LMFDB - Embedded newform 525.4.d.j.274.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,4,Mod(274,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("525.274");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	525.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$30.9760027530$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{41})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 21x^{2} + 100 $ x^4 + 21*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.2
Root			$-2.70156i$ of defining polynomial
Character	$\chi$	$=$	525.274
Dual form			525.4.d.j.274.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.70156i q^{2} -3.00000i q^{3} +5.10469 q^{4} -5.10469 q^{6} +7.00000i q^{7} -22.2984i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-1.70156i q^{2} -3.00000i q^{3} +5.10469 q^{4} -5.10469 q^{6} +7.00000i q^{7} -22.2984i q^{8} -9.00000 q^{9} +37.4031 q^{11} -15.3141i q^{12} -29.0156i q^{13} +11.9109 q^{14} +2.89531 q^{16} +58.4187i q^{17} +15.3141i q^{18} +54.5969 q^{19} +21.0000 q^{21} -63.6437i q^{22} -161.675i q^{23} -66.8953 q^{24} -49.3719 q^{26} +27.0000i q^{27} +35.7328i q^{28} -137.581 q^{29} +154.659 q^{31} -183.314i q^{32} -112.209i q^{33} +99.4031 q^{34} -45.9422 q^{36} -350.125i q^{37} -92.9000i q^{38} -87.0469 q^{39} +353.769 q^{41} -35.7328i q^{42} +518.156i q^{43} +190.931 q^{44} -275.100 q^{46} -542.219i q^{47} -8.68594i q^{48} -49.0000 q^{49} +175.256 q^{51} -148.116i q^{52} -305.309i q^{53} +45.9422 q^{54} +156.089 q^{56} -163.791i q^{57} +234.103i q^{58} -14.6813 q^{59} -171.069 q^{61} -263.163i q^{62} -63.0000i q^{63} -288.758 q^{64} -190.931 q^{66} +551.956i q^{67} +298.209i q^{68} -485.025 q^{69} -120.334 q^{71} +200.686i q^{72} -284.659i q^{73} -595.759 q^{74} +278.700 q^{76} +261.822i q^{77} +148.116i q^{78} -941.612 q^{79} +81.0000 q^{81} -601.959i q^{82} -377.150i q^{83} +107.198 q^{84} +881.675 q^{86} +412.744i q^{87} -834.031i q^{88} +677.725 q^{89} +203.109 q^{91} -825.300i q^{92} -463.978i q^{93} -922.619 q^{94} -549.942 q^{96} -1225.03i q^{97} +83.3765i q^{98} -336.628 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 18 q^{4} + 18 q^{6} - 36 q^{9}+O(q^{10}) $ 4 * q - 18 * q^4 + 18 * q^6 - 36 * q^9	$ 4 q - 18 q^{4} + 18 q^{6} - 36 q^{9} + 124 q^{11} - 42 q^{14} + 50 q^{16} + 244 q^{19} + 84 q^{21} - 306 q^{24} - 428 q^{26} - 704 q^{29} + 132 q^{31} + 372 q^{34} + 162 q^{36} + 36 q^{39} + 32 q^{41} - 312 q^{44} - 1920 q^{46} - 196 q^{49} + 240 q^{51} - 162 q^{54} + 714 q^{56} - 1032 q^{59} - 1760 q^{61} + 958 q^{64} + 312 q^{66} - 96 q^{69} + 620 q^{71} - 2716 q^{74} - 1344 q^{76} - 3664 q^{79} + 324 q^{81} - 378 q^{84} + 2912 q^{86} - 1592 q^{89} - 84 q^{91} - 5176 q^{94} - 1854 q^{96} - 1116 q^{99}+O(q^{100}) $ 4 * q - 18 * q^4 + 18 * q^6 - 36 * q^9 + 124 * q^11 - 42 * q^14 + 50 * q^16 + 244 * q^19 + 84 * q^21 - 306 * q^24 - 428 * q^26 - 704 * q^29 + 132 * q^31 + 372 * q^34 + 162 * q^36 + 36 * q^39 + 32 * q^41 - 312 * q^44 - 1920 * q^46 - 196 * q^49 + 240 * q^51 - 162 * q^54 + 714 * q^56 - 1032 * q^59 - 1760 * q^61 + 958 * q^64 + 312 * q^66 - 96 * q^69 + 620 * q^71 - 2716 * q^74 - 1344 * q^76 - 3664 * q^79 + 324 * q^81 - 378 * q^84 + 2912 * q^86 - 1592 * q^89 - 84 * q^91 - 5176 * q^94 - 1854 * q^96 - 1116 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	− 1.70156i	− 0.601593i	−0.953688	−	0.300797i	$-0.902747\pi$
$2$	− 1.70156i	− 0.601593i	0.953688	−	0.300797i	$-0.0972525\pi$
$3$	− 3.00000i	− 0.577350i
$3$	− 3.00000i	− 0.577350i
$4$	5.10469	0.638086
$5$	0	0
$5$	0	0
$6$	−5.10469	−0.347330
$7$	7.00000i	0.377964i
$7$	7.00000i	0.377964i
$8$	− 22.2984i	− 0.985461i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	37.4031	1.02522	0.512612	−	0.858620i	$-0.328678\pi$
$11$	37.4031	1.02522	0.512612	+	0.858620i	$0.328678\pi$
$12$	− 15.3141i	− 0.368399i
$13$	− 29.0156i	− 0.619037i	−0.950893	−	0.309519i	$-0.899832\pi$
$13$	− 29.0156i	− 0.619037i	0.950893	−	0.309519i	$-0.100168\pi$
$14$	11.9109	0.227381
$15$	0	0
$16$	2.89531	0.0452393
$17$	58.4187i	0.833449i	0.909033	+	0.416724i	$0.136822\pi$
$17$	58.4187i	0.833449i	−0.909033	+	0.416724i	$0.863178\pi$
$18$	15.3141i	0.200531i
$19$	54.5969	0.659231	0.329615	−	0.944115i	$-0.393081\pi$
$19$	54.5969	0.659231	0.329615	+	0.944115i	$0.393081\pi$
$20$	0	0
$21$	21.0000	0.218218
$22$	− 63.6437i	− 0.616768i
$23$	− 161.675i	− 1.46572i	−0.680379	−	0.732860i	$-0.738185\pi$
$23$	− 161.675i	− 1.46572i	0.680379	−	0.732860i	$-0.261815\pi$
$24$	−66.8953	−0.568956
$25$	0	0
$26$	−49.3719	−0.372409
$27$	27.0000i	0.192450i
$28$	35.7328i	0.241174i
$29$	−137.581	−0.880972	−0.440486	−	0.897759i	$-0.645194\pi$
$29$	−137.581	−0.880972	−0.440486	+	0.897759i	$0.645194\pi$
$30$	0	0
$31$	154.659	0.896053	0.448026	−	0.894020i	$-0.352127\pi$
$31$	154.659	0.896053	0.448026	+	0.894020i	$0.352127\pi$
