LMFDB - Embedded newform 294.4.e.k.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,4,Mod(67,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("294.67");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	294.e (of order $3$, degree $2$, 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:	$17.3465615417$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	294.79
Dual form			294.4.e.k.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-2.29289 + 3.97141i) q^{5} +6.00000 q^{6} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-2.29289 + 3.97141i) q^{5} +6.00000 q^{6} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-4.58579 - 7.94282i) q^{10} +(3.24264 + 5.61642i) q^{11} +(-6.00000 + 10.3923i) q^{12} +45.2132 q^{13} +13.7574 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-40.7782 - 70.6299i) q^{17} +(-9.00000 - 15.5885i) q^{18} +(2.52691 - 4.37674i) q^{19} +18.3431 q^{20} -12.9706 q^{22} +(-53.1249 + 92.0150i) q^{23} +(-12.0000 - 20.7846i) q^{24} +(51.9853 + 90.0411i) q^{25} +(-45.2132 + 78.3116i) q^{26} +27.0000 q^{27} -268.132 q^{29} +(-13.7574 + 23.8284i) q^{30} +(-146.184 - 253.198i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(9.72792 - 16.8493i) q^{33} +163.113 q^{34} +36.0000 q^{36} +(-57.2792 + 99.2105i) q^{37} +(5.05382 + 8.75348i) q^{38} +(-67.8198 - 117.467i) q^{39} +(-18.3431 + 31.7713i) q^{40} -161.605 q^{41} -471.294 q^{43} +(12.9706 - 22.4657i) q^{44} +(-20.6360 - 35.7427i) q^{45} +(-106.250 - 184.030i) q^{46} +(-173.002 + 299.648i) q^{47} +48.0000 q^{48} -207.941 q^{50} +(-122.335 + 211.890i) q^{51} +(-90.4264 - 156.623i) q^{52} +(-202.765 - 351.198i) q^{53} +(-27.0000 + 46.7654i) q^{54} -29.7401 q^{55} -15.1615 q^{57} +(268.132 - 464.418i) q^{58} +(126.718 + 219.482i) q^{59} +(-27.5147 - 47.6569i) q^{60} +(375.609 - 650.573i) q^{61} +584.735 q^{62} +64.0000 q^{64} +(-103.669 + 179.560i) q^{65} +(19.4558 + 33.6985i) q^{66} +(-5.82338 - 10.0864i) q^{67} +(-163.113 + 282.519i) q^{68} +318.749 q^{69} -681.661 q^{71} +(-36.0000 + 62.3538i) q^{72} +(-342.729 - 593.623i) q^{73} +(-114.558 - 198.421i) q^{74} +(155.956 - 270.123i) q^{75} -20.2153 q^{76} +271.279 q^{78} +(-0.132034 + 0.228690i) q^{79} +(-36.6863 - 63.5425i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(161.605 - 279.908i) q^{82} -437.137 q^{83} +374.000 q^{85} +(471.294 - 816.304i) q^{86} +(402.198 + 696.627i) q^{87} +(25.9411 + 44.9313i) q^{88} +(29.2563 - 50.6734i) q^{89} +82.5442 q^{90} +424.999 q^{92} +(-438.551 + 759.593i) q^{93} +(-346.004 - 599.297i) q^{94} +(11.5879 + 20.0708i) q^{95} +(-48.0000 + 83.1384i) q^{96} -1280.09 q^{97} -58.3675 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 6 q^{3} - 8 q^{4} - 12 q^{5} + 24 q^{6} + 32 q^{8} - 18 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 6 * q^3 - 8 * q^4 - 12 * q^5 + 24 * q^6 + 32 * q^8 - 18 * q^9	\( 4 q - 4 q^{2} - 6 q^{3} - 8 q^{4} - 12 q^{5} + 24 q^{6} + 32 q^{8} - 18 q^{9} - 24 q^{10} - 4 q^{11} - 24 q^{12} + 96 q^{13} + 72 q^{15} - 32 q^{16} - 132 q^{17} - 36 q^{18} - 120 q^{19} + 96 q^{20} + 16 q^{22} + 76 q^{23} - 48 q^{24} + 174 q^{25} - 96 q^{26} + 108 q^{27} - 224 q^{29} - 72 q^{30} - 432 q^{31} - 64 q^{32} - 12 q^{33} + 528 q^{34} + 144 q^{36} + 280 q^{37} - 240 q^{38} - 144 q^{39} - 96 q^{40} + 72 q^{41} - 256 q^{43} - 16 q^{44} - 108 q^{45} + 152 q^{46} + 264 q^{47} + 192 q^{48} - 696 q^{50} - 396 q^{51} - 192 q^{52} - 268 q^{53} - 108 q^{54} + 96 q^{55} + 720 q^{57} + 224 q^{58} - 336 q^{59} - 144 q^{60} + 504 q^{61} + 1728 q^{62} + 256 q^{64} - 228 q^{65} - 24 q^{66} + 384 q^{67} - 528 q^{68} - 456 q^{69} - 792 q^{71} - 144 q^{72} + 312 q^{73} + 560 q^{74} + 522 q^{75} + 960 q^{76} + 576 q^{78} + 848 q^{79} - 192 q^{80} - 162 q^{81} - 72 q^{82} - 1296 q^{83} + 1496 q^{85} + 256 q^{86} + 336 q^{87} - 32 q^{88} + 612 q^{89} + 432 q^{90} - 608 q^{92} - 1296 q^{93} + 528 q^{94} - 904 q^{95} - 192 q^{96} - 4368 q^{97} + 72 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 6 * q^3 - 8 * q^4 - 12 * q^5 + 24 * q^6 + 32 * q^8 - 18 * q^9 - 24 * q^10 - 4 * q^11 - 24 * q^12 + 96 * q^13 + 72 * q^15 - 32 * q^16 - 132 * q^17 - 36 * q^18 - 120 * q^19 + 96 * q^20 + 16 * q^22 + 76 * q^23 - 48 * q^24 + 174 * q^25 - 96 * q^26 + 108 * q^27 - 224 * q^29 - 72 * q^30 - 432 * q^31 - 64 * q^32 - 12 * q^33 + 528 * q^34 + 144 * q^36 + 280 * q^37 - 240 * q^38 - 144 * q^39 - 96 * q^40 + 72 * q^41 - 256 * q^43 - 16 * q^44 - 108 * q^45 + 152 * q^46 + 264 * q^47 + 192 * q^48 - 696 * q^50 - 396 * q^51 - 192 * q^52 - 268 * q^53 - 108 * q^54 + 96 * q^55 + 720 * q^57 + 224 * q^58 - 336 * q^59 - 144 * q^60 + 504 * q^61 + 1728 * q^62 + 256 * q^64 - 228 * q^65 - 24 * q^66 + 384 * q^67 - 528 * q^68 - 456 * q^69 - 792 * q^71 - 144 * q^72 + 312 * q^73 + 560 * q^74 + 522 * q^75 + 960 * q^76 + 576 * q^78 + 848 * q^79 - 192 * q^80 - 162 * q^81 - 72 * q^82 - 1296 * q^83 + 1496 * q^85 + 256 * q^86 + 336 * q^87 - 32 * q^88 + 612 * q^89 + 432 * q^90 - 608 * q^92 - 1296 * q^93 + 528 * q^94 - 904 * q^95 - 192 * q^96 - 4368 * q^97 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	−2.29289	+	3.97141i	−0.205083	+	0.355213i	−0.950159	−	0.311766i	$-0.899080\pi$
$5$	−2.29289	+	3.97141i	−0.205083	+	0.355213i	0.745076	+	0.666979i	$0.232413\pi$
$6$	6.00000			0.408248
$7$		0			0
$7$		0			0
$8$	8.00000			0.353553
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−4.58579	−	7.94282i	−0.145015	−	0.251174i
$11$	3.24264	+	5.61642i	0.0888812	+	0.153947i	0.907038	−	0.421048i	$-0.138338\pi$
$11$	3.24264	+	5.61642i	0.0888812	+	0.153947i	−0.818157	+	0.574994i	$0.805004\pi$
$12$	−6.00000	+	10.3923i	−0.144338	+	0.250000i
$13$	45.2132			0.964607			0.482303	−	0.876004i	$-0.339800\pi$
$13$	45.2132			0.964607			0.482303	+	0.876004i	$0.339800\pi$
$14$		0			0
$15$	13.7574			0.236809
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−40.7782	−	70.6299i	−0.581774	−	1.00766i	−0.995269	−	0.0971560i	$-0.969025\pi$
$17$	−40.7782	−	70.6299i	−0.581774	−	1.00766i	0.413495	−	0.910506i	$-0.364308\pi$
$18$	−9.00000	−	15.5885i	−0.117851	−	0.204124i
$19$	2.52691	−	4.37674i	0.0305112	−	0.0528470i	−0.850367	−	0.526191i	$-0.823620\pi$
$19$	2.52691	−	4.37674i	0.0305112	−	0.0528470i	0.880878	+	0.473344i	$0.156953\pi$
$20$	18.3431			0.205083
$21$		0			0
$22$	−12.9706			−0.125697
$23$	−53.1249	+	92.0150i	−0.481622	+	0.834194i	−0.999778	−	0.0210927i	$-0.993286\pi$
$23$	−53.1249	+	92.0150i	−0.481622	+	0.834194i	0.518156	+	0.855286i	$0.326619\pi$
$24$	−12.0000	−	20.7846i	−0.102062	−	0.176777i
$25$	51.9853	+	90.0411i	0.415882	+	0.720329i
$26$	−45.2132	+	78.3116i	−0.341040	+	0.590699i
$27$	27.0000			0.192450
$28$		0			0
$29$	−268.132			−1.71693			−0.858463	−	0.512875i	$-0.828580\pi$
$29$	−268.132			−1.71693			−0.858463	+	0.512875i	$0.828580\pi$
$30$	−13.7574	+	23.8284i	−0.0837246	+	0.145015i
$31$	−146.184	−	253.198i	−0.846948	−	1.46696i	−0.883919	−	0.467640i	$-0.845104\pi$
$31$	−146.184	−	253.198i	−0.846948	−	1.46696i	0.0369712	−	0.999316i	$-0.488229\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$	9.72792	−	16.8493i	0.0513156	−	0.0888812i
$34$	163.113			0.822753
$35$		0			0
$36$	36.0000			0.166667
$37$	−57.2792	+	99.2105i	−0.254504	+	0.440814i	−0.964761	−	0.263129i	$-0.915246\pi$
$37$	−57.2792	+	99.2105i	−0.254504	+	0.440814i	0.710257	+	0.703943i	$0.248579\pi$
$38$	5.05382	+	8.75348i	0.0215747	+	0.0373685i
$39$	−67.8198	−	117.467i	−0.278458	−	0.482303i
$40$	−18.3431	+	31.7713i	−0.0725077	+	0.125587i
$41$	−161.605			−0.615573			−0.307786	−	0.951456i	$-0.599588\pi$
$41$	−161.605			−0.615573			−0.307786	+	0.951456i	$0.599588\pi$
$42$		0			0
$43$	−471.294			−1.67143			−0.835716	−	0.549162i	$-0.814947\pi$
$43$	−471.294			−1.67143			−0.835716	+	0.549162i	$0.814947\pi$
$44$	12.9706	−	22.4657i	0.0444406	−	0.0769734i
$45$	−20.6360	−	35.7427i	−0.0683609	−	0.118404i
$46$	−106.250	−	184.030i	−0.340558	−	0.589864i
$47$	−173.002	+	299.648i	−0.536914	+	0.929962i	0.462154	+	0.886800i	$0.347077\pi$
$47$	−173.002	+	299.648i	−0.536914	+	0.929962i	−0.999068	+	0.0431624i	$0.986257\pi$
$48$	48.0000			0.144338
$49$		0			0
$50$	−207.941			−0.588146
$51$	−122.335	+	211.890i	−0.335887	+	0.581774i
$52$	−90.4264	−	156.623i	−0.241152	−	0.417687i
$53$	−202.765	−	351.198i	−0.525507	−	0.910204i	−0.999559	−	0.0297072i	$-0.990543\pi$
$53$	−202.765	−	351.198i	−0.525507	−	0.910204i	0.474052	−	0.880497i	$-0.342791\pi$
