LMFDB - Embedded newform 30.3.d.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [30,3,Mod(11,30)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(30, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("30.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	30.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:	$0.817440793081$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} + 9 $ x^4 - 4*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.1
Root			$-1.58114 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	30.11
Dual form			30.3.d.a.11.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(-0.581139 - 2.94317i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(-4.16228 + 0.821854i) q^{6} +11.4868 q^{7} +2.82843i q^{8} +(-8.32456 + 3.42079i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(-0.581139 - 2.94317i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(-4.16228 + 0.821854i) q^{6} +11.4868 q^{7} +2.82843i q^{8} +(-8.32456 + 3.42079i) q^{9} +3.16228 q^{10} +8.48528i q^{11} +(1.16228 + 5.88635i) q^{12} -10.0000 q^{13} -16.2448i q^{14} +(6.58114 - 1.29947i) q^{15} +4.00000 q^{16} -3.55415i q^{17} +(4.83772 + 11.7727i) q^{18} -10.9737 q^{19} -4.47214i q^{20} +(-6.67544 - 33.8078i) q^{21} +12.0000 q^{22} -17.6590i q^{23} +(8.32456 - 1.64371i) q^{24} -5.00000 q^{25} +14.1421i q^{26} +(14.9057 + 22.5127i) q^{27} -22.9737 q^{28} +26.8328i q^{29} +(-1.83772 - 9.30714i) q^{30} +8.00000 q^{31} -5.65685i q^{32} +(24.9737 - 4.93113i) q^{33} -5.02633 q^{34} +25.6853i q^{35} +(16.6491 - 6.84157i) q^{36} -59.9473 q^{37} +15.5191i q^{38} +(5.81139 + 29.4317i) q^{39} -6.32456 q^{40} +20.5247i q^{41} +(-47.8114 + 9.44050i) q^{42} +42.4605 q^{43} -16.9706i q^{44} +(-7.64911 - 18.6143i) q^{45} -24.9737 q^{46} -88.2952i q^{47} +(-2.32456 - 11.7727i) q^{48} +82.9473 q^{49} +7.07107i q^{50} +(-10.4605 + 2.06546i) q^{51} +20.0000 q^{52} -3.55415i q^{53} +(31.8377 - 21.0798i) q^{54} -18.9737 q^{55} +32.4897i q^{56} +(6.37722 + 32.2974i) q^{57} +37.9473 q^{58} -77.7445i q^{59} +(-13.1623 + 2.59893i) q^{60} +21.9473 q^{61} -11.3137i q^{62} +(-95.6228 + 39.2940i) q^{63} -8.00000 q^{64} -22.3607i q^{65} +(-6.97367 - 35.3181i) q^{66} -53.5395 q^{67} +7.10831i q^{68} +(-51.9737 + 10.2624i) q^{69} +36.3246 q^{70} +69.2592i q^{71} +(-9.67544 - 23.5454i) q^{72} +12.0527 q^{73} +84.7783i q^{74} +(2.90569 + 14.7159i) q^{75} +21.9473 q^{76} +97.4690i q^{77} +(41.6228 - 8.21854i) q^{78} -9.02633 q^{79} +8.94427i q^{80} +(57.5964 - 56.9530i) q^{81} +29.0263 q^{82} -0.688486i q^{83} +(13.3509 + 67.6155i) q^{84} +7.94733 q^{85} -60.0482i q^{86} +(78.9737 - 15.5936i) q^{87} -24.0000 q^{88} +7.10831i q^{89} +(-26.3246 + 10.8175i) q^{90} -114.868 q^{91} +35.3181i q^{92} +(-4.64911 - 23.5454i) q^{93} -124.868 q^{94} -24.5379i q^{95} +(-16.6491 + 3.28742i) q^{96} +111.947 q^{97} -117.305i q^{98} +(-29.0263 - 70.6362i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 8 q^{4} - 4 q^{6} + 8 q^{7} - 8 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 - 8 * q^4 - 4 * q^6 + 8 * q^7 - 8 * q^9	$ 4 q + 4 q^{3} - 8 q^{4} - 4 q^{6} + 8 q^{7} - 8 q^{9} - 8 q^{12} - 40 q^{13} + 20 q^{15} + 16 q^{16} + 32 q^{18} + 32 q^{19} - 52 q^{21} + 48 q^{22} + 8 q^{24} - 20 q^{25} + 28 q^{27} - 16 q^{28} - 20 q^{30} + 32 q^{31} + 24 q^{33} - 96 q^{34} + 16 q^{36} - 88 q^{37} - 40 q^{39} - 128 q^{42} + 56 q^{43} + 20 q^{45} - 24 q^{46} + 16 q^{48} + 180 q^{49} + 72 q^{51} + 80 q^{52} + 140 q^{54} + 152 q^{57} - 40 q^{60} - 64 q^{61} - 256 q^{63} - 32 q^{64} + 48 q^{66} - 328 q^{67} - 132 q^{69} + 120 q^{70} - 64 q^{72} + 200 q^{73} - 20 q^{75} - 64 q^{76} + 40 q^{78} - 112 q^{79} + 28 q^{81} + 192 q^{82} + 104 q^{84} - 120 q^{85} + 240 q^{87} - 96 q^{88} - 80 q^{90} - 80 q^{91} + 32 q^{93} - 120 q^{94} - 16 q^{96} + 296 q^{97} - 192 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 - 8 * q^4 - 4 * q^6 + 8 * q^7 - 8 * q^9 - 8 * q^12 - 40 * q^13 + 20 * q^15 + 16 * q^16 + 32 * q^18 + 32 * q^19 - 52 * q^21 + 48 * q^22 + 8 * q^24 - 20 * q^25 + 28 * q^27 - 16 * q^28 - 20 * q^30 + 32 * q^31 + 24 * q^33 - 96 * q^34 + 16 * q^36 - 88 * q^37 - 40 * q^39 - 128 * q^42 + 56 * q^43 + 20 * q^45 - 24 * q^46 + 16 * q^48 + 180 * q^49 + 72 * q^51 + 80 * q^52 + 140 * q^54 + 152 * q^57 - 40 * q^60 - 64 * q^61 - 256 * q^63 - 32 * q^64 + 48 * q^66 - 328 * q^67 - 132 * q^69 + 120 * q^70 - 64 * q^72 + 200 * q^73 - 20 * q^75 - 64 * q^76 + 40 * q^78 - 112 * q^79 + 28 * q^81 + 192 * q^82 + 104 * q^84 - 120 * q^85 + 240 * q^87 - 96 * q^88 - 80 * q^90 - 80 * q^91 + 32 * q^93 - 120 * q^94 - 16 * q^96 + 296 * q^97 - 192 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	−0.581139	−	2.94317i	−0.193713	−	0.981058i
$3$	−0.581139	−	2.94317i	−0.193713	−	0.981058i
$4$	−2.00000			−0.500000
$5$			2.23607i			0.447214i
$5$			2.23607i			0.447214i
$6$	−4.16228	+	0.821854i	−0.693713	+	0.136976i
$7$	11.4868			1.64098			0.820488	−	0.571664i	$-0.193702\pi$
$7$	11.4868			1.64098			0.820488	+	0.571664i	$0.193702\pi$
$8$			2.82843i			0.353553i
$9$	−8.32456	+	3.42079i	−0.924951	+	0.380087i
$10$	3.16228			0.316228
$11$			8.48528i			0.771389i	0.922627	+	0.385695i	$0.126038\pi$
$11$			8.48528i			0.771389i	−0.922627	+	0.385695i	$0.873962\pi$
$12$	1.16228	+	5.88635i	0.0968565	+	0.490529i
$13$	−10.0000			−0.769231			−0.384615	−	0.923077i	$-0.625666\pi$
$13$	−10.0000			−0.769231			−0.384615	+	0.923077i	$0.625666\pi$
$14$		−	16.2448i		−	1.16035i
$15$	6.58114	−	1.29947i	0.438743	−	0.0866311i
$16$	4.00000			0.250000
$17$		−	3.55415i		−	0.209068i	−0.994521	−	0.104534i	$-0.966665\pi$
$17$		−	3.55415i		−	0.209068i	0.994521	−	0.104534i	$-0.0333351\pi$
$18$	4.83772	+	11.7727i	0.268762	+	0.654039i
$19$	−10.9737			−0.577561			−0.288781	−	0.957395i	$-0.593250\pi$
$19$	−10.9737			−0.577561			−0.288781	+	0.957395i	$0.593250\pi$
$20$		−	4.47214i		−	0.223607i
$21$	−6.67544	−	33.8078i	−0.317878	−	1.60989i
$22$	12.0000			0.545455
$23$		−	17.6590i		−	0.767785i	−0.923378	−	0.383892i	$-0.874583\pi$
$23$		−	17.6590i		−	0.767785i	0.923378	−	0.383892i	$-0.125417\pi$
$24$	8.32456	−	1.64371i	0.346856	−	0.0684879i
$25$	−5.00000			−0.200000
$26$			14.1421i			0.543928i
$27$	14.9057	+	22.5127i	0.552063	+	0.833803i
$28$	−22.9737			−0.820488
$29$			26.8328i			0.925270i	0.886549	+	0.462635i	$0.153096\pi$
$29$			26.8328i			0.925270i	−0.886549	+	0.462635i	$0.846904\pi$
$30$	−1.83772	−	9.30714i	−0.0612574	−	0.310238i
$31$	8.00000			0.258065			0.129032	−	0.991640i	$-0.458813\pi$
$31$	8.00000			0.258065			0.129032	+	0.991640i	$0.458813\pi$
$32$		−	5.65685i		−	0.176777i
$33$	24.9737	−	4.93113i	0.756778	−	0.149428i
$34$	−5.02633			−0.147833
$35$			25.6853i			0.733867i
$36$	16.6491	−	6.84157i	0.462475	−	0.190044i
$37$	−59.9473			−1.62020			−0.810099	−	0.586293i	$-0.800587\pi$
$37$	−59.9473			−1.62020			−0.810099	+	0.586293i	$0.800587\pi$
$38$			15.5191i			0.408398i
$39$	5.81139	+	29.4317i	0.149010	+	0.754660i
$40$	−6.32456			−0.158114
$41$			20.5247i			0.500603i	0.968168	+	0.250301i	$0.0805297\pi$
$41$			20.5247i			0.500603i	−0.968168	+	0.250301i	$0.919470\pi$
$42$	−47.8114	+	9.44050i	−1.13837	+	0.224774i
$43$	42.4605			0.987453			0.493727	−	0.869617i	$-0.335634\pi$
$43$	42.4605			0.987453			0.493727	+	0.869617i	$0.335634\pi$
$44$		−	16.9706i		−	0.385695i
$45$	−7.64911	−	18.6143i	−0.169980	−	0.413650i
$46$	−24.9737			−0.542906
$47$		−	88.2952i		−	1.87862i	−0.343067	−	0.939311i	$-0.611466\pi$
$47$		−	88.2952i		−	1.87862i	0.343067	−	0.939311i	$-0.388534\pi$
$48$	−2.32456	−	11.7727i	−0.0484282	−	0.245265i
$49$	82.9473			1.69280
$50$			7.07107i			0.141421i
$51$	−10.4605	+	2.06546i	−0.205108	+	0.0404992i
$52$	20.0000			0.384615
$53$		−	3.55415i		−	0.0670595i	−0.999438	−	0.0335298i	$-0.989325\pi$
$53$		−	3.55415i		−	0.0670595i	0.999438	−	0.0335298i	$-0.0106749\pi$