$32$	− 183.314i	− 1.01268i
$33$	− 112.209i	− 0.591913i
$34$	99.4031	0.501397
$35$	0	0
$36$	−45.9422	−0.212695
$37$	− 350.125i	− 1.55568i	−0.628462	−	0.777840i	$-0.716315\pi$
$37$	− 350.125i	− 1.55568i	0.628462	−	0.777840i	$-0.283685\pi$
$38$	− 92.9000i	− 0.396589i
$39$	−87.0469	−0.357401
$40$	0	0
$41$	353.769	1.34755	0.673773	−	0.738938i	$-0.264673\pi$
$41$	353.769	1.34755	0.673773	+	0.738938i	$0.264673\pi$
$42$	− 35.7328i	− 0.131278i
$43$	518.156i	1.83763i	0.394689	+	0.918815i	$0.370852\pi$
$43$	518.156i	1.83763i	−0.394689	+	0.918815i	$0.629148\pi$
$44$	190.931	0.654181
$45$	0	0
$46$	−275.100	−0.881767
$47$	− 542.219i	− 1.68278i	−0.540427	−	0.841391i	$-0.681737\pi$
$47$	− 542.219i	− 1.68278i	0.540427	−	0.841391i	$-0.318263\pi$
$48$	− 8.68594i	− 0.0261189i
$49$	−49.0000	−0.142857
$50$	0	0
$51$	175.256	0.481192
$52$	− 148.116i	− 0.394999i
$53$	− 305.309i	− 0.791273i	−0.918407	−	0.395637i	$-0.870524\pi$
$53$	− 305.309i	− 0.791273i	0.918407	−	0.395637i	$-0.129476\pi$
$54$	45.9422	0.115777
$55$	0	0
$56$	156.089	0.372469
$57$	− 163.791i	− 0.380607i
$58$	234.103i	0.529987i
$59$	−14.6813	−0.0323956	−0.0161978	−	0.999869i	$-0.505156\pi$
$59$	−14.6813	−0.0323956	−0.0161978	+	0.999869i	$0.505156\pi$
$60$	0	0
$61$	−171.069	−0.359067	−0.179534	−	0.983752i	$-0.557459\pi$
$61$	−171.069	−0.359067	−0.179534	+	0.983752i	$0.557459\pi$
$62$	− 263.163i	− 0.539059i
$63$	− 63.0000i	− 0.125988i
$64$	−288.758	−0.563980
$65$	0	0
$66$	−190.931	−0.356091
$67$	551.956i	1.00645i	0.864155	+	0.503225i	$0.167853\pi$
$67$	551.956i	1.00645i	−0.864155	+	0.503225i	$0.832147\pi$
$68$	298.209i	0.531812i
$69$	−485.025	−0.846234
$70$	0	0
$71$	−120.334	−0.201142	−0.100571	−	0.994930i	$-0.532067\pi$
$71$	−120.334	−0.201142	−0.100571	+	0.994930i	$0.532067\pi$
$72$	200.686i	0.328487i
$73$	− 284.659i	− 0.456395i	−0.973615	−	0.228198i	$-0.926717\pi$
$73$	− 284.659i	− 0.456395i	0.973615	−	0.228198i	$-0.0732832\pi$
$74$	−595.759	−0.935887
$75$	0	0
$76$	278.700	0.420646
$77$	261.822i	0.387498i
$78$	148.116i	0.215010i
$79$	−941.612	−1.34101	−0.670504	−	0.741906i	$-0.733922\pi$
$79$	−941.612	−1.34101	−0.670504	+	0.741906i	$0.733922\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 601.959i	− 0.810674i
$83$	− 377.150i	− 0.498766i	−0.968405	−	0.249383i	$-0.919772\pi$
$83$	− 377.150i	− 0.498766i	0.968405	−	0.249383i	$-0.0802278\pi$
$84$	107.198	0.139242
$85$	0	0
$86$	881.675	1.10551
$87$	412.744i	0.508630i
$88$	− 834.031i	− 1.01032i
$89$	677.725	0.807176	0.403588	−	0.914941i	$-0.367763\pi$
$89$	677.725	0.807176	0.403588	+	0.914941i	$0.367763\pi$
$90$	0	0
$91$	203.109	0.233974
$92$	− 825.300i	− 0.935255i
$93$	− 463.978i	− 0.517336i
$94$	−922.619	−1.01235
$95$	0	0
$96$	−549.942	−0.584669
$97$	− 1225.03i	− 1.28230i	−0.767414	−	0.641151i	$-0.778457\pi$
$97$	− 1225.03i	− 1.28230i	0.767414	−	0.641151i	$-0.221543\pi$
$98$	83.3765i	0.0859419i
$99$	−336.628	−0.341741
$100$	0	0
$101$	−338.144	−0.333134	−0.166567	−	0.986030i	$-0.553268\pi$
$101$	−338.144	−0.333134	−0.166567	+	0.986030i	$0.553268\pi$
$102$	− 298.209i	− 0.289482i
$103$	566.700i	0.542122i	0.962562	+	0.271061i	$0.0873746\pi$
$103$	566.700i	0.542122i	−0.962562	+	0.271061i	$0.912625\pi$
$104$	−647.003	−0.610037
$105$	0	0
$106$	−519.503	−0.476024
$107$	− 562.531i	− 0.508242i	−0.967172	−	0.254121i	$-0.918214\pi$
$107$	− 562.531i	− 0.508242i	0.967172	−	0.254121i	$-0.0817862\pi$
$108$	137.827i	0.122800i
$109$	−1830.79	−1.60879	−0.804396	−	0.594094i	$-0.797511\pi$
$109$	−1830.79	−1.60879	−0.804396	+	0.594094i	$0.797511\pi$
$110$	0	0
$111$	−1050.37	−0.898173
$112$	20.2672i	0.0170988i
$113$	31.8032i	0.0264761i	0.999912	+	0.0132380i	$0.00421392\pi$
$113$	31.8032i	0.0264761i	−0.999912	+	0.0132380i	$0.995786\pi$
$114$	−278.700	−0.228971
$115$	0	0
$116$	−702.309	−0.562136
$117$	261.141i	0.206346i
$118$	24.9811i	0.0194890i
$119$	−408.931	−0.315014
$120$	0	0
$121$	67.9937	0.0510847
$122$	291.084i	0.216012i
$123$	− 1061.31i	− 0.778006i
$124$	789.488	0.571759
$125$	0	0
$126$	−107.198	−0.0757936
$127$	2220.81i	1.55169i	0.630921	+	0.775847i	$0.282677\pi$
$127$	2220.81i	1.55169i	−0.630921	+	0.775847i	$0.717323\pi$
$128$	− 975.173i	− 0.673390i
$129$	1554.47	1.06096
$130$	0	0
$131$	646.512	0.431191	0.215596	−	0.976483i	$-0.430831\pi$
$131$	646.512	0.431191	0.215596	+	0.976483i	$0.430831\pi$
$132$	− 572.794i	− 0.377692i
$133$	382.178i	0.249166i
$134$	939.188	0.605474
$135$	0	0
$136$	1302.65	0.821331
$137$	− 896.009i	− 0.558768i	−0.960179	−	0.279384i	$-0.909870\pi$
$137$	− 896.009i	− 0.558768i	0.960179	−	0.279384i	$-0.0901303\pi$
$138$	825.300i	0.509088i
$139$	2313.61	1.41178	0.705891	−	0.708320i	$-0.250547\pi$
$139$	2313.61	1.41178	0.705891	+	0.708320i	$0.250547\pi$
$140$	0	0
$141$	−1626.66	−0.971554
$142$	204.756i	0.121005i
$143$	− 1085.27i	− 0.634652i
$144$	−26.0578	−0.0150798
$145$	0	0
$146$	−484.366	−0.274564
