LMFDB - Embedded newform 430.2.g.b.257.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(257,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("430.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.g (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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			257.13
Character	$\chi$	$=$	430.257
Dual form			430.2.g.b.343.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.53278 - 1.53278i) q^{3} -1.00000i q^{4} +(1.06852 - 1.96425i) q^{5} -2.16769 q^{6} +(1.64724 - 1.64724i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.69886i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.53278 - 1.53278i) q^{3} -1.00000i q^{4} +(1.06852 - 1.96425i) q^{5} -2.16769 q^{6} +(1.64724 - 1.64724i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.69886i q^{9} +(-0.633377 - 2.14449i) q^{10} +3.84480 q^{11} +(-1.53278 + 1.53278i) q^{12} +(-2.55562 + 2.55562i) q^{13} -2.32955i q^{14} +(-4.64858 + 1.37296i) q^{15} -1.00000 q^{16} +(-1.69075 - 1.69075i) q^{17} +(1.20128 + 1.20128i) q^{18} +1.66210 q^{19} +(-1.96425 - 1.06852i) q^{20} -5.04974 q^{21} +(2.71869 - 2.71869i) q^{22} +(-4.75893 + 4.75893i) q^{23} +2.16769i q^{24} +(-2.71654 - 4.19767i) q^{25} +3.61420i q^{26} +(-1.99437 + 1.99437i) q^{27} +(-1.64724 - 1.64724i) q^{28} -3.07310 q^{29} +(-2.31621 + 4.25787i) q^{30} +9.51169 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-5.89326 - 5.89326i) q^{33} -2.39108 q^{34} +(-1.47549 - 4.99570i) q^{35} +1.69886 q^{36} +(3.52756 - 3.52756i) q^{37} +(1.17528 - 1.17528i) q^{38} +7.83444 q^{39} +(-2.14449 + 0.633377i) q^{40} +1.30320 q^{41} +(-3.57070 + 3.57070i) q^{42} +(-2.32711 + 6.13062i) q^{43} -3.84480i q^{44} +(3.33698 + 1.81526i) q^{45} +6.73015i q^{46} +(2.14489 + 2.14489i) q^{47} +(1.53278 + 1.53278i) q^{48} +1.57318i q^{49} +(-4.88908 - 1.04731i) q^{50} +5.18310i q^{51} +(2.55562 + 2.55562i) q^{52} +(6.79569 - 6.79569i) q^{53} +2.82046i q^{54} +(4.10824 - 7.55215i) q^{55} -2.32955 q^{56} +(-2.54764 - 2.54764i) q^{57} +(-2.17301 + 2.17301i) q^{58} -5.14916i q^{59} +(1.37296 + 4.64858i) q^{60} -7.55814i q^{61} +(6.72578 - 6.72578i) q^{62} +(2.79843 + 2.79843i) q^{63} +1.00000i q^{64} +(2.28915 + 7.75061i) q^{65} -8.33432 q^{66} +(2.61972 + 2.61972i) q^{67} +(-1.69075 + 1.69075i) q^{68} +14.5888 q^{69} +(-4.57582 - 2.48917i) q^{70} +7.21772i q^{71} +(1.20128 - 1.20128i) q^{72} +(-6.06969 - 6.06969i) q^{73} -4.98873i q^{74} +(-2.27025 + 10.5980i) q^{75} -1.66210i q^{76} +(6.33332 - 6.33332i) q^{77} +(5.53979 - 5.53979i) q^{78} +15.6710i q^{79} +(-1.06852 + 1.96425i) q^{80} +11.2105 q^{81} +(0.921500 - 0.921500i) q^{82} +(12.4307 - 12.4307i) q^{83} +5.04974i q^{84} +(-5.12764 + 1.51445i) q^{85} +(2.68949 + 5.98052i) q^{86} +(4.71041 + 4.71041i) q^{87} +(-2.71869 - 2.71869i) q^{88} +3.54474 q^{89} +(3.64319 - 1.07602i) q^{90} +8.41946i q^{91} +(4.75893 + 4.75893i) q^{92} +(-14.5794 - 14.5794i) q^{93} +3.03333 q^{94} +(1.77598 - 3.26478i) q^{95} +2.16769 q^{96} +(7.33406 + 7.33406i) q^{97} +(1.11241 + 1.11241i) q^{98} +6.53178i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q+O(q^{10}) $ 40 * q	$ 40 q - 8 q^{10} + 16 q^{11} - 24 q^{13} + 8 q^{15} - 40 q^{16} - 12 q^{17} - 16 q^{21} + 44 q^{23} + 24 q^{25} + 32 q^{31} - 64 q^{35} + 48 q^{36} - 28 q^{38} - 4 q^{40} + 8 q^{41} - 16 q^{43} - 28 q^{47} + 24 q^{52} - 80 q^{53} + 24 q^{56} + 64 q^{57} + 12 q^{58} + 24 q^{67} - 12 q^{68} + 40 q^{78} - 120 q^{81} + 48 q^{83} + 28 q^{87} - 44 q^{92} - 16 q^{95} - 60 q^{97}+O(q^{100}) $ 40 * q - 8 * q^10 + 16 * q^11 - 24 * q^13 + 8 * q^15 - 40 * q^16 - 12 * q^17 - 16 * q^21 + 44 * q^23 + 24 * q^25 + 32 * q^31 - 64 * q^35 + 48 * q^36 - 28 * q^38 - 4 * q^40 + 8 * q^41 - 16 * q^43 - 28 * q^47 + 24 * q^52 - 80 * q^53 + 24 * q^56 + 64 * q^57 + 12 * q^58 + 24 * q^67 - 12 * q^68 + 40 * q^78 - 120 * q^81 + 48 * q^83 + 28 * q^87 - 44 * q^92 - 16 * q^95 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−1.53278	−	1.53278i	−0.884954	−	0.884954i	0.109079	−	0.994033i	$-0.465210\pi$
$3$	−1.53278	−	1.53278i	−0.884954	−	0.884954i	−0.994033	+	0.109079i	$0.965210\pi$
$4$		−	1.00000i		−	0.500000i
$5$	1.06852	−	1.96425i	0.477855	−	0.878438i
$5$	1.06852	−	1.96425i	0.477855	−	0.878438i
$6$	−2.16769			−0.884954
$7$	1.64724	−	1.64724i	0.622599	−	0.622599i	−0.323596	−	0.946195i	$-0.604892\pi$
$7$	1.64724	−	1.64724i	0.622599	−	0.622599i	0.946195	+	0.323596i	$0.104892\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$			1.69886i			0.566287i
$10$	−0.633377	−	2.14449i	−0.200292	−	0.678147i
$11$	3.84480			1.15925			0.579626	−	0.814883i	$-0.303199\pi$
$11$	3.84480			1.15925			0.579626	+	0.814883i	$0.303199\pi$
$12$	−1.53278	+	1.53278i	−0.442477	+	0.442477i
$13$	−2.55562	+	2.55562i	−0.708803	+	0.708803i	−0.966283	−	0.257481i	$-0.917108\pi$
$13$	−2.55562	+	2.55562i	−0.708803	+	0.708803i	0.257481	+	0.966283i	$0.417108\pi$
$14$		−	2.32955i		−	0.622599i
$15$	−4.64858	+	1.37296i	−1.20026	+	0.354497i
$16$	−1.00000			−0.250000
$17$	−1.69075	−	1.69075i	−0.410066	−	0.410066i	0.471695	−	0.881762i	$-0.343642\pi$
$17$	−1.69075	−	1.69075i	−0.410066	−	0.410066i	−0.881762	+	0.471695i	$0.843642\pi$
$18$	1.20128	+	1.20128i	0.283143	+	0.283143i
$19$	1.66210			0.381312			0.190656	−	0.981657i	$-0.438938\pi$
$19$	1.66210			0.381312			0.190656	+	0.981657i	$0.438938\pi$
$20$	−1.96425	−	1.06852i	−0.439219	−	0.238928i
$21$	−5.04974			−1.10194
$22$	2.71869	−	2.71869i	0.579626	−	0.579626i
$23$	−4.75893	+	4.75893i	−0.992307	+	0.992307i	−0.999971	−	0.00766412i	$-0.997560\pi$
$23$	−4.75893	+	4.75893i	−0.992307	+	0.992307i	0.00766412	+	0.999971i	$0.497560\pi$
$24$			2.16769i			0.442477i
$25$	−2.71654	−	4.19767i	−0.543308	−	0.839533i
$26$			3.61420i			0.708803i
$27$	−1.99437	+	1.99437i	−0.383816	+	0.383816i
$28$	−1.64724	−	1.64724i	−0.311300	−	0.311300i
$29$	−3.07310			−0.570661			−0.285331	−	0.958429i	$-0.592103\pi$
$29$	−3.07310			−0.570661			−0.285331	+	0.958429i	$0.592103\pi$
$30$	−2.31621	+	4.25787i	−0.422880	+	0.777377i
$31$	9.51169			1.70835			0.854175	−	0.519986i	$-0.174063\pi$
$31$	9.51169			1.70835			0.854175	+	0.519986i	$0.174063\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−5.89326	−	5.89326i	−1.02588	−	1.02588i
$34$	−2.39108			−0.410066
$35$	−1.47549	−	4.99570i	−0.249403	−	0.844427i
$36$	1.69886			0.283143
$37$	3.52756	−	3.52756i	0.579928	−	0.579928i	−0.354955	−	0.934883i	$-0.615504\pi$
$37$	3.52756	−	3.52756i	0.579928	−	0.579928i	0.934883	+	0.354955i	$0.115504\pi$
$38$	1.17528	−	1.17528i	0.190656	−	0.190656i
$39$	7.83444			1.25452
$40$	−2.14449	+	0.633377i	−0.339073	+	0.100146i
$41$	1.30320			0.203525			0.101763	−	0.994809i	$-0.467552\pi$
$41$	1.30320			0.203525			0.101763	+	0.994809i	$0.467552\pi$
$42$	−3.57070	+	3.57070i	−0.550971	+	0.550971i
$43$	−2.32711	+	6.13062i	−0.354881	+	0.934912i
$43$	−2.32711	+	6.13062i	−0.354881	+	0.934912i
$44$		−	3.84480i		−	0.579626i
$45$	3.33698	+	1.81526i	0.497448	+	0.270603i
$46$			6.73015i			0.992307i
$47$	2.14489	+	2.14489i	0.312864	+	0.312864i	0.846018	−	0.533154i	$-0.178993\pi$
$47$	2.14489	+	2.14489i	0.312864	+	0.312864i	−0.533154	+	0.846018i	$0.678993\pi$
$48$	1.53278	+	1.53278i	0.221238	+	0.221238i
$49$			1.57318i			0.224741i
$50$	−4.88908	−	1.04731i	−0.691421	−	0.148112i
$51$			5.18310i			0.725779i
$52$	2.55562	+	2.55562i	0.354401	+	0.354401i
$53$	6.79569	−	6.79569i	0.933460	−	0.933460i	−0.0644599	−	0.997920i	$-0.520532\pi$
$53$	6.79569	−	6.79569i	0.933460	−	0.933460i	0.997920	+	0.0644599i	$0.0205325\pi$
$54$			2.82046i			0.383816i
$55$	4.10824	−	7.55215i	0.553955	−	1.01833i
$56$	−2.32955			−0.311300
$57$	−2.54764	−	2.54764i	−0.337444	−	0.337444i
$58$	−2.17301	+	2.17301i	−0.285331	+	0.285331i
$59$		−	5.14916i		−	0.670363i	−0.942153	−	0.335182i	$-0.891202\pi$
$59$		−	5.14916i		−	0.670363i	0.942153	−	0.335182i	$-0.108798\pi$
$60$	1.37296	+	4.64858i	0.177249	+	0.600129i
$61$		−	7.55814i		−	0.967720i	−0.875145	−	0.483860i	$-0.839234\pi$
$61$		−	7.55814i		−	0.967720i	0.875145	−	0.483860i	$-0.160766\pi$
$62$	6.72578	−	6.72578i	0.854175	−	0.854175i
$63$	2.79843	+	2.79843i	0.352570	+	0.352570i
$64$			1.00000i			0.125000i
$65$	2.28915	+	7.75061i	0.283934	+	0.961345i
$66$	−8.33432			−1.02588
$67$	2.61972	+	2.61972i	0.320050	+	0.320050i	0.848786	−	0.528736i	$-0.177334\pi$
