LMFDB - Embedded newform 175.4.k.e.149.4

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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.4
Character	$\chi$	$=$	175.149
Dual form			175.4.k.e.74.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.52961 - 1.46047i) q^{2} +(-8.70206 + 5.02414i) q^{3} +(0.265967 + 0.460668i) q^{4} +29.3505 q^{6} +(-2.32782 - 18.3734i) q^{7} +21.8138i q^{8} +(36.9839 - 64.0580i) q^{9} +(-7.79680 - 13.5045i) q^{11} +(-4.62892 - 2.67251i) q^{12} -63.9123i q^{13} +(-20.9454 + 49.8773i) q^{14} +(33.9863 - 58.8659i) q^{16} +(-9.16053 + 5.28883i) q^{17} +(-187.110 + 108.028i) q^{18} +(-19.3864 + 33.5782i) q^{19} +(112.567 + 148.191i) q^{21} +45.5481i q^{22} +(20.8909 + 12.0614i) q^{23} +(-109.596 - 189.825i) q^{24} +(-93.3422 + 161.673i) q^{26} +471.945i q^{27} +(7.84491 - 5.95906i) q^{28} -226.731 q^{29} +(71.5651 + 123.954i) q^{31} +(-20.8136 + 12.0168i) q^{32} +(135.697 + 78.3444i) q^{33} +30.8968 q^{34} +39.3460 q^{36} +(-247.036 - 142.626i) q^{37} +(98.0800 - 56.6265i) q^{38} +(321.104 + 556.168i) q^{39} +32.0457 q^{41} +(-68.3225 - 539.268i) q^{42} -235.711i q^{43} +(4.14738 - 7.18348i) q^{44} +(-35.2306 - 61.0212i) q^{46} +(124.964 + 72.1481i) q^{47} +683.006i q^{48} +(-332.163 + 85.5397i) q^{49} +(53.1436 - 92.0475i) q^{51} +(29.4423 - 16.9985i) q^{52} +(275.900 - 159.291i) q^{53} +(689.263 - 1193.84i) q^{54} +(400.794 - 50.7786i) q^{56} -389.599i q^{57} +(573.542 + 331.135i) q^{58} +(224.161 + 388.258i) q^{59} +(-83.3473 + 144.362i) q^{61} -418.076i q^{62} +(-1263.05 - 530.404i) q^{63} -473.580 q^{64} +(-228.840 - 396.362i) q^{66} +(-641.761 + 370.521i) q^{67} +(-4.87279 - 2.81331i) q^{68} -242.392 q^{69} -373.652 q^{71} +(1397.35 + 806.760i) q^{72} +(205.520 - 118.657i) q^{73} +(416.604 + 721.580i) q^{74} -20.6245 q^{76} +(-229.973 + 174.690i) q^{77} -1875.86i q^{78} +(-232.695 + 403.040i) q^{79} +(-1372.55 - 2377.33i) q^{81} +(-81.0631 - 46.8018i) q^{82} +691.289i q^{83} +(-38.3277 + 91.2700i) q^{84} +(-344.249 + 596.257i) q^{86} +(1973.03 - 1139.13i) q^{87} +(294.584 - 170.078i) q^{88} +(506.590 - 877.440i) q^{89} +(-1174.28 + 148.776i) q^{91} +12.8317i q^{92} +(-1245.53 - 719.105i) q^{93} +(-210.741 - 365.014i) q^{94} +(120.748 - 209.141i) q^{96} +1151.67i q^{97} +(965.172 + 268.732i) q^{98} -1153.42 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 54 q^{4} + 16 q^{6} + 84 q^{9} + 130 q^{14} - 382 q^{16} - 84 q^{19} + 604 q^{21} - 584 q^{24} - 46 q^{26} - 1152 q^{29} - 36 q^{31} + 1952 q^{34} - 2844 q^{36} + 44 q^{39} + 672 q^{41} - 1760 q^{44}+ \cdots - 16344 q^{99}+O(q^{100}) $ 32 * q + 54 * q^4 + 16 * q^6 + 84 * q^9 + 130 * q^14 - 382 * q^16 - 84 * q^19 + 604 * q^21 - 584 * q^24 - 46 * q^26 - 1152 * q^29 - 36 * q^31 + 1952 * q^34 - 2844 * q^36 + 44 * q^39 + 672 * q^41 - 1760 * q^44 + 196 * q^46 + 2228 * q^49 - 1256 * q^51 + 4326 * q^54 + 6102 * q^56 + 1116 * q^59 + 2992 * q^61 - 9744 * q^64 + 1364 * q^66 - 3288 * q^69 - 2896 * q^71 + 470 * q^74 - 6036 * q^76 - 1680 * q^79 - 4784 * q^81 + 10542 * q^84 - 3632 * q^86 + 5356 * q^89 + 4092 * q^91 + 7250 * q^94 + 13202 * q^96 - 16344 * q^99

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 $

$2$	−2.52961	−	1.46047i	−0.894354	−	0.516355i	−0.0189897	−	0.999820i	$-0.506045\pi$
$2$	−2.52961	−	1.46047i	−0.894354	−	0.516355i	−0.875364	+	0.483464i	$0.839378\pi$
$3$	−8.70206	+	5.02414i	−1.67471	+	0.966895i	−0.709770	+	0.704434i	$0.751201\pi$
$3$	−8.70206	+	5.02414i	−1.67471	+	0.966895i	−0.964942	+	0.262462i	$0.915466\pi$
$4$	0.265967	+	0.460668i	0.0332459	+	0.0575835i
$5$		0			0
$5$		0			0
$6$	29.3505			1.99705
$7$	−2.32782	−	18.3734i	−0.125690	−	0.992070i
$7$	−2.32782	−	18.3734i	−0.125690	−	0.992070i
$8$			21.8138i			0.964044i
$9$	36.9839	−	64.0580i	1.36977	−	2.37252i
$10$		0			0
$11$	−7.79680	−	13.5045i	−0.213711	−	0.370159i	0.739162	−	0.673528i	$-0.235222\pi$
$11$	−7.79680	−	13.5045i	−0.213711	−	0.370159i	−0.952873	+	0.303369i	$0.901889\pi$
$12$	−4.62892	−	2.67251i	−0.111354	−	0.0642905i
$13$		−	63.9123i		−	1.36354i	−0.731565	−	0.681772i	$-0.761210\pi$
$13$		−	63.9123i		−	1.36354i	0.731565	−	0.681772i	$-0.238790\pi$
$14$	−20.9454	+	49.8773i	−0.399849	+	0.952162i
$15$		0			0
$16$	33.9863	−	58.8659i	0.531035	−	0.919780i
$17$	−9.16053	+	5.28883i	−0.130691	+	0.0754547i	−0.563920	−	0.825829i	$-0.690708\pi$
$17$	−9.16053	+	5.28883i	−0.130691	+	0.0754547i	0.433229	+	0.901284i	$0.357374\pi$
$18$	−187.110	+	108.028i	−2.45012	+	1.41458i
$19$	−19.3864	+	33.5782i	−0.234081	+	0.405440i	−0.959005	−	0.283389i	$-0.908541\pi$
$19$	−19.3864	+	33.5782i	−0.234081	+	0.405440i	0.724924	+	0.688829i	$0.241875\pi$
$20$		0			0
$21$	112.567	+	148.191i	1.16972	+	1.53990i
$22$			45.5481i			0.441404i
$23$	20.8909	+	12.0614i	0.189394	+	0.109346i	0.591699	−	0.806159i	$-0.298458\pi$
$23$	20.8909	+	12.0614i	0.189394	+	0.109346i	−0.402305	+	0.915506i	$0.631791\pi$
$24$	−109.596	−	189.825i	−0.932130	−	1.61450i
$25$		0			0
$26$	−93.3422	+	161.673i	−0.704073	+	1.21949i
$27$			471.945i			3.36392i
$28$	7.84491	−	5.95906i	0.0529482	−	0.0402199i
$29$	−226.731			−1.45182			−0.725912	−	0.687787i	$-0.758582\pi$
$29$	−226.731			−1.45182			−0.725912	+	0.687787i	$0.758582\pi$
$30$		0			0
$31$	71.5651	+	123.954i	0.414628	+	0.718157i	0.995389	−	0.0959171i	$-0.0305784\pi$
$31$	71.5651	+	123.954i	0.414628	+	0.718157i	−0.580761	+	0.814074i	$0.697245\pi$
$32$	−20.8136	+	12.0168i	−0.114980	+	0.0663838i
$33$	135.697	+	78.3444i	0.715810	+	0.413273i
$34$	30.8968			0.155846
$35$		0			0
$36$	39.3460			0.182157
$37$	−247.036	−	142.626i	−1.09764	−	0.633720i	−0.162036	−	0.986785i	$-0.551806\pi$
$37$	−247.036	−	142.626i	−1.09764	−	0.633720i	−0.935599	+	0.353065i	$0.885140\pi$
$38$	98.0800	−	56.6265i	0.418702	−	0.241738i
$39$	321.104	+	556.168i	1.31840	+	2.28354i
$40$		0			0
$41$	32.0457			0.122066			0.0610328	−	0.998136i	$-0.480561\pi$
$41$	32.0457			0.122066			0.0610328	+	0.998136i	$0.480561\pi$
$42$	−68.3225	−	539.268i	−0.251009	−	1.98121i
$43$		−	235.711i		−	0.835942i	−0.908460	−	0.417971i	$-0.862741\pi$
$43$		−	235.711i		−	0.835942i	0.908460	−	0.417971i	$-0.137259\pi$
$44$	4.14738	−	7.18348i	0.0142100	−	0.0246125i
$45$		0			0
$46$	−35.2306	−	61.0212i	−0.112923	−	0.195589i
$47$	124.964	+	72.1481i	0.387828	+	0.223912i	0.681219	−	0.732080i	$-0.261450\pi$
$47$	124.964	+	72.1481i	0.387828	+	0.223912i	−0.293391	+	0.955993i	$0.594784\pi$
$48$			683.006i			2.05382i
$49$	−332.163	+	85.5397i	−0.968404	+	0.249387i
$50$		0			0
$51$	53.1436	−	92.0475i	0.145914	−	0.252730i
$52$	29.4423	−	16.9985i	0.0785177	−	0.0453322i
$53$	275.900	−	159.291i	0.715051	−	0.412835i	−0.0978773	−	0.995198i	$-0.531205\pi$
$53$	275.900	−	159.291i	0.715051	−	0.412835i	0.812928	+	0.582364i	$0.197872\pi$
$54$	689.263	−	1193.84i	1.73698	−	3.00854i
$55$		0			0
$56$	400.794	−	50.7786i	0.956399	−	0.121171i
$57$		−	389.599i		−	0.905327i
$58$	573.542	+	331.135i	1.29844	+	0.749657i
$59$	224.161	+	388.258i	0.494632	+	0.856727i	0.999981	−	0.00618772i	$-0.00196963\pi$
$59$	224.161	+	388.258i	0.494632	+	0.856727i	−0.505349	+	0.862915i	$0.668636\pi$
$60$		0			0
$61$	−83.3473	+	144.362i	−0.174943	+	0.303010i	−0.940142	−	0.340784i	$-0.889307\pi$
$61$	−83.3473	+	144.362i	−0.174943	+	0.303010i	0.765198	+	0.643794i	$0.222641\pi$
$62$		−	418.076i		−	0.856382i
$63$	−1263.05	−	530.404i	−2.52587	−	1.06071i
$64$	−473.580			−0.924960
$65$		0			0
$66$	−228.840	−	396.362i	−0.426792	−	0.739225i
$67$	−641.761	+	370.521i	−1.17020	+	0.675617i	−0.953728	−	0.300671i	$-0.902789\pi$
$67$	−641.761	+	370.521i	−1.17020	+	0.675617i	−0.216475	+	0.976288i	$0.569456\pi$
$68$	−4.87279	−	2.81331i	−0.00868990	−	0.00501711i
$69$	−242.392			−0.422906
$70$		0			0
$71$	−373.652			−0.624567			−0.312284	−	0.949989i	$-0.601094\pi$
$71$	−373.652			−0.624567			−0.312284	+	0.949989i	$0.601094\pi$
