LMFDB - Embedded newform 275.3.c.h.76.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(76,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.76"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,4,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 21x^{6} + 130x^{4} + 215x^{2} + 25 $ x^8 + 21x^6 + 130x^4 + 215*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.2
Root			$-2.78271i$ of defining polynomial
Character	$\chi$	$=$	275.76
Dual form			275.3.c.h.76.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.78271i q^{2} +5.54645 q^{3} -3.74350 q^{4} -15.4342i q^{6} +4.48239i q^{7} -0.713764i q^{8} +21.7632 q^{9} +(2.46337 - 10.7206i) q^{11} -20.7632 q^{12} +15.7063i q^{13} +12.4732 q^{14} -16.9602 q^{16} -25.4820i q^{17} -60.5607i q^{18} +8.44528i q^{19} +24.8614i q^{21} +(-29.8324 - 6.85487i) q^{22} -19.8870 q^{23} -3.95886i q^{24} +43.7063 q^{26} +70.7903 q^{27} -16.7798i q^{28} +21.4524i q^{29} +24.9579 q^{31} +44.3404i q^{32} +(13.6630 - 59.4615i) q^{33} -70.9092 q^{34} -81.4704 q^{36} -30.4659 q^{37} +23.5008 q^{38} +87.1145i q^{39} -10.5577i q^{41} +69.1821 q^{42} +68.3676i q^{43} +(-9.22164 + 40.1327i) q^{44} +55.3397i q^{46} -25.0636 q^{47} -94.0690 q^{48} +28.9082 q^{49} -141.335i q^{51} -58.7967i q^{52} -93.9329 q^{53} -196.989i q^{54} +3.19936 q^{56} +46.8414i q^{57} +59.6960 q^{58} -27.3730 q^{59} +81.1075i q^{61} -69.4507i q^{62} +97.5509i q^{63} +55.5457 q^{64} +(-165.464 - 38.0202i) q^{66} -49.5118 q^{67} +95.3920i q^{68} -110.302 q^{69} +44.0132 q^{71} -15.5338i q^{72} -29.1783i q^{73} +84.7779i q^{74} -31.6149i q^{76} +(48.0540 + 11.0418i) q^{77} +242.415 q^{78} -51.3920i q^{79} +196.767 q^{81} -29.3792 q^{82} +47.2115i q^{83} -93.0685i q^{84} +190.248 q^{86} +118.985i q^{87} +(-7.65199 - 1.75827i) q^{88} +147.455 q^{89} -70.4019 q^{91} +74.4468 q^{92} +138.428 q^{93} +69.7449i q^{94} +245.932i q^{96} +87.8176 q^{97} -80.4433i q^{98} +(53.6108 - 233.315i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 10 q^{4} + 32 q^{9} - q^{11} - 24 q^{12} + 18 q^{14} - 14 q^{16} - 35 q^{22} + 4 q^{23} + 68 q^{26} + 142 q^{27} - 42 q^{31} - 31 q^{33} - 142 q^{34} - 84 q^{36} - 104 q^{37} + 190 q^{38}+ \cdots + 368 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 10 * q^4 + 32 * q^9 - q^11 - 24 * q^12 + 18 * q^14 - 14 * q^16 - 35 * q^22 + 4 * q^23 + 68 * q^26 + 142 * q^27 - 42 * q^31 - 31 * q^33 - 142 * q^34 - 84 * q^36 - 104 * q^37 + 190 * q^38 + 50 * q^42 + 69 * q^44 - 64 * q^47 - 86 * q^48 - 50 * q^49 - 286 * q^53 + 166 * q^56 - 130 * q^58 - 160 * q^59 + 288 * q^64 - 315 * q^66 + 46 * q^67 - 16 * q^69 + 246 * q^71 + 80 * q^77 + 620 * q^78 + 304 * q^81 + 280 * q^82 - 282 * q^86 - 365 * q^88 - 18 * q^89 - 142 * q^91 + 26 * q^92 + 818 * q^93 - 264 * q^97 + 368 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	2.78271i		−	1.39136i	−0.718353	−	0.695679i	$-0.755104\pi$
$2$		−	2.78271i		−	1.39136i	0.718353	−	0.695679i	$-0.244896\pi$
$3$	5.54645			1.84882			0.924409	−	0.381402i	$-0.124559\pi$
$3$	5.54645			1.84882			0.924409	+	0.381402i	$0.124559\pi$
$4$	−3.74350			−0.935875
$5$		0			0
$5$		0			0
$6$		−	15.4342i		−	2.57237i
$7$			4.48239i			0.640341i	0.947360	+	0.320170i	$0.103740\pi$
$7$			4.48239i			0.640341i	−0.947360	+	0.320170i	$0.896260\pi$
$8$		−	0.713764i		−	0.0892205i
$9$	21.7632			2.41813
$10$		0			0
$11$	2.46337	−	10.7206i	0.223943	−	0.974602i
$11$	2.46337	−	10.7206i	0.223943	−	0.974602i
$12$	−20.7632			−1.73026
$13$			15.7063i			1.20818i	0.796916	+	0.604090i	$0.206463\pi$
$13$			15.7063i			1.20818i	−0.796916	+	0.604090i	$0.793537\pi$
$14$	12.4732			0.890943
$15$		0			0
$16$	−16.9602			−1.06001
$17$		−	25.4820i		−	1.49894i	−0.662037	−	0.749471i	$-0.730308\pi$
$17$		−	25.4820i		−	1.49894i	0.662037	−	0.749471i	$-0.269692\pi$
$18$		−	60.5607i		−	3.36448i
$19$			8.44528i			0.444488i	0.974991	+	0.222244i	$0.0713382\pi$
$19$			8.44528i			0.444488i	−0.974991	+	0.222244i	$0.928662\pi$
$20$		0			0
$21$			24.8614i			1.18387i
$22$	−29.8324	−	6.85487i	−1.35602	−	0.311585i
$23$	−19.8870			−0.864650			−0.432325	−	0.901718i	$-0.642307\pi$
$23$	−19.8870			−0.864650			−0.432325	+	0.901718i	$0.642307\pi$
$24$		−	3.95886i		−	0.164952i
$25$		0			0
$26$	43.7063			1.68101
$27$	70.7903			2.62186
$28$		−	16.7798i		−	0.599279i
$29$			21.4524i			0.739739i	0.929084	+	0.369870i	$0.120598\pi$
$29$			21.4524i			0.739739i	−0.929084	+	0.369870i	$0.879402\pi$
$30$		0			0
$31$	24.9579			0.805093			0.402547	−	0.915400i	$-0.368125\pi$
$31$	24.9579			0.805093			0.402547	+	0.915400i	$0.368125\pi$
$32$			44.3404i			1.38564i
$33$	13.6630	−	59.4615i	0.414030	−	1.80186i
$34$	−70.9092			−2.08556
$35$		0			0
$36$	−81.4704			−2.26307
$37$	−30.4659			−0.823403			−0.411701	−	0.911319i	$-0.635065\pi$
$37$	−30.4659			−0.823403			−0.411701	+	0.911319i	$0.635065\pi$
$38$	23.5008			0.618442
$39$			87.1145i			2.23371i
$40$		0			0
$41$		−	10.5577i		−	0.257506i	−0.991677	−	0.128753i	$-0.958903\pi$
$41$		−	10.5577i		−	0.257506i	0.991677	−	0.128753i	$-0.0410974\pi$
$42$	69.1821			1.64719
$43$			68.3676i			1.58994i	0.606645	+	0.794972i	$0.292515\pi$
$43$			68.3676i			1.58994i	−0.606645	+	0.794972i	$0.707485\pi$
$44$	−9.22164	+	40.1327i	−0.209583	+	0.912106i
$45$		0			0
$46$			55.3397i			1.20304i
$47$	−25.0636			−0.533269			−0.266634	−	0.963798i	$-0.585912\pi$
$47$	−25.0636			−0.533269			−0.266634	+	0.963798i	$0.585912\pi$
$48$	−94.0690			−1.95977
$49$	28.9082			0.589964
$50$		0			0
$51$		−	141.335i		−	2.77127i
$52$		−	58.7967i		−	1.13071i
$53$	−93.9329			−1.77232			−0.886159	−	0.463381i	$-0.846636\pi$
$53$	−93.9329			−1.77232			−0.886159	+	0.463381i	$0.846636\pi$
$54$		−	196.989i		−	3.64795i
$55$		0			0
$56$	3.19936			0.0571315
$57$			46.8414i			0.821778i
$58$	59.6960			1.02924
$59$	−27.3730			−0.463949			−0.231974	−	0.972722i	$-0.574519\pi$
$59$	−27.3730			−0.463949			−0.231974	+	0.972722i	$0.574519\pi$
$60$		0			0
$61$			81.1075i			1.32963i	0.747008	+	0.664815i	$0.231490\pi$
$61$			81.1075i			1.32963i	−0.747008	+	0.664815i	$0.768510\pi$
$62$		−	69.4507i		−	1.12017i
$63$			97.5509i			1.54843i
$64$	55.5457			0.867902
$65$		0			0
$66$	−165.464	−	38.0202i	−2.50703	−	0.576064i
