LMFDB - Embedded newform 4025.2.a.t.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$1$
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} - x^{7} - 11x^{6} + 9x^{5} + 36x^{4} - 23x^{3} - 30x^{2} + 17x - 2 $ x^8 - x^7 - 11x^6 + 9x^5 + 36x^4 - 23x^3 - 30x^2 + 17x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.28656$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.28656 q^{2} -2.13745 q^{3} +3.22836 q^{4} +4.88741 q^{6} -1.00000 q^{7} -2.80872 q^{8} +1.56870 q^{9} +O(q^{10})$	\(q-2.28656 q^{2} -2.13745 q^{3} +3.22836 q^{4} +4.88741 q^{6} -1.00000 q^{7} -2.80872 q^{8} +1.56870 q^{9} -3.22604 q^{11} -6.90046 q^{12} +1.60085 q^{13} +2.28656 q^{14} -0.0344172 q^{16} +2.87997 q^{17} -3.58693 q^{18} -4.80956 q^{19} +2.13745 q^{21} +7.37655 q^{22} -1.00000 q^{23} +6.00350 q^{24} -3.66045 q^{26} +3.05933 q^{27} -3.22836 q^{28} +1.87380 q^{29} +3.43651 q^{31} +5.69613 q^{32} +6.89552 q^{33} -6.58522 q^{34} +5.06433 q^{36} -1.21739 q^{37} +10.9973 q^{38} -3.42175 q^{39} +2.67368 q^{41} -4.88741 q^{42} -4.93806 q^{43} -10.4148 q^{44} +2.28656 q^{46} -12.6545 q^{47} +0.0735651 q^{48} +1.00000 q^{49} -6.15579 q^{51} +5.16813 q^{52} +6.12961 q^{53} -6.99535 q^{54} +2.80872 q^{56} +10.2802 q^{57} -4.28456 q^{58} +5.88555 q^{59} +7.75465 q^{61} -7.85778 q^{62} -1.56870 q^{63} -12.9557 q^{64} -15.7670 q^{66} +1.68023 q^{67} +9.29757 q^{68} +2.13745 q^{69} +5.28536 q^{71} -4.40604 q^{72} -8.29066 q^{73} +2.78363 q^{74} -15.5270 q^{76} +3.22604 q^{77} +7.82403 q^{78} -7.14557 q^{79} -11.2453 q^{81} -6.11353 q^{82} -9.49563 q^{83} +6.90046 q^{84} +11.2912 q^{86} -4.00516 q^{87} +9.06104 q^{88} -1.12606 q^{89} -1.60085 q^{91} -3.22836 q^{92} -7.34537 q^{93} +28.9352 q^{94} -12.1752 q^{96} -1.29227 q^{97} -2.28656 q^{98} -5.06070 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 7 q^{3} + 7 q^{4} + q^{6} - 8 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) $ 8 * q - q^2 - 7 * q^3 + 7 * q^4 + q^6 - 8 * q^7 - 3 * q^8 + 9 * q^9	$ 8 q - q^{2} - 7 q^{3} + 7 q^{4} + q^{6} - 8 q^{7} - 3 q^{8} + 9 q^{9} + 6 q^{11} - 8 q^{12} - 8 q^{13} + q^{14} + q^{16} - 4 q^{17} + 11 q^{18} + 7 q^{21} + 8 q^{22} - 8 q^{23} - 8 q^{24} + 2 q^{26} - 28 q^{27} - 7 q^{28} - 3 q^{29} - 16 q^{31} - 12 q^{32} - 5 q^{33} - 4 q^{34} - 14 q^{36} + 7 q^{37} - 11 q^{38} + 16 q^{39} + 7 q^{41} - q^{42} + 10 q^{43} + 7 q^{44} + q^{46} - 19 q^{47} + 6 q^{48} + 8 q^{49} + 7 q^{51} - 18 q^{52} + q^{53} - 25 q^{54} + 3 q^{56} + 25 q^{57} + 9 q^{58} + 21 q^{59} - 7 q^{61} - 18 q^{62} - 9 q^{63} - 37 q^{64} - 43 q^{66} - 11 q^{67} + 17 q^{68} + 7 q^{69} + 8 q^{71} - 4 q^{72} + 3 q^{73} + 12 q^{74} + 8 q^{76} - 6 q^{77} + 50 q^{78} - 15 q^{79} + 28 q^{81} - 41 q^{82} - 25 q^{83} + 8 q^{84} - 12 q^{86} - 21 q^{87} + 29 q^{88} + q^{89} + 8 q^{91} - 7 q^{92} + 5 q^{93} - 36 q^{94} + 30 q^{96} - 10 q^{97} - q^{98} - 18 q^{99}+O(q^{100}) $ 8 * q - q^2 - 7 * q^3 + 7 * q^4 + q^6 - 8 * q^7 - 3 * q^8 + 9 * q^9 + 6 * q^11 - 8 * q^12 - 8 * q^13 + q^14 + q^16 - 4 * q^17 + 11 * q^18 + 7 * q^21 + 8 * q^22 - 8 * q^23 - 8 * q^24 + 2 * q^26 - 28 * q^27 - 7 * q^28 - 3 * q^29 - 16 * q^31 - 12 * q^32 - 5 * q^33 - 4 * q^34 - 14 * q^36 + 7 * q^37 - 11 * q^38 + 16 * q^39 + 7 * q^41 - q^42 + 10 * q^43 + 7 * q^44 + q^46 - 19 * q^47 + 6 * q^48 + 8 * q^49 + 7 * q^51 - 18 * q^52 + q^53 - 25 * q^54 + 3 * q^56 + 25 * q^57 + 9 * q^58 + 21 * q^59 - 7 * q^61 - 18 * q^62 - 9 * q^63 - 37 * q^64 - 43 * q^66 - 11 * q^67 + 17 * q^68 + 7 * q^69 + 8 * q^71 - 4 * q^72 + 3 * q^73 + 12 * q^74 + 8 * q^76 - 6 * q^77 + 50 * q^78 - 15 * q^79 + 28 * q^81 - 41 * q^82 - 25 * q^83 + 8 * q^84 - 12 * q^86 - 21 * q^87 + 29 * q^88 + q^89 + 8 * q^91 - 7 * q^92 + 5 * q^93 - 36 * q^94 + 30 * q^96 - 10 * q^97 - q^98 - 18 * 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 $

$2$	−2.28656	−1.61684	−0.808421	−	0.588604i	$-0.799678\pi$
$2$	−2.28656	−1.61684	−0.808421	+	0.588604i	$0.799678\pi$
$3$	−2.13745	−1.23406	−0.617029	−	0.786940i	$-0.711664\pi$
$3$	−2.13745	−1.23406	−0.617029	+	0.786940i	$0.711664\pi$
$4$	3.22836	1.61418
$5$	0	0
$5$	0	0
$6$	4.88741	1.99528
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.80872	−0.993031
$9$	1.56870	0.522901
$10$	0	0
$11$	−3.22604	−0.972689	−0.486344	−	0.873767i	$-0.661670\pi$
$11$	−3.22604	−0.972689	−0.486344	+	0.873767i	$0.661670\pi$
$12$	−6.90046	−1.99199
$13$	1.60085	0.443997	0.221998	−	0.975047i	$-0.428742\pi$
$13$	1.60085	0.443997	0.221998	+	0.975047i	$0.428742\pi$
$14$	2.28656	0.611109
$15$	0	0
$16$	−0.0344172	−0.00860429
$17$	2.87997	0.698495	0.349247	−	0.937031i	$-0.386437\pi$
$17$	2.87997	0.698495	0.349247	+	0.937031i	$0.386437\pi$
$18$	−3.58693	−0.845448
$19$	−4.80956	−1.10339	−0.551694	−	0.834047i	$-0.686018\pi$
$19$	−4.80956	−1.10339	−0.551694	+	0.834047i	$0.686018\pi$
$20$	0	0
$21$	2.13745	0.466430
$22$	7.37655	1.57268
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	6.00350	1.22546
$25$	0	0
$26$	−3.66045	−0.717873
$27$	3.05933	0.588769
$28$	−3.22836	−0.610102
$29$	1.87380	0.347956	0.173978	−	0.984749i	$-0.444338\pi$
$29$	1.87380	0.347956	0.173978	+	0.984749i	$0.444338\pi$
$30$	0	0
$31$	3.43651	0.617215	0.308608	−	0.951189i	$-0.400137\pi$
$31$	3.43651	0.617215	0.308608	+	0.951189i	$0.400137\pi$
$32$	5.69613	1.00694
$33$	6.89552	1.20036
$34$	−6.58522	−1.12936
$35$	0	0
$36$	5.06433	0.844055
$37$	−1.21739	−0.200138	−0.100069	−	0.994981i	$-0.531906\pi$
$37$	−1.21739	−0.200138	−0.100069	+	0.994981i	$0.531906\pi$
$38$	10.9973	1.78400
$39$	−3.42175	−0.547918
$40$	0	0
$41$	2.67368	0.417559	0.208779	−	0.977963i	$-0.433051\pi$
$41$	2.67368	0.417559	0.208779	+	0.977963i	$0.433051\pi$
