LMFDB - Embedded newform 185.2.e.a.26.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(26,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("185.26"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 11 x^{12} - 2 x^{11} + 86 x^{10} - 18 x^{9} + 332 x^{8} - 110 x^{7} + 935 x^{6} - 290 x^{5} + \cdots + 81 $ x^14 + 11x^12 - 2x^11 + 86x^10 - 18x^9 + 332x^8 - 110x^7 + 935x^6 - 290x^5 + 985x^4 - 441x^3 + 792x^2 - 243x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			26.4
Root			$0.178876 - 0.309823i$ of defining polynomial
Character	$\chi$	$=$	185.26
Dual form			185.2.e.a.121.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.178876 + 0.309823i) q^{2} +(-0.0462746 + 0.0801499i) q^{3} +(0.936006 - 1.62121i) q^{4} +(-0.500000 + 0.866025i) q^{5} -0.0331097 q^{6} +(1.38534 - 2.39948i) q^{7} +1.38522 q^{8} +(1.49572 + 2.59066i) q^{9} -0.357753 q^{10} -2.03649 q^{11} +(0.0866266 + 0.150042i) q^{12} +(3.09620 - 5.36277i) q^{13} +0.991221 q^{14} +(-0.0462746 - 0.0801499i) q^{15} +(-1.62423 - 2.81325i) q^{16} +(2.41732 + 4.18692i) q^{17} +(-0.535097 + 0.926816i) q^{18} +(-3.62153 + 6.27267i) q^{19} +(0.936006 + 1.62121i) q^{20} +(0.128212 + 0.222070i) q^{21} +(-0.364280 - 0.630951i) q^{22} +0.510883 q^{23} +(-0.0641006 + 0.111026i) q^{24} +(-0.500000 - 0.866025i) q^{25} +2.21535 q^{26} -0.554502 q^{27} +(-2.59338 - 4.49186i) q^{28} -8.39445 q^{29} +(0.0165549 - 0.0286739i) q^{30} -4.28667 q^{31} +(1.96630 - 3.40573i) q^{32} +(0.0942375 - 0.163224i) q^{33} +(-0.864804 + 1.49788i) q^{34} +(1.38534 + 2.39948i) q^{35} +5.60000 q^{36} +(2.72642 + 5.43752i) q^{37} -2.59122 q^{38} +(0.286550 + 0.496320i) q^{39} +(-0.692612 + 1.19964i) q^{40} +(1.42197 - 2.46293i) q^{41} +(-0.0458683 + 0.0794462i) q^{42} -4.00472 q^{43} +(-1.90616 + 3.30157i) q^{44} -2.99143 q^{45} +(0.0913850 + 0.158283i) q^{46} -11.1303 q^{47} +0.300642 q^{48} +(-0.338346 - 0.586032i) q^{49} +(0.178876 - 0.309823i) q^{50} -0.447442 q^{51} +(-5.79612 - 10.0392i) q^{52} +(-2.34060 - 4.05405i) q^{53} +(-0.0991874 - 0.171798i) q^{54} +(1.01824 - 1.76365i) q^{55} +(1.91901 - 3.32382i) q^{56} +(-0.335169 - 0.580530i) q^{57} +(-1.50157 - 2.60080i) q^{58} +(5.88440 + 10.1921i) q^{59} -0.173253 q^{60} +(-1.10202 + 1.90875i) q^{61} +(-0.766785 - 1.32811i) q^{62} +8.28832 q^{63} -5.09002 q^{64} +(3.09620 + 5.36277i) q^{65} +0.0674275 q^{66} +(-1.96671 + 3.40645i) q^{67} +9.05051 q^{68} +(-0.0236409 + 0.0409472i) q^{69} +(-0.495610 + 0.858422i) q^{70} +(7.05529 - 12.2201i) q^{71} +(2.07190 + 3.58864i) q^{72} +4.72706 q^{73} +(-1.19698 + 1.81735i) q^{74} +0.0925491 q^{75} +(6.77955 + 11.7425i) q^{76} +(-2.82123 + 4.88651i) q^{77} +(-0.102514 + 0.177560i) q^{78} +(4.77335 - 8.26768i) q^{79} +3.24846 q^{80} +(-4.46149 + 7.72753i) q^{81} +1.01743 q^{82} +(-0.0730402 - 0.126509i) q^{83} +0.480030 q^{84} -4.83464 q^{85} +(-0.716351 - 1.24076i) q^{86} +(0.388450 - 0.672815i) q^{87} -2.82099 q^{88} +(8.28829 + 14.3557i) q^{89} +(-0.535097 - 0.926816i) q^{90} +(-8.57859 - 14.8585i) q^{91} +(0.478190 - 0.828249i) q^{92} +(0.198364 - 0.343576i) q^{93} +(-1.99095 - 3.44842i) q^{94} +(-3.62153 - 6.27267i) q^{95} +(0.181979 + 0.315197i) q^{96} +18.7527 q^{97} +(0.121044 - 0.209655i) q^{98} +(-3.04601 - 5.27584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{3} - 8 q^{4} - 7 q^{5} - 4 q^{6} + 6 q^{8} - 13 q^{9} - 2 q^{11} + 6 q^{12} + 4 q^{13} + 20 q^{14} - 2 q^{15} + 2 q^{16} - 3 q^{17} - 6 q^{18} - 14 q^{19} - 8 q^{20} + q^{21} + 7 q^{22} + 15 q^{24}+ \cdots + 56 q^{99}+O(q^{100}) $ 14 * q - 2 * q^3 - 8 * q^4 - 7 * q^5 - 4 * q^6 + 6 * q^8 - 13 * q^9 - 2 * q^11 + 6 * q^12 + 4 * q^13 + 20 * q^14 - 2 * q^15 + 2 * q^16 - 3 * q^17 - 6 * q^18 - 14 * q^19 - 8 * q^20 + q^21 + 7 * q^22 + 15 * q^24 - 7 * q^25 - 22 * q^26 - 14 * q^27 + 9 * q^28 - 12 * q^29 + 2 * q^30 + 4 * q^32 - 11 * q^33 + 33 * q^34 + 40 * q^36 + 18 * q^37 - 4 * q^38 - 25 * q^39 - 3 * q^40 - 7 * q^41 - 29 * q^42 + 38 * q^43 - 19 * q^44 + 26 * q^45 - 14 * q^46 + 8 * q^47 + 36 * q^48 + 5 * q^49 + 58 * q^51 - 8 * q^52 - 6 * q^53 - 9 * q^54 + q^55 - 25 * q^56 - 44 * q^57 - 12 * q^58 + 2 * q^59 - 12 * q^60 - 4 * q^61 - 25 * q^62 + 10 * q^63 - 62 * q^64 + 4 * q^65 - 2 * q^66 - 8 * q^67 + 26 * q^68 - 11 * q^69 - 10 * q^70 + 33 * q^71 + 43 * q^72 + 18 * q^74 + 4 * q^75 - 12 * q^76 - 5 * q^77 - 22 * q^78 - 9 * q^79 - 4 * q^80 - 35 * q^81 + 152 * q^82 - 11 * q^83 - 80 * q^84 + 6 * q^85 + 17 * q^86 - 29 * q^87 + 40 * q^88 - 12 * q^89 - 6 * q^90 - 24 * q^91 - 7 * q^92 - 47 * q^93 + 10 * q^94 - 14 * q^95 - 15 * q^96 + 30 * q^97 + 54 * q^98 + 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.178876	+	0.309823i	0.126485	+	0.219078i	0.922312	−	0.386445i	$-0.126297\pi$
$2$	0.178876	+	0.309823i	0.126485	+	0.219078i	−0.795828	+	0.605523i	$0.792964\pi$
$3$	−0.0462746	+	0.0801499i	−0.0267166	+	0.0462746i	−0.879075	−	0.476684i	$-0.841839\pi$
$3$	−0.0462746	+	0.0801499i	−0.0267166	+	0.0462746i	0.852358	+	0.522959i	$0.175172\pi$
$4$	0.936006	−	1.62121i	0.468003	−	0.810605i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−0.0331097			−0.0135170
$7$	1.38534	−	2.39948i	0.523610	−	0.906919i	−0.476012	−	0.879439i	$-0.657918\pi$
$7$	1.38534	−	2.39948i	0.523610	−	0.906919i	0.999622	−	0.0274806i	$-0.00874846\pi$
$8$	1.38522			0.489751
$9$	1.49572	+	2.59066i	0.498572	+	0.863553i
$10$	−0.357753			−0.113131
$11$	−2.03649			−0.614024			−0.307012	−	0.951706i	$-0.599329\pi$
$11$	−2.03649			−0.614024			−0.307012	+	0.951706i	$0.599329\pi$
$12$	0.0866266	+	0.150042i	0.0250069	+	0.0433133i
$13$	3.09620	−	5.36277i	0.858731	−	1.48737i	−0.0144096	−	0.999896i	$-0.504587\pi$
$13$	3.09620	−	5.36277i	0.858731	−	1.48737i	0.873140	−	0.487469i	$-0.162080\pi$
$14$	0.991221			0.264915
$15$	−0.0462746	−	0.0801499i	−0.0119480	−	0.0206946i
$16$	−1.62423	−	2.81325i	−0.406057	−	0.703312i
$17$	2.41732	+	4.18692i	0.586286	+	1.01548i	0.994714	+	0.102687i	$0.0327440\pi$
$17$	2.41732	+	4.18692i	0.586286	+	1.01548i	−0.408427	+	0.912791i	$0.633923\pi$
$18$	−0.535097	+	0.926816i	−0.126124	+	0.218453i
$19$	−3.62153	+	6.27267i	−0.830835	+	1.43905i	0.0665413	+	0.997784i	$0.478804\pi$
$19$	−3.62153	+	6.27267i	−0.830835	+	1.43905i	−0.897377	+	0.441265i	$0.854530\pi$
$20$	0.936006	+	1.62121i	0.209297	+	0.362514i
$21$	0.128212	+	0.222070i	0.0279782	+	0.0484597i
$22$	−0.364280	−	0.630951i	−0.0776647	−	0.134519i
$23$	0.510883			0.106526			0.0532632	−	0.998581i	$-0.483038\pi$
$23$	0.510883			0.106526			0.0532632	+	0.998581i	$0.483038\pi$
$24$	−0.0641006	+	0.111026i	−0.0130845	+	0.0226630i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.21535			0.434465
$27$	−0.554502			−0.106714
$28$	−2.59338	−	4.49186i	−0.490102	−	0.848882i
$29$	−8.39445			−1.55881			−0.779405	−	0.626520i	$-0.784479\pi$
$29$	−8.39445			−1.55881			−0.779405	+	0.626520i	$0.784479\pi$
$30$	0.0165549	−	0.0286739i	0.00302249	−	0.00523511i
$31$	−4.28667			−0.769909			−0.384955	−	0.922935i	$-0.625783\pi$
$31$	−4.28667			−0.769909			−0.384955	+	0.922935i	$0.625783\pi$
$32$	1.96630	−	3.40573i	0.347595	−	0.602053i
$33$	0.0942375	−	0.163224i	0.0164046	−	0.0284137i
$34$	−0.864804	+	1.49788i	−0.148313	+	0.256885i
$35$	1.38534	+	2.39948i	0.234166	+	0.405587i
$36$	5.60000			0.933334
$37$	2.72642	+	5.43752i	0.448221	+	0.893923i
$37$	2.72642	+	5.43752i	0.448221	+	0.893923i
$38$	−2.59122			−0.420352
$39$	0.286550	+	0.496320i	0.0458848	+	0.0794748i
$40$	−0.692612	+	1.19964i	−0.109512	+	0.189680i
$41$	1.42197	−	2.46293i	0.222075	−	0.384645i	−0.733363	−	0.679837i	$-0.762050\pi$
$41$	1.42197	−	2.46293i	0.222075	−	0.384645i	0.955438	+	0.295193i	$0.0953838\pi$
$42$	−0.0458683	+	0.0794462i	−0.00707763	+	0.0122588i
$43$	−4.00472			−0.610715			−0.305357	−	0.952238i	$-0.598776\pi$
$43$	−4.00472			−0.610715			−0.305357	+	0.952238i	$0.598776\pi$
$44$	−1.90616	+	3.30157i	−0.287365	+	0.497731i
$45$	−2.99143			−0.445937
$46$	0.0913850	+	0.158283i	0.0134740	+	0.0233376i
$47$	−11.1303			−1.62352			−0.811760	−	0.583991i	$-0.801490\pi$
$47$	−11.1303			−1.62352			−0.811760	+	0.583991i	$0.801490\pi$
$48$	0.300642			0.0433939
$49$	−0.338346	−	0.586032i	−0.0483351	−	0.0837188i
$50$	0.178876	−	0.309823i	0.0252970	−	0.0438156i
$51$	−0.447442			−0.0626544
$52$	−5.79612	−	10.0392i	−0.803777	−	1.39218i
$53$	−2.34060	−	4.05405i	−0.321507	−	0.556866i	0.659292	−	0.751887i	$-0.270856\pi$
$53$	−2.34060	−	4.05405i	−0.321507	−	0.556866i	−0.980799	+	0.195021i	$0.937523\pi$
$54$	−0.0991874	−	0.171798i	−0.0134977	−	0.0233787i
$55$	1.01824	−	1.76365i	0.137300	−	0.237810i
$56$	1.91901	−	3.32382i	0.256438	−	0.444164i
$57$	−0.335169	−	0.580530i	−0.0443942	−	0.0768931i
$58$	−1.50157	−	2.60080i	−0.197166	−	0.341501i
$59$	5.88440	+	10.1921i	0.766084	+	1.32690i	0.939672	+	0.342078i	$0.111131\pi$
$59$	5.88440	+	10.1921i	0.766084	+	1.32690i	−0.173588	+	0.984818i	$0.555536\pi$
$60$	−0.173253			−0.0223669