$67$	−49.5118			−0.738982			−0.369491	−	0.929234i	$-0.620468\pi$
$67$	−49.5118			−0.738982			−0.369491	+	0.929234i	$0.620468\pi$
$68$			95.3920i			1.40282i
$69$	−110.302			−1.59858
$70$		0			0
$71$	44.0132			0.619904			0.309952	−	0.950752i	$-0.399687\pi$
$71$	44.0132			0.619904			0.309952	+	0.950752i	$0.399687\pi$
$72$		−	15.5338i		−	0.215747i
$73$		−	29.1783i		−	0.399703i	−0.979826	−	0.199851i	$-0.935954\pi$
$73$		−	29.1783i		−	0.399703i	0.979826	−	0.199851i	$-0.0640459\pi$
$74$			84.7779i			1.14565i
$75$		0			0
$76$		−	31.6149i		−	0.415986i
$77$	48.0540	+	11.0418i	0.624078	+	0.143400i
$78$	242.415			3.10788
$79$		−	51.3920i		−	0.650532i	−0.945623	−	0.325266i	$-0.894546\pi$
$79$		−	51.3920i		−	0.650532i	0.945623	−	0.325266i	$-0.105454\pi$
$80$		0			0
$81$	196.767			2.42922
$82$	−29.3792			−0.358283
$83$			47.2115i			0.568814i	0.958704	+	0.284407i	$0.0917967\pi$
$83$			47.2115i			0.568814i	−0.958704	+	0.284407i	$0.908203\pi$
$84$		−	93.0685i		−	1.10796i
$85$		0			0
$86$	190.248			2.21218
$87$			118.985i			1.36764i
$88$	−7.65199	−	1.75827i	−0.0869545	−	0.0199803i
$89$	147.455			1.65679			0.828397	−	0.560141i	$-0.189253\pi$
$89$	147.455			1.65679			0.828397	+	0.560141i	$0.189253\pi$
$90$		0			0
$91$	−70.4019			−0.773647
$92$	74.4468			0.809205
$93$	138.428			1.48847
$94$			69.7449i			0.741967i
$95$		0			0
$96$			245.932i			2.56179i
$97$	87.8176			0.905337			0.452668	−	0.891679i	$-0.350472\pi$
$97$	87.8176			0.905337			0.452668	+	0.891679i	$0.350472\pi$
$98$		−	80.4433i		−	0.820850i
$99$	53.6108	−	233.315i	0.541523	−	2.35671i
$100$		0			0
$101$			22.1571i			0.219377i	0.993966	+	0.109688i	$0.0349853\pi$
$101$			22.1571i			0.219377i	−0.993966	+	0.109688i	$0.965015\pi$
$102$	−393.295			−3.85583
$103$	64.5972			0.627158			0.313579	−	0.949562i	$-0.398472\pi$
$103$	64.5972			0.627158			0.313579	+	0.949562i	$0.398472\pi$
$104$	11.2106			0.107794
$105$		0			0
$106$			261.388i			2.46593i
$107$			39.4535i			0.368725i	0.982858	+	0.184362i	$0.0590220\pi$
$107$			39.4535i			0.368725i	−0.982858	+	0.184362i	$0.940978\pi$
$108$	−265.003			−2.45374
$109$			12.6081i			0.115671i	0.998326	+	0.0578355i	$0.0184199\pi$
$109$			12.6081i			0.115671i	−0.998326	+	0.0578355i	$0.981580\pi$
$110$		0			0
$111$	−168.978			−1.52232
$112$		−	76.0222i		−	0.678770i
$113$	−98.6045			−0.872606			−0.436303	−	0.899800i	$-0.643712\pi$
$113$	−98.6045			−0.872606			−0.436303	+	0.899800i	$0.643712\pi$
$114$	130.346			1.14339
$115$		0			0
$116$		−	80.3072i		−	0.692304i
$117$			341.820i			2.92154i
$118$			76.1712i			0.645519i
$119$	114.220			0.959834
$120$		0			0
$121$	−108.864	−	52.8178i	−0.899699	−	0.436511i
$122$	225.699			1.84999
$123$		−	58.5580i		−	0.476081i
$124$	−93.4299			−0.753467
$125$		0			0
$126$	271.456			2.15441
$127$		−	155.235i		−	1.22233i	−0.791505	−	0.611163i	$-0.790702\pi$
$127$		−	155.235i		−	1.22233i	0.791505	−	0.611163i	$-0.209298\pi$
$128$			22.7935i			0.178074i
$129$			379.198i			2.93952i
$130$		0			0
$131$		−	103.068i		−	0.786778i	−0.919372	−	0.393389i	$-0.871302\pi$
$131$		−	103.068i		−	0.786778i	0.919372	−	0.393389i	$-0.128698\pi$
$132$	−51.1474	+	222.594i	−0.387480	+	1.68632i
$133$	−37.8550			−0.284624
$134$			137.777i			1.02819i
$135$		0			0
$136$	−18.1881			−0.133736
$137$	46.4667			0.339173			0.169587	−	0.985515i	$-0.445757\pi$
$137$	46.4667			0.339173			0.169587	+	0.985515i	$0.445757\pi$
$138$			306.939i			2.22420i
$139$		−	113.716i		−	0.818102i	−0.912512	−	0.409051i	$-0.865860\pi$
$139$		−	113.716i		−	0.818102i	0.912512	−	0.409051i	$-0.134140\pi$
$140$		0			0
$141$	−139.014			−0.985917
$142$		−	122.476i		−	0.862508i
$143$	168.382	+	38.6906i	1.17750	+	0.270564i
$144$	−369.108			−2.56325
$145$		0			0
$146$	−81.1949			−0.556129
$147$	160.338			1.09074
$148$	114.049			0.770602
$149$		−	160.233i		−	1.07539i	−0.843139	−	0.537695i	$-0.819295\pi$
$149$		−	160.233i		−	1.07539i	0.843139	−	0.537695i	$-0.180705\pi$
$150$		0			0
$151$		−	166.134i		−	1.10023i	−0.835090	−	0.550113i	$-0.814585\pi$
$151$		−	166.134i		−	1.10023i	0.835090	−	0.550113i	$-0.185415\pi$
$152$	6.02793			0.0396575
$153$		−	554.569i		−	3.62463i
$154$	30.7262	−	133.721i	0.199521	−	0.868315i
$155$		0			0
$156$		−	326.113i		−	2.09047i
$157$	61.2202			0.389937			0.194969	−	0.980809i	$-0.437539\pi$
$157$	61.2202			0.389937			0.194969	+	0.980809i	$0.437539\pi$
$158$	−143.009			−0.905123
$159$	−520.994			−3.27669
$160$		0			0
$161$		−	89.1410i		−	0.553671i
$162$		−	547.545i		−	3.37991i
$163$	−134.800			−0.826995			−0.413498	−	0.910505i	$-0.635693\pi$
$163$	−134.800			−0.826995			−0.413498	+	0.910505i	$0.635693\pi$
$164$			39.5229i			0.240993i
$165$		0			0
$166$	131.376			0.791423
$167$		−	241.427i		−	1.44567i	−0.691021	−	0.722835i	$-0.742839\pi$
$167$		−	241.427i		−	1.44567i	0.691021	−	0.722835i	$-0.257161\pi$
$168$	17.7451			0.105626
$169$	−77.6893			−0.459700
$170$		0			0
$171$			183.796i			1.07483i
$172$		−	255.934i		−	1.48799i
$173$			181.146i			1.04708i	0.852000	+	0.523542i	$0.175390\pi$
$173$			181.146i			1.04708i	−0.852000	+	0.523542i	$0.824610\pi$
$174$	331.101			1.90288
$175$		0			0
$176$	−41.7793	+	181.824i	−0.237383	+	1.03309i
$177$	−151.823			−0.857757
$178$		−	410.324i		−	2.30519i
$179$	109.667			0.612664			0.306332	−	0.951925i	$-0.400898\pi$
$179$	109.667			0.612664			0.306332	+	0.951925i	$0.400898\pi$
$180$		0			0
$181$	−98.6522			−0.545040			−0.272520	−	0.962150i	$-0.587857\pi$
$181$	−98.6522			−0.545040			−0.272520	+	0.962150i	$0.587857\pi$
$182$			195.908i			1.07642i
$183$			449.859i			2.45825i
$184$			14.1946i			0.0771445i
$185$		0			0
$186$		−	385.205i		−	2.07099i
$187$	−273.183	−	62.7717i	−1.46087	−	0.335678i
$188$	93.8257			0.499073
$189$			317.309i			1.67889i
$190$		0			0
$191$	−72.5260			−0.379717			−0.189859	−	0.981811i	$-0.560803\pi$
$191$	−72.5260			−0.379717			−0.189859	+	0.981811i	$0.560803\pi$
$192$	308.082			1.60459
$193$		−	132.224i		−	0.685098i	−0.939500	−	0.342549i	$-0.888710\pi$
$193$		−	132.224i		−	0.685098i	0.939500	−	0.342549i	$-0.111290\pi$
$194$		−	244.371i		−	1.25965i
$195$		0			0
$196$	−108.218			−0.552132
$197$			295.931i			1.50219i	0.660194	+	0.751095i	$0.270474\pi$
