LMFDB - Embedded newform 475.3.c.h.151.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,3,Mod(151,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("475.151");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	475.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.9428125571$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 42x^{12} + 677x^{10} + 5313x^{8} + 21125x^{6} + 40138x^{4} + 30565x^{2} + 3675 $ x^14 + 42x^12 + 677x^10 + 5313x^8 + 21125x^6 + 40138x^4 + 30565x^2 + 3675
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.3
Root			$-2.92865i$ of defining polynomial
Character	$\chi$	$=$	475.151
Dual form			475.3.c.h.151.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.92865i q^{2} -2.02259i q^{3} -4.57698 q^{4} -5.92346 q^{6} +8.32815 q^{7} +1.68976i q^{8} +4.90912 q^{9} +O(q^{10})$	\(q-2.92865i q^{2} -2.02259i q^{3} -4.57698 q^{4} -5.92346 q^{6} +8.32815 q^{7} +1.68976i q^{8} +4.90912 q^{9} -17.3372 q^{11} +9.25736i q^{12} -5.27368i q^{13} -24.3902i q^{14} -13.3592 q^{16} -19.0798 q^{17} -14.3771i q^{18} +(-11.4291 - 15.1781i) q^{19} -16.8445i q^{21} +50.7744i q^{22} -3.32445 q^{23} +3.41769 q^{24} -15.4447 q^{26} -28.1325i q^{27} -38.1178 q^{28} -37.4537i q^{29} -2.86714i q^{31} +45.8834i q^{32} +35.0660i q^{33} +55.8779i q^{34} -22.4689 q^{36} +33.0085i q^{37} +(-44.4513 + 33.4719i) q^{38} -10.6665 q^{39} +20.9092i q^{41} -49.3315 q^{42} +23.9545 q^{43} +79.3518 q^{44} +9.73613i q^{46} +33.8351 q^{47} +27.0202i q^{48} +20.3582 q^{49} +38.5906i q^{51} +24.1375i q^{52} -37.4936i q^{53} -82.3901 q^{54} +14.0726i q^{56} +(-30.6991 + 23.1165i) q^{57} -109.689 q^{58} -32.5574i q^{59} +6.58141 q^{61} -8.39685 q^{62} +40.8839 q^{63} +80.9395 q^{64} +102.696 q^{66} -112.029i q^{67} +87.3276 q^{68} +6.72400i q^{69} +110.992i q^{71} +8.29522i q^{72} +134.981 q^{73} +96.6704 q^{74} +(52.3109 + 69.4698i) q^{76} -144.387 q^{77} +31.2384i q^{78} +48.8335i q^{79} -12.7185 q^{81} +61.2355 q^{82} +44.2971 q^{83} +77.0967i q^{84} -70.1541i q^{86} -75.7535 q^{87} -29.2956i q^{88} -173.577i q^{89} -43.9200i q^{91} +15.2159 q^{92} -5.79906 q^{93} -99.0910i q^{94} +92.8034 q^{96} +50.6952i q^{97} -59.6219i q^{98} -85.1102 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 28 q^{4} - 4 q^{6} - 20 q^{7} - 36 q^{9}+O(q^{10}) $ 14 * q - 28 * q^4 - 4 * q^6 - 20 * q^7 - 36 * q^9	$ 14 q - 28 q^{4} - 4 q^{6} - 20 q^{7} - 36 q^{9} - 4 q^{11} + 36 q^{16} + 22 q^{17} + 39 q^{19} + 12 q^{23} - 44 q^{24} + 30 q^{26} + 98 q^{28} + 4 q^{36} + 37 q^{38} - 32 q^{39} + 250 q^{42} + 90 q^{43} - 52 q^{44} + 148 q^{47} + 234 q^{49} + 98 q^{54} - 195 q^{57} - 274 q^{58} + 222 q^{61} + 518 q^{62} + 198 q^{63} - 218 q^{64} + 92 q^{66} + 80 q^{68} - 228 q^{73} - 92 q^{74} - 351 q^{76} - 260 q^{77} + 402 q^{81} + 58 q^{82} - 280 q^{83} - 282 q^{87} + 302 q^{92} - 358 q^{93} + 190 q^{96} - 180 q^{99}+O(q^{100}) $ 14 * q - 28 * q^4 - 4 * q^6 - 20 * q^7 - 36 * q^9 - 4 * q^11 + 36 * q^16 + 22 * q^17 + 39 * q^19 + 12 * q^23 - 44 * q^24 + 30 * q^26 + 98 * q^28 + 4 * q^36 + 37 * q^38 - 32 * q^39 + 250 * q^42 + 90 * q^43 - 52 * q^44 + 148 * q^47 + 234 * q^49 + 98 * q^54 - 195 * q^57 - 274 * q^58 + 222 * q^61 + 518 * q^62 + 198 * q^63 - 218 * q^64 + 92 * q^66 + 80 * q^68 - 228 * q^73 - 92 * q^74 - 351 * q^76 - 260 * q^77 + 402 * q^81 + 58 * q^82 - 280 * q^83 - 282 * q^87 + 302 * q^92 - 358 * q^93 + 190 * q^96 - 180 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	2.92865i		−	1.46432i	−0.681131	−	0.732162i	$-0.738511\pi$
$2$		−	2.92865i		−	1.46432i	0.681131	−	0.732162i	$-0.261489\pi$
$3$		−	2.02259i		−	0.674198i	−0.941469	−	0.337099i	$-0.890554\pi$
$3$		−	2.02259i		−	0.674198i	0.941469	−	0.337099i	$-0.109446\pi$
$4$	−4.57698			−1.14424
$5$		0			0
$5$		0			0
$6$	−5.92346			−0.987243
$7$	8.32815			1.18974			0.594868	−	0.803823i	$-0.297204\pi$
$7$	8.32815			1.18974			0.594868	+	0.803823i	$0.297204\pi$
$8$			1.68976i			0.211220i
$9$	4.90912			0.545458
$10$		0			0
$11$	−17.3372			−1.57611			−0.788053	−	0.615608i	$-0.788911\pi$
$11$	−17.3372			−1.57611			−0.788053	+	0.615608i	$0.788911\pi$
$12$			9.25736i			0.771446i
$13$		−	5.27368i		−	0.405668i	−0.979213	−	0.202834i	$-0.934985\pi$
$13$		−	5.27368i		−	0.405668i	0.979213	−	0.202834i	$-0.0650151\pi$
$14$		−	24.3902i		−	1.74216i
$15$		0			0
$16$	−13.3592			−0.834950
$17$	−19.0798			−1.12234			−0.561170	−	0.827701i	$-0.689649\pi$
$17$	−19.0798			−1.12234			−0.561170	+	0.827701i	$0.689649\pi$
$18$		−	14.3771i		−	0.798727i
$19$	−11.4291	−	15.1781i	−0.601534	−	0.798847i
$19$	−11.4291	−	15.1781i	−0.601534	−	0.798847i
$20$		0			0
$21$		−	16.8445i		−	0.802117i
$22$			50.7744i			2.30793i
$23$	−3.32445			−0.144541			−0.0722706	−	0.997385i	$-0.523025\pi$
$23$	−3.32445			−0.144541			−0.0722706	+	0.997385i	$0.523025\pi$
$24$	3.41769			0.142404
$25$		0			0
$26$	−15.4447			−0.594029
$27$		−	28.1325i		−	1.04194i
$28$	−38.1178			−1.36135
$29$		−	37.4537i		−	1.29151i	−0.763546	−	0.645753i	$-0.776544\pi$
$29$		−	37.4537i		−	1.29151i	0.763546	−	0.645753i	$-0.223456\pi$
$30$		0			0
$31$		−	2.86714i		−	0.0924885i	−0.998930	−	0.0462443i	$-0.985275\pi$
$31$		−	2.86714i		−	0.0924885i	0.998930	−	0.0462443i	$-0.0147253\pi$
$32$			45.8834i			1.43386i
$33$			35.0660i			1.06261i
$34$			55.8779i			1.64347i
$35$		0			0
$36$	−22.4689			−0.624137
$37$			33.0085i			0.892123i	0.895002	+	0.446061i	$0.147174\pi$
$37$			33.0085i			0.892123i	−0.895002	+	0.446061i	$0.852826\pi$
$38$	−44.4513	+	33.4719i	−1.16977	+	0.880840i
$39$	−10.6665			−0.273500
$40$		0			0
$41$			20.9092i			0.509979i	0.966944	+	0.254990i	$0.0820721\pi$
$41$			20.9092i			0.509979i	−0.966944	+	0.254990i	$0.917928\pi$
$42$	−49.3315			−1.17456
$43$	23.9545			0.557080			0.278540	−	0.960425i	$-0.410149\pi$
$43$	23.9545			0.557080			0.278540	+	0.960425i	$0.410149\pi$
$44$	79.3518			1.80345
$45$		0			0
$46$			9.73613i			0.211655i
$47$	33.8351			0.719895			0.359947	−	0.932973i	$-0.382795\pi$
$47$	33.8351			0.719895			0.359947	+	0.932973i	$0.382795\pi$
$48$			27.0202i			0.562921i
$49$	20.3582			0.415473
$50$		0			0
$51$			38.5906i			0.756679i
$52$			24.1375i			0.464183i
$53$		−	37.4936i		−	0.707426i	−0.935354	−	0.353713i	$-0.884919\pi$
$53$		−	37.4936i		−	0.707426i	0.935354	−	0.353713i	$-0.115081\pi$