$54$	31.8377	−	21.0798i	0.589587	−	0.390367i
$55$	−18.9737			−0.344976
$56$			32.4897i			0.580173i
$57$	6.37722	+	32.2974i	0.111881	+	0.566621i
$58$	37.9473			0.654264
$59$		−	77.7445i		−	1.31770i	−0.752273	−	0.658852i	$-0.771042\pi$
$59$		−	77.7445i		−	1.31770i	0.752273	−	0.658852i	$-0.228958\pi$
$60$	−13.1623	+	2.59893i	−0.219371	+	0.0433155i
$61$	21.9473			0.359792			0.179896	−	0.983686i	$-0.442424\pi$
$61$	21.9473			0.359792			0.179896	+	0.983686i	$0.442424\pi$
$62$		−	11.3137i		−	0.182479i
$63$	−95.6228	+	39.2940i	−1.51782	+	0.623714i
$64$	−8.00000			−0.125000
$65$		−	22.3607i		−	0.344010i
$66$	−6.97367	−	35.3181i	−0.105662	−	0.535123i
$67$	−53.5395			−0.799097			−0.399549	−	0.916712i	$-0.630833\pi$
$67$	−53.5395			−0.799097			−0.399549	+	0.916712i	$0.630833\pi$
$68$			7.10831i			0.104534i
$69$	−51.9737	+	10.2624i	−0.753242	+	0.148730i
$70$	36.3246			0.518922
$71$			69.2592i			0.975482i	0.872988	+	0.487741i	$0.162179\pi$
$71$			69.2592i			0.975482i	−0.872988	+	0.487741i	$0.837821\pi$
$72$	−9.67544	−	23.5454i	−0.134381	−	0.327019i
$73$	12.0527			0.165105			0.0825525	−	0.996587i	$-0.473693\pi$
$73$	12.0527			0.165105			0.0825525	+	0.996587i	$0.473693\pi$
$74$			84.7783i			1.14565i
$75$	2.90569	+	14.7159i	0.0387426	+	0.196212i
$76$	21.9473			0.288781
$77$			97.4690i			1.26583i
$78$	41.6228	−	8.21854i	0.533625	−	0.105366i
$79$	−9.02633			−0.114257			−0.0571287	−	0.998367i	$-0.518195\pi$
$79$	−9.02633			−0.114257			−0.0571287	+	0.998367i	$0.518195\pi$
$80$			8.94427i			0.111803i
$81$	57.5964	−	56.9530i	0.711067	−	0.703124i
$82$	29.0263			0.353980
$83$		−	0.688486i		−	0.00829501i	−0.999991	−	0.00414750i	$-0.998680\pi$
$83$		−	0.688486i		−	0.00829501i	0.999991	−	0.00414750i	$-0.00132020\pi$
$84$	13.3509	+	67.6155i	0.158939	+	0.804947i
$85$	7.94733			0.0934980
$86$		−	60.0482i		−	0.698235i
$87$	78.9737	−	15.5936i	0.907743	−	0.179237i
$88$	−24.0000			−0.272727
$89$			7.10831i			0.0798686i	0.999202	+	0.0399343i	$0.0127149\pi$
$89$			7.10831i			0.0798686i	−0.999202	+	0.0399343i	$0.987285\pi$
$90$	−26.3246	+	10.8175i	−0.292495	+	0.120194i
$91$	−114.868			−1.26229
$92$			35.3181i			0.383892i
$93$	−4.64911	−	23.5454i	−0.0499904	−	0.253176i
$94$	−124.868			−1.32839
$95$		−	24.5379i		−	0.258293i
$96$	−16.6491	+	3.28742i	−0.173428	+	0.0342439i
$97$	111.947			1.15410			0.577048	−	0.816710i	$-0.304205\pi$
$97$	111.947			1.15410			0.577048	+	0.816710i	$0.304205\pi$
$98$		−	117.305i		−	1.19699i
$99$	−29.0263	−	70.6362i	−0.293195	−	0.713497i
$100$	10.0000			0.100000
$101$		−	155.489i		−	1.53950i	−0.638348	−	0.769748i	$-0.720382\pi$
$101$		−	155.489i		−	1.53950i	0.638348	−	0.769748i	$-0.279618\pi$
$102$	2.92100	+	14.7934i	0.0286372	+	0.145033i
$103$	7.59217			0.0737104			0.0368552	−	0.999321i	$-0.488266\pi$
$103$	7.59217			0.0737104			0.0368552	+	0.999321i	$0.488266\pi$
$104$		−	28.2843i		−	0.271964i
$105$	75.5964	−	14.9267i	0.719966	−	0.142160i
$106$	−5.02633			−0.0474182
$107$		−	16.2821i		−	0.152169i	−0.997101	−	0.0760845i	$-0.975758\pi$
$107$		−	16.2821i		−	0.152169i	0.997101	−	0.0760845i	$-0.0242419\pi$
$108$	−29.8114	−	45.0253i	−0.276031	−	0.416901i
$109$	−93.8420			−0.860936			−0.430468	−	0.902606i	$-0.641651\pi$
$109$	−93.8420			−0.860936			−0.430468	+	0.902606i	$0.641651\pi$
$110$			26.8328i			0.243935i
$111$	34.8377	+	176.435i	0.313853	+	1.58951i
$112$	45.9473			0.410244
$113$			195.738i			1.73220i	0.499874	+	0.866098i	$0.333380\pi$
$113$			195.738i			1.73220i	−0.499874	+	0.866098i	$0.666620\pi$
$114$	45.6754	−	9.01876i	0.400662	−	0.0791119i
$115$	39.4868			0.343364
$116$		−	53.6656i		−	0.462635i
$117$	83.2456	−	34.2079i	0.711500	−	0.292375i
$118$	−109.947			−0.931757
$119$		−	40.8260i		−	0.343075i
$120$	3.67544	+	18.6143i	0.0306287	+	0.155119i
$121$	49.0000			0.404959
$122$		−	31.0382i		−	0.254412i
$123$	60.4078	−	11.9277i	0.491121	−	0.0969733i
$124$	−16.0000			−0.129032
$125$		−	11.1803i		−	0.0894427i
$126$	55.5701	+	135.231i	0.441033	+	1.07326i
$127$	−77.5395			−0.610547			−0.305274	−	0.952265i	$-0.598748\pi$
$127$	−77.5395			−0.610547			−0.305274	+	0.952265i	$0.598748\pi$
$128$			11.3137i			0.0883883i
$129$	−24.6754	−	124.969i	−0.191283	−	0.968749i
$130$	−31.6228			−0.243252
$131$			101.600i			0.775572i	0.921749	+	0.387786i	$0.126760\pi$
$131$			101.600i			0.775572i	−0.921749	+	0.387786i	$0.873240\pi$
$132$	−49.9473	+	9.86225i	−0.378389	+	0.0747140i
$133$	−126.053			−0.947764
$134$			75.7163i			0.565047i
$135$	−50.3399	+	33.3301i	−0.372888	+	0.246890i
$136$	10.0527			0.0739167
$137$			176.014i			1.28477i	0.766381	+	0.642386i	$0.222055\pi$
$137$			176.014i			1.28477i	−0.766381	+	0.642386i	$0.777945\pi$
$138$	14.5132	+	73.5019i	0.105168	+	0.532622i
$139$	188.816			1.35839			0.679193	−	0.733960i	$-0.262330\pi$
$139$	188.816			1.35839			0.679193	+	0.733960i	$0.262330\pi$
$140$		−	51.3707i		−	0.366933i
$141$	−259.868	+	51.3118i	−1.84304	+	0.363913i
$142$	97.9473			0.689770
$143$		−	84.8528i		−	0.593376i
$144$	−33.2982	+	13.6831i	−0.231238	+	0.0950218i
$145$	−60.0000			−0.413793
$146$		−	17.0450i		−	0.116747i
$147$	−48.2039	−	244.128i	−0.327918	−	1.66074i
$148$	119.895			0.810099
$149$			72.5899i			0.487181i	0.969878	+	0.243590i	$0.0783252\pi$
$149$			72.5899i			0.487181i	−0.969878	+	0.243590i	$0.921675\pi$
$150$	20.8114	−	4.10927i	0.138743	−	0.0273951i
$151$	93.9473			0.622168			0.311084	−	0.950382i	$-0.399308\pi$
$151$	93.9473			0.622168			0.311084	+	0.950382i	$0.399308\pi$
$152$		−	31.0382i		−	0.204199i
$153$	12.1580	+	29.5868i	0.0794641	+	0.193378i
$154$	137.842			0.895078
$155$			17.8885i			0.115410i
$156$	−11.6228	−	58.8635i	−0.0745050	−	0.377330i
$157$	−123.842			−0.788803			−0.394401	−	0.918938i	$-0.629048\pi$
$157$	−123.842			−0.788803			−0.394401	+	0.918938i	$0.629048\pi$
$158$			12.7652i			0.0807922i
$159$	−10.4605	+	2.06546i	−0.0657893	+	0.0129903i
$160$	12.6491			0.0790569
$161$		−	202.847i		−	1.25992i
$162$	−80.5438	−	81.4537i	−0.497184	−	0.502800i
$163$	159.381			0.977801			0.488900	−	0.872340i	$-0.337398\pi$
$163$	159.381			0.977801			0.488900	+	0.872340i	$0.337398\pi$
$164$		−	41.0494i		−	0.250301i
$165$	11.0263	+	55.8428i	0.0668263	+	0.338441i
$166$	−0.973666			−0.00586546
$167$			10.7742i			0.0645161i	0.999480	+	0.0322581i	$0.0102698\pi$
$167$			10.7742i			0.0645161i	−0.999480	+	0.0322581i	$0.989730\pi$
$168$	95.6228	−	18.8810i	0.569183	−	0.112387i
$169$	−69.0000			−0.408284
$170$		−	11.2392i		−	0.0661131i
$171$	91.3509	−	37.5386i	0.534216	−	0.219524i
$172$	−84.9210			−0.493727
$173$		−	283.345i		−	1.63783i	−0.573913	−	0.818916i	$-0.694575\pi$
$173$		−	283.345i		−	1.63783i	0.573913	−	0.818916i	$-0.305425\pi$
$174$	−22.0527	−	111.686i	−0.126739	−	0.641871i
$175$	−57.4342			−0.328195
$176$			33.9411i			0.192847i
$177$	−228.816	+	45.1804i	−1.29274	+	0.255256i
$178$	10.0527			0.0564757
$179$			306.624i			1.71298i	0.516163	+	0.856491i	$0.327360\pi$
$179$			306.624i			1.71298i	−0.516163	+	0.856491i	$0.672640\pi$
$180$	15.2982	+	37.2285i	0.0849901	+	0.206825i
$181$	265.684			1.46787			0.733934	−	0.679221i	$-0.237682\pi$
$181$	265.684			1.46787			0.733934	+	0.679221i	$0.237682\pi$
$182$			162.448i			0.892573i
$183$	−12.7544	−	64.5948i	−0.0696964	−	0.352977i
$184$	49.9473			0.271453
$185$		−	134.046i		−	0.724575i
$186$	−33.2982	+	6.57484i	−0.179023	+	0.0353486i
$187$	30.1580			0.161273
$188$			176.590i			0.939311i
$189$	171.219	+	258.599i	0.905922	+	1.36825i
$190$	−34.7018			−0.182641
$191$		−	159.620i		−	0.835706i	−0.908515	−	0.417853i	$-0.862783\pi$
$191$		−	159.620i		−	0.835706i	0.908515	−	0.417853i	$-0.137217\pi$
$192$	4.64911	+	23.5454i	0.0242141	+	0.122632i
$193$	−92.0527			−0.476957			−0.238478	−	0.971148i	$-0.576649\pi$
$193$	−92.0527			−0.476957			−0.238478	+	0.971148i	$0.576649\pi$
$194$		−	158.317i		−	0.816069i
$195$	−65.8114	+	12.9947i	−0.337494	+	0.0666393i
