LMFDB - Embedded newform 275.2.y.b.34.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(34,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("275.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.y (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			34.13
Character	$\chi$	$=$	275.34
Dual form			275.2.y.b.89.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.40881 - 1.93906i) q^{2} +(2.16543 - 0.703590i) q^{3} +(-1.15717 - 3.56140i) q^{4} +(-1.75916 - 1.38035i) q^{5} +(1.68637 - 5.19011i) q^{6} +4.20978i q^{7} +(-3.97699 - 1.29220i) q^{8} +(1.76699 - 1.28379i) q^{9} +(-5.15489 + 1.46647i) q^{10} +(0.809017 + 0.587785i) q^{11} +(-5.01153 - 6.89778i) q^{12} +(2.31689 + 3.18892i) q^{13} +(8.16301 + 5.93077i) q^{14} +(-4.78053 - 1.75131i) q^{15} +(-2.04945 + 1.48901i) q^{16} +(-6.53165 - 2.12226i) q^{17} -5.23491i q^{18} +(-0.869785 + 2.67692i) q^{19} +(-2.88032 + 7.86237i) q^{20} +(2.96196 + 9.11598i) q^{21} +(2.27950 - 0.740654i) q^{22} +(3.37458 - 4.64471i) q^{23} -9.52107 q^{24} +(1.18929 + 4.85650i) q^{25} +9.44754 q^{26} +(-1.09190 + 1.50287i) q^{27} +(14.9927 - 4.87143i) q^{28} +(-1.06183 - 3.26798i) q^{29} +(-10.1307 + 6.80246i) q^{30} +(2.67697 - 8.23887i) q^{31} -2.29158i q^{32} +(2.16543 + 0.703590i) q^{33} +(-13.3170 + 9.67538i) q^{34} +(5.81096 - 7.40568i) q^{35} +(-6.61681 - 4.80739i) q^{36} +(-0.386548 - 0.532038i) q^{37} +(3.96535 + 5.45783i) q^{38} +(7.26075 + 5.27524i) q^{39} +(5.21247 + 7.76281i) q^{40} +(-6.79684 + 4.93819i) q^{41} +(21.8492 + 7.09925i) q^{42} +3.58478i q^{43} +(1.15717 - 3.56140i) q^{44} +(-4.88050 - 0.180660i) q^{45} +(-4.25222 - 13.0870i) q^{46} +(-2.23663 + 0.726724i) q^{47} +(-3.39028 + 4.66632i) q^{48} -10.7223 q^{49} +(11.0925 + 4.53577i) q^{50} -15.6370 q^{51} +(8.67599 - 11.9415i) q^{52} +(-4.85542 + 1.57762i) q^{53} +(1.37588 + 4.23451i) q^{54} +(-0.611843 - 2.15073i) q^{55} +(5.43989 - 16.7423i) q^{56} +6.40866i q^{57} +(-7.83271 - 2.54500i) q^{58} +(-1.22105 + 0.887145i) q^{59} +(-0.705240 + 19.0520i) q^{60} +(3.15748 + 2.29404i) q^{61} +(-12.2043 - 16.7978i) q^{62} +(5.40449 + 7.43865i) q^{63} +(-8.54241 - 6.20642i) q^{64} +(0.326040 - 8.80793i) q^{65} +(4.41497 - 3.20767i) q^{66} +(10.3903 + 3.37601i) q^{67} +25.7176i q^{68} +(4.03944 - 12.4321i) q^{69} +(-6.17352 - 21.7010i) q^{70} +(-1.94044 - 5.97206i) q^{71} +(-8.68622 + 2.82232i) q^{72} +(4.96806 - 6.83795i) q^{73} -1.57622 q^{74} +(5.99231 + 9.67963i) q^{75} +10.5401 q^{76} +(-2.47445 + 3.40579i) q^{77} +(20.4580 - 6.64720i) q^{78} +(1.64748 + 5.07042i) q^{79} +(5.66066 + 0.209539i) q^{80} +(-3.33182 + 10.2543i) q^{81} +20.1364i q^{82} +(8.39124 + 2.72648i) q^{83} +(29.0382 - 21.0975i) q^{84} +(8.56076 + 12.7493i) q^{85} +(6.95109 + 5.05026i) q^{86} +(-4.59864 - 6.32948i) q^{87} +(-2.45791 - 3.38303i) q^{88} +(0.324186 + 0.235535i) q^{89} +(-7.22599 + 9.20905i) q^{90} +(-13.4247 + 9.75359i) q^{91} +(-20.4466 - 6.64351i) q^{92} -19.7242i q^{93} +(-1.74182 + 5.36076i) q^{94} +(5.22517 - 3.50853i) q^{95} +(-1.61234 - 4.96226i) q^{96} +(-5.01315 + 1.62887i) q^{97} +(-15.1056 + 20.7911i) q^{98} +2.18412 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 16 q^{4} - 7 q^{5} - 4 q^{6} - 15 q^{8} + 10 q^{9} + 10 q^{10} + 14 q^{11} - 20 q^{12} - 6 q^{14} - 21 q^{15} - 20 q^{16} + 20 q^{17} + 10 q^{19} + 22 q^{20} - 6 q^{21} + 10 q^{23} - 62 q^{24} + 9 q^{25}+ \cdots + 70 q^{99}+O(q^{100}) $ 56 * q + 16 * q^4 - 7 * q^5 - 4 * q^6 - 15 * q^8 + 10 * q^9 + 10 * q^10 + 14 * q^11 - 20 * q^12 - 6 * q^14 - 21 * q^15 - 20 * q^16 + 20 * q^17 + 10 * q^19 + 22 * q^20 - 6 * q^21 + 10 * q^23 - 62 * q^24 + 9 * q^25 - 4 * q^26 + 18 * q^29 - 129 * q^30 - 16 * q^34 + 42 * q^35 - 26 * q^36 - 65 * q^37 - 20 * q^38 + 20 * q^39 - 28 * q^40 - 10 * q^41 + 60 * q^42 - 16 * q^44 - 18 * q^45 + 6 * q^46 - 25 * q^47 + 15 * q^48 - 104 * q^49 + 98 * q^50 + 54 * q^51 + 90 * q^52 + 5 * q^53 + 55 * q^54 - 3 * q^55 + 10 * q^56 - 10 * q^58 + 34 * q^59 + 133 * q^60 - 20 * q^61 - 10 * q^62 + 20 * q^63 + 25 * q^64 - 10 * q^65 + 4 * q^66 - 15 * q^67 - 2 * q^69 - 4 * q^70 - 13 * q^71 - 5 * q^72 - 70 * q^73 - 30 * q^74 - 80 * q^75 + 140 * q^76 - 65 * q^78 + 15 * q^79 - 131 * q^80 - 99 * q^81 + 60 * q^83 + 76 * q^84 + 43 * q^85 + 43 * q^86 - 175 * q^87 + 30 * q^88 + 27 * q^89 + 73 * q^90 - 10 * q^91 - 80 * q^92 - 17 * q^94 + 18 * q^95 - 148 * q^96 - 15 * q^97 - 80 * q^98 + 70 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	1.40881	−	1.93906i	0.996177	−	1.37112i	0.0685353	−	0.997649i	$-0.478167\pi$
$2$	1.40881	−	1.93906i	0.996177	−	1.37112i	0.927642	−	0.373471i	$-0.121833\pi$
$3$	2.16543	−	0.703590i	1.25021	−	0.406218i	0.392214	−	0.919874i	$-0.371709\pi$
$3$	2.16543	−	0.703590i	1.25021	−	0.406218i	0.857996	+	0.513656i	$0.171709\pi$
$4$	−1.15717	−	3.56140i	−0.578585	−	1.78070i
$5$	−1.75916	−	1.38035i	−0.786720	−	0.617310i
$5$	−1.75916	−	1.38035i	−0.786720	−	0.617310i
$6$	1.68637	−	5.19011i	0.688457	−	2.11885i
$7$			4.20978i			1.59115i	0.605856	+	0.795574i	$0.292831\pi$
$7$			4.20978i			1.59115i	−0.605856	+	0.795574i	$0.707169\pi$
$8$	−3.97699	−	1.29220i	−1.40608	−	0.456862i
$9$	1.76699	−	1.28379i	0.588997	−	0.427931i
$10$	−5.15489	+	1.46647i	−1.63012	+	0.463738i
$11$	0.809017	+	0.587785i	0.243928	+	0.177224i
$11$	0.809017	+	0.587785i	0.243928	+	0.177224i
$12$	−5.01153	−	6.89778i	−1.44671	−	1.99122i
$13$	2.31689	+	3.18892i	0.642589	+	0.884447i	0.998750	−	0.0499769i	$-0.0159148\pi$
$13$	2.31689	+	3.18892i	0.642589	+	0.884447i	−0.356162	+	0.934424i	$0.615915\pi$
$14$	8.16301	+	5.93077i	2.18166	+	1.58507i
$15$	−4.78053	−	1.75131i	−1.23433	−	0.452187i
$16$	−2.04945	+	1.48901i	−0.512362	+	0.372253i
$17$	−6.53165	−	2.12226i	−1.58416	−	0.514724i	−0.621034	−	0.783784i	$-0.713287\pi$
$17$	−6.53165	−	2.12226i	−1.58416	−	0.514724i	−0.963123	+	0.269060i	$0.913287\pi$
$18$		−	5.23491i		−	1.23388i
$19$	−0.869785	+	2.67692i	−0.199542	+	0.614129i	0.800351	+	0.599532i	$0.204646\pi$
$19$	−0.869785	+	2.67692i	−0.199542	+	0.614129i	−0.999893	+	0.0145968i	$0.995354\pi$
$20$	−2.88032	+	7.86237i	−0.644059	+	1.75808i
$21$	2.96196	+	9.11598i	0.646353	+	1.98927i
$22$	2.27950	−	0.740654i	0.485991	−	0.157908i
$23$	3.37458	−	4.64471i	0.703648	−	0.968489i	−0.296262	−	0.955107i	$-0.595740\pi$
$23$	3.37458	−	4.64471i	0.703648	−	0.968489i	0.999910	−	0.0133823i	$-0.00425984\pi$
$24$	−9.52107			−1.94348
$25$	1.18929	+	4.85650i	0.237858	+	0.971300i
$26$	9.44754			1.85282
$27$	−1.09190	+	1.50287i	−0.210136	+	0.289228i
$28$	14.9927	−	4.87143i	2.83336	−	0.920614i
$29$	−1.06183	−	3.26798i	−0.197177	−	0.606849i	−0.999944	−	0.0105561i	$-0.996640\pi$
$29$	−1.06183	−	3.26798i	−0.197177	−	0.606849i	0.802767	−	0.596293i	$-0.203360\pi$
$30$	−10.1307	+	6.80246i	−1.84961	+	1.24195i
$31$	2.67697	−	8.23887i	0.480798	−	1.47974i	−0.357177	−	0.934037i	$-0.616261\pi$
$31$	2.67697	−	8.23887i	0.480798	−	1.47974i	0.837976	−	0.545708i	$-0.183739\pi$
$32$		−	2.29158i		−	0.405099i
$33$	2.16543	+	0.703590i	0.376953	+	0.122479i
$34$	−13.3170	+	9.67538i	−2.28385	+	1.65931i
$35$	5.81096	−	7.40568i	0.982231	−	1.25179i
$36$	−6.61681	−	4.80739i	−1.10280	−	0.801232i
$37$	−0.386548	−	0.532038i	−0.0635482	−	0.0874665i	0.776060	−	0.630659i	$-0.217215\pi$
$37$	−0.386548	−	0.532038i	−0.0635482	−	0.0874665i	−0.839608	+	0.543193i	$0.817215\pi$
$38$	3.96535	+	5.45783i	0.643264	+	0.885377i
$39$	7.26075	+	5.27524i	1.16265	+	0.844714i
$40$	5.21247	+	7.76281i	0.824165	+	1.22741i
$41$	−6.79684	+	4.93819i	−1.06149	+	0.771216i	−0.974363	−	0.224982i	$-0.927768\pi$
$41$	−6.79684	+	4.93819i	−1.06149	+	0.771216i	−0.0871244	+	0.996197i	$0.527768\pi$
$42$	21.8492	+	7.09925i	3.37141	+	1.09544i
$43$			3.58478i			0.546674i	0.961918	+	0.273337i	$0.0881274\pi$
$43$			3.58478i			0.546674i	−0.961918	+	0.273337i	$0.911873\pi$
$44$	1.15717	−	3.56140i	0.174450	−	0.536901i
$45$	−4.88050	−	0.180660i	−0.727542	−	0.0269312i
$46$	−4.25222	−	13.0870i	−0.626956	−	1.92957i
$47$	−2.23663	+	0.726724i	−0.326246	+	0.106004i	−0.467561	−	0.883961i	$-0.654867\pi$
$47$	−2.23663	+	0.726724i	−0.326246	+	0.106004i	0.141315	+	0.989965i	$0.454867\pi$
$48$	−3.39028	+	4.66632i	−0.489345	+	0.673525i
$49$	−10.7223			−1.53175
$50$	11.0925	+	4.53577i	1.56872	+	0.641455i
$51$	−15.6370			−2.18962
$52$	8.67599	−	11.9415i	1.20314	−	1.65599i
$53$	−4.85542	+	1.57762i	−0.666944	+	0.216703i	−0.622870	−	0.782325i	$-0.714034\pi$
$53$	−4.85542	+	1.57762i	−0.666944	+	0.216703i	−0.0440735	+	0.999028i	$0.514034\pi$
$54$	1.37588	+	4.23451i	0.187233	+	0.576244i
$55$	−0.611843	−	2.15073i	−0.0825009	−	0.290005i
$56$	5.43989	−	16.7423i	0.726936	−	2.23728i
$57$			6.40866i			0.848848i
$58$	−7.83271	−	2.54500i	−1.02849	−	0.334175i
$59$	−1.22105	+	0.887145i	−0.158967	+	0.115496i	−0.664425	−	0.747355i	$-0.731324\pi$
$59$	−1.22105	+	0.887145i	−0.158967	+	0.115496i	0.505458	+	0.862851i	$0.331324\pi$
$60$	−0.705240	+	19.0520i	−0.0910461	+	2.45960i
$61$	3.15748	+	2.29404i	0.404274	+	0.293722i	0.771279	−	0.636497i	$-0.219617\pi$
$61$	3.15748	+	2.29404i	0.404274	+	0.293722i	−0.367006	+	0.930219i	$0.619617\pi$
$62$	−12.2043	−	16.7978i	−1.54995	−	2.13332i