$54$	−82.3901			−1.52574
$55$		0			0
$56$			14.0726i			0.251296i
$57$	−30.6991	+	23.1165i	−0.538581	+	0.405553i
$58$	−109.689			−1.89118
$59$		−	32.5574i		−	0.551821i	−0.961183	−	0.275910i	$-0.911021\pi$
$59$		−	32.5574i		−	0.551821i	0.961183	−	0.275910i	$-0.0889793\pi$
$60$		0			0
$61$	6.58141			0.107892			0.0539460	−	0.998544i	$-0.482820\pi$
$61$	6.58141			0.107892			0.0539460	+	0.998544i	$0.482820\pi$
$62$	−8.39685			−0.135433
$63$	40.8839			0.648951
$64$	80.9395			1.26468
$65$		0			0
$66$	102.696			1.55600
$67$		−	112.029i		−	1.67208i	−0.548671	−	0.836038i	$-0.684866\pi$
$67$		−	112.029i		−	1.67208i	0.548671	−	0.836038i	$-0.315134\pi$
$68$	87.3276			1.28423
$69$			6.72400i			0.0974493i
$70$		0			0
$71$			110.992i			1.56327i	0.623733	+	0.781637i	$0.285615\pi$
$71$			110.992i			1.56327i	−0.623733	+	0.781637i	$0.714385\pi$
$72$			8.29522i			0.115211i
$73$	134.981			1.84906			0.924530	−	0.381109i	$-0.124458\pi$
$73$	134.981			1.84906			0.924530	+	0.381109i	$0.124458\pi$
$74$	96.6704			1.30636
$75$		0			0
$76$	52.3109	+	69.4698i	0.688301	+	0.914076i
$77$	−144.387			−1.87515
$78$			31.2384i			0.400493i
$79$			48.8335i			0.618145i	0.951038	+	0.309072i	$0.100019\pi$
$79$			48.8335i			0.618145i	−0.951038	+	0.309072i	$0.899981\pi$
$80$		0			0
$81$	−12.7185			−0.157018
$82$	61.2355			0.746775
$83$	44.2971			0.533700			0.266850	−	0.963738i	$-0.414017\pi$
$83$	44.2971			0.533700			0.266850	+	0.963738i	$0.414017\pi$
$84$			77.0967i			0.917818i
$85$		0			0
$86$		−	70.1541i		−	0.815746i
$87$	−75.7535			−0.870730
$88$		−	29.2956i		−	0.332904i
$89$		−	173.577i		−	1.95030i	−0.221538	−	0.975152i	$-0.571108\pi$
$89$		−	173.577i		−	1.95030i	0.221538	−	0.975152i	$-0.428892\pi$
$90$		0			0
$91$		−	43.9200i		−	0.482637i
$92$	15.2159			0.165390
$93$	−5.79906			−0.0623555
$94$		−	99.0910i		−	1.05416i
$95$		0			0
$96$	92.8034			0.966703
$97$			50.6952i			0.522631i	0.965253	+	0.261315i	$0.0841563\pi$
$97$			50.6952i			0.522631i	−0.965253	+	0.261315i	$0.915844\pi$
$98$		−	59.6219i		−	0.608386i
$99$	−85.1102			−0.859699
$100$		0			0
$101$	−100.261			−0.992681			−0.496340	−	0.868128i	$-0.665323\pi$
$101$	−100.261			−0.992681			−0.496340	+	0.868128i	$0.665323\pi$
$102$	113.018			1.10802
$103$		−	31.5721i		−	0.306525i	−0.988185	−	0.153263i	$-0.951022\pi$
$103$		−	31.5721i		−	0.306525i	0.988185	−	0.153263i	$-0.0489780\pi$
$104$	8.91124			0.0856850
$105$		0			0
$106$	−109.805			−1.03590
$107$		−	71.5150i		−	0.668365i	−0.942508	−	0.334182i	$-0.891540\pi$
$107$		−	71.5150i		−	0.668365i	0.942508	−	0.334182i	$-0.108460\pi$
$108$			128.762i			1.19224i
$109$			138.250i			1.26835i	0.773191	+	0.634174i	$0.218660\pi$
$109$			138.250i			1.26835i	−0.773191	+	0.634174i	$0.781340\pi$
$110$		0			0
$111$	66.7628			0.601467
$112$	−111.257			−0.993370
$113$			115.926i			1.02590i	0.858419	+	0.512949i	$0.171447\pi$
$113$			115.926i			1.02590i	−0.858419	+	0.512949i	$0.828553\pi$
$114$	67.7001	+	89.9069i	0.593860	+	0.788657i
$115$		0			0
$116$			171.425i			1.47780i
$117$		−	25.8891i		−	0.221275i
$118$	−95.3492			−0.808044
$119$	−158.899			−1.33529
$120$		0			0
$121$	179.577			1.48411
$122$		−	19.2746i		−	0.157989i
$123$	42.2907			0.343827
$124$			13.1228i			0.105829i
$125$		0			0
$126$		−	119.735i		−	0.950274i
$127$		−	114.758i		−	0.903607i	−0.892117	−	0.451804i	$-0.850781\pi$
$127$		−	114.758i		−	0.903607i	0.892117	−	0.451804i	$-0.149219\pi$
$128$		−	53.5097i		−	0.418045i
$129$		−	48.4501i		−	0.375582i
$130$		0			0
$131$	−203.387			−1.55257			−0.776286	−	0.630381i	$-0.782899\pi$
$131$	−203.387			−1.55257			−0.776286	+	0.630381i	$0.782899\pi$
$132$		−	160.496i		−	1.21588i
$133$	−95.1837	−	126.406i	−0.715667	−	0.950418i
$134$	−328.094			−2.44846
$135$		0			0
$136$		−	32.2402i		−	0.237060i
$137$	152.757			1.11501			0.557507	−	0.830172i	$-0.311758\pi$
$137$	152.757			1.11501			0.557507	+	0.830172i	$0.311758\pi$
$138$	19.6922			0.142697
$139$	155.284			1.11715			0.558575	−	0.829454i	$-0.311348\pi$
$139$	155.284			1.11715			0.558575	+	0.829454i	$0.311348\pi$
$140$		0			0
$141$		−	68.4345i		−	0.485351i
$142$	325.058			2.28914
$143$			91.4306i			0.639375i
$144$	−65.5819			−0.455430
$145$		0			0
$146$		−	395.313i		−	2.70762i
$147$		−	41.1763i		−	0.280111i
$148$		−	151.079i		−	1.02081i
$149$	−106.711			−0.716178			−0.358089	−	0.933687i	$-0.616572\pi$
$149$	−106.711			−0.716178			−0.358089	+	0.933687i	$0.616572\pi$
$150$		0			0
$151$		−	262.585i		−	1.73897i	−0.493955	−	0.869487i	$-0.664449\pi$
$151$		−	262.585i		−	1.73897i	0.493955	−	0.869487i	$-0.335551\pi$
$152$	25.6473	−	19.3125i	0.168732	−	0.127056i
$153$	−93.6649			−0.612189
$154$			422.857i			2.74583i
$155$		0			0
$156$	48.8203			0.312951
$157$	238.486			1.51902			0.759509	−	0.650496i	$-0.225439\pi$
$157$	238.486			1.51902			0.759509	+	0.650496i	$0.225439\pi$
$158$	143.016			0.905164
$159$	−75.8343			−0.476945
$160$		0			0
$161$	−27.6865			−0.171966
$162$			37.2479i			0.229925i
$163$	128.660			0.789328			0.394664	−	0.918826i	$-0.370861\pi$
$163$	128.660			0.789328			0.394664	+	0.918826i	$0.370861\pi$
$164$		−	95.7007i		−	0.583541i
$165$		0			0
$166$		−	129.731i		−	0.781510i
$167$			194.440i			1.16431i	0.813078	+	0.582155i	$0.197790\pi$
$167$			194.440i			1.16431i	−0.813078	+	0.582155i	$0.802210\pi$
$168$	28.4631			0.169423
$169$	141.188			0.835434
$170$		0			0
$171$	−56.1070	−	74.5111i	−0.328111	−	0.435737i
$172$	−109.639			−0.637436
$173$		−	253.484i		−	1.46523i	−0.680646	−	0.732613i	$-0.738301\pi$
$173$		−	253.484i		−	1.46523i	0.680646	−	0.732613i	$-0.261699\pi$
$174$			221.855i			1.27503i
$175$		0			0
$176$	231.611			1.31597
$177$	−65.8504			−0.372036
$178$	−508.346			−2.85588
$179$		−	262.044i		−	1.46393i	−0.681341	−	0.731966i	$-0.738603\pi$
$179$		−	262.044i		−	1.46393i	0.681341	−	0.731966i	$-0.261397\pi$
$180$		0			0
$181$			266.130i			1.47033i	0.677887	+	0.735166i	$0.262896\pi$
$181$			266.130i			1.47033i	−0.677887	+	0.735166i	$0.737104\pi$
$182$	−128.626			−0.706737
$183$		−	13.3115i		−	0.0727405i
$184$		−	5.61751i		−	0.0305299i
$185$		0			0
$186$			16.9834i			0.0913087i
$187$	330.789			1.76893
$188$	−154.862			−0.823735
$189$		−	234.292i		−	1.23964i
$190$		0			0
$191$	−204.892			−1.07273			−0.536366	−	0.843985i	$-0.680203\pi$
