LMFDB - Embedded newform 170.2.n.b.59.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(9,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("170.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.n (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 16 x^{15} + 52 x^{14} + 992 x^{13} + 6181 x^{12} + 8952 x^{11} + 6244 x^{10} - 11448 x^{9} + \cdots + 2048 $ x^20 - 16x^15 + 52x^14 + 992x^13 + 6181x^12 + 8952x^11 + 6244x^10 - 11448x^9 - 14520x^8 + 27936x^7 + 27880x^6 - 121104x^5 + 187460x^4 - 142208x^3 + 73856x^2 - 19456*x + 2048
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			59.1
Root			$1.18678 - 2.86514i$ of defining polynomial
Character	$\chi$	$=$	170.59
Dual form			170.2.n.b.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-2.86514 - 1.18678i) q^{3} +1.00000i q^{4} +(-2.09387 - 0.784666i) q^{5} +(1.18678 + 2.86514i) q^{6} +(1.09360 + 2.64018i) q^{7} +(0.707107 - 0.707107i) q^{8} +(4.67924 + 4.67924i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-2.86514 - 1.18678i) q^{3} +1.00000i q^{4} +(-2.09387 - 0.784666i) q^{5} +(1.18678 + 2.86514i) q^{6} +(1.09360 + 2.64018i) q^{7} +(0.707107 - 0.707107i) q^{8} +(4.67924 + 4.67924i) q^{9} +(0.925748 + 2.03543i) q^{10} +(-0.543661 - 1.31251i) q^{11} +(1.18678 - 2.86514i) q^{12} +3.10930 q^{13} +(1.09360 - 2.64018i) q^{14} +(5.06800 + 4.73314i) q^{15} -1.00000 q^{16} +(-1.10700 + 3.97172i) q^{17} -6.61745i q^{18} +(-5.83686 + 5.83686i) q^{19} +(0.784666 - 2.09387i) q^{20} -8.86232i q^{21} +(-0.543661 + 1.31251i) q^{22} +(-4.30543 + 1.78337i) q^{23} +(-2.86514 + 1.18678i) q^{24} +(3.76860 + 3.28598i) q^{25} +(-2.19860 - 2.19860i) q^{26} +(-4.29311 - 10.3645i) q^{27} +(-2.64018 + 1.09360i) q^{28} +(4.05552 + 1.67985i) q^{29} +(-0.236786 - 6.93045i) q^{30} +(-0.0583565 + 0.140885i) q^{31} +(0.707107 + 0.707107i) q^{32} +4.40573i q^{33} +(3.59120 - 2.02566i) q^{34} +(-0.218195 - 6.38630i) q^{35} +(-4.67924 + 4.67924i) q^{36} +(-3.11322 - 1.28954i) q^{37} +8.25456 q^{38} +(-8.90856 - 3.69005i) q^{39} +(-2.03543 + 0.925748i) q^{40} +(-3.28112 + 1.35908i) q^{41} +(-6.26661 + 6.26661i) q^{42} +(0.136166 - 0.136166i) q^{43} +(1.31251 - 0.543661i) q^{44} +(-6.12609 - 13.4694i) q^{45} +(4.30543 + 1.78337i) q^{46} -5.42173 q^{47} +(2.86514 + 1.18678i) q^{48} +(-0.824830 + 0.824830i) q^{49} +(-0.341262 - 4.98834i) q^{50} +(7.88525 - 10.0658i) q^{51} +3.10930i q^{52} +(6.74377 + 6.74377i) q^{53} +(-4.29311 + 10.3645i) q^{54} +(0.108471 + 3.17483i) q^{55} +(2.64018 + 1.09360i) q^{56} +(23.6504 - 9.79633i) q^{57} +(-1.67985 - 4.05552i) q^{58} +(1.97484 + 1.97484i) q^{59} +(-4.73314 + 5.06800i) q^{60} +(-8.95265 + 3.70831i) q^{61} +(0.140885 - 0.0583565i) q^{62} +(-7.23682 + 17.4712i) q^{63} -1.00000i q^{64} +(-6.51047 - 2.43976i) q^{65} +(3.11532 - 3.11532i) q^{66} +6.86630i q^{67} +(-3.97172 - 1.10700i) q^{68} +14.4521 q^{69} +(-4.36151 + 4.67008i) q^{70} +(1.40347 - 3.38827i) q^{71} +6.61745 q^{72} +(4.32721 - 10.4468i) q^{73} +(1.28954 + 3.11322i) q^{74} +(-6.89782 - 13.8873i) q^{75} +(-5.83686 - 5.83686i) q^{76} +(2.87072 - 2.87072i) q^{77} +(3.69005 + 8.90856i) q^{78} +(4.23263 + 10.2185i) q^{79} +(2.09387 + 0.784666i) q^{80} +14.9383i q^{81} +(3.28112 + 1.35908i) q^{82} +(-3.18264 - 3.18264i) q^{83} +8.86232 q^{84} +(5.43439 - 7.44765i) q^{85} -0.192567 q^{86} +(-9.62601 - 9.62601i) q^{87} +(-1.31251 - 0.543661i) q^{88} -0.619800i q^{89} +(-5.19249 + 13.8561i) q^{90} +(3.40032 + 8.20909i) q^{91} +(-1.78337 - 4.30543i) q^{92} +(0.334399 - 0.334399i) q^{93} +(3.83374 + 3.83374i) q^{94} +(16.8016 - 7.64164i) q^{95} +(-1.18678 - 2.86514i) q^{96} +(-5.75819 + 13.9015i) q^{97} +1.16649 q^{98} +(3.59765 - 8.68549i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{5}+O(q^{10}) $ 20 * q - 4 * q^5	$ 20 q - 4 q^{5} + 8 q^{10} - 8 q^{11} + 24 q^{13} + 16 q^{15} - 20 q^{16} - 4 q^{20} - 8 q^{22} - 16 q^{23} + 8 q^{25} - 12 q^{26} - 24 q^{27} - 12 q^{29} + 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} + 8 q^{37} + 8 q^{38} - 4 q^{40} + 4 q^{41} - 8 q^{42} - 16 q^{43} - 8 q^{44} - 32 q^{45} + 16 q^{46} - 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} - 44 q^{53} - 24 q^{54} + 72 q^{57} + 16 q^{59} + 8 q^{60} + 8 q^{61} + 8 q^{62} + 24 q^{63} - 28 q^{65} - 8 q^{66} - 20 q^{68} - 16 q^{69} + 8 q^{71} + 28 q^{72} + 60 q^{73} + 28 q^{74} - 8 q^{78} + 56 q^{79} + 4 q^{80} - 4 q^{82} + 16 q^{84} + 84 q^{85} + 48 q^{86} + 72 q^{87} + 8 q^{88} - 12 q^{90} - 24 q^{91} + 8 q^{92} - 72 q^{93} + 32 q^{94} + 88 q^{95} - 48 q^{97} + 36 q^{98} + 72 q^{99}+O(q^{100}) $ 20 * q - 4 * q^5 + 8 * q^10 - 8 * q^11 + 24 * q^13 + 16 * q^15 - 20 * q^16 - 4 * q^20 - 8 * q^22 - 16 * q^23 + 8 * q^25 - 12 * q^26 - 24 * q^27 - 12 * q^29 + 8 * q^30 + 8 * q^31 + 8 * q^34 - 8 * q^35 + 8 * q^37 + 8 * q^38 - 4 * q^40 + 4 * q^41 - 8 * q^42 - 16 * q^43 - 8 * q^44 - 32 * q^45 + 16 * q^46 - 40 * q^47 - 56 * q^49 + 8 * q^50 - 8 * q^51 - 44 * q^53 - 24 * q^54 + 72 * q^57 + 16 * q^59 + 8 * q^60 + 8 * q^61 + 8 * q^62 + 24 * q^63 - 28 * q^65 - 8 * q^66 - 20 * q^68 - 16 * q^69 + 8 * q^71 + 28 * q^72 + 60 * q^73 + 28 * q^74 - 8 * q^78 + 56 * q^79 + 4 * q^80 - 4 * q^82 + 16 * q^84 + 84 * q^85 + 48 * q^86 + 72 * q^87 + 8 * q^88 - 12 * q^90 - 24 * q^91 + 8 * q^92 - 72 * q^93 + 32 * q^94 + 88 * q^95 - 48 * q^97 + 36 * q^98 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−2.86514	−	1.18678i	−1.65419	−	0.685187i	−0.656575	−	0.754260i	$-0.727996\pi$
$3$	−2.86514	−	1.18678i	−1.65419	−	0.685187i	−0.997612	+	0.0690736i	$0.977996\pi$
$4$			1.00000i			0.500000i
$5$	−2.09387	−	0.784666i	−0.936408	−	0.350913i
$5$	−2.09387	−	0.784666i	−0.936408	−	0.350913i
$6$	1.18678	+	2.86514i	0.484500	+	1.16969i
$7$	1.09360	+	2.64018i	0.413341	+	0.997893i	0.984234	+	0.176869i	$0.0565969\pi$
$7$	1.09360	+	2.64018i	0.413341	+	0.997893i	−0.570894	+	0.821024i	$0.693403\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	4.67924	+	4.67924i	1.55975	+	1.55975i
$10$	0.925748	+	2.03543i	0.292747	+	0.643661i
$11$	−0.543661	−	1.31251i	−0.163920	−	0.395738i	0.820482	−	0.571672i	$-0.193705\pi$
$11$	−0.543661	−	1.31251i	−0.163920	−	0.395738i	−0.984402	+	0.175935i	$0.943705\pi$
$12$	1.18678	−	2.86514i	0.342593	−	0.827094i
$13$	3.10930			0.862364			0.431182	−	0.902265i	$-0.358097\pi$
$13$	3.10930			0.862364			0.431182	+	0.902265i	$0.358097\pi$
$14$	1.09360	−	2.64018i	0.292276	−	0.705617i
$15$	5.06800	+	4.73314i	1.30855	+	1.22209i
$16$	−1.00000			−0.250000
$17$	−1.10700	+	3.97172i	−0.268487	+	0.963283i
$17$	−1.10700	+	3.97172i	−0.268487	+	0.963283i
$18$		−	6.61745i		−	1.55975i
$19$	−5.83686	+	5.83686i	−1.33907	+	1.33907i	−0.442101	+	0.896965i	$0.645767\pi$
$19$	−5.83686	+	5.83686i	−1.33907	+	1.33907i	−0.896965	+	0.442101i	$0.854233\pi$
$20$	0.784666	−	2.09387i	0.175457	−	0.468204i
$21$		−	8.86232i		−	1.93392i
$22$	−0.543661	+	1.31251i	−0.115909	+	0.279829i
$23$	−4.30543	+	1.78337i	−0.897743	+	0.371857i	−0.783352	−	0.621578i	$-0.786492\pi$
$23$	−4.30543	+	1.78337i	−0.897743	+	0.371857i	−0.114391	+	0.993436i	$0.536492\pi$
$24$	−2.86514	+	1.18678i	−0.584843	+	0.242250i
$25$	3.76860	+	3.28598i	0.753720	+	0.657196i
$26$	−2.19860	−	2.19860i	−0.431182	−	0.431182i
$27$	−4.29311	−	10.3645i	−0.826209	−	1.99464i
$28$	−2.64018	+	1.09360i	−0.498946	+	0.206670i
$29$	4.05552	+	1.67985i	0.753091	+	0.311941i	0.726002	−	0.687692i	$-0.241376\pi$
$29$	4.05552	+	1.67985i	0.753091	+	0.311941i	0.0270891	+	0.999633i	$0.491376\pi$
$30$	−0.236786	−	6.93045i	−0.0432310	−	1.26532i
$31$	−0.0583565	+	0.140885i	−0.0104811	+	0.0253037i	−0.929033	−	0.369996i	$-0.879359\pi$
$31$	−0.0583565	+	0.140885i	−0.0104811	+	0.0253037i	0.918552	+	0.395299i	$0.129359\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$			4.40573i			0.766940i
$34$	3.59120	−	2.02566i	0.615885	−	0.347398i
$35$	−0.218195	−	6.38630i	−0.0368816	−	1.07948i
$36$	−4.67924	+	4.67924i	−0.779874	+	0.779874i
$37$	−3.11322	−	1.28954i	−0.511810	−	0.211999i	0.111805	−	0.993730i	$-0.464337\pi$
$37$	−3.11322	−	1.28954i	−0.511810	−	0.211999i	−0.623615	+	0.781732i	$0.714337\pi$
$38$	8.25456			1.33907
$39$	−8.90856	−	3.69005i	−1.42651	−	0.590880i
$40$	−2.03543	+	0.925748i	−0.321830	+	0.146374i
$41$	−3.28112	+	1.35908i	−0.512424	+	0.212253i	−0.623886	−	0.781516i	$-0.714447\pi$
$41$	−3.28112	+	1.35908i	−0.512424	+	0.212253i	0.111461	+	0.993769i	$0.464447\pi$
$42$	−6.26661	+	6.26661i	−0.966959	+	0.966959i
$43$	0.136166	−	0.136166i	0.0207651	−	0.0207651i	−0.696648	−	0.717413i	$-0.745326\pi$
$43$	0.136166	−	0.136166i	0.0207651	−	0.0207651i	0.717413	+	0.696648i	$0.245326\pi$
$44$	1.31251	−	0.543661i	0.197869	−	0.0819599i
$45$	−6.12609	−	13.4694i	−0.913224	−	2.00790i
$46$	4.30543	+	1.78337i	0.634800	+	0.262943i
$47$	−5.42173			−0.790840			−0.395420	−	0.918500i	$-0.629401\pi$
$47$	−5.42173			−0.790840			−0.395420	+	0.918500i	$0.629401\pi$
$48$	2.86514	+	1.18678i	0.413547	+	0.171297i
$49$	−0.824830	+	0.824830i	−0.117833	+	0.117833i
$50$	−0.341262	−	4.98834i	−0.0482618	−	0.705458i
$51$	7.88525	−	10.0658i	1.10416	−	1.40949i
$52$			3.10930i			0.431182i
$53$	6.74377	+	6.74377i	0.926328	+	0.926328i	0.997466	−	0.0711388i	$-0.0226633\pi$
$53$	6.74377	+	6.74377i	0.926328	+	0.926328i	−0.0711388	+	0.997466i	$0.522663\pi$
$54$	−4.29311	+	10.3645i	−0.584218	+	1.41043i
