LMFDB - Embedded newform 207.2.o.a.113.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(5,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("207.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.o (of order $66$, degree $20$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			113.16
Character	$\chi$	$=$	207.113
Dual form			207.2.o.a.11.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15577 + 0.0550561i) q^{2} +(1.68053 - 0.419325i) q^{3} +(-0.658169 - 0.0628475i) q^{4} +(1.35993 - 1.29669i) q^{5} +(1.96539 - 0.392121i) q^{6} +(-0.328461 + 1.70422i) q^{7} +(-3.04784 - 0.438213i) q^{8} +(2.64833 - 1.40937i) q^{9} +O(q^{10})$	\(q+(1.15577 + 0.0550561i) q^{2} +(1.68053 - 0.419325i) q^{3} +(-0.658169 - 0.0628475i) q^{4} +(1.35993 - 1.29669i) q^{5} +(1.96539 - 0.392121i) q^{6} +(-0.328461 + 1.70422i) q^{7} +(-3.04784 - 0.438213i) q^{8} +(2.64833 - 1.40937i) q^{9} +(1.64316 - 1.42381i) q^{10} +(1.28597 + 0.662964i) q^{11} +(-1.13242 + 0.170370i) q^{12} +(-3.21393 + 0.619434i) q^{13} +(-0.473453 + 1.95160i) q^{14} +(1.74167 - 2.74938i) q^{15} +(-2.20005 - 0.424025i) q^{16} +(-0.539040 + 1.18033i) q^{17} +(3.13846 - 1.48311i) q^{18} +(0.474253 - 0.216584i) q^{19} +(-0.976560 + 0.767975i) q^{20} +(0.162634 + 3.00171i) q^{21} +(1.44979 + 0.837035i) q^{22} +(-4.56694 - 1.46392i) q^{23} +(-5.30573 + 0.541608i) q^{24} +(-0.0699058 + 1.46750i) q^{25} +(-3.74867 + 0.538977i) q^{26} +(3.85960 - 3.47900i) q^{27} +(0.323289 - 1.10102i) q^{28} +(0.911812 + 9.54893i) q^{29} +(2.16434 - 3.08176i) q^{30} +(-4.12585 - 3.24461i) q^{31} +(3.46536 + 0.840688i) q^{32} +(2.43910 + 0.574888i) q^{33} +(-0.687991 + 1.33452i) q^{34} +(1.76316 + 2.74353i) q^{35} +(-1.83163 + 0.761165i) q^{36} +(-1.84227 - 6.27421i) q^{37} +(0.560052 - 0.224211i) q^{38} +(-5.14134 + 2.38865i) q^{39} +(-4.71309 + 3.35617i) q^{40} +(3.29867 + 3.45954i) q^{41} +(0.0227052 + 3.47824i) q^{42} +(-6.23549 - 7.92908i) q^{43} +(-0.804721 - 0.517162i) q^{44} +(1.77403 - 5.35073i) q^{45} +(-5.19774 - 1.94339i) q^{46} +(-0.800711 + 0.462291i) q^{47} +(-3.87504 + 0.209952i) q^{48} +(3.70211 + 1.48210i) q^{49} +(-0.161590 + 1.69225i) q^{50} +(-0.410927 + 2.20961i) q^{51} +(2.15424 - 0.205705i) q^{52} +(6.01642 - 6.94332i) q^{53} +(4.65236 - 3.80843i) q^{54} +(2.60850 - 0.765923i) q^{55} +(1.74791 - 5.05024i) q^{56} +(0.706176 - 0.562842i) q^{57} +(0.528118 + 11.0866i) q^{58} +(1.52043 + 7.88872i) q^{59} +(-1.31910 + 1.70010i) q^{60} +(-1.99225 - 4.97639i) q^{61} +(-4.58990 - 3.97717i) q^{62} +(1.53200 + 4.97626i) q^{63} +(8.25844 + 2.42490i) q^{64} +(-3.56751 + 5.00987i) q^{65} +(2.78739 + 0.798726i) q^{66} +(0.990584 + 1.92146i) q^{67} +(0.428960 - 0.742981i) q^{68} +(-8.28872 - 0.545120i) q^{69} +(1.88676 + 3.26797i) q^{70} +(2.73794 - 4.26031i) q^{71} +(-8.68930 + 3.13501i) q^{72} +(-2.08929 - 4.57490i) q^{73} +(-1.78381 - 7.35297i) q^{74} +(0.497883 + 2.49549i) q^{75} +(-0.325751 + 0.112743i) q^{76} +(-1.55222 + 1.97381i) q^{77} +(-6.07372 + 2.47767i) q^{78} +(-12.2233 - 4.23053i) q^{79} +(-3.54175 + 2.27614i) q^{80} +(5.02733 - 7.46498i) q^{81} +(3.62203 + 4.18005i) q^{82} +(1.97130 + 1.87963i) q^{83} +(0.0816093 - 1.98585i) q^{84} +(0.797471 + 2.30414i) q^{85} +(-6.77026 - 9.50750i) q^{86} +(5.53643 + 15.6649i) q^{87} +(-3.62891 - 2.58414i) q^{88} +(-0.261218 - 1.81681i) q^{89} +(2.34496 - 6.08655i) q^{90} -5.68069i q^{91} +(2.91382 + 1.25053i) q^{92} +(-8.29414 - 3.72257i) q^{93} +(-0.950890 + 0.490218i) q^{94} +(0.364109 - 0.909501i) q^{95} +(6.17615 - 0.0403165i) q^{96} +(11.1861 - 2.71372i) q^{97} +(4.19719 + 1.91679i) q^{98} +(4.34004 - 0.0566640i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.15577	+	0.0550561i	0.817253	+	0.0389306i	0.452045	−	0.891995i	$-0.350695\pi$
$2$	1.15577	+	0.0550561i	0.817253	+	0.0389306i	0.365208	+	0.930926i	$0.380998\pi$
$3$	1.68053	−	0.419325i	0.970252	−	0.242098i
$3$	1.68053	−	0.419325i	0.970252	−	0.242098i
$4$	−0.658169	−	0.0628475i	−0.329085	−	0.0314238i
$5$	1.35993	−	1.29669i	0.608181	−	0.579899i	−0.322119	−	0.946699i	$-0.604395\pi$
$5$	1.35993	−	1.29669i	0.608181	−	0.579899i	0.930300	+	0.366800i	$0.119547\pi$
$6$	1.96539	−	0.392121i	0.802367	−	0.160083i
$7$	−0.328461	+	1.70422i	−0.124147	+	0.644133i	0.865535	+	0.500848i	$0.166979\pi$
$7$	−0.328461	+	1.70422i	−0.124147	+	0.644133i	−0.989681	+	0.143285i	$0.954234\pi$
$8$	−3.04784	−	0.438213i	−1.07757	−	0.154932i
$9$	2.64833	−	1.40937i	0.882778	−	0.469791i
$10$	1.64316	−	1.42381i	0.519613	−	0.450248i
$11$	1.28597	+	0.662964i	0.387735	+	0.199891i	0.641061	−	0.767490i	$-0.278494\pi$
$11$	1.28597	+	0.662964i	0.387735	+	0.199891i	−0.253327	+	0.967381i	$0.581525\pi$
$12$	−1.13242	+	0.170370i	−0.326903	+	0.0491816i
$13$	−3.21393	+	0.619434i	−0.891383	+	0.171800i	−0.614325	−	0.789053i	$-0.710572\pi$
$13$	−3.21393	+	0.619434i	−0.891383	+	0.171800i	−0.277058	+	0.960853i	$0.589359\pi$
$14$	−0.473453	+	1.95160i	−0.126536	+	0.521587i
$15$	1.74167	−	2.74938i	0.449696	−	0.709887i
$16$	−2.20005	−	0.424025i	−0.550012	−	0.106006i
$17$	−0.539040	+	1.18033i	−0.130736	+	0.286273i	−0.963668	−	0.267103i	$-0.913933\pi$
$17$	−0.539040	+	1.18033i	−0.130736	+	0.286273i	0.832932	+	0.553376i	$0.186661\pi$
$18$	3.13846	−	1.48311i	0.739742	−	0.349571i
$19$	0.474253	−	0.216584i	0.108801	−	0.0496878i	−0.360271	−	0.932848i	$-0.617316\pi$
$19$	0.474253	−	0.216584i	0.108801	−	0.0496878i	0.469072	+	0.883160i	$0.344588\pi$
$20$	−0.976560	+	0.767975i	−0.218365	+	0.171725i
$21$	0.162634	+	3.00171i	0.0354897	+	0.655027i
$22$	1.44979	+	0.837035i	0.309096	+	0.178456i
$23$	−4.56694	−	1.46392i	−0.952273	−	0.305248i
$23$	−4.56694	−	1.46392i	−0.952273	−	0.305248i
$24$	−5.30573	+	0.541608i	−1.08303	+	0.110555i
$25$	−0.0699058	+	1.46750i	−0.0139812	+	0.293501i
$26$	−3.74867	+	0.538977i	−0.735174	+	0.105702i
$27$	3.85960	−	3.47900i	0.742781	−	0.669534i
$28$	0.323289	−	1.10102i	0.0610958	−	0.208073i
$29$	0.911812	+	9.54893i	0.169319	+	1.77319i	0.537332	+	0.843371i	$0.319432\pi$
$29$	0.911812	+	9.54893i	0.169319	+	1.77319i	−0.368013	+	0.929821i	$0.619962\pi$
$30$	2.16434	−	3.08176i	0.395152	−	0.562651i
$31$	−4.12585	−	3.24461i	−0.741025	−	0.582748i	0.174668	−	0.984627i	$-0.444115\pi$
$31$	−4.12585	−	3.24461i	−0.741025	−	0.582748i	−0.915693	+	0.401879i	$0.868357\pi$
$32$	3.46536	+	0.840688i	0.612595	+	0.148614i
$33$	2.43910	+	0.574888i	0.424594	+	0.100075i
$34$	−0.687991	+	1.33452i	−0.117989	+	0.228868i
$35$	1.76316	+	2.74353i	0.298029	+	0.463742i
$36$	−1.83163	+	0.761165i	−0.305271	+	0.126861i
$37$	−1.84227	−	6.27421i	−0.302868	−	1.03147i	−0.960534	−	0.278163i	$-0.910274\pi$
$37$	−1.84227	−	6.27421i	−0.302868	−	1.03147i	0.657666	−	0.753310i	$-0.271544\pi$
$38$	0.560052	−	0.224211i	0.0908525	−	0.0363719i
$39$	−5.14134	+	2.38865i	−0.823274	+	0.382491i
$40$	−4.71309	+	3.35617i	−0.745205	+	0.530658i
$41$	3.29867	+	3.45954i	0.515165	+	0.540290i	0.929009	−	0.370058i	$-0.120662\pi$
$41$	3.29867	+	3.45954i	0.515165	+	0.540290i	−0.413843	+	0.910348i	$0.635814\pi$
$42$	0.0227052	+	3.47824i	0.00350349	+	0.536705i
$43$	−6.23549	−	7.92908i	−0.950904	−	1.20917i	−0.977801	−	0.209535i	$-0.932805\pi$
$43$	−6.23549	−	7.92908i	−0.950904	−	1.20917i	0.0268972	−	0.999638i	$-0.491437\pi$
$44$	−0.804721	−	0.517162i	−0.121316	−	0.0779652i
$45$	1.77403	−	5.35073i	0.264457	−	0.797640i
$46$	−5.19774	−	1.94339i	−0.766365	−	0.286538i
$47$	−0.800711	+	0.462291i	−0.116796	+	0.0674320i	−0.557260	−	0.830338i	$-0.688147\pi$
$47$	−0.800711	+	0.462291i	−0.116796	+	0.0674320i	0.440464	+	0.897770i	$0.354814\pi$
$48$	−3.87504	+	0.209952i	−0.559314	+	0.0303039i
$49$	3.70211	+	1.48210i	0.528873	+	0.211729i
$50$	−0.161590	+	1.69225i	−0.0228523	+	0.239320i
$51$	−0.410927	+	2.20961i	−0.0575413	+	0.309407i
$52$	2.15424	−	0.205705i	0.298739	−	0.0285261i
$53$	6.01642	−	6.94332i	0.826419	−	0.953739i	−0.173095	−	0.984905i	$-0.555377\pi$
$53$	6.01642	−	6.94332i	0.826419	−	0.953739i	0.999514	+	0.0311666i	$0.00992224\pi$
$54$	4.65236	−	3.80843i	0.633106	−	0.518262i
$55$	2.60850	−	0.765923i	0.351729	−	0.103277i
$56$	1.74791	−	5.05024i	0.233574	−	0.674867i
$57$	0.706176	−	0.562842i	0.0935352	−	0.0745502i
$58$	0.528118	+	11.0866i	0.0693454	+	1.45574i
$59$	1.52043	+	7.88872i	0.197943	+	1.02702i	0.935924	+	0.352203i	$0.114567\pi$
$59$	1.52043	+	7.88872i	0.197943	+	1.02702i	−0.737981	+	0.674821i	$0.764221\pi$
$60$	−1.31910	+	1.70010i	−0.170295	+	0.219482i
$61$	−1.99225	−	4.97639i	−0.255081	−	0.637162i	0.744453	−	0.667675i	$-0.232710\pi$
$61$	−1.99225	−	4.97639i	−0.255081	−	0.637162i	−0.999534	+	0.0305128i	$0.990286\pi$
$62$	−4.58990	−	3.97717i	−0.582918	−	0.505101i
$63$	1.53200	+	4.97626i	0.193014	+	0.626949i
$64$	8.25844	+	2.42490i	1.03231	+	0.303112i
$65$	−3.56751	+	5.00987i	−0.442495	+	0.621397i
$66$	2.78739	+	0.798726i	0.343104	+	0.0983164i
$67$	0.990584	+	1.92146i	0.121019	+	0.234744i	0.941561	−	0.336842i	$-0.109359\pi$
$67$	0.990584	+	1.92146i	0.121019	+	0.234744i	−0.820542	+	0.571586i	$0.806328\pi$
$68$	0.428960	−	0.742981i	0.0520191	−	0.0900997i
$69$	−8.28872	−	0.545120i	−0.997844	−	0.0656247i
$70$	1.88676	+	3.26797i	0.225511	+	0.390597i
$71$	2.73794	−	4.26031i	0.324933	−	0.505606i	−0.639904	−	0.768455i	$-0.721026\pi$
$71$	2.73794	−	4.26031i	0.324933	−	0.505606i	0.964837	+	0.262849i	$0.0846621\pi$
$72$	−8.68930	+	3.13501i	−1.02404	+	0.369465i
$73$	−2.08929	−	4.57490i	−0.244533	−	0.535452i	0.747074	−	0.664741i	$-0.231458\pi$
$73$	−2.08929	−	4.57490i	−0.244533	−	0.535452i	−0.991607	+	0.129289i	$0.958731\pi$
