	−	3.28448i	−0.595892	−	0.286967i	−0.707419	+	0.706795i	$0.750140\pi$
$132$	−8.10150	−	5.52351i	−0.705145	−	0.480760i
$133$	−6.52794	−	8.18578i	−0.566044	−	0.709797i
$134$	5.05740	−	4.69258i	0.436893	−	0.405377i
$135$	−1.25631	−	2.17600i	−0.108126	−	0.187280i
$136$	1.21542	−	2.10517i	0.104222	−	0.180517i
$137$	4.07666	+	17.8610i	0.348293	+	1.52597i	0.781055	+	0.624463i	$0.214682\pi$
$137$	4.07666	+	17.8610i	0.348293	+	1.52597i	−0.432762	+	0.901508i	$0.642461\pi$
$138$	−5.33932	−	13.6044i	−0.454513	−	1.15808i
$139$	−16.6614	+	5.13936i	−1.41320	+	0.435914i	−0.905032	−	0.425344i	$-0.860153\pi$
$139$	−16.6614	+	5.13936i	−1.41320	+	0.435914i	−0.508168	+	0.861258i	$0.669677\pi$
$140$	2.14000	−	2.68348i	0.180863	−	0.226795i
$141$	0.818241	+	10.9187i	0.0689084	+	0.919518i
$142$	0.370529	+	0.114293i	0.0310941	+	0.00959125i
$143$	0.0987636	−	0.0673359i	0.00825902	−	0.00563091i
$144$	−1.83951	+	0.277261i	−0.153292	+	0.0231051i
$145$	−1.49687	+	6.55819i	−0.124308	+	0.544628i
$146$	8.30850	+	7.70916i	0.687616	+	0.638014i
$147$	0.787615	−	10.5100i	0.0649614	−	0.866850i
$148$	−2.96514	+	7.55506i	−0.243733	+	0.621022i
$149$	−2.81481	−	0.424265i	−0.230599	−	0.0347571i	0.0327263	−	0.999464i	$-0.489581\pi$
$149$	−2.81481	−	0.424265i	−0.230599	−	0.0347571i	−0.263325	+	0.964707i	$0.584819\pi$
$150$	1.98628	−	0.956542i	0.162179	−	0.0781014i
$151$	14.4012	−	6.93527i	1.17196	−	0.564384i	0.256398	−	0.966571i	$-0.417464\pi$
$151$	14.4012	−	6.93527i	1.17196	−	0.564384i	0.915558	+	0.402187i	$0.131750\pi$
$152$	3.01637	+	0.454644i	0.244660	+	0.0368765i
$153$	1.65209	−	4.20946i	0.133564	−	0.340315i
$154$	−1.14080	+	15.2229i	−0.0919283	+	1.22670i
$155$	5.38433	+	4.99592i	0.432479	+	0.401282i
$156$	0.0131845	−	0.0577651i	0.00105560	−	0.00462491i
$157$	22.9754	−	3.46298i	1.83363	−	0.276376i	0.860980	−	0.508638i	$-0.169851\pi$
$157$	22.9754	−	3.46298i	1.83363	−	0.276376i	0.972653	+	0.232262i	$0.0746128\pi$
$158$	−6.62562	+	4.51727i	−0.527106	+	0.359375i
$159$	0.401840	+	0.123951i	0.0318680	+	0.00982996i
$160$	0.0747301	+	0.997204i	0.00590793	+	0.0788359i
$161$	−14.1864	+	17.7891i	−1.11804	+	1.40198i
$162$	10.6262	−	3.27774i	0.834870	−	0.257523i
$163$	5.23425	+	13.3367i	0.409978	+	1.04461i	0.975524	+	0.219891i	$0.0705703\pi$
$163$	5.23425	+	13.3367i	0.409978	+	1.04461i	−0.565546	+	0.824717i	$0.691335\pi$
$164$	−0.297369	−	1.30286i	−0.0232206	−	0.101736i
$165$	−4.90264	+	8.49162i	−0.381670	+	0.661072i
$166$	−2.89759	−	5.01878i	−0.224897	−	0.389533i
$167$	−18.4609	+	17.1293i	−1.42855	+	1.32550i	−0.561316	+	0.827602i	$0.689705\pi$
$167$	−18.4609	+	17.1293i	−1.42855	+	1.32550i	−0.867235	+	0.497899i	$0.834105\pi$
$168$	4.71786	+	5.91601i	0.363991	+	0.456430i
$169$	−10.7405	−	7.32275i	−0.826193	−	0.563289i
$170$	−2.19011	−	1.05470i	−0.167974	−	0.0808920i
$171$	5.67468			0.433954
$172$	−2.05716	−	6.22640i	−0.156857	−	0.474759i
$173$	0.817846			0.0621797			0.0310898	−	0.999517i	$-0.490102\pi$
$173$	0.817846			0.0621797			0.0310898	+	0.999517i	$0.490102\pi$
$174$	−13.3614	−	6.43452i	−1.01293	−	0.487799i
$175$	−2.83590	−	1.93348i	−0.214374	−	0.146157i
$176$	−2.77306	−	3.47730i	−0.209027	−	0.262111i
$177$	13.8297	−	12.8320i	1.03950	−	0.964516i
$178$	4.53551	+	7.85574i	0.339951	+	0.588813i
$179$	−1.41064	+	2.44331i	−0.105437	+	0.182621i	−0.913916	−	0.405902i	$-0.866957\pi$
$179$	−1.41064	+	2.44331i	−0.105437	+	0.182621i	0.808480	+	0.588524i	$0.200291\pi$
$180$	0.413952	+	1.81364i	0.0308542	+	0.135181i
$181$	−4.84101	−	12.3347i	−0.359830	−	0.916831i	−0.990088	−	0.140446i	$-0.955146\pi$
$181$	−4.84101	−	12.3347i	−0.359830	−	0.916831i	0.630259	−	0.776385i	$-0.282949\pi$
$182$	−0.0881476	+	0.0271899i	−0.00653394	+	0.00201545i
$183$	17.3662	−	21.7765i	1.28375	−	1.60977i
$184$	−0.495396	−	6.61059i	−0.0365210	−	0.487339i
$185$	7.75552	+	2.39226i	0.570197	+	0.175883i
$186$	−13.3793	+	9.12184i	−0.981017	+	0.668846i
$187$	10.6907	−	1.61137i	0.781785	−	0.117835i
$188$	−1.10516	+	4.84203i	−0.0806022	+	0.353141i
$189$	−6.32189	−	5.86586i	−0.459850	−	0.426678i
$190$	0.227959	−	3.04191i	0.0165379	−	0.220683i
$191$	−6.84051	+	17.4293i	−0.494962	+	1.26114i	0.437286	+	0.899322i	$0.355940\pi$
$191$	−6.84051	+	17.4293i	−0.494962	+	1.26114i	−0.932248	+	0.361820i	$0.882156\pi$
$192$	−2.17998	−	0.328579i	−0.157327	−	0.0237132i
$193$	5.51416	−	2.65548i	0.396918	−	0.191146i	−0.224768	−	0.974412i	$-0.572162\pi$
$193$	5.51416	−	2.65548i	0.396918	−	0.191146i	0.621686	+	0.783267i	$0.286448\pi$
$194$	7.71988	−	3.71770i	0.554255	−	0.266915i
$195$	−0.0585888	−	0.00883085i	−0.00419563	−	0.000632390i
$196$	1.74657	−	4.45019i	0.124755	−	0.317871i
$197$	1.47901	−	19.7360i	0.105375	−	1.40613i	−0.654498	−	0.756064i	$-0.727120\pi$
$197$	1.47901	−	19.7360i	0.105375	−	1.40613i	0.759873	−	0.650071i	$-0.225261\pi$
$198$	−6.06517	−	5.62766i	−0.431033	−	0.399940i
$199$	−4.79102	+	20.9908i	−0.339627	+	1.48800i	0.460224	+	0.887803i	$0.347769\pi$
$199$	−4.79102	+	20.9908i	−0.339627	+	1.48800i	−0.799851	+	0.600199i	$0.795088\pi$
$200$	0.988831	−	0.149042i	0.0699209	−	0.0105389i
$201$	12.5669	−	8.56798i	0.886402	−	0.604339i
$202$	11.8068	+	3.64191i	0.830723	+	0.256244i
$203$	1.72541	+	23.0240i	0.121100	+	1.61597i
$204$	3.34131	−	4.18987i	0.233939	−	0.293350i
$205$	−1.27699	+	0.393900i	−0.0891891	+	0.0275112i
$206$	1.33907	+	3.41191i	0.0932977	+	0.237719i
$207$	−2.74414	−	12.0229i	−0.190731	−	0.835647i
$208$	0.0134379	−	0.0232752i	0.000931752	−	0.00161384i
$209$	6.78362	+	11.7496i	0.469233	+	0.812735i
$210$	5.54690	−	5.14677i	0.382772	−	0.355161i
$211$	5.72901	+	7.18395i	0.394402	+	0.494564i	0.938896	−	0.344200i	$-0.111850\pi$
$211$	5.72901	+	7.18395i	0.394402	+	0.494564i	−0.544495	+	0.838764i	$0.683279\pi$
$212$	0.157603	+	0.107452i	0.0108242	+	0.00737981i
$213$	0.770191	+	0.370905i	0.0527726	+	0.0254140i
$214$	4.00514			0.273786
$215$	−6.05526	+	2.51671i	−0.412965	+	0.171638i
$216$	2.51262			0.170962
$217$	22.7139	+	10.9384i	1.54192	+	0.742549i
$218$	−12.2710	−	8.36620i	−0.831094	−	0.566630i
$219$	15.5793	+	19.5358i	1.05275	+	1.32011i
$220$	−3.26035	+	3.02516i	−0.219813	+	0.203956i
$221$	0.0326655	+	0.0565782i	0.00219732	+	0.00380586i
$222$	−8.94639	+	15.4956i	−0.600443	+	1.04000i
$223$	3.37867	+	14.8029i	0.226252	+	0.991276i	0.952666	+	0.304019i	$0.0983285\pi$
$223$	3.37867	+	14.8029i	0.226252	+	0.991276i	−0.726414	+	0.687258i	$0.758814\pi$
$224$	1.25396	+	3.19503i	0.0837836	+	0.213477i
$225$	1.77764	−	0.548328i	0.118509	−	0.0365552i
$226$	5.02209	−	6.29750i	0.334064	−	0.418903i
$227$	−0.623288	−	8.31720i	−0.0413691	−	0.552032i	−0.978928	−	0.204205i	$-0.934539\pi$
$227$	−0.623288	−	8.31720i	−0.0413691	−	0.552032i	0.937559	−	0.347826i	$-0.113080\pi$
$228$	6.42624	+	1.98223i	0.425588	+	0.131276i
$229$	19.6229	−	13.3786i	1.29672	−	0.884086i	0.299177	−	0.954198i	$-0.403288\pi$
$229$	19.6229	−	13.3786i	1.29672	−	0.884086i	0.997539	+	0.0701117i	$0.0223356\pi$
$230$	−6.55509	+	0.988021i	−0.432230	+	0.0651481i
$231$	−7.48886	+	32.8108i	−0.492731	+	2.15879i
$232$	−4.93113	−	4.57542i	−0.323745	−	0.300391i
$233$	−0.286607	+	3.82451i	−0.0187763	+	0.250552i	0.979915	+	0.199414i	$0.0639038\pi$
$233$	−0.286607	+	3.82451i	−0.0187763	+	0.250552i	−0.998692	+	0.0511378i	$0.983715\pi$
$234$	0.0182658	−	0.0465406i	0.00119408	−	0.00304245i
$235$	4.91108	+	0.740226i	0.320364	+	0.0482870i
$236$	7.71002	−	3.71295i	0.501880	−	0.241693i
$237$	−15.9280	+	7.67052i	−1.03463	+	0.498254i
$238$	−8.25018	−	1.24352i	−0.534780	−	0.0806051i
$239$	−5.36492	+	13.6696i	−0.347028	+	0.884212i	0.645674	+	0.763613i	$0.276577\pi$
$239$	−5.36492	+	13.6696i	−0.347028	+	0.884212i	−0.992701	+	0.120599i	$0.961519\pi$
$240$	−0.164750	+	2.19844i	−0.0106346	+	0.141909i
