LMFDB - Embedded newform 175.4.k.a.149.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(74,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("175.74");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	175.149
Dual form			175.4.k.a.74.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 + 1.00000i) q^{2} +(6.06218 - 3.50000i) q^{3} +(-2.00000 - 3.46410i) q^{4} +14.0000 q^{6} +(-12.1244 - 14.0000i) q^{7} -24.0000i q^{8} +(11.0000 - 19.0526i) q^{9} +O(q^{10})$	\(q+(1.73205 + 1.00000i) q^{2} +(6.06218 - 3.50000i) q^{3} +(-2.00000 - 3.46410i) q^{4} +14.0000 q^{6} +(-12.1244 - 14.0000i) q^{7} -24.0000i q^{8} +(11.0000 - 19.0526i) q^{9} +(2.50000 + 4.33013i) q^{11} +(-24.2487 - 14.0000i) q^{12} -14.0000i q^{13} +(-7.00000 - 36.3731i) q^{14} +(8.00000 - 13.8564i) q^{16} +(18.1865 - 10.5000i) q^{17} +(38.1051 - 22.0000i) q^{18} +(24.5000 - 42.4352i) q^{19} +(-122.500 - 42.4352i) q^{21} +10.0000i q^{22} +(137.698 + 79.5000i) q^{23} +(-84.0000 - 145.492i) q^{24} +(14.0000 - 24.2487i) q^{26} +35.0000i q^{27} +(-24.2487 + 70.0000i) q^{28} -58.0000 q^{29} +(-73.5000 - 127.306i) q^{31} +(-138.564 + 80.0000i) q^{32} +(30.3109 + 17.5000i) q^{33} +42.0000 q^{34} -88.0000 q^{36} +(189.660 + 109.500i) q^{37} +(84.8705 - 49.0000i) q^{38} +(-49.0000 - 84.8705i) q^{39} +350.000 q^{41} +(-169.741 - 196.000i) q^{42} -124.000i q^{43} +(10.0000 - 17.3205i) q^{44} +(159.000 + 275.396i) q^{46} +(454.663 + 262.500i) q^{47} -112.000i q^{48} +(-49.0000 + 339.482i) q^{49} +(73.5000 - 127.306i) q^{51} +(-48.4974 + 28.0000i) q^{52} +(262.406 - 151.500i) q^{53} +(-35.0000 + 60.6218i) q^{54} +(-336.000 + 290.985i) q^{56} -343.000i q^{57} +(-100.459 - 58.0000i) q^{58} +(-52.5000 - 90.9327i) q^{59} +(206.500 - 357.668i) q^{61} -294.000i q^{62} +(-400.104 + 77.0000i) q^{63} -448.000 q^{64} +(35.0000 + 60.6218i) q^{66} +(-359.401 + 207.500i) q^{67} +(-72.7461 - 42.0000i) q^{68} +1113.00 q^{69} -432.000 q^{71} +(-457.261 - 264.000i) q^{72} +(-963.886 + 556.500i) q^{73} +(219.000 + 379.319i) q^{74} -196.000 q^{76} +(30.3109 - 87.5000i) q^{77} -196.000i q^{78} +(-51.5000 + 89.2006i) q^{79} +(419.500 + 726.595i) q^{81} +(606.218 + 350.000i) q^{82} +1092.00i q^{83} +(98.0000 + 509.223i) q^{84} +(124.000 - 214.774i) q^{86} +(-351.606 + 203.000i) q^{87} +(103.923 - 60.0000i) q^{88} +(-164.500 + 284.922i) q^{89} +(-196.000 + 169.741i) q^{91} -636.000i q^{92} +(-891.140 - 514.500i) q^{93} +(525.000 + 909.327i) q^{94} +(-560.000 + 969.948i) q^{96} +882.000i q^{97} +(-424.352 + 539.000i) q^{98} +110.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{4} + 56 q^{6} + 44 q^{9}+O(q^{10}) $ 4 * q - 8 * q^4 + 56 * q^6 + 44 * q^9	$ 4 q - 8 q^{4} + 56 q^{6} + 44 q^{9} + 10 q^{11} - 28 q^{14} + 32 q^{16} + 98 q^{19} - 490 q^{21} - 336 q^{24} + 56 q^{26} - 232 q^{29} - 294 q^{31} + 168 q^{34} - 352 q^{36} - 196 q^{39} + 1400 q^{41} + 40 q^{44} + 636 q^{46} - 196 q^{49} + 294 q^{51} - 140 q^{54} - 1344 q^{56} - 210 q^{59} + 826 q^{61} - 1792 q^{64} + 140 q^{66} + 4452 q^{69} - 1728 q^{71} + 876 q^{74} - 784 q^{76} - 206 q^{79} + 1678 q^{81} + 392 q^{84} + 496 q^{86} - 658 q^{89} - 784 q^{91} + 2100 q^{94} - 2240 q^{96} + 440 q^{99}+O(q^{100}) $ 4 * q - 8 * q^4 + 56 * q^6 + 44 * q^9 + 10 * q^11 - 28 * q^14 + 32 * q^16 + 98 * q^19 - 490 * q^21 - 336 * q^24 + 56 * q^26 - 232 * q^29 - 294 * q^31 + 168 * q^34 - 352 * q^36 - 196 * q^39 + 1400 * q^41 + 40 * q^44 + 636 * q^46 - 196 * q^49 + 294 * q^51 - 140 * q^54 - 1344 * q^56 - 210 * q^59 + 826 * q^61 - 1792 * q^64 + 140 * q^66 + 4452 * q^69 - 1728 * q^71 + 876 * q^74 - 784 * q^76 - 206 * q^79 + 1678 * q^81 + 392 * q^84 + 496 * q^86 - 658 * q^89 - 784 * q^91 + 2100 * q^94 - 2240 * q^96 + 440 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	1.73205	+	1.00000i	0.612372	+	0.353553i	0.773893	−	0.633316i	$-0.218307\pi$
$2$	1.73205	+	1.00000i	0.612372	+	0.353553i	−0.161521	+	0.986869i	$0.551640\pi$
$3$	6.06218	−	3.50000i	1.16667	−	0.673575i	0.213774	−	0.976883i	$-0.431424\pi$
$3$	6.06218	−	3.50000i	1.16667	−	0.673575i	0.952893	+	0.303308i	$0.0980910\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	14.0000			0.952579
$7$	−12.1244	−	14.0000i	−0.654654	−	0.755929i
$7$	−12.1244	−	14.0000i	−0.654654	−	0.755929i
$8$		−	24.0000i		−	1.06066i
$9$	11.0000	−	19.0526i	0.407407	−	0.705650i
$10$		0			0
$11$	2.50000	+	4.33013i	0.0685253	+	0.118689i	0.898252	−	0.439480i	$-0.144837\pi$
$11$	2.50000	+	4.33013i	0.0685253	+	0.118689i	−0.829727	+	0.558169i	$0.811504\pi$
$12$	−24.2487	−	14.0000i	−0.583333	−	0.336788i
$13$		−	14.0000i		−	0.298685i	−0.988786	−	0.149342i	$-0.952284\pi$
$13$		−	14.0000i		−	0.298685i	0.988786	−	0.149342i	$-0.0477157\pi$
$14$	−7.00000	−	36.3731i	−0.133631	−	0.694365i
$15$		0			0
$16$	8.00000	−	13.8564i	0.125000	−	0.216506i
$17$	18.1865	−	10.5000i	0.259464	−	0.149801i	−0.364626	−	0.931154i	$-0.618803\pi$
$17$	18.1865	−	10.5000i	0.259464	−	0.149801i	0.624090	+	0.781353i	$0.285470\pi$
$18$	38.1051	−	22.0000i	0.498970	−	0.288081i
$19$	24.5000	−	42.4352i	0.295826	−	0.512385i	−0.679351	−	0.733813i	$-0.737739\pi$
$19$	24.5000	−	42.4352i	0.295826	−	0.512385i	0.975177	+	0.221429i	$0.0710720\pi$
$20$		0			0
$21$	−122.500	−	42.4352i	−1.27294	−	0.440959i
$22$			10.0000i			0.0969094i
$23$	137.698	+	79.5000i	1.24835	+	0.720735i	0.970780	−	0.239971i	$-0.0771380\pi$
$23$	137.698	+	79.5000i	1.24835	+	0.720735i	0.277569	+	0.960706i	$0.410471\pi$
$24$	−84.0000	−	145.492i	−0.714435	−	1.23744i
$25$		0			0
$26$	14.0000	−	24.2487i	0.105601	−	0.182906i
$27$			35.0000i			0.249472i
$28$	−24.2487	+	70.0000i	−0.163663	+	0.472456i
$29$	−58.0000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−58.0000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	−73.5000	−	127.306i	−0.425838	−	0.737574i	0.570660	−	0.821186i	$-0.306687\pi$
$31$	−73.5000	−	127.306i	−0.425838	−	0.737574i	−0.996498	+	0.0836128i	$0.973354\pi$
$32$	−138.564	+	80.0000i	−0.765466	+	0.441942i
$33$	30.3109	+	17.5000i	0.159892	+	0.0923139i
$34$	42.0000			0.211851
$35$		0			0
$36$	−88.0000			−0.407407
$37$	189.660	+	109.500i	0.842698	+	0.486532i	0.858181	−	0.513348i	$-0.171595\pi$
$37$	189.660	+	109.500i	0.842698	+	0.486532i	−0.0154821	+	0.999880i	$0.504928\pi$
$38$	84.8705	−	49.0000i	0.362311	−	0.209180i
$39$	−49.0000	−	84.8705i	−0.201187	−	0.348466i
$40$		0			0
$41$	350.000			1.33319			0.666595	−	0.745420i	$-0.267751\pi$
$41$	350.000			1.33319			0.666595	+	0.745420i	$0.267751\pi$
$42$	−169.741	−	196.000i	−0.623610	−	0.720082i
$43$		−	124.000i		−	0.439763i	−0.975527	−	0.219882i	$-0.929433\pi$
$43$		−	124.000i		−	0.439763i	0.975527	−	0.219882i	$-0.0705671\pi$
$44$	10.0000	−	17.3205i	0.0342627	−	0.0593447i
$45$		0			0
$46$	159.000	+	275.396i	0.509636	+	0.882716i
$47$	454.663	+	262.500i	1.41105	+	0.814671i	0.995488	−	0.0948921i	$-0.0302506\pi$
$47$	454.663	+	262.500i	1.41105	+	0.814671i	0.415565	+	0.909564i	$0.363584\pi$
$48$		−	112.000i		−	0.336788i
$49$	−49.0000	+	339.482i	−0.142857	+	0.989743i
$50$		0			0
$51$	73.5000	−	127.306i	0.201805	−	0.349537i
$52$	−48.4974	+	28.0000i	−0.129334	+	0.0746712i
$53$	262.406	−	151.500i	0.680079	−	0.392644i	−0.119806	−	0.992797i	$-0.538227\pi$
$53$	262.406	−	151.500i	0.680079	−	0.392644i	0.799885	+	0.600153i	$0.204894\pi$
$54$	−35.0000	+	60.6218i	−0.0882018	+	0.152770i
$55$		0			0
$56$	−336.000	+	290.985i	−0.801784	+	0.694365i
$57$		−	343.000i		−	0.797043i
$58$	−100.459	−	58.0000i	−0.227429	−	0.131306i
$59$	−52.5000	−	90.9327i	−0.115846	−	0.200651i	0.802272	−	0.596959i	$-0.203625\pi$
$59$	−52.5000	−	90.9327i	−0.115846	−	0.200651i	−0.918118	+	0.396308i	$0.870291\pi$
$60$		0			0
$61$	206.500	−	357.668i	0.433436	−	0.750734i	−0.563730	−	0.825959i	$-0.690634\pi$
$61$	206.500	−	357.668i	0.433436	−	0.750734i	0.997167	+	0.0752252i	$0.0239676\pi$
$62$		−	294.000i		−	0.602226i
$63$	−400.104	+	77.0000i	−0.800132	+	0.153986i
$64$	−448.000			−0.875000
$65$		0			0
$66$	35.0000	+	60.6218i	0.0652758	+	0.113061i
$67$	−359.401	+	207.500i	−0.655340	+	0.378361i	−0.790499	−	0.612463i	$-0.790179\pi$
$67$	−359.401	+	207.500i	−0.655340	+	0.378361i	0.135159	+	0.990824i	$0.456845\pi$
