LMFDB - Embedded newform 171.2.k.a.50.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [171,2,Mod(50,171)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(171, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("171.50"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			50.3
Character	$\chi$	$=$	171.50
Dual form			171.2.k.a.65.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.07540 + 1.86265i) q^{2} +(-1.60489 - 0.651416i) q^{3} +(-1.31298 - 2.27414i) q^{4} -3.02519i q^{5} +(2.93925 - 2.28881i) q^{6} +(1.86959 + 3.23822i) q^{7} +1.34630 q^{8} +(2.15132 + 2.09089i) q^{9} +(5.63486 + 3.25329i) q^{10} +(4.41421 - 2.54855i) q^{11} +(0.625765 + 4.50503i) q^{12} +(1.79312 - 1.03526i) q^{13} -8.04222 q^{14} +(-1.97065 + 4.85508i) q^{15} +(1.17814 - 2.04060i) q^{16} +(-4.50968 + 2.60366i) q^{17} +(-6.20813 + 1.75860i) q^{18} +(4.31830 + 0.593520i) q^{19} +(-6.87970 + 3.97200i) q^{20} +(-0.891046 - 6.41485i) q^{21} +10.9628i q^{22} +(5.49727 - 3.17385i) q^{23} +(-2.16065 - 0.876999i) q^{24} -4.15176 q^{25} +4.45327i q^{26} +(-2.09057 - 4.75705i) q^{27} +(4.90944 - 8.50340i) q^{28} +1.61159 q^{29} +(-6.92407 - 8.89180i) q^{30} +(-1.31340 - 0.758293i) q^{31} +(3.88025 + 6.72078i) q^{32} +(-8.74447 + 1.21464i) q^{33} -11.1999i q^{34} +(9.79622 - 5.65585i) q^{35} +(1.93036 - 7.63769i) q^{36} -4.54399i q^{37} +(-5.74943 + 7.40521i) q^{38} +(-3.55213 + 0.493404i) q^{39} -4.07280i q^{40} +2.02559 q^{41} +(12.9068 + 5.23883i) q^{42} +(0.973250 - 1.68572i) q^{43} +(-11.5915 - 6.69236i) q^{44} +(6.32535 - 6.50813i) q^{45} +13.6527i q^{46} +3.42876i q^{47} +(-3.22006 + 2.50747i) q^{48} +(-3.49070 + 6.04608i) q^{49} +(4.46481 - 7.73327i) q^{50} +(8.93358 - 1.24091i) q^{51} +(-4.70864 - 2.71853i) q^{52} +(-4.49378 + 7.78345i) q^{53} +(11.1089 + 1.22173i) q^{54} +(-7.70983 - 13.3538i) q^{55} +(2.51702 + 4.35961i) q^{56} +(-6.54375 - 3.76554i) q^{57} +(-1.73310 + 3.00183i) q^{58} -7.20907 q^{59} +(13.6286 - 1.89306i) q^{60} -7.75044 q^{61} +(2.82487 - 1.63094i) q^{62} +(-2.74870 + 10.8755i) q^{63} -11.9787 q^{64} +(-3.13185 - 5.42452i) q^{65} +(7.14136 - 17.5941i) q^{66} +(-0.569888 + 0.329025i) q^{67} +(11.8422 + 6.83709i) q^{68} +(-10.8900 + 1.51266i) q^{69} +24.3292i q^{70} +(-2.68449 - 4.64968i) q^{71} +(2.89631 + 2.81497i) q^{72} +(-1.90331 - 3.29663i) q^{73} +(8.46387 + 4.88662i) q^{74} +(6.66310 + 2.70452i) q^{75} +(-4.32008 - 10.5997i) q^{76} +(16.5055 + 9.52945i) q^{77} +(2.90093 - 7.14698i) q^{78} +(9.08384 + 5.24456i) q^{79} +(-6.17320 - 3.56410i) q^{80} +(0.256318 + 8.99635i) q^{81} +(-2.17832 + 3.77297i) q^{82} +(-4.06246 + 2.34546i) q^{83} +(-13.4183 + 10.4489i) q^{84} +(7.87657 + 13.6426i) q^{85} +(2.09327 + 3.62565i) q^{86} +(-2.58642 - 1.04981i) q^{87} +(5.94284 - 3.43110i) q^{88} +(1.49289 - 2.58575i) q^{89} +(5.32008 + 18.7808i) q^{90} +(6.70478 + 3.87100i) q^{91} +(-14.4356 - 8.33438i) q^{92} +(1.61390 + 2.07254i) q^{93} +(-6.38657 - 3.68729i) q^{94} +(1.79551 - 13.0637i) q^{95} +(-1.84933 - 13.3137i) q^{96} +(-4.72908 - 2.73034i) q^{97} +(-7.50782 - 13.0039i) q^{98} +(14.8251 + 3.74692i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} - 6 q^{3} - 15 q^{4} + 4 q^{6} - q^{7} + 12 q^{8} - 4 q^{9} - 6 q^{10} - 9 q^{11} + 15 q^{12} - 6 q^{13} - 6 q^{14} + 9 q^{15} - 9 q^{16} - 27 q^{17} + 6 q^{18} + q^{19} + 9 q^{20} - 3 q^{21}+ \cdots + 28 q^{99}+O(q^{100}) $ 36 * q - 3 * q^2 - 6 * q^3 - 15 * q^4 + 4 * q^6 - q^7 + 12 * q^8 - 4 * q^9 - 6 * q^10 - 9 * q^11 + 15 * q^12 - 6 * q^13 - 6 * q^14 + 9 * q^15 - 9 * q^16 - 27 * q^17 + 6 * q^18 + q^19 + 9 * q^20 - 3 * q^21 + 9 * q^23 - 11 * q^24 - 22 * q^25 + 9 * q^27 + 2 * q^28 - 24 * q^29 - 35 * q^30 + 12 * q^31 - 15 * q^32 - 12 * q^33 + 15 * q^35 + 30 * q^36 - 18 * q^38 - 14 * q^39 + 36 * q^41 - 5 * q^42 + 3 * q^43 + 66 * q^44 + 29 * q^45 + 33 * q^48 - 9 * q^49 + 3 * q^50 - 24 * q^51 + 15 * q^52 - 12 * q^53 - 37 * q^54 - 7 * q^55 + 6 * q^56 + 2 * q^57 - 6 * q^58 - 18 * q^59 + 48 * q^60 - 16 * q^61 - 12 * q^62 - 34 * q^63 + 12 * q^64 - 18 * q^65 + 14 * q^66 + 27 * q^67 + 60 * q^68 - 51 * q^69 + 9 * q^71 - 102 * q^72 - 18 * q^73 + 90 * q^74 - 23 * q^76 - 6 * q^77 + 36 * q^78 - 6 * q^79 - 12 * q^80 + 40 * q^81 - 9 * q^82 - 9 * q^83 - 96 * q^84 + 11 * q^85 + 51 * q^86 - 19 * q^87 + 3 * q^88 - 18 * q^89 + 36 * q^90 + 27 * q^91 - 93 * q^92 - 28 * q^93 + 12 * q^94 - 9 * q^96 + 24 * q^97 - 84 * q^98 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.07540	+	1.86265i	−0.760424	+	1.31709i	0.182209	+	0.983260i	$0.441675\pi$
$2$	−1.07540	+	1.86265i	−0.760424	+	1.31709i	−0.942632	+	0.333832i	$0.891658\pi$
$3$	−1.60489	−	0.651416i	−0.926581	−	0.376095i
$3$	−1.60489	−	0.651416i	−0.926581	−	0.376095i
$4$	−1.31298	−	2.27414i	−0.656488	−	1.13707i
$5$		−	3.02519i		−	1.35290i	−0.736486	−	0.676452i	$-0.763516\pi$
$5$		−	3.02519i		−	1.35290i	0.736486	−	0.676452i	$-0.236484\pi$
$6$	2.93925	−	2.28881i	1.19995	−	0.934401i
$7$	1.86959	+	3.23822i	0.706637	+	1.22393i	0.966097	+	0.258178i	$0.0831220\pi$
$7$	1.86959	+	3.23822i	0.706637	+	1.22393i	−0.259460	+	0.965754i	$0.583545\pi$
$8$	1.34630			0.475988
$9$	2.15132	+	2.09089i	0.717105	+	0.696965i
$10$	5.63486	+	3.25329i	1.78190	+	1.02878i
$11$	4.41421	−	2.54855i	1.33093	−	0.768415i	0.345492	−	0.938422i	$-0.387712\pi$
$11$	4.41421	−	2.54855i	1.33093	−	0.768415i	0.985443	+	0.170006i	$0.0543788\pi$
$12$	0.625765	+	4.50503i	0.180643	+	1.30049i
$13$	1.79312	−	1.03526i	0.497321	−	0.287129i	−0.230285	−	0.973123i	$-0.573966\pi$
$13$	1.79312	−	1.03526i	0.497321	−	0.287129i	0.727607	+	0.685995i	$0.240633\pi$
$14$	−8.04222			−2.14937
$15$	−1.97065	+	4.85508i	−0.508821	+	1.25358i
$16$	1.17814	−	2.04060i	0.294535	−	0.510150i
$17$	−4.50968	+	2.60366i	−1.09376	+	0.631481i	−0.934574	−	0.355768i	$-0.884219\pi$
$17$	−4.50968	+	2.60366i	−1.09376	+	0.631481i	−0.159183	+	0.987249i	$0.550886\pi$
$18$	−6.20813	+	1.75860i	−1.46327	+	0.414505i
$19$	4.31830	+	0.593520i	0.990686	+	0.136163i
$19$	4.31830	+	0.593520i	0.990686	+	0.136163i
$20$	−6.87970	+	3.97200i	−1.53835	+	0.888166i
$21$	−0.891046	−	6.41485i	−0.194442	−	1.39983i
$22$			10.9628i			2.33728i
$23$	5.49727	−	3.17385i	1.14626	−	0.661794i	0.198287	−	0.980144i	$-0.436462\pi$
$23$	5.49727	−	3.17385i	1.14626	−	0.661794i	0.947973	+	0.318350i	$0.103129\pi$
$24$	−2.16065	−	0.876999i	−0.441042	−	0.179017i
$25$	−4.15176			−0.830352
$26$			4.45327i			0.873357i
$27$	−2.09057	−	4.75705i	−0.402331	−	0.915494i
$28$	4.90944	−	8.50340i	0.927797	−	1.60699i
$29$	1.61159			0.299265			0.149632	−	0.988742i	$-0.452191\pi$
$29$	1.61159			0.299265			0.149632	+	0.988742i	$0.452191\pi$
$30$	−6.92407	−	8.89180i	−1.26416	−	1.62341i
$31$	−1.31340	−	0.758293i	−0.235894	−	0.136194i	0.377394	−	0.926053i	$-0.376820\pi$
$31$	−1.31340	−	0.758293i	−0.235894	−	0.136194i	−0.613288	+	0.789859i	$0.710154\pi$
$32$	3.88025	+	6.72078i	0.685937	+	1.18808i
$33$	−8.74447	+	1.21464i	−1.52222	+	0.211442i
$34$		−	11.1999i		−	1.92077i
$35$	9.79622	−	5.65585i	1.65586	−	0.956013i
$36$	1.93036	−	7.63769i	0.321727	−	1.27295i
$37$		−	4.54399i		−	0.747028i	−0.927625	−	0.373514i	$-0.878153\pi$
$37$		−	4.54399i		−	0.747028i	0.927625	−	0.373514i	$-0.121847\pi$
$38$	−5.74943	+	7.40521i	−0.932680	+	1.20128i
$39$	−3.55213	+	0.493404i	−0.568796	+	0.0790079i
$40$		−	4.07280i		−	0.643967i
$41$	2.02559			0.316344			0.158172	−	0.987412i	$-0.449440\pi$
$41$	2.02559			0.316344			0.158172	+	0.987412i	$0.449440\pi$
$42$	12.9068	+	5.23883i	1.99157	+	0.808369i
$43$	0.973250	−	1.68572i	0.148419	−	0.257070i	−0.782224	−	0.622997i	$-0.785915\pi$
$43$	0.973250	−	1.68572i	0.148419	−	0.257070i	0.930643	+	0.365927i	$0.119248\pi$
$44$	−11.5915	−	6.69236i	−1.74748	−	1.00891i
$45$	6.32535	−	6.50813i	0.942927	−	0.970175i
$46$			13.6527i			2.01297i
$47$			3.42876i			0.500136i	0.968228	+	0.250068i	$0.0804529\pi$
$47$			3.42876i			0.500136i	−0.968228	+	0.250068i	$0.919547\pi$
$48$	−3.22006	+	2.50747i	−0.464776	+	0.361922i
$49$	−3.49070	+	6.04608i	−0.498672	+	0.863725i
$50$	4.46481	−	7.73327i	0.631419	−	1.09365i
$51$	8.93358	−	1.24091i	1.25095	−	0.173762i
$52$	−4.70864	−	2.71853i	−0.652971	−	0.376993i
$53$	−4.49378	+	7.78345i	−0.617268	+	1.06914i	0.372714	+	0.927946i	$0.378427\pi$
$53$	−4.49378	+	7.78345i	−0.617268	+	1.06914i	−0.989982	+	0.141193i	$0.954906\pi$
$54$	11.1089	+	1.22173i	1.51173	+	0.166256i
$55$	−7.70983	−	13.3538i	−1.03959	−	1.80063i
$56$	2.51702	+	4.35961i	0.336351	+	0.582577i
$57$	−6.54375	−	3.76554i	−0.866741	−	0.498758i
$58$	−1.73310	+	3.00183i	−0.227568	+	0.394159i
$59$	−7.20907			−0.938541			−0.469271	−	0.883054i	$-0.655483\pi$
$59$	−7.20907			−0.938541			−0.469271	+	0.883054i	$0.655483\pi$
$60$	13.6286	−	1.89306i	1.75944	−	0.244393i
$61$	−7.75044			−0.992342			−0.496171	−	0.868225i	$-0.665261\pi$
$61$	−7.75044			−0.992342			−0.496171	+	0.868225i	$0.665261\pi$
$62$	2.82487	−	1.63094i	0.358759	−	0.207129i
$63$	−2.74870	+	10.8755i	−0.346304	+	1.37019i
$64$	−11.9787			−1.49734
$65$	−3.13185	−	5.42452i	−0.388458	−	0.672829i