$55$	0.108471	+	3.17483i	0.0146263	+	0.428094i
$56$	2.64018	+	1.09360i	0.352808	+	0.146138i
$57$	23.6504	−	9.79633i	3.13258	−	1.29756i
$58$	−1.67985	−	4.05552i	−0.220575	−	0.532516i
$59$	1.97484	+	1.97484i	0.257103	+	0.257103i	0.823875	−	0.566772i	$-0.191808\pi$
$59$	1.97484	+	1.97484i	0.257103	+	0.257103i	−0.566772	+	0.823875i	$0.691808\pi$
$60$	−4.73314	+	5.06800i	−0.611045	+	0.654276i
$61$	−8.95265	+	3.70831i	−1.14627	+	0.474800i	−0.873281	−	0.487217i	$-0.838012\pi$
$61$	−8.95265	+	3.70831i	−1.14627	+	0.474800i	−0.272989	+	0.962017i	$0.588012\pi$
$62$	0.140885	−	0.0583565i	0.0178924	−	0.00741128i
$63$	−7.23682	+	17.4712i	−0.911754	+	2.20117i
$64$		−	1.00000i		−	0.125000i
$65$	−6.51047	−	2.43976i	−0.807524	−	0.302615i
$66$	3.11532	−	3.11532i	0.383470	−	0.383470i
$67$			6.86630i			0.838852i	0.907789	+	0.419426i	$0.137769\pi$
$67$			6.86630i			0.838852i	−0.907789	+	0.419426i	$0.862231\pi$
$68$	−3.97172	−	1.10700i	−0.481642	−	0.134243i
$69$	14.4521			1.73983
$70$	−4.36151	+	4.67008i	−0.521300	+	0.558182i
$71$	1.40347	−	3.38827i	0.166561	−	0.402113i	−0.818457	−	0.574568i	$-0.805170\pi$
$71$	1.40347	−	3.38827i	0.166561	−	0.402113i	0.985017	+	0.172455i	$0.0551699\pi$
$72$	6.61745			0.779874
$73$	4.32721	−	10.4468i	0.506461	−	1.22271i	−0.439446	−	0.898269i	$-0.644825\pi$
$73$	4.32721	−	10.4468i	0.506461	−	1.22271i	0.945907	−	0.324437i	$-0.105175\pi$
$74$	1.28954	+	3.11322i	0.149906	+	0.361904i
$75$	−6.89782	−	13.8873i	−0.796491	−	1.60356i
$76$	−5.83686	−	5.83686i	−0.669533	−	0.669533i
$77$	2.87072	−	2.87072i	0.327149	−	0.327149i
$78$	3.69005	+	8.90856i	0.417815	+	1.00870i
$79$	4.23263	+	10.2185i	0.476208	+	1.14967i	0.961374	+	0.275245i	$0.0887591\pi$
$79$	4.23263	+	10.2185i	0.476208	+	1.14967i	−0.485166	+	0.874422i	$0.661241\pi$
$80$	2.09387	+	0.784666i	0.234102	+	0.0877283i
$81$			14.9383i			1.65981i
$82$	3.28112	+	1.35908i	0.362339	+	0.150086i
$83$	−3.18264	−	3.18264i	−0.349341	−	0.349341i	0.510523	−	0.859864i	$-0.329452\pi$
$83$	−3.18264	−	3.18264i	−0.349341	−	0.349341i	−0.859864	+	0.510523i	$0.829452\pi$
$84$	8.86232			0.966959
$85$	5.43439	−	7.44765i	0.589442	−	0.807811i
$86$	−0.192567			−0.0207651
$87$	−9.62601	−	9.62601i	−1.03202	−	1.03202i
$88$	−1.31251	−	0.543661i	−0.139914	−	0.0579544i
$89$		−	0.619800i		−	0.0656987i	−0.999460	−	0.0328494i	$-0.989542\pi$
$89$		−	0.619800i		−	0.0656987i	0.999460	−	0.0328494i	$-0.0104582\pi$
$90$	−5.19249	+	13.8561i	−0.547336	+	1.46056i
$91$	3.40032	+	8.20909i	0.356450	+	0.860547i
$92$	−1.78337	−	4.30543i	−0.185929	−	0.448872i
$93$	0.334399	−	0.334399i	0.0346755	−	0.0346755i
$94$	3.83374	+	3.83374i	0.395420	+	0.395420i
$95$	16.8016	−	7.64164i	1.72381	−	0.784016i
$96$	−1.18678	−	2.86514i	−0.121125	−	0.292422i
$97$	−5.75819	+	13.9015i	−0.584656	+	1.41148i	0.303895	+	0.952706i	$0.401713\pi$
$97$	−5.75819	+	13.9015i	−0.584656	+	1.41148i	−0.888551	+	0.458778i	$0.848287\pi$
$98$	1.16649			0.117833
$99$	3.59765	−	8.68549i	0.361577	−	0.872924i
$100$	−3.28598	+	3.76860i	−0.328598	+	0.376860i
$101$	−15.7464			−1.56682			−0.783412	−	0.621503i	$-0.786522\pi$
$101$	−15.7464			−1.56682			−0.783412	+	0.621503i	$0.786522\pi$
$102$	−12.6933	+	1.54185i	−1.25682	+	0.152666i
$103$		−	7.01019i		−	0.690735i	−0.938468	−	0.345367i	$-0.887754\pi$
$103$		−	7.01019i		−	0.690735i	0.938468	−	0.345367i	$-0.112246\pi$
$104$	2.19860	−	2.19860i	0.215591	−	0.215591i
$105$	−6.95396	+	18.5566i	−0.678637	+	1.81094i
$106$		−	9.53713i		−	0.926328i
$107$	−1.94964	+	4.70686i	−0.188479	+	0.455029i	−0.989667	−	0.143384i	$-0.954202\pi$
$107$	−1.94964	+	4.70686i	−0.188479	+	0.455029i	0.801188	+	0.598413i	$0.204202\pi$
$108$	10.3645	−	4.29311i	0.997322	−	0.413104i
$109$	−11.0018	+	4.55708i	−1.05378	+	0.436489i	−0.841239	−	0.540664i	$-0.818173\pi$
$109$	−11.0018	+	4.55708i	−1.05378	+	0.436489i	−0.212539	+	0.977153i	$0.568173\pi$
$110$	2.16824	−	2.32164i	0.206734	−	0.221360i
$111$	7.38940	+	7.38940i	0.701370	+	0.701370i
$112$	−1.09360	−	2.64018i	−0.103335	−	0.249473i
$113$	−6.73860	+	2.79122i	−0.633914	+	0.262576i	−0.676415	−	0.736521i	$-0.736467\pi$
$113$	−6.73860	+	2.79122i	−0.633914	+	0.262576i	0.0425012	+	0.999096i	$0.486467\pi$
$114$	−23.6504	−	9.79633i	−2.21507	−	0.917511i
$115$	10.4144	−	0.355817i	0.971144	−	0.0331801i
$116$	−1.67985	+	4.05552i	−0.155970	+	0.376546i
$117$	14.5492	+	14.5492i	1.34507	+	1.34507i
$118$		−	2.79285i		−	0.257103i
$119$	−11.6966	+	1.42079i	−1.07223	+	0.130243i
$120$	6.93045	−	0.236786i	0.632661	−	0.0216155i
$121$	6.35105	−	6.35105i	0.577368	−	0.577368i
$122$	8.95265	+	3.70831i	0.810535	+	0.335735i
$123$	11.0138			0.993079
$124$	−0.140885	−	0.0583565i	−0.0126518	−	0.00524057i
$125$	−5.31256	−	9.83751i	−0.475170	−	0.879894i
$126$	17.4712	−	7.23682i	1.55646	−	0.644707i
$127$	8.30087	−	8.30087i	0.736583	−	0.736583i	−0.235332	−	0.971915i	$-0.575618\pi$
$127$	8.30087	−	8.30087i	0.736583	−	0.736583i	0.971915	+	0.235332i	$0.0756178\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−0.551731	+	0.228535i	−0.0485772	+	0.0201213i
$130$	2.87843	+	6.32877i	0.252455	+	0.555070i
$131$	17.2478	+	7.14427i	1.50695	+	0.624197i	0.974925	−	0.222534i	$-0.0714327\pi$
$131$	17.2478	+	7.14427i	1.50695	+	0.624197i	0.532021	+	0.846731i	$0.321433\pi$
$132$	−4.40573			−0.383470
$133$	−21.7935	−	9.02716i	−1.88974	−	0.782754i
$134$	4.85521	−	4.85521i	0.419426	−	0.419426i
$135$	0.856561	+	25.0705i	0.0737211	+	2.15773i
$136$	2.02566	+	3.59120i	0.173699	+	0.307943i
$137$		−	0.888599i		−	0.0759182i	−0.999279	−	0.0379591i	$-0.987914\pi$
$137$		−	0.888599i		−	0.0759182i	0.999279	−	0.0379591i	$-0.0120857\pi$
$138$	−10.2192	−	10.2192i	−0.869914	−	0.869914i
$139$	4.73615	−	11.4341i	0.401715	−	0.969826i	−0.585535	−	0.810647i	$-0.699115\pi$
$139$	4.73615	−	11.4341i	0.401715	−	0.969826i	0.987250	−	0.159179i	$-0.0508846\pi$
$140$	6.38630	−	0.218195i	0.539741	−	0.0184408i
$141$	15.5340	+	6.43439i	1.30820	+	0.541873i
$142$	−3.38827	+	1.40347i	−0.284337	+	0.117776i
$143$	−1.69040	−	4.08099i	−0.141359	−	0.341270i
$144$	−4.67924	−	4.67924i	−0.389937	−	0.389937i
$145$	−7.17362	−	6.69962i	−0.595736	−	0.556373i
$146$	−10.4468	+	4.32721i	−0.864583	+	0.358122i
$147$	3.34214	−	1.38436i	0.275655	−	0.114180i
$148$	1.28954	−	3.11322i	0.105999	−	0.255905i
$149$		−	12.1316i		−	0.993861i	−0.867790	−	0.496930i	$-0.834460\pi$
$149$		−	12.1316i		−	0.993861i	0.867790	−	0.496930i	$-0.165540\pi$
$150$	−4.94229	+	14.6973i	−0.403536	+	1.20003i
$151$	−2.59324	+	2.59324i	−0.211035	+	0.211035i	−0.804707	−	0.593672i	$-0.797678\pi$
$151$	−2.59324	+	2.59324i	−0.211035	+	0.211035i	0.593672	+	0.804707i	$0.297678\pi$
$152$			8.25456i			0.669533i
$153$	−23.7645	+	13.4047i	−1.92125	+	1.08371i
$154$	−4.05981			−0.327149
$155$	0.232739	−	0.249205i	0.0186940	−	0.0200166i
$156$	3.69005	−	8.90856i	0.295440	−	0.713255i
$157$	−7.67183			−0.612279			−0.306139	−	0.951987i	$-0.599037\pi$
$157$	−7.67183			−0.612279			−0.306139	+	0.951987i	$0.599037\pi$
$158$	4.23263	−	10.2185i	0.336730	−	0.812937i
$159$	−11.3185	−	27.3252i	−0.897612	−	2.16703i
$160$	−0.925748	−	2.03543i	−0.0731868	−	0.160915i
$161$	−9.41680	−	9.41680i	−0.742148	−	0.742148i
$162$	10.5629	−	10.5629i	0.829903	−	0.829903i
$163$	−1.94190	−	4.68816i	−0.152101	−	0.367205i	0.829402	−	0.558653i	$-0.188682\pi$
$163$	−1.94190	−	4.68816i	−0.152101	−	0.367205i	−0.981503	+	0.191448i	$0.938682\pi$
$164$	−1.35908	−	3.28112i	−0.106127	−	0.256212i
$165$	3.45703	−	9.22504i	0.269129	−	0.718168i
$166$			4.50094i			0.349341i
$167$	−4.90482	−	2.03164i	−0.379547	−	0.157213i	0.184750	−	0.982786i	$-0.440853\pi$
$167$	−4.90482	−	2.03164i	−0.379547	−	0.157213i	−0.564296	+	0.825572i	$0.690853\pi$
$168$	−6.26661	−	6.26661i	−0.483479	−	0.483479i
$169$	−3.33227			−0.256329
$170$	−9.10897	+	1.42359i	−0.698626	+	0.109184i
$171$	−54.6241			−4.17721
$172$	0.136166	+	0.136166i	0.0103825	+	0.0103825i
$173$	3.25716	+	1.34916i	0.247637	+	0.102575i	0.503050	−	0.864257i	$-0.332211\pi$
$173$	3.25716	+	1.34916i	0.247637	+	0.102575i	−0.255412	+	0.966832i	$0.582211\pi$
$174$			13.6132i			1.03202i
$175$	−4.55424	+	13.5433i	−0.344268	+	1.02378i
$176$	0.543661	+	1.31251i	0.0409800	+	0.0989344i
$177$	−3.31449	−	8.00190i	−0.249133	−	0.601459i
$178$	−0.438265	+	0.438265i	−0.0328494	+	0.0328494i
$179$	−7.14802	−	7.14802i	−0.534268	−	0.534268i	0.387572	−	0.921840i	$-0.373314\pi$
$179$	−7.14802	−	7.14802i	−0.534268	−	0.534268i	−0.921840	+	0.387572i	$0.873314\pi$
$180$	13.4694	−	6.12609i	1.00395	−	0.456612i
$181$	3.47404	+	8.38708i	0.258224	+	0.623407i	0.998821	−	0.0485420i	$-0.0154575\pi$
$181$	3.47404	+	8.38708i	0.258224	+	0.623407i	−0.740598	+	0.671949i	$0.765457\pi$
$182$	3.40032	−	8.20909i	0.252048	−	0.608498i
$183$	30.0515			2.22147
$184$	−1.78337	+	4.30543i	−0.131471	+	0.317400i
$185$	5.50682	+	5.14296i	0.404870	+	0.378118i
$186$	−0.472911			−0.0346755
$187$	5.81477	−	0.706317i	0.425218	−	0.0516510i
$188$		−	5.42173i		−	0.395420i
$189$	22.6691	−	22.6691i	1.64894	−	1.64894i
$190$	−17.2840	−	6.47707i	−1.25391	−	0.469896i
$191$			9.34726i			0.676344i	0.941084	+	0.338172i	$0.109809\pi$
$191$			9.34726i			0.676344i	−0.941084	+	0.338172i	$0.890191\pi$
$192$	−1.18678	+	2.86514i	−0.0856483	+	0.206773i
$193$	11.6698	−	4.83377i	0.840008	−	0.347943i	0.0791511	−	0.996863i	$-0.474779\pi$
$193$	11.6698	−	4.83377i	0.840008	−	0.347943i	0.760857	+	0.648920i	$0.224779\pi$