$72$	1397.35	+	806.760i	2.28721	+	1.32052i
$73$	205.520	−	118.657i	0.329511	−	0.190243i	−0.326113	−	0.945331i	$-0.605739\pi$
$73$	205.520	−	118.657i	0.329511	−	0.190243i	0.655624	+	0.755088i	$0.272406\pi$
$74$	416.604	+	721.580i	0.654450	+	1.13354i
$75$		0			0
$76$	−20.6245			−0.0311289
$77$	−229.973	+	174.690i	−0.340362	+	0.258542i
$78$		−	1875.86i		−	2.72306i
$79$	−232.695	+	403.040i	−0.331396	+	0.573994i	−0.982786	−	0.184749i	$-0.940853\pi$
$79$	−232.695	+	403.040i	−0.331396	+	0.573994i	0.651390	+	0.758743i	$0.274186\pi$
$80$		0			0
$81$	−1372.55	−	2377.33i	−1.88279	−	3.26108i
$82$	−81.0631	−	46.8018i	−0.109170	−	0.0630292i
$83$			691.289i			0.914202i	0.889415	+	0.457101i	$0.151112\pi$
$83$			691.289i			0.914202i	−0.889415	+	0.457101i	$0.848888\pi$
$84$	−38.3277	+	91.2700i	−0.0497845	+	0.118552i
$85$		0			0
$86$	−344.249	+	596.257i	−0.431643	+	0.747628i
$87$	1973.03	−	1139.13i	2.43139	−	1.40376i
$88$	294.584	−	170.078i	0.356850	−	0.206027i
$89$	506.590	−	877.440i	0.603353	−	1.04504i	−0.388956	−	0.921256i	$-0.627164\pi$
$89$	506.590	−	877.440i	0.603353	−	1.04504i	0.992309	−	0.123782i	$-0.0395024\pi$
$90$		0			0
$91$	−1174.28	+	148.776i	−1.35273	+	0.171384i
$92$			12.8317i			0.0145413i
$93$	−1245.53	−	719.105i	−1.38876	−	0.801804i
$94$	−210.741	−	365.014i	−0.231237	−	0.400514i
$95$		0			0
$96$	120.748	−	209.141i	0.128372	−	0.222348i
$97$			1151.67i			1.20551i	0.797925	+	0.602757i	$0.205931\pi$
$97$			1151.67i			1.20551i	−0.797925	+	0.602757i	$0.794069\pi$
$98$	965.172	+	268.732i	0.994868	+	0.277000i
$99$	−1153.42			−1.17094
$100$		0			0
$101$	600.514	+	1040.12i	0.591618	+	1.02471i	0.994015	+	0.109247i	$0.0348438\pi$
$101$	600.514	+	1040.12i	0.591618	+	1.02471i	−0.402397	+	0.915465i	$0.631823\pi$
$102$	−268.866	+	155.230i	−0.260997	+	0.150687i
$103$	891.184	+	514.525i	0.852534	+	0.492211i	0.861505	−	0.507749i	$-0.169522\pi$
$103$	891.184	+	514.525i	0.852534	+	0.492211i	−0.00897107	+	0.999960i	$0.502856\pi$
$104$	1394.17			1.31452
$105$		0			0
$106$	−930.559			−0.852678
$107$	499.469	+	288.369i	0.451266	+	0.260539i	0.708365	−	0.705846i	$-0.249433\pi$
$107$	499.469	+	288.369i	0.451266	+	0.260539i	−0.257098	+	0.966385i	$0.582766\pi$
$108$	−217.410	+	125.522i	−0.193706	+	0.111836i
$109$	−95.6623	−	165.692i	−0.0840623	−	0.145600i	0.820929	−	0.571030i	$-0.193456\pi$
$109$	−95.6623	−	165.692i	−0.0840623	−	0.145600i	−0.904991	+	0.425430i	$0.860123\pi$
$110$		0			0
$111$	2866.30			2.45096
$112$	−1160.68	−	487.414i	−0.979232	−	0.411217i
$113$			2091.69i			1.74132i	0.491882	+	0.870662i	$0.336309\pi$
$113$			2091.69i			1.74132i	−0.491882	+	0.870662i	$0.663691\pi$
$114$	−568.999	+	985.535i	−0.467470	+	0.809682i
$115$		0			0
$116$	−60.3030	−	104.448i	−0.0482671	−	0.0836012i
$117$	−4094.09	−	2363.72i	−3.23503	−	1.86775i
$118$		−	1309.52i		−	1.02162i
$119$	118.498	+	155.998i	0.0912830	+	0.120171i
$120$		0			0
$121$	543.920	−	942.097i	0.408655	−	0.707811i
$122$	421.673	−	243.453i	0.312922	−	0.180666i
$123$	−278.863	+	161.002i	−0.204425	+	0.118025i
$124$	−38.0679	+	65.9355i	−0.0275693	+	0.0477515i
$125$		0			0
$126$	2420.40	+	3186.37i	1.71132	+	2.25290i
$127$			498.841i			0.348543i	0.984698	+	0.174271i	$0.0557570\pi$
$127$			498.841i			0.348543i	−0.984698	+	0.174271i	$0.944243\pi$
$128$	1364.48	+	787.784i	0.942222	+	0.543992i
$129$	1184.24	+	2051.17i	0.808269	+	1.39996i
$130$		0			0
$131$	−155.825	+	269.897i	−0.103928	+	0.180008i	−0.913300	−	0.407289i	$-0.866474\pi$
$131$	−155.825	+	269.897i	−0.103928	+	0.180008i	0.809372	+	0.587296i	$0.199808\pi$
$132$			83.3481i			0.0549585i
$133$	662.072	+	278.029i	0.431646	+	0.181265i
$134$	2164.55			1.39543
$135$		0			0
$136$	−115.370	−	199.826i	−0.0727417	−	0.125992i
$137$	885.675	−	511.345i	0.552324	−	0.318884i	−0.197735	−	0.980255i	$-0.563359\pi$
$137$	885.675	−	511.345i	0.552324	−	0.318884i	0.750059	+	0.661371i	$0.230025\pi$
$138$	613.157	+	354.007i	0.378228	+	0.218370i
$139$	−1141.29			−0.696424			−0.348212	−	0.937416i	$-0.613211\pi$
$139$	−1141.29			−0.696424			−0.348212	+	0.937416i	$0.613211\pi$
$140$		0			0
$141$	−1449.93			−0.866000
$142$	945.194	+	545.708i	0.558584	+	0.322499i
$143$	−863.101	+	498.311i	−0.504728	+	0.291405i
$144$	−2513.89	−	4354.18i	−1.45480	−	2.51978i
$145$		0			0
$146$	−693.182			−0.392932
$147$	2460.73	−	2413.20i	1.38067	−	1.35400i
$148$		−	151.736i		−	0.0842743i
$149$	645.485	−	1118.01i	0.354900	−	0.614705i	−0.632201	−	0.774805i	$-0.717848\pi$
$149$	645.485	−	1118.01i	0.354900	−	0.614705i	0.987101	+	0.160099i	$0.0511815\pi$
$150$		0			0
$151$	574.974	+	995.885i	0.309873	+	0.536715i	0.978334	−	0.207032i	$-0.0663803\pi$
$151$	574.974	+	995.885i	0.309873	+	0.536715i	−0.668462	+	0.743747i	$0.733047\pi$
$152$	−732.468	−	422.891i	−0.390862	−	0.225664i
$153$			782.407i			0.413424i
$154$	836.873	−	106.028i	0.437904	−	0.0554802i
$155$		0			0
$156$	−170.806	+	295.845i	−0.0876630	+	0.151837i
$157$	−3137.03	+	1811.17i	−1.59467	+	0.920681i	−0.602175	+	0.798364i	$0.705699\pi$
$157$	−3137.03	+	1811.17i	−1.59467	+	0.920681i	−0.992491	+	0.122317i	$0.960968\pi$
$158$	1177.26	−	679.690i	0.592770	−	0.342236i
$159$	−1600.60	+	2772.31i	−0.798337	+	1.38276i
$160$		0			0
$161$	172.978	−	411.913i	0.0846743	−	0.201635i
$162$			8018.30i			3.88875i
$163$	−2343.22	−	1352.86i	−1.12598	−	0.650086i	−0.183060	−	0.983102i	$-0.558600\pi$
$163$	−2343.22	−	1352.86i	−1.12598	−	0.650086i	−0.942921	+	0.333016i	$0.891934\pi$
$164$	8.52308	+	14.7624i	0.00405818	+	0.00702897i
$165$		0			0
$166$	1009.61	−	1748.69i	0.472053	−	0.817620i
$167$			3397.98i			1.57451i	0.616627	+	0.787256i	$0.288499\pi$
$167$			3397.98i			1.57451i	−0.616627	+	0.787256i	$0.711501\pi$
$168$	−3232.61	+	2455.52i	−1.48453	+	1.12766i
$169$	−1887.78			−0.859253
$170$		0			0
$171$	1433.97	+	2483.70i	0.641275	+	1.11072i
$172$	108.584	−	62.6912i	0.0481365	−	0.0277916i
$173$	−3625.88	−	2093.40i	−1.59347	−	0.919991i	−0.992705	−	0.120566i	$-0.961529\pi$
$173$	−3625.88	−	2093.40i	−1.59347	−	0.919991i	−0.600766	−	0.799425i	$-0.705138\pi$
$174$	−6654.67			−2.89936
$175$		0			0
$176$	−1059.94			−0.453953
$177$	−3901.32	−	2252.43i	−1.65673	−	0.956514i
$178$	−2562.96	+	1479.72i	−1.07922	+	0.623089i
$179$	458.926	+	794.884i	0.191630	+	0.331913i	0.945791	−	0.324777i	$-0.105289\pi$
$179$	458.926	+	794.884i	0.191630	+	0.331913i	−0.754161	+	0.656690i	$0.771956\pi$
$180$		0			0
$181$	262.339			0.107732			0.0538661	−	0.998548i	$-0.482846\pi$
$181$	262.339			0.107732			0.0538661	+	0.998548i	$0.482846\pi$
$182$	3187.77	+	1338.67i	1.29832	+	0.545212i
$183$		−	1674.99i		−	0.676607i
$184$	−263.104	+	455.710i	−0.105415	+	0.182584i
$185$		0			0
$186$	2100.47	+	3638.12i	0.828031	+	1.43419i
$187$	142.846	+	82.4720i	0.0558605	+	0.0322511i
$188$			76.7560i			0.0297766i
$189$	8671.23	−	1098.60i	3.33724	−	0.422812i
$190$		0			0
$191$	−723.091	+	1252.43i	−0.273932	+	0.474464i	−0.969865	−	0.243642i	$-0.921658\pi$
$191$	−723.091	+	1252.43i	−0.273932	+	0.474464i	0.695933	+	0.718107i	$0.254991\pi$
$192$	4121.12	−	2379.33i	1.54904	−	0.894340i
$193$	3521.13	−	2032.93i	1.31325	−	0.758204i	0.330615	−	0.943766i	$-0.392744\pi$
$193$	3521.13	−	2032.93i	1.31325	−	0.758204i	0.982633	+	0.185562i	$0.0594106\pi$
$194$	1681.99	−	2913.29i	0.622474	−	1.07816i
$195$		0			0
$196$	−127.750	−	130.266i	−0.0465560	−	0.0474730i
$197$			1073.07i			0.388088i	0.980993	+	0.194044i	$0.0621604\pi$
$197$			1073.07i			0.388088i	−0.980993	+	0.194044i	$0.937840\pi$
$198$	2917.72	+	1684.55i	1.04724	+	0.604624i
$199$	−1488.51	−	2578.18i	−0.530240	−	0.918403i	−0.999378	−	0.0352775i	$-0.988769\pi$
$199$	−1488.51	−	2578.18i	−0.530240	−	0.918403i	0.469138	−	0.883125i	$-0.344565\pi$
$200$		0			0
$201$	3723.10	−	6448.59i	1.30650	−	2.26293i
$202$		−	3508.14i		−	1.22194i
$203$	527.788	+	4165.82i	0.182480	+	1.44031i
$204$	56.5378			0.0194041
$205$		0			0