$63$	5.40449	+	7.43865i	0.680902	+	0.937181i
$64$	−8.54241	−	6.20642i	−1.06780	−	0.775803i
$65$	0.326040	−	8.80793i	0.0404403	−	1.09249i
$66$	4.41497	−	3.20767i	0.543446	−	0.394836i
$67$	10.3903	+	3.37601i	1.26938	+	0.412445i	0.864826	−	0.502071i	$-0.167428\pi$
$67$	10.3903	+	3.37601i	1.26938	+	0.412445i	0.404549	+	0.914516i	$0.367428\pi$
$68$			25.7176i			3.11872i
$69$	4.03944	−	12.4321i	0.486291	−	1.49665i
$70$	−6.17352	−	21.7010i	−0.737877	−	2.59376i
$71$	−1.94044	−	5.97206i	−0.230288	−	0.708753i	−0.997712	−	0.0676126i	$-0.978462\pi$
$71$	−1.94044	−	5.97206i	−0.230288	−	0.708753i	0.767424	−	0.641140i	$-0.221538\pi$
$72$	−8.68622	+	2.82232i	−1.02368	+	0.332614i
$73$	4.96806	−	6.83795i	0.581467	−	0.800321i	−0.412388	−	0.911008i	$-0.635305\pi$
$73$	4.96806	−	6.83795i	0.581467	−	0.800321i	0.993855	+	0.110687i	$0.0353052\pi$
$74$	−1.57622			−0.183232
$75$	5.99231	+	9.67963i	0.691932	+	1.11771i
$76$	10.5401			1.20903
$77$	−2.47445	+	3.40579i	−0.281990	+	0.388125i
$78$	20.4580	−	6.64720i	2.31641	−	0.752647i
$79$	1.64748	+	5.07042i	0.185356	+	0.570467i	0.999954	−	0.00955832i	$-0.00304255\pi$
$79$	1.64748	+	5.07042i	0.185356	+	0.570467i	−0.814598	+	0.580026i	$0.803043\pi$
$80$	5.66066	+	0.209539i	0.632881	+	0.0234271i
$81$	−3.33182	+	10.2543i	−0.370202	+	1.13936i
$82$			20.1364i			2.22369i
$83$	8.39124	+	2.72648i	0.921058	+	0.299270i	0.730901	−	0.682484i	$-0.239100\pi$
$83$	8.39124	+	2.72648i	0.921058	+	0.299270i	0.190157	+	0.981754i	$0.439100\pi$
$84$	29.0382	−	21.0975i	3.16832	−	2.30192i
$85$	8.56076	+	12.7493i	0.928545	+	1.38286i
$86$	6.95109	+	5.05026i	0.749556	+	0.544584i
$87$	−4.59864	−	6.32948i	−0.493026	−	0.678592i
$88$	−2.45791	−	3.38303i	−0.262015	−	0.360632i
$89$	0.324186	+	0.235535i	0.0343636	+	0.0249666i	0.604834	−	0.796351i	$-0.293239\pi$
$89$	0.324186	+	0.235535i	0.0343636	+	0.0249666i	−0.570471	+	0.821318i	$0.693239\pi$
$90$	−7.22599	+	9.20905i	−0.761686	+	0.970719i
$91$	−13.4247	+	9.75359i	−1.40729	+	1.02245i
$92$	−20.4466	−	6.64351i	−2.13171	−	0.692634i
$93$		−	19.7242i		−	2.04530i
$94$	−1.74182	+	5.36076i	−0.179655	+	0.552920i
$95$	5.22517	−	3.50853i	0.536092	−	0.359968i
$96$	−1.61234	−	4.96226i	−0.164558	−	0.506459i
$97$	−5.01315	+	1.62887i	−0.509008	+	0.165387i	−0.552251	−	0.833678i	$-0.686231\pi$
$97$	−5.01315	+	1.62887i	−0.509008	+	0.165387i	0.0432429	+	0.999065i	$0.486231\pi$
$98$	−15.1056	+	20.7911i	−1.52590	+	2.10022i
$99$	2.18412			0.219512
$100$	15.9197	−	9.85533i	1.59197	−	0.985533i
$101$	1.78898			0.178010			0.0890049	−	0.996031i	$-0.471631\pi$
$101$	1.78898			0.178010			0.0890049	+	0.996031i	$0.471631\pi$
$102$	−22.0295	+	30.3211i	−2.18125	+	3.00223i
$103$	−4.75721	+	1.54571i	−0.468742	+	0.152303i	−0.533858	−	0.845574i	$-0.679258\pi$
$103$	−4.75721	+	1.54571i	−0.468742	+	0.152303i	0.0651161	+	0.997878i	$0.479258\pi$
$104$	−5.09350	−	15.6762i	−0.499459	−	1.53718i
$105$	7.37265	−	20.1250i	0.719497	−	1.96400i
$106$	−3.78126	+	11.6375i	−0.367268	+	1.13033i
$107$		−	2.17060i		−	0.209840i	−0.994481	−	0.104920i	$-0.966541\pi$
$107$		−	2.17060i		−	0.209840i	0.994481	−	0.104920i	$-0.0334586\pi$
$108$	6.61583	+	2.14961i	0.636609	+	0.206847i
$109$	12.4243	−	9.02680i	1.19003	−	0.864611i	0.196767	−	0.980450i	$-0.436956\pi$
$109$	12.4243	−	9.02680i	1.19003	−	0.864611i	0.993268	+	0.115840i	$0.0369559\pi$
$110$	−5.03236	−	1.84357i	−0.479817	−	0.175777i
$111$	−1.21138	−	0.880119i	−0.114979	−	0.0835372i
$112$	−6.26841	−	8.62773i	−0.592309	−	0.815244i
$113$	5.02805	+	6.92052i	0.472999	+	0.651028i	0.977141	−	0.212593i	$-0.0681910\pi$
$113$	5.02805	+	6.92052i	0.472999	+	0.651028i	−0.504141	+	0.863621i	$0.668191\pi$
$114$	12.4268	+	9.02857i	1.16387	+	0.845603i
$115$	−12.3477	+	3.51270i	−1.15143	+	0.327561i
$116$	−10.4099	+	7.56321i	−0.966532	+	0.702227i
$117$	8.18783	+	2.66039i	0.756965	+	0.245953i
$118$			3.61750i			0.333018i
$119$	8.93426	−	27.4968i	0.819002	−	2.52063i
$120$	16.7491	+	13.1424i	1.52897	+	1.19973i
$121$	0.309017	+	0.951057i	0.0280925	+	0.0864597i
$122$	8.89656	−	2.89067i	0.805456	−	0.261709i
$123$	−11.2436	+	15.4755i	−1.01380	+	1.39538i
$124$	−32.4396			−2.91316
$125$	4.61150	−	10.1850i	0.412465	−	0.910973i
$126$	22.0378			1.96329
$127$	−2.39855	+	3.30133i	−0.212837	+	0.292945i	−0.902066	−	0.431599i	$-0.857950\pi$
$127$	−2.39855	+	3.30133i	−0.212837	+	0.292945i	0.689228	+	0.724544i	$0.257950\pi$
$128$	−19.7104	+	6.40428i	−1.74217	+	0.566064i
$129$	2.52222	+	7.76259i	0.222069	+	0.683458i
$130$	−16.6197	−	13.0409i	−1.45765	−	1.14376i
$131$	−1.42603	+	4.38886i	−0.124593	+	0.383456i	−0.993827	−	0.110944i	$-0.964612\pi$
$131$	−1.42603	+	4.38886i	−0.124593	+	0.383456i	0.869234	+	0.494401i	$0.164612\pi$
$132$		−	8.52613i		−	0.742104i
$133$	−11.2693	−	3.66161i	−0.977170	−	0.317502i
$134$	21.1842	−	15.3912i	1.83003	−	1.32960i
$135$	3.99531	−	1.13659i	0.343861	−	0.0978221i
$136$	23.2339	+	16.8804i	1.99229	+	1.44748i
$137$	−1.56289	−	2.15113i	−0.133526	−	0.183783i	0.737018	−	0.675873i	$-0.236233\pi$
$137$	−1.56289	−	2.15113i	−0.133526	−	0.183783i	−0.870545	+	0.492090i	$0.836233\pi$
$138$	−18.4158	−	25.3471i	−1.56765	−	2.15769i
$139$	−17.7880	−	12.9237i	−1.50876	−	1.09617i	−0.966726	−	0.255815i	$-0.917656\pi$
$139$	−17.7880	−	12.9237i	−1.50876	−	1.09617i	−0.542029	−	0.840360i	$-0.682344\pi$
$140$	−33.0989	−	12.1255i	−2.79736	−	1.02479i
$141$	−4.33194	+	3.14734i	−0.364815	+	0.265054i
$142$	−14.3139	−	4.65085i	−1.20119	−	0.390291i
$143$			3.94172i			0.329623i
$144$	−1.70977	+	5.26213i	−0.142481	+	0.438511i
$145$	−2.64301	+	7.21460i	−0.219490	+	0.599140i
$146$	−6.26013	−	19.2667i	−0.518092	−	1.59452i
$147$	−23.2183	+	7.54409i	−1.91501	+	0.622226i
$148$	−1.44750	+	1.99231i	−0.118984	+	0.163767i
$149$	−14.6701			−1.20182			−0.600911	−	0.799316i	$-0.705195\pi$
$149$	−14.6701			−1.20182			−0.600911	+	0.799316i	$0.705195\pi$
$150$	27.2114	+	2.01731i	2.22180	+	0.164713i
$151$	2.44581			0.199037			0.0995184	−	0.995036i	$-0.468270\pi$
$151$	2.44581			0.199037			0.0995184	+	0.995036i	$0.468270\pi$
$152$	6.91825	−	9.52216i	0.561145	−	0.772349i
$153$	−14.2659	+	4.63527i	−1.15333	+	0.374740i
$154$	3.11799	+	9.59619i	0.251255	+	0.773283i
$155$	−16.0817	+	10.7983i	−1.29171	+	0.867344i
$156$	10.3853	−	31.9628i	0.831492	−	2.55907i
$157$		−	21.5901i		−	1.72308i	−0.507691	−	0.861539i	$-0.669501\pi$
$157$		−	21.5901i		−	1.72308i	0.507691	−	0.861539i	$-0.330499\pi$
$158$	12.1528	+	3.94869i	0.966827	+	0.314141i
$159$	−9.40407	+	6.83246i	−0.745791	+	0.541849i
$160$	−3.16318	+	4.03126i	−0.250071	+	0.318699i
$161$	19.5532	+	14.2062i	1.54101	+	1.11961i
$162$	15.1897	+	20.9069i	1.19342	+	1.64260i
$163$	−4.88408	−	6.72236i	−0.382551	−	0.526536i	0.573707	−	0.819060i	$-0.305505\pi$
$163$	−4.88408	−	6.72236i	−0.382551	−	0.526536i	−0.956258	+	0.292525i	$0.905505\pi$
$164$	25.4520	+	18.4919i	1.98746	+	1.44398i
$165$	−2.83814	−	4.22677i	−0.220949	−	0.329054i
$166$	17.1084	−	12.4300i	1.32787	−	0.964755i
$167$	17.5754	+	5.71058i	1.36002	+	0.441898i	0.896051	−	0.443952i	$-0.146424\pi$
$167$	17.5754	+	5.71058i	1.36002	+	0.441898i	0.463972	+	0.885850i	$0.346424\pi$
$168$		−	40.0816i		−	3.09236i
$169$	−0.784030	+	2.41300i	−0.0603100	+	0.185615i
$170$	36.7821	+	1.36155i	2.82106	+	0.104426i
$171$	1.89972	+	5.84672i	0.145275	+	0.447110i
$172$	12.7668	−	4.14820i	0.973462	−	0.316297i
$173$	3.57936	−	4.92657i	0.272134	−	0.374560i	−0.650975	−	0.759099i	$-0.725640\pi$
$173$	3.57936	−	4.92657i	0.272134	−	0.374560i	0.923109	+	0.384539i	$0.125640\pi$
$174$	−18.7518			−1.42157
$175$	−20.4448	+	5.00665i	−1.54548	+	0.378467i
$176$	−2.53326			−0.190951
$177$	−2.01991	+	2.78017i	−0.151826	+	0.208970i
$178$	0.913431	−	0.296792i	0.0684645	−	0.0222455i
$179$	−2.00403	−	6.16778i	−0.149789	−	0.461002i	0.847807	−	0.530305i	$-0.177922\pi$
$179$	−2.00403	−	6.16778i	−0.149789	−	0.461002i	−0.997596	+	0.0693029i	$0.977922\pi$
$180$	5.00416	+	17.5905i	0.372988	+	1.31112i
$181$	−6.27791	+	19.3214i	−0.466634	+	1.43615i	0.390283	+	0.920695i	$0.372377\pi$
$181$	−6.27791	+	19.3214i	−0.466634	+	1.43615i	−0.856916	+	0.515456i	$0.827623\pi$
$182$			39.7721i			2.94810i
$183$	8.45136	+	2.74601i	0.624742	+	0.202991i
$184$	−19.4226	+	14.1113i	−1.43185	+	1.04030i
$185$	−0.0543964	+	1.46951i	−0.00399930	+	0.108041i
$186$	−38.2463	−	27.7875i	−2.80435	−	2.03748i
$187$	−4.03678	−	5.55615i	−0.295199	−	0.406306i
$188$	5.17631	+	7.12458i	0.377521	+	0.519614i
$189$	−6.32676	−	4.59666i	−0.460204	−	0.334358i
$190$	0.558017	−	15.0748i	0.0404828	−	1.09364i
$191$	7.30914	−	5.31040i	0.528871	−	0.384247i	−0.291064	−	0.956703i	$-0.594009\pi$
$191$	7.30914	−	5.31040i	0.528871	−	0.384247i	0.819935	+	0.572456i	$0.194009\pi$
$192$	−22.8647	−	7.42921i	−1.65012	−	0.536157i
$193$			7.59265i			0.546531i	0.961939	+	0.273265i	$0.0881038\pi$
$193$			7.59265i			0.546531i	−0.961939	+	0.273265i	$0.911896\pi$
$194$	−3.90409	+	12.0155i	−0.280297	+	0.862666i
$195$	−5.49116	−	19.3023i	−0.393230	−	1.38227i
$196$	12.4075	+	38.1863i	0.886249	+	2.72759i
$197$	14.0949	−	4.57970i	1.00422	−	0.326290i	0.239668	−	0.970855i	$-0.422961\pi$
$197$	14.0949	−	4.57970i	1.00422	−	0.326290i	0.764550	+	0.644565i	$0.222961\pi$
