LMFDB - Embedded newform 224.2.bd.a.109.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(37,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("224.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.bd (of order $24$, degree $8$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			109.17
Character	$\chi$	$=$	224.109
Dual form			224.2.bd.a.37.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.148173 - 1.40643i) q^{2} +(-1.23048 - 1.60359i) q^{3} +(-1.95609 - 0.416790i) q^{4} +(0.591453 + 0.453838i) q^{5} +(-2.43766 + 1.49297i) q^{6} +(-2.18592 - 1.49056i) q^{7} +(-0.876026 + 2.68935i) q^{8} +(-0.280969 + 1.04859i) q^{9} +O(q^{10})$	\(q+(0.148173 - 1.40643i) q^{2} +(-1.23048 - 1.60359i) q^{3} +(-1.95609 - 0.416790i) q^{4} +(0.591453 + 0.453838i) q^{5} +(-2.43766 + 1.49297i) q^{6} +(-2.18592 - 1.49056i) q^{7} +(-0.876026 + 2.68935i) q^{8} +(-0.280969 + 1.04859i) q^{9} +(0.725929 - 0.764591i) q^{10} +(-3.27488 - 0.431146i) q^{11} +(1.73857 + 3.64962i) q^{12} +(0.237482 + 0.0983684i) q^{13} +(-2.42026 + 2.85348i) q^{14} -1.50689i q^{15} +(3.65257 + 1.63056i) q^{16} +(0.237856 + 0.137326i) q^{17} +(1.43314 + 0.550536i) q^{18} +(0.413608 + 3.14167i) q^{19} +(-0.967780 - 1.13426i) q^{20} +(0.299483 + 5.33942i) q^{21} +(-1.09163 + 4.54200i) q^{22} +(1.45977 - 5.44793i) q^{23} +(5.39054 - 1.90439i) q^{24} +(-1.15025 - 4.29278i) q^{25} +(0.173537 - 0.319427i) q^{26} +(-3.57503 + 1.48082i) q^{27} +(3.65460 + 3.82673i) q^{28} +(0.801128 - 1.93409i) q^{29} +(-2.11933 - 0.223280i) q^{30} +(1.52247 - 2.63700i) q^{31} +(2.83448 - 4.89548i) q^{32} +(3.33829 + 5.78208i) q^{33} +(0.228383 - 0.314179i) q^{34} +(-0.616397 - 1.87365i) q^{35} +(0.986643 - 1.93403i) q^{36} +(-6.47662 - 4.96968i) q^{37} +(4.47982 - 0.116200i) q^{38} +(-0.134474 - 0.501865i) q^{39} +(-1.73865 + 1.19305i) q^{40} +(-2.41053 - 2.41053i) q^{41} +(7.55389 + 0.369957i) q^{42} +(-3.81560 - 9.21166i) q^{43} +(6.22626 + 2.20830i) q^{44} +(-0.642070 + 0.492678i) q^{45} +(-7.44583 - 2.86030i) q^{46} +(8.91945 - 5.14965i) q^{47} +(-1.87966 - 7.86360i) q^{48} +(2.55648 + 6.51647i) q^{49} +(-6.20793 + 0.981667i) q^{50} +(-0.0724616 - 0.550400i) q^{51} +(-0.423538 - 0.291398i) q^{52} +(7.96102 + 1.04809i) q^{53} +(1.55295 + 5.24744i) q^{54} +(-1.74127 - 1.74127i) q^{55} +(5.92354 - 4.57292i) q^{56} +(4.52901 - 4.52901i) q^{57} +(-2.60146 - 1.41331i) q^{58} +(-1.51564 + 11.5124i) q^{59} +(-0.628056 + 2.94760i) q^{60} +(-6.27068 + 0.825551i) q^{61} +(-3.48317 - 2.53198i) q^{62} +(2.17716 - 1.87333i) q^{63} +(-6.46516 - 4.71187i) q^{64} +(0.0958163 + 0.165959i) q^{65} +(8.62673 - 3.83832i) q^{66} +(0.961960 + 1.25365i) q^{67} +(-0.408031 - 0.367758i) q^{68} +(-10.5325 + 4.36269i) q^{69} +(-2.72649 + 0.589295i) q^{70} +(-1.35162 + 1.35162i) q^{71} +(-2.57389 - 1.67422i) q^{72} +(-0.883450 + 0.236720i) q^{73} +(-7.94917 + 8.37254i) q^{74} +(-5.46851 + 7.12670i) q^{75} +(0.500361 - 6.31777i) q^{76} +(6.51597 + 5.82384i) q^{77} +(-0.725763 + 0.114766i) q^{78} +(12.0051 - 6.93117i) q^{79} +(1.42032 + 2.62207i) q^{80} +(9.59405 + 5.53913i) q^{81} +(-3.74741 + 3.03306i) q^{82} +(15.5006 + 6.42056i) q^{83} +(1.63960 - 10.5692i) q^{84} +(0.0783567 + 0.189170i) q^{85} +(-13.5209 + 4.00145i) q^{86} +(-4.08727 + 1.09518i) q^{87} +(4.02838 - 8.42958i) q^{88} +(10.2157 + 2.73728i) q^{89} +(0.597779 + 0.976029i) q^{90} +(-0.372493 - 0.569006i) q^{91} +(-5.12608 + 10.0482i) q^{92} +(-6.10204 + 0.803349i) q^{93} +(-5.92099 - 13.3076i) q^{94} +(-1.18118 + 2.04586i) q^{95} +(-11.3381 + 1.47844i) q^{96} -0.0930782 q^{97} +(9.54376 - 2.62995i) q^{98} +(1.37224 - 3.31287i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{8}\right)$

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 $

$2$	0.148173	−	1.40643i	0.104774	−	0.994496i
$2$	0.148173	−	1.40643i	0.104774	−	0.994496i
$3$	−1.23048	−	1.60359i	−0.710417	−	0.925834i	0.289088	−	0.957303i	$-0.406648\pi$
$3$	−1.23048	−	1.60359i	−0.710417	−	0.925834i	−0.999505	+	0.0314690i	$0.989981\pi$
$4$	−1.95609	−	0.416790i	−0.978045	−	0.208395i
$5$	0.591453	+	0.453838i	0.264506	+	0.202962i	0.732496	−	0.680771i	$-0.238355\pi$
$5$	0.591453	+	0.453838i	0.264506	+	0.202962i	−0.467990	+	0.883734i	$0.655022\pi$
$6$	−2.43766	+	1.49297i	−0.995171	+	0.609504i
$7$	−2.18592	−	1.49056i	−0.826200	−	0.563377i
$7$	−2.18592	−	1.49056i	−0.826200	−	0.563377i
$8$	−0.876026	+	2.68935i	−0.309722	+	0.950827i
$9$	−0.280969	+	1.04859i	−0.0936564	+	0.349530i
$10$	0.725929	−	0.764591i	0.229559	−	0.241785i
$11$	−3.27488	−	0.431146i	−0.987413	−	0.129995i	−0.380515	−	0.924775i	$-0.624253\pi$
$11$	−3.27488	−	0.431146i	−0.987413	−	0.129995i	−0.606898	+	0.794780i	$0.707586\pi$
$12$	1.73857	+	3.64962i	0.501881	+	1.05355i
$13$	0.237482	+	0.0983684i	0.0658657	+	0.0272825i	0.415373	−	0.909651i	$-0.363651\pi$
$13$	0.237482	+	0.0983684i	0.0658657	+	0.0272825i	−0.349507	+	0.936934i	$0.613651\pi$
$14$	−2.42026	+	2.85348i	−0.646841	+	0.762625i
$15$		−	1.50689i		−	0.389076i
$16$	3.65257	+	1.63056i	0.913143	+	0.407639i
$17$	0.237856	+	0.137326i	0.0576885	+	0.0333065i	0.528567	−	0.848892i	$-0.322730\pi$
$17$	0.237856	+	0.137326i	0.0576885	+	0.0333065i	−0.470878	+	0.882198i	$0.656063\pi$
$18$	1.43314	+	0.550536i	0.337794	+	0.129763i
$19$	0.413608	+	3.14167i	0.0948882	+	0.720748i	0.971075	+	0.238775i	$0.0767460\pi$
$19$	0.413608	+	3.14167i	0.0948882	+	0.720748i	−0.876187	+	0.481972i	$0.839921\pi$
$20$	−0.967780	−	1.13426i	−0.216402	−	0.253628i
$21$	0.299483	+	5.33942i	0.0653525	+	1.16516i
$22$	−1.09163	+	4.54200i	−0.232735	+	0.968358i
$23$	1.45977	−	5.44793i	0.304383	−	1.13597i	−0.629093	−	0.777330i	$-0.716574\pi$
$23$	1.45977	−	5.44793i	0.304383	−	1.13597i	0.933476	−	0.358641i	$-0.116760\pi$
$24$	5.39054	−	1.90439i	1.10034	−	0.388733i
$25$	−1.15025	−	4.29278i	−0.230049	−	0.858556i
$26$	0.173537	−	0.319427i	0.0340334	−	0.0626447i
$27$	−3.57503	+	1.48082i	−0.688014	+	0.284985i
$28$	3.65460	+	3.82673i	0.690655	+	0.723184i
$29$	0.801128	−	1.93409i	0.148766	−	0.359152i	−0.831876	−	0.554961i	$-0.812733\pi$
$29$	0.801128	−	1.93409i	0.148766	−	0.359152i	0.980642	+	0.195809i	$0.0627332\pi$
$30$	−2.11933	−	0.223280i	−0.386935	−	0.0407652i
$31$	1.52247	−	2.63700i	0.273444	−	0.473619i	−0.696297	−	0.717754i	$-0.745170\pi$
$31$	1.52247	−	2.63700i	0.273444	−	0.473619i	0.969741	+	0.244134i	$0.0785038\pi$
$32$	2.83448	−	4.89548i	0.501070	−	0.865407i
$33$	3.33829	+	5.78208i	0.581121	+	1.00653i
$34$	0.228383	−	0.314179i	0.0391674	−	0.0538813i
$35$	−0.616397	−	1.87365i	−0.104190	−	0.316704i
$36$	0.986643	−	1.93403i	0.164441	−	0.322339i
$37$	−6.47662	−	4.96968i	−1.06475	−	0.817011i	−0.0810282	−	0.996712i	$-0.525820\pi$
$37$	−6.47662	−	4.96968i	−1.06475	−	0.817011i	−0.983721	+	0.179701i	$0.942487\pi$
$38$	4.47982	−	0.116200i	0.726722	−	0.0188502i
$39$	−0.134474	−	0.501865i	−0.0215331	−	0.0803627i
$40$	−1.73865	+	1.19305i	−0.274905	+	0.188637i
$41$	−2.41053	−	2.41053i	−0.376461	−	0.376461i	0.493363	−	0.869824i	$-0.335768\pi$
$41$	−2.41053	−	2.41053i	−0.376461	−	0.376461i	−0.869824	+	0.493363i	$0.835768\pi$
$42$	7.55389	+	0.369957i	1.16559	+	0.0570855i
$43$	−3.81560	−	9.21166i	−0.581873	−	1.40477i	−0.891113	−	0.453781i	$-0.850075\pi$
$43$	−3.81560	−	9.21166i	−0.581873	−	1.40477i	0.309240	−	0.950984i	$-0.399925\pi$
$44$	6.22626	+	2.20830i	0.938643	+	0.332913i
$45$	−0.642070	+	0.492678i	−0.0957142	+	0.0734441i
$46$	−7.44583	−	2.86030i	−1.09783	−	0.421728i
$47$	8.91945	−	5.14965i	1.30104	−	0.751153i	0.320454	−	0.947264i	$-0.396165\pi$
$47$	8.91945	−	5.14965i	1.30104	−	0.751153i	0.980582	+	0.196111i	$0.0628313\pi$
$48$	−1.87966	−	7.86360i	−0.271306	−	1.13501i
$49$	2.55648	+	6.51647i	0.365212	+	0.930925i
$50$	−6.20793	+	0.981667i	−0.877934	+	0.138829i
$51$	−0.0724616	−	0.550400i	−0.0101466	−	0.0770715i
$52$	−0.423538	−	0.291398i	−0.0587341	−	0.0404096i
$53$	7.96102	+	1.04809i	1.09353	+	0.143966i	0.655648	−	0.755066i	$-0.272395\pi$
$53$	7.96102	+	1.04809i	1.09353	+	0.143966i	0.437882	+	0.899032i	$0.355729\pi$
$54$	1.55295	+	5.24744i	0.211330	+	0.714086i
$55$	−1.74127	−	1.74127i	−0.234792	−	0.234792i
$56$	5.92354	−	4.57292i	0.791567	−	0.611083i
$57$	4.52901	−	4.52901i	0.599882	−	0.599882i
$58$	−2.60146	−	1.41331i	−0.341589	−	0.185577i
$59$	−1.51564	+	11.5124i	−0.197320	+	1.49879i	0.550469	+	0.834856i	$0.314449\pi$
$59$	−1.51564	+	11.5124i	−0.197320	+	1.49879i	−0.747789	+	0.663937i	$0.768884\pi$
$60$	−0.628056	+	2.94760i	−0.0810816	+	0.380534i
$61$	−6.27068	+	0.825551i	−0.802878	+	0.105701i	−0.520787	−	0.853687i	$-0.674361\pi$
$61$	−6.27068	+	0.825551i	−0.802878	+	0.105701i	−0.282091	+	0.959388i	$0.591028\pi$
$62$	−3.48317	−	2.53198i	−0.442362	−	0.321562i
$63$	2.17716	−	1.87333i	0.274296	−	0.236018i
$64$	−6.46516	−	4.71187i	−0.808145	−	0.588984i
$65$	0.0958163	+	0.165959i	0.0118846	+	0.0205847i
$66$	8.62673	−	3.83832i	1.06188	−	0.472464i
$67$	0.961960	+	1.25365i	0.117522	+	0.153158i	0.848410	−	0.529340i	$-0.177560\pi$
$67$	0.961960	+	1.25365i	0.117522	+	0.153158i	−0.730888	+	0.682498i	$0.760894\pi$
$68$	−0.408031	−	0.367758i	−0.0494810	−	0.0445972i
$69$	−10.5325	+	4.36269i	−1.26796	+	0.525206i
$70$	−2.72649	+	0.589295i	−0.325877	+	0.0704342i
$71$	−1.35162	+	1.35162i	−0.160408	+	0.160408i	−0.782747	−	0.622340i	$-0.786182\pi$
$71$	−1.35162	+	1.35162i	−0.160408	+	0.160408i	0.622340	+	0.782747i	$0.286182\pi$
$72$	−2.57389	−	1.67422i	−0.303336	−	0.197308i
$73$	−0.883450	+	0.236720i	−0.103400	+	0.0277060i	−0.310148	−	0.950688i	$-0.600379\pi$
