LMFDB - Embedded newform 930.4.d.c.559.13

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			559.13
Root			$-7.62904i$ of defining polynomial
Character	$\chi$	$=$	930.559
Dual form			930.4.d.c.559.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(-7.42511 - 8.35869i) q^{5} +6.00000 q^{6} -7.62904i q^{7} -8.00000i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(-7.42511 - 8.35869i) q^{5} +6.00000 q^{6} -7.62904i q^{7} -8.00000i q^{8} -9.00000 q^{9} +(16.7174 - 14.8502i) q^{10} -39.0265 q^{11} +12.0000i q^{12} -55.9453i q^{13} +15.2581 q^{14} +(-25.0761 + 22.2753i) q^{15} +16.0000 q^{16} -80.2033i q^{17} -18.0000i q^{18} -72.3004 q^{19} +(29.7005 + 33.4348i) q^{20} -22.8871 q^{21} -78.0530i q^{22} -51.5005i q^{23} -24.0000 q^{24} +(-14.7354 + 124.128i) q^{25} +111.891 q^{26} +27.0000i q^{27} +30.5162i q^{28} +59.4680 q^{29} +(-44.5507 - 50.1521i) q^{30} -31.0000 q^{31} +32.0000i q^{32} +117.080i q^{33} +160.407 q^{34} +(-63.7688 + 56.6465i) q^{35} +36.0000 q^{36} +12.6161i q^{37} -144.601i q^{38} -167.836 q^{39} +(-66.8695 + 59.4009i) q^{40} -255.807 q^{41} -45.7742i q^{42} -62.3700i q^{43} +156.106 q^{44} +(66.8260 + 75.2282i) q^{45} +103.001 q^{46} -625.858i q^{47} -48.0000i q^{48} +284.798 q^{49} +(-248.257 - 29.4708i) q^{50} -240.610 q^{51} +223.781i q^{52} +253.941i q^{53} -54.0000 q^{54} +(289.776 + 326.211i) q^{55} -61.0323 q^{56} +216.901i q^{57} +118.936i q^{58} +286.606 q^{59} +(100.304 - 89.1014i) q^{60} +297.628 q^{61} -62.0000i q^{62} +68.6613i q^{63} -64.0000 q^{64} +(-467.629 + 415.400i) q^{65} -234.159 q^{66} +342.744i q^{67} +320.813i q^{68} -154.501 q^{69} +(-113.293 - 127.538i) q^{70} +399.392 q^{71} +72.0000i q^{72} +612.749i q^{73} -25.2323 q^{74} +(372.385 + 44.2062i) q^{75} +289.202 q^{76} +297.735i q^{77} -335.672i q^{78} -623.797 q^{79} +(-118.802 - 133.739i) q^{80} +81.0000 q^{81} -511.613i q^{82} +440.871i q^{83} +91.5485 q^{84} +(-670.394 + 595.518i) q^{85} +124.740 q^{86} -178.404i q^{87} +312.212i q^{88} -409.354 q^{89} +(-150.456 + 133.652i) q^{90} -426.808 q^{91} +206.002i q^{92} +93.0000i q^{93} +1251.72 q^{94} +(536.839 + 604.337i) q^{95} +96.0000 q^{96} +819.010i q^{97} +569.596i q^{98} +351.239 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−7.42511	−	8.35869i	−0.664122	−	0.747624i
$5$	−7.42511	−	8.35869i	−0.664122	−	0.747624i
$6$	6.00000			0.408248
$7$		−	7.62904i		−	0.411929i	−0.978559	−	0.205965i	$-0.933967\pi$
$7$		−	7.62904i		−	0.411929i	0.978559	−	0.205965i	$-0.0660332\pi$
$8$		−	8.00000i		−	0.353553i
$9$	−9.00000			−0.333333
$10$	16.7174	−	14.8502i	0.528650	−	0.469605i
$11$	−39.0265			−1.06972			−0.534861	−	0.844940i	$-0.679636\pi$
$11$	−39.0265			−1.06972			−0.534861	+	0.844940i	$0.679636\pi$
$12$			12.0000i			0.288675i
$13$		−	55.9453i		−	1.19357i	−0.802401	−	0.596785i	$-0.796444\pi$
$13$		−	55.9453i		−	1.19357i	0.802401	−	0.596785i	$-0.203556\pi$
$14$	15.2581			0.291278
$15$	−25.0761	+	22.2753i	−0.431641	+	0.383431i
$16$	16.0000			0.250000
$17$		−	80.2033i		−	1.14424i	−0.820168	−	0.572122i	$-0.806120\pi$
$17$		−	80.2033i		−	1.14424i	0.820168	−	0.572122i	$-0.193880\pi$
$18$		−	18.0000i		−	0.235702i
$19$	−72.3004			−0.872993			−0.436496	−	0.899706i	$-0.643781\pi$
$19$	−72.3004			−0.872993			−0.436496	+	0.899706i	$0.643781\pi$
$20$	29.7005	+	33.4348i	0.332061	+	0.373812i
$21$	−22.8871			−0.237828
$22$		−	78.0530i		−	0.756407i
$23$		−	51.5005i		−	0.466895i	−0.972369	−	0.233448i	$-0.924999\pi$
$23$		−	51.5005i		−	0.466895i	0.972369	−	0.233448i	$-0.0750007\pi$
$24$	−24.0000			−0.204124
$25$	−14.7354	+	124.128i	−0.117883	+	0.993027i
$26$	111.891			0.843982
$27$			27.0000i			0.192450i
$28$			30.5162i			0.205965i
$29$	59.4680			0.380790			0.190395	−	0.981708i	$-0.439023\pi$
$29$	59.4680			0.380790			0.190395	+	0.981708i	$0.439023\pi$
$30$	−44.5507	−	50.1521i	−0.271127	−	0.305216i
$31$	−31.0000			−0.179605
$31$	−31.0000			−0.179605
$32$			32.0000i			0.176777i
$33$			117.080i			0.617604i
$34$	160.407			0.809103
$35$	−63.7688	+	56.6465i	−0.307968	+	0.273571i
$36$	36.0000			0.166667
$37$			12.6161i			0.0560562i	0.999607	+	0.0280281i	$0.00892280\pi$
$37$			12.6161i			0.0560562i	−0.999607	+	0.0280281i	$0.991077\pi$
$38$		−	144.601i		−	0.617299i
$39$	−167.836			−0.689109
$40$	−66.8695	+	59.4009i	−0.264325	+	0.234803i
$41$	−255.807			−0.974397			−0.487199	−	0.873291i	$-0.661981\pi$
$41$	−255.807			−0.974397			−0.487199	+	0.873291i	$0.661981\pi$
$42$		−	45.7742i		−	0.168169i
$43$		−	62.3700i		−	0.221194i	−0.993865	−	0.110597i	$-0.964724\pi$
$43$		−	62.3700i		−	0.221194i	0.993865	−	0.110597i	$-0.0352763\pi$
$44$	156.106			0.534861
$45$	66.8260	+	75.2282i	0.221374	+	0.249208i
$46$	103.001			0.330145
$47$		−	625.858i		−	1.94236i	−0.238353	−	0.971178i	$-0.576608\pi$
$47$		−	625.858i		−	1.94236i	0.238353	−	0.971178i	$-0.423392\pi$
$48$		−	48.0000i		−	0.144338i
$49$	284.798			0.830314
$50$	−248.257	−	29.4708i	−0.702176	−	0.0833560i
$51$	−240.610			−0.660630
$52$			223.781i			0.596785i
$53$			253.941i			0.658141i	0.944305	+	0.329071i	$0.106735\pi$
$53$			253.941i			0.658141i	−0.944305	+	0.329071i	$0.893265\pi$
$54$	−54.0000			−0.136083
$55$	289.776	+	326.211i	0.710426	+	0.799749i
$56$	−61.0323			−0.145639
$57$			216.901i			0.504023i
$58$			118.936i			0.269259i
$59$	286.606			0.632422			0.316211	−	0.948689i	$-0.397589\pi$
$59$	286.606			0.632422			0.316211	+	0.948689i	$0.397589\pi$
$60$	100.304	−	89.1014i	0.215820	−	0.191716i
$61$	297.628			0.624711			0.312355	−	0.949965i	$-0.398882\pi$
$61$	297.628			0.624711			0.312355	+	0.949965i	$0.398882\pi$
$62$		−	62.0000i		−	0.127000i
$63$			68.6613i			0.137310i
$64$	−64.0000			−0.125000
$65$	−467.629	+	415.400i	−0.892342	+	0.792677i
$66$	−234.159			−0.436712
$67$			342.744i			0.624968i	0.949923	+	0.312484i	$0.101161\pi$
$67$			342.744i			0.624968i	−0.949923	+	0.312484i	$0.898839\pi$
$68$			320.813i			0.572122i
$69$	−154.501			−0.269562
$70$	−113.293	−	127.538i	−0.193444	−	0.217766i
$71$	399.392			0.667594			0.333797	−	0.942645i	$-0.391670\pi$
$71$	399.392			0.667594			0.333797	+	0.942645i	$0.391670\pi$
$72$			72.0000i			0.117851i
$73$			612.749i			0.982423i	0.871040	+	0.491212i	$0.163446\pi$
$73$			612.749i			0.982423i	−0.871040	+	0.491212i	$0.836554\pi$
$74$	−25.2323			−0.0396377
$75$	372.385	+	44.2062i	0.573325	+	0.0680599i
$76$	289.202			0.436496
$77$			297.735i			0.440650i
$78$		−	335.672i		−	0.487273i
$79$	−623.797			−0.888388			−0.444194	−	0.895931i	$-0.646510\pi$
$79$	−623.797			−0.888388			−0.444194	+	0.895931i	$0.646510\pi$
$80$	−118.802	−	133.739i	−0.166031	−	0.186906i
$81$	81.0000			0.111111
$82$		−	511.613i		−	0.689003i
$83$			440.871i			0.583035i	0.956566	+	0.291517i	$0.0941601\pi$
$83$			440.871i			0.583035i	−0.956566	+	0.291517i	$0.905840\pi$
