LMFDB - Embedded newform 33.4.e.c.4.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,4,Mod(4,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("33.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	33.e (of order $5$, 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:	$1.94706303019$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
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} - 3 x^{11} + 21 x^{10} - 26 x^{9} + 281 x^{8} + 486 x^{7} + 3506 x^{6} + 15102 x^{5} + \cdots + 1936 $ x^12 - 3x^11 + 21x^10 - 26x^9 + 281x^8 + 486x^7 + 3506x^6 + 15102x^5 + 46669x^4 + 41850x^3 + 16292x^2 + 616*x + 1936
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			4.2
Root			$-0.654357 + 0.475418i$ of defining polynomial
Character	$\chi$	$=$	33.4
Dual form			33.4.e.c.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.46337 - 1.06320i) q^{2} +(-0.927051 + 2.85317i) q^{3} +(-1.46107 - 4.49672i) q^{4} +(17.3626 - 12.6147i) q^{5} +(4.39012 - 3.18961i) q^{6} +(-5.78498 - 17.8043i) q^{7} +(-7.11451 + 21.8962i) q^{8} +(-7.28115 - 5.29007i) q^{9} -38.8200 q^{10} +(30.2087 + 20.4556i) q^{11} +14.1844 q^{12} +(-11.2281 - 8.15769i) q^{13} +(-10.4640 + 32.2050i) q^{14} +(19.8958 + 61.2329i) q^{15} +(3.09019 - 2.24515i) q^{16} +(17.6108 - 12.7950i) q^{17} +(5.03063 + 15.4827i) q^{18} +(-39.0184 + 120.086i) q^{19} +(-82.0928 - 59.6439i) q^{20} +56.1618 q^{21} +(-22.4582 - 62.0523i) q^{22} +1.06620 q^{23} +(-55.8781 - 40.5978i) q^{24} +(103.703 - 319.165i) q^{25} +(7.75762 + 23.8755i) q^{26} +(21.8435 - 15.8702i) q^{27} +(-71.6089 + 52.0269i) q^{28} +(40.3127 + 124.070i) q^{29} +(35.9881 - 110.760i) q^{30} +(156.035 + 113.366i) q^{31} +177.275 q^{32} +(-86.3684 + 67.2272i) q^{33} -39.3748 q^{34} +(-325.038 - 236.154i) q^{35} +(-13.1497 + 40.4705i) q^{36} +(12.8995 + 39.7007i) q^{37} +(184.775 - 134.247i) q^{38} +(33.6843 - 24.4731i) q^{39} +(152.687 + 469.923i) q^{40} +(-18.3159 + 56.3705i) q^{41} +(-82.1857 - 59.7114i) q^{42} -172.713 q^{43} +(47.8461 - 165.727i) q^{44} -193.152 q^{45} +(-1.56025 - 1.13359i) q^{46} +(-41.3932 + 127.395i) q^{47} +(3.54104 + 10.8982i) q^{48} +(-6.03551 + 4.38505i) q^{49} +(-491.094 + 356.801i) q^{50} +(20.1802 + 62.1081i) q^{51} +(-20.2778 + 62.4086i) q^{52} +(32.5881 + 23.6767i) q^{53} -48.8384 q^{54} +(782.544 - 25.9103i) q^{55} +431.005 q^{56} +(-306.454 - 222.652i) q^{57} +(72.9188 - 224.421i) q^{58} +(62.0729 + 191.041i) q^{59} +(246.278 - 178.932i) q^{60} +(-166.055 + 120.646i) q^{61} +(-107.806 - 331.793i) q^{62} +(-52.0648 + 160.239i) q^{63} +(-284.141 - 206.441i) q^{64} -297.856 q^{65} +(197.866 - 6.55140i) q^{66} -474.187 q^{67} +(-83.2661 - 60.4964i) q^{68} +(-0.988421 + 3.04205i) q^{69} +(224.573 + 691.164i) q^{70} +(342.199 - 248.622i) q^{71} +(167.634 - 121.793i) q^{72} +(-335.973 - 1034.02i) q^{73} +(23.3331 - 71.8119i) q^{74} +(814.495 + 591.765i) q^{75} +597.003 q^{76} +(189.442 - 656.182i) q^{77} -75.3125 q^{78} +(-465.201 - 337.988i) q^{79} +(25.3319 - 77.9635i) q^{80} +(25.0304 + 77.0356i) q^{81} +(86.7363 - 63.0176i) q^{82} +(-543.401 + 394.804i) q^{83} +(-82.0565 - 252.544i) q^{84} +(144.365 - 444.309i) q^{85} +(252.744 + 183.629i) q^{86} -391.364 q^{87} +(-662.821 + 515.925i) q^{88} -311.151 q^{89} +(282.654 + 205.360i) q^{90} +(-80.2879 + 247.101i) q^{91} +(-1.55780 - 4.79440i) q^{92} +(-468.104 + 340.097i) q^{93} +(196.021 - 142.417i) q^{94} +(837.387 + 2577.21i) q^{95} +(-164.343 + 505.796i) q^{96} +(-553.683 - 402.274i) q^{97} +13.4944 q^{98} +(-111.743 - 308.747i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 9 q^{3} - 16 q^{4} + 28 q^{5} + 12 q^{7} - 112 q^{8} - 27 q^{9} + 100 q^{10} - 54 q^{11} - 102 q^{12} - 18 q^{13} + 156 q^{14} + 111 q^{15} + 308 q^{16} - 80 q^{17} - 45 q^{18} - 280 q^{19} - 15 q^{20}+ \cdots - 171 q^{99}+O(q^{100}) $ 12 * q + 9 * q^3 - 16 * q^4 + 28 * q^5 + 12 * q^7 - 112 * q^8 - 27 * q^9 + 100 * q^10 - 54 * q^11 - 102 * q^12 - 18 * q^13 + 156 * q^14 + 111 * q^15 + 308 * q^16 - 80 * q^17 - 45 * q^18 - 280 * q^19 - 15 * q^20 - 6 * q^21 - 193 * q^22 - 392 * q^23 - 264 * q^24 + 77 * q^25 + 406 * q^26 + 81 * q^27 - 429 * q^28 + 13 * q^29 + 120 * q^30 + 413 * q^31 + 1314 * q^32 + 177 * q^33 + 1060 * q^34 - 1239 * q^35 - 144 * q^36 + 654 * q^37 + 912 * q^38 + 54 * q^39 - 1803 * q^40 - 1490 * q^41 + 342 * q^42 + 416 * q^43 + 695 * q^44 + 162 * q^45 - 2369 * q^46 - 150 * q^47 + 711 * q^48 - 301 * q^49 - 1878 * q^50 - 1661 * q^52 + 1359 * q^53 - 270 * q^54 + 3300 * q^55 - 858 * q^56 - 1110 * q^57 + 955 * q^58 + 1262 * q^59 + 45 * q^60 - 1044 * q^61 - 701 * q^62 + 108 * q^63 + 78 * q^64 + 4556 * q^65 + 369 * q^66 - 528 * q^67 + 703 * q^68 - 594 * q^69 + 3050 * q^70 + 558 * q^71 + 792 * q^72 - 699 * q^73 - 3224 * q^74 + 1284 * q^75 - 868 * q^76 + 390 * q^77 - 558 * q^78 - 1252 * q^79 - 1914 * q^80 - 243 * q^81 + 2987 * q^82 - 4464 * q^83 - 1443 * q^84 - 2170 * q^85 - 3209 * q^86 - 3474 * q^87 + 1302 * q^88 + 316 * q^89 - 90 * q^90 + 176 * q^91 + 4595 * q^92 - 1239 * q^93 + 1247 * q^94 + 1466 * q^95 + 1398 * q^96 + 1608 * q^97 + 2810 * q^98 - 171 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.46337	−	1.06320i	−0.517381	−	0.375899i	0.298235	−	0.954492i	$-0.403602\pi$
$2$	−1.46337	−	1.06320i	−0.517381	−	0.375899i	−0.815616	+	0.578593i	$0.803602\pi$
$3$	−0.927051	+	2.85317i	−0.178411	+	0.549093i
$3$	−0.927051	+	2.85317i	−0.178411	+	0.549093i
$4$	−1.46107	−	4.49672i	−0.182634	−	0.562090i
$5$	17.3626	−	12.6147i	1.55296	−	1.12829i	0.611460	−	0.791275i	$-0.290582\pi$
$5$	17.3626	−	12.6147i	1.55296	−	1.12829i	0.941499	−	0.337016i	$-0.109418\pi$
$6$	4.39012	−	3.18961i	0.298710	−	0.217026i
$7$	−5.78498	−	17.8043i	−0.312359	−	0.961344i	−0.976828	−	0.214027i	$-0.931342\pi$
$7$	−5.78498	−	17.8043i	−0.312359	−	0.961344i	0.664468	−	0.747317i	$-0.268658\pi$
$8$	−7.11451	+	21.8962i	−0.314420	+	0.967685i
$9$	−7.28115	−	5.29007i	−0.269672	−	0.195928i
$10$	−38.8200			−1.22760
$11$	30.2087	+	20.4556i	0.828025	+	0.560691i
$11$	30.2087	+	20.4556i	0.828025	+	0.560691i
$12$	14.1844			0.341224
$13$	−11.2281	−	8.15769i	−0.239547	−	0.174041i	0.461534	−	0.887122i	$-0.347299\pi$
$13$	−11.2281	−	8.15769i	−0.239547	−	0.174041i	−0.701081	+	0.713081i	$0.747299\pi$
$14$	−10.4640	+	32.2050i	−0.199760	+	0.614797i
$15$	19.8958	+	61.2329i	0.342471	+	1.05402i
$16$	3.09019	−	2.24515i	0.0482842	−	0.0350805i
$17$	17.6108	−	12.7950i	0.251249	−	0.182543i	−0.455031	−	0.890476i	$-0.650372\pi$
$17$	17.6108	−	12.7950i	0.251249	−	0.182543i	0.706280	+	0.707932i	$0.250372\pi$
$18$	5.03063	+	15.4827i	0.0658740	+	0.202739i
$19$	−39.0184	+	120.086i	−0.471128	+	1.44998i	0.379982	+	0.924994i	$0.375930\pi$
$19$	−39.0184	+	120.086i	−0.471128	+	1.44998i	−0.851110	+	0.524988i	$0.824070\pi$
$20$	−82.0928	−	59.6439i	−0.917825	−	0.666839i
$21$	56.1618			0.583595
$22$	−22.4582	−	62.0523i	−0.217641	−	0.601345i
$23$	1.06620			0.00966600			0.00483300	−	0.999988i	$-0.498462\pi$
$23$	1.06620			0.00966600			0.00483300	+	0.999988i	$0.498462\pi$
$24$	−55.8781	−	40.5978i	−0.475253	−	0.345291i
$25$	103.703	−	319.165i	0.829625	−	2.55332i
$26$	7.75762	+	23.8755i	0.0585152	+	0.180091i
$27$	21.8435	−	15.8702i	0.155695	−	0.113119i
$28$	−71.6089	+	52.0269i	−0.483314	+	0.351148i
$29$	40.3127	+	124.070i	0.258134	+	0.794454i	0.993196	+	0.116454i	$0.0371528\pi$
$29$	40.3127	+	124.070i	0.258134	+	0.794454i	−0.735062	+	0.677999i	$0.762847\pi$
$30$	35.9881	−	110.760i	0.219017	−	0.674064i
$31$	156.035	+	113.366i	0.904021	+	0.656810i	0.939496	−	0.342561i	$-0.111294\pi$
$31$	156.035	+	113.366i	0.904021	+	0.656810i	−0.0354747	+	0.999371i	$0.511294\pi$
$32$	177.275			0.979316
$33$	−86.3684	+	67.2272i	−0.455600	+	0.354629i
$34$	−39.3748			−0.198610
$35$	−325.038	−	236.154i	−1.56976	−	1.14050i
$36$	−13.1497	+	40.4705i	−0.0608781	+	0.187363i
$37$	12.8995	+	39.7007i	0.0573155	+	0.176399i	0.975616	−	0.219486i	$-0.0704380\pi$
$37$	12.8995	+	39.7007i	0.0573155	+	0.176399i	−0.918300	+	0.395885i	$0.870438\pi$
$38$	184.775	−	134.247i	0.788800	−	0.573096i
$39$	33.6843	−	24.4731i	0.138303	−	0.100483i
$40$	152.687	+	469.923i	0.603549	+	1.85753i
$41$	−18.3159	+	56.3705i	−0.0697673	+	0.214722i	−0.979861	−	0.199681i	$-0.936009\pi$
$41$	−18.3159	+	56.3705i	−0.0697673	+	0.214722i	0.910094	+	0.414403i	$0.136009\pi$
$42$	−82.1857	−	59.7114i	−0.301941	−	0.219373i
$43$	−172.713			−0.612524			−0.306262	−	0.951947i	$-0.599078\pi$
$43$	−172.713			−0.612524			−0.306262	+	0.951947i	$0.599078\pi$
$44$	47.8461	−	165.727i	0.163933	−	0.567826i
$45$	−193.152			−0.639854
$46$	−1.56025	−	1.13359i	−0.00500100	−	0.00363344i
$47$	−41.3932	+	127.395i	−0.128464	+	0.395372i	−0.994516	−	0.104581i	$-0.966650\pi$
$47$	−41.3932	+	127.395i	−0.128464	+	0.395372i	0.866052	+	0.499954i	$0.166650\pi$
$48$	3.54104	+	10.8982i	0.0106480	+	0.0327713i
$49$	−6.03551	+	4.38505i	−0.0175962	+	0.0127844i
$50$	−491.094	+	356.801i	−1.38902	+	1.00919i
$51$	20.1802	+	62.1081i	0.0554076	+	0.170527i
$52$	−20.2778	+	62.4086i	−0.0540773	+	0.166433i
$53$	32.5881	+	23.6767i	0.0844590	+	0.0613630i	0.629213	−	0.777233i	$-0.283377\pi$
$53$	32.5881	+	23.6767i	0.0844590	+	0.0613630i	−0.544754	+	0.838596i	$0.683377\pi$
$54$	−48.8384			−0.123075
$55$	782.544	−	25.9103i	1.91851	−	0.0635226i