$61$	−1.10202	+	1.90875i	−0.141099	+	0.244390i	−0.927911	−	0.372803i	$-0.878397\pi$
$61$	−1.10202	+	1.90875i	−0.141099	+	0.244390i	0.786812	+	0.617193i	$0.211730\pi$
$62$	−0.766785	−	1.32811i	−0.0973818	−	0.168670i
$63$	8.28832			1.04423
$64$	−5.09002			−0.636252
$65$	3.09620	+	5.36277i	0.384036	+	0.665170i
$66$	0.0674275			0.00829975
$67$	−1.96671	+	3.40645i	−0.240272	+	0.416164i	−0.960792	−	0.277271i	$-0.910570\pi$
$67$	−1.96671	+	3.40645i	−0.240272	+	0.416164i	0.720519	+	0.693435i	$0.243903\pi$
$68$	9.05051			1.09754
$69$	−0.0236409	+	0.0409472i	−0.00284603	+	0.00492947i
$70$	−0.495610	+	0.858422i	−0.0592368	+	0.102601i
$71$	7.05529	−	12.2201i	0.837308	−	1.45026i	−0.0548288	−	0.998496i	$-0.517461\pi$
$71$	7.05529	−	12.2201i	0.837308	−	1.45026i	0.892137	−	0.451765i	$-0.149205\pi$
$72$	2.07190	+	3.58864i	0.244176	+	0.422926i
$73$	4.72706			0.553261			0.276630	−	0.960976i	$-0.410782\pi$
$73$	4.72706			0.553261			0.276630	+	0.960976i	$0.410782\pi$
$74$	−1.19698	+	1.81735i	−0.139146	+	0.211263i
$75$	0.0925491			0.0106867
$76$	6.77955	+	11.7425i	0.777667	+	1.34696i
$77$	−2.82123	+	4.88651i	−0.321509	+	0.556870i
$78$	−0.102514	+	0.177560i	−0.0116075	+	0.0201047i
$79$	4.77335	−	8.26768i	0.537043	−	0.930186i	−0.462018	−	0.886870i	$-0.652875\pi$
$79$	4.77335	−	8.26768i	0.537043	−	0.930186i	0.999061	−	0.0433158i	$-0.0137922\pi$
$80$	3.24846			0.363189
$81$	−4.46149	+	7.72753i	−0.495721	+	0.858615i
$82$	1.01743			0.112356
$83$	−0.0730402	−	0.126509i	−0.00801721	−	0.0138862i	0.861989	−	0.506927i	$-0.169219\pi$
$83$	−0.0730402	−	0.126509i	−0.00801721	−	0.0138862i	−0.870006	+	0.493041i	$0.835885\pi$
$84$	0.480030			0.0523755
$85$	−4.83464			−0.524391
$86$	−0.716351	−	1.24076i	−0.0772461	−	0.133794i
$87$	0.388450	−	0.672815i	0.0416462	−	0.0721333i
$88$	−2.82099			−0.300719
$89$	8.28829	+	14.3557i	0.878557	+	1.52171i	0.852924	+	0.522034i	$0.174827\pi$
$89$	8.28829	+	14.3557i	0.878557	+	1.52171i	0.0256329	+	0.999671i	$0.491840\pi$
$90$	−0.535097	−	0.926816i	−0.0564042	−	0.0976950i
$91$	−8.57859	−	14.8585i	−0.899280	−	1.55760i
$92$	0.478190	−	0.828249i	0.0498547	−	0.0863509i
$93$	0.198364	−	0.343576i	0.0205694	−	0.0356272i
$94$	−1.99095	−	3.44842i	−0.205351	−	0.355678i
$95$	−3.62153	−	6.27267i	−0.371561	−	0.643562i
$96$	0.181979	+	0.315197i	0.0185732	+	0.0321697i
$97$	18.7527			1.90405			0.952023	−	0.306028i	$-0.0990001\pi$
$97$	18.7527			1.90405			0.952023	+	0.306028i	$0.0990001\pi$
$98$	0.121044	−	0.209655i	0.0122273	−	0.0211783i
$99$	−3.04601	−	5.27584i	−0.306135	−	0.530242i
$100$	−1.87201			−0.187201
$101$	4.50006			0.447772			0.223886	−	0.974615i	$-0.428126\pi$
$101$	4.50006			0.447772			0.223886	+	0.974615i	$0.428126\pi$
$102$	−0.0800368	−	0.138628i	−0.00792483	−	0.0137262i
$103$	−3.37545			−0.332593			−0.166297	−	0.986076i	$-0.553181\pi$
$103$	−3.37545			−0.332593			−0.166297	+	0.986076i	$0.553181\pi$
$104$	4.28893	−	7.42864i	0.420564	−	0.728438i
$105$	−0.256424			−0.0250245
$106$	0.837358	−	1.45035i	0.0813314	−	0.140870i
$107$	6.78884	−	11.7586i	0.656302	−	1.13675i	−0.325264	−	0.945623i	$-0.605453\pi$
$107$	6.78884	−	11.7586i	0.656302	−	1.13675i	0.981566	−	0.191125i	$-0.0612134\pi$
$108$	−0.519017	+	0.898965i	−0.0499425	+	0.0865029i
$109$	0.287863	+	0.498593i	0.0275722	+	0.0477565i	0.879482	−	0.475932i	$-0.157889\pi$
$109$	0.287863	+	0.498593i	0.0275722	+	0.0477565i	−0.851910	+	0.523688i	$0.824556\pi$
$110$	0.728559			0.0694654
$111$	−0.561981	−	0.0330964i	−0.0533408	−	0.00314137i
$112$	−9.00045			−0.850463
$113$	−1.77807	−	3.07971i	−0.167267	−	0.289715i	0.770191	−	0.637813i	$-0.220161\pi$
$113$	−1.77807	−	3.07971i	−0.167267	−	0.289715i	−0.937458	+	0.348099i	$0.886827\pi$
$114$	0.119908	−	0.207686i	0.0112304	−	0.0194516i
$115$	−0.255442	+	0.442438i	−0.0238200	+	0.0412575i
$116$	−7.85726	+	13.6092i	−0.729528	+	1.26358i
$117$	18.5241			1.71256
$118$	−2.10516	+	3.64625i	−0.193796	+	0.335664i
$119$	13.3953			1.22794
$120$	−0.0641006	−	0.111026i	−0.00585156	−	0.0101352i
$121$	−6.85272			−0.622975
$122$	−0.788500			−0.0713874
$123$	0.131602	+	0.227942i	0.0118662	+	0.0205528i
$124$	−4.01235	+	6.94960i	−0.360320	+	0.624093i
$125$	1.00000			0.0894427
$126$	1.48259	+	2.56791i	0.132079	+	0.228768i
$127$	0.327318	+	0.566931i	0.0290447	+	0.0503070i	0.880182	−	0.474636i	$-0.157420\pi$
$127$	0.327318	+	0.566931i	0.0290447	+	0.0503070i	−0.851138	+	0.524943i	$0.824087\pi$
$128$	−4.84308	−	8.38846i	−0.428072	−	0.741442i
$129$	0.185317	−	0.320978i	0.0163162	−	0.0282606i
$130$	−1.10767	+	1.91855i	−0.0971494	+	0.168268i
$131$	−1.43266	−	2.48144i	−0.125172	−	0.216805i	0.796628	−	0.604470i	$-0.206615\pi$
$131$	−1.43266	−	2.48144i	−0.125172	−	0.216805i	−0.921800	+	0.387665i	$0.873282\pi$
$132$	−0.176414	−	0.305558i	−0.0153549	−	0.0265954i
$133$	10.0341	+	17.3796i	0.870068	+	1.50700i
$134$	−1.40720			−0.121563
$135$	0.277251	−	0.480213i	0.0238620	−	0.0413301i
$136$	3.34853	+	5.79983i	0.287134	+	0.497331i
$137$	−14.5828			−1.24589			−0.622945	−	0.782265i	$-0.714064\pi$
$137$	−14.5828			−1.24589			−0.622945	+	0.782265i	$0.714064\pi$
$138$	−0.0169152			−0.00143992
$139$	−5.77671	−	10.0056i	−0.489974	−	0.848661i	0.509959	−	0.860199i	$-0.329661\pi$
$139$	−5.77671	−	10.0056i	−0.489974	−	0.848661i	−0.999933	+	0.0115381i	$0.996327\pi$
$140$	5.18676			0.438361
$141$	0.515050	−	0.892092i	0.0433750	−	0.0751277i
$142$	5.04810			0.423627
$143$	−6.30536	+	10.9212i	−0.527281	+	0.913278i
$144$	4.85877	−	8.41564i	0.404898	−	0.701304i
$145$	4.19723	−	7.26981i	0.348561	−	0.603725i
$146$	0.845561	+	1.46455i	0.0699791	+	0.121207i
$147$	0.0626272			0.00516540
$148$	11.3673	+	0.669449i	0.934387	+	0.0550283i
$149$	−0.488881			−0.0400507			−0.0200253	−	0.999799i	$-0.506375\pi$
$149$	−0.488881			−0.0400507			−0.0200253	+	0.999799i	$0.506375\pi$
$150$	0.0165549	+	0.0286739i	0.00135170	+	0.00234121i
$151$	−1.98594	+	3.43975i	−0.161614	+	0.279923i	−0.935448	−	0.353466i	$-0.885003\pi$
$151$	−1.98594	+	3.43975i	−0.161614	+	0.279923i	0.773834	+	0.633388i	$0.218336\pi$
$152$	−5.01663	+	8.68905i	−0.406902	+	0.704775i
$153$	−7.23126	+	12.5249i	−0.584613	+	1.01258i
$154$	−2.01861			−0.162664
$155$	2.14334	−	3.71237i	0.172157	−	0.298185i
$156$	1.07285			0.0858969
$157$	−5.32041	−	9.21522i	−0.424615	−	0.735455i	0.571769	−	0.820414i	$-0.306257\pi$
$157$	−5.32041	−	9.21522i	−0.424615	−	0.735455i	−0.996384	+	0.0849597i	$0.972924\pi$
$158$	3.41536			0.271711
$159$	0.433242			0.0343583
$160$	1.96630	+	3.40573i	0.155449	+	0.269246i
$161$	0.707748	−	1.22586i	0.0557783	−	0.0966109i
$162$	−3.19222			−0.250805
$163$	−11.0589	−	19.1546i	−0.866203	−	1.50031i	−0.865848	−	0.500307i	$-0.833220\pi$
$163$	−11.0589	−	19.1546i	−0.866203	−	1.50031i	−0.000355092	−	1.00000i	$-0.500113\pi$
$164$	−2.66195	−	4.61063i	−0.207863	−	0.360030i
$165$	0.0942375	+	0.163224i	0.00733638	+	0.0127070i
$166$	0.0261304	−	0.0452591i	0.00202811	−	0.00351279i
$167$	−6.29101	+	10.8964i	−0.486813	+	0.843185i	−0.999885	−	0.0151604i	$-0.995174\pi$
$167$	−6.29101	+	10.8964i	−0.486813	+	0.843185i	0.513072	+	0.858346i	$0.328507\pi$
$168$	0.177603	+	0.307617i	0.0137023	+	0.0237332i
$169$	−12.6729	−	21.9501i	−0.974837	−	1.68847i
$170$	−0.864804	−	1.49788i	−0.0663274	−	0.114882i
$171$	−21.6671			−1.65693
$172$	−3.74845	+	6.49250i	−0.285816	+	0.495049i
$173$	−2.01989	−	3.49855i	−0.153569	−	0.265990i	0.778968	−	0.627064i	$-0.215743\pi$
$173$	−2.01989	−	3.49855i	−0.153569	−	0.265990i	−0.932537	+	0.361074i	$0.882410\pi$
$174$	0.277938			0.0210704
$175$	−2.77068			−0.209444
$176$	3.30772	+	5.72914i	0.249329	+	0.431850i
$177$	−1.08919			−0.0818687
$178$	−2.96516	+	5.13581i	−0.222248	+	0.384945i
$179$	−10.6326			−0.794721			−0.397360	−	0.917663i	$-0.630074\pi$
$179$	−10.6326			−0.794721			−0.397360	+	0.917663i	$0.630074\pi$
$180$	−2.80000	+	4.84975i	−0.208700	+	0.361479i
$181$	−0.312453	+	0.541185i	−0.0232245	+	0.0402259i	−0.877404	−	0.479752i	$-0.840727\pi$
$181$	−0.312453	+	0.541185i	−0.0232245	+	0.0402259i	0.854180	+	0.519978i	$0.174060\pi$
$182$	3.06901	−	5.31569i	0.227490	−	0.394025i
$183$	−0.101991	−	0.176653i	−0.00753937	−	0.0130586i
$184$	0.707687			0.0521714
$185$	−6.07224	−	0.357609i	−0.446440	−	0.0262919i
$186$	0.141931			0.0104069
$187$	−4.92284	−	8.52661i	−0.359994	−	0.623528i
$188$	−10.4180	+	18.0446i	−0.759813	+	1.31603i
$189$	−0.768175	+	1.33052i	−0.0558765	+	0.0967810i
$190$	1.29561	−	2.24407i	0.0939936	−	0.162802i
$191$	9.44797			0.683631			0.341816	−	0.939767i	$-0.388958\pi$
$191$	9.44797			0.683631			0.341816	+	0.939767i	$0.388958\pi$
$192$	0.235538	−	0.407964i	0.0169985	−	0.0294423i
$193$	17.1241			1.23262			0.616308	−	0.787505i	$-0.288628\pi$
$193$	17.1241			1.23262			0.616308	+	0.787505i	$0.288628\pi$
$194$	3.35441	+	5.81001i	0.240833	+	0.417135i
$195$	−0.573101			−0.0410406
$196$	−1.26677			−0.0904839
$197$	1.14837	+	1.98903i	0.0818179	+	0.141713i	0.904031	−	0.427467i	$-0.140594\pi$