$84$	91.5485			0.118914
$85$	−670.394	+	595.518i	−0.855464	+	0.759918i
$86$	124.740			0.156408
$87$		−	178.404i		−	0.219849i
$88$			312.212i			0.378204i
$89$	−409.354			−0.487544			−0.243772	−	0.969833i	$-0.578385\pi$
$89$	−409.354			−0.487544			−0.243772	+	0.969833i	$0.578385\pi$
$90$	−150.456	+	133.652i	−0.176217	+	0.156535i
$91$	−426.808			−0.491667
$92$			206.002i			0.233448i
$93$			93.0000i			0.103695i
$94$	1251.72			1.37345
$95$	536.839	+	604.337i	0.579774	+	0.652670i
$96$	96.0000			0.102062
$97$			819.010i			0.857297i	0.903471	+	0.428649i	$0.141010\pi$
$97$			819.010i			0.857297i	−0.903471	+	0.428649i	$0.858990\pi$
$98$			569.596i			0.587121i
$99$	351.239			0.356574
$100$	58.9416	−	496.514i	0.0589416	−	0.496514i
$101$	−249.274			−0.245581			−0.122791	−	0.992433i	$-0.539184\pi$
$101$	−249.274			−0.245581			−0.122791	+	0.992433i	$0.539184\pi$
$102$		−	481.220i		−	0.467136i
$103$		−	235.603i		−	0.225385i	−0.993630	−	0.112692i	$-0.964053\pi$
$103$		−	235.603i		−	0.225385i	0.993630	−	0.112692i	$-0.0359474\pi$
$104$	−447.562			−0.421991
$105$	169.939	+	191.306i	0.157947	+	0.177806i
$106$	−507.882			−0.465376
$107$			271.989i			0.245739i	0.992423	+	0.122870i	$0.0392097\pi$
$107$			271.989i			0.245739i	−0.992423	+	0.122870i	$0.960790\pi$
$108$		−	108.000i		−	0.0962250i
$109$	−1261.72			−1.10872			−0.554361	−	0.832276i	$-0.687037\pi$
$109$	−1261.72			−1.10872			−0.554361	+	0.832276i	$0.687037\pi$
$110$	−652.421	+	579.553i	−0.565508	+	0.502347i
$111$	37.8484			0.0323641
$112$		−	122.065i		−	0.102982i
$113$			1771.25i			1.47456i	0.675589	+	0.737278i	$0.263889\pi$
$113$			1771.25i			1.47456i	−0.675589	+	0.737278i	$0.736111\pi$
$114$	−433.803			−0.356398
$115$	−430.477	+	382.397i	−0.349062	+	0.310076i
$116$	−237.872			−0.190395
$117$			503.507i			0.397857i
$118$			573.212i			0.447190i
$119$	−611.874			−0.471348
$120$	178.203	+	200.609i	0.135563	+	0.152608i
$121$	192.069			0.144304
$122$			595.256i			0.441737i
$123$			767.420i			0.562569i
$124$	124.000			0.0898027
$125$	1146.96	−	798.499i	0.820700	−	0.571359i
$126$	−137.323			−0.0970927
$127$			591.432i			0.413237i	0.978422	+	0.206619i	$0.0662459\pi$
$127$			591.432i			0.413237i	−0.978422	+	0.206619i	$0.933754\pi$
$128$		−	128.000i		−	0.0883883i
$129$	−187.110			−0.127706
$130$	−830.800	−	935.258i	−0.560507	−	0.630981i
$131$	−1453.04			−0.969101			−0.484551	−	0.874763i	$-0.661017\pi$
$131$	−1453.04			−0.969101			−0.484551	+	0.874763i	$0.661017\pi$
$132$		−	468.318i		−	0.308802i
$133$			551.583i			0.359611i
$134$	−685.488			−0.441919
$135$	225.685	−	200.478i	0.143880	−	0.127810i
$136$	−641.626			−0.404551
$137$			519.453i			0.323940i	0.986796	+	0.161970i	$0.0517848\pi$
$137$			519.453i			0.323940i	−0.986796	+	0.161970i	$0.948215\pi$
$138$		−	309.003i		−	0.190609i
$139$	2058.07			1.25585			0.627926	−	0.778273i	$-0.283904\pi$
$139$	2058.07			1.25585			0.627926	+	0.778273i	$0.283904\pi$
$140$	255.075	−	226.586i	0.153984	−	0.136786i
$141$	−1877.57			−1.12142
$142$			798.785i			0.472060i
$143$			2183.35i			1.27679i
$144$	−144.000			−0.0833333
$145$	−441.556	−	497.074i	−0.252891	−	0.284688i
$146$	−1225.50			−0.694678
$147$		−	854.393i		−	0.479382i
$148$		−	50.4646i		−	0.0280281i
$149$	2753.10			1.51371			0.756856	−	0.653582i	$-0.226735\pi$
$149$	2753.10			1.51371			0.756856	+	0.653582i	$0.226735\pi$
$150$	−88.4123	+	744.771i	−0.0481256	+	0.405402i
$151$	−1705.12			−0.918944			−0.459472	−	0.888192i	$-0.651961\pi$
$151$	−1705.12			−0.918944			−0.459472	+	0.888192i	$0.651961\pi$
$152$			578.404i			0.308650i
$153$			721.829i			0.381415i
$154$	−595.469			−0.311586
$155$	230.179	+	259.119i	0.119280	+	0.134277i
$156$	671.343			0.344554
$157$			1795.47i			0.912703i	0.889800	+	0.456351i	$0.150844\pi$
$157$			1795.47i			0.912703i	−0.889800	+	0.456351i	$0.849156\pi$
$158$		−	1247.59i		−	0.628185i
$159$	761.823			0.379978
$160$	267.478	−	237.604i	0.132162	−	0.117401i
$161$	−392.899			−0.192328
$162$			162.000i			0.0785674i
$163$			2121.71i			1.01954i	0.860311	+	0.509770i	$0.170270\pi$
$163$			2121.71i			1.01954i	−0.860311	+	0.509770i	$0.829730\pi$
$164$	1023.23			0.487199
$165$	978.632	−	869.329i	0.461736	−	0.410165i
$166$	−881.742			−0.412268
$167$		−	3425.49i		−	1.58726i	−0.608401	−	0.793630i	$-0.708189\pi$
$167$		−	3425.49i		−	1.58726i	0.608401	−	0.793630i	$-0.291811\pi$
$168$			183.097i			0.0840847i
$169$	−932.872			−0.424612
$170$	−1191.04	−	1340.79i	−0.537343	−	0.604905i
$171$	650.704			0.290998
$172$			249.480i			0.110597i
$173$		−	2982.32i		−	1.31065i	−0.755349	−	0.655323i	$-0.772532\pi$
$173$		−	2982.32i		−	1.31065i	0.755349	−	0.655323i	$-0.227468\pi$
$174$	356.808			0.155457
$175$	946.981	+	112.417i	0.409057	+	0.0485595i
$176$	−624.424			−0.267430
$177$		−	859.817i		−	0.365129i
$178$		−	818.708i		−	0.344746i
$179$	−2422.77			−1.01165			−0.505827	−	0.862635i	$-0.668813\pi$
$179$	−2422.77			−1.01165			−0.505827	+	0.862635i	$0.668813\pi$
$180$	−267.304	−	300.913i	−0.110687	−	0.124604i
$181$	−1045.77			−0.429455			−0.214728	−	0.976674i	$-0.568886\pi$
$181$	−1045.77			−0.429455			−0.214728	+	0.976674i	$0.568886\pi$
$182$		−	853.617i		−	0.347661i
$183$		−	892.884i		−	0.360677i
$184$	−412.004			−0.165072
$185$	105.454	−	93.6763i	0.0419090	−	0.0372282i
$186$	−186.000			−0.0733236
$187$			3130.05i			1.22402i
$188$			2503.43i			0.971178i
$189$	205.984			0.0792758
$190$	−1208.67	+	1073.68i	−0.461508	+	0.409962i
$191$	−1305.14			−0.494433			−0.247217	−	0.968960i	$-0.579516\pi$
$191$	−1305.14			−0.494433			−0.247217	+	0.968960i	$0.579516\pi$
$192$			192.000i			0.0721688i
$193$		−	2333.22i		−	0.870203i	−0.900381	−	0.435101i	$-0.856713\pi$
$193$		−	2333.22i		−	0.870203i	0.900381	−	0.435101i	$-0.143287\pi$
$194$	−1638.02			−0.606201
$195$	1246.20	+	1402.89i	0.457652	+	0.515194i
$196$	−1139.19			−0.415157
$197$		−	2835.01i		−	1.02531i	−0.858594	−	0.512656i	$-0.828662\pi$
$197$		−	2835.01i		−	1.02531i	0.858594	−	0.512656i	$-0.171338\pi$
$198$			702.477i			0.252136i
$199$	698.667			0.248880			0.124440	−	0.992227i	$-0.460287\pi$
$199$	698.667			0.248880			0.124440	+	0.992227i	$0.460287\pi$
$200$	993.027	+	117.883i	0.351088	+	0.0416780i
$201$	1028.23			0.360825
$202$		−	498.548i		−	0.173652i
$203$		−	453.683i		−	0.156859i
$204$	962.439			0.330315
$205$	1899.39	+	2138.21i	0.647119	+	0.728483i
$206$	471.205			0.159371
$207$			463.504i			0.155632i
$208$		−	895.124i		−	0.298393i
$209$	2821.63			0.933859
$210$	−382.613	+	339.879i	−0.125728	+	0.111685i
$211$	2342.96			0.764435			0.382218	−	0.924072i	$-0.375160\pi$
$211$	2342.96			0.764435			0.382218	+	0.924072i	$0.375160\pi$
$212$		−	1015.76i		−	0.329071i
$213$		−	1198.18i		−	0.385435i
$214$	−543.977			−0.173764
