LMFDB - Embedded newform 170.2.h.a.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(21,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("170.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.h (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:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			81.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	170.81
Dual form			170.2.h.a.21.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.292893 + 0.292893i) q^{3} -1.00000 q^{4} +(-0.707107 - 0.707107i) q^{5} +(0.292893 - 0.292893i) q^{6} +(2.41421 - 2.41421i) q^{7} +1.00000i q^{8} -2.82843i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.292893 + 0.292893i) q^{3} -1.00000 q^{4} +(-0.707107 - 0.707107i) q^{5} +(0.292893 - 0.292893i) q^{6} +(2.41421 - 2.41421i) q^{7} +1.00000i q^{8} -2.82843i q^{9} +(-0.707107 + 0.707107i) q^{10} +(1.00000 - 1.00000i) q^{11} +(-0.292893 - 0.292893i) q^{12} +1.00000 q^{13} +(-2.41421 - 2.41421i) q^{14} -0.414214i q^{15} +1.00000 q^{16} +(0.121320 + 4.12132i) q^{17} -2.82843 q^{18} +0.414214i q^{19} +(0.707107 + 0.707107i) q^{20} +1.41421 q^{21} +(-1.00000 - 1.00000i) q^{22} +(-6.24264 + 6.24264i) q^{23} +(-0.292893 + 0.292893i) q^{24} +1.00000i q^{25} -1.00000i q^{26} +(1.70711 - 1.70711i) q^{27} +(-2.41421 + 2.41421i) q^{28} +(2.94975 + 2.94975i) q^{29} -0.414214 q^{30} +(-2.29289 - 2.29289i) q^{31} -1.00000i q^{32} +0.585786 q^{33} +(4.12132 - 0.121320i) q^{34} -3.41421 q^{35} +2.82843i q^{36} +(4.41421 + 4.41421i) q^{37} +0.414214 q^{38} +(0.292893 + 0.292893i) q^{39} +(0.707107 - 0.707107i) q^{40} +(4.65685 - 4.65685i) q^{41} -1.41421i q^{42} +1.75736i q^{43} +(-1.00000 + 1.00000i) q^{44} +(-2.00000 + 2.00000i) q^{45} +(6.24264 + 6.24264i) q^{46} -5.24264 q^{47} +(0.292893 + 0.292893i) q^{48} -4.65685i q^{49} +1.00000 q^{50} +(-1.17157 + 1.24264i) q^{51} -1.00000 q^{52} +13.4853i q^{53} +(-1.70711 - 1.70711i) q^{54} -1.41421 q^{55} +(2.41421 + 2.41421i) q^{56} +(-0.121320 + 0.121320i) q^{57} +(2.94975 - 2.94975i) q^{58} +8.89949i q^{59} +0.414214i q^{60} +(9.77817 - 9.77817i) q^{61} +(-2.29289 + 2.29289i) q^{62} +(-6.82843 - 6.82843i) q^{63} -1.00000 q^{64} +(-0.707107 - 0.707107i) q^{65} -0.585786i q^{66} +3.17157 q^{67} +(-0.121320 - 4.12132i) q^{68} -3.65685 q^{69} +3.41421i q^{70} +(-9.70711 - 9.70711i) q^{71} +2.82843 q^{72} +(-1.53553 - 1.53553i) q^{73} +(4.41421 - 4.41421i) q^{74} +(-0.292893 + 0.292893i) q^{75} -0.414214i q^{76} -4.82843i q^{77} +(0.292893 - 0.292893i) q^{78} +(-0.242641 + 0.242641i) q^{79} +(-0.707107 - 0.707107i) q^{80} -7.48528 q^{81} +(-4.65685 - 4.65685i) q^{82} -9.89949i q^{83} -1.41421 q^{84} +(2.82843 - 3.00000i) q^{85} +1.75736 q^{86} +1.72792i q^{87} +(1.00000 + 1.00000i) q^{88} +3.34315 q^{89} +(2.00000 + 2.00000i) q^{90} +(2.41421 - 2.41421i) q^{91} +(6.24264 - 6.24264i) q^{92} -1.34315i q^{93} +5.24264i q^{94} +(0.292893 - 0.292893i) q^{95} +(0.292893 - 0.292893i) q^{96} +(5.87868 + 5.87868i) q^{97} -4.65685 q^{98} +(-2.82843 - 2.82843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 4 q^{4} + 4 q^{6} + 4 q^{7}+O(q^{10}) $ 4 * q + 4 * q^3 - 4 * q^4 + 4 * q^6 + 4 * q^7	$ 4 q + 4 q^{3} - 4 q^{4} + 4 q^{6} + 4 q^{7} + 4 q^{11} - 4 q^{12} + 4 q^{13} - 4 q^{14} + 4 q^{16} - 8 q^{17} - 4 q^{22} - 8 q^{23} - 4 q^{24} + 4 q^{27} - 4 q^{28} - 8 q^{29} + 4 q^{30} - 12 q^{31} + 8 q^{33} + 8 q^{34} - 8 q^{35} + 12 q^{37} - 4 q^{38} + 4 q^{39} - 4 q^{41} - 4 q^{44} - 8 q^{45} + 8 q^{46} - 4 q^{47} + 4 q^{48} + 4 q^{50} - 16 q^{51} - 4 q^{52} - 4 q^{54} + 4 q^{56} + 8 q^{57} - 8 q^{58} + 8 q^{61} - 12 q^{62} - 16 q^{63} - 4 q^{64} + 24 q^{67} + 8 q^{68} + 8 q^{69} - 36 q^{71} + 8 q^{73} + 12 q^{74} - 4 q^{75} + 4 q^{78} + 16 q^{79} + 4 q^{81} + 4 q^{82} + 24 q^{86} + 4 q^{88} + 36 q^{89} + 8 q^{90} + 4 q^{91} + 8 q^{92} + 4 q^{95} + 4 q^{96} + 32 q^{97} + 4 q^{98}+O(q^{100}) $ 4 * q + 4 * q^3 - 4 * q^4 + 4 * q^6 + 4 * q^7 + 4 * q^11 - 4 * q^12 + 4 * q^13 - 4 * q^14 + 4 * q^16 - 8 * q^17 - 4 * q^22 - 8 * q^23 - 4 * q^24 + 4 * q^27 - 4 * q^28 - 8 * q^29 + 4 * q^30 - 12 * q^31 + 8 * q^33 + 8 * q^34 - 8 * q^35 + 12 * q^37 - 4 * q^38 + 4 * q^39 - 4 * q^41 - 4 * q^44 - 8 * q^45 + 8 * q^46 - 4 * q^47 + 4 * q^48 + 4 * q^50 - 16 * q^51 - 4 * q^52 - 4 * q^54 + 4 * q^56 + 8 * q^57 - 8 * q^58 + 8 * q^61 - 12 * q^62 - 16 * q^63 - 4 * q^64 + 24 * q^67 + 8 * q^68 + 8 * q^69 - 36 * q^71 + 8 * q^73 + 12 * q^74 - 4 * q^75 + 4 * q^78 + 16 * q^79 + 4 * q^81 + 4 * q^82 + 24 * q^86 + 4 * q^88 + 36 * q^89 + 8 * q^90 + 4 * q^91 + 8 * q^92 + 4 * q^95 + 4 * q^96 + 32 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.292893	+	0.292893i	0.169102	+	0.169102i	0.786585	−	0.617483i	$-0.211847\pi$
$3$	0.292893	+	0.292893i	0.169102	+	0.169102i	−0.617483	+	0.786585i	$0.711847\pi$
$4$	−1.00000			−0.500000
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$	0.292893	−	0.292893i	0.119573	−	0.119573i
$7$	2.41421	−	2.41421i	0.912487	−	0.912487i	−0.0839804	−	0.996467i	$-0.526763\pi$
$7$	2.41421	−	2.41421i	0.912487	−	0.912487i	0.996467	+	0.0839804i	$0.0267633\pi$
$8$			1.00000i			0.353553i
$9$		−	2.82843i		−	0.942809i
$10$	−0.707107	+	0.707107i	−0.223607	+	0.223607i
$11$	1.00000	−	1.00000i	0.301511	−	0.301511i	−0.540094	−	0.841605i	$-0.681611\pi$
$11$	1.00000	−	1.00000i	0.301511	−	0.301511i	0.841605	+	0.540094i	$0.181611\pi$
$12$	−0.292893	−	0.292893i	−0.0845510	−	0.0845510i
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$	−2.41421	−	2.41421i	−0.645226	−	0.645226i
$15$		−	0.414214i		−	0.106949i
$16$	1.00000			0.250000
$17$	0.121320	+	4.12132i	0.0294245	+	0.999567i
$17$	0.121320	+	4.12132i	0.0294245	+	0.999567i
$18$	−2.82843			−0.666667
$19$			0.414214i			0.0950271i	0.998871	+	0.0475136i	$0.0151297\pi$
$19$			0.414214i			0.0950271i	−0.998871	+	0.0475136i	$0.984870\pi$
$20$	0.707107	+	0.707107i	0.158114	+	0.158114i
$21$	1.41421			0.308607
$22$	−1.00000	−	1.00000i	−0.213201	−	0.213201i
$23$	−6.24264	+	6.24264i	−1.30168	+	1.30168i	−0.374422	+	0.927258i	$0.622159\pi$
$23$	−6.24264	+	6.24264i	−1.30168	+	1.30168i	−0.927258	+	0.374422i	$0.877841\pi$
$24$	−0.292893	+	0.292893i	−0.0597866	+	0.0597866i
$25$			1.00000i			0.200000i
$26$		−	1.00000i		−	0.196116i
$27$	1.70711	−	1.70711i	0.328533	−	0.328533i
$28$	−2.41421	+	2.41421i	−0.456243	+	0.456243i
$29$	2.94975	+	2.94975i	0.547754	+	0.547754i	0.925791	−	0.378036i	$-0.123401\pi$
$29$	2.94975	+	2.94975i	0.547754	+	0.547754i	−0.378036	+	0.925791i	$0.623401\pi$
$30$	−0.414214			−0.0756247
$31$	−2.29289	−	2.29289i	−0.411816	−	0.411816i	0.470555	−	0.882371i	$-0.344054\pi$
$31$	−2.29289	−	2.29289i	−0.411816	−	0.411816i	−0.882371	+	0.470555i	$0.844054\pi$
$32$		−	1.00000i		−	0.176777i
$33$	0.585786			0.101972
$34$	4.12132	−	0.121320i	0.706801	−	0.0208063i
$35$	−3.41421			−0.577107
$36$			2.82843i			0.471405i
$37$	4.41421	+	4.41421i	0.725692	+	0.725692i	0.969759	−	0.244066i	$-0.0784815\pi$
$37$	4.41421	+	4.41421i	0.725692	+	0.725692i	−0.244066	+	0.969759i	$0.578481\pi$
$38$	0.414214			0.0671943
$39$	0.292893	+	0.292893i	0.0469005	+	0.0469005i
$40$	0.707107	−	0.707107i	0.111803	−	0.111803i
$41$	4.65685	−	4.65685i	0.727278	−	0.727278i	−0.242798	−	0.970077i	$-0.578065\pi$
$41$	4.65685	−	4.65685i	0.727278	−	0.727278i	0.970077	+	0.242798i	$0.0780653\pi$
$42$		−	1.41421i		−	0.218218i
$43$			1.75736i			0.267995i	0.990982	+	0.133997i	$0.0427814\pi$
$43$			1.75736i			0.267995i	−0.990982	+	0.133997i	$0.957219\pi$
$44$	−1.00000	+	1.00000i	−0.150756	+	0.150756i
$45$	−2.00000	+	2.00000i	−0.298142	+	0.298142i
$46$	6.24264	+	6.24264i	0.920427	+	0.920427i
$47$	−5.24264			−0.764718			−0.382359	−	0.924014i	$-0.624888\pi$
$47$	−5.24264			−0.764718			−0.382359	+	0.924014i	$0.624888\pi$
$48$	0.292893	+	0.292893i	0.0422755	+	0.0422755i
$49$		−	4.65685i		−	0.665265i
$50$	1.00000			0.141421
$51$	−1.17157	+	1.24264i	−0.164053	+	0.174005i
$52$	−1.00000			−0.138675
$53$			13.4853i			1.85235i	0.377099	+	0.926173i	$0.376922\pi$
$53$			13.4853i			1.85235i	−0.377099	+	0.926173i	$0.623078\pi$
$54$	−1.70711	−	1.70711i	−0.232308	−	0.232308i
$55$	−1.41421			−0.190693
$56$	2.41421	+	2.41421i	0.322613	+	0.322613i
$57$	−0.121320	+	0.121320i	−0.0160693	+	0.0160693i
$58$	2.94975	−	2.94975i	0.387321	−	0.387321i
$59$			8.89949i			1.15862i	0.815109	+	0.579308i	$0.196677\pi$
$59$			8.89949i			1.15862i	−0.815109	+	0.579308i	$0.803323\pi$
$60$			0.414214i			0.0534747i
$61$	9.77817	−	9.77817i	1.25197	−	1.25197i	0.297130	−	0.954837i	$-0.403971\pi$