$68$	−72.7461	−	42.0000i	−0.129732	−	0.0749007i
$69$	1113.00			1.94188
$70$		0			0
$71$	−432.000			−0.722098			−0.361049	−	0.932547i	$-0.617581\pi$
$71$	−432.000			−0.722098			−0.361049	+	0.932547i	$0.617581\pi$
$72$	−457.261	−	264.000i	−0.748455	−	0.432121i
$73$	−963.886	+	556.500i	−1.54540	+	0.892238i	−0.546919	+	0.837186i	$0.684199\pi$
$73$	−963.886	+	556.500i	−1.54540	+	0.892238i	−0.998483	+	0.0550526i	$0.982467\pi$
$74$	219.000	+	379.319i	0.344030	+	0.595878i
$75$		0			0
$76$	−196.000			−0.295826
$77$	30.3109	−	87.5000i	0.0448603	−	0.129501i
$78$		−	196.000i		−	0.284521i
$79$	−51.5000	+	89.2006i	−0.0733443	+	0.127036i	−0.900365	−	0.435135i	$-0.856701\pi$
$79$	−51.5000	+	89.2006i	−0.0733443	+	0.127036i	0.827021	+	0.562171i	$0.190034\pi$
$80$		0			0
$81$	419.500	+	726.595i	0.575446	+	0.996701i
$82$	606.218	+	350.000i	0.816409	+	0.471354i
$83$			1092.00i			1.44413i	0.691827	+	0.722064i	$0.256806\pi$
$83$			1092.00i			1.44413i	−0.691827	+	0.722064i	$0.743194\pi$
$84$	98.0000	+	509.223i	0.127294	+	0.661438i
$85$		0			0
$86$	124.000	−	214.774i	0.155480	−	0.269299i
$87$	−351.606	+	203.000i	−0.433289	+	0.250160i
$88$	103.923	−	60.0000i	0.125889	−	0.0726821i
$89$	−164.500	+	284.922i	−0.195921	+	0.339345i	−0.947202	−	0.320637i	$-0.896103\pi$
$89$	−164.500	+	284.922i	−0.195921	+	0.339345i	0.751281	+	0.659982i	$0.229436\pi$
$90$		0			0
$91$	−196.000	+	169.741i	−0.225784	+	0.195535i
$92$		−	636.000i		−	0.720735i
$93$	−891.140	−	514.500i	−0.993623	−	0.573668i
$94$	525.000	+	909.327i	0.576060	+	0.997765i
$95$		0			0
$96$	−560.000	+	969.948i	−0.595362	+	1.03120i
$97$			882.000i			0.923232i	0.887080	+	0.461616i	$0.152730\pi$
$97$			882.000i			0.923232i	−0.887080	+	0.461616i	$0.847270\pi$
$98$	−424.352	+	539.000i	−0.437409	+	0.555584i
$99$	110.000			0.111671
$100$		0			0
$101$	−689.500	−	1194.25i	−0.679285	−	1.17656i	−0.975196	−	0.221341i	$-0.928957\pi$
$101$	−689.500	−	1194.25i	−0.679285	−	1.17656i	0.295911	−	0.955215i	$-0.404377\pi$
$102$	254.611	−	147.000i	0.247160	−	0.142698i
$103$	588.031	+	339.500i	0.562529	+	0.324776i	0.754160	−	0.656691i	$-0.228044\pi$
$103$	588.031	+	339.500i	0.562529	+	0.324776i	−0.191631	+	0.981467i	$0.561378\pi$
$104$	−336.000			−0.316803
$105$		0			0
$106$	606.000			0.555282
$107$	395.774	+	228.500i	0.357578	+	0.206448i	0.668018	−	0.744145i	$-0.267143\pi$
$107$	395.774	+	228.500i	0.357578	+	0.206448i	−0.310440	+	0.950593i	$0.600476\pi$
$108$	121.244	−	70.0000i	0.108025	−	0.0623681i
$109$	−562.500	−	974.279i	−0.494291	−	0.856137i	0.505687	−	0.862717i	$-0.331239\pi$
$109$	−562.500	−	974.279i	−0.494291	−	0.856137i	−0.999978	+	0.00657959i	$0.997906\pi$
$110$		0			0
$111$	1533.00			1.31086
$112$	−290.985	+	56.0000i	−0.245495	+	0.0472456i
$113$		−	1538.00i		−	1.28038i	−0.768217	−	0.640190i	$-0.778856\pi$
$113$		−	1538.00i		−	1.28038i	0.768217	−	0.640190i	$-0.221144\pi$
$114$	343.000	−	594.093i	0.281797	−	0.488087i
$115$		0			0
$116$	116.000	+	200.918i	0.0928477	+	0.160817i
$117$	−266.736	−	154.000i	−0.210767	−	0.121686i
$118$		−	210.000i		−	0.163831i
$119$	−367.500	−	127.306i	−0.283098	−	0.0980680i
$120$		0			0
$121$	653.000	−	1131.03i	0.490609	−	0.849759i
$122$	715.337	−	413.000i	0.530849	−	0.306486i
$123$	2121.76	−	1225.00i	1.55539	−	0.898004i
$124$	−294.000	+	509.223i	−0.212919	+	0.368787i
$125$		0			0
$126$	−770.000	−	266.736i	−0.544421	−	0.188593i
$127$		−	72.0000i		−	0.0503068i	−0.999684	−	0.0251534i	$-0.991993\pi$
$127$		−	72.0000i		−	0.0503068i	0.999684	−	0.0251534i	$-0.00800742\pi$
$128$	332.554	+	192.000i	0.229640	+	0.132583i
$129$	−434.000	−	751.710i	−0.296214	−	0.513057i
$130$		0			0
$131$	−1074.50	+	1861.09i	−0.716637	+	1.24125i	0.245687	+	0.969349i	$0.420986\pi$
$131$	−1074.50	+	1861.09i	−0.716637	+	1.24125i	−0.962325	+	0.271903i	$0.912347\pi$
$132$		−	140.000i		−	0.0923139i
$133$	−891.140	+	171.500i	−0.580990	+	0.111812i
$134$	−830.000			−0.535083
$135$		0			0
$136$	−252.000	−	436.477i	−0.158888	−	0.275203i
$137$	974.279	−	562.500i	0.607578	−	0.350786i	−0.164439	−	0.986387i	$-0.552581\pi$
$137$	974.279	−	562.500i	0.607578	−	0.350786i	0.772017	+	0.635602i	$0.219248\pi$
$138$	1927.77	+	1113.00i	1.18915	+	0.686557i
$139$	−252.000			−0.153772			−0.0768862	−	0.997040i	$-0.524498\pi$
$139$	−252.000			−0.153772			−0.0768862	+	0.997040i	$0.524498\pi$
$140$		0			0
$141$	3675.00			2.19497
$142$	−748.246	−	432.000i	−0.442193	−	0.255300i
$143$	60.6218	−	35.0000i	0.0354507	−	0.0204675i
$144$	−176.000	−	304.841i	−0.101852	−	0.176413i
$145$		0			0
$146$	−2226.00			−1.26182
$147$	891.140	+	2229.50i	0.500000	+	1.25093i
$148$		−	876.000i		−	0.486532i
$149$	−100.500	+	174.071i	−0.0552569	+	0.0957078i	−0.892331	−	0.451382i	$-0.850931\pi$
$149$	−100.500	+	174.071i	−0.0552569	+	0.0957078i	0.837074	+	0.547090i	$0.184264\pi$
$150$		0			0
$151$	−809.500	−	1402.10i	−0.436266	−	0.755635i	0.561132	−	0.827726i	$-0.310366\pi$
$151$	−809.500	−	1402.10i	−0.436266	−	0.755635i	−0.997398	+	0.0720914i	$0.977033\pi$
$152$	−1018.45	−	588.000i	−0.543466	−	0.313770i
$153$		−	462.000i		−	0.244121i
$154$	140.000	−	121.244i	0.0732566	−	0.0634421i
$155$		0			0
$156$	−196.000	+	339.482i	−0.100593	+	0.174233i
$157$	−588.031	+	339.500i	−0.298917	+	0.172580i	−0.641956	−	0.766741i	$-0.721877\pi$
$157$	−588.031	+	339.500i	−0.298917	+	0.172580i	0.343039	+	0.939321i	$0.388544\pi$
$158$	−178.401	+	103.000i	−0.0898281	+	0.0518623i
$159$	1060.50	−	1836.84i	0.528950	−	0.916169i
$160$		0			0
$161$	−556.500	−	2891.66i	−0.272412	−	1.41549i
$162$			1678.00i			0.813803i
$163$	404.434	+	233.500i	0.194342	+	0.112203i	0.594014	−	0.804455i	$-0.297543\pi$
$163$	404.434	+	233.500i	0.194342	+	0.112203i	−0.399672	+	0.916658i	$0.630876\pi$
$164$	−700.000	−	1212.44i	−0.333298	−	0.577288i
$165$		0			0
$166$	−1092.00	+	1891.40i	−0.510576	+	0.884344i
$167$		−	1204.00i		−	0.557894i	−0.960306	−	0.278947i	$-0.910015\pi$
$167$		−	1204.00i		−	0.557894i	0.960306	−	0.278947i	$-0.0899854\pi$
$168$	−1018.45	+	2940.00i	−0.467707	+	1.35015i
$169$	2001.00			0.910787
$170$		0			0
$171$	−539.000	−	933.575i	−0.241043	−	0.417499i
$172$	−429.549	+	248.000i	−0.190423	+	0.109941i
$173$	2443.06	+	1410.50i	1.07365	+	0.619875i	0.929178	−	0.369633i	$-0.120517\pi$
$173$	2443.06	+	1410.50i	1.07365	+	0.619875i	0.144477	+	0.989508i	$0.453850\pi$
$174$	−812.000			−0.353779
$175$		0			0
$176$	80.0000			0.0342627
$177$	−636.529	−	367.500i	−0.270307	−	0.156062i
$178$	−569.845	+	329.000i	−0.239953	+	0.138537i
$179$	−1626.50	−	2817.18i	−0.679164	−	1.17635i	−0.975233	−	0.221180i	$-0.929009\pi$
$179$	−1626.50	−	2817.18i	−0.679164	−	1.17635i	0.296069	−	0.955166i	$-0.404324\pi$
$180$		0			0
$181$	1582.00			0.649664			0.324832	−	0.945772i	$-0.394692\pi$
$181$	1582.00			0.649664			0.324832	+	0.945772i	$0.394692\pi$
$182$	−509.223	+	98.0000i	−0.207396	+	0.0399134i
$183$		−	2891.00i		−	1.16781i
$184$	1908.00	−	3304.75i	0.764454	−	1.32407i
$185$		0			0
$186$	−1029.00	−	1782.28i	−0.405645	−	0.702597i
$187$	90.9327	+	52.5000i	0.0355597	+	0.0205304i
$188$		−	2100.00i		−	0.814671i
$189$	490.000	−	424.352i	0.188583	−	0.163318i
$190$		0			0
$191$	−1278.50	+	2214.43i	−0.484340	+	0.838902i	−0.999838	−	0.0179887i	$-0.994274\pi$
$191$	−1278.50	+	2214.43i	−0.484340	+	0.838902i	0.515498	+	0.856891i	$0.327607\pi$
$192$	−2715.86	+	1568.00i	−1.02083	+	0.589378i
$193$	−343.812	+	198.500i	−0.128229	+	0.0740329i	−0.562742	−	0.826632i	$-0.690254\pi$
$193$	−343.812	+	198.500i	−0.128229	+	0.0740329i	0.434514	+	0.900665i	$0.356920\pi$
$194$	−882.000	+	1527.67i	−0.326412	+	0.565362i
$195$		0			0
$196$	1274.00	−	509.223i	0.464286	−	0.185577i
$197$		−	2914.00i		−	1.05388i	−0.849903	−	0.526939i	$-0.823340\pi$
$197$		−	2914.00i		−	1.05388i	0.849903	−	0.526939i	$-0.176660\pi$
$198$	190.526	+	110.000i	0.0683842	+	0.0394816i
$199$	1669.50	+	2891.66i	0.594712	+	1.03007i	0.993587	+	0.113066i	$0.0360673\pi$
$199$	1669.50	+	2891.66i	0.594712	+	1.03007i	−0.398875	+	0.917005i	$0.630599\pi$
$200$		0			0
$201$	−1452.50	+	2515.80i	−0.509709	+	0.882841i
$202$		−	2758.00i		−	0.960654i
$203$	703.213	+	812.000i	0.243132	+	0.280745i