$66$	7.14136	−	17.5941i	0.879041	−	2.16568i
$67$	−0.569888	+	0.329025i	−0.0696229	+	0.0401968i	−0.534407	−	0.845227i	$-0.679465\pi$
$67$	−0.569888	+	0.329025i	−0.0696229	+	0.0401968i	0.464784	+	0.885424i	$0.346132\pi$
$68$	11.8422	+	6.83709i	1.43608	+	0.829119i
$69$	−10.8900	+	1.51266i	−1.31100	+	0.182103i
$70$			24.3292i			2.90790i
$71$	−2.68449	−	4.64968i	−0.318591	−	0.551815i	0.661604	−	0.749854i	$-0.269876\pi$
$71$	−2.68449	−	4.64968i	−0.318591	−	0.551815i	−0.980194	+	0.198039i	$0.936543\pi$
$72$	2.89631	+	2.81497i	0.341334	+	0.331747i
$73$	−1.90331	−	3.29663i	−0.222765	−	0.385841i	0.732881	−	0.680357i	$-0.238175\pi$
$73$	−1.90331	−	3.29663i	−0.222765	−	0.385841i	−0.955647	+	0.294516i	$0.904842\pi$
$74$	8.46387	+	4.88662i	0.983905	+	0.568058i
$75$	6.66310	+	2.70452i	0.769388	+	0.312291i
$76$	−4.32008	−	10.5997i	−0.495547	−	1.21587i
$77$	16.5055	+	9.52945i	1.88098	+	1.08598i
$78$	2.90093	−	7.14698i	0.328465	−	0.809237i
$79$	9.08384	+	5.24456i	1.02201	+	0.590059i	0.914686	−	0.404165i	$-0.132438\pi$
$79$	9.08384	+	5.24456i	1.02201	+	0.590059i	0.107326	+	0.994224i	$0.465771\pi$
$80$	−6.17320	−	3.56410i	−0.690185	−	0.398478i
$81$	0.256318	+	8.99635i	0.0284798	+	0.999594i
$82$	−2.17832	+	3.77297i	−0.240556	+	0.416655i
$83$	−4.06246	+	2.34546i	−0.445913	+	0.257448i	−0.706102	−	0.708110i	$-0.749548\pi$
$83$	−4.06246	+	2.34546i	−0.445913	+	0.257448i	0.260190	+	0.965558i	$0.416215\pi$
$84$	−13.4183	+	10.4489i	−1.46406	+	1.14007i
$85$	7.87657	+	13.6426i	0.854334	+	1.47975i
$86$	2.09327	+	3.62565i	0.225723	+	0.390963i
$87$	−2.58642	−	1.04981i	−0.277293	−	0.112552i
$88$	5.94284	−	3.43110i	0.633509	−	0.365757i
$89$	1.49289	−	2.58575i	0.158246	−	0.274089i	−0.775991	−	0.630745i	$-0.782750\pi$
$89$	1.49289	−	2.58575i	0.158246	−	0.274089i	0.934236	+	0.356655i	$0.116083\pi$
$90$	5.32008	+	18.7808i	0.560786	+	1.97967i
$91$	6.70478	+	3.87100i	0.702851	+	0.405791i
$92$	−14.4356	−	8.33438i	−1.50501	−	0.868919i
$93$	1.61390	+	2.07254i	0.167353	+	0.214913i
$94$	−6.38657	−	3.68729i	−0.658725	−	0.380315i
$95$	1.79551	−	13.0637i	0.184215	−	1.34030i
$96$	−1.84933	−	13.3137i	−0.188746	−	1.35883i
$97$	−4.72908	−	2.73034i	−0.480165	−	0.277224i	0.240320	−	0.970694i	$-0.422748\pi$
$97$	−4.72908	−	2.73034i	−0.480165	−	0.277224i	−0.720485	+	0.693470i	$0.756081\pi$
$98$	−7.50782	−	13.0039i	−0.758404	−	1.31359i
$99$	14.8251	+	3.74692i	1.48998	+	0.376580i
$100$	5.45116	+	9.44168i	0.545116	+	0.944168i
$101$			1.61316i			0.160516i	0.996774	+	0.0802579i	$0.0255744\pi$
$101$			1.61316i			0.160516i	−0.996774	+	0.0802579i	$0.974426\pi$
$102$	−7.29581	+	17.9746i	−0.722393	+	1.77975i
$103$	9.11427	+	5.26213i	0.898056	+	0.518493i	0.876569	−	0.481276i	$-0.159827\pi$
$103$	9.11427	+	5.26213i	0.898056	+	0.518493i	0.0214871	+	0.999769i	$0.493160\pi$
$104$	2.41407	−	1.39376i	0.236719	−	0.136670i
$105$	−19.4061	+	2.69558i	−1.89384	+	0.263062i
$106$	−9.66523	−	16.7407i	−0.938770	−	1.62600i
$107$	10.3237			0.998028			0.499014	−	0.866594i	$-0.333696\pi$
$107$	10.3237			0.998028			0.499014	+	0.866594i	$0.333696\pi$
$108$	−8.07332	+	11.0001i	−0.776856	+	1.05849i
$109$	−5.10016	+	2.94458i	−0.488506	+	0.282039i	−0.723955	−	0.689848i	$-0.757677\pi$
$109$	−5.10016	+	2.94458i	−0.488506	+	0.282039i	0.235448	+	0.971887i	$0.424344\pi$
$110$	33.1646			3.16212
$111$	−2.96003	+	7.29259i	−0.280953	+	0.692182i
$112$	8.81054			0.832518
$113$	−7.68377	+	13.3087i	−0.722828	+	1.25197i	0.237034	+	0.971501i	$0.423825\pi$
$113$	−7.68377	+	13.3087i	−0.722828	+	1.25197i	−0.959862	+	0.280473i	$0.909509\pi$
$114$	14.0510	−	8.13925i	1.31600	−	0.762311i
$115$	−9.60150	−	16.6303i	−0.895344	−	1.55078i
$116$	−2.11598	−	3.66498i	−0.196464	−	0.340285i
$117$	6.02218	+	1.52206i	0.556750	+	0.140714i
$118$	7.75264	−	13.4280i	0.713689	−	1.23615i
$119$	−16.8625	−	9.73555i	−1.54578	−	0.892456i
$120$	−2.65309	+	6.53638i	−0.242193	+	0.596687i
$121$	7.49017	−	12.9734i	0.680925	−	1.17940i
$122$	8.33483	−	14.4364i	0.754600	−	1.30701i
$123$	−3.25084	−	1.31950i	−0.293119	−	0.118976i
$124$			3.98248i			0.357638i
$125$		−	2.56609i		−	0.229518i
$126$	−17.3014	−	16.8154i	−1.54133	−	1.49804i
$127$	1.69680	+	0.979649i	0.150567	+	0.0869298i	0.573391	−	0.819282i	$-0.305628\pi$
$127$	1.69680	+	0.979649i	0.150567	+	0.0869298i	−0.422824	+	0.906212i	$0.638961\pi$
$128$	5.12144	−	8.87060i	0.452676	−	0.784057i
$129$	−2.66006	+	2.07139i	−0.234205	+	0.182376i
$130$	13.4720			1.18157
$131$			13.0386i			1.13919i	0.821926	+	0.569595i	$0.192900\pi$
$131$			13.0386i			1.13919i	−0.821926	+	0.569595i	$0.807100\pi$
$132$	14.2435	+	18.2914i	1.23974	+	1.59206i
$133$	6.15149	+	15.0932i	0.533402	+	1.30875i
$134$		−	1.41534i		−	0.122266i
$135$	−14.3910	+	6.32438i	−1.23858	+	0.544316i
$136$	−6.07137	+	3.50531i	−0.520616	+	0.300578i
$137$			11.4560i			0.978752i	0.872073	+	0.489376i	$0.162775\pi$
$137$			11.4560i			0.978752i	−0.872073	+	0.489376i	$0.837225\pi$
$138$	8.89355	−	21.9110i	0.757069	−	1.86518i
$139$	−9.26139	−	16.0412i	−0.785541	−	1.36060i	−0.928676	−	0.370893i	$-0.879052\pi$
$139$	−9.26139	−	16.0412i	−0.785541	−	1.36060i	0.143135	−	0.989703i	$-0.454282\pi$
$140$	−25.7244	−	14.8520i	−2.17411	−	1.25522i
$141$	2.23355	−	5.50276i	0.188098	−	0.463416i
$142$	11.5476			0.969055
$143$	5.27680	−	9.13968i	0.441268	−	0.764299i
$144$	6.80123	−	1.92661i	0.566769	−	0.160551i
$145$		−	4.87536i		−	0.404876i
$146$	8.18728			0.677584
$147$	9.54069	−	7.42936i	0.786903	−	0.612764i
$148$	−10.3337	+	5.96615i	−0.849423	+	0.490415i
$149$		−	7.28384i		−	0.596716i	−0.954454	−	0.298358i	$-0.903561\pi$
$149$		−	7.28384i		−	0.596716i	0.954454	−	0.298358i	$-0.0964389\pi$
$150$	−12.2031	+	9.50257i	−0.996377	+	0.775882i
$151$	1.90838	−	1.10180i	0.155302	−	0.0896635i	−0.420335	−	0.907369i	$-0.638087\pi$
$151$	1.90838	−	1.10180i	0.155302	−	0.0896635i	0.575637	+	0.817705i	$0.304754\pi$
$152$	5.81372	+	0.799054i	0.471555	+	0.0648118i
$153$	−15.1457	−	3.82796i	−1.22446	−	0.309472i
$154$	−35.5001	+	20.4960i	−2.86068	+	1.65161i
$155$	−2.29398	+	3.97329i	−0.184257	+	0.319142i
$156$	5.78593	+	7.43022i	0.463245	+	0.594894i
$157$	−13.5719			−1.08316			−0.541579	−	0.840650i	$-0.682173\pi$
$157$	−13.5719			−1.08316			−0.541579	+	0.840650i	$0.682173\pi$
$158$	−19.5375	+	11.2800i	−1.55432	+	0.897389i
$159$	12.2823	−	9.56423i	0.974046	−	0.758493i
$160$	20.3316	−	11.7385i	1.60736	−	0.928008i
$161$	20.5552	+	11.8676i	1.61998	+	0.935296i
$162$	−17.0327	−	9.19725i	−1.33821	−	0.722605i
$163$	3.00114			0.235067			0.117534	−	0.993069i	$-0.462501\pi$
$163$	3.00114			0.235067			0.117534	+	0.993069i	$0.462501\pi$
$164$	−2.65955	−	4.60648i	−0.207676	−	0.359706i
$165$	3.67451	+	26.4536i	0.286060	+	2.05941i
$166$		−	10.0892i		−	0.783078i
$167$	−2.98146	−	5.16403i	−0.230712	−	0.399605i	0.727306	−	0.686314i	$-0.240772\pi$
$167$	−2.98146	−	5.16403i	−0.230712	−	0.399605i	−0.958018	+	0.286709i	$0.907439\pi$
$168$	−1.19961	−	8.63629i	−0.0925522	−	0.666305i
$169$	−4.35649	+	7.54566i	−0.335114	+	0.580435i
$170$	−33.8819			−2.59862
$171$	8.04904	+	10.3060i	0.615526	+	0.788117i
$172$	−5.11141			−0.389742
$173$	9.39409	−	16.2710i	0.714220	−	1.23706i	−0.249040	−	0.968493i	$-0.580115\pi$
$173$	9.39409	−	16.2710i	0.714220	−	1.23706i	0.963260	−	0.268572i	$-0.0865516\pi$
$174$	4.73687	−	3.68861i	0.359101	−	0.279633i
$175$	−7.76207	−	13.4443i	−0.586757	−	1.01629i
$176$		−	12.0102i		−	0.905302i
$177$	11.5697	+	4.69610i	0.869634	+	0.352981i
$178$	3.21090	+	5.56144i	0.240667	+	0.416848i
$179$	14.8755			1.11184			0.555922	−	0.831235i	$-0.312365\pi$
$179$	14.8755			1.11184			0.555922	+	0.831235i	$0.312365\pi$
$180$	−23.1054	−	5.83971i	−1.72218	−	0.435266i
$181$	−3.85625	−	2.22640i	−0.286633	−	0.165487i	0.349790	−	0.936828i	$-0.386253\pi$
$181$	−3.85625	−	2.22640i	−0.286633	−	0.165487i	−0.636422	+	0.771341i	$0.719586\pi$
$182$	−14.4206	+	8.32577i	−1.06893	+	0.617147i
$183$	12.4386	+	5.04876i	0.919486	+	0.373215i
$184$	7.40097	−	4.27295i	0.545606	−	0.315006i
$185$	−13.7464			−1.01066
$186$	−5.59601	+	0.777307i	−0.410319	+	0.0569949i
$187$	−13.2711	+	22.9862i	−0.970480	+	1.68092i
$188$	7.79748	−	4.50187i	0.568689	−	0.328333i
$189$	11.4958	−	15.6634i	0.836200	−	1.13935i
$190$	22.4022	+	17.3931i	1.62522	+	1.26183i
$191$	−20.1652	+	11.6424i	−1.45910	+	0.842414i	−0.998967	−	0.0454345i	$-0.985533\pi$
$191$	−20.1652	+	11.6424i	−1.45910	+	0.842414i	−0.460136	+	0.887848i	$0.652199\pi$
$192$	19.2245	+	7.80313i	1.38741	+	0.563142i
$193$		−	22.5699i		−	1.62462i	−0.583229	−	0.812308i	$-0.698211\pi$
$193$		−	22.5699i		−	1.62462i	0.583229	−	0.812308i	$-0.301789\pi$
$194$	10.1713	−	5.87241i	0.730258	−	0.421615i
$195$	1.49264	+	10.7459i	0.106890	+	0.769527i
$196$	18.3328			1.30949
$197$			2.10025i			0.149637i	0.997197	+	0.0748184i	$0.0238377\pi$
$197$			2.10025i			0.149637i	−0.997197	+	0.0748184i	$0.976162\pi$
$198$	−22.9221	+	23.5845i	−1.62901	+	1.67608i
$199$	−6.81724	+	11.8078i	−0.483261	+	0.837033i	−0.999815	−	0.0192216i	$-0.993881\pi$
