LMFDB - Embedded newform 112.2.m.d.85.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,2,Mod(29,112)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("112.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	112.m (of order $4$, degree $2$, 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:	$0.894324502638$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.20138089353117696.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{10} - 2x^{9} + 2x^{8} + 4x^{7} + 2x^{6} + 8x^{5} + 8x^{4} - 16x^{3} - 48x^{2} + 64 $ x^12 - 3x^10 - 2x^9 + 2x^8 + 4x^7 + 2x^6 + 8x^5 + 8x^4 - 16x^3 - 48*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			85.2
Root			$1.35309 - 0.411286i$ of defining polynomial
Character	$\chi$	$=$	112.85
Dual form			112.2.m.d.29.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.411286 + 1.35309i) q^{2} +(2.21570 - 2.21570i) q^{3} +(-1.66169 - 1.11301i) q^{4} +(-0.393125 - 0.393125i) q^{5} +(2.08675 + 3.90932i) q^{6} +1.00000i q^{7} +(2.18943 - 1.79064i) q^{8} -6.81864i q^{9} +O(q^{10})$	\(q+(-0.411286 + 1.35309i) q^{2} +(2.21570 - 2.21570i) q^{3} +(-1.66169 - 1.11301i) q^{4} +(-0.393125 - 0.393125i) q^{5} +(2.08675 + 3.90932i) q^{6} +1.00000i q^{7} +(2.18943 - 1.79064i) q^{8} -6.81864i q^{9} +(0.693620 - 0.370246i) q^{10} +(2.22602 + 2.22602i) q^{11} +(-6.14790 + 1.21570i) q^{12} +(-3.16316 + 3.16316i) q^{13} +(-1.35309 - 0.411286i) q^{14} -1.74209 q^{15} +(1.52241 + 3.69896i) q^{16} +0.980951 q^{17} +(9.22621 + 2.80441i) q^{18} +(-5.26429 + 5.26429i) q^{19} +(0.215698 + 1.09080i) q^{20} +(2.21570 + 2.21570i) q^{21} +(-3.92754 + 2.09647i) q^{22} +1.25951i q^{23} +(0.883601 - 8.81864i) q^{24} -4.69090i q^{25} +(-2.97907 - 5.58100i) q^{26} +(-8.46094 - 8.46094i) q^{27} +(1.11301 - 1.66169i) q^{28} +(3.17349 - 3.17349i) q^{29} +(0.716500 - 2.35720i) q^{30} -4.43140 q^{31} +(-5.63115 + 0.538620i) q^{32} +9.86440 q^{33} +(-0.403452 + 1.32731i) q^{34} +(0.393125 - 0.393125i) q^{35} +(-7.58922 + 11.3304i) q^{36} +(0.645145 + 0.645145i) q^{37} +(-4.95791 - 9.28818i) q^{38} +14.0172i q^{39} +(-1.56467 - 0.156775i) q^{40} -1.21375i q^{41} +(-3.90932 + 2.08675i) q^{42} +(0.966515 + 0.966515i) q^{43} +(-1.22136 - 6.17655i) q^{44} +(-2.68058 + 2.68058i) q^{45} +(-1.70422 - 0.518019i) q^{46} +9.97147 q^{47} +(11.5690 + 4.82257i) q^{48} -1.00000 q^{49} +(6.34720 + 1.92931i) q^{50} +(2.17349 - 2.17349i) q^{51} +(8.77683 - 1.73555i) q^{52} +(-8.07814 - 8.07814i) q^{53} +(14.9283 - 7.96852i) q^{54} -1.75021i q^{55} +(1.79064 + 2.18943i) q^{56} +23.3282i q^{57} +(2.98879 + 5.59922i) q^{58} +(1.81385 + 1.81385i) q^{59} +(2.89482 + 1.93897i) q^{60} +(-2.58783 + 2.58783i) q^{61} +(1.82257 - 5.99606i) q^{62} +6.81864 q^{63} +(1.58722 - 7.84097i) q^{64} +2.48704 q^{65} +(-4.05709 + 13.3474i) q^{66} +(-1.59261 + 1.59261i) q^{67} +(-1.63003 - 1.09181i) q^{68} +(2.79069 + 2.79069i) q^{69} +(0.370246 + 0.693620i) q^{70} -0.934634i q^{71} +(-12.2097 - 14.9289i) q^{72} -0.710511i q^{73} +(-1.13828 + 0.607598i) q^{74} +(-10.3936 - 10.3936i) q^{75} +(14.6068 - 2.88839i) q^{76} +(-2.22602 + 2.22602i) q^{77} +(-18.9665 - 5.76510i) q^{78} +11.8644 q^{79} +(0.855656 - 2.05265i) q^{80} -17.0379 q^{81} +(1.64231 + 0.499198i) q^{82} +(-6.77482 + 6.77482i) q^{83} +(-1.21570 - 6.14790i) q^{84} +(-0.385637 - 0.385637i) q^{85} +(-1.70529 + 0.910265i) q^{86} -14.0630i q^{87} +(8.85973 + 0.887719i) q^{88} -10.2082i q^{89} +(-2.52457 - 4.72954i) q^{90} +(-3.16316 - 3.16316i) q^{91} +(1.40185 - 2.09291i) q^{92} +(-9.81864 + 9.81864i) q^{93} +(-4.10113 + 13.4923i) q^{94} +4.13906 q^{95} +(-11.2835 + 13.6704i) q^{96} -3.03684 q^{97} +(0.411286 - 1.35309i) q^{98} +(15.1784 - 15.1784i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 4 q^{3} - 6 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{8}+O(q^{10}) $ 12 * q + 2 * q^2 + 4 * q^3 - 6 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^8	$ 12 q + 2 q^{2} + 4 q^{3} - 6 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{8} - 4 q^{10} + 8 q^{12} - 24 q^{15} + 10 q^{16} - 8 q^{17} - 20 q^{20} + 4 q^{21} + 14 q^{22} - 8 q^{24} - 20 q^{26} + 4 q^{27} - 4 q^{29} - 28 q^{30} - 8 q^{31} + 12 q^{32} + 8 q^{34} - 4 q^{35} - 16 q^{36} - 20 q^{37} + 16 q^{38} - 8 q^{40} - 12 q^{42} + 16 q^{43} + 14 q^{44} + 40 q^{45} - 28 q^{46} + 16 q^{47} + 16 q^{48} - 12 q^{49} + 44 q^{50} - 16 q^{51} - 16 q^{52} + 4 q^{53} + 64 q^{54} + 6 q^{56} + 14 q^{58} - 16 q^{59} + 60 q^{60} - 20 q^{61} + 8 q^{62} + 12 q^{63} - 18 q^{64} + 32 q^{65} + 12 q^{66} + 24 q^{67} - 28 q^{68} - 4 q^{69} + 20 q^{70} + 6 q^{72} - 38 q^{74} - 40 q^{75} + 48 q^{76} - 76 q^{78} + 24 q^{79} + 24 q^{80} - 44 q^{81} - 16 q^{82} - 20 q^{83} + 8 q^{84} - 8 q^{85} + 38 q^{86} - 14 q^{88} - 40 q^{90} + 32 q^{92} - 48 q^{93} - 24 q^{94} - 16 q^{96} + 48 q^{97} - 2 q^{98} + 32 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 4 * q^3 - 6 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^8 - 4 * q^10 + 8 * q^12 - 24 * q^15 + 10 * q^16 - 8 * q^17 - 20 * q^20 + 4 * q^21 + 14 * q^22 - 8 * q^24 - 20 * q^26 + 4 * q^27 - 4 * q^29 - 28 * q^30 - 8 * q^31 + 12 * q^32 + 8 * q^34 - 4 * q^35 - 16 * q^36 - 20 * q^37 + 16 * q^38 - 8 * q^40 - 12 * q^42 + 16 * q^43 + 14 * q^44 + 40 * q^45 - 28 * q^46 + 16 * q^47 + 16 * q^48 - 12 * q^49 + 44 * q^50 - 16 * q^51 - 16 * q^52 + 4 * q^53 + 64 * q^54 + 6 * q^56 + 14 * q^58 - 16 * q^59 + 60 * q^60 - 20 * q^61 + 8 * q^62 + 12 * q^63 - 18 * q^64 + 32 * q^65 + 12 * q^66 + 24 * q^67 - 28 * q^68 - 4 * q^69 + 20 * q^70 + 6 * q^72 - 38 * q^74 - 40 * q^75 + 48 * q^76 - 76 * q^78 + 24 * q^79 + 24 * q^80 - 44 * q^81 - 16 * q^82 - 20 * q^83 + 8 * q^84 - 8 * q^85 + 38 * q^86 - 14 * q^88 - 40 * q^90 + 32 * q^92 - 48 * q^93 - 24 * q^94 - 16 * q^96 + 48 * q^97 - 2 * q^98 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.411286	+	1.35309i	−0.290823	+	0.956777i
$2$	−0.411286	+	1.35309i	−0.290823	+	0.956777i
$3$	2.21570	−	2.21570i	1.27923	−	1.27923i	0.338137	−	0.941097i	$-0.390203\pi$
$3$	2.21570	−	2.21570i	1.27923	−	1.27923i	0.941097	−	0.338137i	$-0.109797\pi$
$4$	−1.66169	−	1.11301i	−0.830844	−	0.556506i
$5$	−0.393125	−	0.393125i	−0.175811	−	0.175811i	0.613716	−	0.789527i	$-0.289674\pi$
$5$	−0.393125	−	0.393125i	−0.175811	−	0.175811i	−0.789527	+	0.613716i	$0.789674\pi$
$6$	2.08675	+	3.90932i	0.851910	+	1.59597i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	2.18943	−	1.79064i	0.774081	−	0.633087i
$9$		−	6.81864i		−	2.27288i
$10$	0.693620	−	0.370246i	0.219342	−	0.117082i
$11$	2.22602	+	2.22602i	0.671172	+	0.671172i	0.957986	−	0.286815i	$-0.0925964\pi$
$11$	2.22602	+	2.22602i	0.671172	+	0.671172i	−0.286815	+	0.957986i	$0.592596\pi$
$12$	−6.14790	+	1.21570i	−1.77474	+	0.350942i
$13$	−3.16316	+	3.16316i	−0.877304	+	0.877304i	−0.993255	−	0.115951i	$-0.963008\pi$
$13$	−3.16316	+	3.16316i	−0.877304	+	0.877304i	0.115951	+	0.993255i	$0.463008\pi$
$14$	−1.35309	−	0.411286i	−0.361628	−	0.109921i
$15$	−1.74209			−0.449807
$16$	1.52241	+	3.69896i	0.380602	+	0.924739i
$17$	0.980951			0.237915			0.118958	−	0.992899i	$-0.462045\pi$
$17$	0.980951			0.237915			0.118958	+	0.992899i	$0.462045\pi$
$18$	9.22621	+	2.80441i	2.17464	+	0.661006i
$19$	−5.26429	+	5.26429i	−1.20771	+	1.20771i	−0.235946	+	0.971766i	$0.575819\pi$
$19$	−5.26429	+	5.26429i	−1.20771	+	1.20771i	−0.971766	+	0.235946i	$0.924181\pi$
$20$	0.215698	+	1.09080i	0.0482315	+	0.243911i
$21$	2.21570	+	2.21570i	0.483505	+	0.483505i
$22$	−3.92754	+	2.09647i	−0.837354	+	0.446969i
$23$			1.25951i			0.262626i	0.991341	+	0.131313i	$0.0419192\pi$
$23$			1.25951i			0.262626i	−0.991341	+	0.131313i	$0.958081\pi$
$24$	0.883601	−	8.81864i	0.180364	−	1.80010i
$25$		−	4.69090i		−	0.938181i
$26$	−2.97907	−	5.58100i	−0.584244	−	1.09452i
$27$	−8.46094	−	8.46094i	−1.62831	−	1.62831i
$28$	1.11301	−	1.66169i	0.210340	−	0.314029i
$29$	3.17349	−	3.17349i	0.589302	−	0.589302i	−0.348140	−	0.937443i	$-0.613187\pi$
$29$	3.17349	−	3.17349i	0.589302	−	0.589302i	0.937443	+	0.348140i	$0.113187\pi$
$30$	0.716500	−	2.35720i	0.130814	−	0.430365i
$31$	−4.43140			−0.795902			−0.397951	−	0.917407i	$-0.630279\pi$
$31$	−4.43140			−0.795902			−0.397951	+	0.917407i	$0.630279\pi$
$32$	−5.63115	+	0.538620i	−0.995457	+	0.0952155i
$33$	9.86440			1.71717
$34$	−0.403452	+	1.32731i	−0.0691914	+	0.227632i
$35$	0.393125	−	0.393125i	0.0664503	−	0.0664503i
$36$	−7.58922	+	11.3304i	−1.26487	+	1.88841i
$37$	0.645145	+	0.645145i	0.106061	+	0.106061i	0.758146	−	0.652085i	$-0.226105\pi$
$37$	0.645145	+	0.645145i	0.106061	+	0.106061i	−0.652085	+	0.758146i	$0.726105\pi$
$38$	−4.95791	−	9.28818i	−0.804280	−	1.50674i
$39$			14.0172i			2.24455i
$40$	−1.56467	−	0.156775i	−0.247396	−	0.0247883i
$41$		−	1.21375i		−	0.189556i	−0.995498	−	0.0947779i	$-0.969786\pi$
$41$		−	1.21375i		−	0.189556i	0.995498	−	0.0947779i	$-0.0302141\pi$
$42$	−3.90932	+	2.08675i	−0.603221	+	0.321992i
$43$	0.966515	+	0.966515i	0.147392	+	0.147392i	0.776952	−	0.629560i	$-0.216765\pi$
$43$	0.966515	+	0.966515i	0.147392	+	0.147392i	−0.629560	+	0.776952i	$0.716765\pi$
$44$	−1.22136	−	6.17655i	−0.184128	−	0.931150i
$45$	−2.68058	+	2.68058i	−0.399597	+	0.399597i
$46$	−1.70422	−	0.518019i	−0.251274	−	0.0763777i
$47$	9.97147			1.45449			0.727244	−	0.686379i	$-0.240801\pi$
