LMFDB - Embedded newform 150.3.b.b.149.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,3,Mod(149,150)]

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, 1]))

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

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

chi := DirichletCharacter("150.149");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	150.b (of order $2$, degree $1$, not 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:	$8$
Coefficient field:	8.0.40960000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{4} + 1 $ x^8 + 7*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.4
Root			$-0.437016 + 0.437016i$ of defining polynomial
Character	$\chi$	$=$	150.149
Dual form			150.3.b.b.149.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +(2.94317 + 0.581139i) q^{3} +2.00000 q^{4} +(-4.16228 - 0.821854i) q^{6} +11.4868i q^{7} -2.82843 q^{8} +(8.32456 + 3.42079i) q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +(2.94317 + 0.581139i) q^{3} +2.00000 q^{4} +(-4.16228 - 0.821854i) q^{6} +11.4868i q^{7} -2.82843 q^{8} +(8.32456 + 3.42079i) q^{9} -8.48528i q^{11} +(5.88635 + 1.16228i) q^{12} +10.0000i q^{13} -16.2448i q^{14} +4.00000 q^{16} -3.55415 q^{17} +(-11.7727 - 4.83772i) q^{18} +10.9737 q^{19} +(-6.67544 + 33.8078i) q^{21} +12.0000i q^{22} +17.6590 q^{23} +(-8.32456 - 1.64371i) q^{24} -14.1421i q^{26} +(22.5127 + 14.9057i) q^{27} +22.9737i q^{28} +26.8328i q^{29} +8.00000 q^{31} -5.65685 q^{32} +(4.93113 - 24.9737i) q^{33} +5.02633 q^{34} +(16.6491 + 6.84157i) q^{36} -59.9473i q^{37} -15.5191 q^{38} +(-5.81139 + 29.4317i) q^{39} -20.5247i q^{41} +(9.44050 - 47.8114i) q^{42} -42.4605i q^{43} -16.9706i q^{44} -24.9737 q^{46} -88.2952 q^{47} +(11.7727 + 2.32456i) q^{48} -82.9473 q^{49} +(-10.4605 - 2.06546i) q^{51} +20.0000i q^{52} +3.55415 q^{53} +(-31.8377 - 21.0798i) q^{54} -32.4897i q^{56} +(32.2974 + 6.37722i) q^{57} -37.9473i q^{58} -77.7445i q^{59} +21.9473 q^{61} -11.3137 q^{62} +(-39.2940 + 95.6228i) q^{63} +8.00000 q^{64} +(-6.97367 + 35.3181i) q^{66} -53.5395i q^{67} -7.10831 q^{68} +(51.9737 + 10.2624i) q^{69} -69.2592i q^{71} +(-23.5454 - 9.67544i) q^{72} -12.0527i q^{73} +84.7783i q^{74} +21.9473 q^{76} +97.4690 q^{77} +(8.21854 - 41.6228i) q^{78} +9.02633 q^{79} +(57.5964 + 56.9530i) q^{81} +29.0263i q^{82} +0.688486 q^{83} +(-13.3509 + 67.6155i) q^{84} +60.0482i q^{86} +(-15.5936 + 78.9737i) q^{87} +24.0000i q^{88} +7.10831i q^{89} -114.868 q^{91} +35.3181 q^{92} +(23.5454 + 4.64911i) q^{93} +124.868 q^{94} +(-16.6491 - 3.28742i) q^{96} +111.947i q^{97} +117.305 q^{98} +(29.0263 - 70.6362i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{4} - 8 q^{6} + 16 q^{9}+O(q^{10}) $ 8 * q + 16 * q^4 - 8 * q^6 + 16 * q^9	$ 8 q + 16 q^{4} - 8 q^{6} + 16 q^{9} + 32 q^{16} - 64 q^{19} - 104 q^{21} - 16 q^{24} + 64 q^{31} + 192 q^{34} + 32 q^{36} + 80 q^{39} - 48 q^{46} - 360 q^{49} + 144 q^{51} - 280 q^{54} - 128 q^{61} + 64 q^{64} + 96 q^{66} + 264 q^{69} - 128 q^{76} + 224 q^{79} + 56 q^{81} - 208 q^{84} - 160 q^{91} + 240 q^{94} - 32 q^{96} + 384 q^{99}+O(q^{100}) $ 8 * q + 16 * q^4 - 8 * q^6 + 16 * q^9 + 32 * q^16 - 64 * q^19 - 104 * q^21 - 16 * q^24 + 64 * q^31 + 192 * q^34 + 32 * q^36 + 80 * q^39 - 48 * q^46 - 360 * q^49 + 144 * q^51 - 280 * q^54 - 128 * q^61 + 64 * q^64 + 96 * q^66 + 264 * q^69 - 128 * q^76 + 224 * q^79 + 56 * q^81 - 208 * q^84 - 160 * q^91 + 240 * q^94 - 32 * q^96 + 384 * 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 $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$	2.94317	+	0.581139i	0.981058	+	0.193713i
$3$	2.94317	+	0.581139i	0.981058	+	0.193713i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	−4.16228	−	0.821854i	−0.693713	−	0.136976i
$7$			11.4868i			1.64098i	0.571664	+	0.820488i	$0.306298\pi$
$7$			11.4868i			1.64098i	−0.571664	+	0.820488i	$0.693702\pi$
$8$	−2.82843			−0.353553
$9$	8.32456	+	3.42079i	0.924951	+	0.380087i
$10$		0			0
$11$		−	8.48528i		−	0.771389i	−0.922627	−	0.385695i	$-0.873962\pi$
$11$		−	8.48528i		−	0.771389i	0.922627	−	0.385695i	$-0.126038\pi$
$12$	5.88635	+	1.16228i	0.490529	+	0.0968565i
$13$			10.0000i			0.769231i	0.923077	+	0.384615i	$0.125666\pi$
$13$			10.0000i			0.769231i	−0.923077	+	0.384615i	$0.874334\pi$
$14$		−	16.2448i		−	1.16035i
$15$		0			0
$16$	4.00000			0.250000
$17$	−3.55415			−0.209068			−0.104534	−	0.994521i	$-0.533335\pi$
$17$	−3.55415			−0.209068			−0.104534	+	0.994521i	$0.533335\pi$
$18$	−11.7727	−	4.83772i	−0.654039	−	0.268762i
$19$	10.9737			0.577561			0.288781	−	0.957395i	$-0.406750\pi$
$19$	10.9737			0.577561			0.288781	+	0.957395i	$0.406750\pi$
$20$		0			0
$21$	−6.67544	+	33.8078i	−0.317878	+	1.60989i
$22$			12.0000i			0.545455i
$23$	17.6590			0.767785			0.383892	−	0.923378i	$-0.374583\pi$
$23$	17.6590			0.767785			0.383892	+	0.923378i	$0.374583\pi$
$24$	−8.32456	−	1.64371i	−0.346856	−	0.0684879i
$25$		0			0
$26$		−	14.1421i		−	0.543928i
$27$	22.5127	+	14.9057i	0.833803	+	0.552063i
$28$			22.9737i			0.820488i
$29$			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	$0.458813\pi$
$32$	−5.65685			−0.176777
$33$	4.93113	−	24.9737i	0.149428	−	0.756778i
$34$	5.02633			0.147833
$35$		0			0
$36$	16.6491	+	6.84157i	0.462475	+	0.190044i
$37$		−	59.9473i		−	1.62020i	−0.586293	−	0.810099i	$-0.699413\pi$
$37$		−	59.9473i		−	1.62020i	0.586293	−	0.810099i	$-0.300587\pi$
$38$	−15.5191			−0.408398
$39$	−5.81139	+	29.4317i	−0.149010	+	0.754660i
$40$		0			0
$41$		−	20.5247i		−	0.500603i	−0.968168	−	0.250301i	$-0.919470\pi$
$41$		−	20.5247i		−	0.500603i	0.968168	−	0.250301i	$-0.0805297\pi$
$42$	9.44050	−	47.8114i	0.224774	−	1.13837i
$43$		−	42.4605i		−	0.987453i	−0.869617	−	0.493727i	$-0.835634\pi$
$43$		−	42.4605i		−	0.987453i	0.869617	−	0.493727i	$-0.164366\pi$
$44$		−	16.9706i		−	0.385695i
$45$		0			0
$46$	−24.9737			−0.542906
$47$	−88.2952			−1.87862			−0.939311	−	0.343067i	$-0.888534\pi$
$47$	−88.2952			−1.87862			−0.939311	+	0.343067i	$0.888534\pi$
$48$	11.7727	+	2.32456i	0.245265	+	0.0484282i
$49$	−82.9473			−1.69280
$50$		0			0
$51$	−10.4605	−	2.06546i	−0.205108	−	0.0404992i
$52$			20.0000i			0.384615i
$53$	3.55415			0.0670595			0.0335298	−	0.999438i	$-0.489325\pi$
$53$	3.55415			0.0670595			0.0335298	+	0.999438i	$0.489325\pi$
$54$	−31.8377	−	21.0798i	−0.589587	−	0.390367i
$55$		0			0
$56$		−	32.4897i		−	0.580173i
$57$	32.2974	+	6.37722i	0.566621	+	0.111881i
$58$		−	37.9473i		−	0.654264i
