LMFDB - Embedded newform 930.4.d.c.559.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,4,Mod(559,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("930.559");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	930.d (of order $2$, degree $1$, 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:	$54.8717763053$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 2763 x^{18} + 2652899 x^{16} + 1161420105 x^{14} + 247831438280 x^{12} + 26461073949176 x^{10} + \cdots + 34\!\cdots\!00 $ x^20 + 2763x^18 + 2652899x^16 + 1161420105x^14 + 247831438280x^12 + 26461073949176x^10 + 1433368340491408x^8 + 37536884921183444x^6 + 414170668954972900x^4 + 1987578737873500000*x^2 + 3460065015625000000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			559.15
Root			$2.45273i$ of defining polynomial
Character	$\chi$	$=$	930.559
Dual form			930.4.d.c.559.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(1.65380 - 11.0573i) q^{5} +6.00000 q^{6} +2.45273i q^{7} -8.00000i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(1.65380 - 11.0573i) q^{5} +6.00000 q^{6} +2.45273i q^{7} -8.00000i q^{8} -9.00000 q^{9} +(22.1147 + 3.30759i) q^{10} -35.2532 q^{11} +12.0000i q^{12} +31.1443i q^{13} -4.90546 q^{14} +(-33.1720 - 4.96139i) q^{15} +16.0000 q^{16} +47.1144i q^{17} -18.0000i q^{18} +118.399 q^{19} +(-6.61519 + 44.2294i) q^{20} +7.35819 q^{21} -70.5064i q^{22} -57.1501i q^{23} -24.0000 q^{24} +(-119.530 - 36.5732i) q^{25} -62.2886 q^{26} +27.0000i q^{27} -9.81092i q^{28} -298.374 q^{29} +(9.92278 - 66.3441i) q^{30} -31.0000 q^{31} +32.0000i q^{32} +105.760i q^{33} -94.2289 q^{34} +(27.1207 + 4.05632i) q^{35} +36.0000 q^{36} -82.3944i q^{37} +236.798i q^{38} +93.4329 q^{39} +(-88.4588 - 13.2304i) q^{40} -25.0717 q^{41} +14.7164i q^{42} +264.775i q^{43} +141.013 q^{44} +(-14.8842 + 99.5161i) q^{45} +114.300 q^{46} +344.703i q^{47} -48.0000i q^{48} +336.984 q^{49} +(73.1465 - 239.060i) q^{50} +141.343 q^{51} -124.577i q^{52} +422.169i q^{53} -54.0000 q^{54} +(-58.3016 + 389.807i) q^{55} +19.6218 q^{56} -355.198i q^{57} -596.749i q^{58} -43.3724 q^{59} +(132.688 + 19.8456i) q^{60} +96.2068 q^{61} -62.0000i q^{62} -22.0746i q^{63} -64.0000 q^{64} +(344.373 + 51.5064i) q^{65} -211.519 q^{66} -706.568i q^{67} -188.458i q^{68} -171.450 q^{69} +(-8.11264 + 54.2414i) q^{70} +1110.36 q^{71} +72.0000i q^{72} -94.3706i q^{73} +164.789 q^{74} +(-109.720 + 358.590i) q^{75} -473.597 q^{76} -86.4666i q^{77} +186.866i q^{78} +607.265 q^{79} +(26.4608 - 176.918i) q^{80} +81.0000 q^{81} -50.1434i q^{82} +604.212i q^{83} -29.4328 q^{84} +(520.961 + 77.9177i) q^{85} -529.549 q^{86} +895.123i q^{87} +282.026i q^{88} +391.745 q^{89} +(-199.032 - 29.7684i) q^{90} -76.3886 q^{91} +228.600i q^{92} +93.0000i q^{93} -689.405 q^{94} +(195.808 - 1309.18i) q^{95} +96.0000 q^{96} +1048.85i q^{97} +673.968i q^{98} +317.279 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 80 q^{4} - 2 q^{5} + 120 q^{6} - 180 q^{9}+O(q^{10}) $ 20 * q - 80 * q^4 - 2 * q^5 + 120 * q^6 - 180 * q^9	$ 20 q - 80 q^{4} - 2 q^{5} + 120 q^{6} - 180 q^{9} + 8 q^{10} - 114 q^{11} + 52 q^{14} - 12 q^{15} + 320 q^{16} + 370 q^{19} + 8 q^{20} - 78 q^{21} - 480 q^{24} - 90 q^{25} - 368 q^{26} + 368 q^{29} - 12 q^{30} - 620 q^{31} + 712 q^{34} + 374 q^{35} + 720 q^{36} + 552 q^{39} - 32 q^{40} - 872 q^{41} + 456 q^{44} + 18 q^{45} - 1236 q^{46} + 1334 q^{49} + 416 q^{50} - 1068 q^{51} - 1080 q^{54} - 1290 q^{55} - 208 q^{56} + 3228 q^{59} + 48 q^{60} - 2604 q^{61} - 1280 q^{64} + 44 q^{65} - 684 q^{66} + 1854 q^{69} - 852 q^{70} - 2290 q^{71} + 2008 q^{74} - 624 q^{75} - 1480 q^{76} + 4342 q^{79} - 32 q^{80} + 1620 q^{81} + 312 q^{84} + 500 q^{85} - 4 q^{86} + 1390 q^{89} - 72 q^{90} - 5744 q^{91} + 2608 q^{94} - 1136 q^{95} + 1920 q^{96} + 1026 q^{99}+O(q^{100}) $ 20 * q - 80 * q^4 - 2 * q^5 + 120 * q^6 - 180 * q^9 + 8 * q^10 - 114 * q^11 + 52 * q^14 - 12 * q^15 + 320 * q^16 + 370 * q^19 + 8 * q^20 - 78 * q^21 - 480 * q^24 - 90 * q^25 - 368 * q^26 + 368 * q^29 - 12 * q^30 - 620 * q^31 + 712 * q^34 + 374 * q^35 + 720 * q^36 + 552 * q^39 - 32 * q^40 - 872 * q^41 + 456 * q^44 + 18 * q^45 - 1236 * q^46 + 1334 * q^49 + 416 * q^50 - 1068 * q^51 - 1080 * q^54 - 1290 * q^55 - 208 * q^56 + 3228 * q^59 + 48 * q^60 - 2604 * q^61 - 1280 * q^64 + 44 * q^65 - 684 * q^66 + 1854 * q^69 - 852 * q^70 - 2290 * q^71 + 2008 * q^74 - 624 * q^75 - 1480 * q^76 + 4342 * q^79 - 32 * q^80 + 1620 * q^81 + 312 * q^84 + 500 * q^85 - 4 * q^86 + 1390 * q^89 - 72 * q^90 - 5744 * q^91 + 2608 * q^94 - 1136 * q^95 + 1920 * q^96 + 1026 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	−4.00000			−0.500000
$5$	1.65380	−	11.0573i	0.147920	−	0.988999i
$5$	1.65380	−	11.0573i	0.147920	−	0.988999i
$6$	6.00000			0.408248
$7$			2.45273i			0.132435i	0.997805	+	0.0662175i	$0.0210931\pi$
$7$			2.45273i			0.132435i	−0.997805	+	0.0662175i	$0.978907\pi$
$8$		−	8.00000i		−	0.353553i
$9$	−9.00000			−0.333333
$10$	22.1147	+	3.30759i	0.699328	+	0.104595i
$11$	−35.2532			−0.966295			−0.483147	−	0.875539i	$-0.660506\pi$
$11$	−35.2532			−0.966295			−0.483147	+	0.875539i	$0.660506\pi$
$12$			12.0000i			0.288675i
$13$			31.1443i			0.664452i	0.943200	+	0.332226i	$0.107800\pi$
$13$			31.1443i			0.664452i	−0.943200	+	0.332226i	$0.892200\pi$
$14$	−4.90546			−0.0936457
$15$	−33.1720	−	4.96139i	−0.570999	−	0.0854017i
$16$	16.0000			0.250000
$17$			47.1144i			0.672172i	0.941831	+	0.336086i	$0.109103\pi$
$17$			47.1144i			0.672172i	−0.941831	+	0.336086i	$0.890897\pi$
$18$		−	18.0000i		−	0.235702i
$19$	118.399			1.42961			0.714806	−	0.699323i	$-0.246515\pi$
$19$	118.399			1.42961			0.714806	+	0.699323i	$0.246515\pi$
$20$	−6.61519	+	44.2294i	−0.0739601	+	0.494500i
$21$	7.35819			0.0764614
$22$		−	70.5064i		−	0.683273i
$23$		−	57.1501i		−	0.518114i	−0.965862	−	0.259057i	$-0.916588\pi$
$23$		−	57.1501i		−	0.518114i	0.965862	−	0.259057i	$-0.0834117\pi$
$24$	−24.0000			−0.204124
$25$	−119.530	−	36.5732i	−0.956239	−	0.292586i
$26$	−62.2886			−0.469839
$27$			27.0000i			0.192450i
$28$		−	9.81092i		−	0.0662175i
$29$	−298.374			−1.91058			−0.955288	−	0.295676i	$-0.904455\pi$
$29$	−298.374			−1.91058			−0.955288	+	0.295676i	$0.904455\pi$
$30$	9.92278	−	66.3441i	0.0603881	−	0.403757i
$31$	−31.0000			−0.179605
$31$	−31.0000			−0.179605
$32$			32.0000i			0.176777i
$33$			105.760i			0.557890i
$34$	−94.2289			−0.475298
$35$	27.1207	+	4.05632i	0.130978	+	0.0195898i
$36$	36.0000			0.166667
$37$		−	82.3944i		−	0.366096i	−0.983104	−	0.183048i	$-0.941404\pi$
$37$		−	82.3944i		−	0.366096i	0.983104	−	0.183048i	$-0.0585964\pi$
$38$			236.798i			1.01089i
$39$	93.4329			0.383622
$40$	−88.4588	−	13.2304i	−0.349664	−	0.0522977i
$41$	−25.0717			−0.0955009			−0.0477505	−	0.998859i	$-0.515205\pi$
$41$	−25.0717			−0.0955009			−0.0477505	+	0.998859i	$0.515205\pi$
$42$			14.7164i			0.0540664i
$43$			264.775i			0.939018i	0.882928	+	0.469509i	$0.155569\pi$
$43$			264.775i			0.939018i	−0.882928	+	0.469509i	$0.844431\pi$
$44$	141.013			0.483147
$45$	−14.8842	+	99.5161i	−0.0493067	+	0.329666i
$46$	114.300			0.366362
$47$			344.703i			1.06979i	0.844919	+	0.534894i	$0.179648\pi$
$47$			344.703i			1.06979i	−0.844919	+	0.534894i	$0.820352\pi$
$48$		−	48.0000i		−	0.144338i
$49$	336.984			0.982461
