LMFDB - Embedded newform 361.3.f.e.299.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [361,3,Mod(116,361)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("361.116"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(361, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	361.f (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,3,-9,-9,3,9,6,-9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$9.83653754341$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
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} + 24x^{10} + 216x^{8} + 905x^{6} + 1770x^{4} + 1395x^{2} + 361 $ x^12 + 24x^10 + 216x^8 + 905x^6 + 1770x^4 + 1395*x^2 + 361
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			299.2
Root			$0.918492i$ of defining polynomial
Character	$\chi$	$=$	361.299
Dual form			361.3.f.e.262.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.987791 + 2.71393i) q^{2} +(-5.03126 - 0.887147i) q^{3} +(-3.32553 + 2.79045i) q^{4} +(2.44658 + 2.05292i) q^{5} +(-2.56218 - 14.5308i) q^{6} +(3.87208 + 6.70664i) q^{7} +(-0.853313 - 0.492661i) q^{8} +(16.0693 + 5.84876i) q^{9} +(-3.15479 + 8.66771i) q^{10} +(-3.45312 + 5.98097i) q^{11} +(19.2071 - 11.0892i) q^{12} +(-6.01079 + 1.05986i) q^{13} +(-14.3766 + 17.1333i) q^{14} +(-10.4881 - 12.4993i) q^{15} +(-2.52119 + 14.2984i) q^{16} +(-1.18154 + 0.430046i) q^{17} +49.3885i q^{18} -13.8647 q^{20} +(-13.5317 - 37.1780i) q^{21} +(-19.6429 - 3.46358i) q^{22} +(1.45017 - 1.21684i) q^{23} +(3.85618 + 3.23572i) q^{24} +(-2.56995 - 14.5749i) q^{25} +(-8.81380 - 15.2659i) q^{26} +(-35.8406 - 20.6926i) q^{27} +(-31.5912 - 11.4983i) q^{28} +(-4.02691 + 11.0638i) q^{29} +(23.5621 - 40.8108i) q^{30} +(-24.9929 + 14.4296i) q^{31} +(-45.1766 + 7.96586i) q^{32} +(22.6795 - 27.0284i) q^{33} +(-2.33423 - 2.78183i) q^{34} +(-4.29487 + 24.3574i) q^{35} +(-69.7596 + 25.3904i) q^{36} -43.6204i q^{37} +31.1821 q^{39} +(-1.07630 - 2.95712i) q^{40} +(-30.0319 - 5.29544i) q^{41} +(87.5320 - 73.4481i) q^{42} +(4.54356 + 3.81250i) q^{43} +(-5.20616 - 29.5256i) q^{44} +(27.3079 + 47.2986i) q^{45} +(4.73487 + 2.73368i) q^{46} +(-75.3927 - 27.4407i) q^{47} +(25.3695 - 69.7022i) q^{48} +(-5.48600 + 9.50203i) q^{49} +(37.0168 - 21.3716i) q^{50} +(6.32616 - 1.11547i) q^{51} +(17.0315 - 20.2974i) q^{52} +(50.3876 + 60.0496i) q^{53} +(20.7552 - 117.709i) q^{54} +(-20.7268 + 7.54394i) q^{55} -7.63048i q^{56} -34.0042 q^{58} +(25.7737 + 70.8126i) q^{59} +(69.7571 + 12.3001i) q^{60} +(-21.7915 + 18.2852i) q^{61} +(-63.8488 - 53.5755i) q^{62} +(22.9962 + 130.418i) q^{63} +(-37.2060 - 64.4427i) q^{64} +(-16.8817 - 9.74665i) q^{65} +(95.7560 + 34.8523i) q^{66} +(-44.0083 + 120.912i) q^{67} +(2.72923 - 4.72716i) q^{68} +(-8.37569 + 4.83570i) q^{69} +(-70.3468 + 12.4040i) q^{70} +(-3.49628 + 4.16670i) q^{71} +(-10.8307 - 12.9076i) q^{72} +(0.731648 - 4.14938i) q^{73} +(118.383 - 43.0879i) q^{74} +75.6101i q^{75} -53.4830 q^{77} +(30.8014 + 84.6261i) q^{78} +(87.6776 + 15.4599i) q^{79} +(-35.5218 + 29.8063i) q^{80} +(44.0674 + 36.9769i) q^{81} +(-15.2938 - 86.7354i) q^{82} +(10.4759 + 18.1448i) q^{83} +(148.743 + 85.8768i) q^{84} +(-3.77359 - 1.37347i) q^{85} +(-5.85879 + 16.0969i) q^{86} +(30.0757 - 52.0926i) q^{87} +(5.89318 - 3.40243i) q^{88} +(144.671 - 25.5093i) q^{89} +(-101.391 + 120.833i) q^{90} +(-30.3824 - 36.2083i) q^{91} +(-1.42706 + 8.09323i) q^{92} +(138.547 - 50.4269i) q^{93} -231.716i q^{94} +234.362 q^{96} +(-23.7675 - 65.3008i) q^{97} +(-31.2069 - 5.50262i) q^{98} +(-90.4706 + 75.9138i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 9 q^{3} - 9 q^{4} + 3 q^{5} + 9 q^{6} + 6 q^{7} - 9 q^{8} + 39 q^{9} - 30 q^{10} - 18 q^{11} + 63 q^{12} - 51 q^{13} - 90 q^{14} - 54 q^{15} + 51 q^{16} - 75 q^{17} - 90 q^{20} + 48 q^{21}+ \cdots - 366 q^{99}+O(q^{100}) $ 12 * q + 3 * q^2 - 9 * q^3 - 9 * q^4 + 3 * q^5 + 9 * q^6 + 6 * q^7 - 9 * q^8 + 39 * q^9 - 30 * q^10 - 18 * q^11 + 63 * q^12 - 51 * q^13 - 90 * q^14 - 54 * q^15 + 51 * q^16 - 75 * q^17 - 90 * q^20 + 48 * q^21 - 33 * q^22 - 66 * q^23 - 66 * q^24 + 123 * q^25 + 21 * q^26 - 27 * q^27 - 6 * q^28 - 78 * q^29 + 24 * q^30 + 99 * q^31 - 222 * q^32 - 15 * q^33 - 66 * q^34 - 66 * q^35 - 225 * q^36 - 108 * q^39 + 141 * q^40 - 171 * q^41 + 123 * q^42 + 54 * q^43 - 51 * q^44 - 3 * q^45 - 54 * q^46 - 81 * q^47 - 24 * q^48 - 24 * q^49 + 72 * q^50 + 48 * q^51 - 123 * q^52 - 96 * q^53 + 210 * q^54 - 153 * q^55 - 132 * q^58 + 111 * q^59 + 231 * q^60 - 120 * q^61 - 171 * q^62 + 171 * q^63 + 27 * q^64 + 126 * q^65 + 69 * q^66 - 18 * q^67 - 30 * q^68 + 72 * q^69 - 126 * q^70 + 138 * q^71 + 114 * q^72 - 135 * q^73 + 471 * q^74 + 246 * q^77 - 99 * q^78 + 132 * q^79 + 264 * q^80 + 390 * q^81 - 126 * q^82 - 156 * q^83 + 99 * q^84 + 15 * q^85 + 72 * q^86 + 69 * q^87 - 405 * q^88 + 531 * q^89 - 93 * q^90 + 393 * q^91 + 12 * q^92 + 384 * q^93 + 558 * q^96 - 588 * q^97 - 159 * q^98 - 366 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{18}\right)$

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 $

$2$	0.987791	+	2.71393i	0.493895	+	1.35697i	0.897088	+	0.441852i	$0.145678\pi$
$2$	0.987791	+	2.71393i	0.493895	+	1.35697i	−0.403193	+	0.915115i	$0.632100\pi$
$3$	−5.03126	−	0.887147i	−1.67709	−	0.295716i	−0.747485	−	0.664279i	$-0.768739\pi$
$3$	−5.03126	−	0.887147i	−1.67709	−	0.295716i	−0.929603	+	0.368563i	$0.879850\pi$
$4$	−3.32553	+	2.79045i	−0.831381	+	0.697612i
$5$	2.44658	+	2.05292i	0.489316	+	0.410585i	0.853781	−	0.520632i	$-0.174304\pi$
$5$	2.44658	+	2.05292i	0.489316	+	0.410585i	−0.364465	+	0.931217i	$0.618748\pi$
$6$	−2.56218	−	14.5308i	−0.427029	−	2.42180i
$7$	3.87208	+	6.70664i	0.553154	+	0.958091i	0.998045	+	0.0625061i	$0.0199093\pi$
$7$	3.87208	+	6.70664i	0.553154	+	0.958091i	−0.444890	+	0.895585i	$0.646757\pi$
$8$	−0.853313	−	0.492661i	−0.106664	−	0.0615826i
$9$	16.0693	+	5.84876i	1.78548	+	0.649862i
$10$	−3.15479	+	8.66771i	−0.315479	+	0.866771i
$11$	−3.45312	+	5.98097i	−0.313920	+	0.543725i	−0.979207	−	0.202862i	$-0.934976\pi$
$11$	−3.45312	+	5.98097i	−0.313920	+	0.543725i	0.665288	+	0.746587i	$0.268309\pi$
$12$	19.2071	−	11.0892i	1.60059	−	0.924103i
$13$	−6.01079	+	1.05986i	−0.462368	+	0.0815280i	−0.399980	−	0.916524i	$-0.630983\pi$
$13$	−6.01079	+	1.05986i	−0.462368	+	0.0815280i	−0.0623884	+	0.998052i	$0.519872\pi$
$14$	−14.3766	+	17.1333i	−1.02690	+	1.22381i
$15$	−10.4881	−	12.4993i	−0.699209	−	0.833285i
$16$	−2.52119	+	14.2984i	−0.157574	+	0.893648i
$17$	−1.18154	+	0.430046i	−0.0695025	+	0.0252968i	−0.376537	−	0.926401i	$-0.622885\pi$
$17$	−1.18154	+	0.430046i	−0.0695025	+	0.0252968i	0.307035	+	0.951698i	$0.400663\pi$
$18$			49.3885i			2.74380i
$19$		0			0
$19$		0			0
$20$	−13.8647			−0.693237
$21$	−13.5317	−	37.1780i	−0.644365	−	1.77038i
$22$	−19.6429	−	3.46358i	−0.892860	−	0.157435i
$23$	1.45017	−	1.21684i	0.0630508	−	0.0529059i	−0.610718	−	0.791848i	$-0.709119\pi$
$23$	1.45017	−	1.21684i	0.0630508	−	0.0529059i	0.673768	+	0.738943i	$0.264675\pi$
$24$	3.85618	+	3.23572i	0.160674	+	0.134822i
$25$	−2.56995	−	14.5749i	−0.102798	−	0.582996i
$26$	−8.81380	−	15.2659i	−0.338992	−	0.587152i
$27$	−35.8406	−	20.6926i	−1.32743	−	0.766391i
$28$	−31.5912	−	11.4983i	−1.12826	−	0.410652i
$29$	−4.02691	+	11.0638i	−0.138859	+	0.381512i	−0.989557	−	0.144143i	$-0.953957\pi$
$29$	−4.02691	+	11.0638i	−0.138859	+	0.381512i	0.850698	+	0.525655i	$0.176180\pi$
$30$	23.5621	−	40.8108i	0.785404	−	1.36036i
$31$	−24.9929	+	14.4296i	−0.806222	+	0.465472i	−0.845642	−	0.533750i	$-0.820782\pi$
$31$	−24.9929	+	14.4296i	−0.806222	+	0.465472i	0.0394204	+	0.999223i	$0.487449\pi$
$32$	−45.1766	+	7.96586i	−1.41177	+	0.248933i
$33$	22.6795	−	27.0284i	0.687259	−	0.819043i
$34$	−2.33423	−	2.78183i	−0.0686539	−	0.0818186i
$35$	−4.29487	+	24.3574i	−0.122711	+	0.695926i
$36$	−69.7596	+	25.3904i	−1.93777	+	0.705290i
$37$		−	43.6204i		−	1.17893i	−0.807794	−	0.589465i	$-0.799338\pi$
$37$		−	43.6204i		−	1.17893i	0.807794	−	0.589465i	$-0.200662\pi$
$38$		0			0
$39$	31.1821			0.799541
$40$	−1.07630	−	2.95712i	−0.0269076	−	0.0739280i
$41$	−30.0319	−	5.29544i	−0.732485	−	0.129157i	−0.205049	−	0.978752i	$-0.565735\pi$
$41$	−30.0319	−	5.29544i	−0.732485	−	0.129157i	−0.527436	+	0.849595i	$0.676847\pi$
$42$	87.5320	−	73.4481i	2.08410	−	1.74876i
$43$	4.54356	+	3.81250i	0.105664	+	0.0886629i	0.694089	−	0.719889i	$-0.255807\pi$
$43$	4.54356	+	3.81250i	0.105664	+	0.0886629i	−0.588425	+	0.808552i	$0.700252\pi$
$44$	−5.20616	−	29.5256i	−0.118322	−	0.671037i
$45$	27.3079	+	47.2986i	0.606841	+	1.05108i
$46$	4.73487	+	2.73368i	0.102932	+	0.0594278i
$47$	−75.3927	−	27.4407i	−1.60410	−	0.583844i	−0.623839	−	0.781553i	$-0.714428\pi$
$47$	−75.3927	−	27.4407i	−1.60410	−	0.583844i	−0.980261	+	0.197709i	$0.936650\pi$
$48$	25.3695	−	69.7022i	0.528532	−	1.45213i
$49$	−5.48600	+	9.50203i	−0.111959	+	0.193919i
$50$	37.0168	−	21.3716i	0.740335	−	0.427433i
$51$	6.32616	−	1.11547i	0.124042	−	0.0218720i
$52$	17.0315	−	20.2974i	0.327529	−	0.390334i
$53$	50.3876	+	60.0496i	0.950709	+	1.13301i	0.991005	+	0.133823i	$0.0427255\pi$
$53$	50.3876	+	60.0496i	0.950709	+	1.13301i	−0.0402960	+	0.999188i	$0.512830\pi$
$54$	20.7552	−	117.709i	0.384356	−	2.17979i
$55$	−20.7268	+	7.54394i	−0.376851	+	0.137163i
$56$		−	7.63048i		−	0.136259i
$57$		0			0
$58$	−34.0042			−0.586280
