LMFDB - Embedded newform 294.2.m.d.235.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(25,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("294.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.m (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:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			235.3
Character	$\chi$	$=$	294.235
Dual form			294.2.m.d.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.988831 - 0.149042i) q^{2} +(-0.826239 + 0.563320i) q^{3} +(0.955573 + 0.294755i) q^{4} +(0.0491854 + 0.656334i) q^{5} +(0.900969 - 0.433884i) q^{6} +(2.17925 + 1.50029i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(0.365341 - 0.930874i) q^{9} +O(q^{10})$	\(q+(-0.988831 - 0.149042i) q^{2} +(-0.826239 + 0.563320i) q^{3} +(0.955573 + 0.294755i) q^{4} +(0.0491854 + 0.656334i) q^{5} +(0.900969 - 0.433884i) q^{6} +(2.17925 + 1.50029i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(0.365341 - 0.930874i) q^{9} +(0.0491854 - 0.656334i) q^{10} +(-1.06801 - 2.72125i) q^{11} +(-0.955573 + 0.294755i) q^{12} +(-3.41494 + 4.28219i) q^{13} +(-1.93130 - 1.80834i) q^{14} +(-0.410365 - 0.514581i) q^{15} +(0.826239 + 0.563320i) q^{16} +(2.53323 + 2.35049i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(3.54803 + 6.14538i) q^{19} +(-0.146457 + 0.641672i) q^{20} +(-2.64572 - 0.0119878i) q^{21} +(0.650502 + 2.85004i) q^{22} +(-2.94861 + 2.73591i) q^{23} +(0.988831 - 0.149042i) q^{24} +(4.51580 - 0.680647i) q^{25} +(4.01502 - 3.72539i) q^{26} +(0.222521 + 0.974928i) q^{27} +(1.64021 + 2.07598i) q^{28} +(-1.81339 + 7.94500i) q^{29} +(0.329087 + 0.569995i) q^{30} +(2.30409 - 3.99080i) q^{31} +(-0.733052 - 0.680173i) q^{32} +(2.41537 + 1.64677i) q^{33} +(-2.15461 - 2.70180i) q^{34} +(-0.877506 + 1.50411i) q^{35} +(0.623490 - 0.781831i) q^{36} +(-7.33411 + 2.26227i) q^{37} +(-2.59248 - 6.60554i) q^{38} +(0.409306 - 5.46182i) q^{39} +(0.240458 - 0.612677i) q^{40} +(-3.41431 - 1.64425i) q^{41} +(2.61439 + 0.406179i) q^{42} +(3.23626 - 1.55850i) q^{43} +(-0.218461 - 2.91516i) q^{44} +(0.628933 + 0.194000i) q^{45} +(3.32345 - 2.26589i) q^{46} +(5.41168 + 0.815680i) q^{47} -1.00000 q^{48} +(2.49823 + 6.53902i) q^{49} -4.56681 q^{50} +(-3.41713 - 0.515050i) q^{51} +(-4.52542 + 3.08538i) q^{52} +(0.544591 + 0.167984i) q^{53} +(-0.0747301 - 0.997204i) q^{54} +(1.73352 - 0.834818i) q^{55} +(-1.31248 - 2.29726i) q^{56} +(-6.39334 - 3.07887i) q^{57} +(2.97728 - 7.58598i) q^{58} +(0.888645 - 11.8581i) q^{59} +(-0.240458 - 0.612677i) q^{60} +(2.08614 - 0.643489i) q^{61} +(-2.87316 + 3.60282i) q^{62} +(2.19275 - 1.48048i) q^{63} +(0.623490 + 0.781831i) q^{64} +(-2.97851 - 2.03072i) q^{65} +(-2.14295 - 1.98837i) q^{66} +(3.93608 - 6.81749i) q^{67} +(1.72786 + 2.99275i) q^{68} +(0.895064 - 3.92153i) q^{69} +(1.09188 - 1.35652i) q^{70} +(-2.60273 - 11.4033i) q^{71} +(-0.733052 + 0.680173i) q^{72} +(-4.77293 + 0.719403i) q^{73} +(7.58937 - 1.14391i) q^{74} +(-3.34771 + 3.10622i) q^{75} +(1.57902 + 6.91815i) q^{76} +(1.75521 - 7.53261i) q^{77} +(-1.21878 + 5.33981i) q^{78} +(-7.88673 - 13.6602i) q^{79} +(-0.329087 + 0.569995i) q^{80} +(-0.733052 - 0.680173i) q^{81} +(3.13111 + 2.13476i) q^{82} +(9.90788 + 12.4241i) q^{83} +(-2.52465 - 0.791296i) q^{84} +(-1.41811 + 1.77825i) q^{85} +(-3.43239 + 1.05875i) q^{86} +(-2.97728 - 7.58598i) q^{87} +(-0.218461 + 2.91516i) q^{88} +(-1.69707 + 4.32405i) q^{89} +(-0.592994 - 0.285571i) q^{90} +(-13.8665 + 4.20855i) q^{91} +(-3.62404 + 1.74524i) q^{92} +(0.344370 + 4.59530i) q^{93} +(-5.22967 - 1.61314i) q^{94} +(-3.85890 + 2.63096i) q^{95} +(0.988831 + 0.149042i) q^{96} +9.63432 q^{97} +(-1.49574 - 6.83833i) q^{98} -2.92333 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 6 q^{6} - q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 36 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 6 * q^6 - q^7 - 6 * q^8 + 3 * q^9	\( 36 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 6 q^{6} - q^{7} - 6 q^{8} + 3 q^{9} + 13 q^{11} - 3 q^{12} + 2 q^{13} - 4 q^{14} + 3 q^{16} + q^{17} - 18 q^{18} - 2 q^{19} + 7 q^{20} - 12 q^{21} - 12 q^{22} + 42 q^{23} - 3 q^{24} + 33 q^{25} + 34 q^{26} + 6 q^{27} - 9 q^{28} - 4 q^{29} - 7 q^{30} - q^{31} + 3 q^{32} + q^{33} + 5 q^{34} - 4 q^{35} - 6 q^{36} + 45 q^{37} - 30 q^{38} - 6 q^{39} - 58 q^{41} - 20 q^{42} - q^{44} - 14 q^{45} - 7 q^{46} - 68 q^{47} - 36 q^{48} - 29 q^{49} + 74 q^{50} - 8 q^{51} - 15 q^{52} - 19 q^{53} - 3 q^{54} + 48 q^{55} - 15 q^{56} + 3 q^{57} - 40 q^{58} - 123 q^{59} - 13 q^{61} + 2 q^{62} + 10 q^{63} - 6 q^{64} + 9 q^{65} - 6 q^{66} - 7 q^{67} + q^{68} + 21 q^{69} - 16 q^{70} - 38 q^{71} + 3 q^{72} + 65 q^{73} + 38 q^{74} + 9 q^{75} - 17 q^{76} + 25 q^{77} + 5 q^{78} - 71 q^{79} + 7 q^{80} + 3 q^{81} + 29 q^{82} + 8 q^{83} + 4 q^{84} + 73 q^{85} - 14 q^{86} + 40 q^{87} - q^{88} + 45 q^{89} - 35 q^{91} - 7 q^{92} - 6 q^{93} + 9 q^{94} - 144 q^{95} - 3 q^{96} + 56 q^{97} + 24 q^{98} + 30 q^{99}+O(q^{100}) \) 36 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 6 * q^6 - q^7 - 6 * q^8 + 3 * q^9 + 13 * q^11 - 3 * q^12 + 2 * q^13 - 4 * q^14 + 3 * q^16 + q^17 - 18 * q^18 - 2 * q^19 + 7 * q^20 - 12 * q^21 - 12 * q^22 + 42 * q^23 - 3 * q^24 + 33 * q^25 + 34 * q^26 + 6 * q^27 - 9 * q^28 - 4 * q^29 - 7 * q^30 - q^31 + 3 * q^32 + q^33 + 5 * q^34 - 4 * q^35 - 6 * q^36 + 45 * q^37 - 30 * q^38 - 6 * q^39 - 58 * q^41 - 20 * q^42 - q^44 - 14 * q^45 - 7 * q^46 - 68 * q^47 - 36 * q^48 - 29 * q^49 + 74 * q^50 - 8 * q^51 - 15 * q^52 - 19 * q^53 - 3 * q^54 + 48 * q^55 - 15 * q^56 + 3 * q^57 - 40 * q^58 - 123 * q^59 - 13 * q^61 + 2 * q^62 + 10 * q^63 - 6 * q^64 + 9 * q^65 - 6 * q^66 - 7 * q^67 + q^68 + 21 * q^69 - 16 * q^70 - 38 * q^71 + 3 * q^72 + 65 * q^73 + 38 * q^74 + 9 * q^75 - 17 * q^76 + 25 * q^77 + 5 * q^78 - 71 * q^79 + 7 * q^80 + 3 * q^81 + 29 * q^82 + 8 * q^83 + 4 * q^84 + 73 * q^85 - 14 * q^86 + 40 * q^87 - q^88 + 45 * q^89 - 35 * q^91 - 7 * q^92 - 6 * q^93 + 9 * q^94 - 144 * q^95 - 3 * q^96 + 56 * q^97 + 24 * q^98 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{17}{21}\right)$

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 $

$2$	−0.988831	−	0.149042i	−0.699209	−	0.105389i
$2$	−0.988831	−	0.149042i	−0.699209	−	0.105389i
$3$	−0.826239	+	0.563320i	−0.477029	+	0.325233i
$3$	−0.826239	+	0.563320i	−0.477029	+	0.325233i
$4$	0.955573	+	0.294755i	0.477786	+	0.147378i
$5$	0.0491854	+	0.656334i	0.0219964	+	0.293521i	0.997343	+	0.0728443i	$0.0232076\pi$
$5$	0.0491854	+	0.656334i	0.0219964	+	0.293521i	−0.975347	+	0.220677i	$0.929173\pi$
$6$	0.900969	−	0.433884i	0.367819	−	0.177132i
$7$	2.17925	+	1.50029i	0.823678	+	0.567058i
$7$	2.17925	+	1.50029i	0.823678	+	0.567058i
$8$	−0.900969	−	0.433884i	−0.318541	−	0.153401i
$9$	0.365341	−	0.930874i	0.121780	−	0.310291i
$10$	0.0491854	−	0.656334i	0.0155538	−	0.207551i
$11$	−1.06801	−	2.72125i	−0.322018	−	0.820488i	−0.996608	−	0.0822955i	$-0.973775\pi$
$11$	−1.06801	−	2.72125i	−0.322018	−	0.820488i	0.674590	−	0.738192i	$-0.264320\pi$
$12$	−0.955573	+	0.294755i	−0.275850	+	0.0850885i
$13$	−3.41494	+	4.28219i	−0.947133	+	1.18767i	0.0349830	+	0.999388i	$0.488862\pi$
$13$	−3.41494	+	4.28219i	−0.947133	+	1.18767i	−0.982116	+	0.188279i	$0.939709\pi$
$14$	−1.93130	−	1.80834i	−0.516161	−	0.483298i
$15$	−0.410365	−	0.514581i	−0.105956	−	0.132864i
$16$	0.826239	+	0.563320i	0.206560	+	0.140830i
$17$	2.53323	+	2.35049i	0.614398	+	0.570078i	0.924765	−	0.380539i	$-0.124261\pi$
$17$	2.53323	+	2.35049i	0.614398	+	0.570078i	−0.310367	+	0.950617i	$0.600452\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	3.54803	+	6.14538i	0.813975	+	1.40985i	0.910062	+	0.414473i	$0.136034\pi$
$19$	3.54803	+	6.14538i	0.813975	+	1.40985i	−0.0960869	+	0.995373i	$0.530633\pi$
$20$	−0.146457	+	0.641672i	−0.0327489	+	0.143482i
$21$	−2.64572	−	0.0119878i	−0.577344	−	0.00261596i
$22$	0.650502	+	2.85004i	0.138687	+	0.607630i
$23$	−2.94861	+	2.73591i	−0.614828	+	0.570477i	−0.924888	−	0.380240i	$-0.875841\pi$
$23$	−2.94861	+	2.73591i	−0.614828	+	0.570477i	0.310060	+	0.950717i	$0.399651\pi$
$24$	0.988831	−	0.149042i	0.201844	−	0.0304231i
$25$	4.51580	−	0.680647i	0.903160	−	0.136129i
$26$	4.01502	−	3.72539i	0.787410	−	0.730610i
$27$	0.222521	+	0.974928i	0.0428242	+	0.187625i
$28$	1.64021	+	2.07598i	0.309970	+	0.392324i
$29$	−1.81339	+	7.94500i	−0.336739	+	1.47535i	0.469064	+	0.883164i	$0.344591\pi$
$29$	−1.81339	+	7.94500i	−0.336739	+	1.47535i	−0.805802	+	0.592184i	$0.798266\pi$
$30$	0.329087	+	0.569995i	0.0600828	+	0.104066i
$31$	2.30409	−	3.99080i	0.413827	−	0.716770i	−0.581477	−	0.813563i	$-0.697525\pi$
$31$	2.30409	−	3.99080i	0.413827	−	0.716770i	0.995305	+	0.0967929i	$0.0308584\pi$
$32$	−0.733052	−	0.680173i	−0.129586	−	0.120239i
$33$	2.41537	+	1.64677i	0.420462	+	0.286666i
$34$	−2.15461	−	2.70180i	−0.369513	−	0.463354i
$35$	−0.877506	+	1.50411i	−0.148326	+	0.254240i
$36$	0.623490	−	0.781831i	0.103915	−	0.130305i
$37$	−7.33411	+	2.26227i	−1.20572	+	0.371916i	−0.831553	−	0.555445i	$-0.812548\pi$
$37$	−7.33411	+	2.26227i	−1.20572	+	0.371916i	−0.374168	+	0.927361i	$0.622072\pi$
$38$	−2.59248	−	6.60554i	−0.420557	−	1.07156i
$39$	0.409306	−	5.46182i	0.0655415	−	0.874590i
$40$	0.240458	−	0.612677i	0.0380197	−	0.0968727i
$41$	−3.41431	−	1.64425i	−0.533226	−	0.256788i	0.147839	−	0.989011i	$-0.452768\pi$
$41$	−3.41431	−	1.64425i	−0.533226	−	0.256788i	−0.681064	+	0.732223i	$0.738483\pi$
$42$	2.61439	+	0.406179i	0.403409	+	0.0626747i
$43$	3.23626	−	1.55850i	0.493525	−	0.237669i	−0.170531	−	0.985352i	$-0.554548\pi$
$43$	3.23626	−	1.55850i	0.493525	−	0.237669i	0.664055	+	0.747683i	$0.268834\pi$
$44$	−0.218461	−	2.91516i	−0.0329342	−	0.439476i
$45$	0.628933	+	0.194000i	0.0937558	+	0.0289198i
$46$	3.32345	−	2.26589i	0.490015	−	0.334087i
$47$	5.41168	+	0.815680i	0.789375	+	0.118979i	0.531342	−	0.847157i	$-0.321688\pi$
$47$	5.41168	+	0.815680i	0.789375	+	0.118979i	0.258032	+	0.966136i	$0.416926\pi$
$48$	−1.00000			−0.144338
$49$	2.49823	+	6.53902i	0.356891	+	0.934146i