$73$	−0.883450	+	0.236720i	−0.103400	+	0.0277060i	0.206748	+	0.978394i	$0.433712\pi$
$74$	−7.94917	+	8.37254i	−0.924073	+	0.973288i
$75$	−5.46851	+	7.12670i	−0.631449	+	0.822921i
$76$	0.500361	−	6.31777i	0.0573953	−	0.724698i
$77$	6.51597	+	5.82384i	0.742564	+	0.663688i
$78$	−0.725763	+	0.114766i	−0.0821765	+	0.0129947i
$79$	12.0051	−	6.93117i	1.35068	−	0.779818i	0.362339	−	0.932046i	$-0.381978\pi$
$79$	12.0051	−	6.93117i	1.35068	−	0.779818i	0.988345	+	0.152229i	$0.0486450\pi$
$80$	1.42032	+	2.62207i	0.158796	+	0.293157i
$81$	9.59405	+	5.53913i	1.06601	+	0.615459i
$82$	−3.74741	+	3.03306i	−0.413832	+	0.334945i
$83$	15.5006	+	6.42056i	1.70141	+	0.704748i	0.999968	−	0.00797574i	$-0.00253878\pi$
$83$	15.5006	+	6.42056i	1.70141	+	0.704748i	0.701445	+	0.712724i	$0.252539\pi$
$84$	1.63960	−	10.5692i	0.178895	−	1.15319i
$85$	0.0783567	+	0.189170i	0.00849898	+	0.0205184i
$86$	−13.5209	+	4.00145i	−1.45800	+	0.431487i
$87$	−4.08727	+	1.09518i	−0.438201	+	0.117416i
$88$	4.02838	−	8.42958i	0.429427	−	0.898596i
$89$	10.2157	+	2.73728i	1.08286	+	0.290151i	0.755766	−	0.654842i	$-0.227265\pi$
$89$	10.2157	+	2.73728i	1.08286	+	0.290151i	0.327092	+	0.944993i	$0.393931\pi$
$90$	0.597779	+	0.976029i	0.0630115	+	0.102882i
$91$	−0.372493	−	0.569006i	−0.0390479	−	0.0596481i
$92$	−5.12608	+	10.0482i	−0.534431	+	1.04760i
$93$	−6.10204	+	0.803349i	−0.632752	+	0.0833034i
$94$	−5.92099	−	13.3076i	−0.610704	−	1.37258i
$95$	−1.18118	+	2.04586i	−0.121186	+	0.209901i
$96$	−11.3381	+	1.47844i	−1.15719	+	0.150893i
$97$	−0.0930782			−0.00945066			−0.00472533	−	0.999989i	$-0.501504\pi$
$97$	−0.0930782			−0.00945066			−0.00472533	+	0.999989i	$0.501504\pi$
$98$	9.54376	−	2.62995i	0.964066	−	0.265665i
$99$	1.37224	−	3.31287i	0.137915	−	0.332956i
$100$	0.460797	+	8.87648i	0.0460797	+	0.887648i
$101$	1.58229	−	12.0187i	0.157444	−	1.19591i	−0.712110	−	0.702068i	$-0.752260\pi$
$101$	1.58229	−	12.0187i	0.157444	−	1.19591i	0.869554	−	0.493838i	$-0.164406\pi$
$102$	−0.784836	+	0.0203576i	−0.0777104	+	0.00201570i
$103$	0.808836	+	0.216727i	0.0796970	+	0.0213547i	0.298447	−	0.954426i	$-0.403531\pi$
$103$	0.808836	+	0.216727i	0.0796970	+	0.0213547i	−0.218750	+	0.975781i	$0.570198\pi$
$104$	−0.472587	+	0.552499i	−0.0463410	+	0.0541770i
$105$	−2.24610	+	3.29393i	−0.219197	+	0.321455i
$106$	2.65367	−	11.0413i	0.257747	−	1.07243i
$107$	0.106879	−	0.139287i	0.0103324	−	0.0134654i	−0.788159	−	0.615472i	$-0.788965\pi$
$107$	0.106879	−	0.139287i	0.0103324	−	0.0134654i	0.798491	+	0.602007i	$0.205632\pi$
$108$	7.61026	−	1.40659i	0.732298	−	0.135349i
$109$	−7.13445	+	5.47446i	−0.683357	+	0.524358i	−0.891090	−	0.453828i	$-0.850058\pi$
$109$	−7.13445	+	5.47446i	−0.683357	+	0.524358i	0.207733	+	0.978186i	$0.433392\pi$
$110$	−2.70698	+	2.19096i	−0.258100	+	0.208900i
$111$			16.5009i			1.56620i
$112$	−5.55379	−	9.00863i	−0.524783	−	0.851236i
$113$			8.13250i			0.765041i	0.923947	+	0.382520i	$0.124944\pi$
$113$			8.13250i			0.765041i	−0.923947	+	0.382520i	$0.875056\pi$
$114$	−5.69866	−	7.04081i	−0.533728	−	0.659433i
$115$	3.33586	−	2.55969i	0.311070	−	0.238693i
$116$	−2.37319	+	3.44936i	−0.220345	+	0.320265i
$117$	−0.169873	+	0.221383i	−0.0157048	+	0.0204669i
$118$	15.9669	+	3.83748i	1.46987	+	0.353269i
$119$	−0.315241	−	0.654721i	−0.0288981	−	0.0600182i
$120$	4.05254	+	1.32007i	0.369944	+	0.120506i
$121$	−0.0862472	−	0.0231099i	−0.00784065	−	0.00210090i
$122$	0.231933	+	8.94160i	0.0209982	+	0.809534i
$123$	−0.899397	+	6.83160i	−0.0810959	+	0.615984i
$124$	−4.07717	+	4.52366i	−0.366141	+	0.406236i
$125$	2.69438	−	6.50481i	0.240993	−	0.581808i
$126$	−2.31212	−	3.33960i	−0.205980	−	0.297515i
$127$	−13.8415			−1.22824			−0.614119	−	0.789213i	$-0.710489\pi$
$127$	−13.8415			−1.22824			−0.614119	+	0.789213i	$0.710489\pi$
$128$	−7.58488	+	8.39462i	−0.670415	+	0.741986i
$129$	−10.0767	+	17.4534i	−0.887207	+	1.53669i
$130$	0.247607	−	0.110168i	0.0217165	−	0.00966240i
$131$	−19.1663	+	2.52328i	−1.67456	+	0.220460i	−0.907184	−	0.420733i	$-0.861773\pi$
$131$	−19.1663	+	2.52328i	−1.67456	+	0.220460i	−0.767379	+	0.641194i	$0.778439\pi$
$132$	−4.12007	−	12.7016i	−0.358606	−	1.10553i
$133$	3.77872	−	7.48393i	0.327656	−	0.648939i
$134$	1.90571	−	1.16717i	0.164628	−	0.100828i
$135$	−2.78651	−	0.746644i	−0.239825	−	0.0642609i
$136$	−0.577685	+	0.519375i	−0.0495361	+	0.0445361i
$137$	12.1128	−	3.24561i	1.03487	−	0.277291i	0.298881	−	0.954290i	$-0.403386\pi$
$137$	12.1128	−	3.24561i	1.03487	−	0.277291i	0.735984	+	0.676999i	$0.236720\pi$
$138$	4.57519	+	15.4596i	0.389466	+	1.31601i
$139$	7.47093	+	18.0364i	0.633676	+	1.52983i	0.834969	+	0.550297i	$0.185486\pi$
$139$	7.47093	+	18.0364i	0.633676	+	1.52983i	−0.201293	+	0.979531i	$0.564514\pi$
$140$	0.424810	+	3.92193i	0.0359030	+	0.331464i
$141$	−19.2331	−	7.96662i	−1.61972	−	0.670910i
$142$	1.70068	+	2.10123i	0.142718	+	0.176331i
$143$	−0.735314	−	0.424534i	−0.0614901	−	0.0355013i
$144$	−2.73605	+	3.37192i	−0.228004	+	0.280993i
$145$	1.35160	−	0.780344i	0.112244	−	0.0648040i
$146$	0.202026	+	1.27759i	0.0167198	+	0.105734i
$147$	7.30406	−	12.1179i	0.602429	−	0.999470i
$148$	10.5975	+	12.4205i	0.871112	+	1.02096i
$149$	7.46128	−	9.72374i	0.611252	−	0.796599i	−0.380498	−	0.924782i	$-0.624248\pi$
$149$	7.46128	−	9.72374i	0.611252	−	0.796599i	0.991751	+	0.128182i	$0.0409142\pi$
$150$	9.21292	+	8.74706i	0.752232	+	0.714195i
$151$	−19.5217	+	5.23083i	−1.58865	+	0.425679i	−0.941591	−	0.336758i	$-0.890670\pi$
$151$	−19.5217	+	5.23083i	−1.58865	+	0.425679i	−0.647063	+	0.762436i	$0.724003\pi$
$152$	−8.81136	−	1.63985i	−0.714695	−	0.133009i
$153$	−0.210829	+	0.210829i	−0.0170445	+	0.0170445i
$154$	9.15631	−	8.30132i	0.737837	−	0.668939i
$155$	2.09724	−	0.868706i	0.168454	−	0.0697761i
$156$	0.0538714	+	1.03774i	0.00431316	+	0.0830857i
$157$	−11.0151	−	14.3552i	−0.879103	−	1.14567i	−0.988432	−	0.151663i	$-0.951537\pi$
$157$	−11.0151	−	14.3552i	−0.879103	−	1.14567i	0.109330	−	0.994006i	$-0.465130\pi$
$158$	−7.96937	−	17.9114i	−0.634009	−	1.42495i
$159$	−8.11516	−	14.0559i	−0.643574	−	1.11470i
$160$	3.89822	−	1.60905i	0.308181	−	0.127207i
$161$	−11.3114	+	9.73286i	−0.891461	+	0.767057i
$162$	9.21198	−	12.6726i	0.723761	−	0.995654i
$163$	12.9165	−	1.70050i	1.01170	−	0.133193i	0.393593	−	0.919285i	$-0.371232\pi$
$163$	12.9165	−	1.70050i	1.01170	−	0.133193i	0.618110	+	0.786092i	$0.287899\pi$
$164$	3.71052	+	5.71989i	0.289743	+	0.446648i
$165$	−0.649688	+	4.93487i	−0.0505781	+	0.384179i
$166$	11.3268	−	20.8492i	0.879134	−	1.61821i
$167$	8.64632	−	8.64632i	0.669073	−	0.669073i	−0.288429	−	0.957501i	$-0.593133\pi$
$167$	8.64632	−	8.64632i	0.669073	−	0.669073i	0.957501	+	0.288429i	$0.0931328\pi$
$168$	−14.6219	−	3.87206i	−1.12810	−	0.298736i
$169$	−9.14567	−	9.14567i	−0.703513	−	0.703513i
$170$	0.277665	−	0.0821734i	0.0212959	−	0.00630241i
$171$	−3.41053	−	0.449005i	−0.260810	−	0.0343363i
$172$	3.62432	+	19.6091i	0.276351	+	1.49518i
$173$	0.358166	+	2.72054i	0.0272309	+	0.206839i	0.999652	−	0.0263947i	$-0.00840267\pi$
$173$	0.358166	+	2.72054i	0.0272309	+	0.206839i	−0.972421	+	0.233234i	$0.925069\pi$
$174$	0.934671	+	5.91073i	0.0708572	+	0.448091i
$175$	−3.88429	+	11.0982i	−0.293625	+	0.838944i
$176$	−11.2587	−	6.91467i	−0.848658	−	0.521213i
$177$	20.3262	−	11.7353i	1.52781	−	0.882083i
$178$	5.36348	−	13.9620i	0.402010	−	1.04650i
$179$	−0.746441	+	0.572764i	−0.0557916	+	0.0428104i	−0.636281	−	0.771458i	$-0.719528\pi$
$179$	−0.746441	+	0.572764i	−0.0557916	+	0.0428104i	0.580489	+	0.814268i	$0.302861\pi$
$180$	1.46129	−	0.696114i	0.108918	−	0.0518852i
$181$	0.611795	+	1.47700i	0.0454744	+	0.109785i	0.944985	−	0.327115i	$-0.106076\pi$
$181$	0.611795	+	1.47700i	0.0454744	+	0.109785i	−0.899510	+	0.436900i	$0.856076\pi$
$182$	−0.855461	+	0.439574i	−0.0634110	+	0.0325834i
$183$	9.03978	+	9.03978i	0.668240	+	0.668240i
$184$	13.3726	+	8.69834i	0.985838	+	0.641250i
$185$	−1.57518	−	5.87867i	−0.115810	−	0.432208i
$186$	0.225695	+	8.70112i	0.0165488	+	0.637997i
$187$	−0.719741	−	0.552277i	−0.0526327	−	0.0403865i
$188$	−19.5936	+	6.35563i	−1.42901	+	0.463532i
$189$	10.0220	+	2.09182i	0.728991	+	0.152157i
$190$	2.70234	+	1.96438i	0.196048	+	0.142511i
$191$	6.41353	+	11.1086i	0.464067	+	0.803787i	0.999159	−	0.0410064i	$-0.0130564\pi$
$191$	6.41353	+	11.1086i	0.464067	+	0.803787i	−0.535092	+	0.844794i	$0.679723\pi$
$192$	0.399320	+	16.1653i	0.0288185	+	1.16663i
$193$	5.48121	−	9.49374i	0.394546	−	0.683374i	−0.598497	−	0.801125i	$-0.704235\pi$
$193$	5.48121	−	9.49374i	0.394546	−	0.683374i	0.993043	+	0.117751i	$0.0375684\pi$
$194$	−0.0137917	+	0.130908i	−0.000990186	+	0.00939865i
$195$	0.148230	−	0.357859i	0.0106150	−	0.0256268i
$196$	−2.28470	−	13.8123i	−0.163193	−	0.986594i
$197$	21.5255	−	8.91616i	1.53363	−	0.635250i	0.553364	−	0.832939i	$-0.313344\pi$
$197$	21.5255	−	8.91616i	1.53363	−	0.635250i	0.980265	+	0.197690i	$0.0633438\pi$
$198$	−4.45599	−	2.42083i	−0.316673	−	0.172041i
$199$	−1.21074	−	4.51855i	−0.0858271	−	0.320311i	0.909642	−	0.415392i	$-0.136356\pi$
$199$	−1.21074	−	4.51855i	−0.0858271	−	0.320311i	−0.995470	+	0.0950810i	$0.969689\pi$
$200$	12.5524	+	0.667176i	0.887590	+	0.0471765i
$201$	0.826672	−	3.08518i	0.0583089	−	0.217612i
$202$	−16.6690	−	4.00623i	−1.17283	−	0.281877i
$203$	−4.63408	+	3.03365i	−0.325249	+	0.212920i
$204$	−0.0876601	+	1.10683i	−0.00613744	+	0.0774938i
$205$	−0.331725	−	2.51970i	−0.0231687	−	0.175984i
$206$	0.424659	−	1.10546i	0.0295874	−	0.0770209i
