LMFDB - Embedded newform 170.2.n.b.49.3

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			49.3
Root			$0.254075 + 0.613391i$ of defining polynomial
Character	$\chi$	$=$	170.49
Dual form			170.2.n.b.59.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.613391 + 0.254075i) q^{3} -1.00000i q^{4} +(-1.28583 - 1.82938i) q^{5} +(0.254075 - 0.613391i) q^{6} +(-1.97319 + 4.76369i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.80963 + 1.80963i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.613391 + 0.254075i) q^{3} -1.00000i q^{4} +(-1.28583 - 1.82938i) 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} +(2.20279 + 0.384345i) q^{10} +(-0.737928 + 1.78152i) q^{11} +(0.254075 + 0.613391i) q^{12} -3.78187 q^{13} +(-1.97319 - 4.76369i) q^{14} +(1.25352 + 0.795427i) q^{15} -1.00000 q^{16} +(3.13012 - 2.68371i) q^{17} -2.55920i q^{18} +(-2.29711 - 2.29711i) q^{19} +(-1.82938 + 1.28583i) q^{20} -3.42334i q^{21} +(-0.737928 - 1.78152i) q^{22} +(3.23911 + 1.34168i) q^{23} +(-0.613391 - 0.254075i) q^{24} +(-1.69326 + 4.70456i) 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} +(0.384345 - 2.20279i) 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} +(5.63737 + 0.983616i) 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} +(0.795427 - 1.25352i) q^{60} +(1.47400 + 0.610550i) q^{61} +(-6.79928 - 2.81636i) q^{62} +(-5.04977 - 12.1912i) q^{63} +1.00000i q^{64} +(4.86286 + 6.91848i) q^{65} +(0.905276 + 0.905276i) q^{66} +10.2816i q^{67} +(-2.68371 - 3.13012i) q^{68} -2.32773 q^{69} +(-6.17742 + 9.73503i) q^{70} +(0.0895325 + 0.216151i) q^{71} -2.55920 q^{72} +(4.37701 + 10.5670i) q^{73} +(0.213501 - 0.515436i) q^{74} +(-0.156677 - 3.31595i) 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} +(1.28583 + 1.82938i) q^{80} -5.22709i q^{81} +(-3.83779 + 1.58966i) q^{82} +(-7.42776 + 7.42776i) q^{83} -3.42334 q^{84} +(-8.93435 - 2.27537i) q^{85} +4.86039 q^{86} +(1.66339 - 1.66339i) q^{87} +(-1.78152 + 0.737928i) q^{88} -7.56737i q^{89} +(-4.68175 + 3.29070i) 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} +(-1.24858 + 7.15598i) 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} + 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 $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$

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	$-0.686387\pi$
$3$	−0.613391	+	0.254075i	−0.354141	+	0.146690i	0.198518	+	0.980097i	$0.436387\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−1.28583	−	1.82938i	−0.575042	−	0.818124i
$5$	−1.28583	−	1.82938i	−0.575042	−	0.818124i
$6$	0.254075	−	0.613391i	0.103726	−	0.250416i
$7$	−1.97319	+	4.76369i	−0.745794	+	1.80051i	−0.165299	+	0.986244i	$0.552859\pi$
$7$	−1.97319	+	4.76369i	−0.745794	+	1.80051i	−0.580496	+	0.814263i	$0.697141\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.80963	+	1.80963i	−0.603209	+	0.603209i
$10$	2.20279	+	0.384345i	0.696583	+	0.121541i
$11$	−0.737928	+	1.78152i	−0.222494	+	0.537147i	−0.995227	−	0.0975831i	$-0.968889\pi$
$11$	−0.737928	+	1.78152i	−0.222494	+	0.537147i	0.772734	+	0.634730i	$0.218889\pi$
$12$	0.254075	+	0.613391i	0.0733451	+	0.177071i
$13$	−3.78187			−1.04890			−0.524451	−	0.851441i	$-0.675729\pi$
$13$	−3.78187			−1.04890			−0.524451	+	0.851441i	$0.675729\pi$
$14$	−1.97319	−	4.76369i	−0.527356	−	1.27315i
$15$	1.25352	+	0.795427i	0.323657	+	0.205378i
$16$	−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	0.392682	−	0.919674i	$-0.371547\pi$
$19$	−2.29711	−	2.29711i	−0.526992	−	0.526992i	−0.919674	+	0.392682i	$0.871547\pi$
$20$	−1.82938	+	1.28583i	−0.409062	+	0.287521i
$21$		−	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	$-0.255890\pi$
$23$	3.23911	+	1.34168i	0.675402	+	0.279761i	−0.0185016	+	0.999829i	$0.505890\pi$
$24$	−0.613391	−	0.254075i	−0.125208	−	0.0518628i
$25$	−1.69326	+	4.70456i	−0.338653	+	0.940911i
$26$	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	−0.665313	−	0.746565i	$-0.731702\pi$
$29$	−3.27342	+	1.35589i	−0.607859	+	0.251783i	0.0574540	+	0.998348i	$0.481702\pi$
$30$	−1.44882	+	0.323919i	−0.264518	+	0.0591393i
$31$	2.81636	+	6.79928i	0.505832	+	1.22119i	0.946262	+	0.323400i	$0.104826\pi$
$31$	2.81636	+	6.79928i	0.505832	+	1.22119i	−0.440430	+	0.897787i	$0.645174\pi$
$32$	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	$-0.639603\pi$
$37$	−0.515436	+	0.213501i	−0.0847372	+	0.0350993i	0.339912	+	0.940457i	$0.389603\pi$
$38$	3.24860			0.526992
$39$	2.31976	−	0.960878i	0.371460	−	0.153864i
$40$	0.384345	−	2.20279i	0.0607703	−	0.348291i
$41$	3.83779	+	1.58966i	0.599362	+	0.248264i	0.661672	−	0.749793i	$-0.269847\pi$
$41$	3.83779	+	1.58966i	0.599362	+	0.248264i	−0.0623107	+	0.998057i	$0.519847\pi$
$42$	2.42067	+	2.42067i	0.373517	+	0.373517i
$43$	−3.43682	−	3.43682i	−0.524110	−	0.524110i	0.394700	−	0.918810i	$-0.370848\pi$
$43$	−3.43682	−	3.43682i	−0.524110	−	0.524110i	−0.918810	+	0.394700i	$0.870848\pi$
$44$	1.78152	+	0.737928i	0.268574	+	0.111247i
$45$	5.63737	+	0.983616i	0.840370	+	0.146629i
$46$	−3.23911	+	1.34168i	−0.477581	+	0.197821i
$47$	4.24145			0.618679			0.309340	−	0.950952i	$-0.399892\pi$
$47$	4.24145			0.618679			0.309340	+	0.950952i	$0.399892\pi$
$48$	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	$-0.856916\pi$
$53$	−3.39351	+	3.39351i	−0.466135	+	0.466135i	0.434525	+	0.900660i	$0.356916\pi$
$54$	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	−0.104721	−	0.994502i	$-0.533395\pi$
$59$	6.83453	−	6.83453i	0.889780	−	0.889780i	0.994502	+	0.104721i	$0.0333951\pi$
$60$	0.795427	−	1.25352i	0.102689	−	0.161828i
$61$	1.47400	+	0.610550i	0.188726	+	0.0781729i	0.475045	−	0.879961i	$-0.342432\pi$
$61$	1.47400	+	0.610550i	0.188726	+	0.0781729i	−0.286319	+	0.958134i	$0.592432\pi$
$62$	−6.79928	−	2.81636i	−0.863510	−	0.357678i
$63$	−5.04977	−	12.1912i	−0.636212	−	1.53595i
$64$			1.00000i			0.125000i
$65$	4.86286	+	6.91848i	0.603163	+	0.858132i
$66$	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
$70$	−6.17742	+	9.73503i	−0.738342	+	1.16356i