$67$	2.61972	+	2.61972i	0.320050	+	0.320050i	−0.528736	+	0.848786i	$0.677334\pi$
$68$	−1.69075	+	1.69075i	−0.205033	+	0.205033i
$69$	14.5888			1.75629
$70$	−4.57582	−	2.48917i	−0.546915	−	0.297512i
$71$			7.21772i			0.856585i	0.903640	+	0.428293i	$0.140885\pi$
$71$			7.21772i			0.856585i	−0.903640	+	0.428293i	$0.859115\pi$
$72$	1.20128	−	1.20128i	0.141572	−	0.141572i
$73$	−6.06969	−	6.06969i	−0.710403	−	0.710403i	0.256216	−	0.966619i	$-0.417524\pi$
$73$	−6.06969	−	6.06969i	−0.710403	−	0.710403i	−0.966619	+	0.256216i	$0.917524\pi$
$74$		−	4.98873i		−	0.579928i
$75$	−2.27025	+	10.5980i	−0.262145	+	1.22375i
$76$		−	1.66210i		−	0.190656i
$77$	6.33332	−	6.33332i	0.721749	−	0.721749i
$78$	5.53979	−	5.53979i	0.627258	−	0.627258i
$79$			15.6710i			1.76312i	0.472069	+	0.881562i	$0.343507\pi$
$79$			15.6710i			1.76312i	−0.472069	+	0.881562i	$0.656493\pi$
$80$	−1.06852	+	1.96425i	−0.119464	+	0.219610i
$81$	11.2105			1.24561
$82$	0.921500	−	0.921500i	0.101763	−	0.101763i
$83$	12.4307	−	12.4307i	1.36445	−	1.36445i	0.496292	−	0.868156i	$-0.334695\pi$
$83$	12.4307	−	12.4307i	1.36445	−	1.36445i	0.868156	−	0.496292i	$-0.165305\pi$
$84$			5.04974i			0.550971i
$85$	−5.12764	+	1.51445i	−0.556170	+	0.164266i
$86$	2.68949	+	5.98052i	0.290015	+	0.644896i
$87$	4.71041	+	4.71041i	0.505009	+	0.505009i
$88$	−2.71869	−	2.71869i	−0.289813	−	0.289813i
$89$	3.54474			0.375742			0.187871	−	0.982194i	$-0.439841\pi$
$89$	3.54474			0.375742			0.187871	+	0.982194i	$0.439841\pi$
$90$	3.64319	−	1.07602i	0.384025	−	0.113422i
$91$			8.41946i			0.882600i
$92$	4.75893	+	4.75893i	0.496153	+	0.496153i
$93$	−14.5794	−	14.5794i	−1.51181	−	1.51181i
$94$	3.03333			0.312864
$95$	1.77598	−	3.26478i	0.182212	−	0.334959i
$96$	2.16769			0.221238
$97$	7.33406	+	7.33406i	0.744661	+	0.744661i	0.973471	−	0.228810i	$-0.0734835\pi$
$97$	7.33406	+	7.33406i	0.744661	+	0.744661i	−0.228810	+	0.973471i	$0.573483\pi$
$98$	1.11241	+	1.11241i	0.112370	+	0.112370i
$99$			6.53178i			0.656469i
$100$	−4.19767	+	2.71654i	−0.419767	+	0.271654i
$101$	0.259650			0.0258361			0.0129180	−	0.999917i	$-0.495888\pi$
$101$	0.259650			0.0258361			0.0129180	+	0.999917i	$0.495888\pi$
$102$	3.66501	+	3.66501i	0.362890	+	0.362890i
$103$	7.30610	−	7.30610i	0.719892	−	0.719892i	−0.248691	−	0.968583i	$-0.580000\pi$
$103$	7.30610	−	7.30610i	0.719892	−	0.719892i	0.968583	+	0.248691i	$0.0800005\pi$
$104$	3.61420			0.354401
$105$	−5.39573	+	9.91894i	−0.526569	+	0.967989i
$106$		−	9.61056i		−	0.933460i
$107$	−1.59232	−	1.59232i	−0.153936	−	0.153936i	0.625937	−	0.779873i	$-0.284716\pi$
$107$	−1.59232	−	1.59232i	−0.153936	−	0.153936i	−0.779873	+	0.625937i	$0.784716\pi$
$108$	1.99437	+	1.99437i	0.191908	+	0.191908i
$109$		−	1.20517i		−	0.115434i	−0.998333	−	0.0577170i	$-0.981618\pi$
$109$		−	1.20517i		−	0.115434i	0.998333	−	0.0577170i	$-0.0183821\pi$
$110$	−2.43521	−	8.24514i	−0.232188	−	0.786143i
$111$	−10.8140			−1.02642
$112$	−1.64724	+	1.64724i	−0.155650	+	0.155650i
$113$	−11.4616	−	11.4616i	−1.07822	−	1.07822i	−0.996669	−	0.0815516i	$-0.974012\pi$
$113$	−11.4616	−	11.4616i	−1.07822	−	1.07822i	−0.0815516	−	0.996669i	$-0.525988\pi$
$114$	−3.60291			−0.337444
$115$	4.26272	+	14.4327i	0.397501	+	1.34586i
$116$			3.07310i			0.285331i
$117$	−4.34165	−	4.34165i	−0.401385	−	0.401385i
$118$	−3.64101	−	3.64101i	−0.335182	−	0.335182i
$119$	−5.57014			−0.510614
$120$	4.25787	+	2.31621i	0.388689	+	0.211440i
$121$	3.78252			0.343865
$122$	−5.34441	−	5.34441i	−0.483860	−	0.483860i
$123$	−1.99752	−	1.99752i	−0.180110	−	0.180110i
$124$		−	9.51169i		−	0.854175i
$125$	−11.1479	+	0.850683i	−0.997101	+	0.0760874i
$126$	3.95758			0.352570
$127$	1.83113	+	1.83113i	0.162487	+	0.162487i	0.783667	−	0.621181i	$-0.213347\pi$
$127$	1.83113	+	1.83113i	0.162487	+	0.162487i	−0.621181	+	0.783667i	$0.713347\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	12.9639	−	5.82997i	1.14141	−	0.513300i
$130$	7.09918	+	3.86183i	0.622639	+	0.338705i
$131$		−	9.83137i		−	0.858971i	−0.903074	−	0.429485i	$-0.858695\pi$
$131$		−	9.83137i		−	0.858971i	0.903074	−	0.429485i	$-0.141305\pi$
$132$	−5.89326	+	5.89326i	−0.512942	+	0.512942i
$133$	2.73788	−	2.73788i	0.237405	−	0.237405i
$134$	3.70485			0.320050
$135$	1.78642	+	6.04845i	0.153750	+	0.520568i
$136$			2.39108i			0.205033i
$137$	−12.4055	+	12.4055i	−1.05987	+	1.05987i	−0.0617798	+	0.998090i	$0.519678\pi$
$137$	−12.4055	+	12.4055i	−1.05987	+	1.05987i	−0.998090	+	0.0617798i	$0.980322\pi$
$138$	10.3159	−	10.3159i	0.878145	−	0.878145i
$139$		−	5.16869i		−	0.438403i	−0.975680	−	0.219201i	$-0.929655\pi$
$139$		−	5.16869i		−	0.438403i	0.975680	−	0.219201i	$-0.0703452\pi$
$140$	−4.99570	+	1.47549i	−0.422214	+	0.124701i
$141$		−	6.57531i		−	0.553741i
$142$	5.10370	+	5.10370i	0.428293	+	0.428293i
$143$	−9.82587	+	9.82587i	−0.821681	+	0.821681i
$144$		−	1.69886i		−	0.141572i
$145$	−3.28367	+	6.03634i	−0.272694	+	0.501291i
$146$	−8.58383			−0.710403
$147$	2.41135	−	2.41135i	0.198885	−	0.198885i
$148$	−3.52756	−	3.52756i	−0.289964	−	0.289964i
$149$	−7.19846			−0.589721			−0.294860	−	0.955540i	$-0.595273\pi$
$149$	−7.19846			−0.589721			−0.294860	+	0.955540i	$0.595273\pi$
$150$	5.88861	+	9.09922i	0.480803	+	0.742948i
$151$			6.33451i			0.515495i	0.966212	+	0.257747i	$0.0829802\pi$
$151$			6.33451i			0.515495i	−0.966212	+	0.257747i	$0.917020\pi$
$152$	−1.17528	−	1.17528i	−0.0953281	−	0.0953281i
$153$	2.87234	−	2.87234i	0.232215	−	0.232215i
$154$		−	8.95667i		−	0.721749i
$155$	10.1634	−	18.6833i	0.816344	−	1.50068i
$156$		−	7.83444i		−	0.627258i
$157$	−6.31621	+	6.31621i	−0.504088	+	0.504088i	−0.912706	−	0.408617i	$-0.866011\pi$
$157$	−6.31621	+	6.31621i	−0.504088	+	0.504088i	0.408617	+	0.912706i	$0.366011\pi$
$158$	11.0811	+	11.0811i	0.881562	+	0.881562i
$159$	−20.8327			−1.65214
$160$	0.633377	+	2.14449i	0.0500729	+	0.169537i
$161$			15.6782i			1.23562i
$162$	7.92699	−	7.92699i	0.622803	−	0.622803i
$163$	13.1860	+	13.1860i	1.03281	+	1.03281i	0.999443	+	0.0333644i	$0.0106222\pi$
$163$	13.1860	+	13.1860i	1.03281	+	1.03281i	0.0333644	+	0.999443i	$0.489378\pi$
$164$		−	1.30320i		−	0.101763i
$165$	−17.8729	+	5.27877i	−1.39140	+	0.410952i
$166$		−	17.5797i		−	1.36445i
$167$	−16.4897	−	16.4897i	−1.27601	−	1.27601i	−0.942882	−	0.333127i	$-0.891896\pi$
$167$	−16.4897	−	16.4897i	−1.27601	−	1.27601i	−0.333127	−	0.942882i	$-0.608104\pi$
$168$	3.57070	+	3.57070i	0.275486	+	0.275486i
$169$		−	0.0624269i		−	0.00480207i
$170$	−2.55491	+	4.69667i	−0.195952	+	0.360218i
$171$			2.82368i			0.215932i
$172$	6.13062	+	2.32711i	0.467456	+	0.177440i
$173$	4.57076	−	4.57076i	0.347508	−	0.347508i	−0.511672	−	0.859181i	$-0.670974\pi$
$173$	4.57076	−	4.57076i	0.347508	−	0.347508i	0.859181	+	0.511672i	$0.170974\pi$
$174$	6.66152			0.505009
$175$	−11.3894	−	2.43977i	−0.860956	−	0.184429i
$176$	−3.84480			−0.289813
$177$	−7.89255	+	7.89255i	−0.593241	+	0.593241i
$178$	2.50651	−	2.50651i	0.187871	−	0.187871i
$179$	23.1707			1.73186			0.865931	−	0.500164i	$-0.166727\pi$
$179$	23.1707			1.73186			0.865931	+	0.500164i	$0.166727\pi$
$180$	1.81526	−	3.33698i	0.135302	−	0.248724i
$181$	−7.76967			−0.577515			−0.288758	−	0.957402i	$-0.593242\pi$
$181$	−7.76967			−0.577515			−0.288758	+	0.957402i	$0.593242\pi$
$182$	5.95346	+	5.95346i	0.441300	+	0.441300i
$183$	−11.5850	+	11.5850i	−0.856388	+	0.856388i
$184$	6.73015			0.496153
$185$	−3.15975	−	10.6983i	−0.232309	−	0.786553i
$186$	−20.6183			−1.51181
$187$	−6.50059	−	6.50059i	−0.475370	−	0.475370i
$188$	2.14489	−	2.14489i	0.156432	−	0.156432i
$189$			6.57042i			0.477928i
$190$	−1.05274	−	3.56436i	−0.0763736	−	0.258586i
$191$		−	6.27229i		−	0.453847i	−0.973913	−	0.226923i	$-0.927133\pi$
$191$		−	6.27229i		−	0.453847i	0.973913	−	0.226923i	$-0.0728667\pi$
$192$	1.53278	−	1.53278i	0.110619	−	0.110619i
$193$	−14.7084	+	14.7084i	−1.05874	+	1.05874i	−0.0605727	+	0.998164i	$0.519293\pi$
$193$	−14.7084	+	14.7084i	−1.05874	+	1.05874i	−0.998164	+	0.0605727i	$0.980707\pi$
$194$	10.3719			0.744661
$195$	8.37124	−	15.3888i	0.599477	−	1.10201i
$196$	1.57318			0.112370
$197$	12.9920	+	12.9920i	0.925644	+	0.925644i	0.997421	−	0.0717771i	$-0.0228670\pi$
$197$	12.9920	+	12.9920i	0.925644	+	0.925644i	−0.0717771	+	0.997421i	$0.522867\pi$
$198$	4.61867	+	4.61867i	0.328234	+	0.328234i
$199$	−16.8344			−1.19336			−0.596681	−	0.802478i	$-0.703514\pi$
$199$	−16.8344			−1.19336			−0.596681	+	0.802478i	$0.703514\pi$