$47$	9.97147			1.45449			0.727244	+	0.686379i	$0.240801\pi$
$48$	11.5690	+	4.82257i	1.66984	+	0.696078i
$49$	−1.00000			−0.142857
$50$	6.34720	+	1.92931i	0.897630	+	0.272845i
$51$	2.17349	−	2.17349i	0.304350	−	0.304350i
$52$	8.77683	−	1.73555i	1.21713	−	0.240677i
$53$	−8.07814	−	8.07814i	−1.10962	−	1.10962i	−0.993200	−	0.116418i	$-0.962859\pi$
$53$	−8.07814	−	8.07814i	−1.10962	−	1.10962i	−0.116418	−	0.993200i	$-0.537141\pi$
$54$	14.9283	−	7.96852i	2.03148	−	1.08438i
$55$		−	1.75021i		−	0.235999i
$56$	1.79064	+	2.18943i	0.239284	+	0.292575i
$57$			23.3282i			3.08989i
$58$	2.98879	+	5.59922i	0.392448	+	0.735214i
$59$	1.81385	+	1.81385i	0.236143	+	0.236143i	0.815251	−	0.579108i	$-0.196599\pi$
$59$	1.81385	+	1.81385i	0.236143	+	0.236143i	−0.579108	+	0.815251i	$0.696599\pi$
$60$	2.89482	+	1.93897i	0.373719	+	0.250320i
$61$	−2.58783	+	2.58783i	−0.331337	+	0.331337i	−0.853094	−	0.521757i	$-0.825277\pi$
$61$	−2.58783	+	2.58783i	−0.331337	+	0.331337i	0.521757	+	0.853094i	$0.325277\pi$
$62$	1.82257	−	5.99606i	0.231467	−	0.761501i
$63$	6.81864			0.859067
$64$	1.58722	−	7.84097i	0.198402	−	0.980121i
$65$	2.48704			0.308479
$66$	−4.05709	+	13.3474i	−0.499393	+	1.64295i
$67$	−1.59261	+	1.59261i	−0.194568	+	0.194568i	−0.797667	−	0.603098i	$-0.793933\pi$
$67$	−1.59261	+	1.59261i	−0.194568	+	0.194568i	0.603098	+	0.797667i	$0.293933\pi$
$68$	−1.63003	−	1.09181i	−0.197671	−	0.132401i
$69$	2.79069	+	2.79069i	0.335960	+	0.335960i
$70$	0.370246	+	0.693620i	0.0442528	+	0.0829034i
$71$		−	0.934634i		−	0.110921i	−0.998461	−	0.0554603i	$-0.982337\pi$
$71$		−	0.934634i		−	0.110921i	0.998461	−	0.0554603i	$-0.0176626\pi$
$72$	−12.2097	−	14.9289i	−1.43893	−	1.75939i
$73$		−	0.710511i		−	0.0831591i	−0.999135	−	0.0415795i	$-0.986761\pi$
$73$		−	0.710511i		−	0.0831591i	0.999135	−	0.0415795i	$-0.0132390\pi$
$74$	−1.13828	+	0.607598i	−0.132322	+	0.0706318i
$75$	−10.3936	−	10.3936i	−1.20015	−	1.20015i
$76$	14.6068	−	2.88839i	1.67552	−	0.331321i
$77$	−2.22602	+	2.22602i	−0.253679	+	0.253679i
$78$	−18.9665	−	5.76510i	−2.14754	−	0.652769i
$79$	11.8644			1.33485			0.667424	−	0.744678i	$-0.267397\pi$
$79$	11.8644			1.33485			0.667424	+	0.744678i	$0.267397\pi$
$80$	0.855656	−	2.05265i	0.0956653	−	0.229493i
$81$	−17.0379			−1.89310
$82$	1.64231	+	0.499198i	0.181363	+	0.0551273i
$83$	−6.77482	+	6.77482i	−0.743634	+	0.743634i	−0.973275	−	0.229642i	$-0.926245\pi$
$83$	−6.77482	+	6.77482i	−0.743634	+	0.743634i	0.229642	+	0.973275i	$0.426245\pi$
$84$	−1.21570	−	6.14790i	−0.132644	−	0.670790i
$85$	−0.385637	−	0.385637i	−0.0418282	−	0.0418282i
$86$	−1.70529	+	0.910265i	−0.183887	+	0.0981564i
$87$		−	14.0630i		−	1.50771i
$88$	8.85973	+	0.887719i	0.944451	+	0.0946311i
$89$		−	10.2082i		−	1.08206i	−0.841002	−	0.541032i	$-0.818034\pi$
$89$		−	10.2082i		−	1.08206i	0.841002	−	0.541032i	$-0.181966\pi$
$90$	−2.52457	−	4.72954i	−0.266113	−	0.498537i
$91$	−3.16316	−	3.16316i	−0.331590	−	0.331590i
$92$	1.40185	−	2.09291i	0.146153	−	0.218201i
$93$	−9.81864	+	9.81864i	−1.01815	+	1.01815i
$94$	−4.10113	+	13.4923i	−0.422999	+	1.39162i
$95$	4.13906			0.424658
$96$	−11.2835	+	13.6704i	−1.15162	+	1.39522i
$97$	−3.03684			−0.308344			−0.154172	−	0.988044i	$-0.549271\pi$
$97$	−3.03684			−0.308344			−0.154172	+	0.988044i	$0.549271\pi$
$98$	0.411286	−	1.35309i	0.0415462	−	0.136682i
$99$	15.1784	−	15.1784i	1.52549	−	1.52549i
$100$	−5.22103	+	7.79482i	−0.522103	+	0.779482i
$101$	−10.1648	−	10.1648i	−1.01143	−	1.01143i	−0.999934	−	0.0114982i	$-0.996340\pi$
$101$	−10.1648	−	10.1648i	−1.01143	−	1.01143i	−0.0114982	−	0.999934i	$-0.503660\pi$
$102$	2.04699	+	3.83485i	0.202683	+	0.379707i
$103$		−	6.05520i		−	0.596636i	−0.954466	−	0.298318i	$-0.903574\pi$
$103$		−	6.05520i		−	0.596636i	0.954466	−	0.298318i	$-0.0964256\pi$
$104$	−1.26144	+	12.5896i	−0.123695	+	1.23451i
$105$		−	1.74209i		−	0.170011i
$106$	14.2529	−	7.60800i	1.38436	−	0.738954i
$107$	12.4973	+	12.4973i	1.20816	+	1.20816i	0.971624	+	0.236533i	$0.0760111\pi$
$107$	12.4973	+	12.4973i	1.20816	+	1.20816i	0.236533	+	0.971624i	$0.423989\pi$
$108$	4.64231	+	23.4766i	0.446706	+	2.25903i
$109$	10.0575	−	10.0575i	0.963333	−	0.963333i	−0.0360181	−	0.999351i	$-0.511467\pi$
$109$	10.0575	−	10.0575i	0.963333	−	0.963333i	0.999351	+	0.0360181i	$0.0114674\pi$
$110$	2.36819	+	0.719839i	0.225798	+	0.0686339i
$111$	2.85889			0.271354
$112$	−3.69896	+	1.52241i	−0.349518	+	0.143854i
$113$	5.01929			0.472175			0.236088	−	0.971732i	$-0.424135\pi$
$113$	5.01929			0.472175			0.236088	+	0.971732i	$0.424135\pi$
$114$	−31.5650	−	9.59456i	−2.95634	−	0.898613i
$115$	0.495145	−	0.495145i	0.0461725	−	0.0461725i
$116$	−8.80548	+	1.74121i	−0.817568	+	0.161668i
$117$	21.5685	+	21.5685i	1.99401	+	1.99401i
$118$	−3.20031	+	1.70828i	−0.294612	+	0.157260i
$119$			0.980951i			0.0899236i
$120$	−3.81420	+	3.11946i	−0.348187	+	0.284767i
$121$		−	1.08963i		−	0.0990575i
$122$	−2.43721	−	4.56589i	−0.220655	−	0.413376i
$123$	−2.68930	−	2.68930i	−0.242486	−	0.242486i
$124$	7.36359	+	4.93220i	0.661270	+	0.442924i
$125$	−3.80974	+	3.80974i	−0.340754	+	0.340754i
$126$	−2.80441	+	9.22621i	−0.249837	+	0.821936i
$127$	−19.3869			−1.72031			−0.860156	−	0.510031i	$-0.829634\pi$
$127$	−19.3869			−1.72031			−0.860156	+	0.510031i	$0.829634\pi$
$128$	9.95671	+	5.37252i	0.880057	+	0.474869i
$129$	4.28301			0.377098
$130$	−1.02289	+	3.36518i	−0.0897130	+	0.295146i
$131$	8.29224	−	8.29224i	0.724496	−	0.724496i	−0.245021	−	0.969518i	$-0.578795\pi$
$131$	8.29224	−	8.29224i	0.724496	−	0.724496i	0.969518	+	0.245021i	$0.0787950\pi$
$132$	−16.3915	−	10.9792i	−1.42670	−	0.955616i
$133$	−5.26429	−	5.26429i	−0.456472	−	0.456472i
$134$	−1.49992	−	2.80996i	−0.129574	−	0.242744i
$135$			6.65242i			0.572549i
$136$	2.14772	−	1.75653i	0.184166	−	0.150621i
$137$			10.3723i			0.886168i	0.896480	+	0.443084i	$0.146116\pi$
$137$			10.3723i			0.886168i	−0.896480	+	0.443084i	$0.853884\pi$
$138$	−4.92382	+	2.62827i	−0.419143	+	0.223734i
$139$	−4.83290	−	4.83290i	−0.409921	−	0.409921i	0.471790	−	0.881711i	$-0.343608\pi$
$139$	−4.83290	−	4.83290i	−0.409921	−	0.409921i	−0.881711	+	0.471790i	$0.843608\pi$
$140$	−1.09080	+	0.215698i	−0.0921898	+	0.0182298i
$141$	22.0938	−	22.0938i	1.86063	−	1.86063i
$142$	1.26464	+	0.384402i	0.106126	+	0.0322583i
$143$	−14.0826			−1.17764
$144$	25.2218	−	10.3807i	2.10182	−	0.865062i
$145$	−2.49516			−0.207212
$146$	0.961384	+	0.292224i	0.0795647	+	0.0241846i
$147$	−2.21570	+	2.21570i	−0.182748	+	0.182748i
$148$	−0.353975	−	1.79008i	−0.0290966	−	0.147144i
$149$	1.74049	+	1.74049i	0.142587	+	0.142587i	0.774797	−	0.632210i	$-0.217852\pi$
$149$	1.74049	+	1.74049i	0.142587	+	0.142587i	−0.632210	+	0.774797i	$0.717852\pi$
$150$	18.3382	−	9.78872i	1.49731	−	0.799246i
$151$		−	20.8131i		−	1.69374i	−0.531798	−	0.846871i	$-0.678483\pi$
$151$		−	20.8131i		−	1.69374i	0.531798	−	0.846871i	$-0.321517\pi$
$152$	−2.09935	+	20.9523i	−0.170280	+	1.69945i
$153$		−	6.68874i		−	0.540753i
$154$	−2.09647	−	3.92754i	−0.168938	−	0.316490i
$155$	1.74209	+	1.74209i	0.139928	+	0.139928i
$156$	15.6014	−	23.2923i	1.24911	−	1.86487i
$157$	−10.1441	+	10.1441i	−0.809588	+	0.809588i	−0.984571	−	0.174983i	$-0.944013\pi$
$157$	−10.1441	+	10.1441i	−0.809588	+	0.809588i	0.174983	+	0.984571i	$0.444013\pi$
$158$	−4.87966	+	16.0536i	−0.388205	+	1.27715i
$159$	−35.7975			−2.83892
$160$	2.42549	+	2.00200i	0.191752	+	0.158272i
$161$	−1.25951			−0.0992632
$162$	7.00745	−	23.0537i	0.550557	−	1.81127i
$163$	−11.8882	+	11.8882i	−0.931152	+	0.931152i	−0.997778	−	0.0666257i	$-0.978777\pi$
$163$	−11.8882	+	11.8882i	−0.931152	+	0.931152i	0.0666257	+	0.997778i	$0.478777\pi$
$164$	−1.35092	+	2.01687i	−0.105489	+	0.157491i
$165$	−3.87794	−	3.87794i	−0.301898	−	0.301898i
$166$	−6.38053	−	11.9533i	−0.495225	−	0.927757i
$167$		−	1.10868i		−	0.0857923i	−0.999080	−	0.0428962i	$-0.986342\pi$
$167$		−	1.10868i		−	0.0857923i	0.999080	−	0.0428962i	$-0.0136585\pi$
$168$	8.81864	+	0.883601i	0.680373	+	0.0681713i
$169$		−	7.01121i		−	0.539324i
$170$	0.680407	−	0.363193i	0.0521848	−	0.0278556i
$171$	35.8953	+	35.8953i	2.74498	+	2.74498i
$172$	−0.530303	−	2.68179i	−0.0404352	−	0.204485i
$173$	−7.23971	+	7.23971i	−0.550425	+	0.550425i	−0.926563	−	0.376139i	$-0.877252\pi$
$173$	−7.23971	+	7.23971i	−0.550425	+	0.550425i	0.376139	+	0.926563i	$0.377252\pi$
$174$	19.0284	+	5.78392i	1.44254	+	0.438478i
$175$	4.69090			0.354599
$176$	−4.84505	+	11.6229i	−0.365209	+	0.876108i
$177$	8.03789			0.604164
$178$	13.8125	+	4.19848i	1.03529	+	0.314689i
$179$	9.93959	−	9.93959i	0.742920	−	0.742920i	−0.230219	−	0.973139i	$-0.573944\pi$
$179$	9.93959	−	9.93959i	0.742920	−	0.742920i	0.973139	+	0.230219i	$0.0739442\pi$
$180$	7.43780	−	1.47077i	0.554381	−	0.109624i
$181$	7.35342	+	7.35342i	0.546576	+	0.546576i	0.925449	−	0.378873i	$-0.123688\pi$
$181$	7.35342	+	7.35342i	0.546576	+	0.546576i	−0.378873	+	0.925449i	$0.623688\pi$
$182$	5.58100	−	2.97907i	0.413691	−	0.220823i
$183$			11.4677i			0.847715i
$184$	2.25533	+	2.75761i	0.166265	+	0.203294i
$185$		−	0.507246i		−	0.0372935i
$186$	−9.24719	−	17.3237i	−0.678037	−	1.27024i
$187$	2.18362	+	2.18362i	0.159682	+	0.159682i
$188$	−16.5695	−	11.0984i	−1.20845	−	0.809432i
$189$	8.46094	−	8.46094i	0.615443	−	0.615443i
$190$	−1.70234	+	5.60050i	−0.123501	+	0.406303i
$191$	3.54684			0.256640			0.128320	−	0.991733i	$-0.459042\pi$
