LMFDB - Embedded newform 76.4.d.a.75.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,4,Mod(75,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("76.75");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	76.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.48414516044$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.19
Character	$\chi$	$=$	76.75
Dual form			76.4.d.a.75.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60147 - 2.33137i) q^{2} +3.54475 q^{3} +(-2.87062 - 7.46723i) q^{4} +18.5634 q^{5} +(5.67679 - 8.26413i) q^{6} +16.5701i q^{7} +(-22.0061 - 5.26604i) q^{8} -14.4348 q^{9} +O(q^{10})$	\(q+(1.60147 - 2.33137i) q^{2} +3.54475 q^{3} +(-2.87062 - 7.46723i) q^{4} +18.5634 q^{5} +(5.67679 - 8.26413i) q^{6} +16.5701i q^{7} +(-22.0061 - 5.26604i) q^{8} -14.4348 q^{9} +(29.7286 - 43.2782i) q^{10} +9.00860i q^{11} +(-10.1756 - 26.4694i) q^{12} -60.5487i q^{13} +(38.6312 + 26.5365i) q^{14} +65.8025 q^{15} +(-47.5191 + 42.8711i) q^{16} +1.33140 q^{17} +(-23.1168 + 33.6529i) q^{18} +(-82.5710 + 6.40608i) q^{19} +(-53.2884 - 138.617i) q^{20} +58.7369i q^{21} +(21.0024 + 14.4270i) q^{22} +182.865i q^{23} +(-78.0061 - 18.6668i) q^{24} +219.600 q^{25} +(-141.162 - 96.9666i) q^{26} -146.876 q^{27} +(123.733 - 47.5665i) q^{28} -61.1453i q^{29} +(105.380 - 153.410i) q^{30} +111.127 q^{31} +(23.8483 + 179.442i) q^{32} +31.9332i q^{33} +(2.13219 - 3.10399i) q^{34} +307.598i q^{35} +(41.4367 + 107.788i) q^{36} +160.195i q^{37} +(-117.300 + 202.763i) q^{38} -214.630i q^{39} +(-408.508 - 97.7555i) q^{40} +386.315i q^{41} +(136.938 + 94.0652i) q^{42} -300.052i q^{43} +(67.2693 - 25.8602i) q^{44} -267.958 q^{45} +(426.328 + 292.853i) q^{46} -206.981i q^{47} +(-168.443 + 151.967i) q^{48} +68.4308 q^{49} +(351.681 - 511.969i) q^{50} +4.71947 q^{51} +(-452.131 + 173.812i) q^{52} -544.763i q^{53} +(-235.216 + 342.422i) q^{54} +167.230i q^{55} +(87.2589 - 364.644i) q^{56} +(-292.693 + 22.7079i) q^{57} +(-142.553 - 97.9222i) q^{58} +444.988 q^{59} +(-188.894 - 491.363i) q^{60} -252.260 q^{61} +(177.967 - 259.079i) q^{62} -239.186i q^{63} +(456.538 + 231.770i) q^{64} -1123.99i q^{65} +(74.4482 + 51.1399i) q^{66} -530.479 q^{67} +(-3.82194 - 9.94187i) q^{68} +648.211i q^{69} +(717.126 + 492.607i) q^{70} -354.491 q^{71} +(317.653 + 76.0140i) q^{72} +343.873 q^{73} +(373.476 + 256.547i) q^{74} +778.425 q^{75} +(284.865 + 598.187i) q^{76} -149.274 q^{77} +(-500.382 - 343.722i) q^{78} -26.6175 q^{79} +(-882.116 + 795.833i) q^{80} -130.898 q^{81} +(900.646 + 618.671i) q^{82} -1384.46i q^{83} +(438.602 - 168.611i) q^{84} +24.7153 q^{85} +(-699.535 - 480.524i) q^{86} -216.745i q^{87} +(47.4396 - 198.244i) q^{88} -977.352i q^{89} +(-429.126 + 624.711i) q^{90} +1003.30 q^{91} +(1365.50 - 524.936i) q^{92} +393.918 q^{93} +(-482.550 - 331.473i) q^{94} +(-1532.80 + 118.919i) q^{95} +(84.5364 + 636.075i) q^{96} +1185.68i q^{97} +(109.590 - 159.538i) q^{98} -130.037i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 10 q^{4} - 4 q^{5} - 6 q^{6} + 192 q^{9}+O(q^{10}) $ 28 * q + 10 * q^4 - 4 * q^5 - 6 * q^6 + 192 * q^9	$ 28 q + 10 q^{4} - 4 q^{5} - 6 q^{6} + 192 q^{9} - 134 q^{16} - 80 q^{17} - 300 q^{20} - 26 q^{24} + 496 q^{25} - 90 q^{26} + 254 q^{28} - 16 q^{30} - 556 q^{36} - 626 q^{38} - 850 q^{42} + 976 q^{44} - 612 q^{45} + 188 q^{49} + 354 q^{54} - 580 q^{57} + 2534 q^{58} - 948 q^{61} - 1068 q^{62} - 1634 q^{64} + 1244 q^{66} + 1630 q^{68} - 184 q^{73} + 2276 q^{74} + 1688 q^{76} + 308 q^{77} + 3376 q^{80} - 2284 q^{81} - 740 q^{82} + 684 q^{85} + 1810 q^{92} + 824 q^{93} - 5222 q^{96}+O(q^{100}) $ 28 * q + 10 * q^4 - 4 * q^5 - 6 * q^6 + 192 * q^9 - 134 * q^16 - 80 * q^17 - 300 * q^20 - 26 * q^24 + 496 * q^25 - 90 * q^26 + 254 * q^28 - 16 * q^30 - 556 * q^36 - 626 * q^38 - 850 * q^42 + 976 * q^44 - 612 * q^45 + 188 * q^49 + 354 * q^54 - 580 * q^57 + 2534 * q^58 - 948 * q^61 - 1068 * q^62 - 1634 * q^64 + 1244 * q^66 + 1630 * q^68 - 184 * q^73 + 2276 * q^74 + 1688 * q^76 + 308 * q^77 + 3376 * q^80 - 2284 * q^81 - 740 * q^82 + 684 * q^85 + 1810 * q^92 + 824 * q^93 - 5222 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.60147	−	2.33137i	0.566204	−	0.824265i
$2$	1.60147	−	2.33137i	0.566204	−	0.824265i
$3$	3.54475			0.682187			0.341093	−	0.940029i	$-0.389203\pi$
$3$	3.54475			0.682187			0.341093	+	0.940029i	$0.389203\pi$
$4$	−2.87062	−	7.46723i	−0.358827	−	0.933404i
$5$	18.5634			1.66036			0.830180	−	0.557495i	$-0.188238\pi$
$5$	18.5634			1.66036			0.830180	+	0.557495i	$0.188238\pi$
$6$	5.67679	−	8.26413i	0.386257	−	0.562303i
$7$			16.5701i			0.894703i	0.894358	+	0.447351i	$0.147633\pi$
$7$			16.5701i			0.894703i	−0.894358	+	0.447351i	$0.852367\pi$
$8$	−22.0061	−	5.26604i	−0.972542	−	0.232728i
$9$	−14.4348			−0.534621
$10$	29.7286	−	43.2782i	0.940102	−	1.36858i
$11$			9.00860i			0.246927i	0.992349	+	0.123463i	$0.0394002\pi$
$11$			9.00860i			0.246927i	−0.992349	+	0.123463i	$0.960600\pi$
$12$	−10.1756	−	26.4694i	−0.244787	−	0.636756i
$13$		−	60.5487i		−	1.29178i	−0.763429	−	0.645891i	$-0.776486\pi$
$13$		−	60.5487i		−	1.29178i	0.763429	−	0.645891i	$-0.223514\pi$
$14$	38.6312	+	26.5365i	0.737473	+	0.506584i
$15$	65.8025			1.13268
$16$	−47.5191	+	42.8711i	−0.742486	+	0.669861i
$17$	1.33140			0.0189948			0.00949741	−	0.999955i	$-0.496977\pi$
$17$	1.33140			0.0189948			0.00949741	+	0.999955i	$0.496977\pi$
$18$	−23.1168	+	33.6529i	−0.302704	+	0.440670i
$19$	−82.5710	+	6.40608i	−0.997004	+	0.0773503i
$19$	−82.5710	+	6.40608i	−0.997004	+	0.0773503i
$20$	−53.2884	−	138.617i	−0.595782	−	1.54979i
$21$			58.7369i			0.610355i
$22$	21.0024	+	14.4270i	0.203533	+	0.139811i
$23$			182.865i			1.65783i	0.559376	+	0.828914i	$0.311041\pi$
$23$			182.865i			1.65783i	−0.559376	+	0.828914i	$0.688959\pi$
$24$	−78.0061	−	18.6668i	−0.663455	−	0.158764i
$25$	219.600			1.75680
$26$	−141.162	−	96.9666i	−1.06477	−	0.731412i
$27$	−146.876			−1.04690
$28$	123.733	−	47.5665i	0.835119	−	0.321044i
$29$		−	61.1453i		−	0.391531i	−0.980651	−	0.195766i	$-0.937281\pi$
$29$		−	61.1453i		−	0.391531i	0.980651	−	0.195766i	$-0.0627192\pi$
$30$	105.380	−	153.410i	0.641325	−	0.933626i
$31$	111.127			0.643840			0.321920	−	0.946767i	$-0.395672\pi$
$31$	111.127			0.643840			0.321920	+	0.946767i	$0.395672\pi$
$32$	23.8483	+	179.442i	0.131745	+	0.991284i
$33$			31.9332i			0.168450i
$34$	2.13219	−	3.10399i	0.0107549	−	0.0156568i
$35$			307.598i			1.48553i
$36$	41.4367	+	107.788i	0.191836	+	0.499018i
$37$			160.195i			0.711783i	0.934527	+	0.355891i	$0.115823\pi$
$37$			160.195i			0.711783i	−0.934527	+	0.355891i	$0.884177\pi$
$38$	−117.300	+	202.763i	−0.500750	+	0.865592i
$39$		−	214.630i		−	0.881237i
$40$	−408.508	−	97.7555i	−1.61477	−	0.386413i
$41$			386.315i			1.47152i	0.677242	+	0.735760i	$0.263175\pi$
$41$			386.315i			1.47152i	−0.677242	+	0.735760i	$0.736825\pi$
$42$	136.938	+	94.0652i	0.503094	+	0.345585i
$43$		−	300.052i		−	1.06413i	−0.846704	−	0.532065i	$-0.821416\pi$
$43$		−	300.052i		−	1.06413i	0.846704	−	0.532065i	$-0.178584\pi$
$44$	67.2693	−	25.8602i	0.230482	−	0.0886040i
$45$	−267.958			−0.887664
$46$	426.328	+	292.853i	1.36649	+	0.938668i
$47$		−	206.981i		−	0.642367i	−0.947017	−	0.321184i	$-0.895919\pi$
$47$		−	206.981i		−	0.642367i	0.947017	−	0.321184i	$-0.104081\pi$
$48$	−168.443	+	151.967i	−0.506514	+	0.456970i
$49$	68.4308			0.199507
$50$	351.681	−	511.969i	0.994704	−	1.44807i
$51$	4.71947			0.0129580
$52$	−452.131	+	173.812i	−1.20576	+	0.463526i
$53$		−	544.763i		−	1.41187i	−0.708278	−	0.705934i	$-0.750528\pi$
$53$		−	544.763i		−	1.41187i	0.708278	−	0.705934i	$-0.249472\pi$
$54$	−235.216	+	342.422i	−0.592758	+	0.862922i
$55$			167.230i			0.409987i
$56$	87.2589	−	364.644i	0.208223	−	0.870136i
$57$	−292.693	+	22.7079i	−0.680143	+	0.0527674i
$58$	−142.553	−	97.9222i	−0.322726	−	0.221686i
$59$	444.988			0.981907			0.490953	−	0.871186i	$-0.336649\pi$
$59$	444.988			0.981907			0.490953	+	0.871186i	$0.336649\pi$
$60$	−188.894	−	491.363i	−0.406435	−	1.05724i