$50$	−4.56681			−0.645844
$51$	−3.41713	−	0.515050i	−0.478494	−	0.0721214i
$52$	−4.52542	+	3.08538i	−0.627563	+	0.427865i
$53$	0.544591	+	0.167984i	0.0748053	+	0.0230744i	0.331932	−	0.943303i	$-0.392300\pi$
$53$	0.544591	+	0.167984i	0.0748053	+	0.0230744i	−0.257127	+	0.966378i	$0.582776\pi$
$54$	−0.0747301	−	0.997204i	−0.0101695	−	0.135702i
$55$	1.73352	−	0.834818i	0.233747	−	0.112567i
$56$	−1.31248	−	2.29726i	−0.175388	−	0.306984i
$57$	−6.39334	−	3.07887i	−0.846818	−	0.407806i
$58$	2.97728	−	7.58598i	0.390936	−	0.996089i
$59$	0.888645	−	11.8581i	0.115692	−	1.54380i	−0.573492	−	0.819211i	$-0.694412\pi$
$59$	0.888645	−	11.8581i	0.115692	−	1.54380i	0.689183	−	0.724587i	$-0.257969\pi$
$60$	−0.240458	−	0.612677i	−0.0310430	−	0.0790962i
$61$	2.08614	−	0.643489i	0.267103	−	0.0823903i	−0.158311	−	0.987389i	$-0.550605\pi$
$61$	2.08614	−	0.643489i	0.267103	−	0.0823903i	0.425414	+	0.904999i	$0.360129\pi$
$62$	−2.87316	+	3.60282i	−0.364891	+	0.457559i
$63$	2.19275	−	1.48048i	0.276261	−	0.186524i
$64$	0.623490	+	0.781831i	0.0779362	+	0.0977289i
$65$	−2.97851	−	2.03072i	−0.369439	−	0.251879i
$66$	−2.14295	−	1.98837i	−0.263779	−	0.244751i
$67$	3.93608	−	6.81749i	0.480869	−	0.832889i	−0.518890	−	0.854841i	$-0.673655\pi$
$67$	3.93608	−	6.81749i	0.480869	−	0.832889i	0.999759	+	0.0219516i	$0.00698797\pi$
$68$	1.72786	+	2.99275i	0.209534	+	0.362924i
$69$	0.895064	−	3.92153i	0.107753	−	0.472097i
$70$	1.09188	−	1.35652i	0.130505	−	0.162135i
$71$	−2.60273	−	11.4033i	−0.308887	−	1.35332i	−0.856308	−	0.516466i	$-0.827247\pi$
$71$	−2.60273	−	11.4033i	−0.308887	−	1.35332i	0.547420	−	0.836858i	$-0.315610\pi$
$72$	−0.733052	+	0.680173i	−0.0863910	+	0.0801591i
$73$	−4.77293	+	0.719403i	−0.558629	+	0.0841997i	−0.422287	−	0.906462i	$-0.638773\pi$
$73$	−4.77293	+	0.719403i	−0.558629	+	0.0841997i	−0.136342	+	0.990662i	$0.543535\pi$
$74$	7.58937	−	1.14391i	0.882247	−	0.132977i
$75$	−3.34771	+	3.10622i	−0.386560	+	0.358675i
$76$	1.57902	+	6.91815i	0.181126	+	0.793567i
$77$	1.75521	−	7.53261i	0.200025	−	0.858420i
$78$	−1.21878	+	5.33981i	−0.137999	+	0.604614i
$79$	−7.88673	−	13.6602i	−0.887327	−	1.53689i	−0.843024	−	0.537877i	$-0.819227\pi$
$79$	−7.88673	−	13.6602i	−0.887327	−	1.53689i	−0.0443031	−	0.999018i	$-0.514107\pi$
$80$	−0.329087	+	0.569995i	−0.0367930	+	0.0637274i
$81$	−0.733052	−	0.680173i	−0.0814502	−	0.0755747i
$82$	3.13111	+	2.13476i	0.345774	+	0.235745i
$83$	9.90788	+	12.4241i	1.08753	+	1.36372i	0.926292	+	0.376806i	$0.122978\pi$
$83$	9.90788	+	12.4241i	1.08753	+	1.36372i	0.161239	+	0.986915i	$0.448451\pi$
$84$	−2.52465	−	0.791296i	−0.275462	−	0.0863375i
$85$	−1.41811	+	1.77825i	−0.153816	+	0.192879i
$86$	−3.43239	+	1.05875i	−0.370124	+	0.114168i
$87$	−2.97728	−	7.58598i	−0.319198	−	0.813303i
$88$	−0.218461	+	2.91516i	−0.0232880	+	0.310757i
$89$	−1.69707	+	4.32405i	−0.179889	+	0.458349i	−0.992167	−	0.124922i	$-0.960132\pi$
$89$	−1.69707	+	4.32405i	−0.179889	+	0.458349i	0.812278	+	0.583270i	$0.198227\pi$
$90$	−0.592994	−	0.285571i	−0.0625071	−	0.0301018i
$91$	−13.8665	+	4.20855i	−1.45361	+	0.441176i
$92$	−3.62404	+	1.74524i	−0.377832	+	0.181954i
$93$	0.344370	+	4.59530i	0.0357095	+	0.476510i
$94$	−5.22967	−	1.61314i	−0.539399	−	0.166383i
$95$	−3.85890	+	2.63096i	−0.395915	+	0.269930i
$96$	0.988831	+	0.149042i	0.100922	+	0.0152116i
$97$	9.63432			0.978216			0.489108	−	0.872223i	$-0.337322\pi$
$97$	9.63432			0.978216			0.489108	+	0.872223i	$0.337322\pi$
$98$	−1.49574	−	6.83833i	−0.151093	−	0.690776i
$99$	−2.92333			−0.293806
$100$	4.51580	+	0.680647i	0.451580	+	0.0680647i
$101$	5.25182	−	3.58063i	0.522575	−	0.356286i	−0.273123	−	0.961979i	$-0.588057\pi$
$101$	5.25182	−	3.58063i	0.522575	−	0.356286i	0.795698	+	0.605693i	$0.207104\pi$
$102$	3.30220	+	1.01859i	0.326967	+	0.100856i
$103$	−0.836169	−	11.1579i	−0.0823902	−	1.09942i	−0.873201	−	0.487360i	$-0.837960\pi$
$103$	−0.836169	−	11.1579i	−0.0823902	−	1.09942i	0.790811	−	0.612061i	$-0.209659\pi$
$104$	4.93472	−	2.37644i	0.483890	−	0.233029i
$105$	−0.122263	−	1.73707i	−0.0119316	−	0.169520i
$106$	−0.513471	−	0.247275i	−0.0498728	−	0.0240175i
$107$	−0.525752	+	1.33959i	−0.0508263	+	0.129503i	−0.954032	−	0.299704i	$-0.903112\pi$
$107$	−0.525752	+	1.33959i	−0.0508263	+	0.129503i	0.903206	+	0.429208i	$0.141207\pi$
$108$	−0.0747301	+	0.997204i	−0.00719091	+	0.0959560i
$109$	−1.58810	−	4.04640i	−0.152112	−	0.387575i	0.834423	−	0.551124i	$-0.185801\pi$
$109$	−1.58810	−	4.04640i	−0.152112	−	0.387575i	−0.986535	+	0.163549i	$0.947706\pi$
$110$	−1.83858	+	0.567126i	−0.175302	+	0.0540734i
$111$	4.78534	−	6.00063i	0.454205	−	0.569555i
$112$	0.955432	+	2.46721i	0.0902799	+	0.233130i
$113$	11.3717	+	14.2597i	1.06976	+	1.34144i	0.936622	+	0.350342i	$0.113935\pi$
$113$	11.3717	+	14.2597i	1.06976	+	1.34144i	0.133141	+	0.991097i	$0.457494\pi$
$114$	5.86305	+	3.99736i	0.549125	+	0.374387i
$115$	−1.94070	−	1.80071i	−0.180971	−	0.167917i
$116$	−4.07466	+	7.05752i	−0.378323	+	0.655274i
$117$	2.73857	+	4.74333i	0.253180	+	0.438521i
$118$	−2.64608	+	11.5932i	−0.243592	+	1.06724i
$119$	1.99410	+	8.92289i	0.182799	+	0.817960i
$120$	0.146457	+	0.641672i	0.0133697	+	0.0585764i
$121$	1.79902	−	1.66924i	0.163547	−	0.151749i
$122$	−2.15875	+	0.325379i	−0.195444	+	0.0294584i
$123$	3.74727	−	0.564810i	0.337880	−	0.0509272i
$124$	3.37804	−	3.13436i	0.303357	−	0.281474i
$125$	1.40113	+	6.13875i	0.125321	+	0.549067i
$126$	−2.38892	+	1.13714i	−0.212822	+	0.101304i
$127$	1.06715	−	4.67550i	0.0946944	−	0.414883i	−0.905256	−	0.424867i	$-0.860321\pi$
$127$	1.06715	−	4.67550i	0.0946944	−	0.414883i	0.999950	+	0.00998383i	$0.00317801\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−1.79599	+	3.11074i	−0.158128	+	0.273885i
$130$	2.64258	+	2.45196i	0.231770	+	0.215051i
$131$	9.18647	+	6.26323i	0.802625	+	0.547221i	0.893722	−	0.448621i	$-0.148085\pi$
$131$	9.18647	+	6.26323i	0.802625	+	0.547221i	−0.0910967	+	0.995842i	$0.529037\pi$
$132$	1.82267	+	2.28555i	0.158643	+	0.198932i
$133$	−1.48783	+	18.7154i	−0.129011	+	1.62283i
$134$	−4.90821	+	6.15470i	−0.424005	+	0.531686i
$135$	−0.628933	+	0.194000i	−0.0541299	+	0.0166969i
$136$	−1.26252	−	3.21685i	−0.108260	−	0.275842i
$137$	1.16786	−	15.5840i	0.0997770	−	1.33143i	−0.692565	−	0.721355i	$-0.743520\pi$
$137$	1.16786	−	15.5840i	0.0997770	−	1.33143i	0.792342	−	0.610077i	$-0.208861\pi$
$138$	−1.46954	+	3.74433i	−0.125096	+	0.318738i
$139$	−13.5400	−	6.52053i	−1.14845	−	0.553064i	−0.239882	−	0.970802i	$-0.577109\pi$
$139$	−13.5400	−	6.52053i	−1.14845	−	0.553064i	−0.908568	+	0.417738i	$0.862823\pi$
$140$	−1.28186	+	1.17863i	−0.108337	+	0.0996126i
$141$	−4.93083	+	2.37456i	−0.415251	+	0.199974i
$142$	0.874086	+	11.6639i	0.0733516	+	0.978810i
$143$	15.3001	+	4.71946i	1.27946	+	0.394661i
$144$	0.826239	−	0.563320i	0.0688532	−	0.0469433i
$145$	−5.30376	−	0.799413i	−0.440453	−	0.0663876i
$146$	4.82684			0.399472
$147$	−5.74770	−	3.99549i	−0.474062	−	0.329542i
$148$	−7.67510			−0.630889
$149$	−9.60299	−	1.44742i	−0.786708	−	0.118577i	−0.256612	−	0.966515i	$-0.582606\pi$
$149$	−9.60299	−	1.44742i	−0.786708	−	0.118577i	−0.530096	+	0.847938i	$0.677844\pi$
$150$	3.77327	−	2.57257i	0.308086	−	0.210050i
$151$	19.2571	+	5.94003i	1.56712	+	0.483393i	0.952272	−	0.305251i	$-0.0987403\pi$
$151$	19.2571	+	5.94003i	1.56712	+	0.483393i	0.614850	+	0.788644i	$0.289216\pi$
$152$	−0.530290	−	7.07623i	−0.0430122	−	0.573958i
$153$	3.11350	−	1.49938i	0.251712	−	0.121218i
$154$	−2.85829	+	7.18687i	−0.230327	+	0.579135i
$155$	2.73263	+	1.31596i	0.219490	+	0.105701i
$156$	2.00102	−	5.09852i	0.160210	−	0.408208i
$157$	−0.619068	+	8.26089i	−0.0494070	+	0.659291i	0.916439	+	0.400174i	$0.131050\pi$
$157$	−0.619068	+	8.26089i	−0.0494070	+	0.659291i	−0.965846	+	0.259116i	$0.916569\pi$
$158$	5.76269	+	14.6831i	0.458455	+	1.16812i
$159$	−0.544591	+	0.167984i	−0.0431889	+	0.0133220i
$160$	0.410365	−	0.514581i	0.0324422	−	0.0406812i
$161$	−10.5304	+	1.53844i	−0.829914	+	0.121246i
$162$	0.623490	+	0.781831i	0.0489860	+	0.0614265i
$163$	−2.02075	−	1.37772i	−0.158277	−	0.107912i	0.481591	−	0.876396i	$-0.340059\pi$
$163$	−2.02075	−	1.37772i	−0.158277	−	0.107912i	−0.639869	+	0.768484i	$0.721011\pi$
$164$	−2.77797	−	2.57758i	−0.216923	−	0.201275i
$165$	−0.962030	+	1.66628i	−0.0748939	+	0.129720i
$166$	−7.94551	−	13.7620i	−0.616691	−	1.06814i
$167$	−3.57793	+	15.6759i	−0.276869	+	1.21304i	0.624859	+	0.780737i	$0.285156\pi$
$167$	−3.57793	+	15.6759i	−0.276869	+	1.21304i	−0.901728	+	0.432304i	$0.857701\pi$
$168$	2.37851	+	1.15874i	0.183506	+	0.0893985i
$169$	−3.78262	−	16.5728i	−0.290971	−	1.27483i
$170$	1.66731	−	1.54703i	0.127876	−	0.118652i
$171$	7.01681	−	1.05761i	0.536589	−	0.0808778i
$172$	3.55186	−	0.535356i	0.270826	−	0.0408205i
$173$	6.03379	−	5.59854i	0.458741	−	0.425649i	−0.416649	−	0.909068i	$-0.636795\pi$
$173$	6.03379	−	5.59854i	0.458741	−	0.425649i	0.875390	+	0.483418i	$0.160605\pi$
$174$	1.81339	+	7.94500i	0.137473	+	0.602309i
$175$	10.8622	+	5.29173i	0.821106	+	0.400017i
$176$	0.650502	−	2.85004i	0.0490334	−	0.214829i
$177$	5.94570	+	10.2982i	0.446906	+	0.774064i
$178$	2.32258	−	4.02282i	0.174084	−	0.301523i
$179$	−5.83722	−	5.41615i	−0.436294	−	0.404822i	0.431210	−	0.902252i	$-0.358087\pi$
$179$	−5.83722	−	5.41615i	−0.436294	−	0.404822i	−0.867504	+	0.497430i	$0.834277\pi$
$180$	0.543809	+	0.370763i	0.0405331	+	0.0276350i
$181$	−9.94620	−	12.4721i	−0.739295	−	0.927047i	0.259961	−	0.965619i	$-0.416290\pi$
$181$	−9.94620	−	12.4721i	−0.739295	−	0.927047i	−0.999256	+	0.0385723i	$0.987719\pi$
$182$	14.3389	−	2.09484i	1.06287	−	0.155280i
$183$	−1.36116	+	1.70684i	−0.100620	+	0.126173i
$184$	3.84368	−	1.18562i	0.283360	−	0.0874049i
$185$	−1.84554	−	4.70235i	−0.135687	−	0.345724i
$186$	0.344370	−	4.59530i	0.0252504	−	0.336944i
$187$	3.69076	−	9.40390i	0.269895	−	0.687682i
$188$	4.93083	+	2.37456i	0.359618	+	0.173183i
$189$	−0.977751	+	2.45846i	−0.0711209	+	0.178826i
$190$	4.20793	−	2.02643i	0.305275	−	0.147013i
