LMFDB - Embedded newform 170.2.n.a.59.3

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			59.3
Root			$0.254075 + 0.613391i$ of defining polynomial
Character	$\chi$	$=$	170.59
Dual form			170.2.n.a.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.613391 + 0.254075i) q^{3} +1.00000i q^{4} +(0.384345 - 2.20279i) q^{5} +(0.254075 + 0.613391i) q^{6} +(1.97319 + 4.76369i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.80963 - 1.80963i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.613391 + 0.254075i) q^{3} +1.00000i q^{4} +(0.384345 - 2.20279i) q^{5} +(0.254075 + 0.613391i) q^{6} +(1.97319 + 4.76369i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.80963 - 1.80963i) q^{9} +(1.82938 - 1.28583i) q^{10} +(-0.737928 - 1.78152i) q^{11} +(-0.254075 + 0.613391i) q^{12} +3.78187 q^{13} +(-1.97319 + 4.76369i) q^{14} +(0.795427 - 1.25352i) q^{15} -1.00000 q^{16} +(-3.13012 - 2.68371i) q^{17} -2.55920i q^{18} +(-2.29711 + 2.29711i) q^{19} +(2.20279 + 0.384345i) q^{20} +3.42334i q^{21} +(0.737928 - 1.78152i) q^{22} +(-3.23911 + 1.34168i) q^{23} +(-0.613391 + 0.254075i) q^{24} +(-4.70456 - 1.69326i) q^{25} +(2.67419 + 2.67419i) q^{26} +(-1.41245 - 3.40996i) q^{27} +(-4.76369 + 1.97319i) q^{28} +(-3.27342 - 1.35589i) q^{29} +(1.44882 - 0.323919i) q^{30} +(2.81636 - 6.79928i) q^{31} +(-0.707107 - 0.707107i) q^{32} -1.28025i q^{33} +(-0.315659 - 4.11100i) q^{34} +(11.2518 - 2.51561i) q^{35} +(1.80963 - 1.80963i) q^{36} +(0.515436 + 0.213501i) q^{37} -3.24860 q^{38} +(2.31976 + 0.960878i) q^{39} +(1.28583 + 1.82938i) q^{40} +(3.83779 - 1.58966i) q^{41} +(-2.42067 + 2.42067i) q^{42} +(3.43682 - 3.43682i) q^{43} +(1.78152 - 0.737928i) q^{44} +(-4.68175 + 3.29070i) q^{45} +(-3.23911 - 1.34168i) q^{46} -4.24145 q^{47} +(-0.613391 - 0.254075i) q^{48} +(-13.8496 + 13.8496i) q^{49} +(-2.12931 - 4.52394i) q^{50} +(-1.23812 - 2.44145i) q^{51} +3.78187i q^{52} +(3.39351 + 3.39351i) q^{53} +(1.41245 - 3.40996i) q^{54} +(-4.20792 + 0.940782i) q^{55} +(-4.76369 - 1.97319i) q^{56} +(-1.99266 + 0.825387i) q^{57} +(-1.35589 - 3.27342i) q^{58} +(6.83453 + 6.83453i) q^{59} +(1.25352 + 0.795427i) q^{60} +(1.47400 - 0.610550i) q^{61} +(6.79928 - 2.81636i) q^{62} +(5.04977 - 12.1912i) q^{63} -1.00000i q^{64} +(1.45354 - 8.33066i) q^{65} +(0.905276 - 0.905276i) q^{66} +10.2816i q^{67} +(2.68371 - 3.13012i) q^{68} -2.32773 q^{69} +(9.73503 + 6.17742i) q^{70} +(0.0895325 - 0.216151i) q^{71} +2.55920 q^{72} +(-4.37701 + 10.5670i) q^{73} +(0.213501 + 0.515436i) q^{74} +(-2.45552 - 2.23394i) q^{75} +(-2.29711 - 2.29711i) q^{76} +(7.03053 - 7.03053i) q^{77} +(0.960878 + 2.31976i) q^{78} +(-3.43221 - 8.28609i) q^{79} +(-0.384345 + 2.20279i) q^{80} +5.22709i q^{81} +(3.83779 + 1.58966i) q^{82} +(7.42776 + 7.42776i) q^{83} -3.42334 q^{84} +(-7.11471 + 5.86353i) q^{85} +4.86039 q^{86} +(-1.66339 - 1.66339i) q^{87} +(1.78152 + 0.737928i) q^{88} +7.56737i q^{89} +(-5.63737 - 0.983616i) q^{90} +(7.46234 + 18.0157i) q^{91} +(-1.34168 - 3.23911i) q^{92} +(3.45505 - 3.45505i) q^{93} +(-2.99916 - 2.99916i) q^{94} +(4.17716 + 5.94292i) q^{95} +(-0.254075 - 0.613391i) q^{96} +(3.16811 - 7.64850i) q^{97} -19.5862 q^{98} +(-1.88850 + 4.55925i) 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} + 4 q^{10} - 8 q^{11} - 24 q^{13} + 8 q^{15} - 20 q^{16} + 8 q^{20} + 8 q^{22} + 16 q^{23} - 12 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} - 12 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} + 16 q^{60} + 8 q^{61} - 8 q^{62} - 24 q^{63} - 8 q^{65} - 8 q^{66} + 20 q^{68} - 16 q^{69} - 16 q^{70} + 8 q^{71} - 28 q^{72} - 60 q^{73} + 28 q^{74} + 64 q^{75} + 8 q^{78} + 56 q^{79} + 4 q^{80} + 4 q^{82} + 16 q^{84} - 16 q^{85} + 48 q^{86} - 72 q^{87} - 8 q^{88} + 32 q^{90} - 24 q^{91} - 8 q^{92} + 72 q^{93} + 32 q^{94} + 8 q^{95} + 48 q^{97} - 36 q^{98} + 72 q^{99}+O(q^{100}) $ 20 * q - 4 * q^5 + 4 * q^10 - 8 * q^11 - 24 * q^13 + 8 * q^15 - 20 * q^16 + 8 * q^20 + 8 * q^22 + 16 * q^23 - 12 * 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 - 12 * 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 + 16 * q^60 + 8 * q^61 - 8 * q^62 - 24 * q^63 - 8 * q^65 - 8 * q^66 + 20 * q^68 - 16 * q^69 - 16 * q^70 + 8 * q^71 - 28 * q^72 - 60 * q^73 + 28 * q^74 + 64 * q^75 + 8 * q^78 + 56 * q^79 + 4 * q^80 + 4 * q^82 + 16 * q^84 - 16 * q^85 + 48 * q^86 - 72 * q^87 - 8 * q^88 + 32 * q^90 - 24 * q^91 - 8 * q^92 + 72 * q^93 + 32 * q^94 + 8 * 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
$3$	0.613391	+	0.254075i	0.354141	+	0.146690i	0.552660	−	0.833407i	$-0.313613\pi$
$3$	0.613391	+	0.254075i	0.354141	+	0.146690i	−0.198518	+	0.980097i	$0.563613\pi$
$4$			1.00000i			0.500000i
$5$	0.384345	−	2.20279i	0.171884	−	0.985117i
$5$	0.384345	−	2.20279i	0.171884	−	0.985117i
$6$	0.254075	+	0.613391i	0.103726	+	0.250416i
$7$	1.97319	+	4.76369i	0.745794	+	1.80051i	0.580496	+	0.814263i	$0.302859\pi$
$7$	1.97319	+	4.76369i	0.745794	+	1.80051i	0.165299	+	0.986244i	$0.447141\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.80963	−	1.80963i	−0.603209	−	0.603209i
$10$	1.82938	−	1.28583i	0.578501	−	0.406616i
$11$	−0.737928	−	1.78152i	−0.222494	−	0.537147i	0.772734	−	0.634730i	$-0.218889\pi$
$11$	−0.737928	−	1.78152i	−0.222494	−	0.537147i	−0.995227	+	0.0975831i	$0.968889\pi$
$12$	−0.254075	+	0.613391i	−0.0733451	+	0.177071i
$13$	3.78187			1.04890			0.524451	−	0.851441i	$-0.324271\pi$
$13$	3.78187			1.04890			0.524451	+	0.851441i	$0.324271\pi$
$14$	−1.97319	+	4.76369i	−0.527356	+	1.27315i
$15$	0.795427	−	1.25352i	0.205378	−	0.323657i
$16$	−1.00000			−0.250000
$17$	−3.13012	−	2.68371i	−0.759166	−	0.650896i
$17$	−3.13012	−	2.68371i	−0.759166	−	0.650896i
$18$		−	2.55920i		−	0.603209i
$19$	−2.29711	+	2.29711i	−0.526992	+	0.526992i	−0.919674	−	0.392682i	$-0.871547\pi$
$19$	−2.29711	+	2.29711i	−0.526992	+	0.526992i	0.392682	+	0.919674i	$0.371547\pi$
$20$	2.20279	+	0.384345i	0.492559	+	0.0859422i
$21$			3.42334i			0.747035i
$22$	0.737928	−	1.78152i	0.157327	−	0.379820i
$23$	−3.23911	+	1.34168i	−0.675402	+	0.279761i	−0.693903	−	0.720068i	$-0.744110\pi$
$23$	−3.23911	+	1.34168i	−0.675402	+	0.279761i	0.0185016	+	0.999829i	$0.494110\pi$
$24$	−0.613391	+	0.254075i	−0.125208	+	0.0518628i
$25$	−4.70456	−	1.69326i	−0.940911	−	0.338653i
$26$	2.67419	+	2.67419i	0.524451	+	0.524451i
$27$	−1.41245	−	3.40996i	−0.271827	−	0.656247i
$28$	−4.76369	+	1.97319i	−0.900253	+	0.372897i
$29$	−3.27342	−	1.35589i	−0.607859	−	0.251783i	0.0574540	−	0.998348i	$-0.481702\pi$
$29$	−3.27342	−	1.35589i	−0.607859	−	0.251783i	−0.665313	+	0.746565i	$0.731702\pi$
$30$	1.44882	−	0.323919i	0.264518	−	0.0591393i
$31$	2.81636	−	6.79928i	0.505832	−	1.22119i	−0.440430	−	0.897787i	$-0.645174\pi$
$31$	2.81636	−	6.79928i	0.505832	−	1.22119i	0.946262	−	0.323400i	$-0.104826\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		−	1.28025i		−	0.222864i
$34$	−0.315659	−	4.11100i	−0.0541350	−	0.705031i
$35$	11.2518	−	2.51561i	1.90190	−	0.425216i
$36$	1.80963	−	1.80963i	0.301604	−	0.301604i
$37$	0.515436	+	0.213501i	0.0847372	+	0.0350993i	0.424649	−	0.905358i	$-0.360397\pi$
$37$	0.515436	+	0.213501i	0.0847372	+	0.0350993i	−0.339912	+	0.940457i	$0.610397\pi$
$38$	−3.24860			−0.526992
$39$	2.31976	+	0.960878i	0.371460	+	0.153864i
$40$	1.28583	+	1.82938i	0.203308	+	0.289250i
$41$	3.83779	−	1.58966i	0.599362	−	0.248264i	−0.0623107	−	0.998057i	$-0.519847\pi$
$41$	3.83779	−	1.58966i	0.599362	−	0.248264i	0.661672	+	0.749793i	$0.269847\pi$
$42$	−2.42067	+	2.42067i	−0.373517	+	0.373517i
$43$	3.43682	−	3.43682i	0.524110	−	0.524110i	−0.394700	−	0.918810i	$-0.629152\pi$
$43$	3.43682	−	3.43682i	0.524110	−	0.524110i	0.918810	+	0.394700i	$0.129152\pi$
$44$	1.78152	−	0.737928i	0.268574	−	0.111247i
$45$	−4.68175	+	3.29070i	−0.697913	+	0.490549i
$46$	−3.23911	−	1.34168i	−0.477581	−	0.197821i
$47$	−4.24145			−0.618679			−0.309340	−	0.950952i	$-0.600108\pi$
$47$	−4.24145			−0.618679			−0.309340	+	0.950952i	$0.600108\pi$
$48$	−0.613391	−	0.254075i	−0.0885353	−	0.0366725i
$49$	−13.8496	+	13.8496i	−1.97851	+	1.97851i
$50$	−2.12931	−	4.52394i	−0.301129	−	0.639782i
$51$	−1.23812	−	2.44145i	−0.173372	−	0.341872i
$52$			3.78187i			0.524451i
$53$	3.39351	+	3.39351i	0.466135	+	0.466135i	0.900660	−	0.434525i	$-0.143084\pi$
$53$	3.39351	+	3.39351i	0.466135	+	0.466135i	−0.434525	+	0.900660i	$0.643084\pi$
$54$	1.41245	−	3.40996i	0.192210	−	0.464037i
$55$	−4.20792	+	0.940782i	−0.567396	+	0.126855i
$56$	−4.76369	−	1.97319i	−0.636575	−	0.263678i
$57$	−1.99266	+	0.825387i	−0.263934	+	0.109325i
$58$	−1.35589	−	3.27342i	−0.178038	−	0.429821i
$59$	6.83453	+	6.83453i	0.889780	+	0.889780i	0.994502	−	0.104721i	$-0.0333951\pi$
$59$	6.83453	+	6.83453i	0.889780	+	0.889780i	−0.104721	+	0.994502i	$0.533395\pi$
$60$	1.25352	+	0.795427i	0.161828	+	0.102689i
$61$	1.47400	−	0.610550i	0.188726	−	0.0781729i	−0.286319	−	0.958134i	$-0.592432\pi$
$61$	1.47400	−	0.610550i	0.188726	−	0.0781729i	0.475045	+	0.879961i	$0.342432\pi$
$62$	6.79928	−	2.81636i	0.863510	−	0.357678i
$63$	5.04977	−	12.1912i	0.636212	−	1.53595i
$64$		−	1.00000i		−	0.125000i
$65$	1.45354	−	8.33066i	0.180290	−	1.03329i
$66$	0.905276	−	0.905276i	0.111432	−	0.111432i