$199$	−6.81724	+	11.8078i	−0.483261	+	0.837033i	0.516554	+	0.856255i	$0.327215\pi$
$200$	−5.58950			−0.395238
$201$	1.12894	−	0.156814i	0.0796291	−	0.0110608i
$202$	−3.00476	−	1.73480i	−0.211414	−	0.122060i
$203$	3.01300	+	5.21868i	0.211471	+	0.366279i
$204$	−14.5516	−	18.6869i	−1.01881	−	1.30835i
$205$		−	6.12780i		−	0.427984i
$206$	−19.6030	+	11.3178i	−1.36581	+	0.788548i
$207$	18.4626	+	4.66626i	1.28324	+	0.324328i
$208$		−	4.87871i		−	0.338278i
$209$	20.5745	−	8.38547i	1.42317	−	0.580035i
$210$	15.8484	−	39.0456i	1.09365	−	2.69440i
$211$			27.3865i			1.88537i	0.333690	+	0.942683i	$0.391706\pi$
$211$			27.3865i			1.88537i	−0.333690	+	0.942683i	$0.608294\pi$
$212$	23.6009			1.62092
$213$	1.27943	+	9.21092i	0.0876652	+	0.631122i
$214$	−11.1021	+	19.2294i	−0.758924	+	1.31449i
$215$	−5.09961	−	2.94426i	−0.347791	−	0.200797i
$216$	−2.81454	−	6.40440i	−0.191505	−	0.435764i
$217$		−	5.67078i		−	0.384958i
$218$		−	12.6664i		−	0.857877i
$219$	0.907118	+	6.53055i	0.0612974	+	0.441294i
$220$	−20.2456	+	35.0665i	−1.36496	+	2.36418i
$221$	−5.39092	+	9.33735i	−0.362633	+	0.628098i
$222$	−10.4003	−	13.3560i	−0.698024	−	0.896393i
$223$	2.00040	+	1.15493i	0.133956	+	0.0773397i	0.565481	−	0.824762i	$-0.308691\pi$
$223$	2.00040	+	1.15493i	0.133956	+	0.0773397i	−0.431524	+	0.902101i	$0.642024\pi$
$224$	−14.5089	+	25.1302i	−0.969417	+	1.67908i
$225$	−8.93175	−	8.68089i	−0.595450	−	0.578726i
$226$	−16.5263	−	28.6243i	−1.09931	−	1.90406i
$227$	5.87376	+	10.1737i	0.389855	+	0.675249i	0.992430	−	0.122813i	$-0.0391917\pi$
$227$	5.87376	+	10.1737i	0.389855	+	0.675249i	−0.602574	+	0.798063i	$0.705858\pi$
$228$	0.0284214	+	19.8255i	0.00188225	+	1.31297i
$229$	−3.31652	+	5.74438i	−0.219162	+	0.379599i	−0.954552	−	0.298045i	$-0.903666\pi$
$229$	−3.31652	+	5.74438i	−0.219162	+	0.379599i	0.735390	+	0.677644i	$0.236999\pi$
$230$	41.3018			2.72336
$231$	−20.2818	−	26.0456i	−1.33444	−	1.71368i
$232$	2.16968			0.142446
$233$	−3.13882	+	1.81220i	−0.205631	+	0.118721i	−0.599279	−	0.800540i	$-0.704546\pi$
$233$	−3.13882	+	1.81220i	−0.205631	+	0.118721i	0.393648	+	0.919261i	$0.371213\pi$
$234$	−9.31131	+	9.58038i	−0.608699	+	0.626289i
$235$	10.3726			0.676636
$236$	9.46533	+	16.3944i	0.616141	+	1.06719i
$237$	−11.1621	−	14.3343i	−0.725059	−	0.931111i
$238$	36.2678	−	20.9392i	2.35089	−	1.35729i
$239$	13.1428	+	7.58803i	0.850140	+	0.490829i	0.860698	−	0.509116i	$-0.170027\pi$
$239$	13.1428	+	7.58803i	0.850140	+	0.490829i	−0.0105580	+	0.999944i	$0.503361\pi$
$240$	7.58557	+	9.74129i	0.489646	+	0.628797i
$241$		−	24.5234i		−	1.57969i	−0.613308	−	0.789844i	$-0.710161\pi$
$241$		−	24.5234i		−	1.57969i	0.613308	−	0.789844i	$-0.289839\pi$
$242$	16.1099	+	27.9031i	1.03558	+	1.79368i
$243$	5.44900	−	14.6051i	0.349554	−	0.936916i
$244$	10.1761	+	17.6256i	0.651461	+	1.12836i
$245$	18.2905	+	10.5600i	1.16854	+	0.674656i
$246$	5.95373	−	4.63619i	0.379596	−	0.295593i
$247$	8.35767	−	3.40630i	0.531786	−	0.216738i
$248$	−1.76823	−	1.02089i	−0.112283	−	0.0648265i
$249$	8.04765	−	1.11785i	0.509999	−	0.0708408i
$250$	4.77972	+	2.75957i	0.302296	+	0.174531i
$251$	−3.73240	−	2.15490i	−0.235587	−	0.136016i	0.377560	−	0.925985i	$-0.376763\pi$
$251$	−3.73240	−	2.15490i	−0.235587	−	0.136016i	−0.613147	+	0.789969i	$0.710097\pi$
$252$	28.3415	−	8.02838i	1.78535	−	0.505740i
$253$	16.1774	−	28.0201i	1.01707	−	1.76161i
$254$	−3.64949	+	2.10703i	−0.228989	+	0.132207i
$255$	−3.75398	−	27.0258i	−0.235083	−	1.69242i
$256$	−0.963515	−	1.66886i	−0.0602197	−	0.104304i
$257$	−12.6266	−	21.8699i	−0.787626	−	1.36421i	−0.927418	−	0.374027i	$-0.877977\pi$
$257$	−12.6266	−	21.8699i	−0.787626	−	1.36421i	0.139792	−	0.990181i	$-0.455357\pi$
$258$	−0.997653	−	7.18233i	−0.0621112	−	0.447153i
$259$	14.7144	−	8.49539i	0.914311	−	0.527878i
$260$	−8.22408	+	14.2445i	−0.510036	+	0.883408i
$261$	3.46704	+	3.36966i	0.214604	+	0.208577i
$262$	−24.2864	−	14.0217i	−1.50042	−	0.866266i
$263$	−17.4797	−	10.0919i	−1.07784	−	0.622293i	−0.147530	−	0.989058i	$-0.547132\pi$
$263$	−17.4797	−	10.0919i	−1.07784	−	0.622293i	−0.930314	+	0.366764i	$0.880466\pi$
$264$	−11.7727	+	1.63527i	−0.724557	+	0.100644i
$265$	23.5464	+	13.5945i	1.44644	+	0.835105i
$266$	−34.7287	−	4.77322i	−2.12936	−	0.292665i
$267$	−4.08031	+	3.17735i	−0.249711	+	0.194451i
$268$	1.49650	+	0.864004i	0.0914132	+	0.0527774i
$269$	−2.92165	−	5.06044i	−0.178136	−	0.308540i	0.763106	−	0.646273i	$-0.223673\pi$
$269$	−2.92165	−	5.06044i	−0.178136	−	0.308540i	−0.941242	+	0.337733i	$0.890340\pi$
$270$	3.69595	−	33.6066i	0.224929	−	2.04523i
$271$	7.53980	+	13.0593i	0.458010	+	0.793297i	0.998856	−	0.0478248i	$-0.0152289\pi$
$271$	7.53980	+	13.0593i	0.458010	+	0.793297i	−0.540845	+	0.841122i	$0.681896\pi$
$272$			12.2699i			0.743974i
$273$	−8.23877	−	10.5801i	−0.498633	−	0.640338i
$274$	−21.3385	−	12.3198i	−1.28911	−	0.744266i
$275$	−18.3267	+	10.5809i	−1.10514	+	0.638055i
$276$	17.7383	+	22.7793i	1.06772	+	1.37115i
$277$	−8.02211	−	13.8947i	−0.482002	−	0.834852i	0.517785	−	0.855511i	$-0.326757\pi$
$277$	−8.02211	−	13.8947i	−0.482002	−	0.834852i	−0.999787	+	0.0206591i	$0.993424\pi$
$278$	39.8388			2.38937
$279$	−1.24003	−	4.37752i	−0.0742388	−	0.262075i
$280$	13.1886	−	7.61446i	0.788171	−	0.455051i
$281$	−16.9959			−1.01389			−0.506944	−	0.861979i	$-0.669225\pi$
$281$	−16.9959			−1.01389			−0.506944	+	0.861979i	$0.669225\pi$
$282$	7.84776	+	10.0780i	0.467327	+	0.600136i
$283$	−15.5286			−0.923080			−0.461540	−	0.887119i	$-0.652703\pi$
$283$	−15.5286			−0.923080			−0.461540	+	0.887119i	$0.652703\pi$
$284$	−7.04935	+	12.2098i	−0.418302	+	0.724520i
$285$	−11.3915	+	19.7961i	−0.674772	+	1.17262i
$286$	11.3494	+	19.6577i	0.671101	+	1.16238i
$287$	3.78702	+	6.55931i	0.223541	+	0.387184i
$288$	−5.70482	+	22.5717i	−0.336160	+	1.33005i
$289$	5.05813	−	8.76093i	0.297537	−	0.515349i
$290$	9.08108	+	5.24297i	0.533260	+	0.307878i
$291$	5.81105	+	7.46247i	0.340650	+	0.437458i
$292$	−4.99800	+	8.65678i	−0.292486	+	0.506600i
$293$	−15.1343	+	26.2134i	−0.884156	+	1.53140i	−0.0374772	+	0.999297i	$0.511932\pi$
$293$	−15.1343	+	26.2134i	−0.884156	+	1.53140i	−0.846678	+	0.532105i	$0.821401\pi$
$294$	3.57823	+	25.7605i	0.208687	+	1.50238i
$295$			21.8088i			1.26976i
$296$		−	6.11757i		−	0.355576i
$297$	−21.3518	−	15.6707i	−1.23896	−	0.909305i
$298$	13.5672	+	7.83305i	0.785929	+	0.453757i
$299$	6.57150	−	11.3822i	0.380040	−	0.658248i
$300$	−2.59803	−	18.7038i	−0.149997	−	1.07986i
$301$	7.27830			0.419514
$302$			4.73953i			0.272729i
$303$	1.05084	−	2.58894i	0.0603692	−	0.148731i
$304$	6.29871	−	8.11268i	0.361256	−	0.465294i
$305$			23.4465i			1.34254i
$306$	23.4179	−	24.0946i	1.33871	−	1.37740i
$307$	−24.4373	+	14.1089i	−1.39471	+	0.805235i	−0.993832	−	0.110897i	$-0.964628\pi$
$307$	−24.4373	+	14.1089i	−1.39471	+	0.805235i	−0.400876	+	0.916132i	$0.631294\pi$
$308$		−	50.0478i		−	2.85174i
$309$	−11.1995	−	14.3823i	−0.637119	−	0.818180i
$310$	−4.93390	−	8.54576i	−0.280227	−	0.485367i
$311$	16.5220	+	9.53896i	0.936875	+	0.540905i	0.888979	−	0.457947i	$-0.151415\pi$
$311$	16.5220	+	9.53896i	0.936875	+	0.540905i	0.0478956	+	0.998852i	$0.484749\pi$
$312$	−4.78223	+	0.664269i	−0.270740	+	0.0376068i
$313$	−11.2368			−0.635141			−0.317571	−	0.948235i	$-0.602867\pi$
$313$	−11.2368			−0.635141			−0.317571	+	0.948235i	$0.602867\pi$
$314$	14.5953	−	25.2797i	0.823658	−	1.42662i
$315$	32.9005	+	8.31534i	1.85374	+	0.468517i
$316$		−	27.5439i		−	1.54947i
$317$	−0.376061			−0.0211217			−0.0105608	−	0.999944i	$-0.503362\pi$
$317$	−0.376061			−0.0211217			−0.0105608	+	0.999944i	$0.503362\pi$
$318$	4.60646	+	33.1629i	0.258317	+	1.85968i
$319$	7.11389	−	4.10721i	0.398301	−	0.229959i
$320$			36.2379i			2.02576i
$321$	−16.5683	−	6.72500i	−0.924754	−	0.375353i
$322$	−44.2103	+	25.5248i	−2.46374	+	1.42244i
$323$	−21.0195	+	8.56682i	−1.16955	+	0.476671i
$324$	20.1224	−	12.3949i	1.11791	−	0.688605i
$325$	−7.44459	+	4.29814i	−0.412952	+	0.238418i
$326$	−3.22743	+	5.59007i	−0.178751	+	0.309605i
$327$	10.1033	−	1.40339i	0.558714	−	0.0776075i
$328$	2.72705			0.150576
$329$	−11.1031	+	6.41036i	−0.612132	+	0.353414i
$330$	−53.2254	−	21.6040i	−2.92996	−	1.18926i
$331$	−27.1452	+	15.6723i	−1.49204	+	0.861428i	−0.999958	−	0.00912336i	$-0.997096\pi$
$331$	−27.1452	+	15.6723i	−1.49204	+	0.861428i	−0.492078	+	0.870551i	$0.663763\pi$
$332$	10.6678	+	6.15907i	0.585473	+	0.338023i
$333$	9.50101	−	9.77557i	0.520652	−	0.535698i
$334$	12.8250			0.701755
$335$	0.995362	+	1.72402i	0.0543825	+	0.0941932i
$336$	−14.1399	−	5.73933i	−0.771396	−	0.313106i
$337$			1.13840i			0.0620123i	0.999519	+	0.0310062i	$0.00987115\pi$
$337$			1.13840i			0.0620123i	−0.999519	+	0.0310062i	$0.990129\pi$
$338$	−9.36994	−	16.2292i	−0.509658	−	0.882753i
$339$	21.0010	−	16.3536i	1.14062	−	0.888204i
$340$	20.6835	−	35.8249i	1.12172	−	1.94288i
$341$	−7.73018			−0.418613
$342$	−27.8524	+	3.90950i	−1.50608	+	0.211402i
$343$	0.0695125			0.00375332
$344$	1.31028	−	2.26948i	0.0706458	−	0.122362i
$345$	4.57608	+	32.9443i	0.246368	+	1.77366i