$191$	3.54684			0.256640			0.128320	+	0.991733i	$0.459042\pi$
$192$	−13.8564	−	20.8900i	−1.00000	−	1.50761i
$193$	2.99394			0.215509			0.107754	−	0.994178i	$-0.465634\pi$
$193$	2.99394			0.215509			0.107754	+	0.994178i	$0.465634\pi$
$194$	1.24901	−	4.10911i	0.0896737	−	0.295017i
$195$	5.51053	−	5.51053i	0.394617	−	0.394617i
$196$	1.66169	+	1.11301i	0.118692	+	0.0795009i
$197$	3.55345	+	3.55345i	0.253173	+	0.253173i	0.822270	−	0.569097i	$-0.192707\pi$
$197$	3.55345	+	3.55345i	0.253173	+	0.253173i	−0.569097	+	0.822270i	$0.692707\pi$
$198$	14.2951	+	26.7804i	1.01591	+	1.90320i
$199$			1.80109i			0.127676i	0.997960	+	0.0638380i	$0.0203341\pi$
$199$			1.80109i			0.127676i	−0.997960	+	0.0638380i	$0.979666\pi$
$200$	−8.39972	−	10.2704i	−0.593950	−	0.726228i
$201$			7.05749i			0.497797i
$202$	17.9344	−	9.57318i	1.26186	−	0.673567i
$203$	3.17349	+	3.17349i	0.222735	+	0.222735i
$204$	−6.03078	+	1.19254i	−0.422239	+	0.0834945i
$205$	−0.477156	+	0.477156i	−0.0333260	+	0.0333260i
$206$	8.19321	+	2.49042i	0.570848	+	0.173516i
$207$	8.58813			0.596916
$208$	−16.5160	−	6.88478i	−1.14518	−	0.477373i
$209$	−23.4369			−1.62116
$210$	2.35720	+	0.716500i	0.162663	+	0.0494432i
$211$	−15.1022	+	15.1022i	−1.03968	+	1.03968i	−0.0404953	+	0.999180i	$0.512894\pi$
$211$	−15.1022	+	15.1022i	−1.03968	+	1.03968i	−0.999180	+	0.0404953i	$0.987106\pi$
$212$	4.43228	+	22.4144i	0.304410	+	1.53943i
$213$	−2.07087	−	2.07087i	−0.141893	−	0.141893i
$214$	−22.0498	+	11.7699i	−1.50730	+	0.804576i
$215$		−	0.759924i		−	0.0518264i
$216$	−33.6752	−	3.37415i	−2.29130	−	0.229582i
$217$		−	4.43140i		−	0.300823i
$218$	9.47215	+	17.7452i	0.641535	+	1.20185i
$219$	−1.57428	−	1.57428i	−0.106380	−	0.106380i
$220$	−1.94801	+	2.90831i	−0.131335	+	0.196078i
$221$	−3.10291	+	3.10291i	−0.208724	+	0.208724i
$222$	−1.17582	+	3.86833i	−0.0789162	+	0.259625i
$223$	7.11258			0.476294			0.238147	−	0.971229i	$-0.423460\pi$
$223$	7.11258			0.476294			0.238147	+	0.971229i	$0.423460\pi$
$224$	−0.538620	−	5.63115i	−0.0359881	−	0.376247i
$225$	−31.9856			−2.13237
$226$	−2.06437	+	6.79154i	−0.137320	+	0.451767i
$227$	−12.1687	+	12.1687i	−0.807665	+	0.807665i	−0.984280	−	0.176615i	$-0.943485\pi$
$227$	−12.1687	+	12.1687i	−0.807665	+	0.807665i	0.176615	+	0.984280i	$0.443485\pi$
$228$	25.9645	−	38.7641i	1.71954	−	2.56722i
$229$	−0.621484	−	0.621484i	−0.0410688	−	0.0410688i	0.686274	−	0.727343i	$-0.259245\pi$
$229$	−0.621484	−	0.621484i	−0.0410688	−	0.0410688i	−0.727343	+	0.686274i	$0.759245\pi$
$230$	0.466328	+	0.873620i	0.0307487	+	0.0576048i
$231$			9.86440i			0.649030i
$232$	1.26556	−	12.6307i	0.0830881	−	0.829247i
$233$		−	4.85688i		−	0.318185i	−0.987264	−	0.159093i	$-0.949143\pi$
$233$		−	4.85688i		−	0.318185i	0.987264	−	0.159093i	$-0.0508568\pi$
$234$	−38.0548	+	20.3132i	−2.48772	+	1.32791i
$235$	−3.92004	−	3.92004i	−0.255715	−	0.255715i
$236$	−0.995214	−	5.03289i	−0.0647829	−	0.327613i
$237$	26.2879	−	26.2879i	1.70758	−	1.70758i
$238$	−1.32731	−	0.403452i	−0.0860368	−	0.0261519i
$239$	4.91033			0.317623			0.158811	−	0.987309i	$-0.449234\pi$
$239$	4.91033			0.317623			0.158811	+	0.987309i	$0.449234\pi$
$240$	−2.65218	−	6.44393i	−0.171197	−	0.415954i
$241$	10.8591			0.699498			0.349749	−	0.936843i	$-0.386267\pi$
$241$	10.8591			0.699498			0.349749	+	0.936843i	$0.386267\pi$
$242$	1.47437	+	0.448151i	0.0947759	+	0.0288082i
$243$	−12.3680	+	12.3680i	−0.793406	+	0.793406i
$244$	7.18044	−	1.41987i	0.459680	−	0.0908982i
$245$	0.393125	+	0.393125i	0.0251159	+	0.0251159i
$246$	4.74493	−	2.53279i	0.302526	−	0.161484i
$247$		−	33.3037i		−	2.11906i
$248$	−9.70224	+	7.93504i	−0.616093	+	0.503875i
$249$			30.0219i			1.90256i
$250$	−3.58801	−	6.72180i	−0.226926	−	0.425124i
$251$	8.18516	+	8.18516i	0.516643	+	0.516643i	0.916554	−	0.399911i	$-0.130959\pi$
$251$	8.18516	+	8.18516i	0.516643	+	0.516643i	−0.399911	+	0.916554i	$0.630959\pi$
$252$	−11.3304	−	7.58922i	−0.713751	−	0.478076i
$253$	−2.80370	+	2.80370i	−0.176267	+	0.176267i
$254$	7.97358	−	26.2322i	0.500307	−	1.64595i
$255$	−1.70891			−0.107016
$256$	−11.3645	+	11.2626i	−0.710284	+	0.703915i
$257$	20.6130			1.28580			0.642902	−	0.765948i	$-0.277730\pi$
$257$	20.6130			1.28580			0.642902	+	0.765948i	$0.277730\pi$
$258$	−1.76154	+	5.79529i	−0.109669	+	0.360799i
$259$	−0.645145	+	0.645145i	−0.0400874	+	0.0400874i
$260$	−4.13268	−	2.76811i	−0.256298	−	0.171671i
$261$	−21.6389	−	21.6389i	−1.33941	−	1.33941i
$262$	7.80963	+	14.6306i	0.482481	+	0.903882i
$263$			13.6297i			0.840444i	0.907421	+	0.420222i	$0.138048\pi$
$263$			13.6297i			0.840444i	−0.907421	+	0.420222i	$0.861952\pi$
$264$	21.5974	−	17.6636i	1.32923	−	1.08712i
$265$			6.35145i			0.390166i
$266$	9.28818	−	4.95791i	0.569495	−	0.303989i
$267$	−22.6182	−	22.6182i	−1.38421	−	1.38421i
$268$	4.41902	−	0.873826i	0.269934	−	0.0533774i
$269$	4.42999	−	4.42999i	0.270101	−	0.270101i	−0.559040	−	0.829141i	$-0.688830\pi$
$269$	4.42999	−	4.42999i	0.270101	−	0.270101i	0.829141	+	0.559040i	$0.188830\pi$
$270$	−9.00131	−	2.73605i	−0.547802	−	0.166511i
$271$	12.6851			0.770564			0.385282	−	0.922799i	$-0.374104\pi$
$271$	12.6851			0.770564			0.385282	+	0.922799i	$0.374104\pi$
$272$	1.49341	+	3.62849i	0.0905511	+	0.220010i
$273$	−14.0172			−0.848362
$274$	−14.0347	−	4.26600i	−0.847865	−	0.257718i
$275$	10.4421	−	10.4421i	0.629680	−	0.629680i
$276$	−1.53118	−	7.74333i	−0.0921663	−	0.466094i
$277$	17.0842	+	17.0842i	1.02649	+	1.02649i	0.999639	+	0.0268508i	$0.00854789\pi$
$277$	17.0842	+	17.0842i	1.02649	+	1.02649i	0.0268508	+	0.999639i	$0.491452\pi$
$278$	8.52704	−	4.55163i	0.511418	−	0.272988i
$279$			30.2161i			1.80899i
$280$	0.156775	−	1.56467i	0.00936909	−	0.0935067i
$281$			12.8628i			0.767330i	0.923472	+	0.383665i	$0.125338\pi$
$281$			12.8628i			0.767330i	−0.923472	+	0.383665i	$0.874662\pi$
$282$	20.8079	+	38.9817i	1.23909	+	2.32132i
$283$	−0.879091	−	0.879091i	−0.0522565	−	0.0522565i	0.680496	−	0.732752i	$-0.261765\pi$
$283$	−0.879091	−	0.879091i	−0.0522565	−	0.0522565i	−0.732752	+	0.680496i	$0.761765\pi$
$284$	−1.04026	+	1.55307i	−0.0617280	+	0.0921577i
$285$	9.17090	−	9.17090i	0.543237	−	0.543237i
$286$	5.79196	−	19.0549i	0.342486	−	1.12674i
$287$	1.21375			0.0716454
$288$	3.67265	+	38.3968i	0.216413	+	2.26255i
$289$	−16.0377			−0.943396
$290$	1.02622	−	3.37617i	0.0602620	−	0.198255i
$291$	−6.72872	+	6.72872i	−0.394445	+	0.394445i
$292$	−0.790808	+	1.18065i	−0.0462785	+	0.0690922i
$293$	−17.9935	−	17.9935i	−1.05119	−	1.05119i	−0.998617	−	0.0525765i	$-0.983257\pi$
$293$	−17.9935	−	17.9935i	−1.05119	−	1.05119i	−0.0525765	−	0.998617i	$-0.516743\pi$
$294$	−2.08675	−	3.90932i	−0.121701	−	0.227996i
$295$		−	1.42614i		−	0.0830331i
$296$	2.56772	+	0.257278i	0.149246	+	0.0149540i
$297$		−	37.6685i		−	2.18575i
$298$	−3.07088	+	1.63920i	−0.177891	+	0.0949560i
$299$	−3.98403	−	3.98403i	−0.230403	−	0.230403i
$300$	5.70272	+	28.8392i	0.329247	+	1.66503i
$301$	−0.966515	+	0.966515i	−0.0557090	+	0.0557090i
$302$	28.1619	+	8.56013i	1.62053	+	0.492580i
$303$	−45.0441			−2.58772
$304$	−27.4868	−	11.4580i	−1.57648	−	0.657161i
$305$	2.03468			0.116505
$306$	9.05045	+	2.75099i	0.517380	+	0.157264i
$307$	−1.74987	+	1.74987i	−0.0998702	+	0.0998702i	−0.755277	−	0.655406i	$-0.772497\pi$
$307$	−1.74987	+	1.74987i	−0.0998702	+	0.0998702i	0.655406	+	0.755277i	$0.272497\pi$
$308$	6.17655	−	1.22136i	0.351941	−	0.0695937i
$309$	−13.4165	−	13.4165i	−0.763237	−	0.763237i
$310$	−3.07370	+	1.64070i	−0.174575	+	0.0931858i
$311$			17.4288i			0.988296i	0.869378	+	0.494148i	$0.164520\pi$
$311$			17.4288i			0.988296i	−0.869378	+	0.494148i	$0.835480\pi$
$312$	25.0998	+	30.6898i	1.42100	+	1.73747i
$313$			28.3430i			1.60204i	0.598637	+	0.801021i	$0.295709\pi$
$313$			28.3430i			1.60204i	−0.598637	+	0.801021i	$0.704291\pi$
$314$	−9.55373	−	17.8980i	−0.539148	−	1.01004i
$315$	−2.68058	−	2.68058i	−0.151033	−	0.151033i
$316$	−19.7149	−	13.2052i	−1.10905	−	0.742851i
$317$	8.24397	−	8.24397i	0.463028	−	0.463028i	−0.436619	−	0.899647i	$-0.643824\pi$
$317$	8.24397	−	8.24397i	0.463028	−	0.463028i	0.899647	+	0.436619i	$0.143824\pi$
$318$	14.7230	−	48.4371i	0.825625	−	2.71622i
$319$	14.1285			0.791046
$320$	−3.70646	+	2.45851i	−0.207197	+	0.137435i
$321$	55.3803			3.09103
$322$	0.518019	−	1.70422i	0.0288681	−	0.0949727i
$323$	−5.16401	+	5.16401i	−0.287333	+	0.287333i
$324$	28.3116	+	18.9634i	1.57287	+	1.05352i
$325$	14.8381	+	14.8381i	0.823070	+	0.823070i
$326$	−11.1963	−	20.9751i	−0.620104	−	1.16171i
$327$		−	44.5687i		−	2.46466i
$328$	−2.17339	−	2.65742i	−0.120005	−	0.146731i
$329$			9.97147i			0.549745i
$330$	6.84214	−	3.65225i	0.376647	−	0.201050i
$331$	0.235462	+	0.235462i	0.0129422	+	0.0129422i	0.713548	−	0.700606i	$-0.247087\pi$
$331$	0.235462	+	0.235462i	0.0129422	+	0.0129422i	−0.700606	+	0.713548i	$0.747087\pi$
$332$	18.7981	−	3.71718i	1.03168	−	0.204007i
$333$	4.39901	−	4.39901i	0.241064	−	0.241064i
$334$	1.50014	+	0.455986i	0.0820841	+	0.0249504i
$335$	1.25219			0.0684146
$336$	−4.82257	+	11.5690i	−0.263093	+	0.631139i
$337$	9.22099			0.502299			0.251150	−	0.967948i	$-0.419191\pi$
$337$	9.22099			0.502299			0.251150	+	0.967948i	$0.419191\pi$
$338$	9.48678	+	2.88362i	0.516013	+	0.156848i
$339$	11.1212	−	11.1212i	0.604023	−	0.604023i
