LMFDB - Embedded newform 207.4.m.a.4.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,4,Mod(4,207)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([22, 12])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("207.4"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	207.m (of order $33$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.2133953712$
Analytic rank:	$0$
Dimension:	$1400$
Relative dimension:	$70$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			4.13
Character	$\chi$	$=$	207.4
Dual form			207.4.m.a.52.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.19970 + 3.08904i) q^{2} +(-1.31400 - 5.02727i) q^{3} +(-2.08697 - 6.02992i) q^{4} +(7.73363 - 3.98697i) q^{5} +(18.4198 + 6.99946i) q^{6} +(-12.7782 + 10.0489i) q^{7} +(-5.89140 - 1.72987i) q^{8} +(-23.5468 + 13.2117i) q^{9} +(-4.69575 + 32.6597i) q^{10} +(-4.00182 + 0.382128i) q^{11} +(-27.5717 + 18.4151i) q^{12} +(10.6271 + 8.35727i) q^{13} +(-2.93328 - 61.5772i) q^{14} +(-30.2055 - 33.6402i) q^{15} +(58.4285 - 45.9487i) q^{16} +(39.3604 + 45.4243i) q^{17} +(10.9844 - 101.799i) q^{18} +(83.8861 - 96.8098i) q^{19} +(-40.1810 - 38.3125i) q^{20} +(67.3092 + 51.0353i) q^{21} +(7.62239 - 13.2024i) q^{22} +(88.8088 + 65.4217i) q^{23} +(-0.955209 + 31.8907i) q^{24} +(-28.5939 + 40.1545i) q^{25} +(-49.1924 + 14.4442i) q^{26} +(97.3591 + 101.016i) q^{27} +(87.2621 + 56.0799i) q^{28} +(-43.8029 + 126.560i) q^{29} +(170.359 - 19.3081i) q^{30} +(182.068 - 173.602i) q^{31} +(11.0752 + 232.496i) q^{32} +(7.17946 + 19.6161i) q^{33} +(-226.899 + 21.6662i) q^{34} +(-58.7576 + 128.661i) q^{35} +(128.807 + 114.413i) q^{36} +(171.799 - 110.409i) q^{37} +(114.525 + 472.080i) q^{38} +(28.0501 - 64.4069i) q^{39} +(-52.4589 + 10.1106i) q^{40} +(92.3823 - 47.6264i) q^{41} +(-305.710 + 95.6589i) q^{42} +(-19.1162 - 18.2272i) q^{43} +(10.6559 + 23.3332i) q^{44} +(-129.428 + 196.055i) q^{45} +(-397.443 + 130.426i) q^{46} +(317.144 + 549.309i) q^{47} +(-307.771 - 233.359i) q^{48} +(-18.5626 + 76.5161i) q^{49} +(-61.1411 - 176.656i) q^{50} +(176.640 - 257.563i) q^{51} +(28.2151 - 81.5221i) q^{52} +(-3.90199 - 27.1389i) q^{53} +(-526.203 + 78.5423i) q^{54} +(-29.4251 + 18.9104i) q^{55} +(92.6651 - 37.0975i) q^{56} +(-596.915 - 294.510i) q^{57} +(-294.597 - 413.703i) q^{58} +(-3.44028 - 2.70547i) q^{59} +(-139.809 + 252.343i) q^{60} +(118.259 + 487.469i) q^{61} +(135.768 + 944.287i) q^{62} +(168.124 - 405.442i) q^{63} +(-242.299 - 155.716i) q^{64} +(115.506 + 22.2621i) q^{65} +(-76.3877 - 20.9718i) q^{66} +(358.344 + 34.2177i) q^{67} +(191.761 - 332.139i) q^{68} +(212.197 - 532.430i) q^{69} +(-268.191 - 464.520i) q^{70} +(122.875 + 269.060i) q^{71} +(161.578 - 37.1024i) q^{72} +(752.140 - 868.016i) q^{73} +(-36.8493 + 773.561i) q^{74} +(239.440 + 90.9860i) q^{75} +(-758.823 - 303.787i) q^{76} +(47.2963 - 45.0969i) q^{77} +(137.254 + 228.324i) q^{78} +(-298.085 + 119.335i) q^{79} +(268.669 - 588.303i) q^{80} +(379.903 - 622.185i) q^{81} +(-56.0931 + 390.136i) q^{82} +(497.574 + 256.517i) q^{83} +(167.266 - 512.379i) q^{84} +(485.504 + 194.366i) q^{85} +(98.3545 - 18.9563i) q^{86} +(693.808 + 53.9084i) q^{87} +(24.2374 + 4.67137i) q^{88} +(-695.998 + 204.364i) q^{89} +(-320.919 - 831.069i) q^{90} -219.778 q^{91} +(209.146 - 672.043i) q^{92} +(-1111.98 - 687.192i) q^{93} +(-2394.46 - 228.643i) q^{94} +(262.768 - 1083.14i) q^{95} +(1154.27 - 361.178i) q^{96} +(23.7848 - 499.305i) q^{97} +(-195.530 - 225.653i) q^{98} +(89.1816 - 61.8687i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1400 q - 9 q^{2} - 14 q^{3} + 263 q^{4} + 19 q^{5} - 35 q^{6} - 9 q^{7} - 74 q^{8} - 78 q^{9} - 68 q^{10} + 79 q^{11} + 54 q^{12} - 9 q^{13} + 159 q^{14} - 868 q^{15} + 1031 q^{16} - 308 q^{17} - 87 q^{18}+ \cdots + 7484 q^{99}+O(q^{100}) $ 1400 * q - 9 * q^2 - 14 * q^3 + 263 * q^4 + 19 * q^5 - 35 * q^6 - 9 * q^7 - 74 * q^8 - 78 * q^9 - 68 * q^10 + 79 * q^11 + 54 * q^12 - 9 * q^13 + 159 * q^14 - 868 * q^15 + 1031 * q^16 - 308 * q^17 - 87 * q^18 - 36 * q^19 + 119 * q^20 - 660 * q^21 - 52 * q^22 - 116 * q^23 + 2420 * q^24 + 1397 * q^25 + 432 * q^26 + 274 * q^27 - 324 * q^28 - 45 * q^29 + 768 * q^30 - 45 * q^31 + 111 * q^32 - 1664 * q^33 + 403 * q^34 - 536 * q^35 - 121 * q^36 - 180 * q^37 - 117 * q^38 - 46 * q^39 - 473 * q^40 - 333 * q^41 - 332 * q^42 - 9 * q^43 - 1908 * q^44 + 1762 * q^45 + 484 * q^46 + 216 * q^47 + 1072 * q^48 + 4615 * q^49 - 105 * q^50 + 1298 * q^51 - 708 * q^52 - 1380 * q^53 + 4116 * q^54 - 1328 * q^55 - 3971 * q^56 + 2154 * q^57 - 338 * q^58 + 1917 * q^59 + 154 * q^60 + 27 * q^61 - 3854 * q^62 - 4850 * q^63 - 5854 * q^64 + 3363 * q^65 - 2017 * q^66 + 603 * q^67 - 18454 * q^68 - 4653 * q^69 + 542 * q^70 - 5296 * q^71 - 8044 * q^72 - 36 * q^73 + 3243 * q^74 + 5140 * q^75 - 1029 * q^76 - 1661 * q^77 + 14687 * q^78 - 9 * q^79 + 10312 * q^80 - 294 * q^81 - 770 * q^82 - 2735 * q^83 + 2298 * q^84 + 241 * q^85 + 10507 * q^86 - 10268 * q^87 + 2183 * q^88 - 2980 * q^89 + 33928 * q^90 - 1452 * q^91 - 1973 * q^92 - 11406 * q^93 + 2034 * q^94 - 3339 * q^95 - 4446 * q^96 - 5193 * q^97 + 14820 * q^98 + 7484 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.19970	+	3.08904i	−0.777711	+	1.09214i	0.215579	+	0.976486i	$0.430836\pi$
$2$	−2.19970	+	3.08904i	−0.777711	+	1.09214i	−0.993289	+	0.115655i	$0.963103\pi$
$3$	−1.31400	−	5.02727i	−0.252880	−	0.967498i
$3$	−1.31400	−	5.02727i	−0.252880	−	0.967498i
$4$	−2.08697	−	6.02992i	−0.260872	−	0.753740i
$5$	7.73363	−	3.98697i	0.691717	−	0.356605i	−0.0762548	−	0.997088i	$-0.524296\pi$
$5$	7.73363	−	3.98697i	0.691717	−	0.356605i	0.767972	+	0.640483i	$0.221266\pi$
$6$	18.4198	+	6.99946i	1.25331	+	0.476253i
$7$	−12.7782	+	10.0489i	−0.689960	+	0.542591i	−0.900425	−	0.435011i	$-0.856745\pi$
$7$	−12.7782	+	10.0489i	−0.689960	+	0.542591i	0.210465	+	0.977601i	$0.432502\pi$
$8$	−5.89140	−	1.72987i	−0.260366	−	0.0764502i
$9$	−23.5468	+	13.2117i	−0.872104	+	0.489321i
$10$	−4.69575	+	32.6597i	−0.148493	+	1.03279i
$11$	−4.00182	+	0.382128i	−0.109690	+	0.0104742i	−0.149757	−	0.988723i	$-0.547849\pi$
$11$	−4.00182	+	0.382128i	−0.109690	+	0.0104742i	0.0400664	+	0.999197i	$0.487243\pi$
$12$	−27.5717	+	18.4151i	−0.663272	+	0.442999i
$13$	10.6271	+	8.35727i	0.226726	+	0.178299i	0.725060	−	0.688686i	$-0.241812\pi$
$13$	10.6271	+	8.35727i	0.226726	+	0.178299i	−0.498334	+	0.866985i	$0.666055\pi$
$14$	−2.93328	−	61.5772i	−0.0559966	−	1.17551i
$15$	−30.2055	−	33.6402i	−0.519936	−	0.579057i
$16$	58.4285	−	45.9487i	0.912945	−	0.717948i
$17$	39.3604	+	45.4243i	0.561547	+	0.648059i	0.963534	−	0.267586i	$-0.0862259\pi$
$17$	39.3604	+	45.4243i	0.561547	+	0.648059i	−0.401987	+	0.915645i	$0.631680\pi$
$18$	10.9844	−	101.799i	0.143836	−	1.33301i
$19$	83.8861	−	96.8098i	1.01288	−	1.16893i	0.0273204	−	0.999627i	$-0.491303\pi$
$19$	83.8861	−	96.8098i	1.01288	−	1.16893i	0.985564	−	0.169304i	$-0.0541520\pi$
$20$	−40.1810	−	38.3125i	−0.449237	−	0.428347i
$21$	67.3092	+	51.0353i	0.699432	+	0.530325i
$22$	7.62239	−	13.2024i	0.0738682	−	0.127943i
$23$	88.8088	+	65.4217i	0.805127	+	0.593103i
$23$	88.8088	+	65.4217i	0.805127	+	0.593103i
$24$	−0.955209	+	31.8907i	−0.00812422	+	0.271236i
$25$	−28.5939	+	40.1545i	−0.228751	+	0.321236i
$26$	−49.1924	+	14.4442i	−0.371055	+	0.108952i
$27$	97.3591	+	101.016i	0.693955	+	0.720019i
$28$	87.2621	+	56.0799i	0.588964	+	0.378504i
$29$	−43.8029	+	126.560i	−0.280482	+	0.810401i	0.713480	+	0.700676i	$0.247118\pi$
$29$	−43.8029	+	126.560i	−0.280482	+	0.810401i	−0.993962	+	0.109725i	$0.965003\pi$
$30$	170.359	−	19.3081i	1.03677	−	0.117505i
$31$	182.068	−	173.602i	1.05485	−	1.00580i	0.0548780	−	0.998493i	$-0.482523\pi$
$31$	182.068	−	173.602i	1.05485	−	1.00580i	0.999973	−	0.00730567i	$-0.00232549\pi$
$32$	11.0752	+	232.496i	0.0611822	+	1.28437i
$33$	7.17946	+	19.6161i	0.0378722	+	0.103477i
$34$	−226.899	+	21.6662i	−1.14449	+	0.109286i
$35$	−58.7576	+	128.661i	−0.283767	+	0.621363i
$36$	128.807	+	114.413i	0.596328	+	0.529689i
$37$	171.799	−	110.409i	0.763341	−	0.490570i	−0.100126	−	0.994975i	$-0.531925\pi$
$37$	171.799	−	110.409i	0.763341	−	0.490570i	0.863467	+	0.504405i	$0.168288\pi$
$38$	114.525	+	472.080i	0.488907	+	2.01530i
$39$	28.0501	−	64.4069i	0.115170	−	0.264445i
$40$	−52.4589	+	10.1106i	−0.207362	+	0.0399657i
$41$	92.3823	−	47.6264i	0.351895	−	0.181414i	−0.273212	−	0.961954i	$-0.588086\pi$
$41$	92.3823	−	47.6264i	0.351895	−	0.181414i	0.625106	+	0.780540i	$0.285056\pi$
$42$	−305.710	+	95.6589i	−1.12315	+	0.351440i
$43$	−19.1162	−	18.2272i	−0.0677951	−	0.0646425i	0.655424	−	0.755261i	$-0.272490\pi$
$43$	−19.1162	−	18.2272i	−0.0677951	−	0.0646425i	−0.723219	+	0.690619i	$0.757338\pi$
$44$	10.6559	+	23.3332i	0.0365100	+	0.0799456i
$45$	−129.428	+	196.055i	−0.428755	+	0.649469i
$46$	−397.443	+	130.426i	−1.27391	+	0.418050i
$47$	317.144	+	549.309i	0.984259	+	1.70479i	0.645185	+	0.764027i	$0.276780\pi$
$47$	317.144	+	549.309i	0.984259	+	1.70479i	0.339074	+	0.940760i	$0.389886\pi$
$48$	−307.771	−	233.359i	−0.925479	−	0.701718i
$49$	−18.5626	+	76.5161i	−0.0541184	+	0.223079i
$50$	−61.1411	−	176.656i	−0.172933	−	0.499658i
$51$	176.640	−	257.563i	0.484992	−	0.707176i
$52$	28.2151	−	81.5221i	0.0752448	−	0.217406i
$53$	−3.90199	−	27.1389i	−0.0101128	−	0.0703361i	0.984140	−	0.177393i	$-0.0567664\pi$
$53$	−3.90199	−	27.1389i	−0.0101128	−	0.0703361i	−0.994253	+	0.107057i	$0.965857\pi$
$54$	−526.203	+	78.5423i	−1.32606	+	0.197931i
$55$	−29.4251	+	18.9104i	−0.0721396	+	0.0463613i
$56$	92.6651	−	37.0975i	0.221123	−	0.0885244i
$57$	−596.915	−	294.510i	−1.38708	−	0.684364i
$58$	−294.597	−	413.703i	−0.666938	−	0.936584i
$59$	−3.44028	−	2.70547i	−0.00759130	−	0.00596986i	0.614356	−	0.789029i	$-0.289416\pi$
$59$	−3.44028	−	2.70547i	−0.00759130	−	0.00596986i	−0.621947	+	0.783059i	$0.713658\pi$