$74$	−1.78381	−	7.35297i	−0.207364	−	0.854766i
$75$	0.497883	+	2.49549i	0.0574905	+	0.288154i
$76$	−0.325751	+	0.112743i	−0.0373662	+	0.0129326i
$77$	−1.55222	+	1.97381i	−0.176892	+	0.224937i
$78$	−6.07372	+	2.47767i	−0.687714	+	0.280541i
$79$	−12.2233	−	4.23053i	−1.37523	−	0.475972i	−0.463257	−	0.886224i	$-0.653319\pi$
$79$	−12.2233	−	4.23053i	−1.37523	−	0.475972i	−0.911972	+	0.410252i	$0.865441\pi$
$80$	−3.54175	+	2.27614i	−0.395979	+	0.254481i
$81$	5.02733	−	7.46498i	0.558592	−	0.829442i
$82$	3.62203	+	4.18005i	0.399987	+	0.461609i
$83$	1.97130	+	1.87963i	0.216378	+	0.206316i	0.790514	−	0.612444i	$-0.209813\pi$
$83$	1.97130	+	1.87963i	0.216378	+	0.206316i	−0.574136	+	0.818760i	$0.694662\pi$
$84$	0.0816093	−	1.98585i	0.00890431	−	0.216675i
$85$	0.797471	+	2.30414i	0.0864979	+	0.249919i
$86$	−6.77026	−	9.50750i	−0.730056	−	1.02522i
$87$	5.53643	+	15.6649i	0.593568	+	1.67945i
$88$	−3.62891	−	2.58414i	−0.386843	−	0.275470i
$89$	−0.261218	−	1.81681i	−0.0276891	−	0.192582i	0.971282	−	0.237931i	$-0.0764691\pi$
$89$	−0.261218	−	1.81681i	−0.0276891	−	0.192582i	−0.998971	+	0.0453489i	$0.985560\pi$
$90$	2.34496	−	6.08655i	0.247181	−	0.641578i
$91$		−	5.68069i		−	0.595498i
$92$	2.91382	+	1.25053i	0.303786	+	0.130376i
$93$	−8.29414	−	3.72257i	−0.860063	−	0.386012i
$94$	−0.950890	+	0.490218i	−0.0980768	+	0.0505621i
$95$	0.364109	−	0.909501i	0.0373568	−	0.0933129i
$96$	6.17615	−	0.0403165i	0.630351	−	0.00411479i
$97$	11.1861	−	2.71372i	1.13578	−	0.275537i	0.376572	−	0.926387i	$-0.377103\pi$
$97$	11.1861	−	2.71372i	1.13578	−	0.275537i	0.759206	+	0.650851i	$0.225588\pi$
$98$	4.19719	+	1.91679i	0.423980	+	0.193625i
$99$	4.34004	−	0.0566640i	0.436191	−	0.00569495i
$100$	0.138239	−	0.961472i	0.0138239	−	0.0961472i
$101$	−0.281173	+	0.294886i	−0.0279778	+	0.0293422i	−0.737574	−	0.675266i	$-0.764029\pi$
$101$	−0.281173	+	0.294886i	−0.0279778	+	0.0293422i	0.709596	+	0.704608i	$0.248877\pi$
$102$	−0.596590	+	2.53118i	−0.0590712	+	0.250624i
$103$	17.2986	−	0.824032i	1.70448	−	0.0811943i	0.827422	−	0.561581i	$-0.189807\pi$
$103$	17.2986	−	0.824032i	1.70448	−	0.0811943i	0.877057	+	0.480387i	$0.159504\pi$
$104$	10.0670	−	0.479549i	0.987148	−	0.0470237i
$105$	4.11347	+	3.87124i	0.401434	+	0.377794i
$106$	7.33588	−	7.69365i	0.712523	−	0.747273i
$107$	−1.06272	+	7.39141i	−0.102737	+	0.714554i	0.871724	+	0.489998i	$0.163002\pi$
$107$	−1.06272	+	7.39141i	−0.102737	+	0.714554i	−0.974461	+	0.224556i	$0.927907\pi$
$108$	−2.75892	+	2.04720i	−0.265477	+	0.196992i
$109$	17.8758	+	8.16361i	1.71219	+	0.781932i	0.996507	+	0.0835078i	$0.0266124\pi$
$109$	17.8758	+	8.16361i	1.71219	+	0.781932i	0.715684	+	0.698424i	$0.246115\pi$
$110$	3.05699	−	0.741618i	0.291473	−	0.0707105i
$111$	−5.72692	−	9.77145i	−0.543575	−	0.927465i
$112$	1.44526	−	3.61008i	0.136564	−	0.341121i
$113$	10.0367	−	5.17427i	0.944172	−	0.486754i	0.0838345	−	0.996480i	$-0.473283\pi$
$113$	10.0367	−	5.17427i	0.944172	−	0.486754i	0.860337	+	0.509725i	$0.170253\pi$
$114$	0.847165	−	0.611637i	0.0793443	−	0.0572850i
$115$	−8.10899	+	3.93109i	−0.756167	+	0.366576i
$116$		−	6.34211i		−	0.588851i
$117$	−7.63853	+	6.17009i	−0.706183	+	0.570425i
$118$	1.32294	+	9.20126i	0.121787	+	0.847045i
$119$	−1.83449	−	1.30633i	−0.168167	−	0.119751i
$120$	−6.51314	+	7.61645i	−0.594565	+	0.695284i
$121$	−5.16643	−	7.25523i	−0.469675	−	0.659566i
$122$	−2.02860	−	5.86125i	−0.183661	−	0.530653i
$123$	6.99417	+	4.43064i	0.630643	+	0.399497i
$124$	2.51159	+	2.39480i	0.225548	+	0.215059i
$125$	7.96042	+	9.18681i	0.712001	+	0.821694i
$126$	1.49667	+	5.83576i	0.133334	+	0.519891i
$127$	−3.07414	+	1.97563i	−0.272786	+	0.175309i	−0.669881	−	0.742469i	$-0.733655\pi$
$127$	−3.07414	+	1.97563i	−0.272786	+	0.175309i	0.397095	+	0.917778i	$0.370018\pi$
$128$	2.67184	+	0.924733i	0.236159	+	0.0817356i
$129$	−13.8038	−	10.7103i	−1.21535	−	0.942991i
$130$	−4.39905	+	5.59384i	−0.385822	+	0.490612i
$131$	5.33339	−	1.84590i	0.465981	−	0.161277i	−0.0839811	−	0.996467i	$-0.526764\pi$
$131$	5.33339	−	1.84590i	0.465981	−	0.161277i	0.549962	+	0.835190i	$0.314642\pi$
$132$	−1.56921	−	0.531665i	−0.136582	−	0.0462755i
$133$	0.213333	+	0.879370i	0.0184983	+	0.0762510i
$134$	1.03910	+	2.27531i	0.0897645	+	0.196557i
$135$	0.737606	−	9.73593i	0.0634830	−	0.837936i
$136$	2.16014	−	3.36125i	0.185231	−	0.288225i
$137$	−8.34593	−	14.4556i	−0.713041	−	1.23502i	−0.963710	−	0.266950i	$-0.913984\pi$
$137$	−8.34593	−	14.4556i	−0.713041	−	1.23502i	0.250669	−	0.968073i	$-0.419349\pi$
$138$	−9.54984	−	1.08638i	−0.812937	−	0.0924787i
$139$	0.423057	−	0.732756i	0.0358832	−	0.0621515i	−0.847526	−	0.530754i	$-0.821909\pi$
$139$	0.423057	−	0.732756i	0.0358832	−	0.0621515i	0.883409	+	0.468602i	$0.155242\pi$
$140$	−0.988034	−	1.91652i	−0.0835042	−	0.161975i
$141$	−1.15177	+	1.11265i	−0.0969961	+	0.0937020i
$142$	3.39898	−	4.77320i	0.285236	−	0.400558i
$143$	−4.54368	−	1.33414i	−0.379961	−	0.111567i
$144$	−6.42407	+	1.97773i	−0.535339	+	0.164811i
$145$	13.6220	+	11.8036i	1.13125	+	0.980232i
$146$	−2.16286	−	5.40257i	−0.179000	−	0.447120i
$147$	6.84297	+	0.938321i	0.564399	+	0.0773914i
$148$	0.818209	+	4.24527i	0.0672564	+	0.348959i
$149$	−0.434759	−	9.12672i	−0.0356169	−	0.747690i	−0.944078	−	0.329721i	$-0.893045\pi$
$149$	−0.434759	−	9.12672i	−0.0356169	−	0.747690i	0.908461	−	0.417969i	$-0.137258\pi$
$150$	0.438046	+	2.91163i	0.0357663	+	0.237733i
$151$	−5.71783	+	16.5206i	−0.465310	+	1.34443i	0.431541	+	0.902093i	$0.357970\pi$
$151$	−5.71783	+	16.5206i	−0.465310	+	1.34443i	−0.896851	+	0.442332i	$0.854151\pi$
$152$	−1.54036	+	0.452290i	−0.124940	+	0.0366856i
$153$	0.235973	+	3.88562i	0.0190773	+	0.314134i
$154$	−1.90269	+	2.19582i	−0.153323	+	0.176944i
$155$	−9.81814	+	0.937519i	−0.788612	+	0.0753033i
$156$	3.53399	−	1.24902i	0.282946	−	0.100001i
$157$	−0.595043	+	6.23157i	−0.0474896	+	0.497334i	0.940169	+	0.340709i	$0.110667\pi$
$157$	−0.595043	+	6.23157i	−0.0474896	+	0.497334i	−0.987658	+	0.156624i	$0.949939\pi$
$158$	−13.8944	−	5.56249i	−1.10538	−	0.442528i
$159$	7.19924	−	14.1913i	0.570937	−	1.12544i
$160$	5.80278	−	3.35023i	0.458750	−	0.264859i
$161$	3.99490	−	7.30221i	0.314842	−	0.575495i
$162$	6.22144	−	8.35102i	0.488802	−	0.656118i
$163$	−7.45458	−	4.79077i	−0.583888	−	0.375242i	0.215098	−	0.976593i	$-0.430993\pi$
$163$	−7.45458	−	4.79077i	−0.583888	−	0.375242i	−0.798985	+	0.601351i	$0.794629\pi$
$164$	−1.95366	−	2.48428i	−0.152555	−	0.193990i
$165$	4.06247	−	2.38096i	0.316263	−	0.185358i
$166$	2.17488	+	2.28095i	0.168804	+	0.177036i
$167$	−8.05922	+	5.73894i	−0.623641	+	0.444093i	−0.847695	−	0.530484i	$-0.822010\pi$
$167$	−8.05922	+	5.73894i	−0.623641	+	0.444093i	0.224054	+	0.974577i	$0.428071\pi$
$168$	0.819707	−	9.22000i	0.0632417	−	0.711339i
$169$	−2.12316	+	0.849984i	−0.163320	+	0.0653834i
$170$	0.794837	+	2.70696i	0.0609612	+	0.207615i
$171$	0.950732	−	1.24199i	0.0727043	−	0.0949771i
$172$	3.60569	+	5.61056i	0.274931	+	0.427801i
$173$	−0.688046	+	1.33462i	−0.0523112	+	0.101470i	−0.913542	−	0.406745i	$-0.866664\pi$
$173$	−0.688046	+	1.33462i	−0.0523112	+	0.101470i	0.861231	+	0.508214i	$0.169694\pi$
$174$	5.53640	+	18.4098i	0.419713	+	1.39564i
$175$	−2.47798	−	0.601152i	−0.187318	−	0.0454428i
$176$	−2.54808	−	2.00384i	−0.192069	−	0.151045i
$177$	5.86306	+	12.6196i	0.440694	+	0.948551i
$178$	−0.201882	−	2.11420i	−0.0151317	−	0.158466i
$179$	−3.78038	+	12.8748i	−0.282559	+	0.962308i	0.688851	+	0.724902i	$0.258115\pi$
$179$	−3.78038	+	12.8748i	−0.282559	+	0.962308i	−0.971411	+	0.237406i	$0.923703\pi$
$180$	−1.50389	+	3.41019i	−0.112093	+	0.254181i
$181$	−16.9894	+	2.44271i	−1.26281	+	0.181565i	−0.741005	−	0.671499i	$-0.765651\pi$
$181$	−16.9894	+	2.44271i	−1.26281	+	0.181565i	−0.521806	+	0.853064i	$0.674742\pi$
$182$	0.312757	−	6.56557i	0.0231831	−	0.486672i
$183$	−5.43475	−	7.52756i	−0.401748	−	0.556453i
$184$	13.2778	+	6.46308i	0.978852	+	0.476465i
$185$	−10.6411	−	6.14364i	−0.782349	−	0.451689i
$186$	−9.38118	−	4.75908i	−0.687861	−	0.348953i
$187$	−1.47571	+	1.16051i	−0.107914	+	0.0848648i
$188$	0.556057	−	0.253943i	0.0405546	−	0.0185207i
$189$	4.66124	+	7.72032i	0.339055	+	0.561570i
$190$	0.470901	−	1.03113i	0.0341627	−	0.0748059i
$191$	−9.75506	−	1.88013i	−0.705851	−	0.136042i	−0.176321	−	0.984333i	$-0.556420\pi$
$191$	−9.75506	−	1.88013i	−0.705851	−	0.136042i	−0.529530	+	0.848291i	$0.677632\pi$
$192$	14.8953	+	0.612129i	1.07498	+	0.0441766i
$193$	−0.443757	+	1.82919i	−0.0319424	+	0.131668i	−0.985550	−	0.169383i	$-0.945822\pi$
$193$	−0.443757	+	1.82919i	−0.0319424	+	0.131668i	0.953608	+	0.301051i	$0.0973376\pi$
$194$	13.0780	−	2.52058i	0.938945	−	0.180967i
$195$	−3.89453	+	9.91516i	−0.278893	+	0.710039i
$196$	−2.34347	−	1.20814i	−0.167391	−	0.0862958i
$197$	−1.48516	+	1.28690i	−0.105813	+	0.0916876i	−0.706161	−	0.708052i	$-0.749574\pi$
$197$	−1.48516	+	1.28690i	−0.105813	+	0.0916876i	0.600348	+	0.799739i	$0.295029\pi$
$198$	5.01921	+	0.173455i	0.356700	+	0.0123269i
$199$	−24.7090	−	3.55262i	−1.75158	−	0.251839i	−0.809472	−	0.587158i	$-0.800247\pi$
$199$	−24.7090	−	3.55262i	−1.75158	−	0.251839i	−0.942105	+	0.335319i	$0.891156\pi$
$200$	0.856141	−	4.44208i	0.0605383	−	0.314103i
$201$	2.47042	+	2.81369i	0.174250	+	0.198463i
$202$	−0.341207	+	0.325340i	−0.0240072	+	0.0228908i
$203$	−16.5729	−	1.58252i	−1.16319	−	0.111071i
$204$	0.409328	−	1.42847i	0.0286587	−	0.100013i
$205$	8.97194	+	0.427386i	0.626627	+	0.0298499i
$206$	20.0385			1.39615
$207$	−14.1580	+	2.55958i	−0.984048	+	0.177903i
