LMFDB - Embedded newform 430.2.q.c.101.2

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:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			101.2
Character	$\chi$	$=$	430.101
Dual form			430.2.q.c.281.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.623490 + 0.781831i) q^{2} +(-0.399818 + 1.01872i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(0.0747301 + 0.997204i) q^{5} +(-0.547184 - 0.947751i) q^{6} +(0.630880 - 1.09272i) q^{7} +(0.900969 + 0.433884i) q^{8} +(1.32122 + 1.22591i) q^{9} +O(q^{10})$	\(q+(-0.623490 + 0.781831i) q^{2} +(-0.399818 + 1.01872i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(0.0747301 + 0.997204i) q^{5} +(-0.547184 - 0.947751i) q^{6} +(0.630880 - 1.09272i) q^{7} +(0.900969 + 0.433884i) q^{8} +(1.32122 + 1.22591i) q^{9} +(-0.826239 - 0.563320i) q^{10} +(-0.732965 + 3.21133i) q^{11} +(1.08215 + 0.163107i) q^{12} +(2.31740 - 1.57998i) q^{13} +(0.460972 + 1.17454i) q^{14} +(-1.04575 - 0.322571i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-0.182980 + 2.44170i) q^{17} +(-1.78223 + 0.268627i) q^{18} +(-4.49988 + 4.17527i) q^{19} +(0.955573 - 0.294755i) q^{20} +(0.860933 + 1.07958i) q^{21} +(-2.05372 - 2.57529i) q^{22} +(1.64063 - 0.506066i) q^{23} +(-0.802229 + 0.744360i) q^{24} +(-0.988831 + 0.149042i) q^{25} +(-0.209600 + 2.79691i) q^{26} +(-4.73509 + 2.28030i) q^{27} +(-1.20570 - 0.371910i) q^{28} +(1.72132 + 4.38584i) q^{29} +(0.904210 - 0.616480i) q^{30} +(-0.849461 - 0.128036i) q^{31} +(0.222521 - 0.974928i) q^{32} +(-2.97839 - 2.03063i) q^{33} +(-1.79491 - 1.66543i) q^{34} +(1.13681 + 0.547457i) q^{35} +(0.901178 - 1.56089i) q^{36} +(-5.77132 - 9.99623i) q^{37} +(-0.458734 - 6.12139i) q^{38} +(0.683014 + 2.99248i) q^{39} +(-0.365341 + 0.930874i) q^{40} +(-4.93530 + 6.18867i) q^{41} -1.38083 q^{42} +(2.32629 + 6.13094i) q^{43} +3.29392 q^{44} +(-1.12375 + 1.40914i) q^{45} +(-0.627255 + 1.59822i) q^{46} +(-1.78908 - 7.83846i) q^{47} +(-0.0817823 - 1.09131i) q^{48} +(2.70398 + 4.68343i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-2.41425 - 1.16264i) q^{51} +(-2.05603 - 1.90772i) q^{52} +(8.44899 + 5.76042i) q^{53} +(1.16947 - 5.12378i) q^{54} +(-3.25713 - 0.490933i) q^{55} +(1.04251 - 0.710774i) q^{56} +(-2.45430 - 6.25346i) q^{57} +(-4.50221 - 1.38875i) q^{58} +(-0.464629 + 0.223754i) q^{59} +(-0.0817823 + 1.09131i) q^{60} +(0.129724 - 0.0195528i) q^{61} +(0.629732 - 0.584306i) q^{62} +(2.17311 - 0.670315i) q^{63} +(0.623490 + 0.781831i) q^{64} +(1.74874 + 2.19285i) q^{65} +(3.44461 - 1.06252i) q^{66} +(0.380219 - 0.352792i) q^{67} +(2.42120 - 0.364937i) q^{68} +(-0.140412 + 1.87367i) q^{69} +(-1.13681 + 0.547457i) q^{70} +(3.82716 + 1.18052i) q^{71} +(0.658475 + 1.67777i) q^{72} +(10.9116 - 7.43938i) q^{73} +(11.4137 + 1.72034i) q^{74} +(0.243520 - 1.06693i) q^{75} +(5.07191 + 3.45797i) q^{76} +(3.04666 + 2.82689i) q^{77} +(-2.76547 - 1.33178i) q^{78} +(1.61694 - 2.80061i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.0257399 - 0.343476i) q^{81} +(-1.76139 - 7.71715i) q^{82} +(-3.85272 + 9.81656i) q^{83} +(0.860933 - 1.07958i) q^{84} -2.44854 q^{85} +(-6.24378 - 2.00381i) q^{86} -5.15615 q^{87} +(-2.05372 + 2.57529i) q^{88} +(6.81590 - 17.3666i) q^{89} +(-0.401062 - 1.75717i) q^{90} +(-0.264464 - 3.52903i) q^{91} +(-0.858452 - 1.48688i) q^{92} +(0.470062 - 0.814171i) q^{93} +(7.24383 + 3.48844i) q^{94} +(-4.49988 - 4.17527i) q^{95} +(0.904210 + 0.616480i) q^{96} +(-0.162115 + 0.710274i) q^{97} +(-5.34756 - 0.806015i) q^{98} +(-4.90523 + 3.34433i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9}+O(q^{10}) $ 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9} - 4 q^{10} + q^{11} + 14 q^{12} - 23 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{17} - 20 q^{18} - 3 q^{19} + 4 q^{20} - 8 q^{21} - q^{22} + 7 q^{23} + 4 q^{25} - 19 q^{26} + 32 q^{27} + 4 q^{28} + 30 q^{29} + 9 q^{31} + 8 q^{32} + 39 q^{33} - 8 q^{34} - 22 q^{35} - 29 q^{36} - 37 q^{37} - 11 q^{38} - 52 q^{39} - 4 q^{40} - 28 q^{41} - 6 q^{42} + 41 q^{43} + 8 q^{44} + 2 q^{45} - 28 q^{46} + 3 q^{47} - 41 q^{49} + 24 q^{50} - 30 q^{51} - 9 q^{52} - 69 q^{53} + 3 q^{54} + 10 q^{55} - 11 q^{56} + 116 q^{57} + 5 q^{58} + 10 q^{59} - 19 q^{61} - 93 q^{62} + 34 q^{63} - 8 q^{64} - 3 q^{65} - 18 q^{66} + 3 q^{67} + 8 q^{68} + 42 q^{69} + 22 q^{70} - 36 q^{71} + 22 q^{72} - 56 q^{73} + 9 q^{74} - 10 q^{76} + 3 q^{77} + 45 q^{78} + 16 q^{79} - 24 q^{80} - 19 q^{81} + 14 q^{82} + 64 q^{83} - 8 q^{84} - 30 q^{85} + 36 q^{86} + 78 q^{87} - q^{88} - 75 q^{89} + 5 q^{90} + 5 q^{91} + 14 q^{92} - 10 q^{93} - 45 q^{94} - 3 q^{95} + 33 q^{97} - q^{98} - 11 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9 - 4 * q^10 + q^11 + 14 * q^12 - 23 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^17 - 20 * q^18 - 3 * q^19 + 4 * q^20 - 8 * q^21 - q^22 + 7 * q^23 + 4 * q^25 - 19 * q^26 + 32 * q^27 + 4 * q^28 + 30 * q^29 + 9 * q^31 + 8 * q^32 + 39 * q^33 - 8 * q^34 - 22 * q^35 - 29 * q^36 - 37 * q^37 - 11 * q^38 - 52 * q^39 - 4 * q^40 - 28 * q^41 - 6 * q^42 + 41 * q^43 + 8 * q^44 + 2 * q^45 - 28 * q^46 + 3 * q^47 - 41 * q^49 + 24 * q^50 - 30 * q^51 - 9 * q^52 - 69 * q^53 + 3 * q^54 + 10 * q^55 - 11 * q^56 + 116 * q^57 + 5 * q^58 + 10 * q^59 - 19 * q^61 - 93 * q^62 + 34 * q^63 - 8 * q^64 - 3 * q^65 - 18 * q^66 + 3 * q^67 + 8 * q^68 + 42 * q^69 + 22 * q^70 - 36 * q^71 + 22 * q^72 - 56 * q^73 + 9 * q^74 - 10 * q^76 + 3 * q^77 + 45 * q^78 + 16 * q^79 - 24 * q^80 - 19 * q^81 + 14 * q^82 + 64 * q^83 - 8 * q^84 - 30 * q^85 + 36 * q^86 + 78 * q^87 - q^88 - 75 * q^89 + 5 * q^90 + 5 * q^91 + 14 * q^92 - 10 * q^93 - 45 * q^94 - 3 * q^95 + 33 * q^97 - q^98 - 11 * 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
$3$	−0.399818	+	1.01872i	−0.230835	+	0.588158i	−0.998618	−	0.0525518i	$-0.983265\pi$
$3$	−0.399818	+	1.01872i	−0.230835	+	0.588158i	0.767783	+	0.640710i	$0.221360\pi$
$4$	−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
$6$	−0.547184	−	0.947751i	−0.223387	−	0.386918i
$7$	0.630880	−	1.09272i	0.238450	−	0.413008i	−0.721820	−	0.692081i	$-0.756694\pi$
$7$	0.630880	−	1.09272i	0.238450	−	0.413008i	0.960270	+	0.279074i	$0.0900273\pi$
$8$	0.900969	+	0.433884i	0.318541	+	0.153401i
$9$	1.32122	+	1.22591i	0.440407	+	0.408638i
$10$	−0.826239	−	0.563320i	−0.261280	−	0.178137i
$11$	−0.732965	+	3.21133i	−0.220997	+	0.968253i	0.735732	+	0.677273i	$0.236838\pi$
$11$	−0.732965	+	3.21133i	−0.220997	+	0.968253i	−0.956729	+	0.290980i	$0.906019\pi$
$12$	1.08215	+	0.163107i	0.312389	+	0.0470850i
$13$	2.31740	−	1.57998i	0.642731	−	0.438206i	−0.197598	−	0.980283i	$-0.563314\pi$
$13$	2.31740	−	1.57998i	0.642731	−	0.438206i	0.840329	+	0.542077i	$0.182362\pi$
$14$	0.460972	+	1.17454i	0.123200	+	0.313909i
$15$	−1.04575	−	0.322571i	−0.270011	−	0.0832874i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	−0.182980	+	2.44170i	−0.0443791	+	0.592199i	0.930040	+	0.367459i	$0.119772\pi$
$17$	−0.182980	+	2.44170i	−0.0443791	+	0.592199i	−0.974419	+	0.224740i	$0.927847\pi$
$18$	−1.78223	+	0.268627i	−0.420075	+	0.0633161i
$19$	−4.49988	+	4.17527i	−1.03234	+	0.957874i	−0.999135	−	0.0415748i	$-0.986763\pi$
$19$	−4.49988	+	4.17527i	−1.03234	+	0.957874i	−0.0332070	+	0.999448i	$0.510572\pi$
$20$	0.955573	−	0.294755i	0.213673	−	0.0659093i
$21$	0.860933	+	1.07958i	0.187871	+	0.235583i
$22$	−2.05372	−	2.57529i	−0.437855	−	0.549053i
$23$	1.64063	−	0.506066i	0.342094	−	0.105522i	−0.118948	−	0.992901i	$-0.537952\pi$
$23$	1.64063	−	0.506066i	0.342094	−	0.105522i	0.461042	+	0.887378i	$0.347476\pi$
$24$	−0.802229	+	0.744360i	−0.163754	+	0.151942i
$25$	−0.988831	+	0.149042i	−0.197766	+	0.0298085i
$26$	−0.209600	+	2.79691i	−0.0411059	+	0.548520i
$27$	−4.73509	+	2.28030i	−0.911268	+	0.438843i
$28$	−1.20570	−	0.371910i	−0.227856	−	0.0702844i
$29$	1.72132	+	4.38584i	0.319640	+	0.814430i	0.996899	+	0.0786856i	$0.0250723\pi$
$29$	1.72132	+	4.38584i	0.319640	+	0.814430i	−0.677259	+	0.735744i	$0.736832\pi$
$30$	0.904210	−	0.616480i	0.165085	−	0.112553i
$31$	−0.849461	−	0.128036i	−0.152568	−	0.0229959i	0.0723143	−	0.997382i	$-0.476962\pi$
$31$	−0.849461	−	0.128036i	−0.152568	−	0.0229959i	−0.224882	+	0.974386i	$0.572200\pi$
$32$	0.222521	−	0.974928i	0.0393365	−	0.172345i
$33$	−2.97839	−	2.03063i	−0.518471	−	0.353488i
$34$	−1.79491	−	1.66543i	−0.307824	−	0.285619i
$35$	1.13681	+	0.547457i	0.192155	+	0.0925371i
$36$	0.901178	−	1.56089i	0.150196	−	0.260148i
$37$	−5.77132	−	9.99623i	−0.948800	−	1.64337i	−0.747958	−	0.663746i	$-0.768966\pi$
$37$	−5.77132	−	9.99623i	−0.948800	−	1.64337i	−0.200842	−	0.979624i	$-0.564368\pi$
$38$	−0.458734	−	6.12139i	−0.0744166	−	0.993020i
$39$	0.683014	+	2.99248i	0.109370	+	0.479180i
$40$	−0.365341	+	0.930874i	−0.0577655	+	0.147184i
$41$	−4.93530	+	6.18867i	−0.770765	+	0.966509i	−0.999976	−	0.00686802i	$-0.997814\pi$
$41$	−4.93530	+	6.18867i	−0.770765	+	0.966509i	0.229212	+	0.973377i	$0.426385\pi$
$42$	−1.38083			−0.213067
$43$	2.32629	+	6.13094i	0.354755	+	0.934959i
$43$	2.32629	+	6.13094i	0.354755	+	0.934959i
$44$	3.29392			0.496577
$45$	−1.12375	+	1.40914i	−0.167519	+	0.210062i
$46$	−0.627255	+	1.59822i	−0.0924837	+	0.235645i
$47$	−1.78908	−	7.83846i	−0.260964	−	1.14336i	−0.920208	−	0.391429i	$-0.871981\pi$
$47$	−1.78908	−	7.83846i	−0.260964	−	1.14336i	0.659245	−	0.751929i	$-0.270876\pi$
$48$	−0.0817823	−	1.09131i	−0.0118043	−	0.157517i
$49$	2.70398	+	4.68343i	0.386283	+	0.669062i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−2.41425	−	1.16264i	−0.338062	−	0.162802i
$52$	−2.05603	−	1.90772i	−0.285120	−	0.264553i
$53$	8.44899	+	5.76042i	1.16056	+	0.791255i	0.981288	−	0.192545i	$-0.0616741\pi$
$53$	8.44899	+	5.76042i	1.16056	+	0.791255i	0.179270	+	0.983800i	$0.442627\pi$
$54$	1.16947	−	5.12378i	0.159145	−	0.697258i
$55$	−3.25713	−	0.490933i	−0.439191	−	0.0661974i
$56$	1.04251	−	0.710774i	0.139312	−	0.0949812i
$57$	−2.45430	−	6.25346i	−0.325080	−	0.828291i
