LMFDB - Embedded newform 210.2.j.b.197.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(113,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("210.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 16x^{10} + 86x^{8} + 196x^{6} + 185x^{4} + 60x^{2} + 4 $ x^12 + 16x^10 + 86x^8 + 196x^6 + 185x^4 + 60*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.3
Root			$-2.80721i$ of defining polynomial
Character	$\chi$	$=$	210.197
Dual form			210.2.j.b.113.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.53661 + 0.799269i) q^{3} -1.00000i q^{4} +(1.91438 + 1.15549i) q^{5} +(-1.65172 + 0.521378i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.72234 + 2.45633i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.53661 + 0.799269i) q^{3} -1.00000i q^{4} +(1.91438 + 1.15549i) q^{5} +(-1.65172 + 0.521378i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.72234 + 2.45633i) q^{9} +(-2.17073 + 0.536610i) q^{10} -1.70489i q^{11} +(0.799269 - 1.53661i) q^{12} +(0.921665 - 0.921665i) q^{13} +1.00000 q^{14} +(2.01810 + 3.30564i) q^{15} -1.00000 q^{16} +(-4.76445 + 4.76445i) q^{17} +(-2.95476 - 0.519010i) q^{18} -5.94473i q^{19} +(1.15549 - 1.91438i) q^{20} +(-0.521378 - 1.65172i) q^{21} +(1.20554 + 1.20554i) q^{22} +(2.49622 + 2.49622i) q^{23} +(0.521378 + 1.65172i) q^{24} +(2.32966 + 4.42410i) q^{25} +1.30343i q^{26} +(0.683293 + 5.15103i) q^{27} +(-0.707107 + 0.707107i) q^{28} -5.19708 q^{29} +(-3.76445 - 0.910435i) q^{30} -3.40667 q^{31} +(0.707107 - 0.707107i) q^{32} +(1.36267 - 2.61976i) q^{33} -6.73795i q^{34} +(-0.536610 - 2.17073i) q^{35} +(2.45633 - 1.72234i) q^{36} +(-1.02910 - 1.02910i) q^{37} +(4.20356 + 4.20356i) q^{38} +(2.15290 - 0.679581i) q^{39} +(0.536610 + 2.17073i) q^{40} -10.9749i q^{41} +(1.53661 + 0.799269i) q^{42} +(8.17020 - 8.17020i) q^{43} -1.70489 q^{44} +(0.458926 + 6.69249i) q^{45} -3.53019 q^{46} +(-0.436661 + 0.436661i) q^{47} +(-1.53661 - 0.799269i) q^{48} +1.00000i q^{49} +(-4.77563 - 1.48099i) q^{50} +(-11.1292 + 3.51302i) q^{51} +(-0.921665 - 0.921665i) q^{52} +(-6.87196 - 6.87196i) q^{53} +(-4.12549 - 3.15917i) q^{54} +(1.96999 - 3.26380i) q^{55} -1.00000i q^{56} +(4.75144 - 9.13472i) q^{57} +(3.67489 - 3.67489i) q^{58} +0.686337 q^{59} +(3.30564 - 2.01810i) q^{60} -1.74994 q^{61} +(2.40888 - 2.40888i) q^{62} +(0.519010 - 2.95476i) q^{63} +1.00000i q^{64} +(2.82939 - 0.699434i) q^{65} +(0.888895 + 2.81600i) q^{66} +(1.03802 + 1.03802i) q^{67} +(4.76445 + 4.76445i) q^{68} +(1.84056 + 5.83087i) q^{69} +(1.91438 + 1.15549i) q^{70} -12.2611i q^{71} +(-0.519010 + 2.95476i) q^{72} +(-4.59693 + 4.59693i) q^{73} +1.45536 q^{74} +(0.0437379 + 8.66014i) q^{75} -5.94473 q^{76} +(-1.20554 + 1.20554i) q^{77} +(-1.04179 + 2.00286i) q^{78} -7.19515i q^{79} +(-1.91438 - 1.15549i) q^{80} +(-3.06710 + 8.46126i) q^{81} +(7.76040 + 7.76040i) q^{82} +(6.64687 + 6.64687i) q^{83} +(-1.65172 + 0.521378i) q^{84} +(-14.6263 + 3.61565i) q^{85} +11.5544i q^{86} +(-7.98588 - 4.15386i) q^{87} +(1.20554 - 1.20554i) q^{88} -2.25517 q^{89} +(-5.05681 - 4.40779i) q^{90} -1.30343 q^{91} +(2.49622 - 2.49622i) q^{92} +(-5.23472 - 2.72285i) q^{93} -0.617532i q^{94} +(6.86910 - 11.3804i) q^{95} +(1.65172 - 0.521378i) q^{96} +(13.2182 + 13.2182i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(4.18778 - 2.93640i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} + 4 q^{5}+O(q^{10}) $ 12 * q + 4 * q^3 + 4 * q^5	$ 12 q + 4 q^{3} + 4 q^{5} - 4 q^{12} + 12 q^{14} - 12 q^{15} - 12 q^{16} - 28 q^{17} - 8 q^{18} - 4 q^{21} + 4 q^{22} + 24 q^{23} + 4 q^{24} + 20 q^{25} + 28 q^{27} - 8 q^{29} - 16 q^{30} - 8 q^{31} - 36 q^{33} + 8 q^{35} + 4 q^{36} - 20 q^{37} + 4 q^{38} + 40 q^{39} - 8 q^{40} + 4 q^{42} + 8 q^{43} - 8 q^{44} - 48 q^{45} + 8 q^{46} - 16 q^{47} - 4 q^{48} + 16 q^{50} + 8 q^{51} + 24 q^{53} + 4 q^{54} - 16 q^{55} + 44 q^{57} - 8 q^{58} - 32 q^{59} + 4 q^{60} - 28 q^{62} - 8 q^{66} + 28 q^{68} + 32 q^{69} + 4 q^{70} - 24 q^{73} - 8 q^{74} - 4 q^{75} - 4 q^{77} - 8 q^{78} - 4 q^{80} - 36 q^{81} + 32 q^{82} + 24 q^{83} - 36 q^{85} - 16 q^{87} + 4 q^{88} - 48 q^{89} - 8 q^{90} + 24 q^{91} + 24 q^{92} - 20 q^{93} + 8 q^{97} + 40 q^{99}+O(q^{100}) $ 12 * q + 4 * q^3 + 4 * q^5 - 4 * q^12 + 12 * q^14 - 12 * q^15 - 12 * q^16 - 28 * q^17 - 8 * q^18 - 4 * q^21 + 4 * q^22 + 24 * q^23 + 4 * q^24 + 20 * q^25 + 28 * q^27 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 36 * q^33 + 8 * q^35 + 4 * q^36 - 20 * q^37 + 4 * q^38 + 40 * q^39 - 8 * q^40 + 4 * q^42 + 8 * q^43 - 8 * q^44 - 48 * q^45 + 8 * q^46 - 16 * q^47 - 4 * q^48 + 16 * q^50 + 8 * q^51 + 24 * q^53 + 4 * q^54 - 16 * q^55 + 44 * q^57 - 8 * q^58 - 32 * q^59 + 4 * q^60 - 28 * q^62 - 8 * q^66 + 28 * q^68 + 32 * q^69 + 4 * q^70 - 24 * q^73 - 8 * q^74 - 4 * q^75 - 4 * q^77 - 8 * q^78 - 4 * q^80 - 36 * q^81 + 32 * q^82 + 24 * q^83 - 36 * q^85 - 16 * q^87 + 4 * q^88 - 48 * q^89 - 8 * q^90 + 24 * q^91 + 24 * q^92 - 20 * q^93 + 8 * q^97 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	1.53661	+	0.799269i	0.887162	+	0.461458i
$3$	1.53661	+	0.799269i	0.887162	+	0.461458i
$4$		−	1.00000i		−	0.500000i
$5$	1.91438	+	1.15549i	0.856135	+	0.516753i
$5$	1.91438	+	1.15549i	0.856135	+	0.516753i
$6$	−1.65172	+	0.521378i	−0.674310	+	0.212852i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	1.72234	+	2.45633i	0.574113	+	0.818776i
$10$	−2.17073	+	0.536610i	−0.686444	+	0.169691i
$11$		−	1.70489i		−	0.514045i	−0.966405	−	0.257022i	$-0.917259\pi$
$11$		−	1.70489i		−	0.514045i	0.966405	−	0.257022i	$-0.0827414\pi$
$12$	0.799269	−	1.53661i	0.230729	−	0.443581i
$13$	0.921665	−	0.921665i	0.255624	−	0.255624i	−0.567648	−	0.823272i	$-0.692146\pi$
$13$	0.921665	−	0.921665i	0.255624	−	0.255624i	0.823272	+	0.567648i	$0.192146\pi$
$14$	1.00000			0.267261
$15$	2.01810	+	3.30564i	0.521070	+	0.853514i
$16$	−1.00000			−0.250000
$17$	−4.76445	+	4.76445i	−1.15555	+	1.15555i	−0.170128	+	0.985422i	$0.554418\pi$
$17$	−4.76445	+	4.76445i	−1.15555	+	1.15555i	−0.985422	+	0.170128i	$0.945582\pi$
$18$	−2.95476	−	0.519010i	−0.696444	−	0.122332i
$19$		−	5.94473i		−	1.36381i	−0.731439	−	0.681907i	$-0.761151\pi$
$19$		−	5.94473i		−	1.36381i	0.731439	−	0.681907i	$-0.238849\pi$
$20$	1.15549	−	1.91438i	0.258376	−	0.428067i
$21$	−0.521378	−	1.65172i	−0.113774	−	0.360434i
$22$	1.20554	+	1.20554i	0.257022	+	0.257022i
$23$	2.49622	+	2.49622i	0.520498	+	0.520498i	0.917722	−	0.397224i	$-0.130026\pi$
$23$	2.49622	+	2.49622i	0.520498	+	0.520498i	−0.397224	+	0.917722i	$0.630026\pi$
$24$	0.521378	+	1.65172i	0.106426	+	0.337155i
$25$	2.32966	+	4.42410i	0.465933	+	0.884820i
$26$			1.30343i			0.255624i
$27$	0.683293	+	5.15103i	0.131500	+	0.991316i
$28$	−0.707107	+	0.707107i	−0.133631	+	0.133631i
$29$	−5.19708			−0.965073			−0.482536	−	0.875876i	$-0.660284\pi$
$29$	−5.19708			−0.965073			−0.482536	+	0.875876i	$0.660284\pi$
$30$	−3.76445	−	0.910435i	−0.687292	−	0.166222i
$31$	−3.40667			−0.611856			−0.305928	−	0.952055i	$-0.598967\pi$
$31$	−3.40667			−0.611856			−0.305928	+	0.952055i	$0.598967\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	1.36267	−	2.61976i	0.237210	−	0.456041i
$34$		−	6.73795i		−	1.15555i
$35$	−0.536610	−	2.17073i	−0.0907036	−	0.366920i
$36$	2.45633	−	1.72234i	0.409388	−	0.287056i
$37$	−1.02910	−	1.02910i	−0.169183	−	0.169183i	0.617437	−	0.786620i	$-0.288171\pi$
$37$	−1.02910	−	1.02910i	−0.169183	−	0.169183i	−0.786620	+	0.617437i	$0.788171\pi$
$38$	4.20356	+	4.20356i	0.681907	+	0.681907i
$39$	2.15290	−	0.679581i	0.344740	−	0.108820i
$40$	0.536610	+	2.17073i	0.0848454	+	0.343222i
$41$		−	10.9749i		−	1.71399i	−0.515328	−	0.856993i	$-0.672330\pi$
$41$		−	10.9749i		−	1.71399i	0.515328	−	0.856993i	$-0.327670\pi$
$42$	1.53661	+	0.799269i	0.237104	+	0.123330i
$43$	8.17020	−	8.17020i	1.24594	−	1.24594i	0.288449	−	0.957495i	$-0.406861\pi$
$43$	8.17020	−	8.17020i	1.24594	−	1.24594i	0.957495	−	0.288449i	$-0.0931395\pi$
$44$	−1.70489			−0.257022
$45$	0.458926	+	6.69249i	0.0684126	+	0.997657i
$46$	−3.53019			−0.520498
$47$	−0.436661	+	0.436661i	−0.0636935	+	0.0636935i	−0.738236	−	0.674542i	$-0.764341\pi$
$47$	−0.436661	+	0.436661i	−0.0636935	+	0.0636935i	0.674542	+	0.738236i	$0.264341\pi$
$48$	−1.53661	−	0.799269i	−0.221790	−	0.115365i
$49$			1.00000i			0.142857i
$50$	−4.77563	−	1.48099i	−0.675376	−	0.209444i
$51$	−11.1292	+	3.51302i	−1.55840	+	0.491922i
$52$	−0.921665	−	0.921665i	−0.127812	−	0.127812i
$53$	−6.87196	−	6.87196i	−0.943937	−	0.943937i	0.0545729	−	0.998510i	$-0.482620\pi$
$53$	−6.87196	−	6.87196i	−0.943937	−	0.943937i	−0.998510	+	0.0545729i	$0.982620\pi$
$54$	−4.12549	−	3.15917i	−0.561408	−	0.429908i
$55$	1.96999	−	3.26380i	0.265634	−	0.440091i
$56$		−	1.00000i		−	0.133631i
$57$	4.75144	−	9.13472i	0.629343	−	1.20992i
$58$	3.67489	−	3.67489i	0.482536	−	0.482536i
$59$	0.686337			0.0893535			0.0446767	−	0.999001i	$-0.485774\pi$
$59$	0.686337			0.0893535			0.0446767	+	0.999001i	$0.485774\pi$
$60$	3.30564	−	2.01810i	0.426757	−	0.260535i