$198$	3.07700	−	4.23513i	0.218673	−	0.300978i
$199$	−8.43669			−0.598061			−0.299031	−	0.954243i	$-0.596663\pi$
$199$	−8.43669			−0.598061			−0.299031	+	0.954243i	$0.596663\pi$
$200$	1.54579	−	20.8510i	0.109304	−	1.47439i
$201$	24.8747			1.75453
$202$	2.52032	−	3.46893i	0.177329	−	0.244073i
$203$	13.7575	−	4.47008i	0.965586	−	0.313738i
$204$	18.0947	+	55.6897i	1.26688	+	3.89906i
$205$	18.7731	+	0.694919i	1.31117	+	0.0485352i
$206$	−3.70477	+	11.4021i	−0.258123	+	0.794422i
$207$		−	12.5394i		−	0.871550i
$208$	−9.49667	−	3.08566i	−0.658476	−	0.213952i
$209$	−2.27713	+	1.65443i	−0.157512	+	0.114439i
$210$	−28.6369	−	42.6482i	−1.97613	−	2.94301i
$211$	−19.2718	−	14.0018i	−1.32672	−	0.963921i	−0.999822	−	0.0188619i	$-0.993996\pi$
$211$	−19.2718	−	14.0018i	−1.32672	−	0.963921i	−0.326901	−	0.945059i	$-0.606004\pi$
$212$	11.2371	+	15.4665i	0.771767	+	1.06225i
$213$	−8.40376	−	11.5668i	−0.575816	−	0.792543i
$214$	−4.20892	−	3.05796i	−0.287716	−	0.209038i
$215$	4.94824	−	6.30620i	0.337467	−	0.430079i
$216$	6.28448	−	4.56594i	0.427605	−	0.310673i
$217$	34.6838	+	11.2695i	2.35449	+	0.765021i
$218$		−	36.8085i		−	2.49299i
$219$	5.94686	−	18.3026i	0.401852	−	1.23677i
$220$	−6.95161	+	4.66778i	−0.468678	+	0.314702i
$221$	−8.36536	−	25.7459i	−0.562715	−	1.73186i
$222$	−3.41320	+	1.10902i	−0.229079	+	0.0744323i
$223$	7.26054	−	9.99327i	0.486201	−	0.669199i	−0.493480	−	0.869757i	$-0.664276\pi$
$223$	7.26054	−	9.99327i	0.486201	−	0.669199i	0.979682	+	0.200558i	$0.0642755\pi$
$224$	9.64707			0.644572
$225$	8.33620	+	7.05459i	0.555747	+	0.470306i
$226$	20.5028			1.36383
$227$	−3.39634	+	4.67466i	−0.225423	+	0.310268i	−0.906715	−	0.421744i	$-0.861418\pi$
$227$	−3.39634	+	4.67466i	−0.225423	+	0.310268i	0.681292	+	0.732011i	$0.261418\pi$
$228$	22.8238	−	7.41590i	1.51154	−	0.491130i
$229$	−2.74784	−	8.45698i	−0.181582	−	0.558853i	0.818290	−	0.574805i	$-0.194922\pi$
$229$	−2.74784	−	8.45698i	−0.181582	−	0.558853i	−0.999873	+	0.0159519i	$0.994922\pi$
$230$	−10.5842	+	28.8917i	−0.697905	+	1.90506i
$231$	−2.96196	+	9.11598i	−0.194883	+	0.599788i
$232$			14.3688i			0.943359i
$233$	15.6439	+	5.08302i	1.02487	+	0.332999i	0.772759	−	0.634700i	$-0.218876\pi$
$233$	15.6439	+	5.08302i	1.02487	+	0.332999i	0.252108	+	0.967699i	$0.418876\pi$
$234$	16.6937	−	12.1287i	1.09130	−	0.792878i
$235$	4.93772	+	1.80890i	0.322101	+	0.117999i
$236$	4.57244	+	3.32207i	0.297640	+	0.216248i
$237$	7.13500	+	9.82049i	0.463468	+	0.637909i
$238$	−40.7312	−	56.0617i	−2.64021	−	3.63394i
$239$	−1.68956	−	1.22754i	−0.109289	−	0.0794030i	0.531798	−	0.846871i	$-0.321516\pi$
$239$	−1.68956	−	1.22754i	−0.109289	−	0.0794030i	−0.641087	+	0.767468i	$0.721516\pi$
$240$	12.4052	−	3.52904i	0.800751	−	0.227799i
$241$	3.22159	−	2.34062i	0.207521	−	0.150773i	−0.479171	−	0.877722i	$-0.659062\pi$
$241$	3.22159	−	2.34062i	0.207521	−	0.150773i	0.686691	+	0.726949i	$0.259062\pi$
$242$	2.27950	+	0.740654i	0.146532	+	0.0476110i
$243$			18.9762i			1.21732i
$244$	4.51627	−	13.8996i	0.289124	−	0.889833i
$245$	18.8622	+	14.8005i	1.20506	+	0.945566i
$246$	14.1678	+	43.6039i	0.903305	+	2.78009i
$247$	−10.5517	+	3.42845i	−0.671388	+	0.218147i
$248$	−21.2926	+	29.3067i	−1.35208	+	1.86098i
$249$	20.0889			1.27309
$250$	−13.2526	−	23.2907i	−0.838165	−	1.47303i
$251$	−28.3056			−1.78663			−0.893317	−	0.449427i	$-0.851628\pi$
$251$	−28.3056			−1.78663			−0.893317	+	0.449427i	$0.851628\pi$
$252$	20.2381	−	27.8553i	1.27488	−	1.75472i
$253$	5.46018	−	1.77412i	0.343279	−	0.111538i
$254$	3.02236	+	9.30187i	0.189640	+	0.583651i
$255$	27.5080	+	21.5845i	1.72262	+	1.35167i
$256$	−8.82400	+	27.1575i	−0.551500	+	1.69734i
$257$			17.5010i			1.09169i	0.837888	+	0.545843i	$0.183790\pi$
$257$			17.5010i			1.09169i	−0.837888	+	0.545843i	$0.816210\pi$
$258$	18.6054	+	6.04526i	1.15832	+	0.376362i
$259$	2.23977	−	1.62728i	0.139172	−	0.101115i
$260$	−31.7458	+	9.03110i	−1.96879	+	0.560085i
$261$	−6.07166	−	4.41132i	−0.375826	−	0.273054i
$262$	6.50125	+	8.94820i	0.401649	+	0.552822i
$263$	3.70503	+	5.09953i	0.228462	+	0.314450i	0.907823	−	0.419353i	$-0.137743\pi$
$263$	3.70503	+	5.09953i	0.228462	+	0.314450i	−0.679361	+	0.733804i	$0.737743\pi$
$264$	−7.70270	−	5.59634i	−0.474069	−	0.344431i
$265$	10.7191	+	3.92687i	0.658471	+	0.241226i
$266$	−22.9763	+	16.6933i	−1.40877	+	1.02353i
$267$	0.867721	+	0.281940i	0.0531037	+	0.0172544i
$268$		−	40.9106i		−	2.49901i
$269$	−3.01534	+	9.28026i	−0.183848	+	0.565827i	−0.999927	−	0.0121143i	$-0.996144\pi$
$269$	−3.01534	+	9.28026i	−0.183848	+	0.565827i	0.816078	+	0.577941i	$0.196144\pi$
$270$	3.42470	−	9.34836i	0.208421	−	0.568923i
$271$	−5.52369	−	17.0002i	−0.335540	−	1.03269i	−0.966455	−	0.256834i	$-0.917321\pi$
$271$	−5.52369	−	17.0002i	−0.335540	−	1.03269i	0.630915	−	0.775852i	$-0.282679\pi$
$272$	16.5463	−	5.37623i	1.00327	−	0.325982i
$273$	−22.2076	+	30.5662i	−1.34407	+	1.84995i
$274$	−6.37297			−0.385005
$275$	−1.89242	+	4.62804i	−0.114117	+	0.279081i
$276$	−48.9500			−2.94645
$277$	14.9769	−	20.6139i	0.899874	−	1.23857i	−0.0706347	−	0.997502i	$-0.522502\pi$
$277$	14.9769	−	20.6139i	0.899874	−	1.23857i	0.970508	−	0.241068i	$-0.0774975\pi$
$278$	−50.1196	+	16.2848i	−3.00597	+	0.976700i
$279$	−5.84682	−	17.9947i	−0.350040	−	1.07731i
$280$	−32.6798	+	21.9434i	−1.95299	+	1.31137i
$281$	2.07913	−	6.39891i	0.124031	−	0.381727i	−0.869693	−	0.493594i	$-0.835683\pi$
$281$	2.07913	−	6.39891i	0.124031	−	0.381727i	0.993723	+	0.111867i	$0.0356830\pi$
$282$			12.8339i			0.764246i
$283$	17.4731	+	5.67736i	1.03867	+	0.337484i	0.778212	−	0.628002i	$-0.216127\pi$
$283$	17.4731	+	5.67736i	1.03867	+	0.337484i	0.260456	+	0.965486i	$0.416127\pi$
$284$	−19.0235	+	13.8214i	−1.12883	+	0.820147i
$285$	8.84617	−	11.2739i	0.524002	−	0.667806i
$286$	7.64322	+	5.55313i	0.451953	+	0.328363i
$287$	−20.7887	−	28.6132i	−1.22712	−	1.68898i
$288$	−2.94192	−	4.04921i	−0.173354	−	0.238602i
$289$	24.4051	+	17.7314i	1.43560	+	1.04302i
$290$	10.2660	+	15.2889i	0.602841	+	0.897797i
$291$	−9.70956	+	7.05441i	−0.569184	+	0.413537i
$292$	−30.1015	−	9.78059i	−1.76156	−	0.572365i
$293$			23.0137i			1.34447i	0.740337	+	0.672236i	$0.234666\pi$
$293$			23.0137i			1.34447i	−0.740337	+	0.672236i	$0.765334\pi$
$294$	−18.0817	+	55.6498i	−1.05455	+	3.24556i
$295$	3.37259	+	0.124842i	0.196360	+	0.00726858i
$296$	0.849798	+	2.61541i	0.0493935	+	0.152018i
$297$	−1.76673	+	0.574045i	−0.102516	+	0.0333095i
$298$	−20.6674	+	28.4462i	−1.19723	+	1.64784i
$299$	22.6301			1.30873
$300$	27.5389	−	32.5420i	1.58996	−	1.87881i
$301$	−15.0911			−0.869839
$302$	3.44567	−	4.74255i	0.198276	−	0.272903i
$303$	3.87390	−	1.25871i	0.222550	−	0.0723108i
$304$	−2.20339	−	6.78134i	−0.126373	−	0.388936i
$305$	−2.38794	−	8.39400i	−0.136733	−	0.480639i
$306$	−11.1098	+	34.1926i	−0.635108	+	1.95466i
$307$			15.2066i			0.867885i	0.900941	+	0.433943i	$0.142878\pi$
$307$			15.2066i			0.867885i	−0.900941	+	0.433943i	$0.857122\pi$
$308$	14.9927	+	4.87143i	0.854290	+	0.277576i
$309$	−9.21385	+	6.69425i	−0.524157	+	0.380823i
$310$	−1.71743	+	46.3961i	−0.0975434	+	2.63512i
$311$	26.1388	+	18.9910i	1.48220	+	1.07688i	0.976841	+	0.213967i	$0.0686387\pi$
$311$	26.1388	+	18.9910i	1.48220	+	1.07688i	0.505356	+	0.862911i	$0.331361\pi$
$312$	−22.0592	−	30.3619i	−1.24886	−	1.71891i
$313$	9.85514	+	13.5644i	0.557046	+	0.766708i	0.990947	−	0.134253i	$-0.0428634\pi$
$313$	9.85514	+	13.5644i	0.557046	+	0.766708i	−0.433901	+	0.900960i	$0.642863\pi$
$314$	−41.8644	−	30.4163i	−2.36255	−	1.71649i
$315$	0.760538	−	20.5458i	0.0428515	−	1.15763i
$316$	16.1514	−	11.7347i	0.908587	−	0.660127i
$317$	18.9622	+	6.16120i	1.06502	+	0.346047i	0.788548	−	0.614973i	$-0.210833\pi$
$317$	18.9622	+	6.16120i	1.06502	+	0.346047i	0.276476	+	0.961021i	$0.410833\pi$
$318$			27.8606i			1.56235i
$319$	1.06183	−	3.26798i	0.0594511	−	0.182972i
$320$	6.46045	+	22.7096i	0.361150	+	1.26950i
$321$	−1.52721	−	4.70028i	−0.0852408	−	0.262344i
$322$	55.0934	−	17.9009i	3.07024	−	0.997581i
$323$	11.3623	−	15.6388i	0.632213	−	0.870167i
$324$	40.3750			2.24306
$325$	−12.7315	+	15.0445i	−0.706219	+	0.834519i
$326$	−19.9158			−1.10303
$327$	20.5528	−	28.2885i	1.13657	−	1.56436i
$328$	33.4121	−	10.8562i	1.84487	−	0.599436i
$329$	−3.05935	−	9.41572i	−0.168668	−	0.519105i
$330$	−12.1943	−	0.451393i	−0.671276	−	0.0248484i
$331$	8.97073	−	27.6091i	0.493076	−	1.51753i	−0.326858	−	0.945074i	$-0.605990\pi$
$331$	8.97073	−	27.6091i	0.493076	−	1.51753i	0.819934	−	0.572458i	$-0.194010\pi$
$332$		−	33.0396i		−	1.81328i
$333$	−1.36605	−	0.443858i	−0.0748593	−	0.0243233i
$334$	35.8334	−	26.0345i	1.96072	−	1.42455i
$335$	−13.6181	−	20.2811i	−0.744037	−	1.10808i
$336$	−19.6442	−	14.2723i	−1.07168	−	0.778620i
$337$	0.869309	+	1.19650i	0.0473543	+	0.0651776i	0.832037	−	0.554719i	$-0.187174\pi$
$337$	0.869309	+	1.19650i	0.0473543	+	0.0651776i	−0.784683	+	0.619897i	$0.787174\pi$
$338$	3.57439	+	4.91973i	0.194421	+	0.267598i
$339$	15.7571	+	11.4482i	0.855808	+	0.621781i
$340$	35.4992	−	45.2414i	1.92522	−	2.45356i
$341$	7.00840	−	5.09190i	0.379526	−	0.275742i
$342$	14.0135	+	4.55325i	0.757761	+	0.246212i