$147$	147.000i	0.0824786i
$148$	− 1787.28i	− 0.992658i
$149$	−819.337	−0.450488	−0.225244	−	0.974302i	$-0.572318\pi$
$149$	−819.337	−0.450488	−0.225244	+	0.974302i	$0.572318\pi$
$150$	0	0
$151$	534.744	0.288191	0.144095	−	0.989564i	$-0.453973\pi$
$151$	534.744	0.288191	0.144095	+	0.989564i	$0.453973\pi$
$152$	− 1217.43i	− 0.649646i
$153$	− 525.769i	− 0.277816i
$154$	445.506	0.233116
$155$	0	0
$156$	−444.347	−0.228053
$157$	1564.76i	0.795423i	0.917511	+	0.397711i	$0.130195\pi$
$157$	1564.76i	0.795423i	−0.917511	+	0.397711i	$0.869805\pi$
$158$	1602.21i	0.806741i
$159$	−915.928	−0.456842
$160$	0	0
$161$	1131.72	0.553990
$162$	− 137.827i	− 0.0668437i
$163$	1114.31i	0.535455i	0.963495	+	0.267728i	$0.0862727\pi$
$163$	1114.31i	0.535455i	−0.963495	+	0.267728i	$0.913727\pi$
$164$	1805.88	0.859850
$165$	0	0
$166$	−641.744	−0.300054
$167$	− 1774.47i	− 0.822231i	−0.911583	−	0.411115i	$-0.865139\pi$
$167$	− 1774.47i	− 0.822231i	0.911583	−	0.411115i	$-0.134861\pi$
$168$	− 468.267i	− 0.215045i
$169$	1355.09	0.616793
$170$	0	0
$171$	−491.372	−0.219744
$172$	2645.02i	1.17257i
$173$	4215.88i	1.85276i	0.376590	+	0.926380i	$0.377097\pi$
$173$	4215.88i	1.85276i	−0.376590	+	0.926380i	$0.622903\pi$
$174$	702.309	0.305988
$175$	0	0
$176$	108.294	0.0463804
$177$	44.0438i	0.0187036i
$178$	− 1153.19i	− 0.485592i
$179$	2430.70	1.01497	0.507483	−	0.861662i	$-0.330576\pi$
$179$	2430.70	1.01497	0.507483	+	0.861662i	$0.330576\pi$
$180$	0	0
$181$	−2700.91	−1.10916	−0.554578	−	0.832132i	$-0.687120\pi$
$181$	−2700.91	−1.10916	−0.554578	+	0.832132i	$0.687120\pi$
$182$	− 345.603i	− 0.140757i
$183$	513.206i	0.207308i
$184$	−3605.10	−1.44441
$185$	0	0
$186$	−789.488	−0.311226
$187$	2185.04i	0.854472i
$188$	− 2767.86i	− 1.07376i
$189$	−189.000	−0.0727393
$190$	0	0
$191$	3611.10	1.36801	0.684005	−	0.729478i	$-0.260237\pi$
$191$	3611.10	1.36801	0.684005	+	0.729478i	$0.260237\pi$
$192$	866.273i	0.325614i
$193$	4468.33i	1.66651i	0.552886	+	0.833257i	$0.313526\pi$
$193$	4468.33i	1.66651i	−0.552886	+	0.833257i	$0.686474\pi$
$194$	−2084.47	−0.771425
$195$	0	0
$196$	−250.130	−0.0911551
$197$	− 434.422i	− 0.157113i	−0.996910	−	0.0785566i	$-0.974969\pi$
$197$	− 434.422i	− 0.157113i	0.996910	−	0.0785566i	$-0.0250311\pi$
$198$	572.794i	0.205589i
$199$	468.915	0.167038	0.0835189	−	0.996506i	$-0.473384\pi$
$199$	468.915	0.167038	0.0835189	+	0.996506i	$0.473384\pi$
$200$	0	0
$201$	1655.87	0.581074
$202$	575.372i	0.200411i
$203$	− 963.069i	− 0.332976i
$204$	894.628	0.307042
$205$	0	0
$206$	964.275	0.326137
$207$	1455.07i	0.488573i
$208$	− 84.0093i	− 0.0280048i
$209$	2042.09	0.675859
$210$	0	0
$211$	3735.51	1.21878	0.609392	−	0.792869i	$-0.291414\pi$
$211$	3735.51	1.21878	0.609392	+	0.792869i	$0.291414\pi$
$212$	− 1558.51i	− 0.504900i
$213$	361.003i	0.116129i
$214$	−957.182	−0.305755
$215$	0	0
$216$	602.058	0.189652
$217$	1082.62i	0.338676i
$218$	3115.21i	0.967838i
$219$	−853.978	−0.263500
$220$	0	0
$221$	1695.06	0.515936
$222$	1787.28i	0.540334i
$223$	− 842.806i	− 0.253087i	−0.991961	−	0.126544i	$-0.959612\pi$
$223$	− 842.806i	− 0.253087i	0.991961	−	0.126544i	$-0.0403884\pi$
$224$	1283.20	0.382756
$225$	0	0
$226$	54.1152	0.0159278
$227$	992.150i	0.290094i	0.989425	+	0.145047i	$0.0463333\pi$
$227$	992.150i	0.290094i	−0.989425	+	0.145047i	$0.953667\pi$
$228$	− 836.100i	− 0.242860i
$229$	6411.39	1.85012	0.925059	−	0.379825i	$-0.124016\pi$
$229$	6411.39	1.85012	0.925059	+	0.379825i	$0.124016\pi$
$230$	0	0
$231$	785.466	0.223722
$232$	3067.85i	0.868164i
$233$	2274.35i	0.639476i	0.947506	+	0.319738i	$0.103595\pi$
$233$	2274.35i	0.639476i	−0.947506	+	0.319738i	$0.896405\pi$
$234$	444.347	0.124136
$235$	0	0
$236$	−74.9433	−0.0206712
$237$	2824.84i	0.774232i
$238$	695.822i	0.189510i
$239$	−2863.12	−0.774893	−0.387447	−	0.921892i	$-0.626643\pi$
$239$	−2863.12	−0.774893	−0.387447	+	0.921892i	$0.626643\pi$
$240$	0	0
$241$	−5364.23	−1.43378	−0.716889	−	0.697187i	$-0.754435\pi$
$241$	−5364.23	−1.43378	−0.716889	+	0.697187i	$0.754435\pi$
$242$	− 115.696i	− 0.0307322i
$243$	− 243.000i	− 0.0641500i
$244$	−873.252	−0.229116
$245$	0	0
$246$	−1805.88	−0.468043
$247$	− 1584.16i	− 0.408088i
$248$	− 3448.66i	− 0.883025i
$249$	−1131.45	−0.287963
$250$	0	0
$251$	5569.81	1.40065	0.700325	−	0.713824i	$-0.253039\pi$
$251$	5569.81	1.40065	0.700325	+	0.713824i	$0.253039\pi$
$252$	− 321.595i	− 0.0803913i
$253$	− 6047.15i	− 1.50269i
$254$	3778.85	0.933489
$255$	0	0
$256$	−3969.38	−0.969087
$257$	2095.36i	0.508580i	0.967128	+	0.254290i	$0.0818418\pi$
$257$	2095.36i	0.508580i	−0.967128	+	0.254290i	$0.918158\pi$
$258$	− 2645.02i	− 0.638264i
$259$	2450.87	0.587992
$260$	0	0
$261$	1238.23	0.293657
$262$	− 1100.08i	− 0.259402i
$263$	7465.88i	1.75044i	0.483724	+	0.875220i	$0.339284\pi$
$263$	7465.88i	1.75044i	−0.483724	+	0.875220i	$0.660716\pi$
$264$	−2502.09	−0.583308
$265$	0	0