$206$	−1502.90	−	2603.10i	−0.508311	−	0.880421i
$207$	1545.25	−	892.152i	0.518853	−	0.299560i
$208$	−3762.26	−	2172.14i	−1.25416	−	0.724090i
$209$	604.607			0.200103
$210$		0			0
$211$	−521.629			−0.170192			−0.0850958	−	0.996373i	$-0.527120\pi$
$211$	−521.629			−0.170192			−0.0850958	+	0.996373i	$0.527120\pi$
$212$	146.760	+	84.7321i	0.0475450	+	0.0274501i
$213$	3251.54	−	1877.28i	1.04597	−	0.603891i
$214$	−842.310	−	1458.92i	−0.269061	−	0.466028i
$215$		0			0
$216$	−10294.9			−3.24297
$217$	2110.87	−	1603.44i	0.660347	−	0.501605i
$218$			558.849i			0.173624i
$219$	−1192.30	+	2065.12i	−0.367890	+	0.637205i
$220$		0			0
$221$	338.021	+	585.470i	0.102886	+	0.178204i
$222$	−7250.63	−	4186.15i	−2.19203	−	1.26557i
$223$		−	2381.79i		−	0.715229i	−0.933869	−	0.357615i	$-0.883590\pi$
$223$		−	2381.79i		−	0.715229i	0.933869	−	0.357615i	$-0.116410\pi$
$224$	269.239	+	354.444i	0.0803093	+	0.105725i
$225$		0			0
$226$	3054.86	−	5291.17i	0.899142	−	1.55736i
$227$	−295.343	+	170.517i	−0.0863552	+	0.0498572i	−0.542556	−	0.840020i	$-0.682543\pi$
$227$	−295.343	+	170.517i	−0.0863552	+	0.0498572i	0.456201	+	0.889877i	$0.349210\pi$
$228$	179.476	−	103.620i	0.0521319	−	0.0300984i
$229$	387.522	−	671.208i	0.111826	−	0.193688i	−0.804680	−	0.593708i	$-0.797663\pi$
$229$	387.522	−	671.208i	0.111826	−	0.193688i	0.916507	+	0.400020i	$0.130997\pi$
$230$		0			0
$231$	1123.58	−	2675.58i	0.320025	−	0.762078i
$232$		−	4945.87i		−	1.39962i
$233$	−2164.93	−	1249.92i	−0.608709	−	0.351438i	0.163751	−	0.986502i	$-0.447641\pi$
$233$	−2164.93	−	1249.92i	−0.608709	−	0.351438i	−0.772460	+	0.635063i	$0.780974\pi$
$234$	6904.31	+	11958.6i	1.92884	+	3.34085i
$235$		0			0
$236$	−119.239	+	206.528i	−0.0328889	+	0.0569653i
$237$		−	4676.37i		−	1.28170i
$238$	−71.9221	−	567.679i	−0.0195883	−	0.154610i
$239$	2181.70			0.590470			0.295235	−	0.955425i	$-0.404602\pi$
$239$	2181.70			0.590470			0.295235	+	0.955425i	$0.404602\pi$
$240$		0			0
$241$	1135.07	+	1966.00i	0.303387	+	0.525481i	0.976901	−	0.213693i	$-0.0685492\pi$
$241$	1135.07	+	1966.00i	0.303387	+	0.525481i	−0.673514	+	0.739174i	$0.735216\pi$
$242$	−2751.81	+	1588.76i	−0.730964	+	0.422022i
$243$	12852.7	+	7420.51i	3.39301	+	1.95895i
$244$	−88.6705			−0.0232645
$245$		0			0
$246$	940.555			0.243771
$247$	2146.06	+	1239.03i	0.552835	+	0.319180i
$248$	−2703.92	+	1561.11i	−0.692335	+	0.399720i
$249$	−3473.13	−	6015.64i	−0.883938	−	1.53103i
$250$		0			0
$251$	2943.81			0.740286			0.370143	−	0.928975i	$-0.379309\pi$
$251$	2943.81			0.740286			0.370143	+	0.928975i	$0.379309\pi$
$252$	−91.5901	−	722.918i	−0.0228954	−	0.180713i
$253$		−	376.160i		−	0.0934743i
$254$	728.544	−	1261.87i	0.179972	−	0.311721i
$255$		0			0
$256$	−406.759	−	704.527i	−0.0993064	−	0.172004i
$257$	3138.15	+	1811.81i	0.761682	+	0.439757i	0.829899	−	0.557913i	$-0.188398\pi$
$257$	3138.15	+	1811.81i	0.761682	+	0.439757i	−0.0682171	+	0.997670i	$0.521731\pi$
$258$		−	6918.22i		−	1.66942i
$259$	−2045.48	+	4870.90i	−0.490732	+	1.16858i
$260$		0			0
$261$	−8385.40	+	14523.9i	−1.98867	+	3.44448i
$262$	788.355	−	455.157i	0.185896	−	0.107327i
$263$	399.436	−	230.615i	0.0936514	−	0.0540696i	−0.452443	−	0.891793i	$-0.649447\pi$
$263$	399.436	−	230.615i	0.0936514	−	0.0540696i	0.546094	+	0.837724i	$0.316114\pi$
$264$	−1708.99	+	2960.06i	−0.398413	+	0.690072i
$265$		0			0
$266$	−1268.73	−	1670.25i	−0.292447	−	0.384998i
$267$			10180.7i			2.33352i
$268$	−341.374	−	197.093i	−0.0778088	−	0.0449229i
$269$	−2865.16	−	4962.61i	−0.649413	−	1.12482i	−0.983263	−	0.182190i	$-0.941681\pi$
$269$	−2865.16	−	4962.61i	−0.649413	−	1.12482i	0.333851	−	0.942626i	$-0.391652\pi$
$270$		0			0
$271$	217.608	−	376.908i	0.0487777	−	0.0844854i	−0.840606	−	0.541648i	$-0.817801\pi$
$271$	217.608	−	376.908i	0.0487777	−	0.0844854i	0.889383	+	0.457162i	$0.151134\pi$
$272$			718.991i			0.160277i
$273$	9471.22	−	7194.42i	2.09972	−	1.59497i
$274$	−2987.22			−0.658630
$275$		0			0
$276$	−64.4681	−	111.662i	−0.0140599	−	0.0243524i
$277$	93.0980	−	53.7502i	0.0201939	−	0.0116590i	−0.489869	−	0.871796i	$-0.662955\pi$
$277$	93.0980	−	53.7502i	0.0201939	−	0.0116590i	0.510063	+	0.860137i	$0.329622\pi$
$278$	2887.02	+	1666.82i	0.622849	+	0.359602i
$279$	10587.0			2.27179
$280$		0			0
$281$	−8058.94			−1.71088			−0.855438	−	0.517905i	$-0.826712\pi$
$281$	−8058.94			−1.71088			−0.855438	+	0.517905i	$0.826712\pi$
$282$	3667.76	+	2117.58i	0.774510	+	0.447164i
$283$	−5019.80	+	2898.18i	−1.05440	+	0.608760i	−0.923879	−	0.382685i	$-0.874999\pi$
$283$	−5019.80	+	2898.18i	−1.05440	+	0.608760i	−0.130525	+	0.991445i	$0.541666\pi$
$284$	−99.3789	−	172.129i	−0.0207643	−	0.0359648i
$285$		0			0
$286$	2911.08			0.601874
$287$	−74.5964	−	588.787i	−0.0153425	−	0.121098i
$288$			1777.71i			0.363723i
$289$	−2400.56	+	4157.89i	−0.488613	+	0.846303i
$290$		0			0
$291$	−5786.17	−	10021.9i	−1.16561	−	2.01889i
$292$	109.323	+	63.1176i	0.0219097	+	0.0126496i
$293$		−	1250.96i		−	0.249427i	−0.992193	−	0.124713i	$-0.960199\pi$
$293$		−	1250.96i		−	0.249427i	0.992193	−	0.124713i	$-0.0398012\pi$
$294$	−9749.13	+	2510.63i	−1.93395	+	0.498037i
$295$		0			0
$296$	3111.23	−	5388.81i	0.610934	−	1.05817i
$297$	6373.36	−	3679.66i	1.24519	−	0.718908i
$298$	−3265.65	+	1885.43i	−0.634813	+	0.366509i
$299$	770.869	−	1335.18i	0.149099	−	0.258246i
$300$		0			0
$301$	−4330.80	+	548.691i	−0.829313	+	0.105070i
$302$		−	3358.94i		−	0.640018i
$303$	−10451.4	−	6034.13i	−1.98158	−	1.14406i
$304$	1317.74	+	2282.39i	0.248610	+	0.430606i
$305$		0			0
$306$	1142.68	−	1979.19i	0.213474	−	0.369747i
$307$		−	493.727i		−	0.0917865i	−0.998946	−	0.0458933i	$-0.985387\pi$
$307$		−	493.727i		−	0.0917865i	0.998946	−	0.0458933i	$-0.0146134\pi$
$308$	−141.639	−	59.4796i	−0.0262034	−	0.0110038i
$309$	−10340.2			−1.90367
$310$		0			0
$311$	52.7320	+	91.3345i	0.00961466	+	0.0166531i	0.870793	−	0.491650i	$-0.163606\pi$
$311$	52.7320	+	91.3345i	0.00961466	+	0.0166531i	−0.861178	+	0.508303i	$0.830273\pi$
$312$	−12132.2	+	7004.51i	−2.20144	+	1.27100i
$313$	−3213.50	−	1855.32i	−0.580312	−	0.335044i	0.180945	−	0.983493i	$-0.442084\pi$
$313$	−3213.50	−	1855.32i	−0.580312	−	0.335044i	−0.761258	+	0.648450i	$0.775418\pi$
$314$	10580.7			1.90159
$315$		0			0
$316$	−247.557			−0.0440701
$317$	5630.38	+	3250.70i	0.997583	+	0.575955i	0.907532	−	0.419983i	$-0.137964\pi$
$317$	5630.38	+	3250.70i	0.997583	+	0.575955i	0.0900506	+	0.995937i	$0.471297\pi$
$318$	8097.78	−	4675.26i	1.42799	−	0.824451i
$319$	1767.78	+	3061.88i	0.310271	+	0.537406i
$320$		0			0
$321$	−5795.21			−1.00766
$322$	−1039.16	+	789.351i	−0.179844	+	0.136611i
$323$		−	410.125i		−	0.0706500i
$324$	730.106	−	1264.58i	0.125190	−	0.216835i
$325$		0			0
$326$	3951.62	+	6844.42i	0.671350	+	1.16281i
$327$	1664.92	+	961.241i	0.281560	+	0.162559i
$328$			699.038i			0.117677i
$329$	1034.71	−	2463.96i	0.173391	−	0.412896i
$330$		0			0
$331$	54.3441	−	94.1268i	0.00902424	−	0.0156304i	−0.861478	−	0.507795i	$-0.830461\pi$
$331$	54.3441	−	94.1268i	0.00902424	−	0.0156304i	0.870502	+	0.492164i	$0.163794\pi$
$332$	−318.455	+	183.860i	−0.0526430	+	0.0303934i
$333$	−18272.7	+	10549.8i	−3.00702	+	1.73611i
$334$	4962.66	−	8595.57i	0.813007	−	1.40817i
$335$		0			0
$336$	12549.1	−	1589.91i	2.03753	−	0.258145i
$337$		−	8207.88i		−	1.32674i	−0.748291	−	0.663370i	$-0.769125\pi$
$337$		−	8207.88i		−	1.32674i	0.748291	−	0.663370i	$-0.230875\pi$
$338$	4775.35	+	2757.05i	0.768476	+	0.443680i
$339$	−10508.9	−	18202.0i	−1.68368	−	2.91621i
$340$		0			0
$341$	1115.96	−	1932.90i	0.177221	−	0.306956i
$342$		−	8377.08i		−	1.32450i
$343$	2344.87	+	5903.83i	0.369128	+	0.929379i
$344$	5141.75			0.805885
$345$		0			0
$346$	6114.72	+	10591.0i	0.950085	+	1.64560i
$347$	−8142.85	+	4701.28i	−1.25974	+	0.727313i	−0.973025	−	0.230701i	$-0.925898\pi$
$347$	−8142.85	+	4701.28i	−1.25974	+	0.727313i	−0.286719	+	0.958015i	$0.592565\pi$