$42$	−4.88741	−0.754144
$43$	−4.93806	−0.753047	−0.376523	−	0.926407i	$-0.622881\pi$
$43$	−4.93806	−0.753047	−0.376523	+	0.926407i	$0.622881\pi$
$44$	−10.4148	−1.57009
$45$	0	0
$46$	2.28656	0.337135
$47$	−12.6545	−1.84584	−0.922922	−	0.384986i	$-0.874206\pi$
$47$	−12.6545	−1.84584	−0.922922	+	0.384986i	$0.874206\pi$
$48$	0.0735651	0.0106182
$49$	1.00000	0.142857
$50$	0	0
$51$	−6.15579	−0.861983
$52$	5.16813	0.716690
$53$	6.12961	0.841967	0.420984	−	0.907068i	$-0.361685\pi$
$53$	6.12961	0.841967	0.420984	+	0.907068i	$0.361685\pi$
$54$	−6.99535	−0.951946
$55$	0	0
$56$	2.80872	0.375331
$57$	10.2802	1.36165
$58$	−4.28456	−0.562591
$59$	5.88555	0.766233	0.383117	−	0.923700i	$-0.374851\pi$
$59$	5.88555	0.766233	0.383117	+	0.923700i	$0.374851\pi$
$60$	0	0
$61$	7.75465	0.992881	0.496441	−	0.868071i	$-0.334640\pi$
$61$	7.75465	0.992881	0.496441	+	0.868071i	$0.334640\pi$
$62$	−7.85778	−0.997939
$63$	−1.56870	−0.197638
$64$	−12.9557	−1.61946
$65$	0	0
$66$	−15.7670	−1.94079
$67$	1.68023	0.205273	0.102636	−	0.994719i	$-0.467272\pi$
$67$	1.68023	0.205273	0.102636	+	0.994719i	$0.467272\pi$
$68$	9.29757	1.12750
$69$	2.13745	0.257319
$70$	0	0
$71$	5.28536	0.627257	0.313628	−	0.949546i	$-0.398455\pi$
$71$	5.28536	0.627257	0.313628	+	0.949546i	$0.398455\pi$
$72$	−4.40604	−0.519257
$73$	−8.29066	−0.970348	−0.485174	−	0.874418i	$-0.661244\pi$
$73$	−8.29066	−0.970348	−0.485174	+	0.874418i	$0.661244\pi$
$74$	2.78363	0.323591
$75$	0	0
$76$	−15.5270	−1.78107
$77$	3.22604	0.367642
$78$	7.82403	0.885897
$79$	−7.14557	−0.803939	−0.401970	−	0.915653i	$-0.631674\pi$
$79$	−7.14557	−0.803939	−0.401970	+	0.915653i	$0.631674\pi$
$80$	0	0
$81$	−11.2453	−1.24948
$82$	−6.11353	−0.675127
$83$	−9.49563	−1.04228	−0.521140	−	0.853471i	$-0.674493\pi$
$83$	−9.49563	−1.04228	−0.521140	+	0.853471i	$0.674493\pi$
$84$	6.90046	0.752902
$85$	0	0
$86$	11.2912	1.21756
$87$	−4.00516	−0.429399
$88$	9.06104	0.965911
$89$	−1.12606	−0.119362	−0.0596810	−	0.998218i	$-0.519008\pi$
$89$	−1.12606	−0.119362	−0.0596810	+	0.998218i	$0.519008\pi$
$90$	0	0
$91$	−1.60085	−0.167815
$92$	−3.22836	−0.336580
$93$	−7.34537	−0.761680
$94$	28.9352	2.98444
$95$	0	0
$96$	−12.1752	−1.24263
$97$	−1.29227	−0.131210	−0.0656050	−	0.997846i	$-0.520898\pi$
$97$	−1.29227	−0.131210	−0.0656050	+	0.997846i	$0.520898\pi$
$98$	−2.28656	−0.230977
$99$	−5.06070	−0.508620
$100$	0	0
$101$	18.8166	1.87232	0.936158	−	0.351579i	$-0.114355\pi$
$101$	18.8166	1.87232	0.936158	+	0.351579i	$0.114355\pi$
$102$	14.0756	1.39369
$103$	17.2343	1.69815	0.849075	−	0.528272i	$-0.177160\pi$
$103$	17.2343	1.69815	0.849075	+	0.528272i	$0.177160\pi$
$104$	−4.49634	−0.440903
$105$	0	0
$106$	−14.0157	−1.36133
$107$	2.05928	0.199078	0.0995392	−	0.995034i	$-0.468263\pi$
$107$	2.05928	0.199078	0.0995392	+	0.995034i	$0.468263\pi$
$108$	9.87662	0.950378
$109$	−4.40773	−0.422184	−0.211092	−	0.977466i	$-0.567702\pi$
$109$	−4.40773	−0.422184	−0.211092	+	0.977466i	$0.567702\pi$
$110$	0	0
$111$	2.60211	0.246981
$112$	0.0344172	0.00325212
$113$	8.76303	0.824357	0.412178	−	0.911103i	$-0.364768\pi$
$113$	8.76303	0.824357	0.412178	+	0.911103i	$0.364768\pi$
$114$	−23.5063	−2.20157
$115$	0	0
$116$	6.04931	0.561664
$117$	2.51126	0.232166
$118$	−13.4577	−1.23888
$119$	−2.87997	−0.264006
$120$	0	0
$121$	−0.592639	−0.0538763
$122$	−17.7315	−1.60533
$123$	−5.71486	−0.515292
$124$	11.0943	0.996296
$125$	0	0
$126$	3.58693	0.319549
$127$	6.98892	0.620166	0.310083	−	0.950709i	$-0.399643\pi$
$127$	6.98892	0.620166	0.310083	+	0.950709i	$0.399643\pi$
$128$	18.2318	1.61147
$129$	10.5549	0.929304
$130$	0	0
$131$	6.84798	0.598311	0.299155	−	0.954204i	$-0.403295\pi$
$131$	6.84798	0.598311	0.299155	+	0.954204i	$0.403295\pi$
$132$	22.2612	1.93759
$133$	4.80956	0.417041
$134$	−3.84195	−0.331894
$135$	0	0
$136$	−8.08901	−0.693627
$137$	13.4631	1.15023	0.575117	−	0.818071i	$-0.304957\pi$
$137$	13.4631	1.15023	0.575117	+	0.818071i	$0.304957\pi$
$138$	−4.88741	−0.416044
$139$	−16.5134	−1.40065	−0.700323	−	0.713826i	$-0.746961\pi$
$139$	−16.5134	−1.40065	−0.700323	+	0.713826i	$0.746961\pi$
$140$	0	0
$141$	27.0483	2.27788
$142$	−12.0853	−1.01418
$143$	−5.16442	−0.431871
$144$	−0.0539903	−0.00449919
$145$	0	0
$146$	18.9571	1.56890
$147$	−2.13745	−0.176294
$148$	−3.93017	−0.323058
$149$	−1.66498	−0.136400	−0.0682001	−	0.997672i	$-0.521726\pi$
$149$	−1.66498	−0.136400	−0.0682001	+	0.997672i	$0.521726\pi$
$150$	0	0
$151$	22.5049	1.83143	0.915713	−	0.401832i	$-0.131627\pi$
$151$	22.5049	1.83143	0.915713	+	0.401832i	$0.131627\pi$
$152$	13.5087	1.09570
$153$	4.51781	0.365243
$154$	−7.37655	−0.594419
$155$	0	0
$156$	−11.0466	−0.884438
$157$	−7.46109	−0.595460	−0.297730	−	0.954650i	$-0.596229\pi$
$157$	−7.46109	−0.595460	−0.297730	+	0.954650i	$0.596229\pi$
$158$	16.3388	1.29984
$159$	−13.1018	−1.03904
$160$	0	0
$161$	1.00000	0.0788110
$162$	25.7130	2.02021
$163$	−4.93595	−0.386613	−0.193307	−	0.981138i	$-0.561921\pi$
$163$	−4.93595	−0.386613	−0.193307	+	0.981138i	$0.561921\pi$
$164$	8.63160	0.674015
$165$	0	0
$166$	21.7123	1.68520
$167$	8.94358	0.692075	0.346038	−	0.938221i	$-0.387527\pi$
$167$	8.94358	0.692075	0.346038	+	0.938221i	$0.387527\pi$
$168$	−6.00350	−0.463180
$169$	−10.4373	−0.802867
$170$	0	0
$171$	−7.54476	−0.576962
$172$	−15.9418	−1.21555
$173$	19.6528	1.49417	0.747086	−	0.664727i	$-0.231452\pi$
$173$	19.6528	1.49417	0.747086	+	0.664727i	$0.231452\pi$
$174$	9.15805	0.694270
$175$	0	0
$176$	0.111031	0.00836930
$177$	−12.5801	−0.945577
$178$	2.57480	0.192989
$179$	−11.6867	−0.873507	−0.436754	−	0.899581i	$-0.643872\pi$
$179$	−11.6867	−0.873507	−0.436754	+	0.899581i	$0.643872\pi$
$180$	0	0