$200$	−1.04731	+	4.88908i	−0.0740562	+	0.345710i
$201$		−	8.03094i		−	0.566459i
$202$	0.183600	−	0.183600i	0.0129180	−	0.0129180i
$203$	−5.06215	+	5.06215i	−0.355293	+	0.355293i
$204$	5.18310			0.362890
$205$	1.39249	−	2.55980i	0.0972557	−	0.178784i
$206$		−	10.3324i		−	0.719892i
$207$	−8.08476	−	8.08476i	−0.561930	−	0.561930i
$208$	2.55562	−	2.55562i	0.177201	−	0.177201i
$209$	6.39046			0.442037
$210$	3.19839	+	10.8291i	0.220710	+	0.747279i
$211$			5.19150i			0.357398i	0.983904	+	0.178699i	$0.0571888\pi$
$211$			5.19150i			0.357398i	−0.983904	+	0.178699i	$0.942811\pi$
$212$	−6.79569	−	6.79569i	−0.466730	−	0.466730i
$213$	11.0632	−	11.0632i	0.758039	−	0.758039i
$214$	−2.25189			−0.153936
$215$	9.55551	+	11.1217i	0.651680	+	0.758494i
$216$	2.82046			0.191908
$217$	15.6681	−	15.6681i	1.06362	−	1.06362i
$218$	−0.852181	−	0.852181i	−0.0577170	−	0.0577170i
$219$			18.6071i			1.25735i
$220$	−7.55215	−	4.10824i	−0.509166	−	0.276977i
$221$	8.64182			0.581312
$222$	−7.64665	+	7.64665i	−0.513209	+	0.513209i
$223$	18.4789	+	18.4789i	1.23744	+	1.23744i	0.961043	+	0.276399i	$0.0891411\pi$
$223$	18.4789	+	18.4789i	1.23744	+	1.23744i	0.276399	+	0.961043i	$0.410859\pi$
$224$			2.32955i			0.155650i
$225$	7.13125	−	4.61502i	0.475416	−	0.307668i
$226$	−16.2092			−1.07822
$227$	13.4850	−	13.4850i	0.895032	−	0.895032i	−0.0999595	−	0.994992i	$-0.531871\pi$
$227$	13.4850	−	13.4850i	0.895032	−	0.895032i	0.994992	+	0.0999595i	$0.0318713\pi$
$228$	−2.54764	+	2.54764i	−0.168722	+	0.168722i
$229$		−	1.10242i		−	0.0728502i	−0.999336	−	0.0364251i	$-0.988403\pi$
$229$		−	1.10242i		−	0.0728502i	0.999336	−	0.0364251i	$-0.0115970\pi$
$230$	13.2197	+	7.19128i	0.871680	+	0.474179i
$231$	−19.4152			−1.27743
$232$	2.17301	+	2.17301i	0.142665	+	0.142665i
$233$	−3.26223	−	3.26223i	−0.213716	−	0.213716i	0.592128	−	0.805844i	$-0.298288\pi$
$233$	−3.26223	−	3.26223i	−0.213716	−	0.213716i	−0.805844	+	0.592128i	$0.798288\pi$
$234$	−6.14001			−0.401385
$235$	6.50495	−	1.92124i	0.424336	−	0.125328i
$236$	−5.14916			−0.335182
$237$	24.0202	−	24.0202i	1.56028	−	1.56028i
$238$	−3.93868	+	3.93868i	−0.255307	+	0.255307i
$239$			4.15607i			0.268834i	0.990925	+	0.134417i	$0.0429161\pi$
$239$			4.15607i			0.268834i	−0.990925	+	0.134417i	$0.957084\pi$
$240$	4.64858	−	1.37296i	0.300064	−	0.0886244i
$241$			24.4537i			1.57520i	0.616185	+	0.787601i	$0.288677\pi$
$241$			24.4537i			1.57520i	−0.616185	+	0.787601i	$0.711323\pi$
$242$	2.67464	−	2.67464i	0.171933	−	0.171933i
$243$	−11.2001	−	11.2001i	−0.718487	−	0.718487i
$244$	−7.55814			−0.483860
$245$	3.09012	+	1.68097i	0.197421	+	0.107394i
$246$	−2.82492			−0.180110
$247$	−4.24771	+	4.24771i	−0.270275	+	0.270275i
$248$	−6.72578	−	6.72578i	−0.427087	−	0.427087i
$249$	−38.1072			−2.41495
$250$	−7.28125	+	8.48430i	−0.460507	+	0.536594i
$251$	−13.2592			−0.836911			−0.418456	−	0.908237i	$-0.637428\pi$
$251$	−13.2592			−0.836911			−0.418456	+	0.908237i	$0.637428\pi$
$252$	2.79843	−	2.79843i	0.176285	−	0.176285i
$253$	−18.2972	+	18.2972i	−1.15033	+	1.15033i
$254$	2.58961			0.162487
$255$	10.1809	+	5.53823i	0.637553	+	0.346818i
$256$	1.00000			0.0625000
$257$	−8.49382	+	8.49382i	−0.529830	+	0.529830i	−0.920522	−	0.390692i	$-0.872236\pi$
$257$	−8.49382	+	8.49382i	−0.529830	+	0.529830i	0.390692	+	0.920522i	$0.372236\pi$
$258$	5.04444	−	13.2893i	0.314053	−	0.827354i
$259$		−	11.6215i		−	0.722125i
$260$	7.75061	−	2.28915i	0.480672	−	0.141967i
$261$		−	5.22077i		−	0.323158i
$262$	−6.95183	−	6.95183i	−0.429485	−	0.429485i
$263$	8.51531	+	8.51531i	0.525076	+	0.525076i	0.919100	−	0.394024i	$-0.128917\pi$
$263$	8.51531	+	8.51531i	0.525076	+	0.525076i	−0.394024	+	0.919100i	$0.628917\pi$
$264$			8.33432i			0.512942i
$265$	−6.08711	−	20.6097i	−0.373928	−	1.26605i
$266$		−	3.87195i		−	0.237405i
$267$	−5.43333	−	5.43333i	−0.332514	−	0.332514i
$268$	2.61972	−	2.61972i	0.160025	−	0.160025i
$269$			1.98700i			0.121150i	0.998164	+	0.0605748i	$0.0192934\pi$
$269$			1.98700i			0.121150i	−0.998164	+	0.0605748i	$0.980707\pi$
$270$	5.54009	+	3.01371i	0.337159	+	0.183409i
$271$	−15.5685			−0.945719			−0.472860	−	0.881138i	$-0.656778\pi$
$271$	−15.5685			−0.945719			−0.472860	+	0.881138i	$0.656778\pi$
$272$	1.69075	+	1.69075i	0.102517	+	0.102517i
$273$	12.9052	−	12.9052i	0.781060	−	0.781060i
$274$			17.5440i			1.05987i
$275$	−10.4446	−	16.1392i	−0.629831	−	0.973231i
$276$		−	14.5888i		−	0.878145i
$277$	5.51932	−	5.51932i	0.331624	−	0.331624i	−0.521579	−	0.853203i	$-0.674657\pi$
$277$	5.51932	−	5.51932i	0.331624	−	0.331624i	0.853203	+	0.521579i	$0.174657\pi$
$278$	−3.65482	−	3.65482i	−0.219201	−	0.219201i
$279$			16.1590i			0.967415i
$280$	−2.48917	+	4.57582i	−0.148756	+	0.273458i
$281$	11.7996			0.703906			0.351953	−	0.936018i	$-0.385518\pi$
$281$	11.7996			0.703906			0.351953	+	0.936018i	$0.385518\pi$
$282$	−4.64945	−	4.64945i	−0.276870	−	0.276870i
$283$	−3.55227	+	3.55227i	−0.211160	+	0.211160i	−0.804760	−	0.593600i	$-0.797706\pi$
$283$	−3.55227	+	3.55227i	−0.211160	+	0.211160i	0.593600	+	0.804760i	$0.297706\pi$
$284$	7.21772			0.428293
$285$	−7.72641	+	2.28200i	−0.457673	+	0.135174i
$286$			13.8959i			0.821681i
$287$	2.14668	−	2.14668i	0.126715	−	0.126715i
$288$	−1.20128	−	1.20128i	−0.0707858	−	0.0707858i
$289$		−	11.2828i		−	0.663691i
$290$	1.94644	+	6.59024i	0.114299	+	0.386992i
$291$		−	22.4831i		−	1.31798i
$292$	−6.06969	+	6.06969i	−0.355202	+	0.355202i
$293$	13.2848	−	13.2848i	0.776107	−	0.776107i	−0.203059	−	0.979166i	$-0.565088\pi$
$293$	13.2848	−	13.2848i	0.776107	−	0.776107i	0.979166	+	0.203059i	$0.0650885\pi$
$294$		−	3.41017i		−	0.198885i
$295$	−10.1142	−	5.50197i	−0.588873	−	0.320337i
$296$	−4.98873			−0.289964
$297$	−7.66796	+	7.66796i	−0.444940	+	0.444940i
$298$	−5.09008	+	5.09008i	−0.294860	+	0.294860i
$299$		−	24.3241i		−	1.40670i
$300$	10.5980	+	2.27025i	0.611875	+	0.131073i
$301$	6.26531	+	13.9319i	0.361127	+	0.803024i
$302$	4.47917	+	4.47917i	0.257747	+	0.257747i
$303$	−0.397987	−	0.397987i	−0.0228637	−	0.0228637i
$304$	−1.66210			−0.0953281
$305$	−14.8461	−	8.07600i	−0.850083	−	0.462430i
$306$		−	4.06210i		−	0.232215i
$307$	−17.4825	−	17.4825i	−0.997782	−	0.997782i	0.00221572	−	0.999998i	$-0.499295\pi$
$307$	−17.4825	−	17.4825i	−0.997782	−	0.997782i	−0.999998	+	0.00221572i	$0.999295\pi$
$308$	−6.33332	−	6.33332i	−0.360875	−	0.360875i
$309$	−22.3974			−1.27414
$310$	−6.02449	−	20.3977i	−0.342168	−	1.15851i
$311$	3.88765			0.220448			0.110224	−	0.993907i	$-0.464843\pi$
$311$	3.88765			0.220448			0.110224	+	0.993907i	$0.464843\pi$
$312$	−5.53979	−	5.53979i	−0.313629	−	0.313629i
$313$	−6.64674	−	6.64674i	−0.375696	−	0.375696i	0.493851	−	0.869547i	$-0.335589\pi$
$313$	−6.64674	−	6.64674i	−0.375696	−	0.375696i	−0.869547	+	0.493851i	$0.835589\pi$
$314$			8.93247i			0.504088i
$315$	8.48699	−	2.50664i	0.478188	−	0.141233i
$316$	15.6710			0.881562
$317$	−20.8672	−	20.8672i	−1.17202	−	1.17202i	−0.981728	−	0.190290i	$-0.939057\pi$
$317$	−20.8672	−	20.8672i	−1.17202	−	1.17202i	−0.190290	−	0.981728i	$-0.560943\pi$
$318$	−14.7309	+	14.7309i	−0.826069	+	0.826069i
$319$	−11.8155			−0.661540
$320$	1.96425	+	1.06852i	0.109805	+	0.0597319i
$321$			4.88138i			0.272452i
$322$	11.0862	+	11.0862i	0.617809	+	0.617809i
$323$	−2.81019	−	2.81019i	−0.156363	−	0.156363i
$324$		−	11.2105i		−	0.622803i
$325$	17.6701	+	3.78520i	0.980162	+	0.209965i
$326$	18.6478			1.03281
$327$	−1.84726	+	1.84726i	−0.102154	+	0.102154i
$328$	−0.921500	−	0.921500i	−0.0508813	−	0.0508813i
$329$	7.06631			0.389578
$330$	−8.90537	+	16.3707i	−0.490224	+	0.901176i
$331$			31.3197i			1.72149i	0.509040	+	0.860743i	$0.330000\pi$
$331$			31.3197i			1.72149i	−0.509040	+	0.860743i	$0.670000\pi$
$332$	−12.4307	−	12.4307i	−0.682224	−	0.682224i
$333$	5.99284	+	5.99284i	0.328405	+	0.328405i
$334$	−23.3199			−1.27601
$335$	7.94500	−	2.34657i	0.434082	−	0.128207i
$336$	5.04974			0.275486
$337$	21.2365	+	21.2365i	1.15683	+	1.15683i	0.985154	+	0.171673i	$0.0549173\pi$
$337$	21.2365	+	21.2365i	1.15683	+	1.15683i	0.171673	+	0.985154i	$0.445083\pi$
$338$	−0.0441425	−	0.0441425i	−0.00240103	−	0.00240103i
$339$			35.1365i			1.90835i
$340$	1.51445	+	5.12764i	0.0821328	+	0.278085i
$341$	36.5706			1.98041
$342$	1.99664	+	1.99664i	0.107966	+	0.107966i
$343$	14.1221	+	14.1221i	0.762522	+	0.762522i
$344$	5.98052	−	2.68949i	0.322448	−	0.145008i