$340$	0.211589	+	1.07003i	0.0114750	+	0.0580303i
$341$	−9.86440	−	9.86440i	−0.534187	−	0.534187i
$342$	−63.3327	+	33.8062i	−3.42464	+	1.82803i
$343$		−	1.00000i		−	0.0539949i
$344$	3.84680	+	0.385438i	0.207406	+	0.0207814i
$345$		−	2.19418i		−	0.118131i
$346$	−6.81836	−	12.7735i	−0.366557	−	0.686710i
$347$	−8.02721	−	8.02721i	−0.430923	−	0.430923i	0.458019	−	0.888942i	$-0.348559\pi$
$347$	−8.02721	−	8.02721i	−0.430923	−	0.430923i	−0.888942	+	0.458019i	$0.848559\pi$
$348$	−15.6523	+	23.3683i	−0.839050	+	1.25267i
$349$	11.5879	−	11.5879i	0.620287	−	0.620287i	−0.325318	−	0.945605i	$-0.605471\pi$
$349$	11.5879	−	11.5879i	0.620287	−	0.620287i	0.945605	+	0.325318i	$0.105471\pi$
$350$	−1.92931	+	6.34720i	−0.103126	+	0.339272i
$351$	53.5267			2.85704
$352$	−13.7341	−	11.3361i	−0.732028	−	0.604216i
$353$	18.9481			1.00850			0.504252	−	0.863557i	$-0.331768\pi$
$353$	18.9481			1.00850			0.504252	+	0.863557i	$0.331768\pi$
$354$	−3.30587	+	10.8760i	−0.175705	+	0.578051i
$355$	−0.367428	+	0.367428i	−0.0195011	+	0.0195011i
$356$	−11.3618	+	16.9628i	−0.602175	+	0.899026i
$357$	2.17349	+	2.17349i	0.115033	+	0.115033i
$358$	9.36111	+	17.5371i	0.494750	+	0.926867i
$359$		−	3.54172i		−	0.186925i	−0.995623	−	0.0934624i	$-0.970207\pi$
$359$		−	3.54172i		−	0.186925i	0.995623	−	0.0934624i	$-0.0297935\pi$
$360$	−1.06899	+	10.6689i	−0.0563408	+	0.562300i
$361$		−	36.4256i		−	1.91714i
$362$	−12.9742	+	6.92546i	−0.681908	+	0.363994i
$363$	−2.41430	−	2.41430i	−0.126718	−	0.126718i
$364$	1.73555	+	8.77683i	0.0909675	+	0.460031i
$365$	−0.279320	+	0.279320i	−0.0146203	+	0.0146203i
$366$	−15.5168	−	4.71650i	−0.811074	−	0.246535i
$367$	11.1874			0.583979			0.291989	−	0.956422i	$-0.405683\pi$
$367$	11.1874			0.583979			0.291989	+	0.956422i	$0.405683\pi$
$368$	−4.65887	+	1.91749i	−0.242860	+	0.0999559i
$369$	−8.27611			−0.430837
$370$	0.686348	+	0.208623i	0.0356815	+	0.0108458i
$371$	8.07814	−	8.07814i	0.419396	−	0.419396i
$372$	27.2438	−	5.38724i	1.41252	−	0.279315i
$373$	13.8071	+	13.8071i	0.714907	+	0.714907i	0.967558	−	0.252651i	$-0.0813023\pi$
$373$	13.8071	+	13.8071i	0.714907	+	0.714907i	−0.252651	+	0.967558i	$0.581302\pi$
$374$	−3.85272	+	2.05653i	−0.199219	+	0.106341i
$375$			16.8825i			0.871807i
$376$	21.8319	−	17.8553i	1.12589	−	0.920818i
$377$			20.0765i			1.03399i
$378$	7.96852	+	14.9283i	0.409856	+	0.767827i
$379$	−10.9875	−	10.9875i	−0.564391	−	0.564391i	0.366161	−	0.930552i	$-0.380672\pi$
$379$	−10.9875	−	10.9875i	−0.564391	−	0.564391i	−0.930552	+	0.366161i	$0.880672\pi$
$380$	−6.87782	−	4.60682i	−0.352824	−	0.236325i
$381$	−42.9556	+	42.9556i	−2.20068	+	2.20068i
$382$	−1.45877	+	4.79918i	−0.0746369	+	0.245547i
$383$	−4.83945			−0.247284			−0.123642	−	0.992327i	$-0.539458\pi$
$383$	−4.83945			−0.247284			−0.123642	+	0.992327i	$0.539458\pi$
$384$	33.9649	−	10.1572i	1.73327	−	0.518330i
$385$	1.75021			0.0891991
$386$	−1.23137	+	4.05106i	−0.0626750	+	0.206194i
$387$	6.59032	−	6.59032i	0.335005	−	0.335005i
$388$	5.04628	+	3.38004i	0.256186	+	0.171595i
$389$	12.4807	+	12.4807i	0.632795	+	0.632795i	0.948768	−	0.315973i	$-0.102331\pi$
$389$	12.4807	+	12.4807i	0.632795	+	0.632795i	−0.315973	+	0.948768i	$0.602331\pi$
$390$	5.18982	+	9.72263i	0.262797	+	0.492325i
$391$			1.23552i			0.0624827i
$392$	−2.18943	+	1.79064i	−0.110583	+	0.0904410i
$393$		−	36.7462i		−	1.85360i
$394$	−6.26961	+	3.34664i	−0.315859	+	0.168601i
$395$	−4.66419	−	4.66419i	−0.234681	−	0.234681i
$396$	−42.1156	+	8.32803i	−2.11639	+	0.418499i
$397$	−11.7543	+	11.7543i	−0.589931	+	0.589931i	−0.937613	−	0.347682i	$-0.886969\pi$
$397$	−11.7543	+	11.7543i	−0.589931	+	0.589931i	0.347682	+	0.937613i	$0.386969\pi$
$398$	−2.43703	−	0.740764i	−0.122157	−	0.0371311i
$399$	−23.3282			−1.16787
$400$	17.3514	−	7.14147i	0.867572	−	0.357074i
$401$	−25.5823			−1.27752			−0.638760	−	0.769406i	$-0.720552\pi$
$401$	−25.5823			−1.27752			−0.638760	+	0.769406i	$0.720552\pi$
$402$	−9.54940	−	2.90265i	−0.476281	−	0.144771i
$403$	14.0172	−	14.0172i	0.698248	−	0.698248i
$404$	5.57715	+	28.2042i	0.277474	+	1.40321i
$405$	6.69803	+	6.69803i	0.332828	+	0.332828i
$406$	−5.59922	+	2.98879i	−0.277885	+	0.148331i
$407$			2.87222i			0.142371i
$408$	0.866769	−	8.65065i	0.0429114	−	0.428271i
$409$		−	19.2126i		−	0.950001i	−0.879985	−	0.475001i	$-0.842448\pi$
$409$		−	19.2126i		−	0.950001i	0.879985	−	0.475001i	$-0.157552\pi$
$410$	−0.449385	−	0.841881i	−0.0221936	−	0.0415775i
$411$	22.9820	+	22.9820i	1.13362	+	1.13362i
$412$	−6.73951	+	10.0618i	−0.332032	+	0.495711i
$413$	−1.81385	+	1.81385i	−0.0892537	+	0.0892537i
$414$	−3.53218	+	11.6205i	−0.173597	+	0.571116i
$415$	5.32671			0.261478
$416$	16.1085	−	19.5160i	0.789785	−	0.956851i
$417$	−21.4165			−1.04877
$418$	9.63928	−	31.7122i	0.471472	−	1.55109i
$419$	11.2764	−	11.2764i	0.550888	−	0.550888i	−0.375809	−	0.926697i	$-0.622635\pi$
$419$	11.2764	−	11.2764i	0.550888	−	0.550888i	0.926697	+	0.375809i	$0.122635\pi$
$420$	−1.93897	+	2.89482i	−0.0946121	+	0.141253i
$421$	27.1033	+	27.1033i	1.32094	+	1.32094i	0.913019	+	0.407918i	$0.133745\pi$
$421$	27.1033	+	27.1033i	1.32094	+	1.32094i	0.407918	+	0.913019i	$0.366255\pi$
$422$	−14.2232	−	26.6458i	−0.692375	−	1.29710i
$423$		−	67.9918i		−	3.30588i
$424$	−32.1516	−	3.22149i	−1.56142	−	0.156449i
$425$		−	4.60155i		−	0.223208i
$426$	3.65378	−	1.95034i	0.177026	−	0.0944944i
$427$	−2.58783	−	2.58783i	−0.125234	−	0.125234i
$428$	−6.85694	−	34.6762i	−0.331443	−	1.67614i
$429$	−31.2027	+	31.2027i	−1.50648	+	1.50648i
$430$	1.02824	+	0.312546i	0.0495862	+	0.0150723i
$431$	−14.7618			−0.711053			−0.355526	−	0.934666i	$-0.615698\pi$
$431$	−14.7618			−0.711053			−0.355526	+	0.934666i	$0.615698\pi$
$432$	18.4156	−	44.1777i	0.886023	−	2.12550i
$433$	−30.0057			−1.44198			−0.720991	−	0.692944i	$-0.756313\pi$
$433$	−30.0057			−1.44198			−0.720991	+	0.692944i	$0.756313\pi$
$434$	5.99606	+	1.82257i	0.287820	+	0.0874863i
$435$	−5.52852	+	5.52852i	−0.265072	+	0.265072i
$436$	−27.9065	+	5.51829i	−1.33648	+	0.264278i
$437$	−6.63043	−	6.63043i	−0.317176	−	0.317176i
$438$	2.77761	−	1.48266i	0.132720	−	0.0708441i
$439$			33.7523i			1.61091i	0.592659	+	0.805454i	$0.298078\pi$
$439$			33.7523i			1.61091i	−0.592659	+	0.805454i	$0.701922\pi$
$440$	−3.13400	−	3.83197i	−0.149408	−	0.182682i
$441$			6.81864i			0.324697i
$442$	−2.92232	−	5.47469i	−0.139001	−	0.260404i
$443$	5.22020	+	5.22020i	0.248019	+	0.248019i	0.820157	−	0.572138i	$-0.193886\pi$
$443$	5.22020	+	5.22020i	0.248019	+	0.248019i	−0.572138	+	0.820157i	$0.693886\pi$
$444$	−4.75059	−	3.18198i	−0.225453	−	0.151010i
$445$	−4.01309	+	4.01309i	−0.190239	+	0.190239i
$446$	−2.92531	+	9.62394i	−0.138517	+	0.455707i
$447$	7.71281			0.364803
$448$	7.84097	+	1.58722i	0.370451	+	0.0749890i
$449$	−1.59006			−0.0750395			−0.0375197	−	0.999296i	$-0.511946\pi$
$449$	−1.59006			−0.0750395			−0.0375197	+	0.999296i	$0.511946\pi$
$450$	13.1552	−	43.2793i	0.620143	−	2.04020i
$451$	2.70184	−	2.70184i	0.127224	−	0.127224i
$452$	−8.34050	−	5.58654i	−0.392304	−	0.262769i
$453$	−46.1154	−	46.1154i	−2.16669	−	2.16669i
$454$	−11.4605	−	21.4701i	−0.537867	−	1.00764i
$455$			2.48704i			0.116594i
$456$	41.7724	+	51.0754i	1.95617	+	2.39183i
$457$		−	2.14917i		−	0.100534i	−0.998736	−	0.0502671i	$-0.983993\pi$
$457$		−	2.14917i		−	0.100534i	0.998736	−	0.0502671i	$-0.0160072\pi$
$458$	1.09653	−	0.585313i	0.0512374	−	0.0273499i
$459$	−8.29977	−	8.29977i	−0.387400	−	0.387400i
$460$	−1.37388	+	0.271674i	−0.0640574	+	0.0126668i
$461$	−26.7406	+	26.7406i	−1.24543	+	1.24543i	−0.287719	+	0.957715i	$0.592897\pi$
$461$	−26.7406	+	26.7406i	−1.24543	+	1.24543i	−0.957715	+	0.287719i	$0.907103\pi$
$462$	−13.3474	−	4.05709i	−0.620976	−	0.188753i
$463$	16.2686			0.756065			0.378033	−	0.925792i	$-0.376601\pi$
$463$	16.2686			0.756065			0.378033	+	0.925792i	$0.376601\pi$
$464$	16.5699	+	6.90725i	0.769240	+	0.320661i
$465$	7.71991			0.358002
$466$	6.57179	+	1.99757i	0.304432	+	0.0925356i
$467$	17.9285	−	17.9285i	0.829632	−	0.829632i	−0.157834	−	0.987466i	$-0.550451\pi$
$467$	17.9285	−	17.9285i	0.829632	−	0.829632i	0.987466	+	0.157834i	$0.0504511\pi$
$468$	−11.8341	−	59.8460i	−0.547030	−	2.76638i
$469$	−1.59261	−	1.59261i	−0.0735400	−	0.0735400i
$470$	6.91641	−	3.69189i	0.319030	−	0.170294i
$471$			44.9526i			2.07131i
$472$	7.21925	+	0.723347i	0.332293	+	0.0332947i
$473$			4.30297i			0.197851i
$474$	24.7580	+	46.3817i	1.13717	+	2.13038i
$475$	24.6943	+	24.6943i	1.13305	+	1.13305i
$476$	1.09181	−	1.63003i	0.0500430	−	0.0747124i
$477$	−55.0819	+	55.0819i	−2.52203	+	2.52203i
$478$	−2.01955	+	6.64410i	−0.0923721	+	0.303894i
$479$	−16.9860			−0.776112			−0.388056	−	0.921636i	$-0.626853\pi$
$479$	−16.9860			−0.776112			−0.388056	+	0.921636i	$0.626853\pi$
$480$	9.81000	−	0.938327i	0.447763	−	0.0428286i
$481$	−4.08140			−0.186096
$482$	−4.46621	+	14.6933i	−0.203430	+	0.669263i
$483$	−2.79069	+	2.79069i	−0.126981	+	0.126981i
$484$	−1.21277	+	1.81063i	−0.0551261	+	0.0823012i
$485$	1.19386	+	1.19386i	0.0542103	+	0.0542103i
$486$	−11.6482	−	21.8217i	−0.528372	−	0.989854i
$487$			39.0342i			1.76881i	0.466722	+	0.884404i	$0.345435\pi$
$487$			39.0342i			1.76881i	−0.466722	+	0.884404i	$0.654565\pi$
$488$	−1.03200	+	10.2997i	−0.0467165	+	0.466247i
$489$			52.6811i			2.38232i
$490$	−0.693620	+	0.370246i	−0.0313345	+	0.0167260i