$67$			10.2816i			1.25610i	0.778175	+	0.628048i	$0.216146\pi$
$67$			10.2816i			1.25610i	−0.778175	+	0.628048i	$0.783854\pi$
$68$	2.68371	−	3.13012i	0.325448	−	0.379583i
$69$	−2.32773			−0.280226
$70$	9.73503	+	6.17742i	1.16356	+	0.738342i
$71$	0.0895325	−	0.216151i	0.0106256	−	0.0256523i	−0.918478	−	0.395473i	$-0.870581\pi$
$71$	0.0895325	−	0.216151i	0.0106256	−	0.0256523i	0.929103	+	0.369820i	$0.120581\pi$
$72$	2.55920			0.301604
$73$	−4.37701	+	10.5670i	−0.512290	+	1.23678i	0.430258	+	0.902706i	$0.358423\pi$
$73$	−4.37701	+	10.5670i	−0.512290	+	1.23678i	−0.942548	+	0.334072i	$0.891577\pi$
$74$	0.213501	+	0.515436i	0.0248189	+	0.0599182i
$75$	−2.45552	−	2.23394i	−0.283539	−	0.257953i
$76$	−2.29711	−	2.29711i	−0.263496	−	0.263496i
$77$	7.03053	−	7.03053i	0.801203	−	0.801203i
$78$	0.960878	+	2.31976i	0.108798	+	0.262662i
$79$	−3.43221	−	8.28609i	−0.386154	−	0.932258i	−0.990747	−	0.135724i	$-0.956664\pi$
$79$	−3.43221	−	8.28609i	−0.386154	−	0.932258i	0.604593	−	0.796535i	$-0.293336\pi$
$80$	−0.384345	+	2.20279i	−0.0429711	+	0.246279i
$81$			5.22709i			0.580787i
$82$	3.83779	+	1.58966i	0.423813	+	0.175549i
$83$	7.42776	+	7.42776i	0.815303	+	0.815303i	0.985423	−	0.170120i	$-0.0544157\pi$
$83$	7.42776	+	7.42776i	0.815303	+	0.815303i	−0.170120	+	0.985423i	$0.554416\pi$
$84$	−3.42334			−0.373517
$85$	−7.11471	+	5.86353i	−0.771698	+	0.635989i
$86$	4.86039			0.524110
$87$	−1.66339	−	1.66339i	−0.178334	−	0.178334i
$88$	1.78152	+	0.737928i	0.189910	+	0.0786634i
$89$			7.56737i			0.802139i	0.916048	+	0.401070i	$0.131361\pi$
$89$			7.56737i			0.802139i	−0.916048	+	0.401070i	$0.868639\pi$
$90$	−5.63737	−	0.983616i	−0.594231	−	0.103682i
$91$	7.46234	+	18.0157i	0.782266	+	1.88856i
$92$	−1.34168	−	3.23911i	−0.139880	−	0.337701i
$93$	3.45505	−	3.45505i	0.358272	−	0.358272i
$94$	−2.99916	−	2.99916i	−0.309340	−	0.309340i
$95$	4.17716	+	5.94292i	0.428567	+	0.609731i
$96$	−0.254075	−	0.613391i	−0.0259314	−	0.0626039i
$97$	3.16811	−	7.64850i	0.321673	−	0.776588i	−0.677484	−	0.735538i	$-0.736930\pi$
$97$	3.16811	−	7.64850i	0.321673	−	0.776588i	0.999157	−	0.0410503i	$-0.0130704\pi$
$98$	−19.5862			−1.97851
$99$	−1.88850	+	4.55925i	−0.189802	+	0.458222i
$100$	1.69326	−	4.70456i	0.169326	−	0.470456i
$101$	−15.9669			−1.58877			−0.794384	−	0.607416i	$-0.792206\pi$
$101$	−15.9669			−1.58877			−0.794384	+	0.607416i	$0.792206\pi$
$102$	0.850881	−	2.60185i	0.0842497	−	0.257622i
$103$			16.5864i			1.63431i	0.576417	+	0.817155i	$0.304450\pi$
$103$			16.5864i			1.63431i	−0.576417	+	0.817155i	$0.695550\pi$
$104$	−2.67419	+	2.67419i	−0.262226	+	0.262226i
$105$	7.54090	+	1.31575i	0.735917	+	0.128404i
$106$			4.79915i			0.466135i
$107$	−1.46824	+	3.54465i	−0.141940	+	0.342674i	−0.978823	−	0.204708i	$-0.934376\pi$
$107$	−1.46824	+	3.54465i	−0.141940	+	0.342674i	0.836883	+	0.547382i	$0.184376\pi$
$108$	3.40996	−	1.41245i	0.328124	−	0.135913i
$109$	16.2177	−	6.71758i	1.55337	−	0.643428i	0.569450	−	0.822026i	$-0.307156\pi$
$109$	16.2177	−	6.71758i	1.55337	−	0.643428i	0.983922	+	0.178598i	$0.0571563\pi$
$110$	−3.64068	−	2.31022i	−0.347126	−	0.220271i
$111$	0.261919	+	0.261919i	0.0248602	+	0.0248602i
$112$	−1.97319	−	4.76369i	−0.186449	−	0.450127i
$113$	13.0004	−	5.38493i	1.22297	−	0.506571i	0.324618	−	0.945845i	$-0.394764\pi$
$113$	13.0004	−	5.38493i	1.22297	−	0.506571i	0.898353	+	0.439274i	$0.144764\pi$
$114$	−1.99266	−	0.825387i	−0.186630	−	0.0773046i
$115$	1.71051	+	7.65075i	0.159506	+	0.713436i
$116$	1.35589	−	3.27342i	0.125892	−	0.303929i
$117$	−6.84377	−	6.84377i	−0.632707	−	0.632707i
$118$			9.66549i			0.889780i
$119$	6.60808	−	20.2064i	0.605762	−	1.85232i
$120$	0.323919	+	1.44882i	0.0295696	+	0.132259i
$121$	5.14891	−	5.14891i	0.468083	−	0.468083i
$122$	1.47400	+	0.610550i	0.133450	+	0.0552766i
$123$	2.75796			0.248677
$124$	6.79928	+	2.81636i	0.610594	+	0.252916i
$125$	−5.53808	+	9.71235i	−0.495341	+	0.868699i
$126$	12.1912	−	5.04977i	1.08608	−	0.449870i
$127$	6.81394	−	6.81394i	0.604640	−	0.604640i	−0.336900	−	0.941540i	$-0.609379\pi$
$127$	6.81394	−	6.81394i	0.604640	−	0.604640i	0.941540	+	0.336900i	$0.109379\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	2.98132	−	1.23490i	0.262491	−	0.108727i
$130$	6.91848	−	4.86286i	0.606791	−	0.426501i
$131$	−6.30300	−	2.61079i	−0.550695	−	0.228106i	0.0899447	−	0.995947i	$-0.471331\pi$
$131$	−6.30300	−	2.61079i	−0.550695	−	0.228106i	−0.640640	+	0.767841i	$0.721331\pi$
$132$	1.28025			0.111432
$133$	−15.4753	−	6.41009i	−1.34188	−	0.555825i
$134$	−7.27018	+	7.27018i	−0.628048	+	0.628048i
$135$	−8.05429	+	1.80073i	−0.693203	+	0.154982i
$136$	4.11100	−	0.315659i	0.352516	−	0.0270675i
$137$		−	7.15271i		−	0.611097i	−0.952177	−	0.305549i	$-0.901160\pi$
$137$		−	7.15271i		−	0.611097i	0.952177	−	0.305549i	$-0.0988398\pi$
$138$	−1.64595	−	1.64595i	−0.140113	−	0.140113i
$139$	4.83609	−	11.6753i	0.410192	−	0.990290i	−0.574894	−	0.818228i	$-0.694957\pi$
$139$	4.83609	−	11.6753i	0.410192	−	0.990290i	0.985086	−	0.172062i	$-0.0550431\pi$
$140$	2.51561	+	11.2518i	0.212608	+	0.950950i
$141$	−2.60167	−	1.07765i	−0.219100	−	0.0907542i
$142$	0.216151	−	0.0895325i	0.0181390	−	0.00751340i
$143$	−2.79075	−	6.73746i	−0.233374	−	0.563415i
$144$	1.80963	+	1.80963i	0.150802	+	0.150802i
$145$	−4.24487	+	6.68952i	−0.352517	+	0.555534i
$146$	−10.5670	+	4.37701i	−0.874534	+	0.362244i
$147$	−12.0140	+	4.97637i	−0.990900	+	0.410444i
$148$	−0.213501	+	0.515436i	−0.0175496	+	0.0423686i
$149$		−	7.62426i		−	0.624604i	−0.949983	−	0.312302i	$-0.898900\pi$
$149$		−	7.62426i		−	0.624604i	0.949983	−	0.312302i	$-0.101100\pi$
$150$	−0.156677	−	3.31595i	−0.0127927	−	0.270746i
$151$	−0.335898	+	0.335898i	−0.0273350	+	0.0273350i	−0.720642	−	0.693307i	$-0.756153\pi$
$151$	−0.335898	+	0.335898i	−0.0273350	+	0.0273350i	0.693307	+	0.720642i	$0.256153\pi$
$152$		−	3.24860i		−	0.263496i
$153$	0.807833	+	10.5209i	0.0653094	+	0.850562i
$154$	9.94267			0.801203
$155$	−13.8949	−	8.81711i	−1.11607	−	0.708207i
$156$	−0.960878	+	2.31976i	−0.0769318	+	0.185730i
$157$	−14.8313			−1.18367			−0.591835	−	0.806059i	$-0.701596\pi$
$157$	−14.8313			−1.18367			−0.591835	+	0.806059i	$0.701596\pi$
$158$	3.43221	−	8.28609i	0.273052	−	0.659206i
$159$	1.21934	+	2.94376i	0.0967002	+	0.233455i
$160$	−1.82938	+	1.28583i	−0.144625	+	0.101654i
$161$	−12.7827	−	12.7827i	−1.00742	−	1.00742i
$162$	−3.69611	+	3.69611i	−0.290394	+	0.290394i
$163$	−1.70740	−	4.12202i	−0.133734	−	0.322861i	0.842800	−	0.538227i	$-0.180906\pi$
$163$	−1.70740	−	4.12202i	−0.133734	−	0.322861i	−0.976533	+	0.215366i	$0.930906\pi$
$164$	1.58966	+	3.83779i	0.124132	+	0.299681i
$165$	−2.82013	−	0.492060i	−0.219547	−	0.0383068i
$166$			10.5044i			0.815303i
$167$	9.90975	+	4.10475i	0.766839	+	0.317635i	0.731591	−	0.681743i	$-0.238778\pi$
$167$	9.90975	+	4.10475i	0.766839	+	0.317635i	0.0352479	+	0.999379i	$0.488778\pi$
$168$	−2.42067	−	2.42067i	−0.186759	−	0.186759i
$169$	1.30255			0.100196
$170$	−9.17700	−	0.884716i	−0.703844	−	0.0678546i
$171$	8.31380			0.635773
$172$	3.43682	+	3.43682i	0.262055	+	0.262055i
$173$	−5.82171	−	2.41143i	−0.442616	−	0.183338i	0.150234	−	0.988650i	$-0.451997\pi$
$173$	−5.82171	−	2.41143i	−0.442616	−	0.183338i	−0.592850	+	0.805313i	$0.701997\pi$
$174$		−	2.35238i		−	0.178334i
$175$	−1.21678	−	25.7522i	−0.0919801	−	1.94668i
$176$	0.737928	+	1.78152i	0.0556234	+	0.134287i
$177$	2.45576	+	5.92872i	0.184586	+	0.445630i
$178$	−5.35094	+	5.35094i	−0.401070	+	0.401070i
$179$	7.08979	+	7.08979i	0.529916	+	0.529916i	0.920547	−	0.390631i	$-0.127743\pi$
$179$	7.08979	+	7.08979i	0.529916	+	0.529916i	−0.390631	+	0.920547i	$0.627743\pi$
$180$	−3.29070	−	4.68175i	−0.245275	−	0.348957i
$181$	4.70201	+	11.3517i	0.349498	+	0.843762i	0.996679	+	0.0814265i	$0.0259476\pi$
$181$	4.70201	+	11.3517i	0.349498	+	0.843762i	−0.647181	+	0.762336i	$0.724052\pi$
$182$	−7.46234	+	18.0157i	−0.553145	+	1.33541i
$183$	1.05926			0.0783029
$184$	1.34168	−	3.23911i	0.0989103	−	0.238791i
$185$	0.668402	−	1.05334i	0.0491419	−	0.0774430i
$186$	4.88618			0.358272
$187$	−2.47127	+	7.55675i	−0.180718	+	0.552605i
$188$		−	4.24145i		−	0.309340i
$189$	13.4570	−	13.4570i	0.978851	−	0.978851i
$190$	−1.24858	+	7.15598i	−0.0905818	+	0.519149i
$191$		−	5.91808i		−	0.428217i	−0.976810	−	0.214109i	$-0.931315\pi$
$191$		−	5.91808i		−	0.428217i	0.976810	−	0.214109i	$-0.0686847\pi$
$192$	0.254075	−	0.613391i	0.0183363	−	0.0442677i
$193$	−1.13937	+	0.471944i	−0.0820139	+	0.0339713i	−0.423313	−	0.905983i	$-0.639133\pi$
$193$	−1.13937	+	0.471944i	−0.0820139	+	0.0339713i	0.341299	+	0.939955i	$0.389133\pi$
$194$	7.64850	−	3.16811i	0.549131	−	0.227457i
$195$	3.00820	−	4.74064i	0.215422	−	0.339485i
$196$	−13.8496	−	13.8496i	−0.989255	−	0.989255i
$197$	4.28469	+	10.3441i	0.305271	+	0.736990i	0.999846	+	0.0175692i	$0.00559274\pi$
$197$	4.28469	+	10.3441i	0.305271	+	0.736990i	−0.694574	+	0.719421i	$0.744407\pi$
$198$	−4.55925	+	1.88850i	−0.324012	+	0.134210i
$199$	−19.2796	−	7.98588i	−1.36670	−	0.566104i	−0.425806	−	0.904815i	$-0.640009\pi$
$199$	−19.2796	−	7.98588i	−1.36670	−	0.566104i	−0.940891	+	0.338710i	$0.890009\pi$
$200$	4.52394	−	2.12931i	0.319891	−	0.150565i
$201$	−2.61229	+	6.30663i	−0.184257	+	0.444836i
