LMFDB - Embedded newform 575.2.a.k.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(1,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("575.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.a (trivial)

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:	yes
Analytic conductor:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 12x^{5} + 9x^{4} + 43x^{3} - 14x^{2} - 49x - 9 $ x^7 - x^6 - 12x^5 + 9x^4 + 43x^3 - 14x^2 - 49*x - 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.27220$ of defining polynomial
Character	$\chi$	$=$	575.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.27220 q^{2} -3.13672 q^{3} +3.16289 q^{4} +7.12726 q^{6} +4.34930 q^{7} -2.64233 q^{8} +6.83902 q^{9} +O(q^{10})$	\(q-2.27220 q^{2} -3.13672 q^{3} +3.16289 q^{4} +7.12726 q^{6} +4.34930 q^{7} -2.64233 q^{8} +6.83902 q^{9} -3.85039 q^{11} -9.92112 q^{12} +3.05468 q^{13} -9.88249 q^{14} -0.321887 q^{16} -3.04332 q^{17} -15.5396 q^{18} +2.69402 q^{19} -13.6425 q^{21} +8.74885 q^{22} -1.00000 q^{23} +8.28825 q^{24} -6.94085 q^{26} -12.0419 q^{27} +13.7564 q^{28} +3.86561 q^{29} -4.75713 q^{31} +6.01605 q^{32} +12.0776 q^{33} +6.91503 q^{34} +21.6311 q^{36} +1.06605 q^{37} -6.12134 q^{38} -9.58169 q^{39} +10.2468 q^{41} +30.9986 q^{42} -8.40413 q^{43} -12.1784 q^{44} +2.27220 q^{46} +7.89385 q^{47} +1.00967 q^{48} +11.9164 q^{49} +9.54604 q^{51} +9.66164 q^{52} -2.82471 q^{53} +27.3617 q^{54} -11.4923 q^{56} -8.45038 q^{57} -8.78345 q^{58} -7.06900 q^{59} -4.81784 q^{61} +10.8092 q^{62} +29.7450 q^{63} -13.0259 q^{64} -27.4427 q^{66} +12.0038 q^{67} -9.62569 q^{68} +3.13672 q^{69} +7.89385 q^{71} -18.0709 q^{72} -4.83299 q^{73} -2.42227 q^{74} +8.52089 q^{76} -16.7465 q^{77} +21.7715 q^{78} +4.94605 q^{79} +17.2551 q^{81} -23.2829 q^{82} -2.56791 q^{83} -43.1499 q^{84} +19.0959 q^{86} -12.1254 q^{87} +10.1740 q^{88} +11.2622 q^{89} +13.2857 q^{91} -3.16289 q^{92} +14.9218 q^{93} -17.9364 q^{94} -18.8707 q^{96} +6.68955 q^{97} -27.0765 q^{98} -26.3329 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 11 q^{4} + 5 q^{6} + 3 q^{7} - 6 q^{8} + 15 q^{9}+O(q^{10}) $ 7 * q - q^2 + 11 * q^4 + 5 * q^6 + 3 * q^7 - 6 * q^8 + 15 * q^9	$ 7 q - q^{2} + 11 q^{4} + 5 q^{6} + 3 q^{7} - 6 q^{8} + 15 q^{9} - q^{11} + 6 q^{12} - 3 q^{13} + 7 q^{14} + 7 q^{16} + 10 q^{17} - 24 q^{18} + 15 q^{19} + 2 q^{21} + 21 q^{22} - 7 q^{23} + 18 q^{24} - 20 q^{26} - 11 q^{28} + 3 q^{29} + 14 q^{31} + 17 q^{32} + 6 q^{33} + 20 q^{34} - 10 q^{37} - 31 q^{38} - 8 q^{39} + 19 q^{41} + 44 q^{42} + 5 q^{43} - 3 q^{44} + q^{46} - 14 q^{47} - 27 q^{48} + 40 q^{49} + 2 q^{51} + 16 q^{52} + 4 q^{53} - q^{54} - 9 q^{56} - 4 q^{57} - 13 q^{58} - 16 q^{59} + 40 q^{61} - 12 q^{62} + 53 q^{63} - 4 q^{64} - 54 q^{66} - 4 q^{67} + 20 q^{68} - 14 q^{71} - 6 q^{72} - 3 q^{73} - 18 q^{74} + 35 q^{76} - 17 q^{77} + 23 q^{78} - q^{79} + 47 q^{81} - 22 q^{82} + 17 q^{83} - 60 q^{84} - 35 q^{86} - 56 q^{87} + 57 q^{88} + 16 q^{89} + 25 q^{91} - 11 q^{92} + 14 q^{93} + 7 q^{94} - 19 q^{96} - 24 q^{97} - 46 q^{98} - 53 q^{99}+O(q^{100}) $ 7 * q - q^2 + 11 * q^4 + 5 * q^6 + 3 * q^7 - 6 * q^8 + 15 * q^9 - q^11 + 6 * q^12 - 3 * q^13 + 7 * q^14 + 7 * q^16 + 10 * q^17 - 24 * q^18 + 15 * q^19 + 2 * q^21 + 21 * q^22 - 7 * q^23 + 18 * q^24 - 20 * q^26 - 11 * q^28 + 3 * q^29 + 14 * q^31 + 17 * q^32 + 6 * q^33 + 20 * q^34 - 10 * q^37 - 31 * q^38 - 8 * q^39 + 19 * q^41 + 44 * q^42 + 5 * q^43 - 3 * q^44 + q^46 - 14 * q^47 - 27 * q^48 + 40 * q^49 + 2 * q^51 + 16 * q^52 + 4 * q^53 - q^54 - 9 * q^56 - 4 * q^57 - 13 * q^58 - 16 * q^59 + 40 * q^61 - 12 * q^62 + 53 * q^63 - 4 * q^64 - 54 * q^66 - 4 * q^67 + 20 * q^68 - 14 * q^71 - 6 * q^72 - 3 * q^73 - 18 * q^74 + 35 * q^76 - 17 * q^77 + 23 * q^78 - q^79 + 47 * q^81 - 22 * q^82 + 17 * q^83 - 60 * q^84 - 35 * q^86 - 56 * q^87 + 57 * q^88 + 16 * q^89 + 25 * q^91 - 11 * q^92 + 14 * q^93 + 7 * q^94 - 19 * q^96 - 24 * q^97 - 46 * q^98 - 53 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−2.27220	−1.60669	−0.803344	−	0.595515i	$-0.796948\pi$
$2$	−2.27220	−1.60669	−0.803344	+	0.595515i	$0.796948\pi$
$3$	−3.13672	−1.81099	−0.905493	−	0.424360i	$-0.860499\pi$
$3$	−3.13672	−1.81099	−0.905493	+	0.424360i	$0.860499\pi$
$4$	3.16289	1.58145
$5$	0	0
$5$	0	0
$6$	7.12726	2.90969
$7$	4.34930	1.64388	0.821941	−	0.569573i	$-0.192891\pi$
$7$	4.34930	1.64388	0.821941	+	0.569573i	$0.192891\pi$
$8$	−2.64233	−0.934205
$9$	6.83902	2.27967
$10$	0	0
$11$	−3.85039	−1.16093	−0.580467	−	0.814283i	$-0.697130\pi$
$11$	−3.85039	−1.16093	−0.580467	+	0.814283i	$0.697130\pi$
$12$	−9.92112	−2.86398
$13$	3.05468	0.847217	0.423608	−	0.905845i	$-0.360763\pi$
$13$	3.05468	0.847217	0.423608	+	0.905845i	$0.360763\pi$
$14$	−9.88249	−2.64121
$15$	0	0
$16$	−0.321887	−0.0804718
$17$	−3.04332	−0.738113	−0.369057	−	0.929407i	$-0.620319\pi$
$17$	−3.04332	−0.738113	−0.369057	+	0.929407i	$0.620319\pi$
$18$	−15.5396	−3.66272
$19$	2.69402	0.618050	0.309025	−	0.951054i	$-0.399997\pi$
$19$	2.69402	0.618050	0.309025	+	0.951054i	$0.399997\pi$
$20$	0	0
$21$	−13.6425	−2.97705
$22$	8.74885	1.86526
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	8.28825	1.69183
$25$	0	0
$26$	−6.94085	−1.36121
$27$	−12.0419	−2.31747
$28$	13.7564	2.59971
$29$	3.86561	0.717827	0.358913	−	0.933371i	$-0.383147\pi$
$29$	3.86561	0.717827	0.358913	+	0.933371i	$0.383147\pi$
$30$	0	0
$31$	−4.75713	−0.854406	−0.427203	−	0.904156i	$-0.640501\pi$
$31$	−4.75713	−0.854406	−0.427203	+	0.904156i	$0.640501\pi$
$32$	6.01605	1.06350
$33$	12.0776	2.10244
$34$	6.91503	1.18592
$35$	0	0
$36$	21.6311	3.60518
$37$	1.06605	0.175257	0.0876286	−	0.996153i	$-0.472071\pi$