$59$		−	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	$0.442424\pi$
$62$	−11.3137			−0.182479
$63$	−39.2940	+	95.6228i	−0.623714	+	1.51782i
$64$	8.00000			0.125000
$65$		0			0
$66$	−6.97367	+	35.3181i	−0.105662	+	0.535123i
$67$		−	53.5395i		−	0.799097i	−0.916712	−	0.399549i	$-0.869167\pi$
$67$		−	53.5395i		−	0.799097i	0.916712	−	0.399549i	$-0.130833\pi$
$68$	−7.10831			−0.104534
$69$	51.9737	+	10.2624i	0.753242	+	0.148730i
$70$		0			0
$71$		−	69.2592i		−	0.975482i	−0.872988	−	0.487741i	$-0.837821\pi$
$71$		−	69.2592i		−	0.975482i	0.872988	−	0.487741i	$-0.162179\pi$
$72$	−23.5454	−	9.67544i	−0.327019	−	0.134381i
$73$		−	12.0527i		−	0.165105i	−0.996587	−	0.0825525i	$-0.973693\pi$
$73$		−	12.0527i		−	0.165105i	0.996587	−	0.0825525i	$-0.0263072\pi$
$74$			84.7783i			1.14565i
$75$		0			0
$76$	21.9473			0.288781
$77$	97.4690			1.26583
$78$	8.21854	−	41.6228i	0.105366	−	0.533625i
$79$	9.02633			0.114257			0.0571287	−	0.998367i	$-0.481805\pi$
$79$	9.02633			0.114257			0.0571287	+	0.998367i	$0.481805\pi$
$80$		0			0
$81$	57.5964	+	56.9530i	0.711067	+	0.703124i
$82$			29.0263i			0.353980i
$83$	0.688486			0.00829501			0.00414750	−	0.999991i	$-0.498680\pi$
$83$	0.688486			0.00829501			0.00414750	+	0.999991i	$0.498680\pi$
$84$	−13.3509	+	67.6155i	−0.158939	+	0.804947i
$85$		0			0
$86$			60.0482i			0.698235i
$87$	−15.5936	+	78.9737i	−0.179237	+	0.907743i
$88$			24.0000i			0.272727i
$89$			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
$92$	35.3181			0.383892
$93$	23.5454	+	4.64911i	0.253176	+	0.0499904i
$94$	124.868			1.32839
$95$		0			0
$96$	−16.6491	−	3.28742i	−0.173428	−	0.0342439i
$97$			111.947i			1.15410i	0.816710	+	0.577048i	$0.195795\pi$
$97$			111.947i			1.15410i	−0.816710	+	0.577048i	$0.804205\pi$
$98$	117.305			1.19699
$99$	29.0263	−	70.6362i	0.293195	−	0.713497i
$100$		0			0
$101$			155.489i			1.53950i	0.638348	+	0.769748i	$0.279618\pi$
$101$			155.489i			1.53950i	−0.638348	+	0.769748i	$0.720382\pi$
$102$	14.7934	+	2.92100i	0.145033	+	0.0286372i
$103$		−	7.59217i		−	0.0737104i	−0.999321	−	0.0368552i	$-0.988266\pi$
$103$		−	7.59217i		−	0.0737104i	0.999321	−	0.0368552i	$-0.0117340\pi$
$104$		−	28.2843i		−	0.271964i
$105$		0			0
$106$	−5.02633			−0.0474182
$107$	−16.2821			−0.152169			−0.0760845	−	0.997101i	$-0.524242\pi$
$107$	−16.2821			−0.152169			−0.0760845	+	0.997101i	$0.524242\pi$
$108$	45.0253	+	29.8114i	0.416901	+	0.276031i
$109$	93.8420			0.860936			0.430468	−	0.902606i	$-0.358349\pi$
$109$	93.8420			0.860936			0.430468	+	0.902606i	$0.358349\pi$
$110$		0			0
$111$	34.8377	−	176.435i	0.313853	−	1.58951i
$112$			45.9473i			0.410244i
$113$	−195.738			−1.73220			−0.866098	−	0.499874i	$-0.833380\pi$
$113$	−195.738			−1.73220			−0.866098	+	0.499874i	$0.833380\pi$
$114$	−45.6754	−	9.01876i	−0.400662	−	0.0791119i
$115$		0			0
$116$			53.6656i			0.462635i
$117$	−34.2079	+	83.2456i	−0.292375	+	0.711500i
$118$			109.947i			0.931757i
$119$		−	40.8260i		−	0.343075i
$120$		0			0
$121$	49.0000			0.404959
$122$	−31.0382			−0.254412
$123$	11.9277	−	60.4078i	0.0969733	−	0.491121i
$124$	16.0000			0.129032
$125$		0			0
$126$	55.5701	−	135.231i	0.441033	−	1.07326i
$127$		−	77.5395i		−	0.610547i	−0.952265	−	0.305274i	$-0.901252\pi$
$127$		−	77.5395i		−	0.610547i	0.952265	−	0.305274i	$-0.0987479\pi$
$128$	−11.3137			−0.0883883
$129$	24.6754	−	124.969i	0.191283	−	0.968749i
$130$		0			0
$131$		−	101.600i		−	0.775572i	−0.921749	−	0.387786i	$-0.873240\pi$
$131$		−	101.600i		−	0.775572i	0.921749	−	0.387786i	$-0.126760\pi$
$132$	9.86225	−	49.9473i	0.0747140	−	0.378389i
$133$			126.053i			0.947764i
$134$			75.7163i			0.565047i
$135$		0			0
$136$	10.0527			0.0739167
$137$	176.014			1.28477			0.642386	−	0.766381i	$-0.277945\pi$
$137$	176.014			1.28477			0.642386	+	0.766381i	$0.277945\pi$
$138$	−73.5019	−	14.5132i	−0.532622	−	0.105168i
$139$	−188.816			−1.35839			−0.679193	−	0.733960i	$-0.737670\pi$
$139$	−188.816			−1.35839			−0.679193	+	0.733960i	$0.737670\pi$
$140$		0			0
$141$	−259.868	−	51.3118i	−1.84304	−	0.363913i
$142$			97.9473i			0.689770i
$143$	84.8528			0.593376
$144$	33.2982	+	13.6831i	0.231238	+	0.0950218i
$145$		0			0
$146$			17.0450i			0.116747i
$147$	−244.128	−	48.2039i	−1.66074	−	0.327918i
$148$		−	119.895i		−	0.810099i
$149$			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	$0.399308\pi$
$152$	−31.0382			−0.204199
$153$	−29.5868	−	12.1580i	−0.193378	−	0.0794641i
$154$	−137.842			−0.895078
$155$		0			0
$156$	−11.6228	+	58.8635i	−0.0745050	+	0.377330i
$157$		−	123.842i		−	0.788803i	−0.918938	−	0.394401i	$-0.870952\pi$
$157$		−	123.842i		−	0.788803i	0.918938	−	0.394401i	$-0.129048\pi$
$158$	−12.7652			−0.0807922
$159$	10.4605	+	2.06546i	0.0657893	+	0.0129903i
$160$		0			0
$161$			202.847i			1.25992i
$162$	−81.4537	−	80.5438i	−0.502800	−	0.497184i
$163$		−	159.381i		−	0.977801i	−0.872340	−	0.488900i	$-0.837398\pi$
$163$		−	159.381i		−	0.977801i	0.872340	−	0.488900i	$-0.162602\pi$
$164$		−	41.0494i		−	0.250301i
$165$		0			0
$166$	−0.973666			−0.00586546
$167$	10.7742			0.0645161			0.0322581	−	0.999480i	$-0.489730\pi$
$167$	10.7742			0.0645161			0.0322581	+	0.999480i	$0.489730\pi$
$168$	18.8810	−	95.6228i	0.112387	−	0.569183i
$169$	69.0000			0.408284
$170$		0			0
$171$	91.3509	+	37.5386i	0.534216	+	0.219524i
$172$		−	84.9210i		−	0.493727i
$173$	283.345			1.63783			0.818916	−	0.573913i	$-0.194575\pi$
$173$	283.345			1.63783			0.818916	+	0.573913i	$0.194575\pi$
$174$	22.0527	−	111.686i	0.126739	−	0.641871i
$175$		0			0
$176$		−	33.9411i		−	0.192847i
$177$	45.1804	−	228.816i	0.255256	−	1.29274i
$178$		−	10.0527i		−	0.0564757i
$179$			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	$0.237682\pi$
$182$	162.448			0.892573
$183$	64.5948	+	12.7544i	0.352977	+	0.0696964i
$184$	−49.9473			−0.271453
$185$		0			0
$186$	−33.2982	−	6.57484i	−0.179023	−	0.0353486i
$187$			30.1580i			0.161273i
$188$	−176.590			−0.939311
$189$	−171.219	+	258.599i	−0.905922	+	1.36825i
$190$		0			0
$191$			159.620i			0.835706i	0.908515	+	0.417853i	$0.137217\pi$
$191$			159.620i			0.835706i	−0.908515	+	0.417853i	$0.862783\pi$
$192$	23.5454	+	4.64911i	0.122632	+	0.0242141i
$193$			92.0527i			0.476957i	0.971148	+	0.238478i	$0.0766486\pi$
$193$			92.0527i			0.476957i	−0.971148	+	0.238478i	$0.923351\pi$
$194$		−	158.317i		−	0.816069i
$195$		0			0
$196$	−165.895			−0.846401
$197$	−69.8360			−0.354497			−0.177249	−	0.984166i	$-0.556720\pi$
$197$	−69.8360			−0.354497			−0.177249	+	0.984166i	$0.556720\pi$
