LMFDB - Embedded newform 287.3.g.a.132.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,3,Mod(132,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("287.132");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	287.g (of order $4$, degree $2$, 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:	$7.82018358714$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			132.3
Character	$\chi$	$=$	287.132
Dual form			287.3.g.a.237.51

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.66303i q^{2} +(-3.03803 + 3.03803i) q^{3} -9.41780 q^{4} -7.09262 q^{5} +(11.1284 + 11.1284i) q^{6} +(1.44819 + 6.84856i) q^{7} +19.8456i q^{8} -9.45930i q^{9} +O(q^{10})$	\(q-3.66303i q^{2} +(-3.03803 + 3.03803i) q^{3} -9.41780 q^{4} -7.09262 q^{5} +(11.1284 + 11.1284i) q^{6} +(1.44819 + 6.84856i) q^{7} +19.8456i q^{8} -9.45930i q^{9} +25.9805i q^{10} +(-12.8465 - 12.8465i) q^{11} +(28.6116 - 28.6116i) q^{12} +(11.3350 - 11.3350i) q^{13} +(25.0865 - 5.30475i) q^{14} +(21.5476 - 21.5476i) q^{15} +35.0238 q^{16} +(2.53893 + 2.53893i) q^{17} -34.6497 q^{18} +(7.17839 + 7.17839i) q^{19} +66.7969 q^{20} +(-25.2058 - 16.4065i) q^{21} +(-47.0572 + 47.0572i) q^{22} +1.35619 q^{23} +(-60.2915 - 60.2915i) q^{24} +25.3052 q^{25} +(-41.5203 - 41.5203i) q^{26} +(1.39537 + 1.39537i) q^{27} +(-13.6387 - 64.4984i) q^{28} +(22.9859 + 22.9859i) q^{29} +(-78.9296 - 78.9296i) q^{30} +31.7318i q^{31} -48.9108i q^{32} +78.0563 q^{33} +(9.30019 - 9.30019i) q^{34} +(-10.2714 - 48.5742i) q^{35} +89.0858i q^{36} +66.9934 q^{37} +(26.2947 - 26.2947i) q^{38} +68.8720i q^{39} -140.757i q^{40} +(-37.4616 - 16.6623i) q^{41} +(-60.0976 + 92.3296i) q^{42} -61.3960i q^{43} +(120.986 + 120.986i) q^{44} +67.0912i q^{45} -4.96775i q^{46} +(-15.5404 - 15.5404i) q^{47} +(-106.403 + 106.403i) q^{48} +(-44.8055 + 19.8360i) q^{49} -92.6939i q^{50} -15.4267 q^{51} +(-106.750 + 106.750i) q^{52} +(45.0963 + 45.0963i) q^{53} +(5.11127 - 5.11127i) q^{54} +(91.1154 + 91.1154i) q^{55} +(-135.914 + 28.7401i) q^{56} -43.6164 q^{57} +(84.1981 - 84.1981i) q^{58} -64.2882i q^{59} +(-202.931 + 202.931i) q^{60} +53.2723 q^{61} +116.234 q^{62} +(64.7826 - 13.6988i) q^{63} -39.0669 q^{64} +(-80.3945 + 80.3945i) q^{65} -285.923i q^{66} +(-66.6217 + 66.6217i) q^{67} +(-23.9112 - 23.9112i) q^{68} +(-4.12014 + 4.12014i) q^{69} +(-177.929 + 37.6246i) q^{70} +(-24.6353 - 24.6353i) q^{71} +187.725 q^{72} +108.100 q^{73} -245.399i q^{74} +(-76.8782 + 76.8782i) q^{75} +(-67.6046 - 67.6046i) q^{76} +(69.3760 - 106.584i) q^{77} +252.280 q^{78} +(55.6141 + 55.6141i) q^{79} -248.410 q^{80} +76.6554 q^{81} +(-61.0345 + 137.223i) q^{82} -16.3283i q^{83} +(237.383 + 154.513i) q^{84} +(-18.0077 - 18.0077i) q^{85} -224.896 q^{86} -139.664 q^{87} +(254.946 - 254.946i) q^{88} +(-2.86642 + 2.86642i) q^{89} +245.757 q^{90} +(94.0433 + 61.2130i) q^{91} -12.7723 q^{92} +(-96.4022 - 96.4022i) q^{93} +(-56.9250 + 56.9250i) q^{94} +(-50.9136 - 50.9136i) q^{95} +(148.593 + 148.593i) q^{96} +(-34.6667 - 34.6667i) q^{97} +(72.6598 + 164.124i) q^{98} +(-121.519 + 121.519i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 216 q^{4} - 2 q^{7}+O(q^{10}) $ 108 * q - 216 * q^4 - 2 * q^7	$ 108 q - 216 q^{4} - 2 q^{7} - 20 q^{11} - 4 q^{14} - 28 q^{15} + 408 q^{16} + 24 q^{18} + 20 q^{22} - 8 q^{23} + 452 q^{25} - 62 q^{28} + 168 q^{29} - 64 q^{30} - 10 q^{35} - 208 q^{37} - 44 q^{42} + 44 q^{44} + 272 q^{51} - 92 q^{53} + 24 q^{56} - 256 q^{57} + 248 q^{58} - 440 q^{60} - 252 q^{63} - 1104 q^{64} - 644 q^{65} - 348 q^{67} - 30 q^{70} - 564 q^{71} + 796 q^{72} + 1924 q^{78} + 196 q^{79} - 468 q^{81} + 32 q^{85} + 152 q^{86} + 840 q^{88} - 428 q^{92} + 32 q^{93} + 4 q^{95} + 108 q^{98} - 484 q^{99}+O(q^{100}) $ 108 * q - 216 * q^4 - 2 * q^7 - 20 * q^11 - 4 * q^14 - 28 * q^15 + 408 * q^16 + 24 * q^18 + 20 * q^22 - 8 * q^23 + 452 * q^25 - 62 * q^28 + 168 * q^29 - 64 * q^30 - 10 * q^35 - 208 * q^37 - 44 * q^42 + 44 * q^44 + 272 * q^51 - 92 * q^53 + 24 * q^56 - 256 * q^57 + 248 * q^58 - 440 * q^60 - 252 * q^63 - 1104 * q^64 - 644 * q^65 - 348 * q^67 - 30 * q^70 - 564 * q^71 + 796 * q^72 + 1924 * q^78 + 196 * q^79 - 468 * q^81 + 32 * q^85 + 152 * q^86 + 840 * q^88 - 428 * q^92 + 32 * q^93 + 4 * q^95 + 108 * q^98 - 484 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	3.66303i		−	1.83152i	−0.401731	−	0.915758i	$-0.631591\pi$
$2$		−	3.66303i		−	1.83152i	0.401731	−	0.915758i	$-0.368409\pi$
$3$	−3.03803	+	3.03803i	−1.01268	+	1.01268i	−0.0127593	+	0.999919i	$0.504062\pi$
$3$	−3.03803	+	3.03803i	−1.01268	+	1.01268i	−0.999919	+	0.0127593i	$0.995938\pi$
$4$	−9.41780			−2.35445
$5$	−7.09262			−1.41852			−0.709262	−	0.704945i	$-0.750972\pi$
$5$	−7.09262			−1.41852			−0.709262	+	0.704945i	$0.750972\pi$
$6$	11.1284	+	11.1284i	1.85474	+	1.85474i
$7$	1.44819	+	6.84856i	0.206884	+	0.978366i
$7$	1.44819	+	6.84856i	0.206884	+	0.978366i
$8$			19.8456i			2.48070i
$9$		−	9.45930i		−	1.05103i
$10$			25.9805i			2.59805i
$11$	−12.8465	−	12.8465i	−1.16786	−	1.16786i	−0.982709	−	0.185156i	$-0.940721\pi$
$11$	−12.8465	−	12.8465i	−1.16786	−	1.16786i	−0.185156	−	0.982709i	$-0.559279\pi$
$12$	28.6116	−	28.6116i	2.38430	−	2.38430i
$13$	11.3350	−	11.3350i	0.871920	−	0.871920i	−0.120762	−	0.992682i	$-0.538534\pi$
$13$	11.3350	−	11.3350i	0.871920	−	0.871920i	0.992682	+	0.120762i	$0.0385337\pi$
$14$	25.0865	−	5.30475i	1.79189	−	0.378911i
$15$	21.5476	−	21.5476i	1.43651	−	1.43651i
$16$	35.0238			2.18898
$17$	2.53893	+	2.53893i	0.149349	+	0.149349i	0.777827	−	0.628478i	$-0.216322\pi$
$17$	2.53893	+	2.53893i	0.149349	+	0.149349i	−0.628478	+	0.777827i	$0.716322\pi$
$18$	−34.6497			−1.92498
$19$	7.17839	+	7.17839i	0.377810	+	0.377810i	0.870312	−	0.492502i	$-0.163917\pi$
$19$	7.17839	+	7.17839i	0.377810	+	0.377810i	−0.492502	+	0.870312i	$0.663917\pi$
$20$	66.7969			3.33984
$21$	−25.2058	−	16.4065i	−1.20028	−	0.781263i
$22$	−47.0572	+	47.0572i	−2.13896	+	2.13896i
$23$	1.35619			0.0589646			0.0294823	−	0.999565i	$-0.490614\pi$
$23$	1.35619			0.0589646			0.0294823	+	0.999565i	$0.490614\pi$
$24$	−60.2915	−	60.2915i	−2.51215	−	2.51215i
$25$	25.3052			1.01221
$26$	−41.5203	−	41.5203i	−1.59694	−	1.59694i
$27$	1.39537	+	1.39537i	0.0516802	+	0.0516802i
$28$	−13.6387	−	64.4984i	−0.487098	−	2.30351i
$29$	22.9859	+	22.9859i	0.792618	+	0.792618i	0.981919	−	0.189301i	$-0.0606222\pi$
$29$	22.9859	+	22.9859i	0.792618	+	0.792618i	−0.189301	+	0.981919i	$0.560622\pi$
$30$	−78.9296	−	78.9296i	−2.63099	−	2.63099i
$31$			31.7318i			1.02361i	0.859103	+	0.511803i	$0.171022\pi$
$31$			31.7318i			1.02361i	−0.859103	+	0.511803i	$0.828978\pi$
$32$		−	48.9108i		−	1.52846i
$33$	78.0563			2.36534
$34$	9.30019	−	9.30019i	0.273535	−	0.273535i
$35$	−10.2714	−	48.5742i	−0.293470	−	1.38783i
$36$			89.0858i			2.47461i
$37$	66.9934			1.81063			0.905316	−	0.424738i	$-0.139634\pi$
$37$	66.9934			1.81063			0.905316	+	0.424738i	$0.139634\pi$
$38$	26.2947	−	26.2947i	0.691965	−	0.691965i
$39$			68.8720i			1.76595i
$40$		−	140.757i		−	3.51893i
$41$	−37.4616	−	16.6623i	−0.913696	−	0.406397i
$41$	−37.4616	−	16.6623i	−0.913696	−	0.406397i
$42$	−60.0976	+	92.3296i	−1.43089	+	2.19832i
$43$		−	61.3960i		−	1.42781i	−0.700240	−	0.713907i	$-0.746924\pi$
$43$		−	61.3960i		−	1.42781i	0.700240	−	0.713907i	$-0.253076\pi$
$44$	120.986	+	120.986i	2.74968	+	2.74968i
$45$			67.0912i			1.49092i
$46$		−	4.96775i		−	0.107995i
$47$	−15.5404	−	15.5404i	−0.330647	−	0.330647i	0.522185	−	0.852832i	$-0.325117\pi$
$47$	−15.5404	−	15.5404i	−0.330647	−	0.330647i	−0.852832	+	0.522185i	$0.825117\pi$
$48$	−106.403	+	106.403i	−2.21674	+	2.21674i
$49$	−44.8055	+	19.8360i	−0.914398	+	0.404816i
$50$		−	92.6939i		−	1.85388i
$51$	−15.4267			−0.302485
$52$	−106.750	+	106.750i	−2.05289	+	2.05289i
$53$	45.0963	+	45.0963i	0.850873	+	0.850873i	0.990241	−	0.139368i	$-0.0445070\pi$
$53$	45.0963	+	45.0963i	0.850873	+	0.850873i	−0.139368	+	0.990241i	$0.544507\pi$
$54$	5.11127	−	5.11127i	0.0946531	−	0.0946531i
$55$	91.1154	+	91.1154i	1.65664	+	1.65664i
$56$	−135.914	+	28.7401i	−2.42703	+	0.513216i
$57$	−43.6164			−0.765200
$58$	84.1981	−	84.1981i	1.45169	−	1.45169i
$59$		−	64.2882i		−	1.08963i	−0.838556	−	0.544815i	$-0.816600\pi$
$59$		−	64.2882i		−	1.08963i	0.838556	−	0.544815i	$-0.183400\pi$
$60$	−202.931	+	202.931i	−3.38219	+	3.38219i