$215$	−521.332	+	463.104i	−0.165370	+	0.146900i
$216$	216.000			0.0680414
$217$			236.500i			0.0739847i
$218$		−	2523.44i		−	0.783985i
$219$	1838.25			0.567202
$220$	−1159.11	−	1304.84i	−0.355213	−	0.399875i
$221$	−4486.99			−1.36574
$222$			75.6969i			0.0228849i
$223$			1885.26i			0.566126i	0.959101	+	0.283063i	$0.0913505\pi$
$223$			1885.26i			0.566126i	−0.959101	+	0.283063i	$0.908649\pi$
$224$	244.129			0.0728195
$225$	132.619	−	1117.16i	0.0392944	−	0.331009i
$226$	−3542.49			−1.04267
$227$		−	4191.28i		−	1.22548i	−0.790283	−	0.612742i	$-0.790066\pi$
$227$		−	4191.28i		−	1.22548i	0.790283	−	0.612742i	$-0.209934\pi$
$228$		−	867.605i		−	0.252011i
$229$	−728.600			−0.210250			−0.105125	−	0.994459i	$-0.533524\pi$
$229$	−728.600			−0.210250			−0.105125	+	0.994459i	$0.533524\pi$
$230$	−764.794	−	860.953i	−0.219257	−	0.246824i
$231$	893.204			0.254409
$232$		−	475.744i		−	0.134630i
$233$			4473.34i			1.25776i	0.777502	+	0.628881i	$0.216487\pi$
$233$			4473.34i			1.25776i	−0.777502	+	0.628881i	$0.783513\pi$
$234$	−1007.01			−0.281327
$235$	−5231.35	+	4647.07i	−1.45215	+	1.28996i
$236$	−1146.42			−0.316211
$237$			1871.39i			0.512911i
$238$		−	1223.75i		−	0.333293i
$239$	3626.21			0.981422			0.490711	−	0.871322i	$-0.336737\pi$
$239$	3626.21			0.981422			0.490711	+	0.871322i	$0.336737\pi$
$240$	−401.217	+	356.405i	−0.107910	+	0.0958578i
$241$	−523.921			−0.140036			−0.0700181	−	0.997546i	$-0.522306\pi$
$241$	−523.921			−0.140036			−0.0700181	+	0.997546i	$0.522306\pi$
$242$			384.137i			0.102038i
$243$		−	243.000i		−	0.0641500i
$244$	−1190.51			−0.312355
$245$	−2114.66	−	2380.54i	−0.551430	−	0.620763i
$246$	−1534.84			−0.397796
$247$			4044.87i			1.04198i
$248$			248.000i			0.0635001i
$249$	1322.61			0.336615
$250$	1597.00	+	2293.93i	0.404012	+	0.580322i
$251$	−7685.28			−1.93263			−0.966315	−	0.257361i	$-0.917147\pi$
$251$	−7685.28			−1.93263			−0.966315	+	0.257361i	$0.917147\pi$
$252$		−	274.645i		−	0.0686549i
$253$			2009.88i			0.499448i
$254$	−1182.86			−0.292203
$255$	1786.56	+	2011.18i	0.438739	+	0.493903i
$256$	256.000			0.0625000
$257$		−	5199.54i		−	1.26202i	−0.775776	−	0.631009i	$-0.782641\pi$
$257$		−	5199.54i		−	1.26202i	0.775776	−	0.631009i	$-0.217359\pi$
$258$		−	374.220i		−	0.0903020i
$259$	96.2490			0.0230912
$260$	1870.52	−	1661.60i	0.446171	−	0.396339i
$261$	−535.212			−0.126930
$262$		−	2906.07i		−	0.685258i
$263$			1141.54i			0.267644i	0.991005	+	0.133822i	$0.0427250\pi$
$263$			1141.54i			0.267644i	−0.991005	+	0.133822i	$0.957275\pi$
$264$	936.636			0.218356
$265$	2122.61	−	1885.54i	0.492042	−	0.437086i
$266$	−1103.17			−0.254284
$267$			1228.06i			0.281484i
$268$		−	1370.98i		−	0.312484i
$269$	−2532.16			−0.573936			−0.286968	−	0.957940i	$-0.592647\pi$
$269$	−2532.16			−0.573936			−0.286968	+	0.957940i	$0.592647\pi$
$270$	400.956	+	451.369i	0.0903756	+	0.101739i
$271$	4522.96			1.01384			0.506919	−	0.861994i	$-0.330784\pi$
$271$	4522.96			1.01384			0.506919	+	0.861994i	$0.330784\pi$
$272$		−	1283.25i		−	0.286061i
$273$			1280.43i			0.283864i
$274$	−1038.91			−0.229060
$275$	575.071	−	4844.30i	0.126102	−	1.06226i
$276$	618.006			0.134781
$277$		−	1302.86i		−	0.282603i	−0.989967	−	0.141302i	$-0.954871\pi$
$277$		−	1302.86i		−	0.282603i	0.989967	−	0.141302i	$-0.0451288\pi$
$278$			4116.15i			0.888022i
$279$	279.000			0.0598684
$280$	453.172	+	510.150i	0.0967221	+	0.108883i
$281$	8451.15			1.79414			0.897071	−	0.441887i	$-0.145691\pi$
$281$	8451.15			1.79414			0.897071	+	0.441887i	$0.145691\pi$
$282$		−	3755.15i		−	0.792964i
$283$			5256.09i			1.10404i	0.833832	+	0.552018i	$0.186142\pi$
$283$			5256.09i			1.10404i	−0.833832	+	0.552018i	$0.813858\pi$
$284$	−1597.57			−0.333797
$285$	1813.01	−	1610.52i	0.376819	−	0.334733i
$286$	−4366.70			−0.902826
$287$			1951.56i			0.401383i
$288$		−	288.000i		−	0.0589256i
$289$	−1519.56			−0.309295
$290$	994.148	−	883.113i	0.201305	−	0.178821i
$291$	2457.03			0.494961
$292$		−	2451.00i		−	0.491212i
$293$		−	4051.15i		−	0.807749i	−0.914814	−	0.403875i	$-0.867663\pi$
$293$		−	4051.15i		−	0.807749i	0.914814	−	0.403875i	$-0.132337\pi$
$294$	1708.79			0.338974
$295$	−2128.08	−	2395.65i	−0.420006	−	0.472814i
$296$	100.929			0.0198189
$297$		−	1053.72i		−	0.205868i
$298$			5506.21i			1.07036i
$299$	−2881.21			−0.557273
$300$	−1489.54	−	176.825i	−0.286662	−	0.0340299i
$301$	−475.823			−0.0911162
$302$		−	3410.24i		−	0.649792i
$303$			747.822i			0.141786i
$304$	−1156.81			−0.218248
$305$	−2209.92	−	2487.78i	−0.414884	−	0.467049i
$306$	−1443.66			−0.269701
$307$		−	709.903i		−	0.131975i	−0.997820	−	0.0659875i	$-0.978980\pi$
$307$		−	709.903i		−	0.131975i	0.997820	−	0.0659875i	$-0.0210197\pi$
$308$		−	1190.94i		−	0.220325i
$309$	−706.808			−0.130126
$310$	−518.239	+	460.357i	−0.0949483	+	0.0843436i
$311$	−24.5061			−0.00446822			−0.00223411	−	0.999998i	$-0.500711\pi$
$311$	−24.5061			−0.00446822			−0.00223411	+	0.999998i	$0.500711\pi$
$312$			1342.69i			0.243637i
$313$			6646.03i			1.20018i	0.799933	+	0.600089i	$0.204868\pi$
$313$			6646.03i			1.20018i	−0.799933	+	0.600089i	$0.795132\pi$
$314$	−3590.95			−0.645378
$315$	573.919	−	509.818i	0.102656	−	0.0911905i
$316$	2495.19			0.444194
$317$			750.406i			0.132956i	0.997788	+	0.0664779i	$0.0211762\pi$
$317$			750.406i			0.132956i	−0.997788	+	0.0664779i	$0.978824\pi$
$318$			1523.65i			0.268685i
$319$	−2320.83			−0.407340
$320$	475.207	+	534.956i	0.0830153	+	0.0934530i
$321$	815.966			0.141878
$322$		−	785.798i		−	0.135996i
$323$			5798.73i			0.998917i
$324$	−324.000			−0.0555556
$325$	6944.40	+	824.375i	1.18525	+	0.140702i
$326$	−4243.42			−0.720924
$327$			3785.15i			0.640121i
$328$			2046.45i			0.344502i
$329$	−4774.69			−0.800114
$330$	1738.66	+	1957.26i	0.290030	+	0.326496i
$331$	−4259.82			−0.707374			−0.353687	−	0.935364i	$-0.615072\pi$
$331$	−4259.82			−0.707374			−0.353687	+	0.935364i	$0.615072\pi$
$332$		−	1763.48i		−	0.291517i
$333$		−	113.545i		−	0.0186854i
$334$	6850.98			1.12236
$335$	2864.89	−	2544.91i	0.467241	−	0.415055i
$336$	−366.194			−0.0594569
$337$		−	1266.54i		−	0.204726i	−0.994747	−	0.102363i	$-0.967360\pi$
$337$		−	1266.54i		−	0.204726i	0.994747	−	0.102363i	$-0.0326403\pi$
$338$		−	1865.74i		−	0.300246i
$339$	5313.74			0.851335
$340$	2681.58	−	2382.07i	0.427732	−	0.379959i
$341$	1209.82			0.192128
$342$			1301.41i			0.205766i
$343$		−	4789.49i		−	0.753960i
$344$	−498.960			−0.0782038
$345$	1147.19	+	1291.43i	0.179022	+	0.201531i
$346$	5964.65			0.926767
$347$		−	4333.07i		−	0.670349i	−0.942156	−	0.335175i	$-0.891205\pi$
$347$		−	4333.07i		−	0.670349i	0.942156	−	0.335175i	$-0.108795\pi$
$348$			713.615i			0.109925i
$349$	4840.49			0.742423			0.371211	−	0.928548i	$-0.378943\pi$
$349$	4840.49			0.742423			0.371211	+	0.928548i	$0.378943\pi$