$198$	−41.0494	+	99.8947i	−0.207320	+	0.504519i
$199$	−148.921			−0.748347			−0.374173	−	0.927359i	$-0.622074\pi$
$199$	−148.921			−0.748347			−0.374173	+	0.927359i	$0.622074\pi$
$200$		0			0
$201$	31.1139	−	157.576i	0.154795	−	0.783961i
$202$		−	219.895i		−	1.08859i
$203$	−308.224			−1.51835
$204$	−20.9210	−	4.13091i	−0.102554	−	0.0202496i
$205$		0			0
$206$			10.7369i			0.0521211i
$207$	147.004	+	60.4078i	0.710163	+	0.291825i
$208$			40.0000i			0.192308i
$209$		−	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	$0.736872\pi$
$212$	7.10831			0.0335298
$213$	40.2492	−	203.842i	0.188963	−	0.957005i
$214$	23.0263			0.107600
$215$		0			0
$216$	−63.6754	−	42.1597i	−0.294794	−	0.195184i
$217$			91.8947i			0.423478i
$218$	−132.713			−0.608774
$219$	7.00427	−	35.4731i	0.0319830	−	0.161978i
$220$		0			0
$221$		−	35.5415i		−	0.160821i
$222$	−49.2680	+	249.517i	−0.221928	+	1.12395i
$223$			71.3815i			0.320096i	0.987109	+	0.160048i	$0.0511650\pi$
$223$			71.3815i			0.320096i	−0.987109	+	0.160048i	$0.948835\pi$
$224$		−	64.9793i		−	0.290086i
$225$		0			0
$226$	276.816			1.22485
$227$	−29.1217			−0.128290			−0.0641448	−	0.997941i	$-0.520432\pi$
$227$	−29.1217			−0.128290			−0.0641448	+	0.997941i	$0.520432\pi$
$228$	64.5948	+	12.7544i	0.283311	+	0.0559406i
$229$	129.684			0.566306			0.283153	−	0.959075i	$-0.408620\pi$
$229$	129.684			0.566306			0.283153	+	0.959075i	$0.408620\pi$
$230$		0			0
$231$	286.868	+	56.6430i	1.24185	+	0.245208i
$232$		−	75.8947i		−	0.327132i
$233$	185.876			0.797751			0.398875	−	0.917005i	$-0.369401\pi$
$233$	185.876			0.797751			0.398875	+	0.917005i	$0.369401\pi$
$234$	48.3772	−	117.727i	0.206740	−	0.503107i
$235$		0			0
$236$		−	155.489i		−	0.658852i
$237$	26.5661	+	5.24555i	0.112093	+	0.0221331i
$238$			57.7367i			0.242591i
$239$		−	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	$0.664024\pi$
$242$	−69.2965			−0.286349
$243$	136.419	+	201.094i	0.561394	+	0.827549i
$244$	43.8947			0.179896
$245$		0			0
$246$	−16.8683	+	85.4296i	−0.0685704	+	0.347275i
$247$			109.737i			0.444278i
$248$	−22.6274			−0.0912396
$249$	2.02633	+	0.400106i	0.00813789	+	0.00160685i
$250$		0			0
$251$		−	84.6294i		−	0.337169i	−0.985687	−	0.168584i	$-0.946080\pi$
$251$		−	84.6294i		−	0.337169i	0.985687	−	0.168584i	$-0.0539196\pi$
$252$	−78.5880	+	191.246i	−0.311857	+	0.758911i
$253$		−	149.842i		−	0.592261i
$254$			109.657i			0.431722i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−292.054			−1.13640			−0.568198	−	0.822892i	$-0.692359\pi$
$257$	−292.054			−1.13640			−0.568198	+	0.822892i	$0.692359\pi$
$258$	−34.8963	+	176.732i	−0.135257	+	0.685009i
$259$	688.605			2.65871
$260$		0			0
$261$	−91.7893	+	223.371i	−0.351683	+	0.855829i
$262$			143.684i			0.548412i
$263$	277.725			1.05599			0.527995	−	0.849247i	$-0.322944\pi$
$263$	277.725			1.05599			0.527995	+	0.849247i	$0.322944\pi$
$264$	−13.9473	+	70.6362i	−0.0528308	+	0.267561i
$265$		0			0
$266$		−	178.265i		−	0.670171i
$267$	−4.13091	+	20.9210i	−0.0154716	+	0.0783558i
$268$		−	107.079i		−	0.399549i
$269$			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	$0.704030\pi$
$272$	−14.2166			−0.0522670
$273$	−338.078	−	66.7544i	−1.23838	−	0.244522i
$274$	−248.921			−0.908471
$275$		0			0
$276$	103.947	+	20.5247i	0.376621	+	0.0743649i
$277$			415.842i			1.50123i	0.660737	+	0.750617i	$0.270244\pi$
$277$			415.842i			1.50123i	−0.660737	+	0.750617i	$0.729756\pi$
$278$	267.026			0.960524
$279$	66.5964	+	27.3663i	0.238697	+	0.0980871i
$280$		0			0
$281$		−	431.726i		−	1.53639i	−0.640216	−	0.768195i	$-0.721155\pi$
$281$		−	431.726i		−	1.53639i	0.640216	−	0.768195i	$-0.278845\pi$
$282$	367.509	+	72.5658i	1.30322	+	0.257326i
$283$		−	141.540i		−	0.500140i	−0.968228	−	0.250070i	$-0.919546\pi$
$283$		−	141.540i		−	0.500140i	0.968228	−	0.250070i	$-0.0804536\pi$
$284$		−	138.518i		−	0.487741i
$285$		0			0
$286$	−120.000			−0.419580
$287$	235.764			0.821477
$288$	−47.0908	−	19.3509i	−0.163510	−	0.0671906i
$289$	−276.368			−0.956291
$290$		0			0
$291$	−65.0569	+	329.481i	−0.223563	+	1.13224i
$292$		−	24.1053i		−	0.0825525i
$293$	−164.998			−0.563133			−0.281566	−	0.959542i	$-0.590854\pi$
$293$	−164.998			−0.563133			−0.281566	+	0.959542i	$0.590854\pi$
$294$	345.250	+	68.1706i	1.17432	+	0.231873i
$295$		0			0
$296$			169.557i			0.572827i
$297$	126.479	−	191.026i	0.425855	−	0.643186i
$298$		−	102.658i		−	0.344489i
$299$			176.590i			0.590604i
$300$		0			0
$301$	487.737			1.62039
$302$	−132.862			−0.439939
$303$	−90.3607	+	457.631i	−0.298220	+	1.51033i
$304$	43.8947			0.144390
$305$		0			0
$306$	41.8420	+	17.1940i	0.136739	+	0.0561896i
$307$			159.381i			0.519158i	0.965722	+	0.259579i	$0.0835838\pi$
$307$			159.381i			0.519158i	−0.965722	+	0.259579i	$0.916416\pi$
$308$	194.938			0.632916
$309$	4.41210	−	22.3451i	0.0142787	−	0.0723142i
$310$		0			0
$311$		−	143.096i		−	0.460117i	−0.973177	−	0.230058i	$-0.926108\pi$
$311$		−	143.096i		−	0.460117i	0.973177	−	0.230058i	$-0.0738917\pi$
$312$	16.4371	−	83.2456i	0.0526830	−	0.266813i
$313$			501.684i			1.60282i	0.598113	+	0.801412i	$0.295918\pi$
$313$			501.684i			1.60282i	−0.598113	+	0.801412i	$0.704082\pi$
$314$			175.139i			0.557768i
$315$		0			0
$316$	18.0527			0.0571287
$317$	−334.257			−1.05444			−0.527219	−	0.849730i	$-0.676765\pi$
$317$	−334.257			−1.05444			−0.527219	+	0.849730i	$0.676765\pi$
$318$	−14.7934	−	2.92100i	−0.0465201	−	0.00918553i
$319$	227.684			0.713743
$320$		0			0
$321$	−47.9210	−	9.46215i	−0.149287	−	0.0294771i
$322$		−	286.868i		−	0.890895i
$323$	−39.0021			−0.120750
$324$	115.193	+	113.906i	0.355534	+	0.351562i
$325$		0			0
$326$			225.399i			0.691409i
$327$	276.193	+	54.5352i	0.844628	+	0.166774i
$328$			58.0527i			0.176990i
$329$		−	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	$0.299818\pi$
$332$	1.37697			0.00414750
$333$	205.067	−	499.035i	0.615817	−	1.49860i
$334$	−15.2370			−0.0456198
$335$		0			0
$336$	−26.7018	+	135.231i	−0.0794696	+	0.402473i
$337$		−	129.684i		−	0.384819i	−0.981315	−	0.192409i	$-0.938370\pi$
$337$		−	129.684i		−	0.384819i	0.981315	−	0.192409i	$-0.0616302\pi$
$338$	−97.5807			−0.288700
$339$	−576.092	−	113.751i	−1.69939	−	0.335549i
$340$		0			0
$341$		−	67.8823i		−	0.199068i
$342$	−129.190	−	53.0875i	−0.377748	−	0.155227i
$343$		−	389.947i		−	1.13687i
$344$			120.096i			0.349118i
$345$		0			0
$346$	−400.710			−1.15812
$347$	346.985			0.999956			0.499978	−	0.866038i	$-0.333341\pi$
$347$	346.985			0.999956			0.499978	+	0.866038i	$0.333341\pi$