$61$	53.2723			0.873317			0.436658	−	0.899627i	$-0.356162\pi$
$61$	53.2723			0.873317			0.436658	+	0.899627i	$0.356162\pi$
$62$	116.234			1.87475
$63$	64.7826	−	13.6988i	1.02829	−	0.217442i
$64$	−39.0669			−0.610420
$65$	−80.3945	+	80.3945i	−1.23684	+	1.23684i
$66$		−	285.923i		−	4.33216i
$67$	−66.6217	+	66.6217i	−0.994354	+	0.994354i	−0.999984	−	0.00563023i	$-0.998208\pi$
$67$	−66.6217	+	66.6217i	−0.994354	+	0.994354i	0.00563023	+	0.999984i	$0.498208\pi$
$68$	−23.9112	−	23.9112i	−0.351635	−	0.351635i
$69$	−4.12014	+	4.12014i	−0.0597121	+	0.0597121i
$70$	−177.929	+	37.6246i	−2.54184	+	0.537494i
$71$	−24.6353	−	24.6353i	−0.346976	−	0.346976i	0.512006	−	0.858982i	$-0.328903\pi$
$71$	−24.6353	−	24.6353i	−0.346976	−	0.346976i	−0.858982	+	0.512006i	$0.828903\pi$
$72$	187.725			2.60729
$73$	108.100			1.48082			0.740408	−	0.672158i	$-0.234632\pi$
$73$	108.100			1.48082			0.740408	+	0.672158i	$0.234632\pi$
$74$		−	245.399i		−	3.31620i
$75$	−76.8782	+	76.8782i	−1.02504	+	1.02504i
$76$	−67.6046	−	67.6046i	−0.889535	−	0.889535i
$77$	69.3760	−	106.584i	0.900986	−	1.38421i
$78$	252.280			3.23436
$79$	55.6141	+	55.6141i	0.703976	+	0.703976i	0.965261	−	0.261286i	$-0.0841465\pi$
$79$	55.6141	+	55.6141i	0.703976	+	0.703976i	−0.261286	+	0.965261i	$0.584147\pi$
$80$	−248.410			−3.10513
$81$	76.6554			0.946362
$82$	−61.0345	+	137.223i	−0.744323	+	1.67345i
$83$		−	16.3283i		−	0.196727i	−0.995151	−	0.0983633i	$-0.968639\pi$
$83$		−	16.3283i		−	0.196727i	0.995151	−	0.0983633i	$-0.0313607\pi$
$84$	237.383	+	154.513i	2.82599	+	1.83944i
$85$	−18.0077	−	18.0077i	−0.211855	−	0.211855i
$86$	−224.896			−2.61506
$87$	−139.664			−1.60533
$88$	254.946	−	254.946i	2.89712	−	2.89712i
$89$	−2.86642	+	2.86642i	−0.0322070	+	0.0322070i	−0.723027	−	0.690820i	$-0.757250\pi$
$89$	−2.86642	+	2.86642i	−0.0322070	+	0.0322070i	0.690820	+	0.723027i	$0.257250\pi$
$90$	245.757			2.73064
$91$	94.0433	+	61.2130i	1.03344	+	0.672670i
$92$	−12.7723			−0.138829
$93$	−96.4022	−	96.4022i	−1.03658	−	1.03658i
$94$	−56.9250	+	56.9250i	−0.605585	+	0.605585i
$95$	−50.9136	−	50.9136i	−0.535933	−	0.535933i
$96$	148.593	+	148.593i	1.54784	+	1.54784i
$97$	−34.6667	−	34.6667i	−0.357388	−	0.357388i	0.505461	−	0.862849i	$-0.331322\pi$
$97$	−34.6667	−	34.6667i	−0.357388	−	0.357388i	−0.862849	+	0.505461i	$0.831322\pi$
$98$	72.6598	+	164.124i	0.741427	+	1.67473i
$99$	−121.519	+	121.519i	−1.22746	+	1.22746i
$100$	−238.320			−2.38320
$101$	−19.6493	−	19.6493i	−0.194548	−	0.194548i	0.603110	−	0.797658i	$-0.293928\pi$
$101$	−19.6493	−	19.6493i	−0.194548	−	0.194548i	−0.797658	+	0.603110i	$0.793928\pi$
$102$			56.5086i			0.554006i
$103$	−26.1584			−0.253965			−0.126982	−	0.991905i	$-0.540529\pi$
$103$	−26.1584			−0.253965			−0.126982	+	0.991905i	$0.540529\pi$
$104$	224.949	+	224.949i	2.16297	+	2.16297i
$105$	178.775	+	116.365i	1.70262	+	1.10824i
$106$	165.189	−	165.189i	1.55839	−	1.55839i
$107$	−57.3098			−0.535606			−0.267803	−	0.963474i	$-0.586298\pi$
$107$	−57.3098			−0.535606			−0.267803	+	0.963474i	$0.586298\pi$
$108$	−13.1413	−	13.1413i	−0.121678	−	0.121678i
$109$	104.111	−	104.111i	0.955143	−	0.955143i	−0.0438931	−	0.999036i	$-0.513976\pi$
$109$	104.111	−	104.111i	0.955143	−	0.955143i	0.999036	+	0.0438931i	$0.0139761\pi$
$110$	333.759	−	333.759i	3.03417	−	3.03417i
$111$	−203.528	+	203.528i	−1.83359	+	1.83359i
$112$	50.7209	+	239.862i	0.452865	+	2.14163i
$113$	13.8445			0.122517			0.0612587	−	0.998122i	$-0.480489\pi$
$113$	13.8445			0.122517			0.0612587	+	0.998122i	$0.480489\pi$
$114$			159.768i			1.40148i
$115$	−9.61891			−0.0836427
$116$	−216.477	−	216.477i	−1.86618	−	1.86618i
$117$	−107.221	−	107.221i	−0.916417	−	0.916417i
$118$	−235.490			−1.99567
$119$	−13.7112	+	21.0649i	−0.115220	+	0.177016i
$120$	427.625	+	427.625i	3.56354	+	3.56354i
$121$			209.066i			1.72782i
$122$		−	195.138i		−	1.59949i
$123$	164.430	−	63.1888i	1.33683	−	0.513730i
$124$		−	298.843i		−	2.41003i
$125$	−2.16494			−0.0173196
$126$	−50.1792	−	237.301i	−0.398248	−	1.88334i
$127$	65.5796			0.516375			0.258188	−	0.966095i	$-0.416875\pi$
$127$	65.5796			0.516375			0.258188	+	0.966095i	$0.416875\pi$
$128$		−	52.5401i		−	0.410469i
$129$	186.523	+	186.523i	1.44592	+	1.44592i
$130$	294.488	+	294.488i	2.26529	+	2.26529i
$131$	214.335			1.63615			0.818073	−	0.575114i	$-0.195042\pi$
$131$	214.335			1.63615			0.818073	+	0.575114i	$0.195042\pi$
$132$	−735.118			−5.56908
$133$	−38.7660	+	59.5573i	−0.291474	+	0.447799i
$134$	244.037	+	244.037i	1.82117	+	1.82117i
$135$	−9.89679	−	9.89679i	−0.0733096	−	0.0733096i
$136$	−50.3866	+	50.3866i	−0.370490	+	0.370490i
$137$	−101.390	+	101.390i	−0.740073	+	0.740073i	−0.972592	−	0.232519i	$-0.925303\pi$
$137$	−101.390	+	101.390i	−0.740073	+	0.740073i	0.232519	+	0.972592i	$0.425303\pi$
$138$	15.0922	+	15.0922i	0.109364	+	0.109364i
$139$			71.9643i			0.517729i	0.965914	+	0.258864i	$0.0833483\pi$
$139$			71.9643i			0.517729i	−0.965914	+	0.258864i	$0.916652\pi$
$140$	96.7343	+	457.462i	0.690959	+	3.26759i
$141$	94.4246			0.669678
$142$	−90.2398	+	90.2398i	−0.635492	+	0.635492i
$143$	−291.229			−2.03657
$144$		−	331.300i		−	2.30070i
$145$	−163.030	−	163.030i	−1.12435	−	1.12435i
$146$		−	395.972i		−	2.71214i
$147$	75.8583	−	196.383i	0.516043	−	1.33594i
$148$	−630.931			−4.26304
$149$	16.5685	−	16.5685i	0.111198	−	0.111198i	−0.649319	−	0.760516i	$-0.724946\pi$
$149$	16.5685	−	16.5685i	0.111198	−	0.111198i	0.760516	+	0.649319i	$0.224946\pi$
$150$	281.607	+	281.607i	1.87738	+	1.87738i
$151$	−19.7370	−	19.7370i	−0.130708	−	0.130708i	0.638726	−	0.769434i	$-0.279462\pi$
$151$	−19.7370	−	19.7370i	−0.130708	−	0.130708i	−0.769434	+	0.638726i	$0.779462\pi$
$152$	−142.459	+	142.459i	−0.937232	+	0.937232i
$153$	24.0165	−	24.0165i	0.156971	−	0.156971i
$154$	−390.421	−	254.126i	−2.53520	−	1.65017i
$155$		−	225.061i		−	1.45201i
$156$		−	648.622i		−	4.15784i
$157$	32.1380	−	32.1380i	0.204700	−	0.204700i	−0.597310	−	0.802010i	$-0.703764\pi$
$157$	32.1380	−	32.1380i	0.204700	−	0.204700i	0.802010	+	0.597310i	$0.203764\pi$
$158$	203.716	−	203.716i	1.28934	−	1.28934i
$159$	−274.008			−1.72332
$160$			346.906i			2.16816i
$161$	1.96401	+	9.28792i	0.0121988	+	0.0576889i
$162$		−	280.791i		−	1.73328i
$163$	−234.137			−1.43642			−0.718210	−	0.695826i	$-0.755038\pi$
$163$	−234.137			−1.43642			−0.718210	+	0.695826i	$0.755038\pi$
$164$	352.805	+	156.922i	2.15125	+	0.956843i
$165$	−553.623			−3.35529
$166$	−59.8111			−0.360308
$167$	109.400	−	109.400i	0.655089	−	0.655089i	−0.299125	−	0.954214i	$-0.596695\pi$
$167$	109.400	−	109.400i	0.655089	−	0.655089i	0.954214	+	0.299125i	$0.0966948\pi$
$168$	325.597	−	500.223i	1.93808	−	2.97752i
$169$		−	87.9626i		−	0.520489i
$170$	−65.9627	+	65.9627i	−0.388016	+	0.388016i
$171$	67.9025	−	67.9025i	0.397091	−	0.397091i
$172$			578.215i			3.36172i
$173$	210.306			1.21564			0.607820	−	0.794075i	$-0.292044\pi$
$173$	210.306			1.21564			0.607820	+	0.794075i	$0.292044\pi$
$174$			511.594i			2.94019i
$175$	36.6467	+	173.304i	0.209410	+	0.990311i
$176$	−449.933	−	449.933i	−2.55644	−	2.55644i
$177$	195.310	+	195.310i	1.10344	+	1.10344i
$178$	10.4998	+	10.4998i	0.0589875	+	0.0589875i
$179$	102.167	−	102.167i	0.570764	−	0.570764i	−0.361578	−	0.932342i	$-0.617762\pi$
$179$	102.167	−	102.167i	0.570764	−	0.570764i	0.932342	+	0.361578i	$0.117762\pi$
$180$		−	631.851i		−	3.51029i
$181$	−142.554	−	142.554i	−0.787590	−	0.787590i	0.193509	−	0.981099i	$-0.438013\pi$
$181$	−142.554	−	142.554i	−0.787590	−	0.787590i	−0.981099	+	0.193509i	$0.938013\pi$
$182$	224.225	−	344.483i	1.23201	−	1.89277i
$183$	−161.843	+	161.843i	−0.884388	+	0.884388i
$184$			26.9143i			0.146273i
$185$	−475.159			−2.56843
$186$	−353.124	+	353.124i	−1.89852	+	1.89852i
$187$		−	65.2329i		−	0.348839i
$188$	146.356	+	146.356i	0.778492	+	0.778492i
$189$	−7.53549	+	11.5770i	−0.0398703	+	0.0612539i
$190$	−186.498	+	186.498i	−0.981569	+	0.981569i
$191$	−34.8850	+	34.8850i	−0.182644	+	0.182644i	−0.792507	−	0.609863i	$-0.791224\pi$
$191$	−34.8850	+	34.8850i	−0.182644	+	0.182644i	0.609863	+	0.792507i	$0.291224\pi$
$192$	118.687	−	118.687i	0.618159	−	0.618159i
$193$	−141.656	−	141.656i	−0.733968	−	0.733968i	0.237435	−	0.971403i	$-0.423693\pi$
$193$	−141.656	−	141.656i	−0.733968	−	0.733968i	−0.971403	+	0.237435i	$0.923693\pi$
