LMFDB - Embedded newform 75.4.e.c.68.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,4,Mod(32,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("75.32");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	75.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.42514325043$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.28356903014400.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 209x^{4} + 1600 $ x^8 + 209*x^4 + 1600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			68.3
Root			$1.18766 - 1.18766i$ of defining polynomial
Character	$\chi$	$=$	75.68
Dual form			75.4.e.c.32.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18766 + 1.18766i) q^{2} +(-5.11173 + 0.932827i) q^{3} -5.17891i q^{4} +(-7.17891 - 4.96314i) q^{6} +(13.3578 - 13.3578i) q^{7} +(15.6521 - 15.6521i) q^{8} +(25.2597 - 9.53673i) q^{9} +O(q^{10})$	\(q+(1.18766 + 1.18766i) q^{2} +(-5.11173 + 0.932827i) q^{3} -5.17891i q^{4} +(-7.17891 - 4.96314i) q^{6} +(13.3578 - 13.3578i) q^{7} +(15.6521 - 15.6521i) q^{8} +(25.2597 - 9.53673i) q^{9} -28.7164i q^{11} +(4.83102 + 26.4732i) q^{12} +(-14.1789 - 14.1789i) q^{13} +31.7292 q^{14} -4.25236 q^{16} +(18.5587 + 18.5587i) q^{17} +(41.3264 + 18.6736i) q^{18} -49.0735i q^{19} +(-55.8211 + 80.7421i) q^{21} +(34.1055 - 34.1055i) q^{22} +(-37.7738 + 37.7738i) q^{23} +(-65.4088 + 94.6102i) q^{24} -33.6796i q^{26} +(-120.225 + 72.3121i) q^{27} +(-69.1789 - 69.1789i) q^{28} -125.854 q^{29} +247.367 q^{31} +(-130.267 - 130.267i) q^{32} +(26.7874 + 146.791i) q^{33} +44.0829i q^{34} +(-49.3898 - 130.818i) q^{36} +(127.463 - 127.463i) q^{37} +(58.2828 - 58.2828i) q^{38} +(85.7053 + 59.2524i) q^{39} +390.328i q^{41} +(-162.191 + 29.5978i) q^{42} +(39.3993 + 39.3993i) q^{43} -148.720 q^{44} -89.7251 q^{46} +(124.560 + 124.560i) q^{47} +(21.7369 - 3.96671i) q^{48} -13.8625i q^{49} +(-112.179 - 77.5549i) q^{51} +(-73.4313 + 73.4313i) q^{52} +(-160.441 + 160.441i) q^{53} +(-228.669 - 56.9040i) q^{54} -418.156i q^{56} +(45.7770 + 250.850i) q^{57} +(-149.473 - 149.473i) q^{58} +729.423 q^{59} +2.00000 q^{61} +(293.789 + 293.789i) q^{62} +(210.024 - 464.804i) q^{63} -275.409i q^{64} +(-142.524 + 206.153i) q^{66} +(329.987 - 329.987i) q^{67} +(96.1136 - 96.1136i) q^{68} +(157.853 - 228.326i) q^{69} -171.760i q^{71} +(246.097 - 544.637i) q^{72} +(279.927 + 279.927i) q^{73} +302.767 q^{74} -254.147 q^{76} +(-383.589 - 383.589i) q^{77} +(31.4172 + 172.161i) q^{78} -48.0189i q^{79} +(547.102 - 481.789i) q^{81} +(-463.578 + 463.578i) q^{82} +(144.451 - 144.451i) q^{83} +(418.156 + 289.092i) q^{84} +93.5862i q^{86} +(643.334 - 117.400i) q^{87} +(-449.473 - 449.473i) q^{88} -1417.21 q^{89} -378.799 q^{91} +(195.627 + 195.627i) q^{92} +(-1264.48 + 230.751i) q^{93} +295.872i q^{94} +(787.409 + 544.375i) q^{96} +(-908.111 + 908.111i) q^{97} +(16.4640 - 16.4640i) q^{98} +(-273.861 - 725.367i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} - 12 q^{6} + 16 q^{7}+O(q^{10}) $ 8 * q + 6 * q^3 - 12 * q^6 + 16 * q^7	$ 8 q + 6 q^{3} - 12 q^{6} + 16 q^{7} - 132 q^{12} - 68 q^{13} + 284 q^{16} + 240 q^{18} - 492 q^{21} + 500 q^{22} - 702 q^{27} - 508 q^{28} + 616 q^{31} + 240 q^{33} - 804 q^{36} + 1156 q^{37} - 540 q^{42} - 548 q^{43} + 736 q^{46} + 1116 q^{48} - 852 q^{51} - 224 q^{52} - 684 q^{57} - 60 q^{58} + 16 q^{61} - 1428 q^{63} + 2040 q^{66} - 404 q^{67} + 1800 q^{72} + 2512 q^{73} - 1488 q^{76} + 360 q^{78} + 288 q^{81} - 2800 q^{82} + 1680 q^{87} - 2460 q^{88} - 1304 q^{91} - 3408 q^{93} + 4164 q^{96} - 1904 q^{97}+O(q^{100}) $ 8 * q + 6 * q^3 - 12 * q^6 + 16 * q^7 - 132 * q^12 - 68 * q^13 + 284 * q^16 + 240 * q^18 - 492 * q^21 + 500 * q^22 - 702 * q^27 - 508 * q^28 + 616 * q^31 + 240 * q^33 - 804 * q^36 + 1156 * q^37 - 540 * q^42 - 548 * q^43 + 736 * q^46 + 1116 * q^48 - 852 * q^51 - 224 * q^52 - 684 * q^57 - 60 * q^58 + 16 * q^61 - 1428 * q^63 + 2040 * q^66 - 404 * q^67 + 1800 * q^72 + 2512 * q^73 - 1488 * q^76 + 360 * q^78 + 288 * q^81 - 2800 * q^82 + 1680 * q^87 - 2460 * q^88 - 1304 * q^91 - 3408 * q^93 + 4164 * q^96 - 1904 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.18766	+	1.18766i	0.419903	+	0.419903i	0.885170	−	0.465267i	$-0.154042\pi$
$2$	1.18766	+	1.18766i	0.419903	+	0.419903i	−0.465267	+	0.885170i	$0.654042\pi$
$3$	−5.11173	+	0.932827i	−0.983754	+	0.179523i
$3$	−5.11173	+	0.932827i	−0.983754	+	0.179523i
$4$		−	5.17891i		−	0.647364i
$5$		0			0
$5$		0			0
$6$	−7.17891	−	4.96314i	−0.488463	−	0.337699i
$7$	13.3578	−	13.3578i	0.721254	−	0.721254i	−0.247606	−	0.968861i	$-0.579644\pi$
$7$	13.3578	−	13.3578i	0.721254	−	0.721254i	0.968861	+	0.247606i	$0.0796440\pi$
$8$	15.6521	−	15.6521i	0.691732	−	0.691732i
$9$	25.2597	−	9.53673i	0.935543	−	0.353212i
$10$		0			0
$11$		−	28.7164i		−	0.787121i	−0.919299	−	0.393560i	$-0.871243\pi$
$11$		−	28.7164i		−	0.787121i	0.919299	−	0.393560i	$-0.128757\pi$
$12$	4.83102	+	26.4732i	0.116216	+	0.636846i
$13$	−14.1789	−	14.1789i	−0.302502	−	0.302502i	0.539490	−	0.841992i	$-0.318617\pi$
$13$	−14.1789	−	14.1789i	−0.302502	−	0.302502i	−0.841992	+	0.539490i	$0.818617\pi$
$14$	31.7292			0.605713
$15$		0			0
$16$	−4.25236			−0.0664431
$17$	18.5587	+	18.5587i	0.264773	+	0.264773i	0.826990	−	0.562217i	$-0.190051\pi$
$17$	18.5587	+	18.5587i	0.264773	+	0.264773i	−0.562217	+	0.826990i	$0.690051\pi$
$18$	41.3264	+	18.6736i	0.541152	+	0.244522i
$19$		−	49.0735i		−	0.592538i	−0.955105	−	0.296269i	$-0.904258\pi$
$19$		−	49.0735i		−	0.592538i	0.955105	−	0.296269i	$-0.0957425\pi$
$20$		0			0
$21$	−55.8211	+	80.7421i	−0.580055	+	0.839018i
$22$	34.1055	−	34.1055i	0.330514	−	0.330514i
$23$	−37.7738	+	37.7738i	−0.342451	+	0.342451i	−0.857288	−	0.514837i	$-0.827852\pi$
$23$	−37.7738	+	37.7738i	−0.342451	+	0.342451i	0.514837	+	0.857288i	$0.327852\pi$
$24$	−65.4088	+	94.6102i	−0.556313	+	0.804676i
$25$		0			0
$26$		−	33.6796i		−	0.254042i
$27$	−120.225	+	72.3121i	−0.856935	+	0.515425i
$28$	−69.1789	−	69.1789i	−0.466914	−	0.466914i
$29$	−125.854			−0.805882			−0.402941	−	0.915226i	$-0.632012\pi$
$29$	−125.854			−0.805882			−0.402941	+	0.915226i	$0.632012\pi$
$30$		0			0
$31$	247.367			1.43318			0.716588	−	0.697496i	$-0.245703\pi$
$31$	247.367			1.43318			0.716588	+	0.697496i	$0.245703\pi$
$32$	−130.267	−	130.267i	−0.719632	−	0.719632i
$33$	26.7874	+	146.791i	0.141306	+	0.774333i
$34$			44.0829i			0.222357i
$35$		0			0
$36$	−49.3898	−	130.818i	−0.228657	−	0.605637i
$37$	127.463	−	127.463i	0.566347	−	0.566347i	−0.364756	−	0.931103i	$-0.618848\pi$
$37$	127.463	−	127.463i	0.566347	−	0.566347i	0.931103	+	0.364756i	$0.118848\pi$
$38$	58.2828	−	58.2828i	0.248808	−	0.248808i
$39$	85.7053	+	59.2524i	0.351893	+	0.243281i
$40$		0			0
$41$			390.328i			1.48680i	0.668845	+	0.743402i	$0.266789\pi$
$41$			390.328i			1.48680i	−0.668845	+	0.743402i	$0.733211\pi$
$42$	−162.191	+	29.5978i	−0.595873	+	0.108739i
$43$	39.3993	+	39.3993i	0.139729	+	0.139729i	0.773511	−	0.633783i	$-0.218499\pi$
$43$	39.3993	+	39.3993i	0.139729	+	0.139729i	−0.633783	+	0.773511i	$0.718499\pi$
$44$	−148.720			−0.509553
$45$		0			0
$46$	−89.7251			−0.287592
$47$	124.560	+	124.560i	0.386575	+	0.386575i	0.873464	−	0.486889i	$-0.161868\pi$
$47$	124.560	+	124.560i	0.386575	+	0.386575i	−0.486889	+	0.873464i	$0.661868\pi$
$48$	21.7369	−	3.96671i	0.0653637	−	0.0119280i
$49$		−	13.8625i		−	0.0404155i
$50$		0			0
$51$	−112.179	−	77.5549i	−0.308004	−	0.212938i
$52$	−73.4313	+	73.4313i	−0.195829	+	0.195829i
$53$	−160.441	+	160.441i	−0.415816	+	0.415816i	−0.883759	−	0.467943i	$-0.844995\pi$
$53$	−160.441	+	160.441i	−0.415816	+	0.415816i	0.467943	+	0.883759i	$0.344995\pi$
$54$	−228.669	−	56.9040i	−0.576257	−	0.143401i
$55$		0			0
$56$		−	418.156i		−	0.997830i
$57$	45.7770	+	250.850i	0.106374	+	0.582912i
$58$	−149.473	−	149.473i	−0.338392	−	0.338392i
$59$	729.423			1.60954			0.804769	−	0.593588i	$-0.202289\pi$