$61$	−252.260			−0.529485			−0.264743	−	0.964319i	$-0.585287\pi$
$61$	−252.260			−0.529485			−0.264743	+	0.964319i	$0.585287\pi$
$62$	177.967	−	259.079i	0.364545	−	0.530695i
$63$		−	239.186i		−	0.478327i
$64$	456.538	+	231.770i	0.891675	+	0.452676i
$65$		−	1123.99i		−	2.14482i
$66$	74.4482	+	51.1399i	0.138848	+	0.0953771i
$67$	−530.479			−0.967288			−0.483644	−	0.875265i	$-0.660687\pi$
$67$	−530.479			−0.967288			−0.483644	+	0.875265i	$0.660687\pi$
$68$	−3.82194	−	9.94187i	−0.00681585	−	0.0177298i
$69$			648.211i			1.13095i
$70$	717.126	+	492.607i	1.22447	+	0.841112i
$71$	−354.491			−0.592541			−0.296270	−	0.955104i	$-0.595743\pi$
$71$	−354.491			−0.592541			−0.296270	+	0.955104i	$0.595743\pi$
$72$	317.653	+	76.0140i	0.519941	+	0.124421i
$73$	343.873			0.551332			0.275666	−	0.961253i	$-0.411102\pi$
$73$	343.873			0.551332			0.275666	+	0.961253i	$0.411102\pi$
$74$	373.476	+	256.547i	0.586698	+	0.403014i
$75$	778.425			1.19846
$76$	284.865	+	598.187i	0.429951	+	0.902852i
$77$	−149.274			−0.220926
$78$	−500.382	−	343.722i	−0.726373	−	0.498960i
$79$	−26.6175			−0.0379077			−0.0189538	−	0.999820i	$-0.506034\pi$
$79$	−26.6175			−0.0379077			−0.0189538	+	0.999820i	$0.506034\pi$
$80$	−882.116	+	795.833i	−1.23280	+	1.11221i
$81$	−130.898			−0.179559
$82$	900.646	+	618.671i	1.21292	+	0.833180i
$83$		−	1384.46i		−	1.83089i	−0.402438	−	0.915447i	$-0.631837\pi$
$83$		−	1384.46i		−	1.83089i	0.402438	−	0.915447i	$-0.368163\pi$
$84$	438.602	−	168.611i	0.569707	−	0.219012i
$85$	24.7153			0.0315382
$86$	−699.535	−	480.524i	−0.877125	−	0.602514i
$87$		−	216.745i		−	0.267097i
$88$	47.4396	−	198.244i	0.0574668	−	0.240147i
$89$		−	977.352i		−	1.16403i	−0.813177	−	0.582017i	$-0.802264\pi$
$89$		−	977.352i		−	1.16403i	0.813177	−	0.582017i	$-0.197736\pi$
$90$	−429.126	+	624.711i	−0.502598	+	0.731671i
$91$	1003.30			1.15576
$92$	1365.50	−	524.936i	1.54742	−	0.594873i
$93$	393.918			0.439219
$94$	−482.550	−	331.473i	−0.529481	−	0.363711i
$95$	−1532.80	+	118.919i	−1.65539	+	0.128429i
$96$	84.5364	+	636.075i	0.0898745	+	0.676241i
$97$			1185.68i			1.24111i	0.784162	+	0.620556i	$0.213093\pi$
$97$			1185.68i			1.24111i	−0.784162	+	0.620556i	$0.786907\pi$
$98$	109.590	−	159.538i	0.112961	−	0.164446i
$99$		−	130.037i		−	0.132012i
$100$	−630.386	−	1639.80i	−0.630386	−	1.63980i
$101$	−1369.61			−1.34932			−0.674662	−	0.738127i	$-0.735711\pi$
$101$	−1369.61			−1.34932			−0.674662	+	0.738127i	$0.735711\pi$
$102$	7.55808	−	11.0029i	0.00733687	−	0.0106808i
$103$	−1571.46			−1.50331			−0.751654	−	0.659558i	$-0.770744\pi$
$103$	−1571.46			−1.50331			−0.751654	+	0.659558i	$0.770744\pi$
$104$	−318.851	+	1332.44i	−0.300634	+	1.25631i
$105$			1090.36i			1.01341i
$106$	−1270.05	−	872.420i	−1.16375	−	0.799405i
$107$	2132.68			1.92686			0.963430	−	0.267959i	$-0.0863493\pi$
$107$	2132.68			1.92686			0.963430	+	0.267959i	$0.0863493\pi$
$108$	421.624	+	1096.76i	0.375655	+	0.977179i
$109$			326.844i			0.287211i	0.989635	+	0.143605i	$0.0458696\pi$
$109$			326.844i			0.287211i	−0.989635	+	0.143605i	$0.954130\pi$
$110$	389.876	+	267.813i	0.337938	+	0.232136i
$111$			567.852i			0.485569i
$112$	−710.380	−	787.398i	−0.599327	−	0.664305i
$113$			902.048i			0.750951i	0.926832	+	0.375476i	$0.122521\pi$
$113$			902.048i			0.750951i	−0.926832	+	0.375476i	$0.877479\pi$
$114$	−415.797	+	718.743i	−0.341605	+	0.590495i
$115$			3394.60i			2.75259i
$116$	−456.586	+	175.525i	−0.365457	+	0.140492i
$117$			874.006i			0.690614i
$118$	712.633	−	1037.43i	0.555959	−	0.809352i
$119$			22.0615i			0.0169947i
$120$	−1448.06	−	346.519i	−1.10157	−	0.263606i
$121$	1249.85			0.939027
$122$	−403.986	+	588.113i	−0.299796	+	0.436436i
$123$			1369.39i			1.00385i
$124$	−319.004	−	829.813i	−0.231027	−	0.600963i
$125$	1756.09			1.25655
$126$	−557.632	−	383.048i	−0.394269	−	0.270831i
$127$	314.379			0.219658			0.109829	−	0.993950i	$-0.464970\pi$
$127$	314.379			0.219658			0.109829	+	0.993950i	$0.464970\pi$
$128$	1271.47	−	693.189i	0.877995	−	0.478670i
$129$		−	1063.61i		−	0.725935i
$130$	−2620.44	−	1800.03i	−1.76790	−	1.21441i
$131$		−	2009.44i		−	1.34020i	−0.742272	−	0.670099i	$-0.766252\pi$
$131$		−	2009.44i		−	1.34020i	0.742272	−	0.670099i	$-0.233748\pi$
$132$	238.453	−	91.6679i	0.157232	−	0.0604445i
$133$	−106.150	−	1368.21i	−0.0692056	−	0.892022i
$134$	−849.544	+	1236.75i	−0.547682	+	0.797302i
$135$	−2726.51			−1.73823
$136$	−29.2989	−	7.01120i	−0.0184733	−	0.00442063i
$137$	333.563			0.208016			0.104008	−	0.994576i	$-0.466833\pi$
$137$	333.563			0.208016			0.104008	+	0.994576i	$0.466833\pi$
$138$	1511.22	+	1038.09i	0.932202	+	0.640347i
$139$			587.202i			0.358315i	0.983820	+	0.179158i	$0.0573372\pi$
$139$			587.202i			0.358315i	−0.983820	+	0.179158i	$0.942663\pi$
$140$	2296.90	−	882.995i	1.38660	−	0.533048i
$141$		−	733.694i		−	0.438214i
$142$	−567.706	+	826.452i	−0.335499	+	0.488411i
$143$	545.459			0.318976
$144$	685.928	−	618.835i	0.396949	−	0.358122i
$145$		−	1135.06i		−	0.650083i
$146$	550.701	−	801.696i	0.312166	−	0.454444i
$147$	242.570			0.136101
$148$	1196.22	−	459.859i	0.664381	−	0.255407i
$149$	666.945			0.366700			0.183350	−	0.983048i	$-0.441306\pi$
$149$	666.945			0.366700			0.183350	+	0.983048i	$0.441306\pi$
$150$	1246.62	−	1814.80i	0.678574	−	0.987852i
$151$	320.251			0.172594			0.0862969	−	0.996269i	$-0.472497\pi$
$151$	320.251			0.172594			0.0862969	+	0.996269i	$0.472497\pi$
$152$	1850.80	+	293.849i	0.987630	+	0.156804i
$153$	−19.2185			−0.0101550
$154$	−239.057	+	348.013i	−0.125089	+	0.182102i
$155$	2062.90			1.06901
$156$	−1602.69	+	616.119i	−0.822550	+	0.316212i
$157$	2625.22			1.33449			0.667247	−	0.744837i	$-0.267473\pi$
$157$	2625.22			1.33449			0.667247	+	0.744837i	$0.267473\pi$
$158$	−42.6271	+	62.0555i	−0.0214635	+	0.0312460i
$159$		−	1931.05i		−	0.963157i
$160$	442.706	+	3331.04i	0.218744	+	1.64589i
$161$	−3030.10			−1.48326
$162$	−209.629	+	305.173i	−0.101667	+	0.148004i
$163$			536.530i			0.257818i	0.991656	+	0.128909i	$0.0411475\pi$
$163$			536.530i			0.257818i	−0.991656	+	0.128909i	$0.958853\pi$
$164$	2884.71	−	1108.96i	1.37352	−	0.528021i
$165$			592.788i			0.279688i
$166$	−3227.69	−	2217.16i	−1.50914	−	1.03666i
$167$	−1961.24			−0.908774			−0.454387	−	0.890805i	$-0.650142\pi$
$167$	−1961.24			−0.908774			−0.454387	+	0.890805i	$0.650142\pi$
$168$	309.311	−	1292.57i	0.142047	−	0.593595i
$169$	−1469.14			−0.668703
$170$	39.5807	−	57.6206i	0.0178571	−	0.0259959i
$171$	1191.89	−	92.4704i	0.533019	−	0.0413531i
$172$	−2240.56	+	861.335i	−0.993263	+	0.381838i
$173$		−	3371.40i		−	1.48163i	−0.671708	−	0.740816i	$-0.734439\pi$
$173$		−	3371.40i		−	1.48163i	0.671708	−	0.740816i	$-0.265561\pi$
$174$	−505.313	−	347.109i	−0.220159	−	0.151232i
$175$			3638.79i			1.57181i
$176$	−386.209	−	428.081i	−0.165407	−	0.183340i
$177$	1577.37			0.669844
$178$	−2278.57	−	1565.19i	−0.959473	−	0.659080i
$179$	1181.34			0.493280			0.246640	−	0.969107i	$-0.420673\pi$
$179$	1181.34			0.493280			0.246640	+	0.969107i	$0.420673\pi$
$180$	769.205	+	2000.91i	0.318518	+	0.828549i
$181$			1155.85i			0.474661i	0.971429	+	0.237331i	$0.0762725\pi$
$181$			1155.85i			0.474661i	−0.971429	+	0.237331i	$0.923728\pi$
$182$	1606.75	−	2339.07i	0.654397	−	0.952655i
$183$	−894.198			−0.361208
$184$	962.975	−	4024.15i	0.385823	−	1.61231i
$185$			2973.77i			1.18182i
$186$	630.846	−	918.370i	0.248688	−	0.362033i
$187$			11.9940i			0.00469033i
$188$	−1545.57	+	594.162i	−0.599588	+	0.230499i
$189$		−	2433.75i		−	0.936663i
$190$	−2177.48	+	3763.97i	−0.831425	+	1.43719i
$191$			3069.11i			1.16269i	0.813659	+	0.581343i	$0.197472\pi$
$191$			3069.11i			1.16269i	−0.813659	+	0.581343i	$0.802528\pi$
$192$	1618.31	+	821.566i	0.608289	+	0.308809i
$193$		−	986.320i		−	0.367860i	−0.982939	−	0.183930i	$-0.941118\pi$
$193$		−	986.320i		−	0.367860i	0.982939	−	0.183930i	$-0.0588819\pi$
$194$	2764.27	+	1898.83i	1.02301	+	0.702722i
$195$		−	3984.25i		−	1.46317i
$196$	−196.438	−	510.988i	−0.0715883	−	0.186220i
$197$	−2398.07			−0.867285			−0.433642	−	0.901085i	$-0.642772\pi$