$61$	9.77817	−	9.77817i	1.25197	−	1.25197i	0.954837	−	0.297130i	$-0.0960294\pi$
$62$	−2.29289	+	2.29289i	−0.291198	+	0.291198i
$63$	−6.82843	−	6.82843i	−0.860301	−	0.860301i
$64$	−1.00000			−0.125000
$65$	−0.707107	−	0.707107i	−0.0877058	−	0.0877058i
$66$		−	0.585786i		−	0.0721053i
$67$	3.17157			0.387469			0.193735	−	0.981054i	$-0.437940\pi$
$67$	3.17157			0.387469			0.193735	+	0.981054i	$0.437940\pi$
$68$	−0.121320	−	4.12132i	−0.0147123	−	0.499784i
$69$	−3.65685			−0.440234
$70$			3.41421i			0.408077i
$71$	−9.70711	−	9.70711i	−1.15202	−	1.15202i	−0.986147	−	0.165875i	$-0.946955\pi$
$71$	−9.70711	−	9.70711i	−1.15202	−	1.15202i	−0.165875	−	0.986147i	$-0.553045\pi$
$72$	2.82843			0.333333
$73$	−1.53553	−	1.53553i	−0.179721	−	0.179721i	0.611513	−	0.791234i	$-0.290561\pi$
$73$	−1.53553	−	1.53553i	−0.179721	−	0.179721i	−0.791234	+	0.611513i	$0.790561\pi$
$74$	4.41421	−	4.41421i	0.513142	−	0.513142i
$75$	−0.292893	+	0.292893i	−0.0338204	+	0.0338204i
$76$		−	0.414214i		−	0.0475136i
$77$		−	4.82843i		−	0.550250i
$78$	0.292893	−	0.292893i	0.0331636	−	0.0331636i
$79$	−0.242641	+	0.242641i	−0.0272992	+	0.0272992i	−0.720625	−	0.693325i	$-0.756145\pi$
$79$	−0.242641	+	0.242641i	−0.0272992	+	0.0272992i	0.693325	+	0.720625i	$0.256145\pi$
$80$	−0.707107	−	0.707107i	−0.0790569	−	0.0790569i
$81$	−7.48528			−0.831698
$82$	−4.65685	−	4.65685i	−0.514264	−	0.514264i
$83$		−	9.89949i		−	1.08661i	−0.839535	−	0.543305i	$-0.817173\pi$
$83$		−	9.89949i		−	1.08661i	0.839535	−	0.543305i	$-0.182827\pi$
$84$	−1.41421			−0.154303
$85$	2.82843	−	3.00000i	0.306786	−	0.325396i
$86$	1.75736			0.189501
$87$			1.72792i			0.185253i
$88$	1.00000	+	1.00000i	0.106600	+	0.106600i
$89$	3.34315			0.354373			0.177186	−	0.984177i	$-0.443300\pi$
$89$	3.34315			0.354373			0.177186	+	0.984177i	$0.443300\pi$
$90$	2.00000	+	2.00000i	0.210819	+	0.210819i
$91$	2.41421	−	2.41421i	0.253078	−	0.253078i
$92$	6.24264	−	6.24264i	0.650840	−	0.650840i
$93$		−	1.34315i		−	0.139278i
$94$			5.24264i			0.540737i
$95$	0.292893	−	0.292893i	0.0300502	−	0.0300502i
$96$	0.292893	−	0.292893i	0.0298933	−	0.0298933i
$97$	5.87868	+	5.87868i	0.596889	+	0.596889i	0.939484	−	0.342594i	$-0.111306\pi$
$97$	5.87868	+	5.87868i	0.596889	+	0.596889i	−0.342594	+	0.939484i	$0.611306\pi$
$98$	−4.65685			−0.470413
$99$	−2.82843	−	2.82843i	−0.284268	−	0.284268i
$100$		−	1.00000i		−	0.100000i
$101$	−15.6569			−1.55792			−0.778958	−	0.627077i	$-0.784251\pi$
$101$	−15.6569			−1.55792			−0.778958	+	0.627077i	$0.784251\pi$
$102$	1.24264	+	1.17157i	0.123040	+	0.116003i
$103$	−13.6569			−1.34565			−0.672825	−	0.739802i	$-0.734919\pi$
$103$	−13.6569			−1.34565			−0.672825	+	0.739802i	$0.734919\pi$
$104$			1.00000i			0.0980581i
$105$	−1.00000	−	1.00000i	−0.0975900	−	0.0975900i
$106$	13.4853			1.30981
$107$	−3.17157	−	3.17157i	−0.306608	−	0.306608i	0.536985	−	0.843592i	$-0.319563\pi$
$107$	−3.17157	−	3.17157i	−0.306608	−	0.306608i	−0.843592	+	0.536985i	$0.819563\pi$
$108$	−1.70711	+	1.70711i	−0.164266	+	0.164266i
$109$	4.36396	−	4.36396i	0.417992	−	0.417992i	−0.466519	−	0.884511i	$-0.654492\pi$
$109$	4.36396	−	4.36396i	0.417992	−	0.417992i	0.884511	+	0.466519i	$0.154492\pi$
$110$			1.41421i			0.134840i
$111$			2.58579i			0.245432i
$112$	2.41421	−	2.41421i	0.228122	−	0.228122i
$113$	9.53553	−	9.53553i	0.897028	−	0.897028i	−0.0981446	−	0.995172i	$-0.531291\pi$
$113$	9.53553	−	9.53553i	0.897028	−	0.897028i	0.995172	+	0.0981446i	$0.0312908\pi$
$114$	0.121320	+	0.121320i	0.0113627	+	0.0113627i
$115$	8.82843			0.823255
$116$	−2.94975	−	2.94975i	−0.273877	−	0.273877i
$117$		−	2.82843i		−	0.261488i
$118$	8.89949			0.819265
$119$	10.2426	+	9.65685i	0.938941	+	0.885242i
$120$	0.414214			0.0378124
$121$			9.00000i			0.818182i
$122$	−9.77817	−	9.77817i	−0.885274	−	0.885274i
$123$	2.72792			0.245968
$124$	2.29289	+	2.29289i	0.205908	+	0.205908i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$	−6.82843	+	6.82843i	−0.608325	+	0.608325i
$127$			17.7279i			1.57310i	0.617527	+	0.786549i	$0.288134\pi$
$127$			17.7279i			1.57310i	−0.617527	+	0.786549i	$0.711866\pi$
$128$			1.00000i			0.0883883i
$129$	−0.514719	+	0.514719i	−0.0453184	+	0.0453184i
$130$	−0.707107	+	0.707107i	−0.0620174	+	0.0620174i
$131$	−0.0710678	−	0.0710678i	−0.00620922	−	0.00620922i	0.703995	−	0.710205i	$-0.251398\pi$
$131$	−0.0710678	−	0.0710678i	−0.00620922	−	0.00620922i	−0.710205	+	0.703995i	$0.751398\pi$
$132$	−0.585786			−0.0509862
$133$	1.00000	+	1.00000i	0.0867110	+	0.0867110i
$134$		−	3.17157i		−	0.273982i
$135$	−2.41421			−0.207782
$136$	−4.12132	+	0.121320i	−0.353400	+	0.0104031i
$137$	8.72792			0.745677			0.372838	−	0.927896i	$-0.378385\pi$
$137$	8.72792			0.745677			0.372838	+	0.927896i	$0.378385\pi$
$138$			3.65685i			0.311292i
$139$	10.6569	+	10.6569i	0.903903	+	0.903903i	0.995771	−	0.0918686i	$-0.0292840\pi$
$139$	10.6569	+	10.6569i	0.903903	+	0.903903i	−0.0918686	+	0.995771i	$0.529284\pi$
$140$	3.41421			0.288554
$141$	−1.53553	−	1.53553i	−0.129315	−	0.129315i
$142$	−9.70711	+	9.70711i	−0.814602	+	0.814602i
$143$	1.00000	−	1.00000i	0.0836242	−	0.0836242i
$144$		−	2.82843i		−	0.235702i
$145$		−	4.17157i		−	0.346430i
$146$	−1.53553	+	1.53553i	−0.127082	+	0.127082i
$147$	1.36396	−	1.36396i	0.112498	−	0.112498i
$148$	−4.41421	−	4.41421i	−0.362846	−	0.362846i
$149$	−10.2426			−0.839110			−0.419555	−	0.907730i	$-0.637814\pi$
$149$	−10.2426			−0.839110			−0.419555	+	0.907730i	$0.637814\pi$
$150$	0.292893	+	0.292893i	0.0239146	+	0.0239146i
$151$		−	0.828427i		−	0.0674164i	−0.999432	−	0.0337082i	$-0.989268\pi$
$151$		−	0.828427i		−	0.0674164i	0.999432	−	0.0337082i	$-0.0107317\pi$
$152$	−0.414214			−0.0335972
$153$	11.6569	−	0.343146i	0.942401	−	0.0277417i
$154$	−4.82843			−0.389086
$155$			3.24264i			0.260455i
$156$	−0.292893	−	0.292893i	−0.0234502	−	0.0234502i
$157$	−2.82843			−0.225733			−0.112867	−	0.993610i	$-0.536003\pi$
$157$	−2.82843			−0.225733			−0.112867	+	0.993610i	$0.536003\pi$
$158$	0.242641	+	0.242641i	0.0193035	+	0.0193035i
$159$	−3.94975	+	3.94975i	−0.313235	+	0.313235i
$160$	−0.707107	+	0.707107i	−0.0559017	+	0.0559017i
$161$			30.1421i			2.37553i
$162$			7.48528i			0.588099i
$163$	11.6569	−	11.6569i	0.913035	−	0.913035i	−0.0834746	−	0.996510i	$-0.526602\pi$
$163$	11.6569	−	11.6569i	0.913035	−	0.913035i	0.996510	+	0.0834746i	$0.0266017\pi$
$164$	−4.65685	+	4.65685i	−0.363639	+	0.363639i
$165$	−0.414214	−	0.414214i	−0.0322465	−	0.0322465i
$166$	−9.89949			−0.768350
$167$	−14.7279	−	14.7279i	−1.13968	−	1.13968i	−0.988507	−	0.151174i	$-0.951695\pi$
$167$	−14.7279	−	14.7279i	−1.13968	−	1.13968i	−0.151174	−	0.988507i	$-0.548305\pi$
$168$			1.41421i			0.109109i
$169$	−12.0000			−0.923077
$170$	−3.00000	−	2.82843i	−0.230089	−	0.216930i
$171$	1.17157			0.0895924
$172$		−	1.75736i		−	0.133997i
$173$	15.0711	+	15.0711i	1.14583	+	1.14583i	0.987364	+	0.158468i	$0.0506555\pi$
$173$	15.0711	+	15.0711i	1.14583	+	1.14583i	0.158468	+	0.987364i	$0.449345\pi$
$174$	1.72792			0.130993
$175$	2.41421	+	2.41421i	0.182497	+	0.182497i
$176$	1.00000	−	1.00000i	0.0753778	−	0.0753778i
$177$	−2.60660	+	2.60660i	−0.195924	+	0.195924i
$178$		−	3.34315i		−	0.250579i
$179$			1.17157i			0.0875675i	0.999041	+	0.0437837i	$0.0139413\pi$
$179$			1.17157i			0.0875675i	−0.999041	+	0.0437837i	$0.986059\pi$
$180$	2.00000	−	2.00000i	0.149071	−	0.149071i
$181$	1.17157	−	1.17157i	0.0870823	−	0.0870823i	−0.662224	−	0.749306i	$-0.730387\pi$
$181$	1.17157	−	1.17157i	0.0870823	−	0.0870823i	0.749306	+	0.662224i	$0.230387\pi$
$182$	−2.41421	−	2.41421i	−0.178953	−	0.178953i
$183$	5.72792			0.423420
$184$	−6.24264	−	6.24264i	−0.460214	−	0.460214i
$185$		−	6.24264i		−	0.458968i
$186$	−1.34315			−0.0984842
$187$	4.24264	+	4.00000i	0.310253	+	0.292509i
$188$	5.24264			0.382359
$189$		−	8.24264i		−	0.599564i
$190$	−0.292893	−	0.292893i	−0.0212487	−	0.0212487i
$191$	−8.24264			−0.596417			−0.298208	−	0.954501i	$-0.596389\pi$
$191$	−8.24264			−0.596417			−0.298208	+	0.954501i	$0.596389\pi$
$192$	−0.292893	−	0.292893i	−0.0211377	−	0.0211377i
$193$	−2.82843	+	2.82843i	−0.203595	+	0.203595i	−0.801538	−	0.597944i	$-0.795985\pi$
$193$	−2.82843	+	2.82843i	−0.203595	+	0.203595i	0.597944	+	0.801538i	$0.295985\pi$
$194$	5.87868	−	5.87868i	0.422065	−	0.422065i
$195$		−	0.414214i		−	0.0296624i
$196$			4.65685i			0.332632i
$197$	−3.92893	+	3.92893i	−0.279925	+	0.279925i	−0.833079	−	0.553154i	$-0.813424\pi$
$197$	−3.92893	+	3.92893i	−0.279925	+	0.279925i	0.553154	+	0.833079i	$0.313424\pi$