$197$	1.14837	+	1.98903i	0.0818179	+	0.141713i	−0.822213	+	0.569180i	$0.807261\pi$
$198$	1.08972	−	1.88745i	0.0774429	−	0.134135i
$199$	25.5292			1.80971			0.904857	−	0.425715i	$-0.139977\pi$
$199$	25.5292			1.80971			0.904857	+	0.425715i	$0.139977\pi$
$200$	−0.692612	−	1.19964i	−0.0489751	−	0.0848273i
$201$	−0.182018	−	0.315264i	−0.0128385	−	0.0222370i
$202$	0.804954	+	1.39422i	0.0566364	+	0.0980971i
$203$	−11.6292	+	20.1423i	−0.816209	+	1.41372i
$204$	−0.418808	+	0.725398i	−0.0293225	+	0.0507880i
$205$	1.42197	+	2.46293i	0.0993148	+	0.172018i
$206$	−0.603789	−	1.04579i	−0.0420680	−	0.0728638i
$207$	0.764137	+	1.32352i	0.0531112	+	0.0919912i
$208$	−20.1157			−1.39478
$209$	7.37519	−	12.7742i	0.510153	−	0.883610i
$210$	−0.0458683	−	0.0794462i	−0.00316521	−	0.00548231i
$211$	−11.6634			−0.802941			−0.401470	−	0.915872i	$-0.631501\pi$
$211$	−11.6634			−0.802941			−0.401470	+	0.915872i	$0.631501\pi$
$212$	−8.76328			−0.601865
$213$	0.652961	+	1.13096i	0.0447401	+	0.0774922i
$214$	4.85745			0.332049
$215$	2.00236	−	3.46819i	0.136560	−	0.236529i
$216$	−0.768110			−0.0522632
$217$	−5.93851	+	10.2858i	−0.403132	+	0.698246i
$218$	−0.102984	+	0.178373i	−0.00697493	+	0.0120809i
$219$	−0.218743	+	0.378874i	−0.0147813	+	0.0256019i
$220$	−1.90616	−	3.30157i	−0.128514	−	0.222592i
$221$	29.9380			2.01385
$222$	−0.0902711	−	0.180035i	−0.00605860	−	0.0120831i
$223$	−2.49921			−0.167360			−0.0836798	−	0.996493i	$-0.526667\pi$
$223$	−2.49921			−0.167360			−0.0836798	+	0.996493i	$0.526667\pi$
$224$	−5.44799	−	9.43619i	−0.364009	−	0.630482i
$225$	1.49572	−	2.59066i	0.0997145	−	0.172711i
$226$	0.636110	−	1.10177i	0.0423134	−	0.0732890i
$227$	−1.27662	+	2.21117i	−0.0847323	+	0.146761i	−0.905277	−	0.424822i	$-0.860337\pi$
$227$	−1.27662	+	2.21117i	−0.0847323	+	0.146761i	0.820545	+	0.571582i	$0.193670\pi$
$228$	−1.25488			−0.0831066
$229$	0.613571	−	1.06274i	0.0405459	−	0.0702276i	−0.845040	−	0.534703i	$-0.820424\pi$
$229$	0.613571	−	1.06274i	0.0405459	−	0.0702276i	0.885586	+	0.464475i	$0.153757\pi$
$230$	−0.182770			−0.0120515
$231$	−0.261102	−	0.452243i	−0.0171793	−	0.0297554i
$232$	−11.6282			−0.763429
$233$	15.6292			1.02391			0.511953	−	0.859013i	$-0.328922\pi$
$233$	15.6292			1.02391			0.511953	+	0.859013i	$0.328922\pi$
$234$	3.31353	+	5.73921i	0.216612	+	0.375184i
$235$	5.56515	−	9.63912i	0.363030	−	0.628787i
$236$	22.0314			1.43412
$237$	0.441769	+	0.765166i	0.0286960	+	0.0497029i
$238$	2.39610	+	4.15016i	0.155316	+	0.269015i
$239$	−8.31261	−	14.3979i	−0.537698	−	0.931320i	−0.999028	−	0.0440911i	$-0.985961\pi$
$239$	−8.31261	−	14.3979i	−0.537698	−	0.931320i	0.461330	−	0.887229i	$-0.347373\pi$
$240$	−0.150321	+	0.260364i	−0.00970318	+	0.0168064i
$241$	−0.899786	+	1.55847i	−0.0579603	+	0.100390i	−0.893550	−	0.448964i	$-0.851793\pi$
$241$	−0.899786	+	1.55847i	−0.0579603	+	0.100390i	0.835589	+	0.549355i	$0.185126\pi$
$242$	−1.22579	−	2.12313i	−0.0787968	−	0.136480i
$243$	−1.24466	−	2.15582i	−0.0798450	−	0.138296i
$244$	2.06299	+	3.57320i	0.132069	+	0.228751i
$245$	0.676691			0.0432322
$246$	−0.0470811	+	0.0815468i	−0.00300178	+	0.00519924i
$247$	22.4259	+	38.8428i	1.42693	+	2.47151i
$248$	−5.93800			−0.377064
$249$	0.0135196			0.000856771
$250$	0.178876	+	0.309823i	0.0113131	+	0.0195949i
$251$	−6.75316			−0.426256			−0.213128	−	0.977024i	$-0.568365\pi$
$251$	−6.75316			−0.426256			−0.213128	+	0.977024i	$0.568365\pi$
$252$	7.75792	−	13.4371i	0.488703	−	0.846459i
$253$	−1.04041			−0.0654098
$254$	−0.117099	+	0.202821i	−0.00734743	+	0.0127261i
$255$	0.223721	−	0.387496i	0.0140099	−	0.0242659i
$256$	−3.35739	+	5.81517i	−0.209837	+	0.363448i
$257$	4.73362	+	8.19887i	0.295275	+	0.511432i	0.975049	−	0.221990i	$-0.0712553\pi$
$257$	4.73362	+	8.19887i	0.295275	+	0.511432i	−0.679774	+	0.733422i	$0.737922\pi$
$258$	0.132595			0.00825502
$259$	16.8243	+	0.990821i	1.04541	+	0.0615667i
$260$	11.5922			0.718920
$261$	−12.5557	−	21.7472i	−0.777180	−	1.34612i
$262$	0.512539	−	0.887744i	0.0316648	−	0.0548450i
$263$	6.06418	−	10.5035i	0.373933	−	0.647671i	−0.616234	−	0.787563i	$-0.711342\pi$
$263$	6.06418	−	10.5035i	0.373933	−	0.647671i	0.990167	+	0.139892i	$0.0446756\pi$
$264$	0.130540	−	0.226102i	0.00803419	−	0.0139156i
$265$	4.68121			0.287564
$266$	−3.58973	+	6.21760i	−0.220101	+	0.381225i
$267$	−1.53415			−0.0938884
$268$	3.68171	+	6.37692i	0.224896	+	0.389532i
$269$	−18.3226			−1.11715			−0.558574	−	0.829455i	$-0.688651\pi$
$269$	−18.3226			−1.11715			−0.558574	+	0.829455i	$0.688651\pi$
$270$	0.198375			0.0120727
$271$	10.9467	+	18.9602i	0.664964	+	1.15175i	0.979295	+	0.202438i	$0.0648864\pi$
$271$	10.9467	+	18.9602i	0.664964	+	1.15175i	−0.314331	+	0.949313i	$0.601780\pi$
$272$	7.85256	−	13.6010i	0.476132	−	0.824684i
$273$	1.58788			0.0961029
$274$	−2.60852	−	4.51808i	−0.157586	−	0.272947i
$275$	1.01824	+	1.76365i	0.0614024	+	0.106352i
$276$	0.0442560	+	0.0766537i	0.00266390	+	0.00461401i
$277$	9.63350	−	16.6857i	0.578821	−	1.00255i	−0.416794	−	0.909001i	$-0.636846\pi$
$277$	9.63350	−	16.6857i	0.578821	−	1.00255i	0.995615	−	0.0935460i	$-0.0298202\pi$
$278$	2.06664	−	3.57952i	0.123949	−	0.214685i
$279$	−6.41165	−	11.1053i	−0.383856	−	0.664857i
$280$	1.91901	+	3.32382i	0.114683	+	0.198636i
$281$	−2.97557	−	5.15384i	−0.177508	−	0.307452i	0.763519	−	0.645786i	$-0.223470\pi$
$281$	−2.97557	−	5.15384i	−0.177508	−	0.307452i	−0.941026	+	0.338334i	$0.890137\pi$
$282$	0.368521			0.0219451
$283$	4.13549	−	7.16287i	0.245829	−	0.425789i	−0.716535	−	0.697551i	$-0.754273\pi$
$283$	4.13549	−	7.16287i	0.245829	−	0.425789i	0.962364	+	0.271762i	$0.0876064\pi$
$284$	−13.2076	−	22.8762i	−0.783726	−	1.35745i
$285$	0.670338			0.0397074
$286$	−4.51153			−0.266772
$287$	−3.93983	−	6.82399i	−0.232561	−	0.402808i
$288$	11.7641			0.693206
$289$	−3.18688	+	5.51984i	−0.187464	+	0.324696i
$290$	3.00314			0.176351
$291$	−0.867772	+	1.50302i	−0.0508697	+	0.0881089i
$292$	4.42456	−	7.66357i	0.258928	−	0.448476i
$293$	3.74515	−	6.48679i	0.218794	−	0.378963i	−0.735645	−	0.677367i	$-0.763121\pi$
$293$	3.74515	−	6.48679i	0.218794	−	0.378963i	0.954440	+	0.298404i	$0.0964544\pi$
$294$	0.0112025	+	0.0194034i	0.000653345	+	0.00113163i
$295$	−11.7688			−0.685206
$296$	3.77671	+	7.53218i	0.219517	+	0.437799i
$297$	1.12924			0.0655249
$298$	−0.0874493	−	0.151467i	−0.00506580	−	0.00877423i
$299$	1.58179	−	2.73975i	0.0914775	−	0.158444i
$300$	0.0866266	−	0.150042i	0.00500139	−	0.00866266i
$301$	−5.54791	+	9.60927i	−0.319776	+	0.553869i
$302$	−1.42095			−0.0817666
$303$	−0.208238	+	0.360679i	−0.0119630	+	0.0207205i
$304$	23.5288			1.34947
$305$	−1.10202	−	1.90875i	−0.0631013	−	0.109295i
$306$	−5.17401			−0.295778
$307$	10.0716			0.574817			0.287408	−	0.957808i	$-0.407206\pi$
$307$	10.0716			0.574817			0.287408	+	0.957808i	$0.407206\pi$
$308$	5.28138	+	9.14762i	0.300935	+	0.521234i
$309$	0.156198	−	0.270542i	0.00888577	−	0.0153906i
$310$	1.53357			0.0871009
$311$	−2.97981	−	5.16118i	−0.168970	−	0.292664i	0.769088	−	0.639143i	$-0.220711\pi$
$311$	−2.97981	−	5.16118i	−0.168970	−	0.292664i	−0.938058	+	0.346479i	$0.887377\pi$
$312$	0.396937	+	0.687514i	0.0224721	+	0.0389228i
$313$	7.07137	+	12.2480i	0.399698	+	0.692296i	0.993688	−	0.112175i	$-0.0357818\pi$
$313$	7.07137	+	12.2480i	0.399698	+	0.692296i	−0.593991	+	0.804472i	$0.702448\pi$
$314$	1.90339	−	3.29677i	0.107415	−	0.186048i
$315$	−4.14416	+	7.17790i	−0.233497	+	0.404429i
$316$	−8.93576	−	15.4772i	−0.502676	−	0.870660i
$317$	2.44384	+	4.23285i	0.137260	+	0.237741i	0.926458	−	0.376397i	$-0.122837\pi$
$317$	2.44384	+	4.23285i	0.137260	+	0.237741i	−0.789199	+	0.614138i	$0.789504\pi$
$318$	0.0774968	+	0.134228i	0.00434580	+	0.00752715i
$319$	17.0952			0.957147
$320$	2.54501	−	4.40808i	0.142270	−	0.246419i
$321$	0.628301	+	1.08825i	0.0350683	+	0.0607401i
$322$	0.506398			0.0282204
$323$	−35.0176			−1.94843
$324$	8.35197	+	14.4660i	0.463998	+	0.803669i
$325$	−6.19239			−0.343492
$326$	3.95637	−	6.85263i	0.219123	−	0.379532i
$327$	−0.0532829			−0.00294655
$328$	1.96975	−	3.41171i	0.108761	−	0.188380i
$329$	−15.4193	+	26.7070i	−0.850092	+	1.47240i
$330$	−0.0337138	+	0.0583939i	−0.00185588	+	0.00321448i
$331$	12.2406	+	21.2013i	0.672802	+	1.16533i	0.977106	+	0.212753i	$0.0682428\pi$
$331$	12.2406	+	21.2013i	0.672802	+	1.16533i	−0.304304	+	0.952575i	$0.598424\pi$
$332$	−0.273465			−0.0150083
$333$	−10.0088	+	15.1962i	−0.548479	+	0.832748i
$334$	−4.50126			−0.246298
$335$	−1.96671	−	3.40645i	−0.107453	−	0.186114i
$336$	0.416492	−	0.721385i	0.0227215	−	0.0393548i
$337$	4.43827	−	7.68730i	0.241768	−	0.418754i	−0.719450	−	0.694544i	$-0.755606\pi$
$337$	4.43827	−	7.68730i	0.241768	−	0.418754i	0.961218	+	0.275790i	$0.0889394\pi$
$338$	4.53376	−	7.85270i	0.246604	−	0.427131i
$339$	0.329118			0.0178752
$340$	−4.52526	+	7.83797i	−0.245416	+	0.425074i