$191$	0.409506	+	5.46448i	0.0296308	+	0.395396i	0.992226	+	0.124451i	$0.0397170\pi$
$191$	0.409506	+	5.46448i	0.0296308	+	0.395396i	−0.962595	+	0.270945i	$0.912664\pi$
$192$	−0.955573	−	0.294755i	−0.0689625	−	0.0212721i
$193$	−8.78543	+	5.98981i	−0.632389	+	0.431156i	−0.836633	−	0.547764i	$-0.815479\pi$
$193$	−8.78543	+	5.98981i	−0.632389	+	0.431156i	0.204243	+	0.978920i	$0.434527\pi$
$194$	−9.52671	−	1.43592i	−0.683978	−	0.103093i
$195$	3.60490			0.258153
$196$	0.459834	+	6.98488i	0.0328453	+	0.498920i
$197$	−11.2868			−0.804153			−0.402076	−	0.915606i	$-0.631711\pi$
$197$	−11.2868			−0.804153			−0.402076	+	0.915606i	$0.631711\pi$
$198$	2.89068	+	0.435700i	0.205432	+	0.0309638i
$199$	−10.4393	+	7.11737i	−0.740020	+	0.504537i	−0.873687	−	0.486489i	$-0.838277\pi$
$199$	−10.4393	+	7.11737i	−0.740020	+	0.504537i	0.133666	+	0.991026i	$0.457325\pi$
$200$	−4.36392	−	1.34609i	−0.308576	−	0.0951829i
$201$	0.588287	+	7.85015i	0.0414946	+	0.553707i
$202$	−5.72683	+	2.75789i	−0.402938	+	0.194045i
$203$	−15.8717	+	14.5935i	−1.11397	+	1.02426i
$204$	−3.11350	−	1.49938i	−0.217989	−	0.104978i
$205$	0.911239	−	2.32180i	0.0636437	−	0.162162i
$206$	−0.836169	+	11.1579i	−0.0582587	+	0.777408i
$207$	1.46954	+	3.74433i	0.102140	+	0.260249i
$208$	−5.23380	+	1.61441i	−0.362899	+	0.111939i
$209$	12.9338	−	16.2184i	0.894647	−	1.12185i
$210$	−0.137999	+	1.73589i	−0.00952284	+	0.119788i
$211$	−3.65461	−	4.58274i	−0.251594	−	0.315489i	0.639956	−	0.768412i	$-0.278953\pi$
$211$	−3.65461	−	4.58274i	−0.251594	−	0.315489i	−0.891550	+	0.452923i	$0.850381\pi$
$212$	0.470882	+	0.321042i	0.0323403	+	0.0220493i
$213$	8.57419	+	7.95569i	0.587494	+	0.545115i
$214$	0.719536	−	1.24627i	0.0491864	−	0.0851934i
$215$	1.18207	+	2.04741i	0.0806166	+	0.139632i
$216$	0.222521	−	0.974928i	0.0151406	−	0.0663354i
$217$	11.0086	−	5.24013i	0.747310	−	0.355723i
$218$	0.967273	+	4.23790i	0.0655120	+	0.287027i
$219$	3.53832	−	3.28308i	0.239098	−	0.221850i
$220$	1.90257	−	0.286766i	0.128271	−	0.0193338i
$221$	−18.7161	+	2.82099i	−1.25898	+	0.189761i
$222$	−5.62624	+	5.22039i	−0.377609	+	0.350370i
$223$	−2.31626	−	10.1482i	−0.155108	−	0.679573i	−0.991354	−	0.131218i	$-0.958111\pi$
$223$	−2.31626	−	10.1482i	−0.155108	−	0.679573i	0.836246	−	0.548355i	$-0.184746\pi$
$224$	−0.577042	−	2.58206i	−0.0385552	−	0.172521i
$225$	1.01621	−	4.45231i	0.0677473	−	0.296821i
$226$	−9.11942	−	15.7953i	−0.606615	−	1.05069i
$227$	8.03238	−	13.9125i	0.533128	−	0.923404i	−0.466124	−	0.884719i	$-0.654350\pi$
$227$	8.03238	−	13.9125i	0.533128	−	0.923404i	0.999251	−	0.0386845i	$-0.0123167\pi$
$228$	−5.20179	−	4.82655i	−0.344497	−	0.319646i
$229$	17.2508	+	11.7614i	1.13996	+	0.777214i	0.977798	−	0.209550i	$-0.0671999\pi$
$229$	17.2508	+	11.7614i	1.13996	+	0.777214i	0.162165	+	0.986764i	$0.448152\pi$
$230$	1.65064	+	2.06984i	0.108840	+	0.136481i
$231$	2.79304	+	7.21248i	0.183769	+	0.474546i
$232$	5.08102	−	6.37139i	0.333585	−	0.418302i
$233$	17.6579	−	5.44675i	1.15681	−	0.356828i	0.343779	−	0.939050i	$-0.388293\pi$
$233$	17.6579	−	5.44675i	1.15681	−	0.356828i	0.813030	+	0.582222i	$0.197817\pi$
$234$	−2.00102	−	5.09852i	−0.130811	−	0.333300i
$235$	−0.269182	+	3.59199i	−0.0175595	+	0.234315i
$236$	4.34441	−	11.0694i	0.282797	−	0.720555i
$237$	14.2114	+	6.84385i	0.923130	+	0.444556i
$238$	−0.641939	−	9.12044i	−0.0416108	−	0.591190i
$239$	0.117069	−	0.0563776i	0.00757258	−	0.00364676i	−0.430094	−	0.902784i	$-0.641519\pi$
$239$	0.117069	−	0.0563776i	0.00757258	−	0.00364676i	0.437666	+	0.899138i	$0.355805\pi$
$240$	−0.0491854	−	0.656334i	−0.00317490	−	0.0423661i
$241$	−2.90055	−	0.894701i	−0.186841	−	0.0576328i	0.199923	−	0.979812i	$-0.435931\pi$
$241$	−2.90055	−	0.894701i	−0.186841	−	0.0576328i	−0.386764	+	0.922179i	$0.626407\pi$
$242$	−2.02771	+	1.38247i	−0.130346	+	0.0888685i
$243$	0.988831	+	0.149042i	0.0634335	+	0.00956107i
$244$	2.18313			0.139761
$245$	−4.16890	+	1.96130i	−0.266341	+	0.125303i
$246$	−3.78960			−0.241616
$247$	−38.4320	−	5.79269i	−2.44537	−	0.368580i
$248$	−3.80746	+	2.59588i	−0.241774	+	0.164839i
$249$	−15.1850	−	4.68396i	−0.962312	−	0.296834i
$250$	−0.470547	−	6.27902i	−0.0297600	−	0.397120i
$251$	8.69265	−	4.18616i	0.548675	−	0.264228i	−0.138943	−	0.990300i	$-0.544371\pi$
$251$	8.69265	−	4.18616i	0.548675	−	0.264228i	0.687618	+	0.726072i	$0.258656\pi$
$252$	2.53172	−	0.768386i	0.159483	−	0.0484037i
$253$	10.5943	+	5.10193i	0.666055	+	0.320755i
$254$	−1.75208	+	4.46422i	−0.109935	+	0.280110i
$255$	0.169971	−	2.26811i	0.0106440	−	0.142035i
$256$	0.365341	+	0.930874i	0.0228338	+	0.0581796i
$257$	−24.4074	+	7.52868i	−1.52249	+	0.469626i	−0.939412	−	0.342790i	$-0.888628\pi$
$257$	−24.4074	+	7.52868i	−1.52249	+	0.469626i	−0.583078	+	0.812416i	$0.698152\pi$
$258$	2.23956	−	2.80832i	0.139429	−	0.174838i
$259$	−19.3769	−	6.07327i	−1.20402	−	0.377375i
$260$	−2.24762	−	2.81843i	−0.139392	−	0.174791i
$261$	6.73328	+	4.59067i	0.416780	+	0.284156i
$262$	−8.15038	−	7.56244i	−0.503532	−	0.467209i
$263$	1.49229	−	2.58472i	0.0920184	−	0.159381i	−0.816342	−	0.577569i	$-0.804001\pi$
$263$	1.49229	−	2.58472i	0.0920184	−	0.159381i	0.908360	+	0.418188i	$0.137335\pi$
$264$	−1.46166	−	2.53168i	−0.0899592	−	0.155814i
$265$	−0.0834676	+	0.365696i	−0.00512738	+	0.0224645i
$266$	4.26059	−	18.2846i	0.261234	−	1.12110i
$267$	−1.03364	−	4.52869i	−0.0632580	−	0.277151i
$268$	5.77070	−	5.35443i	0.352502	−	0.327074i
$269$	7.14461	−	1.07688i	0.435614	−	0.0656583i	0.0724254	−	0.997374i	$-0.476926\pi$
$269$	7.14461	−	1.07688i	0.435614	−	0.0656583i	0.363189	+	0.931716i	$0.381688\pi$
$270$	0.650823	−	0.0980957i	0.0396078	−	0.00596992i
$271$	−1.84648	+	1.71329i	−0.112166	+	0.104075i	−0.734262	−	0.678866i	$-0.762472\pi$
$271$	−1.84648	+	1.71329i	−0.112166	+	0.104075i	0.622096	+	0.782941i	$0.286281\pi$
$272$	0.768972	+	3.36909i	0.0466258	+	0.204281i
$273$	9.08631	−	11.2886i	0.549929	−	0.683215i
$274$	−3.47749	+	15.2359i	−0.210083	+	0.920434i
$275$	−6.67514	−	11.5617i	−0.402526	−	0.697196i
$276$	2.01119	−	3.48348i	0.121059	−	0.209681i
$277$	−6.01881	−	5.58464i	−0.361635	−	0.335549i	0.478338	−	0.878176i	$-0.341239\pi$
$277$	−6.01881	−	5.58464i	−0.361635	−	0.335549i	−0.839974	+	0.542627i	$0.817430\pi$
$278$	12.4170	+	8.46574i	0.744719	+	0.507741i
$279$	−2.87316	−	3.60282i	−0.172011	−	0.215695i
$280$	1.44321	−	0.974416i	0.0862485	−	0.0582325i
$281$	16.3461	−	20.4973i	0.975126	−	1.22277i	0.000254574	−	1.00000i	$-0.499919\pi$
$281$	16.3461	−	20.4973i	0.975126	−	1.22277i	0.974871	−	0.222769i	$-0.0715096\pi$
$282$	5.22967	−	1.61314i	0.311422	−	0.0960610i
$283$	7.27762	+	18.5431i	0.432610	+	1.10227i	0.966488	+	0.256710i	$0.0826387\pi$
$283$	7.27762	+	18.5431i	0.432610	+	1.10227i	−0.533879	+	0.845561i	$0.679266\pi$
$284$	0.874086	−	11.6639i	0.0518674	−	0.692123i
$285$	1.70631	−	4.34760i	0.101073	−	0.257529i
$286$	−14.4258	−	6.94711i	−0.853017	−	0.410791i
$287$	−4.97377	−	8.70569i	−0.293593	−	0.513881i
$288$	−0.900969	+	0.433884i	−0.0530901	+	0.0255668i
$289$	−0.377980	−	5.04379i	−0.0222341	−	0.296694i
$290$	5.12537	+	1.58097i	0.300972	+	0.0928377i
$291$	−7.96024	+	5.42720i	−0.466638	+	0.318148i
$292$	−4.77293	−	0.719403i	−0.279314	−	0.0420999i
$293$	−16.3095			−0.952814			−0.476407	−	0.879225i	$-0.658061\pi$
$293$	−16.3095			−0.952814			−0.476407	+	0.879225i	$0.658061\pi$
$294$	5.08801	+	4.80751i	0.296739	+	0.280380i
$295$	7.82660			0.455682
$296$	7.58937	+	1.14391i	0.441123	+	0.0664886i
$297$	2.41537	−	1.64677i	0.140154	−	0.0955553i
$298$	9.28001	+	2.86250i	0.537576	+	0.165820i
$299$	−1.64639	−	21.9695i	−0.0952130	−	1.27053i
$300$	−4.11455	+	1.98146i	−0.237554	+	0.114400i
$301$	9.39081	+	1.45898i	0.541277	+	0.0840944i
$302$	−18.1567	−	8.74381i	−1.04480	−	0.503150i
$303$	−2.32222	+	5.91691i	−0.133408	+	0.339918i
$304$	−0.530290	+	7.07623i	−0.0304142	+	0.405849i
$305$	0.524951	+	1.33755i	0.0300586	+	0.0765881i
$306$	−3.30220	+	1.01859i	−0.188774	+	0.0582291i
$307$	5.24061	−	6.57152i	0.299098	−	0.375057i	−0.609460	−	0.792817i	$-0.708614\pi$
$307$	5.24061	−	6.57152i	0.299098	−	0.375057i	0.908557	+	0.417761i	$0.137185\pi$
$308$	3.89751	−	6.68060i	0.222081	−	0.380662i
$309$	6.97634	+	8.74806i	0.396870	+	0.497660i
$310$	−2.50597	−	1.70854i	−0.142330	−	0.0970387i
$311$	13.6691	+	12.6831i	0.775103	+	0.719190i	0.964896	−	0.262634i	$-0.0845911\pi$
$311$	13.6691	+	12.6831i	0.775103	+	0.719190i	−0.189793	+	0.981824i	$0.560782\pi$
$312$	−2.73857	+	4.74333i	−0.155041	+	0.268538i
$313$	−3.38997	−	5.87160i	−0.191613	−	0.331883i	0.754172	−	0.656677i	$-0.228038\pi$
$313$	−3.38997	−	5.87160i	−0.191613	−	0.331883i	−0.945785	+	0.324794i	$0.894705\pi$
$314$	1.84337	−	8.07635i	0.104028	−	0.455775i
$315$	1.07954	+	1.36636i	0.0608254	+	0.0769856i
$316$	−3.50993	−	15.3780i	−0.197449	−	0.865079i
$317$	−5.93997	+	5.51148i	−0.333622	+	0.309556i	−0.829139	−	0.559042i	$-0.811169\pi$
$317$	−5.93997	+	5.51148i	−0.333622	+	0.309556i	0.495517	+	0.868598i	$0.334978\pi$
$318$	0.563545	−	0.0849407i	0.0316020	−	0.00476324i
$319$	23.5571	−	3.55065i	1.31894	−	0.198798i
$320$	−0.482476	+	0.447672i	−0.0269712	+	0.0250256i
$321$	−0.320223	−	1.40299i	−0.0178731	−	0.0783073i
$322$	10.6421	+	0.0482195i	0.593061	+	0.00268717i
$323$	−5.45668	+	23.9073i	−0.303618	+	1.33024i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−12.5065	+	21.6619i	−0.693736	+	1.20159i
$326$	1.79284	+	1.66351i	0.0992963	+	0.0921335i
$327$	3.59157	+	2.44869i	0.198614	+	0.135413i
$328$	2.36278	+	2.96283i	0.130463	+	0.163595i
$329$	10.5696	+	9.89668i	0.582723	+	0.545622i
$330$	1.19963	−	1.50429i	0.0660375	−	0.0828084i
$331$	25.3743	−	7.82692i	1.39470	−	0.430207i	0.495825	−	0.868422i	$-0.334866\pi$
$331$	25.3743	−	7.82692i	1.39470	−	0.430207i	0.898870	+	0.438216i	$0.144389\pi$
$332$	5.80564	+	14.7925i	0.318626	+	0.811845i
$333$	−0.573561	+	7.65364i	−0.0314309	+	0.419417i
$334$	5.87435	−	14.9676i	0.321430	−	0.818991i
$335$	4.66815	+	2.24806i	0.255048	+	0.122825i
$336$	−2.17925	−	1.50029i	−0.118888	−	0.0818478i
$337$	28.9820	−	13.9570i	1.57875	−	0.760285i	0.580218	−	0.814462i	$-0.302968\pi$