$343$		−	15.6700i		−	0.846099i
$344$	4.63226	−	14.2566i	0.249755	−	0.768666i
$345$	−24.2666	+	16.2942i	−1.30647	+	0.877253i
$346$	−4.51027	−	13.8812i	−0.242474	−	0.746257i
$347$	−6.16684	+	2.00373i	−0.331054	+	0.107566i	−0.469827	−	0.882758i	$-0.655684\pi$
$347$	−6.16684	+	2.00373i	−0.331054	+	0.107566i	0.138774	+	0.990324i	$0.455684\pi$
$348$	−17.2204	+	23.7019i	−0.923112	+	1.27055i
$349$	−29.9228			−1.60173			−0.800866	−	0.598843i	$-0.795627\pi$
$349$	−29.9228			−1.60173			−0.800866	+	0.598843i	$0.795627\pi$
$350$	−19.0946	+	46.6970i	−1.02065	+	2.49606i
$351$	−7.32234			−0.390838
$352$	1.34696	−	1.85393i	0.0717932	−	0.0988148i
$353$	4.11321	−	1.33646i	0.218924	−	0.0711327i	−0.197501	−	0.980303i	$-0.563283\pi$
$353$	4.11321	−	1.33646i	0.218924	−	0.0711327i	0.416425	+	0.909170i	$0.363283\pi$
$354$	2.54524	+	7.83344i	0.135278	+	0.416343i
$355$	−4.82996	+	13.1843i	−0.256348	+	0.699749i
$356$	0.463696	−	1.42711i	0.0245758	−	0.0756366i
$357$		−	65.8285i		−	3.48401i
$358$	−14.7830	−	4.80328i	−0.781305	−	0.253861i
$359$	−18.8793	+	13.7166i	−0.996413	+	0.723937i	−0.961316	−	0.275447i	$-0.911174\pi$
$359$	−18.8793	+	13.7166i	−0.996413	+	0.723937i	−0.0350972	+	0.999384i	$0.511174\pi$
$360$	19.1762	+	7.02507i	1.01068	+	0.370254i
$361$	8.96193	+	6.51122i	0.471680	+	0.342696i
$362$	28.6210	+	39.3934i	1.50429	+	2.07047i
$363$	1.33831	+	1.84202i	0.0702430	+	0.0966812i
$364$	50.2710	+	36.5240i	2.63492	+	1.91438i
$365$	−18.1783	+	5.17140i	−0.951498	+	0.270684i
$366$	17.2310	−	12.5191i	0.900679	−	0.654382i
$367$	10.9524	+	3.55866i	0.571712	+	0.185760i	0.580584	−	0.814200i	$-0.302824\pi$
$367$	10.9524	+	3.55866i	0.571712	+	0.185760i	−0.00887246	+	0.999961i	$0.502824\pi$
$368$			14.5439i			0.758152i
$369$	−5.67032	+	17.4515i	−0.295185	+	0.908487i
$370$	2.77283	+	2.17573i	0.144153	+	0.113111i
$371$	−6.64145	−	20.4403i	−0.344807	−	1.06121i
$372$	−70.2457	+	22.8242i	−3.64207	+	1.18338i
$373$	15.2726	−	21.0209i	0.790785	−	1.08842i	−0.203225	−	0.979132i	$-0.565142\pi$
$373$	15.2726	−	21.0209i	0.790785	−	1.08842i	0.994010	−	0.109290i	$-0.0348576\pi$
$374$	−16.4607			−0.851164
$375$	2.81981	−	25.2995i	0.145615	−	1.30646i
$376$	9.83412			0.507156
$377$	7.96119	−	10.9576i	0.410022	−	0.564347i
$378$	−17.8264	+	5.79214i	−0.916889	+	0.297915i
$379$	−0.652852	−	2.00927i	−0.0335347	−	0.103209i	0.932888	−	0.360166i	$-0.117280\pi$
$379$	−0.652852	−	2.00927i	−0.0335347	−	0.103209i	−0.966423	+	0.256957i	$0.917280\pi$
$380$	−18.5417	−	14.5490i	−0.951169	−	0.746346i
$381$	−2.87112	+	8.83639i	−0.147092	+	0.452702i
$382$		−	21.6542i		−	1.10792i
$383$	−6.78889	−	2.20584i	−0.346896	−	0.112713i	0.130387	−	0.991463i	$-0.458378\pi$
$383$	−6.78889	−	2.20584i	−0.346896	−	0.112713i	−0.477282	+	0.878750i	$0.658378\pi$
$384$	−38.1754	+	27.7360i	−1.94813	+	1.41540i
$385$	9.05412	−	2.57573i	0.461440	−	0.131271i
$386$	14.7226	+	10.6966i	0.749360	+	0.544442i
$387$	4.60212	+	6.33427i	0.233939	+	0.321989i
$388$	11.6021	+	15.9690i	0.589009	+	0.810701i
$389$	14.4971	+	10.5327i	0.735030	+	0.534031i	0.891151	−	0.453707i	$-0.149899\pi$
$389$	14.4971	+	10.5327i	0.735030	+	0.534031i	−0.156121	+	0.987738i	$0.549899\pi$
$390$	−45.1643	−	16.5456i	−2.28698	−	0.837819i
$391$	−31.8989	+	23.1759i	−1.61319	+	1.17205i
$392$	42.6424	+	13.8553i	2.15376	+	0.699801i
$393$			10.5071i			0.530013i
$394$	10.9767	−	33.7827i	0.552996	−	1.70195i
$395$	4.10076	−	11.1938i	0.206332	−	0.563220i
$396$	−2.52740	−	7.77853i	−0.127006	−	0.390886i
$397$	0.185465	−	0.0602613i	0.00930823	−	0.00302443i	−0.304359	−	0.952557i	$-0.598442\pi$
$397$	0.185465	−	0.0602613i	0.00930823	−	0.00302443i	0.313667	+	0.949533i	$0.398442\pi$
$398$	−11.8857	+	16.3592i	−0.595775	+	0.820014i
$399$	−26.9791			−1.35064
$400$	−9.66877	−	8.18228i	−0.483438	−	0.409114i
$401$	22.5376			1.12548			0.562738	−	0.826635i	$-0.309748\pi$
$401$	22.5376			1.12548			0.562738	+	0.826635i	$0.309748\pi$
$402$	35.0437	−	48.2335i	1.74782	−	2.40567i
$403$	32.4753	−	10.5519i	1.61771	−	0.525626i
$404$	−2.07015	−	6.37126i	−0.102994	−	0.316982i
$405$	20.0156	−	13.4398i	0.994585	−	0.667831i
$406$	10.7139	−	32.9740i	0.531723	−	1.63647i
$407$		−	0.657635i		−	0.0325978i
$408$	62.1883	+	20.2062i	3.07878	+	1.00036i
$409$	−23.0678	+	16.7597i	−1.14063	+	0.828714i	−0.987207	−	0.159447i	$-0.949029\pi$
$409$	−23.0678	+	16.7597i	−1.14063	+	0.828714i	−0.153421	+	0.988161i	$0.549029\pi$
$410$	27.7952	−	35.4232i	1.37271	−	1.74943i
$411$	−4.89783	−	3.55848i	−0.241592	−	0.175527i
$412$	11.0098	+	15.1537i	0.542413	+	0.746568i
$413$	−3.73469	−	5.14036i	−0.183772	−	0.252940i
$414$	−24.3146	−	17.6656i	−1.19500	−	0.868218i
$415$	−10.9980	−	16.3791i	−0.539873	−	0.804020i
$416$	7.30768	−	5.30934i	0.358288	−	0.260312i
$417$	−47.6116	−	15.4699i	−2.33155	−	0.757566i
$418$			6.74625i			0.329970i
$419$	−6.37045	+	19.6062i	−0.311217	+	0.957828i	0.666067	+	0.745892i	$0.267977\pi$
$419$	−6.37045	+	19.6062i	−0.311217	+	0.957828i	−0.977284	+	0.211935i	$0.932023\pi$
$420$	−80.2046	−	2.96891i	−3.91358	−	0.144868i
$421$	10.8005	+	33.2406i	0.526386	+	1.62005i	0.761559	+	0.648095i	$0.224434\pi$
$421$	10.8005	+	33.2406i	0.526386	+	1.62005i	−0.235174	+	0.971953i	$0.575566\pi$
$422$	−54.3004	+	17.6433i	−2.64330	+	0.858861i
$423$	−3.01913	+	4.15548i	−0.146795	+	0.202046i
$424$	21.3486			1.03678
$425$	2.53874	−	34.2449i	0.123147	−	1.66112i
$426$	−34.2679			−1.66029
$427$	−9.65742	+	13.2923i	−0.467355	+	0.643259i
$428$	−7.73038	+	2.51175i	−0.373662	+	0.121410i
$429$	2.77336	+	8.53552i	0.133899	+	0.412099i
$430$	−5.25697	−	18.4791i	−0.253514	−	0.891143i
$431$	0.453426	−	1.39550i	0.0218408	−	0.0672189i	−0.939542	−	0.342433i	$-0.888749\pi$
$431$	0.453426	−	1.39550i	0.0218408	−	0.0672189i	0.961383	+	0.275215i	$0.0887489\pi$
$432$		−	4.70590i		−	0.226413i
$433$	−21.1639	−	6.87655i	−1.01707	−	0.330466i	−0.247404	−	0.968913i	$-0.579577\pi$
$433$	−21.1639	−	6.87655i	−1.01707	−	0.330466i	−0.769666	+	0.638447i	$0.779577\pi$
$434$	70.7150	−	51.3774i	3.39443	−	2.46620i
$435$	−0.647136	+	17.4823i	−0.0310278	+	0.838212i
$436$	−46.5251	−	33.8025i	−2.22815	−	1.61884i
$437$	9.49838	+	13.0734i	0.454369	+	0.625385i
$438$	−27.1117	−	37.3161i	−1.29545	−	1.78303i
$439$	17.5425	+	12.7454i	0.837257	+	0.608303i	0.921603	−	0.388134i	$-0.126880\pi$
$439$	17.5425	+	12.7454i	0.837257	+	0.608303i	−0.0843463	+	0.996437i	$0.526880\pi$
$440$	−0.345886	+	9.34406i	−0.0164895	+	0.445461i
$441$	−18.9462	+	13.7652i	−0.902198	+	0.655485i
$442$	−61.7080	−	20.0502i	−2.93515	−	0.953688i
$443$		−	19.6968i		−	0.935823i	−0.883775	−	0.467912i	$-0.845007\pi$
$443$		−	19.6968i		−	0.935823i	0.883775	−	0.467912i	$-0.154993\pi$
$444$	−1.73268	+	5.33265i	−0.0822296	+	0.253077i
$445$	−0.245175	−	0.861832i	−0.0116224	−	0.0408548i
$446$	−9.14882	−	28.1572i	−0.433209	−	1.33328i
$447$	−31.7671	+	10.3217i	−1.50253	+	0.488202i
$448$	26.1277	−	35.9617i	1.23442	−	1.69903i
$449$	33.6945			1.59014			0.795070	−	0.606518i	$-0.207434\pi$
$449$	33.6945			1.59014			0.795070	+	0.606518i	$0.207434\pi$
$450$	25.4233	−	6.22582i	1.19847	−	0.293488i
$451$	−8.40135			−0.395604
$452$	18.8284	−	25.9151i	0.885615	−	1.21894i
$453$	5.29622	−	1.72084i	0.248838	−	0.0808523i
$454$	4.27964	+	13.1714i	0.200854	+	0.618164i
$455$	37.0795	+	1.37256i	1.73831	+	0.0643465i
$456$	8.28129	−	25.4872i	0.387807	−	1.19355i
$457$		−	3.95689i		−	0.185095i	−0.995708	−	0.0925477i	$-0.970499\pi$
$457$		−	3.95689i		−	0.185095i	0.995708	−	0.0925477i	$-0.0295011\pi$
$458$	−20.2697	−	6.58604i	−0.947143	−	0.307745i
$459$	10.3214	−	7.49892i	0.481761	−	0.350020i
$460$	26.7986	+	39.9104i	1.24949	+	1.86083i
$461$	−21.0272	−	15.2772i	−0.979334	−	0.711528i	−0.0217744	−	0.999763i	$-0.506932\pi$
$461$	−21.0272	−	15.2772i	−0.979334	−	0.711528i	−0.957560	+	0.288235i	$0.906932\pi$
$462$	13.5036	+	18.5861i	0.628243	+	0.864703i
$463$	−9.12978	−	12.5661i	−0.424297	−	0.583994i	0.542336	−	0.840162i	$-0.317540\pi$
$463$	−9.12978	−	12.5661i	−0.424297	−	0.583994i	−0.966632	+	0.256168i	$0.917540\pi$
$464$	7.04223	+	5.11648i	0.326927	+	0.237526i
$465$	−27.2262	+	34.6980i	−1.26258	+	1.60908i
$466$	31.8955	−	23.1734i	1.47753	−	1.07349i
$467$	31.5649	+	10.2561i	1.46065	+	0.474594i	0.928268	−	0.371911i	$-0.121297\pi$
$467$	31.5649	+	10.2561i	1.46065	+	0.474594i	0.532381	+	0.846505i	$0.321297\pi$
$468$		−	32.2387i		−	1.49023i
$469$	−14.2123	+	43.7409i	−0.656261	+	2.01976i
$470$	10.4638	−	7.02613i	0.482661	−	0.324091i
$471$	−15.1906	−	46.7518i	−0.699945	−	2.15421i
$472$	6.00247	−	1.95032i	0.276286	−	0.0897708i
$473$	−2.10708	+	2.90015i	−0.0968837	+	0.133349i
$474$	29.0943			1.33635
$475$	−14.0349	−	1.04048i	−0.643966	−	0.0477403i
$476$	−108.266			−4.96235
$477$	−6.55414	+	9.02101i	−0.300094	+	0.413043i
$478$	−4.76054	+	1.54679i	−0.217742	+	0.0707487i
$479$	2.49227	+	7.67043i	0.113875	+	0.350471i	0.991711	−	0.128491i	$-0.0410133\pi$
$479$	2.49227	+	7.67043i	0.113875	+	0.350471i	−0.877836	+	0.478962i	$0.841013\pi$
$480$	−4.01328	+	10.9550i	−0.183180	+	0.500025i
$481$	0.801039	−	2.46534i	0.0365242	−	0.112410i
$482$		−	9.54432i		−	0.434732i
$483$	52.3365	+	17.0052i	2.38139	+	0.773761i
$484$	3.02951	−	2.20107i	0.137705	−	0.100048i
