LMFDB - Embedded newform 55.3.i.d.46.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,3,Mod(6,55)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(55, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("55.6");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	55.i (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:	$1.49864145398$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 25x^{10} + 235x^{8} + 1025x^{6} + 2090x^{4} + 1880x^{2} + 605 $ x^12 + 25x^10 + 235x^8 + 1025x^6 + 2090x^4 + 1880*x^2 + 605
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			46.2
Root			$0.914937i$ of defining polynomial
Character	$\chi$	$=$	55.46
Dual form			55.3.i.d.6.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.289909 + 0.0941972i) q^{2} +(-4.17687 + 3.03467i) q^{3} +(-3.16089 - 2.29652i) q^{4} +(-0.690983 - 2.12663i) q^{5} +(-1.49677 + 0.486330i) q^{6} +(-5.94293 + 8.17974i) q^{7} +(-1.41674 - 1.94998i) q^{8} +(5.45583 - 16.7913i) q^{9} -0.681617i q^{10} +(-1.50807 + 10.8961i) q^{11} +20.1718 q^{12} +(4.61316 + 1.49891i) q^{13} +(-2.49342 + 1.81157i) q^{14} +(9.33976 + 6.78573i) q^{15} +(4.60237 + 14.1646i) q^{16} +(-2.71930 + 0.883556i) q^{17} +(3.16339 - 4.35403i) q^{18} +(-12.5616 - 17.2895i) q^{19} +(-2.69973 + 8.30890i) q^{20} -52.2005i q^{21} +(-1.46359 + 3.01683i) q^{22} -12.1155 q^{23} +(11.8351 + 3.84545i) q^{24} +(-4.04508 + 2.93893i) q^{25} +(1.19620 + 0.869094i) q^{26} +(13.8091 + 42.4999i) q^{27} +(37.5699 - 12.2072i) q^{28} +(-28.0610 + 38.6227i) q^{29} +(2.06848 + 2.84702i) q^{30} +(9.63737 - 29.6608i) q^{31} +14.1812i q^{32} +(-26.7672 - 50.0882i) q^{33} -0.871580 q^{34} +(21.5017 + 6.98633i) q^{35} +(-55.8070 + 40.5461i) q^{36} +(-16.0724 - 11.6773i) q^{37} +(-2.01309 - 6.19566i) q^{38} +(-23.8172 + 7.73869i) q^{39} +(-3.16793 + 4.36028i) q^{40} +(23.5474 + 32.4102i) q^{41} +(4.91714 - 15.1334i) q^{42} +28.7133i q^{43} +(29.7901 - 30.9782i) q^{44} -39.4788 q^{45} +(-3.51240 - 1.14125i) q^{46} +(3.18139 - 2.31141i) q^{47} +(-62.2085 - 45.1971i) q^{48} +(-16.4479 - 50.6214i) q^{49} +(-1.44955 + 0.470986i) q^{50} +(8.67687 - 11.9427i) q^{51} +(-11.1394 - 15.3321i) q^{52} +(-19.4659 + 59.9100i) q^{53} +13.6219i q^{54} +(24.2141 - 4.32195i) q^{55} +24.3699 q^{56} +(104.936 + 34.0958i) q^{57} +(-11.7733 + 8.55381i) q^{58} +(41.4758 + 30.1339i) q^{59} +(-13.9384 - 42.8979i) q^{60} +(31.6001 - 10.2675i) q^{61} +(5.58793 - 7.69112i) q^{62} +(104.925 + 144.417i) q^{63} +(17.0737 - 52.5473i) q^{64} -10.8462i q^{65} +(-3.04189 - 17.0424i) q^{66} -90.1298 q^{67} +(10.6245 + 3.45212i) q^{68} +(50.6049 - 36.7666i) q^{69} +(5.57545 + 4.05080i) q^{70} +(1.85591 + 5.71191i) q^{71} +(-40.4722 + 13.1502i) q^{72} +(76.9424 - 105.902i) q^{73} +(-3.55957 - 4.89933i) q^{74} +(7.97710 - 24.5510i) q^{75} +83.4983i q^{76} +(-80.1652 - 77.0905i) q^{77} -7.63380 q^{78} +(85.4604 + 27.7678i) q^{79} +(26.9428 - 19.5751i) q^{80} +(-58.1000 - 42.2121i) q^{81} +(3.77365 + 11.6141i) q^{82} +(-84.0686 + 27.3155i) q^{83} +(-119.880 + 165.000i) q^{84} +(3.75799 + 5.17242i) q^{85} +(-2.70472 + 8.32426i) q^{86} -246.478i q^{87} +(23.3837 - 12.4963i) q^{88} -118.531 q^{89} +(-11.4453 - 3.71879i) q^{90} +(-39.6764 + 28.8266i) q^{91} +(38.2959 + 27.8236i) q^{92} +(49.7567 + 153.135i) q^{93} +(1.14004 - 0.370422i) q^{94} +(-28.0885 + 38.6606i) q^{95} +(-43.0353 - 59.2330i) q^{96} +(-20.6501 + 63.5544i) q^{97} -16.2250i q^{98} +(174.733 + 84.7699i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 5 q^{2} - 13 q^{3} + 13 q^{4} - 15 q^{5} + 20 q^{6} - 5 q^{7} - 35 q^{8} + 4 q^{9} + 12 q^{11} - 2 q^{12} + 70 q^{13} - 60 q^{14} + 35 q^{15} - 43 q^{16} - 15 q^{17} - 30 q^{18} - 80 q^{19} + 20 q^{20}+ \cdots + 669 q^{99}+O(q^{100}) $ 12 * q + 5 * q^2 - 13 * q^3 + 13 * q^4 - 15 * q^5 + 20 * q^6 - 5 * q^7 - 35 * q^8 + 4 * q^9 + 12 * q^11 - 2 * q^12 + 70 * q^13 - 60 * q^14 + 35 * q^15 - 43 * q^16 - 15 * q^17 - 30 * q^18 - 80 * q^19 + 20 * q^20 - 10 * q^22 + 42 * q^23 + 210 * q^24 - 15 * q^25 - 120 * q^26 - 109 * q^27 + 140 * q^28 + 5 * q^29 - 20 * q^30 - 46 * q^31 + 42 * q^33 + 10 * q^34 + 20 * q^35 - 39 * q^36 - 42 * q^37 - 130 * q^38 - 285 * q^39 - 25 * q^40 + 230 * q^41 + 135 * q^42 + 488 * q^44 - 50 * q^45 + 205 * q^46 + 58 * q^47 - 323 * q^48 - 212 * q^49 - 25 * q^50 + 360 * q^51 + 410 * q^52 - 43 * q^53 - 80 * q^55 - 410 * q^56 + 270 * q^57 - 450 * q^58 - 74 * q^59 - 25 * q^60 - 290 * q^61 - 350 * q^62 + 295 * q^63 - 7 * q^64 + 185 * q^66 - 212 * q^67 + 55 * q^68 - 73 * q^69 + 160 * q^70 - 276 * q^71 - 555 * q^72 + 645 * q^73 - 100 * q^74 + 10 * q^75 - 140 * q^77 + 360 * q^78 + 235 * q^79 + 140 * q^80 - 30 * q^81 + 215 * q^82 + 60 * q^83 - 580 * q^84 + 65 * q^85 - 480 * q^86 - 165 * q^88 - 114 * q^89 + 145 * q^90 + 160 * q^91 + 33 * q^92 + 129 * q^93 + 375 * q^94 + 50 * q^95 + 265 * q^96 + 63 * q^97 + 669 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.289909	+	0.0941972i	0.144955	+	0.0470986i	0.380596	−	0.924742i	$-0.375719\pi$
$2$	0.289909	+	0.0941972i	0.144955	+	0.0470986i	−0.235641	+	0.971840i	$0.575719\pi$
$3$	−4.17687	+	3.03467i	−1.39229	+	1.01156i	−0.396679	+	0.917957i	$0.629837\pi$
$3$	−4.17687	+	3.03467i	−1.39229	+	1.01156i	−0.995610	+	0.0935994i	$0.970163\pi$
$4$	−3.16089	−	2.29652i	−0.790223	−	0.574131i
$5$	−0.690983	−	2.12663i	−0.138197	−	0.425325i
$5$	−0.690983	−	2.12663i	−0.138197	−	0.425325i
$6$	−1.49677	+	0.486330i	−0.249462	+	0.0810550i
$7$	−5.94293	+	8.17974i	−0.848990	+	1.16853i	0.135095	+	0.990833i	$0.456866\pi$
$7$	−5.94293	+	8.17974i	−0.848990	+	1.16853i	−0.984084	+	0.177701i	$0.943134\pi$
$8$	−1.41674	−	1.94998i	−0.177093	−	0.243747i
$9$	5.45583	−	16.7913i	0.606203	−	1.86570i
$10$		−	0.681617i		−	0.0681617i
$11$	−1.50807	+	10.8961i	−0.137097	+	0.990558i
$11$	−1.50807	+	10.8961i	−0.137097	+	0.990558i
$12$	20.1718			1.68099
$13$	4.61316	+	1.49891i	0.354859	+	0.115301i	0.481021	−	0.876709i	$-0.340266\pi$
$13$	4.61316	+	1.49891i	0.354859	+	0.115301i	−0.126162	+	0.992010i	$0.540266\pi$
$14$	−2.49342	+	1.81157i	−0.178101	+	0.129398i
$15$	9.33976	+	6.78573i	0.622650	+	0.452382i
$16$	4.60237	+	14.1646i	0.287648	+	0.885290i
$17$	−2.71930	+	0.883556i	−0.159959	+	0.0519739i	−0.387902	−	0.921701i	$-0.626800\pi$
$17$	−2.71930	+	0.883556i	−0.159959	+	0.0519739i	0.227943	+	0.973675i	$0.426800\pi$
$18$	3.16339	−	4.35403i	0.175744	−	0.241891i
$19$	−12.5616	−	17.2895i	−0.661136	−	0.909975i	0.338383	−	0.941009i	$-0.390120\pi$
$19$	−12.5616	−	17.2895i	−0.661136	−	0.909975i	−0.999518	+	0.0310333i	$0.990120\pi$
$20$	−2.69973	+	8.30890i	−0.134986	+	0.415445i
$21$		−	52.2005i		−	2.48574i
$22$	−1.46359	+	3.01683i	−0.0665267	+	0.137129i
$23$	−12.1155			−0.526762			−0.263381	−	0.964692i	$-0.584838\pi$
$23$	−12.1155			−0.526762			−0.263381	+	0.964692i	$0.584838\pi$
$24$	11.8351	+	3.84545i	0.493128	+	0.160227i
$25$	−4.04508	+	2.93893i	−0.161803	+	0.117557i
$26$	1.19620	+	0.869094i	0.0460079	+	0.0334267i
$27$	13.8091	+	42.4999i	0.511447	+	1.57407i
$28$	37.5699	−	12.2072i	1.34178	−	0.435972i
$29$	−28.0610	+	38.6227i	−0.967622	+	1.33182i	−0.0243833	+	0.999703i	$0.507762\pi$
$29$	−28.0610	+	38.6227i	−0.967622	+	1.33182i	−0.943239	+	0.332115i	$0.892238\pi$
$30$	2.06848	+	2.84702i	0.0689495	+	0.0949008i
$31$	9.63737	−	29.6608i	0.310883	−	0.956800i	−0.666533	−	0.745476i	$-0.732222\pi$
$31$	9.63737	−	29.6608i	0.310883	−	0.956800i	0.977416	−	0.211324i	$-0.0677776\pi$
$32$			14.1812i			0.443163i
$33$	−26.7672	−	50.0882i	−0.811127	−	1.51782i
$34$	−0.871580			−0.0256347
$35$	21.5017	+	6.98633i	0.614335	+	0.199609i
$36$	−55.8070	+	40.5461i	−1.55019	+	1.12628i
$37$	−16.0724	−	11.6773i	−0.434389	−	0.315602i	0.349012	−	0.937118i	$-0.386517\pi$
$37$	−16.0724	−	11.6773i	−0.434389	−	0.315602i	−0.783402	+	0.621516i	$0.786517\pi$
$38$	−2.01309	−	6.19566i	−0.0529761	−	0.163044i
$39$	−23.8172	+	7.73869i	−0.610699	+	0.198428i
$40$	−3.16793	+	4.36028i	−0.0791982	+	0.109007i
$41$	23.5474	+	32.4102i	0.574326	+	0.790493i	0.993059	−	0.117617i	$-0.0375255\pi$
$41$	23.5474	+	32.4102i	0.574326	+	0.790493i	−0.418733	+	0.908110i	$0.637526\pi$
$42$	4.91714	−	15.1334i	0.117075	−	0.360319i
$43$			28.7133i			0.667752i	0.942617	+	0.333876i	$0.108357\pi$
$43$			28.7133i			0.667752i	−0.942617	+	0.333876i	$0.891643\pi$
$44$	29.7901	−	30.9782i	0.677047	−	0.704050i
$45$	−39.4788			−0.877306
$46$	−3.51240	−	1.14125i	−0.0763566	−	0.0248098i
$47$	3.18139	−	2.31141i	0.0676891	−	0.0491790i	−0.553426	−	0.832898i	$-0.686680\pi$
$47$	3.18139	−	2.31141i	0.0676891	−	0.0491790i	0.621115	+	0.783719i	$0.286680\pi$
$48$	−62.2085	−	45.1971i	−1.29601	−	0.941607i
$49$	−16.4479	−	50.6214i	−0.335671	−	1.03309i
$50$	−1.44955	+	0.470986i	−0.0289909	+	0.00941972i
$51$	8.67687	−	11.9427i	0.170135	−	0.234170i
$52$	−11.1394	−	15.3321i	−0.214220	−	0.294848i
$53$	−19.4659	+	59.9100i	−0.367282	+	1.13038i	0.581258	+	0.813719i	$0.302561\pi$
$53$	−19.4659	+	59.9100i	−0.367282	+	1.13038i	−0.948540	+	0.316658i	$0.897439\pi$
$54$			13.6219i			0.252257i
$55$	24.2141	−	4.32195i	0.440256	−	0.0785809i
$56$	24.3699			0.435177
$57$	104.936	+	34.0958i	1.84098	+	0.598172i
$58$	−11.7733	+	8.55381i	−0.202988	+	0.147479i
$59$	41.4758	+	30.1339i	0.702979	+	0.510744i	0.880901	−	0.473300i	$-0.156937\pi$