$59$	729.423			1.60954			0.804769	+	0.593588i	$0.202289\pi$
$60$		0			0
$61$	2.00000			0.00419793			0.00209897	−	0.999998i	$-0.499332\pi$
$61$	2.00000			0.00419793			0.00209897	+	0.999998i	$0.499332\pi$
$62$	293.789	+	293.789i	0.601795	+	0.601795i
$63$	210.024	−	464.804i	0.420009	−	0.929520i
$64$		−	275.409i		−	0.537908i
$65$		0			0
$66$	−142.524	+	206.153i	−0.265810	+	0.384479i
$67$	329.987	−	329.987i	0.601706	−	0.601706i	−0.339059	−	0.940765i	$-0.610109\pi$
$67$	329.987	−	329.987i	0.601706	−	0.601706i	0.940765	+	0.339059i	$0.110109\pi$
$68$	96.1136	−	96.1136i	0.171404	−	0.171404i
$69$	157.853	−	228.326i	0.275410	−	0.398365i
$70$		0			0
$71$		−	171.760i		−	0.287100i	−0.989643	−	0.143550i	$-0.954148\pi$
$71$		−	171.760i		−	0.287100i	0.989643	−	0.143550i	$-0.0458518\pi$
$72$	246.097	−	544.637i	0.402817	−	0.891474i
$73$	279.927	+	279.927i	0.448807	+	0.448807i	0.894958	−	0.446151i	$-0.147205\pi$
$73$	279.927	+	279.927i	0.448807	+	0.448807i	−0.446151	+	0.894958i	$0.647205\pi$
$74$	302.767			0.475621
$75$		0			0
$76$	−254.147			−0.383587
$77$	−383.589	−	383.589i	−0.567714	−	0.567714i
$78$	31.4172	+	172.161i	0.0456064	+	0.249915i
$79$		−	48.0189i		−	0.0683866i	−0.999415	−	0.0341933i	$-0.989114\pi$
$79$		−	48.0189i		−	0.0683866i	0.999415	−	0.0341933i	$-0.0108862\pi$
$80$		0			0
$81$	547.102	−	481.789i	0.750483	−	0.660890i
$82$	−463.578	+	463.578i	−0.624313	+	0.624313i
$83$	144.451	−	144.451i	0.191031	−	0.191031i	−0.605111	−	0.796141i	$-0.706871\pi$
$83$	144.451	−	144.451i	0.191031	−	0.191031i	0.796141	+	0.605111i	$0.206871\pi$
$84$	418.156	+	289.092i	0.543150	+	0.375507i
$85$		0			0
$86$			93.5862i			0.117345i
$87$	643.334	−	117.400i	0.792789	−	0.144674i
$88$	−449.473	−	449.473i	−0.544477	−	0.544477i
$89$	−1417.21			−1.68790			−0.843952	−	0.536419i	$-0.819777\pi$
$89$	−1417.21			−1.68790			−0.843952	+	0.536419i	$0.819777\pi$
$90$		0			0
$91$	−378.799			−0.436361
$92$	195.627	+	195.627i	0.221690	+	0.221690i
$93$	−1264.48	+	230.751i	−1.40989	+	0.257288i
$94$			295.872i			0.324647i
$95$		0			0
$96$	787.409	+	544.375i	0.837131	+	0.578751i
$97$	−908.111	+	908.111i	−0.950564	+	0.950564i	−0.998834	−	0.0482702i	$-0.984629\pi$
$97$	−908.111	+	908.111i	−0.950564	+	0.950564i	0.0482702	+	0.998834i	$0.484629\pi$
$98$	16.4640	−	16.4640i	0.0169706	−	0.0169706i
$99$	−273.861	−	725.367i	−0.278020	−	0.736385i
$100$		0			0
$101$			337.668i			0.332665i	0.986070	+	0.166333i	$0.0531926\pi$
$101$			337.668i			0.332665i	−0.986070	+	0.166333i	$0.946807\pi$
$102$	−41.1217	−	225.340i	−0.0399182	−	0.218745i
$103$	933.505	+	933.505i	0.893019	+	0.893019i	0.994806	−	0.101787i	$-0.0324561\pi$
$103$	933.505	+	933.505i	0.893019	+	0.893019i	−0.101787	+	0.994806i	$0.532456\pi$
$104$	−443.860			−0.418500
$105$		0			0
$106$	−381.100			−0.349205
$107$	−596.188	−	596.188i	−0.538651	−	0.538651i	0.384481	−	0.923133i	$-0.374380\pi$
$107$	−596.188	−	596.188i	−0.538651	−	0.538651i	−0.923133	+	0.384481i	$0.874380\pi$
$108$	374.498	+	622.632i	0.333667	+	0.554748i
$109$			2074.60i			1.82303i	0.411264	+	0.911516i	$0.365087\pi$
$109$			2074.60i			1.82303i	−0.411264	+	0.911516i	$0.634913\pi$
$110$		0			0
$111$	−532.657	+	770.460i	−0.455474	+	0.658818i
$112$	−56.8022	+	56.8022i	−0.0479224	+	0.0479224i
$113$	271.193	−	271.193i	0.225767	−	0.225767i	−0.585154	−	0.810922i	$-0.698966\pi$
$113$	271.193	−	271.193i	0.225767	−	0.225767i	0.810922	+	0.585154i	$0.198966\pi$
$114$	−243.558	+	352.294i	−0.200099	+	0.289433i
$115$		0			0
$116$			651.788i			0.521698i
$117$	−493.375	−	222.934i	−0.389851	−	0.176156i
$118$	866.309	+	866.309i	0.675849	+	0.675849i
$119$	495.806			0.381937
$120$		0			0
$121$	506.367			0.380441
$122$	2.37533	+	2.37533i	0.00176272	+	0.00176272i
$123$	−364.108	−	1995.25i	−0.266915	−	1.46265i
$124$		−	1281.09i		−	0.927786i
$125$		0			0
$126$	801.469	−	302.593i	0.566671	−	0.213945i
$127$	−105.588	+	105.588i	−0.0737747	+	0.0737747i	−0.743031	−	0.669257i	$-0.766613\pi$
$127$	−105.588	+	105.588i	−0.0737747	+	0.0737747i	0.669257	+	0.743031i	$0.266613\pi$
$128$	−715.045	+	715.045i	−0.493763	+	0.493763i
$129$	−238.151	−	164.646i	−0.162543	−	0.112374i
$130$		0			0
$131$		−	1979.28i		−	1.32008i	−0.751231	−	0.660039i	$-0.770540\pi$
$131$		−	1979.28i		−	1.32008i	0.751231	−	0.660039i	$-0.229460\pi$
$132$	760.216	−	138.730i	0.501275	−	0.0914763i
$133$	−655.514	−	655.514i	−0.427371	−	0.427371i
$134$	783.827			0.505316
$135$		0			0
$136$	580.964			0.366304
$137$	507.451	+	507.451i	0.316456	+	0.316456i	0.847404	−	0.530948i	$-0.178164\pi$
$137$	507.451	+	507.451i	0.316456	+	0.316456i	−0.530948	+	0.847404i	$0.678164\pi$
$138$	458.651	−	83.6979i	0.282920	−	0.0516293i
$139$		−	68.4333i		−	0.0417585i	−0.999782	−	0.0208793i	$-0.993353\pi$
$139$		−	68.4333i		−	0.0417585i	0.999782	−	0.0208793i	$-0.00664656\pi$
$140$		0			0
$141$	−752.913	−	520.527i	−0.449693	−	0.310895i
$142$	203.993	−	203.993i	0.120554	−	0.120554i
$143$	−407.167	+	407.167i	−0.238105	+	0.238105i
$144$	−107.413	+	40.5536i	−0.0621604	+	0.0234685i
$145$		0			0
$146$			664.917i			0.376911i
$147$	12.9313	+	70.8616i	0.00725550	+	0.0397590i
$148$	−660.121	−	660.121i	−0.366632	−	0.366632i
$149$	−363.356			−0.199780			−0.0998902	−	0.994998i	$-0.531849\pi$
$149$	−363.356			−0.199780			−0.0998902	+	0.994998i	$0.531849\pi$
$150$		0			0
$151$	−2083.14			−1.12267			−0.561337	−	0.827588i	$-0.689713\pi$
$151$	−2083.14			−1.12267			−0.561337	+	0.827588i	$0.689713\pi$
$152$	−768.103	−	768.103i	−0.409878	−	0.409878i
$153$	645.774	+	291.797i	0.341227	+	0.154185i
$154$		−	911.149i		−	0.476769i
$155$		0			0
$156$	306.863	−	443.860i	0.157491	−	0.227803i
$157$	1208.52	−	1208.52i	0.614333	−	0.614333i	−0.329739	−	0.944072i	$-0.606961\pi$
$157$	1208.52	−	1208.52i	0.614333	−	0.614333i	0.944072	+	0.329739i	$0.106961\pi$
$158$	57.0303	−	57.0303i	0.0287157	−	0.0287157i
$159$	670.468	−	969.795i	0.334412	−	0.483709i
$160$		0			0
$161$			1009.15i			0.493989i
$162$	1221.98	+	77.5696i	0.592639	+	0.0376200i
$163$	−626.062	−	626.062i	−0.300840	−	0.300840i	0.540502	−	0.841343i	$-0.318234\pi$
$163$	−626.062	−	626.062i	−0.300840	−	0.300840i	−0.841343	+	0.540502i	$0.818234\pi$
$164$	2021.47			0.962502
$165$		0			0
$166$	343.119			0.160429
$167$	3009.65	+	3009.65i	1.39457	+	1.39457i	0.814724	+	0.579848i	$0.196888\pi$
$167$	3009.65	+	3009.65i	1.39457	+	1.39457i	0.579848	+	0.814724i	$0.303112\pi$
$168$	390.067	+	2137.50i	0.179133	+	0.981619i
$169$		−	1794.92i		−	0.816985i
$170$		0			0
$171$	−468.000	−	1239.58i	−0.209292	−	0.554345i
$172$	204.045	−	204.045i	0.0904552	−	0.0904552i
$173$	1839.23	−	1839.23i	0.808288	−	0.808288i	−0.176086	−	0.984375i	$-0.556344\pi$
$173$	1839.23	−	1839.23i	0.808288	−	0.808288i	0.984375	+	0.176086i	$0.0563438\pi$
$174$	903.497	+	624.633i	0.393643	+	0.272145i
$175$		0			0
$176$			122.113i			0.0522987i
$177$	−3728.61	+	680.425i	−1.58339	+	0.288948i
$178$	−1683.16	−	1683.16i	−0.708755	−	0.708755i
$179$	821.582			0.343061			0.171530	−	0.985179i	$-0.445129\pi$
$179$	821.582			0.343061			0.171530	+	0.985179i	$0.445129\pi$
$180$		0			0
$181$	2314.20			0.950350			0.475175	−	0.879891i	$-0.342385\pi$
$181$	2314.20			0.950350			0.475175	+	0.879891i	$0.342385\pi$
$182$	−449.885	−	449.885i	−0.183229	−	0.183229i
$183$	−10.2235	+	1.86565i	−0.00412973	+	0.000753623i
$184$			1182.48i			0.473769i
$185$		0			0
$186$	−1775.83	−	1227.72i	−0.700053	−	0.483982i
$187$	532.938	−	532.938i	0.208408	−	0.208408i
$188$	645.087	−	645.087i	0.250254	−	0.250254i
$189$	−640.007	+	2571.87i	−0.246316	+	0.989820i
$190$		0			0
$191$		−	931.167i		−	0.352758i	−0.984322	−	0.176379i	$-0.943562\pi$
$191$		−	931.167i		−	0.352758i	0.984322	−	0.176379i	$-0.0564385\pi$
$192$	256.909	+	1407.82i	0.0965666	+	0.529169i
$193$	2623.28	+	2623.28i	0.978382	+	0.978382i	0.999771	−	0.0213891i	$-0.00680888\pi$
$193$	2623.28	+	2623.28i	0.978382	+	0.978382i	−0.0213891	+	0.999771i	$0.506809\pi$
$194$	−2157.06			−0.798289
$195$		0			0