$208$	7.33345			0.508483
$209$	0.753463	+	0.0358919i	0.0521182	+	0.00248269i
$210$	4.54109	+	4.70074i	0.313365	+	0.324382i
$211$	6.91945	+	0.660727i	0.476354	+	0.0454863i	0.330472	−	0.943816i	$-0.392792\pi$
$211$	6.91945	+	0.660727i	0.476354	+	0.0454863i	0.145882	+	0.989302i	$0.453398\pi$
$212$	−4.39619	+	4.19176i	−0.301932	+	0.287891i
$213$	2.81472	−	8.30765i	0.192861	−	0.569231i
$214$	−1.63521	+	8.48426i	−0.111780	+	0.579972i
$215$	−18.7614	−	2.69749i	−1.27952	−	0.183967i
$216$	−13.2880	+	8.91211i	−0.904134	+	0.606392i
$217$	6.88469	−	5.96562i	0.467363	−	0.404973i
$218$	20.2109	+	10.4194i	1.36885	+	0.705693i
$219$	−5.42948	−	6.81215i	−0.366890	−	0.460323i
$220$	−1.76497	+	0.340170i	−0.118994	+	0.0229342i
$221$	1.00130	−	4.12740i	0.0673545	−	0.277639i
$222$	−6.08103	−	11.6089i	−0.408132	−	0.779136i
$223$	−26.3394	−	5.07651i	−1.76382	−	0.339948i	−0.798694	−	0.601737i	$-0.794476\pi$
$223$	−26.3394	−	5.07651i	−1.76382	−	0.339948i	−0.965125	+	0.261789i	$0.915688\pi$
$224$	−2.57095	+	5.62960i	−0.171779	+	0.376143i
$225$	1.88313	+	3.98496i	0.125542	+	0.265664i
$226$	11.8850	−	5.42769i	0.790577	−	0.361044i
$227$	−17.6095	+	13.8482i	−1.16878	+	0.919140i	−0.997811	−	0.0661356i	$-0.978933\pi$
$227$	−17.6095	+	13.8482i	−1.16878	+	0.919140i	−0.170971	+	0.985276i	$0.554691\pi$
$228$	−0.500156	+	0.326064i	−0.0331237	+	0.0215941i
$229$	2.06114	+	1.19000i	0.136204	+	0.0786372i	0.566553	−	0.824025i	$-0.308276\pi$
$229$	2.06114	+	1.19000i	0.136204	+	0.0786372i	−0.430350	+	0.902662i	$0.641610\pi$
$230$	−9.58856	+	4.09699i	−0.632251	+	0.270147i
$231$	−1.78088	+	3.96793i	−0.117174	+	0.261071i
$232$	1.40541	−	29.5032i	0.0922696	−	1.93698i
$233$	25.3965	−	3.65146i	1.66378	−	0.239215i	0.754768	−	0.655991i	$-0.227749\pi$
$233$	25.3965	−	3.65146i	1.66378	−	0.239215i	0.909009	+	0.416776i	$0.136840\pi$
$234$	−9.16809	+	6.71066i	−0.599337	+	0.438690i
$235$	−0.489464	+	1.66696i	−0.0319291	+	0.108741i
$236$	−0.504911	−	5.28767i	−0.0328669	−	0.344198i
$237$	−22.3155	−	1.98397i	−1.44955	−	0.128873i
$238$	−2.04833	−	1.61082i	−0.132773	−	0.104414i
$239$	14.6256	+	3.54813i	0.946051	+	0.229510i	0.678971	−	0.734165i	$-0.262426\pi$
$239$	14.6256	+	3.54813i	0.946051	+	0.229510i	0.267080	+	0.963674i	$0.413941\pi$
$240$	−4.99755	+	5.31026i	−0.322591	+	0.342776i
$241$	−9.12659	+	17.7031i	−0.587895	+	1.14036i	0.387906	+	0.921699i	$0.373198\pi$
$241$	−9.12659	+	17.7031i	−0.587895	+	1.14036i	−0.975801	+	0.218659i	$0.929832\pi$
$242$	−5.57176	−	8.66983i	−0.358166	−	0.557318i
$243$	5.31831	−	14.6532i	0.341169	−	0.940002i
$244$	0.998482	+	3.40052i	0.0639212	+	0.217696i
$245$	6.95645	−	2.78494i	0.444431	−	0.177923i
$246$	7.83972	+	5.50587i	0.499842	+	0.351042i
$247$	−1.39006	+	0.989854i	−0.0884471	+	0.0629829i
$248$	11.1531	+	11.6970i	0.708223	+	0.742763i
$249$	4.10100	+	2.33215i	0.259890	+	0.147794i
$250$	8.69463	+	11.0561i	0.549897	+	0.699250i
$251$	5.89738	+	3.79001i	0.372239	+	0.239224i	0.713363	−	0.700795i	$-0.247171\pi$
$251$	5.89738	+	3.79001i	0.372239	+	0.239224i	−0.341124	+	0.940018i	$0.610808\pi$
$252$	−0.695573	−	3.37150i	−0.0438170	−	0.212385i
$253$	−4.90243	−	4.91027i	−0.308213	−	0.308706i
$254$	−3.66177	+	2.11412i	−0.229760	+	0.132652i
$255$	2.30636	+	3.53777i	0.144430	+	0.221544i
$256$	−12.9440	−	5.18198i	−0.808998	−	0.323874i
$257$	−2.85609	+	29.9103i	−0.178158	+	1.86575i	0.258347	+	0.966052i	$0.416822\pi$
$257$	−2.85609	+	29.9103i	−0.178158	+	1.86575i	−0.436505	+	0.899702i	$0.643784\pi$
$258$	−15.3643	−	13.1387i	−0.956541	−	0.817977i
$259$	11.2977	−	1.07880i	0.702006	−	0.0670335i
$260$	2.66288	−	3.07313i	0.165145	−	0.190587i
$261$	15.8728	+	24.0037i	0.982501	+	1.48579i
$262$	6.26581	−	1.83981i	0.387103	−	0.113664i
$263$	7.41686	−	21.4296i	0.457343	−	1.32141i	−0.446975	−	0.894546i	$-0.647499\pi$
$263$	7.41686	−	21.4296i	0.457343	−	1.32141i	0.904318	−	0.426859i	$-0.140380\pi$
$264$	−7.18208	−	2.82101i	−0.442026	−	0.173621i
$265$	−0.821429	−	17.2439i	−0.0504600	−	1.05928i
$266$	0.198149	+	1.02810i	0.0121493	+	0.0630366i
$267$	−1.20082	−	2.94367i	−0.0734890	−	0.180149i
$268$	−0.531212	−	1.32690i	−0.0324490	−	0.0810536i
$269$	−9.97359	−	8.64216i	−0.608100	−	0.526922i	0.295475	−	0.955350i	$-0.404522\pi$
$269$	−9.97359	−	8.64216i	−0.608100	−	0.526922i	−0.903576	+	0.428428i	$0.859067\pi$
$270$	1.38853	−	11.2119i	0.0845030	−	0.682334i
$271$	−23.2275	−	6.82021i	−1.41097	−	0.414298i	−0.514533	−	0.857470i	$-0.672035\pi$
$271$	−23.2275	−	6.82021i	−1.41097	−	0.414298i	−0.896436	+	0.443172i	$0.853853\pi$
$272$	1.68640	−	2.36822i	0.102253	−	0.143594i
$273$	−2.38206	−	9.54654i	−0.144169	−	0.577783i
$274$	−8.85011	−	17.1668i	−0.534655	−	1.03709i
$275$	−1.06280	+	1.84082i	−0.0640892	+	0.111006i
$276$	5.42112	+	0.879707i	0.326313	+	0.0529521i
$277$	8.67690	+	15.0288i	0.521345	+	0.902995i	0.999692	+	0.0248246i	$0.00790273\pi$
$277$	8.67690	+	15.0288i	0.521345	+	0.902995i	−0.478347	+	0.878171i	$0.658764\pi$
$278$	0.529299	−	0.823606i	0.0317453	−	0.0493966i
$279$	−15.4995	−	2.77793i	−0.927930	−	0.166310i
$280$	−4.17158	−	9.13449i	−0.249300	−	0.545890i
$281$	4.36706	+	18.0012i	0.260517	+	1.07386i	0.940272	+	0.340425i	$0.110571\pi$
$281$	4.36706	+	18.0012i	0.260517	+	1.07386i	−0.679755	+	0.733439i	$0.737914\pi$
$282$	−1.39243	+	1.22256i	−0.0829183	+	0.0728022i
$283$	−9.87814	+	3.41886i	−0.587194	+	0.203230i	−0.604480	−	0.796621i	$-0.706619\pi$
$283$	−9.87814	+	3.41886i	−0.587194	+	0.203230i	0.0172852	+	0.999851i	$0.494498\pi$
$284$	−2.06978	+	2.63193i	−0.122819	+	0.156177i
$285$	0.230518	−	1.68112i	0.0136547	−	0.0995810i
$286$	−5.17800	−	1.79212i	−0.306181	−	0.105970i
$287$	−6.97929	+	4.48532i	−0.411975	+	0.264760i
$288$	10.3623	−	2.65757i	0.610603	−	0.156599i
$289$	10.0300	+	11.5753i	0.590001	+	0.680897i
$290$	15.0941	+	14.3922i	0.886356	+	0.845138i
$291$	17.6606	−	9.25110i	1.03528	−	0.542309i
$292$	1.08758	+	3.14237i	0.0636460	+	0.183893i
$293$	−4.22002	−	5.92618i	−0.246536	−	0.346211i	0.672702	−	0.739913i	$-0.265134\pi$
$293$	−4.22002	−	5.92618i	−0.246536	−	0.346211i	−0.919238	+	0.393702i	$0.871194\pi$
$294$	7.85724	+	1.46123i	0.458244	+	0.0852207i
$295$	12.2969	+	8.75661i	0.715955	+	0.509829i
$296$	2.86551	+	19.9301i	0.166555	+	1.15841i
$297$	7.26979	−	1.91511i	0.421836	−	0.111126i
$298$		−	10.5723i		−	0.612439i
$299$	15.5846	+	1.87601i	0.901281	+	0.108493i
$300$	−0.170856	−	1.67375i	−0.00986436	−	0.0966337i
$301$	15.5610	−	8.02224i	0.896920	−	0.462394i
$302$	−7.51805	+	18.7792i	−0.432615	+	1.08062i
$303$	−0.348865	+	0.613466i	−0.0200418	+	0.0352427i
$304$	−1.13522	+	0.275401i	−0.0651092	+	0.0157953i
$305$	−9.16218	−	4.18423i	−0.524625	−	0.239588i
$306$	0.0588031	+	4.50388i	0.00336155	+	0.257470i
$307$	4.68616	−	32.5929i	0.267453	−	1.86018i	−0.204921	−	0.978778i	$-0.565694\pi$
$307$	4.68616	−	32.5929i	0.267453	−	1.86018i	0.472374	−	0.881398i	$-0.343397\pi$
$308$	1.14568	−	1.20155i	0.0652809	−	0.0684647i
$309$	28.7251	−	8.63853i	1.63412	−	0.491429i
$310$	−11.3991	+	0.543008i	−0.647427	+	0.0308408i
$311$	7.47561	−	0.356107i	0.423903	−	0.0201930i	0.165453	−	0.986218i	$-0.447091\pi$
$311$	7.47561	−	0.356107i	0.423903	−	0.0201930i	0.258450	+	0.966025i	$0.416788\pi$
$312$	16.7167	−	5.02723i	0.946398	−	0.284611i
$313$	15.8348	−	16.6070i	0.895035	−	0.938685i	−0.103399	−	0.994640i	$-0.532972\pi$
$313$	15.8348	−	16.6070i	0.895035	−	0.938685i	0.998433	+	0.0559547i	$0.0178203\pi$
$314$	−1.03082	+	7.16951i	−0.0581725	+	0.404599i
$315$	8.53610	+	4.78084i	0.480955	+	0.269370i
$316$	7.77913	+	3.55261i	0.437610	+	0.199850i
$317$	24.5425	−	5.95395i	1.37845	−	0.334407i	0.523014	−	0.852324i	$-0.324807\pi$
$317$	24.5425	−	5.95395i	1.37845	−	0.334407i	0.855431	+	0.517917i	$0.173292\pi$
$318$	9.10199	−	16.0055i	0.510414	−	0.897543i
$319$	−5.15803	+	12.8841i	−0.288794	+	0.721373i
$320$	14.3753	−	7.41097i	0.803602	−	0.414286i
$321$	1.31347	+	12.8671i	0.0733107	+	0.718170i
$322$	5.01921	−	8.21974i	0.279710	−	0.458068i
$323$			0.676524i			0.0376428i
$324$	−3.77799	+	4.59726i	−0.209888	+	0.255404i
$325$	−0.684349	−	4.75975i	−0.0379608	−	0.264023i
$326$	−8.35202	−	5.94745i	−0.462576	−	0.329399i
$327$	33.4640	+	6.22337i	1.85056	+	0.344153i
$328$	−8.53779	−	11.9897i	−0.471421	−	0.662018i
$329$	−0.524841	−	1.51643i	−0.0289354	−	0.0836035i
$330$	4.82637	−	2.52818i	0.265683	−	0.139172i
$331$	−4.38965	−	4.18552i	−0.241277	−	0.230057i	0.559786	−	0.828637i	$-0.310883\pi$
$331$	−4.38965	−	4.18552i	−0.241277	−	0.230057i	−0.801063	+	0.598580i	$0.795732\pi$
$332$	−1.17932	−	1.36101i	−0.0647235	−	0.0746949i
$333$	−13.7217	−	14.0197i	−0.751942	−	0.768277i
$334$	−9.63057	+	6.18919i	−0.526961	+	0.338657i
$335$	3.83868	+	1.32858i	0.209729	+	0.0725880i
$336$	0.914996	−	6.67287i	0.0499171	−	0.364035i
$337$	11.8480	−	15.0660i	0.645402	−	0.820695i	−0.347743	−	0.937590i	$-0.613052\pi$
$337$	11.8480	−	15.0660i	0.645402	−	0.820695i	0.993144	+	0.116895i	$0.0372941\pi$
$338$	−2.50068	+	0.865494i	−0.136019	+	0.0470767i
$339$	14.6972	−	12.9041i	0.798242	−	0.700856i
$340$	−0.380061	−	1.56663i	−0.0206117	−	0.0849627i
$341$	−3.15467	−	6.90776i	−0.170835	−	0.374076i
$342$	1.16721	−	1.38311i	0.0631154	−	0.0747900i
$343$	−10.3101	+	16.0428i	−0.556693	+	0.866231i
$344$	15.5302	+	26.8990i	0.837330	+	1.45030i
$345$	−11.9790	+	10.0066i	−0.644925	+	0.538737i
$346$	−0.868703	+	1.50464i	−0.0467017	+	0.0808898i
$347$	12.6165	+	24.4726i	0.677288	+	1.31376i	0.937426	+	0.348184i	$0.113202\pi$
$347$	12.6165	+	24.4726i	0.677288	+	1.31376i	−0.260138	+	0.965571i	$0.583768\pi$