$181$	12.5410	0.932165	0.466082	−	0.884741i	$-0.345665\pi$
$181$	12.5410	0.932165	0.466082	+	0.884741i	$0.345665\pi$
$182$	3.66045	0.271330
$183$	−16.5752	−1.22527
$184$	2.80872	0.207061
$185$	0	0
$186$	16.7956	1.23152
$187$	−9.29090	−0.679418
$188$	−40.8532	−2.97952
$189$	−3.05933	−0.222534
$190$	0	0
$191$	10.3939	0.752077	0.376038	−	0.926604i	$-0.377286\pi$
$191$	10.3939	0.752077	0.376038	+	0.926604i	$0.377286\pi$
$192$	27.6922	1.99851
$193$	17.6957	1.27377	0.636883	−	0.770960i	$-0.280223\pi$
$193$	17.6957	1.27377	0.636883	+	0.770960i	$0.280223\pi$
$194$	2.95485	0.212146
$195$	0	0
$196$	3.22836	0.230597
$197$	−0.290459	−0.0206943	−0.0103472	−	0.999946i	$-0.503294\pi$
$197$	−0.290459	−0.0206943	−0.0103472	+	0.999946i	$0.503294\pi$
$198$	11.5716	0.822358
$199$	−12.7516	−0.903936	−0.451968	−	0.892034i	$-0.649278\pi$
$199$	−12.7516	−0.903936	−0.451968	+	0.892034i	$0.649278\pi$
$200$	0	0
$201$	−3.59141	−0.253319
$202$	−43.0252	−3.02724
$203$	−1.87380	−0.131515
$204$	−19.8731	−1.39140
$205$	0	0
$206$	−39.4074	−2.74564
$207$	−1.56870	−0.109032
$208$	−0.0550968	−0.00382028
$209$	15.5158	1.07325
$210$	0	0
$211$	1.18460	0.0815512	0.0407756	−	0.999168i	$-0.487017\pi$
$211$	1.18460	0.0815512	0.0407756	+	0.999168i	$0.487017\pi$
$212$	19.7886	1.35909
$213$	−11.2972	−0.774072
$214$	−4.70867	−0.321878
$215$	0	0
$216$	−8.59280	−0.584666
$217$	−3.43651	−0.233285
$218$	10.0785	0.682604
$219$	17.7209	1.19747
$220$	0	0
$221$	4.61040	0.310129
$222$	−5.94988	−0.399330
$223$	−15.0617	−1.00861	−0.504304	−	0.863526i	$-0.668251\pi$
$223$	−15.0617	−1.00861	−0.504304	+	0.863526i	$0.668251\pi$
$224$	−5.69613	−0.380589
$225$	0	0
$226$	−20.0372	−1.33285
$227$	5.17571	0.343524	0.171762	−	0.985138i	$-0.445054\pi$
$227$	5.17571	0.343524	0.171762	+	0.985138i	$0.445054\pi$
$228$	33.1882	2.19794
$229$	2.76505	0.182720	0.0913598	−	0.995818i	$-0.470879\pi$
$229$	2.76505	0.182720	0.0913598	+	0.995818i	$0.470879\pi$
$230$	0	0
$231$	−6.89552	−0.453692
$232$	−5.26298	−0.345532
$233$	−21.7930	−1.42771	−0.713854	−	0.700295i	$-0.753052\pi$
$233$	−21.7930	−1.42771	−0.713854	+	0.700295i	$0.753052\pi$
$234$	−5.74215	−0.375376
$235$	0	0
$236$	19.0007	1.23684
$237$	15.2733	0.992108
$238$	6.58522	0.426856
$239$	−15.0618	−0.974264	−0.487132	−	0.873328i	$-0.661957\pi$
$239$	−15.0618	−0.974264	−0.487132	+	0.873328i	$0.661957\pi$
$240$	0	0
$241$	−25.8486	−1.66505	−0.832526	−	0.553986i	$-0.813106\pi$
$241$	−25.8486	−1.66505	−0.832526	+	0.553986i	$0.813106\pi$
$242$	1.35510	0.0871094
$243$	14.8583	0.953157
$244$	25.0348	1.60269
$245$	0	0
$246$	13.0674	0.833146
$247$	−7.69939	−0.489901
$248$	−9.65218	−0.612914
$249$	20.2965	1.28624
$250$	0	0
$251$	27.6557	1.74561	0.872805	−	0.488069i	$-0.162299\pi$
$251$	27.6557	1.74561	0.872805	+	0.488069i	$0.162299\pi$
$252$	−5.06433	−0.319023
$253$	3.22604	0.202820
$254$	−15.9806	−1.00271
$255$	0	0
$256$	−15.7766	−0.986037
$257$	0.438926	0.0273795	0.0136897	−	0.999906i	$-0.495642\pi$
$257$	0.438926	0.0273795	0.0136897	+	0.999906i	$0.495642\pi$
$258$	−24.1343	−1.50254
$259$	1.21739	0.0756449
$260$	0	0
$261$	2.93944	0.181947
$262$	−15.6583	−0.967374
$263$	25.5222	1.57376	0.786882	−	0.617103i	$-0.211694\pi$
$263$	25.5222	1.57376	0.786882	+	0.617103i	$0.211694\pi$
$264$	−19.3675	−1.19199
$265$	0	0
$266$	−10.9973	−0.674290
$267$	2.40690	0.147300
$268$	5.42439	0.331347
$269$	14.7177	0.897356	0.448678	−	0.893693i	$-0.351895\pi$
$269$	14.7177	0.897356	0.448678	+	0.893693i	$0.351895\pi$
$270$	0	0
$271$	−6.69131	−0.406468	−0.203234	−	0.979130i	$-0.565145\pi$
$271$	−6.69131	−0.406468	−0.203234	+	0.979130i	$0.565145\pi$
$272$	−0.0991203	−0.00601005
$273$	3.42175	0.207094
$274$	−30.7843	−1.85975
$275$	0	0
$276$	6.90046	0.415359
$277$	30.7540	1.84783	0.923914	−	0.382600i	$-0.124971\pi$
$277$	30.7540	1.84783	0.923914	+	0.382600i	$0.124971\pi$
$278$	37.7588	2.26462
$279$	5.39086	0.322742
$280$	0	0
$281$	8.48665	0.506271	0.253135	−	0.967431i	$-0.418538\pi$
$281$	8.48665	0.506271	0.253135	+	0.967431i	$0.418538\pi$
$282$	−61.8476	−3.68297
$283$	7.27518	0.432464	0.216232	−	0.976342i	$-0.430623\pi$
$283$	7.27518	0.432464	0.216232	+	0.976342i	$0.430623\pi$
$284$	17.0630	1.01251
$285$	0	0
$286$	11.8088	0.698267
$287$	−2.67368	−0.157822
$288$	8.93553	0.526531
$289$	−8.70579	−0.512105
$290$	0	0
$291$	2.76216	0.161921
$292$	−26.7652	−1.56632
$293$	6.00047	0.350551	0.175276	−	0.984519i	$-0.443918\pi$
$293$	6.00047	0.350551	0.175276	+	0.984519i	$0.443918\pi$
$294$	4.88741	0.285040
$295$	0	0
$296$	3.41930	0.198743
$297$	−9.86954	−0.572689
$298$	3.80707	0.220538
$299$	−1.60085	−0.0925797
$300$	0	0
$301$	4.93806	0.284625
$302$	−51.4589	−2.96113
$303$	−40.2195	−2.31055
$304$	0.165531	0.00949387
$305$	0	0
$306$	−10.3302	−0.590541
$307$	−13.9518	−0.796272	−0.398136	−	0.917326i	$-0.630343\pi$
$307$	−13.9518	−0.796272	−0.398136	+	0.917326i	$0.630343\pi$
$308$	10.4148	0.593440
$309$	−36.8376	−2.09562
$310$	0	0
$311$	−33.7772	−1.91533	−0.957663	−	0.287891i	$-0.907046\pi$
$311$	−33.7772	−1.91533	−0.957663	+	0.287891i	$0.907046\pi$
$312$	9.61072	0.544100
$313$	−16.9350	−0.957222	−0.478611	−	0.878027i	$-0.658860\pi$
$313$	−16.9350	−0.957222	−0.478611	+	0.878027i	$0.658860\pi$
$314$	17.0602	0.962764
$315$	0	0
$316$	−23.0685	−1.29770
$317$	−25.4462	−1.42920	−0.714600	−	0.699534i	$-0.753391\pi$
$317$	−25.4462	−1.42920	−0.714600	+	0.699534i	$0.753391\pi$
$318$	29.9580	1.67996
$319$	−6.04497	−0.338453
$320$	0	0
$321$	−4.40162	−0.245674
$322$	−2.28656	−0.127425
$323$	−13.8514	−0.770710
$324$	−36.3038	−2.01688
$325$	0	0
$326$	11.2863	0.625093
$327$	9.42131	0.520999
$328$	−7.50961	−0.414649
$329$	12.6545	0.697664
$330$	0	0