$266$	650.300	0.149896
$267$	− 2033.17i	− 0.466023i
$268$	2817.56i	0.642202i
$269$	6521.38	1.47812	0.739062	−	0.673637i	$-0.235269\pi$
$269$	6521.38	1.47812	0.739062	+	0.673637i	$0.235269\pi$
$270$	0	0
$271$	2409.70	0.540144	0.270072	−	0.962840i	$-0.412952\pi$
$271$	2409.70	0.540144	0.270072	+	0.962840i	$0.412952\pi$
$272$	169.141i	0.0377046i
$273$	− 609.328i	− 0.135085i
$274$	−1524.62	−0.336151
$275$	0	0
$276$	−2475.90	−0.539970
$277$	− 2219.83i	− 0.481503i	−0.970587	−	0.240752i	$-0.922606\pi$
$277$	− 2219.83i	− 0.481503i	0.970587	−	0.240752i	$-0.0773939\pi$
$278$	− 3936.75i	− 0.849319i
$279$	−1391.93	−0.298684
$280$	0	0
$281$	5838.56	1.23950	0.619749	−	0.784800i	$-0.287234\pi$
$281$	5838.56	1.23950	0.619749	+	0.784800i	$0.287234\pi$
$282$	2767.86i	0.584480i
$283$	3645.04i	0.765636i	0.923824	+	0.382818i	$0.125046\pi$
$283$	3645.04i	0.765636i	−0.923824	+	0.382818i	$0.874954\pi$
$284$	−614.269	−0.128346
$285$	0	0
$286$	−1846.66	−0.381802
$287$	2476.38i	0.509325i
$288$	1649.83i	0.337559i
$289$	1500.25	0.305363
$290$	0	0
$291$	−3675.10	−0.740338
$292$	− 1453.10i	− 0.291219i
$293$	− 3777.91i	− 0.753268i	−0.926362	−	0.376634i	$-0.877081\pi$
$293$	− 3777.91i	− 0.753268i	0.926362	−	0.376634i	$-0.122919\pi$
$294$	250.130	0.0496186
$295$	0	0
$296$	−7807.24	−1.53306
$297$	1009.88i	0.197304i
$298$	1394.15i	0.271011i
$299$	−4691.10	−0.907336
$300$	0	0
$301$	−3627.09	−0.694559
$302$	− 909.900i	− 0.173374i
$303$	1014.43i	0.192335i
$304$	158.075	0.0298231
$305$	0	0
$306$	−894.628	−0.167132
$307$	− 4799.64i	− 0.892281i	−0.894963	−	0.446140i	$-0.852798\pi$
$307$	− 4799.64i	− 0.892281i	0.894963	−	0.446140i	$-0.147202\pi$
$308$	1336.52i	0.247257i
$309$	1700.10	0.312994
$310$	0	0
$311$	580.113	0.105772	0.0528861	−	0.998601i	$-0.483158\pi$
$311$	580.113	0.105772	0.0528861	+	0.998601i	$0.483158\pi$
$312$	1941.01i	0.352205i
$313$	6114.78i	1.10424i	0.833764	+	0.552121i	$0.186182\pi$
$313$	6114.78i	1.10424i	−0.833764	+	0.552121i	$0.813818\pi$
$314$	2662.53	0.478521
$315$	0	0
$316$	−4806.64	−0.855679
$317$	− 4300.63i	− 0.761979i	−0.924579	−	0.380989i	$-0.875583\pi$
$317$	− 4300.63i	− 0.761979i	0.924579	−	0.380989i	$-0.124417\pi$
$318$	1558.51i	0.274833i
$319$	−5145.97	−0.903194
$320$	0	0
$321$	−1687.59	−0.293434
$322$	− 1925.70i	− 0.333277i
$323$	3189.48i	0.549435i
$324$	413.480	0.0708984
$325$	0	0
$326$	1896.06	0.322126
$327$	5492.38i	0.928836i
$328$	− 7888.49i	− 1.32795i
$329$	3795.53	0.636032
$330$	0	0
$331$	−6687.54	−1.11051	−0.555257	−	0.831679i	$-0.687380\pi$
$331$	−6687.54	−1.11051	−0.555257	+	0.831679i	$0.687380\pi$
$332$	− 1925.23i	− 0.318256i
$333$	3151.12i	0.518560i
$334$	−3019.37	−0.494648
$335$	0	0
$336$	60.8016	0.00987202
$337$	5869.28i	0.948723i	0.880330	+	0.474362i	$0.157321\pi$
$337$	5869.28i	0.948723i	−0.880330	+	0.474362i	$0.842679\pi$
$338$	− 2305.78i	− 0.371058i
$339$	95.4097	0.0152860
$340$	0	0
$341$	5784.74	0.918655
$342$	836.100i	0.132196i
$343$	− 343.000i	− 0.0539949i
$344$	11554.1	1.81091
$345$	0	0
$346$	7173.58	1.11461
$347$	1937.22i	0.299699i	0.988709	+	0.149850i	$0.0478790\pi$
$347$	1937.22i	0.299699i	−0.988709	+	0.149850i	$0.952121\pi$
$348$	2106.93i	0.324549i
$349$	9748.82	1.49525	0.747625	−	0.664121i	$-0.231194\pi$
$349$	9748.82	1.49525	0.747625	+	0.664121i	$0.231194\pi$
$350$	0	0
$351$	783.422	0.119134
$352$	− 6856.52i	− 1.03822i
$353$	4576.61i	0.690052i	0.938593	+	0.345026i	$0.112130\pi$
$353$	4576.61i	0.690052i	−0.938593	+	0.345026i	$0.887870\pi$
$354$	74.9433	0.0112520
$355$	0	0
$356$	3459.57	0.515048
$357$	1226.79i	0.181873i
$358$	− 4135.98i	− 0.610596i
$359$	−10849.9	−1.59509	−0.797546	−	0.603258i	$-0.793869\pi$
$359$	−10849.9	−1.59509	−0.797546	+	0.603258i	$0.793869\pi$
$360$	0	0
$361$	−3878.18	−0.565415
$362$	4595.77i	0.667261i
$363$	− 203.981i	− 0.0294938i
$364$	1036.81	0.149296
$365$	0	0
$366$	873.252	0.124715
$367$	11467.7i	1.63108i	0.578699	+	0.815541i	$0.303561\pi$
$367$	11467.7i	1.63108i	−0.578699	+	0.815541i	$0.696439\pi$
$368$	− 468.100i	− 0.0663081i
$369$	−3183.92	−0.449182
$370$	0	0
$371$	2137.17	0.299073
$372$	− 2368.46i	− 0.330105i
$373$	− 539.982i	− 0.0749576i	−0.999297	−	0.0374788i	$-0.988067\pi$
$373$	− 539.982i	− 0.0749576i	0.999297	−	0.0374788i	$-0.0119327\pi$
$374$	3717.99	0.514044
$375$	0	0
$376$	−12090.6	−1.65832
$377$	3992.01i	0.545355i
$378$	321.595i	0.0437595i
$379$	−8577.57	−1.16253	−0.581267	−	0.813713i	$-0.697443\pi$
$379$	−8577.57	−1.16253	−0.581267	+	0.813713i	$0.697443\pi$
$380$	0	0
$381$	6662.44	0.895871
$382$	− 6144.51i	− 0.822985i
$383$	− 8627.96i	− 1.15109i	−0.817770	−	0.575546i	$-0.804790\pi$
$383$	− 8627.96i	− 1.15109i	0.817770	−	0.575546i	$-0.195210\pi$
$384$	−2925.52	−0.388782
$385$	0	0
$386$	7603.13	1.00256
$387$	− 4663.41i	− 0.612543i
$388$	− 6253.42i	− 0.818219i
$389$	−9234.06	−1.20356	−0.601781	−	0.798661i	$-0.705542\pi$