$194$	13.9015	−	5.75819i	0.998070	−	0.413414i
$195$	15.7579	+	14.7167i	1.12845	+	1.05389i
$196$	−0.824830	−	0.824830i	−0.0589164	−	0.0589164i
$197$	9.41794	+	22.7369i	0.671001	+	1.61994i	0.779914	+	0.625887i	$0.215263\pi$
$197$	9.41794	+	22.7369i	0.671001	+	1.61994i	−0.108913	+	0.994051i	$0.534737\pi$
$198$	−8.68549	+	3.59765i	−0.617251	+	0.255674i
$199$	1.59821	+	0.662000i	0.113294	+	0.0469279i	0.438610	−	0.898677i	$-0.355471\pi$
$199$	1.59821	+	0.662000i	0.113294	+	0.0469279i	−0.325316	+	0.945605i	$0.605471\pi$
$200$	4.98834	−	0.341262i	0.352729	−	0.0241309i
$201$	8.14878	−	19.6729i	0.574771	−	1.38762i
$202$	11.1344	+	11.1344i	0.783412	+	0.783412i
$203$			12.5444i			0.880442i
$204$	10.0658	+	7.88525i	0.704744	+	0.552078i
$205$	7.93666	−	0.271164i	0.554321	−	0.0189389i
$206$	−4.95696	+	4.95696i	−0.345367	+	0.345367i
$207$	−28.4909	−	11.8013i	−1.98026	−	0.820249i
$208$	−3.10930			−0.215591
$209$	10.8342	+	4.48768i	0.749419	+	0.310419i
$210$	18.0387	−	8.20428i	1.24479	−	0.566149i
$211$	20.0957	−	8.32392i	1.38345	−	0.573042i	0.438046	−	0.898953i	$-0.355671\pi$
$211$	20.0957	−	8.32392i	1.38345	−	0.573042i	0.945401	+	0.325911i	$0.105671\pi$
$212$	−6.74377	+	6.74377i	−0.463164	+	0.463164i
$213$	−8.04225	+	8.04225i	−0.551046	+	0.551046i
$214$	4.70686	−	1.94964i	0.321754	−	0.133275i
$215$	−0.391958	+	0.178269i	−0.0267313	+	0.0121578i
$216$	−10.3645	−	4.29311i	−0.705213	−	0.292109i
$217$	−0.435780			−0.0295827
$218$	11.0018	+	4.55708i	0.745133	+	0.308644i
$219$	−24.7961	+	24.7961i	−1.67556	+	1.67556i
$220$	−3.17483	+	0.108471i	−0.214047	+	0.00731313i
$221$	−3.44199	+	12.3493i	−0.231533	+	0.830701i
$222$		−	10.4502i		−	0.701370i
$223$	5.72265	+	5.72265i	0.383217	+	0.383217i	0.872260	−	0.489043i	$-0.162654\pi$
$223$	5.72265	+	5.72265i	0.383217	+	0.383217i	−0.489043	+	0.872260i	$0.662654\pi$
$224$	−1.09360	+	2.64018i	−0.0730690	+	0.176404i
$225$	2.25828	+	33.0101i	0.150552	+	2.20067i
$226$	6.73860	+	2.79122i	0.448245	+	0.185669i
$227$	−0.436916	+	0.180977i	−0.0289991	+	0.0120118i	−0.397136	−	0.917760i	$-0.629996\pi$
$227$	−0.436916	+	0.180977i	−0.0289991	+	0.0120118i	0.368137	+	0.929772i	$0.379996\pi$
$228$	9.79633	+	23.6504i	0.648778	+	1.56629i
$229$	−3.37412	−	3.37412i	−0.222968	−	0.222968i	0.586779	−	0.809747i	$-0.300396\pi$
$229$	−3.37412	−	3.37412i	−0.222968	−	0.222968i	−0.809747	+	0.586779i	$0.800396\pi$
$230$	−7.61566	−	7.11246i	−0.502162	−	0.468982i
$231$	−11.6319	+	4.81810i	−0.765324	+	0.317007i
$232$	4.05552	−	1.67985i	0.266258	−	0.110288i
$233$	0.178531	−	0.431013i	0.0116960	−	0.0282366i	−0.917924	−	0.396757i	$-0.870136\pi$
$233$	0.178531	−	0.431013i	0.0116960	−	0.0282366i	0.929620	+	0.368520i	$0.120136\pi$
$234$		−	20.5756i		−	1.34507i
$235$	11.3524	+	4.25425i	0.740549	+	0.277516i
$236$	−1.97484	+	1.97484i	−0.128551	+	0.128551i
$237$		−	34.3005i		−	2.22806i
$238$	9.27543	+	7.26613i	0.601237	+	0.470993i
$239$	23.7793			1.53815			0.769077	−	0.639156i	$-0.220716\pi$
$239$	23.7793			1.53815			0.769077	+	0.639156i	$0.220716\pi$
$240$	−5.06800	−	4.73314i	−0.327138	−	0.305523i
$241$	10.2571	−	24.7628i	0.660717	−	1.59511i	−0.135965	−	0.990714i	$-0.543413\pi$
$241$	10.2571	−	24.7628i	0.660717	−	1.59511i	0.796682	−	0.604399i	$-0.206587\pi$
$242$	−8.98174			−0.577368
$243$	4.84908	−	11.7067i	0.311069	−	0.750987i
$244$	−3.70831	−	8.95265i	−0.237400	−	0.573135i
$245$	2.37430	−	1.07987i	0.151689	−	0.0689905i
$246$	−7.78792	−	7.78792i	−0.496539	−	0.496539i
$247$	−18.1485	+	18.1485i	−1.15476	+	1.15476i
$248$	0.0583565	+	0.140885i	0.00370564	+	0.00894621i
$249$	5.34162	+	12.8958i	0.338511	+	0.817238i
$250$	−3.19962	+	10.7127i	−0.202362	+	0.677532i
$251$			28.4608i			1.79643i	0.439553	+	0.898216i	$0.355137\pi$
$251$			28.4608i			1.79643i	−0.439553	+	0.898216i	$0.644863\pi$
$252$	−17.4712	−	7.23682i	−1.10058	−	0.455877i
$253$	4.68138	+	4.68138i	0.294316	+	0.294316i
$254$	−11.7392			−0.736583
$255$	−24.4090	+	14.8891i	−1.52855	+	0.932392i
$256$	1.00000			0.0625000
$257$	9.67576	+	9.67576i	0.603557	+	0.603557i	0.941255	−	0.337697i	$-0.109648\pi$
$257$	9.67576	+	9.67576i	0.603557	+	0.603557i	−0.337697	+	0.941255i	$0.609648\pi$
$258$	0.551731	+	0.228535i	0.0343493	+	0.0142279i
$259$		−	9.62967i		−	0.598359i
$260$	2.43976	−	6.51047i	0.151307	−	0.403762i
$261$	11.1163	+	26.8372i	0.688083	+	1.66118i
$262$	−7.14427	−	17.2478i	−0.441374	−	1.06557i
$263$	−13.5757	+	13.5757i	−0.837116	+	0.837116i	−0.988478	−	0.151362i	$-0.951634\pi$
$263$	−13.5757	+	13.5757i	−0.837116	+	0.837116i	0.151362	+	0.988478i	$0.451634\pi$
$264$	3.11532	+	3.11532i	0.191735	+	0.191735i
$265$	−8.82898	−	19.4122i	−0.542360	−	1.19248i
$266$	9.02716	+	21.7935i	0.553491	+	1.33624i
$267$	−0.735566	+	1.77581i	−0.0450159	+	0.108678i
$268$	−6.86630			−0.419426
$269$	−4.36575	+	10.5399i	−0.266185	+	0.642626i	−0.999297	−	0.0374807i	$-0.988067\pi$
$269$	−4.36575	+	10.5399i	−0.266185	+	0.642626i	0.733113	+	0.680107i	$0.238067\pi$
$270$	17.1219	−	18.3332i	1.04200	−	1.11572i
$271$	8.76735			0.532578			0.266289	−	0.963893i	$-0.414202\pi$
$271$	8.76735			0.532578			0.266289	+	0.963893i	$0.414202\pi$
$272$	1.10700	−	3.97172i	0.0671217	−	0.240821i
$273$		−	27.5556i		−	1.66774i
$274$	−0.628335	+	0.628335i	−0.0379591	+	0.0379591i
$275$	2.26405	−	6.73279i	0.136528	−	0.406003i
$276$			14.4521i			0.869914i
$277$	0.845370	−	2.04090i	0.0507934	−	0.122626i	−0.896446	−	0.443153i	$-0.853860\pi$
$277$	0.845370	−	2.04090i	0.0507934	−	0.122626i	0.947239	+	0.320527i	$0.103860\pi$
$278$	−11.4341	+	4.73615i	−0.685771	+	0.284055i
$279$	−0.932299	+	0.386171i	−0.0558153	+	0.0231194i
$280$	−4.67008	−	4.36151i	−0.279091	−	0.260650i
$281$	−1.10824	−	1.10824i	−0.0661120	−	0.0661120i	0.673278	−	0.739390i	$-0.264886\pi$
$281$	−1.10824	−	1.10824i	−0.0661120	−	0.0661120i	−0.739390	+	0.673278i	$0.764886\pi$
$282$	−6.43439	−	15.5340i	−0.383162	−	0.925036i
$283$	9.47815	−	3.92598i	0.563418	−	0.233375i	−0.0827505	−	0.996570i	$-0.526370\pi$
$283$	9.47815	−	3.92598i	0.563418	−	0.233375i	0.646168	+	0.763195i	$0.276370\pi$
$284$	3.38827	+	1.40347i	0.201057	+	0.0832804i
$285$	−57.2078	+	1.95457i	−3.38870	+	0.115778i
$286$	−1.69040	+	4.08099i	−0.0999556	+	0.241314i
$287$	−7.17644	−	7.17644i	−0.423612	−	0.423612i
$288$			6.61745i			0.389937i
$289$	−14.5491	−	8.79338i	−0.855830	−	0.517257i
$290$	0.335164	+	9.80986i	0.0196815	+	0.576055i
$291$	32.9960	−	32.9960i	1.93426	−	1.93426i
$292$	10.4468	+	4.32721i	0.611353	+	0.253231i
$293$	4.41718			0.258054			0.129027	−	0.991641i	$-0.458815\pi$
$293$	4.41718			0.258054			0.129027	+	0.991641i	$0.458815\pi$
$294$	−3.34214	−	1.38436i	−0.194918	−	0.0807375i
$295$	−2.58548	−	5.68466i	−0.150532	−	0.330974i
$296$	−3.11322	+	1.28954i	−0.180952	+	0.0749528i
$297$	−11.2695	+	11.2695i	−0.653924	+	0.653924i
$298$	−8.57835	+	8.57835i	−0.496930	+	0.496930i
$299$	−13.3868	+	5.54501i	−0.774181	+	0.320676i
$300$	13.8873	−	6.89782i	0.801782	−	0.398246i
$301$	0.508411	+	0.210591i	0.0293043	+	0.0121383i
$302$	3.66739			0.211035
$303$	45.1155	+	18.6875i	2.59182	+	1.07357i
$304$	5.83686	−	5.83686i	0.334767	−	0.334767i
$305$	21.6555	−	0.739883i	1.23999	−	0.0423656i
$306$	26.2826	+	7.32551i	1.50248	+	0.418771i
$307$		−	18.9599i		−	1.08210i	−0.840991	−	0.541049i	$-0.818027\pi$
$307$		−	18.9599i		−	1.08210i	0.840991	−	0.541049i	$-0.181973\pi$
$308$	2.87072	+	2.87072i	0.163574	+	0.163574i
$309$	−8.31955	+	20.0852i	−0.473282	+	1.14260i
$310$	−0.340786	+	0.0116433i	−0.0193553	+	0.000661295i
$311$	−10.1370	−	4.19890i	−0.574819	−	0.238098i	0.0762852	−	0.997086i	$-0.475694\pi$
$311$	−10.1370	−	4.19890i	−0.574819	−	0.238098i	−0.651104	+	0.758988i	$0.725694\pi$
$312$	−8.90856	+	3.69005i	−0.504348	+	0.208908i
$313$	8.33889	+	20.1319i	0.471342	+	1.13792i	0.963571	+	0.267454i	$0.0861823\pi$
$313$	8.33889	+	20.1319i	0.471342	+	1.13792i	−0.492229	+	0.870466i	$0.663818\pi$
$314$	5.42481	+	5.42481i	0.306139	+	0.306139i
$315$	28.8621	−	30.9040i	1.62619	−	1.74124i
$316$	−10.2185	+	4.23263i	−0.574834	+	0.238104i
$317$	−16.7175	+	6.92463i	−0.938950	+	0.388926i	−0.799067	−	0.601242i	$-0.794673\pi$
$317$	−16.7175	+	6.92463i	−0.938950	+	0.388926i	−0.139883	+	0.990168i	$0.544673\pi$
$318$	−11.3185	+	27.3252i	−0.634707	+	1.53232i
$319$		−	6.23619i		−	0.349160i
$320$	−0.784666	+	2.09387i	−0.0438642	+	0.117051i
$321$	11.1720	−	11.1720i	0.623560	−	0.623560i
$322$			13.3174i			0.742148i
$323$	−16.7210	−	29.6437i	−0.930379	−	1.64942i
$324$	−14.9383			−0.829903
$325$	11.7177	+	10.2171i	0.649980	+	0.566742i
$326$	−1.94190	+	4.68816i	−0.107552	+	0.259653i
$327$	36.9298			2.04222
$328$	−1.35908	+	3.28112i	−0.0750428	+	0.181169i
$329$	−5.92919	−	14.3143i	−0.326887	−	0.789174i
$330$	−8.96758	+	4.07860i	−0.493649	+	0.224520i
$331$	−17.7644	−	17.7644i	−0.976417	−	0.976417i	0.0233110	−	0.999728i	$-0.492579\pi$
$331$	−17.7644	−	17.7644i	−0.976417	−	0.976417i	−0.999728	+	0.0233110i	$0.992579\pi$
$332$	3.18264	−	3.18264i	0.174670	−	0.174670i
$333$	−8.53344	−	20.6015i	−0.467630	−	1.12896i
$334$	2.03164	+	4.90482i	0.111167	+	0.268380i
$335$	5.38776	−	14.3772i	0.294365	−	0.785508i
$336$			8.86232i			0.483479i
$337$	−5.61346	−	2.32517i	−0.305785	−	0.126660i	0.224514	−	0.974471i	$-0.427920\pi$
$337$	−5.61346	−	2.32517i	−0.305785	−	0.126660i	−0.530299	+	0.847811i	$0.677920\pi$
