LMFDB - Embedded newform 152.4.b.b.75.48

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,4,Mod(75,152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("152.75");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	152.b (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:	$8.96829032087$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.48
Character	$\chi$	$=$	152.75
Dual form			152.4.b.b.75.47

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.57123 + 1.17846i) q^{2} +5.03936i q^{3} +(5.22247 + 6.06019i) q^{4} +5.72550i q^{5} +(-5.93868 + 12.9574i) q^{6} -3.30417i q^{7} +(6.28649 + 21.7366i) q^{8} +1.60489 q^{9} +O(q^{10})$	\(q+(2.57123 + 1.17846i) q^{2} +5.03936i q^{3} +(5.22247 + 6.06019i) q^{4} +5.72550i q^{5} +(-5.93868 + 12.9574i) q^{6} -3.30417i q^{7} +(6.28649 + 21.7366i) q^{8} +1.60489 q^{9} +(-6.74727 + 14.7216i) q^{10} +18.7882 q^{11} +(-30.5394 + 26.3179i) q^{12} -57.2347 q^{13} +(3.89383 - 8.49579i) q^{14} -28.8528 q^{15} +(-9.45168 + 63.2982i) q^{16} +27.5535 q^{17} +(4.12654 + 1.89129i) q^{18} +(-77.7299 + 28.5842i) q^{19} +(-34.6976 + 29.9012i) q^{20} +16.6509 q^{21} +(48.3087 + 22.1411i) q^{22} -188.477i q^{23} +(-109.539 + 31.6799i) q^{24} +92.2187 q^{25} +(-147.164 - 67.4488i) q^{26} +144.150i q^{27} +(20.0239 - 17.2559i) q^{28} +116.587 q^{29} +(-74.1873 - 34.0019i) q^{30} +20.6754 q^{31} +(-98.8969 + 151.616i) q^{32} +94.6802i q^{33} +(70.8464 + 32.4707i) q^{34} +18.9180 q^{35} +(8.38147 + 9.72591i) q^{36} +96.9185 q^{37} +(-233.547 - 18.1049i) q^{38} -288.426i q^{39} +(-124.453 + 35.9933i) q^{40} +186.285i q^{41} +(42.8133 + 19.6224i) q^{42} +240.906 q^{43} +(98.1205 + 113.860i) q^{44} +9.18878i q^{45} +(222.113 - 484.619i) q^{46} -205.244i q^{47} +(-318.982 - 47.6304i) q^{48} +332.082 q^{49} +(237.116 + 108.676i) q^{50} +138.852i q^{51} +(-298.906 - 346.853i) q^{52} +386.068 q^{53} +(-169.875 + 370.644i) q^{54} +107.572i q^{55} +(71.8214 - 20.7716i) q^{56} +(-144.046 - 391.709i) q^{57} +(299.772 + 137.393i) q^{58} +23.1750i q^{59} +(-150.683 - 174.853i) q^{60} -25.9773i q^{61} +(53.1612 + 24.3651i) q^{62} -5.30282i q^{63} +(-432.960 + 273.294i) q^{64} -327.697i q^{65} +(-111.577 + 243.445i) q^{66} -604.479i q^{67} +(143.897 + 166.979i) q^{68} +949.804 q^{69} +(48.6426 + 22.2941i) q^{70} -828.153 q^{71} +(10.0891 + 34.8848i) q^{72} +824.991 q^{73} +(249.200 + 114.215i) q^{74} +464.723i q^{75} +(-579.168 - 321.777i) q^{76} -62.0793i q^{77} +(339.898 - 741.610i) q^{78} -678.227 q^{79} +(-362.414 - 54.1156i) q^{80} -683.092 q^{81} +(-219.530 + 478.983i) q^{82} +156.548 q^{83} +(86.9587 + 100.907i) q^{84} +157.757i q^{85} +(619.425 + 283.898i) q^{86} +587.522i q^{87} +(118.112 + 408.391i) q^{88} -372.489i q^{89} +(-10.8286 + 23.6265i) q^{90} +189.113i q^{91} +(1142.21 - 984.316i) q^{92} +104.191i q^{93} +(241.872 - 527.731i) q^{94} +(-163.659 - 445.043i) q^{95} +(-764.047 - 498.377i) q^{96} -1456.91i q^{97} +(853.861 + 391.346i) q^{98} +30.1529 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{4} - 14 q^{6} - 528 q^{9}+O(q^{10}) $ 56 * q + 2 * q^4 - 14 * q^6 - 528 * q^9	$ 56 q + 2 q^{4} - 14 q^{6} - 528 q^{9} - 40 q^{11} - 262 q^{16} - 184 q^{17} - 84 q^{19} - 12 q^{20} + 238 q^{24} - 1504 q^{25} + 378 q^{26} - 382 q^{28} + 512 q^{30} + 40 q^{35} + 1464 q^{36} + 958 q^{38} + 1030 q^{42} + 576 q^{43} + 316 q^{44} - 3664 q^{49} - 1314 q^{54} - 648 q^{57} - 1166 q^{58} + 928 q^{62} + 3746 q^{64} + 680 q^{66} + 2538 q^{68} - 432 q^{73} - 4020 q^{74} + 3968 q^{76} + 4608 q^{80} + 2296 q^{81} - 192 q^{82} + 5376 q^{83} - 1906 q^{92} - 1962 q^{96} - 6152 q^{99}+O(q^{100}) $ 56 * q + 2 * q^4 - 14 * q^6 - 528 * q^9 - 40 * q^11 - 262 * q^16 - 184 * q^17 - 84 * q^19 - 12 * q^20 + 238 * q^24 - 1504 * q^25 + 378 * q^26 - 382 * q^28 + 512 * q^30 + 40 * q^35 + 1464 * q^36 + 958 * q^38 + 1030 * q^42 + 576 * q^43 + 316 * q^44 - 3664 * q^49 - 1314 * q^54 - 648 * q^57 - 1166 * q^58 + 928 * q^62 + 3746 * q^64 + 680 * q^66 + 2538 * q^68 - 432 * q^73 - 4020 * q^74 + 3968 * q^76 + 4608 * q^80 + 2296 * q^81 - 192 * q^82 + 5376 * q^83 - 1906 * q^92 - 1962 * q^96 - 6152 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	2.57123	+	1.17846i	0.909068	+	0.416648i
$2$	2.57123	+	1.17846i	0.909068	+	0.416648i
$3$			5.03936i			0.969825i	0.874563	+	0.484912i	$0.161148\pi$
$3$			5.03936i			0.969825i	−0.874563	+	0.484912i	$0.838852\pi$
$4$	5.22247	+	6.06019i	0.652808	+	0.757523i
$5$			5.72550i			0.512104i	0.966663	+	0.256052i	$0.0824219\pi$
$5$			5.72550i			0.512104i	−0.966663	+	0.256052i	$0.917578\pi$
$6$	−5.93868	+	12.9574i	−0.404076	+	0.881636i
$7$		−	3.30417i		−	0.178408i	−0.996013	−	0.0892042i	$-0.971568\pi$
$7$		−	3.30417i		−	0.178408i	0.996013	−	0.0892042i	$-0.0284324\pi$
$8$	6.28649	+	21.7366i	0.277826	+	0.960631i
$9$	1.60489			0.0594402
$10$	−6.74727	+	14.7216i	−0.213367	+	0.465537i
$11$	18.7882			0.514986			0.257493	−	0.966280i	$-0.417104\pi$
$11$	18.7882			0.514986			0.257493	+	0.966280i	$0.417104\pi$
$12$	−30.5394	+	26.3179i	−0.734665	+	0.633110i
$13$	−57.2347			−1.22108			−0.610540	−	0.791985i	$-0.709048\pi$
$13$	−57.2347			−1.22108			−0.610540	+	0.791985i	$0.709048\pi$
$14$	3.89383	−	8.49579i	0.0743336	−	0.162185i
$15$	−28.8528			−0.496651
$16$	−9.45168	+	63.2982i	−0.147683	+	0.989035i
$17$	27.5535			0.393100			0.196550	−	0.980494i	$-0.437026\pi$
$17$	27.5535			0.393100			0.196550	+	0.980494i	$0.437026\pi$
$18$	4.12654	+	1.89129i	0.0540352	+	0.0247657i
$19$	−77.7299	+	28.5842i	−0.938551	+	0.345141i
$19$	−77.7299	+	28.5842i	−0.938551	+	0.345141i
$20$	−34.6976	+	29.9012i	−0.387931	+	0.334306i
$21$	16.6509			0.173025
$22$	48.3087	+	22.1411i	0.468157	+	0.214568i
$23$		−	188.477i		−	1.70871i	−0.519694	−	0.854353i	$-0.673954\pi$
$23$		−	188.477i		−	1.70871i	0.519694	−	0.854353i	$-0.326046\pi$
$24$	−109.539	+	31.6799i	−0.931644	+	0.269443i
$25$	92.2187			0.737749
$26$	−147.164	−	67.4488i	−1.11005	−	0.508761i
$27$			144.150i			1.02747i
$28$	20.0239	−	17.2559i	0.135148	−	0.116466i
$29$	116.587			0.746539			0.373269	−	0.927723i	$-0.378237\pi$
$29$	116.587			0.746539			0.373269	+	0.927723i	$0.378237\pi$
$30$	−74.1873	−	34.0019i	−0.451490	−	0.206929i
$31$	20.6754			0.119787			0.0598937	−	0.998205i	$-0.480924\pi$
$31$	20.6754			0.119787			0.0598937	+	0.998205i	$0.480924\pi$
$32$	−98.8969	+	151.616i	−0.546333	+	0.837568i
$33$			94.6802i			0.499446i
$34$	70.8464	+	32.4707i	0.357355	+	0.163784i
$35$	18.9180			0.0913637
$36$	8.38147	+	9.72591i	0.0388031	+	0.0450274i
$37$	96.9185			0.430630			0.215315	−	0.976545i	$-0.430922\pi$
$37$	96.9185			0.430630			0.215315	+	0.976545i	$0.430922\pi$
$38$	−233.547	−	18.1049i	−0.997009	−	0.0772893i
$39$		−	288.426i		−	1.18423i
$40$	−124.453	+	35.9933i	−0.491943	+	0.142276i
$41$			186.285i			0.709582i	0.934946	+	0.354791i	$0.115448\pi$
$41$			186.285i			0.709582i	−0.934946	+	0.354791i	$0.884552\pi$
$42$	42.8133	+	19.6224i	0.157291	+	0.0720905i
$43$	240.906			0.854368			0.427184	−	0.904165i	$-0.359506\pi$
$43$	240.906			0.854368			0.427184	+	0.904165i	$0.359506\pi$
$44$	98.1205	+	113.860i	0.336187	+	0.390114i
$45$			9.18878i			0.0304396i
$46$	222.113	−	484.619i	0.711929	−	1.55333i
$47$		−	205.244i		−	0.636978i	−0.947927	−	0.318489i	$-0.896825\pi$
$47$		−	205.244i		−	0.636978i	0.947927	−	0.318489i	$-0.103175\pi$
$48$	−318.982	−	47.6304i	−0.959190	−	0.143226i
$49$	332.082			0.968170
$50$	237.116	+	108.676i	0.670664	+	0.307382i
$51$			138.852i			0.381238i
$52$	−298.906	−	346.853i	−0.797132	−	0.924997i
$53$	386.068			1.00057			0.500287	−	0.865859i	$-0.333228\pi$
$53$	386.068			1.00057			0.500287	+	0.865859i	$0.333228\pi$
$54$	−169.875	+	370.644i	−0.428094	+	0.934041i
$55$			107.572i			0.263726i
$56$	71.8214	−	20.7716i	0.171385	−	0.0495665i
$57$	−144.046	−	391.709i	−0.334726	−	0.910230i
$58$	299.772	+	137.393i	0.678654	+	0.311044i
$59$			23.1750i			0.0511378i	0.999673	+	0.0255689i	$0.00813972\pi$
$59$			23.1750i			0.0511378i	−0.999673	+	0.0255689i	$0.991860\pi$
$60$	−150.683	−	174.853i	−0.324218	−	0.376225i
$61$		−	25.9773i		−	0.0545255i	−0.999628	−	0.0272627i	$-0.991321\pi$