$348$	1049.52	+	605.941i	0.161667	+	0.0933386i
$349$	690.530			0.105912			0.0529559	−	0.998597i	$-0.483136\pi$
$349$	690.530			0.105912			0.0529559	+	0.998597i	$0.483136\pi$
$350$		0			0
$351$	30163.1			4.58685
$352$	324.560	+	187.385i	0.0491451	+	0.0283740i
$353$	−3118.89	+	1800.69i	−0.470260	+	0.271505i	−0.716349	−	0.697743i	$-0.754188\pi$
$353$	−3118.89	+	1800.69i	−0.470260	+	0.271505i	0.246088	+	0.969247i	$0.420855\pi$
$354$	6579.23	+	11395.6i	0.987803	+	1.71092i
$355$		0			0
$356$	538.945			0.0802360
$357$	−1814.93	−	762.159i	−0.269066	−	0.112991i
$358$		−	2681.00i		−	0.395797i
$359$	4031.95	−	6983.55i	0.592753	−	1.02668i	−0.401107	−	0.916031i	$-0.631374\pi$
$359$	4031.95	−	6983.55i	0.592753	−	1.02668i	0.993860	−	0.110647i	$-0.0352922\pi$
$360$		0			0
$361$	2677.84	+	4638.15i	0.390412	+	0.676214i
$362$	−663.618	−	383.140i	−0.0963508	−	0.0556281i
$363$			10930.9i			1.58051i
$364$	−380.857	−	501.386i	−0.0548416	−	0.0721972i
$365$		0			0
$366$	−2446.28	+	4237.09i	−0.349370	+	0.605126i
$367$	2935.50	−	1694.81i	0.417526	−	0.241059i	−0.276493	−	0.961016i	$-0.589172\pi$
$367$	2935.50	−	1694.81i	0.417526	−	0.241059i	0.694018	+	0.719958i	$0.255839\pi$
$368$	1420.01	−	819.841i	0.201149	−	0.116134i
$369$	1185.17	−	2052.78i	0.167202	−	0.289603i
$370$		0			0
$371$	−3568.95	−	4698.41i	−0.499436	−	0.657491i
$372$		−	765.033i		−	0.106627i
$373$	7656.74	+	4420.62i	1.06287	+	0.613649i	0.926225	−	0.376971i	$-0.123034\pi$
$373$	7656.74	+	4420.62i	1.06287	+	0.613649i	0.136646	+	0.990620i	$0.456368\pi$
$374$	−240.896	−	417.245i	−0.0333060	−	0.0576877i
$375$		0			0
$376$	−1573.83	+	2725.95i	−0.215862	+	0.373883i
$377$			14490.9i			1.97963i
$378$	−23539.3	−	9885.06i	−3.20300	−	1.34506i
$379$	−3038.06			−0.411754			−0.205877	−	0.978578i	$-0.566005\pi$
$379$	−3038.06			−0.411754			−0.205877	+	0.978578i	$0.566005\pi$
$380$		0			0
$381$	−2506.24	−	4340.94i	−0.337005	−	0.583709i
$382$	3658.28	−	2112.11i	0.489984	−	0.282893i
$383$	2441.05	+	1409.34i	0.325671	+	0.188026i	0.653917	−	0.756566i	$-0.273124\pi$
$383$	2441.05	+	1409.34i	0.325671	+	0.188026i	−0.328247	+	0.944592i	$0.606458\pi$
$384$	−15831.7			−2.10393
$385$		0			0
$386$	−11876.1			−1.56601
$387$	−15099.1	−	8717.49i	−1.98329	−	1.14505i
$388$	−530.540	+	306.307i	−0.0694177	+	0.0400783i
$389$	6094.35	+	10555.7i	0.794334	+	1.37583i	0.923261	+	0.384173i	$0.125513\pi$
$389$	6094.35	+	10555.7i	0.794334	+	1.37583i	−0.128927	+	0.991654i	$0.541153\pi$
$390$		0			0
$391$	−255.162			−0.0330028
$392$	−1865.95	−	7245.74i	−0.240420	−	0.933584i
$393$		−	3131.55i		−	0.401948i
$394$	1567.19	−	2714.46i	0.200391	−	0.347088i
$395$		0			0
$396$	−306.773	−	531.346i	−0.0389291	−	0.0674271i
$397$	8998.29	+	5195.17i	1.13756	+	0.656771i	0.945825	−	0.324676i	$-0.105255\pi$
$397$	8998.29	+	5195.17i	1.13756	+	0.656771i	0.191735	+	0.981447i	$0.438589\pi$
$398$			8695.73i			1.09517i
$399$	−7158.25	+	906.914i	−0.898147	+	0.113791i
$400$		0			0
$401$	−751.138	+	1301.01i	−0.0935413	+	0.162018i	−0.908999	−	0.416799i	$-0.863152\pi$
$401$	−751.138	+	1301.01i	−0.0935413	+	0.162018i	0.815458	+	0.578817i	$0.196485\pi$
$402$	−18836.0	+	10875.0i	−2.33695	+	1.34924i
$403$	7922.20	−	4573.89i	0.979238	−	0.565364i
$404$	−319.434	+	553.275i	−0.0393377	+	0.0681348i
$405$		0			0
$406$	4748.97	−	11308.7i	0.580510	−	1.38237i
$407$			4448.12i			0.541733i
$408$	2007.91	+	1159.27i	0.243643	+	0.140667i
$409$	7048.61	+	12208.5i	0.852155	+	1.47598i	0.879260	+	0.476343i	$0.158038\pi$
$409$	7048.61	+	12208.5i	0.852155	+	1.47598i	−0.0271048	+	0.999633i	$0.508629\pi$
$410$		0			0
$411$	−5138.13	+	8899.50i	−0.616655	+	1.06808i
$412$			547.387i			0.0654559i
$413$	6611.81	−	5022.39i	0.787763	−	0.598391i
$414$	−5211.86			−0.618717
$415$		0			0
$416$	768.018	+	1330.25i	0.0905173	+	0.156781i
$417$	9931.57	−	5733.99i	1.16631	−	0.673369i
$418$	−1529.42	−	883.012i	−0.178963	−	0.103324i
$419$	−11529.9			−1.34433			−0.672163	−	0.740403i	$-0.734635\pi$
$419$	−11529.9			−1.34433			−0.672163	+	0.740403i	$0.734635\pi$
$420$		0			0
$421$	−3370.05			−0.390134			−0.195067	−	0.980790i	$-0.562492\pi$
$421$	−3370.05			−0.390134			−0.195067	+	0.980790i	$0.562492\pi$
$422$	1319.52	+	761.826i	0.152212	+	0.0878794i
$423$	9243.33	−	5336.64i	1.06247	−	0.613419i
$424$	3474.74	+	6018.42i	0.397991	+	0.689341i
$425$		0			0
$426$	−10966.9			−1.24729
$427$	2846.43	+	1195.32i	0.322596	+	0.135470i
$428$			306.786i			0.0346473i
$429$	5007.17	−	8672.67i	0.563516	−	0.976039i
$430$		0			0
$431$	4163.53	+	7211.45i	0.465314	+	0.805948i	0.999216	−	0.0395991i	$-0.0126081\pi$
$431$	4163.53	+	7211.45i	0.465314	+	0.805948i	−0.533902	+	0.845547i	$0.679275\pi$
$432$	27781.5	+	16039.6i	3.09407	+	1.78636i
$433$		−	818.149i		−	0.0908031i	−0.998969	−	0.0454015i	$-0.985543\pi$
$433$		−	818.149i		−	0.0908031i	0.998969	−	0.0454015i	$-0.0144567\pi$
$434$	−7681.46	+	973.203i	−0.849590	+	0.107639i
$435$		0			0
$436$	50.8860	−	88.1372i	0.00558945	−	0.00968120i
$437$	−809.997	+	467.652i	−0.0886668	+	0.0511918i
$438$	6032.11	−	3482.64i	0.658048	−	0.379924i
$439$	4232.89	−	7331.58i	0.460193	−	0.797078i	−0.538777	−	0.842448i	$-0.681114\pi$
$439$	4232.89	−	7331.58i	0.460193	−	0.797078i	0.998970	+	0.0453707i	$0.0144469\pi$
$440$		0			0
$441$	−6805.16	+	24441.3i	−0.734819	+	2.63916i
$442$		−	1974.69i		−	0.212503i
$443$	12617.1	+	7284.47i	1.35317	+	0.781254i	0.988693	−	0.149957i	$-0.0479135\pi$
$443$	12617.1	+	7284.47i	1.35317	+	0.781254i	0.364480	+	0.931211i	$0.381247\pi$
$444$	762.340	+	1320.41i	0.0814844	+	0.141135i
$445$		0			0
$446$	−3478.54	+	6025.00i	−0.369313	+	0.639668i
$447$			12972.0i			1.37261i
$448$	1102.41	+	8701.26i	0.116258	+	0.917625i
$449$	841.211			0.0884169			0.0442084	−	0.999022i	$-0.485923\pi$
$449$	841.211			0.0884169			0.0442084	+	0.999022i	$0.485923\pi$
$450$		0			0
$451$	−249.854	−	432.759i	−0.0260868	−	0.0451837i
$452$	−963.574	+	556.320i	−0.100272	+	0.0578918i
$453$	−10006.9	−	5777.50i	−1.03789	−	0.599229i
$454$	996.140			0.102976
$455$		0			0
$456$	8498.64			0.872775
$457$	−12017.5	−	6938.33i	−1.23010	−	0.710200i	−0.263052	−	0.964782i	$-0.584729\pi$
$457$	−12017.5	−	6938.33i	−1.23010	−	0.710200i	−0.967051	+	0.254581i	$0.918062\pi$
$458$	−1960.56	+	1131.93i	−0.200024	+	0.115484i
$459$	−2496.04	−	4323.27i	−0.253824	−	0.439636i
$460$		0			0
$461$	3053.09			0.308452			0.154226	−	0.988036i	$-0.450712\pi$
$461$	3053.09			0.308452			0.154226	+	0.988036i	$0.450712\pi$
$462$	−6749.82	+	5127.22i	−0.679719	+	0.516320i
$463$		−	9935.80i		−	0.997312i	−0.866800	−	0.498656i	$-0.833827\pi$
$463$		−	9935.80i		−	0.997312i	0.866800	−	0.498656i	$-0.166173\pi$
$464$	−7705.74	+	13346.7i	−0.770970	+	1.33536i
$465$		0			0
$466$	3650.96	+	6323.64i	0.362934	+	0.628620i
$467$	−8597.26	−	4963.63i	−0.851892	−	0.491840i	0.00939651	−	0.999956i	$-0.497009\pi$
$467$	−8597.26	−	4963.63i	−0.851892	−	0.491840i	−0.861289	+	0.508116i	$0.830342\pi$
$468$		−	2514.69i		−	0.248379i
$469$	8301.63	+	10928.8i	0.817342	+	1.07600i
$470$		0			0
$471$	18199.1	−	31521.8i	1.78040	−	3.08375i
$472$	−8469.40	+	4889.81i	−0.825923	+	0.476847i
$473$	−3183.14	+	1837.79i	−0.309432	+	0.178650i
$474$	−6829.71	+	11829.4i	−0.661813	+	1.14629i
$475$		0			0
$476$	−40.3470	+	96.0786i	−0.00388509	+	0.00925159i
$477$		−	23564.8i		−	2.26196i
$478$	−5518.86	−	3186.32i	−0.528089	−	0.304893i
$479$	−6587.12	−	11409.2i	−0.628336	−	1.08831i	−0.987886	−	0.155184i	$-0.950403\pi$
$479$	−6587.12	−	11409.2i	−0.628336	−	1.08831i	0.359549	−	0.933126i	$-0.382931\pi$
$480$		0			0
$481$	−9115.58	+	15788.6i	−0.864105	+	1.49667i
$482$		−	6630.96i		−	0.626622i
$483$	564.243	+	4453.56i	0.0531552	+	0.419552i
$484$	578.658			0.0543443
$485$		0			0
$486$	−21674.9	−	37542.1i	−2.02303	−	3.50400i
$487$	7338.50	−	4236.88i	0.682832	−	0.394233i	−0.118089	−	0.993003i	$-0.537677\pi$