$204$	−588.000			−0.201805
$205$		0			0
$206$	679.000	+	1176.06i	0.229651	+	0.397768i
$207$	3029.36	−	1749.00i	1.01717	−	0.587265i
$208$	−193.990	−	112.000i	−0.0646671	−	0.0373356i
$209$	245.000			0.0810861
$210$		0			0
$211$	1780.00			0.580759			0.290380	−	0.956911i	$-0.406218\pi$
$211$	1780.00			0.580759			0.290380	+	0.956911i	$0.406218\pi$
$212$	−1049.62	−	606.000i	−0.340040	−	0.196322i
$213$	−2618.86	+	1512.00i	−0.842448	+	0.486387i
$214$	457.000	+	791.547i	0.145981	+	0.252846i
$215$		0			0
$216$	840.000			0.264605
$217$	−891.140	+	2572.50i	−0.278777	+	0.804759i
$218$		−	2250.00i		−	0.699033i
$219$	−3895.50	+	6747.20i	−1.20198	+	2.08189i
$220$		0			0
$221$	−147.000	−	254.611i	−0.0447434	−	0.0774978i
$222$	2655.23	+	1533.00i	0.802737	+	0.463460i
$223$		−	1400.00i		−	0.420408i	−0.977658	−	0.210204i	$-0.932587\pi$
$223$		−	1400.00i		−	0.420408i	0.977658	−	0.210204i	$-0.0674128\pi$
$224$	2800.00	+	969.948i	0.835191	+	0.289319i
$225$		0			0
$226$	1538.00	−	2663.89i	0.452682	−	0.784069i
$227$	1909.59	−	1102.50i	0.558342	−	0.322359i	−0.194138	−	0.980974i	$-0.562191\pi$
$227$	1909.59	−	1102.50i	0.558342	−	0.322359i	0.752480	+	0.658615i	$0.228858\pi$
$228$	−1188.19	+	686.000i	−0.345130	+	0.199261i
$229$	143.500	−	248.549i	0.0414094	−	0.0717231i	−0.844578	−	0.535433i	$-0.820149\pi$
$229$	143.500	−	248.549i	0.0414094	−	0.0717231i	0.885987	+	0.463710i	$0.153482\pi$
$230$		0			0
$231$	−122.500	−	636.529i	−0.0348914	−	0.181301i
$232$			1392.00i			0.393919i
$233$	−3972.46	−	2293.50i	−1.11693	−	0.644859i	−0.176314	−	0.984334i	$-0.556417\pi$
$233$	−3972.46	−	2293.50i	−1.11693	−	0.644859i	−0.940615	+	0.339475i	$0.889751\pi$
$234$	−308.000	−	533.472i	−0.0860453	−	0.149035i
$235$		0			0
$236$	−210.000	+	363.731i	−0.0579230	+	0.100326i
$237$			721.000i			0.197612i
$238$	−509.223	−	588.000i	−0.138689	−	0.160144i
$239$	−1668.00			−0.451439			−0.225720	−	0.974192i	$-0.572473\pi$
$239$	−1668.00			−0.451439			−0.225720	+	0.974192i	$0.572473\pi$
$240$		0			0
$241$	1704.50	+	2952.28i	0.455587	+	0.789100i	0.998722	−	0.0505456i	$-0.0160960\pi$
$241$	1704.50	+	2952.28i	0.455587	+	0.789100i	−0.543135	+	0.839646i	$0.682763\pi$
$242$	2262.06	−	1306.00i	0.600870	−	0.346913i
$243$	4267.77	+	2464.00i	1.12666	+	0.650476i
$244$	−1652.00			−0.433436
$245$		0			0
$246$	4900.00			1.26997
$247$	−594.093	−	343.000i	−0.153042	−	0.0883586i
$248$	−3055.34	+	1764.00i	−0.782315	+	0.451670i
$249$	3822.00	+	6619.90i	0.972729	+	1.68482i
$250$		0			0
$251$	−4760.00			−1.19701			−0.598503	−	0.801121i	$-0.704238\pi$
$251$	−4760.00			−1.19701			−0.598503	+	0.801121i	$0.704238\pi$
$252$	1066.94	+	1232.00i	0.266711	+	0.307971i
$253$			795.000i			0.197554i
$254$	72.0000	−	124.708i	0.0177861	−	0.0308065i
$255$		0			0
$256$	2176.00	+	3768.94i	0.531250	+	0.920152i
$257$	−697.150	−	402.500i	−0.169210	−	0.0976936i	0.413003	−	0.910730i	$-0.364480\pi$
$257$	−697.150	−	402.500i	−0.169210	−	0.0976936i	−0.582213	+	0.813036i	$0.697813\pi$
$258$		−	1736.00i		−	0.418909i
$259$	−766.500	−	3982.85i	−0.183892	−	0.955530i
$260$		0			0
$261$	−638.000	+	1105.05i	−0.151307	+	0.262072i
$262$	−3722.18	+	2149.00i	−0.877698	+	0.506739i
$263$	−222.569	+	128.500i	−0.0521831	+	0.0301279i	−0.525865	−	0.850568i	$-0.676258\pi$
$263$	−222.569	+	128.500i	−0.0521831	+	0.0301279i	0.473681	+	0.880696i	$0.342925\pi$
$264$	420.000	−	727.461i	0.0979137	−	0.169591i
$265$		0			0
$266$	−1715.00	−	594.093i	−0.395314	−	0.136941i
$267$			2303.00i			0.527870i
$268$	1437.60	+	830.000i	0.327670	+	0.189180i
$269$	1795.50	+	3109.90i	0.406965	+	0.704884i	0.994548	−	0.104280i	$-0.0332538\pi$
$269$	1795.50	+	3109.90i	0.406965	+	0.704884i	−0.587583	+	0.809164i	$0.699920\pi$
$270$		0			0
$271$	−696.500	+	1206.37i	−0.156123	+	0.270413i	−0.933467	−	0.358662i	$-0.883233\pi$
$271$	−696.500	+	1206.37i	−0.156123	+	0.270413i	0.777344	+	0.629075i	$0.216566\pi$
$272$		−	336.000i		−	0.0749007i
$273$	−594.093	+	1715.00i	−0.131708	+	0.380207i
$274$	2250.00			0.496086
$275$		0			0
$276$	−2226.00	−	3855.55i	−0.485469	−	0.840857i
$277$	−359.401	+	207.500i	−0.0779577	+	0.0450089i	−0.538472	−	0.842643i	$-0.680998\pi$
$277$	−359.401	+	207.500i	−0.0779577	+	0.0450089i	0.460514	+	0.887652i	$0.347665\pi$
$278$	−436.477	−	252.000i	−0.0941660	−	0.0543667i
$279$	−3234.00			−0.693959
$280$		0			0
$281$	−4954.00			−1.05171			−0.525856	−	0.850574i	$-0.676255\pi$
$281$	−4954.00			−1.05171			−0.525856	+	0.850574i	$0.676255\pi$
$282$	6365.29	+	3675.00i	1.34414	+	0.776039i
$283$	−3703.99	+	2138.50i	−0.778019	+	0.449190i	−0.835728	−	0.549144i	$-0.814954\pi$
$283$	−3703.99	+	2138.50i	−0.778019	+	0.449190i	0.0577087	+	0.998333i	$0.481621\pi$
$284$	864.000	+	1496.49i	0.180525	+	0.312678i
$285$		0			0
$286$	140.000			0.0289454
$287$	−4243.52	−	4900.00i	−0.872778	−	1.00780i
$288$			3520.00i			0.720201i
$289$	−2236.00	+	3872.87i	−0.455119	+	0.788289i
$290$		0			0
$291$	3087.00	+	5346.84i	0.621866	+	1.07710i
$292$	3855.55	+	2226.00i	0.772701	+	0.446119i
$293$			7742.00i			1.54366i	0.635829	+	0.771830i	$0.280658\pi$
$293$			7742.00i			1.54366i	−0.635829	+	0.771830i	$0.719342\pi$
$294$	−686.000	+	4752.75i	−0.136083	+	0.942809i
$295$		0			0
$296$	2628.00	−	4551.83i	0.516045	−	0.893817i
$297$	−151.554	+	87.5000i	−0.0296097	+	0.0170952i
$298$	−348.142	+	201.000i	−0.0676756	+	0.0390725i
$299$	1113.00	−	1927.77i	0.215272	−	0.372863i
$300$		0			0
$301$	−1736.00	+	1503.42i	−0.332430	+	0.287893i
$302$		−	3238.00i		−	0.616973i
$303$	−8359.74	−	4826.50i	−1.58500	−	0.915100i
$304$	−392.000	−	678.964i	−0.0739564	−	0.128096i
$305$		0			0
$306$	462.000	−	800.207i	0.0863097	−	0.149493i
$307$			7364.00i			1.36901i	0.729009	+	0.684504i	$0.239981\pi$
$307$			7364.00i			1.36901i	−0.729009	+	0.684504i	$0.760019\pi$
$308$	−363.731	+	70.0000i	−0.0672905	+	0.0129501i
$309$	4753.00			0.875044
$310$		0			0
$311$	−4987.50	−	8638.60i	−0.909374	−	1.57508i	−0.814936	−	0.579550i	$-0.803228\pi$
$311$	−4987.50	−	8638.60i	−0.909374	−	1.57508i	−0.0944372	−	0.995531i	$-0.530105\pi$
$312$	−2036.89	+	1176.00i	−0.369603	+	0.213391i
$313$	4116.22	+	2376.50i	0.743330	+	0.429162i	0.823279	−	0.567637i	$-0.192142\pi$
$313$	4116.22	+	2376.50i	0.743330	+	0.429162i	−0.0799485	+	0.996799i	$0.525476\pi$
$314$	−1358.00			−0.244065
$315$		0			0
$316$	412.000			0.0733443
$317$	−3011.17	−	1738.50i	−0.533515	−	0.308025i	0.208932	−	0.977930i	$-0.433001\pi$
$317$	−3011.17	−	1738.50i	−0.533515	−	0.308025i	−0.742447	+	0.669905i	$0.766335\pi$
$318$	3673.68	−	2121.00i	0.647829	−	0.374024i
$319$	−145.000	−	251.147i	−0.0254497	−	0.0440801i
$320$		0			0
$321$	3199.00			0.556233
$322$	1927.77	−	5565.00i	0.333635	−	0.963122i
$323$		−	1029.00i		−	0.177260i
$324$	1678.00	−	2906.38i	0.287723	−	0.498351i
$325$		0			0
$326$	467.000	+	808.868i	0.0793397	+	0.137420i
$327$	−6819.95	−	3937.50i	−1.15335	−	0.665885i
$328$		−	8400.00i		−	1.41406i
$329$	−1837.50	−	9547.93i	−0.307917	−	1.59998i
$330$		0			0
$331$	−1670.50	+	2893.39i	−0.277399	+	0.480469i	−0.970738	−	0.240143i	$-0.922806\pi$
$331$	−1670.50	+	2893.39i	−0.277399	+	0.480469i	0.693339	+	0.720612i	$0.256139\pi$
$332$	3782.80	−	2184.00i	0.625325	−	0.361032i
$333$	4172.51	−	2409.00i	0.686643	−	0.396434i
$334$	1204.00	−	2085.39i	0.197245	−	0.341639i
$335$		0			0
$336$	−1568.00	+	1357.93i	−0.254588	+	0.220479i
$337$		−	7366.00i		−	1.19066i	−0.803482	−	0.595329i	$-0.797022\pi$
$337$		−	7366.00i		−	1.19066i	0.803482	−	0.595329i	$-0.202978\pi$
$338$	3465.83	+	2001.00i	0.557741	+	0.322012i
$339$	−5383.00	−	9323.63i	−0.862432	−	1.49378i
$340$		0			0
$341$	367.500	−	636.529i	0.0583614	−	0.101085i
$342$		−	2156.00i		−	0.340886i
$343$	5346.84	−	3430.00i	0.841698	−	0.539949i
$344$	−2976.00			−0.466439
$345$		0			0
$346$	2821.00	+	4886.12i	0.438318	+	0.759188i
$347$	−6421.58	+	3707.50i	−0.993454	+	0.573571i	−0.906305	−	0.422625i	$-0.861109\pi$
$347$	−6421.58	+	3707.50i	−0.993454	+	0.573571i	−0.0871487	+	0.996195i	$0.527776\pi$
$348$	1406.43	+	812.000i	0.216645	+	0.125080i
$349$	3878.00			0.594798			0.297399	−	0.954753i	$-0.403881\pi$
$349$	3878.00			0.594798			0.297399	+	0.954753i	$0.403881\pi$