$346$	20.2048	+	34.9958i	1.08622	+	1.88139i
$347$		−	32.4512i		−	1.74207i	−0.491219	−	0.871036i	$-0.663448\pi$
$347$		−	32.4512i		−	1.74207i	0.491219	−	0.871036i	$-0.336552\pi$
$348$	1.00848	+	7.26025i	0.0540600	+	0.389190i
$349$	−3.78030	−	6.54768i	−0.202355	−	0.350489i	0.746932	−	0.664901i	$-0.231526\pi$
$349$	−3.78030	−	6.54768i	−0.202355	−	0.350489i	−0.949287	+	0.314412i	$0.898193\pi$
$350$	33.3894			1.78474
$351$	−8.67341	−	6.36566i	−0.462952	−	0.339774i
$352$	34.2565	+	19.7780i	1.82587	+	1.05417i
$353$	−4.45738	+	2.57347i	−0.237242	+	0.136972i	−0.613909	−	0.789377i	$-0.710404\pi$
$353$	−4.45738	+	2.57347i	−0.237242	+	0.136972i	0.376666	+	0.926349i	$0.377070\pi$
$354$	−21.1893	+	16.5002i	−1.12620	+	0.876974i
$355$	−14.0661	+	8.12109i	−0.746553	+	0.431023i
$356$	−7.84049			−0.415545
$357$	20.7204	+	26.6089i	1.09664	+	1.40829i
$358$	−15.9971	+	27.7078i	−0.845472	+	1.46440i
$359$	5.46349	−	3.15435i	0.288352	−	0.166480i	−0.348846	−	0.937180i	$-0.613426\pi$
$359$	5.46349	−	3.15435i	0.288352	−	0.166480i	0.637198	+	0.770700i	$0.280093\pi$
$360$	8.51580	−	8.76189i	0.448822	−	0.461792i
$361$	18.2955	+	5.12599i	0.962919	+	0.269789i
$362$	8.29402	−	4.78856i	0.435924	−	0.251681i
$363$	−20.4719	+	15.9415i	−1.07450	+	0.836714i
$364$		−	20.3301i		−	1.06559i
$365$	−9.97292	+	5.75787i	−0.522006	+	0.301380i
$366$	−22.7805	+	17.7393i	−1.19076	+	0.927246i
$367$	7.42328			0.387492			0.193746	−	0.981052i	$-0.437936\pi$
$367$	7.42328			0.387492			0.193746	+	0.981052i	$0.437936\pi$
$368$		−	14.9570i		−	0.779686i
$369$	4.35769	+	4.23530i	0.226852	+	0.220481i
$370$	14.7829	−	25.6048i	0.768528	−	1.33113i
$371$	−33.6060			−1.74474
$372$	2.59425	−	6.39143i	0.134506	−	0.331380i
$373$	21.2019	+	12.2409i	1.09779	+	0.633811i	0.935641	−	0.352954i	$-0.114823\pi$
$373$	21.2019	+	12.2409i	1.09779	+	0.633811i	0.162153	+	0.986766i	$0.448156\pi$
$374$	−28.5435	−	49.4389i	−1.47595	−	2.55642i
$375$	−1.67159	+	4.11828i	−0.0863205	+	0.212667i
$376$			4.61613i			0.238059i
$377$	2.88977	−	1.66841i	0.148831	−	0.0859274i
$378$	16.8129	+	38.2572i	0.864760	+	1.96774i
$379$		−	27.3088i		−	1.40276i	−0.712788	−	0.701380i	$-0.752568\pi$
$379$		−	27.3088i		−	1.40276i	0.712788	−	0.701380i	$-0.247432\pi$
$380$	−32.0661	+	13.0690i	−1.64496	+	0.670428i
$381$	−2.08501	−	2.67755i	−0.106819	−	0.137175i
$382$		−	50.0810i		−	2.56237i
$383$	−1.12796			−0.0576362			−0.0288181	−	0.999585i	$-0.509174\pi$
$383$	−1.12796			−0.0576362			−0.0288181	+	0.999585i	$0.509174\pi$
$384$	−13.9978	+	10.9001i	−0.714321	+	0.556244i
$385$	28.8284	−	49.9322i	1.46923	−	2.54478i
$386$	42.0398	+	24.2717i	2.13977	+	1.23540i
$387$	5.61843	−	1.59155i	0.285601	−	0.0809030i
$388$			14.3395i			0.727976i
$389$		−	1.96440i		−	0.0995991i	−0.998759	−	0.0497995i	$-0.984142\pi$
$389$		−	1.96440i		−	0.0995991i	0.998759	−	0.0497995i	$-0.0158582\pi$
$390$	−21.6210	−	8.77585i	−1.09482	−	0.444382i
$391$	−16.5273	+	28.6261i	−0.835821	+	1.44768i
$392$	−4.69953	+	8.13982i	−0.237362	+	0.411123i
$393$	8.49356	−	20.9255i	0.428443	−	1.05555i
$394$	−3.91204	−	2.25862i	−0.197086	−	0.113787i
$395$	15.8658	−	27.4803i	0.798293	−	1.38268i
$396$	−10.9440	−	38.6340i	−0.549955	−	1.94143i
$397$	16.7936	+	29.0874i	0.842848	+	1.45985i	0.887477	+	0.460851i	$0.152456\pi$
$397$	16.7936	+	29.0874i	0.842848	+	1.45985i	−0.0446298	+	0.999004i	$0.514211\pi$
$398$	−14.6625	−	25.3963i	−0.734966	−	1.27300i
$399$	−0.0404700	−	28.2301i	−0.00202604	−	1.41327i
$400$	−4.89136	+	8.47208i	−0.244568	+	0.423604i
$401$	6.15328			0.307280			0.153640	−	0.988127i	$-0.450900\pi$
$401$	6.15328			0.307280			0.153640	+	0.988127i	$0.450900\pi$
$402$	−0.921972	+	2.27145i	−0.0459838	+	0.113290i
$403$	−3.14011			−0.156420
$404$	3.66856	−	2.11805i	0.182518	−	0.105377i
$405$	27.2156	−	0.775411i	1.35236	−	0.0385305i
$406$	−12.9608			−0.643231
$407$	−11.5806	−	20.0581i	−0.574028	−	0.994245i
$408$	12.0273	−	1.67063i	0.595438	−	0.0827086i
$409$	3.24396	−	1.87290i	0.160404	−	0.0926091i	−0.417649	−	0.908608i	$-0.637146\pi$
$409$	3.24396	−	1.87290i	0.160404	−	0.0926091i	0.578053	+	0.815999i	$0.303813\pi$
$410$	11.4139	+	6.58984i	0.563694	+	0.325449i
$411$	7.46261	−	18.3856i	0.368104	−	0.906893i
$412$		−	27.6362i		−	1.36154i
$413$	−13.4780	−	23.3445i	−0.663208	−	1.14871i
$414$	−28.5463	+	29.3712i	−1.40297	+	1.44351i
$415$	7.09546	+	12.2897i	0.348302	+	0.603278i
$416$	13.9155	+	8.03410i	0.682262	+	0.393904i
$417$	4.41398	+	31.7773i	0.216154	+	1.55614i
$418$	−6.50666	+	47.3408i	−0.318251	+	2.31552i
$419$	−3.16792	−	1.82900i	−0.154763	−	0.0893526i	0.420618	−	0.907238i	$-0.361813\pi$
$419$	−3.16792	−	1.82900i	−0.154763	−	0.0893526i	−0.575382	+	0.817885i	$0.695146\pi$
$420$	31.6099	+	40.5930i	1.54240	+	1.98074i
$421$	−6.40584	−	3.69841i	−0.312202	−	0.180250i	0.335710	−	0.941966i	$-0.391024\pi$
$421$	−6.40584	−	3.69841i	−0.312202	−	0.180250i	−0.647911	+	0.761716i	$0.724357\pi$
$422$	−51.0115	−	29.4515i	−2.48320	−	1.43368i
$423$	−7.16917	+	7.37634i	−0.348577	+	0.358650i
$424$	−6.04996	+	10.4788i	−0.293812	+	0.508898i
$425$	18.7231	−	10.8098i	0.908204	−	0.524352i
$426$	−18.5326	−	7.52230i	−0.897908	−	0.364457i
$427$	−14.4901	−	25.0976i	−0.701226	−	1.21456i
$428$	−13.5547	−	23.4775i	−0.655193	−	1.13483i
$429$	−14.4224	+	11.2308i	−0.696320	+	0.542226i
$430$	10.9683	−	6.33253i	0.528936	−	0.305382i
$431$	5.78011	−	10.0114i	0.278418	−	0.482234i	−0.692574	−	0.721347i	$-0.743523\pi$
$431$	5.78011	−	10.0114i	0.278418	−	0.482234i	0.970992	+	0.239113i	$0.0768566\pi$
$432$	−12.1702	−	1.33845i	−0.585540	−	0.0643960i
$433$	−2.95790	−	1.70774i	−0.142148	−	0.0820689i	0.427240	−	0.904138i	$-0.359486\pi$
$433$	−2.95790	−	1.70774i	−0.142148	−	0.0820689i	−0.569387	+	0.822070i	$0.692819\pi$
$434$	10.5627	+	6.09836i	0.507025	+	0.292731i
$435$	−3.17588	+	7.82439i	−0.152272	+	0.375151i
$436$	13.3928	+	7.73231i	0.641397	+	0.370311i
$437$	25.6226	−	10.4429i	1.22570	−	0.499552i
$438$	−13.1397	−	5.33332i	−0.627837	−	0.254836i
$439$	21.1340	+	12.2017i	1.00867	+	0.582355i	0.910802	−	0.412844i	$-0.135465\pi$
$439$	21.1340	+	12.2017i	1.00867	+	0.582355i	0.0978674	+	0.995199i	$0.468798\pi$
$440$	−10.3797	−	17.9782i	−0.494834	−	0.857078i
$441$	−20.1513	+	5.70833i	−0.959587	+	0.271825i
$442$	−11.5948	−	20.0828i	−0.551509	−	0.955241i
$443$		−	38.9864i		−	1.85230i	−0.377157	−	0.926150i	$-0.623098\pi$
$443$		−	38.9864i		−	1.85230i	0.377157	−	0.926150i	$-0.376902\pi$
$444$	20.4708	−	2.84347i	0.971502	−	0.134945i
$445$	−7.82239	−	4.51626i	−0.370817	−	0.214091i
$446$	−4.30245	+	2.48402i	−0.203727	+	0.117622i
$447$	−4.74481	+	11.6897i	−0.224422	+	0.552905i
$448$	−22.3953	−	38.7897i	−1.05808	−	1.83264i
$449$	−26.0848			−1.23102			−0.615509	−	0.788130i	$-0.711050\pi$
$449$	−26.0848			−1.23102			−0.615509	+	0.788130i	$0.711050\pi$
$450$	25.7747	−	7.30127i	1.21503	−	0.344185i
$451$	8.94139	−	5.16231i	0.421034	−	0.243084i
$452$	40.3544			1.89811
$453$	−3.78046	+	0.525121i	−0.177622	+	0.0246723i
$454$	−25.2666			−1.18582
$455$	11.7105	−	20.2832i	0.548997	−	0.950891i
$456$	−8.80984	−	5.06954i	−0.412559	−	0.237403i
$457$	8.91236	+	15.4367i	0.416903	+	0.722096i	0.995626	−	0.0934274i	$-0.0297823\pi$
$457$	8.91236	+	15.4367i	0.416903	+	0.722096i	−0.578724	+	0.815524i	$0.696449\pi$
$458$	−7.13318	−	12.3550i	−0.333312	−	0.577313i
$459$	21.8136	+	16.0096i	1.01817	+	0.747264i
$460$	−25.2131	+	43.6703i	−1.17557	+	2.03614i
$461$	30.8452	+	17.8085i	1.43660	+	0.829424i	0.997612	−	0.0690673i	$-0.0220023\pi$
$461$	30.8452	+	17.8085i	1.43660	+	0.829424i	0.438992	+	0.898491i	$0.355336\pi$
$462$	70.3249	−	9.76840i	3.27181	−	0.454467i
$463$	−5.50447	+	9.53403i	−0.255815	+	0.443084i	−0.965116	−	0.261821i	$-0.915677\pi$
$463$	−5.50447	+	9.53403i	−0.255815	+	0.443084i	0.709302	+	0.704905i	$0.249010\pi$
$464$	1.89868	−	3.28861i	0.0881440	−	0.152670i
$465$	6.26984	−	4.88234i	0.290757	−	0.226413i
$466$		−	7.79537i		−	0.361113i
$467$		−	23.7561i		−	1.09930i	−0.835394	−	0.549651i	$-0.814761\pi$
$467$		−	23.7561i		−	1.09930i	0.835394	−	0.549651i	$-0.185239\pi$
$468$	−4.44560	−	15.6937i	−0.205498	−	0.725441i
$469$	−2.13091	−	1.23028i	−0.0983963	−	0.0568091i
$470$	−11.1547	+	19.3206i	−0.514530	+	0.891192i
$471$	21.7814	+	8.84096i	1.00363	+	0.407370i
$472$	−9.70556			−0.446734
$473$		−	9.92149i		−	0.456190i
$474$	38.7035	−	5.37606i	1.77771	−	0.246931i
$475$	−17.9286	−	2.46415i	−0.822618	−	0.113063i
$476$			51.1301i			2.34355i
$477$	−25.9419	+	7.34864i	−1.18780	+	0.336471i
$478$	−28.2677	+	16.3203i	−1.29293	+	0.746475i
$479$			41.4152i			1.89231i	0.323719	+	0.946153i	$0.395067\pi$
$479$			41.4152i			1.89231i	−0.323719	+	0.946153i	$0.604933\pi$
$480$	−40.2766	+	5.59457i	−1.83837	+	0.255356i
$481$	−4.70420	−	8.14792i	−0.214493	−	0.371513i
$482$	45.6784	+	26.3724i	2.08059	+	1.20123i
$483$	−25.2581	−	32.4361i	−1.14928	−	1.47589i
$484$	−39.3376			−1.78807
$485$	−8.25978	+	14.3064i	−0.375057	+	0.649618i
$486$	21.3443	+	25.8559i	0.968197	+	1.17285i
$487$			15.0755i			0.683134i	0.939857	+	0.341567i	$0.110958\pi$