$207$	5.30250	+	3.06140i	0.368549	+	0.212782i
$208$	0.707026	+	0.746526i	0.0490234	+	0.0517623i
$209$		−	10.4669i		−	0.724010i
$210$	4.29987	+	3.64705i	0.296719	+	0.251671i
$211$	−4.01171	−	1.66171i	−0.276178	−	0.114397i	0.240296	−	0.970700i	$-0.422756\pi$
$211$	−4.01171	−	1.66171i	−0.276178	−	0.114397i	−0.516474	+	0.856303i	$0.672756\pi$
$212$	−15.1356	−	5.36823i	−1.03952	−	0.368692i
$213$	3.83058	+	0.504306i	0.262467	+	0.0345544i
$214$	−0.180061	−	0.170956i	−0.0123087	−	0.0116863i
$215$	1.92386	−	7.17993i	0.131206	−	0.489667i
$216$	−0.850632	−	10.9117i	−0.0578782	−	0.742448i
$217$	−7.25860	+	3.49494i	−0.492746	+	0.237252i
$218$	6.64231	+	10.8453i	0.449874	+	0.734535i
$219$	1.46667	+	1.12541i	0.0991083	+	0.0760484i
$220$	2.68033	+	4.13181i	0.180708	+	0.278567i
$221$	0.0429780	+	0.0560100i	0.00289101	+	0.00376764i
$222$	23.2074	+	2.44500i	1.55758	+	0.164097i
$223$	25.6197			1.71562			0.857810	−	0.513967i	$-0.171825\pi$
$223$	25.6197			1.71562			0.857810	+	0.513967i	$0.171825\pi$
$224$	−13.4929	+	6.47617i	−0.901534	+	0.432708i
$225$	4.82456			0.321637
$226$	11.4378	+	1.20502i	0.760830	+	0.0801566i
$227$	−14.9286	−	19.4553i	−0.990844	−	1.29129i	−0.956454	−	0.291884i	$-0.905718\pi$
$227$	−14.9286	−	19.4553i	−0.990844	−	1.29129i	−0.0343900	−	0.999408i	$-0.510949\pi$
$228$	−10.7468	+	6.97150i	−0.711724	+	0.461699i
$229$	9.05468	+	6.94790i	0.598350	+	0.459130i	0.862993	−	0.505216i	$-0.168587\pi$
$229$	9.05468	+	6.94790i	0.598350	+	0.459130i	−0.264642	+	0.964347i	$0.585254\pi$
$230$	−3.10575	−	5.07093i	−0.204787	−	0.334367i
$231$	1.32130	−	17.6151i	0.0869350	−	1.15899i
$232$	4.49964	+	3.84883i	0.295416	+	0.252688i
$233$	−4.27438	+	15.9522i	−0.280024	+	1.04506i	0.672375	+	0.740211i	$0.265274\pi$
$233$	−4.27438	+	15.9522i	−0.280024	+	1.04506i	−0.952399	+	0.304854i	$0.901392\pi$
$234$	0.286190	+	0.271718i	0.0187088	+	0.0177628i
$235$	7.61254	+	1.00221i	0.496587	+	0.0653770i
$236$	7.76301	−	21.8877i	0.505329	−	1.42477i
$237$	−25.8868	−	10.7227i	−1.68153	−	0.696513i
$238$	−0.967530	+	0.346352i	−0.0627156	+	0.0224507i
$239$			27.6751i			1.79015i	0.445913	+	0.895077i	$0.352879\pi$
$239$			27.6751i			1.79015i	−0.445913	+	0.895077i	$0.647121\pi$
$240$	2.45707	−	5.50401i	0.158603	−	0.355282i
$241$	−22.5676	−	13.0294i	−1.45371	−	0.839298i	−0.455018	−	0.890482i	$-0.650367\pi$
$241$	−22.5676	−	13.0294i	−1.45371	−	0.839298i	−0.998689	+	0.0511845i	$0.983700\pi$
$242$	−0.0452819	+	0.117876i	−0.00291083	+	0.00757738i
$243$	−1.40753	−	10.6913i	−0.0902934	−	0.685846i
$244$	12.6101	+	0.998707i	0.807278	+	0.0639357i
$245$	−1.44538	+	5.01441i	−0.0923421	+	0.320359i
$246$	9.47490	+	2.27720i	0.604097	+	0.145189i
$247$	−0.210816	+	0.786776i	−0.0134139	+	0.0500614i
$248$	5.75808	+	6.40454i	0.365638	+	0.406688i
$249$	−8.77721	−	32.7570i	−0.556233	−	2.07589i
$250$	−8.74933	−	4.75330i	−0.553356	−	0.300625i
$251$	11.7913	−	4.88413i	0.744262	−	0.308283i	0.0218640	−	0.999761i	$-0.493040\pi$
$251$	11.7913	−	4.88413i	0.744262	−	0.308283i	0.722398	+	0.691478i	$0.243040\pi$
$252$	−5.03951	+	2.75699i	−0.317459	+	0.173674i
$253$	−7.12941	+	17.2119i	−0.448222	+	1.08210i
$254$	−2.05094	+	19.4672i	−0.128688	+	1.22148i
$255$	0.206935	−	0.358422i	0.0129588	−	0.0224452i
$256$	10.6826	+	11.9115i	0.667660	+	0.744466i
$257$	−6.19325	−	10.7270i	−0.386325	−	0.669134i	0.605627	−	0.795748i	$-0.292922\pi$
$257$	−6.19325	−	10.7270i	−0.386325	−	0.669134i	−0.991952	+	0.126615i	$0.959589\pi$
$258$	23.0539	+	16.7583i	1.43527	+	1.04333i
$259$	6.74977	+	20.5171i	0.419410	+	1.27487i
$260$	−0.118255	−	0.364566i	−0.00733389	−	0.0226094i
$261$	1.80298	+	1.38348i	0.111602	+	0.0856351i
$262$	0.708900	+	27.3299i	0.0437960	+	1.68845i
$263$	−2.00307	−	7.47556i	−0.123515	−	0.460963i	0.876268	−	0.481825i	$-0.160026\pi$
$263$	−2.00307	−	7.47556i	−0.123515	−	0.460963i	−0.999782	+	0.0208616i	$0.993359\pi$
$264$	−18.4744	+	3.91255i	−1.13702	+	0.240801i
$265$	4.23291	+	4.23291i	0.260025	+	0.260025i
$266$	−9.96572	−	6.42342i	−0.611038	−	0.393845i
$267$	−8.18068	−	19.7499i	−0.500649	−	1.20867i
$268$	−1.35917	−	2.85319i	−0.0830246	−	0.174286i
$269$	6.82470	−	5.23678i	0.416109	−	0.319292i	−0.379401	−	0.925233i	$-0.623870\pi$
$269$	6.82470	−	5.23678i	0.416109	−	0.319292i	0.795510	+	0.605941i	$0.207203\pi$
$270$	−1.46299	+	3.80840i	−0.0890347	+	0.231772i
$271$	22.8091	−	13.1689i	1.38556	−	0.799951i	0.392746	−	0.919647i	$-0.371525\pi$
$271$	22.8091	−	13.1689i	1.38556	−	0.799951i	0.992811	+	0.119696i	$0.0381919\pi$
$272$	0.644867	+	0.889431i	0.0391008	+	0.0539297i
$273$	−0.454108	+	1.29748i	−0.0274839	+	0.0785269i
$274$	−2.76994	−	17.5167i	−0.167338	−	1.05822i
$275$	1.91610	+	14.5543i	0.115545	+	0.877655i
$276$	22.4208	−	4.14398i	1.34957	−	0.249438i
$277$	7.02355	+	0.924667i	0.422004	+	0.0555579i	0.338538	−	0.940953i	$-0.390068\pi$
$277$	7.02355	+	0.924667i	0.422004	+	0.0555579i	0.0834660	+	0.996511i	$0.473401\pi$
$278$	26.4739	−	7.83482i	1.58780	−	0.469901i
$279$	2.33737	+	2.33737i	0.139935	+	0.139935i
$280$	5.57886	−	0.0163413i	0.333401	−	0.000976577i
$281$	3.43098	−	3.43098i	0.204675	−	0.204675i	−0.597324	−	0.802000i	$-0.703770\pi$
$281$	3.43098	−	3.43098i	0.204675	−	0.204675i	0.802000	+	0.597324i	$0.203770\pi$
$282$	−14.0543	+	25.8696i	−0.836923	+	1.54051i
$283$	−2.97231	+	22.5769i	−0.176685	+	1.34206i	0.641508	+	0.767116i	$0.278309\pi$
$283$	−2.97231	+	22.5769i	−0.176685	+	1.34206i	−0.818194	+	0.574943i	$0.805024\pi$
$284$	3.20723	−	2.08055i	0.190314	−	0.123458i
$285$	4.73413	−	0.623260i	0.280426	−	0.0369188i
$286$	−0.706031	+	0.971264i	−0.0417485	+	0.0574320i
$287$	1.67619	+	8.86224i	0.0989422	+	0.523121i
$288$	4.33696	+	4.34769i	0.255558	+	0.256190i
$289$	−8.46228	−	14.6571i	−0.497781	−	0.862183i
$290$	−0.897229	−	2.01655i	−0.0526871	−	0.118416i
$291$	0.114531	+	0.149259i	0.00671391	+	0.00874974i
$292$	1.82677	−	0.0948317i	0.106904	−	0.00554960i
$293$	−7.79492	+	3.22876i	−0.455384	+	0.188626i	−0.598572	−	0.801069i	$-0.704265\pi$
$293$	−7.79492	+	3.22876i	−0.455384	+	0.188626i	0.143187	+	0.989696i	$0.454265\pi$
$294$	−15.9608	−	12.0682i	−0.930850	−	0.703832i
$295$	−6.12121	+	6.12121i	−0.356391	+	0.356391i
$296$	19.0389	−	13.0643i	1.10661	−	0.759347i
$297$	12.3462	−	3.30816i	0.716401	−	0.191959i
$298$	−12.5702	−	11.9346i	−0.728171	−	0.691351i
$299$	0.882573	−	1.15019i	0.0510405	−	0.0665173i
$300$	13.6672	−	11.6612i	0.789078	−	0.673262i
$301$	−5.38992	+	25.8233i	−0.310670	+	1.48843i
$302$	4.46420	+	28.2310i	0.256886	+	1.62451i
$303$	−21.2201	+	12.2514i	−1.21906	+	0.703825i
$304$	−3.61193	+	12.1496i	−0.207159	+	0.696826i
$305$	−4.08348	−	2.35760i	−0.233819	−	0.134996i
$306$	0.265277	+	0.327756i	0.0151649	+	0.0187365i
$307$	−16.3850	−	6.78688i	−0.935141	−	0.387348i	−0.137514	−	0.990500i	$-0.543911\pi$
$307$	−16.3850	−	6.78688i	−0.935141	−	0.387348i	−0.797626	+	0.603152i	$0.793911\pi$
$308$	−10.3185	−	14.1077i	−0.587951	−	0.803863i
$309$	−0.647714	−	1.56372i	−0.0368472	−	0.0889569i
$310$	−0.911019	−	3.07834i	−0.0517424	−	0.174838i
$311$	−16.9964	+	4.55416i	−0.963775	+	0.258243i	−0.706197	−	0.708015i	$-0.749591\pi$
$311$	−16.9964	+	4.55416i	−0.963775	+	0.258243i	−0.257577	+	0.966258i	$0.582924\pi$
$312$	1.46749	+	0.0779989i	0.0830803	+	0.00441582i
$313$	−24.5359	−	6.57439i	−1.38685	−	0.371606i	−0.513248	−	0.858240i	$-0.671558\pi$
$313$	−24.5359	−	6.57439i	−1.38685	−	0.371606i	−0.873606	+	0.486634i	$0.838224\pi$
$314$	−21.8217	+	13.3649i	−1.23147	+	0.754228i
$315$	2.13788	−	0.119912i	0.120456	−	0.00675625i
$316$	−26.3720	+	8.55437i	−1.48354	+	0.481221i
$317$	5.22443	−	0.687809i	0.293433	−	0.0386312i	0.0176274	−	0.999845i	$-0.494389\pi$
$317$	5.22443	−	0.687809i	0.293433	−	0.0386312i	0.275806	+	0.961213i	$0.411055\pi$
$318$	−20.9710	+	9.33070i	−1.17600	+	0.523240i
$319$	−3.45747	+	5.98852i	−0.193581	+	0.335293i
$320$	−1.68541	−	5.72098i	−0.0942173	−	0.319813i
$321$	−0.354872			−0.0198070
$322$	12.0125	+	17.3508i	0.669433	+	0.966923i
$323$	−0.333054	+	0.804063i	−0.0185316	+	0.0447392i
$324$	−16.4582	−	14.8337i	−0.914343	−	0.824097i
$325$	0.149111	−	1.13261i	0.00827117	−	0.0628258i
$326$	−0.477743	−	18.4182i	−0.0264597	−	1.02009i
$327$	17.5576	+	4.70454i	0.970937	+	0.260162i
$328$	8.59442	−	4.37105i	0.474547	−	0.241351i
$329$	−27.1730	−	2.03824i	−1.49810	−	0.112372i
$330$	6.84428	+	1.64496i	0.376765	+	0.0905518i
$331$	3.22524	−	4.20322i	0.177275	−	0.231030i	−0.696261	−	0.717789i	$-0.745154\pi$
$331$	3.22524	−	4.20322i	0.177275	−	0.231030i	0.873536	+	0.486759i	$0.161821\pi$
$332$	−27.6445	−	19.0197i	−1.51719	−	1.04384i
$333$	7.03090	−	5.39500i	0.385291	−	0.295644i
$334$	−10.8793	−	13.4416i	−0.595289	−	0.735492i
$335$			1.17805i			0.0643637i
$336$	−7.61235	+	19.9909i	−0.415288	+	1.09059i
$337$			13.2457i			0.721540i	0.932655	+	0.360770i	$0.117486\pi$
$337$			13.2457i			0.721540i	−0.932655	+	0.360770i	$0.882514\pi$
$338$	−14.2179	+	11.5076i	−0.773351	+	0.625931i
$339$	13.0412	−	10.0069i	0.708301	−	0.543498i
$340$	−0.0744286	−	0.402692i	−0.00403646	−	0.0218390i
$341$	−6.12284	+	7.97944i	−0.331571	+	0.432111i
$342$	−1.13684	+	4.73015i	−0.0614735	+	0.255777i
$343$	4.12491	−	18.0551i	0.222724	−	0.974881i
$344$	28.1159	−	2.19180i	1.51591	−	0.118174i
$345$	−8.20941	−	2.19970i	−0.441980	−	0.118428i
$346$	3.87932	−	0.100624i	0.208554	−	0.00540959i
$347$	−0.339504	+	2.57879i	−0.0182256	+	0.138437i	−0.998138	−	0.0609893i	$-0.980574\pi$
$347$	−0.339504	+	2.57879i	−0.0182256	+	0.138437i	0.979913	+	0.199426i	$0.0639078\pi$