$350$		0			0
$351$	490.000			0.0745136
$352$	−692.820	−	400.000i	−0.104908	−	0.0605684i
$353$	1097.25	−	633.500i	0.165442	−	0.0955179i	−0.414993	−	0.909825i	$-0.636216\pi$
$353$	1097.25	−	633.500i	0.165442	−	0.0955179i	0.580435	+	0.814307i	$0.302883\pi$
$354$	−735.000	−	1273.06i	−0.110353	−	0.191136i
$355$		0			0
$356$	1316.00			0.195921
$357$	−2673.42	+	514.500i	−0.396337	+	0.0762751i
$358$		−	6506.00i		−	0.960483i
$359$	2342.50	−	4057.33i	0.344380	−	0.596484i	−0.640861	−	0.767657i	$-0.721422\pi$
$359$	2342.50	−	4057.33i	0.344380	−	0.596484i	0.985241	+	0.171173i	$0.0547558\pi$
$360$		0			0
$361$	2229.00	+	3860.74i	0.324974	+	0.562872i
$362$	2740.10	+	1582.00i	0.397836	+	0.229691i
$363$		−	9142.00i		−	1.32185i
$364$	980.000	+	339.482i	0.141115	+	0.0488838i
$365$		0			0
$366$	2891.00	−	5007.36i	0.412882	−	0.715133i
$367$	4019.22	−	2320.50i	0.571667	−	0.330052i	−0.186148	−	0.982522i	$-0.559600\pi$
$367$	4019.22	−	2320.50i	0.571667	−	0.330052i	0.757815	+	0.652470i	$0.226267\pi$
$368$	2203.17	−	1272.00i	0.312087	−	0.180184i
$369$	3850.00	−	6668.40i	0.543152	−	0.940766i
$370$		0			0
$371$	−5302.50	−	1836.84i	−0.742027	−	0.257046i
$372$			4116.00i			0.573668i
$373$	7618.43	+	4398.50i	1.05755	+	0.610578i	0.924754	−	0.380565i	$-0.124270\pi$
$373$	7618.43	+	4398.50i	1.05755	+	0.610578i	0.132798	+	0.991143i	$0.457604\pi$
$374$	105.000	+	181.865i	0.0145172	+	0.0251445i
$375$		0			0
$376$	6300.00	−	10911.9i	0.864090	−	1.49665i
$377$			812.000i			0.110929i
$378$	1273.06	−	245.000i	0.173225	−	0.0333371i
$379$	−13680.0			−1.85407			−0.927037	−	0.374969i	$-0.877653\pi$
$379$	−13680.0			−1.85407			−0.927037	+	0.374969i	$0.877653\pi$
$380$		0			0
$381$	−252.000	−	436.477i	−0.0338854	−	0.0586913i
$382$	−4428.85	+	2557.00i	−0.593193	+	0.342480i
$383$	−8456.74	−	4882.50i	−1.12825	−	0.651395i	−0.184755	−	0.982785i	$-0.559149\pi$
$383$	−8456.74	−	4882.50i	−1.12825	−	0.651395i	−0.943494	+	0.331390i	$0.892482\pi$
$384$	2688.00			0.357217
$385$		0			0
$386$	−794.000			−0.104698
$387$	−2362.52	−	1364.00i	−0.310319	−	0.179163i
$388$	3055.34	−	1764.00i	0.399771	−	0.230808i
$389$	865.500	+	1499.09i	0.112809	+	0.195390i	0.916902	−	0.399113i	$-0.130682\pi$
$389$	865.500	+	1499.09i	0.112809	+	0.195390i	−0.804093	+	0.594504i	$0.797349\pi$
$390$		0			0
$391$	3339.00			0.431868
$392$	8147.57	+	1176.00i	1.04978	+	0.151523i
$393$			15043.0i			1.93084i
$394$	2914.00	−	5047.20i	0.372602	−	0.645366i
$395$		0			0
$396$	−220.000	−	381.051i	−0.0279177	−	0.0483549i
$397$	9511.56	+	5491.50i	1.20245	+	0.694233i	0.961099	−	0.276206i	$-0.0890771\pi$
$397$	9511.56	+	5491.50i	1.20245	+	0.694233i	0.241348	+	0.970439i	$0.422410\pi$
$398$			6678.00i			0.841050i
$399$	−4802.00	+	4158.65i	−0.602508	+	0.521787i
$400$		0			0
$401$	−3301.50	+	5718.37i	−0.411145	+	0.712124i	−0.995015	−	0.0997232i	$-0.968204\pi$
$401$	−3301.50	+	5718.37i	−0.411145	+	0.712124i	0.583870	+	0.811847i	$0.301538\pi$
$402$	−5031.61	+	2905.00i	−0.624263	+	0.360418i
$403$	−1782.28	+	1029.00i	−0.220302	+	0.127191i
$404$	−2758.00	+	4777.00i	−0.339643	+	0.588278i
$405$		0			0
$406$	406.000	+	2109.64i	0.0496292	+	0.257881i
$407$			1095.00i			0.133359i
$408$	−3055.34	−	1764.00i	−0.370740	−	0.214047i
$409$	5477.50	+	9487.31i	0.662213	+	1.14699i	0.980033	+	0.198835i	$0.0637158\pi$
$409$	5477.50	+	9487.31i	0.662213	+	1.14699i	−0.317820	+	0.948151i	$0.602951\pi$
$410$		0			0
$411$	3937.50	−	6819.95i	0.472561	−	0.818500i
$412$		−	2716.00i		−	0.324776i
$413$	−636.529	+	1837.50i	−0.0758391	+	0.218928i
$414$	6996.00			0.830518
$415$		0			0
$416$	1120.00	+	1939.90i	0.132001	+	0.228633i
$417$	−1527.67	+	882.000i	−0.179401	+	0.103577i
$418$	424.352	+	245.000i	0.0496549	+	0.0286683i
$419$	−6636.00			−0.773723			−0.386861	−	0.922138i	$-0.626441\pi$
$419$	−6636.00			−0.773723			−0.386861	+	0.922138i	$0.626441\pi$
$420$		0			0
$421$	−16630.0			−1.92517			−0.962585	−	0.270980i	$-0.912652\pi$
$421$	−16630.0			−1.92517			−0.962585	+	0.270980i	$0.912652\pi$
$422$	3083.05	+	1780.00i	0.355641	+	0.205329i
$423$	10002.6	−	5775.00i	1.14975	−	0.663806i
$424$	−3636.00	−	6297.74i	−0.416462	−	0.721333i
$425$		0			0
$426$	−6048.00			−0.687856
$427$	−7511.04	+	1445.50i	−0.851252	+	0.163824i
$428$		−	1828.00i		−	0.206448i
$429$	245.000	−	424.352i	0.0275728	−	0.0477574i
$430$		0			0
$431$	−2461.50	−	4263.44i	−0.275096	−	0.476480i	0.695064	−	0.718948i	$-0.255376\pi$
$431$	−2461.50	−	4263.44i	−0.275096	−	0.476480i	−0.970159	+	0.242468i	$0.922043\pi$
$432$	484.974	+	280.000i	0.0540123	+	0.0311840i
$433$			8974.00i			0.995988i	0.867180	+	0.497994i	$0.165930\pi$
$433$			8974.00i			0.995988i	−0.867180	+	0.497994i	$0.834070\pi$
$434$	−4116.00	+	3564.56i	−0.455240	+	0.394250i
$435$		0			0
$436$	−2250.00	+	3897.11i	−0.247146	+	0.428069i
$437$	6747.20	−	3895.50i	0.738587	−	0.426423i
$438$	−13494.4	+	7791.00i	−1.47212	+	0.849928i
$439$	−2089.50	+	3619.12i	−0.227167	+	0.393465i	−0.956967	−	0.290195i	$-0.906280\pi$
$439$	−2089.50	+	3619.12i	−0.227167	+	0.393465i	0.729800	+	0.683660i	$0.239613\pi$
$440$		0			0
$441$	5929.00	+	4667.88i	0.640212	+	0.504036i
$442$		−	588.000i		−	0.0632767i
$443$	11195.1	+	6463.50i	1.20067	+	0.693206i	0.960704	−	0.277576i	$-0.0895310\pi$
$443$	11195.1	+	6463.50i	1.20067	+	0.693206i	0.239964	+	0.970782i	$0.422864\pi$
$444$	−3066.00	−	5310.47i	−0.327716	−	0.567621i
$445$		0			0
$446$	1400.00	−	2424.87i	0.148637	−	0.257446i
$447$			1407.00i			0.148879i
$448$	5431.71	+	6272.00i	0.572822	+	0.661438i
$449$	2826.00			0.297032			0.148516	−	0.988910i	$-0.452550\pi$
$449$	2826.00			0.297032			0.148516	+	0.988910i	$0.452550\pi$
$450$		0			0
$451$	875.000	+	1515.54i	0.0913573	+	0.158235i
$452$	−5327.79	+	3076.00i	−0.554421	+	0.320095i
$453$	−9814.67	−	5666.50i	−1.01795	−	0.587716i
$454$	4410.00			0.455884
$455$		0			0
$456$	−8232.00			−0.845392
$457$	7343.03	+	4239.50i	0.751625	+	0.433951i	0.826281	−	0.563259i	$-0.190453\pi$
$457$	7343.03	+	4239.50i	0.751625	+	0.433951i	−0.0746560	+	0.997209i	$0.523786\pi$
$458$	497.099	−	287.000i	0.0507159	−	0.0292808i
$459$	367.500	+	636.529i	0.0373713	+	0.0647290i
$460$		0			0
$461$	9338.00			0.943414			0.471707	−	0.881755i	$-0.343638\pi$
$461$	9338.00			0.943414			0.471707	+	0.881755i	$0.343638\pi$
$462$	424.352	−	1225.00i	0.0427330	−	0.123360i
$463$		−	4016.00i		−	0.403109i	−0.979477	−	0.201554i	$-0.935401\pi$
$463$		−	4016.00i		−	0.403109i	0.979477	−	0.201554i	$-0.0645993\pi$
$464$	−464.000	+	803.672i	−0.0464238	+	0.0804084i
$465$		0			0
$466$	−4587.00	−	7944.92i	−0.455984	−	0.789788i
$467$	−5074.04	−	2929.50i	−0.502781	−	0.290281i	0.227080	−	0.973876i	$-0.427082\pi$
$467$	−5074.04	−	2929.50i	−0.502781	−	0.290281i	−0.729861	+	0.683595i	$0.760415\pi$
$468$			1232.00i			0.121686i
$469$	7262.50	+	2515.80i	0.715034	+	0.247695i
$470$		0			0
$471$	−2376.50	+	4116.22i	−0.232491	+	0.402687i
$472$	−2182.38	+	1260.00i	−0.212823	+	0.122873i
$473$	536.936	−	310.000i	0.0521952	−	0.0301349i
$474$	−721.000	+	1248.81i	−0.0698663	+	0.121012i
$475$		0			0
$476$	294.000	+	1527.67i	0.0283098	+	0.147102i
$477$		−	6666.00i		−	0.639864i
$478$	−2889.06	−	1668.00i	−0.276449	−	0.159608i
$479$	3251.50	+	5631.76i	0.310156	+	0.537206i	0.978396	−	0.206740i	$-0.0662853\pi$
$479$	3251.50	+	5631.76i	0.310156	+	0.537206i	−0.668240	+	0.743946i	$0.732952\pi$
$480$		0			0
$481$	1533.00	−	2655.23i	0.145320	−	0.251701i
$482$			6818.00i			0.644297i
$483$	−13494.4	−	15582.0i	−1.27126	−	1.46792i
$484$	−5224.00			−0.490609
$485$		0			0
$486$	4928.00	+	8535.55i	0.459956	+	0.796667i
$487$	13898.8	−	8024.50i	1.29326	−	0.746663i	0.314028	−	0.949414i	$-0.398322\pi$
$487$	13898.8	−	8024.50i	1.29326	−	0.746663i	0.979230	+	0.202751i	$0.0649882\pi$
$488$	−8584.04	−	4956.00i	−0.796273	−	0.459729i
$489$	3269.00			0.302309
$490$		0			0
$491$	8864.00			0.814718			0.407359	−	0.913268i	$-0.366450\pi$
$491$	8864.00			0.814718			0.407359	+	0.913268i	$0.366450\pi$
$492$	−8487.05	−	4900.00i	−0.777695	−	0.449002i
$493$	−1054.82	+	609.000i	−0.0963624	+	0.0556348i
$494$	−686.000	−	1188.19i	−0.0624789	−	0.108217i
$495$		0			0
$496$	−2352.00			−0.212919