$71$	0.0895325	+	0.216151i	0.0106256	+	0.0256523i	0.929103	−	0.369820i	$-0.120581\pi$
$71$	0.0895325	+	0.216151i	0.0106256	+	0.0256523i	−0.918478	+	0.395473i	$0.870581\pi$
$72$	−2.55920			−0.301604
$73$	4.37701	+	10.5670i	0.512290	+	1.23678i	0.942548	+	0.334072i	$0.108423\pi$
$73$	4.37701	+	10.5670i	0.512290	+	1.23678i	−0.430258	+	0.902706i	$0.641577\pi$
$74$	0.213501	−	0.515436i	0.0248189	−	0.0599182i
$75$	−0.156677	−	3.31595i	−0.0180915	−	0.382893i
$76$	−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	0.604593	+	0.796535i	$0.293336\pi$
$79$	−3.43221	+	8.28609i	−0.386154	+	0.932258i	−0.990747	+	0.135724i	$0.956664\pi$
$80$	1.28583	+	1.82938i	0.143761	+	0.204531i
$81$		−	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	$-0.945584\pi$
$83$	−7.42776	+	7.42776i	−0.815303	+	0.815303i	0.170120	+	0.985423i	$0.445584\pi$
$84$	−3.42334			−0.373517
$85$	−8.93435	−	2.27537i	−0.969067	−	0.246799i
$86$	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	$-0.868639\pi$
$89$		−	7.56737i		−	0.802139i	0.916048	−	0.401070i	$-0.131361\pi$
$90$	−4.68175	+	3.29070i	−0.493499	+	0.346871i
$91$	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
$95$	−1.24858	+	7.15598i	−0.128102	+	0.734188i
$96$	−0.254075	+	0.613391i	−0.0259314	+	0.0626039i
$97$	−3.16811	−	7.64850i	−0.321673	−	0.776588i	−0.999157	−	0.0410503i	$-0.986930\pi$
$97$	−3.16811	−	7.64850i	−0.321673	−	0.776588i	0.677484	−	0.735538i	$-0.263070\pi$
$98$	19.5862			1.97851
$99$	−1.88850	−	4.55925i	−0.189802	−	0.458222i
$100$	4.70456	+	1.69326i	0.470456	+	0.169326i
$101$	−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
$105$	−6.26260	+	4.40185i	−0.611167	+	0.429577i
$106$		−	4.79915i		−	0.466135i
$107$	1.46824	+	3.54465i	0.141940	+	0.342674i	0.978823	−	0.204708i	$-0.0656245\pi$
$107$	1.46824	+	3.54465i	0.141940	+	0.342674i	−0.836883	+	0.547382i	$0.815624\pi$
$108$	−3.40996	−	1.41245i	−0.328124	−	0.135913i
$109$	16.2177	+	6.71758i	1.55337	+	0.643428i	0.983922	−	0.178598i	$-0.0571563\pi$
$109$	16.2177	+	6.71758i	1.55337	+	0.643428i	0.569450	+	0.822026i	$0.307156\pi$
$110$	−2.31022	+	3.64068i	−0.220271	+	0.347126i
$111$	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	$-0.605236\pi$
$113$	−13.0004	−	5.38493i	−1.22297	−	0.506571i	−0.898353	+	0.439274i	$0.855236\pi$
$114$	−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
$125$	10.7837	−	2.95166i	0.964522	−	0.264004i
$126$	12.1912	+	5.04977i	1.08608	+	0.449870i
$127$	−6.81394	−	6.81394i	−0.604640	−	0.604640i	0.336900	−	0.941540i	$-0.390621\pi$
$127$	−6.81394	−	6.81394i	−0.604640	−	0.604640i	−0.941540	+	0.336900i	$0.890621\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	2.98132	+	1.23490i	0.262491	+	0.108727i
$130$	−8.33066	−	1.45354i	−0.730648	−	0.127484i
$131$	−6.30300	+	2.61079i	−0.550695	+	0.228106i	−0.640640	−	0.767841i	$-0.721331\pi$
$131$	−6.30300	+	2.61079i	−0.550695	+	0.228106i	0.0899447	+	0.995947i	$0.471331\pi$
$132$	−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	0.985086	+	0.172062i	$0.0550431\pi$
$139$	4.83609	+	11.6753i	0.410192	+	0.990290i	−0.574894	+	0.818228i	$0.694957\pi$
$140$	−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
$145$	6.68952	+	4.24487i	0.555534	+	0.352517i
$146$	−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	$0.101100\pi$
$149$			7.62426i			0.624604i	−0.949983	+	0.312302i	$0.898900\pi$
$150$	2.45552	+	2.23394i	0.200492	+	0.182401i
$151$	−0.335898	−	0.335898i	−0.0273350	−	0.0273350i	0.693307	−	0.720642i	$-0.256153\pi$
$151$	−0.335898	−	0.335898i	−0.0273350	−	0.0273350i	−0.720642	+	0.693307i	$0.756153\pi$
$152$		−	3.24860i		−	0.263496i
$153$	−0.807833	+	10.5209i	−0.0653094	+	0.850562i
$154$	9.94267			0.801203
$155$	8.81711	−	13.8949i	0.708207	−	1.11607i
$156$	−0.960878	−	2.31976i	−0.0769318	−	0.185730i
$157$	14.8313			1.18367			0.591835	−	0.806059i	$-0.298404\pi$
$157$	14.8313			1.18367			0.591835	+	0.806059i	$0.298404\pi$
$158$	−3.43221	−	8.28609i	−0.273052	−	0.659206i
$159$	1.21934	−	2.94376i	0.0967002	−	0.233455i
$160$	−2.20279	−	0.384345i	−0.174146	−	0.0303852i
$161$	−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	$-0.819094\pi$
$163$	1.70740	−	4.12202i	0.133734	−	0.322861i	0.976533	+	0.215366i	$0.0690943\pi$
$164$	1.58966	−	3.83779i	0.124132	−	0.299681i
$165$	−2.34207	+	1.64619i	−0.182330	+	0.128156i
$166$		−	10.5044i		−	0.815303i
$167$	−9.90975	+	4.10475i	−0.766839	+	0.317635i	−0.731591	−	0.681743i	$-0.761222\pi$
$167$	−9.90975	+	4.10475i	−0.766839	+	0.317635i	−0.0352479	+	0.999379i	$0.511222\pi$
$168$	2.42067	−	2.42067i	0.186759	−	0.186759i
$169$	1.30255			0.100196
$170$	7.92647	−	4.70861i	0.607933	−	0.361134i
$171$	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	$-0.548003\pi$
$173$	5.82171	−	2.41143i	0.442616	−	0.183338i	0.592850	+	0.805313i	$0.298003\pi$
$174$			2.35238i			0.178334i
$175$	−19.0699	−	17.3492i	−1.44155	−	1.31147i
$176$	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	−0.390631	−	0.920547i	$-0.627743\pi$
$179$	7.08979	−	7.08979i	0.529916	−	0.529916i	0.920547	+	0.390631i	$0.127743\pi$
$180$	0.983616	−	5.63737i	0.0733144	−	0.420185i
$181$	4.70201	−	11.3517i	0.349498	−	0.843762i	−0.647181	−	0.762336i	$-0.724052\pi$
$181$	4.70201	−	11.3517i	0.349498	−	0.843762i	0.996679	−	0.0814265i	$-0.0259476\pi$
$182$	7.46234	+	18.0157i	0.553145	+	1.33541i
$183$	−1.05926			−0.0783029
$184$	1.34168	+	3.23911i	0.0989103	+	0.238791i
$185$	1.05334	+	0.668402i	0.0774430	+	0.0491419i
$186$	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
$190$	−4.17716	−	5.94292i	−0.303043	−	0.431145i
$191$			5.91808i			0.428217i	0.976810	+	0.214109i	$0.0686847\pi$
$191$			5.91808i			0.428217i	−0.976810	+	0.214109i	$0.931315\pi$
$192$	−0.254075	−	0.613391i	−0.0183363	−	0.0442677i
$193$	1.13937	+	0.471944i	0.0820139	+	0.0339713i	0.423313	−	0.905983i	$-0.360867\pi$
$193$	1.13937	+	0.471944i	0.0820139	+	0.0339713i	−0.341299	+	0.939955i	$0.610867\pi$
$194$	7.64850	+	3.16811i	0.549131	+	0.227457i
$195$	−4.74064	−	3.00820i	−0.339485	−	0.215422i
$196$	−13.8496	+	13.8496i	−0.989255	+	0.989255i