$348$	8.45152	−	0.438737i	0.453049	−	0.0235188i
$349$	−2.18080	+	5.26491i	−0.116735	+	0.281824i	−0.971438	−	0.237294i	$-0.923740\pi$
$349$	−2.18080	+	5.26491i	−0.116735	+	0.281824i	0.854703	+	0.519118i	$0.173740\pi$
$350$	15.0333	+	7.10743i	0.803562	+	0.379908i
$351$	−0.994672			−0.0530917
$352$	−11.3932	+	14.8100i	−0.607261	+	0.789377i
$353$	−12.7963	+	22.1639i	−0.681079	+	1.17966i	0.293573	+	0.955937i	$0.405155\pi$
$353$	−12.7963	+	22.1639i	−0.681079	+	1.17966i	−0.974652	+	0.223726i	$0.928178\pi$
$354$	−13.4931	−	30.3263i	−0.717152	−	1.61182i
$355$	−1.41283	+	0.186003i	−0.0749855	+	0.00987202i
$356$	−18.8419	−	9.61215i	−0.998617	−	0.509443i
$357$	−0.662008	+	1.31114i	−0.0350372	+	0.0693928i
$358$	0.694951	+	1.13469i	0.0367293	+	0.0599700i
$359$	−14.9377	−	4.00253i	−0.788380	−	0.211246i	−0.157904	−	0.987455i	$-0.550474\pi$
$359$	−14.9377	−	4.00253i	−0.788380	−	0.211246i	−0.630476	+	0.776209i	$0.717140\pi$
$360$	−0.762511	−	2.15835i	−0.0401878	−	0.113755i
$361$	8.65360	−	2.31873i	0.455453	−	0.122038i
$362$	2.16795	−	0.641594i	0.113945	−	0.0337215i
$363$	0.0690665	+	0.166741i	0.00362505	+	0.00875165i
$364$	0.491474	+	1.26828i	0.0257602	+	0.0664759i
$365$	−0.629952	−	0.260935i	−0.0329732	−	0.0136579i
$366$	14.0533	−	11.3744i	0.734576	−	0.594548i
$367$	−16.8198	−	9.71092i	−0.877987	−	0.506906i	−0.00799252	−	0.999968i	$-0.502544\pi$
$367$	−16.8198	−	9.71092i	−0.877987	−	0.506906i	−0.869994	+	0.493062i	$0.835877\pi$
$368$	14.2151	−	17.5187i	0.741011	−	0.913226i
$369$	3.20494	−	1.85037i	0.166842	−	0.0963265i
$370$	−8.50134	+	1.34433i	−0.441963	+	0.0698882i
$371$	−15.8399	−	14.1574i	−0.822367	−	0.735015i
$372$	12.2710	+	0.971848i	0.636220	+	0.0503880i
$373$	9.82411	−	12.8030i	0.508673	−	0.662915i	−0.466458	−	0.884543i	$-0.654470\pi$
$373$	9.82411	−	12.8030i	0.508673	−	0.662915i	0.975131	+	0.221628i	$0.0711369\pi$
$374$	−0.883385	+	0.930433i	−0.0456787	+	0.0481115i
$375$	−13.7464	+	3.68335i	−0.709863	+	0.190207i
$376$	6.03551	+	28.4987i	0.311258	+	1.46971i
$377$	0.380508	−	0.380508i	0.0195971	−	0.0195971i
$378$	4.42698	−	13.7852i	0.227699	−	0.709036i
$379$	8.51634	−	3.52758i	0.437455	−	0.181200i	−0.153077	−	0.988214i	$-0.548918\pi$
$379$	8.51634	−	3.52758i	0.437455	−	0.181200i	0.590532	+	0.807015i	$0.298918\pi$
$380$	3.16318	−	3.50958i	0.162268	−	0.180038i
$381$	17.0317	+	22.1962i	0.872561	+	1.13714i
$382$	16.5737	−	7.37419i	0.847986	−	0.377296i
$383$	−5.43130	−	9.40729i	−0.277526	−	0.480690i	0.693243	−	0.720704i	$-0.256181\pi$
$383$	−5.43130	−	9.40729i	−0.277526	−	0.480690i	−0.970769	+	0.240014i	$0.922848\pi$
$384$	22.7946	+	1.83365i	1.16323	+	0.0935731i
$385$	1.21081	+	6.40172i	0.0617086	+	0.326262i
$386$	−12.5401	−	9.11566i	−0.638275	−	0.463975i
$387$	10.7313	−	1.41281i	0.545504	−	0.0718170i
$388$	0.182069	+	0.0387941i	0.00924317	+	0.00196947i
$389$	−1.44322	+	10.9623i	−0.0731741	+	0.555812i	0.915112	+	0.403200i	$0.132102\pi$
$389$	−1.44322	+	10.9623i	−0.0731741	+	0.555812i	−0.988286	+	0.152613i	$0.951231\pi$
$390$	−0.481340	−	0.261500i	−0.0243736	−	0.0132416i
$391$	1.09536	−	1.09536i	0.0553946	−	0.0553946i
$392$	−19.7646	+	1.16666i	−0.998262	+	0.0589253i
$393$	27.6300	+	27.6300i	1.39375	+	1.39375i
$394$	−9.35045	−	31.5952i	−0.471069	−	1.59175i
$395$	10.2461	+	1.34893i	0.515538	+	0.0678718i
$396$	−4.06499	+	5.90833i	−0.204273	+	0.296905i
$397$	2.42512	+	18.4206i	0.121713	+	0.924505i	0.937946	+	0.346781i	$0.112725\pi$
$397$	2.42512	+	18.4206i	0.121713	+	0.924505i	−0.816233	+	0.577723i	$0.803941\pi$
$398$	−6.53442	+	1.03329i	−0.327541	+	0.0517944i
$399$	−16.6508	+	3.14930i	−0.833582	+	0.157662i
$400$	2.79827	−	17.5552i	0.139913	−	0.877762i
$401$	1.21956	−	0.704116i	0.0609022	−	0.0351619i	−0.469240	−	0.883071i	$-0.655472\pi$
$401$	1.21956	−	0.704116i	0.0609022	−	0.0351619i	0.530142	+	0.847909i	$0.322139\pi$
$402$	−4.21660	−	1.61980i	−0.210305	−	0.0807881i
$403$	0.620958	−	0.476478i	0.0309321	−	0.0237350i
$404$	−8.10438	+	22.8502i	−0.403208	+	1.13684i
$405$	3.16056	+	7.63028i	0.157050	+	0.379152i
$406$	3.57996	+	6.96701i	0.177671	+	0.345767i
$407$	19.0675	+	19.0675i	0.945140	+	0.945140i
$408$	1.54369	+	0.287291i	0.0764243	+	0.0142230i
$409$	5.19999	+	19.4066i	0.257123	+	0.959596i	0.966897	+	0.255167i	$0.0821304\pi$
$409$	5.19999	+	19.4066i	0.257123	+	0.959596i	−0.709774	+	0.704429i	$0.751203\pi$
$410$	−3.59293	+	0.0931958i	−0.177442	+	0.00460261i
$411$	−20.1092	−	15.4303i	−0.991912	−	0.761121i
$412$	−1.49183	−	0.761052i	−0.0734970	−	0.0374943i
$413$	20.4730	−	22.9061i	1.00741	−	1.12714i
$414$	5.09133	−	7.00397i	0.250225	−	0.344227i
$415$	6.25399	+	10.8322i	0.306996	+	0.531733i
$416$	1.15470	−	0.883767i	0.0566138	−	0.0433303i
$417$	19.7302	−	34.1737i	0.966193	−	1.67349i
$418$	−14.7210	−	1.55091i	−0.720025	−	0.0758576i
$419$	6.86208	−	16.5665i	0.335235	−	0.809328i	−0.662925	−	0.748686i	$-0.730685\pi$
$419$	6.86208	−	16.5665i	0.335235	−	0.809328i	0.998160	−	0.0606421i	$-0.0193148\pi$
$420$	5.76645	−	5.50707i	0.281374	−	0.268718i
$421$	9.32287	−	3.86166i	0.454369	−	0.188206i	−0.143748	−	0.989614i	$-0.545916\pi$
$421$	9.32287	−	3.86166i	0.454369	−	0.188206i	0.598117	+	0.801408i	$0.295916\pi$
$422$	−2.93150	+	5.39597i	−0.142703	+	0.262672i
$423$	2.89378	+	10.7997i	0.140701	+	0.525102i
$424$	−9.79273	+	20.4918i	−0.475577	+	0.995169i
$425$	0.315918	−	1.17902i	0.0153243	−	0.0571910i
$426$	1.27686	−	5.31272i	0.0618640	−	0.257402i
$427$	14.9377	+	7.54222i	0.722887	+	0.364993i
$428$	−0.267119	+	0.227913i	−0.0129117	+	0.0110166i
$429$	0.224010	+	1.70152i	0.0108153	+	0.0821503i
$430$	−9.81300	−	3.76964i	−0.473225	−	0.181788i
$431$	18.6180	+	10.7491i	0.896798	+	0.517766i	0.876160	−	0.482021i	$-0.160097\pi$
$431$	18.6180	+	10.7491i	0.896798	+	0.517766i	0.0206379	+	0.999787i	$0.493430\pi$
$432$	−15.4726	−	0.420469i	−0.744426	−	0.0202298i
$433$			32.1640i			1.54570i	0.634587	+	0.772852i	$0.281170\pi$
$433$			32.1640i			1.54570i	−0.634587	+	0.772852i	$0.718830\pi$
$434$	3.83985	+	10.7266i	0.184319	+	0.514892i
$435$	−2.91446	−	1.20721i	−0.139738	−	0.0578813i
$436$	16.2373	−	7.73496i	0.777627	−	0.370437i
$437$	17.7193	+	2.33279i	0.847631	+	0.111593i
$438$	1.80014	−	1.89601i	0.0860139	−	0.0905948i
$439$	2.81571	−	10.5084i	0.134386	−	0.501537i	−0.865613	−	0.500713i	$-0.833071\pi$
$439$	2.81571	−	10.5084i	0.134386	−	0.501537i	1.00000		0.000823632i	$-0.000262170\pi$
$440$	6.20826	−	3.15747i	0.295967	−	0.150527i
$441$	−7.55141	+	0.849776i	−0.359591	+	0.0404655i
$442$	0.0851423	−	0.0521464i	0.00404981	−	0.00248035i
$443$	−18.5295	−	14.2182i	−0.880363	−	0.675526i	0.0662832	−	0.997801i	$-0.478886\pi$
$443$	−18.5295	−	14.2182i	−0.880363	−	0.675526i	−0.946646	+	0.322275i	$0.895553\pi$
$444$	6.87743	−	32.2773i	0.326388	−	1.53181i
$445$	4.79980	+	6.25523i	0.227532	+	0.296526i
$446$	3.79615	−	36.0323i	0.179753	−	1.70618i
$447$	−24.7738			−1.17176
$448$	7.10899	+	19.9365i	0.335868	+	0.941909i
$449$	9.55987			0.451158			0.225579	−	0.974225i	$-0.427573\pi$
$449$	9.55987			0.451158			0.225579	+	0.974225i	$0.427573\pi$
$450$	0.714870	−	6.78540i	0.0336993	−	0.319867i
$451$	6.85489	+	8.93346i	0.322784	+	0.420660i
$452$	3.38954	−	15.9079i	0.159431	−	0.748244i
$453$	32.4092	+	24.8684i	1.52272	+	1.16842i
$454$	−29.5745	+	18.1132i	−1.38800	+	0.850096i
$455$	0.0379242	−	0.505592i	0.00177792	−	0.0237025i
$456$	8.21254	+	16.1476i	0.384588	+	0.756181i
$457$	−2.17692	+	8.12438i	−0.101832	+	0.380043i	−0.997967	−	0.0637401i	$-0.979697\pi$
$457$	−2.17692	+	8.12438i	−0.101832	+	0.380043i	0.896134	+	0.443783i	$0.146364\pi$
$458$	11.1134	−	11.7053i	0.519295	−	0.546952i
$459$	−1.05370	−	0.138722i	−0.0491823	−	0.00647498i
$460$	−7.59209	+	3.61664i	−0.353983	+	0.168627i
$461$	20.9004	+	8.65723i	0.973428	+	0.403207i	0.811987	−	0.583675i	$-0.198386\pi$
$461$	20.9004	+	8.65723i	0.973428	+	0.403207i	0.161441	+	0.986882i	$0.448386\pi$
$462$	−24.5786	−	4.46839i	−1.14350	−	0.207888i
$463$		−	33.6055i		−	1.56178i	−0.624668	−	0.780891i	$-0.714765\pi$
$463$		−	33.6055i		−	1.56178i	0.624668	−	0.780891i	$-0.285235\pi$
$464$	6.07983	−	5.75813i	0.282249	−	0.267315i
$465$	−3.97366	−	2.29419i	−0.184274	−	0.106391i
$466$	21.8023	+	8.37531i	1.00997	+	0.387979i
$467$	0.0300771	+	0.228458i	0.00139180	+	0.0105718i	0.992127	−	0.125238i	$-0.0399696\pi$
$467$	0.0300771	+	0.228458i	0.00139180	+	0.0105718i	−0.990735	+	0.135810i	$0.956636\pi$
$468$	0.424558	−	0.362244i	0.0196252	−	0.0167447i
$469$	−0.234129	−	4.17424i	−0.0108111	−	0.192748i
$470$	2.53751	−	10.5580i	0.117047	−	0.487004i
$471$	−9.46598	+	35.3275i	−0.436169	+	1.62781i
$472$	−29.6332	−	14.1613i	−1.36398	−	0.651826i
$473$	8.52404	+	31.8121i	0.391936	+	1.46272i
$474$	−18.9164	+	34.8192i	−0.868860	+	1.59930i
$475$	13.0107	−	5.38922i	0.596973	−	0.247274i
$476$	0.343758	+	1.41208i	0.0157561	+	0.0647227i
$477$	−3.33582	+	8.05338i	−0.152737	+	0.368739i
$478$	38.9231	+	4.10071i	1.78030	+	0.187562i
$479$	2.98768	−	5.17482i	0.136511	−	0.236444i	−0.789663	−	0.613541i	$-0.789744\pi$
$479$	2.98768	−	5.17482i	0.136511	−	0.236444i	0.926174	+	0.377097i	$0.123078\pi$
$480$	−7.37693	−	4.27124i	−0.336709	−	0.194954i
$481$	−1.04922	−	1.81731i	−0.0478404	−	0.0828621i
$482$	−21.6689	+	29.8091i	−0.986990	+	1.35777i
$483$	29.5259	+	6.16275i	1.34348	+	0.280415i
$484$	0.159075	+	0.0811519i	0.00723069	+	0.00368872i
$485$	−0.0550514	−	0.0422424i	−0.00249976	−	0.00191813i
$486$	−15.2451	+	0.395437i	−0.691532	+	0.0179374i
$487$	5.58824	+	20.8556i	0.253227	+	0.945057i	0.969068	+	0.246793i	$0.0793769\pi$