$50$	73.1465	−	239.060i	0.206889	−	0.676163i
$51$	141.343			0.388079
$52$		−	124.577i		−	0.332226i
$53$			422.169i			1.09414i	0.837087	+	0.547069i	$0.184257\pi$
$53$			422.169i			1.09414i	−0.837087	+	0.547069i	$0.815743\pi$
$54$	−54.0000			−0.136083
$55$	−58.3016	+	389.807i	−0.142934	+	0.955665i
$56$	19.6218			0.0468228
$57$		−	355.198i		−	0.825387i
$58$		−	596.749i		−	1.35098i
$59$	−43.3724			−0.0957051			−0.0478526	−	0.998854i	$-0.515238\pi$
$59$	−43.3724			−0.0957051			−0.0478526	+	0.998854i	$0.515238\pi$
$60$	132.688	+	19.8456i	0.285500	+	0.0427009i
$61$	96.2068			0.201935			0.100967	−	0.994890i	$-0.467806\pi$
$61$	96.2068			0.201935			0.100967	+	0.994890i	$0.467806\pi$
$62$		−	62.0000i		−	0.127000i
$63$		−	22.0746i		−	0.0441450i
$64$	−64.0000			−0.125000
$65$	344.373	+	51.5064i	0.657143	+	0.0982858i
$66$	−211.519			−0.394488
$67$		−	706.568i		−	1.28837i	−0.764868	−	0.644186i	$-0.777196\pi$
$67$		−	706.568i		−	1.28837i	0.764868	−	0.644186i	$-0.222804\pi$
$68$		−	188.458i		−	0.336086i
$69$	−171.450			−0.299133
$70$	−8.11264	+	54.2414i	−0.0138521	+	0.0926155i
$71$	1110.36			1.85600			0.928000	−	0.372580i	$-0.121527\pi$
$71$	1110.36			1.85600			0.928000	+	0.372580i	$0.121527\pi$
$72$			72.0000i			0.117851i
$73$		−	94.3706i		−	0.151305i	−0.997134	−	0.0756524i	$-0.975896\pi$
$73$		−	94.3706i		−	0.151305i	0.997134	−	0.0756524i	$-0.0241039\pi$
$74$	164.789			0.258869
$75$	−109.720	+	358.590i	−0.168924	+	0.552085i
$76$	−473.597			−0.714806
$77$		−	86.4666i		−	0.127971i
$78$			186.866i			0.271261i
$79$	607.265			0.864843			0.432422	−	0.901672i	$-0.357659\pi$
$79$	607.265			0.864843			0.432422	+	0.901672i	$0.357659\pi$
$80$	26.4608	−	176.918i	0.0369800	−	0.247250i
$81$	81.0000			0.111111
$82$		−	50.1434i		−	0.0675294i
$83$			604.212i			0.799047i	0.916723	+	0.399523i	$0.130824\pi$
$83$			604.212i			0.799047i	−0.916723	+	0.399523i	$0.869176\pi$
$84$	−29.4328			−0.0382307
$85$	520.961	+	77.9177i	0.664778	+	0.0994278i
$86$	−529.549			−0.663986
$87$			895.123i			1.10307i
$88$			282.026i			0.341637i
$89$	391.745			0.466572			0.233286	−	0.972408i	$-0.425052\pi$
$89$	391.745			0.466572			0.233286	+	0.972408i	$0.425052\pi$
$90$	−199.032	−	29.7684i	−0.233109	−	0.0348651i
$91$	−76.3886			−0.0879967
$92$			228.600i			0.259057i
$93$			93.0000i			0.103695i
$94$	−689.405			−0.756454
$95$	195.808	−	1309.18i	0.211468	−	1.41389i
$96$	96.0000			0.102062
$97$			1048.85i			1.09788i	0.835861	+	0.548942i	$0.184969\pi$
$97$			1048.85i			1.09788i	−0.835861	+	0.548942i	$0.815031\pi$
$98$			673.968i			0.694705i
$99$	317.279			0.322098
$100$	478.120	+	146.293i	0.478120	+	0.146293i
$101$	1284.24			1.26521			0.632605	−	0.774474i	$-0.281986\pi$
$101$	1284.24			1.26521			0.632605	+	0.774474i	$0.281986\pi$
$102$			282.687i			0.274413i
$103$			1975.76i			1.89007i	0.326970	+	0.945035i	$0.393972\pi$
$103$			1975.76i			1.89007i	−0.326970	+	0.945035i	$0.606028\pi$
$104$	249.154			0.234919
$105$	12.1690	−	81.3621i	0.0113102	−	0.0756202i
$106$	−844.338			−0.773673
$107$			1618.89i			1.46266i	0.682026	+	0.731328i	$0.261099\pi$
$107$			1618.89i			1.46266i	−0.682026	+	0.731328i	$0.738901\pi$
$108$		−	108.000i		−	0.0962250i
$109$	2039.14			1.79187			0.895936	−	0.444182i	$-0.146506\pi$
$109$	2039.14			1.79187			0.895936	+	0.444182i	$0.146506\pi$
$110$	−779.614	−	116.603i	−0.675757	−	0.101070i
$111$	−247.183			−0.211366
$112$			39.2437i			0.0331087i
$113$			895.966i			0.745888i	0.927854	+	0.372944i	$0.121652\pi$
$113$			895.966i			0.745888i	−0.927854	+	0.372944i	$0.878348\pi$
$114$	710.395			0.583637
$115$	−631.928	−	94.5146i	−0.512414	−	0.0766394i
$116$	1193.50			0.955288
$117$		−	280.299i		−	0.221484i
$118$		−	86.7447i		−	0.0676737i
$119$	−115.559			−0.0890191
$120$	−39.6911	+	265.376i	−0.0301941	+	0.201879i
$121$	−88.2119			−0.0662749
$122$			192.414i			0.142789i
$123$			75.2150i			0.0551375i
$124$	124.000			0.0898027
$125$	−602.081	+	1261.20i	−0.430814	+	0.902441i
$126$	44.1491			0.0312152
$127$		−	920.890i		−	0.643431i	−0.946836	−	0.321716i	$-0.895740\pi$
$127$		−	920.890i		−	0.643431i	0.946836	−	0.321716i	$-0.104260\pi$
$128$		−	128.000i		−	0.0883883i
$129$	794.324			0.542142
$130$	−103.013	+	688.747i	−0.0694986	+	0.464670i
$131$	−2612.31			−1.74228			−0.871141	−	0.491034i	$-0.836619\pi$
$131$	−2612.31			−1.74228			−0.871141	+	0.491034i	$0.836619\pi$
$132$		−	423.038i		−	0.278945i
$133$			290.401i			0.189331i
$134$	1413.14			0.911017
$135$	298.548	+	44.6525i	0.190333	+	0.0284672i
$136$	376.916			0.237649
$137$		−	2194.36i		−	1.36845i	−0.729273	−	0.684223i	$-0.760141\pi$
$137$		−	2194.36i		−	1.36845i	0.729273	−	0.684223i	$-0.239859\pi$
$138$		−	342.900i		−	0.211519i
$139$	783.660			0.478196			0.239098	−	0.970995i	$-0.423148\pi$
$139$	783.660			0.478196			0.239098	+	0.970995i	$0.423148\pi$
$140$	−108.483	−	16.2253i	−0.0654891	−	0.00979490i
$141$	1034.11			0.617642
$142$			2220.73i			1.31239i
$143$		−	1097.94i		−	0.642056i
$144$	−144.000			−0.0833333
$145$	−493.451	+	3299.23i	−0.282613	+	1.88956i
$146$	188.741			0.106989
$147$		−	1010.95i		−	0.567224i
$148$			329.578i			0.183048i
$149$	−256.065			−0.140790			−0.0703949	−	0.997519i	$-0.522426\pi$
$149$	−256.065			−0.140790			−0.0703949	+	0.997519i	$0.522426\pi$
$150$	−717.179	−	219.439i	−0.390383	−	0.119448i
$151$	−3553.83			−1.91528			−0.957638	−	0.287973i	$-0.907019\pi$
$151$	−3553.83			−1.91528			−0.957638	+	0.287973i	$0.907019\pi$
$152$		−	947.193i		−	0.505444i
$153$		−	424.030i		−	0.224057i
$154$	172.933			0.0904893
$155$	−51.2677	+	342.778i	−0.0265672	+	0.177630i
$156$	−373.732			−0.191811
$157$			345.400i			0.175579i	0.996139	+	0.0877896i	$0.0279803\pi$
$157$			345.400i			0.175579i	−0.996139	+	0.0877896i	$0.972020\pi$
$158$			1214.53i			0.611537i
$159$	1266.51			0.631701
$160$	353.835	+	52.9215i	0.174832	+	0.0261488i
$161$	140.174			0.0686164
$162$			162.000i			0.0785674i
$163$			1410.83i			0.677945i	0.940796	+	0.338972i	$0.110079\pi$
$163$			1410.83i			0.677945i	−0.940796	+	0.338972i	$0.889921\pi$
$164$	100.287			0.0477505
$165$	1169.42	+	174.905i	0.551753	+	0.0825232i
$166$	−1208.42			−0.565011
$167$			1809.73i			0.838569i	0.907855	+	0.419285i	$0.137719\pi$
$167$			1809.73i			0.838569i	−0.907855	+	0.419285i	$0.862281\pi$
$168$		−	58.8655i		−	0.0270332i
$169$	1227.03			0.558503
$170$	−155.835	+	1041.92i	−0.0703061	+	0.470069i
$171$	−1065.59			−0.476537
$172$		−	1059.10i		−	0.469509i
$173$			3916.63i			1.72125i	0.509243	+	0.860623i	$0.329925\pi$
$173$			3916.63i			1.72125i	−0.509243	+	0.860623i	$0.670075\pi$
$174$	−1790.25			−0.779990
$175$	89.7043	−	293.175i	0.0387486	−	0.126640i
$176$	−564.051			−0.241574
$177$			130.117i			0.0552554i
$178$			783.490i			0.329916i
$179$	−265.024			−0.110664			−0.0553320	−	0.998468i	$-0.517622\pi$
$179$	−265.024			−0.110664			−0.0553320	+	0.998468i	$0.517622\pi$
$180$	59.5367	−	398.065i	0.0246534	−	0.164833i
$181$	2535.64			1.04128			0.520642	−	0.853775i	$-0.325693\pi$
$181$	2535.64			1.04128			0.520642	+	0.853775i	$0.325693\pi$
$182$		−	152.777i		−	0.0622231i
$183$		−	288.620i		−	0.116587i
$184$	−457.201			−0.183181
$185$	−911.064	−	136.264i	−0.362069	−	0.0541530i
$186$	−186.000			−0.0733236
$187$		−	1660.93i		−	0.649516i
$188$		−	1378.81i		−	0.534894i