$491$	−26.8828	−	26.8828i	−1.21320	−	1.21320i	−0.969967	−	0.243238i	$-0.921790\pi$
$491$	−26.8828	−	26.8828i	−1.21320	−	1.21320i	−0.243238	−	0.969967i	$-0.578210\pi$
$492$	1.47555	+	7.46200i	0.0665230	+	0.336413i
$493$	3.11304	−	3.11304i	0.140204	−	0.140204i
$494$	45.0627	+	13.6973i	2.02747	+	0.616272i
$495$	−11.9341			−0.536396
$496$	−6.74639	−	16.3915i	−0.302922	−	0.736002i
$497$	0.934634			0.0419241
$498$	−40.6223	−	12.3476i	−1.82033	−	0.553310i
$499$	4.52969	−	4.52969i	0.202777	−	0.202777i	−0.598412	−	0.801189i	$-0.704201\pi$
$499$	4.52969	−	4.52969i	0.202777	−	0.202777i	0.801189	+	0.598412i	$0.204201\pi$
$500$	10.5709	−	2.09031i	0.472744	−	0.0934815i
$501$	−2.45650	−	2.45650i	−0.109748	−	0.109748i
$502$	−14.4417	+	7.70879i	−0.644564	+	0.344060i
$503$		−	35.6215i		−	1.58829i	−0.607731	−	0.794143i	$-0.707920\pi$
$503$		−	35.6215i		−	1.58829i	0.607731	−	0.794143i	$-0.292080\pi$
$504$	14.9289	−	12.2097i	0.664988	−	0.543864i
$505$			7.99206i			0.355642i
$506$	−2.64052	−	4.94677i	−0.117386	−	0.219911i
$507$	−15.5347	−	15.5347i	−0.689922	−	0.689922i
$508$	32.2150	+	21.5779i	1.42931	+	0.957364i
$509$	18.0304	−	18.0304i	0.799183	−	0.799183i	−0.183783	−	0.982967i	$-0.558835\pi$
$509$	18.0304	−	18.0304i	0.799183	−	0.799183i	0.982967	+	0.183783i	$0.0588345\pi$
$510$	0.702851	−	2.31230i	0.0311228	−	0.102390i
$511$	0.710511			0.0314312
$512$	−10.5652	−	20.0094i	−0.466922	−	0.884298i
$513$	89.0818			3.93306
$514$	−8.47785	+	27.8912i	−0.373942	+	1.23023i
$515$	−2.38045	+	2.38045i	−0.104895	+	0.104895i
$516$	−7.11703	−	4.76705i	−0.313310	−	0.209857i
$517$	22.1967	+	22.1967i	0.976212	+	0.976212i
$518$	−0.607598	−	1.13828i	−0.0266963	−	0.0500130i
$519$			32.0820i			1.40824i
$520$	5.44520	−	4.45339i	0.238788	−	0.195294i
$521$		−	15.5300i		−	0.680380i	−0.940357	−	0.340190i	$-0.889509\pi$
$521$		−	15.5300i		−	0.680380i	0.940357	−	0.340190i	$-0.110491\pi$
$522$	38.1790	−	20.3795i	1.67105	−	0.891986i
$523$	7.58074	+	7.58074i	0.331483	+	0.331483i	0.853149	−	0.521667i	$-0.174690\pi$
$523$	7.58074	+	7.58074i	0.331483	+	0.331483i	−0.521667	+	0.853149i	$0.674690\pi$
$524$	−23.0085	+	4.54974i	−1.00513	+	0.198756i
$525$	10.3936	−	10.3936i	0.453615	−	0.453615i
$526$	−18.4422	−	5.60571i	−0.804117	−	0.244421i
$527$	−4.34698			−0.189357
$528$	15.0176	+	36.4880i	0.653559	+	1.58793i
$529$	21.4136			0.931028
$530$	−8.59406	−	2.61226i	−0.373302	−	0.113469i
$531$	12.3680	−	12.3680i	0.536725	−	0.536725i
$532$	2.88839	+	14.6068i	0.125227	+	0.633287i
$533$	3.83929	+	3.83929i	0.166298	+	0.166298i
$534$	39.9070	−	21.3018i	1.72694	−	0.921821i
$535$		−	9.82598i		−	0.424814i
$536$	−0.635119	+	6.33871i	−0.0274330	+	0.273790i
$537$		−	44.0463i		−	1.90074i
$538$	4.17217	+	7.81615i	0.179875	+	0.336978i
$539$	−2.22602	−	2.22602i	−0.0958817	−	0.0958817i
$540$	7.40423	−	11.0542i	0.318627	−	0.475699i
$541$	16.7920	−	16.7920i	0.721944	−	0.721944i	−0.247057	−	0.969001i	$-0.579463\pi$
$541$	16.7920	−	16.7920i	0.721944	−	0.721944i	0.969001	+	0.247057i	$0.0794634\pi$
$542$	−5.21720	+	17.1640i	−0.224098	+	0.737258i
$543$	32.5859			1.39840
$544$	−5.52388	+	0.528360i	−0.236835	+	0.0226532i
$545$	−7.90771			−0.338729
$546$	5.76510	−	18.9665i	0.246723	−	0.811693i
$547$	−28.9159	+	28.9159i	−1.23636	+	1.23636i	−0.274875	+	0.961480i	$0.588637\pi$
$547$	−28.9159	+	28.9159i	−1.23636	+	1.23636i	−0.961480	+	0.274875i	$0.911363\pi$
$548$	11.5445	−	17.2356i	0.493158	−	0.736267i
$549$	17.6454	+	17.6454i	0.753089	+	0.753089i
$550$	9.83434	+	18.4237i	0.419338	+	0.785589i
$551$			33.4124i			1.42342i
$552$	11.1071	+	1.11290i	0.472752	+	0.0473683i
$553$			11.8644i			0.504525i
$554$	−30.1429	+	16.0899i	−1.28065	+	0.683595i
$555$	−1.12390	−	1.12390i	−0.0477071	−	0.0477071i
$556$	2.65169	+	13.4098i	0.112457	+	0.568704i
$557$	11.8756	−	11.8756i	0.503184	−	0.503184i	−0.409242	−	0.912426i	$-0.634207\pi$
$557$	11.8756	−	11.8756i	0.503184	−	0.503184i	0.912426	+	0.409242i	$0.134207\pi$
$558$	−40.8850	−	12.4275i	−1.73080	−	0.526096i
$559$	−6.11449			−0.258616
$560$	2.05265	+	0.855656i	0.0867403	+	0.0361581i
$561$	9.67648			0.408541
$562$	−17.4045	−	5.29029i	−0.734163	−	0.223157i
$563$	−2.51935	+	2.51935i	−0.106178	+	0.106178i	−0.758200	−	0.652022i	$-0.773921\pi$
$563$	−2.51935	+	2.51935i	−0.106178	+	0.106178i	0.652022	+	0.758200i	$0.273921\pi$
$564$	−61.3036	+	12.1223i	−2.58135	+	0.510441i
$565$	−1.97321	−	1.97321i	−0.0830137	−	0.0830137i
$566$	1.55104	−	0.827928i	0.0651952	−	0.0348004i
$567$		−	17.0379i		−	0.715524i
$568$	−1.67359	−	2.04632i	−0.0702224	−	0.0858615i
$569$		−	1.90395i		−	0.0798176i	−0.999203	−	0.0399088i	$-0.987293\pi$
$569$		−	1.90395i		−	0.0798176i	0.999203	−	0.0399088i	$-0.0127067\pi$
$570$	8.63715	+	16.1809i	0.361771	+	0.677743i
$571$	1.94546	+	1.94546i	0.0814148	+	0.0814148i	0.746641	−	0.665227i	$-0.231665\pi$
$571$	1.94546	+	1.94546i	0.0814148	+	0.0814148i	−0.665227	+	0.746641i	$0.731665\pi$
$572$	23.4008	+	15.6741i	0.978437	+	0.655365i
$573$	7.85872	−	7.85872i	0.328303	−	0.328303i
$574$	−0.499198	+	1.64231i	−0.0208361	+	0.0685486i
$575$	5.90824			0.246390
$576$	−53.4647	−	10.8227i	−2.22770	−	0.450944i
$577$	−0.270046			−0.0112422			−0.00562108	−	0.999984i	$-0.501789\pi$
$577$	−0.270046			−0.0112422			−0.00562108	+	0.999984i	$0.501789\pi$
$578$	6.59610	−	21.7004i	0.274362	−	0.902620i
$579$	6.63367	−	6.63367i	0.275686	−	0.275686i
$580$	4.14617	+	2.77714i	0.172160	+	0.115315i
$581$	−6.77482	−	6.77482i	−0.281067	−	0.281067i
$582$	−6.33711	−	11.8720i	−0.262682	−	0.492109i
$583$		−	35.9643i		−	1.48949i
$584$	−1.27227	−	1.55562i	−0.0526469	−	0.0643718i
$585$		−	16.9582i		−	0.701136i
$586$	31.7473	−	16.9463i	1.31147	−	0.700046i
$587$	−22.4556	−	22.4556i	−0.926842	−	0.926842i	0.0706582	−	0.997501i	$-0.477490\pi$
$587$	−22.4556	−	22.4556i	−0.926842	−	0.926842i	−0.997501	+	0.0706582i	$0.977490\pi$
$588$	6.14790	−	1.21570i	0.253535	−	0.0501345i
$589$	23.3282	−	23.3282i	0.961221	−	0.961221i
$590$	1.92969	+	0.586552i	0.0794442	+	0.0241480i
$591$	15.7468			0.647735
$592$	−1.40419	+	3.36854i	−0.0577118	+	0.138446i
$593$	−36.0626			−1.48091			−0.740456	−	0.672105i	$-0.765390\pi$
$593$	−36.0626			−1.48091			−0.740456	+	0.672105i	$0.765390\pi$
$594$	50.9688	+	15.4926i	2.09127	+	0.635667i
$595$	0.385637	−	0.385637i	0.0158096	−	0.0158096i
$596$	−0.954964	−	4.82934i	−0.0391168	−	0.197817i
$597$	3.99067	+	3.99067i	0.163327	+	0.163327i
$598$	7.02932	−	3.75216i	0.287450	−	0.153437i
$599$		−	10.7292i		−	0.438381i	−0.975682	−	0.219191i	$-0.929658\pi$
$599$		−	10.7292i		−	0.438381i	0.975682	−	0.219191i	$-0.0703417\pi$
$600$	−41.3674	−	4.14489i	−1.68882	−	0.169214i
$601$		−	36.0677i		−	1.47123i	−0.677399	−	0.735616i	$-0.736893\pi$
$601$		−	36.0677i		−	1.47123i	0.677399	−	0.735616i	$-0.263107\pi$
$602$	−0.910265	−	1.70529i	−0.0370996	−	0.0695026i
$603$	10.8594	+	10.8594i	0.442230	+	0.442230i
$604$	−23.1652	+	34.5848i	−0.942578	+	1.40724i
$605$	−0.428362	+	0.428362i	−0.0174154	+	0.0174154i
$606$	18.5260	−	60.9486i	0.752568	−	2.47587i
$607$	6.98617			0.283560			0.141780	−	0.989898i	$-0.454717\pi$
$607$	6.98617			0.283560			0.141780	+	0.989898i	$0.454717\pi$
$608$	26.8086	−	32.4795i	1.08723	−	1.31722i
$609$	14.0630			0.569861
$610$	−0.836836	+	2.75310i	−0.0338825	+	0.111470i
$611$	−31.5414	+	31.5414i	−1.27603	+	1.27603i
$612$	−7.44465	+	11.1146i	−0.300932	+	0.449281i
$613$	−23.3560	−	23.3560i	−0.943340	−	0.943340i	0.0551389	−	0.998479i	$-0.482440\pi$
$613$	−23.3560	−	23.3560i	−0.943340	−	0.943340i	−0.998479	+	0.0551389i	$0.982440\pi$
$614$	−1.64803	−	3.08742i	−0.0665089	−	0.124598i
$615$			2.11447i			0.0852635i
$616$	−0.887719	+	8.85973i	−0.0357672	+	0.356969i
$617$		−	41.5107i		−	1.67116i	−0.549370	−	0.835579i	$-0.685132\pi$
$617$		−	41.5107i		−	1.67116i	0.549370	−	0.835579i	$-0.314868\pi$
$618$	23.6717	−	12.6357i	0.952215	−	0.508281i
$619$	−19.3546	−	19.3546i	−0.777929	−	0.777929i	0.201550	−	0.979478i	$-0.435402\pi$
$619$	−19.3546	−	19.3546i	−0.777929	−	0.777929i	−0.979478	+	0.201550i	$0.935402\pi$
$620$	−0.955843	−	4.83379i	−0.0383876	−	0.194130i
$621$	10.6566	−	10.6566i	0.427636	−	0.427636i
$622$	−23.5827	−	7.16822i	−0.945579	−	0.287420i
$623$	10.2082			0.408982
$624$	−51.8491	+	21.3399i	−2.07563	+	0.854282i
$625$	−20.4591			−0.818365
$626$	−38.3505	−	11.6571i	−1.53280	−	0.465911i
$627$	−51.9291	+	51.9291i	−2.07385	+	2.07385i
$628$	28.1469	−	5.56582i	1.12318	−	0.222100i
$629$	0.632856	+	0.632856i	0.0252336	+	0.0252336i
$630$	4.72954	−	2.52457i	0.188429	−	0.100581i
$631$			2.56032i			0.101925i	0.998701	+	0.0509624i	$0.0162289\pi$
$631$			2.56032i			0.101925i	−0.998701	+	0.0509624i	$0.983771\pi$
$632$	25.9763	−	21.2449i	1.03328	−	0.845075i
$633$			66.9236i			2.65997i
$634$	7.76418	+	14.5454i	0.308355	+	0.577673i
$635$	7.62149	+	7.62149i	0.302450	+	0.302450i
$636$	59.4842	+	39.8430i	2.35870	+	1.57988i
$637$	3.16316	−	3.16316i	0.125329	−	0.125329i
$638$	−5.81087	+	19.1171i	−0.230055	+	0.756854i
$639$	−6.37293			−0.252109
$640$	−1.80216	−	6.02631i	−0.0712365	−	0.238211i
$641$	−0.654189			−0.0258389			−0.0129195	−	0.999917i	$-0.504113\pi$
$641$	−0.654189			−0.0258389			−0.0129195	+	0.999917i	$0.504113\pi$
$642$	−22.7772	+	74.9344i	−0.898943	+	2.95742i
$643$	3.21708	−	3.21708i	0.126869	−	0.126869i	−0.640821	−	0.767690i	$-0.721406\pi$