$197$			295.931i			1.50219i	−0.660194	+	0.751095i	$0.729526\pi$
$198$	−649.248	−	149.184i	−3.27903	−	0.753452i
$199$	77.7266			0.390586			0.195293	−	0.980745i	$-0.437434\pi$
$199$	77.7266			0.390586			0.195293	+	0.980745i	$0.437434\pi$
$200$		0			0
$201$	−274.615			−1.36624
$202$	61.6568			0.305232
$203$	−96.1581			−0.473685
$204$			529.087i			2.59356i
$205$		0			0
$206$		−	179.756i		−	0.872600i
$207$	−432.803			−2.09084
$208$		−	266.383i		−	1.28069i
$209$	90.5387	+	20.8039i	0.433199	+	0.0995401i
$210$		0			0
$211$			162.936i			0.772209i	0.922455	+	0.386104i	$0.126180\pi$
$211$			162.936i			0.772209i	−0.922455	+	0.386104i	$0.873820\pi$
$212$	351.638			1.65867
$213$	244.117			1.14609
$214$	109.788			0.513028
$215$		0			0
$216$		−	50.5275i		−	0.233924i
$217$			111.871i			0.515534i
$218$	35.0848			0.160940
$219$		−	161.836i		−	0.738978i
$220$		0			0
$221$	400.229			1.81099
$222$			470.217i			2.11809i
$223$	−27.3536			−0.122662			−0.0613310	−	0.998117i	$-0.519535\pi$
$223$	−27.3536			−0.122662			−0.0613310	+	0.998117i	$0.519535\pi$
$224$	−198.751			−0.887279
$225$		0			0
$226$			274.388i			1.21411i
$227$			69.9378i			0.308096i	0.988063	+	0.154048i	$0.0492310\pi$
$227$			69.9378i			0.308096i	−0.988063	+	0.154048i	$0.950769\pi$
$228$		−	175.351i		−	0.769082i
$229$	−126.890			−0.554103			−0.277052	−	0.960855i	$-0.589357\pi$
$229$	−126.890			−0.554103			−0.277052	+	0.960855i	$0.589357\pi$
$230$		0			0
$231$	266.529	+	61.2428i	1.15381	+	0.265120i
$232$	15.3120			0.0659999
$233$		−	127.078i		−	0.545398i	−0.962099	−	0.272699i	$-0.912084\pi$
$233$		−	127.078i		−	0.545398i	0.962099	−	0.272699i	$-0.0879164\pi$
$234$	951.187			4.06490
$235$		0			0
$236$	102.471			0.434198
$237$		−	285.044i		−	1.20272i
$238$		−	317.842i		−	1.33547i
$239$			242.100i			1.01297i	0.862249	+	0.506485i	$0.169055\pi$
$239$			242.100i			1.01297i	−0.862249	+	0.506485i	$0.830945\pi$
$240$		0			0
$241$			118.029i			0.489748i	0.969555	+	0.244874i	$0.0787466\pi$
$241$			118.029i			0.489748i	−0.969555	+	0.244874i	$0.921253\pi$
$242$	−146.977	+	302.936i	−0.607343	+	1.25180i
$243$	454.245			1.86932
$244$		−	303.626i		−	1.24437i
$245$		0			0
$246$	−162.950			−0.662399
$247$	−132.644			−0.537022
$248$		−	17.8140i		−	0.0718308i
$249$			261.857i			1.05163i
$250$		0			0
$251$	−122.747			−0.489033			−0.244516	−	0.969645i	$-0.578629\pi$
$251$	−122.747			−0.489033			−0.244516	+	0.969645i	$0.578629\pi$
$252$		−	365.182i		−	1.44913i
$253$	−48.9890	+	213.201i	−0.193632	+	0.842690i
$254$	−431.976			−1.70069
$255$		0			0
$256$	285.611			1.11567
$257$	−440.444			−1.71379			−0.856895	−	0.515491i	$-0.827609\pi$
$257$	−440.444			−1.71379			−0.856895	+	0.515491i	$0.827609\pi$
$258$	1055.20			4.08992
$259$		−	136.560i		−	0.527258i
$260$		0			0
$261$			466.873i			1.78878i
$262$	−286.809			−1.09469
$263$			196.653i			0.747729i	0.927483	+	0.373865i	$0.121968\pi$
$263$			196.653i			0.747729i	−0.927483	+	0.373865i	$0.878032\pi$
$264$	−42.4414	−	9.75215i	−0.160763	−	0.0369399i
$265$		0			0
$266$			105.340i			0.396014i
$267$	817.851			3.06311
$268$	185.347			0.691595
$269$	140.084			0.520759			0.260379	−	0.965506i	$-0.416152\pi$
$269$	140.084			0.520759			0.260379	+	0.965506i	$0.416152\pi$
$270$		0			0
$271$		−	122.461i		−	0.451886i	−0.974141	−	0.225943i	$-0.927454\pi$
$271$		−	122.461i		−	0.451886i	0.974141	−	0.225943i	$-0.0725463\pi$
$272$			432.180i			1.58890i
$273$	−390.481			−1.43033
$274$		−	129.304i		−	0.471911i
$275$		0			0
$276$	412.916			1.49607
$277$		−	431.002i		−	1.55596i	−0.628287	−	0.777981i	$-0.716244\pi$
$277$		−	431.002i		−	1.55596i	0.628287	−	0.777981i	$-0.283756\pi$
$278$	−316.440			−1.13827
$279$	543.162			1.94682
$280$		0			0
$281$		−	401.798i		−	1.42989i	−0.699182	−	0.714943i	$-0.746452\pi$
$281$		−	401.798i		−	1.42989i	0.699182	−	0.714943i	$-0.253548\pi$
$282$			386.837i			1.37176i
$283$		−	22.4597i		−	0.0793628i	−0.999212	−	0.0396814i	$-0.987366\pi$
$283$		−	22.4597i		−	0.0793628i	0.999212	−	0.0396814i	$-0.0126343\pi$
$284$	−164.763			−0.580153
$285$		0			0
$286$	107.665	−	468.559i	0.376451	−	1.63832i
$287$	47.3239			0.164892
$288$			964.986i			3.35065i
$289$	−360.333			−1.24683
$290$		0			0
$291$	487.077			1.67380
$292$			109.229i			0.374072i
$293$		−	455.602i		−	1.55496i	−0.628911	−	0.777478i	$-0.716499\pi$
$293$		−	455.602i		−	1.55496i	0.628911	−	0.777478i	$-0.283501\pi$
$294$		−	446.175i		−	1.51760i
$295$		0			0
$296$			21.7454i			0.0734643i
$297$	174.383	−	758.916i	0.587148	−	2.55527i
$298$	−445.883			−1.49625
$299$		−	312.351i		−	1.04465i
$300$		0			0
$301$	−306.450			−1.01811
$302$	−462.304			−1.53081
$303$			122.893i			0.405588i
$304$		−	143.234i		−	0.471163i
$305$		0			0
$306$	−1543.21			−5.04316
$307$			312.438i			1.01771i	0.860851	+	0.508857i	$0.169932\pi$
$307$			312.438i			1.01771i	−0.860851	+	0.508857i	$0.830068\pi$
$308$	−179.890	−	41.3350i	−0.584059	−	0.134204i
$309$	358.286			1.15950
$310$		0			0
$311$	−256.878			−0.825975			−0.412987	−	0.910737i	$-0.635515\pi$
$311$	−256.878			−0.825975			−0.412987	+	0.910737i	$0.635515\pi$
$312$	62.1792			0.199292
$313$	−29.6563			−0.0947485			−0.0473742	−	0.998877i	$-0.515085\pi$
$313$	−29.6563			−0.0947485			−0.0473742	+	0.998877i	$0.515085\pi$
$314$		−	170.358i		−	0.542542i
$315$		0			0
$316$			192.386i			0.608817i
$317$	−99.6748			−0.314431			−0.157216	−	0.987564i	$-0.550252\pi$
$317$	−99.6748			−0.314431			−0.157216	+	0.987564i	$0.550252\pi$
$318$			1449.78i			4.55905i
$319$	229.984	+	52.8454i	0.720952	+	0.165659i
$320$		0			0
$321$			218.827i			0.681705i
$322$	−248.054			−0.770354
$323$	215.203			0.666262
$324$	−736.596			−2.27344
$325$		0			0
$326$			375.111i			1.15065i
$327$			69.9305i			0.213855i
$328$	−7.53573			−0.0229748
$329$		−	112.345i		−	0.341474i
$330$		0			0
$331$	138.630			0.418820			0.209410	−	0.977828i	$-0.432846\pi$
$331$	138.630			0.418820			0.209410	+	0.977828i	$0.432846\pi$
$332$		−	176.736i		−	0.532339i
$333$	−663.034			−1.99109
$334$	−671.822			−2.01144
$335$		0			0
$336$		−	421.654i		−	1.25492i
$337$		−	504.040i		−	1.49567i	−0.663886	−	0.747834i	$-0.731094\pi$
$337$		−	504.040i		−	1.49567i	0.663886	−	0.747834i	$-0.268906\pi$