$487$	5.58824	+	20.8556i	0.253227	+	0.945057i	−0.715841	+	0.698263i	$0.753956\pi$
$488$	3.27309	−	17.5872i	0.148166	−	0.796136i
$489$	−18.6204	−	18.6204i	−0.842045	−	0.842045i
$490$	6.83826	+	2.77583i	0.308921	+	0.125399i
$491$	−10.1495	−	24.5032i	−0.458043	−	1.10581i	−0.969189	−	0.246319i	$-0.920779\pi$
$491$	−10.1495	−	24.5032i	−0.458043	−	1.10581i	0.511146	−	0.859494i	$-0.329221\pi$
$492$	4.60664	−	12.9884i	0.207684	−	0.585560i
$493$	0.456155	−	0.350020i	0.0205442	−	0.0157641i
$494$	1.07531	+	0.413077i	0.0483804	+	0.0185852i
$495$	2.31512	−	1.33663i	0.104057	−	0.0600772i
$496$	9.86072	−	7.14935i	0.442759	−	0.321015i
$497$	4.96919	−	0.939864i	0.222899	−	0.0421587i
$498$	−47.3710	+	7.49082i	−2.12274	+	0.335672i
$499$	−0.883086	−	6.70770i	−0.0395324	−	0.300278i	−0.999777	−	0.0211181i	$-0.993277\pi$
$499$	−0.883086	−	6.70770i	−0.0395324	−	0.300278i	0.960245	−	0.279160i	$-0.0900559\pi$
$500$	−7.98159	+	11.6010i	−0.356948	+	0.518813i
$501$	−24.5043	−	3.22605i	−1.09477	−	0.144129i
$502$	−5.12202	−	17.3074i	−0.228607	−	0.772466i
$503$	−3.04175	−	3.04175i	−0.135625	−	0.135625i	0.636035	−	0.771660i	$-0.280573\pi$
$503$	−3.04175	−	3.04175i	−0.135625	−	0.135625i	−0.771660	+	0.636035i	$0.780573\pi$
$504$	3.13079	+	7.49623i	0.139457	+	0.333908i
$505$	6.39039	−	6.39039i	0.284369	−	0.284369i
$506$	23.1510	+	12.5774i	1.02919	+	0.559132i
$507$	−3.41236	+	25.9195i	−0.151548	+	1.15112i
$508$	27.0753	+	5.76902i	1.20127	+	0.255959i
$509$	−4.11101	+	0.541224i	−0.182217	+	0.0239893i	−0.221082	−	0.975255i	$-0.570959\pi$
$509$	−4.11101	+	0.541224i	−0.182217	+	0.0239893i	0.0388653	+	0.999244i	$0.487626\pi$
$510$	−0.473433	−	0.344148i	−0.0209640	−	0.0152391i
$511$	2.28399	+	0.799382i	0.101038	+	0.0353626i
$512$	18.3355	−	13.2593i	0.810322	−	0.585985i
$513$	−6.13091	−	10.6191i	−0.270686	−	0.468843i
$514$	−16.0045	+	7.12092i	−0.705928	+	0.314090i
$515$	0.380030	+	0.495264i	0.0167461	+	0.0218239i
$516$	26.9854	−	29.9405i	1.18797	−	1.31806i
$517$	−31.4304	+	13.0189i	−1.38231	+	0.572570i
$518$	29.8560	−	6.45299i	1.31180	−	0.283528i
$519$	3.92192	−	3.92192i	0.172153	−	0.172153i
$520$	−0.530258	+	0.112299i	−0.0232534	+	0.00492464i
$521$	42.1708	−	11.2996i	1.84754	−	0.495046i	0.848138	−	0.529775i	$-0.177724\pi$
$521$	42.1708	−	11.2996i	1.84754	−	0.495046i	0.999397	+	0.0347293i	$0.0110569\pi$
$522$	2.21292	−	2.33077i	0.0968567	−	0.102015i
$523$	8.39693	−	10.9431i	0.367172	−	0.478508i	−0.572831	−	0.819673i	$-0.694155\pi$
$523$	8.39693	−	10.9431i	0.367172	−	0.478508i	0.940003	+	0.341165i	$0.110822\pi$
$524$	38.5426	+	3.05253i	1.68374	+	0.133351i
$525$	22.5765	−	7.42727i	0.985318	−	0.324152i
$526$	−10.8107	+	1.70950i	−0.471367	+	0.0745378i
$527$	0.724258	−	0.418150i	0.0315492	−	0.0182149i
$528$	2.76531	+	26.5627i	0.120345	+	1.15599i
$529$	−7.63040	−	4.40541i	−0.331756	−	0.191540i
$530$	6.58049	−	5.32608i	0.285838	−	0.231350i
$531$	−11.6460	−	4.82393i	−0.505393	−	0.209341i
$532$	−10.5107	+	13.0643i	−0.455698	+	0.566410i
$533$	−0.335338	−	0.809577i	−0.0145251	−	0.0350667i
$534$	−28.9890	+	8.57914i	−1.25448	+	0.371256i
$535$	0.126428	−	0.0338762i	0.00546595	−	0.00146460i
$536$	−4.21420	+	1.48881i	−0.182026	+	0.0643069i
$537$	1.83696	+	0.492212i	0.0792707	+	0.0212405i
$538$	−6.35392	−	10.3744i	−0.273937	−	0.447273i
$539$	−5.56261	−	22.4429i	−0.239599	−	0.966683i
$540$	5.13948	+	2.62189i	0.221168	+	0.112828i
$541$	−11.5998	+	1.52714i	−0.498715	+	0.0656570i	−0.375688	−	0.926746i	$-0.622593\pi$
$541$	−11.5998	+	1.52714i	−0.498715	+	0.0656570i	−0.123027	+	0.992403i	$0.539260\pi$
$542$	−15.1414	−	34.0307i	−0.650378	−	1.46174i
$543$	1.61571	−	2.79849i	0.0693367	−	0.120095i
$544$	1.34647	−	0.775171i	0.0577296	−	0.0332352i
$545$	−6.70421			−0.287177
$546$	1.75752	+	0.830922i	0.0752151	+	0.0355602i
$547$	4.82313	−	11.6441i	0.206222	−	0.497865i	−0.786600	−	0.617463i	$-0.788161\pi$
$547$	4.82313	−	11.6441i	0.206222	−	0.497865i	0.992822	+	0.119598i	$0.0381606\pi$
$548$	−25.0464	+	1.30022i	−1.06993	+	0.0555425i
$549$	0.896202	−	6.80733i	0.0382490	−	0.290530i
$550$	20.7535	−	0.538316i	0.884930	−	0.0229539i
$551$	6.40763	+	1.71692i	0.272974	+	0.0731432i
$552$	−2.50606	−	32.1472i	−0.106665	−	1.36828i
$553$	−36.5736	−	2.74337i	−1.55527	−	0.116660i
$554$	2.34118	−	9.74111i	0.0994672	−	0.413860i
$555$	−7.48875	+	9.75953i	−0.317880	+	0.414269i
$556$	−7.09640	−	38.3946i	−0.300954	−	1.62830i
$557$	9.18100	−	7.04483i	0.389011	−	0.298499i	−0.395676	−	0.918390i	$-0.629490\pi$
$557$	9.18100	−	7.04483i	0.389011	−	0.298499i	0.784688	+	0.619891i	$0.212823\pi$
$558$	3.63368	−	2.94101i	0.153826	−	0.124503i
$559$		−	2.56294i		−	0.108401i
$560$	0.803655	−	7.84870i	0.0339606	−	0.331668i
$561$			1.83373i			0.0774204i
$562$	−4.31705	−	5.33381i	−0.182104	−	0.224993i
$563$	8.59744	−	6.59705i	0.362339	−	0.278032i	−0.411507	−	0.911407i	$-0.634997\pi$
$563$	8.59744	−	6.59705i	0.362339	−	0.278032i	0.773846	+	0.633374i	$0.218331\pi$
$564$	34.3013	+	23.5996i	1.44434	+	0.993722i
$565$	−3.69083	+	4.80999i	−0.155275	+	0.202358i
$566$	31.3124	+	7.52564i	1.31616	+	0.316326i
$567$	−12.7154	−	26.4086i	−0.533998	−	1.10906i
$568$	−2.45092	−	4.81902i	−0.102838	−	0.202202i
$569$	22.4880	+	6.02563i	0.942745	+	0.252608i	0.697281	−	0.716798i	$-0.254393\pi$
$569$	22.4880	+	6.02563i	0.942745	+	0.252608i	0.245464	+	0.969406i	$0.421060\pi$
$570$	−0.175101	−	6.75058i	−0.00733416	−	0.282751i
$571$	2.05675	−	15.6226i	0.0860725	−	0.653785i	−0.892968	−	0.450120i	$-0.851381\pi$
$571$	2.05675	−	15.6226i	0.0860725	−	0.653785i	0.979041	−	0.203665i	$-0.0652855\pi$
$572$	1.26140	+	1.13690i	0.0527418	+	0.0475361i
$573$	9.92188	−	23.9535i	0.414492	−	1.00067i
$574$	12.7125	−	1.04429i	0.530609	−	0.0435880i
$575$	−25.0659			−1.04532
$576$	6.75734	−	5.45542i	0.281556	−	0.227309i
$577$	8.37214	−	14.5010i	0.348537	−	0.603683i	−0.637453	−	0.770489i	$-0.720012\pi$
$577$	8.37214	−	14.5010i	0.348537	−	0.603683i	0.985990	+	0.166806i	$0.0533454\pi$
$578$	−21.8681	+	9.72982i	−0.909592	+	0.404707i
$579$	−21.9686	+	2.89222i	−0.912983	+	0.120197i
$580$	−2.96908	+	0.963091i	−0.123284	+	0.0399902i
$581$	−24.3129	−	37.1394i	−1.00867	−	1.54080i
$582$	0.226893	−	0.138963i	0.00940503	−	0.00576021i
$583$	−25.6195	−	6.86472i	−1.06105	−	0.284308i
$584$	0.137304	−	2.58328i	0.00568169	−	0.106897i
$585$	−0.200944	+	0.0538429i	−0.00830803	+	0.00222613i
$586$	3.38603	+	11.4414i	0.139876	+	0.472641i
$587$	−9.89537	−	23.8895i	−0.408426	−	0.986027i	−0.985552	−	0.169372i	$-0.945826\pi$
$587$	−9.89537	−	23.8895i	−0.408426	−	0.986027i	0.577127	−	0.816655i	$-0.304174\pi$
$588$	−19.3380	+	20.6595i	−0.797487	+	0.851983i
$589$	8.91428	+	3.69242i	0.367306	+	0.152143i
$590$	7.70206	+	9.51606i	0.317089	+	0.391770i
$591$	−40.7845	−	23.5470i	−1.67765	−	0.968593i
$592$	−15.5530	−	28.7126i	−0.639223	−	1.18008i
$593$	−28.7707	+	16.6108i	−1.18147	+	0.682122i	−0.956354	−	0.292210i	$-0.905609\pi$
$593$	−28.7707	+	16.6108i	−1.18147	+	0.682122i	−0.225116	+	0.974332i	$0.572276\pi$
$594$	−2.82332	−	17.8543i	−0.115842	−	0.732570i
$595$	0.110687	−	0.530305i	0.00453773	−	0.0217404i
$596$	−18.6477	+	15.9107i	−0.763839	+	0.651728i
$597$	−5.75611	+	7.50151i	−0.235582	+	0.307016i
$598$	−1.48689	−	1.41170i	−0.0608034	−	0.0577289i
$599$	18.1266	−	4.85700i	0.740631	−	0.198452i	0.131273	−	0.991346i	$-0.458094\pi$
$599$	18.1266	−	4.85700i	0.740631	−	0.198452i	0.609359	+	0.792895i	$0.291427\pi$
$600$	−14.3756	−	20.9499i	−0.586882	−	0.855276i
$601$	−18.6060	+	18.6060i	−0.758956	+	0.758956i	−0.976132	−	0.217176i	$-0.930315\pi$
$601$	−18.6060	+	18.6060i	−0.758956	+	0.758956i	0.217176	+	0.976132i	$0.430315\pi$
$602$	35.5200	+	11.4069i	1.44769	+	0.464909i
$603$	−1.58485	+	0.656466i	−0.0645400	+	0.0267334i
$604$	40.3664	−	2.09551i	1.64248	−	0.0852650i
$605$	−0.0405230	−	0.0528106i	−0.00164750	−	0.00214706i
$606$	14.0865	+	31.6598i	0.572225	+	1.28609i
$607$	19.6219	+	33.9861i	0.796427	+	1.37945i	0.921929	+	0.387359i	$0.126612\pi$
$607$	19.6219	+	33.9861i	0.796427	+	1.37945i	−0.125502	+	0.992093i	$0.540054\pi$
$608$	16.5523	+	6.88017i	0.671286	+	0.279028i
$609$	10.5669	+	3.69833i	0.428191	+	0.149864i
$610$	−3.92086	+	5.39379i	−0.158751	+	0.218388i
$611$	2.62477	−	0.345558i	0.106187	−	0.0139798i
$612$	0.500272	−	0.324529i	0.0202223	−	0.0131183i
$613$	−2.08519	+	15.8386i	−0.0842198	+	0.639713i	0.896322	+	0.443403i	$0.146229\pi$
$613$	−2.08519	+	15.8386i	−0.0842198	+	0.639713i	−0.980542	+	0.196310i	$0.937104\pi$
$614$	−11.9731	+	22.0387i	−0.483195	+	0.889410i
$615$	−3.63239	+	3.63239i	−0.146472	+	0.146472i
$616$	−21.3705	+	12.4219i	−0.861041	+	0.500491i
$617$	−13.0001	−	13.0001i	−0.523363	−	0.523363i	0.395223	−	0.918585i	$-0.370667\pi$
$617$	−13.0001	−	13.0001i	−0.523363	−	0.523363i	−0.918585	+	0.395223i	$0.870667\pi$
$618$	−2.29524	+	0.679263i	−0.0923279	+	0.0273240i
$619$	35.2134	+	4.63593i	1.41534	+	0.186334i	0.799089	−	0.601213i	$-0.205316\pi$
$619$	35.2134	+	4.63593i	1.41534	+	0.186334i	0.616255	+	0.787547i	$0.288649\pi$
$620$	−4.46446	+	0.825157i	−0.179297	+	0.0331391i
$621$	2.84871	+	21.6381i	0.114315	+	0.868308i
$622$	3.88670	+	24.5790i	0.155843	+	0.985527i
$623$	−18.2505	−	21.2105i	−0.731192	−	0.849780i
$624$	0.327143	−	2.05237i	0.0130962	−	0.0821604i
$625$	−14.6983	+	8.48606i	−0.587931	+	0.339442i
$626$	−12.8820	+	33.5339i	−0.514868	+	1.34029i
$627$	−16.7846	+	12.8793i	−0.670313	+	0.514349i
$628$	15.5635	+	32.6710i	0.621050	+	1.30372i
$629$	−0.858034	−	2.07148i	−0.0342121	−	0.0825952i