$196$	−165.895			−0.846401
$197$		−	69.8360i		−	0.354497i	−0.984166	−	0.177249i	$-0.943280\pi$
$197$		−	69.8360i		−	0.354497i	0.984166	−	0.177249i	$-0.0567197\pi$
$198$	−99.8947	+	41.0494i	−0.504519	+	0.207320i
$199$	148.921			0.748347			0.374173	−	0.927359i	$-0.377926\pi$
$199$	148.921			0.748347			0.374173	+	0.927359i	$0.377926\pi$
$200$		−	14.1421i		−	0.0707107i
$201$	31.1139	+	157.576i	0.154795	+	0.783961i
$202$	−219.895			−1.08859
$203$			308.224i			1.51835i
$204$	20.9210	−	4.13091i	0.102554	−	0.0202496i
$205$	−45.8947			−0.223876
$206$		−	10.7369i		−	0.0521211i
$207$	60.4078	+	147.004i	0.291825	+	0.710163i
$208$	−40.0000			−0.192308
$209$		−	93.1146i		−	0.445525i
$210$	−21.1096	−	106.910i	−0.100522	−	0.509093i
$211$	−285.842			−1.35470			−0.677351	−	0.735660i	$-0.736872\pi$
$211$	−285.842			−1.35470			−0.677351	+	0.735660i	$0.736872\pi$
$212$			7.10831i			0.0335298i
$213$	203.842	−	40.2492i	0.957005	−	0.188963i
$214$	−23.0263			−0.107600
$215$			94.9446i			0.441603i
$216$	−63.6754	+	42.1597i	−0.294794	+	0.195184i
$217$	91.8947			0.423478
$218$			132.713i			0.608774i
$219$	−7.00427	−	35.4731i	−0.0319830	−	0.161978i
$220$	37.9473			0.172488
$221$			35.5415i			0.160821i
$222$	249.517	−	49.2680i	1.12395	−	0.221928i
$223$	−71.3815			−0.320096			−0.160048	−	0.987109i	$-0.551165\pi$
$223$	−71.3815			−0.320096			−0.160048	+	0.987109i	$0.551165\pi$
$224$		−	64.9793i		−	0.290086i
$225$	41.6228	−	17.1039i	0.184990	−	0.0760175i
$226$	276.816			1.22485
$227$		−	29.1217i		−	0.128290i	−0.997941	−	0.0641448i	$-0.979568\pi$
$227$		−	29.1217i		−	0.128290i	0.997941	−	0.0641448i	$-0.0204319\pi$
$228$	−12.7544	−	64.5948i	−0.0559406	−	0.283311i
$229$	−129.684			−0.566306			−0.283153	−	0.959075i	$-0.591380\pi$
$229$	−129.684			−0.566306			−0.283153	+	0.959075i	$0.591380\pi$
$230$		−	55.8428i		−	0.242795i
$231$	286.868	−	56.6430i	1.24185	−	0.245208i
$232$	−75.8947			−0.327132
$233$		−	185.876i		−	0.797751i	−0.917005	−	0.398875i	$-0.869401\pi$
$233$		−	185.876i		−	0.797751i	0.917005	−	0.398875i	$-0.130599\pi$
$234$	−48.3772	−	117.727i	−0.206740	−	0.503107i
$235$	197.434			0.840145
$236$			155.489i			0.658852i
$237$	5.24555	+	26.5661i	0.0221331	+	0.112093i
$238$	−57.7367			−0.242591
$239$		−	302.716i		−	1.26659i	−0.773908	−	0.633297i	$-0.781701\pi$
$239$		−	302.716i		−	1.26659i	0.773908	−	0.633297i	$-0.218299\pi$
$240$	26.3246	−	5.19786i	0.109686	−	0.0216578i
$241$	−237.526			−0.985585			−0.492793	−	0.870147i	$-0.664024\pi$
$241$	−237.526			−0.985585			−0.492793	+	0.870147i	$0.664024\pi$
$242$		−	69.2965i		−	0.286349i
$243$	−201.094	−	136.419i	−0.827549	−	0.561394i
$244$	−43.8947			−0.179896
$245$			185.476i			0.757044i
$246$	−16.8683	−	85.4296i	−0.0685704	−	0.347275i
$247$	109.737			0.444278
$248$			22.6274i			0.0912396i
$249$	−2.02633	+	0.400106i	−0.00813789	+	0.00160685i
$250$	−15.8114			−0.0632456
$251$			84.6294i			0.337169i	0.985687	+	0.168584i	$0.0539196\pi$
$251$			84.6294i			0.337169i	−0.985687	+	0.168584i	$0.946080\pi$
$252$	191.246	−	78.5880i	0.758911	−	0.311857i
$253$	149.842			0.592261
$254$			109.657i			0.431722i
$255$	−4.61850	−	23.3904i	−0.0181118	−	0.0917270i
$256$	16.0000			0.0625000
$257$		−	292.054i		−	1.13640i	−0.822892	−	0.568198i	$-0.807641\pi$
$257$		−	292.054i		−	1.13640i	0.822892	−	0.568198i	$-0.192359\pi$
$258$	−176.732	+	34.8963i	−0.685009	+	0.135257i
$259$	−688.605			−2.65871
$260$			44.7214i			0.172005i
$261$	−91.7893	−	223.371i	−0.351683	−	0.855829i
$262$	143.684			0.548412
$263$		−	277.725i		−	1.05599i	−0.849247	−	0.527995i	$-0.822944\pi$
$263$		−	277.725i		−	1.05599i	0.849247	−	0.527995i	$-0.177056\pi$
$264$	13.9473	+	70.6362i	0.0528308	+	0.267561i
$265$	7.94733			0.0299899
$266$			178.265i			0.670171i
$267$	20.9210	−	4.13091i	0.0783558	−	0.0154716i
$268$	107.079			0.399549
$269$			286.546i			1.06523i	0.846359	+	0.532613i	$0.178790\pi$
$269$			286.546i			1.06523i	−0.846359	+	0.532613i	$0.821210\pi$
$270$	47.1359	+	71.1913i	0.174578	+	0.263672i
$271$	−324.105			−1.19596			−0.597980	−	0.801511i	$-0.704030\pi$
$271$	−324.105			−1.19596			−0.597980	+	0.801511i	$0.704030\pi$
$272$		−	14.2166i		−	0.0522670i
$273$	66.7544	+	338.078i	0.244522	+	1.23838i
$274$	248.921			0.908471
$275$		−	42.4264i		−	0.154278i
$276$	103.947	−	20.5247i	0.376621	−	0.0743649i
$277$	415.842			1.50123			0.750617	−	0.660737i	$-0.229756\pi$
$277$	415.842			1.50123			0.750617	+	0.660737i	$0.229756\pi$
$278$		−	267.026i		−	0.960524i
$279$	−66.5964	+	27.3663i	−0.238697	+	0.0980871i
$280$	−72.6491			−0.259461
$281$			431.726i			1.53639i	0.640216	+	0.768195i	$0.278845\pi$
$281$			431.726i			1.53639i	−0.640216	+	0.768195i	$0.721155\pi$
$282$	72.5658	+	367.509i	0.257326	+	1.30322i
$283$	141.540			0.500140			0.250070	−	0.968228i	$-0.419546\pi$
$283$	141.540			0.500140			0.250070	+	0.968228i	$0.419546\pi$
$284$		−	138.518i		−	0.487741i
$285$	−72.2192	+	14.2599i	−0.253401	+	0.0500348i
$286$	−120.000			−0.419580
$287$			235.764i			0.821477i
$288$	19.3509	+	47.0908i	0.0671906	+	0.163510i
$289$	276.368			0.956291
$290$			84.8528i			0.292596i
$291$	−65.0569	−	329.481i	−0.223563	−	1.13224i
$292$	−24.1053			−0.0825525
$293$			164.998i			0.563133i	0.959542	+	0.281566i	$0.0908540\pi$
$293$			164.998i			0.563133i	−0.959542	+	0.281566i	$0.909146\pi$
$294$	−345.250	+	68.1706i	−1.17432	+	0.231873i
$295$	173.842			0.589295
$296$		−	169.557i		−	0.572827i
$297$	−191.026	+	126.479i	−0.643186	+	0.425855i
$298$	102.658			0.344489
$299$			176.590i			0.590604i
$300$	−5.81139	−	29.4317i	−0.0193713	−	0.0981058i
$301$	487.737			1.62039
$302$		−	132.862i		−	0.439939i
$303$	−457.631	+	90.3607i	−1.51033	+	0.298220i
$304$	−43.8947			−0.144390
$305$			49.0757i			0.160904i
$306$	41.8420	−	17.1940i	0.136739	−	0.0561896i
$307$	159.381			0.519158			0.259579	−	0.965722i	$-0.416416\pi$
$307$	159.381			0.519158			0.259579	+	0.965722i	$0.416416\pi$
$308$		−	194.938i		−	0.632916i
$309$	−4.41210	−	22.3451i	−0.0142787	−	0.0723142i
$310$	25.2982			0.0816072
$311$			143.096i			0.460117i	0.973177	+	0.230058i	$0.0738917\pi$
$311$			143.096i			0.460117i	−0.973177	+	0.230058i	$0.926108\pi$
$312$	−83.2456	+	16.4371i	−0.266813	+	0.0526830i
$313$	−501.684			−1.60282			−0.801412	−	0.598113i	$-0.795918\pi$
$313$	−501.684			−1.60282			−0.801412	+	0.598113i	$0.795918\pi$
$314$			175.139i			0.557768i
$315$	−87.8641	−	213.819i	−0.278934	−	0.678791i
$316$	18.0527			0.0571287
$317$		−	334.257i		−	1.05444i	−0.849730	−	0.527219i	$-0.823235\pi$
$317$		−	334.257i		−	1.05444i	0.849730	−	0.527219i	$-0.176765\pi$
$318$	2.92100	+	14.7934i	0.00918553	+	0.0465201i
$319$	−227.684			−0.713743
$320$		−	17.8885i		−	0.0559017i
$321$	−47.9210	+	9.46215i	−0.149287	+	0.0294771i
$322$	−286.868			−0.890895
$323$			39.0021i			0.120750i
$324$	−115.193	+	113.906i	−0.355534	+	0.351562i
$325$	50.0000			0.153846
$326$		−	225.399i		−	0.691409i
$327$	54.5352	+	276.193i	0.166774	+	0.844628i
$328$	−58.0527			−0.176990
$329$		−	1014.23i		−	3.08277i
$330$	78.9737	−	15.5936i	0.239314	−	0.0472533i
$331$	389.421			1.17650			0.588249	−	0.808680i	$-0.299818\pi$
$331$	389.421			1.17650			0.588249	+	0.808680i	$0.299818\pi$
$332$			1.37697i			0.00414750i
$333$	499.035	−	205.067i	1.49860	−	0.615817i
$334$	15.2370			0.0456198
$335$		−	119.718i		−	0.357367i
$336$	−26.7018	−	135.231i	−0.0794696	−	0.402473i
$337$	−129.684			−0.384819			−0.192409	−	0.981315i	$-0.561630\pi$
$337$	−129.684			−0.384819			−0.192409	+	0.981315i	$0.561630\pi$
$338$			97.5807i			0.288700i
$339$	576.092	−	113.751i	1.69939	−	0.335549i
$340$	−15.8947			−0.0467490
$341$			67.8823i			0.199068i
$342$	−53.0875	−	129.190i	−0.155227	−	0.377748i
$343$	389.947			1.13687
$344$			120.096i			0.349118i
$345$	−22.9473	−	116.217i	−0.0665140	−	0.336860i
$346$	−400.710			−1.15812
