LMFDB - Embedded newform 150.3.d.c.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,3,Mod(101,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, 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("150.101");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	150.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:	$4.08720396540$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.4
Root			$-1.58114 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	150.101
Dual form			150.3.d.c.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +(0.581139 + 2.94317i) q^{3} -2.00000 q^{4} +(-4.16228 + 0.821854i) q^{6} -11.4868 q^{7} -2.82843i q^{8} +(-8.32456 + 3.42079i) q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +(0.581139 + 2.94317i) q^{3} -2.00000 q^{4} +(-4.16228 + 0.821854i) q^{6} -11.4868 q^{7} -2.82843i q^{8} +(-8.32456 + 3.42079i) q^{9} +8.48528i q^{11} +(-1.16228 - 5.88635i) q^{12} +10.0000 q^{13} -16.2448i q^{14} +4.00000 q^{16} +3.55415i q^{17} +(-4.83772 - 11.7727i) q^{18} -10.9737 q^{19} +(-6.67544 - 33.8078i) q^{21} -12.0000 q^{22} +17.6590i q^{23} +(8.32456 - 1.64371i) q^{24} +14.1421i q^{26} +(-14.9057 - 22.5127i) q^{27} +22.9737 q^{28} +26.8328i q^{29} +8.00000 q^{31} +5.65685i q^{32} +(-24.9737 + 4.93113i) q^{33} -5.02633 q^{34} +(16.6491 - 6.84157i) q^{36} +59.9473 q^{37} -15.5191i q^{38} +(5.81139 + 29.4317i) q^{39} +20.5247i q^{41} +(47.8114 - 9.44050i) q^{42} -42.4605 q^{43} -16.9706i q^{44} -24.9737 q^{46} +88.2952i q^{47} +(2.32456 + 11.7727i) q^{48} +82.9473 q^{49} +(-10.4605 + 2.06546i) q^{51} -20.0000 q^{52} +3.55415i q^{53} +(31.8377 - 21.0798i) q^{54} +32.4897i q^{56} +(-6.37722 - 32.2974i) q^{57} -37.9473 q^{58} -77.7445i q^{59} +21.9473 q^{61} +11.3137i q^{62} +(95.6228 - 39.2940i) q^{63} -8.00000 q^{64} +(-6.97367 - 35.3181i) q^{66} +53.5395 q^{67} -7.10831i q^{68} +(-51.9737 + 10.2624i) q^{69} +69.2592i q^{71} +(9.67544 + 23.5454i) q^{72} -12.0527 q^{73} +84.7783i q^{74} +21.9473 q^{76} -97.4690i q^{77} +(-41.6228 + 8.21854i) q^{78} -9.02633 q^{79} +(57.5964 - 56.9530i) q^{81} -29.0263 q^{82} +0.688486i q^{83} +(13.3509 + 67.6155i) q^{84} -60.0482i q^{86} +(-78.9737 + 15.5936i) q^{87} +24.0000 q^{88} +7.10831i q^{89} -114.868 q^{91} -35.3181i q^{92} +(4.64911 + 23.5454i) q^{93} -124.868 q^{94} +(-16.6491 + 3.28742i) q^{96} -111.947 q^{97} +117.305i q^{98} +(-29.0263 - 70.6362i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 16 q^{16} - 32 q^{18} + 32 q^{19} - 52 q^{21} - 48 q^{22} + 8 q^{24} - 28 q^{27} + 16 q^{28} + 32 q^{31} - 24 q^{33} - 96 q^{34} + 16 q^{36} + 88 q^{37} - 40 q^{39} + 128 q^{42} - 56 q^{43} - 24 q^{46} - 16 q^{48} + 180 q^{49} + 72 q^{51} - 80 q^{52} + 140 q^{54} - 152 q^{57} - 64 q^{61} + 256 q^{63} - 32 q^{64} + 48 q^{66} + 328 q^{67} - 132 q^{69} + 64 q^{72} - 200 q^{73} - 64 q^{76} - 40 q^{78} - 112 q^{79} + 28 q^{81} - 192 q^{82} + 104 q^{84} - 240 q^{87} + 96 q^{88} - 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 + 16 * q^16 - 32 * q^18 + 32 * q^19 - 52 * q^21 - 48 * q^22 + 8 * q^24 - 28 * q^27 + 16 * q^28 + 32 * q^31 - 24 * q^33 - 96 * q^34 + 16 * q^36 + 88 * q^37 - 40 * q^39 + 128 * q^42 - 56 * q^43 - 24 * q^46 - 16 * q^48 + 180 * q^49 + 72 * q^51 - 80 * q^52 + 140 * q^54 - 152 * q^57 - 64 * q^61 + 256 * q^63 - 32 * q^64 + 48 * q^66 + 328 * q^67 - 132 * q^69 + 64 * q^72 - 200 * q^73 - 64 * q^76 - 40 * q^78 - 112 * q^79 + 28 * q^81 - 192 * q^82 + 104 * q^84 - 240 * q^87 + 96 * q^88 - 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 $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$1$

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
$5$		0			0
$5$		0			0
$6$	−4.16228	+	0.821854i	−0.693713	+	0.136976i
$7$	−11.4868			−1.64098			−0.820488	−	0.571664i	$-0.806298\pi$
$7$	−11.4868			−1.64098			−0.820488	+	0.571664i	$0.806298\pi$
$8$		−	2.82843i		−	0.353553i
$9$	−8.32456	+	3.42079i	−0.924951	+	0.380087i
$10$		0			0
$11$			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	$-0.374334\pi$
$13$	10.0000			0.769231			0.384615	+	0.923077i	$0.374334\pi$
$14$		−	16.2448i		−	1.16035i
$15$		0			0
$16$	4.00000			0.250000
$17$			3.55415i			0.209068i	0.994521	+	0.104534i	$0.0333351\pi$
$17$			3.55415i			0.209068i	−0.994521	+	0.104534i	$0.966665\pi$
$18$	−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	$0.593250\pi$
$20$		0			0
$21$	−6.67544	−	33.8078i	−0.317878	−	1.60989i
$22$	−12.0000			−0.545455
$23$			17.6590i			0.767785i	0.923378	+	0.383892i	$0.125417\pi$
$23$			17.6590i			0.767785i	−0.923378	+	0.383892i	$0.874583\pi$
$24$	8.32456	−	1.64371i	0.346856	−	0.0684879i
$25$		0			0
$26$			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	$0.846904\pi$
$30$		0			0
$31$	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
$35$		0			0
$36$	16.6491	−	6.84157i	0.462475	−	0.190044i