$341$	8.72975			0.472743
$342$	−3.87574	−	6.71298i	−0.209576	−	0.362996i
$343$	17.5199			0.945985
$344$	−5.54744			−0.299098
$345$	−0.0236409	−	0.0409472i	−0.00127278	−	0.00220452i
$346$	0.722621	−	1.25162i	0.0388483	−	0.0672873i
$347$	3.32706			0.178606			0.0893029	−	0.996005i	$-0.471536\pi$
$347$	3.32706			0.178606			0.0893029	+	0.996005i	$0.471536\pi$
$348$	−0.727183	−	1.25952i	−0.0389811	−	0.0675172i
$349$	14.3885	+	24.9216i	0.770198	+	1.33402i	0.937454	+	0.348109i	$0.113176\pi$
$349$	14.3885	+	24.9216i	0.770198	+	1.33402i	−0.167256	+	0.985914i	$0.553491\pi$
$350$	−0.495610	−	0.858422i	−0.0264915	−	0.0458846i
$351$	−1.71685	+	2.97367i	−0.0916386	+	0.158723i
$352$	−4.00434	+	6.93572i	−0.213432	+	0.369675i
$353$	−18.0163	−	31.2052i	−0.958912	−	1.66088i	−0.725152	−	0.688589i	$-0.758230\pi$
$353$	−18.0163	−	31.2052i	−0.958912	−	1.66088i	−0.233760	−	0.972294i	$-0.575103\pi$
$354$	−0.194831	−	0.337457i	−0.0103552	−	0.0179356i
$355$	7.05529	+	12.2201i	0.374456	+	0.648576i
$356$	31.0316			1.64467
$357$	−0.619860	+	1.07363i	−0.0328065	+	0.0568225i
$358$	−1.90193	−	3.29424i	−0.100520	−	0.174106i
$359$	−1.95449			−0.103154			−0.0515771	−	0.998669i	$-0.516425\pi$
$359$	−1.95449			−0.103154			−0.0515771	+	0.998669i	$0.516425\pi$
$360$	−4.14381			−0.218398
$361$	−16.7309	−	28.9788i	−0.880575	−	1.52520i
$362$	−0.223562			−0.0117502
$363$	0.317107	−	0.549245i	0.0166438	−	0.0288279i
$364$	−32.1184			−1.68346
$365$	−2.36353	+	4.09376i	−0.123713	+	0.214277i
$366$	0.0364875	−	0.0631982i	0.00190723	−	0.00330342i
$367$	12.6555	−	21.9200i	0.660614	−	1.14422i	−0.319841	−	0.947471i	$-0.603629\pi$
$367$	12.6555	−	21.9200i	0.660614	−	1.14422i	0.980455	−	0.196746i	$-0.0630373\pi$
$368$	−0.829791	−	1.43724i	−0.0432558	−	0.0749213i
$369$	8.50747			0.442881
$370$	−0.975386	−	1.94529i	−0.0507079	−	0.101131i
$371$	−12.9702			−0.673377
$372$	−0.371340	−	0.643180i	−0.0192531	−	0.0333473i
$373$	−11.6839	+	20.2372i	−0.604972	+	1.04784i	0.387084	+	0.922044i	$0.373482\pi$
$373$	−11.6839	+	20.2372i	−0.604972	+	1.04784i	−0.992056	+	0.125797i	$0.959851\pi$
$374$	1.76116	−	3.05042i	0.0910675	−	0.157734i
$375$	−0.0462746	+	0.0801499i	−0.00238961	+	0.00413892i
$376$	−15.4180			−0.795120
$377$	−25.9909	+	45.0175i	−1.33860	+	2.31852i
$378$	−0.549634			−0.0282701
$379$	13.1399	+	22.7590i	0.674953	+	1.16905i	0.976483	+	0.215596i	$0.0691694\pi$
$379$	13.1399	+	22.7590i	0.674953	+	1.16905i	−0.301530	+	0.953457i	$0.597497\pi$
$380$	−13.5591			−0.695567
$381$	−0.0605859			−0.00310391
$382$	1.69002	+	2.92720i	0.0864690	+	0.149769i
$383$	−1.49652	+	2.59204i	−0.0764684	+	0.132447i	−0.901724	−	0.432312i	$-0.857698\pi$
$383$	−1.49652	+	2.59204i	−0.0764684	+	0.132447i	0.825255	+	0.564760i	$0.191031\pi$
$384$	0.896445			0.0457465
$385$	−2.82123	−	4.88651i	−0.143783	−	0.249040i
$386$	3.06309	+	5.30543i	0.155907	+	0.270039i
$387$	−5.98993	−	10.3749i	−0.304485	−	0.527384i
$388$	17.5526	−	30.4020i	0.891099	−	1.54343i
$389$	−0.179623	+	0.311117i	−0.00910727	+	0.0157743i	−0.870543	−	0.492092i	$-0.836232\pi$
$389$	−0.179623	+	0.311117i	−0.00910727	+	0.0157743i	0.861436	+	0.507866i	$0.169566\pi$
$390$	−0.102514	−	0.177560i	−0.00519101	−	0.00899110i
$391$	1.23497	+	2.13903i	0.0624550	+	0.108175i
$392$	−0.468684	−	0.811785i	−0.0236721	−	0.0410013i
$393$	0.265183			0.0133767
$394$	−0.410832	+	0.711583i	−0.0206974	+	0.0358490i
$395$	4.77335	+	8.26768i	0.240173	+	0.415992i
$396$	−11.4043			−0.573089
$397$	−19.0744			−0.957318			−0.478659	−	0.878001i	$-0.658877\pi$
$397$	−19.0744			−0.957318			−0.478659	+	0.878001i	$0.658877\pi$
$398$	4.56657	+	7.90953i	0.228901	+	0.396469i
$399$	−1.85730			−0.0929811
$400$	−1.62423	+	2.81325i	−0.0812114	+	0.140662i
$401$	−16.9963			−0.848755			−0.424378	−	0.905485i	$-0.639507\pi$
$401$	−16.9963			−0.848755			−0.424378	+	0.905485i	$0.639507\pi$
$402$	0.0651174	−	0.112787i	0.00324776	−	0.00562528i
$403$	−13.2724	+	22.9885i	−0.661145	+	1.14514i
$404$	4.21208	−	7.29554i	0.209559	−	0.362967i
$405$	−4.46149	−	7.72753i	−0.221693	−	0.383984i
$406$	−8.32076			−0.412952
$407$	−5.55232	−	11.0734i	−0.275218	−	0.548890i
$408$	−0.619807			−0.0306850
$409$	−0.207634	−	0.359633i	−0.0102668	−	0.0177827i	0.860846	−	0.508865i	$-0.169935\pi$
$409$	−0.207634	−	0.359633i	−0.0102668	−	0.0177827i	−0.871113	+	0.491082i	$0.836601\pi$
$410$	−0.508715	+	0.881120i	−0.0251236	+	0.0435154i
$411$	0.674812	−	1.16881i	0.0332860	−	0.0576531i
$412$	−3.15944	+	5.47232i	−0.155655	+	0.269602i
$413$	32.6076			1.60452
$414$	−0.273372	+	0.473494i	−0.0134355	+	0.0232710i
$415$	0.146080			0.00717081
$416$	−12.1761	−	21.0896i	−0.596982	−	1.03400i
$417$	1.06926			0.0523619
$418$	5.27699			0.258106
$419$	−10.3760	−	17.9718i	−0.506901	−	0.877979i	−0.999968	−	0.00798721i	$-0.997458\pi$
$419$	−10.3760	−	17.9718i	−0.506901	−	0.877979i	0.493067	−	0.869991i	$-0.335876\pi$
$420$	−0.240015	+	0.415718i	−0.0117115	+	0.0202850i
$421$	−11.5314			−0.562008			−0.281004	−	0.959707i	$-0.590667\pi$
$421$	−11.5314			−0.562008			−0.281004	+	0.959707i	$0.590667\pi$
$422$	−2.08631	−	3.61359i	−0.101560	−	0.175907i
$423$	−16.6478	−	28.8348i	−0.809443	−	1.40200i
$424$	−3.24226	−	5.61576i	−0.157458	−	0.272726i
$425$	2.41732	−	4.18692i	0.117257	−	0.203096i
$426$	−0.233599	+	0.404605i	−0.0113179	+	0.0196032i
$427$	3.05334	+	5.28854i	0.147762	+	0.255931i
$428$	−12.7088	−	22.0123i	−0.614303	−	1.06400i
$429$	−0.583556	−	1.01075i	−0.0281743	−	0.0487994i
$430$	1.43270			0.0690910
$431$	0.360230	−	0.623937i	0.0173517	−	0.0300540i	−0.857219	−	0.514952i	$-0.827810\pi$
$431$	0.360230	−	0.623937i	0.0173517	−	0.0300540i	0.874571	+	0.484898i	$0.161143\pi$
$432$	0.900638	+	1.55995i	0.0433320	+	0.0750532i
$433$	28.4761			1.36848			0.684238	−	0.729259i	$-0.260135\pi$
$433$	28.4761			1.36848			0.684238	+	0.729259i	$0.260135\pi$
$434$	−4.24904			−0.203960
$435$	0.388450	+	0.672815i	0.0186247	+	0.0322590i
$436$	1.07776			0.0516156
$437$	−1.85018	+	3.20460i	−0.0885060	+	0.153297i
$438$	−0.156512			−0.00747842
$439$	−11.4437	+	19.8211i	−0.546180	+	0.946011i	0.452352	+	0.891839i	$0.350585\pi$
$439$	−11.4437	+	19.8211i	−0.546180	+	0.946011i	−0.998532	+	0.0541714i	$0.982748\pi$
$440$	1.41050	−	2.44305i	0.0672427	−	0.116468i
$441$	1.01214	−	1.75308i	0.0481971	−	0.0834798i
$442$	5.35521	+	9.27549i	0.254721	+	0.441190i
$443$	2.51641			0.119558			0.0597790	−	0.998212i	$-0.480960\pi$
$443$	2.51641			0.119558			0.0597790	+	0.998212i	$0.480960\pi$
$444$	−0.579674	+	0.880111i	−0.0275101	+	0.0417682i
$445$	−16.5766			−0.785806
$446$	−0.447050	−	0.774313i	−0.0211684	−	0.0366648i
$447$	0.0226228	−	0.0391838i	0.00107002	−	0.00185333i
$448$	−7.05142	+	12.2134i	−0.333148	+	0.577029i
$449$	−18.7859	+	32.5381i	−0.886561	+	1.53557i	−0.0426469	+	0.999090i	$0.513579\pi$
$449$	−18.7859	+	32.5381i	−0.886561	+	1.53557i	−0.843914	+	0.536478i	$0.819754\pi$
$450$	1.07019			0.0504495
$451$	−2.89583	+	5.01572i	−0.136359	+	0.236181i
$452$	−6.65714			−0.313126
$453$	−0.183797	−	0.318346i	−0.00863554	−	0.0149572i
$454$	−0.913430			−0.0428694
$455$	17.1572			0.804341
$456$	−0.464285	−	0.804164i	−0.0217421	−	0.0376584i
$457$	9.71917	−	16.8341i	0.454644	−	0.787466i	−0.544024	−	0.839070i	$-0.683100\pi$
$457$	9.71917	−	16.8341i	0.454644	−	0.787466i	0.998668	+	0.0516036i	$0.0164332\pi$
$458$	0.439014			0.0205138
$459$	−1.34041	−	2.32166i	−0.0625650	−	0.108366i
$460$	0.478190	+	0.828249i	0.0222957	+	0.0386173i
$461$	9.48509	+	16.4287i	0.441765	+	0.765159i	0.997821	−	0.0659862i	$-0.0210193\pi$
$461$	9.48509	+	16.4287i	0.441765	+	0.765159i	−0.556056	+	0.831145i	$0.687686\pi$
$462$	0.0934102	−	0.161791i	0.00434583	−	0.00752721i
$463$	−0.109249	+	0.189225i	−0.00507723	+	0.00879402i	−0.868553	−	0.495597i	$-0.834949\pi$
$463$	−0.109249	+	0.189225i	−0.00507723	+	0.00879402i	0.863476	+	0.504391i	$0.168283\pi$
$464$	13.6345	+	23.6157i	0.632966	+	1.09633i
$465$	0.198364	+	0.343576i	0.00919891	+	0.0159330i
$466$	2.79570	+	4.84230i	0.129509	+	0.224315i
$467$	−11.9630			−0.553580			−0.276790	−	0.960930i	$-0.589271\pi$
$467$	−11.9630			−0.553580			−0.276790	+	0.960930i	$0.589271\pi$
$468$	17.3387	−	30.0315i	0.801483	−	1.38821i
$469$	5.44914	+	9.43819i	0.251618	+	0.435815i
$470$	3.98190			0.183671
$471$	0.984799			0.0453771
$472$	8.15122	+	14.1183i	0.375190	+	0.649848i
$473$	8.15557			0.374993
$474$	−0.158044	+	0.273741i	−0.00725921	+	0.0125733i
$475$	7.24305			0.332334
$476$	12.5381	−	21.7165i	0.574681	−	0.995376i
$477$	7.00177	−	12.1274i	0.320589	−	0.555276i
$478$	2.97386	−	5.15088i	0.136021	−	0.235596i
$479$	8.91840	+	15.4471i	0.407492	+	0.705797i	0.994608	−	0.103706i	$-0.0330700\pi$
$479$	8.91840	+	15.4471i	0.407492	+	0.705797i	−0.587116	+	0.809503i	$0.699737\pi$
$480$	−0.363958			−0.0166123
$481$	37.6017	+	2.21446i	1.71449	+	0.100970i
$482$	−0.643802			−0.0293244
$483$	0.0655014	+	0.113452i	0.00298042	+	0.00516224i
