LMFDB - Embedded newform 825.4.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,4,Mod(1,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("825.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.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:	$48.6765757547$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{97}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 24 $ x^2 - x - 24
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$5.42443$ of defining polynomial
Character	$\chi$	$=$	825.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.42443 q^{2} +3.00000 q^{3} +21.4244 q^{4} -16.2733 q^{6} +7.69772 q^{7} -72.8199 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.42443 q^{2} +3.00000 q^{3} +21.4244 q^{4} -16.2733 q^{6} +7.69772 q^{7} -72.8199 q^{8} +9.00000 q^{9} -11.0000 q^{11} +64.2733 q^{12} -24.8489 q^{13} -41.7557 q^{14} +223.611 q^{16} +15.9420 q^{17} -48.8199 q^{18} +15.1511 q^{19} +23.0931 q^{21} +59.6687 q^{22} -17.7557 q^{23} -218.460 q^{24} +134.791 q^{26} +27.0000 q^{27} +164.919 q^{28} -128.547 q^{29} +219.395 q^{31} -630.402 q^{32} -33.0000 q^{33} -86.4763 q^{34} +192.820 q^{36} -92.0703 q^{37} -82.1863 q^{38} -74.5466 q^{39} -459.942 q^{41} -125.267 q^{42} -64.9648 q^{43} -235.669 q^{44} +96.3146 q^{46} -497.408 q^{47} +670.832 q^{48} -283.745 q^{49} +47.8260 q^{51} -532.373 q^{52} +526.919 q^{53} -146.460 q^{54} -560.547 q^{56} +45.4534 q^{57} +697.292 q^{58} -578.443 q^{59} -221.569 q^{61} -1190.09 q^{62} +69.2794 q^{63} +1630.68 q^{64} +179.006 q^{66} +860.745 q^{67} +341.548 q^{68} -53.2671 q^{69} +580.919 q^{71} -655.379 q^{72} -510.116 q^{73} +499.429 q^{74} +324.605 q^{76} -84.6749 q^{77} +404.373 q^{78} +1035.12 q^{79} +81.0000 q^{81} +2494.92 q^{82} -606.211 q^{83} +494.757 q^{84} +352.397 q^{86} -385.640 q^{87} +801.018 q^{88} -23.4411 q^{89} -191.279 q^{91} -380.406 q^{92} +658.186 q^{93} +2698.15 q^{94} -1891.20 q^{96} -719.490 q^{97} +1539.16 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 6 q^{3} + 33 q^{4} - 3 q^{6} - 24 q^{7} - 57 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q - q^2 + 6 * q^3 + 33 * q^4 - 3 * q^6 - 24 * q^7 - 57 * q^8 + 18 * q^9	$ 2 q - q^{2} + 6 q^{3} + 33 q^{4} - 3 q^{6} - 24 q^{7} - 57 q^{8} + 18 q^{9} - 22 q^{11} + 99 q^{12} - 30 q^{13} - 182 q^{14} + 201 q^{16} - 106 q^{17} - 9 q^{18} + 50 q^{19} - 72 q^{21} + 11 q^{22} - 134 q^{23} - 171 q^{24} + 112 q^{26} + 54 q^{27} - 202 q^{28} - 198 q^{29} + 360 q^{31} - 857 q^{32} - 66 q^{33} - 626 q^{34} + 297 q^{36} + 328 q^{37} + 72 q^{38} - 90 q^{39} - 782 q^{41} - 546 q^{42} - 386 q^{43} - 363 q^{44} - 418 q^{46} - 266 q^{47} + 603 q^{48} + 378 q^{49} - 318 q^{51} - 592 q^{52} + 522 q^{53} - 27 q^{54} - 1062 q^{56} + 150 q^{57} + 390 q^{58} - 172 q^{59} - 778 q^{61} - 568 q^{62} - 216 q^{63} + 809 q^{64} + 33 q^{66} + 776 q^{67} - 1070 q^{68} - 402 q^{69} + 630 q^{71} - 513 q^{72} - 1296 q^{73} + 2358 q^{74} + 728 q^{76} + 264 q^{77} + 336 q^{78} + 652 q^{79} + 162 q^{81} + 1070 q^{82} + 324 q^{83} - 606 q^{84} - 1068 q^{86} - 594 q^{87} + 627 q^{88} - 756 q^{89} - 28 q^{91} - 1726 q^{92} + 1080 q^{93} + 3722 q^{94} - 2571 q^{96} + 452 q^{97} + 4467 q^{98} - 198 q^{99}+O(q^{100}) $ 2 * q - q^2 + 6 * q^3 + 33 * q^4 - 3 * q^6 - 24 * q^7 - 57 * q^8 + 18 * q^9 - 22 * q^11 + 99 * q^12 - 30 * q^13 - 182 * q^14 + 201 * q^16 - 106 * q^17 - 9 * q^18 + 50 * q^19 - 72 * q^21 + 11 * q^22 - 134 * q^23 - 171 * q^24 + 112 * q^26 + 54 * q^27 - 202 * q^28 - 198 * q^29 + 360 * q^31 - 857 * q^32 - 66 * q^33 - 626 * q^34 + 297 * q^36 + 328 * q^37 + 72 * q^38 - 90 * q^39 - 782 * q^41 - 546 * q^42 - 386 * q^43 - 363 * q^44 - 418 * q^46 - 266 * q^47 + 603 * q^48 + 378 * q^49 - 318 * q^51 - 592 * q^52 + 522 * q^53 - 27 * q^54 - 1062 * q^56 + 150 * q^57 + 390 * q^58 - 172 * q^59 - 778 * q^61 - 568 * q^62 - 216 * q^63 + 809 * q^64 + 33 * q^66 + 776 * q^67 - 1070 * q^68 - 402 * q^69 + 630 * q^71 - 513 * q^72 - 1296 * q^73 + 2358 * q^74 + 728 * q^76 + 264 * q^77 + 336 * q^78 + 652 * q^79 + 162 * q^81 + 1070 * q^82 + 324 * q^83 - 606 * q^84 - 1068 * q^86 - 594 * q^87 + 627 * q^88 - 756 * q^89 - 28 * q^91 - 1726 * q^92 + 1080 * q^93 + 3722 * q^94 - 2571 * q^96 + 452 * q^97 + 4467 * q^98 - 198 * 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 $

$2$	−5.42443	−1.91783	−0.958913	−	0.283702i	$-0.908437\pi$
$2$	−5.42443	−1.91783	−0.958913	+	0.283702i	$0.908437\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	21.4244	2.67805
$5$	0	0
$5$	0	0
$6$	−16.2733	−1.10726
$7$	7.69772	0.415638	0.207819	−	0.978167i	$-0.433364\pi$
$7$	7.69772	0.415638	0.207819	+	0.978167i	$0.433364\pi$
$8$	−72.8199	−3.21821
$9$	9.00000	0.333333
$10$	0	0
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	64.2733	1.54617
$13$	−24.8489	−0.530141	−0.265071	−	0.964229i	$-0.585395\pi$
$13$	−24.8489	−0.530141	−0.265071	+	0.964229i	$0.585395\pi$
$14$	−41.7557	−0.797120
$15$	0	0
$16$	223.611	3.49392
$17$	15.9420	0.227441	0.113721	−	0.993513i	$-0.463723\pi$
$17$	15.9420	0.227441	0.113721	+	0.993513i	$0.463723\pi$
$18$	−48.8199	−0.639275
$19$	15.1511	0.182943	0.0914713	−	0.995808i	$-0.470843\pi$
$19$	15.1511	0.182943	0.0914713	+	0.995808i	$0.470843\pi$
$20$	0	0
$21$	23.0931	0.239968
$22$	59.6687	0.578246
$23$	−17.7557	−0.160971	−0.0804853	−	0.996756i	$-0.525647\pi$
$23$	−17.7557	−0.160971	−0.0804853	+	0.996756i	$0.525647\pi$
$24$	−218.460	−1.85804
$25$	0	0
$26$	134.791	1.01672
$27$	27.0000	0.192450
$28$	164.919	1.11310
$29$	−128.547	−0.823121	−0.411560	−	0.911383i	$-0.635016\pi$
$29$	−128.547	−0.823121	−0.411560	+	0.911383i	$0.635016\pi$
$30$	0	0
$31$	219.395	1.27112	0.635558	−	0.772053i	$-0.280770\pi$
$31$	219.395	1.27112	0.635558	+	0.772053i	$0.280770\pi$
$32$	−630.402	−3.48251
$33$	−33.0000	−0.174078
$34$	−86.4763	−0.436193