$58$	−4.50221	−	1.38875i	−0.591169	−	0.182352i
$59$	−0.464629	+	0.223754i	−0.0604896	+	0.0291302i	−0.463884	−	0.885896i	$-0.653545\pi$
$59$	−0.464629	+	0.223754i	−0.0604896	+	0.0291302i	0.403394	+	0.915026i	$0.367830\pi$
$60$	−0.0817823	+	1.09131i	−0.0105580	+	0.140887i
$61$	0.129724	−	0.0195528i	0.0166095	−	0.00250348i	−0.140732	−	0.990048i	$-0.544946\pi$
$61$	0.129724	−	0.0195528i	0.0166095	−	0.00250348i	0.157342	+	0.987544i	$0.449708\pi$
$62$	0.629732	−	0.584306i	0.0799761	−	0.0742070i
$63$	2.17311	−	0.670315i	0.273786	−	0.0844517i
$64$	0.623490	+	0.781831i	0.0779362	+	0.0977289i
$65$	1.74874	+	2.19285i	0.216904	+	0.271989i
$66$	3.44461	−	1.06252i	0.424002	−	0.130787i
$67$	0.380219	−	0.352792i	0.0464512	−	0.0431004i	−0.656606	−	0.754234i	$-0.728008\pi$
$67$	0.380219	−	0.352792i	0.0464512	−	0.0431004i	0.703057	+	0.711134i	$0.251818\pi$
$68$	2.42120	−	0.364937i	0.293613	−	0.0442551i
$69$	−0.140412	+	1.87367i	−0.0169037	+	0.225564i
$70$	−1.13681	+	0.547457i	−0.135874	+	0.0654336i
$71$	3.82716	+	1.18052i	0.454201	+	0.140102i	0.513410	−	0.858143i	$-0.328382\pi$
$71$	3.82716	+	1.18052i	0.454201	+	0.140102i	−0.0592096	+	0.998246i	$0.518858\pi$
$72$	0.658475	+	1.67777i	0.0776020	+	0.197727i
$73$	10.9116	−	7.43938i	1.27710	−	0.870714i	0.281068	−	0.959688i	$-0.409311\pi$
$73$	10.9116	−	7.43938i	1.27710	−	0.870714i	0.996034	+	0.0889741i	$0.0283588\pi$
$74$	11.4137	+	1.72034i	1.32682	+	0.199986i
$75$	0.243520	−	1.06693i	0.0281193	−	0.123199i
$76$	5.07191	+	3.45797i	0.581788	+	0.396656i
$77$	3.04666	+	2.82689i	0.347199	+	0.322154i
$78$	−2.76547	−	1.33178i	−0.313128	−	0.150794i
$79$	1.61694	−	2.80061i	0.181919	−	0.315094i	−0.760615	−	0.649204i	$-0.775102\pi$
$79$	1.61694	−	2.80061i	0.181919	−	0.315094i	0.942534	+	0.334110i	$0.108436\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−0.0257399	−	0.343476i	−0.00285999	−	0.0381639i
$82$	−1.76139	−	7.71715i	−0.194513	−	0.852217i
$83$	−3.85272	+	9.81656i	−0.422891	+	1.07751i	0.547679	+	0.836688i	$0.315511\pi$
$83$	−3.85272	+	9.81656i	−0.422891	+	1.07751i	−0.970570	+	0.240819i	$0.922584\pi$
$84$	0.860933	−	1.07958i	0.0939355	−	0.117791i
$85$	−2.44854			−0.265582
$86$	−6.24378	−	2.00381i	−0.673284	−	0.216077i
$87$	−5.15615			−0.552797
$88$	−2.05372	+	2.57529i	−0.218928	+	0.274527i
$89$	6.81590	−	17.3666i	0.722484	−	1.84086i	0.222192	−	0.975003i	$-0.428679\pi$
$89$	6.81590	−	17.3666i	0.722484	−	1.84086i	0.500292	−	0.865857i	$-0.333226\pi$
$90$	−0.401062	−	1.75717i	−0.0422757	−	0.185222i
$91$	−0.264464	−	3.52903i	−0.0277234	−	0.369943i
$92$	−0.858452	−	1.48688i	−0.0894998	−	0.155018i
$93$	0.470062	−	0.814171i	0.0487431	−	0.0844256i
$94$	7.24383	+	3.48844i	0.747144	+	0.359806i
$95$	−4.49988	−	4.17527i	−0.461678	−	0.428374i
$96$	0.904210	+	0.616480i	0.0922855	+	0.0629192i
$97$	−0.162115	+	0.710274i	−0.0164603	+	0.0721174i	−0.982491	−	0.186310i	$-0.940347\pi$
$97$	−0.162115	+	0.710274i	−0.0164603	+	0.0721174i	0.966031	+	0.258427i	$0.0832043\pi$
$98$	−5.34756	−	0.806015i	−0.540185	−	0.0814198i
$99$	−4.90523	+	3.34433i	−0.492994	+	0.336117i
$100$	0.365341	+	0.930874i	0.0365341	+	0.0930874i
$101$	12.4416	+	3.83773i	1.23799	+	0.381868i	0.843548	−	0.537054i	$-0.180463\pi$
$101$	12.4416	+	3.83773i	1.23799	+	0.381868i	0.394438	+	0.918922i	$0.370939\pi$
$102$	2.41425	−	1.16264i	0.239046	−	0.115118i
$103$	−0.184671	+	2.46426i	−0.0181962	+	0.242811i	0.980688	+	0.195580i	$0.0626589\pi$
$103$	−0.184671	+	2.46426i	−0.0181962	+	0.242811i	−0.998884	+	0.0472314i	$0.984960\pi$
$104$	2.77343	−	0.418027i	0.271957	−	0.0409909i
$105$	−1.01222	+	0.939203i	−0.0987826	+	0.0916568i
$106$	−9.77154	+	3.01412i	−0.949096	+	0.292757i
$107$	−4.80452	−	6.02467i	−0.464470	−	0.582427i	0.493337	−	0.869838i	$-0.335777\pi$
$107$	−4.80452	−	6.02467i	−0.464470	−	0.582427i	−0.957807	+	0.287411i	$0.907205\pi$
$108$	3.27678	+	4.10895i	0.315308	+	0.395384i
$109$	7.20930	−	2.22377i	0.690526	−	0.212999i	0.0704202	−	0.997517i	$-0.477566\pi$
$109$	7.20930	−	2.22377i	0.690526	−	0.212999i	0.620105	+	0.784518i	$0.287090\pi$
$110$	2.41461	−	2.24043i	0.230224	−	0.213617i
$111$	12.4908	−	1.88269i	1.18558	−	0.178697i
$112$	−0.0942914	+	1.25823i	−0.00890970	+	0.118892i
$113$	14.3296	−	6.90079i	1.34802	−	0.649172i	0.386088	−	0.922462i	$-0.373826\pi$
$113$	14.3296	−	6.90079i	1.34802	−	0.649172i	0.961932	+	0.273290i	$0.0881119\pi$
$114$	6.41938	+	1.98012i	0.601230	+	0.185455i
$115$	0.627255	+	1.59822i	0.0584919	+	0.149035i
$116$	3.89285	−	2.65410i	0.361442	−	0.246427i
$117$	4.99871	+	0.753434i	0.462131	+	0.0696550i
$118$	0.114754	−	0.502770i	0.0105640	−	0.0462837i
$119$	2.55264	+	1.74036i	0.234000	+	0.159539i
$120$	−0.802229	−	0.744360i	−0.0732332	−	0.0679504i
$121$	0.135249	+	0.0651324i	0.0122953	+	0.00592112i
$122$	−0.0655948	+	0.113613i	−0.00593867	+	0.0102861i
$123$	−4.33130	−	7.50203i	−0.390540	−	0.676435i
$124$	0.0641973	+	0.856654i	0.00576509	+	0.0769298i
$125$	−0.222521	−	0.974928i	−0.0199029	−	0.0872002i
$126$	−0.830837	+	2.11694i	−0.0740168	+	0.188592i
$127$	2.91062	−	3.64981i	0.258276	−	0.323868i	−0.635740	−	0.771904i	$-0.719305\pi$
$127$	2.91062	−	3.64981i	0.258276	−	0.323868i	0.894016	+	0.448036i	$0.147876\pi$
$128$	−1.00000			−0.0883883
$129$	−7.17579	−	0.0814246i	−0.631793	−	0.00716903i
$130$	−2.80476			−0.245993
$131$	10.7105	−	13.4306i	0.935784	−	1.17344i	−0.0488506	−	0.998806i	$-0.515556\pi$
$131$	10.7105	−	13.4306i	0.935784	−	1.17344i	0.984634	−	0.174629i	$-0.0558727\pi$
$132$	−1.31697	+	3.35558i	−0.114627	+	0.292065i
$133$	1.72351	+	7.55118i	0.149447	+	0.654770i
$134$	0.0387610	+	0.517230i	0.00334844	+	0.0446818i
$135$	−2.62777	−	4.55144i	−0.226163	−	0.391726i
$136$	−1.22427	+	2.12050i	−0.104980	+	0.181831i
$137$	0.634332	+	0.305478i	0.0541946	+	0.0260987i	0.460785	−	0.887512i	$-0.347568\pi$
$137$	0.634332	+	0.305478i	0.0541946	+	0.0260987i	−0.406590	+	0.913611i	$0.633282\pi$
$138$	−1.37735	−	1.27799i	−0.117248	−	0.108790i
$139$	−3.53854	−	2.41253i	−0.300135	−	0.204628i	0.403883	−	0.914811i	$-0.367660\pi$
$139$	−3.53854	−	2.41253i	−0.300135	−	0.204628i	−0.704018	+	0.710182i	$0.748613\pi$
$140$	0.280768	−	1.23012i	0.0237292	−	0.103964i
$141$	8.70050	+	1.31139i	0.732714	+	0.110439i
$142$	−3.30917	+	2.25615i	−0.277699	+	0.189332i
$143$	3.37525	+	8.60000i	0.282253	+	0.719168i
$144$	−1.72228	−	0.531254i	−0.143524	−	0.0442712i
$145$	−4.24494	+	2.04426i	−0.352523	+	0.169766i
$146$	−0.986909	+	13.1694i	−0.0816772	+	1.08991i
$147$	−5.85220	+	0.882078i	−0.482682	+	0.0727526i
$148$	−8.46136	+	7.85100i	−0.695520	+	0.645348i
$149$	9.14253	−	2.82010i	0.748985	−	0.231031i	0.103316	−	0.994649i	$-0.467055\pi$
$149$	9.14253	−	2.82010i	0.748985	−	0.231031i	0.645669	+	0.763617i	$0.276579\pi$
$150$	0.682328	+	0.855612i	0.0557118	+	0.0698604i
$151$	−12.1368	−	15.2190i	−0.987677	−	1.23851i	−0.971107	−	0.238645i	$-0.923297\pi$
$151$	−12.1368	−	15.2190i	−0.987677	−	1.23851i	−0.0165703	−	0.999863i	$-0.505275\pi$
$152$	−5.86583	+	1.80937i	−0.475782	+	0.146759i
$153$	−3.23507	+	3.00170i	−0.261540	+	0.242673i
$154$	−4.10971	+	0.619439i	−0.331170	+	0.0499158i
$155$	0.0641973	−	0.856654i	0.00515645	−	0.0688081i
$156$	2.76547	−	1.33178i	0.221415	−	0.106628i
$157$	−12.5655	−	3.87594i	−1.00283	−	0.309333i	−0.250501	−	0.968116i	$-0.580595\pi$
$157$	−12.5655	−	3.87594i	−1.00283	−	0.309333i	−0.752333	+	0.658783i	$0.771072\pi$
$158$	1.18147	+	3.01033i	0.0939924	+	0.239489i
$159$	−9.24631	+	6.30403i	−0.733280	+	0.499942i
$160$	0.988831	+	0.149042i	0.0781739	+	0.0117828i
$161$	0.482051	−	2.11200i	0.0379910	−	0.166449i
$162$	0.284589	+	0.194029i	0.0223594	+	0.0152444i
$163$	−2.35310	−	2.18336i	−0.184309	−	0.171014i	0.582622	−	0.812743i	$-0.302027\pi$
$163$	−2.35310	−	2.18336i	−0.184309	−	0.171014i	−0.766931	+	0.641729i	$0.778217\pi$
$164$	7.13172	+	3.43446i	0.556894	+	0.268186i
$165$	1.80238	−	3.12181i	0.140315	−	0.243033i
$166$	−5.27277	−	9.13270i	−0.409246	−	0.708835i
$167$	0.0683516	+	0.912089i	0.00528921	+	0.0705796i	0.999224	−	0.0393935i	$-0.0125426\pi$
$167$	0.0683516	+	0.912089i	0.00528921	+	0.0705796i	−0.993935	+	0.109973i	$0.964924\pi$
$168$	0.307264	+	1.34621i	0.0237059	+	0.103862i
$169$	−1.87542	+	4.77850i	−0.144263	+	0.367577i
$170$	1.52664	−	1.91435i	0.117088	−	0.146824i
$171$	−11.0639			−0.846074
$172$	5.45957	−	3.63222i	0.416289	−	0.276954i
$173$	−7.76534			−0.590388			−0.295194	−	0.955437i	$-0.595384\pi$
$173$	−7.76534			−0.590388			−0.295194	+	0.955437i	$0.595384\pi$
$174$	3.21481	−	4.03124i	0.243714	−	0.305608i
$175$	−0.460972	+	1.17454i	−0.0348462	+	0.0887868i
$176$	−0.732965	−	3.21133i	−0.0552493	−	0.242063i
$177$	−0.0421751	−	0.562787i	−0.00317007	−	0.0423017i
$178$	9.32814	+	16.1568i	0.699173	+	1.21100i
$179$	−9.47524	+	16.4116i	−0.708213	+	1.22666i	0.257307	+	0.966330i	$0.417165\pi$
$179$	−9.47524	+	16.4116i	−0.708213	+	1.22666i	−0.965520	+	0.260331i	$0.916168\pi$
$180$	1.62387	+	0.782013i	0.121036	+	0.0582878i
$181$	−3.53362	−	3.27872i	−0.262652	−	0.243706i	0.537843	−	0.843045i	$-0.319239\pi$
$181$	−3.53362	−	3.27872i	−0.262652	−	0.243706i	−0.800495	+	0.599340i	$0.795430\pi$
$182$	2.92400	+	1.99355i	0.216741	+	0.147772i
$183$	−0.0319473	+	0.139970i	−0.00236161	+	0.0103469i
$184$	1.69773	+	0.255891i	0.125158	+	0.0188645i
$185$	9.53698	−	6.50221i	0.701173	−	0.478052i
$186$	0.343466	+	0.875136i	0.0251841	+	0.0641681i
$187$	−7.70698	−	2.37729i	−0.563590	−	0.173845i
$188$	−7.24383	+	3.48844i	−0.528310	+	0.254421i
$189$	−0.495553	+	6.61270i	−0.0360462	+	0.481003i
$190$	6.06999	−	0.914903i	0.440363	−	0.0663741i
$191$	−12.6934	+	11.7778i	−0.918462	+	0.852208i	−0.989392	−	0.145273i	$-0.953594\pi$
$191$	−12.6934	+	11.7778i	−0.918462	+	0.852208i	0.0709296	+	0.997481i	$0.477403\pi$
$192$	−1.04575	+	0.322571i	−0.0754704	+	0.0232795i
$193$	−10.0668	−	12.6233i	−0.724623	−	0.908648i	0.273967	−	0.961739i	$-0.411664\pi$
$193$	−10.0668	−	12.6233i	−0.724623	−	0.908648i	−0.998590	+	0.0530911i	$0.983093\pi$