$643$	3.21708	−	3.21708i	0.126869	−	0.126869i	0.767690	+	0.640821i	$0.221406\pi$
$644$	2.09291	+	1.40185i	0.0824722	+	0.0552406i
$645$	−1.68376	−	1.68376i	−0.0662980	−	0.0662980i
$646$	−4.86347	−	9.11125i	−0.191351	−	0.358477i
$647$			39.4069i			1.54925i	0.632423	+	0.774623i	$0.282061\pi$
$647$			39.4069i			1.54925i	−0.632423	+	0.774623i	$0.717939\pi$
$648$	−37.3033	+	30.5087i	−1.46541	+	1.19850i
$649$			8.07535i			0.316985i
$650$	−26.1799	+	13.9745i	−1.02686	+	0.548126i
$651$	−9.81864	−	9.81864i	−0.384823	−	0.384823i
$652$	32.9861	−	6.52273i	1.29183	−	0.255450i
$653$	25.4270	−	25.4270i	0.995034	−	0.995034i	−0.00495338	−	0.999988i	$-0.501577\pi$
$653$	25.4270	−	25.4270i	0.995034	−	0.995034i	0.999988	+	0.00495338i	$0.00157672\pi$
$654$	60.3054	+	18.3305i	2.35813	+	0.716780i
$655$	−6.51978			−0.254749
$656$	4.48960	−	1.84782i	0.175290	−	0.0721453i
$657$	−4.84472			−0.189010
$658$	−13.4923	−	4.10113i	−0.525983	−	0.159879i
$659$	31.8006	−	31.8006i	1.23877	−	1.23877i	0.278272	−	0.960502i	$-0.410238\pi$
$659$	31.8006	−	31.8006i	1.23877	−	1.23877i	0.960502	−	0.278272i	$-0.0897616\pi$
$660$	2.12773	+	10.7601i	0.0828218	+	0.418837i
$661$	−5.45506	−	5.45506i	−0.212177	−	0.212177i	0.593015	−	0.805192i	$-0.297938\pi$
$661$	−5.45506	−	5.45506i	−0.212177	−	0.212177i	−0.805192	+	0.593015i	$0.797938\pi$
$662$	−0.415443	+	0.221758i	−0.0161467	+	0.00861889i
$663$			13.7502i			0.534014i
$664$	−2.70174	+	26.9643i	−0.104848	+	1.04642i
$665$			4.13906i			0.160506i
$666$	4.14299	+	7.76150i	0.160538	+	0.300752i
$667$	3.99704	+	3.99704i	0.154766	+	0.154766i
$668$	−1.23398	+	1.84228i	−0.0477440	+	0.0712800i
$669$	15.7593	−	15.7593i	0.609291	−	0.609291i
$670$	−0.515009	+	1.69432i	−0.0198965	+	0.0654575i
$671$	−11.5211			−0.444768
$672$	−13.6704	−	11.2835i	−0.527345	−	0.435271i
$673$	−28.3929			−1.09446			−0.547232	−	0.836981i	$-0.684319\pi$
$673$	−28.3929			−1.09446			−0.547232	+	0.836981i	$0.684319\pi$
$674$	−3.79247	+	12.4768i	−0.146080	+	0.480588i
$675$	−39.6895	+	39.6895i	−1.52765	+	1.52765i
$676$	−7.80357	+	11.6504i	−0.300137	+	0.448094i
$677$	7.58622	+	7.58622i	0.291562	+	0.291562i	0.837697	−	0.546135i	$-0.183901\pi$
$677$	7.58622	+	7.58622i	0.291562	+	0.291562i	−0.546135	+	0.837697i	$0.683901\pi$
$678$	10.4740	+	19.6220i	0.402251	+	0.753579i
$679$		−	3.03684i		−	0.116543i
$680$	−1.53486	−	0.153788i	−0.0588592	−	0.00589752i
$681$			53.9243i			2.06639i
$682$	17.4045	−	9.29029i	0.666452	−	0.355744i
$683$	−10.6493	−	10.6493i	−0.407485	−	0.407485i	0.473376	−	0.880861i	$-0.343035\pi$
$683$	−10.6493	−	10.6493i	−0.407485	−	0.407485i	−0.880861	+	0.473376i	$0.843035\pi$
$684$	−19.6949	−	99.5987i	−0.753052	−	3.80825i
$685$	4.07763	−	4.07763i	0.155798	−	0.155798i
$686$	1.35309	+	0.411286i	0.0516611	+	0.0157030i
$687$	−2.75404			−0.105073
$688$	−2.10367	+	5.04653i	−0.0802016	+	0.192397i
$689$	51.1050			1.94695
$690$	2.96892	+	0.902437i	0.113025	+	0.0343552i
$691$	1.31805	−	1.31805i	0.0501409	−	0.0501409i	−0.681592	−	0.731733i	$-0.738712\pi$
$691$	1.31805	−	1.31805i	0.0501409	−	0.0501409i	0.731733	+	0.681592i	$0.238712\pi$
$692$	20.0880	−	3.97225i	0.763631	−	0.151002i
$693$	15.1784	+	15.1784i	0.576582	+	0.576582i
$694$	14.1630	−	7.56003i	0.537620	−	0.286975i
$695$			3.79987i			0.144137i
$696$	−25.1818	−	30.7900i	−0.954512	−	1.16709i
$697$		−	1.19063i		−	0.0450983i
$698$	10.9135	+	20.4454i	0.413082	+	0.773870i
$699$	−10.7614	−	10.7614i	−0.407033	−	0.407033i
$700$	−7.79482	−	5.22103i	−0.294616	−	0.197337i
$701$	5.77893	−	5.77893i	0.218267	−	0.218267i	−0.589501	−	0.807768i	$-0.700675\pi$
$701$	5.77893	−	5.77893i	0.218267	−	0.218267i	0.807768	+	0.589501i	$0.200675\pi$
$702$	−22.0148	+	72.4263i	−0.830895	+	2.73355i
$703$	−6.79247			−0.256183
$704$	20.9874	−	13.9210i	0.790991	−	0.524667i
$705$	−17.3712			−0.654239
$706$	−7.79308	+	25.6384i	−0.293296	+	0.964913i
$707$	10.1648	−	10.1648i	0.382285	−	0.382285i
$708$	−13.3565	−	8.94626i	−0.501966	−	0.336221i
$709$	−27.5392	−	27.5392i	−1.03426	−	1.03426i	−0.999392	−	0.0348642i	$-0.988900\pi$
$709$	−27.5392	−	27.5392i	−1.03426	−	1.03426i	−0.0348642	−	0.999392i	$-0.511100\pi$
$710$	−0.346044	−	0.648281i	−0.0129868	−	0.0243295i
$711$		−	80.8990i		−	3.03395i
$712$	−18.2792	−	22.3501i	−0.685040	−	0.837605i
$713$		−	5.58138i		−	0.209024i
$714$	−3.83485	+	2.04699i	−0.143516	+	0.0766068i
$715$	5.53621	+	5.53621i	0.207043	+	0.207043i
$716$	−27.5794	+	5.45361i	−1.03069	+	0.203811i
$717$	10.8798	−	10.8798i	0.406314	−	0.406314i
$718$	4.79225	+	1.45666i	0.178845	+	0.0543621i
$719$	−3.79808			−0.141645			−0.0708223	−	0.997489i	$-0.522562\pi$
$719$	−3.79808			−0.141645			−0.0708223	+	0.997489i	$0.522562\pi$
$720$	−13.9963	−	5.83441i	−0.521610	−	0.217436i
$721$	6.05520			0.225507
$722$	49.2870	+	14.9814i	1.83427	+	0.557548i
$723$	24.0605	−	24.0605i	0.894821	−	0.894821i
$724$	−4.03464	−	20.4035i	−0.149946	−	0.758292i
$725$	−14.8865	−	14.8865i	−0.552872	−	0.552872i
$726$	4.25972	−	2.27378i	0.158093	−	0.0843881i
$727$			25.5053i			0.945937i	0.881079	+	0.472969i	$0.156818\pi$
$727$			25.5053i			0.945937i	−0.881079	+	0.472969i	$0.843182\pi$
$728$	−12.5896	−	1.26144i	−0.466602	−	0.0467521i
$729$			3.69376i			0.136806i
$730$	−0.263064	−	0.492825i	−0.00973643	−	0.0182403i
$731$	0.948104	+	0.948104i	0.0350669	+	0.0350669i
$732$	12.7637	−	19.0557i	0.471759	−	0.704319i
$733$	−29.0147	+	29.0147i	−1.07168	+	1.07168i	−0.0744582	+	0.997224i	$0.523723\pi$
$733$	−29.0147	+	29.0147i	−1.07168	+	1.07168i	−0.997224	+	0.0744582i	$0.976277\pi$
$734$	−4.60123	+	15.1376i	−0.169835	+	0.558737i
$735$	1.74209			0.0642581
$736$	−0.678397	−	7.09249i	−0.0250060	−	0.261433i
$737$	−7.09038			−0.261178
$738$	3.40385	−	11.1983i	0.125298	−	0.412215i
$739$	1.66971	−	1.66971i	0.0614213	−	0.0614213i	−0.675729	−	0.737150i	$-0.736171\pi$
$739$	1.66971	−	1.66971i	0.0614213	−	0.0614213i	0.737150	+	0.675729i	$0.236171\pi$
$740$	−0.564571	+	0.842884i	−0.0207540	+	0.0309850i
$741$	−73.7909	−	73.7909i	−2.71077	−	2.71077i
$742$	7.60800	+	14.2529i	0.279298	+	0.523239i
$743$		−	24.1373i		−	0.885513i	−0.896642	−	0.442756i	$-0.854001\pi$
$743$		−	24.1373i		−	0.885513i	0.896642	−	0.442756i	$-0.145999\pi$
$744$	−3.91558	+	39.0789i	−0.143552	+	1.43270i
$745$		−	1.36846i		−	0.0501366i
$746$	−24.3610	+	13.0036i	−0.891918	+	0.476095i
$747$	46.1951	+	46.1951i	1.69019	+	1.69019i
$748$	−1.19810	−	6.05889i	−0.0438068	−	0.221535i
$749$	−12.4973	+	12.4973i	−0.456640	+	0.456640i
$750$	−22.8434	−	6.94353i	−0.834125	−	0.253542i
$751$	17.6703			0.644797			0.322398	−	0.946604i	$-0.395511\pi$
$751$	17.6703			0.644797			0.322398	+	0.946604i	$0.395511\pi$
$752$	15.1807	+	36.8840i	0.553581	+	1.34502i
$753$	36.2717			1.32181
$754$	−27.1653	−	8.25721i	−0.989302	−	0.300710i
$755$	−8.18214	+	8.18214i	−0.297779	+	0.297779i
$756$	−23.4766	+	4.64231i	−0.853835	+	0.168839i
$757$	−14.3436	−	14.3436i	−0.521327	−	0.521327i	0.396645	−	0.917972i	$-0.370174\pi$
$757$	−14.3436	−	14.3436i	−0.521327	−	0.521327i	−0.917972	+	0.396645i	$0.870174\pi$
$758$	19.3861	−	10.3480i	0.704134	−	0.375858i
$759$			12.4243i			0.450973i
$760$	9.06218	−	7.41156i	0.328720	−	0.268845i
$761$		−	13.4406i		−	0.487220i	−0.969873	−	0.243610i	$-0.921668\pi$
$761$		−	13.4406i		−	0.487220i	0.969873	−	0.243610i	$-0.0783317\pi$
$762$	−40.4556	−	75.7897i	−1.46555	−	2.74557i
$763$	10.0575	+	10.0575i	0.364106	+	0.364106i
$764$	−5.89373	−	3.94767i	−0.213228	−	0.142822i
$765$	−2.62952	+	2.62952i	−0.0950703	+	0.0950703i
$766$	1.99040	−	6.54820i	0.0719161	−	0.236596i
$767$	−11.4750			−0.414338
$768$	−0.225797	+	50.1350i	−0.00814776	+	1.80909i
$769$	−42.7134			−1.54029			−0.770143	−	0.637871i	$-0.779815\pi$
$769$	−42.7134			−1.54029			−0.770143	+	0.637871i	$0.779815\pi$
$770$	−0.719839	+	2.36819i	−0.0259412	+	0.0853437i
$771$	45.6722	−	45.6722i	1.64484	−	1.64484i
$772$	−4.97500	−	3.33229i	−0.179054	−	0.119932i
$773$	17.6239	+	17.6239i	0.633886	+	0.633886i	0.949040	−	0.315154i	$-0.102056\pi$
$773$	17.6239	+	17.6239i	0.633886	+	0.633886i	−0.315154	+	0.949040i	$0.602056\pi$
$774$	6.20676	+	11.6278i	0.223097	+	0.417952i
$775$			20.7873i			0.746700i
$776$	−6.64895	+	5.43789i	−0.238683	+	0.195209i
$777$			2.85889i			0.102562i
$778$	−22.0206	+	11.7543i	−0.789475	+	0.421412i
$779$	6.38953	+	6.38953i	0.228929	+	0.228929i
$780$	−15.2901	+	3.02349i	−0.547472	+	0.108258i
$781$	2.08052	−	2.08052i	0.0744468	−	0.0744468i
$782$	−1.67176	−	0.508151i	−0.0597820	−	0.0181714i
$783$	−53.7014			−1.91913
$784$	−1.52241	−	3.69896i	−0.0543717	−	0.132106i
$785$	7.97582			0.284669
$786$	49.7208	+	15.1132i	1.77348	+	0.539070i
$787$	27.4590	−	27.4590i	0.978807	−	0.978807i	−0.0209726	−	0.999780i	$-0.506676\pi$
$787$	27.4590	−	27.4590i	0.978807	−	0.978807i	0.999780	+	0.0209726i	$0.00667627\pi$
$788$	−1.94969	−	9.85976i	−0.0694548	−	0.351239i
$789$	30.1993	+	30.1993i	1.07512	+	1.07512i
$790$	8.22938	−	4.39274i	0.292788	−	0.156287i
$791$			5.01929i			0.178466i
$792$	6.05303	−	60.4113i	0.215085	−	2.14662i
$793$		−	16.3714i		−	0.581367i
$794$	−11.0702	−	20.7389i	−0.392866	−	0.735997i
$795$	14.0729	+	14.0729i	0.499114	+	0.499114i
$796$	2.00464	−	2.99285i	0.0710524	−	0.106079i
$797$	37.2933	−	37.2933i	1.32100	−	1.32100i	0.408024	−	0.912971i	$-0.366218\pi$
$797$	37.2933	−	37.2933i	1.32100	−	1.32100i	0.912971	−	0.408024i	$-0.133782\pi$