$56$	431.005			1.02849
$57$	−306.454	−	222.652i	−0.712120	−	0.517386i
$58$	72.9188	−	224.421i	0.165081	−	0.508067i
$59$	62.0729	+	191.041i	0.136969	+	0.421549i	0.995891	−	0.0905583i	$-0.0288652\pi$
$59$	62.0729	+	191.041i	0.136969	+	0.421549i	−0.858922	+	0.512107i	$0.828865\pi$
$60$	246.278	−	178.932i	0.529906	−	0.385000i
$61$	−166.055	+	120.646i	−0.348544	+	0.253232i	−0.748258	−	0.663408i	$-0.769109\pi$
$61$	−166.055	+	120.646i	−0.348544	+	0.253232i	0.399714	+	0.916640i	$0.369109\pi$
$62$	−107.806	−	331.793i	−0.220829	−	0.679642i
$63$	−52.0648	+	160.239i	−0.104120	+	0.320448i
$64$	−284.141	−	206.441i	−0.554964	−	0.403205i
$65$	−297.856			−0.568376
$66$	197.866	−	6.55140i	0.369024	−	0.0122185i
$67$	−474.187			−0.864644			−0.432322	−	0.901719i	$-0.642306\pi$
$67$	−474.187			−0.864644			−0.432322	+	0.901719i	$0.642306\pi$
$68$	−83.2661	−	60.4964i	−0.148493	−	0.107886i
$69$	−0.988421	+	3.04205i	−0.00172452	+	0.00530753i
$70$	224.573	+	691.164i	0.383451	+	1.18014i
$71$	342.199	−	248.622i	0.571994	−	0.415578i	−0.263835	−	0.964568i	$-0.584987\pi$
$71$	342.199	−	248.622i	0.571994	−	0.415578i	0.835829	+	0.548990i	$0.184987\pi$
$72$	167.634	−	121.793i	0.274387	−	0.199354i
$73$	−335.973	−	1034.02i	−0.538667	−	1.65785i	−0.735589	−	0.677428i	$-0.763095\pi$
$73$	−335.973	−	1034.02i	−0.538667	−	1.65785i	0.196922	−	0.980419i	$-0.436905\pi$
$74$	23.3331	−	71.8119i	0.0366543	−	0.112810i
$75$	814.495	+	591.765i	1.25400	+	0.911082i
$76$	597.003			0.901065
$77$	189.442	−	656.182i	0.280375	−	0.971154i
$78$	−75.3125			−0.109326
$79$	−465.201	−	337.988i	−0.662522	−	0.481350i	0.204992	−	0.978764i	$-0.434283\pi$
$79$	−465.201	−	337.988i	−0.662522	−	0.481350i	−0.867514	+	0.497414i	$0.834283\pi$
$80$	25.3319	−	77.9635i	0.0354024	−	0.108957i
$81$	25.0304	+	77.0356i	0.0343352	+	0.105673i
$82$	86.7363	−	63.0176i	0.116810	−	0.0848674i
$83$	−543.401	+	394.804i	−0.718627	+	0.522113i	−0.885945	−	0.463790i	$-0.846489\pi$
$83$	−543.401	+	394.804i	−0.718627	+	0.522113i	0.167318	+	0.985903i	$0.446489\pi$
$84$	−82.0565	−	252.544i	−0.106584	−	0.328033i
$85$	144.365	−	444.309i	0.184218	−	0.566965i
$86$	252.744	+	183.629i	0.316908	+	0.230247i
$87$	−391.364			−0.482283
$88$	−662.821	+	515.925i	−0.802920	+	0.624975i
$89$	−311.151			−0.370584			−0.185292	−	0.982684i	$-0.559323\pi$
$89$	−311.151			−0.370584			−0.185292	+	0.982684i	$0.559323\pi$
$90$	282.654	+	205.360i	0.331048	+	0.240521i
$91$	−80.2879	+	247.101i	−0.0924885	+	0.284650i
$92$	−1.55780	−	4.79440i	−0.00176534	−	0.00543316i
$93$	−468.104	+	340.097i	−0.521937	+	0.379209i
$94$	196.021	−	142.417i	0.215085	−	0.156269i
$95$	837.387	+	2577.21i	0.904359	+	2.78333i
$96$	−164.343	+	505.796i	−0.174721	+	0.537735i
$97$	−553.683	−	402.274i	−0.579567	−	0.421080i	0.259001	−	0.965877i	$-0.416607\pi$
$97$	−553.683	−	402.274i	−0.579567	−	0.421080i	−0.838568	+	0.544797i	$0.816607\pi$
$98$	13.4944			0.0139096
$99$	−111.743	−	308.747i	−0.113440	−	0.313437i
$100$	−1586.72			−1.58672
$101$	939.427	+	682.534i	0.925510	+	0.672422i	0.944889	−	0.327390i	$-0.106169\pi$
$101$	939.427	+	682.534i	0.925510	+	0.672422i	−0.0193793	+	0.999812i	$0.506169\pi$
$102$	36.5025	−	112.343i	0.0354342	−	0.109055i
$103$	138.829	+	427.273i	0.132808	+	0.408742i	0.995243	−	0.0974269i	$-0.0310612\pi$
$103$	138.829	+	427.273i	0.132808	+	0.408742i	−0.862434	+	0.506169i	$0.831061\pi$
$104$	258.505	−	187.815i	0.243735	−	0.177084i
$105$	975.115	−	708.462i	0.906300	−	0.658465i
$106$	−22.5155	−	69.2957i	−0.0206311	−	0.0634961i
$107$	188.651	−	580.607i	0.170444	−	0.524574i	−0.828952	−	0.559320i	$-0.811062\pi$
$107$	188.651	−	580.607i	0.170444	−	0.524574i	0.999396	+	0.0347462i	$0.0110623\pi$
$108$	−103.279	−	75.0364i	−0.0920186	−	0.0668554i
$109$	1128.39			0.991560			0.495780	−	0.868448i	$-0.334882\pi$
$109$	1128.39			0.991560			0.495780	+	0.868448i	$0.334882\pi$
$110$	−1172.70	−	794.087i	−1.01648	−	0.688302i
$111$	−125.231			−0.107085
$112$	−57.8502	−	42.0306i	−0.0488065	−	0.0354600i
$113$	−76.0664	+	234.108i	−0.0633250	+	0.194894i	−0.977714	−	0.209943i	$-0.932672\pi$
$113$	−76.0664	+	234.108i	−0.0633250	+	0.194894i	0.914389	+	0.404838i	$0.132672\pi$
$114$	211.733	+	651.646i	0.173953	+	0.535371i
$115$	18.5120	−	13.4498i	0.0150109	−	0.0109061i
$116$	499.007	−	362.550i	0.399411	−	0.290189i
$117$	38.5987	+	118.795i	0.0304996	+	0.0938682i
$118$	112.279	−	345.560i	0.0875944	−	0.269588i
$119$	−329.684	−	239.529i	−0.253967	−	0.184518i
$120$	−1482.32			−1.12764
$121$	494.135	+	1235.88i	0.371251	+	0.928533i
$122$	371.272			0.275520
$123$	−143.855	−	104.517i	−0.105455	−	0.0766174i
$124$	281.796	−	867.280i	0.204081	−	0.628097i
$125$	−1396.62	−	4298.36i	−0.999340	−	3.07565i
$126$	246.557	−	179.134i	0.174326	−	0.126655i
$127$	−449.478	+	326.565i	−0.314053	+	0.228173i	−0.733633	−	0.679545i	$-0.762177\pi$
$127$	−449.478	+	326.565i	−0.314053	+	0.228173i	0.419581	+	0.907718i	$0.362177\pi$
$128$	−241.932	−	744.589i	−0.167062	−	0.514164i
$129$	160.114	−	492.781i	0.109281	−	0.336333i
$130$	435.874	+	316.681i	0.294067	+	0.213652i
$131$	1958.51			1.30623			0.653113	−	0.757260i	$-0.273463\pi$
$131$	1958.51			1.30623			0.653113	+	0.757260i	$0.273463\pi$
$132$	428.493	+	290.151i	0.282542	+	0.191321i
$133$	2363.77			1.54109
$134$	693.913	+	504.157i	0.447350	+	0.325019i
$135$	179.062	−	551.096i	0.114157	−	0.351339i
$136$	154.869	+	476.639i	0.0976467	+	0.300526i
$137$	−2021.59	+	1468.77i	−1.26070	+	0.915954i	−0.998792	−	0.0491379i	$-0.984353\pi$
$137$	−2021.59	+	1468.77i	−1.26070	+	0.915954i	−0.261911	+	0.965092i	$0.584353\pi$
$138$	4.68075	−	3.40076i	0.00288733	−	0.00209777i
$139$	−686.727	−	2113.53i	−0.419046	−	1.28969i	−0.908581	−	0.417708i	$-0.862834\pi$
$139$	−686.727	−	2113.53i	−0.419046	−	1.28969i	0.489535	−	0.871984i	$-0.337166\pi$
$140$	−587.015	+	1806.65i	−0.354370	+	1.09064i
$141$	−325.107	−	236.204i	−0.194177	−	0.141078i
$142$	−765.102			−0.452155
$143$	−172.316	−	476.111i	−0.100768	−	0.278422i
$144$	−34.3772			−0.0198942
$145$	2265.03	+	1645.64i	1.29725	+	0.942504i
$146$	−607.719	+	1870.37i	−0.344487	+	1.06022i
$147$	−6.91608	−	21.2855i	−0.00388046	−	0.0119428i
$148$	159.676	−	116.011i	0.0886843	−	0.0644329i
$149$	−1974.65	+	1434.67i	−1.08570	+	0.788811i	−0.978669	−	0.205444i	$-0.934136\pi$
$149$	−1974.65	+	1434.67i	−1.08570	+	0.788811i	−0.107036	+	0.994255i	$0.534136\pi$
$150$	−562.744	−	1731.95i	−0.306319	−	0.942753i
$151$	−511.934	+	1575.57i	−0.275898	+	0.849127i	0.713082	+	0.701080i	$0.247299\pi$
$151$	−511.934	+	1575.57i	−0.275898	+	0.849127i	−0.988980	+	0.148047i	$0.952701\pi$
$152$	−2351.83	−	1708.71i	−1.25499	−	0.911806i
$153$	−195.913			−0.103520
$154$	−974.879	+	758.824i	−0.510117	+	0.397064i
$155$	4139.24			2.14498
$156$	−159.264	−	115.712i	−0.0817391	−	0.0593870i
$157$	−803.644	+	2473.36i	−0.408521	+	1.25730i	0.509398	+	0.860531i	$0.329868\pi$
$157$	−803.644	+	2473.36i	−0.408521	+	1.25730i	−0.917919	+	0.396768i	$0.870132\pi$
$158$	321.413	+	989.207i	0.161837	+	0.498083i
$159$	−97.7644	+	71.0300i	−0.0487624	+	0.0354280i
$160$	3077.96	−	2236.27i	1.52084	−	1.10495i
$161$	−6.16794	−	18.9830i	−0.00301927	−	0.00929235i
$162$	45.2757	−	139.344i	0.0219580	−	0.0675798i
$163$	1266.99	+	920.524i	0.608825	+	0.442337i	0.849000	−	0.528392i	$-0.177205\pi$
$163$	1266.99	+	920.524i	0.608825	+	0.442337i	−0.240175	+	0.970730i	$0.577205\pi$
$164$	280.243			0.133435
$165$	−651.531	+	2256.75i	−0.307404	+	1.06477i
$166$	1214.96			0.568066
$167$	−2251.01	−	1635.45i	−1.04304	−	0.757815i	−0.0721653	−	0.997393i	$-0.522991\pi$
$167$	−2251.01	−	1635.45i	−1.04304	−	0.757815i	−0.970877	+	0.239578i	$0.922991\pi$
$168$	−399.563	+	1229.73i	−0.183494	+	0.564736i
$169$	−619.388	−	1906.28i	−0.281925	−	0.867674i
$170$	−683.650	+	496.701i	−0.308433	+	0.224089i
$171$	919.362	−	667.956i	0.411143	−	0.298713i
$172$	252.347	+	776.644i	0.111868	+	0.344294i
$173$	991.075	−	3050.22i	0.435550	−	1.34048i	−0.456973	−	0.889481i	$-0.651066\pi$
$173$	991.075	−	3050.22i	0.435550	−	1.34048i	0.892522	−	0.451003i	$-0.148934\pi$
$174$	572.711	+	416.099i	0.249524	+	0.181290i
$175$	−6282.45			−2.71376
$176$	139.277	−	4.61151i	0.0596499	−	0.00197503i
$177$	−602.616			−0.255906
$178$	455.331	+	330.817i	0.191733	+	0.139302i
$179$	−256.813	+	790.388i	−0.107235	+	0.330035i	−0.990249	−	0.139312i	$-0.955511\pi$
$179$	−256.813	+	790.388i	−0.107235	+	0.330035i	0.883014	+	0.469348i	$0.155511\pi$
$180$	282.210	+	868.552i	0.116859	+	0.359656i
$181$	−3317.87	+	2410.58i	−1.36252	+	0.989926i	−0.364236	+	0.931307i	$0.618670\pi$
$181$	−3317.87	+	2410.58i	−1.36252	+	0.989926i	−0.998280	+	0.0586198i	$0.981330\pi$
$182$	380.210	−	276.238i	0.154852	−	0.112506i
$183$	−190.282	−	585.629i	−0.0768638	−	0.236562i
$184$	−7.58548	+	23.3457i	−0.00303918	+	0.00935364i
$185$	724.782	+	526.585i	0.288038	+	0.209272i
$186$	1046.60			0.412585
$187$	793.729	−	26.2806i	0.310391	−	0.0102772i
$188$	633.339			0.245697
$189$	−408.922	−	297.099i	−0.157379	−	0.114343i
$190$	1514.69	−	4661.74i	0.578354	−	1.77999i
$191$	−568.417	−	1749.41i	−0.215336	−	0.662737i	−0.999130	−	0.0417150i	$-0.986718\pi$
$191$	−568.417	−	1749.41i	−0.215336	−	0.662737i	0.783793	−	0.621022i	$-0.213282\pi$
$192$	852.424	−	619.322i	0.320408	−	0.232790i