$59$	25.7737	+	70.8126i	0.436842	+	1.20021i	0.941535	+	0.336915i	$0.109383\pi$
$59$	25.7737	+	70.8126i	0.436842	+	1.20021i	−0.504693	+	0.863299i	$0.668394\pi$
$60$	69.7571	+	12.3001i	1.16262	+	0.205001i
$61$	−21.7915	+	18.2852i	−0.357237	+	0.299758i	−0.803688	−	0.595050i	$-0.797132\pi$
$61$	−21.7915	+	18.2852i	−0.357237	+	0.299758i	0.446451	+	0.894808i	$0.352688\pi$
$62$	−63.8488	−	53.5755i	−1.02982	−	0.864121i
$63$	22.9962	+	130.418i	0.365020	+	2.07013i
$64$	−37.2060	−	64.4427i	−0.581344	−	1.00692i
$65$	−16.8817	−	9.74665i	−0.259718	−	0.149948i
$66$	95.7560	+	34.8523i	1.45085	+	0.528065i
$67$	−44.0083	+	120.912i	−0.656840	+	1.80465i	−0.0660687	+	0.997815i	$0.521046\pi$
$67$	−44.0083	+	120.912i	−0.656840	+	1.80465i	−0.590772	+	0.806839i	$0.701177\pi$
$68$	2.72923	−	4.72716i	0.0401357	−	0.0695171i
$69$	−8.37569	+	4.83570i	−0.121387	+	0.0700827i
$70$	−70.3468	+	12.4040i	−1.00495	+	0.177201i
$71$	−3.49628	+	4.16670i	−0.0492433	+	0.0586859i	−0.790104	−	0.612973i	$-0.789973\pi$
$71$	−3.49628	+	4.16670i	−0.0492433	+	0.0586859i	0.740861	+	0.671659i	$0.234418\pi$
$72$	−10.8307	−	12.9076i	−0.150427	−	0.179272i
$73$	0.731648	−	4.14938i	0.0100226	−	0.0568408i	−0.979386	−	0.201996i	$-0.935257\pi$
$73$	0.731648	−	4.14938i	0.0100226	−	0.0568408i	0.989409	+	0.145155i	$0.0463682\pi$
$74$	118.383	−	43.0879i	1.59977	−	0.582269i
$75$			75.6101i			1.00813i
$76$		0			0
$77$	−53.4830			−0.694584
$78$	30.8014	+	84.6261i	0.394890	+	1.08495i
$79$	87.6776	+	15.4599i	1.10984	+	0.195695i	0.698377	−	0.715730i	$-0.253906\pi$
$79$	87.6776	+	15.4599i	1.10984	+	0.195695i	0.411466	+	0.911425i	$0.365017\pi$
$80$	−35.5218	+	29.8063i	−0.444022	+	0.372579i
$81$	44.0674	+	36.9769i	0.544042	+	0.456505i
$82$	−15.2938	−	86.7354i	−0.186510	−	1.05775i
$83$	10.4759	+	18.1448i	0.126215	+	0.218611i	0.922207	−	0.386696i	$-0.126384\pi$
$83$	10.4759	+	18.1448i	0.126215	+	0.218611i	−0.795992	+	0.605307i	$0.793050\pi$
$84$	148.743	+	85.8768i	1.77075	+	1.02234i
$85$	−3.77359	−	1.37347i	−0.0443952	−	0.0161585i
$86$	−5.85879	+	16.0969i	−0.0681254	+	0.187173i
$87$	30.0757	−	52.0926i	0.345697	−	0.598765i
$88$	5.89318	−	3.40243i	0.0669679	−	0.0386640i
$89$	144.671	−	25.5093i	1.62551	−	0.286622i	0.714696	−	0.699435i	$-0.246565\pi$
$89$	144.671	−	25.5093i	1.62551	−	0.286622i	0.910815	+	0.412814i	$0.135454\pi$
$90$	−101.391	+	120.833i	−1.12656	+	1.34259i
$91$	−30.3824	−	36.2083i	−0.333872	−	0.397893i
$92$	−1.42706	+	8.09323i	−0.0155115	+	0.0879699i
$93$	138.547	−	50.4269i	1.48975	−	0.542225i
$94$		−	231.716i		−	2.46507i
$95$		0			0
$96$	234.362			2.44128
$97$	−23.7675	−	65.3008i	−0.245026	−	0.673204i	−0.999851	−	0.0172773i	$-0.994500\pi$
$97$	−23.7675	−	65.3008i	−0.245026	−	0.673204i	0.754824	−	0.655927i	$-0.227722\pi$
$98$	−31.2069	−	5.50262i	−0.318438	−	0.0561491i
$99$	−90.4706	+	75.9138i	−0.913844	+	0.766806i
$100$	49.2169	+	41.2979i	0.492169	+	0.412979i
$101$	−4.79407	−	27.1885i	−0.0474660	−	0.269193i	0.951834	−	0.306615i	$-0.0991965\pi$
$101$	−4.79407	−	27.1885i	−0.0474660	−	0.269193i	−0.999300	+	0.0374222i	$0.988085\pi$
$102$	9.27625	+	16.0669i	0.0909436	+	0.157519i
$103$	−112.587	−	65.0023i	−1.09308	−	0.631090i	−0.158686	−	0.987329i	$-0.550726\pi$
$103$	−112.587	−	65.0023i	−1.09308	−	0.631090i	−0.934395	+	0.356239i	$0.884059\pi$
$104$	5.65124	+	2.05688i	0.0543388	+	0.0197777i
$105$	43.2172	−	118.738i	0.411593	−	1.13084i
$106$	−113.198	+	196.065i	−1.06791	+	1.84967i
$107$	69.4189	−	40.0790i	0.648775	−	0.374570i	−0.139212	−	0.990263i	$-0.544457\pi$
$107$	69.4189	−	40.0790i	0.648775	−	0.374570i	0.787987	+	0.615692i	$0.211124\pi$
$108$	176.930	−	31.1976i	1.63824	−	0.288866i
$109$	68.3737	−	81.4846i	0.627282	−	0.747565i	−0.355022	−	0.934858i	$-0.615527\pi$
$109$	68.3737	−	81.4846i	0.627282	−	0.747565i	0.982304	+	0.187292i	$0.0599712\pi$
$110$	−40.9475	−	48.7993i	−0.372250	−	0.443630i
$111$	−38.6978	+	219.466i	−0.348628	+	1.97717i
$112$	−105.656	+	38.4557i	−0.943359	+	0.343355i
$113$			37.9540i			0.335876i	0.985798	+	0.167938i	$0.0537109\pi$
$113$			37.9540i			0.335876i	−0.985798	+	0.167938i	$0.946289\pi$
$114$		0			0
$115$	6.04602			0.0525741
$116$	−17.4815	−	48.0299i	−0.150702	−	0.414051i
$117$	−102.788	−	18.1243i	−0.878532	−	0.154909i
$118$	−166.722	+	139.896i	−1.41290	+	1.18556i
$119$	−7.45919	−	6.25900i	−0.0626823	−	0.0525967i
$120$	2.79177	+	15.8329i	0.0232647	+	0.131941i
$121$	36.6520	+	63.4831i	0.302909	+	0.524654i
$122$	−71.1503	−	41.0786i	−0.583199	−	0.336710i
$123$	146.401	+	53.2854i	1.19025	+	0.433215i
$124$	42.8493	−	117.727i	0.345559	−	0.949415i
$125$	63.5559	−	110.082i	0.508447	−	0.880656i
$126$	−331.231	+	191.236i	−2.62881	+	1.51775i
$127$	−70.8031	+	12.4845i	−0.557505	+	0.0983031i	−0.445299	−	0.895382i	$-0.646903\pi$
$127$	−70.8031	+	12.4845i	−0.557505	+	0.0983031i	−0.112206	+	0.993685i	$0.535792\pi$
$128$	20.1936	−	24.0657i	0.157762	−	0.188014i
$129$	−19.4776	−	23.2125i	−0.150989	−	0.179942i
$130$	9.77617	−	55.4434i	0.0752013	−	0.426488i
$131$	112.482	−	40.9399i	0.858638	−	0.312518i	0.125081	−	0.992147i	$-0.460081\pi$
$131$	112.482	−	40.9399i	0.858638	−	0.312518i	0.733557	+	0.679628i	$0.237859\pi$
$132$			153.170i			1.16038i
$133$		0			0
$134$	−371.618			−2.77327
$135$	−45.2066	−	124.204i	−0.334863	−	0.920030i
$136$	1.22009	+	0.215135i	0.00897127	+	0.00158188i
$137$	126.196	−	105.891i	0.921141	−	0.772929i	−0.0530650	−	0.998591i	$-0.516899\pi$
$137$	126.196	−	105.891i	0.921141	−	0.772929i	0.974206	+	0.225662i	$0.0724546\pi$
$138$	−21.3972	−	17.9544i	−0.155052	−	0.130104i
$139$	36.9075	+	209.313i	0.265522	+	1.50585i	0.767545	+	0.640995i	$0.221478\pi$
$139$	36.9075	+	209.313i	0.265522	+	1.50585i	−0.502023	+	0.864854i	$0.667411\pi$
$140$	−53.6854	−	92.9858i	−0.383467	−	0.664184i
$141$	354.976	+	204.946i	2.51756	+	1.45352i
$142$	−14.7617	−	5.37283i	−0.103956	−	0.0378368i
$143$	14.4169	−	39.6102i	0.100818	−	0.276994i
$144$	−124.142	+	215.020i	−0.862094	+	1.49319i
$145$	−32.5654	+	18.8016i	−0.224589	+	0.129666i
$146$	11.9839	−	2.11308i	0.0820812	−	0.0144731i
$147$	36.0312	−	42.9403i	0.245110	−	0.292111i
$148$	121.721	+	145.061i	0.822436	+	0.980141i
$149$	−10.1090	+	57.3310i	−0.0678456	+	0.384772i	0.931911	+	0.362688i	$0.118141\pi$
$149$	−10.1090	+	57.3310i	−0.0678456	+	0.384772i	−0.999756	+	0.0220834i	$0.992970\pi$
$150$	−205.201	+	74.6870i	−1.36801	+	0.497913i
$151$			54.6073i			0.361638i	0.983516	+	0.180819i	$0.0578748\pi$
$151$			54.6073i			0.361638i	−0.983516	+	0.180819i	$0.942125\pi$
$152$		0			0
$153$	−21.5018			−0.140535
$154$	−52.8300	−	145.149i	−0.343052	−	0.942527i
$155$	−90.7700	−	16.0052i	−0.585613	−	0.103259i
$156$	−103.697	+	87.0120i	−0.664723	+	0.557769i
$157$	−13.5644	−	11.3819i	−0.0863977	−	0.0724963i	0.598566	−	0.801074i	$-0.295737\pi$
$157$	−13.5644	−	11.3819i	−0.0863977	−	0.0724963i	−0.684964	+	0.728577i	$0.740182\pi$
$158$	44.6499	+	253.222i	0.282595	+	1.60267i
$159$	−200.240	−	346.826i	−1.25937	−	2.18130i
$160$	−126.882	−	73.2551i	−0.793010	−	0.457844i
$161$	13.7760	+	5.01407i	0.0855654	+	0.0311433i
$162$	−56.8236	+	156.121i	−0.350763	+	0.963713i
$163$	−101.967	+	176.611i	−0.625562	+	1.08351i	0.362869	+	0.931840i	$0.381797\pi$
$163$	−101.967	+	176.611i	−0.625562	+	1.08351i	−0.988432	+	0.151666i	$0.951536\pi$
$164$	114.648	−	66.1923i	0.699076	−	0.403612i
$165$	110.975	−	19.5678i	0.672573	−	0.118593i
$166$	−38.8957	+	46.3541i	−0.234311	+	0.279241i
$167$	−167.155	−	199.208i	−1.00093	−	1.19286i	−0.981188	−	0.193057i	$-0.938160\pi$
$167$	−167.155	−	199.208i	−1.00093	−	1.19286i	−0.0197423	−	0.999805i	$-0.506285\pi$
$168$	−6.76936	+	38.3910i	−0.0402938	+	0.228518i
$169$	−123.802	+	45.0602i	−0.732555	+	0.266628i
$170$		−	11.5980i		−	0.0682234i
$171$		0			0
$172$	−25.7483			−0.149700
$173$	28.4800	+	78.2481i	0.164624	+	0.452301i	0.994386	−	0.105817i	$-0.0337458\pi$
$173$	28.4800	+	78.2481i	0.164624	+	0.452301i	−0.829761	+	0.558118i	$0.811524\pi$
$174$	171.084	+	30.1668i	0.983243	+	0.173372i
$175$	87.7976	−	73.6709i	0.501700	−	0.420977i
$176$	−76.8122	−	64.4531i	−0.436433	−	0.366211i
$177$	−66.8529	−	379.142i	−0.377700	−	2.14204i
$178$	212.135	+	367.428i	1.19177	+	2.06420i
$179$	196.975	+	113.723i	1.10042	+	0.635327i	0.936331	−	0.351119i	$-0.114199\pi$
$179$	196.975	+	113.723i	1.10042	+	0.635327i	0.164087	+	0.986446i	$0.447532\pi$
$180$	−222.797	−	81.0915i	−1.23776	−	0.450509i
$181$	−13.0048	+	35.7303i	−0.0718496	+	0.197405i	−0.970419	−	0.241426i	$-0.922385\pi$
$181$	−13.0048	+	35.7303i	−0.0718496	+	0.197405i	0.898570	+	0.438831i	$0.144607\pi$
$182$	68.2555	−	118.222i	0.375030	−	0.649571i
$183$	125.860	−	72.6655i	0.687761	−	0.397079i
$184$	−1.83693	+	0.323901i	−0.00998334	+	0.00176033i
$185$	89.5495	−	106.721i	0.484051	−	0.576870i
$186$	273.711	+	326.196i	1.47156	+	1.75374i
$187$	1.50791	−	8.55177i	0.00806368	−	0.0457314i
$188$	327.292	−	119.125i	1.74092	−	0.633641i
$189$		−	320.493i		−	1.69573i
$190$		0			0
$191$	217.732			1.13996			0.569979	−	0.821659i	$-0.306951\pi$
$191$	217.732			1.13996			0.569979	+	0.821659i	$0.306951\pi$
$192$	130.023	+	357.235i	0.677203	+	1.86060i
$193$	166.023	+	29.2742i	0.860220	+	0.151680i	0.586321	−	0.810078i	$-0.300576\pi$
$193$	166.023	+	29.2742i	0.860220	+	0.151680i	0.273899	+	0.961759i	$0.411687\pi$
$194$	153.745	−	129.007i	0.792498	−	0.664985i
$195$	76.2895	+	64.0145i	0.391228	+	0.328279i
$196$	−8.27108	−	46.9076i	−0.0421994	−	0.239325i