$497$	5237.72	+	6048.00i	0.472724	+	0.545855i
$498$			15288.0i			1.37565i
$499$	−5105.50	+	8842.99i	−0.458023	+	0.793319i	−0.998856	−	0.0478104i	$-0.984776\pi$
$499$	−5105.50	+	8842.99i	−0.458023	+	0.793319i	0.540833	+	0.841130i	$0.318109\pi$
$500$		0			0
$501$	−4214.00	−	7298.86i	−0.375784	−	0.650876i
$502$	−8244.56	−	4760.00i	−0.733014	−	0.423206i
$503$		−	1680.00i		−	0.148921i	−0.997224	−	0.0744607i	$-0.976276\pi$
$503$		−	1680.00i		−	0.148921i	0.997224	−	0.0744607i	$-0.0237235\pi$
$504$	1848.00	+	9602.49i	0.163326	+	0.848668i
$505$		0			0
$506$	−795.000	+	1376.98i	−0.0698460	+	0.120977i
$507$	12130.4	−	7003.50i	1.06259	−	0.613484i
$508$	−249.415	+	144.000i	−0.0217835	+	0.0125767i
$509$	−4728.50	+	8190.00i	−0.411762	+	0.713193i	−0.995083	−	0.0990489i	$-0.968420\pi$
$509$	−4728.50	+	8190.00i	−0.411762	+	0.713193i	0.583320	+	0.812242i	$0.301753\pi$
$510$		0			0
$511$	19477.5	+	6747.20i	1.68617	+	0.584107i
$512$			5632.00i			0.486136i
$513$	1485.23	+	857.500i	0.127826	+	0.0738003i
$514$	−805.000	−	1394.30i	−0.0690798	−	0.119650i
$515$		0			0
$516$	−1736.00	+	3006.84i	−0.148107	+	0.256529i
$517$			2625.00i			0.223302i
$518$	2655.23	−	7665.00i	0.225221	−	0.650156i
$519$	19747.0			1.67013
$520$		0			0
$521$	9040.50	+	15658.6i	0.760214	+	1.31673i	0.942740	+	0.333528i	$0.108239\pi$
$521$	9040.50	+	15658.6i	0.760214	+	1.31673i	−0.182526	+	0.983201i	$0.558427\pi$
$522$	−2210.10	+	1276.00i	−0.185313	+	0.106990i
$523$	−17647.0	−	10188.5i	−1.47543	−	0.851839i	−0.475813	−	0.879546i	$-0.657846\pi$
$523$	−17647.0	−	10188.5i	−1.47543	−	0.851839i	−0.999616	+	0.0277071i	$0.991179\pi$
$524$	8596.00			0.716637
$525$		0			0
$526$	−514.000			−0.0426073
$527$	−2673.42	−	1543.50i	−0.220979	−	0.127582i
$528$	484.974	−	280.000i	0.0399731	−	0.0230785i
$529$	6557.00	+	11357.1i	0.538917	+	0.933431i
$530$		0			0
$531$	−2310.00			−0.188786
$532$	2376.37	+	2744.00i	0.193663	+	0.223623i
$533$		−	4900.00i		−	0.398204i
$534$	−2303.00	+	3988.91i	−0.186630	+	0.323253i
$535$		0			0
$536$	4980.00	+	8625.61i	0.401312	+	0.695093i
$537$	−19720.3	−	11385.5i	−1.58472	−	0.914936i
$538$			7182.00i			0.575535i
$539$	−1592.50	+	636.529i	−0.127261	+	0.0508668i
$540$		0			0
$541$	3096.50	−	5363.30i	0.246079	−	0.426222i	−0.716355	−	0.697736i	$-0.754191\pi$
$541$	3096.50	−	5363.30i	0.246079	−	0.426222i	0.962435	+	0.271514i	$0.0875243\pi$
$542$	−2412.75	+	1393.00i	−0.191211	+	0.110396i
$543$	9590.37	−	5537.00i	0.757941	−	0.437597i
$544$	−1680.00	+	2909.85i	−0.132407	+	0.229336i
$545$		0			0
$546$	−2744.00	+	2376.37i	−0.215078	+	0.186263i
$547$			18464.0i			1.44326i	0.692279	+	0.721630i	$0.256607\pi$
$547$			18464.0i			1.44326i	−0.692279	+	0.721630i	$0.743393\pi$
$548$	−3897.11	−	2250.00i	−0.303789	−	0.175393i
$549$	−4543.00	−	7868.71i	−0.353170	−	0.611709i
$550$		0			0
$551$	−1421.00	+	2461.24i	−0.109867	+	0.190295i
$552$		−	26712.0i		−	2.05967i
$553$	1873.21	−	360.500i	0.144045	−	0.0277216i
$554$	−830.000			−0.0636522
$555$		0			0
$556$	504.000	+	872.954i	0.0384431	+	0.0665854i
$557$	8151.90	−	4706.50i	0.620120	−	0.358027i	−0.156796	−	0.987631i	$-0.550116\pi$
$557$	8151.90	−	4706.50i	0.620120	−	0.358027i	0.776916	+	0.629604i	$0.216783\pi$
$558$	−5601.45	−	3234.00i	−0.424961	−	0.245351i
$559$	−1736.00			−0.131351
$560$		0			0
$561$	735.000			0.0553150
$562$	−8580.58	−	4954.00i	−0.644039	−	0.371836i
$563$	2770.42	−	1599.50i	0.207387	−	0.119735i	−0.392709	−	0.919663i	$-0.628462\pi$
$563$	2770.42	−	1599.50i	0.207387	−	0.119735i	0.600097	+	0.799928i	$0.295129\pi$
$564$	−7350.00	−	12730.6i	−0.548743	−	0.950450i
$565$		0			0
$566$	−8554.00			−0.635250
$567$	5086.17	−	14682.5i	0.376718	−	1.08749i
$568$			10368.0i			0.765901i
$569$	10791.5	−	18691.4i	0.795085	−	1.37713i	−0.127701	−	0.991813i	$-0.540760\pi$
$569$	10791.5	−	18691.4i	0.795085	−	1.37713i	0.922785	−	0.385314i	$-0.125907\pi$
$570$		0			0
$571$	−10133.5	−	17551.7i	−0.742686	−	1.28637i	−0.951268	−	0.308365i	$-0.900218\pi$
$571$	−10133.5	−	17551.7i	−0.742686	−	1.28637i	0.208582	−	0.978005i	$-0.433115\pi$
$572$	−242.487	−	140.000i	−0.0177253	−	0.0102337i
$573$			17899.0i			1.30496i
$574$	−2450.00	−	12730.6i	−0.178155	−	0.925721i
$575$		0			0
$576$	−4928.00	+	8535.55i	−0.356481	+	0.617444i
$577$	−12081.9	+	6975.50i	−0.871710	+	0.503282i	−0.867916	−	0.496711i	$-0.834541\pi$
$577$	−12081.9	+	6975.50i	−0.871710	+	0.503282i	−0.00379418	+	0.999993i	$0.501208\pi$
$578$	−7745.73	+	4472.00i	−0.557405	+	0.321818i
$579$	−1389.50	+	2406.68i	−0.0997334	+	0.172743i
$580$		0			0
$581$	15288.0	−	13239.8i	1.09166	−	0.945403i
$582$			12348.0i			0.879452i
$583$	1312.03	+	757.500i	0.0932053	+	0.0538121i
$584$	13356.0	+	23133.3i	0.946362	+	1.63915i
$585$		0			0
$586$	−7742.00	+	13409.5i	−0.545766	+	0.945295i
$587$			20972.0i			1.47463i	0.675550	+	0.737314i	$0.263906\pi$
$587$			20972.0i			1.47463i	−0.675550	+	0.737314i	$0.736094\pi$
$588$	5940.93	−	7546.00i	0.416667	−	0.529238i
$589$	−7203.00			−0.503895
$590$		0			0
$591$	−10199.0	−	17665.2i	−0.709866	−	1.22952i
$592$	3034.55	−	1752.00i	0.210675	−	0.121633i
$593$	163.679	+	94.5000i	0.0113347	+	0.00654410i	0.505657	−	0.862735i	$-0.331250\pi$
$593$	163.679	+	94.5000i	0.0113347	+	0.00654410i	−0.494322	+	0.869279i	$0.664584\pi$
$594$	−350.000			−0.0241762
$595$		0			0
$596$	804.000			0.0552569
$597$	20241.6	+	11686.5i	1.38766	+	0.801167i
$598$	3855.55	−	2226.00i	0.263654	−	0.152221i
$599$	−5140.50	−	8903.61i	−0.350643	−	0.607331i	0.635719	−	0.771920i	$-0.280704\pi$
$599$	−5140.50	−	8903.61i	−0.350643	−	0.607331i	−0.986362	+	0.164589i	$0.947370\pi$
$600$		0			0
$601$	−6090.00			−0.413338			−0.206669	−	0.978411i	$-0.566262\pi$
$601$	−6090.00			−0.413338			−0.206669	+	0.978411i	$0.566262\pi$
$602$	−4510.26	+	868.000i	−0.305356	+	0.0587658i
$603$			9130.00i			0.616588i
$604$	−3238.00	+	5608.38i	−0.218133	+	0.377817i
$605$		0			0
$606$	−9653.00	−	16719.5i	−0.647073	−	1.12076i
$607$	4285.96	+	2474.50i	0.286593	+	0.165464i	0.636404	−	0.771356i	$-0.280421\pi$
$607$	4285.96	+	2474.50i	0.286593	+	0.165464i	−0.349812	+	0.936820i	$0.613754\pi$
$608$			7840.00i			0.522951i
$609$	7105.00	+	2461.24i	0.472757	+	0.163768i
$610$		0			0
$611$	3675.00	−	6365.29i	0.243330	−	0.421460i
$612$	−1600.41	+	924.000i	−0.105707	+	0.0610302i
$613$	−13680.6	+	7898.50i	−0.901394	+	0.520420i	−0.877652	−	0.479298i	$-0.840891\pi$
$613$	−13680.6	+	7898.50i	−0.901394	+	0.520420i	−0.0237416	+	0.999718i	$0.507558\pi$
$614$	−7364.00	+	12754.8i	−0.484018	+	0.838343i
$615$		0			0
$616$	−2100.00	−	727.461i	−0.137356	−	0.0475816i
$617$			9378.00i			0.611903i	0.952047	+	0.305951i	$0.0989745\pi$
$617$			9378.00i			0.611903i	−0.952047	+	0.305951i	$0.901025\pi$
$618$	8232.44	+	4753.00i	0.535853	+	0.309375i
$619$	−12176.5	−	21090.3i	−0.790654	−	1.36945i	−0.925562	−	0.378595i	$-0.876407\pi$
$619$	−12176.5	−	21090.3i	−0.790654	−	1.36945i	0.134908	−	0.990858i	$-0.456926\pi$
$620$		0			0
$621$	−2782.50	+	4819.43i	−0.179803	+	0.311429i
$622$		−	19950.0i		−	1.28605i
$623$	5983.37	−	1151.50i	0.384781	−	0.0740512i
$624$	−1568.00			−0.100593
$625$		0			0
$626$	4753.00	+	8232.44i	0.303463	+	0.525614i
$627$	1485.23	−	857.500i	0.0946005	−	0.0546176i
$628$	2352.12	+	1358.00i	0.149459	+	0.0862900i
$629$	4599.00			0.291533
$630$		0			0
$631$	−12640.0			−0.797449			−0.398725	−	0.917071i	$-0.630547\pi$
$631$	−12640.0			−0.797449			−0.398725	+	0.917071i	$0.630547\pi$
$632$	2140.81	+	1236.00i	0.134742	+	0.0777934i
$633$	10790.7	−	6230.00i	0.677553	−	0.391185i
$634$	−3477.00	−	6022.34i	−0.217806	−	0.377252i
$635$		0			0
$636$	−8484.00			−0.528950
$637$	4752.75	+	686.000i	0.295621	+	0.0426692i
$638$		−	580.000i		−	0.0359913i
$639$	−4752.00	+	8230.71i	−0.294188	+	0.509549i
$640$		0			0
$641$	520.500	+	901.532i	0.0320726	+	0.0555513i	0.881616	−	0.471967i	$-0.156456\pi$
$641$	520.500	+	901.532i	0.0320726	+	0.0555513i	−0.849544	+	0.527518i	$0.823123\pi$
$642$	5540.83	+	3199.00i	0.340622	+	0.196658i
$643$			9548.00i			0.585593i	0.956175	+	0.292797i	$0.0945859\pi$
$643$			9548.00i			0.585593i	−0.956175	+	0.292797i	$0.905414\pi$
$644$	−8904.00	+	7711.09i	−0.544824	+	0.471832i
$645$		0			0