$197$	−2398.07			−0.867285			−0.433642	+	0.901085i	$0.642772\pi$
$198$	−303.165	−	208.250i	−0.108813	−	0.0747458i
$199$		−	1680.59i		−	0.598661i	−0.954149	−	0.299331i	$-0.903237\pi$
$199$		−	1680.59i		−	0.598661i	0.954149	−	0.299331i	$-0.0967633\pi$
$200$	−4832.53	−	1156.42i	−1.70856	−	0.408856i
$201$	−1880.41			−0.659871
$202$	−2193.39	+	3193.08i	−0.763992	+	1.11220i
$203$	1013.19			0.350304
$204$	−13.5478	−	35.2414i	−0.00464968	−	0.0120951i
$205$			7171.33i			2.44325i
$206$	−2516.64	+	3663.67i	−0.851178	+	1.23912i
$207$		−	2639.62i		−	0.886310i
$208$	2595.79	+	2877.22i	0.865315	+	0.959131i
$209$	−57.7098	−	743.849i	−0.0190999	−	0.246187i
$210$	2542.03	+	1746.17i	0.835318	+	0.573796i
$211$	−1142.02			−0.372605			−0.186302	−	0.982492i	$-0.559650\pi$
$211$	−1142.02			−0.372605			−0.186302	+	0.982492i	$0.559650\pi$
$212$	−4067.87	+	1563.81i	−1.31784	+	0.506616i
$213$	−1256.58			−0.404223
$214$	3415.42	−	4972.08i	1.09100	−	1.58824i
$215$		−	5569.99i		−	1.76684i
$216$	3232.16	+	773.453i	1.01815	+	0.243643i
$217$			1841.39i			0.576046i
$218$	761.996	+	523.429i	0.236738	+	0.162620i
$219$	1218.94			0.376112
$220$	1248.75	−	480.053i	0.382684	−	0.147115i
$221$		−	80.6145i		−	0.0245372i
$222$	1323.88	+	909.396i	0.400238	+	0.274931i
$223$	846.144			0.254090			0.127045	−	0.991897i	$-0.459451\pi$
$223$	846.144			0.254090			0.127045	+	0.991897i	$0.459451\pi$
$224$	−2973.37	+	395.170i	−0.886904	+	0.117872i
$225$	−3169.87			−0.939221
$226$	2103.01	+	1444.60i	0.618983	+	0.425191i
$227$	−4967.77			−1.45252			−0.726262	−	0.687418i	$-0.758744\pi$
$227$	−4967.77			−1.45252			−0.726262	+	0.687418i	$0.758744\pi$
$228$	1009.77	+	2120.42i	0.293307	+	0.615914i
$229$	254.337			0.0733933			0.0366966	−	0.999326i	$-0.488316\pi$
$229$	254.337			0.0733933			0.0366966	+	0.999326i	$0.488316\pi$
$230$	7914.09	+	5436.34i	2.26887	+	1.55853i
$231$	−529.137			−0.150713
$232$	−321.994	+	1345.57i	−0.0911203	+	0.380780i
$233$	2411.68			0.678087			0.339044	−	0.940771i	$-0.389897\pi$
$233$	2411.68			0.678087			0.339044	+	0.940771i	$0.389897\pi$
$234$	2037.64	+	1399.69i	0.569250	+	0.391028i
$235$		−	3842.27i		−	1.06656i
$236$	−1277.39	−	3322.83i	−0.352335	−	0.916516i
$237$	−94.3524			−0.0258601
$238$	51.4336	+	35.3307i	0.0140082	+	0.00962247i
$239$		−	3962.47i		−	1.07243i	−0.844081	−	0.536215i	$-0.819854\pi$
$239$		−	3962.47i		−	1.07243i	0.844081	−	0.536215i	$-0.180146\pi$
$240$	−3126.88	+	2821.03i	−0.840996	+	0.758735i
$241$		−	1551.15i		−	0.414600i	−0.978277	−	0.207300i	$-0.933532\pi$
$241$		−	1551.15i		−	0.414600i	0.978277	−	0.207300i	$-0.0664676\pi$
$242$	2001.58	−	2913.86i	0.531681	−	0.774008i
$243$	3501.64			0.924406
$244$	724.142	+	1883.69i	0.189994	+	0.494224i
$245$	1270.31			0.331253
$246$	3192.56	+	2193.03i	0.827440	+	0.568385i
$247$	387.880	+	4999.56i	0.0999198	+	1.28791i
$248$	−2445.48	−	585.200i	−0.626162	−	0.149840i
$249$		−	4907.56i		−	1.24901i
$250$	2812.32	−	4094.10i	0.711466	−	1.03573i
$251$			3214.14i			0.808267i	0.914700	+	0.404133i	$0.132427\pi$
$251$			3214.14i			0.808267i	−0.914700	+	0.404133i	$0.867573\pi$
$252$	−1786.06	+	686.611i	−0.446473	+	0.171637i
$253$	−1647.36			−0.409362
$254$	503.467	−	732.935i	0.124371	−	0.181057i
$255$	87.6095			0.0215150
$256$	420.136	−	4074.40i	0.102572	−	0.994726i
$257$			7181.74i			1.74313i	0.490279	+	0.871565i	$0.336895\pi$
$257$			7181.74i			1.74313i	−0.490279	+	0.871565i	$0.663105\pi$
$258$	−2479.67	−	1703.33i	−0.598363	−	0.411027i
$259$	−2654.46			−0.636834
$260$	−8393.08	+	3226.54i	−2.00199	+	0.769621i
$261$			882.619i			0.209321i
$262$	−4684.77	−	3218.06i	−1.10468	−	0.758825i
$263$			5311.58i			1.24535i	0.782482	+	0.622673i	$0.213953\pi$
$263$			5311.58i			1.24535i	−0.782482	+	0.622673i	$0.786047\pi$
$264$	168.161	−	702.725i	0.0392031	−	0.163825i
$265$		−	10112.7i		−	2.34421i
$266$	−3359.81	−	1943.67i	−0.774448	−	0.448023i
$267$		−	3464.46i		−	0.794089i
$268$	1522.80	+	3961.21i	0.347089	+	0.902871i
$269$		−	316.111i		−	0.0716492i	−0.999358	−	0.0358246i	$-0.988594\pi$
$269$		−	316.111i		−	0.0716492i	0.999358	−	0.0358246i	$-0.0114058\pi$
$270$	−4366.42	+	6356.52i	−0.984191	+	1.43276i
$271$		−	3102.02i		−	0.695330i	−0.937619	−	0.347665i	$-0.886975\pi$
$271$		−	3102.02i		−	0.695330i	0.937619	−	0.347665i	$-0.113025\pi$
$272$	−63.2670	+	57.0786i	−0.0141034	+	0.0127239i
$273$	3556.44			0.788446
$274$	534.190	−	777.660i	0.117779	−	0.171461i
$275$			1978.28i			0.433800i
$276$	4840.34	−	1860.76i	1.05563	−	0.405815i
$277$	5920.52			1.28422			0.642111	−	0.766611i	$-0.278059\pi$
$277$	5920.52			1.28422			0.642111	+	0.766611i	$0.278059\pi$
$278$	1368.99	+	940.384i	0.295347	+	0.202880i
$279$	−1604.10			−0.344211
$280$	1619.82	−	6769.03i	0.345725	−	1.44474i
$281$			2141.11i			0.454548i	0.973831	+	0.227274i	$0.0729813\pi$
$281$			2141.11i			0.454548i	−0.973831	+	0.227274i	$0.927019\pi$
$282$	−1710.52	−	1174.99i	−0.361205	−	0.248119i
$283$			7766.87i			1.63142i	0.578460	+	0.815711i	$0.303654\pi$
$283$			7766.87i			1.63142i	−0.578460	+	0.815711i	$0.696346\pi$
$284$	1017.61	+	2647.07i	0.212619	+	0.553080i
$285$	−5433.38	+	421.536i	−1.12928	+	0.0876129i
$286$	873.533	−	1271.67i	0.180605	−	0.262921i
$287$	−6401.30			−1.31657
$288$	−344.246	−	2590.20i	−0.0704335	−	0.529961i
$289$	−4911.23			−0.999639
$290$	−2646.26	−	1817.77i	−0.535841	−	0.368079i
$291$			4202.94i			0.846670i
$292$	−987.127	−	2567.78i	−0.197833	−	0.514616i
$293$		−	1969.51i		−	0.392697i	−0.980534	−	0.196348i	$-0.937092\pi$
$293$		−	1969.51i		−	0.392697i	0.980534	−	0.196348i	$-0.0629083\pi$
$294$	388.467	−	565.521i	0.0770607	−	0.112183i
$295$	8260.49			1.63032
$296$	843.595	−	3525.28i	0.165652	−	0.692239i
$297$		−	1323.14i		−	0.258507i
$298$	1068.09	−	1554.90i	0.207627	−	0.302258i
$299$	11072.2			2.14155
$300$	−2234.56	−	5812.68i	−0.430041	−	1.11865i
$301$	4971.91			0.952080
$302$	512.871	−	746.625i	0.0977232	−	0.142263i
$303$	−4854.93			−0.920491
$304$	3649.06	−	3844.32i	0.688448	−	0.725286i
$305$	−4682.80			−0.879136
$306$	−30.7777	+	44.8054i	−0.00574982	+	0.00837044i
$307$	5534.00			1.02880			0.514401	−	0.857550i	$-0.328014\pi$
$307$	5534.00			1.02880			0.514401	+	0.857550i	$0.328014\pi$
$308$	428.507	+	1114.66i	0.0792742	+	0.206213i
$309$	−5570.43			−1.02554
$310$	3303.66	−	4809.39i	0.605275	−	0.881145i
$311$		−	2383.59i		−	0.434602i	−0.976105	−	0.217301i	$-0.930275\pi$
$311$		−	2383.59i		−	0.434602i	0.976105	−	0.217301i	$-0.0697252\pi$
$312$	−1130.25	+	4723.16i	−0.205089	+	0.857040i
$313$	9219.27			1.66487			0.832434	−	0.554124i	$-0.186947\pi$
$313$	9219.27			1.66487			0.832434	+	0.554124i	$0.186947\pi$
$314$	4204.20	−	6120.38i	0.755595	−	1.09998i
$315$		−	4440.10i		−	0.794195i
$316$	76.4087	+	198.759i	0.0136023	+	0.0353832i
$317$			7022.50i			1.24424i	0.782923	+	0.622118i	$0.213728\pi$
$317$			7022.50i			1.24424i	−0.782923	+	0.622118i	$0.786272\pi$
$318$	−4502.00	−	3092.51i	−0.793897	−	0.545343i
$319$	550.834			0.0966795
$320$	8474.89	+	4302.44i	1.48050	+	0.751605i
$321$	7559.81			1.31448
$322$	−4852.60	+	7064.30i	−0.839829	+	1.22260i
$323$	−109.935	+	8.52906i	−0.0189379	+	0.00146926i
$324$	375.759	+	977.449i	0.0644306	+	0.167601i
$325$		−	13296.5i		−	2.26940i
$326$	1250.85	+	859.235i	0.212510	+	0.145977i
$327$			1158.58i			0.195931i
$328$	2034.35	−	8501.30i	0.342464	−	1.43112i
$329$	3429.70			0.574728
$330$	1382.01	+	949.330i	0.230537	+	0.158360i
$331$	−4723.08			−0.784302			−0.392151	−	0.919901i	$-0.628269\pi$
$331$	−4723.08			−0.784302			−0.392151	+	0.919901i	$0.628269\pi$
$332$	−10338.1	+	3974.25i	−1.70896	+	0.656974i
$333$		−	2312.38i		−	0.380534i
$334$	−3140.86	+	4572.38i	−0.514551	+	0.749071i
$335$	−9847.49			−1.60605
$336$	−2518.12	−	2791.13i	−0.408853	−	0.453180i
$337$			8175.98i			1.32158i	0.750569	+	0.660792i	$0.229780\pi$
$337$			8175.98i			1.32158i	−0.750569	+	0.660792i	$0.770220\pi$
$338$	−2352.78	+	3425.12i	−0.378622	+	0.551189i
$339$			3197.53i			0.512289i
$340$	−70.9481	−	184.555i	−0.0113168	−	0.0294379i