$191$	−204.892			−1.07273			−0.536366	+	0.843985i	$0.680203\pi$
$192$		−	163.708i		−	0.852644i
$193$		−	239.909i		−	1.24305i	−0.783394	−	0.621526i	$-0.786513\pi$
$193$		−	239.909i		−	1.24305i	0.783394	−	0.621526i	$-0.213487\pi$
$194$	148.468			0.765301
$195$		0			0
$196$	−93.1788			−0.475402
$197$	−10.5701			−0.0536555			−0.0268278	−	0.999640i	$-0.508541\pi$
$197$	−10.5701			−0.0536555			−0.0268278	+	0.999640i	$0.508541\pi$
$198$			249.258i			1.25888i
$199$	−99.3795			−0.499394			−0.249697	−	0.968324i	$-0.580331\pi$
$199$	−99.3795			−0.499394			−0.249697	+	0.968324i	$0.580331\pi$
$200$		0			0
$201$	−226.589			−1.12731
$202$			293.628i			1.45361i
$203$		−	311.920i		−	1.53655i
$204$		−	176.628i		−	0.865825i
$205$		0			0
$206$	−92.4635			−0.448852
$207$	−16.3201			−0.0788411
$208$			70.4521i			0.338712i
$209$	198.149	+	263.145i	0.948081	+	1.25907i
$210$		0			0
$211$			89.7607i			0.425406i	0.977117	+	0.212703i	$0.0682267\pi$
$211$			89.7607i			0.425406i	−0.977117	+	0.212703i	$0.931773\pi$
$212$			171.607i			0.809468i
$213$	224.493			1.05396
$214$	−209.442			−0.978702
$215$		0			0
$216$	47.5371			0.220079
$217$		−	23.8780i		−	0.110037i
$218$	404.885			1.85727
$219$		−	273.012i		−	1.24663i
$220$		0			0
$221$			100.621i			0.455297i
$222$		−	195.525i		−	0.880742i
$223$			104.111i			0.466866i	0.972373	+	0.233433i	$0.0749959\pi$
$223$			104.111i			0.466866i	−0.972373	+	0.233433i	$0.925004\pi$
$224$			382.124i			1.70591i
$225$		0			0
$226$	339.508			1.50225
$227$		−	254.689i		−	1.12198i	−0.827823	−	0.560990i	$-0.810421\pi$
$227$		−	254.689i		−	1.12198i	0.827823	−	0.560990i	$-0.189579\pi$
$228$	140.509	−	105.804i	0.616268	−	0.464051i
$229$	326.228			1.42457			0.712287	−	0.701888i	$-0.247659\pi$
$229$	326.228			1.42457			0.712287	+	0.701888i	$0.247659\pi$
$230$		0			0
$231$			292.035i			1.26422i
$232$	63.2876			0.272791
$233$	−66.9003			−0.287126			−0.143563	−	0.989641i	$-0.545856\pi$
$233$	−66.9003			−0.287126			−0.143563	+	0.989641i	$0.545856\pi$
$234$	−75.8201			−0.324017
$235$		0			0
$236$			149.015i			0.631417i
$237$	98.7702			0.416752
$238$			465.360i			1.95529i
$239$	246.601			1.03180			0.515902	−	0.856647i	$-0.327457\pi$
$239$	246.601			1.03180			0.515902	+	0.856647i	$0.327457\pi$
$240$		0			0
$241$		−	39.9249i		−	0.165663i	−0.996564	−	0.0828317i	$-0.973604\pi$
$241$		−	39.9249i		−	0.165663i	0.996564	−	0.0828317i	$-0.0263964\pi$
$242$		−	525.918i		−	2.17322i
$243$		−	227.468i		−	0.936082i
$244$	−30.1230			−0.123455
$245$		0			0
$246$		−	123.855i		−	0.503474i
$247$	−80.0444	+	60.2736i	−0.324066	+	0.244023i
$248$	4.84478			0.0195354
$249$		−	89.5950i		−	0.359819i
$250$		0			0
$251$	135.552			0.540046			0.270023	−	0.962854i	$-0.412969\pi$
$251$	135.552			0.540046			0.270023	+	0.962854i	$0.412969\pi$
$252$	−187.125			−0.742558
$253$	57.6365			0.227812
$254$	−336.086			−1.32317
$255$		0			0
$256$	167.047			0.652528
$257$		−	315.240i		−	1.22662i	−0.789844	−	0.613308i	$-0.789838\pi$
$257$		−	315.240i		−	1.22662i	0.789844	−	0.613308i	$-0.210162\pi$
$258$	−141.893			−0.549974
$259$			274.900i			1.06139i
$260$		0			0
$261$		−	183.865i		−	0.704462i
$262$			595.649i			2.27347i
$263$	203.024			0.771956			0.385978	−	0.922508i	$-0.373864\pi$
$263$	203.024			0.771956			0.385978	+	0.922508i	$0.373864\pi$
$264$	−59.2530			−0.224443
$265$		0			0
$266$	−370.197	+	278.759i	−1.39172	+	1.04797i
$267$	−351.076			−1.31489
$268$			512.755i			1.91326i
$269$			272.421i			1.01272i	0.862323	+	0.506359i	$0.169009\pi$
$269$			272.421i			1.01272i	−0.862323	+	0.506359i	$0.830991\pi$
$270$		0			0
$271$	225.743			0.833001			0.416501	−	0.909135i	$-0.363256\pi$
$271$	225.743			0.833001			0.416501	+	0.909135i	$0.363256\pi$
$272$	254.890			0.937097
$273$	−88.8323			−0.325393
$274$		−	447.371i		−	1.63274i
$275$		0			0
$276$		−	30.7756i		−	0.111506i
$277$	−133.873			−0.483296			−0.241648	−	0.970364i	$-0.577688\pi$
$277$	−133.873			−0.483296			−0.241648	+	0.970364i	$0.577688\pi$
$278$		−	454.772i		−	1.63587i
$279$		−	14.0752i		−	0.0504486i
$280$		0			0
$281$			272.283i			0.968980i	0.874797	+	0.484490i	$0.160995\pi$
$281$			272.283i			0.968980i	−0.874797	+	0.484490i	$0.839005\pi$
$282$	−200.421			−0.710712
$283$	−307.114			−1.08521			−0.542605	−	0.839988i	$-0.682562\pi$
$283$	−307.114			−1.08521			−0.542605	+	0.839988i	$0.682562\pi$
$284$		−	508.010i		−	1.78877i
$285$		0			0
$286$	267.768			0.936252
$287$			174.135i			0.606741i
$288$			225.247i			0.782108i
$289$	75.0377			0.259646
$290$		0			0
$291$	102.536			0.352356
$292$	−617.807			−2.11578
$293$			272.281i			0.929287i	0.885498	+	0.464644i	$0.153818\pi$
$293$			272.281i			0.929287i	−0.885498	+	0.464644i	$0.846182\pi$
$294$	−120.591			−0.410173
$295$		0			0
$296$	−55.7764			−0.188434
$297$			487.737i			1.64221i
$298$			312.518i			1.04872i
$299$			17.5321i			0.0586357i
$300$		0			0
$301$	199.496			0.662779
$302$	−769.019			−2.54642
$303$			202.787i			0.669263i
$304$	152.684	+	202.767i	0.502251	+	0.666997i
$305$		0			0
$306$			274.311i			0.896443i
$307$		−	41.8126i		−	0.136198i	−0.997679	−	0.0680988i	$-0.978307\pi$
$307$		−	41.8126i		−	0.136198i	0.997679	−	0.0680988i	$-0.0216933\pi$
$308$	660.854			2.14563
$309$	−63.8575			−0.206659
$310$		0			0
$311$	399.316			1.28398			0.641988	−	0.766715i	$-0.278110\pi$
$311$	399.316			1.28398			0.641988	+	0.766715i	$0.278110\pi$
$312$		−	18.0238i		−	0.0577686i
$313$	−273.543			−0.873941			−0.436970	−	0.899476i	$-0.643949\pi$
$313$	−273.543			−0.873941			−0.436970	+	0.899476i	$0.643949\pi$
$314$		−	698.441i		−	2.22434i
$315$		0			0
$316$		−	223.510i		−	0.707309i
$317$			120.459i			0.379996i	0.981784	+	0.189998i	$0.0608482\pi$
$317$			120.459i			0.379996i	−0.981784	+	0.189998i	$0.939152\pi$
$318$			222.092i			0.698402i
$319$			649.340i			2.03555i
$320$		0			0
$321$	−144.646			−0.450610
$322$			81.0840i			0.251814i
$323$	218.065	+	289.595i	0.675125	+	0.896578i
$324$	58.2121			0.179667
$325$		0			0
$326$		−	376.801i		−	1.15583i
$327$	279.623			0.855117
$328$	−35.3314			−0.107718
$329$	281.784			0.856485
$330$		0			0
$331$			55.2508i			0.166921i	0.996511	+	0.0834604i	$0.0265972\pi$
$331$			55.2508i			0.166921i	−0.996511	+	0.0834604i	$0.973403\pi$
$332$	−202.747			−0.610683
$333$			162.043i			0.486615i
$334$	569.445			1.70493