$61$	−1.74994			−0.224056			−0.112028	−	0.993705i	$-0.535735\pi$
$61$	−1.74994			−0.224056			−0.112028	+	0.993705i	$0.535735\pi$
$62$	2.40888	−	2.40888i	0.305928	−	0.305928i
$63$	0.519010	−	2.95476i	0.0653891	−	0.372265i
$64$			1.00000i			0.125000i
$65$	2.82939	−	0.699434i	0.350943	−	0.0867541i
$66$	0.888895	+	2.81600i	0.109415	+	0.346625i
$67$	1.03802	+	1.03802i	0.126814	+	0.126814i	0.767665	−	0.640851i	$-0.221418\pi$
$67$	1.03802	+	1.03802i	0.126814	+	0.126814i	−0.640851	+	0.767665i	$0.721418\pi$
$68$	4.76445	+	4.76445i	0.577775	+	0.577775i
$69$	1.84056	+	5.83087i	0.221578	+	0.701954i
$70$	1.91438	+	1.15549i	0.228812	+	0.138108i
$71$		−	12.2611i		−	1.45513i	−0.686040	−	0.727564i	$-0.740652\pi$
$71$		−	12.2611i		−	1.45513i	0.686040	−	0.727564i	$-0.259348\pi$
$72$	−0.519010	+	2.95476i	−0.0611659	+	0.348222i
$73$	−4.59693	+	4.59693i	−0.538030	+	0.538030i	−0.922950	−	0.384920i	$-0.874229\pi$
$73$	−4.59693	+	4.59693i	−0.538030	+	0.538030i	0.384920	+	0.922950i	$0.374229\pi$
$74$	1.45536			0.169183
$75$	0.0437379	+	8.66014i	0.00505042	+	0.999987i
$76$	−5.94473			−0.681907
$77$	−1.20554	+	1.20554i	−0.137384	+	0.137384i
$78$	−1.04179	+	2.00286i	−0.117960	+	0.226780i
$79$		−	7.19515i		−	0.809517i	−0.914424	−	0.404759i	$-0.867356\pi$
$79$		−	7.19515i		−	0.809517i	0.914424	−	0.404759i	$-0.132644\pi$
$80$	−1.91438	−	1.15549i	−0.214034	−	0.129188i
$81$	−3.06710	+	8.46126i	−0.340789	+	0.940140i
$82$	7.76040	+	7.76040i	0.856993	+	0.856993i
$83$	6.64687	+	6.64687i	0.729589	+	0.729589i	0.970538	−	0.240949i	$-0.0774587\pi$
$83$	6.64687	+	6.64687i	0.729589	+	0.729589i	−0.240949	+	0.970538i	$0.577459\pi$
$84$	−1.65172	+	0.521378i	−0.180217	+	0.0568871i
$85$	−14.6263	+	3.61565i	−1.58644	+	0.392172i
$86$			11.5544i			1.24594i
$87$	−7.98588	−	4.15386i	−0.856176	−	0.445341i
$88$	1.20554	−	1.20554i	0.128511	−	0.128511i
$89$	−2.25517			−0.239048			−0.119524	−	0.992831i	$-0.538137\pi$
$89$	−2.25517			−0.239048			−0.119524	+	0.992831i	$0.538137\pi$
$90$	−5.05681	−	4.40779i	−0.533035	−	0.464622i
$91$	−1.30343			−0.136637
$92$	2.49622	−	2.49622i	0.260249	−	0.260249i
$93$	−5.23472	−	2.72285i	−0.542815	−	0.282346i
$94$		−	0.617532i		−	0.0636935i
$95$	6.86910	−	11.3804i	0.704755	−	1.16761i
$96$	1.65172	−	0.521378i	0.168578	−	0.0532130i
$97$	13.2182	+	13.2182i	1.34210	+	1.34210i	0.893967	+	0.448133i	$0.147911\pi$
$97$	13.2182	+	13.2182i	1.34210	+	1.34210i	0.448133	+	0.893967i	$0.352089\pi$
$98$	−0.707107	−	0.707107i	−0.0714286	−	0.0714286i
$99$	4.18778	−	2.93640i	0.420888	−	0.295120i
$100$	4.42410	−	2.32966i	0.442410	−	0.232966i
$101$			17.8429i			1.77544i	0.460385	+	0.887719i	$0.347711\pi$
$101$			17.8429i			1.77544i	−0.460385	+	0.887719i	$0.652289\pi$
$102$	5.38544	−	10.3536i	0.533238	−	1.02516i
$103$	−11.9006	+	11.9006i	−1.17260	+	1.17260i	−0.191013	+	0.981587i	$0.561177\pi$
$103$	−11.9006	+	11.9006i	−1.17260	+	1.17260i	−0.981587	+	0.191013i	$0.938823\pi$
$104$	1.30343			0.127812
$105$	0.910435	−	3.76445i	0.0888493	−	0.367373i
$106$	9.71842			0.943937
$107$	−3.96954	+	3.96954i	−0.383750	+	0.383750i	−0.872451	−	0.488701i	$-0.837471\pi$
$107$	−3.96954	+	3.96954i	−0.383750	+	0.383750i	0.488701	+	0.872451i	$0.337471\pi$
$108$	5.15103	−	0.683293i	0.495658	−	0.0657499i
$109$			6.66506i			0.638397i	0.947688	+	0.319198i	$0.103414\pi$
$109$			6.66506i			0.638397i	−0.947688	+	0.319198i	$0.896586\pi$
$110$	0.914862	+	3.70086i	0.0872287	+	0.352863i
$111$	−0.758796	−	2.40385i	−0.0720217	−	0.228163i
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	4.33754	+	4.33754i	0.408042	+	0.408042i	0.881055	−	0.473014i	$-0.156834\pi$
$113$	4.33754	+	4.33754i	0.408042	+	0.408042i	−0.473014	+	0.881055i	$0.656834\pi$
$114$	3.09945	+	9.81900i	0.290290	+	0.919633i
$115$	1.89433	+	7.66307i	0.176648	+	0.714585i
$116$			5.19708i			0.482536i
$117$	3.85133	+	0.676494i	0.356056	+	0.0625419i
$118$	−0.485314	+	0.485314i	−0.0446767	+	0.0446767i
$119$	6.73795			0.617667
$120$	−0.910435	+	3.76445i	−0.0831109	+	0.343646i
$121$	8.09334			0.735758
$122$	1.23739	−	1.23739i	0.112028	−	0.112028i
$123$	8.77187	−	16.8641i	0.790933	−	1.52058i
$124$			3.40667i			0.305928i
$125$	−0.652173	+	11.1613i	−0.0583321	+	0.998297i
$126$	1.72234	+	2.45633i	0.153438	+	0.218827i
$127$	−11.2191	−	11.2191i	−0.995531	−	0.995531i	0.00445951	−	0.999990i	$-0.498580\pi$
$127$	−11.2191	−	11.2191i	−0.995531	−	0.995531i	−0.999990	+	0.00445951i	$0.998580\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	19.0846	−	6.02422i	1.68031	−	0.530403i
$130$	−1.50611	+	2.49526i	−0.132094	+	0.218848i
$131$		−	4.60740i		−	0.402550i	−0.979535	−	0.201275i	$-0.935491\pi$
$131$		−	4.60740i		−	0.402550i	0.979535	−	0.201275i	$-0.0645085\pi$
$132$	−2.61976	−	1.36267i	−0.228020	−	0.118605i
$133$	−4.20356	+	4.20356i	−0.364495	+	0.364495i
$134$	−1.46798			−0.126814
$135$	−4.64391	+	10.6505i	−0.399684	+	0.916653i
$136$	−6.73795			−0.577775
$137$	−2.21669	+	2.21669i	−0.189384	+	0.189384i	−0.795430	−	0.606046i	$-0.792755\pi$
$137$	−2.21669	+	2.21669i	−0.189384	+	0.189384i	0.606046	+	0.795430i	$0.292755\pi$
$138$	−5.42452	−	2.82157i	−0.461766	−	0.240188i
$139$			0.322961i			0.0273932i	0.999906	+	0.0136966i	$0.00435990\pi$
$139$			0.322961i			0.0273932i	−0.999906	+	0.0136966i	$0.995640\pi$
$140$	−2.17073	+	0.536610i	−0.183460	+	0.0453518i
$141$	−1.01999	+	0.321968i	−0.0858984	+	0.0271146i
$142$	8.66993	+	8.66993i	0.727564	+	0.727564i
$143$	−1.57134	−	1.57134i	−0.131402	−	0.131402i
$144$	−1.72234	−	2.45633i	−0.143528	−	0.204694i
$145$	−9.94915	−	6.00519i	−0.826232	−	0.498704i
$146$		−	6.50104i		−	0.538030i
$147$	−0.799269	+	1.53661i	−0.0659226	+	0.126737i
$148$	−1.02910	+	1.02910i	−0.0845913	+	0.0845913i
$149$	3.82532			0.313382			0.156691	−	0.987648i	$-0.449917\pi$
$149$	3.82532			0.313382			0.156691	+	0.987648i	$0.449917\pi$
$150$	−6.15457	−	6.09272i	−0.502519	−	0.497468i
$151$	4.75057			0.386596			0.193298	−	0.981140i	$-0.438082\pi$
$151$	4.75057			0.386596			0.193298	+	0.981140i	$0.438082\pi$
$152$	4.20356	−	4.20356i	0.340953	−	0.340953i
$153$	−19.9091	−	3.49707i	−1.60955	−	0.282721i
$154$		−	1.70489i		−	0.137384i
$155$	−6.52164	−	3.93639i	−0.523831	−	0.316178i
$156$	−0.679581	−	2.15290i	−0.0544100	−	0.172370i
$157$	−10.3066	−	10.3066i	−0.822559	−	0.822559i	0.163915	−	0.986474i	$-0.447588\pi$
$157$	−10.3066	−	10.3066i	−0.822559	−	0.822559i	−0.986474	+	0.163915i	$0.947588\pi$
$158$	5.08774	+	5.08774i	0.404759	+	0.404759i
$159$	−5.06698	−	16.0521i	−0.401837	−	1.27301i
$160$	2.17073	−	0.536610i	0.171611	−	0.0424227i
$161$		−	3.53019i		−	0.278218i
$162$	−3.81424	−	8.15178i	−0.299675	−	0.640465i
$163$	4.45269	−	4.45269i	0.348762	−	0.348762i	−0.510887	−	0.859648i	$-0.670683\pi$
$163$	4.45269	−	4.45269i	0.348762	−	0.348762i	0.859648	+	0.510887i	$0.170683\pi$
$164$	−10.9749			−0.856993
$165$	5.63577	−	3.44064i	0.438744	−	0.267853i
$166$	−9.40009			−0.729589
$167$	−8.92259	+	8.92259i	−0.690451	+	0.690451i	−0.962331	−	0.271880i	$-0.912354\pi$
$167$	−8.92259	+	8.92259i	−0.690451	+	0.690451i	0.271880	+	0.962331i	$0.412354\pi$
$168$	0.799269	−	1.53661i	0.0616649	−	0.118552i
$169$			11.3011i			0.869313i
$170$	7.78567	−	12.8990i	0.597134	−	0.989306i
$171$	14.6022	−	10.2388i	1.11666	−	0.782983i
$172$	−8.17020	−	8.17020i	−0.622972	−	0.622972i
$173$	−4.45093	−	4.45093i	−0.338398	−	0.338398i	0.517366	−	0.855764i	$-0.326913\pi$
$173$	−4.45093	−	4.45093i	−0.338398	−	0.338398i	−0.855764	+	0.517366i	$0.826913\pi$
$174$	8.58409	−	2.70964i	0.650758	−	0.205418i
$175$	1.48099	−	4.77563i	0.111952	−	0.361004i
$176$			1.70489i			0.128511i
$177$	1.05463	+	0.548568i	0.0792710	+	0.0412329i
$178$	1.59465	−	1.59465i	0.119524	−	0.119524i
$179$	−10.6798			−0.798243			−0.399121	−	0.916898i	$-0.630685\pi$
$179$	−10.6798			−0.798243			−0.399121	+	0.916898i	$0.630685\pi$
$180$	6.69249	−	0.458926i	0.498829	−	0.0342063i
$181$	12.8215			0.953012			0.476506	−	0.879171i	$-0.341903\pi$
$181$	12.8215			0.953012			0.476506	+	0.879171i	$0.341903\pi$
$182$	0.921665	−	0.921665i	0.0683184	−	0.0683184i
$183$	−2.68897	−	1.39867i	−0.198774	−	0.103393i
$184$			3.53019i			0.260249i
$185$	−0.780962	−	3.15920i	−0.0574175	−	0.232269i
$186$	5.62685	−	1.77616i	0.412581	−	0.130235i
$187$	8.12288	+	8.12288i	0.594004	+	0.594004i
$188$	0.436661	+	0.436661i	0.0318468	+	0.0318468i
$189$	3.15917	−	4.12549i	0.229796	−	0.300085i
$190$	3.19000	+	12.9044i	0.231427	+	0.936181i
$191$		−	8.28637i		−	0.599580i	−0.954005	−	0.299790i	$-0.903083\pi$
$191$		−	8.28637i		−	0.599580i	0.954005	−	0.299790i	$-0.0969167\pi$
$192$	−0.799269	+	1.53661i	−0.0576823	+	0.110895i
$193$	−3.59731	+	3.59731i	−0.258940	+	0.258940i	−0.824623	−	0.565683i	$-0.808613\pi$
$193$	−3.59731	+	3.59731i	−0.258940	+	0.258940i	0.565683	+	0.824623i	$0.308613\pi$
$194$	−18.6933			−1.34210
$195$	4.90671	+	1.18669i	0.351377	+	0.0849806i
$196$	1.00000			0.0714286
$197$	−5.50386	+	5.50386i	−0.392134	+	0.392134i	−0.875447	−	0.483314i	$-0.839433\pi$