$198$	−2.82843	+	2.82843i	−0.201008	+	0.201008i
$199$	−17.9497	−	17.9497i	−1.27242	−	1.27242i	−0.944813	−	0.327611i	$-0.893756\pi$
$199$	−17.9497	−	17.9497i	−1.27242	−	1.27242i	−0.327611	−	0.944813i	$-0.606244\pi$
$200$	−1.00000			−0.0707107
$201$	0.928932	+	0.928932i	0.0655218	+	0.0655218i
$202$			15.6569i			1.10161i
$203$	14.2426			0.999637
$204$	1.17157	−	1.24264i	0.0820265	−	0.0870023i
$205$	−6.58579			−0.459971
$206$			13.6569i			0.951518i
$207$	17.6569	+	17.6569i	1.22724	+	1.22724i
$208$	1.00000			0.0693375
$209$	0.414214	+	0.414214i	0.0286518	+	0.0286518i
$210$	−1.00000	+	1.00000i	−0.0690066	+	0.0690066i
$211$	0.585786	−	0.585786i	0.0403272	−	0.0403272i	−0.686656	−	0.726983i	$-0.740922\pi$
$211$	0.585786	−	0.585786i	0.0403272	−	0.0403272i	0.726983	+	0.686656i	$0.240922\pi$
$212$		−	13.4853i		−	0.926173i
$213$		−	5.68629i		−	0.389618i
$214$	−3.17157	+	3.17157i	−0.216804	+	0.216804i
$215$	1.24264	−	1.24264i	0.0847474	−	0.0847474i
$216$	1.70711	+	1.70711i	0.116154	+	0.116154i
$217$	−11.0711			−0.751553
$218$	−4.36396	−	4.36396i	−0.295565	−	0.295565i
$219$		−	0.899495i		−	0.0607822i
$220$	1.41421			0.0953463
$221$	0.121320	+	4.12132i	0.00816089	+	0.277230i
$222$	2.58579			0.173547
$223$		−	11.3848i		−	0.762381i	−0.924497	−	0.381191i	$-0.875514\pi$
$223$		−	11.3848i		−	0.762381i	0.924497	−	0.381191i	$-0.124486\pi$
$224$	−2.41421	−	2.41421i	−0.161306	−	0.161306i
$225$	2.82843			0.188562
$226$	−9.53553	−	9.53553i	−0.634294	−	0.634294i
$227$	−7.46447	+	7.46447i	−0.495434	+	0.495434i	−0.910013	−	0.414579i	$-0.863929\pi$
$227$	−7.46447	+	7.46447i	−0.495434	+	0.495434i	0.414579	+	0.910013i	$0.363929\pi$
$228$	0.121320	−	0.121320i	0.00803464	−	0.00803464i
$229$		−	7.75736i		−	0.512621i	−0.966595	−	0.256310i	$-0.917493\pi$
$229$		−	7.75736i		−	0.512621i	0.966595	−	0.256310i	$-0.0825069\pi$
$230$		−	8.82843i		−	0.582129i
$231$	1.41421	−	1.41421i	0.0930484	−	0.0930484i
$232$	−2.94975	+	2.94975i	−0.193660	+	0.193660i
$233$	4.36396	+	4.36396i	0.285893	+	0.285893i	0.835454	−	0.549561i	$-0.185205\pi$
$233$	4.36396	+	4.36396i	0.285893	+	0.285893i	−0.549561	+	0.835454i	$0.685205\pi$
$234$	−2.82843			−0.184900
$235$	3.70711	+	3.70711i	0.241825	+	0.241825i
$236$		−	8.89949i		−	0.579308i
$237$	−0.142136			−0.00923270
$238$	9.65685	−	10.2426i	0.625961	−	0.663932i
$239$	24.5858			1.59032			0.795161	−	0.606398i	$-0.207386\pi$
$239$	24.5858			1.59032			0.795161	+	0.606398i	$0.207386\pi$
$240$		−	0.414214i		−	0.0267374i
$241$	−14.1716	−	14.1716i	−0.912871	−	0.912871i	0.0836260	−	0.996497i	$-0.473350\pi$
$241$	−14.1716	−	14.1716i	−0.912871	−	0.912871i	−0.996497	+	0.0836260i	$0.973350\pi$
$242$	9.00000			0.578542
$243$	−7.31371	−	7.31371i	−0.469175	−	0.469175i
$244$	−9.77817	+	9.77817i	−0.625983	+	0.625983i
$245$	−3.29289	+	3.29289i	−0.210375	+	0.210375i
$246$		−	2.72792i		−	0.173926i
$247$			0.414214i			0.0263558i
$248$	2.29289	−	2.29289i	0.145599	−	0.145599i
$249$	2.89949	−	2.89949i	0.183748	−	0.183748i
$250$	−0.707107	−	0.707107i	−0.0447214	−	0.0447214i
$251$	26.1421			1.65008			0.825038	−	0.565077i	$-0.191153\pi$
$251$	26.1421			1.65008			0.825038	+	0.565077i	$0.191153\pi$
$252$	6.82843	+	6.82843i	0.430150	+	0.430150i
$253$			12.4853i			0.784943i
$254$	17.7279			1.11235
$255$	1.70711	−	0.0502525i	0.106903	−	0.00314694i
$256$	1.00000			0.0625000
$257$		−	25.4142i		−	1.58530i	−0.609680	−	0.792648i	$-0.708702\pi$
$257$		−	25.4142i		−	1.58530i	0.609680	−	0.792648i	$-0.291298\pi$
$258$	0.514719	+	0.514719i	0.0320450	+	0.0320450i
$259$	21.3137			1.32437
$260$	0.707107	+	0.707107i	0.0438529	+	0.0438529i
$261$	8.34315	−	8.34315i	0.516428	−	0.516428i
$262$	−0.0710678	+	0.0710678i	−0.00439058	+	0.00439058i
$263$		−	4.27208i		−	0.263428i	−0.991288	−	0.131714i	$-0.957952\pi$
$263$		−	4.27208i		−	0.263428i	0.991288	−	0.131714i	$-0.0420480\pi$
$264$			0.585786i			0.0360527i
$265$	9.53553	−	9.53553i	0.585763	−	0.585763i
$266$	1.00000	−	1.00000i	0.0613139	−	0.0613139i
$267$	0.979185	+	0.979185i	0.0599251	+	0.0599251i
$268$	−3.17157			−0.193735
$269$	−9.53553	−	9.53553i	−0.581392	−	0.581392i	0.353894	−	0.935286i	$-0.384857\pi$
$269$	−9.53553	−	9.53553i	−0.581392	−	0.581392i	−0.935286	+	0.353894i	$0.884857\pi$
$270$			2.41421i			0.146924i
$271$	−17.6569			−1.07258			−0.536289	−	0.844035i	$-0.680174\pi$
$271$	−17.6569			−1.07258			−0.536289	+	0.844035i	$0.680174\pi$
$272$	0.121320	+	4.12132i	0.00735613	+	0.249892i
$273$	1.41421			0.0855921
$274$		−	8.72792i		−	0.527273i
$275$	1.00000	+	1.00000i	0.0603023	+	0.0603023i
$276$	3.65685			0.220117
$277$	−13.8995	−	13.8995i	−0.835140	−	0.835140i	0.153075	−	0.988215i	$-0.451082\pi$
$277$	−13.8995	−	13.8995i	−0.835140	−	0.835140i	−0.988215	+	0.153075i	$0.951082\pi$
$278$	10.6569	−	10.6569i	0.639156	−	0.639156i
$279$	−6.48528	+	6.48528i	−0.388264	+	0.388264i
$280$		−	3.41421i		−	0.204038i
$281$			15.4853i			0.923774i	0.886939	+	0.461887i	$0.152828\pi$
$281$			15.4853i			0.923774i	−0.886939	+	0.461887i	$0.847172\pi$
$282$	−1.53553	+	1.53553i	−0.0914397	+	0.0914397i
$283$	−8.77817	+	8.77817i	−0.521808	+	0.521808i	−0.918117	−	0.396309i	$-0.870291\pi$
$283$	−8.77817	+	8.77817i	−0.521808	+	0.521808i	0.396309	+	0.918117i	$0.370291\pi$
$284$	9.70711	+	9.70711i	0.576011	+	0.576011i
$285$	0.171573			0.0101631
$286$	−1.00000	−	1.00000i	−0.0591312	−	0.0591312i
$287$		−	22.4853i		−	1.32726i
$288$	−2.82843			−0.166667
$289$	−16.9706	+	1.00000i	−0.998268	+	0.0588235i
$290$	−4.17157			−0.244963
$291$			3.44365i			0.201870i
$292$	1.53553	+	1.53553i	0.0898603	+	0.0898603i
$293$	−11.4853			−0.670977			−0.335489	−	0.942044i	$-0.608901\pi$
$293$	−11.4853			−0.670977			−0.335489	+	0.942044i	$0.608901\pi$
$294$	−1.36396	−	1.36396i	−0.0795478	−	0.0795478i
$295$	6.29289	−	6.29289i	0.366386	−	0.366386i
$296$	−4.41421	+	4.41421i	−0.256571	+	0.256571i
$297$		−	3.41421i		−	0.198113i
$298$			10.2426i			0.593340i
$299$	−6.24264	+	6.24264i	−0.361021	+	0.361021i
$300$	0.292893	−	0.292893i	0.0169102	−	0.0169102i
$301$	4.24264	+	4.24264i	0.244542	+	0.244542i
$302$	−0.828427			−0.0476706
$303$	−4.58579	−	4.58579i	−0.263447	−	0.263447i
$304$			0.414214i			0.0237568i
$305$	−13.8284			−0.791813
$306$	−0.343146	−	11.6569i	−0.0196163	−	0.666378i
$307$	−9.89949			−0.564994			−0.282497	−	0.959268i	$-0.591163\pi$
$307$	−9.89949			−0.564994			−0.282497	+	0.959268i	$0.591163\pi$
$308$			4.82843i			0.275125i
$309$	−4.00000	−	4.00000i	−0.227552	−	0.227552i
$310$	3.24264			0.184170
$311$	−5.41421	−	5.41421i	−0.307012	−	0.307012i	0.536737	−	0.843749i	$-0.319657\pi$
$311$	−5.41421	−	5.41421i	−0.307012	−	0.307012i	−0.843749	+	0.536737i	$0.819657\pi$
$312$	−0.292893	+	0.292893i	−0.0165818	+	0.0165818i
$313$	−10.4853	+	10.4853i	−0.592663	+	0.592663i	−0.938350	−	0.345687i	$-0.887646\pi$
$313$	−10.4853	+	10.4853i	−0.592663	+	0.592663i	0.345687	+	0.938350i	$0.387646\pi$
$314$			2.82843i			0.159617i
$315$			9.65685i			0.544102i
$316$	0.242641	−	0.242641i	0.0136496	−	0.0136496i
$317$	−7.51472	+	7.51472i	−0.422069	+	0.422069i	−0.885915	−	0.463847i	$-0.846469\pi$
$317$	−7.51472	+	7.51472i	−0.422069	+	0.422069i	0.463847	+	0.885915i	$0.346469\pi$
$318$	3.94975	+	3.94975i	0.221491	+	0.221491i
$319$	5.89949			0.330308
$320$	0.707107	+	0.707107i	0.0395285	+	0.0395285i
$321$		−	1.85786i		−	0.103696i
$322$	30.1421			1.67976
$323$	−1.70711	+	0.0502525i	−0.0949860	+	0.00279613i
$324$	7.48528			0.415849
$325$			1.00000i			0.0554700i
$326$	−11.6569	−	11.6569i	−0.645613	−	0.645613i
$327$	2.55635			0.141366
$328$	4.65685	+	4.65685i	0.257132	+	0.257132i
$329$	−12.6569	+	12.6569i	−0.697795	+	0.697795i
$330$	−0.414214	+	0.414214i	−0.0228017	+	0.0228017i
$331$			22.5563i			1.23981i	0.784677	+	0.619905i	$0.212829\pi$
$331$			22.5563i			1.23981i	−0.784677	+	0.619905i	$0.787171\pi$
$332$			9.89949i			0.543305i
$333$	12.4853	−	12.4853i	0.684189	−	0.684189i
$334$	−14.7279	+	14.7279i	−0.805876	+	0.805876i
$335$	−2.24264	−	2.24264i	−0.122529	−	0.122529i
$336$	1.41421			0.0771517
$337$	5.43503	+	5.43503i	0.296065	+	0.296065i	0.839470	−	0.543405i	$-0.182865\pi$
$337$	5.43503	+	5.43503i	0.296065	+	0.296065i	−0.543405	+	0.839470i	$0.682865\pi$
$338$			12.0000i			0.652714i
$339$	5.58579			0.303378
$340$	−2.82843	+	3.00000i	−0.153393	+	0.162698i
$341$	−4.58579			−0.248334
$342$		−	1.17157i		−	0.0633514i
$343$	5.65685	+	5.65685i	0.305441	+	0.305441i
$344$	−1.75736			−0.0947505
$345$	2.58579	+	2.58579i	0.139214	+	0.139214i