$61$		−	25.9773i		−	0.0545255i	0.999628	−	0.0272627i	$-0.00867907\pi$
$62$	53.1612	+	24.3651i	0.108895	+	0.0499092i
$63$		−	5.30282i		−	0.0106046i
$64$	−432.960	+	273.294i	−0.845625	+	0.533777i
$65$		−	327.697i		−	0.625320i
$66$	−111.577	+	243.445i	−0.208093	+	0.454030i
$67$		−	604.479i		−	1.10222i	−0.834432	−	0.551111i	$-0.814204\pi$
$67$		−	604.479i		−	1.10222i	0.834432	−	0.551111i	$-0.185796\pi$
$68$	143.897	+	166.979i	0.256619	+	0.297782i
$69$	949.804			1.65714
$70$	48.6426	+	22.2941i	0.0830558	+	0.0380665i
$71$	−828.153			−1.38428			−0.692139	−	0.721765i	$-0.743331\pi$
$71$	−828.153			−1.38428			−0.692139	+	0.721765i	$0.743331\pi$
$72$	10.0891	+	34.8848i	0.0165141	+	0.0571002i
$73$	824.991			1.32271			0.661356	−	0.750073i	$-0.269981\pi$
$73$	824.991			1.32271			0.661356	+	0.750073i	$0.269981\pi$
$74$	249.200	+	114.215i	0.391472	+	0.179421i
$75$			464.723i			0.715487i
$76$	−579.168	−	321.777i	−0.874146	−	0.485663i
$77$		−	62.0793i		−	0.0918778i
$78$	339.898	−	741.610i	0.493409	−	1.07655i
$79$	−678.227			−0.965905			−0.482953	−	0.875647i	$-0.660436\pi$
$79$	−678.227			−0.965905			−0.482953	+	0.875647i	$0.660436\pi$
$80$	−362.414	−	54.1156i	−0.506489	−	0.0756289i
$81$	−683.092			−0.937027
$82$	−219.530	+	478.983i	−0.295646	+	0.645058i
$83$	156.548			0.207029			0.103514	−	0.994628i	$-0.466991\pi$
$83$	156.548			0.207029			0.103514	+	0.994628i	$0.466991\pi$
$84$	86.9587	+	100.907i	0.112952	+	0.131070i
$85$			157.757i			0.201308i
$86$	619.425	+	283.898i	0.776678	+	0.355971i
$87$			587.522i			0.724012i
$88$	118.112	+	408.391i	0.143077	+	0.494711i
$89$		−	372.489i		−	0.443637i	−0.975088	−	0.221819i	$-0.928801\pi$
$89$		−	372.489i		−	0.443637i	0.975088	−	0.221819i	$-0.0711993\pi$
$90$	−10.8286	+	23.6265i	−0.0126826	+	0.0276717i
$91$			189.113i			0.217851i
$92$	1142.21	−	984.316i	1.29438	−	1.11546i
$93$			104.191i			0.116173i
$94$	241.872	−	527.731i	0.265396	−	0.579056i
$95$	−163.659	−	445.043i	−0.176748	−	0.480636i
$96$	−764.047	−	498.377i	−0.812294	−	0.529847i
$97$		−	1456.91i		−	1.52502i	−0.646974	−	0.762512i	$-0.723966\pi$
$97$		−	1456.91i		−	1.52502i	0.646974	−	0.762512i	$-0.276034\pi$
$98$	853.861	+	391.346i	0.880133	+	0.403387i
$99$	30.1529			0.0306109
$100$	481.609	+	558.862i	0.481609	+	0.558862i
$101$		−	743.632i		−	0.732615i	−0.930494	−	0.366308i	$-0.880622\pi$
$101$		−	743.632i		−	0.732615i	0.930494	−	0.366308i	$-0.119378\pi$
$102$	−163.631	+	357.020i	−0.158842	+	0.346571i
$103$	−681.912			−0.652338			−0.326169	−	0.945311i	$-0.605758\pi$
$103$	−681.912			−0.652338			−0.326169	+	0.945311i	$0.605758\pi$
$104$	−359.805	−	1244.09i	−0.339248	−	1.17301i
$105$			95.3346i			0.0886067i
$106$	992.669	+	454.965i	0.909590	+	0.416888i
$107$			1011.28i			0.913684i	0.889548	+	0.456842i	$0.151020\pi$
$107$			1011.28i			0.913684i	−0.889548	+	0.456842i	$0.848980\pi$
$108$	−873.577	+	752.820i	−0.778333	+	0.670742i
$109$	818.210			0.718994			0.359497	−	0.933146i	$-0.382948\pi$
$109$	818.210			0.718994			0.359497	+	0.933146i	$0.382948\pi$
$110$	−126.769	+	276.591i	−0.109881	+	0.239745i
$111$			488.407i			0.417636i
$112$	209.148	+	31.2300i	0.176452	+	0.0263478i
$113$			223.680i			0.186213i	0.995656	+	0.0931064i	$0.0296797\pi$
$113$			223.680i			0.186213i	−0.995656	+	0.0931064i	$0.970320\pi$
$114$	91.2368	−	1176.93i	0.0749571	−	0.966924i
$115$	1079.13			0.875035
$116$	608.871	+	706.538i	0.487347	+	0.565520i
$117$	−91.8552			−0.0725813
$118$	−27.3108	+	59.5883i	−0.0213065	+	0.0464877i
$119$		−	91.0414i		−	0.0701323i
$120$	−181.383	−	627.163i	−0.137983	−	0.477099i
$121$	−978.005			−0.734790
$122$	30.6132	−	66.7937i	0.0227179	−	0.0495673i
$123$	−938.758			−0.688170
$124$	107.977	+	125.297i	0.0781982	+	0.0907417i
$125$			1243.69i			0.889909i
$126$	6.24916	−	13.6348i	0.00441841	−	0.00964034i
$127$	−706.530			−0.493657			−0.246828	−	0.969059i	$-0.579388\pi$
$127$	−706.530			−0.493657			−0.246828	+	0.969059i	$0.579388\pi$
$128$	−1435.31	+	192.476i	−0.991128	+	0.132911i
$129$			1214.01i			0.828587i
$130$	386.178	−	842.585i	0.260539	−	0.568459i
$131$	−2375.61			−1.58441			−0.792207	−	0.610253i	$-0.791068\pi$
$131$	−2375.61			−1.58441			−0.792207	+	0.610253i	$0.791068\pi$
$132$	−573.780	+	494.464i	−0.378342	+	0.326042i
$133$	94.4472	+	256.833i	0.0615760	+	0.167445i
$134$	712.354	−	1554.26i	0.459239	−	1.00199i
$135$	−825.332			−0.526172
$136$	173.215	+	598.919i	0.109214	+	0.377624i
$137$	−1067.76			−0.665878			−0.332939	−	0.942948i	$-0.608040\pi$
$137$	−1067.76			−0.665878			−0.332939	+	0.942948i	$0.608040\pi$
$138$	2442.17	+	1119.31i	1.50646	+	0.690446i
$139$	−2150.99			−1.31255			−0.656276	−	0.754521i	$-0.727869\pi$
$139$	−2150.99			−1.31255			−0.656276	+	0.754521i	$0.727869\pi$
$140$	98.7987	+	114.647i	0.0596430	+	0.0692101i
$141$	1034.30			0.617757
$142$	−2129.37	−	975.945i	−1.25840	−	0.576757i
$143$	−1075.33			−0.628839
$144$	−15.1689	+	101.586i	−0.00877829	+	0.0587885i
$145$			667.518i			0.382306i
$146$	2121.24	+	972.219i	1.20243	+	0.551105i
$147$			1673.48i			0.938956i
$148$	506.154	+	587.344i	0.281119	+	0.326212i
$149$			484.443i			0.266356i	0.991092	+	0.133178i	$0.0425183\pi$
$149$			484.443i			0.266356i	−0.991092	+	0.133178i	$0.957482\pi$
$150$	−547.657	+	1194.91i	−0.298107	+	0.650427i
$151$	2021.09			1.08923			0.544616	−	0.838686i	$-0.316676\pi$
$151$	2021.09			1.08923			0.544616	+	0.838686i	$0.316676\pi$
$152$	−1109.97	−	1509.89i	−0.592307	−	0.805712i
$153$	44.2202			0.0233660
$154$	73.1579	−	159.620i	0.0382807	−	0.0835231i
$155$			118.377i			0.0613436i
$156$	1747.92	−	1506.30i	0.897085	−	0.773078i
$157$			3373.68i			1.71496i	0.514516	+	0.857481i	$0.327972\pi$
$157$			3373.68i			1.71496i	−0.514516	+	0.857481i	$0.672028\pi$
$158$	−1743.88	−	799.263i	−0.878073	−	0.402443i
$159$			1945.53i			0.970382i
$160$	−868.077	−	566.234i	−0.428922	−	0.279779i
$161$	−622.761			−0.304847
$162$	−1756.39	−	804.997i	−0.851821	−	0.390411i
$163$	1488.88			0.715450			0.357725	−	0.933827i	$-0.383553\pi$
$163$	1488.88			0.715450			0.357725	+	0.933827i	$0.383553\pi$
$164$	−1128.92	+	972.869i	−0.537525	+	0.463221i
$165$	−542.092			−0.255768
$166$	402.522	+	184.486i	0.188203	+	0.0862583i
$167$	−12.3994			−0.00574548			−0.00287274	−	0.999996i	$-0.500914\pi$
$167$	−12.3994			−0.00574548			−0.00287274	+	0.999996i	$0.500914\pi$
$168$	104.676	+	361.934i	0.0480708	+	0.166213i
$169$	1078.81			0.491038
$170$	−185.911	+	405.631i	−0.0838747	+	0.183003i
$171$	−124.748	+	45.8745i	−0.0557877	+	0.0205153i
$172$	1258.12	+	1459.93i	0.557738	+	0.647203i
$173$	−273.183			−0.120056			−0.0600280	−	0.998197i	$-0.519119\pi$
$173$	−273.183			−0.120056			−0.0600280	+	0.998197i	$0.519119\pi$
$174$	−692.371	+	1510.66i	−0.301658	+	0.658176i
$175$		−	304.706i		−	0.131621i
$176$	−177.580	+	1189.26i	−0.0760544	+	0.509339i
$177$	−116.787			−0.0495947
$178$	438.963	−	957.755i	0.184841	−	0.403296i
$179$		−	3358.87i		−	1.40253i	−0.712899	−	0.701267i	$-0.752618\pi$
$179$		−	3358.87i		−	1.40253i	0.712899	−	0.701267i	$-0.247382\pi$
$180$	−55.6857	+	47.9881i	−0.0230587	+	0.0198712i
$181$	−2753.17			−1.13062			−0.565308	−	0.824880i	$-0.691243\pi$
$181$	−2753.17			−1.13062			−0.565308	+	0.824880i	$0.691243\pi$
$182$	−222.862	+	486.254i	−0.0907673	+	0.198041i
$183$	130.909			0.0528801
$184$	4096.86	−	1184.86i	1.64144	−	0.474723i
$185$			554.907i			0.220527i
$186$	−122.784	+	267.898i	−0.0484032	+	0.105609i
$187$	517.679			0.202441
$188$	1243.82	−	1071.88i	0.482525	−	0.415824i
$189$	476.297			0.183309
$190$	103.659	−	1337.17i	0.0395802	−	0.510572i
$191$		−	1742.05i		−	0.659950i	−0.943990	−	0.329975i	$-0.892960\pi$
$191$		−	1742.05i		−	0.659950i	0.943990	−	0.329975i	$-0.107040\pi$
$192$	−1377.23	−	2181.84i	−0.517670	−	0.820108i
$193$		−	1861.80i		−	0.694379i	−0.937795	−	0.347189i	$-0.887136\pi$
$193$		−	1861.80i		−	0.694379i	0.937795	−	0.347189i	$-0.112864\pi$
$194$	1716.92	−	3746.07i	0.635399	−	1.38635i
$195$	1651.38			0.606451
$196$	1734.29	+	2012.48i	0.632030	+	0.733412i
$197$			3038.48i			1.09890i	0.835528	+	0.549448i	$0.185162\pi$
$197$			3038.48i			1.09890i	−0.835528	+	0.549448i	$0.814838\pi$