$54$	−27.0000	+	46.7654i	−0.0680414	+	0.117851i
$55$	−29.7401			−0.0729119
$56$		0			0
$57$	−15.1615			−0.0352313
$58$	268.132	−	464.418i	0.607025	−	1.05140i
$59$	126.718	+	219.482i	0.279614	+	0.484307i	0.971289	−	0.237903i	$-0.0764600\pi$
$59$	126.718	+	219.482i	0.279614	+	0.484307i	−0.691674	+	0.722209i	$0.743127\pi$
$60$	−27.5147	−	47.6569i	−0.0592022	−	0.102541i
$61$	375.609	−	650.573i	0.788390	−	1.36553i	−0.138563	−	0.990354i	$-0.544248\pi$
$61$	375.609	−	650.573i	0.788390	−	1.36553i	0.926953	−	0.375177i	$-0.122418\pi$
$62$	584.735			1.19776
$63$		0			0
$64$	64.0000			0.125000
$65$	−103.669	+	179.560i	−0.197824	+	0.342641i
$66$	19.4558	+	33.6985i	0.0362856	+	0.0628485i
$67$	−5.82338	−	10.0864i	−0.0106185	−	0.0183918i	0.860667	−	0.509168i	$-0.170047\pi$
$67$	−5.82338	−	10.0864i	−0.0106185	−	0.0183918i	−0.871286	+	0.490776i	$0.836713\pi$
$68$	−163.113	+	282.519i	−0.290887	+	0.503831i
$69$	318.749			0.556129
$70$		0			0
$71$	−681.661			−1.13941			−0.569706	−	0.821848i	$-0.692943\pi$
$71$	−681.661			−1.13941			−0.569706	+	0.821848i	$0.692943\pi$
$72$	−36.0000	+	62.3538i	−0.0589256	+	0.102062i
$73$	−342.729	−	593.623i	−0.549498	−	0.951758i	−0.998309	−	0.0581315i	$-0.981486\pi$
$73$	−342.729	−	593.623i	−0.549498	−	0.951758i	0.448811	−	0.893627i	$-0.351848\pi$
$74$	−114.558	−	198.421i	−0.179961	−	0.311702i
$75$	155.956	−	270.123i	0.240110	−	0.415882i
$76$	−20.2153			−0.0305112
$77$		0			0
$78$	271.279			0.393799
$79$	−0.132034	+	0.228690i	−0.000188038	+	0.000325692i	−0.866119	−	0.499837i	$-0.833393\pi$
$79$	−0.132034	+	0.228690i	−0.000188038	+	0.000325692i	0.865931	+	0.500163i	$0.166727\pi$
$80$	−36.6863	−	63.5425i	−0.0512707	−	0.0888034i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	161.605	−	279.908i	0.217638	−	0.376960i
$83$	−437.137			−0.578097			−0.289048	−	0.957314i	$-0.593339\pi$
$83$	−437.137			−0.578097			−0.289048	+	0.957314i	$0.593339\pi$
$84$		0			0
$85$	374.000			0.477247
$86$	471.294	−	816.304i	0.590941	−	1.02354i
$87$	402.198	+	696.627i	0.495634	+	0.858463i
$88$	25.9411	+	44.9313i	0.0314242	+	0.0544284i
$89$	29.2563	−	50.6734i	0.0348445	−	0.0603525i	−0.848077	−	0.529873i	$-0.822240\pi$
$89$	29.2563	−	50.6734i	0.0348445	−	0.0603525i	0.882922	+	0.469520i	$0.155573\pi$
$90$	82.5442			0.0966769
$91$		0			0
$92$	424.999			0.481622
$93$	−438.551	+	759.593i	−0.488985	+	0.846948i
$94$	−346.004	−	599.297i	−0.379655	−	0.657582i
$95$	11.5879	+	20.0708i	0.0125146	+	0.0216760i
$96$	−48.0000	+	83.1384i	−0.0510310	+	0.0883883i
$97$	−1280.09			−1.33993			−0.669966	−	0.742391i	$-0.733692\pi$
$97$	−1280.09			−1.33993			−0.669966	+	0.742391i	$0.733692\pi$
$98$		0			0
$99$	−58.3675			−0.0592541
$100$	207.941	−	360.165i	0.207941	−	0.360165i
$101$	653.194	+	1131.37i	0.643518	+	1.11461i	0.984642	+	0.174587i	$0.0558590\pi$
$101$	653.194	+	1131.37i	0.643518	+	1.11461i	−0.341124	+	0.940018i	$0.610808\pi$
$102$	−244.669	−	423.779i	−0.237508	−	0.411376i
$103$	379.487	−	657.291i	0.363029	−	0.628785i	−0.625429	−	0.780281i	$-0.715076\pi$
$103$	379.487	−	657.291i	0.363029	−	0.628785i	0.988458	+	0.151496i	$0.0484092\pi$
$104$	361.706			0.341040
$105$		0			0
$106$	811.058			0.743178
$107$	−631.257	+	1093.37i	−0.570336	+	0.987850i	0.426196	+	0.904631i	$0.359854\pi$
$107$	−631.257	+	1093.37i	−0.570336	+	0.987850i	−0.996531	+	0.0832192i	$0.973480\pi$
$108$	−54.0000	−	93.5307i	−0.0481125	−	0.0833333i
$109$	1052.76	+	1823.44i	0.925105	+	1.60233i	0.791392	+	0.611309i	$0.209357\pi$
$109$	1052.76	+	1823.44i	0.925105	+	1.60233i	0.133713	+	0.991020i	$0.457310\pi$
$110$	29.7401	−	51.5114i	0.0257783	−	0.0446493i
$111$	343.675			0.293876
$112$		0			0
$113$	1535.76			1.27852			0.639258	−	0.768992i	$-0.279241\pi$
$113$	1535.76			1.27852			0.639258	+	0.768992i	$0.279241\pi$
$114$	15.1615	−	26.2604i	0.0124562	−	0.0215747i
$115$	−243.619	−	421.961i	−0.197545	−	0.342157i
$116$	536.264	+	928.837i	0.429232	+	0.743451i
$117$	−203.459	+	352.402i	−0.160768	+	0.278458i
$118$	−506.871			−0.395435
$119$		0			0
$120$	110.059			0.0837246
$121$	644.471	−	1116.26i	0.484200	−	0.838659i
$122$	751.217	+	1301.15i	0.557476	+	0.965576i
$123$	242.408	+	419.862i	0.177701	+	0.307786i
$124$	−584.735	+	1012.79i	−0.423474	+	0.733478i
$125$	−1050.01			−0.751326
$126$		0			0
$127$	24.1749			0.0168911			0.00844557	−	0.999964i	$-0.497312\pi$
$127$	24.1749			0.0168911			0.00844557	+	0.999964i	$0.497312\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$	706.940	+	1224.46i	0.482501	+	0.835716i
$130$	−207.338	−	359.120i	−0.139883	−	0.242284i
$131$	−790.764	+	1369.64i	−0.527400	+	0.913483i	0.472090	+	0.881550i	$0.343500\pi$
$131$	−790.764	+	1369.64i	−0.527400	+	0.913483i	−0.999490	+	0.0319327i	$0.989834\pi$
$132$	−77.8234			−0.0513156
$133$		0			0
$134$	23.2935			0.0150168
$135$	−61.9081	+	107.228i	−0.0394682	+	0.0683609i
$136$	−326.225	−	565.039i	−0.205688	−	0.356262i
$137$	372.594	+	645.352i	0.232357	+	0.402454i	0.958501	−	0.285089i	$-0.0920230\pi$
$137$	372.594	+	645.352i	0.232357	+	0.402454i	−0.726144	+	0.687542i	$0.758690\pi$
$138$	−318.749	+	552.090i	−0.196621	+	0.340558i
$139$	−1373.60			−0.838179			−0.419090	−	0.907945i	$-0.637651\pi$
$139$	−1373.60			−0.838179			−0.419090	+	0.907945i	$0.637651\pi$
$140$		0			0
$141$	1038.01			0.619975
$142$	681.661	−	1180.67i	0.402843	−	0.697745i
$143$	146.610	+	253.936i	0.0857354	+	0.148498i
$144$	−72.0000	−	124.708i	−0.0416667	−	0.0721688i
$145$	614.798	−	1064.86i	0.352112	−	0.609875i
$146$	1370.91			0.777107
$147$		0			0
$148$	458.234			0.254504
$149$	−310.265	+	537.395i	−0.170590	+	0.295470i	−0.938626	−	0.344936i	$-0.887901\pi$
$149$	−310.265	+	537.395i	−0.170590	+	0.295470i	0.768036	+	0.640406i	$0.221234\pi$
$150$	311.912	+	540.247i	0.169783	+	0.294073i
$151$	969.632	+	1679.45i	0.522567	+	0.905112i	0.999655	+	0.0262568i	$0.00835877\pi$
$151$	969.632	+	1679.45i	0.522567	+	0.905112i	−0.477089	+	0.878855i	$0.658308\pi$
$152$	20.2153	−	35.0139i	0.0107873	−	0.0186842i
$153$	734.007			0.387849
$154$		0			0
$155$	1340.74			0.694777
$156$	−271.279	+	469.869i	−0.139229	+	0.241152i
$157$	206.422	+	357.533i	0.104931	+	0.181747i	0.913710	−	0.406366i	$-0.133204\pi$
$157$	206.422	+	357.533i	0.104931	+	0.181747i	−0.808779	+	0.588113i	$0.799871\pi$
$158$	−0.264069	−	0.457380i	−0.000132963	−	0.000230299i
$159$	−608.294	+	1053.60i	−0.303401	+	0.525507i
$160$	146.745			0.0725077
$161$		0			0
$162$	162.000			0.0785674
$163$	1953.72	−	3383.94i	0.938817	−	1.62608i	0.171135	−	0.985248i	$-0.445257\pi$
$163$	1953.72	−	3383.94i	0.938817	−	1.62608i	0.767682	−	0.640831i	$-0.221410\pi$
$164$	323.210	+	559.817i	0.153893	+	0.266551i
$165$	44.6102	+	77.2671i	0.0210479	+	0.0364560i
$166$	437.137	−	757.144i	0.204388	−	0.354011i
$167$	−1286.41			−0.596082			−0.298041	−	0.954553i	$-0.596333\pi$
$167$	−1286.41			−0.596082			−0.298041	+	0.954553i	$0.596333\pi$
$168$		0			0
$169$	−152.766			−0.0695340
$170$	−374.000	+	647.787i	−0.168732	+	0.292253i
$171$	22.7422	+	39.3907i	0.0101704	+	0.0176157i
$172$	942.587	+	1632.61i	0.417858	+	0.723751i
$173$	625.628	−	1083.62i	0.274946	−	0.476220i	−0.695176	−	0.718840i	$-0.744673\pi$
$173$	625.628	−	1083.62i	0.274946	−	0.476220i	0.970121	+	0.242620i	$0.0780068\pi$
$174$	−1608.79			−0.700932
$175$		0			0
$176$	−103.765			−0.0444406
$177$	380.153	−	658.445i	0.161436	−	0.279614i
$178$	58.5126	+	101.347i	0.0246388	+	0.0426757i
$179$	−1811.76	−	3138.05i	−0.756520	−	1.31033i	−0.944615	−	0.328180i	$-0.893565\pi$
$179$	−1811.76	−	3138.05i	−0.756520	−	1.31033i	0.188095	−	0.982151i	$-0.439769\pi$
$180$	−82.5442	+	142.971i	−0.0341804	+	0.0592022i
$181$	181.727			0.0746280			0.0373140	−	0.999304i	$-0.488120\pi$
$181$	181.727			0.0746280			0.0373140	+	0.999304i	$0.488120\pi$
$182$		0			0
$183$	−2253.65			−0.910354
$184$	−424.999	+	736.120i	−0.170279	+	0.294932i
$185$	−262.670	−	454.958i	−0.104389	−	0.180806i
$186$	−877.103	−	1519.19i	−0.345765	−	0.598882i
$187$	264.458	−	458.055i	0.103418	−	0.179124i
$188$	1384.02			0.536914
$189$		0			0
$190$	−46.3515			−0.0176984
$191$	−740.640	+	1282.83i	−0.280580	+	0.485979i	−0.971528	−	0.236926i	$-0.923860\pi$
$191$	−740.640	+	1282.83i	−0.280580	+	0.485979i	0.690948	+	0.722905i	$0.257194\pi$
$192$	−96.0000	−	166.277i	−0.0360844	−	0.0625000i
$193$	178.354	+	308.918i	0.0665192	+	0.115215i	0.897367	−	0.441285i	$-0.145477\pi$