$241$	−3.79902	−	3.52497i	−0.244716	−	0.227064i	0.548272	−	0.836300i	$-0.315286\pi$
$241$	−3.79902	−	3.52497i	−0.244716	−	0.227064i	−0.792989	+	0.609236i	$0.791476\pi$
$242$	1.95406	−	8.56129i	0.125612	−	0.550341i
$243$	16.7881	−	2.53041i	1.07696	−	0.162326i
$244$	10.4388	−	7.11704i	0.668275	−	0.455622i
$245$	−4.56827	−	1.40912i	−0.291856	−	0.0900256i
$246$	−0.220166	−	2.93792i	−0.0140373	−	0.187315i
$247$	−0.0511156	+	0.0640969i	−0.00325241	+	0.00407839i
$248$	−7.01876	+	2.16500i	−0.445692	+	0.137478i
$249$	−4.66763	−	11.8929i	−0.295799	−	0.753684i
$250$	−0.222521	−	0.974928i	−0.0140735	−	0.0616599i
$251$	1.67683	−	2.90436i	0.105841	−	0.183322i	−0.808241	−	0.588852i	$-0.799580\pi$
$251$	1.67683	−	2.90436i	0.105841	−	0.183322i	0.914081	+	0.405531i	$0.132913\pi$
$252$	3.19252	+	5.52961i	0.201110	+	0.348333i
$253$	21.6133	−	20.0542i	1.35881	−	1.26080i
$254$	5.13507	+	6.43917i	0.322203	+	0.404030i
$255$	−4.42785	−	3.01886i	−0.277283	−	0.189048i
$256$	−0.900969	−	0.433884i	−0.0563106	−	0.0271177i
$257$	−8.23680			−0.513797			−0.256899	−	0.966438i	$-0.582701\pi$
$257$	−8.23680			−0.513797			−0.256899	+	0.966438i	$0.582701\pi$
$258$	−2.43870	−	14.2494i	−0.151827	−	0.887128i
$259$	27.8568			1.73094
$260$	−0.0242143	−	0.0116610i	−0.00150171	−	0.000723184i
$261$	−10.3394	−	7.04930i	−0.639995	−	0.436341i
$262$	−4.71979	−	5.91843i	−0.291590	−	0.365642i
$263$	8.25397	−	7.65856i	0.508962	−	0.472247i	−0.383391	−	0.923586i	$-0.625244\pi$
$263$	8.25397	−	7.65856i	0.508962	−	0.472247i	0.892353	+	0.451339i	$0.149053\pi$
$264$	−4.90264	−	8.49162i	−0.301737	−	0.522623i
$265$	0.0953736	−	0.165192i	0.00585875	−	0.0101477i
$266$	−2.32980	−	10.2075i	−0.142849	−	0.625862i
$267$	7.30610	+	18.6156i	0.447126	+	1.13926i
$268$	6.59259	−	2.03355i	0.402707	−	0.124219i
$269$	−12.8713	+	16.1402i	−0.784780	+	0.984083i	0.215192	+	0.976572i	$0.430962\pi$
$269$	−12.8713	+	16.1402i	−0.784780	+	0.984083i	−0.999972	+	0.00751079i	$0.997609\pi$
$270$	−0.187769	−	2.50560i	−0.0114272	−	0.152486i
$271$	−27.4496	−	8.46709i	−1.66745	−	0.514339i	−0.689694	−	0.724101i	$-0.742255\pi$
$271$	−27.4496	−	8.46709i	−1.66745	−	0.514339i	−0.977753	+	0.209762i	$0.932731\pi$
$272$	2.00846	−	1.36934i	0.121781	−	0.0830286i
$273$	−0.201094	+	0.0303101i	−0.0121708	+	0.00183445i
$274$	−4.07666	+	17.8610i	−0.246280	+	1.07902i
$275$	3.26035	+	3.02516i	0.196606	+	0.182424i
$276$	1.09215	−	14.5737i	0.0657398	−	0.877237i
$277$	−6.39012	+	16.2818i	−0.383945	+	0.978277i	0.600031	+	0.799977i	$0.295155\pi$
$277$	−6.39012	+	16.2818i	−0.383945	+	0.978277i	−0.983976	+	0.178300i	$0.942940\pi$
$278$	−17.2413	−	2.59870i	−1.03406	−	0.155860i
$279$	−12.3108	+	5.92856i	−0.737027	+	0.354934i
$280$	3.09239	−	1.48922i	0.184806	−	0.0889978i
$281$	−4.35497	−	0.656406i	−0.259796	−	0.0391579i	0.0178528	−	0.999841i	$-0.494317\pi$
$281$	−4.35497	−	0.656406i	−0.259796	−	0.0391579i	−0.277649	+	0.960683i	$0.589555\pi$
$282$	−4.00022	+	10.1924i	−0.238210	+	0.606949i
$283$	−2.07394	+	27.6748i	−0.123283	+	1.64510i	0.502122	+	0.864797i	$0.332553\pi$
$283$	−2.07394	+	27.6748i	−0.123283	+	1.64510i	−0.625405	+	0.780300i	$0.715066\pi$
$284$	0.284245	+	0.263741i	0.0168668	+	0.0156501i
$285$	1.49646	−	6.55640i	0.0886424	−	0.388368i
$286$	0.118199	−	0.0178156i	0.00698924	−	0.00105346i
$287$	−3.78979	+	2.58384i	−0.223704	+	0.152519i
$288$	−1.77764	−	0.548328i	−0.104748	−	0.0323106i
$289$	−0.828832	−	11.0600i	−0.0487548	−	0.650588i
$290$	−4.19412	+	5.25926i	−0.246287	+	0.308835i
$291$	18.0508	−	5.56792i	1.05815	−	0.326397i
$292$	4.14082	+	10.5506i	0.242323	+	0.617429i
$293$	0.249852	+	1.09467i	0.0145965	+	0.0639514i	0.981702	−	0.190425i	$-0.0609868\pi$
$293$	0.249852	+	1.09467i	0.0145965	+	0.0639514i	−0.967105	+	0.254377i	$0.918130\pi$
$294$	5.26973	−	9.12745i	0.307337	−	0.532323i
$295$	−4.27874	−	7.41099i	−0.249118	−	0.431485i
$296$	−5.94952	+	5.52035i	−0.345809	+	0.320864i
$297$	6.96765	+	8.73715i	0.404304	+	0.506981i
$298$	−2.35198	−	1.60355i	−0.136246	−	0.0928912i
$299$	0.160520	+	0.0773022i	0.00928309	+	0.00447050i
$300$	2.20461			0.127283
$301$	−17.3140	+	14.3803i	−0.997961	+	0.828869i
$302$	15.9842			0.919785
$303$	24.5419	+	11.8188i	1.40990	+	0.678971i
$304$	2.52039	+	1.71837i	0.144554	+	0.0985554i
$305$	−7.87723	−	9.87774i	−0.451049	−	0.565598i
$306$	3.31490	−	3.07578i	0.189500	−	0.175831i
$307$	−9.81214	−	16.9951i	−0.560009	−	0.969963i	−0.997495	−	0.0707382i	$-0.977465\pi$
$307$	−9.81214	−	16.9951i	−0.560009	−	0.969963i	0.437486	−	0.899225i	$-0.355869\pi$
$308$	−7.63280	+	13.2204i	−0.434919	+	0.753302i
$309$	1.79808	+	7.87788i	0.102289	+	0.448157i
$310$	2.68346	+	6.83734i	0.152410	+	0.388335i
$311$	1.29734	−	0.400176i	0.0735654	−	0.0226919i	−0.257754	−	0.966211i	$-0.582982\pi$
$311$	1.29734	−	0.400176i	0.0735654	−	0.0226919i	0.331319	+	0.943519i	$0.392506\pi$
$312$	0.0369422	−	0.0463240i	0.00209144	−	0.00262258i
$313$	−1.00184	−	13.3686i	−0.0566273	−	0.755639i	−0.951172	−	0.308661i	$-0.900119\pi$
$313$	−1.00184	−	13.3686i	−0.0566273	−	0.755639i	0.894545	−	0.446978i	$-0.147500\pi$
$314$	22.2026	+	6.84860i	1.25297	+	0.386489i
$315$	5.27557	−	3.59682i	0.297245	−	0.202658i
$316$	−7.92944	+	1.19517i	−0.446066	+	0.0672336i
$317$	−4.25912	+	18.6604i	−0.239216	+	1.04807i	0.702505	+	0.711679i	$0.252065\pi$
$317$	−4.25912	+	18.6604i	−0.239216	+	1.04807i	−0.941721	+	0.336395i	$0.890792\pi$
$318$	0.308265	+	0.286028i	0.0172866	+	0.0160396i
$319$	2.23582	−	29.8349i	0.125182	−	1.67043i
$320$	−0.365341	+	0.930874i	−0.0204232	+	0.0520374i
$321$	8.73114	+	1.31601i	0.487325	+	0.0734524i
$322$	−20.4999	+	9.87222i	−1.14241	+	0.550157i
$323$	−6.68080	+	3.21731i	−0.371730	+	0.179016i
$324$	10.9960	+	1.65738i	0.610888	+	0.0920766i
$325$	−0.00981885	+	0.0250180i	−0.000544652	+	0.00138775i
$326$	−1.07066	+	14.2870i	−0.0592984	+	0.791282i
$327$	−24.0015	−	22.2701i	−1.32729	−	1.23154i
$328$	0.297369	−	1.30286i	0.0164195	−	0.0719383i
$329$	16.8563	−	2.54068i	0.929317	−	0.140072i
$330$	−8.10150	+	5.52351i	−0.445973	+	0.304059i
$331$	−10.4645	−	3.22787i	−0.575181	−	0.177420i	−0.00650100	−	0.999979i	$-0.502069\pi$
$331$	−10.4645	−	3.22787i	−0.575181	−	0.177420i	−0.568680	+	0.822559i	$0.692546\pi$
$332$	−0.433075	−	5.77898i	−0.0237681	−	0.317163i
$333$	−9.41360	+	11.8043i	−0.515862	+	0.646871i
$334$	−24.0648	+	7.42302i	−1.31677	+	0.406170i
$335$	−2.52053	−	6.42219i	−0.137711	−	0.350882i
$336$	1.68378	+	7.37714i	0.0918580	+	0.402456i
$337$	3.90659	−	6.76641i	0.212806	−	0.368590i	−0.739786	−	0.672842i	$-0.765073\pi$
$337$	3.90659	−	6.76641i	0.212806	−	0.368590i	0.952592	+	0.304252i	$0.0984066\pi$
$338$	−6.49964	−	11.2577i	−0.353534	−	0.612338i
$339$	13.0173	−	12.0783i	0.707002	−	0.656002i
$340$	−1.51561	−	1.90051i	−0.0821952	−	0.103070i
$341$	−26.9918	−	18.4027i	−1.46169	−	0.996561i
$342$	5.11271	+	2.46215i	0.276464	+	0.133138i
$343$	7.61743			0.411303
$344$	0.848100	−	6.50236i	0.0457265	−	0.350584i
$345$	−14.6146			−0.786824
$346$	0.736854	+	0.354850i	0.0396135	+	0.0190769i
$347$	24.3346	+	16.5911i	1.30635	+	0.890656i	0.998158	−	0.0606675i	$-0.0193229\pi$
$347$	24.3346	+	16.5911i	1.30635	+	0.890656i	0.308194	+	0.951323i	$0.400275\pi$
$348$	−9.24638	−	11.5946i	−0.495658	−	0.621536i
$349$	18.0859	−	16.7812i	0.968114	−	0.898278i	−0.0267356	−	0.999643i	$-0.508511\pi$
$349$	18.0859	−	16.7812i	0.968114	−	0.898278i	0.994849	+	0.101364i	$0.0323207\pi$
$350$	−1.71615	−	2.97246i	−0.0917320	−	0.158884i
$351$	−0.0337644	+	0.0584817i	−0.00180221	+	0.00312152i
$352$	−0.989692	−	4.33612i	−0.0527508	−	0.231116i
$353$	6.68757	+	17.0397i	0.355944	+	0.906930i	0.990927	+	0.134404i	$0.0429119\pi$
$353$	6.68757	+	17.0397i	0.355944	+	0.906930i	−0.634983	+	0.772526i	$0.718993\pi$