$487$			15.0755i			0.683134i	−0.939857	+	0.341567i	$0.889042\pi$
$488$	−10.4344			−0.472343
$489$	−4.81648	−	1.95499i	−0.217809	−	0.0884076i
$490$	−39.3393	+	22.7126i	−1.77717	+	1.02605i
$491$			42.3091i			1.90938i	0.297597	+	0.954691i	$0.403815\pi$
$491$			42.3091i			1.90938i	−0.297597	+	0.954691i	$0.596185\pi$
$492$	1.26755	+	9.12535i	0.0571454	+	0.411403i
$493$	−7.26775	+	4.19603i	−0.327323	+	0.188980i
$494$	−2.64310	+	19.2306i	−0.118919	+	0.865223i
$495$	11.3351	−	44.8487i	0.509477	−	2.01580i
$496$	−3.09475	+	1.78675i	−0.138958	+	0.0802276i
$497$	10.0378	−	17.3859i	0.450256	−	0.779866i
$498$	−6.57229	+	16.1921i	−0.294512	+	0.725585i
$499$	43.2590			1.93654			0.968268	−	0.249912i	$-0.0804018\pi$
$499$	43.2590			1.93654			0.968268	+	0.249912i	$0.0804018\pi$
$500$	−5.83564	+	3.36921i	−0.260978	+	0.150676i
$501$	1.42096	+	10.2299i	0.0634840	+	0.457036i
$502$	8.02766	−	4.63477i	0.358292	−	0.206860i
$503$	5.29464	+	3.05686i	0.236077	+	0.136299i	0.613372	−	0.789794i	$-0.289813\pi$
$503$	5.29464	+	3.05686i	0.236077	+	0.136299i	−0.377296	+	0.926093i	$0.623146\pi$
$504$	−3.70057	+	14.6417i	−0.164837	+	0.652194i
$505$	4.88012			0.217163
$506$	34.7944	+	60.2657i	1.54680	+	2.67914i
$507$	11.9070	−	9.27203i	0.528809	−	0.411785i
$508$		−	5.14502i		−	0.228273i
$509$	13.8830	+	24.0460i	0.615353	+	1.06582i	0.990322	+	0.138785i	$0.0443198\pi$
$509$	13.8830	+	24.0460i	0.615353	+	1.06582i	−0.374970	+	0.927037i	$0.622347\pi$
$510$	54.3766	+	22.0712i	2.40783	+	0.977329i
$511$	7.11680	−	12.3267i	0.314829	−	0.545299i
$512$	24.6304			1.08852
$513$	−6.20433	−	21.7832i	−0.273928	−	0.961750i
$514$	54.3147			2.39572
$515$	15.9189	−	27.5724i	0.701472	−	1.21498i
$516$	8.20323	+	3.32965i	0.361127	+	0.146580i
$517$	8.73834	+	15.1353i	0.384312	+	0.665648i
$518$			36.5438i			1.60564i
$519$	−25.6757	+	19.9937i	−1.12704	+	0.877627i
$520$	−4.21640	−	7.30302i	−0.184901	−	0.320258i
$521$	−3.72919			−0.163379			−0.0816894	−	0.996658i	$-0.526032\pi$
$521$	−3.72919			−0.163379			−0.0816894	+	0.996658i	$0.526032\pi$
$522$	−10.0050	+	2.83413i	−0.437905	+	0.124047i
$523$	−38.8829	−	22.4491i	−1.70023	−	0.981629i	−0.945516	−	0.325575i	$-0.894442\pi$
$523$	−38.8829	−	22.4491i	−1.70023	−	0.981629i	−0.754715	−	0.656053i	$-0.772225\pi$
$524$	29.6516	−	17.1194i	1.29534	−	0.747864i
$525$	3.69941	+	26.6329i	0.161455	+	1.16236i
$526$	37.5953	−	21.7057i	1.63924	−	0.946413i
$527$	7.89736			0.344015
$528$	−7.82362	+	19.2750i	−0.340479	+	0.838836i
$529$	8.64667	−	14.9765i	0.375942	−	0.651151i
$530$	−50.6437	+	29.2391i	−2.19982	+	1.27007i
$531$	−15.5090	−	15.0734i	−0.673033	−	0.654130i
$532$	26.2474	−	33.8064i	1.13797	−	1.46569i
$533$	3.63213	−	2.09701i	0.157325	−	0.0908315i
$534$	−1.53032	−	11.0171i	−0.0662234	−	0.476757i
$535$		−	31.2311i		−	1.35024i
$536$	−0.767239	+	0.442966i	−0.0331397	+	0.0191332i
$537$	−23.8734	−	9.69010i	−1.03021	−	0.418159i
$538$	12.5678			0.541835
$539$			35.5849i			1.53275i
$540$	33.2775	+	24.4233i	1.43204	+	1.05101i
$541$	−16.3200	+	28.2670i	−0.701651	+	1.21530i	0.266236	+	0.963908i	$0.414220\pi$
$541$	−16.3200	+	28.2670i	−0.701651	+	1.21530i	−0.967887	+	0.251387i	$0.919113\pi$
$542$	−32.4333			−1.39313
$543$	4.73852	+	6.08514i	0.203349	+	0.261138i
$544$	−34.9973	−	20.2057i	−1.50050	−	0.866313i
$545$	8.90789	+	15.4289i	0.381572	+	0.660903i
$546$	28.5670	−	3.96807i	1.22256	−	0.169818i
$547$		−	10.2878i		−	0.439874i	−0.975514	−	0.219937i	$-0.929415\pi$
$547$		−	10.2878i		−	0.439874i	0.975514	−	0.219937i	$-0.0705851\pi$
$548$	26.0525	−	15.0414i	1.11291	−	0.642539i
$549$	−16.6736	−	16.2054i	−0.711614	−	0.691628i
$550$		−	45.5151i		−	1.94077i
$551$	6.95933	+	0.956509i	0.296477	+	0.0407487i
$552$	−14.6612	+	2.03649i	−0.624021	+	0.0866788i
$553$			39.2206i			1.66783i
$554$	34.5080			1.46610
$555$	22.0615	+	8.95464i	0.936457	+	0.380103i
$556$	−24.3199	+	42.1234i	−1.03140	+	1.78643i
$557$	1.55437	+	0.897418i	0.0658609	+	0.0380248i	0.532569	−	0.846387i	$-0.321227\pi$
$557$	1.55437	+	0.897418i	0.0658609	+	0.0380248i	−0.466708	+	0.884411i	$0.654560\pi$
$558$	9.48731	+	2.39784i	0.401630	+	0.101509i
$559$		−	4.03025i		−	0.170462i
$560$		−	26.6535i		−	1.12632i
$561$	36.2722	−	28.2453i	1.53141	−	1.19252i
$562$	18.2774	−	31.6573i	0.770984	−	1.33538i
$563$	2.51042	−	4.34817i	0.105801	−	0.183254i	−0.808264	−	0.588820i	$-0.799593\pi$
$563$	2.51042	−	4.34817i	0.105801	−	0.183254i	0.914065	+	0.405567i	$0.132926\pi$
$564$	−15.4466	+	2.14560i	−0.650421	+	0.0903460i
$565$	40.2612	+	23.2448i	1.69380	+	0.977918i
$566$	16.6995	−	28.9244i	0.701932	−	1.21578i
$567$	−28.6529	+	17.6495i	−1.20331	+	0.741208i
$568$	−3.61413	−	6.25985i	−0.151645	−	0.262657i
$569$	−10.4266	−	18.0595i	−0.437107	−	0.757092i	0.560358	−	0.828251i	$-0.310664\pi$
$569$	−10.4266	−	18.0595i	−0.437107	−	0.757092i	−0.997465	+	0.0711585i	$0.977330\pi$
$570$	−24.6228	−	42.5070i	−1.03133	−	1.78042i
$571$	−18.2645	+	31.6350i	−0.764345	+	1.32388i	0.176248	+	0.984346i	$0.443604\pi$
$571$	−18.2645	+	31.6350i	−0.764345	+	1.32388i	−0.940592	+	0.339538i	$0.889729\pi$
$572$	−27.7132			−1.15875
$573$	39.9469	−	5.54877i	1.66881	−	0.231803i
$574$	−16.2903			−0.679942
$575$	−22.8234	+	13.1771i	−0.951800	+	0.549522i
$576$	−25.7700	−	25.0463i	−1.07375	−	1.04359i
$577$	−13.8317			−0.575822			−0.287911	−	0.957657i	$-0.592961\pi$
$577$	−13.8317			−0.575822			−0.287911	+	0.957657i	$0.592961\pi$
$578$	10.8790	+	18.8430i	0.452508	+	0.783767i
$579$	−14.7024	+	36.2221i	−0.611010	+	1.50534i
$580$	−11.0872	+	6.40123i	−0.460373	+	0.265796i
$581$	−15.1902	−	8.77008i	−0.630197	−	0.363844i
$582$	−20.1492	+	2.79880i	−0.835211	+	0.116014i
$583$			45.8104i			1.89727i
$584$	−2.56242	−	4.43824i	−0.106034	−	0.183656i
$585$	4.60450	−	18.2182i	0.190373	−	0.753230i
$586$	−32.5509	−	56.3798i	−1.34467	−	2.32903i
$587$	−3.05306	−	1.76269i	−0.126013	−	0.0727539i	0.435668	−	0.900107i	$-0.356512\pi$
$587$	−3.05306	−	1.76269i	−0.126013	−	0.0727539i	−0.561682	+	0.827353i	$0.689845\pi$
$588$	−29.4221	−	11.9423i	−1.21335	−	0.492492i
$589$	−5.22161	−	4.05407i	−0.215153	−	0.167045i
$590$	−40.6221	−	23.4532i	−1.67239	−	0.965553i
$591$	1.36814	−	3.37067i	0.0562777	−	0.138651i
$592$	−9.27247	−	5.35347i	−0.381096	−	0.220026i
$593$	3.25664	+	1.88022i	0.133734	+	0.0772113i	0.565374	−	0.824834i	$-0.308732\pi$
$593$	3.25664	+	1.88022i	0.133734	+	0.0772113i	−0.431640	+	0.902046i	$0.642065\pi$
$594$	52.1507	−	22.9186i	2.13977	−	0.940363i
$595$	−29.4519	+	51.0121i	−1.20741	+	2.09129i
$596$	−16.5645	+	9.56351i	−0.678508	+	0.391737i
$597$	18.6327	−	14.5093i	0.762585	−	0.593827i
$598$	14.1340	+	24.4808i	0.577983	+	1.00110i
$599$	−1.34996	−	2.33820i	−0.0551580	−	0.0955365i	0.837128	−	0.547007i	$-0.184233\pi$
$599$	−1.34996	−	2.33820i	−0.0551580	−	0.0955365i	−0.892286	+	0.451471i	$0.850900\pi$
$600$	8.97052	+	3.64109i	0.366220	+	0.148647i
$601$	3.51336	−	2.02844i	0.143313	−	0.0827417i	−0.426629	−	0.904427i	$-0.640299\pi$
$601$	3.51336	−	2.02844i	0.143313	−	0.0827417i	0.569942	+	0.821685i	$0.306966\pi$
$602$	−7.82709	+	13.5569i	−0.319008	+	0.552539i
$603$	−1.91397	−	0.483739i	−0.0779427	−	0.0196994i
$604$	−5.01131	−	2.89328i	−0.203907	−	0.117726i
$605$	−39.2468	−	22.6592i	−1.59561	−	0.921226i
$606$	3.69222	+	4.74150i	0.149986	+	0.192610i
$607$	4.17611	+	2.41108i	0.169503	+	0.0978627i	0.582352	−	0.812937i	$-0.302133\pi$
$607$	4.17611	+	2.41108i	0.169503	+	0.0978627i	−0.412848	+	0.910800i	$0.635466\pi$
$608$	12.7672	+	31.3254i	0.517777	+	1.27041i
$609$	−1.43600	−	10.3381i	−0.0581897	−	0.418921i
$610$	−43.6727	−	25.2144i	−1.76826	−	1.02090i
$611$	3.54964	+	6.14817i	0.143603	+	0.248728i
$612$	11.1807	+	39.4695i	0.451951	+	1.59546i
$613$	4.89396	+	8.47658i	0.197665	+	0.342366i	0.947771	−	0.318952i	$-0.103331\pi$
$613$	4.89396	+	8.47658i	0.197665	+	0.342366i	−0.750106	+	0.661318i	$0.769997\pi$
$614$		−	60.6907i		−	2.44928i
$615$	−3.99174	+	9.83441i	−0.160963	+	0.396562i
$616$	22.2213	+	12.8295i	0.895322	+	0.516914i
$617$	3.36966	−	1.94547i	0.135657	−	0.0783219i	−0.430635	−	0.902526i	$-0.641710\pi$
$617$	3.36966	−	1.94547i	0.135657	−	0.0783219i	0.566293	+	0.824204i	$0.308377\pi$
$618$	38.8332	−	5.39407i	1.56210	−	0.216981i
$619$	−9.13436	−	15.8212i	−0.367141	−	0.635907i	0.621976	−	0.783036i	$-0.286330\pi$
$619$	−9.13436	−	15.8212i	−0.367141	−	0.635907i	−0.989117	+	0.147129i	$0.952997\pi$
$620$	12.0478			0.483850
$621$	−26.5906	−	19.5156i	−1.06704	−	0.783135i
$622$	−35.5355	+	20.5164i	−1.42484	+	0.822634i
$623$	11.1643			0.447289
$624$	−3.17807	+	7.82978i	−0.127225	+	0.313442i
$625$	−28.5217			−1.14087
$626$	12.0841	−	20.9302i	0.482976	−	0.836540i
$627$	−38.4822	+	0.0551671i	−1.53683	+	0.00220316i
$628$	17.8196	+	30.8645i	0.711079	+	1.23163i
$629$	11.8310	+	20.4919i	0.471734	+	0.817067i
$630$	−50.8699	+	52.3398i	−2.02670	+	2.08527i
$631$	−7.88091	+	13.6501i	−0.313734	+	0.543404i	−0.979168	−	0.203054i	$-0.934913\pi$
$631$	−7.88091	+	13.6501i	−0.313734	+	0.543404i	0.665433	+	0.746457i	$0.268247\pi$