$348$	−2.65941	−	10.6581i	−0.142559	−	0.571333i
$349$	−6.56699	+	9.22204i	−0.351523	+	0.493645i	−0.952043	−	0.305965i	$-0.901021\pi$
$349$	−6.56699	+	9.22204i	−0.351523	+	0.493645i	0.600520	+	0.799610i	$0.294960\pi$
$350$	−2.83088	−	0.831222i	−0.151317	−	0.0444307i
$351$	−10.2495	+	13.5720i	−0.547077	+	0.724421i
$352$	3.89901	+	3.37851i	0.207818	+	0.180075i
$353$	−11.9746	−	29.9110i	−0.637342	−	1.59200i	−0.796424	−	0.604738i	$-0.793278\pi$
$353$	−11.9746	−	29.9110i	−0.637342	−	1.59200i	0.159082	−	0.987265i	$-0.449147\pi$
$354$	6.08156	+	14.9082i	0.323231	+	0.792363i
$355$	−1.80091	−	9.34400i	−0.0955823	−	0.495928i
$356$	0.0577436	+	1.21219i	0.00306040	+	0.0642458i
$357$	−3.63068	−	1.42608i	−0.192156	−	0.0754761i
$358$	−5.07809	+	14.6722i	−0.268386	+	0.775449i
$359$	13.0677	−	3.83703i	0.689687	−	0.202511i	0.0819357	−	0.996638i	$-0.473890\pi$
$359$	13.0677	−	3.83703i	0.689687	−	0.202511i	0.607752	+	0.794127i	$0.292072\pi$
$360$	−7.75172	+	15.5308i	−0.408551	+	0.818543i
$361$	−12.2643	+	14.1538i	−0.645492	+	0.744937i
$362$	−19.7703	+	1.88784i	−1.03911	+	0.0992225i
$363$	−11.7246	−	10.0262i	−0.615383	−	0.526238i
$364$	−0.357017	+	3.73885i	−0.0187128	+	0.195969i
$365$	−8.77354	−	3.51240i	−0.459228	−	0.183847i
$366$	−5.86689	−	8.99935i	−0.306667	−	0.470403i
$367$	25.2677	−	14.5883i	1.31896	−	0.761505i	0.335403	−	0.942075i	$-0.391128\pi$
$367$	25.2677	−	14.5883i	1.31896	−	0.761505i	0.983562	+	0.180570i	$0.0577943\pi$
$368$	9.42675	+	5.15719i	0.491403	+	0.268837i
$369$	13.6118	+	4.51297i	0.708600	+	0.234936i
$370$	−11.9604	−	7.68649i	−0.621792	−	0.399602i
$371$	9.85676	+	12.5339i	0.511738	+	0.650727i
$372$	5.22500	+	2.97135i	0.270903	+	0.154057i
$373$	−14.0824	−	14.7691i	−0.729157	−	0.764718i	0.249907	−	0.968270i	$-0.419600\pi$
$373$	−14.0824	−	14.7691i	−0.729157	−	0.764718i	−0.979064	+	0.203552i	$0.934751\pi$
$374$	−1.76947	+	1.26003i	−0.0914972	+	0.0651549i
$375$	17.2299	+	12.1007i	0.889751	+	0.624876i
$376$	2.64302	−	1.05811i	0.136303	−	0.0545677i
$377$	−8.84542	−	30.1247i	−0.455562	−	1.55150i
$378$	4.96228	+	9.17955i	0.255232	+	0.472145i
$379$	−5.20488	−	8.09896i	−0.267357	−	0.416015i	0.681454	−	0.731861i	$-0.261348\pi$
$379$	−5.20488	−	8.09896i	−0.267357	−	0.416015i	−0.948811	+	0.315846i	$0.897712\pi$
$380$	−0.296806	+	0.575722i	−0.0152258	+	0.0295339i
$381$	−4.33774	+	4.60916i	−0.222229	+	0.236134i
$382$	−11.1711	−	2.71008i	−0.571563	−	0.138660i
$383$	4.56343	+	3.58872i	0.233181	+	0.183375i	0.727912	−	0.685671i	$-0.240491\pi$
$383$	4.56343	+	3.58872i	0.233181	+	0.183375i	−0.494731	+	0.869046i	$0.664733\pi$
$384$	4.87786	+	0.433667i	0.248922	+	0.0221305i
$385$	0.448511	+	4.69702i	0.0228582	+	0.239382i
$386$	−0.613590	+	2.08970i	−0.0312309	+	0.106363i
$387$	−27.6887	−	12.2107i	−1.40750	−	0.620704i
$388$	−7.53291	+	1.08307i	−0.382425	+	0.0549845i
$389$	−0.962602	+	20.2075i	−0.0488059	+	1.02456i	0.833096	+	0.553128i	$0.186566\pi$
$389$	−0.962602	+	20.2075i	−0.0488059	+	1.02456i	−0.881902	+	0.471433i	$0.843737\pi$
$390$	−5.04707	+	11.2452i	−0.255568	+	0.569424i
$391$	4.18967	−	4.60139i	0.211881	−	0.232703i
$392$	−10.6340	−	6.13952i	−0.537096	−	0.310093i
$393$	8.18887	−	5.33852i	0.413074	−	0.269292i
$394$	−1.78735	+	1.40559i	−0.0900456	+	0.0708127i
$395$	−22.1086	+	10.0966i	−1.11240	+	0.508018i
$396$	−2.86004	−	0.235466i	−0.143723	−	0.0118326i
$397$	−13.1820	+	28.8645i	−0.661585	+	1.44867i	0.219454	+	0.975623i	$0.429573\pi$
$397$	−13.1820	+	28.8645i	−0.661585	+	1.44867i	−0.881038	+	0.473045i	$0.843155\pi$
$398$	−28.3624	−	5.46640i	−1.42168	−	0.274006i
$399$	0.727253	+	1.38835i	0.0364082	+	0.0695043i
$400$	0.776054	−	3.19894i	0.0388027	−	0.159947i
$401$	19.7425	−	3.80506i	0.985895	−	0.190016i	0.329272	−	0.944235i	$-0.393197\pi$
$401$	19.7425	−	3.80506i	0.985895	−	0.190016i	0.656623	+	0.754219i	$0.271984\pi$
$402$	2.70033	+	3.38800i	0.134680	+	0.168978i
$403$	15.2700	+	7.87223i	0.760653	+	0.392144i
$404$	0.203592	−	0.176414i	0.0101291	−	0.00877691i
$405$	−2.84296	−	16.6708i	−0.141268	−	0.828378i
$406$	−19.0674	−	2.74148i	−0.946298	−	0.136057i
$407$	1.79046	−	9.28980i	0.0887500	−	0.460478i
$408$	2.22072	−	6.55447i	0.109942	−	0.324494i
$409$	0.204346	−	0.194844i	0.0101043	−	0.00963439i	−0.685010	−	0.728534i	$-0.740202\pi$
$409$	0.204346	−	0.194844i	0.0101043	−	0.00963439i	0.695114	+	0.718899i	$0.255354\pi$
$410$	10.3460	+	0.987920i	0.510951	+	0.0487899i
$411$	−20.0871	−	20.7933i	−0.990825	−	1.02566i
$412$	−11.4372	−	0.544820i	−0.563469	−	0.0268413i
$413$	−13.9435			−0.686114
$414$	−16.5043	+	2.17880i	−0.811142	+	0.107082i
$415$	5.11814			0.251240
$416$	−11.6582	−	0.555347i	−0.571589	−	0.0272281i
$417$	0.403695	−	1.40881i	0.0197690	−	0.0689899i
$418$	0.868855	+	0.0829656i	0.0424971	+	0.00405798i
$419$	−16.0907	+	15.3424i	−0.786080	+	0.749526i	−0.972490	−	0.232946i	$-0.925163\pi$
$419$	−16.0907	+	15.3424i	−0.786080	+	0.749526i	0.186410	+	0.982472i	$0.440315\pi$
$420$	−2.46406	−	2.80645i	−0.120234	−	0.136941i
$421$	−6.04394	+	31.3589i	−0.294564	+	1.52834i	0.469344	+	0.883015i	$0.344490\pi$
$421$	−6.04394	+	31.3589i	−0.294564	+	1.52834i	−0.763908	+	0.645326i	$0.776722\pi$
$422$	7.96092	+	1.14461i	0.387531	+	0.0557186i
$423$	−1.46901	+	2.35280i	−0.0714257	+	0.114397i
$424$	−21.3797	+	18.5257i	−1.03829	+	0.899685i
$425$	−1.69446	−	0.873554i	−0.0821933	−	0.0423736i
$426$	3.71055	−	9.44677i	0.179777	−	0.457697i
$427$	9.13523	−	1.76067i	0.442085	−	0.0852048i
$428$	1.16398	−	4.79801i	0.0562633	−	0.231920i
$429$	−8.19521	−	0.336785i	−0.395668	−	0.0162601i
$430$	−21.5354	−	4.15061i	−1.03853	−	0.200160i
$431$	8.69310	−	19.0352i	0.418732	−	0.916894i	−0.576291	−	0.817245i	$-0.695500\pi$
$431$	8.69310	−	19.0352i	0.418732	−	0.916894i	0.995023	−	0.0996498i	$-0.0317723\pi$
$432$	−9.96650	+	6.01740i	−0.479513	+	0.289512i
$433$	21.9694	−	10.0331i	1.05578	−	0.482159i	0.189585	−	0.981864i	$-0.439286\pi$
$433$	21.9694	−	10.0331i	1.05578	−	0.482159i	0.866196	+	0.499705i	$0.166558\pi$
$434$	8.28557	−	6.51584i	0.397720	−	0.312770i
$435$	27.8417	+	14.1241i	1.33491	+	0.677200i
$436$	−11.2522	−	6.49648i	−0.538885	−	0.311125i
$437$	−2.48295	+	0.294859i	−0.118776	+	0.0141050i
$438$	−5.90018	−	8.17221i	−0.281921	−	0.390483i
$439$	0.139286	−	2.92398i	0.00664778	−	0.139554i	−0.993103	−	0.117243i	$-0.962594\pi$
$439$	0.139286	−	2.92398i	0.00664778	−	0.139554i	0.999751	−	0.0223114i	$-0.00710252\pi$
$440$	−8.28591	+	1.19133i	−0.395015	+	0.0567946i
$441$	11.8932	−	1.29256i	0.566345	−	0.0615504i
$442$	1.38451	−	4.71520i	0.0658543	−	0.224279i
$443$	1.13435	+	11.8795i	0.0538946	+	0.564410i	0.981581	+	0.191048i	$0.0611888\pi$
$443$	1.13435	+	11.8795i	0.0538946	+	0.564410i	−0.927686	+	0.373361i	$0.878205\pi$
$444$	3.15517	+	6.79119i	0.149738	+	0.322296i
$445$	−2.71109	−	2.13202i	−0.128518	−	0.101068i
$446$	−30.1629	−	7.31743i	−1.42825	−	0.346490i
$447$	−4.55769	−	15.1554i	−0.215571	−	0.716825i
$448$	−6.84512	+	13.2777i	−0.323402	+	0.627312i
$449$	7.82720	+	12.1794i	0.369389	+	0.574780i	0.975336	−	0.220725i	$-0.0708422\pi$
$449$	7.82720	+	12.1794i	0.369389	+	0.574780i	−0.605948	+	0.795505i	$0.707206\pi$
$450$	1.95707	+	4.70938i	0.0922570	+	0.222002i
$451$	1.94844	+	6.63577i	0.0917483	+	0.312466i
$452$	−6.93102	+	2.77476i	−0.326008	+	0.130514i
$453$	−2.68146	+	30.1609i	−0.125986	+	1.41708i
$454$	−21.1149	+	15.0359i	−0.990974	+	0.705669i
$455$	−7.36611	−	7.72535i	−0.345329	−	0.362170i
$456$	−2.39896	+	1.40600i	−0.112341	+	0.0658418i
$457$	15.6964	+	19.9596i	0.734247	+	0.933671i	0.999535	−	0.0304981i	$-0.00970935\pi$
$457$	15.6964	+	19.9596i	0.734247	+	0.933671i	−0.265288	+	0.964169i	$0.585467\pi$
$458$	2.31668	+	1.48884i	0.108252	+	0.0695690i
$459$	2.02590	+	6.43093i	0.0945608	+	0.300170i
$460$	5.58414	−	2.07769i	0.260362	−	0.0968729i
$461$	−31.5279	+	18.2026i	−1.46840	+	0.847781i	−0.999373	−	0.0354037i	$-0.988728\pi$
$461$	−31.5279	+	18.2026i	−1.46840	+	0.847781i	−0.469026	+	0.883184i	$0.655395\pi$
$462$	−2.27675	+	4.48797i	−0.105924	+	0.208799i
$463$	26.3657	+	10.5552i	1.22532	+	0.490544i	0.891899	−	0.452234i	$-0.149373\pi$
$463$	26.3657	+	10.5552i	1.22532	+	0.490544i	0.333420	+	0.942778i	$0.391797\pi$
$464$	2.04295	−	21.3947i	0.0948415	−	0.993225i
$465$	−16.1065	+	5.69252i	−0.746922	+	0.263984i
$466$	29.5535	−	2.82202i	1.36904	−	0.130728i
$467$	−5.24350	+	6.05132i	−0.242640	+	0.280022i	−0.863987	−	0.503514i	$-0.832040\pi$
$467$	−5.24350	+	6.05132i	−0.242640	+	0.280022i	0.621347	+	0.783536i	$0.286586\pi$
$468$	5.41522	−	3.58090i	0.250319	−	0.165527i
$469$	−3.59996	+	1.05704i	−0.166231	+	0.0488097i
$470$	−0.657485	+	1.89968i	−0.0303275	+	0.0876256i
$471$	1.61307	+	10.7218i	0.0743264	+	0.494036i
$472$	−1.17707	−	24.7098i	−0.0541793	−	1.13736i
$473$	−2.76197	−	14.3305i	−0.126996	−	0.658916i
$474$	−25.6824	−	3.52162i	−1.17963	−	0.161753i
$475$	0.284685	+	0.711109i	0.0130622	+	0.0326279i
$476$	1.12530	+	0.975081i	0.0515782	+	0.0446928i
$477$	6.14775	−	26.8676i	0.281486	−	1.23018i
$478$	16.7085	+	4.90606i	0.764229	+	0.224398i
$479$	−0.913578	+	1.28294i	−0.0417425	+	0.0586191i	−0.834920	−	0.550372i	$-0.814486\pi$
$479$	−0.913578	+	1.28294i	−0.0417425	+	0.0586191i	0.793177	+	0.608991i	$0.208425\pi$
$480$	8.34688	−	8.06341i	0.380981	−	0.368042i
$481$	9.80738	+	19.0237i	0.447178	+	0.867405i
$482$	−11.5229	+	19.9583i	−0.524854	+	0.909074i
$483$	3.65152	−	13.9467i	0.166150	−	0.634598i
$484$	2.94441	+	5.09987i	0.133837	+	0.231812i
$485$	11.6935	−	18.1954i	0.530975	−	0.826213i
$486$	6.95349	−	16.6429i	0.315417	−	0.754938i