$341$			1001.10i			0.158981i
$342$	1693.19	−	2926.84i	0.267712	−	0.462764i
$343$			6817.46i			1.07320i
$344$	−1580.09	+	6602.99i	−0.247653	+	1.03491i
$345$			12033.0i			1.87778i
$346$	−7859.99	−	5399.17i	−1.22126	−	0.838906i
$347$		−	2376.28i		−	0.367624i	−0.982961	−	0.183812i	$-0.941156\pi$
$347$		−	2376.28i		−	0.367624i	0.982961	−	0.183812i	$-0.0588437\pi$
$348$	−1618.48	+	622.191i	−0.249310	+	0.0958417i
$349$	3240.61			0.497037			0.248518	−	0.968627i	$-0.420056\pi$
$349$	3240.61			0.497037			0.248518	+	0.968627i	$0.420056\pi$
$350$	8483.39	+	5827.40i	1.29559	+	0.889965i
$351$			8893.13i			1.35237i
$352$	−1616.52	+	214.840i	−0.244774	+	0.0325313i
$353$	−4885.62			−0.736645			−0.368322	−	0.929698i	$-0.620068\pi$
$353$	−4885.62			−0.736645			−0.368322	+	0.929698i	$0.620068\pi$
$354$	2526.10	−	3677.44i	0.379268	−	0.552129i
$355$	−6580.56			−0.983831
$356$	−7298.11	+	2805.60i	−1.08651	+	0.417687i
$357$			78.2023i			0.0115936i
$358$	1891.87	−	2754.14i	0.279297	−	0.406594i
$359$		−	7375.74i		−	1.08434i	−0.840270	−	0.542168i	$-0.817604\pi$
$359$		−	7375.74i		−	1.08434i	0.840270	−	0.542168i	$-0.182396\pi$
$360$	5896.72	+	1411.08i	0.863290	+	0.206584i
$361$	6776.92	−	1057.91i	0.988034	−	0.154237i
$362$	2694.72	+	1851.05i	0.391247	+	0.268755i
$363$	4430.38			0.640592
$364$	−2880.09	−	7491.87i	−0.414719	−	1.07879i
$365$	6383.45			0.915411
$366$	−1432.03	+	2084.71i	−0.204517	+	0.297731i
$367$			8077.71i			1.14892i	0.818533	+	0.574459i	$0.194788\pi$
$367$			8077.71i			1.14892i	−0.818533	+	0.574459i	$0.805212\pi$
$368$	−7839.64	−	8689.60i	−1.11051	−	1.23092i
$369$		−	5576.38i		−	0.786706i
$370$	6932.97	+	4762.39i	0.974130	+	0.669149i
$371$	9026.80			1.26320
$372$	−1130.79	−	2941.48i	−0.157604	−	0.409969i
$373$			4658.00i			0.646601i	0.946296	+	0.323301i	$0.104792\pi$
$373$			4658.00i			0.646601i	−0.946296	+	0.323301i	$0.895208\pi$
$374$	27.9626	+	19.2081i	0.00386608	+	0.00265568i
$375$	6224.89			0.857205
$376$	−1089.97	+	4554.84i	−0.149497	+	0.624729i
$377$	−3702.27			−0.505773
$378$	−5673.98	−	3897.57i	−0.772059	−	0.530342i
$379$	−7899.98			−1.07070			−0.535349	−	0.844631i	$-0.679820\pi$
$379$	−7899.98			−1.07070			−0.535349	+	0.844631i	$0.679820\pi$
$380$	5288.06	+	11104.4i	0.713874	+	1.49906i
$381$	1114.39			0.149848
$382$	7155.24	+	4915.07i	0.958361	+	0.658317i
$383$	−7209.44			−0.961841			−0.480920	−	0.876764i	$-0.659697\pi$
$383$	−7209.44			−0.961841			−0.480920	+	0.876764i	$0.659697\pi$
$384$	4507.05	−	2457.18i	0.598956	−	0.326543i
$385$	−2771.03			−0.366817
$386$	−2299.48	−	1579.56i	−0.303214	−	0.208283i
$387$			4331.19i			0.568906i
$388$	8853.77	−	3403.64i	1.15846	−	0.445344i
$389$	−12501.1			−1.62939			−0.814694	−	0.579891i	$-0.803095\pi$
$389$	−12501.1			−1.62939			−0.814694	+	0.579891i	$0.803095\pi$
$390$	−9288.79	−	6380.65i	−1.20604	−	0.828453i
$391$			243.467i			0.0314901i
$392$	−1505.89	−	360.359i	−0.194028	−	0.0464308i
$393$		−	7122.97i		−	0.914266i
$394$	−3840.42	+	5590.79i	−0.491060	+	0.714873i
$395$	−494.112			−0.0629404
$396$	−971.017	+	373.286i	−0.123221	+	0.0473696i
$397$	−11540.2			−1.45891			−0.729456	−	0.684028i	$-0.760227\pi$
$397$	−11540.2			−1.45891			−0.729456	+	0.684028i	$0.760227\pi$
$398$	−3918.07	−	2691.40i	−0.493456	−	0.338964i
$399$	−376.274	−	4849.96i	−0.0472111	−	0.608526i
$400$	−10435.2	+	9414.48i	−1.30440	+	1.17681i
$401$		−	5404.80i		−	0.673074i	−0.941670	−	0.336537i	$-0.890744\pi$
$401$		−	5404.80i		−	0.673074i	0.941670	−	0.336537i	$-0.109256\pi$
$402$	−3011.42	+	4383.95i	−0.373621	+	0.543909i
$403$		−	6728.61i		−	0.831702i
$404$	3931.63	+	10227.2i	0.484174	+	1.25946i
$405$	−2429.92			−0.298133
$406$	1622.58	−	2362.12i	0.198343	−	0.288744i
$407$	−1443.14			−0.175758
$408$	−103.857	−	24.8529i	−0.0126022	−	0.00301569i
$409$			7827.99i			0.946380i	0.880960	+	0.473190i	$0.156898\pi$
$409$			7827.99i			0.946380i	−0.880960	+	0.473190i	$0.843102\pi$
$410$	16719.0	+	11484.6i	2.01389	+	1.38338i
$411$	1182.40			0.141906
$412$	4511.06	+	11734.5i	0.539427	+	1.40319i
$413$			7373.51i			0.878515i
$414$	−6153.94	−	4227.26i	−0.730555	−	0.501832i
$415$		−	25700.3i		−	3.03994i
$416$	10864.9	−	1443.99i	1.28052	−	0.170186i
$417$			2081.48i			0.244438i
$418$	−1826.61	−	1056.70i	−0.213738	−	0.123649i
$419$		−	5007.06i		−	0.583797i	−0.956449	−	0.291898i	$-0.905713\pi$
$419$		−	5007.06i		−	0.583797i	0.956449	−	0.291898i	$-0.0942869\pi$
$420$	8141.95	−	3129.99i	0.945920	−	0.363638i
$421$			11864.9i			1.37353i	0.726878	+	0.686767i	$0.240971\pi$
$421$			11864.9i			1.37353i	−0.726878	+	0.686767i	$0.759029\pi$
$422$	−1828.90	+	2662.47i	−0.210970	+	0.307125i
$423$			2987.72i			0.343423i
$424$	−2868.74	+	11988.1i	−0.328581	+	1.37310i
$425$	292.375			0.0333700
$426$	−2012.37	+	2929.56i	−0.228873	+	0.333187i
$427$		−	4179.98i		−	0.473732i
$428$	−6122.11	−	15925.2i	−0.691409	−	1.79854i
$429$	1933.51			0.217601
$430$	−12985.7	−	8920.15i	−1.45634	−	1.00039i
$431$	−2762.11			−0.308692			−0.154346	−	0.988017i	$-0.549327\pi$
$431$	−2762.11			−0.308692			−0.154346	+	0.988017i	$0.549327\pi$
$432$	6979.41	−	6296.73i	0.777308	−	0.701276i
$433$		−	1352.05i		−	0.150058i	−0.997181	−	0.0750292i	$-0.976095\pi$
$433$		−	1352.05i		−	0.150058i	0.997181	−	0.0750292i	$-0.0239050\pi$
$434$	4292.98	+	2948.93i	0.474815	+	0.326159i
$435$		−	4023.52i		−	0.443478i
$436$	2440.62	−	938.243i	0.268084	−	0.103059i
$437$	−1171.45	−	15099.4i	−0.128234	−	1.65286i
$438$	1952.09	−	2841.81i	0.212956	−	0.310016i
$439$	10054.6			1.09312			0.546558	−	0.837421i	$-0.315938\pi$
$439$	10054.6			1.09312			0.546558	+	0.837421i	$0.315938\pi$
$440$	880.640	−	3680.08i	0.0954156	−	0.398730i
$441$	−987.782			−0.106660
$442$	−187.943	−	129.101i	−0.0202251	−	0.0138930i
$443$			739.747i			0.0793374i	0.999213	+	0.0396687i	$0.0126303\pi$
$443$			739.747i			0.0793374i	−0.999213	+	0.0396687i	$0.987370\pi$
$444$	4240.28	−	1630.09i	0.453232	−	0.174235i
$445$		−	18143.0i		−	1.93272i
$446$	1355.07	−	1972.68i	0.143866	−	0.209437i
$447$	2364.15			0.250158
$448$	−3840.46	+	7564.89i	−0.405010	+	0.797784i
$449$		−	1524.86i		−	0.160273i	−0.996784	−	0.0801365i	$-0.974464\pi$
$449$		−	1524.86i		−	0.160273i	0.996784	−	0.0801365i	$-0.0255356\pi$
$450$	−5076.44	+	7390.15i	−0.531790	+	0.774167i
$451$	−3480.16			−0.363358
$452$	6735.80	−	2589.43i	0.700941	−	0.269462i
$453$	1135.21			0.117741
$454$	−7955.72	+	11581.7i	−0.822424	+	1.19726i
$455$	18624.6			1.91898
$456$	6560.62	+	1041.62i	0.673748	+	0.106970i
$457$	−11675.4			−1.19509			−0.597543	−	0.801837i	$-0.703856\pi$
$457$	−11675.4			−1.19509			−0.597543	+	0.801837i	$0.703856\pi$
$458$	407.312	−	592.955i	0.0415555	−	0.0604955i
$459$	−195.550			−0.0198856
$460$	25348.3	−	9744.59i	2.56928	−	0.987704i
$461$	6801.29			0.687132			0.343566	−	0.939129i	$-0.388365\pi$
$461$	6801.29			0.687132			0.343566	+	0.939129i	$0.388365\pi$
$462$	−847.395	+	1233.62i	−0.0853342	+	0.124227i
$463$			12855.5i			1.29038i	0.764022	+	0.645191i	$0.223222\pi$
$463$			12855.5i			1.29038i	−0.764022	+	0.645191i	$0.776778\pi$
$464$	2621.37	+	2905.57i	0.262271	+	0.290707i
$465$	7312.45			0.729262
$466$	3862.22	−	5622.53i	0.383935	−	0.558924i
$467$			5042.30i			0.499636i	0.968293	+	0.249818i	$0.0803707\pi$
$467$			5042.30i			0.499636i	−0.968293	+	0.249818i	$0.919629\pi$
$468$	6526.41	−	2508.94i	0.644622	−	0.247811i
$469$		−	8790.11i		−	0.865436i
$470$	−8957.76	−	6153.26i	−0.879129	−	0.603891i
$471$	9305.75			0.910374
$472$	−9792.46	−	2343.32i	−0.954946	−	0.228517i
$473$	2703.05			0.262762
$474$	−151.102	+	219.971i	−0.0146421	+	0.0213156i
$475$	−18132.5	+	1406.77i	−1.75153	+	0.135889i
$476$	164.738	−	63.3300i	0.0158629	−	0.00609816i
$477$			7863.53i			0.754814i
$478$	−9238.00	−	6345.76i	−0.883967	−	0.607214i
$479$		−	8819.98i		−	0.841326i	−0.907217	−	0.420663i	$-0.861798\pi$
$479$		−	8819.98i		−	0.841326i	0.907217	−	0.420663i	$-0.138202\pi$
$480$	1569.28	+	11807.7i	0.149224	+	1.12280i
$481$	9699.62			0.919469
$482$	−3616.32	−	2484.12i	−0.341741	−	0.234748i
$483$	−10740.9			−1.01186