$197$	−4.28469	+	10.3441i	−0.305271	+	0.736990i	0.694574	+	0.719421i	$0.255593\pi$
$197$	−4.28469	+	10.3441i	−0.305271	+	0.736990i	−0.999846	+	0.0175692i	$0.994407\pi$
$198$	4.55925	+	1.88850i	0.324012	+	0.134210i
$199$	−19.2796	+	7.98588i	−1.36670	+	0.566104i	−0.940891	−	0.338710i	$-0.890009\pi$
$199$	−19.2796	+	7.98588i	−1.36670	+	0.566104i	−0.425806	+	0.904815i	$0.640009\pi$
$200$	−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
$210$	1.31575	−	7.54090i	0.0907951	−	0.520372i
$211$	−11.2232	−	4.64882i	−0.772640	−	0.320038i	−0.0386985	−	0.999251i	$-0.512321\pi$
$211$	−11.2232	−	4.64882i	−0.772640	−	0.320038i	−0.733941	+	0.679213i	$0.762321\pi$
$212$	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
$215$	−1.86807	+	10.7064i	−0.127401	+	0.730172i
$216$	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	$-0.759458\pi$
$223$	−0.627386	+	0.627386i	−0.0420129	+	0.0420129i	0.685788	+	0.727801i	$0.259458\pi$
$224$	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	$-0.109421\pi$
$227$	20.6249	+	8.54310i	1.36892	+	0.567025i	0.427425	+	0.904051i	$0.359421\pi$
$228$	0.825387	−	1.99266i	0.0546626	−	0.131967i
$229$	4.59129	−	4.59129i	0.303401	−	0.303401i	−0.538942	−	0.842343i	$-0.681176\pi$
$229$	4.59129	−	4.59129i	0.303401	−	0.303401i	0.842343	+	0.538942i	$0.181176\pi$
$230$	6.61941	+	4.20038i	0.436471	+	0.276965i
$231$	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	$-0.142545\pi$
$233$	−0.643616	−	1.55383i	−0.0421647	−	0.101795i	−0.943559	+	0.331205i	$0.892545\pi$
$234$			9.67856i			0.632707i
$235$	−5.45380	−	7.75923i	−0.355767	−	0.506156i
$236$	−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	$0.350794\pi$
$240$	−1.25352	−	0.795427i	−0.0809142	−	0.0513446i
$241$	9.09881	+	21.9665i	0.586106	+	1.41498i	0.887198	+	0.461389i	$0.152649\pi$
$241$	9.09881	+	21.9665i	0.586106	+	1.41498i	−0.301092	+	0.953595i	$0.597351\pi$
$242$	−7.28166			−0.468083
$243$	5.56543	+	13.4361i	0.357022	+	0.861928i
$244$	0.610550	−	1.47400i	0.0390865	−	0.0943631i
$245$	−7.52788	+	43.1444i	−0.480939	+	2.75639i
$246$	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
$250$	−5.53808	+	9.71235i	−0.350259	+	0.614263i
$251$		−	15.0409i		−	0.949375i	−0.880155	−	0.474687i	$-0.842561\pi$
$251$		−	15.0409i		−	0.949375i	0.880155	−	0.474687i	$-0.157439\pi$
$252$	−12.1912	+	5.04977i	−0.767976	+	0.318106i
$253$	−4.78046	+	4.78046i	−0.300545	+	0.300545i
$254$	9.63637			0.604640
$255$	6.05837	−	0.874300i	0.379390	−	0.0547508i
$256$	1.00000			0.0625000
$257$	15.7106	−	15.7106i	0.980002	−	0.980002i	−0.0198022	−	0.999804i	$-0.506304\pi$
$257$	15.7106	−	15.7106i	0.980002	−	0.980002i	0.999804	+	0.0198022i	$0.00630366\pi$
$258$	−2.98132	+	1.23490i	−0.185609	+	0.0768817i
$259$		−	2.87666i		−	0.178747i
$260$	6.91848	−	4.86286i	0.429066	−	0.301582i
$261$	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	$-0.315563\pi$
$263$	−4.69057	−	4.69057i	−0.289233	−	0.289233i	−0.836777	+	0.547544i	$0.815563\pi$
$264$	0.905276	−	0.905276i	0.0557159	−	0.0557159i
$265$	10.5715	+	1.84453i	0.649403	+	0.113309i
$266$	−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	0.973956	+	0.226735i	$0.0728052\pi$
$269$	7.30824	+	17.6437i	0.445591	+	1.07575i	−0.528365	+	0.849017i	$0.677195\pi$
$270$	4.42194	−	6.96855i	0.269110	−	0.424093i
$271$	−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
$275$	−7.13174	−	6.48820i	−0.430060	−	0.391253i
$276$			2.32773i			0.140113i
$277$	−5.15659	−	12.4491i	−0.309829	−	0.747994i	−0.999710	−	0.0240713i	$-0.992337\pi$
$277$	−5.15659	−	12.4491i	−0.309829	−	0.747994i	0.689881	−	0.723923i	$-0.257663\pi$
$278$	−11.6753	−	4.83609i	−0.700241	−	0.290049i
$279$	−17.4007	−	7.20761i	−1.04175	−	0.431508i
$280$	9.73503	+	6.17742i	0.581779	+	0.369171i
$281$	8.18352	−	8.18352i	0.488188	−	0.488188i	−0.419546	−	0.907734i	$-0.637811\pi$
$281$	8.18352	−	8.18352i	0.488188	−	0.488188i	0.907734	+	0.419546i	$0.137811\pi$
$282$	1.07765	−	2.60167i	0.0641729	−	0.154927i
$283$	−0.0268950	−	0.0111403i	−0.00159874	−	0.000662220i	0.381884	−	0.924210i	$-0.375275\pi$
$283$	−0.0268950	−	0.0111403i	−0.00159874	−	0.000662220i	−0.383483	+	0.923548i	$0.625275\pi$
$284$	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	$-0.633285\pi$
$293$	−13.9196			−0.813195			−0.406597	+	0.913607i	$0.633285\pi$
$294$	−12.0140	+	4.97637i	−0.700672	+	0.290228i
$295$	−21.2910	−	3.71489i	−1.23961	−	0.216289i
$296$	−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
$300$	−3.31595	+	0.156677i	−0.191446	+	0.00904577i
$301$	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	−0.344965	−	0.938616i	$-0.612109\pi$
$311$	1.31928	−	0.546462i	0.0748092	−	0.0309870i	0.419774	+	0.907629i	$0.362109\pi$
$312$	2.31976	+	0.960878i	0.131331	+	0.0543990i
$313$	4.25820	−	10.2802i	0.240688	−	0.581072i	−0.756664	−	0.653804i	$-0.773172\pi$
$313$	4.25820	−	10.2802i	0.240688	−	0.581072i	0.997351	+	0.0727326i	$0.0231720\pi$
$314$	−10.4873	+	10.4873i	−0.591835	+	0.591835i
$315$	−15.8092	+	24.9139i	−0.890749	+	1.40374i
$316$	8.28609	+	3.43221i	0.466129	+	0.193077i
$317$	−2.03646	−	0.843531i	−0.114379	−	0.0473774i	0.324760	−	0.945796i	$-0.394716\pi$
$317$	−2.03646	−	0.843531i	−0.114379	−	0.0473774i	−0.439139	+	0.898419i	$0.644716\pi$
$318$	1.21934	+	2.94376i	0.0683774	+	0.165078i
$319$		−	6.83220i		−	0.382530i
$320$	1.82938	−	1.28583i	0.102265	−	0.0718803i
$321$	−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
$325$	6.40370	−	17.7920i	0.355214	−	0.986924i
$326$	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
$330$	0.492060	−	2.82013i	0.0270870	−	0.155243i
$331$	8.47090	−	8.47090i	0.465603	−	0.465603i	−0.434884	−	0.900487i	$-0.643210\pi$
$331$	8.47090	−	8.47090i	0.465603	−	0.465603i	0.900487	+	0.434884i	$0.143210\pi$
$332$	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
$335$	18.8089	−	13.2204i	1.02764	−	0.722308i
$336$			3.42334i			0.186759i
$337$	17.8257	−	7.38363i	0.971026	−	0.402212i	0.159932	−	0.987128i	$-0.448873\pi$
$337$	17.8257	−	7.38363i	0.971026	−	0.402212i	0.811094	+	0.584916i	$0.198873\pi$
$338$	−0.921042	+	0.921042i	−0.0500981	+	0.0500981i