$347$			346.985i			0.999956i	0.866038	+	0.499978i	$0.166659\pi$
$347$			346.985i			0.999956i	−0.866038	+	0.499978i	$0.833341\pi$
$348$	−157.947	+	31.1872i	−0.453872	+	0.0896183i
$349$	509.579			1.46011			0.730055	−	0.683388i	$-0.239494\pi$
$349$	509.579			1.46011			0.730055	+	0.683388i	$0.239494\pi$
$350$			81.2242i			0.232069i
$351$	−149.057	−	225.127i	−0.424664	−	0.641387i
$352$	48.0000			0.136364
$353$			637.679i			1.80646i	0.429159	+	0.903229i	$0.358810\pi$
$353$			637.679i			1.80646i	−0.429159	+	0.903229i	$0.641190\pi$
$354$	63.8947	+	323.594i	0.180493	+	0.914108i
$355$	−154.868			−0.436249
$356$		−	14.2166i		−	0.0399343i
$357$	−120.158	+	23.7256i	−0.336577	+	0.0664582i
$358$	433.631			1.21126
$359$			166.952i			0.465046i	0.972591	+	0.232523i	$0.0746982\pi$
$359$			166.952i			0.465046i	−0.972591	+	0.232523i	$0.925302\pi$
$360$	52.6491	−	21.6350i	0.146248	−	0.0600971i
$361$	−240.579			−0.666423
$362$		−	375.734i		−	1.03794i
$363$	−28.4758	−	144.216i	−0.0784457	−	0.397288i
$364$	229.737			0.631145
$365$			26.9506i			0.0738372i
$366$	−91.3509	+	18.0375i	−0.249593	+	0.0492828i
$367$	−505.828			−1.37828			−0.689140	−	0.724629i	$-0.742011\pi$
$367$	−505.828			−1.37828			−0.689140	+	0.724629i	$0.742011\pi$
$368$		−	70.6362i		−	0.191946i
$369$	−70.2107	−	170.859i	−0.190273	−	0.463033i
$370$	−189.570			−0.512352
$371$		−	40.8260i		−	0.110043i
$372$	9.29822	+	47.0908i	0.0249952	+	0.126588i
$373$	−416.053			−1.11542			−0.557711	−	0.830035i	$-0.688320\pi$
$373$	−416.053			−1.11542			−0.557711	+	0.830035i	$0.688320\pi$
$374$		−	42.6499i		−	0.114037i
$375$	−32.9057	+	6.49733i	−0.0877485	+	0.0173262i
$376$	249.737			0.664193
$377$		−	268.328i		−	0.711746i
$378$	365.715	−	242.141i	0.967499	−	0.640583i
$379$	82.7630			0.218372			0.109186	−	0.994021i	$-0.465176\pi$
$379$	82.7630			0.218372			0.109186	+	0.994021i	$0.465176\pi$
$380$			49.0757i			0.129147i
$381$	45.0612	+	228.212i	0.118271	+	0.598982i
$382$	−225.737			−0.590934
$383$			334.592i			0.873608i	0.899557	+	0.436804i	$0.143890\pi$
$383$			334.592i			0.873608i	−0.899557	+	0.436804i	$0.856110\pi$
$384$	33.2982	−	6.57484i	0.0867141	−	0.0171220i
$385$	−217.947			−0.566097
$386$			130.182i			0.337259i
$387$	−353.465	+	145.248i	−0.913346	+	0.375319i
$388$	−223.895			−0.577048
$389$			542.964i			1.39580i	0.716197	+	0.697898i	$0.245881\pi$
$389$			542.964i			1.39580i	−0.716197	+	0.697898i	$0.754119\pi$
$390$	18.3772	+	93.0714i	0.0471211	+	0.238645i
$391$	−62.7630			−0.160519
$392$			234.610i			0.598496i
$393$	299.026	−	59.0437i	0.760881	−	0.150238i
$394$	−98.7630			−0.250667
$395$		−	20.1835i		−	0.0510975i
$396$	58.0527	+	141.272i	0.146598	+	0.356748i
$397$	−214.000			−0.539043			−0.269521	−	0.962994i	$-0.586865\pi$
$397$	−214.000			−0.539043			−0.269521	+	0.962994i	$0.586865\pi$
$398$		−	210.606i		−	0.529161i
$399$	73.2541	+	370.995i	0.183594	+	0.929812i
$400$	−20.0000			−0.0500000
$401$			726.086i			1.81069i	0.424677	+	0.905345i	$0.360387\pi$
$401$			726.086i			1.81069i	−0.424677	+	0.905345i	$0.639613\pi$
$402$	222.846	−	44.0017i	0.554344	−	0.109457i
$403$	−80.0000			−0.198511
$404$			310.978i			0.769748i
$405$	127.351	+	128.790i	0.314447	+	0.317999i
$406$	435.895			1.07363
$407$		−	508.670i		−	1.24980i
$408$	−5.84200	−	29.5868i	−0.0143186	−	0.0725166i
$409$	−346.158			−0.846352			−0.423176	−	0.906047i	$-0.639085\pi$
$409$	−346.158			−0.846352			−0.423176	+	0.906047i	$0.639085\pi$
$410$			64.9049i			0.158305i
$411$	518.039	−	102.288i	1.26044	−	0.248877i
$412$	−15.1843			−0.0368552
$413$		−	893.038i		−	2.16232i
$414$	207.895	−	85.4296i	0.502161	−	0.206352i
$415$	1.53950			0.00370964
$416$			56.5685i			0.135982i
$417$	−109.728	−	555.717i	−0.263137	−	1.33266i
$418$	−131.684			−0.315033
$419$		−	580.907i		−	1.38641i	−0.720740	−	0.693206i	$-0.756198\pi$
$419$		−	580.907i		−	1.38641i	0.720740	−	0.693206i	$-0.243802\pi$
$420$	−151.193	+	29.8535i	−0.359983	+	0.0710798i
$421$	−269.315			−0.639704			−0.319852	−	0.947468i	$-0.603633\pi$
$421$	−269.315			−0.639704			−0.319852	+	0.947468i	$0.603633\pi$
$422$			404.242i			0.957919i
$423$	302.039	+	735.019i	0.714041	+	1.73763i
$424$	10.0527			0.0237091
$425$			17.7708i			0.0418136i
$426$	−56.9210	−	288.276i	−0.133617	−	0.676704i
$427$	252.105			0.590411
$428$			32.5642i			0.0760845i
$429$	−249.737	+	49.3113i	−0.582137	+	0.114945i
$430$	134.272			0.312260
$431$		−	776.068i		−	1.80062i	−0.435247	−	0.900311i	$-0.643339\pi$
$431$		−	776.068i		−	1.80062i	0.435247	−	0.900311i	$-0.356661\pi$
$432$	59.6228	+	90.0507i	0.138016	+	0.208451i
$433$	−195.526			−0.451561			−0.225781	−	0.974178i	$-0.572493\pi$
$433$	−195.526			−0.451561			−0.225781	+	0.974178i	$0.572493\pi$
$434$		−	129.959i		−	0.299444i
$435$	34.8683	+	176.590i	0.0801571	+	0.405955i
$436$	187.684			0.430468
$437$			193.785i			0.443443i
$438$	−50.1666	+	9.90554i	−0.114536	+	0.0226154i
$439$	598.763			1.36392			0.681962	−	0.731387i	$-0.261127\pi$
$439$	598.763			1.36392			0.681962	+	0.731387i	$0.261127\pi$
$440$		−	53.6656i		−	0.121967i
$441$	−690.500	+	283.745i	−1.56576	+	0.643413i
$442$	50.2633			0.113718
$443$		−	216.728i		−	0.489228i	−0.969621	−	0.244614i	$-0.921339\pi$
$443$		−	216.728i		−	0.489228i	0.969621	−	0.244614i	$-0.0786612\pi$
$444$	−69.6754	−	352.871i	−0.156927	−	0.794754i
$445$	−15.8947			−0.0357183
$446$			100.949i			0.226342i
$447$	213.645	−	42.1848i	0.477953	−	0.0943732i
$448$	−91.8947			−0.205122
$449$		−	246.203i		−	0.548336i	−0.961682	−	0.274168i	$-0.911598\pi$
$449$		−	246.203i		−	0.548336i	0.961682	−	0.274168i	$-0.0884025\pi$
$450$	−24.1886	−	58.8635i	−0.0537525	−	0.130808i
$451$	−174.158			−0.386160
$452$		−	391.476i		−	0.866098i
$453$	−54.5964	−	276.503i	−0.120522	−	0.610383i
$454$	−41.1843			−0.0907144
$455$		−	256.853i		−	0.564513i
$456$	−91.3509	+	18.0375i	−0.200331	+	0.0395559i
$457$	553.052			1.21018			0.605090	−	0.796157i	$-0.293137\pi$
$457$	553.052			1.21018			0.605090	+	0.796157i	$0.293137\pi$
$458$			183.401i			0.400439i
$459$	80.0135	−	52.9771i	0.174321	−	0.115419i
$460$	−78.9737			−0.171682
$461$		−	124.749i		−	0.270605i	−0.990804	−	0.135302i	$-0.956799\pi$
$461$		−	124.749i		−	0.270605i	0.990804	−	0.135302i	$-0.0432006\pi$
$462$	−80.1053	−	405.693i	−0.173388	−	0.878124i
$463$	669.723			1.44649			0.723243	−	0.690593i	$-0.242651\pi$
$463$	669.723			1.44649			0.723243	+	0.690593i	$0.242651\pi$
$464$			107.331i			0.231317i
$465$	52.6491	−	10.3957i	0.113224	−	0.0223564i
$466$	−262.868			−0.564095
$467$			486.880i			1.04257i	0.853383	+	0.521285i	$0.174547\pi$
$467$			486.880i			1.04257i	−0.853383	+	0.521285i	$0.825453\pi$
$468$	−166.491	+	68.4157i	−0.355750	+	0.146187i
$469$	−614.999			−1.31130
$470$		−	279.214i		−	0.594072i
$471$	71.9694	+	364.489i	0.152801	+	0.773861i
$472$	219.895			0.465879
$473$			360.289i			0.761711i
$474$	37.5701	−	7.41833i	0.0792618	−	0.0156505i
$475$	54.8683			0.115512
$476$			81.6520i			0.171538i
$477$	12.1580	+	29.5868i	0.0254885	+	0.0620267i
$478$	−428.105			−0.895618
$479$			520.580i			1.08680i	0.839472	+	0.543402i	$0.182864\pi$
$479$			520.580i			1.08680i	−0.839472	+	0.543402i	$0.817136\pi$
$480$	−7.35089	−	37.2285i	−0.0153144	−	0.0775595i
$481$	599.473			1.24631
$482$			335.912i			0.696914i
$483$	−597.013	+	117.882i	−1.23605	+	0.244062i
$484$	−98.0000			−0.202479
$485$			250.322i			0.516128i
$486$	−192.925	+	284.390i	−0.396966	+	0.585165i
$487$	−263.381			−0.540824			−0.270412	−	0.962745i	$-0.587160\pi$
$487$	−263.381			−0.540824			−0.270412	+	0.962745i	$0.587160\pi$
$488$			62.0764i			0.127206i
$489$	−92.6228	−	469.088i	−0.189413	−	0.959279i
$490$	262.302			0.535311
$491$		−	711.646i		−	1.44938i	−0.689074	−	0.724691i	$-0.741983\pi$
$491$		−	711.646i		−	1.44938i	0.689074	−	0.724691i	$-0.258017\pi$
$492$	−120.816	+	23.8554i	−0.245560	+	0.0484866i
$493$	95.3680			0.193444