$331$	0.346984	0.0190720	0.00953598	−	0.999955i	$-0.496965\pi$
$331$	0.346984	0.0190720	0.00953598	+	0.999955i	$0.496965\pi$
$332$	−30.6553	−1.68243
$333$	−1.90972	−0.104652
$334$	−20.4500	−1.11898
$335$	0	0
$336$	−0.0735651	−0.00401330
$337$	−8.13026	−0.442883	−0.221442	−	0.975174i	$-0.571076\pi$
$337$	−8.13026	−0.442883	−0.221442	+	0.975174i	$0.571076\pi$
$338$	23.8654	1.29811
$339$	−18.7306	−1.01730
$340$	0	0
$341$	−11.0863	−0.600358
$342$	17.2515	0.932857
$343$	−1.00000	−0.0539949
$344$	13.8696	0.747799
$345$	0	0
$346$	−44.9373	−2.41584
$347$	−17.5953	−0.944568	−0.472284	−	0.881447i	$-0.656570\pi$
$347$	−17.5953	−0.944568	−0.472284	+	0.881447i	$0.656570\pi$
$348$	−12.9301	−0.693127
$349$	−15.4523	−0.827145	−0.413572	−	0.910471i	$-0.635719\pi$
$349$	−15.4523	−0.827145	−0.413572	+	0.910471i	$0.635719\pi$
$350$	0	0
$351$	4.89754	0.261411
$352$	−18.3760	−0.979442
$353$	2.34129	0.124614	0.0623070	−	0.998057i	$-0.480154\pi$
$353$	2.34129	0.124614	0.0623070	+	0.998057i	$0.480154\pi$
$354$	28.7651	1.52885
$355$	0	0
$356$	−3.63532	−0.192672
$357$	6.15579	0.325799
$358$	26.7224	1.41232
$359$	−6.54193	−0.345270	−0.172635	−	0.984986i	$-0.555228\pi$
$359$	−6.54193	−0.345270	−0.172635	+	0.984986i	$0.555228\pi$
$360$	0	0
$361$	4.13183	0.217465
$362$	−28.6757	−1.50716
$363$	1.26674	0.0664865
$364$	−5.16813	−0.270884
$365$	0	0
$366$	37.9002	1.98107
$367$	−14.8212	−0.773660	−0.386830	−	0.922151i	$-0.626430\pi$
$367$	−14.8212	−0.773660	−0.386830	+	0.922151i	$0.626430\pi$
$368$	0.0344172	0.00179412
$369$	4.19421	0.218342
$370$	0	0
$371$	−6.12961	−0.318234
$372$	−23.7135	−1.22949
$373$	−27.3528	−1.41627	−0.708137	−	0.706075i	$-0.750464\pi$
$373$	−27.3528	−1.41627	−0.708137	+	0.706075i	$0.750464\pi$
$374$	21.2442	1.09851
$375$	0	0
$376$	35.5428	1.83298
$377$	2.99968	0.154492
$378$	6.99535	0.359802
$379$	9.76267	0.501475	0.250737	−	0.968055i	$-0.419327\pi$
$379$	9.76267	0.501475	0.250737	+	0.968055i	$0.419327\pi$
$380$	0	0
$381$	−14.9385	−0.765322
$382$	−23.7663	−1.21599
$383$	−27.0328	−1.38131	−0.690656	−	0.723183i	$-0.742678\pi$
$383$	−27.0328	−1.38131	−0.690656	+	0.723183i	$0.742678\pi$
$384$	−38.9695	−1.98865
$385$	0	0
$386$	−40.4624	−2.05948
$387$	−7.74634	−0.393769
$388$	−4.17191	−0.211797
$389$	−37.1773	−1.88497	−0.942483	−	0.334255i	$-0.891515\pi$
$389$	−37.1773	−1.88497	−0.942483	+	0.334255i	$0.891515\pi$
$390$	0	0
$391$	−2.87997	−0.145646
$392$	−2.80872	−0.141862
$393$	−14.6372	−0.738351
$394$	0.664152	0.0334595
$395$	0	0
$396$	−16.3378	−0.821003
$397$	−23.8588	−1.19744	−0.598719	−	0.800959i	$-0.704323\pi$
$397$	−23.8588	−1.19744	−0.598719	+	0.800959i	$0.704323\pi$
$398$	29.1573	1.46152
$399$	−10.2802	−0.514653
$400$	0	0
$401$	−8.99020	−0.448949	−0.224475	−	0.974480i	$-0.572067\pi$
$401$	−8.99020	−0.448949	−0.224475	+	0.974480i	$0.572067\pi$
$402$	8.21199	0.409577
$403$	5.50134	0.274041
$404$	60.7466	3.02226
$405$	0	0
$406$	4.28456	0.212639
$407$	3.92735	0.194672
$408$	17.2899	0.855976
$409$	−34.0230	−1.68233	−0.841164	−	0.540781i	$-0.818129\pi$
$409$	−34.0230	−1.68233	−0.841164	+	0.540781i	$0.818129\pi$
$410$	0	0
$411$	−28.7768	−1.41946
$412$	55.6386	2.74112
$413$	−5.88555	−0.289609
$414$	3.58693	0.176288
$415$	0	0
$416$	9.11867	0.447079
$417$	35.2965	1.72848
$418$	−35.4779	−1.73528
$419$	32.5360	1.58949	0.794744	−	0.606945i	$-0.207605\pi$
$419$	32.5360	1.58949	0.794744	+	0.606945i	$0.207605\pi$
$420$	0	0
$421$	8.44345	0.411509	0.205754	−	0.978604i	$-0.434035\pi$
$421$	8.44345	0.411509	0.205754	+	0.978604i	$0.434035\pi$
$422$	−2.70866	−0.131855
$423$	−19.8511	−0.965193
$424$	−17.2163	−0.836100
$425$	0	0
$426$	25.8317	1.25155
$427$	−7.75465	−0.375274
$428$	6.64810	0.321348
$429$	11.0387	0.532954
$430$	0	0
$431$	−40.1626	−1.93457	−0.967283	−	0.253699i	$-0.918353\pi$
$431$	−40.1626	−1.93457	−0.967283	+	0.253699i	$0.918353\pi$
$432$	−0.105294	−0.00506594
$433$	−30.1331	−1.44811	−0.724053	−	0.689744i	$-0.757723\pi$
$433$	−30.1331	−1.44811	−0.724053	+	0.689744i	$0.757723\pi$
$434$	7.85778	0.377186
$435$	0	0
$436$	−14.2297	−0.681480
$437$	4.80956	0.230072
$438$	−40.5199	−1.93611
$439$	−11.2766	−0.538204	−0.269102	−	0.963112i	$-0.586727\pi$
$439$	−11.2766	−0.538204	−0.269102	+	0.963112i	$0.586727\pi$
$440$	0	0
$441$	1.56870	0.0747001
$442$	−10.5420	−0.501430
$443$	−25.5947	−1.21604	−0.608022	−	0.793921i	$-0.708037\pi$
$443$	−25.5947	−1.21604	−0.608022	+	0.793921i	$0.708037\pi$
$444$	8.40055	0.398672
$445$	0	0
$446$	34.4395	1.63076
$447$	3.55881	0.168326
$448$	12.9557	0.612100
$449$	18.6327	0.879333	0.439667	−	0.898161i	$-0.355097\pi$
$449$	18.6327	0.879333	0.439667	+	0.898161i	$0.355097\pi$
$450$	0	0
$451$	−8.62541	−0.406155
$452$	28.2902	1.33066
$453$	−48.1032	−2.26009
$454$	−11.8346	−0.555424
$455$	0	0
$456$	−28.8742	−1.35216
$457$	−1.05675	−0.0494327	−0.0247163	−	0.999695i	$-0.507868\pi$
$457$	−1.05675	−0.0494327	−0.0247163	+	0.999695i	$0.507868\pi$
$458$	−6.32245	−0.295429
$459$	8.81077	0.411252
$460$	0	0
$461$	−26.7221	−1.24457	−0.622285	−	0.782791i	$-0.713796\pi$
$461$	−26.7221	−1.24457	−0.622285	+	0.782791i	$0.713796\pi$
$462$	15.7670	0.733548
$463$	27.0291	1.25615	0.628074	−	0.778154i	$-0.283844\pi$
$463$	27.0291	1.25615	0.628074	+	0.778154i	$0.283844\pi$
$464$	−0.0644910	−0.00299392
$465$	0	0
$466$	49.8310	2.30838
$467$	5.74269	0.265740	0.132870	−	0.991133i	$-0.457581\pi$
$467$	5.74269	0.265740	0.132870	+	0.991133i	$0.457581\pi$
$468$	8.10725	0.374758
$469$	−1.68023	−0.0775859
$470$	0	0
$471$	15.9477	0.734832
$472$	−16.5308	−0.760894
$473$	15.9304	0.732480
$474$	−34.9234	−1.60408
$475$	0	0
$476$	−9.29757	−0.426153
$477$	9.61553	0.440265
$478$	34.4396	1.57523