$193$	178.354	+	308.918i	0.0665192	+	0.115215i	−0.830848	+	0.556500i	$0.812144\pi$
$194$	1280.09	−	2217.18i	0.473738	−	0.820538i
$195$	622.014			0.228428
$196$		0			0
$197$	4890.53			1.76871			0.884355	−	0.466816i	$-0.154599\pi$
$197$	4890.53			1.76871			0.884355	+	0.466816i	$0.154599\pi$
$198$	58.3675	−	101.096i	0.0209495	−	0.0362856i
$199$	−1771.43	−	3068.20i	−0.631020	−	1.09296i	−0.987344	−	0.158596i	$-0.949303\pi$
$199$	−1771.43	−	3068.20i	−0.631020	−	1.09296i	0.356323	−	0.934363i	$-0.384030\pi$
$200$	415.882	+	720.329i	0.147037	+	0.254675i
$201$	−17.4701	+	30.2592i	−0.00613059	+	0.0106185i
$202$	−2612.78			−0.910071
$203$		0			0
$204$	978.676			0.335887
$205$	370.543	−	641.800i	0.126243	−	0.218660i
$206$	758.975	+	1314.58i	0.256700	+	0.444618i
$207$	−478.124	−	828.135i	−0.160541	−	0.278065i
$208$	−361.706	+	626.493i	−0.120576	+	0.208843i
$209$	32.7755			0.0108475
$210$		0			0
$211$	−4289.50			−1.39953			−0.699765	−	0.714373i	$-0.746712\pi$
$211$	−4289.50			−1.39953			−0.699765	+	0.714373i	$0.746712\pi$
$212$	−811.058	+	1404.79i	−0.262753	+	0.455102i
$213$	1022.49	+	1771.01i	0.328920	+	0.569706i
$214$	−1262.51	−	2186.74i	−0.403288	−	0.698516i
$215$	1080.63	−	1871.70i	0.342782	−	0.593715i
$216$	216.000			0.0680414
$217$		0			0
$218$	−4211.05			−1.30830
$219$	−1028.19	+	1780.87i	−0.317253	+	0.549498i
$220$	59.4802	+	103.023i	0.0182280	+	0.0315718i
$221$	−1843.71	−	3193.40i	−0.561183	−	0.971998i
$222$	−343.675	+	595.263i	−0.103901	+	0.179961i
$223$	5795.73			1.74041			0.870204	−	0.492692i	$-0.163987\pi$
$223$	5795.73			1.74041			0.870204	+	0.492692i	$0.163987\pi$
$224$		0			0
$225$	−935.735			−0.277255
$226$	−1535.76	+	2660.02i	−0.452024	+	0.782929i
$227$	−2052.02	−	3554.21i	−0.599989	−	1.03921i	−0.992822	−	0.119601i	$-0.961838\pi$
$227$	−2052.02	−	3554.21i	−0.599989	−	1.03921i	0.392833	−	0.919610i	$-0.371495\pi$
$228$	30.3229	+	52.5209i	0.00880783	+	0.0152556i
$229$	648.416	−	1123.09i	0.187111	−	0.324086i	−0.757175	−	0.653213i	$-0.773421\pi$
$229$	648.416	−	1123.09i	0.187111	−	0.324086i	0.944286	+	0.329126i	$0.106754\pi$
$230$	974.478			0.279370
$231$		0			0
$232$	−2145.06			−0.607025
$233$	739.167	−	1280.27i	0.207830	−	0.359972i	−0.743201	−	0.669069i	$-0.766693\pi$
$233$	739.167	−	1280.27i	0.207830	−	0.359972i	0.951031	+	0.309096i	$0.100027\pi$
$234$	−406.919	−	704.804i	−0.113680	−	0.196900i
$235$	−793.351	−	1374.12i	−0.220223	−	0.381438i
$236$	506.871	−	877.927i	0.139807	−	0.242153i
$237$	0.792206			0.000217128
$238$		0			0
$239$	−3776.92			−1.02221			−0.511106	−	0.859518i	$-0.670764\pi$
$239$	−3776.92			−1.02221			−0.511106	+	0.859518i	$0.670764\pi$
$240$	−110.059	+	190.628i	−0.0296011	+	0.0512707i
$241$	1998.19	+	3460.97i	0.534086	+	0.925065i	0.999207	+	0.0398173i	$0.0126776\pi$
$241$	1998.19	+	3460.97i	0.534086	+	0.925065i	−0.465121	+	0.885247i	$0.653989\pi$
$242$	1288.94	+	2232.51i	0.342381	+	0.593022i
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$	−3004.87			−0.788390
$245$		0			0
$246$	−969.631			−0.251306
$247$	114.250	−	197.886i	0.0294313	−	0.0509766i
$248$	−1169.47	−	2025.58i	−0.299441	−	0.518647i
$249$	655.706	+	1135.72i	0.166882	+	0.289048i
$250$	1050.01	−	1818.67i	0.265634	−	0.460091i
$251$	5423.58			1.36388			0.681939	−	0.731409i	$-0.261137\pi$
$251$	5423.58			1.36388			0.681939	+	0.731409i	$0.261137\pi$
$252$		0			0
$253$	−689.060			−0.171229
$254$	−24.1749	+	41.8721i	−0.00597192	+	0.0103437i
$255$	−561.000	−	971.681i	−0.137769	−	0.238624i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−2982.11	+	5165.17i	−0.723809	+	1.25367i	0.235653	+	0.971837i	$0.424277\pi$
$257$	−2982.11	+	5165.17i	−0.723809	+	1.25367i	−0.959462	+	0.281837i	$0.909056\pi$
$258$	−2827.76			−0.682359
$259$		0			0
$260$	829.352			0.197824
$261$	1206.59	−	2089.88i	0.286154	−	0.495634i
$262$	−1581.53	−	2739.29i	−0.372928	−	0.645930i
$263$	−2583.00	−	4473.89i	−0.605608	−	1.04894i	−0.991955	−	0.126590i	$-0.959597\pi$
$263$	−2583.00	−	4473.89i	−0.605608	−	1.04894i	0.386347	−	0.922353i	$-0.373737\pi$
$264$	77.8234	−	134.794i	0.0181428	−	0.0314242i
$265$	1859.67			0.431089
$266$		0			0
$267$	−175.538			−0.0402350
$268$	−23.2935	+	40.3455i	−0.00530924	+	0.00919588i
$269$	−1941.65	−	3363.03i	−0.440090	−	0.762259i	0.557605	−	0.830106i	$-0.311720\pi$
$269$	−1941.65	−	3363.03i	−0.440090	−	0.762259i	−0.997696	+	0.0678474i	$0.978387\pi$
$270$	−123.816	−	214.456i	−0.0279082	−	0.0483384i
$271$	−2763.83	+	4787.09i	−0.619522	+	1.07304i	0.370051	+	0.929011i	$0.379340\pi$
$271$	−2763.83	+	4787.09i	−0.619522	+	1.07304i	−0.989573	+	0.144032i	$0.953993\pi$
$272$	1304.90			0.290887
$273$		0			0
$274$	−1490.38			−0.328602
$275$	−337.139	+	583.942i	−0.0739282	+	0.128047i
$276$	−637.499	−	1104.18i	−0.139032	−	0.240811i
$277$	−1134.06	−	1964.25i	−0.245989	−	0.426066i	0.716420	−	0.697669i	$-0.245779\pi$
$277$	−1134.06	−	1964.25i	−0.245989	−	0.426066i	−0.962409	+	0.271603i	$0.912446\pi$
$278$	1373.60	−	2379.14i	0.296341	−	0.513278i
$279$	2631.31			0.564632
$280$		0			0
$281$	725.656			0.154053			0.0770267	−	0.997029i	$-0.475457\pi$
$281$	725.656			0.154053			0.0770267	+	0.997029i	$0.475457\pi$
$282$	−1038.01	+	1797.89i	−0.219194	+	0.379655i
$283$	−2118.50	−	3669.35i	−0.444988	−	0.770742i	0.553063	−	0.833139i	$-0.313459\pi$
$283$	−2118.50	−	3669.35i	−0.444988	−	0.770742i	−0.998051	+	0.0623972i	$0.980125\pi$
$284$	1363.32	+	2361.34i	0.284853	+	0.493380i
$285$	34.7636	−	60.2124i	0.00722533	−	0.0125146i
$286$	−586.441			−0.121248
$287$		0			0
$288$	288.000			0.0589256
$289$	−869.219	+	1505.53i	−0.176922	+	0.306438i
$290$	1229.60	+	2129.72i	0.248981	+	0.431247i
$291$	1920.14	+	3325.77i	0.386805	+	0.669966i
$292$	−1370.91	+	2374.49i	−0.274749	+	0.475879i
$293$	−4373.78			−0.872079			−0.436039	−	0.899928i	$-0.643619\pi$
$293$	−4373.78			−0.872079			−0.436039	+	0.899928i	$0.643619\pi$
$294$		0			0
$295$	−1162.20			−0.229376
$296$	−458.234	+	793.684i	−0.0899807	+	0.155851i
$297$	87.5513	+	151.643i	0.0171052	+	0.0296271i
$298$	−620.530	−	1074.79i	−0.120625	−	0.208929i
$299$	−2401.95	+	4160.29i	−0.464576	+	0.804669i
$300$	−1247.65			−0.240110
$301$		0			0
$302$	−3878.53			−0.739021
$303$	1959.58	−	3394.10i	0.371535	−	0.643518i
$304$	40.4306	+	70.0278i	0.00762781	+	0.0132117i
$305$	1722.46	+	2983.39i	0.323370	+	0.560093i
$306$	−734.007	+	1271.34i	−0.137125	+	0.237508i
$307$	4133.47			0.768435			0.384217	−	0.923243i	$-0.374471\pi$
$307$	4133.47			0.768435			0.384217	+	0.923243i	$0.374471\pi$
$308$		0			0
$309$	−2276.92			−0.419190
$310$	−1340.74	+	2322.22i	−0.245641	+	0.425462i
$311$	−2531.62	−	4384.89i	−0.461591	−	0.799499i	0.537450	−	0.843296i	$-0.319388\pi$
$311$	−2531.62	−	4384.89i	−0.461591	−	0.799499i	−0.999040	+	0.0437972i	$0.986054\pi$
$312$	−542.558	−	939.739i	−0.0984498	−	0.170520i
$313$	−3705.78	+	6418.60i	−0.669211	+	1.15911i	0.308914	+	0.951090i	$0.400034\pi$
$313$	−3705.78	+	6418.60i	−0.669211	+	1.15911i	−0.978125	+	0.208017i	$0.933299\pi$
$314$	−825.686			−0.148395
$315$		0			0
$316$	1.05627			0.000188038
$317$	3368.53	−	5834.46i	0.596831	−	1.03374i	−0.396455	−	0.918054i	$-0.629760\pi$
$317$	3368.53	−	5834.46i	0.596831	−	1.03374i	0.993286	−	0.115687i	$-0.0369069\pi$
$318$	−1216.59	−	2107.19i	−0.214537	−	0.371589i
$319$	−869.456	−	1505.94i	−0.152602	−	0.264315i
$320$	−146.745	+	254.170i	−0.0256353	+	0.0444017i
$321$	3787.54			0.658567
$322$		0			0
$323$	−412.171			−0.0710026
$324$	−162.000	+	280.592i	−0.0277778	+	0.0481125i
$325$	2350.42	+	4071.05i	0.401163	+	0.694834i
$326$	3907.44	+	6767.88i	0.663844	+	1.14981i
$327$	3158.29	−	5470.32i	0.534110	−	0.925105i
$328$	−1292.84			−0.217638
$329$		0			0
$330$	−178.441			−0.0297662
$331$	−5587.97	+	9678.65i	−0.927923	+	1.60721i	−0.141132	+	0.989991i	$0.545074\pi$
$331$	−5587.97	+	9678.65i	−0.927923	+	1.60721i	−0.786791	+	0.617219i	$0.788259\pi$
$332$	874.274	+	1514.29i	0.144524	+	0.250323i
$333$	−515.513	−	892.895i	−0.0848346	−	0.146938i
$334$	1286.41	−	2228.14i	0.210747	−	0.365024i
$335$	53.4095			0.00871067
$336$		0			0
$337$	9379.78			1.51617			0.758085	−	0.652156i	$-0.226135\pi$
$337$	9379.78			1.51617			0.758085	+	0.652156i	$0.226135\pi$
$338$	152.766	−	264.599i	0.0245840	−	0.0425807i
$339$	−2303.64	−	3990.03i	−0.369076	−	0.639258i
$340$	−748.000	−	1295.57i	−0.119312	−	0.206654i
$341$	948.043	−	1642.06i	0.150555	−	0.260770i