$197$	−5.50386	+	5.50386i	−0.392134	+	0.392134i	0.483314	+	0.875447i	$0.339433\pi$
$198$	−0.884857	+	5.03756i	−0.0628840	+	0.358004i
$199$			20.7662i			1.47208i	0.676940	+	0.736038i	$0.263306\pi$
$199$			20.7662i			1.47208i	−0.676940	+	0.736038i	$0.736694\pi$
$200$	−1.48099	+	4.77563i	−0.104722	+	0.337688i
$201$	0.765374	+	2.42469i	0.0539853	+	0.171024i
$202$	−12.6169	−	12.6169i	−0.887719	−	0.887719i
$203$	3.67489	+	3.67489i	0.257927	+	0.257927i
$204$	3.51302	+	11.1292i	0.245961	+	0.779199i
$205$	12.6814	−	21.0100i	0.885707	−	1.46740i
$206$		−	16.8300i		−	1.17260i
$207$	−1.83220	+	10.4309i	−0.127347	+	0.724996i
$208$	−0.921665	+	0.921665i	−0.0639060	+	0.0639060i
$209$	−10.1351			−0.701061
$210$	2.01810	+	3.30564i	0.139262	+	0.228111i
$211$	26.0519			1.79349			0.896743	−	0.442551i	$-0.145927\pi$
$211$	26.0519			1.79349			0.896743	+	0.442551i	$0.145927\pi$
$212$	−6.87196	+	6.87196i	−0.471968	+	0.471968i
$213$	9.79994	−	18.8406i	0.671481	−	1.29093i
$214$		−	5.61377i		−	0.383750i
$215$	25.0815	−	6.20021i	1.71054	−	0.422851i
$216$	−3.15917	+	4.12549i	−0.214954	+	0.280704i
$217$	2.40888	+	2.40888i	0.163525	+	0.163525i
$218$	−4.71291	−	4.71291i	−0.319198	−	0.319198i
$219$	−10.7379	+	3.38950i	−0.725598	+	0.229041i
$220$	−3.26380	−	1.96999i	−0.220046	−	0.132817i
$221$			8.78246i			0.590772i
$222$	2.23633	+	1.16323i	0.150092	+	0.0780707i
$223$	−1.49400	+	1.49400i	−0.100045	+	0.100045i	−0.755358	−	0.655312i	$-0.772537\pi$
$223$	−1.49400	+	1.49400i	−0.100045	+	0.100045i	0.655312	+	0.755358i	$0.272537\pi$
$224$	−1.00000			−0.0668153
$225$	−6.85458	+	13.3422i	−0.456972	+	0.889481i
$226$	−6.13421			−0.408042
$227$	7.38425	−	7.38425i	0.490110	−	0.490110i	−0.418231	−	0.908341i	$-0.637350\pi$
$227$	7.38425	−	7.38425i	0.490110	−	0.490110i	0.908341	+	0.418231i	$0.137350\pi$
$228$	−9.13472	−	4.75144i	−0.604962	−	0.314672i
$229$			13.4219i			0.886944i	0.896288	+	0.443472i	$0.146254\pi$
$229$			13.4219i			0.886944i	−0.896288	+	0.443472i	$0.853746\pi$
$230$	−6.75811	−	4.07912i	−0.445616	−	0.268969i
$231$	−2.81600	+	0.888895i	−0.185279	+	0.0584850i
$232$	−3.67489	−	3.67489i	−0.241268	−	0.241268i
$233$	−8.32952	−	8.32952i	−0.545685	−	0.545685i	0.379505	−	0.925190i	$-0.376094\pi$
$233$	−8.32952	−	8.32952i	−0.545685	−	0.545685i	−0.925190	+	0.379505i	$0.876094\pi$
$234$	−3.20166	+	2.24495i	−0.209299	+	0.146757i
$235$	−1.34049	+	0.331373i	−0.0874440	+	0.0216164i
$236$		−	0.686337i		−	0.0446767i
$237$	5.75086	−	11.0561i	0.373558	−	0.718173i
$238$	−4.76445	+	4.76445i	−0.308834	+	0.308834i
$239$	−0.372694			−0.0241076			−0.0120538	−	0.999927i	$-0.503837\pi$
$239$	−0.372694			−0.0241076			−0.0120538	+	0.999927i	$0.503837\pi$
$240$	−2.01810	−	3.30564i	−0.130268	−	0.213378i
$241$	29.4165			1.89489			0.947443	−	0.319924i	$-0.103657\pi$
$241$	29.4165			1.89489			0.947443	+	0.319924i	$0.103657\pi$
$242$	−5.72286	+	5.72286i	−0.367879	+	0.367879i
$243$	−11.4758	+	10.5502i	−0.736171	+	0.676796i
$244$			1.74994i			0.112028i
$245$	−1.15549	+	1.91438i	−0.0738218	+	0.122305i
$246$	5.72206	+	18.1274i	0.364825	+	1.15576i
$247$	−5.47905	−	5.47905i	−0.348623	−	0.348623i
$248$	−2.40888	−	2.40888i	−0.152964	−	0.152964i
$249$	4.90100	+	15.5263i	0.310589	+	0.983938i
$250$	−7.43108	−	8.35339i	−0.469983	−	0.528315i
$251$			2.86106i			0.180589i	0.995915	+	0.0902943i	$0.0287808\pi$
$251$			2.86106i			0.180589i	−0.995915	+	0.0902943i	$0.971219\pi$
$252$	−2.95476	−	0.519010i	−0.186133	−	0.0326946i
$253$	4.25579	−	4.25579i	0.267559	−	0.267559i
$254$	15.8661			0.995531
$255$	−25.3647	−	6.13447i	−1.58840	−	0.384155i
$256$	1.00000			0.0625000
$257$	2.93961	−	2.93961i	0.183368	−	0.183368i	−0.609454	−	0.792822i	$-0.708611\pi$
$257$	2.93961	−	2.93961i	0.183368	−	0.183368i	0.792822	+	0.609454i	$0.208611\pi$
$258$	−9.23508	+	17.7546i	−0.574951	+	1.10535i
$259$			1.45536i			0.0904319i
$260$	−0.699434	−	2.82939i	−0.0433770	−	0.175471i
$261$	−8.95112	−	12.7657i	−0.554061	−	0.790179i
$262$	3.25792	+	3.25792i	0.201275	+	0.201275i
$263$	16.7008	+	16.7008i	1.02982	+	1.02982i	0.999542	+	0.0302760i	$0.00963862\pi$
$263$	16.7008	+	16.7008i	1.02982	+	1.02982i	0.0302760	+	0.999542i	$0.490361\pi$
$264$	2.81600	−	0.888895i	0.173313	−	0.0547077i
$265$	−5.21500	−	21.0960i	−0.320355	−	1.29592i
$266$		−	5.94473i		−	0.364495i
$267$	−3.46532	−	1.80249i	−0.212074	−	0.110311i
$268$	1.03802	−	1.03802i	0.0634072	−	0.0634072i
$269$	1.10509			0.0673783			0.0336891	−	0.999432i	$-0.489274\pi$
$269$	1.10509			0.0673783			0.0336891	+	0.999432i	$0.489274\pi$
$270$	−4.24733	−	10.8148i	−0.258485	−	0.658168i
$271$	−23.9149			−1.45272			−0.726362	−	0.687312i	$-0.758790\pi$
$271$	−23.9149			−1.45272			−0.726362	+	0.687312i	$0.758790\pi$
$272$	4.76445	−	4.76445i	0.288887	−	0.288887i
$273$	−2.00286	−	1.04179i	−0.121219	−	0.0630521i
$274$		−	3.13487i		−	0.189384i
$275$	7.54262	−	3.97183i	0.454837	−	0.239510i
$276$	5.83087	−	1.84056i	0.350977	−	0.110789i
$277$	−10.5902	−	10.5902i	−0.636304	−	0.636304i	0.313338	−	0.949642i	$-0.398553\pi$
$277$	−10.5902	−	10.5902i	−0.636304	−	0.636304i	−0.949642	+	0.313338i	$0.898553\pi$
$278$	−0.228368	−	0.228368i	−0.0136966	−	0.0136966i
$279$	−5.86744	−	8.36790i	−0.351274	−	0.500973i
$280$	1.15549	−	1.91438i	0.0690540	−	0.114406i
$281$			19.4466i			1.16009i	0.814585	+	0.580044i	$0.196964\pi$
$281$			19.4466i			1.16009i	−0.814585	+	0.580044i	$0.803036\pi$
$282$	0.493574	−	0.948905i	0.0293919	−	0.0565065i
$283$	−17.2984	+	17.2984i	−1.02829	+	1.02829i	−0.0286974	+	0.999588i	$0.509136\pi$
$283$	−17.2984	+	17.2984i	−1.02829	+	1.02829i	−0.999588	+	0.0286974i	$0.990864\pi$
$284$	−12.2611			−0.727564
$285$	19.6512	−	11.9970i	1.16403	−	0.710643i
$286$	2.22221			0.131402
$287$	−7.76040	+	7.76040i	−0.458082	+	0.458082i
$288$	2.95476	+	0.519010i	0.174111	+	0.0305830i
$289$		−	28.4000i		−	1.67059i
$290$	11.2814	−	2.78880i	0.662468	−	0.163764i
$291$	9.74628	+	30.8760i	0.571337	+	1.80998i
$292$	4.59693	+	4.59693i	0.269015	+	0.269015i
$293$	17.8992	+	17.8992i	1.04568	+	1.04568i	0.998905	+	0.0467777i	$0.0148953\pi$
$293$	17.8992	+	17.8992i	1.04568	+	1.04568i	0.0467777	+	0.998905i	$0.485105\pi$
$294$	−0.521378	−	1.65172i	−0.0304074	−	0.0963300i
$295$	1.31391	+	0.793059i	0.0764986	+	0.0461737i
$296$		−	1.45536i		−	0.0845913i
$297$	8.78196	−	1.16494i	0.509581	−	0.0675968i
$298$	−2.70491	+	2.70491i	−0.156691	+	0.156691i
$299$	4.60136			0.266103
$300$	8.66014	−	0.0437379i	0.499994	−	0.00252521i
$301$	−11.5544			−0.665985
$302$	−3.35916	+	3.35916i	−0.193298	+	0.193298i
$303$	−14.2613	+	27.4176i	−0.819291	+	1.57510i
$304$			5.94473i			0.340953i
$305$	−3.35003	−	2.02204i	−0.191822	−	0.115782i
$306$	16.5506	−	11.6050i	0.946137	−	0.663416i
$307$	7.54591	+	7.54591i	0.430668	+	0.430668i	0.888856	−	0.458187i	$-0.151501\pi$
$307$	7.54591	+	7.54591i	0.430668	+	0.430668i	−0.458187	+	0.888856i	$0.651501\pi$
$308$	1.20554	+	1.20554i	0.0686921	+	0.0686921i
$309$	−27.7984	+	8.77479i	−1.58139	+	0.499181i
$310$	7.39494	−	1.82805i	0.420005	−	0.103826i
$311$		−	7.09388i		−	0.402257i	−0.979565	−	0.201129i	$-0.935539\pi$
$311$		−	7.09388i		−	0.402257i	0.979565	−	0.201129i	$-0.0644609\pi$
$312$	2.00286	+	1.04179i	0.113390	+	0.0589799i
$313$	13.7044	−	13.7044i	0.774616	−	0.774616i	−0.204293	−	0.978910i	$-0.565490\pi$
$313$	13.7044	−	13.7044i	0.774616	−	0.774616i	0.978910	+	0.204293i	$0.0654897\pi$
$314$	14.5758			0.822559
$315$	4.40779	−	5.05681i	0.248351	−	0.284919i
$316$	−7.19515			−0.404759
$317$	20.1184	−	20.1184i	1.12996	−	1.12996i	0.139778	−	0.990183i	$-0.455361\pi$
$317$	20.1184	−	20.1184i	1.12996	−	1.12996i	0.990183	−	0.139778i	$-0.0446389\pi$
$318$	14.9334	+	7.76764i	0.837425	+	0.435587i
$319$			8.86046i			0.496090i
$320$	−1.15549	+	1.91438i	−0.0645941	+	0.107017i
$321$	−9.27236	+	2.92690i	−0.517533	+	0.163364i
$322$	2.49622	+	2.49622i	0.139109	+	0.139109i
$323$	28.3234	+	28.3234i	1.57595	+	1.57595i
$324$	8.46126	+	3.06710i	0.470070	+	0.170395i
$325$	6.22471	+	1.93037i	0.345285	+	0.107078i
$326$			6.29706i			0.348762i
$327$	−5.32718	+	10.2416i	−0.294593	+	0.566361i
$328$	7.76040	−	7.76040i	0.428497	−	0.428497i
$329$	0.617532			0.0340456
$330$	−1.55219	+	6.41799i	−0.0854454	+	0.353299i
$331$	7.35408			0.404217			0.202108	−	0.979363i	$-0.435221\pi$
$331$	7.35408			0.404217			0.202108	+	0.979363i	$0.435221\pi$
$332$	6.64687	−	6.64687i	0.364794	−	0.364794i
$333$	0.755349	−	4.30026i	0.0413929	−	0.235653i
$334$		−	12.6184i		−	0.690451i
$335$	0.787733	+	3.18659i	0.0430385	+	0.174102i
$336$	0.521378	+	1.65172i	0.0284435	+	0.0901085i
$337$	−22.3830	−	22.3830i	−1.21928	−	1.21928i	−0.967884	−	0.251397i	$-0.919110\pi$
$337$	−22.3830	−	22.3830i	−1.21928	−	1.21928i	−0.251397	−	0.967884i	$-0.580890\pi$
$338$	−7.99106	−	7.99106i	−0.434656	−	0.434656i
$339$	3.19824	+	10.1320i	0.173705	+	0.550293i
$340$	3.61565	+	14.6263i	0.196086	+	0.793220i
$341$			5.80801i			0.314521i
$342$	−3.08537	+	17.5653i	−0.166838	+	0.949821i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	11.5544			0.622972