$630$	0.148129	−	3.02454i	0.00590160	−	0.120501i
$631$	16.4788	+	16.4788i	0.656012	+	0.656012i	0.954434	−	0.298422i	$-0.0964604\pi$
$631$	16.4788	+	16.4788i	0.656012	+	0.656012i	−0.298422	+	0.954434i	$0.596460\pi$
$632$	8.12350	+	38.3579i	0.323135	+	1.52579i
$633$	2.27163	+	8.47784i	0.0902892	+	0.336964i
$634$	−0.193235	−	7.44970i	−0.00767435	−	0.295866i
$635$	−8.18662	−	6.28181i	−0.324876	−	0.249286i
$636$	10.0156	+	30.8769i	0.397146	+	1.22435i
$637$	−0.0338958	+	1.79902i	−0.00134300	+	0.0712799i
$638$	7.91013	+	5.75003i	0.313165	+	0.227646i
$639$	−1.03753	−	1.79706i	−0.0410441	−	0.0710905i
$640$	−8.29590	+	1.52271i	−0.327924	+	0.0601906i
$641$	−13.9878	+	24.2276i	−0.552484	+	0.956931i	0.445610	+	0.895227i	$0.352987\pi$
$641$	−13.9878	+	24.2276i	−0.552484	+	0.956931i	−0.998095	+	0.0617037i	$0.980347\pi$
$642$	−0.0525826	+	0.499103i	−0.00207527	+	0.0196980i
$643$	0.627316	−	1.51447i	0.0247389	−	0.0597251i	−0.911027	−	0.412346i	$-0.864709\pi$
$643$	0.627316	−	1.51447i	0.0247389	−	0.0597251i	0.935766	+	0.352621i	$0.114709\pi$
$644$	26.1826	−	14.3239i	1.03174	−	0.564440i
$645$	−13.8809	+	5.74967i	−0.546561	+	0.226393i
$646$	1.08151	+	0.587557i	0.0425514	+	0.0231171i
$647$	9.24168	+	34.4904i	0.363328	+	1.35596i	0.869674	+	0.493627i	$0.164329\pi$
$647$	9.24168	+	34.4904i	0.363328	+	1.35596i	−0.506346	+	0.862331i	$0.669004\pi$
$648$	−23.3013	+	20.9493i	−0.915360	+	0.822966i
$649$	9.92709	−	37.0484i	0.389672	−	1.45428i
$650$	−1.57084	−	0.377536i	−0.0616134	−	0.0148082i
$651$	14.5360	+	7.33938i	0.569711	+	0.287653i
$652$	−25.9747	−	2.05717i	−1.01725	−	0.0805649i
$653$	−4.43023	−	33.6510i	−0.173368	−	1.31686i	−0.827920	−	0.560847i	$-0.810476\pi$
$653$	−4.43023	−	33.6510i	−0.173368	−	1.31686i	0.654551	−	0.756018i	$-0.272858\pi$
$654$	9.21817	−	23.9964i	0.360459	−	0.938334i
$655$	−12.4811	−	7.20597i	−0.487677	−	0.281560i
$656$	−4.87412	−	12.7351i	−0.190302	−	0.497223i
$657$		−	0.992889i		−	0.0387363i
$658$	−6.89295	+	37.9149i	−0.268715	+	1.47808i
$659$	36.6698	+	15.1891i	1.42845	+	0.591685i	0.956969	−	0.290190i	$-0.0937185\pi$
$659$	36.6698	+	15.1891i	1.42845	+	0.591685i	0.471484	+	0.881875i	$0.343719\pi$
$660$	3.32765	−	9.38226i	0.129529	−	0.365204i
$661$	−45.8806	−	6.04030i	−1.78455	−	0.234940i	−0.835372	−	0.549685i	$-0.814748\pi$
$661$	−45.8806	−	6.04030i	−1.78455	−	0.234940i	−0.949177	+	0.314744i	$0.898081\pi$
$662$	−5.43363	−	5.15888i	−0.211184	−	0.200505i
$663$	0.0369337	−	0.137838i	0.00143438	−	0.00535319i
$664$	−30.8460	+	36.0619i	−1.19706	+	1.39947i
$665$	5.63143	−	2.71147i	0.218377	−	0.105146i
$666$	−6.54589	−	10.6879i	−0.253648	−	0.414146i
$667$	−9.36734	−	7.18782i	−0.362705	−	0.278313i
$668$	−20.5167	+	13.3093i	−0.793814	+	0.514952i
$669$	−31.5245	−	41.0835i	−1.21881	−	1.58838i
$670$	1.65684	+	0.174555i	0.0640095	+	0.00674366i
$671$	20.8916			0.806513
$672$	26.9879	+	13.6683i	1.04108	+	0.527268i
$673$	34.9075			1.34559			0.672793	−	0.739831i	$-0.265095\pi$
$673$	34.9075			1.34559			0.672793	+	0.739831i	$0.265095\pi$
$674$	18.6292	+	1.96266i	0.717569	+	0.0755988i
$675$	10.4690	+	13.6435i	0.402953	+	0.525138i
$676$	14.0779	+	21.7016i	0.541458	+	0.834676i
$677$	4.61281	+	3.53953i	0.177285	+	0.136035i	0.693592	−	0.720368i	$-0.256027\pi$
$677$	4.61281	+	3.53953i	0.177285	+	0.136035i	−0.516307	+	0.856403i	$0.672694\pi$
$678$	−12.1416	−	19.8243i	−0.466295	−	0.761347i
$679$	0.203461	+	0.138738i	0.00780813	+	0.00532429i
$680$	−0.577386	+	0.0450106i	−0.0221417	+	0.00172608i
$681$	−12.8290	+	47.8786i	−0.491610	+	1.83471i
$682$	10.3153	+	9.79369i	0.394993	+	0.375020i
$683$	−25.3273	−	3.33440i	−0.969122	−	0.127587i	−0.370686	−	0.928758i	$-0.620877\pi$
$683$	−25.3273	−	3.33440i	−0.969122	−	0.127587i	−0.598436	+	0.801171i	$0.704211\pi$
$684$	6.48417	+	2.29977i	0.247928	+	0.0879340i
$685$	8.63713	+	3.57762i	0.330008	+	0.136694i
$686$	−24.7820	−	8.47667i	−0.946180	−	0.323641i
$687$		−	23.0693i		−	0.880147i
$688$	1.08341	−	39.8678i	0.0413047	−	1.51995i
$689$	1.78750	+	1.03202i	0.0680985	+	0.0393167i
$690$	−4.31014	+	11.2200i	−0.164084	+	0.427139i
$691$	4.74734	+	36.0596i	0.180597	+	1.37177i	0.806206	+	0.591635i	$0.201517\pi$
$691$	4.74734	+	36.0596i	0.180597	+	1.37177i	−0.625609	+	0.780137i	$0.715149\pi$
$692$	0.433290	−	5.47090i	0.0164712	−	0.207972i
$693$	−7.93761	+	5.19627i	−0.301525	+	0.197390i
$694$	3.57659	+	0.859597i	0.135765	+	0.0326299i
$695$	−3.76690	+	14.0583i	−0.142887	+	0.533261i
$696$	0.635235	−	11.9515i	0.0240785	−	0.453020i
$697$	−0.242329	−	0.904386i	−0.00917888	−	0.0342560i
$698$	7.08159	+	3.84725i	0.268042	+	0.145621i
$699$	30.8404	−	12.7745i	1.16649	−	0.483176i
$700$	12.2236	−	20.0901i	0.462010	−	0.759334i
$701$	−8.73457	+	21.0871i	−0.329900	+	0.796449i	0.668699	+	0.743533i	$0.266852\pi$
$701$	−8.73457	+	21.0871i	−0.329900	+	0.796449i	−0.998599	+	0.0529159i	$0.983148\pi$
$702$	−0.147384	+	1.39894i	−0.00556264	+	0.0527994i
$703$	12.9343	−	22.4029i	0.487827	−	0.844940i
$704$	19.1411	+	18.2182i	0.721407	+	0.686625i
$705$	−7.75993	−	13.4406i	−0.292256	−	0.506202i
$706$	29.2758	+	21.2812i	1.10181	+	0.800928i
$707$	−21.3733	+	23.9134i	−0.803826	+	0.899356i
$708$	−44.6511	+	14.4836i	−1.67809	+	0.544328i
$709$	−0.989203	−	0.759042i	−0.0371503	−	0.0285064i	0.590019	−	0.807389i	$-0.299120\pi$
$709$	−0.989203	−	0.759042i	−0.0371503	−	0.0285064i	−0.627170	+	0.778883i	$0.715787\pi$
$710$	0.0522563	+	2.01461i	0.00196114	+	0.0756071i
$711$	3.89489	+	14.5359i	0.146070	+	0.545140i
$712$	−16.3107	+	25.0755i	−0.611268	+	0.939745i
$713$	−12.1437	−	12.1437i	−0.454786	−	0.454786i
$714$	1.74593	+	1.12534i	0.0653399	+	0.0421149i
$715$	−0.242234	−	0.584805i	−0.00905905	−	0.0218705i
$716$	1.69883	−	0.809269i	0.0634882	−	0.0302438i
$717$	44.3795	−	34.0536i	1.65738	−	1.27176i
$718$	−7.84264	+	20.4157i	−0.292685	+	0.761907i
$719$	−0.246628	+	0.142391i	−0.00919766	+	0.00531027i	−0.504592	−	0.863358i	$-0.668357\pi$
$719$	−0.246628	+	0.142391i	−0.00919766	+	0.00531027i	0.495394	+	0.868668i	$0.335024\pi$
$720$	−3.14855	+	0.752609i	−0.117339	+	0.0280481i
$721$	−1.44501	−	1.67936i	−0.0538148	−	0.0625427i
$722$	−1.97889	−	12.5143i	−0.0736468	−	0.465732i
$723$	6.87510	+	52.2216i	0.255688	+	1.94214i
$724$	−0.581125	−	3.14414i	−0.0215973	−	0.116851i
$725$	−9.22414	−	1.21438i	−0.342576	−	0.0451010i
$726$	0.244744	−	0.0724307i	0.00908330	−	0.00268815i
$727$	−2.93684	−	2.93684i	−0.108921	−	0.108921i	0.650546	−	0.759467i	$-0.274540\pi$
$727$	−2.93684	−	2.93684i	−0.108921	−	0.108921i	−0.759467	+	0.650546i	$0.774540\pi$
$728$	1.85657	−	0.503299i	0.0688090	−	0.0186535i
$729$	8.08802	−	8.08802i	0.299556	−	0.299556i
$730$	−0.460328	+	0.847319i	−0.0170375	+	0.0313607i
$731$	0.357440	−	2.71503i	0.0132204	−	0.100419i
$732$	−13.9149	−	21.4503i	−0.514311	−	0.792827i
$733$	0.107779	−	0.0141894i	0.00398092	−	0.000524097i	−0.128535	−	0.991705i	$-0.541028\pi$
$733$	0.107779	−	0.0141894i	0.00398092	−	0.000524097i	0.132516	+	0.991181i	$0.457694\pi$
$734$	−16.1500	+	22.2170i	−0.596106	+	0.820043i
$735$	9.81958	−	3.85233i	0.362201	−	0.142095i
$736$	−22.5325	−	22.5883i	−0.830560	−	0.832615i
$737$	−2.60980	−	4.52030i	−0.0961331	−	0.166507i
$738$	−2.12753	−	4.78170i	−0.0783156	−	0.176017i
$739$	−22.0513	−	28.7378i	−0.811169	−	1.05714i	−0.997214	−	0.0745946i	$-0.976234\pi$
$739$	−22.0513	−	28.7378i	−0.811169	−	1.05714i	0.186045	−	0.982541i	$-0.440433\pi$
$740$	0.631030	+	12.1557i	0.0231971	+	0.446853i
$741$	1.52107	−	0.630048i	0.0558780	−	0.0231454i
$742$	−22.2584	+	20.1800i	−0.817132	+	0.740830i
$743$	−23.8662	+	23.8662i	−0.875568	+	0.875568i	−0.993072	−	0.117505i	$-0.962511\pi$
$743$	−23.8662	+	23.8662i	−0.875568	+	0.875568i	0.117505	+	0.993072i	$0.462511\pi$
$744$	3.18506	−	17.1142i	0.116770	−	0.627439i
$745$	8.82600	−	2.36492i	0.323360	−	0.0866439i
$746$	−16.5509	−	15.7140i	−0.605971	−	0.575330i
$747$	−11.0877	+	14.4498i	−0.405679	+	0.528691i
$748$	1.17769	+	1.38028i	0.0430608	+	0.0504682i
$749$	−0.441245	+	0.145162i	−0.0161227	+	0.00530410i
$750$	3.14352	+	19.8792i	0.114785	+	0.725885i
$751$	29.5087	−	17.0368i	1.07679	−	0.621683i	0.146759	−	0.989172i	$-0.453116\pi$
$751$	29.5087	−	17.0368i	1.07679	−	0.621683i	0.930028	+	0.367489i	$0.119783\pi$
$752$	40.9757	−	4.26578i	1.49423	−	0.155557i
$753$	−22.3411	−	12.8986i	−0.814155	−	0.470053i
$754$	−0.478776	−	0.591538i	−0.0174360	−	0.0215426i
$755$	−13.9201	−	5.76590i	−0.506605	−	0.209843i
$756$	−18.7320	−	8.26884i	−0.681277	−	0.300735i
$757$	−15.0712	−	36.3851i	−0.547772	−	1.32244i	−0.919132	−	0.393950i	$-0.871108\pi$
$757$	−15.0712	−	36.3851i	−0.547772	−	1.32244i	0.371360	−	0.928489i	$-0.378892\pi$
$758$	−3.69941	−	12.5003i	−0.134368	−	0.454032i
$759$	36.3735	−	9.74624i	1.32027	−	0.353766i
$760$	−4.46728	−	4.96882i	−0.162045	−	0.180238i
$761$	−16.2032	−	4.34164i	−0.587366	−	0.157384i	−0.0471169	−	0.998889i	$-0.515003\pi$
$761$	−16.2032	−	4.34164i	−0.587366	−	0.157384i	−0.540249	+	0.841505i	$0.681670\pi$
$762$	33.7410	−	20.6650i	1.22231	−	0.748615i
$763$	23.7553	−	1.33241i	0.860000	−	0.0482366i
$764$	−7.91550	−	24.4024i	−0.286373	−	0.882849i
$765$	−0.220378	+	0.0290133i	−0.00796777	+	0.00104898i
$766$	−14.0355	+	6.24484i	−0.507122	+	0.225635i
$767$	−1.49240	+	2.58491i	−0.0538874	+	0.0933357i
$768$	5.95644	−	31.7873i	0.214935	−	1.14702i
$769$	44.5030			1.60482			0.802410	−	0.596773i	$-0.203551\pi$
$769$	44.5030			1.60482			0.802410	+	0.596773i	$0.203551\pi$
$770$	9.18298	−	0.754356i	0.330932	−	0.0271851i
$771$	−9.58110	+	23.1308i	−0.345055	+	0.833037i