$354$	18.0277	−	5.56081i	0.958162	−	0.295554i
$355$	0.241762	−	0.303159i	0.0128314	−	0.0160900i
$356$	0.677879	+	9.04566i	0.0359275	+	0.479419i
$357$	−17.5767	−	5.42168i	−0.930255	−	0.286946i
$358$	−2.33106	+	1.58929i	−0.123200	+	0.0839965i
$359$	18.2769	−	2.75480i	0.964618	−	0.145393i	0.352198	−	0.935925i	$-0.385434\pi$
$359$	18.2769	−	2.75480i	0.964618	−	0.145393i	0.612420	+	0.790533i	$0.290196\pi$
$360$	−0.413952	+	1.81364i	−0.0218172	+	0.0955874i
$361$	7.10682	+	6.59416i	0.374043	+	0.347061i
$362$	0.990224	−	13.2136i	0.0520450	−	0.694493i
$363$	7.07288	−	18.0214i	0.371230	−	0.945878i
$364$	−0.0912155	−	0.0137485i	−0.00478099	−	0.000720619i
$365$	10.2117	−	4.91769i	0.534504	−	0.257404i
$366$	25.0949	−	12.0850i	1.31173	−	0.631696i
$367$	−29.1095	−	4.38755i	−1.51950	−	0.229028i	−0.664357	−	0.747416i	$-0.731294\pi$
$367$	−29.1095	−	4.38755i	−1.51950	−	0.229028i	−0.855146	+	0.518388i	$0.826532\pi$
$368$	2.42189	−	6.17088i	0.126250	−	0.321680i
$369$	0.185780	−	2.47906i	0.00967133	−	0.129055i
$370$	5.94952	+	5.52035i	0.309301	+	0.286989i
$371$	0.145685	−	0.638286i	0.00756357	−	0.0331382i
$372$	−16.0121	+	2.41344i	−0.830191	+	0.125131i
$373$	−9.70738	+	6.61838i	−0.502629	+	0.342687i	−0.787944	−	0.615747i	$-0.788854\pi$
$373$	−9.70738	+	6.61838i	−0.502629	+	0.342687i	0.285315	+	0.958434i	$0.407902\pi$
$374$	10.3312	+	3.18675i	0.534212	+	0.164783i
$375$	−0.164750	−	2.19844i	−0.00850767	−	0.113527i
$376$	−3.09660	+	3.88301i	−0.159695	+	0.200251i
$377$	0.172758	−	0.0532887i	0.00889748	−	0.00274451i
$378$	−3.15073	−	8.02792i	−0.162056	−	0.412912i
$379$	−6.38346	−	27.9677i	−0.327896	−	1.43661i	−0.823133	−	0.567849i	$-0.807776\pi$
$379$	−6.38346	−	27.9677i	−0.327896	−	1.43661i	0.495237	−	0.868758i	$-0.335081\pi$
$380$	1.52522	−	2.64176i	0.0782421	−	0.135519i
$381$	9.07857	+	15.7246i	0.465109	+	0.805593i
$382$	−13.7254	+	12.7353i	−0.702252	+	0.651595i
$383$	−14.6227	−	18.3363i	−0.747185	−	0.936940i	0.252344	−	0.967638i	$-0.418799\pi$
$383$	−14.6227	−	18.3363i	−0.747185	−	0.936940i	−0.999529	+	0.0306973i	$0.990227\pi$
$384$	−1.82153	−	1.24190i	−0.0929546	−	0.0633754i
$385$	13.7538	+	6.62350i	0.700960	+	0.337565i
$386$	6.12026			0.311513
$387$	−0.242767	−	12.1963i	−0.0123405	−	0.619972i
$388$	8.56842			0.434996
$389$	11.1993	+	5.39331i	0.567828	+	0.273452i	0.695692	−	0.718340i	$-0.255098\pi$
$389$	11.1993	+	5.39331i	0.567828	+	0.273452i	−0.127864	+	0.991792i	$0.540812\pi$
$390$	−0.0489552	−	0.0333771i	−0.00247894	−	0.00169011i
$391$	10.0471	+	12.5987i	0.508106	+	0.637145i
$392$	3.50447	−	3.25167i	0.177003	−	0.164234i
$393$	−8.34439	−	14.4529i	−0.420919	−	0.729053i
$394$	9.89569	−	17.1398i	0.498538	−	0.863493i
$395$	1.78440	+	7.81795i	0.0897828	+	0.393364i
$396$	−3.02278	−	7.70192i	−0.151901	−	0.387036i
$397$	19.2875	−	5.94939i	0.968010	−	0.298592i	0.229857	−	0.973224i	$-0.426174\pi$
$397$	19.2875	−	5.94939i	0.968010	−	0.298592i	0.738153	+	0.674633i	$0.235698\pi$
$398$	−13.4241	+	16.8333i	−0.672892	+	0.843780i
$399$	−1.72494	−	23.0177i	−0.0863549	−	1.15233i
$400$	0.955573	+	0.294755i	0.0477786	+	0.0147378i
$401$	12.6125	−	8.59906i	0.629839	−	0.429417i	−0.205878	−	0.978578i	$-0.566005\pi$
$401$	12.6125	−	8.59906i	0.629839	−	0.429417i	0.835717	+	0.549161i	$0.185053\pi$
$402$	15.0399	−	2.26690i	0.750123	−	0.113063i
$403$	0.0439268	−	0.192456i	0.00218815	−	0.00958691i
$404$	9.05739	+	8.40403i	0.450622	+	0.418116i
$405$	0.831013	−	11.0891i	0.0412934	−	0.551022i
$406$	−8.43519	+	21.4925i	−0.418632	+	1.06666i
$407$	−35.6943	−	5.38004i	−1.76930	−	0.266679i
$408$	4.82833	−	2.32520i	0.239038	−	0.115115i
$409$	−3.02098	+	1.45483i	−0.149378	+	0.0719366i	−0.507079	−	0.861899i	$-0.669275\pi$
$409$	−3.02098	+	1.45483i	−0.149378	+	0.0719366i	0.357701	+	0.933836i	$0.383561\pi$
$410$	−1.32144	−	0.199175i	−0.0652612	−	0.00983654i
$411$	−14.7558	+	37.5972i	−0.727851	+	1.85453i
$412$	−0.273906	+	3.65502i	−0.0134944	+	0.180070i
$413$	−21.5311	−	19.9779i	−1.05947	−	0.983048i
$414$	2.74414	−	12.0229i	0.134867	−	0.590892i
$415$	−5.73046	+	0.863728i	−0.281297	+	0.0423987i
$416$	0.0222059	−	0.0151397i	0.00108873	−	0.000742285i
$417$	−36.7318	−	11.3303i	−1.79876	−	0.554845i
$418$	1.01388	+	13.5293i	0.0495905	+	0.661739i
$419$	−1.12283	+	1.40799i	−0.0548539	+	0.0687847i	−0.808502	−	0.588494i	$-0.799721\pi$
$419$	−1.12283	+	1.40799i	−0.0548539	+	0.0687847i	0.753648	+	0.657279i	$0.228293\pi$
$420$	7.23068	−	2.23037i	0.352821	−	0.108831i
$421$	−14.0098	−	35.6964i	−0.682797	−	1.73974i	−0.672841	−	0.739787i	$-0.734926\pi$
$421$	−14.0098	−	35.6964i	−0.682797	−	1.73974i	−0.00995510	−	0.999950i	$-0.503169\pi$
$422$	2.04466	+	8.95825i	0.0995325	+	0.436081i
$423$	−4.61960	+	8.00138i	−0.224613	+	0.389040i
$424$	0.0953736	+	0.165192i	0.00463175	+	0.00802243i
$425$	−1.78193	+	1.65339i	−0.0864365	+	0.0802013i
$426$	0.532989	+	0.668347i	0.0258234	+	0.0323815i
$427$	−35.8290	−	24.4278i	−1.73389	−	1.18214i
$428$	3.60851	+	1.73777i	0.174424	+	0.0839981i
$429$	0.263525			0.0127231
$430$	−6.54756	−	0.359806i	−0.315751	−	0.0173514i
$431$	−14.9210			−0.718717			−0.359358	−	0.933200i	$-0.617004\pi$
$431$	−14.9210			−0.718717			−0.359358	+	0.933200i	$0.617004\pi$
$432$	2.26380	+	1.09019i	0.108917	+	0.0524516i
$433$	13.9882	+	9.53698i	0.672229	+	0.458318i	0.850717	−	0.525624i	$-0.176168\pi$
$433$	13.9882	+	9.53698i	0.672229	+	0.458318i	−0.178488	+	0.983942i	$0.557120\pi$
$434$	15.7185	+	19.7104i	0.754512	+	0.946128i
$435$	−10.8712	+	10.0870i	−0.521234	+	0.483634i
$436$	−7.42579	−	12.8619i	−0.355631	−	0.615971i
$437$	−10.1109	+	17.5125i	−0.483669	+	0.837739i
$438$	5.56019	+	24.3608i	0.265676	+	1.16400i
$439$	3.02437	+	7.70596i	0.144345	+	0.367785i	0.984702	−	0.174249i	$-0.0557497\pi$
$439$	3.02437	+	7.70596i	0.144345	+	0.367785i	−0.840357	+	0.542034i	$0.817654\pi$
$440$	−4.25004	+	1.31096i	−0.202613	+	0.0624977i
$441$	5.54493	−	6.95313i	0.264044	−	0.331101i
$442$	0.00488219	+	0.0651482i	0.000232222	+	0.00309879i
$443$	−22.5477	−	6.95503i	−1.07127	−	0.330443i	−0.291541	−	0.956558i	$-0.594168\pi$
$443$	−22.5477	−	6.95503i	−1.07127	−	0.330443i	−0.779731	+	0.626115i	$0.784644\pi$
$444$	−14.7837	+	10.0794i	−0.701604	+	0.478346i
$445$	8.96971	−	1.35197i	0.425205	−	0.0640894i
$446$	−3.37867	+	14.8029i	−0.159985	+	0.700938i
$447$	−4.60038	−	4.26852i	−0.217590	−	0.201894i
$448$	−0.256496	+	3.42270i	−0.0121183	+	0.161707i
$449$	−0.987042	+	2.51494i	−0.0465814	+	0.118688i	−0.952271	−	0.305254i	$-0.901259\pi$
$449$	−0.987042	+	2.51494i	−0.0465814	+	0.118688i	0.905690	+	0.423942i	$0.139354\pi$
$450$	1.83951	+	0.277261i	0.0867151	+	0.0130702i
$451$	5.35505	−	2.57886i	0.252160	−	0.121434i
$452$	7.25713	−	3.49485i	0.341347	−	0.164384i
$453$	34.8452	+	5.25207i	1.63717	+	0.246764i
$454$	3.04713	−	7.76397i	0.143009	−	0.364381i
$455$	−0.00689354	+	0.0919879i	−0.000323174	+	0.00431246i
$456$	4.92978	+	4.57417i	0.230858	+	0.214205i
$457$	−0.583529	+	2.55661i	−0.0272963	+	0.119593i	−0.986741	−	0.162305i	$-0.948107\pi$
$457$	−0.583529	+	2.55661i	−0.0272963	+	0.119593i	0.959444	+	0.281899i	$0.0909641\pi$
$458$	23.4844	−	3.53970i	1.09735	−	0.165399i
$459$	−5.04650	+	3.44064i	−0.235550	+	0.160595i
$460$	−6.33462	−	1.95397i	−0.295353	−	0.0911043i
$461$	−1.76939	−	23.6108i	−0.0824085	−	1.09967i	−0.873129	−	0.487489i	$-0.837913\pi$
$461$	−1.76939	−	23.6108i	−0.0824085	−	1.09967i	0.790721	−	0.612177i	$-0.209706\pi$
$462$	−20.9833	+	26.3122i	−0.976232	+	1.22416i
$463$	−31.9547	+	9.85672i	−1.48506	+	0.458081i	−0.928060	−	0.372431i	$-0.878524\pi$
$463$	−31.9547	+	9.85672i	−1.48506	+	0.458081i	−0.557001	+	0.830512i	$0.688048\pi$
$464$	−2.45759	−	6.26185i	−0.114091	−	0.290699i
$465$	3.60328	+	15.7870i	0.167098	+	0.732105i
