LMFDB - Embedded newform 966.2.y.d.151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			151.2
Character	$\chi$	$=$	966.151
Dual form			966.2.y.d.499.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.327068 + 0.945001i) q^{2} +(-0.888835 + 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-2.76706 + 0.264222i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(2.35671 + 1.20246i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +O(q^{10})$	\(q+(-0.327068 + 0.945001i) q^{2} +(-0.888835 + 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-2.76706 + 0.264222i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(2.35671 + 1.20246i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +(0.655327 - 2.70130i) q^{10} +(0.360684 + 1.04213i) q^{11} +(0.981929 + 0.189251i) q^{12} +(3.29177 - 0.966551i) q^{13} +(-1.90713 + 1.83381i) q^{14} +(2.33839 - 1.50279i) q^{15} +(0.235759 + 0.971812i) q^{16} +(2.72458 + 1.09076i) q^{17} +(0.580057 + 0.814576i) q^{18} +(3.14621 - 1.25955i) q^{19} +(2.33839 + 1.50279i) q^{20} +(-2.64573 + 0.0111152i) q^{21} -1.10278 q^{22} +(-4.78556 - 0.313675i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.67718 - 0.515984i) q^{25} +(-0.163241 + 3.42686i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(-1.10919 - 2.40202i) q^{28} +(0.666438 + 4.63518i) q^{29} +(0.655327 + 2.70130i) q^{30} +(0.124262 + 2.60857i) q^{31} +(-0.995472 - 0.0950560i) q^{32} +(-0.798118 - 0.761004i) q^{33} +(-1.92189 + 2.21798i) q^{34} +(-6.83888 - 2.70460i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-3.85427 + 5.41256i) q^{37} +(0.161254 + 3.38513i) q^{38} +(-2.48294 + 2.36748i) q^{39} +(-2.18495 + 1.71827i) q^{40} +(0.553274 - 1.21150i) q^{41} +(0.854829 - 2.50385i) q^{42} +(-2.98092 - 1.91572i) q^{43} +(0.360684 - 1.04213i) q^{44} +(-1.38982 + 2.40725i) q^{45} +(1.86163 - 4.41977i) q^{46} +(1.68081 + 2.91126i) q^{47} +(-0.654861 - 0.755750i) q^{48} +(4.10816 + 5.66771i) q^{49} +(-0.388014 + 2.69870i) q^{50} +(-2.92152 + 0.278971i) q^{51} +(-3.18499 - 1.27508i) q^{52} +(-6.03201 + 5.75151i) q^{53} +(-0.888835 - 0.458227i) q^{54} +(-1.27339 - 2.78833i) q^{55} +(2.63269 - 0.262557i) q^{56} +(-2.21930 + 2.56121i) q^{57} +(-4.59822 - 0.886234i) q^{58} +(-2.49820 + 10.2977i) q^{59} +(-2.76706 - 0.264222i) q^{60} +(-3.12694 - 1.61205i) q^{61} +(-2.50574 - 0.735753i) q^{62} +(2.34652 - 1.22222i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-8.85316 + 3.54427i) q^{65} +(0.980189 - 0.505322i) q^{66} +(-5.36311 + 1.03365i) q^{67} +(-1.46741 - 2.54162i) q^{68} +(4.39731 - 1.91407i) q^{69} +(4.79262 - 5.57816i) q^{70} +(-9.79945 - 11.3092i) q^{71} +(0.0475819 - 0.998867i) q^{72} +(10.9151 + 8.58373i) q^{73} +(-3.85427 - 5.41256i) q^{74} +(-2.14313 + 1.68538i) q^{75} +(-3.25169 - 0.954784i) q^{76} +(-0.403092 + 2.88970i) q^{77} +(-1.42518 - 3.12071i) q^{78} +(8.49188 + 8.09699i) q^{79} +(-0.909134 - 2.62677i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(0.963912 + 0.919088i) q^{82} +(6.07241 + 13.2967i) q^{83} +(2.08655 + 1.62674i) q^{84} +(-7.82730 - 2.29830i) q^{85} +(2.78532 - 2.19040i) q^{86} +(-2.71631 - 3.81453i) q^{87} +(0.866843 + 0.681692i) q^{88} +(0.308335 - 6.47275i) q^{89} +(-1.82028 - 2.10072i) q^{90} +(8.91999 + 1.68035i) q^{91} +(3.56781 + 3.20480i) q^{92} +(-1.30576 - 2.26165i) q^{93} +(-3.30088 + 0.636192i) q^{94} +(-8.37297 + 4.31656i) q^{95} +(0.928368 - 0.371662i) q^{96} +(-1.27195 + 2.78519i) q^{97} +(-6.69964 + 2.02849i) q^{98} +(1.05811 + 0.310689i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{11}\right)$

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 $

$2$	−0.327068	+	0.945001i	−0.231272	+	0.668216i
$2$	−0.327068	+	0.945001i	−0.231272	+	0.668216i
$3$	−0.888835	+	0.458227i	−0.513169	+	0.264557i
$3$	−0.888835	+	0.458227i	−0.513169	+	0.264557i
$4$	−0.786053	−	0.618159i	−0.393027	−	0.309079i
$5$	−2.76706	+	0.264222i	−1.23747	+	0.118164i	−0.693199	−	0.720747i	$-0.743799\pi$
$5$	−2.76706	+	0.264222i	−1.23747	+	0.118164i	−0.544269	+	0.838910i	$0.683193\pi$
$6$	−0.142315	−	0.989821i	−0.0580998	−	0.404093i
$7$	2.35671	+	1.20246i	0.890753	+	0.454488i
$7$	2.35671	+	1.20246i	0.890753	+	0.454488i
$8$	0.841254	−	0.540641i	0.297428	−	0.191145i
$9$	0.580057	−	0.814576i	0.193352	−	0.271525i
$10$	0.655327	−	2.70130i	0.207233	−	0.854225i
$11$	0.360684	+	1.04213i	0.108750	+	0.314213i	0.986225	−	0.165410i	$-0.0528947\pi$
$11$	0.360684	+	1.04213i	0.108750	+	0.314213i	−0.877475	+	0.479623i	$0.840773\pi$
$12$	0.981929	+	0.189251i	0.283458	+	0.0546321i
$13$	3.29177	−	0.966551i	0.912973	−	0.268073i	0.208681	−	0.977984i	$-0.433083\pi$
$13$	3.29177	−	0.966551i	0.912973	−	0.268073i	0.704292	+	0.709911i	$0.251265\pi$
$14$	−1.90713	+	1.83381i	−0.509703	+	0.490105i
$15$	2.33839	−	1.50279i	0.603770	−	0.388019i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	2.72458	+	1.09076i	0.660809	+	0.264548i	0.677732	−	0.735309i	$-0.262963\pi$
$17$	2.72458	+	1.09076i	0.660809	+	0.264548i	−0.0169234	+	0.999857i	$0.505387\pi$
$18$	0.580057	+	0.814576i	0.136721	+	0.191997i
$19$	3.14621	−	1.25955i	0.721791	−	0.288961i	0.0184654	−	0.999830i	$-0.494122\pi$
$19$	3.14621	−	1.25955i	0.721791	−	0.288961i	0.703325	+	0.710868i	$0.251698\pi$
$20$	2.33839	+	1.50279i	0.522880	+	0.336034i
$21$	−2.64573	+	0.0111152i	−0.577345	+	0.00242554i
$22$	−1.10278			−0.235113
$23$	−4.78556	−	0.313675i	−0.997859	−	0.0654057i
$23$	−4.78556	−	0.313675i	−0.997859	−	0.0654057i
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	2.67718	−	0.515984i	0.535436	−	0.103197i
$26$	−0.163241	+	3.42686i	−0.0320142	+	0.672062i
$27$	−0.142315	+	0.989821i	−0.0273885	+	0.190491i
$28$	−1.10919	−	2.40202i	−0.209616	−	0.453939i
$29$	0.666438	+	4.63518i	0.123754	+	0.860731i	0.953242	+	0.302206i	$0.0977232\pi$
$29$	0.666438	+	4.63518i	0.123754	+	0.860731i	−0.829488	+	0.558524i	$0.811368\pi$
$30$	0.655327	+	2.70130i	0.119646	+	0.493187i
$31$	0.124262	+	2.60857i	0.0223180	+	0.468513i	0.982169	+	0.188002i	$0.0602010\pi$
$31$	0.124262	+	2.60857i	0.0223180	+	0.468513i	−0.959851	+	0.280511i	$0.909496\pi$
$32$	−0.995472	−	0.0950560i	−0.175976	−	0.0168037i
$33$	−0.798118	−	0.761004i	−0.138935	−	0.132474i
$34$	−1.92189	+	2.21798i	−0.329602	+	0.380381i
$35$	−6.83888	−	2.70460i	−1.15598	−	0.457160i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	−3.85427	+	5.41256i	−0.633637	+	0.889819i	−0.999160	−	0.0409833i	$-0.986951\pi$
$37$	−3.85427	+	5.41256i	−0.633637	+	0.889819i	0.365522	+	0.930803i	$0.380890\pi$
$38$	0.161254	+	3.38513i	0.0261588	+	0.549141i
$39$	−2.48294	+	2.36748i	−0.397589	+	0.379101i
$40$	−2.18495	+	1.71827i	−0.345471	+	0.271682i
$41$	0.553274	−	1.21150i	0.0864069	−	0.189205i	−0.861496	−	0.507765i	$-0.830472\pi$
$41$	0.553274	−	1.21150i	0.0864069	−	0.189205i	0.947903	+	0.318560i	$0.103199\pi$
$42$	0.854829	−	2.50385i	0.131903	−	0.386353i
$43$	−2.98092	−	1.91572i	−0.454586	−	0.292145i	0.293240	−	0.956039i	$-0.405266\pi$
$43$	−2.98092	−	1.91572i	−0.454586	−	0.292145i	−0.747827	+	0.663894i	$0.768903\pi$
$44$	0.360684	−	1.04213i	0.0543751	−	0.157107i
$45$	−1.38982	+	2.40725i	−0.207183	+	0.358851i
$46$	1.86163	−	4.41977i	0.274482	−	0.651659i
$47$	1.68081	+	2.91126i	0.245172	+	0.424650i	0.962180	−	0.272415i	$-0.0878223\pi$
$47$	1.68081	+	2.91126i	0.245172	+	0.424650i	−0.717008	+	0.697065i	$0.754489\pi$
$48$	−0.654861	−	0.755750i	−0.0945210	−	0.109083i
$49$	4.10816	+	5.66771i	0.586881	+	0.809673i
$50$	−0.388014	+	2.69870i	−0.0548735	+	0.381654i
$51$	−2.92152	+	0.278971i	−0.409095	+	0.0390638i
$52$	−3.18499	−	1.27508i	−0.441679	−	0.176821i
$53$	−6.03201	+	5.75151i	−0.828560	+	0.790031i	−0.980118	−	0.198418i	$-0.936420\pi$
$53$	−6.03201	+	5.75151i	−0.828560	+	0.790031i	0.151557	+	0.988448i	$0.451571\pi$
$54$	−0.888835	−	0.458227i	−0.120955	−	0.0623567i
$55$	−1.27339	−	2.78833i	−0.171704	−	0.375978i
$56$	2.63269	−	0.262557i	0.351808	−	0.0350857i
$57$	−2.21930	+	2.56121i	−0.293954	+	0.339241i
$58$	−4.59822	−	0.886234i	−0.603775	−	0.116368i
$59$	−2.49820	+	10.2977i	−0.325237	+	1.34065i	0.541003	+	0.841020i	$0.318045\pi$
$59$	−2.49820	+	10.2977i	−0.325237	+	1.34065i	−0.866241	+	0.499627i	$0.833471\pi$
$60$	−2.76706	−	0.264222i	−0.357226	−	0.0341110i
$61$	−3.12694	−	1.61205i	−0.400364	−	0.206402i	0.246272	−	0.969201i	$-0.420794\pi$
$61$	−3.12694	−	1.61205i	−0.400364	−	0.206402i	−0.646636	+	0.762799i	$0.723825\pi$
$62$	−2.50574	−	0.735753i	−0.318230	−	0.0934407i
$63$	2.34652	−	1.22222i	0.295634	−	0.153986i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	−8.85316	+	3.54427i	−1.09810	+	0.439612i
$66$	0.980189	−	0.505322i	0.120653	−	0.0622009i
$67$	−5.36311	+	1.03365i	−0.655208	+	0.126281i	−0.506012	−	0.862527i	$-0.668881\pi$
$67$	−5.36311	+	1.03365i	−0.655208	+	0.126281i	−0.149196	+	0.988808i	$0.547669\pi$
$68$	−1.46741	−	2.54162i	−0.177949	−	0.308217i
$69$	4.39731	−	1.91407i	0.529374	−	0.230427i
$70$	4.79262	−	5.57816i	0.572828	−	0.666718i
$71$	−9.79945	−	11.3092i	−1.16298	−	1.34215i	−0.929075	−	0.369892i	$-0.879395\pi$
$71$	−9.79945	−	11.3092i	−1.16298	−	1.34215i	−0.233906	−	0.972259i	$-0.575151\pi$
$72$	0.0475819	−	0.998867i	0.00560758	−	0.117718i
$73$	10.9151	+	8.58373i	1.27752	+	1.00465i	0.999022	+	0.0442107i	$0.0140773\pi$
$73$	10.9151	+	8.58373i	1.27752	+	1.00465i	0.278493	+	0.960438i	$0.410165\pi$
$74$	−3.85427	−	5.41256i	−0.448049	−	0.629197i
$75$	−2.14313	+	1.68538i	−0.247468	+	0.194611i