$345$	15.5884	−	28.6561i	0.839253	−	1.54279i
$346$		−	6.46403i		−	0.347508i
$347$	−15.9372	+	15.9372i	−0.855553	+	0.855553i	−0.990810	−	0.135258i	$-0.956814\pi$
$347$	−15.9372	+	15.9372i	−0.855553	+	0.855553i	0.135258	+	0.990810i	$0.456814\pi$
$348$	4.71041	−	4.71041i	0.252504	−	0.252504i
$349$	21.5616			1.15417			0.577083	−	0.816685i	$-0.304191\pi$
$349$	21.5616			1.15417			0.577083	+	0.816685i	$0.304191\pi$
$350$	−9.77868	+	6.32833i	−0.522693	+	0.338263i
$351$		−	10.1937i		−	0.544100i
$352$	−2.71869	+	2.71869i	−0.144906	+	0.144906i
$353$	−8.69205	+	8.69205i	−0.462631	+	0.462631i	−0.899517	−	0.436886i	$-0.856081\pi$
$353$	−8.69205	+	8.69205i	−0.462631	+	0.462631i	0.436886	+	0.899517i	$0.356081\pi$
$354$			11.1618i			0.593241i
$355$	14.1774	+	7.71226i	0.752458	+	0.409324i
$356$		−	3.54474i		−	0.187871i
$357$	8.53782	+	8.53782i	0.451870	+	0.451870i
$358$	16.3842	−	16.3842i	0.865931	−	0.865931i
$359$		−	10.4995i		−	0.554142i	−0.960849	−	0.277071i	$-0.910636\pi$
$359$		−	10.4995i		−	0.554142i	0.960849	−	0.277071i	$-0.0893637\pi$
$360$	−1.07602	−	3.64319i	−0.0567112	−	0.192013i
$361$	−16.2374			−0.854601
$362$	−5.49399	+	5.49399i	−0.288758	+	0.288758i
$363$	−5.79778	−	5.79778i	−0.304305	−	0.304305i
$364$	8.41946			0.441300
$365$	−18.4079	+	5.43681i	−0.963516	+	0.284575i
$366$			16.3837i			0.856388i
$367$	15.6821	+	15.6821i	0.818598	+	0.818598i	0.985905	−	0.167307i	$-0.0535070\pi$
$367$	15.6821	+	15.6821i	0.818598	+	0.818598i	−0.167307	+	0.985905i	$0.553507\pi$
$368$	4.75893	−	4.75893i	0.248077	−	0.248077i
$369$			2.21395i			0.115254i
$370$	−9.79910	−	5.33054i	−0.509431	−	0.277122i
$371$		−	22.3883i		−	1.16234i
$372$	−14.5794	+	14.5794i	−0.755905	+	0.755905i
$373$	14.7027	+	14.7027i	0.761277	+	0.761277i	0.976553	−	0.215276i	$-0.0690652\pi$
$373$	14.7027	+	14.7027i	0.761277	+	0.761277i	−0.215276	+	0.976553i	$0.569065\pi$
$374$	−9.19322			−0.475370
$375$	18.3913	+	15.7835i	0.949722	+	0.815055i
$376$		−	3.03333i		−	0.156432i
$377$	7.85370	−	7.85370i	0.404486	−	0.404486i
$378$	4.64599	+	4.64599i	0.238964	+	0.238964i
$379$			21.2603i			1.09207i	0.837763	+	0.546034i	$0.183863\pi$
$379$			21.2603i			1.09207i	−0.837763	+	0.546034i	$0.816137\pi$
$380$	−3.26478	−	1.77598i	−0.167480	−	0.0911061i
$381$		−	5.61346i		−	0.287586i
$382$	−4.43518	−	4.43518i	−0.226923	−	0.226923i
$383$	6.97560	+	6.97560i	0.356437	+	0.356437i	0.862498	−	0.506061i	$-0.168899\pi$
$383$	6.97560	+	6.97560i	0.356437	+	0.356437i	−0.506061	+	0.862498i	$0.668899\pi$
$384$		−	2.16769i		−	0.110619i
$385$	−5.67295	−	19.2075i	−0.289121	−	0.978904i
$386$			20.8009i			1.05874i
$387$	−10.4151	−	3.95343i	−0.529428	−	0.200964i
$388$	7.33406	−	7.33406i	0.372330	−	0.372330i
$389$	23.3306			1.18291			0.591453	−	0.806339i	$-0.298554\pi$
$389$	23.3306			1.18291			0.591453	+	0.806339i	$0.298554\pi$
$390$	−4.96216	−	16.8009i	−0.251269	−	0.850746i
$391$	16.0923			0.813823
$392$	1.11241	−	1.11241i	0.0561852	−	0.0561852i
$393$	−15.0694	+	15.0694i	−0.760149	+	0.760149i
$394$	18.3735			0.925644
$395$	30.7817	+	16.7447i	1.54880	+	0.842518i
$396$	6.53178			0.328234
$397$	12.7402	+	12.7402i	0.639411	+	0.639411i	0.950410	−	0.310999i	$-0.100664\pi$
$397$	12.7402	+	12.7402i	0.639411	+	0.639411i	−0.310999	+	0.950410i	$0.600664\pi$
$398$	−11.9038	+	11.9038i	−0.596681	+	0.596681i
$399$	−8.39318			−0.420184
$400$	2.71654	+	4.19767i	0.135827	+	0.209883i
$401$	27.5573			1.37615			0.688074	−	0.725641i	$-0.258457\pi$
$401$	27.5573			1.37615			0.688074	+	0.725641i	$0.258457\pi$
$402$	−5.67873	−	5.67873i	−0.283229	−	0.283229i
$403$	−24.3083	+	24.3083i	−1.21088	+	1.21088i
$404$		−	0.259650i		−	0.0129180i
$405$	11.9786	−	22.0201i	0.595220	−	1.09419i
$406$			7.15896i			0.355293i
$407$	13.5628	−	13.5628i	0.672283	−	0.672283i
$408$	3.66501	−	3.66501i	0.181445	−	0.181445i
$409$	−5.50882			−0.272394			−0.136197	−	0.990682i	$-0.543488\pi$
$409$	−5.50882			−0.272394			−0.136197	+	0.990682i	$0.543488\pi$
$410$	−0.825416	−	2.79469i	−0.0407644	−	0.138020i
$411$	38.0298			1.87587
$412$	−7.30610	−	7.30610i	−0.359946	−	0.359946i
$413$	−8.48191	−	8.48191i	−0.417368	−	0.417368i
$414$	−11.4336			−0.561930
$415$	−11.1346	−	37.6994i	−0.546575	−	1.85059i
$416$		−	3.61420i		−	0.177201i
$417$	−7.92250	+	7.92250i	−0.387966	+	0.387966i
$418$	4.51873	−	4.51873i	0.221019	−	0.221019i
$419$	−37.5670			−1.83527			−0.917635	−	0.397424i	$-0.869904\pi$
$419$	−37.5670			−1.83527			−0.917635	+	0.397424i	$0.869904\pi$
$420$	9.91894	+	5.39573i	0.483995	+	0.263285i
$421$		−	21.0049i		−	1.02372i	−0.859069	−	0.511859i	$-0.828957\pi$
$421$		−	21.0049i		−	1.02372i	0.859069	−	0.511859i	$-0.171043\pi$
$422$	3.67095	+	3.67095i	0.178699	+	0.178699i
$423$	−3.64387	+	3.64387i	−0.177171	+	0.177171i
$424$	−9.61056			−0.466730
$425$	−2.50421	+	11.6902i	−0.121472	+	0.567057i
$426$		−	15.6457i		−	0.758039i
$427$	−12.4501	−	12.4501i	−0.602502	−	0.602502i
$428$	−1.59232	+	1.59232i	−0.0769679	+	0.0769679i
$429$	30.1219			1.45430
$430$	14.6210	+	1.10746i	0.705087	+	0.0534066i
$431$	4.04866			0.195017			0.0975086	−	0.995235i	$-0.468913\pi$
$431$	4.04866			0.195017			0.0975086	+	0.995235i	$0.468913\pi$
$432$	1.99437	−	1.99437i	0.0959541	−	0.0959541i
$433$	12.3229	+	12.3229i	0.592199	+	0.592199i	0.938225	−	0.346026i	$-0.112469\pi$
$433$	12.3229	+	12.3229i	0.592199	+	0.592199i	−0.346026	+	0.938225i	$0.612469\pi$
$434$		−	22.1580i		−	1.06362i
$435$	14.2856	−	4.21926i	0.684940	−	0.202298i
$436$	−1.20517			−0.0577170
$437$	−7.90983	+	7.90983i	−0.378379	+	0.378379i
$438$	13.1572	+	13.1572i	0.628674	+	0.628674i
$439$		−	33.2306i		−	1.58601i	−0.609216	−	0.793005i	$-0.708516\pi$
$439$		−	33.2306i		−	1.58601i	0.609216	−	0.793005i	$-0.291484\pi$
$440$	−8.24514	+	2.43521i	−0.393072	+	0.116094i
$441$	−2.67262			−0.127268
$442$	6.11069	−	6.11069i	0.290656	−	0.290656i
$443$	−14.1126	+	14.1126i	−0.670509	+	0.670509i	−0.957833	−	0.287324i	$-0.907234\pi$
$443$	−14.1126	+	14.1126i	−0.670509	+	0.670509i	0.287324	+	0.957833i	$0.407234\pi$
$444$			10.8140i			0.513209i
$445$	3.78762	−	6.96275i	0.179550	−	0.330066i
$446$	26.1332			1.23744
$447$	11.0337	+	11.0337i	0.521876	+	0.521876i
$448$	1.64724	+	1.64724i	0.0778249	+	0.0778249i
$449$	−29.8370			−1.40809			−0.704047	−	0.710153i	$-0.748626\pi$
$449$	−29.8370			−1.40809			−0.704047	+	0.710153i	$0.748626\pi$
$450$	1.77924	−	8.30587i	0.0838741	−	0.391542i
$451$	5.01054			0.235937
$452$	−11.4616	+	11.4616i	−0.539110	+	0.539110i
$453$	9.70944	−	9.70944i	0.456189	−	0.456189i
$454$		−	19.0707i		−	0.895032i
$455$	16.5379	+	8.99634i	0.775310	+	0.421755i
$456$			3.60291i			0.168722i
$457$	10.2366	−	10.2366i	0.478850	−	0.478850i	−0.425914	−	0.904764i	$-0.640047\pi$
$457$	10.2366	−	10.2366i	0.478850	−	0.478850i	0.904764	+	0.425914i	$0.140047\pi$
$458$	−0.779531	−	0.779531i	−0.0364251	−	0.0364251i
$459$	6.74394			0.314780
$460$	14.4327	−	4.26272i	0.672930	−	0.198751i
$461$	9.04349			0.421197			0.210599	−	0.977573i	$-0.432459\pi$
$461$	9.04349			0.421197			0.210599	+	0.977573i	$0.432459\pi$
$462$	−13.7287	+	13.7287i	−0.638715	+	0.638715i
$463$	2.84059	+	2.84059i	0.132014	+	0.132014i	0.770026	−	0.638012i	$-0.220243\pi$
$463$	2.84059	+	2.84059i	0.132014	+	0.132014i	−0.638012	+	0.770026i	$0.720243\pi$
$464$	3.07310			0.142665
$465$	−44.2158	+	13.0592i	−2.05046	+	0.605606i
$466$	−4.61349			−0.213716
$467$	−8.98882	+	8.98882i	−0.415953	+	0.415953i	−0.883806	−	0.467853i	$-0.845028\pi$
$467$	−8.98882	+	8.98882i	−0.415953	+	0.415953i	0.467853	+	0.883806i	$0.345028\pi$
$468$	−4.34165	+	4.34165i	−0.200693	+	0.200693i
$469$	8.63064			0.398526
$470$	3.24117	−	5.95822i	0.149504	−	0.274832i
$471$	19.3628			0.892190
$472$	−3.64101	+	3.64101i	−0.167591	+	0.167591i
$473$	−8.94728	+	23.5710i	−0.411396	+	1.08380i
$474$		−	33.9698i		−	1.56028i
$475$	−4.51517	−	6.97695i	−0.207170	−	0.320124i
$476$			5.57014i			0.255307i
$477$	11.5449	+	11.5449i	0.528606	+	0.528606i
$478$	2.93878	+	2.93878i	0.134417	+	0.134417i
$479$			38.3019i			1.75006i	0.484069	+	0.875030i	$0.339158\pi$
$479$			38.3019i			1.75006i	−0.484069	+	0.875030i	$0.660842\pi$
$480$	2.31621	−	4.25787i	0.105720	−	0.194344i
$481$			18.0303i			0.822109i
$482$	17.2914	+	17.2914i	0.787601	+	0.787601i
$483$	24.0314	−	24.0314i	1.09347	−	1.09347i
$484$		−	3.78252i		−	0.171933i
$485$	22.2425	−	6.56934i	1.00998	−	0.298299i
$486$	−15.8393			−0.718487