$487$	−11.6334	−	25.4736i	−0.527159	−	1.15432i	−0.966657	−	0.256074i	$-0.917571\pi$
$487$	−11.6334	−	25.4736i	−0.527159	−	1.15432i	0.439498	−	0.898244i	$-0.355156\pi$
$488$	3.89133	+	16.0403i	0.176152	+	0.726109i
$489$	−14.5365	−	4.92511i	−0.657363	−	0.222721i
$490$	8.19339	−	2.83576i	0.370140	−	0.128107i
$491$	24.5400	−	31.2051i	1.10747	−	1.40827i	0.204345	−	0.978899i	$-0.434493\pi$
$491$	24.5400	−	31.2051i	1.10747	−	1.40827i	0.903129	−	0.429369i	$-0.141264\pi$
$492$	−4.32489	−	3.35567i	−0.194981	−	0.151285i
$493$	−11.7624	−	4.07101i	−0.529752	−	0.183349i
$494$	−1.66108	+	1.06751i	−0.0747357	+	0.0480297i
$495$	5.82869	−	5.70476i	0.261980	−	0.256410i
$496$	7.70128	+	8.88775i	0.345798	+	0.399072i
$497$	6.36119	+	6.06538i	0.285338	+	0.272070i
$498$	4.61141	+	2.92122i	0.206642	+	0.130903i
$499$	0.864089	+	2.49662i	0.0386819	+	0.111764i	0.962688	−	0.270614i	$-0.0872266\pi$
$499$	0.864089	+	2.49662i	0.0386819	+	0.111764i	−0.924006	+	0.382378i	$0.875105\pi$
$500$	−4.66193	−	6.54677i	−0.208488	−	0.292780i
$501$	−11.1372	+	13.0239i	−0.497575	+	0.581864i
$502$	6.60735	+	4.70507i	0.294901	+	0.209998i
$503$	6.13173	+	42.6471i	0.273400	+	1.90154i	0.411987	+	0.911190i	$0.364835\pi$
$503$	6.13173	+	42.6471i	0.273400	+	1.90154i	−0.138586	+	0.990350i	$0.544256\pi$
$504$	−2.48864	−	15.8382i	−0.110853	−	0.705489i
$505$			0.765620i			0.0340697i
$506$	−5.39574	−	5.94506i	−0.239870	−	0.264290i
$507$	−3.21160	+	2.31871i	−0.142632	+	0.102978i
$508$	2.14747	−	1.10710i	0.0952784	−	0.0491194i
$509$	13.4558	−	33.6110i	0.596418	−	1.48978i	−0.255871	−	0.966711i	$-0.582362\pi$
$509$	13.4558	−	33.6110i	0.596418	−	1.48978i	0.852290	−	0.523070i	$-0.175213\pi$
$510$	2.47084	+	4.21583i	0.109411	+	0.186680i
$511$	8.48288	−	2.05792i	0.375260	−	0.0910372i
$512$	−19.8186	−	9.05087i	−0.875868	−	0.399996i
$513$	1.07693	−	2.48586i	0.0475478	−	0.109753i
$514$	−4.94773	+	34.4122i	−0.218235	+	1.51786i
$515$	22.4564	−	23.5516i	0.989546	−	1.03781i
$516$	8.41210	+	7.91673i	0.370322	+	0.348515i
$517$	−1.33617	+	0.0636498i	−0.0587648	+	0.00279931i
$518$	13.1170	−	0.624838i	0.576326	−	0.0274538i
$519$	−0.596638	+	2.53138i	−0.0261895	+	0.111115i
$520$	13.0686	−	13.7059i	0.573096	−	0.601045i
$521$	1.97100	−	13.7086i	0.0863510	−	0.600584i	−0.899995	−	0.435900i	$-0.856430\pi$
$521$	1.97100	−	13.7086i	0.0863510	−	0.600584i	0.986346	−	0.164685i	$-0.0526607\pi$
$522$	17.0238	+	28.6166i	0.745109	+	1.25252i
$523$	11.1918	+	5.11111i	0.489382	+	0.223493i	0.644794	−	0.764357i	$-0.276943\pi$
$523$	11.1918	+	5.11111i	0.489382	+	0.223493i	−0.155412	+	0.987850i	$0.549671\pi$
$524$	−3.62628	+	0.879727i	−0.158415	+	0.0384311i
$525$	−4.41639	+	0.0288292i	−0.192747	+	0.00125821i
$526$	9.75202	−	24.3594i	0.425208	−	1.06212i
$527$	6.05371	−	3.12090i	0.263704	−	0.135949i
$528$	−5.12238	−	2.29902i	−0.222923	−	0.100052i
$529$	18.7139	+	13.3713i	0.813647	+	0.581359i
$530$		−	19.9752i		−	0.867669i
$531$	15.1448	+	18.7491i	0.657226	+	0.813642i
$532$	−0.0851428	−	0.592181i	−0.00369141	−	0.0256743i
$533$	−12.7446	−	9.07541i	−0.552031	−	0.393100i
$534$	−1.22581	−	3.46831i	−0.0530458	−	0.150089i
$535$	8.13916	+	11.4298i	0.351886	+	0.494155i
$536$	−2.17713	−	6.29040i	−0.0940377	−	0.271704i
$537$	−0.954301	+	23.2216i	−0.0411811	+	1.00209i
$538$	−11.0514	−	10.5375i	−0.476459	−	0.454302i
$539$	3.77822	+	4.36030i	0.162740	+	0.187812i
$540$	−1.09735	+	6.36154i	−0.0472224	+	0.273757i
$541$	−0.102617	+	0.0659481i	−0.00441186	+	0.00283533i	−0.542845	−	0.839833i	$-0.682653\pi$
$541$	−0.102617	+	0.0659481i	−0.00441186	+	0.00283533i	0.538433	+	0.842668i	$0.319016\pi$
$542$	−26.4702	−	9.16141i	−1.13699	−	0.393516i
$543$	−27.5268	+	11.2291i	−1.18129	+	0.481887i
$544$	−2.86026	+	3.63711i	−0.122633	+	0.155940i
$545$	34.8956	−	12.0775i	1.49476	−	0.517343i
$546$	−2.22751	−	11.1648i	−0.0953288	−	0.477807i
$547$	−5.89832	−	24.3132i	−0.252194	−	1.03956i	−0.947223	−	0.320576i	$-0.896124\pi$
$547$	−5.89832	−	24.3132i	−0.252194	−	1.03956i	0.695029	−	0.718982i	$-0.255391\pi$
$548$	4.58454	+	10.0387i	0.195842	+	0.428834i
$549$	−12.2897	−	10.3713i	−0.524513	−	0.442637i
$550$	−1.32970	+	2.06905i	−0.0566986	+	0.0882247i
$551$	2.50058	+	4.33113i	0.106528	+	0.184512i
$552$	25.0238	+	5.29366i	1.06508	+	0.225313i
$553$	11.2246	−	19.4416i	0.477319	−	0.826741i
$554$	9.20108	+	17.8476i	0.390916	+	0.758272i
$555$	−20.4588	−	5.86246i	−0.868428	−	0.248848i
$556$	−0.324495	+	0.455689i	−0.0137616	+	0.0193255i
$557$	−26.0980	−	7.66306i	−1.10581	−	0.324694i	−0.322650	−	0.946518i	$-0.604574\pi$
$557$	−26.0980	−	7.66306i	−1.10581	−	0.324694i	−0.783157	+	0.621824i	$0.786392\pi$
$558$	−17.7609	−	4.06399i	−0.751879	−	0.172042i
$559$	24.9520	+	21.6210i	1.05536	+	0.914471i
$560$	−2.71572	−	6.78353i	−0.114760	−	0.286656i
$561$	−1.99333	+	2.56907i	−0.0841585	+	0.108466i
$562$	4.05624	+	21.0457i	0.171102	+	0.887761i
$563$	−0.342428	−	7.18844i	−0.0144316	−	0.302957i	−0.994530	−	0.104447i	$-0.966693\pi$
$563$	−0.342428	−	7.18844i	−0.0144316	−	0.302957i	0.980099	−	0.198510i	$-0.0636102\pi$
$564$	0.827984	−	0.659926i	0.0348644	−	0.0277879i
$565$	6.93977	−	20.0512i	0.291959	−	0.843559i
$566$	−11.6051	+	3.40756i	−0.487798	+	0.143231i
$567$	11.0707	+	11.0196i	0.464924	+	0.462780i
$568$	−10.2117	+	11.7849i	−0.428474	+	0.494485i
$569$	3.10282	−	0.296283i	0.130077	−	0.0124208i	−0.0298146	−	0.999555i	$-0.509492\pi$
$569$	3.10282	−	0.296283i	0.130077	−	0.0124208i	0.159891	+	0.987135i	$0.448886\pi$
$570$	0.358982	−	1.93030i	0.0150361	−	0.0808513i
$571$	−0.138062	+	1.44585i	−0.00577773	+	0.0605071i	−0.997901	−	0.0647586i	$-0.979372\pi$
$571$	−0.138062	+	1.44585i	−0.00577773	+	0.0605071i	0.992123	+	0.125266i	$0.0399783\pi$
$572$	2.90666	+	1.16365i	0.121534	+	0.0486547i
$573$	−17.1820	+	0.930930i	−0.717789	+	0.0388902i
$574$	−8.31341	+	4.79975i	−0.346995	+	0.200338i
$575$	2.46756	−	6.59966i	0.102904	−	0.275225i
$576$	25.2887	−	5.21729i	1.05370	−	0.217387i
$577$	−3.99497	−	2.56741i	−0.166313	−	0.106883i	0.454837	−	0.890575i	$-0.349698\pi$
$577$	−3.99497	−	2.56741i	−0.166313	−	0.106883i	−0.621149	+	0.783692i	$0.713334\pi$
$578$	10.9551	+	13.9306i	0.455672	+	0.579435i
$579$	0.0212811	+	3.26008i	0.000884412	+	0.135484i
$580$	−8.22378	−	8.62485i	−0.341474	−	0.358127i
$581$	−3.85079	+	2.74214i	−0.159758	+	0.113763i
$582$	20.9210	−	9.71982i	0.867202	−	0.402900i
$583$	12.3401	−	4.94024i	0.511075	−	0.204604i
$584$	4.36304	+	14.8591i	0.180544	+	0.614875i
$585$	−2.38718	+	18.2957i	−0.0986977	+	0.756436i
$586$	−4.55110	−	7.08165i	−0.188004	−	0.292540i
$587$	−2.80388	+	5.43876i	−0.115728	+	0.224482i	−0.939584	−	0.342318i	$-0.888788\pi$
$587$	−2.80388	+	5.43876i	−0.115728	+	0.224482i	0.823856	+	0.566799i	$0.191818\pi$
$588$	−4.44486	−	1.04764i	−0.183303	−	0.0432038i
$589$	−2.65943	−	0.645170i	−0.109580	−	0.0265838i
$590$	13.7303	+	10.7977i	0.565269	+	0.444532i
$591$	−1.95622	+	2.78543i	−0.0804681	+	0.114577i
$592$	1.39267	+	14.5847i	0.0572385	+	0.599428i
$593$	3.32831	−	11.3352i	0.136677	−	0.465481i	−0.862499	−	0.506059i	$-0.831102\pi$
$593$	3.32831	−	11.3352i	0.136677	−	0.465481i	0.999176	+	0.0405782i	$0.0129200\pi$
$594$	8.50765	−	1.81319i	0.349073	−	0.0743959i
$595$	−4.18869	+	0.602243i	−0.171720	+	0.0246896i
$596$	−0.287447	+	6.03425i	−0.0117743	+	0.247173i
$597$	−43.0139	+	4.39085i	−1.76044	+	0.179705i
$598$	17.9089	+	3.02627i	0.732351	+	0.123753i
$599$	9.56042	+	5.51971i	0.390628	+	0.225529i	0.682432	−	0.730949i	$-0.260922\pi$
$599$	9.56042	+	5.51971i	0.390628	+	0.225529i	−0.291804	+	0.956478i	$0.594255\pi$
$600$	−0.423910	−	7.82403i	−0.0173061	−	0.319415i
$601$	−4.91253	+	3.86326i	−0.200386	+	0.157585i	−0.713310	−	0.700849i	$-0.752805\pi$
$601$	−4.91253	+	3.86326i	−0.200386	+	0.157585i	0.512924	+	0.858434i	$0.328562\pi$
$602$	18.4266	−	8.41514i	0.751012	−	0.342976i
$603$	5.33146	+	3.69257i	0.217114	+	0.150373i
$604$	4.80157	−	10.5140i	0.195373	−	0.427808i
$605$	−16.4338	−	3.16736i	−0.668129	−	0.128771i
$606$	−0.436984	+	0.689819i	−0.0177512	+	0.0280220i
$607$	−2.77009	+	11.4185i	−0.112435	+	0.463461i	0.887562	+	0.460689i	$0.152398\pi$
$607$	−2.77009	+	11.4185i	−0.112435	+	0.463461i	−0.999996	+	0.00277244i	$0.999118\pi$
$608$	1.82554	−	0.351844i	0.0740354	−	0.0142692i
$609$	−28.5148	+	4.28998i	−1.15548	+	0.173839i
$610$	−10.3590	−	5.34044i	−0.419424	−	0.216228i
$611$	2.28707	−	1.98176i	0.0925249	−	0.0801733i
$612$	0.0888917	−	2.57223i	0.00359323	−	0.103976i
$613$	2.50584	+	0.360286i	0.101210	+	0.0145518i	0.192734	−	0.981251i	$-0.438265\pi$
$613$	2.50584	+	0.360286i	0.101210	+	0.0145518i	−0.0915237	+	0.995803i	$0.529174\pi$
$614$	7.21056	−	37.4119i	0.290995	−	1.50982i
$615$	15.2568	−	3.04393i	0.615213	−	0.122743i
$616$	5.59589	−	5.33567i	0.225465	−	0.214980i
$617$	−31.0517	−	2.96508i	−1.25010	−	0.119370i	−0.551066	−	0.834462i	$-0.685779\pi$
$617$	−31.0517	−	2.96508i	−1.25010	−	0.119370i	−0.699030	+	0.715092i	$0.746385\pi$
$618$	33.6753	−	8.40267i	1.35462	−	0.338005i
$619$	−36.2601	−	1.72728i	−1.45742	−	0.0694253i	−0.696165	−	0.717882i	$-0.745112\pi$
$619$	−36.2601	−	1.72728i	−1.45742	−	0.0694253i	−0.761252	+	0.648457i	$0.775415\pi$
$620$	6.52092			0.261886
$621$	−22.7196	+	10.2382i	−0.911705	+	0.410846i
$622$	8.65970			0.347222
$623$	3.18204	+	0.151579i	0.127486	+	0.00607290i
$624$	12.3240	−	3.07510i	0.493357	−	0.123103i
$625$	15.4255	+	1.47296i	0.617022	+	0.0589184i
$626$	19.2157	−	18.3221i	0.768013	−	0.732299i
$627$	1.28126	−	0.255629i	0.0511688	−	0.0102088i
$628$	0.783278	−	4.06403i	0.0312562	−	0.162173i
$629$	8.39870	+	1.20755i	0.334878	+	0.0481482i