$335$		0			0
$336$			225.029i			0.669728i
$337$			480.908i			1.42703i	0.700642	+	0.713513i	$0.252897\pi$
$337$			480.908i			1.42703i	−0.700642	+	0.713513i	$0.747103\pi$
$338$		−	413.491i		−	1.22335i
$339$	234.472			0.691658
$340$		0			0
$341$			49.7081i			0.145772i
$342$	−218.217	+	164.318i	−0.638061	+	0.480461i
$343$	−238.534			−0.695434
$344$			40.4772i			0.117666i
$345$		0			0
$346$	−742.365			−2.14556
$347$	538.987			1.55328			0.776639	−	0.629946i	$-0.216923\pi$
$347$	538.987			1.55328			0.776639	+	0.629946i	$0.216923\pi$
$348$	346.722			0.996327
$349$	−21.5094			−0.0616315			−0.0308158	−	0.999525i	$-0.509811\pi$
$349$	−21.5094			−0.0616315			−0.0308158	+	0.999525i	$0.509811\pi$
$350$		0			0
$351$	−148.362			−0.422683
$352$		−	795.488i		−	2.25991i
$353$	−91.3380			−0.258748			−0.129374	−	0.991596i	$-0.541297\pi$
$353$	−91.3380			−0.258748			−0.129374	+	0.991596i	$0.541297\pi$
$354$			192.853i			0.544781i
$355$		0			0
$356$			794.458i			2.23162i
$357$			321.389i			0.900248i
$358$	−767.434			−2.14367
$359$	−673.203			−1.87522			−0.937609	−	0.347691i	$-0.886966\pi$
$359$	−673.203			−1.87522			−0.937609	+	0.347691i	$0.886966\pi$
$360$		0			0
$361$	−99.7493	+	346.945i	−0.276314	+	0.961067i
$362$	779.401			2.15304
$363$		−	363.211i		−	1.00058i
$364$			201.021i			0.552255i
$365$		0			0
$366$	−38.9847			−0.106516
$367$	−595.514			−1.62265			−0.811327	−	0.584593i	$-0.801254\pi$
$367$	−595.514			−1.62265			−0.811327	+	0.584593i	$0.801254\pi$
$368$	44.4120			0.120685
$369$			102.646i			0.278172i
$370$		0			0
$371$		−	312.252i		−	0.841651i
$372$	26.5422			0.0713499
$373$		−	228.595i		−	0.612854i	−0.951894	−	0.306427i	$-0.900866\pi$
$373$		−	228.595i		−	0.612854i	0.951894	−	0.306427i	$-0.0991336\pi$
$374$		−	968.765i		−	2.59028i
$375$		0			0
$376$			57.1730i			0.152056i
$377$	−197.519			−0.523922
$378$	−686.158			−1.81523
$379$		−	725.490i		−	1.91422i	−0.289723	−	0.957110i	$-0.593563\pi$
$379$		−	725.490i		−	1.91422i	0.289723	−	0.957110i	$-0.406437\pi$
$380$		0			0
$381$	−232.109			−0.609210
$382$			600.056i			1.57083i
$383$		−	525.150i		−	1.37115i	−0.728003	−	0.685574i	$-0.759551\pi$
$383$		−	525.150i		−	1.37115i	0.728003	−	0.685574i	$-0.240449\pi$
$384$	−108.228			−0.281845
$385$		0			0
$386$	−702.609			−1.82023
$387$	117.595			0.303864
$388$		−	232.031i		−	0.598017i
$389$	135.008			0.347065			0.173533	−	0.984828i	$-0.444482\pi$
$389$	135.008			0.347065			0.173533	+	0.984828i	$0.444482\pi$
$390$		0			0
$391$	63.4297			0.162224
$392$			34.4003i			0.0877560i
$393$			411.369i			1.04674i
$394$			30.9562i			0.0785691i
$395$		0			0
$396$	389.547			0.983705
$397$	344.093			0.866733			0.433366	−	0.901218i	$-0.357326\pi$
$397$	344.093			0.866733			0.433366	+	0.901218i	$0.357326\pi$
$398$			291.047i			0.731275i
$399$	−255.667	+	192.518i	−0.640769	+	0.482501i
$400$		0			0
$401$			66.2162i			0.165128i	0.996586	+	0.0825638i	$0.0263108\pi$
$401$			66.2162i			0.165128i	−0.996586	+	0.0825638i	$0.973689\pi$
$402$			663.600i			1.65075i
$403$	−15.1204			−0.0375196
$404$	458.891			1.13587
$405$		0			0
$406$	−913.503			−2.25001
$407$		−	572.274i		−	1.40608i
$408$	−65.2088			−0.159825
$409$		−	66.1891i		−	0.161832i	−0.996721	−	0.0809158i	$-0.974216\pi$
$409$		−	66.1891i		−	0.161832i	0.996721	−	0.0809158i	$-0.0257845\pi$
$410$		0			0
$411$		−	308.965i		−	0.751739i
$412$			144.505i			0.350740i
$413$		−	271.143i		−	0.656521i
$414$			47.7958i			0.115449i
$415$		0			0
$416$	241.974			0.581669
$417$		−	314.076i		−	0.753180i
$418$	770.659	−	580.308i	1.84368	−	1.38830i
$419$	448.086			1.06942			0.534709	−	0.845036i	$-0.320421\pi$
$419$	448.086			1.06942			0.534709	+	0.845036i	$0.320421\pi$
$420$		0			0
$421$			728.066i			1.72937i	0.502312	+	0.864686i	$0.332483\pi$
$421$			728.066i			1.72937i	−0.502312	+	0.864686i	$0.667517\pi$
$422$	262.877			0.622932
$423$	166.100			0.392672
$424$	63.3551			0.149422
$425$		0			0
$426$		−	657.460i		−	1.54333i
$427$	54.8110			0.128363
$428$			327.323i			0.764772i
$429$	184.927			0.431065
$430$		0			0
$431$		−	623.890i		−	1.44754i	−0.690042	−	0.723770i	$-0.742408\pi$
$431$		−	623.890i		−	1.44754i	0.690042	−	0.723770i	$-0.257592\pi$
$432$			375.827i			0.869971i
$433$			3.90352i			0.00901505i	0.999990	+	0.00450752i	$0.00143479\pi$
$433$			3.90352i			0.00901505i	−0.999990	+	0.00450752i	$0.998565\pi$
$434$	−69.9303			−0.161130
$435$		0			0
$436$		−	632.766i		−	1.45130i
$437$	37.9956	+	50.4588i	0.0869464	+	0.115466i
$438$	−799.557			−1.82547
$439$			748.985i			1.70612i	0.521815	+	0.853059i	$0.325255\pi$
$439$			748.985i			1.70612i	−0.521815	+	0.853059i	$0.674745\pi$
$440$		0			0
$441$	99.9406			0.226623
$442$	294.682			0.666702
$443$	−77.7877			−0.175593			−0.0877965	−	0.996138i	$-0.527983\pi$
$443$	−77.7877			−0.175593			−0.0877965	+	0.996138i	$0.527983\pi$
$444$	−305.572			−0.688225
$445$		0			0
$446$	304.905			0.683642
$447$			215.832i			0.482846i
$448$	674.077			1.50464
$449$		−	112.043i		−	0.249539i	−0.992186	−	0.124770i	$-0.960181\pi$
$449$		−	112.043i		−	0.249539i	0.992186	−	0.124770i	$-0.0398192\pi$
$450$		0			0
$451$		−	362.505i		−	0.803781i
$452$		−	530.593i		−	1.17388i
$453$	−531.103			−1.17241
$454$	−745.895			−1.64294
$455$		0			0
$456$	−39.0613	−	51.8740i	−0.0856607	−	0.113759i
$457$	−563.415			−1.23286			−0.616428	−	0.787412i	$-0.711421\pi$
$457$	−563.415			−1.23286			−0.616428	+	0.787412i	$0.711421\pi$
$458$		−	955.406i		−	2.08604i
$459$			536.761i			1.16941i
$460$		0			0
$461$	−633.225			−1.37359			−0.686795	−	0.726851i	$-0.740983\pi$
$461$	−633.225			−1.37359			−0.686795	+	0.726851i	$0.740983\pi$
$462$	855.268			1.85123
$463$	547.595			1.18271			0.591356	−	0.806411i	$-0.298593\pi$
$463$	547.595			1.18271			0.591356	+	0.806411i	$0.298593\pi$
$464$			500.351i			1.07834i
$465$		0			0
$466$			195.927i			0.420445i
$467$	856.723			1.83453			0.917263	−	0.398283i	$-0.130394\pi$
$467$	856.723			1.83453			0.917263	+	0.398283i	$0.130394\pi$
$468$			118.494i			0.253192i
$469$		−	932.996i		−	1.98933i
$470$		0			0
$471$		−	482.360i		−	1.02412i
$472$	55.0141			0.116555
$473$	−415.302			−0.878017
$474$		−	289.263i		−	0.610260i
$475$		0			0
$476$	727.278			1.52790
$477$		−	184.060i		−	0.385871i
$478$		−	722.208i		−	1.51090i