$484$	−3587.82	−	9332.88i	−0.336948	−	0.876492i
$485$			22010.3i			2.06069i
$486$	5607.76	−	8163.64i	0.523402	−	0.761956i
$487$	16895.2			1.57206			0.786031	−	0.618187i	$-0.212132\pi$
$487$	16895.2			1.57206			0.786031	+	0.618187i	$0.212132\pi$
$488$	5551.26	+	1328.41i	0.514947	+	0.123226i
$489$			1901.86i			0.175880i
$490$	2034.35	−	2961.56i	0.187557	−	0.273040i
$491$			4858.32i			0.446544i	0.974756	+	0.223272i	$0.0716738\pi$
$491$			4858.32i			0.446544i	−0.974756	+	0.223272i	$0.928326\pi$
$492$	10225.6	−	3930.99i	0.936999	−	0.360209i
$493$		−	81.4089i		−	0.00743706i
$494$	12277.0	+	7102.33i	1.11816	+	0.646860i
$495$		−	2413.93i		−	0.219188i
$496$	−5280.67	+	4764.15i	−0.478043	+	0.431284i
$497$		−	5873.97i		−	0.530148i
$498$	−11441.4	−	7859.29i	−1.02952	−	0.707195i
$499$		−	7275.02i		−	0.652654i	−0.945257	−	0.326327i	$-0.894189\pi$
$499$		−	7275.02i		−	0.652654i	0.945257	−	0.326327i	$-0.105811\pi$
$500$	−5041.05	−	13113.1i	−0.450886	−	1.17287i
$501$	−6952.09			−0.619953
$502$	7493.37	+	5147.34i	0.666226	+	0.457644i
$503$			3504.57i			0.310658i	0.987863	+	0.155329i	$0.0496438\pi$
$503$			3504.57i			0.310658i	−0.987863	+	0.155329i	$0.950356\pi$
$504$	−1259.56	+	5263.55i	−0.111320	+	0.465193i
$505$	−25424.7			−2.24036
$506$	−2638.19	+	3840.61i	−0.231782	+	0.337423i
$507$	−5207.73			−0.456180
$508$	−902.461	−	2347.54i	−0.0788193	−	0.205030i
$509$		−	14856.4i		−	1.29371i	−0.762614	−	0.646853i	$-0.776085\pi$
$509$		−	14856.4i		−	1.29371i	0.762614	−	0.646853i	$-0.223915\pi$
$510$	140.304	−	204.250i	0.0121819	−	0.0177340i
$511$			5698.02i			0.493279i
$512$	−8826.11	−	7504.50i	−0.761841	−	0.647764i
$513$	12127.7	−	940.899i	1.04376	−	0.0809779i
$514$	16743.3	+	11501.3i	1.43680	+	0.986967i
$515$	−29171.7			−2.49603
$516$	−7942.22	+	3053.22i	−0.677591	+	0.260485i
$517$	1864.61			0.158618
$518$	−4251.03	+	6188.54i	−0.360578	+	0.524920i
$519$		−	11950.7i		−	1.01075i
$520$	−5918.97	+	24734.6i	−0.499161	+	2.08593i
$521$		−	20204.6i		−	1.69901i	−0.527585	−	0.849503i	$-0.676902\pi$
$521$		−	20204.6i		−	1.69901i	0.527585	−	0.849503i	$-0.323098\pi$
$522$	2057.72	+	1413.48i	0.172536	+	0.118518i
$523$	2735.18			0.228683			0.114341	−	0.993442i	$-0.463524\pi$
$523$	2735.18			0.228683			0.114341	+	0.993442i	$0.463524\pi$
$524$	−15005.0	+	5768.34i	−1.25095	+	0.480899i
$525$			12898.6i			1.07227i
$526$	12383.3	+	8506.32i	1.02650	+	0.705120i
$527$	147.955			0.0122296
$528$	−1369.01	−	1517.44i	−0.112838	−	0.125072i
$529$	−21272.7			−1.74839
$530$	−23576.4	−	16195.1i	−1.93225	−	1.32730i
$531$	−6423.30			−0.524948
$532$	−9912.04	+	4720.25i	−0.807785	+	0.384678i
$533$	23390.9			1.90088
$534$	−8076.96	−	5548.22i	−0.654540	−	0.449616i
$535$	39589.8			3.19928
$536$	11673.8	+	2793.52i	0.940728	+	0.225115i
$537$	4187.54			0.336509
$538$	−736.973	−	506.241i	−0.0590579	−	0.0405680i
$539$			616.465i			0.0492635i
$540$	7826.77	+	20359.5i	0.623723	+	1.62247i
$541$	−1260.78			−0.100194			−0.0500971	−	0.998744i	$-0.515953\pi$
$541$	−1260.78			−0.100194			−0.0500971	+	0.998744i	$0.515953\pi$
$542$	−7231.98	−	4967.78i	−0.573137	−	0.393698i
$543$			4097.20i			0.323808i
$544$	31.7517	+	238.908i	0.00250247	+	0.0188293i
$545$			6067.33i			0.476873i
$546$	5695.52	−	8291.40i	0.446421	−	0.649888i
$547$	−19283.7			−1.50733			−0.753665	−	0.657258i	$-0.771716\pi$
$547$	−19283.7			−1.50733			−0.753665	+	0.657258i	$0.771716\pi$
$548$	−957.531	−	2490.79i	−0.0746418	−	0.194163i
$549$	3641.32			0.283074
$550$	4612.12	+	3168.15i	0.357566	+	0.245619i
$551$	391.702	+	5048.83i	0.0302851	+	0.390358i
$552$	3413.50	−	14264.6i	0.263204	−	1.09989i
$553$		−	441.056i		−	0.0339161i
$554$	9481.51	−	13803.0i	0.727131	−	1.05854i
$555$			10541.3i			0.806219i
$556$	4384.78	−	1685.63i	0.334453	−	0.128573i
$557$	−11962.5			−0.909993			−0.454997	−	0.890493i	$-0.650360\pi$
$557$	−11962.5			−0.909993			−0.454997	+	0.890493i	$0.650360\pi$
$558$	−2568.91	+	3739.75i	−0.194893	+	0.283721i
$559$	−18167.8			−1.37462
$560$	−13187.1	−	14616.8i	−0.995098	−	1.10299i
$561$			42.5159i			0.00319968i
$562$	4991.73	+	3428.92i	0.374668	+	0.257367i
$563$	9757.18			0.730402			0.365201	−	0.930929i	$-0.381000\pi$
$563$	9757.18			0.730402			0.365201	+	0.930929i	$0.381000\pi$
$564$	−5478.67	+	2106.15i	−0.409031	+	0.157243i
$565$			16745.1i			1.24685i
$566$	18107.5	+	12438.4i	1.34472	+	0.923717i
$567$		−	2169.01i		−	0.160652i
$568$	7800.97	+	1866.76i	0.576270	+	0.137901i
$569$			10963.6i			0.807766i	0.914811	+	0.403883i	$0.132340\pi$
$569$			10963.6i			0.807766i	−0.914811	+	0.403883i	$0.867660\pi$
$570$	−7718.61	+	13342.3i	−0.567187	+	0.980435i
$571$		−	21741.8i		−	1.59346i	−0.604337	−	0.796728i	$-0.706562\pi$
$571$		−	21741.8i		−	1.59346i	0.604337	−	0.796728i	$-0.293438\pi$
$572$	−1565.80	−	4073.07i	−0.114457	−	0.297733i
$573$			10879.2i			0.793169i
$574$	−10251.5	+	14923.8i	−0.745449	+	1.08521i
$575$			40157.1i			2.91247i
$576$	−6590.02	−	3345.55i	−0.476708	−	0.242010i
$577$	10398.3			0.750234			0.375117	−	0.926977i	$-0.377602\pi$
$577$	10398.3			0.750234			0.375117	+	0.926977i	$0.377602\pi$
$578$	−7865.16	+	11449.9i	−0.565999	+	0.823968i
$579$		−	3496.26i		−	0.250949i
$580$	−8475.79	+	3258.33i	−0.606790	+	0.233267i
$581$	22940.7			1.63811
$582$	9798.64	+	6730.87i	0.697881	+	0.479388i
$583$	4907.55			0.348628
$584$	−7567.30	−	1810.85i	−0.536194	−	0.128311i
$585$			16224.5i			1.14667i
$586$	−4591.67	−	3154.11i	−0.323686	−	0.222346i
$587$			21602.5i			1.51896i	0.650528	+	0.759482i	$0.274548\pi$
$587$			21602.5i			1.51896i	−0.650528	+	0.759482i	$0.725452\pi$
$588$	−696.324	−	1811.32i	−0.0488366	−	0.127037i
$589$	−9175.88	+	711.891i	−0.641911	+	0.0498013i
$590$	13228.9	−	19258.3i	0.923093	−	1.34382i
$591$	−8500.53			−0.591650
$592$	−6867.76	−	7612.35i	−0.476796	−	0.528489i
$593$	1278.08			0.0885068			0.0442534	−	0.999020i	$-0.485909\pi$
$593$	1278.08			0.0885068			0.0442534	+	0.999020i	$0.485909\pi$
$594$	−3084.75	−	2118.97i	−0.213079	−	0.146368i
$595$			409.536i			0.0282174i
$596$	−1914.54	−	4980.23i	−0.131582	−	0.342279i
$597$		−	5957.25i		−	0.408399i
$598$	17731.8	−	25813.6i	1.21256	−	1.76521i
$599$	12429.7			0.847851			0.423925	−	0.905697i	$-0.360652\pi$
$599$	12429.7			0.847851			0.423925	+	0.905697i	$0.360652\pi$
$600$	−17130.1	−	4099.21i	−1.16556	−	0.278916i
$601$			1884.25i			0.127887i	0.997954	+	0.0639435i	$0.0203677\pi$
$601$			1884.25i			0.127887i	−0.997954	+	0.0639435i	$0.979632\pi$
$602$	7962.34	−	11591.4i	0.539071	−	0.784767i
$603$	7657.34			0.517133
$604$	−919.318	−	2391.39i	−0.0619313	−	0.161100i
$605$	23201.4			1.55912
$606$	−7775.01	+	11318.7i	−0.521185	+	0.758729i
$607$	−13318.6			−0.890583			−0.445291	−	0.895386i	$-0.646900\pi$
$607$	−13318.6			−0.890583			−0.445291	+	0.895386i	$0.646900\pi$
$608$	−3118.70	−	14663.9i	−0.208026	−	0.978123i
$609$	3591.49			0.238973
$610$	−7499.35	+	10917.4i	−0.497770	+	0.724642i
$611$	−12532.4			−0.829799
$612$	55.1688	+	143.509i	0.00364390	+	0.00947875i
$613$	−6904.69			−0.454940			−0.227470	−	0.973785i	$-0.573045\pi$
$613$	−6904.69			−0.454940			−0.227470	+	0.973785i	$0.573045\pi$
$614$	8862.52	−	12901.8i	0.582512	−	0.848006i
$615$			25420.5i			1.66676i
$616$	3284.93	+	786.081i	0.214860	+	0.0514157i
$617$	18048.1			1.17762			0.588810	−	0.808272i	$-0.299597\pi$
$617$	18048.1			1.17762			0.588810	+	0.808272i	$0.299597\pi$
$618$	−8920.86	+	12986.8i	−0.580663	+	0.845314i
$619$		−	5281.51i		−	0.342943i	−0.985189	−	0.171472i	$-0.945148\pi$
$619$		−	5281.51i		−	0.342943i	0.985189	−	0.171472i	$-0.0548522\pi$
$620$	−5921.79	−	15404.1i	−0.383588	−	0.997815i
$621$		−	26858.5i		−	1.73558i
$622$	−5557.05	−	3817.24i	−0.358227	−	0.246073i
$623$	16194.8			1.04146
$624$	9201.41	+	10199.0i	0.590306	+	0.654307i
$625$	5149.01			0.329537
$626$	14764.3	−	21493.6i	0.942655	−	1.37229i
$627$	−204.567	−	2636.75i	−0.0130297	−	0.167946i
$628$	−7536.00	−	19603.1i	−0.478852	−	1.24562i
$629$			213.284i			0.0135202i
$630$	−10351.5	−	7110.68i	−0.654628	−	0.449676i
$631$		−	10792.6i		−	0.680897i	−0.940263	−	0.340449i	$-0.889421\pi$