$348$	−31.1872	+	157.947i	−0.0896183	+	0.453872i
$349$	−509.579			−1.46011			−0.730055	−	0.683388i	$-0.760506\pi$
$349$	−509.579			−1.46011			−0.730055	+	0.683388i	$0.760506\pi$
$350$		0			0
$351$	−149.057	+	225.127i	−0.424664	+	0.641387i
$352$			48.0000i			0.136364i
$353$	−637.679			−1.80646			−0.903229	−	0.429159i	$-0.858810\pi$
$353$	−637.679			−1.80646			−0.903229	+	0.429159i	$0.858810\pi$
$354$	−63.8947	+	323.594i	−0.180493	+	0.914108i
$355$		0			0
$356$			14.2166i			0.0399343i
$357$	23.7256	−	120.158i	0.0664582	−	0.336577i
$358$		−	433.631i		−	1.21126i
$359$			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
$362$	−375.734			−1.03794
$363$	144.216	+	28.4758i	0.397288	+	0.0784457i
$364$	−229.737			−0.631145
$365$		0			0
$366$	−91.3509	−	18.0375i	−0.249593	−	0.0492828i
$367$		−	505.828i		−	1.37828i	−0.724629	−	0.689140i	$-0.757989\pi$
$367$		−	505.828i		−	1.37828i	0.724629	−	0.689140i	$-0.242011\pi$
$368$	70.6362			0.191946
$369$	70.2107	−	170.859i	0.190273	−	0.463033i
$370$		0			0
$371$			40.8260i			0.110043i
$372$	47.0908	+	9.29822i	0.126588	+	0.0249952i
$373$			416.053i			1.11542i	0.830035	+	0.557711i	$0.188320\pi$
$373$			416.053i			1.11542i	−0.830035	+	0.557711i	$0.811680\pi$
$374$		−	42.6499i		−	0.114037i
$375$		0			0
$376$	249.737			0.664193
$377$	−268.328			−0.711746
$378$	242.141	−	365.715i	0.640583	−	0.967499i
$379$	−82.7630			−0.218372			−0.109186	−	0.994021i	$-0.534824\pi$
$379$	−82.7630			−0.218372			−0.109186	+	0.994021i	$0.534824\pi$
$380$		0			0
$381$	45.0612	−	228.212i	0.118271	−	0.598982i
$382$		−	225.737i		−	0.590934i
$383$	−334.592			−0.873608			−0.436804	−	0.899557i	$-0.643890\pi$
$383$	−334.592			−0.873608			−0.436804	+	0.899557i	$0.643890\pi$
$384$	−33.2982	−	6.57484i	−0.0867141	−	0.0171220i
$385$		0			0
$386$		−	130.182i		−	0.337259i
$387$	145.248	−	353.465i	0.375319	−	0.913346i
$388$			223.895i			0.577048i
$389$			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
$392$	234.610			0.598496
$393$	59.0437	−	299.026i	0.150238	−	0.760881i
$394$	98.7630			0.250667
$395$		0			0
$396$	58.0527	−	141.272i	0.146598	−	0.356748i
$397$		−	214.000i		−	0.539043i	−0.962994	−	0.269521i	$-0.913135\pi$
$397$		−	214.000i		−	0.539043i	0.962994	−	0.269521i	$-0.0868655\pi$
$398$	210.606			0.529161
$399$	−73.2541	+	370.995i	−0.183594	+	0.929812i
$400$		0			0
$401$		−	726.086i		−	1.81069i	−0.424677	−	0.905345i	$-0.639613\pi$
$401$		−	726.086i		−	1.81069i	0.424677	−	0.905345i	$-0.360387\pi$
$402$	−44.0017	+	222.846i	−0.109457	+	0.554344i
$403$			80.0000i			0.198511i
$404$			310.978i			0.769748i
$405$		0			0
$406$	435.895			1.07363
$407$	−508.670			−1.24980
$408$	29.5868	+	5.84200i	0.0725166	+	0.0143186i
$409$	346.158			0.846352			0.423176	−	0.906047i	$-0.360915\pi$
$409$	346.158			0.846352			0.423176	+	0.906047i	$0.360915\pi$
$410$		0			0
$411$	518.039	+	102.288i	1.26044	+	0.248877i
$412$		−	15.1843i		−	0.0368552i
$413$	893.038			2.16232
$414$	−207.895	−	85.4296i	−0.502161	−	0.206352i
$415$		0			0
$416$		−	56.5685i		−	0.135982i
$417$	−555.717	−	109.728i	−1.33266	−	0.263137i
$418$			131.684i			0.315033i
$419$		−	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	$0.603633\pi$
$422$	404.242			0.957919
$423$	−735.019	−	302.039i	−1.73763	−	0.714041i
$424$	−10.0527			−0.0237091
$425$		0			0
$426$	−56.9210	+	288.276i	−0.133617	+	0.676704i
$427$			252.105i			0.590411i
$428$	−32.5642			−0.0760845
$429$	249.737	+	49.3113i	0.582137	+	0.114945i
$430$		0			0
$431$			776.068i			1.80062i	0.435247	+	0.900311i	$0.356661\pi$
$431$			776.068i			1.80062i	−0.435247	+	0.900311i	$0.643339\pi$
$432$	90.0507	+	59.6228i	0.208451	+	0.138016i
$433$			195.526i			0.451561i	0.974178	+	0.225781i	$0.0724932\pi$
$433$			195.526i			0.451561i	−0.974178	+	0.225781i	$0.927507\pi$
$434$		−	129.959i		−	0.299444i
$435$		0			0
$436$	187.684			0.430468
$437$	193.785			0.443443
$438$	−9.90554	+	50.1666i	−0.0226154	+	0.114536i
$439$	−598.763			−1.36392			−0.681962	−	0.731387i	$-0.738873\pi$
$439$	−598.763			−1.36392			−0.681962	+	0.731387i	$0.738873\pi$
$440$		0			0
$441$	−690.500	−	283.745i	−1.56576	−	0.643413i
$442$			50.2633i			0.113718i
$443$	216.728			0.489228			0.244614	−	0.969621i	$-0.421339\pi$
$443$	216.728			0.489228			0.244614	+	0.969621i	$0.421339\pi$
$444$	69.6754	−	352.871i	0.156927	−	0.794754i
$445$		0			0
$446$		−	100.949i		−	0.226342i
$447$	−42.1848	+	213.645i	−0.0943732	+	0.477953i
$448$			91.8947i			0.205122i
$449$		−	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
$452$	−391.476			−0.866098
$453$	276.503	+	54.5964i	0.610383	+	0.120522i
$454$	41.1843			0.0907144
$455$		0			0
$456$	−91.3509	−	18.0375i	−0.200331	−	0.0395559i
$457$			553.052i			1.21018i	0.796157	+	0.605090i	$0.206863\pi$
$457$			553.052i			1.21018i	−0.796157	+	0.605090i	$0.793137\pi$
$458$	−183.401			−0.400439
$459$	−80.0135	−	52.9771i	−0.174321	−	0.115419i
$460$		0			0
$461$			124.749i			0.270605i	0.990804	+	0.135302i	$0.0432006\pi$
$461$			124.749i			0.270605i	−0.990804	+	0.135302i	$0.956799\pi$
$462$	−405.693	−	80.1053i	−0.878124	−	0.173388i
$463$		−	669.723i		−	1.44649i	−0.690593	−	0.723243i	$-0.742651\pi$
$463$		−	669.723i		−	1.44649i	0.690593	−	0.723243i	$-0.257349\pi$
$464$			107.331i			0.231317i
$465$		0			0
$466$	−262.868			−0.564095
$467$	486.880			1.04257			0.521285	−	0.853383i	$-0.325453\pi$
$467$	486.880			1.04257			0.521285	+	0.853383i	$0.325453\pi$
$468$	−68.4157	+	166.491i	−0.146187	+	0.355750i
$469$	614.999			1.31130
$470$		0			0
$471$	71.9694	−	364.489i	0.152801	−	0.773861i
$472$			219.895i			0.465879i
$473$	−360.289			−0.761711
$474$	−37.5701	−	7.41833i	−0.0792618	−	0.0156505i
$475$		0			0
$476$		−	81.6520i		−	0.171538i
$477$	29.5868	+	12.1580i	0.0620267	+	0.0254885i
$478$			428.105i			0.895618i
$479$			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
$482$	335.912			0.696914
$483$	−117.882	+	597.013i	−0.244062	+	1.23605i
$484$	98.0000			0.202479
$485$		0			0
$486$	−192.925	−	284.390i	−0.396966	−	0.585165i
$487$		−	263.381i		−	0.540824i	−0.962745	−	0.270412i	$-0.912840\pi$
$487$		−	263.381i		−	0.540824i	0.962745	−	0.270412i	$-0.0871600\pi$
$488$	−62.0764			−0.127206
$489$	92.6228	−	469.088i	0.189413	−	0.959279i
$490$		0			0
$491$			711.646i			1.44938i	0.689074	+	0.724691i	$0.258017\pi$
$491$			711.646i			1.44938i	−0.689074	+	0.724691i	$0.741983\pi$
$492$	23.8554	−	120.816i	0.0484866	−	0.245560i
$493$		−	95.3680i		−	0.193444i
$494$		−	155.191i		−	0.314152i
$495$		0			0