$479$	218.011			0.455137			0.227568	−	0.973762i	$-0.426922\pi$
$479$	218.011			0.455137			0.227568	+	0.973762i	$0.426922\pi$
$480$		0			0
$481$	174.076			0.361905
$482$	−116.926			−0.242585
$483$			55.9985i			0.115939i
$484$	−821.920			−1.69818
$485$		0			0
$486$	−666.174			−1.37073
$487$		−	782.514i		−	1.60680i	−0.595437	−	0.803402i	$-0.703021\pi$
$487$		−	782.514i		−	1.60680i	0.595437	−	0.803402i	$-0.296979\pi$
$488$			11.1210i			0.0227889i
$489$		−	260.228i		−	0.532163i
$490$		0			0
$491$	12.9182			0.0263100			0.0131550	−	0.999913i	$-0.495813\pi$
$491$	12.9182			0.0263100			0.0131550	+	0.999913i	$0.495813\pi$
$492$	−193.563			−0.393422
$493$			714.607i			1.44951i
$494$	176.520	+	234.422i	0.357328	+	0.474538i
$495$		0			0
$496$			38.3027i			0.0772233i
$497$			924.363i			1.85988i
$498$	−262.392			−0.526892
$499$	357.210			0.715851			0.357926	−	0.933750i	$-0.383484\pi$
$499$	357.210			0.715851			0.357926	+	0.933750i	$0.383484\pi$
$500$		0			0
$501$	393.272			0.784974
$502$		−	396.983i		−	0.790802i
$503$	−317.657			−0.631526			−0.315763	−	0.948838i	$-0.602260\pi$
$503$	−317.657			−0.631526			−0.315763	+	0.948838i	$0.602260\pi$
$504$			69.0839i			0.137071i
$505$		0			0
$506$		−	168.797i		−	0.333591i
$507$		−	285.566i		−	0.563247i
$508$			525.245i			1.03395i
$509$			386.897i			0.760112i	0.924964	+	0.380056i	$0.124095\pi$
$509$			386.897i			0.760112i	−0.924964	+	0.380056i	$0.875905\pi$
$510$		0			0
$511$	1124.15			2.19989
$512$		−	703.261i		−	1.37356i
$513$	−426.998	+	321.530i	−0.832354	+	0.626765i
$514$	−923.228			−1.79616
$515$		0			0
$516$			221.755i			0.429758i
$517$	−586.604			−1.13463
$518$	805.086			1.55422
$519$	−512.695			−0.987851
$520$		0			0
$521$			216.069i			0.414719i	0.978265	+	0.207359i	$0.0664870\pi$
$521$			216.069i			0.414719i	−0.978265	+	0.207359i	$0.933513\pi$
$522$	−538.474			−1.03156
$523$			208.535i			0.398728i	0.979926	+	0.199364i	$0.0638875\pi$
$523$			208.535i			0.398728i	−0.979926	+	0.199364i	$0.936112\pi$
$524$	930.897			1.77652
$525$		0			0
$526$		−	594.587i		−	1.13039i
$527$			54.7045i			0.103804i
$528$		−	468.454i		−	0.887223i
$529$	−517.948			−0.979108
$530$		0			0
$531$		−	159.828i		−	0.300995i
$532$	435.653	+	578.555i	0.818897	+	1.08751i
$533$	110.268			0.206882
$534$			1028.18i			1.92542i
$535$		0			0
$536$	189.302			0.353175
$537$	−530.008			−0.986979
$538$	797.826			1.48295
$539$	−352.953			−0.654829
$540$		0			0
$541$	−444.565			−0.821746			−0.410873	−	0.911693i	$-0.634776\pi$
$541$	−444.565			−0.821746			−0.410873	+	0.911693i	$0.634776\pi$
$542$		−	661.123i		−	1.21978i
$543$	538.273			0.991294
$544$		−	875.445i		−	1.60927i
$545$		0			0
$546$			260.158i			0.476481i
$547$		−	57.5311i		−	0.105176i	−0.998616	−	0.0525879i	$-0.983253\pi$
$547$		−	57.5311i		−	0.105176i	0.998616	−	0.0525879i	$-0.0167470\pi$
$548$	−699.164			−1.27585
$549$	32.3089			0.0588505
$550$		0			0
$551$	−568.475	+	428.063i	−1.03172	+	0.776885i
$552$	−11.3619			−0.0205832
$553$			406.693i			0.735430i
$554$			392.067i			0.707702i
$555$		0			0
$556$	−710.731			−1.27829
$557$	−32.9110			−0.0590861			−0.0295430	−	0.999564i	$-0.509405\pi$
$557$	−32.9110			−0.0590861			−0.0295430	+	0.999564i	$0.509405\pi$
$558$	−41.2212			−0.0738730
$559$		−	126.328i		−	0.225989i
$560$		0			0
$561$		−	669.052i		−	1.19261i
$562$	797.422			1.41890
$563$			924.040i			1.64128i	0.571446	+	0.820640i	$0.306383\pi$
$563$			924.040i			1.64128i	−0.571446	+	0.820640i	$0.693617\pi$
$564$			313.223i			0.555360i
$565$		0			0
$566$			899.429i			1.58910i
$567$	−105.921			−0.186810
$568$	−187.550			−0.330194
$569$		−	73.0173i		−	0.128326i	−0.997939	−	0.0641628i	$-0.979562\pi$
$569$		−	73.0173i		−	0.128326i	0.997939	−	0.0641628i	$-0.0204377\pi$
$570$		0			0
$571$	709.971			1.24338			0.621690	−	0.783263i	$-0.286446\pi$
$571$	709.971			1.24338			0.621690	+	0.783263i	$0.286446\pi$
$572$		−	418.476i		−	0.731601i
$573$			414.413i			0.723234i
$574$	509.979			0.888465
$575$		0			0
$576$	397.342			0.689830
$577$	−152.315			−0.263978			−0.131989	−	0.991251i	$-0.542136\pi$
$577$	−152.315			−0.263978			−0.131989	+	0.991251i	$0.542136\pi$
$578$		−	219.759i		−	0.380206i
$579$	−485.238			−0.838062
$580$		0			0
$581$	368.913			0.634962
$582$		−	300.291i		−	0.515964i
$583$			650.032i			1.11498i
$584$			228.086i			0.390558i
$585$		0			0
$586$	797.415			1.36078
$587$	96.2527			0.163974			0.0819870	−	0.996633i	$-0.473873\pi$
$587$	96.2527			0.163974			0.0819870	+	0.996633i	$0.473873\pi$
$588$			188.463i			0.320515i
$589$	−43.5178	+	32.7690i	−0.0738842	+	0.0556350i
$590$		0			0
$591$			21.3791i			0.0361744i
$592$		−	440.968i		−	0.744878i
$593$	707.928			1.19381			0.596904	−	0.802313i	$-0.296397\pi$
$593$	707.928			1.19381			0.596904	+	0.802313i	$0.296397\pi$
$594$	1428.41			2.40473
$595$		0			0
$596$	488.412			0.819483
$597$			201.004i			0.336690i
$598$	51.3452			0.0858616
$599$		−	197.129i		−	0.329097i	−0.986369	−	0.164549i	$-0.947383\pi$
$599$		−	197.129i		−	0.329097i	0.986369	−	0.164549i	$-0.0526168\pi$
$600$		0			0
$601$			828.260i			1.37814i	0.724697	+	0.689068i	$0.241980\pi$
$601$			828.260i			1.37814i	−0.724697	+	0.689068i	$0.758020\pi$
$602$		−	584.255i		−	0.970522i
$603$		−	549.964i		−	0.912047i
$604$			1201.85i			1.98981i
$605$		0			0
$606$	593.891			0.980017
$607$		−	386.555i		−	0.636829i	−0.947952	−	0.318415i	$-0.896850\pi$
$607$		−	386.555i		−	0.636829i	0.947952	−	0.318415i	$-0.103150\pi$
$608$	696.423	−	524.408i	1.14543	−	0.862513i
$609$	−630.887			−1.03594
$610$		0			0
$611$		−	178.435i		−	0.292038i
$612$	428.702			0.700493
$613$	1061.04			1.73090			0.865451	−	0.500993i	$-0.167032\pi$
$613$	1061.04			1.73090			0.865451	+	0.500993i	$0.167032\pi$
$614$	−122.454			−0.199437
$615$		0			0
$616$		−	243.978i		−	0.396068i
$617$	−1188.74			−1.92665			−0.963325	−	0.268337i	$-0.913526\pi$
$617$	−1188.74			−1.92665			−0.963325	+	0.268337i	$0.913526\pi$
$618$			187.016i			0.302615i
$619$	−906.151			−1.46390			−0.731948	−	0.681361i	$-0.761389\pi$
$619$	−906.151			−1.46390			−0.731948	+	0.681361i	$0.761389\pi$
$620$		0			0
$621$			93.5250i			0.150604i
$622$		−	1169.46i		−	1.88016i
$623$		−	1445.58i		−	2.32035i
$624$	142.496			0.228359
$625$		0			0
$626$			801.112i			1.27973i
$627$	532.235	−	400.775i	0.848860	−	0.639194i