$76$	−3.25169	−	0.954784i	−0.372995	−	0.109521i
$77$	−0.403092	+	2.88970i	−0.0459366	+	0.329312i
$78$	−1.42518	−	3.12071i	−0.161370	−	0.353351i
$79$	8.49188	+	8.09699i	0.955411	+	0.910982i	0.996104	−	0.0881894i	$-0.0281081\pi$
$79$	8.49188	+	8.09699i	0.955411	+	0.910982i	−0.0406930	+	0.999172i	$0.512957\pi$
$80$	−0.909134	−	2.62677i	−0.101644	−	0.293682i
$81$	−0.327068	−	0.945001i	−0.0363409	−	0.105000i
$82$	0.963912	+	0.919088i	0.106446	+	0.101496i
$83$	6.07241	+	13.2967i	0.666534	+	1.45951i	0.876306	+	0.481755i	$0.160001\pi$
$83$	6.07241	+	13.2967i	0.666534	+	1.45951i	−0.209772	+	0.977750i	$0.567272\pi$
$84$	2.08655	+	1.62674i	0.227662	+	0.177492i
$85$	−7.82730	−	2.29830i	−0.848990	−	0.249286i
$86$	2.78532	−	2.19040i	0.300349	−	0.236197i
$87$	−2.71631	−	3.81453i	−0.291220	−	0.408961i
$88$	0.866843	+	0.681692i	0.0924057	+	0.0726687i
$89$	0.308335	−	6.47275i	0.0326834	−	0.686110i	−0.921768	−	0.387743i	$-0.873255\pi$
$89$	0.308335	−	6.47275i	0.0326834	−	0.686110i	0.954451	−	0.298367i	$-0.0964420\pi$
$90$	−1.82028	−	2.10072i	−0.191875	−	0.221435i
$91$	8.91999	+	1.68035i	0.935070	+	0.176149i
$92$	3.56781	+	3.20480i	0.371969	+	0.334124i
$93$	−1.30576	−	2.26165i	−0.135401	−	0.234522i
$94$	−3.30088	+	0.636192i	−0.340460	+	0.0656182i
$95$	−8.37297	+	4.31656i	−0.859048	+	0.442870i
$96$	0.928368	−	0.371662i	0.0947512	−	0.0379326i
$97$	−1.27195	+	2.78519i	−0.129147	+	0.282793i	−0.963149	−	0.268969i	$-0.913317\pi$
$97$	−1.27195	+	2.78519i	−0.129147	+	0.282793i	0.834002	+	0.551762i	$0.186044\pi$
$98$	−6.69964	+	2.02849i	−0.676766	+	0.204909i
$99$	1.05811	+	0.310689i	0.106344	+	0.0312254i
$100$	−2.42337	−	1.24933i	−0.242337	−	0.124933i
$101$	5.28789	+	0.504933i	0.526165	+	0.0502427i	0.354759	−	0.934958i	$-0.384563\pi$
$101$	5.28789	+	0.504933i	0.526165	+	0.0502427i	0.171406	+	0.985200i	$0.445169\pi$
$102$	0.691908	−	2.85208i	0.0685091	−	0.282398i
$103$	1.18410	+	0.228216i	0.116673	+	0.0224868i	0.247253	−	0.968951i	$-0.420472\pi$
$103$	1.18410	+	0.228216i	0.116673	+	0.0224868i	−0.130581	+	0.991438i	$0.541684\pi$
$104$	2.24666	−	2.59278i	0.220303	−	0.254243i
$105$	7.31796	−	0.729817i	0.714160	−	0.0712229i
$106$	−3.46230	−	7.58139i	−0.336289	−	0.736370i
$107$	−6.30833	−	3.25217i	−0.609850	−	0.314399i	0.125493	−	0.992094i	$-0.459949\pi$
$107$	−6.30833	−	3.25217i	−0.609850	−	0.314399i	−0.735343	+	0.677695i	$0.762979\pi$
$108$	0.723734	−	0.690079i	0.0696413	−	0.0664029i
$109$	−7.52903	−	3.01417i	−0.721150	−	0.288705i	−0.0180908	−	0.999836i	$-0.505759\pi$
$109$	−7.52903	−	3.01417i	−0.721150	−	0.288705i	−0.703059	+	0.711131i	$0.748183\pi$
$110$	3.05146	−	0.291379i	0.290945	−	0.0277819i
$111$	0.945630	−	6.57700i	0.0897552	−	0.624261i
$112$	−0.612952	+	2.57377i	−0.0579185	+	0.243198i
$113$	2.26609	+	2.61521i	0.213176	+	0.246018i	0.852260	−	0.523119i	$-0.175232\pi$
$113$	2.26609	+	2.61521i	0.213176	+	0.246018i	−0.639084	+	0.769137i	$0.720686\pi$
$114$	−1.69449	−	2.93494i	−0.158703	−	0.274882i
$115$	13.3248	−	0.396496i	1.24255	−	0.0369734i
$116$	2.34142	−	4.05546i	0.217395	−	0.376540i
$117$	1.12209	−	3.24205i	0.103737	−	0.299728i
$118$	−8.91426	−	5.72885i	−0.820624	−	0.527383i
$119$	5.10946	+	5.84681i	0.468383	+	0.535977i
$120$	1.15471	−	2.52846i	0.105410	−	0.230816i
$121$	7.69065	−	6.04799i	0.699150	−	0.549818i
$122$	2.54611	−	2.42771i	0.230514	−	0.219795i
$123$	0.0633724	+	1.33035i	0.00571410	+	0.119954i
$124$	1.51484	−	2.12729i	0.136036	−	0.191036i
$125$	6.06368	−	1.78046i	0.542352	−	0.159249i
$126$	0.387528	+	2.61722i	0.0345238	+	0.233160i
$127$	4.27021	−	4.92809i	0.378920	−	0.437297i	−0.533969	−	0.845504i	$-0.679300\pi$
$127$	4.27021	−	4.92809i	0.378920	−	0.437297i	0.912890	+	0.408207i	$0.133846\pi$
$128$	0.723734	+	0.690079i	0.0639697	+	0.0609949i
$129$	3.52738	+	0.336824i	0.310569	+	0.0296557i
$130$	−0.453753	−	9.52546i	−0.0397968	−	0.835438i
$131$	−1.36339	−	5.61998i	−0.119120	−	0.491020i	−0.999849	−	0.0173983i	$-0.994462\pi$
$131$	−1.36339	−	5.61998i	−0.119120	−	0.491020i	0.880729	−	0.473621i	$-0.157053\pi$
$132$	0.156942	+	1.09155i	0.0136600	+	0.0950076i
$133$	8.92928	+	0.814802i	0.774267	+	0.0706523i
$134$	0.777296	−	5.40621i	0.0671482	−	0.467026i
$135$	0.132261	−	2.77650i	0.0113832	−	0.238963i
$136$	2.88177	−	0.555417i	0.247110	−	0.0476266i
$137$	4.12979	−	7.15301i	0.352832	−	0.611123i	−0.633912	−	0.773405i	$-0.718552\pi$
$137$	4.12979	−	7.15301i	0.352832	−	0.611123i	0.986744	+	0.162282i	$0.0518854\pi$
$138$	0.370575	+	4.78149i	0.0315454	+	0.407028i
$139$	−15.1000			−1.28077			−0.640383	−	0.768056i	$-0.721224\pi$
$139$	−15.1000			−1.28077			−0.640383	+	0.768056i	$0.721224\pi$
$140$	3.70386	+	6.35347i	0.313033	+	0.536966i
$141$	−2.82798	−	1.81743i	−0.238159	−	0.153056i
$142$	13.8923	−	5.56162i	1.16581	−	0.466721i
$143$	2.19456	+	3.08182i	0.183518	+	0.257715i
$144$	0.928368	+	0.371662i	0.0773640	+	0.0309719i
$145$	−3.06879	−	12.6497i	−0.254849	−	1.05050i
$146$	−11.6816	+	7.50731i	−0.966776	+	0.621310i
$147$	−6.24858	−	3.15519i	−0.515374	−	0.260236i
$148$	6.37548	−	1.87201i	0.524061	−	0.153878i
$149$	−11.2895	−	2.17587i	−0.924872	−	0.178254i	−0.295486	−	0.955347i	$-0.595482\pi$
$149$	−11.2895	−	2.17587i	−0.924872	−	0.178254i	−0.629386	+	0.777093i	$0.716694\pi$
$150$	−0.891735	−	2.57650i	−0.0728098	−	0.210370i
$151$	−2.75498	+	11.3562i	−0.224197	+	0.924154i	0.742830	+	0.669480i	$0.233483\pi$
$151$	−2.75498	+	11.3562i	−0.224197	+	0.924154i	−0.967027	+	0.254673i	$0.918032\pi$
$152$	1.96580	−	2.76058i	0.159447	−	0.223912i
$153$	2.46892	−	1.58668i	0.199600	−	0.128275i
$154$	−2.59893	−	1.32605i	−0.209428	−	0.106856i
$155$	−1.03308	−	7.18525i	−0.0829792	−	0.577133i
$156$	3.41521	−	0.326113i	0.273435	−	0.0261099i
$157$	16.2945	+	12.8142i	1.30044	+	1.02268i	0.997571	+	0.0696502i	$0.0221883\pi$
$157$	16.2945	+	12.8142i	1.30044	+	1.02268i	0.302873	+	0.953031i	$0.402054\pi$
$158$	−10.4291	+	5.37656i	−0.829693	+	0.427737i
$159$	2.72597	−	7.87617i	0.216183	−	0.624621i
$160$	2.77965			0.219751
$161$	−10.9010	−	6.49370i	−0.859119	−	0.511775i
$162$	1.00000			0.0785674
$163$	−2.91466	+	8.42135i	−0.228294	+	0.659611i	0.771435	+	0.636308i	$0.219539\pi$
$163$	−2.91466	+	8.42135i	−0.228294	+	0.659611i	−0.999728	+	0.0233027i	$0.992582\pi$
$164$	−1.18380	+	0.610293i	−0.0924395	+	0.0476559i
$165$	2.40952	+	1.89487i	0.187581	+	0.147515i
$166$	−14.5515	+	1.38950i	−1.12942	+	0.107846i
$167$	3.13525	+	21.8061i	0.242613	+	1.68741i	0.638905	+	0.769286i	$0.279388\pi$
$167$	3.13525	+	21.8061i	0.242613	+	1.68741i	−0.396292	+	0.918125i	$0.629703\pi$
$168$	−2.21972	+	1.43974i	−0.171255	+	0.111078i
$169$	−1.03475	+	0.664996i	−0.0795965	+	0.0511536i
$170$	4.73196	−	6.64510i	0.362924	−	0.509656i
$171$	0.798980	−	3.29344i	0.0610996	−	0.251856i
$172$	1.15894	+	3.34854i	0.0883685	+	0.255324i
$173$	−4.04050	−	0.778744i	−0.307194	−	0.0592068i	0.0333246	−	0.999445i	$-0.489390\pi$
$173$	−4.04050	−	0.778744i	−0.307194	−	0.0592068i	−0.340519	+	0.940238i	$0.610603\pi$
$174$	4.49315	−	1.31931i	0.340625	−	0.100017i
$175$	6.92979	+	2.00319i	0.523843	+	0.151427i
$176$	−0.927716	+	0.596207i	−0.0699293	+	0.0449408i
$177$	−2.49820	−	10.2977i	−0.187776	−	0.774023i
$178$	6.01591	+	2.40841i	0.450911	+	0.180518i
$179$	14.4118	+	20.2386i	1.07719	+	1.51270i	0.841028	+	0.540991i	$0.181951\pi$
$179$	14.4118	+	20.2386i	1.07719	+	1.51270i	0.236163	+	0.971713i	$0.424110\pi$
$180$	2.58054	−	1.03309i	0.192342	−	0.0770021i
$181$	−10.4441	−	6.71203i	−0.776306	−	0.498901i	0.0915001	−	0.995805i	$-0.470834\pi$
$181$	−10.4441	−	6.71203i	−0.776306	−	0.498901i	−0.867806	+	0.496904i	$0.834470\pi$
$182$	−4.50538	+	7.87981i	−0.333961	+	0.584091i
$183$	3.51802			0.260060
$184$	−4.19546	+	2.32339i	−0.309293	+	0.171283i
$185$	9.23488	−	15.9953i	0.678962	−	1.17600i
$186$	2.56433	−	0.494235i	0.188026	−	0.0362391i
$187$	−0.153996	+	3.23278i	−0.0112613	+	0.236404i
$188$	0.478410	−	3.32741i	0.0348916	−	0.242676i
$189$	−1.52562	+	2.16159i	−0.110972	+	0.157233i
$190$	−1.34063	−	9.32427i	−0.0972594	−	0.676454i
$191$	5.91450	+	24.3799i	0.427958	+	1.76407i	0.621942	+	0.783064i	$0.286344\pi$
$191$	5.91450	+	24.3799i	0.427958	+	1.76407i	−0.193983	+	0.981005i	$0.562141\pi$
$192$	0.0475819	+	0.998867i	0.00343393	+	0.0720870i
$193$	5.86881	+	0.560404i	0.422447	+	0.0403388i	0.304115	−	0.952635i	$-0.401639\pi$
$193$	5.86881	+	0.560404i	0.422447	+	0.0403388i	0.118332	+	0.992974i	$0.462245\pi$
$194$	−2.21599	−	2.11294i	−0.159099	−	0.151700i
$195$	6.24492	−	7.20702i	0.447208	−	0.516106i
$196$	0.274313	−	6.99462i	0.0195938	−	0.499616i
$197$	3.53115	−	1.03684i	0.251584	−	0.0738718i	−0.153509	−	0.988147i	$-0.549057\pi$
$197$	3.53115	−	1.03684i	0.251584	−	0.0738718i	0.405093	+	0.914276i	$0.367239\pi$
$198$	−0.639674	+	0.898297i	−0.0454597	+	0.0638392i
$199$	−0.967325	−	20.3066i	−0.0685718	−	1.43950i	−0.726887	−	0.686757i	$-0.759033\pi$
$199$	−0.967325	−	20.3066i	−0.0685718	−	1.43950i	0.658315	−	0.752743i	$-0.271270\pi$
$200$	1.97323	−	1.88147i	0.139528	−	0.133040i
$201$	4.29327	−	3.37627i	0.302824	−	0.238143i
$202$	−2.20666	+	4.83192i	−0.155260	+	0.339972i
$203$	−4.00303	+	11.7251i	−0.280958	+	0.822943i
$204$	2.46892	+	1.58668i	0.172859	+	0.111090i
$205$	−1.21084	+	3.49849i	−0.0845687	+	0.244345i
$206$	−0.602945	+	1.04433i	−0.0420092	+	0.0727620i
$207$	−3.03141	+	3.71625i	−0.210698	+	0.258298i
$208$	1.71537	+	2.97111i	0.118940	+	0.206009i
$209$	2.44740	+	2.82445i	0.169290	+	0.195371i
$210$	−1.70379	+	7.15418i	−0.117573	+	0.493685i