$646$	1029.00	−	1782.28i	0.0626710	−	0.108549i
$647$	2806.79	−	1620.50i	0.170551	−	0.0984674i	−0.412295	−	0.911050i	$-0.635273\pi$
$647$	2806.79	−	1620.50i	0.170551	−	0.0984674i	0.582845	+	0.812583i	$0.301939\pi$
$648$	17438.3	−	10068.0i	1.05716	−	0.610352i
$649$	262.500	−	454.663i	0.0158768	−	0.0274994i
$650$		0			0
$651$	3601.50	+	18713.9i	0.216826	+	1.12666i
$652$		−	1868.00i		−	0.112203i
$653$	7666.92	+	4426.50i	0.459464	+	0.265272i	0.711819	−	0.702363i	$-0.247872\pi$
$653$	7666.92	+	4426.50i	0.459464	+	0.265272i	−0.252355	+	0.967635i	$0.581205\pi$
$654$	−7875.00	−	13639.9i	−0.470851	−	0.815539i
$655$		0			0
$656$	2800.00	−	4849.74i	0.166649	−	0.288644i
$657$			24486.0i			1.45402i
$658$	6365.29	−	18375.0i	0.377120	−	1.08865i
$659$	−7044.00			−0.416381			−0.208191	−	0.978088i	$-0.566757\pi$
$659$	−7044.00			−0.416381			−0.208191	+	0.978088i	$0.566757\pi$
$660$		0			0
$661$	6044.50	+	10469.4i	0.355679	+	0.616054i	0.987234	−	0.159277i	$-0.0509163\pi$
$661$	6044.50	+	10469.4i	0.355679	+	0.616054i	−0.631555	+	0.775331i	$0.717583\pi$
$662$	−5786.78	+	3341.00i	−0.339743	+	0.196151i
$663$	−1782.28	−	1029.00i	−0.104401	−	0.0602761i
$664$	26208.0			1.53173
$665$		0			0
$666$	9636.00			0.560642
$667$	−7986.49	−	4611.00i	−0.463625	−	0.267674i
$668$	−4170.78	+	2408.00i	−0.241575	+	0.139474i
$669$	−4900.00	−	8487.05i	−0.283176	−	0.490476i
$670$		0			0
$671$	2065.00			0.118805
$672$	20368.9	−	3920.00i	1.16927	−	0.225026i
$673$			982.000i			0.0562456i	0.999604	+	0.0281228i	$0.00895295\pi$
$673$			982.000i			0.0562456i	−0.999604	+	0.0281228i	$0.991047\pi$
$674$	7366.00	−	12758.3i	0.420961	−	0.729126i
$675$		0			0
$676$	−4002.00	−	6931.67i	−0.227697	−	0.394383i
$677$	−26425.0	−	15256.5i	−1.50014	−	0.866108i	−1.00000		0.000164659i	$-0.999948\pi$
$677$	−26425.0	−	15256.5i	−1.50014	−	0.866108i	−0.500143	−	0.865943i	$-0.666719\pi$
$678$		−	21532.0i		−	1.21966i
$679$	12348.0	−	10693.7i	0.697898	−	0.604397i
$680$		0			0
$681$	7717.50	−	13367.1i	0.434266	−	0.752171i
$682$	1273.06	−	735.000i	0.0714778	−	0.0412677i
$683$	9937.64	−	5737.50i	0.556740	−	0.321434i	−0.195096	−	0.980784i	$-0.562502\pi$
$683$	9937.64	−	5737.50i	0.556740	−	0.321434i	0.751836	+	0.659350i	$0.229169\pi$
$684$	−2156.00	+	3734.30i	−0.120522	+	0.208749i
$685$		0			0
$686$	12691.0	−	594.093i	0.706333	−	0.0330650i
$687$		−	2009.00i		−	0.111569i
$688$	−1718.19	−	992.000i	−0.0952116	−	0.0549704i
$689$	−2121.00	−	3673.68i	−0.117277	−	0.203129i
$690$		0			0
$691$	14157.5	−	24521.5i	0.779416	−	1.34999i	−0.152862	−	0.988248i	$-0.548849\pi$
$691$	14157.5	−	24521.5i	0.779416	−	1.34999i	0.932279	−	0.361741i	$-0.117818\pi$
$692$		−	11284.0i		−	0.619875i
$693$	−1333.68	−	1540.00i	−0.0731057	−	0.0844152i
$694$	−14830.0			−0.811151
$695$		0			0
$696$	4872.00	+	8438.55i	0.265334	+	0.459573i
$697$	6365.29	−	3675.00i	0.345915	−	0.199714i
$698$	6716.89	+	3878.00i	0.364238	+	0.210293i
$699$	−32109.0			−1.73744
$700$		0			0
$701$	10614.0			0.571876			0.285938	−	0.958248i	$-0.407695\pi$
$701$	10614.0			0.571876			0.285938	+	0.958248i	$0.407695\pi$
$702$	848.705	+	490.000i	0.0456301	+	0.0263445i
$703$	9293.32	−	5365.50i	0.498583	−	0.287857i
$704$	−1120.00	−	1939.90i	−0.0599596	−	0.103853i
$705$		0			0
$706$	2534.00			0.135083
$707$	−8359.74	+	24132.5i	−0.444697	+	1.28373i
$708$			2940.00i			0.156062i
$709$	5149.50	−	8919.20i	0.272769	−	0.472451i	−0.696801	−	0.717265i	$-0.745394\pi$
$709$	5149.50	−	8919.20i	0.272769	−	0.472451i	0.969570	+	0.244814i	$0.0787270\pi$
$710$		0			0
$711$	1133.00	+	1962.41i	0.0597621	+	0.103511i
$712$	6838.14	+	3948.00i	0.359930	+	0.207806i
$713$		−	23373.0i		−	1.22767i
$714$	−5145.00	−	1782.28i	−0.269673	−	0.0934176i
$715$		0			0
$716$	−6506.00	+	11268.7i	−0.339582	+	0.588173i
$717$	−10111.7	+	5838.00i	−0.526679	+	0.304078i
$718$	8114.66	−	4685.00i	0.421778	−	0.243513i
$719$	16264.5	−	28170.9i	0.843621	−	1.46119i	−0.0431924	−	0.999067i	$-0.513753\pi$
$719$	16264.5	−	28170.9i	0.843621	−	1.46119i	0.886813	−	0.462128i	$-0.152914\pi$
$720$		0			0
$721$	−2376.50	−	12348.7i	−0.122754	−	0.637847i
$722$			8916.00i			0.459583i
$723$	20666.0	+	11931.5i	1.06304	+	0.613744i
$724$	−3164.00	−	5480.21i	−0.162416	−	0.281313i
$725$		0			0
$726$	9142.00	−	15834.4i	0.467344	−	0.809463i
$727$		−	29456.0i		−	1.50270i	−0.659904	−	0.751350i	$-0.729403\pi$
$727$		−	29456.0i		−	1.50270i	0.659904	−	0.751350i	$-0.270597\pi$
$728$	4073.78	+	4704.00i	0.207396	+	0.239481i
$729$	11843.0			0.601687
$730$		0			0
$731$	−1302.00	−	2255.13i	−0.0658772	−	0.114103i
$732$	−10014.7	+	5782.00i	−0.505676	+	0.291952i
$733$	−24133.5	−	13933.5i	−1.21609	−	0.702109i	−0.252009	−	0.967725i	$-0.581091\pi$
$733$	−24133.5	−	13933.5i	−1.21609	−	0.702109i	−0.964079	+	0.265616i	$0.914425\pi$
$734$	9282.00			0.466764
$735$		0			0
$736$	−25440.0			−1.27409
$737$	−1797.00	−	1037.50i	−0.0898147	−	0.0518546i
$738$	13336.8	−	7700.00i	0.665222	−	0.384066i
$739$	9769.50	+	16921.3i	0.486302	+	0.842299i	0.999876	−	0.0157460i	$-0.00501231\pi$
$739$	9769.50	+	16921.3i	0.486302	+	0.842299i	−0.513574	+	0.858045i	$0.671679\pi$
$740$		0			0
$741$	−4802.00			−0.238065
$742$	−7347.36	−	8484.00i	−0.363518	−	0.419754i
$743$			1248.00i			0.0616214i	0.999525	+	0.0308107i	$0.00980890\pi$
$743$			1248.00i			0.0616214i	−0.999525	+	0.0308107i	$0.990191\pi$
$744$	−12348.0	+	21387.4i	−0.608467	+	1.05390i
$745$		0			0
$746$	8797.00	+	15236.9i	0.431744	+	0.747803i
$747$	20805.4	+	12012.0i	1.01905	+	0.588348i
$748$		−	420.000i		−	0.0205304i
$749$	−1599.50	−	8311.25i	−0.0780300	−	0.405456i
$750$		0			0
$751$	−14046.5	+	24329.3i	−0.682509	+	1.18214i	0.291704	+	0.956509i	$0.405778\pi$
$751$	−14046.5	+	24329.3i	−0.682509	+	1.18214i	−0.974213	+	0.225631i	$0.927556\pi$
$752$	7274.61	−	4200.00i	0.352763	−	0.203668i
$753$	−28856.0	+	16660.0i	−1.39651	+	0.806274i
$754$	−812.000	+	1406.43i	−0.0392192	+	0.0679297i
$755$		0			0
$756$	−2450.00	−	848.705i	−0.117865	−	0.0408295i
$757$		−	35954.0i		−	1.72625i	−0.504991	−	0.863124i	$-0.668504\pi$
$757$		−	35954.0i		−	1.72625i	0.504991	−	0.863124i	$-0.331496\pi$
$758$	−23694.5	−	13680.0i	−1.13538	−	0.655514i
$759$	2782.50	+	4819.43i	0.133068	+	0.230480i
$760$		0			0
$761$	430.500	−	745.648i	0.0205067	−	0.0355187i	−0.855590	−	0.517654i	$-0.826805\pi$
$761$	430.500	−	745.648i	0.0205067	−	0.0355187i	0.876097	+	0.482136i	$0.160139\pi$
$762$		−	1008.00i		−	0.0479212i
$763$	−6819.95	+	19687.5i	−0.323589	+	0.934122i
$764$	10228.0			0.484340
$765$		0			0
$766$	−9765.00	−	16913.5i	−0.460605	−	0.797792i
$767$	−1273.06	+	735.000i	−0.0599315	+	0.0346014i
$768$	26382.6	+	15232.0i	1.23958	+	0.715674i
$769$	−24710.0			−1.15873			−0.579366	−	0.815067i	$-0.696700\pi$
$769$	−24710.0			−1.15873			−0.579366	+	0.815067i	$0.696700\pi$
$770$		0			0
$771$	−5635.00			−0.263216
$772$	1375.25	+	794.000i	0.0641143	+	0.0370164i
$773$	14288.6	−	8249.50i	0.664843	−	0.383847i	−0.129277	−	0.991609i	$-0.541266\pi$
$773$	14288.6	−	8249.50i	0.664843	−	0.383847i	0.794120	+	0.607761i	$0.207932\pi$
$774$	−2728.00	−	4725.03i	−0.126687	−	0.219429i
$775$		0			0
$776$	21168.0			0.979236
$777$	−18586.6	−	21462.0i	−0.858162	−	0.990920i
$778$			3462.00i			0.159536i
$779$	8575.00	−	14852.3i	0.394392	−	0.683107i
$780$		0			0
$781$	−1080.00	−	1870.61i	−0.0494820	−	0.0857053i
$782$	5783.32	+	3339.00i	0.264464	+	0.152688i
$783$		−	2030.00i		−	0.0926517i
$784$	4312.00	+	3394.82i	0.196429	+	0.154647i
$785$		0			0
$786$	−15043.0	+	26055.2i	−0.682654	+	1.18239i
$787$	−14264.3	+	8235.50i	−0.646083	+	0.373016i	−0.786954	−	0.617012i	$-0.788343\pi$
$787$	−14264.3	+	8235.50i	−0.646083	+	0.373016i	0.140871	+	0.990028i	$0.455010\pi$
$788$	−10094.4	+	5828.00i	−0.456342	+	0.263469i
$789$	−899.500	+	1557.98i	−0.0405869	+	0.0702985i
$790$		0			0
$791$	−21532.0	+	18647.3i	−0.967876	+	0.838205i
$792$		−	2640.00i		−	0.118445i
$793$	−5007.36	−	2891.00i	−0.224233	−	0.129461i
$794$	10983.0	+	19023.1i	0.490897	+	0.850258i
$795$		0			0
$796$	6678.00	−	11566.6i	0.297356	−	0.515036i
$797$			36470.0i			1.62087i	0.585828	+	0.810435i	$0.300769\pi$
$797$			36470.0i			1.62087i	−0.585828	+	0.810435i	$0.699231\pi$