$798$	9.59456	−	31.5650i	0.339644	−	1.11739i
$799$	9.78152			0.346045
$800$	2.52662	+	26.4152i	0.0893293	+	0.933919i
$801$	−69.6058			−2.45940
$802$	10.5217	−	34.6151i	0.371533	−	1.22230i
$803$	1.58162	−	1.58162i	0.0558140	−	0.0558140i
$804$	7.85507	−	11.7273i	0.277027	−	0.413592i
$805$	0.495145	+	0.495145i	0.0174516	+	0.0174516i
$806$	13.2014	+	24.7316i	0.465001	+	0.871134i
$807$		−	19.6310i		−	0.691045i
$808$	−40.4565	−	4.05362i	−1.42325	−	0.142606i
$809$			44.3124i			1.55794i	0.627061	+	0.778970i	$0.284258\pi$
$809$			44.3124i			1.55794i	−0.627061	+	0.778970i	$0.715742\pi$
$810$	−11.8178	+	6.30820i	−0.415236	+	0.221648i
$811$	9.44442	+	9.44442i	0.331639	+	0.331639i	0.853209	−	0.521570i	$-0.174653\pi$
$811$	9.44442	+	9.44442i	0.331639	+	0.331639i	−0.521570	+	0.853209i	$0.674653\pi$
$812$	−1.74121	−	8.80548i	−0.0611047	−	0.309012i
$813$	28.1063	−	28.1063i	0.985731	−	0.985731i
$814$	−3.88636	−	1.18130i	−0.136217	−	0.0414047i
$815$	9.34707			0.327414
$816$	11.3486	+	4.73071i	0.397280	+	0.165608i
$817$	−10.1760			−0.356015
$818$	25.9963	+	7.90187i	0.908939	+	0.276283i
$819$	−21.5685	+	21.5685i	−0.753663	+	0.753663i
$820$	1.32396	−	0.261803i	0.0462348	−	0.00914257i
$821$	35.3404	+	35.3404i	1.23339	+	1.23339i	0.962654	+	0.270734i	$0.0872663\pi$
$821$	35.3404	+	35.3404i	1.23339	+	1.23339i	0.270734	+	0.962654i	$0.412734\pi$
$822$	−40.5487	+	21.6444i	−1.41430	+	0.754936i
$823$			23.7136i			0.826605i	0.910594	+	0.413302i	$0.135625\pi$
$823$			23.7136i			0.826605i	−0.910594	+	0.413302i	$0.864375\pi$
$824$	−10.8427	−	13.2574i	−0.377723	−	0.461845i
$825$		−	46.2729i		−	1.61102i
$826$	−1.70828	−	3.20031i	−0.0594388	−	0.111353i
$827$	34.8453	+	34.8453i	1.21169	+	1.21169i	0.970471	+	0.241218i	$0.0775470\pi$
$827$	34.8453	+	34.8453i	1.21169	+	1.21169i	0.241218	+	0.970471i	$0.422453\pi$
$828$	−14.2708	−	9.55869i	−0.495944	−	0.332188i
$829$	11.9866	−	11.9866i	0.416313	−	0.416313i	−0.467618	−	0.883931i	$-0.654888\pi$
$829$	11.9866	−	11.9866i	0.416313	−	0.416313i	0.883931	+	0.467618i	$0.154888\pi$
$830$	−2.19080	+	7.20750i	−0.0760439	+	0.250176i
$831$	75.7069			2.62624
$832$	19.7816	+	29.8229i	0.685805	+	1.03392i
$833$	−0.980951			−0.0339879
$834$	8.80831	−	28.9784i	0.305007	−	1.00344i
$835$	−0.435851	+	0.435851i	−0.0150832	+	0.0150832i
$836$	38.9448	+	26.0856i	1.34693	+	0.902188i
$837$	37.4938	+	37.4938i	1.29598	+	1.29598i
$838$	10.6201	+	19.8958i	0.366866	+	0.687288i
$839$			1.32175i			0.0456320i	0.999740	+	0.0228160i	$0.00726318\pi$
$839$			1.32175i			0.0456320i	−0.999740	+	0.0228160i	$0.992737\pi$
$840$	−3.11946	−	3.81420i	−0.107632	−	0.131602i
$841$			8.85792i			0.305445i
$842$	−47.8204	+	25.5259i	−1.64800	+	0.879682i
$843$	28.5001	+	28.5001i	0.981594	+	0.981594i
$844$	41.9039	−	8.28617i	1.44239	−	0.285222i
$845$	−2.75629	+	2.75629i	−0.0948191	+	0.0948191i
$846$	91.9989	+	27.9641i	3.16299	+	0.961426i
$847$	1.08963			0.0374402
$848$	17.5825	−	42.1789i	0.603784	−	1.44843i
$849$	−3.89560			−0.133697
$850$	6.22629	+	1.89255i	0.213560	+	0.0649140i
$851$	−0.812566	+	0.812566i	−0.0278544	+	0.0278544i
$852$	1.13623	+	5.74603i	0.0389267	+	0.196856i
$853$	33.7981	+	33.7981i	1.15722	+	1.15722i	0.985070	+	0.172153i	$0.0550725\pi$
$853$	33.7981	+	33.7981i	1.15722	+	1.15722i	0.172153	+	0.985070i	$0.444928\pi$
$854$	4.56589	−	2.43721i	0.156242	−	0.0833998i
$855$		−	28.2227i		−	0.965196i
$856$	49.7400	+	4.98380i	1.70008	+	0.170343i
$857$			12.2024i			0.416826i	0.978041	+	0.208413i	$0.0668297\pi$
$857$			12.2024i			0.416826i	−0.978041	+	0.208413i	$0.933170\pi$
$858$	−29.3867	−	55.0532i	−1.00325	−	1.87949i
$859$	−9.62063	−	9.62063i	−0.328252	−	0.328252i	0.523670	−	0.851921i	$-0.324563\pi$
$859$	−9.62063	−	9.62063i	−0.328252	−	0.328252i	−0.851921	+	0.523670i	$0.824563\pi$
$860$	−0.845804	+	1.26276i	−0.0288417	+	0.0430596i
$861$	2.68930	−	2.68930i	0.0916512	−	0.0916512i
$862$	6.07134	−	19.9740i	0.206791	−	0.680319i
$863$	−48.5092			−1.65127			−0.825636	−	0.564204i	$-0.809183\pi$
$863$	−48.5092			−1.65127			−0.825636	+	0.564204i	$0.809183\pi$
$864$	52.2021	+	43.0876i	1.77595	+	1.46587i
$865$	5.69222			0.193541
$866$	12.3409	−	40.6003i	0.419362	−	1.37966i
$867$	−35.5348	+	35.5348i	−1.20682	+	1.20682i
$868$	−4.93220	+	7.36359i	−0.167410	+	0.249937i
$869$	26.4104	+	26.4104i	0.895913	+	0.895913i
$870$	−5.20676	−	9.75437i	−0.176526	−	0.330704i
$871$		−	10.0754i		−	0.341391i
$872$	4.01084	−	40.0295i	0.135824	−	1.35557i
$873$			20.7071i			0.700829i
$874$	11.6985	−	6.24454i	0.395709	−	0.211225i
$875$	−3.80974	−	3.80974i	−0.128793	−	0.128793i
$876$	0.863767	+	4.36815i	0.0291840	+	0.147586i
$877$	−15.6211	+	15.6211i	−0.527487	+	0.527487i	−0.919822	−	0.392336i	$-0.871667\pi$
$877$	−15.6211	+	15.6211i	−0.527487	+	0.527487i	0.392336	+	0.919822i	$0.371667\pi$
$878$	−45.6697	−	13.8818i	−1.54128	−	0.468489i
$879$	−79.7365			−2.68944
$880$	6.47396	−	2.66454i	0.218237	−	0.0898216i
$881$	22.7269			0.765688			0.382844	−	0.923813i	$-0.374945\pi$
$881$	22.7269			0.765688			0.382844	+	0.923813i	$0.374945\pi$
$882$	−9.22621	−	2.80441i	−0.310662	−	0.0944295i
$883$	−30.2833	+	30.2833i	−1.01912	+	1.01912i	−0.0193019	+	0.999814i	$0.506144\pi$
$883$	−30.2833	+	30.2833i	−1.01912	+	1.01912i	−0.999814	+	0.0193019i	$0.993856\pi$
$884$	8.60964	−	1.70249i	0.289573	−	0.0572609i
$885$	−3.15990	−	3.15990i	−0.106219	−	0.106219i
$886$	−9.21038	+	4.91639i	−0.309429	+	0.165169i
$887$		−	38.7161i		−	1.29996i	−0.759951	−	0.649980i	$-0.774777\pi$
$887$		−	38.7161i		−	1.29996i	0.759951	−	0.649980i	$-0.225223\pi$
$888$	6.25935	−	5.11925i	0.210050	−	0.171791i
$889$		−	19.3869i		−	0.650217i
$890$	−3.77953	−	7.08059i	−0.126690	−	0.237342i
$891$	−37.9267	−	37.9267i	−1.27059	−	1.27059i
$892$	−11.8189	−	7.91639i	−0.395725	−	0.265060i
$893$	−52.4928	+	52.4928i	−1.75660	+	1.75660i
$894$	−3.17217	+	10.4361i	−0.106093	+	0.349035i
$895$	−7.81501			−0.261227
$896$	−5.37252	+	9.95671i	−0.179483	+	0.332630i
$897$	−17.6548			−0.589478
$898$	0.653969	−	2.15149i	0.0218232	−	0.0717960i
$899$	−14.0630	+	14.0630i	−0.469027	+	0.469027i
$900$	53.1500	+	35.6003i	1.77167	+	1.18668i
$901$	−7.92426	−	7.92426i	−0.263995	−	0.263995i
$902$	2.54459	+	4.76705i	0.0847256	+	0.158725i
$903$			4.28301i			0.142530i
$904$	10.9894	−	8.98775i	0.365502	−	0.298928i
$905$		−	5.78163i		−	0.192188i
$906$	81.3649	−	43.4315i	2.70317	−	1.44292i
$907$	−25.4724	−	25.4724i	−0.845799	−	0.845799i	0.143807	−	0.989606i	$-0.454065\pi$
$907$	−25.4724	−	25.4724i	−0.845799	−	0.845799i	−0.989606	+	0.143807i	$0.954065\pi$
$908$	33.7645	−	6.67666i	1.12051	−	0.221573i
$909$	−69.3098	+	69.3098i	−2.29886	+	2.29886i
$910$	−3.36518	−	1.02289i	−0.111555	−	0.0339083i
$911$	−52.6922			−1.74577			−0.872886	−	0.487924i	$-0.837754\pi$
$911$	−52.6922			−1.74577			−0.872886	+	0.487924i	$0.837754\pi$
$912$	−86.2899	+	35.5150i	−2.85734	+	1.17602i
$913$	−30.1618			−0.998212
$914$	2.90802	+	0.883926i	0.0961887	+	0.0292377i
$915$	4.50824	−	4.50824i	0.149038	−	0.149038i
$916$	0.340992	+	1.72443i	0.0112667	+	0.0569768i
$917$	8.29224	+	8.29224i	0.273834	+	0.273834i
$918$	14.6439	−	7.81672i	0.483320	−	0.257990i
$919$		−	25.5116i		−	0.841549i	−0.907165	−	0.420775i	$-0.861758\pi$
$919$		−	25.5116i		−	0.841549i	0.907165	−	0.420775i	$-0.138242\pi$
$920$	0.197459	−	1.97071i	0.00651004	−	0.0649724i
$921$			7.75436i			0.255515i
$922$	−25.1843	−	47.1804i	−0.829401	−	1.55380i
$923$	2.95640	+	2.95640i	0.0973111	+	0.0973111i
$924$	10.9792	−	16.3915i	0.361189	−	0.539242i
$925$	3.02632	−	3.02632i	0.0995046	−	0.0995046i
$926$	−6.69105	+	22.0128i	−0.219881	+	0.723386i
$927$	−41.2882			−1.35608
$928$	−16.1611	+	19.5797i	−0.530514	+	0.642736i
$929$	49.1998			1.61419			0.807097	−	0.590419i	$-0.201038\pi$
$929$	49.1998			1.61419			0.807097	+	0.590419i	$0.201038\pi$
$930$	−3.17509	+	10.4457i	−0.104115	+	0.342528i
$931$	5.26429	−	5.26429i	0.172530	−	0.172530i
$932$	−5.40577	+	8.07062i	−0.177072	+	0.264362i
$933$	38.6169	+	38.6169i	1.26426	+	1.26426i
$934$	16.8851	+	31.6325i	0.552496	+	1.03505i
$935$		−	1.71687i		−	0.0561477i
$936$	85.8440	+	8.60131i	2.80590	+	0.281143i
$937$		−	44.3522i		−	1.44892i	−0.689315	−	0.724462i	$-0.742088\pi$
$937$		−	44.3522i		−	1.44892i	0.689315	−	0.724462i	$-0.257912\pi$
$938$	2.80996	−	1.49992i	0.0917485	−	0.0489742i
$939$	62.7995	+	62.7995i	2.04939	+	2.04939i
$940$	2.15083	+	10.8769i	0.0701523	+	0.354766i
$941$	14.0676	−	14.0676i	0.458591	−	0.458591i	−0.439602	−	0.898193i	$-0.644880\pi$
$941$	14.0676	−	14.0676i	0.458591	−	0.458591i	0.898193	+	0.439602i	$0.144880\pi$
$942$	−60.8248	−	18.4884i	−1.98178	−	0.602384i
$943$	1.52873			0.0497822
$944$	−3.94793	+	9.47077i	−0.128494	+	0.308247i
$945$	−6.65242			−0.216403
$946$	−5.82230	−	1.76975i	−0.189299	−	0.0575397i
$947$	−22.2829	+	22.2829i	−0.724098	+	0.724098i	−0.969437	−	0.245340i	$-0.921101\pi$
$947$	−22.2829	+	22.2829i	−0.724098	+	0.724098i	0.245340	+	0.969437i	$0.421101\pi$
$948$	−72.9411	+	14.4235i	−2.36902	+	0.468454i
$949$	2.24746	+	2.24746i	0.0729558	+	0.0729558i
$950$	−43.5700	+	23.2571i	−1.41360	+	0.754560i
$951$		−	36.5323i		−	1.18464i
$952$	1.75653	+	2.14772i	0.0569294	+	0.0696081i
$953$			52.5006i			1.70066i	0.526250	+	0.850330i	$0.323598\pi$
$953$			52.5006i			1.70066i	−0.526250	+	0.850330i	$0.676402\pi$
$954$	−51.8762	−	97.1851i	−1.67955	−	3.14648i