$59$	41.4758	+	30.1339i	0.702979	+	0.510744i	−0.177922	+	0.984045i	$0.556937\pi$
$60$	−13.9384	−	42.8979i	−0.232306	−	0.714966i
$61$	31.6001	−	10.2675i	0.518035	−	0.168320i	−0.0383184	−	0.999266i	$-0.512200\pi$
$61$	31.6001	−	10.2675i	0.518035	−	0.168320i	0.556353	+	0.830946i	$0.312200\pi$
$62$	5.58793	−	7.69112i	0.0901279	−	0.124050i
$63$	104.925	+	144.417i	1.66548	+	2.29233i
$64$	17.0737	−	52.5473i	0.266776	−	0.821052i
$65$		−	10.8462i		−	0.166865i
$66$	−3.04189	−	17.0424i	−0.0460892	−	0.258218i
$67$	−90.1298			−1.34522			−0.672611	−	0.739997i	$-0.734827\pi$
$67$	−90.1298			−1.34522			−0.672611	+	0.739997i	$0.734827\pi$
$68$	10.6245	+	3.45212i	0.156243	+	0.0507665i
$69$	50.6049	−	36.7666i	0.733405	−	0.532850i
$70$	5.57545	+	4.05080i	0.0796493	+	0.0578686i
$71$	1.85591	+	5.71191i	0.0261396	+	0.0804494i	0.963275	−	0.268516i	$-0.0865331\pi$
$71$	1.85591	+	5.71191i	0.0261396	+	0.0804494i	−0.937136	+	0.348965i	$0.886533\pi$
$72$	−40.4722	+	13.1502i	−0.562114	+	0.182642i
$73$	76.9424	−	105.902i	1.05401	−	1.45071i	0.168722	−	0.985664i	$-0.446036\pi$
$73$	76.9424	−	105.902i	1.05401	−	1.45071i	0.885284	−	0.465051i	$-0.153964\pi$
$74$	−3.55957	−	4.89933i	−0.0481023	−	0.0662072i
$75$	7.97710	−	24.5510i	0.106361	−	0.327347i
$76$			83.4983i			1.09866i
$77$	−80.1652	−	77.0905i	−1.04111	−	1.00118i
$78$	−7.63380			−0.0978693
$79$	85.4604	+	27.7678i	1.08178	+	0.351491i	0.795064	−	0.606525i	$-0.207437\pi$
$79$	85.4604	+	27.7678i	1.08178	+	0.351491i	0.286714	+	0.958016i	$0.407437\pi$
$80$	26.9428	−	19.5751i	0.336784	−	0.244688i
$81$	−58.1000	−	42.2121i	−0.717284	−	0.521137i
$82$	3.77365	+	11.6141i	0.0460202	+	0.141636i
$83$	−84.0686	+	27.3155i	−1.01287	+	0.329103i	−0.767999	−	0.640451i	$-0.778747\pi$
$83$	−84.0686	+	27.3155i	−1.01287	+	0.329103i	−0.244876	+	0.969554i	$0.578747\pi$
$84$	−119.880	+	165.000i	−1.42714	+	1.96429i
$85$	3.75799	+	5.17242i	0.0442116	+	0.0608521i
$86$	−2.70472	+	8.32426i	−0.0314502	+	0.0967937i
$87$		−	246.478i		−	2.83308i
$88$	23.3837	−	12.4963i	0.265724	−	0.142003i
$89$	−118.531			−1.33180			−0.665902	−	0.746039i	$-0.731953\pi$
$89$	−118.531			−1.33180			−0.665902	+	0.746039i	$0.731953\pi$
$90$	−11.4453	−	3.71879i	−0.127169	−	0.0413199i
$91$	−39.6764	+	28.8266i	−0.436004	+	0.316775i
$92$	38.2959	+	27.8236i	0.416260	+	0.302430i
$93$	49.7567	+	153.135i	0.535018	+	1.64662i
$94$	1.14004	−	0.370422i	0.0121281	−	0.00394066i
$95$	−28.0885	+	38.6606i	−0.295669	+	0.406953i
$96$	−43.0353	−	59.2330i	−0.448284	−	0.617010i
$97$	−20.6501	+	63.5544i	−0.212887	+	0.655200i	0.786410	+	0.617705i	$0.211938\pi$
$97$	−20.6501	+	63.5544i	−0.212887	+	0.655200i	−0.999297	+	0.0374942i	$0.988062\pi$
$98$		−	16.2250i		−	0.165561i
$99$	174.733	+	84.7699i	1.76498	+	0.856262i
$100$	19.5354			0.195354
$101$	12.3073	+	3.99890i	0.121855	+	0.0395931i	0.369310	−	0.929306i	$-0.379594\pi$
$101$	12.3073	+	3.99890i	0.121855	+	0.0395931i	−0.247455	+	0.968899i	$0.579594\pi$
$102$	3.64047	−	2.64496i	0.0356909	−	0.0259310i
$103$	−91.4263	−	66.4251i	−0.887634	−	0.644904i	0.0476260	−	0.998865i	$-0.484834\pi$
$103$	−91.4263	−	66.4251i	−0.887634	−	0.644904i	−0.935260	+	0.353961i	$0.884834\pi$
$104$	−3.61282	−	11.1191i	−0.0347387	−	0.106915i
$105$	−111.011	+	36.0697i	−1.05725	+	0.343521i
$106$	−11.2867	+	15.5348i	−0.106478	+	0.146555i
$107$	−9.42241	−	12.9688i	−0.0880599	−	0.121204i	0.762714	−	0.646736i	$-0.223866\pi$
$107$	−9.42241	−	12.9688i	−0.0880599	−	0.121204i	−0.850774	+	0.525532i	$0.823866\pi$
$108$	53.9531	−	166.051i	0.499566	−	1.53751i
$109$			156.813i			1.43865i	0.694671	+	0.719327i	$0.255550\pi$
$109$			156.813i			1.43865i	−0.694671	+	0.719327i	$0.744450\pi$
$110$	7.42699	+	1.02792i	0.0675181	+	0.00934477i
$111$	102.569			0.924045
$112$	−143.215	−	46.5333i	−1.27870	−	0.415476i
$113$	−25.8896	+	18.8099i	−0.229112	+	0.166459i	−0.696419	−	0.717636i	$-0.745224\pi$
$113$	−25.8896	+	18.8099i	−0.229112	+	0.166459i	0.467307	+	0.884095i	$0.345224\pi$
$114$	27.2102	+	19.7694i	0.238686	+	0.173416i
$115$	8.37162	+	25.7652i	0.0727967	+	0.224045i
$116$	177.396	−	57.6394i	1.52928	−	0.496892i
$117$	50.3372	−	69.2833i	0.430233	−	0.592165i
$118$	9.18568	+	12.6430i	0.0778447	+	0.107144i
$119$	8.93338	−	27.4941i	0.0750704	−	0.231043i
$120$		−	27.8259i		−	0.231883i
$121$	−116.451	−	32.8642i	−0.962409	−	0.271605i
$122$	10.1283			0.0830192
$123$	−196.709	−	63.9145i	−1.59926	−	0.519630i
$124$	−98.5794	+	71.6221i	−0.794995	+	0.577598i
$125$	9.04508	+	6.57164i	0.0723607	+	0.0525731i
$126$	16.8151	+	51.7514i	0.133453	+	0.410726i
$127$	102.574	−	33.3284i	0.807671	−	0.262428i	0.124060	−	0.992275i	$-0.460408\pi$
$127$	102.574	−	33.3284i	0.807671	−	0.262428i	0.683611	+	0.729846i	$0.260408\pi$
$128$	43.2416	−	59.5170i	0.337825	−	0.464977i
$129$	−87.1355	−	119.932i	−0.675469	−	0.929703i
$130$	1.02168	−	3.14441i	0.00785908	−	0.0241878i
$131$			48.6741i			0.371558i	0.982592	+	0.185779i	$0.0594808\pi$
$131$			48.6741i			0.371558i	−0.982592	+	0.185779i	$0.940519\pi$
$132$	−30.4205	+	219.795i	−0.230458	+	1.66511i
$133$	216.076			1.62463
$134$	−26.1295	−	8.48998i	−0.194996	−	0.0633580i
$135$	80.8397	−	58.7335i	0.598812	−	0.435063i
$136$	5.57546	+	4.05081i	0.0409961	+	0.0297854i
$137$	−23.2157	−	71.4507i	−0.169458	−	0.521538i	0.829879	−	0.557943i	$-0.188409\pi$
$137$	−23.2157	−	71.4507i	−0.169458	−	0.521538i	−0.999337	+	0.0364052i	$0.988409\pi$
$138$	18.1341	−	5.89214i	0.131407	−	0.0426967i
$139$	−28.3745	+	39.0542i	−0.204133	+	0.280965i	−0.898793	−	0.438373i	$-0.855555\pi$
$139$	−28.3745	+	39.0542i	−0.204133	+	0.280965i	0.694660	+	0.719338i	$0.255555\pi$
$140$	−51.9204	−	71.4623i	−0.370860	−	0.510445i
$141$	−6.27385	+	19.3089i	−0.0444954	+	0.136943i
$142$			1.83076i			0.0128926i
$143$	−23.2892	+	48.0052i	−0.162862	+	0.335700i
$144$	262.953			1.82606
$145$	101.526	+	32.9877i	0.700178	+	0.227502i
$146$	32.2820	−	23.4542i	0.221110	−	0.160646i
$147$	222.320	+	161.525i	1.51238	+	1.09881i
$148$	23.9860	+	73.8213i	0.162068	+	0.498793i
$149$	114.600	−	37.2357i	0.769126	−	0.249904i	0.101935	−	0.994791i	$-0.467497\pi$
$149$	114.600	−	37.2357i	0.769126	−	0.249904i	0.667191	+	0.744887i	$0.267497\pi$
$150$	4.62527	−	6.36614i	0.0308351	−	0.0424409i
$151$	−45.4102	−	62.5018i	−0.300730	−	0.413919i	0.631733	−	0.775186i	$-0.282344\pi$
$151$	−45.4102	−	62.5018i	−0.300730	−	0.413919i	−0.932462	+	0.361268i	$0.882344\pi$
$152$	−15.9177	+	48.9896i	−0.104722	+	0.322300i
$153$			50.4812i			0.329943i
$154$	−15.9789	−	29.9006i	−0.103759	−	0.194160i
$155$	−69.7367			−0.449914
$156$	93.0559	+	30.2357i	0.596512	+	0.193819i
$157$	−43.8515	+	31.8599i	−0.279309	+	0.202930i	−0.718616	−	0.695407i	$-0.755224\pi$
$157$	−43.8515	+	31.8599i	−0.279309	+	0.202930i	0.439307	+	0.898337i	$0.355224\pi$
$158$	22.1601	+	16.1003i	0.140254	+	0.101900i
$159$	−100.501	−	309.309i	−0.632079	−	1.94534i
$160$	30.1581	−	9.79897i	0.188488	−	0.0612436i
$161$	72.0017	−	99.1018i	0.447215	−	0.615539i
$162$	−12.8675	−	17.7105i	−0.0794287	−	0.109324i
$163$	−62.7761	+	193.205i	−0.385129	+	1.18531i	0.551257	+	0.834336i	$0.314148\pi$
$163$	−62.7761	+	193.205i	−0.385129	+	1.18531i	−0.936386	+	0.350971i	$0.885852\pi$
$164$		−	156.522i		−	0.954404i
$165$	−88.0232	+	91.5339i	−0.533474	+	0.554751i
$166$	−26.9453			−0.162321
$167$	126.214	+	41.0093i	0.755771	+	0.245565i	0.661462	−	0.749978i	$-0.269936\pi$
$167$	126.214	+	41.0093i	0.755771	+	0.245565i	0.0943081	+	0.995543i	$0.469936\pi$
$168$	−101.790	+	73.9546i	−0.605891	+	0.440206i
$169$	−117.689	−	85.5063i	−0.696387	−	0.505954i
$170$	0.602247	+	1.85353i	0.00354263	+	0.0109031i
$171$	−358.848	+	116.597i	−2.09853	+	0.681852i
$172$	65.9408	−	90.7598i	0.383377	−	0.527673i
$173$	−65.7416	−	90.4855i	−0.380009	−	0.523037i	0.575578	−	0.817747i	$-0.304777\pi$
$173$	−65.7416	−	90.4855i	−0.380009	−	0.523037i	−0.955587	+	0.294709i	$0.904777\pi$
$174$	23.2175	−	71.4562i	0.133434	−	0.410668i
$175$		−	50.5536i		−	0.288878i
$176$	−161.281	+	28.7868i	−0.916367	+	0.163562i
$177$	−264.685			−1.49540
$178$	−34.3631	−	11.1652i	−0.193051	−	0.0627261i
$179$	38.7619	−	28.1621i	0.216547	−	0.157330i	−0.474224	−	0.880404i	$-0.657271\pi$
$179$	38.7619	−	28.1621i	0.216547	−	0.157330i	0.690771	+	0.723074i	$0.257271\pi$
$180$	124.788	+	90.6639i	0.693268	+	0.503688i
$181$	2.09873	+	6.45923i	0.0115952	+	0.0356864i	0.956687	−	0.291119i	$-0.0940277\pi$
$181$	2.09873	+	6.45923i	0.0115952	+	0.0356864i	−0.945092	+	0.326806i	$0.894028\pi$
$182$	−14.2179	+	4.61968i	−0.0781204	+	0.0253829i
$183$	−100.831	+	138.782i	−0.550989	+	0.758371i
$184$	17.1646	+	23.6250i	0.0932857	+	0.128397i
$185$	−13.7275	+	42.2488i	−0.0742026	+	0.228372i
$186$			49.0823i			0.263883i
$187$	−5.52645	−	30.9624i	−0.0295532	−	0.165574i
$188$	−15.3642			−0.0817246
$189$	−429.705	−	139.619i	−2.27357	−	0.738728i
$190$	−11.7848	+	8.56219i	−0.0620255	+	0.0450642i
$191$	60.7195	+	44.1153i	0.317903	+	0.230970i	0.735280	−	0.677763i	$-0.237051\pi$
$191$	60.7195	+	44.1153i	0.317903	+	0.230970i	−0.417377	+	0.908733i	$0.637051\pi$
$192$	88.1494	+	271.296i	0.459112	+	1.41300i
$193$	360.857	−	117.250i	1.86973	−	0.607511i	0.878081	−	0.478513i	$-0.158824\pi$
$193$	360.857	−	117.250i	1.86973	−	0.607511i	0.991645	−	0.128998i	$-0.0411761\pi$
$194$	−11.9733	+	16.4798i	−0.0617180	+	0.0849475i
$195$	32.9146	+	45.3031i	0.168793	+	0.232324i