$35$	0	0
$36$	192.820	0.892685
$37$	−92.0703	−0.409088	−0.204544	−	0.978857i	$-0.565571\pi$
$37$	−92.0703	−0.409088	−0.204544	+	0.978857i	$0.565571\pi$
$38$	−82.1863	−0.350852
$39$	−74.5466	−0.306077
$40$	0	0
$41$	−459.942	−1.75197	−0.875986	−	0.482336i	$-0.839788\pi$
$41$	−459.942	−1.75197	−0.875986	+	0.482336i	$0.839788\pi$
$42$	−125.267	−0.460218
$43$	−64.9648	−0.230396	−0.115198	−	0.993343i	$-0.536750\pi$
$43$	−64.9648	−0.230396	−0.115198	+	0.993343i	$0.536750\pi$
$44$	−235.669	−0.807464
$45$	0	0
$46$	96.3146	0.308713
$47$	−497.408	−1.54371	−0.771855	−	0.635799i	$-0.780671\pi$
$47$	−497.408	−1.54371	−0.771855	+	0.635799i	$0.780671\pi$
$48$	670.832	2.01721
$49$	−283.745	−0.827245
$50$	0	0
$51$	47.8260	0.131313
$52$	−532.373	−1.41975
$53$	526.919	1.36562	0.682811	−	0.730596i	$-0.260757\pi$
$53$	526.919	1.36562	0.682811	+	0.730596i	$0.260757\pi$
$54$	−146.460	−0.369086
$55$	0	0
$56$	−560.547	−1.33761
$57$	45.4534	0.105622
$58$	697.292	1.57860
$59$	−578.443	−1.27639	−0.638194	−	0.769876i	$-0.720318\pi$
$59$	−578.443	−1.27639	−0.638194	+	0.769876i	$0.720318\pi$
$60$	0	0
$61$	−221.569	−0.465067	−0.232533	−	0.972588i	$-0.574701\pi$
$61$	−221.569	−0.465067	−0.232533	+	0.972588i	$0.574701\pi$
$62$	−1190.09	−2.43778
$63$	69.2794	0.138546
$64$	1630.68	3.18493
$65$	0	0
$66$	179.006	0.333851
$67$	860.745	1.56950	0.784752	−	0.619810i	$-0.212790\pi$
$67$	860.745	1.56950	0.784752	+	0.619810i	$0.212790\pi$
$68$	341.548	0.609100
$69$	−53.2671	−0.0929364
$70$	0	0
$71$	580.919	0.971020	0.485510	−	0.874231i	$-0.338634\pi$
$71$	580.919	0.971020	0.485510	+	0.874231i	$0.338634\pi$
$72$	−655.379	−1.07274
$73$	−510.116	−0.817871	−0.408935	−	0.912563i	$-0.634100\pi$
$73$	−510.116	−0.817871	−0.408935	+	0.912563i	$0.634100\pi$
$74$	499.429	0.784560
$75$	0	0
$76$	324.605	0.489930
$77$	−84.6749	−0.125319
$78$	404.373	0.587002
$79$	1035.12	1.47418	0.737088	−	0.675797i	$-0.236200\pi$
$79$	1035.12	1.47418	0.737088	+	0.675797i	$0.236200\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	2494.92	3.35998
$83$	−606.211	−0.801690	−0.400845	−	0.916146i	$-0.631283\pi$
$83$	−606.211	−0.801690	−0.400845	+	0.916146i	$0.631283\pi$
$84$	494.757	0.642648
$85$	0	0
$86$	352.397	0.441860
$87$	−385.640	−0.475229
$88$	801.018	0.970328
$89$	−23.4411	−0.0279186	−0.0139593	−	0.999903i	$-0.504444\pi$
$89$	−23.4411	−0.0279186	−0.0139593	+	0.999903i	$0.504444\pi$
$90$	0	0
$91$	−191.279	−0.220347
$92$	−380.406	−0.431088
$93$	658.186	0.733879
$94$	2698.15	2.96057
$95$	0	0
$96$	−1891.20	−2.01063
$97$	−719.490	−0.753126	−0.376563	−	0.926391i	$-0.622894\pi$
$97$	−719.490	−0.753126	−0.376563	+	0.926391i	$0.622894\pi$
$98$	1539.16	1.58651
$99$	−99.0000	−0.100504
$100$	0	0
$101$	1871.27	1.84355	0.921774	−	0.387727i	$-0.126740\pi$
$101$	1871.27	1.84355	0.921774	+	0.387727i	$0.126740\pi$
$102$	−259.429	−0.251836
$103$	428.745	0.410151	0.205075	−	0.978746i	$-0.434256\pi$
$103$	428.745	0.410151	0.205075	+	0.978746i	$0.434256\pi$
$104$	1809.49	1.70611
$105$	0	0
$106$	−2858.24	−2.61902
$107$	−1148.02	−1.03723	−0.518616	−	0.855008i	$-0.673552\pi$
$107$	−1148.02	−1.03723	−0.518616	+	0.855008i	$0.673552\pi$
$108$	578.460	0.515392
$109$	−1828.32	−1.60662	−0.803308	−	0.595564i	$-0.796929\pi$
$109$	−1828.32	−1.60662	−0.803308	+	0.595564i	$0.796929\pi$
$110$	0	0
$111$	−276.211	−0.236187
$112$	1721.29	1.45220
$113$	−1126.40	−0.937722	−0.468861	−	0.883272i	$-0.655335\pi$
$113$	−1126.40	−0.937722	−0.468861	+	0.883272i	$0.655335\pi$
$114$	−246.559	−0.202565
$115$	0	0
$116$	−2754.04	−2.20436
$117$	−223.640	−0.176714
$118$	3137.72	2.44789
$119$	122.717	0.0945332
$120$	0	0
$121$	121.000	0.0909091
$122$	1201.89	0.891916
$123$	−1379.83	−1.01150
$124$	4700.42	3.40412
$125$	0	0
$126$	−375.801	−0.265707
$127$	−661.304	−0.462057	−0.231029	−	0.972947i	$-0.574209\pi$
$127$	−661.304	−0.462057	−0.231029	+	0.972947i	$0.574209\pi$
$128$	−3802.31	−2.62562
$129$	−194.895	−0.133019
$130$	0	0
$131$	622.186	0.414967	0.207483	−	0.978239i	$-0.433473\pi$
$131$	622.186	0.414967	0.207483	+	0.978239i	$0.433473\pi$
$132$	−707.006	−0.466189
$133$	116.629	0.0760378
$134$	−4669.05	−3.01003
$135$	0	0
$136$	−1160.89	−0.731955
$137$	1872.84	1.16794	0.583969	−	0.811776i	$-0.301499\pi$
$137$	1872.84	1.16794	0.583969	+	0.811776i	$0.301499\pi$
$138$	288.944	0.178236
$139$	−954.058	−0.582174	−0.291087	−	0.956697i	$-0.594017\pi$
$139$	−954.058	−0.582174	−0.291087	+	0.956697i	$0.594017\pi$
$140$	0	0
$141$	−1492.22	−0.891261
$142$	−3151.15	−1.86225
$143$	273.337	0.159844
$144$	2012.50	1.16464
$145$	0	0
$146$	2767.09	1.56853
$147$	−851.236	−0.477610
$148$	−1972.55	−1.09556
$149$	−2047.01	−1.12549	−0.562745	−	0.826631i	$-0.690255\pi$
$149$	−2047.01	−1.12549	−0.562745	+	0.826631i	$0.690255\pi$
$150$	0	0
$151$	475.863	0.256458	0.128229	−	0.991745i	$-0.459071\pi$
$151$	475.863	0.256458	0.128229	+	0.991745i	$0.459071\pi$
$152$	−1103.30	−0.588749
$153$	143.478	0.0758138
$154$	459.313	0.240341
$155$	0	0
$156$	−1597.12	−0.819691
$157$	647.466	0.329130	0.164565	−	0.986366i	$-0.447378\pi$
$157$	647.466	0.329130	0.164565	+	0.986366i	$0.447378\pi$
$158$	−5614.92	−2.82721
$159$	1580.76	0.788442
$160$	0	0
$161$	−136.678	−0.0669054
$162$	−439.379	−0.213092
$163$	−1093.23	−0.525329	−0.262665	−	0.964887i	$-0.584601\pi$
$163$	−1093.23	−0.525329	−0.262665	+	0.964887i	$0.584601\pi$
$164$	−9853.99	−4.69188
$165$	0	0
$166$	3288.35	1.53750
$167$	−1123.25	−0.520479	−0.260240	−	0.965544i	$-0.583802\pi$
$167$	−1123.25	−0.520479	−0.260240	+	0.965544i	$0.583802\pi$
$168$	−1681.64	−0.772270
$169$	−1579.53	−0.718951
$170$	0	0
$171$	136.360	0.0609809
$172$	−1391.83	−0.617014
$173$	−46.0123	−0.0202211	−0.0101106	−	0.999949i	$-0.503218\pi$
$173$	−46.0123	−0.0202211	−0.0101106	+	0.999949i	$0.503218\pi$
$174$	2091.88	0.911406
$175$	0	0
$176$	−2459.72	−1.05346
