LMFDB - Embedded newform 56.4.p.a.37.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,4,Mod(37,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("56.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	56.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.30410696032$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.8
Character	$\chi$	$=$	56.37
Dual form			56.4.p.a.53.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.48377 - 2.40799i) q^{2} +(-2.65541 + 1.53310i) q^{3} +(-3.59684 + 7.14582i) q^{4} +(7.57927 + 4.37589i) q^{5} +(7.63171 + 4.11942i) q^{6} +(17.7736 - 5.20552i) q^{7} +(22.5440 - 1.94162i) q^{8} +(-8.79921 + 15.2407i) q^{9} +(-0.708800 - 24.7436i) q^{10} +(46.4189 - 26.8000i) q^{11} +(-1.40419 - 24.4894i) q^{12} +32.2514i q^{13} +(-38.9069 - 35.0750i) q^{14} -26.8347 q^{15} +(-38.1255 - 51.4047i) q^{16} +(31.9026 + 55.2570i) q^{17} +(49.7554 - 1.42528i) q^{18} +(74.9753 + 43.2870i) q^{19} +(-58.5307 + 38.4207i) q^{20} +(-39.2157 + 41.0716i) q^{21} +(-133.409 - 72.0112i) q^{22} +(-64.1008 + 111.026i) q^{23} +(-56.8867 + 39.7179i) q^{24} +(-24.2031 - 41.9211i) q^{25} +(77.6611 - 47.8538i) q^{26} -136.748i q^{27} +(-26.7312 + 145.731i) q^{28} +82.8256i q^{29} +(39.8166 + 64.6178i) q^{30} +(-118.872 - 205.892i) q^{31} +(-67.2125 + 168.079i) q^{32} +(-82.1740 + 142.330i) q^{33} +(85.7220 - 158.810i) q^{34} +(157.490 + 38.3215i) q^{35} +(-77.2578 - 117.696i) q^{36} +(-183.998 - 106.231i) q^{37} +(-7.01157 - 244.768i) q^{38} +(-49.4447 - 85.6407i) q^{39} +(179.363 + 83.9339i) q^{40} +348.562 q^{41} +(157.087 + 33.4902i) q^{42} -221.770i q^{43} +(24.5464 + 428.096i) q^{44} +(-133.383 + 77.0088i) q^{45} +(362.460 - 10.3829i) q^{46} +(123.164 - 213.326i) q^{47} +(180.047 + 78.0503i) q^{48} +(288.805 - 185.042i) q^{49} +(-65.0336 + 120.482i) q^{50} +(-169.429 - 97.8198i) q^{51} +(-230.463 - 116.003i) q^{52} +(-403.213 + 232.795i) q^{53} +(-329.287 + 202.902i) q^{54} +469.095 q^{55} +(390.581 - 151.863i) q^{56} -265.453 q^{57} +(199.443 - 122.894i) q^{58} +(-163.759 + 94.5465i) q^{59} +(96.5202 - 191.756i) q^{60} +(162.805 + 93.9955i) q^{61} +(-319.407 + 591.739i) q^{62} +(-77.0584 + 316.687i) q^{63} +(504.460 - 87.5435i) q^{64} +(-141.129 + 244.442i) q^{65} +(464.656 - 13.3104i) q^{66} +(-155.578 + 89.8230i) q^{67} +(-509.605 + 29.2200i) q^{68} -393.092i q^{69} +(-141.402 - 436.095i) q^{70} -394.379 q^{71} +(-168.777 + 360.670i) q^{72} +(-428.204 - 741.671i) q^{73} +(17.2072 + 600.688i) q^{74} +(128.538 + 74.2116i) q^{75} +(-578.996 + 380.064i) q^{76} +(685.525 - 717.967i) q^{77} +(-132.857 + 246.134i) q^{78} +(-44.9579 + 77.8694i) q^{79} +(-64.0218 - 556.443i) q^{80} +(-27.9308 - 48.3776i) q^{81} +(-517.186 - 839.334i) q^{82} -199.293i q^{83} +(-152.437 - 427.956i) q^{84} +558.410i q^{85} +(-534.021 + 329.057i) q^{86} +(-126.980 - 219.936i) q^{87} +(994.430 - 694.305i) q^{88} +(-508.742 + 881.168i) q^{89} +(383.347 + 206.922i) q^{90} +(167.886 + 573.225i) q^{91} +(-562.810 - 857.395i) q^{92} +(631.306 + 364.485i) q^{93} +(-696.432 + 19.9498i) q^{94} +(378.839 + 656.168i) q^{95} +(-79.2049 - 549.361i) q^{96} +196.625 q^{97} +(-874.101 - 420.879i) q^{98} +943.274i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{4} - 20 q^{6} - 4 q^{7} - 12 q^{8} + 160 q^{9} - 14 q^{10} - 110 q^{12} + 102 q^{14} - 116 q^{15} - 104 q^{16} - 2 q^{17} - 38 q^{18} + 256 q^{20} - 360 q^{22} + 162 q^{23} + 186 q^{24} + 348 q^{25}+ \cdots - 2670 q^{98}+O(q^{100}) $ 44 * q + 4 * q^4 - 20 * q^6 - 4 * q^7 - 12 * q^8 + 160 * q^9 - 14 * q^10 - 110 * q^12 + 102 * q^14 - 116 * q^15 - 104 * q^16 - 2 * q^17 - 38 * q^18 + 256 * q^20 - 360 * q^22 + 162 * q^23 + 186 * q^24 + 348 * q^25 - 302 * q^26 - 642 * q^28 - 396 * q^30 - 374 * q^31 - 140 * q^32 - 110 * q^33 - 148 * q^34 + 1440 * q^36 + 52 * q^38 + 52 * q^39 + 658 * q^40 - 8 * q^41 - 1710 * q^42 + 374 * q^44 - 486 * q^46 - 738 * q^47 + 936 * q^48 + 356 * q^49 + 2328 * q^50 + 96 * q^52 + 944 * q^54 - 2268 * q^55 + 1848 * q^56 - 452 * q^57 + 918 * q^58 + 410 * q^60 + 1416 * q^62 + 668 * q^63 - 2984 * q^64 + 248 * q^65 + 868 * q^66 - 64 * q^68 + 3422 * q^70 + 1248 * q^71 - 2172 * q^72 - 218 * q^73 - 176 * q^74 - 3028 * q^76 - 3716 * q^78 + 298 * q^79 - 2540 * q^80 - 1050 * q^81 - 146 * q^82 - 4844 * q^84 - 2412 * q^86 + 2140 * q^87 + 1626 * q^88 + 422 * q^89 - 4916 * q^90 + 1652 * q^92 - 2676 * q^94 - 2434 * q^95 - 400 * q^96 + 1672 * q^97 - 2670 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$29$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−1.48377	−	2.40799i	−0.524593	−	0.851353i
$2$	−1.48377	−	2.40799i	−0.524593	−	0.851353i
$3$	−2.65541	+	1.53310i	−0.511033	+	0.295045i	−0.733258	−	0.679950i	$-0.762001\pi$
$3$	−2.65541	+	1.53310i	−0.511033	+	0.295045i	0.222225	+	0.974995i	$0.428668\pi$
$4$	−3.59684	+	7.14582i	−0.449605	+	0.893228i
$5$	7.57927	+	4.37589i	0.677910	+	0.391392i	0.799067	−	0.601242i	$-0.205327\pi$
$5$	7.57927	+	4.37589i	0.677910	+	0.391392i	−0.121157	+	0.992633i	$0.538660\pi$
$6$	7.63171	+	4.11942i	0.519272	+	0.280291i
$7$	17.7736	−	5.20552i	0.959687	−	0.281072i
$7$	17.7736	−	5.20552i	0.959687	−	0.281072i
$8$	22.5440	−	1.94162i	0.996312	−	0.0858081i
$9$	−8.79921	+	15.2407i	−0.325897	+	0.564470i
$10$	−0.708800	−	24.7436i	−0.0224142	−	0.782462i
$11$	46.4189	−	26.8000i	1.27235	−	0.734590i	0.296918	−	0.954903i	$-0.404041\pi$
$11$	46.4189	−	26.8000i	1.27235	−	0.734590i	0.975429	+	0.220313i	$0.0707079\pi$
$12$	−1.40419	−	24.4894i	−0.0337795	−	0.589123i
$13$			32.2514i			0.688072i	0.938956	+	0.344036i	$0.111794\pi$
$13$			32.2514i			0.688072i	−0.938956	+	0.344036i	$0.888206\pi$
$14$	−38.9069	−	35.0750i	−0.742736	−	0.669584i
$15$	−26.8347			−0.461913
$16$	−38.1255	−	51.4047i	−0.595711	−	0.803199i
$17$	31.9026	+	55.2570i	0.455149	+	0.788340i	0.998697	−	0.0510376i	$-0.0162528\pi$
$17$	31.9026	+	55.2570i	0.455149	+	0.788340i	−0.543548	+	0.839378i	$0.682920\pi$
$18$	49.7554	−	1.42528i	0.651526	−	0.0186635i
$19$	74.9753	+	43.2870i	0.905291	+	0.522670i	0.878913	−	0.476982i	$-0.158269\pi$
$19$	74.9753	+	43.2870i	0.905291	+	0.522670i	0.0263778	+	0.999652i	$0.491603\pi$
$20$	−58.5307	+	38.4207i	−0.654394	+	0.429557i
$21$	−39.2157	+	41.0716i	−0.407503	+	0.426788i
$22$	−133.409	−	72.0112i	−1.29286	−	0.697856i
$23$	−64.1008	+	111.026i	−0.581128	+	1.00654i	0.414218	+	0.910178i	$0.364055\pi$
$23$	−64.1008	+	111.026i	−0.581128	+	1.00654i	−0.995346	+	0.0963651i	$0.969278\pi$
$24$	−56.8867	+	39.7179i	−0.483831	+	0.337808i
$25$	−24.2031	−	41.9211i	−0.193625	−	0.335368i
$26$	77.6611	−	47.8538i	0.585792	−	0.360958i
$27$		−	136.748i		−	0.974707i
$28$	−26.7312	+	145.731i	−0.180419	+	0.983590i
$29$			82.8256i			0.530356i	0.964199	+	0.265178i	$0.0854307\pi$
$29$			82.8256i			0.530356i	−0.964199	+	0.265178i	$0.914569\pi$
$30$	39.8166	+	64.6178i	0.242316	+	0.393251i
$31$	−118.872	−	205.892i	−0.688710	−	1.19288i	−0.972255	−	0.233922i	$-0.924844\pi$
$31$	−118.872	−	205.892i	−0.688710	−	1.19288i	0.283546	−	0.958959i	$-0.408489\pi$
$32$	−67.2125	+	168.079i	−0.371300	+	0.928513i
$33$	−82.1740	+	142.330i	−0.433474	+	0.750800i
$34$	85.7220	−	158.810i	0.432389	−	0.801050i
$35$	157.490	+	38.3215i	0.760591	+	0.185072i
$36$	−77.2578	−	117.696i	−0.357675	−	0.544888i
$37$	−183.998	−	106.231i	−0.817542	−	0.472008i	0.0320263	−	0.999487i	$-0.489804\pi$
$37$	−183.998	−	106.231i	−0.817542	−	0.472008i	−0.849568	+	0.527479i	$0.823137\pi$
$38$	−7.01157	−	244.768i	−0.0299323	−	1.04491i
$39$	−49.4447	−	85.6407i	−0.203012	−	0.351628i
$40$	179.363	+	83.9339i	0.708995	+	0.331778i
$41$	348.562			1.32771			0.663856	−	0.747860i	$-0.268919\pi$
$41$	348.562			1.32771			0.663856	+	0.747860i	$0.268919\pi$
$42$	157.087	+	33.4902i	0.577121	+	0.123039i
$43$		−	221.770i		−	0.786504i	−0.919431	−	0.393252i	$-0.871350\pi$
$43$		−	221.770i		−	0.786504i	0.919431	−	0.393252i	$-0.128650\pi$
$44$	24.5464	+	428.096i	0.0841025	+	1.46677i
$45$	−133.383	+	77.0088i	−0.441857	+	0.255106i
$46$	362.460	−	10.3829i	1.16178	−	0.0332800i
$47$	123.164	−	213.326i	0.382239	−	0.662058i	−0.609143	−	0.793061i	$-0.708486\pi$
$47$	123.164	−	213.326i	0.382239	−	0.662058i	0.991382	+	0.131003i	$0.0418197\pi$
$48$	180.047	+	78.0503i	0.541408	+	0.234700i
$49$	288.805	−	185.042i	0.841997	−	0.539482i
$50$	−65.0336	+	120.482i	−0.183943	+	0.340775i
$51$	−169.429	−	97.8198i	−0.465192	−	0.268579i
$52$	−230.463	−	116.003i	−0.614605	−	0.309361i
$53$	−403.213	+	232.795i	−1.04501	+	0.603338i	−0.921249	−	0.388974i	$-0.872829\pi$
$53$	−403.213	+	232.795i	−1.04501	+	0.603338i	−0.123763	+	0.992312i	$0.539496\pi$
$54$	−329.287	+	202.902i	−0.829820	+	0.511324i
$55$	469.095			1.15005
$56$	390.581	−	151.863i	0.932029	−	0.362384i
$57$	−265.453			−0.616845
$58$	199.443	−	122.894i	0.451520	−	0.278221i
$59$	−163.759	+	94.5465i	−0.361350	+	0.208626i	−0.669673	−	0.742656i	$-0.733566\pi$
$59$	−163.759	+	94.5465i	−0.361350	+	0.208626i	0.308323	+	0.951282i	$0.400232\pi$
$60$	96.5202	−	191.756i	0.207678	−	0.412593i
$61$	162.805	+	93.9955i	0.341722	+	0.197293i	0.661033	−	0.750357i	$-0.270118\pi$
$61$	162.805	+	93.9955i	0.341722	+	0.197293i	−0.319311	+	0.947650i	$0.603452\pi$
$62$	−319.407	+	591.739i	−0.654270	+	1.21211i
$63$	−77.0584	+	316.687i	−0.154102	+	0.633314i