$798$	−12476.0	+	2401.00i	−0.553439	+	0.106509i
$799$	11025.0			0.488156
$800$		0			0
$801$	3619.00	+	6268.29i	0.159639	+	0.276503i
$802$	−11436.7	+	6603.00i	−0.503547	+	0.290723i
$803$	−4819.43	−	2782.50i	−0.211798	−	0.122282i
$804$	11620.0			0.509709
$805$		0			0
$806$	−4116.00			−0.179876
$807$	21769.3	+	12568.5i	0.949585	+	0.548243i
$808$	−28662.0	+	16548.0i	−1.24793	+	0.720491i
$809$	17875.5	+	30961.3i	0.776847	+	1.34554i	0.933751	+	0.357924i	$0.116515\pi$
$809$	17875.5	+	30961.3i	0.776847	+	1.34554i	−0.156904	+	0.987614i	$0.550151\pi$
$810$		0			0
$811$	−16492.0			−0.714072			−0.357036	−	0.934091i	$-0.616213\pi$
$811$	−16492.0			−0.714072			−0.357036	+	0.934091i	$0.616213\pi$
$812$	1406.43	−	4060.00i	0.0607831	−	0.175466i
$813$			9751.00i			0.420643i
$814$	−1095.00	+	1896.60i	−0.0471495	+	0.0816654i
$815$		0			0
$816$	−1176.00	−	2036.89i	−0.0504513	−	0.0873842i
$817$	−5261.97	−	3038.00i	−0.225328	−	0.130093i
$818$			21910.0i			0.936510i
$819$	1078.00	+	5601.45i	0.0459931	+	0.238987i
$820$		0			0
$821$	20736.5	−	35916.7i	0.881497	−	1.52680i	0.0318198	−	0.999494i	$-0.489870\pi$
$821$	20736.5	−	35916.7i	0.881497	−	1.52680i	0.849677	−	0.527304i	$-0.176797\pi$
$822$	13639.9	−	7875.00i	0.578767	−	0.334151i
$823$	−21706.9	+	12532.5i	−0.919387	+	0.530809i	−0.883440	−	0.468545i	$-0.844778\pi$
$823$	−21706.9	+	12532.5i	−0.919387	+	0.530809i	−0.0359479	+	0.999354i	$0.511445\pi$
$824$	8148.00	−	14112.7i	0.344477	−	0.596652i
$825$		0			0
$826$	−2940.00	+	2546.11i	−0.123845	+	0.107253i
$827$		−	9732.00i		−	0.409208i	−0.978845	−	0.204604i	$-0.934409\pi$
$827$		−	9732.00i		−	0.409208i	0.978845	−	0.204604i	$-0.0655906\pi$
$828$	−12117.4	−	6996.00i	−0.508587	−	0.293633i
$829$	13877.5	+	24036.5i	0.581406	+	1.00702i	0.995313	+	0.0967055i	$0.0308305\pi$
$829$	13877.5	+	24036.5i	0.581406	+	1.00702i	−0.413907	+	0.910319i	$0.635836\pi$
$830$		0			0
$831$	−1452.50	+	2515.80i	−0.0606338	+	0.105021i
$832$			6272.00i			0.261349i
$833$	2673.42	+	6688.50i	0.111199	+	0.278203i
$834$	−3528.00			−0.146480
$835$		0			0
$836$	−490.000	−	848.705i	−0.0202715	−	0.0351113i
$837$	4455.70	−	2572.50i	0.184004	−	0.106235i
$838$	−11493.9	−	6636.00i	−0.473806	−	0.273552i
$839$	−21112.0			−0.868733			−0.434367	−	0.900736i	$-0.643028\pi$
$839$	−21112.0			−0.868733			−0.434367	+	0.900736i	$0.643028\pi$
$840$		0			0
$841$	−21025.0			−0.862069
$842$	−28804.0	−	16630.0i	−1.17892	−	0.680650i
$843$	−30032.0	+	17339.0i	−1.22700	+	0.708407i
$844$	−3560.00	−	6166.10i	−0.145190	−	0.251476i
$845$		0			0
$846$	23100.0			0.938764
$847$	−23751.6	+	4571.00i	−0.963536	+	0.185433i
$848$		−	4848.00i		−	0.196322i
$849$	−14969.5	+	25927.9i	−0.605126	+	1.04811i
$850$		0			0
$851$	17410.5	+	30155.9i	0.701321	+	1.21472i
$852$	10475.4	+	6048.00i	0.421224	+	0.243194i
$853$		−	21238.0i		−	0.852492i	−0.904607	−	0.426246i	$-0.859836\pi$
$853$		−	21238.0i		−	0.852492i	0.904607	−	0.426246i	$-0.140164\pi$
$854$	−14455.0	−	5007.36i	−0.579204	−	0.200642i
$855$		0			0
$856$	5484.00	−	9498.57i	0.218971	−	0.379269i
$857$	30838.3	−	17804.5i	1.22919	−	0.709673i	0.262330	−	0.964978i	$-0.415509\pi$
$857$	30838.3	−	17804.5i	1.22919	−	0.709673i	0.966861	+	0.255305i	$0.0821758\pi$
$858$	848.705	−	490.000i	0.0337696	−	0.0194969i
$859$	1088.50	−	1885.34i	0.0432353	−	0.0748858i	−0.843598	−	0.536975i	$-0.819567\pi$
$859$	1088.50	−	1885.34i	0.0432353	−	0.0748858i	0.886833	+	0.462090i	$0.152900\pi$
$860$		0			0
$861$	−42875.0	−	14852.3i	−1.69707	−	0.587882i
$862$		−	9846.00i		−	0.389044i
$863$	27926.7	+	16123.5i	1.10155	+	0.635980i	0.936627	−	0.350327i	$-0.113930\pi$
$863$	27926.7	+	16123.5i	1.10155	+	0.635980i	0.164921	+	0.986307i	$0.447263\pi$
$864$	−2800.00	−	4849.74i	−0.110252	−	0.190962i
$865$		0			0
$866$	−8974.00	+	15543.4i	−0.352135	+	0.609916i
$867$			31304.0i			1.22623i
$868$	10693.7	−	2058.00i	0.418165	−	0.0804759i
$869$	−515.000			−0.0201038
$870$		0			0
$871$	2905.00	+	5031.61i	0.113011	+	0.195740i
$872$	−23382.7	+	13500.0i	−0.908071	+	0.524275i
$873$	16804.4	+	9702.00i	0.651479	+	0.376132i
$874$	15582.0			0.603054
$875$		0			0
$876$	31164.0			1.20198
$877$	23929.1	+	13815.5i	0.921357	+	0.531946i	0.884068	−	0.467359i	$-0.154794\pi$
$877$	23929.1	+	13815.5i	0.921357	+	0.531946i	0.0372891	+	0.999305i	$0.488128\pi$
$878$	−7238.24	+	4179.00i	−0.278222	+	0.160631i
$879$	27097.0	+	46933.4i	1.03977	+	1.80094i
$880$		0			0
$881$	24402.0			0.933172			0.466586	−	0.884476i	$-0.345484\pi$
$881$	24402.0			0.933172			0.466586	+	0.884476i	$0.345484\pi$
$882$	5601.45	+	14014.0i	0.213844	+	0.535007i
$883$		−	19612.0i		−	0.747448i	−0.927540	−	0.373724i	$-0.878081\pi$
$883$		−	19612.0i		−	0.747448i	0.927540	−	0.373724i	$-0.121919\pi$
$884$	−588.000	+	1018.45i	−0.0223717	+	0.0387489i
$885$		0			0
$886$	12927.0	+	22390.2i	0.490170	+	0.849000i
$887$	1958.08	+	1130.50i	0.0741218	+	0.0427942i	0.536603	−	0.843835i	$-0.319707\pi$
$887$	1958.08	+	1130.50i	0.0741218	+	0.0427942i	−0.462481	+	0.886629i	$0.653041\pi$
$888$		−	36792.0i		−	1.39038i
$889$	−1008.00	+	872.954i	−0.0380284	+	0.0329335i
$890$		0			0
$891$	−2097.50	+	3632.98i	−0.0788652	+	0.136599i
$892$	−4849.74	+	2800.00i	−0.182042	+	0.105102i
$893$	22278.5	−	12862.5i	0.834851	−	0.482001i
$894$	−1407.00	+	2437.00i	−0.0526366	+	0.0911693i
$895$		0			0
$896$	−1344.00	−	6983.63i	−0.0501115	−	0.260387i
$897$		−	15582.0i		−	0.580009i
$898$	4894.78	+	2826.00i	0.181894	+	0.105017i
$899$	4263.00	+	7383.73i	0.158152	+	0.273928i
$900$		0			0
$901$	3181.50	−	5510.52i	0.117637	−	0.203754i
$902$			3500.00i			0.129199i
$903$	−5261.97	+	15190.0i	−0.193917	+	0.559791i
$904$	−36912.0			−1.35805
$905$		0			0
$906$	−11333.0	−	19629.3i	−0.415578	−	0.719802i
$907$	20640.0	−	11916.5i	0.755611	−	0.436252i	−0.0721066	−	0.997397i	$-0.522972\pi$
$907$	20640.0	−	11916.5i	0.755611	−	0.436252i	0.827718	+	0.561145i	$0.189639\pi$
$908$	−7638.34	−	4410.00i	−0.279171	−	0.161180i
$909$	−30338.0			−1.10698
$910$		0			0
$911$	31824.0			1.15738			0.578692	−	0.815546i	$-0.303563\pi$
$911$	31824.0			1.15738			0.578692	+	0.815546i	$0.303563\pi$
$912$	−4752.75	−	2744.00i	−0.172565	−	0.0996304i
$913$	−4728.50	+	2730.00i	−0.171402	+	0.0989593i
$914$	8479.00	+	14686.1i	0.306849	+	0.531479i
$915$		0			0
$916$	−1148.00			−0.0414094
$917$	39082.9	−	7521.50i	1.40745	−	0.270863i
$918$			1470.00i			0.0528510i
$919$	−8409.50	+	14565.7i	−0.301854	+	0.522826i	−0.976556	−	0.215264i	$-0.930939\pi$
$919$	−8409.50	+	14565.7i	−0.301854	+	0.522826i	0.674702	+	0.738090i	$0.264272\pi$
$920$		0			0
$921$	25774.0	+	44641.9i	0.922130	+	1.59718i
$922$	16173.9	+	9338.00i	0.577721	+	0.333547i
$923$			6048.00i			0.215680i
$924$	−1960.00	+	1697.41i	−0.0697828	+	0.0604336i
$925$		0			0
$926$	4016.00	−	6955.92i	0.142520	−	0.246853i
$927$	12936.7	−	7469.00i	0.458357	−	0.264632i
$928$	8036.72	−	4640.00i	0.284287	−	0.164133i
$929$	899.500	−	1557.98i	0.0317671	−	0.0550222i	−0.849705	−	0.527259i	$-0.823220\pi$
$929$	899.500	−	1557.98i	0.0317671	−	0.0550222i	0.881472	+	0.472237i	$0.156553\pi$
$930$		0			0
$931$	13205.5	+	10396.6i	0.464869	+	0.365989i
$932$			18348.0i			0.644859i
$933$	−60470.2	−	34912.5i	−2.12187	−	1.22506i
$934$	−5859.00	−	10148.1i	−0.205259	−	0.355520i
$935$		0			0
$936$	−3696.00	+	6401.66i	−0.129068	+	0.223552i
$937$		−	14154.0i		−	0.493480i	−0.969082	−	0.246740i	$-0.920641\pi$
$937$		−	14154.0i		−	0.493480i	0.969082	−	0.246740i	$-0.0793594\pi$
$938$	10063.2	+	11620.0i	0.350294	+	0.404484i
$939$	33271.0			1.15629
$940$		0			0
$941$	−6023.50	−	10433.0i	−0.208672	−	0.361431i	0.742624	−	0.669708i	$-0.233581\pi$
$941$	−6023.50	−	10433.0i	−0.208672	−	0.361431i	−0.951296	+	0.308277i	$0.900247\pi$
$942$	−8232.44	+	4753.00i	−0.284742	+	0.164396i
$943$	48194.3	+	27825.0i	1.66429	+	0.960877i
$944$	−1680.00			−0.0579230
$945$		0			0
$946$	1240.00			0.0426172
$947$	−21112.8	−	12189.5i	−0.724472	−	0.418274i	0.0919245	−	0.995766i	$-0.470698\pi$
$947$	−21112.8	−	12189.5i	−0.724472	−	0.418274i	−0.816396	+	0.577492i	$0.804031\pi$
$948$	2497.62	−	1442.00i	0.0855684	−	0.0494029i
$949$	7791.00	+	13494.4i	0.266498	+	0.461588i