$628$	−1091.54			−1.73813
$629$		−	629.795i		−	1.00126i
$630$		0			0
$631$	310.563			0.492176			0.246088	−	0.969247i	$-0.420855\pi$
$631$	310.563			0.492176			0.246088	+	0.969247i	$0.420855\pi$
$632$	−82.5167			−0.130564
$633$	181.549			0.286808
$634$	352.782			0.556438
$635$		0			0
$636$	347.091			0.545741
$637$		−	107.362i		−	0.168544i
$638$	1901.69			2.98070
$639$			544.875i			0.852700i
$640$		0			0
$641$		−	673.349i		−	1.05047i	−0.850958	−	0.525233i	$-0.823978\pi$
$641$		−	673.349i		−	1.05047i	0.850958	−	0.525233i	$-0.176022\pi$
$642$			423.616i			0.659839i
$643$	−454.931			−0.707514			−0.353757	−	0.935337i	$-0.615096\pi$
$643$	−454.931			−0.707514			−0.353757	+	0.935337i	$0.615096\pi$
$644$	126.720			0.196771
$645$		0			0
$646$	848.121	−	638.637i	1.31288	−	0.988602i
$647$	357.358			0.552331			0.276166	−	0.961110i	$-0.410936\pi$
$647$	357.358			0.552331			0.276166	+	0.961110i	$0.410936\pi$
$648$		−	21.4911i		−	0.0331653i
$649$			564.453i			0.869728i
$650$		0			0
$651$	−48.2955			−0.0741866
$652$	−588.875			−0.903183
$653$	−859.520			−1.31626			−0.658132	−	0.752903i	$-0.728653\pi$
$653$	−859.520			−1.31626			−0.658132	+	0.752903i	$0.728653\pi$
$654$		−	818.918i		−	1.25217i
$655$		0			0
$656$		−	279.329i		−	0.425807i
$657$	662.640			1.00858
$658$		−	825.245i		−	1.25417i
$659$			103.485i			0.157033i	0.996913	+	0.0785166i	$0.0250183\pi$
$659$			103.485i			0.157033i	−0.996913	+	0.0785166i	$0.974982\pi$
$660$		0			0
$661$		−	520.372i		−	0.787249i	−0.919271	−	0.393625i	$-0.871221\pi$
$661$		−	520.372i		−	0.787249i	0.919271	−	0.393625i	$-0.128779\pi$
$662$	161.810			0.244426
$663$	203.514			0.306960
$664$			74.8513i			0.112728i
$665$		0			0
$666$	474.566			0.712562
$667$			124.513i			0.186676i
$668$		−	889.945i		−	1.33225i
$669$	210.574			0.314760
$670$		0			0
$671$	−114.103			−0.170049
$672$	772.881			1.15012
$673$			687.475i			1.02151i	0.859727	+	0.510754i	$0.170634\pi$
$673$			687.475i			1.02151i	−0.859727	+	0.510754i	$0.829366\pi$
$674$	1408.41			2.08963
$675$		0			0
$676$	−646.215			−0.955940
$677$			540.624i			0.798558i	0.916830	+	0.399279i	$0.130739\pi$
$677$			540.624i			0.798558i	−0.916830	+	0.399279i	$0.869261\pi$
$678$		−	686.686i		−	1.01281i
$679$			422.197i			0.621793i
$680$		0			0
$681$	−515.133			−0.756436
$682$	145.578			0.213457
$683$		−	405.203i		−	0.593270i	−0.954991	−	0.296635i	$-0.904136\pi$
$683$		−	405.203i		−	0.593270i	0.954991	−	0.296635i	$-0.0958644\pi$
$684$	256.801	+	341.035i	0.375439	+	0.498590i
$685$		0			0
$686$			698.581i			1.01834i
$687$		−	659.826i		−	0.960445i
$688$	−320.012			−0.465134
$689$	−197.729			−0.286980
$690$		0			0
$691$	−252.865			−0.365941			−0.182970	−	0.983118i	$-0.558571\pi$
$691$	−252.865			−0.365941			−0.182970	+	0.983118i	$0.558571\pi$
$692$			1160.19i			1.67657i
$693$	−708.811			−1.02282
$694$		−	1578.50i		−	2.27450i
$695$		0			0
$696$		−	128.005i		−	0.183915i
$697$		−	398.942i		−	0.572370i
$698$			62.9935i			0.0902485i
$699$			135.312i			0.193579i
$700$		0			0
$701$	−77.0624			−0.109932			−0.0549660	−	0.998488i	$-0.517505\pi$
$701$	−77.0624			−0.109932			−0.0549660	+	0.998488i	$0.517505\pi$
$702$			434.499i			0.618944i
$703$	501.007	−	377.259i	0.712670	−	0.536642i
$704$	−1403.26			−1.99327
$705$		0			0
$706$			267.497i			0.378891i
$707$	−834.987			−1.18103
$708$	301.396			0.425700
$709$	876.024			1.23558			0.617788	−	0.786344i	$-0.288029\pi$
$709$	876.024			1.23558			0.617788	+	0.786344i	$0.288029\pi$
$710$		0			0
$711$			239.729i			0.337172i
$712$	293.303			0.411942
$713$			9.53167i			0.0133684i
$714$	941.234			1.31825
$715$		0			0
$716$			1199.37i			1.67510i
$717$		−	498.774i		−	0.695640i
$718$			1971.58i			2.74593i
$719$	819.304			1.13950			0.569752	−	0.821816i	$-0.307039\pi$
$719$	819.304			1.13950			0.569752	+	0.821816i	$0.307039\pi$
$720$		0			0
$721$		−	262.937i		−	0.364684i
$722$	1016.08	+	292.131i	1.40731	+	0.404613i
$723$	−80.7517			−0.111690
$724$		−	1218.07i		−	1.68242i
$725$		0			0
$726$	−1063.72			−1.46518
$727$	−140.643			−0.193457			−0.0967286	−	0.995311i	$-0.530838\pi$
$727$	−140.643			−0.193457			−0.0967286	+	0.995311i	$0.530838\pi$
$728$	74.2141			0.101943
$729$	−574.541			−0.788123
$730$		0			0
$731$	−457.046			−0.625233
$732$			60.9265i			0.0832329i
$733$	693.708			0.946395			0.473197	−	0.880956i	$-0.343100\pi$
$733$	693.708			0.946395			0.473197	+	0.880956i	$0.343100\pi$
$734$			1744.05i			2.37609i
$735$		0			0
$736$		−	152.537i		−	0.207251i
$737$			1942.27i			2.63537i
$738$	300.613			0.407334
$739$	−1424.83			−1.92806			−0.964028	−	0.265801i	$-0.914364\pi$
$739$	−1424.83			−1.92806			−0.964028	+	0.265801i	$0.914364\pi$
$740$		0			0
$741$	121.909	+	161.897i	0.164520	+	0.218485i
$742$	−914.477			−1.23245
$743$			1046.28i			1.40818i	0.710109	+	0.704092i	$0.248646\pi$
$743$			1046.28i			1.40818i	−0.710109	+	0.704092i	$0.751354\pi$
$744$		−	9.79901i		−	0.0131707i
$745$		0			0
$746$	−669.473			−0.897417
$747$	217.460			0.291111
$748$	−1514.01			−2.02408
$749$		−	595.588i		−	0.795178i
$750$		0			0
$751$			70.9338i			0.0944525i	0.998884	+	0.0472262i	$0.0150382\pi$
$751$			70.9338i			0.0944525i	−0.998884	+	0.0472262i	$0.984962\pi$
$752$	−452.009			−0.601076
$753$		−	274.166i		−	0.364098i
$754$			578.462i			0.767191i
$755$		0			0
$756$			1072.35i			1.41845i
$757$	−1422.41			−1.87901			−0.939506	−	0.342532i	$-0.888716\pi$
$757$	−1422.41			−1.87901			−0.939506	+	0.342532i	$0.888716\pi$
$758$	−2124.70			−2.80304
$759$		−	116.575i		−	0.153590i
$760$		0			0
$761$	110.061			0.144627			0.0723136	−	0.997382i	$-0.476962\pi$
$761$	110.061			0.144627			0.0723136	+	0.997382i	$0.476962\pi$
$762$			679.765i			0.892080i
$763$			1151.37i			1.50900i
$764$	937.786			1.22747
$765$		0			0
$766$	−1537.98			−2.00780
$767$	−171.697			−0.223856
$768$		−	337.868i		−	0.439932i
$769$	136.681			0.177739			0.0888693	−	0.996043i	$-0.471675\pi$
$769$	136.681			0.177739			0.0888693	+	0.996043i	$0.471675\pi$
$770$		0			0
$771$	−637.603			−0.826981
$772$			1098.06i			1.42235i
$773$			177.135i			0.229153i	0.993414	+	0.114576i	$0.0365510\pi$
$773$			177.135i			0.229153i	−0.993414	+	0.114576i	$0.963449\pi$
$774$		−	344.395i		−	0.444955i
$775$		0			0
$776$	−85.6625			−0.110390
$777$	556.011			0.715587
$778$		−	395.392i		−	0.508216i