$60$	−139.809	+	252.343i	−0.300821	+	0.542956i
$61$	118.259	+	487.469i	0.248221	+	1.02318i	0.950363	+	0.311144i	$0.100712\pi$
$61$	118.259	+	487.469i	0.248221	+	1.02318i	−0.702142	+	0.712037i	$0.747773\pi$
$62$	135.768	+	944.287i	0.278106	+	1.93427i
$63$	168.124	−	405.442i	0.336216	−	0.810808i
$64$	−242.299	−	155.716i	−0.473241	−	0.304134i
$65$	115.506	+	22.2621i	0.220413	+	0.0424810i
$66$	−76.3877	−	20.9718i	−0.142465	−	0.0391130i
$67$	358.344	+	34.2177i	0.653413	+	0.0623933i	0.416497	−	0.909137i	$-0.363258\pi$
$67$	358.344	+	34.2177i	0.653413	+	0.0623933i	0.236915	+	0.971530i	$0.423864\pi$
$68$	191.761	−	332.139i	0.341976	−	0.592321i
$69$	212.197	−	532.430i	0.370225	−	0.928942i
$70$	−268.191	−	464.520i	−0.457928	−	0.793154i
$71$	122.875	+	269.060i	0.205389	+	0.449740i	0.984093	−	0.177652i	$-0.0568500\pi$
$71$	122.875	+	269.060i	0.205389	+	0.449740i	−0.778704	+	0.627391i	$0.784123\pi$
$72$	161.578	−	37.1024i	0.264475	−	0.0607299i
$73$	752.140	−	868.016i	1.20591	−	1.39169i	0.308073	−	0.951363i	$-0.400316\pi$
$73$	752.140	−	868.016i	1.20591	−	1.39169i	0.897836	−	0.440330i	$-0.145139\pi$
$74$	−36.8493	+	773.561i	−0.0578870	+	1.21520i
$75$	239.440	+	90.9860i	0.368642	+	0.140082i
$76$	−758.823	−	303.787i	−1.14530	−	0.458510i
$77$	47.2963	−	45.0969i	0.0699989	−	0.0667438i
$78$	137.254	+	228.324i	0.199243	+	0.331443i
$79$	−298.085	+	119.335i	−0.424521	+	0.169953i	−0.574078	−	0.818801i	$-0.694639\pi$
$79$	−298.085	+	119.335i	−0.424521	+	0.169953i	0.149557	+	0.988753i	$0.452215\pi$
$80$	268.669	−	588.303i	0.375476	−	0.822178i
$81$	379.903	−	622.185i	0.521129	−	0.853478i
$82$	−56.0931	+	390.136i	−0.0755421	+	0.525407i
$83$	497.574	+	256.517i	0.658022	+	0.339234i	0.754689	−	0.656083i	$-0.227788\pi$
$83$	497.574	+	256.517i	0.658022	+	0.339234i	−0.0966667	+	0.995317i	$0.530818\pi$
$84$	167.266	−	512.379i	0.217265	−	0.665537i
$85$	485.504	+	194.366i	0.619533	+	0.248024i
$86$	98.3545	−	18.9563i	0.123324	−	0.0237687i
$87$	693.808	+	53.9084i	0.854989	+	0.0664321i
$88$	24.2374	+	4.67137i	0.0293604	+	0.00565875i
$89$	−695.998	+	204.364i	−0.828940	+	0.243399i	−0.668562	−	0.743657i	$-0.733090\pi$
$89$	−695.998	+	204.364i	−0.828940	+	0.243399i	−0.160379	+	0.987056i	$0.551271\pi$
$90$	−320.919	−	831.069i	−0.375865	−	0.973359i
$91$	−219.778			−0.253175
$92$	209.146	−	672.043i	0.237010	−	0.761580i
$93$	−1111.98	−	687.192i	−1.23986	−	0.766220i
$94$	−2394.46	−	228.643i	−2.62734	−	0.250880i
$95$	262.768	−	1083.14i	0.283783	−	1.16977i
$96$	1154.27	−	361.178i	1.22715	−	0.383985i
$97$	23.7848	−	499.305i	0.0248968	−	0.522647i	−0.951629	−	0.307248i	$-0.900592\pi$
$97$	23.7848	−	499.305i	0.0248968	−	0.522647i	0.976526	−	0.215399i	$-0.0691052\pi$
$98$	−195.530	−	225.653i	−0.201546	−	0.232596i
$99$	89.1816	−	61.8687i	0.0905362	−	0.0628084i
$100$	301.803	+	88.6174i	0.301803	+	0.0886174i
$101$	−792.152	−	408.383i	−0.780417	−	0.402333i	0.0214997	−	0.999769i	$-0.493156\pi$
$101$	−792.152	−	408.383i	−0.780417	−	0.402333i	−0.801917	+	0.597436i	$0.796186\pi$
$102$	407.067	+	1112.21i	0.395153	+	1.07966i
$103$	70.0618	+	98.3881i	0.0670233	+	0.0941210i	0.846727	−	0.532028i	$-0.178570\pi$
$103$	70.0618	+	98.3881i	0.0670233	+	0.0941210i	−0.779704	+	0.626149i	$0.784630\pi$
$104$	−48.1517	−	67.6196i	−0.0454006	−	0.0637562i
$105$	724.021	+	126.329i	0.672926	+	0.117414i
$106$	92.4165	+	47.6440i	0.0846819	+	0.0436565i
$107$	−1156.70	−	339.639i	−1.04507	−	0.306861i	−0.286248	−	0.958156i	$-0.592408\pi$
$107$	−1156.70	−	339.639i	−1.04507	−	0.306861i	−0.758825	+	0.651295i	$0.774226\pi$
$108$	405.931	−	797.885i	0.361673	−	0.710894i
$109$	−881.042	−	1016.78i	−0.774207	−	0.893482i	0.222470	−	0.974940i	$-0.428588\pi$
$109$	−881.042	−	1016.78i	−0.774207	−	0.893482i	−0.996677	+	0.0814572i	$0.974043\pi$
$110$	6.31140	−	132.493i	0.00547062	−	0.114842i
$111$	−780.799	−	718.603i	−0.667659	−	0.614476i
$112$	−284.879	+	1174.29i	−0.240344	+	0.990712i
$113$	1513.46	+	144.518i	1.25995	+	0.120310i	0.703574	−	0.710622i	$-0.251587\pi$
$113$	1513.46	+	144.518i	1.25995	+	0.120310i	0.556373	+	0.830933i	$0.312193\pi$
$114$	2222.79	−	1196.06i	1.82617	−	0.982646i
$115$	947.649	+	151.870i	0.768424	+	0.123147i
$116$	854.563			0.684001
$117$	−360.648	−	56.3847i	−0.284974	−	0.0445536i
$118$	15.9249	−	4.67597i	0.0124238	−	0.00364795i
$119$	−959.422	−	184.913i	−0.739076	−	0.142445i
$120$	119.760	+	250.439i	0.0911044	+	0.190516i
$121$	−1291.08	+	248.835i	−0.970006	+	0.186953i
$122$	−1765.95	−	706.979i	−1.31050	−	0.524646i
$123$	−360.821	−	401.849i	−0.264505	−	0.294581i
$124$	−1426.77	−	735.553i	−1.03329	−	0.532699i
$125$	−215.823	+	1501.08i	−0.154430	+	1.07409i
$126$	882.607	+	1411.19i	0.624039	+	0.997769i
$127$	606.041	−	1327.04i	0.423444	−	0.927214i	−0.570901	−	0.821019i	$-0.693406\pi$
$127$	606.041	−	1327.04i	0.423444	−	0.927214i	0.994345	−	0.106195i	$-0.0338668\pi$
$128$	−714.693	+	286.120i	−0.493520	+	0.197576i
$129$	−66.5144	+	120.053i	−0.0453974	+	0.0819384i
$130$	−322.848	+	307.835i	−0.217813	+	0.207684i
$131$	383.607	+	153.573i	0.255846	+	0.102425i	0.496040	−	0.868299i	$-0.334787\pi$
$131$	383.607	+	153.573i	0.255846	+	0.102425i	−0.240194	+	0.970725i	$0.577211\pi$
$132$	103.300	−	84.2299i	0.0681146	−	0.0555399i
$133$	−99.0838	+	2080.02i	−0.0645989	+	1.35610i
$134$	−893.948	+	1031.67i	−0.576308	+	0.665095i
$135$	1155.69	+	393.052i	0.736783	+	0.250582i
$136$	−153.310	−	335.701i	−0.0966631	−	0.211663i
$137$	−35.0755	−	60.7525i	−0.0218737	−	0.0378864i	0.854881	−	0.518824i	$-0.173630\pi$
$137$	−35.0755	−	60.7525i	−0.0218737	−	0.0378864i	−0.876755	+	0.480937i	$0.840297\pi$
$138$	1177.93	+	1826.67i	0.726608	+	1.12679i
$139$	−877.578	+	1520.01i	−0.535505	+	0.927522i	0.463633	+	0.886027i	$0.346545\pi$
$139$	−877.578	+	1520.01i	−0.535505	+	0.927522i	−0.999139	+	0.0414952i	$0.986788\pi$
$140$	898.442	+	85.7908i	0.542373	+	0.0517903i
$141$	2344.79	−	2316.16i	1.40048	−	1.38337i
$142$	−1101.43	−	212.283i	−0.650913	−	0.125453i
$143$	−45.7214	−	29.3834i	−0.0267372	−	0.0171830i
$144$	−768.745	+	1853.88i	−0.444876	+	1.07285i
$145$	165.835	+	1153.41i	0.0949785	+	0.660590i
$146$	1026.86	+	4232.77i	0.582078	+	2.39936i
$147$	409.058	−	7.22319i	0.229514	−	0.00405278i
$148$	−1024.30	−	805.516i	−0.568896	−	0.447385i
$149$	−1175.83	−	1651.23i	−0.646497	−	0.907879i	0.353119	−	0.935578i	$-0.385121\pi$
$149$	−1175.83	−	1651.23i	−0.646497	−	0.907879i	−0.999616	+	0.0276999i	$0.991182\pi$
$150$	−807.755	+	539.499i	−0.439686	+	0.293666i
$151$	1580.35	−	632.676i	0.851702	−	0.340970i	0.0955969	−	0.995420i	$-0.469524\pi$
$151$	1580.35	−	632.676i	0.851702	−	0.340970i	0.756105	+	0.654450i	$0.227100\pi$
$152$	−661.675	+	425.233i	−0.353085	+	0.226914i
$153$	−1526.94	−	549.580i	−0.806836	−	0.290398i
$154$	35.2688	+	245.300i	0.0184548	+	0.128356i
$155$	715.904	−	2068.47i	0.370986	−	1.07189i
$156$	−446.908	−	34.7245i	−0.229367	−	0.0178217i
$157$	1053.34	+	3043.42i	0.535449	+	1.54708i	0.810554	+	0.585664i	$0.199166\pi$
$157$	1053.34	+	3043.42i	0.535449	+	1.54708i	−0.275105	+	0.961414i	$0.588713\pi$
$158$	287.065	−	1183.30i	0.144542	−	0.595811i
$159$	−131.307	+	55.2769i	−0.0654927	+	0.0275707i
$160$	1012.61	+	1753.88i	0.500334	+	0.866604i
$161$	−1792.24	+	56.4585i	−0.877318	+	0.0276370i
$162$	1086.29	+	2542.16i	0.526831	+	1.23291i
$163$	307.341	+	672.984i	0.147686	+	0.323387i	0.968989	−	0.247106i	$-0.0794794\pi$
$163$	307.341	+	672.984i	0.147686	+	0.323387i	−0.821302	+	0.570493i	$0.806752\pi$
$164$	−479.983	−	457.662i	−0.228539	−	0.217911i
$165$	133.732	+	123.080i	0.0630971	+	0.0580711i
$166$	−1886.91	+	972.767i	−0.882243	+	0.454828i
$167$	1670.04	−	321.875i	0.773844	−	0.149146i	0.212983	−	0.977056i	$-0.431682\pi$
$167$	1670.04	−	321.875i	0.773844	−	0.149146i	0.560861	+	0.827910i	$0.310470\pi$
$168$	−308.261	−	417.106i	−0.141565	−	0.191550i
$169$	−474.870	−	1957.44i	−0.216145	−	0.890962i
$170$	−1668.37	+	1072.20i	−0.752694	+	0.483727i
$171$	−696.231	+	3387.84i	−0.311357	+	1.51505i
$172$	−70.0137	+	153.309i	−0.0310378	+	0.0679632i
$173$	−1780.12	+	169.981i	−0.782313	+	0.0747018i	−0.478567	−	0.878051i	$-0.658844\pi$
$173$	−1780.12	+	169.981i	−0.782313	+	0.0747018i	−0.303746	+	0.952753i	$0.598237\pi$
$174$	−1692.69	+	2024.62i	−0.737488	+	0.882105i
$175$	−38.1298	−	800.442i	−0.0164705	−	0.345759i
$176$	−216.262	+	206.206i	−0.0926215	+	0.0883144i
$177$	−9.08056	+	20.8502i	−0.00385614	+	0.00885422i
$178$	899.698	−	2599.51i	0.378850	−	1.09461i
$179$	2451.25	+	1575.32i	1.02355	+	0.657793i	0.940865	−	0.338783i	$-0.110015\pi$
$179$	2451.25	+	1575.32i	1.02355	+	0.657793i	0.0826817	+	0.996576i	$0.473652\pi$
$180$	1452.31	+	371.278i	0.601380	+	0.153741i
$181$	−3721.20	+	1092.64i	−1.52815	+	0.448705i	−0.934483	−	0.356007i	$-0.884138\pi$
$181$	−3721.20	+	1092.64i	−1.52815	+	0.448705i	−0.593665	+	0.804712i	$0.702320\pi$
$182$	483.444	−	678.903i	0.196897	−	0.276503i
$183$	2295.25	−	1235.05i	0.927155	−	0.498895i
$184$	−410.037	−	539.053i	−0.164284	−	0.215976i
$185$	888.437	−	1538.82i	0.353077	−	0.611547i
$186$	4568.78	−	1923.34i	1.80107	−	0.758204i
$187$	−174.871	−	166.739i	−0.0683842	−	0.0652042i
$188$	2650.42	−	3058.74i	1.02820	−	1.18661i
$189$	−2259.18	−	312.450i	−0.869477	−	0.120251i
$190$	2767.87	+	3194.29i	1.05685	+	1.21967i
$191$	3018.86	−	2374.06i	1.14365	−	0.899377i	0.147678	−	0.989035i	$-0.452820\pi$
$191$	3018.86	−	2374.06i	1.14365	−	0.899377i	0.995973	+	0.0896585i	$0.0285776\pi$
$192$	−464.446	+	1422.72i	−0.174575	+	0.534769i
$193$	−96.2662	−	2020.88i	−0.0359036	−	0.753709i	−0.943001	−	0.332789i	$-0.892010\pi$
$193$	−96.2662	−	2020.88i	−0.0359036	−	0.753709i	0.907098	−	0.420920i	$-0.138293\pi$
$194$	1490.06	+	1171.79i	0.551442	+	0.433659i
$195$	−39.8585	−	609.934i	−0.0146376	−	0.223991i