$631$		−	10792.6i		−	0.680897i	0.940263	−	0.340449i	$-0.110579\pi$
$632$	585.749	+	140.169i	0.0368668	+	0.00882219i
$633$	−4048.16			−0.254186
$634$	16372.1	+	11246.3i	1.02558	+	0.704491i
$635$	5835.94			0.364712
$636$	−14419.6	+	5543.29i	−0.899015	+	0.345607i
$637$		−	4143.39i		−	0.257719i
$638$	882.141	−	1284.20i	0.0547403	−	0.0796896i
$639$	5117.00			0.316785
$640$	23602.8	−	12867.9i	1.45779	−	0.794765i
$641$			1266.05i			0.0780126i	0.999239	+	0.0390063i	$0.0124192\pi$
$641$			1266.05i			0.0780126i	−0.999239	+	0.0390063i	$0.987581\pi$
$642$	12106.8	−	17624.8i	0.744263	−	1.08348i
$643$			17565.7i			1.07733i	0.842520	+	0.538664i	$0.181071\pi$
$643$			17565.7i			1.07733i	−0.842520	+	0.538664i	$0.818929\pi$
$644$	8698.26	+	22626.5i	0.532235	+	1.38448i
$645$		−	19744.2i		−	1.20531i
$646$	−156.173	+	269.959i	−0.00951166	+	0.0164418i
$647$		−	14039.6i		−	0.853098i	−0.904464	−	0.426549i	$-0.859729\pi$
$647$		−	14039.6i		−	0.853098i	0.904464	−	0.426549i	$-0.140271\pi$
$648$	2880.57	+	689.316i	0.174629	+	0.0417884i
$649$			4008.72i			0.242459i
$650$	−30999.0	−	21293.8i	−1.87059	−	1.28494i
$651$			6527.27i			0.392971i
$652$	4006.40	−	1540.17i	0.240648	−	0.0925119i
$653$	−17339.1			−1.03910			−0.519548	−	0.854441i	$-0.673900\pi$
$653$	−17339.1			−1.03910			−0.519548	+	0.854441i	$0.673900\pi$
$654$	2701.08	+	1855.42i	0.161499	+	0.110937i
$655$		−	37302.1i		−	2.22521i
$656$	−16561.8	−	18357.4i	−0.985714	−	1.09258i
$657$	−4963.73			−0.294754
$658$	5492.54	−	7995.91i	0.325413	−	0.473728i
$659$	9425.92			0.557180			0.278590	−	0.960410i	$-0.410133\pi$
$659$	9425.92			0.557180			0.278590	+	0.960410i	$0.410133\pi$
$660$	4426.49	−	1701.67i	0.261062	−	0.100360i
$661$			27256.9i			1.60389i	0.597397	+	0.801946i	$0.296202\pi$
$661$			27256.9i			1.60389i	−0.597397	+	0.801946i	$0.703798\pi$
$662$	−7563.86	+	11011.3i	−0.444075	+	0.646473i
$663$		−	285.758i		−	0.0167389i
$664$	−7290.62	+	30466.6i	−0.426101	+	1.78062i
$665$	−1970.50	−	25398.6i	−0.114906	−	1.48108i
$666$	−5391.03	−	3703.20i	−0.313661	−	0.215460i
$667$	11181.4			0.649091
$668$	5629.96	+	14645.0i	0.326092	+	0.848253i
$669$	2999.37			0.173337
$670$	−15770.4	+	22958.2i	−0.909350	+	1.32381i
$671$		−	2272.51i		−	0.130744i
$672$	−10539.8	+	1400.78i	−0.605034	+	0.0804110i
$673$			11728.9i			0.671790i	0.941899	+	0.335895i	$0.109039\pi$
$673$			11728.9i			0.671790i	−0.941899	+	0.335895i	$0.890961\pi$
$674$	19061.3	+	13093.6i	1.08934	+	0.748286i
$675$	−32253.8			−1.83919
$676$	4217.34	+	10970.4i	0.239949	+	0.624170i
$677$		−	24867.7i		−	1.41173i	−0.708344	−	0.705867i	$-0.750557\pi$
$677$		−	24867.7i		−	1.41173i	0.708344	−	0.705867i	$-0.249443\pi$
$678$	7454.64	+	5120.73i	0.422262	+	0.290060i
$679$	−19646.9			−1.11043
$680$	−543.888	−	130.152i	−0.0306723	−	0.00733984i
$681$	−17609.5			−0.990892
$682$	2333.94	+	1603.23i	0.131043	+	0.0900158i
$683$	22062.3			1.23600			0.618001	−	0.786177i	$-0.287943\pi$
$683$	22062.3			1.23600			0.618001	+	0.786177i	$0.287943\pi$
$684$	−4111.96	−	8634.70i	−0.229861	−	0.482684i
$685$	6192.06			0.345382
$686$	15894.1	+	10917.9i	0.884603	+	0.607651i
$687$	901.560			0.0500679
$688$	12863.6	+	14258.2i	0.712819	+	0.790102i
$689$	−32984.7			−1.82383
$690$	28053.4	+	19270.4i	1.54779	+	1.06321i
$691$			1661.19i			0.0914537i	0.998954	+	0.0457268i	$0.0145604\pi$
$691$			1661.19i			0.0914537i	−0.998954	+	0.0457268i	$0.985440\pi$
$692$	−25175.0	+	9677.98i	−1.38296	+	0.531650i
$693$	2154.73			0.118112
$694$	−5540.00	−	3805.53i	−0.303019	−	0.208150i
$695$			10900.5i			0.594933i
$696$	−1141.39	+	4769.71i	−0.0621611	+	0.259763i
$697$			514.340i			0.0279513i
$698$	5189.72	−	7555.07i	0.281424	−	0.409690i
$699$	8548.79			0.462582
$700$	27171.7	−	10445.6i	1.46713	−	0.564008i
$701$	−23569.5			−1.26991			−0.634955	−	0.772549i	$-0.718981\pi$
$701$	−23569.5			−1.26991			−0.634955	+	0.772549i	$0.718981\pi$
$702$	20733.2	+	14242.0i	1.11471	+	0.765714i
$703$	−1026.23	−	13227.5i	−0.0550567	−	0.709650i
$704$	−2087.92	+	4112.76i	−0.111778	+	0.220178i
$705$		−	13619.9i		−	0.727594i
$706$	−7824.16	+	11390.2i	−0.417091	+	0.607191i
$707$		−	22694.7i		−	1.20724i
$708$	−4528.02	−	11778.6i	−0.240358	−	0.625235i
$709$	−11337.8			−0.600562			−0.300281	−	0.953851i	$-0.597081\pi$
$709$	−11337.8			−0.600562			−0.300281	+	0.953851i	$0.597081\pi$
$710$	−10538.5	+	15341.8i	−0.557049	+	0.810938i
$711$	384.218			0.0202663
$712$	−5146.77	+	21507.7i	−0.270904	+	1.13207i
$713$			20321.3i			1.06738i
$714$	182.319	+	125.238i	0.00955618	+	0.00656432i
$715$	10125.6			0.529615
$716$	−3391.16	−	8821.31i	−0.177002	−	0.460430i
$717$		−	14046.0i		−	0.731598i
$718$	−17195.6	−	11812.0i	−0.893781	−	0.613955i
$719$			7001.75i			0.363173i	0.983375	+	0.181586i	$0.0581232\pi$
$719$			7001.75i			0.363173i	−0.983375	+	0.181586i	$0.941877\pi$
$720$	12733.1	−	11487.7i	0.659078	−	0.594611i
$721$		−	26039.3i		−	1.34501i
$722$	8386.62	−	17493.8i	0.432296	−	0.901732i
$723$		−	5498.45i		−	0.282835i
$724$	8631.00	−	3318.00i	0.443051	−	0.170321i
$725$		−	13427.5i		−	0.687841i
$726$	7095.11	−	10328.9i	0.362705	−	0.528018i
$727$		−	10143.9i		−	0.517492i	−0.965945	−	0.258746i	$-0.916691\pi$
$727$		−	10143.9i		−	0.517492i	0.965945	−	0.258746i	$-0.0833092\pi$
$728$	−22078.7	−	5283.41i	−1.12403	−	0.268978i
$729$	15946.7			0.810176
$730$	10222.9	−	14882.2i	0.518309	−	0.754541i
$731$		−	399.490i		−	0.0202129i
$732$	2566.90	+	6677.19i	0.129611	+	0.337153i
$733$	8062.55			0.406272			0.203136	−	0.979151i	$-0.434887\pi$
$733$	8062.55			0.406272			0.203136	+	0.979151i	$0.434887\pi$
$734$	18832.2	+	12936.2i	0.947014	+	0.650522i
$735$	4502.92			0.225976
$736$	−32813.6	+	4361.04i	−1.64338	+	0.218410i
$737$		−	4778.87i		−	0.238849i
$738$	−13000.6	−	8930.37i	−0.648455	−	0.445436i
$739$		−	14484.1i		−	0.720982i	−0.932763	−	0.360491i	$-0.882609\pi$
$739$		−	14484.1i		−	0.720982i	0.932763	−	0.360491i	$-0.117391\pi$
$740$	22205.8	−	8536.55i	1.10311	−	0.424067i
$741$	1374.94	+	17722.2i	0.0681640	+	0.878597i
$742$	14456.1	−	21044.8i	0.715230	−	1.04121i
$743$	−28741.3			−1.41913			−0.709566	−	0.704639i	$-0.751109\pi$
$743$	−28741.3			−1.41913			−0.709566	+	0.704639i	$0.751109\pi$
$744$	−8668.60	−	2074.39i	−0.427159	−	0.102219i
$745$	12380.8			0.608854
$746$	10859.5	+	7459.63i	0.532971	+	0.366108i
$747$			19984.4i			0.978835i
$748$	89.5623	−	34.4303i	0.00437797	−	0.00168302i
$749$			35338.8i			1.72397i
$750$	9968.94	−	14512.5i	0.485352	−	0.706564i
$751$	−15219.1			−0.739487			−0.369743	−	0.929134i	$-0.620554\pi$
$751$	−15219.1			−0.739487			−0.369743	+	0.929134i	$0.620554\pi$
$752$	8873.50	+	9835.55i	0.430297	+	0.476949i
$753$			11393.3i			0.551389i
$754$	−5929.06	+	8631.37i	−0.286371	+	0.416891i
$755$	5944.95			0.286568
$756$	−18173.4	+	6986.36i	−0.874285	+	0.336100i
$757$	39653.8			1.90388			0.951942	−	0.306278i	$-0.0990837\pi$
$757$	39653.8			1.90388			0.951942	+	0.306278i	$0.0990837\pi$
$758$	−12651.6	+	18417.8i	−0.606234	+	0.882540i
$759$	−5839.47			−0.279261
$760$	34357.1	+	5454.83i	1.63982	+	0.260352i
$761$	−11503.3			−0.547956			−0.273978	−	0.961736i	$-0.588340\pi$
$761$	−11503.3			−0.547956			−0.273978	+	0.961736i	$0.588340\pi$
$762$	1784.66	−	2598.07i	0.0848445	−	0.123515i
$763$	−5415.85			−0.256968
$764$	22917.7	−	8810.23i	1.08526	−	0.417203i
$765$	−356.760			−0.0168610
$766$	−11545.7	+	16807.9i	−0.544598	+	0.792812i
$767$		−	26943.4i		−	1.26841i
$768$	1489.28	−	14442.7i	0.0699735	−	0.678589i
$769$	−15991.0			−0.749871			−0.374935	−	0.927051i	$-0.622335\pi$
$769$	−15991.0			−0.749871			−0.374935	+	0.927051i	$0.622335\pi$
$770$	−4437.70	+	6460.30i	−0.207693	+	0.302355i
$771$			25457.4i			1.18914i
$772$	−7365.08	+	2831.35i	−0.343362	+	0.131998i
$773$			9356.62i			0.435361i	0.976020	+	0.217681i	$0.0698491\pi$
$773$			9356.62i			0.435361i	−0.976020	+	0.217681i	$0.930151\pi$
$774$	10097.6	+	6936.25i	0.468930	+	0.322117i
$775$	24403.5			1.13110
$776$	6243.85	−	26092.3i	0.288842	−	1.20703i
$777$	−9409.39			−0.434440
$778$	−20020.1	+	29144.8i	−0.922565	+	1.34305i