$202$	−11.2903	−	11.2903i	−0.794384	−	0.794384i
$203$		−	18.2690i		−	1.28223i
$204$	2.44145	−	1.23812i	0.170936	−	0.0866861i
$205$	−2.02666	−	9.06481i	−0.141548	−	0.633114i
$206$	−11.7284	+	11.7284i	−0.817155	+	0.817155i
$207$	8.28953	+	3.43364i	0.576162	+	0.238654i
$208$	−3.78187			−0.262226
$209$	5.78743	+	2.39723i	0.400325	+	0.165820i
$210$	4.40185	+	6.26260i	0.303756	+	0.432160i
$211$	−11.2232	+	4.64882i	−0.772640	+	0.320038i	−0.733941	−	0.679213i	$-0.762321\pi$
$211$	−11.2232	+	4.64882i	−0.772640	+	0.320038i	−0.0386985	+	0.999251i	$0.512321\pi$
$212$	−3.39351	+	3.39351i	−0.233067	+	0.233067i
$213$	0.109837	−	0.109837i	0.00752589	−	0.00752589i
$214$	−3.54465	+	1.46824i	−0.242307	+	0.100367i
$215$	−6.24966	−	8.89151i	−0.426223	−	0.606396i
$216$	3.40996	+	1.41245i	0.232018	+	0.0961052i
$217$	37.9469			2.57600
$218$	16.2177	+	6.71758i	1.09840	+	0.454972i
$219$	−5.36963	+	5.36963i	−0.362846	+	0.362846i
$220$	−0.940782	−	4.20792i	−0.0634275	−	0.283698i
$221$	−11.8377	−	10.1495i	−0.796292	−	0.682727i
$222$			0.370409i			0.0248602i
$223$	0.627386	+	0.627386i	0.0420129	+	0.0420129i	0.727801	−	0.685788i	$-0.240542\pi$
$223$	0.627386	+	0.627386i	0.0420129	+	0.0420129i	−0.685788	+	0.727801i	$0.740542\pi$
$224$	1.97319	−	4.76369i	0.131839	−	0.318288i
$225$	5.44932	+	11.5777i	0.363288	+	0.771844i
$226$	13.0004	+	5.38493i	0.864771	+	0.358200i
$227$	−20.6249	+	8.54310i	−1.36892	+	0.567025i	−0.941495	−	0.337026i	$-0.890579\pi$
$227$	−20.6249	+	8.54310i	−1.36892	+	0.567025i	−0.427425	+	0.904051i	$0.640579\pi$
$228$	−0.825387	−	1.99266i	−0.0546626	−	0.131967i
$229$	4.59129	+	4.59129i	0.303401	+	0.303401i	0.842343	−	0.538942i	$-0.181176\pi$
$229$	4.59129	+	4.59129i	0.303401	+	0.303401i	−0.538942	+	0.842343i	$0.681176\pi$
$230$	−4.20038	+	6.61941i	−0.276965	+	0.436471i
$231$	6.09874	−	2.52618i	0.401268	−	0.166210i
$232$	3.27342	−	1.35589i	0.214910	−	0.0890188i
$233$	0.643616	−	1.55383i	0.0421647	−	0.101795i	−0.901394	−	0.433000i	$-0.857455\pi$
$233$	0.643616	−	1.55383i	0.0421647	−	0.101795i	0.943559	+	0.331205i	$0.107455\pi$
$234$		−	9.67856i		−	0.632707i
$235$	−1.63018	+	9.34302i	−0.106341	+	0.609472i
$236$	−6.83453	+	6.83453i	−0.444890	+	0.444890i
$237$		−	5.95465i		−	0.386796i
$238$	18.9607	−	9.61548i	1.22904	−	0.623279i
$239$	13.9682			0.903530			0.451765	−	0.892137i	$-0.350794\pi$
$239$	13.9682			0.903530			0.451765	+	0.892137i	$0.350794\pi$
$240$	−0.795427	+	1.25352i	−0.0513446	+	0.0809142i
$241$	9.09881	−	21.9665i	0.586106	−	1.41498i	−0.301092	−	0.953595i	$-0.597351\pi$
$241$	9.09881	−	21.9665i	0.586106	−	1.41498i	0.887198	−	0.461389i	$-0.152649\pi$
$242$	7.28166			0.468083
$243$	−5.56543	+	13.4361i	−0.357022	+	0.861928i
$244$	0.610550	+	1.47400i	0.0390865	+	0.0943631i
$245$	25.1847	+	35.8307i	1.60899	+	2.28914i
$246$	1.95017	+	1.95017i	0.124338	+	0.124338i
$247$	−8.68736	+	8.68736i	−0.552763	+	0.552763i
$248$	2.81636	+	6.79928i	0.178839	+	0.431755i
$249$	2.66891	+	6.44333i	0.169136	+	0.408329i
$250$	−10.7837	+	2.95166i	−0.682020	+	0.186679i
$251$			15.0409i			0.949375i	0.880155	+	0.474687i	$0.157439\pi$
$251$			15.0409i			0.949375i	−0.880155	+	0.474687i	$0.842561\pi$
$252$	12.1912	+	5.04977i	0.767976	+	0.318106i
$253$	4.78046	+	4.78046i	0.300545	+	0.300545i
$254$	9.63637			0.604640
$255$	−5.85387	+	1.78897i	−0.366584	+	0.112029i
$256$	1.00000			0.0625000
$257$	−15.7106	−	15.7106i	−0.980002	−	0.980002i	0.0198022	−	0.999804i	$-0.493696\pi$
$257$	−15.7106	−	15.7106i	−0.980002	−	0.980002i	−0.999804	+	0.0198022i	$0.993696\pi$
$258$	2.98132	+	1.23490i	0.185609	+	0.0768817i
$259$			2.87666i			0.178747i
$260$	8.33066	+	1.45354i	0.516646	+	0.0901450i
$261$	3.47000	+	8.37733i	0.214788	+	0.518543i
$262$	−2.61079	−	6.30300i	−0.161295	−	0.389401i
$263$	4.69057	−	4.69057i	0.289233	−	0.289233i	−0.547544	−	0.836777i	$-0.684437\pi$
$263$	4.69057	−	4.69057i	0.289233	−	0.289233i	0.836777	+	0.547544i	$0.184437\pi$
$264$	0.905276	+	0.905276i	0.0557159	+	0.0557159i
$265$	8.77947	−	6.17091i	0.539319	−	0.379076i
$266$	−6.41009	−	15.4753i	−0.393028	−	0.948853i
$267$	−1.92268	+	4.64175i	−0.117666	+	0.284071i
$268$	−10.2816			−0.628048
$269$	7.30824	−	17.6437i	0.445591	−	1.07575i	−0.528365	−	0.849017i	$-0.677195\pi$
$269$	7.30824	−	17.6437i	0.445591	−	1.07575i	0.973956	−	0.226735i	$-0.0728052\pi$
$270$	−6.96855	−	4.42194i	−0.424093	−	0.269110i
$271$	−12.2458			−0.743880			−0.371940	−	0.928257i	$-0.621307\pi$
$271$	−12.2458			−0.743880			−0.371940	+	0.928257i	$0.621307\pi$
$272$	3.13012	+	2.68371i	0.189792	+	0.162724i
$273$			12.9466i			0.783566i
$274$	5.05773	−	5.05773i	0.305549	−	0.305549i
$275$	0.455050	+	9.63075i	0.0274405	+	0.580756i
$276$		−	2.32773i		−	0.140113i
$277$	5.15659	−	12.4491i	0.309829	−	0.747994i	−0.689881	−	0.723923i	$-0.742337\pi$
$277$	5.15659	−	12.4491i	0.309829	−	0.747994i	0.999710	−	0.0240713i	$-0.00766287\pi$
$278$	11.6753	−	4.83609i	0.700241	−	0.290049i
$279$	−17.4007	+	7.20761i	−1.04175	+	0.431508i
$280$	−6.17742	+	9.73503i	−0.369171	+	0.581779i
$281$	8.18352	+	8.18352i	0.488188	+	0.488188i	0.907734	−	0.419546i	$-0.137811\pi$
$281$	8.18352	+	8.18352i	0.488188	+	0.488188i	−0.419546	+	0.907734i	$0.637811\pi$
$282$	−1.07765	−	2.60167i	−0.0641729	−	0.154927i
$283$	0.0268950	−	0.0111403i	0.00159874	−	0.000662220i	−0.381884	−	0.924210i	$-0.624725\pi$
$283$	0.0268950	−	0.0111403i	0.00159874	−	0.000662220i	0.383483	+	0.923548i	$0.374725\pi$
$284$	0.216151	+	0.0895325i	0.0128262	+	0.00531278i
$285$	1.05228	+	4.70664i	0.0623319	+	0.278797i
$286$	2.79075	−	6.73746i	0.165020	−	0.398395i
$287$	15.1453	+	15.1453i	0.894001	+	0.894001i
$288$			2.55920i			0.150802i
$289$	2.59535	+	16.8007i	0.152668	+	0.988278i
$290$	−7.73178	+	1.72863i	−0.454026	+	0.101508i
$291$	3.88658	−	3.88658i	0.227836	−	0.227836i
$292$	−10.5670	−	4.37701i	−0.618389	−	0.256145i
$293$	13.9196			0.813195			0.406597	−	0.913607i	$-0.366715\pi$
$293$	13.9196			0.813195			0.406597	+	0.913607i	$0.366715\pi$
$294$	−12.0140	−	4.97637i	−0.700672	−	0.290228i
$295$	17.6819	−	12.4282i	1.02948	−	0.723598i
$296$	−0.515436	+	0.213501i	−0.0299591	+	0.0124095i
$297$	−5.03261	+	5.03261i	−0.292022	+	0.292022i
$298$	5.39117	−	5.39117i	0.312302	−	0.312302i
$299$	−12.2499	+	5.07408i	−0.708430	+	0.293441i
$300$	2.23394	−	2.45552i	0.128977	−	0.141769i
$301$	23.1534	+	9.59046i	1.33454	+	0.552785i
$302$	−0.475031			−0.0273350
$303$	−9.79396	−	4.05679i	−0.562648	−	0.233057i
$304$	2.29711	−	2.29711i	0.131748	−	0.131748i
$305$	−0.778389	−	3.48157i	−0.0445704	−	0.199354i
$306$	−6.86816	+	8.01061i	−0.392626	+	0.457936i
$307$		−	2.60569i		−	0.148715i	−0.997232	−	0.0743573i	$-0.976309\pi$
$307$		−	2.60569i		−	0.148715i	0.997232	−	0.0743573i	$-0.0236905\pi$
$308$	7.03053	+	7.03053i	0.400601	+	0.400601i
$309$	−4.21420	+	10.1740i	−0.239737	+	0.578777i
$310$	−3.59056	−	16.0598i	−0.203930	−	0.912138i
$311$	1.31928	+	0.546462i	0.0748092	+	0.0309870i	0.419774	−	0.907629i	$-0.362109\pi$
$311$	1.31928	+	0.546462i	0.0748092	+	0.0309870i	−0.344965	+	0.938616i	$0.612109\pi$
$312$	−2.31976	+	0.960878i	−0.131331	+	0.0543990i
$313$	−4.25820	−	10.2802i	−0.240688	−	0.581072i	0.756664	−	0.653804i	$-0.226828\pi$
$313$	−4.25820	−	10.2802i	−0.240688	−	0.581072i	−0.997351	+	0.0727326i	$0.976828\pi$
$314$	−10.4873	−	10.4873i	−0.591835	−	0.591835i
$315$	−24.9139	−	15.8092i	−1.40374	−	0.890749i
$316$	8.28609	−	3.43221i	0.466129	−	0.193077i
$317$	2.03646	−	0.843531i	0.114379	−	0.0473774i	−0.324760	−	0.945796i	$-0.605284\pi$
$317$	2.03646	−	0.843531i	0.114379	−	0.0473774i	0.439139	+	0.898419i	$0.355284\pi$
$318$	−1.21934	+	2.94376i	−0.0683774	+	0.165078i
$319$			6.83220i			0.382530i
$320$	−2.20279	−	0.384345i	−0.123140	−	0.0214856i
$321$	−1.80121	+	1.80121i	−0.100534	+	0.100534i
$322$		−	18.0775i		−	1.00742i
$323$	13.3550	−	1.02545i	0.743092	−	0.0570575i
$324$	−5.22709			−0.290394
$325$	−17.7920	−	6.40370i	−0.986924	−	0.355214i
$326$	1.70740	−	4.12202i	0.0945639	−	0.228297i
$327$	11.6545			0.644498
$328$	−1.58966	+	3.83779i	−0.0877745	+	0.211906i
$329$	−8.36918	−	20.2050i	−0.461408	−	1.11394i
$330$	−1.64619	−	2.34207i	−0.0906200	−	0.128927i
$331$	8.47090	+	8.47090i	0.465603	+	0.465603i	0.900487	−	0.434884i	$-0.143210\pi$
$331$	8.47090	+	8.47090i	0.465603	+	0.465603i	−0.434884	+	0.900487i	$0.643210\pi$
$332$	−7.42776	+	7.42776i	−0.407651	+	0.407651i
$333$	−0.546390	−	1.31910i	−0.0299420	−	0.0722864i
$334$	4.10475	+	9.90975i	0.224602	+	0.542237i
$335$	22.6482	+	3.95168i	1.23740	+	0.215903i
$336$		−	3.42334i		−	0.186759i
$337$	−17.8257	−	7.38363i	−0.971026	−	0.402212i	−0.159932	−	0.987128i	$-0.551127\pi$
$337$	−17.8257	−	7.38363i	−0.971026	−	0.402212i	−0.811094	+	0.584916i	$0.801127\pi$
$338$	0.921042	+	0.921042i	0.0500981	+	0.0500981i
$339$	9.34248			0.507414
$340$	−5.86353	−	7.11471i	−0.317994	−	0.385849i
$341$	−14.1913			−0.768502
$342$	5.87875	+	5.87875i	0.317886	+	0.317886i
$343$	−59.9570	−	24.8350i	−3.23737	−	1.34096i
$344$			4.86039i			0.262055i
$345$	−0.894652	+	5.12750i	−0.0481664	+	0.276055i
$346$	−2.41143	−	5.82171i	−0.129639	−	0.312977i
$347$	2.61715	+	6.31836i	0.140496	+	0.339187i	0.978428	−	0.206587i	$-0.0662356\pi$
$347$	2.61715	+	6.31836i	0.140496	+	0.339187i	−0.837932	+	0.545774i	$0.816236\pi$