$350$	−224.834	+	1893.96i	−0.0343368	+	0.289247i
$351$	1510.52			0.229703
$352$		−	1248.85i		−	0.189102i
$353$			6252.14i			0.942685i	0.881950	+	0.471343i	$0.156230\pi$
$353$			6252.14i			0.942685i	−0.881950	+	0.471343i	$0.843770\pi$
$354$	1719.63			0.258185
$355$	−2965.53	−	3338.40i	−0.443364	−	0.499109i
$356$	1637.42			0.243772
$357$			1835.62i			0.272133i
$358$		−	4845.53i		−	0.715347i
$359$	1619.41			0.238075			0.119038	−	0.992890i	$-0.462019\pi$
$359$	1619.41			0.238075			0.119038	+	0.992890i	$0.462019\pi$
$360$	601.826	−	534.608i	0.0881083	−	0.0782676i
$361$	−1631.65			−0.237884
$362$		−	2091.54i		−	0.303671i
$363$		−	576.206i		−	0.0833140i
$364$	1707.23			0.245833
$365$	5121.78	−	4549.73i	0.734483	−	0.652449i
$366$	1785.77			0.255037
$367$		−	4022.97i		−	0.572200i	−0.958200	−	0.286100i	$-0.907641\pi$
$367$		−	4022.97i		−	0.572200i	0.958200	−	0.286100i	$-0.0923589\pi$
$368$		−	824.008i		−	0.116724i
$369$	2302.26			0.324799
$370$	187.353	+	210.909i	0.0263243	+	0.0296341i
$371$	1937.33			0.271108
$372$		−	372.000i		−	0.0518476i
$373$			5306.55i			0.736629i	0.929701	+	0.368314i	$0.120065\pi$
$373$			5306.55i			0.736629i	−0.929701	+	0.368314i	$0.879935\pi$
$374$	−6260.11			−0.865515
$375$	−2395.50	−	3440.89i	−0.329875	−	0.473831i
$376$	−5006.86			−0.686727
$377$		−	3326.95i		−	0.454500i
$378$			411.968i			0.0560565i
$379$	5378.67			0.728980			0.364490	−	0.931207i	$-0.381243\pi$
$379$	5378.67			0.728980			0.364490	+	0.931207i	$0.381243\pi$
$380$	−2147.36	−	2417.35i	−0.289887	−	0.326335i
$381$	1774.30			0.238583
$382$		−	2610.28i		−	0.349617i
$383$		−	4718.07i		−	0.629457i	−0.949182	−	0.314729i	$-0.898086\pi$
$383$		−	4718.07i		−	0.629457i	0.949182	−	0.314729i	$-0.101914\pi$
$384$	−384.000			−0.0510310
$385$	2488.67	−	2210.71i	0.329440	−	0.292645i
$386$	4666.45			0.615326
$387$			561.330i			0.0737313i
$388$		−	3276.04i		−	0.428649i
$389$	−12059.6			−1.57184			−0.785918	−	0.618331i	$-0.787809\pi$
$389$	−12059.6			−1.57184			−0.785918	+	0.618331i	$0.787809\pi$
$390$	−2805.77	+	2492.40i	−0.364297	+	0.323609i
$391$	−4130.51			−0.534242
$392$		−	2278.38i		−	0.293560i
$393$			4359.11i			0.559511i
$394$	5670.03			0.725004
$395$	4631.76	+	5214.13i	0.589998	+	0.664180i
$396$	−1404.95			−0.178287
$397$		−	443.179i		−	0.0560265i	−0.999608	−	0.0280133i	$-0.991082\pi$
$397$		−	443.179i		−	0.0560265i	0.999608	−	0.0280133i	$-0.00891807\pi$
$398$			1397.33i			0.175985i
$399$	1654.75			0.207622
$400$	−235.766	+	1986.05i	−0.0294708	+	0.248257i
$401$	5995.13			0.746589			0.373295	−	0.927713i	$-0.378228\pi$
$401$	5995.13			0.746589			0.373295	+	0.927713i	$0.378228\pi$
$402$			2056.46i			0.255142i
$403$			1734.30i			0.214372i
$404$	997.097			0.122791
$405$	−601.434	−	677.054i	−0.0737914	−	0.0830693i
$406$	907.367			0.110916
$407$		−	492.364i		−	0.0599646i
$408$			1924.88i			0.233568i
$409$	11302.7			1.36646			0.683228	−	0.730206i	$-0.260576\pi$
$409$	11302.7			1.36646			0.683228	+	0.730206i	$0.260576\pi$
$410$	−4276.42	+	3798.79i	−0.515115	+	0.457582i
$411$	1558.36			0.187027
$412$			942.410i			0.112692i
$413$		−	2186.53i		−	0.260513i
$414$	−927.009			−0.110048
$415$	3685.10	−	3273.52i	0.435891	−	0.387206i
$416$	1790.25			0.210996
$417$		−	6174.22i		−	0.725067i
$418$			5643.27i			0.660338i
$419$	−1626.56			−0.189649			−0.0948243	−	0.995494i	$-0.530229\pi$
$419$	−1626.56			−0.189649			−0.0948243	+	0.995494i	$0.530229\pi$
$420$	−679.758	−	765.225i	−0.0789733	−	0.0889028i
$421$	−3445.25			−0.398839			−0.199420	−	0.979914i	$-0.563906\pi$
$421$	−3445.25			−0.398839			−0.199420	+	0.979914i	$0.563906\pi$
$422$			4685.91i			0.540537i
$423$			5632.72i			0.647452i
$424$	2031.53			0.232688
$425$	9955.51	+	1181.83i	1.13627	+	0.134887i
$426$	2396.35			0.272544
$427$		−	2270.61i		−	0.257337i
$428$		−	1087.95i		−	0.122870i
$429$	6550.04			0.737154
$430$	−926.209	−	1042.66i	−0.103874	−	0.116934i
$431$	6989.06			0.781093			0.390546	−	0.920583i	$-0.372286\pi$
$431$	6989.06			0.781093			0.390546	+	0.920583i	$0.372286\pi$
$432$			432.000i			0.0481125i
$433$			340.725i			0.0378157i	0.999821	+	0.0189078i	$0.00601891\pi$
$433$			340.725i			0.0378157i	−0.999821	+	0.0189078i	$0.993981\pi$
$434$	−473.000			−0.0523151
$435$	−1491.22	+	1324.67i	−0.164365	+	0.146007i
$436$	5046.87			0.554361
$437$			3723.51i			0.407596i
$438$			3676.50i			0.401073i
$439$	10364.3			1.12680			0.563398	−	0.826186i	$-0.309494\pi$
$439$	10364.3			1.12680			0.563398	+	0.826186i	$0.309494\pi$
$440$	2609.68	−	2318.21i	0.282754	−	0.251173i
$441$	−2563.18			−0.276771
$442$		−	8973.99i		−	0.965722i
$443$		−	16757.3i		−	1.79721i	−0.438763	−	0.898603i	$-0.644583\pi$
$443$		−	16757.3i		−	1.79721i	0.438763	−	0.898603i	$-0.355417\pi$
$444$	−151.394			−0.0161820
$445$	3039.50	+	3421.66i	0.323789	+	0.364500i
$446$	−3770.51			−0.400311
$447$		−	8259.31i		−	0.873942i
$448$			488.258i			0.0514912i
$449$	−225.044			−0.0236537			−0.0118268	−	0.999930i	$-0.503765\pi$
$449$	−225.044			−0.0236537			−0.0118268	+	0.999930i	$0.503765\pi$
$450$	2234.31	+	265.237i	0.234059	+	0.0277853i
$451$	9983.24			1.04233
$452$		−	7084.99i		−	0.737278i
$453$			5115.35i			0.530553i
$454$	8382.56			0.866548
$455$	3169.10	+	3567.56i	0.326527	+	0.367582i
$456$	1735.21			0.178199
$457$			13019.7i			1.33268i	0.745649	+	0.666339i	$0.232140\pi$
$457$			13019.7i			1.33268i	−0.745649	+	0.666339i	$0.767860\pi$
$458$		−	1457.20i		−	0.148669i
$459$	2165.49			0.220210
$460$	1721.91	−	1529.59i	0.174531	−	0.155038i
$461$	−11402.4			−1.15198			−0.575990	−	0.817456i	$-0.695383\pi$
$461$	−11402.4			−1.15198			−0.575990	+	0.817456i	$0.695383\pi$
$462$			1786.41i			0.179894i
$463$		−	9664.89i		−	0.970120i	−0.874481	−	0.485060i	$-0.838798\pi$
$463$		−	9664.89i		−	0.970120i	0.874481	−	0.485060i	$-0.161202\pi$
$464$	951.487			0.0951976
$465$	777.358	−	690.536i	0.0775250	−	0.0688663i
$466$	−8946.69			−0.889372
$467$		−	11771.8i		−	1.16646i	−0.812308	−	0.583228i	$-0.801789\pi$
$467$		−	11771.8i		−	1.16646i	0.812308	−	0.583228i	$-0.198211\pi$
$468$		−	2014.03i		−	0.198928i
$469$	2614.81			0.257443
$470$	−9294.13	−	10462.7i	−0.912141	−	1.02683i
$471$	5386.42			0.526949
$472$		−	2292.85i		−	0.223595i
$473$			2434.08i			0.236616i
$474$	−3742.78			−0.362683
$475$	1065.38	−	8974.54i	0.102911	−	0.866906i
$476$	2447.50			0.235674
$477$		−	2285.47i		−	0.219380i
$478$			7252.41i			0.693970i
$479$	375.155			0.0357855			0.0178928	−	0.999840i	$-0.494304\pi$
$479$	375.155			0.0357855			0.0178928	+	0.999840i	$0.494304\pi$
$480$	−712.811	−	802.434i	−0.0677817	−	0.0763040i
$481$	705.813			0.0669071
$482$		−	1047.84i		−	0.0990206i
$483$			1178.70i			0.111041i
$484$	−768.275			−0.0721520
$485$	6845.85	−	6081.24i	0.640936	−	0.569350i
$486$	486.000			0.0453609