$196$	−71.7928			−0.0261636
$197$	−2995.05	−	2995.05i	−1.08319	−	1.08319i	−0.996210	−	0.0869796i	$-0.972279\pi$
$197$	−2995.05	−	2995.05i	−1.08319	−	1.08319i	−0.0869796	−	0.996210i	$-0.527721\pi$
$198$	536.238	−	1186.75i	0.192469	−	0.425952i
$199$			109.458i			0.0389912i	0.999810	+	0.0194956i	$0.00620603\pi$
$199$			109.458i			0.0389912i	−0.999810	+	0.0194956i	$0.993794\pi$
$200$		0			0
$201$	−1378.98	+	1994.63i	−0.483911	+	0.699951i
$202$	−401.036	+	401.036i	−0.139687	+	0.139687i
$203$	−1681.14	+	1681.14i	−0.581246	+	0.581246i
$204$	−401.650	+	580.964i	−0.137849	+	0.199390i
$205$		0			0
$206$			2217.38i			0.749962i
$207$	−593.915	+	1314.39i	−0.199420	+	0.441336i
$208$	60.2938	+	60.2938i	0.0200991	+	0.0200991i
$209$	−1409.21			−0.466399
$210$		0			0
$211$	2714.94			0.885801			0.442901	−	0.896571i	$-0.353949\pi$
$211$	2714.94			0.885801			0.442901	+	0.896571i	$0.353949\pi$
$212$	830.909	+	830.909i	0.269184	+	0.269184i
$213$	160.222	+	877.989i	0.0515409	+	0.282436i
$214$		−	1416.14i		−	0.452362i
$215$		0			0
$216$	−749.932	+	3013.61i	−0.236233	+	0.949305i
$217$	3304.29	−	3304.29i	1.03368	−	1.03368i
$218$	−2463.93	+	2463.93i	−0.765496	+	0.765496i
$219$	−1692.03	−	1169.79i	−0.522087	−	0.360945i
$220$		0			0
$221$		−	526.283i		−	0.160188i
$222$	−1547.67	+	282.429i	−0.467894	+	0.0853847i
$223$	−2830.49	−	2830.49i	−0.849971	−	0.849971i	0.140158	−	0.990129i	$-0.455239\pi$
$223$	−2830.49	−	2830.49i	−0.849971	−	0.849971i	−0.990129	+	0.140158i	$0.955239\pi$
$224$	−3480.17			−1.03808
$225$		0			0
$226$	644.173			0.189601
$227$	−1398.96	−	1398.96i	−0.409042	−	0.409042i	0.472362	−	0.881404i	$-0.343401\pi$
$227$	−1398.96	−	1398.96i	−0.409042	−	0.409042i	−0.881404	+	0.472362i	$0.843401\pi$
$228$	1299.13	−	237.075i	0.377356	−	0.0688626i
$229$			3930.38i			1.13418i	0.823656	+	0.567089i	$0.191931\pi$
$229$			3930.38i			1.13418i	−0.823656	+	0.567089i	$0.808069\pi$
$230$		0			0
$231$	2318.63	+	1602.98i	0.660408	+	0.456573i
$232$	−1969.89	+	1969.89i	−0.557454	+	0.557454i
$233$	−1980.71	+	1980.71i	−0.556912	+	0.556912i	−0.928427	−	0.371515i	$-0.878838\pi$
$233$	−1980.71	+	1980.71i	−0.556912	+	0.556912i	0.371515	+	0.928427i	$0.378838\pi$
$234$	−321.193	−	850.735i	−0.0897309	−	0.237668i
$235$		0			0
$236$		−	3777.61i		−	1.04196i
$237$	44.7933	+	245.460i	0.0122769	+	0.0672756i
$238$	588.851	+	588.851i	0.160376	+	0.160376i
$239$	2976.20			0.805500			0.402750	−	0.915310i	$-0.368054\pi$
$239$	2976.20			0.805500			0.402750	+	0.915310i	$0.368054\pi$
$240$		0			0
$241$	1835.45			0.490587			0.245294	−	0.969449i	$-0.421116\pi$
$241$	1835.45			0.490587			0.245294	+	0.969449i	$0.421116\pi$
$242$	601.394	+	601.394i	0.159748	+	0.159748i
$243$	−2347.21	+	2973.13i	−0.619645	+	0.784882i
$244$		−	10.3578i		−	0.00271759i
$245$		0			0
$246$	1937.25	−	2802.13i	0.502092	−	0.726248i
$247$	−695.808	+	695.808i	−0.179244	+	0.179244i
$248$	3871.82	−	3871.82i	0.991374	−	0.991374i
$249$	−603.648	+	873.143i	−0.153633	+	0.222222i
$250$		0			0
$251$			1542.14i			0.387805i	0.981021	+	0.193902i	$0.0621145\pi$
$251$			1542.14i			0.387805i	−0.981021	+	0.193902i	$0.937885\pi$
$252$	−2407.18	−	1087.70i	−0.601738	−	0.271898i
$253$	1084.73	+	1084.73i	0.269550	+	0.269550i
$254$	−250.805			−0.0619564
$255$		0			0
$256$	−3901.74			−0.952572
$257$	−428.853	−	428.853i	−0.104090	−	0.104090i	0.653144	−	0.757234i	$-0.273450\pi$
$257$	−428.853	−	428.853i	−0.104090	−	0.104090i	−0.757234	+	0.653144i	$0.773450\pi$
$258$	−87.2997	−	478.388i	−0.0210660	−	0.115438i
$259$		−	3405.26i		−	0.816960i
$260$		0			0
$261$	−3179.04	+	1200.24i	−0.753937	+	0.284647i
$262$	2350.72	−	2350.72i	0.554304	−	0.554304i
$263$	5256.99	−	5256.99i	1.23255	−	1.23255i	0.269565	−	0.962982i	$-0.413120\pi$
$263$	5256.99	−	5256.99i	1.23255	−	1.23255i	0.962982	−	0.269565i	$-0.0868798\pi$
$264$	2716.87	+	1878.31i	0.633377	+	0.437885i
$265$		0			0
$266$		−	1557.06i		−	0.358908i
$267$	7244.38	−	1322.01i	1.66048	−	0.303017i
$268$	−1708.97	−	1708.97i	−0.389523	−	0.389523i
$269$	1930.34			0.437528			0.218764	−	0.975778i	$-0.429797\pi$
$269$	1930.34			0.437528			0.218764	+	0.975778i	$0.429797\pi$
$270$		0			0
$271$	−3261.67			−0.731116			−0.365558	−	0.930789i	$-0.619122\pi$
$271$	−3261.67			−0.731116			−0.365558	+	0.930789i	$0.619122\pi$
$272$	−78.9180	−	78.9180i	−0.0175923	−	0.0175923i
$273$	1936.32	−	353.353i	0.429272	−	0.0783367i
$274$			1205.36i			0.265762i
$275$		0			0
$276$	−1182.48	−	817.507i	−0.257887	−	0.178290i
$277$	−4865.57	+	4865.57i	−1.05539	+	1.05539i	−0.0570194	+	0.998373i	$0.518160\pi$
$277$	−4865.57	+	4865.57i	−1.05539	+	1.05539i	−0.998373	+	0.0570194i	$0.981840\pi$
$278$	81.2758	−	81.2758i	0.0175345	−	0.0175345i
$279$	6248.41	−	2359.07i	1.34080	−	0.506215i
$280$		0			0
$281$			3981.96i			0.845351i	0.906281	+	0.422676i	$0.138909\pi$
$281$			3981.96i			0.845351i	−0.906281	+	0.422676i	$0.861091\pi$
$282$	−275.997	−	1512.42i	−0.0582815	−	0.319373i
$283$	4092.66	+	4092.66i	0.859658	+	0.859658i	0.991298	−	0.131640i	$-0.0420242\pi$
$283$	4092.66	+	4092.66i	0.859658	+	0.859658i	−0.131640	+	0.991298i	$0.542024\pi$
$284$	−889.527			−0.185858
$285$		0			0
$286$	−967.156			−0.199962
$287$	5213.93	+	5213.93i	1.07236	+	1.07236i
$288$	−4532.83	−	2048.19i	−0.927429	−	0.419064i
$289$		−	4224.15i		−	0.859791i
$290$		0			0
$291$	3794.91	−	5489.13i	0.764473	−	1.10577i
$292$	1449.71	−	1449.71i	0.290541	−	0.290541i
$293$	−4515.35	+	4515.35i	−0.900305	+	0.900305i	−0.995462	−	0.0951570i	$-0.969665\pi$
$293$	−4515.35	+	4515.35i	−0.900305	+	0.900305i	0.0951570	+	0.995462i	$0.469665\pi$
$294$	−68.8017	+	99.5179i	−0.0136483	+	0.0197415i
$295$		0			0
$296$		−	3990.14i		−	0.783521i
$297$	2076.54	+	3452.42i	0.405701	+	0.674511i
$298$	−431.545	−	431.545i	−0.0838883	−	0.0838883i
$299$	1071.18			0.207184
$300$		0			0
$301$	1052.58			0.201560
$302$	−2474.07	−	2474.07i	−0.471413	−	0.471413i
$303$	−314.986	−	1726.07i	−0.0597210	−	0.327261i
$304$			208.678i			0.0393701i
$305$		0			0
$306$	420.406	+	1113.52i	0.0785393	+	0.208025i
$307$	−1831.07	+	1831.07i	−0.340406	+	0.340406i	−0.856520	−	0.516114i	$-0.827378\pi$
$307$	−1831.07	+	1831.07i	−0.340406	+	0.340406i	0.516114	+	0.856520i	$0.327378\pi$
$308$	−1986.57	+	1986.57i	−0.367517	+	0.367517i
$309$	−5642.63	−	3901.03i	−1.03883	−	0.718194i
$310$		0			0
$311$			4010.21i			0.731184i	0.930775	+	0.365592i	$0.119134\pi$
$311$			4010.21i			0.731184i	−0.930775	+	0.365592i	$0.880866\pi$
$312$	2268.89	−	414.044i	0.411701	−	0.0751303i
$313$	−6072.69	−	6072.69i	−1.09664	−	1.09664i	−0.994801	−	0.101841i	$-0.967527\pi$
$313$	−6072.69	−	6072.69i	−1.09664	−	1.09664i	−0.101841	−	0.994801i	$-0.532473\pi$
$314$	2870.63			0.515920
$315$		0			0
$316$	−248.685			−0.0442710
$317$	3112.10	+	3112.10i	0.551397	+	0.551397i	0.926844	−	0.375447i	$-0.122511\pi$
$317$	3112.10	+	3112.10i	0.551397	+	0.551397i	−0.375447	+	0.926844i	$0.622511\pi$
$318$	1948.08	−	355.500i	0.343531	−	0.0626901i
$319$			3614.09i			0.634326i
$320$		0			0
$321$	3603.70	+	2491.42i	0.626600	+	0.433200i
$322$	−1198.53	+	1198.53i	−0.207427	+	0.207427i
$323$	910.737	−	910.737i	0.156888	−	0.156888i
$324$	−2495.14	−	2833.39i	−0.427836	−	0.485835i
$325$		0			0
$326$		−	1487.10i		−	0.252647i
$327$	−1935.24	−	10604.8i	−0.327275	−	1.79342i
$328$	6109.45	+	6109.45i	1.02847	+	1.02847i
$329$	3327.71			0.557637
$330$		0			0
$331$	−9589.47			−1.59240			−0.796201	−	0.605033i	$-0.793160\pi$
$331$	−9589.47			−1.59240			−0.796201	+	0.605033i	$0.793160\pi$
$332$	−748.099	−	748.099i	−0.123666	−	0.123666i
$333$	2004.10	−	4435.26i	0.329801	−	0.729883i
$334$			7148.90i			1.17117i
$335$		0			0
$336$	237.371	−	343.345i	0.0385407	−	0.0557470i
$337$	2561.34	−	2561.34i	0.414021	−	0.414021i	−0.469115	−	0.883137i	$-0.655427\pi$
$337$	2561.34	−	2561.34i	0.414021	−	0.414021i	0.883137	+	0.469115i	$0.155427\pi$
$338$	2131.76	−	2131.76i	0.343054	−	0.343054i
$339$	−1133.29	+	1639.24i	−0.181569	+	0.262630i