$37$	1.06605	0.175257	0.0876286	+	0.996153i	$0.472071\pi$
$38$	−6.12134	−0.993013
$39$	−9.58169	−1.53430
$40$	0	0
$41$	10.2468	1.60029	0.800144	−	0.599807i	$-0.204756\pi$
$41$	10.2468	1.60029	0.800144	+	0.599807i	$0.204756\pi$
$42$	30.9986	4.78319
$43$	−8.40413	−1.28162	−0.640809	−	0.767700i	$-0.721401\pi$
$43$	−8.40413	−1.28162	−0.640809	+	0.767700i	$0.721401\pi$
$44$	−12.1784	−1.83596
$45$	0	0
$46$	2.27220	0.335018
$47$	7.89385	1.15144	0.575718	−	0.817648i	$-0.304722\pi$
$47$	7.89385	1.15144	0.575718	+	0.817648i	$0.304722\pi$
$48$	1.00967	0.145733
$49$	11.9164	1.70235
$50$	0	0
$51$	9.54604	1.33671
$52$	9.66164	1.33983
$53$	−2.82471	−0.388003	−0.194002	−	0.981001i	$-0.562147\pi$
$53$	−2.82471	−0.388003	−0.194002	+	0.981001i	$0.562147\pi$
$54$	27.3617	3.72346
$55$	0	0
$56$	−11.4923	−1.53572
$57$	−8.45038	−1.11928
$58$	−8.78345	−1.15332
$59$	−7.06900	−0.920305	−0.460152	−	0.887840i	$-0.652205\pi$
$59$	−7.06900	−0.920305	−0.460152	+	0.887840i	$0.652205\pi$
$60$	0	0
$61$	−4.81784	−0.616862	−0.308431	−	0.951247i	$-0.599804\pi$
$61$	−4.81784	−0.616862	−0.308431	+	0.951247i	$0.599804\pi$
$62$	10.8092	1.37276
$63$	29.7450	3.74751
$64$	−13.0259	−1.62824
$65$	0	0
$66$	−27.4427	−3.37796
$67$	12.0038	1.46650	0.733251	−	0.679958i	$-0.238002\pi$
$67$	12.0038	1.46650	0.733251	+	0.679958i	$0.238002\pi$
$68$	−9.62569	−1.16729
$69$	3.13672	0.377617
$70$	0	0
$71$	7.89385	0.936828	0.468414	−	0.883509i	$-0.344826\pi$
$71$	7.89385	0.936828	0.468414	+	0.883509i	$0.344826\pi$
$72$	−18.0709	−2.12968
$73$	−4.83299	−0.565659	−0.282829	−	0.959170i	$-0.591273\pi$
$73$	−4.83299	−0.565659	−0.282829	+	0.959170i	$0.591273\pi$
$74$	−2.42227	−0.281584
$75$	0	0
$76$	8.52089	0.977413
$77$	−16.7465	−1.90844
$78$	21.7715	2.46514
$79$	4.94605	0.556474	0.278237	−	0.960512i	$-0.410250\pi$
$79$	4.94605	0.556474	0.278237	+	0.960512i	$0.410250\pi$
$80$	0	0
$81$	17.2551	1.91724
$82$	−23.2829	−2.57117
$83$	−2.56791	−0.281865	−0.140933	−	0.990019i	$-0.545010\pi$
$83$	−2.56791	−0.281865	−0.140933	+	0.990019i	$0.545010\pi$
$84$	−43.1499	−4.70805
$85$	0	0
$86$	19.0959	2.05916
$87$	−12.1254	−1.29997
$88$	10.1740	1.08455
$89$	11.2622	1.19379	0.596897	−	0.802318i	$-0.296400\pi$
$89$	11.2622	1.19379	0.596897	+	0.802318i	$0.296400\pi$
$90$	0	0
$91$	13.2857	1.39272
$92$	−3.16289	−0.329755
$93$	14.9218	1.54732
$94$	−17.9364	−1.85000
$95$	0	0
$96$	−18.8707	−1.92598
$97$	6.68955	0.679221	0.339611	−	0.940566i	$-0.389705\pi$
$97$	6.68955	0.679221	0.339611	+	0.940566i	$0.389705\pi$
$98$	−27.0765	−2.73514
$99$	−26.3329	−2.64655
$100$	0	0
$101$	7.30446	0.726821	0.363411	−	0.931629i	$-0.381612\pi$
$101$	7.30446	0.726821	0.363411	+	0.931629i	$0.381612\pi$
$102$	−21.6905	−2.14768
$103$	6.02351	0.593514	0.296757	−	0.954953i	$-0.404095\pi$
$103$	6.02351	0.593514	0.296757	+	0.954953i	$0.404095\pi$
$104$	−8.07148	−0.791474
$105$	0	0
$106$	6.41830	0.623400
$107$	1.33701	0.129253	0.0646266	−	0.997910i	$-0.479414\pi$
$107$	1.33701	0.129253	0.0646266	+	0.997910i	$0.479414\pi$
$108$	−38.0874	−3.66496
$109$	13.8590	1.32745	0.663724	−	0.747977i	$-0.268975\pi$
$109$	13.8590	1.32745	0.663724	+	0.747977i	$0.268975\pi$
$110$	0	0
$111$	−3.34389	−0.317388
$112$	−1.39998	−0.132286
$113$	8.57648	0.806807	0.403404	−	0.915022i	$-0.367827\pi$
$113$	8.57648	0.806807	0.403404	+	0.915022i	$0.367827\pi$
$114$	19.2009	1.79833
$115$	0	0
$116$	12.2265	1.13521
$117$	20.8910	1.93138
$118$	16.0622	1.47864
$119$	−13.2363	−1.21337
$120$	0	0
$121$	3.82547	0.347770
$122$	10.9471	0.991104
$123$	−32.1415	−2.89810
$124$	−15.0463	−1.35120
$125$	0	0
$126$	−67.5865	−6.02109
$127$	−7.59522	−0.673967	−0.336983	−	0.941511i	$-0.609407\pi$
$127$	−7.59522	−0.673967	−0.336983	+	0.941511i	$0.609407\pi$
$128$	17.5654	1.55257
$129$	26.3614	2.32099
$130$	0	0
$131$	−11.8353	−1.03406	−0.517029	−	0.855968i	$-0.672962\pi$
$131$	−11.8353	−1.03406	−0.517029	+	0.855968i	$0.672962\pi$
$132$	38.2001	3.32489
$133$	11.7171	1.01600
$134$	−27.2751	−2.35621
$135$	0	0
$136$	8.04145	0.689549
$137$	0.504791	0.0431272	0.0215636	−	0.999767i	$-0.493136\pi$
$137$	0.504791	0.0431272	0.0215636	+	0.999767i	$0.493136\pi$
$138$	−7.12726	−0.606713
$139$	12.3538	1.04784	0.523918	−	0.851769i	$-0.324470\pi$
$139$	12.3538	1.04784	0.523918	+	0.851769i	$0.324470\pi$
$140$	0	0
$141$	−24.7608	−2.08524
$142$	−17.9364	−1.50519
$143$	−11.7617	−0.983563
$144$	−2.20139	−0.183449
$145$	0	0
$146$	10.9815	0.908837
$147$	−37.3785	−3.08293
$148$	3.37180	0.277160
$149$	−5.69696	−0.466714	−0.233357	−	0.972391i	$-0.574971\pi$
$149$	−5.69696	−0.466714	−0.233357	+	0.972391i	$0.574971\pi$
$150$	0	0
$151$	−6.30245	−0.512886	−0.256443	−	0.966559i	$-0.582551\pi$
$151$	−6.30245	−0.512886	−0.256443	+	0.966559i	$0.582551\pi$
$152$	−7.11848	−0.577385
$153$	−20.8133	−1.68266
$154$	38.0514	3.06627
$155$	0	0
$156$	−30.3059	−2.42641
$157$	18.1642	1.44966	0.724830	−	0.688927i	$-0.241918\pi$
$157$	18.1642	1.44966	0.724830	+	0.688927i	$0.241918\pi$
$158$	−11.2384	−0.894080
$159$	8.86032	0.702669
$160$	0	0
$161$	−4.34930	−0.342773
$162$	−39.2071	−3.08040
$163$	2.67049	0.209169	0.104585	−	0.994516i	$-0.466649\pi$
$163$	2.67049	0.209169	0.104585	+	0.994516i	$0.466649\pi$
$164$	32.4097	2.53077
$165$	0	0
$166$	5.83482	0.452870
$167$	3.91511	0.302960	0.151480	−	0.988460i	$-0.451596\pi$
$167$	3.91511	0.302960	0.151480	+	0.988460i	$0.451596\pi$
$168$	36.0481	2.78117
$169$	−3.66891	−0.282224
$170$	0	0
$171$	18.4244	1.40895
$172$	−26.5814	−2.02681
$173$	11.1156	0.845100	0.422550	−	0.906340i	$-0.361135\pi$
$173$	11.1156	0.845100	0.422550	+	0.906340i	$0.361135\pi$
$174$	27.5512	2.08865
$175$	0	0
$176$	1.23939	0.0934225
$177$	22.1735	1.66666
$178$	−25.5900	−1.91805