$487$	15.3510	+	15.3510i	0.695619	+	0.695619i	0.963462	−	0.267843i	$-0.0863110\pi$
$487$	15.3510	+	15.3510i	0.695619	+	0.695619i	−0.267843	+	0.963462i	$0.586311\pi$
$488$	−5.34441	+	5.34441i	−0.241930	+	0.241930i
$489$		−	40.4226i		−	1.82797i
$490$	3.37368	−	0.996419i	0.152407	−	0.0450136i
$491$		−	21.3541i		−	0.963695i	−0.876255	−	0.481848i	$-0.839966\pi$
$491$		−	21.3541i		−	0.963695i	0.876255	−	0.481848i	$-0.160034\pi$
$492$	−1.99752	+	1.99752i	−0.0900552	+	0.0900552i
$493$	5.19584	+	5.19584i	0.234009	+	0.234009i
$494$			6.00716i			0.270275i
$495$	12.8300	+	6.97932i	0.576667	+	0.313697i
$496$	−9.51169			−0.427087
$497$	11.8893	+	11.8893i	0.533309	+	0.533309i
$498$	−26.9459	+	26.9459i	−1.20747	+	1.20747i
$499$	−22.2579			−0.996402			−0.498201	−	0.867062i	$-0.666006\pi$
$499$	−22.2579			−0.996402			−0.498201	+	0.867062i	$0.666006\pi$
$500$	0.850683	+	11.1479i	0.0380437	+	0.498551i
$501$			50.5502i			2.25842i
$502$	−9.37565	+	9.37565i	−0.418456	+	0.418456i
$503$	6.94231	+	6.94231i	0.309542	+	0.309542i	0.844732	−	0.535190i	$-0.179760\pi$
$503$	6.94231	+	6.94231i	0.309542	+	0.309542i	−0.535190	+	0.844732i	$0.679760\pi$
$504$		−	3.95758i		−	0.176285i
$505$	0.277440	−	0.510016i	0.0123459	−	0.0226954i
$506$			25.8761i			1.15033i
$507$	−0.0956870	+	0.0956870i	−0.00424961	+	0.00424961i
$508$	1.83113	−	1.83113i	0.0812433	−	0.0812433i
$509$			20.3841i			0.903508i	0.892142	+	0.451754i	$0.149202\pi$
$509$			20.3841i			0.903508i	−0.892142	+	0.451754i	$0.850798\pi$
$510$	11.1151	−	3.28286i	0.492185	−	0.145367i
$511$	−19.9965			−0.884593
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−3.31484	+	3.31484i	−0.146354	+	0.146354i
$514$			12.0121i			0.529830i
$515$	−6.54430	−	22.1577i	−0.288376	−	0.976384i
$516$	−5.82997	−	12.9639i	−0.256650	−	0.570703i
$517$	8.24668	+	8.24668i	0.362689	+	0.362689i
$518$	−8.21765	−	8.21765i	−0.361063	−	0.361063i
$519$	−14.0120			−0.615058
$520$	3.86183	−	7.09918i	0.169353	−	0.311320i
$521$			9.88863i			0.433229i	0.976257	+	0.216614i	$0.0695014\pi$
$521$			9.88863i			0.433229i	−0.976257	+	0.216614i	$0.930499\pi$
$522$	−3.69164	−	3.69164i	−0.161579	−	0.161579i
$523$	−4.87706	−	4.87706i	−0.213259	−	0.213259i	0.592391	−	0.805650i	$-0.298184\pi$
$523$	−4.87706	−	4.87706i	−0.213259	−	0.213259i	−0.805650	+	0.592391i	$0.798184\pi$
$524$	−9.83137			−0.429485
$525$	13.7178	+	21.1971i	0.598695	+	0.925118i
$526$	12.0425			0.525076
$527$	−16.0819	−	16.0819i	−0.700537	−	0.700537i
$528$	5.89326	+	5.89326i	0.256471	+	0.256471i
$529$		−	22.2949i		−	0.969344i
$530$	−18.8775	−	10.2691i	−0.819988	−	0.446059i
$531$	8.74770			0.379618
$532$	−2.73788	−	2.73788i	−0.118702	−	0.118702i
$533$	−3.33048	+	3.33048i	−0.144259	+	0.144259i
$534$	−7.68389			−0.332514
$535$	−4.82914	+	1.42629i	−0.208782	+	0.0616640i
$536$		−	3.70485i		−	0.160025i
$537$	−35.5157	−	35.5157i	−1.53262	−	1.53262i
$538$	1.40502	+	1.40502i	0.0605748	+	0.0605748i
$539$			6.04858i			0.260531i
$540$	6.04845	−	1.78642i	0.260284	−	0.0768752i
$541$	−45.3312			−1.94894			−0.974470	−	0.224517i	$-0.927920\pi$
$541$	−45.3312			−1.94894			−0.974470	+	0.224517i	$0.927920\pi$
$542$	−11.0086	+	11.0086i	−0.472860	+	0.472860i
$543$	11.9092	+	11.9092i	0.511074	+	0.511074i
$544$	2.39108			0.102517
$545$	−2.36724	−	1.28774i	−0.101402	−	0.0551607i
$546$		−	18.2507i		−	0.781060i
$547$	−12.1066	−	12.1066i	−0.517640	−	0.517640i	0.399217	−	0.916857i	$-0.369282\pi$
$547$	−12.1066	−	12.1066i	−0.517640	−	0.517640i	−0.916857	+	0.399217i	$0.869282\pi$
$548$	12.4055	+	12.4055i	0.529935	+	0.529935i
$549$	12.8402			0.548007
$550$	−18.7976	−	4.02671i	−0.801531	−	0.171700i
$551$	−5.10781			−0.217600
$552$	−10.3159	−	10.3159i	−0.439073	−	0.439073i
$553$	25.8139	+	25.8139i	1.09772	+	1.09772i
$554$		−	7.80549i		−	0.331624i
$555$	−11.5549	+	21.2414i	−0.490480	+	0.901646i
$556$	−5.16869			−0.219201
$557$	−4.95156	−	4.95156i	−0.209804	−	0.209804i	0.594380	−	0.804184i	$-0.297398\pi$
$557$	−4.95156	−	4.95156i	−0.209804	−	0.209804i	−0.804184	+	0.594380i	$0.797398\pi$
$558$	11.4262	+	11.4262i	0.483708	+	0.483708i
$559$	−9.72035	−	21.6148i	−0.411127	−	0.914208i
$560$	1.47549	+	4.99570i	0.0623507	+	0.211107i
$561$			19.9280i			0.841361i
$562$	8.34358	−	8.34358i	0.351953	−	0.351953i
$563$	28.1103	−	28.1103i	1.18471	−	1.18471i	0.206197	−	0.978510i	$-0.433891\pi$
$563$	28.1103	−	28.1103i	1.18471	−	1.18471i	0.978510	−	0.206197i	$-0.0661088\pi$
$564$	−6.57531			−0.276870
$565$	−34.7605	+	10.2665i	−1.46238	+	0.431917i
$566$			5.02367i			0.211160i
$567$	18.4663	−	18.4663i	0.775513	−	0.775513i
$568$	5.10370	−	5.10370i	0.214146	−	0.214146i
$569$		−	13.5280i		−	0.567122i	−0.958954	−	0.283561i	$-0.908484\pi$
$569$		−	13.5280i		−	0.567122i	0.958954	−	0.283561i	$-0.0915159\pi$
$570$	−3.84978	+	7.07702i	−0.161249	+	0.296424i
$571$		−	19.4313i		−	0.813174i	−0.913612	−	0.406587i	$-0.866719\pi$
$571$		−	19.4313i		−	0.813174i	0.913612	−	0.406587i	$-0.133281\pi$
$572$	9.82587	+	9.82587i	0.410840	+	0.410840i
$573$	−9.61407	+	9.61407i	−0.401634	+	0.401634i
$574$		−	3.03587i		−	0.126715i
$575$	32.9043	+	7.04858i	1.37220	+	0.293946i
$576$	−1.69886			−0.0707858
$577$	−28.0204	+	28.0204i	−1.16650	+	1.16650i	−0.183479	+	0.983024i	$0.558736\pi$
$577$	−28.0204	+	28.0204i	−1.16650	+	1.16650i	−0.983024	+	0.183479i	$0.941264\pi$
$578$	−7.97811	−	7.97811i	−0.331846	−	0.331846i
$579$	45.0897			1.87387
$580$	6.03634	+	3.28367i	0.250645	+	0.136347i
$581$		−	40.9528i		−	1.69901i
$582$	−15.8979	−	15.8979i	−0.658991	−	0.658991i
$583$	26.1281	−	26.1281i	1.08212	−	1.08212i
$584$			8.58383i			0.355202i
$585$	−13.1672	+	3.88895i	−0.544396	+	0.160788i
$586$		−	18.7876i		−	0.776107i
$587$	−31.5564	+	31.5564i	−1.30247	+	1.30247i	−0.375752	+	0.926720i	$0.622616\pi$
$587$	−31.5564	+	31.5564i	−1.30247	+	1.30247i	−0.926720	+	0.375752i	$0.877384\pi$
$588$	−2.41135	−	2.41135i	−0.0994425	−	0.0994425i
$589$	15.8094			0.651415
$590$	−11.0423	+	3.26136i	−0.454605	+	0.134268i
$591$		−	39.8280i		−	1.63830i
$592$	−3.52756	+	3.52756i	−0.144982	+	0.144982i
$593$	−18.7470	−	18.7470i	−0.769846	−	0.769846i	0.208233	−	0.978079i	$-0.433229\pi$
$593$	−18.7470	−	18.7470i	−0.769846	−	0.769846i	−0.978079	+	0.208233i	$0.933229\pi$
$594$			10.8441i			0.444940i
$595$	−5.95179	+	10.9411i	−0.244000	+	0.448543i
$596$			7.19846i			0.294860i
$597$	25.8036	+	25.8036i	1.05607	+	1.05607i
$598$	−17.1997	−	17.1997i	−0.703349	−	0.703349i
$599$		−	24.1501i		−	0.986744i	−0.869818	−	0.493372i	$-0.835764\pi$
$599$		−	24.1501i		−	0.986744i	0.869818	−	0.493372i	$-0.164236\pi$
$600$	9.09922	−	5.88861i	0.371474	−	0.240401i
$601$		−	38.5564i		−	1.57275i	−0.617750	−	0.786374i	$-0.711956\pi$
$601$		−	38.5564i		−	1.57275i	0.617750	−	0.786374i	$-0.288044\pi$
$602$	14.2816	+	5.42113i	0.582075	+	0.220949i
$603$	−4.45054	+	4.45054i	−0.181240	+	0.181240i
$604$	6.33451			0.257747
$605$	4.04168	−	7.42980i	0.164318	−	0.302064i
$606$	−0.562838			−0.0228637
$607$	−9.29309	+	9.29309i	−0.377195	+	0.377195i	−0.870089	−	0.492894i	$-0.835939\pi$
$607$	−9.29309	+	9.29309i	−0.377195	+	0.377195i	0.492894	+	0.870089i	$0.335939\pi$
$608$	−1.17528	+	1.17528i	−0.0476640	+	0.0476640i
$609$	15.5184			0.628836
$610$	−16.2083	+	4.78715i	−0.656257	+	0.193826i
$611$	−10.9631			−0.443518
$612$	−2.87234	−	2.87234i	−0.116107	−	0.116107i
$613$	−29.3491	+	29.3491i	−1.18540	+	1.18540i	−0.207076	+	0.978325i	$0.566395\pi$
$613$	−29.3491	+	29.3491i	−1.18540	+	1.18540i	−0.978325	+	0.207076i	$0.933605\pi$
$614$	−24.7241			−0.997782
$615$	−6.05802	+	1.78924i	−0.244283	+	0.0721492i
$616$	−8.95667			−0.360875
$617$	−15.0901	−	15.0901i	−0.607506	−	0.607506i	0.334787	−	0.942294i	$-0.391336\pi$
$617$	−15.0901	−	15.0901i	−0.607506	−	0.607506i	−0.942294	+	0.334787i	$0.891336\pi$
$618$	−15.8373	+	15.8373i	−0.637071	+	0.637071i
$619$			3.11586i			0.125237i	0.998038	+	0.0626185i	$0.0199451\pi$
$619$			3.11586i			0.125237i	−0.998038	+	0.0626185i	$0.980055\pi$
$620$	−18.6833	−	10.1634i	−0.750340	−	0.408172i
$621$		−	18.9821i		−	0.761727i
$622$	2.74898	−	2.74898i	0.110224	−	0.110224i
$623$	5.83905	−	5.83905i	0.233937	−	0.233937i
$624$	−7.83444			−0.313629
$625$	−10.2408	+	22.8063i	−0.409632	+	0.912251i
$626$	−9.39991			−0.375696
$627$	−9.79519	−	9.79519i	−0.391182	−	0.391182i
$628$	6.31621	+	6.31621i	0.252044	+	0.252044i
$629$	−11.9284			−0.475618
$630$	4.22875	−	7.77367i	0.168477	−	0.309711i