$194$	−0.454237	−	0.569595i	−0.0326123	−	0.0408946i
$195$	−2.93307	+	0.904732i	−0.210042	+	0.0647892i
$196$	3.96432	−	3.67835i	0.283166	−	0.262739i
$197$	11.5927	−	1.74732i	0.825947	−	0.124492i	0.277552	−	0.960711i	$-0.410477\pi$
$197$	11.5927	−	1.74732i	0.825947	−	0.124492i	0.548396	+	0.836219i	$0.315239\pi$
$198$	0.443659	−	5.92021i	0.0315294	−	0.420731i
$199$	−6.05308	+	2.91501i	−0.429091	+	0.206640i	−0.635948	−	0.771732i	$-0.719391\pi$
$199$	−6.05308	+	2.91501i	−0.429091	+	0.206640i	0.206857	+	0.978371i	$0.433677\pi$
$200$	−0.955573	−	0.294755i	−0.0675692	−	0.0208423i
$201$	0.207378	+	0.528389i	0.0146273	+	0.0372697i
$202$	−10.7577	+	7.33446i	−0.756907	+	0.516051i
$203$	5.87842	+	0.886029i	0.412584	+	0.0621870i
$204$	−0.596269	+	2.61243i	−0.0417472	+	0.182906i
$205$	−6.54019	−	4.45902i	−0.456786	−	0.311432i
$206$	−1.81150	−	1.68082i	−0.126213	−	0.117109i
$207$	2.78802	+	1.34264i	0.193781	+	0.0933200i
$208$	−1.40238	+	2.42899i	−0.0972374	+	0.168420i
$209$	−10.1099	−	17.5109i	−0.699319	−	1.21126i
$210$	−0.103190	−	1.37697i	−0.00712076	−	0.0950199i
$211$	−1.47380	−	6.45714i	−0.101461	−	0.444528i	−0.999984	−	0.00560288i	$-0.998217\pi$
$211$	−1.47380	−	6.45714i	−0.101461	−	0.444528i	0.898524	−	0.438925i	$-0.144641\pi$
$212$	3.73592	−	9.51897i	0.256584	−	0.653766i
$213$	−2.73279	+	3.42681i	−0.187248	+	0.234801i
$214$	7.70585			0.526761
$215$	−5.93995	+	2.77795i	−0.405101	+	0.189454i
$216$	−5.25555			−0.357595
$217$	−0.675814	+	0.847444i	−0.0458772	+	0.0575282i
$218$	−2.75631	+	7.02296i	−0.186681	+	0.475655i
$219$	3.21600	+	14.0902i	0.217317	+	0.952129i
$220$	0.246155	+	3.28471i	0.0165957	+	0.221455i
$221$	3.43378	+	5.94749i	0.230981	+	0.400071i
$222$	−6.31596	+	10.9396i	−0.423899	+	0.734215i
$223$	6.84509	+	3.29642i	0.458381	+	0.220745i	0.648801	−	0.760958i	$-0.275271\pi$
$223$	6.84509	+	3.29642i	0.458381	+	0.220745i	−0.190420	+	0.981703i	$0.560985\pi$
$224$	−0.924935	−	0.858214i	−0.0617998	−	0.0573419i
$225$	−1.48918	−	1.01530i	−0.0992785	−	0.0676869i
$226$	−3.53913	+	15.5059i	−0.235419	+	1.03144i
$227$	21.5418	+	3.24690i	1.42978	+	0.215505i	0.817861	−	0.575416i	$-0.195160\pi$
$227$	21.5418	+	3.24690i	1.42978	+	0.215505i	0.611919	+	0.790921i	$0.290398\pi$
$228$	−5.55054	+	3.78429i	−0.367593	+	0.250621i
$229$	0.851528	+	2.16966i	0.0562706	+	0.143375i	0.956245	−	0.292569i	$-0.0945100\pi$
$229$	0.851528	+	2.16966i	0.0562706	+	0.143375i	−0.899974	+	0.435944i	$0.856415\pi$
$230$	−1.64063	−	0.506066i	−0.108180	−	0.0333690i
$231$	−4.09791	+	1.97345i	−0.269623	+	0.129843i
$232$	−0.352093	+	4.69836i	−0.0231160	+	0.308462i
$233$	15.0290	−	2.26526i	0.984582	−	0.148402i	0.363032	−	0.931777i	$-0.381742\pi$
$233$	15.0290	−	2.26526i	0.984582	−	0.148402i	0.621550	+	0.783375i	$0.286503\pi$
$234$	−3.70570	+	3.43839i	−0.242249	+	0.224775i
$235$	7.68285	−	2.36984i	0.501174	−	0.154592i
$236$	0.321533	+	0.403190i	0.0209300	+	0.0262454i
$237$	2.20656	+	2.76694i	0.143331	+	0.179732i
$238$	−2.95222	+	0.910638i	−0.191364	+	0.0590279i
$239$	10.6837	−	9.91302i	0.691071	−	0.641220i	−0.254335	−	0.967116i	$-0.581856\pi$
$239$	10.6837	−	9.91302i	0.691071	−	0.641220i	0.945406	+	0.325896i	$0.105666\pi$
$240$	1.08215	−	0.163107i	0.0698522	−	0.0105285i
$241$	0.721272	−	9.62470i	0.0464612	−	0.619981i	−0.924567	−	0.381018i	$-0.875573\pi$
$241$	0.721272	−	9.62470i	0.0464612	−	0.619981i	0.971029	−	0.238963i	$-0.0768075\pi$
$242$	−0.135249	+	0.0651324i	−0.00869412	+	0.00418687i
$243$	−14.7060	−	4.53620i	−0.943389	−	0.290997i
$244$	−0.0479289	−	0.122121i	−0.00306833	−	0.00781799i
$245$	−4.46827	+	3.04641i	−0.285467	+	0.194628i
$246$	8.56584	+	1.29109i	0.546138	+	0.0823171i
$247$	−3.83117	+	16.7855i	−0.243772	+	1.06803i
$248$	−0.709785	−	0.483923i	−0.0450714	−	0.0307292i
$249$	−8.45994	−	7.84967i	−0.536127	−	0.497453i
$250$	0.900969	+	0.433884i	0.0569823	+	0.0274412i
$251$	−11.9046	+	20.6193i	−0.751409	+	1.30148i	0.195730	+	0.980658i	$0.437292\pi$
$251$	−11.9046	+	20.6193i	−0.751409	+	1.30148i	−0.947140	+	0.320821i	$0.896041\pi$
$252$	−1.13707	−	1.96946i	−0.0716287	−	0.124065i
$253$	0.422624	+	5.63952i	0.0265701	+	0.354554i
$254$	1.03879	+	4.55124i	0.0651795	+	0.285570i
$255$	0.978971	−	2.49438i	0.0613056	−	0.156204i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	−23.0135			−1.43554			−0.717771	−	0.696279i	$-0.754838\pi$
$257$	−23.0135			−1.43554			−0.717771	+	0.696279i	$0.754838\pi$
$258$	4.53769	−	5.55949i	0.282505	−	0.346119i
$259$	−14.5640			−0.904966
$260$	1.74874	−	2.19285i	0.108452	−	0.135995i
$261$	−3.10242	+	7.90485i	−0.192035	+	0.489298i
$262$	3.82254	+	16.7477i	0.236158	+	1.03467i
$263$	−0.857825	−	11.4469i	−0.0528958	−	0.705845i	−0.959111	−	0.283029i	$-0.908661\pi$
$263$	−0.857825	−	11.4469i	−0.0528958	−	0.705845i	0.906216	−	0.422816i	$-0.138958\pi$
$264$	−1.80238	−	3.12181i	−0.110929	−	0.192134i
$265$	−5.11292	+	8.85584i	−0.314084	+	0.544010i
$266$	−6.97834	−	3.36059i	−0.427870	−	0.206051i
$267$	14.9666	+	13.8870i	0.915941	+	0.849869i
$268$	−0.428554	−	0.292183i	−0.0261781	−	0.0178479i
$269$	−2.62778	+	11.5131i	−0.160219	+	0.701965i	0.829449	+	0.558583i	$0.188655\pi$
$269$	−2.62778	+	11.5131i	−0.160219	+	0.701965i	−0.989667	+	0.143382i	$0.954202\pi$
$270$	5.19685	+	0.783299i	0.316270	+	0.0476701i
$271$	12.8799	−	8.78136i	0.782397	−	0.533430i	−0.104979	−	0.994474i	$-0.533478\pi$
$271$	12.8799	−	8.78136i	0.782397	−	0.533430i	0.887377	+	0.461045i	$0.152525\pi$
$272$	−0.894553	−	2.27929i	−0.0542403	−	0.138202i
$273$	3.70083	+	1.14155i	0.223984	+	0.0690900i
$274$	−0.634332	+	0.305478i	−0.0383214	+	0.0184546i
$275$	0.246155	−	3.28471i	0.0148437	−	0.198075i
$276$	1.85794	−	0.280039i	0.111835	−	0.0168564i
$277$	−12.9269	+	11.9944i	−0.776704	+	0.720676i	−0.965233	−	0.261392i	$-0.915819\pi$
$277$	−12.9269	+	11.9944i	−0.776704	+	0.720676i	0.188529	+	0.982068i	$0.439628\pi$
$278$	4.09244	−	1.26235i	0.245448	−	0.0757107i
$279$	−0.965365	−	1.21053i	−0.0577949	−	0.0724725i
$280$	0.786694	+	0.986483i	0.0470140	+	0.0589536i
$281$	11.2885	−	3.48205i	0.673418	−	0.207722i	0.0608582	−	0.998146i	$-0.480616\pi$
$281$	11.2885	−	3.48205i	0.673418	−	0.207722i	0.612559	+	0.790425i	$0.290140\pi$
$282$	−6.44996	+	5.98468i	−0.384089	+	0.356383i
$283$	28.6396	−	4.31672i	1.70245	−	0.256602i	0.775378	−	0.631497i	$-0.217559\pi$
$283$	28.6396	−	4.31672i	1.70245	−	0.256602i	0.927068	+	0.374894i	$0.122321\pi$
$284$	0.299302	−	3.99390i	0.0177603	−	0.236994i
$285$	6.05256	−	2.91476i	0.358523	−	0.172656i
$286$	−8.82818	−	2.72313i	−0.522021	−	0.161022i
$287$	3.64888	+	9.29719i	0.215387	+	0.548796i
$288$	1.48918	−	1.01530i	0.0877506	−	0.0598274i
$289$	10.8817	+	1.64016i	0.640101	+	0.0964797i
$290$	1.04841	−	4.59340i	0.0615650	−	0.269734i
$291$	−0.658753	−	0.449130i	−0.0386168	−	0.0263285i
$292$	−9.68091	−	8.98257i	−0.566533	−	0.525665i
$293$	−10.4487	−	5.03182i	−0.610418	−	0.293962i	0.103021	−	0.994679i	$-0.467149\pi$
$293$	−10.4487	−	5.03182i	−0.610418	−	0.293962i	−0.713439	+	0.700717i	$0.752863\pi$
$294$	2.95915	−	5.12540i	0.172581	−	0.298920i
$295$	−0.257850	−	0.446609i	−0.0150126	−	0.0260026i
$296$	−0.862583	−	11.5104i	−0.0501366	−	0.669027i
$297$	−3.85214	−	16.8773i	−0.223524	−	0.979321i
$298$	−3.49543	+	8.90622i	−0.202485	+	0.515923i
$299$	3.00241	−	3.76491i	0.173634	−	0.217730i
$300$	−1.09437			−0.0631834
$301$	8.16698	+	1.32591i	0.470737	+	0.0764244i
$302$	19.4659			1.12014
$303$	−8.88394	+	11.1401i	−0.510369	+	0.639983i
$304$	2.24266	−	5.71422i	0.128626	−	0.327733i
$305$	0.0291924	+	0.127900i	0.00167155	+	0.00732355i
$306$	−0.329795	−	4.40081i	−0.0188531	−	0.251578i
$307$	−1.04782	−	1.81487i	−0.0598021	−	0.103580i	0.834574	−	0.550895i	$-0.185714\pi$
$307$	−1.04782	−	1.81487i	−0.0598021	−	0.103580i	−0.894376	+	0.447315i	$0.852380\pi$
$308$	2.07806	−	3.59931i	0.118409	−	0.205090i
$309$	−2.43656	−	1.17338i	−0.138611	−	0.0667515i
$310$	0.629732	+	0.584306i	0.0357664	+	0.0331864i
$311$	−20.3456	−	13.8714i	−1.15370	−	0.786576i	−0.173544	−	0.984826i	$-0.555522\pi$
$311$	−20.3456	−	13.8714i	−1.15370	−	0.786576i	−0.980151	+	0.198250i	$0.936474\pi$
$312$	−0.683014	+	2.99248i	−0.0386681	+	0.169416i
$313$	7.78079	+	1.17277i	0.439796	+	0.0662886i	0.365208	−	0.930926i	$-0.380998\pi$
$313$	7.78079	+	1.17277i	0.439796	+	0.0662886i	0.0745879	+	0.997214i	$0.476236\pi$
$314$	10.8648	−	7.40748i	0.613135	−	0.418028i
$315$	0.830837	+	2.11694i	0.0468124	+	0.119276i
$316$	−3.09020	−	0.953200i	−0.173837	−	0.0536217i
$317$	−6.38217	+	3.07349i	−0.358459	+	0.172625i	−0.604441	−	0.796650i	$-0.706604\pi$
$317$	−6.38217	+	3.07349i	−0.358459	+	0.172625i	0.245983	+	0.969274i	$0.420889\pi$
$318$	0.836293	−	11.1596i	0.0468970	−	0.625797i
$319$	−15.3460	+	2.31304i	−0.859214	+	0.129506i
$320$	−0.733052	+	0.680173i	−0.0409788	+	0.0380228i
$321$	8.05838	−	2.48568i	0.449775	−	0.138737i
$322$	1.35068	+	1.69370i	0.0752703	+	0.0943860i
$323$	−9.37137	−	11.7513i	−0.521437	−	0.653861i
$324$	−0.329136	+	0.101525i	−0.0182853	+	0.00564028i
$325$	−2.05603	+	1.90772i	−0.114048	+	0.105821i
$326$	3.17415	−	0.478426i	0.175800	−	0.0264976i
$327$	−0.617005	+	8.23336i	−0.0341204	+	0.455306i
$328$	−7.13172	+	3.43446i	−0.393783	+	0.189636i
$329$	−9.69390	−	2.99017i	−0.534442	−	0.164854i
$330$	1.31697	+	3.35558i	0.0724966	+	0.184718i
$331$	5.25150	−	3.58041i	0.288648	−	0.196797i	−0.410335	−	0.911935i	$-0.634588\pi$
$331$	5.25150	−	3.58041i	0.288648	−	0.196797i	0.698984	+	0.715138i	$0.253636\pi$
$332$	10.4278	+	1.57173i	0.572297	+	0.0862599i
$333$	4.62932	−	20.2824i	0.253685	−	1.11147i
$334$	−0.755716	−	0.515239i	−0.0413510	−	0.0281926i
$335$	0.380219	+	0.352792i	0.0207736	+	0.0192751i
$336$	−1.24408	−	0.599120i	−0.0678704	−	0.0326847i
$337$	14.6654	−	25.4011i	0.798873	−	1.38369i	−0.121478	−	0.992594i	$-0.538763\pi$
$337$	14.6654	−	25.4011i	0.798873	−	1.38369i	0.920351	−	0.391094i	$-0.127903\pi$
$338$	−2.56667	−	4.44561i	−0.139609	−	0.241809i