$196$	−64.2633	+	197.782i	−0.327874	+	1.00909i
$197$			91.4898i			0.464415i	0.972666	+	0.232208i	$0.0745949\pi$
$197$			91.4898i			0.464415i	−0.972666	+	0.232208i	$0.925405\pi$
$198$	42.6715	+	41.0349i	0.215513	+	0.207247i
$199$	24.0213			0.120710			0.0603551	−	0.998177i	$-0.480777\pi$
$199$	24.0213			0.120710			0.0603551	+	0.998177i	$0.480777\pi$
$200$	11.4617	+	3.72412i	0.0573084	+	0.0186206i
$201$	376.460	−	273.514i	1.87294	−	1.36077i
$202$	3.19133	+	2.31864i	0.0157987	+	0.0114784i
$203$	−149.159	−	459.064i	−0.734773	−	2.26140i
$204$	−54.8533	+	17.8229i	−0.268889	+	0.0873673i
$205$	52.6536	−	72.4714i	0.256847	−	0.353519i
$206$	−20.2483	−	27.8693i	−0.0982926	−	0.135288i
$207$	−66.1002	+	203.436i	−0.319325	+	0.982781i
$208$			72.2423i			0.347319i
$209$	207.333	−	110.799i	0.992023	−	0.530138i
$210$	−35.5808			−0.169432
$211$	−349.688	−	113.620i	−1.65729	−	0.538486i	−0.676987	−	0.735995i	$-0.736715\pi$
$211$	−349.688	−	113.620i	−1.65729	−	0.538486i	−0.980301	+	0.197509i	$0.936715\pi$
$212$	199.115	−	144.665i	0.939219	−	0.682383i
$213$	−25.0856	−	18.2258i	−0.117773	−	0.0855671i
$214$	−1.51002	−	4.64735i	−0.00705615	−	0.0217166i
$215$	61.0625	−	19.8404i	0.284012	−	0.0922810i
$216$	63.3100	−	87.1387i	0.293102	−	0.403420i
$217$	185.343	+	255.103i	0.854117	+	1.17559i
$218$	−14.7714	+	45.4616i	−0.0677586	+	0.208540i
$219$			675.834i			3.08600i
$220$	−86.4635	−	41.9470i	−0.393016	−	0.190668i
$221$	−13.8690			−0.0627555
$222$	29.7357	+	9.66172i	0.133945	+	0.0435212i
$223$	143.396	−	104.183i	0.643032	−	0.467190i	−0.217858	−	0.975980i	$-0.569907\pi$
$223$	143.396	−	104.183i	0.643032	−	0.467190i	0.860891	+	0.508790i	$0.169907\pi$
$224$	−115.999	−	84.2779i	−0.517851	−	0.376241i
$225$	27.2792	+	83.9566i	0.121241	+	0.373140i
$226$	−9.27747	+	3.01443i	−0.0410508	+	0.0133382i
$227$	10.8732	−	14.9656i	0.0478994	−	0.0659279i	−0.784395	−	0.620261i	$-0.787027\pi$
$227$	10.8732	−	14.9656i	0.0478994	−	0.0659279i	0.832295	+	0.554333i	$0.187027\pi$
$228$	−253.390	−	348.761i	−1.11136	−	1.52966i
$229$	−41.3284	+	127.196i	−0.180473	+	0.555440i	−0.999841	−	0.0178283i	$-0.994325\pi$
$229$	−41.3284	+	127.196i	−0.180473	+	0.555440i	0.819368	+	0.573268i	$0.194325\pi$
$230$			8.25815i			0.0359050i
$231$	568.784	+	78.7219i	2.46227	+	0.340787i
$232$	115.069			0.495985
$233$	−41.8780	−	13.6070i	−0.179734	−	0.0583991i	0.217767	−	0.976001i	$-0.430123\pi$
$233$	−41.8780	−	13.6070i	−0.179734	−	0.0583991i	−0.397501	+	0.917602i	$0.630123\pi$
$234$	21.1195	−	15.3442i	0.0902544	−	0.0655736i
$235$	−7.11379	−	5.16847i	−0.0302715	−	0.0219935i
$236$	−61.8973	−	190.500i	−0.262277	−	0.807204i
$237$	−441.223	+	143.362i	−1.86170	+	0.604903i
$238$	5.17974	−	7.12930i	0.0217636	−	0.0299550i
$239$	97.2433	+	133.844i	0.406876	+	0.560017i	0.962453	−	0.271448i	$-0.0875026\pi$
$239$	97.2433	+	133.844i	0.406876	+	0.560017i	−0.555577	+	0.831465i	$0.687503\pi$
$240$	−53.1324	+	163.525i	−0.221385	+	0.681353i
$241$		−	68.3979i		−	0.283809i	−0.989880	−	0.141904i	$-0.954677\pi$
$241$		−	68.3979i		−	0.283809i	0.989880	−	0.141904i	$-0.0453225\pi$
$242$	−30.6646	−	20.4970i	−0.126713	−	0.0846985i
$243$	−31.4080			−0.129251
$244$	−123.464	−	40.1160i	−0.506001	−	0.164410i
$245$	−96.2877	+	69.9571i	−0.393011	+	0.285539i
$246$	−51.0071	−	37.0588i	−0.207346	−	0.150645i
$247$	−32.0332	−	98.5880i	−0.129689	−	0.399142i
$248$	−71.4915	+	23.2290i	−0.288272	+	0.0936653i
$249$	268.250	−	369.214i	1.07731	−	1.48279i
$250$	2.00322	+	2.75720i	0.00801289	+	0.0110288i
$251$	104.767	−	322.440i	0.417399	−	1.28462i	−0.492688	−	0.870206i	$-0.663986\pi$
$251$	104.767	−	322.440i	0.417399	−	1.28462i	0.910087	−	0.414417i	$-0.136014\pi$
$252$		−	697.449i		−	2.76766i
$253$	18.2710	−	132.012i	0.0722175	−	0.521788i
$254$	32.8767			0.129436
$255$	−31.3932	−	10.2003i	−0.123111	−	0.0400011i
$256$	−160.655	+	116.723i	−0.627559	+	0.455949i
$257$	203.807	+	148.075i	0.793025	+	0.576167i	0.908860	−	0.417102i	$-0.136954\pi$
$257$	203.807	+	148.075i	0.793025	+	0.576167i	−0.115835	+	0.993269i	$0.536954\pi$
$258$	−13.9641	−	42.9772i	−0.0541246	−	0.166578i
$259$	191.034	−	62.0708i	0.737584	−	0.239656i
$260$	−24.9085	+	34.2837i	−0.0958021	+	0.131860i
$261$	495.430	+	681.901i	1.89820	+	2.61265i
$262$	−4.58496	+	14.1111i	−0.0174999	+	0.0538590i
$263$			424.803i			1.61522i	0.589717	+	0.807610i	$0.299239\pi$
$263$			424.803i			1.61522i	−0.589717	+	0.807610i	$0.700761\pi$
$264$	−59.7486	+	123.157i	−0.226320	+	0.466505i
$265$	140.857			0.531535
$266$	62.6425	+	20.3538i	0.235498	+	0.0765180i
$267$	495.086	−	359.701i	1.85426	−	1.34720i
$268$	284.891	+	206.985i	1.06303	+	0.772333i
$269$	154.300	+	474.888i	0.573608	+	1.76538i	0.640872	+	0.767648i	$0.278573\pi$
$269$	154.300	+	474.888i	0.573608	+	1.76538i	−0.0672640	+	0.997735i	$0.521427\pi$
$270$	28.9687	−	9.41250i	0.107291	−	0.0348611i
$271$	−138.031	+	189.983i	−0.509339	+	0.701045i	−0.983808	−	0.179227i	$-0.942640\pi$
$271$	−138.031	+	189.983i	−0.509339	+	0.701045i	0.474468	+	0.880273i	$0.342640\pi$
$272$	−25.0305	−	34.4515i	−0.0920239	−	0.126660i
$273$	78.2437	−	240.809i	0.286607	−	0.882086i
$274$		−	22.9011i		−	0.0835806i
$275$	−25.9227	−	48.5079i	−0.0942643	−	0.176392i
$276$	−244.392			−0.885479
$277$	129.339	+	42.0248i	0.466928	+	0.151714i	0.533026	−	0.846099i	$-0.321055\pi$
$277$	129.339	+	42.0248i	0.466928	+	0.151714i	−0.0660976	+	0.997813i	$0.521055\pi$
$278$	−11.9048	+	8.64937i	−0.0428232	+	0.0311128i
$279$	−445.464	−	323.648i	−1.59664	−	1.16003i
$280$	−16.8392	−	51.8257i	−0.0601399	−	0.185092i
$281$	−287.964	+	93.5652i	−1.02478	+	0.332972i	−0.772726	−	0.634740i	$-0.781107\pi$
$281$	−287.964	+	93.5652i	−1.02478	+	0.332972i	−0.252057	+	0.967712i	$0.581107\pi$
$282$	−3.63769	+	5.00685i	−0.0128996	+	0.0177548i
$283$	−6.25933	−	8.61523i	−0.0221178	−	0.0304425i	0.797815	−	0.602902i	$-0.205989\pi$
$283$	−6.25933	−	8.61523i	−0.0221178	−	0.0304425i	−0.819933	+	0.572460i	$0.805989\pi$
$284$	7.25119	−	22.3169i	0.0255324	−	0.0785805i
$285$		−	246.720i		−	0.865683i
$286$	−11.2737	+	11.7234i	−0.0394186	+	0.0409908i
$287$	−405.047			−1.41131
$288$	238.121	+	77.3703i	0.826810	+	0.268647i
$289$	−227.192	+	165.065i	−0.786131	+	0.571158i
$290$	26.3259	+	19.1269i	0.0907790	+	0.0659548i
$291$	−106.614	−	328.124i	−0.366371	−	1.12757i
$292$	−486.414	+	158.045i	−1.66580	+	0.541251i
$293$	−193.994	+	267.010i	−0.662095	+	0.911296i	−0.999549	−	0.0300463i	$-0.990435\pi$
$293$	−193.994	+	267.010i	−0.662095	+	0.911296i	0.337453	+	0.941342i	$0.390435\pi$
$294$	49.2374	+	67.7695i	0.167474	+	0.230509i
$295$	35.4245	−	109.026i	0.120083	−	0.369578i
$296$			47.8845i			0.161772i
$297$	−483.910	+	86.3727i	−1.62933	+	0.290817i
$298$	36.7310			0.123259
$299$	−55.8909	−	18.1600i	−0.186926	−	0.0607359i
$300$	−81.5967	+	59.2835i	−0.271989	+	0.197612i
$301$	−234.868	−	170.641i	−0.780291	−	0.566914i
$302$	−7.27734	−	22.3973i	−0.0240971	−	0.0741634i
$303$	−63.5415	+	20.6459i	−0.209708	+	0.0681382i
$304$	187.087	−	257.503i	0.615418	−	0.847050i
$305$	−43.6703	−	60.1070i	−0.143181	−	0.197072i
$306$	−4.75519	+	14.6350i	−0.0155398	+	0.0478267i
$307$		−	111.473i		−	0.363104i	−0.983381	−	0.181552i	$-0.941888\pi$
$307$		−	111.473i		−	0.363104i	0.983381	−	0.181552i	$-0.0581121\pi$
$308$	76.3534	+	427.776i	0.247901	+	1.38888i
$309$	583.454			1.88820
$310$	−20.2173	−	6.56900i	−0.0652171	−	0.0211903i
$311$	−327.747	+	238.122i	−1.05385	+	0.765665i	−0.972940	−	0.231057i	$-0.925782\pi$
$311$	−327.747	+	238.122i	−1.05385	+	0.765665i	−0.0809071	+	0.996722i	$0.525782\pi$
$312$	48.8331	+	35.4794i	0.156516	+	0.113716i
$313$	52.4582	+	161.450i	0.167598	+	0.515814i	0.999218	−	0.0395307i	$-0.0125863\pi$
$313$	52.4582	+	161.450i	0.167598	+	0.515814i	−0.831620	+	0.555345i	$0.812586\pi$
$314$	−15.7141	+	5.10581i	−0.0500448	+	0.0162605i
$315$	234.619	−	322.926i	0.744824	−	1.02516i
$316$	−206.362	−	284.033i	−0.653044	−	0.898838i
$317$	−119.372	+	367.389i	−0.376567	+	1.15895i	0.565848	+	0.824510i	$0.308549\pi$
$317$	−119.372	+	367.389i	−0.376567	+	1.15895i	−0.942415	+	0.334445i	$0.891451\pi$
$318$		−	99.1383i		−	0.311756i
$319$	−378.520	−	364.003i	−1.18658	−	1.14107i
$320$	−123.546			−0.386082
$321$	78.7123	+	25.5752i	0.245210	+	0.0796735i
$322$	30.2091	−	21.9482i	0.0938170	−	0.0681620i
$323$	49.4350	+	35.9167i	0.153050	+	0.111197i
$324$	86.7068	+	266.856i	0.267613	+	0.823630i
$325$	−23.0658	+	7.49453i	−0.0709717	+	0.0230601i
$326$	−36.3987	+	50.0986i	−0.111653	+	0.153677i
$327$	−475.877	−	654.988i	−1.45528	−	2.00302i
$328$	29.8386	−	91.8337i	0.0909713	−	0.279981i
$329$			39.7595i			0.120849i
$330$	−34.1410	+	18.2450i	−0.103457	+	0.0552878i
$331$	118.966			0.359413			0.179706	−	0.983720i	$-0.442485\pi$
$331$	118.966			0.359413			0.179706	+	0.983720i	$0.442485\pi$
$332$	328.463	+	106.724i	0.989346	+	0.321458i
$333$	−283.765	+	206.168i	−0.852148	+	0.619122i
$334$	32.7275	+	23.7780i	0.0979867	+	0.0711915i
$335$	62.2782	+	191.672i	0.185905	+	0.572157i
$336$	739.402	−	240.246i	2.20060	−	0.715018i
$337$	260.717	−	358.847i	0.773642	−	1.06483i	−0.222313	−	0.974975i	$-0.571361\pi$
$337$	260.717	−	358.847i	0.773642	−	1.06483i	0.995955	−	0.0898516i	$-0.0286393\pi$
$338$	−26.0648	−	35.8751i	−0.0771147	−	0.106139i
$339$	51.0556	−	157.133i	0.150606	−	0.463519i
$340$		−	24.9798i		−	0.0734700i