$487$	7338.50	−	4236.88i	0.682832	−	0.394233i	0.800921	+	0.598770i	$0.204344\pi$
$488$	−3149.08	−	1818.12i	−0.292115	−	0.168653i
$489$	27187.8			2.51426
$490$		0			0
$491$	−10831.1			−0.995523			−0.497762	−	0.867314i	$-0.665845\pi$
$491$	−10831.1			−0.995523			−0.497762	+	0.867314i	$0.665845\pi$
$492$	−148.337	−	85.6422i	−0.0135926	−	0.00784766i
$493$	2076.98	−	1199.14i	0.189741	−	0.109547i
$494$	−3619.13	−	6268.52i	−0.329620	−	0.570919i
$495$		0			0
$496$	9728.92			0.880728
$497$	869.792	+	6865.24i	0.0785020	+	0.619614i
$498$			20289.7i			1.82571i
$499$	−6046.05	+	10472.1i	−0.542402	+	0.939467i	0.456364	+	0.889793i	$0.349152\pi$
$499$	−6046.05	+	10472.1i	−0.542402	+	0.939467i	−0.998765	+	0.0496738i	$0.984182\pi$
$500$		0			0
$501$	−17071.9	−	29569.4i	−1.52239	−	2.63685i
$502$	−7446.71	−	4299.36i	−0.662078	−	0.382251i
$503$		−	18398.5i		−	1.63091i	−0.578821	−	0.815455i	$-0.696487\pi$
$503$		−	18398.5i		−	1.63091i	0.578821	−	0.815455i	$-0.303513\pi$
$504$	11570.1	−	27552.0i	1.02257	−	2.43505i
$505$		0			0
$506$	−549.372	+	951.540i	−0.0482660	+	0.0835991i
$507$	16427.6	−	9484.46i	1.43900	−	0.830808i
$508$	−229.800	+	132.675i	−0.0200703	+	0.0115876i
$509$	−10351.4	+	17929.1i	−0.901406	+	1.56128i	−0.0757355	+	0.997128i	$0.524130\pi$
$509$	−10351.4	+	17929.1i	−0.901406	+	1.56128i	−0.825670	+	0.564153i	$0.809203\pi$
$510$		0			0
$511$	−2658.54	−	3499.88i	−0.230151	−	0.302986i
$512$		−	10228.3i		−	0.882874i
$513$	−15847.0	−	9149.30i	−1.36387	−	0.787429i
$514$	−5292.20	−	9166.37i	−0.454142	−	0.786598i
$515$		0			0
$516$	−629.938	+	1091.08i	−0.0537432	+	0.0930859i
$517$		−	2250.10i		−	0.191411i
$518$	12288.1	−	9334.14i	1.04229	−	0.791734i
$519$	42070.2			3.55814
$520$		0			0
$521$	7236.53	+	12534.0i	0.608518	+	1.05398i	0.991485	+	0.130222i	$0.0415691\pi$
$521$	7236.53	+	12534.0i	0.608518	+	1.05398i	−0.382967	+	0.923762i	$0.625098\pi$
$522$	42423.7	−	24493.3i	3.55715	−	2.05372i
$523$	13785.3	+	7958.97i	1.15256	+	0.665433i	0.949511	−	0.313734i	$-0.101580\pi$
$523$	13785.3	+	7958.97i	1.15256	+	0.665433i	0.203053	+	0.979168i	$0.434914\pi$
$524$	−165.777			−0.0138206
$525$		0			0
$526$	−1347.23			−0.111677
$527$	−1311.15	−	756.992i	−0.108377	−	0.0625713i
$528$	9223.63	−	5325.27i	0.760241	−	0.438925i
$529$	−5792.55	−	10033.0i	−0.476087	−	0.824606i
$530$		0			0
$531$	33161.4			2.71013
$532$	48.0101	+	378.942i	0.00391260	+	0.0308820i
$533$		−	2048.11i		−	0.166442i
$534$	14868.7	−	25753.3i	1.20492	−	2.08699i
$535$		0			0
$536$	−8082.48	−	13999.3i	−0.651325	−	1.12813i
$537$	−7987.21	−	4611.42i	−0.641850	−	0.370572i
$538$			16738.0i			1.34131i
$539$	3744.97	+	3818.74i	0.299272	+	0.305167i
$540$		0			0
$541$	4419.67	−	7655.09i	0.351232	−	0.608351i	−0.635234	−	0.772320i	$-0.719096\pi$
$541$	4419.67	−	7655.09i	0.351232	−	0.608351i	0.986466	+	0.163969i	$0.0524296\pi$
$542$	−1100.93	+	635.622i	−0.0872490	+	0.0503732i
$543$	−2282.89	+	1318.03i	−0.180421	+	0.104166i
$544$	127.109	−	220.160i	0.0100179	−	0.0173516i
$545$		0			0
$546$	−34465.8	+	4366.65i	−2.70147	+	0.342262i
$547$		−	11349.6i		−	0.887155i	−0.896236	−	0.443577i	$-0.853709\pi$
$547$		−	11349.6i		−	0.887155i	0.896236	−	0.443577i	$-0.146291\pi$
$548$	471.120	+	272.001i	0.0367249	+	0.0212032i
$549$	6165.02	+	10678.1i	0.479265	+	0.830111i
$550$		0			0
$551$	4395.49	−	7613.21i	0.339844	−	0.588628i
$552$		−	5287.49i		−	0.407700i
$553$	7946.88	+	3337.20i	0.611095	+	0.256622i
$554$	−314.003			−0.0240807
$555$		0			0
$556$	−303.545	−	525.756i	−0.0231532	−	0.0401025i
$557$	5725.18	−	3305.43i	0.435518	−	0.251446i	−0.266177	−	0.963924i	$-0.585760\pi$
$557$	5725.18	−	3305.43i	0.435518	−	0.251446i	0.701695	+	0.712478i	$0.252427\pi$
$558$	−26781.1	−	15462.1i	−2.03178	−	1.17305i
$559$	−15064.8			−1.13984
$560$		0			0
$561$	−1657.40			−0.124734
$562$	20386.0	+	11769.9i	1.53013	+	0.883420i
$563$	−11128.4	+	6424.96i	−0.833045	+	0.480959i	−0.854894	−	0.518802i	$-0.826378\pi$
$563$	−11128.4	+	6424.96i	−0.833045	+	0.480959i	0.0218488	+	0.999761i	$0.493045\pi$
$564$	−385.633	−	667.936i	−0.0287909	−	0.0498673i
$565$		0			0
$566$	16930.9			1.25735
$567$	−40484.5	+	30752.4i	−2.99857	+	2.27774i
$568$		−	8150.77i		−	0.602110i
$569$	−4486.52	+	7770.88i	−0.330553	+	0.572535i	−0.982620	−	0.185626i	$-0.940569\pi$
$569$	−4486.52	+	7770.88i	−0.330553	+	0.572535i	0.652067	+	0.758161i	$0.273902\pi$
$570$		0			0
$571$	−661.018	−	1144.92i	−0.0484461	−	0.0839112i	0.840785	−	0.541368i	$-0.182094\pi$
$571$	−661.018	−	1144.92i	−0.0484461	−	0.0839112i	−0.889232	+	0.457457i	$0.848760\pi$
$572$	−459.112	−	265.069i	−0.0335602	−	0.0193760i
$573$		−	14531.6i		−	1.05945i
$574$	−671.208	+	1598.35i	−0.0488078	+	0.116226i
$575$		0			0
$576$	−17514.8	+	30336.5i	−1.26699	+	2.19448i
$577$	−20120.0	+	11616.3i	−1.45166	+	0.838116i	−0.998576	−	0.0533512i	$-0.983010\pi$
$577$	−20120.0	+	11616.3i	−1.45166	+	0.838116i	−0.453084	+	0.891468i	$0.649676\pi$
$578$	12145.0	−	7011.90i	0.873986	−	0.504596i
$579$	−20427.4	+	35381.3i	−1.46621	+	2.53955i
$580$		0			0
$581$	12701.3	−	1609.19i	0.906952	−	0.114906i
$582$			33802.2i			2.40747i
$583$	−4302.27	−	2483.92i	−0.305629	−	0.176455i
$584$	2588.36	+	4483.18i	0.183403	+	0.317663i
$585$		0			0
$586$	−1827.00	+	3164.46i	−0.128793	+	0.223076i
$587$		−	13229.8i		−	0.930244i	−0.885247	−	0.465122i	$-0.846010\pi$
$587$		−	13229.8i		−	0.930244i	0.885247	−	0.465122i	$-0.153990\pi$
$588$	1766.16	+	491.750i	0.123869	+	0.0344889i
$589$	−5549.55			−0.388226
$590$		0			0
$591$	−5391.26	−	9337.94i	−0.375240	−	0.649935i
$592$	−16791.7	+	9694.68i	−1.16577	+	0.673055i
$593$	−22815.7	−	13172.6i	−1.57998	−	0.912201i	−0.994861	−	0.101252i	$-0.967715\pi$
$593$	−22815.7	−	13172.6i	−1.57998	−	0.912201i	−0.585117	−	0.810949i	$-0.698951\pi$
$594$	−21496.2			−1.48485
$595$		0			0
$596$	686.710			0.0471959
$597$	25906.2	+	14957.0i	1.77600	+	1.02537i
$598$	−3900.00	+	2251.67i	−0.266694	+	0.153976i
$599$	−6294.29	−	10902.0i	−0.429345	−	0.743647i	0.567470	−	0.823394i	$-0.307922\pi$
$599$	−6294.29	−	10902.0i	−0.429345	−	0.743647i	−0.996815	+	0.0797468i	$0.974589\pi$
$600$		0			0
$601$	−5027.54			−0.341227			−0.170614	−	0.985338i	$-0.554575\pi$
$601$	−5027.54			−0.341227			−0.170614	+	0.985338i	$0.554575\pi$
$602$	11756.6	+	4937.04i	0.795953	+	0.334251i
$603$			54813.2i			3.70177i
$604$	−305.848	+	529.745i	−0.0206040	+	0.0356871i
$605$		0			0
$606$	17625.4	+	30528.0i	1.18149	+	2.04640i
$607$	1698.78	+	980.794i	0.113594	+	0.0655835i	0.555721	−	0.831369i	$-0.312442\pi$
$607$	1698.78	+	980.794i	0.113594	+	0.0655835i	−0.442127	+	0.896953i	$0.645776\pi$
$608$		−	931.845i		−	0.0621567i
$609$	−25522.5	−	33599.5i	−1.69823	−	2.23567i
$610$		0			0
$611$	4611.15	−	7986.75i	0.305315	−	0.528820i
$612$	−360.430	+	208.094i	−0.0238064	+	0.0137446i
$613$	8066.73	−	4657.33i	0.531504	−	0.306864i	−0.210124	−	0.977675i	$-0.567387\pi$
$613$	8066.73	−	4657.33i	0.531504	−	0.306864i	0.741629	+	0.670810i	$0.234054\pi$
$614$	−721.075	+	1248.94i	−0.0473945	+	0.0820896i
$615$		0			0
$616$	−3810.65	−	5016.59i	−0.249246	−	0.328124i
$617$		−	20829.3i		−	1.35909i	−0.733635	−	0.679544i	$-0.762178\pi$
$617$		−	20829.3i		−	1.35909i	0.733635	−	0.679544i	$-0.237822\pi$
$618$	26156.7	+	15101.6i	1.70255	+	0.982968i
$619$	6682.39	+	11574.2i	0.433906	+	0.751548i	0.997206	−	0.0747050i	$-0.0238015\pi$
$619$	6682.39	+	11574.2i	0.433906	+	0.751548i	−0.563299	+	0.826253i	$0.690468\pi$
$620$		0			0
$621$	−5692.30	+	9859.35i	−0.367833	+	0.637105i
$622$		−	308.055i		−	0.0198583i
$623$	−17300.8	−	7265.26i	−1.11259	−	0.467217i
$624$	43652.5			2.80048
$625$		0			0
$626$	5419.28	+	9386.47i	0.346003	+	0.599295i
$627$	−5261.32	+	3037.63i	−0.335115	+	0.193479i
$628$	−1668.69	−	963.421i	−0.106032	−	0.0612176i
$629$	3017.31			0.191269
$630$		0			0
$631$	−29261.9			−1.84612			−0.923058	−	0.384661i	$-0.874318\pi$