$339$	9.34248			0.507414
$340$	−2.27537	+	8.93435i	−0.123400	+	0.484533i
$341$	−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
$345$	2.99307	+	4.25830i	0.161142	+	0.229259i
$346$	−2.41143	+	5.82171i	−0.129639	+	0.312977i
$347$	−2.61715	+	6.31836i	−0.140496	+	0.339187i	−0.978428	−	0.206587i	$-0.933764\pi$
$347$	−2.61715	+	6.31836i	−0.140496	+	0.339187i	0.837932	+	0.545774i	$0.183764\pi$
$348$	−1.66339	−	1.66339i	−0.0891669	−	0.0891669i
$349$	5.65961	−	5.65961i	0.302952	−	0.302952i	−0.539216	−	0.842168i	$-0.681279\pi$
$349$	5.65961	−	5.65961i	0.302952	−	0.302952i	0.842168	+	0.539216i	$0.181279\pi$
$350$	25.7522	−	1.21678i	1.37651	−	0.0650398i
$351$	−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	$-0.0480241\pi$
$353$	37.1497			1.97728			0.988640	+	0.150300i	$0.0480241\pi$
$354$	−2.45576	−	5.92872i	−0.130522	−	0.315108i
$355$	0.280298	−	0.441723i	0.0148767	−	0.0234442i
$356$	−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	0.612718	−	0.790302i	$-0.290076\pi$
$359$	−3.36474	−	3.36474i	−0.177584	−	0.177584i	−0.790302	+	0.612718i	$0.790076\pi$
$360$	3.29070	+	4.68175i	0.173435	+	0.246750i
$361$		−	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
$365$	13.7030	−	21.5947i	0.717249	−	1.13032i
$366$	0.749012	−	0.749012i	0.0391515	−	0.0391515i
$367$	−1.36037	+	3.28423i	−0.0710110	+	0.171436i	−0.955400	−	0.295315i	$-0.904575\pi$
$367$	−1.36037	+	3.28423i	−0.0710110	+	0.171436i	0.884389	+	0.466751i	$0.154575\pi$
$368$	−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	−0.911839	−	0.410548i	$-0.865338\pi$
$379$	−24.6523	+	10.2113i	−1.26631	+	0.524521i	−0.354467	+	0.935069i	$0.615338\pi$
$380$	7.15598	+	1.24858i	0.367094	+	0.0640510i
$381$	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	$-0.336998\pi$
$383$	−7.47058	−	7.47058i	−0.381729	−	0.381729i	−0.871725	+	0.489996i	$0.836998\pi$
$384$	0.613391	+	0.254075i	0.0313020	+	0.0129657i
$385$	−3.82142	+	21.9016i	−0.194757	+	1.11621i
$386$	−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	0.878708	−	0.477359i	$-0.158406\pi$
$389$	7.91583	+	7.91583i	0.401349	+	0.401349i	−0.477359	+	0.878708i	$0.658406\pi$
$390$	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	$-0.519443\pi$
$397$	−16.1390	−	6.68500i	−0.809994	−	0.335511i	−0.748952	+	0.662625i	$0.769443\pi$
$398$	7.98588	−	19.2796i	0.400296	−	0.966400i
$399$	−7.86378	+	7.86378i	−0.393681	+	0.393681i
$400$	1.69326	−	4.70456i	0.0846632	−	0.235228i
$401$	2.23800	+	0.927011i	0.111760	+	0.0462927i	0.437863	−	0.899042i	$-0.355735\pi$
$401$	2.23800	+	0.927011i	0.111760	+	0.0462927i	−0.326103	+	0.945334i	$0.605735\pi$
$402$	6.30663	+	2.61229i	0.314546	+	0.130289i
$403$	−10.6511	−	25.7140i	−0.530569	−	1.28091i
$404$			15.9669i			0.794384i
$405$	−9.56233	+	6.72116i	−0.475156	+	0.333977i
$406$	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	$0.278473\pi$
$410$	7.84286	+	4.97673i	0.387331	+	0.245783i
$411$	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
$415$	23.1391	+	4.03733i	1.13585	+	0.198185i
$416$	−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	0.0569581	−	0.998377i	$-0.481860\pi$
$419$	14.7921	−	35.7113i	0.722641	−	1.74461i	0.665683	−	0.746234i	$-0.268140\pi$
$420$	4.40185	+	6.26260i	0.214788	+	0.305583i
$421$			32.3783i			1.57802i	0.614380	+	0.789010i	$0.289406\pi$
$421$			32.3783i			1.57802i	−0.614380	+	0.789010i	$0.710594\pi$
$422$	11.2232	−	4.64882i	0.546339	−	0.226301i
$423$	−7.67544	+	7.67544i	−0.373193	+	0.373193i
$424$	−4.79915			−0.233067
$425$	7.32557	+	19.2701i	0.355342	+	0.934736i
$426$	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
$430$	−6.24966	−	8.89151i	−0.301385	−	0.428787i
$431$	−10.4913	+	25.3282i	−0.505347	+	1.22002i	0.441188	+	0.897415i	$0.354557\pi$
$431$	−10.4913	+	25.3282i	−0.505347	+	1.22002i	−0.946535	+	0.322601i	$0.895443\pi$
$432$	−1.41245	+	3.40996i	−0.0679566	+	0.164062i
$433$	−4.97561	−	4.97561i	−0.239113	−	0.239113i	0.577370	−	0.816483i	$-0.304079\pi$
$433$	−4.97561	−	4.97561i	−0.239113	−	0.239113i	−0.816483	+	0.577370i	$0.804079\pi$
$434$	26.8325	−	26.8325i	1.28800	−	1.28800i
$435$	−5.18180	−	0.904127i	−0.248448	−	0.0433496i
$436$	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	0.996987	−	0.0775743i	$-0.0247175\pi$
$439$	4.96900	+	11.9962i	0.237157	+	0.572548i	−0.759829	+	0.650123i	$0.774717\pi$
$440$	3.64068	+	2.31022i	0.173563	+	0.110135i
$441$	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
$445$	−13.8436	+	9.73038i	−0.656249	+	0.461264i
$446$		−	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	−0.466281	−	0.884636i	$-0.654407\pi$
$449$	−30.1216	−	12.4768i	−1.42152	−	0.588815i	−0.955243	+	0.295822i	$0.904407\pi$
$450$	12.0399	+	4.33340i	0.567566	+	0.204278i
$451$	−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	$-0.684865\pi$
$457$	6.14331	−	6.14331i	0.287372	−	0.287372i	0.836040	+	0.548668i	$0.184865\pi$
$458$			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	0.433564	−	0.901123i	$-0.357256\pi$
$461$	−10.0389	−	10.0389i	−0.467558	−	0.467558i	−0.901123	+	0.433564i	$0.857256\pi$
$462$	−6.09874	+	2.52618i	−0.283739	+	0.117529i
$463$	6.24116			0.290051			0.145026	−	0.989428i	$-0.453674\pi$
$463$	6.24116			0.290051			0.145026	+	0.989428i	$0.453674\pi$
$464$	3.27342	−	1.35589i	0.151965	−	0.0629458i
$465$	−1.87798	+	10.7632i	−0.0870893	+	0.499133i
$466$	1.55383	+	0.643616i	0.0719796	+	0.0298149i
$467$	−25.2220	−	25.2220i	−1.16714	−	1.16714i	−0.982878	−	0.184257i	$-0.941012\pi$
$467$	−25.2220	−	25.2220i	−1.16714	−	1.16714i	−0.184257	−	0.982878i	$-0.558988\pi$
$468$	−6.84377	−	6.84377i	−0.316354	−	0.316354i
$469$	−48.9783	−	20.2875i	−2.26161	−	0.936789i
$470$	9.34302	+	1.63018i	0.430962	+	0.0751947i
$471$	−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	−0.849462	−	0.527650i	$-0.823073\pi$
$479$	−13.6111	−	32.8601i	−0.621906	−	1.50141i	0.227556	−	0.973765i	$-0.426927\pi$
$480$	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
$485$	−9.91835	+	15.6304i	−0.450369	+	0.709739i
$486$	−13.4361	−	5.56543i	−0.609475	−	0.252453i