$494$		−	155.191i		−	0.314152i
$495$	157.947	−	64.9049i	0.319086	−	0.131121i
$496$	32.0000			0.0645161
$497$			795.569i			1.60074i
$498$	0.565835	+	2.86567i	0.00113622	+	0.00575436i
$499$	23.0790			0.0462505			0.0231253	−	0.999733i	$-0.492638\pi$
$499$	23.0790			0.0462505			0.0231253	+	0.999733i	$0.492638\pi$
$500$			22.3607i			0.0447214i
$501$	31.7103	−	6.26130i	0.0632941	−	0.0124976i
$502$	119.684			0.238414
$503$			40.5844i			0.0806847i	0.999186	+	0.0403423i	$0.0128449\pi$
$503$			40.5844i			0.0806847i	−0.999186	+	0.0403423i	$0.987155\pi$
$504$	−111.140	−	270.462i	−0.220516	−	0.536631i
$505$	347.684			0.688483
$506$		−	211.909i		−	0.418792i
$507$	40.0986	+	203.079i	0.0790899	+	0.400550i
$508$	155.079			0.305274
$509$			484.591i			0.952045i	0.879433	+	0.476023i	$0.157922\pi$
$509$			484.591i			0.952045i	−0.879433	+	0.476023i	$0.842078\pi$
$510$	−33.0790	+	6.53155i	−0.0648608	+	0.0128070i
$511$	138.447			0.270933
$512$		−	22.6274i		−	0.0441942i
$513$	−163.570	−	247.047i	−0.318850	−	0.481572i
$514$	−413.026			−0.803553
$515$			16.9766i			0.0329643i
$516$	49.3509	+	249.937i	0.0956413	+	0.484375i
$517$	749.210			1.44915
$518$			973.835i			1.87999i
$519$	−833.934	+	164.663i	−1.60681	+	0.317269i
$520$	63.2456			0.121626
$521$		−	539.857i		−	1.03619i	−0.855322	−	0.518097i	$-0.826641\pi$
$521$		−	539.857i		−	1.03619i	0.855322	−	0.518097i	$-0.173359\pi$
$522$	−315.895	+	129.810i	−0.605162	+	0.248678i
$523$	−266.644			−0.509836			−0.254918	−	0.966963i	$-0.582048\pi$
$523$	−266.644			−0.509836			−0.254918	+	0.966963i	$0.582048\pi$
$524$		−	203.200i		−	0.387786i
$525$	33.3772	+	169.039i	0.0635757	+	0.321979i
$526$	−392.763			−0.746698
$527$		−	28.4332i		−	0.0539530i
$528$	99.8947	−	19.7245i	0.189194	−	0.0373570i
$529$	217.158			0.410507
$530$		−	11.2392i		−	0.0212061i
$531$	265.947	+	647.188i	0.500842	+	1.21881i
$532$	252.105			0.473882
$533$		−	205.247i		−	0.385079i
$534$	−5.84200	−	29.5868i	−0.0109401	−	0.0554059i
$535$	36.4078			0.0680520
$536$		−	151.433i		−	0.282523i
$537$	902.447	−	178.191i	1.68053	−	0.331827i
$538$	405.237			0.753229
$539$			703.831i			1.30581i
$540$	100.680	−	66.6603i	0.186444	−	0.123445i
$541$	−337.895			−0.624574			−0.312287	−	0.949988i	$-0.601095\pi$
$541$	−337.895			−0.624574			−0.312287	+	0.949988i	$0.601095\pi$
$542$			458.354i			0.845672i
$543$	−154.399	−	781.954i	−0.284345	−	1.44006i
$544$	−20.1053			−0.0369583
$545$		−	209.837i		−	0.385022i
$546$	478.114	−	94.4050i	0.875666	−	0.172903i
$547$	−214.566			−0.392259			−0.196130	−	0.980578i	$-0.562837\pi$
$547$	−214.566			−0.392259			−0.196130	+	0.980578i	$0.562837\pi$
$548$		−	352.027i		−	0.642386i
$549$	−182.702	+	75.0771i	−0.332790	+	0.136753i
$550$	−60.0000			−0.109091
$551$		−	294.454i		−	0.534400i
$552$	−29.0263	−	147.004i	−0.0525839	−	0.266311i
$553$	−103.684			−0.187494
$554$		−	588.089i		−	1.06153i
$555$	−394.522	+	77.8995i	−0.710850	+	0.140359i
$556$	−377.631			−0.679193
$557$		−	674.821i		−	1.21153i	−0.795644	−	0.605764i	$-0.792867\pi$
$557$		−	674.821i		−	1.21153i	0.795644	−	0.605764i	$-0.207133\pi$
$558$	38.7018	+	94.1816i	0.0693580	+	0.168784i
$559$	−424.605			−0.759580
$560$			102.741i			0.183467i
$561$	−17.5260	−	88.7603i	−0.0312406	−	0.158218i
$562$	610.552			1.08639
$563$		−	718.513i		−	1.27622i	−0.769944	−	0.638111i	$-0.779716\pi$
$563$		−	718.513i		−	1.27622i	0.769944	−	0.638111i	$-0.220284\pi$
$564$	519.737	−	102.624i	0.921519	−	0.181957i
$565$	−437.684			−0.774662
$566$		−	200.167i		−	0.353652i
$567$	661.601	−	654.210i	1.16684	−	1.15381i
$568$	−195.895			−0.344885
$569$			183.122i			0.321831i	0.986968	+	0.160916i	$0.0514447\pi$
$569$			183.122i			0.321831i	−0.986968	+	0.160916i	$0.948555\pi$
$570$	20.1666	+	102.133i	0.0353799	+	0.179181i
$571$	−295.895			−0.518204			−0.259102	−	0.965850i	$-0.583427\pi$
$571$	−295.895			−0.518204			−0.259102	+	0.965850i	$0.583427\pi$
$572$			169.706i			0.296688i
$573$	−469.789	+	92.7613i	−0.819877	+	0.161887i
$574$	333.421			0.580872
$575$			88.2952i			0.153557i
$576$	66.5964	−	27.3663i	0.115619	−	0.0475109i
$577$	−984.947			−1.70701			−0.853507	−	0.521082i	$-0.825529\pi$
$577$	−984.947			−1.70701			−0.853507	+	0.521082i	$0.825529\pi$
$578$		−	390.843i		−	0.676200i
$579$	53.4954	+	270.927i	0.0923927	+	0.467922i
$580$	120.000			0.206897
$581$		−	7.90852i		−	0.0136119i
$582$	−465.956	+	92.0044i	−0.800611	+	0.158083i
$583$	30.1580			0.0517290
$584$			34.0901i			0.0583734i
$585$	76.4911	+	186.143i	0.130754	+	0.318193i
$586$	233.342			0.398195
$587$			378.172i			0.644245i	0.946698	+	0.322122i	$0.104396\pi$
$587$			378.172i			0.644245i	−0.946698	+	0.322122i	$0.895604\pi$
$588$	96.4078	+	488.257i	0.163959	+	0.830369i
$589$	−87.7893			−0.149048
$590$		−	245.850i		−	0.416694i
$591$	−205.540	+	40.5844i	−0.347783	+	0.0686707i
$592$	−239.789			−0.405050
$593$			265.221i			0.447253i	0.974675	+	0.223626i	$0.0717895\pi$
$593$			265.221i			0.447253i	−0.974675	+	0.223626i	$0.928210\pi$
$594$	178.868	+	270.152i	0.301125	+	0.454801i
$595$	91.2897			0.153428
$596$		−	145.180i		−	0.243590i
$597$	−86.5438	−	438.301i	−0.144964	−	0.734172i
$598$	249.737			0.417620
$599$		−	382.061i		−	0.637832i	−0.947783	−	0.318916i	$-0.896681\pi$
$599$		−	382.061i		−	0.637832i	0.947783	−	0.318916i	$-0.103319\pi$
$600$	−41.6228	+	8.21854i	−0.0693713	+	0.0136976i
$601$	1021.53			1.69971			0.849855	−	0.527016i	$-0.176689\pi$
$601$	1021.53			1.69971			0.849855	+	0.527016i	$0.176689\pi$
$602$		−	689.764i		−	1.14579i
$603$	445.693	−	183.147i	0.739125	−	0.303727i
$604$	−187.895			−0.311084
$605$			109.567i			0.181103i
$606$	127.789	+	647.188i	0.210873	+	1.06797i
$607$	−835.487			−1.37642			−0.688210	−	0.725512i	$-0.741603\pi$
$607$	−835.487			−1.37642			−0.688210	+	0.725512i	$0.741603\pi$
$608$			62.0764i			0.102099i
$609$	907.157	−	179.121i	1.48959	−	0.294123i
$610$	69.4036			0.113776
$611$			882.952i			1.44509i
$612$	−24.3160	−	59.1735i	−0.0397320	−	0.0966888i
$613$	833.263			1.35932			0.679660	−	0.733528i	$-0.262128\pi$
$613$	833.263			1.35932			0.679660	+	0.733528i	$0.262128\pi$
$614$		−	225.399i		−	0.367100i
$615$	26.6712	+	135.076i	0.0433678	+	0.219636i
$616$	−275.684			−0.447539
$617$			455.098i			0.737598i	0.929509	+	0.368799i	$0.120231\pi$
$617$			455.098i			0.737598i	−0.929509	+	0.368799i	$0.879769\pi$
$618$	−31.6007	+	6.23966i	−0.0511338	+	0.0100965i
$619$	336.710			0.543959			0.271979	−	0.962303i	$-0.412322\pi$
$619$	336.710			0.543959			0.271979	+	0.962303i	$0.412322\pi$
$620$		−	35.7771i		−	0.0577050i
$621$	397.552	−	263.220i	0.640181	−	0.423865i
$622$	202.369			0.325352
$623$			81.6520i			0.131063i
$624$	23.2456	+	117.727i	0.0372525	+	0.188665i
$625$	25.0000			0.0400000
$626$			709.488i			1.13337i
$627$	−274.053	+	54.1125i	−0.437086	+	0.0863039i
$628$	247.684			0.394401
$629$			213.062i			0.338731i
$630$	−302.386	+	124.259i	−0.479977	+	0.197236i
$631$	−1100.89			−1.74468			−0.872341	−	0.488898i	$-0.837399\pi$
$631$	−1100.89			−1.74468			−0.872341	+	0.488898i	$0.837399\pi$
$632$		−	25.5303i		−	0.0403961i
$633$	166.114	+	841.283i	0.262423	+	1.32904i
$634$	−472.710			−0.745600
$635$		−	173.384i		−	0.273045i
$636$	20.9210	−	4.13091i	0.0328947	−	0.00649515i
$637$	−829.473			−1.30216
$638$			321.994i			0.504692i
$639$	−236.921	−	576.552i	−0.370768	−	0.902273i
$640$	−25.2982			−0.0395285
$641$			337.011i			0.525758i	0.964829	+	0.262879i	$0.0846719\pi$
$641$			337.011i			0.525758i	−0.964829	+	0.262879i	$0.915328\pi$
$642$	13.3815	+	67.7705i	0.0208435	+	0.105562i
$643$	−599.381			−0.932164			−0.466082	−	0.884742i	$-0.654335\pi$
$643$	−599.381			−0.932164			−0.466082	+	0.884742i	$0.654335\pi$
$644$			405.693i			0.629958i
$645$	279.438	−	55.1760i	0.433238	−	0.0855441i
$646$	55.1573			0.0853828
$647$		−	47.0224i		−	0.0726775i	−0.999340	−	0.0363388i	$-0.988430\pi$