$198$	77.5300	+	35.5339i	0.0278274	+	0.0127540i
$199$		−	3019.80i		−	1.07572i	−0.843035	−	0.537859i	$-0.819233\pi$
$199$		−	3019.80i		−	1.07572i	0.843035	−	0.537859i	$-0.180767\pi$
$200$	579.732	+	2004.52i	0.204966	+	0.708705i
$201$	3046.19			1.06896
$202$	876.340	−	1912.05i	0.305243	−	0.665997i
$203$		−	385.223i		−	0.133189i
$204$	−841.468	+	725.149i	−0.288797	+	0.248875i
$205$	−1066.58			−0.363380
$206$	−1753.35	−	803.606i	−0.593019	−	0.271796i
$207$		−	302.485i		−	0.101566i
$208$	540.964	−	3622.85i	0.180332	−	1.20769i
$209$	−1460.40	+	537.045i	−0.483340	+	0.177743i
$210$	−112.348	+	245.127i	−0.0369179	+	0.0805495i
$211$		−	5180.94i		−	1.69038i	−0.534463	−	0.845192i	$-0.679486\pi$
$211$		−	5180.94i		−	1.69038i	0.534463	−	0.845192i	$-0.320514\pi$
$212$	2016.22	+	2339.64i	0.653183	+	0.757958i
$213$		−	4173.36i		−	1.34251i
$214$	−1191.75	+	2600.24i	−0.380685	+	0.830601i
$215$			1379.31i			0.437525i
$216$	−3133.34	+	906.199i	−0.987021	+	0.285458i
$217$		−	68.3150i		−	0.0213711i
$218$	2103.81	+	964.228i	0.653614	+	0.299568i
$219$			4157.42i			1.28280i
$220$	−651.904	+	561.789i	−0.199779	+	0.172163i
$221$	−1577.02			−0.480007
$222$	−575.568	+	1255.81i	−0.174007	+	0.379659i
$223$	6049.57			1.81663			0.908317	−	0.418283i	$-0.137368\pi$
$223$	6049.57			1.81663			0.908317	+	0.418283i	$0.137368\pi$
$224$	500.965	+	326.772i	0.149429	+	0.0974704i
$225$	148.001			0.0438520
$226$	−263.598	+	575.133i	−0.0775853	+	0.169280i
$227$		−	3412.80i		−	0.997867i	−0.866640	−	0.498933i	$-0.833725\pi$
$227$		−	3412.80i		−	0.997867i	0.866640	−	0.498933i	$-0.166275\pi$
$228$	1621.55	−	2918.63i	0.471008	−	0.847768i
$229$		−	5741.64i		−	1.65685i	−0.560101	−	0.828424i	$-0.689238\pi$
$229$		−	5741.64i		−	1.65685i	0.560101	−	0.828424i	$-0.310762\pi$
$230$	2774.68	+	1271.71i	0.795466	+	0.364582i
$231$	312.840			0.0891053
$232$	732.922	+	2534.20i	0.207408	+	0.717149i
$233$	2255.67			0.634223			0.317112	−	0.948388i	$-0.397287\pi$
$233$	2255.67			0.634223			0.317112	+	0.948388i	$0.397287\pi$
$234$	−236.181	−	108.248i	−0.0659814	−	0.0302409i
$235$	1175.13			0.326199
$236$	−140.445	+	121.031i	−0.0387381	+	0.0333832i
$237$		−	3417.83i		−	0.936759i
$238$	107.289	−	234.088i	0.0292205	−	0.0637551i
$239$			1011.60i			0.273785i	0.990586	+	0.136893i	$0.0437115\pi$
$239$			1011.60i			0.273785i	−0.990586	+	0.136893i	$0.956288\pi$
$240$	272.708	−	1826.33i	0.0733467	−	0.491205i
$241$		−	4313.46i		−	1.15292i	−0.817125	−	0.576461i	$-0.804433\pi$
$241$		−	4313.46i		−	1.15292i	0.817125	−	0.576461i	$-0.195567\pi$
$242$	−2514.68	−	1152.54i	−0.667974	−	0.306149i
$243$			449.710i			0.118720i
$244$	157.427	−	135.666i	0.0413043	−	0.0355947i
$245$			1901.34i			0.495804i
$246$	−2413.76	−	1106.29i	−0.625593	−	0.286725i
$247$	4448.85	−	1636.01i	1.14605	−	0.421445i
$248$	129.976	+	449.413i	0.0332801	+	0.115072i
$249$			788.903i			0.200782i
$250$	−1465.63	+	3197.80i	−0.370779	+	0.808987i
$251$	−1821.03			−0.457938			−0.228969	−	0.973434i	$-0.573535\pi$
$251$	−1821.03			−0.457938			−0.228969	+	0.973434i	$0.573535\pi$
$252$	32.1361	−	27.6938i	0.00803326	−	0.00692280i
$253$		−	3541.14i		−	0.879959i
$254$	−1816.65	−	832.617i	−0.448767	−	0.205681i
$255$	−794.996			−0.195234
$256$	−3917.33	−	1196.55i	−0.956380	−	0.292126i
$257$			3365.51i			0.816867i	0.912788	+	0.408434i	$0.133925\pi$
$257$			3365.51i			0.816867i	−0.912788	+	0.408434i	$0.866075\pi$
$258$	−1430.66	+	3121.50i	−0.345229	+	0.753242i
$259$		−	320.235i		−	0.0768280i
$260$	1985.91	−	1711.39i	0.473695	−	0.408214i
$261$	187.109			0.0443745
$262$	−6108.25	−	2799.56i	−1.44034	−	0.660143i
$263$			1894.24i			0.444122i	0.975033	+	0.222061i	$0.0712784\pi$
$263$			1894.24i			0.444122i	−0.975033	+	0.222061i	$0.928722\pi$
$264$	−2058.03	+	595.206i	−0.479783	+	0.138759i
$265$			2210.43i			0.512398i
$266$	−59.8215	+	771.679i	−0.0137891	+	0.177875i
$267$	1877.10			0.430250
$268$	3663.26	−	3156.87i	0.834959	−	0.719540i
$269$	−5932.53			−1.34466			−0.672329	−	0.740253i	$-0.734706\pi$
$269$	−5932.53			−1.34466			−0.672329	+	0.740253i	$0.734706\pi$
$270$	−2122.12	−	972.620i	−0.478326	−	0.219229i
$271$			1212.08i			0.271693i	0.990730	+	0.135847i	$0.0433754\pi$
$271$			1212.08i			0.271693i	−0.990730	+	0.135847i	$0.956625\pi$
$272$	−260.427	+	1744.09i	−0.0580540	+	0.388790i
$273$	−953.009			−0.211277
$274$	−2745.47	−	1258.32i	−0.605328	−	0.277437i
$275$	1732.62			0.379930
$276$	4960.32	+	5755.99i	1.08180	+	1.25533i
$277$			1324.62i			0.287325i	0.989627	+	0.143662i	$0.0458879\pi$
$277$			1324.62i			0.287325i	−0.989627	+	0.143662i	$0.954112\pi$
$278$	−5530.70	−	2534.86i	−1.19320	−	0.546873i
$279$	33.1817			0.00712019
$280$	118.928	+	411.214i	0.0253832	+	0.0877668i
$281$			2675.75i			0.568050i	0.958817	+	0.284025i	$0.0916699\pi$
$281$			2675.75i			0.568050i	−0.958817	+	0.284025i	$0.908330\pi$
$282$	2659.42	+	1218.88i	0.561583	+	0.257387i
$283$	2733.04			0.574073			0.287036	−	0.957920i	$-0.407330\pi$
$283$	2733.04			0.574073			0.287036	+	0.957920i	$0.407330\pi$
$284$	−4325.00	−	5018.76i	−0.903668	−	1.04862i
$285$	2242.73	−	824.736i	0.466132	−	0.171415i
$286$	−2764.93	−	1267.24i	−0.571657	−	0.262005i
$287$	615.518			0.126595
$288$	−158.718	+	243.326i	−0.0324742	+	0.0497852i
$289$	−4153.81			−0.845472
$290$	−786.642	+	1716.34i	−0.159287	+	0.347542i
$291$	7341.91			1.47901
$292$	4308.49	+	4999.60i	0.863477	+	1.00198i
$293$	2897.56			0.577737			0.288869	−	0.957369i	$-0.406721\pi$
$293$	2897.56			0.577737			0.288869	+	0.957369i	$0.406721\pi$
$294$	−1972.13	+	4302.91i	−0.391214	+	0.853574i
$295$	−132.689			−0.0261879
$296$	609.278	+	2106.68i	0.119640	+	0.413677i
$297$			2708.32i			0.529133i
$298$	−570.896	+	1245.61i	−0.110977	+	0.242136i
$299$			10787.4i			2.08647i
$300$	−2816.31	+	2427.00i	−0.541998	+	0.467076i
$301$		−	795.994i		−	0.152426i
$302$	5196.69	+	2381.77i	0.990185	+	0.453826i
$303$	3747.43			0.710508
$304$	−1074.65	−	5190.34i	−0.202749	−	0.979231i
$305$	148.733			0.0279227
$306$	113.700	+	52.1117i	0.0212412	+	0.00973539i
$307$			578.868i			0.107615i	0.998551	+	0.0538074i	$0.0171357\pi$
$307$			578.868i			0.107615i	−0.998551	+	0.0538074i	$0.982864\pi$
$308$	376.212	−	324.207i	0.0695995	−	0.0599786i
$309$		−	3436.40i		−	0.632653i
$310$	−139.502	+	304.375i	−0.0255587	+	0.0557655i
$311$			8292.12i			1.51191i	0.654625	+	0.755954i	$0.272826\pi$
$311$			8292.12i			1.51191i	−0.654625	+	0.755954i	$0.727174\pi$
$312$	6269.40	−	1813.19i	1.13761	−	0.329011i
$313$	8713.54			1.57354			0.786771	−	0.617245i	$-0.211751\pi$
$313$	8713.54			1.57354			0.786771	+	0.617245i	$0.211751\pi$
$314$	−3975.75	+	8674.52i	−0.714536	+	1.55902i
$315$	30.3613			0.00543068
$316$	−3542.02	−	4110.18i	−0.630551	−	0.731696i
$317$	−4416.74			−0.782551			−0.391275	−	0.920274i	$-0.627966\pi$
$317$	−4416.74			−0.782551			−0.391275	+	0.920274i	$0.627966\pi$
$318$	−2292.73	+	5002.41i	−0.404308	+	0.882143i
$319$	2190.45			0.384457
$320$	−1564.74	−	2478.91i	−0.273350	−	0.433048i
$321$	−5096.21			−0.886113
$322$	−1601.26	−	733.898i	−0.277127	−	0.127014i
$323$	−2141.73	+	787.595i	−0.368944	+	0.135675i
$324$	−3567.43	−	4139.67i	−0.611699	−	0.709819i
$325$	−5278.11			−0.900851
$326$	3828.26	+	1754.59i	0.650393	+	0.298091i
$327$			4123.25i			0.697298i
$328$	−4049.21	+	1171.08i	−0.681647	+	0.197141i
$329$	−678.162			−0.113642
$330$	−1393.84	−	638.833i	−0.232511	−	0.106565i
$331$		−	4318.95i		−	0.717194i	−0.933493	−	0.358597i	$-0.883255\pi$
$331$		−	4318.95i		−	0.717194i	0.933493	−	0.358597i	$-0.116745\pi$
$332$	817.568	+	948.712i	0.135150	+	0.156829i
$333$	155.543			0.0255968
$334$	−31.8817	−	14.6122i	−0.00522303	−	0.00239384i
$335$	3460.95			0.564453
$336$	−157.379	+	1053.97i	−0.0255528	+	0.171128i
$337$			9523.11i			1.53934i	0.638443	+	0.769669i	$0.279579\pi$
$337$			9523.11i			1.53934i	−0.638443	+	0.769669i	$0.720421\pi$
$338$	2773.87	+	1271.33i	0.446387	+	0.204590i
$339$	−1127.20			−0.180594
$340$	−956.039	+	823.883i	−0.152496	+	0.131416i
$341$	388.453			0.0616888
$342$	−374.817	−	29.0562i	−0.0592624	−	0.00459410i
$343$		−	2230.59i		−	0.351138i