$337$	28.9820	−	13.9570i	1.57875	−	0.760285i	0.998531	+	0.0541761i	$0.0172532\pi$
$338$	1.27033	+	16.9514i	0.0690971	+	0.922036i
$339$	−17.4285	−	5.37599i	−0.946588	−	0.291984i
$340$	−1.87926	+	1.28125i	−0.101917	+	0.0694858i
$341$	−13.3208	−	2.00778i	−0.721361	−	0.108728i
$342$	−7.09607			−0.383711
$343$	−4.36619	+	17.9982i	−0.235752	+	0.971813i
$344$	−3.59197			−0.193666
$345$	2.61786	+	0.394578i	0.140941	+	0.0212434i
$346$	−6.80082	+	4.63672i	−0.365614	+	0.249272i
$347$	−22.2254	−	6.85564i	−1.19312	−	0.368030i	−0.366303	−	0.930495i	$-0.619377\pi$
$347$	−22.2254	−	6.85564i	−1.19312	−	0.368030i	−0.826821	+	0.562465i	$0.809853\pi$
$348$	−0.608999	−	8.12653i	−0.0326458	−	0.435628i
$349$	−2.73054	+	1.31496i	−0.146163	+	0.0703882i	−0.505535	−	0.862806i	$-0.668705\pi$
$349$	−2.73054	+	1.31496i	−0.146163	+	0.0703882i	0.359373	+	0.933194i	$0.382991\pi$
$350$	−9.95220	−	6.85155i	−0.531967	−	0.366231i
$351$	−4.93472	−	2.37644i	−0.263396	−	0.126845i
$352$	−1.06801	+	2.72125i	−0.0569252	+	0.145043i
$353$	0.0631550	−	0.842745i	0.00336140	−	0.0448548i	−0.995271	−	0.0971386i	$-0.969031\pi$
$353$	0.0631550	−	0.842745i	0.00336140	−	0.0448548i	0.998632	+	0.0522838i	$0.0166500\pi$
$354$	−4.34441	−	11.0694i	−0.230903	−	0.588331i
$355$	7.35636	−	2.26914i	0.390435	−	0.120433i
$356$	−2.89621	+	3.63173i	−0.153499	+	0.192481i
$357$	−6.67405	−	6.24912i	−0.353228	−	0.330739i
$358$	4.96479	+	6.22565i	0.262397	+	0.329036i
$359$	23.7268	+	16.1767i	1.25225	+	0.853772i	0.993683	−	0.112221i	$-0.0357965\pi$
$359$	23.7268	+	16.1767i	1.25225	+	0.853772i	0.258570	+	0.965993i	$0.416749\pi$
$360$	−0.482476	−	0.447672i	−0.0254287	−	0.0235944i
$361$	−15.6771	+	27.1535i	−0.825110	+	1.42913i
$362$	7.97623	+	13.8152i	0.419222	+	0.726113i
$363$	−0.546099	+	2.39262i	−0.0286628	+	0.125580i
$364$	−14.4910	−	0.0656588i	−0.759534	−	0.00344146i
$365$	−0.706927	−	3.09725i	−0.0370022	−	0.162117i
$366$	1.60035	−	1.48491i	0.0836515	−	0.0776172i
$367$	−2.12065	+	0.319636i	−0.110697	+	0.0166849i	−0.204157	−	0.978938i	$-0.565445\pi$
$367$	−2.12065	+	0.319636i	−0.110697	+	0.0166849i	0.0934602	+	0.995623i	$0.470207\pi$
$368$	−3.97745	+	0.599505i	−0.207339	+	0.0312513i
$369$	−2.77797	+	2.57758i	−0.144615	+	0.134184i
$370$	1.12408	+	4.92490i	0.0584379	+	0.256033i
$371$	0.934772	+	1.18313i	0.0485310	+	0.0614248i
$372$	−1.02542	+	4.49265i	−0.0531654	+	0.232933i
$373$	9.13722	+	15.8261i	0.473107	+	0.819446i	0.999526	−	0.0307796i	$-0.00979901\pi$
$373$	9.13722	+	15.8261i	0.473107	+	0.819446i	−0.526419	+	0.850225i	$0.676466\pi$
$374$	−5.05112	+	8.74879i	−0.261187	+	0.452389i
$375$	−4.61575	−	4.28279i	−0.238356	−	0.221162i
$376$	−4.52185	−	3.08294i	−0.233196	−	0.158991i
$377$	−27.8294	−	34.8969i	−1.43329	−	1.79728i
$378$	1.33324	−	2.28527i	0.0685747	−	0.117542i
$379$	−3.37391	+	4.23075i	−0.173306	+	0.217319i	−0.860897	−	0.508779i	$-0.830097\pi$
$379$	−3.37391	+	4.23075i	−0.173306	+	0.217319i	0.687591	+	0.726098i	$0.258668\pi$
$380$	−4.46295	+	1.37664i	−0.228945	+	0.0706201i
$381$	1.75208	+	4.46422i	0.0897617	+	0.228709i
$382$	0.409506	−	5.46448i	0.0209522	−	0.279587i
$383$	−12.1680	+	31.0035i	−0.621755	+	1.58420i	0.178101	+	0.984012i	$0.443005\pi$
$383$	−12.1680	+	31.0035i	−0.621755	+	1.58420i	−0.799856	+	0.600192i	$0.795091\pi$
$384$	0.900969	+	0.433884i	0.0459774	+	0.0221415i
$385$	5.03023	+	0.781512i	0.256365	+	0.0398295i
$386$	9.58004	−	4.61350i	0.487611	−	0.234821i
$387$	−0.268429	−	3.58193i	−0.0136450	−	0.182080i
$388$	9.20629	+	2.83976i	0.467379	+	0.144167i
$389$	−20.4231	+	13.9242i	−1.03549	+	0.705985i	−0.956750	−	0.290910i	$-0.906042\pi$
$389$	−20.4231	+	13.9242i	−1.03549	+	0.705985i	−0.0787395	+	0.996895i	$0.525090\pi$
$390$	−3.56464	−	0.537283i	−0.180503	−	0.0272064i
$391$	−13.9003			−0.702966
$392$	0.586345	−	6.97540i	0.0296149	−	0.352311i
$393$	−11.1184			−0.560850
$394$	11.1608	+	1.68221i	0.562271	+	0.0847487i
$395$	8.57775	−	5.84821i	0.431593	−	0.294255i
$396$	−2.79345	−	0.861666i	−0.140376	−	0.0433004i
$397$	−0.361468	−	4.82346i	−0.0181416	−	0.242083i	−0.998901	−	0.0468637i	$-0.985077\pi$
$397$	−0.361468	−	4.82346i	−0.0181416	−	0.242083i	0.980760	−	0.195219i	$-0.0625417\pi$
$398$	11.3835	−	5.48199i	0.570601	−	0.274787i
$399$	−9.31345	−	16.3015i	−0.466256	−	0.816096i
$400$	4.11455	+	1.98146i	0.205728	+	0.0990732i
$401$	7.10812	−	18.1112i	0.354962	−	0.904429i	−0.636170	−	0.771549i	$-0.719482\pi$
$401$	7.10812	−	18.1112i	0.354962	−	0.904429i	0.991132	−	0.132880i	$-0.0424226\pi$
$402$	0.588287	−	7.85015i	0.0293411	−	0.391530i
$403$	9.22107	+	23.4949i	0.459334	+	1.17036i
$404$	6.07390	−	1.87355i	0.302188	−	0.0932127i
$405$	0.410365	−	0.514581i	0.0203912	−	0.0255697i
$406$	17.8694	−	12.0649i	0.886845	−	0.598773i
$407$	13.9891	+	17.5418i	0.693416	+	0.869516i
$408$	2.85526	+	1.94668i	0.141356	+	0.0963751i
$409$	22.1258	+	20.5298i	1.09405	+	1.01513i	0.999808	+	0.0195817i	$0.00623345\pi$
$409$	22.1258	+	20.5298i	1.09405	+	1.01513i	0.0942427	+	0.995549i	$0.469957\pi$
$410$	−1.24711	+	2.16005i	−0.0615903	+	0.106677i
$411$	7.81385	+	13.5340i	0.385429	+	0.667583i
$412$	2.48983	−	10.9087i	0.122665	−	0.537431i
$413$	19.7273	−	24.5086i	0.970716	−	1.20599i
$414$	−0.895064	−	3.92153i	−0.0439900	−	0.192733i
$415$	−7.66703	+	7.11396i	−0.376360	+	0.349211i
$416$	5.41596	−	0.816324i	0.265539	−	0.0400236i
$417$	14.8604	−	2.23985i	0.727719	−	0.109686i
$418$	−15.2065	+	14.1096i	−0.743776	+	0.690123i
$419$	1.45863	+	6.39066i	0.0712585	+	0.312204i	0.997979	−	0.0635480i	$-0.0202416\pi$
$419$	1.45863	+	6.39066i	0.0712585	+	0.312204i	−0.926720	+	0.375752i	$0.877384\pi$
$420$	0.395178	−	1.69593i	0.0192827	−	0.0827530i
$421$	−5.18868	+	22.7331i	−0.252881	+	1.10794i	0.675807	+	0.737079i	$0.263795\pi$
$421$	−5.18868	+	22.7331i	−0.252881	+	1.10794i	−0.928687	+	0.370864i	$0.879062\pi$
$422$	2.93077	+	5.07624i	0.142668	+	0.247108i
$423$	2.73640	−	4.73959i	0.133049	−	0.230447i
$424$	−0.417774	−	0.387637i	−0.0202889	−	0.0188253i
$425$	13.0394	+	8.89012i	0.632504	+	0.431234i
$426$	−7.29269	−	9.14475i	−0.353332	−	0.443064i
$427$	5.51163	+	1.72750i	0.266727	+	0.0835997i
$428$	−0.897246	+	1.12511i	−0.0433700	+	0.0543843i
$429$	−15.3001	+	4.71946i	−0.738696	+	0.227858i
$430$	−0.863719	−	2.20072i	−0.0416522	−	0.106128i
$431$	0.549121	−	7.32751i	0.0264502	−	0.352954i	−0.968239	−	0.250027i	$-0.919560\pi$
$431$	0.549121	−	7.32751i	0.0264502	−	0.352954i	0.994689	−	0.102926i	$-0.0328206\pi$
$432$	−0.365341	+	0.930874i	−0.0175775	+	0.0447867i
$433$	−26.7794	−	12.8963i	−1.28693	−	0.619755i	−0.339772	−	0.940508i	$-0.610350\pi$
$433$	−26.7794	−	12.8963i	−1.28693	−	0.619755i	−0.947163	+	0.320753i	$0.896064\pi$
$434$	−11.6666	+	3.54086i	−0.560015	+	0.169967i
$435$	4.83250	−	2.32721i	0.231701	−	0.111581i
$436$	−0.324843	−	4.33473i	−0.0155572	−	0.207596i
$437$	−27.2750	−	8.41322i	−1.30474	−	0.402459i
$438$	−3.98812	+	2.71905i	−0.190560	+	0.129921i
$439$	8.13509	+	1.22617i	0.388267	+	0.0585218i	0.340275	−	0.940326i	$-0.389480\pi$
$439$	8.13509	+	1.22617i	0.388267	+	0.0585218i	0.0479917	+	0.998848i	$0.484718\pi$
$440$	−1.92406			−0.0917259
$441$	6.99971	+	0.0634329i	0.333320	+	0.00302061i
$442$	18.9275			0.900288
$443$	22.9805	+	3.46375i	1.09184	+	0.164568i	0.670188	−	0.742192i	$-0.266214\pi$
$443$	22.9805	+	3.46375i	1.09184	+	0.164568i	0.421648	+	0.906759i	$0.361452\pi$
$444$	6.34146	−	4.32354i	0.300952	−	0.205186i
$445$	−2.92149	−	0.901161i	−0.138492	−	0.0427191i
$446$	0.777878	+	10.3801i	0.0368336	+	0.491510i
$447$	8.74972	−	4.21364i	0.413848	−	0.199299i
$448$	0.185761	+	2.63922i	0.00877638	+	0.124692i
$449$	21.5578	+	10.3817i	1.01737	+	0.489941i	0.866799	−	0.498658i	$-0.166173\pi$
$449$	21.5578	+	10.3817i	1.01737	+	0.489941i	0.150574	+	0.988599i	$0.451888\pi$
$450$	−1.66844	+	4.25112i	−0.0786511	+	0.200400i
$451$	−0.827878	+	11.0473i	−0.0389833	+	0.520196i
$452$	6.66340	+	16.9781i	0.313420	+	0.798581i
$453$	−19.2571	+	5.94003i	−0.904778	+	0.279087i
$454$	−10.0162	+	12.5599i	−0.470084	+	0.589467i
$455$	−3.44424	−	8.89407i	−0.161469	−	0.416961i
$456$	4.42433	+	5.54793i	0.207188	+	0.259806i
$457$	1.63972	+	1.11794i	0.0767028	+	0.0522951i	0.601064	−	0.799201i	$-0.294744\pi$
$457$	1.63972	+	1.11794i	0.0767028	+	0.0522951i	−0.524362	+	0.851496i	$0.675696\pi$
$458$	−15.3052	−	14.2011i	−0.715163	−	0.663574i
$459$	−1.72786	+	2.99275i	−0.0806498	+	0.139690i
$460$	−1.32371	−	2.29274i	−0.0617184	−	0.106899i
$461$	1.23374	−	5.40536i	0.0574609	−	0.251753i	−0.938037	−	0.346535i	$-0.887358\pi$
$461$	1.23374	−	5.40536i	0.0574609	−	0.251753i	0.995498	+	0.0947821i	$0.0302154\pi$
$462$	−1.68688	−	7.54821i	−0.0784809	−	0.351174i
$463$	−8.68724	−	38.0613i	−0.403730	−	1.76886i	−0.612072	−	0.790802i	$-0.709664\pi$
$463$	−8.68724	−	38.0613i	−0.403730	−	1.76886i	0.208342	−	0.978056i	$-0.433193\pi$
$464$	−5.97387	+	5.54294i	−0.277330	+	0.257325i
$465$	−2.99911	+	0.452043i	−0.139080	+	0.0209630i
$466$	−18.2725	+	2.75414i	−0.846457	+	0.127583i
$467$	−19.3759	+	17.9782i	−0.896611	+	0.831933i	−0.986457	−	0.164023i	$-0.947553\pi$
$467$	−19.3759	+	17.9782i	−0.896611	+	0.831933i	0.0898459	+	0.995956i	$0.471363\pi$
$468$	1.21878	+	5.33981i	0.0563380	+	0.246833i
$469$	18.8059	−	8.95172i	0.868378	−	0.413352i
$470$	0.801534	−	3.51175i	0.0369720	−	0.161985i
$471$	−4.14203	−	7.17420i	−0.190854	−	0.330570i
$472$	−5.94570	+	10.2982i	−0.273673	+	0.474015i
$473$	−7.69743	−	7.14217i	−0.353928	−	0.328397i
$474$	−13.0326	−	8.88551i	−0.598609	−	0.408125i
$475$	20.2050	+	25.3363i	0.927071	+	1.16251i
$476$	−0.724561	+	9.11424i	−0.0332102	+	0.417751i
$477$	0.355333	−	0.445574i	0.0162696	−	0.0204014i
$478$	−0.124164	+	0.0382996i	−0.00567914	+	0.00175178i
$479$	−5.62601	−	14.3348i	−0.257059	−	0.654975i	0.742836	−	0.669473i	$-0.233480\pi$
$479$	−5.62601	−	14.3348i	−0.257059	−	0.654975i	−0.999895	+	0.0144980i	$0.995385\pi$
$480$	−0.0491854	+	0.656334i	−0.00224500	+	0.0299574i
$481$	15.3580	−	39.1316i	0.700266	−	1.78425i
$482$	2.73480	+	1.31701i	0.124567	+	0.0599883i