$338$	2.35627	+	2.35627i	0.128164	+	0.128164i
$339$	22.6195			1.22853
$340$	7.44765	+	5.43439i	0.403905	+	0.294721i
$341$	0.216640			0.0117317
$342$	38.6251	+	38.6251i	2.08861	+	2.08861i
$343$	15.4015	+	6.37951i	0.831603	+	0.344461i
$344$		−	0.192567i		−	0.0103825i
$345$	−30.2608	−	11.3401i	−1.62919	−	0.610529i
$346$	−1.34916	−	3.25716i	−0.0725313	−	0.175106i
$347$	−6.01683	−	14.5259i	−0.323000	−	0.779792i	−0.999077	−	0.0429601i	$-0.986321\pi$
$347$	−6.01683	−	14.5259i	−0.323000	−	0.779792i	0.676077	−	0.736831i	$-0.263679\pi$
$348$	9.62601	−	9.62601i	0.516008	−	0.516008i
$349$	5.35533	+	5.35533i	0.286664	+	0.286664i	0.835760	−	0.549095i	$-0.185028\pi$
$349$	5.35533	+	5.35533i	0.286664	+	0.286664i	−0.549095	+	0.835760i	$0.685028\pi$
$350$	12.7969	−	6.35623i	0.684023	−	0.339755i
$351$	−13.3485	−	32.2262i	−0.712493	−	1.72011i
$352$	0.543661	−	1.31251i	0.0289772	−	0.0699572i
$353$	11.0090			0.585950			0.292975	−	0.956120i	$-0.405355\pi$
$353$	11.0090			0.585950			0.292975	+	0.956120i	$0.405355\pi$
$354$	−3.31449	+	8.00190i	−0.176163	+	0.425296i
$355$	−5.59734	+	5.99335i	−0.297076	+	0.318094i
$356$	0.619800			0.0328494
$357$	35.1987	+	9.81058i	1.86291	+	0.519231i
$358$			10.1088i			0.534268i
$359$	−13.0823	+	13.0823i	−0.690456	+	0.690456i	−0.962332	−	0.271876i	$-0.912356\pi$
$359$	−13.0823	+	13.0823i	−0.690456	+	0.690456i	0.271876	+	0.962332i	$0.412356\pi$
$360$	−13.8561	−	5.19249i	−0.730280	−	0.273668i
$361$		−	49.1378i		−	2.58620i
$362$	3.47404	−	8.38708i	0.182592	−	0.440815i
$363$	−25.7339	+	10.6593i	−1.35068	+	0.559470i
$364$	−8.20909	+	3.40032i	−0.430273	+	0.178225i
$365$	−17.2579	+	18.4788i	−0.903318	+	0.967227i
$366$	−21.2496	−	21.2496i	−1.11074	−	1.11074i
$367$	10.6352	+	25.6756i	0.555152	+	1.34026i	0.913565	+	0.406693i	$0.133318\pi$
$367$	10.6352	+	25.6756i	0.555152	+	1.34026i	−0.358413	+	0.933563i	$0.616682\pi$
$368$	4.30543	−	1.78337i	0.224436	−	0.0929644i
$369$	−21.7126	−	8.99366i	−1.13031	−	0.468191i
$370$	−0.257289	−	7.53053i	−0.0133758	−	0.391494i
$371$	−10.4298	+	25.1797i	−0.541487	+	1.30726i
$372$	0.334399	+	0.334399i	0.0173378	+	0.0173378i
$373$		−	28.2518i		−	1.46282i	−0.681936	−	0.731412i	$-0.738862\pi$
$373$		−	28.2518i		−	1.46282i	0.681936	−	0.731412i	$-0.261138\pi$
$374$	−4.61110	−	3.61222i	−0.238434	−	0.186783i
$375$	3.54627	+	34.4906i	0.183129	+	1.78109i
$376$	−3.83374	+	3.83374i	−0.197710	+	0.197710i
$377$	12.6098	+	5.22316i	0.649439	+	0.269006i
$378$	−32.0590			−1.64894
$379$	22.6222	+	9.37043i	1.16203	+	0.481327i	0.878549	−	0.477652i	$-0.158512\pi$
$379$	22.6222	+	9.37043i	1.16203	+	0.481327i	0.283477	+	0.958979i	$0.408512\pi$
$380$	7.64164	+	16.8016i	0.392008	+	0.861904i
$381$	−33.6344	+	13.9318i	−1.72314	+	0.713749i
$382$	6.60951	−	6.60951i	0.338172	−	0.338172i
$383$	12.2193	−	12.2193i	0.624379	−	0.624379i	−0.322269	−	0.946648i	$-0.604446\pi$
$383$	12.2193	−	12.2193i	0.624379	−	0.624379i	0.946648	+	0.322269i	$0.104446\pi$
$384$	2.86514	−	1.18678i	0.146211	−	0.0605625i
$385$	−8.26348	+	3.75836i	−0.421146	+	0.191544i
$386$	−11.6698	−	4.83377i	−0.593975	−	0.246033i
$387$	1.27430			0.0647765
$388$	−13.9015	−	5.75819i	−0.705742	−	0.292328i
$389$	−3.55289	+	3.55289i	−0.180139	+	0.180139i	−0.791416	−	0.611278i	$-0.790656\pi$
$389$	−3.55289	+	3.55289i	−0.180139	+	0.180139i	0.611278	+	0.791416i	$0.290656\pi$
$390$	−0.736239	−	21.5488i	−0.0372809	−	1.09117i
$391$	−2.31693	−	19.0741i	−0.117172	−	0.964620i
$392$			1.16649i			0.0589164i
$393$	−40.9386	−	40.9386i	−2.06508	−	2.06508i
$394$	9.41794	−	22.7369i	0.474469	−	1.14547i
$395$	−0.844494	−	24.7174i	−0.0424911	−	1.24367i
$396$	8.68549	+	3.59765i	0.436462	+	0.180789i
$397$	4.22575	−	1.75036i	0.212084	−	0.0878482i	−0.274112	−	0.961698i	$-0.588384\pi$
$397$	4.22575	−	1.75036i	0.212084	−	0.0878482i	0.486196	+	0.873850i	$0.338384\pi$
$398$	−0.662000	−	1.59821i	−0.0331830	−	0.0801110i
$399$	51.7281	+	51.7281i	2.58964	+	2.58964i
$400$	−3.76860	−	3.28598i	−0.188430	−	0.164299i
$401$	16.5494	−	6.85500i	0.826440	−	0.342323i	0.0709474	−	0.997480i	$-0.477398\pi$
$401$	16.5494	−	6.85500i	0.826440	−	0.342323i	0.755492	+	0.655158i	$0.227398\pi$
$402$	−19.6729	+	8.14878i	−0.981195	+	0.406424i
$403$	−0.181448	+	0.438053i	−0.00903855	+	0.0218210i
$404$		−	15.7464i		−	0.783412i
$405$	11.7215	−	31.2788i	0.582448	−	1.55426i
$406$	8.87021	−	8.87021i	0.440221	−	0.440221i
$407$			4.78721i			0.237293i
$408$	−1.54185	−	12.6933i	−0.0763328	−	0.628411i
$409$	−7.28485			−0.360213			−0.180106	−	0.983647i	$-0.557644\pi$
$409$	−7.28485			−0.360213			−0.180106	+	0.983647i	$0.557644\pi$
$410$	−5.80381	−	5.42033i	−0.286630	−	0.267691i
$411$	−1.05457	+	2.54596i	−0.0520181	+	0.125583i
$412$	7.01019			0.345367
$413$	−3.05425	+	7.37362i	−0.150290	+	0.362832i
$414$	11.8013	+	28.4909i	0.580004	+	1.40025i
$415$	4.16674	+	9.16136i	0.204537	+	0.449714i
$416$	2.19860	+	2.19860i	0.107795	+	0.107795i
$417$	−27.1394	+	27.1394i	−1.32902	+	1.32902i
$418$	−4.48768	−	10.8342i	−0.219500	−	0.529919i
$419$	−8.80767	−	21.2636i	−0.430283	−	1.03879i	−0.979196	−	0.202916i	$-0.934958\pi$
$419$	−8.80767	−	21.2636i	−0.430283	−	1.03879i	0.548913	−	0.835879i	$-0.315042\pi$
$420$	−18.5566	−	6.95396i	−0.905468	−	0.339319i
$421$			36.4149i			1.77476i	0.461043	+	0.887378i	$0.347475\pi$
$421$			36.4149i			1.77476i	−0.461043	+	0.887378i	$0.652525\pi$
$422$	−20.0957	−	8.32392i	−0.978244	−	0.405202i
$423$	−25.3696	−	25.3696i	−1.23351	−	1.23351i
$424$	9.53713			0.463164
$425$	−17.2228	+	11.3302i	−0.835430	+	0.549597i
$426$	11.3735			0.551046
$427$	−19.5812	−	19.5812i	−0.947600	−	0.947600i
$428$	−4.70686	−	1.94964i	−0.227515	−	0.0942396i
$429$			13.6987i			0.661381i
$430$	0.403211	+	0.151101i	0.0194446	+	0.00728673i
$431$	6.45751	+	15.5898i	0.311047	+	0.750934i	0.999667	+	0.0258116i	$0.00821700\pi$
$431$	6.45751	+	15.5898i	0.311047	+	0.750934i	−0.688620	+	0.725123i	$0.741783\pi$
$432$	4.29311	+	10.3645i	0.206552	+	0.498661i
$433$	11.9440	−	11.9440i	0.573991	−	0.573991i	−0.359250	−	0.933241i	$-0.616968\pi$
$433$	11.9440	−	11.9440i	0.573991	−	0.573991i	0.933241	+	0.359250i	$0.116968\pi$
$434$	0.308143	+	0.308143i	0.0147913	+	0.0147913i
$435$	12.6024	+	27.7088i	0.604240	+	1.32854i
$436$	−4.55708	−	11.0018i	−0.218244	−	0.526889i
$437$	14.7209	−	35.5394i	0.704196	−	1.70008i
$438$	35.0669			1.67556
$439$	−3.69854	+	8.92906i	−0.176521	+	0.426161i	−0.987232	−	0.159286i	$-0.949081\pi$
$439$	−3.69854	+	8.92906i	−0.176521	+	0.426161i	0.810711	+	0.585447i	$0.199081\pi$
$440$	2.32164	+	2.16824i	0.110680	+	0.103367i
$441$	−7.71916			−0.367579
$442$	11.1661	−	6.29839i	0.531117	−	0.299584i
$443$		−	2.43812i		−	0.115838i	−0.998321	−	0.0579192i	$-0.981553\pi$
$443$		−	2.43812i		−	0.115838i	0.998321	−	0.0579192i	$-0.0184466\pi$
$444$	−7.38940	+	7.38940i	−0.350685	+	0.350685i
$445$	−0.486336	+	1.29778i	−0.0230546	+	0.0615208i
$446$		−	8.09305i		−	0.383217i
$447$	−14.3975	+	34.7587i	−0.680980	+	1.64403i
$448$	2.64018	−	1.09360i	0.124737	−	0.0516676i
$449$	−19.6916	+	8.15655i	−0.929306	+	0.384931i	−0.795415	−	0.606065i	$-0.792747\pi$
$449$	−19.6916	+	8.15655i	−0.929306	+	0.384931i	−0.133891	+	0.990996i	$0.542747\pi$
$450$	21.7448	−	24.9385i	1.02506	−	1.17561i
$451$	3.56763	+	3.56763i	0.167993	+	0.167993i
$452$	−2.79122	−	6.73860i	−0.131288	−	0.316957i
$453$	10.5076	−	4.35238i	0.493689	−	0.204493i
$454$	0.436916	+	0.180977i	0.0205055	+	0.00849365i
$455$	−0.678432	−	19.8569i	−0.0318054	−	0.930906i
$456$	9.79633	−	23.6504i	0.458755	−	1.10753i
$457$	−14.0988	−	14.0988i	−0.659515	−	0.659515i	0.295750	−	0.955265i	$-0.404430\pi$
$457$	−14.0988	−	14.0988i	−0.659515	−	0.659515i	−0.955265	+	0.295750i	$0.904430\pi$
$458$			4.77172i			0.222968i
$459$	45.9173	−	5.57755i	2.14323	−	0.260338i
$460$	0.355817	+	10.4144i	0.0165901	+	0.485572i
$461$	−24.1282	+	24.1282i	−1.12376	+	1.12376i	−0.132594	+	0.991170i	$0.542331\pi$
$461$	−24.1282	+	24.1282i	−1.12376	+	1.12376i	−0.991170	+	0.132594i	$0.957669\pi$
$462$	11.6319	+	4.81810i	0.541166	+	0.224158i
$463$	−32.8930			−1.52867			−0.764333	−	0.644822i	$-0.776932\pi$
$463$	−32.8930			−1.52867			−0.764333	+	0.644822i	$0.776932\pi$
$464$	−4.05552	−	1.67985i	−0.188273	−	0.0779851i
$465$	−0.962579	+	0.437796i	−0.0446385	+	0.0203023i
$466$	−0.431013	+	0.178531i	−0.0199663	+	0.00827030i
$467$	30.3083	−	30.3083i	1.40250	−	1.40250i	0.610435	−	0.792066i	$-0.290994\pi$
$467$	30.3083	−	30.3083i	1.40250	−	1.40250i	0.792066	−	0.610435i	$-0.209006\pi$
$468$	−14.5492	+	14.5492i	−0.672535	+	0.672535i
$469$	−18.1283	+	7.50897i	−0.837085	+	0.346732i
$470$	−5.01916	−	11.0356i	−0.231516	−	0.509033i
$471$	21.9808	+	9.10476i	1.01282	+	0.419525i
$472$	2.79285			0.128551
$473$	−0.252747	−	0.104691i	−0.0116213	−	0.00481371i
$474$	−24.2541	+	24.2541i	−1.11403	+	1.11403i
$475$	−41.1766	+	2.81697i	−1.88931	+	0.129251i
$476$	−1.42079	−	11.6966i	−0.0651217	−	0.536115i
$477$			63.1114i			2.88967i
$478$	−16.8145	−	16.8145i	−0.769077	−	0.769077i
$479$	6.59739	−	15.9275i	0.301443	−	0.727747i	−0.698484	−	0.715626i	$-0.746142\pi$
$479$	6.59739	−	15.9275i	0.301443	−	0.727747i	0.999927	−	0.0121210i	$-0.00385834\pi$
$480$	0.236786	+	6.93045i	0.0108078	+	0.316330i
$481$	−9.67991	−	4.00955i	−0.441366	−	0.182820i
$482$	−24.7628	+	10.2571i	−1.12791	+	0.467198i
$483$	15.8048	+	38.1561i	0.719141	+	1.73616i