$342$	−90.9688			−0.0143831
$343$		0			0
$344$	−3770.35			−0.590941
$345$	−730.858	+	1265.88i	−0.114052	+	0.197545i
$346$	1251.26	+	2167.24i	0.194416	+	0.336738i
$347$	−2840.73	−	4920.29i	−0.439476	−	0.761195i	0.558173	−	0.829725i	$-0.311503\pi$
$347$	−2840.73	−	4920.29i	−0.439476	−	0.761195i	−0.997649	+	0.0685293i	$0.978169\pi$
$348$	1608.79	−	2786.51i	0.247817	−	0.429232i
$349$	−704.250			−0.108016			−0.0540080	−	0.998541i	$-0.517200\pi$
$349$	−704.250			−0.108016			−0.0540080	+	0.998541i	$0.517200\pi$
$350$		0			0
$351$	1220.76			0.185639
$352$	103.765	−	179.725i	0.0157121	−	0.0272142i
$353$	2142.48	+	3710.89i	0.323039	+	0.559520i	0.981114	−	0.193433i	$-0.0619622\pi$
$353$	2142.48	+	3710.89i	0.323039	+	0.559520i	−0.658074	+	0.752953i	$0.728629\pi$
$354$	760.307	+	1316.89i	0.114152	+	0.197717i
$355$	1562.98	−	2707.15i	0.233674	−	0.404735i
$356$	−234.051			−0.0348445
$357$		0			0
$358$	7247.03			1.06988
$359$	−2330.64	+	4036.78i	−0.342636	+	0.593463i	−0.984921	−	0.173003i	$-0.944653\pi$
$359$	−2330.64	+	4036.78i	−0.342636	+	0.593463i	0.642285	+	0.766465i	$0.277986\pi$
$360$	−165.088	−	285.941i	−0.0241692	−	0.0418623i
$361$	3416.73	+	5917.95i	0.498138	+	0.862801i
$362$	−181.727	+	314.760i	−0.0263850	+	0.0457001i
$363$	−3866.82			−0.559106
$364$		0			0
$365$	3143.36			0.450770
$366$	2253.65	−	3903.44i	0.321859	−	0.557476i
$367$	3467.65	+	6006.15i	0.493215	+	0.854274i	0.999969	−	0.00781688i	$-0.00248822\pi$
$367$	3467.65	+	6006.15i	0.493215	+	0.854274i	−0.506754	+	0.862091i	$0.669155\pi$
$368$	−849.998	−	1472.24i	−0.120405	−	0.208548i
$369$	727.223	−	1259.59i	0.102595	−	0.177701i
$370$	1050.68			0.147628
$371$		0			0
$372$	3508.41			0.488985
$373$	1540.55	−	2668.31i	0.213852	−	0.370402i	−0.739065	−	0.673634i	$-0.764732\pi$
$373$	1540.55	−	2668.31i	0.213852	−	0.370402i	0.952917	+	0.303232i	$0.0980657\pi$
$374$	528.916	+	916.109i	0.0731272	+	0.126660i
$375$	1575.02	+	2728.01i	0.216889	+	0.375663i
$376$	−1384.02	+	2397.19i	−0.189828	+	0.328791i
$377$	−12123.1			−1.65616
$378$		0			0
$379$	941.827			0.127647			0.0638237	−	0.997961i	$-0.479670\pi$
$379$	941.827			0.127647			0.0638237	+	0.997961i	$0.479670\pi$
$380$	46.3515	−	80.2832i	0.00625732	−	0.0108380i
$381$	−36.2623	−	62.8082i	−0.00487605	−	0.00844557i
$382$	−1481.28	−	2565.65i	−0.198400	−	0.343639i
$383$	338.763	−	586.755i	0.0451958	−	0.0782814i	−0.842543	−	0.538630i	$-0.818942\pi$
$383$	338.763	−	586.755i	0.0451958	−	0.0782814i	0.887738	+	0.460348i	$0.152276\pi$
$384$	384.000			0.0510310
$385$		0			0
$386$	−713.416			−0.0940724
$387$	2120.82	−	3673.37i	0.278572	−	0.482501i
$388$	2560.18	+	4434.36i	0.334983	+	0.580208i
$389$	5932.71	+	10275.8i	0.773266	+	1.33934i	0.935764	+	0.352627i	$0.114711\pi$
$389$	5932.71	+	10275.8i	0.773266	+	1.33934i	−0.162498	+	0.986709i	$0.551955\pi$
$390$	−622.014	+	1077.36i	−0.0807613	+	0.139883i
$391$	8665.34			1.12078
$392$		0			0
$393$	4744.58			0.608989
$394$	−4890.53	+	8470.64i	−0.625333	+	1.08311i
$395$	−0.605481	−	1.04872i	−7.71268e−5	−	0.000133587i
$396$	116.735	+	202.191i	0.0148135	+	0.0256578i
$397$	2570.38	−	4452.03i	0.324947	−	0.562824i	−0.656555	−	0.754278i	$-0.727987\pi$
$397$	2570.38	−	4452.03i	0.324947	−	0.562824i	0.981502	+	0.191454i	$0.0613203\pi$
$398$	7085.70			0.892397
$399$		0			0
$400$	−1663.53			−0.207941
$401$	6190.99	−	10723.1i	0.770981	−	1.33538i	−0.166045	−	0.986118i	$-0.553100\pi$
$401$	6190.99	−	10723.1i	0.770981	−	1.33538i	0.937026	−	0.349260i	$-0.113567\pi$
$402$	−34.9403	−	60.5183i	−0.00433498	−	0.00750840i
$403$	−6609.44	−	11447.9i	−0.816971	−	1.41504i
$404$	2612.78	−	4525.46i	0.321759	−	0.557303i
$405$	371.449			0.0455739
$406$		0			0
$407$	−742.944			−0.0904824
$408$	−978.676	+	1695.12i	−0.118754	+	0.205688i
$409$	7937.82	+	13748.7i	0.959657	+	1.66217i	0.723331	+	0.690501i	$0.242610\pi$
$409$	7937.82	+	13748.7i	0.959657	+	1.66217i	0.236326	+	0.971674i	$0.424057\pi$
$410$	741.087	+	1283.60i	0.0892675	+	0.154616i
$411$	1117.78	−	1936.06i	0.134151	−	0.232357i
$412$	−3035.90			−0.363029
$413$		0			0
$414$	1912.50			0.227039
$415$	1002.31	−	1736.05i	0.118558	−	0.205348i
$416$	−723.411	−	1252.99i	−0.0852600	−	0.147675i
$417$	2060.39	+	3568.71i	0.241962	+	0.419090i
$418$	−32.7755	+	56.7688i	−0.00383517	+	0.00664271i
$419$	−16111.9			−1.87857			−0.939283	−	0.343145i	$-0.888508\pi$
$419$	−16111.9			−1.87857			−0.939283	+	0.343145i	$0.888508\pi$
$420$		0			0
$421$	8691.58			1.00618			0.503090	−	0.864234i	$-0.332197\pi$
$421$	8691.58			1.00618			0.503090	+	0.864234i	$0.332197\pi$
$422$	4289.50	−	7429.62i	0.494809	−	0.857034i
$423$	−1557.02	−	2696.84i	−0.178971	−	0.309987i
$424$	−1622.12	−	2809.59i	−0.185795	−	0.321806i
$425$	4239.73	−	7343.43i	0.483899	−	0.838138i
$426$	−4089.97			−0.465163
$427$		0			0
$428$	5050.06			0.570336
$429$	439.831	−	761.809i	0.0494993	−	0.0857354i
$430$	2161.25	+	3743.40i	0.242383	+	0.419820i
$431$	2097.55	+	3633.07i	0.234421	+	0.406029i	0.959104	−	0.283053i	$-0.0913472\pi$
$431$	2097.55	+	3633.07i	0.234421	+	0.406029i	−0.724683	+	0.689082i	$0.758014\pi$
$432$	−216.000	+	374.123i	−0.0240563	+	0.0416667i
$433$	−5426.54			−0.602270			−0.301135	−	0.953582i	$-0.597365\pi$
$433$	−5426.54			−0.602270			−0.301135	+	0.953582i	$0.597365\pi$
$434$		0			0
$435$	−3688.79			−0.406584
$436$	4211.05	−	7293.76i	0.462553	−	0.801165i
$437$	268.484	+	465.028i	0.0293898	+	0.0509046i
$438$	−2056.37	−	3561.74i	−0.224332	−	0.388554i
$439$	1885.62	−	3265.99i	0.205002	−	0.355073i	−0.745132	−	0.666917i	$-0.767613\pi$
$439$	1885.62	−	3265.99i	0.205002	−	0.355073i	0.950133	+	0.311844i	$0.100947\pi$
$440$	−237.921			−0.0257783
$441$		0			0
$442$	7374.85			0.793633
$443$	2965.15	−	5135.79i	0.318010	−	0.550810i	−0.662063	−	0.749449i	$-0.730319\pi$
$443$	2965.15	−	5135.79i	0.318010	−	0.550810i	0.980073	+	0.198639i	$0.0636520\pi$
$444$	−687.351	−	1190.53i	−0.0734690	−	0.127252i
$445$	134.163	+	232.377i	0.0142920	+	0.0247545i
$446$	−5795.73	+	10038.5i	−0.615327	+	1.06578i
$447$	1861.59			0.196980
$448$		0			0
$449$	−529.065			−0.0556083			−0.0278041	−	0.999613i	$-0.508851\pi$
$449$	−529.065			−0.0556083			−0.0278041	+	0.999613i	$0.508851\pi$
$450$	935.735	−	1620.74i	0.0980244	−	0.169783i
$451$	−524.027	−	907.642i	−0.0547128	−	0.0947654i
$452$	−3071.53	−	5320.04i	−0.319629	−	0.553614i
$453$	2908.90	−	5038.36i	0.301704	−	0.522567i
$454$	8208.09			0.848512
$455$		0			0
$456$	−121.292			−0.0124562
$457$	−5028.59	+	8709.77i	−0.514721	+	0.891523i	0.485133	+	0.874440i	$0.338771\pi$
$457$	−5028.59	+	8709.77i	−0.514721	+	0.891523i	−0.999854	+	0.0170824i	$0.994562\pi$
$458$	1296.83	+	2246.18i	0.132308	+	0.229164i
$459$	−1101.01	−	1907.01i	−0.111962	−	0.193925i
$460$	−974.478	+	1687.84i	−0.0987723	+	0.171079i
$461$	−5010.31			−0.506190			−0.253095	−	0.967441i	$-0.581448\pi$
$461$	−5010.31			−0.506190			−0.253095	+	0.967441i	$0.581448\pi$
$462$		0			0
$463$	−7124.38			−0.715114			−0.357557	−	0.933891i	$-0.616390\pi$
$463$	−7124.38			−0.715114			−0.357557	+	0.933891i	$0.616390\pi$
$464$	2145.06	−	3715.35i	0.214616	−	0.371725i
$465$	−2011.10	−	3483.33i	−0.200565	−	0.347388i
$466$	1478.33	+	2560.55i	0.146958	+	0.254539i
$467$	−3750.72	+	6496.44i	−0.371654	+	0.643724i	−0.989820	−	0.142323i	$-0.954543\pi$
$467$	−3750.72	+	6496.44i	−0.371654	+	0.643724i	0.618166	+	0.786048i	$0.287876\pi$
$468$	1627.68			0.160768
$469$		0			0
$470$	3173.40			0.311443
$471$	619.265	−	1072.60i	0.0605822	−	0.104931i
$472$	1013.74	+	1755.85i	0.0988587	+	0.171228i
$473$	−1528.24	−	2646.98i	−0.148559	−	0.257312i
$474$	−0.792206	+	1.37214i	−7.67663e−5	+	0.000132963i
$475$	525.449			0.0507563
$476$		0			0
$477$	3649.76			0.350338
$478$	3776.92	−	6541.82i	0.361406	−	0.625974i
$479$	4086.90	+	7078.72i	0.389844	+	0.675230i	0.992428	−	0.122826i	$-0.0391956\pi$
$479$	4086.90	+	7078.72i	0.389844	+	0.675230i	−0.602584	+	0.798055i	$0.705862\pi$
$480$	−220.118	−	381.255i	−0.0209312	−	0.0362538i
$481$	−2589.78	+	4485.63i	−0.245496	+	0.425212i
$482$	−7992.76			−0.755312
$483$		0			0
$484$	−5155.76			−0.484200
$485$	2935.11	−	5083.76i	0.274797	−	0.475962i
$486$	−243.000	−	420.888i	−0.0226805	−	0.0392837i
$487$	5984.39	+	10365.3i	0.556835	+	0.964467i	0.997758	+	0.0669221i	$0.0213179\pi$
$487$	5984.39	+	10365.3i	0.556835	+	0.964467i	−0.440923	+	0.897545i	$0.645349\pi$
$488$	3004.87	−	5204.59i	0.278738	−	0.482788i