$483$	7.83401	−	7.20312i	0.356460	−	0.327753i
$484$	2.21111	−	1.06481i	0.100505	−	0.0484006i
$485$	0.473868	+	6.32332i	0.0215172	+	0.287127i
$486$	−0.955573	−	0.294755i	−0.0433457	−	0.0133704i
$487$	−2.13784	+	1.45756i	−0.0968749	+	0.0660482i	−0.610789	−	0.791794i	$-0.709148\pi$
$487$	−2.13784	+	1.45756i	−0.0968749	+	0.0660482i	0.513914	+	0.857842i	$0.328195\pi$
$488$	−2.15875	−	0.325379i	−0.0977218	−	0.0147292i
$489$	2.44572			0.110599
$490$	4.41466	−	1.31805i	0.199434	−	0.0595434i
$491$	−14.5956			−0.658691			−0.329345	−	0.944210i	$-0.606828\pi$
$491$	−14.5956			−0.658691			−0.329345	+	0.944210i	$0.606828\pi$
$492$	3.74727	+	0.564810i	0.168940	+	0.0254636i
$493$	−23.2684	+	15.8641i	−1.04796	+	0.714484i
$494$	37.1394	+	11.4560i	1.67098	+	0.515429i
$495$	−0.143785	−	1.91868i	−0.00646266	−	0.0862382i
$496$	4.15183	−	1.99942i	0.186423	−	0.0897764i
$497$	11.4363	−	28.7555i	0.512989	−	1.28986i
$498$	14.3173	+	6.89485i	0.641574	+	0.308966i
$499$	−6.61808	+	16.8626i	−0.296266	+	0.754874i	0.702788	+	0.711399i	$0.251938\pi$
$499$	−6.61808	+	16.8626i	−0.296266	+	0.754874i	−0.999055	+	0.0434748i	$0.986157\pi$
$500$	−0.470547	+	6.27902i	−0.0210435	+	0.280806i
$501$	−5.87435	−	14.9676i	−0.262447	−	0.668703i
$502$	−9.21948	+	2.84383i	−0.411485	+	0.126926i
$503$	−9.03318	+	11.3272i	−0.402769	+	0.505057i	−0.941310	−	0.337543i	$-0.890404\pi$
$503$	−9.03318	+	11.3272i	−0.402769	+	0.505057i	0.538541	+	0.842599i	$0.318976\pi$
$504$	−2.61796	+	0.382471i	−0.116613	+	0.0170366i
$505$	2.60840	+	3.27083i	0.116072	+	0.145550i
$506$	−9.71553	−	6.62393i	−0.431908	−	0.294470i
$507$	12.4611	+	11.5622i	0.553418	+	0.513497i
$508$	2.39787	−	4.15323i	0.106388	−	0.184270i
$509$	−12.6237	−	21.8649i	−0.559536	−	0.969144i	−0.997535	−	0.0701688i	$-0.977646\pi$
$509$	−12.6237	−	21.8649i	−0.559536	−	0.969144i	0.438000	−	0.898975i	$-0.355687\pi$
$510$	−0.506117	+	2.21745i	−0.0224113	+	0.0981901i
$511$	−11.4807	−	5.59304i	−0.507876	−	0.247421i
$512$	−0.222521	−	0.974928i	−0.00983413	−	0.0430861i
$513$	−5.20179	+	4.82655i	−0.229664	+	0.213097i
$514$	25.2568	−	3.80686i	1.11403	−	0.167913i
$515$	7.28218	−	1.09761i	0.320891	−	0.0483665i
$516$	−2.63310	+	2.44316i	−0.115916	+	0.107554i
$517$	−3.56007	−	15.5977i	−0.156572	−	0.685986i
$518$	18.2553	+	8.89342i	0.802093	+	0.390754i
$519$	−1.83158	+	8.02469i	−0.0803976	+	0.352245i
$520$	1.80245	+	3.12194i	0.0790428	+	0.136906i
$521$	−6.80886	+	11.7933i	−0.298302	+	0.516674i	−0.975748	−	0.218899i	$-0.929754\pi$
$521$	−6.80886	+	11.7933i	−0.298302	+	0.516674i	0.677446	+	0.735573i	$0.263087\pi$
$522$	−5.97387	−	5.54294i	−0.261469	−	0.242608i
$523$	1.07658	+	0.734003i	0.0470758	+	0.0320957i	0.586629	−	0.809856i	$-0.300455\pi$
$523$	1.07658	+	0.734003i	0.0470758	+	0.0320957i	−0.539554	+	0.841951i	$0.681407\pi$
$524$	6.93222	+	8.69273i	0.302835	+	0.379744i
$525$	−11.9557	+	1.74667i	−0.521790	+	0.0762309i
$526$	−1.86085	+	2.33344i	−0.0811370	+	0.101743i
$527$	15.2172	−	4.69387i	0.662869	−	0.204468i
$528$	1.06801	+	2.72125i	0.0464793	+	0.118427i
$529$	−0.509694	+	6.80139i	−0.0221606	+	0.295713i
$530$	0.137039	−	0.349171i	0.00595261	−	0.0151670i
$531$	−10.7138	−	5.15948i	−0.464938	−	0.223902i
$532$	−6.93819	+	17.4454i	−0.300808	+	0.756353i
$533$	18.7006	−	9.00575i	0.810014	−	0.390082i
$534$	0.347133	+	4.63216i	0.0150219	+	0.200453i
$535$	−0.905080	−	0.279180i	−0.0391300	−	0.0120700i
$536$	−6.50429	+	4.43455i	−0.280942	+	0.191543i
$537$	7.87397	+	1.18681i	0.339787	+	0.0512146i
$538$	−7.22531			−0.311505
$539$	15.1262	−	13.7821i	0.651531	−	0.593636i
$540$	−0.658174			−0.0283233
$541$	3.65121	+	0.550331i	0.156978	+	0.0236606i	0.227061	−	0.973881i	$-0.427088\pi$
$541$	3.65121	+	0.550331i	0.156978	+	0.0236606i	−0.0700832	+	0.997541i	$0.522326\pi$
$542$	2.08121	−	1.41895i	0.0893957	−	0.0609489i
$543$	15.2437	+	4.70207i	0.654172	+	0.201785i
$544$	−0.258247	−	3.44607i	−0.0110722	−	0.147749i
$545$	2.57768	−	1.24134i	0.110416	−	0.0531734i
$546$	−10.6673	+	9.80824i	−0.456518	+	0.419754i
$547$	21.9358	+	10.5637i	0.937908	+	0.451673i	0.839431	−	0.543467i	$-0.182889\pi$
$547$	21.9358	+	10.5637i	0.937908	+	0.451673i	0.0984773	+	0.995139i	$0.468603\pi$
$548$	5.70944	−	14.5474i	0.243895	−	0.621435i
$549$	0.163145	−	2.17703i	0.00696288	−	0.0929132i
$550$	4.87741	+	12.4274i	0.207973	+	0.529907i
$551$	−55.2590	+	17.0451i	−2.35411	+	0.726147i
$552$	−2.50791	+	3.14482i	−0.106744	+	0.133853i
$553$	3.30721	−	41.6014i	0.140637	−	1.76907i
$554$	5.11924	+	6.41932i	0.217496	+	0.272731i
$555$	4.17379	+	2.84564i	0.177167	+	0.120791i
$556$	−11.0165	−	10.2218i	−0.467204	−	0.433502i
$557$	21.6383	−	37.4786i	0.916843	−	1.58802i	0.112663	−	0.993633i	$-0.464062\pi$
$557$	21.6383	−	37.4786i	0.916843	−	1.58802i	0.804180	−	0.594386i	$-0.202605\pi$
$558$	2.30409	+	3.99080i	0.0975400	+	0.168944i
$559$	−4.37781	+	19.1805i	−0.185162	+	0.811247i
$560$	−1.57232	+	0.748433i	−0.0664428	+	0.0316271i
$561$	2.24796	+	9.84895i	0.0949089	+	0.415823i
$562$	−19.2185	+	17.8321i	−0.810683	+	0.752204i
$563$	−33.8756	+	5.10592i	−1.42769	+	0.215189i	−0.816979	−	0.576667i	$-0.804353\pi$
$563$	−33.8756	+	5.10592i	−1.42769	+	0.215189i	−0.610707	+	0.791856i	$0.709115\pi$
$564$	−5.41168	+	0.815680i	−0.227873	+	0.0343463i
$565$	−8.79979	+	8.16502i	−0.370210	+	0.343505i
$566$	−4.43263	−	19.4206i	−0.186318	−	0.816310i
$567$	−0.577042	−	2.58206i	−0.0242335	−	0.108436i
$568$	−2.60273	+	11.4033i	−0.109208	+	0.478472i
$569$	8.27429	+	14.3315i	0.346876	+	0.600807i	0.985693	−	0.168552i	$-0.0539091\pi$
$569$	8.27429	+	14.3315i	0.346876	+	0.600807i	−0.638817	+	0.769359i	$0.720576\pi$
$570$	−2.33522	+	4.04473i	−0.0978117	+	0.169415i
$571$	8.65715	+	8.03266i	0.362290	+	0.336156i	0.840224	−	0.542240i	$-0.182424\pi$
$571$	8.65715	+	8.03266i	0.362290	+	0.336156i	−0.477933	+	0.878396i	$0.658614\pi$
$572$	13.2293	+	9.01957i	0.553144	+	0.377127i
$573$	−3.41660	−	4.28428i	−0.142731	−	0.178979i
$574$	3.62071	+	9.34976i	0.151125	+	0.390251i
$575$	−11.4532	+	14.3618i	−0.477629	+	0.598928i
$576$	0.955573	−	0.294755i	0.0398155	−	0.0122815i
$577$	−1.34065	−	3.41593i	−0.0558121	−	0.142207i	0.900248	−	0.435377i	$-0.143385\pi$
$577$	−1.34065	−	3.41593i	−0.0558121	−	0.142207i	−0.956060	+	0.293170i	$0.905290\pi$
$578$	−0.377980	+	5.04379i	−0.0157219	+	0.209794i
$579$	3.88469	−	9.89802i	0.161442	−	0.411348i
$580$	−4.83250	−	2.32721i	−0.200659	−	0.0966321i
$581$	2.95193	+	41.9399i	0.122467	+	1.73996i
$582$	8.68022	−	4.18017i	0.359807	−	0.173274i
$583$	−0.124503	−	1.66138i	−0.00515639	−	0.0688072i
$584$	4.61240	+	1.42274i	0.190862	+	0.0588732i
$585$	−2.97851	+	2.03072i	−0.123146	+	0.0839597i
$586$	16.1274	+	2.43081i	0.666216	+	0.100416i
$587$	1.33463			0.0550859			0.0275429	−	0.999621i	$-0.491232\pi$
$587$	1.33463			0.0550859			0.0275429	+	0.999621i	$0.491232\pi$
$588$	−4.31466	−	5.51215i	−0.177933	−	0.227317i
$589$	32.7000			1.34738
$590$	−7.73919	−	1.16649i	−0.318617	−	0.0480238i
$591$	9.32561	−	6.35809i	0.383604	−	0.261537i
$592$	−7.33411	−	2.26227i	−0.301430	−	0.0929789i
$593$	−3.25844	−	43.4809i	−0.133808	−	1.78555i	−0.511170	−	0.859480i	$-0.670788\pi$
$593$	−3.25844	−	43.4809i	−0.133808	−	1.78555i	0.377361	−	0.926066i	$-0.376831\pi$
$594$	−2.63383	+	1.26839i	−0.108067	+	0.0520425i
$595$	−5.75831	+	1.74767i	−0.236068	+	0.0716475i
$596$	−8.74972	−	4.21364i	−0.358403	−	0.172598i
$597$	4.61597	−	11.7613i	0.188919	−	0.481358i
$598$	−1.64639	+	21.9695i	−0.0673257	+	0.898399i
$599$	−1.66097	−	4.23209i	−0.0678656	−	0.172919i	0.892917	−	0.450221i	$-0.148655\pi$
$599$	−1.66097	−	4.23209i	−0.0678656	−	0.172919i	−0.960783	+	0.277302i	$0.910560\pi$
$600$	4.36392	−	1.34609i	0.178156	−	0.0549539i
$601$	8.57105	−	10.7478i	0.349621	−	0.438410i	−0.575663	−	0.817687i	$-0.695256\pi$
$601$	8.57105	−	10.7478i	0.349621	−	0.438410i	0.925283	+	0.379277i	$0.123827\pi$
$602$	−9.06847	−	2.84232i	−0.369603	−	0.115844i
$603$	−4.90821	−	6.15470i	−0.199878	−	0.250639i
$604$	16.6507	+	11.3523i	0.677508	+	0.461917i
$605$	1.18407	+	1.09865i	0.0481391	+	0.0446666i
$606$	3.17815	−	5.50471i	0.129103	−	0.223614i
$607$	10.4232	+	18.0534i	0.423063	+	0.732767i	0.996237	−	0.0866668i	$-0.0276215\pi$
$607$	10.4232	+	18.0534i	0.423063	+	0.732767i	−0.573174	+	0.819433i	$0.694288\pi$
$608$	1.57902	−	6.91815i	0.0640379	−	0.280568i
$609$	4.89298	−	20.9985i	0.198274	−	0.850903i
$610$	−0.319736	−	1.40085i	−0.0129457	−	0.0567189i
$611$	−21.9734	+	20.3884i	−0.888950	+	0.824825i
$612$	3.41713	−	0.515050i	0.138129	−	0.0208196i
$613$	46.6913	−	7.03759i	1.88585	−	0.284245i	0.898037	−	0.439920i	$-0.144993\pi$
$613$	46.6913	−	7.03759i	1.88585	−	0.284245i	0.987808	+	0.155675i	$0.0497552\pi$
$614$	−6.16151	+	5.71705i	−0.248658	+	0.230721i
$615$	0.555015	+	2.43168i	0.0223804	+	0.0980548i
$616$	−4.84967	+	6.02509i	−0.195399	+	0.242758i
$617$	7.62277	−	33.3975i	0.306881	−	1.34453i	−0.552634	−	0.833424i	$-0.686377\pi$
$617$	7.62277	−	33.3975i	0.306881	−	1.34453i	0.859515	−	0.511110i	$-0.170765\pi$
$618$	−5.59459	−	9.69012i	−0.225048	−	0.389794i
$619$	19.7068	−	34.1331i	0.792082	−	1.37193i	−0.132593	−	0.991171i	$-0.542330\pi$
$619$	19.7068	−	34.1331i	0.792082	−	1.37193i	0.924676	−	0.380756i	$-0.124336\pi$
$620$	2.22334	+	2.06295i	0.0892913	+	0.0828503i
$621$	−3.32345	−	2.26589i	−0.133365	−	0.0909269i
$622$	−11.6261	−	14.5787i	−0.466164	−	0.584552i
$623$	−10.1857	+	6.87708i	−0.408080	+	0.275524i
$624$	3.41494	−	4.28219i	0.136707	−	0.171425i
$625$	17.8594	−	5.50890i	0.714377	−	0.220356i
$626$	2.47699	+	6.31127i	0.0990005	+	0.252249i
$627$	−1.55021	+	20.6861i	−0.0619095	+	0.826125i
$628$	−3.02650	+	7.71141i	−0.120771	+	0.307719i
$629$	−23.8964	−	11.5079i	−0.952814	−	0.458851i
$630$	−0.863840	−	1.51200i	−0.0344162	−	0.0602393i
$631$	−1.31693	+	0.634198i	−0.0524260	+	0.0252470i	−0.459913	−	0.887964i	$-0.652119\pi$
$631$	−1.31693	+	0.634198i	−0.0524260	+	0.0252470i	0.407487	+	0.913211i	$0.366405\pi$
$632$	1.17875	+	15.7294i	0.0468883	+	0.625680i
$633$	5.60113	+	1.72772i	0.222625	+	0.0686707i
$634$	6.69507	−	4.56462i	0.265895	−	0.181284i