$348$	1.66339	−	1.66339i	0.0891669	−	0.0891669i
$349$	5.65961	+	5.65961i	0.302952	+	0.302952i	0.842168	−	0.539216i	$-0.181279\pi$
$349$	5.65961	+	5.65961i	0.302952	+	0.302952i	−0.539216	+	0.842168i	$0.681279\pi$
$350$	17.3492	−	19.0699i	0.927351	−	1.01933i
$351$	−5.34171	−	12.8960i	−0.285119	−	0.688339i
$352$	−0.737928	+	1.78152i	−0.0393317	+	0.0949551i
$353$	−37.1497			−1.97728			−0.988640	−	0.150300i	$-0.951976\pi$
$353$	−37.1497			−1.97728			−0.988640	+	0.150300i	$0.951976\pi$
$354$	−2.45576	+	5.92872i	−0.130522	+	0.315108i
$355$	−0.441723	−	0.280298i	−0.0234442	−	0.0148767i
$356$	−7.56737			−0.401070
$357$	9.18728	−	10.7155i	0.486242	−	0.567124i
$358$			10.0265i			0.529916i
$359$	−3.36474	+	3.36474i	−0.177584	+	0.177584i	−0.790302	−	0.612718i	$-0.790076\pi$
$359$	−3.36474	+	3.36474i	−0.177584	+	0.177584i	0.612718	+	0.790302i	$0.290076\pi$
$360$	0.983616	−	5.63737i	0.0518411	−	0.297116i
$361$			8.44661i			0.444558i
$362$	−4.70201	+	11.3517i	−0.247132	+	0.596630i
$363$	4.46651	−	1.85009i	0.234431	−	0.0971044i
$364$	−18.0157	+	7.46234i	−0.944278	+	0.391133i
$365$	21.5947	+	13.7030i	1.13032	+	0.717249i
$366$	0.749012	+	0.749012i	0.0391515	+	0.0391515i
$367$	1.36037	+	3.28423i	0.0710110	+	0.171436i	0.955400	−	0.295315i	$-0.0954246\pi$
$367$	1.36037	+	3.28423i	0.0710110	+	0.171436i	−0.884389	+	0.466751i	$0.845425\pi$
$368$	3.23911	−	1.34168i	0.168850	−	0.0699401i
$369$	−9.82166	−	4.06826i	−0.511295	−	0.211785i
$370$	1.21745	−	0.272191i	0.0632925	−	0.0141506i
$371$	−9.46962	+	22.8617i	−0.491638	+	1.18692i
$372$	3.45505	+	3.45505i	0.179136	+	0.179136i
$373$			13.5609i			0.702157i	0.936346	+	0.351078i	$0.114185\pi$
$373$			13.5609i			0.702157i	−0.936346	+	0.351078i	$0.885815\pi$
$374$	−7.09089	+	3.59598i	−0.366661	+	0.185944i
$375$	−5.86467	+	4.55038i	−0.302850	+	0.234981i
$376$	2.99916	−	2.99916i	0.154670	−	0.154670i
$377$	−12.3796	−	5.12782i	−0.637584	−	0.264096i
$378$	19.0310			0.978851
$379$	−24.6523	−	10.2113i	−1.26631	−	0.524521i	−0.354467	−	0.935069i	$-0.615338\pi$
$379$	−24.6523	−	10.2113i	−1.26631	−	0.524521i	−0.911839	+	0.410548i	$0.865338\pi$
$380$	−5.94292	+	4.17716i	−0.304865	+	0.214284i
$381$	5.91086	−	2.44836i	0.302823	−	0.125433i
$382$	4.18472	−	4.18472i	0.214109	−	0.214109i
$383$	7.47058	−	7.47058i	0.381729	−	0.381729i	−0.489996	−	0.871725i	$-0.663002\pi$
$383$	7.47058	−	7.47058i	0.381729	−	0.381729i	0.871725	+	0.489996i	$0.163002\pi$
$384$	0.613391	−	0.254075i	0.0313020	−	0.0129657i
$385$	−12.7846	−	18.1889i	−0.651564	−	0.926993i
$386$	−1.13937	−	0.471944i	−0.0579926	−	0.0240213i
$387$	−12.4387			−0.632295
$388$	7.64850	+	3.16811i	0.388294	+	0.160837i
$389$	7.91583	−	7.91583i	0.401349	−	0.401349i	−0.477359	−	0.878708i	$-0.658406\pi$
$389$	7.91583	−	7.91583i	0.401349	−	0.401349i	0.878708	+	0.477359i	$0.158406\pi$
$390$	5.47926	−	1.22502i	0.277453	−	0.0620313i
$391$	13.7395	+	4.49322i	0.694837	+	0.227232i
$392$		−	19.5862i		−	0.989255i
$393$	−3.20287	−	3.20287i	−0.161563	−	0.161563i
$394$	−4.28469	+	10.3441i	−0.215859	+	0.521131i
$395$	−19.5717	+	4.37572i	−0.984758	+	0.220166i
$396$	−4.55925	−	1.88850i	−0.229111	−	0.0949009i
$397$	16.1390	−	6.68500i	0.809994	−	0.335511i	0.0610426	−	0.998135i	$-0.480557\pi$
$397$	16.1390	−	6.68500i	0.809994	−	0.335511i	0.748952	+	0.662625i	$0.230557\pi$
$398$	−7.98588	−	19.2796i	−0.400296	−	0.966400i
$399$	−7.86378	−	7.86378i	−0.393681	−	0.393681i
$400$	4.70456	+	1.69326i	0.235228	+	0.0846632i
$401$	2.23800	−	0.927011i	0.111760	−	0.0462927i	−0.326103	−	0.945334i	$-0.605735\pi$
$401$	2.23800	−	0.927011i	0.111760	−	0.0462927i	0.437863	+	0.899042i	$0.355735\pi$
$402$	−6.30663	+	2.61229i	−0.314546	+	0.130289i
$403$	10.6511	−	25.7140i	0.530569	−	1.28091i
$404$		−	15.9669i		−	0.794384i
$405$	11.5142	+	2.00901i	0.572144	+	0.0998283i
$406$	12.9181	−	12.9181i	0.641116	−	0.641116i
$407$		−	1.07581i		−	0.0533257i
$408$	2.60185	+	0.850881i	0.128811	+	0.0421249i
$409$	25.9314			1.28222			0.641112	−	0.767447i	$-0.278473\pi$
$409$	25.9314			1.28222			0.641112	+	0.767447i	$0.278473\pi$
$410$	4.97673	−	7.84286i	0.245783	−	0.387331i
$411$	1.81732	−	4.38741i	0.0896419	−	0.216415i
$412$	−16.5864			−0.817155
$413$	−19.0718	+	46.0434i	−0.938462	+	2.26565i
$414$	3.43364	+	8.28953i	0.168754	+	0.407408i
$415$	19.2166	−	13.5070i	0.943307	−	0.663031i
$416$	−2.67419	−	2.67419i	−0.131113	−	0.131113i
$417$	5.93282	−	5.93282i	0.290532	−	0.290532i
$418$	2.39723	+	5.78743i	0.117252	+	0.283072i
$419$	14.7921	+	35.7113i	0.722641	+	1.74461i	0.665683	+	0.746234i	$0.268140\pi$
$419$	14.7921	+	35.7113i	0.722641	+	1.74461i	0.0569581	+	0.998377i	$0.481860\pi$
$420$	−1.31575	+	7.54090i	−0.0642018	+	0.367958i
$421$		−	32.3783i		−	1.57802i	−0.614380	−	0.789010i	$-0.710594\pi$
$421$		−	32.3783i		−	1.57802i	0.614380	−	0.789010i	$-0.289406\pi$
$422$	−11.2232	−	4.64882i	−0.546339	−	0.226301i
$423$	7.67544	+	7.67544i	0.373193	+	0.373193i
$424$	−4.79915			−0.233067
$425$	10.1816	+	17.9258i	0.493881	+	0.869530i
$426$	0.155333			0.00752589
$427$	5.81695	+	5.81695i	0.281502	+	0.281502i
$428$	−3.54465	−	1.46824i	−0.171337	−	0.0709701i
$429$		−	4.84176i		−	0.233762i
$430$	1.86807	−	10.7064i	0.0900863	−	0.516310i
$431$	−10.4913	−	25.3282i	−0.505347	−	1.22002i	−0.946535	−	0.322601i	$-0.895443\pi$
$431$	−10.4913	−	25.3282i	−0.505347	−	1.22002i	0.441188	−	0.897415i	$-0.354557\pi$
$432$	1.41245	+	3.40996i	0.0679566	+	0.164062i
$433$	4.97561	−	4.97561i	0.239113	−	0.239113i	−0.577370	−	0.816483i	$-0.695921\pi$
$433$	4.97561	−	4.97561i	0.239113	−	0.239113i	0.816483	+	0.577370i	$0.195921\pi$
$434$	26.8325	+	26.8325i	1.28800	+	1.28800i
$435$	−4.30340	+	3.02477i	−0.206332	+	0.145027i
$436$	6.71758	+	16.2177i	0.321714	+	0.776686i
$437$	4.35859	−	10.5226i	0.208500	−	0.503363i
$438$	−7.59381			−0.362846
$439$	4.96900	−	11.9962i	0.237157	−	0.572548i	−0.759829	−	0.650123i	$-0.774717\pi$
$439$	4.96900	−	11.9962i	0.237157	−	0.572548i	0.996987	+	0.0775743i	$0.0247175\pi$
$440$	2.31022	−	3.64068i	0.110135	−	0.173563i
$441$	50.1251			2.38691
$442$	−1.19378	−	15.5473i	−0.0567823	−	0.739509i
$443$			32.3529i			1.53713i	0.639769	+	0.768567i	$0.279030\pi$
$443$			32.3529i			1.53713i	−0.639769	+	0.768567i	$0.720970\pi$
$444$	−0.261919	+	0.261919i	−0.0124301	+	0.0124301i
$445$	16.6693	+	2.90848i	0.790201	+	0.137875i
$446$			0.887257i			0.0420129i
$447$	1.93713	−	4.67665i	0.0916232	−	0.221198i
$448$	4.76369	−	1.97319i	0.225063	−	0.0932243i
$449$	−30.1216	+	12.4768i	−1.42152	+	0.588815i	−0.955243	−	0.295822i	$-0.904407\pi$
$449$	−30.1216	+	12.4768i	−1.42152	+	0.588815i	−0.466281	+	0.884636i	$0.654407\pi$
$450$	−4.33340	+	12.0399i	−0.204278	+	0.567566i
$451$	−5.66402	−	5.66402i	−0.266708	−	0.266708i
$452$	5.38493	+	13.0004i	0.253286	+	0.611486i
$453$	−0.291380	+	0.120693i	−0.0136902	+	0.00567067i
$454$	−20.6249	−	8.54310i	−0.967973	−	0.400947i
$455$	42.5528	−	9.51371i	1.99491	−	0.446010i
$456$	0.825387	−	1.99266i	0.0386523	−	0.0933149i
$457$	−6.14331	−	6.14331i	−0.287372	−	0.287372i	0.548668	−	0.836040i	$-0.315135\pi$
$457$	−6.14331	−	6.14331i	−0.287372	−	0.287372i	−0.836040	+	0.548668i	$0.815135\pi$
$458$			6.49307i			0.303401i
$459$	−4.73021	+	14.4642i	−0.220787	+	0.675132i
$460$	−7.65075	+	1.71051i	−0.356718	+	0.0797529i
$461$	−10.0389	+	10.0389i	−0.467558	+	0.467558i	−0.901123	−	0.433564i	$-0.857256\pi$
$461$	−10.0389	+	10.0389i	−0.467558	+	0.467558i	0.433564	+	0.901123i	$0.357256\pi$
$462$	6.09874	+	2.52618i	0.283739	+	0.117529i
$463$	−6.24116			−0.290051			−0.145026	−	0.989428i	$-0.546326\pi$
$463$	−6.24116			−0.290051			−0.145026	+	0.989428i	$0.546326\pi$
$464$	3.27342	+	1.35589i	0.151965	+	0.0629458i
$465$	−6.28282	−	8.93869i	−0.291359	−	0.414522i
$466$	1.55383	−	0.643616i	0.0719796	−	0.0298149i
$467$	25.2220	−	25.2220i	1.16714	−	1.16714i	0.184257	−	0.982878i	$-0.441012\pi$
$467$	25.2220	−	25.2220i	1.16714	−	1.16714i	0.982878	−	0.184257i	$-0.0589879\pi$
$468$	6.84377	−	6.84377i	0.316354	−	0.316354i
$469$	−48.9783	+	20.2875i	−2.26161	+	0.936789i
$470$	−7.75923	+	5.45380i	−0.357907	+	0.251565i
$471$	−9.09741	−	3.76827i	−0.419187	−	0.173633i
$472$	−9.66549			−0.444890
$473$	−8.65887	−	3.58662i	−0.398135	−	0.164913i
$474$	4.21058	−	4.21058i	0.193398	−	0.193398i
$475$	14.6965	−	6.91726i	0.674320	−	0.317386i
$476$	20.2064	+	6.60808i	0.926160	+	0.302881i
$477$		−	12.2820i		−	0.562353i
$478$	9.87704	+	9.87704i	0.451765	+	0.451765i
$479$	−13.6111	+	32.8601i	−0.621906	+	1.50141i	0.227556	+	0.973765i	$0.426927\pi$
$479$	−13.6111	+	32.8601i	−0.621906	+	1.50141i	−0.849462	+	0.527650i	$0.823073\pi$
$480$	−1.44882	+	0.323919i	−0.0661294	+	0.0147848i
$481$	1.94931	+	0.807432i	0.0888810	+	0.0368157i
$482$	21.9665	−	9.09881i	1.00054	−	0.414439i
$483$	−4.59305	−	11.0886i	−0.208991	−	0.504548i
$484$	5.14891	+	5.14891i	0.234042	+	0.234042i
$485$	−15.6304	−	9.91835i	−0.709739	−	0.450369i
$486$	−13.4361	+	5.56543i	−0.609475	+	0.252453i
$487$	1.01960	−	0.422332i	0.0462025	−	0.0191377i	−0.359463	−	0.933160i	$-0.617040\pi$
$487$	1.01960	−	0.422332i	0.0462025	−	0.0191377i	0.405665	+	0.914022i	$0.367040\pi$
$488$	−0.610550	+	1.47400i	−0.0276383	+	0.0667248i
$489$		−	2.96221i		−	0.133956i