$196$	500.126	−	47.7562i	0.182262	−	0.0174039i
$197$	−720.490	+	5011.12i	−0.260573	+	1.81232i	0.267983	+	0.963424i	$0.413643\pi$
$197$	−720.490	+	5011.12i	−0.260573	+	1.81232i	−0.528556	+	0.848899i	$0.677266\pi$
$198$	−5.05747	+	411.578i	−0.00181525	+	0.147725i
$199$	3096.80	+	909.301i	1.10315	+	0.323913i	0.782101	−	0.623151i	$-0.214148\pi$
$199$	3096.80	+	909.301i	1.10315	+	0.323913i	0.321044	+	0.947064i	$0.395966\pi$
$200$	237.920	−	187.103i	0.0841176	−	0.0661508i
$201$	−298.843	−	1846.45i	−0.104869	−	0.647953i
$202$	3004.01	−	1548.67i	1.04634	−	0.539427i
$203$	−712.069	−	2057.39i	−0.246194	−	0.711332i
$204$	−1921.73	−	527.600i	−0.659548	−	0.181075i
$205$	524.566	−	736.650i	0.178718	−	0.250975i
$206$	−458.040			−0.154918
$207$	−2955.49	−	367.158i	−0.992372	−	0.123281i
$208$	1004.93			0.334998
$209$	−298.704	+	419.471i	−0.0988602	+	0.138830i
$210$	−1982.86	+	1958.65i	−0.651574	+	0.643617i
$211$	−246.624	−	712.574i	−0.0804659	−	0.232491i	0.897591	−	0.440829i	$-0.145316\pi$
$211$	−246.624	−	712.574i	−0.0804659	−	0.232491i	−0.978057	+	0.208339i	$0.933194\pi$
$212$	−155.502	+	80.1669i	−0.0503770	+	0.0259712i
$213$	1191.18	−	971.273i	0.383183	−	0.312444i
$214$	3593.56	−	2826.00i	1.14790	−	0.902718i
$215$	−220.509	−	64.7472i	−0.0699469	−	0.0205382i
$216$	−398.837	−	763.544i	−0.125636	−	0.240521i
$217$	−582.002	+	4047.91i	−0.182068	+	1.26631i
$218$	5078.90	−	484.976i	1.57792	−	0.150673i
$219$	−5352.06	−	2640.63i	−1.65141	−	0.814783i
$220$	175.437	+	137.966i	0.0537636	+	0.0422801i
$221$	38.6649	+	811.675i	0.0117687	+	0.247055i
$222$	3937.32	−	831.210i	1.19034	−	0.251294i
$223$	2427.45	−	1908.97i	0.728944	−	0.573248i	−0.183221	−	0.983072i	$-0.558652\pi$
$223$	2427.45	−	1908.97i	0.728944	−	0.573248i	0.912165	+	0.409824i	$0.134410\pi$
$224$	−2477.86	−	2859.60i	−0.739102	−	0.852969i
$225$	142.786	−	1323.28i	0.0423071	−	0.392084i
$226$	−3775.57	+	4357.24i	−1.11127	+	1.28247i
$227$	−1667.70	−	1590.15i	−0.487618	−	0.464943i	0.405934	−	0.913902i	$-0.366946\pi$
$227$	−1667.70	−	1590.15i	−0.487618	−	0.464943i	−0.893552	+	0.448959i	$0.851795\pi$
$228$	−530.122	+	4213.98i	−0.153983	+	1.22403i
$229$	−1800.44	+	3118.45i	−0.519548	+	0.899883i	0.480194	+	0.877162i	$0.340566\pi$
$229$	−1800.44	+	3118.45i	−0.519548	+	0.899883i	−0.999742	+	0.0227210i	$0.992767\pi$
$230$	−2553.67	+	2593.26i	−0.732105	+	0.743455i
$231$	−288.862	−	178.514i	−0.0822758	−	0.0508456i
$232$	476.993	−	669.843i	0.134983	−	0.189558i
$233$	948.116	−	278.392i	0.266580	−	0.0782750i	−0.145711	−	0.989327i	$-0.546547\pi$
$233$	948.116	−	278.392i	0.266580	−	0.0782750i	0.412291	+	0.911052i	$0.364729\pi$
$234$	967.492	−	990.029i	0.270286	−	0.276582i
$235$	4642.75	+	2983.71i	1.28876	+	0.828238i
$236$	−9.13396	+	26.3909i	−0.00251937	+	0.00727923i
$237$	991.614	+	1341.74i	0.271782	+	0.367745i
$238$	2681.64	−	2556.94i	0.730358	−	0.696395i
$239$	67.4734	+	1416.44i	0.0182615	+	0.383355i	0.989435	+	0.144980i	$0.0463118\pi$
$239$	67.4734	+	1416.44i	0.0182615	+	0.383355i	−0.971173	+	0.238375i	$0.923385\pi$
$240$	−3310.59	−	577.639i	−0.890406	−	0.155360i
$241$	−756.765	+	72.2623i	−0.202272	+	0.0193146i	−0.195700	−	0.980664i	$-0.562698\pi$
$241$	−756.765	+	72.2623i	−0.202272	+	0.0193146i	−0.00657177	+	0.999978i	$0.502092\pi$
$242$	2071.32	−	4535.56i	0.550205	−	1.20478i
$243$	−3627.08	−	1092.32i	−0.957521	−	0.288364i
$244$	2692.60	−	1730.43i	0.706458	−	0.454013i
$245$	161.511	+	665.756i	0.0421165	+	0.173607i
$246$	2035.03	−	230.645i	0.527433	−	0.0597780i
$247$	1700.53	−	327.751i	0.438066	−	0.0844304i
$248$	−1372.94	+	707.802i	−0.351541	+	0.181232i
$249$	635.767	−	2838.50i	0.161808	−	0.722420i
$250$	−4162.16	−	3968.61i	−1.05295	−	1.00399i
$251$	−970.247	−	2124.55i	−0.243990	−	0.534263i	0.747528	−	0.664230i	$-0.231240\pi$
$251$	−970.247	−	2124.55i	−0.243990	−	0.534263i	−0.991518	+	0.129966i	$0.958513\pi$
$252$	−2795.65	−	167.624i	−0.698847	−	0.0419022i
$253$	−380.397	−	227.870i	−0.0945270	−	0.0566247i
$254$	2766.19	+	4791.18i	0.683332	+	1.18357i
$255$	339.178	−	2696.15i	0.0832948	−	0.662117i
$256$	1231.50	−	5076.32i	0.300660	−	1.23934i
$257$	1825.50	+	5274.43i	0.443079	+	1.28019i	0.916739	+	0.399486i	$0.130811\pi$
$257$	1825.50	+	5274.43i	0.443079	+	1.28019i	−0.473660	+	0.880708i	$0.657068\pi$
$258$	−224.536	−	469.546i	−0.0541822	−	0.113305i
$259$	−1085.81	+	3137.23i	−0.260497	+	0.752656i
$260$	−106.821	−	742.955i	−0.0254798	−	0.177216i
$261$	−640.654	−	3558.79i	−0.151937	−	0.844000i
$262$	−1318.21	+	847.164i	−0.310838	+	0.199763i
$263$	−1855.67	+	742.897i	−0.435077	+	0.174179i	−0.578853	−	0.815432i	$-0.696500\pi$
$263$	−1855.67	+	742.897i	−0.435077	+	0.174179i	0.143776	+	0.989610i	$0.454075\pi$
$264$	−8.36374	−	127.986i	−0.00194982	−	0.0298371i
$265$	−138.378	−	194.325i	−0.0320774	−	0.0450464i
$266$	−6207.33	−	4881.50i	−1.43081	−	1.12520i
$267$	1941.93	+	3230.43i	0.445110	+	0.740447i
$268$	−541.524	−	2232.19i	−0.123429	−	0.508780i
$269$	−835.632	−	5811.95i	−0.189403	−	1.31733i	−0.833558	−	0.552432i	$-0.813700\pi$
$269$	−835.632	−	5811.95i	−0.189403	−	1.31733i	0.644155	−	0.764895i	$-0.277209\pi$
$270$	−3756.32	+	2705.37i	−0.846674	+	0.609791i
$271$	1157.69	+	744.003i	0.259501	+	0.166771i	0.663922	−	0.747802i	$-0.268891\pi$
$271$	1157.69	+	744.003i	0.259501	+	0.166771i	−0.404421	+	0.914573i	$0.632527\pi$
$272$	4386.96	+	845.516i	0.977935	+	0.188481i
$273$	288.788	+	1104.88i	0.0640229	+	0.244947i
$274$	264.823	+	25.2875i	0.0583887	+	0.00557545i
$275$	99.0836	−	171.618i	0.0217271	−	0.0376325i
$276$	−3653.36	−	168.364i	−0.796762	−	0.0367186i
$277$	1370.16	+	2373.19i	0.297202	+	0.514769i	0.975495	−	0.220023i	$-0.0706132\pi$
$277$	1370.16	+	2373.19i	0.297202	+	0.514769i	−0.678293	+	0.734792i	$0.737280\pi$
$278$	−2764.97	−	6054.44i	−0.596518	−	1.30619i
$279$	−1993.55	+	6493.19i	−0.427781	+	1.39332i
$280$	568.732	−	656.351i	0.121386	−	0.140087i
$281$	−0.831159	+	17.4482i	−0.000176451	+	0.00370416i	−0.998954	−	0.0457298i	$-0.985439\pi$
$281$	−0.831159	+	17.4482i	−0.000176451	+	0.00370416i	0.998777	+	0.0494339i	$0.0157417\pi$
$282$	1996.88	+	12338.0i	0.421675	+	2.60539i
$283$	−5664.55	−	2267.74i	−1.18983	−	0.476337i	−0.309594	−	0.950869i	$-0.600193\pi$
$283$	−5664.55	−	2267.74i	−1.18983	−	0.476337i	−0.880238	+	0.474532i	$0.842617\pi$
$284$	1365.97	−	1302.45i	0.285406	−	0.272134i
$285$	−5790.52	+	102.250i	−1.20351	+	0.0212517i
$286$	191.340	−	76.6009i	0.0395600	−	0.0158374i
$287$	−701.890	+	1536.92i	−0.144360	+	0.316104i
$288$	−3332.45	−	5328.22i	−0.681828	−	1.09017i
$289$	185.065	−	1287.16i	0.0376685	−	0.261990i
$290$	−3927.72	−	2024.88i	−0.795323	−	0.410018i
$291$	−2541.39	+	536.516i	−0.511956	+	0.108079i
$292$	−6803.76	−	2723.82i	−1.36356	−	0.545888i
$293$	232.690	−	44.8473i	0.0463955	−	0.00894200i	−0.166001	−	0.986126i	$-0.553085\pi$
$293$	232.690	−	44.8473i	0.0463955	−	0.00894200i	0.212396	+	0.977184i	$0.431873\pi$
$294$	−877.492	+	1279.49i	−0.174069	+	0.253814i
$295$	−37.3925	−	7.20681i	−0.00737991	−	0.00142236i
$296$	−1203.13	+	353.271i	−0.236252	+	0.0693699i
$297$	−428.215	−	367.044i	−0.0836618	−	0.0717106i
$298$	7687.20			1.49432
$299$	397.036	+	1437.44i	0.0767933	+	0.278025i
$300$	48.9332	−	1633.69i	0.00941720	−	0.314404i
$301$	427.435	+	40.8151i	0.0818503	+	0.00781576i
$302$	−1521.93	+	6273.47i	−0.289990	+	1.19536i
$303$	−1012.16	+	4518.98i	−0.191904	+	0.856793i
$304$	453.060	−	9510.91i	0.0854763	−	1.79437i
$305$	2858.09	+	3298.42i	0.536570	+	0.619235i
$306$	5056.49	−	3507.88i	0.944641	−	0.655334i
$307$	4176.21	+	1226.25i	0.776381	+	0.227966i	0.645836	−	0.763477i	$-0.276509\pi$
$307$	4176.21	+	1226.25i	0.776381	+	0.227966i	0.130545	+	0.991442i	$0.458327\pi$
$308$	−370.637	−	191.077i	−0.0685682	−	0.0353494i
$309$	402.562	−	481.502i	0.0741131	−	0.0886462i
$310$	4814.82	+	6761.47i	0.882140	+	1.23879i
$311$	373.243	+	524.147i	0.0680537	+	0.0955680i	0.847200	−	0.531274i	$-0.178287\pi$
$311$	373.243	+	524.147i	0.0680537	+	0.0955680i	−0.779146	+	0.626842i	$0.784347\pi$
$312$	−276.670	+	330.924i	−0.0502031	+	0.0600476i
$313$	7195.56	+	3709.57i	1.29942	+	0.669895i	0.962408	−	0.271607i	$-0.0875550\pi$
$313$	7195.56	+	3709.57i	1.29942	+	0.669895i	0.337007	+	0.941502i	$0.390585\pi$
$314$	−11718.3	−	3440.80i	−2.10605	−	0.618393i
$315$	−316.277	−	3805.84i	−0.0565720	−	0.680746i
$316$	1341.68	+	1548.38i	0.238846	+	0.275642i
$317$	−433.691	+	9104.30i	−0.0768408	+	1.61309i	0.550836	+	0.834613i	$0.314309\pi$
$317$	−433.691	+	9104.30i	−0.0768408	+	1.61309i	−0.627677	+	0.778474i	$0.715994\pi$
$318$	118.084	−	527.206i	0.0208233	−	0.0929694i
$319$	126.929	−	523.209i	0.0222780	−	0.0918311i
$320$	−2494.69	−	238.214i	−0.435805	−	0.0416143i
$321$	−187.543	+	6261.34i	−0.0326095	+	1.08870i
$322$	3767.98	−	5660.49i	0.652116	−	0.979649i
$323$	7699.31			1.32632
$324$	−4544.57	−	992.300i	−0.779248	−	0.170147i
$325$	−639.453	+	187.760i	−0.109140	+	0.0320464i
$326$	−2754.93	−	530.970i	−0.468042	−	0.0902077i
$327$	−3953.92	+	5765.28i	−0.668661	+	0.974987i
$328$	−626.648	+	120.777i	−0.105490	+	0.0203316i
$329$	−9572.50	−	3832.25i	−1.60410	−	0.642185i
$330$	−674.368	+	142.366i	−0.112493	+	0.0237485i
$331$	4445.47	+	2291.80i	0.738202	+	0.380570i	0.785950	−	0.618290i	$-0.212174\pi$
$331$	4445.47	+	2291.80i	0.738202	+	0.380570i	−0.0477479	+	0.998859i	$0.515204\pi$
$332$	508.353	−	3535.68i	0.0840347	−	0.584474i
$333$	−2586.64	+	4869.53i	−0.425667	+	0.801347i
$334$	−2679.31	+	5866.87i	−0.438938	+	0.961140i
$335$	2907.72	−	1164.08i	0.474227	−	0.189852i
$336$	6277.79	−	110.854i	1.01929	−	0.0179987i
$337$	3875.08	−	3694.89i	0.626378	−	0.597250i	−0.308930	−	0.951085i	$-0.599971\pi$
$337$	3875.08	−	3694.89i	0.626378	−	0.597250i	0.935308	+	0.353835i	$0.115122\pi$
$338$	7091.20	+	2838.89i	1.14115	+	0.456849i
$339$	−1262.16	−	7798.44i	−0.202215	−	1.24942i