$632$	12.2296	+	7.06073i	0.486465	+	0.280861i
$633$	17.8400	−	43.9522i	0.709076	−	1.74694i
$634$	0.404417	−	0.700470i	0.0160614	−	0.0278192i
$635$	2.96362	−	5.13314i	0.117608	−	0.203703i
$636$	−37.8767	−	15.3740i	−1.50191	−	0.609618i
$637$			14.4551i			0.572732i
$638$			17.6676i			0.699466i
$639$	3.94679	−	15.6159i	0.156133	−	0.617756i
$640$	−26.8352	−	15.4933i	−1.06076	−	0.612427i
$641$	−3.93679	+	6.81871i	−0.155494	+	0.269323i	−0.933239	−	0.359257i	$-0.883030\pi$
$641$	−3.93679	+	6.81871i	−0.155494	+	0.269323i	0.777745	+	0.628580i	$0.216363\pi$
$642$	30.3439	−	23.6289i	1.19758	−	0.932558i
$643$	28.1800			1.11131			0.555656	−	0.831413i	$-0.312467\pi$
$643$	28.1800			1.11131			0.555656	+	0.831413i	$0.312467\pi$
$644$		−	62.3274i		−	2.45604i
$645$	6.26636	+	8.04717i	0.246738	+	0.316857i
$646$	6.64738	−	48.3647i	0.261538	−	1.90288i
$647$		−	41.2832i		−	1.62301i	−0.584346	−	0.811504i	$-0.698649\pi$
$647$		−	41.2832i		−	1.62301i	0.584346	−	0.811504i	$-0.301351\pi$
$648$	0.345081	+	12.1118i	0.0135561	+	0.475795i
$649$	−31.8224	+	18.3726i	−1.24914	+	0.721189i
$650$		−	18.4889i		−	0.725194i
$651$	−3.69403	+	9.10095i	−0.144781	+	0.356694i
$652$	−3.94042	−	6.82501i	−0.154319	−	0.267288i
$653$	−30.9349	−	17.8602i	−1.21057	−	0.698925i	−0.247690	−	0.968839i	$-0.579671\pi$
$653$	−30.9349	−	17.8602i	−1.21057	−	0.698925i	−0.962884	+	0.269914i	$0.913005\pi$
$654$	−8.25109	+	20.3281i	−0.322643	+	0.794893i
$655$	39.4443			1.54121
$656$	2.38643	−	4.13342i	0.0931746	−	0.161383i
$657$	2.79828	−	11.0717i	0.109171	−	0.431948i
$658$		−	27.5748i		−	1.07498i
$659$	33.0448			1.28724			0.643621	−	0.765344i	$-0.277431\pi$
$659$	33.0448			1.28724			0.643621	+	0.765344i	$0.277431\pi$
$660$	55.3348	−	43.0893i	2.15390	−	1.67725i
$661$	38.6931	−	22.3395i	1.50499	−	0.868905i	0.505004	−	0.863117i	$-0.331491\pi$
$661$	38.6931	−	22.3395i	1.50499	−	0.868905i	0.999983	−	0.00578816i	$-0.00184244\pi$
$662$		−	67.4161i		−	2.62020i
$663$	14.7343	−	11.4736i	0.572233	−	0.445600i
$664$	−5.46928	+	3.15769i	−0.212249	+	0.122542i
$665$	45.6599	−	18.6094i	1.77061	−	0.721642i
$666$	7.99105	+	28.2097i	0.309647	+	1.09310i
$667$	8.85934	−	5.11494i	0.343035	−	0.198051i
$668$	−7.82916	+	13.5605i	−0.302919	+	0.524672i
$669$	−2.45807	−	3.15662i	−0.0950344	−	0.122042i
$670$	−4.28166			−0.165415
$671$	−34.2121	+	19.7524i	−1.32074	+	0.762531i
$672$	39.6553	−	30.8797i	1.52974	−	1.19121i
$673$	15.8318	−	9.14047i	0.610269	−	0.352339i	−0.162802	−	0.986659i	$-0.552053\pi$
$673$	15.8318	−	9.14047i	0.610269	−	0.352339i	0.773071	+	0.634320i	$0.218720\pi$
$674$	−2.12043	−	1.22423i	−0.0816760	−	0.0471556i
$675$	8.67956	+	19.7501i	0.334076	+	0.760182i
$676$	22.8798			0.879994
$677$	12.5993	+	21.8227i	0.484232	+	0.838715i	0.999836	−	0.0181123i	$-0.00576565\pi$
$677$	12.5993	+	21.8227i	0.484232	+	0.838715i	−0.515604	+	0.856827i	$0.672432\pi$
$678$	7.87643	+	56.7042i	0.302493	+	2.17771i
$679$		−	20.4184i		−	0.783586i
$680$	10.6042	+	18.3670i	0.406653	+	0.704343i
$681$	−2.79944	−	20.1538i	−0.107275	−	0.772296i
$682$	8.31305	−	14.3986i	0.318323	−	0.551352i
$683$	−13.1758			−0.504159			−0.252080	−	0.967706i	$-0.581114\pi$
$683$	−13.1758			−0.504159			−0.252080	+	0.967706i	$0.581114\pi$
$684$	12.8690	−	31.8361i	0.492059	−	1.21729i
$685$	34.6565			1.32416
$686$	−0.0747538	+	0.129477i	−0.00285412	+	0.00494347i
$687$	9.06461	−	7.05864i	0.345837	−	0.269304i
$688$	−2.29325	−	3.97203i	−0.0874294	−	0.151432i
$689$			18.6089i			0.708941i
$690$	−66.2847	−	26.9047i	−2.52342	−	1.02424i
$691$	25.6729	+	44.4667i	0.976641	+	1.69159i	0.674409	+	0.738358i	$0.264399\pi$
$691$	25.6729	+	44.4667i	0.976641	+	1.69159i	0.302233	+	0.953234i	$0.402268\pi$
$692$	−49.3369			−1.87551
$693$	15.5834	+	55.0121i	0.591966	+	2.08974i
$694$	60.4452	+	34.8981i	2.29447	+	1.32471i
$695$	−48.5276	+	28.0174i	−1.84076	+	1.06276i
$696$	−3.48209	−	1.41336i	−0.131988	−	0.0535734i
$697$	−9.13477	+	5.27396i	−0.346004	+	0.199766i
$698$	16.2614			0.615502
$699$	6.21794	−	0.863696i	0.235184	−	0.0326680i
$700$	−20.3828	+	35.3041i	−0.770398	+	1.33437i
$701$	25.4463	−	14.6914i	0.961092	−	0.554887i	0.0645833	−	0.997912i	$-0.479428\pi$
$701$	25.4463	−	14.6914i	0.961092	−	0.554887i	0.896509	+	0.443025i	$0.146095\pi$
$702$	21.1844	−	9.30988i	0.799554	−	0.351379i
$703$	2.69695	−	19.6223i	0.101717	−	0.740071i
$704$	−52.8766	+	30.5283i	−1.99286	+	1.15058i
$705$	−16.6469	−	6.75689i	−0.626958	−	0.254479i
$706$		−	11.0700i		−	0.416626i
$707$	−5.22378	+	3.01595i	−0.196460	+	0.113426i
$708$	−4.51119	−	32.4771i	−0.169541	−	1.22056i
$709$	46.1959			1.73492			0.867462	−	0.497504i	$-0.165750\pi$
$709$	46.1959			1.73492			0.867462	+	0.497504i	$0.165750\pi$
$710$		−	34.9337i		−	1.31104i
$711$	8.57639	+	30.2760i	0.321640	+	1.13544i
$712$	2.00987	−	3.48119i	0.0753230	−	0.130463i
$713$	−9.62684			−0.360528
$714$	−71.8459	+	9.97966i	−2.68876	+	0.373479i
$715$	−27.6493	−	15.9633i	−1.03402	−	0.596994i
$716$	−19.5311	−	33.8289i	−0.729912	−	1.26424i
$717$	−16.1498	−	20.7394i	−0.603126	−	0.774526i
$718$			13.5688i			0.506382i
$719$	−5.87831	+	3.39385i	−0.219224	+	0.126569i	−0.605591	−	0.795776i	$-0.707063\pi$
$719$	−5.87831	+	3.39385i	−0.219224	+	0.126569i	0.386367	+	0.922345i	$0.373730\pi$
$720$	−5.82834	−	20.5750i	−0.217210	−	0.766785i
$721$			39.3520i			1.46555i
$722$	−29.2229	+	28.5655i	−1.08756	+	1.06310i
$723$	−15.9749	+	39.3572i	−0.594113	+	1.46371i
$724$			11.6929i			0.434562i
$725$	−6.69093			−0.248495
$726$	−7.67798	−	55.2755i	−0.284957	−	2.05147i
$727$	−1.33747	+	2.31657i	−0.0496040	+	0.0859167i	−0.889761	−	0.456426i	$-0.849129\pi$
$727$	−1.33747	+	2.31657i	−0.0496040	+	0.0859167i	0.840157	+	0.542343i	$0.182463\pi$
$728$	9.02663	+	5.21152i	0.334549	+	0.193152i
$729$	−18.2590	+	19.8899i	−0.676259	+	0.736664i
$730$		−	24.7681i		−	0.916707i
$731$			10.1361i			0.374896i
$732$	−4.84996	−	34.9160i	−0.179260	−	1.29053i
$733$	11.4965	−	19.9126i	0.424634	−	0.735488i	−0.571752	−	0.820426i	$-0.693736\pi$
$733$	11.4965	−	19.9126i	0.424634	−	0.735488i	0.996386	+	0.0849388i	$0.0270695\pi$
$734$	−7.98301	+	13.8270i	−0.294658	+	0.510363i
$735$	−22.4752	−	28.8624i	−0.829011	−	1.06460i
$736$	42.6615	+	24.6307i	1.57253	+	0.907898i
$737$	−1.67707	+	2.90477i	−0.0617757	+	0.106999i
$738$	−12.5751	+	3.56220i	−0.462897	+	0.131126i
$739$	−14.6521	−	25.3781i	−0.538985	−	0.933550i	−0.998959	−	0.0456175i	$-0.985474\pi$
$739$	−14.6521	−	25.3781i	−0.538985	−	0.933550i	0.459974	−	0.887933i	$-0.347859\pi$
$740$	18.0487	+	31.2613i	0.663485	+	1.14919i
$741$	−15.6320	+	0.0224097i	−0.574257	+	0.000823241i
$742$	36.1400	−	62.5962i	1.32674	−	2.29798i
$743$	13.5165			0.495872			0.247936	−	0.968776i	$-0.420248\pi$
$743$	13.5165			0.495872			0.247936	+	0.968776i	$0.420248\pi$
$744$	2.17279	+	2.79026i	0.0796582	+	0.102296i
$745$	−22.0350			−0.807300
$746$	−45.6011	+	26.3278i	−1.66958	+	0.963930i
$747$	−13.6437	−	3.44835i	−0.499198	−	0.126168i
$748$	69.6986			2.54843
$749$	19.3010	+	33.4303i	0.705243	+	1.22152i
$750$	−5.87328	−	7.54238i	−0.214462	−	0.275409i
$751$	−27.4491	+	15.8478i	−1.00163	+	0.578293i	−0.908731	−	0.417382i	$-0.862948\pi$
$751$	−27.4491	+	15.8478i	−1.00163	+	0.578293i	−0.0929020	+	0.995675i	$0.529614\pi$
$752$	6.99672	+	4.03956i	0.255144	+	0.147308i
$753$	4.58634	+	5.88971i	0.167135	+	0.214633i
$754$			7.17683i			0.261365i
$755$	−3.33316	−	5.77321i	−0.121306	−	0.210109i
$756$	−50.7146	−	5.57745i	−1.84447	−	0.202850i
$757$	−2.36484	−	4.09603i	−0.0859517	−	0.148873i	0.819845	−	0.572586i	$-0.194060\pi$
$757$	−2.36484	−	4.09603i	−0.0859517	−	0.148873i	−0.905796	+	0.423713i	$0.860726\pi$
$758$	50.8668	+	29.3679i	1.84756	+	1.06669i
$759$	−44.2156	+	34.4308i	−1.60493	+	1.24976i
$760$	2.41729	−	17.5876i	0.0876843	−	0.637969i
$761$	0.577494	+	0.333416i	0.0209342	+	0.0120863i	0.510431	−	0.859919i	$-0.329486\pi$
$761$	0.577494	+	0.333416i	0.0209342	+	0.0120863i	−0.489496	+	0.872005i	$0.662819\pi$
$762$	7.22956	−	1.00421i	0.261899	−	0.0363788i
$763$	−19.0704	−	11.0103i	−0.690393	−	0.398599i
$764$	52.9529	+	30.5724i	1.91577	+	1.10607i
$765$	−11.5803	+	45.8187i	−0.418686	+	1.65658i
$766$	1.21301	−	2.10100i	0.0438279	−	0.0759122i
$767$	−12.9267	+	7.46324i	−0.466757	+	0.269482i
$768$	0.459212	+	3.30597i	0.0165704	+	0.119294i
$769$	−11.9041	−	20.6185i	−0.429273	−	0.743523i	0.567536	−	0.823349i	$-0.307897\pi$
$769$	−11.9041	−	20.6185i	−0.429273	−	0.743523i	−0.996809	+	0.0798259i	$0.974564\pi$
$770$	62.0041	+	107.394i	2.23447	+	3.87022i
$771$	6.01785	+	43.3239i	0.216728	+	1.56027i
$772$	−51.3271	+	29.6337i	−1.84730	+	1.06654i
$773$	−5.80883	+	10.0612i	−0.208929	+	0.361876i	−0.951377	−	0.308027i	$-0.900331\pi$
$773$	−5.80883	+	10.0612i	−0.208929	+	0.361876i	0.742448	+	0.669903i	$0.233664\pi$
$774$	−3.07756	+	12.1767i	−0.110621	+	0.437683i
$775$	5.45293	+	3.14825i	0.195875	+	0.113089i
$776$	−6.36675	−	3.67585i	−0.228553	−	0.131955i
$777$	−29.1490	+	4.04891i	−1.04572	+	0.145254i
$778$	3.65899	+	2.11252i	0.131181	+	0.0757375i
$779$	8.74712	+	1.20223i	0.313398	+	0.0430743i