$189$	−66.2237			−0.0254871
$190$	2618.36	+	391.617i	0.999768	+	0.149531i
$191$	−634.288			−0.240290			−0.120145	−	0.992756i	$-0.538336\pi$
$191$	−634.288			−0.240290			−0.120145	+	0.992756i	$0.538336\pi$
$192$			192.000i			0.0721688i
$193$			4931.48i			1.83925i	0.392796	+	0.919626i	$0.371508\pi$
$193$			4931.48i			1.83925i	−0.392796	+	0.919626i	$0.628492\pi$
$194$	−2097.70			−0.776321
$195$	154.519	−	1033.12i	0.0567454	−	0.379401i
$196$	−1347.94			−0.491230
$197$		−	4890.76i		−	1.76879i	−0.466737	−	0.884396i	$-0.654570\pi$
$197$		−	4890.76i		−	1.76879i	0.466737	−	0.884396i	$-0.345430\pi$
$198$			634.558i			0.227758i
$199$	2738.39			0.975474			0.487737	−	0.872991i	$-0.337823\pi$
$199$	2738.39			0.975474			0.487737	+	0.872991i	$0.337823\pi$
$200$	−292.586	+	956.239i	−0.103445	+	0.338082i
$201$	−2119.70			−0.743842
$202$			2568.47i			0.894639i
$203$		−	731.832i		−	0.253027i
$204$	−565.373			−0.194039
$205$	−41.4635	+	277.226i	−0.0141265	+	0.0944504i
$206$	−3951.51			−1.33648
$207$			514.351i			0.172705i
$208$			498.309i			0.166113i
$209$	−4173.95			−1.38143
$210$	162.724	+	24.3379i	0.0534716	+	0.00799750i
$211$	5556.03			1.81276			0.906381	−	0.422460i	$-0.138833\pi$
$211$	5556.03			1.81276			0.906381	+	0.422460i	$0.138833\pi$
$212$		−	1688.68i		−	0.547069i
$213$		−	3331.09i		−	1.07156i
$214$	−3237.78			−1.03425
$215$	2927.71	+	437.884i	0.928688	+	0.138900i
$216$	216.000			0.0680414
$217$		−	76.0346i		−	0.0237860i
$218$			4078.28i			1.26705i
$219$	−283.112			−0.0873559
$220$	233.207	−	1559.23i	0.0714672	−	0.477832i
$221$	−1467.35			−0.446626
$222$		−	494.366i		−	0.149458i
$223$		−	6505.89i		−	1.95366i	−0.214014	−	0.976831i	$-0.568654\pi$
$223$		−	6505.89i		−	1.95366i	0.214014	−	0.976831i	$-0.431346\pi$
$224$	−78.4874			−0.0234114
$225$	1075.77	+	329.159i	0.318746	+	0.0975286i
$226$	−1791.93			−0.527423
$227$			1721.52i			0.503354i	0.967811	+	0.251677i	$0.0809821\pi$
$227$			1721.52i			0.503354i	−0.967811	+	0.251677i	$0.919018\pi$
$228$			1420.79i			0.412694i
$229$	−2074.96			−0.598764			−0.299382	−	0.954133i	$-0.596781\pi$
$229$	−2074.96			−0.598764			−0.299382	+	0.954133i	$0.596781\pi$
$230$	189.029	−	1263.86i	0.0541923	−	0.362331i
$231$	−259.400			−0.0738842
$232$			2386.99i			0.675491i
$233$			4235.01i			1.19075i	0.803448	+	0.595375i	$0.202997\pi$
$233$			4235.01i			1.19075i	−0.803448	+	0.595375i	$0.797003\pi$
$234$	560.598			0.156613
$235$	3811.50	+	570.068i	1.05802	+	0.158243i
$236$	173.489			0.0478526
$237$		−	1821.79i		−	0.499318i
$238$		−	231.118i		−	0.0629460i
$239$	−6106.61			−1.65274			−0.826368	−	0.563131i	$-0.809597\pi$
$239$	−6106.61			−1.65274			−0.826368	+	0.563131i	$0.809597\pi$
$240$	−530.753	−	79.3823i	−0.142750	−	0.0213504i
$241$	−3008.74			−0.804190			−0.402095	−	0.915598i	$-0.631718\pi$
$241$	−3008.74			−0.804190			−0.402095	+	0.915598i	$0.631718\pi$
$242$		−	176.424i		−	0.0468635i
$243$		−	243.000i		−	0.0641500i
$244$	−384.827			−0.100967
$245$	557.303	−	3726.15i	0.145326	−	0.971653i
$246$	−150.430			−0.0389881
$247$			3687.46i			0.949909i
$248$			248.000i			0.0635001i
$249$	1812.64			0.461330
$250$	−2522.40	−	1204.16i	−0.638122	−	0.304632i
$251$	−4410.77			−1.10918			−0.554592	−	0.832122i	$-0.687126\pi$
$251$	−4410.77			−1.10918			−0.554592	+	0.832122i	$0.687126\pi$
$252$			88.2983i			0.0220725i
$253$			2014.72i			0.500650i
$254$	1841.78			0.454975
$255$	233.753	−	1562.88i	0.0574047	−	0.383810i
$256$	256.000			0.0625000
$257$		−	4828.05i		−	1.17185i	−0.810365	−	0.585925i	$-0.800731\pi$
$257$		−	4828.05i		−	1.17185i	0.810365	−	0.585925i	$-0.199269\pi$
$258$			1588.65i			0.383352i
$259$	202.091			0.0484839
$260$	−1377.49	−	206.026i	−0.328571	−	0.0491429i
$261$	2685.37			0.636859
$262$		−	5224.63i		−	1.23198i
$263$		−	4853.47i		−	1.13794i	−0.822359	−	0.568970i	$-0.807342\pi$
$263$		−	4853.47i		−	1.13794i	0.822359	−	0.568970i	$-0.192658\pi$
$264$	846.077			0.197244
$265$	4668.07	+	698.182i	1.08210	+	0.161845i
$266$	−580.803			−0.133877
$267$		−	1175.23i		−	0.269375i
$268$			2826.27i			0.644186i
$269$	1124.63			0.254906			0.127453	−	0.991845i	$-0.459320\pi$
$269$	1124.63			0.254906			0.127453	+	0.991845i	$0.459320\pi$
$270$	−89.3051	+	597.097i	−0.0201294	+	0.134586i
$271$	−2424.69			−0.543503			−0.271751	−	0.962367i	$-0.587603\pi$
$271$	−2424.69			−0.543503			−0.271751	+	0.962367i	$0.587603\pi$
$272$			753.831i			0.168043i
$273$			229.166i			0.0508049i
$274$	4388.73			0.967638
$275$	4213.81	+	1289.32i	0.924009	+	0.282724i
$276$	685.801			0.149567
$277$			5668.85i			1.22963i	0.788671	+	0.614816i	$0.210770\pi$
$277$			5668.85i			1.22963i	−0.788671	+	0.614816i	$0.789230\pi$
$278$			1567.32i			0.338135i
$279$	279.000			0.0598684
$280$	32.4506	−	216.966i	0.00692604	−	0.0463078i
$281$	−3211.25			−0.681733			−0.340866	−	0.940112i	$-0.610720\pi$
$281$	−3211.25			−0.681733			−0.340866	+	0.940112i	$0.610720\pi$
$282$			2068.22i			0.436739i
$283$		−	1030.37i		−	0.216428i	−0.994128	−	0.108214i	$-0.965487\pi$
$283$		−	1030.37i		−	0.216428i	0.994128	−	0.108214i	$-0.0345132\pi$
$284$	−4441.46			−0.928000
$285$	−3927.54	−	587.425i	−0.816307	−	0.122091i
$286$	2195.87			0.454002
$287$		−	61.4941i		−	0.0126477i
$288$		−	288.000i		−	0.0589256i
$289$	2693.23			0.548184
$290$	−6598.46	−	986.901i	−1.33612	−	0.199837i
$291$	3146.55			0.633864
$292$			377.483i			0.0756524i
$293$			899.072i			0.179264i	0.995975	+	0.0896320i	$0.0285691\pi$
$293$			899.072i			0.179264i	−0.995975	+	0.0896320i	$0.971431\pi$
$294$	2021.90			0.401088
$295$	−71.7291	+	479.583i	−0.0141567	+	0.0946523i
$296$	−659.155			−0.129435
$297$		−	951.836i		−	0.185963i
$298$		−	512.130i		−	0.0995534i
$299$	1779.90			0.344262
$300$	438.879	−	1434.36i	0.0844622	−	0.276042i
$301$	−649.421			−0.124359
$302$		−	7107.67i		−	1.35431i
$303$		−	3852.71i		−	0.730470i
$304$	1894.39			0.357403
$305$	159.107	−	1063.79i	0.0298702	−	0.199713i
$306$	848.060			0.158433
$307$			7269.78i			1.35149i	0.737135	+	0.675746i	$0.236178\pi$
$307$			7269.78i			1.35149i	−0.737135	+	0.675746i	$0.763822\pi$
$308$			345.866i			0.0639856i
$309$	5927.27			1.09123
$310$	−685.556	−	102.535i	−0.125603	−	0.0187859i
$311$	−3473.70			−0.633362			−0.316681	−	0.948532i	$-0.602568\pi$
$311$	−3473.70			−0.633362			−0.316681	+	0.948532i	$0.602568\pi$
$312$		−	747.463i		−	0.135631i
$313$			3467.92i			0.626257i	0.949711	+	0.313128i	$0.101377\pi$
$313$			3467.92i			0.626257i	−0.949711	+	0.313128i	$0.898623\pi$
$314$	−690.800			−0.124153
$315$	−244.086	−	36.5069i	−0.0436594	−	0.00652993i
$316$	−2429.06			−0.432422
$317$			1696.27i			0.300542i	0.988645	+	0.150271i	$0.0480147\pi$
$317$			1696.27i			0.300542i	−0.988645	+	0.150271i	$0.951985\pi$
$318$			2533.01i			0.446680i
$319$	10518.7			1.84618
$320$	−105.843	+	707.670i	−0.0184900	+	0.123625i
$321$	4856.67			0.844465
$322$			280.347i			0.0485191i
$323$			5578.31i			0.960946i
$324$	−324.000			−0.0555556
$325$	1139.05	−	3722.68i	0.194409	−	0.635375i
$326$	−2821.67			−0.479379
$327$		−	6117.42i		−	1.03454i
$328$			200.573i			0.0337647i
$329$	−845.462			−0.141677
$330$	−349.810	+	2338.84i	−0.0583527	+	0.390148i
$331$	5986.62			0.994122			0.497061	−	0.867715i	$-0.334412\pi$
$331$	5986.62			0.994122			0.497061	+	0.867715i	$0.334412\pi$
$332$		−	2416.85i		−	0.399523i
