LMFDB - Embedded newform 930.4.d.c.559.5

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

$q$-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	$-0.978907\pi$
$7$		−	2.45273i		−	0.132435i	0.997805	−	0.0662175i	$-0.0210931\pi$
$8$			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	$-0.892200\pi$
$13$		−	31.1443i		−	0.664452i	0.943200	−	0.332226i	$-0.107800\pi$
$14$	−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	$-0.890897\pi$
$17$		−	47.1144i		−	0.672172i	0.941831	−	0.336086i	$-0.109103\pi$
$18$			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	$0.0834117\pi$
$23$			57.1501i			0.518114i	−0.965862	+	0.259057i	$0.916588\pi$
$24$	−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	$0.0585964\pi$
$37$			82.3944i			0.366096i	−0.983104	+	0.183048i	$0.941404\pi$
$38$		−	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	$-0.844431\pi$
$43$		−	264.775i		−	0.939018i	0.882928	−	0.469509i	$-0.155569\pi$
$44$	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	$-0.820352\pi$
$47$		−	344.703i		−	1.06979i	0.844919	−	0.534894i	$-0.179648\pi$
$48$			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	$-0.815743\pi$
$53$		−	422.169i		−	1.09414i	0.837087	−	0.547069i	$-0.184257\pi$
$54$	−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	$0.222804\pi$
$67$			706.568i			1.28837i	−0.764868	+	0.644186i	$0.777196\pi$
$68$			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	$0.0241039\pi$
$73$			94.3706i			0.151305i	−0.997134	+	0.0756524i	$0.975896\pi$
$74$	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	$-0.869176\pi$
$83$		−	604.212i		−	0.799047i	0.916723	−	0.399523i	$-0.130824\pi$
$84$	−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	$-0.815031\pi$
$97$		−	1048.85i		−	1.09788i	0.835861	−	0.548942i	$-0.184969\pi$
$98$		−	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	$-0.606028\pi$
$103$		−	1975.76i		−	1.89007i	0.326970	−	0.945035i	$-0.393972\pi$
$104$	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	$-0.738901\pi$
$107$		−	1618.89i		−	1.46266i	0.682026	−	0.731328i	$-0.261099\pi$
$108$			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	$-0.878348\pi$
$113$		−	895.966i		−	0.745888i	0.927854	−	0.372944i	$-0.121652\pi$
$114$	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	$0.104260\pi$
$127$			920.890i			0.643431i	−0.946836	+	0.321716i	$0.895740\pi$
$128$			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	$0.239859\pi$
$137$			2194.36i			1.36845i	−0.729273	+	0.684223i	$0.760141\pi$
$138$			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	$-0.972020\pi$
$157$		−	345.400i		−	0.175579i	0.996139	−	0.0877896i	$-0.0279803\pi$
$158$		−	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	$-0.889921\pi$
$163$		−	1410.83i		−	0.677945i	0.940796	−	0.338972i	$-0.110079\pi$
$164$	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	$-0.862281\pi$
$167$		−	1809.73i		−	0.838569i	0.907855	−	0.419285i	$-0.137719\pi$
$168$			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	$-0.670075\pi$
$173$		−	3916.63i		−	1.72125i	0.509243	−	0.860623i	$-0.329925\pi$
$174$	−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	$-0.628492\pi$
$193$		−	4931.48i		−	1.83925i	0.392796	−	0.919626i	$-0.371508\pi$
$194$	−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	$0.345430\pi$
$197$			4890.76i			1.76879i	−0.466737	+	0.884396i	$0.654570\pi$
$198$		−	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	$0.431346\pi$
$223$			6505.89i			1.95366i	−0.214014	+	0.976831i	$0.568654\pi$
$224$	−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	$-0.919018\pi$
$227$		−	1721.52i		−	0.503354i	0.967811	−	0.251677i	$-0.0809821\pi$
$228$		−	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	$-0.797003\pi$
$233$		−	4235.01i		−	1.19075i	0.803448	−	0.595375i	$-0.202997\pi$
$234$	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	$0.199269\pi$
$257$			4828.05i			1.17185i	−0.810365	+	0.585925i	$0.800731\pi$
$258$		−	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	$0.192658\pi$
$263$			4853.47i			1.13794i	−0.822359	+	0.568970i	$0.807342\pi$
$264$	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	$-0.789230\pi$
$277$		−	5668.85i		−	1.22963i	0.788671	−	0.614816i	$-0.210770\pi$
$278$		−	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	$0.0345132\pi$