$346$	15.0711	−	15.0711i	0.810226	−	0.810226i
$347$	16.4350	−	16.4350i	0.882279	−	0.882279i	−0.111487	−	0.993766i	$-0.535561\pi$
$347$	16.4350	−	16.4350i	0.882279	−	0.882279i	0.993766	+	0.111487i	$0.0355614\pi$
$348$		−	1.72792i		−	0.0926263i
$349$		−	24.9706i		−	1.33664i	−0.743872	−	0.668322i	$-0.767013\pi$
$349$		−	24.9706i		−	1.33664i	0.743872	−	0.668322i	$-0.232987\pi$
$350$	2.41421	−	2.41421i	0.129045	−	0.129045i
$351$	1.70711	−	1.70711i	0.0911186	−	0.0911186i
$352$	−1.00000	−	1.00000i	−0.0533002	−	0.0533002i
$353$	−17.3137			−0.921516			−0.460758	−	0.887526i	$-0.652422\pi$
$353$	−17.3137			−0.921516			−0.460758	+	0.887526i	$0.652422\pi$
$354$	2.60660	+	2.60660i	0.138539	+	0.138539i
$355$			13.7279i			0.728602i
$356$	−3.34315			−0.177186
$357$	0.171573	+	5.82843i	0.00908060	+	0.308473i
$358$	1.17157			0.0619196
$359$			24.3848i			1.28698i	0.765455	+	0.643490i	$0.222514\pi$
$359$			24.3848i			1.28698i	−0.765455	+	0.643490i	$0.777486\pi$
$360$	−2.00000	−	2.00000i	−0.105409	−	0.105409i
$361$	18.8284			0.990970
$362$	−1.17157	−	1.17157i	−0.0615765	−	0.0615765i
$363$	−2.63604	+	2.63604i	−0.138356	+	0.138356i
$364$	−2.41421	+	2.41421i	−0.126539	+	0.126539i
$365$			2.17157i			0.113665i
$366$		−	5.72792i		−	0.299403i
$367$	−25.5563	+	25.5563i	−1.33403	+	1.33403i	−0.432301	+	0.901729i	$0.642298\pi$
$367$	−25.5563	+	25.5563i	−1.33403	+	1.33403i	−0.901729	+	0.432301i	$0.857702\pi$
$368$	−6.24264	+	6.24264i	−0.325420	+	0.325420i
$369$	−13.1716	−	13.1716i	−0.685685	−	0.685685i
$370$	−6.24264			−0.324539
$371$	32.5563	+	32.5563i	1.69024	+	1.69024i
$372$			1.34315i			0.0696389i
$373$	−32.2843			−1.67162			−0.835808	−	0.549022i	$-0.815000\pi$
$373$	−32.2843			−1.67162			−0.835808	+	0.549022i	$0.815000\pi$
$374$	4.00000	−	4.24264i	0.206835	−	0.219382i
$375$	0.414214			0.0213899
$376$		−	5.24264i		−	0.270369i
$377$	2.94975	+	2.94975i	0.151920	+	0.151920i
$378$	−8.24264			−0.423956
$379$	−4.00000	−	4.00000i	−0.205466	−	0.205466i	0.596871	−	0.802337i	$-0.296410\pi$
$379$	−4.00000	−	4.00000i	−0.205466	−	0.205466i	−0.802337	+	0.596871i	$0.796410\pi$
$380$	−0.292893	+	0.292893i	−0.0150251	+	0.0150251i
$381$	−5.19239	+	5.19239i	−0.266014	+	0.266014i
$382$			8.24264i			0.421730i
$383$		−	20.2132i		−	1.03285i	−0.856333	−	0.516423i	$-0.827263\pi$
$383$		−	20.2132i		−	1.03285i	0.856333	−	0.516423i	$-0.172737\pi$
$384$	−0.292893	+	0.292893i	−0.0149466	+	0.0149466i
$385$	−3.41421	+	3.41421i	−0.174004	+	0.174004i
$386$	2.82843	+	2.82843i	0.143963	+	0.143963i
$387$	4.97056			0.252668
$388$	−5.87868	−	5.87868i	−0.298445	−	0.298445i
$389$			34.6274i			1.75568i	0.478954	+	0.877840i	$0.341016\pi$
$389$			34.6274i			1.75568i	−0.478954	+	0.877840i	$0.658984\pi$
$390$	−0.414214			−0.0209745
$391$	−26.4853	−	24.9706i	−1.33942	−	1.26282i
$392$	4.65685			0.235207
$393$		−	0.0416306i		−	0.00209998i
$394$	3.92893	+	3.92893i	0.197937	+	0.197937i
$395$	0.343146			0.0172655
$396$	2.82843	+	2.82843i	0.142134	+	0.142134i
$397$	0.485281	−	0.485281i	0.0243556	−	0.0243556i	−0.694824	−	0.719180i	$-0.744518\pi$
$397$	0.485281	−	0.485281i	0.0243556	−	0.0243556i	0.719180	+	0.694824i	$0.244518\pi$
$398$	−17.9497	+	17.9497i	−0.899740	+	0.899740i
$399$			0.585786i			0.0293260i
$400$			1.00000i			0.0500000i
$401$	9.17157	−	9.17157i	0.458006	−	0.458006i	−0.439994	−	0.898001i	$-0.645019\pi$
$401$	9.17157	−	9.17157i	0.458006	−	0.458006i	0.898001	+	0.439994i	$0.145019\pi$
$402$	0.928932	−	0.928932i	0.0463309	−	0.0463309i
$403$	−2.29289	−	2.29289i	−0.114217	−	0.114217i
$404$	15.6569			0.778958
$405$	5.29289	+	5.29289i	0.263006	+	0.263006i
$406$		−	14.2426i		−	0.706850i
$407$	8.82843			0.437609
$408$	−1.24264	−	1.17157i	−0.0615199	−	0.0580015i
$409$	−5.48528			−0.271230			−0.135615	−	0.990762i	$-0.543301\pi$
$409$	−5.48528			−0.271230			−0.135615	+	0.990762i	$0.543301\pi$
$410$			6.58579i			0.325249i
$411$	2.55635	+	2.55635i	0.126095	+	0.126095i
$412$	13.6569			0.672825
$413$	21.4853	+	21.4853i	1.05722	+	1.05722i
$414$	17.6569	−	17.6569i	0.867787	−	0.867787i
$415$	−7.00000	+	7.00000i	−0.343616	+	0.343616i
$416$		−	1.00000i		−	0.0490290i
$417$			6.24264i			0.305703i
$418$	0.414214	−	0.414214i	0.0202598	−	0.0202598i
$419$	18.2426	−	18.2426i	0.891211	−	0.891211i	−0.103426	−	0.994637i	$-0.532980\pi$
$419$	18.2426	−	18.2426i	0.891211	−	0.891211i	0.994637	+	0.103426i	$0.0329804\pi$
$420$	1.00000	+	1.00000i	0.0487950	+	0.0487950i
$421$	37.0711			1.80673			0.903367	−	0.428869i	$-0.141088\pi$
$421$	37.0711			1.80673			0.903367	+	0.428869i	$0.141088\pi$
$422$	−0.585786	−	0.585786i	−0.0285156	−	0.0285156i
$423$			14.8284i			0.720983i
$424$	−13.4853			−0.654903
$425$	−4.12132	+	0.121320i	−0.199913	+	0.00588490i
$426$	−5.68629			−0.275502
$427$		−	47.2132i		−	2.28481i
$428$	3.17157	+	3.17157i	0.153304	+	0.153304i
$429$	0.585786			0.0282820
$430$	−1.24264	−	1.24264i	−0.0599255	−	0.0599255i
$431$	16.0000	−	16.0000i	0.770693	−	0.770693i	−0.207535	−	0.978228i	$-0.566544\pi$
$431$	16.0000	−	16.0000i	0.770693	−	0.770693i	0.978228	+	0.207535i	$0.0665440\pi$
$432$	1.70711	−	1.70711i	0.0821332	−	0.0821332i
$433$		−	15.0711i		−	0.724269i	−0.932126	−	0.362135i	$-0.882048\pi$
$433$		−	15.0711i		−	0.724269i	0.932126	−	0.362135i	$-0.117952\pi$
$434$			11.0711i			0.531428i
$435$	1.22183	−	1.22183i	0.0585820	−	0.0585820i
$436$	−4.36396	+	4.36396i	−0.208996	+	0.208996i
$437$	−2.58579	−	2.58579i	−0.123695	−	0.123695i
$438$	−0.899495			−0.0429795
$439$	22.6274	+	22.6274i	1.07995	+	1.07995i	0.996513	+	0.0834344i	$0.0265889\pi$
$439$	22.6274	+	22.6274i	1.07995	+	1.07995i	0.0834344	+	0.996513i	$0.473411\pi$
$440$		−	1.41421i		−	0.0674200i
$441$	−13.1716			−0.627218
$442$	4.12132	−	0.121320i	0.196031	−	0.00577062i
$443$	−20.0000			−0.950229			−0.475114	−	0.879924i	$-0.657593\pi$
$443$	−20.0000			−0.950229			−0.475114	+	0.879924i	$0.657593\pi$
$444$		−	2.58579i		−	0.122716i
$445$	−2.36396	−	2.36396i	−0.112063	−	0.112063i
$446$	−11.3848			−0.539085
$447$	−3.00000	−	3.00000i	−0.141895	−	0.141895i
$448$	−2.41421	+	2.41421i	−0.114061	+	0.114061i
$449$	7.38478	−	7.38478i	0.348509	−	0.348509i	−0.511045	−	0.859554i	$-0.670741\pi$
$449$	7.38478	−	7.38478i	0.348509	−	0.348509i	0.859554	+	0.511045i	$0.170741\pi$
$450$		−	2.82843i		−	0.133333i
$451$		−	9.31371i		−	0.438565i
$452$	−9.53553	+	9.53553i	−0.448514	+	0.448514i
$453$	0.242641	−	0.242641i	0.0114003	−	0.0114003i
$454$	7.46447	+	7.46447i	0.350325	+	0.350325i
$455$	−3.41421			−0.160061
$456$	−0.121320	−	0.121320i	−0.00568135	−	0.00568135i
$457$			3.55635i			0.166359i	0.996535	+	0.0831795i	$0.0265075\pi$
$457$			3.55635i			0.166359i	−0.996535	+	0.0831795i	$0.973493\pi$
$458$	−7.75736			−0.362478
$459$	7.24264	+	6.82843i	0.338058	+	0.318724i
$460$	−8.82843			−0.411628
$461$			26.9706i			1.25614i	0.778155	+	0.628072i	$0.216156\pi$
$461$			26.9706i			1.25614i	−0.778155	+	0.628072i	$0.783844\pi$
$462$	−1.41421	−	1.41421i	−0.0657952	−	0.0657952i
$463$	−20.8995			−0.971282			−0.485641	−	0.874158i	$-0.661414\pi$
$463$	−20.8995			−0.971282			−0.485641	+	0.874158i	$0.661414\pi$
$464$	2.94975	+	2.94975i	0.136939	+	0.136939i
$465$	−0.949747	+	0.949747i	−0.0440435	+	0.0440435i
$466$	4.36396	−	4.36396i	0.202157	−	0.202157i
$467$		−	17.2132i		−	0.796532i	−0.917270	−	0.398266i	$-0.869612\pi$
$467$		−	17.2132i		−	0.796532i	0.917270	−	0.398266i	$-0.130388\pi$
$468$			2.82843i			0.130744i
$469$	7.65685	−	7.65685i	0.353561	−	0.353561i
$470$	3.70711	−	3.70711i	0.170996	−	0.170996i
$471$	−0.828427	−	0.828427i	−0.0381719	−	0.0381719i
$472$	−8.89949			−0.409632
$473$	1.75736	+	1.75736i	0.0808035	+	0.0808035i
$474$			0.142136i			0.00652851i
$475$	−0.414214			−0.0190054
$476$	−10.2426	−	9.65685i	−0.469471	−	0.442621i
$477$	38.1421			1.74641
$478$		−	24.5858i		−	1.12453i
$479$	−5.02082	−	5.02082i	−0.229407	−	0.229407i	0.583038	−	0.812445i	$-0.301864\pi$
$479$	−5.02082	−	5.02082i	−0.229407	−	0.229407i	−0.812445	+	0.583038i	$0.801864\pi$
$480$	−0.414214			−0.0189062
$481$	4.41421	+	4.41421i	0.201271	+	0.201271i
$482$	−14.1716	+	14.1716i	−0.645497	+	0.645497i
$483$	−8.82843	+	8.82843i	−0.401707	+	0.401707i
$484$		−	9.00000i		−	0.409091i
$485$		−	8.31371i		−	0.377506i
$486$	−7.31371	+	7.31371i	−0.331757	+	0.331757i
$487$	11.5858	−	11.5858i	0.525002	−	0.525002i	−0.394076	−	0.919078i	$-0.628935\pi$
$487$	11.5858	−	11.5858i	0.525002	−	0.525002i	0.919078	+	0.394076i	$0.128935\pi$
$488$	9.77817	+	9.77817i	0.442637	+	0.442637i
$489$	6.82843			0.308792