$344$	1514.45	+	5236.48i	0.237366	+	0.820732i
$345$			5438.10i			0.848631i
$346$	−702.416	−	321.935i	−0.109139	−	0.0500211i
$347$	−8490.08			−1.31346			−0.656731	−	0.754125i	$-0.728061\pi$
$347$	−8490.08			−1.31346			−0.656731	+	0.754125i	$0.728061\pi$
$348$	−3560.49	+	3068.32i	−0.548456	+	0.472641i
$349$		−	11160.9i		−	1.71184i	−0.517110	−	0.855919i	$-0.672992\pi$
$349$		−	11160.9i		−	1.71184i	0.517110	−	0.855919i	$-0.327008\pi$
$350$	359.084	−	783.470i	0.0548395	−	0.119652i
$351$		−	8250.39i		−	1.25463i
$352$	−1858.09	+	2848.59i	−0.281354	+	0.431336i
$353$	−6494.13			−0.979172			−0.489586	−	0.871955i	$-0.662852\pi$
$353$	−6494.13			−0.979172			−0.489586	+	0.871955i	$0.662852\pi$
$354$	−300.287	−	137.629i	−0.0450849	−	0.0206636i
$355$		−	4741.59i		−	0.708894i
$356$	2257.35	−	1945.31i	0.336066	−	0.289610i
$357$	458.790			0.0680161
$358$	3958.29	−	8636.42i	0.584363	−	1.27500i
$359$		−	2262.40i		−	0.332604i	−0.986075	−	0.166302i	$-0.946817\pi$
$359$		−	2262.40i		−	0.332604i	0.986075	−	0.166302i	$-0.0531827\pi$
$360$	−199.733	+	57.7652i	−0.0292412	+	0.00845692i
$361$	5224.88	−	4443.70i	0.761756	−	0.647864i
$362$	−7079.04	−	3244.50i	−1.02781	−	0.471069i
$363$		−	4928.52i		−	0.712617i
$364$	−1146.06	+	987.637i	−0.165027	+	0.142215i
$365$			4723.49i			0.677366i
$366$	336.597	+	154.271i	0.0480716	+	0.0220324i
$367$			2224.41i			0.316385i	0.987408	+	0.158192i	$0.0505666\pi$
$367$			2224.41i			0.316385i	−0.987408	+	0.158192i	$0.949433\pi$
$368$	11930.3	+	1781.43i	1.68997	+	0.252346i
$369$			298.967i			0.0421777i
$370$	−653.935	+	1426.79i	−0.0918824	+	0.200474i
$371$		−	1275.63i		−	0.178511i
$372$	−631.415	+	544.132i	−0.0880036	+	0.0758386i
$373$	−63.6398			−0.00883417			−0.00441708	−	0.999990i	$-0.501406\pi$
$373$	−63.6398			−0.00883417			−0.00441708	+	0.999990i	$0.501406\pi$
$374$	1331.07	+	610.064i	0.184033	+	0.0843467i
$375$	−6267.37			−0.863055
$376$	4461.31	−	1290.27i	0.611901	−	0.176969i
$377$	−6672.81			−0.911584
$378$	1224.67	+	561.296i	0.166641	+	0.0763756i
$379$			3252.80i			0.440858i	0.975403	+	0.220429i	$0.0707458\pi$
$379$			3252.80i			0.440858i	−0.975403	+	0.220429i	$0.929254\pi$
$380$	1842.34	−	3316.02i	0.248710	−	0.447654i
$381$		−	3560.46i		−	0.478760i
$382$	2052.94	−	4479.22i	0.274967	−	0.599939i
$383$	−4404.95			−0.587682			−0.293841	−	0.955854i	$-0.594934\pi$
$383$	−4404.95			−0.587682			−0.293841	+	0.955854i	$0.594934\pi$
$384$	−969.956	−	7233.02i	−0.128901	−	0.961220i
$385$	355.435			0.0470510
$386$	2194.05	−	4787.11i	0.289312	−	0.631237i
$387$	386.627			0.0507838
$388$	8829.17	−	7608.69i	1.15524	−	0.995548i
$389$			10114.5i			1.31831i	0.752006	+	0.659156i	$0.229086\pi$
$389$			10114.5i			1.31831i	−0.752006	+	0.659156i	$0.770914\pi$
$390$	4246.09	+	1946.09i	0.551305	+	0.252677i
$391$		−	5193.20i		−	0.671692i
$392$	2087.63	+	7218.35i	0.268983	+	0.930055i
$393$		−	11971.6i		−	1.53660i
$394$	−3580.72	+	7812.63i	−0.457853	+	0.998971i
$395$		−	3883.19i		−	0.494644i
$396$	157.472	+	182.732i	0.0199830	+	0.0231884i
$397$			15279.7i			1.93165i	0.259186	+	0.965827i	$0.416546\pi$
$397$			15279.7i			1.93165i	−0.259186	+	0.965827i	$0.583454\pi$
$398$	3558.71	−	7764.60i	0.448196	−	0.977900i
$399$	−1294.27	+	475.953i	−0.162393	+	0.0597179i
$400$	−871.622	+	5837.28i	−0.108953	+	0.729660i
$401$		−	14208.1i		−	1.76937i	−0.466190	−	0.884684i	$-0.654374\pi$
$401$		−	14208.1i		−	1.76937i	0.466190	−	0.884684i	$-0.345626\pi$
$402$	7832.45	+	3589.81i	0.971759	+	0.445381i
$403$	−1183.35			−0.146270
$404$	4506.55	−	3883.59i	0.554973	−	0.478257i
$405$		−	3911.04i		−	0.479855i
$406$	453.969	−	990.497i	0.0554929	−	0.121078i
$407$	1820.92			0.221768
$408$	−3018.17	+	872.891i	−0.366229	+	0.105918i
$409$			11209.6i			1.35520i	0.735430	+	0.677601i	$0.236980\pi$
$409$			11209.6i			1.35520i	−0.735430	+	0.677601i	$0.763020\pi$
$410$	−2742.41	−	1256.92i	−0.330337	−	0.151402i
$411$		−	5380.85i		−	0.645785i
$412$	−3561.26	−	4132.51i	−0.425852	−	0.494161i
$413$	76.5742			0.00912341
$414$	356.466	−	777.758i	0.0423172	−	0.0923302i
$415$			896.317i			0.106020i
$416$	5660.33	−	8677.70i	0.667117	−	1.02274i
$417$		−	10839.6i		−	1.27295i
$418$	−4387.92	−	340.157i	−0.513445	−	0.0398029i
$419$	−4914.82			−0.573042			−0.286521	−	0.958074i	$-0.592499\pi$
$419$	−4914.82			−0.573042			−0.286521	+	0.958074i	$0.592499\pi$
$420$	−577.746	+	497.882i	−0.0671217	+	0.0578432i
$421$	−6104.34			−0.706668			−0.353334	−	0.935497i	$-0.614952\pi$
$421$	−6104.34			−0.706668			−0.353334	+	0.935497i	$0.614952\pi$
$422$	6105.53	−	13321.4i	0.704295	−	1.53667i
$423$		−	329.394i		−	0.0378621i
$424$	2427.01	+	8391.80i	0.277986	+	0.961183i
$425$	2540.95			0.290009
$426$	4918.13	−	10730.7i	0.559353	−	1.22043i
$427$	−85.8334			−0.00972780
$428$	−6128.55	+	5281.38i	−0.692137	+	0.596461i
$429$		−	5418.99i		−	0.609864i
$430$	−1625.46	+	3546.52i	−0.182294	+	0.397740i
$431$	−11052.2			−1.23519			−0.617595	−	0.786497i	$-0.711893\pi$
$431$	−11052.2			−1.23519			−0.617595	+	0.786497i	$0.711893\pi$
$432$	−9124.45	−	1362.46i	−1.01620	−	0.151740i
$433$			4407.06i			0.489122i	0.969634	+	0.244561i	$0.0786438\pi$
$433$			4407.06i			0.489122i	−0.969634	+	0.244561i	$0.921356\pi$
$434$	80.5065	−	175.654i	0.00890423	−	0.0194278i
$435$	−3363.86			−0.370769
$436$	4273.08	+	4958.51i	0.469365	+	0.544655i
$437$	5387.48	+	14650.3i	0.589744	+	1.60371i
$438$	−4899.36	+	10689.7i	−0.534476	+	1.16615i
$439$	14788.9			1.60782			0.803911	−	0.594750i	$-0.202749\pi$
$439$	14788.9			1.60782			0.803911	+	0.594750i	$0.202749\pi$
$440$	−2338.24	+	676.248i	−0.253344	+	0.0732701i
$441$	532.955			0.0575483
$442$	−4054.87	−	1858.45i	−0.436359	−	0.199994i
$443$	13668.3			1.46592			0.732958	−	0.680274i	$-0.238139\pi$
$443$	13668.3			1.46592			0.732958	+	0.680274i	$0.238139\pi$
$444$	−2959.84	+	2550.69i	−0.316369	+	0.272636i
$445$	2132.68			0.227189
$446$	15554.9	+	7129.18i	1.65144	+	0.756897i
$447$	−2441.28			−0.258319
$448$	903.010	+	1430.57i	0.0952303	+	0.150867i
$449$		−	4433.66i		−	0.466007i	−0.972476	−	0.233003i	$-0.925145\pi$
$449$		−	4433.66i		−	0.466007i	0.972476	−	0.233003i	$-0.0748554\pi$
$450$	380.544	+	174.413i	0.0398644	+	0.0182709i
$451$			3499.96i			0.365425i
$452$	−1355.54	+	1168.16i	−0.141061	+	0.121561i
$453$			10185.0i			1.05636i
$454$	4021.85	−	8775.11i	0.415760	−	0.907129i
$455$	−1082.77			−0.111562
$456$	7608.87	−	5593.55i	0.781400	−	0.574434i
$457$	8045.08			0.823486			0.411743	−	0.911300i	$-0.364920\pi$
$457$	8045.08			0.823486			0.411743	+	0.911300i	$0.364920\pi$
$458$	6766.29	−	14763.1i	0.690323	−	1.50619i
$459$			3971.84i			0.403899i
$460$	5635.70	+	6539.70i	0.571230	+	0.662859i
$461$			11671.8i			1.17919i	0.807698	+	0.589596i	$0.200713\pi$
$461$			11671.8i			1.17919i	−0.807698	+	0.589596i	$0.799287\pi$
$462$	804.383	+	368.669i	0.0810028	+	0.0371256i
$463$			6795.37i			0.682090i	0.940047	+	0.341045i	$0.110781\pi$
$463$			6795.37i			0.682090i	−0.940047	+	0.341045i	$0.889219\pi$
$464$	−1101.94	+	7379.74i	−0.110251	+	0.738353i
$465$	−596.544			−0.0594926
$466$	5799.86	+	2658.22i	0.576552	+	0.264248i
$467$	−7486.56			−0.741834			−0.370917	−	0.928666i	$-0.620957\pi$
$467$	−7486.56			−0.741834			−0.370917	+	0.928666i	$0.620957\pi$
$468$	−479.711	−	556.660i	−0.0473817	−	0.0549820i
$469$	−1997.30			−0.196646
$470$	3021.52	+	1384.84i	0.296537	+	0.135910i
$471$	−17001.2			−1.66321
$472$	−503.746	+	145.690i	−0.0491246	+	0.0142074i
$473$	4526.18			0.439987
$474$	4027.77	−	8788.03i	0.390299	−	0.851577i
$475$	−7168.15	+	2636.00i	−0.692415	+	0.254627i
$476$	551.728	−	475.461i	0.0531269	−	0.0457830i
$477$	619.595			0.0594744
$478$	−1192.12	+	2601.05i	−0.114072	+	0.248889i
$479$			15766.9i			1.50398i	0.659175	+	0.751990i	$0.270906\pi$
$479$			15766.9i			1.50398i	−0.659175	+	0.751990i	$0.729094\pi$
$480$	2853.45	−	4374.55i	0.271337	−	0.415979i
$481$	−5547.10			−0.525834
$482$	5083.24	−	11090.9i	0.480363	−	1.04808i
$483$		−	3138.31i		−	0.295648i
$484$	−5107.60	−	5926.89i	−0.479677	−	0.556620i
$485$	8341.56			0.780971
$486$	−529.965	+	1156.31i	−0.0494644	+	0.107924i
$487$	5904.44			0.549396			0.274698	−	0.961531i	$-0.411422\pi$