$194$	−126.985	+	126.985i	−0.654563	+	0.654563i
$195$		−	488.483i		−	2.50504i
$196$	421.969	−	186.811i	2.15290	−	0.953119i
$197$			140.491i			0.713152i	0.934266	+	0.356576i	$0.116056\pi$
$197$			140.491i			0.713152i	−0.934266	+	0.356576i	$0.883944\pi$
$198$	445.128	+	445.128i	2.24812	+	2.24812i
$199$	190.494	+	190.494i	0.957256	+	0.957256i	0.999123	−	0.0418676i	$-0.0133308\pi$
$199$	190.494	+	190.494i	0.957256	+	0.957256i	−0.0418676	+	0.999123i	$0.513331\pi$
$200$			502.197i			2.51098i
$201$		−	404.798i		−	2.01392i
$202$	−71.9761	+	71.9761i	−0.356317	+	0.356317i
$203$	−124.133	+	190.708i	−0.611490	+	0.939450i
$204$	145.286			0.712186
$205$	265.701	+	118.179i	1.29610	+	0.576484i
$206$			95.8189i			0.465140i
$207$		−	12.8286i		−	0.0619737i
$208$	396.993	−	396.993i	1.90862	−	1.90862i
$209$		−	184.435i		−	0.882462i
$210$	426.249	−	654.859i	2.02976	−	3.11837i
$211$	36.3934	−	36.3934i	0.172480	−	0.172480i	−0.615588	−	0.788068i	$-0.711081\pi$
$211$	36.3934	−	36.3934i	0.172480	−	0.172480i	0.788068	+	0.615588i	$0.211081\pi$
$212$	−424.708	−	424.708i	−2.00334	−	2.00334i
$213$	149.686			0.702750
$214$			209.928i			0.980970i
$215$			435.459i			2.02539i
$216$	−27.6918	+	27.6918i	−0.128203	+	0.128203i
$217$	−217.317	+	45.9535i	−1.00146	+	0.211767i
$218$	−381.360	−	381.360i	−1.74936	−	1.74936i
$219$	−328.410	+	328.410i	−1.49959	+	1.49959i
$220$	−858.107	−	858.107i	−3.90049	−	3.90049i
$221$	57.5574			0.260441
$222$	745.530	+	745.530i	3.35825	+	3.35825i
$223$			7.05032i			0.0316158i	0.999875	+	0.0158079i	$0.00503201\pi$
$223$			7.05032i			0.0316158i	−0.999875	+	0.0158079i	$0.994968\pi$
$224$	334.969	−	70.8320i	1.49540	−	0.316214i
$225$		−	239.370i		−	1.06387i
$226$		−	50.7127i		−	0.224393i
$227$	233.358	+	233.358i	1.02801	+	1.02801i	0.999596	+	0.0284123i	$0.00904512\pi$
$227$	233.358	+	233.358i	1.02801	+	1.02801i	0.0284123	+	0.999596i	$0.490955\pi$
$228$	410.770			1.80162
$229$	−139.559	−	139.559i	−0.609427	−	0.609427i	0.333369	−	0.942796i	$-0.391814\pi$
$229$	−139.559	−	139.559i	−0.609427	−	0.609427i	−0.942796	+	0.333369i	$0.891814\pi$
$230$			35.2344i			0.153193i
$231$	113.040	+	534.573i	0.489351	+	2.31417i
$232$	−456.169	+	456.169i	−1.96624	+	1.96624i
$233$	92.7240	+	92.7240i	0.397957	+	0.397957i	0.877512	−	0.479555i	$-0.159202\pi$
$233$	92.7240	+	92.7240i	0.397957	+	0.397957i	−0.479555	+	0.877512i	$0.659202\pi$
$234$	−392.753	+	392.753i	−1.67843	+	1.67843i
$235$	110.222	+	110.222i	0.469031	+	0.469031i
$236$			605.453i			2.56548i
$237$	−337.915			−1.42580
$238$	77.1613	+	50.2245i	0.324207	+	0.211027i
$239$	24.5715	+	24.5715i	0.102810	+	0.102810i	0.756641	−	0.653831i	$-0.226839\pi$
$239$	24.5715	+	24.5715i	0.102810	+	0.102810i	−0.653831	+	0.756641i	$0.726839\pi$
$240$	754.678	−	754.678i	3.14449	−	3.14449i
$241$	417.262			1.73138			0.865689	−	0.500582i	$-0.166881\pi$
$241$	417.262			1.73138			0.865689	+	0.500582i	$0.166881\pi$
$242$	765.815			3.16452
$243$	−245.440	+	245.440i	−1.01004	+	1.01004i
$244$	−501.708			−2.05618
$245$	317.788	−	140.689i	1.29710	−	0.574241i
$246$	−231.463	−	602.313i	−0.940905	−	2.44843i
$247$	162.734			0.658840
$248$	−629.735			−2.53925
$249$	49.6059	+	49.6059i	0.199221	+	0.199221i
$250$			7.93026i			0.0317210i
$251$	147.310			0.586892			0.293446	−	0.955976i	$-0.405198\pi$
$251$	147.310			0.586892			0.293446	+	0.955976i	$0.405198\pi$
$252$	−610.109	+	129.013i	−2.42107	+	0.511956i
$253$	−17.4223	−	17.4223i	−0.0688627	−	0.0688627i
$254$		−	240.220i		−	0.945749i
$255$	109.416			0.429082
$256$	−348.724			−1.36220
$257$	312.373	−	312.373i	1.21546	−	1.21546i	0.246254	−	0.969205i	$-0.420800\pi$
$257$	312.373	−	312.373i	1.21546	−	1.21546i	0.969205	−	0.246254i	$-0.0791997\pi$
$258$	683.240	−	683.240i	2.64822	−	2.64822i
$259$	97.0190	+	458.808i	0.374591	+	1.77146i
$260$	757.140	−	757.140i	2.91208	−	2.91208i
$261$	217.431	−	217.431i	0.833068	−	0.833068i
$262$		−	785.116i		−	2.99663i
$263$	53.2986	−	53.2986i	0.202656	−	0.202656i	−0.598481	−	0.801137i	$-0.704229\pi$
$263$	53.2986	−	53.2986i	0.202656	−	0.202656i	0.801137	+	0.598481i	$0.204229\pi$
$264$			1549.07i			5.86770i
$265$	−319.851	−	319.851i	−1.20698	−	1.20698i
$266$	218.160	+	142.001i	0.820151	+	0.533838i
$267$		−	17.4166i		−	0.0652305i
$268$	627.430	−	627.430i	2.34116	−	2.34116i
$269$		−	52.4036i		−	0.194809i	−0.995245	−	0.0974045i	$-0.968946\pi$
$269$		−	52.4036i		−	0.194809i	0.995245	−	0.0974045i	$-0.0310540\pi$
$270$	−36.2523	+	36.2523i	−0.134268	+	0.134268i
$271$			172.887i			0.637961i	0.947761	+	0.318980i	$0.103340\pi$
$271$			172.887i			0.637961i	−0.947761	+	0.318980i	$0.896660\pi$
$272$	88.9230	+	88.9230i	0.326923	+	0.326923i
$273$	−471.674	+	99.7395i	−1.72774	+	0.365346i
$274$	371.395	+	371.395i	1.35545	+	1.35545i
$275$	−325.084	−	325.084i	−1.18212	−	1.18212i
$276$	38.8026	−	38.8026i	0.140589	−	0.140589i
$277$	−196.251			−0.708488			−0.354244	−	0.935153i	$-0.615262\pi$
$277$	−196.251			−0.708488			−0.354244	+	0.935153i	$0.615262\pi$
$278$	263.608			0.948229
$279$	300.160			1.07584
$280$	963.983	−	203.842i	3.44280	−	0.728009i
$281$	−22.1933	+	22.1933i	−0.0789797	+	0.0789797i	−0.745493	−	0.666513i	$-0.767786\pi$
$281$	−22.1933	+	22.1933i	−0.0789797	+	0.0789797i	0.666513	+	0.745493i	$0.267786\pi$
$282$		−	345.880i		−	1.22653i
$283$		−	344.373i		−	1.21687i	−0.793605	−	0.608433i	$-0.791798\pi$
$283$		−	344.373i		−	1.21687i	0.793605	−	0.608433i	$-0.208202\pi$
$284$	232.010	+	232.010i	0.816937	+	0.816937i
$285$	309.354			1.08545
$286$			1066.78i			3.73001i
$287$	59.8614	−	280.688i	0.208576	−	0.978006i
$288$	−462.662			−1.60647
$289$		−	276.108i		−	0.955390i
$290$	−597.185	+	597.185i	−2.05926	+	2.05926i
$291$	210.637			0.723839
$292$	−1018.06			−3.48651
$293$	−110.460	−	110.460i	−0.376997	−	0.376997i	0.493020	−	0.870018i	$-0.335893\pi$
$293$	−110.460	−	110.460i	−0.376997	−	0.376997i	−0.870018	+	0.493020i	$0.835893\pi$
$294$	−719.357	−	277.871i	−2.44679	−	0.945140i
$295$			455.971i			1.54567i
$296$			1329.52i			4.49163i
$297$		−	35.8512i		−	0.120711i
$298$	−60.6908	−	60.6908i	−0.203660	−	0.203660i
$299$	15.3723	−	15.3723i	0.0514124	−	0.0514124i
$300$	724.023	−	724.023i	2.41341	−	2.41341i
$301$	420.474	−	88.9129i	1.39692	−	0.295392i
$302$	−72.2971	+	72.2971i	−0.239394	+	0.239394i
$303$	119.391			0.394028
$304$	251.414	+	251.414i	0.827020	+	0.827020i
$305$	−377.840			−1.23882
$306$	−87.9733	−	87.9733i	−0.287494	−	0.287494i
$307$	−390.135			−1.27080			−0.635399	−	0.772184i	$-0.719165\pi$
$307$	−390.135			−1.27080			−0.635399	+	0.772184i	$0.719165\pi$
$308$	−653.369	+	1003.79i	−2.12133	+	3.25906i
$309$	79.4700	−	79.4700i	0.257184	−	0.257184i
$310$	−824.407			−2.65938
$311$	416.561	+	416.561i	1.33942	+	1.33942i	0.896618	+	0.442806i	$0.146017\pi$
$311$	416.561	+	416.561i	1.33942	+	1.33942i	0.442806	+	0.896618i	$0.353983\pi$
$312$	−1366.80			−4.38078
$313$	240.657	+	240.657i	0.768874	+	0.768874i	0.977908	−	0.209035i	$-0.0670321\pi$
$313$	240.657	+	240.657i	0.768874	+	0.768874i	−0.209035	+	0.977908i	$0.567032\pi$
$314$	−117.722	−	117.722i	−0.374912	−	0.374912i
$315$	−459.478	+	97.1606i	−1.45866	+	0.308446i
$316$	−523.762	−	523.762i	−1.65748	−	1.65748i
$317$	50.2547	+	50.2547i	0.158532	+	0.158532i	0.781916	−	0.623384i	$-0.214243\pi$
$317$	50.2547	+	50.2547i	0.158532	+	0.158532i	−0.623384	+	0.781916i	$0.714243\pi$
$318$			1003.70i			3.15629i
$319$		−	590.578i		−	1.85134i
$320$	277.086			0.865895
$321$	174.109	−	174.109i	0.542396	−	0.542396i
$322$	34.0219	−	7.19423i	0.105658	−	0.0223423i
$323$			36.4509i			0.112851i
$324$	−721.925			−2.22816
$325$	286.834	−	286.834i	0.882566	−	0.882566i
$326$			857.650i			2.63083i
$327$			632.583i			1.93450i
$328$	330.673	−	743.446i	1.00815	−	2.26660i
$329$	83.9240	−	128.935i	0.255088	−	0.391899i
$330$			2027.94i			6.14527i
$331$	363.325	+	363.325i	1.09766	+	1.09766i	0.994684	+	0.102974i	$0.0328357\pi$
$331$	363.325	+	363.325i	1.09766	+	1.09766i	0.102974	+	0.994684i	$0.467164\pi$
$332$			153.777i			0.463183i
$333$		−	633.711i		−	1.90304i
$334$	−400.735	−	400.735i	−1.19981	−	1.19981i
$335$	472.522	−	472.522i	1.41051	−	1.41051i
$336$	−882.801	−	574.618i	−2.62739	−	1.71017i
$337$		−	468.607i		−	1.39052i	−0.718756	−	0.695262i	$-0.755288\pi$
$337$		−	468.607i		−	1.39052i	0.718756	−	0.695262i	$-0.244712\pi$
$338$	−322.210			−0.953283