$496$	32.0000			0.0645161
$497$	795.569			1.60074
$498$	−2.86567	−	0.565835i	−0.00575436	−	0.00113622i
$499$	−23.0790			−0.0462505			−0.0231253	−	0.999733i	$-0.507362\pi$
$499$	−23.0790			−0.0462505			−0.0231253	+	0.999733i	$0.507362\pi$
$500$		0			0
$501$	31.7103	+	6.26130i	0.0632941	+	0.0124976i
$502$			119.684i			0.238414i
$503$	−40.5844			−0.0806847			−0.0403423	−	0.999186i	$-0.512845\pi$
$503$	−40.5844			−0.0806847			−0.0403423	+	0.999186i	$0.512845\pi$
$504$	111.140	−	270.462i	0.220516	−	0.536631i
$505$		0			0
$506$			211.909i			0.418792i
$507$	203.079	+	40.0986i	0.400550	+	0.0790899i
$508$		−	155.079i		−	0.305274i
$509$			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
$512$	−22.6274			−0.0441942
$513$	247.047	+	163.570i	0.481572	+	0.318850i
$514$	413.026			0.803553
$515$		0			0
$516$	49.3509	−	249.937i	0.0956413	−	0.484375i
$517$			749.210i			1.44915i
$518$	−973.835			−1.87999
$519$	833.934	+	164.663i	1.60681	+	0.317269i
$520$		0			0
$521$			539.857i			1.03619i	0.855322	+	0.518097i	$0.173359\pi$
$521$			539.857i			1.03619i	−0.855322	+	0.518097i	$0.826641\pi$
$522$	129.810	−	315.895i	0.248678	−	0.605162i
$523$			266.644i			0.509836i	0.966963	+	0.254918i	$0.0820485\pi$
$523$			266.644i			0.509836i	−0.966963	+	0.254918i	$0.917952\pi$
$524$		−	203.200i		−	0.387786i
$525$		0			0
$526$	−392.763			−0.746698
$527$	−28.4332			−0.0539530
$528$	19.7245	−	99.8947i	0.0373570	−	0.189194i
$529$	−217.158			−0.410507
$530$		0			0
$531$	265.947	−	647.188i	0.500842	−	1.21881i
$532$			252.105i			0.473882i
$533$	205.247			0.385079
$534$	5.84200	−	29.5868i	0.0109401	−	0.0554059i
$535$		0			0
$536$			151.433i			0.282523i
$537$	−178.191	+	902.447i	−0.331827	+	1.68053i
$538$		−	405.237i		−	0.753229i
$539$			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	$0.601095\pi$
$542$	458.354			0.845672
$543$	781.954	+	154.399i	1.44006	+	0.284345i
$544$	20.1053			0.0369583
$545$		0			0
$546$	478.114	+	94.4050i	0.875666	+	0.172903i
$547$		−	214.566i		−	0.392259i	−0.980578	−	0.196130i	$-0.937163\pi$
$547$		−	214.566i		−	0.392259i	0.980578	−	0.196130i	$-0.0628373\pi$
$548$	352.027			0.642386
$549$	182.702	+	75.0771i	0.332790	+	0.136753i
$550$		0			0
$551$			294.454i			0.534400i
$552$	−147.004	−	29.0263i	−0.266311	−	0.0525839i
$553$			103.684i			0.187494i
$554$		−	588.089i		−	1.06153i
$555$		0			0
$556$	−377.631			−0.679193
$557$	−674.821			−1.21153			−0.605764	−	0.795644i	$-0.707133\pi$
$557$	−674.821			−1.21153			−0.605764	+	0.795644i	$0.707133\pi$
$558$	−94.1816	−	38.7018i	−0.168784	−	0.0693580i
$559$	424.605			0.759580
$560$		0			0
$561$	−17.5260	+	88.7603i	−0.0312406	+	0.158218i
$562$			610.552i			1.08639i
$563$	718.513			1.27622			0.638111	−	0.769944i	$-0.279716\pi$
$563$	718.513			1.27622			0.638111	+	0.769944i	$0.279716\pi$
$564$	−519.737	−	102.624i	−0.921519	−	0.181957i
$565$		0			0
$566$			200.167i			0.353652i
$567$	−654.210	+	661.601i	−1.15381	+	1.16684i
$568$			195.895i			0.344885i
$569$			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	$0.583427\pi$
$572$	169.706			0.296688
$573$	−92.7613	+	469.789i	−0.161887	+	0.819877i
$574$	−333.421			−0.580872
$575$		0			0
$576$	66.5964	+	27.3663i	0.115619	+	0.0475109i
$577$		−	984.947i		−	1.70701i	−0.521082	−	0.853507i	$-0.674471\pi$
$577$		−	984.947i		−	1.70701i	0.521082	−	0.853507i	$-0.325529\pi$
$578$	390.843			0.676200
$579$	−53.4954	+	270.927i	−0.0923927	+	0.467922i
$580$		0			0
$581$			7.90852i			0.0136119i
$582$	92.0044	−	465.956i	0.158083	−	0.800611i
$583$		−	30.1580i		−	0.0517290i
$584$			34.0901i			0.0583734i
$585$		0			0
$586$	233.342			0.398195
$587$	378.172			0.644245			0.322122	−	0.946698i	$-0.395604\pi$
$587$	378.172			0.644245			0.322122	+	0.946698i	$0.395604\pi$
$588$	−488.257	−	96.4078i	−0.830369	−	0.163959i
$589$	87.7893			0.149048
$590$		0			0
$591$	−205.540	−	40.5844i	−0.347783	−	0.0686707i
$592$		−	239.789i		−	0.405050i
$593$	−265.221			−0.447253			−0.223626	−	0.974675i	$-0.571790\pi$
$593$	−265.221			−0.447253			−0.223626	+	0.974675i	$0.571790\pi$
$594$	−178.868	+	270.152i	−0.301125	+	0.454801i
$595$		0			0
$596$			145.180i			0.243590i
$597$	−438.301	−	86.5438i	−0.734172	−	0.144964i
$598$		−	249.737i		−	0.417620i
$599$		−	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	$0.176689\pi$
$602$	−689.764			−1.14579
$603$	183.147	−	445.693i	0.303727	−	0.739125i
$604$	187.895			0.311084
$605$		0			0
$606$	127.789	−	647.188i	0.210873	−	1.06797i
$607$		−	835.487i		−	1.37642i	−0.725512	−	0.688210i	$-0.758397\pi$
$607$		−	835.487i		−	1.37642i	0.725512	−	0.688210i	$-0.241603\pi$
$608$	−62.0764			−0.102099
$609$	−907.157	−	179.121i	−1.48959	−	0.294123i
$610$		0			0
$611$		−	882.952i		−	1.44509i
$612$	−59.1735	−	24.3160i	−0.0966888	−	0.0397320i
$613$		−	833.263i		−	1.35932i	−0.733528	−	0.679660i	$-0.762128\pi$
$613$		−	833.263i		−	1.35932i	0.733528	−	0.679660i	$-0.237872\pi$
$614$		−	225.399i		−	0.367100i
$615$		0			0
$616$	−275.684			−0.447539
$617$	455.098			0.737598			0.368799	−	0.929509i	$-0.379769\pi$
$617$	455.098			0.737598			0.368799	+	0.929509i	$0.379769\pi$
$618$	−6.23966	+	31.6007i	−0.0100965	+	0.0511338i
$619$	−336.710			−0.543959			−0.271979	−	0.962303i	$-0.587678\pi$
$619$	−336.710			−0.543959			−0.271979	+	0.962303i	$0.587678\pi$
$620$		0			0
$621$	397.552	+	263.220i	0.640181	+	0.423865i
$622$			202.369i			0.325352i
$623$	−81.6520			−0.131063
$624$	−23.2456	+	117.727i	−0.0372525	+	0.188665i
$625$		0			0
$626$		−	709.488i		−	1.13337i
$627$	54.1125	−	274.053i	0.0863039	−	0.437086i
$628$		−	247.684i		−	0.394401i
$629$			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	$0.837399\pi$
$632$	−25.5303			−0.0403961
$633$	−841.283	−	166.114i	−1.32904	−	0.262423i
$634$	472.710			0.745600
$635$		0			0
$636$	20.9210	+	4.13091i	0.0328947	+	0.00649515i
$637$		−	829.473i		−	1.30216i
$638$	−321.994			−0.504692
$639$	236.921	−	576.552i	0.370768	−	0.902273i
$640$		0			0
$641$		−	337.011i		−	0.525758i	−0.964829	−	0.262879i	$-0.915328\pi$
$641$		−	337.011i		−	0.525758i	0.964829	−	0.262879i	$-0.0846719\pi$
$642$	67.7705	+	13.3815i	0.105562	+	0.0208435i
$643$			599.381i			0.932164i	0.884742	+	0.466082i	$0.154335\pi$
$643$			599.381i			0.932164i	−0.884742	+	0.466082i	$0.845665\pi$
$644$			405.693i			0.629958i
$645$		0			0
$646$	55.1573			0.0853828
$647$	−47.0224			−0.0726775			−0.0363388	−	0.999340i	$-0.511570\pi$
$647$	−47.0224			−0.0726775			−0.0363388	+	0.999340i	$0.511570\pi$
$648$	−162.907	−	161.088i	−0.251400	−	0.248592i