$193$	2618.88	−	1902.73i	0.976741	−	0.709644i	0.0197628	−	0.999805i	$-0.493709\pi$
$193$	2618.88	−	1902.73i	0.976741	−	0.709644i	0.956978	+	0.290161i	$0.0937089\pi$
$194$	382.546	+	1177.36i	0.141573	+	0.435717i
$195$	276.127	−	849.832i	0.101405	−	0.312091i
$196$	28.5367	+	20.7331i	0.0103997	+	0.00755580i
$197$	3195.60			1.15572			0.577860	−	0.816136i	$-0.303888\pi$
$197$	3195.60			1.15572			0.577860	+	0.816136i	$0.303888\pi$
$198$	−164.739	+	570.617i	−0.0591288	+	0.204808i
$199$	−2966.11			−1.05659			−0.528296	−	0.849060i	$-0.677169\pi$
$199$	−2966.11			−1.05659			−0.528296	+	0.849060i	$0.677169\pi$
$200$	6250.71	+	4541.41i	2.20996	+	1.60563i
$201$	439.595	−	1352.93i	0.154262	−	0.474770i
$202$	−649.061	−	1997.61i	−0.226078	−	0.695797i
$203$	1975.77	−	1435.48i	0.683112	−	0.496310i
$204$	249.798	−	181.489i	0.0857323	−	0.0622881i
$205$	393.084	+	1209.79i	0.133923	+	0.412172i
$206$	251.119	−	772.864i	0.0849333	−	0.261398i
$207$	−7.76316	−	5.64027i	−0.00260665	−	0.00189384i
$208$	−53.0122			−0.0176718
$209$	−3635.13	+	2829.51i	−1.20310	+	0.936464i
$210$	−2180.20			−0.716419
$211$	−2891.15	−	2100.55i	−0.943295	−	0.685344i	0.00591687	−	0.999982i	$-0.498117\pi$
$211$	−2891.15	−	2100.55i	−0.943295	−	0.685344i	−0.949211	+	0.314639i	$0.898117\pi$
$212$	58.8537	−	181.133i	0.0190665	−	0.0586806i
$213$	392.126	+	1206.84i	0.126141	+	0.388222i
$214$	−893.370	+	649.071i	−0.285372	+	0.207335i
$215$	−2998.76	+	2178.72i	−0.951225	+	0.691106i
$216$	192.092	+	591.198i	0.0605101	+	0.186231i
$217$	1115.75	−	3433.91i	0.349040	−	1.07424i
$218$	−1651.26	−	1199.71i	−0.513014	−	0.372727i
$219$	3261.70			1.00642
$220$	−1259.87	−	3481.02i	−0.386091	−	1.06678i
$221$	−302.113			−0.0919561
$222$	183.260	+	133.147i	0.0554038	+	0.0402532i
$223$	−396.727	+	1221.00i	−0.119134	+	0.366656i	−0.992787	−	0.119894i	$-0.961745\pi$
$223$	−396.727	+	1221.00i	−0.119134	+	0.366656i	0.873653	+	0.486549i	$0.161745\pi$
$224$	−1025.53	−	3156.26i	−0.305899	−	0.941459i
$225$	−2443.48	+	1775.30i	−0.723996	+	0.526014i
$226$	360.219	−	261.714i	0.106024	−	0.0770308i
$227$	−346.743	−	1067.17i	−0.101384	−	0.312027i	0.887481	−	0.460845i	$-0.152453\pi$
$227$	−346.743	−	1067.17i	−0.101384	−	0.312027i	−0.988865	+	0.148817i	$0.952453\pi$
$228$	−553.452	+	1703.35i	−0.160760	+	0.494768i
$229$	3885.80	+	2823.20i	1.12131	+	0.814682i	0.984408	−	0.175902i	$-0.0562841\pi$
$229$	3885.80	+	2823.20i	1.12131	+	0.814682i	0.136906	+	0.990584i	$0.456284\pi$
$230$	−41.3898			−0.0118659
$231$	1696.58	+	1148.82i	0.483231	+	0.327217i
$232$	−3003.46			−0.849943
$233$	85.0596	+	61.7994i	0.0239160	+	0.0173760i	0.599679	−	0.800241i	$-0.295295\pi$
$233$	85.0596	+	61.7994i	0.0239160	+	0.0173760i	−0.575763	+	0.817617i	$0.695295\pi$
$234$	69.8186	−	214.879i	0.0195051	−	0.0600304i
$235$	888.355	+	2734.08i	0.246595	+	0.758942i
$236$	768.363	−	558.249i	0.211933	−	0.153978i
$237$	1395.60	−	1013.97i	0.382507	−	0.277908i
$238$	227.783	+	701.043i	0.0620376	+	0.190932i
$239$	−337.043	+	1037.31i	−0.0912195	+	0.280745i	−0.986250	−	0.165260i	$-0.947154\pi$
$239$	−337.043	+	1037.31i	−0.0912195	+	0.280745i	0.895030	+	0.446005i	$0.147154\pi$
$240$	198.959	+	144.552i	0.0535115	+	0.0388784i
$241$	1068.58			0.285615			0.142808	−	0.989750i	$-0.454387\pi$
$241$	1068.58			0.285615			0.142808	+	0.989750i	$0.454387\pi$
$242$	590.885	−	2333.92i	0.156957	−	0.619958i
$243$	−243.000			−0.0641500
$244$	785.131	+	570.431i	0.205995	+	0.149664i
$245$	−49.4762	+	152.272i	−0.0129017	+	0.0397073i
$246$	99.3909	+	305.894i	0.0257599	+	0.0792808i
$247$	1417.73	−	1030.04i	0.365214	−	0.265343i
$248$	−3592.39	+	2610.02i	−0.919827	+	0.668293i
$249$	−622.682	−	1916.42i	−0.158477	−	0.487743i
$250$	−2526.25	+	7774.99i	−0.639096	+	1.96694i
$251$	−1611.87	−	1171.09i	−0.405339	−	0.294496i	0.366373	−	0.930468i	$-0.380599\pi$
$251$	−1611.87	−	1171.09i	−0.405339	−	0.294496i	−0.771712	+	0.635972i	$0.780599\pi$
$252$	796.621			0.199136
$253$	32.2085	+	21.8098i	0.00800369	+	0.00541964i
$254$	1004.96			0.248255
$255$	1133.85	+	823.793i	0.278450	+	0.202306i
$256$	−1305.87	+	4019.06i	−0.318816	+	0.981216i
$257$	2467.59	+	7594.47i	0.598927	+	1.84331i	0.534117	+	0.845410i	$0.320644\pi$
$257$	2467.59	+	7594.47i	0.598927	+	1.84331i	0.0648096	+	0.997898i	$0.479356\pi$
$258$	−758.233	+	550.888i	−0.182967	+	0.132933i
$259$	632.221	−	459.336i	0.151677	−	0.110200i
$260$	435.189	+	1339.37i	0.103805	+	0.319479i
$261$	362.814	−	1116.63i	0.0860445	−	0.264818i
$262$	−2866.03	−	2082.29i	−0.675817	−	0.491010i
$263$	−3975.12			−0.932002			−0.466001	−	0.884784i	$-0.654306\pi$
$263$	−3975.12			−0.932002			−0.466001	+	0.884784i	$0.654306\pi$
$264$	−857.552	−	2369.43i	−0.199919	−	0.552380i
$265$	864.489			0.200397
$266$	−3459.09	−	2513.17i	−0.797332	−	0.579295i
$267$	288.453	−	887.767i	0.0661163	−	0.203485i
$268$	692.822	+	2132.29i	0.157913	+	0.486008i
$269$	912.180	−	662.738i	0.206753	−	0.150215i	−0.479590	−	0.877493i	$-0.659215\pi$
$269$	912.180	−	662.738i	0.206753	−	0.150215i	0.686343	+	0.727278i	$0.259215\pi$
$270$	−847.962	+	616.081i	−0.191131	+	0.138865i
$271$	−1220.61	−	3756.66i	−0.273605	−	0.842069i	−0.989585	−	0.143949i	$-0.954020\pi$
$271$	−1220.61	−	3756.66i	−0.273605	−	0.842069i	0.715980	−	0.698120i	$-0.245980\pi$
$272$	25.6940	−	79.0779i	0.00572766	−	0.0176279i
$273$	−630.589	−	458.150i	−0.139799	−	0.101570i
$274$	4519.95			0.996570
$275$	9661.47	−	7520.27i	2.11858	−	1.64905i
$276$	15.1234			0.00329827
$277$	−530.792	−	385.643i	−0.115134	−	0.0836500i	0.528728	−	0.848791i	$-0.322669\pi$
$277$	−530.792	−	385.643i	−0.115134	−	0.0836500i	−0.643862	+	0.765141i	$0.722669\pi$
$278$	−1242.17	+	3823.01i	−0.267988	+	0.824781i
$279$	−536.399	−	1650.87i	−0.115102	−	0.354247i
$280$	7483.37	−	5436.98i	1.59720	−	1.16044i
$281$	−695.644	+	505.415i	−0.147682	+	0.107297i	−0.659173	−	0.751992i	$-0.729093\pi$
$281$	−695.644	+	505.415i	−0.147682	+	0.107297i	0.511491	+	0.859289i	$0.329093\pi$
$282$	224.620	+	691.309i	0.0474323	+	0.145982i
$283$	2384.53	−	7338.83i	0.500868	−	1.54151i	−0.306741	−	0.951793i	$-0.599238\pi$
$283$	2384.53	−	7338.83i	0.500868	−	1.54151i	0.807608	−	0.589719i	$-0.200762\pi$
$284$	−1617.96	−	1175.52i	−0.338058	−	0.245614i
$285$	−8129.53			−1.68965
$286$	−254.040	+	879.935i	−0.0525235	+	0.181929i
$287$	1109.60			0.228214
$288$	−1290.77	−	937.797i	−0.264094	−	0.191876i
$289$	−1371.77	+	4221.88i	−0.279213	+	0.859329i
$290$	−1564.94	−	4816.38i	−0.316884	−	0.975268i
$291$	1661.05	−	1206.82i	0.334613	−	0.243111i
$292$	−4158.82	+	3021.56i	−0.833481	+	0.605559i
$293$	−179.790	−	553.336i	−0.0358479	−	0.110328i	0.931531	−	0.363661i	$-0.118473\pi$
$293$	−179.790	−	553.336i	−0.0358479	−	0.110328i	−0.967379	+	0.253333i	$0.918473\pi$
$294$	−12.5100	+	38.5018i	−0.00248163	+	0.00763766i
$295$	3487.66	+	2533.93i	0.688337	+	0.500106i
$296$	−961.069			−0.188720
$297$	984.498	−	32.5971i	0.192345	−	0.00636860i
$298$	4415.01			0.858236
$299$	−11.9714	−	8.69772i	−0.00231546	−	0.00168228i
$300$	1470.97	−	4527.17i	0.283088	−	0.871254i
$301$	999.143	+	3075.05i	0.191328	+	0.588846i
$302$	2424.31	−	1761.36i	0.461931	−	0.335612i
$303$	−2818.28	+	2047.60i	−0.534343	+	0.388223i
$304$	149.038	+	458.691i	0.0281181	+	0.0865387i
$305$	−1361.24	+	4189.47i	−0.255555	+	0.786518i
$306$	286.694	+	208.295i	0.0535595	+	0.0389133i
$307$	2369.06			0.440421			0.220211	−	0.975452i	$-0.429326\pi$
$307$	2369.06			0.440421			0.220211	+	0.975452i	$0.429326\pi$
$308$	−3227.46	+	106.862i	−0.597082	+	0.0197696i
$309$	−1347.78			−0.248132
$310$	−6057.26	−	4400.86i	−1.10977	−	0.806296i
$311$	3247.09	−	9993.50i	0.592043	−	1.82212i	0.0231164	−	0.999733i	$-0.492641\pi$
$311$	3247.09	−	9993.50i	0.592043	−	1.82212i	0.568927	−	0.822388i	$-0.307359\pi$
$312$	296.220	+	911.671i	0.0537505	+	0.165427i
$313$	5874.45	−	4268.04i	1.06084	−	0.770747i	0.0865982	−	0.996243i	$-0.472400\pi$
$313$	5874.45	−	4268.04i	1.06084	−	0.770747i	0.974244	+	0.225496i	$0.0724004\pi$
$314$	3805.72	−	2765.02i	0.683979	−	0.496940i
$315$	1117.38	+	3438.95i	0.199865	+	0.615120i
$316$	−840.147	+	2585.71i	−0.149563	+	0.460308i
$317$	2381.36	+	1730.16i	0.421925	+	0.306547i	0.778412	−	0.627754i	$-0.216025\pi$
$317$	2381.36	+	1730.16i	0.421925	+	0.306547i	−0.356487	+	0.934300i	$0.616025\pi$
$318$	218.585			0.0385461
$319$	−1320.13	+	4572.61i	−0.231702	+	0.802561i
$320$	−7537.62			−1.31677
$321$	1481.68	+	1076.50i	0.257631	+	0.187180i
$322$	−11.1568	+	34.3370i	−0.00193088	+	0.00594262i
$323$	849.356	+	2614.05i	0.146314	+	0.450308i
$324$	309.836	−	225.109i	0.0531269	−	0.0385990i
$325$	−3768.04	+	2737.64i	−0.643118	+	0.467252i
$326$	−875.380	−	2694.14i	−0.148720	−	0.457714i
$327$	−1046.07	+	3219.48i	−0.176905	+	0.544458i
$328$	−1103.99	−	802.096i	−0.185847	−	0.135025i
$329$	2507.65			0.420216
$330$	3352.82	−	2609.76i	0.559293	−	0.435341i
$331$	−6904.52			−1.14655			−0.573273	−	0.819364i	$-0.694327\pi$
$331$	−6904.52			−1.14655			−0.573273	+	0.819364i	$0.694327\pi$
$332$	2569.27	+	1866.69i	0.424720	+	0.308577i
$333$	116.096	−	357.306i	0.0191052	−	0.0587996i
$334$	1555.25	+	4786.56i	0.254788	+	0.784158i
$335$	−8233.12	+	5981.71i	−1.34276	+	0.975570i
$336$	173.551	−	126.092i	0.0281784	−	0.0204728i
$337$	3167.78	+	9749.43i	0.512048	+	1.57592i	0.788590	+	0.614919i	$0.210811\pi$