$485$	11.0673	+	4.05444i	0.502542	+	0.184103i
$486$	36.7959	+	26.7338i	1.66910	+	1.21267i
$487$	9.68848	+	13.3350i	0.439027	+	0.604269i	0.969996	−	0.243123i	$-0.0781718\pi$
$487$	9.68848	+	13.3350i	0.439027	+	0.604269i	−0.530969	+	0.847392i	$0.678172\pi$
$488$	−9.59289	−	13.2035i	−0.434250	−	0.597694i
$489$	−15.3059	−	11.1204i	−0.692157	−	0.502882i
$490$	55.2721	−	15.7239i	2.49694	−	0.710333i
$491$	1.07297	−	0.779560i	0.0484225	−	0.0351810i	−0.563311	−	0.826245i	$-0.690473\pi$
$491$	1.07297	−	0.779560i	0.0484225	−	0.0351810i	0.611733	+	0.791064i	$0.290473\pi$
$492$	68.1251	+	22.1352i	3.07132	+	0.997932i
$493$			23.5988i			1.06284i
$494$	−8.21734	+	25.2904i	−0.369715	+	1.13787i
$495$	−3.84222	−	3.01484i	−0.172695	−	0.135507i
$496$	6.78145	+	20.8712i	0.304496	+	0.937143i
$497$	25.1411	−	8.16882i	1.12773	−	0.366422i
$498$	28.3015	−	38.9536i	1.26822	−	1.74555i
$499$	−43.5559			−1.94983			−0.974916	−	0.222575i	$-0.928554\pi$
$499$	−43.5559			−1.94983			−0.974916	+	0.222575i	$0.928554\pi$
$500$	−41.6091	−	4.63765i	−1.86082	−	0.207402i
$501$	42.0761			1.87982
$502$	−39.8771	+	54.8862i	−1.77980	+	2.44969i
$503$	−40.4049	+	13.1284i	−1.80157	+	0.585365i	−0.999923	−	0.0124368i	$-0.996041\pi$
$503$	−40.4049	+	13.1284i	−1.80157	+	0.585365i	−0.801644	+	0.597801i	$0.796041\pi$
$504$	−11.8814	−	36.5671i	−0.529238	−	1.62883i
$505$	−3.14710	−	2.46941i	−0.140044	−	0.109887i
$506$	4.25222	−	13.0870i	0.189034	−	0.581788i
$507$			5.77681i			0.256557i
$508$	14.5329	+	4.72202i	0.644792	+	0.209506i
$509$	−3.49016	+	2.53575i	−0.154699	+	0.112395i	−0.662442	−	0.749113i	$-0.730480\pi$
$509$	−3.49016	+	2.53575i	−0.154699	+	0.112395i	0.507743	+	0.861508i	$0.330480\pi$
$510$	80.6071	−	22.9312i	3.56934	−	1.01541i
$511$	28.7863	+	20.9144i	1.27343	+	0.925201i
$512$	15.8652	+	21.8366i	0.701152	+	0.965052i
$513$	−3.07335	−	4.23011i	−0.135692	−	0.186764i
$514$	33.9355	+	24.6556i	1.49683	+	1.08751i
$515$	10.5023	+	3.84744i	0.462787	+	0.169539i
$516$	24.7270	−	17.9652i	1.08855	−	0.790876i
$517$	−2.23663	−	0.726724i	−0.0983668	−	0.0319613i
$518$		−	6.63556i		−	0.291550i
$519$	4.28457	−	13.1865i	0.188072	−	0.578825i
$520$	−12.6783	+	34.6077i	−0.555979	+	1.51765i
$521$	−4.02830	−	12.3978i	−0.176483	−	0.543158i	0.823215	−	0.567729i	$-0.192178\pi$
$521$	−4.02830	−	12.3978i	−0.176483	−	0.543158i	−0.999698	+	0.0245711i	$0.992178\pi$
$522$	−17.1076	+	5.55859i	−0.748779	+	0.243293i
$523$	−13.6450	+	18.7807i	−0.596654	+	0.821223i	−0.995397	−	0.0958394i	$-0.969446\pi$
$523$	−13.6450	+	18.7807i	−0.596654	+	0.821223i	0.398743	+	0.917063i	$0.369446\pi$
$524$	17.2806			0.754908
$525$	−40.7491	+	25.2263i	−1.77844	+	1.10097i
$526$	15.1079			0.658738
$527$	−34.9701	+	48.1322i	−1.52332	+	2.09667i
$528$	−5.48559	+	1.78237i	−0.238729	+	0.0775679i
$529$	−3.07815	−	9.47359i	−0.133833	−	0.411895i
$530$	22.7156	−	15.2528i	0.986704	−	0.662539i
$531$	−1.01867	+	3.13515i	−0.0442066	+	0.136054i
$532$			44.3715i			1.92375i
$533$	−31.4950	−	10.2333i	−1.36420	−	0.443255i
$534$	1.76915	−	1.28536i	0.0765586	−	0.0556230i
$535$	−2.99618	+	3.81843i	−0.129536	+	0.165085i
$536$	−36.9596	−	26.8527i	−1.59641	−	1.15986i
$537$	−8.67919	−	11.9459i	−0.374535	−	0.515503i
$538$	13.7469	+	18.9210i	0.592671	+	0.815742i
$539$	−8.67450	−	6.30240i	−0.373637	−	0.271463i
$540$	−8.67110	−	12.9137i	−0.373145	−	0.555715i
$541$	28.2325	−	20.5121i	1.21381	−	0.881886i	0.218240	−	0.975895i	$-0.429968\pi$
$541$	28.2325	−	20.5121i	1.21381	−	0.881886i	0.995571	+	0.0940095i	$0.0299684\pi$
$542$	−40.7461	−	13.2392i	−1.75019	−	0.568672i
$543$			46.2563i			1.98505i
$544$	−4.86334	+	14.9678i	−0.208514	+	0.641740i
$545$	−34.3165	−	1.27028i	−1.46996	−	0.0544129i
$546$	27.9833	+	86.1237i	1.19757	+	3.68575i
$547$	−15.3770	+	4.99630i	−0.657475	+	0.213626i	−0.618707	−	0.785622i	$-0.712343\pi$
$547$	−15.3770	+	4.99630i	−0.657475	+	0.213626i	−0.0387676	+	0.999248i	$0.512343\pi$
$548$	−5.85251	+	8.05529i	−0.250007	+	0.344105i
$549$	8.52431			0.363809
$550$	6.30797	+	10.1895i	0.268973	+	0.434483i
$551$	9.67170			0.412028
$552$	−32.1296	+	44.2226i	−1.36753	+	1.88224i
$553$	−21.3454	+	6.93554i	−0.907698	+	0.294929i
$554$	−18.8720	−	58.0820i	−0.801794	−	2.46767i
$555$	0.916142	+	3.22039i	0.0388881	+	0.136698i
$556$	−25.4428	+	78.3050i	−1.07902	+	3.32087i
$557$		−	37.2055i		−	1.57645i	−0.615390	−	0.788223i	$-0.711001\pi$
$557$		−	37.2055i		−	1.57645i	0.615390	−	0.788223i	$-0.288999\pi$
$558$	−43.1297	−	14.0137i	−1.82583	−	0.593247i
$559$	−11.4316	+	8.30553i	−0.483504	+	0.351286i
$560$	−0.882112	+	23.8301i	−0.0372760	+	1.00701i
$561$	−12.6506	−	9.19121i	−0.534109	−	0.388053i
$562$	−9.47875	−	13.0464i	−0.399837	−	0.550329i
$563$	1.94680	+	2.67955i	0.0820480	+	0.112929i	0.848068	−	0.529887i	$-0.177766\pi$
$563$	1.94680	+	2.67955i	0.0820480	+	0.112929i	−0.766020	+	0.642817i	$0.777766\pi$
$564$	16.2217	+	11.7858i	0.683058	+	0.496271i
$565$	0.707564	−	19.1148i	0.0297675	−	0.804164i
$566$	35.6249	−	25.8830i	1.49743	−	1.08795i
$567$	−43.1683	−	14.0262i	−1.81290	−	0.589046i
$568$			26.2582i			1.10177i
$569$	−3.85413	+	11.8618i	−0.161573	+	0.497272i	−0.998767	−	0.0496340i	$-0.984195\pi$
$569$	−3.85413	+	11.8618i	−0.161573	+	0.497272i	0.837194	+	0.546906i	$0.184195\pi$
$570$	−9.39811	−	33.0359i	−0.393643	−	1.38372i
$571$	2.40689	+	7.40764i	0.100725	+	0.310000i	0.988703	−	0.149885i	$-0.0478904\pi$
$571$	2.40689	+	7.40764i	0.100725	+	0.310000i	−0.887978	+	0.459886i	$0.847890\pi$
$572$	14.0381	−	4.56124i	0.586960	−	0.190715i
$573$	12.0911	−	16.6419i	0.505112	−	0.695227i
$574$	−84.7699			−3.53823
$575$	26.5704	+	10.8647i	1.10806	+	0.453091i
$576$	−23.0621			−0.960921
$577$	8.43379	−	11.6081i	0.351103	−	0.483252i	−0.596540	−	0.802583i	$-0.703458\pi$
$577$	8.43379	−	11.6081i	0.351103	−	0.483252i	0.947643	+	0.319331i	$0.103458\pi$
$578$	68.7643	−	22.3429i	2.86022	−	0.929341i
$579$	5.34212	+	16.4413i	0.222011	+	0.683279i
$580$	28.7525	+	1.06432i	1.19388	+	0.0441935i
$581$	−11.4779	+	35.3253i	−0.476183	+	1.46554i
$582$			28.7657i			1.19238i
$583$	−4.85542	−	1.57762i	−0.201091	−	0.0653385i
$584$	−28.5939	+	20.7747i	−1.18322	+	0.859663i
$585$	−10.7314	−	15.9821i	−0.443691	−	0.660778i
$586$	44.6248	+	32.4218i	1.84343	+	1.33933i
$587$	6.51944	+	8.97324i	0.269086	+	0.370365i	0.922081	−	0.386997i	$-0.126488\pi$
$587$	6.51944	+	8.97324i	0.269086	+	0.370365i	−0.652995	+	0.757362i	$0.726488\pi$
$588$	53.7350	+	73.9599i	2.21600	+	3.05006i
$589$	19.7264	+	14.3321i	0.812814	+	0.590544i
$590$	4.99340	−	6.36376i	0.205575	−	0.261992i
$591$	27.2992	−	19.8340i	1.12294	−	0.815863i
$592$	1.58442	+	0.514810i	0.0651193	+	0.0211585i
$593$		−	23.7947i		−	0.977133i	−0.872527	−	0.488566i	$-0.837520\pi$
$593$		−	23.7947i		−	0.977133i	0.872527	−	0.488566i	$-0.162480\pi$
$594$	−1.37588	+	4.23451i	−0.0564528	+	0.173744i
$595$	−53.6719	+	36.0389i	−2.20033	+	1.47745i
$596$	16.9758	+	52.2461i	0.695356	+	2.14008i
$597$	−18.2691	+	5.93598i	−0.747703	+	0.242943i
$598$	31.8815	−	43.8811i	1.30373	−	1.79443i
$599$	−33.9787			−1.38833			−0.694167	−	0.719814i	$-0.744227\pi$
$599$	−33.9787			−1.38833			−0.694167	+	0.719814i	$0.744227\pi$
$600$	−11.3233	−	46.2391i	−0.462272	−	1.88770i
$601$	39.1273			1.59603			0.798017	−	0.602635i	$-0.205882\pi$
$601$	39.1273			1.59603			0.798017	+	0.602635i	$0.205882\pi$
$602$	−21.2605	+	29.2626i	−0.866514	+	1.19265i
$603$	22.6936	−	7.37361i	0.924156	−	0.300277i
$604$	−2.83021	−	8.71049i	−0.115160	−	0.354425i
$605$	0.769177	−	2.09961i	0.0312715	−	0.0853613i
$606$	3.01688	−	9.28499i	0.122552	−	0.377177i
$607$			33.5583i			1.36209i	0.732243	+	0.681044i	$0.238474\pi$
$607$			33.5583i			1.36209i	−0.732243	+	0.681044i	$0.761526\pi$
$608$	6.13440	+	1.99319i	0.248783	+	0.0808344i
$609$	26.6458	−	19.3593i	1.07974	−	0.784477i
$610$	−19.6406	−	7.19518i	−0.795224	−	0.291324i
$611$	−7.49948	−	5.44869i	−0.303396	−	0.220430i
$612$	33.0161	+	45.4428i	1.33460	+	1.83692i
$613$	−8.46923	−	11.6569i	−0.342069	−	0.470818i	0.602975	−	0.797760i	$-0.293982\pi$
$613$	−8.46923	−	11.6569i	−0.342069	−	0.470818i	−0.945044	+	0.326942i	$0.893982\pi$
$614$	29.4864	+	21.4231i	1.18997	+	0.864567i
$615$	41.1408	−	11.7038i	1.65896	−	0.471943i
$616$	14.2418	−	10.3473i	0.573819	−	0.416904i
$617$	−1.12904	−	0.366848i	−0.0454535	−	0.0147687i	0.286202	−	0.958169i	$-0.407607\pi$
$617$	−1.12904	−	0.366848i	−0.0454535	−	0.0147687i	−0.331655	+	0.943401i	$0.607607\pi$
$618$			27.2971i			1.09805i
$619$	4.93628	−	15.1923i	0.198406	−	0.610630i	−0.801514	−	0.597976i	$-0.795972\pi$
$619$	4.93628	−	15.1923i	0.198406	−	0.610630i	0.999920	−	0.0126545i	$-0.00402817\pi$
$620$	57.0665	+	44.7779i	2.29184	+	1.79832i
$621$	3.29570	+	10.1431i	0.132252	+	0.407029i
$622$	73.6491	−	23.9300i	2.95306	−	0.959507i
$623$	−0.991550	+	1.36475i	−0.0397256	+	0.0546776i
$624$	−22.7354			−0.910145
$625$	−22.1712	+	11.5516i	−0.886847	+	0.462063i
$626$	40.1862			1.60616
$627$	−3.76692	+	5.18472i	−0.150436	+	0.207058i
$628$	−76.8910	+	24.9834i	−3.06829	+	0.996946i
$629$	1.39567	+	4.29544i	0.0556492	+	0.171271i
$630$	−38.7681	−	30.4199i	−1.54456	−	1.21196i