$177$	−1735.33	−0.736923
$178$	127.155	0.0535430
$179$	−831.975	−0.347401	−0.173700	−	0.984799i	$-0.555572\pi$
$179$	−831.975	−0.347401	−0.173700	+	0.984799i	$0.555572\pi$
$180$	0	0
$181$	−1810.63	−0.743553	−0.371776	−	0.928322i	$-0.621251\pi$
$181$	−1810.63	−0.743553	−0.371776	+	0.928322i	$0.621251\pi$
$182$	1037.58	0.422586
$183$	−664.708	−0.268506
$184$	1292.97	0.518037
$185$	0	0
$186$	−3570.28	−1.40745
$187$	−175.362	−0.0685762
$188$	−10656.7	−4.13414
$189$	207.838	0.0799895
$190$	0	0
$191$	458.898	0.173847	0.0869233	−	0.996215i	$-0.472296\pi$
$191$	458.898	0.173847	0.0869233	+	0.996215i	$0.472296\pi$
$192$	4892.05	1.83882
$193$	−1778.91	−0.663465	−0.331733	−	0.943373i	$-0.607633\pi$
$193$	−1778.91	−0.663465	−0.331733	+	0.943373i	$0.607633\pi$
$194$	3902.82	1.44436
$195$	0	0
$196$	−6079.08	−2.21541
$197$	−5304.53	−1.91844	−0.959218	−	0.282666i	$-0.908781\pi$
$197$	−5304.53	−1.91844	−0.959218	+	0.282666i	$0.908781\pi$
$198$	537.018	0.192749
$199$	−5138.40	−1.83041	−0.915205	−	0.402989i	$-0.867971\pi$
$199$	−5138.40	−1.83041	−0.915205	+	0.402989i	$0.867971\pi$
$200$	0	0
$201$	2582.24	0.906153
$202$	−10150.6	−3.53560
$203$	−989.515	−0.342120
$204$	1024.65	0.351664
$205$	0	0
$206$	−2325.70	−0.786597
$207$	−159.801	−0.0536568
$208$	−5556.47	−1.85227
$209$	−166.663	−0.0551593
$210$	0	0
$211$	−4262.36	−1.39068	−0.695339	−	0.718682i	$-0.744746\pi$
$211$	−4262.36	−1.39068	−0.695339	+	0.718682i	$0.744746\pi$
$212$	11288.9	3.65721
$213$	1742.76	0.560619
$214$	6227.38	1.98923
$215$	0	0
$216$	−1966.14	−0.619345
$217$	1688.84	0.528323
$218$	9917.58	3.08121
$219$	−1530.35	−0.472198
$220$	0	0
$221$	−396.141	−0.120576
$222$	1498.29	0.452966
$223$	1377.80	0.413740	0.206870	−	0.978368i	$-0.433672\pi$
$223$	1377.80	0.413740	0.206870	+	0.978368i	$0.433672\pi$
$224$	−4852.65	−1.44746
$225$	0	0
$226$	6110.06	1.79839
$227$	1227.28	0.358843	0.179422	−	0.983772i	$-0.442577\pi$
$227$	1227.28	0.358843	0.179422	+	0.983772i	$0.442577\pi$
$228$	973.814	0.282861
$229$	3890.28	1.12261	0.561304	−	0.827610i	$-0.310300\pi$
$229$	3890.28	1.12261	0.561304	+	0.827610i	$0.310300\pi$
$230$	0	0
$231$	−254.025	−0.0723532
$232$	9360.74	2.64898
$233$	3218.14	0.904837	0.452419	−	0.891806i	$-0.350561\pi$
$233$	3218.14	0.904837	0.452419	+	0.891806i	$0.350561\pi$
$234$	1213.12	0.338906
$235$	0	0
$236$	−12392.8	−3.41823
$237$	3105.35	0.851115
$238$	−665.670	−0.181298
$239$	−428.098	−0.115864	−0.0579318	−	0.998321i	$-0.518451\pi$
$239$	−428.098	−0.115864	−0.0579318	+	0.998321i	$0.518451\pi$
$240$	0	0
$241$	1231.16	0.329070	0.164535	−	0.986371i	$-0.447388\pi$
$241$	1231.16	0.329070	0.164535	+	0.986371i	$0.447388\pi$
$242$	−656.356	−0.174348
$243$	243.000	0.0641500
$244$	−4747.00	−1.24547
$245$	0	0
$246$	7484.77	1.93988
$247$	−376.489	−0.0969854
$248$	−15976.3	−4.09072
$249$	−1818.63	−0.462856
$250$	0	0
$251$	2838.22	0.713732	0.356866	−	0.934156i	$-0.383845\pi$
$251$	2838.22	0.713732	0.356866	+	0.934156i	$0.383845\pi$
$252$	1484.27	0.371033
$253$	195.313	0.0485344
$254$	3587.20	0.886145
$255$	0	0
$256$	7579.90	1.85056
$257$	−342.007	−0.0830110	−0.0415055	−	0.999138i	$-0.513215\pi$
$257$	−342.007	−0.0830110	−0.0415055	+	0.999138i	$0.513215\pi$
$258$	1057.19	0.255108
$259$	−708.731	−0.170032
$260$	0	0
$261$	−1156.92	−0.274374
$262$	−3375.01	−0.795834
$263$	−5895.00	−1.38213	−0.691067	−	0.722791i	$-0.742859\pi$
$263$	−5895.00	−1.38213	−0.691067	+	0.722791i	$0.742859\pi$
$264$	2403.06	0.560219
$265$	0	0
$266$	−632.647	−0.145827
$267$	−70.3234	−0.0161188
$268$	18441.0	4.20322
$269$	−2496.18	−0.565779	−0.282890	−	0.959152i	$-0.591293\pi$
$269$	−2496.18	−0.565779	−0.282890	+	0.959152i	$0.591293\pi$
$270$	0	0
$271$	−2249.68	−0.504274	−0.252137	−	0.967692i	$-0.581133\pi$
$271$	−2249.68	−0.504274	−0.252137	+	0.967692i	$0.581133\pi$
$272$	3564.80	0.794662
$273$	−573.838	−0.127217
$274$	−10159.1	−2.23990
$275$	0	0
$276$	−1141.22	−0.248889
$277$	−4082.59	−0.885556	−0.442778	−	0.896631i	$-0.646007\pi$
$277$	−4082.59	−0.885556	−0.442778	+	0.896631i	$0.646007\pi$
$278$	5175.22	1.11651
$279$	1974.56	0.423705
$280$	0	0
$281$	−1033.79	−0.219468	−0.109734	−	0.993961i	$-0.535000\pi$
$281$	−1033.79	−0.219468	−0.109734	+	0.993961i	$0.535000\pi$
$282$	8094.46	1.70928
$283$	7809.14	1.64030	0.820150	−	0.572148i	$-0.193890\pi$
$283$	7809.14	1.64030	0.820150	+	0.572148i	$0.193890\pi$
$284$	12445.9	2.60044
$285$	0	0
$286$	−1482.70	−0.306552
$287$	−3540.50	−0.728186
$288$	−5673.61	−1.16084
$289$	−4658.85	−0.948270
$290$	0	0
$291$	−2158.47	−0.434817
$292$	−10928.9	−2.19030
$293$	1949.19	0.388645	0.194323	−	0.980938i	$-0.437749\pi$
$293$	1949.19	0.388645	0.194323	+	0.980938i	$0.437749\pi$
$294$	4617.47	0.915973
$295$	0	0
$296$	6704.55	1.31653
$297$	−297.000	−0.0580259
$298$	11103.9	2.15849
$299$	441.209	0.0853371
$300$	0	0
$301$	−500.081	−0.0957614
$302$	−2581.28	−0.491842
$303$	5613.81	1.06437
$304$	3387.96	0.639187
$305$	0	0
$306$	−778.286	−0.145398
$307$	−2364.09	−0.439497	−0.219748	−	0.975557i	$-0.570524\pi$
$307$	−2364.09	−0.439497	−0.219748	+	0.975557i	$0.570524\pi$
$308$	−1814.11	−0.335612
$309$	1286.24	0.236801
$310$	0	0
$311$	−1989.17	−0.362686	−0.181343	−	0.983420i	$-0.558044\pi$
$311$	−1989.17	−0.362686	−0.181343	+	0.983420i	$0.558044\pi$
$312$	5428.47	0.985021
$313$	3878.67	0.700433	0.350216	−	0.936669i	$-0.386108\pi$
$313$	3878.67	0.700433	0.350216	+	0.936669i	$0.386108\pi$
$314$	−3512.13	−0.631214
$315$	0	0
$316$	22176.8	3.94792
$317$	−2913.73	−0.516251	−0.258126	−	0.966111i	$-0.583105\pi$
$317$	−2913.73	−0.516251	−0.258126	+	0.966111i	$0.583105\pi$
$318$	−8574.71	−1.51209
$319$	1414.01	0.248180
$320$	0	0
$321$	−3444.07	−0.598846
$322$	741.402	0.128313
$323$	241.540	0.0416087
$324$	1735.38	0.297562
$325$	0	0
$326$	5930.17	1.00749
$327$	−5484.95	−0.927580