$37$	59.9473			1.62020			0.810099	−	0.586293i	$-0.199413\pi$
$37$	59.9473			1.62020			0.810099	+	0.586293i	$0.199413\pi$
$38$		−	15.5191i		−	0.408398i
$39$	5.81139	+	29.4317i	0.149010	+	0.754660i
$40$		0			0
$41$			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	$-0.664366\pi$
$43$	−42.4605			−0.987453			−0.493727	+	0.869617i	$0.664366\pi$
$44$		−	16.9706i		−	0.385695i
$45$		0			0
$46$	−24.9737			−0.542906
$47$			88.2952i			1.87862i	0.343067	+	0.939311i	$0.388534\pi$
$47$			88.2952i			1.87862i	−0.343067	+	0.939311i	$0.611466\pi$
$48$	2.32456	+	11.7727i	0.0484282	+	0.245265i
$49$	82.9473			1.69280
$50$		0			0
$51$	−10.4605	+	2.06546i	−0.205108	+	0.0404992i
$52$	−20.0000			−0.384615
$53$			3.55415i			0.0670595i	0.999438	+	0.0335298i	$0.0106749\pi$
$53$			3.55415i			0.0670595i	−0.999438	+	0.0335298i	$0.989325\pi$
$54$	31.8377	−	21.0798i	0.589587	−	0.390367i
$55$		0			0
$56$			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	$-0.228958\pi$
$60$		0			0
$61$	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
$65$		0			0
$66$	−6.97367	−	35.3181i	−0.105662	−	0.535123i
$67$	53.5395			0.799097			0.399549	−	0.916712i	$-0.369167\pi$
$67$	53.5395			0.799097			0.399549	+	0.916712i	$0.369167\pi$
$68$		−	7.10831i		−	0.104534i
$69$	−51.9737	+	10.2624i	−0.753242	+	0.148730i
$70$		0			0
$71$			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	$-0.526307\pi$
$73$	−12.0527			−0.165105			−0.0825525	+	0.996587i	$0.526307\pi$
$74$			84.7783i			1.14565i
$75$		0			0
$76$	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	$0.518195\pi$
$80$		0			0
$81$	57.5964	−	56.9530i	0.711067	−	0.703124i
$82$	−29.0263			−0.353980
$83$			0.688486i			0.00829501i	0.999991	+	0.00414750i	$0.00132020\pi$
$83$			0.688486i			0.00829501i	−0.999991	+	0.00414750i	$0.998680\pi$
$84$	13.3509	+	67.6155i	0.158939	+	0.804947i
$85$		0			0
$86$		−	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	$0.987285\pi$
$90$		0			0
$91$	−114.868			−1.26229
$92$		−	35.3181i		−	0.383892i
$93$	4.64911	+	23.5454i	0.0499904	+	0.253176i
$94$	−124.868			−1.32839
$95$		0			0
$96$	−16.6491	+	3.28742i	−0.173428	+	0.0342439i
$97$	−111.947			−1.15410			−0.577048	−	0.816710i	$-0.695795\pi$
$97$	−111.947			−1.15410			−0.577048	+	0.816710i	$0.695795\pi$
$98$			117.305i			1.19699i
$99$	−29.0263	−	70.6362i	−0.293195	−	0.713497i
$100$		0			0
$101$		−	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	$-0.511734\pi$
$103$	−7.59217			−0.0737104			−0.0368552	+	0.999321i	$0.511734\pi$
$104$		−	28.2843i		−	0.271964i
$105$		0			0
$106$	−5.02633			−0.0474182
$107$			16.2821i			0.152169i	0.997101	+	0.0760845i	$0.0242419\pi$
$107$			16.2821i			0.152169i	−0.997101	+	0.0760845i	$0.975758\pi$
$108$	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	$0.641651\pi$
$110$		0			0
$111$	34.8377	+	176.435i	0.313853	+	1.58951i
$112$	−45.9473			−0.410244
$113$		−	195.738i		−	1.73220i	−0.499874	−	0.866098i	$-0.666620\pi$
$113$		−	195.738i		−	1.73220i	0.499874	−	0.866098i	$-0.333380\pi$
$114$	45.6754	−	9.01876i	0.400662	−	0.0791119i
$115$		0			0
$116$		−	53.6656i		−	0.462635i
$117$	−83.2456	+	34.2079i	−0.711500	+	0.292375i
$118$	109.947			0.931757
$119$		−	40.8260i		−	0.343075i
$120$		0			0
$121$	49.0000			0.404959
$122$			31.0382i			0.254412i
$123$	−60.4078	+	11.9277i	−0.491121	+	0.0969733i
$124$	−16.0000			−0.129032
$125$		0			0
$126$	55.5701	+	135.231i	0.441033	+	1.07326i
$127$	77.5395			0.610547			0.305274	−	0.952265i	$-0.401252\pi$
$127$	77.5395			0.610547			0.305274	+	0.952265i	$0.401252\pi$
$128$		−	11.3137i		−	0.0883883i
$129$	−24.6754	−	124.969i	−0.191283	−	0.968749i
$130$		0			0
$131$			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
$135$		0			0
$136$	10.0527			0.0739167
$137$		−	176.014i		−	1.28477i	−0.766381	−	0.642386i	$-0.777945\pi$
$137$		−	176.014i		−	1.28477i	0.766381	−	0.642386i	$-0.222055\pi$
$138$	−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	$0.262330\pi$
$140$		0			0
$141$	−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
$145$		0			0
$146$		−	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	$0.921675\pi$
$150$		0			0
$151$	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
$155$		0			0
$156$	−11.6228	−	58.8635i	−0.0745050	−	0.377330i
$157$	123.842			0.788803			0.394401	−	0.918938i	$-0.370952\pi$
$157$	123.842			0.788803			0.394401	+	0.918938i	$0.370952\pi$
$158$		−	12.7652i		−	0.0807922i
$159$	−10.4605	+	2.06546i	−0.0657893	+	0.0129903i
$160$		0			0
$161$		−	202.847i		−	1.25992i
$162$	80.5438	+	81.4537i	0.497184	+	0.502800i
$163$	−159.381			−0.977801			−0.488900	−	0.872340i	$-0.662602\pi$
$163$	−159.381			−0.977801			−0.488900	+	0.872340i	$0.662602\pi$
$164$		−	41.0494i		−	0.250301i
$165$		0			0
$166$	−0.973666			−0.00586546