$179$	−17.2917	−1.29244	−0.646220	−	0.763152i	$-0.723651\pi$
$179$	−17.2917	−1.29244	−0.646220	+	0.763152i	$0.723651\pi$
$180$	0	0
$181$	20.7989	1.54597	0.772986	−	0.634423i	$-0.218762\pi$
$181$	20.7989	1.54597	0.772986	+	0.634423i	$0.218762\pi$
$182$	−30.1879	−2.23767
$183$	15.1122	1.11713
$184$	2.64233	0.194795
$185$	0	0
$186$	−33.9053	−2.48606
$187$	11.7179	0.856901
$188$	24.9674	1.82094
$189$	−52.3740	−3.80965
$190$	0	0
$191$	25.5384	1.84790	0.923948	−	0.382519i	$-0.124943\pi$
$191$	25.5384	1.84790	0.923948	+	0.382519i	$0.124943\pi$
$192$	40.8586	2.94872
$193$	15.7360	1.13270	0.566349	−	0.824165i	$-0.308355\pi$
$193$	15.7360	1.13270	0.566349	+	0.824165i	$0.308355\pi$
$194$	−15.2000	−1.09130
$195$	0	0
$196$	37.6904	2.69217
$197$	21.5181	1.53310	0.766551	−	0.642183i	$-0.221971\pi$
$197$	21.5181	1.53310	0.766551	+	0.642183i	$0.221971\pi$
$198$	59.8335	4.25218
$199$	0.762929	0.0540826	0.0270413	−	0.999634i	$-0.491391\pi$
$199$	0.762929	0.0540826	0.0270413	+	0.999634i	$0.491391\pi$
$200$	0	0
$201$	−37.6527	−2.65581
$202$	−16.5972	−1.16778
$203$	16.8127	1.18002
$204$	30.1931	2.11394
$205$	0	0
$206$	−13.6866	−0.953593
$207$	−6.83902	−0.475345
$208$	−0.983263	−0.0681770
$209$	−10.3730	−0.717515
$210$	0	0
$211$	−27.4855	−1.89218	−0.946092	−	0.323899i	$-0.895006\pi$
$211$	−27.4855	−1.89218	−0.946092	+	0.323899i	$0.895006\pi$
$212$	−8.93425	−0.613607
$213$	−24.7608	−1.69658
$214$	−3.03794	−0.207670
$215$	0	0
$216$	31.8188	2.16499
$217$	−20.6902	−1.40454
$218$	−31.4904	−2.13280
$219$	15.1597	1.02440
$220$	0	0
$221$	−9.29637	−0.625342
$222$	7.59800	0.509944
$223$	−1.75842	−0.117753	−0.0588764	−	0.998265i	$-0.518752\pi$
$223$	−1.75842	−0.117753	−0.0588764	+	0.998265i	$0.518752\pi$
$224$	26.1656	1.74826
$225$	0	0
$226$	−19.4875	−1.29629
$227$	0.264095	0.0175286	0.00876430	−	0.999962i	$-0.497210\pi$
$227$	0.264095	0.0175286	0.00876430	+	0.999962i	$0.497210\pi$
$228$	−26.7276	−1.77008
$229$	−15.4950	−1.02394	−0.511971	−	0.859003i	$-0.671084\pi$
$229$	−15.4950	−1.02394	−0.511971	+	0.859003i	$0.671084\pi$
$230$	0	0
$231$	52.5291	3.45616
$232$	−10.2142	−0.670597
$233$	2.31823	0.151872	0.0759361	−	0.997113i	$-0.475805\pi$
$233$	2.31823	0.151872	0.0759361	+	0.997113i	$0.475805\pi$
$234$	−47.4686	−3.10312
$235$	0	0
$236$	−22.3585	−1.45541
$237$	−15.5144	−1.00777
$238$	30.0756	1.94951
$239$	19.7582	1.27805	0.639025	−	0.769186i	$-0.279338\pi$
$239$	19.7582	1.27805	0.639025	+	0.769186i	$0.279338\pi$
$240$	0	0
$241$	29.9857	1.93155	0.965776	−	0.259378i	$-0.0835175\pi$
$241$	29.9857	1.93155	0.965776	+	0.259378i	$0.0835175\pi$
$242$	−8.69222	−0.558757
$243$	−17.9988	−1.15462
$244$	−15.2383	−0.975534
$245$	0	0
$246$	73.0319	4.65635
$247$	8.22936	0.523622
$248$	12.5699	0.798190
$249$	8.05483	0.510454
$250$	0	0
$251$	−10.3167	−0.651187	−0.325593	−	0.945510i	$-0.605564\pi$
$251$	−10.3167	−0.651187	−0.325593	+	0.945510i	$0.605564\pi$
$252$	94.0802	5.92650
$253$	3.85039	0.242072
$254$	17.2579	1.08285
$255$	0	0
$256$	−13.8602	−0.866262
$257$	13.3150	0.830567	0.415283	−	0.909692i	$-0.363682\pi$
$257$	13.3150	0.830567	0.415283	+	0.909692i	$0.363682\pi$
$258$	−59.8984	−3.72911
$259$	4.63656	0.288102
$260$	0	0
$261$	26.4370	1.63641
$262$	26.8922	1.66141
$263$	−13.0306	−0.803499	−0.401750	−	0.915750i	$-0.631598\pi$
$263$	−13.0306	−0.803499	−0.401750	+	0.915750i	$0.631598\pi$
$264$	−31.9130	−1.96411
$265$	0	0
$266$	−26.6236	−1.63240
$267$	−35.3265	−2.16194
$268$	37.9668	2.31919
$269$	10.5355	0.642361	0.321180	−	0.947018i	$-0.395920\pi$
$269$	10.5355	0.642361	0.321180	+	0.947018i	$0.395920\pi$
$270$	0	0
$271$	13.1787	0.800547	0.400273	−	0.916396i	$-0.368915\pi$
$271$	13.1787	0.800547	0.400273	+	0.916396i	$0.368915\pi$
$272$	0.979605	0.0593973
$273$	−41.6737	−2.52220
$274$	−1.14699	−0.0692920
$275$	0	0
$276$	9.92112	0.597181
$277$	−11.0930	−0.666512	−0.333256	−	0.942836i	$-0.608147\pi$
$277$	−11.0930	−0.666512	−0.333256	+	0.942836i	$0.608147\pi$
$278$	−28.0703	−1.68355
$279$	−32.5341	−1.94777
$280$	0	0
$281$	−13.3806	−0.798222	−0.399111	−	0.916903i	$-0.630681\pi$
$281$	−13.3806	−0.798222	−0.399111	+	0.916903i	$0.630681\pi$
$282$	56.2615	3.35033
$283$	2.21861	0.131883	0.0659414	−	0.997823i	$-0.478995\pi$
$283$	2.21861	0.131883	0.0659414	+	0.997823i	$0.478995\pi$
$284$	24.9674	1.48154
$285$	0	0
$286$	26.7250	1.58028
$287$	44.5666	2.63069
$288$	41.1439	2.42443
$289$	−7.73821	−0.455189
$290$	0	0
$291$	−20.9833	−1.23006
$292$	−15.2862	−0.894559
$293$	10.8958	0.636540	0.318270	−	0.948000i	$-0.396898\pi$
$293$	10.8958	0.636540	0.318270	+	0.948000i	$0.396898\pi$
$294$	84.9315	4.95331
$295$	0	0
$296$	−2.81685	−0.163726
$297$	46.3661	2.69043
$298$	12.9446	0.749863
$299$	−3.05468	−0.176657
$300$	0	0
$301$	−36.5521	−2.10683
$302$	14.3204	0.824048
$303$	−22.9121	−1.31626
$304$	−0.867169	−0.0497355
$305$	0	0
$306$	47.2920	2.70351
$307$	−25.2621	−1.44178	−0.720891	−	0.693048i	$-0.756267\pi$
$307$	−25.2621	−1.44178	−0.720891	+	0.693048i	$0.756267\pi$
$308$	−52.9674	−3.01810
$309$	−18.8941	−1.07485
$310$	0	0
$311$	5.90035	0.334578	0.167289	−	0.985908i	$-0.446499\pi$
$311$	5.90035	0.334578	0.167289	+	0.985908i	$0.446499\pi$
$312$	25.3180	1.43335
$313$	−17.4846	−0.988290	−0.494145	−	0.869379i	$-0.664519\pi$
$313$	−17.4846	−0.988290	−0.494145	+	0.869379i	$0.664519\pi$
$314$	−41.2727	−2.32915
$315$	0	0
$316$	15.6438	0.880034
$317$	−12.4215	−0.697663	−0.348832	−	0.937185i	$-0.613422\pi$
$317$	−12.4215	−0.697663	−0.348832	+	0.937185i	$0.613422\pi$
$318$	−20.1324	−1.12897
$319$	−14.8841	−0.833350
$320$	0	0
$321$	−4.19381	−0.234076
$322$	9.88249	0.550729
$323$	−8.19875	−0.456190
$324$	54.5762	3.03201
$325$	0	0