$197$	106.287	+	184.094i	0.539527	+	0.934488i	0.998929	+	0.0462599i	$0.0147302\pi$
$197$	106.287	+	184.094i	0.539527	+	0.934488i	−0.459402	+	0.888228i	$0.651936\pi$
$198$	−295.391	−	170.544i	−1.49187	−	0.861334i
$199$	−11.8194	−	4.30192i	−0.0593941	−	0.0216177i	0.312152	−	0.950032i	$-0.398950\pi$
$199$	−11.8194	−	4.30192i	−0.0593941	−	0.0216177i	−0.371546	+	0.928414i	$0.621172\pi$
$200$	−4.98751	+	13.7031i	−0.0249376	+	0.0685154i
$201$	328.684	−	569.297i	1.63524	−	2.83232i
$202$	69.0522	−	39.8673i	0.341843	−	0.197363i
$203$	−89.7936	+	15.8330i	−0.442333	+	0.0779953i
$204$	−17.9251	+	21.3624i	−0.0878684	+	0.104717i
$205$	−62.6043	−	74.6089i	−0.305387	−	0.363946i
$206$	65.1992	−	369.763i	0.316501	−	1.79497i
$207$	30.4202	−	11.0721i	0.146958	−	0.0534882i
$208$		−	88.6166i		−	0.426041i
$209$		0			0
$210$	364.938			1.73780
$211$	97.0678	+	266.692i	0.460037	+	1.26394i	0.925458	+	0.378851i	$0.123681\pi$
$211$	97.0678	+	266.692i	0.460037	+	1.26394i	−0.465421	+	0.885090i	$0.654097\pi$
$212$	−335.130	−	59.0925i	−1.58080	−	0.278738i
$213$	21.2872	−	17.8620i	0.0999397	−	0.0838593i
$214$	177.343	+	148.809i	0.828706	+	0.695367i
$215$	3.28941	+	18.6552i	0.0152996	+	0.0867683i
$216$	20.3888	+	35.3145i	0.0943927	+	0.163493i
$217$	−193.549	−	111.745i	−0.891930	−	0.514956i
$218$	288.683	+	105.072i	1.32423	+	0.481981i
$219$	−7.36223	+	20.2275i	−0.0336175	+	0.0923632i
$220$	47.8766	−	82.9246i	0.217621	−	0.376930i
$221$	6.64621	−	3.83719i	0.0300733	−	0.0173628i
$222$	−633.841	+	111.763i	−2.85514	+	0.503438i
$223$	−59.9557	+	71.4524i	−0.268860	+	0.320414i	−0.883534	−	0.468366i	$-0.844843\pi$
$223$	−59.9557	+	71.4524i	−0.268860	+	0.320414i	0.614675	+	0.788781i	$0.289287\pi$
$224$	−228.352	−	272.139i	−1.01943	−	1.21491i
$225$	43.9478	−	249.240i	0.195323	−	1.10773i
$226$	−103.005	+	37.4906i	−0.455773	+	0.165888i
$227$			1.80854i			0.00796716i	0.999992	+	0.00398358i	$0.00126802\pi$
$227$			1.80854i			0.00796716i	−0.999992	+	0.00398358i	$0.998732\pi$
$228$		0			0
$229$	111.104			0.485169			0.242584	−	0.970130i	$-0.422005\pi$
$229$	111.104			0.485169			0.242584	+	0.970130i	$0.422005\pi$
$230$	5.97220	+	16.4085i	0.0259661	+	0.0713413i
$231$	269.087	+	47.4473i	1.16488	+	0.205399i
$232$	8.88693	−	7.45702i	0.0383057	−	0.0321423i
$233$	−111.036	−	93.1704i	−0.476550	−	0.399873i	0.372627	−	0.927981i	$-0.378457\pi$
$233$	−111.036	−	93.1704i	−0.476550	−	0.399873i	−0.849177	+	0.528108i	$0.822901\pi$
$234$	−52.3450	−	296.863i	−0.223697	−	1.26865i
$235$	−128.121	−	221.911i	−0.545194	−	0.944303i
$236$	−283.310	−	163.569i	−1.20047	−	0.693089i
$237$	−427.414	−	155.566i	−1.80343	−	0.656396i
$238$	9.61840	−	26.4263i	0.0404134	−	0.111035i
$239$	−40.4823	+	70.1174i	−0.169382	+	0.293378i	−0.938203	−	0.346086i	$-0.887510\pi$
$239$	−40.4823	+	70.1174i	−0.169382	+	0.293378i	0.768821	+	0.639464i	$0.220844\pi$
$240$	205.162	−	118.450i	0.854841	−	0.493543i
$241$	198.246	−	34.9562i	0.822598	−	0.145046i	0.253521	−	0.967330i	$-0.418411\pi$
$241$	198.246	−	34.9562i	0.822598	−	0.145046i	0.569078	+	0.822284i	$0.307300\pi$
$242$	−136.084	+	162.179i	−0.562332	+	0.670161i
$243$	50.5060	+	60.1907i	0.207844	+	0.247698i
$244$	21.4442	−	121.616i	0.0878859	−	0.498426i
$245$	−32.9289	+	11.9851i	−0.134404	+	0.0489189i
$246$			449.956i			1.82909i
$247$		0			0
$248$	28.4357			0.114660
$249$	−36.6098	−	100.585i	−0.147027	−	0.403954i
$250$	361.535	+	63.7484i	1.44614	+	0.254994i
$251$	194.262	−	163.005i	0.773952	−	0.649423i	−0.167766	−	0.985827i	$-0.553655\pi$
$251$	194.262	−	163.005i	0.773952	−	0.649423i	0.941718	+	0.336404i	$0.109211\pi$
$252$	−440.399	−	369.539i	−1.74762	−	1.46642i
$253$	2.27026	+	12.8753i	0.00897336	+	0.0508905i
$254$	−103.821	−	179.823i	−0.408743	−	0.707964i
$255$	17.7674	+	10.2580i	0.0696763	+	0.0402276i
$256$	−194.438	−	70.7696i	−0.759523	−	0.276444i
$257$	−76.6506	+	210.596i	−0.298251	+	0.819439i	0.696541	+	0.717517i	$0.254721\pi$
$257$	−76.6506	+	210.596i	−0.298251	+	0.819439i	−0.994792	+	0.101922i	$0.967501\pi$
$258$	43.7574	−	75.7901i	0.169602	−	0.293760i
$259$	292.546	−	168.902i	1.12952	−	0.652130i
$260$	83.3380	−	14.6947i	0.320531	−	0.0565182i
$261$	−129.419	+	154.236i	−0.495860	+	0.590943i
$262$	222.216	+	264.827i	0.848154	+	1.01079i
$263$	24.9180	−	141.317i	0.0947454	−	0.537328i	−0.900080	−	0.435725i	$-0.856492\pi$
$263$	24.9180	−	141.317i	0.0947454	−	0.537328i	0.994825	−	0.101602i	$-0.0323970\pi$
$264$	−32.6686	+	11.8904i	−0.123745	+	0.0450394i
$265$			250.358i			0.944747i
$266$		0			0
$267$	−750.506			−2.81088
$268$	−191.047	−	524.898i	−0.712863	−	1.95858i
$269$	−92.9865	−	16.3960i	−0.345675	−	0.0609518i	−0.00188442	−	0.999998i	$-0.500600\pi$
$269$	−92.9865	−	16.3960i	−0.345675	−	0.0609518i	−0.343790	+	0.939046i	$0.611711\pi$
$270$	292.427	−	245.375i	1.08306	−	0.908797i
$271$	251.338	+	210.898i	0.927446	+	0.778220i	0.975357	−	0.220632i	$-0.0708119\pi$
$271$	251.338	+	210.898i	0.927446	+	0.778220i	−0.0479110	+	0.998852i	$0.515256\pi$
$272$	−3.17007	−	17.9784i	−0.0116547	−	0.0660969i
$273$	120.740	+	209.127i	0.442269	+	0.766033i
$274$	412.037	+	237.890i	1.50379	+	0.868211i
$275$	96.0465	+	34.9580i	0.349260	+	0.127120i
$276$	14.3598	−	39.4532i	0.0520282	−	0.142946i
$277$	−136.885	+	237.092i	−0.494169	+	0.855927i	−0.999977	−	0.00671948i	$-0.997861\pi$
$277$	−136.885	+	237.092i	−0.494169	+	0.855927i	0.505808	+	0.862646i	$0.331194\pi$
$278$	−531.605	+	306.922i	−1.91225	+	1.10404i
$279$	−486.014	+	85.6974i	−1.74199	+	0.307159i
$280$	15.6648	−	18.6686i	0.0559457	−	0.0666735i
$281$	61.1283	+	72.8499i	0.217539	+	0.259252i	0.863767	−	0.503892i	$-0.168099\pi$
$281$	61.1283	+	72.8499i	0.217539	+	0.259252i	−0.646228	+	0.763144i	$0.723655\pi$
$282$	−205.567	+	1165.83i	−0.728959	+	4.13413i
$283$	−431.334	+	156.993i	−1.52415	+	0.554744i	−0.962180	−	0.272415i	$-0.912178\pi$
$283$	−431.334	+	156.993i	−1.52415	+	0.554744i	−0.561968	+	0.827159i	$0.689955\pi$
$284$		−	23.6126i		−	0.0831431i
$285$		0			0
$286$	121.740			0.425665
$287$	−80.7714	−	221.917i	−0.281433	−	0.773232i
$288$	−772.549	−	136.221i	−2.68246	−	0.472990i
$289$	−220.176	+	184.749i	−0.761854	+	0.639271i
$290$	−83.1941	−	69.8081i	−0.286876	−	0.240718i
$291$	61.6493	+	349.631i	0.211853	+	1.20148i
$292$	9.14552	+	15.8405i	0.0313203	+	0.0542483i
$293$	−186.848	−	107.877i	−0.637708	−	0.368181i	0.146023	−	0.989281i	$-0.453353\pi$
$293$	−186.848	−	107.877i	−0.637708	−	0.368181i	−0.783731	+	0.621100i	$0.786686\pi$
$294$	152.128	+	55.3702i	0.517444	+	0.188334i
$295$	−82.3156	+	226.160i	−0.279036	+	0.766645i
$296$	−21.4901	+	37.2219i	−0.0726016	+	0.125750i
$297$	247.523	−	142.908i	0.833412	−	0.481171i
$298$	−165.578	+	29.1959i	−0.555631	+	0.0979727i
$299$	−7.42697	+	8.85111i	−0.0248394	+	0.0296024i
$300$	−210.986	−	251.443i	−0.703287	−	0.838144i
$301$	−7.97604	+	45.2344i	−0.0264985	+	0.150280i
$302$	−148.201	+	53.9406i	−0.490731	+	0.178611i
$303$			141.046i			0.465497i
$304$		0			0
$305$	−90.8527			−0.297878
$306$	−21.2393	−	58.3546i	−0.0694096	−	0.190701i
$307$	−155.999	−	27.5068i	−0.508140	−	0.0895987i	−0.0863000	−	0.996269i	$-0.527504\pi$
$307$	−155.999	−	27.5068i	−0.508140	−	0.0895987i	−0.421840	+	0.906670i	$0.638615\pi$
$308$	177.859	−	149.241i	0.577464	−	0.484550i
$309$	508.790	+	426.925i	1.64657	+	1.38164i
$310$	−46.2247	−	262.154i	−0.149112	−	0.845657i
$311$	−12.3978	−	21.4736i	−0.0398642	−	0.0690469i	0.845405	−	0.534126i	$-0.179359\pi$
$311$	−12.3978	−	21.4736i	−0.0398642	−	0.0690469i	−0.885269	+	0.465079i	$0.846026\pi$
$312$	−26.6081	−	15.3622i	−0.0852823	−	0.0492378i
$313$	102.374	+	37.2610i	0.327072	+	0.119045i	0.500337	−	0.865831i	$-0.333209\pi$
$313$	102.374	+	37.2610i	0.327072	+	0.119045i	−0.173265	+	0.984875i	$0.555432\pi$
$314$	17.4909	−	48.0559i	0.0557036	−	0.153044i
$315$	−211.476	+	366.288i	−0.671354	+	1.16282i
$316$	−334.714	+	193.247i	−1.05922	+	0.611542i
$317$	473.574	−	83.5039i	1.49392	−	0.263419i	0.633797	−	0.773499i	$-0.281495\pi$
$317$	473.574	−	83.5039i	1.49392	−	0.263419i	0.860127	+	0.510080i	$0.170384\pi$
$318$	743.468	−	886.031i	2.33795	−	2.78626i
$319$	−52.2671	−	62.2895i	−0.163847	−	0.195265i
$320$	41.2685	−	234.045i	0.128964	−	0.731391i
$321$	−384.821	+	140.063i	−1.19882	+	0.436334i
$322$			42.3401i			0.131491i
$323$		0			0
$324$	−249.729			−0.770770
$325$	30.8948	+	84.8828i	0.0950610	+	0.261178i
$326$	−580.034	−	102.276i	−1.77924	−	0.313729i
$327$	−416.295	+	349.313i	−1.27307	+	1.06824i
$328$	23.0178	+	19.3142i	0.0701761	+	0.0588848i
$329$	−107.892	−	611.884i	−0.327938	−	1.85983i
$330$	162.725	+	281.849i	0.493107	+	0.854087i
$331$	1.38995	+	0.802488i	0.00419925	+	0.00242444i	0.502098	−	0.864811i	$-0.332562\pi$
$331$	1.38995	+	0.802488i	0.00419925	+	0.00242444i	−0.497899	+	0.867235i	$0.665895\pi$
$332$	−85.4698	−	31.1084i	−0.257439	−	0.0937001i
$333$	255.125	−	700.951i	0.766143	−	2.10496i
$334$	375.523	−	650.424i	1.12432	−	1.94738i
$335$	−355.893	+	205.475i	−1.06237	+	0.613357i
$336$	565.700	−	99.7482i	1.68363	−	0.296870i
$337$	192.589	−	229.519i	0.571481	−	0.681065i	−0.400453	−	0.916317i	$-0.631147\pi$
$337$	192.589	−	229.519i	0.571481	−	0.681065i	0.971934	+	0.235253i	$0.0755917\pi$
$338$	−244.581	−	291.480i	−0.723611	−	0.862366i
$339$	33.6708	−	190.957i	0.0993239	−	0.563294i
$340$	16.3818	−	5.96248i	0.0481817	−	0.0175367i
$341$		−	199.309i		−	0.584484i
$342$		0			0
$343$	294.495			0.858586