$466$	−1.91762	+	3.32141i	−0.0888318	+	0.153861i
$467$	13.0602	+	22.6209i	0.604354	+	1.04677i	0.992153	+	0.125028i	$0.0399022\pi$
$467$	13.0602	+	22.6209i	0.604354	+	1.04677i	−0.387799	+	0.921744i	$0.626765\pi$
$468$	0.0366502	−	0.0340064i	0.00169415	−	0.00157195i
$469$	−14.7641	−	18.5136i	−0.681742	−	0.854878i
$470$	4.10356	+	2.79776i	0.189283	+	0.129051i
$471$	46.1510	+	22.2251i	2.12653	+	1.02408i
$472$	8.55748			0.393890
$473$	24.9625	−	15.0823i	1.14778	−	0.693486i
$474$	−17.6787			−0.812012
$475$	−2.74835	−	1.32354i	−0.126103	−	0.0607280i
$476$	−6.89362	−	4.69999i	−0.315968	−	0.215424i
$477$	0.221242	+	0.277428i	0.0101300	+	0.0127026i
$478$	−10.7646	+	9.98812i	−0.492363	+	0.456846i
$479$	−10.9635	−	18.9894i	−0.500936	−	0.867646i	−0.999999	−	0.00108073i	$-0.999656\pi$
$479$	−10.9635	−	18.9894i	−0.500936	−	0.867646i	0.499064	−	0.866565i	$-0.333677\pi$
$480$	−1.10230	+	1.90924i	−0.0503130	+	0.0871447i
$481$	−0.0485378	−	0.212658i	−0.00221313	−	0.00969637i
$482$	−1.89337	−	4.82423i	−0.0862406	−	0.219737i
$483$	−47.9331	+	14.7854i	−2.18103	+	0.672760i
$484$	5.47515	−	6.86562i	0.248871	−	0.312074i
$485$	−0.640319	−	8.54446i	−0.0290754	−	0.387984i
$486$	16.2235	+	5.00428i	0.735913	+	0.226999i
$487$	4.17237	−	2.84467i	0.189068	−	0.128904i	−0.465087	−	0.885265i	$-0.653977\pi$
$487$	4.17237	−	2.84467i	0.189068	−	0.128904i	0.654155	+	0.756361i	$0.273025\pi$
$488$	12.4930	−	1.88301i	0.565531	−	0.0852401i
$489$	−7.02843	+	30.7935i	−0.317836	+	1.39253i
$490$	−3.50447	−	3.25167i	−0.158316	−	0.146896i
$491$	2.94839	−	39.3435i	0.133059	−	1.77555i	−0.387642	−	0.921810i	$-0.626710\pi$
$491$	2.94839	−	39.3435i	0.133059	−	1.77555i	0.520701	−	0.853739i	$-0.325671\pi$
$492$	1.07635	−	2.74250i	0.0485257	−	0.123641i
$493$	16.1693	+	2.43713i	0.728228	+	0.109763i
$494$	−0.0738642	+	0.0355711i	−0.00332331	+	0.00160042i
$495$	−7.45449	+	3.58990i	−0.335055	+	0.161354i
$496$	−7.26304	−	1.09473i	−0.326120	−	0.0491547i
$497$	0.486229	−	1.23889i	0.0218104	−	0.0555719i
$498$	0.954759	−	12.7404i	0.0427838	−	0.570910i
$499$	−13.9768	−	12.9686i	−0.625689	−	0.580555i	0.302277	−	0.953220i	$-0.402253\pi$
$499$	−13.9768	−	12.9686i	−0.625689	−	0.580555i	−0.927966	+	0.372666i	$0.878444\pi$
$500$	0.222521	−	0.974928i	0.00995144	−	0.0436001i
$501$	−54.9000	+	8.27484i	−2.45275	+	0.369692i
$502$	2.77093	−	1.88919i	0.123673	−	0.0843186i
$503$	8.59457	+	2.65107i	0.383213	+	0.118206i	0.480375	−	0.877063i	$-0.340500\pi$
$503$	8.59457	+	2.65107i	0.383213	+	0.118206i	−0.0971624	+	0.995269i	$0.530977\pi$
$504$	0.477155	+	6.36719i	0.0212542	+	0.283617i
$505$	7.70367	−	9.66010i	0.342809	−	0.429869i
$506$	28.1741	−	8.69055i	1.25249	−	0.386342i
$507$	−10.4700	−	26.6772i	−0.464991	−	1.18478i
$508$	1.83268	+	8.02952i	0.0813122	+	0.356252i
$509$	−11.7957	+	20.4307i	−0.522834	+	0.905574i	0.476813	+	0.879005i	$0.341792\pi$
$509$	−11.7957	+	20.4307i	−0.522834	+	0.905574i	−0.999647	+	0.0265697i	$0.991542\pi$
$510$	−2.67952	−	4.64107i	−0.118651	−	0.205510i
$511$	28.5172	−	26.4601i	1.26153	−	1.17053i
$512$	−0.623490	−	0.781831i	−0.0275546	−	0.0345524i
$513$	−6.33279	−	4.31762i	−0.279600	−	0.190628i
$514$	−7.42110	−	3.57381i	−0.327331	−	0.157634i
$515$	3.66527			0.161511
$516$	3.98538	−	13.8964i	0.175447	−	0.611753i
$517$	−22.0894			−0.971492
$518$	25.0982	+	12.0866i	1.10275	+	0.531056i
$519$	1.48973	+	1.01568i	0.0653919	+	0.0445835i
$520$	−0.0167568	−	0.0210124i	−0.000734835	−	0.000921454i
$521$	14.3995	−	13.3608i	0.630855	−	0.585348i	−0.298557	−	0.954392i	$-0.596505\pi$
$521$	14.3995	−	13.3608i	0.630855	−	0.585348i	0.929412	+	0.369044i	$0.120315\pi$
$522$	−6.25693	−	10.8373i	−0.273858	−	0.474336i
$523$	4.83908	−	8.38153i	0.211598	−	0.366499i	−0.740617	−	0.671928i	$-0.765467\pi$
$523$	4.83908	−	8.38153i	0.211598	−	0.366499i	0.952215	+	0.305429i	$0.0987999\pi$
$524$	−1.68447	−	7.38017i	−0.0735866	−	0.322404i
$525$	−2.76448	−	7.04379i	−0.120652	−	0.307416i
$526$	10.7595	−	3.31886i	0.469136	−	0.144709i
$527$	11.1322	−	13.9594i	0.484928	−	0.608081i
$528$	−0.732749	−	9.77786i	−0.0318888	−	0.425527i
$529$	20.0148	+	6.17375i	0.870210	+	0.268424i
$530$	0.157603	−	0.107452i	0.00684583	−	0.00466740i
$531$	15.7415	−	2.37265i	0.683124	−	0.102964i
$532$	2.32980	−	10.2075i	0.101009	−	0.442551i
$533$	0.0263282	+	0.0244290i	0.00114040	+	0.00105814i
$534$	−1.49445	+	19.9421i	−0.0646714	+	0.862980i
$535$	1.46324	−	3.72828i	0.0632615	−	0.161188i
$536$	6.82204	+	1.02826i	0.294667	+	0.0444140i
$537$	−5.60387	+	2.69868i	−0.241825	+	0.116457i
$538$	−18.5996	+	8.95711i	−0.801887	+	0.386168i
$539$	21.0251	+	3.16903i	0.905617	+	0.136500i
$540$	0.917965	−	2.33894i	0.0395029	−	0.100652i
$541$	−1.59229	+	21.2476i	−0.0684579	+	0.913508i	0.852220	+	0.523184i	$0.175256\pi$
$541$	−1.59229	+	21.2476i	−0.0684579	+	0.913508i	−0.920678	+	0.390324i	$0.872363\pi$
$542$	−21.0575	−	19.5385i	−0.904499	−	0.839252i
$543$	6.50039	−	28.4801i	0.278959	−	1.22220i
$544$	2.40369	−	0.362298i	0.103057	−	0.0155334i
$545$	−12.2710	+	8.36620i	−0.525630	+	0.358369i
$546$	−0.194331	−	0.0599431i	−0.00831659	−	0.00256533i
$547$	−0.675112	−	9.00875i	−0.0288657	−	0.385186i	−0.992862	−	0.119270i	$-0.961945\pi$
$547$	−0.675112	−	9.00875i	−0.0288657	−	0.385186i	0.963996	−	0.265916i	$-0.0856745\pi$
$548$	−11.4226	+	14.3234i	−0.487948	+	0.611867i
$549$	22.4588	−	6.92763i	0.958520	−	0.295664i
$550$	1.62490	+	4.14019i	0.0692861	+	0.176538i
$551$	4.56609	+	20.0054i	0.194522	+	0.852257i
$552$	7.30731	−	12.6566i	0.311020	−	0.538702i
$553$	13.7618	+	23.8361i	0.585212	+	1.01362i
$554$	−12.8217	+	11.8968i	−0.544742	+	0.505446i
$555$	11.1560	+	13.9891i	0.473545	+	0.593806i
$556$	−14.4063	−	9.82206i	−0.610964	−	0.416548i
$557$	29.8611	+	14.3804i	1.26526	+	0.609315i	0.941560	−	0.336846i	$-0.109360\pi$
$557$	29.8611	+	14.3804i	1.26526	+	0.609315i	0.323696	+	0.946161i	$0.395074\pi$
$558$	−13.6639			−0.578441
$559$	0.139947	+	0.107118i	0.00591912	+	0.00453060i
$560$	3.43230			0.145041
$561$	21.4747	+	10.3417i	0.906661	+	0.436625i
$562$	−3.63889	−	2.48095i	−0.153497	−	0.104653i
$563$	−6.11471	−	7.66760i	−0.257704	−	0.323151i	0.636101	−	0.771605i	$-0.280546\pi$
$563$	−6.11471	−	7.66760i	−0.257704	−	0.323151i	−0.893806	+	0.448455i	$0.851975\pi$
$564$	−8.02640	+	7.44741i	−0.337972	+	0.313592i
$565$	−4.02740	−	6.97566i	−0.169434	−	0.293468i
$566$	−13.8762	+	24.0343i	−0.583260	+	1.01024i
$567$	−8.49314	−	37.2109i	−0.356678	−	1.56271i
$568$	0.141663	+	0.360951i	0.00594405	+	0.0151452i
$569$	6.23337	−	1.92274i	0.261316	−	0.0806054i	−0.161329	−	0.986901i	$-0.551578\pi$
$569$	6.23337	−	1.92274i	0.261316	−	0.0806054i	0.422645	+	0.906295i	$0.361102\pi$
$570$	4.19297	−	5.25782i	0.175624	−	0.220226i
$571$	−2.94912	−	39.3533i	−0.123417	−	1.64688i	−0.624166	−	0.781291i	$-0.714561\pi$
$571$	−2.94912	−	39.3533i	−0.123417	−	1.64688i	0.500750	−	0.865592i	$-0.333058\pi$
$572$	0.114223	+	0.0352332i	0.00477592	+	0.00147318i
$573$	−34.1057	+	23.2528i	−1.42478	+	0.971401i
$574$	−4.53557	+	0.683627i	−0.189311	+	0.0285340i
$575$	−1.47512	+	6.46292i	−0.0615168	+	0.269523i
$576$	−1.36368	−	1.26531i	−0.0568202	−	0.0527214i
$577$	−2.27967	+	30.4201i	−0.0949039	+	1.26640i	0.722918	+	0.690933i	$0.242800\pi$
$577$	−2.27967	+	30.4201i	−0.0949039	+	1.26640i	−0.817822	+	0.575471i	$0.804819\pi$
$578$	4.05200	−	10.3243i	0.168541	−	0.429435i
$579$	13.3420	+	2.01099i	0.554476	+	0.0835739i
$580$	−6.06068	+	2.91867i	−0.251656	+	0.121191i
$581$	−17.9210	+	8.63030i	−0.743488	+	0.358045i
$582$	18.6790	+	2.81541i	0.774269	+	0.116702i
$583$	−0.309946	+	0.789729i	−0.0128366	+	0.0327072i
$584$	−0.847000	+	11.3024i	−0.0350491	+	0.467698i
$585$	−0.0366502	−	0.0340064i	−0.00151530	−	0.00140599i
$586$	−0.249852	+	1.09467i	−0.0103213	+	0.0452205i