$64$	504.460	−	87.5435i	0.985274	−	0.170983i
$65$	−141.129	+	244.442i	−0.269306	+	0.466451i
$66$	464.656	−	13.3104i	0.866593	−	0.0248242i
$67$	−155.578	+	89.8230i	−0.283685	+	0.163786i	−0.635090	−	0.772438i	$-0.719037\pi$
$67$	−155.578	+	89.8230i	−0.283685	+	0.163786i	0.351406	+	0.936223i	$0.385704\pi$
$68$	−509.605	+	29.2200i	−0.908804	+	0.0521095i
$69$		−	393.092i		−	0.685836i
$70$	−141.402	−	436.095i	−0.241439	−	0.744619i
$71$	−394.379			−0.659214			−0.329607	−	0.944118i	$-0.606916\pi$
$71$	−394.379			−0.659214			−0.329607	+	0.944118i	$0.606916\pi$
$72$	−168.777	+	360.670i	−0.276259	+	0.590352i
$73$	−428.204	−	741.671i	−0.686541	−	1.18912i	−0.972950	−	0.231016i	$-0.925795\pi$
$73$	−428.204	−	741.671i	−0.686541	−	1.18912i	0.286409	−	0.958107i	$-0.407538\pi$
$74$	17.2072	+	600.688i	0.0270310	+	0.943629i
$75$	128.538	+	74.2116i	0.197898	+	0.114256i
$76$	−578.996	+	380.064i	−0.873886	+	0.573636i
$77$	685.525	−	717.967i	1.01458	−	1.06260i
$78$	−132.857	+	246.134i	−0.192861	+	0.357297i
$79$	−44.9579	+	77.8694i	−0.0640273	+	0.110899i	−0.896262	−	0.443525i	$-0.853728\pi$
$79$	−44.9579	+	77.8694i	−0.0640273	+	0.110899i	0.832235	+	0.554423i	$0.187061\pi$
$80$	−64.0218	−	556.443i	−0.0894732	−	0.777653i
$81$	−27.9308	−	48.3776i	−0.0383139	−	0.0663616i
$82$	−517.186	−	839.334i	−0.696508	−	1.13035i
$83$		−	199.293i		−	0.263557i	−0.991279	−	0.131778i	$-0.957931\pi$
$83$		−	199.293i		−	0.263557i	0.991279	−	0.131778i	$-0.0420688\pi$
$84$	−152.437	−	427.956i	−0.198003	−	0.555879i
$85$			558.410i			0.712565i
$86$	−534.021	+	329.057i	−0.669593	+	0.412594i
$87$	−126.980	−	219.936i	−0.156479	−	0.271030i
$88$	994.430	−	694.305i	1.20462	−	0.841058i
$89$	−508.742	+	881.168i	−0.605917	+	1.04948i	0.385989	+	0.922503i	$0.373860\pi$
$89$	−508.742	+	881.168i	−0.605917	+	1.04948i	−0.991906	+	0.126975i	$0.959473\pi$
$90$	383.347	+	206.922i	0.448981	+	0.242350i
$91$	167.886	+	573.225i	0.193398	+	0.660334i
$92$	−562.810	−	857.395i	−0.637794	−	0.971626i
$93$	631.306	+	364.485i	0.703907	+	0.406401i
$94$	−696.432	+	19.9498i	−0.764165	+	0.0218901i
$95$	378.839	+	656.168i	0.409137	+	0.708647i
$96$	−79.2049	−	549.361i	−0.0842064	−	0.584051i
$97$	196.625			0.205816			0.102908	−	0.994691i	$-0.467185\pi$
$97$	196.625			0.205816			0.102908	+	0.994691i	$0.467185\pi$
$98$	−874.101	−	420.879i	−0.900995	−	0.433829i
$99$			943.274i			0.957602i
$100$	386.615	−	22.1680i	0.386615	−	0.0221680i
$101$	1741.62	−	1005.52i	1.71582	−	0.990627i	0.789609	−	0.613610i	$-0.210283\pi$
$101$	1741.62	−	1005.52i	1.71582	−	0.990627i	0.926207	−	0.377017i	$-0.123050\pi$
$102$	15.8447	+	553.126i	0.0153810	+	0.536937i
$103$	−298.306	+	516.681i	−0.285369	+	0.494273i	−0.972698	−	0.232073i	$-0.925449\pi$
$103$	−298.306	+	516.681i	−0.285369	+	0.494273i	0.687330	+	0.726345i	$0.258783\pi$
$104$	62.6199	+	727.075i	0.0590422	+	0.685534i
$105$	−476.951	+	139.689i	−0.443292	+	0.129831i
$106$	1158.85	+	625.519i	1.06186	+	0.573167i
$107$	−355.200	−	205.075i	−0.320920	−	0.185283i	0.330882	−	0.943672i	$-0.392654\pi$
$107$	−355.200	−	205.075i	−0.320920	−	0.185283i	−0.651803	+	0.758389i	$0.725987\pi$
$108$	977.174	+	491.859i	0.870636	+	0.438233i
$109$	−755.806	+	436.365i	−0.664156	+	0.383451i	−0.793859	−	0.608102i	$-0.791931\pi$
$109$	−755.806	+	436.365i	−0.664156	+	0.383451i	0.129702	+	0.991553i	$0.458598\pi$
$110$	−696.030	−	1129.58i	−0.603308	−	0.979099i
$111$	651.452			0.557055
$112$	−945.218	−	715.186i	−0.797452	−	0.603382i
$113$	1088.92			0.906521			0.453261	−	0.891378i	$-0.350261\pi$
$113$	1088.92			0.906521			0.453261	+	0.891378i	$0.350261\pi$
$114$	393.872	+	639.209i	0.323592	+	0.525153i
$115$	−971.674	+	560.996i	−0.787905	+	0.454897i
$116$	−591.857	−	297.910i	−0.473729	−	0.238451i
$117$	−491.534	−	283.787i	−0.388396	−	0.224240i
$118$	470.649	+	254.046i	0.367176	+	0.198193i
$119$	854.668	+	816.048i	0.658380	+	0.628630i
$120$	−604.961	+	52.1027i	−0.460209	+	0.0396359i
$121$	770.975	−	1335.37i	0.579245	−	1.00328i
$122$	−15.2252	−	531.501i	−0.0112986	−	0.394425i
$123$	−925.573	+	534.380i	−0.678505	+	0.391735i
$124$	1898.83	−	108.876i	1.37516	−	0.0788498i
$125$		−	1517.61i		−	1.08592i
$126$	876.916	−	284.335i	0.620015	−	0.201037i
$127$	−1223.26			−0.854699			−0.427349	−	0.904087i	$-0.640553\pi$
$127$	−1223.26			−0.854699			−0.427349	+	0.904087i	$0.640553\pi$
$128$	−959.308	−	1084.84i	−0.662435	−	0.749120i
$129$	339.996	+	588.891i	0.232054	+	0.401930i
$130$	798.017	−	22.8598i	0.538390	−	0.0154226i
$131$	2126.40	+	1227.68i	1.41820	+	0.818798i	0.996141	−	0.0877697i	$-0.0279740\pi$
$131$	2126.40	+	1227.68i	1.41820	+	0.818798i	0.422060	+	0.906568i	$0.361307\pi$
$132$	−721.495	−	1099.14i	−0.475743	−	0.724755i
$133$	1557.92	+	379.083i	1.01570	+	0.247148i
$134$	447.135	+	241.354i	0.288258	+	0.155595i
$135$	598.393	−	1036.45i	0.381492	−	0.660764i
$136$	826.499	+	1183.77i	0.521116	+	0.746377i
$137$	−1219.84	−	2112.83i	−0.760716	−	1.31760i	−0.942482	−	0.334257i	$-0.891515\pi$
$137$	−1219.84	−	2112.83i	−0.760716	−	1.31760i	0.181766	−	0.983342i	$-0.441819\pi$
$138$	−946.561	+	583.258i	−0.583889	+	0.359784i
$139$		−	2783.96i		−	1.69879i	−0.527756	−	0.849396i	$-0.676967\pi$
$139$		−	2783.96i		−	1.69879i	0.527756	−	0.849396i	$-0.323033\pi$
$140$	−840.305	+	987.559i	−0.507277	+	0.596171i
$141$			755.288i			0.451112i
$142$	585.169	+	949.661i	0.345819	+	0.561224i
$143$	864.337	+	1497.07i	0.505451	+	0.875466i
$144$	1118.92	−	128.737i	0.647522	−	0.0745009i
$145$	−362.436	+	627.757i	−0.207577	+	0.359534i
$146$	−1150.58	+	2131.58i	−0.652210	+	1.20829i
$147$	−483.207	+	934.129i	−0.271117	+	0.524120i
$148$	1420.92	−	932.719i	0.789181	−	0.518034i
$149$	−1086.95	−	627.552i	−0.597628	−	0.345041i	0.170480	−	0.985361i	$-0.445468\pi$
$149$	−1086.95	−	627.552i	−0.597628	−	0.345041i	−0.768108	+	0.640320i	$0.778802\pi$
$150$	−12.0207	−	419.632i	−0.00654323	−	0.228419i
$151$	−1374.36	−	2380.46i	−0.740689	−	1.28291i	−0.952182	−	0.305531i	$-0.901166\pi$
$151$	−1374.36	−	2380.46i	−0.740689	−	1.28291i	0.211493	−	0.977379i	$-0.432167\pi$
$152$	1774.29	+	830.288i	0.946801	+	0.443061i
$153$	−1122.87			−0.593325
$154$	−2746.02	−	585.438i	−1.43689	−	0.306337i
$155$		−	2080.68i		−	1.07822i
$156$	789.817	−	45.2870i	0.405359	−	0.0232427i
$157$	−2173.05	+	1254.61i	−1.10464	+	0.637764i	−0.937436	−	0.348158i	$-0.886807\pi$
$157$	−2173.05	+	1254.61i	−1.10464	+	0.637764i	−0.167204	+	0.985922i	$0.553474\pi$
$158$	254.216	−	7.28221i	0.128002	−	0.00366672i
$159$	713.797	−	1236.33i	0.356024	−	0.616651i
$160$	−1244.92	+	979.799i	−0.615121	+	0.484125i
$161$	−561.357	+	2307.01i	−0.274790	+	1.12930i
$162$	−75.0499	+	139.039i	−0.0363980	+	0.0674315i
$163$	−2259.90	−	1304.75i	−1.08594	−	0.626971i	−0.153451	−	0.988156i	$-0.549039\pi$
$163$	−2259.90	−	1304.75i	−1.08594	−	0.626971i	−0.932494	+	0.361186i	$0.882372\pi$
$164$	−1253.72	+	2490.76i	−0.596946	+	1.18595i
$165$	−1245.64	+	719.169i	−0.587714	+	0.339317i
$166$	−479.895	+	295.705i	−0.224380	+	0.138260i
$167$	−695.155			−0.322112			−0.161056	−	0.986945i	$-0.551490\pi$
$167$	−695.155			−0.322112			−0.161056	+	0.986945i	$0.551490\pi$
$168$	−804.331	+	1002.06i	−0.369378	+	0.460181i
$169$	1156.85			0.526557
$170$	1344.65	−	828.553i	0.606645	−	0.373807i
$171$	−1319.45	+	761.783i	−0.590062	+	0.340673i
$172$	1584.73	+	797.672i	0.702527	+	0.353616i
$173$	−1543.24	−	890.989i	−0.678209	−	0.391564i	0.120971	−	0.992656i	$-0.461399\pi$
$173$	−1543.24	−	890.989i	−0.678209	−	0.391564i	−0.799180	+	0.601092i	$0.794733\pi$
$174$	−341.194	+	632.101i	−0.148654	+	0.275399i
$175$	−648.399	−	619.100i	−0.280082	−	0.267426i
$176$	−3147.39	−	1364.39i	−1.34797	−	0.584345i
$177$	289.899	−	502.119i	0.123108	−	0.213229i
$178$	2876.70	−	82.4053i	1.21134	−	0.0346997i
$179$	2087.67	−	1205.32i	0.871730	−	0.503293i	0.00380701	−	0.999993i	$-0.498788\pi$
$179$	2087.67	−	1205.32i	0.871730	−	0.503293i	0.867923	+	0.496699i	$0.165455\pi$
$180$	−70.5333	−	1230.12i	−0.0292069	−	0.509376i
$181$			2234.05i			0.917435i	0.888582	+	0.458717i	$0.151691\pi$
$181$			2234.05i			0.917435i	−0.888582	+	0.458717i	$0.848309\pi$
$182$	1131.22	−	1254.80i	0.460722	−	0.511056i
$183$	−576.418			−0.232842
$184$	−1229.52	+	2627.42i	−0.492615	+	1.05270i
$185$	−929.712	−	1610.31i	−0.369480	−	0.639958i
$186$	−59.0387	−	2060.99i	−0.0232738	−	0.812469i
$187$	2961.77	+	1709.98i	1.15821	+	0.668695i
$188$	1081.39	+	1647.40i	0.419512	+	0.639091i
$189$	−711.843	−	2430.50i	−0.273963	−	0.935414i
$190$	1017.94	−	1885.84i	0.388678	−	0.720071i
$191$	364.827	−	631.899i	0.138209	−	0.239385i	−0.788610	−	0.614894i	$-0.789199\pi$
$191$	364.827	−	631.899i	0.138209	−	0.239385i	0.926819	+	0.375509i	$0.122532\pi$
$192$	−1205.33	+	1005.85i	−0.453060	+	0.378079i
$193$	2388.81	+	4137.54i	0.890934	+	1.54314i	0.838757	+	0.544506i	$0.183283\pi$
$193$	2388.81	+	4137.54i	0.890934	+	1.54314i	0.0521772	+	0.998638i	$0.483384\pi$
$194$	−291.746	−	473.470i	−0.107970	−	0.175223i
$195$		−	865.458i		−	0.317829i
$196$	283.493	+	2729.32i	0.103314	+	0.994649i
$197$			2330.88i			0.842987i	0.906832	+	0.421493i	$0.138494\pi$
$197$			2330.88i			0.842987i	−0.906832	+	0.421493i	$0.861506\pi$
$198$	2271.39	−	1399.60i	0.815257	−	0.502351i