$333$			741.550i			0.122032i
$334$	−3619.46			−0.592958
$335$	−7812.77	−	1168.52i	−1.27420	−	0.190576i
$336$	117.731			0.0191153
$337$		−	2762.05i		−	0.446464i	−0.974765	−	0.223232i	$-0.928339\pi$
$337$		−	2762.05i		−	0.446464i	0.974765	−	0.223232i	$-0.0716608\pi$
$338$			2454.06i			0.394922i
$339$	2687.90			0.430639
$340$	−2083.84	−	311.671i	−0.332389	−	0.0497139i
$341$	1092.85			0.173552
$342$		−	2131.19i		−	0.336963i
$343$			1667.82i			0.262547i
$344$	2118.20			0.331993
$345$	−283.544	+	1895.78i	−0.0442478	+	0.295842i
$346$	−7833.25			−1.21710
$347$		−	348.734i		−	0.0539511i	−0.999636	−	0.0269756i	$-0.991412\pi$
$347$		−	348.734i		−	0.0539511i	0.999636	−	0.0269756i	$-0.00858763\pi$
$348$		−	3580.49i		−	0.551536i
$349$	−3247.11			−0.498034			−0.249017	−	0.968499i	$-0.580108\pi$
$349$	−3247.11			−0.498034			−0.249017	+	0.968499i	$0.580108\pi$
$350$	586.349	+	179.409i	0.0895477	+	0.0273994i
$351$	−840.896			−0.127874
$352$		−	1128.10i		−	0.170818i
$353$		−	8034.97i		−	1.21150i	−0.795656	−	0.605749i	$-0.792874\pi$
$353$		−	8034.97i		−	1.21150i	0.795656	−	0.605749i	$-0.207126\pi$
$354$	−260.234			−0.0390714
$355$	1836.32	−	12277.7i	0.274540	−	1.83558i
$356$	−1566.98			−0.233286
$357$			346.677i			0.0513952i
$358$		−	530.049i		−	0.0782512i
$359$	−5821.40			−0.855826			−0.427913	−	0.903820i	$-0.640751\pi$
$359$	−5821.40			−0.855826			−0.427913	+	0.903820i	$0.640751\pi$
$360$	796.129	+	119.073i	0.116555	+	0.0174326i
$361$	7159.37			1.04379
$362$			5071.27i			0.736299i
$363$			264.636i			0.0382639i
$364$	305.554			0.0439984
$365$	−1043.49	−	156.070i	−0.149640	−	0.0223810i
$366$	577.241			0.0824395
$367$			5139.43i			0.730997i	0.930812	+	0.365499i	$0.119102\pi$
$367$			5139.43i			0.730997i	−0.930812	+	0.365499i	$0.880898\pi$
$368$		−	914.401i		−	0.129528i
$369$	225.645			0.0318336
$370$	272.527	−	1822.13i	0.0382919	−	0.256021i
$371$	−1035.47			−0.144902
$372$		−	372.000i		−	0.0518476i
$373$			895.837i			0.124356i	0.998065	+	0.0621779i	$0.0198046\pi$
$373$			895.837i			0.124356i	−0.998065	+	0.0621779i	$0.980195\pi$
$374$	3321.87			0.459277
$375$	3783.60	+	1806.24i	0.521024	+	0.248731i
$376$	2757.62			0.378227
$377$		−	9292.66i		−	1.26949i
$378$		−	132.447i		−	0.0180221i
$379$	−14266.0			−1.93350			−0.966748	−	0.255732i	$-0.917684\pi$
$379$	−14266.0			−1.93350			−0.966748	+	0.255732i	$0.917684\pi$
$380$	−783.233	+	5236.72i	−0.105734	+	0.706943i
$381$	−2762.67			−0.371485
$382$		−	1268.58i		−	0.169911i
$383$			7255.84i			0.968032i	0.875059	+	0.484016i	$0.160822\pi$
$383$			7255.84i			0.968032i	−0.875059	+	0.484016i	$0.839178\pi$
$384$	−384.000			−0.0510310
$385$	−956.091	−	142.998i	−0.126563	−	0.0189295i
$386$	−9862.96			−1.30055
$387$		−	2382.97i		−	0.313006i
$388$		−	4195.41i		−	0.548942i
$389$	4258.04			0.554990			0.277495	−	0.960727i	$-0.410496\pi$
$389$	4258.04			0.554990			0.277495	+	0.960727i	$0.410496\pi$
$390$	2066.24	+	309.038i	0.268277	+	0.0401250i
$391$	2692.59			0.348262
$392$		−	2695.87i		−	0.347352i
$393$			7836.94i			1.00591i
$394$	9781.52			1.25073
$395$	1004.29	−	6714.74i	0.127928	−	0.855329i
$396$	−1269.12			−0.161049
$397$		−	2197.33i		−	0.277786i	−0.990307	−	0.138893i	$-0.955646\pi$
$397$		−	2197.33i		−	0.277786i	0.990307	−	0.138893i	$-0.0443544\pi$
$398$			5476.78i			0.689764i
$399$	871.204			0.109310
$400$	−1912.48	−	585.172i	−0.239060	−	0.0731465i
$401$	−1315.27			−0.163794			−0.0818970	−	0.996641i	$-0.526098\pi$
$401$	−1315.27			−0.163794			−0.0818970	+	0.996641i	$0.526098\pi$
$402$		−	4239.41i		−	0.525976i
$403$		−	965.474i		−	0.119339i
$404$	−5136.95			−0.632605
$405$	133.958	−	895.645i	0.0164356	−	0.109889i
$406$	1463.66			0.178917
$407$			2904.67i			0.353757i
$408$		−	1130.75i		−	0.137207i
$409$	4484.14			0.542118			0.271059	−	0.962563i	$-0.412626\pi$
$409$	4484.14			0.542118			0.271059	+	0.962563i	$0.412626\pi$
$410$	−554.453	−	82.9270i	−0.0667865	−	0.00998895i
$411$	−6583.09			−0.790073
$412$		−	7903.03i		−	0.945035i
$413$		−	106.381i		−	0.0126747i
$414$	−1028.70			−0.122121
$415$	6680.98	+	999.244i	0.790256	+	0.118195i
$416$	−996.618			−0.117460
$417$		−	2350.98i		−	0.276086i
$418$		−	8347.90i		−	0.976816i
$419$	3807.12			0.443891			0.221945	−	0.975059i	$-0.428759\pi$
$419$	3807.12			0.443891			0.221945	+	0.975059i	$0.428759\pi$
$420$	−48.6758	+	325.448i	−0.00565509	+	0.0378101i
$421$	3033.45			0.351167			0.175584	−	0.984465i	$-0.443819\pi$
$421$	3033.45			0.351167			0.175584	+	0.984465i	$0.443819\pi$
$422$			11112.1i			1.28182i
$423$		−	3102.32i		−	0.356596i
$424$	3377.35			0.386837
$425$	1723.13	−	5631.58i	0.196668	−	0.642758i
$426$	6662.19			0.757709
$427$			235.969i			0.0267432i
$428$		−	6475.57i		−	0.731328i
$429$	−3293.81			−0.370691
$430$	−875.767	+	5855.41i	−0.0982169	+	0.656681i
$431$	5569.05			0.622393			0.311197	−	0.950346i	$-0.399270\pi$
$431$	5569.05			0.622393			0.311197	+	0.950346i	$0.399270\pi$
$432$			432.000i			0.0481125i
$433$		−	11093.0i		−	1.23116i	−0.788073	−	0.615582i	$-0.788921\pi$
$433$		−	11093.0i		−	1.23116i	0.788073	−	0.615582i	$-0.211079\pi$
$434$	152.069			0.0168193
$435$	9897.69	+	1480.35i	1.09094	+	0.163167i
$436$	−8156.56			−0.895936
$437$		−	6766.52i		−	0.740702i
$438$		−	566.224i		−	0.0617699i
$439$	−2915.40			−0.316958			−0.158479	−	0.987362i	$-0.550659\pi$
$439$	−2915.40			−0.316958			−0.158479	+	0.987362i	$0.550659\pi$
$440$	3118.46	+	466.413i	0.337878	+	0.0505349i
$441$	−3032.86			−0.327487
$442$		−	2934.69i		−	0.315812i
$443$		−	1390.52i		−	0.149132i	−0.997216	−	0.0745661i	$-0.976243\pi$
$443$		−	1390.52i		−	0.149132i	0.997216	−	0.0745661i	$-0.0237572\pi$
$444$	988.733			0.105683
$445$	647.867	−	4331.66i	0.0690153	−	0.461439i
$446$	13011.8			1.38145
$447$			768.195i			0.0812850i
$448$		−	156.975i		−	0.0165544i
$449$	11386.2			1.19677			0.598383	−	0.801210i	$-0.295810\pi$
$449$	11386.2			1.19677			0.598383	+	0.801210i	$0.295810\pi$
$450$	−658.318	+	2151.54i	−0.0689631	+	0.225388i
$451$	883.857			0.0922820
$452$		−	3583.86i		−	0.372944i
$453$			10661.5i			1.10579i
$454$	−3443.04			−0.355925
$455$	−126.331	+	844.655i	−0.0130165	+	0.0870287i
$456$	−2841.58			−0.291818
$457$		−	18212.5i		−	1.86421i	−0.362191	−	0.932104i	$-0.617971\pi$
$457$		−	18212.5i		−	1.86421i	0.362191	−	0.932104i	$-0.382029\pi$
$458$		−	4149.92i		−	0.423390i
$459$	−1272.09			−0.129360
$460$	2527.71	+	378.059i	0.256207	+	0.0383197i
$461$	8974.30			0.906670			0.453335	−	0.891340i	$-0.350234\pi$
$461$	8974.30			0.906670			0.453335	+	0.891340i	$0.350234\pi$
$462$		−	518.800i		−	0.0522440i
$463$			10970.1i			1.10113i	0.834792	+	0.550566i	$0.185588\pi$
$463$			10970.1i			1.10113i	−0.834792	+	0.550566i	$0.814412\pi$
$464$	−4773.99			−0.477644
$465$	1028.33	+	153.803i	0.102554	+	0.0153386i
$466$	−8470.02			−0.841988
$467$			4721.07i			0.467805i	0.972260	+	0.233903i	$0.0751497\pi$
$467$			4721.07i			0.467805i	−0.972260	+	0.233903i	$0.924850\pi$
$468$			1121.20i			0.110742i
$469$	1733.02			0.170626
$470$	−1140.14	+	7622.99i	−0.111895	+	0.748133i
$471$	1036.20			0.101371
$472$			346.979i			0.0338369i
$473$		−	9334.15i		−	0.907368i
$474$	3643.59			0.353071
$475$	−14152.2	−	4330.24i	−1.36705	−	0.418284i
$476$	462.236			0.0445096
$477$		−	3799.52i		−	0.364713i
$478$		−	12213.2i		−	1.16866i