$479$	8.55745	0.391000	0.195500	−	0.980704i	$-0.437367\pi$
$479$	8.55745	0.391000	0.195500	+	0.980704i	$0.437367\pi$
$480$	0	0
$481$	−1.94886	−0.0888604
$482$	59.1043	2.69213
$483$	−2.13745	−0.0972574
$484$	−1.91325	−0.0869659
$485$	0	0
$486$	−33.9743	−1.54111
$487$	−14.2506	−0.645757	−0.322879	−	0.946440i	$-0.604651\pi$
$487$	−14.2506	−0.645757	−0.322879	+	0.946440i	$0.604651\pi$
$488$	−21.7806	−0.985962
$489$	10.5504	0.477103
$490$	0	0
$491$	28.9970	1.30862	0.654309	−	0.756228i	$-0.272960\pi$
$491$	28.9970	1.30862	0.654309	+	0.756228i	$0.272960\pi$
$492$	−18.4496	−0.831774
$493$	5.39649	0.243046
$494$	17.6051	0.792092
$495$	0	0
$496$	−0.118275	−0.00531070
$497$	−5.28536	−0.237081
$498$	−46.4091	−2.07964
$499$	2.12569	0.0951591	0.0475796	−	0.998867i	$-0.484849\pi$
$499$	2.12569	0.0951591	0.0475796	+	0.998867i	$0.484849\pi$
$500$	0	0
$501$	−19.1165	−0.854061
$502$	−63.2363	−2.82238
$503$	−3.95977	−0.176558	−0.0882788	−	0.996096i	$-0.528137\pi$
$503$	−3.95977	−0.176558	−0.0882788	+	0.996096i	$0.528137\pi$
$504$	4.40604	0.196261
$505$	0	0
$506$	−7.37655	−0.327927
$507$	22.3092	0.990785
$508$	22.5627	1.00106
$509$	36.7628	1.62948	0.814740	−	0.579826i	$-0.196880\pi$
$509$	36.7628	1.62948	0.814740	+	0.579826i	$0.196880\pi$
$510$	0	0
$511$	8.29066	0.366757
$512$	−0.389381	−0.0172084
$513$	−14.7140	−0.649640
$514$	−1.00363	−0.0442683
$515$	0	0
$516$	34.0749	1.50006
$517$	40.8239	1.79543
$518$	−2.78363	−0.122306
$519$	−42.0069	−1.84390
$520$	0	0
$521$	7.51748	0.329347	0.164673	−	0.986348i	$-0.447343\pi$
$521$	7.51748	0.329347	0.164673	+	0.986348i	$0.447343\pi$
$522$	−6.72120	−0.294179
$523$	−31.1427	−1.36178	−0.680889	−	0.732387i	$-0.738406\pi$
$523$	−31.1427	−1.36178	−0.680889	+	0.732387i	$0.738406\pi$
$524$	22.1077	0.965781
$525$	0	0
$526$	−58.3580	−2.54453
$527$	9.89703	0.431121
$528$	−0.237324	−0.0103282
$529$	1.00000	0.0434783
$530$	0	0
$531$	9.23267	0.400664
$532$	15.5270	0.673180
$533$	4.28017	0.185395
$534$	−5.50351	−0.238160
$535$	0	0
$536$	−4.71929	−0.203842
$537$	24.9798	1.07796
$538$	−33.6530	−1.45088
$539$	−3.22604	−0.138956
$540$	0	0
$541$	−20.0581	−0.862367	−0.431183	−	0.902264i	$-0.641904\pi$
$541$	−20.0581	−0.862367	−0.431183	+	0.902264i	$0.641904\pi$
$542$	15.3001	0.657195
$543$	−26.8058	−1.15035
$544$	16.4047	0.703344
$545$	0	0
$546$	−7.82403	−0.334838
$547$	−26.0505	−1.11384	−0.556920	−	0.830566i	$-0.688017\pi$
$547$	−26.0505	−1.11384	−0.556920	+	0.830566i	$0.688017\pi$
$548$	43.4638	1.85668
$549$	12.1647	0.519178
$550$	0	0
$551$	−9.01216	−0.383931
$552$	−6.00350	−0.255526
$553$	7.14557	0.303861
$554$	−70.3209	−2.98765
$555$	0	0
$556$	−53.3111	−2.26089
$557$	19.3397	0.819450	0.409725	−	0.912209i	$-0.365625\pi$
$557$	19.3397	0.819450	0.409725	+	0.912209i	$0.365625\pi$
$558$	−12.3265	−0.521823
$559$	−7.90510	−0.334350
$560$	0	0
$561$	19.8589	0.838442
$562$	−19.4052	−0.818560
$563$	−35.7358	−1.50608	−0.753041	−	0.657973i	$-0.771414\pi$
$563$	−35.7358	−1.50608	−0.753041	+	0.657973i	$0.771414\pi$
$564$	87.3217	3.67691
$565$	0	0
$566$	−16.6351	−0.699227
$567$	11.2453	0.472257
$568$	−14.8451	−0.622886
$569$	28.7169	1.20388	0.601938	−	0.798543i	$-0.294396\pi$
$569$	28.7169	1.20388	0.601938	+	0.798543i	$0.294396\pi$
$570$	0	0
$571$	13.1638	0.550888	0.275444	−	0.961317i	$-0.411175\pi$
$571$	13.1638	0.550888	0.275444	+	0.961317i	$0.411175\pi$
$572$	−16.6726	−0.697117
$573$	−22.2165	−0.928107
$574$	6.11353	0.255174
$575$	0	0
$576$	−20.3236	−0.846819
$577$	6.48506	0.269977	0.134988	−	0.990847i	$-0.456900\pi$
$577$	6.48506	0.269977	0.134988	+	0.990847i	$0.456900\pi$
$578$	19.9063	0.827994
$579$	−37.8238	−1.57190
$580$	0	0
$581$	9.49563	0.393945
$582$	−6.31585	−0.261801
$583$	−19.7744	−0.818972
$584$	23.2861	0.963586
$585$	0	0
$586$	−13.7204	−0.566786
$587$	−7.02681	−0.290028	−0.145014	−	0.989430i	$-0.546323\pi$
$587$	−7.02681	−0.290028	−0.145014	+	0.989430i	$0.546323\pi$
$588$	−6.90046	−0.284570
$589$	−16.5281	−0.681028
$590$	0	0
$591$	0.620842	0.0255380
$592$	0.0418991	0.00172204
$593$	−12.4275	−0.510338	−0.255169	−	0.966896i	$-0.582131\pi$
$593$	−12.4275	−0.510338	−0.255169	+	0.966896i	$0.582131\pi$
$594$	22.5673	0.925947
$595$	0	0
$596$	−5.37514	−0.220174
$597$	27.2559	1.11551
$598$	3.66045	0.149687
$599$	43.9384	1.79527	0.897637	−	0.440735i	$-0.145282\pi$
$599$	43.9384	1.79527	0.897637	+	0.440735i	$0.145282\pi$
$600$	0	0
$601$	−21.1916	−0.864425	−0.432212	−	0.901772i	$-0.642267\pi$
$601$	−21.1916	−0.864425	−0.432212	+	0.901772i	$0.642267\pi$
$602$	−11.2912	−0.460194
$603$	2.63578	0.107337
$604$	72.6540	2.95625
$605$	0	0
$606$	91.9643	3.73579
$607$	8.15513	0.331007	0.165503	−	0.986209i	$-0.447075\pi$
$607$	8.15513	0.331007	0.165503	+	0.986209i	$0.447075\pi$
$608$	−27.3959	−1.11105
$609$	4.00516	0.162297
$610$	0	0
$611$	−20.2580	−0.819549
$612$	14.5851	0.589568
$613$	34.7975	1.40546	0.702728	−	0.711458i	$-0.251965\pi$
$613$	34.7975	1.40546	0.702728	+	0.711458i	$0.251965\pi$
$614$	31.9017	1.28745
$615$	0	0
$616$	−9.06104	−0.365080
$617$	−0.384474	−0.0154784	−0.00773918	−	0.999970i	$-0.502463\pi$
$617$	−0.384474	−0.0154784	−0.00773918	+	0.999970i	$0.502463\pi$
$618$	84.2313	3.38828
$619$	−47.0599	−1.89150	−0.945748	−	0.324900i	$-0.894669\pi$
$619$	−47.0599	−1.89150	−0.945748	+	0.324900i	$0.894669\pi$
$620$	0	0
$621$	−3.05933	−0.122767
$622$	77.2335	3.09678
$623$	1.12606	0.0451146
$624$	0.117767	0.00471445
$625$	0	0
$626$	38.7229	1.54768
$627$	−33.1644	−1.32446
$628$	−24.0871	−0.961179
$629$	−3.50604	−0.139795
$630$	0	0
$631$	35.8320	1.42645	0.713225	−	0.700935i	$-0.247234\pi$
$631$	35.8320	1.42645	0.713225	+	0.700935i	$0.247234\pi$