$345$	−3.21401	+	13.2892i	−0.173036	+	0.715468i
$346$	6.29457			0.338398
$347$	13.9437	−	13.9437i	0.748536	−	0.748536i	−0.225668	−	0.974204i	$-0.572457\pi$
$347$	13.9437	−	13.9437i	0.748536	−	0.748536i	0.974204	+	0.225668i	$0.0724566\pi$
$348$	−4.15386	+	7.98588i	−0.222670	+	0.428088i
$349$		−	4.36703i		−	0.233762i	−0.993146	−	0.116881i	$-0.962710\pi$
$349$		−	4.36703i		−	0.233762i	0.993146	−	0.116881i	$-0.0372896\pi$
$350$	2.32966	+	4.42410i	0.124526	+	0.236478i
$351$	5.37729	+	4.11776i	0.287019	+	0.219790i
$352$	−1.20554	−	1.20554i	−0.0642556	−	0.0642556i
$353$	−9.91003	−	9.91003i	−0.527458	−	0.527458i	0.392356	−	0.919814i	$-0.371660\pi$
$353$	−9.91003	−	9.91003i	−0.527458	−	0.527458i	−0.919814	+	0.392356i	$0.871660\pi$
$354$	−1.13363	+	0.357841i	−0.0602520	+	0.0190191i
$355$	14.1677	−	23.4724i	0.751942	−	1.24579i
$356$			2.25517i			0.119524i
$357$	10.3536	+	5.38544i	0.547971	+	0.285028i
$358$	7.55173	−	7.55173i	0.399121	−	0.399121i
$359$	−31.8147			−1.67912			−0.839559	−	0.543269i	$-0.817186\pi$
$359$	−31.8147			−1.67912			−0.839559	+	0.543269i	$0.817186\pi$
$360$	−4.40779	+	5.05681i	−0.232311	+	0.266517i
$361$	−16.3398			−0.859988
$362$	−9.06614	+	9.06614i	−0.476506	+	0.476506i
$363$	12.4363	+	6.46876i	0.652737	+	0.339522i
$364$			1.30343i			0.0683184i
$365$	−14.1120	+	3.48852i	−0.738655	+	0.182598i
$366$	2.89040	−	0.912379i	0.151083	−	0.0476908i
$367$	−14.4435	−	14.4435i	−0.753945	−	0.753945i	0.221268	−	0.975213i	$-0.428980\pi$
$367$	−14.4435	−	14.4435i	−0.753945	−	0.753945i	−0.975213	+	0.221268i	$0.928980\pi$
$368$	−2.49622	−	2.49622i	−0.130125	−	0.130125i
$369$	26.9579	−	18.9024i	1.40337	−	0.984021i
$370$	2.78611	+	1.68167i	0.144843	+	0.0874256i
$371$			9.71842i			0.504555i
$372$	−2.72285	+	5.23472i	−0.141173	+	0.271408i
$373$	−13.5553	+	13.5553i	−0.701867	+	0.701867i	−0.964811	−	0.262944i	$-0.915307\pi$
$373$	−13.5553	+	13.5553i	−0.701867	+	0.701867i	0.262944	+	0.964811i	$0.415307\pi$
$374$	−11.4875			−0.594004
$375$	−9.92302	+	16.6293i	−0.512422	+	0.858733i
$376$	−0.617532			−0.0318468
$377$	−4.78996	+	4.78996i	−0.246696	+	0.246696i
$378$	0.683293	+	5.15103i	0.0351448	+	0.264940i
$379$			15.1496i			0.778182i	0.921199	+	0.389091i	$0.127211\pi$
$379$			15.1496i			0.778182i	−0.921199	+	0.389091i	$0.872789\pi$
$380$	−11.3804	−	6.86910i	−0.583804	−	0.352377i
$381$	−8.27227	−	26.2064i	−0.423801	−	1.34259i
$382$	5.85935	+	5.85935i	0.299790	+	0.299790i
$383$	−16.7428	−	16.7428i	−0.855519	−	0.855519i	0.135287	−	0.990806i	$-0.456804\pi$
$383$	−16.7428	−	16.7428i	−0.855519	−	0.855519i	−0.990806	+	0.135287i	$0.956804\pi$
$384$	−0.521378	−	1.65172i	−0.0266065	−	0.0842888i
$385$	−3.70086	+	0.914862i	−0.188613	+	0.0466257i
$386$		−	5.08736i		−	0.258940i
$387$	34.1406	+	5.99686i	1.73546	+	0.304837i
$388$	13.2182	−	13.2182i	0.671050	−	0.671050i
$389$	10.3633			0.525439			0.262719	−	0.964872i	$-0.415381\pi$
$389$	10.3633			0.525439			0.262719	+	0.964872i	$0.415381\pi$
$390$	−4.30868	+	2.63045i	−0.218179	+	0.133198i
$391$	−23.7863			−1.20292
$392$	−0.707107	+	0.707107i	−0.0357143	+	0.0357143i
$393$	3.68255	−	7.07977i	0.185760	−	0.357127i
$394$		−	7.78363i		−	0.392134i
$395$	8.31395	−	13.7742i	0.418320	−	0.693056i
$396$	−2.93640	−	4.18778i	−0.147560	−	0.210444i
$397$	10.6075	+	10.6075i	0.532373	+	0.532373i	0.921278	−	0.388905i	$-0.127147\pi$
$397$	10.6075	+	10.6075i	0.532373	+	0.532373i	−0.388905	+	0.921278i	$0.627147\pi$
$398$	−14.6839	−	14.6839i	−0.736038	−	0.736038i
$399$	−9.81900	+	3.09945i	−0.491565	+	0.155167i
$400$	−2.32966	−	4.42410i	−0.116483	−	0.221205i
$401$			9.37124i			0.467977i	0.972239	+	0.233989i	$0.0751779\pi$
$401$			9.37124i			0.467977i	−0.972239	+	0.233989i	$0.924822\pi$
$402$	−2.25572	−	1.17331i	−0.112505	−	0.0585195i
$403$	−3.13981	+	3.13981i	−0.156405	+	0.156405i
$404$	17.8429			0.887719
$405$	−15.6485	+	12.6540i	−0.777581	+	0.628782i
$406$	−5.19708			−0.257927
$407$	−1.75450	+	1.75450i	−0.0869674	+	0.0869674i
$408$	−10.3536	−	5.38544i	−0.512580	−	0.266619i
$409$		−	23.1943i		−	1.14689i	−0.819245	−	0.573443i	$-0.805607\pi$
$409$		−	23.1943i		−	1.14689i	0.819245	−	0.573443i	$-0.194393\pi$
$410$	5.88922	+	23.8234i	0.290848	+	1.17655i
$411$	−5.17791	+	1.63445i	−0.255408	+	0.0806216i
$412$	11.9006	+	11.9006i	0.586300	+	0.586300i
$413$	−0.485314	−	0.485314i	−0.0238807	−	0.0238807i
$414$	−6.08018	−	8.67131i	−0.298825	−	0.426171i
$415$	5.04418	+	20.4050i	0.247609	+	1.00164i
$416$		−	1.30343i		−	0.0639060i
$417$	−0.258133	+	0.496265i	−0.0126408	+	0.0243022i
$418$	7.16661	−	7.16661i	0.350531	−	0.350531i
$419$	−1.64096			−0.0801662			−0.0400831	−	0.999196i	$-0.512762\pi$
$419$	−1.64096			−0.0801662			−0.0400831	+	0.999196i	$0.512762\pi$
$420$	−3.76445	−	0.910435i	−0.183687	−	0.0444247i
$421$	3.92047			0.191072			0.0955359	−	0.995426i	$-0.469544\pi$
$421$	3.92047			0.191072			0.0955359	+	0.995426i	$0.469544\pi$
$422$	−18.4215	+	18.4215i	−0.896743	+	0.896743i
$423$	−1.82466	−	0.320505i	−0.0887180	−	0.0155835i
$424$		−	9.71842i		−	0.471968i
$425$	−32.1780	−	9.97884i	−1.56086	−	0.484045i
$426$	6.39269	+	20.2519i	0.309727	+	0.981208i
$427$	1.23739	+	1.23739i	0.0598815	+	0.0598815i
$428$	3.96954	+	3.96954i	0.191875	+	0.191875i
$429$	−1.15861	−	3.67046i	−0.0559384	−	0.177212i
$430$	−13.3511	+	22.1195i	−0.643845	+	1.06670i
$431$		−	28.0498i		−	1.35111i	−0.737308	−	0.675557i	$-0.763903\pi$
$431$		−	28.0498i		−	1.35111i	0.737308	−	0.675557i	$-0.236097\pi$
$432$	−0.683293	−	5.15103i	−0.0328750	−	0.247829i
$433$	−7.42460	+	7.42460i	−0.356804	+	0.356804i	−0.862633	−	0.505830i	$-0.831186\pi$
$433$	−7.42460	+	7.42460i	−0.356804	+	0.356804i	0.505830	+	0.862633i	$0.331186\pi$
$434$	−3.40667			−0.163525
$435$	−10.4882	−	17.1797i	−0.502871	−	0.823703i
$436$	6.66506			0.319198
$437$	14.8394	−	14.8394i	0.709862	−	0.709862i
$438$	5.19608	−	9.98957i	0.248278	−	0.477320i
$439$			23.4410i			1.11878i	0.828905	+	0.559389i	$0.188964\pi$
$439$			23.4410i			1.11878i	−0.828905	+	0.559389i	$0.811036\pi$
$440$	3.70086	−	0.914862i	0.176431	−	0.0436143i
$441$	−2.45633	+	1.72234i	−0.116968	+	0.0820161i
$442$	−6.21014	−	6.21014i	−0.295386	−	0.295386i
$443$	−10.0545	−	10.0545i	−0.477706	−	0.477706i	0.426692	−	0.904397i	$-0.359679\pi$
$443$	−10.0545	−	10.0545i	−0.477706	−	0.477706i	−0.904397	+	0.426692i	$0.859679\pi$
$444$	−2.40385	+	0.758796i	−0.114082	+	0.0360108i
$445$	−4.31724	−	2.60584i	−0.204657	−	0.123529i
$446$		−	2.11283i		−	0.100045i
$447$	5.87802	+	3.05746i	0.278021	+	0.144613i
$448$	0.707107	−	0.707107i	0.0334077	−	0.0334077i
$449$	29.2933			1.38244			0.691218	−	0.722646i	$-0.257074\pi$
$449$	29.2933			1.38244			0.691218	+	0.722646i	$0.257074\pi$
$450$	−4.58745	−	14.2813i	−0.216255	−	0.673226i
$451$	−18.7110			−0.881065
$452$	4.33754	−	4.33754i	0.204021	−	0.204021i
$453$	7.29977	+	3.79699i	0.342973	+	0.178398i
$454$			10.4429i			0.490110i
$455$	−2.49526	−	1.50611i	−0.116979	−	0.0706074i
$456$	9.81900	−	3.09945i	0.459817	−	0.145145i
$457$	21.3134	+	21.3134i	0.996997	+	0.996997i	0.999996	−	0.00299860i	$-0.000954486\pi$
$457$	21.3134	+	21.3134i	0.996997	+	0.996997i	−0.00299860	+	0.999996i	$0.500954\pi$
$458$	−9.49072	−	9.49072i	−0.443472	−	0.443472i
$459$	−27.7974	−	21.2863i	−1.29747	−	0.993561i
$460$	7.66307	−	1.89433i	0.357293	−	0.0883238i
$461$		−	9.53108i		−	0.443907i	−0.975057	−	0.221953i	$-0.928757\pi$
$461$		−	9.53108i		−	0.443907i	0.975057	−	0.221953i	$-0.0712433\pi$
$462$	1.36267	−	2.61976i	0.0633971	−	0.121882i
$463$	19.8492	−	19.8492i	0.922471	−	0.922471i	−0.0747323	−	0.997204i	$-0.523810\pi$
$463$	19.8492	−	19.8492i	0.922471	−	0.922471i	0.997204	+	0.0747323i	$0.0238102\pi$
$464$	5.19708			0.241268
$465$	−6.87499	−	11.2612i	−0.318820	−	0.522227i
$466$	11.7797			0.545685
$467$	−16.9197	+	16.9197i	−0.782949	+	0.782949i	−0.980327	−	0.197379i	$-0.936757\pi$
$467$	−16.9197	+	16.9197i	−0.782949	+	0.782949i	0.197379	+	0.980327i	$0.436757\pi$
$468$	0.676494	−	3.85133i	0.0312709	−	0.178028i
$469$		−	1.46798i		−	0.0677851i
$470$	0.713554	−	1.18219i	0.0329138	−	0.0545302i
$471$	−7.59950	−	24.0751i	−0.350167	−	1.10932i
$472$	0.485314	+	0.485314i	0.0223384	+	0.0223384i
$473$	−13.9293	−	13.9293i	−0.640471	−	0.640471i
$474$	3.75139	+	11.8843i	0.172307	+	0.545866i
$475$	26.3001	−	13.8492i	1.20673	−	0.635446i
$476$		−	6.73795i		−	0.308834i
$477$	5.04396	−	28.7156i	0.230947	−	1.31480i
$478$	0.263534	−	0.263534i	0.0120538	−	0.0120538i
$479$	−5.16727			−0.236099			−0.118049	−	0.993008i	$-0.537664\pi$
$479$	−5.16727			−0.236099			−0.118049	+	0.993008i	$0.537664\pi$
$480$	3.76445	+	0.910435i	0.171823	+	0.0415555i
$481$	−1.89697			−0.0864943
$482$	−20.8006	+	20.8006i	−0.947443	+	0.947443i
$483$	2.82157	−	5.42452i	0.128386	−	0.246824i
$484$		−	8.09334i		−	0.367879i
$485$	10.0310	+	40.5780i	0.455484	+	1.84255i
$486$	0.654467	−	15.5747i	0.0296872	−	0.706483i
$487$	−16.2445	−	16.2445i	−0.736107	−	0.736107i	0.235715	−	0.971822i	$-0.424257\pi$
$487$	−16.2445	−	16.2445i	−0.736107	−	0.736107i	−0.971822	+	0.235715i	$0.924257\pi$