$328$	33492.9	5.63822
$329$	−3828.90	−0.641624
$330$	0	0
$331$	8104.46	1.34580	0.672902	−	0.739731i	$-0.265047\pi$
$331$	8104.46	1.34580	0.672902	+	0.739731i	$0.265047\pi$
$332$	−12987.7	−2.14697
$333$	−828.633	−0.136363
$334$	6093.02	0.998189
$335$	0	0
$336$	5163.88	0.838430
$337$	−5919.19	−0.956792	−0.478396	−	0.878144i	$-0.658782\pi$
$337$	−5919.19	−0.956792	−0.478396	+	0.878144i	$0.658782\pi$
$338$	8568.07	1.37882
$339$	−3379.19	−0.541394
$340$	0	0
$341$	−2413.35	−0.383256
$342$	−739.677	−0.116951
$343$	−4824.51	−0.759472
$344$	4730.73	0.741465
$345$	0	0
$346$	249.590	0.0387805
$347$	8540.59	1.32128	0.660638	−	0.750705i	$-0.270286\pi$
$347$	8540.59	1.32128	0.660638	+	0.750705i	$0.270286\pi$
$348$	−8262.11	−1.27269
$349$	937.337	0.143767	0.0718833	−	0.997413i	$-0.477099\pi$
$349$	937.337	0.143767	0.0718833	+	0.997413i	$0.477099\pi$
$350$	0	0
$351$	−670.919	−0.102026
$352$	6934.42	1.05002
$353$	211.118	0.0318319	0.0159160	−	0.999873i	$-0.494934\pi$
$353$	211.118	0.0318319	0.0159160	+	0.999873i	$0.494934\pi$
$354$	9413.17	1.41329
$355$	0	0
$356$	−502.213	−0.0747675
$357$	368.151	0.0545788
$358$	4512.99	0.666254
$359$	−1376.31	−0.202337	−0.101169	−	0.994869i	$-0.532258\pi$
$359$	−1376.31	−0.202337	−0.101169	+	0.994869i	$0.532258\pi$
$360$	0	0
$361$	−6629.44	−0.966532
$362$	9821.63	1.42600
$363$	363.000	0.0524864
$364$	−4098.05	−0.590100
$365$	0	0
$366$	3605.66	0.514948
$367$	−1030.45	−0.146564	−0.0732821	−	0.997311i	$-0.523347\pi$
$367$	−1030.45	−0.146564	−0.0732821	+	0.997311i	$0.523347\pi$
$368$	−3970.37	−0.562418
$369$	−4139.48	−0.583991
$370$	0	0
$371$	4056.07	0.567603
$372$	14101.3	1.96537
$373$	−9365.39	−1.30006	−0.650029	−	0.759909i	$-0.725243\pi$
$373$	−9365.39	−1.30006	−0.650029	+	0.759909i	$0.725243\pi$
$374$	951.239	0.131517
$375$	0	0
$376$	36221.2	4.96799
$377$	3194.24	0.436370
$378$	−1127.40	−0.153406
$379$	−7120.23	−0.965017	−0.482509	−	0.875891i	$-0.660274\pi$
$379$	−7120.23	−0.965017	−0.482509	+	0.875891i	$0.660274\pi$
$380$	0	0
$381$	−1983.91	−0.266769
$382$	−2489.26	−0.333407
$383$	1163.56	0.155235	0.0776176	−	0.996983i	$-0.475269\pi$
$383$	1163.56	0.155235	0.0776176	+	0.996983i	$0.475269\pi$
$384$	−11406.9	−1.51590
$385$	0	0
$386$	9649.57	1.27241
$387$	−584.684	−0.0767988
$388$	−15414.7	−2.01691
$389$	−10958.9	−1.42838	−0.714188	−	0.699954i	$-0.753204\pi$
$389$	−10958.9	−1.42838	−0.714188	+	0.699954i	$0.753204\pi$
$390$	0	0
$391$	−283.062	−0.0366114
$392$	20662.3	2.66225
$393$	1866.56	0.239581
$394$	28774.0	3.67923
$395$	0	0
$396$	−2121.02	−0.269155
$397$	2172.09	0.274595	0.137298	−	0.990530i	$-0.456158\pi$
$397$	2172.09	0.274595	0.137298	+	0.990530i	$0.456158\pi$
$398$	27872.9	3.51041
$399$	349.888	0.0439005
$400$	0	0
$401$	7830.71	0.975180	0.487590	−	0.873073i	$-0.337876\pi$
$401$	7830.71	0.975180	0.487590	+	0.873073i	$0.337876\pi$
$402$	−14007.2	−1.73784
$403$	−5451.73	−0.673870
$404$	40090.9	4.93712
$405$	0	0
$406$	5367.55	0.656126
$407$	1012.77	0.123345
$408$	−3482.68	−0.422594
$409$	−10731.2	−1.29736	−0.648682	−	0.761060i	$-0.724679\pi$
$409$	−10731.2	−1.29736	−0.648682	+	0.761060i	$0.724679\pi$
$410$	0	0
$411$	5618.52	0.674309
$412$	9185.62	1.09841
$413$	−4452.69	−0.530515
$414$	866.831	0.102904
$415$	0	0
$416$	15664.8	1.84622
$417$	−2862.17	−0.336118
$418$	904.049	0.105786
$419$	−7315.88	−0.852994	−0.426497	−	0.904489i	$-0.640252\pi$
$419$	−7315.88	−0.852994	−0.426497	+	0.904489i	$0.640252\pi$
$420$	0	0
$421$	−12495.7	−1.44657	−0.723284	−	0.690551i	$-0.757368\pi$
$421$	−12495.7	−1.44657	−0.723284	+	0.690551i	$0.757368\pi$
$422$	23120.9	2.66708
$423$	−4476.67	−0.514570
$424$	−38370.2	−4.39486
$425$	0	0
$426$	−9453.46	−1.07517
$427$	−1705.58	−0.193299
$428$	−24595.8	−2.77776
$429$	820.012	0.0922857
$430$	0	0
$431$	6075.01	0.678939	0.339470	−	0.940617i	$-0.389752\pi$
$431$	6075.01	0.678939	0.339470	+	0.940617i	$0.389752\pi$
$432$	6037.49	0.672405
$433$	−5641.79	−0.626160	−0.313080	−	0.949727i	$-0.601361\pi$
$433$	−5641.79	−0.626160	−0.313080	+	0.949727i	$0.601361\pi$
$434$	−9161.01	−1.01323
$435$	0	0
$436$	−39170.7	−4.30260
$437$	−269.019	−0.0294484
$438$	8301.26	0.905593
$439$	10897.0	1.18470	0.592351	−	0.805680i	$-0.298200\pi$
$439$	10897.0	1.18470	0.592351	+	0.805680i	$0.298200\pi$
$440$	0	0
$441$	−2553.71	−0.275748
$442$	2148.84	0.231244
$443$	7720.83	0.828054	0.414027	−	0.910265i	$-0.364122\pi$
$443$	7720.83	0.828054	0.414027	+	0.910265i	$0.364122\pi$
$444$	−5917.66	−0.632522
$445$	0	0
$446$	−7473.76	−0.793481
$447$	−6141.04	−0.649802
$448$	12552.5	1.32378
$449$	−7473.86	−0.785553	−0.392776	−	0.919634i	$-0.628485\pi$
$449$	−7473.86	−0.785553	−0.392776	+	0.919634i	$0.628485\pi$
$450$	0	0
$451$	5059.36	0.528240
$452$	−24132.4	−2.51127
$453$	1427.59	0.148066
$454$	−6657.29	−0.688198
$455$	0	0
$456$	−3309.91	−0.339914
$457$	−11140.5	−1.14033	−0.570167	−	0.821529i	$-0.693121\pi$
$457$	−11140.5	−1.14033	−0.570167	+	0.821529i	$0.693121\pi$
$458$	−21102.6	−2.15296
$459$	430.434	0.0437711
$460$	0	0
$461$	14328.8	1.44763	0.723817	−	0.689992i	$-0.242386\pi$
$461$	14328.8	1.44763	0.723817	+	0.689992i	$0.242386\pi$
$462$	1377.94	0.138761
$463$	−11760.7	−1.18049	−0.590246	−	0.807223i	$-0.700969\pi$
$463$	−11760.7	−1.18049	−0.590246	+	0.807223i	$0.700969\pi$
$464$	−28744.4	−2.87592
$465$	0	0
$466$	−17456.5	−1.73532
$467$	−11854.9	−1.17469	−0.587343	−	0.809338i	$-0.699826\pi$
$467$	−11854.9	−1.17469	−0.587343	+	0.809338i	$0.699826\pi$
$468$	−4791.35	−0.473249
$469$	6625.77	0.652345
$470$	0	0
$471$	1942.40	0.190023
$472$	42122.1	4.10769
$473$	714.613	0.0694671
$474$	−16844.8	−1.63229
$475$	0	0
$476$	2629.14	0.253165
$477$	4742.27	0.455207
$478$	2322.19	0.222206
$479$	−1324.68	−0.126359	−0.0631796	−	0.998002i	$-0.520124\pi$
$479$	−1324.68	−0.126359	−0.0631796	+	0.998002i	$0.520124\pi$
$480$	0	0