$344$	−1.99881	−	5.49169i	−0.00581050	−	0.0159642i
$345$	−30.4191	−	5.36371i	−0.0881714	−	0.0155470i
$346$	−184.228	+	154.585i	−0.532450	+	0.446779i
$347$	−296.655	−	248.923i	−0.854915	−	0.717359i	0.105951	−	0.994371i	$-0.466211\pi$
$347$	−296.655	−	248.923i	−0.854915	−	0.717359i	−0.960866	+	0.277013i	$0.910656\pi$
$348$	45.3442	+	257.160i	0.130299	+	0.738965i
$349$	−118.007	−	204.393i	−0.338128	−	0.585654i	0.645953	−	0.763377i	$-0.276460\pi$
$349$	−118.007	−	204.393i	−0.338128	−	0.585654i	−0.984081	+	0.177723i	$0.943127\pi$
$350$	286.664	+	165.505i	0.819039	+	0.472872i
$351$	237.361	+	86.3925i	0.676243	+	0.246132i
$352$	108.357	−	297.707i	0.307831	−	0.845759i
$353$	−151.713	+	262.775i	−0.429782	+	0.744405i	−0.996854	−	0.0792640i	$-0.974743\pi$
$353$	−151.713	+	262.775i	−0.429782	+	0.744405i	0.567071	+	0.823669i	$0.308076\pi$
$354$	962.929	−	555.947i	2.72014	−	1.57047i
$355$	−17.1078	+	3.01657i	−0.0481911	+	0.00849739i
$356$	−409.923	+	488.527i	−1.15147	+	1.37227i
$357$	31.9765	+	38.1081i	0.0895700	+	0.106745i
$358$	−114.068	+	646.912i	−0.318626	+	1.80702i
$359$	148.484	−	54.0436i	0.413603	−	0.150539i	−0.126833	−	0.991924i	$-0.540481\pi$
$359$	148.484	−	54.0436i	0.413603	−	0.150539i	0.540437	+	0.841385i	$0.318259\pi$
$360$		−	53.8140i		−	0.149483i
$361$		0			0
$362$	−109.816			−0.303358
$363$	−128.087	−	351.916i	−0.352856	−	0.969465i
$364$	202.075	+	35.6312i	0.555150	+	0.0978879i
$365$	10.3084	−	8.64978i	0.0282422	−	0.0236980i
$366$	321.533	+	269.798i	0.878505	+	0.737153i
$367$	23.0487	+	130.716i	0.0628031	+	0.356174i	0.999973	+	0.00730175i	$0.00232424\pi$
$367$	23.0487	+	130.716i	0.0628031	+	0.356174i	−0.937170	+	0.348872i	$0.886565\pi$
$368$	13.7426	+	23.8029i	0.0373441	+	0.0646818i
$369$	−451.621	−	260.744i	−1.22391	−	0.706622i
$370$	378.089	+	137.613i	1.02186	+	0.371928i
$371$	−207.626	+	570.448i	−0.559639	+	1.53760i
$372$	−320.027	+	554.304i	−0.860289	+	1.49006i
$373$	−278.822	+	160.978i	−0.747513	+	0.431577i	−0.824794	−	0.565433i	$-0.808709\pi$
$373$	−278.822	+	160.978i	−0.747513	+	0.431577i	0.0772818	+	0.997009i	$0.475376\pi$
$374$	24.6984	−	4.35500i	0.0660386	−	0.0116444i
$375$	−417.425	+	497.468i	−1.11313	+	1.32658i
$376$	50.8146	+	60.5585i	0.135145	+	0.161060i
$377$	12.4787	−	70.7703i	0.0331000	−	0.187720i
$378$	869.797	−	316.580i	2.30105	−	0.837514i
$379$			241.981i			0.638471i	0.947675	+	0.319236i	$0.103426\pi$
$379$			241.981i			0.638471i	−0.947675	+	0.319236i	$0.896574\pi$
$380$		0			0
$381$	367.305			0.964054
$382$	215.074	+	590.910i	0.563020	+	1.54689i
$383$	406.851	+	71.7388i	1.06227	+	0.187307i	0.677365	−	0.735647i	$-0.263122\pi$
$383$	406.851	+	71.7388i	1.06227	+	0.187307i	0.384909	+	0.922955i	$0.374233\pi$
$384$	−122.949	+	103.166i	−0.320179	+	0.268662i
$385$	−130.850	−	109.796i	−0.339871	−	0.285186i
$386$	84.5472	+	479.491i	0.219034	+	1.24220i
$387$	50.7137	+	87.8386i	0.131043	+	0.226973i
$388$	261.258	+	150.837i	0.673345	+	0.388756i
$389$	−78.4491	−	28.5531i	−0.201669	−	0.0734013i	0.239211	−	0.970968i	$-0.423111\pi$
$389$	−78.4491	−	28.5531i	−0.201669	−	0.0734013i	−0.440880	+	0.897566i	$0.645333\pi$
$390$	−98.3730	+	270.277i	−0.252238	+	0.693019i
$391$	−1.19014	+	2.06138i	−0.00304383	+	0.00527208i
$392$	9.36255	−	5.40547i	0.0238840	−	0.0137895i
$393$	−602.244	+	106.192i	−1.53243	+	0.270208i
$394$	−394.630	+	470.302i	−1.00160	+	1.19366i
$395$	182.772	+	217.819i	0.462715	+	0.551442i
$396$	89.0287	−	504.907i	0.224820	−	1.27502i
$397$	617.189	−	224.638i	1.55463	−	0.565840i	0.585133	−	0.810937i	$-0.301042\pi$
$397$	617.189	−	224.638i	1.55463	−	0.565840i	0.969498	+	0.245098i	$0.0788200\pi$
$398$		−	36.3265i		−	0.0912726i
$399$		0			0
$400$	214.877			0.537192
$401$	−118.782	−	326.352i	−0.296215	−	0.813845i	−0.995124	−	0.0986340i	$-0.968553\pi$
$401$	−118.782	−	326.352i	−0.296215	−	0.813845i	0.698908	−	0.715211i	$-0.253670\pi$
$402$	1869.71	+	329.680i	4.65101	+	0.820098i
$403$	134.933	−	113.223i	0.334822	−	0.280949i
$404$	91.8109	+	77.0385i	0.227255	+	0.190689i
$405$	31.9036	+	180.934i	0.0787742	+	0.446751i
$406$	−131.667	−	228.054i	−0.324303	−	0.561710i
$407$	260.893	+	150.626i	0.641014	+	0.370089i
$408$	−5.94775	−	2.16480i	−0.0145778	−	0.00530589i
$409$	22.7840	−	62.5986i	0.0557067	−	0.153053i	−0.908718	−	0.417410i	$-0.862938\pi$
$409$	22.7840	−	62.5986i	0.0557067	−	0.153053i	0.964425	+	0.264358i	$0.0851600\pi$
$410$	140.644	−	243.602i	0.343033	−	0.594151i
$411$	−728.868	+	420.812i	−1.77340	+	1.02387i
$412$	555.798	−	98.0021i	1.34902	−	0.237869i
$413$	−375.117	+	447.047i	−0.908273	+	1.08244i
$414$	60.0976	+	71.6215i	0.145163	+	0.172999i
$415$	−11.6197	+	65.8988i	−0.0279993	+	0.158792i
$416$	263.104	−	95.7622i	0.632462	−	0.230197i
$417$		−	1085.85i		−	2.60396i
$418$		0			0
$419$	−154.857			−0.369586			−0.184793	−	0.982777i	$-0.559161\pi$
$419$	−154.857			−0.369586			−0.184793	+	0.982777i	$0.559161\pi$
$420$	187.613	+	515.463i	0.446698	+	1.22729i
$421$	−520.244	−	91.7330i	−1.23573	−	0.217893i	−0.482647	−	0.875815i	$-0.660325\pi$
$421$	−520.244	−	91.7330i	−1.23573	−	0.217893i	−0.753086	+	0.657922i	$0.771436\pi$
$422$	−627.900	+	526.871i	−1.48792	+	1.24851i
$423$	−1051.02	−	881.907i	−2.48467	−	2.08489i
$424$	−13.4123	−	76.0651i	−0.0316328	−	0.179399i
$425$	9.30439	+	16.1157i	0.0218927	+	0.0379192i
$426$	69.5036	+	40.1279i	0.163154	+	0.0941971i
$427$	−207.011	−	75.3457i	−0.484802	−	0.176454i
$428$	−119.016	+	326.993i	−0.278075	+	0.764003i
$429$	−107.675	+	186.499i	−0.250992	+	0.434730i
$430$	−47.3797	+	27.3547i	−0.110185	+	0.0636155i
$431$	345.366	−	60.8974i	0.801313	−	0.141293i	0.242029	−	0.970269i	$-0.422187\pi$
$431$	345.366	−	60.8974i	0.801313	−	0.141293i	0.559284	+	0.828976i	$0.311076\pi$
$432$	386.231	−	460.292i	0.894053	−	1.06549i
$433$	104.460	+	124.491i	0.241248	+	0.287508i	0.873059	−	0.487614i	$-0.162133\pi$
$433$	104.460	+	124.491i	0.241248	+	0.287508i	−0.631811	+	0.775122i	$0.717688\pi$
$434$	112.084	−	635.660i	0.258258	−	1.46465i
$435$	180.525	−	65.7056i	0.414999	−	0.151047i
$436$			461.772i			1.05911i
$437$		0			0
$438$	−62.1686			−0.141937
$439$	147.241	+	404.541i	0.335401	+	0.921506i	0.986681	+	0.162669i	$0.0520101\pi$
$439$	147.241	+	404.541i	0.335401	+	0.921506i	−0.651280	+	0.758838i	$0.725768\pi$
$440$	21.4031	+	3.77394i	0.0486433	+	0.00857713i
$441$	−143.731	+	120.605i	−0.325922	+	0.273481i
$442$	16.9789	+	14.2470i	0.0384139	+	0.0322331i
$443$	−37.6724	−	213.651i	−0.0850394	−	0.482282i	−0.997348	−	0.0727792i	$-0.976813\pi$
$443$	−37.6724	−	213.651i	−0.0850394	−	0.482282i	0.912309	−	0.409503i	$-0.134298\pi$
$444$	−483.718	−	837.823i	−1.08945	−	1.88699i
$445$	406.317	+	234.587i	0.913071	+	0.527162i
$446$	−253.141	−	92.1357i	−0.567580	−	0.206582i
$447$	101.722	−	279.479i	0.227566	−	0.625233i
$448$	288.129	−	499.054i	0.643145	−	1.11396i
$449$	182.412	−	105.316i	0.406262	−	0.234556i	−0.282920	−	0.959143i	$-0.591303\pi$
$449$	182.412	−	105.316i	0.406262	−	0.234556i	0.689183	+	0.724588i	$0.257970\pi$
$450$	719.832	−	126.926i	1.59963	−	0.282057i
$451$	135.375	−	161.334i	0.300167	−	0.357726i
$452$	−105.909	−	126.217i	−0.234311	−	0.279241i
$453$	48.4448	−	274.744i	0.106942	−	0.606499i
$454$	−4.90827	+	1.78646i	−0.0108112	+	0.00393494i
$455$		−	150.959i		−	0.331778i
$456$		0			0
$457$	627.841			1.37383			0.686916	−	0.726737i	$-0.258964\pi$
$457$	627.841			1.37383			0.686916	+	0.726737i	$0.258964\pi$
$458$	109.747	+	301.528i	0.239623	+	0.658358i
$459$	51.2459	+	9.03604i	0.111647	+	0.0196864i
$460$	−20.1062	+	16.8711i	−0.0437091	+	0.0366763i
$461$	578.501	+	485.420i	1.25488	+	1.05297i	0.996208	+	0.0870063i	$0.0277300\pi$
$461$	578.501	+	485.420i	1.25488	+	1.05297i	0.258674	+	0.965965i	$0.416714\pi$
$462$	137.033	+	777.152i	0.296608	+	1.68215i
$463$	−6.58305	−	11.4022i	−0.0142182	−	0.0246267i	0.858829	−	0.512263i	$-0.171193\pi$
$463$	−6.58305	−	11.4022i	−0.0142182	−	0.0246267i	−0.873047	+	0.487636i	$0.837859\pi$
$464$	−148.042	−	85.4722i	−0.319056	−	0.184207i
$465$	442.489	+	161.053i	0.951589	+	0.346350i
$466$	143.178	−	393.377i	0.307248	−	0.844158i
$467$	9.80331	−	16.9798i	0.0209921	−	0.0363594i	−0.855339	−	0.518070i	$-0.826651\pi$
$467$	9.80331	−	16.9798i	0.0209921	−	0.0363594i	0.876331	+	0.481710i	$0.159984\pi$
$468$	392.400	−	226.552i	0.838461	−	0.484086i
$469$	−981.315	+	173.032i	−2.09236	+	0.368939i
$470$	475.696	−	566.913i	1.01212	−	1.20620i
$471$	58.1488	+	69.2990i	0.123458	+	0.147132i
$472$	12.8936	−	73.1230i	0.0273169	−	0.154922i
$473$	−38.4919	+	14.0099i	−0.0813783	+	0.0296193i
$474$		−	1313.64i		−	2.77139i
$475$		0			0
$476$	42.2711			0.0888049
$477$	458.479	+	1259.66i	0.961173	+	2.64080i
$478$	−230.282	−	40.6049i	−0.481761	−	0.0849475i
$479$	584.362	−	490.338i	1.21996	−	1.02367i	0.221135	−	0.975243i	$-0.429024\pi$
$479$	584.362	−	490.338i	1.21996	−	1.02367i	0.998827	−	0.0484261i	$-0.0154205\pi$
$480$	573.386	+	481.128i	1.19455	+	1.00235i
$481$	46.2317	+	262.193i	0.0961158	+	0.545100i
$482$	290.695	+	503.498i	0.603101	+	1.04460i
$483$	−64.8626	−	37.4485i	−0.134291	−	0.0775330i
$484$	−299.033	−	108.839i	−0.617837	−	0.224874i
$485$	75.9084	−	208.557i	0.156512	−	0.430014i
$486$	−113.464	+	196.526i	−0.233465	+	0.404374i
$487$	−220.903	+	127.539i	−0.453601	+	0.261886i	−0.709350	−	0.704857i	$-0.751011\pi$
$487$	−220.903	+	127.539i	−0.453601	+	0.261886i	0.255749	+	0.966743i	$0.417678\pi$