$631$	−29261.9			−1.84612			−0.923058	+	0.384661i	$0.874318\pi$
$632$	−8791.84	−	5075.97i	−0.553356	−	0.319480i
$633$	4539.25	−	2620.74i	0.285022	−	0.164558i
$634$	−9495.13	−	16446.0i	−0.594795	−	1.03021i
$635$		0			0
$636$	−1702.82			−0.106166
$637$	5467.04	+	21229.3i	0.340050	+	1.32046i
$638$		−	10327.2i		−	0.640841i
$639$	−13819.1	+	23935.4i	−0.855516	+	1.48180i
$640$		0			0
$641$	6224.26	+	10780.7i	0.383531	+	0.664296i	0.991564	−	0.129616i	$-0.0413745\pi$
$641$	6224.26	+	10780.7i	0.383531	+	0.664296i	−0.608033	+	0.793912i	$0.708041\pi$
$642$	14659.7	+	8463.76i	0.901200	+	0.520308i
$643$			13458.0i			0.825397i	0.910868	+	0.412698i	$0.135414\pi$
$643$			13458.0i			0.825397i	−0.910868	+	0.412698i	$0.864586\pi$
$644$	235.762	−	29.8698i	0.0144259	−	0.00182769i
$645$		0			0
$646$	−598.977	+	1037.46i	−0.0364805	+	0.0631861i
$647$	−1591.58	+	918.898i	−0.0967101	+	0.0558356i	−0.547575	−	0.836757i	$-0.684449\pi$
$647$	−1591.58	+	918.898i	−0.0967101	+	0.0558356i	0.450865	+	0.892592i	$0.351116\pi$
$648$	51858.6	−	29940.6i	3.14383	−	1.81509i
$649$	3495.48	−	6054.35i	0.211417	−	0.366185i
$650$		0			0
$651$	−10313.0	+	24558.5i	−0.620891	+	1.47853i
$652$		−	1439.26i		−	0.0864506i
$653$	10503.5	+	6064.19i	0.629454	+	0.363415i	0.780540	−	0.625105i	$-0.214944\pi$
$653$	10503.5	+	6064.19i	0.629454	+	0.363415i	−0.151087	+	0.988520i	$0.548277\pi$
$654$	−2807.73	−	4863.14i	−0.167876	−	0.290770i
$655$		0			0
$656$	1089.11	−	1886.40i	0.0648211	−	0.112274i
$657$		−	17553.6i		−	1.04236i
$658$	−6215.98	+	4721.71i	−0.368273	+	0.279744i
$659$	−4131.14			−0.244198			−0.122099	−	0.992518i	$-0.538962\pi$
$659$	−4131.14			−0.244198			−0.122099	+	0.992518i	$0.538962\pi$
$660$		0			0
$661$	−10681.3	−	18500.6i	−0.628525	−	1.08864i	−0.987848	−	0.155424i	$-0.950326\pi$
$661$	−10681.3	−	18500.6i	−0.628525	−	1.08864i	0.359323	−	0.933213i	$-0.383008\pi$
$662$	−274.939	+	158.736i	−0.0161417	+	0.00931943i
$663$	−5882.96	−	3396.53i	−0.344608	−	0.198960i
$664$	−15079.7			−0.881331
$665$		0			0
$666$	61630.6			3.58579
$667$	−4736.61	−	2734.69i	−0.274966	−	0.158752i
$668$	−1565.34	+	903.749i	−0.0906659	+	0.0523460i
$669$	11966.4	+	20726.4i	0.691552	+	1.19780i
$670$		0			0
$671$	2599.37			0.149549
$672$	−4123.71	−	1731.70i	−0.236719	−	0.0994075i
$673$		−	26260.3i		−	1.50410i	−0.659104	−	0.752052i	$-0.729064\pi$
$673$		−	26260.3i		−	1.50410i	0.659104	−	0.752052i	$-0.270936\pi$
$674$	−11987.4	+	20762.8i	−0.685070	+	1.18658i
$675$		0			0
$676$	−502.086	−	869.639i	−0.0285666	−	0.0494788i
$677$	−26428.1	−	15258.3i	−1.50032	−	0.866208i	−1.00000		0.000364836i	$-0.999884\pi$
$677$	−26428.1	−	15258.3i	−1.50032	−	0.866208i	−0.500316	−	0.865843i	$-0.666783\pi$
$678$			61392.1i			3.47750i
$679$	21160.2	−	2680.89i	1.19595	−	0.151521i
$680$		0			0
$681$	1713.40	−	2967.69i	0.0964134	−	0.166993i
$682$	−5645.89	+	3259.65i	−0.316997	+	0.183018i
$683$	−25294.3	+	14603.7i	−1.41707	+	0.818147i	−0.996041	−	0.0888993i	$-0.971665\pi$
$683$	−25294.3	+	14603.7i	−1.41707	+	0.818147i	−0.421031	+	0.907046i	$0.638332\pi$
$684$	−762.775	+	1321.16i	−0.0426395	+	0.0738538i
$685$		0			0
$686$	2690.78	−	18359.0i	0.149759	−	1.02179i
$687$			7787.85i			0.432497i
$688$	−13875.3	−	8010.92i	−0.768883	−	0.443915i
$689$	−10180.6	−	17633.4i	−0.562919	−	0.975004i
$690$		0			0
$691$	−5312.39	+	9201.33i	−0.292464	+	0.506563i	−0.974392	−	0.224857i	$-0.927809\pi$
$691$	−5312.39	+	9201.33i	−0.292464	+	0.506563i	0.681928	+	0.731420i	$0.261142\pi$
$692$		−	2227.10i		−	0.122344i
$693$	2684.96	+	21192.3i	0.147176	+	1.16166i
$694$	27464.4			1.50221
$695$		0			0
$696$	24848.7	+	43039.3i	1.35329	+	2.34397i
$697$	−293.555	+	169.484i	−0.0159529	+	0.00921043i
$698$	−1746.78	−	1008.50i	−0.0947227	−	0.0546881i
$699$	25119.1			1.35922
$700$		0			0
$701$	22033.0			1.18712			0.593562	−	0.804788i	$-0.297721\pi$
$701$	22033.0			1.18712			0.593562	+	0.804788i	$0.297721\pi$
$702$	−76301.0	−	44052.4i	−4.10227	−	2.36845i
$703$	9578.27	−	5530.01i	0.513871	−	0.296683i
$704$	3692.41	+	6395.44i	0.197674	+	0.342382i
$705$		0			0
$706$	10519.5			0.560772
$707$	17712.7	−	13454.7i	0.942225	−	0.715722i
$708$		−	2396.29i		−	0.127201i
$709$	12433.7	−	21535.8i	0.658614	−	1.14075i	−0.322361	−	0.946617i	$-0.604477\pi$
$709$	12433.7	−	21535.8i	0.658614	−	1.14075i	0.980975	−	0.194136i	$-0.0621902\pi$
$710$		0			0
$711$	17211.9	+	29812.0i	0.907874	+	1.57248i
$712$	19140.3	+	11050.7i	1.00746	+	0.581659i
$713$			3452.69i			0.181352i
$714$	3477.97	+	4578.63i	0.182296	+	0.239987i
$715$		0			0
$716$	−244.118	+	422.825i	−0.0127418	+	0.0220694i
$717$	−18985.3	+	10961.2i	−0.988868	+	0.570923i
$718$	−20398.6	+	11777.1i	−1.06026	+	0.612142i
$719$	−702.482	+	1216.74i	−0.0364370	+	0.0631107i	−0.883669	−	0.468113i	$-0.844934\pi$
$719$	−702.482	+	1216.74i	−0.0364370	+	0.0631107i	0.847232	+	0.531223i	$0.178267\pi$
$720$		0			0
$721$	7379.06	−	17571.8i	0.381152	−	0.907639i
$722$		−	15643.6i		−	0.806366i
$723$	−19754.9	−	11405.5i	−1.01617	−	0.586687i
$724$	69.7736	+	120.851i	0.00358165	+	0.00620360i
$725$		0			0
$726$	15964.3	−	27651.0i	0.816103	−	1.41353i
$727$			28384.6i			1.44804i	0.689779	+	0.724020i	$0.257708\pi$
$727$			28384.6i			1.44804i	−0.689779	+	0.724020i	$0.742292\pi$
$728$	−3245.37	−	25615.6i	−0.165222	−	1.30409i
$729$	−75008.8			−3.81084
$730$		0			0
$731$	1246.63	+	2159.23i	0.0630758	+	0.109251i
$732$	771.616	−	445.493i	0.0389614	−	0.0224944i
$733$	17729.1	+	10235.9i	0.893369	+	0.515787i	0.875043	−	0.484045i	$-0.160833\pi$
$733$	17729.1	+	10235.9i	0.893369	+	0.515787i	0.0183260	+	0.999832i	$0.494166\pi$
$734$	−9900.91			−0.497887
$735$		0			0
$736$	−579.754			−0.0290353
$737$	10007.4	+	5777.76i	0.500171	+	0.288774i
$738$	−5996.06	+	3461.83i	−0.299076	+	0.172672i
$739$	−16590.5	−	28735.6i	−0.825834	−	1.43039i	−0.901280	−	0.433236i	$-0.857372\pi$
$739$	−16590.5	−	28735.6i	−0.825834	−	1.43039i	0.0754464	−	0.997150i	$-0.475962\pi$
$740$		0			0
$741$	−24900.1			−1.23445
$742$	2166.17	+	17097.5i	0.107173	+	0.845916i
$743$			30844.1i			1.52296i	0.648188	+	0.761481i	$0.275527\pi$
$743$			30844.1i			1.52296i	−0.648188	+	0.761481i	$0.724473\pi$
$744$	15686.4	−	27169.7i	0.772974	−	1.33883i
$745$		0			0
$746$	−12912.4	−	22364.9i	−0.633722	−	1.09764i
$747$	44282.6	+	25566.5i	2.16896	+	1.25225i
$748$			87.7393i			0.00428886i
$749$	4135.64	−	9848.21i	0.201753	−	0.480435i
$750$		0			0
$751$	12346.5	−	21384.7i	0.599906	−	1.03907i	−0.392928	−	0.919569i	$-0.628538\pi$
$751$	12346.5	−	21384.7i	0.599906	−	1.03907i	0.992834	−	0.119499i	$-0.0381289\pi$
$752$	8494.13	−	4904.09i	0.411900	−	0.237811i
$753$	−25617.2	+	14790.1i	−1.23977	+	0.715779i
$754$	21163.6	−	36656.4i	1.02219	−	1.77049i
$755$		0			0
$756$	2812.35	+	3702.37i	0.135297	+	0.178113i
$757$			6870.57i			0.329875i	0.986304	+	0.164937i	$0.0527422\pi$
$757$			6870.57i			0.329875i	−0.986304	+	0.164937i	$0.947258\pi$
$758$	7685.12	+	4437.01i	0.368253	+	0.212611i
$759$	1889.88	+	3273.37i	0.0903799	+	0.156542i
$760$		0			0
$761$	−15441.3	+	26745.1i	−0.735540	+	1.27399i	0.218946	+	0.975737i	$0.429738\pi$
$761$	−15441.3	+	26745.1i	−0.735540	+	1.27399i	−0.954486	+	0.298256i	$0.903595\pi$
$762$			14641.2i			0.696057i
$763$	−2821.64	+	2143.34i	−0.133880	+	0.101696i
$764$	−769.273			−0.0364284
$765$		0			0
$766$	−4116.62	−	7130.19i	−0.194177	−	0.336324i
$767$	24814.5	−	14326.6i	1.16819	−	0.674452i
$768$	7079.28	+	4087.22i	0.332619	+	0.192038i
$769$	13536.3			0.634761			0.317380	−	0.948298i	$-0.397197\pi$
$769$	13536.3			0.634761			0.317380	+	0.948298i	$0.397197\pi$
$770$		0			0
$771$	−36411.1			−1.70080
$772$	1873.01	+	1081.38i	0.0873201	+	0.0504143i
$773$	−12371.8	+	7142.87i	−0.575657	+	0.332356i	−0.759406	−	0.650617i	$-0.774510\pi$
$773$	−12371.8	+	7142.87i	−0.575657	+	0.332356i	0.183748	+	0.982973i	$0.441177\pi$
$774$	25463.3	+	44103.8i	1.18251	+	2.04816i
$775$		0			0
$776$	−25122.4			−1.16217