$950$		0			0
$951$	−24339.0			−0.829912
$952$	−3055.34	+	8820.00i	−0.104017	+	0.300271i
$953$		−	52330.0i		−	1.77874i	−0.457192	−	0.889368i	$-0.651145\pi$
$953$		−	52330.0i		−	1.77874i	0.457192	−	0.889368i	$-0.348855\pi$
$954$	6666.00	−	11545.9i	0.226226	−	0.391835i
$955$		0			0
$956$	3336.00	+	5778.12i	0.112860	+	0.195479i
$957$	−1758.03	−	1015.00i	−0.0593825	−	0.0342845i
$958$			13006.0i			0.438627i
$959$	−19687.5	−	6819.95i	−0.662922	−	0.229643i
$960$		0			0
$961$	4091.00	−	7085.82i	0.137323	−	0.237851i
$962$	5310.47	−	3066.00i	0.177980	−	0.102757i
$963$	8707.02	−	5027.00i	0.291360	−	0.168217i
$964$	6818.00	−	11809.1i	0.227794	−	0.394550i
$965$		0			0
$966$	−7791.00	−	40483.2i	−0.259494	−	1.34837i
$967$			12416.0i			0.412897i	0.978457	+	0.206449i	$0.0661906\pi$
$967$			12416.0i			0.412897i	−0.978457	+	0.206449i	$0.933809\pi$
$968$	−27144.7	−	15672.0i	−0.901305	−	0.520369i
$969$	−3601.50	−	6237.98i	−0.119398	−	0.206804i
$970$		0			0
$971$	−18406.5	+	31881.0i	−0.608334	+	1.05367i	0.383181	+	0.923673i	$0.374829\pi$
$971$	−18406.5	+	31881.0i	−0.608334	+	1.05367i	−0.991515	+	0.129993i	$0.958505\pi$
$972$		−	19712.0i		−	0.650476i
$973$	3055.34	+	3528.00i	0.100668	+	0.116241i
$974$	32098.0			1.05594
$975$		0			0
$976$	−3304.00	−	5722.70i	−0.108359	−	0.187683i
$977$	−30306.6	+	17497.5i	−0.992418	+	0.572973i	−0.905996	−	0.423286i	$-0.860877\pi$
$977$	−30306.6	+	17497.5i	−0.992418	+	0.572973i	−0.0864221	+	0.996259i	$0.527543\pi$
$978$	5662.07	+	3269.00i	0.185126	+	0.106883i
$979$	−1645.00			−0.0537022
$980$		0			0
$981$	−24750.0			−0.805511
$982$	15352.9	+	8864.00i	0.498911	+	0.288046i
$983$	−12385.0	+	7150.50i	−0.401853	+	0.232010i	−0.687283	−	0.726390i	$-0.741197\pi$
$983$	−12385.0	+	7150.50i	−0.401853	+	0.232010i	0.285430	+	0.958399i	$0.407863\pi$
$984$	−29400.0	−	50922.3i	−0.952477	−	1.64974i
$985$		0			0
$986$	−2436.00			−0.0786796
$987$	−44557.0	−	51450.0i	−1.43695	−	1.65924i
$988$			2744.00i			0.0883586i
$989$	9858.00	−	17074.6i	0.316953	−	0.548978i
$990$		0			0
$991$	1332.50	+	2307.96i	0.0427127	+	0.0739805i	0.886591	−	0.462553i	$-0.153067\pi$
$991$	1332.50	+	2307.96i	0.0427127	+	0.0739805i	−0.843879	+	0.536534i	$0.819733\pi$
$992$	20368.9	+	11760.0i	0.651929	+	0.376392i
$993$			23387.0i			0.747396i
$994$	3024.00	+	15713.2i	0.0964944	+	0.501400i
$995$		0			0
$996$	15288.0	−	26479.6i	0.486364	−	0.842408i
$997$	−21538.9	+	12435.5i	−0.684197	+	0.395021i	−0.801434	−	0.598083i	$-0.795929\pi$
$997$	−21538.9	+	12435.5i	−0.684197	+	0.395021i	0.117237	+	0.993104i	$0.462596\pi$
$998$	−17686.0	+	10211.0i	−0.560962	+	0.323871i
$999$	−3832.50	+	6638.08i	−0.121376	+	0.210230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.k.a.149.2		4
5.2	odd	4		7.4.c.a.2.1	✓	2
5.3	odd	4		175.4.e.a.51.1		2
5.4	even	2	inner	175.4.k.a.149.1		4
7.4	even	3	inner	175.4.k.a.74.1		4
15.2	even	4		63.4.e.b.37.1		2
20.7	even	4		112.4.i.c.65.1		2
35.2	odd	12		49.4.a.d.1.1		1
35.4	even	6	inner	175.4.k.a.74.2		4
35.12	even	12		49.4.a.c.1.1		1
35.17	even	12		49.4.c.a.18.1		2
35.18	odd	12		175.4.e.a.151.1		2
35.23	odd	12		1225.4.a.c.1.1		1
35.27	even	4		49.4.c.a.30.1		2
35.32	odd	12		7.4.c.a.4.1	yes	2
35.33	even	12		1225.4.a.d.1.1		1
40.27	even	4		448.4.i.a.65.1		2
40.37	odd	4		448.4.i.f.65.1		2
105.2	even	12		441.4.a.d.1.1		1
105.17	odd	12		441.4.e.k.361.1		2
105.32	even	12		63.4.e.b.46.1		2
105.47	odd	12		441.4.a.e.1.1		1
105.62	odd	4		441.4.e.k.226.1		2
140.47	odd	12		784.4.a.r.1.1		1
140.67	even	12		112.4.i.c.81.1		2
140.107	even	12		784.4.a.b.1.1		1
280.67	even	12		448.4.i.a.193.1		2
280.277	odd	12		448.4.i.f.193.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.4.c.a.2.1	✓	2	5.2	odd	4
7.4.c.a.4.1	yes	2	35.32	odd	12
49.4.a.c.1.1		1	35.12	even	12
49.4.a.d.1.1		1	35.2	odd	12
49.4.c.a.18.1		2	35.17	even	12
49.4.c.a.30.1		2	35.27	even	4
63.4.e.b.37.1		2	15.2	even	4
63.4.e.b.46.1		2	105.32	even	12
112.4.i.c.65.1		2	20.7	even	4
112.4.i.c.81.1		2	140.67	even	12
175.4.e.a.51.1		2	5.3	odd	4
175.4.e.a.151.1		2	35.18	odd	12
175.4.k.a.74.1		4	7.4	even	3	inner
175.4.k.a.74.2		4	35.4	even	6	inner
175.4.k.a.149.1		4	5.4	even	2	inner
175.4.k.a.149.2		4	1.1	even	1	trivial
441.4.a.d.1.1		1	105.2	even	12
441.4.a.e.1.1		1	105.47	odd	12
441.4.e.k.226.1		2	105.62	odd	4
441.4.e.k.361.1		2	105.17	odd	12
448.4.i.a.65.1		2	40.27	even	4
448.4.i.a.193.1		2	280.67	even	12
448.4.i.f.65.1		2	40.37	odd	4
448.4.i.f.193.1		2	280.277	odd	12
784.4.a.b.1.1		1	140.107	even	12
784.4.a.r.1.1		1	140.47	odd	12
1225.4.a.c.1.1		1	35.23	odd	12
1225.4.a.d.1.1		1	35.33	even	12

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 + 1.00000i) q^{2} +(6.06218 - 3.50000i) q^{3} +(-2.00000 - 3.46410i) q^{4} +14.0000 q^{6} +(-12.1244 - 14.0000i) q^{7} -24.0000i q^{8} +(11.0000 - 19.0526i) q^{9} +O(q^{10})\)	\(q+(1.73205 + 1.00000i) q^{2} +(6.06218 - 3.50000i) q^{3} +(-2.00000 - 3.46410i) q^{4} +14.0000 q^{6} +(-12.1244 - 14.0000i) q^{7} -24.0000i q^{8} +(11.0000 - 19.0526i) q^{9} +(2.50000 + 4.33013i) q^{11} +(-24.2487 - 14.0000i) q^{12} -14.0000i q^{13} +(-7.00000 - 36.3731i) q^{14} +(8.00000 - 13.8564i) q^{16} +(18.1865 - 10.5000i) q^{17} +(38.1051 - 22.0000i) q^{18} +(24.5000 - 42.4352i) q^{19} +(-122.500 - 42.4352i) q^{21} +10.0000i q^{22} +(137.698 + 79.5000i) q^{23} +(-84.0000 - 145.492i) q^{24} +(14.0000 - 24.2487i) q^{26} +35.0000i q^{27} +(-24.2487 + 70.0000i) q^{28} -58.0000 q^{29} +(-73.5000 - 127.306i) q^{31} +(-138.564 + 80.0000i) q^{32} +(30.3109 + 17.5000i) q^{33} +42.0000 q^{34} -88.0000 q^{36} +(189.660 + 109.500i) q^{37} +(84.8705 - 49.0000i) q^{38} +(-49.0000 - 84.8705i) q^{39} +350.000 q^{41} +(-169.741 - 196.000i) q^{42} -124.000i q^{43} +(10.0000 - 17.3205i) q^{44} +(159.000 + 275.396i) q^{46} +(454.663 + 262.500i) q^{47} -112.000i q^{48} +(-49.0000 + 339.482i) q^{49} +(73.5000 - 127.306i) q^{51} +(-48.4974 + 28.0000i) q^{52} +(262.406 - 151.500i) q^{53} +(-35.0000 + 60.6218i) q^{54} +(-336.000 + 290.985i) q^{56} -343.000i q^{57} +(-100.459 - 58.0000i) q^{58} +(-52.5000 - 90.9327i) q^{59} +(206.500 - 357.668i) q^{61} -294.000i q^{62} +(-400.104 + 77.0000i) q^{63} -448.000 q^{64} +(35.0000 + 60.6218i) q^{66} +(-359.401 + 207.500i) q^{67} +(-72.7461 - 42.0000i) q^{68} +1113.00 q^{69} -432.000 q^{71} +(-457.261 - 264.000i) q^{72} +(-963.886 + 556.500i) q^{73} +(219.000 + 379.319i) q^{74} -196.000 q^{76} +(30.3109 - 87.5000i) q^{77} -196.000i q^{78} +(-51.5000 + 89.2006i) q^{79} +(419.500 + 726.595i) q^{81} +(606.218 + 350.000i) q^{82} +1092.00i q^{83} +(98.0000 + 509.223i) q^{84} +(124.000 - 214.774i) q^{86} +(-351.606 + 203.000i) q^{87} +(103.923 - 60.0000i) q^{88} +(-164.500 + 284.922i) q^{89} +(-196.000 + 169.741i) q^{91} -636.000i q^{92} +(-891.140 - 514.500i) q^{93} +(525.000 + 909.327i) q^{94} +(-560.000 + 969.948i) q^{96} +882.000i q^{97} +(-424.352 + 539.000i) q^{98} +110.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{4} + 56 q^{6} + 44 q^{9}+O(q^{10}) \) 4 * q - 8 * q^4 + 56 * q^6 + 44 * q^9	\( 4 q - 8 q^{4} + 56 q^{6} + 44 q^{9} + 10 q^{11} - 28 q^{14} + 32 q^{16} + 98 q^{19} - 490 q^{21} - 336 q^{24} + 56 q^{26} - 232 q^{29} - 294 q^{31} + 168 q^{34} - 352 q^{36} - 196 q^{39} + 1400 q^{41} + 40 q^{44} + 636 q^{46} - 196 q^{49} + 294 q^{51} - 140 q^{54} - 1344 q^{56} - 210 q^{59} + 826 q^{61} - 1792 q^{64} + 140 q^{66} + 4452 q^{69} - 1728 q^{71} + 876 q^{74} - 784 q^{76} - 206 q^{79} + 1678 q^{81} + 392 q^{84} + 496 q^{86} - 658 q^{89} - 784 q^{91} + 2100 q^{94} - 2240 q^{96} + 440 q^{99}+O(q^{100}) \) 4 * q - 8 * q^4 + 56 * q^6 + 44 * q^9 + 10 * q^11 - 28 * q^14 + 32 * q^16 + 98 * q^19 - 490 * q^21 - 336 * q^24 + 56 * q^26 - 232 * q^29 - 294 * q^31 + 168 * q^34 - 352 * q^36 - 196 * q^39 + 1400 * q^41 + 40 * q^44 + 636 * q^46 - 196 * q^49 + 294 * q^51 - 140 * q^54 - 1344 * q^56 - 210 * q^59 + 826 * q^61 - 1792 * q^64 + 140 * q^66 + 4452 * q^69 - 1728 * q^71 + 876 * q^74 - 784 * q^76 - 206 * q^79 + 1678 * q^81 + 392 * q^84 + 496 * q^86 - 658 * q^89 - 784 * q^91 + 2100 * q^94 - 2240 * q^96 + 440 * q^99

Introduction

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