$479$	−18909.3			−1.80373			−0.901865	−	0.432018i	$-0.857802\pi$
$479$	−18909.3			−1.80373			−0.901865	+	0.432018i	$0.857802\pi$
$480$	158.765	−	1061.51i	0.0150970	−	0.100939i
$481$	2566.12			0.243253
$482$		−	6017.47i		−	0.568648i
$483$		−	420.521i		−	0.0396157i
$484$	352.848			0.0331375
$485$	11597.5	+	1734.59i	1.08581	+	0.162399i
$486$	486.000			0.0453609
$487$			5928.26i			0.551612i	0.961213	+	0.275806i	$0.0889448\pi$
$487$			5928.26i			0.551612i	−0.961213	+	0.275806i	$0.911055\pi$
$488$		−	769.654i		−	0.0713947i
$489$	4232.50			0.391412
$490$	7452.30	+	1114.61i	0.687063	+	0.102761i
$491$	−16523.9			−1.51876			−0.759382	−	0.650645i	$-0.774498\pi$
$491$	−16523.9			−1.51876			−0.759382	+	0.650645i	$0.774498\pi$
$492$		−	300.860i		−	0.0275687i
$493$		−	14057.7i		−	1.28424i
$494$	−7374.92			−0.671687
$495$	524.715	−	3508.26i	0.0476448	−	0.318555i
$496$	−496.000			−0.0449013
$497$			2723.42i			0.245799i
$498$			3625.27i			0.326209i
$499$	874.688			0.0784698			0.0392349	−	0.999230i	$-0.487508\pi$
$499$	874.688			0.0784698			0.0392349	+	0.999230i	$0.487508\pi$
$500$	2408.32	−	5044.80i	0.215407	−	0.451220i
$501$	5429.19			0.484148
$502$		−	8821.54i		−	0.784312i
$503$		−	15289.9i		−	1.35536i	−0.735359	−	0.677678i	$-0.762986\pi$
$503$		−	15289.9i		−	1.35536i	0.735359	−	0.677678i	$-0.237014\pi$
$504$	−176.597			−0.0156076
$505$	2123.87	−	14200.2i	0.187150	−	1.25129i
$506$	−4029.45			−0.354013
$507$		−	3681.10i		−	0.322452i
$508$			3683.56i			0.321716i
$509$	−17458.2			−1.52027			−0.760137	−	0.649763i	$-0.774868\pi$
$509$	−17458.2			−1.52027			−0.760137	+	0.649763i	$0.774868\pi$
$510$	3125.76	+	467.506i	0.271394	+	0.0405912i
$511$	231.466			0.0200380
$512$			512.000i			0.0441942i
$513$			3196.78i			0.275129i
$514$	9656.10			0.828623
$515$	21846.6	+	3267.50i	1.86928	+	0.279579i
$516$	−3177.30			−0.271071
$517$		−	12151.9i		−	1.03373i
$518$			404.182i			0.0342833i
$519$	11749.9			0.993762
$520$	412.051	−	2754.99i	0.0347493	−	0.232335i
$521$	−7380.17			−0.620597			−0.310298	−	0.950639i	$-0.600429\pi$
$521$	−7380.17			−0.620597			−0.310298	+	0.950639i	$0.600429\pi$
$522$			5370.74i			0.450327i
$523$			7990.31i			0.668053i	0.942564	+	0.334027i	$0.108408\pi$
$523$			7990.31i			0.668053i	−0.942564	+	0.334027i	$0.891592\pi$
$524$	10449.3			0.871141
$525$	−879.524	−	269.113i	−0.0731154	−	0.0223715i
$526$	9706.95			0.804645
$527$		−	1460.55i		−	0.120726i
$528$			1692.15i			0.139473i
$529$	8900.87			0.731558
$530$	−1396.36	+	9336.14i	−0.114442	+	0.765162i
$531$	390.351			0.0319017
$532$		−	1161.61i		−	0.0946654i
$533$		−	780.840i		−	0.0634558i
$534$	2350.47			0.190477
$535$	17900.6	+	2677.32i	1.44657	+	0.216356i
$536$	−5652.54			−0.455509
$537$			795.073i			0.0638919i
$538$			2249.25i			0.180246i
$539$	−11879.8			−0.949347
$540$	−1194.19	−	178.610i	−0.0951665	−	0.0142336i
$541$	5396.99			0.428900			0.214450	−	0.976735i	$-0.431204\pi$
$541$	5396.99			0.428900			0.214450	+	0.976735i	$0.431204\pi$
$542$		−	4849.37i		−	0.384315i
$543$		−	7606.91i		−	0.601185i
$544$	−1507.66			−0.118824
$545$	3372.32	−	22547.5i	0.265054	−	1.77216i
$546$	−458.332			−0.0359245
$547$		−	9629.59i		−	0.752708i	−0.926476	−	0.376354i	$-0.877178\pi$
$547$		−	9629.59i		−	0.752708i	0.926476	−	0.376354i	$-0.122822\pi$
$548$			8777.45i			0.684223i
$549$	−865.861			−0.0673116
$550$	−2578.65	+	8427.62i	−0.199916	+	0.653373i
$551$	−35327.3			−2.73138
$552$			1371.60i			0.105760i
$553$			1489.46i			0.114536i
$554$	−11337.7			−0.869481
$555$	−408.791	+	2733.19i	−0.0312652	+	0.209041i
$556$	−3134.64			−0.239098
$557$			22557.4i			1.71596i	0.513684	+	0.857980i	$0.328281\pi$
$557$			22557.4i			1.71596i	−0.513684	+	0.857980i	$0.671719\pi$
$558$			558.000i			0.0423334i
$559$	−8246.22			−0.623932
$560$	433.931	+	64.9011i	0.0327445	+	0.00489745i
$561$	−4982.80			−0.374998
$562$		−	6422.49i		−	0.482058i
$563$			19572.7i			1.46517i	0.680677	+	0.732584i	$0.261686\pi$
$563$			19572.7i			1.46517i	−0.680677	+	0.732584i	$0.738314\pi$
$564$	−4136.43			−0.308821
$565$	9907.00	+	1481.75i	0.737683	+	0.110332i
$566$	2060.74			0.153038
$567$			198.671i			0.0147150i
$568$		−	8882.92i		−	0.656195i
$569$	20027.6			1.47557			0.737784	−	0.675036i	$-0.235872\pi$
$569$	20027.6			1.47557			0.737784	+	0.675036i	$0.235872\pi$
$570$	1174.85	−	7855.09i	0.0863316	−	0.577216i
$571$	2789.72			0.204459			0.102230	−	0.994761i	$-0.467402\pi$
$571$	2789.72			0.204459			0.102230	+	0.994761i	$0.467402\pi$
$572$			4391.75i			0.321028i
$573$			1902.86i			0.138732i
$574$	122.988			0.00894325
$575$	−2090.16	+	6831.14i	−0.151593	+	0.495441i
$576$	576.000			0.0416667
$577$			24541.5i			1.77067i	0.464955	+	0.885335i	$0.346071\pi$
$577$			24541.5i			1.77067i	−0.464955	+	0.885335i	$0.653929\pi$
$578$			5386.46i			0.387625i
$579$	14794.4			1.06189
$580$	1973.80	−	13196.9i	0.141306	−	0.944780i
$581$	−1481.97			−0.105822
$582$			6293.11i			0.448209i
$583$		−	14882.8i		−	1.05726i
$584$	−754.965			−0.0534943
$585$	−3099.36	−	463.557i	−0.219048	−	0.0327619i
$586$	−1798.14			−0.126759
$587$		−	10482.0i		−	0.737030i	−0.929622	−	0.368515i	$-0.879866\pi$
$587$		−	10482.0i		−	0.737030i	0.929622	−	0.368515i	$-0.120134\pi$
$588$			4043.81i			0.283612i
$589$	−3670.37			−0.256766
$590$	−959.167	−	143.458i	−0.0669293	−	0.0100103i
$591$	−14672.3			−1.02121
$592$		−	1318.31i		−	0.0915240i
$593$			15003.7i			1.03900i	0.854469	+	0.519502i	$0.173882\pi$
$593$			15003.7i			1.03900i	−0.854469	+	0.519502i	$0.826118\pi$
$594$	1903.67			0.131496
$595$	−191.111	+	1277.78i	−0.0131677	+	0.0880399i
$596$	1024.26			0.0703949
$597$		−	8215.17i		−	0.563190i
$598$			3559.80i			0.243430i
$599$	11891.8			0.811164			0.405582	−	0.914059i	$-0.367069\pi$
$599$	11891.8			0.811164			0.405582	+	0.914059i	$0.367069\pi$
$600$	2868.72	+	877.757i	0.195192	+	0.0597238i
$601$	−20918.4			−1.41976			−0.709882	−	0.704321i	$-0.751252\pi$
$601$	−20918.4			−1.41976			−0.709882	+	0.704321i	$0.751252\pi$
$602$		−	1298.84i		−	0.0879349i
$603$			6359.11i			0.429458i
$604$	14215.3			0.957638
$605$	−145.885	+	975.390i	−0.00980340	+	0.0655459i
$606$	7705.42			0.516520
$607$			5661.21i			0.378553i	0.981924	+	0.189276i	$0.0606142\pi$
$607$			5661.21i			0.378553i	−0.981924	+	0.189276i	$0.939386\pi$
$608$			3788.77i			0.252722i
$609$	−2195.50			−0.146085
$610$	2127.58	+	318.213i	0.141219	+	0.0211214i
$611$	−10735.5			−0.710823
$612$			1696.12i			0.112029i
$613$			7829.80i			0.515893i	0.966159	+	0.257947i	$0.0830459\pi$
$613$			7829.80i			0.515893i	−0.966159	+	0.257947i	$0.916954\pi$
$614$	−14539.6			−0.955649
$615$	831.679	+	124.390i	0.0545309	+	0.00815595i
$616$	−691.733			−0.0452447
$617$		−	11841.8i		−	0.772662i	−0.922360	−	0.386331i	$-0.873742\pi$
$617$		−	11841.8i		−	0.772662i	0.922360	−	0.386331i	$-0.126258\pi$
$618$			11854.5i			0.771618i
$619$	21332.4			1.38517			0.692585	−	0.721337i	$-0.256472\pi$
$619$	21332.4			1.38517			0.692585	+	0.721337i	$0.256472\pi$
$620$	205.071	−	1371.11i	0.0132836	−	0.0888148i
$621$	1543.05			0.0997110
$622$		−	6947.40i		−	0.447854i
$623$			960.844i			0.0617904i
$624$	1494.93			0.0959054
$625$	12949.8	+	8743.19i	0.828787	+	0.559564i
$626$	−6935.84			−0.442830
$627$			12521.9i			0.797567i
$628$		−	1381.60i		−	0.0877896i
$629$	3881.97			0.246080
$630$	73.0137	−	488.172i	0.00461736	−	0.0308718i