$649$	−659.684			−1.01646
$650$		0			0
$651$	−53.4036	+	270.462i	−0.0820331	+	0.415456i
$652$		−	318.763i		−	0.488900i
$653$	−559.228			−0.856399			−0.428199	−	0.903684i	$-0.640852\pi$
$653$	−559.228			−0.856399			−0.428199	+	0.903684i	$0.640852\pi$
$654$	−390.596	−	77.1245i	−0.597242	−	0.117927i
$655$		0			0
$656$		−	82.0989i		−	0.125151i
$657$	41.2296	−	100.333i	0.0627543	−	0.152714i
$658$			1434.34i			2.17985i
$659$		−	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	$0.638689\pi$
$662$	−550.724			−0.831909
$663$	20.6546	−	104.605i	0.0311532	−	0.157775i
$664$	−1.94733			−0.00293273
$665$		0			0
$666$	−290.009	+	705.742i	−0.435448	+	1.05967i
$667$			473.842i			0.710408i
$668$	21.5484			0.0322581
$669$	−41.4826	+	210.088i	−0.0620068	+	0.314033i
$670$		0			0
$671$		−	186.229i		−	0.277540i
$672$	37.7620	−	191.246i	0.0561935	−	0.284592i
$673$		−	1019.42i		−	1.51474i	−0.652985	−	0.757370i	$-0.726484\pi$
$673$		−	1019.42i		−	1.51474i	0.652985	−	0.757370i	$-0.273516\pi$
$674$			183.401i			0.272108i
$675$		0			0
$676$	138.000			0.204142
$677$	624.616			0.922624			0.461312	−	0.887238i	$-0.347379\pi$
$677$	624.616			0.922624			0.461312	+	0.887238i	$0.347379\pi$
$678$	814.717	+	160.868i	1.20165	+	0.237269i
$679$	−1285.92			−1.89384
$680$		0			0
$681$	−85.7103	−	16.9238i	−0.125860	−	0.0248513i
$682$			96.0000i			0.140762i
$683$	−525.882			−0.769959			−0.384980	−	0.922925i	$-0.625792\pi$
$683$	−525.882			−0.769959			−0.384980	+	0.922925i	$0.625792\pi$
$684$	182.702	+	75.0771i	0.267108	+	0.109762i
$685$		0			0
$686$			551.469i			0.803890i
$687$	381.683	+	75.3644i	0.555579	+	0.109701i
$688$		−	169.842i		−	0.246863i
$689$			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	$0.264409\pi$
$692$	566.690			0.818916
$693$	811.386	+	333.421i	1.17083	+	0.481126i
$694$	−490.710			−0.707075
$695$		0			0
$696$	44.1053	−	223.371i	0.0633697	−	0.320936i
$697$			72.9480i			0.104660i
$698$	720.653			1.03245
$699$	547.065	+	108.020i	0.782640	+	0.154535i
$700$		0			0
$701$			606.045i			0.864544i	0.901743	+	0.432272i	$0.142288\pi$
$701$			606.045i			0.864544i	−0.901743	+	0.432272i	$0.857712\pi$
$702$	210.798	−	318.377i	0.300283	−	0.453529i
$703$		−	657.842i		−	0.935764i
$704$		−	67.8823i		−	0.0964237i
$705$		0			0
$706$	901.815			1.27736
$707$	−1786.08			−2.52627
$708$	90.3607	−	457.631i	0.127628	−	0.646372i
$709$	−489.473			−0.690371			−0.345186	−	0.938534i	$-0.612184\pi$
$709$	−489.473			−0.690371			−0.345186	+	0.938534i	$0.612184\pi$
$710$		0			0
$711$	75.1402	+	30.8772i	0.105682	+	0.0434278i
$712$		−	20.1053i		−	0.0282378i
$713$	141.272			0.198138
$714$	−33.5530	+	169.929i	−0.0469930	+	0.237996i
$715$		0			0
$716$			613.247i			0.856491i
$717$	175.920	−	890.947i	0.245356	−	1.24260i
$718$		−	236.105i		−	0.328838i
$719$		−	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
$722$	340.230			0.471232
$723$	−699.080	−	138.036i	−0.966916	−	0.190921i
$724$	531.368			0.733934
$725$		0			0
$726$	−203.952	−	40.2709i	−0.280925	−	0.0554695i
$727$		−	150.172i		−	0.206563i	−0.994652	−	0.103282i	$-0.967066\pi$
$727$		−	150.172i		−	0.206563i	0.994652	−	0.103282i	$-0.0329343\pi$
$728$	324.897			0.446287
$729$	284.641	+	671.134i	0.390453	+	0.920623i
$730$		0			0
$731$			150.911i			0.206445i
$732$	129.190	+	25.5089i	0.176489	+	0.0348482i
$733$			675.526i			0.921591i	0.887506	+	0.460795i	$0.152436\pi$
$733$			675.526i			0.921591i	−0.887506	+	0.460795i	$0.847564\pi$
$734$			715.349i			0.974591i
$735$		0			0
$736$	−99.8947			−0.135726
$737$	−454.298			−0.616415
$738$	−99.2929	+	241.631i	−0.134543	+	0.327414i
$739$	936.921			1.26782			0.633911	−	0.773406i	$-0.281448\pi$
$739$	936.921			1.26782			0.633911	+	0.773406i	$0.281448\pi$
$740$		0			0
$741$	−63.7722	+	322.974i	−0.0860624	+	0.435863i
$742$		−	57.7367i		−	0.0778122i
$743$	−452.939			−0.609608			−0.304804	−	0.952415i	$-0.598591\pi$
$743$	−452.939			−0.609608			−0.304804	+	0.952415i	$0.598591\pi$
$744$	−66.5964	−	13.1497i	−0.0895113	−	0.0176743i
$745$		0			0
$746$		−	588.387i		−	0.788723i
$747$	5.73134	+	2.35516i	0.00767247	+	0.00315283i
$748$			60.3160i			0.0806364i
$749$		−	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	$0.356513\pi$
$752$	−353.181			−0.469656
$753$	49.1814	−	249.079i	0.0653140	−	0.330782i
$754$	379.473			0.503280
$755$		0			0
$756$	−342.438	+	517.199i	−0.452961	+	0.684125i
$757$			123.315i			0.162900i	0.996677	+	0.0814500i	$0.0259551\pi$
$757$			123.315i			0.162900i	−0.996677	+	0.0814500i	$0.974045\pi$
$758$	117.045			0.154412
$759$	87.0790	−	441.011i	0.114729	−	0.581042i
$760$		0			0
$761$			502.715i			0.660598i	0.943876	+	0.330299i	$0.107150\pi$
$761$			502.715i			0.660598i	−0.943876	+	0.330299i	$0.892850\pi$
$762$	−63.7262	+	322.741i	−0.0836302	+	0.423545i
$763$			1077.95i			1.41278i
$764$			319.240i			0.417853i
$765$		0			0
$766$	473.184			0.617734
$767$	777.445			1.01362
$768$	47.0908	+	9.29822i	0.0613161	+	0.0121071i
$769$	286.316			0.372323			0.186161	−	0.982519i	$-0.440395\pi$
$769$	286.316			0.372323			0.186161	+	0.982519i	$0.440395\pi$
$770$		0			0
$771$	−859.565	−	169.724i	−1.11487	−	0.220135i
$772$			184.105i			0.238478i
$773$	972.030			1.25748			0.628739	−	0.777617i	$-0.283572\pi$
$773$	972.030			1.25748			0.628739	+	0.777617i	$0.283572\pi$
$774$	−205.412	+	499.875i	−0.265390	+	0.645833i
$775$		0			0
$776$		−	316.635i		−	0.408035i
$777$	2026.68	+	400.175i	2.60835	+	0.515026i
$778$		−	767.868i		−	0.986976i
$779$		−	225.231i		−	0.289129i
$780$		0			0
$781$	−587.684			−0.752476
$782$	88.7603			0.113504
$783$	−399.962	+	604.078i	−0.510807	+	0.771492i
$784$	−331.789			−0.423201
$785$		0			0
$786$	−83.5003	+	422.887i	−0.106235	+	0.538024i
$787$			1492.70i			1.89669i	0.317237	+	0.948346i	$0.397245\pi$
$787$			1492.70i			1.89669i	−0.317237	+	0.948346i	$0.602755\pi$
$788$	−139.672			−0.177249
$789$	817.394	+	161.397i	1.03599	+	0.204559i
$790$		0			0
$791$		−	2248.41i		−	2.84249i
$792$	−82.0989	+	199.789i	−0.103660	+	0.252259i
$793$			219.473i			0.276763i
$794$			302.642i			0.381161i
$795$		0			0
$796$	−297.842			−0.374173
$797$	−94.3618			−0.118396			−0.0591981	−	0.998246i	$-0.518854\pi$
$797$	−94.3618			−0.118396			−0.0591981	+	0.998246i	$0.518854\pi$
$798$	103.597	−	524.666i	0.129821	−	0.657476i
$799$	313.815			0.392760
$800$		0			0
$801$	−24.3160	+	59.1735i	−0.0303571	+	0.0738746i
$802$			1026.84i			1.28035i
$803$	−102.270			−0.127360
$804$	62.2278	−	315.152i	0.0773977	−	0.391980i
$805$		0			0