$487$	−1.01960	−	0.422332i	−0.0462025	−	0.0191377i	0.359463	−	0.933160i	$-0.382960\pi$
$487$	−1.01960	−	0.422332i	−0.0462025	−	0.0191377i	−0.405665	+	0.914022i	$0.632960\pi$
$488$	0.610550	+	1.47400i	0.0276383	+	0.0667248i
$489$			2.96221i			0.133956i
$490$	−25.1847	−	35.8307i	−1.13773	−	1.61867i
$491$	6.88078	+	6.88078i	0.310525	+	0.310525i	0.845113	−	0.534588i	$-0.179533\pi$
$491$	6.88078	+	6.88078i	0.310525	+	0.310525i	−0.534588	+	0.845113i	$0.679533\pi$
$492$			2.75796i			0.124338i
$493$	−6.60737	+	13.0290i	−0.297581	+	0.586798i
$494$	−12.2858			−0.552763
$495$	−5.91230	+	9.31723i	−0.265738	+	0.418778i
$496$	−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	0.556633	+	0.830758i	$0.312093\pi$
$499$	−9.48039	+	22.8877i	−0.424401	+	1.02459i	−0.981034	+	0.193836i	$0.937907\pi$
$500$	−2.95166	−	10.7837i	−0.132002	−	0.482261i
$501$	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	$-0.937396\pi$
$503$	−3.34332	+	8.07150i	−0.149071	+	0.359890i	0.831650	+	0.555300i	$0.187396\pi$
$504$	5.04977	−	12.1912i	0.224935	−	0.543041i
$505$	20.5308	+	29.2096i	0.913609	+	1.29981i
$506$		−	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	$0.538477\pi$
$510$	−3.66569	+	4.90213i	−0.162319	+	0.217070i
$511$	−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
$515$	30.3429	−	21.3274i	1.33707	−	0.939798i
$516$	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
$520$	−1.45354	+	8.33066i	−0.0637421	+	0.365324i
$521$	−10.9210	+	26.3656i	−0.478457	+	1.15510i	0.481875	+	0.876240i	$0.339956\pi$
$521$	−10.9210	+	26.3656i	−0.478457	+	1.15510i	−0.960332	+	0.278858i	$0.910044\pi$
$522$	3.47000	+	8.37733i	0.151878	+	0.366666i
$523$	6.67355			0.291814			0.145907	−	0.989298i	$-0.453390\pi$
$523$	6.67355			0.291814			0.145907	+	0.989298i	$0.453390\pi$
$524$	2.61079	+	6.30300i	0.114053	+	0.275348i
$525$	16.1053	+	5.79662i	0.702893	+	0.252985i
$526$	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
$530$	−8.77947	+	6.17091i	−0.381356	+	0.268047i
$531$			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
$535$	4.59660	−	7.24380i	0.198728	−	0.313177i
$536$	−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	0.896813	−	0.442410i	$-0.145876\pi$
$541$	−1.16670	−	2.81667i	−0.0501605	−	0.121098i	−0.946974	+	0.321312i	$0.895876\pi$
$542$	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	−0.729885	+	0.683570i	$0.760426\pi$
$547$	−40.4461	+	16.7533i	−1.72935	+	0.716320i	−0.999464	+	0.0327496i	$0.989574\pi$
$548$	−7.15271			−0.305549
$549$	−3.77225	+	1.56252i	−0.160996	+	0.0666867i
$550$	9.63075	−	0.455050i	0.410657	−	0.0194034i
$551$	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
$555$	−0.815933	−	0.142365i	−0.0346344	−	0.00604305i
$556$	11.6753	−	4.83609i	0.495145	−	0.205096i
$557$	−24.8597			−1.05334			−0.526669	−	0.850071i	$-0.676559\pi$
$557$	−24.8597			−1.05334			−0.526669	+	0.850071i	$0.676559\pi$
$558$	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	$-0.808567\pi$
$563$	−6.13933	+	6.13933i	−0.258742	+	0.258742i	0.565800	+	0.824542i	$0.308567\pi$
$564$	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	−0.999600	−	0.0282640i	$-0.991002\pi$
$569$	−23.1700	+	23.1700i	−0.971336	+	0.971336i	0.0282640	+	0.999600i	$0.491002\pi$
$570$	4.07218	+	2.58402i	0.170565	+	0.108233i
$571$	28.2865	+	11.7166i	1.18375	+	0.490326i	0.885716	−	0.464228i	$-0.153668\pi$
$571$	28.2865	+	11.7166i	1.18375	+	0.490326i	0.298037	+	0.954554i	$0.403668\pi$
$572$	−6.73746	−	2.79075i	−0.281707	−	0.116687i
$573$	−1.50364	−	3.63010i	−0.0628153	−	0.151650i
$574$		−	21.4187i		−	0.894001i
$575$	−11.7967	+	12.9668i	−0.491956	+	0.540752i
$576$	−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
$580$	4.24487	−	6.68952i	0.176259	−	0.277767i
$581$	−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
$585$	−21.3198	−	3.71991i	−0.881466	−	0.153799i
$586$	9.84268	−	9.84268i	0.406597	−	0.406597i
$587$	33.4139	+	33.4139i	1.37914	+	1.37914i	0.846074	+	0.533065i	$0.178960\pi$
$587$	33.4139	+	33.4139i	1.37914	+	1.37914i	0.533065	+	0.846074i	$0.321040\pi$
$588$	4.97637	−	12.0140i	0.205222	−	0.495450i
$589$	9.14921	−	22.0881i	0.376987	−	0.910126i
$590$	17.6819	−	12.4282i	0.727950	−	0.511661i
$591$		−	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	$-0.586237\pi$
$593$	16.9464	−	16.9464i	0.695906	−	0.695906i	0.963525	+	0.267619i	$0.0862368\pi$
$594$	−7.11719			−0.292022
$595$	28.4683	−	38.0708i	1.16709	−	1.56075i
$596$	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	$0.0926159\pi$
$599$			14.0422i			0.573747i	−0.957969	+	0.286873i	$0.907384\pi$
$600$	2.23394	−	2.45552i	0.0912003	−	0.100246i
$601$	13.1098	−	31.6498i	0.534759	−	1.29102i	−0.393582	−	0.919290i	$-0.628764\pi$
$601$	13.1098	−	31.6498i	0.534759	−	1.29102i	0.928340	−	0.371732i	$-0.121236\pi$
$602$	−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
$605$	2.79867	−	16.0400i	0.113782	−	0.652117i
$606$	−4.05679	+	9.79396i	−0.164796	+	0.397852i
$607$	6.63626	+	16.0213i	0.269357	+	0.650286i	0.999453	−	0.0330584i	$-0.0105247\pi$
$607$	6.63626	+	16.0213i	0.269357	+	0.650286i	−0.730096	+	0.683345i	$0.760525\pi$
$608$	−3.24860			−0.131748
$609$	4.64169	+	11.2060i	0.188091	+	0.454091i
$610$	3.01225	+	1.91144i	0.121962	+	0.0773919i
$611$	−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
$615$	3.54627	+	5.04535i	0.143000	+	0.203448i
$616$		−	9.94267i		−	0.400601i
$617$	−10.5097	−	25.3727i	−0.423106	−	1.02147i	−0.981426	−	0.191842i	$-0.938554\pi$
$617$	−10.5097	−	25.3727i	−0.423106	−	1.02147i	0.558320	−	0.829626i	$-0.311446\pi$
$618$	10.1740	+	4.21420i	0.409257	+	0.169520i
$619$	4.94993	+	2.05033i	0.198955	+	0.0824097i	0.479936	−	0.877304i	$-0.340660\pi$
$619$	4.94993	+	2.05033i	0.198955	+	0.0824097i	−0.280981	+	0.959713i	$0.590660\pi$
$620$	−13.8949	−	8.81711i	−0.558034	−	0.354104i
$621$	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	1.00000		0.000175956i	$-5.60084e-5\pi$
$631$	25.1153	+	25.1153i	0.999824	+	0.999824i	−0.000175956		1.00000i	$0.500056\pi$
$632$	−8.28609	+	3.43221i	−0.329603	+	0.136526i