$326$	−6.06790	−0.336070
$327$	−43.4717	−2.40399
$328$	−27.0755	−1.49500
$329$	34.3327	1.89283
$330$	0	0
$331$	18.8830	1.03790	0.518952	−	0.854804i	$-0.326322\pi$
$331$	18.8830	1.03790	0.518952	+	0.854804i	$0.326322\pi$
$332$	−8.12204	−0.445755
$333$	7.29072	0.399529
$334$	−8.89592	−0.486763
$335$	0	0
$336$	4.39136	0.239568
$337$	−16.5669	−0.902458	−0.451229	−	0.892408i	$-0.649014\pi$
$337$	−16.5669	−0.902458	−0.451229	+	0.892408i	$0.649014\pi$
$338$	8.33651	0.453446
$339$	−26.9020	−1.46112
$340$	0	0
$341$	18.3168	0.991909
$342$	−41.8640	−2.26375
$343$	21.3831	1.15458
$344$	22.2065	1.19729
$345$	0	0
$346$	−25.2568	−1.35781
$347$	−10.9584	−0.588278	−0.294139	−	0.955763i	$-0.595033\pi$
$347$	−10.9584	−0.588278	−0.294139	+	0.955763i	$0.595033\pi$
$348$	−38.3512	−2.05584
$349$	20.1395	1.07804	0.539020	−	0.842293i	$-0.318795\pi$
$349$	20.1395	1.07804	0.539020	+	0.842293i	$0.318795\pi$
$350$	0	0
$351$	−36.7843	−1.96340
$352$	−23.1641	−1.23465
$353$	−20.3789	−1.08466	−0.542331	−	0.840165i	$-0.682458\pi$
$353$	−20.3789	−1.08466	−0.542331	+	0.840165i	$0.682458\pi$
$354$	−50.3826	−2.67780
$355$	0	0
$356$	35.6212	1.88792
$357$	41.5186	2.19740
$358$	39.2901	2.07655
$359$	−25.6854	−1.35562	−0.677812	−	0.735235i	$-0.737072\pi$
$359$	−25.6854	−1.35562	−0.677812	+	0.735235i	$0.737072\pi$
$360$	0	0
$361$	−11.7423	−0.618015
$362$	−47.2593	−2.48389
$363$	−11.9994	−0.629806
$364$	42.0214	2.20252
$365$	0	0
$366$	−34.3380	−1.79488
$367$	27.5629	1.43877	0.719385	−	0.694611i	$-0.244424\pi$
$367$	27.5629	1.43877	0.719385	+	0.694611i	$0.244424\pi$
$368$	0.321887	0.0167795
$369$	70.0784	3.64814
$370$	0	0
$371$	−12.2855	−0.637832
$372$	47.1961	2.44700
$373$	−21.0418	−1.08950	−0.544752	−	0.838597i	$-0.683376\pi$
$373$	−21.0418	−1.08950	−0.544752	+	0.838597i	$0.683376\pi$
$374$	−26.6255	−1.37677
$375$	0	0
$376$	−20.8582	−1.07568
$377$	11.8082	0.608155
$378$	119.004	6.12092
$379$	0.466139	0.0239440	0.0119720	−	0.999928i	$-0.496189\pi$
$379$	0.466139	0.0239440	0.0119720	+	0.999928i	$0.496189\pi$
$380$	0	0
$381$	23.8241	1.22054
$382$	−58.0284	−2.96899
$383$	31.6866	1.61911	0.809556	−	0.587043i	$-0.199708\pi$
$383$	31.6866	1.61911	0.809556	+	0.587043i	$0.199708\pi$
$384$	−55.0976	−2.81169
$385$	0	0
$386$	−35.7552	−1.81989
$387$	−57.4760	−2.92167
$388$	21.1584	1.07415
$389$	10.9053	0.552919	0.276460	−	0.961026i	$-0.410839\pi$
$389$	10.9053	0.552919	0.276460	+	0.961026i	$0.410839\pi$
$390$	0	0
$391$	3.04332	0.153907
$392$	−31.4871	−1.59034
$393$	37.1241	1.87266
$394$	−48.8935	−2.46322
$395$	0	0
$396$	−83.2881	−4.18538
$397$	−17.4395	−0.875265	−0.437632	−	0.899154i	$-0.644183\pi$
$397$	−17.4395	−0.875265	−0.437632	+	0.899154i	$0.644183\pi$
$398$	−1.73353	−0.0868939
$399$	−36.7532	−1.83996
$400$	0	0
$401$	26.9622	1.34643	0.673215	−	0.739447i	$-0.264913\pi$
$401$	26.9622	1.34643	0.673215	+	0.739447i	$0.264913\pi$
$402$	85.5544	4.26707
$403$	−14.5315	−0.723867
$404$	23.1032	1.14943
$405$	0	0
$406$	−38.2019	−1.89593
$407$	−4.10469	−0.203462
$408$	−25.2238	−1.24876
$409$	−18.7559	−0.927419	−0.463709	−	0.885987i	$-0.653482\pi$
$409$	−18.7559	−0.927419	−0.463709	+	0.885987i	$0.653482\pi$
$410$	0	0
$411$	−1.58339	−0.0781028
$412$	19.0517	0.938612
$413$	−30.7452	−1.51287
$414$	15.5396	0.763731
$415$	0	0
$416$	18.3771	0.901013
$417$	−38.7504	−1.89762
$418$	23.5695	1.15282
$419$	17.3762	0.848882	0.424441	−	0.905456i	$-0.360471\pi$
$419$	17.3762	0.848882	0.424441	+	0.905456i	$0.360471\pi$
$420$	0	0
$421$	−7.50489	−0.365766	−0.182883	−	0.983135i	$-0.558543\pi$
$421$	−7.50489	−0.365766	−0.182883	+	0.983135i	$0.558543\pi$
$422$	62.4527	3.04015
$423$	53.9862	2.62490
$424$	7.46381	0.362474
$425$	0	0
$426$	56.2615	2.72588
$427$	−20.9543	−1.01405
$428$	4.22881	0.204407
$429$	36.8932	1.78122
$430$	0	0
$431$	−19.5065	−0.939593	−0.469796	−	0.882775i	$-0.655673\pi$
$431$	−19.5065	−0.939593	−0.469796	+	0.882775i	$0.655673\pi$
$432$	3.87614	0.186491
$433$	−38.7163	−1.86058	−0.930292	−	0.366819i	$-0.880447\pi$
$433$	−38.7163	−1.86058	−0.930292	+	0.366819i	$0.880447\pi$
$434$	47.0123	2.25666
$435$	0	0
$436$	43.8345	2.09929
$437$	−2.69402	−0.128872
$438$	−34.4460	−1.64589
$439$	24.4249	1.16574	0.582868	−	0.812567i	$-0.301931\pi$
$439$	24.4249	1.16574	0.582868	+	0.812567i	$0.301931\pi$
$440$	0	0
$441$	81.4967	3.88080
$442$	21.1232	1.00473
$443$	−8.28001	−0.393395	−0.196698	−	0.980464i	$-0.563022\pi$
$443$	−8.28001	−0.393395	−0.196698	+	0.980464i	$0.563022\pi$
$444$	−10.5764	−0.501933
$445$	0	0
$446$	3.99549	0.189192
$447$	17.8698	0.845212
$448$	−56.6536	−2.67663
$449$	−13.0618	−0.616423	−0.308212	−	0.951318i	$-0.599731\pi$
$449$	−13.0618	−0.616423	−0.308212	+	0.951318i	$0.599731\pi$
$450$	0	0
$451$	−39.4543	−1.85783
$452$	27.1265	1.27592
$453$	19.7690	0.928830
$454$	−0.600077	−0.0281630
$455$	0	0
$456$	22.3287	1.04564
$457$	23.1582	1.08329	0.541646	−	0.840606i	$-0.317801\pi$
$457$	23.1582	1.08329	0.541646	+	0.840606i	$0.317801\pi$
$458$	35.2078	1.64515
$459$	36.6474	1.71056
$460$	0	0
$461$	−15.6153	−0.727277	−0.363638	−	0.931540i	$-0.618466\pi$
$461$	−15.6153	−0.727277	−0.363638	+	0.931540i	$0.618466\pi$
$462$	−119.357	−5.55297
$463$	25.4444	1.18250	0.591251	−	0.806487i	$-0.298634\pi$
$463$	25.4444	1.18250	0.591251	+	0.806487i	$0.298634\pi$
$464$	−1.24429	−0.0577648
$465$	0	0
$466$	−5.26748	−0.244011
$467$	−0.938838	−0.0434443	−0.0217221	−	0.999764i	$-0.506915\pi$
$467$	−0.938838	−0.0434443	−0.0217221	+	0.999764i	$0.506915\pi$
$468$	66.0762	3.05437
$469$	52.2083	2.41075
$470$	0	0
$471$	−56.9760	−2.62532
$472$	18.6786	0.859753
$473$	32.3592	1.48788
$474$	35.2518	1.61917
$475$	0	0
$476$	−41.8651	−1.91888
$477$	−19.3182	−0.884521