$489$	−11722.3			−1.08405
$490$		0			0
$491$	2079.96			0.191176			0.0955878	−	0.995421i	$-0.469527\pi$
$491$	2079.96			0.191176			0.0955878	+	0.995421i	$0.469527\pi$
$492$	969.631	−	1679.45i	0.0888503	−	0.153893i
$493$	10933.9	+	18938.1i	0.998863	+	1.73008i
$494$	228.500	+	395.773i	0.0208111	+	0.0360459i
$495$	133.831	−	231.801i	0.0121520	−	0.0210479i
$496$	4677.88			0.423474
$497$		0			0
$498$	−2622.82			−0.236007
$499$	−6417.21	+	11114.9i	−0.575699	+	0.997140i	0.420266	+	0.907401i	$0.361937\pi$
$499$	−6417.21	+	11114.9i	−0.575699	+	0.997140i	−0.995965	+	0.0897390i	$0.971397\pi$
$500$	2100.02	+	3637.34i	0.187832	+	0.325334i
$501$	1929.62	+	3342.20i	0.172074	+	0.298041i
$502$	−5423.58	+	9393.92i	−0.482204	+	0.835202i
$503$	16808.8			1.48999			0.744997	−	0.667068i	$-0.232451\pi$
$503$	16808.8			1.48999			0.744997	+	0.667068i	$0.232451\pi$
$504$		0			0
$505$	−5990.82			−0.527897
$506$	689.060	−	1193.49i	0.0605384	−	0.104856i
$507$	229.149	+	396.898i	0.0200727	+	0.0347670i
$508$	−48.3498	−	83.7443i	−0.00422278	−	0.00731408i
$509$	2135.13	−	3698.16i	0.185929	−	0.322039i	−0.757960	−	0.652301i	$-0.773804\pi$
$509$	2135.13	−	3698.16i	0.185929	−	0.322039i	0.943889	+	0.330262i	$0.107137\pi$
$510$	2244.00			0.194835
$511$		0			0
$512$	512.000			0.0441942
$513$	68.2266	−	118.172i	0.00587189	−	0.0101704i
$514$	−5964.22	−	10330.3i	−0.511811	−	0.886482i
$515$	1740.25	+	3014.20i	0.148902	+	0.257906i
$516$	2827.76	−	4897.83i	0.241250	−	0.417858i
$517$	−2243.93			−0.190886
$518$		0			0
$519$	−3753.77			−0.317480
$520$	−829.352	+	1436.48i	−0.0699414	+	0.121142i
$521$	−7641.64	−	13235.7i	−0.642584	−	1.11299i	−0.984854	−	0.173386i	$-0.944529\pi$
$521$	−7641.64	−	13235.7i	−0.642584	−	1.11299i	0.342270	−	0.939602i	$-0.388804\pi$
$522$	2413.19	+	4179.76i	0.202342	+	0.350466i
$523$	2249.66	−	3896.53i	0.188090	−	0.325781i	−0.756524	−	0.653966i	$-0.773104\pi$
$523$	2249.66	−	3896.53i	0.188090	−	0.325781i	0.944613	+	0.328185i	$0.106437\pi$
$524$	6326.11			0.527400
$525$		0			0
$526$	10332.0			0.856459
$527$	−11922.2	+	20649.9i	−0.985465	+	1.70687i
$528$	155.647	+	269.588i	0.0128289	+	0.0222203i
$529$	438.992	+	760.356i	0.0360805	+	0.0624933i
$530$	−1859.67	+	3221.04i	−0.152413	+	0.263987i
$531$	−2280.92			−0.186410
$532$		0			0
$533$	−7306.69			−0.593785
$534$	175.538	−	304.041i	0.0142252	−	0.0246388i
$535$	−2894.81	−	5013.96i	−0.233932	−	0.405182i
$536$	−46.5870	−	80.6911i	−0.00375420	−	0.00650247i
$537$	−5435.27	+	9414.16i	−0.436777	+	0.756520i
$538$	7766.59			0.622382
$539$		0			0
$540$	495.265			0.0394682
$541$	−1985.41	+	3438.83i	−0.157781	+	0.273284i	−0.934068	−	0.357095i	$-0.883767\pi$
$541$	−1985.41	+	3438.83i	−0.157781	+	0.273284i	0.776287	+	0.630379i	$0.217101\pi$
$542$	−5527.65	−	9574.18i	−0.438068	−	0.758757i
$543$	−272.591	−	472.141i	−0.0215432	−	0.0373140i
$544$	−1304.90	+	2260.16i	−0.102844	+	0.178131i
$545$	−9655.50			−0.758892
$546$		0			0
$547$	−2703.90			−0.211353			−0.105677	−	0.994401i	$-0.533701\pi$
$547$	−2703.90			−0.211353			−0.105677	+	0.994401i	$0.533701\pi$
$548$	1490.38	−	2581.41i	0.116178	−	0.201227i
$549$	3380.48	+	5855.16i	0.262797	+	0.455177i
$550$	−674.278	−	1167.88i	−0.0522751	−	0.0905432i
$551$	−677.546	+	1173.54i	−0.0523855	+	0.0907344i
$552$	2549.99			0.196621
$553$		0			0
$554$	4536.24			0.347881
$555$	−788.011	+	1364.87i	−0.0602688	+	0.104389i
$556$	2747.19	+	4758.28i	0.209545	+	0.362942i
$557$	−395.412	−	684.874i	−0.0300793	−	0.0520988i	0.850594	−	0.525823i	$-0.176243\pi$
$557$	−395.412	−	684.874i	−0.0300793	−	0.0520988i	−0.880673	+	0.473724i	$0.842909\pi$
$558$	−2631.31	+	4557.56i	−0.199627	+	0.345765i
$559$	−21308.7			−1.61227
$560$		0			0
$561$	−1586.75			−0.119416
$562$	−725.656	+	1256.87i	−0.0544661	+	0.0943380i
$563$	−3758.58	−	6510.05i	−0.281359	−	0.487328i	0.690361	−	0.723465i	$-0.257452\pi$
$563$	−3758.58	−	6510.05i	−0.281359	−	0.487328i	−0.971720	+	0.236137i	$0.924119\pi$
$564$	−2076.03	−	3595.78i	−0.154994	−	0.268457i
$565$	−3521.34	+	6099.14i	−0.262202	+	0.454146i
$566$	8473.99			0.629308
$567$		0			0
$568$	−5453.29			−0.402843
$569$	−6972.72	+	12077.1i	−0.513728	+	0.889804i	0.486145	+	0.873878i	$0.338403\pi$
$569$	−6972.72	+	12077.1i	−0.513728	+	0.889804i	−0.999873	+	0.0159254i	$0.994931\pi$
$570$	69.5273	+	120.425i	0.00510908	+	0.00884919i
$571$	1059.25	+	1834.67i	0.0776323	+	0.134463i	0.902228	−	0.431259i	$-0.141931\pi$
$571$	1059.25	+	1834.67i	0.0776323	+	0.134463i	−0.824596	+	0.565723i	$0.808597\pi$
$572$	586.441	−	1015.75i	0.0428677	−	0.0742490i
$573$	4443.84			0.323986
$574$		0			0
$575$	−11046.8			−0.801192
$576$	−288.000	+	498.831i	−0.0208333	+	0.0360844i
$577$	−11428.9	−	19795.4i	−0.824592	−	1.42823i	−0.902231	−	0.431253i	$-0.858072\pi$
$577$	−11428.9	−	19795.4i	−0.824592	−	1.42823i	0.0776391	−	0.996982i	$-0.475262\pi$
$578$	−1738.44	−	3011.06i	−0.125103	−	0.216685i
$579$	535.062	−	926.755i	0.0384049	−	0.0665192i
$580$	−4918.38			−0.352112
$581$		0			0
$582$	−7680.54			−0.547025
$583$	1314.98	−	2277.62i	0.0934153	−	0.161800i
$584$	−2741.83	−	4748.99i	−0.194277	−	0.336497i
$585$	−933.021	−	1616.04i	−0.0659413	−	0.114214i
$586$	4373.78	−	7575.61i	0.308326	−	0.534037i
$587$	23955.3			1.68440			0.842199	−	0.539167i	$-0.181261\pi$
$587$	23955.3			1.68440			0.842199	+	0.539167i	$0.181261\pi$
$588$		0			0
$589$	−1477.57			−0.103366
$590$	1162.20	−	2012.99i	0.0810968	−	0.140464i
$591$	−7335.79	−	12706.0i	−0.510582	−	0.884355i
$592$	−916.468	−	1587.37i	−0.0636260	−	0.110203i
$593$	5388.99	−	9334.01i	0.373186	−	0.646378i	−0.616867	−	0.787067i	$-0.711599\pi$
$593$	5388.99	−	9334.01i	0.373186	−	0.646378i	0.990054	+	0.140689i	$0.0449319\pi$
$594$	−350.205			−0.0241904
$595$		0			0
$596$	2482.12			0.170590
$597$	−5314.28	+	9204.60i	−0.364320	+	0.631020i
$598$	−4803.89	−	8320.59i	−0.328505	−	0.568987i
$599$	−3798.79	−	6579.69i	−0.259122	−	0.448813i	0.706885	−	0.707329i	$-0.250100\pi$
$599$	−3798.79	−	6579.69i	−0.259122	−	0.448813i	−0.966007	+	0.258516i	$0.916767\pi$
$600$	1247.65	−	2160.99i	0.0848916	−	0.147037i
$601$	19956.1			1.35445			0.677225	−	0.735776i	$-0.263182\pi$
$601$	19956.1			1.35445			0.677225	+	0.735776i	$0.263182\pi$
$602$		0			0
$603$	104.821			0.00707899
$604$	3878.53	−	6717.81i	0.261283	−	0.452556i
$605$	2955.40	+	5118.91i	0.198602	+	0.343989i
$606$	3919.17	+	6788.20i	0.262715	+	0.455036i
$607$	118.155	−	204.651i	0.00790079	−	0.0136846i	−0.862048	−	0.506827i	$-0.830818\pi$
$607$	118.155	−	204.651i	0.00790079	−	0.0136846i	0.869949	+	0.493142i	$0.164152\pi$
$608$	−161.722			−0.0107873
$609$		0			0
$610$	−6889.85			−0.457314
$611$	−7821.98	+	13548.1i	−0.517911	+	0.897048i
$612$	−1468.01	−	2542.68i	−0.0969624	−	0.167944i
$613$	−13207.5	−	22876.0i	−0.870219	−	1.50726i	−0.861770	−	0.507300i	$-0.830644\pi$
$613$	−13207.5	−	22876.0i	−0.870219	−	1.50726i	−0.00844986	−	0.999964i	$-0.502690\pi$
$614$	−4133.47	+	7159.38i	−0.271683	+	0.470568i
$615$	−2223.26			−0.145773
$616$		0			0
$617$	18473.6			1.20538			0.602689	−	0.797976i	$-0.294096\pi$
$617$	18473.6			1.20538			0.602689	+	0.797976i	$0.294096\pi$
$618$	2276.92	−	3943.75i	0.148206	−	0.256700i
$619$	−8023.96	−	13897.9i	−0.521018	−	0.902430i	−0.999701	−	0.0244421i	$-0.992219\pi$
$619$	−8023.96	−	13897.9i	−0.521018	−	0.902430i	0.478683	−	0.877988i	$-0.341114\pi$
$620$	−2681.47	−	4644.44i	−0.173694	−	0.300847i
$621$	−1434.37	+	2484.41i	−0.0926882	+	0.160541i
$622$	10126.5			0.652788
$623$		0			0
$624$	2170.23			0.139229
$625$	−4090.60	+	7085.13i	−0.261798	+	0.453448i
$626$	−7411.56	−	12837.2i	−0.473204	−	0.819613i
$627$	−49.1632	−	85.1532i	−0.00313140	−	0.00542375i
$628$	825.686	−	1430.13i	0.0524657	−	0.0908733i
$629$	9342.97			0.592255
$630$		0			0
$631$	−15065.7			−0.950487			−0.475243	−	0.879854i	$-0.657640\pi$
$631$	−15065.7			−0.950487			−0.475243	+	0.879854i	$0.657640\pi$
$632$	−1.05627	+	1.82952i	−6.64816e−5	+	0.000115149i
$633$	6434.24	+	11144.4i	0.404010	+	0.699765i
$634$	6737.05	+	11668.9i	0.422023	+	0.730965i
$635$	−55.4304	+	96.0083i	−0.00346408	+	0.00599996i
$636$	4866.35			0.303401
$637$		0			0
$638$	3477.82			0.215812
$639$	3067.47	−	5313.02i	0.189902	−	0.328920i
$640$	−293.490	−	508.340i	−0.0181269	−	0.0313967i
$641$	15599.2	+	27018.6i	0.961203	+	1.66485i	0.719488	+	0.694505i	$0.244377\pi$
$641$	15599.2	+	27018.6i	0.961203	+	1.66485i	0.241715	+	0.970347i	$0.422290\pi$