$490$	3.29289	+	3.29289i	0.148758	+	0.148758i
$491$		−	33.7279i		−	1.52212i	−0.648682	−	0.761060i	$-0.724679\pi$
$491$		−	33.7279i		−	1.52212i	0.648682	−	0.761060i	$-0.275321\pi$
$492$	−2.72792			−0.122984
$493$	−11.7990	+	12.5147i	−0.531400	+	0.563635i
$494$	0.414214			0.0186363
$495$			4.00000i			0.179787i
$496$	−2.29289	−	2.29289i	−0.102954	−	0.102954i
$497$	−46.8701			−2.10241
$498$	−2.89949	−	2.89949i	−0.129929	−	0.129929i
$499$	−10.7574	+	10.7574i	−0.481566	+	0.481566i	−0.905631	−	0.424066i	$-0.860603\pi$
$499$	−10.7574	+	10.7574i	−0.481566	+	0.481566i	0.424066	+	0.905631i	$0.360603\pi$
$500$	−0.707107	+	0.707107i	−0.0316228	+	0.0316228i
$501$		−	8.62742i		−	0.385445i
$502$		−	26.1421i		−	1.16678i
$503$	−2.14214	+	2.14214i	−0.0955131	+	0.0955131i	−0.753249	−	0.657736i	$-0.771514\pi$
$503$	−2.14214	+	2.14214i	−0.0955131	+	0.0955131i	0.657736	+	0.753249i	$0.271514\pi$
$504$	6.82843	−	6.82843i	0.304162	−	0.304162i
$505$	11.0711	+	11.0711i	0.492656	+	0.492656i
$506$	12.4853			0.555038
$507$	−3.51472	−	3.51472i	−0.156094	−	0.156094i
$508$		−	17.7279i		−	0.786549i
$509$	32.0000			1.41838			0.709188	−	0.705020i	$-0.249062\pi$
$509$	32.0000			1.41838			0.709188	+	0.705020i	$0.249062\pi$
$510$	−0.0502525	−	1.70711i	−0.00222522	−	0.0755920i
$511$	−7.41421			−0.327985
$512$		−	1.00000i		−	0.0441942i
$513$	0.707107	+	0.707107i	0.0312195	+	0.0312195i
$514$	−25.4142			−1.12097
$515$	9.65685	+	9.65685i	0.425532	+	0.425532i
$516$	0.514719	−	0.514719i	0.0226592	−	0.0226592i
$517$	−5.24264	+	5.24264i	−0.230571	+	0.230571i
$518$		−	21.3137i		−	0.936471i
$519$			8.82843i			0.387525i
$520$	0.707107	−	0.707107i	0.0310087	−	0.0310087i
$521$	27.3137	−	27.3137i	1.19664	−	1.19664i	0.221468	−	0.975168i	$-0.428915\pi$
$521$	27.3137	−	27.3137i	1.19664	−	1.19664i	0.975168	−	0.221468i	$-0.0710847\pi$
$522$	−8.34315	−	8.34315i	−0.365170	−	0.365170i
$523$	−0.828427			−0.0362246			−0.0181123	−	0.999836i	$-0.505766\pi$
$523$	−0.828427			−0.0362246			−0.0181123	+	0.999836i	$0.505766\pi$
$524$	0.0710678	+	0.0710678i	0.00310461	+	0.00310461i
$525$			1.41421i			0.0617213i
$526$	−4.27208			−0.186271
$527$	9.17157	−	9.72792i	0.399520	−	0.423755i
$528$	0.585786			0.0254931
$529$		−	54.9411i		−	2.38874i
$530$	−9.53553	−	9.53553i	−0.414197	−	0.414197i
$531$	25.1716			1.09235
$532$	−1.00000	−	1.00000i	−0.0433555	−	0.0433555i
$533$	4.65685	−	4.65685i	0.201711	−	0.201711i
$534$	0.979185	−	0.979185i	0.0423735	−	0.0423735i
$535$			4.48528i			0.193916i
$536$			3.17157i			0.136991i
$537$	−0.343146	+	0.343146i	−0.0148078	+	0.0148078i
$538$	−9.53553	+	9.53553i	−0.411106	+	0.411106i
$539$	−4.65685	−	4.65685i	−0.200585	−	0.200585i
$540$	2.41421			0.103891
$541$	11.3137	+	11.3137i	0.486414	+	0.486414i	0.907173	−	0.420758i	$-0.138236\pi$
$541$	11.3137	+	11.3137i	0.486414	+	0.486414i	−0.420758	+	0.907173i	$0.638236\pi$
$542$			17.6569i			0.758427i
$543$	0.686292			0.0294516
$544$	4.12132	−	0.121320i	0.176700	−	0.00520157i
$545$	−6.17157			−0.264361
$546$		−	1.41421i		−	0.0605228i
$547$	18.5355	+	18.5355i	0.792522	+	0.792522i	0.981904	−	0.189381i	$-0.0606483\pi$
$547$	18.5355	+	18.5355i	0.792522	+	0.792522i	−0.189381	+	0.981904i	$0.560648\pi$
$548$	−8.72792			−0.372838
$549$	−27.6569	−	27.6569i	−1.18037	−	1.18037i
$550$	1.00000	−	1.00000i	0.0426401	−	0.0426401i
$551$	−1.22183	+	1.22183i	−0.0520515	+	0.0520515i
$552$		−	3.65685i		−	0.155646i
$553$			1.17157i			0.0498203i
$554$	−13.8995	+	13.8995i	−0.590533	+	0.590533i
$555$	1.82843	−	1.82843i	0.0776124	−	0.0776124i
$556$	−10.6569	−	10.6569i	−0.451951	−	0.451951i
$557$	2.17157			0.0920125			0.0460062	−	0.998941i	$-0.485351\pi$
$557$	2.17157			0.0920125			0.0460062	+	0.998941i	$0.485351\pi$
$558$	6.48528	+	6.48528i	0.274544	+	0.274544i
$559$			1.75736i			0.0743284i
$560$	−3.41421			−0.144277
$561$	0.0710678	+	2.41421i	0.00300049	+	0.101928i
$562$	15.4853			0.653207
$563$		−	3.85786i		−	0.162590i	−0.996690	−	0.0812948i	$-0.974094\pi$
$563$		−	3.85786i		−	0.162590i	0.996690	−	0.0812948i	$-0.0259055\pi$
$564$	1.53553	+	1.53553i	0.0646576	+	0.0646576i
$565$	−13.4853			−0.567330
$566$	8.77817	+	8.77817i	0.368974	+	0.368974i
$567$	−18.0711	+	18.0711i	−0.758914	+	0.758914i
$568$	9.70711	−	9.70711i	0.407301	−	0.407301i
$569$		−	7.97056i		−	0.334143i	−0.985945	−	0.167072i	$-0.946569\pi$
$569$		−	7.97056i		−	0.334143i	0.985945	−	0.167072i	$-0.0534311\pi$
$570$		−	0.171573i		−	0.00718640i
$571$	−25.0416	+	25.0416i	−1.04796	+	1.04796i	−0.0491692	+	0.998790i	$0.515657\pi$
$571$	−25.0416	+	25.0416i	−1.04796	+	1.04796i	−0.998790	+	0.0491692i	$0.984343\pi$
$572$	−1.00000	+	1.00000i	−0.0418121	+	0.0418121i
$573$	−2.41421	−	2.41421i	−0.100855	−	0.100855i
$574$	−22.4853			−0.938518
$575$	−6.24264	−	6.24264i	−0.260336	−	0.260336i
$576$			2.82843i			0.117851i
$577$	29.6569			1.23463			0.617315	−	0.786716i	$-0.288220\pi$
$577$	29.6569			1.23463			0.617315	+	0.786716i	$0.288220\pi$
$578$	1.00000	+	16.9706i	0.0415945	+	0.705882i
$579$	−1.65685			−0.0688565
$580$			4.17157i			0.173215i
$581$	−23.8995	−	23.8995i	−0.991518	−	0.991518i
$582$	3.44365			0.142744
$583$	13.4853	+	13.4853i	0.558503	+	0.558503i
$584$	1.53553	−	1.53553i	0.0635408	−	0.0635408i
$585$	−2.00000	+	2.00000i	−0.0826898	+	0.0826898i
$586$			11.4853i			0.474453i
$587$		−	8.82843i		−	0.364388i	−0.983263	−	0.182194i	$-0.941680\pi$
$587$		−	8.82843i		−	0.364388i	0.983263	−	0.182194i	$-0.0583199\pi$
$588$	−1.36396	+	1.36396i	−0.0562488	+	0.0562488i
$589$	0.949747	−	0.949747i	0.0391337	−	0.0391337i
$590$	−6.29289	−	6.29289i	−0.259074	−	0.259074i
$591$	−2.30152			−0.0946717
$592$	4.41421	+	4.41421i	0.181423	+	0.181423i
$593$			42.2843i			1.73641i	0.496208	+	0.868203i	$0.334725\pi$
$593$			42.2843i			1.73641i	−0.496208	+	0.868203i	$0.665275\pi$
$594$	−3.41421			−0.140087
$595$	−0.414214	−	14.0711i	−0.0169811	−	0.576858i
$596$	10.2426			0.419555
$597$		−	10.5147i		−	0.430339i
$598$	6.24264	+	6.24264i	0.255281	+	0.255281i
$599$	−30.7696			−1.25721			−0.628605	−	0.777725i	$-0.716374\pi$
$599$	−30.7696			−1.25721			−0.628605	+	0.777725i	$0.716374\pi$
$600$	−0.292893	−	0.292893i	−0.0119573	−	0.0119573i
$601$	18.8284	−	18.8284i	0.768028	−	0.768028i	−0.209731	−	0.977759i	$-0.567259\pi$
$601$	18.8284	−	18.8284i	0.768028	−	0.768028i	0.977759	+	0.209731i	$0.0672590\pi$
$602$	4.24264	−	4.24264i	0.172917	−	0.172917i
$603$		−	8.97056i		−	0.365310i
$604$			0.828427i			0.0337082i
$605$	6.36396	−	6.36396i	0.258732	−	0.258732i
$606$	−4.58579	+	4.58579i	−0.186285	+	0.186285i
$607$	10.0711	+	10.0711i	0.408772	+	0.408772i	0.881310	−	0.472538i	$-0.156662\pi$
$607$	10.0711	+	10.0711i	0.408772	+	0.408772i	−0.472538	+	0.881310i	$0.656662\pi$
$608$	0.414214			0.0167986
$609$	4.17157	+	4.17157i	0.169041	+	0.169041i
$610$			13.8284i			0.559897i
$611$	−5.24264			−0.212095
$612$	−11.6569	+	0.343146i	−0.471200	+	0.0138708i
$613$	33.2843			1.34434			0.672170	−	0.740397i	$-0.265363\pi$
$613$	33.2843			1.34434			0.672170	+	0.740397i	$0.265363\pi$
$614$			9.89949i			0.399511i
$615$	−1.92893	−	1.92893i	−0.0777821	−	0.0777821i
$616$	4.82843			0.194543
$617$	27.4350	+	27.4350i	1.10449	+	1.10449i	0.993862	+	0.110631i	$0.0352872\pi$
$617$	27.4350	+	27.4350i	1.10449	+	1.10449i	0.110631	+	0.993862i	$0.464713\pi$
$618$	−4.00000	+	4.00000i	−0.160904	+	0.160904i
$619$	−1.75736	+	1.75736i	−0.0706342	+	0.0706342i	−0.741541	−	0.670907i	$-0.765905\pi$
$619$	−1.75736	+	1.75736i	−0.0706342	+	0.0706342i	0.670907	+	0.741541i	$0.265905\pi$
$620$		−	3.24264i		−	0.130228i
$621$			21.3137i			0.855290i
$622$	−5.41421	+	5.41421i	−0.217090	+	0.217090i
$623$	8.07107	−	8.07107i	0.323361	−	0.323361i
$624$	0.292893	+	0.292893i	0.0117251	+	0.0117251i
$625$	−1.00000			−0.0400000
$626$	10.4853	+	10.4853i	0.419076	+	0.419076i
$627$			0.242641i			0.00969014i
$628$	2.82843			0.112867
$629$	−17.6569	+	18.7279i	−0.704025	+	0.746731i
$630$	9.65685			0.384738
$631$			38.3431i			1.52642i	0.646153	+	0.763208i	$0.276377\pi$
$631$			38.3431i			1.52642i	−0.646153	+	0.763208i	$0.723623\pi$
$632$	−0.242641	−	0.242641i	−0.00965173	−	0.00965173i
$633$	0.343146			0.0136388
$634$	7.51472	+	7.51472i	0.298448	+	0.298448i
$635$	12.5355	−	12.5355i	0.497457	−	0.497457i
$636$	3.94975	−	3.94975i	0.156618	−	0.156618i
$637$		−	4.65685i		−	0.184511i
$638$		−	5.89949i		−	0.233563i
$639$	−27.4558	+	27.4558i	−1.08614	+	1.08614i
$640$	0.707107	−	0.707107i	0.0279508	−	0.0279508i
$641$	3.07107	+	3.07107i	0.121300	+	0.121300i	0.765151	−	0.643851i	$-0.222664\pi$