$630$	9.60256	+	5.99551i	0.382575	+	0.238867i
$631$	−2.48964	+	2.15728i	−0.0991109	+	0.0858801i	−0.703007	−	0.711183i	$-0.748160\pi$
$631$	−2.48964	+	2.15728i	−0.0991109	+	0.0858801i	0.603896	+	0.797063i	$0.293614\pi$
$632$	35.4008	+	18.2504i	1.40817	+	0.725961i
$633$	11.9054	−	1.79113i	0.473196	−	0.0711910i
$634$	28.6933	−	5.53019i	1.13956	−	0.219632i
$635$	−1.61884	+	6.67294i	−0.0642416	+	0.264808i
$636$	−5.63021	+	8.88780i	−0.223252	+	0.352424i
$637$	−12.8164	−	2.47015i	−0.507803	−	0.0978710i
$638$	−6.67085	+	14.6071i	−0.264102	+	0.578302i
$639$	1.24659	−	15.1415i	0.0493145	−	0.598988i
$640$	4.83262	−	2.20698i	0.191026	−	0.0872386i
$641$	33.4117	−	26.2752i	1.31968	−	1.03781i	0.323898	−	0.946092i	$-0.395007\pi$
$641$	33.4117	−	26.2752i	1.31968	−	1.03781i	0.995785	−	0.0917178i	$-0.0292358\pi$
$642$	0.809657	+	14.9437i	0.0319546	+	0.589781i
$643$	0.559980	+	0.323304i	0.0220834	+	0.0127499i	0.511001	−	0.859580i	$-0.329275\pi$
$643$	0.559980	+	0.323304i	0.0220834	+	0.0127499i	−0.488918	+	0.872330i	$0.662608\pi$
$644$	−3.08824	+	4.55502i	−0.121694	+	0.179493i
$645$	−32.6602	+	3.33395i	−1.28599	+	0.131274i
$646$	−0.0372468	+	0.781906i	−0.00146546	+	0.0307637i
$647$	−34.2620	+	4.92614i	−1.34698	+	0.193666i	−0.777782	−	0.628534i	$-0.783655\pi$
$647$	−34.2620	+	4.92614i	−1.34698	+	0.193666i	−0.569198	+	0.822201i	$0.692746\pi$
$648$	−18.5938	+	20.5490i	−0.730432	+	0.807242i
$649$	−3.27471	+	11.1527i	−0.128544	+	0.437780i
$650$	−0.528897	−	5.53886i	−0.0207450	−	0.217252i
$651$	9.06836	−	12.9123i	0.355417	−	0.506073i
$652$	4.60529	+	3.62164i	0.180357	+	0.141834i
$653$	−19.8771	−	4.82214i	−0.777853	−	0.188705i	−0.172871	−	0.984944i	$-0.555304\pi$
$653$	−19.8771	−	4.82214i	−0.777853	−	0.188705i	−0.604982	+	0.796239i	$0.706820\pi$
$654$	38.3340	+	9.03519i	1.49898	+	0.353304i
$655$	4.85948	−	9.42608i	0.189876	−	0.368307i
$656$	−5.79030	−	9.00988i	−0.226073	−	0.351777i
$657$	−11.9809	−	9.17128i	−0.467419	−	0.357806i
$658$	−0.523107	−	1.78154i	−0.0203929	−	0.0694517i
$659$	−4.59536	+	1.83971i	−0.179010	+	0.0716647i	−0.459436	−	0.888211i	$-0.651948\pi$
$659$	−4.59536	+	1.83971i	−0.179010	+	0.0716647i	0.280426	+	0.959876i	$0.409524\pi$
$660$	−2.82343	+	1.31176i	−0.109902	+	0.0510602i
$661$	−12.2943	+	8.75473i	−0.478193	+	0.340520i	−0.793603	−	0.608436i	$-0.791797\pi$
$661$	−12.2943	+	8.75473i	−0.478193	+	0.340520i	0.315410	+	0.948955i	$0.397858\pi$
$662$	−4.84299	−	5.07918i	−0.188228	−	0.197408i
$663$	−0.0480188	−	7.35607i	−0.00186489	−	0.285686i
$664$	−5.18453	−	6.59266i	−0.201199	−	0.255845i
$665$	1.43039	+	0.919257i	0.0554682	+	0.0356472i
$666$	−15.0872	−	16.9591i	−0.584617	−	0.657150i
$667$	9.81466	−	44.9442i	0.380025	−	1.74025i
$668$	5.66501	−	3.27069i	0.219186	−	0.126547i
$669$	−46.3928	+	2.51359i	−1.79365	+	0.0971808i
$670$	4.36349	+	1.74688i	0.168576	+	0.0674877i
$671$	0.737198	−	7.72028i	0.0284592	−	0.298038i
$672$	−1.95992	+	10.5387i	−0.0756054	+	0.406541i
$673$	3.16517	−	0.302237i	0.122008	−	0.0116504i	−0.0338733	−	0.999426i	$-0.510784\pi$
$673$	3.16517	−	0.302237i	0.122008	−	0.0116504i	0.155882	+	0.987776i	$0.450178\pi$
$674$	14.5230	−	16.7605i	0.559407	−	0.645590i
$675$	4.83564	+	5.90719i	0.186124	+	0.227368i
$676$	1.45082	−	0.425998i	0.0558006	−	0.0163845i
$677$	9.82519	−	28.3880i	0.377613	−	1.09104i	−0.582838	−	0.812589i	$-0.698058\pi$
$677$	9.82519	−	28.3880i	0.377613	−	1.09104i	0.960450	−	0.278451i	$-0.0898211\pi$
$678$	17.6970	−	14.1050i	0.679651	−	0.541701i
$679$	0.950570	+	19.9549i	0.0364795	+	0.765799i
$680$	−1.42086	−	7.37212i	−0.0544875	−	0.282708i
$681$	−23.7863	+	30.6564i	−0.911491	+	1.17476i
$682$	−3.26576	−	8.15747i	−0.125052	−	0.312366i
$683$	−6.63743	−	5.75137i	−0.253974	−	0.220070i	0.518563	−	0.855039i	$-0.326467\pi$
$683$	−6.63743	−	5.75137i	−0.253974	−	0.220070i	−0.772537	+	0.634970i	$0.781013\pi$
$684$	−0.703799	+	0.757687i	−0.0269104	+	0.0289709i
$685$	−30.0944	−	8.83650i	−1.14985	−	0.337625i
$686$	−12.7994	+	17.9742i	−0.488682	+	0.686258i
$687$	3.96279	+	1.13553i	0.151190	+	0.0433233i
$688$	10.3563	+	20.0884i	0.394829	+	0.765861i
$689$	−15.0354	+	26.0421i	−0.572804	+	0.992125i
$690$	−14.3959	+	10.9058i	−0.548041	+	0.415178i
$691$	18.8143	+	32.5874i	0.715731	+	1.23968i	0.962677	+	0.270653i	$0.0872396\pi$
$691$	18.8143	+	32.5874i	0.715731	+	1.23968i	−0.246946	+	0.969029i	$0.579427\pi$
$692$	0.536728	−	0.835166i	0.0204034	−	0.0317482i
$693$	−1.32897	+	7.41498i	−0.0504832	+	0.281672i
$694$	13.2344	+	28.9793i	0.502371	+	1.10004i
$695$	−0.374831	−	1.54507i	−0.0142181	−	0.0586080i
$696$	−10.0096	−	50.1702i	−0.379413	−	1.90170i
$697$	−5.86152	+	2.02869i	−0.222021	+	0.0768422i
$698$	−8.09766	+	10.2970i	−0.306501	+	0.389748i
$699$	41.1483	−	16.7858i	1.55637	−	0.634895i
$700$	1.59315	+	0.551395i	0.0602154	+	0.0208408i
$701$	8.38636	−	5.38959i	0.316749	−	0.203562i	−0.372599	−	0.927992i	$-0.621533\pi$
$701$	8.38636	−	5.38959i	0.316749	−	0.203562i	0.689348	+	0.724430i	$0.257897\pi$
$702$	−12.5933	+	15.1218i	−0.475302	+	0.570737i
$703$	−2.23260	−	2.57656i	−0.0842040	−	0.0971766i
$704$	9.01249	+	8.59339i	0.339671	+	0.323876i
$705$	−0.123558	+	3.00662i	−0.00465346	+	0.113236i
$706$	−12.1931	−	35.2296i	−0.458892	−	1.32588i
$707$	−0.410195	−	0.576038i	−0.0154270	−	0.0216641i
$708$	−3.06577	−	8.67434i	−0.115219	−	0.326002i
$709$	20.7818	+	14.7987i	0.780477	+	0.555775i	0.899399	−	0.437129i	$-0.144005\pi$
$709$	20.7818	+	14.7987i	0.780477	+	0.555775i	−0.118922	+	0.992904i	$0.537944\pi$
$710$	−1.56699	−	10.8987i	−0.0588082	−	0.409020i
$711$	−38.3338	+	6.02336i	−1.43763	+	0.225894i
$712$			5.65183i			0.211811i
$713$	14.0927	+	20.8578i	0.527775	+	0.781132i
$714$	−4.11772	−	1.84811i	−0.154102	−	0.0691638i
$715$	−7.90907	+	4.07741i	−0.295783	+	0.152487i
$716$	3.29728	−	8.23621i	0.123225	−	0.307802i
$717$	26.0665	−	0.170156i	0.973472	−	0.00635460i
$718$	15.3145	−	3.71526i	0.571533	−	0.138652i
$719$	45.2679	+	20.6732i	1.68821	+	0.770979i	0.998919	+	0.0464933i	$0.0148046\pi$
$719$	45.2679	+	20.6732i	1.68821	+	0.770979i	0.689290	+	0.724486i	$0.257923\pi$
$720$	−6.17179	+	11.0196i	−0.230009	+	0.410677i
$721$	−4.27757	+	29.7512i	−0.159305	+	1.10799i
$722$	−14.9540	+	15.6833i	−0.556531	+	0.583673i
$723$	−7.91410	+	33.5775i	−0.294329	+	1.24876i
$724$	11.3354	−	0.539972i	0.421277	−	0.0200679i
$725$	−14.0768	+	0.670562i	−0.522800	+	0.0249040i
$726$	−12.9990	−	12.2335i	−0.482437	−	0.454027i
$727$	21.6586	−	22.7149i	0.803272	−	0.842447i	−0.186889	−	0.982381i	$-0.559840\pi$
$727$	21.6586	−	22.7149i	0.803272	−	0.842447i	0.990161	+	0.139934i	$0.0446889\pi$
$728$	−2.48935	+	17.3138i	−0.0922615	+	0.641693i
$729$	2.79310	−	26.8551i	0.103448	−	0.994635i
$730$	−9.94682	−	4.54256i	−0.368149	−	0.168128i
$731$	12.7201	−	3.08587i	0.470471	−	0.114135i
$732$	3.10390	+	5.29597i	0.114723	+	0.195745i
$733$	−8.37924	+	20.9303i	−0.309494	+	0.773079i	0.689323	+	0.724454i	$0.257908\pi$
$733$	−8.37924	+	20.9303i	−0.309494	+	0.773079i	−0.998817	+	0.0486249i	$0.984516\pi$
$734$	30.0069	−	15.4696i	1.10757	−	0.570994i
$735$	10.5227	−	7.59718i	0.388135	−	0.280226i
$736$	−14.5954	−	8.91238i	−0.537994	−	0.328515i
$737$			3.12767i			0.115209i
$738$	15.4836	+	5.96536i	0.569959	+	0.219588i
$739$	−5.79117	−	40.2785i	−0.213032	−	1.48167i	−0.762954	−	0.646452i	$-0.776252\pi$
$739$	−5.79117	−	40.2785i	−0.213032	−	1.48167i	0.549923	−	0.835216i	$-0.314657\pi$
$740$	6.61753	+	4.71232i	0.243265	+	0.173228i
$741$	−1.92095	+	2.24636i	−0.0705680	+	0.0825221i
$742$	10.7021	+	15.0290i	0.392886	+	0.551731i
$743$	−3.93442	−	11.3678i	−0.144340	−	0.417043i	0.849538	−	0.527528i	$-0.176881\pi$
$743$	−3.93442	−	11.3678i	−0.144340	−	0.417043i	−0.993878	+	0.110485i	$0.964760\pi$
$744$	23.6479	+	14.9804i	0.866976	+	0.549208i
$745$	−12.4258	−	11.8480i	−0.455246	−	0.434076i
$746$	−15.4628	−	17.8451i	−0.566135	−	0.653354i
$747$	7.86976	+	2.19959i	0.287939	+	0.0804787i
$748$	1.04420	−	0.671066i	0.0381797	−	0.0245366i
$749$	−12.2475	−	4.23890i	−0.447514	−	0.154886i
$750$	19.2477	+	14.9342i	0.702825	+	0.545320i
$751$	17.5861	−	22.3626i	0.641727	−	0.816022i	−0.351004	−	0.936374i	$-0.614160\pi$
$751$	17.5861	−	22.3626i	0.641727	−	0.816022i	0.992731	+	0.120351i	$0.0384021\pi$
$752$	1.95763	−	0.677541i	0.0713873	−	0.0247074i
$753$	11.4999	+	3.89630i	0.419081	+	0.141989i
$754$	−8.56473	−	35.3043i	−0.311909	−	1.28571i
$755$	13.6463	+	29.8811i	0.496638	+	1.08749i
$756$	−2.58268	−	5.37422i	−0.0939313	−	0.195459i
$757$	21.0120	−	32.6954i	0.763696	−	1.18833i	−0.213697	−	0.976900i	$-0.568550\pi$
$757$	21.0120	−	32.6954i	0.763696	−	1.18833i	0.977392	−	0.211433i	$-0.0678132\pi$
$758$	−5.56975	−	9.64710i	−0.202303	−	0.350398i
$759$	−10.2977	−	6.19613i	−0.373781	−	0.224905i
$760$	−1.50830	+	2.61246i	−0.0547119	+	0.0947638i
$761$	18.3371	+	35.5689i	0.664718	+	1.28937i	0.944248	+	0.329236i	$0.106791\pi$
$761$	18.3371	+	35.5689i	0.664718	+	1.28937i	−0.279530	+	0.960137i	$0.590179\pi$
$762$	−5.26719	+	5.08831i	−0.190810	+	0.184330i
$763$	−19.7841	+	27.7828i	−0.716231	+	1.00581i
$764$	6.30232	+	1.85053i	0.228010	+	0.0669497i
$765$	5.35937	+	4.97820i	0.193768	+	0.179987i
$766$	5.07670	+	4.39899i	0.183429	+	0.158942i
$767$	−9.77308	−	24.4120i	−0.352885	−	0.881465i
$768$	−23.9256	−	3.28072i	−0.863341	−	0.118383i
$769$	−4.13424	−	21.4505i	−0.149085	−	0.773524i	−0.977094	−	0.212810i	$-0.931739\pi$
$769$	−4.13424	−	21.4505i	−0.149085	−	0.773524i	0.828009	−	0.560715i	$-0.189474\pi$
$770$	0.259776	+	5.45337i	0.00936167	+	0.196526i
$771$	7.74242	+	51.4627i	0.278836	+	1.85338i