$631$	−0.393342	+	1.21058i	−0.0156587	+	0.0481926i	−0.958581	−	0.284822i	$-0.908066\pi$
$631$	−0.393342	+	1.21058i	−0.0156587	+	0.0481926i	0.942922	+	0.333014i	$0.108066\pi$
$632$		−	22.2939i		−	0.886804i
$633$	−51.5831	−	16.7604i	−2.05025	−	0.666165i
$634$	38.6610	−	28.0889i	1.53543	−	1.11555i
$635$	8.77642	−	2.49673i	0.348281	−	0.0990796i
$636$	35.2152	+	25.5854i	1.39637	+	1.01453i
$637$	−24.8423	−	34.1925i	−0.984287	−	1.35476i
$638$	−4.84088	−	6.66290i	−0.191652	−	0.263787i
$639$	−11.0956	−	8.06144i	−0.438936	−	0.318906i
$640$	43.5138	+	15.9410i	1.72003	+	0.630121i
$641$	−25.6417	+	18.6298i	−1.01279	+	0.735832i	−0.964792	−	0.263015i	$-0.915283\pi$
$641$	−25.6417	+	18.6298i	−1.01279	+	0.735832i	−0.0479948	+	0.998848i	$0.515283\pi$
$642$	−11.2657	−	3.66043i	−0.444620	−	0.144466i
$643$			36.2850i			1.43094i	0.698642	+	0.715471i	$0.253788\pi$
$643$			36.2850i			1.43094i	−0.698642	+	0.715471i	$0.746212\pi$
$644$	27.9677	−	86.0759i	1.10208	−	3.39186i
$645$	6.27807	−	17.1372i	0.247199	−	0.674775i
$646$	−14.3173	−	44.0641i	−0.563307	−	1.73368i
$647$	4.19189	−	1.36203i	0.164800	−	0.0535468i	−0.225455	−	0.974254i	$-0.572387\pi$
$647$	4.19189	−	1.36203i	0.164800	−	0.0535468i	0.390255	+	0.920707i	$0.372387\pi$
$648$	26.5012	−	36.4758i	1.04106	−	1.43290i
$649$	−1.50930			−0.0592452
$650$	11.2359	+	45.8820i	0.440707	+	1.79964i
$651$	83.0345			3.25438
$652$	−18.2893	+	25.1731i	−0.716265	+	0.985854i
$653$	−17.3498	+	5.63729i	−0.678950	+	0.220604i	−0.628136	−	0.778104i	$-0.716182\pi$
$653$	−17.3498	+	5.63729i	−0.678950	+	0.220604i	−0.0508144	+	0.998708i	$0.516182\pi$
$654$	−25.8981	−	79.7061i	−1.01270	−	3.11676i
$655$	8.56676	−	5.75230i	0.334731	−	0.224761i
$656$	6.57674	−	20.2411i	0.256779	−	0.790283i
$657$		−	18.4605i		−	0.720214i
$658$	−22.5676	−	7.33267i	−0.879778	−	0.285857i
$659$	−25.7664	+	18.7204i	−1.00372	+	0.729242i	−0.962882	−	0.269924i	$-0.913001\pi$
$659$	−25.7664	+	18.7204i	−1.00372	+	0.729242i	−0.0408340	+	0.999166i	$0.513001\pi$
$660$	−11.7690	+	14.9988i	−0.458108	+	0.583829i
$661$	6.00269	+	4.36121i	0.233478	+	0.169631i	0.698373	−	0.715734i	$-0.253908\pi$
$661$	6.00269	+	4.36121i	0.233478	+	0.169631i	−0.464895	+	0.885366i	$0.653908\pi$
$662$	−40.8975	−	56.2906i	−1.58953	−	2.18780i
$663$	−36.2292	−	49.8652i	−1.40703	−	1.93660i
$664$	−29.8487	−	21.6863i	−1.15835	−	0.841594i
$665$	14.7702	+	21.9969i	0.572762	+	0.853001i
$666$	−2.78517	+	2.02355i	−0.107923	+	0.0784108i
$667$	−18.7621	−	6.09616i	−0.726470	−	0.236044i
$668$		−	69.2010i		−	2.67747i
$669$	8.69100	−	26.7482i	0.336014	−	1.03414i
$670$	−58.5116	−	2.16590i	−2.26050	−	0.0836761i
$671$	1.20605	+	3.71184i	0.0465590	+	0.143294i
$672$	20.8900	−	6.78759i	0.805851	−	0.261837i
$673$	−6.16517	+	8.48563i	−0.237650	+	0.327097i	−0.911138	−	0.412101i	$-0.864795\pi$
$673$	−6.16517	+	8.48563i	−0.237650	+	0.327097i	0.673488	+	0.739198i	$0.264795\pi$
$674$	3.54477			0.136540
$675$	−8.59727	−	3.51546i	−0.330909	−	0.135310i
$676$	9.50090			0.365419
$677$	10.4763	−	14.4194i	0.402638	−	0.554184i	−0.558766	−	0.829326i	$-0.688725\pi$
$677$	10.4763	−	14.4194i	0.402638	−	0.554184i	0.961404	+	0.275142i	$0.0887248\pi$
$678$	44.3974	−	14.4256i	1.70507	−	0.554012i
$679$	−6.85719	−	21.1043i	−0.263155	−	0.809908i
$680$	−17.5713	−	61.7662i	−0.673830	−	2.36863i
$681$	−4.06548	+	12.5123i	−0.155790	+	0.479471i
$682$		−	20.7632i		−	0.795064i
$683$	−11.4693	−	3.72660i	−0.438860	−	0.142594i	0.0812495	−	0.996694i	$-0.474109\pi$
$683$	−11.4693	−	3.72660i	−0.438860	−	0.142594i	−0.520110	+	0.854099i	$0.674109\pi$
$684$	18.6242	−	13.5313i	0.712115	−	0.517382i
$685$	−0.219935	+	5.94151i	−0.00840327	+	0.227013i
$686$	−30.3850	−	22.0760i	−1.16010	−	0.842864i
$687$	−11.9005	−	16.3796i	−0.454032	−	0.624922i
$688$	−5.33778	−	7.34682i	−0.203501	−	0.280095i
$689$	−16.2804	−	11.8284i	−0.620233	−	0.450626i
$690$	−2.59153	+	70.0098i	−0.0986579	+	2.66523i
$691$	−2.81242	+	2.04334i	−0.106989	+	0.0777324i	−0.639994	−	0.768380i	$-0.721063\pi$
$691$	−2.81242	+	2.04334i	−0.106989	+	0.0777324i	0.533004	+	0.846113i	$0.321063\pi$
$692$	−21.6874	−	7.04667i	−0.824432	−	0.267874i
$693$			9.19467i			0.349277i
$694$	−4.80255	+	14.7807i	−0.182302	+	0.561069i
$695$	13.4527	+	47.2884i	0.510289	+	1.79375i
$696$	10.1098	+	31.1147i	0.383210	+	1.17940i
$697$	54.8747	−	17.8299i	2.07853	−	0.675354i
$698$	−42.1555	+	58.0221i	−1.59561	+	2.19617i
$699$	37.4521			1.41657
$700$	41.4888	+	67.0186i	1.56813	+	2.53307i
$701$	−20.8506			−0.787515			−0.393757	−	0.919214i	$-0.628825\pi$
$701$	−20.8506			−0.787515			−0.393757	+	0.919214i	$0.628825\pi$
$702$	−10.3158	+	14.1984i	−0.389343	+	0.535885i
$703$	1.76044	−	0.572002i	0.0663963	−	0.0215735i
$704$	−3.26291	−	10.0422i	−0.122976	−	0.378480i
$705$	11.9650	+	0.442904i	0.450628	+	0.0166807i
$706$	3.20324	−	9.85856i	0.120555	−	0.371032i
$707$			7.53120i			0.283240i
$708$	12.2387	+	3.97658i	0.459957	+	0.149449i
$709$	−11.1794	+	8.12232i	−0.419852	+	0.305040i	−0.777578	−	0.628786i	$-0.783552\pi$
$709$	−11.1794	+	8.12232i	−0.419852	+	0.305040i	0.357727	+	0.933826i	$0.383552\pi$
$710$	18.7606	+	27.9397i	0.704072	+	1.04856i
$711$	9.42046	+	6.84436i	0.353295	+	0.256684i
$712$	−0.984925	−	1.35563i	−0.0369116	−	0.0508045i
$713$	−29.2335	−	40.2365i	−1.09480	−	1.50687i
$714$	−127.645	−	92.7396i	−4.77700	−	3.47069i
$715$	5.44094	−	6.93412i	0.203480	−	0.259321i
$716$	−19.6469	+	14.2743i	−0.734241	+	0.533457i
$717$	−4.52232	−	1.46939i	−0.168889	−	0.0548754i
$718$			55.9322i			2.08737i
$719$	9.05895	−	27.8806i	0.337842	−	1.03977i	−0.627463	−	0.778646i	$-0.715907\pi$
$719$	9.05895	−	27.8806i	0.337842	−	1.03977i	0.965305	−	0.261124i	$-0.0840933\pi$
$720$	10.2713	−	6.89686i	0.382790	−	0.257031i
$721$	−6.50711	−	20.0268i	−0.242337	−	0.745838i
$722$	25.2512	−	8.20463i	0.939754	−	0.305345i
$723$	5.32928	−	7.33512i	0.198198	−	0.272796i
$724$	76.0760			2.82734
$725$	14.6081	−	9.04336i	0.542532	−	0.335862i
$726$	5.45721			0.202536
$727$	15.3054	−	21.0661i	0.567645	−	0.781297i	−0.424628	−	0.905368i	$-0.639595\pi$
$727$	15.3054	−	21.0661i	0.567645	−	0.781297i	0.992273	+	0.124071i	$0.0395951\pi$
$728$	65.9933	−	21.4425i	2.44588	−	0.794713i
$729$	3.35601	+	10.3287i	0.124297	+	0.382546i
$730$	−15.5821	+	42.5343i	−0.576721	+	1.57427i
$731$	7.60784	−	23.4145i	0.281386	−	0.866017i
$732$		−	33.2763i		−	1.22993i
$733$	35.2904	+	11.4666i	1.30348	+	0.423527i	0.876791	−	0.480871i	$-0.159679\pi$
$733$	35.2904	+	11.4666i	1.30348	+	0.423527i	0.426690	+	0.904398i	$0.359679\pi$
$734$	22.3303	−	16.2239i	0.824226	−	0.598835i
$735$	51.2582	+	18.7781i	1.89069	+	0.692639i
$736$	−10.6437	−	7.73313i	−0.392334	−	0.285047i
$737$	6.42155	+	8.83850i	0.236541	+	0.325571i
$738$	25.8510	+	35.5808i	0.951588	+	1.30975i
$739$	14.1699	+	10.2951i	0.521249	+	0.378710i	0.817074	−	0.576532i	$-0.195594\pi$
$739$	14.1699	+	10.2951i	0.521249	+	0.378710i	−0.295825	+	0.955242i	$0.595594\pi$
$740$	5.29646	−	1.50675i	0.194702	−	0.0553891i
$741$	−20.4367	+	14.8481i	−0.750761	+	0.545460i
$742$	−48.9914	−	15.9183i	−1.79853	−	0.584378i
$743$		−	29.0508i		−	1.06577i	−0.846187	−	0.532886i	$-0.821107\pi$
$743$		−	29.0508i		−	1.06577i	0.846187	−	0.532886i	$-0.178893\pi$
$744$	−25.4876	+	78.4428i	−0.934421	+	2.87585i
$745$	25.8071	+	20.2498i	0.945498	+	0.741896i
$746$	−19.2446	−	59.2288i	−0.704595	−	2.16852i
$747$	18.3275	−	5.95496i	0.670567	−	0.217880i
$748$	−15.1164	+	20.8060i	−0.552712	+	0.760743i
$749$	9.13776			0.333886
$750$	−45.0845	−	41.1099i	−1.64625	−	1.50112i
$751$	31.2748			1.14123			0.570617	−	0.821216i	$-0.306704\pi$
$751$	31.2748			1.14123			0.570617	+	0.821216i	$0.306704\pi$
$752$	3.50175	−	4.81975i	0.127696	−	0.175758i
$753$	−61.2938	+	19.9155i	−2.23367	+	0.725763i
$754$	−10.0317	−	30.8744i	−0.365333	−	1.12438i
$755$	−4.30256	−	3.37606i	−0.156586	−	0.122867i
$756$	−9.04941	+	27.8512i	−0.329124	+	1.01294i
$757$		−	0.250510i		−	0.00910493i	−0.999990	−	0.00455247i	$-0.998551\pi$
$757$		−	0.250510i		−	0.00910493i	0.999990	−	0.00455247i	$-0.00144910\pi$
$758$	−4.81583	−	1.56476i	−0.174919	−	0.0568346i
$759$	10.5754	−	7.68347i	0.383862	−	0.278892i
$760$	−25.3142	+	7.20142i	−0.918242	+	0.261223i
$761$	−26.7104	−	19.4063i	−0.968252	−	0.703476i	−0.0131995	−	0.999913i	$-0.504202\pi$
$761$	−26.7104	−	19.4063i	−0.968252	−	0.703476i	−0.955053	+	0.296437i	$0.904202\pi$
$762$	13.0894	+	18.0160i	0.474179	+	0.652652i
$763$	38.0009	+	52.3037i	1.37572	+	1.89352i
$764$	−27.3704	−	19.8857i	−0.990226	−	0.719441i
$765$	31.4943	+	11.5377i	1.13868	+	0.417146i
$766$	−13.8415	+	10.0564i	−0.500113	+	0.363354i
$767$	−5.65807	−	1.83842i	−0.204301	−	0.0663814i
$768$			65.0161i			2.34607i
$769$	−8.53238	+	26.2600i	−0.307685	+	0.946958i	0.670976	+	0.741479i	$0.265875\pi$
$769$	−8.53238	+	26.2600i	−0.307685	+	0.946958i	−0.978661	+	0.205479i	$0.934125\pi$
$770$	7.76102	−	21.1851i	0.279688	−	0.763460i
$771$	12.3136	+	37.8973i	0.443462	+	1.36484i
$772$	27.0405	−	8.78598i	0.973208	−	0.316214i
$773$	2.46518	−	3.39302i	0.0886662	−	0.122039i	−0.762379	−	0.647130i	$-0.775969\pi$
$773$	2.46518	−	3.39302i	0.0886662	−	0.122039i	0.851046	+	0.525092i	$0.175969\pi$
$774$	18.7660			0.674530