$955$	−1.39435	−	1.39435i	−0.0451202	−	0.0451202i
$956$	−8.15943	−	5.46526i	−0.263895	−	0.176759i
$957$	31.3046	−	31.3046i	1.01193	−	1.01193i
$958$	6.98613	−	22.9836i	0.225712	−	0.742566i
$959$	−10.3723			−0.334940
$960$	−2.76508	+	13.6597i	−0.0892426	+	0.440865i
$961$	−11.3627			−0.366540
$962$	1.67862	−	5.52249i	0.0541210	−	0.178052i
$963$	85.2143	−	85.2143i	2.74599	−	2.74599i
$964$	−18.0445	−	12.0863i	−0.581173	−	0.389275i
$965$	−1.17699	−	1.17699i	−0.0378888	−	0.0378888i
$966$	−2.62827	−	4.92382i	−0.0845633	−	0.158421i
$967$			22.7183i			0.730572i	0.930895	+	0.365286i	$0.119029\pi$
$967$			22.7183i			0.730572i	−0.930895	+	0.365286i	$0.880971\pi$
$968$	−1.95114	−	2.38567i	−0.0627120	−	0.0766785i
$969$			22.8838i			0.735133i
$970$	−2.10641	+	1.12438i	−0.0676328	+	0.0361016i
$971$	−8.51367	−	8.51367i	−0.273217	−	0.273217i	0.557177	−	0.830394i	$-0.311884\pi$
$971$	−8.51367	−	8.51367i	−0.273217	−	0.273217i	−0.830394	+	0.557177i	$0.811884\pi$
$972$	34.3174	−	6.78600i	1.10073	−	0.217661i
$973$	4.83290	−	4.83290i	0.154936	−	0.154936i
$974$	−52.8166	−	16.0542i	−1.69235	−	0.514411i
$975$	65.7535			2.10580
$976$	−13.5120	−	5.63253i	−0.432508	−	0.180293i
$977$	−37.7274			−1.20701			−0.603503	−	0.797361i	$-0.706229\pi$
$977$	−37.7274			−1.20701			−0.603503	+	0.797361i	$0.706229\pi$
$978$	−71.2821	−	21.6670i	−2.27935	−	0.692835i
$979$	22.7236	−	22.7236i	0.726250	−	0.726250i
$980$	−0.215698	−	1.09080i	−0.00689022	−	0.0348445i
$981$	−68.5784	−	68.5784i	−2.18954	−	2.18954i
$982$	47.4313	−	25.3183i	1.51359	−	0.807938i
$983$			45.1569i			1.44028i	0.693828	+	0.720141i	$0.255923\pi$
$983$			45.1569i			1.44028i	−0.693828	+	0.720141i	$0.744077\pi$
$984$	−10.7036	−	1.07247i	−0.341219	−	0.0341891i
$985$		−	2.79390i		−	0.0890212i
$986$	2.93186	+	5.49256i	0.0933694	+	0.174919i
$987$	22.0938	+	22.0938i	0.703253	+	0.703253i
$988$	−37.0674	+	55.3403i	−1.17927	+	1.76061i
$989$	−1.21733	+	1.21733i	−0.0387090	+	0.0387090i
$990$	4.90832	−	16.1478i	0.155997	−	0.513212i
$991$	−46.2280			−1.46848			−0.734240	−	0.678890i	$-0.762462\pi$
$991$	−46.2280			−1.46848			−0.734240	+	0.678890i	$0.762462\pi$
$992$	24.9539	−	2.38684i	0.792286	−	0.0757822i
$993$	1.04343			0.0331121
$994$	−0.384402	+	1.26464i	−0.0121925	+	0.0401120i
$995$	0.708054	−	0.708054i	0.0224468	−	0.0224468i
$996$	33.4148	−	49.8871i	1.05879	−	1.58073i
$997$	−27.2458	−	27.2458i	−0.862885	−	0.862885i	0.128788	−	0.991672i	$-0.458891\pi$
$997$	−27.2458	−	27.2458i	−0.862885	−	0.862885i	−0.991672	+	0.128788i	$0.958891\pi$
$998$	4.26606	+	7.99206i	0.135040	+	0.252984i
$999$		−	10.9171i		−	0.345401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.2.m.d.85.2	yes	12
4.3	odd	2		448.2.m.d.113.1		12
7.2	even	3		784.2.x.l.165.6		24
7.3	odd	6		784.2.x.m.373.3		24
7.4	even	3		784.2.x.l.373.3		24
7.5	odd	6		784.2.x.m.165.6		24
7.6	odd	2		784.2.m.h.197.2		12
8.3	odd	2		896.2.m.h.225.6		12
8.5	even	2		896.2.m.g.225.1		12
16.3	odd	4		448.2.m.d.337.1		12
16.5	even	4		896.2.m.g.673.1		12
16.11	odd	4		896.2.m.h.673.6		12
16.13	even	4	inner	112.2.m.d.29.2	✓	12
32.3	odd	8		7168.2.a.bi.1.1		12
32.13	even	8		7168.2.a.bj.1.1		12
32.19	odd	8		7168.2.a.bi.1.12		12
32.29	even	8		7168.2.a.bj.1.12		12
112.13	odd	4		784.2.m.h.589.2		12
112.45	odd	12		784.2.x.m.765.6		24
112.61	odd	12		784.2.x.m.557.3		24
112.93	even	12		784.2.x.l.557.3		24
112.109	even	12		784.2.x.l.765.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.d.29.2	✓	12	16.13	even	4	inner
112.2.m.d.85.2	yes	12	1.1	even	1	trivial
448.2.m.d.113.1		12	4.3	odd	2
448.2.m.d.337.1		12	16.3	odd	4
784.2.m.h.197.2		12	7.6	odd	2
784.2.m.h.589.2		12	112.13	odd	4
784.2.x.l.165.6		24	7.2	even	3
784.2.x.l.373.3		24	7.4	even	3
784.2.x.l.557.3		24	112.93	even	12
784.2.x.l.765.6		24	112.109	even	12
784.2.x.m.165.6		24	7.5	odd	6
784.2.x.m.373.3		24	7.3	odd	6
784.2.x.m.557.3		24	112.61	odd	12
784.2.x.m.765.6		24	112.45	odd	12
896.2.m.g.225.1		12	8.5	even	2
896.2.m.g.673.1		12	16.5	even	4
896.2.m.h.225.6		12	8.3	odd	2
896.2.m.h.673.6		12	16.11	odd	4
7168.2.a.bi.1.1		12	32.3	odd	8
7168.2.a.bi.1.12		12	32.19	odd	8
7168.2.a.bj.1.1		12	32.13	even	8
7168.2.a.bj.1.12		12	32.29	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	112.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.411286 + 1.35309i) q^{2} +(2.21570 - 2.21570i) q^{3} +(-1.66169 - 1.11301i) q^{4} +(-0.393125 - 0.393125i) q^{5} +(2.08675 + 3.90932i) q^{6} +1.00000i q^{7} +(2.18943 - 1.79064i) q^{8} -6.81864i q^{9} +O(q^{10})\)	\(q+(-0.411286 + 1.35309i) q^{2} +(2.21570 - 2.21570i) q^{3} +(-1.66169 - 1.11301i) q^{4} +(-0.393125 - 0.393125i) q^{5} +(2.08675 + 3.90932i) q^{6} +1.00000i q^{7} +(2.18943 - 1.79064i) q^{8} -6.81864i q^{9} +(0.693620 - 0.370246i) q^{10} +(2.22602 + 2.22602i) q^{11} +(-6.14790 + 1.21570i) q^{12} +(-3.16316 + 3.16316i) q^{13} +(-1.35309 - 0.411286i) q^{14} -1.74209 q^{15} +(1.52241 + 3.69896i) q^{16} +0.980951 q^{17} +(9.22621 + 2.80441i) q^{18} +(-5.26429 + 5.26429i) q^{19} +(0.215698 + 1.09080i) q^{20} +(2.21570 + 2.21570i) q^{21} +(-3.92754 + 2.09647i) q^{22} +1.25951i q^{23} +(0.883601 - 8.81864i) q^{24} -4.69090i q^{25} +(-2.97907 - 5.58100i) q^{26} +(-8.46094 - 8.46094i) q^{27} +(1.11301 - 1.66169i) q^{28} +(3.17349 - 3.17349i) q^{29} +(0.716500 - 2.35720i) q^{30} -4.43140 q^{31} +(-5.63115 + 0.538620i) q^{32} +9.86440 q^{33} +(-0.403452 + 1.32731i) q^{34} +(0.393125 - 0.393125i) q^{35} +(-7.58922 + 11.3304i) q^{36} +(0.645145 + 0.645145i) q^{37} +(-4.95791 - 9.28818i) q^{38} +14.0172i q^{39} +(-1.56467 - 0.156775i) q^{40} -1.21375i q^{41} +(-3.90932 + 2.08675i) q^{42} +(0.966515 + 0.966515i) q^{43} +(-1.22136 - 6.17655i) q^{44} +(-2.68058 + 2.68058i) q^{45} +(-1.70422 - 0.518019i) q^{46} +9.97147 q^{47} +(11.5690 + 4.82257i) q^{48} -1.00000 q^{49} +(6.34720 + 1.92931i) q^{50} +(2.17349 - 2.17349i) q^{51} +(8.77683 - 1.73555i) q^{52} +(-8.07814 - 8.07814i) q^{53} +(14.9283 - 7.96852i) q^{54} -1.75021i q^{55} +(1.79064 + 2.18943i) q^{56} +23.3282i q^{57} +(2.98879 + 5.59922i) q^{58} +(1.81385 + 1.81385i) q^{59} +(2.89482 + 1.93897i) q^{60} +(-2.58783 + 2.58783i) q^{61} +(1.82257 - 5.99606i) q^{62} +6.81864 q^{63} +(1.58722 - 7.84097i) q^{64} +2.48704 q^{65} +(-4.05709 + 13.3474i) q^{66} +(-1.59261 + 1.59261i) q^{67} +(-1.63003 - 1.09181i) q^{68} +(2.79069 + 2.79069i) q^{69} +(0.370246 + 0.693620i) q^{70} -0.934634i q^{71} +(-12.2097 - 14.9289i) q^{72} -0.710511i q^{73} +(-1.13828 + 0.607598i) q^{74} +(-10.3936 - 10.3936i) q^{75} +(14.6068 - 2.88839i) q^{76} +(-2.22602 + 2.22602i) q^{77} +(-18.9665 - 5.76510i) q^{78} +11.8644 q^{79} +(0.855656 - 2.05265i) q^{80} -17.0379 q^{81} +(1.64231 + 0.499198i) q^{82} +(-6.77482 + 6.77482i) q^{83} +(-1.21570 - 6.14790i) q^{84} +(-0.385637 - 0.385637i) q^{85} +(-1.70529 + 0.910265i) q^{86} -14.0630i q^{87} +(8.85973 + 0.887719i) q^{88} -10.2082i q^{89} +(-2.52457 - 4.72954i) q^{90} +(-3.16316 - 3.16316i) q^{91} +(1.40185 - 2.09291i) q^{92} +(-9.81864 + 9.81864i) q^{93} +(-4.10113 + 13.4923i) q^{94} +4.13906 q^{95} +(-11.2835 + 13.6704i) q^{96} -3.03684 q^{97} +(0.411286 - 1.35309i) q^{98} +(15.1784 - 15.1784i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 4 q^{3} - 6 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{8}+O(q^{10}) \) 12 * q + 2 * q^2 + 4 * q^3 - 6 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^8	\( 12 q + 2 q^{2} + 4 q^{3} - 6 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{8} - 4 q^{10} + 8 q^{12} - 24 q^{15} + 10 q^{16} - 8 q^{17} - 20 q^{20} + 4 q^{21} + 14 q^{22} - 8 q^{24} - 20 q^{26} + 4 q^{27} - 4 q^{29} - 28 q^{30} - 8 q^{31} + 12 q^{32} + 8 q^{34} - 4 q^{35} - 16 q^{36} - 20 q^{37} + 16 q^{38} - 8 q^{40} - 12 q^{42} + 16 q^{43} + 14 q^{44} + 40 q^{45} - 28 q^{46} + 16 q^{47} + 16 q^{48} - 12 q^{49} + 44 q^{50} - 16 q^{51} - 16 q^{52} + 4 q^{53} + 64 q^{54} + 6 q^{56} + 14 q^{58} - 16 q^{59} + 60 q^{60} - 20 q^{61} + 8 q^{62} + 12 q^{63} - 18 q^{64} + 32 q^{65} + 12 q^{66} + 24 q^{67} - 28 q^{68} - 4 q^{69} + 20 q^{70} + 6 q^{72} - 38 q^{74} - 40 q^{75} + 48 q^{76} - 76 q^{78} + 24 q^{79} + 24 q^{80} - 44 q^{81} - 16 q^{82} - 20 q^{83} + 8 q^{84} - 8 q^{85} + 38 q^{86} - 14 q^{88} - 40 q^{90} + 32 q^{92} - 48 q^{93} - 24 q^{94} - 16 q^{96} + 48 q^{97} - 2 q^{98} + 32 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 4 * q^3 - 6 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^8 - 4 * q^10 + 8 * q^12 - 24 * q^15 + 10 * q^16 - 8 * q^17 - 20 * q^20 + 4 * q^21 + 14 * q^22 - 8 * q^24 - 20 * q^26 + 4 * q^27 - 4 * q^29 - 28 * q^30 - 8 * q^31 + 12 * q^32 + 8 * q^34 - 4 * q^35 - 16 * q^36 - 20 * q^37 + 16 * q^38 - 8 * q^40 - 12 * q^42 + 16 * q^43 + 14 * q^44 + 40 * q^45 - 28 * q^46 + 16 * q^47 + 16 * q^48 - 12 * q^49 + 44 * q^50 - 16 * q^51 - 16 * q^52 + 4 * q^53 + 64 * q^54 + 6 * q^56 + 14 * q^58 - 16 * q^59 + 60 * q^60 - 20 * q^61 + 8 * q^62 + 12 * q^63 - 18 * q^64 + 32 * q^65 + 12 * q^66 + 24 * q^67 - 28 * q^68 - 4 * q^69 + 20 * q^70 + 6 * q^72 - 38 * q^74 - 40 * q^75 + 48 * q^76 - 76 * q^78 + 24 * q^79 + 24 * q^80 - 44 * q^81 - 16 * q^82 - 20 * q^83 + 8 * q^84 - 8 * q^85 + 38 * q^86 - 14 * q^88 - 40 * q^90 + 32 * q^92 - 48 * q^93 - 24 * q^94 - 16 * q^96 + 48 * q^97 - 2 * q^98 + 32 * q^99

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