$780$	22.4778	−	17.5035i	0.804834	−	0.626727i
$781$	−23.6998	−	13.6831i	−0.848046	−	0.489620i
$782$	−35.5469	−	61.5691i	−1.27116	−	2.20171i
$783$	−3.36915	−	7.66640i	−0.120403	−	0.273975i
$784$	8.22509	+	14.2463i	0.293753	+	0.508795i
$785$			41.0576i			1.46541i
$786$	29.8429	+	38.3238i	1.06446	+	1.36697i
$787$	8.15629	+	4.70904i	0.290740	+	0.167859i	0.638276	−	0.769808i	$-0.279648\pi$
$787$	8.15629	+	4.70904i	0.290740	+	0.167859i	−0.347535	+	0.937667i	$0.612981\pi$
$788$	4.77627	−	2.75758i	0.170148	−	0.0982348i
$789$	21.4789	+	27.5829i	0.764668	+	0.981977i
$790$	34.1241	+	59.1047i	1.21408	+	2.10285i
$791$	−57.4619			−2.04311
$792$	19.9590	+	5.04447i	0.709212	+	0.179248i
$793$	−13.8975	+	8.02370i	−0.493513	+	0.284930i
$794$	−72.2395			−2.56368
$795$	−28.9336	−	37.1561i	−1.02617	−	1.31779i
$796$	35.8035			1.26902
$797$	22.1959	−	38.4444i	0.786218	−	1.36177i	−0.142051	−	0.989859i	$-0.545370\pi$
$797$	22.1959	−	38.4444i	0.786218	−	1.36177i	0.928269	−	0.371910i	$-0.121297\pi$
$798$	52.6263	+	30.2833i	1.86295	+	1.07202i
$799$	−8.92733	−	15.4626i	−0.315826	−	0.547027i
$800$	−16.1099	−	27.9031i	−0.569569	−	0.986523i
$801$	8.61821	−	2.44131i	0.304509	−	0.0862593i
$802$	−6.61724	+	11.4614i	−0.233663	+	0.404716i
$803$	−16.8032	−	9.70134i	−0.592972	−	0.342353i
$804$	−1.83888	−	2.36147i	−0.0648524	−	0.0832826i
$805$	35.9016	−	62.1835i	1.26537	−	2.19168i
$806$	3.37688	−	5.84893i	0.118946	−	0.206020i
$807$	1.39246	+	10.0246i	0.0490169	+	0.352884i
$808$			2.17180i			0.0764036i
$809$			4.81244i			0.169196i	0.996415	+	0.0845982i	$0.0269607\pi$
$809$			4.81244i			0.169196i	−0.996415	+	0.0845982i	$0.973039\pi$
$810$	−27.8234	+	51.5271i	−0.977615	+	1.81048i
$811$	−17.1253	−	9.88731i	−0.601351	−	0.347190i	0.168222	−	0.985749i	$-0.446198\pi$
$811$	−17.1253	−	9.88731i	−0.601351	−	0.347190i	−0.769573	+	0.638559i	$0.779531\pi$
$812$	7.91200	−	13.7040i	0.277657	−	0.480916i
$813$	−3.59348	−	25.8703i	−0.126029	−	0.907310i
$814$	49.8151			1.74602
$815$		−	9.07901i		−	0.318024i
$816$	7.99282	−	19.6918i	0.279805	−	0.689352i
$817$	5.20329	−	6.70180i	0.182040	−	0.234466i
$818$			8.05649i			0.281689i
$819$	6.33023	+	22.3467i	0.221196	+	0.780858i
$820$	−13.9355	+	8.04565i	−0.486648	+	0.280966i
$821$		−	6.25639i		−	0.218350i	−0.994023	−	0.109175i	$-0.965179\pi$
$821$		−	6.25639i		−	0.218350i	0.994023	−	0.109175i	$-0.0348208\pi$
$822$	26.2206	+	33.6721i	0.914547	+	1.17445i
$823$	−7.11827	−	12.3292i	−0.248127	−	0.429769i	0.714879	−	0.699248i	$-0.246482\pi$
$823$	−7.11827	−	12.3292i	−0.248127	−	0.429769i	−0.963006	+	0.269479i	$0.913148\pi$
$824$	12.2705	+	7.08439i	0.427464	+	0.246796i
$825$	36.3049	−	5.04289i	1.26397	−	0.175571i
$826$	57.9769			2.01728
$827$	6.98747	−	12.1027i	0.242978	−	0.420851i	−0.718583	−	0.695441i	$-0.755209\pi$
$827$	6.98747	−	12.1027i	0.242978	−	0.420851i	0.961561	+	0.274590i	$0.0885423\pi$
$828$	−13.6292	−	48.1131i	−0.473646	−	1.67205i
$829$		−	6.20264i		−	0.215427i	−0.994182	−	0.107713i	$-0.965647\pi$
$829$		−	6.20264i		−	0.215427i	0.994182	−	0.107713i	$-0.0343529\pi$
$830$	−30.5219			−1.05943
$831$	3.82335	+	27.5251i	0.132630	+	0.954837i
$832$	−21.4793	+	12.4011i	−0.744659	+	0.429929i
$833$		−	36.3545i		−	1.25961i
$834$	−63.9368	−	25.9516i	−2.21395	−	0.898631i
$835$	−15.6222	+	9.01946i	−0.540628	+	0.312131i
$836$	−46.0836	−	35.7794i	−1.59383	−	1.23746i
$837$	−0.861472	+	7.83319i	−0.0297768	+	0.270755i
$838$	6.81358	−	3.93382i	0.235371	−	0.135892i
$839$	−11.2033	+	19.4047i	−0.386781	+	0.669925i	−0.992015	−	0.126123i	$-0.959747\pi$
$839$	−11.2033	+	19.4047i	−0.386781	+	0.669925i	0.605233	+	0.796048i	$0.293080\pi$
$840$	−26.1264	+	3.62906i	−0.901447	+	0.125214i
$841$	−26.4028			−0.910441
$842$	13.7777	−	7.95456i	0.474811	−	0.274132i
$843$	27.2764	+	11.0714i	0.939449	+	0.381318i
$844$	62.2808	−	35.9578i	2.14379	−	1.23772i
$845$	22.8270	+	13.1792i	0.785273	+	0.453378i
$846$	−6.02980	−	21.2862i	−0.207309	−	0.731834i
$847$	56.0141			1.92467
$848$	10.5886	+	18.3400i	0.363614	+	0.629798i
$849$	24.9216	+	10.1156i	0.855309	+	0.347166i
$850$			46.4994i			1.59492i
$851$	−14.4220	−	24.9796i	−0.494379	−	0.856289i
$852$	19.2671	−	15.0033i	0.660079	−	0.514005i
$853$	−6.00853	+	10.4071i	−0.205728	+	0.356332i	−0.950365	−	0.311139i	$-0.899290\pi$
$853$	−6.00853	+	10.4071i	−0.205728	+	0.356332i	0.744636	+	0.667471i	$0.232623\pi$
$854$	62.3308			2.13291
$855$	31.1775	−	24.3499i	1.06625	−	0.832748i
$856$	13.8987			0.475049
$857$	18.0738	−	31.3047i	0.617389	−	1.06935i	−0.372571	−	0.928004i	$-0.621524\pi$
$857$	18.0738	−	31.3047i	0.617389	−	1.06935i	0.989960	−	0.141346i	$-0.0451430\pi$
$858$	−5.40911	−	38.9414i	−0.184664	−	1.32944i
$859$	−17.8252	−	30.8741i	−0.608187	−	1.05341i	−0.991539	−	0.129809i	$-0.958564\pi$
$859$	−17.8252	−	30.8741i	−0.608187	−	1.05341i	0.383352	−	0.923602i	$-0.374770\pi$
$860$			15.4630i			0.527283i
$861$	−1.80490	−	12.9939i	−0.0615107	−	0.442830i
$862$	12.4319	+	21.5326i	0.423431	+	0.733404i
$863$	21.0718			0.717294			0.358647	−	0.933473i	$-0.383238\pi$
$863$	21.0718			0.717294			0.358647	+	0.933473i	$0.383238\pi$
$864$	23.8591	−	32.5088i	0.811705	−	1.10597i
$865$	−49.2230	−	28.4189i	−1.67363	−	0.966271i
$866$	6.36186	−	3.67302i	0.216185	−	0.124814i
$867$	−13.8247	+	10.7654i	−0.469512	+	0.365611i
$868$	−12.8961	+	7.44560i	−0.437724	+	0.252720i
$869$	53.4640			1.81364
$870$	−11.1588	−	14.3299i	−0.378317	−	0.485830i
$871$	−0.681251	+	1.17996i	−0.0230833	+	0.0399815i
$872$	−6.86633	+	3.96428i	−0.232523	+	0.134247i
$873$	−4.46490	−	15.7618i	−0.151114	−	0.533457i
$874$	−8.10312	+	58.9563i	−0.274092	+	1.99423i
$875$	8.30955	−	4.79752i	0.280914	−	0.162186i
$876$	13.6604	−	10.6374i	0.461541	−	0.359404i
$877$			51.2369i			1.73015i	0.501645	+	0.865073i	$0.332728\pi$
$877$			51.2369i			1.73015i	−0.501645	+	0.865073i	$0.667272\pi$
$878$	−45.4550	+	26.2434i	−1.53403	+	0.885673i
$879$	41.3646	−	32.2108i	1.39519	−	1.08644i
$880$	−36.3331			−1.22479
$881$		−	11.1100i		−	0.374304i	−0.982331	−	0.187152i	$-0.940074\pi$
$881$		−	11.1100i		−	0.374304i	0.982331	−	0.187152i	$-0.0599257\pi$
$882$	11.0381	−	43.6736i	0.371674	−	1.47057i
$883$	15.1216	−	26.1914i	0.508883	−	0.881411i	−0.491064	−	0.871123i	$-0.663392\pi$
$883$	15.1216	−	26.1914i	0.508883	−	0.881411i	0.999947	−	0.0102875i	$-0.00327469\pi$
$884$	28.3126			0.952256
$885$	14.2066	−	35.0006i	0.477549	−	1.17653i
$886$	72.6180	+	41.9260i	2.43965	+	1.40853i
$887$	0.648824	+	1.12380i	0.0217854	+	0.0377334i	0.876713	−	0.481015i	$-0.159732\pi$
$887$	0.648824	+	1.12380i	0.0217854	+	0.0377334i	−0.854927	+	0.518748i	$0.826398\pi$
$888$	−3.98508	+	9.81800i	−0.133731	+	0.329470i
$889$			7.32615i			0.245711i
$890$	16.8244	−	9.71358i	0.563956	−	0.325600i
$891$	24.0590	+	39.0585i	0.806008	+	1.30851i
$892$		−	6.06557i		−	0.203090i
$893$	−2.03503	+	14.8064i	−0.0680998	+	0.495478i
$894$	−16.6713	−	21.4091i	−0.557572	−	0.716026i
$895$		−	45.0010i		−	1.50422i
$896$	38.2999			1.27951
$897$	−17.9610	+	13.9863i	−0.599702	+	0.466989i
$898$	28.0516	−	48.5869i	0.936096	−	1.62137i
$899$	−2.11666	−	1.22206i	−0.0705947	−	0.0407579i
$900$	−8.01440	+	31.7098i	−0.267147	+	1.05699i
$901$		−	46.8011i		−	1.55917i
$902$			22.2062i			0.739387i
$903$	−11.6808	−	4.74120i	−0.388714	−	0.157777i
$904$	−10.3446	+	17.9174i	−0.344058	+	0.595925i
$905$	−6.73529	+	11.6659i	−0.223889	+	0.387787i
$906$	3.08740	−	7.60640i	0.102572	−	0.252706i
$907$	−31.1588	−	17.9895i	−1.03461	−	0.597333i	−0.116309	−	0.993213i	$-0.537106\pi$
$907$	−31.1588	−	17.9895i	−1.03461	−	0.597333i	−0.918302	+	0.395880i	$0.870440\pi$
$908$	15.4242	−	26.7155i	0.511871	−	0.886586i
$909$	−3.37296	+	3.47043i	−0.111874	+	0.115107i
$910$	25.1870	+	43.6252i	0.834941	+	1.44616i
$911$	−6.18966	−	10.7208i	−0.205073	−	0.355196i	0.745083	−	0.666972i	$-0.232410\pi$
$911$	−6.18966	−	10.7208i	−0.205073	−	0.355196i	−0.950156	+	0.311775i	$0.899076\pi$
$912$	−15.3934	+	8.91685i	−0.509727	+	0.295266i
$913$	−11.9550	+	20.7067i	−0.395654	+	0.685292i
$914$	−38.3374			−1.26809
$915$	15.2734	−	37.6290i	0.504924	−	1.24398i
$916$	17.4180			0.575508
$917$	−42.2219	+	24.3768i	−1.39429	+	0.804993i
$918$	−53.2786	+	23.4143i	−1.75846	+	0.772787i
$919$	−10.1943			−0.336279			−0.168139	−	0.985763i	$-0.553776\pi$
$919$	−10.1943			−0.336279			−0.168139	+	0.985763i	$0.553776\pi$
$920$	−12.9265	−	22.3893i	−0.426173	−	0.738154i
$921$	48.4097	−	6.72429i	1.59516	−	0.221573i
$922$	−66.3419	+	38.3025i	−2.18485	+	1.26143i
$923$	−9.62722	−	5.55828i	−0.316884	−	0.182953i
$924$	−32.6019	+	80.3209i	−1.07252	+	2.64236i
$925$			18.8656i			0.620296i
$926$	−11.8390	−	20.5058i	−0.389055	−	0.673863i
$927$	8.60512	+	30.3775i	0.282629	+	0.997728i
$928$	6.25336	+	10.8311i	0.205277	+	0.355550i
$929$	0.786138	+	0.453877i	0.0257924	+	0.0148912i	0.512841	−	0.858484i	$-0.328593\pi$
$929$	0.786138	+	0.453877i	0.0257924	+	0.0148912i	−0.487048	+	0.873375i	$0.661926\pi$
$930$	2.35150	+	16.9290i	0.0771087	+	0.555123i
$931$	−18.6624	+	24.0370i	−0.611635	+	0.787781i