$484$	−6.41419	+	11.1097i	−0.291554	+	0.504987i
$485$	−9.37633	+	16.2403i	−0.425757	+	0.737433i
$486$	0.445281	−	0.771249i	0.0201984	−	0.0349846i
$487$	−19.0241			−0.862062			−0.431031	−	0.902337i	$-0.641850\pi$
$487$	−19.0241			−0.862062			−0.431031	+	0.902337i	$0.641850\pi$
$488$	−1.52654	+	2.64405i	−0.0691033	+	0.119690i
$489$	2.04699			0.0925681
$490$	0.121044	+	0.209655i	0.00546822	+	0.00947123i
$491$	31.9253			1.44077			0.720385	−	0.693575i	$-0.243965\pi$
$491$	31.9253			1.44077			0.720385	+	0.693575i	$0.243965\pi$
$492$	0.492722			0.0222136
$493$	−20.2921	−	35.1469i	−0.913910	−	1.58294i
$494$	−8.02294	+	13.8961i	−0.360969	+	0.625217i
$495$	6.09202			0.273816
$496$	6.96254	+	12.0595i	0.312627	+	0.541486i
$497$	−19.5480	−	33.8581i	−0.876846	−	1.51874i
$498$	0.00241834	+	0.00418869i	0.000108369	+	0.000187700i
$499$	−4.55248	+	7.88512i	−0.203797	+	0.352987i	−0.949749	−	0.313013i	$-0.898662\pi$
$499$	−4.55248	+	7.88512i	−0.203797	+	0.352987i	0.745952	+	0.666000i	$0.231995\pi$
$500$	0.936006	−	1.62121i	0.0418595	−	0.0725027i
$501$	−0.582228	−	1.00845i	−0.0260120	−	0.0450541i
$502$	−1.20798	−	2.09229i	−0.0539148	−	0.0933833i
$503$	9.13175	+	15.8166i	0.407164	+	0.705230i	0.994571	−	0.104063i	$-0.0331842\pi$
$503$	9.13175	+	15.8166i	0.407164	+	0.705230i	−0.587406	+	0.809292i	$0.699851\pi$
$504$	11.4812			0.511413
$505$	−2.25003	+	3.89716i	−0.100125	+	0.173421i
$506$	−0.186104	−	0.322342i	−0.00827334	−	0.0143299i
$507$	2.34573			0.104177
$508$	1.22549			0.0543721
$509$	−13.5136	−	23.4062i	−0.598978	−	1.03746i	−0.992972	−	0.118348i	$-0.962240\pi$
$509$	−13.5136	−	23.4062i	−0.598978	−	1.03746i	0.393994	−	0.919113i	$-0.371093\pi$
$510$	0.160074			0.00708818
$511$	6.54860	−	11.3425i	0.289693	−	0.501763i
$512$	−21.7745			−0.962308
$513$	2.00814	−	3.47821i	0.0886617	−	0.153567i
$514$	−1.69347	+	2.93317i	−0.0746956	+	0.129377i
$515$	1.68773	−	2.92323i	0.0743701	−	0.128813i
$516$	−0.346916	−	0.600875i	−0.0152721	−	0.0264521i
$517$	22.6667			0.996880
$518$	2.70249	+	5.38978i	0.118740	+	0.236813i
$519$	0.373878			0.0164114
$520$	4.28893	+	7.42864i	0.188082	+	0.325767i
$521$	12.2187	−	21.1634i	0.535311	−	0.927186i	−0.463837	−	0.885921i	$-0.653528\pi$
$521$	12.2187	−	21.1634i	0.535311	−	0.927186i	0.999148	−	0.0412658i	$-0.0131390\pi$
$522$	4.49185	−	7.78011i	0.196603	−	0.340526i
$523$	−6.43876	+	11.1523i	−0.281547	+	0.487654i	−0.971766	−	0.235947i	$-0.924181\pi$
$523$	−6.43876	+	11.1523i	−0.281547	+	0.487654i	0.690219	+	0.723601i	$0.257514\pi$
$524$	−5.36393			−0.234324
$525$	0.128212	−	0.222070i	0.00559564	−	0.00969193i
$526$	4.33896			0.189187
$527$	−10.3623	−	17.9480i	−0.451387	−	0.781826i
$528$	−0.612253			−0.0266449
$529$	−22.7390			−0.988652
$530$	0.837358	+	1.45035i	0.0363725	+	0.0629991i
$531$	−17.6028	+	30.4890i	−0.763897	+	1.32311i
$532$	37.5680			1.62878
$533$	−8.80541	−	15.2514i	−0.381405	−	0.660612i
$534$	−0.274423	−	0.475315i	−0.0118755	−	0.0205689i
$535$	6.78884	+	11.7586i	0.293507	+	0.508369i
$536$	−2.72434	+	4.71869i	−0.117674	+	0.203817i
$537$	0.492021	−	0.852205i	0.0212323	−	0.0367753i
$538$	−3.27748	−	5.67676i	−0.141302	−	0.244742i
$539$	0.689036	+	1.19345i	0.0296789	+	0.0514053i
$540$	−0.519017	−	0.898965i	−0.0223350	−	0.0386853i
$541$	27.7984			1.19515			0.597573	−	0.801815i	$-0.296132\pi$
$541$	27.7984			1.19515			0.597573	+	0.801815i	$0.296132\pi$
$542$	−3.91621	+	6.78307i	−0.168216	+	0.291358i
$543$	−0.0289173	−	0.0500862i	−0.00124096	−	0.00214940i
$544$	19.0127			0.815162
$545$	−0.575725			−0.0246614
$546$	0.284035	+	0.491962i	0.0121556	+	0.0210540i
$547$	13.2756			0.567623			0.283811	−	0.958880i	$-0.408401\pi$
$547$	13.2756			0.567623			0.283811	+	0.958880i	$0.408401\pi$
$548$	−13.6496	+	23.6418i	−0.583081	+	1.00993i
$549$	−6.59323			−0.281392
$550$	−0.364280	+	0.630951i	−0.0155329	+	0.0269038i
$551$	30.4007	−	52.6556i	1.29512	−	2.24321i
$552$	−0.0327479	+	0.0567211i	−0.00139384	+	0.00241421i
$553$	−13.2254	−	22.9071i	−0.562403	−	0.974110i
$554$	6.89282			0.292848
$555$	0.309653	−	0.470141i	0.0131440	−	0.0199564i
$556$	−21.6282			−0.917238
$557$	9.83840	+	17.0406i	0.416866	+	0.722034i	0.995622	−	0.0934671i	$-0.0297950\pi$
$557$	9.83840	+	17.0406i	0.416866	+	0.722034i	−0.578756	+	0.815501i	$0.696462\pi$
$558$	2.29379	−	3.97296i	0.0971038	−	0.168189i
$559$	−12.3994	+	21.4764i	−0.524439	+	0.908356i
$560$	4.50023	−	7.79462i	0.190169	−	0.329383i
$561$	0.911209			0.0384713
$562$	1.06452	−	1.84380i	0.0449040	−	0.0777760i
$563$	11.5785			0.487975			0.243988	−	0.969778i	$-0.421544\pi$
$563$	11.5785			0.487975			0.243988	+	0.969778i	$0.421544\pi$
$564$	−0.964180	−	1.67001i	−0.0405993	−	0.0703200i
$565$	3.55614			0.149608
$566$	2.95897			0.124375
$567$	12.3614	+	21.4106i	0.519129	+	0.899159i
$568$	9.77315	−	16.9276i	0.410072	−	0.710266i
$569$	−7.13372			−0.299061			−0.149530	−	0.988757i	$-0.547776\pi$
$569$	−7.13372			−0.299061			−0.149530	+	0.988757i	$0.547776\pi$
$570$	0.119908	+	0.207686i	0.00502238	+	0.00869903i
$571$	−7.75168	−	13.4263i	−0.324398	−	0.561873i	0.656993	−	0.753897i	$-0.271828\pi$
$571$	−7.75168	−	13.4263i	−0.324398	−	0.561873i	−0.981390	+	0.192024i	$0.938495\pi$
$572$	11.8037	+	20.4446i	0.493538	+	0.854834i
$573$	−0.437201	+	0.757254i	−0.0182643	+	0.0316347i
$574$	1.40949	−	2.44130i	0.0588309	−	0.101898i
$575$	−0.255442	−	0.442438i	−0.0106526	−	0.0184509i
$576$	−7.61323	−	13.1865i	−0.317218	−	0.549437i
$577$	−9.83190	−	17.0294i	−0.409308	−	0.708941i	0.585505	−	0.810669i	$-0.300896\pi$
$577$	−9.83190	−	17.0294i	−0.409308	−	0.708941i	−0.994812	+	0.101728i	$0.967563\pi$
$578$	−2.28023			−0.0948452
$579$	−0.792408	+	1.37249i	−0.0329314	+	0.0570388i
$580$	−7.85726	−	13.6092i	−0.326255	−	0.565090i
$581$	−0.404743			−0.0167916
$582$	−0.620896			−0.0257370
$583$	4.76661	+	8.25601i	0.197413	+	0.341929i
$584$	6.54804			0.270960
$585$	−9.26207	+	16.0424i	−0.382940	+	0.663271i
$586$	2.67968			0.110697
$587$	−6.19424	+	10.7287i	−0.255664	+	0.442822i	−0.965076	−	0.261972i	$-0.915627\pi$
$587$	−6.19424	+	10.7287i	−0.255664	+	0.442822i	0.709412	+	0.704794i	$0.248961\pi$
$588$	0.0586194	−	0.101532i	0.00241742	−	0.00418710i
$589$	15.5243	−	26.8889i	0.639668	−	1.10794i
$590$	−2.10516	−	3.64625i	−0.0866682	−	0.150114i
$591$	−0.212561			−0.00874359
$592$	10.8688	−	16.5019i	0.446703	−	0.678223i
$593$	27.8062			1.14186			0.570931	−	0.820998i	$-0.306582\pi$
$593$	27.8062			1.14186			0.570931	+	0.820998i	$0.306582\pi$
$594$	0.201994	+	0.349863i	0.00828791	+	0.0143551i
$595$	−6.69763	+	11.6006i	−0.274576	+	0.475580i
$596$	−0.457596	+	0.792579i	−0.0187439	+	0.0324653i
$597$	−1.18135	+	2.04616i	−0.0483495	+	0.0837437i
$598$	1.13178			0.0462821
$599$	0.663341	−	1.14894i	0.0271034	−	0.0469444i	−0.852156	−	0.523289i	$-0.824705\pi$
$599$	0.663341	−	1.14894i	0.0271034	−	0.0469444i	0.879259	+	0.476344i	$0.158038\pi$
$600$	0.128201			0.00523380
$601$	2.96671	+	5.13850i	0.121015	+	0.209604i	0.920168	−	0.391523i	$-0.128052\pi$
$601$	2.96671	+	5.13850i	0.121015	+	0.209604i	−0.799153	+	0.601127i	$0.794718\pi$
$602$	−3.96956			−0.161787
$603$	−11.7666			−0.479173
$604$	3.71771	+	6.43925i	0.151271	+	0.262010i
$605$	3.42636	−	5.93463i	0.139301	−	0.241277i
$606$	−0.148996			−0.00605253
$607$	9.97311	+	17.2739i	0.404796	+	0.701127i	0.994298	−	0.106640i	$-0.0340092\pi$
$607$	9.97311	+	17.2739i	0.404796	+	0.701127i	−0.589502	+	0.807767i	$0.700676\pi$
$608$	14.2420	+	24.6679i	0.577589	+	1.00041i
$609$	−1.07627	−	1.86416i	−0.0436127	−	0.0755394i
$610$	0.394250	−	0.682861i	0.0159627	−	0.0276482i
$611$	−34.4616	+	59.6892i	−1.39417	+	2.41477i
$612$	13.5370	+	23.4468i	0.547201	+	0.947780i
$613$	−2.49236	−	4.31689i	−0.100665	−	0.174358i	0.811294	−	0.584639i	$-0.198764\pi$
$613$	−2.49236	−	4.31689i	−0.100665	−	0.174358i	−0.911959	+	0.410281i	$0.865430\pi$
$614$	1.80157	+	3.12042i	0.0727056	+	0.125930i
$615$	−0.263204			−0.0106134
$616$	−3.90804	+	6.76892i	−0.157459	+	0.272727i
$617$	−12.3127	−	21.3262i	−0.495691	−	0.858561i	0.504297	−	0.863530i	$-0.331752\pi$
$617$	−12.3127	−	21.3262i	−0.495691	−	0.858561i	−0.999988	+	0.00496889i	$0.998418\pi$
$618$	0.111760			0.00449566
$619$	13.5019			0.542688			0.271344	−	0.962482i	$-0.412532\pi$
$619$	13.5019			0.542688			0.271344	+	0.962482i	$0.412532\pi$
$620$	−4.01235	−	6.94960i	−0.161140	−	0.279103i
$621$	−0.283286			−0.0113679
$622$	1.06604	−	1.84643i	0.0427442	−	0.0740350i
$623$	45.9285			1.84009
$624$	0.930847	−	1.61227i	0.0372637	−	0.0645426i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−2.52980	+	4.38175i	−0.101111	+	0.175130i
$627$	0.682568	+	1.18224i	0.0272591	+	0.0472142i
$628$	−19.9197			−0.794885
$629$	−16.1758	+	24.5595i	−0.644973	+	0.979253i
$630$	−2.96517			−0.118135
$631$	−16.2924	−	28.2193i	−0.648592	−	1.12339i	−0.983459	−	0.181129i	$-0.942025\pi$
$631$	−16.2924	−	28.2193i	−0.648592	−	1.12339i	0.334868	−	0.942265i	$-0.391308\pi$