$487$	5904.44			0.549396			0.274698	+	0.961531i	$0.411422\pi$
$488$	564.659	−	163.306i	0.0523789	−	0.0151486i
$489$			7503.01i			0.693861i
$490$	−2240.65	+	4888.78i	−0.206576	+	0.450720i
$491$	−15452.6			−1.42029			−0.710147	−	0.704053i	$-0.751372\pi$
$491$	−15452.6			−1.42029			−0.710147	+	0.704053i	$0.751372\pi$
$492$	−4902.63	−	5689.05i	−0.449243	−	0.521305i
$493$	3212.37			0.293464
$494$	13367.0	+	1036.23i	1.21743	+	0.0943765i
$495$			172.640i			0.0156760i
$496$	−195.417	+	1308.72i	−0.0176905	+	0.118474i
$497$			2736.36i			0.246967i
$498$	−929.690	+	2028.45i	−0.0836554	+	0.182524i
$499$	600.472			0.0538694			0.0269347	−	0.999637i	$-0.491425\pi$
$499$	600.472			0.0538694			0.0269347	+	0.999637i	$0.491425\pi$
$500$	−7536.96	+	6495.10i	−0.674126	+	0.580940i
$501$		−	62.4850i		−	0.00557210i
$502$	−4682.29	−	2146.01i	−0.416297	−	0.190799i
$503$		−	11018.5i		−	0.976725i	−0.872641	−	0.488362i	$-0.837594\pi$
$503$		−	11018.5i		−	0.976725i	0.872641	−	0.488362i	$-0.162406\pi$
$504$	115.265	−	33.3361i	0.0101871	−	0.00294625i
$505$	4257.66			0.375175
$506$	4173.09	−	9105.09i	0.366633	−	0.799942i
$507$			5436.51i			0.476221i
$508$	−3689.83	−	4281.70i	−0.322263	−	0.373956i
$509$	19114.7			1.66452			0.832262	−	0.554382i	$-0.187045\pi$
$509$	19114.7			1.66452			0.832262	+	0.554382i	$0.187045\pi$
$510$	−2044.12	−	936.870i	−0.177481	−	0.0813438i
$511$		−	2725.91i		−	0.235983i
$512$	−8662.28	−	7693.02i	−0.747700	−	0.664037i
$513$	−4120.42	−	11204.8i	−0.354622	−	0.964334i
$514$	−3966.12	+	8653.51i	−0.340346	+	0.742588i
$515$		−	3904.29i		−	0.334065i
$516$	−7357.13	+	6340.13i	−0.627674	+	0.540908i
$517$		−	3856.16i		−	0.328034i
$518$	377.384	−	823.399i	0.0320103	−	0.0698419i
$519$		−	1376.66i		−	0.116433i
$520$	7123.02	−	2060.07i	0.600702	−	0.173730i
$521$		−	19202.9i		−	1.61477i	−0.590028	−	0.807383i	$-0.700883\pi$
$521$		−	19202.9i		−	1.61477i	0.590028	−	0.807383i	$-0.299117\pi$
$522$	481.100	+	220.500i	0.0403394	+	0.0184885i
$523$			6024.44i			0.503691i	0.967767	+	0.251846i	$0.0810375\pi$
$523$			6024.44i			0.503691i	−0.967767	+	0.251846i	$0.918962\pi$
$524$	−12406.6	−	14396.6i	−1.03432	−	1.20023i
$525$	1535.52			0.127649
$526$	−2232.29	+	4870.54i	−0.185043	+	0.403737i
$527$	569.679			0.0470884
$528$	−5993.09	−	894.888i	−0.493969	−	0.0737594i
$529$	−23356.7			−1.91967
$530$	−2604.90	+	5683.53i	−0.213490	+	0.465805i
$531$			37.1933i			0.00303964i
$532$	−1063.21	+	1913.67i	−0.0866464	+	0.155955i
$533$		−	10662.0i		−	0.866457i
$534$	4826.47	+	2212.09i	0.391127	+	0.179263i
$535$	−5790.09			−0.467902
$536$	13139.3	−	3800.05i	1.05883	−	0.306226i
$537$	16926.5			1.36021
$538$	−15253.9	−	6991.25i	−1.22238	−	0.560249i
$539$	6239.22			0.498594
$540$	−4310.27	−	5001.66i	−0.343490	−	0.398588i
$541$		−	1031.76i		−	0.0819938i	−0.999159	−	0.0409969i	$-0.986947\pi$
$541$		−	1031.76i		−	0.0819938i	0.999159	−	0.0409969i	$-0.0130534\pi$
$542$	−1428.39	+	3116.55i	−0.113201	+	0.246987i
$543$		−	13874.2i		−	1.09650i
$544$	−2724.95	+	4177.55i	−0.214764	+	0.329248i
$545$			4684.66i			0.368200i
$546$	−2450.41	−	1123.08i	−0.192065	−	0.0880283i
$547$			15015.5i			1.17371i	0.809693	+	0.586853i	$0.199633\pi$
$547$			15015.5i			1.17371i	−0.809693	+	0.586853i	$0.800367\pi$
$548$	−5576.37	−	6470.85i	−0.434691	−	0.504418i
$549$		−	41.6906i		−	0.00324101i
$550$	4454.97	+	2041.82i	0.345382	+	0.158297i
$551$	−9062.28	+	3332.55i	−0.700665	+	0.257661i
$552$	5970.93	+	20645.5i	0.460398	+	1.59190i
$553$			2240.98i			0.172326i
$554$	−1561.02	+	3405.91i	−0.119713	+	0.261198i
$555$	−2796.37			−0.213873
$556$	−11233.5	−	13035.4i	−0.856845	−	0.994289i
$557$		−	12817.8i		−	0.975062i	−0.873106	−	0.487531i	$-0.837898\pi$
$557$		−	12817.8i		−	0.975062i	0.873106	−	0.487531i	$-0.162102\pi$
$558$	85.3177	+	39.1032i	0.00647274	+	0.00296662i
$559$	−13788.2			−1.04325
$560$	−178.807	+	1197.48i	−0.0134928	+	0.0903619i
$561$			2608.77i			0.196332i
$562$	−3153.27	+	6879.98i	−0.236677	+	0.516396i
$563$			8471.22i			0.634137i	0.948403	+	0.317069i	$0.102699\pi$
$563$			8471.22i			0.634137i	−0.948403	+	0.317069i	$0.897301\pi$
$564$	5401.59	+	6268.04i	0.403277	+	0.467965i
$565$	−1280.68			−0.0953604
$566$	7027.29	+	3220.78i	0.521871	+	0.239186i
$567$			2257.05i			0.167173i
$568$	−5206.18	−	18001.2i	−0.384588	−	1.32978i
$569$			6730.08i			0.495852i	0.968779	+	0.247926i	$0.0797489\pi$
$569$			6730.08i			0.495852i	−0.968779	+	0.247926i	$0.920251\pi$
$570$	6738.49	+	522.376i	0.495166	+	0.0383858i
$571$	20384.8			1.49400			0.747001	−	0.664822i	$-0.231493\pi$
$571$	20384.8			1.49400			0.747001	+	0.664822i	$0.231493\pi$
$572$	−5615.90	−	6516.73i	−0.410511	−	0.476360i
$573$	8778.82			0.640036
$574$	1582.64	+	725.363i	0.115084	+	0.0527458i
$575$		−	17381.1i		−	1.26060i
$576$	−694.852	+	438.606i	−0.0502642	+	0.0317278i
$577$	−8621.00			−0.622005			−0.311002	−	0.950409i	$-0.600665\pi$
$577$	−8621.00			−0.622005			−0.311002	+	0.950409i	$0.600665\pi$
$578$	−10680.4	−	4895.09i	−0.768592	−	0.352265i
$579$	9382.26			0.673425
$580$	−4045.28	+	3486.09i	−0.289605	+	0.249572i
$581$		−	517.262i		−	0.0369357i
$582$	18877.8	+	8652.15i	1.34452	+	0.616225i
$583$	7253.50			0.515282
$584$	5186.30	+	17932.5i	0.367484	+	1.27064i
$585$		−	525.917i		−	0.0371692i
$586$	7450.29	+	3414.65i	0.525203	+	0.240713i
$587$	−9852.46			−0.692768			−0.346384	−	0.938093i	$-0.612591\pi$
$587$	−9852.46			−0.692768			−0.346384	+	0.938093i	$0.612591\pi$
$588$	−10141.6	+	8739.70i	−0.711281	+	0.612958i
$589$	−1607.10	+	590.990i	−0.112427	+	0.0413435i
$590$	−341.173	−	156.368i	−0.0238066	−	0.0109111i
$591$	−15312.0			−1.06574
$592$	−916.044	+	6134.77i	−0.0635966	+	0.425908i
$593$	−15120.2			−1.04707			−0.523536	−	0.852004i	$-0.675387\pi$
$593$	−15120.2			−1.04707			−0.523536	+	0.852004i	$0.675387\pi$
$594$	−3191.64	+	6963.71i	−0.220462	+	0.481018i
$595$	521.257			0.0359151
$596$	−2935.81	+	2529.99i	−0.201771	+	0.173880i
$597$	15217.8			1.04326
$598$	−12712.6	+	27737.0i	−0.869323	+	1.89674i
$599$	−22742.6			−1.55131			−0.775657	−	0.631155i	$-0.782581\pi$
$599$	−22742.6			−1.55131			−0.775657	+	0.631155i	$0.782581\pi$
$600$	−10101.5	+	2921.47i	−0.687320	+	0.198781i
$601$			24084.6i			1.63466i	0.576169	+	0.817331i	$0.304547\pi$
$601$			24084.6i			1.63466i	−0.576169	+	0.817331i	$0.695453\pi$
$602$	938.047	−	2046.69i	0.0635082	−	0.138566i
$603$		−	970.121i		−	0.0655164i
$604$	10555.1	+	12248.2i	0.711059	+	0.825118i
$605$		−	5599.57i		−	0.376289i
$606$	9635.50	+	4416.19i	0.645900	+	0.296032i
$607$	12023.0			0.803954			0.401977	−	0.915650i	$-0.368323\pi$
$607$	12023.0			0.803954			0.401977	+	0.915650i	$0.368323\pi$
$608$	3353.42	−	14612.0i	0.223683	−	0.974662i
$609$	1941.27			0.129170
$610$	382.427	+	175.276i	0.0253836	+	0.0116340i
$611$			11747.1i			0.777801i
$612$	230.939	+	267.983i	0.0152535	+	0.0177003i
$613$		−	10246.4i		−	0.675117i	−0.941304	−	0.337559i	$-0.890399\pi$
$613$		−	10246.4i		−	0.675117i	0.941304	−	0.337559i	$-0.109601\pi$
$614$	−682.173	+	1488.40i	−0.0448375	+	0.0978292i
$615$		−	5374.86i		−	0.352415i
$616$	1349.39	−	390.261i	0.0882607	−	0.0255261i
$617$	21866.3			1.42675			0.713374	−	0.700783i	$-0.247166\pi$
$617$	21866.3			1.42675			0.713374	+	0.700783i	$0.247166\pi$
$618$	4049.66	−	8835.78i	0.263594	−	0.575125i
$619$	12728.3			0.826482			0.413241	−	0.910622i	$-0.364397\pi$
$619$	12728.3			0.826482			0.413241	+	0.910622i	$0.364397\pi$
$620$	−717.386	+	618.220i	−0.0464692	+	0.0400456i
$621$	27169.0			1.75565
$622$	−9771.93	+	21321.0i	−0.629934	+	1.37443i
$623$	−1230.77			−0.0791486
$624$	18256.9	+	2726.11i	1.17125	+	0.174891i
$625$	4406.62			0.282023
$626$	22404.5	+	10268.6i	1.43046	+	0.655613i
$627$	−2706.36	−	7359.49i	−0.172379	−	0.468755i
$628$	−20445.1	+	17618.9i	−1.29912	+	1.11954i
$629$	2670.44			0.169281
$630$	78.0659	+	35.7795i	0.00493686	+	0.00226268i
$631$			30417.2i			1.91900i	0.281704	+	0.959501i	$0.409100\pi$
$631$			30417.2i			1.91900i	−0.281704	+	0.959501i	$0.590900\pi$
$632$	−4263.67	−	14742.4i	−0.268354	−	0.927879i
$633$	26108.6			1.63938
$634$	−11356.5	−	5204.94i	−0.711392	−	0.326048i