$488$	−1.23739	−	1.23739i	−0.0560141	−	0.0560141i
$489$	10.4009	−	3.28315i	0.470347	−	0.148469i
$490$	−0.536610	−	2.17073i	−0.0242415	−	0.0980634i
$491$		−	9.61274i		−	0.433817i	−0.976192	−	0.216908i	$-0.930403\pi$
$491$		−	9.61274i		−	0.433817i	0.976192	−	0.216908i	$-0.0695973\pi$
$492$	−16.8641	−	8.77187i	−0.760292	−	0.395466i
$493$	24.7612	−	24.7612i	1.11519	−	1.11519i
$494$	7.74854			0.348623
$495$	11.4100	−	0.782420i	0.512840	−	0.0351671i
$496$	3.40667			0.152964
$497$	−8.66993	+	8.66993i	−0.388899	+	0.388899i
$498$	−14.4443	−	7.51320i	−0.647263	−	0.336675i
$499$			6.60885i			0.295853i	0.988998	+	0.147926i	$0.0472599\pi$
$499$			6.60885i			0.295853i	−0.988998	+	0.147926i	$0.952740\pi$
$500$	11.1613	+	0.652173i	0.499149	+	0.0291660i
$501$	−20.8421	+	6.57899i	−0.931156	+	0.293927i
$502$	−2.02308	−	2.02308i	−0.0902943	−	0.0902943i
$503$	−14.3231	−	14.3231i	−0.638634	−	0.638634i	0.311584	−	0.950219i	$-0.399140\pi$
$503$	−14.3231	−	14.3231i	−0.638634	−	0.638634i	−0.950219	+	0.311584i	$0.899140\pi$
$504$	2.45633	−	1.72234i	0.109414	−	0.0767190i
$505$	−20.6174	+	34.1581i	−0.917463	+	1.52001i
$506$			6.01860i			0.267559i
$507$	−9.03259	+	17.3653i	−0.401152	+	0.771221i
$508$	−11.2191	+	11.2191i	−0.497765	+	0.497765i
$509$	21.9532			0.973058			0.486529	−	0.873664i	$-0.338263\pi$
$509$	21.9532			0.973058			0.486529	+	0.873664i	$0.338263\pi$
$510$	22.2733	−	13.5978i	0.986278	−	0.602122i
$511$	6.50104			0.287589
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	30.6215	−	4.06199i	1.35197	−	0.179341i
$514$			4.15724i			0.183368i
$515$	−36.5333	+	9.03113i	−1.60985	+	0.397959i
$516$	−6.02422	−	19.0846i	−0.265202	−	0.840153i
$517$	0.744460	+	0.744460i	0.0327413	+	0.0327413i
$518$	−1.02910	−	1.02910i	−0.0452160	−	0.0452160i
$519$	−3.28185	−	10.3968i	−0.144057	−	0.456371i
$520$	2.49526	+	1.50611i	0.109424	+	0.0660472i
$521$			33.6715i			1.47518i	0.675251	+	0.737588i	$0.264035\pi$
$521$			33.6715i			1.47518i	−0.675251	+	0.737588i	$0.735965\pi$
$522$	15.3561	+	2.69734i	0.672120	+	0.118059i
$523$	6.88874	−	6.88874i	0.301223	−	0.301223i	−0.540269	−	0.841492i	$-0.681677\pi$
$523$	6.88874	−	6.88874i	0.301223	−	0.301223i	0.841492	+	0.540269i	$0.181677\pi$
$524$	−4.60740			−0.201275
$525$	6.09272	−	6.15457i	0.265908	−	0.268608i
$526$	−23.6185			−1.02982
$527$	16.2309	−	16.2309i	0.707030	−	0.707030i
$528$	−1.36267	+	2.61976i	−0.0593025	+	0.114010i
$529$		−	10.5378i		−	0.458164i
$530$	18.6047	+	11.2296i	0.808137	+	0.487782i
$531$	1.18210	+	1.68587i	0.0512990	+	0.0731605i
$532$	4.20356	+	4.20356i	0.182247	+	0.182247i
$533$	−10.1152	−	10.1152i	−0.438136	−	0.438136i
$534$	3.72490	−	1.17580i	0.161192	−	0.0508817i
$535$	−12.1860	+	3.01240i	−0.526845	+	0.130238i
$536$			1.46798i			0.0634072i
$537$	−16.4106	−	8.53600i	−0.708170	−	0.368356i
$538$	−0.781414	+	0.781414i	−0.0336891	+	0.0336891i
$539$	1.70489			0.0734349
$540$	10.6505	+	4.64391i	0.458326	+	0.199842i
$541$	1.57604			0.0677593			0.0338797	−	0.999426i	$-0.489214\pi$
$541$	1.57604			0.0677593			0.0338797	+	0.999426i	$0.489214\pi$
$542$	16.9104	−	16.9104i	0.726362	−	0.726362i
$543$	19.7016	+	10.2478i	0.845476	+	0.439775i
$544$			6.73795i			0.288887i
$545$	−7.70144	+	12.7594i	−0.329893	+	0.546554i
$546$	2.15290	−	0.679581i	0.0921355	−	0.0290834i
$547$	5.30755	+	5.30755i	0.226934	+	0.226934i	0.811411	−	0.584476i	$-0.198700\pi$
$547$	5.30755	+	5.30755i	0.226934	+	0.226934i	−0.584476	+	0.811411i	$0.698700\pi$
$548$	2.21669	+	2.21669i	0.0946922	+	0.0946922i
$549$	−3.01398	−	4.29842i	−0.128634	−	0.183452i
$550$	−2.52493	+	8.14194i	−0.107663	+	0.347174i
$551$			30.8952i			1.31618i
$552$	−2.82157	+	5.42452i	−0.120094	+	0.230883i
$553$	−5.08774	+	5.08774i	−0.216353	+	0.216353i
$554$	14.9768			0.636304
$555$	1.32501	−	5.47865i	0.0562437	−	0.232556i
$556$	0.322961			0.0136966
$557$	−5.78892	+	5.78892i	−0.245284	+	0.245284i	−0.819032	−	0.573748i	$-0.805489\pi$
$557$	−5.78892	+	5.78892i	−0.245284	+	0.245284i	0.573748	+	0.819032i	$0.305489\pi$
$558$	10.0659	+	1.76810i	0.426124	+	0.0748495i
$559$		−	15.0604i		−	0.636986i
$560$	0.536610	+	2.17073i	0.0226759	+	0.0917299i
$561$	5.98933	+	18.9741i	0.252870	+	0.801086i
$562$	−13.7508	−	13.7508i	−0.580044	−	0.580044i
$563$	1.00705	+	1.00705i	0.0424423	+	0.0424423i	0.728009	−	0.685567i	$-0.240446\pi$
$563$	1.00705	+	1.00705i	0.0424423	+	0.0424423i	−0.685567	+	0.728009i	$0.740446\pi$
$564$	0.321968	+	1.01999i	0.0135573	+	0.0429492i
$565$	3.29168	+	13.3157i	0.138482	+	0.560195i
$566$		−	24.4637i		−	1.02829i
$567$	8.15178	−	3.81424i	0.342343	−	0.160183i
$568$	8.66993	−	8.66993i	0.363782	−	0.363782i
$569$	−13.9047			−0.582917			−0.291459	−	0.956583i	$-0.594141\pi$
$569$	−13.9047			−0.582917			−0.291459	+	0.956583i	$0.594141\pi$
$570$	−5.41228	+	22.3786i	−0.226696	+	0.937338i
$571$	34.8923			1.46020			0.730098	−	0.683343i	$-0.239475\pi$
$571$	34.8923			1.46020			0.730098	+	0.683343i	$0.239475\pi$
$572$	−1.57134	+	1.57134i	−0.0657010	+	0.0657010i
$573$	6.62304	−	12.7329i	0.276681	−	0.531925i
$574$		−	10.9749i		−	0.458082i
$575$	−5.22818	+	16.8589i	−0.218030	+	0.703064i
$576$	−2.45633	+	1.72234i	−0.102347	+	0.0717641i
$577$	11.6857	+	11.6857i	0.486482	+	0.486482i	0.907194	−	0.420712i	$-0.138220\pi$
$577$	11.6857	+	11.6857i	0.486482	+	0.486482i	−0.420712	+	0.907194i	$0.638220\pi$
$578$	20.0819	+	20.0819i	0.835295	+	0.835295i
$579$	−8.40287	+	2.65244i	−0.349212	+	0.110232i
$580$	−6.00519	+	9.94915i	−0.249352	+	0.413116i
$581$		−	9.40009i		−	0.389981i
$582$	−28.7243	−	14.9410i	−1.19066	−	0.619323i
$583$	−11.7160	+	11.7160i	−0.485226	+	0.485226i
$584$	−6.50104			−0.269015
$585$	6.59121	+	5.74526i	0.272513	+	0.237537i
$586$	−25.3133			−1.04568
$587$	19.5496	−	19.5496i	0.806898	−	0.806898i	−0.177265	−	0.984163i	$-0.556725\pi$
$587$	19.5496	−	19.5496i	0.806898	−	0.806898i	0.984163	+	0.177265i	$0.0567249\pi$
$588$	1.53661	+	0.799269i	0.0633687	+	0.0329613i
$589$			20.2517i			0.834457i
$590$	−1.48985	+	0.368295i	−0.0613361	+	0.0151625i
$591$	−12.8563	+	4.05822i	−0.528840	+	0.166933i
$592$	1.02910	+	1.02910i	0.0422957	+	0.0422957i
$593$	−11.8939	−	11.8939i	−0.488424	−	0.488424i	0.419385	−	0.907809i	$-0.362246\pi$
$593$	−11.8939	−	11.8939i	−0.488424	−	0.488424i	−0.907809	+	0.419385i	$0.862246\pi$
$594$	−5.38604	+	7.03352i	−0.220992	+	0.288589i
$595$	12.8990	+	7.78567i	0.528806	+	0.319181i
$596$		−	3.82532i		−	0.156691i
$597$	−16.5978	+	31.9095i	−0.679302	+	1.30597i
$598$	−3.25365	+	3.25365i	−0.133052	+	0.133052i
$599$	33.0557			1.35062			0.675309	−	0.737535i	$-0.264010\pi$
$599$	33.0557			1.35062			0.675309	+	0.737535i	$0.264010\pi$
$600$	−6.09272	+	6.15457i	−0.248734	+	0.251259i
$601$	−39.7500			−1.62144			−0.810718	−	0.585436i	$-0.800923\pi$
$601$	−39.7500			−1.62144			−0.810718	+	0.585436i	$0.800923\pi$
$602$	8.17020	−	8.17020i	0.332993	−	0.332993i
$603$	−0.761898	+	4.33754i	−0.0310269	+	0.176638i
$604$		−	4.75057i		−	0.193298i
$605$	15.4937	+	9.35181i	0.629908	+	0.380205i
$606$	−9.30292	−	29.4715i	−0.377905	−	1.19720i
$607$	22.5491	+	22.5491i	0.915238	+	0.915238i	0.996678	−	0.0814398i	$-0.0259518\pi$
$607$	22.5491	+	22.5491i	0.915238	+	0.915238i	−0.0814398	+	0.996678i	$0.525952\pi$
$608$	−4.20356	−	4.20356i	−0.170477	−	0.170477i
$609$	2.70964	+	8.58409i	0.109800	+	0.347845i
$610$	3.79863	−	0.939032i	0.153802	−	0.0380203i
$611$			0.804910i			0.0325632i
$612$	−3.49707	+	19.9091i	−0.141361	+	0.804776i
$613$	−0.341141	+	0.341141i	−0.0137786	+	0.0137786i	−0.713962	−	0.700184i	$-0.753101\pi$
$613$	−0.341141	+	0.341141i	−0.0137786	+	0.0137786i	0.700184	+	0.713962i	$0.253101\pi$
$614$	−10.6715			−0.430668
$615$	36.2790	−	22.1483i	1.46291	−	0.893107i
$616$	−1.70489			−0.0686921
$617$	24.0144	−	24.0144i	0.966784	−	0.966784i	−0.0326817	−	0.999466i	$-0.510405\pi$
$617$	24.0144	−	24.0144i	0.966784	−	0.966784i	0.999466	+	0.0326817i	$0.0104048\pi$
$618$	13.4517	−	25.8611i	0.541106	−	1.04029i
$619$			15.8572i			0.637355i	0.947863	+	0.318677i	$0.103239\pi$
$619$			15.8572i			0.637355i	−0.947863	+	0.318677i	$0.896761\pi$
$620$	−3.93639	+	6.52164i	−0.158089	+	0.261915i
$621$	−11.1525	+	14.5638i	−0.447533	+	0.584424i
$622$	5.01613	+	5.01613i	0.201129	+	0.201129i
$623$	1.59465	+	1.59465i	0.0638882	+	0.0638882i
$624$	−2.15290	+	0.679581i	−0.0861849	+	0.0272050i
$625$	−14.1453	+	20.6133i	−0.565813	+	0.824534i
$626$			19.3809i			0.774616i
$627$	−15.5737	−	8.10069i	−0.621955	−	0.323510i
$628$	−10.3066	+	10.3066i	−0.411280	+	0.411280i
$629$	9.80618			0.390998
$630$	0.458926	+	6.69249i	0.0182840	+	0.266635i
$631$	9.22404			0.367203			0.183602	−	0.983001i	$-0.441224\pi$
$631$	9.22404			0.367203			0.183602	+	0.983001i	$0.441224\pi$
$632$	5.08774	−	5.08774i	0.202379	−	0.202379i
$633$	40.0316	+	20.8225i	1.59111	+	0.827619i
$634$			28.4517i			1.12996i
$635$	−8.51393	−	34.4411i	−0.337865	−	1.36675i
$636$	−16.0521	+	5.06698i	−0.636506	+	0.200919i
$637$	0.921665	+	0.921665i	0.0365177	+	0.0365177i
$638$	−6.26529	−	6.26529i	−0.248045	−	0.248045i