$340$	158.779	−	3333.19i	0.0253265	−	0.531669i
$341$	−662.266	+	764.296i	−0.105172	+	0.121375i
$342$	−8933.68	−	9602.90i	−1.41251	−	1.51832i
$343$	−2848.01	−	6236.28i	−0.448333	−	0.981712i
$344$	81.0902	+	140.452i	0.0127096	+	0.0220136i
$345$	−481.723	−	4963.64i	−0.0751742	−	0.774589i
$346$	3390.65	−	5872.78i	0.526828	−	0.912493i
$347$	−5974.65	−	570.510i	−0.924311	−	0.0882610i	−0.377965	−	0.925820i	$-0.623376\pi$
$347$	−5974.65	−	570.510i	−0.924311	−	0.0882610i	−0.546347	+	0.837559i	$0.683982\pi$
$348$	−1122.90	−	4296.11i	−0.172970	−	0.661770i
$349$	4009.07	+	772.684i	0.614901	+	0.118512i	0.487186	−	0.873298i	$-0.338023\pi$
$349$	4009.07	+	772.684i	0.614901	+	0.118512i	0.127715	+	0.991811i	$0.459236\pi$
$350$	2556.48	+	1642.95i	0.390427	+	0.250912i
$351$	190.432	+	1887.17i	0.0289587	+	0.286978i
$352$	−133.164	−	926.176i	−0.0201638	−	0.140242i
$353$	−1734.95	−	7151.57i	−0.261593	−	1.07830i	−0.939335	−	0.343000i	$-0.888557\pi$
$353$	−1734.95	−	7151.57i	−0.261593	−	1.07830i	0.677743	−	0.735299i	$-0.262958\pi$
$354$	−44.4327	−	73.9144i	−0.00667110	−	0.0110975i
$355$	2023.01	+	1590.91i	0.302451	+	0.237850i
$356$	2684.83	+	3770.31i	0.399706	+	0.561309i
$357$	331.074	+	5066.25i	0.0490820	+	0.751076i
$358$	−10258.2	+	4106.78i	−1.51443	+	0.606285i
$359$	4741.71	−	3047.31i	0.697097	−	0.447997i	−0.143506	−	0.989649i	$-0.545838\pi$
$359$	4741.71	−	3047.31i	0.697097	−	0.447997i	0.840602	+	0.541653i	$0.182201\pi$
$360$	1101.66	−	931.142i	0.161285	−	0.136321i
$361$	−1359.11	−	9452.81i	−0.198150	−	1.37816i
$362$	4810.30	−	13898.4i	0.698408	−	2.01792i
$363$	2947.44	+	6163.62i	0.426172	+	0.891202i
$364$	458.670	+	1325.24i	0.0660463	+	0.190828i
$365$	2356.03	−	9711.67i	0.337863	−	1.39269i
$366$	−1233.71	+	9806.86i	−0.176194	+	1.40058i
$367$	785.831	+	1361.10i	0.111771	+	0.193593i	0.916484	−	0.400070i	$-0.131014\pi$
$367$	785.831	+	1361.10i	0.111771	+	0.193593i	−0.804713	+	0.593664i	$0.797681\pi$
$368$	8195.01	−	258.157i	1.16085	−	0.0365689i
$369$	−1546.08	+	2341.97i	−0.218119	+	0.330402i
$370$	2799.18	+	6129.36i	0.393304	+	0.861216i
$371$	322.577	+	307.577i	0.0451412	+	0.0430420i
$372$	−1823.04	+	8139.29i	−0.254086	+	1.13442i
$373$	−5811.50	+	2996.03i	−0.806723	+	0.415895i	−0.811687	−	0.584093i	$-0.801450\pi$
$373$	−5811.50	+	2996.03i	−0.806723	+	0.415895i	0.00496338	+	0.999988i	$0.498420\pi$
$374$	899.729	−	173.408i	0.124395	−	0.0239752i
$375$	7829.92	−	887.425i	1.07823	−	0.122204i
$376$	−918.187	−	3784.82i	−0.125936	−	0.519115i
$377$	−1523.20	+	978.899i	−0.208086	+	0.133729i
$378$	5934.68	−	6291.41i	0.807532	−	0.856072i
$379$	1794.94	−	3930.37i	0.243271	−	0.532690i	−0.748129	−	0.663553i	$-0.769048\pi$
$379$	1794.94	−	3930.37i	0.243271	−	0.532690i	0.991400	+	0.130863i	$0.0417749\pi$
$380$	−7079.65	+	676.025i	−0.955733	+	0.0912614i
$381$	−7467.74	−	1302.99i	−1.00416	−	0.175208i
$382$	692.988	+	14547.6i	0.0928177	+	1.94848i
$383$	−389.259	+	371.158i	−0.0519327	+	0.0495177i	−0.715601	−	0.698509i	$-0.753847\pi$
$383$	−389.259	+	371.158i	−0.0519327	+	0.0495177i	0.663668	+	0.748027i	$0.268999\pi$
$384$	2377.51	+	3216.99i	0.315955	+	0.427516i
$385$	185.972	−	537.332i	0.0246183	−	0.0711298i
$386$	6454.33	+	4147.95i	0.851080	+	0.546956i
$387$	690.937	+	176.636i	0.0907553	+	0.0232014i
$388$	−3060.41	+	898.617i	−0.400435	+	0.117578i
$389$	7891.97	−	11082.7i	1.02863	−	1.44451i	0.137650	−	0.990481i	$-0.456045\pi$
$389$	7891.97	−	11082.7i	1.02863	−	1.44451i	0.890984	−	0.454034i	$-0.150015\pi$
$390$	1971.79	+	1218.55i	0.256014	+	0.158214i
$391$	523.814	+	6609.10i	0.0677504	+	0.854825i
$392$	241.723	−	418.676i	0.0311450	−	0.0539448i
$393$	267.992	−	2130.29i	0.0343980	−	0.273432i
$394$	−13894.7	−	13248.6i	−1.77666	−	1.69404i
$395$	−1829.49	+	2111.35i	−0.233043	+	0.268945i
$396$	−559.183	−	408.639i	−0.0709596	−	0.0518558i
$397$	4874.46	+	5625.43i	0.616227	+	0.711164i	0.974986	−	0.222266i	$-0.0713454\pi$
$397$	4874.46	+	5625.43i	0.616227	+	0.711164i	−0.358759	+	0.933430i	$0.616800\pi$
$398$	−9620.89	+	7565.95i	−1.21169	+	0.952881i
$399$	10587.0	−	2235.04i	1.32836	−	0.280430i
$400$	174.348	+	3660.02i	0.0217935	+	0.457503i
$401$	300.127	+	236.023i	0.0373757	+	0.0293925i	0.636672	−	0.771135i	$-0.280310\pi$
$401$	300.127	+	236.023i	0.0373757	+	0.0293925i	−0.599296	+	0.800527i	$0.704553\pi$
$402$	6361.13	+	3138.49i	0.789215	+	0.389388i
$403$	3385.70	−	323.295i	0.418495	−	0.0399614i
$404$	−809.314	+	5628.90i	−0.0996655	+	0.693189i
$405$	457.401	−	6326.41i	0.0561196	−	0.776203i
$406$	7921.70	+	2326.02i	0.968343	+	0.284331i
$407$	−645.320	+	507.485i	−0.0785930	+	0.0618062i
$408$	−1486.21	+	1211.84i	−0.180339	+	0.147047i
$409$	2369.84	−	1221.74i	0.286507	−	0.147704i	−0.308983	−	0.951068i	$-0.599989\pi$
$409$	2369.84	−	1221.74i	0.286507	−	0.147704i	0.595489	+	0.803363i	$0.296958\pi$
$410$	1121.66	+	3240.81i	0.135109	+	0.390372i
$411$	−259.330	+	256.163i	−0.0311236	+	0.0307435i
$412$	447.055	−	627.801i	0.0534583	−	0.0750716i
$413$	71.1478			0.00847689
$414$	7635.36	−	8322.01i	0.906419	−	0.987933i
$415$	4870.78			0.576138
$416$	−1825.34	+	2563.32i	−0.215131	+	0.302109i
$417$	8794.64	+	2414.52i	1.03279	+	0.283548i
$418$	−638.705	−	1845.42i	−0.0747371	−	0.215939i
$419$	3797.94	−	1957.98i	0.442820	−	0.228290i	−0.222372	−	0.974962i	$-0.571380\pi$
$419$	3797.94	−	1957.98i	0.442820	−	0.228290i	0.665192	+	0.746672i	$0.268350\pi$
$420$	−749.261	−	4629.43i	−0.0870481	−	0.537841i
$421$	−9091.05	+	7149.28i	−1.05242	+	0.827636i	−0.985424	−	0.170117i	$-0.945585\pi$
$421$	−9091.05	+	7149.28i	−1.05242	+	0.827636i	−0.0670004	+	0.997753i	$0.521343\pi$
$422$	2743.67	+	805.614i	0.316492	+	0.0929305i
$423$	−14725.0	−	8744.47i	−1.69256	−	1.00513i
$424$	−23.9587	+	166.636i	−0.00274419	+	0.0190862i
$425$	−2949.46	+	281.639i	−0.336635	+	0.0321447i
$426$	380.076	+	5816.10i	0.0432271	+	0.661481i
$427$	−6409.68	−	5040.63i	−0.726431	−	0.571272i
$428$	366.017	+	7683.64i	0.0413367	+	0.867764i
$429$	−87.6400	+	268.464i	−0.00986317	+	0.0302134i
$430$	685.060	−	538.737i	0.0768291	−	0.0604191i
$431$	−3220.04	−	3716.13i	−0.359870	−	0.415312i	0.546726	−	0.837312i	$-0.315874\pi$
$431$	−3220.04	−	3716.13i	−0.359870	−	0.415312i	−0.906596	+	0.421999i	$0.861328\pi$
$432$	10330.1	+	1428.68i	1.15048	+	0.159114i
$433$	−10412.8	+	12017.1i	−1.15568	+	1.33372i	−0.222238	+	0.974992i	$0.571336\pi$
$433$	−10412.8	+	12017.1i	−1.15568	+	1.33372i	−0.933441	+	0.358732i	$0.883209\pi$
$434$	−11223.9	−	10702.0i	−1.24140	−	1.18367i
$435$	5580.59	−	2349.28i	0.615101	−	0.258941i
$436$	−4292.37	+	7434.60i	−0.471484	+	0.816635i
$437$	13783.3	−	3109.59i	1.50880	−	0.340393i
$438$	19929.9	−	10724.2i	2.17418	−	1.16991i
$439$	−3086.39	+	4334.22i	−0.335547	+	0.471210i	−0.947533	−	0.319659i	$-0.896432\pi$
$439$	−3086.39	+	4334.22i	−0.335547	+	0.471210i	0.611986	+	0.790869i	$0.290371\pi$
$440$	206.068	−	60.5069i	0.0223270	−	0.00655580i
$441$	−573.816	−	2046.95i	−0.0619605	−	0.221029i
$442$	−2592.35	−	1666.00i	−0.278972	−	0.179284i
$443$	677.244	−	1956.77i	0.0726339	−	0.209862i	−0.902840	−	0.429976i	$-0.858522\pi$
$443$	677.244	−	1956.77i	0.0726339	−	0.209862i	0.975474	+	0.220114i	$0.0706431\pi$
$444$	−2703.61	+	6207.86i	−0.288981	+	0.663540i
$445$	−4567.81	+	4355.39i	−0.486595	+	0.463967i
$446$	557.229	+	11697.7i	0.0591604	+	1.24193i
$447$	−6756.11	+	8080.95i	−0.714884	+	0.855069i
$448$	4660.94	−	445.066i	0.491538	−	0.0469362i
$449$	−1979.58	+	4334.68i	−0.208067	+	0.455604i	−0.984679	−	0.174375i	$-0.944209\pi$
$449$	−1979.58	+	4334.68i	−0.208067	+	0.455604i	0.776612	+	0.629979i	$0.216937\pi$
$450$	3773.59	+	3351.90i	0.395309	+	0.351133i
$451$	−351.498	+	225.894i	−0.0366993	+	0.0235852i
$452$	−2287.12	−	9427.62i	−0.238002	−	0.981057i
$453$	−5257.22	−	7113.50i	−0.545266	−	0.737795i
$454$	8580.49	−	1653.75i	0.887009	−	0.170957i
$455$	−1699.68	+	876.246i	−0.175126	+	0.0902836i
$456$	3007.20	+	2767.66i	0.308827	+	0.284227i
$457$	−11265.3	−	10741.5i	−1.15311	−	1.09949i	−0.993677	−	0.112278i	$-0.964185\pi$
$457$	−11265.3	−	10741.5i	−1.15311	−	1.09949i	−0.159432	−	0.987209i	$-0.550966\pi$
$458$	−5672.62	−	12421.3i	−0.578742	−	1.26727i
$459$	−756.480	+	8398.49i	−0.0769269	+	0.854048i
$460$	−1061.96	−	6031.19i	−0.107639	−	0.611317i
$461$	−2248.31	−	3894.18i	−0.227146	−	0.393428i	0.729815	−	0.683644i	$-0.239606\pi$
$461$	−2248.31	−	3894.18i	−0.227146	−	0.393428i	−0.956961	+	0.290217i	$0.906273\pi$
$462$	1186.84	−	499.630i	0.119517	−	0.0503137i
$463$	−4328.94	+	17844.1i	−0.434521	+	1.79112i	0.160088	+	0.987103i	$0.448822\pi$
$463$	−4328.94	+	17844.1i	−0.434521	+	1.79112i	−0.594609	+	0.804015i	$0.702693\pi$
$464$	3255.93	+	9407.40i	0.325761	+	0.941224i
$465$	−11339.4	−	881.067i	−1.13087	−	0.0878678i
$466$	−1225.60	+	3541.15i	−0.121835	+	0.352018i
$467$	1805.58	+	12558.1i	0.178913	+	1.24437i	0.859283	+	0.511500i	$0.170910\pi$
$467$	1805.58	+	12558.1i	0.178913	+	1.24437i	−0.680370	+	0.732869i	$0.738181\pi$
$468$	412.669	+	2292.35i	0.0407599	+	0.226419i
$469$	−4922.85	+	3163.73i	−0.484683	+	0.311487i
$470$	−19429.5	+	7778.39i	−1.90684	+	0.763383i
$471$	13916.0	−	9294.47i	1.36139	−	0.909271i
$472$	15.5880	+	21.8902i	0.00152012	+	0.00213470i
$473$	83.4646	+	65.6373i	0.00811355	+	0.00638057i
$474$	−6325.96	+	111.704i	−0.612998	+	0.0108244i
$475$	1488.72	+	6136.58i	0.143804	+	0.592769i
$476$	887.277	+	6171.15i	0.0854375	+	0.594231i
$477$	450.430	+	587.483i	0.0432364	+	0.0563920i
$478$	−4523.87	−	2907.31i	−0.432880	−	0.278195i
$479$	16453.5	+	3171.14i	1.56947	+	0.302491i	0.898494	−	0.438986i	$-0.144662\pi$
$479$	16453.5	+	3171.14i	1.56947	+	0.302491i	0.670979	+	0.741477i	$0.265874\pi$
$480$	7486.67	−	7395.24i	0.711913	−	0.703219i
$481$	2748.45	+	262.445i	0.260537	+	0.0248783i
$482$	1441.43	−	2496.64i	0.136215	−	0.235931i