$772$	−14.6786	+	16.2861i	−0.528296	+	0.586149i
$773$	0.0533595	−	0.405306i	0.00191921	−	0.0145778i	−0.990458	−	0.137812i	$-0.955993\pi$
$773$	0.0533595	−	0.405306i	0.00191921	−	0.0145778i	0.992378	+	0.123234i	$0.0393265\pi$
$774$	−0.396918	−	15.3022i	−0.0142669	−	0.550026i
$775$	−13.0713	−	3.50244i	−0.469534	−	0.125811i
$776$	0.0815390	−	0.250320i	0.00292708	−	0.00898595i
$777$	24.5956	−	36.0697i	0.882362	−	1.29399i
$778$	15.2039	+	3.65411i	0.545086	+	0.131006i
$779$	6.57605	−	8.57008i	0.235612	−	0.307055i
$780$	−0.439103	+	0.638223i	−0.0157224	+	0.0228521i
$781$	5.00913	−	3.84364i	0.179241	−	0.137536i
$782$	−1.37824	−	1.70284i	−0.0492858	−	0.0608936i
$783$			8.10077i			0.289498i
$784$	−1.28775	+	27.9704i	−0.0459912	+	0.998942i
$785$		−	13.4895i		−	0.481461i
$786$	42.9536	−	34.7656i	1.53211	−	1.24005i
$787$	10.9927	−	8.43497i	0.391846	−	0.300674i	−0.393983	−	0.919118i	$-0.628903\pi$
$787$	10.9927	−	8.43497i	0.391846	−	0.300674i	0.785829	+	0.618443i	$0.212236\pi$
$788$	−45.8220	+	8.46918i	−1.63234	+	0.301702i
$789$	−9.52301	+	12.4106i	−0.339028	+	0.441830i
$790$	3.41537	−	14.2106i	0.121513	−	0.505589i
$791$	12.1219	−	17.7770i	0.431007	−	0.632077i
$792$	7.70734	+	6.59257i	0.273868	+	0.234257i
$793$	−1.57038	−	0.420783i	−0.0557660	−	0.0149424i
$794$	26.2667	−	0.681321i	0.932169	−	0.0241792i
$795$	1.57935	−	11.9964i	0.0560138	−	0.425467i
$796$	0.485032	+	9.34330i	0.0171915	+	0.331165i
$797$	11.9672	−	28.8914i	0.423901	−	1.02339i	−0.557285	−	0.830321i	$-0.688157\pi$
$797$	11.9672	−	28.8914i	0.423901	−	1.02339i	0.981186	−	0.193065i	$-0.0618430\pi$
$798$	1.96207	+	23.8848i	0.0694566	+	0.845513i
$799$	2.82872			0.100073
$800$	−24.2756	−	6.53678i	−0.858271	−	0.231110i
$801$	−5.74057	+	9.94296i	−0.202833	+	0.351317i
$802$	−0.809583	−	1.81956i	−0.0285874	−	0.0642510i
$803$	2.99525	−	0.394332i	0.105700	−	0.0139157i
$804$	−2.90292	+	5.69034i	−0.102378	+	0.200683i
$805$	−11.1073	+	0.622997i	−0.391480	+	0.0219578i
$806$	−0.578123	−	0.943935i	−0.0203635	−	0.0332487i
$807$	−16.7953	−	4.50029i	−0.591222	−	0.158418i
$808$	30.9363	+	14.7840i	1.08834	+	0.520100i
$809$	−46.2127	+	12.3827i	−1.62475	+	0.435351i	−0.952393	−	0.304874i	$-0.901386\pi$
$809$	−46.2127	+	12.3827i	−1.62475	+	0.435351i	−0.672359	+	0.740225i	$0.734719\pi$
$810$	11.1998	−	3.31451i	0.393520	−	0.116460i
$811$	6.70708	+	16.1923i	0.235517	+	0.568589i	0.996809	−	0.0798201i	$-0.0254346\pi$
$811$	6.70708	+	16.1923i	0.235517	+	0.568589i	−0.761292	+	0.648409i	$0.775435\pi$
$812$	10.3291	−	4.00265i	0.362479	−	0.140465i
$813$	−49.1836	−	20.3725i	−1.72494	−	0.714496i
$814$	29.6424	−	23.9918i	1.03896	−	0.840911i
$815$	8.41128	+	4.85626i	0.294634	+	0.170107i
$816$	0.632788	−	2.12853i	0.0221520	−	0.0745134i
$817$	27.3618	−	15.7973i	0.957268	−	0.552679i
$818$	28.0646	−	4.43788i	0.981255	−	0.155167i
$819$	0.701314	−	0.230720i	0.0245059	−	0.00806201i
$820$	−0.401303	+	5.06702i	−0.0140141	+	0.176948i
$821$	−6.84321	+	8.91825i	−0.238830	+	0.311249i	−0.897355	−	0.441310i	$-0.854514\pi$
$821$	−6.84321	+	8.91825i	−0.238830	+	0.311249i	0.658525	+	0.752559i	$0.271181\pi$
$822$	−24.6813	+	25.9958i	−0.860858	+	0.906707i
$823$	39.1733	−	10.4965i	1.36550	−	0.365884i	0.499665	−	0.866219i	$-0.333456\pi$
$823$	39.1733	−	10.4965i	1.36550	−	0.365884i	0.865832	+	0.500335i	$0.166790\pi$
$824$	−1.29141	+	1.98538i	−0.0449886	+	0.0691640i
$825$	20.9814	−	20.9814i	0.730477	−	0.730477i
$826$	−29.1823	−	32.1879i	−1.01538	−	1.11996i
$827$	−17.2925	+	7.16278i	−0.601319	+	0.249074i	−0.662512	−	0.749052i	$-0.730509\pi$
$827$	−17.2925	+	7.16278i	−0.601319	+	0.249074i	0.0611930	+	0.998126i	$0.480509\pi$
$828$	−9.09620	−	8.19840i	−0.316115	−	0.284914i
$829$	31.0278	+	40.4362i	1.07764	+	1.40441i	0.908034	+	0.418897i	$0.137583\pi$
$829$	31.0278	+	40.4362i	1.07764	+	1.40441i	0.169607	+	0.985512i	$0.445750\pi$
$830$	16.1614	−	7.19075i	0.560972	−	0.249595i
$831$	−7.15953	−	12.4007i	−0.248362	−	0.430175i
$832$	−1.07186	−	1.75495i	−0.0371601	−	0.0608421i
$833$	−0.286808	+	1.90105i	−0.00993730	+	0.0658676i
$834$	−45.1395	−	32.8128i	−1.56305	−	1.13621i
$835$	9.03792	−	1.18987i	0.312770	−	0.0411770i
$836$	−4.36250	+	20.4742i	−0.150880	+	0.708114i
$837$	−1.53795	+	11.6819i	−0.0531592	+	0.403784i
$838$	−22.2829	−	12.1058i	−0.769750	−	0.418186i
$839$	3.61471	−	3.61471i	0.124794	−	0.124794i	−0.641951	−	0.766745i	$-0.721875\pi$
$839$	3.61471	−	3.61471i	0.124794	−	0.124794i	0.766745	+	0.641951i	$0.221875\pi$
$840$	−6.89088	−	8.92611i	−0.237758	−	0.307980i
$841$	17.4072	+	17.4072i	0.600248	+	0.600248i
$842$	−4.04975	−	13.6842i	−0.139564	−	0.471587i
$843$	−9.72364	−	1.28014i	−0.334900	−	0.0440904i
$844$	7.15469	+	4.92249i	0.246275	+	0.169439i
$845$	−1.25858	−	9.55988i	−0.0432965	−	0.328870i
$846$	15.6179	−	2.46967i	0.536953	−	0.0849090i
$847$	0.154083	+	0.179073i	0.00529435	+	0.00615301i
$848$	27.3692	+	16.8091i	0.939863	+	0.577228i
$849$	39.8615	−	23.0141i	1.36804	−	0.789840i
$850$	−1.61140	−	0.619016i	−0.0552706	−	0.0212321i
$851$	−36.5288	+	28.0296i	−1.25219	+	0.960841i
$852$	−7.28277	−	2.58302i	−0.249504	−	0.0884926i
$853$	−16.8601	−	40.7039i	−0.577279	−	1.39368i	−0.895245	−	0.445573i	$-0.853000\pi$
$853$	−16.8601	−	40.7039i	−0.577279	−	1.39368i	0.317966	−	0.948102i	$-0.397000\pi$
$854$	12.8210	−	19.8913i	0.438725	−	0.680667i
$855$	−1.81339	−	1.81339i	−0.0620168	−	0.0620168i
$856$	0.280963	+	0.409454i	0.00960313	+	0.0139949i
$857$	14.1851	+	52.9396i	0.484555	+	1.80838i	0.582057	+	0.813148i	$0.302248\pi$
$857$	14.1851	+	52.9396i	0.484555	+	1.80838i	−0.0975024	+	0.995235i	$0.531085\pi$
$858$	2.42627	−	0.0629340i	0.0828313	−	0.00214853i
$859$	18.7830	+	14.4127i	0.640868	+	0.491755i	0.877331	−	0.479885i	$-0.159322\pi$
$859$	18.7830	+	14.4127i	0.640868	+	0.491755i	−0.236464	+	0.971640i	$0.575988\pi$
$860$	−6.75576	+	13.2427i	−0.230369	+	0.451574i
$861$	12.1489	−	13.5927i	0.414033	−	0.463238i
$862$	17.8766	−	24.5922i	0.608878	−	0.837613i
$863$	−7.71814	−	13.3682i	−0.262728	−	0.455059i	0.704238	−	0.709964i	$-0.251289\pi$
$863$	−7.71814	−	13.3682i	−0.262728	−	0.455059i	−0.966966	+	0.254905i	$0.917956\pi$
$864$	−2.88399	+	21.6988i	−0.0981152	+	0.738209i
$865$	−1.02285	+	1.77162i	−0.0347778	+	0.0602369i
$866$	45.2364	+	4.76584i	1.53720	+	0.161950i
$867$	−13.0913	+	31.6053i	−0.444605	+	1.07337i
$868$	15.6551	−	3.81109i	0.531370	−	0.129357i
$869$	−42.3037	+	17.5228i	−1.43506	+	0.594419i
$870$	−2.12970	+	3.92011i	−0.0722036	+	0.132904i
$871$	0.105129	+	0.392347i	0.00356216	+	0.0132942i
$872$	−8.47274	−	23.9828i	−0.286923	−	0.812159i
$873$	0.0261521	−	0.0976010i	0.000885115	−	0.00330329i
$874$	5.90644	−	24.5753i	0.199788	−	0.831273i
$875$	−15.5855	+	10.2029i	−0.526886	+	0.344920i
$876$	−2.39987	−	2.81270i	−0.0810842	−	0.0950324i
$877$	−0.467158	−	3.54842i	−0.0157748	−	0.119821i	0.981746	−	0.190198i	$-0.0609131\pi$
$877$	−0.467158	−	3.54842i	−0.0157748	−	0.119821i	−0.997520	+	0.0703769i	$0.977580\pi$
$878$	−14.3621	−	5.51715i	−0.484696	−	0.186195i
$879$	14.7691	+	8.52695i	0.498149	+	0.287607i
$880$	−3.52086	−	9.19933i	−0.118688	−	0.310109i
$881$		−	35.8359i		−	1.20734i	−0.797234	−	0.603671i	$-0.793704\pi$
$881$		−	35.8359i		−	1.20734i	0.797234	−	0.603671i	$-0.206296\pi$
$882$	0.0762347	+	10.7464i	0.00256696	+	0.361851i
$883$	−32.8847	−	13.6213i	−1.10666	−	0.458393i	−0.246872	−	0.969048i	$-0.579403\pi$
$883$	−32.8847	−	13.6213i	−1.10666	−	0.458393i	−0.859786	+	0.510655i	$0.829403\pi$
$884$	−0.0607244	−	0.127473i	−0.00204238	−	0.00428740i
$885$	17.3479	+	2.28390i	0.583145	+	0.0767725i
$886$	−22.7425	+	23.9537i	−0.764048	+	0.804740i
$887$	−1.60582	+	5.99300i	−0.0539181	+	0.201225i	−0.987631	−	0.156799i	$-0.949883\pi$
$887$	−1.60582	+	5.99300i	−0.0539181	+	0.201225i	0.933712	+	0.358024i	$0.116549\pi$
$888$	−44.3767	−	14.4553i	−1.48919	−	0.485086i
$889$	30.2565	+	20.6316i	1.01477	+	0.691962i
$890$	9.50874	−	5.82373i	0.318734	−	0.195212i
$891$	−29.0312	−	22.2764i	−0.972581	−	0.746288i
$892$	−50.1144	−	10.6780i	−1.67795	−	0.357527i
$893$	19.8676	+	25.8920i	0.664845	+	0.866442i
$894$	−3.67082	+	34.8427i	−0.122771	+	1.16531i
$895$	−0.701427			−0.0234461
$896$	29.0926	−	7.04425i	0.971915	−	0.235332i
$897$	−2.93042			−0.0978440
$898$	1.41652	−	13.4453i	0.0472698	−	0.448675i
$899$	−3.88051	−	5.05718i	−0.129422	−	0.168666i
$900$	−9.43726	−	2.01083i	−0.314575	−	0.0670276i
$901$	1.74965	+	1.34255i	0.0582891	+	0.0447268i
$902$	13.5800	−	8.31722i	0.452165	−	0.276933i
$903$	48.0422	−	23.1318i	1.59874	−	0.769778i
$904$	−21.8711	−	7.12428i	−0.727422	−	0.236950i
$905$	−0.308472	+	1.15123i	−0.0102540	+	0.0382683i
$906$	39.7779	−	41.8964i	1.32153	−	1.39191i
$907$	−2.55719	−	0.336660i	−0.0849100	−	0.0111786i	0.0879515	−	0.996125i	$-0.471968\pi$
$907$	−2.55719	−	0.336660i	−0.0849100	−	0.0111786i	−0.172861	+	0.984946i	$0.555301\pi$
$908$	21.0928	+	44.2784i	0.699990	+	1.46943i
$909$	12.1581	+	5.03606i	0.403260	+	0.167036i
$910$	−0.705460	−	0.128253i	−0.0233858	−	0.00425154i
$911$			28.7357i			0.952055i	0.879430	+	0.476027i	$0.157924\pi$
$911$			28.7357i			0.952055i	−0.879430	+	0.476027i	$0.842076\pi$
$912$	23.9273	−	9.15772i	0.792314	−	0.303243i
$913$	−47.9944	−	27.7096i	−1.58838	−	0.917053i
$914$	11.1038	+	4.26550i	0.367281	+	0.141090i
$915$	1.24401	+	9.44920i	0.0411257	+	0.312381i
$916$	−14.8160	−	17.3646i	−0.489533	−	0.573743i
$917$	45.6570	+	23.0527i	1.50773	+	0.761267i
$918$	−0.351232	+	1.46140i	−0.0115924	+	0.0482332i
$919$	4.36031	−	16.2729i	0.143833	−	0.536794i	−0.855971	−	0.517024i	$-0.827040\pi$