$478$	−44.8945	−2.05343
$479$	19.6836	0.899365	0.449683	−	0.893188i	$-0.351537\pi$
$479$	19.6836	0.899365	0.449683	+	0.893188i	$0.351537\pi$
$480$	0	0
$481$	3.25644	0.148481
$482$	−68.1336	−3.10340
$483$	13.6425	0.620758
$484$	12.0995	0.549979
$485$	0	0
$486$	40.8968	1.85512
$487$	−4.56458	−0.206841	−0.103420	−	0.994638i	$-0.532979\pi$
$487$	−4.56458	−0.206841	−0.103420	+	0.994638i	$0.532979\pi$
$488$	12.7303	0.576275
$489$	−8.37660	−0.378803
$490$	0	0
$491$	−25.8288	−1.16564	−0.582818	−	0.812603i	$-0.698050\pi$
$491$	−25.8288	−1.16564	−0.582818	+	0.812603i	$0.698050\pi$
$492$	−101.660	−4.58320
$493$	−11.7643	−0.529837
$494$	−18.6988	−0.841297
$495$	0	0
$496$	1.53126	0.0687555
$497$	34.3327	1.54003
$498$	−18.3022	−0.820141
$499$	30.9105	1.38375	0.691873	−	0.722019i	$-0.256786\pi$
$499$	30.9105	1.38375	0.691873	+	0.722019i	$0.256786\pi$
$500$	0	0
$501$	−12.2806	−0.548657
$502$	23.4417	1.04625
$503$	−12.6811	−0.565422	−0.282711	−	0.959205i	$-0.591234\pi$
$503$	−12.6811	−0.565422	−0.282711	+	0.959205i	$0.591234\pi$
$504$	−78.5960	−3.50094
$505$	0	0
$506$	−8.74885	−0.388934
$507$	11.5084	0.511104
$508$	−24.0229	−1.06584
$509$	5.17101	0.229201	0.114601	−	0.993412i	$-0.463441\pi$
$509$	5.17101	0.229201	0.114601	+	0.993412i	$0.463441\pi$
$510$	0	0
$511$	−21.0201	−0.929876
$512$	−3.63755	−0.160759
$513$	−32.4412	−1.43231
$514$	−30.2543	−1.33446
$515$	0	0
$516$	83.3784	3.67053
$517$	−30.3944	−1.33674
$518$	−10.5352	−0.462890
$519$	−34.8664	−1.53047
$520$	0	0
$521$	−41.5944	−1.82229	−0.911143	−	0.412090i	$-0.864799\pi$
$521$	−41.5944	−1.82229	−0.911143	+	0.412090i	$0.864799\pi$
$522$	−60.0702	−2.62920
$523$	−15.7162	−0.687222	−0.343611	−	0.939112i	$-0.611650\pi$
$523$	−15.7162	−0.687222	−0.343611	+	0.939112i	$0.611650\pi$
$524$	−37.4339	−1.63531
$525$	0	0
$526$	29.6081	1.29097
$527$	14.4775	0.630648
$528$	−3.88762	−0.169187
$529$	1.00000	0.0434783
$530$	0	0
$531$	−48.3450	−2.09799
$532$	37.0599	1.60675
$533$	31.3009	1.35579
$534$	80.2688	3.47357
$535$	0	0
$536$	−31.7181	−1.37001
$537$	54.2391	2.34059
$538$	−23.9388	−1.03207
$539$	−45.8829	−1.97631
$540$	0	0
$541$	−1.96134	−0.0843248	−0.0421624	−	0.999111i	$-0.513425\pi$
$541$	−1.96134	−0.0843248	−0.0421624	+	0.999111i	$0.513425\pi$
$542$	−29.9446	−1.28623
$543$	−65.2404	−2.79973
$544$	−18.3088	−0.784981
$545$	0	0
$546$	94.6909	4.05240
$547$	4.36601	0.186677	0.0933386	−	0.995634i	$-0.470246\pi$
$547$	4.36601	0.186677	0.0933386	+	0.995634i	$0.470246\pi$
$548$	1.59660	0.0682034
$549$	−32.9493	−1.40624
$550$	0	0
$551$	10.4140	0.443652
$552$	−8.28825	−0.352771
$553$	21.5119	0.914778
$554$	25.2054	1.07088
$555$	0	0
$556$	39.0738	1.65710
$557$	22.3234	0.945875	0.472937	−	0.881096i	$-0.343194\pi$
$557$	22.3234	0.945875	0.472937	+	0.881096i	$0.343194\pi$
$558$	73.9240	3.12945
$559$	−25.6720	−1.08581
$560$	0	0
$561$	−36.7559	−1.55184
$562$	30.4035	1.28249
$563$	20.2690	0.854237	0.427118	−	0.904196i	$-0.359529\pi$
$563$	20.2690	0.854237	0.427118	+	0.904196i	$0.359529\pi$
$564$	−78.3158	−3.29769
$565$	0	0
$566$	−5.04113	−0.211895
$567$	75.0478	3.15171
$568$	−20.8582	−0.875189
$569$	−46.5440	−1.95122	−0.975612	−	0.219500i	$-0.929557\pi$
$569$	−46.5440	−1.95122	−0.975612	+	0.219500i	$0.929557\pi$
$570$	0	0
$571$	−15.3392	−0.641925	−0.320963	−	0.947092i	$-0.604006\pi$
$571$	−15.3392	−0.641925	−0.320963	+	0.947092i	$0.604006\pi$
$572$	−37.2010	−1.55545
$573$	−80.1069	−3.34651
$574$	−101.264	−4.22669
$575$	0	0
$576$	−89.0844	−3.71185
$577$	−39.0456	−1.62549	−0.812745	−	0.582620i	$-0.802028\pi$
$577$	−39.0456	−1.62549	−0.812745	+	0.582620i	$0.802028\pi$
$578$	17.5828	0.731347
$579$	−49.3593	−2.05130
$580$	0	0
$581$	−11.1686	−0.463353
$582$	47.6782	1.97632
$583$	10.8762	0.450447
$584$	12.7704	0.528441
$585$	0	0
$586$	−24.7575	−1.02272
$587$	17.8923	0.738495	0.369248	−	0.929331i	$-0.379615\pi$
$587$	17.8923	0.738495	0.369248	+	0.929331i	$0.379615\pi$
$588$	−118.224	−4.87549
$589$	−12.8158	−0.528065
$590$	0	0
$591$	−67.4964	−2.77643
$592$	−0.343147	−0.0141032
$593$	9.82459	0.403448	0.201724	−	0.979442i	$-0.435346\pi$
$593$	9.82459	0.403448	0.201724	+	0.979442i	$0.435346\pi$
$594$	−105.353	−4.32269
$595$	0	0
$596$	−18.0189	−0.738083
$597$	−2.39310	−0.0979429
$598$	6.94085	0.283833
$599$	−41.7073	−1.70411	−0.852057	−	0.523448i	$-0.824645\pi$
$599$	−41.7073	−1.70411	−0.852057	+	0.523448i	$0.824645\pi$
$600$	0	0
$601$	44.4299	1.81234	0.906168	−	0.422919i	$-0.138994\pi$
$601$	44.4299	1.81234	0.906168	+	0.422919i	$0.138994\pi$
$602$	83.0537	3.38502
$603$	82.0944	3.34314
$604$	−19.9340	−0.811102
$605$	0	0
$606$	52.0608	2.11483
$607$	19.2044	0.779481	0.389741	−	0.920925i	$-0.372565\pi$
$607$	19.2044	0.779481	0.389741	+	0.920925i	$0.372565\pi$
$608$	16.2073	0.657294
$609$	−52.7368	−2.13700
$610$	0	0
$611$	24.1132	0.975516
$612$	−65.8303	−2.66103
$613$	−48.7625	−1.96950	−0.984749	−	0.173980i	$-0.944337\pi$
$613$	−48.7625	−1.96950	−0.984749	+	0.173980i	$0.944337\pi$
$614$	57.4005	2.31650
$615$	0	0
$616$	44.2497	1.78287
$617$	−21.5623	−0.868065	−0.434032	−	0.900897i	$-0.642910\pi$
$617$	−21.5623	−0.868065	−0.434032	+	0.900897i	$0.642910\pi$
$618$	42.9311	1.72694
$619$	47.0797	1.89229	0.946147	−	0.323737i	$-0.104939\pi$
$619$	47.0797	1.89229	0.946147	+	0.323737i	$0.104939\pi$
$620$	0	0
$621$	12.0419	0.483226
$622$	−13.4068	−0.537563
$623$	48.9828	1.96246
$624$	3.08422	0.123468
$625$	0	0
$626$	39.7286	1.58787
$627$	32.5372	1.29941
$628$	57.4514	2.29256
$629$	−3.24432	−0.129360
$630$	0	0
$631$	−13.7810	−0.548611	−0.274305	−	0.961643i	$-0.588448\pi$
$631$	−13.7810	−0.548611	−0.274305	+	0.961643i	$0.588448\pi$
$632$	−13.0691	−0.519861
$633$	86.2145	3.42672