$167$		−	10.7742i		−	0.0645161i	−0.999480	−	0.0322581i	$-0.989730\pi$
$167$		−	10.7742i		−	0.0645161i	0.999480	−	0.0322581i	$-0.0102698\pi$
$168$	−95.6228	+	18.8810i	−0.569183	+	0.112387i
$169$	−69.0000			−0.408284
$170$		0			0
$171$	91.3509	−	37.5386i	0.534216	−	0.219524i
$172$	84.9210			0.493727
$173$			283.345i			1.63783i	0.573913	+	0.818916i	$0.305425\pi$
$173$			283.345i			1.63783i	−0.573913	+	0.818916i	$0.694575\pi$
$174$	−22.0527	−	111.686i	−0.126739	−	0.641871i
$175$		0			0
$176$			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	$0.672640\pi$
$180$		0			0
$181$	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
$185$		0			0
$186$	−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
$190$		0			0
$191$		−	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	$-0.423351\pi$
$193$	92.0527			0.476957			0.238478	+	0.971148i	$0.423351\pi$
$194$		−	158.317i		−	0.816069i
$195$		0			0
$196$	−165.895			−0.846401
$197$			69.8360i			0.354497i	0.984166	+	0.177249i	$0.0567197\pi$
$197$			69.8360i			0.354497i	−0.984166	+	0.177249i	$0.943280\pi$
$198$	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	$0.377926\pi$
$200$		0			0
$201$	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
$205$		0			0
$206$		−	10.7369i		−	0.0521211i
$207$	−60.4078	−	147.004i	−0.291825	−	0.710163i
$208$	40.0000			0.192308
$209$		−	93.1146i		−	0.445525i
$210$		0			0
$211$	−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
$215$		0			0
$216$	−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
$220$		0			0
$221$			35.5415i			0.160821i
$222$	−249.517	+	49.2680i	−1.12395	+	0.221928i
$223$	71.3815			0.320096			0.160048	−	0.987109i	$-0.448835\pi$
$223$	71.3815			0.320096			0.160048	+	0.987109i	$0.448835\pi$
$224$		−	64.9793i		−	0.290086i
$225$		0			0
$226$	276.816			1.22485
$227$			29.1217i			0.128290i	0.997941	+	0.0641448i	$0.0204319\pi$
$227$			29.1217i			0.128290i	−0.997941	+	0.0641448i	$0.979568\pi$
$228$	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	$0.591380\pi$
$230$		0			0
$231$	286.868	−	56.6430i	1.24185	−	0.245208i
$232$	75.8947			0.327132
$233$			185.876i			0.797751i	0.917005	+	0.398875i	$0.130599\pi$
$233$			185.876i			0.797751i	−0.917005	+	0.398875i	$0.869401\pi$
$234$	−48.3772	−	117.727i	−0.206740	−	0.503107i
$235$		0			0
$236$			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	$-0.218299\pi$
$240$		0			0
$241$	−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
$245$		0			0
$246$	−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
$250$		0			0
$251$			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
$255$		0			0
$256$	16.0000			0.0625000
$257$			292.054i			1.13640i	0.822892	+	0.568198i	$0.192359\pi$
$257$			292.054i			1.13640i	−0.822892	+	0.568198i	$0.807641\pi$
$258$	176.732	−	34.8963i	0.685009	−	0.135257i
$259$	−688.605			−2.65871
$260$		0			0
$261$	−91.7893	−	223.371i	−0.351683	−	0.855829i
$262$	−143.684			−0.548412
$263$			277.725i			1.05599i	0.849247	+	0.527995i	$0.177056\pi$
$263$			277.725i			1.05599i	−0.849247	+	0.527995i	$0.822944\pi$
$264$	13.9473	+	70.6362i	0.0528308	+	0.267561i
$265$		0			0
$266$			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	$0.821210\pi$
$270$		0			0
$271$	−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
$275$		0			0
$276$	103.947	−	20.5247i	0.376621	−	0.0743649i
$277$	−415.842			−1.50123			−0.750617	−	0.660737i	$-0.770244\pi$
$277$	−415.842			−1.50123			−0.750617	+	0.660737i	$0.770244\pi$
$278$			267.026i			0.960524i
$279$	−66.5964	+	27.3663i	−0.238697	+	0.0980871i
$280$		0			0
$281$			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	$-0.580454\pi$
$283$	−141.540			−0.500140			−0.250070	+	0.968228i	$0.580454\pi$
$284$		−	138.518i		−	0.487741i
$285$		0			0
$286$	−120.000			−0.419580
$287$		−	235.764i		−	0.821477i
$288$	−19.3509	−	47.0908i	−0.0671906	−	0.163510i
$289$	276.368			0.956291
$290$		0			0
$291$	−65.0569	−	329.481i	−0.223563	−	1.13224i
$292$	24.1053			0.0825525
$293$		−	164.998i		−	0.563133i	−0.959542	−	0.281566i	$-0.909146\pi$
$293$		−	164.998i		−	0.563133i	0.959542	−	0.281566i	$-0.0908540\pi$
$294$	−345.250	+	68.1706i	−1.17432	+	0.231873i
$295$		0			0
$296$		−	169.557i		−	0.572827i
$297$	191.026	−	126.479i	0.643186	−	0.425855i
$298$	−102.658			−0.344489
$299$			176.590i			0.590604i
$300$		0			0
$301$	487.737			1.62039
$302$			132.862i			0.439939i
$303$	457.631	−	90.3607i	1.51033	−	0.298220i
$304$	−43.8947			−0.144390
$305$		0			0
$306$	41.8420	−	17.1940i	0.136739	−	0.0561896i
$307$	−159.381			−0.519158			−0.259579	−	0.965722i	$-0.583584\pi$
$307$	−159.381			−0.519158			−0.259579	+	0.965722i	$0.583584\pi$
$308$			194.938i			0.632916i
$309$	−4.41210	−	22.3451i	−0.0142787	−	0.0723142i
$310$		0			0
$311$			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	$-0.204082\pi$