$211$	1.70495	−	11.8582i	0.117374	−	0.816351i	−0.843055	−	0.537827i	$-0.819245\pi$
$211$	1.70495	−	11.8582i	0.117374	−	0.816351i	0.960429	−	0.278525i	$-0.0898454\pi$
$212$	8.29683	−	0.792251i	0.569828	−	0.0544120i
$213$	13.8923	+	5.56162i	0.951882	+	0.381076i
$214$	5.13656	−	4.89770i	0.351128	−	0.334800i
$215$	8.75458	+	4.51330i	0.597057	+	0.307804i
$216$	0.415415	+	0.909632i	0.0282654	+	0.0618926i
$217$	−2.84386	+	6.29706i	−0.193054	+	0.427473i
$218$	5.31089	−	6.12910i	0.359699	−	0.415115i
$219$	−13.6350	−	2.62793i	−0.921369	−	0.177579i
$220$	−0.722681	+	2.97893i	−0.0487231	+	0.200839i
$221$	10.0230	+	0.957079i	0.674219	+	0.0643801i
$222$	5.90599	+	3.04475i	0.396384	+	0.204350i
$223$	−5.92181	−	1.73880i	−0.396553	−	0.116439i	0.0773748	−	0.997002i	$-0.475346\pi$
$223$	−5.92181	−	1.73880i	−0.396553	−	0.116439i	−0.473928	+	0.880563i	$0.657164\pi$
$224$	−2.23174	−	1.42104i	−0.149114	−	0.0949471i
$225$	1.13261	−	2.48007i	0.0755072	−	0.165338i
$226$	−3.21254	+	1.28611i	−0.213695	+	0.0855506i
$227$	7.74050	−	3.99051i	0.513755	−	0.264859i	−0.181795	−	0.983336i	$-0.558191\pi$
$227$	7.74050	−	3.99051i	0.513755	−	0.264859i	0.695551	+	0.718477i	$0.255161\pi$
$228$	3.32773	−	0.641367i	0.220384	−	0.0424756i
$229$	1.49811	+	2.59481i	0.0989980	+	0.171470i	0.911270	−	0.411809i	$-0.135103\pi$
$229$	1.49811	+	2.59481i	0.0989980	+	0.171470i	−0.812272	+	0.583279i	$0.801770\pi$
$230$	−3.98344	+	12.7217i	−0.262660	+	0.838841i
$231$	−0.965854	−	2.75317i	−0.0635485	−	0.181146i
$232$	3.06661	+	3.53906i	0.201333	+	0.232350i
$233$	0.594916	−	12.4888i	0.0389742	−	0.818170i	−0.891768	−	0.452493i	$-0.850535\pi$
$233$	0.594916	−	12.4888i	0.0389742	−	0.818170i	0.930742	−	0.365676i	$-0.119162\pi$
$234$	2.69674	+	2.12074i	0.176292	+	0.138637i
$235$	−5.42014	−	7.61152i	−0.353571	−	0.496521i
$236$	8.32933	−	6.55026i	0.542193	−	0.426386i
$237$	−11.2581	−	3.30569i	−0.731294	−	0.214727i
$238$	−7.19638	+	2.91614i	−0.466472	+	0.189025i
$239$	5.87654	+	12.8678i	0.380121	+	0.832350i	0.998905	+	0.0467883i	$0.0148986\pi$
$239$	5.87654	+	12.8678i	0.380121	+	0.832350i	−0.618783	+	0.785562i	$0.712374\pi$
$240$	2.01173	+	1.91818i	0.129856	+	0.123818i
$241$	0.488272	+	1.41077i	0.0314524	+	0.0908756i	0.959634	−	0.281252i	$-0.0907496\pi$
$241$	0.488272	+	1.41077i	0.0314524	+	0.0908756i	−0.928182	+	0.372127i	$0.878628\pi$
$242$	3.19999	+	9.24577i	0.205703	+	0.594341i
$243$	0.723734	+	0.690079i	0.0464276	+	0.0442686i
$244$	1.46144	+	3.20011i	0.0935591	+	0.204866i
$245$	−12.8651	−	14.5975i	−0.821920	−	0.932597i
$246$	−1.27791	−	0.375228i	−0.0814765	−	0.0239237i
$247$	9.13919	−	7.18714i	0.581513	−	0.457307i
$248$	1.51484	+	2.12729i	0.0961921	+	0.135083i
$249$	−11.4903	−	9.03606i	−0.728168	−	0.572637i
$250$	−0.300702	+	6.31251i	−0.0190181	+	0.399238i
$251$	−2.74858	−	3.17203i	−0.173489	−	0.200217i	0.662346	−	0.749199i	$-0.269561\pi$
$251$	−2.74858	−	3.17203i	−0.173489	−	0.200217i	−0.835834	+	0.548982i	$0.815016\pi$
$252$	−2.60002	−	0.489793i	−0.163786	−	0.0308541i
$253$	−1.39918	−	5.10030i	−0.0879660	−	0.320653i
$254$	3.26040	+	5.64718i	0.204576	+	0.354335i
$255$	8.01032	−	1.54386i	0.501626	−	0.0966805i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	20.4871	−	8.20181i	1.27795	−	0.511615i	0.369355	−	0.929288i	$-0.379579\pi$
$257$	20.4871	−	8.20181i	1.27795	−	0.511615i	0.908597	+	0.417673i	$0.137154\pi$
$258$	−1.47199	+	3.22322i	−0.0916423	+	0.200669i
$259$	−15.5918	+	8.12122i	−0.968827	+	0.504628i
$260$	9.14997	+	2.68667i	0.567457	+	0.166620i
$261$	4.16228	+	2.14580i	0.257638	+	0.132822i
$262$	5.75681	+	0.549708i	0.355657	+	0.0339611i
$263$	−4.42992	+	18.2604i	−0.273160	+	1.12598i	0.655543	+	0.755158i	$0.272440\pi$
$263$	−4.42992	+	18.2604i	−0.273160	+	1.12598i	−0.928703	+	0.370824i	$0.879075\pi$
$264$	−1.08285	−	0.208702i	−0.0666448	−	0.0128447i
$265$	15.1713	−	17.5086i	0.931964	−	1.07554i
$266$	−3.69047	+	8.17168i	−0.226277	+	0.501038i
$267$	2.69193	+	5.89450i	0.164743	+	0.360737i
$268$	4.85465	+	2.50275i	0.296545	+	0.152880i
$269$	−0.904703	+	0.862633i	−0.0551607	+	0.0525957i	−0.717158	−	0.696910i	$-0.754557\pi$
$269$	−0.904703	+	0.862633i	−0.0551607	+	0.0525957i	0.661997	+	0.749506i	$0.269709\pi$
$270$	2.58054	+	1.03309i	0.157047	+	0.0628719i
$271$	22.0323	−	2.10383i	1.33836	−	0.127798i	0.598808	−	0.800893i	$-0.295641\pi$
$271$	22.0323	−	2.10383i	1.33836	−	0.127798i	0.739556	+	0.673095i	$0.235035\pi$
$272$	−0.417667	+	2.90494i	−0.0253248	+	0.176138i
$273$	−8.69839	+	2.59382i	−0.526451	+	0.156985i
$274$	5.40888	+	6.24218i	0.326762	+	0.377104i
$275$	1.50334	+	2.60385i	0.0906546	+	0.157018i
$276$	−4.63972	−	1.21368i	−0.279278	−	0.0730549i
$277$	6.41919	−	11.1184i	0.385692	−	0.668037i	−0.606173	−	0.795333i	$-0.707296\pi$
$277$	6.41919	−	11.1184i	0.385692	−	0.668037i	0.991865	+	0.127295i	$0.0406295\pi$
$278$	4.93873	−	14.2695i	0.296205	−	0.855829i
$279$	2.19696	+	1.41190i	0.131528	+	0.0845282i
$280$	−7.21545	+	1.42213i	−0.431206	+	0.0849885i
$281$	6.01569	−	13.1725i	0.358866	−	0.785807i	−0.640967	−	0.767568i	$-0.721467\pi$
$281$	6.01569	−	13.1725i	0.358866	−	0.785807i	0.999834	−	0.0182393i	$-0.00580608\pi$
$282$	2.64242	−	2.07802i	0.157354	−	0.123744i
$283$	−18.3212	+	17.4693i	−1.08908	+	1.03844i	−0.0899871	+	0.995943i	$0.528683\pi$
$283$	−18.3212	+	17.4693i	−1.08908	+	1.03844i	−0.999097	+	0.0424963i	$0.986469\pi$
$284$	0.712024	+	14.9472i	0.0422509	+	0.886955i
$285$	5.46423	−	7.67343i	0.323673	−	0.454535i
$286$	−3.63010	+	1.06589i	−0.214652	+	0.0630275i
$287$	2.76069	−	2.18987i	0.162959	−	0.129264i
$288$	−0.654861	+	0.755750i	−0.0385880	+	0.0445330i
$289$	−6.06988	−	5.78761i	−0.357051	−	0.340448i
$290$	12.9577	+	1.23731i	0.760903	+	0.0726575i
$291$	−0.145690	−	3.05842i	−0.00854052	−	0.179288i
$292$	−3.27374	−	13.4945i	−0.191581	−	0.789707i
$293$	−3.06928	−	21.3473i	−0.179309	−	1.24712i	−0.858366	−	0.513038i	$-0.828520\pi$
$293$	−3.06928	−	21.3473i	−0.179309	−	1.24712i	0.679056	−	0.734086i	$-0.262389\pi$
$294$	5.02537	−	4.87295i	0.293086	−	0.284196i
$295$	4.19178	−	29.1545i	0.244055	−	1.69744i
$296$	−0.316164	+	6.63711i	−0.0183767	+	0.385774i
$297$	−1.08285	+	0.208702i	−0.0628333	+	0.0121101i
$298$	5.74864	−	9.95693i	0.333010	−	0.576789i
$299$	−16.0562	+	3.59295i	−0.928552	+	0.207786i
$300$	2.72645			0.157412
$301$	−4.72158	−	8.09925i	−0.272148	−	0.466833i
$302$	−9.83054	−	6.31771i	−0.565684	−	0.363543i
$303$	−4.93144	+	1.97425i	−0.283304	+	0.113418i
$304$	1.96580	+	2.76058i	0.112746	+	0.158330i
$305$	9.07839	+	3.63444i	0.519827	+	0.208107i
$306$	0.691908	+	2.85208i	0.0395537	+	0.163043i
$307$	5.51574	−	3.54475i	0.314800	−	0.202310i	−0.373693	−	0.927552i	$-0.621909\pi$
$307$	5.51574	−	3.54475i	0.314800	−	0.202310i	0.688493	+	0.725243i	$0.258272\pi$
$308$	2.10315	−	2.02228i	0.119838	−	0.115230i
$309$	−1.15704	+	0.339739i	−0.0658219	+	0.0193271i
$310$	7.12795	+	1.37380i	0.404840	+	0.0780266i
$311$	−7.02446	−	20.2959i	−0.398321	−	1.15087i	−0.948760	−	0.315997i	$-0.897661\pi$
$311$	−7.02446	−	20.2959i	−0.398321	−	1.15087i	0.550439	−	0.834875i	$-0.314460\pi$
$312$	−0.808828	+	3.33403i	−0.0457909	+	0.188753i
$313$	9.58035	−	13.4537i	0.541513	−	0.760449i	−0.449634	−	0.893213i	$-0.648446\pi$
$313$	9.58035	−	13.4537i	0.541513	−	0.760449i	0.991148	+	0.132764i	$0.0423851\pi$
$314$	−17.4388	+	11.2072i	−0.984129	+	0.632461i
$315$	−6.17004	+	4.00197i	−0.347642	+	0.225485i
$316$	−1.66984	−	11.6140i	−0.0939358	−	0.653338i
$317$	0.298082	−	0.0284634i	0.0167420	−	0.00159866i	−0.0866817	−	0.996236i	$-0.527626\pi$
$317$	0.298082	−	0.0284634i	0.0167420	−	0.00159866i	0.103424	+	0.994637i	$0.467020\pi$
$318$	6.55141	+	5.15209i	0.367385	+	0.288915i
$319$	−4.59007	+	2.36634i	−0.256995	+	0.132490i
$320$	−0.909134	+	2.62677i	−0.0508221	+	0.146841i
$321$	7.09730			0.396133
$322$	9.70192	−	8.17757i	0.540667	−	0.455718i
$323$	9.94599			0.553410
$324$	−0.327068	+	0.945001i	−0.0181704	+	0.0525000i
$325$	8.31394	−	4.28613i	0.461174	−	0.237752i
$326$	−7.00489	−	5.50871i	−0.387965	−	0.305099i
$327$	8.07324	−	0.770901i	0.446451	−	0.0426309i
$328$	−0.189543	−	1.31830i	−0.0104658	−	0.0727911i
$329$	0.460514	+	8.88210i	0.0253890	+	0.489686i
$330$	−2.57873	+	1.65725i	−0.141954	+	0.0912284i
$331$	−15.9208	+	22.3576i	−0.875087	+	1.22889i	0.0972399	+	0.995261i	$0.468999\pi$
$331$	−15.9208	+	22.3576i	−0.875087	+	1.22889i	−0.972326	+	0.233626i	$0.924941\pi$
$332$	3.44625	−	14.2057i	0.189138	−	0.779636i
$333$	2.17325	+	6.27918i	0.119093	+	0.344097i
$334$	−21.6323	−	4.16928i	−1.18367	−	0.228133i
$335$	14.5669	−	4.27724i	0.795877	−	0.233691i
$336$	−0.634556	−	2.56853i	−0.0346179	−	0.140125i
$337$	24.2854	−	15.6073i	1.32291	−	0.850183i	0.327405	−	0.944884i	$-0.393826\pi$
$337$	24.2854	−	15.6073i	1.32291	−	0.850183i	0.995506	+	0.0947014i	$0.0301896\pi$
$338$	−0.289987	−	1.19534i	−0.0157732	−	0.0650181i
$339$	−3.21254	−	1.28611i	−0.174481	−	0.0698518i
$340$	4.73196	+	6.64510i	0.256626	+	0.360381i
$341$	−2.67364	+	1.07036i	−0.144786	+	0.0579635i
$342$	2.85098	+	1.83222i	0.154164	+	0.0990749i
$343$	2.86654	+	18.2971i	0.154778	+	0.987949i
$344$	−3.54343			−0.191049
$345$	−11.6619	+	6.45821i	−0.627856	+	0.347698i
$346$	2.05743	−	3.56358i	0.110608	−	0.191579i
$347$	−2.11770	+	0.408153i	−0.113684	+	0.0219108i	−0.245776	−	0.969327i	$-0.579043\pi$
$347$	−2.11770	+	0.408153i	−0.113684	+	0.0219108i	0.132092	+	0.991237i	$0.457831\pi$
$348$	−0.222819	+	4.67754i	−0.0119443	+	0.250742i