$634$	28.2242	1.12093
$635$	0	0
$636$	28.0242	1.11123
$637$	36.4009	1.44226
$638$	33.8197	1.33893
$639$	53.9862	2.13566
$640$	0	0
$641$	−16.1054	−0.636124	−0.318062	−	0.948070i	$-0.603032\pi$
$641$	−16.1054	−0.636124	−0.318062	+	0.948070i	$0.603032\pi$
$642$	9.52919	0.376087
$643$	0.504543	0.0198972	0.00994861	−	0.999951i	$-0.496833\pi$
$643$	0.504543	0.0198972	0.00994861	+	0.999951i	$0.496833\pi$
$644$	−13.7564	−0.542078
$645$	0	0
$646$	18.6292	0.732956
$647$	14.0128	0.550901	0.275450	−	0.961315i	$-0.411173\pi$
$647$	14.0128	0.550901	0.275450	+	0.961315i	$0.411173\pi$
$648$	−45.5938	−1.79109
$649$	27.2184	1.06841
$650$	0	0
$651$	64.8994	2.54361
$652$	8.44649	0.330790
$653$	31.2463	1.22276	0.611380	−	0.791337i	$-0.290615\pi$
$653$	31.2463	1.22276	0.611380	+	0.791337i	$0.290615\pi$
$654$	98.7765	3.86247
$655$	0	0
$656$	−3.29833	−0.128778
$657$	−33.0529	−1.28952
$658$	−78.0109	−3.04118
$659$	−6.53474	−0.254557	−0.127279	−	0.991867i	$-0.540624\pi$
$659$	−6.53474	−0.254557	−0.127279	+	0.991867i	$0.540624\pi$
$660$	0	0
$661$	10.5596	0.410721	0.205360	−	0.978686i	$-0.434163\pi$
$661$	10.5596	0.410721	0.205360	+	0.978686i	$0.434163\pi$
$662$	−42.9060	−1.66759
$663$	29.1601	1.13249
$664$	6.78528	0.263320
$665$	0	0
$666$	−16.5660	−0.641919
$667$	−3.86561	−0.149677
$668$	12.3831	0.479116
$669$	5.51568	0.213249
$670$	0	0
$671$	18.5506	0.716136
$672$	−82.0743	−3.16608
$673$	−14.0478	−0.541504	−0.270752	−	0.962649i	$-0.587272\pi$
$673$	−14.0478	−0.541504	−0.270752	+	0.962649i	$0.587272\pi$
$674$	37.6434	1.44997
$675$	0	0
$676$	−11.6044	−0.446323
$677$	23.1788	0.890835	0.445417	−	0.895323i	$-0.353055\pi$
$677$	23.1788	0.890835	0.445417	+	0.895323i	$0.353055\pi$
$678$	61.1268	2.34756
$679$	29.0949	1.11656
$680$	0	0
$681$	−0.828392	−0.0317441
$682$	−41.6194	−1.59369
$683$	26.2195	1.00326	0.501631	−	0.865081i	$-0.332733\pi$
$683$	26.2195	1.00326	0.501631	+	0.865081i	$0.332733\pi$
$684$	58.2745	2.22818
$685$	0	0
$686$	−48.5866	−1.85504
$687$	48.6036	1.85434
$688$	2.70518	0.103134
$689$	−8.62858	−0.328723
$690$	0	0
$691$	−12.6788	−0.482324	−0.241162	−	0.970485i	$-0.577529\pi$
$691$	−12.6788	−0.482324	−0.241162	+	0.970485i	$0.577529\pi$
$692$	35.1573	1.33648
$693$	−114.530	−4.35062
$694$	24.8997	0.945179
$695$	0	0
$696$	32.0392	1.21444
$697$	−31.1844	−1.18119
$698$	−45.7609	−1.73207
$699$	−7.27164	−0.275039
$700$	0	0
$701$	23.1324	0.873700	0.436850	−	0.899534i	$-0.356094\pi$
$701$	23.1324	0.873700	0.436850	+	0.899534i	$0.356094\pi$
$702$	83.5813	3.15457
$703$	2.87195	0.108318
$704$	50.1547	1.89028
$705$	0	0
$706$	46.3050	1.74271
$707$	31.7693	1.19481
$708$	70.1324	2.63574
$709$	−20.9777	−0.787834	−0.393917	−	0.919146i	$-0.628880\pi$
$709$	−20.9777	−0.787834	−0.393917	+	0.919146i	$0.628880\pi$
$710$	0	0
$711$	33.8261	1.26858
$712$	−29.7585	−1.11525
$713$	4.75713	0.178156
$714$	−94.3386	−3.53053
$715$	0	0
$716$	−54.6917	−2.04392
$717$	−61.9759	−2.31453
$718$	58.3624	2.17806
$719$	−3.02524	−0.112822	−0.0564111	−	0.998408i	$-0.517966\pi$
$719$	−3.02524	−0.112822	−0.0564111	+	0.998408i	$0.517966\pi$
$720$	0	0
$721$	26.1981	0.975668
$722$	26.6808	0.992957
$723$	−94.0569	−3.49802
$724$	65.7848	2.44487
$725$	0	0
$726$	27.2651	1.01190
$727$	43.3149	1.60646	0.803230	−	0.595669i	$-0.203113\pi$
$727$	43.3149	1.60646	0.803230	+	0.595669i	$0.203113\pi$
$728$	−35.1053	−1.30109
$729$	4.69165	0.173765
$730$	0	0
$731$	25.5765	0.945979
$732$	47.7984	1.76668
$733$	−19.3359	−0.714186	−0.357093	−	0.934069i	$-0.616232\pi$
$733$	−19.3359	−0.714186	−0.357093	+	0.934069i	$0.616232\pi$
$734$	−62.6284	−2.31166
$735$	0	0
$736$	−6.01605	−0.221755
$737$	−46.2194	−1.70251
$738$	−159.232	−5.86142
$739$	14.4819	0.532725	0.266363	−	0.963873i	$-0.414178\pi$
$739$	14.4819	0.532725	0.266363	+	0.963873i	$0.414178\pi$
$740$	0	0
$741$	−25.8132	−0.948272
$742$	27.9151	1.02480
$743$	47.0441	1.72588	0.862941	−	0.505305i	$-0.168620\pi$
$743$	47.0441	1.72588	0.862941	+	0.505305i	$0.168620\pi$
$744$	−39.4283	−1.44551
$745$	0	0
$746$	47.8112	1.75049
$747$	−17.5620	−0.642561
$748$	37.0626	1.35514
$749$	5.81504	0.212477
$750$	0	0
$751$	9.47856	0.345878	0.172939	−	0.984933i	$-0.444674\pi$
$751$	9.47856	0.345878	0.172939	+	0.984933i	$0.444674\pi$
$752$	−2.54093	−0.0926581
$753$	32.3607	1.17929
$754$	−26.8307	−0.977115
$755$	0	0
$756$	−165.654	−6.02476
$757$	42.4538	1.54301	0.771505	−	0.636223i	$-0.219504\pi$
$757$	42.4538	1.54301	0.771505	+	0.636223i	$0.219504\pi$
$758$	−1.05916	−0.0384705
$759$	−12.0776	−0.438389
$760$	0	0
$761$	15.6711	0.568076	0.284038	−	0.958813i	$-0.408326\pi$
$761$	15.6711	0.568076	0.284038	+	0.958813i	$0.408326\pi$
$762$	−54.1331	−1.96103
$763$	60.2769	2.18217
$764$	80.7753	2.92235
$765$	0	0
$766$	−71.9984	−2.60141
$767$	−21.5935	−0.779698
$768$	43.4756	1.56879
$769$	12.7546	0.459944	0.229972	−	0.973197i	$-0.426137\pi$
$769$	12.7546	0.459944	0.229972	+	0.973197i	$0.426137\pi$
$770$	0	0
$771$	−41.7654	−1.50415
$772$	49.7712	1.79130
$773$	16.4845	0.592907	0.296454	−	0.955047i	$-0.404196\pi$
$773$	16.4845	0.592907	0.296454	+	0.955047i	$0.404196\pi$
$774$	130.597	4.69422
$775$	0	0
$776$	−17.6760	−0.634532
$777$	−14.5436	−0.521749
$778$	−24.7790	−0.888369
$779$	27.6052	0.989058
$780$	0	0
$781$	−30.3944	−1.08760
$782$	−6.91503	−0.247281
$783$	−46.5495	−1.66354
$784$	−3.83575	−0.136991
$785$	0	0
$786$	−84.3534	−3.00879
$787$	−5.32270	−0.189734	−0.0948668	−	0.995490i	$-0.530243\pi$
$787$	−5.32270	−0.189734	−0.0948668	+	0.995490i	$0.530243\pi$
$788$	68.0596	2.42452
$789$	40.8732	1.45513
$790$	0	0
$791$	37.3017	1.32630
$792$	69.5801	2.47242
$793$	−14.7170	−0.522615
$794$	39.6261	1.40628
$795$	0	0