$631$			7.67629i			0.305588i	0.988258	+	0.152794i	$0.0488272\pi$
$631$			7.67629i			0.305588i	−0.988258	+	0.152794i	$0.951173\pi$
$632$	11.0811	−	11.0811i	0.440781	−	0.440781i
$633$	7.95746	−	7.95746i	0.316281	−	0.316281i
$634$	−29.5107			−1.17202
$635$	5.55339	−	1.64020i	0.220380	−	0.0650894i
$636$			20.8327i			0.826069i
$637$	−4.02047	−	4.02047i	−0.159297	−	0.159297i
$638$	−8.35481	+	8.35481i	−0.330770	+	0.330770i
$639$	−12.2619			−0.485073
$640$	2.14449	−	0.633377i	0.0847684	−	0.0250364i
$641$			2.97256i			0.117409i	0.998275	+	0.0587045i	$0.0186970\pi$
$641$			2.97256i			0.117409i	−0.998275	+	0.0587045i	$0.981303\pi$
$642$	3.45166	+	3.45166i	0.136226	+	0.136226i
$643$	21.3956	−	21.3956i	0.843759	−	0.843759i	−0.145587	−	0.989346i	$-0.546507\pi$
$643$	21.3956	−	21.3956i	0.843759	−	0.843759i	0.989346	+	0.145587i	$0.0465070\pi$
$644$	15.6782			0.617809
$645$	2.40063	−	31.6937i	0.0945247	−	1.24794i
$646$	−3.97421			−0.156363
$647$	−27.1527	+	27.1527i	−1.06748	+	1.06748i	−0.0699308	+	0.997552i	$0.522278\pi$
$647$	−27.1527	+	27.1527i	−1.06748	+	1.06748i	−0.997552	+	0.0699308i	$0.977722\pi$
$648$	−7.92699	−	7.92699i	−0.311402	−	0.311402i
$649$		−	19.7975i		−	0.777120i
$650$	15.1712	−	9.81812i	0.595063	−	0.385098i
$651$	−48.0315			−1.88250
$652$	13.1860	−	13.1860i	0.516404	−	0.516404i
$653$	−30.8481	−	30.8481i	−1.20718	−	1.20718i	−0.971936	−	0.235245i	$-0.924411\pi$
$653$	−30.8481	−	30.8481i	−1.20718	−	1.20718i	−0.235245	−	0.971936i	$-0.575589\pi$
$654$			2.61242i			0.102154i
$655$	−19.3112	−	10.5050i	−0.754553	−	0.410464i
$656$	−1.30320			−0.0508813
$657$	10.3115	−	10.3115i	0.402292	−	0.402292i
$658$	4.99663	−	4.99663i	0.194789	−	0.194789i
$659$			18.4981i			0.720584i	0.932840	+	0.360292i	$0.117323\pi$
$659$			18.4981i			0.720584i	−0.932840	+	0.360292i	$0.882677\pi$
$660$	5.27877	+	17.8729i	0.205476	+	0.695700i
$661$	23.4341			0.911481			0.455741	−	0.890113i	$-0.349374\pi$
$661$	23.4341			0.911481			0.455741	+	0.890113i	$0.349374\pi$
$662$	22.1464	+	22.1464i	0.860743	+	0.860743i
$663$	−13.2461	−	13.2461i	−0.514434	−	0.514434i
$664$	−17.5797			−0.682224
$665$	−2.45241	−	8.30336i	−0.0951003	−	0.321991i
$666$	8.47515			0.328405
$667$	14.6247	−	14.6247i	0.566271	−	0.566271i
$668$	−16.4897	+	16.4897i	−0.638005	+	0.638005i
$669$		−	56.6485i		−	2.19016i
$670$	3.95869	−	7.27724i	0.152938	−	0.281144i
$671$		−	29.0596i		−	1.12183i
$672$	3.57070	−	3.57070i	0.137743	−	0.137743i
$673$	−25.7625	−	25.7625i	−0.993072	−	0.993072i	0.00690410	−	0.999976i	$-0.497802\pi$
$673$	−25.7625	−	25.7625i	−0.993072	−	0.993072i	−0.999976	+	0.00690410i	$0.997802\pi$
$674$	30.0330			1.15683
$675$	13.7895	+	2.95391i	0.530757	+	0.113696i
$676$	−0.0624269			−0.00240103
$677$	5.07007	−	5.07007i	0.194859	−	0.194859i	−0.602933	−	0.797792i	$-0.706001\pi$
$677$	5.07007	−	5.07007i	0.194859	−	0.194859i	0.797792	+	0.602933i	$0.206001\pi$
$678$	24.8452	+	24.8452i	0.954176	+	0.954176i
$679$	24.1620			0.927251
$680$	4.69667	+	2.55491i	0.180109	+	0.0979762i
$681$	−41.3393			−1.58412
$682$	25.8593	−	25.8593i	0.990204	−	0.990204i
$683$	−8.32050	+	8.32050i	−0.318375	+	0.318375i	−0.848143	−	0.529768i	$-0.822279\pi$
$683$	−8.32050	+	8.32050i	−0.318375	+	0.318375i	0.529768	+	0.848143i	$0.322279\pi$
$684$	2.82368			0.107966
$685$	11.1119	+	37.6228i	0.424566	+	1.43749i
$686$	19.9717			0.762522
$687$	−1.68978	+	1.68978i	−0.0644691	+	0.0644691i
$688$	2.32711	−	6.13062i	0.0887202	−	0.233728i
$689$			34.7345i			1.32328i
$690$	−9.24025	−	31.2856i	−0.351770	−	1.19102i
$691$		−	1.40467i		−	0.0534363i	−0.999643	−	0.0267182i	$-0.991494\pi$
$691$		−	1.40467i		−	0.0534363i	0.999643	−	0.0267182i	$-0.00850567\pi$
$692$	−4.57076	−	4.57076i	−0.173754	−	0.173754i
$693$	10.7594	+	10.7594i	0.408717	+	0.408717i
$694$			22.5386i			0.855553i
$695$	−10.1526	−	5.52284i	−0.385110	−	0.209493i
$696$		−	6.66152i		−	0.252504i
$697$	−2.20338	−	2.20338i	−0.0834588	−	0.0834588i
$698$	15.2464	−	15.2464i	0.577083	−	0.577083i
$699$			10.0006i			0.378257i
$700$	−2.43977	+	11.3894i	−0.0922147	+	0.430478i
$701$	−35.9418			−1.35750			−0.678751	−	0.734369i	$-0.737478\pi$
$701$	−35.9418			−1.35750			−0.678751	+	0.734369i	$0.737478\pi$
$702$	−7.20804	−	7.20804i	−0.272050	−	0.272050i
$703$	5.86317	−	5.86317i	0.221134	−	0.221134i
$704$			3.84480i			0.144906i
$705$	−12.9155	−	7.02583i	−0.486427	−	0.264608i
$706$			12.2924i			0.462631i
$707$	0.427706	−	0.427706i	0.0160855	−	0.0160855i
$708$	7.89255	+	7.89255i	0.296620	+	0.296620i
$709$		−	7.84566i		−	0.294650i	−0.989088	−	0.147325i	$-0.952934\pi$
$709$		−	7.84566i		−	0.294650i	0.989088	−	0.147325i	$-0.0470663\pi$
$710$	15.4783	−	4.57154i	0.580891	−	0.171567i
$711$	−26.6228			−0.998433
$712$	−2.50651	−	2.50651i	−0.0939355	−	0.0939355i
$713$	−45.2655	+	45.2655i	−1.69521	+	1.69521i
$714$	12.0743			0.451870
$715$	8.80134	+	29.7996i	0.329151	+	1.11444i
$716$		−	23.1707i		−	0.865931i
$717$	6.37036	−	6.37036i	0.237905	−	0.237905i
$718$	−7.42426	−	7.42426i	−0.277071	−	0.277071i
$719$		−	13.8662i		−	0.517121i	−0.965995	−	0.258561i	$-0.916752\pi$
$719$		−	13.8662i		−	0.517121i	0.965995	−	0.258561i	$-0.0832482\pi$
$720$	−3.33698	−	1.81526i	−0.124362	−	0.0676508i
$721$		−	24.0698i		−	0.896408i
$722$	−11.4816	+	11.4816i	−0.427300	+	0.427300i
$723$	37.4823	−	37.4823i	1.39398	−	1.39398i
$724$			7.76967i			0.288758i
$725$	8.34822	+	12.8999i	0.310045	+	0.479089i
$726$	−8.19930			−0.304305
$727$	4.07497	−	4.07497i	0.151132	−	0.151132i	−0.627491	−	0.778624i	$-0.715918\pi$
$727$	4.07497	−	4.07497i	0.151132	−	0.151132i	0.778624	+	0.627491i	$0.215918\pi$
$728$	5.95346	−	5.95346i	0.220650	−	0.220650i
$729$			0.703360i			0.0260504i
$730$	−9.17198	+	16.8608i	−0.339470	+	0.624045i
$731$	14.2999	−	6.43078i	0.528900	−	0.237851i
$732$	11.5850	+	11.5850i	0.428194	+	0.428194i
$733$	3.24048	+	3.24048i	0.119690	+	0.119690i	0.764415	−	0.644725i	$-0.223028\pi$
$733$	3.24048	+	3.24048i	0.119690	+	0.119690i	−0.644725	+	0.764415i	$0.723028\pi$
$734$	22.1778			0.818598
$735$	−2.15992	−	7.31307i	−0.0796700	−	0.269747i
$736$		−	6.73015i		−	0.248077i
$737$	10.0723	+	10.0723i	0.371019	+	0.371019i
$738$	1.56550	+	1.56550i	0.0576268	+	0.0576268i
$739$	−42.6019			−1.56714			−0.783568	−	0.621306i	$-0.786602\pi$
$739$	−42.6019			−1.56714			−0.783568	+	0.621306i	$0.786602\pi$
$740$	−10.6983	+	3.15975i	−0.393276	+	0.116155i
$741$	13.0216			0.478362
$742$	−15.8309	−	15.8309i	−0.581172	−	0.581172i
$743$	−0.172076	−	0.172076i	−0.00631284	−	0.00631284i	0.703943	−	0.710256i	$-0.251421\pi$
$743$	−0.172076	−	0.172076i	−0.00631284	−	0.00631284i	−0.710256	+	0.703943i	$0.751421\pi$
$744$			20.6183i			0.755905i
$745$	−7.69168	+	14.1396i	−0.281801	+	0.518033i
$746$	20.7928			0.761277
$747$	21.1180	+	21.1180i	0.772668	+	0.772668i
$748$	−6.50059	+	6.50059i	−0.237685	+	0.237685i
$749$	−5.24589			−0.191681
$750$	24.1652	−	1.84401i	0.882388	−	0.0673338i
$751$			45.0021i			1.64215i	0.570820	+	0.821075i	$0.306625\pi$
$751$			45.0021i			1.64215i	−0.570820	+	0.821075i	$0.693375\pi$
$752$	−2.14489	−	2.14489i	−0.0782161	−	0.0782161i
$753$	20.3235	+	20.3235i	0.740628	+	0.740628i
$754$		−	11.1068i		−	0.404486i
$755$	12.4425	+	6.76853i	0.452831	+	0.246332i
$756$	6.57042			0.238964
$757$	0.679016	−	0.679016i	0.0246793	−	0.0246793i	−0.694659	−	0.719339i	$-0.744445\pi$
$757$	0.679016	−	0.679016i	0.0246793	−	0.0246793i	0.719339	+	0.694659i	$0.244445\pi$
$758$	15.0333	+	15.0333i	0.546034	+	0.546034i
$759$	56.0913			2.03598
$760$	−3.56436	+	1.05274i	−0.129293	+	0.0381868i
$761$			32.6905i			1.18503i	0.805560	+	0.592514i	$0.201865\pi$
$761$			32.6905i			1.18503i	−0.805560	+	0.592514i	$0.798135\pi$
$762$	−3.96932	−	3.96932i	−0.143793	−	0.143793i
$763$	−1.98520	−	1.98520i	−0.0718691	−	0.0718691i
$764$	−6.27229			−0.226923
$765$	−2.57284	−	8.71114i	−0.0930214	−	0.314952i
$766$	9.86499			0.356437
$767$	13.1593	+	13.1593i	0.475155	+	0.475155i
$768$	−1.53278	−	1.53278i	−0.0553096	−	0.0553096i
$769$		−	34.2546i		−	1.23525i	−0.786471	−	0.617627i	$-0.788094\pi$
$769$		−	34.2546i		−	1.23525i	0.786471	−	0.617627i	$-0.211906\pi$
$770$	−17.5931	−	9.57036i	−0.634012	−	0.344892i
$771$	26.0384			0.937750
$772$	14.7084	+	14.7084i	0.529368	+	0.529368i
$773$	23.0214	+	23.0214i	0.828021	+	0.828021i	0.987243	−	0.159222i	$-0.0508986\pi$
$773$	23.0214	+	23.0214i	0.828021	+	0.828021i	−0.159222	+	0.987243i	$0.550899\pi$