$587$	−34.1283	+	5.14402i	−1.40863	+	0.212316i	−0.808927	−	0.587909i	$-0.799952\pi$
$587$	−34.1283	+	5.14402i	−1.40863	+	0.212316i	−0.599700	+	0.800225i	$0.704713\pi$
$588$	8.70812	−	5.93709i	0.359117	−	0.244842i
$589$	21.4103	+	6.60420i	0.882195	+	0.272121i
$590$	−0.639501	−	8.53355i	−0.0263278	−	0.351321i
$591$	27.2042	−	34.1130i	1.11903	−	1.40322i
$592$	−7.75552	+	2.39226i	−0.318750	+	0.0983213i
$593$	−7.96925	−	20.3053i	−0.327258	−	0.833840i	−0.995917	−	0.0902707i	$-0.971227\pi$
$593$	−7.96925	−	20.3053i	−0.327258	−	0.833840i	0.668659	−	0.743569i	$-0.266868\pi$
$594$	2.48672	+	10.8950i	0.102032	+	0.447029i
$595$	−4.17169	+	7.22557i	−0.171022	+	0.296220i
$596$	−1.42330	−	2.46524i	−0.0583008	−	0.100980i
$597$	−34.7955	+	32.2855i	−1.42408	+	1.32136i
$598$	0.111083	+	0.139294i	0.00454253	+	0.00569615i
$599$	35.1485	+	23.9638i	1.43613	+	0.979136i	0.996727	+	0.0808453i	$0.0257620\pi$
$599$	35.1485	+	23.9638i	1.43613	+	0.979136i	0.439402	+	0.898291i	$0.355190\pi$
$600$	1.98628	+	0.956542i	0.0810896	+	0.0390507i
$601$	25.1929			1.02764			0.513821	−	0.857898i	$-0.328230\pi$
$601$	25.1929			1.02764			0.513821	+	0.857898i	$0.328230\pi$
$602$	−21.8388	+	5.44399i	−0.890081	+	0.221880i
$603$	12.8343			0.522653
$604$	14.4012	+	6.93527i	0.585978	+	0.282192i
$605$	−7.25558	−	4.94677i	−0.294981	−	0.201115i
$606$	16.9835	+	21.2967i	0.689910	+	0.865119i
$607$	−7.23874	+	6.71657i	−0.293812	+	0.272617i	−0.813280	−	0.581872i	$-0.802320\pi$
$607$	−7.23874	+	6.71657i	−0.293812	+	0.272617i	0.519469	+	0.854490i	$0.326130\pi$
$608$	1.52522	+	2.64176i	0.0618558	+	0.107137i
$609$	−25.4506	+	44.0817i	−1.03131	+	1.78628i
$610$	−2.81135	−	12.3173i	−0.113828	−	0.498714i
$611$	−0.0487658	−	0.124253i	−0.00197285	−	0.00502675i
$612$	4.32115	−	1.33290i	0.174672	−	0.0538793i
$613$	−6.50068	+	8.15159i	−0.262560	+	0.329240i	−0.895584	−	0.444892i	$-0.853242\pi$
$613$	−6.50068	+	8.15159i	−0.262560	+	0.329240i	0.633024	+	0.774132i	$0.281813\pi$
$614$	−1.46652	−	19.5694i	−0.0591841	−	0.789757i
$615$	−2.81527	−	0.868394i	−0.113522	−	0.0350170i
$616$	−12.6130	+	8.59942i	−0.508194	+	0.346481i
$617$	7.79698	−	1.17521i	0.313895	−	0.0473120i	0.00979434	−	0.999952i	$-0.496882\pi$
$617$	7.79698	−	1.17521i	0.313895	−	0.0473120i	0.304100	+	0.952640i	$0.401644\pi$
$618$	−1.79808	+	7.87788i	−0.0723292	+	0.316895i
$619$	10.1406	+	9.40912i	0.407586	+	0.378185i	0.857153	−	0.515062i	$-0.172231\pi$
$619$	10.1406	+	9.40912i	0.407586	+	0.378185i	−0.449567	+	0.893247i	$0.648422\pi$
$620$	−0.548899	+	7.32454i	−0.0220443	+	0.294161i
$621$	−6.08531	+	15.5051i	−0.244195	+	0.622199i
$622$	1.34249	+	0.202348i	0.0538291	+	0.00811343i
$623$	28.0512	−	13.5087i	1.12385	−	0.541216i
$624$	0.0533830	−	0.0257079i	0.00213703	−	0.00102914i
$625$	−0.988831	−	0.149042i	−0.0395532	−	0.00596169i
$626$	4.89780	−	12.4794i	0.195756	−	0.498777i
$627$	−2.23521	+	29.8268i	−0.0892655	+	1.19117i
$628$	17.0324	+	15.8037i	0.679666	+	0.630637i
$629$	4.39010	−	19.2343i	0.175045	−	0.766922i
$630$	6.31373	−	0.951642i	0.251545	−	0.0379143i
$631$	14.5277	−	9.90483i	0.578339	−	0.394305i	−0.238524	−	0.971137i	$-0.576664\pi$
$631$	14.5277	−	9.90483i	0.578339	−	0.394305i	0.816863	+	0.576832i	$0.195711\pi$
$632$	−7.66275	−	2.36364i	−0.304808	−	0.0940207i
$633$	1.51383	+	20.2006i	0.0601693	+	0.802903i
$634$	−11.9338	+	14.9645i	−0.473951	+	0.594316i
$635$	7.87011	−	2.42761i	0.312316	−	0.0963366i
$636$	0.153634	+	0.391453i	0.00609199	+	0.0155221i
$637$	0.0285904	+	0.125263i	0.00113279	+	0.00496310i
$638$	14.9593	−	25.9102i	0.592244	−	1.02580i
$639$	0.360668	+	0.624695i	0.0142678	+	0.0247125i
$640$	−0.733052	+	0.680173i	−0.0289764	+	0.0268862i
$641$	−26.4959	−	33.2248i	−1.04653	−	1.31230i	−0.948382	−	0.317130i	$-0.897281\pi$
$641$	−26.4959	−	33.2248i	−1.04653	−	1.31230i	−0.0981438	−	0.995172i	$-0.531291\pi$
$642$	7.29549	+	4.97398i	0.287930	+	0.196307i
$643$	25.3948	+	12.2295i	1.00147	+	0.482283i	0.861438	−	0.507863i	$-0.169564\pi$
$643$	25.3948	+	12.2295i	1.00147	+	0.482283i	0.140034	+	0.990147i	$0.455279\pi$
$644$	−22.7531			−0.896599
$645$	−14.1553	−	2.93576i	−0.557366	−	0.115596i
$646$	−7.41513			−0.291744
$647$	30.3649	+	14.6230i	1.19377	+	0.574888i	0.921893	−	0.387445i	$-0.126642\pi$
$647$	30.3649	+	14.6230i	1.19377	+	0.574888i	0.271874	+	0.962333i	$0.412356\pi$
$648$	9.18794	+	6.26423i	0.360936	+	0.246082i
$649$	23.7304	+	29.7569i	0.931498	+	1.16806i
$650$	−0.0197014	+	0.0182802i	−0.000772752	+	0.000717009i
$651$	27.7896	+	48.1330i	1.08916	+	1.88648i
$652$	−7.16352	+	12.4076i	−0.280545	+	0.485918i
$653$	5.49238	+	24.0637i	0.214933	+	0.941685i	0.961160	+	0.275992i	$0.0890065\pi$
$653$	5.49238	+	24.0637i	0.214933	+	0.941685i	−0.746226	+	0.665692i	$0.768136\pi$
$654$	−11.9620	−	30.4786i	−0.467749	−	1.19181i
$655$	−7.23365	+	2.23129i	−0.282642	+	0.0871835i
$656$	0.833209	−	1.04481i	0.0325314	−	0.0407930i
$657$	1.57566	+	21.0257i	0.0614723	+	0.820291i
$658$	16.2893	+	5.02460i	0.635025	+	0.195879i
$659$	−32.5450	+	22.1888i	−1.26777	+	0.864353i	−0.995208	−	0.0977840i	$-0.968825\pi$
$659$	−32.5450	+	22.1888i	−1.26777	+	0.864353i	−0.272566	+	0.962137i	$0.587872\pi$
$660$	−9.69576	+	1.46140i	−0.377407	+	0.0568850i
$661$	−1.66550	+	7.29704i	−0.0647805	+	0.283822i	−0.996935	−	0.0782399i	$-0.975070\pi$
$661$	−1.66550	+	7.29704i	−0.0647805	+	0.283822i	0.932154	+	0.362062i	$0.117927\pi$
$662$	−8.02766	−	7.44858i	−0.312004	−	0.289497i
$663$	−0.0107633	+	0.143626i	−0.000418012	+	0.00557798i
$664$	2.11722	−	5.39459i	0.0821641	−	0.209351i
$665$	−10.3531	−	1.56047i	−0.401475	−	0.0605126i
$666$	−13.6030	+	6.55088i	−0.527107	+	0.253841i
$667$	40.1771	−	19.3482i	1.55566	−	0.749167i
$668$	−24.9024	−	3.75343i	−0.963503	−	0.145225i
$669$	−12.2294	+	31.1599i	−0.472814	+	1.20471i
$670$	0.515571	−	6.87981i	0.0199182	−	0.265790i
$671$	41.1915	+	38.2202i	1.59018	+	1.47547i
$672$	−1.68378	+	7.37714i	−0.0649534	+	0.284579i
$673$	28.7469	−	4.33290i	1.10811	−	0.167021i	0.430607	−	0.902539i	$-0.358299\pi$
$673$	28.7469	−	4.33290i	1.10811	−	0.167021i	0.677505	+	0.735518i	$0.263061\pi$
$674$	6.45555	−	4.40132i	0.248659	−	0.169533i
$675$	−2.40100	−	0.740609i	−0.0924143	−	0.0285061i
$676$	−0.971437	−	12.9629i	−0.0373630	−	0.498574i
$677$	−7.91418	+	9.92406i	−0.304166	+	0.381413i	−0.910299	−	0.413951i	$-0.864149\pi$
$677$	−7.91418	+	9.92406i	−0.304166	+	0.381413i	0.606133	+	0.795363i	$0.292720\pi$
$678$	16.9687	−	5.23416i	0.651680	−	0.201017i
$679$	−10.7444	−	27.3764i	−0.412334	−	1.05061i
$680$	−0.540913	−	2.36990i	−0.0207431	−	0.0908814i
$681$	9.19377	−	15.9241i	0.352306	−	0.610212i
$682$	−16.3341	−	28.2915i	−0.625466	−	1.08334i
$683$	34.2950	−	31.8211i	1.31226	−	1.21760i	0.352820	−	0.935691i	$-0.385223\pi$
$683$	34.2950	−	31.8211i	1.31226	−	1.21760i	0.959441	−	0.281909i	$-0.0909677\pi$
$684$	3.53810	+	4.43664i	0.135283	+	0.169639i
$685$	15.1370	+	10.3202i	0.578355	+	0.394316i
$686$	6.86307	+	3.30508i	0.262033	+	0.126189i
$687$	52.3586			1.99760
$688$	3.58538	−	5.49045i	0.136691	−	0.209321i
$689$	−0.00512649			−0.000195304
$690$	−13.1673	−	6.34104i	−0.501271	−	0.241399i
$691$	−26.9728	−	18.3897i	−1.02609	−	0.699578i	−0.0714841	−	0.997442i	$-0.522774\pi$
$691$	−26.9728	−	18.3897i	−1.02609	−	0.699578i	−0.954608	+	0.297864i	$0.903726\pi$
$692$	0.509919	+	0.639418i	0.0193842	+	0.0243070i
$693$	−20.8175	+	19.3158i	−0.790790	+	0.733746i
$694$	14.7262	+	25.5065i	0.558997	+	0.968212i
$695$	−8.71801	+	15.1000i	−0.330693	+	0.572777i
$696$	−3.30000	−	14.4582i	−0.125086	−	0.548038i
$697$	1.18681	+	3.02393i	0.0449535	+	0.114540i
$698$	23.5759	−	7.27220i	0.892361	−	0.275257i
$699$	−5.27171	+	6.61052i	−0.199394	+	0.250033i
$700$	−0.256496	−	3.42270i	−0.00969463	−	0.129366i