$633$	8.06538			0.320570
$634$	2.03646	−	0.843531i	0.0808783	−	0.0335009i
$635$	−3.70369	+	21.2269i	−0.146977	+	0.842364i
$636$	−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
$640$	−0.384345	+	2.20279i	−0.0151926	+	0.0870729i
$641$	11.8092	−	4.89153i	0.466435	−	0.193204i	−0.137072	−	0.990561i	$-0.543769\pi$
$641$	11.8092	−	4.89153i	0.466435	−	0.193204i	0.603508	+	0.797357i	$0.293769\pi$
$642$	2.54730			0.100534
$643$	−11.5049	+	4.76547i	−0.453708	+	0.187932i	−0.597822	−	0.801629i	$-0.703967\pi$
$643$	−11.5049	+	4.76547i	−0.453708	+	0.187932i	0.144114	+	0.989561i	$0.453967\pi$
$644$	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	−0.549988	−	0.835173i	$-0.685368\pi$
$653$	10.9746	−	26.4950i	0.429468	−	1.03683i	0.979456	−	0.201656i	$-0.0646323\pi$
$654$	8.24101	−	8.24101i	0.322249	−	0.322249i
$655$	12.8807	+	8.17354i	0.503292	+	0.319367i
$656$	−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	$0.138066\pi$
$659$			21.5776i			0.840546i	−0.907398	+	0.420273i	$0.861934\pi$
$660$	1.64619	+	2.34207i	0.0640780	+	0.0911650i
$661$	19.0645	+	19.0645i	0.741522	+	0.741522i	0.972871	−	0.231349i	$-0.0743138\pi$
$661$	19.0645	+	19.0645i	0.741522	+	0.741522i	−0.231349	+	0.972871i	$0.574314\pi$
$662$			11.9797i			0.465603i
$663$	4.68243	−	9.23326i	0.181850	−	0.358590i
$664$	−10.5044			−0.407651
$665$	−31.6252	−	20.0679i	−1.22637	−	0.778201i
$666$	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
$670$	−3.95168	+	22.6482i	−0.152667	+	0.874975i
$671$	−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	0.423942	+	0.905689i	$0.360646\pi$
$673$	−13.3927	+	32.3328i	−0.516249	+	1.24634i	−0.940191	+	0.340647i	$0.889354\pi$
$674$	−7.38363	+	17.8257i	−0.284407	+	0.686619i
$675$	13.6507	+	12.4189i	0.525416	+	0.478005i
$676$		−	1.30255i		−	0.0500981i
$677$	13.1663	−	5.45364i	0.506020	−	0.209600i	−0.115044	−	0.993360i	$-0.536701\pi$
$677$	13.1663	−	5.45364i	0.506020	−	0.209600i	0.621064	+	0.783760i	$0.286701\pi$
$678$	−6.60613	+	6.60613i	−0.253707	+	0.253707i
$679$	42.6864			1.63815
$680$	−4.70861	−	7.92647i	−0.180567	−	0.303966i
$681$	−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	$-0.617803\pi$
$683$	1.09176	−	0.452223i	0.0417751	−	0.0173038i	0.403473	+	0.914991i	$0.367803\pi$
$684$		−	8.31380i		−	0.317886i
$685$	−13.0850	+	9.19719i	−0.499953	+	0.351407i
$686$	−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
$690$	−5.12750	−	0.894652i	−0.195200	−	0.0340588i
$691$	9.65140	−	23.3005i	0.367156	−	0.886394i	−0.627057	−	0.778973i	$-0.715741\pi$
$691$	9.65140	−	23.3005i	0.367156	−	0.886394i	0.994214	−	0.107421i	$-0.0342592\pi$
$692$	−2.41143	−	5.82171i	−0.0916688	−	0.221308i
$693$	25.4452			0.966585
$694$	−2.61715	−	6.31836i	−0.0993457	−	0.239842i
$695$	15.1402	−	23.8596i	0.574302	−	0.905046i
$696$	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
$700$	−17.3492	+	19.0699i	−0.655736	+	0.720776i
$701$			44.5531i			1.68275i	0.540453	+	0.841374i	$0.318253\pi$
$701$			44.5531i			1.68275i	−0.540453	+	0.841374i	$0.681747\pi$
$702$	−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
$705$	5.31674	+	3.37377i	0.200240	+	0.127063i
$706$	−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	−0.226277	−	0.974063i	$-0.572655\pi$
$709$	8.05437	−	3.33623i	0.302488	−	0.125295i	0.528765	+	0.848768i	$0.322655\pi$
$710$	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	0.0326277	−	0.999468i	$-0.489612\pi$
$719$	20.4439	−	8.46815i	0.762429	−	0.315809i	0.729802	+	0.683659i	$0.239612\pi$
$720$	−5.63737	−	0.983616i	−0.210092	−	0.0366572i
$721$	−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
$725$	−0.836124	−	17.6959i	−0.0310529	−	0.657208i
$726$	4.46651	−	1.85009i	0.165768	−	0.0686632i
$727$	13.9152			0.516088			0.258044	−	0.966133i	$-0.416922\pi$
$727$	13.9152			0.516088			0.258044	+	0.966133i	$0.416922\pi$
$728$	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	$-0.769705\pi$
$733$	−2.36873	+	2.36873i	−0.0874912	+	0.0874912i	0.662007	+	0.749498i	$0.269705\pi$
$734$	−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	−0.523145	−	0.852243i	$-0.675242\pi$
$739$	8.94639	−	8.94639i	0.329098	−	0.329098i	0.852243	+	0.523145i	$0.175242\pi$
$740$	0.668402	−	1.05334i	0.0245710	−	0.0387215i
$741$	−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	−0.997061	−	0.0766080i	$-0.975591\pi$
$743$	−9.43680	−	22.7824i	−0.346203	−	0.835807i	0.650859	−	0.759199i	$-0.274409\pi$
$744$		−	4.88618i		−	0.179136i
$745$	13.9477	−	9.80353i	0.511003	−	0.359174i
$746$	−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
$750$	0.929342	−	7.36455i	0.0339348	−	0.268915i
$751$	−0.492767	−	1.18965i	−0.0179813	−	0.0434108i	0.914634	−	0.404283i	$-0.132479\pi$
$751$	−0.492767	−	1.18965i	−0.0179813	−	0.0434108i	−0.932615	+	0.360872i	$0.882479\pi$
$752$	−4.24145			−0.154670
$753$	3.82152	+	9.22596i	0.139264	+	0.336213i
$754$	−5.12782	+	12.3796i	−0.186744	+	0.450840i
$755$	−0.182576	+	1.04639i	−0.00664462	+	0.0380822i
$756$	13.4570	−	13.4570i	0.489426	−	0.489426i
$757$	−18.6875	−	18.6875i	−0.679208	−	0.679208i	0.280613	−	0.959821i	$-0.409462\pi$
$757$	−18.6875	−	18.6875i	−0.679208	−	0.679208i	−0.959821	+	0.280613i	$0.909462\pi$
$758$	10.2113	−	24.6523i	0.370892	−	0.895414i
$759$	1.71770	−	4.14689i	0.0623485	−	0.150522i
$760$	−5.94292	+	4.17716i	−0.215572	+	0.151521i
$761$		−	9.94599i		−	0.360542i	−0.983617	−	0.180271i	$-0.942303\pi$
$761$		−	9.94599i		−	0.360542i	0.983617	−	0.180271i	$-0.0576974\pi$
$762$	−5.91086	+	2.44836i	−0.214128	+	0.0886947i
$763$	−64.0010	+	64.0010i	−2.31699	+	2.31699i
$764$	5.91808			0.214109
$765$	20.2854	−	12.0503i	0.733421	−	0.435678i
$766$	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	$0.215523\pi$
$769$			34.7481i			1.25305i	−0.779402	+	0.626525i	$0.784477\pi$
$770$	−12.7846	−	18.1889i	−0.460726	−	0.655483i
$771$	−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	$-0.173784\pi$
$773$	9.32492	+	9.32492i	0.335394	+	0.335394i	−0.519236	+	0.854631i	$0.673784\pi$
$774$	−8.79550	+	8.79550i	−0.316148	+	0.316148i