$199$	1720.27	+	2979.60i	0.612799	+	1.06140i	0.990766	+	0.135580i	$0.0432898\pi$
$199$	1720.27	+	2979.60i	0.612799	+	1.06140i	−0.377967	+	0.925819i	$0.623377\pi$
$200$	−627.029	−	898.073i	−0.221688	−	0.317517i
$201$	275.415	−	477.033i	0.0966483	−	0.167400i
$202$	−5005.45	−	2701.83i	−1.74348	−	0.941090i
$203$	431.150	+	1472.11i	0.149068	+	0.508976i
$204$	1308.41	−	858.867i	0.449055	−	0.294768i
$205$	2641.84	+	1525.27i	0.900070	+	0.519656i
$206$	1686.78	−	48.3191i	0.570503	−	0.0163425i
$207$	−1128.07	−	1953.88i	−0.378775	−	0.656058i
$208$	1657.88	−	1229.60i	0.552659	−	0.409892i
$209$	4640.36			1.53579
$210$	1044.06	+	941.227i	0.343079	+	0.309290i
$211$		−	4280.43i		−	1.39657i	−0.715818	−	0.698287i	$-0.753946\pi$
$211$		−	4280.43i		−	1.39657i	0.715818	−	0.698287i	$-0.246054\pi$
$212$	−213.220	−	3718.62i	−0.0690756	−	1.20470i
$213$	1047.24	−	604.623i	0.336880	−	0.194498i
$214$	33.2177	+	1159.60i	0.0106108	+	0.370415i
$215$	970.443	−	1680.86i	0.307831	−	0.533179i
$216$	−265.512	−	3082.83i	−0.0836378	−	0.971112i
$217$	−3184.56	−	3040.66i	−0.996231	−	0.951215i
$218$	2172.21	+	1172.51i	0.674864	+	0.364276i
$219$	2274.11	+	1312.96i	0.701690	+	0.405121i
$220$	−1687.26	+	3352.07i	−0.517068	+	1.02726i
$221$	−1782.12	+	1028.91i	−0.542435	+	0.313175i
$222$	−966.606	−	1568.69i	−0.292227	−	0.474250i
$223$	−3964.54			−1.19052			−0.595258	−	0.803535i	$-0.702950\pi$
$223$	−3964.54			−1.19052			−0.595258	+	0.803535i	$0.702950\pi$
$224$	−319.674	+	3337.25i	−0.0953533	+	0.995443i
$225$	851.874			0.252407
$226$	−1615.71	−	2622.11i	−0.475555	−	0.771770i
$227$	1560.76	−	901.104i	0.456349	−	0.263473i	−0.254159	−	0.967162i	$-0.581799\pi$
$227$	1560.76	−	901.104i	0.456349	−	0.263473i	0.710508	+	0.703689i	$0.248465\pi$
$228$	954.793	−	1896.88i	0.277336	−	0.550983i
$229$	−3326.21	−	1920.39i	−0.959835	−	0.554161i	−0.0637125	−	0.997968i	$-0.520294\pi$
$229$	−3326.21	−	1920.39i	−0.959835	−	0.554161i	−0.896122	+	0.443807i	$0.853627\pi$
$230$	2792.62	+	1507.39i	0.800607	+	0.432150i
$231$	−719.632	+	2957.47i	−0.204971	+	0.842370i
$232$	160.816	+	1867.22i	0.0455089	+	0.528400i
$233$	−282.326	+	489.004i	−0.0793812	+	0.137492i	−0.902983	−	0.429676i	$-0.858628\pi$
$233$	−282.326	+	489.004i	−0.0793812	+	0.137492i	0.823602	+	0.567168i	$0.191961\pi$
$234$	45.9674	+	1604.68i	0.0128418	+	0.448297i
$235$	1866.98	−	1077.90i	0.518248	−	0.299211i
$236$	−86.5964	−	1510.26i	−0.0238854	−	0.416567i
$237$		−	275.700i		−	0.0755638i
$238$	696.904	−	3268.86i	0.189805	−	0.890289i
$239$	1560.15			0.422250			0.211125	−	0.977459i	$-0.432287\pi$
$239$	1560.15			0.422250			0.211125	+	0.977459i	$0.432287\pi$
$240$	1023.09	+	1379.43i	0.275167	+	0.371008i
$241$	2108.53	+	3652.08i	0.563578	+	0.976147i	0.997180	+	0.0750420i	$0.0239091\pi$
$241$	2108.53	+	3652.08i	0.563578	+	0.976147i	−0.433602	+	0.901105i	$0.642758\pi$
$242$	−4359.50	+	124.881i	−1.15801	+	0.0331722i
$243$	3345.86	+	1931.73i	0.883281	+	0.509962i
$244$	−1257.26	+	825.288i	−0.329868	+	0.216531i
$245$	2998.66	−	138.705i	0.781947	−	0.0361695i
$246$	2660.12	+	1435.87i	0.689444	+	0.372146i
$247$	−1396.07	+	2418.06i	−0.359634	+	0.622905i
$248$	−3079.60	−	4410.82i	−0.788529	−	1.12938i
$249$	305.536	+	529.204i	0.0777612	+	0.134686i
$250$	−3654.40	+	2251.79i	−0.924498	+	0.569664i
$251$			6029.33i			1.51621i	0.652134	+	0.758104i	$0.273874\pi$
$251$			6029.33i			1.51621i	−0.652134	+	0.758104i	$0.726126\pi$
$252$	−1985.82	−	1689.72i	−0.496409	−	0.422390i
$253$			6871.59i			1.70756i
$254$	1815.04	+	2945.60i	0.448369	+	0.727651i
$255$	−856.098	−	1482.81i	−0.210239	−	0.364145i
$256$	−1188.89	+	3919.66i	−0.290257	+	0.956949i
$257$	−1537.80	+	2663.55i	−0.373250	+	0.646489i	−0.990064	−	0.140621i	$-0.955090\pi$
$257$	−1537.80	+	2663.55i	−0.373250	+	0.646489i	0.616813	+	0.787110i	$0.288423\pi$
$258$	913.566	−	1692.49i	0.220450	−	0.408409i
$259$	−3823.30	−	930.311i	−0.917252	−	0.223192i
$260$	−1239.12	−	1887.70i	−0.295566	−	0.450270i
$261$	−1262.32	−	728.800i	−0.299370	−	0.172841i
$262$	−198.857	−	6941.94i	−0.0468910	−	1.63693i
$263$	−208.250	−	360.700i	−0.0488260	−	0.0845691i	0.840579	−	0.541688i	$-0.182215\pi$
$263$	−208.250	−	360.700i	−0.0488260	−	0.0845691i	−0.889406	+	0.457119i	$0.848881\pi$
$264$	−1576.18	+	3368.22i	−0.367451	+	0.785226i
$265$	−4074.75			−0.944565
$266$	−1398.77	−	4313.92i	−0.322421	−	0.994374i
$267$		−	3119.81i		−	0.715091i
$268$	−82.2701	−	1434.81i	−0.0187517	−	0.327034i
$269$	6849.24	−	3954.41i	1.55244	−	0.896300i	0.554495	−	0.832187i	$-0.312911\pi$
$269$	6849.24	−	3954.41i	1.55244	−	0.896300i	0.997943	−	0.0641134i	$-0.0204219\pi$
$270$	−3383.63	+	96.9268i	−0.762672	+	0.0218473i
$271$	−100.871	+	174.714i	−0.0226107	+	0.0391629i	−0.877109	−	0.480291i	$-0.840531\pi$
$271$	−100.871	+	174.714i	−0.0226107	+	0.0391629i	0.854499	+	0.519454i	$0.173864\pi$
$272$	1624.17	−	3746.65i	0.362057	−	0.835198i
$273$	−1324.62	−	1264.76i	−0.293661	−	0.280391i
$274$	−3277.70	+	6072.32i	−0.722676	+	1.33884i
$275$	−2246.96	−	1297.29i	−0.492717	−	0.284470i
$276$	2808.96	+	1413.89i	0.612607	+	0.308355i
$277$	2478.67	−	1431.06i	0.537650	−	0.310413i	−0.206476	−	0.978452i	$-0.566199\pi$
$277$	2478.67	−	1431.06i	0.537650	−	0.310413i	0.744126	+	0.668039i	$0.232866\pi$
$278$	−6703.74	+	4130.76i	−1.44627	+	0.891174i
$279$	4183.91			0.897793
$280$	3624.85	+	558.134i	0.773666	+	0.119124i
$281$	−3676.81			−0.780569			−0.390284	−	0.920694i	$-0.627623\pi$
$281$	−3676.81			−0.780569			−0.390284	+	0.920694i	$0.627623\pi$
$282$	1818.73	−	1120.68i	0.384055	−	0.236650i
$283$	−5065.23	+	2924.41i	−1.06395	+	0.614270i	−0.926521	−	0.376243i	$-0.877216\pi$
$283$	−5065.23	+	2924.41i	−1.06395	+	0.614270i	−0.137425	+	0.990512i	$0.543883\pi$
$284$	1418.52	−	2818.16i	0.296386	−	0.588828i
$285$	−2011.94	−	1161.60i	−0.418166	−	0.241428i
$286$	2322.46	−	4302.63i	0.480175	−	0.889580i
$287$	6195.21	−	1814.45i	1.27419	−	0.373182i
$288$	−1970.22	−	2503.33i	−0.403112	−	0.512187i
$289$	420.944	−	729.097i	0.0856797	−	0.148402i
$290$	2049.41	−	58.7068i	0.414984	−	0.0118875i
$291$	−522.118	+	301.445i	−0.105179	+	0.0607252i
$292$	6840.03	−	392.197i	1.37083	−	0.0786014i
$293$			1025.09i			0.204391i	0.994764	+	0.102196i	$0.0325867\pi$
$293$			1025.09i			0.204391i	−0.994764	+	0.102196i	$0.967413\pi$
$294$	2966.34	−	222.478i	0.588438	−	0.0441333i
$295$	−1654.90			−0.326617
$296$	−4354.30	−	2037.62i	−0.855028	−	0.400115i
$297$	−3664.83	−	6347.67i	−0.716010	−	1.24017i
$298$	101.650	+	3548.52i	0.0197598	+	0.689799i
$299$	−3580.74	−	2067.34i	−0.692574	−	0.399858i
$300$	−992.635	+	651.585i	−0.191033	+	0.125398i
$301$	−1154.43	−	3941.67i	−0.221064	−	0.754797i
$302$	−3692.90	+	6841.52i	−0.703650	+	1.30359i
$303$	−3083.13	+	5340.15i	−0.584559	+	1.01249i
$304$	−633.314	−	5504.43i	−0.119484	−	1.03849i
$305$	822.628	+	1424.83i	0.154438	+	0.267494i
$306$	1666.09	+	2703.86i	0.311254	+	0.505130i
$307$		−	2028.66i		−	0.377140i	−0.982060	−	0.188570i	$-0.939615\pi$
$307$		−	2028.66i		−	0.377140i	0.982060	−	0.188570i	$-0.0603852\pi$
$308$	2664.74	+	7481.05i	0.492980	+	1.38400i
$309$		−	1829.33i		−	0.336787i
$310$	−5010.26	+	3087.26i	−0.917947	+	0.565627i
$311$	−1802.47	−	3121.96i	−0.328644	−	0.569229i	0.653599	−	0.756841i	$-0.273258\pi$
$311$	−1802.47	−	3121.96i	−0.328644	−	0.569229i	−0.982243	+	0.187612i	$0.939925\pi$
$312$	−1280.96	−	1834.68i	−0.232436	−	0.332911i
$313$	1447.00	−	2506.27i	0.261307	−	0.452597i	−0.705283	−	0.708926i	$-0.749180\pi$
$313$	1447.00	−	2506.27i	0.261307	−	0.452597i	0.966589	+	0.256330i	$0.0825132\pi$
$314$	6245.41	+	3371.13i	1.12245	+	0.605872i
$315$	−1969.83	+	2063.06i	−0.352341	+	0.369016i
$316$	−394.734	−	601.345i	−0.0702707	−	0.107052i
$317$	1058.34	+	611.032i	0.187515	+	0.108262i	0.590819	−	0.806804i	$-0.298805\pi$
$317$	1058.34	+	611.032i	0.187515	+	0.108262i	−0.403304	+	0.915066i	$0.632138\pi$
$318$	−4036.19	+	115.620i	−0.711755	+	0.0203888i
$319$	2219.72	+	3844.67i	0.389594	+	0.674797i
$320$	4206.52	+	1543.95i	0.734849	+	0.269717i
$321$	1257.60			0.218668
$322$	6388.19	−	2071.34i	1.10559	−	0.358482i
$323$			5523.88i			0.951570i
$324$	446.160	−	25.5822i	0.0765021	−	0.00438652i
$325$	1352.01	−	780.586i	0.230758	−	0.133228i
$326$	211.342	+	7377.78i	0.0359054	+	1.25343i
$327$	1337.98	−	2317.45i	0.226271	−	0.391912i
$328$	7857.96	−	676.773i	1.32282	−	0.113929i
$329$	1078.59	−	4432.70i	0.180744	−	0.742805i
$330$	3580.00	+	1932.40i	0.597189	+	0.322349i
$331$	332.286	+	191.845i	0.0551785	+	0.0318573i	0.527335	−	0.849657i	$-0.323191\pi$
$331$	332.286	+	191.845i	0.0551785	+	0.0318573i	−0.472157	+	0.881514i	$0.656524\pi$
$332$	1424.11	+	716.824i	0.235416	+	0.118497i
$333$	3238.07	−	1869.50i	0.532868	−	0.307652i
$334$	1031.45	+	1673.93i	0.168978	+	0.274231i
$335$	−1572.22			−0.256417
$336$	3606.39	+	449.998i	0.585550	+	0.0730637i
$337$	7826.94			1.26517			0.632583	−	0.774493i	$-0.281995\pi$
$337$	7826.94			1.26517			0.632583	+	0.774493i	$0.281995\pi$
$338$	−1716.50	−	2785.67i	−0.276228	−	0.448286i
$339$	−2891.52	+	1669.42i	−0.463263	+	0.267465i
$340$	−3990.30	−	2008.51i	−0.636483	−	0.320373i
$341$	−11035.8	−	6371.52i	−1.75256	−	1.01184i
$342$	3792.13	+	2046.90i	0.599575	+	0.323637i
$343$	4169.88	−	4792.26i	0.656421	−	0.754395i
$344$	−430.593	−	4999.58i	−0.0674884	−	0.783603i