$806$		−	113.137i		−	0.140369i
$807$	−166.523	+	843.354i	−0.206348	+	1.04505i
$808$		−	439.789i		−	0.544294i
$809$		−	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	$0.501993\pi$
$812$	−616.448			−0.759173
$813$	−953.899	−	188.350i	−1.17331	−	0.231673i
$814$	719.368			0.883744
$815$		0			0
$816$	−41.8420	−	8.26183i	−0.0512770	−	0.0101248i
$817$		−	465.947i		−	0.570315i
$818$	−489.541			−0.598461
$819$	−956.228	−	392.940i	−1.16756	−	0.479780i
$820$		0			0
$821$		−	337.011i		−	0.410488i	−0.978711	−	0.205244i	$-0.934201\pi$
$821$		−	337.011i		−	0.410488i	0.978711	−	0.205244i	$-0.0657988\pi$
$822$	−732.618	−	144.658i	−0.891263	−	0.175983i
$823$			901.512i			1.09540i	0.836675	+	0.547699i	$0.184496\pi$
$823$			901.512i			1.09540i	−0.836675	+	0.547699i	$0.815504\pi$
$824$			21.4739i			0.0260606i
$825$		0			0
$826$	−1262.95			−1.52899
$827$	−531.354			−0.642508			−0.321254	−	0.946993i	$-0.604104\pi$
$827$	−531.354			−0.642508			−0.321254	+	0.946993i	$0.604104\pi$
$828$	294.007	+	120.816i	0.355081	+	0.145913i
$829$	197.631			0.238397			0.119199	−	0.992870i	$-0.461967\pi$
$829$	197.631			0.238397			0.119199	+	0.992870i	$0.461967\pi$
$830$		0			0
$831$	−241.662	+	1223.90i	−0.290809	+	1.47280i
$832$			80.0000i			0.0961538i
$833$	294.808			0.353911
$834$	785.903	+	155.179i	0.942330	+	0.186066i
$835$		0			0
$836$		−	186.229i		−	0.222762i
$837$	180.101	+	119.246i	0.215175	+	0.142468i
$838$			821.526i			0.980341i
$839$		−	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
$842$	380.869			0.452339
$843$	250.893	−	1270.64i	0.297619	−	1.50729i
$844$	−571.684			−0.677351
$845$		0			0
$846$	1039.47	+	427.148i	1.22869	+	0.504903i
$847$			562.855i			0.664528i
$848$	14.2166			0.0167649
$849$	82.2541	−	416.575i	0.0968835	−	0.490666i
$850$		0			0
$851$		−	1058.61i		−	1.24396i
$852$	80.4984	−	407.684i	0.0944817	−	0.478502i
$853$			1196.42i			1.40260i	0.712865	+	0.701301i	$0.247397\pi$
$853$			1196.42i			1.40260i	−0.712865	+	0.701301i	$0.752603\pi$
$854$		−	356.531i		−	0.417483i
$855$		0			0
$856$	46.0527			0.0537998
$857$	−1266.04			−1.47729			−0.738645	−	0.674095i	$-0.764534\pi$
$857$	−1266.04			−1.47729			−0.738645	+	0.674095i	$0.764534\pi$
$858$	−353.181	−	69.7367i	−0.411633	−	0.0812782i
$859$	470.868			0.548159			0.274079	−	0.961707i	$-0.411627\pi$
$859$	470.868			0.548159			0.274079	+	0.961707i	$0.411627\pi$
$860$		0			0
$861$	693.895	+	137.012i	0.805917	+	0.159131i
$862$		−	1097.53i		−	1.27323i
$863$	285.057			0.330310			0.165155	−	0.986268i	$-0.447188\pi$
$863$	285.057			0.330310			0.165155	+	0.986268i	$0.447188\pi$
$864$	−127.351	−	84.3193i	−0.147397	−	0.0975918i
$865$		0			0
$866$		−	276.516i		−	0.319302i
$867$	−813.399	−	160.608i	−0.938177	−	0.185246i
$868$			183.789i			0.211739i
$869$		−	76.5910i		−	0.0881369i
$870$		0			0
$871$	535.395			0.614690
$872$	−265.425			−0.304387
$873$	−382.948	+	931.912i	−0.438657	+	1.06748i
$874$	−274.053			−0.313561
$875$		0			0
$876$	14.0085	−	70.9462i	0.0159915	−	0.0809888i
$877$			244.579i			0.278882i	0.990230	+	0.139441i	$0.0445305\pi$
$877$			244.579i			0.278882i	−0.990230	+	0.139441i	$0.955469\pi$
$878$	846.779			0.964440
$879$	−485.618	−	95.8867i	−0.552466	−	0.109086i
$880$		0			0
$881$			137.271i			0.155813i	0.996961	+	0.0779065i	$0.0248236\pi$
$881$			137.271i			0.155813i	−0.996961	+	0.0779065i	$0.975176\pi$
$882$	976.514	+	401.276i	1.10716	+	0.454962i
$883$		−	1647.75i		−	1.86608i	−0.359772	−	0.933040i	$-0.617146\pi$
$883$		−	1647.75i		−	1.86608i	0.359772	−	0.933040i	$-0.382854\pi$
$884$		−	71.0831i		−	0.0804107i
$885$		0			0
$886$	−306.500			−0.345936
$887$	514.419			0.579954			0.289977	−	0.957034i	$-0.406352\pi$
$887$	514.419			0.579954			0.289977	+	0.957034i	$0.406352\pi$
$888$	−98.5360	+	499.035i	−0.110964	+	0.561976i
$889$	890.683			1.00189
$890$		0			0
$891$	483.263	−	488.722i	0.542382	−	0.548510i
$892$			142.763i			0.160048i
$893$	−968.923			−1.08502
$894$	59.6584	−	302.139i	0.0667319	−	0.337964i
$895$		0			0
$896$		−	129.959i		−	0.145043i
$897$	−102.624	+	519.737i	−0.114408	+	0.579417i
$898$			348.184i			0.387732i
$899$			214.663i			0.238779i
$900$		0			0
$901$	−12.6320			−0.0140200
$902$	246.297			0.273056
$903$	1435.49	+	283.443i	1.58969	+	0.313890i
$904$	553.631			0.612424
$905$		0			0
$906$	−391.035	−	77.2110i	−0.431606	−	0.0852219i
$907$			347.303i			0.382914i	0.981501	+	0.191457i	$0.0613213\pi$
$907$			347.303i			0.382914i	−0.981501	+	0.191457i	$0.938679\pi$
$908$	−58.2434			−0.0641448
$909$	−531.895	+	1294.38i	−0.585143	+	1.42396i
$910$		0			0
$911$		−	304.540i		−	0.334292i	−0.985932	−	0.167146i	$-0.946545\pi$
$911$		−	304.540i		−	0.334292i	0.985932	−	0.167146i	$-0.0534551\pi$
$912$	129.190	+	25.5089i	0.141655	+	0.0279703i
$913$		−	5.84200i		−	0.00639868i
$914$		−	782.134i		−	0.855726i
$915$		0			0
$916$	259.368			0.283153
$917$	1167.06			1.27270
$918$	113.156	+	74.9210i	0.123264	+	0.0816133i
$919$	−244.289			−0.265820			−0.132910	−	0.991128i	$-0.542432\pi$
$919$	−244.289			−0.265820			−0.132910	+	0.991128i	$0.542432\pi$
$920$		0			0
$921$	−92.6228	+	469.088i	−0.100568	+	0.509324i
$922$		−	176.421i		−	0.191346i
$923$	692.592			0.750371
$924$	573.737	+	113.286i	0.620927	+	0.122604i
$925$		0			0
$926$			947.132i			1.02282i
$927$	25.9712	−	63.2014i	0.0280164	−	0.0681785i
$928$		−	151.789i		−	0.163566i
$929$			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
$932$	371.752			0.398875
$933$	83.1588	−	421.157i	0.0891305	−	0.451401i
$934$	−688.552			−0.737208
$935$		0			0
$936$	96.7544	−	235.454i	0.103370	−	0.251553i
$937$		−	332.053i		−	0.354379i	−0.984177	−	0.177189i	$-0.943300\pi$
$937$		−	332.053i		−	0.354379i	0.984177	−	0.177189i	$-0.0567005\pi$
$938$	−869.740			−0.927229
$939$	−291.548	+	1476.54i	−0.310488	+	1.57246i
$940$		0			0
$941$			1636.99i			1.73963i	0.493381	+	0.869813i	$0.335761\pi$
$941$			1636.99i			1.73963i	−0.493381	+	0.869813i	$0.664239\pi$
$942$	−101.780	+	515.465i	−0.108047	+	0.547203i
$943$		−	362.447i		−	0.384355i
$944$		−	310.978i		−	0.329426i
$945$		0			0
$946$	509.526			0.538611
$947$	−1209.32			−1.27700			−0.638500	−	0.769622i	$-0.720445\pi$
$947$	−1209.32			−1.27700			−0.638500	+	0.769622i	$0.720445\pi$
$948$	53.1322	+	10.4911i	0.0560466	+	0.0110666i
$949$	120.527			0.127004
$950$		0			0
$951$	−983.776	−	194.250i	−1.03446	−	0.204258i
$952$			115.473i			0.121296i
$953$	−1205.26			−1.26470			−0.632352	−	0.774681i	$-0.717910\pi$
$953$	−1205.26			−1.26470			−0.632352	+	0.774681i	$0.717910\pi$