$488$	27.6034	−	4.86722i	0.0565642	−	0.00997380i
$489$	669.702	−	798.119i	1.36953	−	1.63215i
$490$	−65.0537	−	77.5280i	−0.132763	−	0.158220i
$491$	40.3360	−	228.757i	0.0821507	−	0.465900i	−0.915784	−	0.401670i	$-0.868430\pi$
$491$	40.3360	−	228.757i	0.0821507	−	0.465900i	0.997935	−	0.0642298i	$-0.0204591\pi$
$492$	−635.549	+	231.321i	−1.29177	+	0.470164i
$493$		−	14.8041i		−	0.0300287i
$494$		0			0
$495$	−377.189			−0.761997
$496$	−143.309	−	393.737i	−0.288929	−	0.793825i
$497$	−41.4824	−	7.31447i	−0.0834656	−	0.0147172i
$498$	236.817	−	198.713i	0.475537	−	0.399023i
$499$	−440.620	−	369.724i	−0.883006	−	0.740930i	0.0837892	−	0.996484i	$-0.473298\pi$
$499$	−440.620	−	369.724i	−0.883006	−	0.740930i	−0.966795	+	0.255554i	$0.917742\pi$
$500$	95.8213	+	543.430i	0.191643	+	1.08686i
$501$	664.275	+	1150.56i	1.32590	+	2.29652i
$502$	634.275	+	366.199i	1.26350	+	0.729480i
$503$	−103.931	−	37.8276i	−0.206621	−	0.0752040i	0.236636	−	0.971598i	$-0.423955\pi$
$503$	−103.931	−	37.8276i	−0.206621	−	0.0752040i	−0.443258	+	0.896394i	$0.646177\pi$
$504$	44.6289	−	122.617i	0.0885493	−	0.243287i
$505$	44.0869	−	76.3607i	0.0873007	−	0.151209i
$506$	−32.7001	+	18.8794i	−0.0646247	+	0.0373111i
$507$	662.854	−	116.879i	1.30741	−	0.230531i
$508$	200.620	−	239.090i	0.394922	−	0.470649i
$509$	448.339	+	534.309i	0.880822	+	1.04972i	0.998394	+	0.0566587i	$0.0180447\pi$
$509$	448.339	+	534.309i	0.880822	+	1.04972i	−0.117571	+	0.993064i	$0.537511\pi$
$510$	−10.2891	+	58.3525i	−0.0201747	+	0.114417i
$511$	30.6614	−	11.1598i	0.0600027	−	0.0218392i
$512$		−	723.259i		−	1.41262i
$513$		0			0
$514$	−647.257			−1.25926
$515$	−142.009	−	390.167i	−0.275746	−	0.757605i
$516$	129.547	+	22.8426i	0.251059	+	0.0442685i
$517$	424.462	−	356.166i	0.821009	−	0.688908i
$518$	747.363	+	627.112i	1.44279	+	1.21064i
$519$	−73.8726	−	418.953i	−0.142336	−	0.807230i
$520$	9.60358	+	16.6339i	0.0184684	+	0.0319882i
$521$	−787.086	−	454.424i	−1.51072	−	0.872215i	−0.999922	−	0.0125152i	$-0.996016\pi$
$521$	−787.086	−	454.424i	−1.51072	−	0.872215i	−0.510799	−	0.859700i	$-0.670650\pi$
$522$	−546.426	−	198.883i	−1.04679	−	0.381001i
$523$	214.496	−	589.322i	0.410125	−	1.12681i	−0.546999	−	0.837133i	$-0.684230\pi$
$523$	214.496	−	589.322i	0.410125	−	1.12681i	0.957125	−	0.289677i	$-0.0935478\pi$
$524$	−259.819	+	450.020i	−0.495839	+	0.858818i
$525$	−507.090	+	292.768i	−0.965885	+	0.557654i
$526$	408.139	−	71.9660i	0.775930	−	0.136817i
$527$	23.3247	−	27.7973i	0.0442594	−	0.0527463i
$528$	329.283	+	392.424i	0.623642	+	0.743228i
$529$	−91.2376	+	517.434i	−0.172472	+	0.978136i
$530$	−679.455	+	247.301i	−1.28199	+	0.466606i
$531$			1288.66i			2.42685i
$532$		0			0
$533$	186.128			0.349208
$534$	−741.343	−	2036.82i	−1.38828	−	3.81427i
$535$	252.118	+	44.4552i	0.471249	+	0.0830938i
$536$	97.1213	−	81.4945i	0.181197	−	0.152042i
$537$	−890.143	−	746.918i	−1.65762	−	1.39091i
$538$	−47.3535	−	268.555i	−0.0880176	−	0.499173i
$539$	−37.8876	−	65.6232i	−0.0702923	−	0.121750i
$540$	496.920	+	286.897i	0.920223	+	0.531291i
$541$	938.477	+	341.578i	1.73471	+	0.631382i	0.998948	−	0.0458600i	$-0.0146028\pi$
$541$	938.477	+	341.578i	1.73471	+	0.631382i	0.735760	+	0.677242i	$0.236825\pi$
$542$	−324.093	+	890.437i	−0.597957	+	1.64287i
$543$	97.1284	−	168.231i	0.178874	−	0.309818i
$544$	49.9524	−	28.8400i	0.0918243	−	0.0530148i
$545$	334.563	−	58.9926i	0.613878	−	0.108243i
$546$	−448.291	+	534.253i	−0.821046	+	0.978485i
$547$	14.3815	+	17.1392i	0.0262916	+	0.0313332i	0.779030	−	0.626987i	$-0.215712\pi$
$547$	14.3815	+	17.1392i	0.0262916	+	0.0313332i	−0.752738	+	0.658320i	$0.771267\pi$
$548$	−124.185	+	704.288i	−0.226615	+	1.28520i
$549$	−457.120	+	166.378i	−0.832642	+	0.303057i
$550$			295.195i			0.536718i
$551$		0			0
$552$	9.52944			0.0172635
$553$	235.811	+	647.884i	0.426421	+	1.17158i
$554$	−778.665	−	137.300i	−1.40553	−	0.247833i
$555$	−545.224	+	457.497i	−0.982385	+	0.824319i
$556$	−706.814	−	593.087i	−1.27125	−	1.06670i
$557$	164.359	+	932.127i	0.295079	+	1.67348i	0.666880	+	0.745165i	$0.267629\pi$
$557$	164.359	+	932.127i	0.295079	+	1.67348i	−0.371800	+	0.928313i	$0.621259\pi$
$558$	−712.658	−	1234.36i	−1.27716	−	2.21211i
$559$	−31.3511	−	18.1006i	−0.0560843	−	0.0323803i
$560$	−337.443	−	122.819i	−0.602577	−	0.219320i
$561$	−15.1734	+	41.6885i	−0.0270470	+	0.0743110i
$562$	−137.328	+	237.859i	−0.244355	+	0.423236i
$563$	375.791	−	216.963i	0.667479	−	0.385369i	−0.127642	−	0.991820i	$-0.540741\pi$
$563$	375.791	−	216.963i	0.667479	−	0.385369i	0.795121	+	0.606451i	$0.207407\pi$
$564$	−1752.37	+	308.991i	−3.10704	+	0.547856i
$565$	−77.9167	+	92.8575i	−0.137906	+	0.164350i
$566$	−852.135	−	1015.54i	−1.50554	−	1.79423i
$567$	−77.3585	+	438.722i	−0.136435	+	0.773760i
$568$	5.03619	−	1.83302i	0.00886652	−	0.00322715i
$569$			966.317i			1.69827i	0.528174	+	0.849136i	$0.322877\pi$
$569$			966.317i			1.69827i	−0.528174	+	0.849136i	$0.677123\pi$
$570$		0			0
$571$	−249.882			−0.437623			−0.218811	−	0.975767i	$-0.570218\pi$
$571$	−249.882			−0.437623			−0.218811	+	0.975767i	$0.570218\pi$
$572$	62.5862	+	171.954i	0.109417	+	0.300619i
$573$	−1095.47	−	193.160i	−1.91181	−	0.337104i
$574$	522.484	−	438.416i	0.910251	−	0.763791i
$575$	−21.4621	−	18.0089i	−0.0373254	−	0.0313197i
$576$	−220.966	−	1253.16i	−0.383621	−	2.17563i
$577$	−452.337	−	783.471i	−0.783946	−	1.35783i	−0.929626	−	0.368503i	$-0.879870\pi$
$577$	−452.337	−	783.471i	−0.783946	−	1.35783i	0.145680	−	0.989332i	$-0.453463\pi$
$578$	−718.885	−	415.049i	−1.24375	−	0.718077i
$579$	−809.332	−	294.573i	−1.39781	−	0.508761i
$580$	55.8320	−	153.397i	0.0962621	−	0.264478i
$581$	−81.1269	+	140.516i	−0.139633	+	0.241852i
$582$	−887.978	+	512.674i	−1.52574	+	0.880884i
$583$	−533.149	+	94.0086i	−0.914492	+	0.161250i
$584$	−2.66856	+	3.18027i	−0.00456945	+	0.00544566i
$585$	−214.272	−	255.359i	−0.366276	−	0.436511i
$586$	108.204	−	613.654i	0.184648	−	1.04719i
$587$	644.432	−	234.554i	1.09784	−	0.399581i	0.271321	−	0.962489i	$-0.412540\pi$
$587$	644.432	−	234.554i	1.09784	−	0.399581i	0.826520	+	0.562908i	$0.190317\pi$
$588$			243.342i			0.413847i
$589$		0			0
$590$	−695.094			−1.17813
$591$	−371.438	−	1020.52i	−0.628491	−	1.72676i
$592$	623.701	+	109.975i	1.05355	+	0.185769i
$593$	−825.335	+	692.539i	−1.39180	+	1.16786i	−0.427190	+	0.904162i	$0.640497\pi$
$593$	−825.335	+	692.539i	−1.39180	+	1.16786i	−0.964606	+	0.263694i	$0.915059\pi$
$594$	632.343	+	530.599i	1.06455	+	0.893264i
$595$	−5.40024	−	30.6263i	−0.00907604	−	0.0514728i
$596$	−126.361	−	218.864i	−0.212016	−	0.367222i
$597$	55.6502	+	32.1296i	0.0932163	+	0.0538185i
$598$	−31.3576	−	11.4132i	−0.0524375	−	0.0190857i
$599$	205.734	−	565.250i	0.343463	−	0.943656i	−0.640919	−	0.767608i	$-0.721447\pi$
$599$	205.734	−	565.250i	0.343463	−	0.943656i	0.984382	−	0.176047i	$-0.0563312\pi$
$600$	37.2501	−	64.5191i	0.0620835	−	0.107532i
$601$	450.991	−	260.380i	0.750401	−	0.433244i	−0.0754379	−	0.997151i	$-0.524035\pi$
$601$	450.991	−	260.380i	0.750401	−	0.433244i	0.825839	+	0.563906i	$0.190702\pi$
$602$	−130.642	+	23.0357i	−0.217013	+	0.0382652i
$603$	−1414.37	+	1685.58i	−2.34555	+	2.79532i
$604$	−152.379	−	181.598i	−0.252283	−	0.300659i
$605$	−40.6540	+	230.560i	−0.0671967	+	0.381091i
$606$	−382.788	+	139.323i	−0.631664	+	0.229907i
$607$			841.425i			1.38620i	0.720840	+	0.693102i	$0.243756\pi$
$607$			841.425i			1.38620i	−0.720840	+	0.693102i	$0.756244\pi$
$608$		0			0
$609$	465.822			0.764896
$610$	−89.7435	−	246.568i	−0.147121	−	0.404210i
$611$	482.253	+	85.0341i	0.789284	+	0.139172i
$612$	71.5049	−	59.9997i	0.116838	−	0.0980388i
$613$	564.080	+	473.319i	0.920195	+	0.772135i	0.974031	−	0.226414i	$-0.0727003\pi$
$613$	564.080	+	473.319i	0.920195	+	0.772135i	−0.0538359	+	0.998550i	$0.517145\pi$
$614$	−79.4426	−	450.541i	−0.129385	−	0.733781i
$615$	248.790	+	430.916i	0.404536	+	0.700677i
$616$	45.6377	+	26.3489i	0.0740872	+	0.0427743i
$617$	−219.234	−	79.7947i	−0.355323	−	0.129327i	0.158190	−	0.987409i	$-0.449434\pi$
$617$	−219.234	−	79.7947i	−0.355323	−	0.129327i	−0.513513	+	0.858082i	$0.671656\pi$
$618$	−656.069	+	1802.53i	−1.06160	+	2.91672i
$619$	449.457	−	778.482i	0.726102	−	1.25765i	−0.232417	−	0.972616i	$-0.574663\pi$
$619$	449.457	−	778.482i	0.726102	−	1.25765i	0.958519	−	0.285029i	$-0.0920032\pi$
$620$	346.520	−	200.063i	0.558903	−	0.322683i
$621$	−77.1543	+	13.6044i	−0.124242	+	0.0219072i
$622$	46.0314	−	54.8581i	0.0740055	−	0.0881963i
$623$	731.257	+	871.479i	1.17377	+	1.39884i
$624$	−78.6159	+	445.853i	−0.125987	+	0.714508i
$625$	33.8042	−	12.3037i	0.0540868	−	0.0196860i
$626$			314.641i			0.502622i
$627$		0			0
$628$	76.8695			0.122404
$629$	18.7588	+	51.5394i	0.0298232	+	0.0819386i
$630$	−1202.98	−	212.117i	−1.90948	−	0.336694i
$631$	134.303	−	112.694i	0.212842	−	0.178596i	−0.530133	−	0.847914i	$-0.677858\pi$
$631$	134.303	−	112.694i	0.212842	−	0.178596i	0.742976	+	0.669318i	$0.233414\pi$
$632$	−67.2000	−	56.3875i	−0.106329	−	0.0892207i
$633$	−251.779	−	1427.91i	−0.397755	−	2.25578i
$634$	694.416	+	1202.76i	1.09529	+	1.89710i
$635$	−198.855	−	114.809i	−0.313158	−	0.180802i
$636$	1633.71	+	594.620i	2.56872	+	0.934937i
$637$	22.9043	−	62.9291i	0.0359565	−	0.0987897i
$638$	117.421	−	203.378i	0.184045	−	0.318775i
$639$	−80.5528	+	46.5072i	−0.126061	+	0.0727812i