$641$	3.07107	+	3.07107i	0.121300	+	0.121300i	−0.643851	+	0.765151i	$0.722664\pi$
$642$	−1.85786			−0.0733241
$643$	18.3848	+	18.3848i	0.725025	+	0.725025i	0.969624	−	0.244599i	$-0.0786565\pi$
$643$	18.3848	+	18.3848i	0.725025	+	0.725025i	−0.244599	+	0.969624i	$0.578656\pi$
$644$		−	30.1421i		−	1.18777i
$645$	0.727922			0.0286619
$646$	0.0502525	+	1.70711i	0.00197716	+	0.0671652i
$647$	5.78680			0.227502			0.113751	−	0.993509i	$-0.463713\pi$
$647$	5.78680			0.227502			0.113751	+	0.993509i	$0.463713\pi$
$648$		−	7.48528i		−	0.294050i
$649$	8.89949	+	8.89949i	0.349336	+	0.349336i
$650$	1.00000			0.0392232
$651$	−3.24264	−	3.24264i	−0.127089	−	0.127089i
$652$	−11.6569	+	11.6569i	−0.456518	+	0.456518i
$653$	23.4853	−	23.4853i	0.919050	−	0.919050i	−0.0779103	−	0.996960i	$-0.524825\pi$
$653$	23.4853	−	23.4853i	0.919050	−	0.919050i	0.996960	+	0.0779103i	$0.0248248\pi$
$654$		−	2.55635i		−	0.0999612i
$655$			0.100505i			0.00392706i
$656$	4.65685	−	4.65685i	0.181820	−	0.181820i
$657$	−4.34315	+	4.34315i	−0.169442	+	0.169442i
$658$	12.6569	+	12.6569i	0.493416	+	0.493416i
$659$	−19.2426			−0.749587			−0.374793	−	0.927108i	$-0.622286\pi$
$659$	−19.2426			−0.749587			−0.374793	+	0.927108i	$0.622286\pi$
$660$	0.414214	+	0.414214i	0.0161232	+	0.0161232i
$661$			11.3137i			0.440052i	0.975494	+	0.220026i	$0.0706143\pi$
$661$			11.3137i			0.440052i	−0.975494	+	0.220026i	$0.929386\pi$
$662$	22.5563			0.876677
$663$	−1.17157	+	1.24264i	−0.0455001	+	0.0482602i
$664$	9.89949			0.384175
$665$		−	1.41421i		−	0.0548408i
$666$	−12.4853	−	12.4853i	−0.483795	−	0.483795i
$667$	−36.8284			−1.42600
$668$	14.7279	+	14.7279i	0.569840	+	0.569840i
$669$	3.33452	−	3.33452i	0.128920	−	0.128920i
$670$	−2.24264	+	2.24264i	−0.0866408	+	0.0866408i
$671$		−	19.5563i		−	0.754964i
$672$		−	1.41421i		−	0.0545545i
$673$	−15.5355	+	15.5355i	−0.598851	+	0.598851i	−0.940007	−	0.341156i	$-0.889182\pi$
$673$	−15.5355	+	15.5355i	−0.598851	+	0.598851i	0.341156	+	0.940007i	$0.389182\pi$
$674$	5.43503	−	5.43503i	0.209349	−	0.209349i
$675$	1.70711	+	1.70711i	0.0657066	+	0.0657066i
$676$	12.0000			0.461538
$677$	−26.1716	−	26.1716i	−1.00586	−	1.00586i	−0.999983	−	0.00587250i	$-0.998131\pi$
$677$	−26.1716	−	26.1716i	−1.00586	−	1.00586i	−0.00587250	−	0.999983i	$-0.501869\pi$
$678$		−	5.58579i		−	0.214521i
$679$	28.3848			1.08931
$680$	3.00000	+	2.82843i	0.115045	+	0.108465i
$681$	−4.37258			−0.167558
$682$			4.58579i			0.175599i
$683$	−10.1924	−	10.1924i	−0.390001	−	0.390001i	0.484687	−	0.874688i	$-0.338934\pi$
$683$	−10.1924	−	10.1924i	−0.390001	−	0.390001i	−0.874688	+	0.484687i	$0.838934\pi$
$684$	−1.17157			−0.0447962
$685$	−6.17157	−	6.17157i	−0.235804	−	0.235804i
$686$	5.65685	−	5.65685i	0.215980	−	0.215980i
$687$	2.27208	−	2.27208i	0.0866852	−	0.0866852i
$688$			1.75736i			0.0669987i
$689$			13.4853i			0.513748i
$690$	2.58579	−	2.58579i	0.0984392	−	0.0984392i
$691$	−18.1716	+	18.1716i	−0.691279	+	0.691279i	−0.962513	−	0.271234i	$-0.912568\pi$
$691$	−18.1716	+	18.1716i	−0.691279	+	0.691279i	0.271234	+	0.962513i	$0.412568\pi$
$692$	−15.0711	−	15.0711i	−0.572916	−	0.572916i
$693$	−13.6569			−0.518781
$694$	−16.4350	−	16.4350i	−0.623865	−	0.623865i
$695$		−	15.0711i		−	0.571678i
$696$	−1.72792			−0.0654967
$697$	19.7574	+	18.6274i	0.748363	+	0.705564i
$698$	−24.9706			−0.945150
$699$			2.55635i			0.0966900i
$700$	−2.41421	−	2.41421i	−0.0912487	−	0.0912487i
$701$	−24.9706			−0.943125			−0.471563	−	0.881833i	$-0.656310\pi$
$701$	−24.9706			−0.943125			−0.471563	+	0.881833i	$0.656310\pi$
$702$	−1.70711	−	1.70711i	−0.0644306	−	0.0644306i
$703$	−1.82843	+	1.82843i	−0.0689604	+	0.0689604i
$704$	−1.00000	+	1.00000i	−0.0376889	+	0.0376889i
$705$			2.17157i			0.0817862i
$706$			17.3137i			0.651610i
$707$	−37.7990	+	37.7990i	−1.42158	+	1.42158i
$708$	2.60660	−	2.60660i	0.0979621	−	0.0979621i
$709$	24.5061	+	24.5061i	0.920346	+	0.920346i	0.997054	−	0.0767078i	$-0.0244409\pi$
$709$	24.5061	+	24.5061i	0.920346	+	0.920346i	−0.0767078	+	0.997054i	$0.524441\pi$
$710$	13.7279			0.515200
$711$	0.686292	+	0.686292i	0.0257379	+	0.0257379i
$712$			3.34315i			0.125290i
$713$	28.6274			1.07211
$714$	5.82843	−	0.171573i	0.218123	−	0.00642095i
$715$	−1.41421			−0.0528886
$716$		−	1.17157i		−	0.0437837i
$717$	7.20101	+	7.20101i	0.268927	+	0.268927i
$718$	24.3848			0.910032
$719$	−1.32233	−	1.32233i	−0.0493146	−	0.0493146i	0.682019	−	0.731334i	$-0.261102\pi$
$719$	−1.32233	−	1.32233i	−0.0493146	−	0.0493146i	−0.731334	+	0.682019i	$0.761102\pi$
$720$	−2.00000	+	2.00000i	−0.0745356	+	0.0745356i
$721$	−32.9706	+	32.9706i	−1.22789	+	1.22789i
$722$		−	18.8284i		−	0.700721i
$723$		−	8.30152i		−	0.308737i
$724$	−1.17157	+	1.17157i	−0.0435412	+	0.0435412i
$725$	−2.94975	+	2.94975i	−0.109551	+	0.109551i
$726$	2.63604	+	2.63604i	0.0978326	+	0.0978326i
$727$	20.2132			0.749666			0.374833	−	0.927092i	$-0.377700\pi$
$727$	20.2132			0.749666			0.374833	+	0.927092i	$0.377700\pi$
$728$	2.41421	+	2.41421i	0.0894767	+	0.0894767i
$729$			18.1716i			0.673021i
$730$	2.17157			0.0803735
$731$	−7.24264	+	0.213203i	−0.267879	+	0.00788561i
$732$	−5.72792			−0.211710
$733$		−	5.17157i		−	0.191016i	−0.995429	−	0.0955082i	$-0.969552\pi$
$733$		−	5.17157i		−	0.191016i	0.995429	−	0.0955082i	$-0.0304476\pi$
$734$	25.5563	+	25.5563i	0.943302	+	0.943302i
$735$	−1.92893			−0.0711497
$736$	6.24264	+	6.24264i	0.230107	+	0.230107i
$737$	3.17157	−	3.17157i	0.116826	−	0.116826i
$738$	−13.1716	+	13.1716i	−0.484852	+	0.484852i
$739$		−	47.8701i		−	1.76093i	−0.474113	−	0.880464i	$-0.657231\pi$
$739$		−	47.8701i		−	1.76093i	0.474113	−	0.880464i	$-0.342769\pi$
$740$			6.24264i			0.229484i
$741$	−0.121320	+	0.121320i	−0.00445681	+	0.00445681i
$742$	32.5563	−	32.5563i	1.19518	−	1.19518i
$743$	−26.5563	−	26.5563i	−0.974258	−	0.974258i	0.0254189	−	0.999677i	$-0.491908\pi$
$743$	−26.5563	−	26.5563i	−0.974258	−	0.974258i	−0.999677	+	0.0254189i	$0.991908\pi$
$744$	1.34315			0.0492421
$745$	7.24264	+	7.24264i	0.265350	+	0.265350i
$746$			32.2843i			1.18201i
$747$	−28.0000			−1.02447
$748$	−4.24264	−	4.00000i	−0.155126	−	0.146254i
$749$	−15.3137			−0.559551
$750$		−	0.414214i		−	0.0151249i
$751$	−31.8492	−	31.8492i	−1.16220	−	1.16220i	−0.983994	−	0.178201i	$-0.942972\pi$
$751$	−31.8492	−	31.8492i	−1.16220	−	1.16220i	−0.178201	−	0.983994i	$-0.557028\pi$
$752$	−5.24264			−0.191179
$753$	7.65685	+	7.65685i	0.279031	+	0.279031i
$754$	2.94975	−	2.94975i	0.107423	−	0.107423i
$755$	−0.585786	+	0.585786i	−0.0213190	+	0.0213190i
$756$			8.24264i			0.299782i
$757$			34.1716i			1.24199i	0.783816	+	0.620993i	$0.213271\pi$
$757$			34.1716i			1.24199i	−0.783816	+	0.620993i	$0.786729\pi$
$758$	−4.00000	+	4.00000i	−0.145287	+	0.145287i
$759$	−3.65685	+	3.65685i	−0.132735	+	0.132735i
$760$	0.292893	+	0.292893i	0.0106244	+	0.0106244i
$761$	−19.1127			−0.692835			−0.346417	−	0.938080i	$-0.612602\pi$
$761$	−19.1127			−0.692835			−0.346417	+	0.938080i	$0.612602\pi$
$762$	5.19239	+	5.19239i	0.188100	+	0.188100i
$763$		−	21.0711i		−	0.762824i
$764$	8.24264			0.298208
$765$	−8.48528	−	8.00000i	−0.306786	−	0.289241i
$766$	−20.2132			−0.730333
$767$			8.89949i			0.321342i
$768$	0.292893	+	0.292893i	0.0105689	+	0.0105689i
$769$	−5.14214			−0.185430			−0.0927151	−	0.995693i	$-0.529555\pi$
$769$	−5.14214			−0.185430			−0.0927151	+	0.995693i	$0.529555\pi$
$770$	3.41421	+	3.41421i	0.123040	+	0.123040i
$771$	7.44365	−	7.44365i	0.268077	−	0.268077i
$772$	2.82843	−	2.82843i	0.101797	−	0.101797i
$773$		−	40.4853i		−	1.45615i	−0.685495	−	0.728077i	$-0.740414\pi$
$773$		−	40.4853i		−	1.45615i	0.685495	−	0.728077i	$-0.259586\pi$
$774$		−	4.97056i		−	0.178663i
$775$	2.29289	−	2.29289i	0.0823632	−	0.0823632i
$776$	−5.87868	+	5.87868i	−0.211032	+	0.211032i
$777$	6.24264	+	6.24264i	0.223953	+	0.223953i
$778$	34.6274			1.24145
$779$	1.92893	+	1.92893i	0.0691112	+	0.0691112i
$780$			0.414214i			0.0148312i
$781$	−19.4142			−0.694695
$782$	−24.9706	+	26.4853i	−0.892946	+	0.947112i
$783$	10.0711			0.359911
$784$		−	4.65685i		−	0.166316i
$785$	2.00000	+	2.00000i	0.0713831	+	0.0713831i
$786$	−0.0416306			−0.00148491
$787$	−21.6066	−	21.6066i	−0.770192	−	0.770192i	0.207948	−	0.978140i	$-0.433322\pi$
$787$	−21.6066	−	21.6066i	−0.770192	−	0.770192i	−0.978140	+	0.207948i	$0.933322\pi$
$788$	3.92893	−	3.92893i	0.139962	−	0.139962i
$789$	1.25126	−	1.25126i	0.0445461	−	0.0445461i
$790$		−	0.343146i		−	0.0122086i
$791$		−	46.0416i		−	1.63705i
$792$	2.82843	−	2.82843i	0.100504	−	0.100504i