$313$	501.684			1.60282			0.801412	+	0.598113i	$0.204082\pi$
$314$			175.139i			0.557768i
$315$		0			0
$316$	18.0527			0.0571287
$317$			334.257i			1.05444i	0.849730	+	0.527219i	$0.176765\pi$
$317$			334.257i			1.05444i	−0.849730	+	0.527219i	$0.823235\pi$
$318$	−2.92100	−	14.7934i	−0.00918553	−	0.0465201i
$319$	−227.684			−0.713743
$320$		0			0
$321$	−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
$325$		0			0
$326$		−	225.399i		−	0.691409i
$327$	−54.5352	−	276.193i	−0.166774	−	0.844628i
$328$	58.0527			0.176990
$329$		−	1014.23i		−	3.08277i
$330$		0			0
$331$	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
$335$		0			0
$336$	−26.7018	−	135.231i	−0.0794696	−	0.402473i
$337$	129.684			0.384819			0.192409	−	0.981315i	$-0.438370\pi$
$337$	129.684			0.384819			0.192409	+	0.981315i	$0.438370\pi$
$338$		−	97.5807i		−	0.288700i
$339$	576.092	−	113.751i	1.69939	−	0.335549i
$340$		0			0
$341$			67.8823i			0.199068i
$342$	53.0875	+	129.190i	0.155227	+	0.377748i
$343$	−389.947			−1.13687
$344$			120.096i			0.349118i
$345$		0			0
$346$	−400.710			−1.15812
$347$		−	346.985i		−	0.999956i	−0.866038	−	0.499978i	$-0.833341\pi$
$347$		−	346.985i		−	0.999956i	0.866038	−	0.499978i	$-0.166659\pi$
$348$	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	$0.239494\pi$
$350$		0			0
$351$	−149.057	−	225.127i	−0.424664	−	0.641387i
$352$	−48.0000			−0.136364
$353$		−	637.679i		−	1.80646i	−0.429159	−	0.903229i	$-0.641190\pi$
$353$		−	637.679i		−	1.80646i	0.429159	−	0.903229i	$-0.358810\pi$
$354$	63.8947	+	323.594i	0.180493	+	0.914108i
$355$		0			0
$356$		−	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	$0.925302\pi$
$360$		0			0
$361$	−240.579			−0.666423
$362$			375.734i			1.03794i
$363$	28.4758	+	144.216i	0.0784457	+	0.397288i
$364$	229.737			0.631145
$365$		0			0
$366$	−91.3509	+	18.0375i	−0.249593	+	0.0492828i
$367$	505.828			1.37828			0.689140	−	0.724629i	$-0.257989\pi$
$367$	505.828			1.37828			0.689140	+	0.724629i	$0.257989\pi$
$368$			70.6362i			0.191946i
$369$	−70.2107	−	170.859i	−0.190273	−	0.463033i
$370$		0			0
$371$		−	40.8260i		−	0.110043i
$372$	−9.29822	−	47.0908i	−0.0249952	−	0.126588i
$373$	416.053			1.11542			0.557711	−	0.830035i	$-0.311680\pi$
$373$	416.053			1.11542			0.557711	+	0.830035i	$0.311680\pi$
$374$		−	42.6499i		−	0.114037i
$375$		0			0
$376$	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	$0.465176\pi$
$380$		0			0
$381$	45.0612	+	228.212i	0.118271	+	0.598982i
$382$	225.737			0.590934
$383$		−	334.592i		−	0.873608i	−0.899557	−	0.436804i	$-0.856110\pi$
$383$		−	334.592i		−	0.873608i	0.899557	−	0.436804i	$-0.143890\pi$
$384$	33.2982	−	6.57484i	0.0867141	−	0.0171220i
$385$		0			0
$386$			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	$0.754119\pi$
$390$		0			0
$391$	−62.7630			−0.160519
$392$		−	234.610i		−	0.598496i
$393$	−299.026	+	59.0437i	−0.760881	+	0.150238i
$394$	−98.7630			−0.250667
$395$		0			0
$396$	58.0527	+	141.272i	0.146598	+	0.356748i
$397$	214.000			0.539043			0.269521	−	0.962994i	$-0.413135\pi$
$397$	214.000			0.539043			0.269521	+	0.962994i	$0.413135\pi$
$398$			210.606i			0.529161i
$399$	73.2541	+	370.995i	0.183594	+	0.929812i
$400$		0			0
$401$			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
$405$		0			0
$406$	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	$0.639085\pi$
$410$		0			0
$411$	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
$415$		0			0
$416$			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	$-0.243802\pi$
$420$		0			0
$421$	−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
$425$		0			0
$426$	−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
$430$		0			0
$431$		−	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	$-0.427507\pi$
$433$	195.526			0.451561			0.225781	+	0.974178i	$0.427507\pi$
$434$		−	129.959i		−	0.299444i
$435$		0			0
$436$	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	$0.261127\pi$
$440$		0			0
$441$	−690.500	+	283.745i	−1.56576	+	0.643413i
$442$	−50.2633			−0.113718
$443$			216.728i			0.489228i	0.969621	+	0.244614i	$0.0786612\pi$
$443$			216.728i			0.489228i	−0.969621	+	0.244614i	$0.921339\pi$
$444$	−69.6754	−	352.871i	−0.156927	−	0.794754i
$445$		0			0
$446$			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	$-0.0884025\pi$
$450$		0			0
$451$	−174.158			−0.386160
$452$			391.476i			0.866098i
$453$	54.5964	+	276.503i	0.120522	+	0.610383i
$454$	−41.1843			−0.0907144
$455$		0			0
$456$	−91.3509	+	18.0375i	−0.200331	+	0.0395559i
$457$	−553.052			−1.21018			−0.605090	−	0.796157i	$-0.706863\pi$
$457$	−553.052			−1.21018			−0.605090	+	0.796157i	$0.706863\pi$
$458$		−	183.401i		−	0.400439i
$459$	80.0135	−	52.9771i	0.174321	−	0.115419i
$460$		0			0
$461$		−	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	$-0.757349\pi$