$487$			17907.7i			1.66627i	0.553067	+	0.833137i	$0.313457\pi$
$487$			17907.7i			1.66627i	−0.553067	+	0.833137i	$0.686543\pi$
$488$		−	2381.02i		−	0.220869i
$489$	6365.13			0.588632
$490$	4761.07	−	4229.31i	0.438946	−	0.389920i
$491$	−7655.95			−0.703683			−0.351842	−	0.936060i	$-0.614444\pi$
$491$	−7655.95			−0.703683			−0.351842	+	0.936060i	$0.614444\pi$
$492$		−	3069.68i		−	0.281284i
$493$		−	4769.52i		−	0.435717i
$494$	−8089.73			−0.736790
$495$	−2607.99	−	2935.89i	−0.236809	−	0.266583i
$496$	−496.000			−0.0449013
$497$		−	3046.98i		−	0.275001i
$498$			2645.23i			0.238023i
$499$	5727.03			0.513782			0.256891	−	0.966440i	$-0.417302\pi$
$499$	5727.03			0.513782			0.256891	+	0.966440i	$0.417302\pi$
$500$	−4587.85	+	3194.00i	−0.410350	+	0.285680i
$501$	−10276.5			−0.916405
$502$		−	15370.6i		−	1.36658i
$503$		−	22538.2i		−	1.99787i	−0.0461606	−	0.998934i	$-0.514699\pi$
$503$		−	22538.2i		−	1.99787i	0.0461606	−	0.998934i	$-0.485301\pi$
$504$	549.291			0.0485463
$505$	1850.89	+	2083.61i	0.163096	+	0.183602i
$506$	−4019.77			−0.353163
$507$			2798.62i			0.245150i
$508$		−	2365.73i		−	0.206619i
$509$	16676.5			1.45220			0.726102	−	0.687587i	$-0.241330\pi$
$509$	16676.5			1.45220			0.726102	+	0.687587i	$0.241330\pi$
$510$	−4022.37	+	3573.11i	−0.349242	+	0.310235i
$511$	4674.69			0.404689
$512$			512.000i			0.0441942i
$513$		−	1952.11i		−	0.168008i
$514$	10399.1			0.892381
$515$	−1969.33	+	1749.38i	−0.168503	+	0.149683i
$516$	748.440			0.0638532
$517$			24425.1i			2.07778i
$518$			192.498i			0.0163280i
$519$	−8946.97			−0.756702
$520$	3323.20	+	3741.03i	0.280254	+	0.315491i
$521$	3309.25			0.278274			0.139137	−	0.990273i	$-0.455567\pi$
$521$	3309.25			0.278274			0.139137	+	0.990273i	$0.455567\pi$
$522$		−	1070.42i		−	0.0897532i
$523$			11322.7i			0.946668i	0.880883	+	0.473334i	$0.156950\pi$
$523$			11322.7i			0.946668i	−0.880883	+	0.473334i	$0.843050\pi$
$524$	5812.14			0.484551
$525$	337.251	−	2840.94i	0.0280358	−	0.236169i
$526$	−2283.08			−0.189253
$527$			2486.30i			0.205512i
$528$			1873.27i			0.154401i
$529$	9514.70			0.782009
$530$	3771.08	+	4245.23i	0.309067	+	0.347926i
$531$	−2579.45			−0.210807
$532$		−	2206.33i		−	0.179806i
$533$			14311.2i			1.16301i
$534$	−2456.12			−0.199039
$535$	2273.47	−	2019.55i	0.183721	−	0.163201i
$536$	2741.95			0.220960
$537$			7268.30i			0.584079i
$538$		−	5064.33i		−	0.405834i
$539$	−11114.7			−0.888205
$540$	−902.738	+	801.912i	−0.0719401	+	0.0639052i
$541$	−593.797			−0.0471892			−0.0235946	−	0.999722i	$-0.507511\pi$
$541$	−593.797			−0.0471892			−0.0235946	+	0.999722i	$0.507511\pi$
$542$			9045.92i			0.716892i
$543$			3137.31i			0.247946i
$544$	2566.50			0.202276
$545$	9368.40	+	10546.3i	0.736327	+	0.828907i
$546$	−2560.85			−0.200722
$547$			8249.30i			0.644816i	0.946601	+	0.322408i	$0.104492\pi$
$547$			8249.30i			0.644816i	−0.946601	+	0.322408i	$0.895508\pi$
$548$		−	2077.81i		−	0.161970i
$549$	−2678.65			−0.208237
$550$	9688.60	+	1150.14i	0.751133	+	0.0891677i
$551$	−4299.56			−0.332427
$552$			1236.01i			0.0953046i
$553$			4758.97i			0.365953i
$554$	2605.72			0.199831
$555$	−281.029	−	316.363i	−0.0214937	−	0.0241962i
$556$	−8232.30			−0.627926
$557$		−	1718.31i		−	0.130713i	−0.997862	−	0.0653565i	$-0.979182\pi$
$557$		−	1718.31i		−	0.130713i	0.997862	−	0.0653565i	$-0.0208184\pi$
$558$			558.000i			0.0423334i
$559$	−3489.31			−0.264011
$560$	−1020.30	+	906.343i	−0.0769921	+	0.0683929i
$561$	9390.16			0.706690
$562$			16902.3i			1.26865i
$563$		−	15970.3i		−	1.19550i	−0.801681	−	0.597752i	$-0.796061\pi$
$563$		−	15970.3i		−	1.19550i	0.801681	−	0.597752i	$-0.203939\pi$
$564$	7510.30			0.560710
$565$	14805.3	−	13151.7i	1.10241	−	0.979286i
$566$	−10512.2			−0.780671
$567$		−	617.952i		−	0.0457699i
$568$		−	3195.14i		−	0.236030i
$569$	−6532.00			−0.481258			−0.240629	−	0.970617i	$-0.577354\pi$
$569$	−6532.00			−0.481258			−0.240629	+	0.970617i	$0.577354\pi$
$570$	3221.03	+	3626.02i	0.236692	+	0.266452i
$571$	−18289.5			−1.34044			−0.670222	−	0.742161i	$-0.733801\pi$
$571$	−18289.5			−1.34044			−0.670222	+	0.742161i	$0.733801\pi$
$572$		−	8733.39i		−	0.638394i
$573$			3915.43i			0.285461i
$574$	−3903.12			−0.283821
$575$	6392.67	+	758.880i	0.463640	+	0.0550391i
$576$	576.000			0.0416667
$577$		−	23031.5i		−	1.66173i	−0.556477	−	0.830863i	$-0.687847\pi$
$577$		−	23031.5i		−	1.66173i	0.556477	−	0.830863i	$-0.312153\pi$
$578$		−	3039.13i		−	0.218704i
$579$	−6999.67			−0.502412
$580$	1766.23	+	1988.30i	0.126446	+	0.142344i
$581$	3363.42			0.240169
$582$			4914.06i			0.349990i
$583$		−	9910.44i		−	0.704028i
$584$	4902.00			0.347339
$585$	4208.66	−	3738.60i	0.297447	−	0.264226i
$586$	8102.29			0.571165
$587$			22124.5i			1.55567i	0.628471	+	0.777833i	$0.283681\pi$
$587$			22124.5i			1.55567i	−0.628471	+	0.777833i	$0.716319\pi$
$588$			3417.57i			0.239691i
$589$	2241.31			0.156794
$590$	4791.30	−	4256.16i	0.334330	−	0.296989i
$591$	−8505.04			−0.591964
$592$			201.858i			0.0140141i
$593$			13304.4i			0.921329i	0.887574	+	0.460665i	$0.152389\pi$
$593$			13304.4i			0.921329i	−0.887574	+	0.460665i	$0.847611\pi$
$594$	2107.43			0.145571
$595$	4543.23	+	5114.46i	0.313033	+	0.352391i
$596$	−11012.4			−0.756856
$597$		−	2096.00i		−	0.143691i
$598$		−	5762.41i		−	0.394051i
$599$	−24963.9			−1.70284			−0.851418	−	0.524489i	$-0.824257\pi$
$599$	−24963.9			−1.70284			−0.851418	+	0.524489i	$0.824257\pi$
$600$	353.649	−	2979.08i	0.0240628	−	0.202701i
$601$	−97.2639			−0.00660146			−0.00330073	−	0.999995i	$-0.501051\pi$
$601$	−97.2639			−0.00660146			−0.00330073	+	0.999995i	$0.501051\pi$
$602$		−	951.646i		−	0.0644289i
$603$		−	3084.70i		−	0.208323i
$604$	6820.47			0.459472
$605$	−1426.13	−	1605.44i	−0.0958355	−	0.107885i
$606$	−1495.64			−0.100258
$607$			18295.4i			1.22337i	0.791101	+	0.611686i	$0.209508\pi$
$607$			18295.4i			1.22337i	−0.791101	+	0.611686i	$0.790492\pi$
$608$		−	2313.61i		−	0.154325i
$609$	−1361.05			−0.0905624
$610$	4975.56	−	4419.84i	0.330253	−	0.293367i
$611$	−35013.8			−2.31834
$612$		−	2887.32i		−	0.190707i
$613$		−	5957.70i		−	0.392544i	−0.980550	−	0.196272i	$-0.937116\pi$
$613$		−	5957.70i		−	0.392544i	0.980550	−	0.196272i	$-0.0628835\pi$
$614$	1419.81			0.0933204
$615$	6414.63	−	5698.18i	0.420590	−	0.373614i
$616$	2381.88			0.155793
$617$			22695.9i			1.48088i	0.672123	+	0.740440i	$0.265383\pi$
$617$			22695.9i			1.48088i	−0.672123	+	0.740440i	$0.734617\pi$
$618$		−	1413.62i		−	0.0920129i
$619$	−14684.2			−0.953484			−0.476742	−	0.879043i	$-0.658182\pi$
$619$	−14684.2			−0.953484			−0.476742	+	0.879043i	$0.658182\pi$
$620$	−920.714	−	1036.48i	−0.0596399	−	0.0671386i
$621$	1390.51			0.0898540
$622$		−	49.0123i		−	0.00315951i
$623$			3122.98i			0.200834i
$624$	−2685.37			−0.172277