$349$	−0.935800	+	6.50863i	−0.0500922	+	0.348399i	0.949326	+	0.314293i	$0.101767\pi$
$349$	−0.935800	+	6.50863i	−0.0500922	+	0.348399i	−0.999418	+	0.0341061i	$0.989142\pi$
$350$	−4.15952	+	5.89348i	−0.222336	+	0.315020i
$351$	0.488245	+	3.39582i	0.0260606	+	0.181256i
$352$	−0.259990	−	1.07169i	−0.0138575	−	0.0571214i
$353$	−0.972677	−	20.4190i	−0.0517704	−	1.08679i	−0.864012	−	0.503472i	$-0.832056\pi$
$353$	−0.972677	−	20.4190i	−0.0517704	−	1.08679i	0.812241	−	0.583322i	$-0.198247\pi$
$354$	10.5484	+	1.00725i	0.560642	+	0.0535348i
$355$	30.1038	+	28.7039i	1.59775	+	1.52345i
$356$	−4.24356	+	4.89732i	−0.224908	+	0.259558i
$357$	−7.22063	−	2.85557i	−0.382156	−	0.151133i
$358$	−23.8391	+	6.99981i	−1.25994	+	0.369951i
$359$	−6.11699	+	8.59011i	−0.322843	+	0.453369i	−0.943820	−	0.330459i	$-0.892796\pi$
$359$	−6.11699	+	8.59011i	−0.322843	+	0.453369i	0.620978	+	0.783828i	$0.286736\pi$
$360$	0.132261	+	2.77650i	0.00697077	+	0.146334i
$361$	−5.43877	+	5.18585i	−0.286251	+	0.272940i
$362$	9.75881	−	7.67441i	0.512912	−	0.403358i
$363$	−4.06437	+	8.89973i	−0.213324	+	0.467115i
$364$	−5.97286	−	6.83482i	−0.313063	−	0.358242i
$365$	−32.4708	−	20.8677i	−1.69960	−	1.09227i
$366$	−1.15063	+	3.32453i	−0.0601445	+	0.173776i
$367$	4.19605	−	7.26777i	0.219032	−	0.379375i	−0.735480	−	0.677546i	$-0.763043\pi$
$367$	4.19605	−	7.26777i	0.219032	−	0.379375i	0.954512	+	0.298171i	$0.0963767\pi$
$368$	−0.823406	−	4.72462i	−0.0429230	−	0.246288i
$369$	−0.665930	−	1.15342i	−0.0346669	−	0.0600449i
$370$	12.0951	+	13.9585i	0.628795	+	0.725668i
$371$	−21.1317	+	6.30137i	−1.09710	+	0.327151i
$372$	−0.371659	+	2.58495i	−0.0192696	+	0.134023i
$373$	−19.5924	+	1.87084i	−1.01445	+	0.0968686i	−0.589018	−	0.808120i	$-0.700485\pi$
$373$	−19.5924	+	1.87084i	−1.01445	+	0.0968686i	−0.425436	+	0.904988i	$0.639879\pi$
$374$	−3.00461	−	1.20287i	−0.155365	−	0.0621987i
$375$	−4.57376	+	4.36107i	−0.236188	+	0.225205i
$376$	2.98793	+	1.54039i	0.154091	+	0.0794394i
$377$	6.67390	+	14.6138i	0.343723	+	0.752649i
$378$	−1.54373	−	2.14870i	−0.0794007	−	0.110517i
$379$	−18.0499	+	20.8307i	−0.927160	+	1.07000i	0.0702111	+	0.997532i	$0.477633\pi$
$379$	−18.0499	+	20.8307i	−0.927160	+	1.07000i	−0.997371	+	0.0724671i	$0.976913\pi$
$380$	9.24992	+	1.78278i	0.474511	+	0.0914545i
$381$	−1.53734	+	6.33699i	−0.0787601	+	0.324654i
$382$	−24.9735	−	2.38468i	−1.27775	−	0.122011i
$383$	−2.18465	−	1.12627i	−0.111630	−	0.0575495i	0.401507	−	0.915856i	$-0.368487\pi$
$383$	−2.18465	−	1.12627i	−0.111630	−	0.0575495i	−0.513137	+	0.858306i	$0.671517\pi$
$384$	−0.959493	−	0.281733i	−0.0489639	−	0.0143771i
$385$	0.351858	−	8.10249i	0.0179324	−	0.412941i
$386$	−2.44908	+	5.36274i	−0.124655	+	0.272957i
$387$	−3.28961	+	1.31696i	−0.167220	+	0.0669448i
$388$	2.72151	−	1.40304i	0.138164	−	0.0712284i
$389$	25.0157	−	4.82138i	1.26835	−	0.244454i	0.489685	−	0.871899i	$-0.337112\pi$
$389$	25.0157	−	4.82138i	1.26835	−	0.244454i	0.778660	+	0.627446i	$0.215900\pi$
$390$	4.76813	+	8.25864i	0.241444	+	0.418193i
$391$	−12.6965	−	6.07453i	−0.642091	−	0.307202i
$392$	6.52021	+	2.54694i	0.329320	+	0.128640i
$393$	3.78705	+	4.37049i	0.191032	+	0.220462i
$394$	−0.175112	+	3.67606i	−0.00882203	+	0.185197i
$395$	−25.6370	−	20.1611i	−1.28994	−	1.01442i
$396$	−0.639674	−	0.898297i	−0.0321448	−	0.0451411i
$397$	−5.46048	+	4.29417i	−0.274054	+	0.215518i	−0.745721	−	0.666258i	$-0.767895\pi$
$397$	−5.46048	+	4.29417i	−0.274054	+	0.215518i	0.471667	+	0.881777i	$0.343652\pi$
$398$	19.5062	+	5.72753i	0.977756	+	0.287095i
$399$	−8.31002	+	3.36741i	−0.416022	+	0.168581i
$400$	1.13261	+	2.48007i	0.0566304	+	0.124003i
$401$	−8.25650	−	7.87256i	−0.412310	−	0.393137i	0.455336	−	0.890320i	$-0.349519\pi$
$401$	−8.25650	−	7.87256i	−0.412310	−	0.393137i	−0.867646	+	0.497183i	$0.834368\pi$
$402$	1.78638	+	5.16141i	0.0890967	+	0.257428i
$403$	2.93036	+	8.46671i	0.145972	+	0.421757i
$404$	−3.84444	−	3.66566i	−0.191268	−	0.182374i
$405$	1.15471	+	2.52846i	0.0573779	+	0.125640i
$406$	−9.77100	−	7.61778i	−0.484927	−	0.378064i
$407$	−7.03074	−	2.06441i	−0.348501	−	0.102329i
$408$	−2.30692	+	1.81418i	−0.114209	+	0.0898153i
$409$	8.70896	+	12.2300i	0.430631	+	0.604736i	0.971693	−	0.236246i	$-0.0759172\pi$
$409$	8.70896	+	12.2300i	0.430631	+	0.604736i	−0.541063	+	0.840982i	$0.681978\pi$
$410$	−2.91005	−	2.28849i	−0.143717	−	0.113020i
$411$	−0.393007	+	8.25023i	−0.0193856	+	0.406954i
$412$	−0.789690	−	0.911351i	−0.0389053	−	0.0448991i
$413$	−18.2701	+	21.2647i	−0.899015	+	1.04637i
$414$	−2.52039	−	4.08015i	−0.123870	−	0.200529i
$415$	−20.3160	−	35.1884i	−0.997275	−	1.72733i
$416$	−3.36874	+	0.649272i	−0.165166	+	0.0318332i
$417$	13.4214	−	6.91922i	0.657250	−	0.338836i
$418$	−3.46958	+	1.38901i	−0.169703	+	0.0679386i
$419$	−12.5396	+	27.4578i	−0.612598	+	1.34140i	0.308184	+	0.951327i	$0.400279\pi$
$419$	−12.5396	+	27.4578i	−0.612598	+	1.34140i	−0.920782	+	0.390077i	$0.872449\pi$
$420$	−6.20345	−	3.94999i	−0.302697	−	0.192740i
$421$	−10.2792	−	3.01825i	−0.500978	−	0.147101i	0.0214733	−	0.999769i	$-0.493164\pi$
$421$	−10.2792	−	3.01825i	−0.500978	−	0.147101i	−0.522452	+	0.852669i	$0.674983\pi$
$422$	10.6484	+	5.48961i	0.518354	+	0.267230i
$423$	3.34641	+	0.319543i	0.162708	+	0.0155367i
$424$	−1.96495	+	8.09963i	−0.0954263	+	0.393353i
$425$	7.85702	+	1.51432i	0.381121	+	0.0734551i
$426$	−9.79945	+	11.3092i	−0.474785	+	0.547931i
$427$	−5.43087	−	7.55917i	−0.262818	−	0.365814i
$428$	2.94833	+	6.45593i	0.142513	+	0.312059i
$429$	−3.36277	−	1.73363i	−0.162356	−	0.0837005i
$430$	−7.12841	+	6.79693i	−0.343763	+	0.327777i
$431$	1.13536	+	0.454531i	0.0546885	+	0.0218940i	0.398845	−	0.917018i	$-0.369411\pi$
$431$	1.13536	+	0.454531i	0.0546885	+	0.0218940i	−0.344157	+	0.938912i	$0.611835\pi$
$432$	−0.995472	+	0.0950560i	−0.0478947	+	0.00457339i
$433$	0.882145	−	6.13545i	0.0423932	−	0.294851i	−0.957584	−	0.288153i	$-0.906959\pi$
$433$	0.882145	−	6.13545i	0.0423932	−	0.294851i	0.999978	−	0.00669803i	$-0.00213207\pi$
$434$	−5.02059	−	4.74702i	−0.240996	−	0.227864i
$435$	8.52410	+	9.83733i	0.408699	+	0.471664i
$436$	4.05498	+	7.02343i	0.194198	+	0.336361i
$437$	−15.4515	+	5.04079i	−0.739145	+	0.241133i
$438$	6.94298	−	12.0256i	0.331748	−	0.574605i
$439$	−7.67738	+	22.1823i	−0.366421	+	1.05871i	0.599613	+	0.800290i	$0.295321\pi$
$439$	−7.67738	+	22.1823i	−0.366421	+	1.05871i	−0.966034	+	0.258415i	$0.916800\pi$
$440$	−2.57873	−	1.65725i	−0.122936	−	0.0790061i
$441$	6.99975	−	0.0588156i	0.333322	−	0.00280075i
$442$	−4.18264	+	9.15870i	−0.198948	+	0.435635i
$443$	19.0728	−	14.9990i	0.906177	−	0.712625i	−0.0520469	−	0.998645i	$-0.516575\pi$
$443$	19.0728	−	14.9990i	0.906177	−	0.712625i	0.958224	+	0.286019i	$0.0923321\pi$
$444$	−4.80895	+	4.58532i	−0.228223	+	0.217610i
$445$	0.857063	+	17.9920i	0.0406287	+	0.852901i
$446$	3.58000	−	5.02741i	0.169518	−	0.238055i
$447$	11.0316	−	3.23916i	0.521774	−	0.153207i
$448$	2.07281	−	1.64422i	0.0979311	−	0.0776820i
$449$	23.6983	−	27.3493i	1.11839	−	1.29069i	0.165895	−	0.986143i	$-0.446949\pi$
$449$	23.6983	−	27.3493i	1.11839	−	1.29069i	0.952497	−	0.304549i	$-0.0985057\pi$
$450$	1.97323	+	1.88147i	0.0930187	+	0.0886932i
$451$	1.46210	+	0.139613i	0.0688474	+	0.00657413i
$452$	−0.164653	−	3.45650i	−0.00774464	−	0.162580i
$453$	−2.75498	−	11.3562i	−0.129440	−	0.533560i
$454$	1.23936	+	8.61995i	0.0581661	+	0.404554i
$455$	−25.1262	−	2.29278i	−1.17793	−	0.107487i
$456$	−0.482301	+	3.35448i	−0.0225858	+	0.157088i
$457$	−1.97506	+	41.4616i	−0.0923894	+	1.93949i	0.193237	+	0.981152i	$0.438101\pi$
$457$	−1.97506	+	41.4616i	−0.0923894	+	1.93949i	−0.285627	+	0.958341i	$0.592202\pi$
$458$	−2.94208	+	0.567039i	−0.137474	+	0.0264960i
$459$	−1.46741	+	2.54162i	−0.0684926	+	0.118633i
$460$	−10.7191	−	7.92520i	−0.499782	−	0.369514i
$461$	3.66529			0.170710			0.0853549	−	0.996351i	$-0.472798\pi$
$461$	3.66529			0.170710			0.0853549	+	0.996351i	$0.472798\pi$
$462$	2.91765	−	0.0122576i	0.135741	−	0.000570276i
$463$	8.25333	+	5.30409i	0.383565	+	0.246502i	0.718187	−	0.695850i	$-0.244972\pi$
$463$	8.25333	+	5.30409i	0.383565	+	0.246502i	−0.334622	+	0.942352i	$0.608609\pi$
$464$	−4.34740	+	1.74044i	−0.201823	+	0.0807977i
$465$	4.21071	+	5.91312i	0.195267	+	0.274214i
$466$	11.6074	+	4.64689i	0.537701	+	0.215263i
$467$	−6.03069	−	24.8588i	−0.279067	−	1.15033i	−0.922862	−	0.385132i	$-0.874156\pi$
$467$	−6.03069	−	24.8588i	−0.279067	−	1.15033i	0.643795	−	0.765198i	$-0.277359\pi$
$468$	−2.88612	+	1.85480i	−0.133411	+	0.0857381i
$469$	−13.8822	−	4.01291i	−0.641021	−	0.185299i
$470$	8.96564	−	2.63255i	0.413554	−	0.121431i
$471$	−20.3549	−	3.92309i	−0.937906	−	0.180767i
$472$	3.46574	+	10.0136i	0.159524	+	0.460914i
$473$	0.921256	−	3.79747i	0.0423594	−	0.174608i
$474$	6.80605	−	9.55776i	0.312612	−	0.439003i
$475$	7.77307	−	4.99545i	0.356653	−	0.229207i
$476$	−0.402044	−	7.75436i	−0.0184277	−	0.355421i
$477$	1.18613	+	8.24973i	0.0543093	+	0.377729i
$478$	−14.0821	+	1.34468i	−0.644101	+	0.0615042i
$479$	−18.8152	−	14.7965i	−0.859689	−	0.676067i	0.0877013	−	0.996147i	$-0.472048\pi$
$479$	−18.8152	−	14.7965i	−0.859689	−	0.676067i	−0.947391	+	0.320080i	$0.896290\pi$
$480$	−2.47065	+	1.27371i	−0.112769	+	0.0581366i
$481$	−7.45585	+	21.5423i	−0.339957	+	0.982242i
$482$	−1.49288			−0.0679986
$483$	12.6648	+	0.776705i	0.576268	+	0.0353413i
$484$	−9.78388			−0.444722
$485$	2.78366	−	8.04287i	0.126400	−	0.365208i