$793$	9.77817	−	9.77817i	0.347233	−	0.347233i
$794$	−0.485281	−	0.485281i	−0.0172220	−	0.0172220i
$795$	5.58579			0.198107
$796$	17.9497	+	17.9497i	0.636212	+	0.636212i
$797$		−	18.6274i		−	0.659817i	−0.944013	−	0.329908i	$-0.892982\pi$
$797$		−	18.6274i		−	0.659817i	0.944013	−	0.329908i	$-0.107018\pi$
$798$	0.585786			0.0207366
$799$	−0.636039	−	21.6066i	−0.0225014	−	0.764387i
$800$	1.00000			0.0353553
$801$		−	9.45584i		−	0.334106i
$802$	−9.17157	−	9.17157i	−0.323859	−	0.323859i
$803$	−3.07107			−0.108376
$804$	−0.928932	−	0.928932i	−0.0327609	−	0.0327609i
$805$	21.3137	−	21.3137i	0.751210	−	0.751210i
$806$	−2.29289	+	2.29289i	−0.0807637	+	0.0807637i
$807$		−	5.58579i		−	0.196629i
$808$		−	15.6569i		−	0.550806i
$809$	20.1716	−	20.1716i	0.709195	−	0.709195i	−0.257171	−	0.966366i	$-0.582790\pi$
$809$	20.1716	−	20.1716i	0.709195	−	0.709195i	0.966366	+	0.257171i	$0.0827904\pi$
$810$	5.29289	−	5.29289i	0.185973	−	0.185973i
$811$	21.9289	+	21.9289i	0.770029	+	0.770029i	0.978111	−	0.208082i	$-0.0667222\pi$
$811$	21.9289	+	21.9289i	0.770029	+	0.770029i	−0.208082	+	0.978111i	$0.566722\pi$
$812$	−14.2426			−0.499819
$813$	−5.17157	−	5.17157i	−0.181375	−	0.181375i
$814$		−	8.82843i		−	0.309436i
$815$	−16.4853			−0.577454
$816$	−1.17157	+	1.24264i	−0.0410133	+	0.0435011i
$817$	−0.727922			−0.0254668
$818$			5.48528i			0.191788i
$819$	−6.82843	−	6.82843i	−0.238605	−	0.238605i
$820$	6.58579			0.229986
$821$	39.9203	+	39.9203i	1.39323	+	1.39323i	0.817976	+	0.575253i	$0.195096\pi$
$821$	39.9203	+	39.9203i	1.39323	+	1.39323i	0.575253	+	0.817976i	$0.304904\pi$
$822$	2.55635	−	2.55635i	0.0891629	−	0.0891629i
$823$	11.4142	−	11.4142i	0.397874	−	0.397874i	−0.479608	−	0.877483i	$-0.659221\pi$
$823$	11.4142	−	11.4142i	0.397874	−	0.397874i	0.877483	+	0.479608i	$0.159221\pi$
$824$		−	13.6569i		−	0.475759i
$825$			0.585786i			0.0203945i
$826$	21.4853	−	21.4853i	0.747569	−	0.747569i
$827$	−18.1421	+	18.1421i	−0.630864	+	0.630864i	−0.948285	−	0.317421i	$-0.897183\pi$
$827$	−18.1421	+	18.1421i	−0.630864	+	0.630864i	0.317421	+	0.948285i	$0.397183\pi$
$828$	−17.6569	−	17.6569i	−0.613618	−	0.613618i
$829$	11.3137			0.392941			0.196471	−	0.980510i	$-0.437052\pi$
$829$	11.3137			0.392941			0.196471	+	0.980510i	$0.437052\pi$
$830$	7.00000	+	7.00000i	0.242974	+	0.242974i
$831$		−	8.14214i		−	0.282448i
$832$	−1.00000			−0.0346688
$833$	19.1924	−	0.564971i	0.664977	−	0.0195751i
$834$	6.24264			0.216165
$835$			20.8284i			0.720797i
$836$	−0.414214	−	0.414214i	−0.0143259	−	0.0143259i
$837$	−7.82843			−0.270590
$838$	−18.2426	−	18.2426i	−0.630182	−	0.630182i
$839$	−13.1213	+	13.1213i	−0.452998	+	0.452998i	−0.896348	−	0.443350i	$-0.853790\pi$
$839$	−13.1213	+	13.1213i	−0.452998	+	0.452998i	0.443350	+	0.896348i	$0.353790\pi$
$840$	1.00000	−	1.00000i	0.0345033	−	0.0345033i
$841$		−	11.5980i		−	0.399930i
$842$		−	37.0711i		−	1.27755i
$843$	−4.53553	+	4.53553i	−0.156212	+	0.156212i
$844$	−0.585786	+	0.585786i	−0.0201636	+	0.0201636i
$845$	8.48528	+	8.48528i	0.291903	+	0.291903i
$846$	14.8284			0.509812
$847$	21.7279	+	21.7279i	0.746580	+	0.746580i
$848$			13.4853i			0.463086i
$849$	−5.14214			−0.176478
$850$	0.121320	+	4.12132i	0.00416125	+	0.141360i
$851$	−55.1127			−1.88924
$852$			5.68629i			0.194809i
$853$	−17.4853	−	17.4853i	−0.598685	−	0.598685i	0.341278	−	0.939962i	$-0.389140\pi$
$853$	−17.4853	−	17.4853i	−0.598685	−	0.598685i	−0.939962	+	0.341278i	$0.889140\pi$
$854$	−47.2132			−1.61560
$855$	−0.828427	−	0.828427i	−0.0283316	−	0.0283316i
$856$	3.17157	−	3.17157i	0.108402	−	0.108402i
$857$	11.4350	−	11.4350i	0.390613	−	0.390613i	−0.484293	−	0.874906i	$-0.660923\pi$
$857$	11.4350	−	11.4350i	0.390613	−	0.390613i	0.874906	+	0.484293i	$0.160923\pi$
$858$		−	0.585786i		−	0.0199984i
$859$			5.87006i			0.200284i	0.994973	+	0.100142i	$0.0319297\pi$
$859$			5.87006i			0.200284i	−0.994973	+	0.100142i	$0.968070\pi$
$860$	−1.24264	+	1.24264i	−0.0423737	+	0.0423737i
$861$	6.58579	−	6.58579i	0.224443	−	0.224443i
$862$	−16.0000	−	16.0000i	−0.544962	−	0.544962i
$863$	49.4558			1.68350			0.841748	−	0.539870i	$-0.181527\pi$
$863$	49.4558			1.68350			0.841748	+	0.539870i	$0.181527\pi$
$864$	−1.70711	−	1.70711i	−0.0580770	−	0.0580770i
$865$		−	21.3137i		−	0.724688i
$866$	−15.0711			−0.512136
$867$	−5.26346	−	4.67767i	−0.178756	−	0.158862i
$868$	11.0711			0.375777
$869$			0.485281i			0.0164620i
$870$	−1.22183	−	1.22183i	−0.0414238	−	0.0414238i
$871$	3.17157			0.107465
$872$	4.36396	+	4.36396i	0.147782	+	0.147782i
$873$	16.6274	−	16.6274i	0.562753	−	0.562753i
$874$	−2.58579	+	2.58579i	−0.0874655	+	0.0874655i
$875$		−	3.41421i		−	0.115421i
$876$			0.899495i			0.0303911i
$877$	8.21320	−	8.21320i	0.277340	−	0.277340i	−0.554706	−	0.832046i	$-0.687169\pi$
$877$	8.21320	−	8.21320i	0.277340	−	0.277340i	0.832046	+	0.554706i	$0.187169\pi$
$878$	22.6274	−	22.6274i	0.763638	−	0.763638i
$879$	−3.36396	−	3.36396i	−0.113464	−	0.113464i
$880$	−1.41421			−0.0476731
$881$	−20.0416	−	20.0416i	−0.675220	−	0.675220i	0.283695	−	0.958915i	$-0.408440\pi$
$881$	−20.0416	−	20.0416i	−0.675220	−	0.675220i	−0.958915	+	0.283695i	$0.908440\pi$
$882$			13.1716i			0.443510i
$883$	43.4975			1.46381			0.731903	−	0.681409i	$-0.238632\pi$
$883$	43.4975			1.46381			0.731903	+	0.681409i	$0.238632\pi$
$884$	−0.121320	−	4.12132i	−0.00408044	−	0.138615i
$885$	3.68629			0.123913
$886$			20.0000i			0.671913i
$887$	17.1005	+	17.1005i	0.574179	+	0.574179i	0.933293	−	0.359115i	$-0.116921\pi$
$887$	17.1005	+	17.1005i	0.574179	+	0.574179i	−0.359115	+	0.933293i	$0.616921\pi$
$888$	−2.58579			−0.0867733
$889$	42.7990	+	42.7990i	1.43543	+	1.43543i
$890$	−2.36396	+	2.36396i	−0.0792402	+	0.0792402i
$891$	−7.48528	+	7.48528i	−0.250766	+	0.250766i
$892$			11.3848i			0.381191i
$893$		−	2.17157i		−	0.0726689i
$894$	−3.00000	+	3.00000i	−0.100335	+	0.100335i
$895$	0.828427	−	0.828427i	0.0276913	−	0.0276913i
$896$	2.41421	+	2.41421i	0.0806532	+	0.0806532i
$897$	−3.65685			−0.122099
$898$	−7.38478	−	7.38478i	−0.246433	−	0.246433i
$899$		−	13.5269i		−	0.451148i
$900$	−2.82843			−0.0942809
$901$	−55.5772	+	1.63604i	−1.85154	+	0.0545044i
$902$	−9.31371			−0.310113
$903$			2.48528i			0.0827050i
$904$	9.53553	+	9.53553i	0.317147	+	0.317147i
$905$	−1.65685			−0.0550757
$906$	−0.242641	−	0.242641i	−0.00806120	−	0.00806120i
$907$	27.0208	−	27.0208i	0.897211	−	0.897211i	−0.0979772	−	0.995189i	$-0.531237\pi$
$907$	27.0208	−	27.0208i	0.897211	−	0.897211i	0.995189	+	0.0979772i	$0.0312372\pi$
$908$	7.46447	−	7.46447i	0.247717	−	0.247717i
$909$			44.2843i			1.46882i
$910$			3.41421i			0.113180i
$911$	19.3137	−	19.3137i	0.639892	−	0.639892i	−0.310637	−	0.950529i	$-0.600542\pi$
$911$	19.3137	−	19.3137i	0.639892	−	0.639892i	0.950529	+	0.310637i	$0.100542\pi$
$912$	−0.121320	+	0.121320i	−0.00401732	+	0.00401732i
$913$	−9.89949	−	9.89949i	−0.327625	−	0.327625i
$914$	3.55635			0.117634
$915$	−4.05025	−	4.05025i	−0.133897	−	0.133897i
$916$			7.75736i			0.256310i
$917$	−0.343146			−0.0113317
$918$	6.82843	−	7.24264i	0.225372	−	0.239043i
$919$	39.0122			1.28689			0.643447	−	0.765491i	$-0.277504\pi$
$919$	39.0122			1.28689			0.643447	+	0.765491i	$0.277504\pi$
$920$			8.82843i			0.291065i
$921$	−2.89949	−	2.89949i	−0.0955416	−	0.0955416i
$922$	26.9706			0.888228
$923$	−9.70711	−	9.70711i	−0.319513	−	0.319513i
$924$	−1.41421	+	1.41421i	−0.0465242	+	0.0465242i
$925$	−4.41421	+	4.41421i	−0.145138	+	0.145138i
$926$			20.8995i			0.686800i
$927$			38.6274i			1.26869i
$928$	2.94975	−	2.94975i	0.0968302	−	0.0968302i
$929$	−3.48528	+	3.48528i	−0.114348	+	0.114348i	−0.761966	−	0.647617i	$-0.775766\pi$
$929$	−3.48528	+	3.48528i	−0.114348	+	0.114348i	0.647617	+	0.761966i	$0.275766\pi$
$930$	0.949747	+	0.949747i	0.0311434	+	0.0311434i
$931$	1.92893			0.0632182
$932$	−4.36396	−	4.36396i	−0.142946	−	0.142946i
$933$		−	3.17157i		−	0.103833i
$934$	−17.2132			−0.563233
$935$	−0.171573	−	5.82843i	−0.00561103	−	0.190610i
$936$	2.82843			0.0924500
$937$		−	41.8406i		−	1.36687i	−0.730010	−	0.683437i	$-0.760485\pi$
$937$		−	41.8406i		−	1.36687i	0.730010	−	0.683437i	$-0.239515\pi$
$938$	−7.65685	−	7.65685i	−0.250005	−	0.250005i
$939$	−6.14214			−0.200441
$940$	−3.70711	−	3.70711i	−0.120912	−	0.120912i
$941$	22.4056	−	22.4056i	0.730401	−	0.730401i	−0.240298	−	0.970699i	$-0.577245\pi$
$941$	22.4056	−	22.4056i	0.730401	−	0.730401i	0.970699	+	0.240298i	$0.0772451\pi$
$942$	−0.828427	+	0.828427i	−0.0269916	+	0.0269916i
$943$			58.1421i			1.89337i