$796$	2.41307	0.0855288
$797$	28.3536	1.00433	0.502167	−	0.864770i	$-0.332536\pi$
$797$	28.3536	1.00433	0.502167	+	0.864770i	$0.332536\pi$
$798$	83.5107	2.95625
$799$	−24.0235	−0.849890
$800$	0	0
$801$	77.0226	2.72146
$802$	−61.2636	−2.16329
$803$	18.6089	0.656693
$804$	−119.091	−4.20003
$805$	0	0
$806$	33.0185	1.16303
$807$	−33.0469	−1.16331
$808$	−19.3008	−0.679000
$809$	−7.59007	−0.266853	−0.133426	−	0.991059i	$-0.542598\pi$
$809$	−7.59007	−0.266853	−0.133426	+	0.991059i	$0.542598\pi$
$810$	0	0
$811$	25.8314	0.907063	0.453532	−	0.891240i	$-0.350164\pi$
$811$	25.8314	0.907063	0.453532	+	0.891240i	$0.350164\pi$
$812$	53.1769	1.86614
$813$	−41.3378	−1.44978
$814$	9.32669	0.326900
$815$	0	0
$816$	−3.07275	−0.107568
$817$	−22.6409	−0.792104
$818$	42.6171	1.49007
$819$	90.8614	3.17496
$820$	0	0
$821$	7.76281	0.270924	0.135462	−	0.990783i	$-0.456748\pi$
$821$	7.76281	0.270924	0.135462	+	0.990783i	$0.456748\pi$
$822$	3.59778	0.125487
$823$	−6.53060	−0.227642	−0.113821	−	0.993501i	$-0.536309\pi$
$823$	−6.53060	−0.227642	−0.113821	+	0.993501i	$0.536309\pi$
$824$	−15.9161	−0.554464
$825$	0	0
$826$	69.8593	2.43071
$827$	−31.6531	−1.10069	−0.550343	−	0.834938i	$-0.685503\pi$
$827$	−31.6531	−1.10069	−0.550343	+	0.834938i	$0.685503\pi$
$828$	−21.6311	−0.751733
$829$	36.8740	1.28069	0.640344	−	0.768088i	$-0.278792\pi$
$829$	36.8740	1.28069	0.640344	+	0.768088i	$0.278792\pi$
$830$	0	0
$831$	34.7955	1.20704
$832$	−39.7900	−1.37947
$833$	−36.2655	−1.25652
$834$	88.0488	3.04888
$835$	0	0
$836$	−32.8087	−1.13471
$837$	57.2851	1.98006
$838$	−39.4822	−1.36389
$839$	20.8121	0.718512	0.359256	−	0.933239i	$-0.383030\pi$
$839$	20.8121	0.718512	0.359256	+	0.933239i	$0.383030\pi$
$840$	0	0
$841$	−14.0570	−0.484725
$842$	17.0526	0.587672
$843$	41.9713	1.44557
$844$	−86.9339	−2.99239
$845$	0	0
$846$	−122.667	−4.21740
$847$	16.6381	0.571692
$848$	0.909236	0.0312233
$849$	−6.95917	−0.238838
$850$	0	0
$851$	−1.06605	−0.0365436
$852$	−78.3158	−2.68306
$853$	−40.4842	−1.38615	−0.693077	−	0.720864i	$-0.743745\pi$
$853$	−40.4842	−1.38615	−0.693077	+	0.720864i	$0.743745\pi$
$854$	47.6123	1.62926
$855$	0	0
$856$	−3.53281	−0.120749
$857$	−35.4839	−1.21211	−0.606054	−	0.795423i	$-0.707249\pi$
$857$	−35.4839	−1.21211	−0.606054	+	0.795423i	$0.707249\pi$
$858$	−83.8287	−2.86187
$859$	−21.2494	−0.725019	−0.362510	−	0.931980i	$-0.618080\pi$
$859$	−21.2494	−0.725019	−0.362510	+	0.931980i	$0.618080\pi$
$860$	0	0
$861$	−139.793	−4.76414
$862$	44.3226	1.50963
$863$	−20.1312	−0.685274	−0.342637	−	0.939468i	$-0.611320\pi$
$863$	−20.1312	−0.685274	−0.342637	+	0.939468i	$0.611320\pi$
$864$	−72.4449	−2.46463
$865$	0	0
$866$	87.9711	2.98938
$867$	24.2726	0.824341
$868$	−65.4409	−2.22121
$869$	−19.0442	−0.646030
$870$	0	0
$871$	36.6679	1.24244
$872$	−36.6200	−1.24011
$873$	45.7500	1.54840
$874$	6.12134	0.207058
$875$	0	0
$876$	47.9487	1.62004
$877$	16.9571	0.572600	0.286300	−	0.958140i	$-0.407575\pi$
$877$	16.9571	0.572600	0.286300	+	0.958140i	$0.407575\pi$
$878$	−55.4982	−1.87297
$879$	−34.1771	−1.15277
$880$	0	0
$881$	−22.0047	−0.741356	−0.370678	−	0.928762i	$-0.620875\pi$
$881$	−22.0047	−0.741356	−0.370678	+	0.928762i	$0.620875\pi$
$882$	−185.177	−6.23523
$883$	−43.0831	−1.44986	−0.724931	−	0.688821i	$-0.758129\pi$
$883$	−43.0831	−1.44986	−0.724931	+	0.688821i	$0.758129\pi$
$884$	−29.4034	−0.988945
$885$	0	0
$886$	18.8139	0.632064
$887$	−41.4084	−1.39036	−0.695179	−	0.718837i	$-0.744675\pi$
$887$	−41.4084	−1.39036	−0.695179	+	0.718837i	$0.744675\pi$
$888$	8.83567	0.296506
$889$	−33.0339	−1.10792
$890$	0	0
$891$	−66.4389	−2.22579
$892$	−5.56171	−0.186220
$893$	21.2662	0.711645
$894$	−40.6037	−1.35799
$895$	0	0
$896$	76.3970	2.55225
$897$	9.58169	0.319923
$898$	29.6790	0.990400
$899$	−18.3892	−0.613315
$900$	0	0
$901$	8.59648	0.286390
$902$	89.6481	2.98496
$903$	114.654	3.81544
$904$	−22.6619	−0.753723
$905$	0	0
$906$	−44.9192	−1.49234
$907$	−44.5134	−1.47804	−0.739022	−	0.673681i	$-0.764712\pi$
$907$	−44.5134	−1.47804	−0.739022	+	0.673681i	$0.764712\pi$
$908$	0.835305	0.0277206
$909$	49.9554	1.65692
$910$	0	0
$911$	36.1026	1.19613	0.598066	−	0.801447i	$-0.295936\pi$
$911$	36.1026	1.19613	0.598066	+	0.801447i	$0.295936\pi$
$912$	2.72007	0.0900704
$913$	9.88746	0.327227
$914$	−52.6200	−1.74051
$915$	0	0
$916$	−49.0092	−1.61931
$917$	−51.4754	−1.69987
$918$	−83.2703	−2.74833
$919$	−47.8205	−1.57745	−0.788727	−	0.614743i	$-0.789260\pi$
$919$	−47.8205	−1.57745	−0.788727	+	0.614743i	$0.789260\pi$
$920$	0	0
$921$	79.2401	2.61105
$922$	35.4811	1.16851
$923$	24.1132	0.793696
$924$	166.144	5.46573
$925$	0	0
$926$	−57.8148	−1.89991
$927$	41.1949	1.35302
$928$	23.2557	0.763407
$929$	−19.8647	−0.651739	−0.325870	−	0.945415i	$-0.605657\pi$
$929$	−19.8647	−0.651739	−0.325870	+	0.945415i	$0.605657\pi$
$930$	0	0
$931$	32.1031	1.05214
$932$	7.33232	0.240178
$933$	−18.5077	−0.605916
$934$	2.13323	0.0698014
$935$	0	0
$936$	−55.2010	−1.80430
$937$	11.8180	0.386077	0.193039	−	0.981191i	$-0.438166\pi$
$937$	11.8180	0.386077	0.193039	+	0.981191i	$0.438166\pi$
$938$	−118.628	−3.87333
$939$	54.8445	1.78978
$940$	0	0
$941$	12.8621	0.419292	0.209646	−	0.977777i	$-0.432769\pi$
$941$	12.8621	0.419292	0.209646	+	0.977777i	$0.432769\pi$
$942$	129.461	4.21807
$943$	−10.2468	−0.333683
$944$	2.27542	0.0740586
$945$	0	0
$946$	−73.5265	−2.39055
$947$	21.8068	0.708626	0.354313	−	0.935127i	$-0.384715\pi$
$947$	21.8068	0.708626	0.354313	+	0.935127i	$0.384715\pi$
$948$	−49.0703	−1.59373
$949$	−14.7633	−0.479235
$950$	0	0
$951$	38.9629	1.26346
$952$	34.9747	1.13354
$953$	6.34377	0.205495	0.102747	−	0.994707i	$-0.467237\pi$
$953$	6.34377	0.205495	0.102747	+	0.994707i	$0.467237\pi$