$631$	−19975.5			−1.26024			−0.630121	−	0.776497i	$-0.716995\pi$
$631$	−19975.5			−1.26024			−0.630121	+	0.776497i	$0.716995\pi$
$632$		−	4858.12i		−	0.305768i
$633$		−	16668.1i		−	1.04660i
$634$	−3392.54			−0.212516
$635$	−10182.6	−	1522.97i	−0.636353	−	0.0951765i
$636$	−5066.03			−0.315851
$637$			10495.1i			0.652798i
$638$			21037.3i			1.30545i
$639$	−9993.28			−0.618667
$640$	−1415.34	−	211.686i	−0.0874160	−	0.0130744i
$641$	−642.218			−0.0395727			−0.0197863	−	0.999804i	$-0.506299\pi$
$641$	−642.218			−0.0395727			−0.0197863	+	0.999804i	$0.506299\pi$
$642$			9713.35i			0.597127i
$643$			14350.3i			0.880125i	0.897967	+	0.440063i	$0.145044\pi$
$643$			14350.3i			0.880125i	−0.897967	+	0.440063i	$0.854956\pi$
$644$	−560.695			−0.0343082
$645$	1313.65	−	8783.12i	0.0801937	−	0.536178i
$646$	−11156.6			−0.679491
$647$		−	9666.18i		−	0.587352i	−0.955905	−	0.293676i	$-0.905121\pi$
$647$		−	9666.18i		−	0.587352i	0.955905	−	0.293676i	$-0.0948787\pi$
$648$		−	648.000i		−	0.0392837i
$649$	1529.01			0.0924793
$650$	7445.35	+	2278.10i	0.449278	+	0.137468i
$651$	−228.104			−0.0137329
$652$		−	5643.33i		−	0.338972i
$653$		−	3146.94i		−	0.188590i	−0.995544	−	0.0942950i	$-0.969940\pi$
$653$		−	3146.94i		−	0.188590i	0.995544	−	0.0942950i	$-0.0300597\pi$
$654$	12234.8			0.731529
$655$	−4320.24	+	28885.3i	−0.257718	+	1.72312i
$656$	−401.147			−0.0238752
$657$			849.336i			0.0504349i
$658$		−	1690.92i		−	0.100181i
$659$	−33398.3			−1.97422			−0.987111	−	0.160040i	$-0.948838\pi$
$659$	−33398.3			−1.97422			−0.987111	+	0.160040i	$0.948838\pi$
$660$	−4677.68	−	699.620i	−0.275877	−	0.0412616i
$661$	−28820.2			−1.69588			−0.847939	−	0.530094i	$-0.822157\pi$
$661$	−28820.2			−1.69588			−0.847939	+	0.530094i	$0.822157\pi$
$662$			11973.2i			0.702951i
$663$			4402.04i			0.257860i
$664$	4833.69			0.282506
$665$	3211.07	+	480.265i	0.187248	+	0.0280058i
$666$	−1483.10			−0.0862897
$667$			17052.1i			0.989896i
$668$		−	7238.92i		−	0.419285i
$669$	−19517.7			−1.12795
$670$	2337.04	−	15625.5i	0.134758	−	0.900995i
$671$	−3391.60			−0.195128
$672$			235.462i			0.0135166i
$673$		−	7808.13i		−	0.447223i	−0.974678	−	0.223612i	$-0.928215\pi$
$673$		−	7808.13i		−	0.447223i	0.974678	−	0.223612i	$-0.0717847\pi$
$674$	5524.10			0.315698
$675$	987.477	−	3227.31i	0.0563082	−	0.184028i
$676$	−4908.13			−0.279252
$677$			21793.5i			1.23721i	0.785702	+	0.618606i	$0.212302\pi$
$677$			21793.5i			1.23721i	−0.785702	+	0.618606i	$0.787698\pi$
$678$			5375.79i			0.304508i
$679$	−2572.55			−0.145398
$680$	623.342	−	4167.69i	0.0351530	−	0.235035i
$681$	5164.57			0.290612
$682$			2185.70i			0.122720i
$683$			4067.07i			0.227851i	0.993489	+	0.113925i	$0.0363425\pi$
$683$			4067.07i			0.227851i	−0.993489	+	0.113925i	$0.963658\pi$
$684$	4262.37			0.238269
$685$	−24263.8	−	3629.03i	−1.35339	−	0.202421i
$686$	−3335.64			−0.185649
$687$			6224.87i			0.345697i
$688$			4236.39i			0.234754i
$689$	−13148.2			−0.727003
$690$	−3791.57	−	567.088i	−0.209192	−	0.0312879i
$691$	−12621.9			−0.694878			−0.347439	−	0.937703i	$-0.612949\pi$
$691$	−12621.9			−0.694878			−0.347439	+	0.937703i	$0.612949\pi$
$692$		−	15666.5i		−	0.860623i
$693$			778.199i			0.0426571i
$694$	697.469			0.0381492
$695$	1296.02	−	8665.20i	0.0707348	−	0.472935i
$696$	7160.98			0.389995
$697$		−	1181.24i		−	0.0641931i
$698$		−	6494.23i		−	0.352164i
$699$	12705.0			0.687480
$700$	−358.817	+	1172.70i	−0.0193743	+	0.0633198i
$701$	5058.76			0.272563			0.136282	−	0.990670i	$-0.456485\pi$
$701$	5058.76			0.272563			0.136282	+	0.990670i	$0.456485\pi$
$702$		−	1681.79i		−	0.0904205i
$703$		−	9755.43i		−	0.523376i
$704$	2256.20			0.120787
$705$	1710.20	−	11434.5i	0.0913617	−	0.610848i
$706$	16069.9			0.856658
$707$			3149.89i			0.167558i
$708$		−	520.468i		−	0.0276277i
$709$	−13023.0			−0.689829			−0.344915	−	0.938634i	$-0.612092\pi$
$709$	−13023.0			−0.689829			−0.344915	+	0.938634i	$0.612092\pi$
$710$	24555.4	+	3672.64i	1.29795	+	0.194129i
$711$	−5465.38			−0.288281
$712$		−	3133.96i		−	0.164958i
$713$			1771.65i			0.0930560i
$714$	−693.354			−0.0363419
$715$	−12140.3	−	1815.76i	−0.634993	−	0.0949731i
$716$	1060.10			0.0553320
$717$			18319.8i			0.954207i
$718$		−	11642.8i		−	0.605161i
$719$	17673.7			0.916717			0.458358	−	0.888767i	$-0.348438\pi$
$719$	17673.7			0.916717			0.458358	+	0.888767i	$0.348438\pi$
$720$	−238.147	+	1592.26i	−0.0123267	+	0.0824166i
$721$	−4846.00			−0.250311
$722$			14318.7i			0.738072i
$723$			9026.21i			0.464299i
$724$	−10142.5			−0.520642
$725$	35664.7	+	10912.5i	1.82697	+	0.559008i
$726$	−529.272			−0.0270566
$727$			26012.9i			1.32705i	0.748155	+	0.663524i	$0.230940\pi$
$727$			26012.9i			1.32705i	−0.748155	+	0.663524i	$0.769060\pi$
$728$			611.109i			0.0311115i
$729$	−729.000			−0.0370370
$730$	312.140	−	2086.98i	0.0158258	−	0.105812i
$731$	−12474.7			−0.631182
$732$			1154.48i			0.0582935i
$733$		−	15642.6i		−	0.788229i	−0.919061	−	0.394115i	$-0.871051\pi$
$733$		−	15642.6i		−	0.788229i	0.919061	−	0.394115i	$-0.128949\pi$
$734$	−10278.9			−0.516893
$735$	−11178.5	−	1671.91i	−0.560984	−	0.0839039i
$736$	1828.80			0.0915904
$737$			24908.8i			1.24495i
$738$			451.290i			0.0225098i
$739$	−17297.5			−0.861028			−0.430514	−	0.902584i	$-0.641668\pi$
$739$	−17297.5			−0.861028			−0.430514	+	0.902584i	$0.641668\pi$
$740$	3644.25	+	545.055i	0.181034	+	0.0270765i
$741$	11062.4			0.548430
$742$		−	2070.93i		−	0.102461i
$743$		−	20564.7i		−	1.01540i	−0.861533	−	0.507702i	$-0.830495\pi$
$743$		−	20564.7i		−	1.01540i	0.861533	−	0.507702i	$-0.169505\pi$
$744$	744.000			0.0366618
$745$	−423.480	+	2831.40i	−0.0208256	+	0.139241i
$746$	−1791.67			−0.0879328
$747$		−	5437.91i		−	0.266349i
$748$			6643.74i			0.324758i
$749$	−3970.70			−0.193707
$750$	−3612.49	+	7567.19i	−0.175879	+	0.368420i
$751$	−27970.2			−1.35905			−0.679526	−	0.733652i	$-0.737814\pi$
$751$	−27970.2			−1.35905			−0.679526	+	0.733652i	$0.737814\pi$
$752$			5515.24i			0.267447i
$753$			13232.3i			0.640388i
$754$	18585.3			0.897663
$755$	−5877.32	+	39296.0i	−0.283308	+	1.89421i
$756$	264.895			0.0127436
$757$			16261.9i			0.780780i	0.920650	+	0.390390i	$0.127660\pi$
$757$			16261.9i			0.780780i	−0.920650	+	0.390390i	$0.872340\pi$
$758$		−	28532.0i		−	1.36719i
$759$	6044.17			0.289051
$760$	−10473.4	−	1566.47i	−0.499884	−	0.0747654i
$761$	−23922.9			−1.13956			−0.569779	−	0.821798i	$-0.692971\pi$
$761$	−23922.9			−1.13956			−0.569779	+	0.821798i	$0.692971\pi$
$762$		−	5525.34i		−	0.262680i
$763$			5001.46i			0.237307i
$764$	2537.15			0.120145
$765$	−4688.65	−	701.260i	−0.221593	−	0.0331426i
$766$	−14511.7			−0.684502
$767$		−	1350.80i		−	0.0635915i
$768$		−	768.000i		−	0.0360844i
$769$	31811.9			1.49176			0.745881	−	0.666079i	$-0.232029\pi$
$769$	31811.9			1.49176			0.745881	+	0.666079i	$0.232029\pi$
$770$	285.996	−	1912.18i	0.0133852	−	0.0894939i
$771$	−14484.1			−0.676568
$772$		−	19725.9i		−	0.919626i
$773$		−	22660.3i		−	1.05438i	−0.849747	−	0.527190i	$-0.823246\pi$
$773$		−	22660.3i		−	1.05438i	0.849747	−	0.527190i	$-0.176754\pi$
$774$	4765.94			0.221329
$775$	3705.43	+	1133.77i	0.171746	+	0.0525500i
$776$	8390.81			0.388161
$777$		−	606.274i		−	0.0279922i
$778$			8516.08i			0.392437i
$779$	−2968.47			−0.136529