$775$	43.1958	+	3.20231i	1.55164	+	0.115030i
$776$	22.0421			0.791264
$777$	3.70511	−	5.09965i	0.132920	−	0.182949i
$778$	40.8471	−	13.2720i	1.46444	−	0.475826i
$779$	−7.30737	−	22.4898i	−0.261814	−	0.805780i
$780$	−62.3891	+	41.8923i	−2.23389	+	1.49998i
$781$	1.94044	−	5.97206i	0.0694343	−	0.213697i
$782$			94.5040i			3.37946i
$783$	6.07076	+	1.97251i	0.216951	+	0.0704918i
$784$	21.9747	−	15.9656i	0.784812	−	0.570199i
$785$	−29.8018	+	37.9805i	−1.06367	+	1.35558i
$786$	20.3739	+	14.8025i	0.726712	+	0.527987i
$787$	−6.48763	−	8.92946i	−0.231259	−	0.318301i	0.677579	−	0.735450i	$-0.263029\pi$
$787$	−6.48763	−	8.92946i	−0.231259	−	0.318301i	−0.908838	+	0.417149i	$0.863029\pi$
$788$	−32.6203	−	44.8980i	−1.16205	−	1.59942i
$789$	11.6109	+	8.43585i	0.413361	+	0.300324i
$790$	−15.9282	−	23.7215i	−0.566700	−	0.843972i
$791$	−29.1339	+	21.1670i	−1.03588	+	0.752612i
$792$	−8.68622	−	2.82232i	−0.308651	−	0.100287i
$793$			15.3840i			0.546301i
$794$	0.144435	−	0.444524i	0.00512579	−	0.0157756i
$795$	25.9744	+	0.961487i	0.921218	+	0.0341004i
$796$	9.76268	+	30.0464i	0.346029	+	1.06497i
$797$	−9.69003	+	3.14848i	−0.343238	+	0.111525i	−0.475563	−	0.879681i	$-0.657756\pi$
$797$	−9.69003	+	3.14848i	−0.343238	+	0.111525i	0.132325	+	0.991206i	$0.457756\pi$
$798$	−38.0083	+	52.3140i	−1.34548	+	1.85189i
$799$	16.1512			0.571387
$800$	11.1291	−	2.72536i	0.393472	−	0.0963559i
$801$	0.875211			0.0309241
$802$	31.7512	−	43.7018i	1.12117	−	1.54316i
$803$	8.03849	−	2.61186i	0.283672	−	0.0921706i
$804$	−28.7843	−	88.5889i	−1.01514	−	3.12429i
$805$	−14.7877	−	51.9813i	−0.521198	−	1.83210i
$806$	25.2908	−	77.8371i	0.890830	−	2.74169i
$807$			22.2173i			0.782086i
$808$	−7.11474	−	2.31172i	−0.250296	−	0.0813260i
$809$	−18.4245	+	13.3862i	−0.647770	+	0.470633i	−0.862511	−	0.506039i	$-0.831109\pi$
$809$	−18.4245	+	13.3862i	−0.647770	+	0.470633i	0.214741	+	0.976671i	$0.431109\pi$
$810$	2.13755	−	57.7456i	0.0751058	−	2.02897i
$811$	−25.1080	−	18.2420i	−0.881662	−	0.640565i	0.0520288	−	0.998646i	$-0.483431\pi$
$811$	−25.1080	−	18.2420i	−0.881662	−	0.640565i	−0.933691	+	0.358081i	$0.883431\pi$
$812$	−31.8395	−	43.8233i	−1.11735	−	1.53790i
$813$	−23.9223	−	32.9262i	−0.838991	−	1.15477i
$814$	−1.27519	−	0.926481i	−0.0446955	−	0.0324732i
$815$	−0.687304	+	18.5674i	−0.0240752	+	0.650389i
$816$	32.0472	−	23.2837i	1.12188	−	0.815092i
$817$	−9.59619	−	3.11799i	−0.335728	−	0.109085i
$818$			68.3409i			2.38948i
$819$	−11.1997	+	34.4690i	−0.391348	+	1.20444i
$820$	−19.2488	−	67.6628i	−0.672197	−	2.36289i
$821$	1.33858	+	4.11971i	0.0467166	+	0.143779i	0.971694	−	0.236243i	$-0.0759163\pi$
$821$	1.33858	+	4.11971i	0.0467166	+	0.143779i	−0.924977	+	0.380022i	$0.875916\pi$
$822$	−13.8002	+	4.48396i	−0.481337	+	0.156396i
$823$	2.20798	−	3.03902i	0.0769652	−	0.105934i	−0.768799	−	0.639491i	$-0.779145\pi$
$823$	2.20798	−	3.03902i	0.0769652	−	0.105934i	0.845764	+	0.533557i	$0.179145\pi$
$824$	20.9167			0.728669
$825$	−0.841667	+	11.3532i	−0.0293031	+	0.395267i
$826$	−15.2289			−0.529881
$827$	6.84844	−	9.42607i	0.238144	−	0.327777i	−0.673171	−	0.739487i	$-0.735068\pi$
$827$	6.84844	−	9.42607i	0.238144	−	0.327777i	0.911315	+	0.411710i	$0.135068\pi$
$828$	−44.6579	+	14.5102i	−1.55197	+	0.504265i
$829$	−12.2574	−	37.7243i	−0.425716	−	1.31022i	−0.902307	−	0.431095i	$-0.858127\pi$
$829$	−12.2574	−	37.7243i	−0.425716	−	1.31022i	0.476590	−	0.879125i	$-0.341873\pi$
$830$	−47.2542	−	1.74919i	−1.64022	−	0.0607153i
$831$	17.9276	−	55.1755i	0.621902	−	1.91402i
$832$		−	41.6206i		−	1.44294i
$833$	70.0341	+	22.7555i	2.42654	+	0.788430i
$834$	−97.0726	+	70.5273i	−3.36135	+	2.44216i
$835$	−23.0353	−	34.3059i	−0.797169	−	1.18721i
$836$	8.52711	+	6.19531i	0.294916	+	0.214269i
$837$	9.45897	+	13.0192i	0.326950	+	0.450008i
$838$	29.0429	+	39.9741i	1.00327	+	1.38088i
$839$	−32.1188	−	23.3356i	−1.10886	−	0.805636i	−0.126379	−	0.991982i	$-0.540335\pi$
$839$	−32.1188	−	23.3356i	−1.10886	−	0.805636i	−0.982484	+	0.186346i	$0.940335\pi$
$840$	−55.3265	+	70.5100i	−1.90895	+	2.43283i
$841$	13.9093	−	10.1057i	0.479630	−	0.348472i
$842$	79.6713	+	25.8868i	2.74565	+	0.892117i
$843$		−	15.3192i		−	0.527623i
$844$	−27.5652	+	84.8369i	−0.948832	+	2.92021i
$845$	4.71001	−	3.16261i	0.162029	−	0.108797i
$846$	3.80434	+	11.7085i	0.130796	+	0.402548i
$847$	−4.00374	+	1.30089i	−0.137570	+	0.0446993i
$848$	7.60184	−	10.4630i	0.261048	−	0.359302i
$849$	41.8313			1.43565
$850$	−62.8263	−	53.1673i	−2.15492	−	1.82362i
$851$	−3.77560			−0.129426
$852$	−31.4694	+	43.3139i	−1.07812	+	1.48391i
$853$	0.766623	−	0.249091i	0.0262487	−	0.00852872i	−0.295863	−	0.955230i	$-0.595607\pi$
$853$	0.766623	−	0.249091i	0.0262487	−	0.00852872i	0.322112	+	0.946702i	$0.395607\pi$
$854$	12.1691	+	37.4526i	0.416417	+	1.28160i
$855$	4.72860	−	12.9076i	0.161715	−	0.441430i
$856$	−2.80485	+	8.63246i	−0.0958680	+	0.295051i
$857$			47.0807i			1.60824i	0.594464	+	0.804122i	$0.297364\pi$
$857$			47.0807i			1.60824i	−0.594464	+	0.804122i	$0.702636\pi$
$858$	20.4580	+	6.64720i	0.698424	+	0.226932i
$859$	−2.10778	+	1.53139i	−0.0719164	+	0.0522503i	−0.623163	−	0.782092i	$-0.714153\pi$
$859$	−2.10778	+	1.53139i	−0.0719164	+	0.0522503i	0.551246	+	0.834343i	$0.314153\pi$
$860$	−28.1849	−	10.3253i	−0.961096	−	0.352090i
$861$	−65.1484	−	47.3331i	−2.22025	−	1.61311i
$862$	−2.06717	−	2.84521i	−0.0704080	−	0.0969083i
$863$	−12.8302	−	17.6593i	−0.436746	−	0.601130i	0.532739	−	0.846280i	$-0.321163\pi$
$863$	−12.8302	−	17.6593i	−0.436746	−	0.601130i	−0.969485	+	0.245150i	$0.921163\pi$
$864$	3.44395	+	2.50218i	0.117166	+	0.0851259i
$865$	−13.0971	+	3.72587i	−0.445313	+	0.126683i
$866$	−43.1498	+	31.3502i	−1.46629	+	1.06532i
$867$	65.3232	+	21.2248i	2.21849	+	0.720832i
$868$		−	136.564i		−	4.63528i
$869$	−1.64748	+	5.07042i	−0.0558869	+	0.172002i
$870$	32.9875	+	25.8840i	1.11838	+	0.877550i
$871$	13.3073	+	40.9556i	0.450900	+	1.38773i
$872$	−61.0759	+	19.8447i	−2.06829	+	0.672028i
$873$	−6.76705	+	9.31405i	−0.229030	+	0.315233i
$874$	38.7314			1.31011
$875$	42.8766	+	19.4134i	1.44949	+	0.656293i
$876$	−72.0643			−2.43483
$877$	−18.3028	+	25.1916i	−0.618040	+	0.850659i	−0.997208	−	0.0746684i	$-0.976210\pi$
$877$	−18.3028	+	25.1916i	−0.618040	+	0.850659i	0.379168	+	0.925328i	$0.376210\pi$
$878$	49.4279	−	16.0601i	1.66811	−	0.542002i
$879$	16.1922	+	49.8344i	0.546149	+	1.68087i
$880$	4.45640	+	3.49677i	0.150225	+	0.117876i
$881$	−4.84065	+	14.8980i	−0.163086	+	0.501926i	−0.998890	−	0.0471010i	$-0.985002\pi$
$881$	−4.84065	+	14.8980i	−0.163086	+	0.501926i	0.835804	+	0.549027i	$0.185002\pi$
$882$			56.1302i			1.89000i
$883$	−44.9420	−	14.6026i	−1.51242	−	0.491415i	−0.568808	−	0.822470i	$-0.692595\pi$
$883$	−44.9420	−	14.6026i	−1.51242	−	0.491415i	−0.943611	+	0.331055i	$0.892595\pi$
$884$	−82.0115	+	59.5848i	−2.75834	+	2.00405i
$885$	7.39094	−	2.10259i	0.248444	−	0.0706776i
$886$	−38.1932	−	27.7490i	−1.28313	−	0.932246i
$887$	17.5382	+	24.1392i	0.588874	+	0.810515i	0.994633	−	0.103465i	$-0.0329929\pi$
$887$	17.5382	+	24.1392i	0.588874	+	0.810515i	−0.405759	+	0.913980i	$0.632993\pi$
$888$	3.68035	+	5.06557i	0.123505	+	0.169989i
$889$	−13.8979	−	10.0974i	−0.466120	−	0.338656i
$890$	−2.01655	−	0.738746i	−0.0675948	−	0.0247628i
$891$	−8.72280	+	6.33749i	−0.292225	+	0.212314i
$892$	−43.9917	−	14.2938i	−1.47295	−	0.478591i
$893$		−	6.61938i		−	0.221509i
$894$	−24.7392	+	76.1395i	−0.827403	+	2.54649i
$895$	−4.98826	+	13.6164i	−0.166739	+	0.455145i
$896$	−26.9606	−	82.9763i	−0.900692	−	2.77204i
$897$	49.0039	−	15.9223i	1.63619	−	0.531631i
$898$	47.4690	−	65.3354i	1.58406	−	2.18027i
$899$	−29.7669			−0.992783
$900$	15.4778	−	37.8519i	0.515927	−	1.26173i
$901$	35.0620			1.16809
$902$	−11.8359	+	16.2907i	−0.394092	+	0.542421i
$903$	−32.6788	+	10.6180i	−1.08748	+	0.353344i
$904$	−11.0538	−	34.0201i	−0.367644	−	1.13149i
$905$	37.7141	−	25.3238i	1.25366	−	0.841792i
$906$	4.12453	−	12.6940i	0.137028	−	0.421730i
$907$		−	20.2923i		−	0.673795i	−0.941541	−	0.336898i	$-0.890622\pi$
$907$		−	20.2923i		−	0.673795i	0.941541	−	0.336898i	$-0.109378\pi$
$908$	20.5785	+	6.68635i	0.682920	+	0.221894i
$909$	3.16110	−	2.29668i	0.104847	−	0.0761759i
$910$	54.8993	−	69.9655i	1.81989	−	2.31933i
$911$	23.6315	+	17.1693i	0.782946	+	0.568844i	0.905862	−	0.423573i	$-0.139224\pi$
$911$	23.6315	+	17.1693i	0.782946	+	0.568844i	−0.122916	+	0.992417i	$0.539224\pi$
$912$	−9.54257	−	13.1342i	−0.315986	−	0.434917i
$913$	5.18607	+	7.13801i	0.171634	+	0.236234i
$914$	−7.67263	−	5.57449i	−0.253788	−	0.184388i
$915$	−11.0768	−	16.4965i	−0.366189	−	0.545357i
$916$	−26.9390	+	19.5723i	−0.890089	+	0.646688i
$917$	−18.4761	−	6.00326i	−0.610136	−	0.198245i
$918$		−	30.5783i		−	1.00923i
$919$	−0.101692	+	0.312977i	−0.00335452	+	0.0103242i	−0.952720	−	0.303850i	$-0.901728\pi$
$919$	−0.101692	+	0.312977i	−0.00335452	+	0.0103242i	0.949365	+	0.314175i	$0.101728\pi$
$920$	53.6459	+	1.98579i	1.76865	+	0.0654697i
$921$	10.6992	+	32.9288i	0.352551	+	1.08504i
$922$	−59.2465	+	19.2504i	−1.95118	+	0.633977i
$923$	14.5486	−	20.0245i	0.478874	−	0.659114i
$924$	35.8932			1.18080
$925$	2.12413	−	2.51002i	0.0698408	−	0.0825289i