$340$		0			0
$341$		−	7103.50i		−	1.12808i
$342$	916.377	−	2028.03i	0.144889	−	0.320653i
$343$	4396.56	+	4396.56i	0.692104	+	0.692104i
$344$	1233.36			0.193310
$345$		0			0
$346$	4368.77			0.678805
$347$	−8177.44	−	8177.44i	−1.26509	−	1.26509i	−0.948592	−	0.316503i	$-0.897491\pi$
$347$	−8177.44	−	8177.44i	−1.26509	−	1.26509i	−0.316503	−	0.948592i	$-0.602509\pi$
$348$	−608.005	−	3331.77i	−0.0936566	−	0.513223i
$349$		−	2766.04i		−	0.424249i	−0.977243	−	0.212124i	$-0.931962\pi$
$349$		−	2766.04i		−	0.424249i	0.977243	−	0.212124i	$-0.0680382\pi$
$350$		0			0
$351$	2729.96	+	679.347i	0.415141	+	0.103307i
$352$	−3740.81	+	3740.81i	−0.566437	+	0.566437i
$353$	−6338.53	+	6338.53i	−0.955711	+	0.955711i	−0.999060	−	0.0433491i	$-0.986197\pi$
$353$	−6338.53	+	6338.53i	−0.955711	+	0.955711i	0.0433491	+	0.999060i	$0.486197\pi$
$354$	−5236.46	−	3620.23i	−0.786199	−	0.543539i
$355$		0			0
$356$			7339.58i			1.09269i
$357$	−2534.43	+	462.501i	−0.375732	+	0.0685663i
$358$	975.763	+	975.763i	0.144052	+	0.144052i
$359$	−8827.47			−1.29776			−0.648880	−	0.760890i	$-0.724762\pi$
$359$	−8827.47			−1.29776			−0.648880	+	0.760890i	$0.724762\pi$
$360$		0			0
$361$	4450.80			0.648899
$362$	2748.50	+	2748.50i	0.399055	+	0.399055i
$363$	−2588.42	+	472.353i	−0.374261	+	0.0682978i
$364$			1961.76i			0.282484i
$365$		0			0
$366$	−14.3578	−	9.92628i	−0.00205053	−	0.00141764i
$367$	−6191.27	+	6191.27i	−0.880605	+	0.880605i	−0.993596	−	0.112991i	$-0.963957\pi$
$367$	−6191.27	+	6191.27i	−0.880605	+	0.880605i	0.112991	+	0.993596i	$0.463957\pi$
$368$	160.628	−	160.628i	0.0227535	−	0.0227535i
$369$	3722.45	+	9859.55i	0.525157	+	1.39097i
$370$		0			0
$371$			4286.28i			0.599818i
$372$	1195.04	+	6548.60i	0.166559	+	0.912713i
$373$	−3584.46	−	3584.46i	−0.497577	−	0.497577i	0.413106	−	0.910683i	$-0.364444\pi$
$373$	−3584.46	−	3584.46i	−0.497577	−	0.497577i	−0.910683	+	0.413106i	$0.864444\pi$
$374$	1265.90			0.175022
$375$		0			0
$376$	3899.27			0.534812
$377$	1784.48	+	1784.48i	0.243781	+	0.243781i
$378$	−3814.63	+	2294.40i	−0.519057	+	0.312200i
$379$			7110.48i			0.963695i	0.876255	+	0.481848i	$0.160034\pi$
$379$			7110.48i			0.963695i	−0.876255	+	0.481848i	$0.839966\pi$
$380$		0			0
$381$	441.241	−	638.231i	0.0593319	−	0.0858203i
$382$	1105.91	−	1105.91i	0.148124	−	0.148124i
$383$	1695.77	−	1695.77i	0.226240	−	0.226240i	−0.584880	−	0.811120i	$-0.698858\pi$
$383$	1695.77	−	1695.77i	0.226240	−	0.226240i	0.811120	+	0.584880i	$0.198858\pi$
$384$	2988.11	−	4322.14i	0.397100	−	0.574383i
$385$		0			0
$386$			6231.15i			0.821650i
$387$	1370.95	+	619.472i	0.180076	+	0.0813683i
$388$	4703.02	+	4703.02i	0.615361	+	0.615361i
$389$	−12362.2			−1.61128			−0.805640	−	0.592405i	$-0.798178\pi$
$389$	−12362.2			−1.61128			−0.805640	+	0.592405i	$0.798178\pi$
$390$		0			0
$391$	−1402.06			−0.181343
$392$	−216.978	−	216.978i	−0.0279567	−	0.0279567i
$393$	1846.32	+	10117.5i	0.236984	+	1.29863i
$394$		−	7114.22i		−	0.909668i
$395$		0			0
$396$	−3756.61	+	1418.30i	−0.476709	+	0.179980i
$397$	1340.12	−	1340.12i	0.169417	−	0.169417i	−0.617306	−	0.786723i	$-0.711776\pi$
$397$	1340.12	−	1340.12i	0.169417	−	0.169417i	0.786723	+	0.617306i	$0.211776\pi$
$398$	−129.999	+	129.999i	−0.0163725	+	0.0163725i
$399$	3962.30	+	2739.33i	0.497150	+	0.343705i
$400$		0			0
$401$		−	2281.30i		−	0.284096i	−0.989860	−	0.142048i	$-0.954631\pi$
$401$		−	2281.30i		−	0.284096i	0.989860	−	0.142048i	$-0.0453688\pi$
$402$	−4006.72	+	731.175i	−0.497107	+	0.0907156i
$403$	−3507.40	−	3507.40i	−0.433538	−	0.433538i
$404$	1748.75			0.215356
$405$		0			0
$406$	−3993.26			−0.488133
$407$	−3660.29	−	3660.29i	−0.445783	−	0.445783i
$408$	−2969.74	+	541.939i	−0.360352	+	0.0657597i
$409$		−	4614.82i		−	0.557917i	−0.960303	−	0.278959i	$-0.910011\pi$
$409$		−	4614.82i		−	0.557917i	0.960303	−	0.278959i	$-0.0899892\pi$
$410$		0			0
$411$	−3067.32	−	2120.59i	−0.368126	−	0.254504i
$412$	4834.54	−	4834.54i	0.578108	−	0.578108i
$413$	9743.49	−	9743.49i	1.16089	−	1.16089i
$414$	−2266.43	+	855.683i	−0.269055	+	0.101581i
$415$		0			0
$416$			3694.10i			0.435380i
$417$	63.8364	+	349.813i	0.00749660	+	0.0410801i
$418$	−1673.67	−	1673.67i	−0.195842	−	0.195842i
$419$	−2142.28			−0.249779			−0.124889	−	0.992171i	$-0.539858\pi$
$419$	−2142.28			−0.249779			−0.124889	+	0.992171i	$0.539858\pi$
$420$		0			0
$421$	−8889.30			−1.02907			−0.514534	−	0.857470i	$-0.672035\pi$
$421$	−8889.30			−1.02907			−0.514534	+	0.857470i	$0.672035\pi$
$422$	3224.43	+	3224.43i	0.371950	+	0.371950i
$423$	4334.26	+	1958.46i	0.498200	+	0.225115i
$424$			5022.48i			0.575267i
$425$		0			0
$426$	−852.466	+	1233.05i	−0.0969534	+	0.140238i
$427$	26.7156	−	26.7156i	0.00302778	−	0.00302778i
$428$	−3087.60	+	3087.60i	−0.348703	+	0.348703i
$429$	1701.52	−	2461.15i	0.191492	−	0.276982i
$430$		0			0
$431$		−	15707.3i		−	1.75543i	−0.479179	−	0.877717i	$-0.659065\pi$
$431$		−	15707.3i		−	1.75543i	0.479179	−	0.877717i	$-0.340935\pi$
$432$	511.238	−	307.497i	0.0569374	−	0.0342464i
$433$	−5430.81	−	5430.81i	−0.602744	−	0.602744i	0.338296	−	0.941040i	$-0.390149\pi$
$433$	−5430.81	−	5430.81i	−0.602744	−	0.602744i	−0.941040	+	0.338296i	$0.890149\pi$
$434$	7848.76			0.868094
$435$		0			0
$436$	10744.2			1.18016
$437$	1853.69	+	1853.69i	0.202915	+	0.202915i
$438$	−620.253	−	3398.88i	−0.0676640	−	0.370787i
$439$		−	8221.92i		−	0.893874i	−0.894565	−	0.446937i	$-0.852515\pi$
$439$		−	8221.92i		−	0.893874i	0.894565	−	0.446937i	$-0.147485\pi$
$440$		0			0
$441$	−132.203	−	350.163i	−0.0142753	−	0.0378105i
$442$	625.047	−	625.047i	0.0672635	−	0.0672635i
$443$	1960.53	−	1960.53i	0.210265	−	0.210265i	−0.594115	−	0.804380i	$-0.702498\pi$
$443$	1960.53	−	1960.53i	0.210265	−	0.210265i	0.804380	+	0.594115i	$0.202498\pi$
$444$	3990.14	+	2758.58i	0.426495	+	0.294857i
$445$		0			0
$446$		−	6723.34i		−	0.713810i
$447$	1857.38	−	338.948i	0.196535	−	0.0358651i
$448$	−3678.86	−	3678.86i	−0.387968	−	0.387968i
$449$	17849.2			1.87607			0.938036	−	0.346537i	$-0.112643\pi$
$449$	17849.2			1.87607			0.938036	+	0.346537i	$0.112643\pi$
$450$		0			0
$451$	11208.8			1.17029
$452$	−1404.49	−	1404.49i	−0.146154	−	0.146154i
$453$	10648.5	−	1943.21i	1.10443	−	0.201545i
$454$		−	3323.00i		−	0.343516i
$455$		0			0
$456$	4642.85	+	3209.83i	0.476801	+	0.329636i
$457$	6346.80	−	6346.80i	0.649652	−	0.649652i	−0.303257	−	0.952909i	$-0.598074\pi$
$457$	6346.80	−	6346.80i	0.649652	−	0.649652i	0.952909	+	0.303257i	$0.0980740\pi$
$458$	−4667.97	+	4667.97i	−0.476245	+	0.476245i
$459$	−3573.22	−	889.192i	−0.363363	−	0.0904225i
$460$		0			0
$461$		−	8848.20i		−	0.893930i	−0.894552	−	0.446965i	$-0.852505\pi$
$461$		−	8848.20i		−	0.893930i	0.894552	−	0.446965i	$-0.147495\pi$
$462$	849.944	+	4657.55i	0.0855908	+	0.469024i
$463$	−1329.43	−	1329.43i	−0.133443	−	0.133443i	0.637230	−	0.770673i	$-0.280080\pi$
$463$	−1329.43	−	1329.43i	−0.133443	−	0.133443i	−0.770673	+	0.637230i	$0.780080\pi$
$464$	535.178			0.0535453
$465$		0			0
$466$	−4704.83			−0.467697
$467$	1479.96	+	1479.96i	0.146647	+	0.146647i	0.776618	−	0.629971i	$-0.216933\pi$
$467$	1479.96	+	1479.96i	0.146647	+	0.146647i	−0.629971	+	0.776618i	$0.716933\pi$
$468$	−1154.56	+	2555.14i	−0.114037	+	0.252375i
$469$		−	8815.81i		−	0.867966i
$470$		0			0
$471$	−5050.29	+	7304.96i	−0.494066	+	0.714639i
$472$	11417.0	−	11417.0i	1.11337	−	1.11337i
$473$	1131.41	−	1131.41i	0.109983	−	0.109983i
$474$	−238.324	+	344.723i	−0.0230941	+	0.0334043i
$475$		0			0
$476$		−	2567.73i		−	0.247252i
$477$	−2522.60	+	5582.76i	−0.242143	+	0.535885i
$478$	3534.73	+	3534.73i	0.338231	+	0.338231i
$479$	−5039.60			−0.480720			−0.240360	−	0.970684i	$-0.577266\pi$
$479$	−5039.60			−0.480720			−0.240360	+	0.970684i	$0.577266\pi$
$480$		0			0
$481$	−3614.58			−0.342642
$482$	2179.89	+	2179.89i	0.205999	+	0.205999i
$483$	−941.362	−	5158.51i	−0.0886821	−	0.485963i
$484$		−	2622.43i		−	0.246284i