$780$	−618.077	+	4132.48i	−0.0283727	+	0.189701i
$781$	−39143.9			−1.79344
$782$			5385.19i			0.246258i
$783$		−	8056.11i		−	0.367691i
$784$	5391.75			0.245615
$785$	3819.21	+	571.222i	0.173648	+	0.0259717i
$786$	−15673.9			−0.711283
$787$			27806.5i			1.25946i	0.776814	+	0.629730i	$0.216834\pi$
$787$			27806.5i			1.25946i	−0.776814	+	0.629730i	$0.783166\pi$
$788$			19563.0i			0.884396i
$789$	−14560.4			−0.656990
$790$	13429.5	+	2008.59i	0.604809	+	0.0904586i
$791$	−2197.56			−0.0987817
$792$		−	2538.23i		−	0.113879i
$793$			2996.29i			0.134176i
$794$	4394.66			0.196424
$795$	2094.55	−	14004.2i	0.0934414	−	0.624752i
$796$	−10953.6			−0.487737
$797$			5939.37i			0.263969i	0.991252	+	0.131985i	$0.0421349\pi$
$797$			5939.37i			0.263969i	−0.991252	+	0.131985i	$0.957865\pi$
$798$			1742.41i			0.0772939i
$799$	−16240.5			−0.719082
$800$	1170.34	−	3824.96i	0.0517224	−	0.169041i
$801$	−3525.70			−0.155524
$802$		−	2630.54i		−	0.115820i
$803$			3326.87i			0.146205i
$804$	8478.81			0.371921
$805$	231.819	−	1549.95i	0.0101497	−	0.0678616i
$806$	1930.95			0.0843855
$807$		−	3373.88i		−	0.147170i
$808$		−	10273.9i		−	0.447320i
$809$	−10715.4			−0.465678			−0.232839	−	0.972515i	$-0.574802\pi$
$809$	−10715.4			−0.465678			−0.232839	+	0.972515i	$0.574802\pi$
$810$	1791.29	+	267.915i	0.0777031	+	0.0116217i
$811$	−337.734			−0.0146233			−0.00731163	−	0.999973i	$-0.502327\pi$
$811$	−337.734			−0.0146233			−0.00731163	+	0.999973i	$0.502327\pi$
$812$			2927.33i			0.126514i
$813$			7274.06i			0.313791i
$814$	−5809.33			−0.250144
$815$	15600.1	+	2333.23i	0.670487	+	0.100282i
$816$	2261.49			0.0970197
$817$			31349.1i			1.34243i
$818$			8968.27i			0.383335i
$819$	687.497			0.0293322
$820$	165.854	−	1108.91i	0.00706326	−	0.0472252i
$821$	21168.8			0.899876			0.449938	−	0.893060i	$-0.351446\pi$
$821$	21168.8			0.899876			0.449938	+	0.893060i	$0.351446\pi$
$822$		−	13166.2i		−	0.558666i
$823$		−	9764.68i		−	0.413579i	−0.978385	−	0.206789i	$-0.933698\pi$
$823$		−	9764.68i		−	0.413579i	0.978385	−	0.206789i	$-0.0663015\pi$
$824$	15806.1			0.668240
$825$	3867.97	−	12641.4i	0.163231	−	0.533477i
$826$	212.761			0.00896237
$827$			29508.6i			1.24077i	0.784299	+	0.620383i	$0.213023\pi$
$827$			29508.6i			1.24077i	−0.784299	+	0.620383i	$0.786977\pi$
$828$		−	2057.40i		−	0.0863523i
$829$	45144.8			1.89137			0.945683	−	0.325089i	$-0.105394\pi$
$829$	45144.8			1.89137			0.945683	+	0.325089i	$0.105394\pi$
$830$	−1998.49	+	13362.0i	−0.0835765	+	0.558796i
$831$	17006.5			0.709928
$832$		−	1993.24i		−	0.0830565i
$833$			15876.8i			0.660383i
$834$	4701.96			0.195223
$835$	20010.8	+	2992.93i	0.829345	+	0.124041i
$836$	16695.8			0.690713
$837$		−	837.000i		−	0.0345651i
$838$			7614.25i			0.313878i
$839$	7063.92			0.290672			0.145336	−	0.989382i	$-0.453574\pi$
$839$	7063.92			0.290672			0.145336	+	0.989382i	$0.453574\pi$
$840$	−650.897	−	97.3517i	−0.0267358	−	0.00399875i
$841$	64638.3			2.65030
$842$			6066.91i			0.248313i
$843$			9633.74i			0.393598i
$844$	−22224.1			−0.906381
$845$	2029.26	−	13567.7i	0.0826139	−	0.552360i
$846$	6204.65			0.252151
$847$		−	216.360i		−	0.00877712i
$848$			6754.70i			0.273535i
$849$	−3091.11			−0.124955
$850$	11263.2	+	3446.25i	0.454498	+	0.139065i
$851$	−4708.85			−0.189679
$852$			13324.4i			0.535781i
$853$		−	2292.91i		−	0.0920374i	−0.998941	−	0.0460187i	$-0.985347\pi$
$853$		−	2292.91i		−	0.0920374i	0.998941	−	0.0460187i	$-0.0146534\pi$
$854$	−471.939			−0.0189103
$855$	−1762.27	+	11782.6i	−0.0704895	+	0.471295i
$856$	12951.1			0.517127
$857$			17174.5i			0.684562i	0.939598	+	0.342281i	$0.111199\pi$
$857$			17174.5i			0.684562i	−0.939598	+	0.342281i	$0.888801\pi$
$858$		−	6587.62i		−	0.262118i
$859$	−4819.24			−0.191421			−0.0957103	−	0.995409i	$-0.530512\pi$
$859$	−4819.24			−0.191421			−0.0957103	+	0.995409i	$0.530512\pi$
$860$	−11710.8	−	1751.53i	−0.464344	−	0.0694498i
$861$	−184.482			−0.00730213
$862$			11138.1i			0.440099i
$863$		−	30921.9i		−	1.21969i	−0.792521	−	0.609845i	$-0.791232\pi$
$863$		−	30921.9i		−	1.21969i	0.792521	−	0.609845i	$-0.208768\pi$
$864$	−864.000			−0.0340207
$865$	43307.5	+	6477.30i	1.70231	+	0.254607i
$866$	22185.9			0.870565
$867$		−	8079.69i		−	0.316494i
$868$			304.139i			0.0118930i
$869$	−21408.0			−0.835693
$870$	−2960.70	+	19795.4i	−0.115376	+	0.771409i
$871$	22005.6			0.856062
$872$		−	16313.1i		−	0.633523i
$873$		−	9439.66i		−	0.365961i
$874$	13533.0			0.523755
$875$	−3093.38	−	1476.74i	−0.119515	−	0.0570549i
$876$	1132.45			0.0436779
$877$			1565.05i			0.0602601i	0.999546	+	0.0301301i	$0.00959215\pi$
$877$			1565.05i			0.0602601i	−0.999546	+	0.0301301i	$0.990408\pi$
$878$		−	5830.81i		−	0.224123i
$879$	2697.22			0.103498
$880$	−932.826	+	6236.91i	−0.0357336	+	0.238916i
$881$	−11050.9			−0.422605			−0.211302	−	0.977421i	$-0.567770\pi$
$881$	−11050.9			−0.422605			−0.211302	+	0.977421i	$0.567770\pi$
$882$		−	6065.71i		−	0.231568i
$883$		−	39459.8i		−	1.50388i	−0.659231	−	0.751941i	$-0.729118\pi$
$883$		−	39459.8i		−	1.50388i	0.659231	−	0.751941i	$-0.270882\pi$
$884$	5869.39			0.223313
$885$	1438.75	+	215.187i	0.0546475	+	0.00817338i
$886$	2781.04			0.105452
$887$		−	30714.7i		−	1.16268i	−0.813660	−	0.581340i	$-0.802528\pi$
$887$		−	30714.7i		−	1.16268i	0.813660	−	0.581340i	$-0.197472\pi$
$888$			1977.47i			0.0747291i
$889$	2258.70			0.0852128
$890$	8663.32	+	1295.73i	0.326287	+	0.0488012i
$891$	−2855.51			−0.107366
$892$			26023.5i			0.976831i
$893$			40812.5i			1.52938i
$894$	−1536.39			−0.0574772
$895$	−438.297	+	2930.47i	−0.0163694	+	0.109447i
$896$	313.949			0.0117057
$897$		−	5339.70i		−	0.198760i
$898$			22772.4i			0.846242i
$899$	9249.61			0.343150
$900$	−4303.08	−	1316.64i	−0.159373	−	0.0487643i
$901$	−19890.3			−0.735450
$902$			1767.71i			0.0652533i
$903$			1948.26i			0.0717986i
$904$	7167.72			0.263711
$905$	4193.43	−	28037.4i	0.154027	−	1.02983i
$906$	−21323.0			−0.781909
$907$			39300.1i			1.43874i	0.694627	+	0.719370i	$0.255569\pi$
$907$			39300.1i			1.43874i	−0.694627	+	0.719370i	$0.744431\pi$
$908$		−	6886.09i		−	0.251677i
$909$	−11558.1			−0.421737
$910$	−1689.31	−	252.662i	−0.0615386	−	0.00920404i
$911$	18582.8			0.675825			0.337912	−	0.941178i	$-0.390279\pi$
$911$	18582.8			0.675825			0.337912	+	0.941178i	$0.390279\pi$
$912$		−	5683.16i		−	0.206347i
$913$		−	21300.4i		−	0.772114i
$914$	36424.9			1.31819
$915$	−3191.38	−	477.320i	−0.115305	−	0.0172456i
$916$	8299.83			0.299382
$917$		−	6407.30i		−	0.230739i
$918$		−	2544.18i		−	0.0914711i
$919$	38456.3			1.38037			0.690183	−	0.723635i	$-0.257530\pi$
$919$	38456.3			1.38037			0.690183	+	0.723635i	$0.257530\pi$
$920$	−756.117	+	5055.43i	−0.0270961	+	0.181166i
$921$	21809.3			0.780284
$922$			17948.6i			0.641113i
$923$			34581.5i			1.23322i
$924$	1037.60			0.0369421
$925$	−3013.43	+	9848.60i	−0.107115	+	0.350075i
$926$	−21940.2			−0.778618
$927$		−	17781.8i		−	0.630023i
$928$		−	9547.98i		−	0.337745i
$929$	13511.1			0.477164			0.238582	−	0.971122i	$-0.423317\pi$
$929$	13511.1			0.477164			0.238582	+	0.971122i	$0.423317\pi$
$930$	−307.606	+	2056.67i	−0.0108460	+	0.0725169i
$931$	39898.6			1.40454
$932$		−	16940.0i		−	0.595375i
$933$			10421.1i			0.365672i
$934$	−9442.14			−0.330788
$935$	−18365.5	−	2746.85i	−0.642371	−	0.0960766i