$490$	−7.52788	+	43.1444i	−0.340075	+	1.94906i
$491$	6.88078	−	6.88078i	0.310525	−	0.310525i	−0.534588	−	0.845113i	$-0.679533\pi$
$491$	6.88078	−	6.88078i	0.310525	−	0.310525i	0.845113	+	0.534588i	$0.179533\pi$
$492$			2.75796i			0.124338i
$493$	6.60737	+	13.0290i	0.297581	+	0.586798i
$494$	−12.2858			−0.552763
$495$	9.31723	+	5.91230i	0.418778	+	0.265738i
$496$	−2.81636	+	6.79928i	−0.126458	+	0.305297i
$497$	1.20634			0.0541117
$498$	−2.66891	+	6.44333i	−0.119597	+	0.288732i
$499$	−9.48039	−	22.8877i	−0.424401	−	1.02459i	−0.981034	−	0.193836i	$-0.937907\pi$
$499$	−9.48039	−	22.8877i	−0.424401	−	1.02459i	0.556633	−	0.830758i	$-0.312093\pi$
$500$	−9.71235	−	5.53808i	−0.434349	−	0.247670i
$501$	5.03563	+	5.03563i	0.224976	+	0.224976i
$502$	−10.6355	+	10.6355i	−0.474687	+	0.474687i
$503$	3.34332	+	8.07150i	0.149071	+	0.359890i	0.980722	−	0.195409i	$-0.0626036\pi$
$503$	3.34332	+	8.07150i	0.149071	+	0.359890i	−0.831650	+	0.555300i	$0.812604\pi$
$504$	5.04977	+	12.1912i	0.224935	+	0.543041i
$505$	−6.13681	+	35.1717i	−0.273084	+	1.56512i
$506$			6.76060i			0.300545i
$507$	0.798972	+	0.330945i	0.0354836	+	0.0146978i
$508$	6.81394	+	6.81394i	0.302320	+	0.302320i
$509$	−5.44103			−0.241169			−0.120585	−	0.992703i	$-0.538477\pi$
$509$	−5.44103			−0.241169			−0.120585	+	0.992703i	$0.538477\pi$
$510$	−5.40430	−	2.87432i	−0.239306	−	0.127277i
$511$	−58.9748			−2.60889
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	11.0776	+	4.58849i	0.489088	+	0.202587i
$514$		−	22.2182i		−	0.980002i
$515$	36.5364	+	6.37492i	1.60999	+	0.280913i
$516$	1.23490	+	2.98132i	0.0543636	+	0.131245i
$517$	3.12989	+	7.55621i	0.137652	+	0.332322i
$518$	−2.03410	+	2.03410i	−0.0893734	+	0.0893734i
$519$	−2.95830	−	2.95830i	−0.129855	−	0.129855i
$520$	4.86286	+	6.91848i	0.213250	+	0.303395i
$521$	−10.9210	−	26.3656i	−0.478457	−	1.15510i	−0.960332	−	0.278858i	$-0.910044\pi$
$521$	−10.9210	−	26.3656i	−0.478457	−	1.15510i	0.481875	−	0.876240i	$-0.339956\pi$
$522$	−3.47000	+	8.37733i	−0.151878	+	0.366666i
$523$	−6.67355			−0.291814			−0.145907	−	0.989298i	$-0.546610\pi$
$523$	−6.67355			−0.291814			−0.145907	+	0.989298i	$0.546610\pi$
$524$	2.61079	−	6.30300i	0.114053	−	0.275348i
$525$	5.79662	−	16.1053i	0.252985	−	0.702893i
$526$	6.63347			0.289233
$527$	−27.0629	+	13.7243i	−1.17888	+	0.597840i
$528$			1.28025i			0.0557159i
$529$	−7.57172	+	7.57172i	−0.329205	+	0.329205i
$530$	10.5715	+	1.84453i	0.459197	+	0.0801213i
$531$		−	24.7359i		−	1.07345i
$532$	6.41009	−	15.4753i	0.277913	−	0.670940i
$533$	14.5140	−	6.01190i	0.628672	−	0.260404i
$534$	−4.64175	+	1.92268i	−0.200868	+	0.0832024i
$535$	7.24380	+	4.59660i	0.313177	+	0.198728i
$536$	−7.27018	−	7.27018i	−0.314024	−	0.314024i
$537$	2.54747	+	6.15015i	0.109932	+	0.265398i
$538$	17.6437	−	7.30824i	0.760672	−	0.315081i
$539$	34.8932	+	14.4532i	1.50296	+	0.622545i
$540$	−1.80073	−	8.05429i	−0.0774911	−	0.346602i
$541$	−1.16670	+	2.81667i	−0.0501605	+	0.121098i	−0.946974	−	0.321312i	$-0.895876\pi$
$541$	−1.16670	+	2.81667i	−0.0501605	+	0.121098i	0.896813	+	0.442410i	$0.145876\pi$
$542$	−8.65910	−	8.65910i	−0.371940	−	0.371940i
$543$			8.15767i			0.350079i
$544$	0.315659	+	4.11100i	0.0135338	+	0.176258i
$545$	−8.56423	−	38.3060i	−0.366851	−	1.64085i
$546$	−9.15466	+	9.15466i	−0.391783	+	0.391783i
$547$	40.4461	+	16.7533i	1.72935	+	0.716320i	0.999464	+	0.0327496i	$0.0104264\pi$
$547$	40.4461	+	16.7533i	1.72935	+	0.716320i	0.729885	+	0.683570i	$0.239574\pi$
$548$	7.15271			0.305549
$549$	−3.77225	−	1.56252i	−0.160996	−	0.0666867i
$550$	−6.48820	+	7.13174i	−0.276658	+	0.304098i
$551$	10.6340	−	4.40476i	0.453025	−	0.187649i
$552$	1.64595	−	1.64595i	0.0700564	−	0.0700564i
$553$	32.7000	−	32.7000i	1.39055	−	1.39055i
$554$	12.4491	−	5.15659i	0.528912	−	0.219082i
$555$	0.677619	−	0.476284i	0.0287633	−	0.0202171i
$556$	11.6753	+	4.83609i	0.495145	+	0.205096i
$557$	24.8597			1.05334			0.526669	−	0.850071i	$-0.323441\pi$
$557$	24.8597			1.05334			0.526669	+	0.850071i	$0.323441\pi$
$558$	−17.4007	−	7.20761i	−0.736631	−	0.305123i
$559$	12.9976	−	12.9976i	0.549740	−	0.549740i
$560$	−11.2518	+	2.51561i	−0.475475	+	0.106304i
$561$	−3.43584	+	4.00735i	−0.145061	+	0.169191i
$562$			11.5732i			0.488188i
$563$	6.13933	+	6.13933i	0.258742	+	0.258742i	0.824542	−	0.565800i	$-0.191433\pi$
$563$	6.13933	+	6.13933i	0.258742	+	0.258742i	−0.565800	+	0.824542i	$0.691433\pi$
$564$	1.07765	−	2.60167i	0.0453771	−	0.109550i
$565$	−6.86523	−	30.7067i	−0.288822	−	1.29184i
$566$	0.0268950	+	0.0111403i	0.00113048	+	0.000468260i
$567$	−24.9002	+	10.3140i	−1.04571	+	0.433148i
$568$	0.0895325	+	0.216151i	0.00375670	+	0.00906948i
$569$	−23.1700	−	23.1700i	−0.971336	−	0.971336i	0.0282640	−	0.999600i	$-0.491002\pi$
$569$	−23.1700	−	23.1700i	−0.971336	−	0.971336i	−0.999600	+	0.0282640i	$0.991002\pi$
$570$	−2.58402	+	4.07218i	−0.108233	+	0.170565i
$571$	28.2865	−	11.7166i	1.18375	−	0.490326i	0.298037	−	0.954554i	$-0.403668\pi$
$571$	28.2865	−	11.7166i	1.18375	−	0.490326i	0.885716	+	0.464228i	$0.153668\pi$
$572$	6.73746	−	2.79075i	0.281707	−	0.116687i
$573$	1.50364	−	3.63010i	0.0628153	−	0.151650i
$574$			21.4187i			0.894001i
$575$	17.5104	−	0.827361i	0.730235	−	0.0345033i
$576$	−1.80963	+	1.80963i	−0.0754011	+	0.0754011i
$577$			33.2782i			1.38539i	0.721231	+	0.692694i	$0.243576\pi$
$577$			33.2782i			1.38539i	−0.721231	+	0.692694i	$0.756424\pi$
$578$	−10.0447	+	13.7151i	−0.417805	+	0.570473i
$579$	−0.818790			−0.0340278
$580$	−6.68952	−	4.24487i	−0.277767	−	0.176259i
$581$	−20.7272	+	50.0399i	−0.859910	+	2.07601i
$582$	5.49646			0.227836
$583$	3.54143	−	8.54976i	0.146671	−	0.354095i
$584$	−4.37701	−	10.5670i	−0.181122	−	0.437267i
$585$	−17.7058	+	12.4450i	−0.732043	+	0.514538i
$586$	9.84268	+	9.84268i	0.406597	+	0.406597i
$587$	−33.4139	+	33.4139i	−1.37914	+	1.37914i	−0.533065	+	0.846074i	$0.678960\pi$
$587$	−33.4139	+	33.4139i	−1.37914	+	1.37914i	−0.846074	+	0.533065i	$0.821040\pi$
$588$	−4.97637	−	12.0140i	−0.205222	−	0.495450i
$589$	9.14921	+	22.0881i	0.376987	+	0.910126i
$590$	21.2910	+	3.71489i	0.876538	+	0.152939i
$591$			7.43364i			0.305779i
$592$	−0.515436	−	0.213501i	−0.0211843	−	0.00877482i
$593$	−16.9464	−	16.9464i	−0.695906	−	0.695906i	0.267619	−	0.963525i	$-0.413763\pi$
$593$	−16.9464	−	16.9464i	−0.695906	−	0.695906i	−0.963525	+	0.267619i	$0.913763\pi$
$594$	−7.11719			−0.292022
$595$	−41.9707	−	22.3224i	−1.72063	−	0.915131i
$596$	7.62426			0.312302
$597$	−9.79693	−	9.79693i	−0.400962	−	0.400962i
$598$	−12.2499	−	5.07408i	−0.500936	−	0.207494i
$599$		−	14.0422i		−	0.573747i	−0.957969	−	0.286873i	$-0.907384\pi$
$599$		−	14.0422i		−	0.573747i	0.957969	−	0.286873i	$-0.0926159\pi$
$600$	3.31595	−	0.156677i	0.135373	−	0.00639633i
$601$	13.1098	+	31.6498i	0.534759	+	1.29102i	0.928340	+	0.371732i	$0.121236\pi$
$601$	13.1098	+	31.6498i	0.534759	+	1.29102i	−0.393582	+	0.919290i	$0.628764\pi$
$602$	9.59046	+	23.1534i	0.390878	+	0.943663i
$603$	18.6058	−	18.6058i	0.757688	−	0.757688i
$604$	−0.335898	−	0.335898i	−0.0136675	−	0.0136675i
$605$	−9.36301	−	13.3209i	−0.380660	−	0.541573i
$606$	−4.05679	−	9.79396i	−0.164796	−	0.397852i
$607$	−6.63626	+	16.0213i	−0.269357	+	0.650286i	−0.999453	−	0.0330584i	$-0.989475\pi$
$607$	−6.63626	+	16.0213i	−0.269357	+	0.650286i	0.730096	+	0.683345i	$0.239475\pi$
$608$	3.24860			0.131748
$609$	4.64169	−	11.2060i	0.188091	−	0.454091i
$610$	1.91144	−	3.01225i	0.0773919	−	0.121962i
$611$	−16.0406			−0.648934
$612$	−10.5209	+	0.807833i	−0.425281	+	0.0326547i
$613$		−	30.2454i		−	1.22160i	−0.791784	−	0.610801i	$-0.790848\pi$
$613$		−	30.2454i		−	1.22160i	0.791784	−	0.610801i	$-0.209152\pi$
$614$	1.84250	−	1.84250i	0.0743573	−	0.0743573i
$615$	1.06001	−	6.07520i	0.0427436	−	0.244976i
$616$			9.94267i			0.400601i
$617$	10.5097	−	25.3727i	0.423106	−	1.02147i	−0.558320	−	0.829626i	$-0.688554\pi$
$617$	10.5097	−	25.3727i	0.423106	−	1.02147i	0.981426	−	0.191842i	$-0.0614461\pi$
$618$	−10.1740	+	4.21420i	−0.409257	+	0.169520i
$619$	4.94993	−	2.05033i	0.198955	−	0.0824097i	−0.280981	−	0.959713i	$-0.590660\pi$
$619$	4.94993	−	2.05033i	0.198955	−	0.0824097i	0.479936	+	0.877304i	$0.340660\pi$
$620$	8.81711	−	13.8949i	0.354104	−	0.558034i
$621$	9.15018	+	9.15018i	0.367184	+	0.367184i
$622$	0.546462	+	1.31928i	0.0219111	+	0.0528981i
$623$	−36.0486	+	14.9318i	−1.44426	+	0.598231i
$624$	−2.31976	−	0.960878i	−0.0928649	−	0.0384659i
$625$	19.2657	+	15.9321i	0.770629	+	0.637284i
$626$	4.25820	−	10.2802i	0.170192	−	0.410880i
$627$	2.94088	+	2.94088i	0.117447	+	0.117447i
$628$		−	14.8313i		−	0.591835i
$629$	−1.04040	−	2.05157i	−0.0414836	−	0.0818013i
$630$	−6.43794	−	28.7956i	−0.256494	−	1.14724i
$631$	25.1153	−	25.1153i	0.999824	−	0.999824i	−0.000175956	−	1.00000i	$-0.500056\pi$
$631$	25.1153	−	25.1153i	0.999824	−	0.999824i	1.00000		0.000175956i	$5.60084e-5\pi$
$632$	8.28609	+	3.43221i	0.329603	+	0.136526i
$633$	−8.06538			−0.320570
$634$	2.03646	+	0.843531i	0.0808783	+	0.0335009i
$635$	−12.3908	−	17.6286i	−0.491713	−	0.699569i
$636$	−2.94376	+	1.21934i	−0.116727	+	0.0483501i
$637$	−52.3773	+	52.3773i	−2.07526	+	2.07526i
$638$	−4.83109	+	4.83109i	−0.191265	+	0.191265i
$639$	−0.553172	+	0.229131i	−0.0218831	+	0.00906430i