$339$	−42.0599	+	42.0599i	−0.124071	+	0.124071i
$340$	169.593	+	169.593i	0.498802	+	0.498802i
$341$	407.642	−	407.642i	1.19543	−	1.19543i
$342$	−248.729	−	248.729i	−0.727278	−	0.727278i
$343$	−200.735	−	278.127i	−0.585232	−	0.810866i
$344$	1218.44			3.54197
$345$	29.2226	−	29.2226i	0.0847031	−	0.0847031i
$346$		−	770.356i		−	2.22646i
$347$	−24.8444	+	24.8444i	−0.0715976	+	0.0715976i	−0.741999	−	0.670401i	$-0.766122\pi$
$347$	−24.8444	+	24.8444i	−0.0715976	+	0.0715976i	0.670401	+	0.741999i	$0.266122\pi$
$348$	1315.33			3.77968
$349$	518.846			1.48667			0.743333	−	0.668922i	$-0.233244\pi$
$349$	518.846			1.48667			0.743333	+	0.668922i	$0.233244\pi$
$350$	634.820	−	134.238i	1.81377	−	0.383537i
$351$	31.6328			0.0901220
$352$	−628.334	+	628.334i	−1.78504	+	1.78504i
$353$			128.748i			0.364726i	0.983231	+	0.182363i	$0.0583746\pi$
$353$			128.748i			0.364726i	−0.983231	+	0.182363i	$0.941625\pi$
$354$	715.425	−	715.425i	2.02097	−	2.02097i
$355$	174.729	+	174.729i	0.492194	+	0.492194i
$356$	26.9954	−	26.9954i	0.0758297	−	0.0758297i
$357$	−22.3408	−	105.651i	−0.0625792	−	0.295941i
$358$	−374.240	−	374.240i	−1.04536	−	1.04536i
$359$	239.699			0.667684			0.333842	−	0.942629i	$-0.391655\pi$
$359$	239.699			0.667684			0.333842	+	0.942629i	$0.391655\pi$
$360$	−1331.46			−3.69851
$361$		−	257.941i		−	0.714519i
$362$	−522.179	+	522.179i	−1.44248	+	1.44248i
$363$	−635.149	−	635.149i	−1.74972	−	1.74972i
$364$	−885.681	−	576.492i	−2.43319	−	1.58377i
$365$	−766.709			−2.10057
$366$	592.836	+	592.836i	1.61977	+	1.61977i
$367$	−582.536			−1.58729			−0.793646	−	0.608380i	$-0.791820\pi$
$367$	−582.536			−1.58729			−0.793646	+	0.608380i	$0.791820\pi$
$368$	47.4987			0.129073
$369$	−157.614	+	354.360i	−0.427137	+	0.960325i
$370$			1740.52i			4.70411i
$371$	−243.537	+	374.152i	−0.656433	+	1.00850i
$372$	907.896	+	907.896i	2.44058	+	2.44058i
$373$	39.6698			0.106353			0.0531767	−	0.998585i	$-0.483065\pi$
$373$	39.6698			0.106353			0.0531767	+	0.998585i	$0.483065\pi$
$374$	−238.950			−0.638904
$375$	6.57717	−	6.57717i	0.0175391	−	0.0175391i
$376$	308.408	−	308.408i	0.820235	−	0.820235i
$377$	521.089			1.38220
$378$	42.4069	+	27.6027i	0.112188	+	0.0730231i
$379$	681.134			1.79719			0.898594	−	0.438781i	$-0.144590\pi$
$379$	681.134			1.79719			0.898594	+	0.438781i	$0.144590\pi$
$380$	479.494	+	479.494i	1.26183	+	1.26183i
$381$	−199.233	+	199.233i	−0.522922	+	0.522922i
$382$	127.785	+	127.785i	0.334515	+	0.334515i
$383$	11.7057	+	11.7057i	0.0305633	+	0.0305633i	0.722223	−	0.691660i	$-0.243120\pi$
$383$	11.7057	+	11.7057i	0.0305633	+	0.0305633i	−0.691660	+	0.722223i	$0.743120\pi$
$384$	159.619	+	159.619i	0.415673	+	0.415673i
$385$	−492.057	+	755.961i	−1.27807	+	1.96354i
$386$	−518.890	+	518.890i	−1.34427	+	1.34427i
$387$	−580.763			−1.50068
$388$	326.484	+	326.484i	0.841453	+	0.841453i
$389$		−	644.017i		−	1.65557i	−0.561045	−	0.827785i	$-0.689601\pi$
$389$		−	644.017i		−	1.65557i	0.561045	−	0.827785i	$-0.310399\pi$
$390$	−1789.33			−4.58802
$391$	3.44326	+	3.44326i	0.00880630	+	0.00880630i
$392$	−393.656	−	889.191i	−1.00423	−	2.26834i
$393$	−651.157	+	651.157i	−1.65689	+	1.65689i
$394$	514.623			1.30615
$395$	−394.449	−	394.449i	−0.998606	−	0.998606i
$396$	1144.44	−	1144.44i	2.89000	−	2.89000i
$397$	57.5334	−	57.5334i	0.144920	−	0.144920i	−0.630924	−	0.775844i	$-0.717324\pi$
$397$	57.5334	−	57.5334i	0.144920	−	0.144920i	0.775844	+	0.630924i	$0.217324\pi$
$398$	697.785	−	697.785i	1.75323	−	1.75323i
$399$	−63.1647	−	298.709i	−0.158307	−	0.748645i
$400$	886.284			2.21571
$401$			272.871i			0.680477i	0.940339	+	0.340239i	$0.110508\pi$
$401$			272.871i			0.680477i	−0.940339	+	0.340239i	$0.889492\pi$
$402$	−1482.79			−3.68853
$403$	359.678	+	359.678i	0.892502	+	0.892502i
$404$	185.053	+	185.053i	0.458053	+	0.458053i
$405$	−543.687			−1.34244
$406$	698.571	+	454.701i	1.72062	+	1.11995i
$407$	−860.632	−	860.632i	−2.11457	−	2.11457i
$408$		−	306.152i		−	0.750373i
$409$			682.473i			1.66864i	0.551282	+	0.834319i	$0.314139\pi$
$409$			682.473i			1.66864i	−0.551282	+	0.834319i	$0.685861\pi$
$410$	432.895	−	973.269i	1.05584	−	2.37383i
$411$		−	616.052i		−	1.49891i
$412$	246.354			0.597947
$413$	440.281	−	93.1012i	1.06606	−	0.225427i
$414$	−46.9914			−0.113506
$415$			115.810i			0.279061i
$416$	−554.402	−	554.402i	−1.33270	−	1.33270i
$417$	−218.630	−	218.630i	−0.524293	−	0.524293i
$418$	−675.590			−1.61624
$419$	18.2600			0.0435800			0.0217900	−	0.999763i	$-0.493063\pi$
$419$	18.2600			0.0435800			0.0217900	+	0.999763i	$0.493063\pi$
$420$	−1683.67	−	1095.90i	−4.00873	−	2.60929i
$421$	−43.7128	−	43.7128i	−0.103831	−	0.103831i	0.653283	−	0.757114i	$-0.273391\pi$
$421$	−43.7128	−	43.7128i	−0.103831	−	0.103831i	−0.757114	+	0.653283i	$0.773391\pi$
$422$	−133.310	−	133.310i	−0.315901	−	0.315901i
$423$	−147.001	+	147.001i	−0.347521	+	0.347521i
$424$	−894.961	+	894.961i	−2.11076	+	2.11076i
$425$	64.2483	+	64.2483i	0.151173	+	0.151173i
$426$		−	548.303i		−	1.28710i
$427$	77.1482	+	364.839i	0.180675	+	0.854423i
$428$	539.732			1.26106
$429$	884.765	−	884.765i	2.06239	−	2.06239i
$430$	1595.10			3.70953
$431$			87.2817i			0.202510i	0.994861	+	0.101255i	$0.0322858\pi$
$431$			87.2817i			0.202510i	−0.994861	+	0.101255i	$0.967714\pi$
$432$	48.8709	+	48.8709i	0.113127	+	0.113127i
$433$		−	107.199i		−	0.247574i	−0.992309	−	0.123787i	$-0.960496\pi$
$433$		−	107.199i		−	0.247574i	0.992309	−	0.123787i	$-0.0395039\pi$
$434$	168.329	+	796.038i	0.387855	+	1.83419i
$435$	990.583			2.27720
$436$	−980.493	+	980.493i	−2.24884	+	2.24884i
$437$	9.73523	+	9.73523i	0.0222774	+	0.0222774i
$438$	1202.98	+	1202.98i	2.74652	+	2.74652i
$439$	165.471	−	165.471i	0.376928	−	0.376928i	−0.493065	−	0.869993i	$-0.664123\pi$
$439$	165.471	−	165.471i	0.376928	−	0.376928i	0.869993	+	0.493065i	$0.164123\pi$
$440$	−1808.24	+	1808.24i	−4.10963	+	4.10963i
$441$	187.634	+	423.829i	0.425475	+	0.961063i
$442$		−	210.835i		−	0.477001i
$443$		−	457.820i		−	1.03345i	−0.856150	−	0.516727i	$-0.827150\pi$
$443$		−	457.820i		−	1.03345i	0.856150	−	0.516727i	$-0.172850\pi$
$444$	1916.79	−	1916.79i	4.31709	−	4.31709i
$445$	20.3304	−	20.3304i	0.0456863	−	0.0456863i
$446$	25.8255			0.0579048
$447$			100.671i			0.225215i
$448$	−56.5761	−	267.552i	−0.126286	−	0.597214i
$449$			267.238i			0.595184i	0.954693	+	0.297592i	$0.0961835\pi$
$449$			267.238i			0.595184i	−0.954693	+	0.297592i	$0.903816\pi$
$450$	−876.819			−1.94849
$451$	267.198	+	695.303i	0.592457	+	1.54169i
$452$	−130.384			−0.288461
$453$	119.923			0.264731
$454$	854.797	−	854.797i	1.88281	−	1.88281i
$455$	−667.013	−	434.160i	−1.46596	−	0.954199i
$456$		−	865.592i		−	1.89823i
$457$	312.552	−	312.552i	0.683921	−	0.683921i	−0.276960	−	0.960881i	$-0.589327\pi$
$457$	312.552	−	312.552i	0.683921	−	0.683921i	0.960881	+	0.276960i	$0.0893271\pi$
$458$	−511.208	+	511.208i	−1.11618	+	1.11618i
$459$			7.08548i			0.0154368i
$460$	90.5889			0.196932
$461$			286.451i			0.621369i	0.950513	+	0.310684i	$0.100558\pi$
$461$			286.451i			0.621369i	−0.950513	+	0.310684i	$0.899442\pi$
$462$	1958.16	−	414.069i	4.23844	−	0.896254i
$463$	164.428	+	164.428i	0.355136	+	0.355136i	0.862016	−	0.506881i	$-0.169201\pi$
$463$	164.428	+	164.428i	0.355136	+	0.355136i	−0.506881	+	0.862016i	$0.669201\pi$
$464$	805.053	+	805.053i	1.73503	+	1.73503i
$465$	683.744	+	683.744i	1.47042	+	1.47042i
$466$	339.651	−	339.651i	0.728864	−	0.728864i
$467$		−	76.2876i		−	0.163357i	−0.996659	−	0.0816783i	$-0.973972\pi$
$467$		−	76.2876i		−	0.163357i	0.996659	−	0.0816783i	$-0.0260280\pi$
$468$	1009.78	+	1009.78i	2.15766	+	2.15766i
$469$	−552.743	−	359.782i	−1.17856	−	0.767126i
$470$	403.747	−	403.747i	0.859037	−	0.859037i
$471$			195.272i			0.414591i
$472$	1275.84			2.70304
$473$	−788.725	+	788.725i	−1.66749	+	1.66749i
$474$			1237.79i			2.61138i
$475$	181.651	+	181.651i	0.382423	+	0.382423i
$476$	129.129	−	198.385i	0.271280	−	0.416775i
$477$	426.579	−	426.579i	0.894296	−	0.894296i
$478$	90.0063	−	90.0063i	0.188298	−	0.188298i
$479$	−318.637	+	318.637i	−0.665214	+	0.665214i	−0.956604	−	0.291390i	$-0.905882\pi$
$479$	−318.637	+	318.637i	−0.665214	+	0.665214i	0.291390	+	0.956604i	$0.405882\pi$
$480$	−1053.91	−	1053.91i	−2.19565	−	2.19565i
$481$	759.368	−	759.368i	1.57873	−	1.57873i
$482$		−	1528.44i		−	3.17105i