$481$	2287.84	0.216874
$482$	−6678.34	−0.631100
$483$	−410.035	−0.0386278
$484$	2592.36	0.243459
$485$	0	0
$486$	−1318.14	−0.123029
$487$	−18636.4	−1.73408	−0.867040	−	0.498239i	$-0.833980\pi$
$487$	−18636.4	−1.73408	−0.867040	+	0.498239i	$0.833980\pi$
$488$	16134.7	1.49668
$489$	−3279.70	−0.303299
$490$	0	0
$491$	124.552	0.0114480	0.00572398	−	0.999984i	$-0.498178\pi$
$491$	124.552	0.0114480	0.00572398	+	0.999984i	$0.498178\pi$
$492$	−29562.0	−2.70886
$493$	−2049.29	−0.187212
$494$	2042.24	0.186001
$495$	0	0
$496$	49059.2	4.44117
$497$	4471.75	0.403592
$498$	9865.04	0.887677
$499$	10230.2	0.917768	0.458884	−	0.888496i	$-0.348249\pi$
$499$	10230.2	0.917768	0.458884	+	0.888496i	$0.348249\pi$
$500$	0	0
$501$	−3369.76	−0.300499
$502$	−15395.7	−1.36881
$503$	−5150.81	−0.456587	−0.228294	−	0.973592i	$-0.573315\pi$
$503$	−5150.81	−0.456587	−0.228294	+	0.973592i	$0.573315\pi$
$504$	−5044.92	−0.445870
$505$	0	0
$506$	−1059.46	−0.0930806
$507$	−4738.60	−0.415086
$508$	−14168.1	−1.23741
$509$	−22.7715	−0.00198296	−0.000991481	−	1.00000i	$-0.500316\pi$
$509$	−22.7715	−0.00198296	−0.000991481		1.00000i	$0.500316\pi$
$510$	0	0
$511$	−3926.73	−0.339938
$512$	−10698.1	−0.923429
$513$	409.081	0.0352073
$514$	1855.19	0.159201
$515$	0	0
$516$	−4175.50	−0.356233
$517$	5471.49	0.465446
$518$	3844.46	0.326093
$519$	−138.037	−0.0116747
$520$	0	0
$521$	21521.7	1.80976	0.904879	−	0.425669i	$-0.139961\pi$
$521$	21521.7	1.80976	0.904879	+	0.425669i	$0.139961\pi$
$522$	6275.63	0.526201
$523$	−2923.36	−0.244416	−0.122208	−	0.992504i	$-0.538998\pi$
$523$	−2923.36	−0.244416	−0.122208	+	0.992504i	$0.538998\pi$
$524$	13330.0	1.11130
$525$	0	0
$526$	31977.0	2.65069
$527$	3497.60	0.289104
$528$	−7379.15	−0.608213
$529$	−11851.7	−0.974088
$530$	0	0
$531$	−5205.99	−0.425462
$532$	2498.71	0.203633
$533$	11429.0	0.928792
$534$	381.464	0.0309130
$535$	0	0
$536$	−62679.3	−5.05100
$537$	−2495.93	−0.200572
$538$	13540.3	1.08507
$539$	3121.20	0.249424
$540$	0	0
$541$	21272.8	1.69056	0.845278	−	0.534327i	$-0.179435\pi$
$541$	21272.8	1.69056	0.845278	+	0.534327i	$0.179435\pi$
$542$	12203.2	0.967108
$543$	−5431.89	−0.429290
$544$	−10049.9	−0.792067
$545$	0	0
$546$	3112.75	0.243980
$547$	18730.5	1.46409	0.732046	−	0.681256i	$-0.238566\pi$
$547$	18730.5	1.46409	0.732046	+	0.681256i	$0.238566\pi$
$548$	40124.5	3.12780
$549$	−1994.12	−0.155022
$550$	0	0
$551$	−1947.63	−0.150584
$552$	3878.91	0.299089
$553$	7968.04	0.612723
$554$	22145.7	1.69834
$555$	0	0
$556$	−20440.1	−1.55909
$557$	18885.0	1.43659	0.718297	−	0.695736i	$-0.244922\pi$
$557$	18885.0	1.43659	0.718297	+	0.695736i	$0.244922\pi$
$558$	−10710.9	−0.812593
$559$	1614.30	0.122143
$560$	0	0
$561$	−526.086	−0.0395925
$562$	5607.71	0.420902
$563$	−10285.1	−0.769922	−0.384961	−	0.922933i	$-0.625785\pi$
$563$	−10285.1	−0.769922	−0.384961	+	0.922933i	$0.625785\pi$
$564$	−31970.0	−2.38685
$565$	0	0
$566$	−42360.1	−3.14581
$567$	623.515	0.0461820
$568$	−42302.5	−3.12495
$569$	18008.8	1.32683	0.663415	−	0.748251i	$-0.269106\pi$
$569$	18008.8	1.32683	0.663415	+	0.748251i	$0.269106\pi$
$570$	0	0
$571$	−7010.79	−0.513822	−0.256911	−	0.966435i	$-0.582705\pi$
$571$	−7010.79	−0.513822	−0.256911	+	0.966435i	$0.582705\pi$
$572$	5856.10	0.428070
$573$	1376.69	0.100370
$574$	19205.2	1.39653
$575$	0	0
$576$	14676.1	1.06164
$577$	16398.9	1.18318	0.591589	−	0.806240i	$-0.298501\pi$
$577$	16398.9	1.18318	0.591589	+	0.806240i	$0.298501\pi$
$578$	25271.6	1.81862
$579$	−5336.73	−0.383052
$580$	0	0
$581$	−4666.44	−0.333213
$582$	11708.5	0.833903
$583$	−5796.11	−0.411750
$584$	37146.6	2.63208
$585$	0	0
$586$	−10573.3	−0.745354
$587$	−12823.5	−0.901671	−0.450836	−	0.892607i	$-0.648874\pi$
$587$	−12823.5	−0.901671	−0.450836	+	0.892607i	$0.648874\pi$
$588$	−18237.2	−1.27907
$589$	3324.09	0.232541
$590$	0	0
$591$	−15913.6	−1.10761
$592$	−20587.9	−1.42932
$593$	−16899.5	−1.17029	−0.585144	−	0.810929i	$-0.698962\pi$
$593$	−16899.5	−1.17029	−0.585144	+	0.810929i	$0.698962\pi$
$594$	1611.06	0.111284
$595$	0	0
$596$	−43856.1	−3.01412
$597$	−15415.2	−1.05679
$598$	−2393.31	−0.163662
$599$	−15074.9	−1.02829	−0.514143	−	0.857704i	$-0.671890\pi$
$599$	−15074.9	−1.02829	−0.514143	+	0.857704i	$0.671890\pi$
$600$	0	0
$601$	−11418.8	−0.775014	−0.387507	−	0.921867i	$-0.626664\pi$
$601$	−11418.8	−0.775014	−0.387507	+	0.921867i	$0.626664\pi$
$602$	2712.65	0.183654
$603$	7746.71	0.523168
$604$	10195.1	0.686809
$605$	0	0
$606$	−30451.7	−2.04128
$607$	17952.8	1.20046	0.600232	−	0.799826i	$-0.295075\pi$
$607$	17952.8	1.20046	0.600232	+	0.799826i	$0.295075\pi$
$608$	−9551.30	−0.637100
$609$	−2968.54	−0.197523
$610$	0	0
$611$	12360.0	0.818384
$612$	3073.94	0.203033
$613$	−12528.9	−0.825507	−0.412753	−	0.910843i	$-0.635433\pi$
$613$	−12528.9	−0.825507	−0.412753	+	0.910843i	$0.635433\pi$
$614$	12823.8	0.842878
$615$	0	0
$616$	6166.01	0.403305
$617$	8586.10	0.560232	0.280116	−	0.959966i	$-0.409627\pi$
$617$	8586.10	0.560232	0.280116	+	0.959966i	$0.409627\pi$
$618$	−6977.09	−0.454142
$619$	18415.4	1.19576	0.597882	−	0.801584i	$-0.296009\pi$
$619$	18415.4	1.19576	0.597882	+	0.801584i	$0.296009\pi$
$620$	0	0
$621$	−479.404	−0.0309788
$622$	10790.1	0.695569
$623$	−180.443	−0.0116040
$624$	−16669.4	−1.06941
$625$	0	0
$626$	−21039.6	−1.34331
$627$	−499.988	−0.0318462
$628$	13871.6	0.881427
$629$	−1467.79	−0.0930436
$630$	0	0
$631$	2374.38	0.149798	0.0748989	−	0.997191i	$-0.476137\pi$
$631$	2374.38	0.149798	0.0748989	+	0.997191i	$0.476137\pi$
$632$	−75377.1	−4.74421
$633$	−12787.1	−0.802909
$634$	15805.3	0.990080
$635$	0	0
$636$	33866.8	2.11149
$637$	7050.74	0.438557
$638$	−7670.21	−0.475966
$639$	5228.27	0.323673
$640$	0	0
$641$	11086.0	0.683104	0.341552	−	0.939863i	$-0.389047\pi$
$641$	11086.0	0.683104	0.341552	+	0.939863i	$0.389047\pi$
$642$	18682.1	1.14848