$338$			216.187i			0.639607i
$339$	−546.905			−1.61329
$340$		0			0
$341$	61.4806	−	267.564i	0.180295	−	0.784646i
$342$	511.452			1.49547
$343$			349.215i			1.01812i
$344$	48.7983			0.141856
$345$		0			0
$346$	504.076			1.45687
$347$		−	305.042i		−	0.879083i	−0.898222	−	0.439542i	$-0.855141\pi$
$347$		−	305.042i		−	0.879083i	0.898222	−	0.439542i	$-0.144859\pi$
$348$		−	445.420i		−	1.27994i
$349$		−	383.638i		−	1.09925i	−0.835412	−	0.549625i	$-0.814771\pi$
$349$		−	383.638i		−	1.09925i	0.835412	−	0.549625i	$-0.185229\pi$
$350$		0			0
$351$			1111.86i			3.16768i
$352$	475.356	+	109.227i	1.35044	+	0.310304i
$353$	571.115			1.61789			0.808945	−	0.587884i	$-0.200039\pi$
$353$	571.115			1.61789			0.808945	+	0.587884i	$0.200039\pi$
$354$			422.480i			1.19345i
$355$		0			0
$356$	−551.997			−1.55055
$357$	633.517			1.77456
$358$		−	305.172i		−	0.852434i
$359$			105.966i			0.295169i	0.989049	+	0.147585i	$0.0471499\pi$
$359$			105.966i			0.295169i	−0.989049	+	0.147585i	$0.952850\pi$
$360$		0			0
$361$	289.677			0.802430
$362$			274.521i			0.758345i
$363$	−603.807	−	292.952i	−1.66338	−	0.807029i
$364$	263.550			0.724037
$365$		0			0
$366$	1251.83			3.42030
$367$	409.176			1.11492			0.557461	−	0.830203i	$-0.311776\pi$
$367$	409.176			1.11492			0.557461	+	0.830203i	$0.311776\pi$
$368$	337.287			0.916540
$369$		−	229.770i		−	0.622682i
$370$		0			0
$371$		−	421.043i		−	1.13489i
$372$	−518.205			−1.39302
$373$			286.691i			0.768608i	0.923207	+	0.384304i	$0.125559\pi$
$373$			286.691i			0.768608i	−0.923207	+	0.384304i	$0.874441\pi$
$374$	−174.676	+	760.191i	−0.467048	+	2.03260i
$375$		0			0
$376$			17.8895i			0.0475785i
$377$	−336.939			−0.893738
$378$	882.981			2.33593
$379$	−396.663			−1.04660			−0.523302	−	0.852147i	$-0.675300\pi$
$379$	−396.663			−1.04660			−0.523302	+	0.852147i	$0.675300\pi$
$380$		0			0
$381$		−	861.006i		−	2.25986i
$382$			201.819i			0.528322i
$383$	423.356			1.10537			0.552684	−	0.833391i	$-0.313604\pi$
$383$	423.356			1.10537			0.552684	+	0.833391i	$0.313604\pi$
$384$			126.423i			0.329227i
$385$		0			0
$386$	−367.941			−0.953216
$387$			1487.90i			3.84469i
$388$	−328.745			−0.847282
$389$	−453.620			−1.16612			−0.583059	−	0.812430i	$-0.698145\pi$
$389$	−453.620			−1.16612			−0.583059	+	0.812430i	$0.698145\pi$
$390$		0			0
$391$			506.760i			1.29606i
$392$		−	20.6336i		−	0.0526368i
$393$		−	571.662i		−	1.45461i
$394$	823.493			2.09008
$395$		0			0
$396$	−200.692	+	873.414i	−0.506798	+	2.20559i
$397$	535.740			1.34947			0.674735	−	0.738060i	$-0.264258\pi$
$397$	535.740			1.34947			0.674735	+	0.738060i	$0.264258\pi$
$398$		−	216.291i		−	0.543445i
$399$	−209.961			−0.526218
$400$		0			0
$401$	−611.297			−1.52443			−0.762216	−	0.647323i	$-0.775889\pi$
$401$	−611.297			−1.52443			−0.762216	+	0.647323i	$0.775889\pi$
$402$			764.175i			1.90093i
$403$			391.997i			0.972698i
$404$		−	82.9450i		−	0.205309i
$405$		0			0
$406$			267.581i			0.659066i
$407$	−75.0489	+	326.613i	−0.184395	+	0.802490i
$408$	−100.880			−0.247254
$409$		−	748.695i		−	1.83055i	−0.402831	−	0.915275i	$-0.631974\pi$
$409$		−	748.695i		−	1.83055i	0.402831	−	0.915275i	$-0.368026\pi$
$410$		0			0
$411$	257.725			0.627069
$412$	−241.820			−0.586941
$413$		−	122.696i		−	0.297085i
$414$			1204.37i			2.90910i
$415$		0			0
$416$	−696.425			−1.67410
$417$		−	630.721i		−	1.51252i
$418$	57.8913	−	251.943i	0.138496	−	0.602735i
$419$	1.63966			0.00391327			0.00195663	−	0.999998i	$-0.499377\pi$
$419$	1.63966			0.00391327			0.00195663	+	0.999998i	$0.499377\pi$
$420$		0			0
$421$	587.016			1.39434			0.697169	−	0.716907i	$-0.254443\pi$
$421$	587.016			1.39434			0.697169	+	0.716907i	$0.254443\pi$
$422$	453.404			1.07442
$423$	−545.464			−1.28951
$424$			67.0459i			0.158127i
$425$		0			0
$426$		−	679.308i		−	1.59462i
$427$	−363.555			−0.851417
$428$		−	147.694i		−	0.345080i
$429$	933.922	+	214.596i	2.17697	+	0.500223i
$430$		0			0
$431$			709.692i			1.64662i	0.567595	+	0.823308i	$0.307874\pi$
$431$			709.692i			1.64662i	−0.567595	+	0.823308i	$0.692126\pi$
$432$	−1200.62			−2.77921
$433$	−821.863			−1.89807			−0.949034	−	0.315175i	$-0.897937\pi$
$433$	−821.863			−1.89807			−0.949034	+	0.315175i	$0.897937\pi$
$434$	311.305			0.717292
$435$		0			0
$436$		−	47.1986i		−	0.108254i
$437$		−	167.951i		−	0.384327i
$438$	−450.344			−1.02818
$439$			522.233i			1.18960i	0.803875	+	0.594798i	$0.202768\pi$
$439$			522.233i			1.18960i	−0.803875	+	0.594798i	$0.797232\pi$
$440$		0			0
$441$	629.134			1.42661
$442$		−	1113.72i		−	2.51974i
$443$	−377.862			−0.852963			−0.426481	−	0.904496i	$-0.640247\pi$
$443$	−377.862			−0.852963			−0.426481	+	0.904496i	$0.640247\pi$
$444$	632.568			1.42470
$445$		0			0
$446$			76.1173i			0.170667i
$447$		−	888.726i		−	1.98820i
$448$			248.977i			0.555753i
$449$	565.531			1.25953			0.629767	−	0.776784i	$-0.283150\pi$
$449$	565.531			1.25953			0.629767	+	0.776784i	$0.283150\pi$
$450$		0			0
$451$	−113.186	−	26.0077i	−0.250966	−	0.0576667i
$452$	369.126			0.816650
$453$		−	921.455i		−	2.03412i
$454$	194.617			0.428672
$455$		0			0
$456$	33.4337			0.0733194
$457$			311.699i			0.682054i	0.940054	+	0.341027i	$0.110775\pi$
$457$			311.699i			0.682054i	−0.940054	+	0.341027i	$0.889225\pi$
$458$			353.098i			0.770955i
$459$		−	1803.88i		−	3.93002i
$460$		0			0
$461$		−	125.484i		−	0.272200i	−0.990695	−	0.136100i	$-0.956543\pi$
$461$		−	125.484i		−	0.272200i	0.990695	−	0.136100i	$-0.0434569\pi$
$462$	170.421	−	741.675i	0.368877	−	1.60536i
$463$	478.622			1.03374			0.516871	−	0.856063i	$-0.327097\pi$
$463$	478.622			1.03374			0.516871	+	0.856063i	$0.327097\pi$
$464$		−	363.838i		−	0.784133i
$465$		0			0
$466$	−353.621			−0.758844
$467$	−422.419			−0.904538			−0.452269	−	0.891882i	$-0.649385\pi$
$467$	−422.419			−0.904538			−0.452269	+	0.891882i	$0.649385\pi$
$468$		−	1279.60i		−	2.73419i
$469$		−	221.931i		−	0.473200i
$470$		0			0
$471$	339.555			0.720923
$472$			19.5378i			0.0413937i
$473$	732.944	+	168.415i	1.54956	+	0.356057i
$474$	−793.195			−1.67341
$475$		0			0
$476$	−427.584			−0.898285
$477$	−2044.28			−4.28569
$478$	673.695			1.40940
$479$			158.064i			0.329987i	0.986295	+	0.164993i	$0.0527603\pi$