$483$	−34.1837	−	22.2503i	−0.0707738	−	0.0460668i
$484$		−	1968.94i		−	4.06806i
$485$	245.878	+	245.878i	0.506964	+	0.506964i
$486$	899.054	+	899.054i	1.84991	+	1.84991i
$487$			540.300i			1.10945i	0.832035	+	0.554723i	$0.187176\pi$
$487$			540.300i			1.10945i	−0.832035	+	0.554723i	$0.812824\pi$
$488$			1057.22i			2.16643i
$489$	711.315	−	711.315i	1.45463	−	1.45463i
$490$	−515.348	−	1164.07i	−1.05173	−	2.37565i
$491$	476.130			0.969714			0.484857	−	0.874593i	$-0.338872\pi$
$491$	476.130			0.969714			0.484857	+	0.874593i	$0.338872\pi$
$492$	−1548.57	+	595.100i	−3.14750	+	1.20955i
$493$			116.719i			0.236753i
$494$		−	596.098i		−	1.20668i
$495$	861.888	−	861.888i	1.74119	−	1.74119i
$496$			1111.37i			2.24066i
$497$	133.040	−	204.393i	0.267686	−	0.411253i
$498$	181.708	−	181.708i	0.364876	−	0.364876i
$499$	−254.392	−	254.392i	−0.509804	−	0.509804i	0.404662	−	0.914466i	$-0.367389\pi$
$499$	−254.392	−	254.392i	−0.509804	−	0.509804i	−0.914466	+	0.404662i	$0.867389\pi$
$500$	20.3890			0.0407780
$501$			664.721i			1.32679i
$502$		−	539.600i		−	1.07490i
$503$	194.183	−	194.183i	0.386050	−	0.386050i	−0.487226	−	0.873276i	$-0.661991\pi$
$503$	194.183	−	194.183i	0.386050	−	0.386050i	0.873276	+	0.487226i	$0.161991\pi$
$504$	271.861	+	1285.65i	0.539407	+	2.55089i
$505$	139.365	+	139.365i	0.275971	+	0.275971i
$506$	−63.8183	+	63.8183i	−0.126123	+	0.126123i
$507$	267.233	+	267.233i	0.527087	+	0.527087i
$508$	−617.616			−1.21578
$509$	−309.403	−	309.403i	−0.607864	−	0.607864i	0.334524	−	0.942387i	$-0.391425\pi$
$509$	−309.403	−	309.403i	−0.607864	−	0.607864i	−0.942387	+	0.334524i	$0.891425\pi$
$510$		−	400.794i		−	0.785870i
$511$	156.548	+	740.326i	0.306357	+	1.44878i
$512$			1067.22i			2.08442i
$513$			20.0330i			0.0390506i
$514$	−1144.23	−	1144.23i	−2.22613	−	2.22613i
$515$	185.531			0.360255
$516$	−1756.64	−	1756.64i	−3.40434	−	3.40434i
$517$			399.280i			0.772302i
$518$	1680.63	−	355.384i	3.24446	−	0.686069i
$519$	−638.916	+	638.916i	−1.23105	+	1.23105i
$520$	−1595.48	−	1595.48i	−3.06822	−	3.06822i
$521$	−279.710	+	279.710i	−0.536871	+	0.536871i	−0.922609	−	0.385737i	$-0.873947\pi$
$521$	−279.710	+	279.710i	−0.536871	+	0.536871i	0.385737	+	0.922609i	$0.373947\pi$
$522$	−796.455	−	796.455i	−1.52578	−	1.52578i
$523$		−	199.643i		−	0.381726i	−0.981617	−	0.190863i	$-0.938871\pi$
$523$		−	199.643i		−	0.381726i	0.981617	−	0.190863i	$-0.0611286\pi$
$524$	−2018.57			−3.85222
$525$	−637.839	−	415.171i	−1.21493	−	0.790801i
$526$	−195.234	−	195.234i	−0.371168	−	0.371168i
$527$	−80.5648	+	80.5648i	−0.152874	+	0.152874i
$528$	2733.82			5.17770
$529$	−527.161			−0.996523
$530$	−1171.62	+	1171.62i	−2.21061	+	2.21061i
$531$	−608.121			−1.14524
$532$	365.090	−	560.899i	0.686260	−	1.05432i
$533$	−613.492	+	235.759i	−1.15102	+	0.442324i
$534$	−63.7974			−0.119471
$535$	406.477			0.759769
$536$	−1322.15	−	1322.15i	−2.46669	−	2.46669i
$537$			620.772i			1.15600i
$538$	−191.956			−0.356796
$539$	830.418	+	320.771i	1.54066	+	0.595123i
$540$	93.2060	+	93.2060i	0.172604	+	0.172604i
$541$			149.305i			0.275980i	0.990434	+	0.137990i	$0.0440642\pi$
$541$			149.305i			0.275980i	−0.990434	+	0.137990i	$0.955936\pi$
$542$	633.292			1.16844
$543$	866.166			1.59515
$544$	124.181	−	124.181i	0.228274	−	0.228274i
$545$	−738.417	+	738.417i	−1.35489	+	1.35489i
$546$	365.349	+	1727.76i	0.669137	+	3.16439i
$547$	−107.586	+	107.586i	−0.196683	+	0.196683i	−0.798577	−	0.601893i	$-0.794413\pi$
$547$	−107.586	+	107.586i	−0.196683	+	0.196683i	0.601893	+	0.798577i	$0.294413\pi$
$548$	954.870	−	954.870i	1.74246	−	1.74246i
$549$		−	503.919i		−	0.917885i
$550$	−1190.79	+	1190.79i	−2.16508	+	2.16508i
$551$			330.004i			0.598918i
$552$	−81.7665	−	81.7665i	−0.148128	−	0.148128i
$553$	−300.337	+	461.416i	−0.543104	+	0.834387i
$554$			718.874i			1.29761i
$555$	1443.55	−	1443.55i	2.60099	−	2.60099i
$556$		−	677.746i		−	1.21897i
$557$	−226.774	+	226.774i	−0.407135	+	0.407135i	−0.880738	−	0.473603i	$-0.842953\pi$
$557$	−226.774	+	226.774i	−0.407135	+	0.407135i	0.473603	+	0.880738i	$0.342953\pi$
$558$		−	1099.50i		−	1.97042i
$559$	−695.921	−	695.921i	−1.24494	−	1.24494i
$560$	−359.744	−	1701.25i	−0.642400	−	3.03795i
$561$	198.180	+	198.180i	0.353261	+	0.353261i
$562$	81.2948	+	81.2948i	0.144653	+	0.144653i
$563$	243.984	−	243.984i	0.433364	−	0.433364i	−0.456407	−	0.889771i	$-0.650864\pi$
$563$	243.984	−	243.984i	0.433364	−	0.433364i	0.889771	+	0.456407i	$0.150864\pi$
$564$	−889.272			−1.57672
$565$	−98.1935			−0.173794
$566$	−1261.45			−2.22871
$567$	111.011	+	524.979i	0.195787	+	0.925888i
$568$	488.901	−	488.901i	0.860742	−	0.860742i
$569$			406.254i			0.713979i	0.934108	+	0.356990i	$0.116197\pi$
$569$			406.254i			0.713979i	−0.934108	+	0.356990i	$0.883803\pi$
$570$		−	1133.17i		−	1.98803i
$571$	106.781	+	106.781i	0.187008	+	0.187008i	0.794401	−	0.607393i	$-0.207785\pi$
$571$	106.781	+	106.781i	0.187008	+	0.187008i	−0.607393	+	0.794401i	$0.707785\pi$
$572$	2742.74			4.79500
$573$		−	211.963i		−	0.369919i
$574$	−1028.17	−	219.274i	−1.79123	−	0.382011i
$575$	34.3186			0.0596845
$576$			369.545i			0.641572i
$577$	−464.850	+	464.850i	−0.805633	+	0.805633i	−0.983970	−	0.178337i	$-0.942928\pi$
$577$	−464.850	+	464.850i	−0.805633	+	0.805633i	0.178337	+	0.983970i	$0.442928\pi$
$578$	−1011.39			−1.74981
$579$	860.711			1.48655
$580$	1535.39	+	1535.39i	2.64722	+	2.64722i
$581$	111.825	−	23.6464i	0.192470	−	0.0406995i
$582$		−	771.570i		−	1.32572i
$583$		−	1158.66i		−	1.98741i
$584$			2145.30i			3.67345i
$585$	760.476	+	760.476i	1.29996	+	1.29996i
$586$	−404.619	+	404.619i	−0.690477	+	0.690477i
$587$	−564.714	+	564.714i	−0.962034	+	0.962034i	−0.999305	−	0.0372709i	$-0.988134\pi$
$587$	−564.714	+	564.714i	−0.962034	+	0.962034i	0.0372709	+	0.999305i	$0.488134\pi$
$588$	−714.418	+	1849.50i	−1.21500	+	3.14540i
$589$	−227.783	+	227.783i	−0.386728	+	0.386728i
$590$	1670.24			2.83091
$591$	−426.816	−	426.816i	−0.722193	−	0.722193i
$592$	2346.36			3.96345
$593$	−249.741	−	249.741i	−0.421149	−	0.421149i	0.464450	−	0.885599i	$-0.346252\pi$
$593$	−249.741	−	249.741i	−0.421149	−	0.421149i	−0.885599	+	0.464450i	$0.846252\pi$
$594$	−131.324			−0.221084
$595$	97.2482	−	149.405i	0.163442	−	0.251101i
$596$	−156.039	+	156.039i	−0.261810	+	0.261810i
$597$	−1157.45			−1.93878
$598$	−56.3092	−	56.3092i	−0.0941626	−	0.0941626i
$599$	−640.487			−1.06926			−0.534631	−	0.845086i	$-0.679549\pi$
$599$	−640.487			−1.06926			−0.534631	+	0.845086i	$0.679549\pi$
$600$	−1525.69	−	1525.69i	−2.54282	−	2.54282i
$601$	371.946	+	371.946i	0.618879	+	0.618879i	0.945244	−	0.326365i	$-0.105824\pi$
$601$	371.946	+	371.946i	0.618879	+	0.618879i	−0.326365	+	0.945244i	$0.605824\pi$
$602$	−325.691	−	1540.21i	−0.541015	−	2.55849i
$603$	630.195	+	630.195i	1.04510	+	1.04510i
$604$	185.879	+	185.879i	0.307746	+	0.307746i
$605$		−	1482.82i		−	2.45095i
$606$		−	437.332i		−	0.721669i
$607$	−369.079			−0.608037			−0.304019	−	0.952666i	$-0.598329\pi$
$607$	−369.079			−0.608037			−0.304019	+	0.952666i	$0.598329\pi$
$608$	351.101	−	351.101i	0.577469	−	0.577469i
$609$	−202.260	−	956.497i	−0.332117	−	1.57060i
$610$			1384.04i			2.26892i
$611$	−352.300			−0.576595
$612$	−226.183	+	226.183i	−0.369580	+	0.369580i
$613$		−	174.335i		−	0.284397i	−0.989838	−	0.142198i	$-0.954583\pi$
$613$		−	174.335i		−	0.284397i	0.989838	−	0.142198i	$-0.0454171\pi$
$614$			1429.08i			2.32749i
$615$	−1166.24	+	448.174i	−1.89632	+	0.728739i
$616$	2115.23	+	1376.81i	3.43381	+	2.23507i
$617$		−	98.7411i		−	0.160034i	−0.996793	−	0.0800171i	$-0.974503\pi$
$617$		−	98.7411i		−	0.160034i	0.996793	−	0.0800171i	$-0.0254975\pi$
$618$	−291.101	−	291.101i	−0.471037	−	0.471037i
$619$		−	1184.97i		−	1.91433i	−0.289541	−	0.957166i	$-0.593503\pi$
$619$		−	1184.97i		−	1.91433i	0.289541	−	0.957166i	$-0.406497\pi$
$620$			2119.58i			3.41868i
$621$	1.89237	+	1.89237i	0.00304730	+	0.00304730i
$622$	1525.87	−	1525.87i	2.45317	−	2.45317i
$623$	−23.7819	−	15.4797i	−0.0381733	−	0.0248471i
$624$			2412.15i			3.86563i
$625$	−617.276			−0.987641
$626$	881.536	−	881.536i	1.40820	−	1.40820i
$627$	560.319	+	560.319i	0.893650	+	0.893650i
$628$	−302.669	+	302.669i	−0.481957	+	0.481957i
$629$	170.092	+	170.092i	0.270416	+	0.270416i
$630$	355.902	+	1683.08i	0.564924	+	2.67156i