$647$		−	47.0224i		−	0.0726775i	0.999340	−	0.0363388i	$-0.0115695\pi$
$648$	161.088	+	162.907i	0.248592	+	0.251400i
$649$	659.684			1.01646
$650$		−	70.7107i		−	0.108786i
$651$	−53.4036	−	270.462i	−0.0820331	−	0.415456i
$652$	−318.763			−0.488900
$653$			559.228i			0.856399i	0.903684	+	0.428199i	$0.140852\pi$
$653$			559.228i			0.856399i	−0.903684	+	0.428199i	$0.859148\pi$
$654$	390.596	−	77.1245i	0.597242	−	0.117927i
$655$	−227.184			−0.346846
$656$			82.0989i			0.125151i
$657$	−100.333	+	41.2296i	−0.152714	+	0.0627543i
$658$	−1434.34			−2.17985
$659$		−	665.759i		−	1.01026i	−0.863044	−	0.505129i	$-0.831445\pi$
$659$		−	665.759i		−	1.01026i	0.863044	−	0.505129i	$-0.168555\pi$
$660$	−22.0527	−	111.686i	−0.0334131	−	0.169221i
$661$	−557.947			−0.844096			−0.422048	−	0.906574i	$-0.638689\pi$
$661$	−557.947			−0.844096			−0.422048	+	0.906574i	$0.638689\pi$
$662$		−	550.724i		−	0.831909i
$663$	104.605	−	20.6546i	0.157775	−	0.0311532i
$664$	1.94733			0.00293273
$665$		−	281.862i		−	0.423853i
$666$	−290.009	−	705.742i	−0.435448	−	1.05967i
$667$	473.842			0.710408
$668$		−	21.5484i		−	0.0322581i
$669$	41.4826	+	210.088i	0.0620068	+	0.314033i
$670$	−169.307			−0.252697
$671$			186.229i			0.277540i
$672$	−191.246	+	37.7620i	−0.284592	+	0.0561935i
$673$	1019.42			1.51474			0.757370	−	0.652985i	$-0.226484\pi$
$673$	1019.42			1.51474			0.757370	+	0.652985i	$0.226484\pi$
$674$			183.401i			0.272108i
$675$	−74.5285	−	112.563i	−0.110413	−	0.166761i
$676$	138.000			0.204142
$677$			624.616i			0.922624i	0.887238	+	0.461312i	$0.152621\pi$
$677$			624.616i			0.922624i	−0.887238	+	0.461312i	$0.847379\pi$
$678$	−160.868	−	814.717i	−0.237269	−	1.20165i
$679$	1285.92			1.89384
$680$			22.4784i			0.0330565i
$681$	−85.7103	+	16.9238i	−0.125860	+	0.0248513i
$682$	96.0000			0.140762
$683$			525.882i			0.769959i	0.922925	+	0.384980i	$0.125792\pi$
$683$			525.882i			0.769959i	−0.922925	+	0.384980i	$0.874208\pi$
$684$	−182.702	+	75.0771i	−0.267108	+	0.109762i
$685$	−393.579			−0.574567
$686$		−	551.469i		−	0.803890i
$687$	75.3644	+	381.683i	0.109701	+	0.555579i
$688$	169.842			0.246863
$689$			35.5415i			0.0515843i
$690$	−164.355	+	32.4524i	−0.238196	+	0.0470325i
$691$	932.000			1.34877			0.674385	−	0.738380i	$-0.264409\pi$
$691$	932.000			1.34877			0.674385	+	0.738380i	$0.264409\pi$
$692$			566.690i			0.818916i
$693$	−333.421	−	811.386i	−0.481126	−	1.17083i
$694$	490.710			0.707075
$695$			422.205i			0.607489i
$696$	44.1053	+	223.371i	0.0633697	+	0.320936i
$697$	72.9480			0.104660
$698$		−	720.653i		−	1.03245i
$699$	−547.065	+	108.020i	−0.782640	+	0.154535i
$700$	114.868			0.164098
$701$		−	606.045i		−	0.864544i	−0.901743	−	0.432272i	$-0.857712\pi$
$701$		−	606.045i		−	0.864544i	0.901743	−	0.432272i	$-0.142288\pi$
$702$	−318.377	+	210.798i	−0.453529	+	0.300283i
$703$	657.842			0.935764
$704$		−	67.8823i		−	0.0964237i
$705$	−114.737	−	581.083i	−0.162747	−	0.824232i
$706$	901.815			1.27736
$707$		−	1786.08i		−	2.52627i
$708$	457.631	−	90.3607i	0.646372	−	0.127628i
$709$	489.473			0.690371			0.345186	−	0.938534i	$-0.387816\pi$
$709$	489.473			0.690371			0.345186	+	0.938534i	$0.387816\pi$
$710$			219.017i			0.308474i
$711$	75.1402	−	30.8772i	0.105682	−	0.0434278i
$712$	−20.1053			−0.0282378
$713$		−	141.272i		−	0.198138i
$714$	33.5530	+	169.929i	0.0469930	+	0.237996i
$715$	189.737			0.265366
$716$		−	613.247i		−	0.856491i
$717$	−890.947	+	175.920i	−1.24260	+	0.245356i
$718$	236.105			0.328838
$719$		−	107.778i		−	0.149900i	−0.997187	−	0.0749500i	$-0.976120\pi$
$719$		−	107.778i		−	0.149900i	0.997187	−	0.0749500i	$-0.0238797\pi$
$720$	−30.5964	−	74.4571i	−0.0424951	−	0.103413i
$721$	87.2100			0.120957
$722$			340.230i			0.471232i
$723$	138.036	+	699.080i	0.190921	+	0.966916i
$724$	−531.368			−0.733934
$725$		−	134.164i		−	0.185054i
$726$	−203.952	+	40.2709i	−0.280925	+	0.0554695i
$727$	−150.172			−0.206563			−0.103282	−	0.994652i	$-0.532934\pi$
$727$	−150.172			−0.206563			−0.103282	+	0.994652i	$0.532934\pi$
$728$		−	324.897i		−	0.446287i
$729$	−284.641	+	671.134i	−0.390453	+	0.920623i
$730$	38.1139			0.0522108
$731$		−	150.911i		−	0.206445i
$732$	25.5089	+	129.190i	0.0348482	+	0.176489i
$733$	−675.526			−0.921591			−0.460795	−	0.887506i	$-0.652436\pi$
$733$	−675.526			−0.921591			−0.460795	+	0.887506i	$0.652436\pi$
$734$			715.349i			0.974591i
$735$	545.888	−	107.787i	0.742705	−	0.146649i
$736$	−99.8947			−0.135726
$737$		−	454.298i		−	0.616415i
$738$	−241.631	+	99.2929i	−0.327414	+	0.134543i
$739$	−936.921			−1.26782			−0.633911	−	0.773406i	$-0.718552\pi$
$739$	−936.921			−1.26782			−0.633911	+	0.773406i	$0.718552\pi$
$740$			268.093i			0.362287i
$741$	−63.7722	−	322.974i	−0.0860624	−	0.435863i
$742$	−57.7367			−0.0778122
$743$			452.939i			0.609608i	0.952415	+	0.304804i	$0.0985910\pi$
$743$			452.939i			0.609608i	−0.952415	+	0.304804i	$0.901409\pi$
$744$	66.5964	−	13.1497i	0.0895113	−	0.0176743i
$745$	−162.316			−0.217874
$746$			588.387i			0.788723i
$747$	2.35516	+	5.73134i	0.00315283	+	0.00767247i
$748$	−60.3160			−0.0806364
$749$		−	187.029i		−	0.249706i
$750$	9.18861	+	46.5357i	0.0122515	+	0.0620476i
$751$	654.369			0.871330			0.435665	−	0.900109i	$-0.356513\pi$
$751$	654.369			0.871330			0.435665	+	0.900109i	$0.356513\pi$
$752$		−	353.181i		−	0.469656i
$753$	249.079	−	49.1814i	0.330782	−	0.0653140i
$754$	−379.473			−0.503280
$755$			210.073i			0.278242i
$756$	−342.438	−	517.199i	−0.452961	−	0.684125i
$757$	123.315			0.162900			0.0814500	−	0.996677i	$-0.474045\pi$
$757$	123.315			0.162900			0.0814500	+	0.996677i	$0.474045\pi$
$758$		−	117.045i		−	0.154412i
$759$	−87.0790	−	441.011i	−0.114729	−	0.581042i
$760$	69.4036			0.0913205
$761$		−	502.715i		−	0.660598i	−0.943876	−	0.330299i	$-0.892850\pi$
$761$		−	502.715i		−	0.660598i	0.943876	−	0.330299i	$-0.107150\pi$
$762$	322.741	−	63.7262i	0.423545	−	0.0836302i
$763$	−1077.95			−1.41278
$764$			319.240i			0.417853i
$765$	−66.1580	+	27.1861i	−0.0864811	+	0.0355374i
$766$	473.184			0.617734
$767$			777.445i			1.01362i
$768$	−9.29822	−	47.0908i	−0.0121071	−	0.0613161i
$769$	−286.316			−0.372323			−0.186161	−	0.982519i	$-0.559605\pi$
$769$	−286.316			−0.372323			−0.186161	+	0.982519i	$0.559605\pi$
$770$			308.224i			0.400291i
$771$	−859.565	+	169.724i	−1.11487	+	0.220135i
$772$	184.105			0.238478
$773$		−	972.030i		−	1.25748i	−0.777617	−	0.628739i	$-0.783572\pi$
$773$		−	972.030i		−	1.25748i	0.777617	−	0.628739i	$-0.216428\pi$
$774$	205.412	+	499.875i	0.265390	+	0.645833i
$775$	−40.0000			−0.0516129
$776$			316.635i			0.408035i
$777$	400.175	+	2026.68i	0.515026	+	2.60835i
$778$	767.868			0.986976
$779$		−	225.231i		−	0.289129i
$780$	131.623	−	25.9893i	0.168747	−	0.0333196i
$781$	−587.684			−0.752476
$782$			88.7603i			0.113504i
$783$	−604.078	+	399.962i	−0.771492	+	0.510807i
$784$	331.789			0.423201
$785$		−	276.919i		−	0.352763i
$786$	−83.5003	−	422.887i	−0.106235	−	0.538024i
$787$	1492.70			1.89669			0.948346	−	0.317237i	$-0.102755\pi$
$787$	1492.70			1.89669			0.948346	+	0.317237i	$0.102755\pi$
$788$			139.672i			0.177249i
$789$	−817.394	+	161.397i	−1.03599	+	0.204559i
$790$	−28.5438			−0.0361314
$791$			2248.41i			2.84249i
$792$	199.789	−	82.0989i	0.252259	−	0.103660i
$793$	−219.473			−0.276763
$794$			302.642i			0.381161i
$795$	−4.61850	−	23.3904i	−0.00580944	−	0.0294219i
$796$	−297.842			−0.374173
$797$		−	94.3618i		−	0.118396i	−0.998246	−	0.0591981i	$-0.981146\pi$
$797$		−	94.3618i		−	0.118396i	0.998246	−	0.0591981i	$-0.0188544\pi$
$798$	524.666	−	103.597i	0.657476	−	0.129821i
$799$	−313.815			−0.392760
$800$			28.2843i			0.0353553i
$801$	−24.3160	−	59.1735i	−0.0303571	−	0.0738746i
$802$	1026.84			1.28035
$803$			102.270i			0.127360i
$804$	−62.2278	−	315.152i	−0.0773977	−	0.391980i
$805$	453.579			0.563452
$806$			113.137i			0.140369i