$463$	−669.723			−1.44649			−0.723243	+	0.690593i	$0.757349\pi$
$464$			107.331i			0.231317i
$465$		0			0
$466$	−262.868			−0.564095
$467$		−	486.880i		−	1.04257i	−0.853383	−	0.521285i	$-0.825453\pi$
$467$		−	486.880i		−	1.04257i	0.853383	−	0.521285i	$-0.174547\pi$
$468$	166.491	−	68.4157i	0.355750	−	0.146187i
$469$	−614.999			−1.31130
$470$		0			0
$471$	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
$475$		0			0
$476$			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	$0.817136\pi$
$480$		0			0
$481$	599.473			1.24631
$482$		−	335.912i		−	0.696914i
$483$	597.013	−	117.882i	1.23605	−	0.244062i
$484$	−98.0000			−0.202479
$485$		0			0
$486$	−192.925	+	284.390i	−0.396966	+	0.585165i
$487$	263.381			0.540824			0.270412	−	0.962745i	$-0.412840\pi$
$487$	263.381			0.540824			0.270412	+	0.962745i	$0.412840\pi$
$488$		−	62.0764i		−	0.127206i
$489$	−92.6228	−	469.088i	−0.189413	−	0.959279i
$490$		0			0
$491$		−	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
$495$		0			0
$496$	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	$0.492638\pi$
$500$		0			0
$501$	31.7103	−	6.26130i	0.0632941	−	0.0124976i
$502$	−119.684			−0.238414
$503$		−	40.5844i		−	0.0806847i	−0.999186	−	0.0403423i	$-0.987155\pi$
$503$		−	40.5844i		−	0.0806847i	0.999186	−	0.0403423i	$-0.0128449\pi$
$504$	−111.140	−	270.462i	−0.220516	−	0.536631i
$505$		0			0
$506$		−	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	$0.842078\pi$
$510$		0			0
$511$	138.447			0.270933
$512$			22.6274i			0.0441942i
$513$	163.570	+	247.047i	0.318850	+	0.481572i
$514$	−413.026			−0.803553
$515$		0			0
$516$	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
$520$		0			0
$521$		−	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	$-0.417952\pi$
$523$	266.644			0.509836			0.254918	+	0.966963i	$0.417952\pi$
$524$		−	203.200i		−	0.387786i
$525$		0			0
$526$	−392.763			−0.746698
$527$			28.4332i			0.0539530i
$528$	−99.8947	+	19.7245i	−0.189194	+	0.0373570i
$529$	217.158			0.410507
$530$		0			0
$531$	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
$535$		0			0
$536$		−	151.433i		−	0.282523i
$537$	−902.447	+	178.191i	−1.68053	+	0.331827i
$538$	−405.237			−0.753229
$539$			703.831i			1.30581i
$540$		0			0
$541$	−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
$545$		0			0
$546$	478.114	−	94.4050i	0.875666	−	0.172903i
$547$	214.566			0.392259			0.196130	−	0.980578i	$-0.437163\pi$
$547$	214.566			0.392259			0.196130	+	0.980578i	$0.437163\pi$
$548$			352.027i			0.642386i
$549$	−182.702	+	75.0771i	−0.332790	+	0.136753i
$550$		0			0
$551$		−	294.454i		−	0.534400i
$552$	29.0263	+	147.004i	0.0525839	+	0.266311i
$553$	103.684			0.187494
$554$		−	588.089i		−	1.06153i
$555$		0			0
$556$	−377.631			−0.679193
$557$			674.821i			1.21153i	0.795644	+	0.605764i	$0.207133\pi$
$557$			674.821i			1.21153i	−0.795644	+	0.605764i	$0.792867\pi$
$558$	−38.7018	−	94.1816i	−0.0693580	−	0.168784i
$559$	−424.605			−0.759580
$560$		0			0
$561$	−17.5260	−	88.7603i	−0.0312406	−	0.158218i
$562$	−610.552			−1.08639
$563$			718.513i			1.27622i	0.769944	+	0.638111i	$0.220284\pi$
$563$			718.513i			1.27622i	−0.769944	+	0.638111i	$0.779716\pi$
$564$	519.737	−	102.624i	0.921519	−	0.181957i
$565$		0			0
$566$		−	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	$0.948555\pi$
$570$		0			0
$571$	−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
$575$		0			0
$576$	66.5964	−	27.3663i	0.115619	−	0.0475109i
$577$	984.947			1.70701			0.853507	−	0.521082i	$-0.174471\pi$
$577$	984.947			1.70701			0.853507	+	0.521082i	$0.174471\pi$
$578$			390.843i			0.676200i
$579$	53.4954	+	270.927i	0.0923927	+	0.467922i
$580$		0			0
$581$		−	7.90852i		−	0.0136119i
$582$	465.956	−	92.0044i	0.800611	−	0.158083i
$583$	−30.1580			−0.0517290
$584$			34.0901i			0.0583734i
$585$		0			0
$586$	233.342			0.398195
$587$		−	378.172i		−	0.644245i	−0.946698	−	0.322122i	$-0.895604\pi$
$587$		−	378.172i		−	0.644245i	0.946698	−	0.322122i	$-0.104396\pi$
$588$	−96.4078	−	488.257i	−0.163959	−	0.830369i
$589$	−87.7893			−0.149048
$590$		0			0
$591$	−205.540	+	40.5844i	−0.347783	+	0.0686707i
$592$	239.789			0.405050
$593$		−	265.221i		−	0.447253i	−0.974675	−	0.223626i	$-0.928210\pi$
$593$		−	265.221i		−	0.447253i	0.974675	−	0.223626i	$-0.0717895\pi$
$594$	178.868	+	270.152i	0.301125	+	0.454801i
$595$		0			0
$596$		−	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	$-0.103319\pi$
$600$		0			0
$601$	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
$605$		0			0
$606$	127.789	+	647.188i	0.210873	+	1.06797i
$607$	835.487			1.37642			0.688210	−	0.725512i	$-0.258397\pi$
$607$	835.487			1.37642			0.688210	+	0.725512i	$0.258397\pi$
$608$		−	62.0764i		−	0.102099i
$609$	907.157	−	179.121i	1.48959	−	0.294123i
$610$		0			0
$611$			882.952i			1.44509i
$612$	24.3160	+	59.1735i	0.0397320	+	0.0966888i