$775$	−36.7565	+	1.73673i	−1.32033	+	0.0623852i
$776$	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
$780$	−3.00820	+	4.74064i	−0.107711	+	0.169742i
$781$	−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
$785$	−19.0706	−	27.1322i	−0.680660	−	0.968389i
$786$			4.52954i			0.161563i
$787$	4.47652	+	10.8073i	0.159571	+	0.385238i	0.983362	−	0.181655i	$-0.0581453\pi$
$787$	4.47652	+	10.8073i	0.159571	+	0.385238i	−0.823792	+	0.566893i	$0.808145\pi$
$788$	10.3441	+	4.28469i	0.368495	+	0.152636i
$789$	4.06891	+	1.68540i	0.144857	+	0.0600018i
$790$	−10.7452	+	16.9334i	−0.382296	+	0.602462i
$791$	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	$-0.736153\pi$
$797$	1.73623	−	1.73623i	0.0615003	−	0.0615003i	0.737188	+	0.675688i	$0.236153\pi$
$798$		−	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
$805$	39.8210	+	6.94801i	1.40351	+	0.244885i
$806$	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	0.921114	−	0.389293i	$-0.127281\pi$
$809$	36.8953	+	15.2825i	1.29717	+	0.537305i	0.376054	+	0.926598i	$0.377281\pi$
$810$	2.00901	−	11.5142i	0.0705893	−	0.404567i
$811$	5.85899	−	2.42687i	0.205737	−	0.0852190i	−0.277435	−	0.960744i	$-0.589484\pi$
$811$	5.85899	−	2.42687i	0.205737	−	0.0852190i	0.483172	+	0.875525i	$0.339484\pi$
$812$	−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	−0.996999	−	0.0774174i	$-0.975333\pi$
$821$	−47.1986	+	19.5503i	−1.64724	+	0.682310i	−0.650242	+	0.759727i	$0.725333\pi$
$822$	−4.38741	−	1.81732i	−0.153028	−	0.0633864i
$823$	11.3375	−	27.3712i	0.395201	−	0.954099i	−0.593587	−	0.804770i	$-0.702289\pi$
$823$	11.3375	−	27.3712i	0.395201	−	0.954099i	0.988788	−	0.149329i	$-0.0477114\pi$
$824$	−11.7284	+	11.7284i	−0.408578	+	0.408578i
$825$	6.02303	+	2.16781i	0.209695	+	0.0754734i
$826$	−46.0434	−	19.0718i	−1.60206	−	0.663593i
$827$	34.3113	+	14.2122i	1.19312	+	0.494206i	0.888770	−	0.458354i	$-0.151561\pi$
$827$	34.3113	+	14.2122i	1.19312	+	0.494206i	0.304350	+	0.952560i	$0.401561\pi$
$828$	3.43364	+	8.28953i	0.119327	+	0.288081i
$829$			5.88822i			0.204506i	0.994758	+	0.102253i	$0.0326052\pi$
$829$			5.88822i			0.204506i	−0.994758	+	0.102253i	$0.967395\pi$
$830$	−19.2166	+	13.5070i	−0.667019	+	0.468834i
$831$	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
$835$	20.2514	+	12.8507i	0.700830	+	0.444716i
$836$	−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	−0.975995	−	0.217792i	$-0.930114\pi$
$839$	−3.81939	+	9.22081i	−0.131860	+	0.318338i	0.844135	+	0.536130i	$0.180114\pi$
$840$	−7.54090	−	1.31575i	−0.260186	−	0.0453975i
$841$	−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
$845$	−1.67486	−	2.38286i	−0.0576170	−	0.0819729i
$846$		−	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
$850$	−18.8060	−	8.44605i	−0.645039	−	0.289697i
$851$	−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	$-0.492207\pi$
$853$	21.8663	−	9.05730i	0.748686	−	0.310116i	0.724205	+	0.689584i	$0.242207\pi$
$854$		−	8.22641i		−	0.281502i
$855$	−10.6902	−	15.2091i	−0.365596	−	0.520141i
$856$	−1.46824	+	3.54465i	−0.0501835	+	0.121154i
$857$	3.44244	−	8.31079i	0.117592	−	0.283891i	−0.854114	−	0.520085i	$-0.825900\pi$
$857$	3.44244	−	8.31079i	0.117592	−	0.283891i	0.971706	+	0.236194i	$0.0759001\pi$
$858$	−3.42364	−	3.42364i	−0.116881	−	0.116881i
$859$	−17.1482	+	17.1482i	−0.585090	+	0.585090i	−0.936298	−	0.351207i	$-0.885771\pi$
$859$	−17.1482	+	17.1482i	−0.585090	+	0.585090i	0.351207	+	0.936298i	$0.385771\pi$
$860$	10.7064	+	1.86807i	0.365086	+	0.0637006i
$861$	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	$-0.299032\pi$
$863$	34.6790			1.18049			0.590243	+	0.807225i	$0.299032\pi$
$864$	−1.41245	−	3.40996i	−0.0480526	−	0.116009i
$865$	−11.8972	−	7.54942i	−0.404516	−	0.256688i
$866$	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
$870$	4.30340	−	3.02477i	0.145899	−	0.102549i
$871$		−	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
$875$	−7.21742	+	57.1943i	−0.243993	+	1.93352i
$876$	−5.36963	+	5.36963i	−0.181423	+	0.181423i
$877$	−9.96344	+	24.0539i	−0.336442	+	0.812242i	0.661610	+	0.749848i	$0.269873\pi$
$877$	−9.96344	+	24.0539i	−0.336442	+	0.812242i	−0.998052	+	0.0623936i	$0.980127\pi$
$878$	−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	−0.991979	−	0.126402i	$-0.959657\pi$
$881$	−11.2768	−	27.2245i	−0.379924	−	0.917217i	0.612055	−	0.790815i	$-0.290343\pi$
$882$	−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	$-0.635339\pi$
$887$	−1.78717	+	0.740272i	−0.0600074	+	0.0248559i	0.352478	+	0.935820i	$0.385339\pi$
$888$	0.370409			0.0124301
$889$	45.9047	−	19.0144i	1.53960	−	0.637721i
$890$	2.90848	−	16.6693i	0.0974925	−	0.558757i
$891$	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
$895$	−22.0862	−	3.85363i	−0.738260	−	0.128813i
$896$	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	$-0.519647\pi$
$907$	−24.4262	−	10.1177i	−0.811060	−	0.335952i	−0.749377	+	0.662144i	$0.769647\pi$
$908$	8.54310	−	20.6249i	0.283513	−	0.684460i
$909$	28.8941	−	28.8941i	0.958358	−	0.958358i
$910$	23.3622	−	36.8166i	0.774449	−	1.22046i
$911$	42.3697	+	17.5501i	1.40377	+	0.581461i	0.950728	−	0.310027i	$-0.100338\pi$
$911$	42.3697	+	17.5501i	1.40377	+	0.581461i	0.453043	+	0.891488i	$0.350338\pi$
$912$	−1.99266	−	0.825387i	−0.0659836	−	0.0273313i
$913$	−7.75152	−	18.7138i	−0.256538	−	0.619337i
$914$			8.68795i			0.287372i
$915$	1.36204	+	1.93779i	0.0450275	+	0.0640615i
$916$	−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	$0.738321\pi$
$920$	4.20038	−	6.61941i	0.138483	−	0.218236i
$921$	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
$925$	−0.131657	−	2.78641i	−0.00432886	−	0.0916166i
$926$	−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	0.291125	+	0.956685i	$0.405971\pi$
$929$	−18.0198	+	43.5036i	−0.591210	+	1.42731i	−0.882335	+	0.470622i	$0.844029\pi$
$930$	−6.28282	−	8.93869i	−0.206022	−	0.293111i
$931$			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
$935$	10.6465	−	14.2376i	0.348179	−	0.465620i
$936$	9.67856			0.316354
$937$	−8.14787	+	8.14787i	−0.266179	+	0.266179i	−0.827559	−	0.561379i	$-0.810271\pi$