$479$			158.064i			0.329987i	−0.986295	+	0.164993i	$0.947240\pi$
$480$		0			0
$481$		−	478.508i		−	0.994819i
$482$	328.442			0.681414
$483$		−	494.417i		−	1.02364i
$484$	407.531	+	197.724i	0.842006	+	0.408520i
$485$		0			0
$486$		−	1264.03i		−	2.60089i
$487$	840.800			1.72649			0.863245	−	0.504786i	$-0.168429\pi$
$487$	840.800			1.72649			0.863245	+	0.504786i	$0.168429\pi$
$488$	57.8916			0.118630
$489$	−747.663			−1.52896
$490$		0			0
$491$			327.239i			0.666476i	0.942843	+	0.333238i	$0.108141\pi$
$491$			327.239i			0.666476i	−0.942843	+	0.333238i	$0.891859\pi$
$492$			219.212i			0.445553i
$493$	546.651			1.10883
$494$			369.112i			0.747190i
$495$		0			0
$496$	−423.291			−0.853409
$497$			197.284i			0.396950i
$498$	728.673			1.46320
$499$	551.123			1.10445			0.552227	−	0.833693i	$-0.313778\pi$
$499$	551.123			1.10445			0.552227	+	0.833693i	$0.313778\pi$
$500$		0			0
$501$		−	1339.06i		−	2.67278i
$502$			341.571i			0.680420i
$503$		−	399.050i		−	0.793340i	−0.917961	−	0.396670i	$-0.870166\pi$
$503$		−	399.050i		−	0.793340i	0.917961	−	0.396670i	$-0.129834\pi$
$504$	69.6283			0.138151
$505$		0			0
$506$	593.276	+	136.322i	1.17248	+	0.269412i
$507$	−430.900			−0.849901
$508$			581.124i			1.14394i
$509$	−18.2410			−0.0358370			−0.0179185	−	0.999839i	$-0.505704\pi$
$509$	−18.2410			−0.0358370			−0.0179185	+	0.999839i	$0.505704\pi$
$510$		0			0
$511$	130.788			0.255946
$512$		−	703.599i		−	1.37422i
$513$			597.844i			1.16539i
$514$			1225.63i			2.38449i
$515$		0			0
$516$		−	1419.53i		−	2.75102i
$517$	−61.7411	+	268.698i	−0.119422	+	0.519725i
$518$	−380.007			−0.733605
$519$			1004.72i			1.93587i
$520$		0			0
$521$	673.198			1.29213			0.646064	−	0.763284i	$-0.276414\pi$
$521$	673.198			1.29213			0.646064	+	0.763284i	$0.276414\pi$
$522$	1299.17			2.48884
$523$			102.262i			0.195529i	0.995210	+	0.0977645i	$0.0311692\pi$
$523$			102.262i			0.195529i	−0.995210	+	0.0977645i	$0.968831\pi$
$524$			385.835i			0.736326i
$525$		0			0
$526$	547.229			1.04036
$527$		−	635.977i		−	1.20679i
$528$	−231.727	+	1008.48i	−0.438877	+	1.91000i
$529$	−133.509			−0.252380
$530$		0			0
$531$	−595.723			−1.12189
$532$	141.710			0.266373
$533$	165.824			0.311114
$534$		−	2275.84i		−	4.26188i
$535$		0			0
$536$			35.3397i			0.0659323i
$537$	608.262			1.13270
$538$		−	389.814i		−	0.724561i
$539$	71.2117	−	309.914i	0.132118	−	0.574980i
$540$		0			0
$541$		−	822.873i		−	1.52102i	−0.649324	−	0.760512i	$-0.724948\pi$
$541$		−	822.873i		−	1.52102i	0.649324	−	0.760512i	$-0.275052\pi$
$542$	−340.774			−0.628735
$543$	−547.170			−1.00768
$544$	1129.88			2.07699
$545$		0			0
$546$			1086.60i			1.99010i
$547$			641.446i			1.17266i	0.810071	+	0.586331i	$0.199428\pi$
$547$			641.446i			1.17266i	−0.810071	+	0.586331i	$0.800572\pi$
$548$	−173.948			−0.317424
$549$			1765.15i			3.21522i
$550$		0			0
$551$	−181.172			−0.328805
$552$			78.7296i			0.142626i
$553$	230.359			0.416562
$554$	−1199.35			−2.16490
$555$		0			0
$556$			425.696i			0.765641i
$557$		−	523.719i		−	0.940250i	−0.882600	−	0.470125i	$-0.844209\pi$
$557$		−	523.719i		−	0.940250i	0.882600	−	0.470125i	$-0.155791\pi$
$558$		−	1511.47i		−	2.70872i
$559$	−1073.81			−1.92094
$560$		0			0
$561$	−1515.20	−	348.161i	−2.70089	−	0.620607i
$562$	−1118.09			−1.98948
$563$		−	1008.31i		−	1.79095i	−0.445111	−	0.895475i	$-0.646836\pi$
$563$		−	1008.31i		−	1.79095i	0.445111	−	0.895475i	$-0.353164\pi$
$564$	520.400			0.922695
$565$		0			0
$566$	−62.4988			−0.110422
$567$			881.984i			1.55553i
$568$		−	31.4150i		−	0.0553081i
$569$			369.577i			0.649521i	0.945796	+	0.324760i	$0.105284\pi$
$569$			369.577i			0.649521i	−0.945796	+	0.324760i	$0.894716\pi$
$570$		0			0
$571$			456.385i			0.799273i	0.916674	+	0.399636i	$0.130864\pi$
$571$			456.385i			0.799273i	−0.916674	+	0.399636i	$0.869136\pi$
$572$	−630.338	−	144.838i	−1.10199	−	0.253214i
$573$	−402.262			−0.702028
$574$		−	131.689i		−	0.229423i
$575$		0			0
$576$	1208.85			2.09870
$577$	886.043			1.53560			0.767802	−	0.640687i	$-0.221351\pi$
$577$	886.043			1.53560			0.767802	+	0.640687i	$0.221351\pi$
$578$			1002.70i			1.73478i
$579$		−	733.373i		−	1.26662i
$580$		0			0
$581$	−211.620			−0.364235
$582$		−	1355.40i		−	2.32886i
$583$	−231.392	+	1007.02i	−0.396898	+	1.72731i
$584$	−20.8264			−0.0356617
$585$		0			0
$586$	−1267.81			−2.16350
$587$	497.919			0.848243			0.424121	−	0.905605i	$-0.360583\pi$
$587$	497.919			0.848243			0.424121	+	0.905605i	$0.360583\pi$
$588$	−600.226			−1.02079
$589$			210.776i			0.357855i
$590$		0			0
$591$			1641.37i			2.77728i
$592$	516.708			0.872817
$593$			60.1067i			0.101360i	0.998715	+	0.0506802i	$0.0161389\pi$
$593$			60.1067i			0.101360i	−0.998715	+	0.0506802i	$0.983861\pi$
$594$	−2111.85	−	485.258i	−3.55530	−	0.816933i
$595$		0			0
$596$			599.833i			1.00643i
$597$	431.107			0.722122
$598$	−869.185			−1.45349
$599$	935.800			1.56227			0.781135	−	0.624362i	$-0.214641\pi$
$599$	935.800			1.56227			0.781135	+	0.624362i	$0.214641\pi$
$600$		0			0
$601$			925.265i			1.53954i	0.638320	+	0.769771i	$0.279630\pi$
$601$			925.265i			1.53954i	−0.638320	+	0.769771i	$0.720370\pi$
$602$			852.763i			1.41655i
$603$	−1077.53			−1.78695
$604$			621.923i			1.02967i
$605$		0			0
$606$	341.976			0.564318
$607$		−	790.264i		−	1.30192i	−0.759113	−	0.650959i	$-0.774367\pi$
$607$		−	790.264i		−	1.30192i	0.759113	−	0.650959i	$-0.225633\pi$
$608$	−374.467			−0.615899
$609$	−533.337			−0.875758
$610$		0			0
$611$		−	393.658i		−	0.644285i
$612$			2076.03i			3.39221i
$613$		−	390.665i		−	0.637300i	−0.947872	−	0.318650i	$-0.896770\pi$
$613$		−	390.665i		−	0.637300i	0.947872	−	0.318650i	$-0.103230\pi$
$614$	869.427			1.41600
$615$		0			0
$616$	7.88123	−	34.2992i	0.0127942	−	0.0556805i
$617$	−283.723			−0.459843			−0.229922	−	0.973209i	$-0.573847\pi$
$617$	−283.723			−0.459843			−0.229922	+	0.973209i	$0.573847\pi$
$618$		−	997.007i		−	1.61328i
$619$	−774.717			−1.25156			−0.625781	−	0.779999i	$-0.715220\pi$
$619$	−774.717			−1.25156			−0.625781	+	0.779999i	$0.715220\pi$
$620$		0			0
$621$	−1407.80			−2.26699
$622$			714.818i			1.14923i
$623$			660.949i			1.06091i
$624$		−	1477.48i		−	2.36776i