$485$		0			0
$486$	−6318.78	+	743.377i	−0.589765	+	0.0693833i
$487$	−1292.93	+	1292.93i	−0.120305	+	0.120305i	−0.764696	−	0.644391i	$-0.777111\pi$
$487$	−1292.93	+	1292.93i	−0.120305	+	0.120305i	0.644391	+	0.764696i	$0.277111\pi$
$488$	31.3042	−	31.3042i	0.00290384	−	0.00290384i
$489$	3784.27	+	2616.26i	0.349961	+	0.241945i
$490$		0			0
$491$			13865.7i			1.27444i	0.770681	+	0.637221i	$0.219916\pi$
$491$			13865.7i			1.27444i	−0.770681	+	0.637221i	$0.780084\pi$
$492$	−10333.2	+	1885.68i	−0.946865	+	0.172791i
$493$	−2335.69	−	2335.69i	−0.213375	−	0.213375i
$494$	−1652.77			−0.150530
$495$		0			0
$496$	−1051.89			−0.0952247
$497$	−2294.33	−	2294.33i	−0.207072	−	0.207072i
$498$	−1753.93	+	320.070i	−0.157822	+	0.0288006i
$499$			10884.3i			0.976453i	0.872717	+	0.488226i	$0.162356\pi$
$499$			10884.3i			0.976453i	−0.872717	+	0.488226i	$0.837644\pi$
$500$		0			0
$501$	−18192.0	−	12577.0i	−1.62227	−	1.12156i
$502$	−1831.54	+	1831.54i	−0.162840	+	0.162840i
$503$	−7880.86	+	7880.86i	−0.698589	+	0.698589i	−0.964106	−	0.265517i	$-0.914457\pi$
$503$	−7880.86	+	7880.86i	−0.698589	+	0.698589i	0.265517	+	0.964106i	$0.414457\pi$
$504$	−3987.84	−	10562.5i	−0.352445	−	0.933513i
$505$		0			0
$506$			2576.58i			0.226370i
$507$	1674.35	+	9175.14i	0.146667	+	0.803713i
$508$	546.829	+	546.829i	0.0477590	+	0.0477590i
$509$	−1788.46			−0.155741			−0.0778704	−	0.996963i	$-0.524812\pi$
$509$	−1788.46			−0.155741			−0.0778704	+	0.996963i	$0.524812\pi$
$510$		0			0
$511$	7478.42			0.647408
$512$	1086.41	+	1086.41i	0.0937754	+	0.0937754i
$513$	3548.60	+	5899.84i	0.305409	+	0.507766i
$514$		−	1018.67i		−	0.0874153i
$515$		0			0
$516$	−852.686	+	1233.36i	−0.0727469	+	0.105224i
$517$	3576.93	−	3576.93i	0.304281	−	0.304281i
$518$	4044.31	−	4044.31i	0.343044	−	0.343044i
$519$	−7685.96	+	11117.3i	−0.650051	+	0.940263i
$520$		0			0
$521$			18251.6i			1.53478i	0.641183	+	0.767388i	$0.278444\pi$
$521$			18251.6i			1.53478i	−0.641183	+	0.767388i	$0.721556\pi$
$522$	−5201.11	−	2350.15i	−0.436104	−	0.197056i
$523$	2125.69	+	2125.69i	0.177725	+	0.177725i	0.790363	−	0.612639i	$-0.209892\pi$
$523$	2125.69	+	2125.69i	0.177725	+	0.177725i	−0.612639	+	0.790363i	$0.709892\pi$
$524$	−10250.5			−0.854570
$525$		0			0
$526$	12487.1			1.03510
$527$	4590.80	+	4590.80i	0.379466	+	0.379466i
$528$	−113.910	−	624.207i	−0.00938880	−	0.0514491i
$529$			9313.29i			0.765455i
$530$		0			0
$531$	18425.0	−	6956.30i	1.50579	−	0.568508i
$532$	−3394.85	+	3394.85i	−0.276664	+	0.276664i
$533$	5534.42	−	5534.42i	0.449761	−	0.449761i
$534$	10174.0	+	7033.79i	0.824478	+	0.570003i
$535$		0			0
$536$		−	10330.0i		−	0.832439i
$537$	−4199.71	+	766.393i	−0.337488	+	0.0615872i
$538$	2292.60	+	2292.60i	0.183719	+	0.183719i
$539$	−398.082			−0.0318119
$540$		0			0
$541$	−2214.16			−0.175960			−0.0879798	−	0.996122i	$-0.528041\pi$
$541$	−2214.16			−0.175960			−0.0879798	+	0.996122i	$0.528041\pi$
$542$	−3873.77	−	3873.77i	−0.306998	−	0.306998i
$543$	−11829.6	+	2158.75i	−0.934911	+	0.170609i
$544$		−	4835.17i		−	0.381078i
$545$		0			0
$546$	2719.36	+	1880.03i	0.213146	+	0.147359i
$547$	−12385.1	+	12385.1i	−0.968098	+	0.968098i	−0.999507	−	0.0314090i	$-0.990001\pi$
$547$	−12385.1	+	12385.1i	−0.968098	+	0.968098i	0.0314090	+	0.999507i	$0.490001\pi$
$548$	2628.04	−	2628.04i	0.204862	−	0.204862i
$549$	50.5193	−	19.0735i	0.00392735	−	0.00148276i
$550$		0			0
$551$			6176.11i			0.477516i
$552$	−1103.05	−	6044.52i	−0.0850522	−	0.466072i
$553$	−641.427	−	641.427i	−0.0493242	−	0.0493242i
$554$	−11557.3			−0.886324
$555$		0			0
$556$	−354.410			−0.0270329
$557$	−8716.96	−	8716.96i	−0.663105	−	0.663105i	0.293006	−	0.956111i	$-0.405344\pi$
$557$	−8716.96	−	8716.96i	−0.663105	−	0.663105i	−0.956111	+	0.293006i	$0.905344\pi$
$558$	10222.8	+	4619.23i	0.775566	+	0.350444i
$559$		−	1117.28i		−	0.0845363i
$560$		0			0
$561$	−2227.10	+	3221.38i	−0.167608	+	0.242436i
$562$	−4729.23	+	4729.23i	−0.354965	+	0.354965i
$563$	−11697.0	+	11697.0i	−0.875615	+	0.875615i	−0.993077	−	0.117462i	$-0.962524\pi$
$563$	−11697.0	+	11697.0i	−0.875615	+	0.875615i	0.117462	+	0.993077i	$0.462524\pi$
$564$	−2695.76	+	3899.27i	−0.201262	+	0.291115i
$565$		0			0
$566$			9721.40i			0.721945i
$567$	872.435	−	13743.7i	0.0646188	−	1.01796i
$568$	−2688.40	−	2688.40i	−0.198596	−	0.198596i
$569$	11517.5			0.848576			0.424288	−	0.905527i	$-0.360524\pi$
$569$	11517.5			0.848576			0.424288	+	0.905527i	$0.360524\pi$
$570$		0			0
$571$	−11093.9			−0.813072			−0.406536	−	0.913635i	$-0.633263\pi$
$571$	−11093.9			−0.813072			−0.406536	+	0.913635i	$0.633263\pi$
$572$	2108.68	+	2108.68i	0.154141	+	0.154141i
$573$	868.617	+	4759.88i	0.0633281	+	0.347027i
$574$			12384.8i			0.900577i
$575$		0			0
$576$	−2626.50	−	6956.73i	−0.189995	−	0.503236i
$577$	14119.4	−	14119.4i	1.01871	−	1.01871i	0.0188920	−	0.999822i	$-0.493986\pi$
$577$	14119.4	−	14119.4i	1.01871	−	1.01871i	0.999822	−	0.0188920i	$-0.00601387\pi$
$578$	5016.87	−	5016.87i	0.361028	−	0.361028i
$579$	−15856.6	−	10962.4i	−1.13813	−	0.786846i
$580$		0			0
$581$		−	3859.10i		−	0.275564i
$582$	11026.3	−	2012.16i	0.785320	−	0.143311i
$583$	4607.29	+	4607.29i	0.327297	+	0.327297i
$584$	8762.89			0.620909
$585$		0			0
$586$	−10725.4			−0.756081
$587$	−8524.33	−	8524.33i	−0.599381	−	0.599381i	0.340767	−	0.940148i	$-0.389313\pi$
$587$	−8524.33	−	8524.33i	−0.599381	−	0.599381i	−0.940148	+	0.340767i	$0.889313\pi$
$588$	366.986	−	66.9702i	0.0257385	−	0.00469695i
$589$		−	12139.2i		−	0.849211i
$590$		0			0
$591$	18103.8	+	12516.0i	1.26005	+	0.871135i
$592$	−542.020	+	542.020i	−0.0376298	+	0.0376298i
$593$	4580.53	−	4580.53i	0.317200	−	0.317200i	−0.530491	−	0.847691i	$-0.677992\pi$
$593$	4580.53	−	4580.53i	0.317200	−	0.317200i	0.847691	+	0.530491i	$0.177992\pi$
$594$	−1634.08	+	6566.55i	−0.112874	+	0.453584i
$595$		0			0
$596$			1881.79i			0.129331i
$597$	−102.105	−	559.518i	−0.00699979	−	0.0383577i
$598$	1272.20	+	1272.20i	0.0869971	+	0.0869971i
$599$	−10195.8			−0.695477			−0.347738	−	0.937592i	$-0.613050\pi$
$599$	−10195.8			−0.695477			−0.347738	+	0.937592i	$0.613050\pi$
$600$		0			0
$601$	18915.8			1.28385			0.641923	−	0.766769i	$-0.278137\pi$
$601$	18915.8			1.28385			0.641923	+	0.766769i	$0.278137\pi$
$602$	1250.11	+	1250.11i	0.0846355	+	0.0846355i
$603$	5188.36	−	11482.4i	0.350392	−	0.775452i
$604$			10788.4i			0.726778i
$605$		0			0
$606$	1675.89	−	2424.09i	0.112341	−	0.162495i
$607$	−12758.2	+	12758.2i	−0.853113	+	0.853113i	−0.990515	−	0.137402i	$-0.956125\pi$
$607$	−12758.2	+	12758.2i	−0.853113	+	0.853113i	0.137402	+	0.990515i	$0.456125\pi$
$608$	−6392.67	+	6392.67i	−0.426409	+	0.426409i
$609$	7025.33	−	10161.8i	0.467456	−	0.676149i
$610$		0			0
$611$		−	3532.26i		−	0.233879i
$612$	1511.19	−	3344.41i	0.0998140	−	0.220898i
$613$	−7340.02	−	7340.02i	−0.483622	−	0.483622i	0.422664	−	0.906286i	$-0.361095\pi$
$613$	−7340.02	−	7340.02i	−0.483622	−	0.483622i	−0.906286	+	0.422664i	$0.861095\pi$
$614$	−4349.39			−0.285875
$615$		0			0
$616$	−12007.9			−0.785412
$617$	17118.9	+	17118.9i	1.11698	+	1.11698i	0.992182	+	0.124803i	$0.0398299\pi$
$617$	17118.9	+	17118.9i	1.11698	+	1.11698i	0.124803	+	0.992182i	$0.460170\pi$
$618$	−2068.43	−	11334.7i	−0.134635	−	0.737778i
$619$		−	3176.16i		−	0.206237i	−0.994669	−	0.103118i	$-0.967118\pi$
$619$		−	3176.16i		−	0.206237i	0.994669	−	0.103118i	$-0.0328820\pi$
$620$		0			0
$621$	1809.84	−	7272.84i	0.116950	−	0.469966i
$622$	−4762.79	+	4762.79i	−0.307026	+	0.307026i
$623$	−18930.8	+	18930.8i	−1.21741	+	1.21741i
$624$	−364.450	−	251.962i	−0.0233809	−	0.0161644i
$625$		0			0
$626$		−	14424.6i		−	0.920965i
$627$	7203.53	−	1314.55i	0.458822	−	0.0837291i
$628$	−6258.80	−	6258.80i	−0.397697	−	0.397697i
$629$	4731.09			0.299906
$630$		0			0
$631$	−11467.2			−0.723459			−0.361729	−	0.932283i	$-0.617814\pi$
$631$	−11467.2			−0.723459			−0.361729	+	0.932283i	$0.617814\pi$