$779$	−2474.77	−	31898.4i	−0.113823	−	1.46711i
$780$	−29751.4	+	11437.3i	−1.36573	+	0.525025i
$781$		−	3193.47i		−	0.146314i
$782$	567.612	+	389.904i	0.0259562	+	0.0178298i
$783$			8980.77i			0.409893i
$784$	−3251.77	+	2933.70i	−0.148131	+	0.133642i
$785$	48733.0			2.21574
$786$	−16606.3	−	11407.2i	−0.753598	−	0.517661i
$787$	16427.1			0.744045			0.372023	−	0.928224i	$-0.378664\pi$
$787$	16427.1			0.744045			0.372023	+	0.928224i	$0.378664\pi$
$788$	6883.92	+	17906.9i	0.311205	+	0.809527i
$789$			18828.2i			0.849559i
$790$	−791.303	+	1151.96i	−0.0356371	+	0.0518796i
$791$	−14947.0			−0.671878
$792$	−684.780	+	2861.61i	−0.0307230	+	0.128387i
$793$			15274.0i			0.683980i
$794$	−18481.3	+	26904.6i	−0.826041	+	1.20253i
$795$		−	35846.8i		−	1.59919i
$796$	−12549.3	+	4824.32i	−0.558793	+	0.214816i
$797$			13391.8i			0.595183i	0.954693	+	0.297591i	$0.0961833\pi$
$797$			13391.8i			0.595183i	−0.954693	+	0.297591i	$0.903817\pi$
$798$	−11909.7	−	6889.81i	−0.528318	−	0.305635i
$799$		−	275.574i		−	0.0122016i
$800$	5237.09	+	39405.3i	0.231449	+	1.74148i
$801$			14107.8i			0.622317i
$802$	−12600.6	−	8655.60i	−0.554792	−	0.381097i
$803$			3097.81i			0.136139i
$804$	5397.94	+	14041.5i	0.236780	+	0.615927i
$805$	−56249.0			−2.46275
$806$	−15686.9	−	10775.6i	−0.685543	−	0.470913i
$807$		−	1120.53i		−	0.0488781i
$808$	30139.9	+	7212.44i	1.31227	+	0.314026i
$809$	−22763.6			−0.989279			−0.494640	−	0.869098i	$-0.664700\pi$
$809$	−22763.6			−0.989279			−0.494640	+	0.869098i	$0.664700\pi$
$810$	−3891.43	+	5665.05i	−0.168804	+	0.245740i
$811$	31860.0			1.37948			0.689739	−	0.724058i	$-0.257725\pi$
$811$	31860.0			1.37948			0.689739	+	0.724058i	$0.257725\pi$
$812$	−2908.47	−	7565.70i	−0.125699	−	0.326975i
$813$		−	10995.9i		−	0.474345i
$814$	−2311.13	+	3364.49i	−0.0995150	+	0.144871i
$815$			9959.82i			0.428070i
$816$	−224.265	+	202.329i	−0.00962115	+	0.00868007i
$817$	1922.16	+	24775.6i	0.0823108	+	1.06094i
$818$	18250.0	+	12536.3i	0.780068	+	0.535844i
$819$	−14482.4			−0.617895
$820$	53550.0	−	20586.1i	2.28054	−	0.876705i
$821$	−26858.4			−1.14173			−0.570867	−	0.821042i	$-0.693393\pi$
$821$	−26858.4			−1.14173			−0.570867	+	0.821042i	$0.693393\pi$
$822$	1893.57	−	2756.61i	0.0803476	−	0.116968i
$823$			6752.33i			0.285992i	0.989723	+	0.142996i	$0.0456736\pi$
$823$			6752.33i			0.285992i	−0.989723	+	0.142996i	$0.954326\pi$
$824$	34581.8	+	8275.37i	1.46203	+	0.349862i
$825$			7012.52i			0.295933i
$826$	17190.4	+	11808.4i	0.724130	+	0.497418i
$827$	21649.4			0.910304			0.455152	−	0.890414i	$-0.349585\pi$
$827$	21649.4			0.910304			0.455152	+	0.890414i	$0.349585\pi$
$828$	−19710.7	+	7577.33i	−0.827286	+	0.318032i
$829$		−	25084.0i		−	1.05091i	−0.850821	−	0.525455i	$-0.823895\pi$
$829$		−	25084.0i		−	1.05091i	0.850821	−	0.525455i	$-0.176105\pi$
$830$	−59917.0	−	41158.1i	−2.50572	−	1.72123i
$831$	20986.7			0.876080
$832$	14033.4	−	27642.7i	0.584759	−	1.15185i
$833$	91.1087			0.00378959
$834$	4852.72	+	3333.42i	0.201482	+	0.138402i
$835$	−36407.2			−1.50889
$836$	−5388.83	+	2566.24i	−0.222938	+	0.106166i
$837$	−16321.9			−0.674035
$838$	−11673.3	−	8018.63i	−0.481204	−	0.330548i
$839$	−12037.6			−0.495332			−0.247666	−	0.968845i	$-0.579664\pi$
$839$	−12037.6			−0.495332			−0.247666	+	0.968845i	$0.579664\pi$
$840$	5741.86	−	23994.5i	0.235849	−	0.985582i
$841$	20650.2			0.846703
$842$	27661.4	+	19001.2i	1.13216	+	0.777700i
$843$			7589.70i			0.310087i
$844$	3278.29	+	8527.70i	0.133701	+	0.347791i
$845$	−27272.2			−1.11029
$846$	6965.50	+	4784.73i	0.283072	+	0.194447i
$847$			20710.1i			0.840150i
$848$	23354.6	+	25886.7i	0.945755	+	1.04829i
$849$			27531.6i			1.11293i
$850$	468.228	−	681.635i	0.0188942	−	0.0275058i
$851$	−29294.2			−1.18001
$852$	3607.16	+	9383.19i	0.145046	+	0.377304i
$853$	32873.9			1.31955			0.659777	−	0.751461i	$-0.270651\pi$
$853$	32873.9			1.31955			0.659777	+	0.751461i	$0.270651\pi$
$854$	−9745.11	−	6694.10i	−0.390481	−	0.268229i
$855$	22125.6	−	1716.56i	0.885004	−	0.0686611i
$856$	−46932.0	−	11230.8i	−1.87395	−	0.448435i
$857$		−	39474.6i		−	1.57343i	−0.617319	−	0.786713i	$-0.711781\pi$
$857$		−	39474.6i		−	1.57343i	0.617319	−	0.786713i	$-0.288219\pi$
$858$	3096.45	−	4507.74i	0.123207	−	0.179361i
$859$		−	26364.2i		−	1.04719i	−0.851968	−	0.523594i	$-0.824591\pi$
$859$		−	26364.2i		−	1.04719i	0.851968	−	0.523594i	$-0.175409\pi$
$860$	−41592.4	+	15989.3i	−1.64917	+	0.633989i
$861$	−22691.0			−0.898149
$862$	−4423.43	+	6439.52i	−0.174783	+	0.254444i
$863$	−12489.7			−0.492646			−0.246323	−	0.969188i	$-0.579222\pi$
$863$	−12489.7			−0.492646			−0.246323	+	0.969188i	$0.579222\pi$
$864$	−3502.74	−	26355.6i	−0.137923	−	1.03777i
$865$		−	62584.5i		−	2.46004i
$866$	−3152.13	−	2165.26i	−0.123688	−	0.0849636i
$867$	−17409.1			−0.681941
$868$	13750.1	−	5285.93i	0.537684	−	0.206701i
$869$		−	239.787i		−	0.00936042i
$870$	−9380.33	−	6443.52i	−0.365543	−	0.251099i
$871$			32119.8i			1.24953i
$872$	1721.17	−	7192.56i	0.0668420	−	0.279325i
$873$		−	17115.1i		−	0.663525i
$874$	−37078.3	−	21450.0i	−1.43500	−	0.830158i
$875$			29098.6i			1.12424i
$876$	−3499.11	−	9102.12i	−0.134959	−	0.351064i
$877$		−	28313.8i		−	1.09018i	−0.838377	−	0.545091i	$-0.816495\pi$
$877$		−	28313.8i		−	1.09018i	0.838377	−	0.545091i	$-0.183505\pi$
$878$	16102.0	−	23440.9i	0.618926	−	0.901018i
$879$		−	6981.42i		−	0.267892i
$880$	−7169.34	−	7946.63i	−0.274635	−	0.304410i
$881$	20614.3			0.788323			0.394161	−	0.919041i	$-0.371035\pi$
$881$	20614.3			0.788323			0.394161	+	0.919041i	$0.371035\pi$
$882$	−1581.90	+	2302.89i	−0.0603915	+	0.0879165i
$883$			36289.6i			1.38306i	0.722348	+	0.691529i	$0.243063\pi$
$883$			36289.6i			1.38306i	−0.722348	+	0.691529i	$0.756937\pi$
$884$	−601.967	+	231.413i	−0.0229031	+	0.00880460i
$885$	29281.3			1.11218
$886$	1724.63	+	1184.68i	0.0653951	+	0.0449211i
$887$	−8327.83			−0.315244			−0.157622	−	0.987500i	$-0.550383\pi$
$887$	−8327.83			−0.315244			−0.157622	+	0.987500i	$0.550383\pi$
$888$	2990.33	−	12496.2i	0.113006	−	0.472236i
$889$			5209.30i			0.196529i
$890$	−42298.0	−	29055.3i	−1.59307	−	1.09431i
$891$		−	1179.21i		−	0.0443379i
$892$	−2428.95	−	6318.35i	−0.0911742	−	0.237168i
$893$	1325.94	+	17090.6i	0.0496873	+	0.640442i
$894$	3786.11	−	5511.72i	0.141640	−	0.206196i
$895$	21929.6			0.819023
$896$	11486.2	+	21068.5i	0.428268	+	0.785544i
$897$	39248.3			1.46094
$898$	−3555.02	−	2442.01i	−0.132108	−	0.0907472i
$899$		−	6794.91i		−	0.252084i
$900$	9099.48	+	23670.2i	0.337018	+	0.876672i
$901$		−	725.298i		−	0.0268182i
$902$	−5573.36	+	8113.56i	−0.205735	+	0.299503i
$903$	17624.2			0.649496
$904$	4750.22	−	19850.6i	0.174768	−	0.730332i
$905$			21456.5i			0.788109i
$906$	1818.00	−	2646.60i	0.0666655	−	0.0970500i
$907$	23918.1			0.875619			0.437809	−	0.899068i	$-0.355755\pi$
$907$	23918.1			0.875619			0.437809	+	0.899068i	$0.355755\pi$
$908$	14260.6	+	37095.5i	0.521204	+	1.35579i
$909$	19770.1			0.721377
$910$	29826.7	−	43421.0i	1.08653	−	1.58175i
$911$	3413.00			0.124125			0.0620624	−	0.998072i	$-0.480232\pi$
$911$	3413.00			0.124125			0.0620624	+	0.998072i	$0.480232\pi$
$912$	12935.0	−	13627.1i	0.469650	−	0.494780i
$913$	12472.0			0.452097
$914$	−18697.8	+	27219.8i	−0.676662	+	0.985067i
$915$	−16599.4			−0.599735
$916$	−730.104	−	1899.19i	−0.0263355	−	0.0685056i
$917$	33296.8			1.19908
$918$	−313.167	+	455.901i	−0.0112593	+	0.0163910i
$919$			1739.29i			0.0624308i	0.999513	+	0.0312154i	$0.00993779\pi$
$919$			1739.29i			0.0624308i	−0.999513	+	0.0312154i	$0.990062\pi$
$920$	17876.1	−	74701.9i	0.640606	−	2.67701i
$921$	19616.6			0.701835
$922$	10892.0	−	15856.4i	0.389057	−	0.566379i
$923$			21464.0i			0.765434i
$924$	1518.95	+	3951.19i	0.0540798	+	0.140676i
$925$			35178.8i			1.25046i
$926$	29971.0	+	20587.7i	1.06362	+	0.730618i
$927$	22683.7			0.803700
$928$	10972.0	−	1458.22i	0.388118	−	0.0515822i
$929$	11322.2			0.399860			0.199930	−	0.979810i	$-0.435929\pi$
$929$	11322.2			0.399860			0.199930	+	0.979810i	$0.435929\pi$