$389$	−9234.06	−1.20356	−0.601781	+	0.798661i	$0.705542\pi$
$390$	0	0
$391$	9444.85	1.22160
$392$	1092.62i	0.140780i
$393$	− 1939.54i	− 0.248948i
$394$	−739.196	−0.0945182
$395$	0	0
$396$	−1718.38	−0.218060
$397$	11618.0i	1.46874i	0.678747	+	0.734372i	$0.262523\pi$
$397$	11618.0i	1.46874i	−0.678747	+	0.734372i	$0.737477\pi$
$398$	− 797.889i	− 0.100489i
$399$	1146.53	0.143856
$400$	0	0
$401$	11157.1	1.38942	0.694711	−	0.719289i	$-0.255532\pi$
$401$	11157.1	1.38942	0.694711	+	0.719289i	$0.255532\pi$
$402$	− 2817.56i	− 0.349570i
$403$	− 4487.54i	− 0.554690i
$404$	−1726.12	−0.212568
$405$	0	0
$406$	−1638.72	−0.200316
$407$	− 13095.8i	− 1.59492i
$408$	− 3907.94i	− 0.474196i
$409$	7428.08	0.898031	0.449015	−	0.893524i	$-0.351775\pi$
$409$	7428.08	0.898031	0.449015	+	0.893524i	$0.351775\pi$
$410$	0	0
$411$	−2688.03	−0.322605
$412$	2892.83i	0.345921i
$413$	− 102.769i	− 0.0122444i
$414$	2475.90	0.293922
$415$	0	0
$416$	−5318.97	−0.626885
$417$	− 6940.83i	− 0.815093i
$418$	− 3474.75i	− 0.406592i
$419$	−9644.74	−1.12453	−0.562263	−	0.826959i	$-0.690069\pi$
$419$	−9644.74	−1.12453	−0.562263	+	0.826959i	$0.690069\pi$
$420$	0	0
$421$	9918.18	1.14818	0.574088	−	0.818793i	$-0.305357\pi$
$421$	9918.18	1.14818	0.574088	+	0.818793i	$0.305357\pi$
$422$	− 6356.21i	− 0.733212i
$423$	4879.97i	0.560927i
$424$	−6807.92	−0.779769
$425$	0	0
$426$	614.269	0.0698625
$427$	− 1197.48i	− 0.135715i
$428$	− 2871.54i	− 0.324302i
$429$	−3255.82	−0.366417
$430$	0	0
$431$	−16324.1	−1.82437	−0.912185	−	0.409779i	$-0.865606\pi$
$431$	−16324.1	−1.82437	−0.912185	+	0.409779i	$0.865606\pi$
$432$	78.1735i	0.00870630i
$433$	5168.75i	0.573659i	0.957982	+	0.286829i	$0.0926012\pi$
$433$	5168.75i	0.573659i	−0.957982	+	0.286829i	$0.907399\pi$
$434$	1842.14	0.203745
$435$	0	0
$436$	−9345.63	−1.02655
$437$	− 8826.95i	− 0.966248i
$438$	1453.10i	0.158520i
$439$	−18339.0	−1.99378	−0.996892	−	0.0787782i	$-0.974898\pi$
$439$	−18339.0	−1.99378	−0.996892	+	0.0787782i	$0.974898\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	− 2884.24i	− 0.310383i
$443$	1613.28i	0.173023i	0.996251	+	0.0865113i	$0.0275719\pi$
$443$	1613.28i	0.173023i	−0.996251	+	0.0865113i	$0.972428\pi$
$444$	−5361.83	−0.573111
$445$	0	0
$446$	−1434.09	−0.152256
$447$	2458.01i	0.260089i
$448$	− 2021.30i	− 0.213164i
$449$	886.750	0.0932034	0.0466017	−	0.998914i	$-0.485161\pi$
$449$	886.750	0.0932034	0.0466017	+	0.998914i	$0.485161\pi$
$450$	0	0
$451$	13232.1	1.38154
$452$	162.345i	0.0168940i
$453$	− 1604.23i	− 0.166387i
$454$	1688.21	0.174518
$455$	0	0
$456$	−3652.28	−0.375073
$457$	7391.22i	0.756557i	0.925692	+	0.378279i	$0.123484\pi$
$457$	7391.22i	0.756557i	−0.925692	+	0.378279i	$0.876516\pi$
$458$	− 10909.4i	− 1.11302i
$459$	−1577.31	−0.160397
$460$	0	0
$461$	−7133.35	−0.720679	−0.360340	−	0.932821i	$-0.617339\pi$
$461$	−7133.35	−0.720679	−0.360340	+	0.932821i	$0.617339\pi$
$462$	− 1336.52i	− 0.134590i
$463$	− 14461.8i	− 1.45162i	−0.687897	−	0.725808i	$-0.741466\pi$
$463$	− 14461.8i	− 1.45162i	0.687897	−	0.725808i	$-0.258534\pi$
$464$	−398.341	−0.0398546
$465$	0	0
$466$	3869.95	0.384704
$467$	− 16393.5i	− 1.62441i	−0.583370	−	0.812206i	$-0.698266\pi$
$467$	− 16393.5i	− 1.62441i	0.583370	−	0.812206i	$-0.301734\pi$
$468$	1333.04i	0.131666i
$469$	−3863.69	−0.380403
$470$	0	0
$471$	4694.28	0.459238
$472$	327.370i	0.0319246i
$473$	19380.7i	1.88398i
$474$	4806.64	0.465772
$475$	0	0
$476$	−2087.47	−0.201006
$477$	2747.78i	0.263758i
$478$	4871.77i	0.466171i
$479$	12991.4	1.23923	0.619617	−	0.784904i	$-0.287288\pi$
$479$	12991.4	1.23923	0.619617	+	0.784904i	$0.287288\pi$
$480$	0	0
$481$	−10159.1	−0.963025
$482$	9127.57i	0.862551i
$483$	− 3395.17i	− 0.319846i
$484$	347.087	0.0325964
$485$	0	0
$486$	−413.480	−0.0385922
$487$	− 12863.5i	− 1.19692i	−0.801152	−	0.598461i	$-0.795779\pi$
$487$	− 12863.5i	− 1.19692i	0.801152	−	0.598461i	$-0.204221\pi$
$488$	3814.57i	0.353847i
$489$	3342.92	0.309145
$490$	0	0
$491$	−4898.10	−0.450200	−0.225100	−	0.974336i	$-0.572271\pi$
$491$	−4898.10	−0.450200	−0.225100	+	0.974336i	$0.572271\pi$
$492$	− 5417.63i	− 0.496435i
$493$	− 8037.32i	− 0.734245i
$494$	−2695.55	−0.245503
$495$	0	0
$496$	447.787	0.0405368
$497$	− 842.340i	− 0.0760244i
$498$	1925.23i	0.173236i
$499$	−10308.0	−0.924746	−0.462373	−	0.886686i	$-0.653002\pi$
$499$	−10308.0	−0.924746	−0.462373	+	0.886686i	$0.653002\pi$
$500$	0	0
$501$	−5323.41	−0.474715
$502$	− 9477.37i	− 0.842621i
$503$	15119.6i	1.34026i	0.742244	+	0.670130i	$0.233762\pi$
$503$	15119.6i	1.34026i	−0.742244	+	0.670130i	$0.766238\pi$
$504$	−1404.80	−0.124156
$505$	0	0
$506$	−10289.6	−0.904009
$507$	− 4065.28i	− 0.356105i
$508$	11336.6i	0.990114i
$509$	−14183.8	−1.23514	−0.617571	−	0.786515i	$-0.711883\pi$
$509$	−14183.8	−1.23514	−0.617571	+	0.786515i	$0.711883\pi$
$510$	0	0
$511$	1992.62	0.172501
$512$	− 1047.24i	− 0.0903943i