$345$	1720.13	−	2979.35i	0.268430	−	0.464935i
$346$	144.321	+	5038.13i	0.0224241	+	0.782807i
$347$	584.362	−	337.382i	0.0904040	−	0.0521948i	−0.454116	−	0.890942i	$-0.650045\pi$
$347$	584.362	−	337.382i	0.0904040	−	0.0521948i	0.544520	+	0.838748i	$0.316712\pi$
$348$	2028.35	−	116.303i	0.312445	−	0.0179151i
$349$			7024.54i			1.07741i	0.842496	+	0.538703i	$0.181086\pi$
$349$			7024.54i			1.07741i	−0.842496	+	0.538703i	$0.818914\pi$
$350$	−528.711	+	2479.94i	−0.0807451	+	0.378739i
$351$	4410.31			0.670669
$352$	1384.57	+	9603.32i	0.209653	+	1.45414i
$353$	−1569.65	−	2718.71i	−0.236668	−	0.409921i	0.723088	−	0.690756i	$-0.242722\pi$
$353$	−1569.65	−	2718.71i	−0.236668	−	0.409921i	−0.959756	+	0.280835i	$0.909389\pi$
$354$	−1639.24	+	46.9573i	−0.246115	+	0.00705015i
$355$	−2989.11	−	1725.76i	−0.446888	−	0.258011i
$356$	−4466.80	−	6804.80i	−0.665000	−	1.01307i
$357$	−3520.57	−	856.649i	−0.521929	−	0.126999i
$358$	−6000.01	−	3238.67i	−0.885784	−	0.478126i
$359$	−535.877	+	928.166i	−0.0787814	+	0.136453i	−0.902724	−	0.430219i	$-0.858436\pi$
$359$	−535.877	+	928.166i	−0.0787814	+	0.136453i	0.823943	+	0.566673i	$0.191770\pi$
$360$	−2857.46	+	1995.06i	−0.418337	+	0.292081i
$361$	318.035	+	550.853i	0.0463676	+	0.0803110i
$362$	5379.57	−	3314.82i	0.781061	−	0.481280i
$363$			4727.92i			0.683614i
$364$	−4700.02	−	862.120i	−0.676781	−	0.124141i
$365$		−	7495.09i		−	1.07483i
$366$	855.273	+	1388.01i	0.122147	+	0.198231i
$367$	885.623	+	1533.94i	0.125965	+	0.218178i	0.922110	−	0.386928i	$-0.126464\pi$
$367$	885.623	+	1533.94i	0.125965	+	0.218178i	−0.796145	+	0.605106i	$0.793131\pi$
$368$	8151.13	−	937.831i	1.15464	−	0.132847i
$369$	−3067.07	+	5312.32i	−0.432697	+	0.749453i
$370$	−2498.13	+	4628.07i	−0.351004	+	0.650275i
$371$	−5954.75	+	6236.56i	−0.833302	+	0.872738i
$372$	−4875.25	+	3200.21i	−0.679489	+	0.446030i
$373$	9657.76	+	5575.91i	1.34064	+	0.774021i	0.986902	−	0.161323i	$-0.0515760\pi$
$373$	9657.76	+	5575.91i	1.34064	+	0.774021i	0.353741	+	0.935343i	$0.384909\pi$
$374$	−276.980	−	9669.13i	−0.0382948	−	1.33684i
$375$	2326.65	+	4029.88i	0.320394	+	0.554939i
$376$	2362.40	−	5048.34i	0.324020	−	0.692415i
$377$	−2671.24			−0.364923
$378$	−4796.42	+	5320.43i	−0.652649	+	0.723950i
$379$		−	11982.3i		−	1.62399i	−0.583667	−	0.811993i	$-0.698383\pi$
$379$		−	11982.3i		−	1.62399i	0.583667	−	0.811993i	$-0.301617\pi$
$380$	−6051.48	+	346.983i	−0.816933	+	0.0468418i
$381$	3248.25	−	1875.38i	0.436780	−	0.252175i
$382$	−2062.93	+	59.0941i	−0.276305	+	0.00791497i
$383$	168.027	−	291.031i	0.0224172	−	0.0388277i	−0.854599	−	0.519288i	$-0.826197\pi$
$383$	168.027	−	291.031i	0.0224172	−	0.0388277i	0.877016	+	0.480460i	$0.159530\pi$
$384$	4210.52	+	1409.98i	0.559550	+	0.187377i
$385$	8337.53	−	2441.88i	1.10369	−	0.323246i
$386$	6418.71	−	11891.4i	0.846383	−	1.56802i
$387$	3379.93	+	1951.40i	0.443957	+	0.256319i
$388$	−707.227	+	1405.04i	−0.0925361	+	0.183841i
$389$	3352.87	−	1935.78i	0.437010	−	0.252308i	−0.265318	−	0.964161i	$-0.585477\pi$
$389$	3352.87	−	1935.78i	0.437010	−	0.252308i	0.702329	+	0.711853i	$0.252144\pi$
$390$	−2084.01	+	1284.14i	−0.270585	+	0.166731i
$391$	−8179.93			−1.05800
$392$	6151.53	−	4732.33i	0.792600	−	0.609742i
$393$	−7528.60			−0.966330
$394$	5612.74	−	3458.50i	0.717679	−	0.442225i
$395$	−681.496	+	393.462i	−0.0868096	+	0.0501195i
$396$	−6740.46	−	3392.80i	−0.855356	−	0.430542i
$397$	5876.75	+	3392.94i	0.742936	+	0.428934i	0.823136	−	0.567844i	$-0.192222\pi$
$397$	5876.75	+	3392.94i	0.742936	+	0.428934i	−0.0801996	+	0.996779i	$0.525556\pi$
$398$	4622.36	−	8563.46i	0.582156	−	1.07851i
$399$	−4718.08	+	1381.82i	−0.591978	+	0.173378i
$400$	−1232.18	+	2842.42i	−0.154023	+	0.355302i
$401$	−6141.21	+	10636.9i	−0.764782	+	1.32464i	0.175581	+	0.984465i	$0.443820\pi$
$401$	−6141.21	+	10636.9i	−0.764782	+	1.32464i	−0.940362	+	0.340175i	$0.889514\pi$
$402$	−1557.35	+	44.6114i	−0.193217	+	0.00553486i
$403$	6640.31	−	3833.78i	0.820788	−	0.473882i
$404$	920.972	+	16062.0i	0.113416	+	1.97800i
$405$		−	488.889i		−	0.0599830i
$406$	2905.10	−	3222.49i	0.355118	−	0.393915i
$407$	−11388.0			−1.38693
$408$	−4009.53	−	1876.28i	−0.486523	−	0.227671i
$409$	−1572.28	−	2723.27i	−0.190084	−	0.329234i	0.755194	−	0.655501i	$-0.227543\pi$
$409$	−1572.28	−	2723.27i	−0.190084	−	0.329234i	−0.945278	+	0.326267i	$0.894209\pi$
$410$	−247.061	−	8624.69i	−0.0297597	−	1.03889i
$411$	6478.35	+	3740.28i	0.777502	+	0.448891i
$412$	−2619.15	−	3990.06i	−0.313195	−	0.477127i
$413$	−2418.44	+	2532.89i	−0.288144	+	0.301781i
$414$	−3031.12	+	5615.50i	−0.359834	+	0.666635i
$415$	872.084	−	1510.49i	0.103154	−	0.178668i
$416$	−5420.78	−	2167.70i	−0.638884	−	0.255481i
$417$	4268.08	+	7392.53i	0.501220	+	0.868139i
$418$	−6885.24	−	11173.9i	−0.805665	−	1.30750i
$419$			2133.06i			0.248704i	0.992238	+	0.124352i	$0.0396852\pi$
$419$			2133.06i			0.248704i	−0.992238	+	0.124352i	$0.960315\pi$
$420$	717.325	−	3910.64i	0.0833378	−	0.454333i
$421$			4230.88i			0.489787i	0.969550	+	0.244893i	$0.0787530\pi$
$421$			4230.88i			0.489787i	−0.969550	+	0.244893i	$0.921247\pi$
$422$	−10307.2	+	6351.19i	−1.18898	+	0.732633i
$423$	2167.48	+	3754.19i	0.249141	+	0.431525i
$424$	−8638.02	+	6031.01i	−0.989386	+	0.690783i
$425$	1544.29	−	2674.78i	0.176256	−	0.305285i
$426$	−3009.79	−	1624.61i	−0.342311	−	0.184772i
$427$	3382.93	+	823.158i	0.383400	+	0.0932913i
$428$	2743.02	−	1800.57i	0.309787	−	0.203350i
$429$	−4590.33	−	2650.23i	−0.516604	−	0.298262i
$430$	−5487.41	+	157.191i	−0.615410	+	0.0176289i
$431$	−92.2433	−	159.770i	−0.0103091	−	0.0178558i	0.860825	−	0.508901i	$-0.169948\pi$
$431$	−92.2433	−	159.770i	−0.0103091	−	0.0178558i	−0.871134	+	0.491046i	$0.836615\pi$
$432$	−7029.48	+	5213.57i	−0.782884	+	0.580644i
$433$	−5972.94			−0.662912			−0.331456	−	0.943471i	$-0.607540\pi$
$433$	−5972.94			−0.662912			−0.331456	+	0.943471i	$0.607540\pi$
$434$	−2596.72	+	12180.0i	−0.287204	+	1.34714i
$435$		−	2222.60i		−	0.244978i
$436$	−399.672	−	6970.38i	−0.0439009	−	0.765644i
$437$	−9611.96	+	5549.47i	−1.05218	+	0.607476i
$438$	−212.671	−	7424.17i	−0.0232005	−	0.809910i
$439$	5535.24	−	9587.32i	0.601783	−	1.04232i	−0.390768	−	0.920489i	$-0.627791\pi$
$439$	5535.24	−	9587.32i	0.601783	−	1.04232i	0.992551	−	0.121829i	$-0.0388761\pi$
$440$	10575.3	−	910.802i	1.14581	−	0.0986836i
$441$	278.913	+	6029.81i	0.0301169	+	0.651097i
$442$	5121.85	+	2764.66i	0.551180	+	0.297514i
$443$	−1854.17	−	1070.51i	−0.198858	−	0.114811i	0.397264	−	0.917704i	$-0.369960\pi$
$443$	−1854.17	−	1070.51i	−0.198858	−	0.114811i	−0.596123	+	0.802893i	$0.703293\pi$
$444$	−2343.17	+	4655.16i	−0.250455	+	0.497577i
$445$	−7711.79	+	4452.40i	−0.821514	+	0.474302i
$446$	5882.47	+	9546.57i	0.624536	+	1.01355i
$447$	3848.40			0.407211
$448$	8510.39	−	4181.95i	0.897496	−	0.441023i
$449$	5106.95			0.536775			0.268387	−	0.963311i	$-0.413509\pi$
$449$	5106.95			0.536775			0.268387	+	0.963311i	$0.413509\pi$
$450$	−1263.99	−	2051.30i	−0.132411	−	0.214888i
$451$	16179.8	−	9341.44i	1.68931	−	0.975324i
$452$	−3916.67	+	7781.22i	−0.407576	+	0.809730i
$453$	7298.98	+	4214.07i	0.757033	+	0.437073i
$454$	−4485.66	−	2421.26i	−0.463706	−	0.250298i
$455$	−1235.92	+	5079.28i	−0.127343	+	0.523341i
$456$	−5984.37	+	515.409i	−0.614570	+	0.0529303i
$457$	−3095.20	+	5361.05i	−0.316822	+	0.548751i	−0.979823	−	0.199867i	$-0.935949\pi$
$457$	−3095.20	+	5361.05i	−0.316822	+	0.548751i	0.663001	+	0.748618i	$0.269282\pi$
$458$	311.062	+	10858.9i	0.0317357	+	1.10787i
$459$	7556.26	−	4362.61i	0.768401	−	0.443637i
$460$	−513.824	−	8961.22i	−0.0520808	−	0.908302i
$461$			10592.5i			1.07016i	0.844803	+	0.535078i	$0.179718\pi$
$461$			10592.5i			1.07016i	−0.844803	+	0.535078i	$0.820282\pi$
$462$	8189.34	−	2655.35i	0.824681	−	0.267398i
$463$	−4511.99			−0.452894			−0.226447	−	0.974023i	$-0.572711\pi$
$463$	−4511.99			−0.452894			−0.226447	+	0.974023i	$0.572711\pi$
$464$	4257.63	−	3157.77i	0.425981	−	0.315939i
$465$	3189.89	+	5525.05i	0.318124	+	0.551007i
$466$	1596.42	−	45.7308i	0.158697	−	0.00454600i
$467$	3025.77	+	1746.93i	0.299820	+	0.173101i	0.642362	−	0.766401i	$-0.277955\pi$
$467$	3025.77	+	1746.93i	0.299820	+	0.173101i	−0.342542	+	0.939502i	$0.611288\pi$
$468$	3795.86	−	2491.67i	0.374922	−	0.246106i
$469$	−2297.61	+	2406.35i	−0.226213	+	0.236919i
$470$	−5365.75	−	2896.31i	−0.526603	−	0.284248i
$471$	3846.89	−	6663.01i	0.376338	−	0.651837i
$472$	−3508.21	+	2449.41i	−0.342116	+	0.238863i
$473$	−5943.44	−	10294.3i	−0.577758	−	1.00071i
$474$	−663.883	+	409.076i	−0.0643315	+	0.0396402i
$475$		−	4190.73i		−	0.404808i
$476$	−8905.44	+	3172.11i	−0.857521	+	0.305448i
$477$		−	8193.66i		−	0.786503i
$478$	−2314.91	−	3756.83i	−0.221509	−	0.359484i
$479$	−1024.99	−	1775.34i	−0.0977729	−	0.169348i	0.812990	−	0.582278i	$-0.197839\pi$
$479$	−1024.99	−	1775.34i	−0.0977729	−	0.169348i	−0.910762	+	0.412931i	$0.864505\pi$
$480$	1803.63	−	4510.35i	0.171508	−	0.428892i
$481$	3426.11	−	5934.19i	0.324775	−	0.562528i
$482$	5665.60	−	10496.2i	0.535396	−	0.991884i
$483$	−2046.25	−	6986.67i	−0.192769	−	0.658187i
$484$	6769.22	+	10312.3i	0.635727	+	0.968477i
$485$	1490.27	+	860.408i	0.139525	+	0.0805549i
$486$	−312.899	−	10923.1i	−0.0292045	−	1.01951i