$642$	−3787.54	+	6560.21i	−0.232839	+	0.403288i
$643$	−12497.9			−0.766517			−0.383259	−	0.923641i	$-0.625198\pi$
$643$	−12497.9			−0.766517			−0.383259	+	0.923641i	$0.625198\pi$
$644$		0			0
$645$	−6483.75			−0.395810
$646$	412.171	−	713.902i	0.0251032	−	0.0434800i
$647$	4964.86	+	8599.39i	0.301683	+	0.522530i	0.976517	−	0.215439i	$-0.0691183\pi$
$647$	4964.86	+	8599.39i	0.301683	+	0.522530i	−0.674834	+	0.737969i	$0.735785\pi$
$648$	−324.000	−	561.184i	−0.0196419	−	0.0340207i
$649$	−821.801	+	1423.40i	−0.0497049	+	0.0860915i
$650$	−9401.68			−0.567330
$651$		0			0
$652$	−15629.8			−0.938817
$653$	4072.79	−	7054.28i	0.244075	−	0.422750i	−0.717796	−	0.696253i	$-0.754849\pi$
$653$	4072.79	−	7054.28i	0.244075	−	0.422750i	0.961871	+	0.273503i	$0.0881825\pi$
$654$	6316.58	+	10940.6i	0.377673	+	0.654148i
$655$	−3626.27	−	6280.89i	−0.216321	−	0.374679i
$656$	1292.84	−	2239.27i	0.0769466	−	0.133275i
$657$	6169.11			0.366332
$658$		0			0
$659$	−16975.8			−1.00347			−0.501733	−	0.865022i	$-0.667304\pi$
$659$	−16975.8			−1.00347			−0.501733	+	0.865022i	$0.667304\pi$
$660$	178.441	−	309.068i	0.0105239	−	0.0182280i
$661$	−10318.9	−	17872.8i	−0.607199	−	1.05170i	−0.991700	−	0.128574i	$-0.958960\pi$
$661$	−10318.9	−	17872.8i	−0.607199	−	1.05170i	0.384501	−	0.923124i	$-0.374373\pi$
$662$	−11175.9	−	19357.3i	−0.656141	−	1.13647i
$663$	−5531.14	+	9580.21i	−0.323999	+	0.561183i
$664$	−3497.10			−0.204388
$665$		0			0
$666$	2062.05			0.119974
$667$	14244.5	−	24672.2i	0.826910	−	1.43225i
$668$	2572.83	+	4456.27i	0.149021	+	0.258111i
$669$	−8693.60	−	15057.8i	−0.502412	−	0.870204i
$670$	−53.4095	+	92.5080i	−0.00307969	+	0.00533417i
$671$	4871.86			0.280292
$672$		0			0
$673$	−2150.29			−0.123161			−0.0615807	−	0.998102i	$-0.519614\pi$
$673$	−2150.29			−0.123161			−0.0615807	+	0.998102i	$0.519614\pi$
$674$	−9379.78	+	16246.3i	−0.536047	+	0.928461i
$675$	1403.60	+	2431.11i	0.0800366	+	0.138627i
$676$	305.532	+	529.198i	0.0173835	+	0.0301091i
$677$	13891.7	−	24061.1i	0.788628	−	1.36594i	−0.138180	−	0.990407i	$-0.544125\pi$
$677$	13891.7	−	24061.1i	0.788628	−	1.36594i	0.926808	−	0.375536i	$-0.122541\pi$
$678$	9214.58			0.521952
$679$		0			0
$680$	2992.00			0.168732
$681$	−6156.06	+	10662.6i	−0.346404	+	0.599989i
$682$	1896.09	+	3284.12i	0.106459	+	0.184392i
$683$	−9090.89	−	15745.9i	−0.509302	−	0.882137i	−0.999942	−	0.0107743i	$-0.996570\pi$
$683$	−9090.89	−	15745.9i	−0.509302	−	0.882137i	0.490640	−	0.871362i	$-0.336763\pi$
$684$	90.9688	−	157.563i	0.00508520	−	0.00880783i
$685$	−3417.27			−0.190609
$686$		0			0
$687$	−3890.49			−0.216058
$688$	3770.35	−	6530.43i	0.208929	−	0.361876i
$689$	−9167.63	−	15878.8i	−0.506907	−	0.877989i
$690$	−1461.72	−	2531.77i	−0.0806472	−	0.139685i
$691$	−11967.6	+	20728.4i	−0.658853	+	1.14117i	0.322060	+	0.946719i	$0.395625\pi$
$691$	−11967.6	+	20728.4i	−0.658853	+	1.14117i	−0.980913	+	0.194447i	$0.937709\pi$
$692$	−5005.02			−0.274946
$693$		0			0
$694$	11362.9			0.621513
$695$	3149.51	−	5455.11i	0.171896	−	0.297733i
$696$	3217.58	+	5573.02i	0.175233	+	0.303513i
$697$	6589.96	+	11414.1i	0.358124	+	0.620289i
$698$	704.250	−	1219.80i	0.0381895	−	0.0661461i
$699$	−4435.00			−0.239982
$700$		0			0
$701$	−20627.2			−1.11138			−0.555691	−	0.831389i	$-0.687546\pi$
$701$	−20627.2			−1.11138			−0.555691	+	0.831389i	$0.687546\pi$
$702$	−1220.76	+	2114.41i	−0.0656332	+	0.113680i
$703$	289.479	+	501.392i	0.0155305	+	0.0268995i
$704$	207.529	+	359.451i	0.0111101	+	0.0192433i
$705$	−2380.05	+	4122.37i	−0.127146	+	0.220223i
$706$	−8569.93			−0.456846
$707$		0			0
$708$	−3041.23			−0.161436
$709$	3292.32	−	5702.46i	0.174394	−	0.302060i	−0.765557	−	0.643368i	$-0.777537\pi$
$709$	3292.32	−	5702.46i	0.174394	−	0.302060i	0.939952	+	0.341308i	$0.110870\pi$
$710$	3125.95	+	5414.31i	0.165232	+	0.286191i
$711$	−1.18831	−	2.05821i	−6.26794e−5	−	0.000108564i
$712$	234.051	−	405.387i	0.0123194	−	0.0213378i
$713$	31064.0			1.63163
$714$		0			0
$715$	−1344.65			−0.0703313
$716$	−7247.03	+	12552.2i	−0.378260	+	0.655165i
$717$	5665.38	+	9812.72i	0.295087	+	0.511106i
$718$	−4661.27	−	8073.56i	−0.242280	−	0.419642i
$719$	−85.4430	+	147.992i	−0.00443183	+	0.00767616i	−0.868233	−	0.496157i	$-0.834744\pi$
$719$	−85.4430	+	147.992i	−0.00443183	+	0.00767616i	0.863801	+	0.503833i	$0.168077\pi$
$720$	660.353			0.0341804
$721$		0			0
$722$	−13666.9			−0.704474
$723$	5994.57	−	10382.9i	0.308355	−	0.534086i
$724$	−363.454	−	629.521i	−0.0186570	−	0.0323149i
$725$	−13938.9	−	24142.9i	−0.714039	−	1.23675i
$726$	3866.82	−	6697.53i	0.197674	−	0.342381i
$727$	−11127.5			−0.567671			−0.283836	−	0.958873i	$-0.591607\pi$
$727$	−11127.5			−0.567671			−0.283836	+	0.958873i	$0.591607\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	−3143.36	+	5444.46i	−0.159371	+	0.276039i
$731$	19218.5	+	33287.4i	0.972396	+	1.68424i
$732$	4507.30	+	7806.88i	0.227588	+	0.394195i
$733$	11288.0	−	19551.3i	0.568800	−	0.985191i	−0.427885	−	0.903833i	$-0.640741\pi$
$733$	11288.0	−	19551.3i	0.568800	−	0.985191i	0.996685	−	0.0813578i	$-0.0259256\pi$
$734$	−13870.6			−0.697511
$735$		0			0
$736$	3399.99			0.170279
$737$	37.7662	−	65.4130i	0.00188757	−	0.00326936i
$738$	1454.45	+	2519.17i	0.0725459	+	0.125653i
$739$	11468.2	+	19863.5i	0.570860	+	0.988758i	0.996478	+	0.0838550i	$0.0267233\pi$
$739$	11468.2	+	19863.5i	0.570860	+	0.988758i	−0.425618	+	0.904903i	$0.639943\pi$
$740$	−1050.68	+	1819.83i	−0.0521943	+	0.0904032i
$741$	−685.499			−0.0339844
$742$		0			0
$743$	16973.4			0.838081			0.419041	−	0.907967i	$-0.362366\pi$
$743$	16973.4			0.838081			0.419041	+	0.907967i	$0.362366\pi$
$744$	−3508.41	+	6076.75i	−0.172882	+	0.299441i
$745$	−1422.81	−	2464.38i	−0.0699700	−	0.121192i
$746$	3081.10	+	5336.63i	0.151216	+	0.261914i
$747$	1967.12	−	3407.15i	0.0963495	−	0.166882i
$748$	−2115.66			−0.103418
$749$		0			0
$750$	−6300.06			−0.306728
$751$	10598.9	−	18357.9i	0.514994	−	0.891995i	−0.484855	−	0.874595i	$-0.661128\pi$
$751$	10598.9	−	18357.9i	0.514994	−	0.891995i	0.999849	−	0.0174007i	$-0.00553909\pi$
$752$	−2768.03	−	4794.37i	−0.134228	−	0.232490i
$753$	−8135.38	−	14090.9i	−0.393718	−	0.681939i
$754$	12123.1	−	20997.8i	0.585541	−	1.01419i
$755$	−8893.05			−0.428677
$756$		0			0
$757$	−7962.24			−0.382289			−0.191144	−	0.981562i	$-0.561220\pi$
$757$	−7962.24			−0.382289			−0.191144	+	0.981562i	$0.561220\pi$
$758$	−941.827	+	1631.29i	−0.0451302	+	0.0781678i
$759$	1033.59	+	1790.23i	0.0494294	+	0.0856143i
$760$	92.7030	+	160.566i	0.00442460	+	0.00766362i
$761$	−13428.1	+	23258.1i	−0.639642	+	1.10789i	0.345869	+	0.938283i	$0.387584\pi$
$761$	−13428.1	+	23258.1i	−0.639642	+	1.10789i	−0.985511	+	0.169610i	$0.945749\pi$
$762$	145.049			0.00689578
$763$		0			0
$764$	5925.12			0.280580
$765$	−1683.00	+	2915.04i	−0.0795412	+	0.137769i
$766$	677.526	+	1173.51i	0.0319582	+	0.0553533i
$767$	5729.32	+	9923.47i	0.269718	+	0.467165i
$768$	−384.000	+	665.108i	−0.0180422	+	0.0312500i
$769$	−12183.6			−0.571331			−0.285666	−	0.958329i	$-0.592215\pi$
$769$	−12183.6			−0.571331			−0.285666	+	0.958329i	$0.592215\pi$
$770$		0			0
$771$	17892.7			0.835783
$772$	713.416	−	1235.67i	0.0332596	−	0.0576073i
$773$	8727.61	+	15116.7i	0.406093	+	0.703374i	0.994448	−	0.105229i	$-0.0335574\pi$
$773$	8727.61	+	15116.7i	0.406093	+	0.703374i	−0.588355	+	0.808603i	$0.700224\pi$
$774$	4241.64	+	7346.74i	0.196980	+	0.341180i
$775$	15198.8	−	26325.1i	0.704461	−	1.22016i
$776$	−10240.7			−0.473738
$777$		0			0
$778$	−23730.8			−1.09356
$779$	−408.362	+	707.304i	−0.0187819	+	0.0325312i
$780$	−1244.03	−	2154.72i	−0.0571069	−	0.0989120i
$781$	−2210.38	−	3828.49i	−0.101272	−	0.175409i
$782$	−8665.34	+	15008.8i	−0.396256	+	0.686335i
$783$	−7239.56			−0.330423
$784$		0			0
$785$	−1893.21			−0.0860785
$786$	−4744.58	+	8217.86i	−0.215310	+	0.372928i
$787$	−15490.5	−	26830.3i	−0.701622	−	1.21524i	−0.967897	−	0.251348i	$-0.919126\pi$
$787$	−15490.5	−	26830.3i	−0.701622	−	1.21524i	0.266275	−	0.963897i	$-0.414207\pi$
$788$	−9781.06	−	16941.3i	−0.442177	−	0.765874i
$789$	−7749.01	+	13421.7i	−0.349648	+	0.605608i
$790$	2.42193			0.000109074
$791$		0			0
$792$	−466.940			−0.0209495
$793$	16982.5	−	29414.5i	0.760486	−	1.31720i
$794$	5140.76	+	8904.07i	0.229772	+	0.397977i
$795$	−2789.50	−	4831.56i	−0.124445	−	0.215544i
$796$	−7085.70	+	12272.8i	−0.315510	+	0.546480i