$486$	−0.888835	+	0.458227i	−0.0403184	+	0.0207856i
$487$	−19.3629	−	15.2271i	−0.877415	−	0.690007i	0.0742189	−	0.997242i	$-0.476354\pi$
$487$	−19.3629	−	15.2271i	−0.877415	−	0.690007i	−0.951634	+	0.307235i	$0.900596\pi$
$488$	−3.50209	+	0.334409i	−0.158532	+	0.0151380i
$489$	−1.26823	−	8.82077i	−0.0573516	−	0.398889i
$490$	18.0024	−	7.38316i	0.813264	−	0.333537i
$491$	17.4320	−	11.2029i	0.786695	−	0.505578i	−0.0845543	−	0.996419i	$-0.526947\pi$
$491$	17.4320	−	11.2029i	0.786695	−	0.505578i	0.871249	+	0.490841i	$0.163310\pi$
$492$	0.772554	−	1.08490i	0.0348294	−	0.0489111i
$493$	−3.24010	+	13.3559i	−0.145927	+	0.601517i
$494$	3.80272	+	10.9872i	0.171092	+	0.494339i
$495$	−3.00994	−	0.580119i	−0.135287	−	0.0260744i
$496$	−2.50574	+	0.735753i	−0.112511	+	0.0330363i
$497$	−9.49560	−	38.4359i	−0.425936	−	1.72409i
$498$	12.2972	−	7.90293i	0.551050	−	0.354139i
$499$	−3.15574	−	13.0081i	−0.141270	−	0.582325i	−0.997804	−	0.0662336i	$-0.978902\pi$
$499$	−3.15574	−	13.0081i	−0.141270	−	0.582325i	0.856534	−	0.516091i	$-0.172613\pi$
$500$	−5.86698	−	2.34878i	−0.262379	−	0.105041i
$501$	−12.7789	−	17.9454i	−0.570918	−	0.801742i
$502$	3.89654	−	1.55994i	0.173911	−	0.0696236i
$503$	0.549284	+	0.353004i	0.0244914	+	0.0157397i	0.552829	−	0.833295i	$-0.313548\pi$
$503$	0.549284	+	0.353004i	0.0244914	+	0.0157397i	−0.528338	+	0.849034i	$0.677185\pi$
$504$	1.31324	−	2.29683i	0.0584963	−	0.102309i
$505$	−14.7653			−0.657049
$506$	5.27742	+	0.345914i	0.234610	+	0.0153777i
$507$	0.615007	−	1.06522i	0.0273134	−	0.0473083i
$508$	−6.40296	+	1.23407i	−0.284085	+	0.0547530i
$509$	0.880338	−	18.4806i	0.0390203	−	0.819137i	−0.891527	−	0.452967i	$-0.850366\pi$
$509$	0.880338	−	18.4806i	0.0390203	−	0.819137i	0.930548	−	0.366170i	$-0.119331\pi$
$510$	−1.16097	+	8.07471i	−0.0514085	+	0.357554i
$511$	15.4021	+	33.3543i	0.681349	+	1.47551i
$512$	−0.142315	−	0.989821i	−0.00628949	−	0.0437443i
$513$	0.798980	+	3.29344i	0.0352758	+	0.145409i
$514$	1.05003	+	22.0429i	0.0463150	+	0.972271i
$515$	−3.33677	−	0.318623i	−0.147036	−	0.0140402i
$516$	−2.56450	−	2.44525i	−0.112896	−	0.107646i
$517$	−2.42765	+	2.80166i	−0.106768	+	0.123217i
$518$	−2.57498	−	17.3904i	−0.113138	−	0.764092i
$519$	3.94818	−	1.15929i	0.173306	−	0.0508873i
$520$	−5.53157	+	7.76801i	−0.242575	+	0.340650i
$521$	−1.38111	−	28.9932i	−0.0605077	−	1.27021i	−0.801211	−	0.598381i	$-0.795811\pi$
$521$	−1.38111	−	28.9932i	−0.0605077	−	1.27021i	0.740704	−	0.671832i	$-0.234492\pi$
$522$	−3.38913	+	3.23153i	−0.148338	+	0.141440i
$523$	−16.3015	+	12.8196i	−0.712815	+	0.560564i	−0.907373	−	0.420327i	$-0.861915\pi$
$523$	−16.3015	+	12.8196i	−0.712815	+	0.560564i	0.194558	+	0.980891i	$0.437673\pi$
$524$	−2.40234	+	5.26039i	−0.104947	+	0.229801i
$525$	−7.07735	+	1.39491i	−0.308881	+	0.0608789i
$526$	−15.8072	−	10.1587i	−0.689226	−	0.442938i
$527$	−2.50676	+	7.24281i	−0.109196	+	0.315502i
$528$	0.551389	−	0.955034i	0.0239961	−	0.0415625i
$529$	22.8032	+	3.00222i	0.991444	+	0.130531i
$530$	11.5836	+	20.0634i	0.503159	+	0.871497i
$531$	6.93917	+	8.00823i	0.301134	+	0.347527i
$532$	−6.51521	−	6.16019i	−0.282470	−	0.267078i
$533$	0.650274	−	4.52276i	0.0281665	−	0.195902i
$534$	−6.45075	+	0.615972i	−0.279151	+	0.0266557i
$535$	18.3148	+	7.33216i	0.791820	+	0.316997i
$536$	−3.95290	+	3.76908i	−0.170739	+	0.162799i
$537$	−22.0836	−	11.3849i	−0.952979	−	0.491295i
$538$	−0.519289	−	1.13708i	−0.0223882	−	0.0490232i
$539$	−4.42473	+	6.32548i	−0.190587	+	0.272458i
$540$	−1.82028	+	2.10072i	−0.0783325	+	0.0904005i
$541$	−30.9811	−	5.97113i	−1.33198	−	0.256719i	−0.526924	−	0.849913i	$-0.676655\pi$
$541$	−30.9811	−	5.97113i	−1.33198	−	0.256719i	−0.805060	+	0.593194i	$0.797867\pi$
$542$	−5.21793	+	21.5086i	−0.224129	+	0.923873i
$543$	12.3587	+	1.18012i	0.530364	+	0.0506436i
$544$	−2.60856	−	1.34481i	−0.111841	−	0.0576582i
$545$	21.6297	+	6.35105i	0.926514	+	0.272049i
$546$	0.393802	−	9.06834i	0.0168532	−	0.388089i
$547$	11.9224	−	26.1064i	0.509764	−	1.11623i	−0.463407	−	0.886146i	$-0.653373\pi$
$547$	11.9224	−	26.1064i	0.509764	−	1.11623i	0.973171	−	0.230083i	$-0.0738997\pi$
$548$	−7.66794	+	3.06978i	−0.327558	+	0.131134i
$549$	−3.12694	+	1.61205i	−0.133455	+	0.0688007i
$550$	−2.95234	+	0.569016i	−0.125888	+	0.0242629i
$551$	7.93501	+	13.7438i	0.338043	+	0.585507i
$552$	2.66443	−	3.98758i	0.113406	−	0.169723i
$553$	10.2766	+	29.2934i	0.437004	+	1.24568i
$554$	8.40735	+	9.70260i	0.357194	+	0.412224i
$555$	−0.878826	+	18.4488i	−0.0373041	+	0.783109i
$556$	11.8694	+	9.33420i	0.503375	+	0.395858i
$557$	2.57144	+	3.61108i	0.108955	+	0.153006i	0.865453	−	0.500990i	$-0.167031\pi$
$557$	2.57144	+	3.61108i	0.108955	+	0.153006i	−0.756498	+	0.653996i	$0.773091\pi$
$558$	−2.05280	+	1.61434i	−0.0869020	+	0.0683405i
$559$	−11.6642	−	3.42491i	−0.493342	−	0.144858i
$560$	1.01603	−	7.28374i	0.0429351	−	0.307794i
$561$	−1.34447	−	2.94398i	−0.0567635	−	0.124295i
$562$	10.4805	+	9.99315i	0.442094	+	0.421536i
$563$	2.12795	+	6.14831i	0.0896824	+	0.259120i	0.980919	−	0.194419i	$-0.0622823\pi$
$563$	2.12795	+	6.14831i	0.0896824	+	0.259120i	−0.891236	+	0.453540i	$0.850161\pi$
$564$	1.09948	+	3.17674i	0.0462965	+	0.133765i
$565$	−6.96142	−	6.63770i	−0.292869	−	0.279250i
$566$	−10.5162	−	23.0272i	−0.442028	−	0.967906i
$567$	0.365524	−	2.62038i	0.0153506	−	0.110046i
$568$	−14.3580	−	4.21589i	−0.602449	−	0.176895i
$569$	−10.9848	+	8.63851i	−0.460505	+	0.362145i	−0.821297	−	0.570501i	$-0.806749\pi$
$569$	−10.9848	+	8.63851i	−0.460505	+	0.362145i	0.360792	+	0.932646i	$0.382507\pi$
$570$	5.46423	+	7.67343i	0.228871	+	0.321405i
$571$	−14.1428	−	11.1220i	−0.591856	−	0.465441i	0.276751	−	0.960942i	$-0.410742\pi$
$571$	−14.1428	−	11.1220i	−0.591856	−	0.465441i	−0.868608	+	0.495501i	$0.834985\pi$
$572$	0.180019	−	3.77906i	0.00752697	−	0.158011i
$573$	−16.4285	−	18.9595i	−0.686312	−	0.792046i
$574$	1.16649	+	3.32509i	0.0486884	+	0.138787i
$575$	−12.9737	+	1.62951i	−0.541039	+	0.0679553i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	24.6397	−	4.74892i	1.02577	−	0.197700i	0.351499	−	0.936188i	$-0.385672\pi$
$577$	24.6397	−	4.74892i	1.02577	−	0.197700i	0.674267	+	0.738488i	$0.264460\pi$
$578$	7.45456	−	3.84309i	0.310069	−	0.159852i
$579$	−5.47320	+	2.19114i	−0.227459	+	0.0910607i
$580$	−5.40732	+	11.8404i	−0.224527	+	0.491645i
$581$	−1.67791	+	38.6384i	−0.0696114	+	1.60299i
$582$	2.93786	+	0.862633i	0.121778	+	0.0357573i
$583$	−8.16945	−	4.21164i	−0.338344	−	0.174428i
$584$	13.8231	+	1.31994i	0.572003	+	0.0546197i
$585$	−2.24826	+	9.26745i	−0.0929540	+	0.383162i
$586$	21.1771	+	4.08155i	0.874818	+	0.168607i
$587$	26.0743	−	30.0914i	1.07620	−	1.24200i	0.107388	−	0.994217i	$-0.465751\pi$
$587$	26.0743	−	30.0914i	1.07620	−	1.24200i	0.968814	−	0.247787i	$-0.0797034\pi$
$588$	2.96130	+	6.34277i	0.122122	+	0.261571i
$589$	3.67659	+	8.05060i	0.151491	+	0.331719i
$590$	26.1800	+	13.4967i	1.07781	+	0.555652i
$591$	−2.66350	+	2.53965i	−0.109562	+	0.104467i
$592$	−6.16867	−	2.46956i	−0.253531	−	0.101498i
$593$	25.2279	−	2.40897i	1.03598	−	0.0989245i	0.436819	−	0.899549i	$-0.356105\pi$
$593$	25.2279	−	2.40897i	1.03598	−	0.0989245i	0.599166	+	0.800625i	$0.295499\pi$
$594$	0.156942	−	1.09155i	0.00643940	−	0.0447870i
$595$	−15.6830	−	14.8285i	−0.642942	−	0.607908i
$596$	7.52911	+	8.68906i	0.308404	+	0.355918i
$597$	10.1648	+	17.6060i	0.416019	+	0.720566i
$598$	1.85612	−	16.3482i	0.0759023	−	0.668529i
$599$	18.5142	−	32.0676i	0.756471	−	1.31025i	−0.188168	−	0.982137i	$-0.560255\pi$
$599$	18.5142	−	32.0676i	0.756471	−	1.31025i	0.944640	−	0.328110i	$-0.106412\pi$
$600$	−0.891735	+	2.57650i	−0.0364049	+	0.105185i
$601$	7.60043	+	4.88450i	0.310028	+	0.199243i	0.686397	−	0.727227i	$-0.259191\pi$
$601$	7.60043	+	4.88450i	0.310028	+	0.199243i	−0.376369	+	0.926470i	$0.622828\pi$
$602$	9.19808	−	1.81290i	0.374886	−	0.0738881i
$603$	−2.26892	+	4.96824i	−0.0923974	+	0.202322i
$604$	9.18549	−	7.22355i	0.373752	−	0.293922i
$605$	−19.6825	+	18.7672i	−0.800207	+	0.762996i
$606$	−0.252753	−	5.30593i	−0.0102674	−	0.215539i
$607$	11.0622	−	15.5347i	0.449002	−	0.630535i	−0.526592	−	0.850118i	$-0.676530\pi$
$607$	11.0622	−	15.5347i	0.449002	−	0.630535i	0.975594	+	0.219583i	$0.0704698\pi$
$608$	−3.25169	+	0.954784i	−0.131874	+	0.0387216i
$609$	−1.81473	−	12.2560i	−0.0735367	−	0.496639i
$610$	−6.40380	+	7.39038i	−0.259282	+	0.299228i
$611$	8.34674	+	7.95860i	0.337673	+	0.321970i
$612$	−2.92152	−	0.278971i	−0.118096	−	0.0112768i
$613$	−1.38468	−	29.0680i	−0.0559267	−	1.17405i	−0.836134	−	0.548526i	$-0.815189\pi$
$613$	−1.38468	−	29.0680i	−0.0559267	−	1.17405i	0.780207	−	0.625521i	$-0.215114\pi$
$614$	1.54577	+	6.37176i	0.0623823	+	0.257143i
$615$	−0.526864	−	3.66442i	−0.0212452	−	0.147764i
$616$	1.22319	+	2.64890i	0.0492836	+	0.106727i
$617$	2.24418	−	15.6086i	0.0903471	−	0.628378i	−0.893459	−	0.449144i	$-0.851729\pi$
$617$	2.24418	−	15.6086i	0.0903471	−	0.628378i	0.983806	−	0.179234i	$-0.0573619\pi$
$618$	0.0573786	−	1.20452i	0.00230811	−	0.0484531i
$619$	−25.8490	+	4.98198i	−1.03896	+	0.200243i	−0.680077	−	0.733140i	$-0.738054\pi$
$619$	−25.8490	+	4.98198i	−1.03896	+	0.200243i	−0.358881	+	0.933383i	$0.616842\pi$
$620$	−3.62957	+	6.28659i	−0.145767	+	0.252476i
$621$	0.991538	−	4.69221i	0.0397891	−	0.188292i
$622$	21.4771			0.861152
$623$	8.50990	−	14.8836i	0.340942	−	0.596300i
$624$	−2.88612	−	1.85480i	−0.115537	−	0.0742514i
$625$	−28.9639	+	11.5954i	−1.15856	+	0.463816i