$944$			8.89949i			0.289654i
$945$	−5.82843	+	5.82843i	−0.189599	+	0.189599i
$946$	1.75736	−	1.75736i	0.0571367	−	0.0571367i
$947$	0.778175	+	0.778175i	0.0252873	+	0.0252873i	0.719637	−	0.694350i	$-0.244308\pi$
$947$	0.778175	+	0.778175i	0.0252873	+	0.0252873i	−0.694350	+	0.719637i	$0.744308\pi$
$948$	0.142136			0.00461635
$949$	−1.53553	−	1.53553i	−0.0498455	−	0.0498455i
$950$			0.414214i			0.0134389i
$951$	−4.40202			−0.142745
$952$	−9.65685	+	10.2426i	−0.312980	+	0.331966i
$953$	−23.4142			−0.758461			−0.379230	−	0.925302i	$-0.623811\pi$
$953$	−23.4142			−0.758461			−0.379230	+	0.925302i	$0.623811\pi$
$954$		−	38.1421i		−	1.23490i
$955$	5.82843	+	5.82843i	0.188603	+	0.188603i
$956$	−24.5858			−0.795161
$957$	1.72792	+	1.72792i	0.0558558	+	0.0558558i
$958$	−5.02082	+	5.02082i	−0.162215	+	0.162215i
$959$	21.0711	−	21.0711i	0.680420	−	0.680420i
$960$			0.414214i			0.0133687i
$961$		−	20.4853i		−	0.660816i
$962$	4.41421	−	4.41421i	0.142320	−	0.142320i
$963$	−8.97056	+	8.97056i	−0.289072	+	0.289072i
$964$	14.1716	+	14.1716i	0.456436	+	0.456436i
$965$	4.00000			0.128765
$966$	8.82843	+	8.82843i	0.284050	+	0.284050i
$967$			45.5980i			1.46633i	0.680050	+	0.733166i	$0.261958\pi$
$967$			45.5980i			1.46633i	−0.680050	+	0.733166i	$0.738042\pi$
$968$	−9.00000			−0.289271
$969$	−0.514719	−	0.485281i	−0.0165351	−	0.0155895i
$970$	−8.31371			−0.266937
$971$			60.0122i			1.92588i	0.269710	+	0.962941i	$0.413072\pi$
$971$			60.0122i			1.92588i	−0.269710	+	0.962941i	$0.586928\pi$
$972$	7.31371	+	7.31371i	0.234587	+	0.234587i
$973$	51.4558			1.64960
$974$	−11.5858	−	11.5858i	−0.371233	−	0.371233i
$975$	−0.292893	+	0.292893i	−0.00938009	+	0.00938009i
$976$	9.77817	−	9.77817i	0.312992	−	0.312992i
$977$		−	25.7574i		−	0.824051i	−0.911172	−	0.412025i	$-0.864821\pi$
$977$		−	25.7574i		−	0.824051i	0.911172	−	0.412025i	$-0.135179\pi$
$978$		−	6.82843i		−	0.218349i
$979$	3.34315	−	3.34315i	0.106847	−	0.106847i
$980$	3.29289	−	3.29289i	0.105188	−	0.105188i
$981$	−12.3431	−	12.3431i	−0.394086	−	0.394086i
$982$	−33.7279			−1.07630
$983$	6.07107	+	6.07107i	0.193637	+	0.193637i	0.797266	−	0.603629i	$-0.206279\pi$
$983$	6.07107	+	6.07107i	0.193637	+	0.193637i	−0.603629	+	0.797266i	$0.706279\pi$
$984$			2.72792i			0.0869630i
$985$	5.55635			0.177040
$986$	12.5147	+	11.7990i	0.398550	+	0.375756i
$987$	−7.41421			−0.235997
$988$		−	0.414214i		−	0.0131779i
$989$	−10.9706	−	10.9706i	−0.348844	−	0.348844i
$990$	4.00000			0.127128
$991$	−16.0919	−	16.0919i	−0.511176	−	0.511176i	0.403711	−	0.914887i	$-0.367720\pi$
$991$	−16.0919	−	16.0919i	−0.511176	−	0.511176i	−0.914887	+	0.403711i	$0.867720\pi$
$992$	−2.29289	+	2.29289i	−0.0727994	+	0.0727994i
$993$	−6.60660	+	6.60660i	−0.209654	+	0.209654i
$994$			46.8701i			1.48663i
$995$			25.3848i			0.804752i
$996$	−2.89949	+	2.89949i	−0.0918740	+	0.0918740i
$997$	−23.2843	+	23.2843i	−0.737420	+	0.737420i	−0.972078	−	0.234658i	$-0.924603\pi$
$997$	−23.2843	+	23.2843i	−0.737420	+	0.737420i	0.234658	+	0.972078i	$0.424603\pi$
$998$	10.7574	+	10.7574i	0.340518	+	0.340518i
$999$	15.0711			0.476827

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.h.a.81.1	yes	4
3.2	odd	2		1530.2.q.c.1441.2		4
4.3	odd	2		1360.2.bt.a.81.2		4
5.2	odd	4		850.2.g.h.149.1		4
5.3	odd	4		850.2.g.e.149.2		4
5.4	even	2		850.2.h.g.251.2		4
17.2	even	8		2890.2.a.t.1.2		2
17.4	even	4	inner	170.2.h.a.21.1	✓	4
17.8	even	8		2890.2.b.j.2311.2		4
17.9	even	8		2890.2.b.j.2311.3		4
17.15	even	8		2890.2.a.v.1.1		2
51.38	odd	4		1530.2.q.c.361.2		4
68.55	odd	4		1360.2.bt.a.1041.2		4
85.4	even	4		850.2.h.g.701.2		4
85.38	odd	4		850.2.g.h.599.1		4
85.72	odd	4		850.2.g.e.599.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.h.a.21.1	✓	4	17.4	even	4	inner
170.2.h.a.81.1	yes	4	1.1	even	1	trivial
850.2.g.e.149.2		4	5.3	odd	4
850.2.g.e.599.2		4	85.72	odd	4
850.2.g.h.149.1		4	5.2	odd	4
850.2.g.h.599.1		4	85.38	odd	4
850.2.h.g.251.2		4	5.4	even	2
850.2.h.g.701.2		4	85.4	even	4
1360.2.bt.a.81.2		4	4.3	odd	2
1360.2.bt.a.1041.2		4	68.55	odd	4
1530.2.q.c.361.2		4	51.38	odd	4
1530.2.q.c.1441.2		4	3.2	odd	2
2890.2.a.t.1.2		2	17.2	even	8
2890.2.a.v.1.1		2	17.15	even	8
2890.2.b.j.2311.2		4	17.8	even	8
2890.2.b.j.2311.3		4	17.9	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.292893 + 0.292893i) q^{3} -1.00000 q^{4} +(-0.707107 - 0.707107i) q^{5} +(0.292893 - 0.292893i) q^{6} +(2.41421 - 2.41421i) q^{7} +1.00000i q^{8} -2.82843i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.292893 + 0.292893i) q^{3} -1.00000 q^{4} +(-0.707107 - 0.707107i) q^{5} +(0.292893 - 0.292893i) q^{6} +(2.41421 - 2.41421i) q^{7} +1.00000i q^{8} -2.82843i q^{9} +(-0.707107 + 0.707107i) q^{10} +(1.00000 - 1.00000i) q^{11} +(-0.292893 - 0.292893i) q^{12} +1.00000 q^{13} +(-2.41421 - 2.41421i) q^{14} -0.414214i q^{15} +1.00000 q^{16} +(0.121320 + 4.12132i) q^{17} -2.82843 q^{18} +0.414214i q^{19} +(0.707107 + 0.707107i) q^{20} +1.41421 q^{21} +(-1.00000 - 1.00000i) q^{22} +(-6.24264 + 6.24264i) q^{23} +(-0.292893 + 0.292893i) q^{24} +1.00000i q^{25} -1.00000i q^{26} +(1.70711 - 1.70711i) q^{27} +(-2.41421 + 2.41421i) q^{28} +(2.94975 + 2.94975i) q^{29} -0.414214 q^{30} +(-2.29289 - 2.29289i) q^{31} -1.00000i q^{32} +0.585786 q^{33} +(4.12132 - 0.121320i) q^{34} -3.41421 q^{35} +2.82843i q^{36} +(4.41421 + 4.41421i) q^{37} +0.414214 q^{38} +(0.292893 + 0.292893i) q^{39} +(0.707107 - 0.707107i) q^{40} +(4.65685 - 4.65685i) q^{41} -1.41421i q^{42} +1.75736i q^{43} +(-1.00000 + 1.00000i) q^{44} +(-2.00000 + 2.00000i) q^{45} +(6.24264 + 6.24264i) q^{46} -5.24264 q^{47} +(0.292893 + 0.292893i) q^{48} -4.65685i q^{49} +1.00000 q^{50} +(-1.17157 + 1.24264i) q^{51} -1.00000 q^{52} +13.4853i q^{53} +(-1.70711 - 1.70711i) q^{54} -1.41421 q^{55} +(2.41421 + 2.41421i) q^{56} +(-0.121320 + 0.121320i) q^{57} +(2.94975 - 2.94975i) q^{58} +8.89949i q^{59} +0.414214i q^{60} +(9.77817 - 9.77817i) q^{61} +(-2.29289 + 2.29289i) q^{62} +(-6.82843 - 6.82843i) q^{63} -1.00000 q^{64} +(-0.707107 - 0.707107i) q^{65} -0.585786i q^{66} +3.17157 q^{67} +(-0.121320 - 4.12132i) q^{68} -3.65685 q^{69} +3.41421i q^{70} +(-9.70711 - 9.70711i) q^{71} +2.82843 q^{72} +(-1.53553 - 1.53553i) q^{73} +(4.41421 - 4.41421i) q^{74} +(-0.292893 + 0.292893i) q^{75} -0.414214i q^{76} -4.82843i q^{77} +(0.292893 - 0.292893i) q^{78} +(-0.242641 + 0.242641i) q^{79} +(-0.707107 - 0.707107i) q^{80} -7.48528 q^{81} +(-4.65685 - 4.65685i) q^{82} -9.89949i q^{83} -1.41421 q^{84} +(2.82843 - 3.00000i) q^{85} +1.75736 q^{86} +1.72792i q^{87} +(1.00000 + 1.00000i) q^{88} +3.34315 q^{89} +(2.00000 + 2.00000i) q^{90} +(2.41421 - 2.41421i) q^{91} +(6.24264 - 6.24264i) q^{92} -1.34315i q^{93} +5.24264i q^{94} +(0.292893 - 0.292893i) q^{95} +(0.292893 - 0.292893i) q^{96} +(5.87868 + 5.87868i) q^{97} -4.65685 q^{98} +(-2.82843 - 2.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{4} + 4 q^{6} + 4 q^{7}+O(q^{10}) \) 4 * q + 4 * q^3 - 4 * q^4 + 4 * q^6 + 4 * q^7	\( 4 q + 4 q^{3} - 4 q^{4} + 4 q^{6} + 4 q^{7} + 4 q^{11} - 4 q^{12} + 4 q^{13} - 4 q^{14} + 4 q^{16} - 8 q^{17} - 4 q^{22} - 8 q^{23} - 4 q^{24} + 4 q^{27} - 4 q^{28} - 8 q^{29} + 4 q^{30} - 12 q^{31} + 8 q^{33} + 8 q^{34} - 8 q^{35} + 12 q^{37} - 4 q^{38} + 4 q^{39} - 4 q^{41} - 4 q^{44} - 8 q^{45} + 8 q^{46} - 4 q^{47} + 4 q^{48} + 4 q^{50} - 16 q^{51} - 4 q^{52} - 4 q^{54} + 4 q^{56} + 8 q^{57} - 8 q^{58} + 8 q^{61} - 12 q^{62} - 16 q^{63} - 4 q^{64} + 24 q^{67} + 8 q^{68} + 8 q^{69} - 36 q^{71} + 8 q^{73} + 12 q^{74} - 4 q^{75} + 4 q^{78} + 16 q^{79} + 4 q^{81} + 4 q^{82} + 24 q^{86} + 4 q^{88} + 36 q^{89} + 8 q^{90} + 4 q^{91} + 8 q^{92} + 4 q^{95} + 4 q^{96} + 32 q^{97} + 4 q^{98}+O(q^{100}) \) 4 * q + 4 * q^3 - 4 * q^4 + 4 * q^6 + 4 * q^7 + 4 * q^11 - 4 * q^12 + 4 * q^13 - 4 * q^14 + 4 * q^16 - 8 * q^17 - 4 * q^22 - 8 * q^23 - 4 * q^24 + 4 * q^27 - 4 * q^28 - 8 * q^29 + 4 * q^30 - 12 * q^31 + 8 * q^33 + 8 * q^34 - 8 * q^35 + 12 * q^37 - 4 * q^38 + 4 * q^39 - 4 * q^41 - 4 * q^44 - 8 * q^45 + 8 * q^46 - 4 * q^47 + 4 * q^48 + 4 * q^50 - 16 * q^51 - 4 * q^52 - 4 * q^54 + 4 * q^56 + 8 * q^57 - 8 * q^58 + 8 * q^61 - 12 * q^62 - 16 * q^63 - 4 * q^64 + 24 * q^67 + 8 * q^68 + 8 * q^69 - 36 * q^71 + 8 * q^73 + 12 * q^74 - 4 * q^75 + 4 * q^78 + 16 * q^79 + 4 * q^81 + 4 * q^82 + 24 * q^86 + 4 * q^88 + 36 * q^89 + 8 * q^90 + 4 * q^91 + 8 * q^92 + 4 * q^95 + 4 * q^96 + 32 * q^97 + 4 * q^98

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