$625$	−15190.7	−	3658.16i	−0.972207	−	0.234122i
$626$	−13292.1			−0.848654
$627$		−	8464.90i		−	0.539164i
$628$		−	7181.89i		−	0.456351i
$629$	1011.86			0.0641420
$630$	1019.64	+	1147.84i	0.0644814	+	0.0725888i
$631$	−11854.6			−0.747898			−0.373949	−	0.927449i	$-0.621996\pi$
$631$	−11854.6			−0.747898			−0.373949	+	0.927449i	$0.621996\pi$
$632$			4990.38i			0.314093i
$633$		−	7028.87i		−	0.441347i
$634$	−1500.81			−0.0940139
$635$	4943.60	−	4391.45i	0.308946	−	0.274440i
$636$	−3047.29			−0.189989
$637$		−	15933.1i		−	0.991039i
$638$		−	4641.65i		−	0.288033i
$639$	−3594.53			−0.222531
$640$	−1069.91	+	950.414i	−0.0660812	+	0.0587007i
$641$	−20428.6			−1.25879			−0.629394	−	0.777086i	$-0.716697\pi$
$641$	−20428.6			−1.25879			−0.629394	+	0.777086i	$0.716697\pi$
$642$			1631.93i			0.100323i
$643$		−	14603.3i		−	0.895641i	−0.894123	−	0.447821i	$-0.852200\pi$
$643$		−	14603.3i		−	0.895641i	0.894123	−	0.447821i	$-0.147800\pi$
$644$	1571.60			0.0961639
$645$	1389.31	+	1563.99i	0.0848126	+	0.0954763i
$646$	−11597.5			−0.706341
$647$		−	3053.87i		−	0.185564i	−0.995686	−	0.0927822i	$-0.970424\pi$
$647$		−	3053.87i		−	0.185564i	0.995686	−	0.0927822i	$-0.0295760\pi$
$648$		−	648.000i		−	0.0392837i
$649$	−11185.2			−0.676515
$650$	−1648.75	+	13888.8i	−0.0994913	+	0.838097i
$651$	709.501			0.0427151
$652$		−	8486.83i		−	0.509770i
$653$		−	8940.36i		−	0.535778i	−0.963450	−	0.267889i	$-0.913674\pi$
$653$		−	8940.36i		−	0.535778i	0.963450	−	0.267889i	$-0.0863261\pi$
$654$	−7570.31			−0.452634
$655$	10789.0	+	12145.5i	0.643602	+	0.724523i
$656$	−4092.91			−0.243599
$657$		−	5514.75i		−	0.327474i
$658$		−	9549.39i		−	0.565766i
$659$	−29011.5			−1.71491			−0.857457	−	0.514556i	$-0.827957\pi$
$659$	−29011.5			−1.71491			−0.857457	+	0.514556i	$0.827957\pi$
$660$	−3914.53	+	3477.32i	−0.230868	+	0.205082i
$661$	−5084.29			−0.299177			−0.149588	−	0.988748i	$-0.547795\pi$
$661$	−5084.29			−0.299177			−0.149588	+	0.988748i	$0.547795\pi$
$662$		−	8519.63i		−	0.500189i
$663$			13461.0i			0.788508i
$664$	3526.97			0.206134
$665$	4610.51	−	4095.57i	0.268854	−	0.238826i
$666$	227.091			0.0132126
$667$		−	3062.63i		−	0.177789i
$668$			13702.0i			0.793630i
$669$	5655.77			0.326853
$670$	5089.83	+	5729.78i	0.293488	+	0.330389i
$671$	−11615.4			−0.668266
$672$		−	732.388i		−	0.0420424i
$673$		−	32246.1i		−	1.84695i	−0.383662	−	0.923474i	$-0.625337\pi$
$673$		−	32246.1i		−	1.84695i	0.383662	−	0.923474i	$-0.374663\pi$
$674$	2533.07			0.144763
$675$	−3351.47	−	397.856i	−0.191108	−	0.0226866i
$676$	3731.49			0.212306
$677$		−	24788.7i		−	1.40725i	−0.710572	−	0.703625i	$-0.751564\pi$
$677$		−	24788.7i		−	1.40725i	0.710572	−	0.703625i	$-0.248436\pi$
$678$			10627.5i			0.601985i
$679$	6248.26			0.353146
$680$	4764.15	+	5363.15i	0.268672	+	0.302452i
$681$	−12573.8			−0.707534
$682$			2419.64i			0.135855i
$683$			8617.87i			0.482802i	0.970425	+	0.241401i	$0.0776068\pi$
$683$			8617.87i			0.482802i	−0.970425	+	0.241401i	$0.922393\pi$
$684$	−2602.82			−0.145499
$685$	4341.94	−	3856.99i	0.242186	−	0.215136i
$686$	9578.99			0.533130
$687$			2185.80i			0.121388i
$688$		−	997.920i		−	0.0552985i
$689$	14206.8			0.785538
$690$	−2582.86	+	2294.38i	−0.142504	+	0.126588i
$691$	−19440.4			−1.07026			−0.535129	−	0.844771i	$-0.679737\pi$
$691$	−19440.4			−1.07026			−0.535129	+	0.844771i	$0.679737\pi$
$692$			11929.3i			0.655323i
$693$		−	2679.61i		−	0.146883i
$694$	8666.13			0.474009
$695$	−15281.4	−	17202.8i	−0.834040	−	0.938906i
$696$	−1427.23			−0.0777285
$697$			20516.5i			1.11495i
$698$			9680.98i			0.524972i
$699$	13420.0			0.726169
$700$	−3787.92	−	449.667i	−0.204529	−	0.0242798i
$701$	−29674.8			−1.59886			−0.799431	−	0.600758i	$-0.794865\pi$
$701$	−29674.8			−1.59886			−0.799431	+	0.600758i	$0.794865\pi$
$702$			3021.04i			0.162424i
$703$		−	912.153i		−	0.0489367i
$704$	2497.70			0.133715
$705$	13941.2	+	15694.1i	0.744760	+	0.838401i
$706$	−12504.3			−0.666579
$707$			1901.72i			0.101162i
$708$			3439.27i			0.182565i
$709$	14362.2			0.760766			0.380383	−	0.924829i	$-0.375792\pi$
$709$	14362.2			0.760766			0.380383	+	0.924829i	$0.375792\pi$
$710$	6676.79	−	5931.07i	0.352923	−	0.313506i
$711$	5614.17			0.296129
$712$			3274.83i			0.172373i
$713$			1596.51i			0.0838569i
$714$	−3671.24			−0.192427
$715$	18249.9	−	16211.6i	0.954558	−	0.847944i
$716$	9691.06			0.505827
$717$		−	10878.6i		−	0.566624i
$718$			3238.81i			0.168345i
$719$	−8230.15			−0.426888			−0.213444	−	0.976955i	$-0.568468\pi$
$719$	−8230.15			−0.426888			−0.213444	+	0.976955i	$0.568468\pi$
$720$	1069.22	+	1203.65i	0.0553435	+	0.0623020i
$721$	−1797.42			−0.0928425
$722$		−	3263.29i		−	0.168209i
$723$			1571.76i			0.0808499i
$724$	4183.07			0.214728
$725$	−876.284	+	7381.66i	−0.0448888	+	0.378135i
$726$	1152.41			0.0589119
$727$		−	12621.0i		−	0.643859i	−0.946764	−	0.321930i	$-0.895669\pi$
$727$		−	12621.0i		−	0.643859i	0.946764	−	0.321930i	$-0.104331\pi$
$728$			3414.47i			0.173830i
$729$	−729.000			−0.0370370
$730$	9099.47	+	10243.6i	0.461351	+	0.519358i
$731$	−5002.28			−0.253100
$732$			3571.53i			0.180338i
$733$			25685.4i			1.29428i	0.762370	+	0.647142i	$0.224036\pi$
$733$			25685.4i			1.29428i	−0.762370	+	0.647142i	$0.775964\pi$
$734$	8045.94			0.404606
$735$	−7141.61	+	6343.97i	−0.358398	+	0.318368i
$736$	1648.02			0.0825362
$737$		−	13376.1i		−	0.668542i
$738$			4604.52i			0.229668i
$739$	−35092.5			−1.74682			−0.873408	−	0.486989i	$-0.838095\pi$
$739$	−35092.5			−1.74682			−0.873408	+	0.486989i	$0.838095\pi$
$740$	−421.818	+	374.705i	−0.0209545	+	0.0186141i
$741$	12134.6			0.601587
$742$			3874.65i			0.191702i
$743$		−	18125.0i		−	0.894941i	−0.894299	−	0.447471i	$-0.852325\pi$
$743$		−	18125.0i		−	0.894941i	0.894299	−	0.447471i	$-0.147675\pi$
$744$	744.000			0.0366618
$745$	−20442.1	−	23012.3i	−1.00529	−	1.13169i
$746$	−10613.1			−0.520875
$747$		−	3967.84i		−	0.194345i
$748$		−	12520.2i		−	0.612011i
$749$	2075.01			0.101227
$750$	6881.78	−	4790.99i	0.335049	−	0.233257i
$751$	−18850.7			−0.915941			−0.457971	−	0.888967i	$-0.651424\pi$
$751$	−18850.7			−0.915941			−0.457971	+	0.888967i	$0.651424\pi$
$752$		−	10013.7i		−	0.485589i
$753$			23055.8i			1.11580i
$754$	6653.90			0.321380
$755$	12660.7	+	14252.6i	0.610291	+	0.687025i
$756$	−823.936			−0.0396379
$757$			8541.13i			0.410083i	0.978753	+	0.205041i	$0.0657329\pi$
$757$			8541.13i			0.410083i	−0.978753	+	0.205041i	$0.934267\pi$
$758$			10757.3i			0.515467i
$759$	6029.65			0.288356
$760$	4834.70	−	4294.71i	0.230754	−	0.204981i
$761$	35530.0			1.69246			0.846231	−	0.532817i	$-0.178866\pi$
$761$	35530.0			1.69246			0.846231	+	0.532817i	$0.178866\pi$
$762$			3548.59i			0.168703i
$763$			9625.69i			0.456715i
$764$	5220.57			0.247217