$797$	−10517.6			−0.467446			−0.233723	−	0.972303i	$-0.575091\pi$
$797$	−10517.6			−0.467446			−0.233723	+	0.972303i	$0.575091\pi$
$798$		0			0
$799$	28218.8			1.24945
$800$	1663.53	−	2881.32i	0.0735183	−	0.127337i
$801$	263.307	+	456.061i	0.0116148	+	0.0201175i
$802$	12382.0	+	21446.2i	0.545166	+	0.944255i
$803$	2222.69	−	3849.81i	0.0976800	−	0.169187i
$804$	139.761			0.00613059
$805$		0			0
$806$	26437.7			1.15537
$807$	−5824.94	+	10089.1i	−0.254086	+	0.440090i
$808$	5225.56	+	9050.93i	0.227518	+	0.394072i
$809$	20889.2	+	36181.2i	0.907819	+	1.57239i	0.817087	+	0.576514i	$0.195587\pi$
$809$	20889.2	+	36181.2i	0.907819	+	1.57239i	0.0907320	+	0.995875i	$0.471079\pi$
$810$	−371.449	+	643.368i	−0.0161128	+	0.0279082i
$811$	−12935.4			−0.560079			−0.280039	−	0.959988i	$-0.590348\pi$
$811$	−12935.4			−0.560079			−0.280039	+	0.959988i	$0.590348\pi$
$812$		0			0
$813$	16583.0			0.715363
$814$	742.944	−	1286.82i	0.0319904	−	0.0554090i
$815$	8959.34	+	15518.0i	0.385070	+	0.666961i
$816$	−1957.35	−	3390.23i	−0.0839719	−	0.145444i
$817$	−1190.92	+	2062.73i	−0.0509975	+	0.0883302i
$818$	−31751.3			−1.35716
$819$		0			0
$820$	−2964.35			−0.126243
$821$	7249.61	−	12556.7i	0.308177	−	0.533778i	−0.669787	−	0.742554i	$-0.733614\pi$
$821$	7249.61	−	12556.7i	0.308177	−	0.533778i	0.977964	+	0.208776i	$0.0669478\pi$
$822$	2235.56	+	3872.11i	0.0948592	+	0.164301i
$823$	5988.57	+	10372.5i	0.253643	+	0.439323i	0.964526	−	0.263987i	$-0.0850377\pi$
$823$	5988.57	+	10372.5i	0.253643	+	0.439323i	−0.710883	+	0.703310i	$0.751704\pi$
$824$	3035.90	−	5258.33i	0.128350	−	0.222309i
$825$	2022.84			0.0853649
$826$		0			0
$827$	27613.5			1.16108			0.580541	−	0.814231i	$-0.302841\pi$
$827$	27613.5			1.16108			0.580541	+	0.814231i	$0.302841\pi$
$828$	−1912.50	+	3312.54i	−0.0802703	+	0.139032i
$829$	338.918	+	587.023i	0.0141992	+	0.0245937i	0.873038	−	0.487653i	$-0.162147\pi$
$829$	338.918	+	587.023i	0.0141992	+	0.0245937i	−0.858839	+	0.512246i	$0.828813\pi$
$830$	2004.62	+	3472.10i	0.0838329	+	0.145203i
$831$	−3402.18	+	5892.75i	−0.142022	+	0.245989i
$832$	2893.65			0.120576
$833$		0			0
$834$	−8241.58			−0.342185
$835$	2949.61	−	5108.88i	0.122246	−	0.211736i
$836$	−65.5509	−	113.538i	−0.00271187	−	0.00469710i
$837$	−3946.96	−	6836.34i	−0.162995	−	0.282316i
$838$	16111.9	−	27906.7i	0.664173	−	1.15038i
$839$	42209.6			1.73687			0.868436	−	0.495801i	$-0.165126\pi$
$839$	42209.6			1.73687			0.868436	+	0.495801i	$0.165126\pi$
$840$		0			0
$841$	47505.8			1.94784
$842$	−8691.58	+	15054.3i	−0.355738	+	0.616157i
$843$	−1088.48	−	1885.31i	−0.0444714	−	0.0770267i
$844$	8578.99	+	14859.2i	0.349883	+	0.606015i
$845$	350.277	−	606.697i	0.0142602	−	0.0246994i
$846$	6228.08			0.253104
$847$		0			0
$848$	6488.46			0.262753
$849$	−6355.50	+	11008.0i	−0.256914	+	0.444988i
$850$	8479.46	+	14686.9i	0.342168	+	0.592653i
$851$	−6085.90	−	10541.1i	−0.245149	−	0.424611i
$852$	4089.97	−	7084.03i	0.164460	−	0.284853i
$853$	−2796.45			−0.112249			−0.0561247	−	0.998424i	$-0.517874\pi$
$853$	−2796.45			−0.112249			−0.0561247	+	0.998424i	$0.517874\pi$
$854$		0			0
$855$	−208.582			−0.00834310
$856$	−5050.06	+	8746.95i	−0.201644	+	0.349258i
$857$	−11590.5	−	20075.4i	−0.461989	−	0.800189i	0.537071	−	0.843537i	$-0.319531\pi$
$857$	−11590.5	−	20075.4i	−0.461989	−	0.800189i	−0.999060	+	0.0433483i	$0.986197\pi$
$858$	879.661	+	1523.62i	0.0350013	+	0.0606241i
$859$	5948.75	−	10303.5i	0.236285	−	0.409257i	−0.723361	−	0.690471i	$-0.757404\pi$
$859$	5948.75	−	10303.5i	0.236285	−	0.409257i	0.959645	+	0.281213i	$0.0907369\pi$
$860$	−8645.01			−0.342782
$861$		0			0
$862$	−8390.21			−0.331521
$863$	14907.9	−	25821.3i	0.588033	−	1.01850i	−0.406457	−	0.913670i	$-0.633236\pi$
$863$	14907.9	−	25821.3i	0.588033	−	1.01850i	0.994490	−	0.104833i	$-0.0334308\pi$
$864$	−432.000	−	748.246i	−0.0170103	−	0.0294628i
$865$	2869.00	+	4969.25i	0.112773	+	0.195329i
$866$	5426.54	−	9399.04i	0.212934	−	0.368813i
$867$	5215.31			0.204292
$868$		0			0
$869$	−1.71256			−6.68523e−5
$870$	3688.79	−	6389.17i	0.143749	−	0.248981i
$871$	−263.294	−	456.038i	−0.0102427	−	0.0177408i
$872$	8422.11	+	14587.5i	0.327074	+	0.566509i
$873$	5760.41	−	9977.32i	0.223322	−	0.386805i
$874$	−1073.94			−0.0415634
$875$		0			0
$876$	8225.48			0.317253
$877$	5169.42	−	8953.70i	0.199041	−	0.344749i	−0.749177	−	0.662370i	$-0.769551\pi$
$877$	5169.42	−	8953.70i	0.199041	−	0.344749i	0.948218	+	0.317621i	$0.102884\pi$
$878$	3771.24	+	6531.98i	0.144958	+	0.251075i
$879$	6560.67	+	11363.4i	0.251747	+	0.436039i
$880$	237.921	−	412.091i	0.00911399	−	0.0157859i
$881$	24140.2			0.923160			0.461580	−	0.887099i	$-0.347283\pi$
$881$	24140.2			0.923160			0.461580	+	0.887099i	$0.347283\pi$
$882$		0			0
$883$	12997.6			0.495361			0.247681	−	0.968842i	$-0.420332\pi$
$883$	12997.6			0.495361			0.247681	+	0.968842i	$0.420332\pi$
$884$	−7374.85	+	12773.6i	−0.280592	+	0.485999i
$885$	1743.30	+	3019.49i	0.0662152	+	0.114688i
$886$	5930.30	+	10271.6i	0.224867	+	0.389481i
$887$	−22633.3	+	39202.0i	−0.856766	+	1.48396i	0.0182306	+	0.999834i	$0.494197\pi$
$887$	−22633.3	+	39202.0i	−0.856766	+	1.48396i	−0.874997	+	0.484129i	$0.839137\pi$
$888$	2749.40			0.103901
$889$		0			0
$890$	−536.653			−0.0202120
$891$	262.654	−	454.930i	0.00987569	−	0.0171052i
$892$	−11591.5	−	20077.0i	−0.435102	−	0.753619i
$893$	874.322	+	1514.37i	0.0327638	+	0.0567486i
$894$	−1861.59	+	3224.37i	−0.0696430	+	0.120625i
$895$	16616.7			0.620596
$896$		0			0
$897$	14411.7			0.536446
$898$	529.065	−	916.367i	0.0196605	−	0.0340530i
$899$	39196.6	+	67890.4i	1.45415	+	2.51866i
$900$	1871.47	+	3241.48i	0.0693137	+	0.120055i
$901$	−16536.7	+	28642.5i	−0.611452	+	1.05907i
$902$	2096.11			0.0773756
$903$		0			0
$904$	12286.1			0.452024
$905$	−416.681	+	721.712i	−0.0153049	+	0.0265089i
$906$	5817.79	+	10076.7i	0.213337	+	0.369510i
$907$	13883.2	+	24046.5i	0.508253	+	0.880319i	0.999954	+	0.00955575i	$0.00304174\pi$
$907$	13883.2	+	24046.5i	0.508253	+	0.880319i	−0.491702	+	0.870764i	$0.663625\pi$
$908$	−8208.09	+	14216.8i	−0.299994	+	0.519605i
$909$	−11757.5			−0.429012
$910$		0			0
$911$	18531.2			0.673948			0.336974	−	0.941514i	$-0.390597\pi$
$911$	18531.2			0.673948			0.336974	+	0.941514i	$0.390597\pi$
$912$	121.292	−	210.084i	0.00440392	−	0.00762781i
$913$	−1417.48	−	2455.14i	−0.0513819	−	0.0889961i
$914$	−10057.2	−	17419.5i	−0.363963	−	0.630402i
$915$	5167.38	−	8950.17i	0.186698	−	0.323370i
$916$	−5187.33			−0.187111
$917$		0			0
$918$	4404.04			0.158339
$919$	9046.70	−	15669.3i	0.324726	−	0.562442i	−0.656731	−	0.754125i	$-0.728061\pi$
$919$	9046.70	−	15669.3i	0.324726	−	0.562442i	0.981457	+	0.191683i	$0.0613947\pi$
$920$	−1948.96	−	3375.69i	−0.0698426	−	0.120971i
$921$	−6200.20	−	10739.1i	−0.221828	−	0.384217i
$922$	5010.31	−	8678.11i	0.178965	−	0.309977i
$923$	−30820.1			−1.09908
$924$		0			0
$925$	−11910.7			−0.423375
$926$	7124.38	−	12339.8i	0.252831	−	0.437916i
$927$	3415.39	+	5915.62i	0.121010	+	0.209595i
$928$	4290.11	+	7430.69i	0.151756	+	0.262850i
$929$	−5311.26	+	9199.37i	−0.187574	+	0.324888i	−0.944441	−	0.328681i	$-0.893396\pi$
$929$	−5311.26	+	9199.37i	−0.187574	+	0.324888i	0.756867	+	0.653569i	$0.226729\pi$
$930$	8044.41			0.283642
$931$		0			0
$932$	−5913.34			−0.207830
$933$	−7594.85	+	13154.7i	−0.266500	+	0.461591i
$934$	−7501.44	−	12992.9i	−0.262799	−	0.455182i
$935$	1212.75	+	2100.54i	0.0424183	+	0.0734706i
$936$	−1627.68	+	2819.22i	−0.0568400	+	0.0984498i
$937$	16057.6			0.559851			0.279925	−	0.960022i	$-0.409690\pi$
$937$	16057.6			0.559851			0.279925	+	0.960022i	$0.409690\pi$
$938$		0			0
$939$	22234.7			0.772738
$940$	−3173.40	+	5496.49i	−0.110112	+	0.190719i
$941$	−27576.6	−	47764.1i	−0.955338	−	1.65469i	−0.733593	−	0.679589i	$-0.762158\pi$
$941$	−27576.6	−	47764.1i	−0.955338	−	1.65469i	−0.221745	−	0.975105i	$-0.571175\pi$
$942$	1238.53	+	2145.20i	0.0428381	+	0.0741977i
$943$	8585.25	−	14870.1i	0.296473	−	0.513507i
$944$	−4054.97			−0.139807
$945$		0			0
$946$	6112.94			0.210094
$947$	−9392.86	+	16268.9i	−0.322309	+	0.558256i	−0.980964	−	0.194189i	$-0.937792\pi$
$947$	−9392.86	+	16268.9i	−0.322309	+	0.558256i	0.658655	+	0.752445i	$0.271126\pi$
$948$	−1.58441	−	2.74428i	−5.42820e−5	−	9.40191e-5i
$949$	−15495.9	−	26839.6i	−0.530049	−	0.918072i
$950$	−525.449	+	910.104i	−0.0179451	+	0.0310818i
$951$	−20211.2			−0.689161