$640$	98.8103	−	17.4229i	0.154391	−	0.0272233i
$641$	251.452	−	299.669i	0.392281	−	0.467502i	−0.533370	−	0.845882i	$-0.679074\pi$
$641$	251.452	−	299.669i	0.392281	−	0.467502i	0.925650	+	0.378381i	$0.123519\pi$
$642$	−760.245	−	906.024i	−1.18418	−	1.41125i
$643$	3.88097	−	22.0101i	0.00603573	−	0.0342303i	−0.981641	−	0.190737i	$-0.938912\pi$
$643$	3.88097	−	22.0101i	0.00603573	−	0.0342303i	0.987677	+	0.156507i	$0.0500233\pi$
$644$	−59.8040	+	21.7669i	−0.0928634	+	0.0337995i
$645$		−	96.7773i		−	0.150042i
$646$		0			0
$647$	−599.186			−0.926100			−0.463050	−	0.886332i	$-0.653245\pi$
$647$	−599.186			−0.926100			−0.463050	+	0.886332i	$0.653245\pi$
$648$	−19.3862	−	53.2632i	−0.0299170	−	0.0821963i
$649$	−512.528	−	90.3725i	−0.789719	−	0.139249i
$650$	−199.849	+	167.693i	−0.307460	+	0.257989i
$651$	874.660	+	733.927i	1.34356	+	1.12738i
$652$	−153.732	−	871.859i	−0.235786	−	1.33721i
$653$	152.832	+	264.713i	0.234046	+	0.405380i	0.958995	−	0.283423i	$-0.0914700\pi$
$653$	152.832	+	264.713i	0.234046	+	0.405380i	−0.724949	+	0.688803i	$0.758137\pi$
$654$	−1359.22	−	784.749i	−2.07832	−	1.19992i
$655$	359.242	+	130.753i	0.548460	+	0.199623i
$656$	151.432	−	416.057i	0.230842	−	0.634233i
$657$	36.0258	−	62.3986i	0.0548338	−	0.0949750i
$658$	1554.04	−	897.224i	2.36176	−	1.36356i
$659$	−44.1686	+	7.78811i	−0.0670237	+	0.0118181i	−0.207059	−	0.978328i	$-0.566389\pi$
$659$	−44.1686	+	7.78811i	−0.0670237	+	0.0118181i	0.140036	+	0.990146i	$0.455278\pi$
$660$	−314.446	+	374.742i	−0.476433	+	0.567791i
$661$	−623.467	−	743.019i	−0.943217	−	1.12408i	−0.992122	−	0.125279i	$-0.960017\pi$
$661$	−623.467	−	743.019i	−0.943217	−	1.12408i	0.0489043	−	0.998803i	$-0.484427\pi$
$662$	−0.804919	+	4.56492i	−0.00121589	+	0.00689565i
$663$	−36.8430	+	13.4097i	−0.0555701	+	0.0202259i
$664$		−	20.6442i		−	0.0310907i
$665$		0			0
$666$	2154.35			3.23475
$667$	7.62317	+	20.9445i	0.0114290	+	0.0314010i
$668$	1111.76	+	196.033i	1.66431	+	0.293463i
$669$	365.042	−	306.306i	0.545653	−	0.457857i
$670$	−909.192	−	762.903i	−1.35700	−	1.13866i
$671$	−34.1149	−	193.475i	−0.0508419	−	0.288339i
$672$	907.470	+	1571.78i	1.35040	+	2.33896i
$673$	−374.338	−	216.124i	−0.556224	−	0.321136i	0.195405	−	0.980723i	$-0.437398\pi$
$673$	−374.338	−	216.124i	−0.556224	−	0.321136i	−0.751628	+	0.659587i	$0.770731\pi$
$674$	813.136	+	295.957i	1.20643	+	0.439106i
$675$	−209.484	+	575.552i	−0.310346	+	0.852670i
$676$	285.968	−	495.311i	0.423030	−	0.732709i
$677$	1085.71	−	626.838i	1.60371	−	0.925905i	0.612980	−	0.790099i	$-0.289971\pi$
$677$	1085.71	−	626.838i	1.60371	−	0.925905i	0.990735	−	0.135806i	$-0.0433625\pi$
$678$	551.503	−	97.2449i	0.813427	−	0.143429i
$679$	345.919	−	412.250i	0.509454	−	0.607143i
$680$	2.54340	+	3.03110i	0.00374029	+	0.00445750i
$681$	1.60445	−	9.09926i	0.00235601	−	0.0133616i
$682$	540.911	−	196.876i	0.793125	−	0.288674i
$683$		−	708.508i		−	1.03735i	−0.854972	−	0.518674i	$-0.826426\pi$
$683$		−	708.508i		−	1.03735i	0.854972	−	0.518674i	$-0.173574\pi$
$684$		0			0
$685$	526.136			0.768082
$686$	290.899	+	799.240i	0.424052	+	1.16507i
$687$	−558.992	−	98.5653i	−0.813670	−	0.143472i
$688$	−65.9678	+	55.3535i	−0.0958834	+	0.0804557i
$689$	−366.513	−	307.541i	−0.531950	−	0.446359i
$690$	−15.4910	−	87.8537i	−0.0224507	−	0.127324i
$691$	−272.140	−	471.360i	−0.393835	−	0.682142i	0.599117	−	0.800661i	$-0.295518\pi$
$691$	−272.140	−	471.360i	−0.393835	−	0.682142i	−0.992952	+	0.118520i	$0.962185\pi$
$692$	−313.058	−	180.744i	−0.452396	−	0.261191i
$693$	−859.436	−	312.809i	−1.24017	−	0.451384i
$694$	382.528	−	1050.99i	0.551193	−	1.51439i
$695$	−339.407	+	587.869i	−0.488355	+	0.845855i
$696$	−51.3279	+	29.6342i	−0.0737470	+	0.0425779i
$697$	37.7612	−	6.65833i	0.0541768	−	0.00955284i
$698$	438.144	−	522.160i	0.627713	−	0.748080i
$699$	475.996	+	567.270i	0.680967	+	0.811545i
$700$	−86.3983	+	489.989i	−0.123426	+	0.699984i
$701$	−292.347	+	106.405i	−0.417042	+	0.151791i	−0.542014	−	0.840369i	$-0.682338\pi$
$701$	−292.347	+	106.405i	−0.417042	+	0.151791i	0.124972	+	0.992160i	$0.460116\pi$
$702$			729.520i			1.03920i
$703$		0			0
$704$	513.906			0.729981
$705$	447.740	+	1230.16i	0.635092	+	1.74490i
$706$	−863.014	−	152.173i	−1.22240	−	0.215542i
$707$	163.780	−	137.428i	0.231655	−	0.194382i
$708$	1280.30	+	1074.30i	1.80833	+	1.51737i
$709$	13.5503	+	76.8474i	0.0191118	+	0.108388i	0.992871	−	0.119191i	$-0.0380300\pi$
$709$	13.5503	+	76.8474i	0.0191118	+	0.108388i	−0.973760	+	0.227579i	$0.926919\pi$
$710$	−25.0857	−	43.4498i	−0.0353320	−	0.0611969i
$711$	1318.50	+	761.236i	1.85443	+	1.07066i
$712$	−136.017	−	49.5060i	−0.191035	−	0.0695309i
$713$	−18.6854	+	51.3376i	−0.0262067	+	0.0720022i
$714$	−71.8367	+	124.425i	−0.100612	+	0.174265i
$715$	116.589	−	67.3126i	0.163061	−	0.0941435i
$716$	−972.384	+	171.458i	−1.35808	+	0.239466i
$717$	265.881	−	316.865i	0.370825	−	0.441932i
$718$	293.342	+	349.591i	0.408554	+	0.486895i
$719$	94.9085	−	538.253i	0.132001	−	0.748613i	−0.844901	−	0.534923i	$-0.820341\pi$
$719$	94.9085	−	538.253i	0.132001	−	0.748613i	0.976901	−	0.213690i	$-0.0685483\pi$
$720$	−745.141	+	271.209i	−1.03492	+	0.376679i
$721$		−	1006.78i		−	1.39636i
$722$		0			0
$723$	−1028.44			−1.42246
$724$	−56.4558	−	155.111i	−0.0779777	−	0.214242i
$725$	171.603	+	30.2583i	0.236694	+	0.0417356i
$726$	828.553	−	695.238i	1.14126	−	0.957629i
$727$	−276.631	−	232.121i	−0.380510	−	0.319286i	0.432392	−	0.901686i	$-0.357670\pi$
$727$	−276.631	−	232.121i	−0.380510	−	0.319286i	−0.812903	+	0.582399i	$0.802114\pi$
$728$	8.08727	+	45.8652i	0.0111089	+	0.0630016i
$729$	−459.577	−	796.012i	−0.630422	−	1.09192i
$730$	33.6575	+	19.4321i	0.0461061	+	0.0266194i
$731$	−7.00797	−	2.55069i	−0.00958682	−	0.00348932i
$732$	−215.782	+	592.857i	−0.294785	+	0.809914i
$733$	−333.779	+	578.122i	−0.455360	+	0.788707i	−0.998709	−	0.0508002i	$-0.983823\pi$
$733$	−333.779	+	578.122i	−0.455360	+	0.788707i	0.543349	+	0.839507i	$0.317156\pi$
$734$	−331.987	+	191.673i	−0.452298	+	0.261135i
$735$	176.306	−	31.0876i	0.239873	−	0.0422960i
$736$	−55.8206	+	66.5244i	−0.0758432	+	0.0903864i
$737$	−571.204	−	680.735i	−0.775040	−	0.923657i
$738$	261.533	−	1483.23i	0.354381	−	2.00980i
$739$	1185.50	−	431.487i	1.60420	−	0.583880i	0.623916	−	0.781492i	$-0.285541\pi$
$739$	1185.50	−	431.487i	1.60420	−	0.583880i	0.980280	+	0.197612i	$0.0633186\pi$
$740$			604.786i			0.817278i
$741$		0			0
$742$	−1753.25			−2.36287
$743$	−449.989	−	1236.33i	−0.605637	−	1.66397i	−0.739647	−	0.672995i	$-0.765008\pi$
$743$	−449.989	−	1236.33i	−0.605637	−	1.66397i	0.134010	−	0.990980i	$-0.457215\pi$
$744$	−143.067	−	25.2266i	−0.192295	−	0.0339067i
$745$	−142.429	+	119.512i	−0.191179	+	0.160419i
$746$	−712.302	−	597.692i	−0.954828	−	0.801196i
$747$	62.2161	+	352.845i	0.0832879	+	0.472349i
$748$	18.8487	+	32.6469i	0.0251988	+	0.0436455i
$749$	537.591	+	310.378i	0.717745	+	0.414390i
$750$	−1762.42	−	641.470i	−2.34990	−	0.855293i
$751$	−323.384	+	888.490i	−0.430604	+	1.18308i	0.514838	+	0.857287i	$0.327852\pi$
$751$	−323.384	+	888.490i	−0.430604	+	1.18308i	−0.945443	+	0.325788i	$0.894370\pi$
$752$	582.436	−	1008.81i	0.774516	−	1.34150i
$753$	−1121.99	+	647.783i	−1.49003	+	0.860269i
$754$	204.392	−	36.0399i	0.271077	−	0.0477982i
$755$	−112.105	+	133.601i	−0.148483	+	0.176955i
$756$	894.319	+	1065.81i	1.18296	+	1.40980i
$757$	−51.6383	+	292.855i	−0.0682144	+	0.386863i	0.931517	+	0.363697i	$0.118486\pi$
$757$	−51.6383	+	292.855i	−0.0682144	+	0.386863i	−0.999732	+	0.0231658i	$0.992625\pi$
$758$	−656.719	+	239.026i	−0.866384	+	0.315338i
$759$		−	66.7930i		−	0.0880013i
$760$		0			0
$761$	−402.072			−0.528348			−0.264174	−	0.964475i	$-0.585099\pi$
$761$	−402.072			−0.528348			−0.264174	+	0.964475i	$0.585099\pi$
$762$	362.820	+	996.840i	0.476142	+	1.30819i
$763$	811.236	+	143.043i	1.06322	+	0.187474i
$764$	−724.073	+	607.570i	−0.947740	+	0.795248i
$765$	−52.6060	−	44.1416i	−0.0687660	−	0.0577015i
$766$	207.189	+	1175.03i	0.270482	+	1.53398i
$767$	−229.972	−	398.323i	−0.299833	−	0.519326i
$768$	915.485	+	528.555i	1.19204	+	0.688223i
$769$	817.621	+	297.590i	1.06323	+	0.386983i	0.813640	−	0.581370i	$-0.197483\pi$
$769$	817.621	+	297.590i	1.06323	+	0.386983i	0.249587	+	0.968352i	$0.419705\pi$
$770$	168.727	−	463.575i	0.219127	−	0.602045i
$771$	572.479	−	991.562i	0.742514	−	1.28607i
$772$	−633.800	+	365.925i	−0.820985	+	0.473996i
$773$	−1049.39	+	185.035i	−1.35755	+	0.239373i	−0.804588	−	0.593834i	$-0.797614\pi$
$773$	−1049.39	+	185.035i	−1.35755	+	0.239373i	−0.552962	+	0.833206i	$0.686503\pi$
$774$	−188.294	+	224.400i	−0.243274	+	0.289922i
$775$	274.541	+	327.185i	0.354247	+	0.422175i
$776$	−11.8900	+	67.4314i	−0.0153221	+	0.0868961i
$777$	−1621.72	+	590.257i	−2.08715	+	0.759662i
$778$		−	241.110i		−	0.309910i
$779$		0			0
$780$	−432.332			−0.554271
$781$	−12.8479	−	35.2992i	−0.0164505	−	0.0451975i
$782$	−6.77006	−	1.19374i	−0.00865737	−	0.00152653i
$783$	373.266	−	313.207i	0.476712	−	0.400009i
$784$	−122.032	−	102.397i	−0.155653	−	0.130609i
$785$	−9.82027	−	55.6935i	−0.0125099	−	0.0709472i
$786$	−883.088	−	1529.55i	−1.12352	−	1.94600i
$787$	−686.096	−	396.118i	−0.871786	−	0.503326i	−0.00384484	−	0.999993i	$-0.501224\pi$
$787$	−686.096	−	396.118i	−0.871786	−	0.503326i	−0.867941	+	0.496667i	$0.834557\pi$
$788$	−867.164	−	315.622i	−1.10046	−	0.400536i
$789$	−250.738	+	688.898i	−0.317793	+	0.873128i