$483$	2638.84	+	8935.87i	0.248595	+	0.841814i
$484$	4194.90	+	7265.79i	0.393962	+	0.682362i
$485$	−1806.77	−	3956.27i	−0.169157	−	0.370402i
$486$	11352.7	−	8801.44i	1.05961	−	0.821485i
$487$	1204.10	−	1389.60i	0.112039	−	0.129299i	−0.696960	−	0.717110i	$-0.745464\pi$
$487$	1204.10	−	1389.60i	0.112039	−	0.129299i	0.808999	+	0.587811i	$0.200010\pi$
$488$	146.549	−	3076.45i	0.0135942	−	0.285378i
$489$	2979.42	−	2429.39i	0.275530	−	0.224664i
$490$	−2411.83	−	965.549i	−0.222357	−	0.0890185i
$491$	−12474.1	+	11894.0i	−1.14653	+	1.09322i	−0.152045	+	0.988374i	$0.548586\pi$
$491$	−12474.1	+	11894.0i	−1.14653	+	1.09322i	−0.994489	+	0.104844i	$0.966566\pi$
$492$	−1670.09	+	3014.37i	−0.153036	+	0.276216i
$493$	−7473.00	+	2991.74i	−0.682692	+	0.273309i
$494$	−2728.22	+	5973.98i	−0.248479	+	0.544093i
$495$	443.029	−	834.033i	0.0402276	−	0.0757313i
$496$	2661.20	−	18509.1i	0.240910	−	1.67557i
$497$	−4273.89	−	2203.35i	−0.385735	−	0.198860i
$498$	7369.76	+	8207.76i	0.663146	+	0.738551i
$499$	−10799.6	−	4323.50i	−0.968849	−	0.387869i	−0.167372	−	0.985894i	$-0.553528\pi$
$499$	−10799.6	−	4323.50i	−0.968849	−	0.387869i	−0.801477	+	0.598025i	$0.795952\pi$
$500$	9501.81	−	1831.32i	0.849868	−	0.163799i
$501$	−3812.59	−	7972.81i	−0.339988	−	0.710976i
$502$	8697.06	+	1676.22i	0.773245	+	0.149031i
$503$	20525.9	−	6026.95i	1.81949	−	0.534251i	0.820209	−	0.572065i	$-0.193857\pi$
$503$	20525.9	−	6026.95i	1.81949	−	0.534251i	0.999285	+	0.0378130i	$0.0120391\pi$
$504$	−1691.85	+	2097.79i	−0.149525	+	0.185403i
$505$	−7754.43			−0.683302
$506$	1540.66	−	673.817i	0.135357	−	0.0591992i
$507$	−9216.60	+	4959.38i	−0.807345	+	0.434426i
$508$	−9266.76	−	884.868i	−0.809343	−	0.0772829i
$509$	−173.871	+	716.705i	−0.0151408	+	0.0624114i	−0.978881	−	0.204432i	$-0.934465\pi$
$509$	−173.871	+	716.705i	−0.0151408	+	0.0624114i	0.963740	+	0.266843i	$0.0859805\pi$
$510$	7582.45	+	6978.46i	0.658346	+	0.605905i
$511$	−888.405	+	18649.9i	−0.0769094	+	1.61453i
$512$	8938.95	+	10316.1i	0.771581	+	0.890452i
$513$	17946.4	−	951.489i	1.54455	−	0.0818894i
$514$	−20308.5	−	5963.11i	−1.74274	−	0.511715i
$515$	934.103	+	481.563i	0.0799252	+	0.0412043i
$516$	862.722	+	150.530i	0.0736031	+	0.0128424i
$517$	−1479.06	−	2077.05i	−0.125820	−	0.176689i
$518$	−7302.59	−	10255.1i	−0.619416	−	0.869848i
$519$	3193.62	+	8725.79i	0.270105	+	0.737995i
$520$	−641.985	−	330.966i	−0.0541402	−	0.0279112i
$521$	−3668.02	−	1077.03i	−0.308443	−	0.0905670i	0.123848	−	0.992301i	$-0.460476\pi$
$521$	−3668.02	−	1077.03i	−0.308443	−	0.0905670i	−0.432291	+	0.901734i	$0.642295\pi$
$522$	12402.5	+	5849.27i	1.03993	+	0.490451i
$523$	7151.34	+	8253.08i	0.597909	+	0.690023i	0.971356	−	0.237628i	$-0.0763699\pi$
$523$	7151.34	+	8253.08i	0.597909	+	0.690023i	−0.373448	+	0.927651i	$0.621824\pi$
$524$	125.455	−	2633.62i	0.0104590	−	0.219562i
$525$	−3973.93	+	1243.47i	−0.330356	+	0.103371i
$526$	1787.06	−	7366.38i	0.148136	−	0.610626i
$527$	15052.0	+	1437.29i	1.24417	+	0.118803i
$528$	1320.82	+	816.253i	0.108866	+	0.0672781i
$529$	3607.01	+	11620.0i	0.296458	+	0.955046i
$530$	904.670			0.0741441
$531$	116.751	+	18.2532i	0.00954158	+	0.00149175i
$532$	12749.2	−	3743.49i	1.03900	−	0.305077i
$533$	1379.78	+	265.932i	0.112130	+	0.0216112i
$534$	−14250.6	−	1107.26i	−1.15484	−	0.0897303i
$535$	−10299.6	+	1985.09i	−0.832323	+	0.160417i
$536$	−2051.95	−	821.478i	−0.165356	−	0.0661986i
$537$	4698.61	−	14393.0i	0.377579	−	1.15662i
$538$	19791.5	+	10203.2i	1.58601	+	0.817644i
$539$	45.0454	−	313.297i	0.00359970	−	0.0250365i
$540$	−41.8185	−	7788.99i	−0.00333256	−	0.620712i
$541$	−5375.14	+	11769.9i	−0.427163	+	0.935357i	0.566615	+	0.823982i	$0.308253\pi$
$541$	−5375.14	+	11769.9i	−0.427163	+	0.935357i	−0.993779	+	0.111374i	$0.964475\pi$
$542$	−4844.83	+	1939.58i	−0.383954	+	0.153712i
$543$	10382.7	+	17271.7i	0.820559	+	1.36501i
$544$	−10125.1	+	9654.22i	−0.797993	+	0.760884i
$545$	−10867.5	−	4350.70i	−0.854153	−	0.341951i
$546$	−4048.27	−	1538.32i	−0.317308	−	0.120575i
$547$	121.418	−	2548.89i	0.00949082	−	0.199237i	−0.989142	−	0.146963i	$-0.953050\pi$
$547$	121.418	−	2548.89i	0.00949082	−	0.199237i	0.998633	−	0.0522737i	$-0.0166468\pi$
$548$	−293.131	+	338.291i	−0.0228502	+	0.0263706i
$549$	−9224.90	−	9915.94i	−0.717139	−	0.770860i
$550$	312.181	+	683.581i	0.0242026	+	0.0529963i
$551$	8577.80	+	14857.2i	0.663206	+	1.14871i
$552$	−2171.17	+	2769.68i	−0.167412	+	0.213561i
$553$	2609.81	−	4520.32i	0.200688	−	0.347602i
$554$	−10344.8	−	987.810i	−0.793338	−	0.0757546i
$555$	−8903.46	−	2444.40i	−0.680956	−	0.186953i
$556$	10997.0	+	2119.50i	0.838809	+	0.161667i
$557$	7760.82	+	4987.57i	0.590371	+	0.379408i	0.801451	−	0.598061i	$-0.204062\pi$
$557$	7760.82	+	4987.57i	0.590371	+	0.379408i	−0.211080	+	0.977469i	$0.567698\pi$
$558$	−15672.5	−	20441.2i	−1.18902	−	1.55080i
$559$	−50.8202	−	353.462i	−0.00384520	−	0.0267439i
$560$	2478.69	+	10217.3i	0.187043	+	0.771000i
$561$	−608.462	+	1098.22i	−0.0457919	+	0.0826504i
$562$	−52.0698	−	40.9482i	−0.00390824	−	0.00307348i
$563$	−3847.65	−	5403.27i	−0.288027	−	0.404477i	0.645058	−	0.764134i	$-0.276833\pi$
$563$	−3847.65	−	5403.27i	−0.288027	−	0.404477i	−0.933085	+	0.359656i	$0.882894\pi$
$564$	−18859.8	−	9305.15i	−1.40805	−	0.694712i
$565$	12280.7	−	4916.45i	0.914430	−	0.366083i
$566$	19465.5	−	12509.7i	1.44557	−	0.929013i
$567$	1397.80	+	11768.1i	0.103531	+	0.871626i
$568$	−258.470	−	1797.70i	−0.0190936	−	0.132799i
$569$	4495.71	−	12989.5i	0.331230	−	0.957027i	−0.649278	−	0.760551i	$-0.724929\pi$
$569$	4495.71	−	12989.5i	0.331230	−	0.957027i	0.980509	−	0.196476i	$-0.0629499\pi$
$570$	12421.5	−	18112.1i	0.912774	−	1.33093i
$571$	−2636.03	−	7616.30i	−0.193195	−	0.558200i	0.806248	−	0.591578i	$-0.201495\pi$
$571$	−2636.03	−	7616.30i	−0.193195	−	0.558200i	−0.999443	+	0.0333778i	$0.989374\pi$
$572$	−81.7599	+	337.019i	−0.00597649	+	0.0246354i
$573$	−15901.8	−	12057.1i	−1.15935	−	0.879045i
$574$	−3203.68	−	5548.93i	−0.232960	−	0.403498i
$575$	−5166.37	+	1695.41i	−0.374700	+	0.122963i
$576$	7762.65	+	465.441i	0.561534	+	0.0336690i
$577$	−6522.53	−	14282.3i	−0.470600	−	1.03047i	−0.984942	−	0.172886i	$-0.944691\pi$
$577$	−6522.53	−	14282.3i	−0.470600	−	1.03047i	0.514341	−	0.857585i	$-0.328036\pi$
$578$	3569.00	+	3403.03i	0.256835	+	0.244892i
$579$	−10033.0	+	3139.39i	−0.720133	+	0.225334i
$580$	6608.88	−	3407.11i	0.473136	−	0.243918i
$581$	−8935.84	+	1722.24i	−0.638075	+	0.122979i
$582$	3932.98	−	9030.65i	0.280115	−	0.643183i
$583$	25.9856	+	107.114i	0.00184599	+	0.00760928i
$584$	−5932.71	+	3812.72i	−0.420372	+	0.270157i
$585$	−3013.93	+	1001.83i	−0.213009	+	0.0708047i
$586$	−373.312	+	817.440i	−0.0263164	+	0.0576248i
$587$	−22688.1	+	2166.45i	−1.59529	+	0.152332i	−0.854519	−	0.519421i	$-0.826148\pi$
$587$	−22688.1	+	2166.45i	−1.59529	+	0.152332i	−0.740775	+	0.671753i	$0.765542\pi$
$588$	−897.250	−	2451.51i	−0.0629285	−	0.171937i
$589$	−1533.34	−	32188.7i	−0.107267	−	2.25181i
$590$	104.514	−	99.6542i	0.00729286	−	0.00695373i
$591$	26139.0	−	2962.53i	1.81931	−	0.206196i
$592$	4964.84	−	14345.0i	0.344685	−	0.995903i
$593$	1434.38	+	921.821i	0.0993305	+	0.0638359i	0.589363	−	0.807868i	$-0.299379\pi$
$593$	1434.38	+	921.821i	0.0993305	+	0.0638359i	−0.490033	+	0.871704i	$0.663015\pi$
$594$	2075.76	−	515.389i	0.143383	−	0.0356005i
$595$	−8157.06	+	2395.13i	−0.562028	+	0.165026i
$596$	−7502.84	+	10536.3i	−0.515651	+	0.724131i
$597$	502.102	−	16763.2i	0.0344216	−	1.14920i
$598$	−5313.69	−	1935.48i	−0.363366	−	0.132354i
$599$	12485.3	−	21625.2i	0.851648	−	1.47510i	−0.0280724	−	0.999606i	$-0.508937\pi$
$599$	12485.3	−	21625.2i	0.851648	−	1.47510i	0.879720	−	0.475492i	$-0.157730\pi$
$600$	−1253.24	−	950.236i	−0.0852724	−	0.0646553i
$601$	−20212.7	−	19272.8i	−1.37187	−	1.30808i	−0.906034	−	0.423206i	$-0.860905\pi$
$601$	−20212.7	−	19272.8i	−1.37187	−	1.30808i	−0.465837	−	0.884870i	$-0.654247\pi$
$602$	−1066.31	+	1230.58i	−0.0721918	+	0.0833138i
$603$	−8889.92	+	3928.60i	−0.600374	+	0.265315i
$604$	−7113.14	−	8209.00i	−0.479188	−	0.553012i
$605$	−8992.63	+	7071.88i	−0.604302	+	0.475228i
$606$	−11732.9	−	13067.0i	−0.786494	−	0.875924i
$607$	−1088.22	−	22844.5i	−0.0727668	−	1.52756i	−0.680102	−	0.733117i	$-0.738065\pi$
$607$	−1088.22	−	22844.5i	−0.0727668	−	1.52756i	0.607335	−	0.794446i	$-0.292238\pi$
$608$	23436.9	+	18431.0i	1.56331	+	1.22940i
$609$	−9407.38	+	6283.17i	−0.625954	+	0.418074i
$610$	−16475.9	+	1573.26i	−1.09359	+	0.104425i
$611$	−1220.40	+	8488.03i	−0.0808051	+	0.562012i
$612$	−127.234	+	10354.3i	−0.00840378	+	0.683901i
$613$	12194.4	+	3580.59i	0.803467	+	0.235919i	0.657583	−	0.753382i	$-0.271579\pi$
$613$	12194.4	+	3580.59i	0.803467	+	0.235919i	0.145884	+	0.989302i	$0.453397\pi$
$614$	−12974.3	+	10203.1i	−0.852770	+	0.670626i
$615$	−4392.61	−	1669.17i	−0.288012	−	0.109443i
$616$	−356.653	+	183.868i	−0.0233279	+	0.0120264i
$617$	4599.88	+	13290.5i	0.300137	+	0.867188i	0.989725	+	0.142986i	$0.0456704\pi$
$617$	4599.88	+	13290.5i	0.300137	+	0.867188i	−0.689588	+	0.724202i	$0.742208\pi$
$618$	601.866	+	2302.69i	0.0391757	+	0.149883i
$619$	6740.48	−	9465.68i	0.437678	−	0.614633i	−0.535542	−	0.844509i	$-0.679893\pi$
$619$	6740.48	−	9465.68i	0.437678	−	0.614633i	0.973220	+	0.229876i	$0.0738320\pi$
$620$	−13966.8			−0.904709
$621$	2037.72	+	15340.5i	0.131676	+	0.991293i
$622$	−2440.14			−0.157300
$623$	6840.00	−	9605.44i	0.439870	−	0.617711i
$624$	−1320.48	−	5052.06i	−0.0847142	−	0.324110i
$625$	2300.31	+	6646.31i	0.147220	+	0.425364i
$626$	−27287.1	+	14067.5i	−1.74219	+	0.898161i
$627$	2501.29	+	950.478i	0.159317	+	0.0605397i
$628$	16153.3	−	12703.1i	1.02641	−	0.807179i
$629$	11777.3	+	3458.13i	0.746570	+	0.219213i
$630$	12452.1	+	7394.71i	0.787468	+	0.467639i
$631$	1177.25	−	8187.94i	0.0742718	−	0.516571i	−0.918393	−	0.395670i	$-0.870512\pi$