$774$	−10.1601	+	4.56907i	−0.365196	+	0.164232i
$775$	−25.8389	−	39.9269i	−0.928161	−	1.43422i
$776$		−	10.3719i		−	0.372330i
$777$	−17.8133	+	17.8133i	−0.639048	+	0.639048i
$778$	16.4972	−	16.4972i	0.591453	−	0.591453i
$779$	2.16605			0.0776067
$780$	−15.3888	−	8.37124i	−0.551007	−	0.299738i
$781$			27.7507i			0.992998i
$782$	11.3790	−	11.3790i	0.406911	−	0.406911i
$783$	6.12890	−	6.12890i	0.219029	−	0.219029i
$784$		−	1.57318i		−	0.0561852i
$785$	5.65762	+	19.1556i	0.201929	+	0.683692i
$786$			21.3113i			0.760149i
$787$	9.55195	+	9.55195i	0.340490	+	0.340490i	0.856552	−	0.516061i	$-0.172602\pi$
$787$	9.55195	+	9.55195i	0.340490	+	0.340490i	−0.516061	+	0.856552i	$0.672602\pi$
$788$	12.9920	−	12.9920i	0.462822	−	0.462822i
$789$		−	26.1043i		−	0.929337i
$790$	33.6062	−	9.92565i	1.19566	−	0.353139i
$791$	−37.7602			−1.34260
$792$	4.61867	−	4.61867i	0.164117	−	0.164117i
$793$	19.3158	+	19.3158i	0.685923	+	0.685923i
$794$	18.0173			0.639411
$795$	−22.2601	+	40.9205i	−0.789484	+	1.45130i
$796$			16.8344i			0.596681i
$797$	3.35493	+	3.35493i	0.118838	+	0.118838i	0.764025	−	0.645187i	$-0.223221\pi$
$797$	3.35493	+	3.35493i	0.118838	+	0.118838i	−0.645187	+	0.764025i	$0.723221\pi$
$798$	−5.93487	+	5.93487i	−0.210092	+	0.210092i
$799$		−	7.25293i		−	0.256590i
$800$	4.88908	+	1.04731i	0.172855	+	0.0370281i
$801$			6.02202i			0.212778i
$802$	19.4860	−	19.4860i	0.688074	−	0.688074i
$803$	−23.3368	−	23.3368i	−0.823536	−	0.823536i
$804$	−8.03094			−0.283229
$805$	30.7960	+	16.7525i	1.08541	+	0.590447i
$806$			34.3771i			1.21088i
$807$	3.04564	−	3.04564i	0.107212	−	0.107212i
$808$	−0.183600	−	0.183600i	−0.00645902	−	0.00645902i
$809$			33.1114i			1.16413i	0.813141	+	0.582067i	$0.197756\pi$
$809$			33.1114i			1.16413i	−0.813141	+	0.582067i	$0.802244\pi$
$810$	−7.10045	−	24.0407i	−0.249484	−	0.844704i
$811$		−	39.6877i		−	1.39363i	−0.717253	−	0.696813i	$-0.754601\pi$
$811$		−	39.6877i		−	1.39363i	0.717253	−	0.696813i	$-0.245399\pi$
$812$	5.06215	+	5.06215i	0.177647	+	0.177647i
$813$	23.8632	+	23.8632i	0.836918	+	0.836918i
$814$		−	19.1807i		−	0.672283i
$815$	39.9901	−	11.8111i	1.40079	−	0.413725i
$816$		−	5.18310i		−	0.181445i
$817$	−3.86789	+	10.1897i	−0.135320	+	0.356493i
$818$	−3.89533	+	3.89533i	−0.136197	+	0.136197i
$819$	−14.3035			−0.499804
$820$	−2.55980	−	1.39249i	−0.0893922	−	0.0486278i
$821$	17.8747			0.623832			0.311916	−	0.950110i	$-0.399029\pi$
$821$	17.8747			0.623832			0.311916	+	0.950110i	$0.399029\pi$
$822$	26.8911	−	26.8911i	0.937936	−	0.937936i
$823$	−0.287982	+	0.287982i	−0.0100384	+	0.0100384i	−0.712108	−	0.702070i	$-0.752259\pi$
$823$	−0.287982	+	0.287982i	−0.0100384	+	0.0100384i	0.702070	+	0.712108i	$0.252259\pi$
$824$	−10.3324			−0.359946
$825$	−8.72865	+	40.7472i	−0.303893	+	1.41864i
$826$	−11.9952			−0.417368
$827$	−25.6902	−	25.6902i	−0.893334	−	0.893334i	0.101501	−	0.994835i	$-0.467635\pi$
$827$	−25.6902	−	25.6902i	−0.893334	−	0.893334i	−0.994835	+	0.101501i	$0.967635\pi$
$828$	−8.08476	+	8.08476i	−0.280965	+	0.280965i
$829$	2.66476			0.0925511			0.0462755	−	0.998929i	$-0.485265\pi$
$829$	2.66476			0.0925511			0.0462755	+	0.998929i	$0.485265\pi$
$830$	−34.5309	−	18.7842i	−1.19858	−	0.652009i
$831$	−16.9198			−0.586943
$832$	−2.55562	−	2.55562i	−0.0886003	−	0.0886003i
$833$	2.65986	−	2.65986i	0.0921585	−	0.0921585i
$834$			11.2041i			0.387966i
$835$	−50.0093	+	14.7703i	−1.73064	+	0.511148i
$836$		−	6.39046i		−	0.221019i
$837$	−18.9698	+	18.9698i	−0.655693	+	0.655693i
$838$	−26.5639	+	26.5639i	−0.917635	+	0.917635i
$839$	−8.70050			−0.300375			−0.150187	−	0.988658i	$-0.547988\pi$
$839$	−8.70050			−0.300375			−0.150187	+	0.988658i	$0.547988\pi$
$840$	10.8291	−	3.19839i	0.373640	−	0.110355i
$841$	−19.5560			−0.674346
$842$	−14.8527	−	14.8527i	−0.511859	−	0.511859i
$843$	−18.0863	−	18.0863i	−0.622924	−	0.622924i
$844$	5.19150			0.178699
$845$	−0.122622	−	0.0667042i	−0.00421832	−	0.00229469i
$846$			5.15320i			0.177171i
$847$	6.23072	−	6.23072i	0.214090	−	0.214090i
$848$	−6.79569	+	6.79569i	−0.233365	+	0.233365i
$849$	10.8897			0.373735
$850$	6.49546	+	10.0369i	0.222792	+	0.344264i
$851$			33.5749i			1.15093i
$852$	−11.0632	−	11.0632i	−0.379019	−	0.379019i
$853$	19.7386	−	19.7386i	0.675836	−	0.675836i	−0.283219	−	0.959055i	$-0.591402\pi$
$853$	19.7386	−	19.7386i	0.675836	−	0.675836i	0.959055	+	0.283219i	$0.0914023\pi$
$854$	−17.6071			−0.602502
$855$	5.54640	+	3.01715i	0.189683	+	0.103184i
$856$			2.25189i			0.0769679i
$857$	−29.9277	−	29.9277i	−1.02231	−	1.02231i	−0.999745	−	0.0225648i	$-0.992817\pi$
$857$	−29.9277	−	29.9277i	−1.02231	−	1.02231i	−0.0225648	−	0.999745i	$-0.507183\pi$
$858$	21.2994	−	21.2994i	0.727149	−	0.727149i
$859$	16.3092			0.556464			0.278232	−	0.960514i	$-0.410252\pi$
$859$	16.3092			0.556464			0.278232	+	0.960514i	$0.410252\pi$
$860$	11.1217	−	9.55551i	0.379247	−	0.325840i
$861$	−6.58081			−0.224273
$862$	2.86284	−	2.86284i	0.0975086	−	0.0975086i
$863$	−22.8860	−	22.8860i	−0.779049	−	0.779049i	0.200620	−	0.979669i	$-0.435704\pi$
$863$	−22.8860	−	22.8860i	−0.779049	−	0.779049i	−0.979669	+	0.200620i	$0.935704\pi$
$864$		−	2.82046i		−	0.0959541i
$865$	−4.09417	−	13.8620i	−0.139206	−	0.471324i
$866$	17.4272			0.592199
$867$	−17.2940	+	17.2940i	−0.587336	+	0.587336i
$868$	−15.6681	−	15.6681i	−0.531809	−	0.531809i
$869$			60.2519i			2.04390i
$870$	7.11795	−	13.0849i	0.241321	−	0.443619i
$871$	−13.3900			−0.453705
$872$	−0.852181	+	0.852181i	−0.0288585	+	0.0288585i
$873$	−12.4595	+	12.4595i	−0.421691	+	0.421691i
$874$			11.1862i			0.378379i
$875$	−16.9621	+	19.7646i	−0.573422	+	0.668166i
$876$	18.6071			0.628674
$877$	32.2397	+	32.2397i	1.08866	+	1.08866i	0.995667	+	0.0929909i	$0.0296427\pi$
$877$	32.2397	+	32.2397i	1.08866	+	1.08866i	0.0929909	+	0.995667i	$0.470357\pi$
$878$	−23.4976	−	23.4976i	−0.793005	−	0.793005i
$879$	−40.7255			−1.37364
$880$	−4.10824	+	7.55215i	−0.138489	+	0.254583i
$881$	−15.0583			−0.507328			−0.253664	−	0.967292i	$-0.581636\pi$
$881$	−15.0583			−0.507328			−0.253664	+	0.967292i	$0.581636\pi$
$882$	−1.88983	+	1.88983i	−0.0636338	+	0.0636338i
$883$	−0.318941	+	0.318941i	−0.0107332	+	0.0107332i	−0.712453	−	0.701720i	$-0.752416\pi$
$883$	−0.318941	+	0.318941i	−0.0107332	+	0.0107332i	0.701720	+	0.712453i	$0.252416\pi$
$884$		−	8.64182i		−	0.290656i
$885$	7.06960	+	23.9363i	0.237642	+	0.804609i
$886$			19.9582i			0.670509i
$887$	25.9133	−	25.9133i	0.870082	−	0.870082i	−0.122399	−	0.992481i	$-0.539059\pi$
$887$	25.9133	−	25.9133i	0.870082	−	0.870082i	0.992481	+	0.122399i	$0.0390588\pi$
$888$	7.64665	+	7.64665i	0.256605	+	0.256605i
$889$	6.03263			0.202328
$890$	−2.24516	−	7.60166i	−0.0752579	−	0.254808i
$891$	43.1020			1.44397
$892$	18.4789	−	18.4789i	0.618721	−	0.618721i
$893$	3.56502	+	3.56502i	0.119299	+	0.119299i
$894$	15.6040			0.521876
$895$	24.7583	−	45.5131i	0.827579	−	1.52133i
$896$	2.32955			0.0778249
$897$	−37.2836	+	37.2836i	−1.24486	+	1.24486i
$898$	−21.0979	+	21.0979i	−0.704047	+	0.704047i
$899$	−29.2304			−0.974889
$900$	−4.61502	−	7.13125i	−0.153834	−	0.237708i
$901$	−22.9796			−0.765561
$902$	3.54299	−	3.54299i	0.117969	−	0.117969i
$903$	11.7513	−	30.9580i	0.391059	−	1.03022i
$904$			16.2092i			0.539110i
$905$	−8.30203	+	15.2616i	−0.275969	+	0.507312i
$906$		−	13.7312i		−	0.456189i
$907$	23.1991	+	23.1991i	0.770313	+	0.770313i	0.978161	−	0.207848i	$-0.0666461\pi$
$907$	23.1991	+	23.1991i	0.770313	+	0.770313i	−0.207848	+	0.978161i	$0.566646\pi$
$908$	−13.4850	−	13.4850i	−0.447516	−	0.447516i
$909$			0.441108i			0.0146306i
$910$	18.0554	−	5.33270i	0.598532	−	0.176777i
$911$		−	38.6940i		−	1.28199i	−0.767546	−	0.640994i	$-0.778522\pi$
$911$		−	38.6940i		−	1.28199i	0.767546	−	0.640994i	$-0.221478\pi$
$912$	2.54764	+	2.54764i	0.0843609	+	0.0843609i
$913$	47.7936	−	47.7936i	1.58174	−	1.58174i
$914$		−	14.4768i		−	0.478850i
$915$	10.3770	+	35.1346i	0.343054	+	1.16151i
$916$	−1.10242			−0.0364251
$917$	−16.1946	−	16.1946i	−0.534794	−	0.534794i
$918$	4.76869	−	4.76869i	0.157390	−	0.157390i
$919$		−	10.4640i		−	0.345176i	−0.984994	−	0.172588i	$-0.944787\pi$
$919$		−	10.4640i		−	0.345176i	0.984994	−	0.172588i	$-0.0552129\pi$
$920$	7.19128	−	13.2197i	0.237090	−	0.435840i
$921$			53.5940i			1.76598i
$922$	6.39471	−	6.39471i	0.210599	−	0.210599i
$923$	−18.4458	−	18.4458i	−0.607150	−	0.607150i
$924$			19.4152i			0.638715i