$631$	77.7274			0.123181			0.0615906	−	0.998101i	$-0.480383\pi$
$631$	77.7274			0.123181			0.0615906	+	0.998101i	$0.480383\pi$
$632$	−1103.69	+	1103.69i	−1.74635	+	1.74635i
$633$			221.129i			0.349334i
$634$	184.085	−	184.085i	0.290354	−	0.290354i
$635$	−465.131			−0.732490
$636$	2580.55			4.05747
$637$	−283.029	+	732.709i	−0.444315	+	1.15025i
$638$	−2163.31			−3.39076
$639$	−233.033	+	233.033i	−0.364683	+	0.364683i
$640$			372.647i			0.582261i
$641$	51.8782	−	51.8782i	0.0809332	−	0.0809332i	−0.665481	−	0.746415i	$-0.731774\pi$
$641$	51.8782	−	51.8782i	0.0809332	−	0.0809332i	0.746415	+	0.665481i	$0.231774\pi$
$642$	−637.767	−	637.767i	−0.993407	−	0.993407i
$643$	−692.229	+	692.229i	−1.07656	+	1.07656i	−0.0797469	+	0.996815i	$0.525411\pi$
$643$	−692.229	+	692.229i	−1.07656	+	1.07656i	−0.996815	+	0.0797469i	$0.974589\pi$
$644$	−18.4966	−	87.4717i	−0.0287215	−	0.135826i
$645$	−1322.94	−	1322.94i	−2.05107	−	2.05107i
$646$	133.521			0.206689
$647$	−534.403			−0.825971			−0.412985	−	0.910738i	$-0.635514\pi$
$647$	−534.403			−0.825971			−0.412985	+	0.910738i	$0.635514\pi$
$648$			1521.27i			2.34764i
$649$	−825.879	+	825.879i	−1.27254	+	1.27254i
$650$	−1050.68	−	1050.68i	−1.61643	−	1.61643i
$651$	520.608	−	799.824i	0.799704	−	1.22861i
$652$	2205.05			3.38198
$653$	473.656	+	473.656i	0.725354	+	0.725354i	0.969690	−	0.244337i	$-0.0785702\pi$
$653$	473.656	+	473.656i	0.725354	+	0.725354i	−0.244337	+	0.969690i	$0.578570\pi$
$654$	2317.17			3.54308
$655$	−1520.20			−2.32091
$656$	−1312.04	−	583.576i	−2.00007	−	0.889598i
$657$		−	1022.55i		−	1.55639i
$658$	−472.292	−	307.416i	−0.717769	−	0.467198i
$659$	206.382	+	206.382i	0.313175	+	0.313175i	0.846138	−	0.532963i	$-0.178922\pi$
$659$	206.382	+	206.382i	0.313175	+	0.313175i	−0.532963	+	0.846138i	$0.678922\pi$
$660$	5213.91			7.89987
$661$	−758.294			−1.14719			−0.573596	−	0.819138i	$-0.694452\pi$
$661$	−758.294			−1.14719			−0.573596	+	0.819138i	$0.694452\pi$
$662$	1330.87	−	1330.87i	2.01038	−	2.01038i
$663$	−174.861	+	174.861i	−0.263743	+	0.263743i
$664$	324.044			0.488019
$665$	274.952	−	422.417i	0.413462	−	0.635214i
$666$	−2321.30			−3.48544
$667$	31.1732	+	31.1732i	0.0467364	+	0.0467364i
$668$	−1030.31	+	1030.31i	−1.54237	+	1.54237i
$669$	−21.4191	−	21.4191i	−0.0320166	−	0.0320166i
$670$	−1730.86	−	1730.86i	−2.58338	−	2.58338i
$671$	−684.363	−	684.363i	−1.01992	−	1.01992i
$672$	−802.456	+	1232.84i	−1.19413	+	1.83458i
$673$	454.029	−	454.029i	0.674634	−	0.674634i	−0.284147	−	0.958781i	$-0.591710\pi$
$673$	454.029	−	454.029i	0.674634	−	0.674634i	0.958781	+	0.284147i	$0.0917103\pi$
$674$	−1716.52			−2.54677
$675$	35.3101	+	35.3101i	0.0523112	+	0.0523112i
$676$			828.414i			1.22546i
$677$	1195.22			1.76546			0.882731	−	0.469879i	$-0.155703\pi$
$677$	1195.22			1.76546			0.882731	+	0.469879i	$0.155703\pi$
$678$	154.067	+	154.067i	0.227237	+	0.227237i
$679$	187.213	−	287.621i	0.275719	−	0.423594i
$680$	357.373	−	357.373i	0.525548	−	0.525548i
$681$	−1417.90			−2.08208
$682$	−1493.21	−	1493.21i	−2.18945	−	2.18945i
$683$	501.798	−	501.798i	0.734697	−	0.734697i	−0.236850	−	0.971546i	$-0.576115\pi$
$683$	501.798	−	501.798i	0.734697	−	0.734697i	0.971546	+	0.236850i	$0.0761149\pi$
$684$	−639.493	+	639.493i	−0.934931	+	0.934931i
$685$	719.120	−	719.120i	1.04981	−	1.04981i
$686$	−1018.79	+	735.297i	−1.48511	+	1.07186i
$687$	847.969			1.23431
$688$		−	2150.32i		−	3.12546i
$689$	1022.33			1.48379
$690$	−107.043	−	107.043i	−0.155135	−	0.155135i
$691$	2.03631	+	2.03631i	0.00294690	+	0.00294690i	0.708579	−	0.705632i	$-0.249337\pi$
$691$	2.03631	+	2.03631i	0.00294690	+	0.00294690i	−0.705632	+	0.708579i	$0.749337\pi$
$692$	−1980.62			−2.86216
$693$	−1008.21	−	656.248i	−1.45485	−	0.946967i
$694$	91.0056	+	91.0056i	0.131132	+	0.131132i
$695$		−	510.416i		−	0.734411i
$696$		−	2771.71i		−	3.98234i
$697$	−52.8079	−	137.417i	−0.0757646	−	0.197155i
$698$		−	1900.55i		−	2.72285i
$699$	−563.397			−0.806004
$700$	−345.131	−	1632.15i	−0.493045	−	2.33164i
$701$	553.402			0.789446			0.394723	−	0.918800i	$-0.370840\pi$
$701$	553.402			0.789446			0.394723	+	0.918800i	$0.370840\pi$
$702$		−	115.872i		−	0.165060i
$703$	480.905	+	480.905i	0.684075	+	0.684075i
$704$	501.873	+	501.873i	0.712888	+	0.712888i
$705$	−669.718			−0.949954
$706$	471.609			0.668001
$707$	106.114	−	163.025i	0.150090	−	0.230588i
$708$	−1839.39	−	1839.39i	−2.59800	−	2.59800i
$709$	982.833	+	982.833i	1.38622	+	1.38622i	0.833096	+	0.553129i	$0.186566\pi$
$709$	982.833	+	982.833i	1.38622	+	1.38622i	0.553129	+	0.833096i	$0.313434\pi$
$710$	640.037	−	640.037i	0.901460	−	0.901460i
$711$	526.070	−	526.070i	0.739902	−	0.739902i
$712$	−56.8857	−	56.8857i	−0.0798957	−	0.0798957i
$713$			43.0342i			0.0603565i
$714$	−387.002	+	81.8350i	−0.542020	+	0.114615i
$715$	2065.58			2.88892
$716$	−962.186	+	962.186i	−1.34384	+	1.34384i
$717$	−149.298			−0.208226
$718$		−	878.023i		−	1.22287i
$719$	−149.529	−	149.529i	−0.207968	−	0.207968i	0.595435	−	0.803403i	$-0.296980\pi$
$719$	−149.529	−	149.529i	−0.207968	−	0.207968i	−0.803403	+	0.595435i	$0.796980\pi$
$720$			2349.79i			3.26359i
$721$	−37.8822	−	179.147i	−0.0525412	−	0.248470i
$722$	−944.848			−1.30865
$723$	−1267.66	+	1267.66i	−1.75333	+	1.75333i
$724$	1342.54	+	1342.54i	1.85434	+	1.85434i
$725$	581.664	+	581.664i	0.802295	+	0.802295i
$726$	−2326.57	+	2326.57i	−3.20464	+	3.20464i
$727$	−423.310	+	423.310i	−0.582270	+	0.582270i	−0.935527	−	0.353256i	$-0.885074\pi$
$727$	−423.310	+	423.310i	−0.582270	+	0.582270i	0.353256	+	0.935527i	$0.385074\pi$
$728$	−1214.81	+	1866.34i	−1.66869	+	2.56366i
$729$		−	801.411i		−	1.09933i
$730$			2808.48i			3.84723i
$731$	155.880	−	155.880i	0.213243	−	0.213243i
$732$	1524.21	−	1524.21i	2.08225	−	2.08225i
$733$	1107.13			1.51041			0.755204	−	0.655489i	$-0.227538\pi$
$733$	1107.13			1.51041			0.755204	+	0.655489i	$0.227538\pi$
$734$			2133.85i			2.90715i
$735$	−538.034	+	1392.87i	−0.732019	+	1.89506i
$736$		−	66.3322i		−	0.0901252i
$737$	1711.71			2.32254
$738$	1298.03	+	577.344i	1.75885	+	0.782309i
$739$	−523.414			−0.708273			−0.354137	−	0.935194i	$-0.615225\pi$
$739$	−523.414			−0.708273			−0.354137	+	0.935194i	$0.615225\pi$
$740$	4474.95			6.04723
$741$	−494.390	+	494.390i	−0.667193	+	0.667193i
$742$	1370.53	+	892.082i	1.84708	+	1.20227i
$743$			434.057i			0.584196i	0.956388	+	0.292098i	$0.0943533\pi$
$743$			434.057i			0.584196i	−0.956388	+	0.292098i	$0.905647\pi$
$744$	1913.16	−	1913.16i	2.57145	−	2.57145i
$745$	−117.514	+	117.514i	−0.157737	+	0.157737i
$746$		−	145.312i		−	0.194788i
$747$	−154.454			−0.206766
$748$			614.350i			0.821324i
$749$	−82.9953	−	392.490i	−0.110808	−	0.524018i
$750$	−24.0924	−	24.0924i	−0.0321232	−	0.0321232i
$751$	−648.991	−	648.991i	−0.864169	−	0.864169i	0.127650	−	0.991819i	$-0.459256\pi$
$751$	−648.991	−	648.991i	−0.864169	−	0.864169i	−0.991819	+	0.127650i	$0.959256\pi$
$752$	−544.283	−	544.283i	−0.723781	−	0.723781i
$753$	−447.532	+	447.532i	−0.594332	+	0.594332i
$754$		−	1908.77i		−	2.53152i
$755$	139.987	+	139.987i	0.185413	+	0.185413i
$756$	70.9678	−	109.030i	0.0938727	−	0.144219i
$757$	−748.308	+	748.308i	−0.988518	+	0.988518i	−0.999935	−	0.0114172i	$-0.996366\pi$
$757$	−748.308	+	748.308i	−0.988518	+	0.988518i	0.0114172	+	0.999935i	$0.496366\pi$
$758$		−	2495.02i		−	3.29158i
$759$	105.859			0.139471
$760$	1010.41	−	1010.41i	1.32949	−	1.32949i
$761$		−	893.923i		−	1.17467i	−0.809344	−	0.587334i	$-0.800177\pi$
$761$		−	893.923i		−	1.17467i	0.809344	−	0.587334i	$-0.199823\pi$
$762$	729.797	+	729.797i	0.957739	+	0.957739i
$763$	863.779	+	562.236i	1.13208	+	0.736875i
$764$	328.540	−	328.540i	0.430026	−	0.430026i
$765$	−170.340	+	170.340i	−0.222667	+	0.222667i
$766$	42.8785	−	42.8785i	0.0559771	−	0.0559771i
$767$	−728.704	−	728.704i	−0.950070	−	0.950070i
$768$	1059.43	−	1059.43i	1.37947	−	1.37947i
$769$			1095.01i			1.42394i	0.702210	+	0.711970i	$0.252197\pi$
$769$			1095.01i			1.42394i	−0.702210	+	0.711970i	$0.747803\pi$
$770$	2769.11	+	1802.42i	3.59625	+	2.34081i
$771$			1898.00i			2.46174i
$772$	1334.09	+	1334.09i	1.72809	+	1.72809i
$773$	−1006.47	−	1006.47i	−1.30203	−	1.30203i	−0.927023	−	0.375004i	$-0.877641\pi$
$773$	−1006.47	−	1006.47i	−1.30203	−	1.30203i	−0.375004	−	0.927023i	$-0.622359\pi$
$774$			2127.35i			2.74852i
$775$			802.980i			1.03610i