$487$	3873.91	+	6709.80i	0.360459	+	0.624333i	0.988036	−	0.154221i	$-0.0492868\pi$
$487$	3873.91	+	6709.80i	0.360459	+	0.624333i	−0.627577	+	0.778554i	$0.715953\pi$
$488$	3852.77	+	1802.93i	0.357391	+	0.167243i
$489$	8001.27			0.739939
$490$	−4783.32	−	7014.93i	−0.440997	−	0.646739i
$491$			10491.3i			0.964291i	0.876091	+	0.482146i	$0.160142\pi$
$491$			10491.3i			0.964291i	−0.876091	+	0.482146i	$0.839858\pi$
$492$	−489.446	−	8536.06i	−0.0448494	−	0.782186i
$493$	−4576.69	+	2642.35i	−0.418101	+	0.241391i
$494$	7894.12	−	226.133i	0.718974	−	0.0205956i
$495$	−4127.66	+	7149.32i	−0.374797	+	0.649168i
$496$	−6051.78	+	13960.3i	−0.547848	+	1.26378i
$497$	−7009.56	+	2052.95i	−0.632639	+	0.185286i
$498$	820.972	−	1520.95i	0.0738727	−	0.136858i
$499$	−1725.97	−	996.491i	−0.154840	−	0.0893969i	0.420578	−	0.907256i	$-0.361827\pi$
$499$	−1725.97	−	996.491i	−0.154840	−	0.0893969i	−0.575418	+	0.817859i	$0.695161\pi$
$500$	10844.6	+	5458.61i	0.969970	+	0.488233i
$501$	1845.92	−	1065.74i	0.164610	−	0.0950377i
$502$	14518.6	−	8946.16i	1.29083	−	0.795392i
$503$	3940.26			0.349279			0.174640	−	0.984632i	$-0.444124\pi$
$503$	3940.26			0.349279			0.174640	+	0.984632i	$0.444124\pi$
$504$	−1122.32	+	7288.99i	−0.0991903	+	0.644202i
$505$	17600.2			1.55089
$506$	16546.7	−	10195.9i	1.45374	−	0.895775i
$507$	−3071.90	+	1773.56i	−0.269088	+	0.155358i
$508$	4399.87	−	8741.19i	0.384277	−	0.763440i
$509$	−5019.62	−	2898.08i	−0.437114	−	0.252368i	0.265259	−	0.964177i	$-0.414543\pi$
$509$	−5019.62	−	2898.08i	−0.437114	−	0.252368i	−0.702373	+	0.711810i	$0.747876\pi$
$510$	−2300.33	+	4261.62i	−0.199726	+	0.370015i
$511$	−11471.5	−	10953.2i	−0.993093	−	0.948219i
$512$	11202.6	−	2953.04i	0.966968	−	0.254897i
$513$	5919.40	−	10252.7i	0.509450	−	0.882394i
$514$	8695.55	−	249.091i	0.746195	−	0.0213753i
$515$	−4521.88	+	2610.71i	−0.386909	+	0.223382i
$516$	−5431.02	+	311.407i	−0.463347	+	0.0265677i
$517$		−	13203.1i		−	1.12316i
$518$	3432.73	+	10586.8i	0.291169	+	0.897990i
$519$	5463.90			0.462117
$520$	−2706.99	+	5784.71i	−0.228287	+	0.487839i
$521$	7361.53	+	12750.5i	0.619030	+	1.07219i	0.989663	+	0.143412i	$0.0458074\pi$
$521$	7361.53	+	12750.5i	0.619030	+	1.07219i	−0.370633	+	0.928779i	$0.620859\pi$
$522$	118.050	+	4121.02i	0.00989828	+	0.345541i
$523$	−14898.2	−	8601.49i	−1.24561	−	0.719153i	−0.275379	−	0.961336i	$-0.588803\pi$
$523$	−14898.2	−	8601.49i	−1.24561	−	0.719153i	−0.970231	+	0.242183i	$0.922137\pi$
$524$	−16421.1	+	10779.1i	−1.36900	+	0.898640i
$525$	2670.91	+	649.902i	0.222034	+	0.0540268i
$526$	−559.566	+	1036.66i	−0.0463844	+	0.0859325i
$527$	7584.65	−	13137.0i	0.626931	−	1.08588i
$528$	10449.3	−	1202.25i	0.861267	−	0.0990934i
$529$	−2134.32	−	3696.75i	−0.175419	−	0.303834i
$530$	6046.00	+	9811.96i	0.495512	+	0.804159i
$531$		−	3327.74i		−	0.271962i
$532$	−8312.43	+	9769.10i	−0.677424	+	0.796135i
$533$			11241.6i			0.913562i
$534$	−7512.48	+	4629.09i	−0.608795	+	0.375132i
$535$	−1794.77	−	3108.63i	−0.145037	−	0.251211i
$536$	−3332.94	+	2327.04i	−0.268584	+	0.187524i
$537$	−3695.74	+	6401.21i	−0.296989	+	0.514399i
$538$	−19684.9	−	10625.5i	−1.57747	−	0.851480i
$539$	8446.88	−	16329.4i	0.675015	−	1.30493i
$540$	5253.94	+	8003.94i	0.418692	+	0.637842i
$541$	−12396.0	−	7156.85i	−0.985114	−	0.568756i	−0.0813037	−	0.996689i	$-0.525908\pi$
$541$	−12396.0	−	7156.85i	−0.985114	−	0.568756i	−0.903810	+	0.427934i	$0.859242\pi$
$542$	570.380	−	16.3390i	0.0452028	−	0.00129487i
$543$	−3425.02	−	5932.31i	−0.270685	−	0.468840i
$544$	−11431.8	+	1648.19i	−0.900981	+	0.129900i
$545$	−7637.94			−0.600318
$546$	−1080.11	+	5066.28i	−0.0846598	+	0.397100i
$547$			18243.6i			1.42604i	0.701145	+	0.713018i	$0.252672\pi$
$547$			18243.6i			1.42604i	−0.701145	+	0.713018i	$0.747328\pi$
$548$	19485.5	−	1117.27i	1.51894	−	0.0870937i
$549$	−2865.11	+	1654.17i	−0.222732	+	0.128594i
$550$	210.132	+	7335.55i	0.0162910	+	0.568707i
$551$	−3585.27	+	6209.88i	−0.277201	+	0.480126i
$552$	−763.233	−	8861.84i	−0.0588503	−	0.683306i
$553$	−393.715	+	1618.05i	−0.0302757	+	0.124424i
$554$	−7123.78	−	3845.25i	−0.546318	−	0.294890i
$555$	4937.53	+	2850.68i	0.377633	+	0.218027i
$556$	19893.6	+	10013.4i	1.51741	+	0.763785i
$557$	−16086.0	+	9287.24i	−1.22367	+	0.706486i	−0.965698	−	0.259666i	$-0.916387\pi$
$557$	−16086.0	+	9287.24i	−1.22367	+	0.706486i	−0.257972	+	0.966152i	$0.583054\pi$
$558$	−6207.97	−	10074.8i	−0.470976	−	0.764339i
$559$	7152.41			0.541171
$560$	−4034.48	−	9556.76i	−0.304443	−	0.721155i
$561$	−10486.3			−0.789181
$562$	5455.54	+	8853.71i	0.409481	+	0.664540i
$563$	−4972.40	+	2870.82i	−0.372224	+	0.214903i	−0.674429	−	0.738339i	$-0.735610\pi$
$563$	−4972.40	+	2870.82i	−0.372224	+	0.214903i	0.302206	+	0.953243i	$0.402277\pi$
$564$	−5397.15	−	2716.65i	−0.402945	−	0.202822i
$565$	8253.21	+	4764.99i	0.614540	+	0.354805i
$566$	14557.6	+	7857.87i	1.08110	+	0.583553i
$567$	−748.264	−	714.452i	−0.0554217	−	0.0529174i
$568$	−8890.87	+	765.733i	−0.656783	+	0.0565659i
$569$	3623.14	−	6275.46i	0.266942	−	0.462356i	−0.701129	−	0.713035i	$-0.747320\pi$
$569$	3623.14	−	6275.46i	0.266942	−	0.462356i	0.968070	+	0.250678i	$0.0806536\pi$
$570$	188.153	+	6568.28i	0.0138261	+	0.482658i
$571$	−7153.20	+	4129.90i	−0.524259	+	0.302681i	−0.738676	−	0.674061i	$-0.764548\pi$
$571$	−7153.20	+	4129.90i	−0.524259	+	0.302681i	0.214416	+	0.976742i	$0.431215\pi$
$572$	−13806.7	+	791.657i	−1.00924	+	0.0578686i
$573$			2237.26i			0.163112i
$574$	−13561.5	−	12225.8i	−0.986140	−	0.889015i
$575$	6205.76			0.450084
$576$	−3104.63	+	8458.63i	−0.224583	+	0.611880i
$577$	1280.85	+	2218.49i	0.0924132	+	0.160064i	0.908526	−	0.417828i	$-0.137209\pi$
$577$	1280.85	+	2218.49i	0.0924132	+	0.160064i	−0.816113	+	0.577893i	$0.803875\pi$
$578$	−2380.24	+	68.1839i	−0.171289	+	0.00490671i
$579$	−12686.5	−	7324.57i	−0.910594	−	0.525732i
$580$	−3182.22	−	4847.84i	−0.227818	−	0.347062i
$581$	−1037.42	−	3542.16i	−0.0740784	−	0.252932i
$582$	1500.58	+	809.980i	0.106875	+	0.0576886i
$583$	−12477.8	+	21612.2i	−0.886411	+	1.53531i
$584$	−11093.4	−	15888.8i	−0.786045	−	1.12583i
$585$	−2483.64	−	4301.80i	−0.175532	−	0.304030i
$586$	2468.42	−	1521.01i	0.174009	−	0.107222i
$587$		−	2146.44i		−	0.150925i	−0.997149	−	0.0754624i	$-0.975957\pi$
$587$		−	2146.44i		−	0.150925i	0.997149	−	0.0754624i	$-0.0240433\pi$
$588$	−4937.10	−	6812.82i	−0.346263	−	0.477816i
$589$		−	20582.4i		−	1.43987i
$590$	2455.50	+	3984.99i	0.171341	+	0.278067i
$591$	−3573.47	−	6189.44i	−0.248719	−	0.430794i
$592$	1554.22	+	13508.5i	0.107902	+	0.937829i
$593$	7900.80	−	13684.6i	0.547128	−	0.947653i	−0.451342	−	0.892351i	$-0.649055\pi$
$593$	7900.80	−	13684.6i	0.547128	−	0.947653i	0.998470	−	0.0553020i	$-0.0176122\pi$
$594$	−9847.36	+	18243.4i	−0.680206	+	1.26016i
$595$	2906.82	+	9924.98i	0.200282	+	0.683840i
$596$	8393.97	−	5509.96i	0.576897	−	0.378686i
$597$	−9136.06	−	5274.70i	−0.626321	−	0.361607i
$598$	334.865	+	11689.9i	0.0228991	+	0.799387i
$599$	−11161.4	−	19332.1i	−0.761339	−	1.31868i	−0.942160	−	0.335162i	$-0.891209\pi$
$599$	−11161.4	−	19332.1i	−0.761339	−	1.31868i	0.180821	−	0.983516i	$-0.442124\pi$
$600$	3041.85	+	1423.45i	0.206972	+	0.0968536i
$601$	−12041.0			−0.817242			−0.408621	−	0.912704i	$-0.633990\pi$
$601$	−12041.0			−0.817242			−0.408621	+	0.912704i	$0.633990\pi$
$602$	−7778.59	+	8628.40i	−0.526631	+	0.584165i
$603$		−	3161.49i		−	0.213509i
$604$	21953.7	−	1258.80i	1.47895	−	0.0848008i
$605$	11686.8	−	6747.40i	0.785352	−	0.453423i
$606$	17433.7	−	499.401i	1.16864	−	0.0334766i
$607$	−3607.64	+	6248.62i	−0.241235	+	0.417832i	−0.961066	−	0.276318i	$-0.910886\pi$
$607$	−3607.64	+	6248.62i	−0.241235	+	0.417832i	0.719831	+	0.694149i	$0.244219\pi$
$608$	−12314.9	+	9692.33i	−0.821440	+	0.646507i
$609$	−3401.78	−	3248.06i	−0.226350	−	0.216122i
$610$	2210.39	−	4095.01i	0.146715	−	0.271807i
$611$	6880.05	+	3972.20i	0.455544	+	0.263008i
$612$	4038.79	−	8023.84i	0.266762	−	0.529975i
$613$	24381.6	−	14076.7i	1.60646	−	0.927493i	0.616312	−	0.787502i	$-0.288626\pi$
$613$	24381.6	−	14076.7i	1.60646	−	0.927493i	0.990153	−	0.139991i	$-0.0447072\pi$
$614$	−4885.00	+	3010.08i	−0.321079	+	0.197845i
$615$	−9353.56			−0.613288
$616$	14060.4	−	17516.9i	0.919661	−	1.14574i
$617$	−8547.35			−0.557704			−0.278852	−	0.960334i	$-0.589954\pi$
$617$	−8547.35			−0.557704			−0.278852	+	0.960334i	$0.589954\pi$
$618$	−4405.01	+	2714.31i	−0.286724	+	0.176676i
$619$	4572.60	−	2639.99i	0.296912	−	0.171422i	−0.344143	−	0.938917i	$-0.611830\pi$
$619$	4572.60	−	2639.99i	0.296912	−	0.171422i	0.641055	+	0.767495i	$0.278497\pi$
$620$	14868.2	+	7483.87i	0.963097	+	0.484774i
$621$	15182.5	+	8765.63i	0.981085	+	0.566429i
$622$	−4843.21	+	8972.60i	−0.312210	+	0.578406i
$623$	−4455.27	+	18309.8i	−0.286511	+	1.17748i
$624$	−2517.23	+	5806.78i	−0.161490	+	0.372528i
$625$	3615.52	−	6262.27i	0.231394	−	0.400785i
$626$	−8182.09	+	234.382i	−0.522399	+	0.0149645i
$627$	−12322.0	+	7114.14i	−0.784841	+	0.453128i
$628$	−1149.12	−	20040.9i	−0.0730170	−	1.27344i
$629$		−	13556.2i		−	0.859335i
$630$	7890.60	+	1682.24i	0.498999	+	0.106384i
$631$	26983.8			1.70239			0.851194	−	0.524852i	$-0.175879\pi$
$631$	26983.8			1.70239			0.851194	+	0.524852i	$0.175879\pi$