$339$	1.30072	+	17.3569i	0.0706456	+	0.942700i
$340$	0.544852	+	2.38715i	0.0295488	+	0.129462i
$341$	1.03379	−	2.63405i	0.0559829	−	0.142642i
$342$	6.89820	−	8.65007i	0.373012	−	0.467742i
$343$	15.6559			0.845337
$344$	−0.564202	+	6.53312i	−0.0304197	+	0.352242i
$345$	−1.87893			−0.101158
$346$	4.84161	−	6.07119i	0.260287	−	0.326389i
$347$	−4.24921	+	10.8268i	−0.228110	+	0.581214i	−0.998404	−	0.0564744i	$-0.982014\pi$
$347$	−4.24921	+	10.8268i	−0.228110	+	0.581214i	0.770294	+	0.637689i	$0.220109\pi$
$348$	1.14735	+	5.02688i	0.0615045	+	0.269469i
$349$	−0.938279	−	12.5205i	−0.0502249	−	0.670205i	−0.964326	−	0.264718i	$-0.914721\pi$
$349$	−0.938279	−	12.5205i	−0.0502249	−	0.670205i	0.914101	−	0.405487i	$-0.132898\pi$
$350$	−0.630880	−	1.09272i	−0.0337219	−	0.0584081i
$351$	−7.37027	+	12.7657i	−0.393396	+	0.681381i
$352$	2.96772	+	1.42918i	0.158180	+	0.0761754i
$353$	−9.38649	−	8.70939i	−0.499592	−	0.463554i	0.389668	−	0.920955i	$-0.372590\pi$
$353$	−9.38649	−	8.70939i	−0.499592	−	0.463554i	−0.889260	+	0.457401i	$0.848780\pi$
$354$	0.466301	+	0.317918i	0.0247836	+	0.0168972i
$355$	−0.891219	+	3.90468i	−0.0473010	+	0.207239i
$356$	−18.4479	−	2.78057i	−0.977737	−	0.147370i
$357$	−2.79353	+	1.90460i	−0.147849	+	0.100802i
$358$	−6.92339	−	17.6405i	−0.365912	−	0.932330i
$359$	−1.04868	−	0.323474i	−0.0553470	−	0.0170723i	0.266958	−	0.963708i	$-0.413981\pi$
$359$	−1.04868	−	0.323474i	−0.0553470	−	0.0170723i	−0.322305	+	0.946636i	$0.604458\pi$
$360$	−1.62387	+	0.782013i	−0.0855853	+	0.0412157i
$361$	1.39609	−	18.6296i	0.0734786	−	0.980503i
$362$	4.76659	−	0.718448i	0.250526	−	0.0377608i
$363$	−0.120426	+	0.111739i	−0.00632075	+	0.00586480i
$364$	−3.38170	+	1.04312i	−0.177249	+	0.0546742i
$365$	8.23400	+	10.3251i	0.430987	+	0.540441i
$366$	−0.0895143	−	0.112247i	−0.00467899	−	0.00586726i
$367$	21.0099	−	6.48070i	1.09671	−	0.338290i	0.306961	−	0.951722i	$-0.400688\pi$
$367$	21.0099	−	6.48070i	1.09671	−	0.338290i	0.789747	+	0.613433i	$0.210212\pi$
$368$	−1.25858	+	1.16779i	−0.0656080	+	0.0608753i
$369$	−14.1074	+	2.12635i	−0.734402	+	0.110693i
$370$	−0.862583	+	11.5104i	−0.0448436	+	0.598396i
$371$	11.6248	−	5.59821i	0.603530	−	0.290645i
$372$	−0.898357	−	0.277106i	−0.0465776	−	0.0143673i
$373$	0.604100	+	1.53922i	0.0312791	+	0.0796979i	0.945660	−	0.325157i	$-0.105417\pi$
$373$	0.604100	+	1.53922i	0.0312791	+	0.0796979i	−0.914381	+	0.404855i	$0.867322\pi$
$374$	6.66386	−	4.54334i	0.344580	−	0.234931i
$375$	1.08215	+	0.163107i	0.0558818	+	0.00842282i
$376$	1.78908	−	7.83846i	0.0922646	−	0.404238i
$377$	10.9185	+	7.44410i	0.562331	+	0.383391i
$378$	−4.86104	−	4.51039i	−0.250025	−	0.231989i
$379$	23.4384	+	11.2873i	1.20395	+	0.579792i	0.924799	−	0.380455i	$-0.124233\pi$
$379$	23.4384	+	11.2873i	1.20395	+	0.579792i	0.279151	+	0.960247i	$0.409947\pi$
$380$	−3.06928	+	5.31614i	−0.157451	+	0.272712i
$381$	2.55441	+	4.42437i	0.130866	+	0.226667i
$382$	−1.29401	−	17.2674i	−0.0662075	−	0.883477i
$383$	−4.27113	−	18.7130i	−0.218245	−	0.956192i	−0.958774	−	0.284168i	$-0.908283\pi$
$383$	−4.27113	−	18.7130i	−0.218245	−	0.956192i	0.740530	−	0.672023i	$-0.234575\pi$
$384$	0.399818	−	1.01872i	0.0204031	−	0.0519863i
$385$	−2.59130	+	3.24939i	−0.132065	+	0.165604i
$386$	16.1459			0.821803
$387$	−4.44246	+	10.9522i	−0.225823	+	0.556729i
$388$	0.728540			0.0369860
$389$	8.08037	−	10.1325i	0.409691	−	0.513736i	−0.533585	−	0.845747i	$-0.679156\pi$
$389$	8.08037	−	10.1325i	0.409691	−	0.513736i	0.943276	+	0.332010i	$0.107727\pi$
$390$	1.12139	−	2.85726i	0.0567839	−	0.144683i
$391$	0.935459	+	4.09851i	0.0473082	+	0.207271i
$392$	0.404138	+	5.39284i	0.0204120	+	0.272380i
$393$	9.39973	+	16.2808i	0.474154	+	0.821258i
$394$	−5.86183	+	10.1530i	−0.295315	+	0.511501i
$395$	2.91362	+	1.40312i	0.146600	+	0.0705988i
$396$	4.35199	+	4.03806i	0.218696	+	0.202920i
$397$	14.1176	+	9.62519i	0.708540	+	0.483074i	0.863180	−	0.504897i	$-0.168469\pi$
$397$	14.1176	+	9.62519i	0.708540	+	0.483074i	−0.154640	+	0.987971i	$0.549422\pi$
$398$	1.49499	−	6.54997i	0.0749369	−	0.328320i
$399$	−8.38162	−	1.26333i	−0.419606	−	0.0632454i
$400$	0.826239	−	0.563320i	0.0413119	−	0.0281660i
$401$	10.3649	+	26.4093i	0.517597	+	1.31882i	0.915843	+	0.401538i	$0.131524\pi$
$401$	10.3649	+	26.4093i	0.517597	+	1.31882i	−0.398245	+	0.917279i	$0.630381\pi$
$402$	−0.542409	−	0.167311i	−0.0270529	−	0.00834472i
$403$	−2.17083	+	1.04542i	−0.108137	+	0.0520759i
$404$	0.972990	−	12.9836i	0.0484080	−	0.645960i
$405$	0.340592	−	0.0513359i	0.0169241	−	0.00255090i
$406$	−4.35786	+	4.04350i	−0.216277	+	0.200676i
$407$	36.3314	−	11.2067i	1.80088	−	0.555498i
$408$	−1.67071	−	2.09500i	−0.0827124	−	0.103718i
$409$	−5.56907	−	6.98339i	−0.275373	−	0.345306i	0.624843	−	0.780750i	$-0.285163\pi$
$409$	−5.56907	−	6.98339i	−0.275373	−	0.345306i	−0.900216	+	0.435444i	$0.856591\pi$
$410$	7.56394	−	2.33317i	0.373557	−	0.115227i
$411$	−0.564813	+	0.524070i	−0.0278602	+	0.0258505i
$412$	2.44357	−	0.368309i	0.120386	−	0.0181453i
$413$	−0.0486260	+	0.648869i	−0.00239273	+	0.0319288i
$414$	−2.78802	+	1.34264i	−0.137024	+	0.0659872i
$415$	−10.0770	−	3.10835i	−0.494662	−	0.152583i
$416$	−1.02469	−	2.61087i	−0.0502397	−	0.128009i
$417$	3.87247	−	2.64020i	0.189635	−	0.129291i
$418$	19.9940	+	3.01362i	0.977940	+	0.147401i
$419$	5.42746	−	23.7792i	0.265149	−	1.16169i	−0.650434	−	0.759562i	$-0.725413\pi$
$419$	5.42746	−	23.7792i	0.265149	−	1.16169i	0.915583	−	0.402129i	$-0.131730\pi$
$420$	1.14090	+	0.777849i	0.0556700	+	0.0379552i
$421$	15.1286	+	14.0373i	0.737322	+	0.684135i	0.956560	−	0.291537i	$-0.0941665\pi$
$421$	15.1286	+	14.0373i	0.737322	+	0.684135i	−0.219238	+	0.975672i	$0.570357\pi$
$422$	5.96729	+	2.87370i	0.290483	+	0.139889i
$423$	7.24551	−	12.5496i	0.352289	−	0.610182i
$424$	5.11292	+	8.85584i	0.248305	+	0.430078i
$425$	−0.182980	−	2.44170i	−0.00887583	−	0.118440i
$426$	−0.975322	−	4.27316i	−0.0472545	−	0.207035i
$427$	0.0604748	−	0.154087i	0.00292658	−	0.00745680i
$428$	−4.80452	+	6.02467i	−0.232235	+	0.291214i
$429$	−10.1105			−0.488138
$430$	1.53161	−	6.37606i	0.0738609	−	0.307481i
$431$	35.6281			1.71615			0.858073	−	0.513528i	$-0.171662\pi$
$431$	35.6281			1.71615			0.858073	+	0.513528i	$0.171662\pi$
$432$	3.27678	−	4.10895i	0.157654	−	0.197692i
$433$	−2.94821	+	7.51191i	−0.141682	+	0.361000i	−0.984047	−	0.177907i	$-0.943067\pi$
$433$	−2.94821	+	7.51191i	−0.141682	+	0.361000i	0.842365	+	0.538907i	$0.181163\pi$
$434$	−0.241195	−	1.05675i	−0.0115777	−	0.0507254i
$435$	−0.385320	−	5.14173i	−0.0184747	−	0.246527i
$436$	−3.77224	−	6.53371i	−0.180658	−	0.312908i
$437$	−5.26965	+	9.12730i	−0.252082	+	0.436618i
$438$	−13.0213	−	6.27074i	−0.622183	−	0.299627i
$439$	−17.5527	−	16.2865i	−0.837745	−	0.777314i	0.139321	−	0.990247i	$-0.455508\pi$
$439$	−17.5527	−	16.2865i	−0.837745	−	0.777314i	−0.977067	+	0.212933i	$0.931698\pi$
$440$	−2.72156	−	1.85553i	−0.129745	−	0.0884589i
$441$	−2.16893	+	9.50270i	−0.103282	+	0.452510i
$442$	−6.79086	−	1.02356i	−0.323008	−	0.0486857i
$443$	−10.2594	+	6.99471i	−0.487437	+	0.332329i	−0.781974	−	0.623311i	$-0.785787\pi$
$443$	−10.2594	+	6.99471i	−0.487437	+	0.332329i	0.294537	+	0.955640i	$0.404835\pi$
$444$	−4.61496	−	11.7587i	−0.219016	−	0.558044i
$445$	17.8274	+	5.49903i	0.845101	+	0.260679i
$446$	−6.84509	+	3.29642i	−0.324124	+	0.156090i
$447$	−0.782459	+	10.4412i	−0.0370091	+	0.493852i
$448$	1.24767	−	0.188055i	0.0589467	−	0.00888479i
$449$	−28.6992	+	26.6290i	−1.35440	+	1.25670i	−0.416791	+	0.909002i	$0.636845\pi$
$449$	−28.6992	+	26.6290i	−1.35440	+	1.25670i	−0.937607	+	0.347696i	$0.886964\pi$
$450$	1.72228	−	0.531254i	0.0811892	−	0.0250436i
$451$	−16.2565	−	20.3850i	−0.765488	−	0.959891i
$452$	−9.91642	−	12.4348i	−0.466429	−	0.584884i
$453$	20.3564	−	6.27913i	0.956429	−	0.295019i
$454$	−15.9696	+	14.8176i	−0.749492	+	0.695427i
$455$	3.49940	−	0.527450i	0.164054	−	0.0247272i
$456$	0.502025	−	6.69905i	0.0235095	−	0.313712i
$457$	11.0558	−	5.32419i	0.517169	−	0.249055i	−0.157045	−	0.987591i	$-0.550197\pi$
$457$	11.0558	−	5.32419i	0.517169	−	0.249055i	0.674214	+	0.738536i	$0.264483\pi$
$458$	−2.22723	−	0.687008i	−0.104071	−	0.0321018i
$459$	−4.70137	−	11.9789i	−0.219441	−	0.559127i
$460$	1.41857	−	0.967166i	0.0661413	−	0.0450944i
$461$	9.29795	+	1.40144i	0.433049	+	0.0652716i	0.361950	−	0.932198i	$-0.382111\pi$
$461$	9.29795	+	1.40144i	0.433049	+	0.0652716i	0.0710992	+	0.997469i	$0.477349\pi$
$462$	1.01210	−	4.43430i	0.0470872	−	0.206302i
$463$	−5.89715	−	4.02061i	−0.274064	−	0.186854i	0.418487	−	0.908223i	$-0.362561\pi$
$463$	−5.89715	−	4.02061i	−0.274064	−	0.186854i	−0.692551	+	0.721369i	$0.743513\pi$
$464$	−3.45380	−	3.20465i	−0.160338	−	0.148772i
$465$	0.847022	+	0.407904i	0.0392797	+	0.0189161i
$466$	−7.59937	+	13.1625i	−0.352034	+	0.609741i
$467$	−4.96612	−	8.60158i	−0.229805	−	0.398034i	0.727945	−	0.685635i	$-0.240475\pi$
$467$	−4.96612	−	8.60158i	−0.229805	−	0.398034i	−0.957750	+	0.287602i	$0.907142\pi$
$468$	−0.377773	−	5.04104i	−0.0174626	−	0.233022i
$469$	−0.145629	−	0.638041i	−0.00672451	−	0.0294620i
$470$	−2.93736	+	7.48426i	−0.135490	+	0.345223i
$471$	8.97239	−	11.2510i	0.413426	−	0.518420i
$472$	−0.515699			−0.0237370
$473$	−21.3936	+	2.97671i	−0.983677	+	0.136869i
$474$	−3.53905			−0.162554
$475$	3.82732	−	4.79931i	0.175610	−	0.220208i
$476$	1.12871	−	2.87591i	0.0517344	−	0.131817i
$477$	4.10120	+	17.9685i	0.187781	+	0.822722i
$478$	1.08914	+	14.5335i	0.0498160	+	0.664748i
$479$	17.0910	+	29.6024i	0.780907	+	1.35257i	0.931414	+	0.363961i	$0.118576\pi$
$479$	17.0910	+	29.6024i	0.780907	+	1.35257i	−0.150507	+	0.988609i	$0.548091\pi$
$480$	−0.547184	+	0.947751i	−0.0249754	+	0.0432587i
$481$	−29.1682	−	14.0467i	−1.32996	−	0.640474i
$482$	7.07519	+	6.56482i	0.322266	+	0.299019i
$483$	1.95881	+	1.33549i	0.0891288	+	0.0607670i
$484$	0.0334037	−	0.146351i	0.00151835	−	0.00665232i