$765$	6033.55	−	5359.67i	0.285155	−	0.253306i
$766$	9436.14			0.445093
$767$		−	16034.2i		−	0.754841i
$768$		−	768.000i		−	0.0360844i
$769$	−2010.38			−0.0942734			−0.0471367	−	0.998888i	$-0.515010\pi$
$769$	−2010.38			−0.0942734			−0.0471367	+	0.998888i	$0.515010\pi$
$770$	4421.43	+	4977.34i	0.206931	+	0.232949i
$771$	−15598.6			−0.728626
$772$			9332.90i			0.435101i
$773$			38781.8i			1.80451i	0.431204	+	0.902255i	$0.358089\pi$
$773$			38781.8i			1.80451i	−0.431204	+	0.902255i	$0.641911\pi$
$774$	−1122.66			−0.0521359
$775$	456.797	−	3847.98i	0.0211724	−	0.178353i
$776$	6552.08			0.303100
$777$		−	288.747i		−	0.0133317i
$778$		−	24119.1i		−	1.11146i
$779$	18494.9			0.850642
$780$	−4984.80	−	5611.55i	−0.228826	−	0.257597i
$781$	−15586.9			−0.714139
$782$		−	8261.01i		−	0.377766i
$783$			1605.63i			0.0732832i
$784$	4556.76			0.207579
$785$	15007.8	−	13331.6i	0.682359	−	0.606146i
$786$	−8718.21			−0.395634
$787$			12057.1i			0.546111i	0.961998	+	0.273056i	$0.0880343\pi$
$787$			12057.1i			0.546111i	−0.961998	+	0.273056i	$0.911966\pi$
$788$			11340.1i			0.512656i
$789$	3424.62			0.154524
$790$	−10428.3	+	9263.53i	−0.469646	+	0.417192i
$791$	13512.9			0.607413
$792$		−	2809.91i		−	0.126068i
$793$		−	16650.9i		−	0.745636i
$794$	886.359			0.0396167
$795$	−5656.62	−	6367.84i	−0.252352	−	0.284081i
$796$	−2794.67			−0.124440
$797$			12778.8i			0.567942i	0.958833	+	0.283971i	$0.0916519\pi$
$797$			12778.8i			0.567942i	−0.958833	+	0.283971i	$0.908348\pi$
$798$			3309.50i			0.146811i
$799$	−50195.9			−2.22253
$800$	−3972.11	−	471.533i	−0.175544	−	0.0208390i
$801$	3684.19			0.162515
$802$			11990.3i			0.527918i
$803$		−	23913.5i		−	1.05092i
$804$	−4112.93			−0.180413
$805$	2917.32	+	3284.12i	0.127729	+	0.143789i
$806$	−3468.61			−0.151584
$807$			7596.49i			0.331362i
$808$			1994.19i			0.0868261i
$809$	−29397.1			−1.27756			−0.638781	−	0.769389i	$-0.720561\pi$
$809$	−29397.1			−1.27756			−0.638781	+	0.769389i	$0.720561\pi$
$810$	1354.11	−	1202.87i	0.0587389	−	0.0521784i
$811$	−13598.6			−0.588792			−0.294396	−	0.955683i	$-0.595118\pi$
$811$	−13598.6			−0.588792			−0.294396	+	0.955683i	$0.595118\pi$
$812$			1814.73i			0.0784294i
$813$		−	13568.9i		−	0.585340i
$814$	984.728			0.0424014
$815$	17734.7	−	15753.9i	0.762233	−	0.677099i
$816$	−3849.76			−0.165157
$817$			4509.38i			0.193101i
$818$			22605.3i			0.966230i
$819$	3841.28			0.163889
$820$	−7597.57	−	8552.84i	−0.323560	−	0.364241i
$821$	−24508.2			−1.04183			−0.520916	−	0.853608i	$-0.674409\pi$
$821$	−24508.2			−1.04183			−0.520916	+	0.853608i	$0.674409\pi$
$822$			3116.72i			0.132248i
$823$			12594.5i			0.533434i	0.963775	+	0.266717i	$0.0859388\pi$
$823$			12594.5i			0.533434i	−0.963775	+	0.266717i	$0.914061\pi$
$824$	−1884.82			−0.0796855
$825$	−14532.9	−	1725.21i	−0.613298	−	0.0728051i
$826$	4373.05			0.184211
$827$			13929.9i			0.585720i	0.956155	+	0.292860i	$0.0946070\pi$
$827$			13929.9i			0.585720i	−0.956155	+	0.292860i	$0.905393\pi$
$828$		−	1854.02i		−	0.0778159i
$829$	−2667.26			−0.111746			−0.0558731	−	0.998438i	$-0.517794\pi$
$829$	−2667.26			−0.111746			−0.0558731	+	0.998438i	$0.517794\pi$
$830$	6547.03	+	7370.21i	0.273796	+	0.308221i
$831$	−3908.57			−0.163161
$832$			3580.50i			0.149196i
$833$		−	22841.7i		−	0.950082i
$834$	12348.4			0.512700
$835$	−28632.6	+	25434.7i	−1.18667	+	1.05413i
$836$	−11286.5			−0.466930
$837$		−	837.000i		−	0.0345651i
$838$		−	3253.13i		−	0.134102i
$839$	3088.90			0.127104			0.0635522	−	0.997979i	$-0.479757\pi$
$839$	3088.90			0.127104			0.0635522	+	0.997979i	$0.479757\pi$
$840$	1530.45	−	1359.52i	0.0628638	−	0.0558425i
$841$	−20852.6			−0.854999
$842$		−	6890.50i		−	0.282022i
$843$		−	25353.5i		−	1.03585i
$844$	−9371.83			−0.382218
$845$	6926.68	+	7797.59i	0.281994	+	0.317450i
$846$	−11265.4			−0.457818
$847$		−	1465.30i		−	0.0594431i
$848$			4063.06i			0.164535i
$849$	15768.3			0.637415
$850$	−2363.65	+	19911.0i	−0.0953796	+	0.803461i
$851$	649.737			0.0261724
$852$			4792.71i			0.192718i
$853$		−	9484.57i		−	0.380710i	−0.981715	−	0.190355i	$-0.939036\pi$
$853$		−	9484.57i		−	0.380710i	0.981715	−	0.190355i	$-0.0609639\pi$
$854$	4541.23			0.181964
$855$	−4831.55	−	5439.03i	−0.193258	−	0.217557i
$856$	2175.91			0.0868820
$857$			15479.4i			0.616997i	0.951225	+	0.308499i	$0.0998265\pi$
$857$			15479.4i			0.616997i	−0.951225	+	0.308499i	$0.900173\pi$
$858$			13100.1i			0.521247i
$859$	−46217.5			−1.83576			−0.917882	−	0.396852i	$-0.870102\pi$
$859$	−46217.5			−1.83576			−0.917882	+	0.396852i	$0.870102\pi$
$860$	2085.33	−	1852.42i	0.0826849	−	0.0734499i
$861$	5854.68			0.231739
$862$			13978.1i			0.552316i
$863$		−	29082.3i		−	1.14713i	−0.819160	−	0.573566i	$-0.805560\pi$
$863$		−	29082.3i		−	1.14713i	0.819160	−	0.573566i	$-0.194440\pi$
$864$	−864.000			−0.0340207
$865$	−24928.3	+	22144.1i	−0.979871	+	0.870429i
$866$	−681.450			−0.0267397
$867$			4558.69i			0.178571i
$868$		−	946.001i		−	0.0369923i
$869$	24344.6			0.950328
$870$	−2649.34	−	2982.45i	−0.103242	−	0.116223i
$871$	19174.9			0.745944
$872$			10093.7i			0.391992i
$873$		−	7371.09i		−	0.285766i
$874$	−7447.02			−0.288214
$875$	−6091.78	−	8750.22i	−0.235360	−	0.338070i
$876$	−7352.99			−0.283601
$877$			38717.9i			1.49078i	0.666631	+	0.745388i	$0.267736\pi$
$877$			38717.9i			1.49078i	−0.666631	+	0.745388i	$0.732264\pi$
$878$			20728.7i			0.796765i
$879$	−12153.4			−0.466354
$880$	4636.42	+	5219.37i	0.177606	+	0.199937i
$881$	−8217.95			−0.314267			−0.157134	−	0.987577i	$-0.550225\pi$
$881$	−8217.95			−0.314267			−0.157134	+	0.987577i	$0.550225\pi$
$882$		−	5126.36i		−	0.195707i
$883$			29799.1i			1.13570i	0.823133	+	0.567848i	$0.192224\pi$
$883$			29799.1i			1.13570i	−0.823133	+	0.567848i	$0.807776\pi$
$884$	17948.0			0.682868
$885$	−7186.95	+	6384.24i	−0.272979	+	0.242490i
$886$	33514.6			1.27082
$887$			23943.7i			0.906371i	0.891416	+	0.453185i	$0.149712\pi$
$887$			23943.7i			0.906371i	−0.891416	+	0.453185i	$0.850288\pi$
$888$		−	302.787i		−	0.0114424i
$889$	4512.06			0.170224
$890$	−6843.33	+	6079.00i	−0.257740	+	0.228953i
$891$	−3161.15			−0.118858
$892$		−	7541.02i		−	0.283063i
$893$			45249.8i			1.69566i
$894$	16518.6			0.617970
$895$	17989.3	+	20251.1i	0.671862	+	0.756337i
$896$	−976.517			−0.0364098
$897$			8643.62i			0.321742i
$898$		−	450.089i		−	0.0167257i
$899$	−1843.51			−0.0683920
$900$	−530.474	+	4468.62i	−0.0196472	+	0.165505i
$901$	20366.9			0.753074
$902$			19966.5i			0.737041i
$903$			1427.47i			0.0526060i
$904$	14170.0			0.521334
$905$	7764.95	+	8741.25i	0.285211	+	0.321071i
$906$	−10230.7			−0.375157
$907$		−	21952.2i		−	0.803652i	−0.915716	−	0.401826i	$-0.868376\pi$
$907$		−	21952.2i		−	0.803652i	0.915716	−	0.401826i	$-0.131624\pi$
$908$			16765.1i			0.612742i