$701$	32.9182	+	10.1539i	1.24330	+	0.383508i	0.845506	−	0.533966i	$-0.179299\pi$
$701$	32.9182	+	10.1539i	1.24330	+	0.383508i	0.397796	+	0.917474i	$0.369775\pi$
$702$	−0.0557950	+	0.0380404i	−0.00210585	+	0.00143574i
$703$	24.4811	−	3.68993i	0.923323	−	0.139169i
$704$	0.989692	−	4.33612i	0.0373004	−	0.163424i
$705$	8.02640	+	7.44741i	0.302292	+	0.280486i
$706$	−1.36794	+	18.2538i	−0.0514829	+	0.686992i
$707$	15.4936	−	39.4770i	0.582696	−	1.48468i
$708$	18.6551	+	2.81181i	0.701103	+	0.105674i
$709$	−33.9414	+	16.3453i	−1.27470	+	0.613862i	−0.944022	−	0.329883i	$-0.892991\pi$
$709$	−33.9414	+	16.3453i	−1.27470	+	0.613862i	−0.330675	+	0.943745i	$0.607277\pi$
$710$	0.349356	−	0.168241i	0.0131111	−	0.00631397i
$711$	−14.7510	−	2.22336i	−0.553206	−	0.0833824i
$712$	−3.31402	+	8.44398i	−0.124198	+	0.316452i
$713$	3.63872	−	48.5553i	0.136271	−	1.81841i
$714$	−13.4836	−	12.5110i	−0.504612	−	0.468212i
$715$	0.0265988	−	0.116537i	0.000994739	−	0.00435824i
$716$	−2.78978	+	0.420491i	−0.104259	+	0.0157145i
$717$	−26.7486	+	18.2369i	−0.998945	+	0.681069i
$718$	17.6622	+	5.44806i	0.659147	+	0.203320i
$719$	0.714167	+	9.52989i	0.0266339	+	0.355405i	0.994560	+	0.104169i	$0.0332181\pi$
$719$	0.714167	+	9.52989i	0.0266339	+	0.355405i	−0.967926	+	0.251236i	$0.919163\pi$
$720$	−1.15987	+	1.45443i	−0.0432257	+	0.0542033i
$721$	12.0214	−	3.70811i	0.447700	−	0.138097i
$722$	3.54192	+	9.02466i	0.131817	+	0.335863i
$723$	−2.54237	−	11.1388i	−0.0945517	−	0.414258i
$724$	6.62534	−	11.4754i	0.246229	−	0.426481i
$725$	3.36343	+	5.82562i	0.124914	+	0.216358i
$726$	14.1916	−	13.1679i	0.526701	−	0.488707i
$727$	18.3319	+	22.9875i	0.679893	+	0.852559i	0.995344	−	0.0963831i	$-0.0307274\pi$
$727$	18.3319	+	22.9875i	0.679893	+	0.852559i	−0.315452	+	0.948942i	$0.602156\pi$
$728$	−0.0762171	−	0.0519639i	−0.00282479	−	0.00192591i
$729$	3.66576	+	1.76534i	0.135769	+	0.0653829i
$730$	11.3341			0.419494
$731$	7.20059	+	14.2210i	0.266323	+	0.525985i
$732$	27.8532			1.02948
$733$	−37.7345	−	18.1720i	−1.39376	−	0.671197i	−0.421871	−	0.906656i	$-0.638626\pi$
$733$	−37.7345	−	18.1720i	−1.39376	−	0.671197i	−0.971884	+	0.235459i	$0.924341\pi$
$734$	−24.3230	−	16.5832i	−0.897780	−	0.612096i
$735$	−6.57125	−	8.24009i	−0.242384	−	0.303940i
$736$	4.85950	−	4.50895i	0.179123	−	0.166202i
$737$	15.3423	+	26.5737i	0.565143	+	0.978856i
$738$	1.24301	−	2.15295i	0.0457558	−	0.0792513i
$739$	−4.32764	−	18.9606i	−0.159195	−	0.697478i	−0.990018	−	0.140941i	$-0.954987\pi$
$739$	−4.32764	−	18.9606i	−0.159195	−	0.697478i	0.830823	−	0.556536i	$-0.187870\pi$
$740$	2.96514	+	7.55506i	0.109001	+	0.277730i
$741$	−0.172710	+	0.0532741i	−0.00634468	+	0.00195707i
$742$	0.408199	−	0.511866i	0.0149855	−	0.0187912i
$743$	−3.15309	−	42.0751i	−0.115676	−	1.54359i	−0.689305	−	0.724471i	$-0.742084\pi$
$743$	−3.15309	−	42.0751i	−0.115676	−	1.54359i	0.573630	−	0.819115i	$-0.305535\pi$
$744$	−15.4736	−	4.77297i	−0.567289	−	0.174986i
$745$	−2.35198	+	1.60355i	−0.0861698	+	0.0587496i
$746$	−11.6177	+	1.75108i	−0.425353	+	0.0641116i
$747$	2.39893	−	10.5104i	0.0877723	−	0.384555i
$748$	7.92539	+	7.35369i	0.289781	+	0.268877i
$749$	1.02730	−	13.7084i	0.0375368	−	0.500894i
$750$	0.805433	−	2.05221i	0.0294102	−	0.0749361i
$751$	−34.7267	−	5.23421i	−1.26720	−	0.190999i	−0.519172	−	0.854670i	$-0.673760\pi$
$751$	−34.7267	−	5.23421i	−1.26720	−	0.190999i	−0.748025	+	0.663671i	$0.768998\pi$
$752$	−4.47471	+	2.15491i	−0.163176	+	0.0785814i
$753$	6.66132	−	3.20792i	0.242752	−	0.116903i
$754$	0.178770	+	0.0269453i	0.00651044	+	0.000981290i
$755$	5.83967	−	14.8792i	0.212527	−	0.541511i
$756$	0.644478	−	8.59996i	0.0234394	−	0.312777i
$757$	−11.2316	−	10.4214i	−0.408221	−	0.378773i	0.449164	−	0.893449i	$-0.351722\pi$
$757$	−11.2316	−	10.4214i	−0.408221	−	0.378773i	−0.857385	+	0.514676i	$0.827912\pi$
$758$	6.38346	−	27.9677i	0.231858	−	1.01583i
$759$	64.2745	−	9.68782i	2.33302	−	0.351646i
$760$	2.52039	−	1.71837i	0.0914241	−	0.0623319i
$761$	−1.98409	−	0.612011i	−0.0719232	−	0.0221854i	0.258585	−	0.965989i	$-0.416744\pi$
$761$	−1.98409	−	0.612011i	−0.0719232	−	0.0221854i	−0.330508	+	0.943803i	$0.607220\pi$
$762$	1.35689	+	18.1064i	0.0491548	+	0.655925i
$763$	−31.7824	+	39.8539i	−1.15060	+	1.44281i
$764$	−17.8918	+	5.51889i	−0.647302	+	0.199666i
$765$	−1.65209	−	4.20946i	−0.0597315	−	0.152193i
$766$	−5.21878	−	22.8650i	−0.188562	−	0.826145i
$767$	−0.114995	+	0.199177i	−0.00415222	+	0.00719185i
$768$	−1.10230	−	1.90924i	−0.0397759	−	0.0688939i
$769$	−10.6241	+	9.85775i	−0.383116	+	0.355479i	−0.848097	−	0.529841i	$-0.822252\pi$
$769$	−10.6241	+	9.85775i	−0.383116	+	0.355479i	0.464981	+	0.885321i	$0.346061\pi$
$770$	9.51795	+	11.9351i	0.343003	+	0.430112i
$771$	−15.0036	−	10.2293i	−0.540341	−	0.368398i
$772$	5.51416	+	2.65548i	0.198459	+	0.0955728i
$773$	−16.8070			−0.604504			−0.302252	−	0.953228i	$-0.597738\pi$
$773$	−16.8070			−0.604504			−0.302252	+	0.953228i	$0.597738\pi$
$774$	5.07304	−	11.0938i	0.182347	−	0.398758i
$775$	7.34508			0.263843
$776$	7.71988	+	3.71770i	0.277127	+	0.133458i
$777$	50.7421	+	34.5954i	1.82036	+	1.24110i
$778$	7.75017	+	9.71840i	0.277857	+	0.348422i
$779$	−2.98828	+	2.77272i	−0.107066	+	0.0993430i
$780$	−0.0296253	−	0.0513125i	−0.00106076	−	0.00183728i
$781$	−0.862298	+	1.49354i	−0.0308554	+	0.0534432i
$782$	3.58578	+	15.7103i	0.128227	+	0.561801i
$783$	6.17501	+	15.7337i	0.220677	+	0.562276i
$784$	4.56827	−	1.40912i	0.163152	−	0.0503259i
$785$	14.4867	−	18.1658i	0.517053	−	0.648364i
$786$	−1.24715	−	16.6421i	−0.0444845	−	0.593604i
$787$	−8.70176	−	2.68414i	−0.310184	−	0.0956791i	0.135755	−	0.990742i	$-0.456654\pi$
$787$	−8.70176	−	2.68414i	−0.310184	−	0.0956791i	−0.445939	+	0.895063i	$0.647130\pi$
$788$	16.3524	−	11.1489i	0.582530	−	0.397162i
$789$	24.5460	−	3.69972i	0.873861	−	0.131713i
$790$	−1.78440	+	7.81795i	−0.0634860	+	0.278150i
$791$	−20.2663	−	18.8044i	−0.720587	−	0.668607i
$792$	0.618307	−	8.25073i	0.0219706	−	0.293177i
$793$	−0.124052	+	0.316080i	−0.00440523	+	0.0112243i
$794$	19.9587	+	3.00830i	0.708309	+	0.106760i
$795$	0.378877	−	0.182458i	0.0134374	−	0.00647111i
$796$	−19.3985	+	9.34180i	−0.687560	+	0.331111i
$797$	3.09572	+	0.466605i	0.109656	+	0.0165280i	0.203641	−	0.979046i	$-0.434722\pi$
$797$	3.09572	+	0.466605i	0.109656	+	0.0165280i	−0.0939850	+	0.995574i	$0.529961\pi$
$798$	8.43288	−	21.4866i	0.298521	−	0.760619i
$799$	0.902210	−	12.0391i	0.0319179	−	0.425915i
$800$	0.733052	+	0.680173i	0.0259173	+	0.0240477i
$801$	−3.75497	+	16.4516i	−0.132675	+	0.581289i
$802$	15.0945	−	2.27513i	0.533004	−	0.0803375i
$803$	−41.6507	+	28.3970i	−1.46982	+	1.00211i
$804$	14.5341	+	4.48317i	0.512577	+	0.158109i
$805$	1.70034	+	22.6895i	0.0599293	+	0.799700i
$806$	0.123080	−	0.154338i	0.00433531	−	0.00543631i
$807$	−43.4900	+	13.4149i	−1.53092	+	0.472226i
$808$	4.51405	+	11.5016i	0.158804	+	0.404626i
$809$	−8.03486	−	35.2030i	−0.282491	−	1.23767i	−0.894589	−	0.446890i	$-0.852531\pi$
$809$	−8.03486	−	35.2030i	−0.282491	−	1.23767i	0.612098	−	0.790782i	$-0.290326\pi$
$810$	5.56010	−	9.63037i	0.195362	−	0.338377i
$811$	21.9608	+	38.0371i	0.771147	+	1.33566i	0.936935	+	0.349504i	$0.113650\pi$
$811$	21.9608	+	38.0371i	0.771147	+	1.33566i	−0.165788	+	0.986161i	$0.553017\pi$
$812$	−16.9251	+	15.7042i	−0.593955	+	0.551109i
$813$	−39.4851	−	49.5127i	−1.38480	−	1.73649i
$814$	−29.8251	−	20.3344i	−1.04537	−	0.712721i
$815$	12.9082	+	6.21627i	0.452155	+	0.217746i
$816$	5.35905			0.187604
$817$	−13.3110	+	14.9311i	−0.465694	+	0.522374i
$818$	−3.35303			−0.117236
$819$	−0.154609	−	0.0744560i	−0.00540249	−	0.00260170i
$820$	−1.10416	−	0.752801i	−0.0385588	−	0.0262889i
$821$	1.84546	+	2.31413i	0.0644069	+	0.0807637i	0.812991	−	0.582276i	$-0.197838\pi$