$513$	1474.12i	0.126869i
$514$	3565.39	0.305958
$515$	0	0
$516$	7935.07	0.676981
$517$	− 20280.7i	− 1.72523i
$518$	− 4170.32i	− 0.353732i
$519$	12647.6	1.06969
$520$	0	0
$521$	−7464.08	−0.627653	−0.313827	−	0.949480i	$-0.601611\pi$
$521$	−7464.08	−0.627653	−0.313827	+	0.949480i	$0.601611\pi$
$522$	− 2106.93i	− 0.176662i
$523$	16642.9i	1.39148i	0.718295	+	0.695739i	$0.244923\pi$
$523$	16642.9i	1.39148i	−0.718295	+	0.695739i	$0.755077\pi$
$524$	3300.24	0.275137
$525$	0	0
$526$	12703.7	1.05305
$527$	9035.01i	0.746814i
$528$	− 324.881i	− 0.0267777i
$529$	−13971.8	−1.14834
$530$	0	0
$531$	132.132	0.0107985
$532$	1950.90i	0.158989i
$533$	− 10264.8i	− 0.834181i
$534$	−3459.57	−0.280356
$535$	0	0
$536$	12307.8	0.991818
$537$	− 7292.09i	− 0.585991i
$538$	− 11096.5i	− 0.889230i
$539$	−1832.75	−0.146461
$540$	0	0
$541$	67.8755	0.00539408	0.00269704	−	0.999996i	$-0.499142\pi$
$541$	67.8755	0.00539408	0.00269704	+	0.999996i	$0.499142\pi$
$542$	− 4100.26i	− 0.324947i
$543$	8102.74i	0.640372i
$544$	10709.0	0.844014
$545$	0	0
$546$	−1036.81	−0.0812662
$547$	− 9212.91i	− 0.720138i	−0.932926	−	0.360069i	$-0.882753\pi$
$547$	− 9212.91i	− 0.720138i	0.932926	−	0.360069i	$-0.117247\pi$
$548$	− 4573.85i	− 0.356542i
$549$	1539.62	0.119689
$550$	0	0
$551$	−7511.51	−0.580764
$552$	10815.3i	0.833931i
$553$	− 6591.29i	− 0.506854i
$554$	−3777.17	−0.289669
$555$	0	0
$556$	11810.2	0.900838
$557$	16699.6i	1.27035i	0.772370	+	0.635173i	$0.219071\pi$
$557$	16699.6i	1.27035i	−0.772370	+	0.635173i	$0.780929\pi$
$558$	2368.46i	0.179686i
$559$	15034.6	1.13756
$560$	0	0
$561$	6555.13	0.493329
$562$	− 9934.67i	− 0.745674i
$563$	− 14772.8i	− 1.10586i	−0.833227	−	0.552931i	$-0.813509\pi$
$563$	− 14772.8i	− 1.10586i	0.833227	−	0.552931i	$-0.186491\pi$
$564$	−8303.57	−0.619935
$565$	0	0
$566$	6202.26	0.460601
$567$	567.000i	0.0419961i
$568$	2683.27i	0.198217i
$569$	−5663.76	−0.417289	−0.208644	−	0.977992i	$-0.566905\pi$
$569$	−5663.76	−0.417289	−0.208644	+	0.977992i	$0.566905\pi$
$570$	0	0
$571$	5579.58	0.408929	0.204464	−	0.978874i	$-0.434455\pi$
$571$	5579.58	0.408929	0.204464	+	0.978874i	$0.434455\pi$
$572$	− 5539.99i	− 0.404962i
$573$	− 10833.3i	− 0.789821i
$574$	4213.72	0.306406
$575$	0	0
$576$	2598.82	0.187993
$577$	− 2301.23i	− 0.166034i	−0.996548	−	0.0830170i	$-0.973544\pi$
$577$	− 2301.23i	− 0.166034i	0.996548	−	0.0830170i	$-0.0264556\pi$
$578$	− 2552.77i	− 0.183704i
$579$	13405.0	0.962162
$580$	0	0
$581$	2640.05	0.188516
$582$	6253.42i	0.445382i
$583$	− 11419.5i	− 0.811232i
$584$	−6347.46	−0.449760
$585$	0	0
$586$	−6428.34	−0.453161
$587$	− 16470.4i	− 1.15810i	−0.815291	−	0.579052i	$-0.803423\pi$
$587$	− 16470.4i	− 1.15810i	0.815291	−	0.579052i	$-0.196577\pi$
$588$	750.389i	0.0526284i
$589$	8443.92	0.590706
$590$	0	0
$591$	−1303.27	−0.0907093
$592$	− 1013.72i	− 0.0703779i
$593$	13570.0i	0.939715i	0.882742	+	0.469858i	$0.155695\pi$
$593$	13570.0i	0.939715i	−0.882742	+	0.469858i	$0.844305\pi$
$594$	1718.38	0.118697
$595$	0	0
$596$	−4182.46	−0.287450
$597$	− 1406.75i	− 0.0964393i
$598$	7982.20i	0.545847i
$599$	−27814.1	−1.89725	−0.948625	−	0.316403i	$-0.897525\pi$
$599$	−27814.1	−1.89725	−0.948625	+	0.316403i	$0.897525\pi$
$600$	0	0
$601$	20646.1	1.40128	0.700641	−	0.713514i	$-0.252898\pi$
$601$	20646.1	1.40128	0.700641	+	0.713514i	$0.252898\pi$
$602$	6171.72i	0.417842i
$603$	− 4967.61i	− 0.335483i
$604$	2729.70	0.183891
$605$	0	0
$606$	1726.12	0.115707
$607$	3315.28i	0.221686i	0.993838	+	0.110843i	$0.0353550\pi$
$607$	3315.28i	0.221686i	−0.993838	+	0.110843i	$0.964645\pi$
$608$	− 10008.4i	− 0.667588i
$609$	−2889.21	−0.192244
$610$	0	0
$611$	−15732.8	−1.04170
$612$	− 2683.88i	− 0.177271i
$613$	11113.9i	0.732278i	0.930560	+	0.366139i	$0.119320\pi$
$613$	11113.9i	0.732278i	−0.930560	+	0.366139i	$0.880680\pi$
$614$	−8166.89	−0.536790
$615$	0	0
$616$	5838.22	0.381865
$617$	7871.34i	0.513595i	0.966465	+	0.256797i	$0.0826673\pi$
$617$	7871.34i	0.513595i	−0.966465	+	0.256797i	$0.917333\pi$
$618$	− 2892.83i	− 0.188295i
$619$	19107.1	1.24068	0.620339	−	0.784334i	$-0.286995\pi$
$619$	19107.1	1.24068	0.620339	+	0.784334i	$0.286995\pi$
$620$	0	0
$621$	4365.22	0.282078
$622$	− 987.098i	− 0.0636319i
$623$	4744.07i	0.305084i
$624$	−252.028	−0.0161686
$625$	0	0
$626$	10404.7	0.664305
$627$	− 6126.28i	− 0.390208i
$628$	7987.60i	0.507548i
$629$	20453.9	1.29658
$630$	0	0
$631$	−25769.9	−1.62580	−0.812902	−	0.582401i	$-0.802113\pi$
$631$	−25769.9	−1.62580	−0.812902	+	0.582401i	$0.802113\pi$
$632$	20996.5i	1.32151i
$633$	− 11206.5i	− 0.703665i
$634$	−7317.79	−0.458401
$635$	0	0
$636$	−4675.53	−0.291504
$637$	1421.77i	0.0884339i
$638$	8756.19i	0.543355i
$639$	1083.01	0.0670472
$640$	0	0
$641$	−1954.61	−0.120440	−0.0602202	−	0.998185i	$-0.519180\pi$
$641$	−1954.61	−0.120440	−0.0602202	+	0.998185i	$0.519180\pi$
$642$	2871.54i	0.176528i