$909$	2243.47			0.0818604
$910$	−7135.12	+	6338.20i	−0.259920	+	0.230889i
$911$	−2327.62			−0.0846516			−0.0423258	−	0.999104i	$-0.513477\pi$
$911$	−2327.62			−0.0846516			−0.0423258	+	0.999104i	$0.513477\pi$
$912$			3470.42i			0.126006i
$913$		−	17205.7i		−	0.623685i
$914$	−26039.3			−0.942345
$915$	−7463.34	+	6629.76i	−0.269651	+	0.239534i
$916$	2914.40			0.105125
$917$			11085.3i			0.399201i
$918$			4330.98i			0.155712i
$919$	8343.96			0.299501			0.149751	−	0.988724i	$-0.452153\pi$
$919$	8343.96			0.299501			0.149751	+	0.988724i	$0.452153\pi$
$920$	3059.17	+	3443.81i	0.109628	+	0.123412i
$921$	−2129.71			−0.0761958
$922$		−	22804.8i		−	0.814573i
$923$		−	22344.1i		−	0.796820i
$924$	−3572.82			−0.127205
$925$	−1566.02	−	185.904i	−0.0556654	−	0.00660808i
$926$	19329.8			0.685978
$927$			2120.42i			0.0751282i
$928$			1902.97i			0.0673149i
$929$	21961.1			0.775585			0.387793	−	0.921747i	$-0.373238\pi$
$929$	21961.1			0.775585			0.387793	+	0.921747i	$0.373238\pi$
$930$	1381.07	+	1554.72i	0.0486958	+	0.0548184i
$931$	−20591.0			−0.724858
$932$		−	17893.4i		−	0.628881i
$933$			73.5184i			0.00257973i
$934$	23543.7			0.824809
$935$	26163.2	−	23241.0i	0.915109	−	0.812901i
$936$	4028.06			0.140664
$937$			8952.90i			0.312144i	0.987746	+	0.156072i	$0.0498831\pi$
$937$			8952.90i			0.312144i	−0.987746	+	0.156072i	$0.950117\pi$
$938$			5229.61i			0.182039i
$939$	19938.1			0.692923
$940$	20925.4	−	18588.3i	0.726076	−	0.644981i
$941$	38315.1			1.32735			0.663674	−	0.748022i	$-0.268996\pi$
$941$	38315.1			1.32735			0.663674	+	0.748022i	$0.268996\pi$
$942$			10772.8i			0.372609i
$943$			13174.2i			0.454942i
$944$	4585.69			0.158106
$945$	−1529.45	−	1721.76i	−0.0526489	−	0.0592685i
$946$	−4868.17			−0.167313
$947$			40226.4i			1.38034i	0.723647	+	0.690170i	$0.242464\pi$
$947$			40226.4i			1.38034i	−0.723647	+	0.690170i	$0.757536\pi$
$948$		−	7485.57i		−	0.256456i
$949$	34280.4			1.17259
$950$	17949.1	+	2130.75i	0.612995	+	0.0727691i
$951$	2251.22			0.0767621
$952$			4894.99i			0.166647i
$953$			36928.2i			1.25522i	0.778529	+	0.627609i	$0.215966\pi$
$953$			36928.2i			1.25522i	−0.778529	+	0.627609i	$0.784034\pi$
$954$	4570.94			0.155125
$955$	9690.83	+	10909.3i	0.328364	+	0.369650i
$956$	−14504.8			−0.490711
$957$			6962.48i			0.235178i
$958$			750.310i			0.0253042i
$959$	3962.92			0.133441
$960$	1604.87	−	1425.62i	0.0539551	−	0.0479289i
$961$	961.000			0.0322581
$962$			1411.63i			0.0473105i
$963$		−	2447.90i		−	0.0819132i
$964$	2095.68			0.0700181
$965$	−19502.7	+	17324.5i	−0.650584	+	0.577921i
$966$	−2357.39			−0.0785175
$967$			13500.7i			0.448969i	0.974478	+	0.224485i	$0.0720699\pi$
$967$			13500.7i			0.448969i	−0.974478	+	0.224485i	$0.927930\pi$
$968$		−	1536.55i		−	0.0510192i
$969$	17396.2			0.576725
$970$	12162.5	+	13691.7i	0.402591	+	0.453210i
$971$	−35367.4			−1.16889			−0.584446	−	0.811433i	$-0.698688\pi$
$971$	−35367.4			−1.16889			−0.584446	+	0.811433i	$0.698688\pi$
$972$			972.000i			0.0320750i
$973$		−	15701.1i		−	0.517323i
$974$	−35815.4			−1.17823
$975$	2473.13	−	20833.2i	0.0812343	−	0.684304i
$976$	4762.05			0.156178
$977$			41040.5i			1.34391i	0.740592	+	0.671955i	$0.234545\pi$
$977$			41040.5i			1.34391i	−0.740592	+	0.671955i	$0.765455\pi$
$978$			12730.3i			0.416226i
$979$	15975.7			0.521537
$980$	8458.62	+	9522.15i	0.275715	+	0.310381i
$981$	11355.5			0.369574
$982$		−	15311.9i		−	0.497579i
$983$		−	11792.2i		−	0.382618i	−0.981530	−	0.191309i	$-0.938727\pi$
$983$		−	11792.2i		−	0.382618i	0.981530	−	0.191309i	$-0.0612733\pi$
$984$	6139.36			0.198898
$985$	−23697.0	+	21050.3i	−0.766547	+	0.680932i
$986$	9539.05			0.308099
$987$			14324.1i			0.461946i
$988$		−	16179.5i		−	0.520989i
$989$	−3212.09			−0.103274
$990$	5871.79	−	5215.97i	0.188503	−	0.167449i
$991$	23311.8			0.747250			0.373625	−	0.927580i	$-0.378115\pi$
$991$	23311.8			0.747250			0.373625	+	0.927580i	$0.378115\pi$
$992$		−	992.000i		−	0.0317500i
$993$			12779.5i			0.408402i
$994$	6093.96			0.194455
$995$	−5187.68	−	5839.94i	−0.165287	−	0.186069i
$996$	−5290.45			−0.168308
$997$			41966.0i			1.33308i	0.745471	+	0.666538i	$0.232224\pi$
$997$			41966.0i			1.33308i	−0.745471	+	0.666538i	$0.767776\pi$
$998$			11454.1i			0.363299i
$999$	−340.636			−0.0107880

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.4.d.c.559.13	yes	20
5.4	even	2	inner	930.4.d.c.559.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.4.d.c.559.3	✓	20	5.4	even	2	inner
930.4.d.c.559.13	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)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(-7.42511 - 8.35869i) q^{5} +6.00000 q^{6} -7.62904i q^{7} -8.00000i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(-7.42511 - 8.35869i) q^{5} +6.00000 q^{6} -7.62904i q^{7} -8.00000i q^{8} -9.00000 q^{9} +(16.7174 - 14.8502i) q^{10} -39.0265 q^{11} +12.0000i q^{12} -55.9453i q^{13} +15.2581 q^{14} +(-25.0761 + 22.2753i) q^{15} +16.0000 q^{16} -80.2033i q^{17} -18.0000i q^{18} -72.3004 q^{19} +(29.7005 + 33.4348i) q^{20} -22.8871 q^{21} -78.0530i q^{22} -51.5005i q^{23} -24.0000 q^{24} +(-14.7354 + 124.128i) q^{25} +111.891 q^{26} +27.0000i q^{27} +30.5162i q^{28} +59.4680 q^{29} +(-44.5507 - 50.1521i) q^{30} -31.0000 q^{31} +32.0000i q^{32} +117.080i q^{33} +160.407 q^{34} +(-63.7688 + 56.6465i) q^{35} +36.0000 q^{36} +12.6161i q^{37} -144.601i q^{38} -167.836 q^{39} +(-66.8695 + 59.4009i) q^{40} -255.807 q^{41} -45.7742i q^{42} -62.3700i q^{43} +156.106 q^{44} +(66.8260 + 75.2282i) q^{45} +103.001 q^{46} -625.858i q^{47} -48.0000i q^{48} +284.798 q^{49} +(-248.257 - 29.4708i) q^{50} -240.610 q^{51} +223.781i q^{52} +253.941i q^{53} -54.0000 q^{54} +(289.776 + 326.211i) q^{55} -61.0323 q^{56} +216.901i q^{57} +118.936i q^{58} +286.606 q^{59} +(100.304 - 89.1014i) q^{60} +297.628 q^{61} -62.0000i q^{62} +68.6613i q^{63} -64.0000 q^{64} +(-467.629 + 415.400i) q^{65} -234.159 q^{66} +342.744i q^{67} +320.813i q^{68} -154.501 q^{69} +(-113.293 - 127.538i) q^{70} +399.392 q^{71} +72.0000i q^{72} +612.749i q^{73} -25.2323 q^{74} +(372.385 + 44.2062i) q^{75} +289.202 q^{76} +297.735i q^{77} -335.672i q^{78} -623.797 q^{79} +(-118.802 - 133.739i) q^{80} +81.0000 q^{81} -511.613i q^{82} +440.871i q^{83} +91.5485 q^{84} +(-670.394 + 595.518i) q^{85} +124.740 q^{86} -178.404i q^{87} +312.212i q^{88} -409.354 q^{89} +(-150.456 + 133.652i) q^{90} -426.808 q^{91} +206.002i q^{92} +93.0000i q^{93} +1251.72 q^{94} +(536.839 + 604.337i) q^{95} +96.0000 q^{96} +819.010i q^{97} +569.596i q^{98} +351.239 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 80 q^{4} - 2 q^{5} + 120 q^{6} - 180 q^{9}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

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