$485$	−0.720403	−	0.108583i	−0.0327118	−	0.00493051i
$486$	12.7156	−	8.66933i	0.576790	−	0.393249i
$487$	10.6831	+	27.2201i	0.484098	+	1.23346i	0.939307	+	0.343077i	$0.111469\pi$
$487$	10.6831	+	27.2201i	0.484098	+	1.23346i	−0.455209	+	0.890384i	$0.650436\pi$
$488$	0.125361	+	0.0386688i	0.00567483	+	0.00175045i
$489$	3.16504	−	1.52420i	0.143128	−	0.0689268i
$490$	0.404138	−	5.39284i	0.0182571	−	0.243624i
$491$	−25.0543	+	3.77633i	−1.13068	+	0.170423i	−0.687623	−	0.726068i	$-0.741346\pi$
$491$	−25.0543	+	3.77633i	−1.13068	+	0.170423i	−0.443062	+	0.896491i	$0.646108\pi$
$492$	−6.35013	+	5.89206i	−0.286286	+	0.265635i
$493$	−11.0239	+	3.40041i	−0.496490	+	0.153147i
$494$	−10.7347	−	13.4609i	−0.482977	−	0.605634i
$495$	−3.70154	−	4.64159i	−0.166372	−	0.208624i
$496$	0.820890	−	0.253211i	0.0368591	−	0.0113695i
$497$	3.70446	−	3.43723i	0.166168	−	0.154181i
$498$	11.4118	−	1.72005i	0.511375	−	0.0770774i
$499$	1.92086	−	25.6321i	0.0859895	−	1.14745i	−0.772637	−	0.634848i	$-0.781063\pi$
$499$	1.92086	−	25.6321i	0.0859895	−	1.14745i	0.858626	−	0.512602i	$-0.171318\pi$
$500$	−0.900969	+	0.433884i	−0.0402926	+	0.0194039i
$501$	−0.956491	−	0.295038i	−0.0427328	−	0.0131813i
$502$	−8.69845	−	22.1633i	−0.388231	−	0.989196i
$503$	−32.3546	+	22.0590i	−1.44262	+	0.983561i	−0.446571	+	0.894748i	$0.647355\pi$
$503$	−32.3546	+	22.0590i	−1.44262	+	0.983561i	−0.996048	+	0.0888126i	$0.971693\pi$
$504$	2.24874	+	0.338943i	0.100167	+	0.0150977i
$505$	−2.89723	+	12.6936i	−0.128925	+	0.564858i
$506$	−4.67266	−	3.18576i	−0.207725	−	0.141625i
$507$	−4.11812	−	3.82106i	−0.182892	−	0.169699i
$508$	−4.20597	−	2.02549i	−0.186610	−	0.0898666i
$509$	8.33944	−	14.4443i	0.369639	−	0.640234i	−0.619870	−	0.784705i	$-0.712815\pi$
$509$	8.33944	−	14.4443i	0.369639	−	0.640234i	0.989509	+	0.144471i	$0.0461479\pi$
$510$	1.33980	+	2.32061i	0.0593276	+	0.102758i
$511$	−1.24524	−	16.6166i	−0.0550862	−	0.735075i
$512$	0.222521	+	0.974928i	0.00983413	+	0.0430861i
$513$	11.7864	−	30.0313i	0.520384	−	1.32592i
$514$	14.3487	−	17.9927i	0.632893	−	0.793623i
$515$	−2.47117			−0.108893
$516$	1.51738	+	7.01400i	0.0667990	+	0.308774i
$517$	26.4832			1.16473
$518$	9.08053	−	11.3866i	0.398976	−	0.500300i
$519$	3.10472	−	7.91070i	0.136282	−	0.347241i
$520$	0.624117	+	2.73443i	0.0273693	+	0.119913i
$521$	2.47715	+	33.0552i	0.108526	+	1.44818i	0.739910	+	0.672706i	$0.234868\pi$
$521$	2.47715	+	33.0552i	0.108526	+	1.44818i	−0.631384	+	0.775470i	$0.717513\pi$
$522$	−4.24593	−	7.35417i	−0.185839	−	0.321883i
$523$	−3.83697	+	6.64582i	−0.167779	+	0.290601i	−0.937639	−	0.347612i	$-0.886993\pi$
$523$	−3.83697	+	6.64582i	−0.167779	+	0.290601i	0.769860	+	0.638213i	$0.220326\pi$
$524$	−15.4772	−	7.45341i	−0.676123	−	0.325604i
$525$	−1.01222	−	0.939203i	−0.0441769	−	0.0409902i
$526$	9.48438	+	6.46634i	0.413539	+	0.281946i
$527$	0.468058	−	2.05070i	0.0203889	−	0.0893298i
$528$	3.56450	+	0.537261i	0.155125	+	0.0233813i
$529$	−16.5679	+	11.2958i	−0.720345	+	0.491123i
$530$	−3.73592	−	9.51897i	−0.162278	−	0.413478i
$531$	−0.888180	−	0.273967i	−0.0385437	−	0.0118892i
$532$	6.97834	−	3.36059i	0.302549	−	0.145700i
$533$	−1.65911	+	22.1393i	−0.0718640	+	0.958959i
$534$	−20.1888	+	3.04297i	−0.873655	+	0.131682i
$535$	5.64879	−	5.24131i	0.244218	−	0.226601i
$536$	0.495637	−	0.152884i	0.0214082	−	0.00660357i
$537$	−12.9304	−	16.2143i	−0.557990	−	0.699697i
$538$	−7.36289	−	9.23277i	−0.317437	−	0.398053i
$539$	−17.0220	+	5.25059i	−0.733189	+	0.226159i
$540$	−3.85259	+	3.57468i	−0.165789	+	0.153830i
$541$	6.95067	−	1.04764i	0.298833	−	0.0450418i	0.00208535	−	0.999998i	$-0.499336\pi$
$541$	6.95067	−	1.04764i	0.298833	−	0.0450418i	0.296747	+	0.954956i	$0.404098\pi$
$542$	−1.16494	+	15.5450i	−0.0500383	+	0.667714i
$543$	4.75290	−	2.28888i	0.203967	−	0.0982252i
$544$	2.33976	+	0.721721i	0.100316	+	0.0309435i
$545$	2.75631	+	7.02296i	0.118067	+	0.300830i
$546$	−3.19993	+	2.18168i	−0.136944	+	0.0933672i
$547$	37.7053	+	5.68315i	1.61216	+	0.242994i	0.892405	−	0.451234i	$-0.149016\pi$
$547$	37.7053	+	5.68315i	1.61216	+	0.242994i	0.719755	+	0.694228i	$0.244254\pi$
$548$	0.156667	−	0.686403i	0.00669248	−	0.0293217i
$549$	0.195364	+	0.133197i	0.00833795	+	0.00568472i
$550$	2.41461	+	2.24043i	0.102959	+	0.0955323i
$551$	−26.0578	−	12.5488i	−1.11010	−	0.534596i
$552$	−0.939463	+	1.62720i	−0.0399862	+	0.0692581i
$553$	−2.04018	−	3.53370i	−0.0867574	−	0.150268i
$554$	−1.31782	−	17.5851i	−0.0559888	−	0.747119i
$555$	2.81087	+	12.3152i	0.119315	+	0.522751i
$556$	−1.56465	+	3.98666i	−0.0663559	+	0.169072i
$557$	−6.48018	+	8.12589i	−0.274574	+	0.344305i	−0.899930	−	0.436035i	$-0.856382\pi$
$557$	−6.48018	+	8.12589i	−0.274574	+	0.344305i	0.625356	+	0.780340i	$0.284954\pi$
$558$	1.54832			0.0655458
$559$	15.0777	+	10.5323i	0.637717	+	0.445471i
$560$	−1.26176			−0.0533191
$561$	5.50318	−	6.90077i	0.232344	−	0.291351i
$562$	−4.31591	+	10.9968i	−0.182056	+	0.463870i
$563$	2.85273	+	12.4986i	0.120228	+	0.526754i	0.998792	+	0.0491298i	$0.0156448\pi$
$563$	2.85273	+	12.4986i	0.120228	+	0.526754i	−0.878564	+	0.477624i	$0.841498\pi$
$564$	−0.657533	−	8.77417i	−0.0276871	−	0.369459i
$565$	7.95235	+	13.7739i	0.334558	+	0.579471i
$566$	−14.4815	+	25.0828i	−0.608704	+	1.05431i
$567$	−0.391560	−	0.188565i	−0.0164440	−	0.00791900i
$568$	2.93595	+	2.72416i	0.123190	+	0.114303i
$569$	−25.4992	−	17.3850i	−1.06898	−	0.728818i	−0.104914	−	0.994481i	$-0.533457\pi$
$569$	−25.4992	−	17.3850i	−1.06898	−	0.728818i	−0.964066	+	0.265663i	$0.914409\pi$
$570$	−1.49486	+	6.54941i	−0.0626128	+	0.274325i
$571$	−4.80666	−	0.724487i	−0.201152	−	0.0303188i	0.0476931	−	0.998862i	$-0.484813\pi$
$571$	−4.80666	−	0.724487i	−0.201152	−	0.0303188i	−0.248846	+	0.968543i	$0.580051\pi$
$572$	7.63331	−	5.20431i	0.319165	−	0.217603i
$573$	−6.92317	−	17.6400i	−0.289220	−	0.736920i
$574$	−9.54388	−	2.94390i	−0.398354	−	0.122876i
$575$	−1.54688	+	0.744937i	−0.0645092	+	0.0310660i
$576$	−0.134690	+	1.79732i	−0.00561210	+	0.0748882i
$577$	−28.8069	+	4.34194i	−1.19925	+	0.180758i	−0.718137	−	0.695902i	$-0.755005\pi$
$577$	−28.8069	+	4.34194i	−1.19925	+	0.180758i	−0.481111	+	0.876660i	$0.659767\pi$
$578$	−8.06697	+	7.48505i	−0.335542	+	0.311337i
$579$	16.8845	−	5.20818i	0.701697	−	0.216445i
$580$	2.93759	+	3.68362i	0.121977	+	0.152954i
$581$	8.29611	+	10.4030i	0.344181	+	0.431589i
$582$	0.761870	−	0.235006i	0.0315805	−	0.00974130i
$583$	−24.6914	+	22.9103i	−1.02262	+	0.948848i
$584$	13.0588	−	1.96830i	0.540377	−	0.0814488i
$585$	−0.377773	+	5.04104i	−0.0156190	+	0.208421i
$586$	10.4487	−	5.03182i	0.431631	−	0.207862i
$587$	−0.476268	−	0.146909i	−0.0196577	−	0.00606359i	0.284911	−	0.958554i	$-0.408036\pi$
$587$	−0.476268	−	0.146909i	−0.0196577	−	0.00606359i	−0.304568	+	0.952490i	$0.598512\pi$
$588$	2.16220	+	5.50920i	0.0891676	+	0.227195i
$589$	4.35705	−	2.97059i	0.179529	−	0.122401i
$590$	0.509939	+	0.0768610i	0.0209939	+	0.00316432i
$591$	−2.85495	+	12.5083i	−0.117437	+	0.514524i
$592$	9.53698	+	6.50221i	0.391968	+	0.267239i
$593$	−18.2395	−	16.9238i	−0.749008	−	0.694978i	0.210206	−	0.977657i	$-0.432586\pi$
$593$	−18.2395	−	16.9238i	−0.749008	−	0.694978i	−0.959215	+	0.282679i	$0.908777\pi$
$594$	15.5970	+	7.51111i	0.639952	+	0.308185i
$595$	−1.54474	+	2.67556i	−0.0633280	+	0.109687i
$596$	−4.78380	−	8.28578i	−0.195952	−	0.339399i
$597$	−0.549447	−	7.33186i	−0.0224874	−	0.300073i
$598$	1.07155	+	4.69476i	0.0438189	+	0.191983i
$599$	4.95986	−	12.6375i	0.202654	−	0.516355i	−0.793027	−	0.609186i	$-0.791496\pi$
$599$	4.95986	−	12.6375i	0.202654	−	0.516355i	0.995682	+	0.0928308i	$0.0295916\pi$
$600$	0.682328	−	0.855612i	0.0278559	−	0.0349302i
$601$	−6.81861			−0.278137			−0.139069	−	0.990283i	$-0.544411\pi$
$601$	−6.81861			−0.278137			−0.139069	+	0.990283i	$0.544411\pi$
$602$	−6.12867	+	5.55851i	−0.249786	+	0.226548i
$603$	0.934847			0.0380699
$604$	−12.1368	+	15.2190i	−0.493839	+	0.619254i
$605$	−0.0548431	+	0.139738i	−0.00222969	+	0.00568115i
$606$	−3.17064	−	13.8915i	−0.128799	−	0.564303i
$607$	−1.84961	−	24.6813i	−0.0750733	−	1.00178i	−0.899814	−	0.436273i	$-0.856298\pi$
$607$	−1.84961	−	24.6813i	−0.0750733	−	1.00178i	0.824741	−	0.565510i	$-0.191321\pi$
$608$	3.06928	+	5.31614i	0.124476	+	0.215598i
$609$	−3.25291	+	5.63421i	−0.131815	+	0.228310i
$610$	−0.118198	−	0.0569210i	−0.00478568	−	0.00230466i
$611$	−16.5306	−	15.3381i	−0.668756	−	0.620515i
$612$	3.64632	+	2.48602i	0.147394	+	0.100491i
$613$	−7.29622	+	31.9668i	−0.294692	+	1.29113i	0.583224	+	0.812312i	$0.301791\pi$
$613$	−7.29622	+	31.9668i	−0.294692	+	1.29113i	−0.877915	+	0.478816i	$0.841066\pi$
$614$	2.07223	+	0.312338i	0.0836283	+	0.0126049i
$615$	7.15738	−	4.87982i	0.288613	−	0.196773i
$616$	1.51840	+	3.86883i	0.0611783	+	0.155880i
$617$	−43.1527	−	13.3108i	−1.73726	−	0.535875i	−0.745789	−	0.666182i	$-0.767927\pi$
$617$	−43.1527	−	13.3108i	−1.73726	−	0.535875i	−0.991474	+	0.130307i	$0.958404\pi$
$618$	2.43656	−	1.17338i	0.0980127	−	0.0472004i
$619$	0.261652	−	3.49151i	0.0105167	−	0.140335i	−0.989474	−	0.144713i	$-0.953774\pi$
$619$	0.261652	−	3.49151i	0.0105167	−	0.140335i	0.999990	+	0.00437712i	$0.00139329\pi$
$620$	−0.849461	+	0.128036i	−0.0341152	+	0.00514203i
$621$	−6.61453	+	6.13738i	−0.265432	+	0.246285i
$622$	23.5304	−	7.25817i	0.943484	−	0.291026i
$623$	−14.6768	−	18.4041i	−0.588013	−	0.737345i
$624$	−1.91376	−	2.39978i	−0.0766118	−	0.0960682i
$625$	0.955573	−	0.294755i	0.0382229	−	0.0117902i
$626$	−5.76815	+	5.35206i	−0.230542	+	0.213911i
$627$	21.8808	−	3.29801i	0.873837	−	0.131710i
$628$	−0.982677	+	13.1129i	−0.0392131	+	0.523262i
$629$	25.4638	−	12.2627i	1.01531	−	0.488947i
$630$	−2.17311	−	0.670315i	−0.0865787	−	0.0267060i
$631$	17.1799	+	43.7738i	0.683923	+	1.74261i	0.669615	+	0.742709i	$0.266459\pi$
$631$	17.1799	+	43.7738i	0.683923	+	1.74261i	0.0143080	+	0.999898i	$0.495445\pi$
$632$	2.67195	−	1.82170i	0.106284	−	0.0724635i