$341$	308.654	+	149.741i	0.905144	+	0.439122i
$342$	−115.016			−0.336305
$343$	40.6417	+	13.2053i	0.118489	+	0.0384993i
$344$	55.9903	−	40.6793i	0.162763	−	0.118254i
$345$	−113.156	−	82.2127i	−0.327989	−	0.238298i
$346$	−10.5356	−	32.4252i	−0.0304497	−	0.0937146i
$347$	501.898	−	163.076i	1.44639	−	0.469961i	0.522507	−	0.852635i	$-0.324997\pi$
$347$	501.898	−	163.076i	1.44639	−	0.469961i	0.923883	+	0.382674i	$0.124997\pi$
$348$	−566.042	+	779.091i	−1.62656	+	2.23877i
$349$	318.255	+	438.040i	0.911905	+	1.25513i	0.966512	+	0.256622i	$0.0826096\pi$
$349$	318.255	+	438.040i	0.911905	+	1.25513i	−0.0546065	+	0.998508i	$0.517390\pi$
$350$	4.76200	−	14.6559i	0.0136057	−	0.0418741i
$351$			216.758i			0.617543i
$352$	−154.520	−	21.3862i	−0.438978	−	0.0607563i
$353$	216.813			0.614201			0.307101	−	0.951677i	$-0.400641\pi$
$353$	216.813			0.614201			0.307101	+	0.951677i	$0.400641\pi$
$354$	−76.7347	−	24.9326i	−0.216765	−	0.0704311i
$355$	10.8647	−	7.89366i	0.0306048	−	0.0222357i
$356$	374.662	+	272.208i	1.05242	+	0.764630i
$357$	46.1221	+	141.949i	0.129193	+	0.397616i
$358$	13.8902	−	4.51321i	0.0387995	−	0.0126067i
$359$	−329.315	+	453.263i	−0.917311	+	1.26257i	0.0472967	+	0.998881i	$0.484939\pi$
$359$	−329.315	+	453.263i	−0.917311	+	1.26257i	−0.964608	+	0.263689i	$0.915061\pi$
$360$	55.9312	+	76.9827i	0.155364	+	0.213841i
$361$	−29.5795	+	91.0363i	−0.0819376	+	0.252178i
$362$			2.07029i			0.00571902i
$363$	586.134	−	216.123i	1.61469	−	0.595379i
$364$	191.614			0.526411
$365$	−278.380	−	90.4512i	−0.762686	−	0.247812i
$366$	−42.3047	+	30.7362i	−0.115587	+	0.0839786i
$367$	−25.0380	−	18.1911i	−0.0682233	−	0.0495671i	0.553151	−	0.833081i	$-0.313425\pi$
$367$	−25.0380	−	18.1911i	−0.0682233	−	0.0495671i	−0.621374	+	0.783514i	$0.713425\pi$
$368$	−55.7602	−	171.612i	−0.151522	−	0.466337i
$369$	672.680	−	218.567i	1.82298	−	0.592323i
$370$	−7.95944	+	10.9552i	−0.0215120	+	0.0296087i
$371$	−374.364	−	515.267i	−1.00907	−	1.38886i
$372$	194.403	−	598.312i	0.522590	−	1.60837i
$373$		−	483.806i		−	1.29707i	−0.761186	−	0.648534i	$-0.775383\pi$
$373$		−	483.806i		−	1.29707i	0.761186	−	0.648534i	$-0.224617\pi$
$374$	1.31440	−	9.49685i	0.00351444	−	0.0253927i
$375$	−57.7229			−0.153928
$376$	−9.01440	−	2.92896i	−0.0239745	−	0.00778977i
$377$	−187.342	+	136.112i	−0.496928	+	0.361040i
$378$	−111.424	−	80.9540i	−0.294771	−	0.214164i
$379$	25.3368	+	77.9786i	0.0668517	+	0.205748i	0.978902	−	0.204330i	$-0.0655015\pi$
$379$	25.3368	+	77.9786i	0.0668517	+	0.205748i	−0.912050	+	0.410078i	$0.865501\pi$
$380$	177.570	−	57.6959i	0.467289	−	0.151831i
$381$	−327.298	+	450.487i	−0.859050	+	1.18238i
$382$	13.4476	+	18.5090i	0.0352031	+	0.0484530i
$383$	225.261	−	693.283i	0.588150	−	1.81014i	0.00191562	−	0.999998i	$-0.499390\pi$
$383$	225.261	−	693.283i	0.588150	−	1.81014i	0.586234	−	0.810141i	$-0.300610\pi$
$384$			379.819i			0.989111i
$385$	−108.550	+	223.750i	−0.281948	+	0.581168i
$386$	115.660			0.299638
$387$	482.135	+	156.655i	1.24583	+	0.404793i
$388$	211.227	−	153.465i	0.544399	−	0.395529i
$389$	−193.321	−	140.456i	−0.496969	−	0.361069i	0.310889	−	0.950446i	$-0.399373\pi$
$389$	−193.321	−	140.456i	−0.496969	−	0.361069i	−0.807858	+	0.589377i	$0.799373\pi$
$390$	5.27483	+	16.2342i	0.0135252	+	0.0416263i
$391$	32.9458	−	10.7047i	0.0842604	−	0.0273779i
$392$	−75.4082	+	103.790i	−0.192368	+	0.264772i
$393$	−147.710	−	203.305i	−0.375852	−	0.517316i
$394$	−8.61808	+	26.5237i	−0.0218733	+	0.0673191i
$395$		−	200.930i		−	0.508682i
$396$	−357.635	−	669.226i	−0.903120	−	1.68997i
$397$	−354.733			−0.893535			−0.446768	−	0.894650i	$-0.647425\pi$
$397$	−354.733			−0.893535			−0.446768	+	0.894650i	$0.647425\pi$
$398$	6.96401	+	2.26274i	0.0174975	+	0.00568528i
$399$	−902.522	+	655.721i	−2.26196	+	1.64341i
$400$	−60.2458	−	43.7712i	−0.150615	−	0.109428i
$401$	79.1417	+	243.573i	0.197361	+	0.607414i	0.999941	+	0.0108700i	$0.00346008\pi$
$401$	79.1417	+	243.573i	0.197361	+	0.607414i	−0.802580	+	0.596545i	$0.796540\pi$
$402$	134.904	−	43.8328i	0.335581	−	0.109037i
$403$	88.9175	−	122.384i	0.220639	−	0.303684i
$404$	−29.7187	−	40.9042i	−0.0735610	−	0.101248i
$405$	−49.6233	+	152.725i	−0.122527	+	0.377098i
$406$		−	147.137i		−	0.362407i
$407$	151.476	−	157.517i	0.372176	−	0.387020i
$408$	−35.5808			−0.0872079
$409$	261.500	+	84.9666i	0.639365	+	0.207742i	0.610719	−	0.791847i	$-0.290881\pi$
$409$	261.500	+	84.9666i	0.639365	+	0.207742i	0.0286458	+	0.999590i	$0.490881\pi$
$410$	22.0914	−	16.0503i	0.0538813	−	0.0391471i
$411$	313.798	+	227.988i	0.763500	+	0.554715i
$412$	136.442	+	419.925i	0.331170	+	1.01924i
$413$	−492.975	+	160.177i	−1.19364	+	0.387839i
$414$	−38.3261	+	52.7514i	−0.0925752	+	0.127419i
$415$	116.180	+	159.908i	0.279952	+	0.385320i
$416$	−21.2563	+	65.4202i	−0.0510969	+	0.157260i
$417$		−	249.232i		−	0.597678i
$418$	70.5446	−	12.5914i	0.168767	−	0.0301231i
$419$	44.0757			0.105193			0.0525963	−	0.998616i	$-0.483250\pi$
$419$	44.0757			0.105193			0.0525963	+	0.998616i	$0.483250\pi$
$420$	433.729	+	140.927i	1.03269	+	0.335541i
$421$	65.8608	−	47.8507i	0.156439	−	0.113660i	−0.506812	−	0.862057i	$-0.669176\pi$
$421$	65.8608	−	47.8507i	0.156439	−	0.113660i	0.663251	+	0.748397i	$0.269176\pi$
$422$	−90.6750	−	65.8792i	−0.214870	−	0.156112i
$423$	−21.4546	−	66.0303i	−0.0507200	−	0.156100i
$424$	144.401	−	46.9188i	0.340569	−	0.110658i
$425$	8.40311	−	11.5659i	0.0197720	−	0.0272139i
$426$	−5.55574	−	7.64682i	−0.0130416	−	0.0179503i
$427$	−103.812	+	319.500i	−0.243119	+	0.748243i
$428$			62.6319i			0.146336i
$429$	−48.4038	−	271.186i	−0.112829	−	0.632136i
$430$	19.5715			0.0455151
$431$	690.547	+	224.372i	1.60220	+	0.520585i	0.967649	−	0.252299i	$-0.0811866\pi$
$431$	690.547	+	224.372i	1.60220	+	0.520585i	0.634547	+	0.772884i	$0.281187\pi$
$432$	−538.442	+	391.201i	−1.24639	+	0.905558i
$433$	−280.828	−	204.033i	−0.648563	−	0.471208i	0.214218	−	0.976786i	$-0.431280\pi$
$433$	−280.828	−	204.033i	−0.648563	−	0.471208i	−0.862781	+	0.505577i	$0.831280\pi$
$434$	29.7027	+	91.4156i	0.0684394	+	0.210635i
$435$	−524.167	+	170.312i	−1.20498	+	0.391522i
$436$	360.126	−	495.670i	0.825976	−	1.13686i
$437$	152.190	+	209.472i	0.348261	+	0.479340i
$438$	−63.6617	+	195.930i	−0.145346	+	0.447330i
$439$		−	72.1914i		−	0.164445i	−0.996614	−	0.0822226i	$-0.973798\pi$
$439$		−	72.1914i		−	0.164445i	0.996614	−	0.0822226i	$-0.0262018\pi$
$440$	−42.7327	−	41.0938i	−0.0971199	−	0.0933949i
$441$	−939.738			−2.13092
$442$	−4.02074	−	1.30642i	−0.00909669	−	0.00295569i
$443$	304.024	−	220.886i	0.686284	−	0.498614i	−0.189153	−	0.981948i	$-0.560574\pi$
$443$	304.024	−	220.886i	0.686284	−	0.498614i	0.875436	+	0.483333i	$0.160574\pi$
$444$	−324.210	−	235.552i	−0.730202	−	0.530523i
$445$	81.9026	+	252.070i	0.184051	+	0.566450i
$446$	51.3857	−	16.6962i	0.115214	−	0.0374355i
$447$	−365.670	+	503.301i	−0.818053	+	1.12595i
$448$	328.356	+	451.943i	0.732937	+	1.00880i
$449$	34.6764	−	106.723i	0.0772302	−	0.237690i	−0.904987	−	0.425440i	$-0.860119\pi$
$449$	34.6764	−	106.723i	0.0772302	−	0.237690i	0.982217	+	0.187750i	$0.0601194\pi$
$450$			26.9094i			0.0597987i
$451$	−388.657	+	207.699i	−0.861767	+	0.460529i
$452$	125.032			0.276619
$453$	379.344	+	123.256i	0.837405	+	0.272089i
$454$	4.56195	−	3.31445i	0.0100483	−	0.00730055i
$455$	88.7190	+	64.4581i	0.194987	+	0.141666i
$456$	−82.1812	−	252.928i	−0.180222	−	0.554666i
$457$	−177.567	+	57.6949i	−0.388549	+	0.126247i	−0.496775	−	0.867879i	$-0.665483\pi$
$457$	−177.567	+	57.6949i	−0.388549	+	0.126247i	0.108227	+	0.994126i	$0.465483\pi$
$458$	−23.9630	+	32.9822i	−0.0523209	+	0.0720136i
$459$	−75.1021	−	103.369i	−0.163621	−	0.225205i
$460$	32.7086	−	100.667i	0.0711056	−	0.218841i
$461$		−	559.922i		−	1.21458i	−0.794479	−	0.607291i	$-0.792256\pi$
$461$		−	559.922i		−	1.21458i	0.794479	−	0.607291i	$-0.207744\pi$
$462$	157.480	+	76.4000i	0.340866	+	0.165368i
$463$	−648.611			−1.40089			−0.700444	−	0.713708i	$-0.747014\pi$
$463$	−648.611			−1.40089			−0.700444	+	0.713708i	$0.747014\pi$
$464$	−676.224	−	219.719i	−1.45738	−	0.473532i
$465$	291.281	−	211.628i	0.626410	−	0.455114i
$466$	−10.8591	−	7.88958i	−0.0233028	−	0.0169304i
$467$	−278.242	−	856.339i	−0.595806	−	1.83370i	−0.550671	−	0.834722i	$-0.685628\pi$
$467$	−278.242	−	856.339i	−0.595806	−	1.83370i	−0.0451348	−	0.998981i	$-0.514372\pi$
$468$	−318.221	+	103.396i	−0.679960	+	0.220932i
$469$	535.635	−	737.238i	1.14208	−	1.57194i
$470$	−1.57550	−	2.16849i	−0.00335212	−	0.00461380i
$471$	86.4772	−	266.149i	0.183603	−	0.565073i
$472$		−	123.569i		−	0.261798i
$473$	−312.864	−	43.3016i	−0.661447	−	0.0915468i
$474$	−141.419			−0.298352
$475$	101.625	+	33.0201i	0.213948	+	0.0695159i
$476$	−91.3783	+	66.3902i	−0.191971	+	0.139475i
$477$	899.765	+	653.718i	1.88630	+	1.37048i
$478$	15.5840	+	47.9626i	0.0326025	+	0.100340i
$479$	−441.790	+	143.546i	−0.922317	+	0.299679i	−0.731417	−	0.681930i	$-0.761141\pi$
$479$	−441.790	+	143.546i	−0.922317	+	0.299679i	−0.190900	+	0.981609i	$0.561141\pi$
$480$	−96.2298	+	132.449i	−0.200479	+	0.275935i
$481$	−56.6415	−	77.9603i	−0.117758	−	0.162080i
$482$	6.44289	−	19.8292i	0.0133670	−	0.0411394i
$483$			632.437i			1.30939i
$484$	292.617	+	371.314i	0.604581	+	0.767177i
$485$	149.425			0.308093