$632$	20.0699	0.798337
$633$	−2.53203	−0.100639
$634$	58.1842	2.31079
$635$	0	0
$636$	−42.2972	−1.67719
$637$	1.60085	0.0634281
$638$	13.8222	0.547226
$639$	8.29115	0.327993
$640$	0	0
$641$	14.9793	0.591645	0.295822	−	0.955243i	$-0.404406\pi$
$641$	14.9793	0.591645	0.295822	+	0.955243i	$0.404406\pi$
$642$	10.0646	0.397217
$643$	−11.1190	−0.438491	−0.219246	−	0.975670i	$-0.570360\pi$
$643$	−11.1190	−0.438491	−0.219246	+	0.975670i	$0.570360\pi$
$644$	3.22836	0.127215
$645$	0	0
$646$	31.6720	1.24612
$647$	−32.7707	−1.28835	−0.644174	−	0.764879i	$-0.722799\pi$
$647$	−32.7707	−1.28835	−0.644174	+	0.764879i	$0.722799\pi$
$648$	31.5848	1.24077
$649$	−18.9870	−0.745307
$650$	0	0
$651$	7.34537	0.287888
$652$	−15.9350	−0.624063
$653$	19.0708	0.746298	0.373149	−	0.927771i	$-0.378278\pi$
$653$	19.0708	0.746298	0.373149	+	0.927771i	$0.378278\pi$
$654$	−21.5424	−0.842374
$655$	0	0
$656$	−0.0920205	−0.00359280
$657$	−13.0056	−0.507396
$658$	−28.9352	−1.12801
$659$	26.6960	1.03993	0.519963	−	0.854189i	$-0.325946\pi$
$659$	26.6960	1.03993	0.519963	+	0.854189i	$0.325946\pi$
$660$	0	0
$661$	−19.8123	−0.770609	−0.385305	−	0.922789i	$-0.625904\pi$
$661$	−19.8123	−0.770609	−0.385305	+	0.922789i	$0.625904\pi$
$662$	−0.793400	−0.0308363
$663$	−9.85452	−0.382718
$664$	26.6705	1.03502
$665$	0	0
$666$	4.36669	0.169206
$667$	−1.87380	−0.0725539
$668$	28.8731	1.11713
$669$	32.1937	1.24468
$670$	0	0
$671$	−25.0168	−0.965765
$672$	12.1752	0.469669
$673$	9.88201	0.380923	0.190462	−	0.981695i	$-0.439001\pi$
$673$	9.88201	0.380923	0.190462	+	0.981695i	$0.439001\pi$
$674$	18.5903	0.716073
$675$	0	0
$676$	−33.6953	−1.29597
$677$	4.84985	0.186395	0.0931975	−	0.995648i	$-0.470291\pi$
$677$	4.84985	0.186395	0.0931975	+	0.995648i	$0.470291\pi$
$678$	42.8286	1.64482
$679$	1.29227	0.0495927
$680$	0	0
$681$	−11.0628	−0.423929
$682$	25.3496	0.970685
$683$	−31.1120	−1.19047	−0.595233	−	0.803553i	$-0.702940\pi$
$683$	−31.1120	−1.19047	−0.595233	+	0.803553i	$0.702940\pi$
$684$	−24.3572	−0.931320
$685$	0	0
$686$	2.28656	0.0873013
$687$	−5.91016	−0.225487
$688$	0.169954	0.00647943
$689$	9.81261	0.373831
$690$	0	0
$691$	26.5435	1.00976	0.504880	−	0.863189i	$-0.331537\pi$
$691$	26.5435	1.00976	0.504880	+	0.863189i	$0.331537\pi$
$692$	63.4462	2.41186
$693$	5.06070	0.192240
$694$	40.2328	1.52722
$695$	0	0
$696$	11.2494	0.426406
$697$	7.70011	0.291663
$698$	35.3327	1.33736
$699$	46.5815	1.76187
$700$	0	0
$701$	−25.7796	−0.973682	−0.486841	−	0.873491i	$-0.661851\pi$
$701$	−25.7796	−0.973682	−0.486841	+	0.873491i	$0.661851\pi$
$702$	−11.1985	−0.422661
$703$	5.85510	0.220829
$704$	41.7957	1.57523
$705$	0	0
$706$	−5.35349	−0.201481
$707$	−18.8166	−0.707669
$708$	−40.6130	−1.52633
$709$	5.22878	0.196371	0.0981854	−	0.995168i	$-0.468696\pi$
$709$	5.22878	0.196371	0.0981854	+	0.995168i	$0.468696\pi$
$710$	0	0
$711$	−11.2093	−0.420380
$712$	3.16278	0.118530
$713$	−3.43651	−0.128698
$714$	−14.0756	−0.526766
$715$	0	0
$716$	−37.7289	−1.41000
$717$	32.1938	1.20230
$718$	14.9585	0.558247
$719$	−22.5634	−0.841473	−0.420737	−	0.907183i	$-0.638228\pi$
$719$	−22.5634	−0.841473	−0.420737	+	0.907183i	$0.638228\pi$
$720$	0	0
$721$	−17.2343	−0.641840
$722$	−9.44767	−0.351606
$723$	55.2501	2.05477
$724$	40.4868	1.50468
$725$	0	0
$726$	−2.89647	−0.107498
$727$	11.4002	0.422811	0.211405	−	0.977398i	$-0.432196\pi$
$727$	11.4002	0.422811	0.211405	+	0.977398i	$0.432196\pi$
$728$	4.49634	0.166646
$729$	1.97704	0.0732236
$730$	0	0
$731$	−14.2214	−0.525999
$732$	−53.5107	−1.97781
$733$	33.4318	1.23483	0.617416	−	0.786637i	$-0.288179\pi$
$733$	33.4318	1.23483	0.617416	+	0.786637i	$0.288179\pi$
$734$	33.8895	1.25089
$735$	0	0
$736$	−5.69613	−0.209962
$737$	−5.42050	−0.199667
$738$	−9.59031	−0.353024
$739$	−32.1459	−1.18251	−0.591253	−	0.806486i	$-0.701367\pi$
$739$	−32.1459	−1.18251	−0.591253	+	0.806486i	$0.701367\pi$
$740$	0	0
$741$	16.4571	0.604566
$742$	14.0157	0.514534
$743$	−47.0917	−1.72763	−0.863813	−	0.503812i	$-0.831931\pi$
$743$	−47.0917	−1.72763	−0.863813	+	0.503812i	$0.831931\pi$
$744$	20.6311	0.756372
$745$	0	0
$746$	62.5438	2.28989
$747$	−14.8958	−0.545009
$748$	−29.9944	−1.09670
$749$	−2.05928	−0.0752446
$750$	0	0
$751$	−45.7539	−1.66959	−0.834793	−	0.550565i	$-0.814412\pi$
$751$	−45.7539	−1.66959	−0.834793	+	0.550565i	$0.814412\pi$
$752$	0.435531	0.0158822
$753$	−59.1127	−2.15418
$754$	−6.85896	−0.249789
$755$	0	0
$756$	−9.87662	−0.359209
$757$	37.4438	1.36092	0.680459	−	0.732786i	$-0.261780\pi$
$757$	37.4438	1.36092	0.680459	+	0.732786i	$0.261780\pi$
$758$	−22.3229	−0.810806
$759$	−6.89552	−0.250291
$760$	0	0
$761$	−47.7567	−1.73118	−0.865589	−	0.500756i	$-0.833056\pi$
$761$	−47.7567	−1.73118	−0.865589	+	0.500756i	$0.833056\pi$
$762$	34.1577	1.23740
$763$	4.40773	0.159570
$764$	33.5553	1.21399
$765$	0	0
$766$	61.8122	2.23336
$767$	9.42190	0.340205
$768$	33.7217	1.21683
$769$	−7.42831	−0.267872	−0.133936	−	0.990990i	$-0.542762\pi$
$769$	−7.42831	−0.267872	−0.133936	+	0.990990i	$0.542762\pi$
$770$	0	0
$771$	−0.938184	−0.0337879
$772$	57.1282	2.05609
$773$	−2.79260	−0.100443	−0.0502215	−	0.998738i	$-0.515993\pi$
$773$	−2.79260	−0.100443	−0.0502215	+	0.998738i	$0.515993\pi$
$774$	17.7125	0.636662
$775$	0	0
$776$	3.62962	0.130296
$777$	−2.60211	−0.0933502
$778$	85.0082	3.04769
$779$	−12.8592	−0.460729
$780$	0	0
$781$	−17.0508	−0.610126
$782$	6.58522	0.235487
$783$	5.73259	0.204866
$784$	−0.0344172	−0.00122918
$785$	0	0
$786$	33.4689	1.19380
$787$	36.6263	1.30559	0.652793	−	0.757536i	$-0.273597\pi$
$787$	36.6263	1.30559	0.652793	+	0.757536i	$0.273597\pi$
$788$	−0.937705	−0.0334044
$789$	−54.5524	−1.94212
$790$	0	0