$632$	−862.337	+	1842.78i	−0.0542752	+	0.115984i
$633$	6562.33	+	11366.3i	0.412053	+	0.713696i
$634$	−98.9740	−	3455.10i	−0.00619994	−	0.216435i
$635$	−9271.41	−	5352.85i	−0.579409	−	0.334522i
$636$	6267.20	+	9547.55i	0.390740	+	0.595260i
$637$	5967.88	+	9314.38i	0.371202	+	0.579355i
$638$	5964.37	−	11049.7i	0.370112	−	0.685676i
$639$	3470.22	−	6010.61i	0.214836	−	0.372106i
$640$	−2523.70	−	12420.1i	−0.155872	−	0.767107i
$641$	−11038.3	−	19118.9i	−0.680166	−	1.17808i	−0.974930	−	0.222512i	$-0.928574\pi$
$641$	−11038.3	−	19118.9i	−0.680166	−	1.17808i	0.294764	−	0.955570i	$-0.404759\pi$
$642$	−1865.99	−	3028.29i	−0.114712	−	0.186164i
$643$			7248.12i			0.444538i	0.974985	+	0.222269i	$0.0713464\pi$
$643$			7248.12i			0.444538i	−0.974985	+	0.222269i	$0.928654\pi$
$644$	−14466.4	−	12309.3i	−0.885179	−	0.753190i
$645$			5951.15i			0.363296i
$646$	13301.5	−	8196.18i	0.810122	−	0.499187i
$647$	13986.9	+	24226.0i	0.849893	+	1.47206i	0.881303	+	0.472551i	$0.156667\pi$
$647$	13986.9	+	24226.0i	0.849893	+	1.47206i	−0.0314105	+	0.999507i	$0.510000\pi$
$648$	−723.602	−	1036.39i	−0.0438670	−	0.0628292i
$649$	−5067.69	+	8777.49i	−0.306509	+	0.530888i
$650$	−3885.72	−	2097.43i	−0.234478	−	0.126566i
$651$	13117.9	+	3191.94i	0.789758	+	0.192169i
$652$	17452.0	−	11455.8i	1.04827	−	0.688107i
$653$	16345.2	+	9436.90i	0.979536	+	0.565535i	0.902130	−	0.431464i	$-0.142003\pi$
$653$	16345.2	+	9436.90i	0.979536	+	0.565535i	0.0774060	+	0.997000i	$0.475336\pi$
$654$	−7565.66	+	216.724i	−0.452356	+	0.0129581i
$655$	10744.4	+	18609.8i	0.640942	+	1.11014i
$656$	−13289.1	−	17917.7i	−0.790933	−	1.06642i
$657$	15071.4			0.894965
$658$	−12274.3	+	3979.88i	−0.727207	+	0.235793i
$659$			12594.1i			0.744455i	0.928141	+	0.372228i	$0.121406\pi$
$659$			12594.1i			0.744455i	−0.928141	+	0.372228i	$0.878594\pi$
$660$	−658.696	−	11487.8i	−0.0388481	−	0.677520i
$661$	−16194.5	+	9349.92i	−0.952941	+	0.550181i	−0.893993	−	0.448080i	$-0.852108\pi$
$661$	−16194.5	+	9349.92i	−0.952941	+	0.550181i	−0.0589480	+	0.998261i	$0.518775\pi$
$662$	−31.0748	−	1084.80i	−0.00182441	−	0.0636885i
$663$	3154.83	−	5464.32i	0.184802	−	0.320086i
$664$	−386.950	−	4492.85i	−0.0226153	−	0.262585i
$665$	10149.0	+	9690.45i	0.591824	+	0.565082i
$666$	−9306.30	−	5023.33i	−0.541459	−	0.292267i
$667$	−9195.78	−	5309.18i	−0.533826	−	0.308205i
$668$	2500.36	−	4967.46i	0.144823	−	0.287719i
$669$	10527.5	−	6078.03i	0.608393	−	0.351256i
$670$	2332.82	+	3785.90i	0.134515	+	0.218302i
$671$	10076.3			0.579719
$672$	−4267.47	−	9351.85i	−0.244972	−	0.536838i
$673$	−26792.3			−1.53457			−0.767286	−	0.641305i	$-0.778393\pi$
$673$	−26792.3			−1.53457			−0.767286	+	0.641305i	$0.778393\pi$
$674$	−11613.4	−	18847.2i	−0.663697	−	1.07710i
$675$	−5732.61	+	3309.72i	−0.326886	+	0.188728i
$676$	−4160.99	+	8266.61i	−0.236743	+	0.470335i
$677$	9315.61	+	5378.37i	0.528845	+	0.305329i	0.740546	−	0.672006i	$-0.234567\pi$
$677$	9315.61	+	5378.37i	0.528845	+	0.305329i	−0.211701	+	0.977334i	$0.567900\pi$
$678$	8310.32	+	4485.72i	0.470731	+	0.254090i
$679$	3494.74	−	1023.53i	0.197519	−	0.0578492i
$680$	1084.22	+	12588.8i	0.0611439	+	0.709937i
$681$	−2762.96	+	4785.59i	−0.155473	+	0.269287i
$682$	1032.05	+	36028.0i	0.0579460	+	2.02285i
$683$	−27340.4	+	15785.0i	−1.53170	+	0.884328i	−0.532417	+	0.846482i	$0.678716\pi$
$683$	−27340.4	+	15785.0i	−1.53170	+	0.884328i	−0.999284	+	0.0378455i	$0.987951\pi$
$684$	−697.727	−	12168.5i	−0.0390033	−	0.680228i
$685$		−	21351.6i		−	1.19095i
$686$	−17726.9	−	2930.41i	−0.986610	−	0.163096i
$687$	11776.6			0.654010
$688$	−11400.0	+	8455.11i	−0.631719	+	0.468529i
$689$	−7507.98	−	13004.2i	−0.415140	−	0.719043i
$690$	−9726.51	+	278.623i	−0.536641	+	0.0153725i
$691$	24576.0	+	14189.0i	1.35299	+	0.781149i	0.988667	−	0.150123i	$-0.0479671\pi$
$691$	24576.0	+	14189.0i	1.35299	+	0.781149i	0.364323	+	0.931273i	$0.381300\pi$
$692$	11917.6	−	7822.96i	0.654682	−	0.429746i
$693$	4910.23	+	16765.4i	0.269155	+	0.918998i
$694$	−1679.47	−	906.541i	−0.0918615	−	0.0495848i
$695$	12182.3	−	21100.3i	0.664893	−	1.15163i
$696$	−3289.66	−	4711.67i	−0.179158	−	0.256603i
$697$	11120.0	+	19260.5i	0.604306	+	1.04669i
$698$	16915.0	−	10422.8i	0.917254	−	0.565200i
$699$		−	1731.34i		−	0.0936841i
$700$	6756.16	−	2406.54i	0.364799	−	0.129941i
$701$		−	3313.45i		−	0.178527i	−0.996008	−	0.0892634i	$-0.971549\pi$
$701$		−	3313.45i		−	0.178527i	0.996008	−	0.0892634i	$-0.0284513\pi$
$702$	−6543.89	−	10620.0i	−0.351828	−	0.570976i
$703$	−9196.86	−	15929.4i	−0.493409	−	0.854609i
$704$	21070.3	−	17583.2i	1.12801	−	0.941322i
$705$	−3305.06	+	5724.53i	−0.176561	+	0.305813i
$706$	−4217.63	+	7813.64i	−0.224834	+	0.416530i
$707$	25720.6	−	26937.8i	1.36821	−	1.43296i
$708$	2545.33	+	3877.60i	0.135112	+	0.205832i
$709$	−11822.5	−	6825.73i	−0.626239	−	0.361559i	0.153055	−	0.988218i	$-0.451089\pi$
$709$	−11822.5	−	6825.73i	−0.626239	−	0.361559i	−0.779294	+	0.626658i	$0.784422\pi$
$710$	279.536	+	9758.37i	0.0147758	+	0.515810i
$711$	−791.188	−	1370.38i	−0.0417326	−	0.0722830i
$712$	−9758.18	+	20852.8i	−0.513628	+	1.09760i
$713$	30479.1			1.60091
$714$	3160.93	+	9748.58i	0.165679	+	0.510968i
$715$			15129.0i			0.791317i
$716$	1103.96	+	19253.4i	0.0576216	+	1.00494i
$717$	−4142.84	+	2391.87i	−0.215784	+	0.124583i
$718$	3030.14	−	86.8005i	0.157498	−	0.00451165i
$719$	−17155.5	+	29714.1i	−0.889834	+	1.54124i	−0.0497630	+	0.998761i	$0.515847\pi$
$719$	−17155.5	+	29714.1i	−0.889834	+	1.54124i	−0.840071	+	0.542477i	$0.817487\pi$
$720$	9043.91	+	3920.53i	0.468121	+	0.202930i
$721$	−2612.39	+	10736.1i	−0.134938	+	0.554556i
$722$	854.557	−	1583.17i	0.0440489	−	0.0816057i
$723$	−11198.0	−	6465.18i	−0.576015	−	0.332562i
$724$	−15964.1	−	8035.52i	−0.819478	−	0.412483i
$725$	3472.14	−	2004.64i	0.177865	−	0.102690i
$726$	11384.8	−	7015.16i	0.581997	−	0.358619i
$727$	−5988.54			−0.305506			−0.152753	−	0.988264i	$-0.548814\pi$
$727$	−5988.54			−0.305506			−0.152753	+	0.988264i	$0.548814\pi$
$728$	4897.79	+	12596.8i	0.249346	+	0.641303i
$729$	−10337.9			−0.525220
$730$	−18048.1	+	11121.0i	−0.915056	+	0.563845i
$731$	12254.4	−	7075.06i	0.620033	−	0.357976i
$732$	2073.28	−	4118.98i	0.104687	−	0.207981i
$733$	30860.2	+	17817.1i	1.55504	+	0.897804i	0.997719	+	0.0675083i	$0.0215049\pi$
$733$	30860.2	+	17817.1i	1.55504	+	0.897804i	0.557323	+	0.830296i	$0.311828\pi$
$734$	2379.66	−	4408.60i	0.119666	−	0.221695i
$735$	−7750.00	+	4965.56i	−0.388929	+	0.249194i
$736$	−14352.7	−	18236.3i	−0.718815	−	0.913314i
$737$	−4814.51	+	8338.97i	−0.240630	+	0.416784i
$738$	17342.8	−	496.799i	0.865039	−	0.0247797i
$739$	−16663.6	+	9620.75i	−0.829474	+	0.478897i	−0.853673	−	0.520810i	$-0.825630\pi$
$739$	−16663.6	+	9620.75i	−0.829474	+	0.478897i	0.0241983	+	0.999707i	$0.492297\pi$
$740$	14851.0	−	851.535i	0.737748	−	0.0423014i
$741$		−	8561.25i		−	0.424434i
$742$	23853.1	+	5085.35i	1.18015	+	0.251602i
$743$	−33062.3			−1.63249			−0.816244	−	0.577707i	$-0.803948\pi$
$743$	−33062.3			−1.63249			−0.816244	+	0.577707i	$0.803948\pi$
$744$	14939.8	+	6991.17i	0.736184	+	0.344501i
$745$	−5492.20	−	9512.77i	−0.270092	−	0.467814i
$746$	−903.177	−	31529.2i	−0.0443266	−	1.54741i
$747$	3037.36	+	1753.62i	0.148770	+	0.0858923i
$748$	−22872.2	+	15013.8i	−1.11804	+	0.733900i
$749$	−7380.72	−	1795.92i	−0.360061	−	0.0876124i
$750$	6251.70	−	11582.0i	0.304373	−	0.563886i
$751$	653.983	−	1132.73i	0.0317765	−	0.0550386i	−0.849700	−	0.527267i	$-0.823217\pi$
$751$	653.983	−	1132.73i	0.0317765	−	0.0550386i	0.881476	+	0.472228i	$0.156550\pi$
$752$	−15661.6	+	1801.95i	−0.759468	+	0.0873810i
$753$	−9243.57	−	16010.3i	−0.447350	−	0.774833i
$754$	3963.52	+	6432.33i	0.191436	+	0.310678i
$755$		−	24056.2i		−	1.15960i
$756$	19928.3	+	3655.43i	0.958712	+	0.175856i
$757$		−	22928.8i		−	1.10087i	−0.834877	−	0.550437i	$-0.814461\pi$
$757$		−	22928.8i		−	1.10087i	0.834877	−	0.550437i	$-0.185539\pi$
$758$	−28853.3	+	17779.0i	−1.38259	+	0.851931i
$759$	−10534.8	−	18246.9i	−0.503808	−	0.872621i
$760$	9814.55	+	14057.1i	0.468436	+	0.670926i
$761$	12998.0	−	22513.1i	0.619154	−	1.07241i	−0.370487	−	0.928838i	$-0.620809\pi$
$761$	12998.0	−	22513.1i	0.619154	−	1.07241i	0.989640	−	0.143568i	$-0.0458576\pi$
$762$	−9335.56	−	5039.12i	−0.443821	−	0.239565i
$763$	−11161.9	+	11690.2i	−0.529605	+	0.554668i
$764$	3203.21	+	4879.83i	0.151686	+	0.231081i
$765$	−8510.55	−	4913.57i	−0.402221	−	0.232223i
$766$	−950.115	+	27.2168i	−0.0448160	+	0.00128379i
$767$	−3049.26	−	5281.47i	−0.143549	−	0.248635i
$768$	−2852.24	−	12231.0i	−0.134012	−	0.574672i
$769$	−7834.78			−0.367398			−0.183699	−	0.982982i	$-0.558807\pi$
$769$	−7834.78			−0.367398			−0.183699	+	0.982982i	$0.558807\pi$
$770$	−18251.0	−	16453.5i	−0.854183	−	0.770055i
$771$		−	9430.41i		−	0.440503i
$772$	−38158.3	+	2187.94i	−1.77895	+	0.102002i
$773$	−5328.06	+	3076.15i	−0.247913	+	0.143133i	−0.618808	−	0.785542i	$-0.712384\pi$
$773$	−5328.06	+	3076.15i	−0.247913	+	0.143133i	0.370895	+	0.928675i	$0.379051\pi$
$774$	−316.085	−	11034.3i	−0.0146789	−	0.512428i
$775$	−5754.14	+	9966.46i	−0.266703	+	0.461943i
$776$	4432.70	−	381.769i	0.205057	−	0.0176607i
$777$	11578.7	−	3391.15i	0.534598	−	0.156572i
$778$	−9636.23	−	5201.42i	−0.444056	−	0.239691i