$807$	843.354	−	166.523i	1.04505	−	0.206348i
$808$	439.789			0.544294
$809$		−	1103.35i		−	1.36384i	−0.731427	−	0.681920i	$-0.761145\pi$
$809$		−	1103.35i		−	1.36384i	0.731427	−	0.681920i	$-0.238855\pi$
$810$	182.136	−	180.101i	0.224859	−	0.222347i
$811$	−10.1580			−0.0125253			−0.00626264	−	0.999980i	$-0.501993\pi$
$811$	−10.1580			−0.0125253			−0.00626264	+	0.999980i	$0.501993\pi$
$812$		−	616.448i		−	0.759173i
$813$	188.350	+	953.899i	0.231673	+	1.17331i
$814$	−719.368			−0.883744
$815$			356.388i			0.437286i
$816$	−41.8420	+	8.26183i	−0.0512770	+	0.0101248i
$817$	−465.947			−0.570315
$818$			489.541i			0.598461i
$819$	956.228	−	392.940i	1.16756	−	0.479780i
$820$	91.7893			0.111938
$821$			337.011i			0.410488i	0.978711	+	0.205244i	$0.0657988\pi$
$821$			337.011i			0.410488i	−0.978711	+	0.205244i	$0.934201\pi$
$822$	−144.658	−	732.618i	−0.175983	−	0.891263i
$823$	−901.512			−1.09540			−0.547699	−	0.836675i	$-0.684496\pi$
$823$	−901.512			−1.09540			−0.547699	+	0.836675i	$0.684496\pi$
$824$			21.4739i			0.0260606i
$825$	−124.868	+	24.6556i	−0.151356	+	0.0298856i
$826$	−1262.95			−1.52899
$827$		−	531.354i		−	0.642508i	−0.946993	−	0.321254i	$-0.895896\pi$
$827$		−	531.354i		−	0.642508i	0.946993	−	0.321254i	$-0.104104\pi$
$828$	−120.816	−	294.007i	−0.145913	−	0.355081i
$829$	−197.631			−0.238397			−0.119199	−	0.992870i	$-0.538033\pi$
$829$	−197.631			−0.238397			−0.119199	+	0.992870i	$0.538033\pi$
$830$		−	2.17718i		−	0.00262311i
$831$	−241.662	−	1223.90i	−0.290809	−	1.47280i
$832$	80.0000			0.0961538
$833$		−	294.808i		−	0.353911i
$834$	−785.903	+	155.179i	−0.942330	+	0.186066i
$835$	−24.0918			−0.0288525
$836$			186.229i			0.222762i
$837$	119.246	+	180.101i	0.142468	+	0.215175i
$838$	−821.526			−0.980341
$839$		−	943.950i		−	1.12509i	−0.826767	−	0.562545i	$-0.809822\pi$
$839$		−	943.950i		−	1.12509i	0.826767	−	0.562545i	$-0.190178\pi$
$840$	42.2192	+	213.819i	0.0502610	+	0.254546i
$841$	121.000			0.143876
$842$			380.869i			0.452339i
$843$	1270.64	−	250.893i	1.50729	−	0.297619i
$844$	571.684			0.677351
$845$		−	154.289i		−	0.182590i
$846$	1039.47	−	427.148i	1.22869	−	0.504903i
$847$	562.855			0.664528
$848$		−	14.2166i		−	0.0167649i
$849$	−82.2541	−	416.575i	−0.0968835	−	0.490666i
$850$	25.1317			0.0295667
$851$			1058.61i			1.24396i
$852$	−407.684	+	80.4984i	−0.478502	+	0.0944817i
$853$	−1196.42			−1.40260			−0.701301	−	0.712865i	$-0.747397\pi$
$853$	−1196.42			−1.40260			−0.701301	+	0.712865i	$0.747397\pi$
$854$		−	356.531i		−	0.417483i
$855$	83.9388	+	204.267i	0.0981740	+	0.238909i
$856$	46.0527			0.0537998
$857$		−	1266.04i		−	1.47729i	−0.674095	−	0.738645i	$-0.735466\pi$
$857$		−	1266.04i		−	1.47729i	0.674095	−	0.738645i	$-0.264534\pi$
$858$	69.7367	+	353.181i	0.0812782	+	0.411633i
$859$	−470.868			−0.548159			−0.274079	−	0.961707i	$-0.588373\pi$
$859$	−470.868			−0.548159			−0.274079	+	0.961707i	$0.588373\pi$
$860$		−	189.889i		−	0.220801i
$861$	693.895	−	137.012i	0.805917	−	0.159131i
$862$	−1097.53			−1.27323
$863$		−	285.057i		−	0.330310i	−0.986268	−	0.165155i	$-0.947188\pi$
$863$		−	285.057i		−	0.330310i	0.986268	−	0.165155i	$-0.0528124\pi$
$864$	127.351	−	84.3193i	0.147397	−	0.0975918i
$865$	633.579			0.732461
$866$			276.516i			0.319302i
$867$	−160.608	−	813.399i	−0.185246	−	0.938177i
$868$	−183.789			−0.211739
$869$		−	76.5910i		−	0.0881369i
$870$	249.737	−	49.3113i	0.287054	−	0.0566796i
$871$	535.395			0.614690
$872$		−	265.425i		−	0.304387i
$873$	−931.912	+	382.948i	−1.06748	+	0.438657i
$874$	274.053			0.313561
$875$		−	128.427i		−	0.146773i
$876$	14.0085	+	70.9462i	0.0159915	+	0.0809888i
$877$	244.579			0.278882			0.139441	−	0.990230i	$-0.455469\pi$
$877$	244.579			0.278882			0.139441	+	0.990230i	$0.455469\pi$
$878$		−	846.779i		−	0.964440i
$879$	485.618	−	95.8867i	0.552466	−	0.109086i
$880$	−75.8947			−0.0862439
$881$		−	137.271i		−	0.155813i	−0.996961	−	0.0779065i	$-0.975176\pi$
$881$		−	137.271i		−	0.155813i	0.996961	−	0.0779065i	$-0.0248236\pi$
$882$	401.276	+	976.514i	0.454962	+	1.10716i
$883$	1647.75			1.86608			0.933040	−	0.359772i	$-0.117146\pi$
$883$	1647.75			1.86608			0.933040	+	0.359772i	$0.117146\pi$
$884$		−	71.0831i		−	0.0804107i
$885$	−101.026	−	511.647i	−0.114154	−	0.578133i
$886$	−306.500			−0.345936
$887$			514.419i			0.579954i	0.957034	+	0.289977i	$0.0936477\pi$
$887$			514.419i			0.579954i	−0.957034	+	0.289977i	$0.906352\pi$
$888$	−499.035	+	98.5360i	−0.561976	+	0.110964i
$889$	−890.683			−1.00189
$890$			22.4784i			0.0252567i
$891$	483.263	+	488.722i	0.542382	+	0.548510i
$892$	142.763			0.160048
$893$			968.923i			1.08502i
$894$	−59.6584	−	302.139i	−0.0667319	−	0.337964i
$895$	−685.631			−0.766069
$896$			129.959i			0.145043i
$897$	519.737	−	102.624i	0.579417	−	0.114408i
$898$	−348.184			−0.387732
$899$			214.663i			0.238779i
$900$	−83.2456	+	34.2079i	−0.0924951	+	0.0380087i
$901$	−12.6320			−0.0140200
$902$			246.297i			0.273056i
$903$	−283.443	−	1435.49i	−0.313890	−	1.58969i
$904$	−553.631			−0.612424
$905$			594.087i			0.656450i
$906$	−391.035	+	77.2110i	−0.431606	+	0.0852219i
$907$	347.303			0.382914			0.191457	−	0.981501i	$-0.438679\pi$
$907$	347.303			0.382914			0.191457	+	0.981501i	$0.438679\pi$
$908$			58.2434i			0.0641448i
$909$	531.895	+	1294.38i	0.585143	+	1.42396i
$910$	−363.246			−0.399171
$911$			304.540i			0.334292i	0.985932	+	0.167146i	$0.0534551\pi$
$911$			304.540i			0.334292i	−0.985932	+	0.167146i	$0.946545\pi$
$912$	25.5089	+	129.190i	0.0279703	+	0.141655i
$913$	5.84200			0.00639868
$914$		−	782.134i		−	0.855726i
$915$	144.438	−	28.5198i	0.157856	−	0.0311692i
$916$	259.368			0.283153
$917$			1167.06i			1.27270i
$918$	−74.9210	−	113.156i	−0.0816133	−	0.123264i
$919$	244.289			0.265820			0.132910	−	0.991128i	$-0.457568\pi$
$919$	244.289			0.265820			0.132910	+	0.991128i	$0.457568\pi$
$920$			111.686i			0.121397i
$921$	−92.6228	−	469.088i	−0.100568	−	0.509324i
$922$	−176.421			−0.191346
$923$		−	692.592i		−	0.750371i
$924$	−573.737	+	113.286i	−0.620927	+	0.122604i
$925$	299.737			0.324040
$926$		−	947.132i		−	1.02282i
$927$	−63.2014	+	25.9712i	−0.0681785	+	0.0280164i
$928$	151.789			0.163566
$929$			1025.96i			1.10437i	0.833723	+	0.552183i	$0.186205\pi$
$929$			1025.96i			1.10437i	−0.833723	+	0.552183i	$0.813795\pi$
$930$	−14.7018	−	74.4571i	−0.0158084	−	0.0800614i
$931$	−910.236			−0.977697
$932$			371.752i			0.398875i
$933$	421.157	−	83.1588i	0.451401	−	0.0891305i
$934$	688.552			0.737208
$935$			67.4353i			0.0721234i
$936$	96.7544	+	235.454i	0.103370	+	0.251553i
$937$	−332.053			−0.354379			−0.177189	−	0.984177i	$-0.556700\pi$
$937$	−332.053			−0.354379			−0.177189	+	0.984177i	$0.556700\pi$
$938$			869.740i			0.927229i
$939$	291.548	+	1476.54i	0.310488	+	1.57246i
$940$	−394.868			−0.420073
$941$		−	1636.99i		−	1.73963i	−0.493381	−	0.869813i	$-0.664239\pi$
$941$		−	1636.99i		−	1.73963i	0.493381	−	0.869813i	$-0.335761\pi$
$942$	515.465	−	101.780i	0.547203	−	0.108047i
$943$	362.447			0.384355
$944$		−	310.978i		−	0.329426i
$945$	−578.246	+	382.858i	−0.611900	+	0.405141i
$946$	509.526			0.538611
$947$		−	1209.32i		−	1.27700i	−0.769622	−	0.638500i	$-0.779555\pi$
$947$		−	1209.32i		−	1.27700i	0.769622	−	0.638500i	$-0.220445\pi$
$948$	−10.4911	−	53.1322i	−0.0110666	−	0.0560466i
$949$	−120.527			−0.127004
$950$		−	77.5955i		−	0.0816795i
$951$	−983.776	+	194.250i	−1.03446	+	0.204258i
$952$	115.473			0.121296
$953$			1205.26i			1.26470i	0.774681	+	0.632352i	$0.217910\pi$
$953$			1205.26i			1.26470i	−0.774681	+	0.632352i	$0.782090\pi$
$954$	41.8420	−	17.1940i	0.0438595	−	0.0180231i
$955$	356.921			0.373739
$956$			605.432i			0.633297i
$957$	132.316	+	670.114i	0.138261	+	0.700223i
$958$	736.211			0.768487
$959$			2021.84i			2.10828i
$960$	−52.6491	+	10.3957i	−0.0548428	+	0.0108289i
$961$	−897.000			−0.933403