$954$	−41.8420	−	17.1940i	−0.0438595	−	0.0180231i
$955$		0			0
$956$		−	605.432i		−	0.633297i
$957$	670.114	+	132.316i	0.700223	+	0.138261i
$958$		−	736.211i		−	0.768487i
$959$			2021.84i			2.10828i
$960$		0			0
$961$	−897.000			−0.933403
$962$	−847.783			−0.881272
$963$	−135.541	−	55.6975i	−0.140749	−	0.0578375i
$964$	−475.052			−0.492793
$965$		0			0
$966$	166.710	−	844.304i	0.172578	−	0.874020i
$967$		−	1845.93i		−	1.90893i	−0.298325	−	0.954464i	$-0.596428\pi$
$967$		−	1845.93i		−	1.90893i	0.298325	−	0.954464i	$-0.403572\pi$
$968$	−138.593			−0.143175
$969$	−114.790	−	22.6656i	−0.118462	−	0.0233908i
$970$		0			0
$971$			1057.91i			1.08950i	0.838598	+	0.544751i	$0.183376\pi$
$971$			1057.91i			1.08950i	−0.838598	+	0.544751i	$0.816624\pi$
$972$	272.838	+	402.189i	0.280697	+	0.413774i
$973$		−	2168.89i		−	2.22908i
$974$			372.478i			0.382421i
$975$		0			0
$976$	87.7893			0.0899481
$977$	964.028			0.986722			0.493361	−	0.869825i	$-0.335768\pi$
$977$	964.028			0.986722			0.493361	+	0.869825i	$0.335768\pi$
$978$	−130.988	+	663.390i	−0.133935	+	0.678313i
$979$	60.3160			0.0616098
$980$		0			0
$981$	781.193	+	321.013i	0.796323	+	0.327231i
$982$		−	1006.42i		−	1.02487i
$983$	460.718			0.468685			0.234343	−	0.972154i	$-0.424706\pi$
$983$	460.718			0.468685			0.234343	+	0.972154i	$0.424706\pi$
$984$	−33.7367	+	170.859i	−0.0342852	+	0.173637i
$985$		0			0
$986$			134.871i			0.136786i
$987$	589.410	−	2985.06i	0.597173	−	3.02438i
$988$			219.473i			0.222139i
$989$		−	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	$0.285275\pi$
$992$	−45.2548			−0.0456198
$993$	1146.13	+	226.307i	1.15421	+	0.227903i
$994$	−1125.10			−1.13190
$995$		0			0
$996$	4.05267	+	0.800212i	0.00406894	+	0.000803425i
$997$		−	9.36798i		−	0.00939617i	−0.999989	−	0.00469809i	$-0.998505\pi$
$997$		−	9.36798i		−	0.00939617i	0.999989	−	0.00469809i	$-0.00149545\pi$
$998$	32.6386			0.0327040
$999$	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.b.b.149.4		8
3.2	odd	2	inner	150.3.b.b.149.6		8
4.3	odd	2		1200.3.c.k.449.1		8
5.2	odd	4		150.3.d.c.101.2		4
5.3	odd	4		30.3.d.a.11.3	yes	4
5.4	even	2	inner	150.3.b.b.149.5		8
12.11	even	2		1200.3.c.k.449.7		8
15.2	even	4		150.3.d.c.101.4		4
15.8	even	4		30.3.d.a.11.1	✓	4
15.14	odd	2	inner	150.3.b.b.149.3		8
20.3	even	4		240.3.l.c.161.3		4
20.7	even	4		1200.3.l.u.401.2		4
20.19	odd	2		1200.3.c.k.449.8		8
40.3	even	4		960.3.l.f.641.2		4
40.13	odd	4		960.3.l.e.641.3		4
45.13	odd	12		810.3.h.a.431.1		8
45.23	even	12		810.3.h.a.431.4		8
45.38	even	12		810.3.h.a.701.1		8
45.43	odd	12		810.3.h.a.701.4		8
60.23	odd	4		240.3.l.c.161.4		4
60.47	odd	4		1200.3.l.u.401.1		4
60.59	even	2		1200.3.c.k.449.2		8
120.53	even	4		960.3.l.e.641.4		4
120.83	odd	4		960.3.l.f.641.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.3.d.a.11.1	✓	4	15.8	even	4
30.3.d.a.11.3	yes	4	5.3	odd	4
150.3.b.b.149.3		8	15.14	odd	2	inner
150.3.b.b.149.4		8	1.1	even	1	trivial
150.3.b.b.149.5		8	5.4	even	2	inner
150.3.b.b.149.6		8	3.2	odd	2	inner
150.3.d.c.101.2		4	5.2	odd	4
150.3.d.c.101.4		4	15.2	even	4
240.3.l.c.161.3		4	20.3	even	4
240.3.l.c.161.4		4	60.23	odd	4
810.3.h.a.431.1		8	45.13	odd	12
810.3.h.a.431.4		8	45.23	even	12
810.3.h.a.701.1		8	45.38	even	12
810.3.h.a.701.4		8	45.43	odd	12
960.3.l.e.641.3		4	40.13	odd	4
960.3.l.e.641.4		4	120.53	even	4
960.3.l.f.641.1		4	120.83	odd	4
960.3.l.f.641.2		4	40.3	even	4
1200.3.c.k.449.1		8	4.3	odd	2
1200.3.c.k.449.2		8	60.59	even	2
1200.3.c.k.449.7		8	12.11	even	2
1200.3.c.k.449.8		8	20.19	odd	2
1200.3.l.u.401.1		4	60.47	odd	4
1200.3.l.u.401.2		4	20.7	even	4

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.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +(2.94317 + 0.581139i) q^{3} +2.00000 q^{4} +(-4.16228 - 0.821854i) q^{6} +11.4868i q^{7} -2.82843 q^{8} +(8.32456 + 3.42079i) q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +(2.94317 + 0.581139i) q^{3} +2.00000 q^{4} +(-4.16228 - 0.821854i) q^{6} +11.4868i q^{7} -2.82843 q^{8} +(8.32456 + 3.42079i) q^{9} -8.48528i q^{11} +(5.88635 + 1.16228i) q^{12} +10.0000i q^{13} -16.2448i q^{14} +4.00000 q^{16} -3.55415 q^{17} +(-11.7727 - 4.83772i) q^{18} +10.9737 q^{19} +(-6.67544 + 33.8078i) q^{21} +12.0000i q^{22} +17.6590 q^{23} +(-8.32456 - 1.64371i) q^{24} -14.1421i q^{26} +(22.5127 + 14.9057i) q^{27} +22.9737i q^{28} +26.8328i q^{29} +8.00000 q^{31} -5.65685 q^{32} +(4.93113 - 24.9737i) q^{33} +5.02633 q^{34} +(16.6491 + 6.84157i) q^{36} -59.9473i q^{37} -15.5191 q^{38} +(-5.81139 + 29.4317i) q^{39} -20.5247i q^{41} +(9.44050 - 47.8114i) q^{42} -42.4605i q^{43} -16.9706i q^{44} -24.9737 q^{46} -88.2952 q^{47} +(11.7727 + 2.32456i) q^{48} -82.9473 q^{49} +(-10.4605 - 2.06546i) q^{51} +20.0000i q^{52} +3.55415 q^{53} +(-31.8377 - 21.0798i) q^{54} -32.4897i q^{56} +(32.2974 + 6.37722i) q^{57} -37.9473i q^{58} -77.7445i q^{59} +21.9473 q^{61} -11.3137 q^{62} +(-39.2940 + 95.6228i) q^{63} +8.00000 q^{64} +(-6.97367 + 35.3181i) q^{66} -53.5395i q^{67} -7.10831 q^{68} +(51.9737 + 10.2624i) q^{69} -69.2592i q^{71} +(-23.5454 - 9.67544i) q^{72} -12.0527i q^{73} +84.7783i q^{74} +21.9473 q^{76} +97.4690 q^{77} +(8.21854 - 41.6228i) q^{78} +9.02633 q^{79} +(57.5964 + 56.9530i) q^{81} +29.0263i q^{82} +0.688486 q^{83} +(-13.3509 + 67.6155i) q^{84} +60.0482i q^{86} +(-15.5936 + 78.9737i) q^{87} +24.0000i q^{88} +7.10831i q^{89} -114.868 q^{91} +35.3181 q^{92} +(23.5454 + 4.64911i) q^{93} +124.868 q^{94} +(-16.6491 - 3.28742i) q^{96} +111.947i q^{97} +117.305 q^{98} +(29.0263 - 70.6362i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{4} - 8 q^{6} + 16 q^{9}+O(q^{10}) \) 8 * q + 16 * q^4 - 8 * q^6 + 16 * q^9	\( 8 q + 16 q^{4} - 8 q^{6} + 16 q^{9} + 32 q^{16} - 64 q^{19} - 104 q^{21} - 16 q^{24} + 64 q^{31} + 192 q^{34} + 32 q^{36} + 80 q^{39} - 48 q^{46} - 360 q^{49} + 144 q^{51} - 280 q^{54} - 128 q^{61} + 64 q^{64} + 96 q^{66} + 264 q^{69} - 128 q^{76} + 224 q^{79} + 56 q^{81} - 208 q^{84} - 160 q^{91} + 240 q^{94} - 32 q^{96} + 384 q^{99}+O(q^{100}) \) 8 * q + 16 * q^4 - 8 * q^6 + 16 * q^9 + 32 * q^16 - 64 * q^19 - 104 * q^21 - 16 * q^24 + 64 * q^31 + 192 * q^34 + 32 * q^36 + 80 * q^39 - 48 * q^46 - 360 * q^49 + 144 * q^51 - 280 * q^54 - 128 * q^61 + 64 * q^64 + 96 * q^66 + 264 * q^69 - 128 * q^76 + 224 * q^79 + 56 * q^81 - 208 * q^84 - 160 * q^91 + 240 * q^94 - 32 * q^96 + 384 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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