$337$	3167.78	+	9749.43i	0.512048	+	1.57592i	−0.276543	+	0.961002i	$0.589189\pi$
$338$	−1120.37	+	3448.14i	−0.180296	+	0.554893i
$339$	−597.433	−	434.061i	−0.0957172	−	0.0695426i
$340$	−2208.86			−0.352330
$341$	2394.64	+	6616.42i	0.380285	+	1.05073i
$342$	−2055.54			−0.325003
$343$	−5081.84	−	3692.17i	−0.799981	−	0.581220i
$344$	1228.77	−	3781.77i	0.192590	−	0.592730i
$345$	21.2129	+	65.2865i	0.00331033	+	0.0101881i
$346$	−4693.32	+	3409.89i	−0.729232	+	0.529818i
$347$	−4255.33	+	3091.68i	−0.658324	+	0.478300i	−0.866096	−	0.499877i	$-0.833379\pi$
$347$	−4255.33	+	3091.68i	−0.658324	+	0.478300i	0.207773	+	0.978177i	$0.433379\pi$
$348$	571.811	+	1759.85i	0.0880813	+	0.271086i
$349$	3265.12	−	10049.0i	0.500795	−	1.54129i	−0.306931	−	0.951732i	$-0.599302\pi$
$349$	3265.12	−	10049.0i	0.500795	−	1.54129i	0.807726	−	0.589558i	$-0.200698\pi$
$350$	9193.57	+	6679.52i	1.40405	+	1.02010i
$351$	−374.724			−0.0569838
$352$	5355.26	+	3626.27i	0.810898	+	0.549094i
$353$	−1822.89			−0.274852			−0.137426	−	0.990512i	$-0.543883\pi$
$353$	−1822.89			−0.274852			−0.137426	+	0.990512i	$0.543883\pi$
$354$	881.853	+	640.703i	0.132401	+	0.0961949i
$355$	2805.19	−	8633.47i	0.419391	−	1.29075i
$356$	454.615	+	1399.16i	0.0676813	+	0.208302i
$357$	989.052	−	718.588i	0.146628	−	0.106531i
$358$	1216.16	−	883.589i	0.179541	−	0.130444i
$359$	3561.11	+	10960.0i	0.523532	+	1.61127i	0.767200	+	0.641408i	$0.221649\pi$
$359$	3561.11	+	10960.0i	0.523532	+	1.61127i	−0.243668	+	0.969859i	$0.578351\pi$
$360$	1374.18	−	4229.30i	0.201183	−	0.619177i
$361$	−7349.20	−	5339.51i	−1.07147	−	0.778468i
$362$	7418.22			1.07705
$363$	−3984.25	+	264.130i	−0.576086	+	0.0381907i
$364$	1228.45			0.176891
$365$	−18877.2	−	13715.1i	−2.70706	−	1.96680i
$366$	−344.188	+	1059.30i	−0.0491558	+	0.151286i
$367$	−797.036	−	2453.02i	−0.113365	−	0.348901i	0.878238	−	0.478225i	$-0.158720\pi$
$367$	−797.036	−	2453.02i	−0.113365	−	0.348901i	−0.991602	+	0.129323i	$0.958720\pi$
$368$	3.29476	−	2.39378i	0.000466715	−	0.000339088i
$369$	431.564	−	313.550i	0.0608844	−	0.0442351i
$370$	−500.760	−	1541.18i	−0.0703602	−	0.216546i
$371$	233.026	−	717.179i	0.0326094	−	0.100361i
$372$	2213.26	+	1608.03i	0.308473	+	0.224119i
$373$	6084.16			0.844573			0.422287	−	0.906462i	$-0.361228\pi$
$373$	6084.16			0.844573			0.422287	+	0.906462i	$0.361228\pi$
$374$	−1189.46	−	805.437i	−0.164454	−	0.111359i
$375$	13558.7			1.86711
$376$	−2494.98	−	1812.71i	−0.342204	−	0.248626i
$377$	559.487	−	1721.92i	0.0764325	−	0.235235i
$378$	282.529	+	869.535i	0.0384437	+	0.118318i
$379$	−4772.34	+	3467.31i	−0.646803	+	0.469930i	−0.862181	−	0.506601i	$-0.830902\pi$
$379$	−4772.34	+	3467.31i	−0.646803	+	0.469930i	0.215377	+	0.976531i	$0.430902\pi$
$380$	10365.5	−	7531.00i	1.39932	−	1.01666i
$381$	−515.056	−	1585.18i	−0.0692575	−	0.213153i
$382$	−1028.17	+	3164.38i	−0.137711	+	0.423832i
$383$	1294.36	+	940.409i	0.172686	+	0.125464i	0.670771	−	0.741664i	$-0.265963\pi$
$383$	1294.36	+	940.409i	0.172686	+	0.125464i	−0.498085	+	0.867128i	$0.665963\pi$
$384$	2348.72			0.312129
$385$	−4988.31	−	13782.8i	−0.660333	−	1.82451i
$386$	−5855.38			−0.772102
$387$	1257.55	+	913.665i	0.165181	+	0.120011i
$388$	−999.943	+	3077.51i	−0.130836	+	0.402672i
$389$	777.053	+	2391.52i	0.101281	+	0.311710i	0.988840	−	0.148985i	$-0.0476005\pi$
$389$	777.053	+	2391.52i	0.101281	+	0.311710i	−0.887559	+	0.460694i	$0.847600\pi$
$390$	−1307.62	+	950.043i	−0.169780	+	0.123352i
$391$	18.7766	−	13.6420i	0.00242858	−	0.00176446i
$392$	−53.0763	−	163.352i	−0.00683867	−	0.0210473i
$393$	−1815.64	+	5587.96i	−0.233045	+	0.717240i
$394$	−4676.35	−	3397.57i	−0.597947	−	0.434434i
$395$	−12340.7			−1.57197
$396$	−1225.08	+	953.578i	−0.155462	+	0.121008i
$397$	5486.84			0.693644			0.346822	−	0.937931i	$-0.387261\pi$
$397$	5486.84			0.693644			0.346822	+	0.937931i	$0.387261\pi$
$398$	4340.53	+	3153.58i	0.546661	+	0.397172i
$399$	−2191.34	+	6744.25i	−0.274948	+	0.846202i
$400$	−396.113	−	1219.11i	−0.0495142	−	0.152389i
$401$	11903.1	−	8648.10i	1.48232	−	1.07697i	0.505526	−	0.862812i	$-0.331299\pi$
$401$	11903.1	−	8648.10i	1.48232	−	1.07697i	0.976799	−	0.214160i	$-0.0687014\pi$
$402$	−2081.74	+	1512.47i	−0.258278	+	0.187650i
$403$	−827.168	−	2545.76i	−0.102244	−	0.314674i
$404$	1696.59	−	5221.58i	0.208932	−	0.643028i
$405$	1406.37	+	1021.79i	0.172551	+	0.125366i
$406$	−4417.50			−0.539992
$407$	−422.424	+	1463.18i	−0.0514466	+	0.178199i
$408$	−1503.50			−0.182438
$409$	6434.60	+	4675.01i	0.777923	+	0.565194i	0.904355	−	0.426781i	$-0.140353\pi$
$409$	6434.60	+	4675.01i	0.777923	+	0.565194i	−0.126432	+	0.991975i	$0.540353\pi$
$410$	711.022	−	2188.30i	0.0856460	−	0.263591i
$411$	−2316.54	−	7129.57i	−0.278021	−	0.855659i
$412$	1718.49	−	1248.55i	0.205495	−	0.149301i
$413$	3042.26	−	2210.33i	0.362469	−	0.263349i
$414$	5.36366	+	16.5076i	0.000636738	+	0.00195968i
$415$	−4454.54	+	13709.7i	−0.526903	+	1.62164i
$416$	−1990.46	−	1446.15i	−0.234592	−	0.170441i
$417$	6666.88			0.782923
$418$	8327.90	−	275.740i	0.974476	−	0.0322653i
$419$	7289.12			0.849873			0.424936	−	0.905223i	$-0.360296\pi$
$419$	7289.12			0.849873			0.424936	+	0.905223i	$0.360296\pi$
$420$	−4610.47	−	3349.70i	−0.535638	−	0.389164i
$421$	1716.98	−	5284.32i	0.198766	−	0.611739i	−0.801146	−	0.598469i	$-0.795776\pi$
$421$	1716.98	−	5284.32i	0.198766	−	0.611739i	0.999912	−	0.0132699i	$-0.00422405\pi$
$422$	1997.53	+	6147.77i	0.230422	+	0.709167i
$423$	975.320	−	708.611i	0.112108	−	0.0814512i
$424$	−750.278	+	545.109i	−0.0859356	+	0.0624359i
$425$	−2257.42	−	6947.63i	−0.257650	−	0.792964i
$426$	709.289	−	2182.97i	0.0806694	−	0.248275i
$427$	3108.65	+	2258.57i	0.352314	+	0.255971i
$428$	−2886.46			−0.325987
$429$	1518.17	−	50.2672i	0.170858	−	0.00565716i
$430$	6704.73			0.751932
$431$	10555.7	+	7669.16i	1.17970	+	0.857101i	0.992138	−	0.125152i	$-0.0399418\pi$
$431$	10555.7	+	7669.16i	1.17970	+	0.857101i	0.187561	+	0.982253i	$0.439942\pi$
$432$	31.8694	−	98.0839i	0.00354934	−	0.0109238i
$433$	−4501.50	−	13854.2i	−0.499603	−	1.53762i	−0.809658	−	0.586902i	$-0.800347\pi$
$433$	−4501.50	−	13854.2i	−0.499603	−	1.53762i	0.310054	−	0.950719i	$-0.399653\pi$
$434$	−5283.70	+	3838.83i	−0.584391	+	0.424585i
$435$	−6795.10	+	4936.93i	−0.748965	+	0.544155i
$436$	−1648.66	−	5074.05i	−0.181093	−	0.557346i
$437$	−41.6013	+	128.036i	−0.00455392	+	0.0140155i
$438$	−4773.08	−	3467.85i	−0.520700	−	0.378311i
$439$	−9451.64			−1.02757			−0.513784	−	0.857920i	$-0.671757\pi$
$439$	−9451.64			−1.02757			−0.513784	+	0.857920i	$0.671757\pi$
$440$	−5000.08	+	17319.1i	−0.541748	+	1.87649i
$441$	67.1427			0.00725005
$442$	442.104	+	321.207i	0.0475764	+	0.0345662i
$443$	−3959.92	+	12187.4i	−0.424698	+	1.30709i	0.478585	+	0.878041i	$0.341150\pi$
$443$	−3959.92	+	12187.4i	−0.424698	+	1.30709i	−0.903283	+	0.429045i	$0.858850\pi$
$444$	182.972	+	563.131i	0.0195574	+	0.0601915i
$445$	−5402.40	+	3925.07i	−0.575502	+	0.418127i
$446$	1878.73	−	1364.98i	0.199463	−	0.144918i
$447$	−2262.75	−	6964.04i	−0.239429	−	0.736885i
$448$	−2031.79	+	6253.20i	−0.214270	+	0.659456i
$449$	−4913.87	−	3570.14i	−0.516481	−	0.375245i	0.298796	−	0.954317i	$-0.403415\pi$
$449$	−4913.87	−	3570.14i	−0.516481	−	0.375245i	−0.815277	+	0.579072i	$0.803415\pi$
$450$	5463.23			0.572310
$451$	−1706.39	+	1328.22i	−0.178162	+	0.138677i
$452$	1163.86			0.121114
$453$	−4020.78	−	2921.27i	−0.417026	−	0.302987i
$454$	−627.199	+	1930.32i	−0.0648368	+	0.199547i
$455$	1723.09	+	5303.12i	0.177538	+	0.546405i
$456$	7055.50	−	5126.12i	0.724571	−	0.526431i
$457$	−12443.3	+	9040.61i	−1.27369	+	0.925387i	−0.999343	−	0.0362443i	$-0.988461\pi$
$457$	−12443.3	+	9040.61i	−1.27369	+	0.925387i	−0.274344	+	0.961632i	$0.588461\pi$
$458$	−2684.74	−	8262.79i	−0.273908	−	0.843002i
$459$	181.621	−	558.973i	0.0184692	−	0.0568423i
$460$	−87.5272	−	63.5923i	−0.00887169	−	0.00644566i
$461$	−3156.66			−0.318916			−0.159458	−	0.987205i	$-0.550975\pi$
$461$	−3156.66			−0.318916			−0.159458	+	0.987205i	$0.550975\pi$
$462$	−1261.29	−	3484.96i	−0.127014	−	0.350942i
$463$	4925.34			0.494384			0.247192	−	0.968966i	$-0.420492\pi$
$463$	4925.34			0.494384			0.247192	+	0.968966i	$0.420492\pi$
$464$	403.129	+	292.891i	0.0403336	+	0.0293041i
$465$	−3837.29	+	11810.0i	−0.382688	+	1.17779i
$466$	−58.7687	−	180.871i	−0.00584207	−	0.0179800i
$467$	9426.38	−	6848.67i	0.934049	−	0.678626i	−0.0129319	−	0.999916i	$-0.504116\pi$
$467$	9426.38	−	6848.67i	0.934049	−	0.678626i	0.946981	+	0.321290i	$0.104116\pi$
$468$	477.791	−	347.136i	0.0471921	−	0.0342871i
$469$	2743.16	+	8442.58i	0.270080	+	0.831220i
$470$	1606.88	−	4945.48i	0.157702	−	0.485357i
$471$	−6311.91	−	4585.87i	−0.617489	−	0.448632i
$472$	−4624.68			−0.450992
$473$	−5217.45	−	3532.96i	−0.507185	−	0.343437i
$474$	−3120.34			−0.302367
$475$	34281.0	+	24906.6i	3.31141	+	2.40588i
$476$	−595.405	+	1832.47i	−0.0573326	+	0.176452i
$477$	−112.028	−	344.787i	−0.0107535	−	0.0330958i
$478$	1596.09	−	1159.63i	0.152727	−	0.110963i
$479$	10614.2	−	7711.64i	1.01247	−	0.735603i	0.0477449	−	0.998860i	$-0.484797\pi$
$479$	10614.2	−	7711.64i	1.01247	−	0.735603i	0.964726	+	0.263256i	$0.0847965\pi$
$480$	3527.03	+	10855.1i	0.335388	+	1.03222i
$481$	179.029	−	550.994i	0.0169709	−	0.0522311i
$482$	−1563.73	−	1136.12i	−0.147772	−	0.107363i