$635$		−	4045.24i		−	0.252804i
$636$	−11790.3	+	10160.5i	−0.735087	+	0.633473i
$637$	−19006.6			−1.18221
$638$	5632.16	+	2581.36i	0.349497	+	0.160183i
$639$	−1329.09			−0.0822818
$640$	−1102.02	−	8217.85i	−0.0680644	−	0.507561i
$641$		−	21789.6i		−	1.34265i	−0.741165	−	0.671323i	$-0.765727\pi$
$641$		−	21789.6i		−	1.34265i	0.741165	−	0.671323i	$-0.234273\pi$
$642$	−13103.5	−	6005.67i	−0.805537	−	0.369198i
$643$	5470.19			0.335495			0.167747	−	0.985830i	$-0.446351\pi$
$643$	5470.19			0.335495			0.167747	+	0.985830i	$0.446351\pi$
$644$	−3252.35	−	3774.05i	−0.199007	−	0.230929i
$645$	−6950.82			−0.424323
$646$	−6435.03	−	498.852i	−0.391924	−	0.0303824i
$647$			3431.69i			0.208522i	0.994550	+	0.104261i	$0.0332477\pi$
$647$			3431.69i			0.208522i	−0.994550	+	0.104261i	$0.966752\pi$
$648$	−4294.25	−	14848.1i	−0.260331	−	0.900137i
$649$			435.416i			0.0263352i
$650$	−13571.2	−	6220.04i	−0.818935	−	0.375338i
$651$	344.264			0.0207262
$652$	7775.64	+	9022.91i	0.467052	+	0.541970i
$653$		−	24252.9i		−	1.45343i	−0.686939	−	0.726715i	$-0.741046\pi$
$653$		−	24252.9i		−	1.45343i	0.686939	−	0.726715i	$-0.258954\pi$
$654$	−4859.09	+	10601.8i	−0.290528	+	0.633891i
$655$		−	13601.6i		−	0.811385i
$656$	−11791.5	−	1760.71i	−0.701802	−	0.104793i
$657$	1324.02			0.0786223
$658$	−1743.71	−	799.186i	−0.103308	−	0.0473488i
$659$			21052.9i			1.24447i	0.782832	+	0.622233i	$0.213775\pi$
$659$			21052.9i			1.24447i	−0.782832	+	0.622233i	$0.786225\pi$
$660$	−2831.05	−	3285.17i	−0.166968	−	0.193750i
$661$	−9819.28			−0.577800			−0.288900	−	0.957359i	$-0.593290\pi$
$661$	−9819.28			−0.577800			−0.288900	+	0.957359i	$0.593290\pi$
$662$	5089.71	−	11105.0i	0.298818	−	0.651978i
$663$		−	7947.14i		−	0.465522i
$664$	984.139	+	3402.83i	0.0575181	+	0.198879i
$665$	−1470.50	+	540.757i	−0.0857495	+	0.0315333i
$666$	399.938	+	183.301i	0.0232692	+	0.0106648i
$667$		−	21974.0i		−	1.27561i
$668$	−64.7554	−	75.1427i	−0.00375069	−	0.00435233i
$669$			30485.9i			1.76182i
$670$	8898.89	+	4078.58i	0.513126	+	0.235178i
$671$		−	488.066i		−	0.0280798i
$672$	−1646.72	+	2524.54i	−0.0945292	+	0.144920i
$673$		−	1913.83i		−	0.109618i	−0.998497	−	0.0548088i	$-0.982545\pi$
$673$		−	1913.83i		−	0.109618i	0.998497	−	0.0548088i	$-0.0174549\pi$
$674$	−11222.6	+	24486.1i	−0.641363	+	1.39936i
$675$			13293.3i			0.758016i
$676$	5634.05	+	6537.79i	0.320554	+	0.371973i
$677$	−11272.2			−0.639918			−0.319959	−	0.947431i	$-0.603669\pi$
$677$	−11272.2			−0.639918			−0.319959	+	0.947431i	$0.603669\pi$
$678$	−2898.30	−	1328.36i	−0.164172	−	0.0752441i
$679$	−4813.89			−0.272077
$680$	−3429.11	+	991.740i	−0.193383	+	0.0559287i
$681$	17198.3			0.967756
$682$	998.802	+	457.776i	0.0560793	+	0.0257025i
$683$		−	30566.3i		−	1.71243i	−0.516622	−	0.856214i	$-0.672811\pi$
$683$		−	30566.3i		−	1.71243i	0.516622	−	0.856214i	$-0.327189\pi$
$684$	−929.499	−	516.416i	−0.0519595	−	0.0288679i
$685$		−	6113.49i		−	0.340999i
$686$	2628.66	−	5735.36i	0.146301	−	0.319208i
$687$	28934.2			1.60685
$688$	−2276.97	+	15248.9i	−0.126175	+	0.845000i
$689$	−22096.5			−1.22178
$690$	−6408.58	+	13982.6i	−0.353581	+	0.771463i
$691$	−3125.68			−0.172079			−0.0860393	−	0.996292i	$-0.527421\pi$
$691$	−3125.68			−0.172079			−0.0860393	+	0.996292i	$0.527421\pi$
$692$	−1426.69	−	1655.54i	−0.0783736	−	0.0909452i
$693$		−	99.6302i		−	0.00546124i
$694$	−21830.0	−	10005.2i	−1.19403	−	0.547252i
$695$		−	12315.5i		−	0.672163i
$696$	−12770.7	+	3693.45i	−0.695508	+	0.201149i
$697$			5132.81i			0.278937i
$698$	13152.7	−	28697.4i	0.713234	−	1.55618i
$699$			11367.1i			0.615085i
$700$	1846.58	−	1591.32i	0.0997057	−	0.0859231i
$701$			23361.6i			1.25871i	0.777117	+	0.629356i	$0.216681\pi$
$701$			23361.6i			1.25871i	−0.777117	+	0.629356i	$0.783319\pi$
$702$	9722.75	−	21213.7i	0.522738	−	1.14054i
$703$	−7533.47	+	2770.34i	−0.404168	+	0.148628i
$704$	−8134.52	+	5134.69i	−0.435485	+	0.274888i
$705$			5921.88i			0.316356i
$706$	−16697.9	−	7653.07i	−0.890134	−	0.407970i
$707$	−2457.09			−0.130705
$708$	−609.917	−	707.752i	−0.0323758	−	0.0375691i
$709$		−	34656.4i		−	1.83575i	−0.396866	−	0.917877i	$-0.629902\pi$
$709$		−	34656.4i		−	1.83575i	0.396866	−	0.917877i	$-0.370098\pi$
$710$	5587.77	−	12191.7i	0.295360	−	0.644433i
$711$	−1088.48			−0.0574136
$712$	8096.64	−	2341.65i	0.426172	−	0.123254i
$713$		−	3896.84i		−	0.204681i
$714$	1179.66	+	540.665i	0.0618312	+	0.0283388i
$715$		−	6156.83i		−	0.322031i
$716$	20355.3	−	17541.6i	1.06245	−	0.915585i
$717$	−5097.79			−0.265524
$718$	2666.15	−	5817.16i	0.138579	−	0.302360i
$719$			21824.0i			1.13198i	0.824411	+	0.565992i	$0.191507\pi$
$719$			21824.0i			1.13198i	−0.824411	+	0.565992i	$0.808493\pi$
$720$	−581.633	−	86.8494i	−0.0301058	−	0.00449540i
$721$			2253.15i			0.116383i
$722$	18671.1	−	5268.48i	0.962419	−	0.271568i
$723$	21737.1			1.11813
$724$	−14378.3	−	16684.7i	−0.738075	−	0.856468i
$725$	10751.5			0.550759
$726$	5808.06	−	12672.4i	0.296911	−	0.647817i
$727$		−	32538.0i		−	1.65993i	−0.557817	−	0.829964i	$-0.688361\pi$
$727$		−	32538.0i		−	1.65993i	0.557817	−	0.829964i	$-0.311639\pi$
$728$	−4110.68	+	1188.86i	−0.209275	+	0.0605247i
$729$	−20709.7			−1.05216
$730$	−5566.44	+	12145.2i	−0.282223	+	0.615771i
$731$	6637.80			0.335852
$732$	683.667	+	793.332i	0.0345206	+	0.0400579i
$733$		−	14353.4i		−	0.723267i	−0.932320	−	0.361633i	$-0.882219\pi$
$733$		−	14353.4i		−	0.723267i	0.932320	−	0.361633i	$-0.117781\pi$
$734$	−2621.38	+	5719.47i	−0.131821	+	0.287615i
$735$	−9581.52			−0.480843
$736$	28576.2	+	18639.8i	1.43116	+	0.933522i
$737$		−	11357.1i		−	0.567629i
$738$	−352.320	+	768.713i	−0.0175733	+	0.0383424i
$739$	−20256.9			−1.00834			−0.504169	−	0.863605i	$-0.668201\pi$
$739$	−20256.9			−1.00834			−0.504169	+	0.863605i	$0.668201\pi$
$740$	−3362.84	+	2897.98i	−0.167055	+	0.143962i
$741$	8244.44	+	22419.3i	0.408727	+	1.11146i
$742$	1503.28	−	3279.95i	0.0743763	−	0.162278i
$743$	34092.1			1.68334			0.841668	−	0.539995i	$-0.181574\pi$
$743$	34092.1			1.68334			0.841668	+	0.539995i	$0.181574\pi$
$744$	−2264.75	+	654.994i	−0.111599	+	0.0322758i
$745$	−2773.68			−0.136402
$746$	−163.633	−	74.9969i	−0.00803086	−	0.00368074i
$747$	251.242			0.0123059
$748$	2703.56	+	3137.23i	0.132155	+	0.153354i
$749$	3341.44			0.163009
$750$	−16114.9	−	7385.84i	−0.784576	−	0.359591i
$751$	37961.1			1.84450			0.922250	−	0.386595i	$-0.126349\pi$
$751$	37961.1			1.84450			0.922250	+	0.386595i	$0.126349\pi$
$752$	12991.6	+	1939.90i	0.629993	+	0.0940705i
$753$		−	9176.82i		−	0.444119i
$754$	−17157.3	−	7863.64i	−0.828692	−	0.379810i
$755$			11571.7i			0.557800i
$756$	2487.44	+	2886.45i	0.119666	+	0.138861i
$757$			27811.9i			1.33532i	0.744464	+	0.667662i	$0.232705\pi$
$757$			27811.9i			1.33532i	−0.744464	+	0.667662i	$0.767295\pi$
$758$	−3833.30	+	8363.71i	−0.183683	+	0.400770i
$759$	17845.1			0.853406
$760$	8644.87	−	6355.15i	0.412609	−	0.303323i
$761$	14158.7			0.674447			0.337223	−	0.941425i	$-0.390512\pi$
$761$	14158.7			0.674447			0.337223	+	0.941425i	$0.390512\pi$
$762$	4195.85	−	9154.76i	0.199475	−	0.435226i
$763$		−	2703.51i		−	0.128275i
$764$	10557.2	−	9097.81i	0.499927	−	0.430821i
$765$			253.183i			0.0119658i
$766$	−11326.1	−	5191.05i	−0.534243	−	0.244857i
$767$		−	1326.42i		−	0.0624434i
$768$	6029.84	−	19740.8i	0.283311	−	0.927521i
$769$	13553.8			0.635584			0.317792	−	0.948160i	$-0.397059\pi$
$769$	13553.8			0.635584			0.317792	+	0.948160i	$0.397059\pi$
$770$	913.905	+	418.865i	0.0427725	+	0.0196037i
$771$	−16960.0			−0.792218
$772$	11282.8	−	9723.17i	0.526008	−	0.453296i
$773$	23092.4			1.07448			0.537241	−	0.843429i	$-0.319467\pi$
$773$	23092.4			1.07448			0.537241	+	0.843429i	$0.319467\pi$
$774$	994.107	+	455.624i	0.0461659	+	0.0211590i
$775$	1906.66			0.0883731
$776$	31668.4	−	9158.88i	1.46499	−	0.423692i
$777$	1613.78			0.0745097
$778$	−11919.5	+	26006.6i	−0.549273	+	1.19844i
$779$	−5324.82	−	14479.9i	−0.244906	−	0.665979i
$780$	8624.29	+	10007.7i	0.395896	+	0.459401i
$781$	−15559.5			−0.712883
$782$	6119.98	−	13352.9i	0.279859	−	0.610614i
$783$			16806.0i			0.767047i