$925$	−24.3903	−	5.22476i	−0.801949	−	0.171789i
$926$	4.01721			0.132014
$927$	12.4120	+	12.4120i	0.407665	+	0.407665i
$928$	2.17301	−	2.17301i	0.0713327	−	0.0713327i
$929$	16.5770			0.543875			0.271937	−	0.962315i	$-0.412336\pi$
$929$	16.5770			0.543875			0.271937	+	0.962315i	$0.412336\pi$
$930$	−22.0311	+	40.4996i	−0.722427	+	1.32803i
$931$			2.61479i			0.0856964i
$932$	−3.26223	+	3.26223i	−0.106858	+	0.106858i
$933$	−5.95893	−	5.95893i	−0.195087	−	0.195087i
$934$			12.7121i			0.415953i
$935$	−19.7148	+	5.82278i	−0.644742	+	0.190425i
$936$			6.14001i			0.200693i
$937$	−2.84438	+	2.84438i	−0.0929219	+	0.0929219i	−0.752040	−	0.659118i	$-0.770930\pi$
$937$	−2.84438	+	2.84438i	−0.0929219	+	0.0929219i	0.659118	+	0.752040i	$0.270930\pi$
$938$	6.10278	−	6.10278i	0.199263	−	0.199263i
$939$			20.3760i			0.664947i
$940$	−1.92124	−	6.50495i	−0.0626641	−	0.212168i
$941$	10.4169			0.339581			0.169790	−	0.985480i	$-0.445691\pi$
$941$	10.4169			0.339581			0.169790	+	0.985480i	$0.445691\pi$
$942$	13.6916	−	13.6916i	0.446095	−	0.446095i
$943$	−6.20183	+	6.20183i	−0.201959	+	0.201959i
$944$			5.14916i			0.167591i
$945$	12.9059	+	7.02060i	0.419830	+	0.228380i
$946$	10.3406	+	22.9939i	0.336201	+	0.747597i
$947$	22.6334	+	22.6334i	0.735488	+	0.735488i	0.971701	−	0.236213i	$-0.0759063\pi$
$947$	22.6334	+	22.6334i	0.735488	+	0.735488i	−0.236213	+	0.971701i	$0.575906\pi$
$948$	−24.0202	−	24.0202i	−0.780141	−	0.780141i
$949$	31.0237			1.00707
$950$	−8.12615	−	1.74074i	−0.263647	−	0.0564771i
$951$			63.9698i			2.07436i
$952$	3.93868	+	3.93868i	0.127653	+	0.127653i
$953$	11.8799	+	11.8799i	0.384829	+	0.384829i	0.872838	−	0.488009i	$-0.162277\pi$
$953$	11.8799	+	11.8799i	0.384829	+	0.384829i	−0.488009	+	0.872838i	$0.662277\pi$
$954$	16.3270			0.528606
$955$	−12.3203	−	6.70205i	−0.398677	−	0.216873i
$956$	4.15607			0.134417
$957$	18.1106	+	18.1106i	0.585432	+	0.585432i
$958$	27.0836	+	27.0836i	0.875030	+	0.875030i
$959$			40.8696i			1.31975i
$960$	−1.37296	−	4.64858i	−0.0443122	−	0.150032i
$961$	59.4722			1.91846
$962$	12.7493	+	12.7493i	0.411054	+	0.411054i
$963$	2.70513	−	2.70513i	0.0871717	−	0.0871717i
$964$	24.4537			0.787601
$965$	13.1748	+	44.6072i	0.424112	+	1.43596i
$966$		−	33.9855i		−	1.09347i
$967$	−16.6142	−	16.6142i	−0.534276	−	0.534276i	0.387566	−	0.921842i	$-0.373316\pi$
$967$	−16.6142	−	16.6142i	−0.534276	−	0.534276i	−0.921842	+	0.387566i	$0.873316\pi$
$968$	−2.67464	−	2.67464i	−0.0859663	−	0.0859663i
$969$			8.61484i			0.276749i
$970$	11.0826	−	20.3730i	0.355840	−	0.654139i
$971$	2.84461			0.0912878			0.0456439	−	0.998958i	$-0.485466\pi$
$971$	2.84461			0.0912878			0.0456439	+	0.998958i	$0.485466\pi$
$972$	−11.2001	+	11.2001i	−0.359244	+	0.359244i
$973$	−8.51409	−	8.51409i	−0.272949	−	0.272949i
$974$	21.7096			0.695619
$975$	−21.2826	−	32.8864i	−0.681588	−	1.05321i
$976$			7.55814i			0.241930i
$977$	3.31373	+	3.31373i	0.106016	+	0.106016i	0.758125	−	0.652109i	$-0.226116\pi$
$977$	3.31373	+	3.31373i	0.106016	+	0.106016i	−0.652109	+	0.758125i	$0.726116\pi$
$978$	−28.5831	−	28.5831i	−0.913987	−	0.913987i
$979$	13.6288			0.435580
$980$	1.68097	−	3.09012i	0.0536968	−	0.0987104i
$981$	2.04741			0.0653687
$982$	−15.0996	−	15.0996i	−0.481848	−	0.481848i
$983$	38.5220	+	38.5220i	1.22866	+	1.22866i	0.964471	+	0.264190i	$0.0851044\pi$
$983$	38.5220	+	38.5220i	1.22866	+	1.22866i	0.264190	+	0.964471i	$0.414896\pi$
$984$			2.82492i			0.0900552i
$985$	39.4018	−	11.6374i	1.25544	−	0.370797i
$986$	7.34803			0.234009
$987$	−10.8311	−	10.8311i	−0.344759	−	0.344759i
$988$	4.24771	+	4.24771i	0.135138	+	0.135138i
$989$	−18.1007	−	40.2498i	−0.575568	−	1.27987i
$990$	14.0073	−	4.13708i	0.445182	−	0.131485i
$991$			30.2353i			0.960455i	0.877144	+	0.480227i	$0.159446\pi$
$991$			30.2353i			0.960455i	−0.877144	+	0.480227i	$0.840554\pi$
$992$	−6.72578	+	6.72578i	−0.213544	+	0.213544i
$993$	48.0063	−	48.0063i	1.52344	−	1.52344i
$994$	16.8141			0.533309
$995$	−17.9879	+	33.0670i	−0.570255	+	1.04830i
$996$			38.1072i			1.20747i
$997$	40.6672	−	40.6672i	1.28794	−	1.28794i	0.351908	−	0.936035i	$-0.385533\pi$
$997$	40.6672	−	40.6672i	1.28794	−	1.28794i	0.936035	−	0.351908i	$-0.114467\pi$
$998$	−15.7387	+	15.7387i	−0.498201	+	0.498201i
$999$			14.0705i			0.445172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.g.b.257.13	yes	40
5.3	odd	4	inner	430.2.g.b.343.8	yes	40
43.42	odd	2	inner	430.2.g.b.257.8	✓	40
215.128	even	4	inner	430.2.g.b.343.13	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.g.b.257.8	✓	40	43.42	odd	2	inner
430.2.g.b.257.13	yes	40	1.1	even	1	trivial
430.2.g.b.343.8	yes	40	5.3	odd	4	inner
430.2.g.b.343.13	yes	40	215.128	even	4	inner

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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.53278 - 1.53278i) q^{3} -1.00000i q^{4} +(1.06852 - 1.96425i) q^{5} -2.16769 q^{6} +(1.64724 - 1.64724i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.69886i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.53278 - 1.53278i) q^{3} -1.00000i q^{4} +(1.06852 - 1.96425i) q^{5} -2.16769 q^{6} +(1.64724 - 1.64724i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.69886i q^{9} +(-0.633377 - 2.14449i) q^{10} +3.84480 q^{11} +(-1.53278 + 1.53278i) q^{12} +(-2.55562 + 2.55562i) q^{13} -2.32955i q^{14} +(-4.64858 + 1.37296i) q^{15} -1.00000 q^{16} +(-1.69075 - 1.69075i) q^{17} +(1.20128 + 1.20128i) q^{18} +1.66210 q^{19} +(-1.96425 - 1.06852i) q^{20} -5.04974 q^{21} +(2.71869 - 2.71869i) q^{22} +(-4.75893 + 4.75893i) q^{23} +2.16769i q^{24} +(-2.71654 - 4.19767i) q^{25} +3.61420i q^{26} +(-1.99437 + 1.99437i) q^{27} +(-1.64724 - 1.64724i) q^{28} -3.07310 q^{29} +(-2.31621 + 4.25787i) q^{30} +9.51169 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-5.89326 - 5.89326i) q^{33} -2.39108 q^{34} +(-1.47549 - 4.99570i) q^{35} +1.69886 q^{36} +(3.52756 - 3.52756i) q^{37} +(1.17528 - 1.17528i) q^{38} +7.83444 q^{39} +(-2.14449 + 0.633377i) q^{40} +1.30320 q^{41} +(-3.57070 + 3.57070i) q^{42} +(-2.32711 + 6.13062i) q^{43} -3.84480i q^{44} +(3.33698 + 1.81526i) q^{45} +6.73015i q^{46} +(2.14489 + 2.14489i) q^{47} +(1.53278 + 1.53278i) q^{48} +1.57318i q^{49} +(-4.88908 - 1.04731i) q^{50} +5.18310i q^{51} +(2.55562 + 2.55562i) q^{52} +(6.79569 - 6.79569i) q^{53} +2.82046i q^{54} +(4.10824 - 7.55215i) q^{55} -2.32955 q^{56} +(-2.54764 - 2.54764i) q^{57} +(-2.17301 + 2.17301i) q^{58} -5.14916i q^{59} +(1.37296 + 4.64858i) q^{60} -7.55814i q^{61} +(6.72578 - 6.72578i) q^{62} +(2.79843 + 2.79843i) q^{63} +1.00000i q^{64} +(2.28915 + 7.75061i) q^{65} -8.33432 q^{66} +(2.61972 + 2.61972i) q^{67} +(-1.69075 + 1.69075i) q^{68} +14.5888 q^{69} +(-4.57582 - 2.48917i) q^{70} +7.21772i q^{71} +(1.20128 - 1.20128i) q^{72} +(-6.06969 - 6.06969i) q^{73} -4.98873i q^{74} +(-2.27025 + 10.5980i) q^{75} -1.66210i q^{76} +(6.33332 - 6.33332i) q^{77} +(5.53979 - 5.53979i) q^{78} +15.6710i q^{79} +(-1.06852 + 1.96425i) q^{80} +11.2105 q^{81} +(0.921500 - 0.921500i) q^{82} +(12.4307 - 12.4307i) q^{83} +5.04974i q^{84} +(-5.12764 + 1.51445i) q^{85} +(2.68949 + 5.98052i) q^{86} +(4.71041 + 4.71041i) q^{87} +(-2.71869 - 2.71869i) q^{88} +3.54474 q^{89} +(3.64319 - 1.07602i) q^{90} +8.41946i q^{91} +(4.75893 + 4.75893i) q^{92} +(-14.5794 - 14.5794i) q^{93} +3.03333 q^{94} +(1.77598 - 3.26478i) q^{95} +2.16769 q^{96} +(7.33406 + 7.33406i) q^{97} +(1.11241 + 1.11241i) q^{98} +6.53178i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q+O(q^{10}) \) 40 * q	\( 40 q - 8 q^{10} + 16 q^{11} - 24 q^{13} + 8 q^{15} - 40 q^{16} - 12 q^{17} - 16 q^{21} + 44 q^{23} + 24 q^{25} + 32 q^{31} - 64 q^{35} + 48 q^{36} - 28 q^{38} - 4 q^{40} + 8 q^{41} - 16 q^{43} - 28 q^{47} + 24 q^{52} - 80 q^{53} + 24 q^{56} + 64 q^{57} + 12 q^{58} + 24 q^{67} - 12 q^{68} + 40 q^{78} - 120 q^{81} + 48 q^{83} + 28 q^{87} - 44 q^{92} - 16 q^{95} - 60 q^{97}+O(q^{100}) \) 40 * q - 8 * q^10 + 16 * q^11 - 24 * q^13 + 8 * q^15 - 40 * q^16 - 12 * q^17 - 16 * q^21 + 44 * q^23 + 24 * q^25 + 32 * q^31 - 64 * q^35 + 48 * q^36 - 28 * q^38 - 4 * q^40 + 8 * q^41 - 16 * q^43 - 28 * q^47 + 24 * q^52 - 80 * q^53 + 24 * q^56 + 64 * q^57 + 12 * q^58 + 24 * q^67 - 12 * q^68 + 40 * q^78 - 120 * q^81 + 48 * q^83 + 28 * q^87 - 44 * q^92 - 16 * q^95 - 60 * q^97

Introduction

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