$631$	1177.25	−	8187.94i	0.0742718	−	0.516571i	0.992665	−	0.120901i	$-0.0385785\pi$
$632$	1962.57	−	187.403i	0.123524	−	0.0117951i
$633$	−3258.23	+	2176.17i	−0.204586	+	0.136643i
$634$	−27169.6	−	21366.4i	−1.70196	−	1.33844i
$635$	−603.982	−	12679.1i	−0.0377453	−	0.792372i
$636$	607.350	+	676.411i	0.0378664	+	0.0421721i
$637$	−836.733	+	658.014i	−0.0520449	+	0.0409285i
$638$	1337.01	+	1542.99i	0.0829667	+	0.0957487i
$639$	−6448.05	−	4712.10i	−0.399188	−	0.291718i
$640$	−4386.42	+	5062.20i	−0.270920	+	0.312658i
$641$	8290.13	+	7904.62i	0.510827	+	0.487073i	0.901091	−	0.433630i	$-0.142768\pi$
$641$	8290.13	+	7904.62i	0.510827	+	0.487073i	−0.390264	+	0.920703i	$0.627616\pi$
$642$	−18929.0	−	14352.4i	−1.16366	−	0.882311i
$643$	11915.7	−	20638.6i	0.730808	−	1.26580i	−0.225731	−	0.974190i	$-0.572477\pi$
$643$	11915.7	−	20638.6i	0.730808	−	1.26580i	0.956538	−	0.291606i	$-0.0941897\pi$
$644$	4080.80	+	10689.2i	0.249699	+	0.654060i
$645$	−35.7524	+	1193.63i	−0.00218256	+	0.0728671i
$646$	−16936.1	+	23783.5i	−1.03149	+	1.44853i
$647$	−6740.36	+	1979.15i	−0.409569	+	0.120260i	−0.480025	−	0.877255i	$-0.659373\pi$
$647$	−6740.36	+	1979.15i	−0.409569	+	0.120260i	0.0704566	+	0.997515i	$0.477554\pi$
$648$	−3314.46	+	3008.36i	−0.200933	+	0.182376i
$649$	14.8012	+	9.51217i	0.000895222	+	0.000575324i
$650$	826.604	−	2388.32i	0.0498801	−	0.144119i
$651$	21114.7	−	2393.09i	1.27120	−	0.144074i
$652$	3416.62	−	3257.74i	0.205223	−	0.195680i
$653$	−949.913	−	19941.1i	−0.0569265	−	1.19503i	−0.828907	−	0.559387i	$-0.811037\pi$
$653$	−949.913	−	19941.1i	−0.0569265	−	1.19503i	0.771980	−	0.635647i	$-0.219266\pi$
$654$	−9111.78	−	24895.7i	−0.544799	−	1.48853i
$655$	3578.96	−	341.750i	0.213499	−	0.0203867i
$656$	3209.39	−	7027.58i	0.191015	−	0.418264i
$657$	−6242.54	+	30376.0i	−0.370692	+	1.80378i
$658$	32894.6	−	21140.1i	1.94888	−	1.25247i
$659$	871.677	+	3593.10i	0.0515262	+	0.212394i	0.991755	−	0.128150i	$-0.0409040\pi$
$659$	871.677	+	3593.10i	0.0515262	+	0.212394i	−0.940229	+	0.340544i	$0.889389\pi$
$660$	463.064	−	1063.26i	0.0273102	−	0.0627079i
$661$	27010.7	−	5205.89i	1.58940	−	0.306332i	0.683542	−	0.729911i	$-0.260439\pi$
$661$	27010.7	−	5205.89i	1.58940	−	0.306332i	0.905859	+	0.423579i	$0.139226\pi$
$662$	−16858.1	+	8690.98i	−0.989744	+	0.510249i
$663$	4029.70	−	1260.92i	0.236049	−	0.0738614i
$664$	−2487.67	−	2371.98i	−0.145392	−	0.138631i
$665$	7526.71	+	16481.2i	0.438907	+	0.961072i
$666$	−9352.36	−	18701.7i	−0.544139	−	1.08810i
$667$	−12169.9	+	8373.99i	−0.706475	+	0.486120i
$668$	−5426.22	−	9398.49i	−0.314291	−	0.544369i
$669$	−12786.6	−	9695.07i	−0.738951	−	0.560288i
$670$	−2800.23	+	11542.7i	−0.161466	+	0.665572i
$671$	−659.526	−	1905.58i	−0.0379445	−	0.109633i
$672$	−11120.1	+	16214.4i	−0.638341	+	0.930778i
$673$	−1912.97	+	5527.17i	−0.109569	+	0.316578i	−0.986434	−	0.164158i	$-0.947509\pi$
$673$	−1912.97	+	5527.17i	−0.109569	+	0.316578i	0.876865	+	0.480736i	$0.159630\pi$
$674$	2889.65	+	20097.9i	0.165141	+	1.14858i
$675$	−6840.12	+	1020.97i	−0.390039	+	0.0582182i
$676$	−10812.2	+	6948.56i	−0.615167	+	0.395344i
$677$	11112.2	−	4448.63i	0.630834	−	0.252548i	−0.0341368	−	0.999417i	$-0.510868\pi$
$677$	11112.2	−	4448.63i	0.630834	−	0.252548i	0.664971	+	0.746869i	$0.268444\pi$
$678$	26866.1	+	13255.4i	1.52181	+	0.750839i
$679$	4713.55	+	6619.26i	0.266406	+	0.374115i
$680$	−2524.07	−	1984.95i	−0.142344	−	0.111940i
$681$	−5802.75	+	10473.4i	−0.326522	+	0.589344i
$682$	−904.158	−	3726.99i	−0.0507654	−	0.209258i
$683$	425.260	+	2957.75i	0.0238245	+	0.165703i	0.998260	−	0.0589640i	$-0.0187797\pi$
$683$	425.260	+	2957.75i	0.0238245	+	0.165703i	−0.974436	+	0.224667i	$0.927871\pi$
$684$	21881.4	−	2872.12i	1.22318	−	0.160553i
$685$	−513.479	−	329.993i	−0.0286409	−	0.0184064i
$686$	25528.9	+	4920.29i	1.42084	+	0.273845i
$687$	18043.1	+	4953.64i	1.00202	+	0.275099i
$688$	−1954.45	−	186.627i	−0.108303	−	0.0103417i
$689$	185.340	−	321.019i	0.0102480	−	0.0177501i
$690$	16392.5	+	9430.44i	0.904425	+	0.520306i
$691$	−2953.40	−	5115.43i	−0.162594	−	0.281621i	0.773204	−	0.634157i	$-0.218653\pi$
$691$	−2953.40	−	5115.43i	−0.162594	−	0.281621i	−0.935798	+	0.352536i	$0.885319\pi$
$692$	4740.04	+	10379.2i	0.260389	+	0.570173i
$693$	−517.870	+	1686.75i	−0.0283871	+	0.0924595i
$694$	14904.8	−	17201.0i	0.815240	−	0.940838i
$695$	−726.641	+	15254.1i	−0.0396591	+	0.832547i
$696$	−3994.25	−	1517.80i	−0.217531	−	0.0826608i
$697$	5799.59	+	2321.81i	0.315173	+	0.126176i
$698$	−11205.6	+	10684.5i	−0.607647	+	0.579391i
$699$	−2645.38	−	4400.62i	−0.143144	−	0.238121i
$700$	−4747.03	+	1900.42i	−0.256315	+	0.102613i
$701$	7350.81	−	16096.0i	0.396057	−	0.867244i	−0.601598	−	0.798799i	$-0.705469\pi$
$701$	7350.81	−	16096.0i	0.396057	−	0.867244i	0.997655	−	0.0684452i	$-0.0218038\pi$
$702$	−6248.43	−	3562.94i	−0.335943	−	0.191559i
$703$	3722.94	−	25893.6i	0.199734	−	1.38918i
$704$	1029.14	+	530.560i	0.0550956	+	0.0284037i
$705$	8899.34	−	27260.9i	0.475416	−	1.45632i
$706$	25907.9	+	10371.9i	1.38110	+	0.552908i
$707$	14226.1	−	2741.86i	0.756759	−	0.145853i
$708$	144.676	+	11.2412i	0.00767974	+	0.000596710i
$709$	−23387.4	−	4507.55i	−1.23883	−	0.238765i	−0.472570	−	0.881293i	$-0.656674\pi$
$709$	−23387.4	−	4507.55i	−1.23883	−	0.238765i	−0.766262	+	0.642528i	$0.777886\pi$
$710$	−9364.39	+	2749.63i	−0.494985	+	0.145341i
$711$	5442.32	−	6748.16i	0.287065	−	0.355943i
$712$	4453.93			0.234435
$713$	27526.6	−	3506.15i	1.44583	−	0.184160i
$714$	−16378.1	−	10121.5i	−0.858453	−	0.530515i
$715$	−470.743	−	44.9506i	−0.0246221	−	0.00235113i
$716$	4383.36	−	18068.5i	0.228791	−	0.943087i
$717$	7032.16	−	2200.41i	0.366277	−	0.114611i
$718$	−1017.05	+	21350.5i	−0.0528634	+	1.10974i
$719$	−22455.0	−	25914.4i	−1.16471	−	1.34415i	−0.928003	−	0.372573i	$-0.878476\pi$
$719$	−22455.0	−	25914.4i	−1.16471	−	1.34415i	−0.236712	−	0.971580i	$-0.576070\pi$
$720$	1446.17	+	17402.2i	0.0748552	+	0.900753i
$721$	−1883.96	−	553.181i	−0.0973126	−	0.0285736i
$722$	32189.8	+	16595.0i	1.65925	+	0.855403i
$723$	1357.67	+	3709.51i	0.0698374	+	0.190813i
$724$	14354.6	+	20158.2i	0.736858	+	1.03477i
$725$	−3829.47	−	5377.73i	−0.196169	−	0.275481i
$726$	−25523.2	−	4453.34i	−1.30476	−	0.227657i
$727$	22150.2	+	11419.2i	1.12999	+	0.582552i	0.918733	−	0.394878i	$-0.129213\pi$
$727$	22150.2	+	11419.2i	1.12999	+	0.582552i	0.211259	+	0.977430i	$0.432244\pi$
$728$	1294.80	+	380.187i	0.0659182	+	0.0193553i
$729$	−725.393	+	19669.6i	−0.0368538	+	0.999321i
$730$	24817.2	+	28640.6i	1.25826	+	1.45211i
$731$	75.5395	−	1585.77i	0.00382206	−	0.0802350i
$732$	−12237.4	−	11262.6i	−0.617906	−	0.568686i
$733$	−5734.70	+	23638.8i	−0.288971	+	1.19116i	0.623437	+	0.781874i	$0.285736\pi$
$733$	−5734.70	+	23638.8i	−0.288971	+	1.19116i	−0.912408	+	0.409282i	$0.865779\pi$
$734$	−5933.08	−	566.541i	−0.298357	−	0.0284897i
$735$	3134.71	−	1686.76i	0.157314	−	0.0846492i
$736$	−14226.7	+	21372.3i	−0.712505	+	1.07037i
$737$	−1447.10			−0.0723266
$738$	−3833.54	−	9927.55i	−0.191212	−	0.495174i
$739$	−27954.5	+	8208.18i	−1.39151	+	0.408583i	−0.889759	−	0.456431i	$-0.849128\pi$
$739$	−27954.5	+	8208.18i	−1.39151	+	0.408583i	−0.501748	+	0.865014i	$0.667309\pi$
$740$	−11133.1	−	2145.73i	−0.553055	−	0.106593i
$741$	−3882.20	−	8118.37i	−0.192464	−	0.402478i
$742$	−1659.69	+	319.879i	−0.0821148	+	0.0158263i
$743$	−9988.49	−	3998.79i	−0.493193	−	0.197445i	0.111715	−	0.993740i	$-0.464366\pi$
$743$	−9988.49	−	3998.79i	−0.493193	−	0.197445i	−0.604907	+	0.796296i	$0.706790\pi$
$744$	5362.36	+	5972.10i	0.264239	+	0.294285i
$745$	−15676.9	−	8081.99i	−0.770947	−	0.397451i
$746$	3528.66	−	24542.3i	0.173181	−	1.20450i
$747$	−15105.3	+	533.628i	−0.739858	+	0.0261371i
$748$	−640.473	+	1402.44i	−0.0313075	+	0.0685538i
$749$	18193.6	−	7283.64i	0.887559	−	0.355325i
$750$	−14482.2	+	26139.0i	−0.705086	+	1.27262i
$751$	17563.7	−	16747.0i	0.853407	−	0.813722i	−0.130677	−	0.991425i	$-0.541715\pi$
$751$	17563.7	−	16747.0i	0.853407	−	0.813722i	0.984084	+	0.177703i	$0.0568665\pi$
$752$	43770.3	+	17523.0i	2.12252	+	0.849730i
$753$	−9405.75	+	7669.35i	−0.455198	+	0.371164i
$754$	326.711	−	6858.50i	0.0157800	−	0.331262i
$755$	9699.39	−	11193.7i	0.467545	−	0.539576i
$756$	2830.80	+	14274.7i	0.136184	+	0.686729i
$757$	−8162.68	−	17873.8i	−0.391912	−	0.858168i	−0.998027	−	0.0627907i	$-0.980000\pi$
$757$	−8162.68	−	17873.8i	−0.391912	−	0.858168i	0.606114	−	0.795377i	$-0.292727\pi$
$758$	8192.76	+	14190.3i	0.392578	+	0.679966i
$759$	−645.719	+	2211.78i	−0.0308803	+	0.105774i
$760$	−3421.77	+	5926.67i	−0.163316	+	0.282872i
$761$	−23798.3	−	2272.46i	−1.13362	−	0.108248i	−0.488668	−	0.872470i	$-0.662517\pi$
$761$	−23798.3	−	2272.46i	−1.13362	−	0.108248i	−0.644953	+	0.764222i	$0.723123\pi$
$762$	20451.8	−	20202.0i	0.972296	−	0.960422i
$763$	21475.7	+	4139.10i	1.01897	+	0.196390i
$764$	−20615.7	−	13248.9i	−0.976242	−	0.627393i
$765$	−14000.0	+	1837.61i	−0.661660	+	0.0868484i
$766$	−290.270	−	2018.87i	−0.0136918	−	0.0952283i
$767$	−13.9500	−	57.5027i	−0.000656722	−	0.00270704i
$768$	−27138.2	+	479.209i	−1.27509	+	0.0225156i
$769$	22241.0	+	17490.5i	1.04295	+	0.820186i	0.984017	−	0.178076i	$-0.0569872\pi$
$769$	22241.0	+	17490.5i	1.04295	+	0.820186i	0.0589347	+	0.998262i	$0.481230\pi$
$770$	1250.76	+	1756.44i	0.0585379	+	0.0822050i
$771$	24117.2	−	16107.9i	1.12654	−	0.752413i
$772$	−11984.8	+	4798.00i	−0.558734	+	0.223683i
$773$	−21696.2	+	13943.3i	−1.00952	+	0.648778i	−0.937269	−	0.348608i	$-0.886654\pi$
$773$	−21696.2	+	13943.3i	−1.00952	+	0.648778i	−0.0722503	+	0.997387i	$0.523018\pi$
$774$	−2065.49	+	1745.79i	−0.0959205	+	0.0810737i
$775$	1764.85	+	12274.8i	0.0818004	+	0.568934i
$776$	−1003.86	+	2900.46i	−0.0464388	+	0.134176i
$777$	17198.4	+	1336.31i	0.794067	+	0.0616985i