$777$	−6672.22	−	52663.6i	−0.308062	−	2.43153i
$778$		−	35602.6i		−	1.64064i
$779$	−621.249	+	1076.03i	−0.0285732	+	0.0494903i
$780$		0			0
$781$	2913.29	+	5045.96i	0.133477	+	0.231189i
$782$	645.462	+	372.658i	0.0295162	+	0.0170412i
$783$		−	107005.i		−	4.88382i
$784$	−6253.59	+	22460.2i	−0.284876	+	1.02315i
$785$		0			0
$786$	−4573.54	+	7921.61i	−0.207548	+	0.359484i
$787$	−7321.06	+	4226.82i	−0.331598	+	0.191448i	−0.656550	−	0.754282i	$-0.727985\pi$
$787$	−7321.06	+	4226.82i	−0.331598	+	0.191448i	0.324952	+	0.945730i	$0.394652\pi$
$788$	−494.330	+	285.402i	−0.0223474	+	0.0129023i
$789$	−2317.28	+	4013.65i	−0.104559	+	0.181102i
$790$		0			0
$791$	38431.4	−	4869.07i	1.72751	−	0.218867i
$792$		−	25160.6i		−	1.12884i
$793$	9226.49	+	5326.92i	0.413168	+	0.238543i
$794$	−15174.8	−	26283.5i	−0.678254	−	1.17477i
$795$		0			0
$796$	791.789	−	1371.42i	0.0352566	−	0.0610662i
$797$			5465.35i			0.242902i	0.992597	+	0.121451i	$0.0387547\pi$
$797$			5465.35i			0.242902i	−0.992597	+	0.121451i	$0.961245\pi$
$798$	19432.1	+	8160.29i	0.862018	+	0.361994i
$799$	−1526.32			−0.0675810
$800$		0			0
$801$	−37471.3	−	64902.3i	−1.65291	−	2.86293i
$802$	3800.18	−	2194.04i	0.167318	−	0.0966011i
$803$	−3204.80	−	1850.29i	−0.140840	−	0.0813142i
$804$	3960.88			0.173743
$805$		0			0
$806$	−26720.2			−1.16771
$807$	49865.6	+	28789.9i	2.17516	+	1.25583i
$808$	−22689.0	+	13099.5i	−0.987867	+	0.570346i
$809$	8300.53	+	14376.9i	0.360731	+	0.624804i	0.988081	−	0.153933i	$-0.0491940\pi$
$809$	8300.53	+	14376.9i	0.360731	+	0.624804i	−0.627350	+	0.778737i	$0.715861\pi$
$810$		0			0
$811$	−24613.6			−1.06572			−0.532861	−	0.846203i	$-0.678883\pi$
$811$	−24613.6			−1.06572			−0.532861	+	0.846203i	$0.678883\pi$
$812$	−1778.69	+	1351.10i	−0.0768714	+	0.0583922i
$813$			4373.17i			0.188652i
$814$	6496.37	−	11252.0i	0.279727	−	0.484501i
$815$		0			0
$816$	−3612.31	−	6256.70i	−0.154971	−	0.268417i
$817$	7914.73	+	4569.57i	0.338924	+	0.195678i
$818$		−	41177.2i		−	1.76006i
$819$	−33899.3	+	80724.6i	−1.44632	+	3.44413i
$820$		0			0
$821$	8970.29	−	15537.0i	0.381322	−	0.660469i	−0.609930	−	0.792456i	$-0.708802\pi$
$821$	8970.29	−	15537.0i	0.381322	−	0.660469i	0.991251	+	0.131987i	$0.0421357\pi$
$822$	25995.0	−	15008.2i	1.10302	−	0.636827i
$823$	−39758.4	+	22954.5i	−1.68395	+	0.972229i	−0.724960	+	0.688791i	$0.758142\pi$
$823$	−39758.4	+	22954.5i	−1.68395	+	0.972229i	−0.958990	+	0.283439i	$0.908525\pi$
$824$	−11223.8	+	19440.1i	−0.474513	+	0.821880i
$825$		0			0
$826$	−24060.4	+	3048.33i	−1.01352	+	0.128408i
$827$			36696.8i			1.54301i	0.636221	+	0.771507i	$0.280497\pi$
$827$			36696.8i			1.54301i	−0.636221	+	0.771507i	$0.719503\pi$
$828$	821.972	+	474.566i	0.0344994	+	0.0199182i
$829$	14460.2	+	25045.9i	0.605820	+	1.04931i	0.991921	+	0.126855i	$0.0404883\pi$
$829$	14460.2	+	25045.9i	0.605820	+	1.04931i	−0.386101	+	0.922457i	$0.626178\pi$
$830$		0			0
$831$	−540.096	+	935.474i	−0.0225460	+	0.0390508i
$832$			30267.5i			1.26122i
$833$	2590.38	−	2540.34i	0.107745	−	0.105663i
$834$	−33497.4			−1.39079
$835$		0			0
$836$	160.805	+	278.523i	0.00665259	+	0.0115226i
$837$	−58499.6	+	33774.8i	−2.41582	+	1.39478i
$838$	29166.2	+	16839.1i	1.20230	+	0.694150i
$839$	−5852.41			−0.240820			−0.120410	−	0.992724i	$-0.538421\pi$
$839$	−5852.41			−0.240820			−0.120410	+	0.992724i	$0.538421\pi$
$840$		0			0
$841$	27018.0			1.10779
$842$	8524.93	+	4921.87i	0.348918	+	0.201448i
$843$	70129.4	−	40489.2i	2.86523	−	1.65424i
$844$	−138.736	−	240.298i	−0.00565817	−	0.00980023i
$845$		0			0
$846$	−31176.1			−1.26697
$847$	−18575.6	−	7800.62i	−0.753562	−	0.316449i
$848$		−	21654.8i		−	0.876920i
$849$	29121.7	−	50440.3i	1.17721	−	2.03900i
$850$		0			0
$851$	−3440.54	−	5959.19i	−0.138590	−	0.240045i
$852$	1729.60	+	998.586i	0.0695484	+	0.0401538i
$853$		−	18715.7i		−	0.751245i	−0.926773	−	0.375623i	$-0.877429\pi$
$853$		−	18715.7i		−	0.751245i	0.926773	−	0.375623i	$-0.122571\pi$
$854$	−5454.64	−	7180.85i	−0.218564	−	0.287733i
$855$		0			0
$856$	−6290.42	+	10895.3i	−0.251171	+	0.435041i
$857$	−14979.8	+	8648.57i	−0.597081	+	0.344725i	−0.767893	−	0.640579i	$-0.778695\pi$
$857$	−14979.8	+	8648.57i	−0.597081	+	0.344725i	0.170811	+	0.985304i	$0.445361\pi$
$858$	−25332.4	+	14625.7i	−1.00797	+	0.581949i
$859$	15366.4	−	26615.3i	0.610354	−	1.05716i	−0.380827	−	0.924646i	$-0.624361\pi$
$859$	15366.4	−	26615.3i	0.610354	−	1.05716i	0.991181	−	0.132518i	$-0.0423061\pi$
$860$		0			0
$861$	3607.29	+	4748.88i	0.142783	+	0.187969i
$862$		−	24322.9i		−	0.961070i
$863$	−9347.02	−	5396.51i	−0.368686	−	0.212861i	0.304198	−	0.952609i	$-0.401612\pi$
$863$	−9347.02	−	5396.51i	−0.368686	−	0.212861i	−0.672884	+	0.739748i	$0.734945\pi$
$864$	−5671.25	−	9822.89i	−0.223310	−	0.386784i
$865$		0			0
$866$	−1194.89	+	2069.60i	−0.0468867	+	0.0812101i
$867$		−	48242.9i		−	1.88975i
$868$	1300.07	+	545.950i	0.0508380	+	0.0213488i
$869$	7257.12			0.283292
$870$		0			0
$871$	23680.8	+	41016.4i	0.921234	+	1.59562i
$872$	3614.38	−	2086.76i	0.140365	−	0.0810398i
$873$	73773.9	+	42593.4i	2.86010	+	1.65128i
$874$	2731.97			0.105733
$875$		0			0
$876$	−1268.45			−0.0489233
$877$	−16945.3	−	9783.36i	−0.652453	−	0.376694i	0.136942	−	0.990579i	$-0.456272\pi$
$877$	−16945.3	−	9783.36i	−0.652453	−	0.376694i	−0.789395	+	0.613885i	$0.789606\pi$
$878$	−21415.1	+	12364.0i	−0.823151	+	0.475246i
$879$	6285.01	+	10886.0i	0.241170	+	0.417718i
$880$		0			0
$881$	27700.5			1.05931			0.529656	−	0.848213i	$-0.322321\pi$
$881$	27700.5			1.05931			0.529656	+	0.848213i	$0.322321\pi$
$882$	52910.2	−	51888.2i	2.01993	−	1.98091i
$883$			5071.61i			0.193288i	0.995319	+	0.0966440i	$0.0308108\pi$
$883$			5071.61i			0.193288i	−0.995319	+	0.0966440i	$0.969189\pi$
$884$	−179.805	+	311.431i	−0.00684106	+	0.0118491i
$885$		0			0
$886$	−21277.6	−	36853.8i	−0.806810	−	1.39744i
$887$	−19527.9	−	11274.4i	−0.739212	−	0.426784i	0.0825707	−	0.996585i	$-0.473687\pi$
$887$	−19527.9	−	11274.4i	−0.739212	−	0.426784i	−0.821783	+	0.569801i	$0.807020\pi$
$888$			62525.0i			2.36284i
$889$	9165.39	−	1161.21i	0.345779	−	0.0438084i
$890$		0			0
$891$	−21403.0	+	37071.1i	−0.804745	+	1.39386i
$892$	1097.21	−	633.476i	0.0411854	−	0.0237784i
$893$	−4845.20	+	2797.38i	−0.181566	+	0.104827i
$894$	18945.3	−	32814.2i	0.708753	−	1.22760i
$895$		0			0
$896$	11298.0	−	26904.0i	0.421250	−	1.00312i
$897$			15491.8i			0.576651i
$898$	−2127.94	−	1228.57i	−0.0790760	−	0.0456545i
$899$	−16226.0	−	28104.3i	−0.601967	−	1.04264i
$900$		0			0
$901$	−1684.92	+	2918.37i	−0.0623007	+	0.107908i
$902$			1459.62i			0.0538803i
$903$	34930.2	−	26533.3i	1.28727	−	0.977821i
$904$	−45627.7			−1.67871
$905$		0			0
$906$	16875.8	+	29229.7i	0.618830	+	1.07185i
$907$	20994.3	−	12121.1i	0.768584	−	0.443742i	−0.0637854	−	0.997964i	$-0.520317\pi$
$907$	20994.3	−	12121.1i	0.768584	−	0.443742i	0.832369	+	0.554222i	$0.186984\pi$
$908$	−157.103	−	90.7035i	−0.00574191	−	0.00331509i
$909$	88837.4			3.24153
$910$		0			0
$911$	6574.69			0.239110			0.119555	−	0.992828i	$-0.461853\pi$
$911$	6574.69			0.239110			0.119555	+	0.992828i	$0.461853\pi$
$912$	−22934.1	−	13241.0i	−0.832702	−	0.480760i
$913$	9335.48	−	5389.84i	0.338400	−	0.195375i
$914$	20266.5	+	35102.6i	0.733432	+	1.27034i
$915$		0			0
$916$	412.272			0.0148710
$917$	5321.66	+	2234.76i	0.191643	+	0.0804781i
$918$			14581.6i			0.524253i
$919$	−20956.1	+	36297.1i	−0.752208	+	1.30286i	0.194542	+	0.980894i	$0.437678\pi$
$919$	−20956.1	+	36297.1i	−0.752208	+	1.30286i	−0.946750	+	0.321969i	$0.895655\pi$
$920$		0			0
$921$	2480.55	+	4296.44i	0.0887480	+	0.153716i
$922$	−7723.13	−	4458.95i	−0.275865	−	0.159271i
$923$			23880.9i			0.851625i
$924$	1531.39	−	194.019i	0.0545226	−	0.00690774i
$925$		0			0
$926$	−14511.0	+	25133.7i	−0.514968	+	0.891950i
$927$	65918.9	−	38058.3i	2.33556	−	1.34843i