$779$	317.361	−	238.974i	0.407396	−	0.306770i
$780$		0			0
$781$		−	1924.29i		−	2.46389i
$782$		−	185.763i		−	0.237549i
$783$	−1053.66			−1.34568
$784$	−271.969			−0.346899
$785$		0			0
$786$	1204.75			1.53277
$787$		−	210.259i		−	0.267166i	−0.991038	−	0.133583i	$-0.957352\pi$
$787$		−	210.259i		−	0.267166i	0.991038	−	0.133583i	$-0.0426482\pi$
$788$	48.3793			0.0613950
$789$		−	410.636i		−	0.520451i
$790$		0			0
$791$			965.453i			1.22055i
$792$		−	143.816i		−	0.181585i
$793$		−	34.7083i		−	0.0437683i
$794$		−	1007.73i		−	1.26918i
$795$		0			0
$796$	454.857			0.571429
$797$			474.092i			0.594845i	0.954746	+	0.297423i	$0.0961270\pi$
$797$			474.092i			0.594845i	−0.954746	+	0.297423i	$0.903873\pi$
$798$	563.817	+	748.758i	0.706537	+	0.938293i
$799$	−645.565			−0.807967
$800$		0			0
$801$		−	852.110i		−	1.06381i
$802$	193.924			0.241800
$803$	−2340.19			−2.91431
$804$	1037.09			1.28992
$805$		0			0
$806$			44.2823i			0.0549408i
$807$	550.997			0.682772
$808$		−	169.416i		−	0.209674i
$809$	−1279.92			−1.58210			−0.791050	−	0.611751i	$-0.790465\pi$
$809$	−1279.92			−1.58210			−0.791050	+	0.611751i	$0.790465\pi$
$810$		0			0
$811$		−	869.604i		−	1.07226i	−0.844135	−	0.536130i	$-0.819886\pi$
$811$		−	869.604i		−	1.07226i	0.844135	−	0.536130i	$-0.180114\pi$
$812$			1427.65i			1.75819i
$813$		−	456.587i		−	0.561607i
$814$	−1675.99			−2.05896
$815$		0			0
$816$		−	515.540i		−	0.631789i
$817$	−273.779	−	363.583i	−0.335103	−	0.445022i
$818$	−193.845			−0.236974
$819$		−	215.609i		−	0.263258i
$820$		0			0
$821$	−1061.20			−1.29257			−0.646287	−	0.763094i	$-0.723679\pi$
$821$	−1061.20			−1.29257			−0.646287	+	0.763094i	$0.723679\pi$
$822$	−904.849			−1.10079
$823$	458.926			0.557626			0.278813	−	0.960345i	$-0.410059\pi$
$823$	458.926			0.557626			0.278813	+	0.960345i	$0.410059\pi$
$824$	53.3492			0.0647441
$825$		0			0
$826$	−794.083			−0.961359
$827$			746.165i			0.902255i	0.892459	+	0.451128i	$0.148978\pi$
$827$			746.165i			0.902255i	−0.892459	+	0.451128i	$0.851022\pi$
$828$	74.6967			0.0902134
$829$			200.255i			0.241562i	0.992679	+	0.120781i	$0.0385399\pi$
$829$			200.255i			0.241562i	−0.992679	+	0.120781i	$0.961460\pi$
$830$		0			0
$831$			270.771i			0.325837i
$832$		−	426.849i		−	0.513040i
$833$	−388.429			−0.466301
$834$	−919.818			−1.10290
$835$		0			0
$836$	−906.923	−	1204.41i	−1.08484	−	1.44068i
$837$	−80.6599			−0.0963678
$838$		−	1312.29i		−	1.56597i
$839$			247.657i			0.295181i	0.989049	+	0.147591i	$0.0471518\pi$
$839$			247.657i			0.295181i	−0.989049	+	0.147591i	$0.952848\pi$
$840$		0			0
$841$	−561.777			−0.667987
$842$	2132.25			2.53236
$843$	550.718			0.653284
$844$		−	410.832i		−	0.486768i
$845$		0			0
$846$		−	486.449i		−	0.574999i
$847$	1495.55			1.76570
$848$			500.884i			0.590665i
$849$			621.167i			0.731645i
$850$		0			0
$851$		−	109.735i		−	0.128948i
$852$	−1027.50			−1.20598
$853$	172.802			0.202581			0.101291	−	0.994857i	$-0.467703\pi$
$853$	172.802			0.202581			0.101291	+	0.994857i	$0.467703\pi$
$854$		−	160.522i		−	0.187965i
$855$		0			0
$856$	120.843			0.141172
$857$			795.527i			0.928270i	0.885765	+	0.464135i	$0.153635\pi$
$857$			795.527i			0.928270i	−0.885765	+	0.464135i	$0.846365\pi$
$858$		−	541.586i		−	0.631219i
$859$	−104.671			−0.121852			−0.0609260	−	0.998142i	$-0.519405\pi$
$859$	−104.671			−0.121852			−0.0609260	+	0.998142i	$0.519405\pi$
$860$		0			0
$861$	352.203			0.409063
$862$	−1827.15			−2.11967
$863$			887.350i			1.02822i	0.857725	+	0.514108i	$0.171877\pi$
$863$			887.350i			1.02822i	−0.857725	+	0.514108i	$0.828123\pi$
$864$	1290.81			1.49400
$865$		0			0
$866$	11.4320			0.0132009
$867$		−	151.771i		−	0.175053i
$868$			109.289i			0.125909i
$869$		−	846.633i		−	0.974262i
$870$		0			0
$871$	−590.806			−0.678307
$872$	−233.609			−0.267900
$873$			248.869i			0.285073i
$874$	147.776	−	111.276i	0.169080	−	0.127318i
$875$		0			0
$876$			1249.57i			1.42645i
$877$		−	82.4212i		−	0.0939809i	−0.998895	−	0.0469904i	$-0.985037\pi$
$877$		−	82.4212i		−	0.0939809i	0.998895	−	0.0469904i	$-0.0149630\pi$
$878$	2193.51			2.49831
$879$	550.714			0.626523
$880$		0			0
$881$	1311.40			1.48853			0.744267	−	0.667883i	$-0.232799\pi$
$881$	1311.40			1.48853			0.744267	+	0.667883i	$0.232799\pi$
$882$		−	292.691i		−	0.331849i
$883$	61.4085			0.0695453			0.0347727	−	0.999395i	$-0.488929\pi$
$883$	61.4085			0.0695453			0.0347727	+	0.999395i	$0.488929\pi$
$884$		−	460.538i		−	0.520971i
$885$		0			0
$886$			227.813i			0.257125i
$887$		−	70.9500i		−	0.0799887i	−0.999200	−	0.0399943i	$-0.987266\pi$
$887$		−	70.9500i		−	0.0799887i	0.999200	−	0.0399943i	$-0.0127340\pi$
$888$			112.813i			0.127042i
$889$		−	955.723i		−	1.07505i
$890$		0			0
$891$	220.502			0.247477
$892$		−	476.514i		−	0.534208i
$893$	−386.706	−	513.552i	−0.433041	−	0.575086i
$894$	632.096			0.707042
$895$		0			0
$896$		−	445.637i		−	0.497363i
$897$	35.4602			0.0395320
$898$	−328.135			−0.365407
$899$	−107.385			−0.119449
$900$		0			0
$901$			715.369i			0.793972i
$902$	−1061.65			−1.17700
$903$		−	403.500i		−	0.446844i
$904$	−195.888			−0.216690
$905$		0			0
$906$			1555.41i			1.71679i
$907$			658.755i			0.726301i	0.931730	+	0.363151i	$0.118299\pi$
$907$			658.755i			0.726301i	−0.931730	+	0.363151i	$0.881701\pi$
$908$			1165.71i			1.28382i
$909$	−492.192			−0.541465
$910$		0			0
$911$		−	445.396i		−	0.488909i	−0.969661	−	0.244454i	$-0.921391\pi$
$911$		−	445.396i		−	0.488909i	0.969661	−	0.244454i	$-0.0786089\pi$
$912$	410.115	−	308.818i	0.449688	−	0.338616i
$913$	−767.986			−0.841168
$914$			1650.04i			1.80530i
$915$		0			0
$916$	−1493.14			−1.63006
$917$	−1693.84			−1.84715
$918$	1571.98			1.71240
$919$	423.867			0.461226			0.230613	−	0.973046i	$-0.425927\pi$
$919$	423.867			0.461226			0.230613	+	0.973046i	$0.425927\pi$
$920$		0			0
$921$	−84.5699			−0.0918240
$922$			1854.49i			2.01138i
$923$	585.339			0.634170
$924$		−	1336.64i		−	1.44658i
$925$		0			0
$926$		−	1603.71i		−	1.73187i
$927$		−	154.991i		−	0.167197i
$928$	1718.50			1.85183
$929$	976.138			1.05074			0.525370	−	0.850874i	$-0.323927\pi$
$929$	976.138			1.05074			0.525370	+	0.850874i	$0.323927\pi$
$930$		0			0
$931$	−232.676	−	308.998i	−0.249921	−	0.331899i
$932$	306.201			0.328542
$933$		−	807.654i		−	0.865653i