$919$	4.36031	−	16.2729i	0.143833	−	0.536794i	0.999805	−	0.0197702i	$-0.00629344\pi$
$920$	3.96160	+	11.2136i	0.130610	+	0.369703i
$921$	9.27799	+	34.6259i	0.305720	+	1.14096i
$922$	15.2727	−	28.1122i	0.502978	−	0.925825i
$923$	−0.453942	+	0.188029i	−0.0149417	+	0.00618905i
$924$	−9.92636	+	33.9059i	−0.326553	+	1.11542i
$925$	−13.8841	+	33.5191i	−0.456505	+	1.10210i
$926$	−47.2638	−	4.97944i	−1.55319	−	0.163634i
$927$	−0.454516	+	0.787244i	−0.0149283	+	0.0258565i
$928$	−7.19754	−	9.40406i	−0.236271	−	0.308703i
$929$	−19.9628	−	34.5767i	−0.654960	−	1.13442i	−0.981904	−	0.189380i	$-0.939352\pi$
$929$	−19.9628	−	34.5767i	−0.654960	−	1.13442i	0.326944	−	0.945044i	$-0.393981\pi$
$930$	−3.81541	+	5.24874i	−0.125112	+	0.172113i
$931$	−19.4152	+	10.7269i	−0.636307	+	0.351559i
$932$	15.0098	−	29.4224i	0.491662	−	0.963764i
$933$	28.2167	+	21.6514i	0.923772	+	0.708835i
$934$	0.325767	−	0.00844995i	0.0106594	−	0.000276491i
$935$	−0.175049	−	0.653292i	−0.00572471	−	0.0213649i
$936$	−0.446563	−	0.650786i	−0.0145964	−	0.0212716i
$937$	−7.07585	−	7.07585i	−0.231158	−	0.231158i	0.582018	−	0.813176i	$-0.302263\pi$
$937$	−7.07585	−	7.07585i	−0.231158	−	0.231158i	−0.813176	+	0.582018i	$0.802263\pi$
$938$	−5.90546	−	0.289224i	−0.192820	−	0.00944349i
$939$	19.6483	+	47.4353i	0.641199	+	1.54799i
$940$	−14.4731	−	5.13324i	−0.472060	−	0.167428i
$941$	−14.6630	+	11.2513i	−0.478001	+	0.366783i	−0.819481	−	0.573106i	$-0.805738\pi$
$941$	−14.6630	+	11.2513i	−0.478001	+	0.366783i	0.341480	+	0.939889i	$0.389072\pi$
$942$	48.2831	+	18.5478i	1.57315	+	0.604321i
$943$	−16.6512	+	9.61356i	−0.542237	+	0.313061i
$944$	−24.3077	+	39.5787i	−0.791148	+	1.28818i
$945$	4.97818	+	5.78556i	0.161940	+	0.188204i
$946$	46.0046	−	7.27476i	1.49574	−	0.236523i
$947$	2.60499	+	19.7869i	0.0846509	+	0.642987i	0.980198	+	0.198020i	$0.0634512\pi$
$947$	2.60499	+	19.7869i	0.0846509	+	0.642987i	−0.895547	+	0.444967i	$0.853215\pi$
$948$	46.1679	+	31.7639i	1.49946	+	1.03164i
$949$	−0.233090	−	0.0306868i	−0.00756641	−	0.000996136i
$950$	−5.65172	−	19.0972i	−0.183366	−	0.619596i
$951$	−7.53151	−	7.53151i	−0.244226	−	0.244226i
$952$	2.03693	−	0.274239i	0.0660173	−	0.00888815i
$953$	−4.20814	+	4.20814i	−0.136315	+	0.136315i	−0.771972	−	0.635657i	$-0.780729\pi$
$953$	−4.20814	+	4.20814i	−0.136315	+	0.136315i	0.635657	+	0.771972i	$0.280729\pi$
$954$	10.8322	+	5.88489i	0.350706	+	0.190530i
$955$	−1.24818	+	9.48090i	−0.0403903	+	0.306795i
$956$	11.5347	−	54.1350i	0.373059	−	1.75085i
$957$	13.8575	−	1.82437i	0.447949	−	0.0589736i
$958$	−6.83533	−	4.96874i	−0.220839	−	0.160533i
$959$	−31.3153	−	10.9602i	−1.01123	−	0.353922i
$960$	−7.10026	+	9.74226i	−0.229160	+	0.314430i
$961$	10.8642	+	18.8173i	0.350457	+	0.607009i
$962$	−2.71138	+	1.20638i	−0.0874184	+	0.0388953i
$963$	0.116026	+	0.151208i	0.00373888	+	0.00487261i
$964$	38.7137	+	34.8926i	1.24688	+	1.12382i
$965$	7.55050	−	3.12752i	0.243059	−	0.100678i
$966$	13.0424	−	40.6130i	0.419633	−	1.30670i
$967$	−20.1730	+	20.1730i	−0.648720	+	0.648720i	−0.952684	−	0.303964i	$-0.901690\pi$
$967$	−20.1730	+	20.1730i	−0.648720	+	0.648720i	0.303964	+	0.952684i	$0.401690\pi$
$968$	0.137705	−	0.211704i	0.00442601	−	0.00680441i
$969$	1.69920	−	0.455300i	0.0545863	−	0.0146263i
$970$	−0.0675682	+	0.0711667i	−0.00216948	+	0.00228503i
$971$	−14.9238	+	19.4491i	−0.478928	+	0.624151i	−0.968860	−	0.247610i	$-0.920355\pi$
$971$	−14.9238	+	19.4491i	−0.478928	+	0.624151i	0.489932	+	0.871761i	$0.337022\pi$
$972$	−1.70276	+	21.4998i	−0.0546161	+	0.689605i
$973$	10.5535	−	50.5620i	0.338328	−	1.62094i
$974$	30.1599	−	4.76923i	0.966387	−	0.152816i
$975$	−1.99972	+	1.15454i	−0.0640422	+	0.0369748i
$976$	−24.2502	−	7.20932i	−0.776231	−	0.230765i
$977$	33.3963	+	19.2814i	1.06844	+	0.616865i	0.927755	−	0.373189i	$-0.121736\pi$
$977$	33.3963	+	19.2814i	1.06844	+	0.616865i	0.140687	+	0.990054i	$0.455069\pi$
$978$	−28.9474	+	23.4293i	−0.925635	+	0.749186i
$979$	−32.2749	−	13.3687i	−1.03151	−	0.427265i
$980$	4.91726	−	9.20622i	0.157076	−	0.294082i
$981$	−3.73591	−	9.01928i	−0.119278	−	0.287963i
$982$	−35.9659	+	10.6439i	−1.14772	+	0.339661i
$983$	56.5639	−	15.1562i	1.80411	−	0.483409i	0.809500	−	0.587119i	$-0.199738\pi$
$983$	56.5639	−	15.1562i	1.80411	−	0.483409i	0.994608	+	0.103710i	$0.0330714\pi$
$984$	−17.5846	−	8.40345i	−0.560578	−	0.267892i
$985$	16.7778	+	4.49560i	0.534586	+	0.143242i
$986$	−0.424688	−	0.693413i	−0.0135248	−	0.0220828i
$987$	30.1673	+	46.0824i	0.960237	+	1.46682i
$988$	0.740296	−	1.45114i	0.0235519	−	0.0461669i
$989$	−55.7543	+	7.34020i	−1.77288	+	0.233405i
$990$	−1.53684	−	3.45410i	−0.0488441	−	0.109779i
$991$	12.2087	−	21.1461i	0.387823	−	0.671729i	−0.604333	−	0.796732i	$-0.706560\pi$
$991$	12.2087	−	21.1461i	0.387823	−	0.671729i	0.992156	+	0.125002i	$0.0398938\pi$
$992$	−8.59397	−	14.9278i	−0.272859	−	0.473957i
$993$	−10.7088			−0.339834
$994$	−0.585552	−	7.12808i	−0.0185726	−	0.226089i
$995$	1.33459	−	3.22199i	0.0423094	−	0.102144i
$996$	3.51621	+	67.7339i	0.111416	+	2.14623i
$997$	6.04778	−	45.9374i	0.191535	−	1.45485i	−0.577889	−	0.816115i	$-0.696123\pi$
$997$	6.04778	−	45.9374i	0.191535	−	1.45485i	0.769424	−	0.638738i	$-0.220543\pi$
$998$	−9.56476	+	0.248097i	−0.302767	+	0.00785337i
$999$	30.5133	+	8.17602i	0.965398	+	0.258678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.bd.a.109.17	yes	240
4.3	odd	2		896.2.bh.a.529.25		240
7.2	even	3	inner	224.2.bd.a.205.4	yes	240
28.23	odd	6		896.2.bh.a.401.6		240
32.5	even	8	inner	224.2.bd.a.165.4	yes	240
32.27	odd	8		896.2.bh.a.753.6		240
224.37	even	24	inner	224.2.bd.a.37.17	✓	240
224.219	odd	24		896.2.bh.a.625.25		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.17	✓	240	224.37	even	24	inner
224.2.bd.a.109.17	yes	240	1.1	even	1	trivial
224.2.bd.a.165.4	yes	240	32.5	even	8	inner
224.2.bd.a.205.4	yes	240	7.2	even	3	inner
896.2.bh.a.401.6		240	28.23	odd	6
896.2.bh.a.529.25		240	4.3	odd	2
896.2.bh.a.625.25		240	224.219	odd	24
896.2.bh.a.753.6		240	32.27	odd	8

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.bd (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.148173 - 1.40643i) q^{2} +(-1.23048 - 1.60359i) q^{3} +(-1.95609 - 0.416790i) q^{4} +(0.591453 + 0.453838i) q^{5} +(-2.43766 + 1.49297i) q^{6} +(-2.18592 - 1.49056i) q^{7} +(-0.876026 + 2.68935i) q^{8} +(-0.280969 + 1.04859i) q^{9} +O(q^{10})\)	\(q+(0.148173 - 1.40643i) q^{2} +(-1.23048 - 1.60359i) q^{3} +(-1.95609 - 0.416790i) q^{4} +(0.591453 + 0.453838i) q^{5} +(-2.43766 + 1.49297i) q^{6} +(-2.18592 - 1.49056i) q^{7} +(-0.876026 + 2.68935i) q^{8} +(-0.280969 + 1.04859i) q^{9} +(0.725929 - 0.764591i) q^{10} +(-3.27488 - 0.431146i) q^{11} +(1.73857 + 3.64962i) q^{12} +(0.237482 + 0.0983684i) q^{13} +(-2.42026 + 2.85348i) q^{14} -1.50689i q^{15} +(3.65257 + 1.63056i) q^{16} +(0.237856 + 0.137326i) q^{17} +(1.43314 + 0.550536i) q^{18} +(0.413608 + 3.14167i) q^{19} +(-0.967780 - 1.13426i) q^{20} +(0.299483 + 5.33942i) q^{21} +(-1.09163 + 4.54200i) q^{22} +(1.45977 - 5.44793i) q^{23} +(5.39054 - 1.90439i) q^{24} +(-1.15025 - 4.29278i) q^{25} +(0.173537 - 0.319427i) q^{26} +(-3.57503 + 1.48082i) q^{27} +(3.65460 + 3.82673i) q^{28} +(0.801128 - 1.93409i) q^{29} +(-2.11933 - 0.223280i) q^{30} +(1.52247 - 2.63700i) q^{31} +(2.83448 - 4.89548i) q^{32} +(3.33829 + 5.78208i) q^{33} +(0.228383 - 0.314179i) q^{34} +(-0.616397 - 1.87365i) q^{35} +(0.986643 - 1.93403i) q^{36} +(-6.47662 - 4.96968i) q^{37} +(4.47982 - 0.116200i) q^{38} +(-0.134474 - 0.501865i) q^{39} +(-1.73865 + 1.19305i) q^{40} +(-2.41053 - 2.41053i) q^{41} +(7.55389 + 0.369957i) q^{42} +(-3.81560 - 9.21166i) q^{43} +(6.22626 + 2.20830i) q^{44} +(-0.642070 + 0.492678i) q^{45} +(-7.44583 - 2.86030i) q^{46} +(8.91945 - 5.14965i) q^{47} +(-1.87966 - 7.86360i) q^{48} +(2.55648 + 6.51647i) q^{49} +(-6.20793 + 0.981667i) q^{50} +(-0.0724616 - 0.550400i) q^{51} +(-0.423538 - 0.291398i) q^{52} +(7.96102 + 1.04809i) q^{53} +(1.55295 + 5.24744i) q^{54} +(-1.74127 - 1.74127i) q^{55} +(5.92354 - 4.57292i) q^{56} +(4.52901 - 4.52901i) q^{57} +(-2.60146 - 1.41331i) q^{58} +(-1.51564 + 11.5124i) q^{59} +(-0.628056 + 2.94760i) q^{60} +(-6.27068 + 0.825551i) q^{61} +(-3.48317 - 2.53198i) q^{62} +(2.17716 - 1.87333i) q^{63} +(-6.46516 - 4.71187i) q^{64} +(0.0958163 + 0.165959i) q^{65} +(8.62673 - 3.83832i) q^{66} +(0.961960 + 1.25365i) q^{67} +(-0.408031 - 0.367758i) q^{68} +(-10.5325 + 4.36269i) q^{69} +(-2.72649 + 0.589295i) q^{70} +(-1.35162 + 1.35162i) q^{71} +(-2.57389 - 1.67422i) q^{72} +(-0.883450 + 0.236720i) q^{73} +(-7.94917 + 8.37254i) q^{74} +(-5.46851 + 7.12670i) q^{75} +(0.500361 - 6.31777i) q^{76} +(6.51597 + 5.82384i) q^{77} +(-0.725763 + 0.114766i) q^{78} +(12.0051 - 6.93117i) q^{79} +(1.42032 + 2.62207i) q^{80} +(9.59405 + 5.53913i) q^{81} +(-3.74741 + 3.03306i) q^{82} +(15.5006 + 6.42056i) q^{83} +(1.63960 - 10.5692i) q^{84} +(0.0783567 + 0.189170i) q^{85} +(-13.5209 + 4.00145i) q^{86} +(-4.08727 + 1.09518i) q^{87} +(4.02838 - 8.42958i) q^{88} +(10.2157 + 2.73728i) q^{89} +(0.597779 + 0.976029i) q^{90} +(-0.372493 - 0.569006i) q^{91} +(-5.12608 + 10.0482i) q^{92} +(-6.10204 + 0.803349i) q^{93} +(-5.92099 - 13.3076i) q^{94} +(-1.18118 + 2.04586i) q^{95} +(-11.3381 + 1.47844i) q^{96} -0.0930782 q^{97} +(9.54376 - 2.62995i) q^{98} +(1.37224 - 3.31287i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

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