$483$	59.8796			0.00564103
$484$	4835.43	−	4027.69i	0.454116	−	0.378258i
$485$	−14687.9			−1.37514
$486$	355.600	+	258.358i	0.0331900	+	0.0241139i
$487$	858.224	−	2641.34i	0.0798560	−	0.245771i	−0.903156	−	0.429312i	$-0.858756\pi$
$487$	858.224	−	2641.34i	0.0798560	−	0.245771i	0.983012	+	0.183541i	$0.0587560\pi$
$488$	−1460.29	−	4494.32i	−0.135460	−	0.416902i
$489$	−3800.98	+	2761.57i	−0.351505	+	0.255384i
$490$	234.298	−	170.228i	0.0216010	−	0.0156941i
$491$	−3911.56	−	12038.6i	−0.359524	−	1.10650i	−0.953340	−	0.301900i	$-0.902379\pi$
$491$	−3911.56	−	12038.6i	−0.359524	−	1.10650i	0.593815	−	0.804601i	$-0.297621\pi$
$492$	−259.800	+	799.581i	−0.0238062	+	0.0732681i
$493$	2297.41	+	1669.16i	0.209878	+	0.152485i
$494$	−3169.81			−0.288697
$495$	−5834.89	−	3951.05i	−0.529815	−	0.358761i
$496$	736.701			0.0666912
$497$	−6406.17	−	4654.36i	−0.578181	−	0.420073i
$498$	−1126.33	+	3466.48i	−0.101349	+	0.311921i
$499$	−3133.14	−	9642.80i	−0.281079	−	0.865073i	−0.987547	−	0.157327i	$-0.949712\pi$
$499$	−3133.14	−	9642.80i	−0.281079	−	0.865073i	0.706467	−	0.707746i	$-0.250288\pi$
$500$	−17287.9	+	12560.4i	−1.54628	+	1.12344i
$501$	6753.02	−	4906.36i	0.602201	−	0.437525i
$502$	1113.66	+	3427.48i	0.0990138	+	0.304733i
$503$	−46.4233	+	142.876i	−0.00411513	+	0.0126651i	−0.953093	−	0.302678i	$-0.902119\pi$
$503$	−46.4233	+	142.876i	−0.00411513	+	0.0126651i	0.948978	+	0.315343i	$0.102119\pi$
$504$	−3138.21	−	2280.04i	−0.277355	−	0.201510i
$505$	24920.9			2.19597
$506$	−23.9449	−	66.1601i	−0.00210372	−	0.00581260i
$507$	6013.15			0.526732
$508$	2125.19	+	1544.04i	0.185610	+	0.134854i
$509$	2260.06	−	6955.76i	0.196809	−	0.605715i	−0.803142	−	0.595787i	$-0.796840\pi$
$509$	2260.06	−	6955.76i	0.196809	−	0.605715i	0.999951	−	0.00992707i	$-0.00315994\pi$
$510$	−783.393	−	2411.04i	−0.0680181	−	0.209338i
$511$	−16466.4	+	11963.6i	−1.42550	+	1.03569i
$512$	1116.98	−	811.532i	0.0964139	−	0.0700488i
$513$	1053.50	+	3242.33i	0.0906686	+	0.279049i
$514$	4463.46	−	13737.1i	0.383025	−	1.17883i
$515$	7800.35	+	5667.28i	0.667426	+	0.484913i
$516$	−2449.84			−0.209008
$517$	−3856.39	+	3001.72i	−0.328053	+	0.255349i
$518$	−1413.54			−0.119899
$519$	7784.01	+	5655.41i	0.658343	+	0.478314i
$520$	2119.10	−	6521.91i	0.178709	−	0.550009i
$521$	5466.02	+	16822.7i	0.459637	+	1.41462i	0.865604	+	0.500729i	$0.166935\pi$
$521$	5466.02	+	16822.7i	0.459637	+	1.41462i	−0.405967	+	0.913888i	$0.633065\pi$
$522$	−1718.13	+	1248.30i	−0.144063	+	0.104668i
$523$	17344.7	−	12601.7i	1.45016	−	1.05360i	0.464362	−	0.885646i	$-0.346284\pi$
$523$	17344.7	−	12601.7i	1.45016	−	1.05360i	0.985795	−	0.167955i	$-0.0537163\pi$
$524$	−2861.53	−	8806.87i	−0.238562	−	0.734217i
$525$	5824.15	−	17924.9i	0.484165	−	1.49011i
$526$	5817.09	+	4226.36i	0.482200	+	0.350339i
$527$	4198.40			0.347031
$528$	−115.959	+	401.655i	−0.00955773	+	0.0331057i
$529$	−12165.9			−0.999907
$530$	−1265.07	−	919.128i	−0.103681	−	0.0753290i
$531$	558.656	−	1719.37i	0.0456565	−	0.140516i
$532$	−3453.65	−	10629.2i	−0.281456	−	0.866233i
$533$	665.505	−	483.517i	0.0540829	−	0.0392936i
$534$	−1365.99	+	992.452i	−0.110697	+	0.0804262i
$535$	−4048.70	−	12460.6i	−0.327179	−	1.00695i
$536$	3373.60	−	10382.9i	0.271861	−	0.836702i
$537$	−2017.03	−	1465.46i	−0.162088	−	0.117764i
$538$	−2039.49			−0.163436
$539$	−272.024	+	9.00681i	−0.0217382	+	0.000719761i
$540$	−2739.75			−0.218333
$541$	−5815.91	−	4225.51i	−0.462191	−	0.335802i	0.332199	−	0.943209i	$-0.392209\pi$
$541$	−5815.91	−	4225.51i	−0.462191	−	0.335802i	−0.794390	+	0.607408i	$0.792209\pi$
$542$	−2207.88	+	6795.16i	−0.174975	+	0.538518i
$543$	−3801.94	−	11701.2i	−0.300473	−	0.924762i
$544$	3121.95	−	2268.23i	0.246053	−	0.178768i
$545$	19591.8	−	14234.3i	1.53985	−	1.11877i
$546$	435.681	+	1340.89i	0.0341492	+	0.105100i
$547$	−1719.61	+	5292.42i	−0.134416	+	0.413689i	−0.995499	−	0.0947756i	$-0.969787\pi$
$547$	−1719.61	+	5292.42i	−0.134416	+	0.413689i	0.861083	+	0.508464i	$0.169787\pi$
$548$	9558.36	+	6944.55i	0.745096	+	0.541344i
$549$	1847.30			0.143608
$550$	−22133.9	+	732.862i	−1.71599	+	0.0568170i
$551$	−16472.0			−1.27356
$552$	−59.5772	−	43.2853i	−0.00459379	−	0.00333758i
$553$	−3326.48	+	10237.9i	−0.255798	+	0.787265i
$554$	366.731	+	1128.68i	0.0281243	+	0.0865578i
$555$	−2174.34	+	1579.75i	−0.166299	+	0.120823i
$556$	−8500.59	+	6176.04i	−0.648391	+	0.471084i
$557$	−457.077	−	1406.74i	−0.0347702	−	0.107012i	0.932165	−	0.362033i	$-0.117917\pi$
$557$	−457.077	−	1406.74i	−0.0347702	−	0.107012i	−0.966935	+	0.255022i	$0.917917\pi$
$558$	−970.255	+	2986.14i	−0.0736096	+	0.226547i
$559$	1939.24	+	1408.94i	0.146728	+	0.106604i
$560$	−1534.63			−0.115804
$561$	−660.844	+	2289.01i	−0.0497341	+	0.172267i
$562$	1555.35			0.116741
$563$	4700.69	+	3415.25i	0.351884	+	0.255659i	0.749659	−	0.661824i	$-0.230218\pi$
$563$	4700.69	+	3415.25i	0.351884	+	0.255659i	−0.397775	+	0.917483i	$0.630218\pi$
$564$	−587.138	+	1807.02i	−0.0438351	+	0.134910i
$565$	1632.49	+	5024.29i	0.121556	+	0.374112i
$566$	−11292.1	+	8204.21i	−0.838593	+	0.609273i
$567$	1226.77	−	891.298i	0.0908631	−	0.0660159i
$568$	3009.31	+	9261.70i	0.222302	+	0.684176i
$569$	−5295.96	+	16299.3i	−0.390190	+	1.20088i	0.542454	+	0.840086i	$0.317495\pi$
$569$	−5295.96	+	16299.3i	−0.390190	+	1.20088i	−0.932644	+	0.360797i	$0.882505\pi$
$570$	11896.5	+	8643.34i	0.874195	+	0.635140i
$571$	−4065.88			−0.297989			−0.148994	−	0.988838i	$-0.547604\pi$
$571$	−4065.88			−0.297989			−0.148994	+	0.988838i	$0.547604\pi$
$572$	−1889.17	+	1470.49i	−0.138095	+	0.107490i
$573$	5518.31			0.402322
$574$	−1623.75	−	1179.73i	−0.118073	−	0.0857854i
$575$	110.568	−	340.294i	0.00801915	−	0.0246804i
$576$	976.791	+	3006.25i	0.0706591	+	0.217466i
$577$	4411.11	−	3204.86i	0.318261	−	0.231230i	−0.417172	−	0.908828i	$-0.636979\pi$
$577$	4411.11	−	3204.86i	0.318261	−	0.231230i	0.735433	+	0.677597i	$0.236979\pi$
$578$	6496.14	−	4719.72i	0.467480	−	0.339644i
$579$	3000.97	+	9236.03i	0.215399	+	0.662929i
$580$	4090.62	−	12589.6i	0.292851	−	0.901303i
$581$	10172.8	+	7390.96i	0.726400	+	0.527760i
$582$	−3713.83			−0.264507
$583$	500.125	+	1381.85i	0.0355284	+	0.0981655i
$584$	25031.4			1.77364
$585$	2168.73	+	1575.68i	0.153275	+	0.111361i
$586$	−325.209	+	1000.89i	−0.0229254	+	0.0705570i
$587$	−4153.31	−	12782.6i	−0.292037	−	0.898797i	−0.984201	−	0.177057i	$-0.943342\pi$
$587$	−4153.31	−	12782.6i	−0.292037	−	0.898797i	0.692164	−	0.721740i	$-0.256658\pi$
$588$	−85.6100	+	62.1993i	−0.00600425	+	0.00436234i
$589$	−19701.9	+	14314.3i	−1.37827	+	1.00137i
$590$	−2409.67	−	7416.19i	−0.168143	−	0.517491i
$591$	−2962.48	+	9117.58i	−0.206193	+	0.634597i
$592$	128.996	+	93.7213i	0.00895560	+	0.00650663i
$593$	−12395.2			−0.858367			−0.429183	−	0.903217i	$-0.641199\pi$
$593$	−12395.2			−0.858367			−0.429183	+	0.903217i	$0.641199\pi$
$594$	−1475.35	−	999.020i	−0.101909	−	0.0690072i
$595$	−8745.76			−0.602591
$596$	9336.43	+	6783.31i	0.641670	+	0.466200i
$597$	2749.73	−	8462.81i	0.188508	−	0.580167i
$598$	8.27117	+	25.4560i	0.000565607	+	0.00174076i
$599$	−10758.7	+	7816.69i	−0.733874	+	0.533191i	−0.890787	−	0.454422i	$-0.849846\pi$
$599$	−10758.7	+	7816.69i	−0.733874	+	0.533191i	0.156913	+	0.987612i	$0.449846\pi$
$600$	−18752.1	+	13624.2i	−1.27592	+	0.927011i
$601$	−4110.00	−	12649.3i	−0.278953	−	0.858528i	−0.988146	−	0.153514i	$-0.950941\pi$
$601$	−4110.00	−	12649.3i	−0.278953	−	0.858528i	0.709194	−	0.705013i	$-0.249059\pi$
$602$	1807.28	−	5562.24i	0.122358	−	0.376578i
$603$	3452.63	+	2508.48i	0.233170	+	0.169408i
$604$	7832.88			0.527675
$605$	24169.7	+	15224.7i	1.62419	+	1.02309i
$606$	6301.22			0.422392
$607$	−1134.88	−	824.542i	−0.0758872	−	0.0551353i	0.549195	−	0.835694i	$-0.314934\pi$
$607$	−1134.88	−	824.542i	−0.0758872	−	0.0551353i	−0.625082	+	0.780559i	$0.714934\pi$
$608$	−6916.98	+	21288.3i	−0.461383	+	1.41999i
$609$	2264.03	+	6967.97i	0.150646	+	0.463639i
$610$	6446.26	−	4683.48i	0.427871	−	0.310867i
$611$	1504.02	−	1092.73i	0.0995843	−	0.0723522i
$612$	286.243	+	880.967i	0.0189064	+	0.0581879i
$613$	5282.82	−	16258.8i	0.348077	−	1.07127i	−0.611839	−	0.790982i	$-0.709570\pi$
$613$	5282.82	−	16258.8i	0.348077	−	1.07127i	0.959916	−	0.280288i	$-0.0904298\pi$
$614$	−3466.82	−	2518.79i	−0.227866	−	0.165554i
$615$	−3816.14			−0.250214
$616$	13020.1	+	8816.47i	0.851615	+	0.576665i
$617$	−5567.24			−0.363255			−0.181628	−	0.983367i	$-0.558137\pi$
$617$	−5567.24			−0.363255			−0.181628	+	0.983367i	$0.558137\pi$
$618$	1972.31	+	1432.97i	0.128379	+	0.0932725i
$619$	−2134.75	+	6570.08i	−0.138615	+	0.426614i	−0.996135	−	0.0878376i	$-0.972004\pi$
$619$	−2134.75	+	6570.08i	−0.138615	+	0.426614i	0.857520	+	0.514451i	$0.172004\pi$
$620$	−6047.74	−	18613.0i	−0.391747	−	1.20567i
$621$	23.2895	−	16.9208i	0.00150495	−	0.00109341i
$622$	−15376.8	+	11171.9i	−0.991246	+	0.720182i
$623$	1800.00	+	5539.84i	0.115755	+	0.356259i
$624$	49.1450	−	151.253i	0.00315285	−	0.00970346i
$625$	−44534.0	−	32355.9i	−2.85018	−	2.07078i
$626$	−13134.3			−0.838583
$627$	−4703.11	−	12994.7i	−0.299560	−	0.827688i
$628$	12296.2			0.781325
$629$	735.141	+	534.111i	0.0466009	+	0.0338576i
$630$	2021.15	−	6220.47i	0.127817	−	0.393380i
$631$	7423.16	+	22846.1i	0.468322	+	1.44135i	0.854756	+	0.519031i	$0.173707\pi$