$639$	30.1174	−	21.1178i	1.19142	−	0.835408i
$640$	−0.536610	−	2.17073i	−0.0212114	−	0.0858055i
$641$		−	46.8024i		−	1.84858i	−0.381688	−	0.924291i	$-0.624657\pi$
$641$		−	46.8024i		−	1.84858i	0.381688	−	0.924291i	$-0.375343\pi$
$642$	4.48692	−	8.62618i	0.177084	−	0.340448i
$643$	−15.5179	+	15.5179i	−0.611968	+	0.611968i	−0.943458	−	0.331491i	$-0.892448\pi$
$643$	−15.5179	+	15.5179i	−0.611968	+	0.611968i	0.331491	+	0.943458i	$0.392448\pi$
$644$	−3.53019			−0.139109
$645$	43.4960	+	10.5195i	1.71265	+	0.414206i
$646$	−40.0553			−1.57595
$647$	−13.4045	+	13.4045i	−0.526986	+	0.526986i	−0.919672	−	0.392687i	$-0.871546\pi$
$647$	−13.4045	+	13.4045i	−0.526986	+	0.526986i	0.392687	+	0.919672i	$0.371546\pi$
$648$	−8.15178	+	3.81424i	−0.320232	+	0.149838i
$649$		−	1.17013i		−	0.0459317i
$650$	−5.76651	+	3.03656i	−0.226181	+	0.119104i
$651$	1.77616	+	5.62685i	0.0696134	+	0.220534i
$652$	−4.45269	−	4.45269i	−0.174381	−	0.174381i
$653$	22.3383	+	22.3383i	0.874165	+	0.874165i	0.992923	−	0.118758i	$-0.0378914\pi$
$653$	22.3383	+	22.3383i	0.874165	+	0.874165i	−0.118758	+	0.992923i	$0.537891\pi$
$654$	−3.47502	−	11.0088i	−0.135884	−	0.430477i
$655$	5.32382	−	8.82029i	0.208019	−	0.344637i
$656$			10.9749i			0.428497i
$657$	−19.2090	−	3.37411i	−0.749416	−	0.131636i
$658$	−0.436661	+	0.436661i	−0.0170228	+	0.0170228i
$659$	−9.99021			−0.389163			−0.194582	−	0.980886i	$-0.562335\pi$
$659$	−9.99021			−0.389163			−0.194582	+	0.980886i	$0.562335\pi$
$660$	−3.44064	−	5.63577i	−0.133927	−	0.219372i
$661$	−0.298368			−0.0116052			−0.00580259	−	0.999983i	$-0.501847\pi$
$661$	−0.298368			−0.0116052			−0.00580259	+	0.999983i	$0.501847\pi$
$662$	−5.20012	+	5.20012i	−0.202108	+	0.202108i
$663$	−7.01955	+	13.4952i	−0.272617	+	0.524111i
$664$			9.40009i			0.364794i
$665$	−12.9044	+	3.19000i	−0.500410	+	0.123703i
$666$	2.50663	+	3.57485i	0.0971299	+	0.138523i
$667$	−12.9731	−	12.9731i	−0.502319	−	0.502319i
$668$	8.92259	+	8.92259i	0.345225	+	0.345225i
$669$	−3.48980	+	1.10158i	−0.134923	+	0.0425897i
$670$	−2.81027	−	1.69625i	−0.108570	−	0.0655317i
$671$			2.98345i			0.115175i
$672$	−1.53661	−	0.799269i	−0.0592760	−	0.0308325i
$673$	3.14231	−	3.14231i	0.121127	−	0.121127i	−0.643945	−	0.765072i	$-0.722703\pi$
$673$	3.14231	−	3.14231i	0.121127	−	0.121127i	0.765072	+	0.643945i	$0.222703\pi$
$674$	31.6544			1.21928
$675$	−21.1968	+	15.0231i	−0.815866	+	0.578240i
$676$	11.3011			0.434656
$677$	−4.61132	+	4.61132i	−0.177227	+	0.177227i	−0.790146	−	0.612919i	$-0.789995\pi$
$677$	−4.61132	+	4.61132i	−0.177227	+	0.177227i	0.612919	+	0.790146i	$0.289995\pi$
$678$	−9.42588	−	4.90288i	−0.361999	−	0.188294i
$679$		−	18.6933i		−	0.717383i
$680$	−12.8990	−	7.78567i	−0.494653	−	0.298567i
$681$	17.2487	−	5.44471i	0.660972	−	0.208642i
$682$	−4.10688	−	4.10688i	−0.157261	−	0.157261i
$683$	8.26190	+	8.26190i	0.316133	+	0.316133i	0.847280	−	0.531147i	$-0.178239\pi$
$683$	8.26190	+	8.26190i	0.316133	+	0.316133i	−0.531147	+	0.847280i	$0.678239\pi$
$684$	−10.2388	−	14.6022i	−0.391491	−	0.558329i
$685$	−6.80494	+	1.68220i	−0.260003	+	0.0642736i
$686$			1.00000i			0.0381802i
$687$	−10.7277	+	20.6242i	−0.409288	+	0.786863i
$688$	−8.17020	+	8.17020i	−0.311486	+	0.311486i
$689$	−12.6673			−0.482586
$690$	−7.12426	−	11.6696i	−0.271216	−	0.444252i
$691$	−21.6167			−0.822338			−0.411169	−	0.911559i	$-0.634879\pi$
$691$	−21.6167			−0.822338			−0.411169	+	0.911559i	$0.634879\pi$
$692$	−4.45093	+	4.45093i	−0.169199	+	0.169199i
$693$	−5.03756	−	0.884857i	−0.191361	−	0.0336129i
$694$			19.7193i			0.748536i
$695$	−0.373179	+	0.618268i	−0.0141555	+	0.0234522i
$696$	−2.70964	−	8.58409i	−0.102709	−	0.325379i
$697$	52.2892	+	52.2892i	1.98060	+	1.98060i
$698$	3.08796	+	3.08796i	0.116881	+	0.116881i
$699$	−6.14169	−	19.4567i	−0.232300	−	0.735922i
$700$	−4.77563	−	1.48099i	−0.180502	−	0.0559762i
$701$			1.45001i			0.0547660i	0.999625	+	0.0273830i	$0.00871737\pi$
$701$			1.45001i			0.0547660i	−0.999625	+	0.0273830i	$0.991283\pi$
$702$	−6.71401	+	0.890626i	−0.253404	+	0.0336145i
$703$	−6.11771	+	6.11771i	−0.230734	+	0.230734i
$704$	1.70489			0.0642556
$705$	−2.32467	−	0.562222i	−0.0875521	−	0.0211745i
$706$	14.0149			0.527458
$707$	12.6169	−	12.6169i	0.474506	−	0.474506i
$708$	0.548568	−	1.05463i	0.0206165	−	0.0396355i
$709$		−	0.737376i		−	0.0276927i	−0.999904	−	0.0138464i	$-0.995592\pi$
$709$		−	0.737376i		−	0.0276927i	0.999904	−	0.0138464i	$-0.00440758\pi$
$710$	6.57944	+	26.6156i	0.246922	+	0.998864i
$711$	17.6736	−	12.3925i	0.662814	−	0.464754i
$712$	−1.59465	−	1.59465i	−0.0597619	−	0.0597619i
$713$	−8.50380	−	8.50380i	−0.318470	−	0.318470i
$714$	−11.1292	+	3.51302i	−0.416499	+	0.131472i
$715$	−1.19246	−	4.82381i	−0.0445955	−	0.180400i
$716$			10.6798i			0.399121i
$717$	−0.572685	−	0.297883i	−0.0213873	−	0.0111246i
$718$	22.4964	−	22.4964i	0.839559	−	0.839559i
$719$	24.2873			0.905762			0.452881	−	0.891571i	$-0.350396\pi$
$719$	24.2873			0.905762			0.452881	+	0.891571i	$0.350396\pi$
$720$	−0.458926	−	6.69249i	−0.0171032	−	0.249414i
$721$	16.8300			0.626781
$722$	11.5540	−	11.5540i	0.429994	−	0.429994i
$723$	45.2017	+	23.5117i	1.68107	+	0.874411i
$724$		−	12.8215i		−	0.476506i
$725$	−12.1074	−	22.9924i	−0.449659	−	0.853916i
$726$	−13.3679	+	4.21969i	−0.496129	+	0.156607i
$727$	0.423061	+	0.423061i	0.0156905	+	0.0156905i	0.714908	−	0.699218i	$-0.246468\pi$
$727$	0.423061	+	0.423061i	0.0156905	+	0.0156905i	−0.699218	+	0.714908i	$0.746468\pi$
$728$	−0.921665	−	0.921665i	−0.0341592	−	0.0341592i
$729$	−26.0662	+	7.03933i	−0.965416	+	0.260716i
$730$	7.51192	−	12.4454i	0.278029	−	0.460626i
$731$			77.8531i			2.87950i
$732$	−1.39867	+	2.68897i	−0.0516963	+	0.0993871i
$733$	−0.238162	+	0.238162i	−0.00879670	+	0.00879670i	−0.711491	−	0.702695i	$-0.751980\pi$
$733$	−0.238162	+	0.238162i	−0.00879670	+	0.00879670i	0.702695	+	0.711491i	$0.251980\pi$
$734$	20.4262			0.753945
$735$	−3.30564	+	2.01810i	−0.121931	+	0.0744386i
$736$	3.53019			0.130125
$737$	1.76971	−	1.76971i	0.0651882	−	0.0651882i
$738$	−5.69607	+	32.4281i	−0.209675	+	1.19370i
$739$		−	41.6831i		−	1.53334i	−0.642042	−	0.766669i	$-0.721913\pi$
$739$		−	41.6831i		−	1.53334i	0.642042	−	0.766669i	$-0.278087\pi$
$740$	−3.15920	+	0.780962i	−0.116134	+	0.0287088i
$741$	−4.03992	−	12.7984i	−0.148410	−	0.470161i
$742$	−6.87196	−	6.87196i	−0.252278	−	0.252278i
$743$	−1.84534	−	1.84534i	−0.0676990	−	0.0676990i	0.672447	−	0.740146i	$-0.265243\pi$
$743$	−1.84534	−	1.84534i	−0.0676990	−	0.0676990i	−0.740146	+	0.672447i	$0.765243\pi$
$744$	−1.77616	−	5.62685i	−0.0651173	−	0.206290i
$745$	7.32309	+	4.42013i	0.268297	+	0.161941i
$746$		−	19.1701i		−	0.701867i
$747$	−4.87874	+	27.7750i	−0.178504	+	1.01624i
$748$	8.12288	−	8.12288i	0.297002	−	0.297002i
$749$	5.61377			0.205123
$750$	−4.74206	−	18.7753i	−0.173156	−	0.685578i
$751$	27.4131			1.00032			0.500160	−	0.865933i	$-0.333275\pi$
$751$	27.4131			1.00032			0.500160	+	0.865933i	$0.333275\pi$
$752$	0.436661	−	0.436661i	0.0159234	−	0.0159234i
$753$	−2.28676	+	4.39633i	−0.0833341	+	0.160211i
$754$		−	6.77403i		−	0.246696i
$755$	9.09438	+	5.48926i	0.330978	+	0.199775i
$756$	−4.12549	−	3.15917i	−0.150043	−	0.114898i
$757$	28.1863	+	28.1863i	1.02445	+	1.02445i	0.999694	+	0.0247547i	$0.00788046\pi$
$757$	28.1863	+	28.1863i	1.02445	+	1.02445i	0.0247547	+	0.999694i	$0.492120\pi$
$758$	−10.7124	−	10.7124i	−0.389091	−	0.389091i
$759$	9.94101	−	3.13797i	0.360836	−	0.113901i
$760$	12.9044	−	3.19000i	0.468091	−	0.115713i
$761$		−	17.7595i		−	0.643782i	−0.946777	−	0.321891i	$-0.895682\pi$
$761$		−	17.7595i		−	0.643782i	0.946777	−	0.321891i	$-0.104318\pi$
$762$	24.3801	+	12.6813i	0.883197	+	0.459396i
$763$	4.71291	−	4.71291i	0.170619	−	0.170619i
$764$	−8.28637			−0.299790
$765$	−34.0726	−	29.6995i	−1.23190	−	1.07379i
$766$	23.6779			0.855519
$767$	0.632573	−	0.632573i	0.0228409	−	0.0228409i
$768$	1.53661	+	0.799269i	0.0554476	+	0.0288411i
$769$		−	31.6783i		−	1.14235i	−0.820828	−	0.571175i	$-0.806488\pi$
$769$		−	31.6783i		−	1.14235i	0.820828	−	0.571175i	$-0.193512\pi$
$770$	1.96999	−	3.26380i	0.0709937	−	0.117619i
$771$	6.86658	−	2.16750i	0.247294	−	0.0780605i
$772$	3.59731	+	3.59731i	0.129470	+	0.129470i
$773$	−24.0703	−	24.0703i	−0.865748	−	0.865748i	0.126250	−	0.991998i	$-0.459706\pi$
$773$	−24.0703	−	24.0703i	−0.865748	−	0.865748i	−0.991998	+	0.126250i	$0.959706\pi$
$774$	−28.3814	+	19.9006i	−1.02015	+	0.715312i
$775$	−7.93640	−	15.0714i	−0.285084	−	0.541382i
$776$			18.6933i			0.671050i
$777$	−1.16323	+	2.23633i	−0.0417306	+	0.0802278i
$778$	−7.32794	+	7.32794i	−0.262719	+	0.262719i
$779$	−65.2426			−2.33756
$780$	1.18669	−	4.90671i	0.0424903	−	0.175688i
$781$	−20.9039			−0.748001
$782$	16.8194	−	16.8194i	0.601461	−	0.601461i
$783$	−3.55113	−	26.7703i	−0.126907	−	0.956692i
$784$		−	1.00000i		−	0.0357143i
$785$	−7.82151	−	31.6400i	−0.279162	−	1.12928i
$786$	2.40220	+	7.61011i	0.0856836	+	0.271444i
$787$	−19.3092	−	19.3092i	−0.688297	−	0.688297i	0.273558	−	0.961855i	$-0.411799\pi$