$283$			1030.37i			0.216428i	−0.994128	+	0.108214i	$0.965487\pi$
$284$	−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	$-0.971431\pi$
$293$		−	899.072i		−	0.179264i	0.995975	−	0.0896320i	$-0.0285691\pi$
$294$	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	$-0.763822\pi$
$307$		−	7269.78i		−	1.35149i	0.737135	−	0.675746i	$-0.236178\pi$
$308$		−	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	$-0.898623\pi$
$313$		−	3467.92i		−	0.626257i	0.949711	−	0.313128i	$-0.101377\pi$
$314$	−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	$-0.951985\pi$
$317$		−	1696.27i		−	0.300542i	0.988645	−	0.150271i	$-0.0480147\pi$
$318$		−	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	$0.0716608\pi$
$337$			2762.05i			0.446464i	−0.974765	+	0.223232i	$0.928339\pi$
$338$		−	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	$0.00858763\pi$
$347$			348.734i			0.0539511i	−0.999636	+	0.0269756i	$0.991412\pi$
$348$			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	$0.207126\pi$
$353$			8034.97i			1.21150i	−0.795656	+	0.605749i	$0.792874\pi$
$354$	−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	$-0.880898\pi$
$367$		−	5139.43i		−	0.730997i	0.930812	−	0.365499i	$-0.119102\pi$
$368$			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	$-0.980195\pi$
$373$		−	895.837i		−	0.124356i	0.998065	−	0.0621779i	$-0.0198046\pi$
$374$	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	$-0.839178\pi$
$383$		−	7255.84i		−	0.968032i	0.875059	−	0.484016i	$-0.160822\pi$
$384$	−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	$0.0443544\pi$
$397$			2197.33i			0.277786i	−0.990307	+	0.138893i	$0.955646\pi$
$398$		−	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	$0.211079\pi$
$433$			11093.0i			1.23116i	−0.788073	+	0.615582i	$0.788921\pi$
$434$	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	$0.0237572\pi$
$443$			1390.52i			0.149132i	−0.997216	+	0.0745661i	$0.976243\pi$
$444$	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	$0.382029\pi$
$457$			18212.5i			1.86421i	−0.362191	+	0.932104i	$0.617971\pi$
$458$			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	$-0.814412\pi$
$463$		−	10970.1i		−	1.10113i	0.834792	−	0.550566i	$-0.185588\pi$
$464$	−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	$-0.924850\pi$
$467$		−	4721.07i		−	0.467805i	0.972260	−	0.233903i	$-0.0751497\pi$
$468$		−	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	$-0.911055\pi$
$487$		−	5928.26i		−	0.551612i	0.961213	−	0.275806i	$-0.0889448\pi$
$488$			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	$0.237014\pi$
$503$			15289.9i			1.35536i	−0.735359	+	0.677678i	$0.762986\pi$
$504$	−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	$-0.891592\pi$
$523$		−	7990.31i		−	0.668053i	0.942564	−	0.334027i	$-0.108408\pi$
$524$	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	$0.122822\pi$
$547$			9629.59i			0.752708i	−0.926476	+	0.376354i	$0.877178\pi$
$548$		−	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	$-0.671719\pi$
$557$		−	22557.4i		−	1.71596i	0.513684	−	0.857980i	$-0.328281\pi$
$558$		−	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	$-0.738314\pi$
$563$		−	19572.7i		−	1.46517i	0.680677	−	0.732584i	$-0.261686\pi$
$564$	−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	$-0.653929\pi$
$577$		−	24541.5i		−	1.77067i	0.464955	−	0.885335i	$-0.346071\pi$
$578$		−	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	$0.120134\pi$
$587$			10482.0i			0.737030i	−0.929622	+	0.368515i	$0.879866\pi$
$588$		−	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	$-0.826118\pi$
$593$		−	15003.7i		−	1.03900i	0.854469	−	0.519502i	$-0.173882\pi$
$594$	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	$-0.939386\pi$
$607$		−	5661.21i		−	0.378553i	0.981924	−	0.189276i	$-0.0606142\pi$
$608$		−	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	$-0.916954\pi$
$613$		−	7829.80i		−	0.515893i	0.966159	−	0.257947i	$-0.0830459\pi$
$614$	−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	$0.126258\pi$
$617$			11841.8i			0.772662i	−0.922360	+	0.386331i	$0.873742\pi$
$618$		−	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	$-0.854956\pi$
$643$		−	14350.3i		−	0.880125i	0.897967	−	0.440063i	$-0.145044\pi$