$484$	6.35105	+	6.35105i	0.288684	+	0.288684i
$485$	22.9650	−	24.5897i	1.04278	−	1.11656i
$486$	−11.7067	+	4.84908i	−0.531028	+	0.219959i
$487$	−0.559836	+	0.231892i	−0.0253686	+	0.0105080i	−0.395332	−	0.918538i	$-0.629370\pi$
$487$	−0.559836	+	0.231892i	−0.0253686	+	0.0105080i	0.369963	+	0.929046i	$0.379370\pi$
$488$	−3.70831	+	8.95265i	−0.167867	+	0.405268i
$489$			15.7368i			0.711643i
$490$	−2.44247	−	0.915302i	−0.110340	−	0.0413491i
$491$	7.58558	−	7.58558i	0.342332	−	0.342332i	−0.514911	−	0.857244i	$-0.672175\pi$
$491$	7.58558	−	7.58558i	0.342332	−	0.342332i	0.857244	+	0.514911i	$0.172175\pi$
$492$			11.0138i			0.496539i
$493$	−11.1614	+	14.2478i	−0.502682	+	0.641688i
$494$	25.6659			1.15476
$495$	−14.3482	+	15.3633i	−0.644904	+	0.690531i
$496$	0.0583565	−	0.140885i	0.00262028	−	0.00632592i
$497$	10.4805			0.470113
$498$	5.34162	−	12.8958i	0.239363	−	0.577875i
$499$	12.9866	+	31.3524i	0.581359	+	1.40353i	0.891581	+	0.452861i	$0.149597\pi$
$499$	12.9866	+	31.3524i	0.581359	+	1.40353i	−0.310222	+	0.950664i	$0.600403\pi$
$500$	9.83751	−	5.31256i	0.439947	−	0.237585i
$501$	11.6419	+	11.6419i	0.520121	+	0.520121i
$502$	20.1249	−	20.1249i	0.898216	−	0.898216i
$503$	−6.59797	−	15.9289i	−0.294189	−	0.710235i	−0.999998	−	0.00183309i	$-0.999417\pi$
$503$	−6.59797	−	15.9289i	−0.294189	−	0.710235i	0.705809	−	0.708402i	$-0.250583\pi$
$504$	7.23682	+	17.4712i	0.322354	+	0.778230i
$505$	32.9709	+	12.3557i	1.46719	+	0.549819i
$506$		−	6.62047i		−	0.294316i
$507$	9.54742	+	3.95467i	0.424016	+	0.175633i
$508$	8.30087	+	8.30087i	0.368291	+	0.368291i
$509$	29.7197			1.31730			0.658651	−	0.752448i	$-0.271127\pi$
$509$	29.7197			1.31730			0.658651	+	0.752448i	$0.271127\pi$
$510$	27.7879	+	6.73155i	1.23047	+	0.298078i
$511$	32.3136			1.42947
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	85.5542	+	35.4377i	3.77731	+	1.56461i
$514$		−	13.6836i		−	0.603557i
$515$	−5.50066	+	14.6784i	−0.242388	+	0.646810i
$516$	−0.228535	−	0.551731i	−0.0100607	−	0.0242886i
$517$	2.94758	+	7.11609i	0.129634	+	0.312965i
$518$	−6.80921	+	6.80921i	−0.299179	+	0.299179i
$519$	−7.73106	−	7.73106i	−0.339356	−	0.339356i
$520$	−6.32877	+	2.87843i	−0.277535	+	0.126227i
$521$	11.0879	+	26.7685i	0.485769	+	1.17275i	0.956830	+	0.290649i	$0.0938712\pi$
$521$	11.0879	+	26.7685i	0.485769	+	1.17275i	−0.471061	+	0.882101i	$0.656129\pi$
$522$	11.1163	−	26.8372i	0.486548	−	1.17463i
$523$	2.06831			0.0904407			0.0452204	−	0.998977i	$-0.485601\pi$
$523$	2.06831			0.0904407			0.0452204	+	0.998977i	$0.485601\pi$
$524$	−7.14427	+	17.2478i	−0.312099	+	0.753473i
$525$	29.1214	−	33.3985i	1.27096	−	1.45763i
$526$	19.1990			0.837116
$527$	−0.494955	−	0.387735i	−0.0215606	−	0.0168900i
$528$		−	4.40573i		−	0.191735i
$529$	−0.907159	+	0.907159i	−0.0394417	+	0.0394417i
$530$	−7.48346	+	19.9695i	−0.325061	+	0.867421i
$531$			18.4815i			0.802031i
$532$	9.02716	−	21.7935i	0.391377	−	0.944868i
$533$	−10.2020	+	4.22579i	−0.441896	+	0.183039i
$534$	1.77581	−	0.735566i	0.0768469	−	0.0318310i
$535$	7.77562	−	8.32574i	0.336169	−	0.359953i
$536$	4.85521	+	4.85521i	0.209713	+	0.209713i
$537$	11.9969	+	28.9632i	0.517706	+	1.24985i
$538$	10.5399	−	4.36575i	0.454406	−	0.188221i
$539$	1.53103	+	0.634172i	0.0659460	+	0.0273157i
$540$	−25.0705	+	0.856561i	−1.07886	+	0.0368605i
$541$	7.00518	−	16.9120i	0.301176	−	0.727103i	−0.698755	−	0.715361i	$-0.746262\pi$
$541$	7.00518	−	16.9120i	0.301176	−	0.727103i	0.999931	−	0.0117424i	$-0.00373780\pi$
$542$	−6.19945	−	6.19945i	−0.266289	−	0.266289i
$543$		−	28.1530i		−	1.20816i
$544$	−3.59120	+	2.02566i	−0.153971	+	0.0868496i
$545$	26.6121	−	0.909229i	1.13994	−	0.0389471i
$546$	−19.4847	+	19.4847i	−0.833870	+	0.833870i
$547$	−24.5635	−	10.1745i	−1.05026	−	0.435031i	−0.210275	−	0.977642i	$-0.567436\pi$
$547$	−24.5635	−	10.1745i	−1.05026	−	0.435031i	−0.839984	+	0.542611i	$0.817436\pi$
$548$	0.888599			0.0379591
$549$	−59.2437	−	24.5395i	−2.52846	−	1.04732i
$550$	−6.36173	+	3.15988i	−0.271265	+	0.134738i
$551$	−33.4765	+	13.8664i	−1.42615	+	0.590730i
$552$	10.2192	−	10.2192i	0.434957	−	0.434957i
$553$	−22.3498	+	22.3498i	−0.950409	+	0.950409i
$554$	−2.04090	+	0.845370i	−0.0867097	+	0.0359163i
$555$	−9.67424	−	21.2707i	−0.410649	−	0.902889i
$556$	11.4341	+	4.73615i	0.484913	+	0.200858i
$557$	−26.4035			−1.11875			−0.559375	−	0.828914i	$-0.688959\pi$
$557$	−26.4035			−1.11875			−0.559375	+	0.828914i	$0.688959\pi$
$558$	0.932299	+	0.386171i	0.0394674	+	0.0163479i
$559$	0.423379	−	0.423379i	0.0179070	−	0.0179070i
$560$	0.218195	+	6.38630i	0.00922041	+	0.269870i
$561$	−17.4983	−	4.87714i	−0.738780	−	0.205913i
$562$			1.56729i			0.0661120i
$563$	21.2367	+	21.2367i	0.895019	+	0.895019i	0.994990	−	0.0999709i	$-0.0318750\pi$
$563$	21.2367	+	21.2367i	0.895019	+	0.895019i	−0.0999709	+	0.994990i	$0.531875\pi$
$564$	−6.43439	+	15.5340i	−0.270937	+	0.654099i
$565$	16.2999	−	0.556904i	0.685743	−	0.0234291i
$566$	−9.47815	−	3.92598i	−0.398396	−	0.165021i
$567$	−39.4396	+	16.3364i	−1.65631	+	0.686066i
$568$	−1.40347	−	3.38827i	−0.0588882	−	0.142169i
$569$	−4.00087	−	4.00087i	−0.167725	−	0.167725i	0.618253	−	0.785979i	$-0.287841\pi$
$569$	−4.00087	−	4.00087i	−0.167725	−	0.167725i	−0.785979	+	0.618253i	$0.787841\pi$
$570$	41.8341	+	39.0700i	1.75224	+	1.63646i
$571$	−15.9703	+	6.61510i	−0.668335	+	0.276833i	−0.690941	−	0.722911i	$-0.742804\pi$
$571$	−15.9703	+	6.61510i	−0.668335	+	0.276833i	0.0226061	+	0.999744i	$0.492804\pi$
$572$	4.08099	−	1.69040i	0.170635	−	0.0706793i
$573$	11.0931	−	26.7812i	0.463422	−	1.11880i
$574$			10.1490i			0.423612i
$575$	−22.0855	−	7.42676i	−0.921030	−	0.309717i
$576$	4.67924	−	4.67924i	0.194968	−	0.194968i
$577$		−	18.3530i		−	0.764047i	−0.924153	−	0.382024i	$-0.875227\pi$
$577$		−	18.3530i		−	0.764047i	0.924153	−	0.382024i	$-0.124773\pi$
$578$	4.06992	+	16.5056i	0.169286	+	0.686544i
$579$	−39.1721			−1.62794
$580$	6.69962	−	7.17362i	0.278187	−	0.297868i
$581$	4.92221	−	11.8833i	0.204208	−	0.493001i
$582$	−46.6634			−1.93426
$583$	5.18496	−	12.5176i	0.214739	−	0.518426i
$584$	−4.32721	−	10.4468i	−0.179061	−	0.432292i
$585$	−19.0478	−	41.8803i	−0.787531	−	1.73154i
$586$	−3.12342	−	3.12342i	−0.129027	−	0.129027i
$587$	17.7752	−	17.7752i	0.733660	−	0.733660i	−0.237683	−	0.971343i	$-0.576388\pi$
$587$	17.7752	−	17.7752i	0.733660	−	0.733660i	0.971343	+	0.237683i	$0.0763880\pi$
$588$	1.38436	+	3.34214i	0.0570900	+	0.137828i
$589$	−0.481707	−	1.16294i	−0.0198484	−	0.0479183i
$590$	−2.19146	+	5.84787i	−0.0902208	+	0.240753i
$591$		−	76.3214i		−	3.13944i
$592$	3.11322	+	1.28954i	0.127952	+	0.0529996i
$593$	3.43407	+	3.43407i	0.141020	+	0.141020i	0.774093	−	0.633072i	$-0.218206\pi$
$593$	3.43407	+	3.43407i	0.141020	+	0.141020i	−0.633072	+	0.774093i	$0.718206\pi$
$594$	15.9375			0.653924
$595$	25.6061	+	6.20302i	1.04975	+	0.254299i
$596$	12.1316			0.496930
$597$	−3.79344	−	3.79344i	−0.155255	−	0.155255i
$598$	13.3868	+	5.54501i	0.547429	+	0.226752i
$599$			4.34894i			0.177693i	0.996045	+	0.0888465i	$0.0283180\pi$
$599$			4.34894i			0.177693i	−0.996045	+	0.0888465i	$0.971682\pi$
$600$	−14.6973	−	4.94229i	−0.600014	−	0.201768i
$601$	−0.860720	−	2.07796i	−0.0351095	−	0.0847619i	0.905352	−	0.424662i	$-0.139607\pi$
$601$	−0.860720	−	2.07796i	−0.0351095	−	0.0847619i	−0.940462	+	0.339900i	$0.889607\pi$
$602$	−0.210591	−	0.508411i	−0.00858304	−	0.0207213i
$603$	−32.1291	+	32.1291i	−1.30840	+	1.30840i
$604$	−2.59324	−	2.59324i	−0.105517	−	0.105517i
$605$	−18.2817	+	8.31483i	−0.743258	+	0.338046i
$606$	−18.6875	−	45.1155i	−0.759126	−	1.83269i
$607$	−7.92457	+	19.1316i	−0.321648	+	0.776528i	0.677510	+	0.735513i	$0.263059\pi$
$607$	−7.92457	+	19.1316i	−0.321648	+	0.776528i	−0.999159	+	0.0410146i	$0.986941\pi$
$608$	−8.25456			−0.334767
$609$	14.8874	−	35.9413i	0.603267	−	1.45642i
$610$	−15.8359	−	14.7896i	−0.641178	−	0.598812i
$611$	−16.8578			−0.681992
$612$	−13.4047	−	23.7645i	−0.541854	−	0.960625i
$613$			26.3783i			1.06541i	0.846302	+	0.532704i	$0.178824\pi$
$613$			26.3783i			1.06541i	−0.846302	+	0.532704i	$0.821176\pi$
$614$	−13.4067	+	13.4067i	−0.541049	+	0.541049i
$615$	−23.0614	−	8.64214i	−0.929927	−	0.348485i
$616$		−	4.05981i		−	0.163574i
$617$	12.1971	−	29.4464i	0.491037	−	1.18547i	−0.463156	−	0.886277i	$-0.653283\pi$
$617$	12.1971	−	29.4464i	0.491037	−	1.18547i	0.954193	−	0.299191i	$-0.0967168\pi$
$618$	20.0852	−	8.31955i	0.807944	−	0.334661i
$619$	14.7541	−	6.11135i	0.593018	−	0.245636i	−0.0659305	−	0.997824i	$-0.521002\pi$
$619$	14.7541	−	6.11135i	0.593018	−	0.245636i	0.658948	+	0.752188i	$0.271002\pi$
$620$	0.249205	+	0.232739i	0.0100083	+	0.00934701i
$621$	36.9673	+	36.9673i	1.48345	+	1.48345i
$622$	4.19890	+	10.1370i	0.168361	+	0.406459i
$623$	1.63638	−	0.677812i	0.0655603	−	0.0271560i
$624$	8.90856	+	3.69005i	0.356628	+	0.147720i
$625$	3.40466	+	24.7671i	0.136187	+	0.990683i
$626$	8.33889	−	20.1319i	0.333289	−	0.804631i
$627$	−25.7156	−	25.7156i	−1.02698	−	1.02698i
$628$		−	7.67183i		−	0.306139i
$629$	8.56800	−	10.9373i	0.341629	−	0.436099i
$630$	−42.2610	+	1.44389i	−1.68372	+	0.0575260i
$631$	−8.23073	+	8.23073i	−0.327660	+	0.327660i	−0.851696	−	0.524036i	$-0.824426\pi$
$631$	−8.23073	+	8.23073i	−0.327660	+	0.327660i	0.524036	+	0.851696i	$0.324426\pi$
$632$	10.2185	+	4.23263i	0.406469	+	0.168365i