$635$	3.12117	+	0.470441i	0.123860	+	0.0186689i
$636$	−0.569910			−0.0225984
$637$	−36.5327	−	11.6324i	−1.44748	−	0.460893i
$638$	−23.8231			−0.943167
$639$	−11.5659	−	1.74328i	−0.457541	−	0.0689632i
$640$	0.543809	−	0.370763i	0.0214959	−	0.0146557i
$641$	−24.9737	−	7.70336i	−0.986401	−	0.304264i	−0.240740	−	0.970590i	$-0.577390\pi$
$641$	−24.9737	−	7.70336i	−0.986401	−	0.304264i	−0.745661	+	0.666325i	$0.767866\pi$
$642$	0.107542	+	1.43505i	0.00424434	+	0.0566368i
$643$	3.00377	−	1.44654i	0.118457	−	0.0570460i	−0.373717	−	0.927543i	$-0.621917\pi$
$643$	3.00377	−	1.44654i	0.118457	−	0.0570460i	0.492174	+	0.870497i	$0.336202\pi$
$644$	−10.5161	−	1.63380i	−0.414391	−	0.0643809i
$645$	−2.13002	−	1.02576i	−0.0838695	−	0.0403894i
$646$	8.95892	−	22.8270i	0.352484	−	0.898115i
$647$	3.45636	−	46.1219i	0.135884	−	1.81324i	−0.347336	−	0.937741i	$-0.612914\pi$
$647$	3.45636	−	46.1219i	0.135884	−	1.81324i	0.483220	−	0.875499i	$-0.339467\pi$
$648$	0.365341	+	0.930874i	0.0143520	+	0.0365682i
$649$	−33.2181	+	10.2464i	−1.30392	+	0.402207i
$650$	15.5954	−	19.5560i	0.611700	−	0.767047i
$651$	−6.14383	+	10.5309i	−0.240796	+	0.412740i
$652$	−1.52488	−	1.91214i	−0.0597190	−	0.0748853i
$653$	39.8015	+	27.1362i	1.55755	+	1.06192i	0.966953	+	0.254956i	$0.0820609\pi$
$653$	39.8015	+	27.1362i	1.55755	+	1.06192i	0.590599	+	0.806965i	$0.298892\pi$
$654$	−3.18649	−	2.95663i	−0.124602	−	0.115614i
$655$	−3.65893	+	6.33744i	−0.142966	+	0.247624i
$656$	−1.89480	−	3.28189i	−0.0739795	−	0.128136i
$657$	−1.07407	+	4.70582i	−0.0419036	+	0.183592i
$658$	−8.97655	−	11.3615i	−0.349942	−	0.442916i
$659$	−10.5689	−	46.3053i	−0.411705	−	1.80380i	−0.576073	−	0.817399i	$-0.695415\pi$
$659$	−10.5689	−	46.3053i	−0.411705	−	1.80380i	0.164367	−	0.986399i	$-0.447442\pi$
$660$	−1.41044	+	1.30869i	−0.0549011	+	0.0509408i
$661$	8.90979	−	1.34294i	0.346551	−	0.0522341i	0.0265392	−	0.999648i	$-0.491551\pi$
$661$	8.90979	−	1.34294i	0.346551	−	0.0522341i	0.320012	+	0.947414i	$0.396313\pi$
$662$	−26.2574	+	3.95766i	−1.02052	+	0.153819i
$663$	13.8748	−	12.8740i	0.538854	−	0.499983i
$664$	−3.53608	−	15.4926i	−0.137227	−	0.601229i
$665$	−12.3567	−	0.0559884i	−0.479173	−	0.00217114i
$666$	1.70787	−	7.48267i	0.0661786	−	0.289947i
$667$	−16.3898	−	28.3880i	−0.634616	−	1.09919i
$668$	−8.03954	+	13.9249i	−0.311059	+	0.538770i
$669$	7.63046	+	7.08003i	0.295011	+	0.273730i
$670$	−4.28095	−	2.91870i	−0.165388	−	0.112759i
$671$	−3.97912	−	4.98965i	−0.153612	−	0.192623i
$672$	1.93130	+	1.80834i	0.0745015	+	0.0697581i
$673$	−12.1554	+	15.2424i	−0.468555	+	0.587550i	−0.958817	−	0.284026i	$-0.908330\pi$
$673$	−12.1554	+	15.2424i	−0.468555	+	0.587550i	0.490261	+	0.871575i	$0.336901\pi$
$674$	−30.7385	+	9.48156i	−1.18400	+	0.365216i
$675$	1.66844	+	4.25112i	0.0642184	+	0.163626i
$676$	1.27033	−	16.9514i	0.0488590	−	0.651978i
$677$	4.45901	−	11.3614i	0.171374	−	0.436653i	−0.819222	−	0.573477i	$-0.805594\pi$
$677$	4.45901	−	11.3614i	0.171374	−	0.436653i	0.990595	+	0.136824i	$0.0436894\pi$
$678$	16.4326	+	7.91354i	0.631091	+	0.303917i
$679$	20.9956	+	14.4543i	0.805735	+	0.554705i
$680$	2.04923	−	0.986856i	0.0785843	−	0.0378442i
$681$	1.20052	+	16.0198i	0.0460040	+	0.613881i
$682$	12.8728	+	3.97072i	0.492923	+	0.152047i
$683$	22.4391	−	15.2987i	0.858609	−	0.585389i	−0.0520057	−	0.998647i	$-0.516561\pi$
$683$	22.4391	−	15.2987i	0.858609	−	0.585389i	0.910614	+	0.413257i	$0.135609\pi$
$684$	7.01681	+	1.05761i	0.268294	+	0.0404389i
$685$	10.2857			0.392998
$686$	6.99992	−	17.1465i	0.267258	−	0.654655i
$687$	−20.8787			−0.796571
$688$	3.55186	+	0.535356i	0.135413	+	0.0204103i
$689$	−2.57908	+	1.75839i	−0.0982552	+	0.0669893i
$690$	−2.52981	−	0.780342i	−0.0963081	−	0.0297071i
$691$	−1.11259	−	14.8464i	−0.0423248	−	0.564785i	−0.977546	−	0.210722i	$-0.932419\pi$
$691$	−1.11259	−	14.8464i	−0.0423248	−	0.564785i	0.935221	−	0.354064i	$-0.115200\pi$
$692$	7.41593	−	3.57132i	0.281911	−	0.135761i
$693$	−6.37066	−	4.38585i	−0.242001	−	0.166605i
$694$	20.9554	+	10.0916i	0.795457	+	0.383072i
$695$	3.61367	−	9.20748i	0.137074	−	0.349260i
$696$	−0.608999	+	8.12653i	−0.0230841	+	0.308035i
$697$	−4.78444	−	12.1906i	−0.181224	−	0.461750i
$698$	2.89603	−	0.893307i	0.109616	−	0.0338122i
$699$	−11.5214	+	14.4474i	−0.435779	+	0.546450i
$700$	8.81987	+	8.25833i	0.333360	+	0.312135i
$701$	1.29453	+	1.62329i	0.0488939	+	0.0613110i	0.805677	−	0.592355i	$-0.201802\pi$
$701$	1.29453	+	1.62329i	0.0488939	+	0.0613110i	−0.756783	+	0.653666i	$0.773230\pi$
$702$	4.52542	+	3.08538i	0.170801	+	0.116450i
$703$	−39.9242	−	37.0443i	−1.50577	−	1.39715i
$704$	1.46166	−	2.53168i	0.0550886	−	0.0954162i
$705$	−1.80103	−	3.11947i	−0.0678307	−	0.117486i
$706$	−0.188054	+	0.823919i	−0.00707751	+	0.0310086i
$707$	16.8170	+	0.0761981i	0.632469	+	0.00286572i
$708$	2.64608	+	11.5932i	0.0994459	+	0.435701i
$709$	−23.0796	+	21.4148i	−0.866774	+	0.804249i	−0.981959	−	0.189095i	$-0.939444\pi$
$709$	−23.0796	+	21.4148i	−0.866774	+	0.804249i	0.115185	+	0.993344i	$0.463254\pi$
$710$	−7.61239	+	1.14738i	−0.285688	+	0.0430605i
$711$	−15.5973	+	2.35091i	−0.584944	+	0.0881661i
$712$	3.40514	−	3.15951i	0.127613	−	0.118408i
$713$	4.12462	+	18.0711i	0.154468	+	0.676769i
$714$	5.66812	+	7.17404i	0.212124	+	0.268482i
$715$	−2.34500	+	10.2741i	−0.0876979	+	0.384230i
$716$	−3.98145	−	6.89608i	−0.148794	−	0.257719i
$717$	−0.0649685	+	0.112529i	−0.00242629	+	0.00420246i
$718$	−21.0508	−	19.5323i	−0.785609	−	0.728938i
$719$	28.5142	+	19.4407i	1.06340	+	0.725014i	0.962882	−	0.269921i	$-0.0869976\pi$
$719$	28.5142	+	19.4407i	1.06340	+	0.725014i	0.100518	+	0.994935i	$0.467950\pi$
$720$	0.410365	+	0.514581i	0.0152934	+	0.0191773i
$721$	14.9179	−	25.5703i	0.555572	−	0.952289i
$722$	19.5490	−	24.5137i	0.727539	−	0.912305i
$723$	2.90055	−	0.894701i	0.107873	−	0.0332743i
$724$	−5.82809	−	14.8497i	−0.216599	−	0.551886i
$725$	−2.78118	+	37.1123i	−0.103290	+	1.37832i
$726$	0.896600	−	2.28450i	0.0332760	−	0.0847858i
$727$	−11.7435	−	5.65537i	−0.435542	−	0.209746i	0.203248	−	0.979127i	$-0.434850\pi$
$727$	−11.7435	−	5.65537i	−0.435542	−	0.209746i	−0.638790	+	0.769381i	$0.720565\pi$
$728$	14.3193	+	2.22469i	0.530710	+	0.0824526i
$729$	−0.900969	+	0.433884i	−0.0333692	+	0.0160698i
$730$	0.237410	+	3.16802i	0.00878694	+	0.117254i
$731$	11.8614	+	3.65876i	0.438711	+	0.135324i
$732$	−1.80379	+	1.22980i	−0.0666699	+	0.0454547i
$733$	−49.4283	−	7.45012i	−1.82568	−	0.275176i	−0.855540	−	0.517737i	$-0.826775\pi$
$733$	−49.4283	−	7.45012i	−1.82568	−	0.275176i	−0.970136	+	0.242560i	$0.922013\pi$
$734$	2.14460			0.0791586
$735$	2.33967	−	3.96893i	0.0863000	−	0.146396i
$736$	4.02238			0.148267
$737$	−22.7559	−	3.42990i	−0.838224	−	0.126342i
$738$	3.13111	−	2.13476i	0.115258	−	0.0785815i
$739$	−32.5957	−	10.0544i	−1.19905	−	0.369858i	−0.370001	−	0.929032i	$-0.620643\pi$
$739$	−32.5957	−	10.0544i	−1.19905	−	0.369858i	−0.829051	+	0.559173i	$0.811119\pi$
$740$	−0.377503	−	5.03742i	−0.0138773	−	0.185179i
$741$	35.0171	−	16.8634i	1.28639	−	0.619491i
$742$	−0.747996	−	1.30923i	−0.0274598	−	0.0480634i
$743$	−5.09216	−	2.45225i	−0.186813	−	0.0899644i	0.338139	−	0.941096i	$-0.390203\pi$
$743$	−5.09216	−	2.45225i	−0.186813	−	0.0899644i	−0.524952	+	0.851132i	$0.675917\pi$
$744$	1.68356	−	4.28964i	0.0617223	−	0.157266i
$745$	0.477662	−	6.37396i	0.0175002	−	0.233524i
$746$	−6.67640	−	17.0112i	−0.244440	−	0.622824i
$747$	15.1850	−	4.68396i	0.555591	−	0.171377i
$748$	6.29864	−	7.89824i	0.230301	−	0.288788i
$749$	−3.15553	+	2.13052i	−0.115300	+	0.0778476i
$750$	3.92588	+	4.92290i	0.143353	+	0.179759i
$751$	−17.6345	−	12.0230i	−0.643492	−	0.438726i	0.197108	−	0.980382i	$-0.436845\pi$
$751$	−17.6345	−	12.0230i	−0.643492	−	0.438726i	−0.840600	+	0.541656i	$0.817797\pi$
$752$	4.01185	+	3.72245i	0.146297	+	0.135744i
$753$	−4.82406	+	8.35551i	−0.175798	+	0.304492i
$754$	22.3174	+	38.6549i	0.812753	+	1.40773i
$755$	−2.95147	+	12.9313i	−0.107415	+	0.470617i
$756$	−1.65895	+	2.06104i	−0.0603356	+	0.0749592i
$757$	−6.68756	−	29.3001i	−0.243064	−	1.06493i	−0.938211	−	0.346064i	$-0.887518\pi$
$757$	−6.68756	−	29.3001i	−0.243064	−	1.06493i	0.695147	−	0.718867i	$-0.255339\pi$
$758$	3.96678	−	3.68064i	0.144080	−	0.133687i
$759$	−11.6274	+	1.75255i	−0.422048	+	0.0636135i
$760$	4.61828	−	0.696094i	0.167523	−	0.0252500i
$761$	8.70843	−	8.08024i	0.315680	−	0.292909i	−0.506378	−	0.862311i	$-0.669016\pi$
$761$	8.70843	−	8.08024i	0.315680	−	0.292909i	0.822059	+	0.569403i	$0.192826\pi$
$762$	−1.06715	−	4.67550i	−0.0386588	−	0.169375i
$763$	2.60994	−	11.2007i	0.0944862	−	0.405493i
$764$	−1.21937	+	5.34242i	−0.0441153	+	0.193282i
$765$	1.13724	+	1.96975i	0.0411168	+	0.0712164i
$766$	16.6529	−	28.8437i	0.601694	−	1.04216i
$767$	47.7442	+	44.3001i	1.72394	+	1.59958i
$768$	−0.826239	−	0.563320i	−0.0298143	−	0.0203271i
$769$	29.4359	+	36.9115i	1.06149	+	1.33106i	0.941023	+	0.338343i	$0.109867\pi$
$769$	29.4359	+	36.9115i	1.06149	+	1.33106i	0.120463	+	0.992718i	$0.461562\pi$
$770$	−4.85757	−	1.52250i	−0.175055	−	0.0548671i
$771$	15.9253	−	19.9696i	0.573534	−	0.719189i
$772$	−10.1606	+	3.13414i	−0.365690	+	0.112800i
$773$	14.1825	+	36.1363i	0.510108	+	1.29973i	0.921537	+	0.388291i	$0.126935\pi$
$773$	14.1825	+	36.1363i	0.510108	+	1.29973i	−0.411429	+	0.911442i	$0.634970\pi$
$774$	−0.268429	+	3.58193i	−0.00964847	+	0.128750i
$775$	7.68849	−	19.5899i	0.276179	−	0.703692i
$776$	−8.68022	−	4.18017i	−0.311602	−	0.150059i
$777$	19.4312	−	5.89743i	0.697089	−	0.211569i
$778$	22.2702	−	10.7248i	0.798427	−	0.384502i
$779$	−2.00959	−	26.8161i	−0.0720009	−	0.960785i
$780$	3.44475	+	1.06256i	0.123342	+	0.0380459i
$781$	−28.2515	+	19.2616i	−1.01092	+	0.689233i
$782$	13.7450	+	2.07173i	0.491520	+	0.0740847i
$783$	−8.14932			−0.291233
$784$	−1.61943	+	6.81010i	−0.0578366	+	0.243218i
$785$	−5.45235			−0.194603
$786$	10.9942	+	1.65711i	0.392151	+	0.0591073i
$787$	−16.2760	+	11.0968i	−0.580178	+	0.395559i	−0.817548	−	0.575860i	$-0.804667\pi$