$632$	6.61215	−	11.4526i	0.263017	−	0.455559i
$633$	0.539718	−	0.934819i	0.0214519	−	0.0371557i
$634$	−0.874290	+	1.51431i	−0.0347225	+	0.0601411i
$635$	−0.654635			−0.0259784
$636$	0.405517	−	0.702376i	0.0160798	−	0.0278510i
$637$	−4.19034			−0.166027
$638$	3.05793	+	5.29649i	0.121065	+	0.209690i
$639$	42.2108			1.66984
$640$	9.68616			0.382879
$641$	−1.15179	−	1.99496i	−0.0454930	−	0.0787962i	0.842382	−	0.538880i	$-0.181153\pi$
$641$	−1.15179	−	1.99496i	−0.0454930	−	0.0787962i	−0.887875	+	0.460084i	$0.847819\pi$
$642$	−0.224777	+	0.389324i	−0.00887122	+	0.0153654i
$643$	1.78059			0.0702197			0.0351098	−	0.999383i	$-0.488822\pi$
$643$	1.78059			0.0702197			0.0351098	+	0.999383i	$0.488822\pi$
$644$	−1.32491	−	2.29482i	−0.0522089	−	0.0904284i
$645$	0.185317	+	0.320978i	0.00729684	+	0.0126385i
$646$	−6.26382	−	10.8493i	−0.246447	−	0.426858i
$647$	8.69575	−	15.0615i	0.341865	−	0.592128i	−0.642914	−	0.765938i	$-0.722275\pi$
$647$	8.69575	−	15.0615i	0.341865	−	0.592128i	0.984779	+	0.173811i	$0.0556081\pi$
$648$	−6.18017	+	10.7044i	−0.242780	+	0.420507i
$649$	−11.9835	−	20.7560i	−0.470394	−	0.814746i
$650$	−1.10767	−	1.91855i	−0.0434465	−	0.0752516i
$651$	−0.549604	−	0.951942i	−0.0215407	−	0.0373095i
$652$	−41.4049			−1.62154
$653$	3.75990	−	6.51235i	0.147136	−	0.254848i	−0.783032	−	0.621982i	$-0.786328\pi$
$653$	3.75990	−	6.51235i	0.147136	−	0.254848i	0.930168	+	0.367134i	$0.119661\pi$
$654$	−0.00953105	−	0.0165083i	−0.000372694	−	0.000645524i
$655$	2.86533			0.111958
$656$	−9.23843			−0.360700
$657$	7.07035	+	12.2462i	0.275841	+	0.477770i
$658$	−11.0326			−0.430095
$659$	13.9067	−	24.0871i	0.541729	−	0.938302i	−0.457076	−	0.889428i	$-0.651103\pi$
$659$	13.9067	−	24.0871i	0.541729	−	0.938302i	0.998805	−	0.0488744i	$-0.0155634\pi$
$660$	0.352828			0.0137338
$661$	0.907354	−	1.57158i	0.0352920	−	0.0611275i	−0.847840	−	0.530252i	$-0.822097\pi$
$661$	0.907354	−	1.57158i	0.0352920	−	0.0611275i	0.883132	+	0.469125i	$0.155431\pi$
$662$	−4.37910	+	7.58482i	−0.170198	+	0.294792i
$663$	−1.38537	+	2.39953i	−0.0538033	+	0.0931900i
$664$	−0.101177	−	0.175244i	−0.00392643	−	0.00680078i
$665$	−20.0682			−0.778212
$666$	−6.49848	−	0.382711i	−0.251811	−	0.0148298i
$667$	−4.28858			−0.166055
$668$	11.7769	+	20.3981i	0.455660	+	0.789227i
$669$	0.115650	−	0.200311i	0.00447128	−	0.00774449i
$670$	0.703598	−	1.21867i	0.0271824	−	0.0470812i
$671$	2.24424	−	3.88714i	0.0866381	−	0.150062i
$672$	1.00841			0.0389004
$673$	12.1457	−	21.0369i	0.468182	−	0.810915i	−0.531157	−	0.847273i	$-0.678243\pi$
$673$	12.1457	−	21.0369i	0.468182	−	0.810915i	0.999339	+	0.0363587i	$0.0115759\pi$
$674$	3.17561			0.122320
$675$	0.277251	+	0.480213i	0.0106714	+	0.0184834i
$676$	−47.4476			−1.82491
$677$	−36.8733			−1.41716			−0.708578	−	0.705633i	$-0.750663\pi$
$677$	−36.8733			−1.41716			−0.708578	+	0.705633i	$0.750663\pi$
$678$	0.0588714	+	0.101968i	0.00226094	+	0.00391607i
$679$	25.9789	−	44.9967i	0.996977	−	1.72682i
$680$	−6.69706			−0.256821
$681$	−0.118150	−	0.204642i	−0.00452753	−	0.00784190i
$682$	1.56155	+	2.70468i	0.0597948	+	0.103568i
$683$	−15.2416	−	26.3993i	−0.583204	−	1.01014i	−0.995097	−	0.0989072i	$-0.968465\pi$
$683$	−15.2416	−	26.3993i	−0.583204	−	1.01014i	0.411892	−	0.911233i	$-0.364868\pi$
$684$	−20.2806	+	35.1270i	−0.775447	+	1.34311i
$685$	7.29139	−	12.6291i	0.278590	−	0.482532i
$686$	3.13390	+	5.42807i	0.119653	+	0.207245i
$687$	0.0567854	+	0.0983553i	0.00216650	+	0.00375249i
$688$	6.50459	+	11.2663i	0.247985	+	0.429523i
$689$	−28.9879			−1.10435
$690$	0.00845760	−	0.0146490i	0.000321975	−	0.000557678i
$691$	10.0536	+	17.4133i	0.382456	+	0.662433i	0.991413	−	0.130771i	$-0.0417452\pi$
$691$	10.0536	+	17.4133i	0.382456	+	0.662433i	−0.608957	+	0.793203i	$0.708412\pi$
$692$	−7.56251			−0.287484
$693$	−16.8791			−0.641182
$694$	0.595132	+	1.03080i	0.0225909	+	0.0391286i
$695$	11.5534			0.438246
$696$	0.538090	−	0.931999i	0.0203962	−	0.0353273i
$697$	13.7494			0.520797
$698$	−5.14753	+	8.91578i	−0.194837	+	0.337467i
$699$	−0.723237	+	1.25268i	−0.0273553	+	0.0473808i
$700$	−2.59338	+	4.49186i	−0.0980205	+	0.169776i
$701$	6.28918	+	10.8932i	0.237539	+	0.411430i	0.960008	−	0.279974i	$-0.0903259\pi$
$701$	6.28918	+	10.8932i	0.237539	+	0.411430i	−0.722469	+	0.691404i	$0.756993\pi$
$702$	−1.22841			−0.0463635
$703$	−43.9816	−	2.59018i	−1.65880	−	0.0976905i
$704$	10.3658			0.390674
$705$	0.515050	+	0.892092i	0.0193979	+	0.0335981i
$706$	6.44539	−	11.1637i	0.242575	−	0.420153i
$707$	6.23412	−	10.7978i	0.234458	−	0.406093i
$708$	−1.01949	+	1.76581i	−0.0383148	+	0.0663632i
$709$	−8.41335			−0.315970			−0.157985	−	0.987442i	$-0.550500\pi$
$709$	−8.41335			−0.315970			−0.157985	+	0.987442i	$0.550500\pi$
$710$	−2.52405	+	4.37178i	−0.0947259	+	0.164070i
$711$	28.5583			1.07102
$712$	11.4811	+	19.8859i	0.430274	+	0.745257i
$713$	−2.18999			−0.0820157
$714$	−0.443514			−0.0165981
$715$	−6.30536	−	10.9212i	−0.235807	−	0.408430i
$716$	−9.95222	+	17.2377i	−0.371932	+	0.644205i
$717$	1.53865			0.0574619
$718$	−0.349613	−	0.605548i	−0.0130474	−	0.0225988i
$719$	0.582394	+	1.00874i	0.0217196	+	0.0376195i	0.876681	−	0.481072i	$-0.159753\pi$
$719$	0.582394	+	1.00874i	0.0217196	+	0.0376195i	−0.854961	+	0.518692i	$0.826419\pi$
$720$	4.85877	+	8.41564i	0.181076	+	0.313633i
$721$	−4.67615	+	8.09934i	−0.174149	+	0.301635i
$722$	5.98554	−	10.3673i	0.222759	−	0.385829i
$723$	−0.0832744	−	0.144235i	−0.00309701	−	0.00536418i
$724$	0.584916	+	1.01310i	0.0217382	+	0.0376517i
$725$	4.19723	+	7.26981i	0.155881	+	0.269994i
$726$	0.226892			0.00842074
$727$	−13.7157	+	23.7564i	−0.508689	+	0.881075i	0.491261	+	0.871013i	$0.336536\pi$
$727$	−13.7157	+	23.7564i	−0.508689	+	0.881075i	−0.999949	+	0.0100623i	$0.996797\pi$
$728$	−11.8833	−	20.5824i	−0.440423	−	0.762835i
$729$	−26.5386			−0.982910
$730$	−1.69112			−0.0625912
$731$	−9.68070	−	16.7675i	−0.358054	−	0.620167i
$732$	−0.381856			−0.0141138
$733$	10.2010	−	17.6686i	0.376781	−	0.652604i	−0.613811	−	0.789453i	$-0.710364\pi$
$733$	10.2010	−	17.6686i	0.376781	−	0.652604i	0.990592	+	0.136849i	$0.0436975\pi$
$734$	9.05512			0.334230
$735$	−0.0313136	+	0.0542367i	−0.00115502	+	0.00200055i
$736$	1.00455	−	1.73993i	0.0370281	−	0.0641346i
$737$	4.00519	−	6.93719i	0.147533	−	0.255535i
$738$	1.52179	+	2.63581i	0.0560177	+	0.0970256i
$739$	31.3170			1.15201			0.576006	−	0.817445i	$-0.304610\pi$
$739$	31.3170			1.15201			0.576006	+	0.817445i	$0.304610\pi$
$740$	−6.26342	+	9.50966i	−0.230248	+	0.349582i
$741$	−4.15100			−0.152491
$742$	−2.32006	−	4.01845i	−0.0851719	−	0.147522i
$743$	−23.2252	+	40.2272i	−0.852049	+	1.47579i	0.0273061	+	0.999627i	$0.491307\pi$
$743$	−23.2252	+	40.2272i	−0.852049	+	1.47579i	−0.879356	+	0.476166i	$0.842026\pi$
$744$	0.274779	−	0.475930i	0.0100739	−	0.0174485i
$745$	0.244441	−	0.423383i	0.00895561	−	0.0155116i
$746$	−8.35993			−0.306079
$747$	0.218495	−	0.378445i	0.00799432	−	0.0138466i
$748$	−18.4312			−0.673913
$749$	−18.8097	−	32.5794i	−0.687292	−	1.19043i
$750$	−0.0331097			−0.00120900
$751$	−29.1714			−1.06448			−0.532239	−	0.846594i	$-0.678649\pi$
$751$	−29.1714			−1.06448			−0.532239	+	0.846594i	$0.678649\pi$
$752$	18.0782	+	31.3123i	0.659242	+	1.14184i
$753$	0.312499	−	0.541265i	0.0113881	−	0.0197248i
$754$	−18.5966			−0.677249
$755$	−1.98594	−	3.43975i	−0.0722758	−	0.125185i
$756$	1.43803	+	2.49075i	0.0523008	+	0.0905876i
$757$	−5.70362	−	9.87896i	−0.207302	−	0.359057i	0.743562	−	0.668667i	$-0.233135\pi$
$757$	−5.70362	−	9.87896i	−0.207302	−	0.359057i	−0.950864	+	0.309610i	$0.899801\pi$
$758$	−4.70085	+	8.14211i	−0.170743	+	0.295735i
$759$	0.0481444	−	0.0833885i	0.00174753	−	0.00302681i
$760$	−5.01663	−	8.68905i	−0.181972	−	0.315185i
$761$	18.2391	+	31.5910i	0.661165	+	1.14517i	0.980310	+	0.197466i	$0.0632711\pi$
$761$	18.2391	+	31.5910i	0.661165	+	1.14517i	−0.319145	+	0.947706i	$0.603396\pi$
$762$	−0.0108374	−	0.0187709i	−0.000392597	−	0.000679999i
$763$	1.59515			0.0577484
$764$	8.84336	−	15.3172i	0.319942	−	0.554155i
$765$	−7.23126	−	12.5249i	−0.261447	−	0.452839i
$766$	−1.07077			−0.0386883
$767$	72.8771			2.63144
$768$	−0.310724	−	0.538189i	−0.0112123	−	0.0194202i
$769$	−30.2067			−1.08928			−0.544641	−	0.838669i	$-0.683334\pi$
$769$	−30.2067			−1.08928			−0.544641	+	0.838669i	$0.683334\pi$
$770$	1.00930	−	1.74817i	0.0363728	−	0.0629995i
$771$	−0.876185			−0.0315550
$772$	16.0282	−	27.7617i	0.576868	−	0.999165i
$773$	−20.7496	+	35.9394i	−0.746311	+	1.29265i	0.203268	+	0.979123i	$0.434844\pi$
$773$	−20.7496	+	35.9394i	−0.746311	+	1.29265i	−0.949580	+	0.313526i	$0.898490\pi$
$774$	2.14292	−	3.71164i	0.0770256	−	0.133412i
$775$	2.14334	+	3.71237i	0.0769909	+	0.133352i
$776$	25.9767			0.932507
$777$	−0.857950	+	1.30261i	−0.0307788	+	0.0467310i
$778$	−0.128522			−0.00460773
$779$	10.2994	+	17.8391i	0.369015	+	0.639153i