$626$	9.58035	+	13.4537i	0.382908	+	0.537719i
$627$	−3.46958	−	1.38901i	−0.138562	−	0.0554717i
$628$	−4.88718	−	20.1452i	−0.195020	−	0.803882i
$629$	−16.4051	+	10.5429i	−0.654113	+	0.420373i
$630$	−1.76384	−	7.13961i	−0.0702732	−	0.284449i
$631$	4.91199	−	1.44229i	0.195543	−	0.0574167i	−0.182494	−	0.983207i	$-0.558417\pi$
$631$	4.91199	−	1.44229i	0.195543	−	0.0574167i	0.378038	+	0.925790i	$0.376599\pi$
$632$	11.5214	+	2.22056i	0.458296	+	0.0883293i
$633$	3.91832	+	11.3212i	0.155739	+	0.449979i
$634$	−0.0705952	+	0.290997i	−0.00280369	+	0.0115570i
$635$	−10.5138	+	14.7646i	−0.417229	+	0.585916i
$636$	−7.01148	+	4.50601i	−0.278023	+	0.178675i
$637$	19.0013	+	14.6861i	0.752858	+	0.581883i
$638$	−0.734933	−	5.11157i	−0.0290963	−	0.202369i
$639$	−14.8964	+	1.42244i	−0.589293	+	0.0562707i
$640$	−2.18495	−	1.71827i	−0.0863678	−	0.0679204i
$641$	−27.6182	+	14.2382i	−1.09085	+	0.562374i	−0.907235	−	0.420623i	$-0.861811\pi$
$641$	−27.6182	+	14.2382i	−1.09085	+	0.562374i	−0.183619	+	0.982998i	$0.558781\pi$
$642$	−2.32130	+	6.70695i	−0.0916144	+	0.264702i
$643$	44.2523			1.74514			0.872571	−	0.488487i	$-0.162451\pi$
$643$	44.2523			1.74514			0.872571	+	0.488487i	$0.162451\pi$
$644$	4.55463	+	11.8429i	0.179477	+	0.466677i
$645$	−9.84949			−0.387823
$646$	−3.25302	+	9.39897i	−0.127988	+	0.369798i
$647$	−12.8346	+	6.61669i	−0.504580	+	0.260129i	−0.691670	−	0.722214i	$-0.743125\pi$
$647$	−12.8346	+	6.61669i	−0.504580	+	0.260129i	0.187090	+	0.982343i	$0.440094\pi$
$648$	−0.786053	−	0.618159i	−0.0308791	−	0.0242836i
$649$	−11.6326	+	1.11078i	−0.456618	+	0.0436018i
$650$	1.33118	+	9.25854i	0.0522131	+	0.363150i
$651$	−0.357757	−	6.90019i	−0.0140216	−	0.270440i
$652$	7.49681	−	4.81791i	0.293598	−	0.188684i
$653$	1.99708	−	2.80450i	0.0781517	−	0.109749i	−0.773650	−	0.633614i	$-0.781571\pi$
$653$	1.99708	−	2.80450i	0.0781517	−	0.109749i	0.851801	+	0.523865i	$0.175510\pi$
$654$	−1.91200	+	7.88135i	−0.0747649	+	0.308185i
$655$	5.25752	+	15.1906i	0.205428	+	0.593546i
$656$	1.30779	+	0.252056i	0.0510607	+	0.00984114i
$657$	13.3235	−	3.91212i	0.519798	−	0.152627i
$658$	−8.54421	−	2.46986i	−0.333088	−	0.0962853i
$659$	6.73961	−	4.33128i	0.262538	−	0.168723i	−0.402749	−	0.915310i	$-0.631945\pi$
$659$	6.73961	−	4.33128i	0.262538	−	0.168723i	0.665287	+	0.746587i	$0.268309\pi$
$660$	−0.722681	−	2.97893i	−0.0281303	−	0.115955i
$661$	20.6022	+	8.24787i	0.801332	+	0.320805i	0.735933	−	0.677054i	$-0.236744\pi$
$661$	20.6022	+	8.24787i	0.801332	+	0.320805i	0.0653992	+	0.997859i	$0.479168\pi$
$662$	−15.9208	−	22.3576i	−0.618780	−	0.868954i
$663$	−9.34734	+	3.74211i	−0.363021	+	0.145332i
$664$	12.2972	+	7.90293i	0.477224	+	0.306693i
$665$	−24.9232	+	0.104707i	−0.966479	+	0.00406036i
$666$	−6.64463			−0.257474
$667$	−1.73534	−	22.3910i	−0.0671927	−	0.866982i
$668$	11.0152	−	19.0789i	0.426191	−	0.738184i
$669$	6.06027	−	1.16802i	0.234304	−	0.0451583i
$670$	−0.722384	+	15.1647i	−0.0279081	+	0.585864i
$671$	0.552125	−	3.84011i	0.0213145	−	0.148246i
$672$	2.63480	+	0.240428i	0.101640	+	0.00927469i
$673$	3.21568	+	22.3656i	0.123955	+	0.862129i	0.953005	+	0.302954i	$0.0979729\pi$
$673$	3.21568	+	22.3656i	0.123955	+	0.862129i	−0.829050	+	0.559175i	$0.811118\pi$
$674$	6.80592	+	28.0544i	0.262154	+	1.08061i
$675$	0.129730	+	2.72336i	0.00499330	+	0.104822i
$676$	1.22445	+	0.116920i	0.0470940	+	0.00449694i
$677$	22.7743	+	21.7152i	0.875286	+	0.834584i	0.987258	−	0.159128i	$-0.0508682\pi$
$677$	22.7743	+	21.7152i	0.875286	+	0.834584i	−0.111972	+	0.993711i	$0.535717\pi$
$678$	2.26609	−	2.61521i	0.0870288	−	0.100437i
$679$	−6.34671	+	5.03441i	−0.243564	+	0.193203i
$680$	−7.82730	+	2.29830i	−0.300163	+	0.0881359i
$681$	−5.05148	+	7.09381i	−0.193573	+	0.271835i
$682$	−0.137033	−	2.87668i	−0.00524726	−	0.110154i
$683$	20.6952	−	19.7329i	0.791881	−	0.755057i	−0.181711	−	0.983352i	$-0.558164\pi$
$683$	20.6952	−	19.7329i	0.791881	−	0.755057i	0.973592	+	0.228295i	$0.0733151\pi$
$684$	−2.66391	+	2.09492i	−0.101857	+	0.0801014i
$685$	−9.53741	+	20.8840i	−0.364406	+	0.797937i
$686$	−18.2283	−	3.27551i	−0.695960	−	0.125059i
$687$	−2.52058	−	1.61988i	−0.0961663	−	0.0618023i
$688$	1.15894	−	3.34854i	0.0441843	−	0.127662i
$689$	−14.2969	+	24.7629i	−0.544667	+	0.943392i
$690$	−2.28878	−	13.1328i	−0.0871324	−	0.499956i
$691$	−18.7479	−	32.4724i	−0.713205	−	1.23531i	−0.963648	−	0.267176i	$-0.913909\pi$
$691$	−18.7479	−	32.4724i	−0.713205	−	1.23531i	0.250442	−	0.968132i	$-0.419424\pi$
$692$	2.69466	+	3.10981i	0.102436	+	0.118217i
$693$	2.12006	+	2.00454i	0.0805345	+	0.0761461i
$694$	0.306926	−	2.13472i	0.0116508	−	0.0810329i
$695$	41.7827	−	3.98976i	1.58491	−	0.151340i
$696$	−4.34740	−	1.74044i	−0.164788	−	0.0659711i
$697$	2.82890	−	2.69735i	0.107152	−	0.102169i
$698$	−5.84459	−	3.01310i	−0.221221	−	0.114047i
$699$	5.19392	+	11.3731i	0.196452	+	0.430170i
$700$	−4.20890	−	5.85832i	−0.159081	−	0.221424i
$701$	−7.23983	+	8.35521i	−0.273445	+	0.315572i	−0.875817	−	0.482643i	$-0.839677\pi$
$701$	−7.23983	+	8.35521i	−0.273445	+	0.315572i	0.602372	+	0.798215i	$0.294222\pi$
$702$	−3.36874	−	0.649272i	−0.127145	−	0.0245052i
$703$	−5.30893	+	21.8837i	−0.200230	+	0.825360i
$704$	1.09779	+	0.104826i	0.0413743	+	0.00395077i
$705$	8.30541	+	4.28174i	0.312800	+	0.161260i
$706$	19.6141	+	5.75922i	0.738186	+	0.216751i
$707$	11.8549	+	7.54848i	0.445848	+	0.283890i
$708$	−4.40190	+	9.63883i	−0.165434	+	0.362249i
$709$	−37.4258	+	14.9830i	−1.40556	+	0.562700i	−0.945626	−	0.325255i	$-0.894550\pi$
$709$	−37.4258	+	14.9830i	−1.40556	+	0.562700i	−0.459930	+	0.887955i	$0.652126\pi$
$710$	−36.9712	+	19.0600i	−1.38751	+	0.715309i
$711$	11.5214	−	2.22056i	0.432086	−	0.0832777i
$712$	−3.24004	−	5.61192i	−0.121426	−	0.210316i
$713$	0.223581	−	12.5225i	0.00837318	−	0.468970i
$714$	5.06015	−	5.88954i	0.189371	−	0.220410i
$715$	−6.88676	−	7.94775i	−0.257550	−	0.297229i
$716$	1.18220	−	24.8174i	0.0441809	−	0.927471i
$717$	−11.1196	−	8.74459i	−0.415271	−	0.326573i
$718$	−6.11699	−	8.59011i	−0.228284	−	0.320580i
$719$	−22.5429	+	17.7279i	−0.840709	+	0.661141i	−0.942699	−	0.333645i	$-0.891721\pi$
$719$	−22.5429	+	17.7279i	−0.840709	+	0.661141i	0.101990	+	0.994785i	$0.467479\pi$
$720$	−2.66705	−	0.783118i	−0.0993952	−	0.0291851i
$721$	2.51616	+	1.96167i	0.0937065	+	0.0730566i
$722$	−3.12179	−	6.83576i	−0.116181	−	0.254401i
$723$	−1.08045	−	1.03020i	−0.0401822	−	0.0383136i
$724$	4.06053	+	11.7321i	0.150909	+	0.436022i
$725$	4.17585	+	12.0653i	0.155087	+	0.448095i
$726$	−7.08093	−	6.75165i	−0.262798	−	0.250577i
$727$	−12.4937	−	27.3573i	−0.463364	−	1.01463i	−0.986708	−	0.162504i	$-0.948043\pi$
$727$	−12.4937	−	27.3573i	−0.463364	−	1.01463i	0.523344	−	0.852122i	$-0.324684\pi$
$728$	8.41244	−	3.40891i	0.311786	−	0.126343i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	30.3401	−	23.8597i	1.12294	−	0.883089i
$731$	−6.03218	−	8.47102i	−0.223108	−	0.313312i
$732$	−2.76535	−	2.17470i	−0.102210	−	0.0803791i
$733$	−2.18454	+	45.8592i	−0.0806879	+	1.69385i	0.489237	+	0.872151i	$0.337275\pi$
$733$	−2.18454	+	45.8592i	−0.0806879	+	1.69385i	−0.569925	+	0.821697i	$0.693028\pi$
$734$	5.49566	+	6.34233i	0.202848	+	0.234100i
$735$	18.1239	+	7.07961i	0.668510	+	0.261135i
$736$	4.73408	+	0.767151i	0.174500	+	0.0282776i
$737$	−3.01158	−	5.21621i	−0.110933	−	0.192142i
$738$	1.30779	−	0.252056i	0.0481404	−	0.00927831i
$739$	14.2018	−	7.32154i	0.522422	−	0.269327i	−0.176781	−	0.984250i	$-0.556569\pi$
$739$	14.2018	−	7.32154i	0.522422	−	0.269327i	0.699203	+	0.714923i	$0.253538\pi$
$740$	−17.1467	+	6.86451i	−0.630326	+	0.252345i
$741$	−4.82990	+	10.5760i	−0.177431	+	0.388519i
$742$	0.956693	−	22.0304i	0.0351213	−	0.808763i
$743$	4.75079	+	1.39496i	0.174290	+	0.0511760i	0.367713	−	0.929939i	$-0.380141\pi$
$743$	4.75079	+	1.39496i	0.174290	+	0.0511760i	−0.193423	+	0.981115i	$0.561959\pi$
$744$	−2.32122	−	1.19667i	−0.0851000	−	0.0438721i
$745$	31.8137	+	3.03784i	1.16556	+	0.111298i
$746$	4.64009	−	19.1267i	0.169886	−	0.700278i
$747$	14.3535	+	2.76642i	0.525169	+	0.101218i
$748$	2.11942	−	2.44594i	0.0774937	−	0.0894325i
$749$	−10.9563	−	15.2500i	−0.400334	−	0.557221i
$750$	−2.62529	−	5.74857i	−0.0958619	−	0.209908i
$751$	30.7838	+	15.8702i	1.12332	+	0.579111i	0.916806	−	0.399333i	$-0.130758\pi$
$751$	30.7838	+	15.8702i	1.12332	+	0.579111i	0.206513	+	0.978444i	$0.433789\pi$
$752$	−2.43292	+	2.31979i	−0.0887196	+	0.0845940i
$753$	3.89654	+	1.55994i	0.141998	+	0.0568474i
$754$	−15.9929	+	1.52713i	−0.582426	+	0.0556149i
$755$	4.62265	−	32.1512i	0.168235	−	1.17010i
$756$	2.53543	−	0.756053i	0.0922125	−	0.0274974i
$757$	2.56228	+	2.95702i	0.0931275	+	0.107475i	0.800400	−	0.599466i	$-0.204620\pi$
$757$	2.56228	+	2.95702i	0.0931275	+	0.107475i	−0.707273	+	0.706941i	$0.750075\pi$
$758$	−13.7815	−	23.8702i	−0.500565	−	0.867004i
$759$	3.58074	+	3.89218i	0.129973	+	0.141277i
$760$	−4.71008	+	8.15809i	−0.170852	+	0.295925i
$761$	16.8396	−	48.6548i	0.610434	−	1.76373i	−0.0343960	−	0.999408i	$-0.510951\pi$
$761$	16.8396	−	48.6548i	0.610434	−	1.76373i	0.644830	−	0.764326i	$-0.276928\pi$
$762$	−5.48564	−	3.52541i	−0.198724	−	0.127712i
$763$	−14.1193	−	16.1569i	−0.511153	−	0.584919i
$764$	10.4215	−	22.8200i	0.377038	−	0.825599i
$765$	−6.41242	+	5.04278i	−0.231842	+	0.182322i
$766$	1.77885	−	1.69613i	0.0642725	−	0.0612837i
$767$	1.72977	+	36.3123i	0.0624584	+	1.31116i
$768$	0.580057	−	0.814576i	0.0209310	−	0.0293935i