$643$	−19934.1	−1.22259	−0.611294	−	0.791403i	$-0.709351\pi$
$643$	−19934.1	−1.22259	−0.611294	+	0.791403i	$0.709351\pi$
$644$	−2928.26	−0.179176
$645$	0	0
$646$	−1310.21	−0.0797983
$647$	30634.8	1.86148	0.930739	−	0.365684i	$-0.119165\pi$
$647$	30634.8	1.86148	0.930739	+	0.365684i	$0.119165\pi$
$648$	−5898.41	−0.357579
$649$	6362.87	0.384845
$650$	0	0
$651$	5066.53	0.305028
$652$	−23421.9	−1.40686
$653$	9818.07	0.588378	0.294189	−	0.955747i	$-0.404951\pi$
$653$	9818.07	0.588378	0.294189	+	0.955747i	$0.404951\pi$
$654$	29752.7	1.77894
$655$	0	0
$656$	−102848.	−6.12125
$657$	−4591.04	−0.272624
$658$	20769.6	1.23052
$659$	16478.5	0.974070	0.487035	−	0.873383i	$-0.338078\pi$
$659$	16478.5	0.974070	0.487035	+	0.873383i	$0.338078\pi$
$660$	0	0
$661$	2958.12	0.174066	0.0870328	−	0.996205i	$-0.472262\pi$
$661$	2958.12	0.174066	0.0870328	+	0.996205i	$0.472262\pi$
$662$	−43962.1	−2.58102
$663$	−1188.42	−0.0696146
$664$	44144.2	2.58001
$665$	0	0
$666$	4494.86	0.261520
$667$	2282.44	0.132498
$668$	−24065.1	−1.39387
$669$	4133.39	0.238873
$670$	0	0
$671$	2437.26	0.140223
$672$	−14558.0	−0.835692
$673$	29960.3	1.71602	0.858012	−	0.513630i	$-0.171700\pi$
$673$	29960.3	1.71602	0.858012	+	0.513630i	$0.171700\pi$
$674$	32108.2	1.83496
$675$	0	0
$676$	−33840.6	−1.92539
$677$	4514.73	0.256300	0.128150	−	0.991755i	$-0.459096\pi$
$677$	4514.73	0.256300	0.128150	+	0.991755i	$0.459096\pi$
$678$	18330.2	1.03830
$679$	−5538.43	−0.313027
$680$	0	0
$681$	3681.84	0.207178
$682$	13091.0	0.735018
$683$	13555.7	0.759438	0.379719	−	0.925102i	$-0.376021\pi$
$683$	13555.7	0.759438	0.379719	+	0.925102i	$0.376021\pi$
$684$	2921.44	0.163310
$685$	0	0
$686$	26170.2	1.45653
$687$	11670.8	0.648137
$688$	−14526.8	−0.804986
$689$	−13093.3	−0.723972
$690$	0	0
$691$	−11471.3	−0.631535	−0.315768	−	0.948837i	$-0.602262\pi$
$691$	−11471.3	−0.631535	−0.315768	+	0.948837i	$0.602262\pi$
$692$	−985.787	−0.0541532
$693$	−762.074	−0.0417731
$694$	−46327.8	−2.53398
$695$	0	0
$696$	28082.2	1.52939
$697$	−7332.40	−0.398471
$698$	−5084.52	−0.275719
$699$	9654.41	0.522408
$700$	0	0
$701$	22229.0	1.19769	0.598843	−	0.800866i	$-0.295627\pi$
$701$	22229.0	1.19769	0.598843	+	0.800866i	$0.295627\pi$
$702$	3639.35	0.195667
$703$	−1394.97	−0.0748397
$704$	−17937.5	−0.960292
$705$	0	0
$706$	−1145.19	−0.0610480
$707$	14404.5	0.766248
$708$	−37178.4	−1.97352
$709$	−15081.2	−0.798851	−0.399426	−	0.916766i	$-0.630790\pi$
$709$	−15081.2	−0.798851	−0.399426	+	0.916766i	$0.630790\pi$
$710$	0	0
$711$	9316.06	0.491392
$712$	1706.98	0.0898480
$713$	−3895.52	−0.204612
$714$	−1997.01	−0.104673
$715$	0	0
$716$	−17824.6	−0.930358
$717$	−1284.30	−0.0668938
$718$	7465.71	0.388047
$719$	−7399.80	−0.383819	−0.191910	−	0.981413i	$-0.561468\pi$
$719$	−7399.80	−0.383819	−0.191910	+	0.981413i	$0.561468\pi$
$720$	0	0
$721$	3300.36	0.170474
$722$	35960.9	1.85364
$723$	3693.48	0.189989
$724$	−38791.7	−1.99127
$725$	0	0
$726$	−1969.07	−0.100660
$727$	−1705.77	−0.0870202	−0.0435101	−	0.999053i	$-0.513854\pi$
$727$	−1705.77	−0.0870202	−0.0435101	+	0.999053i	$0.513854\pi$
$728$	13928.9	0.709122
$729$	729.000	0.0370370
$730$	0	0
$731$	−1035.67	−0.0524017
$732$	−14241.0	−0.719074
$733$	−37122.6	−1.87061	−0.935303	−	0.353847i	$-0.884873\pi$
$733$	−37122.6	−1.87061	−0.935303	+	0.353847i	$0.884873\pi$
$734$	5589.60	0.281084
$735$	0	0
$736$	11193.2	0.560581
$737$	−9468.20	−0.473223
$738$	22454.3	1.11999
$739$	34256.3	1.70520	0.852598	−	0.522568i	$-0.175026\pi$
$739$	34256.3	1.70520	0.852598	+	0.522568i	$0.175026\pi$
$740$	0	0
$741$	−1129.47	−0.0559945
$742$	−22001.9	−1.08856
$743$	−1567.88	−0.0774160	−0.0387080	−	0.999251i	$-0.512324\pi$
$743$	−1567.88	−0.0774160	−0.0387080	+	0.999251i	$0.512324\pi$
$744$	−47929.0	−2.36178
$745$	0	0
$746$	50801.9	2.49328
$747$	−5455.90	−0.267230
$748$	−3757.03	−0.183651
$749$	−8837.17	−0.431112
$750$	0	0
$751$	−955.613	−0.0464325	−0.0232163	−	0.999730i	$-0.507391\pi$
$751$	−955.613	−0.0464325	−0.0232163	+	0.999730i	$0.507391\pi$
$752$	−111226.	−5.39360
$753$	8514.65	0.412073
$754$	−17326.9	−0.836881
$755$	0	0
$756$	4452.82	0.214216
$757$	14015.4	0.672918	0.336459	−	0.941698i	$-0.390771\pi$
$757$	14015.4	0.672918	0.336459	+	0.941698i	$0.390771\pi$
$758$	38623.2	1.85073
$759$	585.938	0.0280214
$760$	0	0
$761$	−36271.0	−1.72776	−0.863879	−	0.503699i	$-0.831972\pi$
$761$	−36271.0	−1.72776	−0.863879	+	0.503699i	$0.831972\pi$
$762$	10761.6	0.511616
$763$	−14073.9	−0.667770
$764$	9831.63	0.465571
$765$	0	0
$766$	−6311.64	−0.297714
$767$	14373.6	0.676665
$768$	22739.7	1.06842
$769$	−18163.6	−0.851749	−0.425874	−	0.904782i	$-0.640033\pi$
$769$	−18163.6	−0.851749	−0.425874	+	0.904782i	$0.640033\pi$
$770$	0	0
$771$	−1026.02	−0.0479264
$772$	−38112.1	−1.77680
$773$	8345.65	0.388321	0.194160	−	0.980970i	$-0.437802\pi$
$773$	8345.65	0.388321	0.194160	+	0.980970i	$0.437802\pi$
$774$	3171.57	0.147287
$775$	0	0
$776$	52393.2	2.42372
$777$	−2126.19	−0.0981683
$778$	59445.7	2.73937
$779$	−6968.65	−0.320510
$780$	0	0
$781$	−6390.11	−0.292774
$782$	1535.45	0.0702142
$783$	−3470.76	−0.158410
$784$	−63448.5	−2.89033
$785$	0	0
$786$	−10125.0	−0.459475
$787$	22996.2	1.04158	0.520791	−	0.853684i	$-0.325637\pi$
$787$	22996.2	1.04158	0.520791	+	0.853684i	$0.325637\pi$
$788$	−113647.	−5.13768
$789$	−17685.0	−0.797975
$790$	0	0
$791$	−8670.69	−0.389752
$792$	7209.17	0.323443
$793$	5505.75	0.246551
$794$	−11782.4	−0.526626
$795$	0	0
$796$	−110087.	−4.90194
$797$	2743.82	0.121946	0.0609730	−	0.998139i	$-0.480580\pi$
$797$	2743.82	0.121946	0.0609730	+	0.998139i	$0.480580\pi$
$798$	−1897.94	−0.0841934
$799$	−7929.68	−0.351104
$800$	0	0
$801$	−210.970	−0.00930619
$802$	−42477.1	−1.87022
$803$	5611.28	0.246597
$804$	55322.9	2.42673
$805$	0	0
$806$	29572.5	1.29237
$807$	−7488.53	−0.326653
$808$	−136266.	−5.93293