$962$		−	847.783i		−	0.881272i
$963$	55.6975	+	135.541i	0.0578375	+	0.140749i
$964$	475.052			0.492793
$965$		−	205.836i		−	0.213302i
$966$	166.710	+	844.304i	0.172578	+	0.874020i
$967$	−1845.93			−1.90893			−0.954464	−	0.298325i	$-0.903572\pi$
$967$	−1845.93			−1.90893			−0.954464	+	0.298325i	$0.903572\pi$
$968$			138.593i			0.143175i
$969$	114.790	−	22.6656i	0.118462	−	0.0233908i
$970$	354.009			0.364957
$971$		−	1057.91i		−	1.08950i	−0.838598	−	0.544751i	$-0.816624\pi$
$971$		−	1057.91i		−	1.08950i	0.838598	−	0.544751i	$-0.183376\pi$
$972$	402.189	+	272.838i	0.413774	+	0.280697i
$973$	2168.89			2.22908
$974$			372.478i			0.382421i
$975$	−29.0569	−	147.159i	−0.0298020	−	0.150932i
$976$	87.7893			0.0899481
$977$			964.028i			0.986722i	0.869825	+	0.493361i	$0.164232\pi$
$977$			964.028i			0.986722i	−0.869825	+	0.493361i	$0.835768\pi$
$978$	−663.390	+	130.988i	−0.678313	+	0.133935i
$979$	−60.3160			−0.0616098
$980$		−	370.952i		−	0.378522i
$981$	781.193	−	321.013i	0.796323	−	0.327231i
$982$	−1006.42			−1.02487
$983$		−	460.718i		−	0.468685i	−0.972154	−	0.234343i	$-0.924706\pi$
$983$		−	460.718i		−	0.468685i	0.972154	−	0.234343i	$-0.0752937\pi$
$984$	33.7367	+	170.859i	0.0342852	+	0.173637i
$985$	156.158			0.158536
$986$		−	134.871i		−	0.136786i
$987$	−2985.06	+	589.410i	−3.02438	+	0.597173i
$988$	−219.473			−0.222139
$989$		−	749.812i		−	0.758152i
$990$	−91.7893	−	223.371i	−0.0927165	−	0.225628i
$991$	1237.89			1.24914			0.624568	−	0.780971i	$-0.285275\pi$
$991$	1237.89			1.24914			0.624568	+	0.780971i	$0.285275\pi$
$992$		−	45.2548i		−	0.0456198i
$993$	−226.307	−	1146.13i	−0.227903	−	1.15421i
$994$	1125.10			1.13190
$995$			332.997i			0.334671i
$996$	4.05267	−	0.800212i	0.00406894	−	0.000803425i
$997$	−9.36798			−0.00939617			−0.00469809	−	0.999989i	$-0.501495\pi$
$997$	−9.36798			−0.00939617			−0.00469809	+	0.999989i	$0.501495\pi$
$998$		−	32.6386i		−	0.0327040i
$999$	−893.557	−	1349.57i	−0.894451	−	1.35093i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.3.d.a.11.1	✓	4
3.2	odd	2	inner	30.3.d.a.11.3	yes	4
4.3	odd	2		240.3.l.c.161.4		4
5.2	odd	4		150.3.b.b.149.6		8
5.3	odd	4		150.3.b.b.149.3		8
5.4	even	2		150.3.d.c.101.4		4
8.3	odd	2		960.3.l.f.641.1		4
8.5	even	2		960.3.l.e.641.4		4
9.2	odd	6		810.3.h.a.701.4		8
9.4	even	3		810.3.h.a.431.4		8
9.5	odd	6		810.3.h.a.431.1		8
9.7	even	3		810.3.h.a.701.1		8
12.11	even	2		240.3.l.c.161.3		4
15.2	even	4		150.3.b.b.149.4		8
15.8	even	4		150.3.b.b.149.5		8
15.14	odd	2		150.3.d.c.101.2		4
20.3	even	4		1200.3.c.k.449.2		8
20.7	even	4		1200.3.c.k.449.7		8
20.19	odd	2		1200.3.l.u.401.1		4
24.5	odd	2		960.3.l.e.641.3		4
24.11	even	2		960.3.l.f.641.2		4
60.23	odd	4		1200.3.c.k.449.8		8
60.47	odd	4		1200.3.c.k.449.1		8
60.59	even	2		1200.3.l.u.401.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.3.d.a.11.1	✓	4	1.1	even	1	trivial
30.3.d.a.11.3	yes	4	3.2	odd	2	inner
150.3.b.b.149.3		8	5.3	odd	4
150.3.b.b.149.4		8	15.2	even	4
150.3.b.b.149.5		8	15.8	even	4
150.3.b.b.149.6		8	5.2	odd	4
150.3.d.c.101.2		4	15.14	odd	2
150.3.d.c.101.4		4	5.4	even	2
240.3.l.c.161.3		4	12.11	even	2
240.3.l.c.161.4		4	4.3	odd	2
810.3.h.a.431.1		8	9.5	odd	6
810.3.h.a.431.4		8	9.4	even	3
810.3.h.a.701.1		8	9.7	even	3
810.3.h.a.701.4		8	9.2	odd	6
960.3.l.e.641.3		4	24.5	odd	2
960.3.l.e.641.4		4	8.5	even	2
960.3.l.f.641.1		4	8.3	odd	2
960.3.l.f.641.2		4	24.11	even	2
1200.3.c.k.449.1		8	60.47	odd	4
1200.3.c.k.449.2		8	20.3	even	4
1200.3.c.k.449.7		8	20.7	even	4
1200.3.c.k.449.8		8	60.23	odd	4
1200.3.l.u.401.1		4	20.19	odd	2
1200.3.l.u.401.2		4	60.59	even	2

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:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	30.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(-0.581139 - 2.94317i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(-4.16228 + 0.821854i) q^{6} +11.4868 q^{7} +2.82843i q^{8} +(-8.32456 + 3.42079i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(-0.581139 - 2.94317i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(-4.16228 + 0.821854i) q^{6} +11.4868 q^{7} +2.82843i q^{8} +(-8.32456 + 3.42079i) q^{9} +3.16228 q^{10} +8.48528i q^{11} +(1.16228 + 5.88635i) q^{12} -10.0000 q^{13} -16.2448i q^{14} +(6.58114 - 1.29947i) q^{15} +4.00000 q^{16} -3.55415i q^{17} +(4.83772 + 11.7727i) q^{18} -10.9737 q^{19} -4.47214i q^{20} +(-6.67544 - 33.8078i) q^{21} +12.0000 q^{22} -17.6590i q^{23} +(8.32456 - 1.64371i) q^{24} -5.00000 q^{25} +14.1421i q^{26} +(14.9057 + 22.5127i) q^{27} -22.9737 q^{28} +26.8328i q^{29} +(-1.83772 - 9.30714i) q^{30} +8.00000 q^{31} -5.65685i q^{32} +(24.9737 - 4.93113i) q^{33} -5.02633 q^{34} +25.6853i q^{35} +(16.6491 - 6.84157i) q^{36} -59.9473 q^{37} +15.5191i q^{38} +(5.81139 + 29.4317i) q^{39} -6.32456 q^{40} +20.5247i q^{41} +(-47.8114 + 9.44050i) q^{42} +42.4605 q^{43} -16.9706i q^{44} +(-7.64911 - 18.6143i) q^{45} -24.9737 q^{46} -88.2952i q^{47} +(-2.32456 - 11.7727i) q^{48} +82.9473 q^{49} +7.07107i q^{50} +(-10.4605 + 2.06546i) q^{51} +20.0000 q^{52} -3.55415i q^{53} +(31.8377 - 21.0798i) q^{54} -18.9737 q^{55} +32.4897i q^{56} +(6.37722 + 32.2974i) q^{57} +37.9473 q^{58} -77.7445i q^{59} +(-13.1623 + 2.59893i) q^{60} +21.9473 q^{61} -11.3137i q^{62} +(-95.6228 + 39.2940i) q^{63} -8.00000 q^{64} -22.3607i q^{65} +(-6.97367 - 35.3181i) q^{66} -53.5395 q^{67} +7.10831i q^{68} +(-51.9737 + 10.2624i) q^{69} +36.3246 q^{70} +69.2592i q^{71} +(-9.67544 - 23.5454i) q^{72} +12.0527 q^{73} +84.7783i q^{74} +(2.90569 + 14.7159i) q^{75} +21.9473 q^{76} +97.4690i q^{77} +(41.6228 - 8.21854i) q^{78} -9.02633 q^{79} +8.94427i q^{80} +(57.5964 - 56.9530i) q^{81} +29.0263 q^{82} -0.688486i q^{83} +(13.3509 + 67.6155i) q^{84} +7.94733 q^{85} -60.0482i q^{86} +(78.9737 - 15.5936i) q^{87} -24.0000 q^{88} +7.10831i q^{89} +(-26.3246 + 10.8175i) q^{90} -114.868 q^{91} +35.3181i q^{92} +(-4.64911 - 23.5454i) q^{93} -124.868 q^{94} -24.5379i q^{95} +(-16.6491 + 3.28742i) q^{96} +111.947 q^{97} -117.305i q^{98} +(-29.0263 - 70.6362i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 8 q^{4} - 4 q^{6} + 8 q^{7} - 8 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 - 8 * q^4 - 4 * q^6 + 8 * q^7 - 8 * q^9	\( 4 q + 4 q^{3} - 8 q^{4} - 4 q^{6} + 8 q^{7} - 8 q^{9} - 8 q^{12} - 40 q^{13} + 20 q^{15} + 16 q^{16} + 32 q^{18} + 32 q^{19} - 52 q^{21} + 48 q^{22} + 8 q^{24} - 20 q^{25} + 28 q^{27} - 16 q^{28} - 20 q^{30} + 32 q^{31} + 24 q^{33} - 96 q^{34} + 16 q^{36} - 88 q^{37} - 40 q^{39} - 128 q^{42} + 56 q^{43} + 20 q^{45} - 24 q^{46} + 16 q^{48} + 180 q^{49} + 72 q^{51} + 80 q^{52} + 140 q^{54} + 152 q^{57} - 40 q^{60} - 64 q^{61} - 256 q^{63} - 32 q^{64} + 48 q^{66} - 328 q^{67} - 132 q^{69} + 120 q^{70} - 64 q^{72} + 200 q^{73} - 20 q^{75} - 64 q^{76} + 40 q^{78} - 112 q^{79} + 28 q^{81} + 192 q^{82} + 104 q^{84} - 120 q^{85} + 240 q^{87} - 96 q^{88} - 80 q^{90} - 80 q^{91} + 32 q^{93} - 120 q^{94} - 16 q^{96} + 296 q^{97} - 192 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 - 8 * q^4 - 4 * q^6 + 8 * q^7 - 8 * q^9 - 8 * q^12 - 40 * q^13 + 20 * q^15 + 16 * q^16 + 32 * q^18 + 32 * q^19 - 52 * q^21 + 48 * q^22 + 8 * q^24 - 20 * q^25 + 28 * q^27 - 16 * q^28 - 20 * q^30 + 32 * q^31 + 24 * q^33 - 96 * q^34 + 16 * q^36 - 88 * q^37 - 40 * q^39 - 128 * q^42 + 56 * q^43 + 20 * q^45 - 24 * q^46 + 16 * q^48 + 180 * q^49 + 72 * q^51 + 80 * q^52 + 140 * q^54 + 152 * q^57 - 40 * q^60 - 64 * q^61 - 256 * q^63 - 32 * q^64 + 48 * q^66 - 328 * q^67 - 132 * q^69 + 120 * q^70 - 64 * q^72 + 200 * q^73 - 20 * q^75 - 64 * q^76 + 40 * q^78 - 112 * q^79 + 28 * q^81 + 192 * q^82 + 104 * q^84 - 120 * q^85 + 240 * q^87 - 96 * q^88 - 80 * q^90 - 80 * q^91 + 32 * q^93 - 120 * q^94 - 16 * q^96 + 296 * q^97 - 192 * q^99

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