$632$	−751.597	−	751.597i	−0.0473052	−	0.0473052i
$633$	−13878.0	+	2532.57i	−0.871410	+	0.159021i
$634$			7392.26i			0.463066i
$635$		0			0
$636$	−5022.48	−	3472.29i	−0.313136	−	0.216486i
$637$	−196.556	+	196.556i	−0.0122258	+	0.0122258i
$638$	−4292.32	+	4292.32i	−0.266355	+	0.266355i
$639$	−1638.02	−	4338.59i	−0.101407	−	0.268595i
$640$		0			0
$641$		−	12383.2i		−	0.763035i	−0.924362	−	0.381518i	$-0.875402\pi$
$641$		−	12383.2i		−	0.763035i	0.924362	−	0.381518i	$-0.124598\pi$
$642$	1321.02	+	7238.95i	0.0812092	+	0.445013i
$643$	11142.9	+	11142.9i	0.683413	+	0.683413i	0.960768	−	0.277354i	$-0.0894576\pi$
$643$	11142.9	+	11142.9i	0.683413	+	0.683413i	−0.277354	+	0.960768i	$0.589458\pi$
$644$	5226.29			0.319790
$645$		0			0
$646$	2163.30			0.131755
$647$	2391.21	+	2391.21i	0.145299	+	0.145299i	0.776014	−	0.630716i	$-0.217239\pi$
$647$	2391.21	+	2391.21i	0.145299	+	0.145299i	−0.630716	+	0.776014i	$0.717239\pi$
$648$	1022.28	−	16104.3i	0.0619738	−	0.976292i
$649$		−	20946.4i		−	1.26690i
$650$		0			0
$651$	−13808.3	+	19973.0i	−0.831322	+	1.20246i
$652$	−3242.32	+	3242.32i	−0.194753	+	0.194753i
$653$	16623.3	−	16623.3i	0.996201	−	0.996201i	−0.00379136	−	0.999993i	$-0.501207\pi$
$653$	16623.3	−	16623.3i	0.996201	−	0.996201i	0.999993	+	0.00379136i	$0.00120683\pi$
$654$	10296.5	−	14893.4i	0.615636	−	0.890484i
$655$		0			0
$656$		−	1659.81i		−	0.0987878i
$657$	9740.43	+	4401.27i	0.578403	+	0.261354i
$658$	3952.20	+	3952.20i	0.234153	+	0.234153i
$659$	20089.8			1.18754			0.593768	−	0.804636i	$-0.297640\pi$
$659$	20089.8			1.18754			0.593768	+	0.804636i	$0.297640\pi$
$660$		0			0
$661$	541.434			0.0318598			0.0159299	−	0.999873i	$-0.494929\pi$
$661$	541.434			0.0318598			0.0159299	+	0.999873i	$0.494929\pi$
$662$	−11389.1	−	11389.1i	−0.668654	−	0.668654i
$663$	490.931	+	2690.22i	0.0287574	+	0.157586i
$664$		−	4521.93i		−	0.264284i
$665$		0			0
$666$	7647.80	−	2887.41i	0.444964	−	0.167995i
$667$	4753.99	−	4753.99i	0.275975	−	0.275975i
$668$	15586.7	−	15586.7i	0.902796	−	0.902796i
$669$	17109.1	+	11828.3i	0.988751	+	0.683573i
$670$		0			0
$671$		−	57.4328i		−	0.00330428i
$672$	17789.7	−	3246.40i	1.02121	−	0.186358i
$673$	24314.3	+	24314.3i	1.39264	+	1.39264i	0.819354	+	0.573288i	$0.194332\pi$
$673$	24314.3	+	24314.3i	1.39264	+	1.39264i	0.573288	+	0.819354i	$0.305668\pi$
$674$	6084.03			0.347697
$675$		0			0
$676$	−9295.71			−0.528887
$677$	14662.4	+	14662.4i	0.832380	+	0.832380i	0.987842	−	0.155462i	$-0.0496867\pi$
$677$	14662.4	+	14662.4i	0.832380	+	0.832380i	−0.155462	+	0.987842i	$0.549687\pi$
$678$	−3292.84	+	600.902i	−0.186520	+	0.0340376i
$679$			24260.8i			1.37120i
$680$		0			0
$681$	8456.13	+	5846.14i	0.475829	+	0.328964i
$682$	8436.57	−	8436.57i	0.473685	−	0.473685i
$683$	15981.2	−	15981.2i	0.895320	−	0.895320i	−0.0996976	−	0.995018i	$-0.531788\pi$
$683$	15981.2	−	15981.2i	0.895320	−	0.895320i	0.995018	+	0.0996976i	$0.0317875\pi$
$684$	−6419.67	+	2423.73i	−0.358863	+	0.135488i
$685$		0			0
$686$			10443.3i			0.581233i
$687$	−3666.36	−	20091.1i	−0.203611	−	1.11575i
$688$	−167.540	−	167.540i	−0.00928400	−	0.00928400i
$689$	4549.75			0.251570
$690$		0			0
$691$	−16714.9			−0.920209			−0.460105	−	0.887865i	$-0.652188\pi$
$691$	−16714.9			−0.920209			−0.460105	+	0.887865i	$0.652188\pi$
$692$	−9525.19	−	9525.19i	−0.523256	−	0.523256i
$693$	−13347.5	−	6031.14i	−0.731645	−	0.330598i
$694$		−	19424.1i		−	1.06243i
$695$		0			0
$696$	8231.98	−	11907.1i	0.448322	−	0.648474i
$697$	−7243.96	+	7243.96i	−0.393665	+	0.393665i
$698$	3285.13	−	3285.13i	0.178143	−	0.178143i
$699$	8277.19	−	11972.5i	0.447886	−	0.647842i
$700$		0			0
$701$		−	6990.49i		−	0.376643i	−0.982107	−	0.188322i	$-0.939695\pi$
$701$		−	6990.49i		−	0.376643i	0.982107	−	0.188322i	$-0.0603048\pi$
$702$	2435.44	+	4049.11i	0.130940	+	0.217698i
$703$	−6255.06	−	6255.06i	−0.335582	−	0.335582i
$704$	−7908.75			−0.423398
$705$		0			0
$706$	−15056.1			−0.802611
$707$	4510.51	+	4510.51i	0.239936	+	0.239936i
$708$	3523.86	+	19310.2i	0.187055	+	1.02503i
$709$			28175.0i			1.49243i	0.665705	+	0.746215i	$0.268131\pi$
$709$			28175.0i			1.49243i	−0.665705	+	0.746215i	$0.731869\pi$
$710$		0			0
$711$	−457.943	−	1212.94i	−0.0241550	−	0.0639787i
$712$	−22182.3	+	22182.3i	−1.16758	+	1.16758i
$713$	−9343.99	+	9343.99i	−0.490793	+	0.490793i
$714$	−3559.35	−	2460.75i	−0.186562	−	0.128980i
$715$		0			0
$716$		−	4254.90i		−	0.222085i
$717$	−15213.6	+	2776.28i	−0.792414	+	0.144605i
$718$	−10484.1	−	10484.1i	−0.544933	−	0.544933i
$719$	−20143.8			−1.04484			−0.522418	−	0.852690i	$-0.674970\pi$
$719$	−20143.8			−1.04484			−0.522418	+	0.852690i	$0.674970\pi$
$720$		0			0
$721$	24939.2			1.28819
$722$	5286.05	+	5286.05i	0.272474	+	0.272474i
$723$	−9382.32	+	1712.15i	−0.482617	+	0.0880715i
$724$		−	11985.0i		−	0.615222i
$725$		0			0
$726$	−3635.16	−	2513.17i	−0.185831	−	0.128475i
$727$	9805.90	−	9805.90i	0.500249	−	0.500249i	−0.411267	−	0.911515i	$-0.634913\pi$
$727$	9805.90	−	9805.90i	0.500249	−	0.500249i	0.911515	+	0.411267i	$0.134913\pi$
$728$	−5929.00	+	5929.00i	−0.301845	+	0.301845i
$729$	9224.92	−	17387.4i	0.468674	−	0.883371i
$730$		0			0
$731$			1462.39i			0.0739926i
$732$	9.66205	+	52.9464i	0.000487868	+	0.00267344i
$733$	−16533.1	−	16533.1i	−0.833100	−	0.833100i	0.154840	−	0.987940i	$-0.450514\pi$
$733$	−16533.1	−	16533.1i	−0.833100	−	0.833100i	−0.987940	+	0.154840i	$0.950514\pi$
$734$	−14706.3			−0.739536
$735$		0			0
$736$	9841.37			0.492877
$737$	−9476.04	−	9476.04i	−0.473615	−	0.473615i
$738$	−7288.81	+	16130.8i	−0.363557	+	0.804586i
$739$			15250.1i			0.759114i	0.925168	+	0.379557i	$0.123924\pi$
$739$			15250.1i			0.759114i	−0.925168	+	0.379557i	$0.876076\pi$
$740$		0			0
$741$	2907.72	−	4205.85i	0.144153	−	0.208510i
$742$	−5090.66	+	5090.66i	−0.251865	+	0.251865i
$743$	5438.49	−	5438.49i	0.268531	−	0.268531i	−0.559977	−	0.828508i	$-0.689190\pi$
$743$	5438.49	−	5438.49i	0.268531	−	0.268531i	0.828508	+	0.559977i	$0.189190\pi$
$744$	−16180.0	+	23403.5i	−0.797294	+	1.15324i
$745$		0			0
$746$		−	8514.27i		−	0.417868i
$747$	2271.20	−	5026.38i	0.111243	−	0.246192i
$748$	−2760.04	−	2760.04i	−0.134916	−	0.134916i
$749$	−15927.5			−0.777009
$750$		0			0
$751$	2087.82			0.101446			0.0507228	−	0.998713i	$-0.483848\pi$
$751$	2087.82			0.101446			0.0507228	+	0.998713i	$0.483848\pi$
$752$	−529.676	−	529.676i	−0.0256852	−	0.0256852i
$753$	−1438.55	−	7883.01i	−0.0696197	−	0.381505i
$754$			4238.72i			0.204728i
$755$		0			0
$756$	13319.5	+	3314.54i	0.640774	+	0.159456i
$757$	10258.6	−	10258.6i	0.492546	−	0.492546i	−0.416562	−	0.909107i	$-0.636765\pi$
$757$	10258.6	−	10258.6i	0.492546	−	0.492546i	0.909107	+	0.416562i	$0.136765\pi$
$758$	−8444.86	+	8444.86i	−0.404658	+	0.404658i
$759$	−6556.70	−	4532.98i	−0.313561	−	0.216781i
$760$		0			0
$761$			26879.5i			1.28040i	0.768210	+	0.640198i	$0.221148\pi$
$761$			26879.5i			1.28040i	−0.768210	+	0.640198i	$0.778852\pi$
$762$	1282.05	−	233.958i	0.0609498	−	0.0111226i
$763$	27712.1	+	27712.1i	1.31487	+	1.31487i
$764$	−4822.43			−0.228363
$765$		0			0
$766$	4028.02			0.189998
$767$	−10342.4	−	10342.4i	−0.486888	−	0.486888i
$768$	19944.6	−	3639.64i	0.937097	−	0.171008i
$769$		−	25180.9i		−	1.18082i	−0.807105	−	0.590408i	$-0.798967\pi$
$769$		−	25180.9i		−	1.18082i	0.807105	−	0.590408i	$-0.201033\pi$
$770$		0			0
$771$	2592.23	+	1792.14i	0.121085	+	0.0837124i
$772$	13585.7	−	13585.7i	0.633369	−	0.633369i
$773$	−18871.2	+	18871.2i	−0.878072	+	0.878072i	−0.993335	−	0.115263i	$-0.963229\pi$
$773$	−18871.2	+	18871.2i	−0.878072	+	0.878072i	0.115263	+	0.993335i	$0.463229\pi$
$774$	892.506	+	2363.96i	0.0414476	+	0.109781i
$775$		0			0
$776$			28427.7i			1.31507i
$777$	3176.52	+	17406.8i	0.146663	+	0.803688i
$778$	−14682.1	−	14682.1i	−0.676581	−	0.676581i
$779$	19154.7			0.880988
$780$		0			0
$781$	−4932.32			−0.225982
$782$	−1665.18	−	1665.18i	−0.0761465	−	0.0761465i