$625$		0			0
$626$			82.5250i			0.131829i
$627$	502.169	+	115.388i	0.800907	+	0.184032i
$628$	−229.178			−0.364933
$629$			776.332i			1.23423i
$630$		0			0
$631$	392.301			0.621712			0.310856	−	0.950457i	$-0.399384\pi$
$631$	392.301			0.621712			0.310856	+	0.950457i	$0.399384\pi$
$632$	−36.6818			−0.0580408
$633$			903.717i			1.42767i
$634$			277.366i			0.437487i
$635$		0			0
$636$	1950.34			3.06658
$637$			454.042i			0.712782i
$638$	147.054	−	639.979i	0.230492	−	1.00310i
$639$	957.865			1.49901
$640$		0			0
$641$	−685.356			−1.06920			−0.534599	−	0.845106i	$-0.679537\pi$
$641$	−685.356			−1.06920			−0.534599	+	0.845106i	$0.679537\pi$
$642$	608.934			0.948495
$643$	747.072			1.16185			0.580927	−	0.813956i	$-0.302690\pi$
$643$	747.072			1.16185			0.580927	+	0.813956i	$0.302690\pi$
$644$			333.699i			0.518167i
$645$		0			0
$646$		−	598.848i		−	0.927009i
$647$	−190.791			−0.294885			−0.147443	−	0.989071i	$-0.547104\pi$
$647$	−190.791			−0.294885			−0.147443	+	0.989071i	$0.547104\pi$
$648$		−	140.445i		−	0.216736i
$649$	−67.4299	+	293.456i	−0.103898	+	0.452166i
$650$		0			0
$651$			620.487i			0.953129i
$652$	504.625			0.773964
$653$	142.136			0.217666			0.108833	−	0.994060i	$-0.465289\pi$
$653$	142.136			0.217666			0.108833	+	0.994060i	$0.465289\pi$
$654$	194.596			0.297548
$655$		0			0
$656$			179.061i			0.272959i
$657$		−	635.012i		−	0.966533i
$658$	−312.624			−0.475112
$659$			528.247i			0.801589i	0.916168	+	0.400794i	$0.131266\pi$
$659$			528.247i			0.801589i	−0.916168	+	0.400794i	$0.868734\pi$
$660$		0			0
$661$	2.43838			0.00368892			0.00184446	−	0.999998i	$-0.499413\pi$
$661$	2.43838			0.00368892			0.00184446	+	0.999998i	$0.499413\pi$
$662$		−	385.766i		−	0.582729i
$663$	2219.85			3.34820
$664$	33.6979			0.0507498
$665$		0			0
$666$			1845.03i			2.77032i
$667$		−	426.624i		−	0.639616i
$668$			903.781i			1.35297i
$669$	−151.716			−0.226780
$670$		0			0
$671$	869.523	+	199.798i	1.29586	+	0.297762i
$672$	−1102.36			−1.64042
$673$			684.594i			1.01723i	0.860995	+	0.508614i	$0.169842\pi$
$673$			684.594i			1.01723i	−0.860995	+	0.508614i	$0.830158\pi$
$674$	−1402.60			−2.08101
$675$		0			0
$676$	290.830			0.430222
$677$			326.416i			0.482151i	0.970506	+	0.241076i	$0.0775002\pi$
$677$			326.416i			0.482151i	−0.970506	+	0.241076i	$0.922500\pi$
$678$			1521.88i			2.24466i
$679$			393.633i			0.579724i
$680$		0			0
$681$			387.907i			0.569614i
$682$	−744.555	−	171.083i	−1.09172	−	0.250855i
$683$	1162.56			1.70213			0.851067	−	0.525058i	$-0.175956\pi$
$683$	1162.56			1.70213			0.851067	+	0.525058i	$0.175956\pi$
$684$		−	688.040i		−	1.00591i
$685$		0			0
$686$	971.765			1.41657
$687$	−703.787			−1.02444
$688$		−	1159.53i		−	1.68536i
$689$		−	1475.34i		−	2.14128i
$690$		0			0
$691$	−400.519			−0.579623			−0.289811	−	0.957084i	$-0.593593\pi$
$691$	−400.519			−0.579623			−0.289811	+	0.957084i	$0.593593\pi$
$692$		−	678.118i		−	0.979940i
$693$	1045.81	+	240.304i	1.50910	+	0.346759i
$694$	−848.845			−1.22312
$695$		0			0
$696$	84.9271			0.122022
$697$	−269.032			−0.385986
$698$	−1067.55			−1.52945
$699$		−	704.831i		−	1.00834i
$700$		0			0
$701$		−	819.099i		−	1.16847i	−0.811584	−	0.584236i	$-0.801394\pi$
$701$		−	819.099i		−	1.16847i	0.811584	−	0.584236i	$-0.198606\pi$
$702$	3093.98			4.40738
$703$		−	257.293i		−	0.365993i
$704$	136.830	−	595.485i	0.194361	−	0.845859i
$705$		0			0
$706$		−	1589.25i		−	2.25106i
$707$	−99.3165			−0.140476
$708$	568.350			0.802754
$709$	516.432			0.728395			0.364198	−	0.931322i	$-0.381343\pi$
$709$	516.432			0.728395			0.364198	+	0.931322i	$0.381343\pi$
$710$		0			0
$711$		−	1118.45i		−	1.57307i
$712$		−	105.248i		−	0.147820i
$713$	−496.336			−0.696124
$714$		−	1762.90i		−	2.46904i
$715$		0			0
$716$	−410.538			−0.573377
$717$			1342.80i			1.87280i
$718$	294.873			0.410686
$719$	382.550			0.532058			0.266029	−	0.963965i	$-0.414288\pi$
$719$	382.550			0.532058			0.266029	+	0.963965i	$0.414288\pi$
$720$		0			0
$721$			289.550i			0.401595i
$722$		−	806.089i		−	1.11647i
$723$			654.644i			0.905455i
$724$	369.305			0.510089
$725$		0			0
$726$	−815.201	+	1680.22i	−1.12287	+	2.31436i
$727$	−890.685			−1.22515			−0.612575	−	0.790412i	$-0.709866\pi$
$727$	−890.685			−1.22515			−0.612575	+	0.790412i	$0.709866\pi$
$728$			50.2503i			0.0690252i
$729$	748.548			1.02681
$730$		0			0
$731$	1742.15			2.38324
$732$		−	1684.05i		−	2.30061i
$733$			17.9184i			0.0244454i	0.999925	+	0.0122227i	$0.00389070\pi$
$733$			17.9184i			0.0244454i	−0.999925	+	0.0122227i	$0.996109\pi$
$734$		−	1138.62i		−	1.55126i
$735$		0			0
$736$		−	881.795i		−	1.19809i
$737$	−121.966	+	530.797i	−0.165490	+	0.720214i
$738$	−639.384			−0.866374
$739$			765.890i			1.03639i	0.855263	+	0.518194i	$0.173395\pi$
$739$			765.890i			1.03639i	−0.855263	+	0.518194i	$0.826605\pi$
$740$		0			0
$741$	−735.706			−0.992856
$742$	−1171.64			−1.57903
$743$			402.876i			0.542229i	0.962547	+	0.271114i	$0.0873922\pi$
$743$			402.876i			0.542229i	−0.962547	+	0.271114i	$0.912608\pi$
$744$		−	98.8047i		−	0.132802i
$745$		0			0
$746$	797.779			1.06941
$747$			1027.47i			1.37547i
$748$	1022.66	+	234.986i	1.36719	+	0.314152i
$749$	−176.846			−0.236109
$750$		0			0
$751$	−884.758			−1.17811			−0.589053	−	0.808094i	$-0.700499\pi$
$751$	−884.758			−1.17811			−0.589053	+	0.808094i	$0.700499\pi$
$752$	425.084			0.565272
$753$	−680.812			−0.904133
$754$			937.606i			1.24351i
$755$		0			0
$756$		−	1187.85i		−	1.57123i
$757$	−752.068			−0.993485			−0.496742	−	0.867898i	$-0.665471\pi$
$757$	−752.068			−0.993485			−0.496742	+	0.867898i	$0.665471\pi$
$758$			1103.80i			1.45620i
$759$	−271.715	+	1182.51i	−0.357991	+	1.55798i
$760$		0			0
$761$			876.298i			1.15151i	0.817623	+	0.575754i	$0.195292\pi$
$761$			876.298i			1.15151i	−0.817623	+	0.575754i	$0.804708\pi$
$762$	−2395.93			−3.14427
$763$	−56.5145			−0.0740689
$764$	271.501			0.355368
$765$		0			0
$766$		−	1178.08i		−	1.53796i
$767$		−	429.930i		−	0.560534i
$768$	1584.13			2.06267
$769$		−	794.557i		−	1.03323i	−0.856217	−	0.516617i	$-0.827191\pi$
$769$		−	794.557i		−	1.03323i	0.856217	−	0.516617i	$-0.172809\pi$
$770$		0			0
$771$	−2442.90			−3.16849