$631$	7423.16	+	22846.1i	0.468322	+	1.44135i	−0.386433	+	0.922317i	$0.626293\pi$
$632$	10710.3	−	7781.52i	0.674105	−	0.489766i
$633$	8673.46	−	6301.64i	0.544611	−	0.395683i
$634$	−1645.31	−	5063.73i	−0.103065	−	0.317203i
$635$	−3684.60	+	11340.0i	−0.230266	+	0.708686i
$636$	462.243	+	335.839i	0.0288194	+	0.0209385i
$637$	103.539			0.00644014
$638$	6793.45	−	5287.87i	0.421560	−	0.328133i
$639$	−3806.84			−0.235675
$640$	−13593.3	−	9876.12i	−0.839567	−	0.609981i
$641$	5231.17	−	16099.9i	0.322338	−	0.992055i	−0.650289	−	0.759687i	$-0.725352\pi$
$641$	5231.17	−	16099.9i	0.322338	−	0.992055i	0.972628	−	0.232369i	$-0.0746476\pi$
$642$	−1023.71	−	3150.66i	−0.0629325	−	0.193686i
$643$	−267.790	+	194.561i	−0.0164240	+	0.0119327i	−0.595967	−	0.803009i	$-0.703231\pi$
$643$	−267.790	+	194.561i	−0.0164240	+	0.0119327i	0.579543	+	0.814942i	$0.303231\pi$
$644$	−76.3493	+	55.4710i	−0.00467172	+	0.00339420i
$645$	−3436.27	−	10575.7i	−0.209772	−	0.645612i
$646$	1536.34	−	4728.37i	0.0935705	−	0.287980i
$647$	−11650.4	−	8464.48i	−0.707918	−	0.514333i	0.174583	−	0.984642i	$-0.444142\pi$
$647$	−11650.4	−	8464.48i	−0.707918	−	0.514333i	−0.882501	+	0.470310i	$0.844142\pi$
$648$	−1864.87			−0.113054
$649$	−2032.71	+	7040.83i	−0.122944	+	0.425850i
$650$	8424.72			0.508377
$651$	8763.18	+	6366.82i	0.527582	+	0.383311i
$652$	2288.17	−	7042.27i	0.137441	−	0.423001i
$653$	4062.15	+	12502.0i	0.243437	+	0.749222i	0.995890	+	0.0905757i	$0.0288707\pi$
$653$	4062.15	+	12502.0i	0.243437	+	0.749222i	−0.752453	+	0.658647i	$0.771129\pi$
$654$	4953.77	−	3599.12i	0.296189	−	0.215194i
$655$	34004.8	−	24706.0i	2.02852	−	1.47380i
$656$	69.9609	+	215.317i	0.00416389	+	0.0128151i
$657$	−3023.76	+	9306.18i	−0.179556	+	0.552616i
$658$	−3669.62	−	2666.14i	−0.217412	−	0.157959i
$659$	−3909.26			−0.231082			−0.115541	−	0.993303i	$-0.536860\pi$
$659$	−3909.26			−0.231082			−0.115541	+	0.993303i	$0.536860\pi$
$660$	11099.9	−	367.522i	0.654642	−	0.0216754i
$661$	20672.6			1.21645			0.608224	−	0.793765i	$-0.291882\pi$
$661$	20672.6			1.21645			0.608224	+	0.793765i	$0.291882\pi$
$662$	10103.9	+	7340.91i	0.593201	+	0.430986i
$663$	280.074	−	861.979i	0.0164060	−	0.0504924i
$664$	−4778.68	−	14707.3i	−0.279290	−	0.859567i
$665$	41041.3	−	29818.2i	2.39325	−	1.73880i
$666$	−549.781	+	399.440i	−0.0319874	+	0.0232402i
$667$	42.9813	+	132.283i	0.00249512	+	0.00767919i
$668$	−4065.29	+	12511.7i	−0.235465	+	0.724687i
$669$	−3115.94	−	2263.86i	−0.180073	−	0.130831i
$670$	18407.9			1.06143
$671$	−7484.21	+	247.805i	−0.430588	+	0.0142569i
$672$	9956.08			0.571524
$673$	−15636.8	−	11360.8i	−0.895624	−	0.650709i	0.0417141	−	0.999130i	$-0.486718\pi$
$673$	−15636.8	−	11360.8i	−0.895624	−	0.650709i	−0.937338	+	0.348420i	$0.886718\pi$
$674$	5729.98	−	17635.1i	0.327464	−	1.00783i
$675$	−2799.98	−	8617.47i	−0.159661	−	0.491387i
$676$	−7667.04	+	5570.43i	−0.436222	+	0.316934i
$677$	−25536.2	+	18553.1i	−1.44968	+	1.05326i	−0.463776	+	0.885953i	$0.653506\pi$
$677$	−25536.2	+	18553.1i	−1.44968	+	1.05326i	−0.985906	+	0.167302i	$0.946494\pi$
$678$	412.774	+	1270.39i	0.0233812	+	0.0719601i
$679$	−3959.18	+	12185.1i	−0.223769	+	0.688691i
$680$	8701.59	+	6322.07i	0.490722	+	0.356530i
$681$	3366.25			0.189420
$682$	3530.35	−	12228.3i	0.198217	−	0.686577i
$683$	−17726.5			−0.993096			−0.496548	−	0.868009i	$-0.665399\pi$
$683$	−17726.5			−0.993096			−0.496548	+	0.868009i	$0.665399\pi$
$684$	−4346.87	−	3158.18i	−0.242992	−	0.176544i
$685$	−16572.0	+	51003.5i	−0.924357	+	2.84488i
$686$	3511.10	+	10806.1i	0.195415	+	0.601425i
$687$	−11657.4	+	8469.60i	−0.647391	+	0.470357i
$688$	−533.717	+	387.768i	−0.0295753	+	0.0214877i
$689$	−172.756	−	531.688i	−0.00955221	−	0.0293987i
$690$	38.3705	−	118.092i	0.00211701	−	0.00651550i
$691$	18710.1	+	13593.7i	1.03005	+	0.748375i	0.968319	−	0.249717i	$-0.0803377\pi$
$691$	18710.1	+	13593.7i	1.03005	+	0.748375i	0.0617317	+	0.998093i	$0.480338\pi$
$692$	−15164.0			−0.833019
$693$	−4850.60	+	3775.60i	−0.265886	+	0.206960i
$694$	9514.23			0.520397
$695$	−38584.8	−	28033.5i	−2.10591	−	1.53003i
$696$	2784.36	−	8569.38i	0.151639	−	0.466697i
$697$	398.702	+	1227.08i	0.0216670	+	0.0666843i
$698$	−15462.2	+	11234.0i	−0.838472	+	0.609185i
$699$	−255.179	+	185.398i	−0.0138079	+	0.0100321i
$700$	9179.12	+	28250.4i	0.495626	+	1.52538i
$701$	−684.567	+	2106.88i	−0.0368841	+	0.113518i	−0.967803	−	0.251707i	$-0.919008\pi$
$701$	−684.567	+	2106.88i	−0.0368841	+	0.113518i	0.930919	+	0.365225i	$0.119008\pi$
$702$	548.362	+	398.408i	0.0294823	+	0.0214202i
$703$	−5270.83			−0.282778
$704$	−4360.67	−	12048.6i	−0.233450	−	0.645027i
$705$	−8624.33			−0.460725
$706$	2667.57	+	1938.10i	0.142203	+	0.103317i
$707$	6717.49	−	20674.3i	0.357337	−	1.09977i
$708$	880.466	+	2709.80i	0.0467372	+	0.143842i
$709$	8708.18	−	6326.86i	0.461273	−	0.335134i	−0.332758	−	0.943012i	$-0.607979\pi$
$709$	8708.18	−	6326.86i	0.461273	−	0.335134i	0.794030	+	0.607878i	$0.207979\pi$
$710$	−13284.2	+	9651.52i	−0.702178	+	0.510162i
$711$	1599.22	+	4921.89i	0.0843536	+	0.259614i
$712$	2213.69	−	6813.03i	0.116519	−	0.358608i
$713$	166.364	+	120.871i	0.00873826	+	0.00634872i
$714$	−2211.36			−0.115908
$715$	−8997.84	−	6092.82i	−0.470629	−	0.318683i
$716$	3929.38			0.205094
$717$	−2647.17	−	1923.28i	−0.137880	−	0.100176i
$718$	6441.44	−	19824.7i	0.334808	−	1.03043i
$719$	−4842.20	−	14902.8i	−0.251159	−	0.772989i	−0.994562	−	0.104145i	$-0.966789\pi$
$719$	−4842.20	−	14902.8i	−0.251159	−	0.772989i	0.743403	−	0.668844i	$-0.233211\pi$
$720$	−596.878	+	433.657i	−0.0308949	+	0.0224464i
$721$	6804.18	−	4943.53i	0.351458	−	0.255349i
$722$	5077.65	+	15627.4i	0.261732	+	0.805529i
$723$	−990.628	+	3048.84i	−0.0509569	+	0.156829i
$724$	15687.3	+	11397.5i	0.805270	+	0.585063i
$725$	43779.3			2.24265
$726$	6111.28	+	3849.55i	0.312412	+	0.196791i
$727$	7671.66			0.391370			0.195685	−	0.980667i	$-0.437307\pi$
$727$	7671.66			0.391370			0.195685	+	0.980667i	$0.437307\pi$
$728$	−4839.36	−	3516.00i	−0.246372	−	0.178999i
$729$	225.273	−	693.320i	0.0114451	−	0.0352243i
$730$	13042.5	+	40140.6i	0.661265	+	2.03517i
$731$	−3041.62	+	2209.86i	−0.153896	+	0.111812i
$732$	−2355.39	+	1711.29i	−0.118931	+	0.0864088i
$733$	6045.47	+	18606.1i	0.304631	+	0.937558i	0.979815	+	0.199909i	$0.0640645\pi$
$733$	6045.47	+	18606.1i	0.304631	+	0.937558i	−0.675183	+	0.737650i	$0.735935\pi$
$734$	−1441.70	+	4437.10i	−0.0724989	+	0.223129i
$735$	−388.591	−	282.328i	−0.0195012	−	0.0141685i
$736$	189.011			0.00946606
$737$	−14324.6	−	9699.78i	−0.715947	−	0.484798i
$738$	−964.907			−0.0481284
$739$	−4832.25	−	3510.84i	−0.240538	−	0.174761i	0.460985	−	0.887408i	$-0.347496\pi$
$739$	−4832.25	−	3510.84i	−0.240538	−	0.174761i	−0.701523	+	0.712647i	$0.747496\pi$
$740$	1308.95	−	4028.52i	0.0650241	−	0.200123i
$741$	1624.57	+	4999.91i	0.0805399	+	0.247876i
$742$	−1103.51	+	801.748i	−0.0545973	+	0.0396672i
$743$	−1067.51	+	775.593i	−0.0527096	+	0.0382957i	−0.613828	−	0.789440i	$-0.710371\pi$
$743$	−1067.51	+	775.593i	−0.0527096	+	0.0382957i	0.561119	+	0.827735i	$0.310371\pi$
$744$	−4116.51	−	12669.3i	−0.202848	−	0.624301i
$745$	−16187.3	+	49819.3i	−0.796047	+	2.44998i
$746$	−8903.40	−	6468.70i	−0.436966	−	0.317474i
$747$	6045.13			0.296091
$748$	−1277.87	−	3530.78i	−0.0624648	−	0.172591i
$749$	−11428.7			−0.557536
$750$	−19841.4	−	14415.6i	−0.966008	−	0.701846i
$751$	10028.3	−	30863.9i	0.487267	−	1.49965i	−0.341404	−	0.939917i	$-0.610902\pi$
$751$	10028.3	−	30863.9i	0.487267	−	1.49965i	0.828671	−	0.559736i	$-0.189098\pi$
$752$	158.109	+	486.610i	0.00766708	+	0.0235969i
$753$	4835.60	−	3513.27i	0.234022	−	0.170027i
$754$	−2649.49	+	1924.97i	−0.127969	+	0.0929752i
$755$	10986.8	+	33813.9i	0.529604	+	1.62995i
$756$	−738.508	+	2272.89i	−0.0355281	+	0.109344i
$757$	−2338.96	−	1699.36i	−0.112300	−	0.0815906i	0.530218	−	0.847861i	$-0.322110\pi$
$757$	−2338.96	−	1699.36i	−0.112300	−	0.0815906i	−0.642518	+	0.766271i	$0.722110\pi$
$758$	10670.2			0.511290
$759$	−92.0859	+	71.6776i	−0.00440383	+	0.00342784i
$760$	−62388.8			−2.97774
$761$	18145.2	+	13183.2i	0.864338	+	0.627979i	0.929062	−	0.369925i	$-0.120616\pi$
$761$	18145.2	+	13183.2i	0.864338	+	0.627979i	−0.0647233	+	0.997903i	$0.520616\pi$
$762$	−931.648	+	2867.32i	−0.0442914	+	0.136315i
$763$	−6527.71	−	20090.2i	−0.309723	−	0.953230i
$764$	−7036.10	+	5112.03i	−0.333190	+	0.242077i
$765$	−3401.56	+	2471.38i	−0.160763	+	0.116801i
$766$	−894.290	−	2752.34i	−0.0421828	−	0.129825i
$767$	861.489	−	2651.39i	0.0405562	−	0.124819i
$768$	−10256.5	−	7451.75i	−0.481898	−	0.350119i
$769$	5386.04			0.252569			0.126285	−	0.991994i	$-0.459695\pi$
$769$	5386.04			0.252569			0.126285	+	0.991994i	$0.459695\pi$
$770$	−7354.13	+	25473.0i	−0.344188	+	1.19218i
$771$	−23955.9			−1.11900
$772$	−12382.4	−	8996.34i	−0.577270	−	0.419411i
$773$	2320.68	−	7142.31i	0.107981	−	0.332330i	−0.882438	−	0.470429i	$-0.844099\pi$
$773$	2320.68	−	7142.31i	0.107981	−	0.332330i	0.990418	+	0.138099i	$0.0440992\pi$
$774$	−868.858	−	2674.07i	−0.0403494	−	0.124183i
$775$	52363.7	−	38044.5i	2.42705	−	1.76335i
$776$	12747.5	−	9261.57i	0.589700	−	0.428442i
$777$	724.461	+	2229.66i	0.0334490	+	0.102946i
$778$	1405.56	−	4325.86i	0.0647708	−	0.199344i