$644$	−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	$0.0948787\pi$
$647$			9666.18i			0.587352i	−0.955905	+	0.293676i	$0.905121\pi$
$648$			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	$0.0300597\pi$
$653$			3146.94i			0.188590i	−0.995544	+	0.0942950i	$0.969940\pi$
$654$	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	$0.0717847\pi$
$673$			7808.13i			0.447223i	−0.974678	+	0.223612i	$0.928215\pi$
$674$	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	$-0.787698\pi$
$677$		−	21793.5i		−	1.23721i	0.785702	−	0.618606i	$-0.212302\pi$
$678$		−	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	$-0.963658\pi$
$683$		−	4067.07i		−	0.227851i	0.993489	−	0.113925i	$-0.0363425\pi$
$684$	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	$-0.769060\pi$
$727$		−	26012.9i		−	1.32705i	0.748155	−	0.663524i	$-0.230940\pi$
$728$		−	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	$0.128949\pi$
$733$			15642.6i			0.788229i	−0.919061	+	0.394115i	$0.871051\pi$
$734$	−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	$0.169505\pi$
$743$			20564.7i			1.01540i	−0.861533	+	0.507702i	$0.830495\pi$
$744$	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	$-0.872340\pi$
$757$		−	16261.9i		−	0.780780i	0.920650	−	0.390390i	$-0.127660\pi$
$758$			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	$0.176754\pi$
$773$			22660.3i			1.05438i	−0.849747	+	0.527190i	$0.823246\pi$
$774$	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	$-0.783166\pi$
$787$		−	27806.5i		−	1.25946i	0.776814	−	0.629730i	$-0.216834\pi$
$788$		−	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	$-0.957865\pi$
$797$		−	5939.37i		−	0.263969i	0.991252	−	0.131985i	$-0.0421349\pi$
$798$		−	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	$0.0663015\pi$
$823$			9764.68i			0.413579i	−0.978385	+	0.206789i	$0.933698\pi$
$824$	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	$-0.786977\pi$
$827$		−	29508.6i		−	1.24077i	0.784299	−	0.620383i	$-0.213023\pi$
$828$			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	$0.0146534\pi$
$853$			2292.91i			0.0920374i	−0.998941	+	0.0460187i	$0.985347\pi$
$854$	−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	$-0.888801\pi$
$857$		−	17174.5i		−	0.684562i	0.939598	−	0.342281i	$-0.111199\pi$
$858$			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	$0.208768\pi$
$863$			30921.9i			1.21969i	−0.792521	+	0.609845i	$0.791232\pi$
$864$	−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	$-0.990408\pi$
$877$		−	1565.05i		−	0.0602601i	0.999546	−	0.0301301i	$-0.00959215\pi$
$878$			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	$0.270882\pi$
$883$			39459.8i			1.50388i	−0.659231	+	0.751941i	$0.729118\pi$
$884$	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	$0.197472\pi$
$887$			30714.7i			1.16268i	−0.813660	+	0.581340i	$0.802528\pi$
$888$		−	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	$-0.744431\pi$
$907$		−	39300.1i		−	1.43874i	0.694627	−	0.719370i	$-0.255569\pi$
$908$			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	$0.0435100\pi$
$937$			7816.72i			0.272531i	−0.990672	+	0.136265i	$0.956490\pi$
$938$		−	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	$0.0123334\pi$
$947$			2257.77i			0.0774739i	−0.999249	+	0.0387370i	$0.987667\pi$
$948$		−	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	$0.0478494\pi$
$953$			8811.68i			0.299516i	−0.988723	+	0.149758i	$0.952151\pi$
$954$	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	$-0.933627\pi$
$967$		−	12449.8i		−	0.414020i	0.978339	−	0.207010i	$-0.0663733\pi$
$968$		−	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	$0.322417\pi$
$977$			51815.4i			1.69675i	−0.529399	+	0.848373i	$0.677583\pi$
$978$		−	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	$-0.862111\pi$
$983$		−	25874.4i		−	0.839537i	0.907631	−	0.419768i	$-0.137889\pi$
$984$	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	$-0.870771\pi$
$997$		−	24864.9i		−	0.789848i	0.918714	−	0.394924i	$-0.129229\pi$
$998$		−	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.559.5	✓	20
5.4	even	2	inner	930.4.d.c.559.15	yes	20

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

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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