$772$			494.980i			0.641166i
$773$	−911.736			−1.17948			−0.589738	−	0.807594i	$-0.700769\pi$
$773$	−911.736			−1.17948			−0.589738	+	0.807594i	$0.700769\pi$
$774$	4140.39			5.34934
$775$		0			0
$776$		−	62.6810i		−	0.0807745i
$777$		−	757.423i		−	0.974805i
$778$			1262.30i			1.62249i
$779$	89.1631			0.114458
$780$		0			0
$781$	108.421	−	471.849i	0.138823	−	0.604160i
$782$	1410.17			1.80328
$783$			1518.62i			1.93949i
$784$	−490.289			−0.625369
$785$		0			0
$786$	−1590.77			−2.02388
$787$			1566.53i			1.99050i	0.0973313	+	0.995252i	$0.468969\pi$
$787$			1566.53i			1.99050i	−0.0973313	+	0.995252i	$0.531031\pi$
$788$		−	1107.82i		−	1.40586i
$789$			1090.73i			1.38242i
$790$		0			0
$791$		−	441.983i		−	0.558765i
$792$	−166.532	−	38.2654i	−0.210267	−	0.0483149i
$793$	−1273.90			−1.60643
$794$		−	1490.81i		−	1.87760i
$795$		0			0
$796$	−290.970			−0.365540
$797$	−488.561			−0.613001			−0.306500	−	0.951871i	$-0.599158\pi$
$797$	−488.561			−0.613001			−0.306500	+	0.951871i	$0.599158\pi$
$798$			584.262i			0.732158i
$799$			638.672i			0.799339i
$800$		0			0
$801$	3209.08			4.00634
$802$			1701.07i			2.12103i
$803$	−312.810	−	71.8771i	−0.389551	−	0.0895107i
$804$	1028.02			1.27863
$805$		0			0
$806$	1090.82			1.35337
$807$	776.970			0.962788
$808$	15.8149			0.0195729
$809$			177.955i			0.219969i	0.993933	+	0.109984i	$0.0350801\pi$
$809$			177.955i			0.219969i	−0.993933	+	0.109984i	$0.964920\pi$
$810$		0			0
$811$		−	148.090i		−	0.182602i	−0.995823	−	0.0913009i	$-0.970897\pi$
$811$		−	148.090i		−	0.182602i	0.995823	−	0.0913009i	$-0.0291025\pi$
$812$	359.968			0.443310
$813$		−	679.225i		−	0.835455i
$814$	908.872	+	208.840i	1.11655	+	0.256560i
$815$		0			0
$816$			2397.07i			2.93758i
$817$	−577.384			−0.706712
$818$	−2083.40			−2.54695
$819$	−1532.17			−1.87078
$820$		0			0
$821$		−	95.9583i		−	0.116880i	−0.998291	−	0.0584399i	$-0.981387\pi$
$821$		−	95.9583i		−	0.116880i	0.998291	−	0.0584399i	$-0.0186126\pi$
$822$		−	717.177i		−	0.872478i
$823$	780.102			0.947876			0.473938	−	0.880558i	$-0.342832\pi$
$823$	780.102			0.947876			0.473938	+	0.880558i	$0.342832\pi$
$824$		−	46.1072i		−	0.0559553i
$825$		0			0
$826$	−341.429			−0.413352
$827$		−	51.5115i		−	0.0622872i	−0.999515	−	0.0311436i	$-0.990085\pi$
$827$		−	51.5115i		−	0.0622872i	0.999515	−	0.0311436i	$-0.00991492\pi$
$828$	1620.20			1.95676
$829$	−1102.12			−1.32945			−0.664726	−	0.747087i	$-0.731452\pi$
$829$	−1102.12			−1.32945			−0.664726	+	0.747087i	$0.731452\pi$
$830$		0			0
$831$		−	2390.53i		−	2.87669i
$832$			872.421i			1.04858i
$833$		−	736.640i		−	0.884321i
$834$	−1755.12			−2.10446
$835$		0			0
$836$	−338.932	−	77.8793i	−0.405421	−	0.0931571i
$837$	1766.78			2.11084
$838$		−	4.56271i		−	0.00544476i
$839$	727.457			0.867052			0.433526	−	0.901141i	$-0.357269\pi$
$839$	727.457			0.867052			0.433526	+	0.901141i	$0.357269\pi$
$840$		0			0
$841$	380.793			0.452786
$842$		−	1633.50i		−	1.94002i
$843$		−	2228.56i		−	2.64360i
$844$		−	609.951i		−	0.722691i
$845$		0			0
$846$			1517.87i			1.79417i
$847$	236.750	−	487.969i	0.279516	−	0.576114i
$848$	1593.12			1.87868
$849$		−	124.571i		−	0.146727i
$850$		0			0
$851$	605.874			0.711955
$852$	−913.852			−1.07260
$853$		−	942.330i		−	1.10472i	−0.833604	−	0.552362i	$-0.813726\pi$
$853$		−	942.330i		−	1.10472i	0.833604	−	0.552362i	$-0.186274\pi$
$854$			1011.67i			1.18463i
$855$		0			0
$856$	28.1605			0.0328978
$857$			584.440i			0.681960i	0.940070	+	0.340980i	$0.110759\pi$
$857$			584.440i			0.681960i	−0.940070	+	0.340980i	$0.889241\pi$
$858$	597.158	−	2598.84i	0.695989	−	3.02895i
$859$	209.717			0.244141			0.122070	−	0.992521i	$-0.461047\pi$
$859$	209.717			0.244141			0.122070	+	0.992521i	$0.461047\pi$
$860$		0			0
$861$	262.480			0.304854
$862$	1974.87			2.29103
$863$	−1655.39			−1.91818			−0.959090	−	0.283101i	$-0.908637\pi$
$863$	−1655.39			−1.91818			−0.959090	+	0.283101i	$0.908637\pi$
$864$			3138.87i			3.63295i
$865$		0			0
$866$			2287.01i			2.64089i
$867$	−1998.57			−2.30516
$868$		−	418.789i		−	0.482476i
$869$	−550.955	−	126.598i	−0.634010	−	0.145682i
$870$		0			0
$871$		−	777.649i		−	0.892824i
$872$	8.99923			0.0103202
$873$	1911.19			2.18922
$874$	−467.359			−0.534736
$875$		0			0
$876$			605.834i			0.691591i
$877$			265.595i			0.302845i	0.988469	+	0.151422i	$0.0483853\pi$
$877$			265.595i			0.302845i	−0.988469	+	0.151422i	$0.951615\pi$
$878$	1453.22			1.65515
$879$		−	2526.98i		−	2.87483i
$880$		0			0
$881$	187.558			0.212892			0.106446	−	0.994319i	$-0.466053\pi$
$881$	187.558			0.212892			0.106446	+	0.994319i	$0.466053\pi$
$882$		−	1750.70i		−	1.98492i
$883$	36.3595			0.0411773			0.0205886	−	0.999788i	$-0.493446\pi$
$883$	36.3595			0.0411773			0.0205886	+	0.999788i	$0.493446\pi$
$884$	−1498.26			−1.69486
$885$		0			0
$886$			1051.48i			1.18678i
$887$			666.369i			0.751261i	0.926769	+	0.375631i	$0.122574\pi$
$887$			666.369i			0.751261i	−0.926769	+	0.375631i	$0.877426\pi$
$888$			120.610i			0.135822i
$889$	695.825			0.782705
$890$		0			0
$891$	484.710	−	2109.46i	0.544006	−	2.36752i
$892$	102.398			0.114796
$893$		−	211.669i		−	0.237032i
$894$	−2473.07			−2.76630
$895$		0			0
$896$	−102.169			−0.114028
$897$		−	1732.44i		−	1.93137i
$898$		−	1573.71i		−	1.75246i
$899$			535.408i			0.595559i
$900$		0			0
$901$			2393.60i			2.65660i
$902$	−72.3719	+	314.963i	−0.0802349	+	0.349183i
$903$	−1699.71			−1.88229
$904$			70.3803i			0.0778543i
$905$		0			0
$906$	−2564.15			−2.83018
$907$	667.718			0.736182			0.368091	−	0.929790i	$-0.380011\pi$
$907$	667.718			0.736182			0.368091	+	0.929790i	$0.380011\pi$
$908$		−	261.812i		−	0.288339i
$909$			482.208i			0.530481i
$910$		0			0
$911$	218.396			0.239732			0.119866	−	0.992790i	$-0.461754\pi$
$911$	218.396			0.239732			0.119866	+	0.992790i	$0.461754\pi$
$912$		−	794.439i		−	0.871095i
$913$	506.137	+	116.300i	0.554367	+	0.127382i
$914$	867.368			0.948981
$915$		0			0
$916$	475.011			0.518571
$917$	461.990			0.503806
$918$	−5019.68			−5.46806
$919$			197.616i			0.215034i	0.994203	+	0.107517i	$0.0342900\pi$
$919$			197.616i			0.215034i	−0.994203	+	0.107517i	$0.965710\pi$
$920$		0			0
$921$			1732.93i			1.88157i