$613$	−833.263			−1.35932			−0.679660	−	0.733528i	$-0.737872\pi$
$613$	−833.263			−1.35932			−0.679660	+	0.733528i	$0.737872\pi$
$614$		−	225.399i		−	0.367100i
$615$		0			0
$616$	−275.684			−0.447539
$617$		−	455.098i		−	0.737598i	−0.929509	−	0.368799i	$-0.879769\pi$
$617$		−	455.098i		−	0.737598i	0.929509	−	0.368799i	$-0.120231\pi$
$618$	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	$0.412322\pi$
$620$		0			0
$621$	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
$625$		0			0
$626$			709.488i			1.13337i
$627$	274.053	−	54.1125i	0.437086	−	0.0863039i
$628$	−247.684			−0.394401
$629$			213.062i			0.338731i
$630$		0			0
$631$	−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
$635$		0			0
$636$	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
$640$		0			0
$641$			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	$-0.345665\pi$
$643$	599.381			0.932164			0.466082	+	0.884742i	$0.345665\pi$
$644$			405.693i			0.629958i
$645$		0			0
$646$	55.1573			0.0853828
$647$			47.0224i			0.0726775i	0.999340	+	0.0363388i	$0.0115695\pi$
$647$			47.0224i			0.0726775i	−0.999340	+	0.0363388i	$0.988430\pi$
$648$	−161.088	−	162.907i	−0.248592	−	0.251400i
$649$	659.684			1.01646
$650$		0			0
$651$	−53.4036	−	270.462i	−0.0820331	−	0.415456i
$652$	318.763			0.488900
$653$		−	559.228i		−	0.856399i	−0.903684	−	0.428199i	$-0.859148\pi$
$653$		−	559.228i		−	0.856399i	0.903684	−	0.428199i	$-0.140852\pi$
$654$	390.596	−	77.1245i	0.597242	−	0.117927i
$655$		0			0
$656$			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	$-0.168555\pi$
$660$		0			0
$661$	−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
$665$		0			0
$666$	−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
$670$		0			0
$671$			186.229i			0.277540i
$672$	191.246	−	37.7620i	0.284592	−	0.0561935i
$673$	−1019.42			−1.51474			−0.757370	−	0.652985i	$-0.773516\pi$
$673$	−1019.42			−1.51474			−0.757370	+	0.652985i	$0.773516\pi$
$674$			183.401i			0.272108i
$675$		0			0
$676$	138.000			0.204142
$677$		−	624.616i		−	0.922624i	−0.887238	−	0.461312i	$-0.847379\pi$
$677$		−	624.616i		−	0.922624i	0.887238	−	0.461312i	$-0.152621\pi$
$678$	160.868	+	814.717i	0.237269	+	1.20165i
$679$	1285.92			1.89384
$680$		0			0
$681$	−85.7103	+	16.9238i	−0.125860	+	0.0248513i
$682$	−96.0000			−0.140762
$683$		−	525.882i		−	0.769959i	−0.922925	−	0.384980i	$-0.874208\pi$
$683$		−	525.882i		−	0.769959i	0.922925	−	0.384980i	$-0.125792\pi$
$684$	−182.702	+	75.0771i	−0.267108	+	0.109762i
$685$		0			0
$686$		−	551.469i		−	0.803890i
$687$	−75.3644	−	381.683i	−0.109701	−	0.555579i
$688$	−169.842			−0.246863
$689$			35.5415i			0.0515843i
$690$		0			0
$691$	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
$695$		0			0
$696$	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
$700$		0			0
$701$		−	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
$705$		0			0
$706$	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	$0.387816\pi$
$710$		0			0
$711$	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
$715$		0			0
$716$		−	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	$-0.0238797\pi$
$720$		0			0
$721$	87.2100			0.120957
$722$		−	340.230i		−	0.471232i
$723$	−138.036	−	699.080i	−0.190921	−	0.966916i
$724$	−531.368			−0.733934
$725$		0			0
$726$	−203.952	+	40.2709i	−0.280925	+	0.0554695i
$727$	150.172			0.206563			0.103282	−	0.994652i	$-0.467066\pi$
$727$	150.172			0.206563			0.103282	+	0.994652i	$0.467066\pi$
$728$			324.897i			0.446287i
$729$	−284.641	+	671.134i	−0.390453	+	0.920623i
$730$		0			0
$731$		−	150.911i		−	0.206445i
$732$	−25.5089	−	129.190i	−0.0348482	−	0.176489i
$733$	675.526			0.921591			0.460795	−	0.887506i	$-0.347564\pi$
$733$	675.526			0.921591			0.460795	+	0.887506i	$0.347564\pi$
$734$			715.349i			0.974591i
$735$		0			0
$736$	−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	$0.718552\pi$
$740$		0			0
$741$	−63.7722	−	322.974i	−0.0860624	−	0.435863i
$742$	57.7367			0.0778122
$743$		−	452.939i		−	0.609608i	−0.952415	−	0.304804i	$-0.901409\pi$
$743$		−	452.939i		−	0.609608i	0.952415	−	0.304804i	$-0.0985910\pi$
$744$	66.5964	−	13.1497i	0.0895113	−	0.0176743i
$745$		0			0
$746$			588.387i			0.788723i
$747$	−2.35516	−	5.73134i	−0.00315283	−	0.00767247i
$748$	60.3160			0.0806364
$749$		−	187.029i		−	0.249706i
$750$		0			0
$751$	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
$755$		0			0
$756$	−342.438	−	517.199i	−0.452961	−	0.684125i
$757$	−123.315			−0.162900			−0.0814500	−	0.996677i	$-0.525955\pi$
$757$	−123.315			−0.162900			−0.0814500	+	0.996677i	$0.525955\pi$
$758$			117.045i			0.154412i
$759$	−87.0790	−	441.011i	−0.114729	−	0.581042i
$760$		0			0
$761$		−	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
$765$		0			0