$780$	−0.536426	+	0.929117i	−0.0192071	+	0.0332677i
$781$	−14.3680	+	24.8861i	−0.514127	+	0.890494i
$782$	−0.441814	+	0.765244i	−0.0157992	+	0.0273651i
$783$	4.65474			0.166347
$784$	−1.09910	+	1.90370i	−0.0392536	+	0.0679893i
$785$	10.6408			0.379787
$786$	0.0474351	+	0.0821600i	0.00169195	+	0.00293055i
$787$	−47.6784			−1.69955			−0.849777	−	0.527143i	$-0.823263\pi$
$787$	−47.6784			−1.69955			−0.849777	+	0.527143i	$0.823263\pi$
$788$	4.29952			0.153164
$789$	0.561234	+	0.972086i	0.0199805	+	0.0346072i
$790$	−1.70768	+	2.95779i	−0.0607565	+	0.105233i
$791$	−9.85294			−0.350330
$792$	−4.21940	−	7.30822i	−0.149930	−	0.259686i
$793$	6.82413	+	11.8197i	0.242332	+	0.419731i
$794$	−3.41196	−	5.90970i	−0.121086	−	0.209727i
$795$	−0.216621	+	0.375198i	−0.00768275	+	0.0133069i
$796$	23.8955	−	41.3882i	0.846952	−	1.46696i
$797$	−25.2032	−	43.6533i	−0.892745	−	1.54628i	−0.836571	−	0.547859i	$-0.815443\pi$
$797$	−25.2032	−	43.6533i	−0.892745	−	1.54628i	−0.0561739	−	0.998421i	$-0.517890\pi$
$798$	−0.332227	−	0.575433i	−0.0117607	−	0.0203701i
$799$	−26.9055	−	46.6017i	−0.951848	−	1.64865i
$800$	−3.93259			−0.139038
$801$	−24.7939	+	42.9443i	−0.876049	+	1.51736i
$802$	−3.04024	−	5.26585i	−0.107355	−	0.185944i
$803$	−9.62660			−0.339715
$804$	−0.681479			−0.0240339
$805$	0.707748	+	1.22586i	0.0249448	+	0.0432057i
$806$	−9.49647			−0.334499
$807$	0.847869	−	1.46855i	0.0298464	−	0.0516955i
$808$	6.23359			0.219297
$809$	17.5875	−	30.4624i	0.618344	−	1.07100i	−0.371444	−	0.928455i	$-0.621137\pi$
$809$	17.5875	−	30.4624i	0.618344	−	1.07100i	0.989788	−	0.142547i	$-0.0455293\pi$
$810$	1.59611	−	2.76455i	0.0560817	−	0.0971363i
$811$	−14.6305	+	25.3407i	−0.513745	+	0.889832i	0.486128	+	0.873888i	$0.338409\pi$
$811$	−14.6305	+	25.3407i	−0.513745	+	0.889832i	−0.999873	+	0.0159445i	$0.994924\pi$
$812$	21.7700	+	37.7067i	0.763977	+	1.32325i
$813$	−2.02621			−0.0710624
$814$	2.43763	−	3.70102i	0.0854388	−	0.129721i
$815$	22.1179			0.774755
$816$	0.726748	+	1.25876i	0.0254413	+	0.0440656i
$817$	14.5032	−	25.1203i	0.507403	−	0.878848i
$818$	0.0742817	−	0.128660i	0.00259720	−	0.00449848i
$819$	25.6623	−	44.4484i	0.896713	−	1.55315i
$820$	5.32390			0.185919
$821$	9.22305	−	15.9748i	0.321887	−	0.557524i	−0.658991	−	0.752151i	$-0.729016\pi$
$821$	9.22305	−	15.9748i	0.321887	−	0.557524i	0.980877	+	0.194627i	$0.0623496\pi$
$822$	0.482832			0.0168407
$823$	9.85134	+	17.0630i	0.343396	+	0.594780i	0.985061	−	0.172205i	$-0.0550893\pi$
$823$	9.85134	+	17.0630i	0.343396	+	0.594780i	−0.641665	+	0.766985i	$0.721756\pi$
$824$	−4.67576			−0.162888
$825$	−0.188475			−0.00656186
$826$	5.83274	+	10.1026i	0.202947	+	0.351515i
$827$	−18.8318	+	32.6177i	−0.654847	+	1.13423i	0.327085	+	0.944995i	$0.393934\pi$
$827$	−18.8318	+	32.6177i	−0.654847	+	1.13423i	−0.981932	+	0.189233i	$0.939400\pi$
$828$	2.86095			0.0994248
$829$	2.91402	+	5.04724i	0.101208	+	0.175298i	0.912183	−	0.409784i	$-0.134396\pi$
$829$	2.91402	+	5.04724i	0.101208	+	0.175298i	−0.810974	+	0.585082i	$0.801062\pi$
$830$	0.0261304	+	0.0452591i	0.000906998	+	0.00157097i
$831$	0.891572	+	1.54425i	0.0309283	+	0.0535694i
$832$	−15.7597	+	27.2966i	−0.546369	+	0.946339i
$833$	1.63578	−	2.83325i	0.0566764	−	0.0981664i
$834$	0.191265	+	0.331281i	0.00662298	+	0.0114713i
$835$	−6.29101	−	10.8964i	−0.217710	−	0.377084i
$836$	−13.8065	−	23.9135i	−0.477506	−	0.827065i
$837$	2.37697			0.0821601
$838$	3.71205	−	6.42946i	0.128231	−	0.222102i
$839$	20.4051	+	35.3427i	0.704462	+	1.22016i	0.966885	+	0.255211i	$0.0821450\pi$
$839$	20.4051	+	35.3427i	0.704462	+	1.22016i	−0.262423	+	0.964953i	$0.584522\pi$
$840$	−0.355205			−0.0122557
$841$	41.4669			1.42989
$842$	−2.06270	−	3.57271i	−0.0710855	−	0.123124i
$843$	0.550773			0.0189696
$844$	−10.9170	+	18.9088i	−0.375779	+	0.650868i
$845$	25.3458			0.871920
$846$	5.95579	−	10.3157i	0.204764	−	0.354662i
$847$	−9.49337	+	16.4430i	−0.326196	+	0.564988i
$848$	−7.60335	+	13.1694i	−0.261100	+	0.452239i
$849$	0.382736	+	0.662918i	0.0131355	+	0.0227513i
$850$	1.72961			0.0593251
$851$	1.39288	+	2.77794i	0.0477474	+	0.0952264i
$852$	2.44470			0.0837541
$853$	7.13107	+	12.3514i	0.244163	+	0.422903i	0.961896	−	0.273415i	$-0.0881534\pi$
$853$	7.13107	+	12.3514i	0.244163	+	0.422903i	−0.717733	+	0.696319i	$0.754820\pi$
$854$	−1.09234	+	1.89199i	−0.0373792	+	0.0647426i
$855$	10.8336	−	18.7643i	0.370500	−	0.641725i
$856$	9.40406	−	16.2883i	0.321424	−	0.556723i
$857$	25.9914			0.887851			0.443925	−	0.896064i	$-0.353586\pi$
$857$	25.9914			0.887851			0.443925	+	0.896064i	$0.353586\pi$
$858$	0.208769	−	0.361598i	0.00712725	−	0.0123448i
$859$	−29.8786			−1.01944			−0.509722	−	0.860339i	$-0.670252\pi$
$859$	−29.8786			−1.01944			−0.509722	+	0.860339i	$0.670252\pi$
$860$	−3.74845	−	6.49250i	−0.127821	−	0.221392i
$861$	0.729256			0.0248530
$862$	0.257747			0.00877889
$863$	20.1684	+	34.9327i	0.686540	+	1.18912i	0.972950	+	0.231015i	$0.0742047\pi$
$863$	20.1684	+	34.9327i	0.686540	+	1.18912i	−0.286410	+	0.958107i	$0.592462\pi$
$864$	−1.09032	+	1.88848i	−0.0370933	+	0.0642475i
$865$	4.03977			0.137356
$866$	5.09371	+	8.82256i	0.173091	+	0.299803i
$867$	−0.294943	−	0.510856i	−0.0100168	−	0.0173496i
$868$	11.1170	+	19.2552i	0.377334	+	0.653562i
$869$	−9.72085	+	16.8370i	−0.329757	+	0.571157i
$870$	−0.138969	+	0.240701i	−0.00471149	+	0.00816054i
$871$	12.1787	+	21.0941i	0.412658	+	0.714745i
$872$	0.398754	+	0.690662i	0.0135035	+	0.0233888i
$873$	28.0487	+	48.5818i	0.949304	+	1.64424i
$874$	−1.32381			−0.0447786
$875$	1.38534	−	2.39948i	0.0468331	−	0.0811173i
$876$	0.409489	+	0.709256i	0.0138354	+	0.0239636i
$877$	−14.2522			−0.481262			−0.240631	−	0.970617i	$-0.577354\pi$
$877$	−14.2522			−0.481262			−0.240631	+	0.970617i	$0.577354\pi$
$878$	−8.18806			−0.276334
$879$	0.346611	+	0.600347i	0.0116909	+	0.0202492i
$880$	−6.61544			−0.223006
$881$	4.96811	−	8.60501i	0.167380	−	0.289910i	−0.770118	−	0.637901i	$-0.779803\pi$
$881$	4.96811	−	8.60501i	0.167380	−	0.289910i	0.937498	+	0.347991i	$0.113136\pi$
$882$	0.724191			0.0243848
$883$	−21.1285	+	36.5957i	−0.711031	+	1.23154i	0.253439	+	0.967351i	$0.418438\pi$
$883$	−21.1285	+	36.5957i	−0.711031	+	1.23154i	−0.964470	+	0.264191i	$0.914895\pi$
$884$	28.0222	−	48.5358i	0.942488	−	1.63244i
$885$	0.544596	−	0.943269i	0.0183064	−	0.0317076i
$886$	0.450126	+	0.779641i	0.0151223	+	0.0261926i
$887$	−28.2372			−0.948113			−0.474056	−	0.880494i	$-0.657211\pi$
$887$	−28.2372			−0.948113			−0.474056	+	0.880494i	$0.657211\pi$
$888$	−0.778469	−	0.0458459i	−0.0261237	−	0.00153849i
$889$	1.81379			0.0608325
$890$	−2.96516	−	5.13581i	−0.0993924	−	0.172153i
$891$	9.08577	−	15.7370i	0.304385	−	0.527210i
$892$	−2.33928	+	4.05175i	−0.0783248	+	0.135663i
$893$	40.3087	−	69.8167i	1.34888	−	2.33633i
$894$	0.0161867			0.000541365
$895$	5.31632	−	9.20813i	0.177705	−	0.307794i
$896$	−26.8373			−0.896571
$897$	0.146394	+	0.253561i	0.00488794	+	0.00846617i
$898$	−13.4414			−0.448546
$899$	35.9843			1.20014
$900$	−2.80000	−	4.84975i	−0.0933334	−	0.161658i
$901$	11.3160	−	19.5999i	0.376990	−	0.652966i
$902$	−2.07198			−0.0689894
$903$	−0.513454	−	0.889329i	−0.0170867	−	0.0295950i
$904$	−2.46303	−	4.26609i	−0.0819190	−	0.141888i
$905$	−0.312453	−	0.541185i	−0.0103863	−	0.0179896i
$906$	0.0657539	−	0.113889i	0.00218453	−	0.00378371i
$907$	10.5036	−	18.1928i	0.348767	−	0.604081i	−0.637264	−	0.770645i	$-0.719934\pi$
$907$	10.5036	−	18.1928i	0.348767	−	0.604081i	0.986031	+	0.166564i	$0.0532673\pi$
$908$	2.38985	+	4.13934i	0.0793100	+	0.137369i
$909$	6.73081	+	11.6581i	0.223247	+	0.386675i
$910$	3.06901	+	5.31569i	0.101737	+	0.176213i
$911$	10.1234			0.335403			0.167701	−	0.985838i	$-0.446366\pi$
$911$	10.1234			0.335403			0.167701	+	0.985838i	$0.446366\pi$
$912$	−1.08878	+	1.88583i	−0.0360532	+	0.0624460i
$913$	0.148745	+	0.257635i	0.00492276	+	0.00852646i
$914$	6.95413			0.230022
$915$	0.203981			0.00674342
$916$	−1.14861	−	1.98945i	−0.0379512	−	0.0657334i
$917$	−7.93891			−0.262166
$918$	0.479536	−	0.830580i	0.0158270	−	0.0274132i
$919$	32.6466			1.07691			0.538456	−	0.842654i	$-0.319008\pi$
$919$	32.6466			1.07691			0.538456	+	0.842654i	$0.319008\pi$
$920$	−0.353844	+	0.612875i	−0.0116659	+	0.0202059i
$921$	−0.466059	+	0.807238i	−0.0153572	+	0.0265994i
$922$	−3.39332	+	5.87740i	−0.111753	+	0.193562i
$923$	−43.6891	−	75.6718i	−1.43804	−	2.49077i
$924$	−0.977574			−0.0321598
$925$	3.34582	−	5.07991i	0.110010	−	0.167026i
$926$	−0.0781683			−0.00256877
$927$	−5.04872	−	8.74464i	−0.165822	−	0.287212i
$928$	−16.5060	+	28.5892i	−0.541836	+	0.938487i
$929$	20.7398	−	35.9224i	0.680451	−	1.17858i	−0.294392	−	0.955685i	$-0.595117\pi$
$929$	20.7398	−	35.9224i	0.680451	−	1.17858i	0.974843	−	0.222891i	$-0.0715494\pi$
$930$	−0.0709653	+	0.122916i	−0.00232704	+	0.00403056i
$931$	4.90131			0.160634
$932$	14.6291	−	25.3383i	0.479191	−	0.829984i