$778$	16875.1	+	48757.3i	0.777635	+	2.24683i
$779$	3138.89	−	12938.7i	0.144368	−	0.595092i
$780$	−3594.67	+	1513.26i	−0.165013	+	0.0694659i
$781$	−594.541	−	1029.78i	−0.0272399	−	0.0471809i
$782$	−21568.0	−	12919.9i	−0.986280	−	0.590813i
$783$	−17049.2	+	7897.00i	−0.778146	+	0.360429i
$784$	2431.23	+	5323.65i	0.110752	+	0.242513i
$785$	20280.1	+	19337.1i	0.922075	+	0.879197i
$786$	5991.05	+	5513.83i	0.271875	+	0.250219i
$787$	−6844.33	+	3528.50i	−0.310005	+	0.159819i	−0.606208	−	0.795306i	$-0.707310\pi$
$787$	−6844.33	+	3528.50i	−0.310005	+	0.159819i	0.296203	+	0.955125i	$0.404280\pi$
$788$	31720.3	−	6113.58i	1.43400	−	0.276380i
$789$	6173.09	+	8352.76i	0.278540	+	0.376890i
$790$	−2497.71	−	10295.7i	−0.112487	−	0.463677i
$791$	−20791.6	+	13361.9i	−0.934593	+	0.600626i
$792$	−632.429	+	210.221i	−0.0283742	+	0.00943164i
$793$	−2817.16	+	6168.72i	−0.126154	+	0.276239i
$794$	−28099.5	+	2683.18i	−1.25594	+	0.119928i
$795$	−795.095	+	951.009i	−0.0354706	+	0.0424262i
$796$	−979.923	−	20571.1i	−0.0436337	−	0.915985i
$797$	19475.7	−	18570.0i	0.865575	−	0.825324i	−0.120312	−	0.992736i	$-0.538390\pi$
$797$	19475.7	−	18570.0i	0.865575	−	0.825324i	0.985887	+	0.167412i	$0.0535411\pi$
$798$	−16384.1	+	37620.2i	−0.726808	+	1.66885i
$799$	−12469.1	+	36027.0i	−0.552096	+	1.59518i
$800$	−9652.45	−	6203.26i	−0.426582	−	0.274148i
$801$	13688.5	−	14007.4i	0.603821	−	0.617887i
$802$	−1389.27	+	407.927i	−0.0611683	+	0.0179606i
$803$	−2678.24	+	3761.06i	−0.117700	+	0.165286i
$804$	−10510.3	+	5655.50i	−0.461031	+	0.248077i
$805$	−13635.4	+	7582.22i	−0.597000	+	0.331973i
$806$	−6448.84	+	11169.7i	−0.281825	+	0.488134i
$807$	−28120.2	+	11837.9i	−1.22661	+	0.516372i
$808$	3960.44	+	3776.27i	0.172435	+	0.164417i
$809$	−24553.9	+	28336.7i	−1.06708	+	1.23148i	−0.0953355	+	0.995445i	$0.530392\pi$
$809$	−24553.9	+	28336.7i	−1.06708	+	1.23148i	−0.971745	+	0.236032i	$0.924153\pi$
$810$	18536.4	+	15329.1i	0.804078	+	0.664952i
$811$	19294.6	+	22267.2i	0.835421	+	0.964128i	0.999752	−	0.0222778i	$-0.00709184\pi$
$811$	19294.6	+	22267.2i	0.835421	+	0.964128i	−0.164331	+	0.986405i	$0.552546\pi$
$812$	−10919.8	+	8587.44i	−0.471934	+	0.371133i
$813$	2219.09	−	6797.64i	0.0957281	−	0.293239i
$814$	−148.135	−	3109.74i	−0.00637854	−	0.133902i
$815$	5060.03	+	3979.25i	0.217479	+	0.171027i
$816$	−1513.83	−	23165.4i	−0.0649446	−	0.993813i
$817$	−3368.16	+	321.620i	−0.144231	+	0.0137724i
$818$	−1438.93	+	10008.0i	−0.0615050	+	0.427777i
$819$	5175.06	−	2903.63i	0.220795	−	0.123884i
$820$	−5536.69	−	1625.72i	−0.235792	−	0.0692349i
$821$	−20185.1	+	15873.7i	−0.858056	+	0.674783i	−0.946993	−	0.321255i	$-0.895895\pi$
$821$	−20185.1	+	15873.7i	−0.858056	+	0.674783i	0.0889371	+	0.996037i	$0.471653\pi$
$822$	−220.850	−	1364.56i	−0.00937110	−	0.0579009i
$823$	−6144.31	+	3167.61i	−0.260240	+	0.134163i	−0.583410	−	0.812178i	$-0.698282\pi$
$823$	−6144.31	+	3167.61i	−0.260240	+	0.134163i	0.323170	+	0.946341i	$0.395251\pi$
$824$	−242.564	−	700.842i	−0.0102550	−	0.0296298i
$825$	−992.964	−	272.613i	−0.0419037	−	0.0115045i
$826$	−156.504	+	219.779i	−0.00659256	+	0.00925796i
$827$	−3138.07			−0.131948			−0.0659742	−	0.997821i	$-0.521015\pi$
$827$	−3138.07			−0.131948			−0.0659742	+	0.997821i	$0.521015\pi$
$828$	3954.11	+	18587.6i	0.165960	+	0.780151i
$829$	−34448.7			−1.44325			−0.721625	−	0.692285i	$-0.756604\pi$
$829$	−34448.7			−1.44325			−0.721625	+	0.692285i	$0.756604\pi$
$830$	−10714.2	+	15046.1i	−0.448069	+	0.629224i
$831$	10130.2	−	10006.5i	0.422881	−	0.417717i
$832$	−1273.58	−	3679.78i	−0.0530692	−	0.153333i
$833$	−4206.32	+	2168.51i	−0.174959	+	0.0901974i
$834$	−26804.1	+	21855.8i	−1.11289	+	0.907439i
$835$	11632.2	−	9147.67i	0.482095	−	0.379124i
$836$	3152.76	+	925.734i	0.130431	+	0.0382981i
$837$	35262.5	+	1490.06i	1.45621	+	0.0615339i
$838$	−2306.06	+	16039.0i	−0.0950613	+	0.661166i
$839$	−17164.2	+	1638.98i	−0.706286	+	0.0674421i	−0.442017	−	0.897007i	$-0.645737\pi$
$839$	−17164.2	+	1638.98i	−0.706286	+	0.0674421i	−0.264269	+	0.964449i	$0.585131\pi$
$840$	−4046.97	−	1996.72i	−0.166230	−	0.0820158i
$841$	5072.28	+	3988.88i	0.207974	+	0.163553i
$842$	−2086.87	−	43808.9i	−0.0854138	−	1.79306i
$843$	88.8087	−	18.7485i	0.00362839	−	0.000765993i
$844$	−3782.06	+	2974.25i	−0.154246	+	0.121301i
$845$	−11476.7	−	13244.9i	−0.467233	−	0.539215i
$846$	59402.6	−	26251.0i	2.41407	−	1.06682i
$847$	13997.2	−	16153.6i	0.567827	−	0.655307i
$848$	−1474.98	−	1406.39i	−0.0597302	−	0.0569526i
$849$	−3957.32	+	31457.0i	−0.159970	+	1.27162i
$850$	5617.92	−	9730.53i	0.226698	−	0.392652i
$851$	22480.4	+	1434.13i	0.905545	+	0.0577691i
$852$	−8342.65	−	5155.67i	−0.335463	−	0.207313i
$853$	856.397	−	1202.64i	0.0343757	−	0.0482739i	−0.797030	−	0.603939i	$-0.793597\pi$
$853$	856.397	−	1202.64i	0.0343757	−	0.0482739i	0.831406	+	0.555665i	$0.187536\pi$
$854$	29670.1	−	8711.92i	1.18886	−	0.349082i
$855$	8122.79	+	28976.1i	0.324905	+	1.15902i
$856$	6227.07	+	4001.90i	0.248641	+	0.159792i
$857$	15938.9	−	46052.4i	0.635312	−	1.83561i	0.0925830	−	0.995705i	$-0.470488\pi$
$857$	15938.9	−	46052.4i	0.635312	−	1.83561i	0.542729	−	0.839908i	$-0.317391\pi$
$858$	−636.514	−	861.263i	−0.0253266	−	0.0342693i
$859$	23224.0	−	22144.1i	0.922460	−	0.879564i	−0.0705601	−	0.997508i	$-0.522479\pi$
$859$	23224.0	−	22144.1i	0.922460	−	0.879564i	0.993020	+	0.117943i	$0.0376302\pi$
$860$	69.7759	+	1464.78i	0.00276667	+	0.0580796i
$861$	8648.81	+	1509.06i	0.342335	+	0.0597314i
$862$	18562.4	−	1772.49i	0.733455	−	0.0700364i
$863$	255.596	−	559.677i	0.0100818	−	0.0220760i	−0.904524	−	0.426422i	$-0.859774\pi$
$863$	255.596	−	559.677i	0.0100818	−	0.0220760i	0.914606	+	0.404346i	$0.132501\pi$
$864$	−22407.5	+	23754.4i	−0.882314	+	0.935348i
$865$	−13089.1	+	8411.85i	−0.514500	+	0.330649i
$866$	−14216.1	−	58599.6i	−0.557832	−	2.29942i
$867$	−6714.06	+	760.955i	−0.263000	+	0.0298078i
$868$	25623.2	−	4938.47i	1.00197	−	0.193113i
$869$	1147.28	−	591.465i	0.0447858	−	0.0230887i
$870$	−5018.58	+	22406.4i	−0.195570	+	0.873159i
$871$	3522.20	+	3358.41i	0.137021	+	0.130649i
$872$	3431.68	+	7514.33i	0.133270	+	0.291820i
$873$	6036.60	+	12071.3i	0.234030	+	0.467985i
$874$	−20713.4	+	49417.3i	−0.801650	+	1.91255i
$875$	−12326.4	−	21350.0i	−0.476238	−	0.824869i
$876$	−4753.18	+	37783.4i	−0.183328	+	1.45729i
$877$	7122.46	−	29359.2i	0.274240	−	1.13043i	−0.653417	−	0.756998i	$-0.726665\pi$
$877$	7122.46	−	29359.2i	0.274240	−	1.13043i	0.927657	−	0.373434i	$-0.121820\pi$
$878$	−6599.48	−	19068.0i	−0.253669	−	0.732930i
$879$	−531.214	−	1110.86i	−0.0203839	−	0.0426263i
$880$	−850.358	+	2456.95i	−0.0325745	+	0.0941179i
$881$	−5458.30	−	37963.3i	−0.208734	−	1.45178i	−0.777295	−	0.629137i	$-0.783409\pi$
$881$	−5458.30	−	37963.3i	−0.208734	−	1.45178i	0.568561	−	0.822641i	$-0.307500\pi$
$882$	7585.35	+	2730.14i	0.289583	+	0.104227i
$883$	30309.8	−	19478.9i	1.15516	−	0.742377i	0.184501	−	0.982832i	$-0.440933\pi$
$883$	30309.8	−	19478.9i	1.15516	−	0.742377i	0.970660	+	0.240455i	$0.0772968\pi$
$884$	4813.64	−	1927.09i	0.183145	−	0.0733203i
$885$	12.9033	+	197.452i	0.000490100	+	0.00749974i
$886$	4554.81	+	6396.34i	0.172711	+	0.242538i
$887$	−32667.3	−	25689.8i	−1.23659	−	0.972468i	−1.00000		0.000859848i	$-0.999726\pi$
$887$	−32667.3	−	25689.8i	−1.23659	−	0.972468i	−0.236594	−	0.971608i	$-0.576031\pi$
$888$	3356.91	+	5584.26i	0.126859	+	0.211031i
$889$	5591.23	+	23047.4i	0.210938	+	0.869498i
$890$	−3406.21	−	23690.7i	−0.128288	−	0.892263i
$891$	−1282.55	+	2635.05i	−0.0482234	+	0.0990768i
$892$	−16577.0	−	10653.4i	−0.622240	−	0.399890i
$893$	79782.4	+	15376.8i	2.98972	+	0.576221i
$894$	−10101.0	−	38645.6i	−0.377883	−	1.44575i
$895$	25237.8	+	2409.92i	0.942577	+	0.0900052i
$896$	6257.33	−	10838.0i	0.233306	−	0.404099i
$897$	6704.71	−	3884.81i	0.249569	−	0.144604i
$898$	−9035.53	−	15650.0i	−0.335768	−	0.581567i
$899$	13995.9	+	30646.8i	0.519233	+	1.13696i
$900$	−8277.29	+	1900.67i	−0.306566	+	0.0703952i
$901$	1079.18	−	1245.44i	0.0399032	−	0.0460507i
$902$	75.3929	−	1582.69i	0.00278305	−	0.0584234i
$903$	−356.462	−	2202.46i	−0.0131366	−	0.0811665i
$904$	−8666.38	−	3469.49i	−0.318849	−	0.127648i
$905$	−24422.1	+	23286.4i	−0.897036	+	0.855322i
$906$	33538.2	−	592.220i	1.22984	−	0.0217166i
$907$	33557.5	−	13434.4i	1.22851	−	0.491822i	0.335579	−	0.942012i	$-0.391068\pi$
$907$	33557.5	−	13434.4i	1.22851	−	0.491822i	0.892933	+	0.450190i	$0.148644\pi$
$908$	−6108.03	+	13374.7i	−0.223240	+	0.488828i
$909$	24048.1	−	849.551i	0.877474	−	0.0309987i
$910$	1032.02	−	7177.86i	0.0375947	−	0.261477i
$911$	−15993.3	−	8245.12i	−0.581648	−	0.299861i	0.142180	−	0.989841i	$-0.454589\pi$
$911$	−15993.3	−	8245.12i	−0.581648	−	0.299861i	−0.723828	+	0.689980i	$0.757619\pi$
$912$	−48409.2	+	10219.7i	−1.75766	+	0.371062i
$913$	−2089.23	−	836.400i	−0.0757319	−	0.0303185i
$914$	57961.3	−	11171.1i	2.09758	−	0.404275i
$915$	12826.5	−	18702.5i	0.463421	−	0.675723i
$916$	22561.5	+	4348.37i	0.813813	+	0.156850i
$917$	−6445.06	+	1892.44i	−0.232099	+	0.0681504i
$918$	−24279.3	−	20810.9i	−0.872915	−	0.748217i
$919$	−47015.1			−1.68758			−0.843789	−	0.536674i	$-0.819680\pi$
$919$	−47015.1			−1.68758			−0.843789	+	0.536674i	$0.819680\pi$
$920$	−5320.26	−	2534.04i	−0.190656	−	0.0908095i
$921$	677.114	−	22606.2i	0.0242255	−	0.808794i
$922$	16974.9	+	1620.91i	0.606333	+	0.0578977i
$923$	−942.791	+	3886.24i	−0.0336212	+	0.138588i
$924$	−473.575	+	2114.37i	−0.0168609	+	0.0752787i
$925$	−479.004	+	10055.5i	−0.0170266	+	0.357431i
$926$	−45599.0	−	52624.0i	−1.61822	−	1.86753i
$927$	−2949.60	−	1391.09i	−0.104507	−	0.0492874i
$928$	−29909.9	−	8782.33i	−1.05802	−	0.310662i
$929$	24165.6	+	12458.2i	0.853441	+	0.439979i	0.828686	−	0.559714i	$-0.189089\pi$