$791$	−8.76303	−0.311577
$792$	14.2141	0.505075
$793$	12.4141	0.440836
$794$	54.5546	1.93607
$795$	0	0
$796$	−41.1667	−1.45912
$797$	1.09829	0.0389033	0.0194517	−	0.999811i	$-0.493808\pi$
$797$	1.09829	0.0389033	0.0194517	+	0.999811i	$0.493808\pi$
$798$	23.5063	0.832114
$799$	−36.4445	−1.28931
$800$	0	0
$801$	−1.76645	−0.0624144
$802$	20.5566	0.725880
$803$	26.7460	0.943847
$804$	−11.5944	−0.408902
$805$	0	0
$806$	−12.5792	−0.443082
$807$	−31.4585	−1.10739
$808$	−52.8504	−1.85927
$809$	−17.6686	−0.621194	−0.310597	−	0.950542i	$-0.600529\pi$
$809$	−17.6686	−0.621194	−0.310597	+	0.950542i	$0.600529\pi$
$810$	0	0
$811$	−30.3486	−1.06568	−0.532842	−	0.846214i	$-0.678876\pi$
$811$	−30.3486	−1.06568	−0.532842	+	0.846214i	$0.678876\pi$
$812$	−6.04931	−0.212289
$813$	14.3024	0.501606
$814$	−8.98013	−0.314753
$815$	0	0
$816$	0.211865	0.00741676
$817$	23.7499	0.830902
$818$	77.7956	2.72006
$819$	−2.51126	−0.0877506
$820$	0	0
$821$	−42.9172	−1.49782	−0.748910	−	0.662672i	$-0.769422\pi$
$821$	−42.9172	−1.49782	−0.748910	+	0.662672i	$0.769422\pi$
$822$	65.7999	2.29504
$823$	22.7189	0.791930	0.395965	−	0.918266i	$-0.370410\pi$
$823$	22.7189	0.791930	0.395965	+	0.918266i	$0.370410\pi$
$824$	−48.4064	−1.68632
$825$	0	0
$826$	13.4577	0.468252
$827$	−19.0458	−0.662286	−0.331143	−	0.943581i	$-0.607434\pi$
$827$	−19.0458	−0.662286	−0.331143	+	0.943581i	$0.607434\pi$
$828$	−5.06433	−0.175998
$829$	−48.0021	−1.66718	−0.833591	−	0.552382i	$-0.813719\pi$
$829$	−48.0021	−1.66718	−0.833591	+	0.552382i	$0.813719\pi$
$830$	0	0
$831$	−65.7352	−2.28033
$832$	−20.7402	−0.719037
$833$	2.87997	0.0997849
$834$	−80.7077	−2.79468
$835$	0	0
$836$	50.0907	1.73242
$837$	10.5134	0.363397
$838$	−74.3955	−2.56995
$839$	6.77487	0.233895	0.116947	−	0.993138i	$-0.462689\pi$
$839$	6.77487	0.233895	0.116947	+	0.993138i	$0.462689\pi$
$840$	0	0
$841$	−25.4889	−0.878926
$842$	−19.3065	−0.665345
$843$	−18.1398	−0.624768
$844$	3.82431	0.131638
$845$	0	0
$846$	45.3907	1.56057
$847$	0.592639	0.0203633
$848$	−0.210964	−0.00724453
$849$	−15.5503	−0.533686
$850$	0	0
$851$	1.21739	0.0417316
$852$	−36.4714	−1.24949
$853$	17.4880	0.598777	0.299389	−	0.954131i	$-0.403217\pi$
$853$	17.4880	0.598777	0.299389	+	0.954131i	$0.403217\pi$
$854$	17.7315	0.606759
$855$	0	0
$856$	−5.78394	−0.197691
$857$	11.7696	0.402043	0.201021	−	0.979587i	$-0.435574\pi$
$857$	11.7696	0.402043	0.201021	+	0.979587i	$0.435574\pi$
$858$	−25.2407	−0.861702
$859$	−11.0000	−0.375316	−0.187658	−	0.982234i	$-0.560090\pi$
$859$	−11.0000	−0.375316	−0.187658	+	0.982234i	$0.560090\pi$
$860$	0	0
$861$	5.71486	0.194762
$862$	91.8343	3.12789
$863$	14.5533	0.495400	0.247700	−	0.968837i	$-0.420325\pi$
$863$	14.5533	0.495400	0.247700	+	0.968837i	$0.420325\pi$
$864$	17.4264	0.592857
$865$	0	0
$866$	68.9013	2.34136
$867$	18.6082	0.631968
$868$	−11.0943	−0.376564
$869$	23.0519	0.781983
$870$	0	0
$871$	2.68980	0.0911405
$872$	12.3801	0.419242
$873$	−2.02718	−0.0686098
$874$	−10.9973	−0.371991
$875$	0	0
$876$	57.2094	1.93293
$877$	21.3486	0.720890	0.360445	−	0.932780i	$-0.382625\pi$
$877$	21.3486	0.720890	0.360445	+	0.932780i	$0.382625\pi$
$878$	25.7847	0.870191
$879$	−12.8257	−0.432601
$880$	0	0
$881$	−45.4235	−1.53036	−0.765178	−	0.643818i	$-0.777349\pi$
$881$	−45.4235	−1.53036	−0.765178	+	0.643818i	$0.777349\pi$
$882$	−3.58693	−0.120778
$883$	−1.94612	−0.0654921	−0.0327460	−	0.999464i	$-0.510425\pi$
$883$	−1.94612	−0.0654921	−0.0327460	+	0.999464i	$0.510425\pi$
$884$	14.8840	0.500604
$885$	0	0
$886$	58.5239	1.96615
$887$	−46.8470	−1.57297	−0.786484	−	0.617610i	$-0.788101\pi$
$887$	−46.8470	−1.57297	−0.786484	+	0.617610i	$0.788101\pi$
$888$	−7.30859	−0.245260
$889$	−6.98892	−0.234401
$890$	0	0
$891$	36.2778	1.21535
$892$	−48.6246	−1.62807
$893$	60.8624	2.03668
$894$	−8.13743	−0.272156
$895$	0	0
$896$	−18.2318	−0.609080
$897$	3.42175	0.114249
$898$	−42.6049	−1.42174
$899$	6.43934	0.214764
$900$	0	0
$901$	17.6531	0.588109
$902$	19.7225	0.656688
$903$	−10.5549	−0.351244
$904$	−24.6129	−0.818612
$905$	0	0
$906$	109.991	3.65421
$907$	12.9865	0.431211	0.215605	−	0.976481i	$-0.430828\pi$
$907$	12.9865	0.431211	0.215605	+	0.976481i	$0.430828\pi$
$908$	16.7090	0.554509
$909$	29.5176	0.979035
$910$	0	0
$911$	58.9789	1.95406	0.977029	−	0.213108i	$-0.0683585\pi$
$911$	58.9789	1.95406	0.977029	+	0.213108i	$0.0683585\pi$
$912$	−0.353815	−0.0117160
$913$	30.6333	1.01382
$914$	2.41632	0.0799248
$915$	0	0
$916$	8.92657	0.294942
$917$	−6.84798	−0.226140
$918$	−20.1464	−0.664929
$919$	−6.21873	−0.205137	−0.102568	−	0.994726i	$-0.532706\pi$
$919$	−6.21873	−0.205137	−0.102568	+	0.994726i	$0.532706\pi$
$920$	0	0
$921$	29.8213	0.982646
$922$	61.1016	2.01227
$923$	8.46109	0.278500
$924$	−22.2612	−0.732340
$925$	0	0
$926$	−61.8036	−2.03099
$927$	27.0355	0.887963
$928$	10.6734	0.350372
$929$	−11.8842	−0.389908	−0.194954	−	0.980812i	$-0.562456\pi$
$929$	−11.8842	−0.389908	−0.194954	+	0.980812i	$0.562456\pi$
$930$	0	0
$931$	−4.80956	−0.157627
$932$	−70.3556	−2.30458
$933$	72.1970	2.36363
$934$	−13.1310	−0.429659
$935$	0	0
$936$	−7.05342	−0.230548
$937$	−23.5211	−0.768401	−0.384200	−	0.923250i	$-0.625523\pi$
$937$	−23.5211	−0.768401	−0.384200	+	0.923250i	$0.625523\pi$
$938$	3.84195	0.125444
$939$	36.1977	1.18127
$940$	0	0
$941$	9.19002	0.299586	0.149793	−	0.988717i	$-0.452139\pi$
$941$	9.19002	0.299586	0.149793	+	0.988717i	$0.452139\pi$
$942$	−36.4654	−1.18811
$943$	−2.67368	−0.0870670
$944$	−0.202564	−0.00659290
$945$	0	0
$946$	−36.4258	−1.18430
$947$	27.5216	0.894333	0.447167	−	0.894451i	$-0.352433\pi$
$947$	27.5216	0.894333	0.447167	+	0.894451i	$0.352433\pi$
$948$	49.3077	1.60144