$633$	7.16726	+	1.08029i	0.284873	+	0.0429377i
$634$	1.57627	−	6.90608i	0.0626016	−	0.274275i
$635$	3.85711	+	2.62973i	0.153065	+	0.104358i
$636$	8.20347	+	7.61171i	0.325289	+	0.301824i
$637$	13.6659	+	6.58116i	0.541463	+	0.260755i
$638$	7.75969	−	13.4402i	0.307209	−	0.532102i
$639$	3.60931	+	6.25151i	0.142782	+	0.247306i
$640$	−0.0747301	−	0.997204i	−0.00295397	−	0.0394179i
$641$	8.32913	+	36.4923i	0.328981	+	1.44136i	0.821077	+	0.570818i	$0.193374\pi$
$641$	8.32913	+	36.4923i	0.328981	+	1.44136i	−0.492096	+	0.870541i	$0.663769\pi$
$642$	−3.08094	+	7.85009i	−0.121595	+	0.309819i
$643$	−0.786841	+	0.986668i	−0.0310300	+	0.0389104i	−0.797104	−	0.603842i	$-0.793636\pi$
$643$	−0.786841	+	0.986668i	−0.0310300	+	0.0389104i	0.766074	+	0.642752i	$0.222207\pi$
$644$	−2.16632			−0.0853649
$645$	−0.455051	−	7.16181i	−0.0179176	−	0.281996i
$646$	15.0305			0.591367
$647$	−21.8711	+	27.4255i	−0.859843	+	1.07821i	0.136318	+	0.990665i	$0.456473\pi$
$647$	−21.8711	+	27.4255i	−0.859843	+	1.07821i	−0.996161	+	0.0875439i	$0.972098\pi$
$648$	0.125838	−	0.320629i	0.00494337	−	0.0125955i
$649$	−0.377990	−	1.65608i	−0.0148374	−	0.0650069i
$650$	−0.209600	−	2.79691i	−0.00822117	−	0.109704i
$651$	−0.593105	−	1.02729i	−0.0232456	−	0.0402626i
$652$	−1.60500	+	2.77995i	−0.0628567	+	0.108871i
$653$	2.55676	+	1.23127i	0.100054	+	0.0481834i	0.483241	−	0.875487i	$-0.339459\pi$
$653$	2.55676	+	1.23127i	0.100054	+	0.0481834i	−0.383187	+	0.923671i	$0.625174\pi$
$654$	−6.05240	−	5.61581i	−0.236668	−	0.219595i
$655$	14.1934	+	9.67692i	0.554583	+	0.378108i
$656$	1.76139	−	7.71715i	0.0687707	−	0.301304i
$657$	23.5366	+	3.54758i	0.918252	+	0.138404i
$658$	8.38186	−	5.71466i	0.326759	−	0.222780i
$659$	2.54332	+	6.48028i	0.0990738	+	0.252436i	0.971814	−	0.235749i	$-0.0757544\pi$
$659$	2.54332	+	6.48028i	0.0990738	+	0.252436i	−0.872740	+	0.488185i	$0.837659\pi$
$660$	−3.44461	−	1.06252i	−0.134081	−	0.0413586i
$661$	−33.4080	+	16.0885i	−1.29942	+	0.625768i	−0.950308	−	0.311312i	$-0.899232\pi$
$661$	−33.4080	+	16.0885i	−1.29942	+	0.625768i	−0.349114	+	0.937080i	$0.613517\pi$
$662$	−0.474977	+	6.33813i	−0.0184605	+	0.246339i
$663$	−7.43171	+	1.12015i	−0.288624	+	0.0435030i
$664$	−7.73042	+	7.17279i	−0.299999	+	0.278358i
$665$	−7.40127	+	2.28299i	−0.287009	+	0.0885305i
$666$	12.9711	+	16.2652i	0.502619	+	0.630264i
$667$	5.04356	+	6.32442i	0.195287	+	0.244883i
$668$	0.874011	−	0.269597i	0.0338165	−	0.0104310i
$669$	−6.09492	+	5.65526i	−0.235643	+	0.218645i
$670$	−0.512887	+	0.0773053i	−0.0198145	+	0.00298656i
$671$	−0.0322929	+	0.430919i	−0.00124665	+	0.0166354i
$672$	1.24408	−	0.599120i	0.0479916	−	0.0231115i
$673$	1.16280	+	0.358676i	0.0448225	+	0.0138259i	0.317085	−	0.948397i	$-0.397296\pi$
$673$	1.16280	+	0.358676i	0.0448225	+	0.0138259i	−0.272263	+	0.962223i	$0.587772\pi$
$674$	10.7157	+	27.3032i	0.412754	+	1.05168i
$675$	4.34234	−	2.96056i	0.167137	−	0.113952i
$676$	5.07601	+	0.765085i	0.195231	+	0.0294264i
$677$	−7.73790	+	33.9019i	−0.297391	+	1.30296i	0.576604	+	0.817024i	$0.304377\pi$
$677$	−7.73790	+	33.9019i	−0.297391	+	1.30296i	−0.873996	+	0.485934i	$0.838480\pi$
$678$	−14.3812	−	9.80493i	−0.552306	−	0.376556i
$679$	0.673852	+	0.625243i	0.0258601	+	0.0239946i
$680$	−2.20606	−	1.06238i	−0.0845986	−	0.0407405i
$681$	−11.9205	+	20.6469i	−0.456794	+	0.791190i
$682$	1.41483	+	2.45056i	0.0541766	+	0.0938366i
$683$	−2.12602	−	28.3697i	−0.0813498	−	1.08554i	−0.877226	−	0.480078i	$-0.840608\pi$
$683$	−2.12602	−	28.3697i	−0.0813498	−	1.08554i	0.795876	−	0.605460i	$-0.207011\pi$
$684$	2.46194	+	10.7865i	0.0941346	+	0.412431i
$685$	−0.257220	+	0.655386i	−0.00982788	+	0.0250410i
$686$	−9.76127	+	12.2402i	−0.372687	+	0.467335i
$687$	−2.55073			−0.0973164
$688$	−4.75603	−	4.51445i	−0.181322	−	0.172112i
$689$	28.6810			1.09266
$690$	1.17149	−	1.46900i	0.0445979	−	0.0559240i
$691$	3.45759	−	8.80979i	0.131533	−	0.335140i	−0.849901	−	0.526943i	$-0.823338\pi$
$691$	3.45759	−	8.80979i	0.131533	−	0.335140i	0.981433	+	0.191803i	$0.0614334\pi$
$692$	1.72795	+	7.57065i	0.0656868	+	0.287793i
$693$	0.559790	+	7.46988i	0.0212647	+	0.283757i
$694$	−5.81541	−	10.0726i	−0.220750	−	0.382350i
$695$	2.14135	−	3.70893i	0.0812262	−	0.140688i
$696$	−4.64553	−	2.23717i	−0.176088	−	0.0847997i
$697$	−14.2078	−	13.1829i	−0.538159	−	0.499339i
$698$	10.3739	+	7.07281i	0.392658	+	0.267710i
$699$	−3.70120	+	16.2160i	−0.139992	+	0.613346i
$700$	1.24767	+	0.188055i	0.0471574	+	0.00710783i
$701$	5.38006	−	3.66806i	0.203202	−	0.138541i	−0.457444	−	0.889239i	$-0.651235\pi$
$701$	5.38006	−	3.66806i	0.203202	−	0.138541i	0.660646	+	0.750698i	$0.270283\pi$
$702$	−5.38532	−	13.7216i	−0.203256	−	0.517887i
$703$	67.7072	+	20.8849i	2.55363	+	0.787690i
$704$	−2.96772	+	1.42918i	−0.111850	+	0.0538641i
$705$	−0.657533	+	8.77417i	−0.0247641	+	0.330454i
$706$	12.6617	−	1.90844i	0.476528	−	0.0718250i
$707$	12.0427	−	11.1740i	0.452912	−	0.420241i
$708$	−0.539292	+	0.166350i	−0.0202678	+	0.00625180i
$709$	−27.4039	−	34.3634i	−1.02918	−	1.29055i	−0.956044	−	0.293223i	$-0.905272\pi$
$709$	−27.4039	−	34.3634i	−1.02918	−	1.29055i	−0.0731318	−	0.997322i	$-0.523299\pi$
$710$	−2.49714	−	3.13131i	−0.0937160	−	0.117516i
$711$	5.56964	−	1.71801i	0.208878	−	0.0644303i
$712$	13.6760	−	12.6895i	0.512530	−	0.475559i
$713$	−1.45844	+	0.219825i	−0.0546191	+	0.00823250i
$714$	0.252664	−	3.37157i	0.00945572	−	0.126178i
$715$	−8.32372	+	4.00849i	−0.311289	+	0.149909i
$716$	18.1086	+	5.58575i	0.676749	+	0.208749i
$717$	5.82705	+	14.8471i	0.217615	+	0.554475i
$718$	0.906740	−	0.618205i	0.0338392	−	0.0230712i
$719$	−30.8877	−	4.65557i	−1.15192	−	0.173624i	−0.454809	−	0.890589i	$-0.650292\pi$
$719$	−30.8877	−	4.65557i	−1.15192	−	0.173624i	−0.697109	+	0.716966i	$0.745530\pi$
$720$	0.401062	−	1.75717i	0.0149467	−	0.0654858i
$721$	2.57623	+	1.75645i	0.0959440	+	0.0654135i
$722$	13.6947	+	12.7069i	0.509665	+	0.472900i
$723$	9.51649	+	4.58290i	0.353922	+	0.170440i
$724$	−2.41021	+	4.17461i	−0.0895749	+	0.155148i
$725$	−2.35577	−	4.08030i	−0.0874909	−	0.151539i
$726$	−0.0122767	−	0.163822i	−0.000455632	−	0.00607999i
$727$	−7.60605	−	33.3243i	−0.282093	−	1.23593i	−0.895105	−	0.445855i	$-0.852900\pi$
$727$	−7.60605	−	33.3243i	−0.282093	−	1.23593i	0.613012	−	0.790073i	$-0.289958\pi$
$728$	1.29292	−	3.29429i	0.0479186	−	0.122095i
$729$	11.1451	−	13.9755i	0.412781	−	0.517611i
$730$	−13.2063			−0.488788
$731$	−15.3956	+	4.55825i	−0.569425	+	0.168593i
$732$	0.143570			0.00530649
$733$	−30.2923	+	37.9853i	−1.11887	+	1.40302i	−0.214262	+	0.976776i	$0.568735\pi$
$733$	−30.2923	+	37.9853i	−1.11887	+	1.40302i	−0.904608	+	0.426244i	$0.859837\pi$
$734$	−8.03265	+	20.4668i	−0.296490	+	0.755445i
$735$	−1.31695	−	5.76992i	−0.0485763	−	0.212827i
$736$	−0.128304	−	1.71210i	−0.00472936	−	0.0631089i
$737$	0.854244	+	1.47959i	0.0314665	+	0.0545016i
$738$	7.13338	−	12.3554i	0.262583	−	0.454808i
$739$	41.6207	+	20.0435i	1.53104	+	0.737310i	0.994318	−	0.106448i	$-0.0339479\pi$
$739$	41.6207	+	20.0435i	1.53104	+	0.737310i	0.536723	+	0.843759i	$0.319662\pi$
$740$	−8.46136	−	7.85100i	−0.311046	−	0.288608i
$741$	−15.5679	−	10.6140i	−0.571901	−	0.389916i
$742$	−2.87109	+	12.5791i	−0.105401	+	0.461792i
$743$	1.31843	+	0.198721i	0.0483684	+	0.00729036i	0.173182	−	0.984890i	$-0.444595\pi$
$743$	1.31843	+	0.198721i	0.0483684	+	0.00729036i	−0.124814	+	0.992180i	$0.539833\pi$
$744$	0.776767	−	0.529591i	0.0284776	−	0.0194157i
$745$	3.49543	+	8.90622i	0.128063	+	0.326299i
$746$	−1.58006	−	0.487385i	−0.0578502	−	0.0178444i
$747$	−17.1246	+	8.24675i	−0.626555	+	0.301733i
$748$	−0.602721	+	8.04275i	−0.0220376	+	0.294072i
$749$	−9.61433	+	1.44913i	−0.351300	+	0.0529499i
$750$	−0.802229	+	0.744360i	−0.0292933	+	0.0271802i
$751$	28.5906	−	8.81902i	1.04328	−	0.321811i	0.274680	−	0.961536i	$-0.411428\pi$
$751$	28.5906	−	8.81902i	1.04328	−	0.321811i	0.768604	+	0.639725i	$0.220952\pi$
$752$	5.01288	+	6.28596i	0.182801	+	0.229225i
$753$	−16.2456	−	20.3714i	−0.592024	−	0.742374i
$754$	−12.6276	+	3.89510i	−0.459870	+	0.141851i
$755$	14.2695	−	13.2402i	0.519320	−	0.481859i
$756$	6.55717	−	0.988335i	0.238482	−	0.0359454i
$757$	3.27663	−	43.7236i	0.119091	−	1.58916i	−0.542997	−	0.839734i	$-0.682711\pi$
$757$	3.27663	−	43.7236i	0.119091	−	1.58916i	0.662088	−	0.749426i	$-0.269670\pi$
$758$	−23.4384	+	11.2873i	−0.851322	+	0.409975i
$759$	−5.91406	−	1.82425i	−0.214667	−	0.0662160i
$760$	−2.24266	−	5.71422i	−0.0813500	−	0.207276i
$761$	−10.9905	+	7.49322i	−0.398407	+	0.271629i	−0.745906	−	0.666051i	$-0.767983\pi$
$761$	−10.9905	+	7.49322i	−0.398407	+	0.271629i	0.347499	+	0.937680i	$0.387031\pi$
$762$	−5.05176	−	0.761430i	−0.183006	−	0.0275837i
$763$	2.11825	−	9.28065i	0.0766857	−	0.335982i
$764$	14.3070	+	9.75435i	0.517609	+	0.352900i
$765$	−3.23507	−	3.00170i	−0.116964	−	0.108527i
$766$	17.2935	+	8.32809i	0.624838	+	0.300906i
$767$	−0.723205	+	1.25263i	−0.0261134	+	0.0452298i
$768$	0.547184	+	0.947751i	0.0197448	+	0.0341990i
$769$	−3.54423	−	47.2945i	−0.127808	−	1.70548i	−0.580865	−	0.814000i	$-0.697286\pi$
$769$	−3.54423	−	47.2945i	−0.127808	−	1.70548i	0.453057	−	0.891482i	$-0.350333\pi$
$770$	−0.924826	−	4.05193i	−0.0333284	−	0.146021i
$771$	9.20121	−	23.4443i	0.331373	−	0.844326i
$772$	−10.0668	+	12.6233i	−0.362311	+	0.454324i
$773$	−30.3274			−1.09080			−0.545400	−	0.838176i	$-0.683622\pi$
$773$	−30.3274			−1.09080			−0.545400	+	0.838176i	$0.683622\pi$
$774$	−5.79291	−	10.3018i	−0.208222	−	0.370291i
$775$	0.859056			0.0308582
$776$	−0.454237	+	0.569595i	−0.0163062	+	0.0204473i
$777$	5.82296	−	14.8367i	0.208898	−	0.532263i
$778$	2.88385	+	12.6350i	0.103391	+	0.452986i
$779$	−3.63116	−	48.4545i	−0.130100	−	1.73606i
$780$	1.53472	+	2.65821i	0.0549517	+	0.0951792i
$781$	−6.59623	+	11.4250i	−0.236032	+	0.408819i
$782$	−3.78760	−	1.82401i	−0.135444	−	0.0652265i
$783$	−18.1516	−	16.8422i	−0.648685	−	0.601892i
$784$	−4.46827	−	3.04641i	−0.159581	−	0.108801i