$769$	17.6464	−	5.18145i	0.636346	−	0.186848i	0.0523812	−	0.998627i	$-0.483319\pi$
$769$	17.6464	−	5.18145i	0.636346	−	0.186848i	0.583964	+	0.811779i	$0.301501\pi$
$770$	7.54177	+	2.98257i	0.271787	+	0.107484i
$771$	−14.4514	+	16.6778i	−0.520455	+	0.600637i
$772$	−4.26678	−	4.06837i	−0.153565	−	0.146424i
$773$	8.55705	+	0.817099i	0.307776	+	0.0293890i	0.247801	−	0.968811i	$-0.420292\pi$
$773$	8.55705	+	0.817099i	0.307776	+	0.0293890i	0.0599745	+	0.998200i	$0.480898\pi$
$774$	−0.168603	−	3.53942i	−0.00606032	−	0.127222i
$775$	1.67865	+	6.91950i	0.0602989	+	0.248556i
$776$	0.435752	+	3.03072i	0.0156426	+	0.108796i
$777$	10.1372	−	14.3630i	0.363669	−	0.515270i
$778$	−3.62562	+	25.2168i	−0.129985	+	0.904065i
$779$	0.214767	−	4.50852i	0.00769484	−	0.161535i
$780$	−9.36392	+	1.80475i	−0.335282	+	0.0646204i
$781$	8.25108	−	14.2913i	0.295247	−	0.511383i
$782$	9.89306	−	10.0114i	0.353775	−	0.358008i
$783$	−4.68284			−0.167351
$784$	−4.53941	+	5.32858i	−0.162122	+	0.190306i
$785$	−48.4738	−	31.1522i	−1.73010	−	1.11187i
$786$	−5.36874	+	2.14932i	−0.191497	+	0.0766637i
$787$	17.8126	+	25.0143i	0.634952	+	0.891665i	0.999214	−	0.0396315i	$-0.0126184\pi$
$787$	17.8126	+	25.0143i	0.634952	+	0.891665i	−0.364263	+	0.931296i	$0.618679\pi$
$788$	−3.41660	−	1.36780i	−0.121711	−	0.0487259i
$789$	−4.42992	−	18.2604i	−0.157709	−	0.650086i
$790$	27.4373	−	17.6329i	0.976176	−	0.627350i
$791$	2.19583	+	8.88819i	0.0780747	+	0.316028i
$792$	1.05811	−	0.310689i	0.0375982	−	0.0110398i
$793$	−11.8513	−	2.28415i	−0.420853	−	0.0811127i
$794$	−2.27204	−	6.56464i	−0.0806318	−	0.232970i
$795$	−5.46187	+	22.5141i	−0.193713	+	0.798494i
$796$	−11.7924	+	16.5601i	−0.417969	+	0.586956i
$797$	−11.5637	+	7.43153i	−0.409607	+	0.263238i	−0.729178	−	0.684324i	$-0.760097\pi$
$797$	−11.5637	+	7.43153i	−0.409607	+	0.263238i	0.319571	+	0.947562i	$0.396461\pi$
$798$	−0.464260	−	8.95435i	−0.0164346	−	0.316981i
$799$	1.40404	+	9.76532i	0.0496714	+	0.345472i
$800$	−2.71410	+	0.259166i	−0.0959581	+	0.00916289i
$801$	−5.09369	−	4.00572i	−0.179977	−	0.141535i
$802$	10.1400	−	5.22754i	0.358056	−	0.184591i
$803$	−5.00843	+	14.4709i	−0.176744	+	0.510668i
$804$	−5.46181			−0.192623
$805$	31.8795	+	15.0882i	1.12361	+	0.531789i
$806$	−8.95948			−0.315584
$807$	0.408851	−	1.18130i	0.0143922	−	0.0415836i
$808$	4.72145	−	2.43407i	0.166100	−	0.0856304i
$809$	−1.40976	−	1.10865i	−0.0495646	−	0.0389780i	0.593069	−	0.805151i	$-0.297916\pi$
$809$	−1.40976	−	1.10865i	−0.0495646	−	0.0389780i	−0.642634	+	0.766173i	$0.722158\pi$
$810$	−2.76706	+	0.264222i	−0.0972247	+	0.00928383i
$811$	1.52866	+	10.6321i	0.0536786	+	0.373343i	0.998899	+	0.0469104i	$0.0149375\pi$
$811$	1.52866	+	10.6321i	0.0536786	+	0.373343i	−0.945220	+	0.326433i	$0.894153\pi$
$812$	10.3946	−	6.74207i	0.364779	−	0.236600i
$813$	−18.6190	+	11.9657i	−0.652998	+	0.419656i
$814$	4.25040	−	5.96885i	0.148977	−	0.209208i
$815$	5.83993	−	24.0725i	0.204564	−	0.843224i
$816$	−0.959883	−	2.77340i	−0.0336026	−	0.0970884i
$817$	−11.7916	−	2.27264i	−0.412535	−	0.0795096i
$818$	−14.4058	+	4.22993i	−0.503687	+	0.147896i
$819$	6.54288	−	6.29131i	0.228627	−	0.219836i
$820$	3.11441	−	2.00151i	0.108760	−	0.0698957i
$821$	3.83523	+	15.8090i	0.133850	+	0.551739i	0.998759	+	0.0498089i	$0.0158612\pi$
$821$	3.83523	+	15.8090i	0.133850	+	0.551739i	−0.864908	+	0.501930i	$0.832624\pi$
$822$	−7.66794	−	3.06978i	−0.267450	−	0.107071i
$823$	17.8577	+	25.0777i	0.622481	+	0.874152i	0.998626	−	0.0524088i	$-0.0166899\pi$
$823$	17.8577	+	25.0777i	0.622481	+	0.874152i	−0.376145	+	0.926561i	$0.622750\pi$
$824$	1.11951	−	0.448184i	0.0390000	−	0.0156132i
$825$	−2.52937	−	1.62553i	−0.0880615	−	0.0565937i
$826$	−14.1196	−	24.2203i	−0.491284	−	0.842732i
$827$	15.1022			0.525154			0.262577	−	0.964911i	$-0.415428\pi$
$827$	15.1022			0.525154			0.262577	+	0.964911i	$0.415428\pi$
$828$	4.68009	−	1.04728i	0.162644	−	0.0363955i
$829$	22.2674	−	38.5683i	0.773380	−	1.33953i	−0.162321	−	0.986738i	$-0.551898\pi$
$829$	22.2674	−	38.5683i	0.773380	−	1.33953i	0.935701	−	0.352795i	$-0.114769\pi$
$830$	39.8978	−	7.68967i	1.38487	−	0.266912i
$831$	−0.610874	+	12.8238i	−0.0211910	+	0.444854i
$832$	0.488245	−	3.39582i	0.0169269	−	0.117729i
$833$	5.01093	+	19.9232i	0.173618	+	0.690297i
$834$	2.14895	+	14.9463i	0.0744122	+	0.517548i
$835$	−14.4371	−	59.5106i	−0.499617	−	2.05945i
$836$	−0.177827	−	3.73305i	−0.00615028	−	0.129110i
$837$	−2.59970	−	0.248242i	−0.0898589	−	0.00858048i
$838$	−21.8464	−	20.8305i	−0.754671	−	0.719577i
$839$	−22.1373	+	25.5478i	−0.764264	+	0.882008i	−0.995869	−	0.0908021i	$-0.971057\pi$
$839$	−22.1373	+	25.5478i	−0.764264	+	0.882008i	0.231605	+	0.972810i	$0.425602\pi$
$840$	5.76169	−	4.57035i	0.198797	−	0.157692i
$841$	6.78457	−	1.99213i	0.233951	−	0.0686941i
$842$	6.21425	−	8.72670i	0.214157	−	0.300742i
$843$	0.689042	+	14.4648i	0.0237319	+	0.498193i
$844$	−8.67043	+	8.26724i	−0.298448	+	0.284570i
$845$	2.68752	−	2.11349i	0.0924536	−	0.0727063i
$846$	−1.39647	+	3.05784i	−0.0480117	+	0.105131i
$847$	25.3971	−	5.00564i	0.872655	−	0.171996i
$848$	−7.01148	−	4.50601i	−0.240775	−	0.154737i
$849$	8.27968	−	23.9226i	0.284158	−	0.821020i
$850$	−4.00081	+	6.92960i	−0.137227	+	0.237683i
$851$	20.1426	−	24.6932i	0.690480	−	0.846470i
$852$	−7.48209	−	12.9594i	−0.256332	−	0.443980i
$853$	27.7201	+	31.9908i	0.949120	+	1.09534i	0.995342	+	0.0964113i	$0.0307364\pi$
$853$	27.7201	+	31.9908i	0.949120	+	1.09534i	−0.0462219	+	0.998931i	$0.514718\pi$
$854$	8.91969	−	2.65981i	0.305225	−	0.0910168i
$855$	−1.34063	+	9.32427i	−0.0458485	+	0.318883i
$856$	−7.06516	+	0.674641i	−0.241482	+	0.0230588i
$857$	−5.65709	−	2.26476i	−0.193242	−	0.0773626i	0.273023	−	0.962008i	$-0.411977\pi$
$857$	−5.65709	−	2.26476i	−0.193242	−	0.0773626i	−0.466265	+	0.884645i	$0.654401\pi$
$858$	2.73814	−	2.61081i	0.0934785	−	0.0891315i
$859$	36.3928	+	18.7618i	1.24171	+	0.640145i	0.948764	−	0.315985i	$-0.102335\pi$
$859$	36.3928	+	18.7618i	1.24171	+	0.640145i	0.292943	+	0.956130i	$0.405365\pi$
$860$	−4.09163	−	8.95941i	−0.139523	−	0.305513i
$861$	−1.45035	+	3.21145i	−0.0494277	+	0.109446i
$862$	−0.800873	+	0.924256i	−0.0272778	+	0.0314803i
$863$	37.6123	+	7.24917i	1.28034	+	0.246765i	0.783671	−	0.621177i	$-0.213345\pi$
$863$	37.6123	+	7.24917i	1.28034	+	0.246765i	0.496667	+	0.867941i	$0.334557\pi$
$864$	0.235759	−	0.971812i	0.00802068	−	0.0330617i
$865$	11.3861	+	1.08724i	0.387139	+	0.0369673i
$866$	5.50949	+	2.84034i	0.187220	+	0.0965186i
$867$	8.04716	+	2.36286i	0.273296	+	0.0802469i
$868$	6.12801	−	3.19187i	0.207998	−	0.108339i
$869$	−5.37521	+	11.7701i	−0.182341	+	0.399272i
$870$	−12.0842	+	4.83780i	−0.409694	+	0.164017i
$871$	−16.6550	+	8.58627i	−0.564335	+	0.290935i
$872$	−7.96340	+	1.53482i	−0.269675	+	0.0519756i
$873$	1.53094	+	2.65167i	0.0518146	+	0.0897454i
$874$	0.290140	−	16.2503i	0.00981414	−	0.549676i
$875$	16.4313	+	3.09533i	0.555478	+	0.104641i
$876$	9.09336	+	10.4943i	0.307236	+	0.354570i
$877$	2.40204	−	50.4250i	0.0811111	−	1.70273i	−0.481854	−	0.876251i	$-0.660037\pi$
$877$	2.40204	−	50.4250i	0.0811111	−	1.70273i	0.562965	−	0.826481i	$-0.309660\pi$
$878$	−18.4513	−	14.5103i	−0.622701	−	0.489698i
$879$	12.5100	+	17.5678i	0.421952	+	0.592548i
$880$	2.40952	−	1.89487i	0.0812248	−	0.0638759i
$881$	26.6513	+	7.82553i	0.897905	+	0.263649i	0.697942	−	0.716154i	$-0.254099\pi$
$881$	26.6513	+	7.82553i	0.897905	+	0.263649i	0.199964	+	0.979803i	$0.435918\pi$
$882$	−2.23381	+	6.63401i	−0.0752164	+	0.223379i
$883$	10.7946	+	23.6368i	0.363266	+	0.795441i	0.999709	+	0.0241175i	$0.00767758\pi$
$883$	10.7946	+	23.6368i	0.363266	+	0.795441i	−0.636443	+	0.771323i	$0.719595\pi$
$884$	−7.28697	−	6.94811i	−0.245087	−	0.233690i
$885$	9.63355	+	27.8343i	0.323828	+	0.935640i
$886$	7.93599	+	22.9295i	0.266615	+	0.770333i
$887$	18.0920	+	17.2507i	0.607472	+	0.579223i	0.930102	−	0.367302i	$-0.119719\pi$
$887$	18.0920	+	17.2507i	0.607472	+	0.579223i	−0.322630	+	0.946525i	$0.604567\pi$
$888$	−2.76028	−	6.04417i	−0.0926290	−	0.202829i
$889$	15.9895	−	6.47931i	0.536271	−	0.217309i
$890$	−17.2827	−	5.07467i	−0.579319	−	0.170103i
$891$	0.866843	−	0.681692i	0.0290403	−	0.0228376i
$892$	3.58000	+	5.02741i	0.119867	+	0.168330i
$893$	8.95508	+	7.04235i	0.299670	+	0.235663i
$894$	−0.547062	+	11.4842i	−0.0182965	+	0.384091i
$895$	−45.2260	−	52.1936i	−1.51174	−	1.74464i
$896$	0.875837	+	2.49658i	0.0292597	+	0.0834049i
$897$	12.6249	−	10.5509i	0.421533	−	0.352284i
$898$	18.0941	+	31.3400i	0.603809	+	1.04583i
$899$	−12.0084	+	2.31442i	−0.400502	+	0.0771904i
$900$	−2.42337	+	1.24933i	−0.0807789	+	0.0416444i
$901$	−22.7082	+	9.09100i	−0.756521	+	0.302865i
$902$	−0.610139	+	1.33602i	−0.0203154	+	0.0444845i
$903$	7.90800	+	5.03535i	0.263162	+	0.167566i
$904$	3.32025	+	0.974913i	0.110430	+	0.0324251i
$905$	30.6730	+	15.8130i	1.01961	+	0.525643i
$906$	11.6327	+	1.11079i	0.386470	+	0.0369034i
$907$	10.7893	−	44.4742i	0.358253	−	1.47674i	−0.452717	−	0.891654i	$-0.649545\pi$
$907$	10.7893	−	44.4742i	0.358253	−	1.47674i	0.810971	−	0.585087i	$-0.198940\pi$
$908$	−8.55121	−	1.64811i	−0.283782	−	0.0546945i
$909$	3.47858	−	4.01450i	0.115377	−	0.133153i
$910$	10.3846	−	22.9944i	0.344248	−	0.762256i
$911$	−19.2933	−	42.2465i	−0.639217	−	1.39969i	−0.900683	−	0.434477i	$-0.856933\pi$
$911$	−19.2933	−	42.2465i	−0.639217	−	1.39969i	0.261466	−	0.965213i	$-0.415794\pi$
$912$	−3.01224	−	1.55292i	−0.0997452	−	0.0514222i