$809$	41241.7	1.79231	0.896156	−	0.443738i	$-0.146348\pi$
$809$	41241.7	1.79231	0.896156	+	0.443738i	$0.146348\pi$
$810$	0	0
$811$	12832.9	0.555641	0.277820	−	0.960633i	$-0.410388\pi$
$811$	12832.9	0.555641	0.277820	+	0.960633i	$0.410388\pi$
$812$	−21199.8	−0.916215
$813$	−6749.03	−0.291142
$814$	−5493.72	−0.236554
$815$	0	0
$816$	10694.4	0.458798
$817$	−984.292	−0.0421493
$818$	58210.4	2.48812
$819$	−1721.51	−0.0734488
$820$	0	0
$821$	16368.5	0.695817	0.347908	−	0.937529i	$-0.386892\pi$
$821$	16368.5	0.695817	0.347908	+	0.937529i	$0.386892\pi$
$822$	−30477.3	−1.29321
$823$	−3869.53	−0.163892	−0.0819461	−	0.996637i	$-0.526114\pi$
$823$	−3869.53	−0.163892	−0.0819461	+	0.996637i	$0.526114\pi$
$824$	−31221.2	−1.31995
$825$	0	0
$826$	24153.3	1.01743
$827$	−7388.69	−0.310677	−0.155339	−	0.987861i	$-0.549647\pi$
$827$	−7388.69	−0.310677	−0.155339	+	0.987861i	$0.549647\pi$
$828$	−3423.65	−0.143696
$829$	23990.1	1.00508	0.502539	−	0.864554i	$-0.332399\pi$
$829$	23990.1	1.00508	0.502539	+	0.864554i	$0.332399\pi$
$830$	0	0
$831$	−12247.8	−0.511276
$832$	−40520.6	−1.68846
$833$	−4523.47	−0.188150
$834$	15525.7	0.644616
$835$	0	0
$836$	−3570.65	−0.147720
$837$	5923.68	0.244626
$838$	39684.5	1.63589
$839$	−18228.3	−0.750074	−0.375037	−	0.927010i	$-0.622370\pi$
$839$	−18228.3	−0.750074	−0.375037	+	0.927010i	$0.622370\pi$
$840$	0	0
$841$	−7864.78	−0.322472
$842$	67782.3	2.77427
$843$	−3101.36	−0.126710
$844$	−91318.7	−3.72431
$845$	0	0
$846$	24283.4	0.986855
$847$	931.424	0.0377852
$848$	117825.	4.77137
$849$	23427.4	0.947028
$850$	0	0
$851$	1634.77	0.0658511
$852$	37337.6	1.50137
$853$	21737.3	0.872534	0.436267	−	0.899817i	$-0.356300\pi$
$853$	21737.3	0.872534	0.436267	+	0.899817i	$0.356300\pi$
$854$	9251.79	0.370714
$855$	0	0
$856$	83599.0	3.33803
$857$	18712.2	0.745852	0.372926	−	0.927861i	$-0.378355\pi$
$857$	18712.2	0.745852	0.372926	+	0.927861i	$0.378355\pi$
$858$	−4448.10	−0.176988
$859$	30527.6	1.21256	0.606279	−	0.795252i	$-0.292661\pi$
$859$	30527.6	1.21256	0.606279	+	0.795252i	$0.292661\pi$
$860$	0	0
$861$	−10621.5	−0.420418
$862$	−32953.4	−1.30209
$863$	−10906.4	−0.430196	−0.215098	−	0.976592i	$-0.569007\pi$
$863$	−10906.4	−0.430196	−0.215098	+	0.976592i	$0.569007\pi$
$864$	−17020.8	−0.670209
$865$	0	0
$866$	30603.5	1.20087
$867$	−13976.6	−0.547484
$868$	36182.5	1.41488
$869$	−11386.3	−0.444481
$870$	0	0
$871$	−21388.5	−0.832058
$872$	133138.	5.17043
$873$	−6475.41	−0.251042
$874$	1459.28	0.0564768
$875$	0	0
$876$	−32786.8	−1.26457
$877$	−21770.9	−0.838256	−0.419128	−	0.907927i	$-0.637664\pi$
$877$	−21770.9	−0.838256	−0.419128	+	0.907927i	$0.637664\pi$
$878$	−59109.8	−2.27205
$879$	5847.58	0.224384
$880$	0	0
$881$	47206.9	1.80527	0.902634	−	0.430409i	$-0.141631\pi$
$881$	47206.9	1.80527	0.902634	+	0.430409i	$0.141631\pi$
$882$	13852.4	0.528837
$883$	6059.68	0.230945	0.115473	−	0.993311i	$-0.463162\pi$
$883$	6059.68	0.230945	0.115473	+	0.993311i	$0.463162\pi$
$884$	−8487.09	−0.322909
$885$	0	0
$886$	−41881.1	−1.58806
$887$	37130.2	1.40553	0.702767	−	0.711420i	$-0.251948\pi$
$887$	37130.2	1.40553	0.702767	+	0.711420i	$0.251948\pi$
$888$	20113.6	0.760101
$889$	−5090.53	−0.192048
$890$	0	0
$891$	−891.000	−0.0335013
$892$	29518.5	1.10802
$893$	−7536.30	−0.282410
$894$	33311.6	1.24621
$895$	0	0
$896$	−29269.1	−1.09131
$897$	1323.63	0.0492694
$898$	40541.4	1.50655
$899$	−28202.5	−1.04628
$900$	0	0
$901$	8400.15	0.310599
$902$	−27444.1	−1.01307
$903$	−1500.24	−0.0552879
$904$	82024.1	3.01779
$905$	0	0
$906$	−7743.85	−0.283965
$907$	−1182.94	−0.0433064	−0.0216532	−	0.999766i	$-0.506893\pi$
$907$	−1182.94	−0.0433064	−0.0216532	+	0.999766i	$0.506893\pi$
$908$	26293.8	0.961001
$909$	16841.4	0.614516
$910$	0	0
$911$	37676.4	1.37022	0.685112	−	0.728438i	$-0.259753\pi$
$911$	37676.4	1.37022	0.685112	+	0.728438i	$0.259753\pi$
$912$	10163.9	0.369035
$913$	6668.32	0.241719
$914$	60431.1	2.18696
$915$	0	0
$916$	83347.1	3.00640
$917$	4789.41	0.172476
$918$	−2334.86	−0.0839454
$919$	8697.82	0.312203	0.156101	−	0.987741i	$-0.450107\pi$
$919$	8697.82	0.312203	0.156101	+	0.987741i	$0.450107\pi$
$920$	0	0
$921$	−7092.26	−0.253744
$922$	−77725.7	−2.77631
$923$	−14435.2	−0.514778
$924$	−5442.33	−0.193766
$925$	0	0
$926$	63795.3	2.26398
$927$	3858.71	0.136717
$928$	81036.0	2.86653
$929$	−17247.5	−0.609119	−0.304559	−	0.952493i	$-0.598509\pi$
$929$	−17247.5	−0.609119	−0.304559	+	0.952493i	$0.598509\pi$
$930$	0	0
$931$	−4299.06	−0.151338
$932$	68946.7	2.42320
$933$	−5967.51	−0.209397
$934$	64306.0	2.25284
$935$	0	0
$936$	16285.4	0.568702
$937$	41812.4	1.45779	0.728896	−	0.684624i	$-0.240034\pi$
$937$	41812.4	1.45779	0.728896	+	0.684624i	$0.240034\pi$
$938$	−35941.0	−1.25108
$939$	11636.0	0.404395
$940$	0	0
$941$	37655.9	1.30451	0.652257	−	0.757998i	$-0.273822\pi$
$941$	37655.9	1.30451	0.652257	+	0.757998i	$0.273822\pi$
$942$	−10536.4	−0.364431
$943$	8166.60	0.282016
$944$	−129346.	−4.45959
$945$	0	0
$946$	−3876.37	−0.133226
$947$	21244.4	0.728986	0.364493	−	0.931206i	$-0.381242\pi$
$947$	21244.4	0.728986	0.364493	+	0.931206i	$0.381242\pi$
$948$	66530.4	2.27933
$949$	12675.8	0.433587
$950$	0	0
$951$	−8741.20	−0.298058
$952$	−8936.24	−0.304228
$953$	−1324.27	−0.0450130	−0.0225065	−	0.999747i	$-0.507165\pi$
$953$	−1324.27	−0.0450130	−0.0225065	+	0.999747i	$0.507165\pi$
$954$	−25724.1	−0.873007
$955$	0	0
$956$	−9171.77	−0.310289
$957$	4242.04	0.143287
$958$	7185.62	0.242335
$959$	14416.6	0.485439
$960$	0	0
$961$	18343.4	0.615735
$962$	−12410.2	−0.415927
$963$	−10332.2	−0.345744
$964$	26376.9	0.881268
$965$	0	0
$966$	2224.21	0.0740815
$967$	−52267.1	−1.73815	−0.869077	−	0.494676i	$-0.835287\pi$
$967$	−52267.1	−1.73815	−0.869077	+	0.494676i	$0.835287\pi$
$968$	−8811.20	−0.292565
$969$	724.619	0.0240228
$970$	0	0
$971$	−52489.8	−1.73479	−0.867394	−	0.497622i	$-0.834207\pi$