$772$	0.407028	−	1.17603i	0.0146492	−	0.0423262i
$773$	3.33187	−	0.978324i	0.119839	−	0.0351879i	−0.221263	−	0.975214i	$-0.571018\pi$
$773$	3.33187	−	0.978324i	0.119839	−	0.0351879i	0.341102	+	0.940026i	$0.389200\pi$
$774$	−31.3295	−	15.6372i	−1.12612	−	0.562067i
$775$	5.04989	−	5.82788i	0.181397	−	0.209344i
$776$	−35.2827	+	3.36909i	−1.26657	+	0.120943i
$777$	18.5337	−	6.55037i	0.664894	−	0.234993i
$778$	−2.22509	+	23.3022i	−0.0797735	+	0.835426i
$779$	2.31369	+	0.926260i	0.0828964	+	0.0331867i
$780$	3.18640	−	6.28109i	0.114091	−	0.224899i
$781$	6.34534	−	3.66348i	0.227054	−	0.131090i
$782$	5.09563	−	5.08749i	0.182220	−	0.181928i
$783$	36.7400	+	33.6829i	1.31298	+	1.20373i
$784$	−7.51637	−	4.83048i	−0.268442	−	0.172517i
$785$	7.27122	+	9.24611i	0.259521	+	0.330008i
$786$	9.75837	−	5.71925i	0.348070	−	0.203999i
$787$	−1.36484	−	1.43140i	−0.0486512	−	0.0510239i	0.698959	−	0.715162i	$-0.253647\pi$
$787$	−1.36484	−	1.43140i	−0.0486512	−	0.0510239i	−0.747610	+	0.664138i	$0.768799\pi$
$788$	1.05836	−	0.753658i	0.0377027	−	0.0268479i
$789$	3.47825	−	39.1231i	0.123829	−	1.39282i
$790$	−26.1083	+	10.4522i	−0.928893	+	0.371873i
$791$	5.52142	+	18.8042i	0.196319	+	0.668601i
$792$	−13.2526	−	1.72916i	−0.470910	−	0.0614431i
$793$	9.48548	+	14.7597i	0.336839	+	0.524132i
$794$	−16.8245	+	32.6350i	−0.597080	+	1.15817i
$795$	−8.61124	−	28.6344i	−0.305409	−	1.01556i
$796$	16.0395	+	3.89113i	0.568503	+	0.137917i
$797$	−5.88407	−	4.62728i	−0.208424	−	0.163907i	0.508490	−	0.861068i	$-0.330204\pi$
$797$	−5.88407	−	4.62728i	−0.208424	−	0.163907i	−0.716915	+	0.697161i	$0.754446\pi$
$798$	0.764101	+	1.64465i	0.0270489	+	0.0582200i
$799$	−0.114042	−	1.19430i	−0.00403450	−	0.0422512i
$800$	−1.47596	+	5.02666i	−0.0521831	+	0.177719i
$801$	−3.25236	−	4.44337i	−0.114917	−	0.156999i
$802$	23.0273	−	3.31083i	0.813123	−	0.116909i
$803$	0.346233	−	7.26832i	0.0122183	−	0.256493i
$804$	−1.44912	−	2.00715i	−0.0511065	−	0.0707866i
$805$	−4.03594	−	15.1107i	−0.142248	−	0.532581i
$806$	17.2152	+	9.93920i	0.606380	+	0.350093i
$807$	−20.3847	−	10.3412i	−0.717577	−	0.364027i
$808$	0.986193	−	0.775551i	0.0346942	−	0.0272838i
$809$	−3.10955	+	1.42008i	−0.109326	+	0.0499275i	−0.469327	−	0.883024i	$-0.655504\pi$
$809$	−3.10955	+	1.42008i	−0.109326	+	0.0499275i	0.360001	+	0.932952i	$0.382776\pi$
$810$	−2.36798	−	19.4241i	−0.0832023	−	0.682494i
$811$	9.35486	−	20.4843i	0.328494	−	0.719301i	−0.671266	−	0.741216i	$-0.734249\pi$
$811$	9.35486	−	20.4843i	0.328494	−	0.719301i	0.999760	+	0.0219156i	$0.00697651\pi$
$812$	10.8083	+	2.08314i	0.379298	+	0.0731037i
$813$	−41.8943	−	1.72166i	−1.46930	−	0.0603812i
$814$	2.58083	−	10.6383i	0.0904579	−	0.372872i
$815$	−16.3499	+	3.15118i	−0.572711	+	0.110381i
$816$	1.84099	−	4.68701i	0.0644475	−	0.164078i
$817$	−4.67452	−	2.40988i	−0.163541	−	0.0843111i
$818$	0.246905	−	0.213944i	0.00863281	−	0.00748038i
$819$	−8.00621	−	15.0443i	−0.279760	−	0.525692i
$820$	−5.87819	−	0.845156i	−0.205275	−	0.0295141i
$821$	2.60897	−	13.5366i	0.0910536	−	0.472431i	−0.907566	−	0.419909i	$-0.862062\pi$
$821$	2.60897	−	13.5366i	0.0910536	−	0.472431i	0.998620	−	0.0525217i	$-0.0167259\pi$
$822$	−22.0713	−	25.1382i	−0.769826	−	0.876796i
$823$	−18.5987	+	17.7338i	−0.648308	+	0.618161i	−0.941146	−	0.338002i	$-0.890249\pi$
$823$	−18.5987	+	17.7338i	−0.648308	+	0.618161i	0.292837	+	0.956162i	$0.405401\pi$
$824$	−53.0844	−	5.06894i	−1.84928	−	0.176585i
$825$	−1.01416	+	3.53921i	−0.0353084	+	0.123219i
$826$	−16.1155	−	0.767675i	−0.560729	−	0.0267108i
$827$	−4.89430			−0.170191			−0.0850957	−	0.996373i	$-0.527120\pi$
$827$	−4.89430			−0.170191			−0.0850957	+	0.996373i	$0.527120\pi$
$828$	9.47921	−	0.794843i	0.329425	−	0.0276227i
$829$	−14.1498			−0.491442			−0.245721	−	0.969341i	$-0.579025\pi$
$829$	−14.1498			−0.491442			−0.245721	+	0.969341i	$0.579025\pi$
$830$	5.91540	+	0.281785i	0.205326	+	0.00978090i
$831$	20.8837	+	21.6179i	0.724449	+	0.749917i
$832$	−28.0441	−	2.67789i	−0.972254	−	0.0928390i
$833$	−3.74495	+	3.57081i	−0.129755	+	0.123721i
$834$	0.544142	−	1.60604i	0.0188421	−	0.0556126i
$835$	−3.51835	+	18.2549i	−0.121757	+	0.631737i
$836$	−0.493651	−	0.0709762i	−0.0170733	−	0.00245476i
$837$	−27.2121	+	1.83095i	−0.940589	+	0.0632868i
$838$	−19.4418	+	16.8464i	−0.671606	+	0.581950i
$839$	−45.2488	−	23.3274i	−1.56216	−	0.805351i	−0.562395	−	0.826869i	$-0.690120\pi$
$839$	−45.2488	−	23.3274i	−1.56216	−	0.805351i	−0.999768	+	0.0215172i	$0.993150\pi$
$840$	−10.8408	−	13.6015i	−0.374042	−	0.469296i
$841$	−61.8747	+	11.9254i	−2.13361	+	0.411220i
$842$	−8.71191	+	35.9110i	−0.300232	+	1.23757i
$843$	14.8873	+	28.4203i	0.512747	+	0.978849i
$844$	−4.51264	−	0.869741i	−0.155332	−	0.0299377i
$845$	−1.78518	+	3.90901i	−0.0614122	+	0.134474i
$846$	−1.82737	+	2.63842i	−0.0628264	+	0.0907108i
$847$	14.0615	−	6.42165i	0.483157	−	0.220651i
$848$	−16.1806	+	12.7245i	−0.555643	+	0.436962i
$849$	−15.1669	+	9.88763i	−0.520525	+	0.339343i
$850$	−1.91031	−	1.10292i	−0.0655231	−	0.0378298i
$851$	−0.771378	+	31.3509i	−0.0264425	+	1.07469i
$852$	−2.37467	+	5.29094i	−0.0813550	+	0.181265i
$853$	−0.838427	+	17.6008i	−0.0287072	+	0.602638i	0.937982	+	0.346685i	$0.112693\pi$
$853$	−0.838427	+	17.6008i	−0.0287072	+	0.602638i	−0.966689	+	0.255954i	$0.917610\pi$
$854$	10.6552	−	1.53198i	0.364612	−	0.0524233i
$855$	−0.317544	−	2.92183i	−0.0108598	−	0.0999244i
$856$	6.47802	−	22.0621i	0.221414	−	0.754068i
$857$	0.287654	+	3.01245i	0.00982607	+	0.102903i	0.999054	−	0.0434773i	$-0.0138436\pi$
$857$	0.287654	+	3.01245i	0.00982607	+	0.102903i	−0.989228	+	0.146381i	$0.953238\pi$
$858$	−9.45324	−	0.840442i	−0.322728	−	0.0286922i
$859$	−24.0531	−	18.9156i	−0.820681	−	0.645391i	0.116905	−	0.993143i	$-0.462703\pi$
$859$	−24.0531	−	18.9156i	−0.820681	−	0.645391i	−0.937586	+	0.347752i	$0.886945\pi$
$860$	12.1787	+	2.95451i	0.415289	+	0.100748i
$861$	−9.84807	+	10.4643i	−0.335621	+	0.356622i
$862$	11.0952	−	21.5217i	0.377905	−	0.733034i
$863$	0.528620	+	0.822548i	0.0179944	+	0.0279999i	0.850134	−	0.526566i	$-0.176521\pi$
$863$	0.528620	+	0.822548i	0.0179944	+	0.0279999i	−0.832140	+	0.554566i	$0.812884\pi$
$864$	16.2997	−	8.81128i	0.554527	−	0.299766i
$865$	0.794901	+	2.70718i	0.0270274	+	0.0920470i
$866$	25.9439	−	10.3864i	0.881611	−	0.352944i
$867$	21.7095	+	15.2467i	0.737293	+	0.517804i
$868$	−4.90621	+	3.49370i	−0.166528	+	0.118584i
$869$	−12.9141	−	13.5439i	−0.438082	−	0.459447i
$870$	31.4010	+	17.8571i	1.06459	+	0.605413i
$871$	−4.37388	−	5.56184i	−0.148203	−	0.188456i
$872$	−50.9052	−	32.7148i	−1.72387	−	1.10786i
$873$	25.7999	−	22.9523i	0.873194	−	0.776816i
$874$	−2.88595	+	0.204088i	−0.0976188	+	0.00690337i
$875$	−18.2710	+	10.5488i	−0.617673	+	0.356613i
$876$	3.14539	+	4.82478i	0.106273	+	0.163014i
$877$	6.39768	+	2.56125i	0.216034	+	0.0864871i	0.477155	−	0.878819i	$-0.341668\pi$
$877$	6.39768	+	2.56125i	0.216034	+	0.0864871i	−0.261121	+	0.965306i	$0.584092\pi$
$878$	0.321967	−	3.37179i	0.0108658	−	0.113792i
$879$	−9.57684	−	8.18954i	−0.323019	−	0.276226i
$880$	−6.06359	+	0.579002i	−0.204403	+	0.0195182i
$881$	−7.90850	+	9.12690i	−0.266444	+	0.307493i	−0.873168	−	0.487420i	$-0.837938\pi$
$881$	−7.90850	+	9.12690i	−0.266444	+	0.307493i	0.606723	+	0.794913i	$0.292484\pi$
$882$	13.8170	−	0.839105i	0.465244	−	0.0282541i
$883$	−16.7641	+	4.92238i	−0.564157	+	0.165651i	−0.551361	−	0.834267i	$-0.685891\pi$
$883$	−16.7641	+	4.92238i	−0.564157	+	0.165651i	−0.0127958	+	0.999918i	$0.504073\pi$
$884$	−0.918419	+	2.65360i	−0.0308898	+	0.0892502i
$885$	24.3372	+	9.55929i	0.818085	+	0.321332i
$886$	0.657012	+	13.7924i	0.0220727	+	0.463364i
$887$	−5.20086	−	26.9846i	−0.174628	−	0.906055i	−0.958491	−	0.285122i	$-0.907966\pi$
$887$	−5.20086	−	26.9846i	−0.174628	−	0.906055i	0.783864	−	0.620933i	$-0.213246\pi$
$888$	13.1728	+	32.2914i	0.442049	+	1.08363i
$889$	−2.35717	−	5.88791i	−0.0790568	−	0.197474i
$890$	−3.01602	−	2.61339i	−0.101097	−	0.0876011i
$891$	11.4140	−	6.26681i	0.382384	−	0.209946i
$892$	17.0168	+	4.99657i	0.569763	+	0.167298i
$893$	−0.279615	+	0.392664i	−0.00935696	+	0.0131400i
$894$	−4.43325	−	17.7671i	−0.148270	−	0.594220i
$895$	11.5536	+	22.4109i	0.386195	+	0.749113i
$896$	−2.45354	+	4.24965i	−0.0819670	+	0.141971i
$897$	26.9770	−	3.38233i	0.900736	−	0.112933i
$898$	8.37590	+	14.5075i	0.279508	+	0.484121i
$899$	27.2205	−	42.3559i	0.907854	−	1.41265i
$900$	−0.988971	−	2.74113i	−0.0329657	−	0.0913709i
$901$	4.95233	+	10.8441i	0.164986	+	0.361269i
$902$	1.88661	+	7.77670i	0.0628171	+	0.258936i
$903$	22.7867	−	20.0067i	0.758294	−	0.665781i
$904$	−32.8576	+	11.3721i	−1.09283	+	0.378232i
$905$	−19.9370	+	25.3520i	−0.662728	+	0.842727i
$906$	−4.75969	+	34.7114i	−0.158130	+	1.15321i
$907$	−35.0218	−	12.1212i	−1.16288	−	0.402476i	−0.323609	−	0.946191i	$-0.604896\pi$
$907$	−35.0218	−	12.1212i	−1.16288	−	0.402476i	−0.839270	+	0.543714i	$0.817017\pi$
$908$	12.4603	−	8.00778i	0.413511	−	0.265747i
$909$	−0.329035	+	1.17723i	−0.0109134	+	0.0390464i
$910$	−8.08820	−	9.33429i	−0.268121	−	0.309429i
$911$	12.6891	+	12.0990i	0.420409	+	0.400859i	0.870535	−	0.492106i	$-0.163773\pi$
$911$	12.6891	+	12.0990i	0.420409	+	0.400859i	−0.450127	+	0.892965i	$0.648621\pi$
$912$	−1.79228	+	0.938843i	−0.0593483	+	0.0310882i
$913$	1.28891	+	3.72405i	0.0426566	+	0.123248i
$914$	17.0426	+	23.9329i	0.563718	+	0.791631i
$915$	−17.1518	−	3.18977i	−0.567022	−	0.105450i
$916$	−1.28179	−	0.912757i	−0.0423514	−	0.0301583i
$917$	1.39401	+	9.69556i	0.0460343	+	0.320176i