$922$	−349.187			−0.378728
$923$			691.286i			0.748956i
$924$	−997.752	−	229.263i	−1.07982	−	0.248120i
$925$		0			0
$926$		−	1331.87i		−	1.43830i
$927$	1405.84			1.51655
$928$	−951.209			−1.02501
$929$	298.522			0.321337			0.160669	−	0.987008i	$-0.448635\pi$
$929$	298.522			0.321337			0.160669	+	0.987008i	$0.448635\pi$
$930$		0			0
$931$			244.138i			0.262232i
$932$			475.716i			0.510425i
$933$	−1424.76			−1.52708
$934$			1175.47i			1.25854i
$935$		0			0
$936$	243.978			0.260661
$937$			708.598i			0.756241i	0.925756	+	0.378120i	$0.123429\pi$
$937$			708.598i			0.756241i	−0.925756	+	0.378120i	$0.876571\pi$
$938$	−617.571			−0.658391
$939$	−164.487			−0.175173
$940$		0			0
$941$		−	286.193i		−	0.304137i	−0.988370	−	0.152069i	$-0.951407\pi$
$941$		−	286.193i		−	0.304137i	0.988370	−	0.152069i	$-0.0485934\pi$
$942$		−	944.884i		−	1.00306i
$943$			209.961i			0.222652i
$944$	464.251			0.491792
$945$		0			0
$946$	468.651	−	2039.57i	0.495403	−	2.15600i
$947$	1220.02			1.28829			0.644147	−	0.764901i	$-0.277212\pi$
$947$	1220.02			1.28829			0.644147	+	0.764901i	$0.277212\pi$
$948$			1067.06i			1.12559i
$949$	458.284			0.482913
$950$		0			0
$951$	−552.842			−0.581327
$952$		−	81.5263i		−	0.0856368i
$953$		−	1539.71i		−	1.61564i	−0.589428	−	0.807821i	$-0.700647\pi$
$953$		−	1539.71i		−	1.61564i	0.589428	−	0.807821i	$-0.299353\pi$
$954$			5688.64i			5.96293i
$955$		0			0
$956$		−	906.301i		−	0.948013i
$957$	1275.59	+	293.104i	1.33291	+	0.306274i
$958$	439.846			0.459130
$959$			208.282i			0.217186i
$960$		0			0
$961$	−338.104			−0.351825
$962$	−1331.55			−1.38415
$963$			858.633i			0.891623i
$964$		−	441.843i		−	0.458343i
$965$		0			0
$966$	−1375.82			−1.42424
$967$			1504.21i			1.55555i	0.628546	+	0.777773i	$0.283651\pi$
$967$			1504.21i			1.55555i	−0.628546	+	0.777773i	$0.716349\pi$
$968$	−37.6994	+	77.7029i	−0.0389457	+	0.0802716i
$969$	1193.61			1.23180
$970$		0			0
$971$	−676.492			−0.696696			−0.348348	−	0.937365i	$-0.613257\pi$
$971$	−676.492			−0.696696			−0.348348	+	0.937365i	$0.613257\pi$
$972$	−1700.47			−1.74945
$973$	509.720			0.523864
$974$		−	2339.71i		−	2.40216i
$975$		0			0
$976$		−	1375.60i		−	1.40943i
$977$	588.072			0.601916			0.300958	−	0.953637i	$-0.402694\pi$
$977$	588.072			0.601916			0.300958	+	0.953637i	$0.402694\pi$
$978$			2080.53i			2.12734i
$979$	363.236	−	1580.81i	0.371028	−	1.61472i
$980$		0			0
$981$			274.393i			0.279707i
$982$	910.614			0.927306
$983$	−824.978			−0.839245			−0.419622	−	0.907699i	$-0.637838\pi$
$983$	−824.978			−0.839245			−0.419622	+	0.907699i	$0.637838\pi$
$984$	−41.7966			−0.0424762
$985$		0			0
$986$		−	1521.17i		−	1.54277i
$987$		−	623.116i		−	0.631323i
$988$	496.555			0.502586
$989$		−	1359.62i		−	1.37475i
$990$		0			0
$991$	−1747.44			−1.76331			−0.881653	−	0.471899i	$-0.843569\pi$
$991$	−1747.44			−1.76331			−0.881653	+	0.471899i	$0.843569\pi$
$992$			1106.64i			1.11557i
$993$	768.902			0.774323
$994$	548.985			0.552299
$995$		0			0
$996$		−	980.261i		−	0.984198i
$997$			1069.45i			1.07267i	0.844007	+	0.536333i	$0.180191\pi$
$997$			1069.45i			1.07267i	−0.844007	+	0.536333i	$0.819809\pi$
$998$		−	1533.62i		−	1.53669i
$999$	−2156.69			−2.15885

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.c.h.76.2	yes	8
5.2	odd	4		275.3.d.b.274.13		16
5.3	odd	4		275.3.d.b.274.4		16
5.4	even	2		275.3.c.g.76.7	yes	8
11.10	odd	2	inner	275.3.c.h.76.7	yes	8
55.32	even	4		275.3.d.b.274.3		16
55.43	even	4		275.3.d.b.274.14		16
55.54	odd	2		275.3.c.g.76.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.c.g.76.2	✓	8	55.54	odd	2
275.3.c.g.76.7	yes	8	5.4	even	2
275.3.c.h.76.2	yes	8	1.1	even	1	trivial
275.3.c.h.76.7	yes	8	11.10	odd	2	inner
275.3.d.b.274.3		16	55.32	even	4
275.3.d.b.274.4		16	5.3	odd	4
275.3.d.b.274.13		16	5.2	odd	4
275.3.d.b.274.14		16	55.43	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.78271i q^{2} +5.54645 q^{3} -3.74350 q^{4} -15.4342i q^{6} +4.48239i q^{7} -0.713764i q^{8} +21.7632 q^{9} +(2.46337 - 10.7206i) q^{11} -20.7632 q^{12} +15.7063i q^{13} +12.4732 q^{14} -16.9602 q^{16} -25.4820i q^{17} -60.5607i q^{18} +8.44528i q^{19} +24.8614i q^{21} +(-29.8324 - 6.85487i) q^{22} -19.8870 q^{23} -3.95886i q^{24} +43.7063 q^{26} +70.7903 q^{27} -16.7798i q^{28} +21.4524i q^{29} +24.9579 q^{31} +44.3404i q^{32} +(13.6630 - 59.4615i) q^{33} -70.9092 q^{34} -81.4704 q^{36} -30.4659 q^{37} +23.5008 q^{38} +87.1145i q^{39} -10.5577i q^{41} +69.1821 q^{42} +68.3676i q^{43} +(-9.22164 + 40.1327i) q^{44} +55.3397i q^{46} -25.0636 q^{47} -94.0690 q^{48} +28.9082 q^{49} -141.335i q^{51} -58.7967i q^{52} -93.9329 q^{53} -196.989i q^{54} +3.19936 q^{56} +46.8414i q^{57} +59.6960 q^{58} -27.3730 q^{59} +81.1075i q^{61} -69.4507i q^{62} +97.5509i q^{63} +55.5457 q^{64} +(-165.464 - 38.0202i) q^{66} -49.5118 q^{67} +95.3920i q^{68} -110.302 q^{69} +44.0132 q^{71} -15.5338i q^{72} -29.1783i q^{73} +84.7779i q^{74} -31.6149i q^{76} +(48.0540 + 11.0418i) q^{77} +242.415 q^{78} -51.3920i q^{79} +196.767 q^{81} -29.3792 q^{82} +47.2115i q^{83} -93.0685i q^{84} +190.248 q^{86} +118.985i q^{87} +(-7.65199 - 1.75827i) q^{88} +147.455 q^{89} -70.4019 q^{91} +74.4468 q^{92} +138.428 q^{93} +69.7449i q^{94} +245.932i q^{96} +87.8176 q^{97} -80.4433i q^{98} +(53.6108 - 233.315i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 10 q^{4} + 32 q^{9} - q^{11} - 24 q^{12} + 18 q^{14} - 14 q^{16} - 35 q^{22} + 4 q^{23} + 68 q^{26} + 142 q^{27} - 42 q^{31} - 31 q^{33} - 142 q^{34} - 84 q^{36} - 104 q^{37} + 190 q^{38}+ \cdots + 368 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 10 * q^4 + 32 * q^9 - q^11 - 24 * q^12 + 18 * q^14 - 14 * q^16 - 35 * q^22 + 4 * q^23 + 68 * q^26 + 142 * q^27 - 42 * q^31 - 31 * q^33 - 142 * q^34 - 84 * q^36 - 104 * q^37 + 190 * q^38 + 50 * q^42 + 69 * q^44 - 64 * q^47 - 86 * q^48 - 50 * q^49 - 286 * q^53 + 166 * q^56 - 130 * q^58 - 160 * q^59 + 288 * q^64 - 315 * q^66 + 46 * q^67 - 16 * q^69 + 246 * q^71 + 80 * q^77 + 620 * q^78 + 304 * q^81 + 280 * q^82 - 282 * q^86 - 365 * q^88 - 18 * q^89 - 142 * q^91 + 26 * q^92 + 818 * q^93 - 264 * q^97 + 368 * q^99

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