$971$	−52489.8	−1.73479	−0.867394	+	0.497622i	$0.834207\pi$
$972$	5206.14	0.171797
$973$	−7344.07	−0.241973
$974$	101092.	3.32566
$975$	0	0
$976$	−49545.3	−1.62490
$977$	−8324.11	−0.272581	−0.136291	−	0.990669i	$-0.543518\pi$
$977$	−8324.11	−0.272581	−0.136291	+	0.990669i	$0.543518\pi$
$978$	17790.5	0.581675
$979$	257.852	0.00841777
$980$	0	0
$981$	−16454.9	−0.535539
$982$	−675.623	−0.0219552
$983$	44407.1	1.44086	0.720431	−	0.693527i	$-0.243944\pi$
$983$	44407.1	1.44086	0.720431	+	0.693527i	$0.243944\pi$
$984$	100479.	3.25523
$985$	0	0
$986$	11116.2	0.359039
$987$	−11486.7	−0.370442
$988$	−8066.05	−0.259732
$989$	1153.50	0.0370870
$990$	0	0
$991$	−45124.7	−1.44645	−0.723226	−	0.690612i	$-0.757341\pi$
$991$	−45124.7	−1.44645	−0.723226	+	0.690612i	$0.757341\pi$
$992$	−138307.	−4.42667
$993$	24313.4	0.777001
$994$	−24256.7	−0.774020
$995$	0	0
$996$	−38963.2	−1.23955
$997$	−5480.61	−0.174095	−0.0870474	−	0.996204i	$-0.527743\pi$
$997$	−5480.61	−0.174095	−0.0870474	+	0.996204i	$0.527743\pi$
$998$	−55492.9	−1.76012
$999$	−2485.90	−0.0787291

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.a.l.1.1		2
3.2	odd	2		2475.4.a.p.1.2		2
5.2	odd	4		825.4.c.h.199.1		4
5.3	odd	4		825.4.c.h.199.4		4
5.4	even	2		33.4.a.c.1.2	✓	2
15.14	odd	2		99.4.a.f.1.1		2
20.19	odd	2		528.4.a.p.1.1		2
35.34	odd	2		1617.4.a.k.1.2		2
40.19	odd	2		2112.4.a.bg.1.2		2
40.29	even	2		2112.4.a.bn.1.2		2
55.54	odd	2		363.4.a.i.1.1		2
60.59	even	2		1584.4.a.bj.1.2		2
165.164	even	2		1089.4.a.u.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.a.c.1.2	✓	2	5.4	even	2
99.4.a.f.1.1		2	15.14	odd	2
363.4.a.i.1.1		2	55.54	odd	2
528.4.a.p.1.1		2	20.19	odd	2
825.4.a.l.1.1		2	1.1	even	1	trivial
825.4.c.h.199.1		4	5.2	odd	4
825.4.c.h.199.4		4	5.3	odd	4
1089.4.a.u.1.2		2	165.164	even	2
1584.4.a.bj.1.2		2	60.59	even	2
1617.4.a.k.1.2		2	35.34	odd	2
2112.4.a.bg.1.2		2	40.19	odd	2
2112.4.a.bn.1.2		2	40.29	even	2
2475.4.a.p.1.2		2	3.2	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.a (trivial)

\(f(q)\)	\(=\)	\(q-5.42443 q^{2} +3.00000 q^{3} +21.4244 q^{4} -16.2733 q^{6} +7.69772 q^{7} -72.8199 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.42443 q^{2} +3.00000 q^{3} +21.4244 q^{4} -16.2733 q^{6} +7.69772 q^{7} -72.8199 q^{8} +9.00000 q^{9} -11.0000 q^{11} +64.2733 q^{12} -24.8489 q^{13} -41.7557 q^{14} +223.611 q^{16} +15.9420 q^{17} -48.8199 q^{18} +15.1511 q^{19} +23.0931 q^{21} +59.6687 q^{22} -17.7557 q^{23} -218.460 q^{24} +134.791 q^{26} +27.0000 q^{27} +164.919 q^{28} -128.547 q^{29} +219.395 q^{31} -630.402 q^{32} -33.0000 q^{33} -86.4763 q^{34} +192.820 q^{36} -92.0703 q^{37} -82.1863 q^{38} -74.5466 q^{39} -459.942 q^{41} -125.267 q^{42} -64.9648 q^{43} -235.669 q^{44} +96.3146 q^{46} -497.408 q^{47} +670.832 q^{48} -283.745 q^{49} +47.8260 q^{51} -532.373 q^{52} +526.919 q^{53} -146.460 q^{54} -560.547 q^{56} +45.4534 q^{57} +697.292 q^{58} -578.443 q^{59} -221.569 q^{61} -1190.09 q^{62} +69.2794 q^{63} +1630.68 q^{64} +179.006 q^{66} +860.745 q^{67} +341.548 q^{68} -53.2671 q^{69} +580.919 q^{71} -655.379 q^{72} -510.116 q^{73} +499.429 q^{74} +324.605 q^{76} -84.6749 q^{77} +404.373 q^{78} +1035.12 q^{79} +81.0000 q^{81} +2494.92 q^{82} -606.211 q^{83} +494.757 q^{84} +352.397 q^{86} -385.640 q^{87} +801.018 q^{88} -23.4411 q^{89} -191.279 q^{91} -380.406 q^{92} +658.186 q^{93} +2698.15 q^{94} -1891.20 q^{96} -719.490 q^{97} +1539.16 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 6 q^{3} + 33 q^{4} - 3 q^{6} - 24 q^{7} - 57 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q - q^2 + 6 * q^3 + 33 * q^4 - 3 * q^6 - 24 * q^7 - 57 * q^8 + 18 * q^9	\( 2 q - q^{2} + 6 q^{3} + 33 q^{4} - 3 q^{6} - 24 q^{7} - 57 q^{8} + 18 q^{9} - 22 q^{11} + 99 q^{12} - 30 q^{13} - 182 q^{14} + 201 q^{16} - 106 q^{17} - 9 q^{18} + 50 q^{19} - 72 q^{21} + 11 q^{22} - 134 q^{23} - 171 q^{24} + 112 q^{26} + 54 q^{27} - 202 q^{28} - 198 q^{29} + 360 q^{31} - 857 q^{32} - 66 q^{33} - 626 q^{34} + 297 q^{36} + 328 q^{37} + 72 q^{38} - 90 q^{39} - 782 q^{41} - 546 q^{42} - 386 q^{43} - 363 q^{44} - 418 q^{46} - 266 q^{47} + 603 q^{48} + 378 q^{49} - 318 q^{51} - 592 q^{52} + 522 q^{53} - 27 q^{54} - 1062 q^{56} + 150 q^{57} + 390 q^{58} - 172 q^{59} - 778 q^{61} - 568 q^{62} - 216 q^{63} + 809 q^{64} + 33 q^{66} + 776 q^{67} - 1070 q^{68} - 402 q^{69} + 630 q^{71} - 513 q^{72} - 1296 q^{73} + 2358 q^{74} + 728 q^{76} + 264 q^{77} + 336 q^{78} + 652 q^{79} + 162 q^{81} + 1070 q^{82} + 324 q^{83} - 606 q^{84} - 1068 q^{86} - 594 q^{87} + 627 q^{88} - 756 q^{89} - 28 q^{91} - 1726 q^{92} + 1080 q^{93} + 3722 q^{94} - 2571 q^{96} + 452 q^{97} + 4467 q^{98} - 198 q^{99}+O(q^{100}) \) 2 * q - q^2 + 6 * q^3 + 33 * q^4 - 3 * q^6 - 24 * q^7 - 57 * q^8 + 18 * q^9 - 22 * q^11 + 99 * q^12 - 30 * q^13 - 182 * q^14 + 201 * q^16 - 106 * q^17 - 9 * q^18 + 50 * q^19 - 72 * q^21 + 11 * q^22 - 134 * q^23 - 171 * q^24 + 112 * q^26 + 54 * q^27 - 202 * q^28 - 198 * q^29 + 360 * q^31 - 857 * q^32 - 66 * q^33 - 626 * q^34 + 297 * q^36 + 328 * q^37 + 72 * q^38 - 90 * q^39 - 782 * q^41 - 546 * q^42 - 386 * q^43 - 363 * q^44 - 418 * q^46 - 266 * q^47 + 603 * q^48 + 378 * q^49 - 318 * q^51 - 592 * q^52 + 522 * q^53 - 27 * q^54 - 1062 * q^56 + 150 * q^57 + 390 * q^58 - 172 * q^59 - 778 * q^61 - 568 * q^62 - 216 * q^63 + 809 * q^64 + 33 * q^66 + 776 * q^67 - 1070 * q^68 - 402 * q^69 + 630 * q^71 - 513 * q^72 - 1296 * q^73 + 2358 * q^74 + 728 * q^76 + 264 * q^77 + 336 * q^78 + 652 * q^79 + 162 * q^81 + 1070 * q^82 + 324 * q^83 - 606 * q^84 - 1068 * q^86 - 594 * q^87 + 627 * q^88 - 756 * q^89 - 28 * q^91 - 1726 * q^92 + 1080 * q^93 + 3722 * q^94 - 2571 * q^96 + 452 * q^97 + 4467 * q^98 - 198 * q^99

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