$779$	26133.5	+	15088.2i	1.20197	+	0.693955i
$780$	6184.41	+	3112.91i	0.283894	+	0.142898i
$781$	−18306.6	+	10569.3i	−0.838749	+	0.484252i
$782$	12137.2	+	19697.2i	0.555018	+	0.900730i
$783$	11326.2			0.516942
$784$	−20522.9	−	7791.12i	−0.934898	−	0.354916i
$785$	−21960.2			−0.998462
$786$	11170.7	+	18128.8i	0.506930	+	0.822688i
$787$	9159.31	−	5288.13i	0.414859	−	0.239519i	−0.278016	−	0.960576i	$-0.589677\pi$
$787$	9159.31	−	5288.13i	0.414859	−	0.239519i	0.692875	+	0.721057i	$0.256344\pi$
$788$	−16656.1	−	8383.80i	−0.752979	−	0.379011i
$789$	1105.98	+	638.536i	0.0499034	+	0.0288118i
$790$	1958.64	+	1057.23i	0.0882091	+	0.0476133i
$791$	19354.1	−	5668.39i	0.869977	−	0.254798i
$792$	1831.48	+	21265.1i	0.0821700	+	0.954070i
$793$	−3031.49	+	5250.69i	−0.135752	+	0.235129i
$794$	−549.584	−	19185.5i	−0.0245642	−	0.857517i
$795$	10820.1	−	6247.00i	0.482704	−	0.278689i
$796$	−27479.3	+	1575.62i	−1.22359	+	0.0701588i
$797$		−	11570.5i		−	0.514241i	−0.966379	−	0.257120i	$-0.917226\pi$
$797$		−	11570.5i		−	0.514241i	0.966379	−	0.257120i	$-0.0827737\pi$
$798$	10328.0	+	9310.77i	0.458153	+	0.413030i
$799$	15717.0			0.695903
$800$	8672.79	−	1250.41i	0.383287	−	0.0552609i
$801$	−8953.06	−	15507.2i	−0.394933	−	0.684043i
$802$	34725.7	−	994.744i	1.52894	−	0.0437975i
$803$	−39753.5	−	22951.7i	−1.74704	−	1.00865i
$804$	2418.17	+	3683.88i	0.106072	+	0.161593i
$805$	−14349.9	+	15029.0i	−0.628283	+	0.658017i
$806$	−19084.4	−	10301.3i	−0.834020	−	0.450185i
$807$	−12125.0	+	21001.1i	−0.528898	+	0.916079i
$808$	37310.6	−	26050.0i	1.62448	−	1.13420i
$809$	20835.6	+	36088.3i	0.905488	+	1.56835i	0.820261	+	0.571989i	$0.193828\pi$
$809$	20835.6	+	36088.3i	0.905488	+	1.56835i	0.0852262	+	0.996362i	$0.472839\pi$
$810$	−1177.24	+	725.400i	−0.0510667	+	0.0314666i
$811$			4576.16i			0.198139i	0.995081	+	0.0990696i	$0.0315866\pi$
$811$			4576.16i			0.198139i	−0.995081	+	0.0990696i	$0.968413\pi$
$812$	−12070.2	−	2214.03i	−0.521653	−	0.0956862i
$813$		−	618.583i		−	0.0266847i
$814$	16897.1	+	27422.1i	0.727573	+	1.18077i
$815$	−11418.9	−	19778.2i	−0.490782	−	0.850060i
$816$	1431.16	+	12438.9i	0.0613978	+	0.533637i
$817$	9599.78	−	16627.3i	0.411082	−	0.712015i
$818$	−4224.70	+	7826.74i	−0.180578	+	0.334542i
$819$	−10213.6	−	2485.24i	−0.435766	−	0.106033i
$820$	−20401.6	+	13392.0i	−0.868847	+	0.570328i
$821$	−16660.8	−	9619.13i	−0.708242	−	0.408904i	0.102168	−	0.994767i	$-0.467422\pi$
$821$	−16660.8	−	9619.13i	−0.708242	−	0.408904i	−0.810410	+	0.585863i	$0.800756\pi$
$822$	−605.844	−	21149.5i	−0.0257071	−	0.897414i
$823$	−5624.38	−	9741.71i	−0.238218	−	0.412606i	0.721985	−	0.691909i	$-0.243230\pi$
$823$	−5624.38	−	9741.71i	−0.238218	−	0.412606i	−0.960203	+	0.279303i	$0.909897\pi$
$824$	−5721.80	+	12227.2i	−0.241903	+	0.516937i
$825$	7955.47			0.335726
$826$	9687.59	+	2065.34i	0.408080	+	0.0870006i
$827$			17626.7i			0.741163i	0.928800	+	0.370582i	$0.120842\pi$
$827$			17626.7i			0.741163i	−0.928800	+	0.370582i	$0.879158\pi$
$828$	18019.6	−	1033.22i	0.756308	−	0.0433656i
$829$	−28478.1	+	16441.8i	−1.19310	+	0.688839i	−0.959009	−	0.283374i	$-0.908546\pi$
$829$	−28478.1	+	16441.8i	−1.19310	+	0.688839i	−0.234095	+	0.972214i	$0.575213\pi$
$830$	−4931.23	+	141.259i	−0.206223	+	0.00590743i
$831$	−4387.93	+	7600.11i	−0.183171	+	0.317262i
$832$	2823.40	+	16269.6i	0.117649	+	0.677939i
$833$	19438.5	+	10055.2i	0.808529	+	0.418236i
$834$	11468.3	−	21246.3i	0.476156	−	0.882135i
$835$	−5268.77	−	3041.92i	−0.218363	−	0.126072i
$836$	−16690.6	+	33159.2i	−0.690500	+	1.37181i
$837$	−28155.2	+	16255.4i	−1.16271	+	0.671291i
$838$	5136.39	−	3164.98i	0.211735	−	0.130468i
$839$	8483.06			0.349068			0.174534	−	0.984651i	$-0.444158\pi$
$839$	8483.06			0.349068			0.174534	+	0.984651i	$0.444158\pi$
$840$	−10481.1	+	4075.19i	−0.430516	+	0.167390i
$841$	17528.9			0.718723
$842$	10187.9	−	6277.66i	0.416982	−	0.256939i
$843$	9763.41	−	5636.91i	0.398897	−	0.230303i
$844$	30587.2	+	15396.0i	1.24746	+	0.627907i
$845$	8768.04	+	5062.23i	0.356958	+	0.206090i
$846$	5824.01	−	10789.6i	0.236683	−	0.438482i
$847$	6751.75	−	27747.7i	0.273899	−	1.12565i
$848$	27339.5	+	11851.6i	1.10712	+	0.479937i
$849$	8966.83	−	15531.0i	0.362475	−	0.627824i
$850$	−8732.23	+	250.141i	−0.352368	+	0.0100939i
$851$	23588.8	−	13619.0i	0.950192	−	0.548594i
$852$	553.782	+	9658.10i	0.0222679	+	0.388358i
$853$			1148.92i			0.0461176i	0.999734	+	0.0230588i	$0.00734049\pi$
$853$			1148.92i			0.0461176i	−0.999734	+	0.0230588i	$0.992660\pi$
$854$	−3037.35	−	9367.45i	−0.121705	−	0.375348i
$855$	−13333.9			−0.533346
$856$	−8405.79	−	3933.53i	−0.335635	−	0.157062i
$857$	19525.6	+	33819.3i	0.778275	+	1.34801i	0.932935	+	0.360044i	$0.117238\pi$
$857$	19525.6	+	33819.3i	0.778275	+	1.34801i	−0.154661	+	0.987968i	$0.549428\pi$
$858$	429.280	+	14985.8i	0.0170809	+	0.596279i
$859$	12358.3	+	7135.08i	0.490874	+	0.283406i	0.724937	−	0.688815i	$-0.241869\pi$
$859$	12358.3	+	7135.08i	0.490874	+	0.283406i	−0.234063	+	0.972221i	$0.575202\pi$
$860$	8520.57	+	12980.4i	0.337848	+	0.514683i
$861$	−13669.1	+	14316.0i	−0.541047	+	0.566652i
$862$	−247.857	+	459.184i	−0.00979355	+	0.0181437i
$863$	−3995.09	+	6919.69i	−0.157583	+	0.272942i	−0.933997	−	0.357282i	$-0.883704\pi$
$863$	−3995.09	+	6919.69i	−0.157583	+	0.272942i	0.776413	+	0.630224i	$0.217037\pi$
$864$	22984.4	+	9191.16i	0.905028	+	0.361909i
$865$	−7797.74	−	13506.1i	−0.306510	−	0.530891i
$866$	8862.48	+	14382.8i	0.347759	+	0.564372i
$867$			2581.40i			0.101118i
$868$	33182.4	−	11819.5i	1.29756	−	0.462190i
$869$			4819.48i			0.188135i
$870$	−5352.00	+	3297.83i	−0.208563	+	0.128514i
$871$	−2896.92	−	5017.61i	−0.112696	−	0.195196i
$872$	−16191.6	+	11304.9i	−0.628804	+	0.439027i
$873$	−1730.14	+	2996.69i	−0.0670749	+	0.116177i
$874$	27625.0	+	14911.4i	1.06914	+	0.577099i
$875$	−7899.97	−	26973.5i	−0.305220	−	1.04214i
$876$	−17561.8	+	11527.9i	−0.677349	+	0.444625i
$877$	−9621.74	−	5555.12i	−0.370471	−	0.213892i	0.303193	−	0.952929i	$-0.401947\pi$
$877$	−9621.74	−	5555.12i	−0.370471	−	0.213892i	−0.673664	+	0.739038i	$0.735281\pi$
$878$	−31299.2	+	896.590i	−1.20307	+	0.0344629i
$879$	−1571.57	−	2722.04i	−0.0603046	−	0.104451i
$880$	−17884.5	−	24113.7i	−0.685097	−	0.923719i
$881$	−17590.4			−0.672683			−0.336342	−	0.941740i	$-0.609190\pi$
$881$	−17590.4			−0.672683			−0.336342	+	0.941740i	$0.609190\pi$
$882$	14105.9	−	9618.49i	0.538515	−	0.367201i
$883$		−	22009.6i		−	0.838826i	−0.907796	−	0.419413i	$-0.862236\pi$
$883$		−	22009.6i		−	0.838826i	0.907796	−	0.419413i	$-0.137764\pi$
$884$	−942.388	−	16435.5i	−0.0358551	−	0.625323i
$885$	4394.44	−	2537.13i	0.166912	−	0.0963669i
$886$	173.399	+	6053.21i	0.00657500	+	0.229528i
$887$	22650.3	−	39231.5i	0.857410	−	1.48508i	−0.0169818	−	0.999856i	$-0.505406\pi$
$887$	22650.3	−	39231.5i	0.857410	−	1.48508i	0.874391	−	0.485221i	$-0.161261\pi$
$888$	14686.3	−	1264.87i	0.555000	−	0.0477998i
$889$	−21741.8	+	6367.71i	−0.820243	+	0.240232i
$890$	22163.9	+	11963.6i	0.834759	+	0.450584i
$891$	−2593.04	−	1497.09i	−0.0974972	−	0.0562900i
$892$	14259.8	−	28329.9i	0.535262	−	1.06340i
$893$	18468.5	−	10662.8i	0.692075	−	0.399570i
$894$	−5710.15	−	9266.92i	−0.213620	−	0.346680i
$895$	21097.3			0.787939
$896$	−22697.6	−	14287.9i	−0.846286	−	0.532728i
$897$	12677.8			0.471904
$898$	−7577.55	−	12297.5i	−0.281588	−	0.456985i
$899$	17053.1	−	9845.63i	0.632651	−	0.365261i
$900$	−3064.05	+	6087.34i	−0.113483	+	0.225457i
$901$	−25727.1	−	14853.6i	−0.951271	−	0.549216i
$902$	−46501.3	−	25100.4i	−1.71655	−	0.926552i
$903$	9108.45	+	8696.88i	0.335670	+	0.320503i
$904$	24548.6	−	2114.26i	0.903178	−	0.0777869i
$905$	−9775.97	+	16932.5i	−0.359076	+	0.621938i
$906$	−682.588	−	23828.6i	−0.0250303	−	0.873788i
$907$	−9627.87	+	5558.65i	−0.352468	+	0.203497i	−0.665772	−	0.746156i	$-0.731897\pi$
$907$	−9627.87	+	5558.65i	−0.352468	+	0.203497i	0.313304	+	0.949653i	$0.398564\pi$
$908$	825.332	+	14394.0i	0.0301648	+	0.526082i
$909$			35391.2i			1.29137i
$910$	14064.7	−	4560.40i	0.512351	−	0.166127i
$911$	4926.27			0.179160			0.0895800	−	0.995980i	$-0.471448\pi$
$911$	4926.27			0.179160			0.0895800	+	0.995980i	$0.471448\pi$
$912$	10120.5	+	13645.6i	0.367461	+	0.495449i
$913$	−5341.04	−	9250.95i	−0.193606	−	0.335336i
$914$	17501.9	−	501.356i	0.633384	−	0.0181438i
$915$	−4368.83	−	2522.34i	−0.157846	−	0.0911323i
$916$	25686.6	−	16861.2i	0.926538	−	0.608197i
$917$	44184.5	+	10751.3i	1.59117	+	0.387174i
$918$	−21716.9	−	11722.3i	−0.780789	−	0.421452i
$919$	12450.7	−	21565.2i	0.446910	−	0.774070i	−0.551274	−	0.834325i	$-0.685858\pi$
$919$	12450.7	−	21565.2i	0.446910	−	0.774070i	0.998183	+	0.0602546i	$0.0191913\pi$
$920$	−20816.1	+	14533.7i	−0.745965	+	0.520828i
$921$	3110.14	+	5386.93i	0.111273	+	0.192731i
$922$	25506.6	−	15716.9i	0.911081	−	0.561396i
$923$		−	12719.3i		−	0.453587i
$924$	−18545.2	−	15779.9i	−0.660272	−	0.561819i
$925$			10284.5i			0.365570i
$926$	6694.77	+	10864.8i	0.237585	+	0.385573i
$927$	−5249.71	−	9092.77i	−0.186001	−	0.322164i
$928$	−13921.2	−	5566.92i	−0.492442	−	0.196921i
$929$	−5730.85	+	9926.12i	−0.202393	+	0.350555i	−0.949299	−	0.314375i	$-0.898205\pi$
$929$	−5730.85	+	9926.12i	−0.202393	+	0.350555i	0.746906	+	0.664930i	$0.231538\pi$