$640$	−1.28583	−	1.82938i	−0.0508270	−	0.0723126i
$641$	11.8092	+	4.89153i	0.466435	+	0.193204i	0.603508	−	0.797357i	$-0.293769\pi$
$641$	11.8092	+	4.89153i	0.466435	+	0.193204i	−0.137072	+	0.990561i	$0.543769\pi$
$642$	−2.54730			−0.100534
$643$	11.5049	+	4.76547i	0.453708	+	0.187932i	0.597822	−	0.801629i	$-0.296033\pi$
$643$	11.5049	+	4.76547i	0.453708	+	0.187932i	−0.144114	+	0.989561i	$0.546033\pi$
$644$	12.7827	−	12.7827i	0.503711	−	0.503711i
$645$	−1.57438	−	7.04185i	−0.0619910	−	0.277273i
$646$	10.1685	+	8.71831i	0.400075	+	0.343017i
$647$		−	5.80461i		−	0.228203i	−0.993469	−	0.114101i	$-0.963601\pi$
$647$		−	5.80461i		−	0.228203i	0.993469	−	0.114101i	$-0.0363989\pi$
$648$	−3.69611	−	3.69611i	−0.145197	−	0.145197i
$649$	7.13243	−	17.2192i	0.279973	−	0.675914i
$650$	−8.05276	−	17.1090i	−0.315855	−	0.671069i
$651$	23.2763	+	9.64135i	0.912269	+	0.377874i
$652$	4.12202	−	1.70740i	0.161431	−	0.0668668i
$653$	−10.9746	−	26.4950i	−0.429468	−	1.03683i	−0.979456	−	0.201656i	$-0.935368\pi$
$653$	−10.9746	−	26.4950i	−0.429468	−	1.03683i	0.549988	−	0.835173i	$-0.314632\pi$
$654$	8.24101	+	8.24101i	0.322249	+	0.322249i
$655$	−8.17354	+	12.8807i	−0.319367	+	0.503292i
$656$	−3.83779	+	1.58966i	−0.149840	+	0.0620659i
$657$	27.0431	−	11.2016i	1.05505	−	0.437017i
$658$	8.36918	−	20.2050i	0.326264	−	0.787672i
$659$		−	21.5776i		−	0.840546i	−0.907398	−	0.420273i	$-0.861934\pi$
$659$		−	21.5776i		−	0.840546i	0.907398	−	0.420273i	$-0.138066\pi$
$660$	0.492060	−	2.82013i	0.0191534	−	0.109773i
$661$	19.0645	−	19.0645i	0.741522	−	0.741522i	−0.231349	−	0.972871i	$-0.574314\pi$
$661$	19.0645	−	19.0645i	0.741522	−	0.741522i	0.972871	+	0.231349i	$0.0743138\pi$
$662$			11.9797i			0.465603i
$663$	−4.68243	−	9.23326i	−0.181850	−	0.358590i
$664$	−10.5044			−0.407651
$665$	−20.0679	+	31.6252i	−0.778201	+	1.22637i
$666$	0.546390	−	1.31910i	0.0211722	−	0.0511142i
$667$	12.4222			0.480988
$668$	−4.10475	+	9.90975i	−0.158818	+	0.383420i
$669$	0.225430	+	0.544236i	0.00871562	+	0.0210414i
$670$	13.2204	+	18.8089i	0.510749	+	0.726653i
$671$	−2.17541	−	2.17541i	−0.0839808	−	0.0839808i
$672$	2.42067	−	2.42067i	0.0933793	−	0.0933793i
$673$	13.3927	+	32.3328i	0.516249	+	1.24634i	0.940191	+	0.340647i	$0.110646\pi$
$673$	13.3927	+	32.3328i	0.516249	+	1.24634i	−0.423942	+	0.905689i	$0.639354\pi$
$674$	−7.38363	−	17.8257i	−0.284407	−	0.686619i
$675$	0.871001	+	18.4340i	0.0335248	+	0.709525i
$676$			1.30255i			0.0500981i
$677$	−13.1663	−	5.45364i	−0.506020	−	0.209600i	0.115044	−	0.993360i	$-0.463299\pi$
$677$	−13.1663	−	5.45364i	−0.506020	−	0.209600i	−0.621064	+	0.783760i	$0.713299\pi$
$678$	6.60613	+	6.60613i	0.253707	+	0.253707i
$679$	42.6864			1.63815
$680$	0.884716	−	9.17700i	0.0339273	−	0.351922i
$681$	−14.8217			−0.567968
$682$	−10.0348	−	10.0348i	−0.384251	−	0.384251i
$683$	−1.09176	−	0.452223i	−0.0417751	−	0.0173038i	0.361698	−	0.932295i	$-0.382197\pi$
$683$	−1.09176	−	0.452223i	−0.0417751	−	0.0173038i	−0.403473	+	0.914991i	$0.632197\pi$
$684$			8.31380i			0.317886i
$685$	−15.7559	−	2.74911i	−0.602002	−	0.105038i
$686$	−24.8350	−	59.9570i	−0.948205	−	2.28917i
$687$	1.64972	+	3.98279i	0.0629409	+	0.151953i
$688$	−3.43682	+	3.43682i	−0.131027	+	0.131027i
$689$	12.8338	+	12.8338i	0.488930	+	0.488930i
$690$	−4.25830	+	2.99307i	−0.162111	+	0.113944i
$691$	9.65140	+	23.3005i	0.367156	+	0.886394i	0.994214	+	0.107421i	$0.0342592\pi$
$691$	9.65140	+	23.3005i	0.367156	+	0.886394i	−0.627057	+	0.778973i	$0.715741\pi$
$692$	2.41143	−	5.82171i	0.0916688	−	0.221308i
$693$	−25.4452			−0.966585
$694$	−2.61715	+	6.31836i	−0.0993457	+	0.239842i
$695$	−23.8596	−	15.1402i	−0.905046	−	0.574302i
$696$	2.35238			0.0891669
$697$	−16.2790	−	5.32368i	−0.616609	−	0.201649i
$698$			8.00389i			0.302952i
$699$	0.789576	−	0.789576i	0.0298645	−	0.0298645i
$700$	25.7522	−	1.21678i	0.973341	−	0.0459901i
$701$		−	44.5531i		−	1.68275i	−0.540453	−	0.841374i	$-0.681747\pi$
$701$		−	44.5531i		−	1.68275i	0.540453	−	0.841374i	$-0.318253\pi$
$702$	5.34171	−	12.8960i	0.201610	−	0.486729i
$703$	−1.67444	+	0.693578i	−0.0631529	+	0.0261588i
$704$	−1.78152	+	0.737928i	−0.0671434	+	0.0278117i
$705$	−3.37377	+	5.31674i	−0.127063	+	0.200240i
$706$	−26.2688	−	26.2688i	−0.988640	−	0.988640i
$707$	−31.5057	−	76.0615i	−1.18489	−	2.86059i
$708$	−5.92872	+	2.45576i	−0.222815	+	0.0922930i
$709$	8.05437	+	3.33623i	0.302488	+	0.125295i	0.528765	−	0.848768i	$-0.322655\pi$
$709$	8.05437	+	3.33623i	0.302488	+	0.125295i	−0.226277	+	0.974063i	$0.572655\pi$
$710$	−0.114145	−	0.510545i	−0.00428377	−	0.0191604i
$711$	−8.78371	+	21.2058i	−0.329415	+	0.795278i
$712$	−5.35094	−	5.35094i	−0.200535	−	0.200535i
$713$			25.8023i			0.966304i
$714$	14.0734	−	1.08061i	0.526683	−	0.0404407i
$715$	−15.9138	+	3.55792i	−0.595143	+	0.133059i
$716$	−7.08979	+	7.08979i	−0.264958	+	0.264958i
$717$	8.56799	+	3.54898i	0.319977	+	0.132539i
$718$	−4.75846			−0.177584
$719$	20.4439	+	8.46815i	0.762429	+	0.315809i	0.729802	−	0.683659i	$-0.239612\pi$
$719$	20.4439	+	8.46815i	0.762429	+	0.315809i	0.0326277	+	0.999468i	$0.489612\pi$
$720$	4.68175	−	3.29070i	0.174478	−	0.122637i
$721$	−79.0127	+	32.7281i	−2.94259	+	1.21886i
$722$	−5.97266	+	5.97266i	−0.222279	+	0.222279i
$723$	11.1622	−	11.1622i	0.415128	−	0.415128i
$724$	−11.3517	+	4.70201i	−0.421881	+	0.174749i
$725$	13.1041	+	11.9216i	0.486674	+	0.442759i
$726$	4.46651	+	1.85009i	0.165768	+	0.0686632i
$727$	−13.9152			−0.516088			−0.258044	−	0.966133i	$-0.583078\pi$
$727$	−13.9152			−0.516088			−0.258044	+	0.966133i	$0.583078\pi$
$728$	−18.0157	−	7.46234i	−0.667705	−	0.276573i
$729$	4.26076	−	4.26076i	0.157806	−	0.157806i
$730$	5.58024	+	24.9592i	0.206534	+	0.923782i
$731$	−19.9811	+	1.53423i	−0.739028	+	0.0567454i
$732$			1.05926i			0.0391515i
$733$	2.36873	+	2.36873i	0.0874912	+	0.0874912i	0.749498	−	0.662007i	$-0.230295\pi$
$733$	2.36873	+	2.36873i	0.0874912	+	0.0874912i	−0.662007	+	0.749498i	$0.730295\pi$
$734$	−1.36037	+	3.28423i	−0.0502123	+	0.121223i
$735$	6.34436	+	28.3770i	0.234015	+	1.04670i
$736$	3.23911	+	1.34168i	0.119395	+	0.0494551i
$737$	18.3168	−	7.58707i	0.674709	−	0.279473i
$738$	−4.06826	−	9.82166i	−0.149755	−	0.361540i
$739$	8.94639	+	8.94639i	0.329098	+	0.329098i	0.852243	−	0.523145i	$-0.175242\pi$
$739$	8.94639	+	8.94639i	0.329098	+	0.329098i	−0.523145	+	0.852243i	$0.675242\pi$
$740$	1.05334	+	0.668402i	0.0387215	+	0.0245710i
$741$	−7.53598	+	3.12151i	−0.276841	+	0.114671i
$742$	−22.8617	+	9.46962i	−0.839279	+	0.347641i
$743$	9.43680	−	22.7824i	0.346203	−	0.835807i	−0.650859	−	0.759199i	$-0.725591\pi$
$743$	9.43680	−	22.7824i	0.346203	−	0.835807i	0.997061	−	0.0766080i	$-0.0244090\pi$
$744$			4.88618i			0.179136i
$745$	−16.7946	−	2.93035i	−0.615308	−	0.107360i
$746$	−9.58900	+	9.58900i	−0.351078	+	0.351078i
$747$		−	26.8829i		−	0.983595i
$748$	−7.55675	−	2.47127i	−0.276302	−	0.0903588i
$749$	−19.7827			−0.722846
$750$	−7.36455	−	0.929342i	−0.268915	−	0.0339348i
$751$	−0.492767	+	1.18965i	−0.0179813	+	0.0434108i	−0.932615	−	0.360872i	$-0.882479\pi$
$751$	−0.492767	+	1.18965i	−0.0179813	+	0.0434108i	0.914634	+	0.404283i	$0.132479\pi$
$752$	4.24145			0.154670
$753$	−3.82152	+	9.22596i	−0.139264	+	0.336213i
$754$	−5.12782	−	12.3796i	−0.186744	−	0.450840i
$755$	0.610811	+	0.869013i	0.0222297	+	0.0316266i
$756$	13.4570	+	13.4570i	0.489426	+	0.489426i
$757$	18.6875	−	18.6875i	0.679208	−	0.679208i	−0.280613	−	0.959821i	$-0.590538\pi$
$757$	18.6875	−	18.6875i	0.679208	−	0.679208i	0.959821	+	0.280613i	$0.0905378\pi$
$758$	−10.2113	−	24.6523i	−0.370892	−	0.895414i
$759$	1.71770	+	4.14689i	0.0623485	+	0.150522i
$760$	−7.15598	−	1.24858i	−0.259575	−	0.0452909i
$761$			9.94599i			0.360542i	0.983617	+	0.180271i	$0.0576974\pi$
$761$			9.94599i			0.360542i	−0.983617	+	0.180271i	$0.942303\pi$
$762$	5.91086	+	2.44836i	0.214128	+	0.0886947i
$763$	64.0010	+	64.0010i	2.31699	+	2.31699i
$764$	5.91808			0.214109
$765$	23.4858	+	2.26416i	0.849129	+	0.0818610i
$766$	10.5650			0.381729
$767$	25.8473	+	25.8473i	0.933293	+	0.933293i
$768$	0.613391	+	0.254075i	0.0221338	+	0.00916813i
$769$		−	34.7481i		−	1.25305i	−0.779402	−	0.626525i	$-0.784477\pi$
$769$		−	34.7481i		−	1.25305i	0.779402	−	0.626525i	$-0.215523\pi$
$770$	3.82142	−	21.9016i	0.137714	−	0.789279i
$771$	−5.64508	−	13.6284i	−0.203303	−	0.490816i
$772$	−0.471944	−	1.13937i	−0.0169856	−	0.0410070i
$773$	−9.32492	+	9.32492i	−0.335394	+	0.335394i	−0.854631	−	0.519236i	$-0.826216\pi$
$773$	−9.32492	+	9.32492i	−0.335394	+	0.335394i	0.519236	+	0.854631i	$0.326216\pi$
$774$	−8.79550	−	8.79550i	−0.316148	−	0.316148i
$775$	−24.7627	+	27.2188i	−0.889502	+	0.977728i
$776$	3.16811	+	7.64850i	0.113729	+	0.274565i
$777$	−0.730886	+	1.76451i	−0.0262204	+	0.0633016i
$778$	11.1947			0.401349
$779$	−5.16418	+	12.4674i	−0.185026	+	0.446692i
$780$	4.74064	+	3.00820i	0.169742	+	0.107711i
$781$	−0.451144			−0.0161432
$782$	6.53812	+	12.8925i	0.233803	+	0.461035i
$783$			13.0774i			0.467347i
$784$	13.8496	−	13.8496i	0.494627	−	0.494627i
$785$	−5.70036	+	32.6703i	−0.203454	+	1.16605i
$786$		−	4.52954i		−	0.161563i
$787$	−4.47652	+	10.8073i	−0.159571	+	0.385238i	−0.983362	−	0.181655i	$-0.941855\pi$