$932$	8.24239	+	4.75875i	0.269989	+	0.155878i
$933$	−20.3020	−	26.0716i	−0.664659	−	0.853546i
$934$	44.2493	+	25.5474i	1.44788	+	0.835935i
$935$	69.5377	+	40.1476i	2.27413	+	1.31297i
$936$	8.10764	+	2.04914i	0.265007	+	0.0669782i
$937$	−23.0292	+	39.8878i	−0.752332	+	1.30308i	0.194358	+	0.980931i	$0.437738\pi$
$937$	−23.0292	+	39.8878i	−0.752332	+	1.30308i	−0.946690	+	0.322146i	$0.895596\pi$
$938$	4.58317	−	2.64609i	0.149646	−	0.0863980i
$939$	18.0338	+	7.31983i	0.588510	+	0.238873i
$940$	−13.6190	−	23.5888i	−0.444203	−	0.769383i
$941$	26.4298	+	45.7778i	0.861587	+	1.49231i	0.870396	+	0.492352i	$0.163863\pi$
$941$	26.4298	+	45.7778i	0.861587	+	1.49231i	−0.00880912	+	0.999961i	$0.502804\pi$
$942$	−39.8913	+	31.0635i	−1.29973	+	1.01210i
$943$	11.1352	−	6.42893i	0.362613	−	0.209355i
$944$	−8.49330	+	14.7108i	−0.276433	+	0.478797i
$945$	−47.3849	−	34.7771i	−1.54143	−	1.13130i
$946$	18.4803	+	10.6696i	0.600845	+	0.346898i
$947$	5.73555	+	3.31142i	0.186380	+	0.107607i	0.590287	−	0.807193i	$-0.299015\pi$
$947$	5.73555	+	3.31142i	0.186380	+	0.107607i	−0.403907	+	0.914800i	$0.632348\pi$
$948$	−17.9425	+	44.2048i	−0.582746	+	1.43571i
$949$	−6.82571	−	3.94083i	−0.221572	−	0.127925i
$950$	23.8702	−	30.7447i	0.774453	−	0.997488i
$951$	0.603535	+	0.244972i	0.0195710	+	0.00794376i
$952$	−22.7019	−	13.1069i	−0.735773	−	0.424799i
$953$	−7.59011	−	13.1465i	−0.245868	−	0.425855i	0.716508	−	0.697579i	$-0.245740\pi$
$953$	−7.59011	−	13.1465i	−0.245868	−	0.425855i	−0.962375	+	0.271724i	$0.912406\pi$
$954$	14.2100	−	56.2234i	0.460066	−	1.82030i
$955$	35.2204	+	61.0035i	1.13971	+	1.97403i
$956$		−	39.8516i		−	1.28889i
$957$	−14.0925	+	1.95750i	−0.455545	+	0.0632769i
$958$	−77.1419	−	44.5379i	−2.49234	−	1.43895i
$959$	−37.0970	+	21.4180i	−1.19793	+	0.691622i
$960$	23.6059	−	58.1577i	0.761878	−	1.87703i
$961$	−14.3500	−	24.8549i	−0.462903	−	0.801771i
$962$	20.2356			0.652422
$963$	22.2095	+	21.5857i	0.715691	+	0.695590i
$964$	−55.7696	+	32.1986i	−1.79622	+	1.03705i
$965$	−68.2781			−2.19795
$966$	87.5797	−	12.1651i	2.81783	−	0.391407i
$967$	29.5659			0.950775			0.475387	−	0.879777i	$-0.342308\pi$
$967$	29.5659			0.950775			0.475387	+	0.879777i	$0.342308\pi$
$968$	10.0840	−	17.4660i	0.324112	−	0.561378i
$969$	39.3144	−	0.0563603i	1.26296	−	0.00181055i
$970$	−17.7652	−	30.7702i	−0.570405	−	0.987970i
$971$	−17.8609	−	30.9360i	−0.573184	−	0.992784i	−0.996236	−	0.0866789i	$-0.972375\pi$
$971$	−17.8609	−	30.9360i	−0.573184	−	0.992784i	0.423052	−	0.906105i	$-0.360959\pi$
$972$	−40.3684	+	6.78432i	−1.29482	+	0.217607i
$973$	34.6299	−	59.9808i	1.11018	−	1.92290i
$974$	−28.0803	−	16.2122i	−0.899750	−	0.519471i
$975$	14.7476	−	2.04850i	0.472301	−	0.0656044i
$976$	−9.13111	+	15.8155i	−0.292280	+	0.506243i
$977$	0.303010	−	0.524829i	0.00969416	−	0.0167908i	−0.861138	−	0.508372i	$-0.830248\pi$
$977$	0.303010	−	0.524829i	0.00969416	−	0.0167908i	0.870832	+	0.491581i	$0.163581\pi$
$978$	8.82111	−	6.86903i	0.282068	−	0.219647i
$979$		−	15.2187i		−	0.486393i
$980$		−	55.4603i		−	1.77161i
$981$	−17.1288	−	4.32918i	−0.546882	−	0.138220i
$982$	−78.8070	−	45.4993i	−2.51483	−	1.45194i
$983$	−14.1525	+	24.5129i	−0.451395	+	0.781839i	−0.998473	−	0.0552427i	$-0.982407\pi$
$983$	−14.1525	+	24.5129i	−0.451395	+	0.781839i	0.547078	+	0.837082i	$0.315740\pi$
$984$	−4.37660	−	1.77644i	−0.139521	−	0.0566309i
$985$	6.35366			0.202444
$986$		−	18.0497i		−	0.574819i
$987$	21.9950	−	3.05518i	0.700107	−	0.0972475i
$988$	−18.7198	−	14.5341i	−0.595557	−	0.462392i
$989$		−	12.3558i		−	0.392892i
$990$	71.3476	+	69.3438i	2.26758	+	2.20389i
$991$	49.4706	−	28.5619i	1.57149	−	0.907298i	0.575498	−	0.817803i	$-0.304808\pi$
$991$	49.4706	−	28.5619i	1.57149	−	0.907298i	0.995987	−	0.0894946i	$-0.0285252\pi$
$992$		−	11.7695i		−	0.373681i
$993$	53.7742	−	7.46943i	1.70647	−	0.237035i
$994$	21.5893	+	37.3937i	0.684770	+	1.18606i
$995$	35.7208	+	20.6234i	1.13243	+	0.653806i
$996$	−13.1085	−	16.8338i	−0.415359	−	0.533399i
$997$	−36.7425			−1.16365			−0.581823	−	0.813316i	$-0.697660\pi$
$997$	−36.7425			−1.16365			−0.581823	+	0.813316i	$0.697660\pi$
$998$	−46.5207	+	80.5763i	−1.47259	+	2.55060i
$999$	−21.6160	+	9.49956i	−0.683900	+	0.300553i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.k.a.50.3	✓	36
3.2	odd	2		513.2.k.a.449.16		36
9.2	odd	6		171.2.t.a.164.3	yes	36
9.7	even	3		513.2.t.a.278.16		36
19.8	odd	6		171.2.t.a.122.3	yes	36
57.8	even	6		513.2.t.a.179.16		36
171.65	even	6	inner	171.2.k.a.65.3	yes	36
171.160	odd	6		513.2.k.a.8.16		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.k.a.50.3	✓	36	1.1	even	1	trivial
171.2.k.a.65.3	yes	36	171.65	even	6	inner
171.2.t.a.122.3	yes	36	19.8	odd	6
171.2.t.a.164.3	yes	36	9.2	odd	6
513.2.k.a.8.16		36	171.160	odd	6
513.2.k.a.449.16		36	3.2	odd	2
513.2.t.a.179.16		36	57.8	even	6
513.2.t.a.278.16		36	9.7	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07540 + 1.86265i) q^{2} +(-1.60489 - 0.651416i) q^{3} +(-1.31298 - 2.27414i) q^{4} -3.02519i q^{5} +(2.93925 - 2.28881i) q^{6} +(1.86959 + 3.23822i) q^{7} +1.34630 q^{8} +(2.15132 + 2.09089i) q^{9} +(5.63486 + 3.25329i) q^{10} +(4.41421 - 2.54855i) q^{11} +(0.625765 + 4.50503i) q^{12} +(1.79312 - 1.03526i) q^{13} -8.04222 q^{14} +(-1.97065 + 4.85508i) q^{15} +(1.17814 - 2.04060i) q^{16} +(-4.50968 + 2.60366i) q^{17} +(-6.20813 + 1.75860i) q^{18} +(4.31830 + 0.593520i) q^{19} +(-6.87970 + 3.97200i) q^{20} +(-0.891046 - 6.41485i) q^{21} +10.9628i q^{22} +(5.49727 - 3.17385i) q^{23} +(-2.16065 - 0.876999i) q^{24} -4.15176 q^{25} +4.45327i q^{26} +(-2.09057 - 4.75705i) q^{27} +(4.90944 - 8.50340i) q^{28} +1.61159 q^{29} +(-6.92407 - 8.89180i) q^{30} +(-1.31340 - 0.758293i) q^{31} +(3.88025 + 6.72078i) q^{32} +(-8.74447 + 1.21464i) q^{33} -11.1999i q^{34} +(9.79622 - 5.65585i) q^{35} +(1.93036 - 7.63769i) q^{36} -4.54399i q^{37} +(-5.74943 + 7.40521i) q^{38} +(-3.55213 + 0.493404i) q^{39} -4.07280i q^{40} +2.02559 q^{41} +(12.9068 + 5.23883i) q^{42} +(0.973250 - 1.68572i) q^{43} +(-11.5915 - 6.69236i) q^{44} +(6.32535 - 6.50813i) q^{45} +13.6527i q^{46} +3.42876i q^{47} +(-3.22006 + 2.50747i) q^{48} +(-3.49070 + 6.04608i) q^{49} +(4.46481 - 7.73327i) q^{50} +(8.93358 - 1.24091i) q^{51} +(-4.70864 - 2.71853i) q^{52} +(-4.49378 + 7.78345i) q^{53} +(11.1089 + 1.22173i) q^{54} +(-7.70983 - 13.3538i) q^{55} +(2.51702 + 4.35961i) q^{56} +(-6.54375 - 3.76554i) q^{57} +(-1.73310 + 3.00183i) q^{58} -7.20907 q^{59} +(13.6286 - 1.89306i) q^{60} -7.75044 q^{61} +(2.82487 - 1.63094i) q^{62} +(-2.74870 + 10.8755i) q^{63} -11.9787 q^{64} +(-3.13185 - 5.42452i) q^{65} +(7.14136 - 17.5941i) q^{66} +(-0.569888 + 0.329025i) q^{67} +(11.8422 + 6.83709i) q^{68} +(-10.8900 + 1.51266i) q^{69} +24.3292i q^{70} +(-2.68449 - 4.64968i) q^{71} +(2.89631 + 2.81497i) q^{72} +(-1.90331 - 3.29663i) q^{73} +(8.46387 + 4.88662i) q^{74} +(6.66310 + 2.70452i) q^{75} +(-4.32008 - 10.5997i) q^{76} +(16.5055 + 9.52945i) q^{77} +(2.90093 - 7.14698i) q^{78} +(9.08384 + 5.24456i) q^{79} +(-6.17320 - 3.56410i) q^{80} +(0.256318 + 8.99635i) q^{81} +(-2.17832 + 3.77297i) q^{82} +(-4.06246 + 2.34546i) q^{83} +(-13.4183 + 10.4489i) q^{84} +(7.87657 + 13.6426i) q^{85} +(2.09327 + 3.62565i) q^{86} +(-2.58642 - 1.04981i) q^{87} +(5.94284 - 3.43110i) q^{88} +(1.49289 - 2.58575i) q^{89} +(5.32008 + 18.7808i) q^{90} +(6.70478 + 3.87100i) q^{91} +(-14.4356 - 8.33438i) q^{92} +(1.61390 + 2.07254i) q^{93} +(-6.38657 - 3.68729i) q^{94} +(1.79551 - 13.0637i) q^{95} +(-1.84933 - 13.3137i) q^{96} +(-4.72908 - 2.73034i) q^{97} +(-7.50782 - 13.0039i) q^{98} +(14.8251 + 3.74692i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} - 6 q^{3} - 15 q^{4} + 4 q^{6} - q^{7} + 12 q^{8} - 4 q^{9} - 6 q^{10} - 9 q^{11} + 15 q^{12} - 6 q^{13} - 6 q^{14} + 9 q^{15} - 9 q^{16} - 27 q^{17} + 6 q^{18} + q^{19} + 9 q^{20} - 3 q^{21}+ \cdots + 28 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 6 * q^3 - 15 * q^4 + 4 * q^6 - q^7 + 12 * q^8 - 4 * q^9 - 6 * q^10 - 9 * q^11 + 15 * q^12 - 6 * q^13 - 6 * q^14 + 9 * q^15 - 9 * q^16 - 27 * q^17 + 6 * q^18 + q^19 + 9 * q^20 - 3 * q^21 + 9 * q^23 - 11 * q^24 - 22 * q^25 + 9 * q^27 + 2 * q^28 - 24 * q^29 - 35 * q^30 + 12 * q^31 - 15 * q^32 - 12 * q^33 + 15 * q^35 + 30 * q^36 - 18 * q^38 - 14 * q^39 + 36 * q^41 - 5 * q^42 + 3 * q^43 + 66 * q^44 + 29 * q^45 + 33 * q^48 - 9 * q^49 + 3 * q^50 - 24 * q^51 + 15 * q^52 - 12 * q^53 - 37 * q^54 - 7 * q^55 + 6 * q^56 + 2 * q^57 - 6 * q^58 - 18 * q^59 + 48 * q^60 - 16 * q^61 - 12 * q^62 - 34 * q^63 + 12 * q^64 - 18 * q^65 + 14 * q^66 + 27 * q^67 + 60 * q^68 - 51 * q^69 + 9 * q^71 - 102 * q^72 - 18 * q^73 + 90 * q^74 - 23 * q^76 - 6 * q^77 + 36 * q^78 - 6 * q^79 - 12 * q^80 + 40 * q^81 - 9 * q^82 - 9 * q^83 - 96 * q^84 + 11 * q^85 + 51 * q^86 - 19 * q^87 + 3 * q^88 - 18 * q^89 + 36 * q^90 + 27 * q^91 - 93 * q^92 - 28 * q^93 + 12 * q^94 - 9 * q^96 + 24 * q^97 - 84 * q^98 + 28 * q^99

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