$936$	−2242.39			−0.0783064
$937$		−	7816.72i		−	0.272531i	−0.990672	−	0.136265i	$-0.956490\pi$
$937$		−	7816.72i		−	0.272531i	0.990672	−	0.136265i	$-0.0435100\pi$
$938$			3466.04i			0.120651i
$939$	10403.8			0.361569
$940$	−15246.0	−	2280.27i	−0.529010	−	0.0791216i
$941$	−32868.5			−1.13866			−0.569332	−	0.822108i	$-0.692798\pi$
$941$	−32868.5			−1.13866			−0.569332	+	0.822108i	$0.692798\pi$
$942$			2072.40i			0.0716799i
$943$			1432.85i			0.0494803i
$944$	−693.958			−0.0239263
$945$	−109.521	+	732.259i	−0.00377006	+	0.0252067i
$946$	18668.3			0.641606
$947$		−	2257.77i		−	0.0774739i	−0.999249	−	0.0387370i	$-0.987667\pi$
$947$		−	2257.77i		−	0.0774739i	0.999249	−	0.0387370i	$-0.0123334\pi$
$948$			7287.18i			0.249659i
$949$	2939.11			0.100535
$950$	8660.48	−	28304.5i	0.295772	−	0.966651i
$951$	5088.81			0.173518
$952$			924.472i			0.0314730i
$953$		−	8811.68i		−	0.299516i	−0.988723	−	0.149758i	$-0.952151\pi$
$953$		−	8811.68i		−	0.299516i	0.988723	−	0.149758i	$-0.0478494\pi$
$954$	7599.04			0.257891
$955$	−1048.98	+	7013.54i	−0.0355438	+	0.237647i
$956$	24426.4			0.826368
$957$		−	31556.0i		−	1.06589i
$958$		−	37818.5i		−	1.27543i
$959$	5382.18			0.181230
$960$	2123.01	+	317.529i	0.0713749	+	0.0106752i
$961$	961.000			0.0322581
$962$			5132.23i			0.172006i
$963$		−	14570.0i		−	0.487552i
$964$	12034.9			0.402095
$965$	54529.1	+	8155.67i	1.81902	+	0.272062i
$966$	841.042			0.0280125
$967$			12449.8i			0.414020i	0.978339	+	0.207010i	$0.0663733\pi$
$967$			12449.8i			0.414020i	−0.978339	+	0.207010i	$0.933627\pi$
$968$			705.696i			0.0234317i
$969$	16734.9			0.554802
$970$	−3469.18	+	23195.0i	−0.114834	+	0.767781i
$971$	−38799.1			−1.28231			−0.641154	−	0.767412i	$-0.721544\pi$
$971$	−38799.1			−1.28231			−0.641154	+	0.767412i	$0.721544\pi$
$972$			972.000i			0.0320750i
$973$			1922.11i			0.0633298i
$974$	−11856.5			−0.390049
$975$	−11168.0	−	3417.14i	−0.366834	−	0.112242i
$976$	1539.31			0.0504837
$977$		−	51815.4i		−	1.69675i	−0.529399	−	0.848373i	$-0.677583\pi$
$977$		−	51815.4i		−	1.69675i	0.529399	−	0.848373i	$-0.322417\pi$
$978$			8465.00i			0.276770i
$979$	−13810.3			−0.450845
$980$	−2229.21	+	14904.6i	−0.0726629	+	0.485827i
$981$	−18352.3			−0.597291
$982$		−	33047.8i		−	1.07393i
$983$			25874.4i			0.839537i	0.907631	+	0.419768i	$0.137889\pi$
$983$			25874.4i			0.839537i	−0.907631	+	0.419768i	$0.862111\pi$
$984$	601.720			0.0194940
$985$	−54078.8	−	8088.32i	−1.74933	−	0.261640i
$986$	28115.5			0.908093
$987$			2536.39i			0.0817975i
$988$		−	14749.8i		−	0.474954i
$989$	15131.9			0.486518
$990$	7016.52	+	1049.43i	0.225252	+	0.0336900i
$991$	−56846.5			−1.82219			−0.911094	−	0.412199i	$-0.864761\pi$
$991$	−56846.5			−1.82219			−0.911094	+	0.412199i	$0.864761\pi$
$992$		−	992.000i		−	0.0317500i
$993$		−	17959.9i		−	0.573957i
$994$	−5446.85			−0.173806
$995$	4528.74	−	30279.3i	0.144292	−	0.964743i
$996$	−7250.54			−0.230665
$997$			24864.9i			0.789848i	0.918714	+	0.394924i	$0.129229\pi$
$997$			24864.9i			0.789848i	−0.918714	+	0.394924i	$0.870771\pi$
$998$			1749.38i			0.0554865i
$999$	2224.65			0.0704552

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.4.d.c.559.15	yes	20
5.4	even	2	inner	930.4.d.c.559.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.4.d.c.559.5	✓	20	5.4	even	2	inner
930.4.d.c.559.15	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	930.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(1.65380 - 11.0573i) q^{5} +6.00000 q^{6} +2.45273i q^{7} -8.00000i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(1.65380 - 11.0573i) q^{5} +6.00000 q^{6} +2.45273i q^{7} -8.00000i q^{8} -9.00000 q^{9} +(22.1147 + 3.30759i) q^{10} -35.2532 q^{11} +12.0000i q^{12} +31.1443i q^{13} -4.90546 q^{14} +(-33.1720 - 4.96139i) q^{15} +16.0000 q^{16} +47.1144i q^{17} -18.0000i q^{18} +118.399 q^{19} +(-6.61519 + 44.2294i) q^{20} +7.35819 q^{21} -70.5064i q^{22} -57.1501i q^{23} -24.0000 q^{24} +(-119.530 - 36.5732i) q^{25} -62.2886 q^{26} +27.0000i q^{27} -9.81092i q^{28} -298.374 q^{29} +(9.92278 - 66.3441i) q^{30} -31.0000 q^{31} +32.0000i q^{32} +105.760i q^{33} -94.2289 q^{34} +(27.1207 + 4.05632i) q^{35} +36.0000 q^{36} -82.3944i q^{37} +236.798i q^{38} +93.4329 q^{39} +(-88.4588 - 13.2304i) q^{40} -25.0717 q^{41} +14.7164i q^{42} +264.775i q^{43} +141.013 q^{44} +(-14.8842 + 99.5161i) q^{45} +114.300 q^{46} +344.703i q^{47} -48.0000i q^{48} +336.984 q^{49} +(73.1465 - 239.060i) q^{50} +141.343 q^{51} -124.577i q^{52} +422.169i q^{53} -54.0000 q^{54} +(-58.3016 + 389.807i) q^{55} +19.6218 q^{56} -355.198i q^{57} -596.749i q^{58} -43.3724 q^{59} +(132.688 + 19.8456i) q^{60} +96.2068 q^{61} -62.0000i q^{62} -22.0746i q^{63} -64.0000 q^{64} +(344.373 + 51.5064i) q^{65} -211.519 q^{66} -706.568i q^{67} -188.458i q^{68} -171.450 q^{69} +(-8.11264 + 54.2414i) q^{70} +1110.36 q^{71} +72.0000i q^{72} -94.3706i q^{73} +164.789 q^{74} +(-109.720 + 358.590i) q^{75} -473.597 q^{76} -86.4666i q^{77} +186.866i q^{78} +607.265 q^{79} +(26.4608 - 176.918i) q^{80} +81.0000 q^{81} -50.1434i q^{82} +604.212i q^{83} -29.4328 q^{84} +(520.961 + 77.9177i) q^{85} -529.549 q^{86} +895.123i q^{87} +282.026i q^{88} +391.745 q^{89} +(-199.032 - 29.7684i) q^{90} -76.3886 q^{91} +228.600i q^{92} +93.0000i q^{93} -689.405 q^{94} +(195.808 - 1309.18i) q^{95} +96.0000 q^{96} +1048.85i q^{97} +673.968i q^{98} +317.279 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 80 q^{4} - 2 q^{5} + 120 q^{6} - 180 q^{9}+O(q^{10}) \) 20 * q - 80 * q^4 - 2 * q^5 + 120 * q^6 - 180 * q^9	\( 20 q - 80 q^{4} - 2 q^{5} + 120 q^{6} - 180 q^{9} + 8 q^{10} - 114 q^{11} + 52 q^{14} - 12 q^{15} + 320 q^{16} + 370 q^{19} + 8 q^{20} - 78 q^{21} - 480 q^{24} - 90 q^{25} - 368 q^{26} + 368 q^{29} - 12 q^{30} - 620 q^{31} + 712 q^{34} + 374 q^{35} + 720 q^{36} + 552 q^{39} - 32 q^{40} - 872 q^{41} + 456 q^{44} + 18 q^{45} - 1236 q^{46} + 1334 q^{49} + 416 q^{50} - 1068 q^{51} - 1080 q^{54} - 1290 q^{55} - 208 q^{56} + 3228 q^{59} + 48 q^{60} - 2604 q^{61} - 1280 q^{64} + 44 q^{65} - 684 q^{66} + 1854 q^{69} - 852 q^{70} - 2290 q^{71} + 2008 q^{74} - 624 q^{75} - 1480 q^{76} + 4342 q^{79} - 32 q^{80} + 1620 q^{81} + 312 q^{84} + 500 q^{85} - 4 q^{86} + 1390 q^{89} - 72 q^{90} - 5744 q^{91} + 2608 q^{94} - 1136 q^{95} + 1920 q^{96} + 1026 q^{99}+O(q^{100}) \) 20 * q - 80 * q^4 - 2 * q^5 + 120 * q^6 - 180 * q^9 + 8 * q^10 - 114 * q^11 + 52 * q^14 - 12 * q^15 + 320 * q^16 + 370 * q^19 + 8 * q^20 - 78 * q^21 - 480 * q^24 - 90 * q^25 - 368 * q^26 + 368 * q^29 - 12 * q^30 - 620 * q^31 + 712 * q^34 + 374 * q^35 + 720 * q^36 + 552 * q^39 - 32 * q^40 - 872 * q^41 + 456 * q^44 + 18 * q^45 - 1236 * q^46 + 1334 * q^49 + 416 * q^50 - 1068 * q^51 - 1080 * q^54 - 1290 * q^55 - 208 * q^56 + 3228 * q^59 + 48 * q^60 - 2604 * q^61 - 1280 * q^64 + 44 * q^65 - 684 * q^66 + 1854 * q^69 - 852 * q^70 - 2290 * q^71 + 2008 * q^74 - 624 * q^75 - 1480 * q^76 + 4342 * q^79 - 32 * q^80 + 1620 * q^81 + 312 * q^84 + 500 * q^85 - 4 * q^86 + 1390 * q^89 - 72 * q^90 - 5744 * q^91 + 2608 * q^94 - 1136 * q^95 + 1920 * q^96 + 1026 * q^99

Introduction

L-functions

Modular forms

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Database

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