$954$	43.8949	1.42115
$955$	0	0
$956$	62.4930	2.02117
$957$	46.6873	1.50919
$958$	−44.7250	−1.44500
$959$	2.19549	0.0708961
$960$	0	0
$961$	−8.36971	−0.269991
$962$	−7.39928	−0.238562
$963$	9.14381	0.294655
$964$	94.8418	3.05465
$965$	0	0
$966$	−30.9986	−0.997364
$967$	−10.5486	−0.339221	−0.169611	−	0.985511i	$-0.554251\pi$
$967$	−10.5486	−0.339221	−0.169611	+	0.985511i	$0.554251\pi$
$968$	−10.1081	−0.324888
$969$	25.7172	0.826155
$970$	0	0
$971$	−26.8501	−0.861661	−0.430830	−	0.902433i	$-0.641779\pi$
$971$	−26.8501	−0.861661	−0.430830	+	0.902433i	$0.641779\pi$
$972$	−56.9282	−1.82597
$973$	53.7304	1.72252
$974$	10.3716	0.332329
$975$	0	0
$976$	1.55080	0.0496399
$977$	−43.3776	−1.38777	−0.693886	−	0.720084i	$-0.744103\pi$
$977$	−43.3776	−1.38777	−0.693886	+	0.720084i	$0.744103\pi$
$978$	19.0333	0.608618
$979$	−43.3639	−1.38592
$980$	0	0
$981$	94.7818	3.02615
$982$	58.6881	1.87281
$983$	−57.7079	−1.84060	−0.920299	−	0.391216i	$-0.872054\pi$
$983$	−57.7079	−1.84060	−0.920299	+	0.391216i	$0.872054\pi$
$984$	84.9285	2.70742
$985$	0	0
$986$	26.7308	0.851283
$987$	−107.692	−3.42788
$988$	26.0286	0.828080
$989$	8.40413	0.267236
$990$	0	0
$991$	−32.2625	−1.02485	−0.512427	−	0.858731i	$-0.671253\pi$
$991$	−32.2625	−1.02485	−0.512427	+	0.858731i	$0.671253\pi$
$992$	−28.6191	−0.908659
$993$	−59.2307	−1.87963
$994$	−78.0109	−2.47435
$995$	0	0
$996$	25.4766	0.807256
$997$	−13.5410	−0.428847	−0.214424	−	0.976741i	$-0.568787\pi$
$997$	−13.5410	−0.428847	−0.214424	+	0.976741i	$0.568787\pi$
$998$	−70.2350	−2.22325
$999$	−12.8373	−0.406153

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.a.k.1.2	✓	7
3.2	odd	2		5175.2.a.cg.1.6		7
4.3	odd	2		9200.2.a.da.1.7		7
5.2	odd	4		575.2.b.f.24.3		14
5.3	odd	4		575.2.b.f.24.12		14
5.4	even	2		575.2.a.l.1.6	yes	7
15.14	odd	2		5175.2.a.cb.1.2		7
20.19	odd	2		9200.2.a.db.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
575.2.a.k.1.2	✓	7	1.1	even	1	trivial
575.2.a.l.1.6	yes	7	5.4	even	2
575.2.b.f.24.3		14	5.2	odd	4
575.2.b.f.24.12		14	5.3	odd	4
5175.2.a.cb.1.2		7	15.14	odd	2
5175.2.a.cg.1.6		7	3.2	odd	2
9200.2.a.da.1.7		7	4.3	odd	2
9200.2.a.db.1.1		7	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.a (trivial)

\(f(q)\)	\(=\)	\(q-2.27220 q^{2} -3.13672 q^{3} +3.16289 q^{4} +7.12726 q^{6} +4.34930 q^{7} -2.64233 q^{8} +6.83902 q^{9} +O(q^{10})\)	\(q-2.27220 q^{2} -3.13672 q^{3} +3.16289 q^{4} +7.12726 q^{6} +4.34930 q^{7} -2.64233 q^{8} +6.83902 q^{9} -3.85039 q^{11} -9.92112 q^{12} +3.05468 q^{13} -9.88249 q^{14} -0.321887 q^{16} -3.04332 q^{17} -15.5396 q^{18} +2.69402 q^{19} -13.6425 q^{21} +8.74885 q^{22} -1.00000 q^{23} +8.28825 q^{24} -6.94085 q^{26} -12.0419 q^{27} +13.7564 q^{28} +3.86561 q^{29} -4.75713 q^{31} +6.01605 q^{32} +12.0776 q^{33} +6.91503 q^{34} +21.6311 q^{36} +1.06605 q^{37} -6.12134 q^{38} -9.58169 q^{39} +10.2468 q^{41} +30.9986 q^{42} -8.40413 q^{43} -12.1784 q^{44} +2.27220 q^{46} +7.89385 q^{47} +1.00967 q^{48} +11.9164 q^{49} +9.54604 q^{51} +9.66164 q^{52} -2.82471 q^{53} +27.3617 q^{54} -11.4923 q^{56} -8.45038 q^{57} -8.78345 q^{58} -7.06900 q^{59} -4.81784 q^{61} +10.8092 q^{62} +29.7450 q^{63} -13.0259 q^{64} -27.4427 q^{66} +12.0038 q^{67} -9.62569 q^{68} +3.13672 q^{69} +7.89385 q^{71} -18.0709 q^{72} -4.83299 q^{73} -2.42227 q^{74} +8.52089 q^{76} -16.7465 q^{77} +21.7715 q^{78} +4.94605 q^{79} +17.2551 q^{81} -23.2829 q^{82} -2.56791 q^{83} -43.1499 q^{84} +19.0959 q^{86} -12.1254 q^{87} +10.1740 q^{88} +11.2622 q^{89} +13.2857 q^{91} -3.16289 q^{92} +14.9218 q^{93} -17.9364 q^{94} -18.8707 q^{96} +6.68955 q^{97} -27.0765 q^{98} -26.3329 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 11 q^{4} + 5 q^{6} + 3 q^{7} - 6 q^{8} + 15 q^{9}+O(q^{10}) \) 7 * q - q^2 + 11 * q^4 + 5 * q^6 + 3 * q^7 - 6 * q^8 + 15 * q^9	\( 7 q - q^{2} + 11 q^{4} + 5 q^{6} + 3 q^{7} - 6 q^{8} + 15 q^{9} - q^{11} + 6 q^{12} - 3 q^{13} + 7 q^{14} + 7 q^{16} + 10 q^{17} - 24 q^{18} + 15 q^{19} + 2 q^{21} + 21 q^{22} - 7 q^{23} + 18 q^{24} - 20 q^{26} - 11 q^{28} + 3 q^{29} + 14 q^{31} + 17 q^{32} + 6 q^{33} + 20 q^{34} - 10 q^{37} - 31 q^{38} - 8 q^{39} + 19 q^{41} + 44 q^{42} + 5 q^{43} - 3 q^{44} + q^{46} - 14 q^{47} - 27 q^{48} + 40 q^{49} + 2 q^{51} + 16 q^{52} + 4 q^{53} - q^{54} - 9 q^{56} - 4 q^{57} - 13 q^{58} - 16 q^{59} + 40 q^{61} - 12 q^{62} + 53 q^{63} - 4 q^{64} - 54 q^{66} - 4 q^{67} + 20 q^{68} - 14 q^{71} - 6 q^{72} - 3 q^{73} - 18 q^{74} + 35 q^{76} - 17 q^{77} + 23 q^{78} - q^{79} + 47 q^{81} - 22 q^{82} + 17 q^{83} - 60 q^{84} - 35 q^{86} - 56 q^{87} + 57 q^{88} + 16 q^{89} + 25 q^{91} - 11 q^{92} + 14 q^{93} + 7 q^{94} - 19 q^{96} - 24 q^{97} - 46 q^{98} - 53 q^{99}+O(q^{100}) \) 7 * q - q^2 + 11 * q^4 + 5 * q^6 + 3 * q^7 - 6 * q^8 + 15 * q^9 - q^11 + 6 * q^12 - 3 * q^13 + 7 * q^14 + 7 * q^16 + 10 * q^17 - 24 * q^18 + 15 * q^19 + 2 * q^21 + 21 * q^22 - 7 * q^23 + 18 * q^24 - 20 * q^26 - 11 * q^28 + 3 * q^29 + 14 * q^31 + 17 * q^32 + 6 * q^33 + 20 * q^34 - 10 * q^37 - 31 * q^38 - 8 * q^39 + 19 * q^41 + 44 * q^42 + 5 * q^43 - 3 * q^44 + q^46 - 14 * q^47 - 27 * q^48 + 40 * q^49 + 2 * q^51 + 16 * q^52 + 4 * q^53 - q^54 - 9 * q^56 - 4 * q^57 - 13 * q^58 - 16 * q^59 + 40 * q^61 - 12 * q^62 + 53 * q^63 - 4 * q^64 - 54 * q^66 - 4 * q^67 + 20 * q^68 - 14 * q^71 - 6 * q^72 - 3 * q^73 - 18 * q^74 + 35 * q^76 - 17 * q^77 + 23 * q^78 - q^79 + 47 * q^81 - 22 * q^82 + 17 * q^83 - 60 * q^84 - 35 * q^86 - 56 * q^87 + 57 * q^88 + 16 * q^89 + 25 * q^91 - 11 * q^92 + 14 * q^93 + 7 * q^94 - 19 * q^96 - 24 * q^97 - 46 * q^98 - 53 * q^99

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