$918$	1.98741	+	7.54422i	0.0655943	+	0.248996i
$919$			16.5181i			0.544881i	0.962173	+	0.272440i	$0.0878308\pi$
$919$			16.5181i			0.544881i	−0.962173	+	0.272440i	$0.912169\pi$
$920$	26.4376	−	8.42787i	0.871620	−	0.277859i
$921$	−5.79183	−	56.7383i	−0.190847	−	1.86959i
$922$	−37.4411	+	19.3023i	−1.23306	+	0.635686i
$923$	−6.16054	+	15.3883i	−0.202777	+	0.506512i
$924$	1.42150	−	2.49965i	0.0467638	−	0.0822324i
$925$	9.33620	−	2.26494i	0.306972	−	0.0744707i
$926$	29.8916	+	13.6510i	0.982299	+	0.448601i
$927$	44.6510	−	26.5625i	1.46653	−	0.872425i
$928$	−4.86791	+	33.8570i	−0.159797	+	1.11141i
$929$	14.3313	−	15.0302i	0.470195	−	0.493126i	−0.445342	−	0.895361i	$-0.646918\pi$
$929$	14.3313	−	15.0302i	0.470195	−	0.493126i	0.915537	+	0.402234i	$0.131766\pi$
$930$	−18.9288	+	5.69248i	−0.620701	+	0.186664i
$931$	2.07674	−	0.0989272i	0.0680623	−	0.00324221i
$932$	−16.9447	+	0.807173i	−0.555041	+	0.0264398i
$933$	12.4136	−	3.73316i	0.406404	−	0.122218i
$934$	−6.39345	+	6.70525i	−0.209200	+	0.219403i
$935$	−0.502038	+	3.49175i	−0.0164184	+	0.114193i
$936$	25.9848	−	15.4581i	0.849341	−	0.505265i
$937$	38.0565	+	17.3798i	1.24325	+	0.567775i	0.924905	−	0.380199i	$-0.124144\pi$
$937$	38.0565	+	17.3798i	1.24325	+	0.567775i	0.318349	+	0.947974i	$0.396872\pi$
$938$	−4.21892	+	1.02350i	−0.137753	+	0.0334185i
$939$	19.6470	−	34.5485i	0.641156	−	1.12745i
$940$	0.426915	−	1.06638i	0.0139244	−	0.0347815i
$941$	−36.4454	+	18.7889i	−1.18809	+	0.612501i	−0.934898	−	0.354917i	$-0.884509\pi$
$941$	−36.4454	+	18.7889i	−1.18809	+	0.612501i	−0.253188	+	0.967417i	$0.581479\pi$
$942$	1.27404	+	12.4808i	0.0415104	+	0.406646i
$943$	−10.0003	−	20.6285i	−0.325655	−	0.671757i
$944$		−	18.0003i		−	0.585859i
$945$	16.3499	+	4.45491i	0.531861	+	0.144918i
$946$	−2.40323	−	16.7148i	−0.0781356	−	0.543445i
$947$	17.0710	+	12.1562i	0.554734	+	0.395025i	0.822761	−	0.568387i	$-0.192432\pi$
$947$	17.0710	+	12.1562i	0.554734	+	0.395025i	−0.268027	+	0.963411i	$0.586372\pi$
$948$	14.5627	+	2.70826i	0.472975	+	0.0879603i
$949$	9.54867	+	13.4092i	0.309963	+	0.435282i
$950$	0.289880	+	0.837552i	0.00940494	+	0.0271738i
$951$	38.7477	−	20.2971i	1.25648	−	0.658178i
$952$	5.01877	+	4.78539i	0.162659	+	0.155095i
$953$	11.3526	+	13.1017i	0.367748	+	0.424404i	0.909221	−	0.416314i	$-0.136678\pi$
$953$	11.3526	+	13.1017i	0.367748	+	0.424404i	−0.541472	+	0.840718i	$0.682133\pi$
$954$	8.58462	−	30.7143i	0.277937	−	0.994413i
$955$	−15.7042	+	10.0925i	−0.508175	+	0.326585i
$956$	−9.40313	−	3.25445i	−0.304119	−	0.105257i
$957$	−3.26556	+	23.8150i	−0.105561	+	0.769830i
$958$	−1.12652	+	1.43249i	−0.0363962	+	0.0462816i
$959$	27.3767	−	9.47518i	0.884041	−	0.305970i
$960$	21.0504	−	18.4822i	0.679399	−	0.596512i
$961$	−0.813343	−	3.35264i	−0.0262369	−	0.108150i
$962$	10.2877	+	22.5270i	0.331689	+	0.726298i
$963$	7.60281	+	21.0727i	0.244997	+	0.679058i
$964$	7.11943	−	11.0781i	0.229302	−	0.356800i
$965$	1.76842	+	3.06300i	0.0569275	+	0.0986014i
$966$	4.98817	−	15.9182i	0.160492	−	0.512159i
$967$	−7.71994	+	13.3713i	−0.248257	+	0.429993i	−0.963042	−	0.269351i	$-0.913191\pi$
$967$	−7.71994	+	13.3713i	−0.248257	+	0.429993i	0.714786	+	0.699344i	$0.246524\pi$
$968$	12.5671	+	24.3768i	0.403922	+	0.783499i
$969$	0.283684	+	1.13692i	0.00911323	+	0.0365230i
$970$	14.5168	−	20.3860i	0.466106	−	0.654554i
$971$	−45.8951	−	13.4760i	−1.47285	−	0.432466i	−0.555822	−	0.831301i	$-0.687596\pi$
$971$	−45.8951	−	13.4760i	−1.47285	−	0.432466i	−0.917023	+	0.398835i	$0.869415\pi$
$972$	−4.42126	+	9.31003i	−0.141812	+	0.298619i
$973$	1.10982	+	0.961662i	0.0355791	+	0.0308295i
$974$	−12.0431	−	30.0821i	−0.385884	−	0.963893i
$975$	−3.14595	−	7.71192i	−0.100751	−	0.246979i
$976$	2.27293	+	11.7931i	0.0727546	+	0.377487i
$977$	−1.19291	−	25.0423i	−0.0381646	−	0.801174i	−0.934105	−	0.356999i	$-0.883800\pi$
$977$	−1.19291	−	25.0423i	−0.0381646	−	0.801174i	0.895940	−	0.444175i	$-0.146503\pi$
$978$	−16.5297	−	6.49262i	−0.528562	−	0.207611i
$979$	0.868563	−	2.50955i	0.0277594	−	0.0802055i
$980$	−4.75355	+	1.39577i	−0.151847	+	0.0445862i
$981$	58.8466	−	3.57374i	1.87883	−	0.114101i
$982$	30.0806	−	34.7149i	0.959912	−	1.10780i
$983$	−3.42910	+	0.327439i	−0.109371	+	0.0104437i	−0.149598	−	0.988747i	$-0.547798\pi$
$983$	−3.42910	+	0.327439i	−0.109371	+	0.0104437i	0.0402269	+	0.999191i	$0.487192\pi$
$984$	−19.3755	−	16.5688i	−0.617670	−	0.528194i
$985$	−0.351005	+	3.67589i	−0.0111839	+	0.117124i
$986$	−13.3705	−	5.35274i	−0.425804	−	0.170466i
$987$	−1.51789	−	2.32832i	−0.0483149	−	0.0741112i
$988$	0.977102	−	0.564130i	0.0310857	−	0.0179474i
$989$	16.8696	+	45.3399i	0.536422	+	1.44172i
$990$	7.05071	−	6.27249i	0.224086	−	0.199353i
$991$	−16.6507	−	10.7008i	−0.528928	−	0.339921i	0.248767	−	0.968563i	$-0.419975\pi$
$991$	−16.6507	−	10.7008i	−0.528928	−	0.339921i	−0.777695	+	0.628642i	$0.783611\pi$
$992$	−11.5699	−	14.7123i	−0.367344	−	0.467116i
$993$	−9.13201	−	5.19318i	−0.289795	−	0.164801i
$994$	7.01814	+	7.36041i	0.222602	+	0.233458i
$995$	−38.2093	+	27.2087i	−1.21132	+	0.862574i
$996$	−2.55258	−	1.79269i	−0.0808816	−	0.0568035i
$997$	−33.5373	+	13.4263i	−1.06214	+	0.425215i	−0.835914	−	0.548861i	$-0.815062\pi$
$997$	−33.5373	+	13.4263i	−1.06214	+	0.425215i	−0.226222	+	0.974076i	$0.572637\pi$
$998$	0.861235	+	2.93310i	0.0272619	+	0.0928455i
$999$	−28.9384	−	17.8067i	−0.915571	−	0.563379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.o.a.113.16	yes	440
3.2	odd	2		621.2.s.a.44.7		440
9.2	odd	6	inner	207.2.o.a.182.16	yes	440
9.7	even	3		621.2.s.a.251.7		440
23.11	odd	22	inner	207.2.o.a.149.16	yes	440
69.11	even	22		621.2.s.a.287.7		440
207.11	even	66	inner	207.2.o.a.11.16	✓	440
207.34	odd	66		621.2.s.a.494.7		440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.16	✓	440	207.11	even	66	inner
207.2.o.a.113.16	yes	440	1.1	even	1	trivial
207.2.o.a.149.16	yes	440	23.11	odd	22	inner
207.2.o.a.182.16	yes	440	9.2	odd	6	inner
621.2.s.a.44.7		440	3.2	odd	2
621.2.s.a.251.7		440	9.7	even	3
621.2.s.a.287.7		440	69.11	even	22
621.2.s.a.494.7		440	207.34	odd	66

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.15577 + 0.0550561i) q^{2} +(1.68053 - 0.419325i) q^{3} +(-0.658169 - 0.0628475i) q^{4} +(1.35993 - 1.29669i) q^{5} +(1.96539 - 0.392121i) q^{6} +(-0.328461 + 1.70422i) q^{7} +(-3.04784 - 0.438213i) q^{8} +(2.64833 - 1.40937i) q^{9} +O(q^{10})\)	\(q+(1.15577 + 0.0550561i) q^{2} +(1.68053 - 0.419325i) q^{3} +(-0.658169 - 0.0628475i) q^{4} +(1.35993 - 1.29669i) q^{5} +(1.96539 - 0.392121i) q^{6} +(-0.328461 + 1.70422i) q^{7} +(-3.04784 - 0.438213i) q^{8} +(2.64833 - 1.40937i) q^{9} +(1.64316 - 1.42381i) q^{10} +(1.28597 + 0.662964i) q^{11} +(-1.13242 + 0.170370i) q^{12} +(-3.21393 + 0.619434i) q^{13} +(-0.473453 + 1.95160i) q^{14} +(1.74167 - 2.74938i) q^{15} +(-2.20005 - 0.424025i) q^{16} +(-0.539040 + 1.18033i) q^{17} +(3.13846 - 1.48311i) q^{18} +(0.474253 - 0.216584i) q^{19} +(-0.976560 + 0.767975i) q^{20} +(0.162634 + 3.00171i) q^{21} +(1.44979 + 0.837035i) q^{22} +(-4.56694 - 1.46392i) q^{23} +(-5.30573 + 0.541608i) q^{24} +(-0.0699058 + 1.46750i) q^{25} +(-3.74867 + 0.538977i) q^{26} +(3.85960 - 3.47900i) q^{27} +(0.323289 - 1.10102i) q^{28} +(0.911812 + 9.54893i) q^{29} +(2.16434 - 3.08176i) q^{30} +(-4.12585 - 3.24461i) q^{31} +(3.46536 + 0.840688i) q^{32} +(2.43910 + 0.574888i) q^{33} +(-0.687991 + 1.33452i) q^{34} +(1.76316 + 2.74353i) q^{35} +(-1.83163 + 0.761165i) q^{36} +(-1.84227 - 6.27421i) q^{37} +(0.560052 - 0.224211i) q^{38} +(-5.14134 + 2.38865i) q^{39} +(-4.71309 + 3.35617i) q^{40} +(3.29867 + 3.45954i) q^{41} +(0.0227052 + 3.47824i) q^{42} +(-6.23549 - 7.92908i) q^{43} +(-0.804721 - 0.517162i) q^{44} +(1.77403 - 5.35073i) q^{45} +(-5.19774 - 1.94339i) q^{46} +(-0.800711 + 0.462291i) q^{47} +(-3.87504 + 0.209952i) q^{48} +(3.70211 + 1.48210i) q^{49} +(-0.161590 + 1.69225i) q^{50} +(-0.410927 + 2.20961i) q^{51} +(2.15424 - 0.205705i) q^{52} +(6.01642 - 6.94332i) q^{53} +(4.65236 - 3.80843i) q^{54} +(2.60850 - 0.765923i) q^{55} +(1.74791 - 5.05024i) q^{56} +(0.706176 - 0.562842i) q^{57} +(0.528118 + 11.0866i) q^{58} +(1.52043 + 7.88872i) q^{59} +(-1.31910 + 1.70010i) q^{60} +(-1.99225 - 4.97639i) q^{61} +(-4.58990 - 3.97717i) q^{62} +(1.53200 + 4.97626i) q^{63} +(8.25844 + 2.42490i) q^{64} +(-3.56751 + 5.00987i) q^{65} +(2.78739 + 0.798726i) q^{66} +(0.990584 + 1.92146i) q^{67} +(0.428960 - 0.742981i) q^{68} +(-8.28872 - 0.545120i) q^{69} +(1.88676 + 3.26797i) q^{70} +(2.73794 - 4.26031i) q^{71} +(-8.68930 + 3.13501i) q^{72} +(-2.08929 - 4.57490i) q^{73} +(-1.78381 - 7.35297i) q^{74} +(0.497883 + 2.49549i) q^{75} +(-0.325751 + 0.112743i) q^{76} +(-1.55222 + 1.97381i) q^{77} +(-6.07372 + 2.47767i) q^{78} +(-12.2233 - 4.23053i) q^{79} +(-3.54175 + 2.27614i) q^{80} +(5.02733 - 7.46498i) q^{81} +(3.62203 + 4.18005i) q^{82} +(1.97130 + 1.87963i) q^{83} +(0.0816093 - 1.98585i) q^{84} +(0.797471 + 2.30414i) q^{85} +(-6.77026 - 9.50750i) q^{86} +(5.53643 + 15.6649i) q^{87} +(-3.62891 - 2.58414i) q^{88} +(-0.261218 - 1.81681i) q^{89} +(2.34496 - 6.08655i) q^{90} -5.68069i q^{91} +(2.91382 + 1.25053i) q^{92} +(-8.29414 - 3.72257i) q^{93} +(-0.950890 + 0.490218i) q^{94} +(0.364109 - 0.909501i) q^{95} +(6.17615 - 0.0403165i) q^{96} +(11.1861 - 2.71372i) q^{97} +(4.19719 + 1.91679i) q^{98} +(4.34004 - 0.0566640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Introduction

L-functions

Modular forms

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