$930$	11710.6	−	17048.1i	0.412911	−	0.601106i
$931$	−5650.39	+	438.373i	−0.198909	+	0.0154319i
$932$	−6923.00	−	18008.6i	−0.243316	−	0.632929i
$933$		−	8449.23i		−	0.296479i
$934$	11755.5	+	8075.07i	0.411832	+	0.282895i
$935$			222.650i			0.00778764i
$936$	4602.55	−	19233.5i	0.160725	−	0.671651i
$937$	−11388.0			−0.397045			−0.198522	−	0.980096i	$-0.563614\pi$
$937$	−11388.0			−0.397045			−0.198522	+	0.980096i	$0.563614\pi$
$938$	−20493.0	−	14077.1i	−0.713349	−	0.490013i
$939$	32680.0			1.13575
$940$	−28691.1	+	11029.7i	−0.995532	+	0.382711i
$941$			12400.7i			0.429596i	0.976658	+	0.214798i	$0.0689093\pi$
$941$			12400.7i			0.429596i	−0.976658	+	0.214798i	$0.931091\pi$
$942$	14902.8	−	21695.2i	0.515457	−	0.750390i
$943$	−70643.7			−2.43953
$944$	−21145.4	+	19077.1i	−0.729053	+	0.657741i
$945$		−	45178.7i		−	1.55520i
$946$	4328.85	−	6301.83i	0.148777	−	0.216586i
$947$		−	772.531i		−	0.0265089i	−0.999912	−	0.0132544i	$-0.995781\pi$
$947$		−	772.531i		−	0.0265089i	0.999912	−	0.0132544i	$-0.00421914\pi$
$948$	270.850	+	704.552i	0.00927931	+	0.0241379i
$949$		−	20821.0i		−	0.712202i
$950$	−25758.9	+	44526.6i	−0.879716	+	1.52067i
$951$			24893.0i			0.848801i
$952$	116.177	−	485.487i	0.00395515	−	0.0165281i
$953$		−	23999.4i		−	0.815756i	−0.913036	−	0.407878i	$-0.866269\pi$
$953$		−	23999.4i		−	0.815756i	0.913036	−	0.407878i	$-0.133731\pi$
$954$	18332.8	+	12593.2i	0.622167	+	0.427379i
$955$			56973.1i			1.93048i
$956$	−29588.7	+	11374.7i	−1.00101	+	0.384817i
$957$	1952.57			0.0659535
$958$	−20562.7	−	14124.9i	−0.693476	−	0.476362i
$959$			5527.18i			0.186113i
$960$	30041.3	+	15251.0i	1.00998	+	0.512735i
$961$	−17441.7			−0.585470
$962$	15533.6	−	22613.4i	0.520607	−	0.757886i
$963$	−30784.8			−1.03014
$964$	−11582.8	+	4452.77i	−0.386989	+	0.148770i
$965$		−	18309.4i		−	0.610779i
$966$	−17201.3	+	25041.2i	−0.572921	+	0.834044i
$967$		−	22253.4i		−	0.740043i	−0.929023	−	0.370021i	$-0.879350\pi$
$967$		−	22253.4i		−	0.740043i	0.929023	−	0.370021i	$-0.120650\pi$
$968$	−27504.2	−	6581.73i	−0.913243	−	0.218538i
$969$	−389.692	+	30.2334i	−0.0129192	+	0.00100231i
$970$	51314.2	+	35248.7i	1.69856	+	1.16677i
$971$	53216.5			1.75881			0.879403	−	0.476079i	$-0.157942\pi$
$971$	53216.5			1.75881			0.879403	+	0.476079i	$0.157942\pi$
$972$	−10051.9	−	26147.6i	−0.331702	−	0.862844i
$973$	−9730.02			−0.320586
$974$	27057.1	−	39389.0i	0.890107	−	1.29580i
$975$		−	47132.6i		−	1.54815i
$976$	11987.2	−	10814.7i	0.393136	−	0.354682i
$977$			17416.5i			0.570320i	0.958480	+	0.285160i	$0.0920467\pi$
$977$			17416.5i			0.570320i	−0.958480	+	0.285160i	$0.907953\pi$
$978$	4433.96	+	3045.77i	0.144972	+	0.0995838i
$979$	8804.57			0.287431
$980$	−3646.56	−	9485.68i	−0.118862	−	0.309193i
$981$		−	4717.92i		−	0.153549i
$982$	11326.6	+	7780.44i	0.368071	+	0.252835i
$983$	−23665.3			−0.767859			−0.383929	−	0.923362i	$-0.625429\pi$
$983$	−23665.3			−0.767859			−0.383929	+	0.923362i	$0.625429\pi$
$984$	7211.26	−	30135.0i	0.233625	−	0.976288i
$985$	−44516.2			−1.44001
$986$	−189.795	−	130.374i	−0.00613011	−	0.00421089i
$987$	12157.4			0.392072
$988$	36219.4	−	17248.2i	1.16629	−	0.555403i
$989$	54869.2			1.76414
$990$	−5627.77	−	3865.82i	−0.180669	−	0.124105i
$991$	−21696.9			−0.695484			−0.347742	−	0.937590i	$-0.613051\pi$
$991$	−21696.9			−0.695484			−0.347742	+	0.937590i	$0.613051\pi$
$992$	2650.20	+	19940.8i	0.0848226	+	0.638228i
$993$	−16742.1			−0.535041
$994$	−13694.4	−	9406.96i	−0.436982	−	0.300172i
$995$		−	31197.4i		−	0.993993i
$996$	−36645.9	+	14087.7i	−1.16583	+	0.448179i
$997$	−1748.49			−0.0555419			−0.0277709	−	0.999614i	$-0.508841\pi$
$997$	−1748.49			−0.0555419			−0.0277709	+	0.999614i	$0.508841\pi$
$998$	−16960.8	−	11650.7i	−0.537960	−	0.369535i
$999$		−	23528.8i		−	0.745164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.4.d.a.75.19	yes	28
4.3	odd	2	inner	76.4.d.a.75.9	✓	28
19.18	odd	2	inner	76.4.d.a.75.10	yes	28
76.75	even	2	inner	76.4.d.a.75.20	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.4.d.a.75.9	✓	28	4.3	odd	2	inner
76.4.d.a.75.10	yes	28	19.18	odd	2	inner
76.4.d.a.75.19	yes	28	1.1	even	1	trivial
76.4.d.a.75.20	yes	28	76.75	even	2	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	76.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.60147 - 2.33137i) q^{2} +3.54475 q^{3} +(-2.87062 - 7.46723i) q^{4} +18.5634 q^{5} +(5.67679 - 8.26413i) q^{6} +16.5701i q^{7} +(-22.0061 - 5.26604i) q^{8} -14.4348 q^{9} +O(q^{10})\)	\(q+(1.60147 - 2.33137i) q^{2} +3.54475 q^{3} +(-2.87062 - 7.46723i) q^{4} +18.5634 q^{5} +(5.67679 - 8.26413i) q^{6} +16.5701i q^{7} +(-22.0061 - 5.26604i) q^{8} -14.4348 q^{9} +(29.7286 - 43.2782i) q^{10} +9.00860i q^{11} +(-10.1756 - 26.4694i) q^{12} -60.5487i q^{13} +(38.6312 + 26.5365i) q^{14} +65.8025 q^{15} +(-47.5191 + 42.8711i) q^{16} +1.33140 q^{17} +(-23.1168 + 33.6529i) q^{18} +(-82.5710 + 6.40608i) q^{19} +(-53.2884 - 138.617i) q^{20} +58.7369i q^{21} +(21.0024 + 14.4270i) q^{22} +182.865i q^{23} +(-78.0061 - 18.6668i) q^{24} +219.600 q^{25} +(-141.162 - 96.9666i) q^{26} -146.876 q^{27} +(123.733 - 47.5665i) q^{28} -61.1453i q^{29} +(105.380 - 153.410i) q^{30} +111.127 q^{31} +(23.8483 + 179.442i) q^{32} +31.9332i q^{33} +(2.13219 - 3.10399i) q^{34} +307.598i q^{35} +(41.4367 + 107.788i) q^{36} +160.195i q^{37} +(-117.300 + 202.763i) q^{38} -214.630i q^{39} +(-408.508 - 97.7555i) q^{40} +386.315i q^{41} +(136.938 + 94.0652i) q^{42} -300.052i q^{43} +(67.2693 - 25.8602i) q^{44} -267.958 q^{45} +(426.328 + 292.853i) q^{46} -206.981i q^{47} +(-168.443 + 151.967i) q^{48} +68.4308 q^{49} +(351.681 - 511.969i) q^{50} +4.71947 q^{51} +(-452.131 + 173.812i) q^{52} -544.763i q^{53} +(-235.216 + 342.422i) q^{54} +167.230i q^{55} +(87.2589 - 364.644i) q^{56} +(-292.693 + 22.7079i) q^{57} +(-142.553 - 97.9222i) q^{58} +444.988 q^{59} +(-188.894 - 491.363i) q^{60} -252.260 q^{61} +(177.967 - 259.079i) q^{62} -239.186i q^{63} +(456.538 + 231.770i) q^{64} -1123.99i q^{65} +(74.4482 + 51.1399i) q^{66} -530.479 q^{67} +(-3.82194 - 9.94187i) q^{68} +648.211i q^{69} +(717.126 + 492.607i) q^{70} -354.491 q^{71} +(317.653 + 76.0140i) q^{72} +343.873 q^{73} +(373.476 + 256.547i) q^{74} +778.425 q^{75} +(284.865 + 598.187i) q^{76} -149.274 q^{77} +(-500.382 - 343.722i) q^{78} -26.6175 q^{79} +(-882.116 + 795.833i) q^{80} -130.898 q^{81} +(900.646 + 618.671i) q^{82} -1384.46i q^{83} +(438.602 - 168.611i) q^{84} +24.7153 q^{85} +(-699.535 - 480.524i) q^{86} -216.745i q^{87} +(47.4396 - 198.244i) q^{88} -977.352i q^{89} +(-429.126 + 624.711i) q^{90} +1003.30 q^{91} +(1365.50 - 524.936i) q^{92} +393.918 q^{93} +(-482.550 - 331.473i) q^{94} +(-1532.80 + 118.919i) q^{95} +(84.5364 + 636.075i) q^{96} +1185.68i q^{97} +(109.590 - 159.538i) q^{98} -130.037i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 10 q^{4} - 4 q^{5} - 6 q^{6} + 192 q^{9}+O(q^{10}) \) 28 * q + 10 * q^4 - 4 * q^5 - 6 * q^6 + 192 * q^9	\( 28 q + 10 q^{4} - 4 q^{5} - 6 q^{6} + 192 q^{9} - 134 q^{16} - 80 q^{17} - 300 q^{20} - 26 q^{24} + 496 q^{25} - 90 q^{26} + 254 q^{28} - 16 q^{30} - 556 q^{36} - 626 q^{38} - 850 q^{42} + 976 q^{44} - 612 q^{45} + 188 q^{49} + 354 q^{54} - 580 q^{57} + 2534 q^{58} - 948 q^{61} - 1068 q^{62} - 1634 q^{64} + 1244 q^{66} + 1630 q^{68} - 184 q^{73} + 2276 q^{74} + 1688 q^{76} + 308 q^{77} + 3376 q^{80} - 2284 q^{81} - 740 q^{82} + 684 q^{85} + 1810 q^{92} + 824 q^{93} - 5222 q^{96}+O(q^{100}) \) 28 * q + 10 * q^4 - 4 * q^5 - 6 * q^6 + 192 * q^9 - 134 * q^16 - 80 * q^17 - 300 * q^20 - 26 * q^24 + 496 * q^25 - 90 * q^26 + 254 * q^28 - 16 * q^30 - 556 * q^36 - 626 * q^38 - 850 * q^42 + 976 * q^44 - 612 * q^45 + 188 * q^49 + 354 * q^54 - 580 * q^57 + 2534 * q^58 - 948 * q^61 - 1068 * q^62 - 1634 * q^64 + 1244 * q^66 + 1630 * q^68 - 184 * q^73 + 2276 * q^74 + 1688 * q^76 + 308 * q^77 + 3376 * q^80 - 2284 * q^81 - 740 * q^82 + 684 * q^85 + 1810 * q^92 + 824 * q^93 - 5222 * q^96

Introduction

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