$633$	−67.4556			−2.68112
$634$	16.7175	+	6.92463i	0.663938	+	0.275012i
$635$	−23.8944	+	10.8675i	−0.948219	+	0.431265i
$636$	27.3252	−	11.3185i	1.08351	−	0.448806i
$637$	−2.56464	+	2.56464i	−0.101615	+	0.101615i
$638$	−4.40965	+	4.40965i	−0.174580	+	0.174580i
$639$	22.4217	−	9.28737i	0.886988	−	0.367403i
$640$	2.03543	−	0.925748i	0.0804576	−	0.0365934i
$641$	−11.2760	−	4.67068i	−0.445376	−	0.184481i	0.148712	−	0.988880i	$-0.452487\pi$
$641$	−11.2760	−	4.67068i	−0.445376	−	0.184481i	−0.594089	+	0.804400i	$0.702487\pi$
$642$	−15.7996			−0.623560
$643$	25.2352	+	10.4528i	0.995180	+	0.412217i	0.820027	−	0.572324i	$-0.193958\pi$
$643$	25.2352	+	10.4528i	0.995180	+	0.412217i	0.175152	+	0.984541i	$0.443958\pi$
$644$	9.41680	−	9.41680i	0.371074	−	0.371074i
$645$	1.33458	−	0.0455972i	0.0525489	−	0.00179539i
$646$	−9.13779	+	32.7848i	−0.359521	+	1.28990i
$647$			4.28386i			0.168416i	0.996448	+	0.0842080i	$0.0268360\pi$
$647$			4.28386i			0.168416i	−0.996448	+	0.0842080i	$0.973164\pi$
$648$	10.5629	+	10.5629i	0.414952	+	0.414952i
$649$	1.51836	−	3.66565i	0.0596010	−	0.143889i
$650$	−1.06109	−	15.5102i	−0.0416192	−	0.608361i
$651$	1.24857	+	0.517174i	0.0489352	+	0.0202696i
$652$	4.68816	−	1.94190i	0.183602	−	0.0760506i
$653$	4.87695	+	11.7740i	0.190850	+	0.460753i	0.990121	−	0.140219i	$-0.0447806\pi$
$653$	4.87695	+	11.7740i	0.190850	+	0.460753i	−0.799271	+	0.600971i	$0.794781\pi$
$654$	−26.1133	−	26.1133i	−1.02111	−	1.02111i
$655$	−30.5088	−	28.4929i	−1.19208	−	1.11331i
$656$	3.28112	−	1.35908i	0.128106	−	0.0530633i
$657$	69.1311	−	28.6351i	2.69706	−	1.11716i
$658$	−5.92919	+	14.3143i	−0.231144	+	0.558030i
$659$		−	0.677458i		−	0.0263900i	−0.999913	−	0.0131950i	$-0.995800\pi$
$659$		−	0.677458i		−	0.0263900i	0.999913	−	0.0131950i	$-0.00420023\pi$
$660$	9.22504	+	3.45703i	0.359084	+	0.134565i
$661$	−12.6544	+	12.6544i	−0.492200	+	0.492200i	−0.908999	−	0.416799i	$-0.863152\pi$
$661$	−12.6544	+	12.6544i	−0.492200	+	0.492200i	0.416799	+	0.908999i	$0.363152\pi$
$662$			25.1226i			0.976417i
$663$	24.5176	−	31.2974i	0.952184	−	1.21549i
$664$	−4.50094			−0.174670
$665$	38.5495	+	36.0023i	1.49488	+	1.39611i
$666$	−8.53344	+	20.6015i	−0.330664	+	0.798294i
$667$	−20.4565			−0.792080
$668$	2.03164	−	4.90482i	0.0786067	−	0.189773i
$669$	−9.60465	−	23.1877i	−0.371337	−	0.896488i
$670$	−13.9759	+	6.35647i	−0.539936	+	0.245572i
$671$	9.73441	+	9.73441i	0.375793	+	0.375793i
$672$	6.26661	−	6.26661i	0.241740	−	0.241740i
$673$	17.2508	+	41.6470i	0.664968	+	1.60538i	0.789918	+	0.613213i	$0.210123\pi$
$673$	17.2508	+	41.6470i	0.664968	+	1.60538i	−0.124949	+	0.992163i	$0.539877\pi$
$674$	2.32517	+	5.61346i	0.0895623	+	0.216223i
$675$	17.8785	−	53.1666i	0.688143	−	2.04638i
$676$		−	3.33227i		−	0.128164i
$677$	35.5853	+	14.7399i	1.36766	+	0.566501i	0.941152	−	0.337984i	$-0.109745\pi$
$677$	35.5853	+	14.7399i	1.36766	+	0.566501i	0.426504	+	0.904486i	$0.359745\pi$
$678$	−15.9944	−	15.9944i	−0.614263	−	0.614263i
$679$	−42.9996			−1.65017
$680$	−1.42359	−	9.10897i	−0.0545922	−	0.349313i
$681$	1.46660			0.0562004
$682$	−0.153187	−	0.153187i	−0.00586585	−	0.00586585i
$683$	31.7607	+	13.1557i	1.21529	+	0.503390i	0.895909	−	0.444237i	$-0.146525\pi$
$683$	31.7607	+	13.1557i	1.21529	+	0.503390i	0.319381	+	0.947626i	$0.396525\pi$
$684$		−	54.6241i		−	2.08861i
$685$	−0.697254	+	1.86061i	−0.0266407	+	0.0710904i
$686$	−6.37951	−	15.4015i	−0.243571	−	0.588032i
$687$	5.66298	+	13.6716i	0.216056	+	0.521605i
$688$	−0.136166	+	0.136166i	−0.00519126	+	0.00519126i
$689$	20.9684	+	20.9684i	0.798831	+	0.798831i
$690$	13.3790	+	29.4163i	0.509330	+	1.11986i
$691$	4.51976	+	10.9117i	0.171940	+	0.415100i	0.986235	−	0.165352i	$-0.0528760\pi$
$691$	4.51976	+	10.9117i	0.171940	+	0.415100i	−0.814295	+	0.580452i	$0.802876\pi$
$692$	−1.34916	+	3.25716i	−0.0512874	+	0.123819i
$693$	26.8656			1.02054
$694$	−6.01683	+	14.5259i	−0.228396	+	0.551396i
$695$	−18.8888	+	20.2252i	−0.716494	+	0.767186i
$696$	−13.6132			−0.516008
$697$	−1.76570	−	14.5362i	−0.0668808	−	0.550597i
$698$		−	7.57358i		−	0.286664i
$699$	−1.02303	+	1.02303i	−0.0386946	+	0.0386946i
$700$	−13.5433	−	4.55424i	−0.511889	−	0.172134i
$701$		−	7.71882i		−	0.291536i	−0.989319	−	0.145768i	$-0.953435\pi$
$701$		−	7.71882i		−	0.291536i	0.989319	−	0.145768i	$-0.0465653\pi$
$702$	−13.3485	+	32.2262i	−0.503808	+	1.21630i
$703$	25.6982	−	10.6446i	0.969227	−	0.401467i
$704$	−1.31251	+	0.543661i	−0.0494672	+	0.0204900i
$705$	−27.4773	−	25.6618i	−1.03486	−	0.966479i
$706$	−7.78454	−	7.78454i	−0.292975	−	0.292975i
$707$	−17.2202	−	41.5732i	−0.647632	−	1.56352i
$708$	8.00190	−	3.31449i	0.300730	−	0.124566i
$709$	9.40945	+	3.89752i	0.353379	+	0.146375i	0.552309	−	0.833639i	$-0.313747\pi$
$709$	9.40945	+	3.89752i	0.353379	+	0.146375i	−0.198930	+	0.980014i	$0.563747\pi$
$710$	8.19585	−	0.280020i	0.307585	−	0.0105090i
$711$	−28.0092	+	67.6202i	−1.05043	+	2.53595i
$712$	−0.438265	−	0.438265i	−0.0164247	−	0.0164247i
$713$		−	0.710641i		−	0.0266137i
$714$	−17.9521	−	31.8263i	−0.671840	−	1.19107i
$715$	0.337269	+	9.87148i	0.0126132	+	0.369172i
$716$	7.14802	−	7.14802i	0.267134	−	0.267134i
$717$	−68.1309	−	28.2207i	−2.54440	−	1.05392i
$718$	18.5011			0.690456
$719$	24.2288	+	10.0359i	0.903580	+	0.374275i	0.785596	−	0.618740i	$-0.212357\pi$
$719$	24.2288	+	10.0359i	0.903580	+	0.374275i	0.117985	+	0.993015i	$0.462357\pi$
$720$	6.12609	+	13.4694i	0.228306	+	0.501974i
$721$	18.5081	−	7.66633i	0.689279	−	0.285509i
$722$	−34.7456	+	34.7456i	−1.29310	+	1.29310i
$723$	−58.7759	+	58.7759i	−2.18590	+	2.18590i
$724$	−8.38708	+	3.47404i	−0.311703	+	0.129112i
$725$	9.76367	+	19.6570i	0.362613	+	0.730044i
$726$	25.7339	+	10.6593i	0.955075	+	0.395605i
$727$	−34.1904			−1.26805			−0.634026	−	0.773312i	$-0.718599\pi$
$727$	−34.1904			−1.26805			−0.634026	+	0.773312i	$0.718599\pi$
$728$	8.20909	+	3.40032i	0.304249	+	0.126024i
$729$	3.90227	−	3.90227i	0.144529	−	0.144529i
$730$	25.2697	−	0.863365i	0.935273	−	0.0319546i
$731$	0.390076	+	0.691546i	0.0144275	+	0.0255778i
$732$			30.0515i			1.11074i
$733$	0.290284	+	0.290284i	0.0107219	+	0.0107219i	0.712447	−	0.701726i	$-0.247587\pi$
$733$	0.290284	+	0.290284i	0.0107219	+	0.0107219i	−0.701726	+	0.712447i	$0.747587\pi$
$734$	10.6352	−	25.6756i	0.392552	−	0.947704i
$735$	−8.08427	+	0.276208i	−0.298193	+	0.0101881i
$736$	−4.30543	−	1.78337i	−0.158700	−	0.0657357i
$737$	9.01211	−	3.73294i	0.331965	−	0.137505i
$738$	8.99366	+	21.7126i	0.331061	+	0.799252i
$739$	−14.1478	−	14.1478i	−0.520435	−	0.520435i	0.397268	−	0.917703i	$-0.369958\pi$
$739$	−14.1478	−	14.1478i	−0.520435	−	0.520435i	−0.917703	+	0.397268i	$0.869958\pi$
$740$	−5.14296	+	5.50682i	−0.189059	+	0.202435i
$741$	73.5362	−	30.4597i	2.70142	−	1.11897i
$742$	25.1797	−	10.4298i	0.924376	−	0.382889i
$743$	−4.43181	+	10.6993i	−0.162588	+	0.392521i	−0.984087	−	0.177689i	$-0.943138\pi$
$743$	−4.43181	+	10.6993i	−0.162588	+	0.392521i	0.821499	+	0.570210i	$0.193138\pi$
$744$		−	0.472911i		−	0.0173378i
$745$	−9.51927	+	25.4020i	−0.348759	+	0.930659i
$746$	−19.9771	+	19.9771i	−0.731412	+	0.731412i
$747$		−	29.7847i		−	1.08977i
$748$	0.706317	+	5.81477i	0.0258255	+	0.212609i
$749$	−14.5591			−0.531977
$750$	21.8810	−	26.8962i	0.798980	−	0.982109i
$751$	−5.40995	+	13.0608i	−0.197412	+	0.476594i	−0.991324	−	0.131438i	$-0.958041\pi$
$751$	−5.40995	+	13.0608i	−0.197412	+	0.476594i	0.793913	+	0.608032i	$0.208041\pi$
$752$	5.42173			0.197710
$753$	33.7767	−	81.5442i	1.23089	−	2.97164i
$754$	−5.22316	−	12.6098i	−0.190216	−	0.459222i
$755$	7.46473	−	3.39508i	0.271669	−	0.123560i
$756$	22.6691	+	22.6691i	0.824468	+	0.824468i
$757$	30.4429	−	30.4429i	1.10647	−	1.10647i	0.112856	−	0.993611i	$-0.464000\pi$
$757$	30.4429	−	30.4429i	1.10647	−	1.10647i	0.993611	−	0.112856i	$-0.0359999\pi$
$758$	−9.37043	−	22.6222i	−0.340349	−	0.821676i
$759$	−7.85703	−	18.9686i	−0.285192	−	0.688515i
$760$	6.47707	−	17.2840i	0.234948	−	0.626956i
$761$		−	46.1433i		−	1.67269i	−0.548200	−	0.836347i	$-0.684687\pi$
$761$		−	46.1433i		−	1.67269i	0.548200	−	0.836347i	$-0.315313\pi$
$762$	33.6344	+	13.9318i	1.21845	+	0.504697i
$763$	−24.0630	−	24.0630i	−0.871138	−	0.871138i
$764$	−9.34726			−0.338172
$765$	60.2781	−	9.42053i	2.17936	−	0.340600i
$766$	−17.2807			−0.624379
$767$	6.14038	+	6.14038i	0.221716	+	0.221716i
$768$	−2.86514	−	1.18678i	−0.103387	−	0.0428242i
$769$			39.3018i			1.41726i	0.705580	+	0.708630i	$0.250687\pi$
$769$			39.3018i			1.41726i	−0.705580	+	0.708630i	$0.749313\pi$
$770$	8.50073	+	3.18560i	0.306345	+	0.114801i
$771$	−16.2394	−	39.2054i	−0.584847	−	1.41195i
$772$	4.83377	+	11.6698i	0.173971	+	0.420004i
$773$	−9.84072	+	9.84072i	−0.353946	+	0.353946i	−0.861576	−	0.507629i	$-0.830522\pi$
$773$	−9.84072	+	9.84072i	−0.353946	+	0.353946i	0.507629	+	0.861576i	$0.330522\pi$
$774$	−0.901068	−	0.901068i	−0.0323882	−	0.0323882i
$775$	−0.682868	+	0.339181i	−0.0245293	+	0.0121837i
$776$	5.75819	+	13.9015i	0.206707	+	0.499035i
$777$	−11.4283	+	27.5903i	−0.409988	+	0.989798i
$778$	5.02454			0.180139
$779$	11.2186	−	27.0842i	0.401949	−	0.970391i
$780$	−14.7167	+	15.7579i	−0.526943	+	0.564224i
$781$	−5.21016			−0.186434
$782$	−11.8491	+	15.1258i	−0.423724	+	0.540896i
$783$		−	49.2451i		−	1.75988i
$784$	0.824830	−	0.824830i	0.0294582	−	0.0294582i