$785$	2.92608	−	12.8200i	0.104436	−	0.457565i
$786$	−18.5895	−	2.80191i	−0.663065	−	0.0999410i
$787$	−8.52830	+	5.81449i	−0.304001	+	0.207264i	−0.705706	−	0.708505i	$-0.749370\pi$
$787$	−8.52830	+	5.81449i	−0.304001	+	0.207264i	0.401705	+	0.915769i	$0.368418\pi$
$788$	−4.28314	−	10.9133i	−0.152580	−	0.388769i
$789$	12.0041	+	3.70278i	0.427358	+	0.131823i
$790$	−2.91362	+	1.40312i	−0.103662	+	0.0499209i
$791$	1.49968	−	20.0118i	0.0533224	−	0.711537i
$792$	−5.87050	+	0.884836i	−0.208599	+	0.0314413i
$793$	0.269730	−	0.250273i	0.00957839	−	0.00888744i
$794$	−16.3274	+	5.03634i	−0.579439	+	0.178733i
$795$	−6.97738	−	8.74936i	−0.247462	−	0.310308i
$796$	4.18886	+	5.25267i	0.148470	+	0.186176i
$797$	−15.6899	+	4.83968i	−0.555763	+	0.171430i	−0.559899	−	0.828561i	$-0.689160\pi$
$797$	−15.6899	+	4.83968i	−0.555763	+	0.171430i	0.00413527	+	0.999991i	$0.498684\pi$
$798$	6.21356	−	5.76534i	0.219958	−	0.204091i
$799$	19.4665	−	2.93411i	0.688676	−	0.103801i
$800$	−0.0747301	+	0.997204i	−0.00264211	+	0.0352565i
$801$	30.2953	−	14.5895i	1.07043	−	0.515493i
$802$	−27.1100	−	8.36233i	−0.957288	−	0.295284i
$803$	15.8925	+	40.4935i	0.560835	+	1.42898i
$804$	0.468996	−	0.319756i	0.0165402	−	0.0112769i
$805$	2.14212	+	0.322873i	0.0754999	+	0.0113798i
$806$	0.536151	−	2.34903i	0.0188851	−	0.0827411i
$807$	−10.6780	−	7.28011i	−0.375882	−	0.256272i
$808$	9.54437	+	8.85588i	0.335770	+	0.311549i
$809$	−10.2986	−	4.95953i	−0.362078	−	0.174368i	0.243995	−	0.969776i	$-0.421542\pi$
$809$	−10.2986	−	4.95953i	−0.362078	−	0.174368i	−0.606073	+	0.795409i	$0.707256\pi$
$810$	−0.172219	+	0.298293i	−0.00605117	+	0.0104809i
$811$	−22.2909	−	38.6089i	−0.782739	−	1.35574i	−0.930341	−	0.366696i	$-0.880489\pi$
$811$	−22.2909	−	38.6089i	−0.782739	−	1.35574i	0.147602	−	0.989047i	$-0.452845\pi$
$812$	−0.444257	−	5.92819i	−0.0155904	−	0.208039i
$813$	3.79613	+	16.6319i	0.133136	+	0.583307i
$814$	−13.8905	+	35.3923i	−0.486860	+	1.24050i
$815$	2.00141	−	2.50968i	0.0701062	−	0.0879104i
$816$	2.67961			0.0938051
$817$	−36.0664	−	17.8756i	−1.26180	−	0.625387i
$818$	8.93209			0.312303
$819$	3.97687	−	4.98684i	0.138963	−	0.174254i
$820$	−2.89190	+	7.36844i	−0.100989	+	0.257317i
$821$	5.31470	+	23.2852i	0.185484	+	0.812659i	0.978959	+	0.204056i	$0.0654126\pi$
$821$	5.31470	+	23.2852i	0.185484	+	0.812659i	−0.793475	+	0.608603i	$0.791730\pi$
$822$	−0.0575792	−	0.768341i	−0.00200831	−	0.0267990i
$823$	0.131660	+	0.228041i	0.00458937	+	0.00794901i	0.868311	−	0.496020i	$-0.165206\pi$
$823$	0.131660	+	0.228041i	0.00458937	+	0.00794901i	−0.863722	+	0.503969i	$0.831872\pi$
$824$	−1.23559	+	2.14010i	−0.0430437	+	0.0745539i
$825$	3.24778	+	1.56405i	0.113073	+	0.0544531i
$826$	−0.476988	−	0.442581i	−0.0165965	−	0.0153993i
$827$	15.5650	+	10.6120i	0.541247	+	0.369016i	0.802870	−	0.596154i	$-0.203305\pi$
$827$	15.5650	+	10.6120i	0.541247	+	0.369016i	−0.261623	+	0.965170i	$0.584258\pi$
$828$	0.688585	−	3.01689i	0.0239300	−	0.104844i
$829$	49.5025	+	7.46131i	1.71929	+	0.259142i	0.933301	−	0.359094i	$-0.116914\pi$
$829$	49.5025	+	7.46131i	1.71929	+	0.259142i	0.785993	+	0.618236i	$0.212152\pi$
$830$	8.71313	−	5.94051i	0.302437	−	0.206198i
$831$	−7.05055	−	17.9645i	−0.244581	−	0.623182i
$832$	2.68015	+	0.826716i	0.0929174	+	0.0286612i
$833$	−11.9303	+	5.74533i	−0.413360	+	0.199064i
$834$	−0.350250	+	4.67375i	−0.0121281	+	0.161839i
$835$	−0.904431	+	0.136321i	−0.0312991	+	0.00471758i
$836$	−14.8222	+	13.7530i	−0.512637	+	0.475658i
$837$	4.31423	−	1.33076i	0.149122	−	0.0459979i
$838$	15.2074	+	19.0695i	0.525331	+	0.658744i
$839$	21.8402	+	27.3867i	0.754006	+	0.945493i	0.999716	−	0.0238500i	$-0.00759242\pi$
$839$	21.8402	+	27.3867i	0.754006	+	0.945493i	−0.245710	+	0.969343i	$0.579021\pi$
$840$	−1.31948	+	0.407007i	−0.0455265	+	0.0140431i
$841$	4.98584	−	4.62618i	0.171926	−	0.159524i
$842$	−20.4073	+	3.07591i	−0.703282	+	0.106003i
$843$	−0.966124	+	12.8920i	−0.0332751	+	0.444025i
$844$	−5.96729	+	2.87370i	−0.205403	+	0.0989167i
$845$	−4.90529	−	1.51308i	−0.168747	−	0.0520515i
$846$	5.29417	+	13.4893i	0.182017	+	0.463772i
$847$	0.156497	−	0.106698i	0.00537730	−	0.00366618i
$848$	−10.1116	−	1.52408i	−0.347235	−	0.0523372i
$849$	−7.05309	+	30.9016i	−0.242061	+	1.06054i
$850$	2.02308	+	1.37931i	0.0693911	+	0.0473101i
$851$	−14.5273	−	13.4794i	−0.497991	−	0.462068i
$852$	3.94900	+	1.90174i	0.135290	+	0.0651524i
$853$	−4.36154	+	7.55440i	−0.149336	+	0.258658i	−0.930982	−	0.365064i	$-0.881047\pi$
$853$	−4.36154	+	7.55440i	−0.149336	+	0.258658i	0.781646	+	0.623722i	$0.214380\pi$
$854$	0.0827648	+	0.143353i	0.00283215	+	0.00490543i
$855$	−0.826803	−	11.0329i	−0.0282761	−	0.377318i
$856$	−1.71471	−	7.51265i	−0.0586077	−	0.256777i
$857$	11.9215	−	30.3754i	0.407229	−	1.03760i	−0.569283	−	0.822142i	$-0.692779\pi$
$857$	11.9215	−	30.3754i	0.407229	−	1.03760i	0.976512	−	0.215462i	$-0.0691256\pi$
$858$	6.30377	−	7.90468i	0.215207	−	0.269861i
$859$	−27.8980			−0.951867			−0.475933	−	0.879481i	$-0.657890\pi$
$859$	−27.8980			−0.951867			−0.475933	+	0.879481i	$0.657890\pi$
$860$	4.03006	+	5.17287i	0.137424	+	0.176393i
$861$	−10.9301			−0.372497
$862$	−22.2138	+	27.8552i	−0.756604	+	0.948751i
$863$	21.2028	−	54.0239i	0.721753	−	1.83900i	0.215790	−	0.976440i	$-0.430767\pi$
$863$	21.2028	−	54.0239i	0.721753	−	1.83900i	0.505962	−	0.862556i	$-0.331138\pi$
$864$	1.16947	+	5.12378i	0.0397862	+	0.174315i
$865$	−0.580305	−	7.74363i	−0.0197310	−	0.263291i
$866$	−4.03487	−	6.98861i	−0.137111	−	0.237482i
$867$	−6.02156	+	10.4297i	−0.204503	+	0.354210i
$868$	0.976580	+	0.470296i	0.0331473	+	0.0159629i
$869$	7.80854	+	7.24527i	0.264887	+	0.245779i
$870$	4.26021	+	2.90456i	0.144435	+	0.0984739i
$871$	0.323717	−	1.41830i	0.0109687	−	0.0480572i
$872$	7.46021	+	1.12445i	0.252635	+	0.0380786i
$873$	−1.08492	+	0.739689i	−0.0367191	+	0.0250347i
$874$	−3.85044	−	9.81076i	−0.130243	−	0.331854i
$875$	−1.20570	−	0.371910i	−0.0407602	−	0.0125729i
$876$	13.0213	−	6.27074i	0.439950	−	0.211869i
$877$	2.55080	−	34.0381i	0.0861345	−	1.14939i	−0.771883	−	0.635765i	$-0.780685\pi$
$877$	2.55080	−	34.0381i	0.0861345	−	1.14939i	0.858017	−	0.513621i	$-0.171696\pi$
$878$	23.6773	−	3.56877i	0.799069	−	0.120440i
$879$	9.30358	−	8.63246i	0.313802	−	0.291166i
$880$	3.14758	−	0.970899i	0.106105	−	0.0327290i
$881$	−22.8404	−	28.6410i	−0.769514	−	0.964940i	0.230453	−	0.973083i	$-0.425979\pi$
$881$	−22.8404	−	28.6410i	−0.769514	−	0.964940i	−0.999967	+	0.00814388i	$0.997408\pi$
$882$	−6.07721	−	7.62057i	−0.204630	−	0.256598i
$883$	52.0462	−	16.0541i	1.75149	−	0.540264i	0.757810	−	0.652476i	$-0.226270\pi$
$883$	52.0462	−	16.0541i	1.75149	−	0.540264i	0.993684	+	0.112211i	$0.0357934\pi$
$884$	5.03428	−	4.67113i	0.169321	−	0.157107i
$885$	0.558062	−	0.0841143i	0.0187590	−	0.00282747i
$886$	0.927919	−	12.3822i	0.0311740	−	0.415989i
$887$	−22.5119	+	10.8412i	−0.755876	+	0.364011i	−0.771802	−	0.635862i	$-0.780645\pi$
$887$	−22.5119	+	10.8412i	−0.755876	+	0.364011i	0.0159264	+	0.999873i	$0.494930\pi$
$888$	12.0707	+	3.72332i	0.405067	+	0.124947i
$889$	−2.15195	−	5.48307i	−0.0721740	−	0.183896i
$890$	−15.4145	+	10.5095i	−0.516696	+	0.352278i
$891$	1.12188	+	0.169096i	0.0375844	+	0.00566494i
$892$	1.69060	−	7.40699i	0.0566054	−	0.248004i
$893$	40.7784	+	27.8022i	1.36460	+	0.930366i
$894$	−7.67540	−	7.12173i	−0.256704	−	0.238186i
$895$	−17.0738	−	8.22230i	−0.570714	−	0.274841i
$896$	−0.630880	+	1.09272i	−0.0210762	+	0.0365051i
$897$	2.63496	+	4.56389i	0.0879789	+	0.152384i
$898$	−2.92570	−	39.0408i	−0.0976320	−	1.30281i
$899$	−0.900646	−	3.94599i	−0.0300382	−	0.131606i
$900$	−0.658475	+	1.67777i	−0.0219492	+	0.0559256i
$901$	−15.6112	+	19.5758i	−0.520085	+	0.652165i
$902$	26.0734			0.868148
$903$	−4.61604	+	7.78973i	−0.153612	+	0.259226i
$904$	15.9047			0.528983
$905$	3.00549	−	3.76876i	0.0999058	−	0.125278i
$906$	−7.78281	+	19.8303i	−0.258566	+	0.658817i
$907$	8.80859	+	38.5930i	0.292485	+	1.28146i	0.881055	+	0.473013i	$0.156834\pi$
$907$	8.80859	+	38.5930i	0.292485	+	1.28146i	−0.588571	+	0.808446i	$0.700309\pi$
$908$	−1.62800	−	21.7242i	−0.0540272	−	0.720943i
$909$	11.7334	+	20.3228i	0.389172	+	0.674066i
$910$	−1.76946	+	3.06480i	−0.0586571	+	0.101597i
$911$	−17.4415	−	8.39940i	−0.577864	−	0.278284i	0.122036	−	0.992526i	$-0.461058\pi$
$911$	−17.4415	−	8.39940i	−0.577864	−	0.278284i	−0.699900	+	0.714241i	$0.746772\pi$
$912$	4.92452	+	4.56929i	0.163067	+	0.151304i
$913$	−28.7003	−	19.5675i	−0.949842	−	0.647591i
$914$	−2.73056	+	11.9634i	−0.0903188	+	0.395713i
$915$	−0.141966	−	0.0213980i	−0.00469326	−	0.000707395i
$916$	1.92578	−	1.31297i	0.0636295	−	0.0433818i
$917$	−7.91875	−	20.1766i	−0.261500	−	0.666292i
$918$	12.2967	+	3.79304i	0.405853	+	0.125189i
$919$	13.9387	−	6.71253i	0.459796	−	0.221426i	−0.189623	−	0.981857i	$-0.560727\pi$
$919$	13.9387	−	6.71253i	0.459796	−	0.221426i	0.649419	+	0.760431i	$0.275012\pi$
$920$	−0.128304	+	1.71210i	−0.00423007	+	0.0564464i
$921$	2.26778	−	0.341813i	0.0747259	−	0.0112631i
$922$	−6.89287	+	6.39565i	−0.227005	+	0.210629i
$923$	10.7343	−	3.31108i	0.353323	−	0.108986i
$924$	2.83584	+	3.55603i	0.0932924	+	0.116985i
$925$	7.19672	+	9.02441i	0.236627	+	0.296721i
$926$	6.82025	−	2.10377i	0.224127	−	0.0691342i
$927$	−3.26497	+	3.02945i	−0.107236	+	0.0995001i
$928$	4.65891	−	0.702217i	0.152936	−	0.0230514i
$929$	−0.725093	+	9.67570i	−0.0237895	+	0.317449i	0.972596	+	0.232502i	$0.0746912\pi$
$929$	−0.725093	+	9.67570i	−0.0237895	+	0.317449i	−0.996385	+	0.0849473i	$0.972928\pi$
$930$	−0.847022	+	0.407904i	−0.0277750	+	0.0133757i
$931$	−31.7222	−	9.78500i	−1.03965	−	0.320691i
$932$	−5.55272	−	14.1481i	−0.181886	−	0.463437i
$933$	22.2656	−	15.1805i	0.728944	−	0.496986i
$934$	9.82131	+	1.48032i	0.321363	+	0.0484377i
$935$	1.79470	−	7.86308i	0.0586929	−	0.257150i
$936$	4.17678	+	2.84768i	0.136522	+	0.0930793i
$937$	27.6862	+	25.6890i	0.904469	+	0.839224i	0.987548	−	0.157319i	$-0.0502850\pi$