$776$	687.980	−	687.980i	0.886572	−	0.886572i
$777$	−1688.62	−	1099.13i	−2.17326	−	1.41458i
$778$	−2359.05			−3.03220
$779$	−149.305	−	388.522i	−0.191663	−	0.498745i
$780$			4600.43i			5.89799i
$781$			632.955i			0.810442i
$782$	12.6128	−	12.6128i	0.0161289	−	0.0161289i
$783$			64.1475i			0.0819253i
$784$	−1569.26	+	694.731i	−2.00160	+	0.886136i
$785$	−227.942	+	227.942i	−0.290372	+	0.290372i
$786$	2385.21	+	2385.21i	3.03462	+	3.03462i
$787$	118.790			0.150940			0.0754698	−	0.997148i	$-0.475954\pi$
$787$	118.790			0.150940			0.0754698	+	0.997148i	$0.475954\pi$
$788$		−	1323.12i		−	1.67908i
$789$			323.846i			0.410451i
$790$	−1444.88	+	1444.88i	−1.82896	+	1.82896i
$791$	20.0494	+	94.8146i	0.0253469	+	0.119867i
$792$	−2411.61	−	2411.61i	−3.04497	−	3.04497i
$793$	603.839	−	603.839i	0.761462	−	0.761462i
$794$	−210.746	−	210.746i	−0.265424	−	0.265424i
$795$	1943.43			2.44457
$796$	−1794.03	−	1794.03i	−2.25381	−	2.25381i
$797$		−	958.713i		−	1.20290i	−0.798910	−	0.601451i	$-0.794590\pi$
$797$		−	958.713i		−	1.20290i	0.798910	−	0.601451i	$-0.205410\pi$
$798$	−1094.18	+	231.374i	−1.37116	+	0.289943i
$799$		−	78.9121i		−	0.0987636i
$800$		−	1237.70i		−	1.54713i
$801$	27.1143	+	27.1143i	0.0338506	+	0.0338506i
$802$	999.536			1.24630
$803$	−1388.70	−	1388.70i	−1.72939	−	1.72939i
$804$			3812.31i			4.74168i
$805$	−13.9300	−	65.8756i	−0.0173043	−	0.0818331i
$806$	1317.51	−	1317.51i	1.63463	−	1.63463i
$807$	159.204	+	159.204i	0.197279	+	0.197279i
$808$	389.952	−	389.952i	0.482614	−	0.482614i
$809$	1059.97	+	1059.97i	1.31022	+	1.31022i	0.921252	+	0.388967i	$0.127168\pi$
$809$	1059.97	+	1059.97i	1.31022	+	1.31022i	0.388967	+	0.921252i	$0.372832\pi$
$810$			1991.54i			2.45870i
$811$	702.870			0.866671			0.433335	−	0.901233i	$-0.357337\pi$
$811$	702.870			0.866671			0.433335	+	0.901233i	$0.357337\pi$
$812$	1169.06	−	1796.05i	1.43972	−	2.21189i
$813$	−525.238	−	525.238i	−0.646049	−	0.646049i
$814$	−3152.52	+	3152.52i	−3.87288	+	3.87288i
$815$	1660.64			2.03760
$816$	−540.302			−0.662135
$817$	440.725	−	440.725i	0.539443	−	0.539443i
$818$	2499.92			3.05614
$819$	579.032	−	889.583i	0.706999	−	1.08618i
$820$	−2502.31	−	1112.99i	−3.05160	−	1.35730i
$821$	−812.015			−0.989056			−0.494528	−	0.869162i	$-0.664659\pi$
$821$	−812.015			−0.989056			−0.494528	+	0.869162i	$0.664659\pi$
$822$	−2256.62			−2.74528
$823$	276.645	+	276.645i	0.336142	+	0.336142i	0.854913	−	0.518771i	$-0.173610\pi$
$823$	276.645	+	276.645i	0.336142	+	0.336142i	−0.518771	+	0.854913i	$0.673610\pi$
$824$		−	519.128i		−	0.630009i
$825$	1975.23			2.39422
$826$	−341.033	−	1612.76i	−0.412873	−	1.95250i
$827$	553.860	+	553.860i	0.669722	+	0.669722i	0.957652	−	0.287929i	$-0.0929668\pi$
$827$	553.860	+	553.860i	0.669722	+	0.669722i	−0.287929	+	0.957652i	$0.592967\pi$
$828$			120.817i			0.145914i
$829$	330.699			0.398914			0.199457	−	0.979907i	$-0.436082\pi$
$829$	330.699			0.398914			0.199457	+	0.979907i	$0.436082\pi$
$830$	424.217			0.511105
$831$	596.217	−	596.217i	0.717470	−	0.717470i
$832$	−442.821	+	442.821i	−0.532237	+	0.532237i
$833$	−164.120	−	63.3960i	−0.197023	−	0.0761056i
$834$	−800.849	+	800.849i	−0.960250	+	0.960250i
$835$	−775.931	+	775.931i	−0.929259	+	0.929259i
$836$			1736.97i			2.07771i
$837$	−44.2774	+	44.2774i	−0.0529001	+	0.0529001i
$838$		−	66.8870i		−	0.0798174i
$839$	−209.798	−	209.798i	−0.250058	−	0.250058i	0.570936	−	0.820994i	$-0.306580\pi$
$839$	−209.798	−	209.798i	−0.250058	−	0.250058i	−0.820994	+	0.570936i	$0.806580\pi$
$840$	−2309.33	+	3547.89i	−2.74921	+	4.22368i
$841$			215.705i			0.256486i
$842$	−160.121	+	160.121i	−0.190168	+	0.190168i
$843$		−	134.848i		−	0.159962i
$844$	−342.745	+	342.745i	−0.406096	+	0.406096i
$845$			623.885i			0.738325i
$846$	538.471	+	538.471i	0.636490	+	0.636490i
$847$	−1431.80	+	302.766i	−1.69044	+	0.357457i
$848$	1579.44	+	1579.44i	1.86255	+	1.86255i
$849$	1046.22	+	1046.22i	1.23229	+	1.23229i
$850$	235.344	−	235.344i	0.276875	−	0.276875i
$851$	90.8555			0.106763
$852$	−1409.71			−1.65459
$853$	−188.527			−0.221016			−0.110508	−	0.993875i	$-0.535248\pi$
$853$	−188.527			−0.221016			−0.110508	+	0.993875i	$0.535248\pi$
$854$	1336.42	−	282.596i	1.56489	−	0.330909i
$855$	−481.607	+	481.607i	−0.563283	+	0.563283i
$856$		−	1137.35i		−	1.32868i
$857$			705.739i			0.823500i	0.911297	+	0.411750i	$0.135082\pi$
$857$			705.739i			0.823500i	−0.911297	+	0.411750i	$0.864918\pi$
$858$	−3240.92	−	3240.92i	−3.77730	−	3.77730i
$859$	95.9665			0.111719			0.0558595	−	0.998439i	$-0.482210\pi$
$859$	95.9665			0.111719			0.0558595	+	0.998439i	$0.482210\pi$
$860$		−	4101.06i		−	4.76868i
$861$	670.878	+	1034.60i	0.779185	+	1.20163i
$862$	319.716			0.370900
$863$			201.280i			0.233233i	0.993177	+	0.116617i	$0.0372049\pi$
$863$			201.280i			0.233233i	−0.993177	+	0.116617i	$0.962795\pi$
$864$	68.2485	−	68.2485i	0.0789913	−	0.0789913i
$865$	−1491.62			−1.72441
$866$	−392.675			−0.453435
$867$	838.824	+	838.824i	0.967502	+	0.967502i
$868$	2046.65	−	432.781i	2.35789	−	0.498596i
$869$		−	1428.89i		−	1.64430i
$870$		−	3628.54i		−	4.17073i
$871$			1510.31i			1.73399i
$872$	2066.13	+	2066.13i	2.36942	+	2.36942i
$873$	−327.922	+	327.922i	−0.375627	+	0.375627i
$874$	35.6605	−	35.6605i	0.0408014	−	0.0408014i
$875$	−3.13524	−	14.8267i	−0.00358313	−	0.0169449i
$876$	3092.90	−	3092.90i	3.53071	−	3.53071i
$877$	−205.575			−0.234407			−0.117204	−	0.993108i	$-0.537393\pi$
$877$	−205.575			−0.234407			−0.117204	+	0.993108i	$0.537393\pi$
$878$	−606.127	−	606.127i	−0.690350	−	0.690350i
$879$	671.164			0.763554
$880$	3191.20	+	3191.20i	3.62637	+	3.62637i
$881$	793.334			0.900492			0.450246	−	0.892905i	$-0.351336\pi$
$881$	793.334			0.900492			0.450246	+	0.892905i	$0.351336\pi$
$882$	1552.50	−	687.311i	1.76020	−	0.779264i
$883$	1027.75	−	1027.75i	1.16393	−	1.16393i	0.180326	−	0.983607i	$-0.442285\pi$
$883$	1027.75	−	1027.75i	1.16393	−	1.16393i	0.983607	−	0.180326i	$-0.0577153\pi$
$884$	−542.064			−0.613195
$885$	−1385.26	−	1385.26i	−1.56526	−	1.56526i
$886$	−1677.01			−1.89279
$887$	245.276	+	245.276i	0.276523	+	0.276523i	0.831719	−	0.555196i	$-0.187357\pi$
$887$	245.276	+	245.276i	0.276523	+	0.276523i	−0.555196	+	0.831719i	$0.687357\pi$
$888$	−4039.13	−	4039.13i	−4.54858	−	4.54858i
$889$	94.9716	+	449.126i	0.106830	+	0.505204i
$890$	−74.4710	−	74.4710i	−0.0836752	−	0.0836752i
$891$	−984.754	−	984.754i	−1.10522	−	1.10522i
$892$		−	66.3985i		−	0.0744377i
$893$		−	223.110i		−	0.249844i
$894$	368.762			0.412485
$895$	−724.630	+	724.630i	−0.809642	+	0.809642i
$896$	359.824	−	76.0878i	0.401589	−	0.0849195i
$897$			93.4032i			0.104128i
$898$	978.900			1.09009
$899$	−729.384	+	729.384i	−0.811328	+	0.811328i
$900$			2254.34i			2.50482i
$901$			228.993i			0.254154i
$902$	2546.92	−	978.754i	2.82363	−	1.08509i
$903$	−1007.29	+	1547.54i	−1.11550	+	1.71377i
$904$			274.751i			0.303928i
$905$	1011.08	+	1011.08i	1.11721	+	1.11721i
$906$		−	439.282i		−	0.484859i
$907$		−	1618.46i		−	1.78441i	−0.451634	−	0.892203i	$-0.649159\pi$
$907$		−	1618.46i		−	1.78441i	0.451634	−	0.892203i	$-0.350841\pi$
$908$	−2197.72	−	2197.72i	−2.42039	−	2.42039i
$909$	−185.869	+	185.869i	−0.204476	+	0.204476i
$910$	−1590.34	+	2443.29i	−1.74763	+	2.68493i
$911$		−	1265.30i		−	1.38892i	−0.719533	−	0.694458i	$-0.755644\pi$
$911$		−	1265.30i		−	1.38892i	0.719533	−	0.694458i	$-0.244356\pi$
$912$	−1527.61			−1.67501
$913$	−209.762	+	209.762i	−0.229750	+	0.229750i
$914$	−1144.89	−	1144.89i	−1.25261	−	1.25261i
$915$	1147.89	−	1147.89i	1.25453	−	1.25453i
$916$	1314.34	+	1314.34i	1.43487	+	1.43487i
$917$	310.397	+	1467.89i	0.338492	+	1.60075i
$918$	25.9543			0.0282727
$919$	−168.031	+	168.031i	−0.182842	+	0.182842i	−0.792593	−	0.609751i	$-0.791269\pi$
$919$	−168.031	+	168.031i	−0.182842	+	0.182842i	0.609751	+	0.792593i	$0.291269\pi$
$920$		−	190.893i		−	0.207492i
$921$	1185.24	−	1185.24i	1.28691	−	1.28691i
$922$	1049.28			1.13805
$923$	−558.480			−0.605070
$924$	−1064.59	−	5034.50i	−1.15215	−	5.44859i
$925$	1695.28			1.83274
$926$	602.304	−	602.304i	0.650437	−	0.650437i
$927$			247.440i			0.266925i
$928$	1124.26	−	1124.26i	1.21149	−	1.21149i
$929$	571.700	+	571.700i	0.615393	+	0.615393i	0.944346	−	0.328953i	$-0.106696\pi$
$929$	571.700	+	571.700i	0.615393	+	0.615393i	−0.328953	+	0.944346i	$0.606696\pi$