$787$	−16.2760	+	11.0968i	−0.580178	+	0.395559i	0.237370	+	0.971419i	$0.423715\pi$
$788$	−10.7854	−	3.32685i	−0.384213	−	0.118514i
$789$	0.223038	+	2.97623i	0.00794035	+	0.105957i
$790$	−9.35357	+	4.50444i	−0.332785	+	0.160261i
$791$	3.38806	+	48.1363i	0.120466	+	1.71153i
$792$	2.63383	+	1.26839i	0.0935890	+	0.0450701i
$793$	−4.36849	+	11.1307i	−0.155130	+	0.395264i
$794$	−0.361468	+	4.82346i	−0.0128280	+	0.171178i
$795$	−0.137039	−	0.349171i	−0.00486029	−	0.0123838i
$796$	−12.0734	+	3.72414i	−0.427929	+	0.131999i
$797$	−3.77829	+	4.73783i	−0.133834	+	0.167823i	−0.844233	−	0.535977i	$-0.819943\pi$
$797$	−3.77829	+	4.73783i	−0.133834	+	0.167823i	0.710398	+	0.703800i	$0.248515\pi$
$798$	6.77981	+	17.5075i	0.240003	+	0.619760i
$799$	11.7918	+	14.7864i	0.417163	+	0.523106i
$800$	−3.77327	−	2.57257i	−0.133405	−	0.0909542i
$801$	3.40514	+	3.15951i	0.120315	+	0.111636i
$802$	−9.72806	+	16.8495i	−0.343510	+	0.594976i
$803$	7.05522	+	12.2200i	0.248973	+	0.431234i
$804$	−1.75172	+	7.67479i	−0.0617784	+	0.270669i
$805$	−1.52767	−	6.83580i	−0.0538435	−	0.240930i
$806$	−5.61635	−	24.6068i	−0.197827	−	0.866738i
$807$	−5.29652	+	4.91446i	−0.186446	+	0.172997i
$808$	−6.28530	+	0.947357i	−0.221116	+	0.0333279i
$809$	11.3564	−	1.71169i	0.399268	−	0.0601800i	0.0536608	−	0.998559i	$-0.482911\pi$
$809$	11.3564	−	1.71169i	0.399268	−	0.0601800i	0.345607	+	0.938379i	$0.387673\pi$
$810$	−0.482476	+	0.447672i	−0.0169525	+	0.0157296i
$811$	6.55734	+	28.7296i	0.230259	+	1.00883i	0.949425	+	0.313993i	$0.101667\pi$
$811$	6.55734	+	28.7296i	0.230259	+	1.00883i	−0.719166	+	0.694838i	$0.755476\pi$
$812$	−19.4680	+	9.26688i	−0.683194	+	0.325204i
$813$	0.560508	−	2.45574i	0.0196579	−	0.0861267i
$814$	−11.2184	−	19.4309i	−0.393205	−	0.681052i
$815$	0.804856	−	1.39405i	0.0281929	−	0.0488315i
$816$	−2.53323	−	2.35049i	−0.0886807	−	0.0822837i
$817$	21.0599	+	14.3584i	0.736793	+	0.502337i
$818$	−18.8189	−	23.5981i	−0.657987	−	0.825089i
$819$	−1.14839	+	14.4456i	−0.0401279	+	0.504768i
$820$	1.55512	−	1.95006i	0.0543071	−	0.0680989i
$821$	50.0327	−	15.4331i	1.74615	−	0.538617i	0.753271	−	0.657710i	$-0.228475\pi$
$821$	50.0327	−	15.4331i	1.74615	−	0.538617i	0.992883	+	0.119092i	$0.0379985\pi$
$822$	−5.70944	−	14.5474i	−0.199140	−	0.507400i
$823$	1.10562	−	14.7534i	0.0385393	−	0.514272i	−0.944212	−	0.329339i	$-0.893174\pi$
$823$	1.10562	−	14.7534i	0.0385393	−	0.514272i	0.982751	−	0.184933i	$-0.0592068\pi$
$824$	−4.08787	+	10.4157i	−0.142408	+	0.362849i
$825$	12.0282	+	5.79247i	0.418768	+	0.201668i
$826$	−23.1598	+	21.2946i	−0.805831	+	0.740936i
$827$	−19.9833	+	9.62343i	−0.694886	+	0.334639i	−0.747767	−	0.663961i	$-0.768874\pi$
$827$	−19.9833	+	9.62343i	−0.694886	+	0.334639i	0.0528809	+	0.998601i	$0.483160\pi$
$828$	0.300593	+	4.01113i	0.0104463	+	0.139396i
$829$	24.0825	+	7.42847i	0.836420	+	0.258001i	0.683237	−	0.730196i	$-0.260571\pi$
$829$	24.0825	+	7.42847i	0.836420	+	0.258001i	0.153183	+	0.988198i	$0.451048\pi$
$830$	8.64167	−	5.89179i	0.299957	−	0.204507i
$831$	8.11892	+	1.22373i	0.281642	+	0.0424507i
$832$	−5.47713			−0.189885
$833$	−9.04133	+	22.4369i	−0.313263	+	0.777393i
$834$	−15.0283			−0.520387
$835$	−10.4646	−	1.57729i	−0.362144	−	0.0545844i
$836$	17.1396	−	11.6856i	0.592786	−	0.404155i
$837$	4.40346	+	1.35829i	0.152206	+	0.0469492i
$838$	−0.489856	−	6.53668i	−0.0169218	−	0.225806i
$839$	−25.6658	+	12.3600i	−0.886082	+	0.426715i	−0.820842	−	0.571155i	$-0.806496\pi$
$839$	−25.6658	+	12.3600i	−0.886082	+	0.426715i	−0.0652400	+	0.997870i	$0.520781\pi$
$840$	−0.643530	+	1.61809i	−0.0222039	+	0.0558295i
$841$	−33.7065	−	16.2322i	−1.16229	−	0.559730i
$842$	8.51892	−	21.7058i	0.293581	−	0.748033i
$843$	−1.95921	+	26.1438i	−0.0674786	+	0.900440i
$844$	−2.14146	−	5.45635i	−0.0737121	−	0.187815i
$845$	10.6912	−	3.29780i	0.367789	−	0.113448i
$846$	−3.41224	+	4.27881i	−0.117315	+	0.147109i
$847$	6.42486	−	0.938639i	0.220761	−	0.0322520i
$848$	0.355333	+	0.445574i	0.0122022	+	0.0153011i
$849$	−16.4587	−	11.2214i	−0.564862	−	0.385117i
$850$	−11.5688	−	10.7342i	−0.396805	−	0.368182i
$851$	15.4361	−	26.7361i	0.529142	−	0.916501i
$852$	5.84828	+	10.1295i	0.200359	+	0.347032i
$853$	4.82253	−	21.1289i	0.165120	−	0.723439i	−0.822781	−	0.568358i	$-0.807579\pi$
$853$	4.82253	−	21.1289i	0.165120	−	0.723439i	0.987902	−	0.155081i	$-0.0495640\pi$
$854$	−5.19260	−	2.52967i	−0.177687	−	0.0865637i
$855$	1.03927	+	4.55335i	0.0355424	+	0.155721i
$856$	1.05491	−	0.978817i	0.0360562	−	0.0334553i
$857$	−42.7720	+	6.44684i	−1.46106	+	0.220220i	−0.830978	−	0.556305i	$-0.812218\pi$
$857$	−42.7720	+	6.44684i	−1.46106	+	0.220220i	−0.630086	+	0.776525i	$0.716980\pi$
$858$	15.8326	−	2.38638i	0.540517	−	0.0814698i
$859$	−14.8726	+	13.7998i	−0.507447	+	0.470842i	−0.891855	−	0.452321i	$-0.850596\pi$
$859$	−14.8726	+	13.7998i	−0.507447	+	0.470842i	0.384408	+	0.923163i	$0.374406\pi$
$860$	0.526072	+	2.30487i	0.0179389	+	0.0785954i
$861$	9.01361	+	4.39115i	0.307183	+	0.149650i
$862$	−1.63510	+	7.16383i	−0.0556916	+	0.244001i
$863$	8.98669	+	15.5654i	0.305911	+	0.529853i	0.977464	−	0.211104i	$-0.0677058\pi$
$863$	8.98669	+	15.5654i	0.305911	+	0.529853i	−0.671553	+	0.740957i	$0.734372\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	3.97129	+	3.68482i	0.135028	+	0.125287i
$866$	24.5582	+	16.7435i	0.834521	+	0.568967i
$867$	3.15357	+	3.95445i	0.107101	+	0.134300i
$868$	12.0640	−	1.76250i	0.409480	−	0.0598230i
$869$	−28.7498	+	36.0511i	−0.975269	+	1.22295i
$870$	−5.12537	+	1.58097i	−0.173766	+	0.0535999i
$871$	15.7524	+	40.1364i	0.533748	+	1.35997i
$872$	−0.324843	+	4.33473i	−0.0110006	+	0.146793i
$873$	3.51981	−	8.96833i	0.119128	−	0.303532i
$874$	25.7164	+	12.3844i	0.869871	+	0.418908i
$875$	−6.15653	+	15.4800i	−0.208129	+	0.523318i
$876$	4.34883	−	2.09429i	0.146933	−	0.0707594i
$877$	1.58109	+	21.0982i	0.0533898	+	0.712437i	0.958104	+	0.286419i	$0.0924649\pi$
$877$	1.58109	+	21.0982i	0.0533898	+	0.712437i	−0.904715	+	0.426018i	$0.859916\pi$
$878$	−7.86148	−	2.42495i	−0.265312	−	0.0818380i
$879$	13.4756	−	9.18749i	0.454520	−	0.309886i
$880$	1.90257	+	0.286766i	0.0641356	+	0.00966688i
$881$	30.2372			1.01872			0.509358	−	0.860555i	$-0.329883\pi$
$881$	30.2372			1.01872			0.509358	+	0.860555i	$0.329883\pi$
$882$	−6.91208	−	1.10598i	−0.232742	−	0.0372402i
$883$	−55.2520			−1.85938			−0.929689	−	0.368345i	$-0.879924\pi$
$883$	−55.2520			−1.85938			−0.929689	+	0.368345i	$0.879924\pi$
$884$	−18.7161	−	2.82099i	−0.629490	−	0.0948803i
$885$	−6.46664	+	4.40888i	−0.217374	+	0.148203i
$886$	−22.2076	−	6.85013i	−0.746078	−	0.230135i
$887$	2.90336	+	38.7427i	0.0974854	+	1.30085i	0.804627	+	0.593780i	$0.202365\pi$
$887$	2.90336	+	38.7427i	0.0974854	+	1.30085i	−0.707142	+	0.707072i	$0.750016\pi$
$888$	−6.91502	+	3.33010i	−0.232053	+	0.111751i
$889$	9.34021	−	8.58802i	0.313260	−	0.288033i
$890$	2.75455	+	1.32652i	0.0923327	+	0.0444651i
$891$	−1.06801	+	2.72125i	−0.0357798	+	0.0911653i
$892$	0.777878	−	10.3801i	0.0260453	−	0.347550i
$893$	14.1882	+	36.1509i	0.474789	+	1.20974i
$894$	−9.28001	+	2.86250i	−0.310370	+	0.0957364i
$895$	3.26770	−	4.09756i	0.109227	−	0.136966i
$896$	0.209670	−	2.63743i	0.00700457	−	0.0881104i
$897$	13.7362	+	17.2246i	0.458637	+	0.575113i
$898$	−19.7697	−	13.4787i	−0.659722	−	0.449791i
$899$	27.5287	+	25.5429i	0.918134	+	0.851904i
$900$	2.28340	−	3.95497i	0.0761135	−	0.131832i
$901$	0.984728	+	1.70560i	0.0328060	+	0.0568217i
$902$	2.46514	−	10.8005i	0.0820802	−	0.359617i
$903$	−8.58093	+	4.08456i	−0.285555	+	0.135926i
$904$	−4.05852	−	17.7816i	−0.134984	−	0.591406i
$905$	7.69668	−	7.14147i	0.255846	−	0.237391i
$906$	19.9273	−	3.00356i	0.662042	−	0.0997868i
$907$	−23.0531	+	3.47470i	−0.765467	+	0.115376i	−0.520159	−	0.854070i	$-0.674127\pi$
$907$	−23.0531	+	3.47470i	−0.765467	+	0.115376i	−0.245308	+	0.969445i	$0.578889\pi$
$908$	11.7763	−	10.9268i	0.390810	−	0.362619i
$909$	−1.41441	−	6.19693i	−0.0469130	−	0.205539i
$910$	2.08018	+	9.30807i	0.0689573	+	0.308560i
$911$	−9.88793	+	43.3218i	−0.327602	+	1.43532i	0.496086	+	0.868273i	$0.334770\pi$
$911$	−9.88793	+	43.3218i	−0.327602	+	1.43532i	−0.823688	+	0.567044i	$0.808087\pi$
$912$	−3.54803	−	6.14538i	−0.117487	−	0.203494i
$913$	23.2273	−	40.2309i	0.768712	−	1.33145i
$914$	−1.45478	−	1.34984i	−0.0481199	−	0.0446488i
$915$	−1.18721	−	0.809423i	−0.0392478	−	0.0267587i
$916$	13.0176	+	16.3236i	0.430115	+	0.539347i
$917$	10.6229	+	27.4315i	0.350799	+	0.905869i
$918$	2.15461	−	2.70180i	0.0711128	−	0.0891726i
$919$	49.3471	−	15.2216i	1.62781	−	0.502113i	0.659467	−	0.751734i	$-0.270782\pi$
$919$	49.3471	−	15.2216i	1.62781	−	0.502113i	0.968344	+	0.249621i	$0.0803060\pi$
$920$	0.967213	+	2.46442i	0.0318881	+	0.0812495i
$921$	−0.628128	+	8.38179i	−0.0206975	+	0.276189i
$922$	−2.02558	+	5.16110i	−0.0667091	+	0.169972i
$923$	57.7193	+	27.7962i	1.89986	+	0.914922i
$924$	0.543040	+	7.71531i	0.0178647	+	0.253815i
$925$	−31.5796	+	15.2079i	−1.03833	+	0.500033i
$926$	2.91747	+	38.9309i	0.0958740	+	1.27935i
$927$	−10.6921	−	3.29807i	−0.351174	−	0.108323i
$928$	6.73328	−	4.59067i	0.221031	−	0.150696i
$929$	−24.0574	−	3.62607i	−0.789298	−	0.118967i	−0.257991	−	0.966147i	$-0.583061\pi$
$929$	−24.0574	−	3.62607i	−0.789298	−	0.118967i	−0.531306	+	0.847180i	$0.678299\pi$
$930$	3.03299			0.0994556
$931$	−31.3209	+	38.5533i	−1.02650	+	1.26353i
$932$	18.4789			0.605296
$933$	−18.4386	−	2.77916i	−0.603651	−	0.0909858i
$934$	21.8390	−	14.8896i	0.714595	−	0.487202i
$935$	6.35363	+	1.95984i	0.207786	+	0.0640935i
$936$	−0.409306	−	5.46182i	−0.0133786	−	0.178525i
$937$	−32.6444	+	15.7207i	−1.06644	+	0.513573i	−0.882959	−	0.469450i	$-0.844452\pi$
$937$	−32.6444	+	15.7207i	−1.06644	+	0.513573i	−0.183485	+	0.983022i	$0.558738\pi$
$938$	−19.9301	+	6.04886i	−0.650740	+	0.197502i
$939$	6.10852	+	2.94171i	0.199344	+	0.0959990i
$940$	−1.31598	+	3.35306i	−0.0429225	+	0.109365i
$941$	1.32029	−	17.6180i	0.0430401	−	0.574330i	−0.933441	−	0.358730i	$-0.883210\pi$
$941$	1.32029	−	17.6180i	0.0430401	−	0.574330i	0.976482	−	0.215601i	$-0.0691710\pi$