$937$	27.6862	+	25.6890i	0.904469	+	0.839224i	−0.0830794	+	0.996543i	$0.526475\pi$
$938$	0.589639	+	0.283955i	0.0192524	+	0.00927146i
$939$	−4.30562	+	7.45755i	−0.140508	+	0.243368i
$940$	−4.02002	−	6.96288i	−0.131119	−	0.227104i
$941$	1.03197	+	13.7707i	0.0336413	+	0.448912i	0.988435	+	0.151643i	$0.0484565\pi$
$941$	1.03197	+	13.7707i	0.0336413	+	0.448912i	−0.954794	+	0.297268i	$0.903924\pi$
$942$	3.20221	+	14.0298i	0.104334	+	0.457116i
$943$	−4.96511	+	12.6509i	−0.161686	+	0.411970i
$944$	0.321533	−	0.403190i	0.0104650	−	0.0131227i
$945$	−6.63124			−0.215714
$946$	11.0114	−	18.5821i	0.358011	−	0.604156i
$947$	−17.9379			−0.582904			−0.291452	−	0.956585i	$-0.594138\pi$
$947$	−17.9379			−0.582904			−0.291452	+	0.956585i	$0.594138\pi$
$948$	2.20656	−	2.76694i	0.0716657	−	0.0898660i
$949$	13.5324	−	34.4800i	0.439281	−	1.11927i
$950$	1.36596	+	5.98464i	0.0443175	+	0.194168i
$951$	−0.579319	−	7.73048i	−0.0187857	−	0.250678i
$952$	1.54474	+	2.67556i	0.0500652	+	0.0867155i
$953$	3.50940	−	6.07846i	0.113681	−	0.196901i	−0.803571	−	0.595209i	$-0.797069\pi$
$953$	3.50940	−	6.07846i	0.113681	−	0.196901i	0.917252	+	0.398308i	$0.130403\pi$
$954$	−16.6054	−	7.99675i	−0.537620	−	0.258904i
$955$	−12.6934	−	11.7778i	−0.410749	−	0.381119i
$956$	−12.0418	−	8.20998i	−0.389461	−	0.265530i
$957$	3.77928	−	16.5581i	0.122167	−	0.535248i
$958$	−33.8002	−	5.09456i	−1.09203	−	0.164598i
$959$	0.733987	−	0.500424i	0.0237017	−	0.0161595i
$960$	−0.399818	−	1.01872i	−0.0129041	−	0.0328790i
$961$	−28.9176	−	8.91989i	−0.932825	−	0.287738i
$962$	29.1682	−	14.0467i	0.940422	−	0.452883i
$963$	1.03790	−	13.8499i	0.0334460	−	0.446305i
$964$	−9.54389	+	1.43851i	−0.307388	+	0.0463313i
$965$	11.8358	−	10.9820i	0.381006	−	0.353522i
$966$	−2.26543	+	0.698791i	−0.0728889	+	0.0224832i
$967$	21.4291	+	26.8712i	0.689112	+	0.864119i	0.996158	−	0.0875757i	$-0.0279120\pi$
$967$	21.4291	+	26.8712i	0.689112	+	0.864119i	−0.307046	+	0.951695i	$0.599341\pi$
$968$	0.0935951	+	0.117364i	0.00300826	+	0.00377224i
$969$	15.7181	−	4.84840i	0.504939	−	0.155753i
$970$	0.534058	−	0.495533i	0.0171476	−	0.0159106i
$971$	40.7689	−	6.14493i	1.30834	−	0.197200i	0.542403	−	0.840118i	$-0.317515\pi$
$971$	40.7689	−	6.14493i	1.30834	−	0.197200i	0.765935	+	0.642918i	$0.222276\pi$
$972$	−1.15007	+	15.3467i	−0.0368886	+	0.492245i
$973$	−4.86861	+	2.34460i	−0.156080	+	0.0751643i
$974$	−27.9424	−	8.61908i	−0.895331	−	0.276173i
$975$	−1.12139	−	2.85726i	−0.0359133	−	0.0915055i
$976$	−0.108394	+	0.0739017i	−0.00346960	+	0.00236554i
$977$	−45.0952	−	6.79701i	−1.44272	−	0.217456i	−0.619422	−	0.785058i	$-0.712633\pi$
$977$	−45.0952	−	6.79701i	−1.44272	−	0.217456i	−0.823303	+	0.567603i	$0.807871\pi$
$978$	−0.781700	+	3.42485i	−0.0249960	+	0.109515i
$979$	50.7742	+	34.6173i	1.62275	+	1.10637i
$980$	3.96432	+	3.67835i	0.126635	+	0.117501i
$981$	12.2512	+	5.89988i	0.391152	+	0.188369i
$982$	12.6686	−	21.9427i	0.404273	−	0.700221i
$983$	−14.8273	−	25.6816i	−0.472916	−	0.819114i	0.526604	−	0.850111i	$-0.323465\pi$
$983$	−14.8273	−	25.6816i	−0.472916	−	0.819114i	−0.999519	+	0.0309966i	$0.990132\pi$
$984$	−0.647357	−	8.63838i	−0.0206370	−	0.275381i
$985$	2.60876	+	11.4297i	0.0831221	+	0.364182i
$986$	4.21472	−	10.7389i	0.134224	−	0.341997i
$987$	6.92194	−	8.67984i	0.220328	−	0.276282i
$988$	17.2171			0.547750
$989$	6.91923	+	8.88132i	0.220019	+	0.282410i
$990$	5.93681			0.188684
$991$	37.7543	−	47.3424i	1.19931	−	1.50388i	0.385537	−	0.922692i	$-0.374016\pi$
$991$	37.7543	−	47.3424i	1.19931	−	1.50388i	0.813769	−	0.581189i	$-0.197412\pi$
$992$	−0.313848	+	0.799672i	−0.00996469	+	0.0253896i
$993$	1.54779	+	6.78131i	0.0491176	+	0.215198i
$994$	0.377646	+	5.03934i	0.0119782	+	0.159838i
$995$	−3.35921	−	5.81831i	−0.106494	−	0.184453i
$996$	−5.77035	+	9.99454i	−0.182841	+	0.316689i
$997$	−19.3517	−	9.31927i	−0.612873	−	0.295144i	0.101580	−	0.994827i	$-0.467610\pi$
$997$	−19.3517	−	9.31927i	−0.612873	−	0.295144i	−0.714453	+	0.699683i	$0.753324\pi$
$998$	18.8423	+	17.4831i	0.596444	+	0.553419i
$999$	50.1221	+	34.1727i	1.58579	+	1.08118i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.c.101.2	✓	48
43.23	even	21	inner	430.2.q.c.281.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.c.101.2	✓	48	1.1	even	1	trivial
430.2.q.c.281.2	yes	48	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)

\(f(q)\)	\(=\)	\(q+(-0.623490 + 0.781831i) q^{2} +(-0.399818 + 1.01872i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(0.0747301 + 0.997204i) q^{5} +(-0.547184 - 0.947751i) q^{6} +(0.630880 - 1.09272i) q^{7} +(0.900969 + 0.433884i) q^{8} +(1.32122 + 1.22591i) q^{9} +O(q^{10})\)	\(q+(-0.623490 + 0.781831i) q^{2} +(-0.399818 + 1.01872i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(0.0747301 + 0.997204i) q^{5} +(-0.547184 - 0.947751i) q^{6} +(0.630880 - 1.09272i) q^{7} +(0.900969 + 0.433884i) q^{8} +(1.32122 + 1.22591i) q^{9} +(-0.826239 - 0.563320i) q^{10} +(-0.732965 + 3.21133i) q^{11} +(1.08215 + 0.163107i) q^{12} +(2.31740 - 1.57998i) q^{13} +(0.460972 + 1.17454i) q^{14} +(-1.04575 - 0.322571i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-0.182980 + 2.44170i) q^{17} +(-1.78223 + 0.268627i) q^{18} +(-4.49988 + 4.17527i) q^{19} +(0.955573 - 0.294755i) q^{20} +(0.860933 + 1.07958i) q^{21} +(-2.05372 - 2.57529i) q^{22} +(1.64063 - 0.506066i) q^{23} +(-0.802229 + 0.744360i) q^{24} +(-0.988831 + 0.149042i) q^{25} +(-0.209600 + 2.79691i) q^{26} +(-4.73509 + 2.28030i) q^{27} +(-1.20570 - 0.371910i) q^{28} +(1.72132 + 4.38584i) q^{29} +(0.904210 - 0.616480i) q^{30} +(-0.849461 - 0.128036i) q^{31} +(0.222521 - 0.974928i) q^{32} +(-2.97839 - 2.03063i) q^{33} +(-1.79491 - 1.66543i) q^{34} +(1.13681 + 0.547457i) q^{35} +(0.901178 - 1.56089i) q^{36} +(-5.77132 - 9.99623i) q^{37} +(-0.458734 - 6.12139i) q^{38} +(0.683014 + 2.99248i) q^{39} +(-0.365341 + 0.930874i) q^{40} +(-4.93530 + 6.18867i) q^{41} -1.38083 q^{42} +(2.32629 + 6.13094i) q^{43} +3.29392 q^{44} +(-1.12375 + 1.40914i) q^{45} +(-0.627255 + 1.59822i) q^{46} +(-1.78908 - 7.83846i) q^{47} +(-0.0817823 - 1.09131i) q^{48} +(2.70398 + 4.68343i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-2.41425 - 1.16264i) q^{51} +(-2.05603 - 1.90772i) q^{52} +(8.44899 + 5.76042i) q^{53} +(1.16947 - 5.12378i) q^{54} +(-3.25713 - 0.490933i) q^{55} +(1.04251 - 0.710774i) q^{56} +(-2.45430 - 6.25346i) q^{57} +(-4.50221 - 1.38875i) q^{58} +(-0.464629 + 0.223754i) q^{59} +(-0.0817823 + 1.09131i) q^{60} +(0.129724 - 0.0195528i) q^{61} +(0.629732 - 0.584306i) q^{62} +(2.17311 - 0.670315i) q^{63} +(0.623490 + 0.781831i) q^{64} +(1.74874 + 2.19285i) q^{65} +(3.44461 - 1.06252i) q^{66} +(0.380219 - 0.352792i) q^{67} +(2.42120 - 0.364937i) q^{68} +(-0.140412 + 1.87367i) q^{69} +(-1.13681 + 0.547457i) q^{70} +(3.82716 + 1.18052i) q^{71} +(0.658475 + 1.67777i) q^{72} +(10.9116 - 7.43938i) q^{73} +(11.4137 + 1.72034i) q^{74} +(0.243520 - 1.06693i) q^{75} +(5.07191 + 3.45797i) q^{76} +(3.04666 + 2.82689i) q^{77} +(-2.76547 - 1.33178i) q^{78} +(1.61694 - 2.80061i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.0257399 - 0.343476i) q^{81} +(-1.76139 - 7.71715i) q^{82} +(-3.85272 + 9.81656i) q^{83} +(0.860933 - 1.07958i) q^{84} -2.44854 q^{85} +(-6.24378 - 2.00381i) q^{86} -5.15615 q^{87} +(-2.05372 + 2.57529i) q^{88} +(6.81590 - 17.3666i) q^{89} +(-0.401062 - 1.75717i) q^{90} +(-0.264464 - 3.52903i) q^{91} +(-0.858452 - 1.48688i) q^{92} +(0.470062 - 0.814171i) q^{93} +(7.24383 + 3.48844i) q^{94} +(-4.49988 - 4.17527i) q^{95} +(0.904210 + 0.616480i) q^{96} +(-0.162115 + 0.710274i) q^{97} +(-5.34756 - 0.806015i) q^{98} +(-4.90523 + 3.34433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9}+O(q^{10}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9} - 4 q^{10} + q^{11} + 14 q^{12} - 23 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{17} - 20 q^{18} - 3 q^{19} + 4 q^{20} - 8 q^{21} - q^{22} + 7 q^{23} + 4 q^{25} - 19 q^{26} + 32 q^{27} + 4 q^{28} + 30 q^{29} + 9 q^{31} + 8 q^{32} + 39 q^{33} - 8 q^{34} - 22 q^{35} - 29 q^{36} - 37 q^{37} - 11 q^{38} - 52 q^{39} - 4 q^{40} - 28 q^{41} - 6 q^{42} + 41 q^{43} + 8 q^{44} + 2 q^{45} - 28 q^{46} + 3 q^{47} - 41 q^{49} + 24 q^{50} - 30 q^{51} - 9 q^{52} - 69 q^{53} + 3 q^{54} + 10 q^{55} - 11 q^{56} + 116 q^{57} + 5 q^{58} + 10 q^{59} - 19 q^{61} - 93 q^{62} + 34 q^{63} - 8 q^{64} - 3 q^{65} - 18 q^{66} + 3 q^{67} + 8 q^{68} + 42 q^{69} + 22 q^{70} - 36 q^{71} + 22 q^{72} - 56 q^{73} + 9 q^{74} - 10 q^{76} + 3 q^{77} + 45 q^{78} + 16 q^{79} - 24 q^{80} - 19 q^{81} + 14 q^{82} + 64 q^{83} - 8 q^{84} - 30 q^{85} + 36 q^{86} + 78 q^{87} - q^{88} - 75 q^{89} + 5 q^{90} + 5 q^{91} + 14 q^{92} - 10 q^{93} - 45 q^{94} - 3 q^{95} + 33 q^{97} - q^{98} - 11 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9 - 4 * q^10 + q^11 + 14 * q^12 - 23 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^17 - 20 * q^18 - 3 * q^19 + 4 * q^20 - 8 * q^21 - q^22 + 7 * q^23 + 4 * q^25 - 19 * q^26 + 32 * q^27 + 4 * q^28 + 30 * q^29 + 9 * q^31 + 8 * q^32 + 39 * q^33 - 8 * q^34 - 22 * q^35 - 29 * q^36 - 37 * q^37 - 11 * q^38 - 52 * q^39 - 4 * q^40 - 28 * q^41 - 6 * q^42 + 41 * q^43 + 8 * q^44 + 2 * q^45 - 28 * q^46 + 3 * q^47 - 41 * q^49 + 24 * q^50 - 30 * q^51 - 9 * q^52 - 69 * q^53 + 3 * q^54 + 10 * q^55 - 11 * q^56 + 116 * q^57 + 5 * q^58 + 10 * q^59 - 19 * q^61 - 93 * q^62 + 34 * q^63 - 8 * q^64 - 3 * q^65 - 18 * q^66 + 3 * q^67 + 8 * q^68 + 42 * q^69 + 22 * q^70 - 36 * q^71 + 22 * q^72 - 56 * q^73 + 9 * q^74 - 10 * q^76 + 3 * q^77 + 45 * q^78 + 16 * q^79 - 24 * q^80 - 19 * q^81 + 14 * q^82 + 64 * q^83 - 8 * q^84 - 30 * q^85 + 36 * q^86 + 78 * q^87 - q^88 - 75 * q^89 + 5 * q^90 + 5 * q^91 + 14 * q^92 - 10 * q^93 - 45 * q^94 - 3 * q^95 + 33 * q^97 - q^98 - 11 * q^99

Introduction

L-functions

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