$643$	19396.5i	1.18961i	0.803868	+	0.594807i	$0.202772\pi$
$643$	19396.5i	1.18961i	−0.803868	+	0.594807i	$0.797228\pi$
$644$	5777.10	0.353493
$645$	0	0
$646$	5427.10	0.330536
$647$	31264.3i	1.89973i	0.312661	+	0.949865i	$0.398780\pi$
$647$	31264.3i	1.89973i	−0.312661	+	0.949865i	$0.601220\pi$
$648$	− 1806.17i	− 0.109496i
$649$	−549.126	−0.0332127
$650$	0	0
$651$	3247.85	0.195535
$652$	5688.18i	0.341666i
$653$	− 6442.75i	− 0.386102i	−0.981189	−	0.193051i	$-0.938162\pi$
$653$	− 6442.75i	− 0.386102i	0.981189	−	0.193051i	$-0.0618382\pi$
$654$	9345.63	0.558781
$655$	0	0
$656$	1024.27	0.0609620
$657$	2561.93i	0.152132i
$658$	− 6458.33i	− 0.382632i
$659$	3584.70	0.211897	0.105949	−	0.994372i	$-0.466212\pi$
$659$	3584.70	0.211897	0.105949	+	0.994372i	$0.466212\pi$
$660$	0	0
$661$	6294.43	0.370386	0.185193	−	0.982702i	$-0.440709\pi$
$661$	6294.43	0.370386	0.185193	+	0.982702i	$0.440709\pi$
$662$	11379.3i	0.668078i
$663$	− 5085.17i	− 0.297876i
$664$	−8409.85	−0.491514
$665$	0	0
$666$	5361.83	0.311962
$667$	22243.4i	1.29126i
$668$	− 9058.11i	− 0.524654i
$669$	−2528.42	−0.146120
$670$	0	0
$671$	−6398.51	−0.368125
$672$	− 3849.60i	− 0.220984i
$673$	10233.9i	0.586162i	0.956088	+	0.293081i	$0.0946806\pi$
$673$	10233.9i	0.586162i	−0.956088	+	0.293081i	$0.905319\pi$
$674$	9986.94	0.570745
$675$	0	0
$676$	6917.33	0.393567
$677$	− 7100.75i	− 0.403108i	−0.979477	−	0.201554i	$-0.935401\pi$
$677$	− 7100.75i	− 0.403108i	0.979477	−	0.201554i	$-0.0645992\pi$
$678$	− 162.345i	− 0.00919593i
$679$	8575.24	0.484665
$680$	0	0
$681$	2976.45	0.167486
$682$	− 9843.10i	− 0.552657i
$683$	35274.6i	1.97620i	0.153813	+	0.988100i	$0.450845\pi$
$683$	35274.6i	1.97620i	−0.153813	+	0.988100i	$0.549155\pi$
$684$	−2508.30	−0.140215
$685$	0	0
$686$	−583.636	−0.0324830
$687$	− 19234.2i	− 1.06817i
$688$	1500.22i	0.0831330i
$689$	−8858.74	−0.489828
$690$	0	0
$691$	4945.12	0.272245	0.136122	−	0.990692i	$-0.456536\pi$
$691$	4945.12	0.272245	0.136122	+	0.990692i	$0.456536\pi$
$692$	21520.8i	1.18222i
$693$	− 2356.40i	− 0.129166i
$694$	3296.31	0.180297
$695$	0	0
$696$	9203.54	0.501235
$697$	20666.7i	1.12311i
$698$	− 16588.2i	− 0.899532i
$699$	6823.06	0.369201
$700$	0	0
$701$	−15300.4	−0.824379	−0.412190	−	0.911098i	$-0.635236\pi$
$701$	−15300.4	−0.824379	−0.412190	+	0.911098i	$0.635236\pi$
$702$	− 1333.04i	− 0.0716701i
$703$	− 19115.7i	− 1.02555i
$704$	−10800.4	−0.578206
$705$	0	0
$706$	7787.38	0.415130
$707$	− 2367.01i	− 0.125913i
$708$	224.830i	0.0119345i
$709$	28297.4	1.49892	0.749458	−	0.662052i	$-0.230314\pi$
$709$	28297.4	1.49892	0.749458	+	0.662052i	$0.230314\pi$
$710$	0	0
$711$	8474.51	0.447003
$712$	− 15112.2i	− 0.795441i
$713$	− 25004.5i	− 1.31336i
$714$	2087.47	0.109414
$715$	0	0
$716$	12407.9	0.647635
$717$	8589.35i	0.447385i
$718$	18461.9i	0.959597i
$719$	−8548.96	−0.443425	−0.221712	−	0.975112i	$-0.571165\pi$
$719$	−8548.96	−0.443425	−0.221712	+	0.975112i	$0.571165\pi$
$720$	0	0
$721$	−3966.90	−0.204903
$722$	6598.97i	0.340150i
$723$	16092.7i	0.827792i
$724$	−13787.3	−0.707737
$725$	0	0
$726$	−347.087	−0.0177432
$727$	14345.3i	0.731827i	0.930649	+	0.365913i	$0.119243\pi$
$727$	14345.3i	0.731827i	−0.930649	+	0.365913i	$0.880757\pi$
$728$	− 4529.02i	− 0.230572i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−30270.0	−1.53157
$732$	2619.76i	0.132280i
$733$	22624.0i	1.14002i	0.821637	+	0.570012i	$0.193061\pi$
$733$	22624.0i	1.14002i	−0.821637	+	0.570012i	$0.806939\pi$
$734$	19512.9	0.981248
$735$	0	0
$736$	−29637.3	−1.48430
$737$	20644.9i	1.03184i
$738$	5417.63i	0.270225i
$739$	−14837.3	−0.738566	−0.369283	−	0.929317i	$-0.620397\pi$
$739$	−14837.3	−0.738566	−0.369283	+	0.929317i	$0.620397\pi$
$740$	0	0
$741$	−4752.49	−0.235610
$742$	− 3636.52i	− 0.179920i
$743$	− 13073.1i	− 0.645497i	−0.946485	−	0.322749i	$-0.895393\pi$
$743$	− 13073.1i	− 0.645497i	0.946485	−	0.322749i	$-0.104607\pi$
$744$	−10346.0	−0.509815
$745$	0	0
$746$	−918.813	−0.0450940
$747$	3394.35i	0.166255i
$748$	11154.0i	0.545226i
$749$	3937.72	0.192098
$750$	0	0
$751$	16213.3	0.787791	0.393895	−	0.919155i	$-0.371127\pi$
$751$	16213.3	0.787791	0.393895	+	0.919155i	$0.371127\pi$
$752$	− 1569.89i	− 0.0761278i
$753$	− 16709.4i	− 0.808665i
$754$	6792.65	0.328082
$755$	0	0
$756$	−964.786	−0.0464139
$757$	19903.9i	0.955642i	0.878457	+	0.477821i	$0.158573\pi$
$757$	19903.9i	0.955642i	−0.878457	+	0.477821i	$0.841427\pi$
$758$	14595.3i	0.699372i
$759$	−18141.4	−0.867580
$760$	0	0
$761$	−30125.5	−1.43502	−0.717509	−	0.696549i	$-0.754718\pi$
$761$	−30125.5	−1.43502	−0.717509	+	0.696549i	$0.754718\pi$
$762$	− 11336.6i	− 0.538950i
$763$	− 12815.6i	− 0.608066i
$764$	18433.5	0.872907
$765$	0	0
$766$	−14681.0	−0.692489
$767$	425.986i	0.0200541i
$768$	11908.1i	0.559503i
$769$	36049.1	1.69046	0.845230	−	0.534402i	$-0.179463\pi$
$769$	36049.1	1.69046	0.845230	+	0.534402i	$0.179463\pi$
$770$	0	0