$766$	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	$0.559605\pi$
$770$		0			0
$771$	−859.565	+	169.724i	−1.11487	+	0.220135i
$772$	−184.105			−0.238478
$773$			972.030i			1.25748i	0.777617	+	0.628739i	$0.216428\pi$
$773$			972.030i			1.25748i	−0.777617	+	0.628739i	$0.783572\pi$
$774$	205.412	+	499.875i	0.265390	+	0.645833i
$775$		0			0
$776$			316.635i			0.408035i
$777$	−400.175	−	2026.68i	−0.515026	−	2.60835i
$778$	−767.868			−0.986976
$779$		−	225.231i		−	0.289129i
$780$		0			0
$781$	−587.684			−0.752476
$782$		−	88.7603i		−	0.113504i
$783$	604.078	−	399.962i	0.771492	−	0.510807i
$784$	331.789			0.423201
$785$		0			0
$786$	−83.5003	−	422.887i	−0.106235	−	0.538024i
$787$	−1492.70			−1.89669			−0.948346	−	0.317237i	$-0.897245\pi$
$787$	−1492.70			−1.89669			−0.948346	+	0.317237i	$0.897245\pi$
$788$		−	139.672i		−	0.177249i
$789$	−817.394	+	161.397i	−1.03599	+	0.204559i
$790$		0			0
$791$			2248.41i			2.84249i
$792$	−199.789	+	82.0989i	−0.252259	+	0.103660i
$793$	219.473			0.276763
$794$			302.642i			0.381161i
$795$		0			0
$796$	−297.842			−0.374173
$797$			94.3618i			0.118396i	0.998246	+	0.0591981i	$0.0188544\pi$
$797$			94.3618i			0.118396i	−0.998246	+	0.0591981i	$0.981146\pi$
$798$	−524.666	+	103.597i	−0.657476	+	0.129821i
$799$	−313.815			−0.392760
$800$		0			0
$801$	−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
$805$		0			0
$806$			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	$-0.238855\pi$
$810$		0			0
$811$	−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
$815$		0			0
$816$	−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
$820$		0			0
$821$			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	$-0.315504\pi$
$823$	901.512			1.09540			0.547699	+	0.836675i	$0.315504\pi$
$824$			21.4739i			0.0260606i
$825$		0			0
$826$	−1262.95			−1.52899
$827$			531.354i			0.642508i	0.946993	+	0.321254i	$0.104104\pi$
$827$			531.354i			0.642508i	−0.946993	+	0.321254i	$0.895896\pi$
$828$	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	$0.538033\pi$
$830$		0			0
$831$	−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
$835$		0			0
$836$			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	$-0.190178\pi$
$840$		0			0
$841$	121.000			0.143876
$842$		−	380.869i		−	0.452339i
$843$	−1270.64	+	250.893i	−1.50729	+	0.297619i
$844$	571.684			0.677351
$845$		0			0
$846$	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
$850$		0			0
$851$			1058.61i			1.24396i
$852$	407.684	−	80.4984i	0.478502	−	0.0944817i
$853$	1196.42			1.40260			0.701301	−	0.712865i	$-0.252603\pi$
$853$	1196.42			1.40260			0.701301	+	0.712865i	$0.252603\pi$
$854$		−	356.531i		−	0.417483i
$855$		0			0
$856$	46.0527			0.0537998
$857$			1266.04i			1.47729i	0.674095	+	0.738645i	$0.264534\pi$
$857$			1266.04i			1.47729i	−0.674095	+	0.738645i	$0.735466\pi$
$858$	−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	$0.588373\pi$
$860$		0			0
$861$	693.895	−	137.012i	0.805917	−	0.159131i
$862$	1097.53			1.27323
$863$			285.057i			0.330310i	0.986268	+	0.165155i	$0.0528124\pi$
$863$			285.057i			0.330310i	−0.986268	+	0.165155i	$0.947188\pi$
$864$	127.351	−	84.3193i	0.147397	−	0.0975918i
$865$		0			0
$866$			276.516i			0.319302i
$867$	160.608	+	813.399i	0.185246	+	0.938177i
$868$	183.789			0.211739
$869$		−	76.5910i		−	0.0881369i
$870$		0			0
$871$	535.395			0.614690
$872$			265.425i			0.304387i
$873$	931.912	−	382.948i	1.06748	−	0.438657i
$874$	274.053			0.313561
$875$		0			0
$876$	14.0085	+	70.9462i	0.0159915	+	0.0809888i
$877$	−244.579			−0.278882			−0.139441	−	0.990230i	$-0.544531\pi$
$877$	−244.579			−0.278882			−0.139441	+	0.990230i	$0.544531\pi$
$878$			846.779i			0.964440i
$879$	485.618	−	95.8867i	0.552466	−	0.109086i
$880$		0			0
$881$		−	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	$-0.882854\pi$
$883$	−1647.75			−1.86608			−0.933040	+	0.359772i	$0.882854\pi$
$884$		−	71.0831i		−	0.0804107i
$885$		0			0
$886$	−306.500			−0.345936
$887$		−	514.419i		−	0.579954i	−0.957034	−	0.289977i	$-0.906352\pi$
$887$		−	514.419i		−	0.579954i	0.957034	−	0.289977i	$-0.0936477\pi$
$888$	499.035	−	98.5360i	0.561976	−	0.110964i
$889$	−890.683			−1.00189
$890$		0			0
$891$	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
$895$		0			0
$896$			129.959i			0.145043i
$897$	−519.737	+	102.624i	−0.579417	+	0.114408i
$898$	348.184			0.387732
$899$			214.663i			0.238779i
$900$		0			0
$901$	−12.6320			−0.0140200
$902$		−	246.297i		−	0.273056i
$903$	283.443	+	1435.49i	0.313890	+	1.58969i
$904$	−553.631			−0.612424
$905$		0			0
$906$	−391.035	+	77.2110i	−0.431606	+	0.0852219i
$907$	−347.303			−0.382914			−0.191457	−	0.981501i	$-0.561321\pi$
$907$	−347.303			−0.382914			−0.191457	+	0.981501i	$0.561321\pi$
$908$		−	58.2434i		−	0.0641448i
$909$	531.895	+	1294.38i	0.585143	+	1.42396i
$910$		0			0