$928$	4719.10	−	2724.57i	0.166931	−	0.0963777i
$929$	−24085.7	+	41717.7i	−0.850621	+	1.47332i	0.0300283	+	0.999549i	$0.490440\pi$
$929$	−24085.7	+	41717.7i	−0.850621	+	1.47332i	−0.880649	+	0.473769i	$0.842893\pi$
$930$		0			0
$931$	3567.16	−	12811.7i	0.125573	−	0.451006i
$932$		−	1329.75i		−	0.0467355i
$933$	−917.754	−	529.866i	−0.0322036	−	0.0185927i
$934$	14498.5	+	25112.1i	0.507929	+	0.879759i
$935$		0			0
$936$	51561.9	−	89307.8i	1.80059	−	3.11871i
$937$		−	48696.8i		−	1.69782i	−0.528539	−	0.848909i	$-0.677260\pi$
$937$		−	48696.8i		−	1.69782i	0.528539	−	0.848909i	$-0.322740\pi$
$938$	−5038.66	−	39770.0i	−0.175392	−	1.38437i
$939$	37285.4			1.29581
$940$		0			0
$941$	1000.15	+	1732.31i	0.0346482	+	0.0600124i	0.882830	−	0.469694i	$-0.155636\pi$
$941$	1000.15	+	1732.31i	0.0346482	+	0.0600124i	−0.848181	+	0.529706i	$0.822302\pi$
$942$	−92073.4	+	53158.6i	−3.18462	+	1.83864i
$943$	669.462	+	386.514i	0.0231184	+	0.0133474i
$944$	30473.6			1.05067
$945$		0			0
$946$	10736.2			0.368988
$947$	−36802.1	−	21247.7i	−1.26284	−	0.729101i	−0.289216	−	0.957264i	$-0.593395\pi$
$947$	−36802.1	−	21247.7i	−1.26284	−	0.729101i	−0.973623	+	0.228163i	$0.926728\pi$
$948$	2154.25	−	1243.76i	0.0738048	−	0.0426112i
$949$	−7583.64	−	13135.2i	−0.259405	−	0.449303i
$950$		0			0
$951$	−65327.9			−2.22755
$952$	−3402.92	+	2584.89i	−0.115850	+	0.0880008i
$953$		−	51166.5i		−	1.73919i	−0.493768	−	0.869594i	$-0.664381\pi$
$953$		−	51166.5i		−	1.73919i	0.493768	−	0.869594i	$-0.335619\pi$
$954$	−34415.7	+	59609.7i	−1.16798	+	2.02299i
$955$		0			0
$956$	580.260	+	1005.04i	0.0196307	+	0.0340014i
$957$	−30766.6	−	17763.1i	−1.03923	−	0.600000i
$958$			38481.3i			1.29778i
$959$	−11456.8	−	15082.5i	−0.385777	−	0.507863i
$960$		0			0
$961$	4652.38	−	8058.16i	0.156167	−	0.270490i
$962$	46117.8	−	26626.1i	1.54563	−	0.892371i
$963$	36944.6	−	21330.0i	1.23627	−	0.713758i
$964$	−603.782	+	1045.78i	−0.0201727	+	0.0349402i
$965$		0			0
$966$	5076.98	−	12089.8i	0.169099	−	0.402675i
$967$		−	26324.2i		−	0.875418i	−0.899117	−	0.437709i	$-0.855790\pi$
$967$		−	26324.2i		−	0.875418i	0.899117	−	0.437709i	$-0.144210\pi$
$968$	20550.7	+	11865.0i	0.682361	+	0.393961i
$969$	2060.52	+	3568.93i	0.0683112	+	0.118318i
$970$		0			0
$971$	2617.28	−	4533.27i	0.0865012	−	0.149824i	−0.819529	−	0.573038i	$-0.805765\pi$
$971$	2617.28	−	4533.27i	0.0865012	−	0.149824i	0.906030	+	0.423214i	$0.139098\pi$
$972$			7894.44i			0.260508i
$973$	2656.71	+	20969.3i	0.0875337	+	0.690901i
$974$	−24751.4			−0.814257
$975$		0			0
$976$	5665.33	+	9812.63i	0.185802	+	0.321818i
$977$	−38954.3	+	22490.3i	−1.27560	+	0.736467i	−0.976036	−	0.217610i	$-0.930174\pi$
$977$	−38954.3	+	22490.3i	−1.27560	+	0.736467i	−0.299562	+	0.954077i	$0.596841\pi$
$978$	−68774.5	−	39707.0i	−2.24864	−	1.29825i
$979$	−15799.1			−0.515774
$980$		0			0
$981$	−14151.9			−0.460585
$982$	27398.6	+	15818.6i	0.890350	+	0.514044i
$983$	−14197.0	+	8196.66i	−0.460646	+	0.265954i	−0.712316	−	0.701859i	$-0.752354\pi$
$983$	−14197.0	+	8196.66i	−0.460646	+	0.265954i	0.251670	+	0.967813i	$0.419020\pi$
$984$	−3512.06	−	6083.07i	−0.113781	−	0.197074i
$985$		0			0
$986$	−7005.27			−0.226261
$987$	3375.17	+	26640.1i	0.108848	+	0.859132i
$988$			1318.16i			0.0424456i
$989$	2842.99	−	4924.20i	0.0914073	−	0.158322i
$990$		0			0
$991$	1941.67	+	3363.07i	0.0622393	+	0.107802i	0.895466	−	0.445130i	$-0.146842\pi$
$991$	1941.67	+	3363.07i	0.0622393	+	0.107802i	−0.833227	+	0.552931i	$0.813509\pi$
$992$	−2979.06	−	1719.96i	−0.0953480	−	0.0550492i
$993$			1092.13i			0.0349020i
$994$	7826.27	−	18636.7i	0.249733	−	0.594689i
$995$		0			0
$996$	1847.47	−	3199.92i	0.0587746	−	0.101801i
$997$	−12092.9	+	6981.81i	−0.384137	+	0.221781i	−0.679617	−	0.733567i	$-0.737854\pi$
$997$	−12092.9	+	6981.81i	−0.384137	+	0.221781i	0.295480	+	0.955349i	$0.404521\pi$
$998$	30588.4	−	17660.2i	0.970198	−	0.560144i
$999$	67311.8	−	116588.i	2.13178	−	3.69236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.k.e.149.4		32
5.2	odd	4		175.4.e.e.51.7	✓	16
5.3	odd	4		175.4.e.f.51.2	yes	16
5.4	even	2	inner	175.4.k.e.149.13		32
7.4	even	3	inner	175.4.k.e.74.13		32
35.2	odd	12		1225.4.a.bn.1.2		8
35.4	even	6	inner	175.4.k.e.74.4		32
35.12	even	12		1225.4.a.bo.1.2		8
35.18	odd	12		175.4.e.f.151.2	yes	16
35.23	odd	12		1225.4.a.bl.1.7		8
35.32	odd	12		175.4.e.e.151.7	yes	16
35.33	even	12		1225.4.a.bk.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.4.e.e.51.7	✓	16	5.2	odd	4
175.4.e.e.151.7	yes	16	35.32	odd	12
175.4.e.f.51.2	yes	16	5.3	odd	4
175.4.e.f.151.2	yes	16	35.18	odd	12
175.4.k.e.74.4		32	35.4	even	6	inner
175.4.k.e.74.13		32	7.4	even	3	inner
175.4.k.e.149.4		32	1.1	even	1	trivial
175.4.k.e.149.13		32	5.4	even	2	inner
1225.4.a.bk.1.7		8	35.33	even	12
1225.4.a.bl.1.7		8	35.23	odd	12
1225.4.a.bn.1.2		8	35.2	odd	12
1225.4.a.bo.1.2		8	35.12	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+(-2.52961 - 1.46047i) q^{2} +(-8.70206 + 5.02414i) q^{3} +(0.265967 + 0.460668i) q^{4} +29.3505 q^{6} +(-2.32782 - 18.3734i) q^{7} +21.8138i q^{8} +(36.9839 - 64.0580i) q^{9} +(-7.79680 - 13.5045i) q^{11} +(-4.62892 - 2.67251i) q^{12} -63.9123i q^{13} +(-20.9454 + 49.8773i) q^{14} +(33.9863 - 58.8659i) q^{16} +(-9.16053 + 5.28883i) q^{17} +(-187.110 + 108.028i) q^{18} +(-19.3864 + 33.5782i) q^{19} +(112.567 + 148.191i) q^{21} +45.5481i q^{22} +(20.8909 + 12.0614i) q^{23} +(-109.596 - 189.825i) q^{24} +(-93.3422 + 161.673i) q^{26} +471.945i q^{27} +(7.84491 - 5.95906i) q^{28} -226.731 q^{29} +(71.5651 + 123.954i) q^{31} +(-20.8136 + 12.0168i) q^{32} +(135.697 + 78.3444i) q^{33} +30.8968 q^{34} +39.3460 q^{36} +(-247.036 - 142.626i) q^{37} +(98.0800 - 56.6265i) q^{38} +(321.104 + 556.168i) q^{39} +32.0457 q^{41} +(-68.3225 - 539.268i) q^{42} -235.711i q^{43} +(4.14738 - 7.18348i) q^{44} +(-35.2306 - 61.0212i) q^{46} +(124.964 + 72.1481i) q^{47} +683.006i q^{48} +(-332.163 + 85.5397i) q^{49} +(53.1436 - 92.0475i) q^{51} +(29.4423 - 16.9985i) q^{52} +(275.900 - 159.291i) q^{53} +(689.263 - 1193.84i) q^{54} +(400.794 - 50.7786i) q^{56} -389.599i q^{57} +(573.542 + 331.135i) q^{58} +(224.161 + 388.258i) q^{59} +(-83.3473 + 144.362i) q^{61} -418.076i q^{62} +(-1263.05 - 530.404i) q^{63} -473.580 q^{64} +(-228.840 - 396.362i) q^{66} +(-641.761 + 370.521i) q^{67} +(-4.87279 - 2.81331i) q^{68} -242.392 q^{69} -373.652 q^{71} +(1397.35 + 806.760i) q^{72} +(205.520 - 118.657i) q^{73} +(416.604 + 721.580i) q^{74} -20.6245 q^{76} +(-229.973 + 174.690i) q^{77} -1875.86i q^{78} +(-232.695 + 403.040i) q^{79} +(-1372.55 - 2377.33i) q^{81} +(-81.0631 - 46.8018i) q^{82} +691.289i q^{83} +(-38.3277 + 91.2700i) q^{84} +(-344.249 + 596.257i) q^{86} +(1973.03 - 1139.13i) q^{87} +(294.584 - 170.078i) q^{88} +(506.590 - 877.440i) q^{89} +(-1174.28 + 148.776i) q^{91} +12.8317i q^{92} +(-1245.53 - 719.105i) q^{93} +(-210.741 - 365.014i) q^{94} +(120.748 - 209.141i) q^{96} +1151.67i q^{97} +(965.172 + 268.732i) q^{98} -1153.42 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 54 q^{4} + 16 q^{6} + 84 q^{9} + 130 q^{14} - 382 q^{16} - 84 q^{19} + 604 q^{21} - 584 q^{24} - 46 q^{26} - 1152 q^{29} - 36 q^{31} + 1952 q^{34} - 2844 q^{36} + 44 q^{39} + 672 q^{41} - 1760 q^{44}+ \cdots - 16344 q^{99}+O(q^{100}) \) 32 * q + 54 * q^4 + 16 * q^6 + 84 * q^9 + 130 * q^14 - 382 * q^16 - 84 * q^19 + 604 * q^21 - 584 * q^24 - 46 * q^26 - 1152 * q^29 - 36 * q^31 + 1952 * q^34 - 2844 * q^36 + 44 * q^39 + 672 * q^41 - 1760 * q^44 + 196 * q^46 + 2228 * q^49 - 1256 * q^51 + 4326 * q^54 + 6102 * q^56 + 1116 * q^59 + 2992 * q^61 - 9744 * q^64 + 1364 * q^66 - 3288 * q^69 - 2896 * q^71 + 470 * q^74 - 6036 * q^76 - 1680 * q^79 - 4784 * q^81 + 10542 * q^84 - 3632 * q^86 + 5356 * q^89 + 4092 * q^91 + 7250 * q^94 + 13202 * q^96 - 16344 * q^99

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