$929$	24165.6	+	12458.2i	0.853441	+	0.439979i	0.0247553	+	0.999694i	$0.492119\pi$
$930$	27665.0	−	33090.0i	0.975453	−	1.16673i
$931$	5850.36	+	8215.69i	0.205948	+	0.289214i
$932$	−3657.38	−	5136.06i	−0.128542	−	0.180512i
$933$	2144.58	−	2565.12i	0.0752524	−	0.0900090i
$934$	−42764.3	−	22046.5i	−1.49817	−	0.772360i
$935$	−2017.17	−	592.296i	−0.0705547	−	0.0207167i
$936$	2027.19	+	956.060i	0.0707913	+	0.0333865i
$937$	−22521.0	−	25990.7i	−0.785198	−	0.906167i	0.212275	−	0.977210i	$-0.431913\pi$
$937$	−22521.0	−	25990.7i	−0.785198	−	0.906167i	−0.997473	+	0.0710434i	$0.977367\pi$
$938$	1055.90	−	22166.2i	0.0367553	−	0.771589i
$939$	9194.00	−	41048.4i	0.319526	−	1.42658i
$940$	8302.25	−	34222.3i	0.288074	−	1.18746i
$941$	−26913.0	−	2569.88i	−0.932346	−	0.0890282i	−0.382184	−	0.924086i	$-0.624828\pi$
$941$	−26913.0	−	2569.88i	−0.932346	−	0.0890282i	−0.550162	+	0.835058i	$0.685434\pi$
$942$	−1899.96	+	63432.1i	−0.0657154	+	2.19398i
$943$	11320.2	+	1814.16i	0.390917	+	0.0626482i
$944$	−325.323			−0.0112165
$945$	−18717.4	+	6590.89i	−0.644314	+	0.226880i
$946$	−386.354	+	113.444i	−0.0132785	+	0.00389891i
$947$	−39471.5	−	7607.51i	−1.35444	−	0.261046i	−0.540179	−	0.841550i	$-0.681643\pi$
$947$	−39471.5	−	7607.51i	−1.35444	−	0.261046i	−0.814257	+	0.580504i	$0.802856\pi$
$948$	6021.14	−	8779.54i	0.206284	−	0.300787i
$949$	15247.3	−	2938.68i	0.521548	−	0.100520i
$950$	−22230.9	−	8899.90i	−0.759226	−	0.303948i
$951$	46339.6	−	9782.79i	1.58009	−	0.333574i
$952$	5332.46	+	2749.08i	0.181540	+	0.0935904i
$953$	−6253.40	+	43493.4i	−0.212558	+	1.47837i	0.552015	+	0.833834i	$0.313859\pi$
$953$	−6253.40	+	43493.4i	−0.212558	+	1.47837i	−0.764572	+	0.644538i	$0.777050\pi$
$954$	−2805.57	+	99.1129i	−0.0952135	+	0.00336362i
$955$	13881.5	−	30396.2i	0.470361	−	1.02995i
$956$	8400.20	−	3362.93i	0.284186	−	0.113771i
$957$	−2797.10	+	49.3914i	−0.0944800	+	0.00166834i
$958$	−45988.4	+	43849.9i	−1.55096	+	1.47884i
$959$	1058.70	+	423.840i	0.0356488	+	0.0142716i
$960$	2080.46	+	12854.5i	0.0699445	+	0.432163i
$961$	1593.77	−	33457.3i	0.0534984	−	1.12307i
$962$	−6856.46	+	7912.78i	−0.229793	+	0.265196i
$963$	31723.9	−	7284.59i	1.06156	−	0.243762i
$964$	2015.09	+	4412.42i	0.0673253	+	0.147422i
$965$	−8801.65	−	15244.9i	−0.293612	−	0.508550i
$966$	−33407.9	−	11504.7i	−1.11272	−	0.383187i
$967$	7165.60	−	12411.2i	0.238294	−	0.412737i	−0.721931	−	0.691965i	$-0.756745\pi$
$967$	7165.60	−	12411.2i	0.238294	−	0.412737i	0.960225	+	0.279228i	$0.0900785\pi$
$968$	8036.71	+	767.413i	0.266849	+	0.0254810i
$969$	−10116.9	−	38706.5i	−0.335399	−	1.28321i
$970$	16195.4	+	3121.42i	0.536087	+	0.103322i
$971$	−35988.6	−	23128.4i	−1.18942	−	0.764395i	−0.212326	−	0.977199i	$-0.568104\pi$
$971$	−35988.6	−	23128.4i	−1.18942	−	0.764395i	−0.977095	+	0.212804i	$0.931740\pi$
$972$	983.025	+	24150.7i	0.0324388	+	0.796948i
$973$	−4060.56	−	28241.8i	−0.133788	−	0.930514i
$974$	1643.89	+	6776.21i	0.0540797	+	0.222920i
$975$	1784.16	+	2967.98i	0.0586041	+	0.0974888i
$976$	29308.3	+	23048.3i	0.961203	+	0.755899i
$977$	4216.31	+	5920.97i	0.138067	+	0.193888i	0.877820	−	0.478990i	$-0.158997\pi$
$977$	4216.31	+	5920.97i	0.138067	+	0.193888i	−0.739753	+	0.672878i	$0.765058\pi$
$978$	950.662	+	14547.5i	0.0310826	+	0.475641i
$979$	2707.17	−	1083.79i	0.0883774	−	0.0353810i
$980$	3677.39	−	2363.31i	0.119867	−	0.0770340i
$981$	34179.1	+	12301.8i	1.11239	+	0.400373i
$982$	−9301.92	−	64696.3i	−0.302277	−	2.10238i
$983$	6243.97	−	18040.8i	0.202596	−	0.585362i	−0.797237	−	0.603667i	$-0.793706\pi$
$983$	6243.97	−	18040.8i	0.202596	−	0.585362i	0.999832	+	0.0183047i	$0.00582688\pi$
$984$	1430.59	+	2991.63i	0.0463472	+	0.0969203i
$985$	14407.2	+	41626.7i	0.466041	+	1.34654i
$986$	7196.74	−	29665.4i	0.232445	−	0.958151i
$987$	−6687.46	+	53159.1i	−0.215668	+	1.71436i
$988$	−5525.28	−	9570.07i	−0.177918	−	0.308163i
$989$	−505.228	−	2869.35i	−0.0162440	−	0.0922548i
$990$	1601.84	+	3203.16i	0.0514239	+	0.102831i
$991$	5645.57	+	12362.1i	0.180966	+	0.396261i	0.978275	−	0.207311i	$-0.0664711\pi$
$991$	5645.57	+	12362.1i	0.180966	+	0.396261i	−0.797309	+	0.603571i	$0.793744\pi$
$992$	42378.1	+	40407.5i	1.35636	+	1.29328i
$993$	5680.12	−	25360.0i	0.181524	−	0.810448i
$994$	16207.5	−	8355.55i	0.517174	−	0.266622i
$995$	27574.8	−	5314.61i	0.878574	−	0.169331i
$996$	−18442.8	+	2090.26i	−0.586728	+	0.0664984i
$997$	5839.90	+	24072.4i	0.185508	+	0.764674i	0.986195	+	0.165591i	$0.0529530\pi$
$997$	5839.90	+	24072.4i	0.185508	+	0.764674i	−0.800687	+	0.599083i	$0.795532\pi$
$998$	37111.3	−	23850.0i	1.17709	−	0.756471i
$999$	27879.3	+	6605.15i	0.882944	+	0.209187i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.m.a.4.13	✓	1400
9.7	even	3	inner	207.4.m.a.142.58	yes	1400
23.6	even	11	inner	207.4.m.a.121.58	yes	1400
207.52	even	33	inner	207.4.m.a.52.13	yes	1400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.4.m.a.4.13	✓	1400	1.1	even	1	trivial
207.4.m.a.52.13	yes	1400	207.52	even	33	inner
207.4.m.a.121.58	yes	1400	23.6	even	11	inner
207.4.m.a.142.58	yes	1400	9.7	even	3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	207.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.19970 + 3.08904i) q^{2} +(-1.31400 - 5.02727i) q^{3} +(-2.08697 - 6.02992i) q^{4} +(7.73363 - 3.98697i) q^{5} +(18.4198 + 6.99946i) q^{6} +(-12.7782 + 10.0489i) q^{7} +(-5.89140 - 1.72987i) q^{8} +(-23.5468 + 13.2117i) q^{9} +(-4.69575 + 32.6597i) q^{10} +(-4.00182 + 0.382128i) q^{11} +(-27.5717 + 18.4151i) q^{12} +(10.6271 + 8.35727i) q^{13} +(-2.93328 - 61.5772i) q^{14} +(-30.2055 - 33.6402i) q^{15} +(58.4285 - 45.9487i) q^{16} +(39.3604 + 45.4243i) q^{17} +(10.9844 - 101.799i) q^{18} +(83.8861 - 96.8098i) q^{19} +(-40.1810 - 38.3125i) q^{20} +(67.3092 + 51.0353i) q^{21} +(7.62239 - 13.2024i) q^{22} +(88.8088 + 65.4217i) q^{23} +(-0.955209 + 31.8907i) q^{24} +(-28.5939 + 40.1545i) q^{25} +(-49.1924 + 14.4442i) q^{26} +(97.3591 + 101.016i) q^{27} +(87.2621 + 56.0799i) q^{28} +(-43.8029 + 126.560i) q^{29} +(170.359 - 19.3081i) q^{30} +(182.068 - 173.602i) q^{31} +(11.0752 + 232.496i) q^{32} +(7.17946 + 19.6161i) q^{33} +(-226.899 + 21.6662i) q^{34} +(-58.7576 + 128.661i) q^{35} +(128.807 + 114.413i) q^{36} +(171.799 - 110.409i) q^{37} +(114.525 + 472.080i) q^{38} +(28.0501 - 64.4069i) q^{39} +(-52.4589 + 10.1106i) q^{40} +(92.3823 - 47.6264i) q^{41} +(-305.710 + 95.6589i) q^{42} +(-19.1162 - 18.2272i) q^{43} +(10.6559 + 23.3332i) q^{44} +(-129.428 + 196.055i) q^{45} +(-397.443 + 130.426i) q^{46} +(317.144 + 549.309i) q^{47} +(-307.771 - 233.359i) q^{48} +(-18.5626 + 76.5161i) q^{49} +(-61.1411 - 176.656i) q^{50} +(176.640 - 257.563i) q^{51} +(28.2151 - 81.5221i) q^{52} +(-3.90199 - 27.1389i) q^{53} +(-526.203 + 78.5423i) q^{54} +(-29.4251 + 18.9104i) q^{55} +(92.6651 - 37.0975i) q^{56} +(-596.915 - 294.510i) q^{57} +(-294.597 - 413.703i) q^{58} +(-3.44028 - 2.70547i) q^{59} +(-139.809 + 252.343i) q^{60} +(118.259 + 487.469i) q^{61} +(135.768 + 944.287i) q^{62} +(168.124 - 405.442i) q^{63} +(-242.299 - 155.716i) q^{64} +(115.506 + 22.2621i) q^{65} +(-76.3877 - 20.9718i) q^{66} +(358.344 + 34.2177i) q^{67} +(191.761 - 332.139i) q^{68} +(212.197 - 532.430i) q^{69} +(-268.191 - 464.520i) q^{70} +(122.875 + 269.060i) q^{71} +(161.578 - 37.1024i) q^{72} +(752.140 - 868.016i) q^{73} +(-36.8493 + 773.561i) q^{74} +(239.440 + 90.9860i) q^{75} +(-758.823 - 303.787i) q^{76} +(47.2963 - 45.0969i) q^{77} +(137.254 + 228.324i) q^{78} +(-298.085 + 119.335i) q^{79} +(268.669 - 588.303i) q^{80} +(379.903 - 622.185i) q^{81} +(-56.0931 + 390.136i) q^{82} +(497.574 + 256.517i) q^{83} +(167.266 - 512.379i) q^{84} +(485.504 + 194.366i) q^{85} +(98.3545 - 18.9563i) q^{86} +(693.808 + 53.9084i) q^{87} +(24.2374 + 4.67137i) q^{88} +(-695.998 + 204.364i) q^{89} +(-320.919 - 831.069i) q^{90} -219.778 q^{91} +(209.146 - 672.043i) q^{92} +(-1111.98 - 687.192i) q^{93} +(-2394.46 - 228.643i) q^{94} +(262.768 - 1083.14i) q^{95} +(1154.27 - 361.178i) q^{96} +(23.7848 - 499.305i) q^{97} +(-195.530 - 225.653i) q^{98} +(89.1816 - 61.8687i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1400 q - 9 q^{2} - 14 q^{3} + 263 q^{4} + 19 q^{5} - 35 q^{6} - 9 q^{7} - 74 q^{8} - 78 q^{9} - 68 q^{10} + 79 q^{11} + 54 q^{12} - 9 q^{13} + 159 q^{14} - 868 q^{15} + 1031 q^{16} - 308 q^{17} - 87 q^{18}+ \cdots + 7484 q^{99}+O(q^{100}) \) 1400 * q - 9 * q^2 - 14 * q^3 + 263 * q^4 + 19 * q^5 - 35 * q^6 - 9 * q^7 - 74 * q^8 - 78 * q^9 - 68 * q^10 + 79 * q^11 + 54 * q^12 - 9 * q^13 + 159 * q^14 - 868 * q^15 + 1031 * q^16 - 308 * q^17 - 87 * q^18 - 36 * q^19 + 119 * q^20 - 660 * q^21 - 52 * q^22 - 116 * q^23 + 2420 * q^24 + 1397 * q^25 + 432 * q^26 + 274 * q^27 - 324 * q^28 - 45 * q^29 + 768 * q^30 - 45 * q^31 + 111 * q^32 - 1664 * q^33 + 403 * q^34 - 536 * q^35 - 121 * q^36 - 180 * q^37 - 117 * q^38 - 46 * q^39 - 473 * q^40 - 333 * q^41 - 332 * q^42 - 9 * q^43 - 1908 * q^44 + 1762 * q^45 + 484 * q^46 + 216 * q^47 + 1072 * q^48 + 4615 * q^49 - 105 * q^50 + 1298 * q^51 - 708 * q^52 - 1380 * q^53 + 4116 * q^54 - 1328 * q^55 - 3971 * q^56 + 2154 * q^57 - 338 * q^58 + 1917 * q^59 + 154 * q^60 + 27 * q^61 - 3854 * q^62 - 4850 * q^63 - 5854 * q^64 + 3363 * q^65 - 2017 * q^66 + 603 * q^67 - 18454 * q^68 - 4653 * q^69 + 542 * q^70 - 5296 * q^71 - 8044 * q^72 - 36 * q^73 + 3243 * q^74 + 5140 * q^75 - 1029 * q^76 - 1661 * q^77 + 14687 * q^78 - 9 * q^79 + 10312 * q^80 - 294 * q^81 - 770 * q^82 - 2735 * q^83 + 2298 * q^84 + 241 * q^85 + 10507 * q^86 - 10268 * q^87 + 2183 * q^88 - 2980 * q^89 + 33928 * q^90 - 1452 * q^91 - 1973 * q^92 - 11406 * q^93 + 2034 * q^94 - 3339 * q^95 - 4446 * q^96 - 5193 * q^97 + 14820 * q^98 + 7484 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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