$821$	1.84546	+	2.31413i	0.0644069	+	0.0807637i	−0.748584	+	0.663039i	$0.769266\pi$
$822$	−29.6074	+	27.4716i	−1.03268	+	0.958183i
$823$	0.541135	+	0.937274i	0.0188628	+	0.0326713i	0.875303	−	0.483575i	$-0.160662\pi$
$823$	0.541135	+	0.937274i	0.0188628	+	0.0326713i	−0.856440	+	0.516247i	$0.827329\pi$
$824$	−1.83264	+	3.17422i	−0.0638429	+	0.110579i
$825$	2.18188	+	9.55944i	0.0759633	+	0.332817i
$826$	−10.7307	−	27.3414i	−0.373370	−	0.951331i
$827$	30.9919	−	9.55975i	1.07770	−	0.332425i	0.295426	−	0.955366i	$-0.404538\pi$
$827$	30.9919	−	9.55975i	1.07770	−	0.332425i	0.782269	+	0.622941i	$0.214062\pi$
$828$	7.68892	−	9.64160i	0.267208	−	0.335069i
$829$	0.594726	+	7.93606i	0.0206557	+	0.275631i	0.997963	+	0.0638025i	$0.0203228\pi$
$829$	0.594726	+	7.93606i	0.0206557	+	0.275631i	−0.977307	+	0.211828i	$0.932058\pi$
$830$	−5.53772	−	1.70816i	−0.192217	−	0.0592912i
$831$	−31.8601	+	21.7219i	−1.10521	+	0.753523i
$832$	0.0265757	−	0.00400564i	0.000921345	−	0.000138870i
$833$	−2.58592	+	11.3297i	−0.0895969	+	0.392550i
$834$	−28.1782	−	26.1455i	−0.975730	−	0.905345i
$835$	−1.88198	+	25.1133i	−0.0651286	+	0.869080i
$836$	−4.95667	+	12.6294i	−0.171430	+	0.436796i
$837$	18.2493	+	2.75064i	0.630788	+	0.0950760i
$838$	−1.62254	+	0.781374i	−0.0560497	+	0.0269921i
$839$	4.16860	−	2.00749i	0.143916	−	0.0693063i	−0.360540	−	0.932744i	$-0.617407\pi$
$839$	4.16860	−	2.00749i	0.143916	−	0.0693063i	0.504456	+	0.863438i	$0.331693\pi$
$840$	7.48234	+	1.12778i	0.258165	+	0.0389122i
$841$	5.93698	−	15.1272i	0.204723	−	0.521627i
$842$	2.86569	−	38.2400i	0.0987583	−	1.31784i
$843$	−7.11752	−	6.60409i	−0.245140	−	0.227457i
$844$	−2.04466	+	8.95825i	−0.0703801	+	0.308356i
$845$	−12.8541	+	1.93744i	−0.442194	+	0.0666500i
$846$	−7.63378	+	5.20463i	−0.262455	+	0.178939i
$847$	−28.8015	−	8.88409i	−0.989632	−	0.305261i
$848$	0.0142546	+	0.190214i	0.000489503	+	0.00653197i
$849$	−38.1470	+	47.8349i	−1.30920	+	1.64169i
$850$	−2.32285	+	0.716503i	−0.0796730	+	0.0245759i
$851$	−19.6563	−	50.0835i	−0.673810	−	1.71684i
$852$	0.190222	+	0.833415i	0.00651688	+	0.0285523i
$853$	−27.5520	+	47.7214i	−0.943362	+	1.63395i	−0.184362	+	0.982858i	$0.559022\pi$
$853$	−27.5520	+	47.7214i	−0.943362	+	1.63395i	−0.758999	+	0.651092i	$0.774311\pi$
$854$	−21.6820	−	37.5543i	−0.741942	−	1.28508i
$855$	4.15983	−	3.85976i	0.142263	−	0.132001i
$856$	2.49717	+	3.13135i	0.0853514	+	0.107027i
$857$	−42.8889	−	29.2411i	−1.46506	−	0.998858i	−0.993104	−	0.117233i	$-0.962597\pi$
$857$	−42.8889	−	29.2411i	−1.46506	−	0.998858i	−0.471951	−	0.881625i	$-0.656450\pi$
$858$	0.237428	+	0.114339i	0.00810566	+	0.00390348i
$859$	−11.6396			−0.397140			−0.198570	−	0.980087i	$-0.563630\pi$
$859$	−11.6396			−0.397140			−0.198570	+	0.980087i	$0.563630\pi$
$860$	−5.74303	−	3.16505i	−0.195836	−	0.107927i
$861$	−10.1121			−0.344619
$862$	−13.4433	−	6.47396i	−0.457881	−	0.220504i
$863$	−28.7918	−	19.6299i	−0.980084	−	0.668210i	−0.0364967	−	0.999334i	$-0.511620\pi$
$863$	−28.7918	−	19.6299i	−0.980084	−	0.668210i	−0.943587	+	0.331124i	$0.892572\pi$
$864$	1.56660	+	1.96445i	0.0532967	+	0.0668319i
$865$	0.599524	−	0.556277i	0.0203844	−	0.0189140i
$866$	8.46498	+	14.6618i	0.287652	+	0.498227i
$867$	12.2256	−	21.1754i	0.415205	−	0.719156i
$868$	5.60986	+	24.5784i	0.190411	+	0.834246i
$869$	−13.0301	−	33.2002i	−0.442016	−	1.12624i
$870$	−14.1712	+	4.37123i	−0.480448	+	0.148199i
$871$	−0.115607	+	0.144967i	−0.00391719	+	0.00491200i
$872$	−1.10986	−	14.8101i	−0.0375846	−	0.501532i
$873$	15.2315	+	4.69831i	0.515509	+	0.159014i
$874$	−16.7080	+	11.3913i	−0.565156	+	0.385317i
$875$	−3.39396	+	0.511557i	−0.114737	+	0.0172938i
$876$	−5.56019	+	24.3608i	−0.187861	+	0.823074i
$877$	−26.9792	−	25.0330i	−0.911023	−	0.845305i	0.0774049	−	0.997000i	$-0.475337\pi$
$877$	−26.9792	−	25.0330i	−0.911023	−	0.845305i	−0.988427	+	0.151694i	$0.951527\pi$
$878$	−0.618630	+	8.25505i	−0.0208778	+	0.278594i
$879$	−0.904359	+	2.30427i	−0.0305033	+	0.0777211i
$880$	−4.39796	−	0.662886i	−0.148255	−	0.0223459i
$881$	−0.396666	+	0.191024i	−0.0133640	+	0.00643578i	−0.440554	−	0.897726i	$-0.645218\pi$
$881$	−0.396666	+	0.191024i	−0.0133640	+	0.00643578i	0.427190	+	0.904162i	$0.359504\pi$
$882$	8.01266	−	3.85869i	0.269800	−	0.129929i
$883$	−1.87721	−	0.282944i	−0.0631731	−	0.00952182i	0.117380	−	0.993087i	$-0.462551\pi$
$883$	−1.87721	−	0.282944i	−0.0631731	−	0.00952182i	−0.180553	+	0.983565i	$0.557789\pi$
$884$	−0.0238681	+	0.0608148i	−0.000802770	+	0.00204542i
$885$	1.40985	−	18.8131i	0.0473915	−	0.632396i
$886$	−17.2971	−	16.0493i	−0.581106	−	0.539188i
$887$	11.7084	−	51.2977i	0.393128	−	1.72241i	−0.260397	−	0.965502i	$-0.583853\pi$
$887$	11.7084	−	51.2977i	0.393128	−	1.72241i	0.653525	−	0.756905i	$-0.273289\pi$
$888$	−17.6929	+	2.66678i	−0.593736	+	0.0894913i
$889$	23.3565	−	15.9242i	0.783351	−	0.534080i
$890$	8.66803	+	2.67373i	0.290553	+	0.0896237i
$891$	3.69604	+	49.3203i	0.123822	+	1.65229i
$892$	−9.46682	+	11.8710i	−0.316972	+	0.397471i
$893$	14.4771	−	4.46559i	0.484457	−	0.149435i
$894$	−2.29275	−	5.84184i	−0.0766811	−	0.195380i
$895$	0.627796	+	2.75055i	0.0209849	+	0.0919409i
$896$	−1.71615	+	2.97246i	−0.0573325	+	0.0993028i
$897$	0.196390	+	0.340157i	0.00655727	+	0.0113575i
$898$	−1.98049	+	1.83762i	−0.0660897	+	0.0613223i
$899$	−30.8062	−	38.6297i	−1.02744	−	1.28837i
$900$	1.53704	+	1.04794i	0.0512346	+	0.0349312i
$901$	−0.417758	−	0.201182i	−0.0139175	−	0.00670233i
$902$	5.94366			0.197902
$903$	−49.3969	+	4.69203i	−1.64382	+	0.156141i
$904$	8.05480			0.267899
$905$	−11.9384	−	5.74925i	−0.396847	−	0.191112i
$906$	29.1156	+	19.8507i	0.967302	+	0.659496i
$907$	−29.8441	−	37.4233i	−0.990957	−	1.24262i	−0.970067	−	0.242839i	$-0.921921\pi$
$907$	−29.8441	−	37.4233i	−0.990957	−	1.24262i	−0.0208906	−	0.999782i	$-0.506650\pi$
$908$	6.11403	−	5.67299i	0.202901	−	0.188265i
$909$	11.4926	+	19.9057i	0.381185	+	0.660231i
$910$	−0.0461229	+	0.0798872i	−0.00152896	+	0.00264824i
$911$	8.21247	+	35.9812i	0.272091	+	1.19211i	0.907540	+	0.419966i	$0.137958\pi$
$911$	8.21247	+	35.9812i	0.272091	+	1.19211i	−0.635449	+	0.772143i	$0.719185\pi$
$912$	2.45692	+	6.26014i	0.0813568	+	0.207294i
$913$	24.6298	−	7.59728i	0.815127	−	0.251433i
$914$	−1.63501	+	2.05024i	−0.0540814	+	0.0678159i
$915$	−2.08147	−	27.7753i	−0.0688113	−	0.918224i
$916$	22.6945	+	7.00033i	0.749848	+	0.231297i
$917$	−21.4676	+	14.6364i	−0.708923	+	0.483336i
$918$	−6.03957	+	0.910319i	−0.199336	+	0.0300450i
$919$	−2.93792	+	12.8719i	−0.0969132	+	0.424604i	−0.999988	−	0.00487869i	$-0.998447\pi$
$919$	−2.93792	+	12.8719i	−0.0969132	+	0.424604i	0.903075	+	0.429483i	$0.141304\pi$
$920$	−4.85950	−	4.50895i	−0.160213	−	0.148656i
$921$	3.23311	−	43.1428i	0.106535	−	1.42160i
$922$	8.65019	−	22.0403i	0.284879	−	0.725859i
$923$	−0.0103049	−	0.00155321i	−0.000339189	−	5.11244e-5i
$924$	−30.3218	+	14.6022i	−0.997513	+	0.480377i
$925$	7.31235	−	3.52144i	0.240429	−	0.115784i
$926$	−33.0669	−	4.98403i	−1.08664	−	0.163785i
$927$	−2.49106	+	6.34711i	−0.0818171	+	0.208467i
$928$	0.502698	−	6.70804i	0.0165019	−	0.220202i
$929$	−26.5136	−	24.6010i	−0.869883	−	0.807133i	0.112570	−	0.993644i	$-0.464092\pi$
$929$	−26.5136	−	24.6010i	−0.869883	−	0.807133i	−0.982453	+	0.186511i	$0.940282\pi$
$930$	−3.60328	+	15.7870i	−0.118156	+	0.517676i
$931$	−14.4202	+	2.17350i	−0.472604	+	0.0712335i
$932$	−3.16882	+	2.16046i	−0.103798	+	0.0707683i
$933$	2.86012	+	0.882231i	0.0936362	+	0.0288829i
$934$	1.95198	+	26.0474i	0.0638708	+	0.852296i
$935$	6.74086	−	8.45277i	0.220450	−	0.276435i
$936$	0.0477755	−	0.0147368i	0.00156159	−	0.000481687i
$937$	17.9858	+	45.8271i	0.587570	+	1.49710i	0.847134	+	0.531379i	$0.178326\pi$