$785$	16.0638	+	6.01983i	0.573343	+	0.214857i
$786$			57.8959i			2.06508i
$787$	−14.2061	+	34.2966i	−0.506394	+	1.22254i	0.439552	+	0.898217i	$0.355137\pi$
$787$	−14.2061	+	34.2966i	−0.506394	+	1.22254i	−0.945946	+	0.324325i	$0.894863\pi$
$788$	−22.7369	+	9.41794i	−0.809969	+	0.335500i
$789$	55.0078	−	22.7850i	1.95833	−	0.811166i
$790$	−16.8807	+	18.0750i	−0.600587	+	0.643078i
$791$	−14.7386	−	14.7386i	−0.524045	−	0.524045i
$792$	−3.59765	−	8.68549i	−0.127837	−	0.308625i
$793$	−27.8365	+	11.5302i	−0.988501	+	0.409451i
$794$	−4.22575	−	1.75036i	−0.149966	−	0.0621181i
$795$	2.25826	+	66.0966i	0.0800922	+	2.34420i
$796$	−0.662000	+	1.59821i	−0.0234640	+	0.0566470i
$797$	10.6688	+	10.6688i	0.377909	+	0.377909i	0.870347	−	0.492439i	$-0.163894\pi$
$797$	10.6688	+	10.6688i	0.377909	+	0.377909i	−0.492439	+	0.870347i	$0.663894\pi$
$798$		−	73.1546i		−	2.58964i
$799$	6.00185	−	21.5336i	0.212330	−	0.761804i
$800$	0.341262	+	4.98834i	0.0120654	+	0.176364i
$801$	2.90020	−	2.90020i	0.102473	−	0.102473i
$802$	−16.5494	−	6.85500i	−0.584381	−	0.242059i
$803$	−16.0641			−0.566890
$804$	19.6729	+	8.14878i	0.693809	+	0.287385i
$805$	12.3285	+	27.1066i	0.434524	+	0.955383i
$806$	0.438053	−	0.181448i	0.0154298	−	0.00639122i
$807$	25.0169	−	25.0169i	0.880638	−	0.880638i
$808$	−11.1344	+	11.1344i	−0.391706	+	0.391706i
$809$	−12.8751	+	5.33306i	−0.452666	+	0.187500i	−0.597355	−	0.801977i	$-0.703782\pi$
$809$	−12.8751	+	5.33306i	−0.452666	+	0.187500i	0.144689	+	0.989477i	$0.453782\pi$
$810$	−30.4058	+	13.8291i	−1.06835	+	0.485904i
$811$	−14.3402	−	5.93992i	−0.503554	−	0.208579i	0.116422	−	0.993200i	$-0.462858\pi$
$811$	−14.3402	−	5.93992i	−0.503554	−	0.208579i	−0.619976	+	0.784621i	$0.712858\pi$
$812$	−12.5444			−0.440221
$813$	−25.1196	−	10.4049i	−0.880984	−	0.364916i
$814$	3.38507	−	3.38507i	0.118647	−	0.118647i
$815$	0.387448	+	11.3401i	0.0135717	+	0.397228i
$816$	−7.88525	+	10.0658i	−0.276039	+	0.352372i
$817$			1.58956i			0.0556116i
$818$	5.15117	+	5.15117i	0.180106	+	0.180106i
$819$	−22.5014	+	54.3232i	−0.786263	+	1.89821i
$820$	0.271164	+	7.93666i	0.00946947	+	0.277160i
$821$	−18.6515	−	7.72572i	−0.650943	−	0.269630i	0.0326785	−	0.999466i	$-0.489596\pi$
$821$	−18.6515	−	7.72572i	−0.650943	−	0.269630i	−0.683622	+	0.729836i	$0.739596\pi$
$822$	2.54596	−	1.05457i	0.0888005	−	0.0367824i
$823$	−4.57040	−	11.0339i	−0.159314	−	0.384618i	0.823986	−	0.566610i	$-0.191745\pi$
$823$	−4.57040	−	11.0339i	−0.159314	−	0.384618i	−0.983300	+	0.181992i	$0.941745\pi$
$824$	−4.95696	−	4.95696i	−0.172684	−	0.172684i
$825$	−14.4772	+	16.6034i	−0.504030	+	0.578058i
$826$	7.37362	−	3.05425i	0.256561	−	0.106271i
$827$	−18.1526	+	7.51905i	−0.631227	+	0.261463i	−0.675275	−	0.737566i	$-0.735975\pi$
$827$	−18.1526	+	7.51905i	−0.631227	+	0.261463i	0.0440471	+	0.999029i	$0.485975\pi$
$828$	11.8013	−	28.4909i	0.410124	−	0.990128i
$829$			3.19831i			0.111082i	0.998456	+	0.0555410i	$0.0176883\pi$
$829$			3.19831i			0.111082i	−0.998456	+	0.0555410i	$0.982312\pi$
$830$	3.53173	−	9.42439i	0.122588	−	0.327125i
$831$	−4.84420	+	4.84420i	−0.168043	+	0.168043i
$832$		−	3.10930i		−	0.107795i
$833$	−2.36291	−	4.18908i	−0.0818699	−	0.145143i
$834$	38.3810			1.32902
$835$	8.67591	+	8.10265i	0.300242	+	0.280404i
$836$	−4.48768	+	10.8342i	−0.155210	+	0.374709i
$837$	1.71073			0.0591315
$838$	−8.80767	+	21.2636i	−0.304256	+	0.734539i
$839$	−16.8215	−	40.6108i	−0.580744	−	1.40204i	−0.892140	−	0.451760i	$-0.850796\pi$
$839$	−16.8215	−	40.6108i	−0.580744	−	1.40204i	0.311395	−	0.950280i	$-0.399204\pi$
$840$	8.20428	+	18.0387i	0.283074	+	0.622393i
$841$	−6.88075	−	6.88075i	−0.237267	−	0.237267i
$842$	25.7493	−	25.7493i	0.887378	−	0.887378i
$843$	1.86002	+	4.49049i	0.0640625	+	0.154661i
$844$	8.32392	+	20.0957i	0.286521	+	0.691723i
$845$	6.97735	+	2.61472i	0.240028	+	0.0899492i
$846$			35.8780i			1.23351i
$847$	23.7134	+	9.82241i	0.814802	+	0.337502i
$848$	−6.74377	−	6.74377i	−0.231582	−	0.231582i
$849$	−31.8155			−1.09190
$850$	20.1901	+	4.16669i	0.692513	+	0.142916i
$851$	15.7034			0.538307
$852$	−8.04225	−	8.04225i	−0.275523	−	0.275523i
$853$	−30.8517	−	12.7792i	−1.05634	−	0.437551i	−0.214191	−	0.976792i	$-0.568711\pi$
$853$	−30.8517	−	12.7792i	−1.05634	−	0.437551i	−0.842152	+	0.539241i	$0.818711\pi$
$854$			27.6920i			0.947600i
$855$	114.376	+	42.8617i	3.91157	+	1.46584i
$856$	1.94964	+	4.70686i	0.0666375	+	0.160877i
$857$	16.6682	+	40.2406i	0.569375	+	1.37459i	0.902083	+	0.431563i	$0.142038\pi$
$857$	16.6682	+	40.2406i	0.569375	+	1.37459i	−0.332707	+	0.943030i	$0.607962\pi$
$858$	9.68647	−	9.68647i	0.330691	−	0.330691i
$859$	10.5216	+	10.5216i	0.358992	+	0.358992i	0.863441	−	0.504449i	$-0.168304\pi$
$859$	10.5216	+	10.5216i	0.358992	+	0.358992i	−0.504449	+	0.863441i	$0.668304\pi$
$860$	−0.178269	−	0.391958i	−0.00607891	−	0.0133656i
$861$	12.0446	+	29.0783i	0.410480	+	0.990986i
$862$	6.45751	−	15.5898i	0.219944	−	0.530991i
$863$	−5.56154			−0.189317			−0.0946585	−	0.995510i	$-0.530176\pi$
$863$	−5.56154			−0.189317			−0.0946585	+	0.995510i	$0.530176\pi$
$864$	4.29311	−	10.3645i	0.146054	−	0.352607i
$865$	−5.76144	−	5.38075i	−0.195895	−	0.182951i
$866$	−16.8913			−0.573991
$867$	31.2494	+	42.4608i	1.06128	+	1.44204i
$868$		−	0.435780i		−	0.0147913i
$869$	11.1108	−	11.1108i	0.376907	−	0.376907i
$870$	10.6818	−	28.5044i	0.362148	−	0.966388i
$871$			21.3494i			0.723396i
$872$	−4.55708	+	11.0018i	−0.154322	+	0.372567i
$873$	−91.9925	+	38.1045i	−3.11347	+	1.28964i
$874$	−35.5394	+	14.7209i	−1.20214	+	0.497942i
$875$	20.1630	−	24.7844i	0.681633	−	0.837865i
$876$	−24.7961	−	24.7961i	−0.837782	−	0.837782i
$877$	−9.61142	−	23.2040i	−0.324555	−	0.783544i	−0.998978	−	0.0451995i	$-0.985608\pi$
$877$	−9.61142	−	23.2040i	−0.324555	−	0.783544i	0.674423	−	0.738345i	$-0.264392\pi$
$878$	8.92906	−	3.69854i	0.301341	−	0.124820i
$879$	−12.6558	−	5.24221i	−0.426870	−	0.176815i
$880$	−0.108471	−	3.17483i	−0.00365657	−	0.107023i
$881$	−0.438491	+	1.05861i	−0.0147731	+	0.0356655i	−0.931094	−	0.364779i	$-0.881144\pi$
$881$	−0.438491	+	1.05861i	−0.0147731	+	0.0356655i	0.916321	+	0.400445i	$0.131144\pi$
$882$	5.45827	+	5.45827i	0.183789	+	0.183789i
$883$			31.8311i			1.07120i	0.844471	+	0.535601i	$0.179915\pi$
$883$			31.8311i			1.07120i	−0.844471	+	0.535601i	$0.820085\pi$
$884$	−12.3493	−	3.44199i	−0.415350	−	0.115767i
$885$	0.661309	+	19.3557i	0.0222296	+	0.650635i
$886$	−1.72401	+	1.72401i	−0.0579192	+	0.0579192i
$887$	41.9931	+	17.3941i	1.40999	+	0.584038i	0.952325	−	0.305086i	$-0.0986852\pi$
$887$	41.9931	+	17.3941i	1.40999	+	0.584038i	0.457667	+	0.889124i	$0.348685\pi$
$888$	10.4502			0.350685
$889$	30.9936	+	12.8380i	1.03949	+	0.430571i
$890$	1.26156	−	0.573779i	0.0422877	−	0.0192331i
$891$	19.6067	−	8.12135i	0.656848	−	0.272075i
$892$	−5.72265	+	5.72265i	−0.191608	+	0.191608i
$893$	31.6458	−	31.6458i	1.05899	−	1.05899i
$894$	34.7587	−	14.3975i	1.16251	−	0.481526i
$895$	9.35823	+	20.5758i	0.312811	+	0.687775i
$896$	−2.64018	−	1.09360i	−0.0882021	−	0.0365345i
$897$	44.9358			1.50036
$898$	19.6916	+	8.15655i	0.657119	+	0.272187i
$899$	−0.473332	+	0.473332i	−0.0157865	+	0.0157865i
$900$	−33.0101	+	2.25828i	−1.10034	+	0.0752761i
$901$	−34.2497	+	19.3190i	−1.14102	+	0.643609i
$902$		−	5.04539i		−	0.167993i
$903$	−1.20674	−	1.20674i	−0.0401579	−	0.0401579i
$904$	−2.79122	+	6.73860i	−0.0928345	+	0.224122i
$905$	−0.693142	−	20.2874i	−0.0230408	−	0.674377i
$906$	−10.5076	−	4.35238i	−0.349091	−	0.144598i
$907$	13.3124	−	5.51416i	0.442030	−	0.183095i	−0.150557	−	0.988601i	$-0.548107\pi$
$907$	13.3124	−	5.51416i	0.442030	−	0.183095i	0.592587	+	0.805507i	$0.298107\pi$
$908$	−0.180977	−	0.436916i	−0.00600592	−	0.0144996i
$909$	−73.6811	−	73.6811i	−2.44385	−	2.44385i
$910$	−13.5612	+	14.5207i	−0.449550	+	0.481356i
$911$	45.1179	−	18.6884i	1.49482	−	0.619176i	0.522462	−	0.852663i	$-0.325014\pi$
$911$	45.1179	−	18.6884i	1.49482	−	0.619176i	0.972360	+	0.233487i	$0.0750136\pi$
$912$	−23.6504	+	9.79633i	−0.783144	+	0.324389i
$913$	−2.44698	+	5.90754i	−0.0809833	+	0.195511i
$914$			19.9387i			0.659515i
$915$	−62.9240	−	23.5804i	−2.08020	−	0.779544i
$916$	3.37412	−	3.37412i	0.111484	−	0.111484i
$917$			53.3501i			1.76178i
$918$	−36.4123	−	28.5245i	−1.20179	−	0.941448i
$919$	−28.2398			−0.931547			−0.465773	−	0.884904i	$-0.654224\pi$
$919$	−28.2398			−0.931547			−0.465773	+	0.884904i	$0.654224\pi$
$920$	7.11246	−	7.61566i	0.234491	−	0.251081i
$921$	−22.5012	+	54.3227i	−0.741439	+	1.78999i
$922$	34.1225			1.12376
$923$	4.36379	−	10.5351i	0.143636	−	0.346768i
$924$	−4.81810	−	11.6319i	−0.158504	−	0.382662i
$925$	−7.49507	−	15.0897i	−0.246436	−	0.496147i
$926$	23.2588	+	23.2588i	0.764333	+	0.764333i
$927$	32.8024	−	32.8024i	1.07737	−	1.07737i
$928$	1.67985	+	4.05552i	0.0551438	+	0.133129i
$929$	7.54682	+	18.2196i	0.247603	+	0.597767i	0.998000	−	0.0632214i	$-0.0201374\pi$
$929$	7.54682	+	18.2196i	0.247603	+	0.597767i	−0.750397	+	0.660988i	$0.770137\pi$
$930$	0.990215	+	0.371077i	0.0324704	+	0.0121681i
$931$		−	9.62883i		−	0.315572i
$932$	0.431013	+	0.178531i	0.0141183	+	0.00584799i
$933$	24.0609	+	24.0609i	0.787717	+	0.787717i
$934$	−42.8624			−1.40250
$935$	−12.7296	−	3.08371i	−0.416302	−	0.100848i
$936$	20.5756			0.672535
$937$	−28.9551	−	28.9551i	−0.945923	−	0.945923i	0.0526883	−	0.998611i	$-0.483221\pi$