$933$	0.551558			0.0180572
$934$	−2.13989	−	3.70640i	−0.0700194	−	0.121277i
$935$	9.84568			0.321988
$936$	25.6601			0.838726
$937$	−22.6417	−	39.2166i	−0.739673	−	1.28115i	−0.952643	−	0.304092i	$-0.901647\pi$
$937$	−22.6417	−	39.2166i	−0.739673	−	1.28115i	0.212970	−	0.977059i	$-0.431686\pi$
$938$	−1.94945	+	3.37654i	−0.0636517	+	0.110248i
$939$	−1.30890			−0.0427143
$940$	−10.4180	−	18.0446i	−0.339799	−	0.588549i
$941$	1.90807	+	3.30488i	0.0622014	+	0.107736i	0.895449	−	0.445164i	$-0.146855\pi$
$941$	1.90807	+	3.30488i	0.0622014	+	0.107736i	−0.833248	+	0.552900i	$0.813521\pi$
$942$	0.176157	+	0.305113i	0.00573952	+	0.00994113i
$943$	0.726461	−	1.25827i	0.0236568	−	0.0409748i
$944$	19.1152	−	33.1086i	0.622148	−	1.07759i
$945$	−0.768175	−	1.33052i	−0.0249887	−	0.0432818i
$946$	1.45884	+	2.52678i	0.0474309	+	0.0821528i
$947$	2.88363	+	4.99460i	0.0937055	+	0.162303i	0.909068	−	0.416649i	$-0.136795\pi$
$947$	2.88363	+	4.99460i	0.0937055	+	0.162303i	−0.815362	+	0.578951i	$0.803462\pi$
$948$	1.65399			0.0537192
$949$	14.6359	−	25.3502i	0.475102	−	0.822901i
$950$	1.29561	+	2.24407i	0.0420352	+	0.0728071i
$951$	−0.452350			−0.0146685
$952$	18.5554			0.601385
$953$	17.0826	+	29.5879i	0.553359	+	0.958446i	0.998029	+	0.0627517i	$0.0199876\pi$
$953$	17.0826	+	29.5879i	0.553359	+	0.958446i	−0.444670	+	0.895694i	$0.646679\pi$
$954$	5.00981			0.162198
$955$	−4.72399	+	8.18218i	−0.152865	+	0.264769i
$956$	−31.1226			−1.00658
$957$	−0.791073	+	1.37018i	−0.0255717	+	0.0442916i
$958$	−3.19059	+	5.52626i	−0.103083	+	0.178545i
$959$	−20.2021	+	34.9911i	−0.652361	+	1.12992i
$960$	0.235538	+	0.407964i	0.00760197	+	0.0131670i
$961$	−12.6244			−0.407240
$962$	6.03997	+	12.0460i	0.194737	+	0.388379i
$963$	40.6167			1.30886
$964$	1.68441	+	2.91748i	0.0542512	+	0.0939659i
$965$	−8.56203	+	14.8299i	−0.275621	+	0.477390i
$966$	−0.0234333	+	0.0405877i	−0.000753955	+	0.00130589i
$967$	−16.2464	+	28.1396i	−0.522449	+	0.904908i	0.477210	+	0.878789i	$0.341648\pi$
$967$	−16.2464	+	28.1396i	−0.522449	+	0.904908i	−0.999659	+	0.0261184i	$0.991685\pi$
$968$	−9.49256			−0.305102
$969$	1.62042	−	2.80666i	0.0520555	−	0.0901628i
$970$	−6.70882			−0.215407
$971$	16.8070	+	29.1106i	0.539362	+	0.934203i	0.998938	+	0.0460644i	$0.0146680\pi$
$971$	16.8070	+	29.1106i	0.539362	+	0.934203i	−0.459576	+	0.888138i	$0.651999\pi$
$972$	−4.66004			−0.149471
$973$	−32.0109			−1.02622
$974$	−3.40296	−	5.89409i	−0.109038	−	0.188859i
$975$	0.286550	−	0.496320i	0.00917696	−	0.0158950i
$976$	7.15971			0.229177
$977$	25.2908	+	43.8050i	0.809126	+	1.40145i	0.913470	+	0.406906i	$0.133392\pi$
$977$	25.2908	+	43.8050i	0.809126	+	1.40145i	−0.104344	+	0.994541i	$0.533274\pi$
$978$	0.366158	+	0.634205i	0.0117085	+	0.0202796i
$979$	−16.8790	−	29.2353i	−0.539455	−	0.934364i
$980$	0.633387	−	1.09706i	0.0202328	−	0.0350443i
$981$	−0.861122	+	1.49151i	−0.0274935	+	0.0476202i
$982$	5.71069	+	9.89120i	0.182235	+	0.315641i
$983$	−15.5754	−	26.9773i	−0.496777	−	0.860442i	0.503217	−	0.864160i	$-0.332150\pi$
$983$	−15.5754	−	26.9773i	−0.496777	−	0.860442i	−0.999993	+	0.00371817i	$0.998816\pi$
$984$	0.182299	+	0.315750i	0.00581147	+	0.0100658i
$985$	−2.29674			−0.0731802
$986$	7.25956	−	12.5739i	0.231191	−	0.400435i
$987$	−1.42704	−	2.47171i	−0.0454232	−	0.0786753i
$988$	83.9632			2.67123
$989$	−2.04595			−0.0650573
$990$	1.08972	+	1.88745i	0.0346335	+	0.0599870i
$991$	−16.6891			−0.530146			−0.265073	−	0.964228i	$-0.585396\pi$
$991$	−16.6891			−0.530146			−0.265073	+	0.964228i	$0.585396\pi$
$992$	−8.42887	+	14.5992i	−0.267617	+	0.463526i
$993$	−2.26571			−0.0719000
$994$	6.99334	−	12.1128i	0.221815	−	0.384196i
$995$	−12.7646	+	22.1089i	−0.404664	+	0.700899i
$996$	0.0126545	−	0.0219182i	0.000400972	−	0.000694503i
$997$	−5.87262	−	10.1717i	−0.185988	−	0.322140i	0.757921	−	0.652346i	$-0.226215\pi$
$997$	−5.87262	−	10.1717i	−0.185988	−	0.322140i	−0.943909	+	0.330206i	$0.892882\pi$
$998$	−3.25732			−0.103109
$999$	−1.51181	−	3.01512i	−0.0478315	−	0.0953940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.e.a.26.4	✓	14
5.2	odd	4		925.2.o.b.174.7		28
5.3	odd	4		925.2.o.b.174.8		28
5.4	even	2		925.2.e.c.26.4		14
37.10	even	3	inner	185.2.e.a.121.4	yes	14
37.11	even	6		6845.2.a.k.1.4		7
37.26	even	3		6845.2.a.l.1.4		7
185.47	odd	12		925.2.o.b.824.8		28
185.84	even	6		925.2.e.c.676.4		14
185.158	odd	12		925.2.o.b.824.7		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.e.a.26.4	✓	14	1.1	even	1	trivial
185.2.e.a.121.4	yes	14	37.10	even	3	inner
925.2.e.c.26.4		14	5.4	even	2
925.2.e.c.676.4		14	185.84	even	6
925.2.o.b.174.7		28	5.2	odd	4
925.2.o.b.174.8		28	5.3	odd	4
925.2.o.b.824.7		28	185.158	odd	12
925.2.o.b.824.8		28	185.47	odd	12
6845.2.a.k.1.4		7	37.11	even	6
6845.2.a.l.1.4		7	37.26	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:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.178876 + 0.309823i) q^{2} +(-0.0462746 + 0.0801499i) q^{3} +(0.936006 - 1.62121i) q^{4} +(-0.500000 + 0.866025i) q^{5} -0.0331097 q^{6} +(1.38534 - 2.39948i) q^{7} +1.38522 q^{8} +(1.49572 + 2.59066i) q^{9} -0.357753 q^{10} -2.03649 q^{11} +(0.0866266 + 0.150042i) q^{12} +(3.09620 - 5.36277i) q^{13} +0.991221 q^{14} +(-0.0462746 - 0.0801499i) q^{15} +(-1.62423 - 2.81325i) q^{16} +(2.41732 + 4.18692i) q^{17} +(-0.535097 + 0.926816i) q^{18} +(-3.62153 + 6.27267i) q^{19} +(0.936006 + 1.62121i) q^{20} +(0.128212 + 0.222070i) q^{21} +(-0.364280 - 0.630951i) q^{22} +0.510883 q^{23} +(-0.0641006 + 0.111026i) q^{24} +(-0.500000 - 0.866025i) q^{25} +2.21535 q^{26} -0.554502 q^{27} +(-2.59338 - 4.49186i) q^{28} -8.39445 q^{29} +(0.0165549 - 0.0286739i) q^{30} -4.28667 q^{31} +(1.96630 - 3.40573i) q^{32} +(0.0942375 - 0.163224i) q^{33} +(-0.864804 + 1.49788i) q^{34} +(1.38534 + 2.39948i) q^{35} +5.60000 q^{36} +(2.72642 + 5.43752i) q^{37} -2.59122 q^{38} +(0.286550 + 0.496320i) q^{39} +(-0.692612 + 1.19964i) q^{40} +(1.42197 - 2.46293i) q^{41} +(-0.0458683 + 0.0794462i) q^{42} -4.00472 q^{43} +(-1.90616 + 3.30157i) q^{44} -2.99143 q^{45} +(0.0913850 + 0.158283i) q^{46} -11.1303 q^{47} +0.300642 q^{48} +(-0.338346 - 0.586032i) q^{49} +(0.178876 - 0.309823i) q^{50} -0.447442 q^{51} +(-5.79612 - 10.0392i) q^{52} +(-2.34060 - 4.05405i) q^{53} +(-0.0991874 - 0.171798i) q^{54} +(1.01824 - 1.76365i) q^{55} +(1.91901 - 3.32382i) q^{56} +(-0.335169 - 0.580530i) q^{57} +(-1.50157 - 2.60080i) q^{58} +(5.88440 + 10.1921i) q^{59} -0.173253 q^{60} +(-1.10202 + 1.90875i) q^{61} +(-0.766785 - 1.32811i) q^{62} +8.28832 q^{63} -5.09002 q^{64} +(3.09620 + 5.36277i) q^{65} +0.0674275 q^{66} +(-1.96671 + 3.40645i) q^{67} +9.05051 q^{68} +(-0.0236409 + 0.0409472i) q^{69} +(-0.495610 + 0.858422i) q^{70} +(7.05529 - 12.2201i) q^{71} +(2.07190 + 3.58864i) q^{72} +4.72706 q^{73} +(-1.19698 + 1.81735i) q^{74} +0.0925491 q^{75} +(6.77955 + 11.7425i) q^{76} +(-2.82123 + 4.88651i) q^{77} +(-0.102514 + 0.177560i) q^{78} +(4.77335 - 8.26768i) q^{79} +3.24846 q^{80} +(-4.46149 + 7.72753i) q^{81} +1.01743 q^{82} +(-0.0730402 - 0.126509i) q^{83} +0.480030 q^{84} -4.83464 q^{85} +(-0.716351 - 1.24076i) q^{86} +(0.388450 - 0.672815i) q^{87} -2.82099 q^{88} +(8.28829 + 14.3557i) q^{89} +(-0.535097 - 0.926816i) q^{90} +(-8.57859 - 14.8585i) q^{91} +(0.478190 - 0.828249i) q^{92} +(0.198364 - 0.343576i) q^{93} +(-1.99095 - 3.44842i) q^{94} +(-3.62153 - 6.27267i) q^{95} +(0.181979 + 0.315197i) q^{96} +18.7527 q^{97} +(0.121044 - 0.209655i) q^{98} +(-3.04601 - 5.27584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{3} - 8 q^{4} - 7 q^{5} - 4 q^{6} + 6 q^{8} - 13 q^{9} - 2 q^{11} + 6 q^{12} + 4 q^{13} + 20 q^{14} - 2 q^{15} + 2 q^{16} - 3 q^{17} - 6 q^{18} - 14 q^{19} - 8 q^{20} + q^{21} + 7 q^{22} + 15 q^{24}+ \cdots + 56 q^{99}+O(q^{100}) \) 14 * q - 2 * q^3 - 8 * q^4 - 7 * q^5 - 4 * q^6 + 6 * q^8 - 13 * q^9 - 2 * q^11 + 6 * q^12 + 4 * q^13 + 20 * q^14 - 2 * q^15 + 2 * q^16 - 3 * q^17 - 6 * q^18 - 14 * q^19 - 8 * q^20 + q^21 + 7 * q^22 + 15 * q^24 - 7 * q^25 - 22 * q^26 - 14 * q^27 + 9 * q^28 - 12 * q^29 + 2 * q^30 + 4 * q^32 - 11 * q^33 + 33 * q^34 + 40 * q^36 + 18 * q^37 - 4 * q^38 - 25 * q^39 - 3 * q^40 - 7 * q^41 - 29 * q^42 + 38 * q^43 - 19 * q^44 + 26 * q^45 - 14 * q^46 + 8 * q^47 + 36 * q^48 + 5 * q^49 + 58 * q^51 - 8 * q^52 - 6 * q^53 - 9 * q^54 + q^55 - 25 * q^56 - 44 * q^57 - 12 * q^58 + 2 * q^59 - 12 * q^60 - 4 * q^61 - 25 * q^62 + 10 * q^63 - 62 * q^64 + 4 * q^65 - 2 * q^66 - 8 * q^67 + 26 * q^68 - 11 * q^69 - 10 * q^70 + 33 * q^71 + 43 * q^72 + 18 * q^74 + 4 * q^75 - 12 * q^76 - 5 * q^77 - 22 * q^78 - 9 * q^79 - 4 * q^80 - 35 * q^81 + 152 * q^82 - 11 * q^83 - 80 * q^84 + 6 * q^85 + 17 * q^86 - 29 * q^87 + 40 * q^88 - 12 * q^89 - 6 * q^90 - 24 * q^91 - 7 * q^92 - 47 * q^93 + 10 * q^94 - 14 * q^95 - 15 * q^96 + 30 * q^97 + 54 * q^98 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more