$952$		0			0
$953$	−36499.4			−1.24064			−0.620321	−	0.784348i	$-0.712998\pi$
$953$	−36499.4			−1.24064			−0.620321	+	0.784348i	$0.712998\pi$
$954$	−3649.76	+	6321.57i	−0.123863	+	0.214537i
$955$	−3396.42	−	5882.76i	−0.115084	−	0.199332i
$956$	7553.84	+	13083.6i	0.255553	+	0.442631i
$957$	−2608.37	+	4517.83i	−0.0881051	+	0.152602i
$958$	−16347.6			−0.551323
$959$		0			0
$960$	880.471			0.0296011
$961$	−27843.9	+	48227.0i	−0.934641	+	1.61885i
$962$	−5179.55	−	8971.25i	−0.173592	−	0.300670i
$963$	−5681.31	−	9840.32i	−0.190112	−	0.329283i
$964$	7992.76	−	13843.9i	0.267043	−	0.462532i
$965$	−1635.79			−0.0545677
$966$		0			0
$967$	26059.9			0.866627			0.433314	−	0.901243i	$-0.357344\pi$
$967$	26059.9			0.866627			0.433314	+	0.901243i	$0.357344\pi$
$968$	5155.76	−	8930.05i	0.171191	−	0.296511i
$969$	618.257	+	1070.85i	0.0204967	+	0.0355013i
$970$	5870.22	+	10167.5i	0.194311	+	0.336556i
$971$	−10844.5	+	18783.2i	−0.358410	+	0.620785i	−0.987695	−	0.156390i	$-0.950014\pi$
$971$	−10844.5	+	18783.2i	−0.358410	+	0.620785i	0.629285	+	0.777174i	$0.283348\pi$
$972$	972.000			0.0320750
$973$		0			0
$974$	−23937.6			−0.787484
$975$	7051.26	−	12213.1i	0.231611	−	0.401163i
$976$	6009.74	+	10409.2i	0.197097	+	0.341383i
$977$	−1059.59	−	1835.27i	−0.0346975	−	0.0600978i	0.848155	−	0.529748i	$-0.177713\pi$
$977$	−1059.59	−	1835.27i	−0.0346975	−	0.0600978i	−0.882853	+	0.469650i	$0.844380\pi$
$978$	11722.3	−	20303.7i	0.383270	−	0.663844i
$979$	379.471			0.0123881
$980$		0			0
$981$	−18949.7			−0.616737
$982$	−2079.96	+	3602.59i	−0.0675908	+	0.117071i
$983$	24252.1	+	42005.8i	0.786898	+	1.36295i	0.927859	+	0.372932i	$0.121648\pi$
$983$	24252.1	+	42005.8i	0.786898	+	1.36295i	−0.140960	+	0.990015i	$0.545019\pi$
$984$	1939.26	+	3358.90i	0.0628266	+	0.108819i
$985$	−11213.5	+	19422.3i	−0.362731	+	0.628269i
$986$	−43735.7			−1.41261
$987$		0			0
$988$	−913.998			−0.0294313
$989$	25037.4	−	43366.1i	0.804999	−	1.39430i
$990$	267.661	+	463.603i	0.00859275	+	0.0148831i
$991$	−1021.92	−	1770.02i	−0.0327572	−	0.0567372i	0.849182	−	0.528100i	$-0.177095\pi$
$991$	−1021.92	−	1770.02i	−0.0327572	−	0.0567372i	−0.881939	+	0.471363i	$0.843762\pi$
$992$	−4677.88	+	8102.33i	−0.149721	+	0.259324i
$993$	33527.8			1.07147
$994$		0			0
$995$	16246.8			0.517645
$996$	2622.82	−	4542.86i	0.0834411	−	0.144524i
$997$	13369.5	+	23156.6i	0.424689	+	0.735583i	0.996391	−	0.0848782i	$-0.0270501\pi$
$997$	13369.5	+	23156.6i	0.424689	+	0.735583i	−0.571702	+	0.820461i	$0.693717\pi$
$998$	−12834.4	−	22229.9i	−0.407081	−	0.705084i
$999$	−1546.54	+	2678.68i	−0.0489793	+	0.0848346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.4.e.k.79.2		4
3.2	odd	2		882.4.g.bk.667.1		4
7.2	even	3		294.4.a.o.1.1	yes	2
7.3	odd	6		294.4.e.m.67.1		4
7.4	even	3	inner	294.4.e.k.67.2		4
7.5	odd	6		294.4.a.l.1.2	✓	2
7.6	odd	2		294.4.e.m.79.1		4
21.2	odd	6		882.4.a.t.1.2		2
21.5	even	6		882.4.a.bb.1.1		2
21.11	odd	6		882.4.g.bk.361.1		4
21.17	even	6		882.4.g.be.361.2		4
21.20	even	2		882.4.g.be.667.2		4
28.19	even	6		2352.4.a.bw.1.2		2
28.23	odd	6		2352.4.a.bu.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.4.a.l.1.2	✓	2	7.5	odd	6
294.4.a.o.1.1	yes	2	7.2	even	3
294.4.e.k.67.2		4	7.4	even	3	inner
294.4.e.k.79.2		4	1.1	even	1	trivial
294.4.e.m.67.1		4	7.3	odd	6
294.4.e.m.79.1		4	7.6	odd	2
882.4.a.t.1.2		2	21.2	odd	6
882.4.a.bb.1.1		2	21.5	even	6
882.4.g.be.361.2		4	21.17	even	6
882.4.g.be.667.2		4	21.20	even	2
882.4.g.bk.361.1		4	21.11	odd	6
882.4.g.bk.667.1		4	3.2	odd	2
2352.4.a.bu.1.1		2	28.23	odd	6
2352.4.a.bw.1.2		2	28.19	even	6

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	294.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-2.29289 + 3.97141i) q^{5} +6.00000 q^{6} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-2.29289 + 3.97141i) q^{5} +6.00000 q^{6} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-4.58579 - 7.94282i) q^{10} +(3.24264 + 5.61642i) q^{11} +(-6.00000 + 10.3923i) q^{12} +45.2132 q^{13} +13.7574 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-40.7782 - 70.6299i) q^{17} +(-9.00000 - 15.5885i) q^{18} +(2.52691 - 4.37674i) q^{19} +18.3431 q^{20} -12.9706 q^{22} +(-53.1249 + 92.0150i) q^{23} +(-12.0000 - 20.7846i) q^{24} +(51.9853 + 90.0411i) q^{25} +(-45.2132 + 78.3116i) q^{26} +27.0000 q^{27} -268.132 q^{29} +(-13.7574 + 23.8284i) q^{30} +(-146.184 - 253.198i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(9.72792 - 16.8493i) q^{33} +163.113 q^{34} +36.0000 q^{36} +(-57.2792 + 99.2105i) q^{37} +(5.05382 + 8.75348i) q^{38} +(-67.8198 - 117.467i) q^{39} +(-18.3431 + 31.7713i) q^{40} -161.605 q^{41} -471.294 q^{43} +(12.9706 - 22.4657i) q^{44} +(-20.6360 - 35.7427i) q^{45} +(-106.250 - 184.030i) q^{46} +(-173.002 + 299.648i) q^{47} +48.0000 q^{48} -207.941 q^{50} +(-122.335 + 211.890i) q^{51} +(-90.4264 - 156.623i) q^{52} +(-202.765 - 351.198i) q^{53} +(-27.0000 + 46.7654i) q^{54} -29.7401 q^{55} -15.1615 q^{57} +(268.132 - 464.418i) q^{58} +(126.718 + 219.482i) q^{59} +(-27.5147 - 47.6569i) q^{60} +(375.609 - 650.573i) q^{61} +584.735 q^{62} +64.0000 q^{64} +(-103.669 + 179.560i) q^{65} +(19.4558 + 33.6985i) q^{66} +(-5.82338 - 10.0864i) q^{67} +(-163.113 + 282.519i) q^{68} +318.749 q^{69} -681.661 q^{71} +(-36.0000 + 62.3538i) q^{72} +(-342.729 - 593.623i) q^{73} +(-114.558 - 198.421i) q^{74} +(155.956 - 270.123i) q^{75} -20.2153 q^{76} +271.279 q^{78} +(-0.132034 + 0.228690i) q^{79} +(-36.6863 - 63.5425i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(161.605 - 279.908i) q^{82} -437.137 q^{83} +374.000 q^{85} +(471.294 - 816.304i) q^{86} +(402.198 + 696.627i) q^{87} +(25.9411 + 44.9313i) q^{88} +(29.2563 - 50.6734i) q^{89} +82.5442 q^{90} +424.999 q^{92} +(-438.551 + 759.593i) q^{93} +(-346.004 - 599.297i) q^{94} +(11.5879 + 20.0708i) q^{95} +(-48.0000 + 83.1384i) q^{96} -1280.09 q^{97} -58.3675 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 6 q^{3} - 8 q^{4} - 12 q^{5} + 24 q^{6} + 32 q^{8} - 18 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 6 * q^3 - 8 * q^4 - 12 * q^5 + 24 * q^6 + 32 * q^8 - 18 * q^9	\( 4 q - 4 q^{2} - 6 q^{3} - 8 q^{4} - 12 q^{5} + 24 q^{6} + 32 q^{8} - 18 q^{9} - 24 q^{10} - 4 q^{11} - 24 q^{12} + 96 q^{13} + 72 q^{15} - 32 q^{16} - 132 q^{17} - 36 q^{18} - 120 q^{19} + 96 q^{20} + 16 q^{22} + 76 q^{23} - 48 q^{24} + 174 q^{25} - 96 q^{26} + 108 q^{27} - 224 q^{29} - 72 q^{30} - 432 q^{31} - 64 q^{32} - 12 q^{33} + 528 q^{34} + 144 q^{36} + 280 q^{37} - 240 q^{38} - 144 q^{39} - 96 q^{40} + 72 q^{41} - 256 q^{43} - 16 q^{44} - 108 q^{45} + 152 q^{46} + 264 q^{47} + 192 q^{48} - 696 q^{50} - 396 q^{51} - 192 q^{52} - 268 q^{53} - 108 q^{54} + 96 q^{55} + 720 q^{57} + 224 q^{58} - 336 q^{59} - 144 q^{60} + 504 q^{61} + 1728 q^{62} + 256 q^{64} - 228 q^{65} - 24 q^{66} + 384 q^{67} - 528 q^{68} - 456 q^{69} - 792 q^{71} - 144 q^{72} + 312 q^{73} + 560 q^{74} + 522 q^{75} + 960 q^{76} + 576 q^{78} + 848 q^{79} - 192 q^{80} - 162 q^{81} - 72 q^{82} - 1296 q^{83} + 1496 q^{85} + 256 q^{86} + 336 q^{87} - 32 q^{88} + 612 q^{89} + 432 q^{90} - 608 q^{92} - 1296 q^{93} + 528 q^{94} - 904 q^{95} - 192 q^{96} - 4368 q^{97} + 72 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 6 * q^3 - 8 * q^4 - 12 * q^5 + 24 * q^6 + 32 * q^8 - 18 * q^9 - 24 * q^10 - 4 * q^11 - 24 * q^12 + 96 * q^13 + 72 * q^15 - 32 * q^16 - 132 * q^17 - 36 * q^18 - 120 * q^19 + 96 * q^20 + 16 * q^22 + 76 * q^23 - 48 * q^24 + 174 * q^25 - 96 * q^26 + 108 * q^27 - 224 * q^29 - 72 * q^30 - 432 * q^31 - 64 * q^32 - 12 * q^33 + 528 * q^34 + 144 * q^36 + 280 * q^37 - 240 * q^38 - 144 * q^39 - 96 * q^40 + 72 * q^41 - 256 * q^43 - 16 * q^44 - 108 * q^45 + 152 * q^46 + 264 * q^47 + 192 * q^48 - 696 * q^50 - 396 * q^51 - 192 * q^52 - 268 * q^53 - 108 * q^54 + 96 * q^55 + 720 * q^57 + 224 * q^58 - 336 * q^59 - 144 * q^60 + 504 * q^61 + 1728 * q^62 + 256 * q^64 - 228 * q^65 - 24 * q^66 + 384 * q^67 - 528 * q^68 - 456 * q^69 - 792 * q^71 - 144 * q^72 + 312 * q^73 + 560 * q^74 + 522 * q^75 + 960 * q^76 + 576 * q^78 + 848 * q^79 - 192 * q^80 - 162 * q^81 - 72 * q^82 - 1296 * q^83 + 1496 * q^85 + 256 * q^86 + 336 * q^87 - 32 * q^88 + 612 * q^89 + 432 * q^90 - 608 * q^92 - 1296 * q^93 + 528 * q^94 - 904 * q^95 - 192 * q^96 - 4368 * q^97 + 72 * q^99

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