$937$	−28.9551	−	28.9551i	−0.945923	−	0.945923i	−0.998611	+	0.0526883i	$0.983221\pi$
$938$	18.1283	+	7.50897i	0.591908	+	0.245176i
$939$		−	67.5769i		−	2.20529i
$940$	−4.25425	+	11.3524i	−0.138758	+	0.370275i
$941$	−13.5792	−	32.7830i	−0.442669	−	1.06870i	−0.975009	−	0.222166i	$-0.928687\pi$
$941$	−13.5792	−	32.7830i	−0.442669	−	1.06870i	0.532340	−	0.846531i	$-0.321313\pi$
$942$	−9.10476	−	21.9808i	−0.296649	−	0.716175i
$943$	11.7029	−	11.7029i	0.381098	−	0.381098i
$944$	−1.97484	−	1.97484i	−0.0642757	−	0.0642757i
$945$	−65.2539	+	29.6785i	−2.12271	+	0.965443i
$946$	0.104691	+	0.252747i	0.00340381	+	0.00821751i
$947$	12.8388	−	30.9955i	0.417204	−	1.00722i	−0.565950	−	0.824440i	$-0.691490\pi$
$947$	12.8388	−	30.9955i	0.417204	−	1.00722i	0.983154	−	0.182780i	$-0.0585096\pi$
$948$	34.3005			1.11403
$949$	13.4546	−	32.4822i	0.436754	−	1.05442i
$950$	31.1081	+	27.1243i	1.00928	+	0.880029i
$951$	56.1160			1.81969
$952$	−7.26613	+	9.27543i	−0.235497	+	0.300618i
$953$		−	16.2347i		−	0.525892i	−0.964811	−	0.262946i	$-0.915306\pi$
$953$		−	16.2347i		−	0.525892i	0.964811	−	0.262946i	$-0.0846941\pi$
$954$	44.6265	−	44.6265i	1.44484	−	1.44484i
$955$	7.33448	−	19.5720i	0.237338	−	0.633334i
$956$			23.7793i			0.769077i
$957$	−7.40098	+	17.8675i	−0.239240	+	0.577576i
$958$	−15.9275	+	6.59739i	−0.514595	+	0.213152i
$959$	2.34606	−	0.971770i	0.0757582	−	0.0313801i
$960$	4.73314	−	5.06800i	0.152761	−	0.163569i
$961$	21.9039	+	21.9039i	0.706576	+	0.706576i
$962$	4.00955	+	9.67991i	0.129273	+	0.312093i
$963$	−31.1474	+	12.9017i	−1.00371	+	0.415750i
$964$	24.7628	+	10.2571i	0.797556	+	0.330359i
$965$	−28.2279	+	0.964435i	−0.908688	+	0.0310463i
$966$	15.8048	−	38.1561i	0.508510	−	1.22765i
$967$	28.8558	+	28.8558i	0.927939	+	0.927939i	0.997573	−	0.0696339i	$-0.0221831\pi$
$967$	28.8558	+	28.8558i	0.927939	+	0.927939i	−0.0696339	+	0.997573i	$0.522183\pi$
$968$		−	8.98174i		−	0.288684i
$969$	12.7273	+	104.777i	0.408859	+	3.36594i
$970$	−33.6262	+	1.14888i	−1.07967	+	0.0368882i
$971$	35.4161	−	35.4161i	1.13656	−	1.13656i	0.147496	−	0.989063i	$-0.452879\pi$
$971$	35.4161	−	35.4161i	1.13656	−	1.13656i	0.989063	−	0.147496i	$-0.0471212\pi$
$972$	11.7067	+	4.84908i	0.375493	+	0.155534i
$973$	35.3674			1.13383
$974$	0.559836	+	0.231892i	0.0179383	+	0.00743028i
$975$	−21.4474	−	43.1796i	−0.686865	−	1.38286i
$976$	8.95265	−	3.70831i	0.286567	−	0.118700i
$977$	−18.7097	+	18.7097i	−0.598575	+	0.598575i	−0.939933	−	0.341358i	$-0.889113\pi$
$977$	−18.7097	+	18.7097i	−0.598575	+	0.598575i	0.341358	+	0.939933i	$0.389113\pi$
$978$	11.1276	−	11.1276i	0.355822	−	0.355822i
$979$	−0.813496	+	0.336961i	−0.0259995	+	0.0107693i
$980$	1.07987	+	2.37430i	0.0344952	+	0.0758444i
$981$	−72.8036	−	30.1562i	−2.32444	−	0.962814i
$982$	−10.7276			−0.342332
$983$	−41.9521	−	17.3771i	−1.33807	−	0.554245i	−0.405120	−	0.914263i	$-0.632770\pi$
$983$	−41.9521	−	17.3771i	−1.33807	−	0.554245i	−0.932945	+	0.360018i	$0.882770\pi$
$984$	7.78792	−	7.78792i	0.248270	−	0.248270i
$985$	−1.87907	−	54.9981i	−0.0598721	−	1.75239i
$986$	17.9670	−	2.18244i	0.572185	−	0.0695031i
$987$			48.0491i			1.52942i
$988$	−18.1485	−	18.1485i	−0.577381	−	0.577381i
$989$	−0.343418	+	0.829084i	−0.0109200	+	0.0263633i
$990$	21.0092	−	0.717803i	0.667718	−	0.0228133i
$991$	22.1320	+	9.16737i	0.703046	+	0.291211i	0.705424	−	0.708786i	$-0.250757\pi$
$991$	22.1320	+	9.16737i	0.703046	+	0.291211i	−0.00237764	+	0.999997i	$0.500757\pi$
$992$	−0.140885	+	0.0583565i	−0.00447310	+	0.00185282i
$993$	29.8149	+	71.9796i	0.946149	+	2.28420i
$994$	−7.41080	−	7.41080i	−0.235056	−	0.235056i
$995$	−2.82700	−	2.64020i	−0.0896218	−	0.0837001i
$996$	−12.8958	+	5.34162i	−0.408619	+	0.169256i
$997$	−21.3244	+	8.83285i	−0.675350	+	0.279739i	−0.693882	−	0.720089i	$-0.744101\pi$
$997$	−21.3244	+	8.83285i	−0.675350	+	0.279739i	0.0185315	+	0.999828i	$0.494101\pi$
$998$	12.9866	−	31.3524i	0.411083	−	0.992442i
$999$			37.8030i			1.19603i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.n.b.59.1	yes	20
5.2	odd	4		850.2.l.h.501.1		20
5.3	odd	4		850.2.l.i.501.5		20
5.4	even	2		170.2.n.a.59.5	yes	20
17.15	even	8		170.2.n.a.49.5	✓	20
85.32	odd	8		850.2.l.h.151.1		20
85.49	even	8	inner	170.2.n.b.49.1	yes	20
85.83	odd	8		850.2.l.i.151.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.n.a.49.5	✓	20	17.15	even	8
170.2.n.a.59.5	yes	20	5.4	even	2
170.2.n.b.49.1	yes	20	85.49	even	8	inner
170.2.n.b.59.1	yes	20	1.1	even	1	trivial
850.2.l.h.151.1		20	85.32	odd	8
850.2.l.h.501.1		20	5.2	odd	4
850.2.l.i.151.5		20	85.83	odd	8
850.2.l.i.501.5		20	5.3	odd	4

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-2.86514 - 1.18678i) q^{3} +1.00000i q^{4} +(-2.09387 - 0.784666i) q^{5} +(1.18678 + 2.86514i) q^{6} +(1.09360 + 2.64018i) q^{7} +(0.707107 - 0.707107i) q^{8} +(4.67924 + 4.67924i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-2.86514 - 1.18678i) q^{3} +1.00000i q^{4} +(-2.09387 - 0.784666i) q^{5} +(1.18678 + 2.86514i) q^{6} +(1.09360 + 2.64018i) q^{7} +(0.707107 - 0.707107i) q^{8} +(4.67924 + 4.67924i) q^{9} +(0.925748 + 2.03543i) q^{10} +(-0.543661 - 1.31251i) q^{11} +(1.18678 - 2.86514i) q^{12} +3.10930 q^{13} +(1.09360 - 2.64018i) q^{14} +(5.06800 + 4.73314i) q^{15} -1.00000 q^{16} +(-1.10700 + 3.97172i) q^{17} -6.61745i q^{18} +(-5.83686 + 5.83686i) q^{19} +(0.784666 - 2.09387i) q^{20} -8.86232i q^{21} +(-0.543661 + 1.31251i) q^{22} +(-4.30543 + 1.78337i) q^{23} +(-2.86514 + 1.18678i) q^{24} +(3.76860 + 3.28598i) q^{25} +(-2.19860 - 2.19860i) q^{26} +(-4.29311 - 10.3645i) q^{27} +(-2.64018 + 1.09360i) q^{28} +(4.05552 + 1.67985i) q^{29} +(-0.236786 - 6.93045i) q^{30} +(-0.0583565 + 0.140885i) q^{31} +(0.707107 + 0.707107i) q^{32} +4.40573i q^{33} +(3.59120 - 2.02566i) q^{34} +(-0.218195 - 6.38630i) q^{35} +(-4.67924 + 4.67924i) q^{36} +(-3.11322 - 1.28954i) q^{37} +8.25456 q^{38} +(-8.90856 - 3.69005i) q^{39} +(-2.03543 + 0.925748i) q^{40} +(-3.28112 + 1.35908i) q^{41} +(-6.26661 + 6.26661i) q^{42} +(0.136166 - 0.136166i) q^{43} +(1.31251 - 0.543661i) q^{44} +(-6.12609 - 13.4694i) q^{45} +(4.30543 + 1.78337i) q^{46} -5.42173 q^{47} +(2.86514 + 1.18678i) q^{48} +(-0.824830 + 0.824830i) q^{49} +(-0.341262 - 4.98834i) q^{50} +(7.88525 - 10.0658i) q^{51} +3.10930i q^{52} +(6.74377 + 6.74377i) q^{53} +(-4.29311 + 10.3645i) q^{54} +(0.108471 + 3.17483i) q^{55} +(2.64018 + 1.09360i) q^{56} +(23.6504 - 9.79633i) q^{57} +(-1.67985 - 4.05552i) q^{58} +(1.97484 + 1.97484i) q^{59} +(-4.73314 + 5.06800i) q^{60} +(-8.95265 + 3.70831i) q^{61} +(0.140885 - 0.0583565i) q^{62} +(-7.23682 + 17.4712i) q^{63} -1.00000i q^{64} +(-6.51047 - 2.43976i) q^{65} +(3.11532 - 3.11532i) q^{66} +6.86630i q^{67} +(-3.97172 - 1.10700i) q^{68} +14.4521 q^{69} +(-4.36151 + 4.67008i) q^{70} +(1.40347 - 3.38827i) q^{71} +6.61745 q^{72} +(4.32721 - 10.4468i) q^{73} +(1.28954 + 3.11322i) q^{74} +(-6.89782 - 13.8873i) q^{75} +(-5.83686 - 5.83686i) q^{76} +(2.87072 - 2.87072i) q^{77} +(3.69005 + 8.90856i) q^{78} +(4.23263 + 10.2185i) q^{79} +(2.09387 + 0.784666i) q^{80} +14.9383i q^{81} +(3.28112 + 1.35908i) q^{82} +(-3.18264 - 3.18264i) q^{83} +8.86232 q^{84} +(5.43439 - 7.44765i) q^{85} -0.192567 q^{86} +(-9.62601 - 9.62601i) q^{87} +(-1.31251 - 0.543661i) q^{88} -0.619800i q^{89} +(-5.19249 + 13.8561i) q^{90} +(3.40032 + 8.20909i) q^{91} +(-1.78337 - 4.30543i) q^{92} +(0.334399 - 0.334399i) q^{93} +(3.83374 + 3.83374i) q^{94} +(16.8016 - 7.64164i) q^{95} +(-1.18678 - 2.86514i) q^{96} +(-5.75819 + 13.9015i) q^{97} +1.16649 q^{98} +(3.59765 - 8.68549i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{5}+O(q^{10}) \) 20 * q - 4 * q^5	\( 20 q - 4 q^{5} + 8 q^{10} - 8 q^{11} + 24 q^{13} + 16 q^{15} - 20 q^{16} - 4 q^{20} - 8 q^{22} - 16 q^{23} + 8 q^{25} - 12 q^{26} - 24 q^{27} - 12 q^{29} + 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} + 8 q^{37} + 8 q^{38} - 4 q^{40} + 4 q^{41} - 8 q^{42} - 16 q^{43} - 8 q^{44} - 32 q^{45} + 16 q^{46} - 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} - 44 q^{53} - 24 q^{54} + 72 q^{57} + 16 q^{59} + 8 q^{60} + 8 q^{61} + 8 q^{62} + 24 q^{63} - 28 q^{65} - 8 q^{66} - 20 q^{68} - 16 q^{69} + 8 q^{71} + 28 q^{72} + 60 q^{73} + 28 q^{74} - 8 q^{78} + 56 q^{79} + 4 q^{80} - 4 q^{82} + 16 q^{84} + 84 q^{85} + 48 q^{86} + 72 q^{87} + 8 q^{88} - 12 q^{90} - 24 q^{91} + 8 q^{92} - 72 q^{93} + 32 q^{94} + 88 q^{95} - 48 q^{97} + 36 q^{98} + 72 q^{99}+O(q^{100}) \) 20 * q - 4 * q^5 + 8 * q^10 - 8 * q^11 + 24 * q^13 + 16 * q^15 - 20 * q^16 - 4 * q^20 - 8 * q^22 - 16 * q^23 + 8 * q^25 - 12 * q^26 - 24 * q^27 - 12 * q^29 + 8 * q^30 + 8 * q^31 + 8 * q^34 - 8 * q^35 + 8 * q^37 + 8 * q^38 - 4 * q^40 + 4 * q^41 - 8 * q^42 - 16 * q^43 - 8 * q^44 - 32 * q^45 + 16 * q^46 - 40 * q^47 - 56 * q^49 + 8 * q^50 - 8 * q^51 - 44 * q^53 - 24 * q^54 + 72 * q^57 + 16 * q^59 + 8 * q^60 + 8 * q^61 + 8 * q^62 + 24 * q^63 - 28 * q^65 - 8 * q^66 - 20 * q^68 - 16 * q^69 + 8 * q^71 + 28 * q^72 + 60 * q^73 + 28 * q^74 - 8 * q^78 + 56 * q^79 + 4 * q^80 - 4 * q^82 + 16 * q^84 + 84 * q^85 + 48 * q^86 + 72 * q^87 + 8 * q^88 - 12 * q^90 - 24 * q^91 + 8 * q^92 - 72 * q^93 + 32 * q^94 + 88 * q^95 - 48 * q^97 + 36 * q^98 + 72 * q^99

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