$784$	−3138.74	+	21020.2i	−0.142982	+	0.957554i
$785$	−19316.0			−0.878239
$786$	14108.0	−	30781.6i	0.640223	−	1.39688i
$787$			5587.77i			0.253091i	0.991961	+	0.126545i	$0.0403889\pi$
$787$			5587.77i			0.253091i	−0.991961	+	0.126545i	$0.959611\pi$
$788$	−18413.7	+	15868.3i	−0.832439	+	0.717369i
$789$	−9545.77			−0.430721
$790$	4576.18	−	9984.58i	0.206093	−	0.449665i
$791$	739.077			0.0332219
$792$	189.556	+	655.421i	0.00850451	+	0.0294058i
$793$			1486.80i			0.0665800i
$794$	−18006.5	+	39287.7i	−0.804821	+	1.75600i
$795$	−11139.1			−0.496937
$796$	18300.5	−	15770.8i	0.814881	−	0.702237i
$797$	−37059.9			−1.64709			−0.823543	−	0.567254i	$-0.808006\pi$
$797$	−37059.9			−1.64709			−0.823543	+	0.567254i	$0.808006\pi$
$798$	−3888.77	−	301.462i	−0.172507	−	0.0133730i
$799$		−	5655.19i		−	0.250396i
$800$	−9120.14	+	13981.8i	−0.403057	+	0.617915i
$801$		−	597.802i		−	0.0263699i
$802$	16743.6	−	36532.2i	0.737205	−	1.60848i
$803$	15500.1			0.681177
$804$	15908.6	+	18460.5i	0.697828	+	0.809764i
$805$		−	3565.62i		−	0.156114i
$806$	−3042.67	−	1394.53i	−0.132969	−	0.0609432i
$807$		−	29896.1i		−	1.30408i
$808$	16164.0	−	4674.83i	0.703773	−	0.203540i
$809$	44631.5			1.93963			0.969816	−	0.243840i	$-0.0784071\pi$
$809$	44631.5			1.93963			0.969816	+	0.243840i	$0.0784071\pi$
$810$	4609.01	−	10056.2i	0.199931	−	0.436221i
$811$		−	15500.9i		−	0.671158i	−0.942012	−	0.335579i	$-0.891068\pi$
$811$		−	15500.9i		−	0.671158i	0.942012	−	0.335579i	$-0.108932\pi$
$812$	2334.52	−	2011.81i	0.100894	−	0.0869468i
$813$	−6108.12			−0.263495
$814$	4682.01	+	2145.88i	0.201602	+	0.0923994i
$815$			8524.60i			0.366385i
$816$	−8789.07	−	1312.38i	−0.377058	−	0.0563022i
$817$	−18725.6	+	6886.11i	−0.801868	+	0.294877i
$818$	−13210.0	+	28822.4i	−0.564642	+	1.23197i
$819$			303.505i			0.0129491i
$820$	−5570.16	−	6463.65i	−0.237218	−	0.275269i
$821$		−	1010.46i		−	0.0429541i	−0.999769	−	0.0214770i	$-0.993163\pi$
$821$		−	1010.46i		−	0.0429541i	0.999769	−	0.0214770i	$-0.00683688\pi$
$822$	6341.11	−	13835.4i	0.269065	−	0.587062i
$823$			23113.5i			0.978962i	0.872014	+	0.489481i	$0.162814\pi$
$823$			23113.5i			0.978962i	−0.872014	+	0.489481i	$0.837186\pi$
$824$	−4286.84	−	14822.5i	−0.181237	−	0.626656i
$825$			8731.28i			0.368466i
$826$	196.890	+	90.2396i	0.00829380	+	0.00380126i
$827$		−	8617.64i		−	0.362352i	−0.983451	−	0.181176i	$-0.942010\pi$
$827$		−	8617.64i		−	0.362352i	0.983451	−	0.181176i	$-0.0579903\pi$
$828$	1833.11	−	1579.72i	0.0769385	−	0.0663030i
$829$	−35920.9			−1.50493			−0.752463	−	0.658634i	$-0.771135\pi$
$829$	−35920.9			−1.50493			−0.752463	+	0.658634i	$0.771135\pi$
$830$	−1056.27	+	2304.64i	−0.0441732	+	0.0963797i
$831$	−6675.25			−0.278654
$832$	24780.3	−	15641.9i	1.03258	−	0.651785i
$833$	9150.03			0.380588
$834$	12774.0	−	27871.2i	0.530371	−	1.15719i
$835$		−	70.9927i		−	0.00294228i
$836$	−10881.5	−	6045.61i	−0.450173	−	0.250110i
$837$			2980.36i			0.123078i
$838$	−12637.1	−	5791.91i	−0.520934	−	0.238757i
$839$	5510.57			0.226753			0.113377	−	0.993552i	$-0.463833\pi$
$839$	5510.57			0.226753			0.113377	+	0.993552i	$0.463833\pi$
$840$	−2072.25	+	599.320i	−0.0851184	+	0.0246173i
$841$	−10796.5			−0.442680
$842$	−15695.7	−	7193.71i	−0.642409	−	0.294432i
$843$	−13484.1			−0.550909
$844$	31397.5	−	27057.3i	1.28050	−	1.10350i
$845$			6176.73i			0.251463i
$846$	388.177	−	846.948i	0.0157752	−	0.0344192i
$847$			3231.49i			0.131093i
$848$	−3648.99	+	24437.4i	−0.147767	+	0.989603i
$849$			13772.8i			0.556750i
$850$	6533.36	+	2994.40i	0.263638	+	0.120832i
$851$		−	18266.9i		−	0.735820i
$852$	25291.3	−	21795.2i	1.01698	−	0.876399i
$853$		−	13875.8i		−	0.556975i	−0.960440	−	0.278488i	$-0.910167\pi$
$853$		−	13875.8i		−	0.556975i	0.960440	−	0.278488i	$-0.0898331\pi$
$854$	−220.698	−	101.151i	−0.00884323	−	0.00405307i
$855$	−262.654	−	714.243i	−0.0105059	−	0.0285691i
$856$	−21981.8	+	6357.41i	−0.877714	+	0.253845i
$857$			29552.2i			1.17793i	0.808160	+	0.588964i	$0.200464\pi$
$857$			29552.2i			1.17793i	−0.808160	+	0.588964i	$0.799536\pi$
$858$	6386.07	−	13933.5i	0.254099	−	0.554407i
$859$	5040.17			0.200196			0.100098	−	0.994978i	$-0.468084\pi$
$859$	5040.17			0.200196			0.100098	+	0.994978i	$0.468084\pi$
$860$	−8358.85	+	7203.38i	−0.331436	+	0.285620i
$861$			3101.82i			0.122775i
$862$	−28417.8	−	13024.6i	−1.12287	−	0.514640i
$863$	−22745.6			−0.897185			−0.448593	−	0.893736i	$-0.648075\pi$
$863$	−22745.6			−0.897185			−0.448593	+	0.893736i	$0.648075\pi$
$864$	−21855.5	−	14256.0i	−0.860577	−	0.561342i
$865$		−	1564.11i		−	0.0614812i
$866$	−5193.54	+	11331.6i	−0.203792	+	0.444645i
$867$		−	20932.5i		−	0.819960i
$868$	414.002	−	356.773i	0.0161891	−	0.0139512i
$869$	−12742.6			−0.497427
$870$	−8649.26	−	3964.17i	−0.337055	−	0.154480i
$871$			34597.2i			1.34590i
$872$	5143.67	+	17785.1i	0.199755	+	0.690688i
$873$		−	2338.18i		−	0.0906478i
$874$	−3412.35	+	44018.3i	−0.132065	+	1.70359i
$875$	4109.35			0.158767
$876$	−25194.8	+	21712.0i	−0.971749	+	0.837421i
$877$	−44944.1			−1.73051			−0.865253	−	0.501336i	$-0.832842\pi$
$877$	−44944.1			−1.73051			−0.865253	+	0.501336i	$0.832842\pi$
$878$	38025.6	+	17428.1i	1.46162	+	0.669896i
$879$			14601.8i			0.560304i
$880$	−6809.09	−	1016.73i	−0.260835	−	0.0389478i
$881$	−37214.5			−1.42314			−0.711570	−	0.702615i	$-0.752016\pi$
$881$	−37214.5			−1.42314			−0.711570	+	0.702615i	$0.752016\pi$
$882$	1370.35	+	628.066i	0.0523153	+	0.0239774i
$883$	−15692.1			−0.598053			−0.299027	−	0.954245i	$-0.596662\pi$
$883$	−15692.1			−0.598053			−0.299027	+	0.954245i	$0.596662\pi$
$884$	−8235.91	−	9557.00i	−0.313352	−	0.363616i
$885$		−	668.665i		−	0.0253977i
$886$	35144.4	+	16107.5i	1.33262	+	0.610771i
$887$	7657.20			0.289858			0.144929	−	0.989442i	$-0.453705\pi$
$887$	7657.20			0.289858			0.144929	+	0.989442i	$0.453705\pi$
$888$	−10616.3	+	3070.37i	−0.401194	+	0.116030i
$889$			2334.49i			0.0880725i
$890$	5483.62	+	2513.28i	0.206530	+	0.0946577i
$891$	−12834.0			−0.482555
$892$	31593.7	+	36661.5i	1.18591	+	1.37614i
$893$	5866.75	+	15953.6i	0.219847	+	0.597836i
$894$	−6277.10	−	2876.95i	−0.234829	−	0.107628i
$895$	19231.2			0.718243
$896$	635.974	+	4742.50i	0.0237125	+	0.176826i
$897$	−54361.7			−2.02351
$898$	5224.88	−	11400.0i	0.194161	−	0.423632i
$899$	2410.48			0.0894260
$900$	772.928	+	896.910i	0.0286270	+	0.0332189i
$901$	10637.5			0.393326
$902$	−4124.56	+	8999.20i	−0.152254	+	0.332196i
$903$	4011.30			0.147827
$904$	−4862.05	+	1406.16i	−0.178882	+	0.0517348i
$905$		−	15763.3i		−	0.578993i
$906$	−12002.6	+	26188.0i	−0.440132	+	0.960306i
$907$		−	34016.8i		−	1.24533i	−0.782490	−	0.622663i	$-0.786051\pi$
$907$		−	34016.8i		−	1.24533i	0.782490	−	0.622663i	$-0.213949\pi$
$908$	20682.2	−	17823.3i	0.755907	−	0.651416i
$909$		−	1193.44i		−	0.0435468i
$910$	−2784.05	−	1276.00i	−0.101418	−	0.0464823i
$911$	−20171.8			−0.733612			−0.366806	−	0.930297i	$-0.619549\pi$
$911$	−20171.8			−0.733612			−0.366806	+	0.930297i	$0.619549\pi$
$912$	26156.0	−	5415.56i	0.949682	−	0.196631i
$913$	2941.25			0.106617
$914$	20685.8	+	9480.80i	0.748604	+	0.343104i
$915$			749.519i			0.0270801i
$916$	34795.4	−	29985.5i	1.25510	−	1.08160i
$917$			7849.43i			0.282673i
$918$	−4680.65	+	10212.5i	−0.168284	+	0.367172i
$919$			52191.5i			1.87338i	0.350158	+	0.936691i	$0.386128\pi$
$919$			52191.5i			1.87338i	−0.350158	+	0.936691i	$0.613872\pi$
$920$	6783.92	+	23456.5i	0.243108	+	0.840586i
$921$	−2917.12			−0.104367
$922$	−13754.7	+	30010.8i	−0.491309	+	1.07197i
$923$	47399.1			1.69031
$924$	1633.79	+	1895.87i	0.0581687	+	0.0674993i
$925$	8937.70			0.317697
$926$	−8008.07	+	17472.5i	−0.284192	+	0.620066i
$927$	−1094.39			−0.0387751
$928$	−11530.1	+	17676.4i	−0.407859	+	0.625277i
$929$	−15362.2			−0.542538			−0.271269	−	0.962504i	$-0.587443\pi$
$929$	−15362.2			−0.542538			−0.271269	+	0.962504i	$0.587443\pi$
$930$	−1533.85	−	703.002i	−0.0540828	−	0.0247875i
$931$	−25812.7	+	9492.33i	−0.908677	+	0.334155i
$932$	11780.2	+	13669.8i	0.414026	+	0.480439i
$933$	−41787.0			−1.46628
$934$	−19249.7	−	8822.61i	−0.674378	−	0.309084i