$937$	17.9858	+	45.8271i	0.587570	+	1.49710i	−0.259564	+	0.965726i	$0.583579\pi$
$938$	−5.26924	−	23.0861i	−0.172047	−	0.753787i
$939$	14.7776	−	25.5955i	0.482249	−	0.835279i
$940$	2.48328	+	4.30116i	0.0809956	+	0.140288i
$941$	−14.3622	+	13.3262i	−0.468196	+	0.434422i	−0.878655	−	0.477457i	$-0.841559\pi$
$941$	−14.3622	+	13.3262i	−0.468196	+	0.434422i	0.410459	+	0.911879i	$0.365368\pi$
$942$	31.9375	+	40.0483i	1.04058	+	1.30484i
$943$	7.31959	+	4.99041i	0.238359	+	0.162510i
$944$	7.71002	+	3.71295i	0.250940	+	0.120846i
$945$	−8.62407			−0.280541
$946$	29.0344	−	2.75787i	0.943990	−	0.0896661i
$947$	0.0496601			0.00161374			0.000806869	−	1.00000i	$-0.499743\pi$
$947$	0.0496601			0.00161374			0.000806869		1.00000i	$0.499743\pi$
$948$	−15.9280	−	7.67052i	−0.517317	−	0.249127i
$949$	−0.251684	−	0.171595i	−0.00817000	−	0.00557021i
$950$	−1.90192	−	2.38493i	−0.0617063	−	0.0773773i
$951$	−30.9325	+	28.7011i	−1.00305	+	0.930698i
$952$	−4.17169	−	7.22557i	−0.135205	−	0.234182i
$953$	7.68906	−	13.3178i	0.249073	−	0.431407i	−0.714196	−	0.699946i	$-0.753207\pi$
$953$	7.68906	−	13.3178i	0.249073	−	0.431407i	0.963269	+	0.268539i	$0.0865407\pi$
$954$	0.0789602	+	0.345947i	0.00255643	+	0.0112005i
$955$	6.84051	+	17.4293i	0.221354	+	0.564000i
$956$	−14.0323	+	4.32839i	−0.453837	+	0.139990i
$957$	41.1245	−	51.5685i	1.32937	−	1.66697i
$958$	−1.63861	−	21.8657i	−0.0529410	−	0.706449i
$959$	60.0873	+	18.5345i	1.94032	+	0.598510i
$960$	−1.82153	+	1.24190i	−0.0587896	+	0.0400821i
$961$	−22.6939	+	3.42055i	−0.732061	+	0.110340i
$962$	0.0485378	−	0.212658i	0.00156492	−	0.00685637i
$963$	5.46175	+	5.06777i	0.176003	+	0.163306i
$964$	0.387286	−	5.16798i	0.0124737	−	0.166449i
$965$	2.23598	−	5.69719i	0.0719788	−	0.183399i
$966$	−49.6014	−	7.47621i	−1.59590	−	0.240543i
$967$	43.8621	−	21.1229i	1.41051	−	0.679266i	0.435246	−	0.900311i	$-0.356661\pi$
$967$	43.8621	−	21.1229i	1.41051	−	0.679266i	0.975263	+	0.221046i	$0.0709471\pi$
$968$	7.91182	−	3.81013i	0.254296	−	0.122462i
$969$	−16.1649	−	2.43646i	−0.519290	−	0.0782703i
$970$	3.13039	−	7.97612i	0.100511	−	0.256098i
$971$	0.875463	−	11.6822i	0.0280950	−	0.374901i	−0.965380	−	0.260848i	$-0.915998\pi$
$971$	0.875463	−	11.6822i	0.0280950	−	0.374901i	0.993475	−	0.114053i	$-0.0363832\pi$
$972$	12.4456	+	11.5478i	0.399192	+	0.370396i
$973$	−13.3169	+	58.3451i	−0.426920	+	1.87046i
$974$	4.99343	−	0.752638i	0.160000	−	0.0241161i
$975$	−0.0489552	+	0.0333771i	−0.00156782	+	0.00106892i
$976$	12.0728	+	3.72397i	0.386441	+	0.119201i
$977$	−3.25328	−	43.4120i	−0.104082	−	1.38887i	−0.767704	−	0.640804i	$-0.778601\pi$
$977$	−3.25328	−	43.4120i	−0.104082	−	1.38887i	0.663623	−	0.748067i	$-0.269018\pi$
$978$	−19.6932	+	24.6945i	−0.629719	+	0.789643i
$979$	−38.5522	+	11.8918i	−1.23213	+	0.380063i
$980$	−1.74657	−	4.45019i	−0.0557922	−	0.142156i
$981$	−6.14785	−	26.9355i	−0.196286	−	0.859983i
$982$	19.7269	−	34.1680i	0.629512	−	1.09035i
$983$	1.52815	+	2.64683i	0.0487403	+	0.0844207i	0.889366	−	0.457195i	$-0.151146\pi$
$983$	1.52815	+	2.64683i	0.0487403	+	0.0844207i	−0.840626	+	0.541616i	$0.817813\pi$
$984$	2.15968	−	2.00389i	0.0688482	−	0.0638818i
$985$	−12.3397	−	15.4735i	−0.393176	−	0.493027i
$986$	13.5106	+	9.21136i	0.430265	+	0.293349i
$987$	33.8595	+	16.3059i	1.07776	+	0.519022i
$988$	−0.0819831			−0.00260823
$989$	38.0713	+	20.9816i	1.21060	+	0.667175i
$990$	−8.27386			−0.262961
$991$	−40.5784	−	19.5415i	−1.28901	−	0.620756i	−0.341323	−	0.939946i	$-0.610875\pi$
$991$	−40.5784	−	19.5415i	−1.28901	−	0.620756i	−0.947691	+	0.319190i	$0.896589\pi$
$992$	−6.06879	−	4.13763i	−0.192684	−	0.131370i
$993$	−15.0527	−	18.8755i	−0.477683	−	0.598996i
$994$	0.975613	−	0.905236i	0.0309446	−	0.0287124i
$995$	10.7653	+	18.6461i	0.341284	+	0.591121i
$996$	6.38805	−	11.0644i	0.202413	−	0.350590i
$997$	−5.11288	−	22.4010i	−0.161927	−	0.709446i	−0.989069	−	0.147454i	$-0.952892\pi$
$997$	−5.11288	−	22.4010i	−0.161927	−	0.709446i	0.827142	−	0.561992i	$-0.189965\pi$
$998$	−6.96583	−	17.7486i	−0.220499	−	0.561823i
$999$	19.4867	−	6.01085i	0.616532	−	0.190175i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.d.111.5	yes	60
43.31	even	21	inner	430.2.q.d.31.5	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.d.31.5	✓	60	43.31	even	21	inner
430.2.q.d.111.5	yes	60	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.900969 + 0.433884i) q^{2} +(1.82153 + 1.24190i) q^{3} +(0.623490 + 0.781831i) q^{4} +(0.733052 - 0.680173i) q^{5} +(1.10230 + 1.90924i) q^{6} +(1.71615 - 2.97246i) q^{7} +(0.222521 + 0.974928i) q^{8} +(0.679638 + 1.73169i) q^{9} +O(q^{10})\)	\(q+(0.900969 + 0.433884i) q^{2} +(1.82153 + 1.24190i) q^{3} +(0.623490 + 0.781831i) q^{4} +(0.733052 - 0.680173i) q^{5} +(1.10230 + 1.90924i) q^{6} +(1.71615 - 2.97246i) q^{7} +(0.222521 + 0.974928i) q^{8} +(0.679638 + 1.73169i) q^{9} +(0.955573 - 0.294755i) q^{10} +(-2.77306 + 3.47730i) q^{11} +(0.164750 + 2.19844i) q^{12} +(-0.0256818 - 0.00792179i) q^{13} +(2.83590 - 1.93348i) q^{14} +(2.17998 - 0.328579i) q^{15} +(-0.222521 + 0.974928i) q^{16} +(-1.78193 - 1.65339i) q^{17} +(-0.139019 + 1.85508i) q^{18} +(1.11445 - 2.83957i) q^{19} +(0.988831 + 0.149042i) q^{20} +(6.81750 - 3.28314i) q^{21} +(-4.00718 + 1.92976i) q^{22} +(-6.55509 - 0.988021i) q^{23} +(-0.805433 + 2.05221i) q^{24} +(0.0747301 - 0.997204i) q^{25} +(-0.0197014 - 0.0182802i) q^{26} +(0.559111 - 2.44963i) q^{27} +(3.39396 - 0.511557i) q^{28} +(-5.55798 + 3.78937i) q^{29} +(2.10666 + 0.649819i) q^{30} +(0.548899 + 7.32454i) q^{31} +(-0.623490 + 0.781831i) q^{32} +(-9.36966 + 2.89016i) q^{33} +(-0.888086 - 2.26281i) q^{34} +(-0.763758 - 3.34624i) q^{35} +(-0.930142 + 1.61105i) q^{36} +(4.05805 + 7.02874i) q^{37} +(2.23613 - 2.07482i) q^{38} +(-0.0369422 - 0.0463240i) q^{39} +(0.826239 + 0.563320i) q^{40} +(-1.20402 - 0.579827i) q^{41} +7.56686 q^{42} +(-6.15062 - 2.27375i) q^{43} -4.44764 q^{44} +(1.67606 + 0.807147i) q^{45} +(-5.47724 - 3.73432i) q^{46} +(3.09660 + 3.88301i) q^{47} +(-1.61609 + 1.49951i) q^{48} +(-2.39033 - 4.14017i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-1.19250 - 5.22468i) q^{51} +(-0.00981885 - 0.0250180i) q^{52} +(0.182273 - 0.0562237i) q^{53} +(1.56660 - 1.96445i) q^{54} +(0.332372 + 4.43520i) q^{55} +(3.27981 + 1.01169i) q^{56} +(5.55646 - 3.78833i) q^{57} +(-6.65172 + 1.00259i) q^{58} +(1.90422 - 8.34293i) q^{59} +(1.61609 + 1.49951i) q^{60} +(0.944147 - 12.5988i) q^{61} +(-2.68346 + 6.83734i) q^{62} +(6.31373 + 0.951642i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(-0.0242143 + 0.0116610i) q^{65} +(-9.69576 - 1.46140i) q^{66} +(2.52053 - 6.42219i) q^{67} +(0.181657 - 2.42405i) q^{68} +(-10.7133 - 9.94046i) q^{69} +(0.763758 - 3.34624i) q^{70} +(0.383425 - 0.0577920i) q^{71} +(-1.53704 + 1.04794i) q^{72} +(10.8306 + 3.34079i) q^{73} +(0.606517 + 8.09340i) q^{74} +(1.37455 - 1.72363i) q^{75} +(2.91491 - 0.899132i) q^{76} +(5.57715 + 14.2103i) q^{77} +(-0.0131845 - 0.0577651i) q^{78} +(-4.00950 + 6.94466i) q^{79} +(0.500000 + 0.866025i) q^{80} +(8.15168 - 7.56365i) q^{81} +(-0.833209 - 1.04481i) q^{82} +(-4.78821 - 3.26455i) q^{83} +(6.81750 + 3.28314i) q^{84} -2.43084 q^{85} +(-4.55497 - 4.71723i) q^{86} -14.8300 q^{87} +(-4.00718 - 1.92976i) q^{88} +(7.49483 + 5.10989i) q^{89} +(1.15987 + 1.45443i) q^{90} +(-0.0676210 + 0.0627431i) q^{91} +(-3.31457 - 5.74100i) q^{92} +(-8.09650 + 14.0236i) q^{93} +(1.10516 + 4.84203i) q^{94} +(-1.11445 - 2.83957i) q^{95} +(-2.10666 + 0.649819i) q^{96} +(5.34232 - 6.69906i) q^{97} +(-0.357259 - 4.76729i) q^{98} +(-7.90628 - 2.43876i) 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

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