$787$	−19.3092	−	19.3092i	−0.688297	−	0.688297i	−0.961855	+	0.273558i	$0.911799\pi$
$788$	5.50386	+	5.50386i	0.196067	+	0.196067i
$789$	12.3142	+	39.0111i	0.438397	+	1.38883i
$790$	3.86098	+	15.6187i	0.137368	+	0.555688i
$791$		−	6.13421i		−	0.218107i
$792$	5.03756	+	0.884857i	0.179002	+	0.0314420i
$793$	−1.61285	+	1.61285i	−0.0572741	+	0.0572741i
$794$	−15.0012			−0.532373
$795$	8.84799	−	36.5846i	0.313806	−	1.29752i
$796$	20.7662			0.736038
$797$	16.7052	−	16.7052i	0.591727	−	0.591727i	−0.346371	−	0.938098i	$-0.612586\pi$
$797$	16.7052	−	16.7052i	0.591727	−	0.591727i	0.938098	+	0.346371i	$0.112586\pi$
$798$	4.75144	−	9.13472i	0.168199	−	0.323366i
$799$		−	4.16090i		−	0.147202i
$800$	4.77563	+	1.48099i	0.168844	+	0.0523609i
$801$	−3.88417	−	5.53944i	−0.137240	−	0.195727i
$802$	−6.62647	−	6.62647i	−0.233989	−	0.233989i
$803$	7.83728	+	7.83728i	0.276572	+	0.276572i
$804$	2.42469	−	0.765374i	0.0855122	−	0.0269927i
$805$	4.07912	−	6.75811i	0.143770	−	0.238192i
$806$		−	4.44036i		−	0.156405i
$807$	1.69809	+	0.883261i	0.0597754	+	0.0310923i
$808$	−12.6169	+	12.6169i	−0.443860	+	0.443860i
$809$	12.8721			0.452560			0.226280	−	0.974062i	$-0.427343\pi$
$809$	12.8721			0.452560			0.226280	+	0.974062i	$0.427343\pi$
$810$	2.11745	−	20.0129i	0.0743996	−	0.703182i
$811$	−1.25946			−0.0442256			−0.0221128	−	0.999755i	$-0.507039\pi$
$811$	−1.25946			−0.0442256			−0.0221128	+	0.999755i	$0.507039\pi$
$812$	3.67489	−	3.67489i	0.128963	−	0.128963i
$813$	−36.7478	−	19.1144i	−1.28880	−	0.670372i
$814$		−	2.48124i		−	0.0869674i
$815$	13.6692	−	3.37906i	0.478811	−	0.118363i
$816$	11.1292	−	3.51302i	0.389599	−	0.122980i
$817$	−48.5696	−	48.5696i	−1.69924	−	1.69924i
$818$	16.4009	+	16.4009i	0.573443	+	0.573443i
$819$	−2.24495	−	3.20166i	−0.0784449	−	0.111875i
$820$	−21.0100	−	12.6814i	−0.733701	−	0.442854i
$821$		−	26.4873i		−	0.924415i	−0.886772	−	0.462207i	$-0.847058\pi$
$821$		−	26.4873i		−	0.924415i	0.886772	−	0.462207i	$-0.152942\pi$
$822$	2.50560	−	4.81707i	0.0873930	−	0.168015i
$823$	2.53245	−	2.53245i	0.0882758	−	0.0882758i	−0.661590	−	0.749866i	$-0.730118\pi$
$823$	2.53245	−	2.53245i	0.0882758	−	0.0882758i	0.749866	+	0.661590i	$0.230118\pi$
$824$	−16.8300			−0.586300
$825$	14.7646	−	0.0745685i	0.514038	−	0.00259614i
$826$	0.686337			0.0238807
$827$	−9.56258	+	9.56258i	−0.332524	+	0.332524i	−0.853544	−	0.521021i	$-0.825551\pi$
$827$	−9.56258	+	9.56258i	−0.332524	+	0.332524i	0.521021	+	0.853544i	$0.325551\pi$
$828$	10.4309	+	1.83220i	0.362498	+	0.0636735i
$829$		−	38.5455i		−	1.33874i	−0.742928	−	0.669371i	$-0.766564\pi$
$829$		−	38.5455i		−	1.33874i	0.742928	−	0.669371i	$-0.233436\pi$
$830$	−17.9953	−	10.8618i	−0.624626	−	0.377017i
$831$	−7.80859	−	24.7374i	−0.270877	−	0.858132i
$832$	0.921665	+	0.921665i	0.0319530	+	0.0319530i
$833$	−4.76445	−	4.76445i	−0.165079	−	0.165079i
$834$	−0.168385	−	0.533439i	−0.00583069	−	0.0184715i
$835$	−27.3912	+	6.77118i	−0.947911	+	0.234326i
$836$			10.1351i			0.350531i
$837$	−2.32775	−	17.5479i	−0.0804589	−	0.606543i
$838$	1.16034	−	1.16034i	0.0400831	−	0.0400831i
$839$	−18.9721			−0.654989			−0.327495	−	0.944853i	$-0.606204\pi$
$839$	−18.9721			−0.654989			−0.327495	+	0.944853i	$0.606204\pi$
$840$	3.30564	−	2.01810i	0.114056	−	0.0696309i
$841$	−1.99040			−0.0686344
$842$	−2.77219	+	2.77219i	−0.0955359	+	0.0955359i
$843$	−15.5431	+	29.8818i	−0.535332	+	1.02919i
$844$		−	26.0519i		−	0.896743i
$845$	−13.0583	+	21.6345i	−0.449220	+	0.744249i
$846$	1.51686	−	1.06360i	0.0521507	−	0.0365673i
$847$	−5.72286	−	5.72286i	−0.196640	−	0.196640i
$848$	6.87196	+	6.87196i	0.235984	+	0.235984i
$849$	−40.4071	+	12.7548i	−1.38677	+	0.437745i
$850$	29.8094	−	15.6972i	1.02245	−	0.538409i
$851$		−	5.13771i		−	0.176119i
$852$	−18.8406	−	9.79994i	−0.645467	−	0.335741i
$853$	−25.7974	+	25.7974i	−0.883284	+	0.883284i	−0.993867	−	0.110582i	$-0.964728\pi$
$853$	−25.7974	+	25.7974i	−0.883284	+	0.883284i	0.110582	+	0.993867i	$0.464728\pi$
$854$	−1.74994			−0.0598815
$855$	39.7850	−	2.72819i	1.36062	−	0.0933021i
$856$	−5.61377			−0.191875
$857$	−13.3333	+	13.3333i	−0.455458	+	0.455458i	−0.897161	−	0.441703i	$-0.854374\pi$
$857$	−13.3333	+	13.3333i	−0.455458	+	0.455458i	0.441703	+	0.897161i	$0.354374\pi$
$858$	3.41467	+	1.77614i	0.116575	+	0.0606366i
$859$			7.46319i			0.254641i	0.991862	+	0.127320i	$0.0406377\pi$
$859$			7.46319i			0.254641i	−0.991862	+	0.127320i	$0.959362\pi$
$860$	−6.20021	−	25.0815i	−0.211425	−	0.855271i
$861$	−18.1274	+	5.72206i	−0.617779	+	0.195007i
$862$	19.8342	+	19.8342i	0.675557	+	0.675557i
$863$	−14.6455	−	14.6455i	−0.498539	−	0.498539i	0.412444	−	0.910983i	$-0.364675\pi$
$863$	−14.6455	−	14.6455i	−0.498539	−	0.498539i	−0.910983	+	0.412444i	$0.864675\pi$
$864$	4.12549	+	3.15917i	0.140352	+	0.107477i
$865$	−3.37773	−	13.6638i	−0.114846	−	0.464583i
$866$		−	10.5000i		−	0.356804i
$867$	22.6993	−	43.6398i	0.770908	−	1.48208i
$868$	2.40888	−	2.40888i	0.0817627	−	0.0817627i
$869$	−12.2670			−0.416128
$870$	19.5642	+	4.73160i	0.663287	+	0.160416i
$871$	1.91341			0.0648336
$872$	−4.71291	+	4.71291i	−0.159599	+	0.159599i
$873$	−9.70201	+	55.2343i	−0.328363	+	1.86940i
$874$			20.9860i			0.709862i
$875$	8.35339	−	7.43108i	0.282396	−	0.251216i
$876$	3.38950	+	10.7379i	0.114521	+	0.362799i
$877$	3.06648	+	3.06648i	0.103548	+	0.103548i	0.756983	−	0.653435i	$-0.226673\pi$
$877$	3.06648	+	3.06648i	0.103548	+	0.103548i	−0.653435	+	0.756983i	$0.726673\pi$
$878$	−16.5753	−	16.5753i	−0.559389	−	0.559389i
$879$	13.1978	+	41.8104i	0.445151	+	1.41023i
$880$	−1.96999	+	3.26380i	−0.0664085	+	0.110023i
$881$			4.11283i			0.138565i	0.997597	+	0.0692824i	$0.0220710\pi$
$881$			4.11283i			0.138565i	−0.997597	+	0.0692824i	$0.977929\pi$
$882$	0.519010	−	2.95476i	0.0174760	−	0.0994921i
$883$	−8.74068	+	8.74068i	−0.294147	+	0.294147i	−0.838716	−	0.544569i	$-0.816693\pi$
$883$	−8.74068	+	8.74068i	−0.294147	+	0.294147i	0.544569	+	0.838716i	$0.316693\pi$
$884$	8.78246			0.295386
$885$	1.38509	+	2.26879i	0.0465594	+	0.0762644i
$886$	14.2193			0.477706
$887$	2.49148	−	2.49148i	0.0836558	−	0.0836558i	−0.664041	−	0.747696i	$-0.731160\pi$
$887$	2.49148	−	2.49148i	0.0836558	−	0.0836558i	0.747696	+	0.664041i	$0.231160\pi$
$888$	1.16323	−	2.23633i	0.0390354	−	0.0750462i
$889$			15.8661i			0.532133i
$890$	4.89536	−	1.21015i	0.164093	−	0.0405642i
$891$	14.4255	+	5.22909i	0.483274	+	0.175181i
$892$	1.49400	+	1.49400i	0.0500227	+	0.0500227i
$893$	2.59583	+	2.59583i	0.0868661	+	0.0868661i
$894$	−6.31833	+	1.99444i	−0.211317	+	0.0667040i
$895$	−20.4451	−	12.3404i	−0.683403	−	0.412494i
$896$			1.00000i			0.0334077i
$897$	7.07049	+	3.67772i	0.236077	+	0.122796i
$898$	−20.7135	+	20.7135i	−0.691218	+	0.691218i
$899$	17.7047			0.590485
$900$	13.3422	+	6.85458i	0.444741	+	0.228486i
$901$	65.4823			2.18153
$902$	13.2307	−	13.2307i	0.440533	−	0.440533i
$903$	−17.7546	−	9.23508i	−0.590837	−	0.307324i
$904$			6.13421i			0.204021i
$905$	24.5451	+	14.8151i	0.815906	+	0.492472i
$906$	−7.84659	+	2.47685i	−0.260686	+	0.0822877i
$907$	−28.0384	−	28.0384i	−0.931001	−	0.931001i	0.0667678	−	0.997769i	$-0.478731\pi$
$907$	−28.0384	−	28.0384i	−0.931001	−	0.931001i	−0.997769	+	0.0667678i	$0.978731\pi$
$908$	−7.38425	−	7.38425i	−0.245055	−	0.245055i
$909$	−43.8281	+	30.7316i	−1.45369	+	1.01930i
$910$	2.82939	−	0.699434i	0.0937934	−	0.0231860i
$911$		−	35.7595i		−	1.18476i	−0.805657	−	0.592382i	$-0.798188\pi$
$911$		−	35.7595i		−	1.18476i	0.805657	−	0.592382i	$-0.201812\pi$
$912$	−4.75144	+	9.13472i	−0.157336	+	0.302481i
$913$	11.3322	−	11.3322i	0.375041	−	0.375041i
$914$	−30.1416			−0.996997
$915$	−3.53154	−	5.78466i	−0.116749	−	0.191235i
$916$	13.4219			0.443472
$917$	−3.25792	+	3.25792i	−0.107586	+	0.107586i
$918$	34.7074	−	4.60400i	1.14552	−	0.151955i
$919$			55.1175i			1.81816i	0.416623	+	0.909079i	$0.363214\pi$
$919$			55.1175i			1.81816i	−0.416623	+	0.909079i	$0.636786\pi$
$920$	−4.07912	+	6.75811i	−0.134484	+	0.222808i
$921$	5.56391	+	17.6263i	0.183337	+	0.580808i
$922$	6.73949	+	6.73949i	0.221953	+	0.221953i
$923$	−11.3007	−	11.3007i	−0.371966	−	0.371966i
$924$	0.888895	+	2.81600i	0.0292425	+	0.0926396i
$925$	2.15538	−	6.95029i	0.0708685	−	0.228524i
$926$			28.0710i			0.922471i
$927$	−49.7286	−	8.73493i	−1.63330	−	0.286893i
$928$	−3.67489	+	3.67489i	−0.120634	+	0.120634i
$929$	−6.70076			−0.219845			−0.109922	−	0.993940i	$-0.535060\pi$
$929$	−6.70076			−0.219845			−0.109922	+	0.993940i	$0.535060\pi$
$930$	12.8242	+	3.10155i	0.420524	+	0.101704i
$931$	5.94473			0.194831
$932$	−8.32952	+	8.32952i	−0.272842	+	0.272842i
$933$	5.66992	−	10.9005i	0.185625	−	0.356867i
$934$		−	23.9280i		−	0.782949i
$935$	6.16430	+	24.9362i	0.201594	+	0.815501i
$936$	2.24495	+	3.20166i	0.0733785	+	0.104649i
$937$	9.53939	+	9.53939i	0.311638	+	0.311638i	0.845544	−	0.533906i	$-0.179276\pi$
$937$	9.53939	+	9.53939i	0.311638	+	0.311638i	−0.533906	+	0.845544i	$0.679276\pi$