$935$			2963.97i			0.103671i
$936$	−577.447	−	1996.62i	−0.0201650	−	0.0697239i
$937$	17961.4			0.626227			0.313113	−	0.949716i	$-0.398628\pi$
$937$	17961.4			0.626227			0.313113	+	0.949716i	$0.398628\pi$
$938$	−5135.53	−	2353.74i	−0.178764	−	0.0819321i
$939$			43910.6i			1.52606i
$940$	6137.05	+	7121.48i	0.212945	+	0.247103i
$941$	34823.8			1.20640			0.603201	−	0.797589i	$-0.293892\pi$
$941$	34823.8			1.20640			0.603201	+	0.797589i	$0.293892\pi$
$942$	−43714.0	−	20035.2i	−1.51197	−	0.692975i
$943$	35110.5			1.21247
$944$	−1466.94	−	219.043i	−0.0505771	−	0.00755216i
$945$			2727.04i			0.0938736i
$946$	11637.9	+	5333.92i	0.399978	+	0.183320i
$947$	−17274.2			−0.592751			−0.296375	−	0.955072i	$-0.595778\pi$
$947$	−17274.2			−0.592751			−0.296375	+	0.955072i	$0.595778\pi$
$948$	20712.7	−	17849.5i	0.709616	−	0.611524i
$949$	−47218.1			−1.61514
$950$	−21537.4	−	1669.61i	−0.735543	−	0.0570202i
$951$		−	22257.5i		−	0.758937i
$952$	1978.93	−	572.331i	0.0673713	−	0.0194846i
$953$			50134.8i			1.70412i	0.523444	+	0.852060i	$0.324647\pi$
$953$			50134.8i			1.70412i	−0.523444	+	0.852060i	$0.675353\pi$
$954$	1593.12	+	730.167i	0.0540663	+	0.0247799i
$955$	9974.11			0.337963
$956$	−6130.46	+	5283.03i	−0.207399	+	0.178729i
$957$			11038.5i			0.372856i
$958$	−18580.6	+	40540.2i	−0.626630	+	1.36722i
$959$			3528.08i			0.118798i
$960$	12492.1	−	7885.30i	0.419981	−	0.265101i
$961$	−29363.5			−0.985651
$962$	−14262.9	−	6537.04i	−0.478019	−	0.219088i
$963$			1622.99i			0.0543096i
$964$	26140.4	−	22526.9i	0.873365	−	0.752637i
$965$	10659.7			0.355594
$966$	3698.38	−	8069.33i	0.123181	−	0.268764i
$967$			12466.9i			0.414590i	0.978278	+	0.207295i	$0.0664660\pi$
$967$			12466.9i			0.414590i	−0.978278	+	0.207295i	$0.933534\pi$
$968$	−6148.22	−	21258.5i	−0.204144	−	0.705862i
$969$	−3968.97	−	10792.9i	−0.131581	−	0.357811i
$970$	21448.1	+	9830.20i	0.709956	+	0.325390i
$971$			35033.1i			1.15784i	0.815383	+	0.578922i	$0.196526\pi$
$971$			35033.1i			1.15784i	−0.815383	+	0.578922i	$0.803474\pi$
$972$	−2725.32	+	2348.59i	−0.0899330	+	0.0775012i
$973$			7107.24i			0.234170i
$974$	15181.7	+	6958.15i	0.499438	+	0.228905i
$975$		−	26598.3i		−	0.873668i
$976$	1644.32	+	245.529i	0.0539276	+	0.00805246i
$977$		−	21109.5i		−	0.691250i	−0.938373	−	0.345625i	$-0.887667\pi$
$977$		−	21109.5i		−	0.691250i	0.938373	−	0.345625i	$-0.112333\pi$
$978$	−8842.00	+	19292.0i	−0.289096	+	0.630767i
$979$		−	6998.38i		−	0.228467i
$980$	−11522.5	+	9929.67i	−0.375583	+	0.323665i
$981$	1313.13			0.0427372
$982$	−39732.1	−	18210.2i	−1.29114	−	0.591763i
$983$	−55306.0			−1.79449			−0.897247	−	0.441530i	$-0.854436\pi$
$983$	−55306.0			−1.79449			−0.897247	+	0.441530i	$0.854436\pi$
$984$	−5901.49	−	20405.4i	−0.191192	−	0.661078i
$985$	−17396.8			−0.562749
$986$	8259.75	+	3785.65i	0.266779	+	0.122271i
$987$		−	3417.50i		−	0.110213i
$988$	33148.5	+	18416.8i	1.06740	+	0.593034i
$989$		−	45405.3i		−	1.45986i
$990$	−203.449	+	443.898i	−0.00653136	+	0.0142505i
$991$	29330.3			0.940170			0.470085	−	0.882621i	$-0.344223\pi$
$991$	29330.3			0.940170			0.470085	+	0.882621i	$0.344223\pi$
$992$	−2044.73	+	3134.72i	−0.0654438	+	0.100330i
$993$	21764.7			0.695552
$994$	−3224.69	+	7035.81i	−0.102898	+	0.224509i
$995$	17289.8			0.550879
$996$	−4780.90	+	4120.02i	−0.152097	+	0.131072i
$997$		−	42823.7i		−	1.36032i	−0.733063	−	0.680161i	$-0.761910\pi$
$997$		−	42823.7i		−	1.36032i	0.733063	−	0.680161i	$-0.238090\pi$
$998$	1543.95	+	707.632i	0.0489709	+	0.0224446i
$999$			13970.8i			0.442460i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.4.b.b.75.48	yes	56
4.3	odd	2		608.4.b.b.303.16		56
8.3	odd	2	inner	152.4.b.b.75.10	yes	56
8.5	even	2		608.4.b.b.303.15		56
19.18	odd	2	inner	152.4.b.b.75.9	✓	56
76.75	even	2		608.4.b.b.303.42		56
152.37	odd	2		608.4.b.b.303.41		56
152.75	even	2	inner	152.4.b.b.75.47	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.4.b.b.75.9	✓	56	19.18	odd	2	inner
152.4.b.b.75.10	yes	56	8.3	odd	2	inner
152.4.b.b.75.47	yes	56	152.75	even	2	inner
152.4.b.b.75.48	yes	56	1.1	even	1	trivial
608.4.b.b.303.15		56	8.5	even	2
608.4.b.b.303.16		56	4.3	odd	2
608.4.b.b.303.41		56	152.37	odd	2
608.4.b.b.303.42		56	76.75	even	2

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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	152.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.57123 + 1.17846i) q^{2} +5.03936i q^{3} +(5.22247 + 6.06019i) q^{4} +5.72550i q^{5} +(-5.93868 + 12.9574i) q^{6} -3.30417i q^{7} +(6.28649 + 21.7366i) q^{8} +1.60489 q^{9} +O(q^{10})\)	\(q+(2.57123 + 1.17846i) q^{2} +5.03936i q^{3} +(5.22247 + 6.06019i) q^{4} +5.72550i q^{5} +(-5.93868 + 12.9574i) q^{6} -3.30417i q^{7} +(6.28649 + 21.7366i) q^{8} +1.60489 q^{9} +(-6.74727 + 14.7216i) q^{10} +18.7882 q^{11} +(-30.5394 + 26.3179i) q^{12} -57.2347 q^{13} +(3.89383 - 8.49579i) q^{14} -28.8528 q^{15} +(-9.45168 + 63.2982i) q^{16} +27.5535 q^{17} +(4.12654 + 1.89129i) q^{18} +(-77.7299 + 28.5842i) q^{19} +(-34.6976 + 29.9012i) q^{20} +16.6509 q^{21} +(48.3087 + 22.1411i) q^{22} -188.477i q^{23} +(-109.539 + 31.6799i) q^{24} +92.2187 q^{25} +(-147.164 - 67.4488i) q^{26} +144.150i q^{27} +(20.0239 - 17.2559i) q^{28} +116.587 q^{29} +(-74.1873 - 34.0019i) q^{30} +20.6754 q^{31} +(-98.8969 + 151.616i) q^{32} +94.6802i q^{33} +(70.8464 + 32.4707i) q^{34} +18.9180 q^{35} +(8.38147 + 9.72591i) q^{36} +96.9185 q^{37} +(-233.547 - 18.1049i) q^{38} -288.426i q^{39} +(-124.453 + 35.9933i) q^{40} +186.285i q^{41} +(42.8133 + 19.6224i) q^{42} +240.906 q^{43} +(98.1205 + 113.860i) q^{44} +9.18878i q^{45} +(222.113 - 484.619i) q^{46} -205.244i q^{47} +(-318.982 - 47.6304i) q^{48} +332.082 q^{49} +(237.116 + 108.676i) q^{50} +138.852i q^{51} +(-298.906 - 346.853i) q^{52} +386.068 q^{53} +(-169.875 + 370.644i) q^{54} +107.572i q^{55} +(71.8214 - 20.7716i) q^{56} +(-144.046 - 391.709i) q^{57} +(299.772 + 137.393i) q^{58} +23.1750i q^{59} +(-150.683 - 174.853i) q^{60} -25.9773i q^{61} +(53.1612 + 24.3651i) q^{62} -5.30282i q^{63} +(-432.960 + 273.294i) q^{64} -327.697i q^{65} +(-111.577 + 243.445i) q^{66} -604.479i q^{67} +(143.897 + 166.979i) q^{68} +949.804 q^{69} +(48.6426 + 22.2941i) q^{70} -828.153 q^{71} +(10.0891 + 34.8848i) q^{72} +824.991 q^{73} +(249.200 + 114.215i) q^{74} +464.723i q^{75} +(-579.168 - 321.777i) q^{76} -62.0793i q^{77} +(339.898 - 741.610i) q^{78} -678.227 q^{79} +(-362.414 - 54.1156i) q^{80} -683.092 q^{81} +(-219.530 + 478.983i) q^{82} +156.548 q^{83} +(86.9587 + 100.907i) q^{84} +157.757i q^{85} +(619.425 + 283.898i) q^{86} +587.522i q^{87} +(118.112 + 408.391i) q^{88} -372.489i q^{89} +(-10.8286 + 23.6265i) q^{90} +189.113i q^{91} +(1142.21 - 984.316i) q^{92} +104.191i q^{93} +(241.872 - 527.731i) q^{94} +(-163.659 - 445.043i) q^{95} +(-764.047 - 498.377i) q^{96} -1456.91i q^{97} +(853.861 + 391.346i) q^{98} +30.1529 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{4} - 14 q^{6} - 528 q^{9}+O(q^{10}) \) 56 * q + 2 * q^4 - 14 * q^6 - 528 * q^9	\( 56 q + 2 q^{4} - 14 q^{6} - 528 q^{9} - 40 q^{11} - 262 q^{16} - 184 q^{17} - 84 q^{19} - 12 q^{20} + 238 q^{24} - 1504 q^{25} + 378 q^{26} - 382 q^{28} + 512 q^{30} + 40 q^{35} + 1464 q^{36} + 958 q^{38} + 1030 q^{42} + 576 q^{43} + 316 q^{44} - 3664 q^{49} - 1314 q^{54} - 648 q^{57} - 1166 q^{58} + 928 q^{62} + 3746 q^{64} + 680 q^{66} + 2538 q^{68} - 432 q^{73} - 4020 q^{74} + 3968 q^{76} + 4608 q^{80} + 2296 q^{81} - 192 q^{82} + 5376 q^{83} - 1906 q^{92} - 1962 q^{96} - 6152 q^{99}+O(q^{100}) \) 56 * q + 2 * q^4 - 14 * q^6 - 528 * q^9 - 40 * q^11 - 262 * q^16 - 184 * q^17 - 84 * q^19 - 12 * q^20 + 238 * q^24 - 1504 * q^25 + 378 * q^26 - 382 * q^28 + 512 * q^30 + 40 * q^35 + 1464 * q^36 + 958 * q^38 + 1030 * q^42 + 576 * q^43 + 316 * q^44 - 3664 * q^49 - 1314 * q^54 - 648 * q^57 - 1166 * q^58 + 928 * q^62 + 3746 * q^64 + 680 * q^66 + 2538 * q^68 - 432 * q^73 - 4020 * q^74 + 3968 * q^76 + 4608 * q^80 + 2296 * q^81 - 192 * q^82 + 5376 * q^83 - 1906 * q^92 - 1962 * q^96 - 6152 * q^99

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