$790$	−410.607	+	711.192i	−0.519755	+	0.900243i
$791$	−254.544	+	146.961i	−0.321800	+	0.185791i
$792$	114.599	−	20.2070i	0.144696	−	0.0255139i
$793$	111.604	−	133.004i	0.140736	−	0.167723i
$794$	1219.31	+	1453.11i	1.53565	+	1.83012i
$795$	222.104	−	1259.62i	0.279377	−	1.58442i
$796$	51.3100	−	18.6753i	0.0644598	−	0.0234615i
$797$		−	194.822i		−	0.244444i	−0.992503	−	0.122222i	$-0.960998\pi$
$797$		−	194.822i		−	0.244444i	0.992503	−	0.122222i	$-0.0390019\pi$
$798$		0			0
$799$	100.880			0.126258
$800$	232.203	+	637.974i	0.290254	+	0.797467i
$801$	2473.96	+	436.225i	3.08859	+	0.544601i
$802$	768.365	−	644.735i	0.958061	−	0.803909i
$803$	22.2909	+	18.7043i	0.0277595	+	0.0232930i
$804$	495.547	+	2810.39i	0.616352	+	3.49551i
$805$	23.4107	+	40.5485i	0.0290816	+	0.0503708i
$806$	440.564	+	254.360i	0.546606	+	0.315583i
$807$	453.294	+	164.985i	0.561702	+	0.204443i
$808$	−9.30386	+	25.5622i	−0.0115147	+	0.0316363i
$809$	−304.775	+	527.886i	−0.376731	+	0.652517i	−0.990584	−	0.136903i	$-0.956285\pi$
$809$	−304.775	+	527.886i	−0.376731	+	0.652517i	0.613854	+	0.789420i	$0.289618\pi$
$810$	−459.529	+	265.309i	−0.567320	+	0.327542i
$811$	−533.654	+	94.0976i	−0.658020	+	0.116027i	−0.492681	−	0.870210i	$-0.663983\pi$
$811$	−533.654	+	94.0976i	−0.658020	+	0.116027i	−0.165339	+	0.986237i	$0.552872\pi$
$812$	254.430	−	303.218i	0.313337	−	0.373421i
$813$	−1077.45	−	1284.05i	−1.32528	−	1.57940i
$814$	−151.083	+	856.833i	−0.185605	+	1.05262i
$815$	−612.040	+	222.764i	−0.750969	+	0.273330i
$816$			93.2662i			0.114297i
$817$		0			0
$818$	192.394			0.235201
$819$	−276.451	−	759.542i	−0.337547	−	0.927402i
$820$	416.385	+	73.4198i	0.507786	+	0.0895364i
$821$	1161.33	−	974.471i	1.41453	−	1.18693i	0.460337	−	0.887744i	$-0.347729\pi$
$821$	1161.33	−	974.471i	1.41453	−	1.18693i	0.954194	−	0.299188i	$-0.0967158\pi$
$822$	−1862.02	−	1562.42i	−2.26524	−	1.90076i
$823$	116.331	+	659.747i	0.141350	+	0.801637i	0.970226	+	0.242203i	$0.0778701\pi$
$823$	116.331	+	659.747i	0.141350	+	0.801637i	−0.828875	+	0.559433i	$0.811019\pi$
$824$	64.0482	+	110.935i	0.0777283	+	0.134629i
$825$	−452.222	−	261.090i	−0.548148	−	0.316473i
$826$	−1583.79	−	576.453i	−1.91742	−	0.697885i
$827$	233.282	−	640.938i	0.282083	−	0.775016i	−0.715031	−	0.699093i	$-0.753587\pi$
$827$	233.282	−	640.938i	0.282083	−	0.775016i	0.997114	−	0.0759229i	$-0.0241903\pi$
$828$	−70.2672	+	121.706i	−0.0848638	+	0.146988i
$829$	−373.918	+	215.882i	−0.451047	+	0.260412i	−0.708272	−	0.705939i	$-0.750525\pi$
$829$	−373.918	+	215.882i	−0.451047	+	0.260412i	0.257225	+	0.966352i	$0.417192\pi$
$830$	−190.323	+	33.5590i	−0.229304	+	0.0404326i
$831$	899.039	−	1071.43i	1.08188	−	1.28933i
$832$	291.938	+	347.918i	0.350887	+	0.418170i
$833$	2.39563	−	13.5863i	0.00287590	−	0.0163101i
$834$	2946.93	−	1072.59i	3.53349	−	1.28608i
$835$		−	830.535i		−	0.994653i
$836$		0			0
$837$	1194.35			1.42694
$838$	−152.966	−	420.270i	−0.182537	−	0.501516i
$839$	−165.775	−	29.2306i	−0.197587	−	0.0348399i	0.0739789	−	0.997260i	$-0.476430\pi$
$839$	−165.775	−	29.2306i	−0.197587	−	0.0348399i	−0.271566	+	0.962420i	$0.587541\pi$
$840$	−95.3755	+	80.0296i	−0.113542	+	0.0952733i
$841$	538.051	+	451.478i	0.639775	+	0.536835i
$842$	−264.935	−	1502.52i	−0.314649	−	1.78446i
$843$	−242.924	−	420.757i	−0.288166	−	0.499118i
$844$	−1066.99	−	616.027i	−1.26421	−	0.729890i
$845$	−395.396	−	143.912i	−0.467924	−	0.170311i
$846$	1355.25	−	3723.53i	1.60195	−	4.40133i
$847$	−283.839	+	491.623i	−0.335111	+	0.580429i
$848$	−985.648	+	569.064i	−1.16232	+	0.671066i
$849$	2309.43	−	407.215i	2.72018	−	0.479640i
$850$	−34.5461	+	41.1704i	−0.0406424	+	0.0484358i
$851$	−53.0789	−	63.2569i	−0.0623724	−	0.0743325i
$852$	−20.9479	+	118.801i	−0.0245867	+	0.139438i
$853$	−481.841	+	175.376i	−0.564879	+	0.205599i	−0.608645	−	0.793443i	$-0.708287\pi$
$853$	−481.841	+	175.376i	−0.564879	+	0.205599i	0.0437662	+	0.999042i	$0.486064\pi$
$854$		−	636.239i		−	0.745010i
$855$		0			0
$856$	−78.9814			−0.0922680
$857$	−295.375	−	811.537i	−0.344662	−	0.946951i	−0.984023	−	0.178044i	$-0.943023\pi$
$857$	−295.375	−	811.537i	−0.344662	−	0.946951i	0.639360	−	0.768907i	$-0.279199\pi$
$858$	−612.507	−	108.002i	−0.713878	−	0.125876i
$859$	−662.975	+	556.302i	−0.771799	+	0.647616i	−0.941169	−	0.337936i	$-0.890271\pi$
$859$	−662.975	+	556.302i	−0.771799	+	0.647616i	0.169370	+	0.985553i	$0.445827\pi$
$860$	−62.9953	−	52.8594i	−0.0732504	−	0.0614644i
$861$	209.508	+	1188.18i	0.243331	+	1.38000i
$862$	506.421	+	877.147i	0.587495	+	1.01757i
$863$	1358.98	+	784.608i	1.57472	+	0.909163i	0.995578	+	0.0939340i	$0.0299443\pi$
$863$	1358.98	+	784.608i	1.57472	+	0.909163i	0.579138	+	0.815229i	$0.303389\pi$
$864$	1783.99	+	649.320i	2.06480	+	0.751527i
$865$	−90.9589	+	249.907i	−0.105155	+	0.288910i
$866$	−234.675	+	406.470i	−0.270988	+	0.469364i
$867$	1271.66	−	734.194i	1.46674	−	0.846822i
$868$	955.471	−	168.475i	1.10077	−	0.194096i
$869$	−395.226	+	471.012i	−0.454806	+	0.542017i
$870$	356.641	+	425.029i	0.409933	+	0.488539i
$871$	136.374	−	773.418i	0.156572	−	0.887965i
$872$	−98.4884	+	35.8469i	−0.112945	+	0.0411088i
$873$		−	1188.35i		−	1.36123i
$874$		0			0
$875$	984.374			1.12500
$876$	−31.9606	−	87.8111i	−0.0364847	−	0.100241i
$877$	−1076.64	−	189.840i	−1.22764	−	0.216465i	−0.478026	−	0.878346i	$-0.658648\pi$
$877$	−1076.64	−	189.840i	−1.22764	−	0.216465i	−0.749609	+	0.661880i	$0.769759\pi$
$878$	−952.454	+	799.204i	−1.08480	+	0.910255i
$879$	844.381	+	708.520i	0.960615	+	0.806052i
$880$	−55.6099	−	315.379i	−0.0631930	−	0.358386i
$881$	800.040	+	1385.71i	0.908104	+	1.57288i	0.816695	+	0.577069i	$0.195804\pi$
$881$	800.040	+	1385.71i	0.908104	+	1.57288i	0.0914086	+	0.995813i	$0.470863\pi$
$882$	−469.290	−	270.945i	−0.532075	−	0.307194i
$883$	−1600.70	−	582.609i	−1.81280	−	0.659806i	−0.996633	−	0.0819931i	$-0.973871\pi$
$883$	−1600.70	−	582.609i	−1.81280	−	0.659806i	−0.816169	−	0.577813i	$-0.803906\pi$
$884$	−11.3947	+	31.3066i	−0.0128899	+	0.0354147i
$885$	614.789	−	1064.84i	0.694676	−	1.20321i
$886$	542.622	−	313.283i	0.612440	−	0.353593i
$887$	423.758	−	74.7199i	0.477743	−	0.0842389i	0.0704088	−	0.997518i	$-0.477570\pi$
$887$	423.758	−	74.7199i	0.477743	−	0.0842389i	0.407334	+	0.913279i	$0.366459\pi$
$888$	141.143	−	168.208i	0.158945	−	0.189424i
$889$	−357.884	−	426.510i	−0.402569	−	0.479763i
$890$	−235.298	+	1334.44i	−0.264379	+	1.49937i
$891$	−373.328	+	135.880i	−0.418999	+	0.152503i
$892$		−	404.920i		−	0.453946i
$893$		0			0
$894$	858.968			0.960814
$895$	248.449	+	682.608i	0.277597	+	0.762690i
$896$	239.591	+	42.2464i	0.267401	+	0.0471500i
$897$	45.2193	−	37.9435i	0.0504117	−	0.0423004i
$898$	466.004	+	391.024i	0.518936	+	0.435439i
$899$	−59.0032	−	334.624i	−0.0656320	−	0.372218i
$900$	549.342	+	951.488i	0.610380	+	1.05721i
$901$	−85.3592	−	49.2821i	−0.0947383	−	0.0546972i
$902$	571.573	+	208.036i	0.633673	+	0.230638i
$903$	80.2591	−	220.510i	0.0888805	−	0.244197i
$904$	18.6984	−	32.3867i	0.0206841	−	0.0358260i
$905$	−105.169	+	60.7192i	−0.116209	+	0.0670931i
$906$	793.490	−	139.914i	0.875817	−	0.154430i
$907$	−207.524	+	247.318i	−0.228803	+	0.272677i	−0.868216	−	0.496187i	$-0.834733\pi$
$907$	−207.524	+	247.318i	−0.228803	+	0.272677i	0.639413	+	0.768864i	$0.279178\pi$
$908$	−5.04665	−	6.01436i	−0.00555798	−	0.00662374i
$909$	81.9816	−	464.941i	0.0901887	−	0.511486i
$910$	409.693	−	149.116i	0.450212	−	0.163864i
$911$		−	1176.87i		−	1.29185i	−0.763401	−	0.645924i	$-0.776472\pi$
$911$		−	1176.87i		−	1.29185i	0.763401	−	0.645924i	$-0.223528\pi$
$912$		0			0
$913$	−144.698			−0.158486
$914$	620.176	+	1703.92i	0.678529	+	1.86424i
$915$	457.104	+	80.5998i	0.499567	+	0.0880872i
$916$	−369.478	+	310.029i	−0.403360	+	0.338459i
$917$	710.107	+	595.850i	0.774380	+	0.649782i
$918$	26.0971	+	148.004i	0.0284282	+	0.161224i
$919$	−227.393	−	393.857i	−0.247436	−	0.428571i	0.715378	−	0.698738i	$-0.246255\pi$
$919$	−227.393	−	393.857i	−0.247436	−	0.428571i	−0.962814	+	0.270167i	$0.912921\pi$
$920$	−5.15915	−	2.97864i	−0.00560777	−	0.00323765i
$921$	760.469	+	276.788i	0.825699	+	0.300530i
$922$	−745.959	+	2049.50i	−0.809066	+	2.22289i
$923$	16.5992	−	28.7507i	0.0179840	−	0.0311492i
$924$	−1027.25	+	593.085i	−1.11175	+	0.641867i
$925$	−635.764	+	112.102i	−0.687312	+	0.121192i
$926$	24.4421	−	29.1289i	0.0263953	−	0.0314567i
$927$	−1429.02	−	1703.04i	−1.54155	−	1.83715i
$928$	93.7891	−	531.905i	0.101066	−	0.573173i
$929$	1226.24	−	446.315i	1.31996	−	0.480425i	0.416513	−	0.909130i	$-0.363252\pi$
$929$	1226.24	−	446.315i	1.31996	−	0.480425i	0.903445	+	0.428704i	$0.141030\pi$
$930$			1359.97i			1.46233i
$931$		0			0
$932$	629.240			0.675151
$933$	43.3262	+	119.038i	0.0464375	+	0.127586i
$934$	55.7658	+	9.83301i	0.0597064	+	0.0105278i
$935$	21.2454	−	17.8270i	0.0227223	−	0.0190663i
$936$	78.7814	+	66.1054i	0.0841682	+	0.0706255i
$937$	−113.823	−	645.521i	−0.121476	−	0.688923i	−0.983339	−	0.181782i	$-0.941813\pi$
$937$	−113.823	−	645.521i	−0.121476	−	0.688923i	0.861863	−	0.507141i	$-0.169298\pi$
$938$	−1438.93	−	2492.30i	−1.53404	−	2.65704i
$939$	−482.013	−	278.290i	−0.513326	−	0.296369i
$940$	1045.30	+	380.458i	1.11202	+	0.404743i
$941$	76.0510	−	208.948i	0.0808193	−	0.222049i	−0.892701	−	0.450649i	$-0.851193\pi$
$941$	76.0510	−	208.948i	0.0808193	−	0.222049i	0.973520	+	0.228600i	$0.0734148\pi$