$913$	−11.6667	+	11.1241i	−0.386110	+	0.368155i
$914$	−38.5353	−	15.4272i	−1.27463	−	0.510287i
$915$	−9.73459	+	0.929541i	−0.321816	+	0.0307297i
$916$	0.426407	−	2.96573i	0.0140889	−	0.0979904i
$917$	3.54470	−	14.8841i	0.117056	−	0.491516i
$918$	−1.92189	−	2.21798i	−0.0634319	−	0.0732043i
$919$	−21.8543	−	37.8528i	−0.720908	−	1.24865i	−0.960636	−	0.277809i	$-0.910392\pi$
$919$	−21.8543	−	37.8528i	−0.720908	−	1.24865i	0.239729	−	0.970840i	$-0.422942\pi$
$920$	10.9952	−	7.53750i	0.362501	−	0.248504i
$921$	−3.27829	+	5.67816i	−0.108023	+	0.187102i
$922$	−1.19880	+	3.46371i	−0.0394804	+	0.114071i
$923$	−43.1884	−	27.7555i	−1.42157	−	0.913584i
$924$	−0.942687	+	2.76119i	−0.0310121	+	0.0908366i
$925$	−7.52577	+	16.4791i	−0.247446	+	0.541831i
$926$	−7.71177	+	6.06461i	−0.253425	+	0.199295i
$927$	0.872744	−	0.832160i	0.0286647	−	0.0273317i
$928$	−0.222819	−	4.67754i	−0.00731438	−	0.153548i
$929$	29.6499	−	41.6375i	0.972782	−	1.36608i	0.0425563	−	0.999094i	$-0.486450\pi$
$929$	29.6499	−	41.6375i	0.972782	−	1.36608i	0.930226	−	0.366987i	$-0.119611\pi$
$930$	−6.96509	+	2.04513i	−0.228394	+	0.0670626i
$931$	20.0640	+	12.6574i	0.657569	+	0.414829i
$932$	−8.18771	+	9.44912i	−0.268197	+	0.309516i
$933$	15.5437	+	14.8209i	0.508878	+	0.485214i
$934$	25.4641	+	2.43152i	0.833210	+	0.0795619i
$935$	−0.428056	−	8.98600i	−0.0139989	−	0.293874i
$936$	−0.808828	−	3.33403i	−0.0264374	−	0.108976i
$937$	0.754490	+	5.24759i	0.0246481	+	0.171431i	0.998427	−	0.0560645i	$-0.0178553\pi$
$937$	0.754490	+	5.24759i	0.0246481	+	0.171431i	−0.973779	+	0.227496i	$0.926946\pi$
$938$	8.33264	−	11.8062i	0.272070	−	0.385486i
$939$	−2.35050	+	16.3481i	−0.0767058	+	0.533501i
$940$	−0.444612	+	9.33356i	−0.0145017	+	0.304427i
$941$	18.2584	−	3.51903i	0.595208	−	0.114717i	0.117254	−	0.993102i	$-0.462591\pi$
$941$	18.2584	−	3.51903i	0.595208	−	0.114717i	0.477954	+	0.878385i	$0.341379\pi$
$942$	10.3648	−	17.9523i	0.337703	−	0.584918i
$943$	−3.02775	+	5.62417i	−0.0985970	+	0.183148i
$944$	−10.5964			−0.344883
$945$	3.65034	−	6.38437i	0.118746	−	0.207684i
$946$	3.28730	+	2.11262i	0.106879	+	0.0686871i
$947$	47.5903	−	19.0523i	1.54648	−	0.619116i	0.567552	−	0.823338i	$-0.307891\pi$
$947$	47.5903	−	19.0523i	1.54648	−	0.619116i	0.978925	+	0.204222i	$0.0654665\pi$
$948$	6.80605	+	9.55776i	0.221050	+	0.310422i
$949$	44.2266	+	17.7057i	1.43566	+	0.574750i
$950$	2.17838	+	8.97941i	0.0706760	+	0.291330i
$951$	−0.251903	+	0.161888i	−0.00816852	+	0.00524959i
$952$	7.45938	+	2.15627i	0.241760	+	0.0698852i
$953$	31.3993	−	9.21966i	1.01712	−	0.298654i	0.269658	−	0.962956i	$-0.413089\pi$
$953$	31.3993	−	9.21966i	1.01712	−	0.298654i	0.747464	+	0.664302i	$0.231271\pi$
$954$	−8.18395	−	1.57733i	−0.264965	−	0.0510679i
$955$	−22.8075	−	65.8980i	−0.738034	−	2.13241i
$956$	3.33509	−	13.7474i	0.107864	−	0.444623i
$957$	2.99549	−	4.20658i	0.0968306	−	0.135980i
$958$	20.1365	−	12.9410i	0.650581	−	0.418103i
$959$	18.3340	−	11.8917i	0.592034	−	0.384001i
$960$	−0.395585	−	2.75136i	−0.0127675	−	0.0887997i
$961$	24.0704	−	2.29845i	0.776466	−	0.0741435i
$962$	−17.9189	−	14.0916i	−0.577728	−	0.454330i
$963$	−6.30833	+	3.25217i	−0.203283	+	0.104800i
$964$	0.488272	−	1.41077i	0.0157262	−	0.0454378i
$965$	−16.3875			−0.527531
$966$	−4.87623	+	11.7142i	−0.156890	+	0.376898i
$967$	20.6924			0.665423			0.332712	−	0.943029i	$-0.392036\pi$
$967$	20.6924			0.665423			0.332712	+	0.943029i	$0.392036\pi$
$968$	3.19999	−	9.24577i	0.102852	−	0.297170i
$969$	−8.84035	+	4.55752i	−0.283993	+	0.146409i
$970$	6.69007	+	5.26113i	0.214805	+	0.168925i
$971$	45.2023	−	4.31630i	1.45061	−	0.138517i	0.660198	−	0.751091i	$-0.270472\pi$
$971$	45.2023	−	4.31630i	1.45061	−	0.138517i	0.790413	+	0.612575i	$0.209866\pi$
$972$	−0.142315	−	0.989821i	−0.00456475	−	0.0317485i
$973$	−35.5863	−	18.1572i	−1.14085	−	0.582093i
$974$	20.7226	−	13.3176i	0.663995	−	0.426724i
$975$	−5.42571	+	7.61934i	−0.173762	+	0.244014i
$976$	0.829405	−	3.41886i	0.0265486	−	0.109435i
$977$	15.0326	+	43.4340i	0.480937	+	1.38958i	0.881012	+	0.473093i	$0.156863\pi$
$977$	15.0326	+	43.4340i	0.480937	+	1.38958i	−0.400076	+	0.916482i	$0.631016\pi$
$978$	8.75043	+	1.68651i	0.279808	+	0.0539286i
$979$	6.85663	−	2.01329i	0.219139	−	0.0643450i
$980$	1.08910	+	19.4270i	0.0347899	+	0.620574i
$981$	−6.82253	+	4.38457i	−0.217827	+	0.139989i
$982$	4.88527	+	20.1373i	0.155895	+	0.642609i
$983$	−20.7968	−	8.32580i	−0.663316	−	0.265552i	0.0154780	−	0.999880i	$-0.495073\pi$
$983$	−20.7968	−	8.32580i	−0.663316	−	0.265552i	−0.678794	+	0.734328i	$0.737497\pi$
$984$	0.772554	+	1.08490i	0.0246281	+	0.0345854i
$985$	−9.49696	+	3.80201i	−0.302598	+	0.121142i
$986$	−11.5616	−	7.43016i	−0.368195	−	0.236625i
$987$	−4.47934	−	7.68371i	−0.142579	−	0.244575i
$988$	−11.6267			−0.369894
$989$	13.6645	+	10.1029i	0.434505	+	0.321252i
$990$	1.53267	−	2.65466i	0.0487114	−	0.0843706i
$991$	−14.5253	+	2.79951i	−0.461410	+	0.0889295i	−0.414659	−	0.909977i	$-0.636099\pi$
$991$	−14.5253	+	2.79951i	−0.461410	+	0.0889295i	−0.0467514	+	0.998907i	$0.514887\pi$
$992$	0.124262	−	2.60857i	0.00394531	−	0.0828222i
$993$	3.90611	−	27.1676i	0.123957	−	0.862138i
$994$	39.4277	+	3.59780i	1.25057	+	0.114115i
$995$	8.04212	+	55.9342i	0.254952	+	1.77323i
$996$	3.44625	+	14.2057i	0.109199	+	0.450123i
$997$	−1.19639	−	25.1154i	−0.0378902	−	0.795413i	−0.935223	−	0.354059i	$-0.884801\pi$
$997$	−1.19639	−	25.1154i	−0.0378902	−	0.795413i	0.897333	−	0.441354i	$-0.145502\pi$
$998$	13.3249	+	1.27237i	0.421791	+	0.0402761i
$999$	−4.80895	−	4.58532i	−0.152148	−	0.145073i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.d.151.2	✓	160
7.2	even	3	inner	966.2.y.d.289.7	yes	160
23.16	even	11	inner	966.2.y.d.361.7	yes	160
161.16	even	33	inner	966.2.y.d.499.2	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.d.151.2	✓	160	1.1	even	1	trivial
966.2.y.d.289.7	yes	160	7.2	even	3	inner
966.2.y.d.361.7	yes	160	23.16	even	11	inner
966.2.y.d.499.2	yes	160	161.16	even	33	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.327068 + 0.945001i) q^{2} +(-0.888835 + 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-2.76706 + 0.264222i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(2.35671 + 1.20246i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +O(q^{10})\)	\(q+(-0.327068 + 0.945001i) q^{2} +(-0.888835 + 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-2.76706 + 0.264222i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(2.35671 + 1.20246i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +(0.655327 - 2.70130i) q^{10} +(0.360684 + 1.04213i) q^{11} +(0.981929 + 0.189251i) q^{12} +(3.29177 - 0.966551i) q^{13} +(-1.90713 + 1.83381i) q^{14} +(2.33839 - 1.50279i) q^{15} +(0.235759 + 0.971812i) q^{16} +(2.72458 + 1.09076i) q^{17} +(0.580057 + 0.814576i) q^{18} +(3.14621 - 1.25955i) q^{19} +(2.33839 + 1.50279i) q^{20} +(-2.64573 + 0.0111152i) q^{21} -1.10278 q^{22} +(-4.78556 - 0.313675i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.67718 - 0.515984i) q^{25} +(-0.163241 + 3.42686i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(-1.10919 - 2.40202i) q^{28} +(0.666438 + 4.63518i) q^{29} +(0.655327 + 2.70130i) q^{30} +(0.124262 + 2.60857i) q^{31} +(-0.995472 - 0.0950560i) q^{32} +(-0.798118 - 0.761004i) q^{33} +(-1.92189 + 2.21798i) q^{34} +(-6.83888 - 2.70460i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-3.85427 + 5.41256i) q^{37} +(0.161254 + 3.38513i) q^{38} +(-2.48294 + 2.36748i) q^{39} +(-2.18495 + 1.71827i) q^{40} +(0.553274 - 1.21150i) q^{41} +(0.854829 - 2.50385i) q^{42} +(-2.98092 - 1.91572i) q^{43} +(0.360684 - 1.04213i) q^{44} +(-1.38982 + 2.40725i) q^{45} +(1.86163 - 4.41977i) q^{46} +(1.68081 + 2.91126i) q^{47} +(-0.654861 - 0.755750i) q^{48} +(4.10816 + 5.66771i) q^{49} +(-0.388014 + 2.69870i) q^{50} +(-2.92152 + 0.278971i) q^{51} +(-3.18499 - 1.27508i) q^{52} +(-6.03201 + 5.75151i) q^{53} +(-0.888835 - 0.458227i) q^{54} +(-1.27339 - 2.78833i) q^{55} +(2.63269 - 0.262557i) q^{56} +(-2.21930 + 2.56121i) q^{57} +(-4.59822 - 0.886234i) q^{58} +(-2.49820 + 10.2977i) q^{59} +(-2.76706 - 0.264222i) q^{60} +(-3.12694 - 1.61205i) q^{61} +(-2.50574 - 0.735753i) q^{62} +(2.34652 - 1.22222i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-8.85316 + 3.54427i) q^{65} +(0.980189 - 0.505322i) q^{66} +(-5.36311 + 1.03365i) q^{67} +(-1.46741 - 2.54162i) q^{68} +(4.39731 - 1.91407i) q^{69} +(4.79262 - 5.57816i) q^{70} +(-9.79945 - 11.3092i) q^{71} +(0.0475819 - 0.998867i) q^{72} +(10.9151 + 8.58373i) q^{73} +(-3.85427 - 5.41256i) q^{74} +(-2.14313 + 1.68538i) q^{75} +(-3.25169 - 0.954784i) q^{76} +(-0.403092 + 2.88970i) q^{77} +(-1.42518 - 3.12071i) q^{78} +(8.49188 + 8.09699i) q^{79} +(-0.909134 - 2.62677i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(0.963912 + 0.919088i) q^{82} +(6.07241 + 13.2967i) q^{83} +(2.08655 + 1.62674i) q^{84} +(-7.82730 - 2.29830i) q^{85} +(2.78532 - 2.19040i) q^{86} +(-2.71631 - 3.81453i) q^{87} +(0.866843 + 0.681692i) q^{88} +(0.308335 - 6.47275i) q^{89} +(-1.82028 - 2.10072i) q^{90} +(8.91999 + 1.68035i) q^{91} +(3.56781 + 3.20480i) q^{92} +(-1.30576 - 2.26165i) q^{93} +(-3.30088 + 0.636192i) q^{94} +(-8.37297 + 4.31656i) q^{95} +(0.928368 - 0.371662i) q^{96} +(-1.27195 + 2.78519i) q^{97} +(-6.69964 + 2.02849i) q^{98} +(1.05811 + 0.310689i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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