$930$	2504.58	−	2504.58i	2.69309	−	2.69309i
$931$	−464.022	−	179.241i	−0.498412	−	0.192525i
$932$	−873.256	−	873.256i	−0.936970	−	0.936970i
$933$	−2531.05			−2.71281
$934$	−279.444			−0.299190
$935$			462.672i			0.494836i
$936$	2127.86	−	2127.86i	2.27335	−	2.27335i
$937$	218.711	+	218.711i	0.233416	+	0.233416i	0.814117	−	0.580701i	$-0.197221\pi$
$937$	218.711	+	218.711i	0.233416	+	0.233416i	−0.580701	+	0.814117i	$0.697221\pi$
$938$	−1317.89	+	2024.72i	−1.40500	+	2.15855i
$939$	−1462.25			−1.55724
$940$	−1038.05	−	1038.05i	−1.10431	−	1.10431i
$941$	321.081			0.341212			0.170606	−	0.985339i	$-0.445427\pi$
$941$	321.081			0.341212			0.170606	+	0.985339i	$0.445427\pi$
$942$	715.289			0.759330
$943$	−50.8048	−	22.5972i	−0.0538757	−	0.0239631i
$944$		−	2251.61i		−	2.38518i
$945$	53.4464	−	82.1112i	0.0565570	−	0.0868901i
$946$	2889.12	+	2889.12i	3.05404	+	3.05404i
$947$	−1611.51			−1.70170			−0.850850	−	0.525409i	$-0.823912\pi$
$947$	−1611.51			−1.70170			−0.850850	+	0.525409i	$0.823912\pi$
$948$	3182.41			3.35698
$949$	1225.30	−	1225.30i	1.29115	−	1.29115i
$950$	665.393	−	665.393i	0.700414	−	0.700414i
$951$	−305.351			−0.321084
$952$	−418.045	−	272.106i	−0.439122	−	0.285826i
$953$	919.465			0.964811			0.482406	−	0.875948i	$-0.339763\pi$
$953$	919.465			0.964811			0.482406	+	0.875948i	$0.339763\pi$
$954$	−1562.57	−	1562.57i	−1.63792	−	1.63792i
$955$	247.426	−	247.426i	0.259085	−	0.259085i
$956$	−231.410	−	231.410i	−0.242061	−	0.242061i
$957$	1794.20	+	1794.20i	1.87481	+	1.87481i
$958$	1167.18	+	1167.18i	1.21835	+	1.21835i
$959$	−841.207	−	547.543i	−0.877171	−	0.570953i
$960$	−841.798	+	841.798i	−0.876873	+	0.876873i
$961$	−45.9047			−0.0477677
$962$	−2781.59	−	2781.59i	−2.89146	−	2.89146i
$963$			542.111i			0.562939i
$964$	−3929.69			−4.07644
$965$	1004.71	+	1004.71i	1.04115	+	1.04115i
$966$	−81.5035	+	125.216i	−0.0843721	+	0.129623i
$967$	622.594	−	622.594i	0.643841	−	0.643841i	−0.307657	−	0.951497i	$-0.599545\pi$
$967$	622.594	−	622.594i	0.643841	−	0.643841i	0.951497	+	0.307657i	$0.0995448\pi$
$968$	−4149.03			−4.28619
$969$	−110.739	−	110.739i	−0.114282	−	0.114282i
$970$	900.657	−	900.657i	0.928513	−	0.928513i
$971$	−632.591	+	632.591i	−0.651484	+	0.651484i	−0.953350	−	0.301866i	$-0.902390\pi$
$971$	−632.591	+	632.591i	−0.651484	+	0.651484i	0.301866	+	0.953350i	$0.402390\pi$
$972$	2311.50	−	2311.50i	2.37809	−	2.37809i
$973$	−492.852	+	104.218i	−0.506528	+	0.107110i
$974$	1979.14			2.03197
$975$			1742.82i			1.78751i
$976$	1865.80			1.91168
$977$	−842.093	−	842.093i	−0.861917	−	0.861917i	0.129644	−	0.991561i	$-0.458617\pi$
$977$	−842.093	−	842.093i	−0.861917	−	0.861917i	−0.991561	+	0.129644i	$0.958617\pi$
$978$	−2605.57	−	2605.57i	−2.66418	−	2.66418i
$979$	73.6470			0.0752267
$980$	−2992.87	+	1324.98i	−3.05395	+	1.35202i
$981$	−984.813	−	984.813i	−1.00389	−	1.00389i
$982$		−	1744.08i		−	1.77605i
$983$			267.896i			0.272529i	0.990672	+	0.136265i	$0.0435098\pi$
$983$			267.896i			0.272529i	−0.990672	+	0.136265i	$0.956490\pi$
$984$	1254.02	+	3263.21i	1.27441	+	3.31627i
$985$		−	996.449i		−	1.01162i
$986$	427.547			0.433618
$987$	136.744	+	646.672i	0.138546	+	0.655190i
$988$	−1532.59			−1.55121
$989$		−	83.2644i		−	0.0841905i
$990$	−3157.12	−	3157.12i	−3.18901	−	3.18901i
$991$	−259.620	−	259.620i	−0.261977	−	0.261977i	0.563880	−	0.825857i	$-0.309308\pi$
$991$	−259.620	−	259.620i	−0.261977	−	0.261977i	−0.825857	+	0.563880i	$0.809308\pi$
$992$	1552.03			1.56454
$993$	−2207.59			−2.22315
$994$	−748.697	−	487.329i	−0.753216	−	0.490270i
$995$	−1351.10	−	1351.10i	−1.35789	−	1.35789i
$996$	−467.179	−	467.179i	−0.469055	−	0.469055i
$997$	114.852	−	114.852i	0.115198	−	0.115198i	−0.647158	−	0.762356i	$-0.724043\pi$
$997$	114.852	−	114.852i	0.115198	−	0.115198i	0.762356	+	0.647158i	$0.224043\pi$
$998$	−931.847	+	931.847i	−0.933715	+	0.933715i
$999$	93.4803	+	93.4803i	0.0935739	+	0.0935739i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.g.a.132.3	✓	108
7.6	odd	2	inner	287.3.g.a.132.4	yes	108
41.32	even	4	inner	287.3.g.a.237.52	yes	108
287.237	odd	4	inner	287.3.g.a.237.51	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.g.a.132.3	✓	108	1.1	even	1	trivial
287.3.g.a.132.4	yes	108	7.6	odd	2	inner
287.3.g.a.237.51	yes	108	287.237	odd	4	inner
287.3.g.a.237.52	yes	108	41.32	even	4	inner

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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-3.66303i q^{2} +(-3.03803 + 3.03803i) q^{3} -9.41780 q^{4} -7.09262 q^{5} +(11.1284 + 11.1284i) q^{6} +(1.44819 + 6.84856i) q^{7} +19.8456i q^{8} -9.45930i q^{9} +O(q^{10})\)	\(q-3.66303i q^{2} +(-3.03803 + 3.03803i) q^{3} -9.41780 q^{4} -7.09262 q^{5} +(11.1284 + 11.1284i) q^{6} +(1.44819 + 6.84856i) q^{7} +19.8456i q^{8} -9.45930i q^{9} +25.9805i q^{10} +(-12.8465 - 12.8465i) q^{11} +(28.6116 - 28.6116i) q^{12} +(11.3350 - 11.3350i) q^{13} +(25.0865 - 5.30475i) q^{14} +(21.5476 - 21.5476i) q^{15} +35.0238 q^{16} +(2.53893 + 2.53893i) q^{17} -34.6497 q^{18} +(7.17839 + 7.17839i) q^{19} +66.7969 q^{20} +(-25.2058 - 16.4065i) q^{21} +(-47.0572 + 47.0572i) q^{22} +1.35619 q^{23} +(-60.2915 - 60.2915i) q^{24} +25.3052 q^{25} +(-41.5203 - 41.5203i) q^{26} +(1.39537 + 1.39537i) q^{27} +(-13.6387 - 64.4984i) q^{28} +(22.9859 + 22.9859i) q^{29} +(-78.9296 - 78.9296i) q^{30} +31.7318i q^{31} -48.9108i q^{32} +78.0563 q^{33} +(9.30019 - 9.30019i) q^{34} +(-10.2714 - 48.5742i) q^{35} +89.0858i q^{36} +66.9934 q^{37} +(26.2947 - 26.2947i) q^{38} +68.8720i q^{39} -140.757i q^{40} +(-37.4616 - 16.6623i) q^{41} +(-60.0976 + 92.3296i) q^{42} -61.3960i q^{43} +(120.986 + 120.986i) q^{44} +67.0912i q^{45} -4.96775i q^{46} +(-15.5404 - 15.5404i) q^{47} +(-106.403 + 106.403i) q^{48} +(-44.8055 + 19.8360i) q^{49} -92.6939i q^{50} -15.4267 q^{51} +(-106.750 + 106.750i) q^{52} +(45.0963 + 45.0963i) q^{53} +(5.11127 - 5.11127i) q^{54} +(91.1154 + 91.1154i) q^{55} +(-135.914 + 28.7401i) q^{56} -43.6164 q^{57} +(84.1981 - 84.1981i) q^{58} -64.2882i q^{59} +(-202.931 + 202.931i) q^{60} +53.2723 q^{61} +116.234 q^{62} +(64.7826 - 13.6988i) q^{63} -39.0669 q^{64} +(-80.3945 + 80.3945i) q^{65} -285.923i q^{66} +(-66.6217 + 66.6217i) q^{67} +(-23.9112 - 23.9112i) q^{68} +(-4.12014 + 4.12014i) q^{69} +(-177.929 + 37.6246i) q^{70} +(-24.6353 - 24.6353i) q^{71} +187.725 q^{72} +108.100 q^{73} -245.399i q^{74} +(-76.8782 + 76.8782i) q^{75} +(-67.6046 - 67.6046i) q^{76} +(69.3760 - 106.584i) q^{77} +252.280 q^{78} +(55.6141 + 55.6141i) q^{79} -248.410 q^{80} +76.6554 q^{81} +(-61.0345 + 137.223i) q^{82} -16.3283i q^{83} +(237.383 + 154.513i) q^{84} +(-18.0077 - 18.0077i) q^{85} -224.896 q^{86} -139.664 q^{87} +(254.946 - 254.946i) q^{88} +(-2.86642 + 2.86642i) q^{89} +245.757 q^{90} +(94.0433 + 61.2130i) q^{91} -12.7723 q^{92} +(-96.4022 - 96.4022i) q^{93} +(-56.9250 + 56.9250i) q^{94} +(-50.9136 - 50.9136i) q^{95} +(148.593 + 148.593i) q^{96} +(-34.6667 - 34.6667i) q^{97} +(72.6598 + 164.124i) q^{98} +(-121.519 + 121.519i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 216 q^{4} - 2 q^{7}+O(q^{10}) \) 108 * q - 216 * q^4 - 2 * q^7	\( 108 q - 216 q^{4} - 2 q^{7} - 20 q^{11} - 4 q^{14} - 28 q^{15} + 408 q^{16} + 24 q^{18} + 20 q^{22} - 8 q^{23} + 452 q^{25} - 62 q^{28} + 168 q^{29} - 64 q^{30} - 10 q^{35} - 208 q^{37} - 44 q^{42} + 44 q^{44} + 272 q^{51} - 92 q^{53} + 24 q^{56} - 256 q^{57} + 248 q^{58} - 440 q^{60} - 252 q^{63} - 1104 q^{64} - 644 q^{65} - 348 q^{67} - 30 q^{70} - 564 q^{71} + 796 q^{72} + 1924 q^{78} + 196 q^{79} - 468 q^{81} + 32 q^{85} + 152 q^{86} + 840 q^{88} - 428 q^{92} + 32 q^{93} + 4 q^{95} + 108 q^{98} - 484 q^{99}+O(q^{100}) \) 108 * q - 216 * q^4 - 2 * q^7 - 20 * q^11 - 4 * q^14 - 28 * q^15 + 408 * q^16 + 24 * q^18 + 20 * q^22 - 8 * q^23 + 452 * q^25 - 62 * q^28 + 168 * q^29 - 64 * q^30 - 10 * q^35 - 208 * q^37 - 44 * q^42 + 44 * q^44 + 272 * q^51 - 92 * q^53 + 24 * q^56 - 256 * q^57 + 248 * q^58 - 440 * q^60 - 252 * q^63 - 1104 * q^64 - 644 * q^65 - 348 * q^67 - 30 * q^70 - 564 * q^71 + 796 * q^72 + 1924 * q^78 + 196 * q^79 - 468 * q^81 + 32 * q^85 + 152 * q^86 + 840 * q^88 - 428 * q^92 + 32 * q^93 + 4 * q^95 + 108 * q^98 - 484 * q^99

Introduction

L-functions

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