$486$	−9.10546	−	2.95854i	−0.0187355	−	0.00608753i
$487$	−26.6567	+	19.3672i	−0.0547366	+	0.0397685i	−0.614817	−	0.788670i	$-0.710770\pi$
$487$	−26.6567	+	19.3672i	−0.0547366	+	0.0397685i	0.560081	+	0.828438i	$0.310770\pi$
$488$	−64.7906	−	47.0731i	−0.132768	−	0.0964613i
$489$	−324.106	−	997.496i	−0.662794	−	2.03987i
$490$	−34.5044	+	11.2112i	−0.0704172	+	0.0228799i
$491$	−469.003	+	645.528i	−0.955200	+	1.31472i	−0.00602158	+	0.999982i	$0.501917\pi$
$491$	−469.003	+	645.528i	−0.955200	+	1.31472i	−0.949179	+	0.314738i	$0.898083\pi$
$492$	474.994	+	653.773i	0.965434	+	1.32881i
$493$	42.1812	−	129.820i	0.0855603	−	0.263327i
$494$		−	31.5990i		−	0.0639656i
$495$	59.5366	−	430.166i	0.120276	−	0.869022i
$496$	464.489			0.936470
$497$	−57.7514	−	18.7646i	−0.116200	−	0.0377557i
$498$	112.547	−	81.7701i	0.225998	−	0.164197i
$499$	−479.816	−	348.607i	−0.961555	−	0.698611i	−0.00804363	−	0.999968i	$-0.502560\pi$
$499$	−479.816	−	348.607i	−0.961555	−	0.698611i	−0.953511	+	0.301357i	$0.902560\pi$
$500$	−13.4986	−	41.5445i	−0.0269973	−	0.0830890i
$501$	−651.627	+	211.727i	−1.30065	+	0.422608i
$502$	60.7459	−	83.6096i	0.121008	−	0.166553i
$503$	461.015	+	634.532i	0.916530	+	1.26150i	0.964887	+	0.262665i	$0.0846015\pi$
$503$	461.015	+	634.532i	0.916530	+	1.26150i	−0.0483569	+	0.998830i	$0.515398\pi$
$504$	132.958	−	409.203i	0.263806	−	0.811910i
$505$		−	28.9363i		−	0.0572996i
$506$	17.7321	−	36.5505i	0.0350437	−	0.0722342i
$507$	751.056			1.48137
$508$	−400.766	−	130.217i	−0.788909	−	0.256332i
$509$	639.768	−	464.819i	1.25691	−	0.913200i	0.258310	−	0.966062i	$-0.416835\pi$
$509$	639.768	−	464.819i	1.25691	−	0.913200i	0.998602	+	0.0528625i	$0.0168345\pi$
$510$	−8.14034	−	5.91431i	−0.0159615	−	0.0115967i
$511$	408.989	+	1258.74i	0.800369	+	2.46328i
$512$	−337.436	+	109.640i	−0.659055	+	0.214140i
$513$	561.340	−	772.619i	1.09423	−	1.50608i
$514$	45.1374	+	62.1263i	0.0878160	+	0.120868i
$515$	−78.0874	+	240.328i	−0.151626	+	0.466657i
$516$			579.200i			1.12248i
$517$	20.3877	+	38.1506i	0.0394346	+	0.0737922i
$518$	61.2295			0.118204
$519$	549.187	+	178.442i	1.05816	+	0.343818i
$520$	−21.1498	+	15.3662i	−0.0406727	+	0.0295505i
$521$	−514.280	−	373.646i	−0.987101	−	0.717171i	−0.0278170	−	0.999613i	$-0.508856\pi$
$521$	−514.280	−	373.646i	−0.987101	−	0.717171i	−0.959284	+	0.282442i	$0.908856\pi$
$522$	79.3966	+	244.357i	0.152101	+	0.468118i
$523$	180.831	−	58.7556i	0.345757	−	0.112343i	−0.130990	−	0.991384i	$-0.541816\pi$
$523$	180.831	−	58.7556i	0.345757	−	0.112343i	0.476747	+	0.879040i	$0.341816\pi$
$524$	111.781	−	153.854i	0.213323	−	0.293614i
$525$	153.413	+	211.155i	0.292216	+	0.402201i
$526$	−40.0152	+	123.154i	−0.0760746	+	0.234134i
$527$			89.1719i			0.169207i
$528$	586.289	−	609.672i	1.11040	−	1.15468i
$529$	−382.214			−0.722522
$530$	40.8357	+	13.2683i	0.0770485	+	0.0250346i
$531$	732.273	−	532.027i	1.37905	−	1.00193i
$532$	−682.995	−	496.225i	−1.28382	−	0.932753i
$533$	60.0480	+	184.809i	0.112660	+	0.346733i
$534$	177.413	−	57.6449i	0.332234	−	0.107949i
$535$	−21.0692	+	28.9992i	−0.0393816	+	0.0542041i
$536$	127.691	+	175.751i	0.238229	+	0.327894i
$537$	−76.4403	+	235.259i	−0.142347	+	0.438099i
$538$			152.209i			0.282917i
$539$	576.382	−	102.878i	1.06936	−	0.190868i
$540$	−390.408			−0.722979
$541$	37.6026	+	12.2178i	0.0695058	+	0.0225838i	0.343563	−	0.939129i	$-0.388366\pi$
$541$	37.6026	+	12.2178i	0.0695058	+	0.0225838i	−0.274058	+	0.961713i	$0.588366\pi$
$542$	−57.9123	+	42.0758i	−0.106849	+	0.0776306i
$543$	−28.3678	−	20.6104i	−0.0522427	−	0.0379565i
$544$	−12.5299	−	38.5630i	−0.0230329	−	0.0708879i
$545$	333.484	−	108.355i	0.611896	−	0.198817i
$546$	45.3671	−	62.4425i	0.0830900	−	0.114364i
$547$	347.554	+	478.368i	0.635383	+	0.874529i	0.998359	−	0.0572690i	$-0.0182393\pi$
$547$	347.554	+	478.368i	0.635383	+	0.874529i	−0.362976	+	0.931799i	$0.618239\pi$
$548$	−90.7057	+	279.164i	−0.165521	+	0.509423i
$549$		−	586.626i		−	1.06853i
$550$	−2.94591	−	16.5047i	−0.00535621	−	0.0300086i
$551$	1020.26			1.85165
$552$	−143.388	−	46.5896i	−0.259761	−	0.0844015i
$553$	−735.018	+	534.022i	−1.32915	+	0.965682i
$554$	33.5380	+	24.3668i	0.0605379	+	0.0439833i
$555$	−70.8735	−	218.126i	−0.127700	−	0.393020i
$556$	179.378	−	58.2834i	0.322622	−	0.104826i
$557$	128.305	−	176.596i	0.230350	−	0.317049i	−0.678159	−	0.734915i	$-0.737222\pi$
$557$	128.305	−	176.596i	0.230350	−	0.317049i	0.908509	+	0.417866i	$0.137222\pi$
$558$	−98.6573	−	135.790i	−0.176805	−	0.243351i
$559$	−43.0386	+	132.459i	−0.0769921	+	0.236957i
$560$			336.718i			0.601282i
$561$	117.044	+	112.555i	0.208634	+	0.200632i
$562$	−92.2970			−0.164229
$563$	−356.595	−	115.865i	−0.633383	−	0.205799i	−0.0253101	−	0.999680i	$-0.508057\pi$
$563$	−356.595	−	115.865i	−0.633383	−	0.205799i	−0.608073	+	0.793881i	$0.708057\pi$
$564$	64.1743	−	46.6254i	0.113784	−	0.0826691i
$565$	57.8909	+	42.0602i	0.102462	+	0.0744428i
$566$	−1.00311	−	3.08725i	−0.00177227	−	0.00545450i
$567$	690.568	−	224.379i	1.21793	−	0.395730i
$568$	8.50874	−	11.7113i	0.0149802	−	0.0206184i
$569$	−131.674	−	181.234i	−0.231413	−	0.318513i	0.677480	−	0.735541i	$-0.263072\pi$
$569$	−131.674	−	181.234i	−0.231413	−	0.318513i	−0.908894	+	0.417028i	$0.863072\pi$
$570$	23.2403	−	71.5263i	0.0407724	−	0.125485i
$571$		−	176.017i		−	0.308262i	−0.988050	−	0.154131i	$-0.950742\pi$
$571$		−	176.017i		−	0.308262i	0.988050	−	0.154131i	$-0.0492577\pi$
$572$	183.860	−	98.2549i	0.321433	−	0.171774i
$573$	−387.492			−0.676252
$574$	−117.427	−	38.1543i	−0.204577	−	0.0664710i
$575$	49.0083	−	35.6066i	0.0852319	−	0.0619246i
$576$	−789.188	−	573.378i	−1.37012	−	0.995449i
$577$	206.377	+	635.162i	0.357672	+	1.10080i	0.954444	+	0.298391i	$0.0964498\pi$
$577$	206.377	+	635.162i	0.357672	+	1.10080i	−0.596772	+	0.802411i	$0.703550\pi$
$578$	−81.4137	+	26.4529i	−0.140854	+	0.0457663i
$579$	−1151.44	+	1584.82i	−1.98867	+	2.73716i
$580$	−245.155	−	337.427i	−0.422681	−	0.581771i
$581$	276.180	−	849.994i	0.475352	−	1.46298i
$582$		−	105.169i		−	0.180703i
$583$	−623.432	−	302.452i	−1.06935	−	0.518785i
$584$	−315.514			−0.540264
$585$	−182.122	−	59.1750i	−0.311319	−	0.101154i
$586$	−81.3922	+	59.1349i	−0.138895	+	0.100913i
$587$	79.0311	+	57.4195i	0.134636	+	0.0978185i	0.653065	−	0.757302i	$-0.273483\pi$
$587$	79.0311	+	57.4195i	0.134636	+	0.0978185i	−0.518429	+	0.855121i	$0.673483\pi$
$588$	−331.784	−	1021.13i	−0.564259	−	1.73661i
$589$	−633.882	+	205.961i	−1.07620	+	0.349679i
$590$	20.5398	−	28.2706i	0.0348132	−	0.0479163i
$591$	−277.641	−	382.141i	−0.469782	−	0.646600i
$592$	91.4335	−	281.403i	0.154448	−	0.475343i
$593$		−	479.081i		−	0.807893i	−0.914783	−	0.403947i	$-0.867638\pi$
$593$		−	479.081i		−	0.807893i	0.914783	−	0.403947i	$-0.132362\pi$
$594$	−148.426	−	20.5427i	−0.249875	−	0.0345837i
$595$	−64.6425			−0.108643
$596$	−447.751	−	145.483i	−0.751259	−	0.244099i
$597$	−100.334	+	72.8968i	−0.168063	+	0.122105i
$598$	−14.4927	−	10.5295i	−0.0242352	−	0.0176079i
$599$	146.829	+	451.894i	0.245124	+	0.754414i	0.995616	+	0.0935345i	$0.0298165\pi$
$599$	146.829	+	451.894i	0.245124	+	0.754414i	−0.750492	+	0.660879i	$0.770183\pi$
$600$	−59.1754	+	19.2272i	−0.0986256	+	0.0320454i
$601$	316.409	−	435.499i	0.526470	−	0.724624i	−0.460117	−	0.887858i	$-0.652193\pi$
$601$	316.409	−	435.499i	0.526470	−	0.724624i	0.986587	+	0.163234i	$0.0521926\pi$
$602$	−52.0163	−	71.5943i	−0.0864059	−	0.118927i
$603$	−491.733	+	1513.40i	−0.815477	+	2.50978i
$604$			301.847i			0.499747i
$605$	10.5761	+	270.357i	0.0174811	+	0.446872i
$606$	−20.3660			−0.0336073
$607$	−391.027	−	127.052i	−0.644196	−	0.209312i	−0.0313426	−	0.999509i	$-0.509978\pi$
$607$	−391.027	−	127.052i	−0.644196	−	0.209312i	−0.612853	+	0.790197i	$0.709978\pi$
$608$	245.186	−	178.138i	0.403267	−	0.292991i
$609$	2016.13	+	1464.80i	3.31055	+	2.40526i
$610$	−6.99851	−	21.5392i	−0.0114730	−	0.0353102i
$611$	18.1408	−	5.89431i	0.0296904	−	0.00964700i
$612$	115.931	−	159.566i	0.189430	−	0.260728i
$613$	146.092	+	201.079i	0.238324	+	0.328025i	0.911379	−	0.411567i	$-0.135019\pi$
$613$	146.092	+	201.079i	0.238324	+	0.328025i	−0.673056	+	0.739592i	$0.735019\pi$
$614$	10.5004	−	32.3170i	0.0171017	−	0.0526336i
$615$			462.490i			0.752016i
$616$	−36.7514	+	265.538i	−0.0596614	+	0.431067i
$617$	−1141.96			−1.85082			−0.925411	−	0.378964i	$-0.876280\pi$
$617$	−1141.96			−1.85082			−0.925411	+	0.378964i	$0.876280\pi$
$618$	169.149	+	54.9597i	0.273703	+	0.0889316i
$619$	−4.57281	+	3.32234i	−0.00738742	+	0.00536727i	−0.591473	−	0.806325i	$-0.701453\pi$
$619$	−4.57281	+	3.32234i	−0.00738742	+	0.00536727i	0.584085	+	0.811692i	$0.301453\pi$
$620$	220.430	+	160.152i	0.355533	+	0.258310i
$621$	−167.304	−	514.909i	−0.269411	−	0.829161i
$622$	−117.447	+	38.1609i	−0.188822	+	0.0613519i
$623$	704.418	−	969.549i	1.13069	−	1.55626i
$624$	−219.232	−	301.746i	−0.351333	−	0.483568i
$625$	7.72542	−	23.7764i	0.0123607	−	0.0380423i
$626$			51.7472i			0.0826633i
$627$	−529.763	+	1091.98i	−0.844917	+	1.74159i
$628$	211.777			0.337224
$629$	54.0233	+	17.5532i	0.0858876	+	0.0279066i
$630$	98.4370	−	71.5187i	0.156249	−	0.113522i
$631$	601.402	+	436.944i	0.953094	+	0.692463i	0.951537	−	0.307536i	$-0.0995043\pi$
$631$	601.402	+	436.944i	0.953094	+	0.692463i	0.00155713	+	0.999999i	$0.499504\pi$