$942$	−130.634	+	226.265i	−0.138677	+	0.240196i
$943$	−49.9950	+	28.8646i	−0.0530169	+	0.0306093i
$944$	−1077.49	+	189.990i	−1.14140	+	0.201260i
$945$	657.948	−	784.112i	0.696241	−	0.829748i
$946$	−76.0440	−	90.6257i	−0.0803847	−	0.0957988i
$947$	−245.316	+	1391.26i	−0.259046	+	1.46912i	0.526425	+	0.850222i	$0.323532\pi$
$947$	−245.316	+	1391.26i	−0.259046	+	1.46912i	−0.785470	+	0.618899i	$0.787579\pi$
$948$	1855.47	−	675.337i	1.95725	−	0.712381i
$949$			25.7165i			0.0270985i
$950$		0			0
$951$	−2456.76			−2.58334
$952$	3.28146	+	9.01574i	0.00344691	+	0.00947031i
$953$	562.349	+	99.1573i	0.590083	+	0.104048i	0.460713	−	0.887549i	$-0.347594\pi$
$953$	562.349	+	99.1573i	0.590083	+	0.104048i	0.129369	+	0.991596i	$0.458705\pi$
$954$	−2965.76	+	2488.57i	−3.10876	+	2.60856i
$955$	532.699	+	446.987i	0.557800	+	0.468050i
$956$	−61.0339	−	346.141i	−0.0638430	−	0.362072i
$957$	207.710	+	359.764i	0.217042	+	0.375928i
$958$	1907.97	+	1101.57i	1.99162	+	1.14986i
$959$	1198.82	+	436.333i	1.25007	+	0.454988i
$960$	−415.265	+	1140.93i	−0.432568	+	1.18847i
$961$	−64.0710	+	110.974i	−0.0666712	+	0.115478i
$962$	−665.907	+	384.462i	−0.692211	+	0.399648i
$963$	1349.93	−	238.029i	1.40179	−	0.247174i
$964$	−561.730	+	669.443i	−0.582707	+	0.694443i
$965$	346.090	+	412.453i	0.358642	+	0.427413i
$966$	37.5619	−	213.024i	0.0388840	−	0.220522i
$967$	−1486.56	+	541.064i	−1.53729	+	0.559528i	−0.965394	−	0.260797i	$-0.916015\pi$
$967$	−1486.56	+	541.064i	−1.53729	+	0.559528i	−0.571897	+	0.820325i	$0.693792\pi$
$968$		−	72.2279i		−	0.0746156i
$969$		0			0
$970$	640.990			0.660815
$971$	278.580	+	765.391i	0.286900	+	0.788251i	0.996496	+	0.0836420i	$0.0266552\pi$
$971$	278.580	+	765.391i	0.286900	+	0.788251i	−0.709596	+	0.704609i	$0.751123\pi$
$972$	−335.918	−	59.2314i	−0.345595	−	0.0609376i
$973$	−1260.88	+	1058.00i	−1.29587	+	1.08736i
$974$	−564.338	−	473.536i	−0.579402	−	0.486176i
$975$	−80.1364	−	454.476i	−0.0821912	−	0.466129i
$976$	−206.508	−	357.683i	−0.211586	−	0.366478i
$977$	818.544	+	472.586i	0.837813	+	0.483712i	0.856520	−	0.516113i	$-0.172622\pi$
$977$	818.544	+	472.586i	0.837813	+	0.483712i	−0.0187071	+	0.999825i	$0.505955\pi$
$978$	2827.57	+	1029.15i	2.89117	+	1.05230i
$979$	−346.994	+	953.357i	−0.354437	+	0.973807i
$980$	76.0619	−	131.743i	0.0776142	−	0.134432i
$981$	1575.30	−	909.502i	1.60581	−	0.927118i
$982$	660.675	−	116.495i	0.672785	−	0.118630i
$983$	−10.7647	+	12.8289i	−0.0109509	+	0.0130507i	−0.771492	−	0.636239i	$-0.780489\pi$
$983$	−10.7647	+	12.8289i	−0.0109509	+	0.0130507i	0.760541	+	0.649290i	$0.224934\pi$
$984$	−98.6739	−	117.595i	−0.100278	−	0.119507i
$985$	−117.892	+	668.600i	−0.119687	+	0.678782i
$986$	40.1775	−	14.6234i	0.0407479	−	0.0148310i
$987$			3174.26i			3.21607i
$988$		0			0
$989$	11.2281			0.0113530
$990$	−372.584	−	1023.67i	−0.376347	−	1.03401i
$991$	−382.587	−	67.4604i	−0.386061	−	0.0680730i	−0.0227508	−	0.999741i	$-0.507242\pi$
$991$	−382.587	−	67.4604i	−0.386061	−	0.0680730i	−0.363310	+	0.931668i	$0.618354\pi$
$992$	1014.15	−	850.972i	1.02233	−	0.857835i
$993$	−6.28128	−	5.27062i	−0.00632556	−	0.00530777i
$994$	−21.1250	−	119.806i	−0.0212525	−	0.120529i
$995$	−20.0856	−	34.7893i	−0.0201866	−	0.0349642i
$996$	402.423	+	232.339i	0.404039	+	0.233272i
$997$	−1383.15	−	503.427i	−1.38732	−	0.504942i	−0.462928	−	0.886396i	$-0.653201\pi$
$997$	−1383.15	−	503.427i	−1.38732	−	0.504942i	−0.924388	+	0.381454i	$0.875423\pi$
$998$	568.166	−	1561.02i	0.569304	−	1.56415i
$999$	−902.619	+	1563.38i	−0.903522	+	1.56495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.3.f.e.299.2		12
19.2	odd	18		361.3.b.c.360.12		12
19.3	odd	18		361.3.d.f.69.6		12
19.4	even	9		361.3.f.c.262.1		12
19.5	even	9		361.3.d.f.293.6		12
19.6	even	9		361.3.f.g.333.2		12
19.7	even	3		19.3.f.a.2.1	✓	12
19.8	odd	6		361.3.f.b.307.1		12
19.9	even	9		361.3.f.b.127.1		12
19.10	odd	18		361.3.f.f.127.2		12
19.11	even	3		361.3.f.f.307.2		12
19.12	odd	6		361.3.f.g.116.2		12
19.13	odd	18		19.3.f.a.10.1	yes	12
19.14	odd	18		361.3.d.d.293.1		12
19.15	odd	18	inner	361.3.f.e.262.2		12
19.16	even	9		361.3.d.d.69.1		12
19.17	even	9		361.3.b.c.360.1		12
19.18	odd	2		361.3.f.c.299.1		12
57.26	odd	6		171.3.ba.b.154.2		12
57.32	even	18		171.3.ba.b.10.2		12
76.7	odd	6		304.3.z.a.97.1		12
76.51	even	18		304.3.z.a.257.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.3.f.a.2.1	✓	12	19.7	even	3
19.3.f.a.10.1	yes	12	19.13	odd	18
171.3.ba.b.10.2		12	57.32	even	18
171.3.ba.b.154.2		12	57.26	odd	6
304.3.z.a.97.1		12	76.7	odd	6
304.3.z.a.257.1		12	76.51	even	18
361.3.b.c.360.1		12	19.17	even	9
361.3.b.c.360.12		12	19.2	odd	18
361.3.d.d.69.1		12	19.16	even	9
361.3.d.d.293.1		12	19.14	odd	18
361.3.d.f.69.6		12	19.3	odd	18
361.3.d.f.293.6		12	19.5	even	9
361.3.f.b.127.1		12	19.9	even	9
361.3.f.b.307.1		12	19.8	odd	6
361.3.f.c.262.1		12	19.4	even	9
361.3.f.c.299.1		12	19.18	odd	2
361.3.f.e.262.2		12	19.15	odd	18	inner
361.3.f.e.299.2		12	1.1	even	1	trivial
361.3.f.f.127.2		12	19.10	odd	18
361.3.f.f.307.2		12	19.11	even	3
361.3.f.g.116.2		12	19.12	odd	6
361.3.f.g.333.2		12	19.6	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	361.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.987791 + 2.71393i) q^{2} +(-5.03126 - 0.887147i) q^{3} +(-3.32553 + 2.79045i) q^{4} +(2.44658 + 2.05292i) q^{5} +(-2.56218 - 14.5308i) q^{6} +(3.87208 + 6.70664i) q^{7} +(-0.853313 - 0.492661i) q^{8} +(16.0693 + 5.84876i) q^{9} +(-3.15479 + 8.66771i) q^{10} +(-3.45312 + 5.98097i) q^{11} +(19.2071 - 11.0892i) q^{12} +(-6.01079 + 1.05986i) q^{13} +(-14.3766 + 17.1333i) q^{14} +(-10.4881 - 12.4993i) q^{15} +(-2.52119 + 14.2984i) q^{16} +(-1.18154 + 0.430046i) q^{17} +49.3885i q^{18} -13.8647 q^{20} +(-13.5317 - 37.1780i) q^{21} +(-19.6429 - 3.46358i) q^{22} +(1.45017 - 1.21684i) q^{23} +(3.85618 + 3.23572i) q^{24} +(-2.56995 - 14.5749i) q^{25} +(-8.81380 - 15.2659i) q^{26} +(-35.8406 - 20.6926i) q^{27} +(-31.5912 - 11.4983i) q^{28} +(-4.02691 + 11.0638i) q^{29} +(23.5621 - 40.8108i) q^{30} +(-24.9929 + 14.4296i) q^{31} +(-45.1766 + 7.96586i) q^{32} +(22.6795 - 27.0284i) q^{33} +(-2.33423 - 2.78183i) q^{34} +(-4.29487 + 24.3574i) q^{35} +(-69.7596 + 25.3904i) q^{36} -43.6204i q^{37} +31.1821 q^{39} +(-1.07630 - 2.95712i) q^{40} +(-30.0319 - 5.29544i) q^{41} +(87.5320 - 73.4481i) q^{42} +(4.54356 + 3.81250i) q^{43} +(-5.20616 - 29.5256i) q^{44} +(27.3079 + 47.2986i) q^{45} +(4.73487 + 2.73368i) q^{46} +(-75.3927 - 27.4407i) q^{47} +(25.3695 - 69.7022i) q^{48} +(-5.48600 + 9.50203i) q^{49} +(37.0168 - 21.3716i) q^{50} +(6.32616 - 1.11547i) q^{51} +(17.0315 - 20.2974i) q^{52} +(50.3876 + 60.0496i) q^{53} +(20.7552 - 117.709i) q^{54} +(-20.7268 + 7.54394i) q^{55} -7.63048i q^{56} -34.0042 q^{58} +(25.7737 + 70.8126i) q^{59} +(69.7571 + 12.3001i) q^{60} +(-21.7915 + 18.2852i) q^{61} +(-63.8488 - 53.5755i) q^{62} +(22.9962 + 130.418i) q^{63} +(-37.2060 - 64.4427i) q^{64} +(-16.8817 - 9.74665i) q^{65} +(95.7560 + 34.8523i) q^{66} +(-44.0083 + 120.912i) q^{67} +(2.72923 - 4.72716i) q^{68} +(-8.37569 + 4.83570i) q^{69} +(-70.3468 + 12.4040i) q^{70} +(-3.49628 + 4.16670i) q^{71} +(-10.8307 - 12.9076i) q^{72} +(0.731648 - 4.14938i) q^{73} +(118.383 - 43.0879i) q^{74} +75.6101i q^{75} -53.4830 q^{77} +(30.8014 + 84.6261i) q^{78} +(87.6776 + 15.4599i) q^{79} +(-35.5218 + 29.8063i) q^{80} +(44.0674 + 36.9769i) q^{81} +(-15.2938 - 86.7354i) q^{82} +(10.4759 + 18.1448i) q^{83} +(148.743 + 85.8768i) q^{84} +(-3.77359 - 1.37347i) q^{85} +(-5.85879 + 16.0969i) q^{86} +(30.0757 - 52.0926i) q^{87} +(5.89318 - 3.40243i) q^{88} +(144.671 - 25.5093i) q^{89} +(-101.391 + 120.833i) q^{90} +(-30.3824 - 36.2083i) q^{91} +(-1.42706 + 8.09323i) q^{92} +(138.547 - 50.4269i) q^{93} -231.716i q^{94} +234.362 q^{96} +(-23.7675 - 65.3008i) q^{97} +(-31.2069 - 5.50262i) q^{98} +(-90.4706 + 75.9138i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 9 q^{3} - 9 q^{4} + 3 q^{5} + 9 q^{6} + 6 q^{7} - 9 q^{8} + 39 q^{9} - 30 q^{10} - 18 q^{11} + 63 q^{12} - 51 q^{13} - 90 q^{14} - 54 q^{15} + 51 q^{16} - 75 q^{17} - 90 q^{20} + 48 q^{21}+ \cdots - 366 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - 9 * q^3 - 9 * q^4 + 3 * q^5 + 9 * q^6 + 6 * q^7 - 9 * q^8 + 39 * q^9 - 30 * q^10 - 18 * q^11 + 63 * q^12 - 51 * q^13 - 90 * q^14 - 54 * q^15 + 51 * q^16 - 75 * q^17 - 90 * q^20 + 48 * q^21 - 33 * q^22 - 66 * q^23 - 66 * q^24 + 123 * q^25 + 21 * q^26 - 27 * q^27 - 6 * q^28 - 78 * q^29 + 24 * q^30 + 99 * q^31 - 222 * q^32 - 15 * q^33 - 66 * q^34 - 66 * q^35 - 225 * q^36 - 108 * q^39 + 141 * q^40 - 171 * q^41 + 123 * q^42 + 54 * q^43 - 51 * q^44 - 3 * q^45 - 54 * q^46 - 81 * q^47 - 24 * q^48 - 24 * q^49 + 72 * q^50 + 48 * q^51 - 123 * q^52 - 96 * q^53 + 210 * q^54 - 153 * q^55 - 132 * q^58 + 111 * q^59 + 231 * q^60 - 120 * q^61 - 171 * q^62 + 171 * q^63 + 27 * q^64 + 126 * q^65 + 69 * q^66 - 18 * q^67 - 30 * q^68 + 72 * q^69 - 126 * q^70 + 138 * q^71 + 114 * q^72 - 135 * q^73 + 471 * q^74 + 246 * q^77 - 99 * q^78 + 132 * q^79 + 264 * q^80 + 390 * q^81 - 126 * q^82 - 156 * q^83 + 99 * q^84 + 15 * q^85 + 72 * q^86 + 69 * q^87 - 405 * q^88 + 531 * q^89 - 93 * q^90 + 393 * q^91 + 12 * q^92 + 384 * q^93 + 558 * q^96 - 588 * q^97 - 159 * q^98 - 366 * q^99

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