$783$	15130.8	−	9100.79i	0.690588	−	0.415371i
$784$			58.9485i			0.00268533i
$785$		0			0
$786$	−9823.43	+	14209.0i	−0.445789	+	0.644809i
$787$	−14716.0	+	14716.0i	−0.666542	+	0.666542i	−0.956914	−	0.290372i	$-0.906221\pi$
$787$	−14716.0	+	14716.0i	−0.666542	+	0.666542i	0.290372	+	0.956914i	$0.406221\pi$
$788$	−15511.1	+	15511.1i	−0.701217	+	0.701217i
$789$	−21968.5	+	31776.2i	−0.991253	+	1.43379i
$790$		0			0
$791$		−	7245.10i		−	0.325672i
$792$	−15640.0	−	7067.03i	−0.701697	−	0.317066i
$793$	−28.3578	−	28.3578i	−0.00126988	−	0.00126988i
$794$	3183.22			0.142277
$795$		0			0
$796$	566.871			0.0252415
$797$	−17463.9	−	17463.9i	−0.776163	−	0.776163i	0.203013	−	0.979176i	$-0.434927\pi$
$797$	−17463.9	−	17463.9i	−0.776163	−	0.776163i	−0.979176	+	0.203013i	$0.934927\pi$
$798$	1452.47	+	7959.28i	0.0644321	+	0.353077i
$799$			4623.35i			0.204709i
$800$		0			0
$801$	−35798.1	+	13515.5i	−1.57911	+	0.596188i
$802$	2709.42	−	2709.42i	0.119293	−	0.119293i
$803$	8038.49	−	8038.49i	0.353265	−	0.353265i
$804$	10330.0	+	7141.64i	0.453122	+	0.313266i
$805$		0			0
$806$		−	8331.22i		−	0.364088i
$807$	−9867.40	+	1800.68i	−0.430420	+	0.0785462i
$808$	5285.22	+	5285.22i	0.230115	+	0.230115i
$809$	−24097.9			−1.04727			−0.523633	−	0.851944i	$-0.675424\pi$
$809$	−24097.9			−1.04727			−0.523633	+	0.851944i	$0.675424\pi$
$810$		0			0
$811$	25302.7			1.09556			0.547780	−	0.836622i	$-0.315473\pi$
$811$	25302.7			1.09556			0.547780	+	0.836622i	$0.315473\pi$
$812$	8706.47	+	8706.47i	0.376277	+	0.376277i
$813$	16672.8	−	3042.57i	0.719238	−	0.131252i
$814$		−	8694.39i		−	0.374371i
$815$		0			0
$816$	477.025	+	329.791i	0.0204647	+	0.0141483i
$817$	1933.46	−	1933.46i	0.0827945	−	0.0827945i
$818$	5480.85	−	5480.85i	0.234271	−	0.234271i
$819$	−9568.33	+	3612.50i	−0.408235	+	0.154128i
$820$		0			0
$821$		−	27925.3i		−	1.18709i	−0.804802	−	0.593544i	$-0.797728\pi$
$821$		−	27925.3i		−	1.18709i	0.804802	−	0.593544i	$-0.202272\pi$
$822$	−1124.39	−	6161.50i	−0.0477102	−	0.261444i
$823$	−997.907	−	997.907i	−0.0422659	−	0.0422659i	0.685658	−	0.727924i	$-0.259515\pi$
$823$	−997.907	−	997.907i	−0.0422659	−	0.0422659i	−0.727924	+	0.685658i	$0.759515\pi$
$824$	29222.6			1.23546
$825$		0			0
$826$	23144.0			0.974918
$827$	18683.3	+	18683.3i	0.785590	+	0.785590i	0.980768	−	0.195178i	$-0.0625285\pi$
$827$	18683.3	+	18683.3i	0.785590	+	0.785590i	−0.195178	+	0.980768i	$0.562529\pi$
$828$	6807.11	+	3075.83i	0.285705	+	0.129097i
$829$			21146.9i			0.885962i	0.896531	+	0.442981i	$0.146079\pi$
$829$			21146.9i			0.885962i	−0.896531	+	0.442981i	$0.853921\pi$
$830$		0			0
$831$	20332.8	−	29410.2i	0.848780	−	1.22771i
$832$	−3904.99	+	3904.99i	−0.162718	+	0.162718i
$833$	257.270	−	257.270i	0.0107009	−	0.0107009i
$834$	−339.644	+	491.276i	−0.0141018	+	0.0203975i
$835$		0			0
$836$			7298.19i			0.301930i
$837$	−29739.6	+	17887.6i	−1.22814	+	0.738695i
$838$	−2544.31	−	2544.31i	−0.104883	−	0.104883i
$839$	30903.4			1.27164			0.635820	−	0.771838i	$-0.280662\pi$
$839$	30903.4			1.27164			0.635820	+	0.771838i	$0.280662\pi$
$840$		0			0
$841$	−8549.68			−0.350555
$842$	−10557.5	−	10557.5i	−0.432109	−	0.432109i
$843$	−3714.48	−	20354.7i	−0.151760	−	0.831618i
$844$		−	14060.4i		−	0.573435i
$845$		0			0
$846$	2821.65	+	7473.63i	0.114669	+	0.303722i
$847$	6763.96	−	6763.96i	0.274395	−	0.274395i
$848$	682.252	−	682.252i	0.0276281	−	0.0276281i
$849$	−24738.3	−	17102.8i	−1.00002	−	0.691364i
$850$		0			0
$851$			9629.53i			0.387892i
$852$	4547.02	−	829.774i	0.182839	−	0.0333657i
$853$	−181.224	−	181.224i	−0.00727432	−	0.00727432i	0.703460	−	0.710735i	$-0.251637\pi$
$853$	−181.224	−	181.224i	−0.00727432	−	0.00727432i	−0.710735	+	0.703460i	$0.751637\pi$
$854$	63.4584			0.00254274
$855$		0			0
$856$	−18663.2			−0.745205
$857$	13852.9	+	13852.9i	0.552167	+	0.552167i	0.927066	−	0.374899i	$-0.122323\pi$
$857$	13852.9	+	13852.9i	0.552167	+	0.552167i	−0.374899	+	0.927066i	$0.622323\pi$
$858$	4943.85	−	902.189i	0.196713	−	0.0358977i
$859$		−	8910.47i		−	0.353925i	−0.984218	−	0.176962i	$-0.943373\pi$
$859$		−	8910.47i		−	0.353925i	0.984218	−	0.176962i	$-0.0566271\pi$
$860$		0			0
$861$	−31515.9	−	21788.5i	−1.24746	−	0.862428i
$862$	18655.0	−	18655.0i	0.737112	−	0.737112i
$863$	6487.75	−	6487.75i	0.255905	−	0.255905i	−0.567481	−	0.823386i	$-0.692082\pi$
$863$	6487.75	−	6487.75i	0.255905	−	0.255905i	0.823386	+	0.567481i	$0.192082\pi$
$864$	25081.2	+	6241.43i	0.987594	+	0.245761i
$865$		0			0
$866$		−	12900.0i		−	0.506187i
$867$	3940.40	+	21592.8i	0.154352	+	0.845823i
$868$	−17112.6	−	17112.6i	−0.669170	−	0.669170i
$869$	−1378.93			−0.0538285
$870$		0			0
$871$	−9357.71			−0.364034
$872$	32471.9	+	32471.9i	1.26105	+	1.26105i
$873$	−14278.2	+	31599.0i	−0.553543	+	1.22504i
$874$			4403.12i			0.170409i
$875$		0			0
$876$	−6058.22	+	8762.89i	−0.233662	+	0.337980i
$877$	20231.6	−	20231.6i	0.778987	−	0.778987i	−0.200672	−	0.979659i	$-0.564312\pi$
$877$	20231.6	−	20231.6i	0.778987	−	0.778987i	0.979659	+	0.200672i	$0.0643124\pi$
$878$	9764.88	−	9764.88i	0.375340	−	0.375340i
$879$	18869.2	−	27293.3i	0.724054	−	1.04730i
$880$		0			0
$881$			33209.0i			1.26996i	0.772527	+	0.634982i	$0.218993\pi$
$881$			33209.0i			1.26996i	−0.772527	+	0.634982i	$0.781007\pi$
$882$	258.863	−	572.889i	0.00988251	−	0.0218709i
$883$	−26984.3	−	26984.3i	−1.02842	−	1.02842i	−0.999584	−	0.0288331i	$-0.990821\pi$
$883$	−26984.3	−	26984.3i	−1.02842	−	1.02842i	−0.0288331	−	0.999584i	$-0.509179\pi$
$884$	−2725.57			−0.103700
$885$		0			0
$886$	4656.90			0.176582
$887$	−24008.9	−	24008.9i	−0.908838	−	0.908838i	0.0873406	−	0.996179i	$-0.472163\pi$
$887$	−24008.9	−	24008.9i	−0.908838	−	0.908838i	−0.996179	+	0.0873406i	$0.972163\pi$
$888$	3722.11	+	20396.5i	0.140660	+	0.770792i
$889$			2820.84i			0.106421i
$890$		0			0
$891$	−13835.3	−	15710.8i	−0.520200	−	0.590720i
$892$	−14658.8	+	14658.8i	−0.550240	+	0.550240i
$893$	6112.61	−	6112.61i	0.229060	−	0.229060i
$894$	2608.50	+	1803.39i	0.0975853	+	0.0674656i
$895$		0			0
$896$			19102.9i			0.712258i
$897$	−5475.59	+	999.226i	−0.203818	+	0.0371942i
$898$	21198.9	+	21198.9i	0.787768	+	0.787768i
$899$	−31132.2			−1.15497
$900$		0			0
$901$	−5955.13			−0.220193
$902$	13312.3	+	13312.3i	0.491409	+	0.491409i
$903$	−5380.49	+	981.871i	−0.198285	+	0.0361845i
$904$		−	8489.50i		−	0.312341i
$905$		0			0
$906$	14954.7	+	10338.9i	0.548384	+	0.379125i
$907$	23026.7	−	23026.7i	0.842989	−	0.842989i	−0.146258	−	0.989246i	$-0.546723\pi$
$907$	23026.7	−	23026.7i	0.842989	−	0.842989i	0.989246	+	0.146258i	$0.0467229\pi$
$908$	−7245.11	+	7245.11i	−0.264799	+	0.264799i
$909$	3220.25	+	8529.38i	0.117501	+	0.311223i
$910$		0			0
$911$		−	33422.1i		−	1.21550i	−0.794127	−	0.607752i	$-0.792071\pi$
$911$		−	33422.1i		−	1.21550i	0.794127	−	0.607752i	$-0.207929\pi$
$912$	−194.660	−	1066.71i	−0.00706781	−	0.0387304i
$913$	−4148.12	−	4148.12i	−0.150364	−	0.150364i
$914$	15075.7			0.545581
$915$		0			0
$916$	20355.1			0.734226
$917$	−26438.8	−	26438.8i	−0.952112	−	0.952112i
$918$	−3187.73	−	5299.85i	−0.114609	−	0.190546i
$919$		−	42542.2i		−	1.52703i	−0.645792	−	0.763513i	$-0.723473\pi$
$919$		−	42542.2i		−	1.52703i	0.645792	−	0.763513i	$-0.276527\pi$
$920$		0			0
$921$	7651.86	−	11068.0i	0.273765	−	0.395986i
$922$	10508.7	−	10508.7i	0.375363	−	0.375363i
$923$	−2435.36	+	2435.36i	−0.0868482	+	0.0868482i
$924$	8301.70	−	12007.9i	0.295569	−	0.427524i
$925$		0			0
$926$		−	3157.84i		−	0.112066i
$927$	32482.6	+	14677.4i	1.15088	+	0.520033i
$928$	16394.7	+	16394.7i	0.579938	+	0.579938i
$929$	5721.21			0.202053			0.101026	−	0.994884i	$-0.467787\pi$
$929$	5721.21			0.202053			0.101026	+	0.994884i	$0.467787\pi$
$930$		0			0
$931$	−680.282			−0.0239477
$932$	10257.9	+	10257.9i	0.360524	+	0.360524i
$933$	−3740.83	−	20499.1i	−0.131264	−	0.719305i
$934$			3515.38i			0.123155i
$935$		0			0
$936$	−11211.8	+	4232.97i	−0.391525	+	0.147819i