$938$	1.03802	+	1.03802i	0.0338926	+	0.0338926i
$939$	32.0117	−	10.1048i	1.04466	−	0.329757i
$940$	0.331373	+	1.34049i	0.0108082	+	0.0437220i
$941$			44.9315i			1.46472i	0.680915	+	0.732362i	$0.261582\pi$
$941$			44.9315i			1.46472i	−0.680915	+	0.732362i	$0.738418\pi$
$942$	22.3973	+	11.6500i	0.729743	+	0.379577i
$943$	27.3957	−	27.3957i	0.892126	−	0.892126i
$944$	−0.686337			−0.0223384
$945$	10.8148	−	4.24733i	0.351806	−	0.138166i
$946$	19.6990			0.640471
$947$	−1.70096	+	1.70096i	−0.0552738	+	0.0552738i	−0.734203	−	0.678930i	$-0.762444\pi$
$947$	−1.70096	+	1.70096i	−0.0552738	+	0.0552738i	0.678930	+	0.734203i	$0.262444\pi$
$948$	−11.0561	−	5.75086i	−0.359086	−	0.186779i
$949$			8.47366i			0.275067i
$950$	−8.80408	+	28.3898i	−0.285642	+	0.921088i
$951$	46.9941	−	14.8341i	1.52389	−	0.481029i
$952$	4.76445	+	4.76445i	0.154417	+	0.154417i
$953$	−31.9131	−	31.9131i	−1.03377	−	1.03377i	−0.999410	−	0.0343567i	$-0.989062\pi$
$953$	−31.9131	−	31.9131i	−1.03377	−	1.03377i	−0.0343567	−	0.999410i	$-0.510938\pi$
$954$	16.7384	+	23.8716i	0.541926	+	0.772873i
$955$	9.57485	−	15.8632i	0.309835	−	0.513322i
$956$			0.372694i			0.0120538i
$957$	−7.08189	+	13.6151i	−0.228925	+	0.440113i
$958$	3.65381	−	3.65381i	0.118049	−	0.118049i
$959$	3.13487			0.101230
$960$	−3.30564	+	2.01810i	−0.106689	+	0.0651338i
$961$	−19.3946			−0.625632
$962$	1.34136	−	1.34136i	0.0432471	−	0.0432471i
$963$	−16.5874	−	2.91361i	−0.534521	−	0.0938896i
$964$		−	29.4165i		−	0.947443i
$965$	−11.0433	+	2.72993i	−0.355495	+	0.0878795i
$966$	1.84056	+	5.83087i	0.0592192	+	0.187605i
$967$	−24.6132	−	24.6132i	−0.791508	−	0.791508i	0.190232	−	0.981739i	$-0.439076\pi$
$967$	−24.6132	−	24.6132i	−0.791508	−	0.791508i	−0.981739	+	0.190232i	$0.939076\pi$
$968$	5.72286	+	5.72286i	0.183940	+	0.183940i
$969$	20.8840	+	66.1600i	0.670890	+	2.12536i
$970$	−35.7860	−	21.6000i	−1.14902	−	0.693534i
$971$		−	17.9560i		−	0.576235i	−0.957595	−	0.288117i	$-0.906971\pi$
$971$		−	17.9560i		−	0.576235i	0.957595	−	0.288117i	$-0.0930293\pi$
$972$	10.5502	+	11.4758i	0.338398	+	0.368085i
$973$	0.228368	−	0.228368i	0.00732113	−	0.00732113i
$974$	22.9731			0.736107
$975$	8.02206	+	7.94144i	0.256912	+	0.254330i
$976$	1.74994			0.0560141
$977$	−14.6134	+	14.6134i	−0.467526	+	0.467526i	−0.901112	−	0.433586i	$-0.857248\pi$
$977$	−14.6134	+	14.6134i	−0.467526	+	0.467526i	0.433586	+	0.901112i	$0.357248\pi$
$978$	−5.03304	+	9.67612i	−0.160939	+	0.309408i
$979$			3.84483i			0.122881i
$980$	1.91438	+	1.15549i	0.0611525	+	0.0369109i
$981$	−16.3716	+	11.4795i	−0.522704	+	0.366512i
$982$	6.79723	+	6.79723i	0.216908	+	0.216908i
$983$	−1.53415	−	1.53415i	−0.0489318	−	0.0489318i	0.682217	−	0.731149i	$-0.261016\pi$
$983$	−1.53415	−	1.53415i	−0.0489318	−	0.0489318i	−0.731149	+	0.682217i	$0.761016\pi$
$984$	18.1274	−	5.72206i	0.577879	−	0.182413i
$985$	−16.8961	+	4.17677i	−0.538356	+	0.133083i
$986$			35.0177i			1.11519i
$987$	0.948905	+	0.493574i	0.0302040	+	0.0157106i
$988$	−5.47905	+	5.47905i	−0.174312	+	0.174312i
$989$	40.7893			1.29702
$990$	−7.51482	+	8.62133i	−0.238837	+	0.274004i
$991$	−6.06527			−0.192670			−0.0963348	−	0.995349i	$-0.530712\pi$
$991$	−6.06527			−0.192670			−0.0963348	+	0.995349i	$0.530712\pi$
$992$	−2.40888	+	2.40888i	−0.0764820	+	0.0764820i
$993$	11.3003	+	5.87789i	0.358606	+	0.186529i
$994$		−	12.2611i		−	0.388899i
$995$	−23.9952	+	39.7543i	−0.760700	+	1.26030i
$996$	15.5263	−	4.90100i	0.491969	−	0.155294i
$997$	12.6897	+	12.6897i	0.401887	+	0.401887i	0.878897	−	0.477011i	$-0.158280\pi$
$997$	12.6897	+	12.6897i	0.401887	+	0.401887i	−0.477011	+	0.878897i	$0.658280\pi$
$998$	−4.67316	−	4.67316i	−0.147926	−	0.147926i
$999$	4.59774	−	6.00409i	0.145466	−	0.189961i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.j.b.197.3	yes	12
3.2	odd	2		210.2.j.a.197.4	yes	12
5.2	odd	4		1050.2.j.c.743.3		12
5.3	odd	4		210.2.j.a.113.4	✓	12
5.4	even	2		1050.2.j.d.407.4		12
15.2	even	4		1050.2.j.d.743.4		12
15.8	even	4	inner	210.2.j.b.113.3	yes	12
15.14	odd	2		1050.2.j.c.407.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.j.a.113.4	✓	12	5.3	odd	4
210.2.j.a.197.4	yes	12	3.2	odd	2
210.2.j.b.113.3	yes	12	15.8	even	4	inner
210.2.j.b.197.3	yes	12	1.1	even	1	trivial
1050.2.j.c.407.3		12	15.14	odd	2
1050.2.j.c.743.3		12	5.2	odd	4
1050.2.j.d.407.4		12	5.4	even	2
1050.2.j.d.743.4		12	15.2	even	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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.53661 + 0.799269i) q^{3} -1.00000i q^{4} +(1.91438 + 1.15549i) q^{5} +(-1.65172 + 0.521378i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.72234 + 2.45633i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.53661 + 0.799269i) q^{3} -1.00000i q^{4} +(1.91438 + 1.15549i) q^{5} +(-1.65172 + 0.521378i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.72234 + 2.45633i) q^{9} +(-2.17073 + 0.536610i) q^{10} -1.70489i q^{11} +(0.799269 - 1.53661i) q^{12} +(0.921665 - 0.921665i) q^{13} +1.00000 q^{14} +(2.01810 + 3.30564i) q^{15} -1.00000 q^{16} +(-4.76445 + 4.76445i) q^{17} +(-2.95476 - 0.519010i) q^{18} -5.94473i q^{19} +(1.15549 - 1.91438i) q^{20} +(-0.521378 - 1.65172i) q^{21} +(1.20554 + 1.20554i) q^{22} +(2.49622 + 2.49622i) q^{23} +(0.521378 + 1.65172i) q^{24} +(2.32966 + 4.42410i) q^{25} +1.30343i q^{26} +(0.683293 + 5.15103i) q^{27} +(-0.707107 + 0.707107i) q^{28} -5.19708 q^{29} +(-3.76445 - 0.910435i) q^{30} -3.40667 q^{31} +(0.707107 - 0.707107i) q^{32} +(1.36267 - 2.61976i) q^{33} -6.73795i q^{34} +(-0.536610 - 2.17073i) q^{35} +(2.45633 - 1.72234i) q^{36} +(-1.02910 - 1.02910i) q^{37} +(4.20356 + 4.20356i) q^{38} +(2.15290 - 0.679581i) q^{39} +(0.536610 + 2.17073i) q^{40} -10.9749i q^{41} +(1.53661 + 0.799269i) q^{42} +(8.17020 - 8.17020i) q^{43} -1.70489 q^{44} +(0.458926 + 6.69249i) q^{45} -3.53019 q^{46} +(-0.436661 + 0.436661i) q^{47} +(-1.53661 - 0.799269i) q^{48} +1.00000i q^{49} +(-4.77563 - 1.48099i) q^{50} +(-11.1292 + 3.51302i) q^{51} +(-0.921665 - 0.921665i) q^{52} +(-6.87196 - 6.87196i) q^{53} +(-4.12549 - 3.15917i) q^{54} +(1.96999 - 3.26380i) q^{55} -1.00000i q^{56} +(4.75144 - 9.13472i) q^{57} +(3.67489 - 3.67489i) q^{58} +0.686337 q^{59} +(3.30564 - 2.01810i) q^{60} -1.74994 q^{61} +(2.40888 - 2.40888i) q^{62} +(0.519010 - 2.95476i) q^{63} +1.00000i q^{64} +(2.82939 - 0.699434i) q^{65} +(0.888895 + 2.81600i) q^{66} +(1.03802 + 1.03802i) q^{67} +(4.76445 + 4.76445i) q^{68} +(1.84056 + 5.83087i) q^{69} +(1.91438 + 1.15549i) q^{70} -12.2611i q^{71} +(-0.519010 + 2.95476i) q^{72} +(-4.59693 + 4.59693i) q^{73} +1.45536 q^{74} +(0.0437379 + 8.66014i) q^{75} -5.94473 q^{76} +(-1.20554 + 1.20554i) q^{77} +(-1.04179 + 2.00286i) q^{78} -7.19515i q^{79} +(-1.91438 - 1.15549i) q^{80} +(-3.06710 + 8.46126i) q^{81} +(7.76040 + 7.76040i) q^{82} +(6.64687 + 6.64687i) q^{83} +(-1.65172 + 0.521378i) q^{84} +(-14.6263 + 3.61565i) q^{85} +11.5544i q^{86} +(-7.98588 - 4.15386i) q^{87} +(1.20554 - 1.20554i) q^{88} -2.25517 q^{89} +(-5.05681 - 4.40779i) q^{90} -1.30343 q^{91} +(2.49622 - 2.49622i) q^{92} +(-5.23472 - 2.72285i) q^{93} -0.617532i q^{94} +(6.86910 - 11.3804i) q^{95} +(1.65172 - 0.521378i) q^{96} +(13.2182 + 13.2182i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(4.18778 - 2.93640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} + 4 q^{5}+O(q^{10}) \) 12 * q + 4 * q^3 + 4 * q^5	\( 12 q + 4 q^{3} + 4 q^{5} - 4 q^{12} + 12 q^{14} - 12 q^{15} - 12 q^{16} - 28 q^{17} - 8 q^{18} - 4 q^{21} + 4 q^{22} + 24 q^{23} + 4 q^{24} + 20 q^{25} + 28 q^{27} - 8 q^{29} - 16 q^{30} - 8 q^{31} - 36 q^{33} + 8 q^{35} + 4 q^{36} - 20 q^{37} + 4 q^{38} + 40 q^{39} - 8 q^{40} + 4 q^{42} + 8 q^{43} - 8 q^{44} - 48 q^{45} + 8 q^{46} - 16 q^{47} - 4 q^{48} + 16 q^{50} + 8 q^{51} + 24 q^{53} + 4 q^{54} - 16 q^{55} + 44 q^{57} - 8 q^{58} - 32 q^{59} + 4 q^{60} - 28 q^{62} - 8 q^{66} + 28 q^{68} + 32 q^{69} + 4 q^{70} - 24 q^{73} - 8 q^{74} - 4 q^{75} - 4 q^{77} - 8 q^{78} - 4 q^{80} - 36 q^{81} + 32 q^{82} + 24 q^{83} - 36 q^{85} - 16 q^{87} + 4 q^{88} - 48 q^{89} - 8 q^{90} + 24 q^{91} + 24 q^{92} - 20 q^{93} + 8 q^{97} + 40 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 + 4 * q^5 - 4 * q^12 + 12 * q^14 - 12 * q^15 - 12 * q^16 - 28 * q^17 - 8 * q^18 - 4 * q^21 + 4 * q^22 + 24 * q^23 + 4 * q^24 + 20 * q^25 + 28 * q^27 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 36 * q^33 + 8 * q^35 + 4 * q^36 - 20 * q^37 + 4 * q^38 + 40 * q^39 - 8 * q^40 + 4 * q^42 + 8 * q^43 - 8 * q^44 - 48 * q^45 + 8 * q^46 - 16 * q^47 - 4 * q^48 + 16 * q^50 + 8 * q^51 + 24 * q^53 + 4 * q^54 - 16 * q^55 + 44 * q^57 - 8 * q^58 - 32 * q^59 + 4 * q^60 - 28 * q^62 - 8 * q^66 + 28 * q^68 + 32 * q^69 + 4 * q^70 - 24 * q^73 - 8 * q^74 - 4 * q^75 - 4 * q^77 - 8 * q^78 - 4 * q^80 - 36 * q^81 + 32 * q^82 + 24 * q^83 - 36 * q^85 - 16 * q^87 + 4 * q^88 - 48 * q^89 - 8 * q^90 + 24 * q^91 + 24 * q^92 - 20 * q^93 + 8 * q^97 + 40 * q^99

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