$949$	−13.2721	−0.430832
$950$	0	0
$951$	54.3900	1.76372
$952$	8.08901	0.262166
$953$	50.6738	1.64149	0.820743	−	0.571297i	$-0.193560\pi$
$953$	50.6738	1.64149	0.820743	+	0.571297i	$0.193560\pi$
$954$	−21.9865	−0.711839
$955$	0	0
$956$	−48.6247	−1.57264
$957$	12.9208	0.417671
$958$	−19.5671	−0.632185
$959$	−13.4631	−0.434747
$960$	0	0
$961$	−19.1904	−0.619046
$962$	4.45619	0.143673
$963$	3.23040	0.104098
$964$	−83.4484	−2.68769
$965$	0	0
$966$	4.88741	0.157250
$967$	13.6766	0.439809	0.219904	−	0.975521i	$-0.429425\pi$
$967$	13.6766	0.439809	0.219904	+	0.975521i	$0.429425\pi$
$968$	1.66455	0.0535008
$969$	29.6066	0.951102
$970$	0	0
$971$	40.2562	1.29188	0.645942	−	0.763386i	$-0.276465\pi$
$971$	40.2562	1.29188	0.645942	+	0.763386i	$0.276465\pi$
$972$	47.9678	1.53857
$973$	16.5134	0.529394
$974$	32.5849	1.04409
$975$	0	0
$976$	−0.266893	−0.00854304
$977$	−31.6538	−1.01269	−0.506347	−	0.862330i	$-0.669005\pi$
$977$	−31.6538	−1.01269	−0.506347	+	0.862330i	$0.669005\pi$
$978$	−24.1240	−0.771401
$979$	3.63271	0.116102
$980$	0	0
$981$	−6.91441	−0.220760
$982$	−66.3035	−2.11583
$983$	13.0349	0.415750	0.207875	−	0.978155i	$-0.433345\pi$
$983$	13.0349	0.415750	0.207875	+	0.978155i	$0.433345\pi$
$984$	16.0514	0.511701
$985$	0	0
$986$	−12.3394	−0.392967
$987$	−27.0483	−0.860958
$988$	−24.8564	−0.790787
$989$	4.93806	0.157021
$990$	0	0
$991$	48.3404	1.53558	0.767792	−	0.640699i	$-0.221356\pi$
$991$	48.3404	1.53558	0.767792	+	0.640699i	$0.221356\pi$
$992$	19.5748	0.621500
$993$	−0.741661	−0.0235359
$994$	12.0853	0.383322
$995$	0	0
$996$	65.5242	2.07621
$997$	−21.3534	−0.676268	−0.338134	−	0.941098i	$-0.609796\pi$
$997$	−21.3534	−0.676268	−0.338134	+	0.941098i	$0.609796\pi$
$998$	−4.86053	−0.153857
$999$	−3.72440	−0.117835

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.t.1.2		8
5.4	even	2		805.2.a.m.1.7	✓	8
15.14	odd	2		7245.2.a.bp.1.2		8
35.34	odd	2		5635.2.a.bb.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.m.1.7	✓	8	5.4	even	2
4025.2.a.t.1.2		8	1.1	even	1	trivial
5635.2.a.bb.1.7		8	35.34	odd	2
7245.2.a.bp.1.2		8	15.14	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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q-2.28656 q^{2} -2.13745 q^{3} +3.22836 q^{4} +4.88741 q^{6} -1.00000 q^{7} -2.80872 q^{8} +1.56870 q^{9} +O(q^{10})\)	\(q-2.28656 q^{2} -2.13745 q^{3} +3.22836 q^{4} +4.88741 q^{6} -1.00000 q^{7} -2.80872 q^{8} +1.56870 q^{9} -3.22604 q^{11} -6.90046 q^{12} +1.60085 q^{13} +2.28656 q^{14} -0.0344172 q^{16} +2.87997 q^{17} -3.58693 q^{18} -4.80956 q^{19} +2.13745 q^{21} +7.37655 q^{22} -1.00000 q^{23} +6.00350 q^{24} -3.66045 q^{26} +3.05933 q^{27} -3.22836 q^{28} +1.87380 q^{29} +3.43651 q^{31} +5.69613 q^{32} +6.89552 q^{33} -6.58522 q^{34} +5.06433 q^{36} -1.21739 q^{37} +10.9973 q^{38} -3.42175 q^{39} +2.67368 q^{41} -4.88741 q^{42} -4.93806 q^{43} -10.4148 q^{44} +2.28656 q^{46} -12.6545 q^{47} +0.0735651 q^{48} +1.00000 q^{49} -6.15579 q^{51} +5.16813 q^{52} +6.12961 q^{53} -6.99535 q^{54} +2.80872 q^{56} +10.2802 q^{57} -4.28456 q^{58} +5.88555 q^{59} +7.75465 q^{61} -7.85778 q^{62} -1.56870 q^{63} -12.9557 q^{64} -15.7670 q^{66} +1.68023 q^{67} +9.29757 q^{68} +2.13745 q^{69} +5.28536 q^{71} -4.40604 q^{72} -8.29066 q^{73} +2.78363 q^{74} -15.5270 q^{76} +3.22604 q^{77} +7.82403 q^{78} -7.14557 q^{79} -11.2453 q^{81} -6.11353 q^{82} -9.49563 q^{83} +6.90046 q^{84} +11.2912 q^{86} -4.00516 q^{87} +9.06104 q^{88} -1.12606 q^{89} -1.60085 q^{91} -3.22836 q^{92} -7.34537 q^{93} +28.9352 q^{94} -12.1752 q^{96} -1.29227 q^{97} -2.28656 q^{98} -5.06070 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 7 q^{3} + 7 q^{4} + q^{6} - 8 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) \) 8 * q - q^2 - 7 * q^3 + 7 * q^4 + q^6 - 8 * q^7 - 3 * q^8 + 9 * q^9	\( 8 q - q^{2} - 7 q^{3} + 7 q^{4} + q^{6} - 8 q^{7} - 3 q^{8} + 9 q^{9} + 6 q^{11} - 8 q^{12} - 8 q^{13} + q^{14} + q^{16} - 4 q^{17} + 11 q^{18} + 7 q^{21} + 8 q^{22} - 8 q^{23} - 8 q^{24} + 2 q^{26} - 28 q^{27} - 7 q^{28} - 3 q^{29} - 16 q^{31} - 12 q^{32} - 5 q^{33} - 4 q^{34} - 14 q^{36} + 7 q^{37} - 11 q^{38} + 16 q^{39} + 7 q^{41} - q^{42} + 10 q^{43} + 7 q^{44} + q^{46} - 19 q^{47} + 6 q^{48} + 8 q^{49} + 7 q^{51} - 18 q^{52} + q^{53} - 25 q^{54} + 3 q^{56} + 25 q^{57} + 9 q^{58} + 21 q^{59} - 7 q^{61} - 18 q^{62} - 9 q^{63} - 37 q^{64} - 43 q^{66} - 11 q^{67} + 17 q^{68} + 7 q^{69} + 8 q^{71} - 4 q^{72} + 3 q^{73} + 12 q^{74} + 8 q^{76} - 6 q^{77} + 50 q^{78} - 15 q^{79} + 28 q^{81} - 41 q^{82} - 25 q^{83} + 8 q^{84} - 12 q^{86} - 21 q^{87} + 29 q^{88} + q^{89} + 8 q^{91} - 7 q^{92} + 5 q^{93} - 36 q^{94} + 30 q^{96} - 10 q^{97} - q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q - q^2 - 7 * q^3 + 7 * q^4 + q^6 - 8 * q^7 - 3 * q^8 + 9 * q^9 + 6 * q^11 - 8 * q^12 - 8 * q^13 + q^14 + q^16 - 4 * q^17 + 11 * q^18 + 7 * q^21 + 8 * q^22 - 8 * q^23 - 8 * q^24 + 2 * q^26 - 28 * q^27 - 7 * q^28 - 3 * q^29 - 16 * q^31 - 12 * q^32 - 5 * q^33 - 4 * q^34 - 14 * q^36 + 7 * q^37 - 11 * q^38 + 16 * q^39 + 7 * q^41 - q^42 + 10 * q^43 + 7 * q^44 + q^46 - 19 * q^47 + 6 * q^48 + 8 * q^49 + 7 * q^51 - 18 * q^52 + q^53 - 25 * q^54 + 3 * q^56 + 25 * q^57 + 9 * q^58 + 21 * q^59 - 7 * q^61 - 18 * q^62 - 9 * q^63 - 37 * q^64 - 43 * q^66 - 11 * q^67 + 17 * q^68 + 7 * q^69 + 8 * q^71 - 4 * q^72 + 3 * q^73 + 12 * q^74 + 8 * q^76 - 6 * q^77 + 50 * q^78 - 15 * q^79 + 28 * q^81 - 41 * q^82 - 25 * q^83 + 8 * q^84 - 12 * q^86 - 21 * q^87 + 29 * q^88 + q^89 + 8 * q^91 - 7 * q^92 + 5 * q^93 - 36 * q^94 + 30 * q^96 - 10 * q^97 - q^98 - 18 * q^99

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