$779$	−6054.66	−	4398.97i	−0.278473	−	0.202323i
$780$	−4224.90			−0.193943
$781$	15423.1	−	510.666i	0.706637	−	0.0233970i
$782$	−41.9814			−0.00191976
$783$	2849.58	+	2070.34i	0.130058	+	0.0944929i
$784$	−8.80575	+	27.1013i	−0.000401136	+	0.00123457i
$785$	17247.3	+	53081.8i	0.784182	+	2.41346i
$786$	8598.09	−	6246.88i	0.390183	−	0.283485i
$787$	−614.522	+	446.476i	−0.0278340	+	0.0202226i	−0.601615	−	0.798786i	$-0.705476\pi$
$787$	−614.522	+	446.476i	−0.0278340	+	0.0202226i	0.573781	+	0.819009i	$0.305476\pi$
$788$	−4669.00	−	14369.7i	−0.211074	−	0.649619i
$789$	3685.14	−	11341.7i	0.166279	−	0.511755i
$790$	18059.1	+	13120.7i	0.813308	+	0.590903i
$791$	4608.19			0.207141
$792$	7555.38	−	250.161i	0.338976	−	0.0112236i
$793$	2848.68			0.127566
$794$	−8029.30	−	5833.63i	−0.358878	−	0.260740i
$795$	−801.425	+	2466.53i	−0.0357530	+	0.110036i
$796$	4333.70	+	13337.8i	0.192970	+	0.593900i
$797$	−21073.0	+	15310.4i	−0.936566	+	0.680455i	−0.947592	−	0.319484i	$-0.896490\pi$
$797$	−21073.0	+	15310.4i	−0.936566	+	0.680455i	0.0110254	+	0.999939i	$0.496490\pi$
$798$	10377.3	−	7539.52i	0.460340	−	0.334456i
$799$	901.052	+	2773.15i	0.0398961	+	0.122787i
$800$	18384.0	−	56580.1i	0.812465	−	2.50051i
$801$	2265.54	+	1646.01i	0.0999362	+	0.0726079i
$802$	−26613.4			−1.17176
$803$	11002.2	−	38109.0i	0.483510	−	1.67476i
$804$	−6726.05			−0.295037
$805$	−346.556	−	251.787i	−0.0151733	−	0.0110240i
$806$	−1496.21	+	4604.85i	−0.0653867	+	0.201239i
$807$	1045.27	+	3217.00i	0.0455949	+	0.140327i
$808$	−21628.5	+	15714.0i	−0.941692	+	0.684179i
$809$	−9091.99	+	6605.72i	−0.395126	+	0.287076i	−0.767553	−	0.640986i	$-0.778526\pi$
$809$	−9091.99	+	6605.72i	−0.395126	+	0.287076i	0.372427	+	0.928062i	$0.378526\pi$
$810$	−971.679	−	2990.52i	−0.0421498	−	0.129724i
$811$	1215.55	−	3741.07i	0.0526309	−	0.161981i	−0.921286	−	0.388885i	$-0.872860\pi$
$811$	1215.55	−	3741.07i	0.0526309	−	0.161981i	0.973917	+	0.226904i	$0.0728603\pi$
$812$	−9341.70	−	6787.14i	−0.403731	−	0.293328i
$813$	11850.0			0.511188
$814$	2173.82	−	1692.05i	0.0936024	−	0.0728580i
$815$	33610.4			1.44457
$816$	201.803	+	146.618i	0.00865749	+	0.00629004i
$817$	6738.99	−	20740.5i	0.288577	−	0.888149i
$818$	−4445.74	−	13682.6i	−0.190026	−	0.584841i
$819$	1891.77	−	1374.45i	0.0807127	−	0.0586412i
$820$	4865.75	−	3535.18i	0.207219	−	0.150553i
$821$	3905.94	+	12021.2i	0.166039	+	0.511016i	0.999111	−	0.0421481i	$-0.0134201\pi$
$821$	3905.94	+	12021.2i	0.166039	+	0.511016i	−0.833072	+	0.553164i	$0.813420\pi$
$822$	−4190.22	+	12896.2i	−0.177799	+	0.547209i
$823$	21878.1	+	15895.3i	0.926636	+	0.673240i	0.945167	−	0.326588i	$-0.105899\pi$
$823$	21878.1	+	15895.3i	0.926636	+	0.673240i	−0.0185310	+	0.999828i	$0.505899\pi$
$824$	−10343.4			−0.437291
$825$	12499.9	+	34537.5i	0.527505	+	1.45750i
$826$	−6802.00			−0.286528
$827$	−6088.25	−	4423.37i	−0.255997	−	0.185992i	0.452384	−	0.891823i	$-0.350574\pi$
$827$	−6088.25	−	4423.37i	−0.255997	−	0.185992i	−0.708380	+	0.705831i	$0.750574\pi$
$828$	−14.0202	+	43.1496i	−0.000588447	+	0.00181105i
$829$	−7731.25	−	23794.3i	−0.323905	−	0.996877i	−0.971932	−	0.235260i	$-0.924406\pi$
$829$	−7731.25	−	23794.3i	−0.323905	−	0.996877i	0.648027	−	0.761617i	$-0.275594\pi$
$830$	21094.8	−	15326.3i	0.882183	−	0.640943i
$831$	1592.38	−	1156.93i	0.0664728	−	0.0482953i
$832$	1506.29	+	4635.87i	0.0627657	+	0.193173i
$833$	−50.1833	+	154.448i	−0.00208733	+	0.00642415i
$834$	−9756.15	−	7088.26i	−0.405069	−	0.294300i
$835$	−59714.0			−2.47484
$836$	18034.7	+	12212.1i	0.746104	+	0.505219i
$837$	5207.47			0.215050
$838$	−10666.7	−	7749.82i	−0.439708	−	0.319466i
$839$	3826.85	−	11777.8i	0.157470	−	0.484644i	−0.840932	−	0.541140i	$-0.817993\pi$
$839$	3826.85	−	11777.8i	0.157470	−	0.484644i	0.998403	+	0.0564960i	$0.0179928\pi$
$840$	8575.17	+	26391.7i	0.352228	+	1.08405i
$841$	5962.95	−	4332.34i	0.244493	−	0.177635i
$842$	−8130.90	+	5907.44i	−0.332790	+	0.241786i
$843$	−797.137	−	2453.34i	−0.0325680	−	0.100234i
$844$	−5221.38	+	16069.8i	−0.212947	+	0.655384i
$845$	−34801.3	−	25284.6i	−1.41681	−	1.02937i
$846$	−2180.66			−0.0886200
$847$	19145.4	−	15947.3i	0.776675	−	0.646936i
$848$	153.861			0.00623069
$849$	18728.3	+	13606.9i	0.757073	+	0.550046i
$850$	−4083.29	+	12567.1i	−0.164772	+	0.507115i
$851$	13.7535	+	42.3289i	0.000554011	+	0.00170507i
$852$	4853.89	−	3526.56i	0.195178	−	0.141805i
$853$	−17186.5	+	12486.7i	−0.689864	+	0.501216i	−0.876616	−	0.481191i	$-0.840204\pi$
$853$	−17186.5	+	12486.7i	−0.689864	+	0.501216i	0.186751	+	0.982407i	$0.440204\pi$
$854$	−2147.80	−	6610.26i	−0.0860612	−	0.264869i
$855$	7536.49	−	23194.9i	0.301453	−	0.927777i
$856$	11370.9	+	8261.47i	0.454031	+	0.329873i
$857$	44030.0			1.75500			0.877501	−	0.479575i	$-0.159209\pi$
$857$	44030.0			1.75500			0.877501	+	0.479575i	$0.159209\pi$
$858$	−2275.10	−	1540.56i	−0.0905251	−	0.0612984i
$859$	16585.2			0.658764			0.329382	−	0.944197i	$-0.393160\pi$
$859$	16585.2			0.658764			0.329382	+	0.944197i	$0.393160\pi$
$860$	14178.5	+	10301.3i	0.562190	+	0.408455i
$861$	−1028.65	+	3165.86i	−0.0407159	+	0.125311i
$862$	−7293.05	−	22445.7i	−0.288170	−	0.886896i
$863$	29456.2	−	21401.2i	1.16188	−	0.844154i	0.171864	−	0.985121i	$-0.445021\pi$
$863$	29456.2	−	21401.2i	1.16188	−	0.844154i	0.990014	+	0.140966i	$0.0450209\pi$
$864$	3872.30	−	2813.39i	0.152475	−	0.110780i
$865$	−21269.8	−	65461.8i	−0.836065	−	2.57314i
$866$	−8142.45	+	25059.9i	−0.319505	+	0.983336i
$867$	−10774.0	−	7827.80i	−0.422036	−	0.306627i
$868$	−17071.5			−0.667564
$869$	−7139.37	−	19726.2i	−0.278696	−	0.770040i
$870$	15192.7			0.592048
$871$	5324.21	+	3868.27i	0.207123	+	0.150484i
$872$	−8027.93	+	24707.4i	−0.311766	+	0.959517i
$873$	1903.39	+	5858.04i	0.0737916	+	0.227107i
$874$	197.006	−	143.134i	0.00762453	−	0.00553955i
$875$	−68449.9	+	49731.8i	−2.64461	+	1.92142i
$876$	−4765.58	−	14666.9i	−0.183806	−	0.565697i
$877$	3913.92	−	12045.8i	0.150700	−	0.463806i	−0.847000	−	0.531593i	$-0.821594\pi$
$877$	3913.92	−	12045.8i	0.150700	−	0.463806i	0.997700	+	0.0677866i	$0.0215937\pi$
$878$	13831.3	+	10049.0i	0.531644	+	0.386262i
$879$	1745.44			0.0669762
$880$	2360.04	−	1837.00i	0.0904055	−	0.0703696i
$881$	−33584.8			−1.28434			−0.642169	−	0.766563i	$-0.721965\pi$
$881$	−33584.8			−1.28434			−0.642169	+	0.766563i	$0.721965\pi$
$882$	−98.2549	−	71.3863i	−0.00375104	−	0.00272529i
$883$	−5095.02	+	15680.9i	−0.194180	+	0.597626i	0.805805	+	0.592181i	$0.201733\pi$
$883$	−5095.02	+	15680.9i	−0.194180	+	0.597626i	−0.999985	+	0.00544444i	$0.998267\pi$
$884$	441.409	+	1358.52i	0.0167943	+	0.0516877i
$885$	−10463.0	+	7601.80i	−0.397412	+	0.288737i
$886$	18752.5	−	13624.5i	0.711064	−	0.516618i
$887$	2892.13	+	8901.06i	0.109479	+	0.336943i	0.990756	−	0.135659i	$-0.0433150\pi$
$887$	2892.13	+	8901.06i	0.109479	+	0.336943i	−0.881276	+	0.472601i	$0.843315\pi$
$888$	890.960	−	2742.09i	0.0336697	−	0.103625i
$889$	8414.48	+	6113.48i	0.317450	+	0.230641i
$890$	12078.9			0.454927
$891$	−819.675	+	2839.16i	−0.0308195	+	0.106751i
$892$	6070.15			0.227852
$893$	−13683.3	−	9941.50i	−0.512760	−	0.372542i
$894$	−4092.94	+	12596.8i	−0.153119	+	0.471251i
$895$	5511.55	+	16962.8i	0.205844	+	0.633524i
$896$	−11857.3	+	8614.86i	−0.442105	+	0.321208i
$897$	35.9142	−	26.0932i	0.00133683	−	0.000971266i
$898$	3395.05	+	10448.9i	0.126163	+	0.388290i
$899$	−7775.08	+	23929.2i	−0.288447	+	0.887747i
$900$	11553.1	+	8393.84i	0.427893	+	0.310883i
$901$	876.845			0.0324217
$902$	3909.26	−	129.437i	0.144306	−	0.00477802i
$903$	−9699.89			−0.357466
$904$	−4584.91	−	3331.13i	−0.168686	−	0.122557i
$905$	−27198.3	+	83707.8i	−0.999008	+	3.07463i
$906$	2778.01	+	8549.83i	0.101869	+	0.313520i
$907$	−29465.6	+	21408.0i	−1.07871	+	0.783728i	−0.977457	−	0.211133i	$-0.932285\pi$
$907$	−29465.6	+	21408.0i	−1.07871	+	0.783728i	−0.101251	+	0.994861i	$0.532285\pi$
$908$	−4292.13	+	3118.41i	−0.156871	+	0.113974i
$909$	−3229.46	−	9939.27i	−0.117838	−	0.362667i
$910$	3116.77	−	9592.44i	0.113539	−	0.349436i
$911$	39662.7	+	28816.7i	1.44246	+	1.04801i	0.987520	+	0.157491i	$0.0503406\pi$
$911$	39662.7	+	28816.7i	1.44246	+	1.04801i	0.454944	+	0.890520i	$0.349659\pi$
$912$	−1446.89			−0.0525343
$913$	−24491.4	+	810.920i	−0.887785	+	0.0293949i
$914$	27821.3			1.00683
$915$	−10691.3	−	7767.70i	−0.386278	−	0.280647i
$916$	7017.70	−	21598.3i	0.253135	−	0.779069i
$917$	−11329.9	−	34869.9i	−0.408012	−	1.25573i
$918$	−860.082	+	624.886i	−0.0309226	+	0.0224666i
$919$	−10465.7	+	7603.75i	−0.375659	+	0.272932i	−0.759554	−	0.650445i	$-0.774583\pi$
$919$	−10465.7	+	7603.75i	−0.375659	+	0.272932i	0.383895	+	0.923377i	$0.374583\pi$
$920$	162.795	+	501.031i	0.00583390	+	0.0179549i
$921$	−2196.24	+	6759.33i	−0.0785760	+	0.241832i
$922$	4619.37	+	3356.17i	0.165001	+	0.119880i
$923$	−5870.43			−0.209347
$924$	2687.12	−	9307.54i	0.0956707	−	0.331381i
$925$	14008.8			0.497954
$926$	−7207.61	−	5236.64i	−0.255785	−	0.185839i
$927$	1249.46	−	3845.45i	0.0442694	−	0.136247i
$928$	7146.43	+	21994.5i	0.252794	+	0.778021i
$929$	1839.17	−	1336.24i	0.0649530	−	0.0471911i	−0.554835	−	0.831960i	$-0.687219\pi$
$929$	1839.17	−	1336.24i	0.0649530	−	0.0471911i	0.619788	+	0.784769i	$0.287219\pi$
$930$	18171.8	−	13202.6i	0.640727	−	0.465515i