$926$	−37.2284			−1.22340
$927$	−6.42157	+	8.83853i	−0.210912	+	0.290295i
$928$	−7.48885	+	2.43328i	−0.245834	+	0.0798762i
$929$	3.15123	+	9.69848i	0.103388	+	0.318197i	0.989349	−	0.145564i	$-0.0464997\pi$
$929$	3.15123	+	9.69848i	0.103388	+	0.318197i	−0.885960	+	0.463761i	$0.846500\pi$
$930$	28.9249	+	101.676i	0.948485	+	3.33408i
$931$	9.32608	−	28.7027i	0.305650	−	0.940694i
$932$		−	61.5962i		−	2.01765i
$933$	69.9636	+	22.7326i	2.29051	+	0.744230i
$934$	64.3559	−	46.7573i	2.10579	−	1.52995i
$935$	−0.568069	+	15.3463i	−0.0185779	+	0.501878i
$936$	−29.1252	−	21.1607i	−0.951985	−	0.691658i
$937$	4.96263	+	6.83047i	0.162122	+	0.223142i	0.882348	−	0.470598i	$-0.155962\pi$
$937$	4.96263	+	6.83047i	0.162122	+	0.223142i	−0.720226	+	0.693740i	$0.755962\pi$
$938$	64.7936	+	89.1808i	2.11559	+	2.91186i
$939$	30.8844	+	22.4388i	1.00787	+	0.732264i
$940$	0.728428	−	19.6784i	0.0237587	−	0.641838i
$941$	−31.2286	+	22.6889i	−1.01802	+	0.739636i	−0.965876	−	0.259003i	$-0.916606\pi$
$941$	−31.2286	+	22.6889i	−1.01802	+	0.739636i	−0.0521453	+	0.998640i	$0.516606\pi$
$942$	−112.055	−	36.4089i	−3.65095	−	1.18627i
$943$			48.2336i			1.57070i
$944$	1.18151	−	3.63631i	0.0384549	−	0.118352i
$945$	4.78480	+	16.8194i	0.155650	+	0.547134i
$946$	2.65508	+	8.17150i	0.0863241	+	0.265678i
$947$	30.8561	−	10.0257i	1.00269	−	0.325793i	0.238749	−	0.971081i	$-0.423263\pi$
$947$	30.8561	−	10.0257i	1.00269	−	0.325793i	0.763939	+	0.645288i	$0.223263\pi$
$948$	26.7183	−	36.7746i	0.867770	−	1.19438i
$949$	33.3161			1.08149
$950$	−21.7900	+	25.7487i	−0.706962	+	0.835397i
$951$	45.3963			1.47208
$952$	−71.0629	+	97.8097i	−2.30316	+	3.17003i
$953$	−39.1298	+	12.7141i	−1.26754	+	0.411849i	−0.864175	−	0.503191i	$-0.832159\pi$
$953$	−39.1298	+	12.7141i	−1.26754	+	0.411849i	−0.403365	+	0.915039i	$0.632159\pi$
$954$	8.25872	+	25.4177i	0.267386	+	0.822929i
$955$	−20.1881	−	0.747298i	−0.653273	−	0.0241820i
$956$	−2.41665	+	7.43769i	−0.0781601	+	0.240552i
$957$		−	7.82367i		−	0.252903i
$958$	18.3845	+	5.97350i	0.593977	+	0.192995i
$959$	9.05579	−	6.57941i	0.292427	−	0.212460i
$960$	29.9679	+	44.6304i	0.967209	+	1.44044i
$961$	−35.6332	−	25.8891i	−1.14946	−	0.835131i
$962$	−3.65193	−	5.02645i	−0.117743	−	0.162059i
$963$	−2.78660	−	3.83543i	−0.0897970	−	0.123595i
$964$	−12.0638	−	8.76487i	−0.388549	−	0.282297i
$965$	10.4805	−	13.3567i	0.337379	−	0.429967i
$966$	106.706	−	77.5264i	3.43321	−	2.49437i
$967$	43.3325	+	14.0796i	1.39348	+	0.452769i	0.907077	−	0.420965i	$-0.138309\pi$
$967$	43.3325	+	14.0796i	1.39348	+	0.452769i	0.486403	+	0.873735i	$0.338309\pi$
$968$		−	4.18165i		−	0.134403i
$969$	13.6009	−	41.8591i	0.436922	−	1.34471i
$970$	23.4535	−	15.7483i	0.753047	−	0.505647i
$971$	−8.59617	−	26.4563i	−0.275864	−	0.849023i	−0.988989	−	0.147986i	$-0.952721\pi$
$971$	−8.59617	−	26.4563i	−0.275864	−	0.849023i	0.713125	−	0.701037i	$-0.247279\pi$
$972$	67.5818	−	21.9586i	2.16769	−	0.704324i
$973$	54.4060	−	74.8835i	1.74418	−	2.40065i
$974$	39.5066			1.26587
$975$	−16.9841	+	41.5356i	−0.543926	+	1.33020i
$976$	−9.88694			−0.316473
$977$	−15.8426	+	21.8054i	−0.506849	+	0.697618i	−0.983384	−	0.181538i	$-0.941893\pi$
$977$	−15.8426	+	21.8054i	−0.506849	+	0.697618i	0.476535	+	0.879155i	$0.341893\pi$
$978$	−43.1262	+	14.0125i	−1.37902	+	0.448072i
$979$	0.123828	+	0.381103i	0.00395756	+	0.0121801i
$980$	30.8836	−	84.3025i	0.986540	−	2.69294i
$981$	10.3651	−	31.9005i	0.330933	−	1.01851i
$982$		−	3.17880i		−	0.101440i
$983$	−52.3042	−	16.9947i	−1.66825	−	0.542046i	−0.685670	−	0.727912i	$-0.740491\pi$
$983$	−52.3042	−	16.9947i	−1.66825	−	0.542046i	−0.982575	+	0.185867i	$0.940491\pi$
$984$	64.7131	−	47.0168i	2.06298	−	1.49884i
$985$	−31.1167	−	11.3994i	−0.991461	−	0.363214i
$986$	45.7594	+	33.2461i	1.45728	+	1.05877i
$987$	−13.2496	−	18.2365i	−0.421740	−	0.580475i
$988$	24.4202	+	33.6115i	0.776910	+	1.06932i
$989$	16.6503	+	12.0971i	0.529448	+	0.384666i
$990$	−11.2589	+	3.20295i	−0.357831	+	0.101796i
$991$	13.4087	−	9.74196i	0.425940	−	0.309464i	−0.354083	−	0.935214i	$-0.615207\pi$
$991$	13.4087	−	9.74196i	0.425940	−	0.309464i	0.780023	+	0.625750i	$0.215207\pi$
$992$	−18.8801	−	6.13450i	−0.599442	−	0.194771i
$993$		−	66.0972i		−	2.09753i
$994$	19.5791	−	60.2582i	0.621011	−	1.91128i
$995$	14.8415	+	11.6456i	0.470507	+	0.369189i
$996$	−23.2463	−	71.5448i	−0.736587	−	2.26698i
$997$	16.4127	−	5.33280i	0.519795	−	0.168892i	−0.0373574	−	0.999302i	$-0.511894\pi$
$997$	16.4127	−	5.33280i	0.519795	−	0.168892i	0.557152	+	0.830410i	$0.311894\pi$
$998$	−61.3619	+	84.4574i	−1.94238	+	2.67345i
$999$	1.22166			0.0386515

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.y.b.34.13	✓	56
25.8	odd	20		6875.2.a.n.1.49		56
25.14	even	10	inner	275.2.y.b.89.13	yes	56
25.17	odd	20		6875.2.a.n.1.8		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.y.b.34.13	✓	56	1.1	even	1	trivial
275.2.y.b.89.13	yes	56	25.14	even	10	inner
6875.2.a.n.1.8		56	25.17	odd	20
6875.2.a.n.1.49		56	25.8	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40881 - 1.93906i) q^{2} +(2.16543 - 0.703590i) q^{3} +(-1.15717 - 3.56140i) q^{4} +(-1.75916 - 1.38035i) q^{5} +(1.68637 - 5.19011i) q^{6} +4.20978i q^{7} +(-3.97699 - 1.29220i) q^{8} +(1.76699 - 1.28379i) q^{9} +(-5.15489 + 1.46647i) q^{10} +(0.809017 + 0.587785i) q^{11} +(-5.01153 - 6.89778i) q^{12} +(2.31689 + 3.18892i) q^{13} +(8.16301 + 5.93077i) q^{14} +(-4.78053 - 1.75131i) q^{15} +(-2.04945 + 1.48901i) q^{16} +(-6.53165 - 2.12226i) q^{17} -5.23491i q^{18} +(-0.869785 + 2.67692i) q^{19} +(-2.88032 + 7.86237i) q^{20} +(2.96196 + 9.11598i) q^{21} +(2.27950 - 0.740654i) q^{22} +(3.37458 - 4.64471i) q^{23} -9.52107 q^{24} +(1.18929 + 4.85650i) q^{25} +9.44754 q^{26} +(-1.09190 + 1.50287i) q^{27} +(14.9927 - 4.87143i) q^{28} +(-1.06183 - 3.26798i) q^{29} +(-10.1307 + 6.80246i) q^{30} +(2.67697 - 8.23887i) q^{31} -2.29158i q^{32} +(2.16543 + 0.703590i) q^{33} +(-13.3170 + 9.67538i) q^{34} +(5.81096 - 7.40568i) q^{35} +(-6.61681 - 4.80739i) q^{36} +(-0.386548 - 0.532038i) q^{37} +(3.96535 + 5.45783i) q^{38} +(7.26075 + 5.27524i) q^{39} +(5.21247 + 7.76281i) q^{40} +(-6.79684 + 4.93819i) q^{41} +(21.8492 + 7.09925i) q^{42} +3.58478i q^{43} +(1.15717 - 3.56140i) q^{44} +(-4.88050 - 0.180660i) q^{45} +(-4.25222 - 13.0870i) q^{46} +(-2.23663 + 0.726724i) q^{47} +(-3.39028 + 4.66632i) q^{48} -10.7223 q^{49} +(11.0925 + 4.53577i) q^{50} -15.6370 q^{51} +(8.67599 - 11.9415i) q^{52} +(-4.85542 + 1.57762i) q^{53} +(1.37588 + 4.23451i) q^{54} +(-0.611843 - 2.15073i) q^{55} +(5.43989 - 16.7423i) q^{56} +6.40866i q^{57} +(-7.83271 - 2.54500i) q^{58} +(-1.22105 + 0.887145i) q^{59} +(-0.705240 + 19.0520i) q^{60} +(3.15748 + 2.29404i) q^{61} +(-12.2043 - 16.7978i) q^{62} +(5.40449 + 7.43865i) q^{63} +(-8.54241 - 6.20642i) q^{64} +(0.326040 - 8.80793i) q^{65} +(4.41497 - 3.20767i) q^{66} +(10.3903 + 3.37601i) q^{67} +25.7176i q^{68} +(4.03944 - 12.4321i) q^{69} +(-6.17352 - 21.7010i) q^{70} +(-1.94044 - 5.97206i) q^{71} +(-8.68622 + 2.82232i) q^{72} +(4.96806 - 6.83795i) q^{73} -1.57622 q^{74} +(5.99231 + 9.67963i) q^{75} +10.5401 q^{76} +(-2.47445 + 3.40579i) q^{77} +(20.4580 - 6.64720i) q^{78} +(1.64748 + 5.07042i) q^{79} +(5.66066 + 0.209539i) q^{80} +(-3.33182 + 10.2543i) q^{81} +20.1364i q^{82} +(8.39124 + 2.72648i) q^{83} +(29.0382 - 21.0975i) q^{84} +(8.56076 + 12.7493i) q^{85} +(6.95109 + 5.05026i) q^{86} +(-4.59864 - 6.32948i) q^{87} +(-2.45791 - 3.38303i) q^{88} +(0.324186 + 0.235535i) q^{89} +(-7.22599 + 9.20905i) q^{90} +(-13.4247 + 9.75359i) q^{91} +(-20.4466 - 6.64351i) q^{92} -19.7242i q^{93} +(-1.74182 + 5.36076i) q^{94} +(5.22517 - 3.50853i) q^{95} +(-1.61234 - 4.96226i) q^{96} +(-5.01315 + 1.62887i) q^{97} +(-15.1056 + 20.7911i) q^{98} +2.18412 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 16 q^{4} - 7 q^{5} - 4 q^{6} - 15 q^{8} + 10 q^{9} + 10 q^{10} + 14 q^{11} - 20 q^{12} - 6 q^{14} - 21 q^{15} - 20 q^{16} + 20 q^{17} + 10 q^{19} + 22 q^{20} - 6 q^{21} + 10 q^{23} - 62 q^{24} + 9 q^{25}+ \cdots + 70 q^{99}+O(q^{100}) \) 56 * q + 16 * q^4 - 7 * q^5 - 4 * q^6 - 15 * q^8 + 10 * q^9 + 10 * q^10 + 14 * q^11 - 20 * q^12 - 6 * q^14 - 21 * q^15 - 20 * q^16 + 20 * q^17 + 10 * q^19 + 22 * q^20 - 6 * q^21 + 10 * q^23 - 62 * q^24 + 9 * q^25 - 4 * q^26 + 18 * q^29 - 129 * q^30 - 16 * q^34 + 42 * q^35 - 26 * q^36 - 65 * q^37 - 20 * q^38 + 20 * q^39 - 28 * q^40 - 10 * q^41 + 60 * q^42 - 16 * q^44 - 18 * q^45 + 6 * q^46 - 25 * q^47 + 15 * q^48 - 104 * q^49 + 98 * q^50 + 54 * q^51 + 90 * q^52 + 5 * q^53 + 55 * q^54 - 3 * q^55 + 10 * q^56 - 10 * q^58 + 34 * q^59 + 133 * q^60 - 20 * q^61 - 10 * q^62 + 20 * q^63 + 25 * q^64 - 10 * q^65 + 4 * q^66 - 15 * q^67 - 2 * q^69 - 4 * q^70 - 13 * q^71 - 5 * q^72 - 70 * q^73 - 30 * q^74 - 80 * q^75 + 140 * q^76 - 65 * q^78 + 15 * q^79 - 131 * q^80 - 99 * q^81 + 60 * q^83 + 76 * q^84 + 43 * q^85 + 43 * q^86 - 175 * q^87 + 30 * q^88 + 27 * q^89 + 73 * q^90 - 10 * q^91 - 80 * q^92 - 17 * q^94 + 18 * q^95 - 148 * q^96 - 15 * q^97 - 80 * q^98 + 70 * q^99

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