$937$	−8.14787	+	8.14787i	−0.266179	+	0.266179i	0.561379	+	0.827559i	$0.310271\pi$
$938$	48.9783	−	20.2875i	1.59920	−	0.662410i
$939$			7.38769i			0.241088i
$940$	−7.75923	+	5.45380i	−0.253078	+	0.177883i
$941$	−1.91451	+	4.62203i	−0.0624111	+	0.150674i	−0.952008	−	0.306072i	$-0.900985\pi$
$941$	−1.91451	+	4.62203i	−0.0624111	+	0.150674i	0.889597	+	0.456746i	$0.150985\pi$
$942$	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
$945$	7.31449	−	41.9214i	0.237940	−	1.36370i
$946$	−3.58662	+	8.65887i	−0.116611	+	0.281524i
$947$	5.74762	+	13.8760i	0.186773	+	0.450909i	0.989335	−	0.145660i	$-0.0465304\pi$
$947$	5.74762	+	13.8760i	0.186773	+	0.450909i	−0.802562	+	0.596568i	$0.796530\pi$
$948$	−5.95465			−0.193398
$949$	−16.5533	−	39.9632i	−0.537342	−	1.29726i
$950$	−5.50073	+	15.2832i	−0.178467	+	0.495853i
$951$	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
$955$	10.8264	−	7.60967i	0.350335	−	0.246243i
$956$		−	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
$960$	−0.795427	+	1.25352i	−0.0256723	+	0.0404571i
$961$	−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	$-0.671559\pi$
$967$	10.7280	−	10.7280i	0.344989	−	0.344989i	0.858239	+	0.513250i	$0.171559\pi$
$968$			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	0.204162	−	0.978937i	$-0.434553\pi$
$971$	−24.1427	−	24.1427i	−0.774775	−	0.774775i	−0.978937	+	0.204162i	$0.934553\pi$
$972$	13.4361	−	5.56543i	0.430964	−	0.178511i
$973$	−65.1603			−2.08894
$974$	1.01960	−	0.422332i	0.0326701	−	0.0135324i
$975$	0.592534	+	12.5405i	0.0189763	+	0.401617i
$976$	−1.47400	−	0.610550i	−0.0471815	−	0.0195432i
$977$	23.0505	+	23.0505i	0.737451	+	0.737451i	0.972084	−	0.234633i	$-0.0753889\pi$
$977$	23.0505	+	23.0505i	0.737451	+	0.737451i	−0.234633	+	0.972084i	$0.575389\pi$
$978$	−2.09460	−	2.09460i	−0.0669780	−	0.0669780i
$979$	13.4814	+	5.58417i	0.430867	+	0.178471i
$980$	43.1444	+	7.52788i	1.37820	+	0.240469i
$981$	−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	$-0.685909\pi$
$983$	−11.0179	+	4.56376i	−0.351416	+	0.145561i	0.199991	+	0.979798i	$0.435909\pi$
$984$	−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	−0.0544717	−	0.998515i	$-0.517347\pi$
$991$	19.2995	−	7.99410i	0.613068	−	0.253941i	0.667540	+	0.744574i	$0.267347\pi$
$992$	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
$995$	39.3996	+	25.0012i	1.24905	+	0.792593i
$996$	−6.44333	−	2.66891i	−0.204165	−	0.0845678i
$997$	−6.60154	−	2.73445i	−0.209073	−	0.0866009i	0.275689	−	0.961247i	$-0.411094\pi$
$997$	−6.60154	−	2.73445i	−0.209073	−	0.0866009i	−0.484762	+	0.874646i	$0.661094\pi$
$998$	−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.b.49.3	yes	20
5.2	odd	4		850.2.l.i.151.3		20
5.3	odd	4		850.2.l.h.151.3		20
5.4	even	2		170.2.n.a.49.3	✓	20
17.8	even	8		170.2.n.a.59.3	yes	20
85.8	odd	8		850.2.l.h.501.3		20
85.42	odd	8		850.2.l.i.501.3		20
85.59	even	8	inner	170.2.n.b.59.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.n.a.49.3	✓	20	5.4	even	2
170.2.n.a.59.3	yes	20	17.8	even	8
170.2.n.b.49.3	yes	20	1.1	even	1	trivial
170.2.n.b.59.3	yes	20	85.59	even	8	inner
850.2.l.h.151.3		20	5.3	odd	4
850.2.l.h.501.3		20	85.8	odd	8
850.2.l.i.151.3		20	5.2	odd	4
850.2.l.i.501.3		20	85.42	odd	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.613391 + 0.254075i) q^{3} -1.00000i q^{4} +(-1.28583 - 1.82938i) q^{5} +(0.254075 - 0.613391i) q^{6} +(-1.97319 + 4.76369i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.80963 + 1.80963i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.613391 + 0.254075i) q^{3} -1.00000i q^{4} +(-1.28583 - 1.82938i) 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} +(2.20279 + 0.384345i) q^{10} +(-0.737928 + 1.78152i) q^{11} +(0.254075 + 0.613391i) q^{12} -3.78187 q^{13} +(-1.97319 - 4.76369i) q^{14} +(1.25352 + 0.795427i) q^{15} -1.00000 q^{16} +(3.13012 - 2.68371i) q^{17} -2.55920i q^{18} +(-2.29711 - 2.29711i) q^{19} +(-1.82938 + 1.28583i) q^{20} -3.42334i q^{21} +(-0.737928 - 1.78152i) q^{22} +(3.23911 + 1.34168i) q^{23} +(-0.613391 - 0.254075i) q^{24} +(-1.69326 + 4.70456i) 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} +(0.384345 - 2.20279i) 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} +(5.63737 + 0.983616i) 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} +(0.795427 - 1.25352i) q^{60} +(1.47400 + 0.610550i) q^{61} +(-6.79928 - 2.81636i) q^{62} +(-5.04977 - 12.1912i) q^{63} +1.00000i q^{64} +(4.86286 + 6.91848i) q^{65} +(0.905276 + 0.905276i) q^{66} +10.2816i q^{67} +(-2.68371 - 3.13012i) q^{68} -2.32773 q^{69} +(-6.17742 + 9.73503i) q^{70} +(0.0895325 + 0.216151i) q^{71} -2.55920 q^{72} +(4.37701 + 10.5670i) q^{73} +(0.213501 - 0.515436i) q^{74} +(-0.156677 - 3.31595i) 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} +(1.28583 + 1.82938i) q^{80} -5.22709i q^{81} +(-3.83779 + 1.58966i) q^{82} +(-7.42776 + 7.42776i) q^{83} -3.42334 q^{84} +(-8.93435 - 2.27537i) q^{85} +4.86039 q^{86} +(1.66339 - 1.66339i) q^{87} +(-1.78152 + 0.737928i) q^{88} -7.56737i q^{89} +(-4.68175 + 3.29070i) 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} +(-1.24858 + 7.15598i) 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	\( 20 q - 4 q^{5} + 8 q^{10} - 8 q^{11} + 24 q^{13} + 16 q^{15} - 20 q^{16} - 4 q^{20} - 8 q^{22} - 16 q^{23} + 8 q^{25} - 12 q^{26} - 24 q^{27} - 12 q^{29} + 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} + 8 q^{37} + 8 q^{38} - 4 q^{40} + 4 q^{41} - 8 q^{42} - 16 q^{43} - 8 q^{44} - 32 q^{45} + 16 q^{46} - 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} - 44 q^{53} - 24 q^{54} + 72 q^{57} + 16 q^{59} + 8 q^{60} + 8 q^{61} + 8 q^{62} + 24 q^{63} - 28 q^{65} - 8 q^{66} - 20 q^{68} - 16 q^{69} + 8 q^{71} + 28 q^{72} + 60 q^{73} + 28 q^{74} - 8 q^{78} + 56 q^{79} + 4 q^{80} - 4 q^{82} + 16 q^{84} + 84 q^{85} + 48 q^{86} + 72 q^{87} + 8 q^{88} - 12 q^{90} - 24 q^{91} + 8 q^{92} - 72 q^{93} + 32 q^{94} + 88 q^{95} - 48 q^{97} + 36 q^{98} + 72 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more