$931$	−291.089	−	895.878i	−0.0102471	−	0.0315373i
$932$	153.616	−	472.783i	0.00539901	−	0.0166164i
$933$	25502.9	+	18529.0i	0.894886	+	0.650173i
$934$	−21075.8			−0.738354
$935$	13449.7	−	10468.9i	0.470429	−	0.366172i
$936$	−2875.76			−0.100424
$937$	13914.2	+	10109.3i	0.485120	+	0.352460i	0.803305	−	0.595568i	$-0.203073\pi$
$937$	13914.2	+	10109.3i	0.485120	+	0.352460i	−0.318184	+	0.948029i	$0.603073\pi$
$938$	4961.91	−	15271.2i	0.172721	−	0.531580i
$939$	6731.52	+	20717.5i	0.233946	+	0.720011i
$940$	10996.4	−	7989.37i	0.381557	−	0.277218i
$941$	26864.0	−	19517.8i	0.930649	−	0.676156i	−0.0155024	−	0.999880i	$-0.504935\pi$
$941$	26864.0	−	19517.8i	0.930649	−	0.676156i	0.946152	+	0.323723i	$0.104935\pi$
$942$	4360.97	+	13421.7i	0.150837	+	0.464227i
$943$	−19.5284	+	60.1022i	−0.000674370	+	0.00207550i
$944$	620.733	+	450.989i	0.0214016	+	0.0155492i
$945$	−10847.8			−0.373416
$946$	3878.83	+	10717.3i	0.133310	+	0.368338i
$947$	23096.7			0.792546			0.396273	−	0.918133i	$-0.370303\pi$
$947$	23096.7			0.792546			0.396273	+	0.918133i	$0.370303\pi$
$948$	−6598.60	−	4794.16i	−0.226068	−	0.164248i
$949$	−4662.87	+	14350.8i	−0.159497	+	0.490883i
$950$	−23685.2	−	72895.4i	−0.808893	−	2.48952i
$951$	−7144.07	+	5190.47i	−0.243599	+	0.176985i
$952$	7590.33	−	5514.70i	0.258407	−	0.187744i
$953$	2716.30	+	8359.91i	0.0923290	+	0.284159i	0.986548	−	0.163470i	$-0.0522685\pi$
$953$	2716.30	+	8359.91i	0.0923290	+	0.284159i	−0.894219	+	0.447629i	$0.852269\pi$
$954$	−202.640	+	623.661i	−0.00687705	+	0.0211654i
$955$	−31937.4	−	23203.9i	−1.08217	−	0.786241i
$956$	5156.94			0.174464
$957$	−11822.6	−	8005.59i	−0.399342	−	0.270412i
$958$	−23731.5			−0.800346
$959$	37845.4	+	27496.3i	1.27434	+	0.925862i
$960$	6987.76	−	21506.1i	0.234926	−	0.723028i
$961$	2289.08	+	7045.06i	0.0768379	+	0.236483i
$962$	−847.805	+	615.966i	−0.0284141	+	0.0206440i
$963$	−4445.05	+	3229.51i	−0.148743	+	0.108068i
$964$	−1561.27	−	4805.11i	−0.0521631	−	0.160542i
$965$	21468.3	−	66072.6i	0.716154	−	2.20410i
$966$	−87.6263	−	63.6642i	−0.00291856	−	0.00212046i
$967$	29582.8			0.983785			0.491892	−	0.870656i	$-0.336305\pi$
$967$	29582.8			0.983785			0.491892	+	0.870656i	$0.336305\pi$
$968$	−30576.5	+	2027.02i	−1.01526	+	0.0673047i
$969$	−8245.72			−0.273365
$970$	21494.0	+	15616.3i	0.711473	+	0.516916i
$971$	10668.1	−	32833.0i	0.352580	−	1.08513i	−0.604819	−	0.796363i	$-0.706755\pi$
$971$	10668.1	−	32833.0i	0.352580	−	1.08513i	0.957399	−	0.288767i	$-0.0932453\pi$
$972$	355.041	+	1092.70i	0.0117160	+	0.0360581i
$973$	−33657.3	+	24453.4i	−1.10894	+	0.805695i
$974$	−4064.19	+	2952.81i	−0.133701	+	0.0971396i
$975$	−4317.79	−	13288.8i	−0.141826	−	0.436494i
$976$	−242.273	+	745.639i	−0.00794566	+	0.0244542i
$977$	−46932.3	−	34098.3i	−1.53684	−	1.11658i	−0.952276	−	0.305239i	$-0.901264\pi$
$977$	−46932.3	−	34098.3i	−1.53684	−	1.11658i	−0.584569	−	0.811344i	$-0.698736\pi$
$978$	8498.37			0.277861
$979$	−9399.49	−	6364.79i	−0.306853	−	0.207783i
$980$	757.013			0.0246754
$981$	−8215.97	−	5969.25i	−0.267396	−	0.194275i
$982$	−7075.35	+	21775.7i	−0.229922	+	0.707628i
$983$	−6795.98	−	20915.9i	−0.220507	−	0.678650i	−0.998717	−	0.0506455i	$-0.983872\pi$
$983$	−6795.98	−	20915.9i	−0.220507	−	0.678650i	0.778210	−	0.628004i	$-0.216128\pi$
$984$	3311.97	−	2406.29i	0.107299	−	0.0779570i
$985$	55483.9	−	40311.4i	1.79479	−	1.30399i
$986$	−1587.30	−	4885.22i	−0.0512678	−	0.157786i
$987$	−2324.72	+	7154.74i	−0.0749711	+	0.230737i
$988$	−6703.20	−	4870.16i	−0.215847	−	0.156822i
$989$	−184.147			−0.00592066
$990$	4337.85	+	11985.5i	0.139259	+	0.384773i
$991$	−48417.3			−1.55199			−0.775997	−	0.630737i	$-0.782753\pi$
$991$	−48417.3			−1.55199			−0.775997	+	0.630737i	$0.782753\pi$
$992$	27661.1	+	20096.9i	0.885322	+	0.643224i
$993$	6400.84	−	19699.8i	0.204556	−	0.629560i
$994$	4426.10	+	13622.1i	0.141235	+	0.434676i
$995$	−51499.4	+	37416.5i	−1.64084	+	1.19214i
$996$	−7707.82	+	5600.06i	−0.245212	+	0.178157i
$997$	7998.17	+	24615.8i	0.254067	+	0.781937i	0.994012	+	0.109270i	$0.0348514\pi$
$997$	7998.17	+	24615.8i	0.254067	+	0.781937i	−0.739945	+	0.672667i	$0.765149\pi$
$998$	−5667.31	+	17442.2i	−0.179755	+	0.553230i
$999$	911.829	+	662.483i	0.0288779	+	0.0209810i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.4.e.c.4.2	✓	12
3.2	odd	2		99.4.f.d.37.2		12
11.3	even	5	inner	33.4.e.c.25.2	yes	12
11.5	even	5		363.4.a.v.1.4		6
11.6	odd	10		363.4.a.u.1.3		6
33.5	odd	10		1089.4.a.bi.1.3		6
33.14	odd	10		99.4.f.d.91.2		12
33.17	even	10		1089.4.a.bk.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.e.c.4.2	✓	12	1.1	even	1	trivial
33.4.e.c.25.2	yes	12	11.3	even	5	inner
99.4.f.d.37.2		12	3.2	odd	2
99.4.f.d.91.2		12	33.14	odd	10
363.4.a.u.1.3		6	11.6	odd	10
363.4.a.v.1.4		6	11.5	even	5
1089.4.a.bi.1.3		6	33.5	odd	10
1089.4.a.bk.1.4		6	33.17	even	10

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	33.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.46337 - 1.06320i) q^{2} +(-0.927051 + 2.85317i) q^{3} +(-1.46107 - 4.49672i) q^{4} +(17.3626 - 12.6147i) q^{5} +(4.39012 - 3.18961i) q^{6} +(-5.78498 - 17.8043i) q^{7} +(-7.11451 + 21.8962i) q^{8} +(-7.28115 - 5.29007i) q^{9} -38.8200 q^{10} +(30.2087 + 20.4556i) q^{11} +14.1844 q^{12} +(-11.2281 - 8.15769i) q^{13} +(-10.4640 + 32.2050i) q^{14} +(19.8958 + 61.2329i) q^{15} +(3.09019 - 2.24515i) q^{16} +(17.6108 - 12.7950i) q^{17} +(5.03063 + 15.4827i) q^{18} +(-39.0184 + 120.086i) q^{19} +(-82.0928 - 59.6439i) q^{20} +56.1618 q^{21} +(-22.4582 - 62.0523i) q^{22} +1.06620 q^{23} +(-55.8781 - 40.5978i) q^{24} +(103.703 - 319.165i) q^{25} +(7.75762 + 23.8755i) q^{26} +(21.8435 - 15.8702i) q^{27} +(-71.6089 + 52.0269i) q^{28} +(40.3127 + 124.070i) q^{29} +(35.9881 - 110.760i) q^{30} +(156.035 + 113.366i) q^{31} +177.275 q^{32} +(-86.3684 + 67.2272i) q^{33} -39.3748 q^{34} +(-325.038 - 236.154i) q^{35} +(-13.1497 + 40.4705i) q^{36} +(12.8995 + 39.7007i) q^{37} +(184.775 - 134.247i) q^{38} +(33.6843 - 24.4731i) q^{39} +(152.687 + 469.923i) q^{40} +(-18.3159 + 56.3705i) q^{41} +(-82.1857 - 59.7114i) q^{42} -172.713 q^{43} +(47.8461 - 165.727i) q^{44} -193.152 q^{45} +(-1.56025 - 1.13359i) q^{46} +(-41.3932 + 127.395i) q^{47} +(3.54104 + 10.8982i) q^{48} +(-6.03551 + 4.38505i) q^{49} +(-491.094 + 356.801i) q^{50} +(20.1802 + 62.1081i) q^{51} +(-20.2778 + 62.4086i) q^{52} +(32.5881 + 23.6767i) q^{53} -48.8384 q^{54} +(782.544 - 25.9103i) q^{55} +431.005 q^{56} +(-306.454 - 222.652i) q^{57} +(72.9188 - 224.421i) q^{58} +(62.0729 + 191.041i) q^{59} +(246.278 - 178.932i) q^{60} +(-166.055 + 120.646i) q^{61} +(-107.806 - 331.793i) q^{62} +(-52.0648 + 160.239i) q^{63} +(-284.141 - 206.441i) q^{64} -297.856 q^{65} +(197.866 - 6.55140i) q^{66} -474.187 q^{67} +(-83.2661 - 60.4964i) q^{68} +(-0.988421 + 3.04205i) q^{69} +(224.573 + 691.164i) q^{70} +(342.199 - 248.622i) q^{71} +(167.634 - 121.793i) q^{72} +(-335.973 - 1034.02i) q^{73} +(23.3331 - 71.8119i) q^{74} +(814.495 + 591.765i) q^{75} +597.003 q^{76} +(189.442 - 656.182i) q^{77} -75.3125 q^{78} +(-465.201 - 337.988i) q^{79} +(25.3319 - 77.9635i) q^{80} +(25.0304 + 77.0356i) q^{81} +(86.7363 - 63.0176i) q^{82} +(-543.401 + 394.804i) q^{83} +(-82.0565 - 252.544i) q^{84} +(144.365 - 444.309i) q^{85} +(252.744 + 183.629i) q^{86} -391.364 q^{87} +(-662.821 + 515.925i) q^{88} -311.151 q^{89} +(282.654 + 205.360i) q^{90} +(-80.2879 + 247.101i) q^{91} +(-1.55780 - 4.79440i) q^{92} +(-468.104 + 340.097i) q^{93} +(196.021 - 142.417i) q^{94} +(837.387 + 2577.21i) q^{95} +(-164.343 + 505.796i) q^{96} +(-553.683 - 402.274i) q^{97} +13.4944 q^{98} +(-111.743 - 308.747i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 9 q^{3} - 16 q^{4} + 28 q^{5} + 12 q^{7} - 112 q^{8} - 27 q^{9} + 100 q^{10} - 54 q^{11} - 102 q^{12} - 18 q^{13} + 156 q^{14} + 111 q^{15} + 308 q^{16} - 80 q^{17} - 45 q^{18} - 280 q^{19} - 15 q^{20}+ \cdots - 171 q^{99}+O(q^{100}) \) 12 * q + 9 * q^3 - 16 * q^4 + 28 * q^5 + 12 * q^7 - 112 * q^8 - 27 * q^9 + 100 * q^10 - 54 * q^11 - 102 * q^12 - 18 * q^13 + 156 * q^14 + 111 * q^15 + 308 * q^16 - 80 * q^17 - 45 * q^18 - 280 * q^19 - 15 * q^20 - 6 * q^21 - 193 * q^22 - 392 * q^23 - 264 * q^24 + 77 * q^25 + 406 * q^26 + 81 * q^27 - 429 * q^28 + 13 * q^29 + 120 * q^30 + 413 * q^31 + 1314 * q^32 + 177 * q^33 + 1060 * q^34 - 1239 * q^35 - 144 * q^36 + 654 * q^37 + 912 * q^38 + 54 * q^39 - 1803 * q^40 - 1490 * q^41 + 342 * q^42 + 416 * q^43 + 695 * q^44 + 162 * q^45 - 2369 * q^46 - 150 * q^47 + 711 * q^48 - 301 * q^49 - 1878 * q^50 - 1661 * q^52 + 1359 * q^53 - 270 * q^54 + 3300 * q^55 - 858 * q^56 - 1110 * q^57 + 955 * q^58 + 1262 * q^59 + 45 * q^60 - 1044 * q^61 - 701 * q^62 + 108 * q^63 + 78 * q^64 + 4556 * q^65 + 369 * q^66 - 528 * q^67 + 703 * q^68 - 594 * q^69 + 3050 * q^70 + 558 * q^71 + 792 * q^72 - 699 * q^73 - 3224 * q^74 + 1284 * q^75 - 868 * q^76 + 390 * q^77 - 558 * q^78 - 1252 * q^79 - 1914 * q^80 - 243 * q^81 + 2987 * q^82 - 4464 * q^83 - 1443 * q^84 - 2170 * q^85 - 3209 * q^86 - 3474 * q^87 + 1302 * q^88 + 316 * q^89 - 90 * q^90 + 176 * q^91 + 4595 * q^92 - 1239 * q^93 + 1247 * q^94 + 1466 * q^95 + 1398 * q^96 + 1608 * q^97 + 2810 * q^98 - 171 * q^99

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