$632$	−66.9288	−	205.986i	−0.105900	−	0.325927i
$633$	1805.40	−	586.610i	2.85213	−	0.926714i
$634$	−69.2140	+	95.2649i	−0.109170	+	0.150260i
$635$	−141.754	−	195.108i	−0.223235	−	0.307256i
$636$	−392.664	+	1208.49i	−0.617396	+	1.90015i
$637$		−	258.179i		−	0.405304i
$638$	−75.4485	−	141.183i	−0.118258	−	0.221290i
$639$	106.036			0.165940
$640$	−156.450	−	50.8336i	−0.244453	−	0.0794275i
$641$	−292.789	+	212.724i	−0.456769	+	0.331862i	−0.792263	−	0.610180i	$-0.791097\pi$
$641$	−292.789	+	212.724i	−0.456769	+	0.331862i	0.335493	+	0.942043i	$0.391097\pi$
$642$	20.4103	+	14.8290i	0.0317918	+	0.0230981i
$643$	200.009	+	615.565i	0.311056	+	0.957333i	0.977347	+	0.211641i	$0.0678809\pi$
$643$	200.009	+	615.565i	0.311056	+	0.957333i	−0.666291	+	0.745692i	$0.732119\pi$
$644$	−455.179	+	147.897i	−0.706800	+	0.229653i
$645$	−194.841	+	268.175i	−0.302079	+	0.415776i
$646$	10.9484	+	15.0692i	0.0169480	+	0.0233269i
$647$	225.784	−	694.892i	0.348971	−	1.07402i	−0.610453	−	0.792053i	$-0.709012\pi$
$647$	225.784	−	694.892i	0.348971	−	1.07402i	0.959423	−	0.281969i	$-0.0909876\pi$
$648$			173.097i			0.267125i
$649$	−390.891	+	406.482i	−0.602298	+	0.626320i
$650$	−7.39295			−0.0113738
$651$	−1548.31	−	503.076i	−2.37835	−	0.772774i
$652$	642.128	−	466.534i	0.984859	−	0.715542i
$653$	−243.570	−	176.964i	−0.373001	−	0.271001i	0.385453	−	0.922727i	$-0.374045\pi$
$653$	−243.570	−	176.964i	−0.373001	−	0.271001i	−0.758454	+	0.651726i	$0.774045\pi$
$654$	−76.2630	−	234.713i	−0.116610	−	0.358889i
$655$	103.512	−	33.6330i	0.158033	−	0.0513480i
$656$	−350.705	+	482.704i	−0.534611	+	0.735829i
$657$	−1358.45	−	1869.75i	−2.06766	−	2.84589i
$658$	−3.74523	+	11.5266i	−0.00569184	+	0.0175177i
$659$		−	596.433i		−	0.905057i	−0.891750	−	0.452529i	$-0.850522\pi$
$659$		−	596.433i		−	0.905057i	0.891750	−	0.452529i	$-0.149478\pi$
$660$	488.442	−	87.1816i	0.740063	−	0.132093i
$661$	882.175			1.33461			0.667303	−	0.744786i	$-0.267449\pi$
$661$	882.175			1.33461			0.667303	+	0.744786i	$0.267449\pi$
$662$	34.4892	+	11.2062i	0.0520985	+	0.0169278i
$663$	57.9288	−	42.0877i	0.0873737	−	0.0634807i
$664$	172.368	+	125.233i	0.259591	+	0.188604i
$665$	−149.305	−	459.514i	−0.224519	−	0.690998i
$666$	−101.687	+	33.0400i	−0.152683	+	0.0496096i
$667$	339.974	−	467.934i	0.509707	−	0.701551i
$668$	−304.769	−	419.479i	−0.456241	−	0.627962i
$669$	−282.784	+	870.320i	−0.422697	+	1.30093i
$670$			61.4340i			0.0916926i
$671$	64.2210	+	359.803i	0.0957094	+	0.536220i
$672$	740.266			1.10159
$673$	383.533	+	124.617i	0.569886	+	0.185167i	0.579764	−	0.814784i	$-0.303145\pi$
$673$	383.533	+	124.617i	0.569886	+	0.185167i	−0.00987877	+	0.999951i	$0.503145\pi$
$674$	109.387	−	79.4741i	0.162295	−	0.117914i
$675$	−180.763	−	131.332i	−0.267797	−	0.194566i
$676$	175.636	+	540.553i	0.259817	+	0.799634i
$677$	−595.604	+	193.523i	−0.879769	+	0.285854i	−0.713861	−	0.700287i	$-0.753055\pi$
$677$	−595.604	+	193.523i	−0.879769	+	0.285854i	−0.165908	+	0.986141i	$0.553055\pi$
$678$	29.6029	−	40.7450i	0.0436622	−	0.0600958i
$679$	−397.136	−	546.611i	−0.584884	−	0.805024i
$680$	4.76201	−	14.6560i	0.00700296	−	0.0215529i
$681$			95.5059i			0.140244i
$682$	75.3765	+	72.4855i	0.110523	+	0.106284i
$683$	935.585			1.36982			0.684909	−	0.728629i	$-0.259842\pi$
$683$	935.585			1.36982			0.684909	+	0.728629i	$0.259842\pi$
$684$	1402.05	+	455.553i	2.04978	+	0.666013i
$685$	−135.907	+	98.7424i	−0.198405	+	0.144150i
$686$	10.5385	+	7.65666i	0.0153622	+	0.0111613i
$687$	−213.374	−	656.698i	−0.310588	−	0.955892i
$688$	−406.714	+	132.149i	−0.591154	+	0.192078i
$689$	−179.599	+	247.197i	−0.260666	+	0.358776i
$690$	−25.0608	−	34.4932i	−0.0363200	−	0.0499901i
$691$	255.366	−	785.937i	0.369561	−	1.13739i	−0.577515	−	0.816380i	$-0.695977\pi$
$691$	255.366	−	785.937i	0.369561	−	1.13739i	0.947076	−	0.321011i	$-0.104023\pi$
$692$			436.992i			0.631491i
$693$	−1731.82	+	925.486i	−2.49902	+	1.33548i
$694$	160.866			0.231795
$695$	102.660	+	33.3563i	0.147712	+	0.0479946i
$696$	−480.626	+	349.195i	−0.690555	+	0.501718i
$697$	−92.6687	−	67.3278i	−0.132954	−	0.0965965i
$698$	51.0029	+	156.971i	0.0730700	+	0.224886i
$699$	216.212	−	70.2514i	0.309316	−	0.100503i
$700$	−116.097	+	159.794i	−0.165854	+	0.228278i
$701$	−139.111	−	191.469i	−0.198446	−	0.273138i	0.698184	−	0.715919i	$-0.253992\pi$
$701$	−139.111	−	191.469i	−0.198446	−	0.273138i	−0.896630	+	0.442781i	$0.853992\pi$
$702$	−20.4180	+	62.8400i	−0.0290854	+	0.0895157i
$703$			424.570i			0.603940i
$704$	546.814	+	265.282i	0.776725	+	0.376821i
$705$	45.3980			0.0643943
$706$	62.8561	+	20.4232i	0.0890313	+	0.0289280i
$707$	−105.852	+	76.9057i	−0.149719	+	0.108778i
$708$	836.642	+	607.856i	1.18170	+	0.858554i
$709$	−278.848	−	858.205i	−0.393297	−	1.21044i	−0.930280	−	0.366851i	$-0.880436\pi$
$709$	−278.848	−	858.205i	−0.393297	−	1.21044i	0.536982	−	0.843593i	$-0.319564\pi$
$710$	3.89333	−	1.26502i	0.00548357	−	0.00178172i
$711$	932.515	−	1283.50i	1.31155	−	1.80520i
$712$	167.927	+	231.132i	0.235853	+	0.324623i
$713$	−116.762	+	359.356i	−0.163761	+	0.504006i
$714$			45.4969i			0.0637212i
$715$	118.182	+	16.3568i	0.165289	+	0.0228766i
$716$	−187.197			−0.261449
$717$	−812.345	−	263.947i	−1.13298	−	0.368127i
$718$	−138.167	+	100.385i	−0.192434	+	0.139811i
$719$	318.157	+	231.154i	0.442499	+	0.321494i	0.786627	−	0.617428i	$-0.211826\pi$
$719$	318.157	+	231.154i	0.442499	+	0.321494i	−0.344128	+	0.938923i	$0.611826\pi$
$720$	−181.696	−	559.203i	−0.252355	−	0.776670i
$721$	1086.68	−	353.084i	1.50718	−	0.489714i
$722$	−17.1507	+	23.6060i	−0.0237545	+	0.0326952i
$723$	207.565	+	285.689i	0.287089	+	0.395144i
$724$	8.19991	−	25.2367i	0.0113258	−	0.0348574i
$725$		−	238.702i		−	0.329243i
$726$	190.284	−	7.44370i	0.262099	−	0.0102530i
$727$	1284.55			1.76691			0.883456	−	0.468514i	$-0.155210\pi$
$727$	1284.55			1.76691			0.883456	+	0.468514i	$0.155210\pi$
$728$	112.422	+	36.5282i	0.154426	+	0.0501761i
$729$	654.087	−	475.222i	0.897238	−	0.651882i
$730$	−72.1847	−	52.4453i	−0.0988832	−	0.0718429i
$731$	−25.3698	−	78.0803i	−0.0347056	−	0.106813i
$732$	637.432	−	207.114i	0.870809	−	0.282943i
$733$	−246.425	+	339.175i	−0.336187	+	0.462722i	−0.943323	−	0.331876i	$-0.892318\pi$
$733$	−246.425	+	339.175i	−0.336187	+	0.462722i	0.607136	+	0.794598i	$0.292318\pi$
$734$	−5.54518	−	7.63228i	−0.00755474	−	0.0103982i
$735$	189.884	−	584.403i	0.258346	−	0.795106i
$736$		−	171.813i		−	0.233441i
$737$	135.922	−	982.066i	0.184426	−	1.33252i
$738$	215.605			0.292147
$739$	−269.243	−	87.4823i	−0.364334	−	0.118379i	0.121128	−	0.992637i	$-0.461349\pi$
$739$	−269.243	−	87.4823i	−0.364334	−	0.118379i	−0.485462	+	0.874258i	$0.661349\pi$
$740$	140.417	−	102.019i	0.189752	−	0.137863i
$741$	432.981	+	314.579i	0.584319	+	0.424533i
$742$	−59.9947	−	184.645i	−0.0808554	−	0.248847i
$743$	−10.6813	+	3.47057i	−0.0143759	+	0.00467102i	−0.316196	−	0.948694i	$-0.602406\pi$
$743$	−10.6813	+	3.47057i	−0.0143759	+	0.00467102i	0.301820	+	0.953365i	$0.402406\pi$
$744$	228.118	−	313.978i	0.306610	−	0.422013i
$745$	−158.373	−	217.982i	−0.212581	−	0.292593i
$746$	45.5732	−	140.260i	0.0610901	−	0.188016i
$747$			1560.65i			2.08923i
$748$	−53.6373	+	110.560i	−0.0717076	+	0.147808i
$749$	162.078			0.216393
$750$	−16.7344	−	5.43733i	−0.0223125	−	0.00724978i
$751$	−700.813	+	509.171i	−0.933174	+	0.677990i	−0.946768	−	0.321917i	$-0.895673\pi$
$751$	−700.813	+	509.171i	−0.933174	+	0.677990i	0.0135942	+	0.999908i	$0.495673\pi$
$752$	47.3822	+	34.4252i	0.0630083	+	0.0457782i
$753$	540.902	+	1664.72i	0.718329	+	2.21079i
$754$	−67.1335	+	21.8130i	−0.0890365	+	0.0289297i
$755$	−101.540	+	139.758i	−0.134490	+	0.185110i
$756$	1037.61	+	1428.15i	1.37250	+	1.88909i
$757$	38.2121	−	117.605i	0.0504783	−	0.155356i	−0.922640	−	0.385663i	$-0.873973\pi$
$757$	38.2121	−	117.605i	0.0504783	−	0.155356i	0.973118	+	0.230306i	$0.0739728\pi$
$758$			24.9934i			0.0329728i
$759$	324.299	+	606.845i	0.427271	+	0.799532i
$760$	115.181			0.151554
$761$	627.999	+	204.049i	0.825228	+	0.268133i	0.691034	−	0.722822i	$-0.257155\pi$
$761$	627.999	+	204.049i	0.825228	+	0.268133i	0.134194	+	0.990955i	$0.457155\pi$
$762$	−137.321	+	99.7698i	−0.180212	+	0.130932i
$763$	−1282.69	−	931.931i	−1.68112	−	1.22140i
$764$	−90.6160	−	278.887i	−0.118607	−	0.365036i
$765$	107.355	−	34.8817i	0.140333	−	0.0455970i
$766$	130.611	−	179.770i	0.170510	−	0.234687i
$767$	146.167	+	201.181i	0.190569	+	0.262296i
$768$	316.820	−	975.071i	0.412526	−	1.26962i
$769$			753.219i			0.979479i	0.871869	+	0.489739i	$0.162908\pi$
$769$			753.219i			0.979479i	−0.871869	+	0.489739i	$0.837092\pi$
$770$	−52.5462	+	54.6420i	−0.0682419	+	0.0709636i
$771$	−1300.63			−1.68695
$772$	−1409.90	−	458.103i	−1.82629	−	0.593398i
$773$	134.737	−	97.8922i	0.174304	−	0.126639i	−0.497213	−	0.867629i	$-0.665643\pi$
$773$	134.737	−	97.8922i	0.174304	−	0.126639i	0.671517	+	0.740989i	$0.265643\pi$
$774$	125.019	+	90.8315i	0.161523	+	0.117353i
$775$	48.1869	+	148.304i	0.0621766	+	0.191360i
$776$	153.185	−	49.7729i	0.197404	−	0.0641404i
$777$	−609.560	+	838.988i	−0.784505	+	1.07978i
$778$	−42.8149	−	58.9297i	−0.0550320	−	0.0757451i
$779$	264.565	−	814.247i	0.339621	−	1.04525i
$780$		−	218.787i		−	0.280497i
$781$	−65.0365	+	11.6083i	−0.0832734	+	0.0148634i