$930$	8571.21	−	15879.2i	0.302216	−	0.559890i
$931$	29663.2	−	1372.09i	1.04422	−	0.0483012i
$932$	−2478.85	−	3776.32i	−0.0871217	−	0.132723i
$933$	9572.56	+	5526.72i	0.335896	+	0.193930i
$934$	−282.965	−	9878.06i	−0.00991315	−	0.346060i
$935$	14965.4	+	25920.8i	0.523443	+	0.906630i
$936$	−11632.1	−	5443.31i	−0.406205	−	0.190086i
$937$	−5527.69			−0.192723			−0.0963617	−	0.995346i	$-0.530721\pi$
$937$	−5527.69			−0.192723			−0.0963617	+	0.995346i	$0.530721\pi$
$938$	9203.60	+	1962.16i	0.320371	+	0.0683015i
$939$			8873.55i			0.308389i
$940$	987.263	+	17218.1i	0.0342564	+	0.597440i
$941$	1517.92	−	876.373i	0.0525854	−	0.0303602i	−0.473477	−	0.880806i	$-0.657001\pi$
$941$	1517.92	−	876.373i	0.0525854	−	0.0303602i	0.526062	+	0.850446i	$0.323668\pi$
$942$	−21752.4	+	623.114i	−0.752368	+	0.0215522i
$943$	−22343.1	+	38699.4i	−0.771570	+	1.33640i
$944$	11103.5	+	4813.37i	0.382828	+	0.165955i
$945$	5240.38	−	21536.4i	0.180391	−	0.741353i
$946$	−15969.9	+	29586.2i	−0.548867	+	1.01684i
$947$	17093.0	+	9868.64i	0.586533	+	0.338635i	0.763726	−	0.645541i	$-0.223368\pi$
$947$	17093.0	+	9868.64i	0.586533	+	0.338635i	−0.177192	+	0.984176i	$0.556701\pi$
$948$	1970.10	+	991.648i	0.0674957	+	0.0339739i
$949$	23919.9	−	13810.2i	0.818202	−	0.472389i
$950$	−10091.2	+	6218.09i	−0.344635	+	0.212359i
$951$	−3747.09			−0.127768
$952$	20852.0	+	16737.5i	0.709893	+	0.569817i
$953$	17751.6			0.603389			0.301694	−	0.953405i	$-0.402448\pi$
$953$	17751.6			0.603389			0.301694	+	0.953405i	$0.402448\pi$
$954$	−19730.3	+	12157.5i	−0.669592	+	0.412594i
$955$	5530.24	−	3192.89i	0.187387	−	0.108188i
$956$	−5611.61	+	11148.6i	−0.189846	+	0.377166i
$957$	−11788.5	−	6806.11i	−0.398191	−	0.229896i
$958$	−2754.15	+	5102.38i	−0.0928837	+	0.172078i
$959$	−32679.4	−	31202.7i	−1.10039	−	1.05067i
$960$	−13537.0	+	2349.20i	−0.455111	+	0.0789794i
$961$	−13365.5	+	23149.7i	−0.448642	+	0.777072i
$962$	−19373.0	+	554.955i	−0.649285	+	0.0185993i
$963$	6250.96	−	3608.99i	0.209174	−	0.120766i
$964$	−33681.2	+	1931.23i	−1.12531	+	0.0645236i
$965$			41812.7i			1.39482i
$966$	−13787.7	+	15294.0i	−0.459225	+	0.509395i
$967$	−31083.0			−1.03367			−0.516836	−	0.856085i	$-0.672890\pi$
$967$	−31083.0			−1.03367			−0.516836	+	0.856085i	$0.672890\pi$
$968$	14788.1	−	31601.4i	0.491019	−	1.04928i
$969$	−8468.66	−	14668.2i	−0.280756	−	0.486284i
$970$	−139.368	−	4865.21i	−0.00461322	−	0.161044i
$971$	−10899.2	−	6292.63i	−0.360217	−	0.207971i	0.308959	−	0.951075i	$-0.400019\pi$
$971$	−10899.2	−	6292.63i	−0.360217	−	0.207971i	−0.669176	+	0.743104i	$0.733353\pi$
$972$	−25838.4	+	16960.8i	−0.852640	+	0.559689i
$973$	−14491.9	−	49481.0i	−0.477482	−	1.63031i
$974$	10409.1	−	19284.2i	0.342434	−	0.634399i
$975$	−2393.43	+	4145.54i	−0.0786166	+	0.136168i
$976$	−1375.21	−	11952.6i	−0.0451018	−	0.392000i
$977$	−10203.6	−	17673.1i	−0.334126	−	0.578722i	0.649191	−	0.760625i	$-0.275108\pi$
$977$	−10203.6	−	17673.1i	−0.334126	−	0.578722i	−0.983316	+	0.181903i	$0.941774\pi$
$978$	−11872.1	−	19267.0i	−0.388166	−	0.629949i
$979$			54537.1i			1.78040i
$980$	−9794.52	+	21926.8i	−0.319260	+	0.714719i
$981$		−	15358.7i		−	0.499861i
$982$	25263.0	−	15566.7i	0.820952	−	0.505860i
$983$	23381.3	+	40497.5i	0.758643	+	1.31401i	0.943543	+	0.331251i	$0.107471\pi$
$983$	23381.3	+	40497.5i	0.758643	+	1.31401i	−0.184900	+	0.982757i	$0.559196\pi$
$984$	−19828.5	+	13844.2i	−0.642389	+	0.448512i
$985$	−10199.7	+	17666.4i	−0.329938	+	0.571469i
$986$	13153.5	+	7099.98i	0.424842	+	0.229320i
$987$	3931.67	+	13424.2i	0.126795	+	0.432926i
$988$	−12257.6	−	18673.4i	−0.394703	−	0.601297i
$989$	24622.2	+	14215.7i	0.791650	+	0.457059i
$990$	23340.0	−	668.593i	0.749287	−	0.0214639i
$991$	3271.64	+	5666.64i	0.104871	+	0.181641i	0.913685	−	0.406422i	$-0.133224\pi$
$991$	3271.64	+	5666.64i	0.104871	+	0.181641i	−0.808815	+	0.588064i	$0.799890\pi$
$992$	42595.7	−	6141.30i	1.36332	−	0.196559i
$993$	−1176.47			−0.0375974
$994$	15344.1	+	13832.8i	0.489622	+	0.441399i
$995$			30110.9i			0.959378i
$996$	−4880.56	+	279.844i	−0.155267	+	0.00890281i
$997$	11066.6	−	6389.30i	0.351537	−	0.202960i	−0.313825	−	0.949481i	$-0.601611\pi$
$997$	11066.6	−	6389.30i	0.351537	−	0.202960i	0.665362	+	0.746521i	$0.268277\pi$
$998$	161.410	+	5634.69i	0.00511959	+	0.178721i
$999$	−14526.9	+	25161.3i	−0.460070	+	0.796864i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.4.p.a.37.8	✓	44
4.3	odd	2		224.4.t.a.177.15		44
7.4	even	3	inner	56.4.p.a.53.22	yes	44
8.3	odd	2		224.4.t.a.177.8		44
8.5	even	2	inner	56.4.p.a.37.22	yes	44
28.11	odd	6		224.4.t.a.81.8		44
56.11	odd	6		224.4.t.a.81.15		44
56.53	even	6	inner	56.4.p.a.53.8	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.4.p.a.37.8	✓	44	1.1	even	1	trivial
56.4.p.a.37.22	yes	44	8.5	even	2	inner
56.4.p.a.53.8	yes	44	56.53	even	6	inner
56.4.p.a.53.22	yes	44	7.4	even	3	inner
224.4.t.a.81.8		44	28.11	odd	6
224.4.t.a.81.15		44	56.11	odd	6
224.4.t.a.177.8		44	8.3	odd	2
224.4.t.a.177.15		44	4.3	odd	2

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:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	56.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.48377 - 2.40799i) q^{2} +(-2.65541 + 1.53310i) q^{3} +(-3.59684 + 7.14582i) q^{4} +(7.57927 + 4.37589i) q^{5} +(7.63171 + 4.11942i) q^{6} +(17.7736 - 5.20552i) q^{7} +(22.5440 - 1.94162i) q^{8} +(-8.79921 + 15.2407i) q^{9} +(-0.708800 - 24.7436i) q^{10} +(46.4189 - 26.8000i) q^{11} +(-1.40419 - 24.4894i) q^{12} +32.2514i q^{13} +(-38.9069 - 35.0750i) q^{14} -26.8347 q^{15} +(-38.1255 - 51.4047i) q^{16} +(31.9026 + 55.2570i) q^{17} +(49.7554 - 1.42528i) q^{18} +(74.9753 + 43.2870i) q^{19} +(-58.5307 + 38.4207i) q^{20} +(-39.2157 + 41.0716i) q^{21} +(-133.409 - 72.0112i) q^{22} +(-64.1008 + 111.026i) q^{23} +(-56.8867 + 39.7179i) q^{24} +(-24.2031 - 41.9211i) q^{25} +(77.6611 - 47.8538i) q^{26} -136.748i q^{27} +(-26.7312 + 145.731i) q^{28} +82.8256i q^{29} +(39.8166 + 64.6178i) q^{30} +(-118.872 - 205.892i) q^{31} +(-67.2125 + 168.079i) q^{32} +(-82.1740 + 142.330i) q^{33} +(85.7220 - 158.810i) q^{34} +(157.490 + 38.3215i) q^{35} +(-77.2578 - 117.696i) q^{36} +(-183.998 - 106.231i) q^{37} +(-7.01157 - 244.768i) q^{38} +(-49.4447 - 85.6407i) q^{39} +(179.363 + 83.9339i) q^{40} +348.562 q^{41} +(157.087 + 33.4902i) q^{42} -221.770i q^{43} +(24.5464 + 428.096i) q^{44} +(-133.383 + 77.0088i) q^{45} +(362.460 - 10.3829i) q^{46} +(123.164 - 213.326i) q^{47} +(180.047 + 78.0503i) q^{48} +(288.805 - 185.042i) q^{49} +(-65.0336 + 120.482i) q^{50} +(-169.429 - 97.8198i) q^{51} +(-230.463 - 116.003i) q^{52} +(-403.213 + 232.795i) q^{53} +(-329.287 + 202.902i) q^{54} +469.095 q^{55} +(390.581 - 151.863i) q^{56} -265.453 q^{57} +(199.443 - 122.894i) q^{58} +(-163.759 + 94.5465i) q^{59} +(96.5202 - 191.756i) q^{60} +(162.805 + 93.9955i) q^{61} +(-319.407 + 591.739i) q^{62} +(-77.0584 + 316.687i) q^{63} +(504.460 - 87.5435i) q^{64} +(-141.129 + 244.442i) q^{65} +(464.656 - 13.3104i) q^{66} +(-155.578 + 89.8230i) q^{67} +(-509.605 + 29.2200i) q^{68} -393.092i q^{69} +(-141.402 - 436.095i) q^{70} -394.379 q^{71} +(-168.777 + 360.670i) q^{72} +(-428.204 - 741.671i) q^{73} +(17.2072 + 600.688i) q^{74} +(128.538 + 74.2116i) q^{75} +(-578.996 + 380.064i) q^{76} +(685.525 - 717.967i) q^{77} +(-132.857 + 246.134i) q^{78} +(-44.9579 + 77.8694i) q^{79} +(-64.0218 - 556.443i) q^{80} +(-27.9308 - 48.3776i) q^{81} +(-517.186 - 839.334i) q^{82} -199.293i q^{83} +(-152.437 - 427.956i) q^{84} +558.410i q^{85} +(-534.021 + 329.057i) q^{86} +(-126.980 - 219.936i) q^{87} +(994.430 - 694.305i) q^{88} +(-508.742 + 881.168i) q^{89} +(383.347 + 206.922i) q^{90} +(167.886 + 573.225i) q^{91} +(-562.810 - 857.395i) q^{92} +(631.306 + 364.485i) q^{93} +(-696.432 + 19.9498i) q^{94} +(378.839 + 656.168i) q^{95} +(-79.2049 - 549.361i) q^{96} +196.625 q^{97} +(-874.101 - 420.879i) q^{98} +943.274i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{4} - 20 q^{6} - 4 q^{7} - 12 q^{8} + 160 q^{9} - 14 q^{10} - 110 q^{12} + 102 q^{14} - 116 q^{15} - 104 q^{16} - 2 q^{17} - 38 q^{18} + 256 q^{20} - 360 q^{22} + 162 q^{23} + 186 q^{24} + 348 q^{25}+ \cdots - 2670 q^{98}+O(q^{100}) \) 44 * q + 4 * q^4 - 20 * q^6 - 4 * q^7 - 12 * q^8 + 160 * q^9 - 14 * q^10 - 110 * q^12 + 102 * q^14 - 116 * q^15 - 104 * q^16 - 2 * q^17 - 38 * q^18 + 256 * q^20 - 360 * q^22 + 162 * q^23 + 186 * q^24 + 348 * q^25 - 302 * q^26 - 642 * q^28 - 396 * q^30 - 374 * q^31 - 140 * q^32 - 110 * q^33 - 148 * q^34 + 1440 * q^36 + 52 * q^38 + 52 * q^39 + 658 * q^40 - 8 * q^41 - 1710 * q^42 + 374 * q^44 - 486 * q^46 - 738 * q^47 + 936 * q^48 + 356 * q^49 + 2328 * q^50 + 96 * q^52 + 944 * q^54 - 2268 * q^55 + 1848 * q^56 - 452 * q^57 + 918 * q^58 + 410 * q^60 + 1416 * q^62 + 668 * q^63 - 2984 * q^64 + 248 * q^65 + 868 * q^66 - 64 * q^68 + 3422 * q^70 + 1248 * q^71 - 2172 * q^72 - 218 * q^73 - 176 * q^74 - 3028 * q^76 - 3716 * q^78 + 298 * q^79 - 2540 * q^80 - 1050 * q^81 - 146 * q^82 - 4844 * q^84 - 2412 * q^86 + 2140 * q^87 + 1626 * q^88 + 422 * q^89 - 4916 * q^90 + 1652 * q^92 - 2676 * q^94 - 2434 * q^95 - 400 * q^96 + 1672 * q^97 - 2670 * q^98

Introduction

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