$911$			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
$915$		0			0
$916$	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	$0.457568\pi$
$920$		0			0
$921$	−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
$925$		0			0
$926$		−	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	$0.813795\pi$
$930$		0			0
$931$	−910.236			−0.977697
$932$		−	371.752i		−	0.398875i
$933$	−421.157	+	83.1588i	−0.451401	+	0.0891305i
$934$	688.552			0.737208
$935$		0			0
$936$	96.7544	+	235.454i	0.103370	+	0.251553i
$937$	332.053			0.354379			0.177189	−	0.984177i	$-0.443300\pi$
$937$	332.053			0.354379			0.177189	+	0.984177i	$0.443300\pi$
$938$		−	869.740i		−	0.927229i
$939$	291.548	+	1476.54i	0.310488	+	1.57246i
$940$		0			0
$941$		−	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
$945$		0			0
$946$	509.526			0.538611
$947$			1209.32i			1.27700i	0.769622	+	0.638500i	$0.220445\pi$
$947$			1209.32i			1.27700i	−0.769622	+	0.638500i	$0.779555\pi$
$948$	10.4911	+	53.1322i	0.0110666	+	0.0560466i
$949$	−120.527			−0.127004
$950$		0			0
$951$	−983.776	+	194.250i	−1.03446	+	0.204258i
$952$	−115.473			−0.121296
$953$		−	1205.26i		−	1.26470i	−0.774681	−	0.632352i	$-0.782090\pi$
$953$		−	1205.26i		−	1.26470i	0.774681	−	0.632352i	$-0.217910\pi$
$954$	41.8420	−	17.1940i	0.0438595	−	0.0180231i
$955$		0			0
$956$			605.432i			0.633297i
$957$	−132.316	−	670.114i	−0.138261	−	0.700223i
$958$	−736.211			−0.768487
$959$			2021.84i			2.10828i
$960$		0			0
$961$	−897.000			−0.933403
$962$			847.783i			0.881272i
$963$	−55.6975	−	135.541i	−0.0578375	−	0.140749i
$964$	475.052			0.492793
$965$		0			0
$966$	166.710	+	844.304i	0.172578	+	0.874020i
$967$	1845.93			1.90893			0.954464	−	0.298325i	$-0.0964281\pi$
$967$	1845.93			1.90893			0.954464	+	0.298325i	$0.0964281\pi$
$968$		−	138.593i		−	0.143175i
$969$	114.790	−	22.6656i	0.118462	−	0.0233908i
$970$		0			0
$971$		−	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
$975$		0			0
$976$	87.7893			0.0899481
$977$		−	964.028i		−	0.986722i	−0.869825	−	0.493361i	$-0.835768\pi$
$977$		−	964.028i		−	0.986722i	0.869825	−	0.493361i	$-0.164232\pi$
$978$	663.390	−	130.988i	0.678313	−	0.133935i
$979$	−60.3160			−0.0616098
$980$		0			0
$981$	781.193	−	321.013i	0.796323	−	0.327231i
$982$	1006.42			1.02487
$983$			460.718i			0.468685i	0.972154	+	0.234343i	$0.0752937\pi$
$983$			460.718i			0.468685i	−0.972154	+	0.234343i	$0.924706\pi$
$984$	33.7367	+	170.859i	0.0342852	+	0.173637i
$985$		0			0
$986$		−	134.871i		−	0.136786i
$987$	2985.06	−	589.410i	3.02438	−	0.597173i
$988$	219.473			0.222139
$989$		−	749.812i		−	0.758152i
$990$		0			0
$991$	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
$995$		0			0
$996$	4.05267	−	0.800212i	0.00406894	−	0.000803425i
$997$	9.36798			0.00939617			0.00469809	−	0.999989i	$-0.498505\pi$
$997$	9.36798			0.00939617			0.00469809	+	0.999989i	$0.498505\pi$
$998$			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	150.3.d.c.101.4		4
3.2	odd	2	inner	150.3.d.c.101.2		4
4.3	odd	2		1200.3.l.u.401.1		4
5.2	odd	4		150.3.b.b.149.3		8
5.3	odd	4		150.3.b.b.149.6		8
5.4	even	2		30.3.d.a.11.1	✓	4
12.11	even	2		1200.3.l.u.401.2		4
15.2	even	4		150.3.b.b.149.5		8
15.8	even	4		150.3.b.b.149.4		8
15.14	odd	2		30.3.d.a.11.3	yes	4
20.3	even	4		1200.3.c.k.449.7		8
20.7	even	4		1200.3.c.k.449.2		8
20.19	odd	2		240.3.l.c.161.4		4
40.19	odd	2		960.3.l.f.641.1		4
40.29	even	2		960.3.l.e.641.4		4
45.4	even	6		810.3.h.a.431.4		8
45.14	odd	6		810.3.h.a.431.1		8
45.29	odd	6		810.3.h.a.701.4		8
45.34	even	6		810.3.h.a.701.1		8
60.23	odd	4		1200.3.c.k.449.1		8
60.47	odd	4		1200.3.c.k.449.8		8
60.59	even	2		240.3.l.c.161.3		4
120.29	odd	2		960.3.l.e.641.3		4
120.59	even	2		960.3.l.f.641.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.3.d.a.11.1	✓	4	5.4	even	2
30.3.d.a.11.3	yes	4	15.14	odd	2
150.3.b.b.149.3		8	5.2	odd	4
150.3.b.b.149.4		8	15.8	even	4
150.3.b.b.149.5		8	15.2	even	4
150.3.b.b.149.6		8	5.3	odd	4
150.3.d.c.101.2		4	3.2	odd	2	inner
150.3.d.c.101.4		4	1.1	even	1	trivial
240.3.l.c.161.3		4	60.59	even	2
240.3.l.c.161.4		4	20.19	odd	2
810.3.h.a.431.1		8	45.14	odd	6
810.3.h.a.431.4		8	45.4	even	6
810.3.h.a.701.1		8	45.34	even	6
810.3.h.a.701.4		8	45.29	odd	6
960.3.l.e.641.3		4	120.29	odd	2
960.3.l.e.641.4		4	40.29	even	2
960.3.l.f.641.1		4	40.19	odd	2
960.3.l.f.641.2		4	120.59	even	2
1200.3.c.k.449.1		8	60.23	odd	4
1200.3.c.k.449.2		8	20.7	even	4
1200.3.c.k.449.7		8	20.3	even	4
1200.3.c.k.449.8		8	60.47	odd	4
1200.3.l.u.401.1		4	4.3	odd	2
1200.3.l.u.401.2		4	12.11	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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	150.d (of order \(2\), degree \(1\), minimal)

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

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