$782$	10.5596			0.0135034
$783$	−2028.96	−	659.249i	−2.59126	−	0.841953i
$784$	641.335	−	465.957i	0.818030	−	0.594333i
$785$	98.0548	+	71.2410i	0.124911	+	0.0907529i
$786$	−23.6717	−	72.8539i	−0.0301166	−	0.0926894i
$787$	329.445	−	107.043i	0.418609	−	0.136014i	−0.0921365	−	0.995746i	$-0.529370\pi$
$787$	329.445	−	107.043i	0.418609	−	0.136014i	0.510745	+	0.859732i	$0.329370\pi$
$788$	210.108	−	289.190i	0.266635	−	0.366992i
$789$	−1289.14	−	1774.34i	−1.63389	−	2.24885i
$790$	18.9270	−	58.2513i	0.0239582	−	0.0737359i
$791$		−	323.556i		−	0.409047i
$792$	−82.2517	−	460.822i	−0.103853	−	0.581846i
$793$	161.167			0.203236
$794$	−102.840	−	33.4149i	−0.129522	−	0.0420843i
$795$	−588.340	+	427.454i	−0.740051	+	0.537678i
$796$	−75.9289	−	55.1656i	−0.0953880	−	0.0693035i
$797$	13.9224	+	42.8487i	0.0174685	+	0.0537625i	0.959411	−	0.282012i	$-0.0910019\pi$
$797$	13.9224	+	42.8487i	0.0174685	+	0.0537625i	−0.941942	+	0.335775i	$0.891002\pi$
$798$	−323.417	+	105.084i	−0.405284	+	0.131685i
$799$	−6.60890	+	9.09636i	−0.00827146	+	0.0113847i
$800$	−41.6775	−	57.3642i	−0.0520969	−	0.0717052i
$801$	−646.683	+	1990.28i	−0.807344	+	2.48475i
$802$			78.0690i			0.0973429i
$803$	1037.89	+	998.082i	1.29252	+	1.24294i
$804$	−1818.08			−2.26130
$805$	−260.505	−	84.6431i	−0.323608	−	0.105147i
$806$	37.3063	−	27.1046i	0.0462857	−	0.0336285i
$807$	−2085.62	−	1515.29i	−2.58441	−	1.87769i
$808$	−9.63856	−	29.6644i	−0.0119289	−	0.0367134i
$809$	−1187.16	+	385.731i	−1.46744	+	0.476800i	−0.930333	−	0.366715i	$-0.880482\pi$
$809$	−1187.16	+	385.731i	−1.46744	+	0.476800i	−0.537106	+	0.843515i	$0.680482\pi$
$810$	−28.7725	+	39.6020i	−0.0355216	+	0.0488913i
$811$	−62.7425	−	86.3577i	−0.0773644	−	0.106483i	0.768581	−	0.639753i	$-0.220963\pi$
$811$	−62.7425	−	86.3577i	−0.0773644	−	0.106483i	−0.845945	+	0.533270i	$0.820963\pi$
$812$	−582.776	+	1793.60i	−0.717704	+	2.20887i
$813$		−	1212.41i		−	1.49128i
$814$	58.7518	−	31.3971i	0.0721767	−	0.0385713i
$815$	454.252			0.557365
$816$	209.098	+	67.9401i	0.256248	+	0.0832599i
$817$	496.440	−	360.685i	0.607638	−	0.441475i
$818$	67.8077	+	49.2652i	0.0828945	+	0.0602264i
$819$	267.568	+	823.491i	0.326701	+	1.00548i
$820$	−332.865	+	108.154i	−0.405932	+	0.131895i
$821$	−361.534	+	497.608i	−0.440358	+	0.606100i	−0.970292	−	0.241939i	$-0.922217\pi$
$821$	−361.534	+	497.608i	−0.440358	+	0.606100i	0.529934	+	0.848039i	$0.322217\pi$
$822$	69.4972	+	95.6547i	0.0845465	+	0.116368i
$823$	−118.117	+	363.528i	−0.143521	+	0.441711i	−0.996818	−	0.0797139i	$-0.974599\pi$
$823$	−118.117	+	363.528i	−0.143521	+	0.441711i	0.853297	+	0.521425i	$0.174599\pi$
$824$			272.386i			0.330566i
$825$	255.481	+	123.944i	0.309674	+	0.150235i
$826$	−158.006			−0.191291
$827$	909.438	+	295.494i	1.09968	+	0.357309i	0.801981	−	0.597350i	$-0.203780\pi$
$827$	909.438	+	295.494i	1.09968	+	0.357309i	0.297703	+	0.954659i	$0.403780\pi$
$828$	676.131	−	491.238i	0.816583	−	0.593282i
$829$	591.020	+	429.401i	0.712931	+	0.517975i	0.884118	−	0.467264i	$-0.154760\pi$
$829$	591.020	+	429.401i	0.712931	+	0.517975i	−0.171187	+	0.985239i	$0.554760\pi$
$830$	18.6187	+	57.3026i	0.0224322	+	0.0690393i
$831$	−667.764	+	216.970i	−0.803566	+	0.261095i
$832$	157.527	−	216.817i	0.189335	−	0.260598i
$833$	89.4537	+	123.122i	0.107387	+	0.147806i
$834$	23.4769	−	72.2545i	0.0281498	−	0.0866361i
$835$		−	296.746i		−	0.355385i
$836$	−909.809	−	125.921i	−1.08829	−	0.150623i
$837$	1393.66			1.66507
$838$	12.7780	+	4.15181i	0.0152482	+	0.00495443i
$839$	739.591	−	537.345i	0.881515	−	0.640458i	−0.0521367	−	0.998640i	$-0.516603\pi$
$839$	739.591	−	537.345i	0.881515	−	0.640458i	0.933652	+	0.358182i	$0.116603\pi$
$840$	227.609	+	165.367i	0.270963	+	0.196866i
$841$	−444.409	−	1367.75i	−0.528429	−	1.62634i
$842$	23.6010	−	7.66845i	0.0280297	−	0.00910742i
$843$	918.847	−	1264.68i	1.08997	−	1.50022i
$844$	844.394	+	1162.21i	1.00047	+	1.37702i
$845$	−100.519	+	309.365i	−0.118957	+	0.366112i
$846$		−	21.1638i		−	0.0250163i
$847$	960.883	−	757.233i	1.13445	−	0.894018i
$848$	−938.193			−1.10636
$849$	52.2888	+	16.9896i	0.0615887	+	0.0200114i
$850$	3.52561	−	2.56151i	0.00414778	−	0.00301354i
$851$	194.726	+	141.476i	0.228820	+	0.166247i
$852$	37.4371	+	115.220i	0.0439403	+	0.135234i
$853$	−1041.09	+	338.270i	−1.22050	+	0.396565i	−0.847265	−	0.531171i	$-0.821752\pi$
$853$	−1041.09	+	338.270i	−1.22050	+	0.396565i	−0.373237	+	0.927736i	$0.621752\pi$
$854$	−60.1920	+	82.8472i	−0.0704824	+	0.0970107i
$855$	495.916	+	682.569i	0.580018	+	0.798327i
$856$	−11.9398	+	36.7470i	−0.0139484	+	0.0429287i
$857$			1161.22i			1.35499i	0.735528	+	0.677494i	$0.236934\pi$
$857$			1161.22i			1.35499i	−0.735528	+	0.677494i	$0.763066\pi$
$858$	11.5123	−	83.1789i	0.0134176	−	0.0969451i
$859$	−465.631			−0.542061			−0.271031	−	0.962571i	$-0.587364\pi$
$859$	−465.631			−0.542061			−0.271031	+	0.962571i	$0.587364\pi$
$860$	−238.576	−	77.5181i	−0.277414	−	0.0901373i
$861$	1691.83	−	1229.19i	1.96496	−	1.42763i
$862$	179.061	+	130.095i	0.207727	+	0.150922i
$863$	240.025	+	738.720i	0.278128	+	0.855990i	0.988375	+	0.152037i	$0.0485834\pi$
$863$	240.025	+	738.720i	0.278128	+	0.855990i	−0.710247	+	0.703953i	$0.751417\pi$
$864$	−602.700	+	195.829i	−0.697570	+	0.226654i
$865$	−147.003	+	202.332i	−0.169945	+	0.233909i
$866$	−62.1952	−	85.6043i	−0.0718189	−	0.0988502i
$867$	448.034	−	1378.91i	0.516763	−	1.59043i
$868$		−	1232.00i		−	1.41935i
$869$	−431.442	+	889.313i	−0.496480	+	1.02337i
$870$	−168.004			−0.193108
$871$	−415.783	−	135.096i	−0.477363	−	0.155105i
$872$	305.782	−	222.164i	0.350668	−	0.254775i
$873$	954.498	+	693.484i	1.09335	+	0.794368i
$874$	24.3897	+	75.0637i	0.0279058	+	0.0858852i
$875$	−107.509	+	34.9317i	−0.122867	+	0.0399219i
$876$	1552.07	−	2136.24i	1.77177	−	2.43863i
$877$	814.144	+	1120.57i	0.928329	+	1.27773i	0.960508	+	0.278253i	$0.0897553\pi$
$877$	814.144	+	1120.57i	0.928329	+	1.27773i	−0.0321793	+	0.999482i	$0.510245\pi$
$878$	6.80023	−	20.9290i	0.00774514	−	0.0238371i
$879$		−	1703.97i		−	1.93853i
$880$	172.661	+	323.092i	0.196206	+	0.367150i
$881$	−1570.42			−1.78255			−0.891273	−	0.453467i	$-0.850187\pi$
$881$	−1570.42			−1.78255			−0.891273	+	0.453467i	$0.850187\pi$
$882$	−272.439	−	88.5206i	−0.308887	−	0.100364i
$883$	−885.963	+	643.690i	−1.00336	+	0.728981i	−0.962805	−	0.270197i	$-0.912911\pi$
$883$	−885.963	+	643.690i	−1.00336	+	0.728981i	−0.0405507	+	0.999177i	$0.512911\pi$
$884$	43.8383	+	31.8504i	0.0495908	+	0.0360299i
$885$	182.893	+	562.887i	0.206659	+	0.636030i
$886$	108.946	−	35.3987i	0.122964	−	0.0399534i
$887$	−520.530	+	716.448i	−0.586843	+	0.807720i	−0.994425	−	0.105449i	$-0.966372\pi$
$887$	−520.530	+	716.448i	−0.586843	+	0.807720i	0.407582	+	0.913169i	$0.366372\pi$
$888$	−145.314	−	200.007i	−0.163642	−	0.225233i
$889$	−336.974	+	1037.10i	−0.379048	+	1.16659i
$890$			80.7925i			0.0907781i
$891$	547.567	−	569.407i	0.614554	−	0.639065i
$892$	−692.520			−0.776368
$893$	−79.9265	−	25.9697i	−0.0895033	−	0.0290814i
$894$	−153.421	+	111.467i	−0.171611	+	0.124683i
$895$	−86.6742	−	62.9725i	−0.0968427	−	0.0703603i
$896$	229.852	+	707.411i	0.256531	+	0.789521i
$897$	288.558	−	93.7583i	0.321693	−	0.104524i
$898$	20.1060	−	27.6735i	0.0223897	−	0.0308168i
$899$	875.145	+	1204.53i	0.973465	+	1.33986i
$900$	106.582	−	328.025i	0.118424	−	0.364472i
$901$		−	180.113i		−	0.199903i
$902$	−132.240	+	23.6034i	−0.146607	+	0.0261678i
$903$	1498.85			1.65986
$904$	73.3577	+	23.8354i	0.0811479	+	0.0263666i
$905$	12.2862	−	8.92644i	0.0135759	−	0.00986347i
$906$	98.3650	+	71.4664i	0.108571	+	0.0788812i
$907$	−96.6622	−	297.496i	−0.106573	−	0.327999i	0.883523	−	0.468388i	$-0.155165\pi$
$907$	−96.6622	−	297.496i	−0.106573	−	0.327999i	−0.990097	+	0.140388i	$0.955165\pi$
$908$	−68.7378	+	22.3343i	−0.0757025	+	0.0245972i
$909$	134.294	−	184.839i	0.147738	−	0.203344i
$910$	19.6487	+	27.0441i	0.0215920	+	0.0297188i
$911$	−140.671	+	432.942i	−0.154414	+	0.475238i	−0.998101	−	0.0615976i	$-0.980380\pi$
$911$	−140.671	+	432.942i	−0.154414	+	0.475238i	0.843687	+	0.536836i	$0.180380\pi$
$912$			1643.30i			1.80187i
$913$	−170.853	−	957.216i	−0.187133	−	1.04843i
$914$	−56.9129			−0.0622680
$915$	364.810	+	118.534i	0.398699	+	0.129545i
$916$	422.743	−	307.141i	0.461510	−	0.335306i
$917$	−398.141	−	289.267i	−0.434178	−	0.315449i
$918$	−12.0357	−	37.0421i	−0.0131108	−	0.0403509i
$919$	981.783	−	319.001i	1.06832	−	0.347117i	0.278485	−	0.960441i	$-0.410168\pi$
$919$	981.783	−	319.001i	1.06832	−	0.347117i	0.789832	+	0.613324i	$0.210168\pi$
$920$	38.3811	−	52.8271i	0.0417186	−	0.0574207i
$921$	338.284	+	465.607i	0.367300	+	0.505545i
$922$	52.7431	−	162.327i	0.0572051	−	0.176059i
$923$			29.1318i			0.0315621i
$924$	−1617.08	−	1555.06i	−1.75008	−	1.68296i
$925$	99.3330			0.107387
$926$	−188.038	−	61.0973i	−0.203065	−	0.0659798i
$927$	−1614.17	+	1172.76i	−1.74129	+	1.26512i
$928$	−547.717	−	397.939i	−0.590212	−	0.428814i
$929$	−431.640	−	1328.45i	−0.464629	−	1.42998i	−0.859449	−	0.511222i	$-0.829193\pi$
$929$	−431.640	−	1328.45i	−0.464629	−	1.42998i	0.394820	−	0.918758i	$-0.370807\pi$
$930$	104.380	−	33.9150i	0.112236	−	0.0364678i
$931$	−668.609	+	920.262i	−0.718162	+	0.988466i
$932$	101.123	+	139.184i	0.108501	+	0.149339i