$942$	3.02650	+	7.71141i	0.0986088	+	0.251251i
$943$	14.5660	−	4.49301i	0.474334	−	0.146313i
$944$	7.41416	−	9.29706i	0.241310	−	0.302594i
$945$	−1.66166	−	0.520810i	−0.0540537	−	0.0169420i
$946$	6.54697	+	8.20964i	0.212860	+	0.266918i
$947$	−6.87298	−	4.68592i	−0.223342	−	0.152272i	0.446480	−	0.894793i	$-0.352677\pi$
$947$	−6.87298	−	4.68592i	−0.223342	−	0.152272i	−0.669822	+	0.742522i	$0.733630\pi$
$948$	11.5628	+	10.7287i	0.375541	+	0.348451i
$949$	13.2186	−	22.8953i	0.429094	−	0.743213i
$950$	−16.2032	−	28.0647i	−0.525701	−	0.910540i
$951$	1.80310	−	7.89990i	0.0584696	−	0.256172i
$952$	2.07488	−	8.90446i	0.0672471	−	0.288595i
$953$	12.0240	+	52.6805i	0.389495	+	1.70649i	0.666401	+	0.745593i	$0.267834\pi$
$953$	12.0240	+	52.6805i	0.389495	+	1.70649i	−0.276906	+	0.960897i	$0.589309\pi$
$954$	−0.417774	+	0.387637i	−0.0135259	+	0.0125502i
$955$	−3.56638	+	0.537546i	−0.115405	+	0.0173946i
$956$	0.128486	−	0.0193661i	0.00415553	−	0.000626345i
$957$	−17.4636	+	16.2038i	−0.564518	+	0.523796i
$958$	3.42667	+	15.0132i	0.110711	+	0.485056i
$959$	25.9257	−	32.2093i	0.837183	−	1.04009i
$960$	0.146457	−	0.641672i	0.00472689	−	0.0207099i
$961$	4.88232	+	8.45642i	0.157494	+	0.272788i
$962$	−21.0188	+	36.4055i	−0.677672	+	1.17376i
$963$	1.05491	+	0.978817i	0.0339941	+	0.0315419i
$964$	−2.50797	−	1.70990i	−0.0807762	−	0.0550723i
$965$	−4.36343	−	5.47156i	−0.140464	−	0.176136i
$966$	−8.82008	+	5.95507i	−0.283782	+	0.191601i
$967$	−31.3621	+	39.3269i	−1.00854	+	1.26467i	−0.0444698	+	0.999011i	$0.514160\pi$
$967$	−31.3621	+	39.3269i	−1.00854	+	1.26467i	−0.964068	+	0.265656i	$0.914412\pi$
$968$	−2.34512	+	0.723372i	−0.0753749	+	0.0232501i
$969$	−8.95892	−	22.8270i	−0.287802	−	0.733308i
$970$	0.473868	−	6.32332i	0.0152150	−	0.203030i
$971$	22.7345	−	57.9264i	0.729583	−	1.85895i	0.313763	−	0.949501i	$-0.398410\pi$
$971$	22.7345	−	57.9264i	0.729583	−	1.85895i	0.415821	−	0.909447i	$-0.363494\pi$
$972$	0.900969	+	0.433884i	0.0288986	+	0.0139168i
$973$	−19.7243	−	34.5239i	−0.632333	−	1.10678i
$974$	2.33120	−	1.12265i	0.0746965	−	0.0359720i
$975$	−1.86922	−	24.9431i	−0.0598631	−	0.798817i
$976$	2.08614	+	0.643489i	0.0667757	+	0.0205976i
$977$	17.3175	−	11.8069i	0.554037	−	0.377736i	−0.253696	−	0.967284i	$-0.581646\pi$
$977$	17.3175	−	11.8069i	0.554037	−	0.377736i	0.807733	+	0.589548i	$0.200694\pi$
$978$	−2.41841	−	0.364516i	−0.0773321	−	0.0116559i
$979$	13.5793			0.433997
$980$	−4.56179	+	0.645358i	−0.145721	+	0.0206152i
$981$	−4.34689			−0.138785
$982$	14.4326	+	2.17536i	0.460562	+	0.0694186i
$983$	46.2257	−	31.5161i	1.47437	−	1.00521i	0.482787	−	0.875738i	$-0.339625\pi$
$983$	46.2257	−	31.5161i	1.47437	−	1.00521i	0.991583	−	0.129471i	$-0.0413278\pi$
$984$	−3.62124	−	1.11700i	−0.115441	−	0.0356088i
$985$	−0.555147	−	7.40792i	−0.0176884	−	0.236036i
$986$	25.3729	−	12.2190i	0.808039	−	0.389131i
$987$	−14.3080	−	2.22294i	−0.455430	−	0.0707569i
$988$	−35.0171	−	16.8634i	−1.11404	−	0.536495i
$989$	−5.27855	+	13.4495i	−0.167848	+	0.427670i
$990$	−0.143785	+	1.91868i	−0.00456979	+	0.0609796i
$991$	−11.7794	−	30.0135i	−0.374186	−	0.953410i	−0.986642	−	0.162905i	$-0.947914\pi$
$991$	−11.7794	−	30.0135i	−0.374186	−	0.953410i	0.612456	−	0.790505i	$-0.290182\pi$
$992$	−4.40346	+	1.35829i	−0.139810	+	0.0431256i
$993$	−16.5561	+	20.7607i	−0.525393	+	0.658822i
$994$	−15.5944	+	26.7298i	−0.494624	+	0.847819i
$995$	−5.18483	−	6.50157i	−0.164370	−	0.206114i
$996$	−13.1298	−	8.95173i	−0.416033	−	0.283646i
$997$	−18.1494	−	16.8402i	−0.574797	−	0.533334i	0.338320	−	0.941031i	$-0.390141\pi$
$997$	−18.1494	−	16.8402i	−0.574797	−	0.533334i	−0.913117	+	0.407697i	$0.866332\pi$
$998$	9.05741	−	15.6879i	0.286707	−	0.496591i
$999$	−3.83755	−	6.64683i	−0.121415	−	0.210296i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.m.d.235.3	✓	36
3.2	odd	2		882.2.z.e.235.1		36
49.44	even	21	inner	294.2.m.d.289.3	yes	36
147.44	odd	42		882.2.z.e.289.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.m.d.235.3	✓	36	1.1	even	1	trivial
294.2.m.d.289.3	yes	36	49.44	even	21	inner
882.2.z.e.235.1		36	3.2	odd	2
882.2.z.e.289.1		36	147.44	odd	42

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.m (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.988831 - 0.149042i) q^{2} +(-0.826239 + 0.563320i) q^{3} +(0.955573 + 0.294755i) q^{4} +(0.0491854 + 0.656334i) q^{5} +(0.900969 - 0.433884i) q^{6} +(2.17925 + 1.50029i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(0.365341 - 0.930874i) q^{9} +O(q^{10})\)	\(q+(-0.988831 - 0.149042i) q^{2} +(-0.826239 + 0.563320i) q^{3} +(0.955573 + 0.294755i) q^{4} +(0.0491854 + 0.656334i) q^{5} +(0.900969 - 0.433884i) q^{6} +(2.17925 + 1.50029i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(0.365341 - 0.930874i) q^{9} +(0.0491854 - 0.656334i) q^{10} +(-1.06801 - 2.72125i) q^{11} +(-0.955573 + 0.294755i) q^{12} +(-3.41494 + 4.28219i) q^{13} +(-1.93130 - 1.80834i) q^{14} +(-0.410365 - 0.514581i) q^{15} +(0.826239 + 0.563320i) q^{16} +(2.53323 + 2.35049i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(3.54803 + 6.14538i) q^{19} +(-0.146457 + 0.641672i) q^{20} +(-2.64572 - 0.0119878i) q^{21} +(0.650502 + 2.85004i) q^{22} +(-2.94861 + 2.73591i) q^{23} +(0.988831 - 0.149042i) q^{24} +(4.51580 - 0.680647i) q^{25} +(4.01502 - 3.72539i) q^{26} +(0.222521 + 0.974928i) q^{27} +(1.64021 + 2.07598i) q^{28} +(-1.81339 + 7.94500i) q^{29} +(0.329087 + 0.569995i) q^{30} +(2.30409 - 3.99080i) q^{31} +(-0.733052 - 0.680173i) q^{32} +(2.41537 + 1.64677i) q^{33} +(-2.15461 - 2.70180i) q^{34} +(-0.877506 + 1.50411i) q^{35} +(0.623490 - 0.781831i) q^{36} +(-7.33411 + 2.26227i) q^{37} +(-2.59248 - 6.60554i) q^{38} +(0.409306 - 5.46182i) q^{39} +(0.240458 - 0.612677i) q^{40} +(-3.41431 - 1.64425i) q^{41} +(2.61439 + 0.406179i) q^{42} +(3.23626 - 1.55850i) q^{43} +(-0.218461 - 2.91516i) q^{44} +(0.628933 + 0.194000i) q^{45} +(3.32345 - 2.26589i) q^{46} +(5.41168 + 0.815680i) q^{47} -1.00000 q^{48} +(2.49823 + 6.53902i) q^{49} -4.56681 q^{50} +(-3.41713 - 0.515050i) q^{51} +(-4.52542 + 3.08538i) q^{52} +(0.544591 + 0.167984i) q^{53} +(-0.0747301 - 0.997204i) q^{54} +(1.73352 - 0.834818i) q^{55} +(-1.31248 - 2.29726i) q^{56} +(-6.39334 - 3.07887i) q^{57} +(2.97728 - 7.58598i) q^{58} +(0.888645 - 11.8581i) q^{59} +(-0.240458 - 0.612677i) q^{60} +(2.08614 - 0.643489i) q^{61} +(-2.87316 + 3.60282i) q^{62} +(2.19275 - 1.48048i) q^{63} +(0.623490 + 0.781831i) q^{64} +(-2.97851 - 2.03072i) q^{65} +(-2.14295 - 1.98837i) q^{66} +(3.93608 - 6.81749i) q^{67} +(1.72786 + 2.99275i) q^{68} +(0.895064 - 3.92153i) q^{69} +(1.09188 - 1.35652i) q^{70} +(-2.60273 - 11.4033i) q^{71} +(-0.733052 + 0.680173i) q^{72} +(-4.77293 + 0.719403i) q^{73} +(7.58937 - 1.14391i) q^{74} +(-3.34771 + 3.10622i) q^{75} +(1.57902 + 6.91815i) q^{76} +(1.75521 - 7.53261i) q^{77} +(-1.21878 + 5.33981i) q^{78} +(-7.88673 - 13.6602i) q^{79} +(-0.329087 + 0.569995i) q^{80} +(-0.733052 - 0.680173i) q^{81} +(3.13111 + 2.13476i) q^{82} +(9.90788 + 12.4241i) q^{83} +(-2.52465 - 0.791296i) q^{84} +(-1.41811 + 1.77825i) q^{85} +(-3.43239 + 1.05875i) q^{86} +(-2.97728 - 7.58598i) q^{87} +(-0.218461 + 2.91516i) q^{88} +(-1.69707 + 4.32405i) q^{89} +(-0.592994 - 0.285571i) q^{90} +(-13.8665 + 4.20855i) q^{91} +(-3.62404 + 1.74524i) q^{92} +(0.344370 + 4.59530i) q^{93} +(-5.22967 - 1.61314i) q^{94} +(-3.85890 + 2.63096i) q^{95} +(0.988831 + 0.149042i) q^{96} +9.63432 q^{97} +(-1.49574 - 6.83833i) q^{98} -2.92333 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 6 q^{6} - q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 36 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 6 * q^6 - q^7 - 6 * q^8 + 3 * q^9	\( 36 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 6 q^{6} - q^{7} - 6 q^{8} + 3 q^{9} + 13 q^{11} - 3 q^{12} + 2 q^{13} - 4 q^{14} + 3 q^{16} + q^{17} - 18 q^{18} - 2 q^{19} + 7 q^{20} - 12 q^{21} - 12 q^{22} + 42 q^{23} - 3 q^{24} + 33 q^{25} + 34 q^{26} + 6 q^{27} - 9 q^{28} - 4 q^{29} - 7 q^{30} - q^{31} + 3 q^{32} + q^{33} + 5 q^{34} - 4 q^{35} - 6 q^{36} + 45 q^{37} - 30 q^{38} - 6 q^{39} - 58 q^{41} - 20 q^{42} - q^{44} - 14 q^{45} - 7 q^{46} - 68 q^{47} - 36 q^{48} - 29 q^{49} + 74 q^{50} - 8 q^{51} - 15 q^{52} - 19 q^{53} - 3 q^{54} + 48 q^{55} - 15 q^{56} + 3 q^{57} - 40 q^{58} - 123 q^{59} - 13 q^{61} + 2 q^{62} + 10 q^{63} - 6 q^{64} + 9 q^{65} - 6 q^{66} - 7 q^{67} + q^{68} + 21 q^{69} - 16 q^{70} - 38 q^{71} + 3 q^{72} + 65 q^{73} + 38 q^{74} + 9 q^{75} - 17 q^{76} + 25 q^{77} + 5 q^{78} - 71 q^{79} + 7 q^{80} + 3 q^{81} + 29 q^{82} + 8 q^{83} + 4 q^{84} + 73 q^{85} - 14 q^{86} + 40 q^{87} - q^{88} + 45 q^{89} - 35 q^{91} - 7 q^{92} - 6 q^{93} + 9 q^{94} - 144 q^{95} - 3 q^{96} + 56 q^{97} + 24 q^{98} + 30 q^{99}+O(q^{100}) \) 36 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 6 * q^6 - q^7 - 6 * q^8 + 3 * q^9 + 13 * q^11 - 3 * q^12 + 2 * q^13 - 4 * q^14 + 3 * q^16 + q^17 - 18 * q^18 - 2 * q^19 + 7 * q^20 - 12 * q^21 - 12 * q^22 + 42 * q^23 - 3 * q^24 + 33 * q^25 + 34 * q^26 + 6 * q^27 - 9 * q^28 - 4 * q^29 - 7 * q^30 - q^31 + 3 * q^32 + q^33 + 5 * q^34 - 4 * q^35 - 6 * q^36 + 45 * q^37 - 30 * q^38 - 6 * q^39 - 58 * q^41 - 20 * q^42 - q^44 - 14 * q^45 - 7 * q^46 - 68 * q^47 - 36 * q^48 - 29 * q^49 + 74 * q^50 - 8 * q^51 - 15 * q^52 - 19 * q^53 - 3 * q^54 + 48 * q^55 - 15 * q^56 + 3 * q^57 - 40 * q^58 - 123 * q^59 - 13 * q^61 + 2 * q^62 + 10 * q^63 - 6 * q^64 + 9 * q^65 - 6 * q^66 - 7 * q^67 + q^68 + 21 * q^69 - 16 * q^70 - 38 * q^71 + 3 * q^72 + 65 * q^73 + 38 * q^74 + 9 * q^75 - 17 * q^76 + 25 * q^77 + 5 * q^78 - 71 * q^79 + 7 * q^80 + 3 * q^81 + 29 * q^82 + 8 * q^83 + 4 * q^84 + 73 * q^85 - 14 * q^86 + 40 * q^87 - q^88 + 45 * q^89 - 35 * q^91 - 7 * q^92 - 6 * q^93 + 9 * q^94 - 144 * q^95 - 3 * q^96 + 56 * q^97 + 24 * q^98 + 30 * q^99

Introduction

L-functions

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Database

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