$937$	−1344.01	+	1344.01i	−0.0468589	+	0.0468589i	−0.730148	−	0.683289i	$-0.760549\pi$
$937$	−1344.01	+	1344.01i	−0.0468589	+	0.0468589i	0.683289	+	0.730148i	$0.260549\pi$
$938$	10470.2	−	10470.2i	0.364461	−	0.364461i
$939$	36706.8	+	25377.2i	1.27570	+	0.881953i
$940$		0			0
$941$		−	9625.77i		−	0.333466i	−0.986002	−	0.166733i	$-0.946678\pi$
$941$		−	9625.77i		−	0.333466i	0.986002	−	0.166733i	$-0.0533217\pi$
$942$	−14673.9	+	2677.80i	−0.507538	+	0.0926192i
$943$	−14744.1	−	14744.1i	−0.509157	−	0.509157i
$944$	−3101.77			−0.106943
$945$		0			0
$946$	2687.46			0.0923645
$947$	2234.24	+	2234.24i	0.0766664	+	0.0766664i	0.744400	−	0.667734i	$-0.232736\pi$
$947$	2234.24	+	2234.24i	0.0766664	+	0.0766664i	−0.667734	+	0.744400i	$0.732736\pi$
$948$	1271.21	−	231.980i	0.0435518	−	0.00794765i
$949$		−	7938.11i		−	0.271530i
$950$		0			0
$951$	−18811.3	−	13005.2i	−0.641427	−	0.443451i
$952$	7760.41	−	7760.41i	0.264198	−	0.264198i
$953$	−6457.14	+	6457.14i	−0.219483	+	0.219483i	−0.808281	−	0.588798i	$-0.799602\pi$
$953$	−6457.14	+	6457.14i	−0.219483	+	0.219483i	0.588798	+	0.808281i	$0.299602\pi$
$954$	−9626.45	+	3634.44i	−0.326696	+	0.123343i
$955$		0			0
$956$		−	15413.5i		−	0.521451i
$957$	−3371.32	−	18474.3i	−0.113876	−	0.624021i
$958$	−5985.35	−	5985.35i	−0.201856	−	0.201856i
$959$	13556.9			0.456491
$960$		0			0
$961$	31399.6			1.05399
$962$	−4292.91	−	4292.91i	−0.143876	−	0.143876i
$963$	−20745.2	−	9373.84i	−0.694190	−	0.313674i
$964$		−	9505.61i		−	0.317588i
$965$		0			0
$966$	5008.55	−	7244.59i	0.166819	−	0.241295i
$967$	−13166.9	+	13166.9i	−0.437869	+	0.437869i	−0.891294	−	0.453425i	$-0.850202\pi$
$967$	−13166.9	+	13166.9i	−0.437869	+	0.437869i	0.453425	+	0.891294i	$0.350202\pi$
$968$	7925.72	−	7925.72i	0.263163	−	0.263163i
$969$	−3805.89	+	5505.01i	−0.126174	+	0.182504i
$970$		0			0
$971$		−	21504.3i		−	0.710716i	−0.934730	−	0.355358i	$-0.884359\pi$
$971$		−	21504.3i		−	0.710716i	0.934730	−	0.355358i	$-0.115641\pi$
$972$	15397.6	+	12156.0i	0.508104	+	0.401136i
$973$	−914.119	−	914.119i	−0.0301185	−	0.0301185i
$974$	−3071.14			−0.101032
$975$		0			0
$976$	−8.50472			−0.000278924
$977$	8996.19	+	8996.19i	0.294589	+	0.294589i	0.838890	−	0.544301i	$-0.183205\pi$
$977$	8996.19	+	8996.19i	0.294589	+	0.294589i	−0.544301	+	0.838890i	$0.683205\pi$
$978$	1387.21	+	7601.68i	0.0453559	+	0.248543i
$979$			40697.1i			1.32858i
$980$		0			0
$981$	19784.9	+	52403.7i	0.643917	+	1.70553i
$982$	−16467.8	+	16467.8i	−0.535142	+	0.535142i
$983$	16337.3	−	16337.3i	0.530090	−	0.530090i	−0.390509	−	0.920599i	$-0.627701\pi$
$983$	16337.3	−	16337.3i	0.530090	−	0.530090i	0.920599	+	0.390509i	$0.127701\pi$
$984$	−36929.0	−	25530.8i	−1.19639	−	0.827128i
$985$		0			0
$986$		−	5548.02i		−	0.179194i
$987$	−17010.4	+	3104.18i	−0.548578	+	0.100108i
$988$	3603.53	+	3603.53i	0.116036	+	0.116036i
$989$	−2976.52			−0.0957004
$990$		0			0
$991$	−18296.9			−0.586500			−0.293250	−	0.956036i	$-0.594737\pi$
$991$	−18296.9			−0.586500			−0.293250	+	0.956036i	$0.594737\pi$
$992$	−32223.9	−	32223.9i	−1.03136	−	1.03136i
$993$	49018.8	−	8945.31i	1.56653	−	0.285872i
$994$		−	5449.79i		−	0.173900i
$995$		0			0
$996$	4521.93	+	3126.24i	0.143858	+	0.0994564i
$997$	−20406.0	+	20406.0i	−0.648210	+	0.648210i	−0.952560	−	0.304350i	$-0.901561\pi$
$997$	−20406.0	+	20406.0i	−0.648210	+	0.648210i	0.304350	+	0.952560i	$0.401561\pi$
$998$	−12926.9	+	12926.9i	−0.410015	+	0.410015i
$999$	−6107.09	+	24541.4i	−0.193413	+	0.777232i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.4.e.c.68.3		8
3.2	odd	2	inner	75.4.e.c.68.2		8
5.2	odd	4	inner	75.4.e.c.32.2		8
5.3	odd	4		15.4.e.a.2.3	yes	8
5.4	even	2		15.4.e.a.8.2	yes	8
15.2	even	4	inner	75.4.e.c.32.3		8
15.8	even	4		15.4.e.a.2.2	✓	8
15.14	odd	2		15.4.e.a.8.3	yes	8
20.3	even	4		240.4.v.c.17.2		8
20.19	odd	2		240.4.v.c.113.1		8
60.23	odd	4		240.4.v.c.17.1		8
60.59	even	2		240.4.v.c.113.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.4.e.a.2.2	✓	8	15.8	even	4
15.4.e.a.2.3	yes	8	5.3	odd	4
15.4.e.a.8.2	yes	8	5.4	even	2
15.4.e.a.8.3	yes	8	15.14	odd	2
75.4.e.c.32.2		8	5.2	odd	4	inner
75.4.e.c.32.3		8	15.2	even	4	inner
75.4.e.c.68.2		8	3.2	odd	2	inner
75.4.e.c.68.3		8	1.1	even	1	trivial
240.4.v.c.17.1		8	60.23	odd	4
240.4.v.c.17.2		8	20.3	even	4
240.4.v.c.113.1		8	20.19	odd	2
240.4.v.c.113.2		8	60.59	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	75.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18766 + 1.18766i) q^{2} +(-5.11173 + 0.932827i) q^{3} -5.17891i q^{4} +(-7.17891 - 4.96314i) q^{6} +(13.3578 - 13.3578i) q^{7} +(15.6521 - 15.6521i) q^{8} +(25.2597 - 9.53673i) q^{9} +O(q^{10})\)	\(q+(1.18766 + 1.18766i) q^{2} +(-5.11173 + 0.932827i) q^{3} -5.17891i q^{4} +(-7.17891 - 4.96314i) q^{6} +(13.3578 - 13.3578i) q^{7} +(15.6521 - 15.6521i) q^{8} +(25.2597 - 9.53673i) q^{9} -28.7164i q^{11} +(4.83102 + 26.4732i) q^{12} +(-14.1789 - 14.1789i) q^{13} +31.7292 q^{14} -4.25236 q^{16} +(18.5587 + 18.5587i) q^{17} +(41.3264 + 18.6736i) q^{18} -49.0735i q^{19} +(-55.8211 + 80.7421i) q^{21} +(34.1055 - 34.1055i) q^{22} +(-37.7738 + 37.7738i) q^{23} +(-65.4088 + 94.6102i) q^{24} -33.6796i q^{26} +(-120.225 + 72.3121i) q^{27} +(-69.1789 - 69.1789i) q^{28} -125.854 q^{29} +247.367 q^{31} +(-130.267 - 130.267i) q^{32} +(26.7874 + 146.791i) q^{33} +44.0829i q^{34} +(-49.3898 - 130.818i) q^{36} +(127.463 - 127.463i) q^{37} +(58.2828 - 58.2828i) q^{38} +(85.7053 + 59.2524i) q^{39} +390.328i q^{41} +(-162.191 + 29.5978i) q^{42} +(39.3993 + 39.3993i) q^{43} -148.720 q^{44} -89.7251 q^{46} +(124.560 + 124.560i) q^{47} +(21.7369 - 3.96671i) q^{48} -13.8625i q^{49} +(-112.179 - 77.5549i) q^{51} +(-73.4313 + 73.4313i) q^{52} +(-160.441 + 160.441i) q^{53} +(-228.669 - 56.9040i) q^{54} -418.156i q^{56} +(45.7770 + 250.850i) q^{57} +(-149.473 - 149.473i) q^{58} +729.423 q^{59} +2.00000 q^{61} +(293.789 + 293.789i) q^{62} +(210.024 - 464.804i) q^{63} -275.409i q^{64} +(-142.524 + 206.153i) q^{66} +(329.987 - 329.987i) q^{67} +(96.1136 - 96.1136i) q^{68} +(157.853 - 228.326i) q^{69} -171.760i q^{71} +(246.097 - 544.637i) q^{72} +(279.927 + 279.927i) q^{73} +302.767 q^{74} -254.147 q^{76} +(-383.589 - 383.589i) q^{77} +(31.4172 + 172.161i) q^{78} -48.0189i q^{79} +(547.102 - 481.789i) q^{81} +(-463.578 + 463.578i) q^{82} +(144.451 - 144.451i) q^{83} +(418.156 + 289.092i) q^{84} +93.5862i q^{86} +(643.334 - 117.400i) q^{87} +(-449.473 - 449.473i) q^{88} -1417.21 q^{89} -378.799 q^{91} +(195.627 + 195.627i) q^{92} +(-1264.48 + 230.751i) q^{93} +295.872i q^{94} +(787.409 + 544.375i) q^{96} +(-908.111 + 908.111i) q^{97} +(16.4640 - 16.4640i) q^{98} +(-273.861 - 725.367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} - 12 q^{6} + 16 q^{7}+O(q^{10}) \) 8 * q + 6 * q^3 - 12 * q^6 + 16 * q^7	\( 8 q + 6 q^{3} - 12 q^{6} + 16 q^{7} - 132 q^{12} - 68 q^{13} + 284 q^{16} + 240 q^{18} - 492 q^{21} + 500 q^{22} - 702 q^{27} - 508 q^{28} + 616 q^{31} + 240 q^{33} - 804 q^{36} + 1156 q^{37} - 540 q^{42} - 548 q^{43} + 736 q^{46} + 1116 q^{48} - 852 q^{51} - 224 q^{52} - 684 q^{57} - 60 q^{58} + 16 q^{61} - 1428 q^{63} + 2040 q^{66} - 404 q^{67} + 1800 q^{72} + 2512 q^{73} - 1488 q^{76} + 360 q^{78} + 288 q^{81} - 2800 q^{82} + 1680 q^{87} - 2460 q^{88} - 1304 q^{91} - 3408 q^{93} + 4164 q^{96} - 1904 q^{97}+O(q^{100}) \) 8 * q + 6 * q^3 - 12 * q^6 + 16 * q^7 - 132 * q^12 - 68 * q^13 + 284 * q^16 + 240 * q^18 - 492 * q^21 + 500 * q^22 - 702 * q^27 - 508 * q^28 + 616 * q^31 + 240 * q^33 - 804 * q^36 + 1156 * q^37 - 540 * q^42 - 548 * q^43 + 736 * q^46 + 1116 * q^48 - 852 * q^51 - 224 * q^52 - 684 * q^57 - 60 * q^58 + 16 * q^61 - 1428 * q^63 + 2040 * q^66 - 404 * q^67 + 1800 * q^72 + 2512 * q^73 - 1488 * q^76 + 360 * q^78 + 288 * q^81 - 2800 * q^82 + 1680 * q^87 - 2460 * q^88 - 1304 * q^91 - 3408 * q^93 + 4164 * q^96 - 1904 * q^97

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