$787$	−4.47652	+	10.8073i	−0.159571	+	0.385238i	0.823792	+	0.566893i	$0.191855\pi$
$788$	−10.3441	+	4.28469i	−0.368495	+	0.152636i
$789$	4.06891	−	1.68540i	0.144857	−	0.0600018i
$790$	−16.9334	−	10.7452i	−0.602462	−	0.382296i
$791$	51.3043	+	51.3043i	1.82417	+	1.82417i
$792$	−1.88850	−	4.55925i	−0.0671051	−	0.162006i
$793$	5.57447	−	2.30902i	0.197955	−	0.0819958i
$794$	16.1390	+	6.68500i	0.572752	+	0.237242i
$795$	6.95312	−	1.55454i	0.246602	−	0.0551338i
$796$	7.98588	−	19.2796i	0.283052	−	0.683348i
$797$	−1.73623	−	1.73623i	−0.0615003	−	0.0615003i	0.675688	−	0.737188i	$-0.263847\pi$
$797$	−1.73623	−	1.73623i	−0.0615003	−	0.0615003i	−0.737188	+	0.675688i	$0.763847\pi$
$798$		−	11.1211i		−	0.393681i
$799$	13.2763	+	11.3828i	0.469681	+	0.402696i
$800$	2.12931	+	4.52394i	0.0752824	+	0.159946i
$801$	13.6941	−	13.6941i	0.483857	−	0.483857i
$802$	2.23800	+	0.927011i	0.0790266	+	0.0327339i
$803$	22.0553			0.778313
$804$	−6.30663	−	2.61229i	−0.222418	−	0.0921285i
$805$	−33.0707	+	23.2447i	−1.16559	+	0.819268i
$806$	25.7140	−	10.6511i	0.905738	−	0.375169i
$807$	8.96561	−	8.96561i	0.315605	−	0.315605i
$808$	11.2903	−	11.2903i	0.397192	−	0.397192i
$809$	36.8953	−	15.2825i	1.29717	−	0.537305i	0.376054	−	0.926598i	$-0.377281\pi$
$809$	36.8953	−	15.2825i	1.29717	−	0.537305i	0.921114	+	0.389293i	$0.127281\pi$
$810$	6.72116	+	9.56233i	0.236158	+	0.335986i
$811$	5.85899	+	2.42687i	0.205737	+	0.0852190i	0.483172	−	0.875525i	$-0.339484\pi$
$811$	5.85899	+	2.42687i	0.205737	+	0.0852190i	−0.277435	+	0.960744i	$0.589484\pi$
$812$	18.2690			0.641116
$813$	−7.51147	−	3.11135i	−0.263439	−	0.109120i
$814$	0.760709	−	0.760709i	0.0266629	−	0.0266629i
$815$	−9.73616	+	2.17675i	−0.341043	+	0.0762484i
$816$	1.23812	+	2.44145i	0.0433430	+	0.0854679i
$817$			15.7895i			0.552404i
$818$	18.3363	+	18.3363i	0.641112	+	0.641112i
$819$	19.0976	−	46.1057i	0.667324	−	1.61106i
$820$	9.06481	−	2.02666i	0.316557	−	0.0707740i
$821$	−47.1986	−	19.5503i	−1.64724	−	0.682310i	−0.650242	−	0.759727i	$-0.725333\pi$
$821$	−47.1986	−	19.5503i	−1.64724	−	0.682310i	−0.996999	+	0.0774174i	$0.975333\pi$
$822$	4.38741	−	1.81732i	0.153028	−	0.0633864i
$823$	−11.3375	−	27.3712i	−0.395201	−	0.954099i	−0.988788	−	0.149329i	$-0.952289\pi$
$823$	−11.3375	−	27.3712i	−0.395201	−	0.954099i	0.593587	−	0.804770i	$-0.297711\pi$
$824$	−11.7284	−	11.7284i	−0.408578	−	0.408578i
$825$	−2.16781	+	6.02303i	−0.0754734	+	0.209695i
$826$	−46.0434	+	19.0718i	−1.60206	+	0.663593i
$827$	−34.3113	+	14.2122i	−1.19312	+	0.494206i	−0.888770	−	0.458354i	$-0.848439\pi$
$827$	−34.3113	+	14.2122i	−1.19312	+	0.494206i	−0.304350	+	0.952560i	$0.598439\pi$
$828$	−3.43364	+	8.28953i	−0.119327	+	0.288081i
$829$		−	5.88822i		−	0.204506i	−0.994758	−	0.102253i	$-0.967395\pi$
$829$		−	5.88822i		−	0.204506i	0.994758	−	0.102253i	$-0.0326052\pi$
$830$	23.1391	+	4.03733i	0.803169	+	0.140138i
$831$	6.32601	−	6.32601i	0.219447	−	0.219447i
$832$		−	3.78187i		−	0.131113i
$833$	80.5191	−	6.18257i	2.78982	−	0.214213i
$834$	8.39028			0.290532
$835$	12.8507	−	20.2514i	0.444716	−	0.700830i
$836$	−2.39723	+	5.78743i	−0.0829100	+	0.200162i
$837$	−27.1633			−0.938900
$838$	−14.7921	+	35.7113i	−0.510985	+	1.23363i
$839$	−3.81939	−	9.22081i	−0.131860	−	0.318338i	0.844135	−	0.536130i	$-0.180114\pi$
$839$	−3.81939	−	9.22081i	−0.131860	−	0.318338i	−0.975995	+	0.217792i	$0.930114\pi$
$840$	−6.26260	+	4.40185i	−0.216080	+	0.151878i
$841$	−11.6293	−	11.6293i	−0.401010	−	0.401010i
$842$	22.8949	−	22.8949i	0.789010	−	0.789010i
$843$	2.94047	+	7.09892i	0.101275	+	0.244500i
$844$	−4.64882	−	11.2232i	−0.160019	−	0.386320i
$845$	0.500629	−	2.86924i	0.0172222	−	0.0987050i
$846$			10.8547i			0.373193i
$847$	34.6876	+	14.3681i	1.19188	+	0.493693i
$848$	−3.39351	−	3.39351i	−0.116534	−	0.116534i
$849$	0.0193276			0.000663321
$850$	−5.47598	+	19.8750i	−0.187825	+	0.681705i
$851$	−1.95601			−0.0670510
$852$	0.109837	+	0.109837i	0.00376295	+	0.00376295i
$853$	−21.8663	−	9.05730i	−0.748686	−	0.310116i	−0.0244808	−	0.999700i	$-0.507793\pi$
$853$	−21.8663	−	9.05730i	−0.748686	−	0.310116i	−0.724205	+	0.689584i	$0.757793\pi$
$854$			8.22641i			0.281502i
$855$	3.19537	−	18.3136i	0.109279	−	0.626310i
$856$	−1.46824	−	3.54465i	−0.0501835	−	0.121154i
$857$	−3.44244	−	8.31079i	−0.117592	−	0.283891i	0.854114	−	0.520085i	$-0.174100\pi$
$857$	−3.44244	−	8.31079i	−0.117592	−	0.283891i	−0.971706	+	0.236194i	$0.924100\pi$
$858$	3.42364	−	3.42364i	0.116881	−	0.116881i
$859$	−17.1482	−	17.1482i	−0.585090	−	0.585090i	0.351207	−	0.936298i	$-0.385771\pi$
$859$	−17.1482	−	17.1482i	−0.585090	−	0.585090i	−0.936298	+	0.351207i	$0.885771\pi$
$860$	8.89151	−	6.24966i	0.303198	−	0.213112i
$861$	5.44196	+	13.1381i	0.185462	+	0.447744i
$862$	10.4913	−	25.3282i	0.357334	−	0.862681i
$863$	−34.6790			−1.18049			−0.590243	−	0.807225i	$-0.700968\pi$
$863$	−34.6790			−1.18049			−0.590243	+	0.807225i	$0.700968\pi$
$864$	−1.41245	+	3.40996i	−0.0480526	+	0.116009i
$865$	−7.54942	+	11.8972i	−0.256688	+	0.404516i
$866$	7.03658			0.239113
$867$	−2.67668	+	10.9648i	−0.0909047	+	0.372385i
$868$			37.9469i			1.28800i
$869$	−12.2291	+	12.2291i	−0.414843	+	0.414843i
$870$	−5.18180	−	0.904127i	−0.175680	−	0.0306528i
$871$			38.8836i			1.31752i
$872$	−6.71758	+	16.2177i	−0.227486	+	0.549200i
$873$	−19.5740	+	8.10783i	−0.662481	+	0.274409i
$874$	10.5226	−	4.35859i	0.355931	−	0.147432i
$875$	−57.1943	−	7.21742i	−1.93352	−	0.243993i
$876$	−5.36963	−	5.36963i	−0.181423	−	0.181423i
$877$	9.96344	+	24.0539i	0.336442	+	0.812242i	0.998052	+	0.0623936i	$0.0198734\pi$
$877$	9.96344	+	24.0539i	0.336442	+	0.812242i	−0.661610	+	0.749848i	$0.730127\pi$
$878$	11.9962	−	4.96900i	0.404853	−	0.167696i
$879$	8.53818	+	3.53663i	0.287986	+	0.119288i
$880$	4.20792	−	0.940782i	0.141849	−	0.0317138i
$881$	−11.2768	+	27.2245i	−0.379924	+	0.917217i	0.612055	+	0.790815i	$0.290343\pi$
$881$	−11.2768	+	27.2245i	−0.379924	+	0.917217i	−0.991979	+	0.126402i	$0.959657\pi$
$882$	35.4438	+	35.4438i	1.19345	+	1.19345i
$883$			44.8515i			1.50937i	0.656086	+	0.754687i	$0.272211\pi$
$883$			44.8515i			1.50937i	−0.656086	+	0.754687i	$0.727789\pi$
$884$	10.1495	−	11.8377i	0.341363	−	0.398146i
$885$	14.0036	−	3.13084i	0.470725	−	0.105242i
$886$	−22.8770	+	22.8770i	−0.768567	+	0.768567i
$887$	1.78717	+	0.740272i	0.0600074	+	0.0248559i	0.412485	−	0.910964i	$-0.364661\pi$
$887$	1.78717	+	0.740272i	0.0600074	+	0.0248559i	−0.352478	+	0.935820i	$0.614661\pi$
$888$	−0.370409			−0.0124301
$889$	45.9047	+	19.0144i	1.53960	+	0.637721i
$890$	9.73038	+	13.8436i	0.326163	+	0.464038i
$891$	9.31214	−	3.85721i	0.311968	−	0.129222i
$892$	−0.627386	+	0.627386i	−0.0210064	+	0.0210064i
$893$	9.74307	−	9.74307i	0.326039	−	0.326039i
$894$	4.67665	−	1.93713i	0.156411	−	0.0647874i
$895$	18.3422	−	12.8924i	0.613113	−	0.430945i
$896$	4.76369	+	1.97319i	0.159144	+	0.0659195i
$897$	−8.80317			−0.293929
$898$	−30.1216	−	12.4768i	−1.00517	−	0.416355i
$899$	−18.4382	+	18.4382i	−0.614949	+	0.614949i
$900$	−11.5777	+	5.44932i	−0.385922	+	0.181644i
$901$	−1.51489	−	19.7293i	−0.0504684	−	0.657279i
$902$		−	8.01014i		−	0.266708i
$903$	11.7654	+	11.7654i	0.391528	+	0.391528i
$904$	−5.38493	+	13.0004i	−0.179100	+	0.432386i
$905$	26.8125	−	5.99458i	0.891278	−	0.199267i
$906$	−0.291380	−	0.120693i	−0.00968045	−	0.00400977i
$907$	24.4262	−	10.1177i	0.811060	−	0.335952i	0.0616832	−	0.998096i	$-0.480353\pi$
$907$	24.4262	−	10.1177i	0.811060	−	0.335952i	0.749377	+	0.662144i	$0.230353\pi$
$908$	−8.54310	−	20.6249i	−0.283513	−	0.684460i
$909$	28.8941	+	28.8941i	0.958358	+	0.958358i
$910$	36.8166	+	23.3622i	1.22046	+	0.774449i
$911$	42.3697	−	17.5501i	1.40377	−	0.581461i	0.453043	−	0.891488i	$-0.350338\pi$
$911$	42.3697	−	17.5501i	1.40377	−	0.581461i	0.950728	+	0.310027i	$0.100338\pi$
$912$	1.99266	−	0.825387i	0.0659836	−	0.0273313i
$913$	7.75152	−	18.7138i	0.256538	−	0.619337i
$914$		−	8.68795i		−	0.287372i
$915$	0.407123	−	2.33333i	0.0134591	−	0.0771376i
$916$	−4.59129	+	4.59129i	−0.151701	+	0.151701i
$917$		−	35.1771i		−	1.16165i
$918$	−13.5725	+	6.88298i	−0.447960	+	0.227172i
$919$	−41.2704			−1.36139			−0.680693	−	0.732569i	$-0.738321\pi$
$919$	−41.2704			−1.36139			−0.680693	+	0.732569i	$0.738321\pi$
$920$	−6.61941	−	4.20038i	−0.218236	−	0.138483i
$921$	0.662040	−	1.59831i	0.0218150	−	0.0526660i
$922$	−14.1971			−0.467558
$923$	0.338600	−	0.817454i	0.0111452	−	0.0269068i
$924$	2.52618	+	6.09874i	0.0831052	+	0.200634i
$925$	−2.06339	−	1.87719i	−0.0678437	−	0.0617218i
$926$	−4.41317	−	4.41317i	−0.145026	−	0.145026i
$927$	30.0153	−	30.0153i	0.985831	−	0.985831i
$928$	1.35589	+	3.27342i	0.0445094	+	0.107455i
$929$	−18.0198	−	43.5036i	−0.591210	−	1.42731i	−0.882335	−	0.470622i	$-0.844029\pi$
$929$	−18.0198	−	43.5036i	−0.591210	−	1.42731i	0.291125	−	0.956685i	$-0.405971\pi$
$930$	1.87798	−	10.7632i	0.0615814	−	0.352940i
$931$		−	63.6278i		−	2.08532i
$932$	1.55383	+	0.643616i	0.0508973	+	0.0210823i
$933$	0.670389	+	0.670389i	0.0219476	+	0.0219476i
$934$	35.6693			1.16714
$935$	15.6961	+	8.34810i	0.513318	+	0.273012i
$936$	9.67856			0.316354
$937$	8.14787	+	8.14787i	0.266179	+	0.266179i	0.827559	−	0.561379i	$-0.189729\pi$