$934$		−	2509.04i		−	2.68634i
$935$		0			0
$936$	43.7463			0.0467375
$937$	383.017			0.408770			0.204385	−	0.978891i	$-0.434481\pi$
$937$	383.017			0.408770			0.204385	+	0.978891i	$0.434481\pi$
$938$	−2732.42			−2.91302
$939$			553.267i			0.589209i
$940$		0			0
$941$			1515.60i			1.61062i	0.592851	+	0.805312i	$0.298002\pi$
$941$			1515.60i			1.61062i	−0.592851	+	0.805312i	$0.701998\pi$
$942$	−1412.66			−1.49964
$943$		−	69.5114i		−	0.0737130i
$944$			434.941i			0.460743i
$945$		0			0
$946$			1216.27i			1.28570i
$947$	−33.4812			−0.0353550			−0.0176775	−	0.999844i	$-0.505627\pi$
$947$	−33.4812			−0.0353550			−0.0176775	+	0.999844i	$0.505627\pi$
$948$	−452.069			−0.476866
$949$		−	711.849i		−	0.750104i
$950$		0			0
$951$	243.639			0.256193
$952$		−	268.501i		−	0.282039i
$953$			1337.39i			1.40335i	0.712499	+	0.701674i	$0.247563\pi$
$953$			1337.39i			1.40335i	−0.712499	+	0.701674i	$0.752437\pi$
$954$	−539.048			−0.565040
$955$		0			0
$956$	−1128.69			−1.18064
$957$	1313.35			1.37236
$958$		−	638.476i		−	0.666468i
$959$	1272.18			1.32657
$960$		0			0
$961$	952.779			0.991446
$962$		−	509.808i		−	0.529946i
$963$		−	351.076i		−	0.364565i
$964$			182.735i			0.189559i
$965$		0			0
$966$	164.000			0.169772
$967$	−146.380			−0.151375			−0.0756877	−	0.997132i	$-0.524115\pi$
$967$	−146.380			−0.151375			−0.0756877	+	0.997132i	$0.524115\pi$
$968$			303.442i			0.313473i
$969$	585.732	−	441.058i	0.604471	−	0.455168i
$970$		0			0
$971$		−	1118.48i		−	1.15188i	−0.817492	−	0.575940i	$-0.804636\pi$
$971$		−	1118.48i		−	1.15188i	0.817492	−	0.575940i	$-0.195364\pi$
$972$			1041.12i			1.07111i
$973$	1293.23			1.32912
$974$	−2291.71			−2.35288
$975$		0			0
$976$	−87.9224			−0.0900844
$977$		−	850.328i		−	0.870346i	−0.900347	−	0.435173i	$-0.856687\pi$
$977$		−	850.328i		−	0.870346i	0.900347	−	0.435173i	$-0.143313\pi$
$978$	−762.115			−0.779258
$979$			3009.33i			3.07388i
$980$		0			0
$981$			678.685i			0.691830i
$982$		−	37.8328i		−	0.0385263i
$983$		−	1064.58i		−	1.08299i	−0.840705	−	0.541493i	$-0.817859\pi$
$983$		−	1064.58i		−	1.08299i	0.840705	−	0.541493i	$-0.182141\pi$
$984$			71.4610i			0.0726230i
$985$		0			0
$986$	2092.83			2.12255
$987$		−	569.933i		−	0.577440i
$988$	366.361	−	275.871i	0.370811	−	0.279222i
$989$	−79.6353			−0.0805210
$990$		0			0
$991$			1750.89i			1.76679i	0.468631	+	0.883394i	$0.344747\pi$
$991$			1750.89i			1.76679i	−0.468631	+	0.883394i	$0.655253\pi$
$992$	131.554			0.132615
$993$	111.750			0.112538
$994$	2707.13			2.72347
$995$		0			0
$996$			410.074i			0.411721i
$997$	444.357			0.445695			0.222847	−	0.974853i	$-0.428465\pi$
$997$	444.357			0.445695			0.222847	+	0.974853i	$0.428465\pi$
$998$		−	1046.14i		−	1.04824i
$999$	928.612			0.929542

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.3.c.h.151.3	✓	14
5.2	odd	4		475.3.d.d.474.24		28
5.3	odd	4		475.3.d.d.474.5		28
5.4	even	2		475.3.c.i.151.12	yes	14
19.18	odd	2	inner	475.3.c.h.151.12	yes	14
95.18	even	4		475.3.d.d.474.23		28
95.37	even	4		475.3.d.d.474.6		28
95.94	odd	2		475.3.c.i.151.3	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.3.c.h.151.3	✓	14	1.1	even	1	trivial
475.3.c.h.151.12	yes	14	19.18	odd	2	inner
475.3.c.i.151.3	yes	14	95.94	odd	2
475.3.c.i.151.12	yes	14	5.4	even	2
475.3.d.d.474.5		28	5.3	odd	4
475.3.d.d.474.6		28	95.37	even	4
475.3.d.d.474.23		28	95.18	even	4
475.3.d.d.474.24		28	5.2	odd	4

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	475.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.92865i q^{2} -2.02259i q^{3} -4.57698 q^{4} -5.92346 q^{6} +8.32815 q^{7} +1.68976i q^{8} +4.90912 q^{9} +O(q^{10})\)	\(q-2.92865i q^{2} -2.02259i q^{3} -4.57698 q^{4} -5.92346 q^{6} +8.32815 q^{7} +1.68976i q^{8} +4.90912 q^{9} -17.3372 q^{11} +9.25736i q^{12} -5.27368i q^{13} -24.3902i q^{14} -13.3592 q^{16} -19.0798 q^{17} -14.3771i q^{18} +(-11.4291 - 15.1781i) q^{19} -16.8445i q^{21} +50.7744i q^{22} -3.32445 q^{23} +3.41769 q^{24} -15.4447 q^{26} -28.1325i q^{27} -38.1178 q^{28} -37.4537i q^{29} -2.86714i q^{31} +45.8834i q^{32} +35.0660i q^{33} +55.8779i q^{34} -22.4689 q^{36} +33.0085i q^{37} +(-44.4513 + 33.4719i) q^{38} -10.6665 q^{39} +20.9092i q^{41} -49.3315 q^{42} +23.9545 q^{43} +79.3518 q^{44} +9.73613i q^{46} +33.8351 q^{47} +27.0202i q^{48} +20.3582 q^{49} +38.5906i q^{51} +24.1375i q^{52} -37.4936i q^{53} -82.3901 q^{54} +14.0726i q^{56} +(-30.6991 + 23.1165i) q^{57} -109.689 q^{58} -32.5574i q^{59} +6.58141 q^{61} -8.39685 q^{62} +40.8839 q^{63} +80.9395 q^{64} +102.696 q^{66} -112.029i q^{67} +87.3276 q^{68} +6.72400i q^{69} +110.992i q^{71} +8.29522i q^{72} +134.981 q^{73} +96.6704 q^{74} +(52.3109 + 69.4698i) q^{76} -144.387 q^{77} +31.2384i q^{78} +48.8335i q^{79} -12.7185 q^{81} +61.2355 q^{82} +44.2971 q^{83} +77.0967i q^{84} -70.1541i q^{86} -75.7535 q^{87} -29.2956i q^{88} -173.577i q^{89} -43.9200i q^{91} +15.2159 q^{92} -5.79906 q^{93} -99.0910i q^{94} +92.8034 q^{96} +50.6952i q^{97} -59.6219i q^{98} -85.1102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 28 q^{4} - 4 q^{6} - 20 q^{7} - 36 q^{9}+O(q^{10}) \) 14 * q - 28 * q^4 - 4 * q^6 - 20 * q^7 - 36 * q^9	\( 14 q - 28 q^{4} - 4 q^{6} - 20 q^{7} - 36 q^{9} - 4 q^{11} + 36 q^{16} + 22 q^{17} + 39 q^{19} + 12 q^{23} - 44 q^{24} + 30 q^{26} + 98 q^{28} + 4 q^{36} + 37 q^{38} - 32 q^{39} + 250 q^{42} + 90 q^{43} - 52 q^{44} + 148 q^{47} + 234 q^{49} + 98 q^{54} - 195 q^{57} - 274 q^{58} + 222 q^{61} + 518 q^{62} + 198 q^{63} - 218 q^{64} + 92 q^{66} + 80 q^{68} - 228 q^{73} - 92 q^{74} - 351 q^{76} - 260 q^{77} + 402 q^{81} + 58 q^{82} - 280 q^{83} - 282 q^{87} + 302 q^{92} - 358 q^{93} + 190 q^{96} - 180 q^{99}+O(q^{100}) \) 14 * q - 28 * q^4 - 4 * q^6 - 20 * q^7 - 36 * q^9 - 4 * q^11 + 36 * q^16 + 22 * q^17 + 39 * q^19 + 12 * q^23 - 44 * q^24 + 30 * q^26 + 98 * q^28 + 4 * q^36 + 37 * q^38 - 32 * q^39 + 250 * q^42 + 90 * q^43 - 52 * q^44 + 148 * q^47 + 234 * q^49 + 98 * q^54 - 195 * q^57 - 274 * q^58 + 222 * q^61 + 518 * q^62 + 198 * q^63 - 218 * q^64 + 92 * q^66 + 80 * q^68 - 228 * q^73 - 92 * q^74 - 351 * q^76 - 260 * q^77 + 402 * q^81 + 58 * q^82 - 280 * q^83 - 282 * q^87 + 302 * q^92 - 358 * q^93 + 190 * q^96 - 180 * q^99

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