$933$	646.332	−	1989.21i	0.692746	−	2.13205i
$934$		−	274.470i		−	0.293865i
$935$	−62.0267	+	33.1472i	−0.0663387	+	0.0354515i
$936$	−206.416			−0.220530
$937$	1141.42	+	370.868i	1.21816	+	0.395804i	0.846411	−	0.532530i	$-0.178759\pi$
$937$	1141.42	+	370.868i	1.21816	+	0.395804i	0.371748	+	0.928334i	$0.378759\pi$
$938$	224.731	−	163.277i	0.239586	−	0.174069i
$939$	−709.058	−	515.161i	−0.755120	−	0.548627i
$940$	10.6164	+	32.6740i	0.0112941	+	0.0347596i
$941$	29.9217	−	9.72215i	0.0317978	−	0.0103317i	−0.293075	−	0.956089i	$-0.594679\pi$
$941$	29.9217	−	9.72215i	0.0317978	−	0.0103317i	0.324873	+	0.945758i	$0.394679\pi$
$942$	50.1411	−	69.0133i	0.0532283	−	0.0732625i
$943$	−285.289	−	392.667i	−0.302533	−	0.416401i
$944$	−235.949	+	726.177i	−0.249946	+	0.769255i
$945$			1010.30i			1.06910i
$946$	−86.6233	−	42.0245i	−0.0915680	−	0.0444233i
$947$	−540.682			−0.570942			−0.285471	−	0.958387i	$-0.592150\pi$
$947$	−540.682			−0.570942			−0.285471	+	0.958387i	$0.592150\pi$
$948$	1723.89	+	560.127i	1.81845	+	0.590851i
$949$	513.685	−	373.214i	0.541291	−	0.393271i
$950$	26.3517	+	19.1456i	0.0277386	+	0.0201533i
$951$	−616.304	−	1896.79i	−0.648059	−	1.99452i
$952$	−66.2692	+	21.5322i	−0.0696105	+	0.0226178i
$953$	−335.865	+	462.279i	−0.352429	+	0.485077i	−0.948020	−	0.318211i	$-0.896918\pi$
$953$	−335.865	+	462.279i	−0.352429	+	0.485077i	0.595591	+	0.803288i	$0.296918\pi$
$954$	199.272	+	274.274i	0.208880	+	0.287499i
$955$	51.8606	−	159.611i	0.0543043	−	0.167132i
$956$		−	646.388i		−	0.676138i
$957$	2685.66	+	371.705i	2.80633	+	0.388407i
$958$	−141.601			−0.147809
$959$	722.418	+	234.728i	0.753303	+	0.244763i
$960$	516.036	−	374.922i	0.537537	−	0.390544i
$961$	−9.41808	−	6.84263i	−0.00980029	−	0.00712033i
$962$	−9.07724	−	27.9369i	−0.00943580	−	0.0290404i
$963$	−269.171	+	87.4590i	−0.279513	+	0.0908193i
$964$	−157.077	+	216.198i	−0.162943	+	0.224272i
$965$	−498.692	−	686.391i	−0.516779	−	0.711286i
$966$	−59.5738	+	183.349i	−0.0616705	+	0.189802i
$967$			1228.33i			1.27025i	0.772410	+	0.635125i	$0.219051\pi$
$967$			1228.33i			1.27025i	−0.772410	+	0.635125i	$0.780949\pi$
$968$	100.897	+	273.638i	0.104233	+	0.282684i
$969$	−315.479			−0.325571
$970$	43.3198	+	14.0754i	0.0446595	+	0.0145108i
$971$	−1282.98	+	932.137i	−1.32129	+	0.959976i	−0.321379	+	0.946951i	$0.604146\pi$
$971$	−1282.98	+	932.137i	−1.32129	+	0.959976i	−0.999915	+	0.0130253i	$0.995854\pi$
$972$	99.2772	+	72.1291i	0.102137	+	0.0742069i
$973$	−150.825	−	464.193i	−0.155011	−	0.477074i
$974$	−9.55237	+	3.10375i	−0.00980736	+	0.00318660i
$975$	73.5993	−	101.301i	0.0754865	−	0.103898i
$976$	290.871	+	400.350i	0.298024	+	0.410194i
$977$	290.915	−	895.345i	0.297764	−	0.916422i	−0.684515	−	0.728998i	$-0.739986\pi$
$977$	290.915	−	895.345i	0.297764	−	0.916422i	0.982279	−	0.187424i	$-0.0600139\pi$
$978$		−	319.713i		−	0.326905i
$979$	178.752	−	1291.52i	0.182586	−	1.31923i
$980$	465.013			0.474503
$981$	2633.10	+	855.547i	2.68410	+	0.872117i
$982$	−196.775	+	142.966i	−0.200382	+	0.145586i
$983$	564.528	+	410.154i	0.574291	+	0.417247i	0.836662	−	0.547720i	$-0.184504\pi$
$983$	564.528	+	410.154i	0.574291	+	0.417247i	−0.262370	+	0.964967i	$0.584504\pi$
$984$	154.053	+	474.127i	0.156558	+	0.481837i
$985$	194.565	−	63.2179i	0.197528	−	0.0641806i
$986$	24.4574	−	33.6628i	0.0248047	−	0.0341408i
$987$	−120.657	−	166.070i	−0.122246	−	0.168257i
$988$	−125.156	+	385.191i	−0.126676	+	0.389870i
$989$		−	347.877i		−	0.351746i
$990$	57.7806	−	119.101i	0.0583643	−	0.120304i
$991$	1202.24			1.21315			0.606577	−	0.795025i	$-0.292542\pi$
$991$	1202.24			1.21315			0.606577	+	0.795025i	$0.292542\pi$
$992$	420.626	+	136.670i	0.424018	+	0.137772i
$993$	−496.903	+	361.021i	−0.500406	+	0.363566i
$994$	−14.9751	−	10.8800i	−0.0150655	−	0.0109457i
$995$	−16.5983	−	51.0844i	−0.0166817	−	0.0513411i
$996$	−1695.82	+	551.004i	−1.70263	+	0.553217i
$997$	−476.323	+	655.602i	−0.477756	+	0.657575i	−0.978072	−	0.208268i	$-0.933217\pi$
$997$	−476.323	+	655.602i	−0.477756	+	0.657575i	0.500316	+	0.865843i	$0.333217\pi$
$998$	−106.265	−	146.262i	−0.106478	−	0.146555i
$999$	274.339	−	844.329i	0.274614	−	0.845174i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.3.i.d.46.2	yes	12
5.2	odd	4		275.3.q.f.24.3		24
5.3	odd	4		275.3.q.f.24.4		24
5.4	even	2		275.3.x.f.101.2		12
11.4	even	5		605.3.c.d.241.8		12
11.6	odd	10	inner	55.3.i.d.6.2	✓	12
11.7	odd	10		605.3.c.d.241.5		12
55.17	even	20		275.3.q.f.149.4		24
55.28	even	20		275.3.q.f.149.3		24
55.39	odd	10		275.3.x.f.226.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.i.d.6.2	✓	12	11.6	odd	10	inner
55.3.i.d.46.2	yes	12	1.1	even	1	trivial
275.3.q.f.24.3		24	5.2	odd	4
275.3.q.f.24.4		24	5.3	odd	4
275.3.q.f.149.3		24	55.28	even	20
275.3.q.f.149.4		24	55.17	even	20
275.3.x.f.101.2		12	5.4	even	2
275.3.x.f.226.2		12	55.39	odd	10
605.3.c.d.241.5		12	11.7	odd	10
605.3.c.d.241.8		12	11.4	even	5

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:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	55.i (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.289909 + 0.0941972i) q^{2} +(-4.17687 + 3.03467i) q^{3} +(-3.16089 - 2.29652i) q^{4} +(-0.690983 - 2.12663i) q^{5} +(-1.49677 + 0.486330i) q^{6} +(-5.94293 + 8.17974i) q^{7} +(-1.41674 - 1.94998i) q^{8} +(5.45583 - 16.7913i) q^{9} -0.681617i q^{10} +(-1.50807 + 10.8961i) q^{11} +20.1718 q^{12} +(4.61316 + 1.49891i) q^{13} +(-2.49342 + 1.81157i) q^{14} +(9.33976 + 6.78573i) q^{15} +(4.60237 + 14.1646i) q^{16} +(-2.71930 + 0.883556i) q^{17} +(3.16339 - 4.35403i) q^{18} +(-12.5616 - 17.2895i) q^{19} +(-2.69973 + 8.30890i) q^{20} -52.2005i q^{21} +(-1.46359 + 3.01683i) q^{22} -12.1155 q^{23} +(11.8351 + 3.84545i) q^{24} +(-4.04508 + 2.93893i) q^{25} +(1.19620 + 0.869094i) q^{26} +(13.8091 + 42.4999i) q^{27} +(37.5699 - 12.2072i) q^{28} +(-28.0610 + 38.6227i) q^{29} +(2.06848 + 2.84702i) q^{30} +(9.63737 - 29.6608i) q^{31} +14.1812i q^{32} +(-26.7672 - 50.0882i) q^{33} -0.871580 q^{34} +(21.5017 + 6.98633i) q^{35} +(-55.8070 + 40.5461i) q^{36} +(-16.0724 - 11.6773i) q^{37} +(-2.01309 - 6.19566i) q^{38} +(-23.8172 + 7.73869i) q^{39} +(-3.16793 + 4.36028i) q^{40} +(23.5474 + 32.4102i) q^{41} +(4.91714 - 15.1334i) q^{42} +28.7133i q^{43} +(29.7901 - 30.9782i) q^{44} -39.4788 q^{45} +(-3.51240 - 1.14125i) q^{46} +(3.18139 - 2.31141i) q^{47} +(-62.2085 - 45.1971i) q^{48} +(-16.4479 - 50.6214i) q^{49} +(-1.44955 + 0.470986i) q^{50} +(8.67687 - 11.9427i) q^{51} +(-11.1394 - 15.3321i) q^{52} +(-19.4659 + 59.9100i) q^{53} +13.6219i q^{54} +(24.2141 - 4.32195i) q^{55} +24.3699 q^{56} +(104.936 + 34.0958i) q^{57} +(-11.7733 + 8.55381i) q^{58} +(41.4758 + 30.1339i) q^{59} +(-13.9384 - 42.8979i) q^{60} +(31.6001 - 10.2675i) q^{61} +(5.58793 - 7.69112i) q^{62} +(104.925 + 144.417i) q^{63} +(17.0737 - 52.5473i) q^{64} -10.8462i q^{65} +(-3.04189 - 17.0424i) q^{66} -90.1298 q^{67} +(10.6245 + 3.45212i) q^{68} +(50.6049 - 36.7666i) q^{69} +(5.57545 + 4.05080i) q^{70} +(1.85591 + 5.71191i) q^{71} +(-40.4722 + 13.1502i) q^{72} +(76.9424 - 105.902i) q^{73} +(-3.55957 - 4.89933i) q^{74} +(7.97710 - 24.5510i) q^{75} +83.4983i q^{76} +(-80.1652 - 77.0905i) q^{77} -7.63380 q^{78} +(85.4604 + 27.7678i) q^{79} +(26.9428 - 19.5751i) q^{80} +(-58.1000 - 42.2121i) q^{81} +(3.77365 + 11.6141i) q^{82} +(-84.0686 + 27.3155i) q^{83} +(-119.880 + 165.000i) q^{84} +(3.75799 + 5.17242i) q^{85} +(-2.70472 + 8.32426i) q^{86} -246.478i q^{87} +(23.3837 - 12.4963i) q^{88} -118.531 q^{89} +(-11.4453 - 3.71879i) q^{90} +(-39.6764 + 28.8266i) q^{91} +(38.2959 + 27.8236i) q^{92} +(49.7567 + 153.135i) q^{93} +(1.14004 - 0.370422i) q^{94} +(-28.0885 + 38.6606i) q^{95} +(-43.0353 - 59.2330i) q^{96} +(-20.6501 + 63.5544i) q^{97} -16.2250i q^{98} +(174.733 + 84.7699i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 5 q^{2} - 13 q^{3} + 13 q^{4} - 15 q^{5} + 20 q^{6} - 5 q^{7} - 35 q^{8} + 4 q^{9} + 12 q^{11} - 2 q^{12} + 70 q^{13} - 60 q^{14} + 35 q^{15} - 43 q^{16} - 15 q^{17} - 30 q^{18} - 80 q^{19} + 20 q^{20}+ \cdots + 669 q^{99}+O(q^{100}) \) 12 * q + 5 * q^2 - 13 * q^3 + 13 * q^4 - 15 * q^5 + 20 * q^6 - 5 * q^7 - 35 * q^8 + 4 * q^9 + 12 * q^11 - 2 * q^12 + 70 * q^13 - 60 * q^14 + 35 * q^15 - 43 * q^16 - 15 * q^17 - 30 * q^18 - 80 * q^19 + 20 * q^20 - 10 * q^22 + 42 * q^23 + 210 * q^24 - 15 * q^25 - 120 * q^26 - 109 * q^27 + 140 * q^28 + 5 * q^29 - 20 * q^30 - 46 * q^31 + 42 * q^33 + 10 * q^34 + 20 * q^35 - 39 * q^36 - 42 * q^37 - 130 * q^38 - 285 * q^39 - 25 * q^40 + 230 * q^41 + 135 * q^42 + 488 * q^44 - 50 * q^45 + 205 * q^46 + 58 * q^47 - 323 * q^48 - 212 * q^49 - 25 * q^50 + 360 * q^51 + 410 * q^52 - 43 * q^53 - 80 * q^55 - 410 * q^56 + 270 * q^57 - 450 * q^58 - 74 * q^59 - 25 * q^60 - 290 * q^61 - 350 * q^62 + 295 * q^63 - 7 * q^64 + 185 * q^66 - 212 * q^67 + 55 * q^68 - 73 * q^69 + 160 * q^70 - 276 * q^71 - 555 * q^72 + 645 * q^73 - 100 * q^74 + 10 * q^75 - 140 * q^77 + 360 * q^78 + 235 * q^79 + 140 * q^80 - 30 * q^81 + 215 * q^82 + 60 * q^83 - 580 * q^84 + 65 * q^85 - 480 * q^86 - 165 * q^88 - 114 * q^89 + 145 * q^90 + 160 * q^91 + 33 * q^92 + 129 * q^93 + 375 * q^94 + 50 * q^95 + 265 * q^96 + 63 * q^97 + 669 * q^99

Introduction

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