$937$	8.14787	+	8.14787i	0.266179	+	0.266179i	−0.561379	+	0.827559i	$0.689729\pi$
$938$	−48.9783	−	20.2875i	−1.59920	−	0.662410i
$939$		−	7.38769i		−	0.241088i
$940$	−9.34302	−	1.63018i	−0.304736	−	0.0531707i
$941$	−1.91451	−	4.62203i	−0.0624111	−	0.150674i	0.889597	−	0.456746i	$-0.150985\pi$
$941$	−1.91451	−	4.62203i	−0.0624111	−	0.150674i	−0.952008	+	0.306072i	$0.900985\pi$
$942$	−3.76827	−	9.09741i	−0.122777	−	0.296410i
$943$	−10.2982	+	10.2982i	−0.335355	+	0.335355i
$944$	−6.83453	−	6.83453i	−0.222445	−	0.222445i
$945$	−24.4708	−	34.8150i	−0.796034	−	1.13253i
$946$	−3.58662	−	8.65887i	−0.116611	−	0.281524i
$947$	−5.74762	+	13.8760i	−0.186773	+	0.450909i	−0.989335	−	0.145660i	$-0.953470\pi$
$947$	−5.74762	+	13.8760i	−0.186773	+	0.450909i	0.802562	+	0.596568i	$0.203470\pi$
$948$	5.95465			0.193398
$949$	−16.5533	+	39.9632i	−0.537342	+	1.29726i
$950$	15.2832	+	5.50073i	0.495853	+	0.178467i
$951$	1.46347			0.0474562
$952$	9.61548	+	18.9607i	0.311639	+	0.614520i
$953$			1.92919i			0.0624927i	0.999512	+	0.0312464i	$0.00994764\pi$
$953$			1.92919i			0.0624927i	−0.999512	+	0.0312464i	$0.990052\pi$
$954$	8.68467	−	8.68467i	0.281177	−	0.281177i
$955$	−13.0363	−	2.27459i	−0.421844	−	0.0736039i
$956$			13.9682i			0.451765i
$957$	−1.73589	+	4.19081i	−0.0561133	+	0.135470i
$958$	−32.8601	+	13.6111i	−1.06166	+	0.439754i
$959$	34.0733	−	14.1136i	1.10028	−	0.455753i
$960$	−1.25352	−	0.795427i	−0.0404571	−	0.0256723i
$961$	−16.3781	−	16.3781i	−0.528326	−	0.528326i
$962$	0.807432	+	1.94931i	0.0260326	+	0.0628484i
$963$	9.07146	−	3.75752i	0.292324	−	0.121084i
$964$	21.9665	+	9.09881i	0.707492	+	0.293053i
$965$	0.601680	+	2.69119i	0.0193688	+	0.0866324i
$966$	4.59305	−	11.0886i	0.147779	−	0.356770i
$967$	−10.7280	−	10.7280i	−0.344989	−	0.344989i	0.513250	−	0.858239i	$-0.328441\pi$
$967$	−10.7280	−	10.7280i	−0.344989	−	0.344989i	−0.858239	+	0.513250i	$0.828441\pi$
$968$			7.28166i			0.234042i
$969$	8.45238	+	2.76417i	0.271529	+	0.0887979i
$970$	−4.03902	−	18.0657i	−0.129685	−	0.580054i
$971$	−24.1427	+	24.1427i	−0.774775	+	0.774775i	−0.978937	−	0.204162i	$-0.934553\pi$
$971$	−24.1427	+	24.1427i	−0.774775	+	0.774775i	0.204162	+	0.978937i	$0.434553\pi$
$972$	−13.4361	−	5.56543i	−0.430964	−	0.178511i
$973$	65.1603			2.08894
$974$	1.01960	+	0.422332i	0.0326701	+	0.0135324i
$975$	−9.28645	−	8.44848i	−0.297404	−	0.270568i
$976$	−1.47400	+	0.610550i	−0.0471815	+	0.0195432i
$977$	−23.0505	+	23.0505i	−0.737451	+	0.737451i	−0.972084	−	0.234633i	$-0.924611\pi$
$977$	−23.0505	+	23.0505i	−0.737451	+	0.737451i	0.234633	+	0.972084i	$0.424611\pi$
$978$	2.09460	−	2.09460i	0.0669780	−	0.0669780i
$979$	13.4814	−	5.58417i	0.430867	−	0.178471i
$980$	−35.8307	+	25.1847i	−1.14457	+	0.804494i
$981$	−41.5042	−	17.1916i	−1.32513	−	0.548886i
$982$	9.73089			0.310525
$983$	11.0179	+	4.56376i	0.351416	+	0.145561i	0.551407	−	0.834236i	$-0.314091\pi$
$983$	11.0179	+	4.56376i	0.351416	+	0.145561i	−0.199991	+	0.979798i	$0.564091\pi$
$984$	−1.95017	+	1.95017i	−0.0621691	+	0.0621691i
$985$	24.4328	−	5.46254i	0.778493	−	0.174051i
$986$	−4.54081	+	13.8850i	−0.144609	+	0.442190i
$987$		−	14.5199i		−	0.462175i
$988$	−8.68736	−	8.68736i	−0.276382	−	0.276382i
$989$	−6.52111	+	15.7434i	−0.207359	+	0.500610i
$990$	2.40765	+	10.7689i	0.0765201	+	0.342258i
$991$	19.2995	+	7.99410i	0.613068	+	0.253941i	0.667540	−	0.744574i	$-0.267347\pi$
$991$	19.2995	+	7.99410i	0.613068	+	0.253941i	−0.0544717	+	0.998515i	$0.517347\pi$
$992$	−6.79928	+	2.81636i	−0.215877	+	0.0894194i
$993$	3.04373	+	7.34822i	0.0965899	+	0.233189i
$994$	0.853011	+	0.853011i	0.0270559	+	0.0270559i
$995$	−25.0012	+	39.3996i	−0.792593	+	1.24905i
$996$	−6.44333	+	2.66891i	−0.204165	+	0.0845678i
$997$	6.60154	−	2.73445i	0.209073	−	0.0866009i	−0.275689	−	0.961247i	$-0.588906\pi$
$997$	6.60154	−	2.73445i	0.209073	−	0.0866009i	0.484762	+	0.874646i	$0.338906\pi$
$998$	9.48039	−	22.8877i	0.300097	−	0.724497i
$999$		−	2.05918i		−	0.0651495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.n.a.59.3	yes	20
5.2	odd	4		850.2.l.i.501.3		20
5.3	odd	4		850.2.l.h.501.3		20
5.4	even	2		170.2.n.b.59.3	yes	20
17.15	even	8		170.2.n.b.49.3	yes	20
85.32	odd	8		850.2.l.i.151.3		20
85.49	even	8	inner	170.2.n.a.49.3	✓	20
85.83	odd	8		850.2.l.h.151.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.n.a.49.3	✓	20	85.49	even	8	inner
170.2.n.a.59.3	yes	20	1.1	even	1	trivial
170.2.n.b.49.3	yes	20	17.15	even	8
170.2.n.b.59.3	yes	20	5.4	even	2
850.2.l.h.151.3		20	85.83	odd	8
850.2.l.h.501.3		20	5.3	odd	4
850.2.l.i.151.3		20	85.32	odd	8
850.2.l.i.501.3		20	5.2	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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.613391 + 0.254075i) q^{3} +1.00000i q^{4} +(0.384345 - 2.20279i) q^{5} +(0.254075 + 0.613391i) q^{6} +(1.97319 + 4.76369i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.80963 - 1.80963i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.613391 + 0.254075i) q^{3} +1.00000i q^{4} +(0.384345 - 2.20279i) q^{5} +(0.254075 + 0.613391i) q^{6} +(1.97319 + 4.76369i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.80963 - 1.80963i) q^{9} +(1.82938 - 1.28583i) q^{10} +(-0.737928 - 1.78152i) q^{11} +(-0.254075 + 0.613391i) q^{12} +3.78187 q^{13} +(-1.97319 + 4.76369i) q^{14} +(0.795427 - 1.25352i) q^{15} -1.00000 q^{16} +(-3.13012 - 2.68371i) q^{17} -2.55920i q^{18} +(-2.29711 + 2.29711i) q^{19} +(2.20279 + 0.384345i) q^{20} +3.42334i q^{21} +(0.737928 - 1.78152i) q^{22} +(-3.23911 + 1.34168i) q^{23} +(-0.613391 + 0.254075i) q^{24} +(-4.70456 - 1.69326i) q^{25} +(2.67419 + 2.67419i) q^{26} +(-1.41245 - 3.40996i) q^{27} +(-4.76369 + 1.97319i) q^{28} +(-3.27342 - 1.35589i) q^{29} +(1.44882 - 0.323919i) q^{30} +(2.81636 - 6.79928i) q^{31} +(-0.707107 - 0.707107i) q^{32} -1.28025i q^{33} +(-0.315659 - 4.11100i) q^{34} +(11.2518 - 2.51561i) q^{35} +(1.80963 - 1.80963i) q^{36} +(0.515436 + 0.213501i) q^{37} -3.24860 q^{38} +(2.31976 + 0.960878i) q^{39} +(1.28583 + 1.82938i) q^{40} +(3.83779 - 1.58966i) q^{41} +(-2.42067 + 2.42067i) q^{42} +(3.43682 - 3.43682i) q^{43} +(1.78152 - 0.737928i) q^{44} +(-4.68175 + 3.29070i) q^{45} +(-3.23911 - 1.34168i) q^{46} -4.24145 q^{47} +(-0.613391 - 0.254075i) q^{48} +(-13.8496 + 13.8496i) q^{49} +(-2.12931 - 4.52394i) q^{50} +(-1.23812 - 2.44145i) q^{51} +3.78187i q^{52} +(3.39351 + 3.39351i) q^{53} +(1.41245 - 3.40996i) q^{54} +(-4.20792 + 0.940782i) q^{55} +(-4.76369 - 1.97319i) q^{56} +(-1.99266 + 0.825387i) q^{57} +(-1.35589 - 3.27342i) q^{58} +(6.83453 + 6.83453i) q^{59} +(1.25352 + 0.795427i) q^{60} +(1.47400 - 0.610550i) q^{61} +(6.79928 - 2.81636i) q^{62} +(5.04977 - 12.1912i) q^{63} -1.00000i q^{64} +(1.45354 - 8.33066i) q^{65} +(0.905276 - 0.905276i) q^{66} +10.2816i q^{67} +(2.68371 - 3.13012i) q^{68} -2.32773 q^{69} +(9.73503 + 6.17742i) q^{70} +(0.0895325 - 0.216151i) q^{71} +2.55920 q^{72} +(-4.37701 + 10.5670i) q^{73} +(0.213501 + 0.515436i) q^{74} +(-2.45552 - 2.23394i) q^{75} +(-2.29711 - 2.29711i) q^{76} +(7.03053 - 7.03053i) q^{77} +(0.960878 + 2.31976i) q^{78} +(-3.43221 - 8.28609i) q^{79} +(-0.384345 + 2.20279i) q^{80} +5.22709i q^{81} +(3.83779 + 1.58966i) q^{82} +(7.42776 + 7.42776i) q^{83} -3.42334 q^{84} +(-7.11471 + 5.86353i) q^{85} +4.86039 q^{86} +(-1.66339 - 1.66339i) q^{87} +(1.78152 + 0.737928i) q^{88} +7.56737i q^{89} +(-5.63737 - 0.983616i) q^{90} +(7.46234 + 18.0157i) q^{91} +(-1.34168 - 3.23911i) q^{92} +(3.45505 - 3.45505i) q^{93} +(-2.99916 - 2.99916i) q^{94} +(4.17716 + 5.94292i) q^{95} +(-0.254075 - 0.613391i) q^{96} +(3.16811 - 7.64850i) q^{97} -19.5862 q^{98} +(-1.88850 + 4.55925i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{5}+O(q^{10}) \) 20 * q - 4 * q^5	\( 20 q - 4 q^{5} + 4 q^{10} - 8 q^{11} - 24 q^{13} + 8 q^{15} - 20 q^{16} + 8 q^{20} + 8 q^{22} + 16 q^{23} - 12 q^{25} - 12 q^{26} + 24 q^{27} - 12 q^{29} - 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} - 8 q^{37} - 8 q^{38} + 4 q^{40} + 4 q^{41} + 8 q^{42} + 16 q^{43} - 8 q^{44} - 12 q^{45} + 16 q^{46} + 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} + 44 q^{53} - 24 q^{54} - 72 q^{57} + 16 q^{59} + 16 q^{60} + 8 q^{61} - 8 q^{62} - 24 q^{63} - 8 q^{65} - 8 q^{66} + 20 q^{68} - 16 q^{69} - 16 q^{70} + 8 q^{71} - 28 q^{72} - 60 q^{73} + 28 q^{74} + 64 q^{75} + 8 q^{78} + 56 q^{79} + 4 q^{80} + 4 q^{82} + 16 q^{84} - 16 q^{85} + 48 q^{86} - 72 q^{87} - 8 q^{88} + 32 q^{90} - 24 q^{91} - 8 q^{92} + 72 q^{93} + 32 q^{94} + 8 q^{95} + 48 q^{97} - 36 q^{98} + 72 q^{99}+O(q^{100}) \) 20 * q - 4 * q^5 + 4 * q^10 - 8 * q^11 - 24 * q^13 + 8 * q^15 - 20 * q^16 + 8 * q^20 + 8 * q^22 + 16 * q^23 - 12 * 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 - 12 * 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 + 16 * q^60 + 8 * q^61 - 8 * q^62 - 24 * q^63 - 8 * q^65 - 8 * q^66 + 20 * q^68 - 16 * q^69 - 16 * q^70 + 8 * q^71 - 28 * q^72 - 60 * q^73 + 28 * q^74 + 64 * q^75 + 8 * q^78 + 56 * q^79 + 4 * q^80 + 4 * q^82 + 16 * q^84 - 16 * q^85 + 48 * q^86 - 72 * q^87 - 8 * q^88 + 32 * q^90 - 24 * q^91 - 8 * q^92 + 72 * q^93 + 32 * q^94 + 8 * q^95 + 48 * q^97 - 36 * q^98 + 72 * q^99

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