$771$	6286.09	0.293629
$772$	22809.4i	1.06338i
$773$	9644.77i	0.448769i	0.974501	+	0.224384i	$0.0720371\pi$
$773$	9644.77i	0.448769i	−0.974501	+	0.224384i	$0.927963\pi$
$774$	−7935.07	−0.368502
$775$	0	0
$776$	−27316.4	−1.26366
$777$	− 7352.62i	− 0.339477i
$778$	15712.3i	0.724054i
$779$	19314.7	0.888344
$780$	0	0
$781$	−4500.88	−0.206215
$782$	− 16071.0i	− 0.734908i
$783$	− 3714.69i	− 0.169543i
$784$	−141.870	−0.00646275
$785$	0	0
$786$	−3300.24	−0.149766
$787$	− 25218.6i	− 1.14224i	−0.820865	−	0.571122i	$-0.806508\pi$
$787$	− 25218.6i	− 1.14224i	0.820865	−	0.571122i	$-0.193492\pi$
$788$	− 2217.59i	− 0.100252i
$789$	22397.6	1.01062
$790$	0	0
$791$	−222.623	−0.0100070
$792$	7506.28i	0.336773i
$793$	4963.67i	0.222276i
$794$	19768.8	0.883586
$795$	0	0
$796$	2393.67	0.106584
$797$	32042.3i	1.42409i	0.702135	+	0.712044i	$0.252230\pi$
$797$	32042.3i	1.42409i	−0.702135	+	0.712044i	$0.747770\pi$
$798$	− 1950.90i	− 0.0865427i
$799$	31675.7	1.40251
$800$	0	0
$801$	−6099.52	−0.269059
$802$	− 18984.5i	− 0.835867i
$803$	− 10647.1i	− 0.467908i
$804$	8452.69	0.370775
$805$	0	0
$806$	−7635.82	−0.333698
$807$	− 19564.1i	− 0.853396i
$808$	7540.07i	0.328291i
$809$	−3427.90	−0.148972	−0.0744860	−	0.997222i	$-0.523732\pi$
$809$	−3427.90	−0.148972	−0.0744860	+	0.997222i	$0.523732\pi$
$810$	0	0
$811$	23094.4	0.999943	0.499972	−	0.866042i	$-0.333344\pi$
$811$	23094.4	0.999943	0.499972	+	0.866042i	$0.333344\pi$
$812$	− 4916.16i	− 0.212467i
$813$	− 7229.11i	− 0.311852i
$814$	−22283.3	−0.959494
$815$	0	0
$816$	507.422	0.0217688
$817$	28289.7i	1.21142i
$818$	− 12639.3i	− 0.540249i
$819$	−1827.98	−0.0779914
$820$	0	0
$821$	474.741	0.0201810	0.0100905	−	0.999949i	$-0.496788\pi$
$821$	474.741	0.0201810	0.0100905	+	0.999949i	$0.496788\pi$
$822$	4573.85i	0.194077i
$823$	− 24159.8i	− 1.02328i	−0.859201	−	0.511638i	$-0.829039\pi$
$823$	− 24159.8i	− 1.02328i	0.859201	−	0.511638i	$-0.170961\pi$
$824$	12636.5	0.534240
$825$	0	0
$826$	−174.868	−0.00736613
$827$	− 7566.35i	− 0.318147i	−0.987267	−	0.159074i	$-0.949149\pi$
$827$	− 7566.35i	− 0.318147i	0.987267	−	0.159074i	$-0.0508507\pi$
$828$	7427.70i	0.311752i
$829$	10580.9	0.443295	0.221648	−	0.975127i	$-0.428857\pi$
$829$	10580.9	0.443295	0.221648	+	0.975127i	$0.428857\pi$
$830$	0	0
$831$	−6659.48	−0.277996
$832$	8378.49i	0.349125i
$833$	− 2862.52i	− 0.119064i
$834$	−11810.2	−0.490354
$835$	0	0
$836$	10424.2	0.431256
$837$	4175.80i	0.172445i
$838$	16411.1i	0.676507i
$839$	−15315.6	−0.630218	−0.315109	−	0.949055i	$-0.602041\pi$
$839$	−15315.6	−0.630218	−0.315109	+	0.949055i	$0.602041\pi$
$840$	0	0
$841$	−5460.40	−0.223888
$842$	− 16876.4i	− 0.690735i
$843$	− 17515.7i	− 0.715625i
$844$	19068.6	0.777688
$845$	0	0
$846$	8303.57	0.337450
$847$	475.956i	0.0193082i
$848$	− 883.966i	− 0.0357966i
$849$	10935.1	0.442040
$850$	0	0
$851$	−56606.4	−2.28019
$852$	1842.81i	0.0741004i
$853$	− 18598.2i	− 0.746528i	−0.927725	−	0.373264i	$-0.878239\pi$
$853$	− 18598.2i	− 0.746528i	0.927725	−	0.373264i	$-0.121761\pi$
$854$	−2037.59	−0.0816450
$855$	0	0
$856$	−12543.6	−0.500853
$857$	41775.3i	1.66513i	0.553926	+	0.832566i	$0.313129\pi$
$857$	41775.3i	1.66513i	−0.553926	+	0.832566i	$0.686871\pi$
$858$	5539.99i	0.220434i
$859$	−32414.7	−1.28752	−0.643758	−	0.765229i	$-0.722626\pi$
$859$	−32414.7	−1.28752	−0.643758	+	0.765229i	$0.722626\pi$
$860$	0	0
$861$	7429.14	0.294059
$862$	27776.4i	1.09753i
$863$	31299.7i	1.23459i	0.786730	+	0.617297i	$0.211772\pi$
$863$	31299.7i	1.23459i	−0.786730	+	0.617297i	$0.788228\pi$
$864$	4949.48	0.194890
$865$	0	0
$866$	8794.94	0.345109
$867$	− 4500.75i	− 0.176302i
$868$	5526.41i	0.216104i
$869$	−35219.2	−1.37483
$870$	0	0
$871$	16015.4	0.623030
$872$	40823.8i	1.58540i
$873$	11025.3i	0.427434i
$874$	−15019.6	−0.581288
$875$	0	0
$876$	−4359.29	−0.168136
$877$	− 19973.0i	− 0.769031i	−0.923119	−	0.384515i	$-0.874369\pi$
$877$	− 19973.0i	− 0.769031i	0.923119	−	0.384515i	$-0.125631\pi$
$878$	31204.9i	1.19945i
$879$	−11333.7	−0.434900
$880$	0	0
$881$	17367.9	0.664176	0.332088	−	0.943248i	$-0.392247\pi$
$881$	17367.9	0.664176	0.332088	+	0.943248i	$0.392247\pi$
$882$	− 750.389i	− 0.0286473i
$883$	14364.2i	0.547446i	0.961809	+	0.273723i	$0.0882551\pi$
$883$	14364.2i	0.547446i	−0.961809	+	0.273723i	$0.911745\pi$
$884$	8652.73	0.329211
$885$	0	0
$886$	2745.09	0.104089
$887$	− 33738.1i	− 1.27713i	−0.769568	−	0.638564i	$-0.779529\pi$
$887$	− 33738.1i	− 1.27713i	0.769568	−	0.638564i	$-0.220471\pi$
$888$	23421.7i	0.885114i
$889$	−15545.7	−0.586485
$890$	0	0
$891$	3029.65	0.113914
$892$	− 4302.26i	− 0.161491i
$893$	− 29603.4i	− 1.10934i
$894$	4182.46	0.156468
$895$	0	0
$896$	6826.21	0.254518
$897$	14073.3i	0.523850i
$898$	− 1508.86i	− 0.0560705i
$899$	−21278.2	−0.789398
$900$	0	0
$901$	17835.8	0.659485
$902$	− 22515.2i	− 0.831123i
$903$	10881.3i	0.401004i
$904$	709.162	0.0260911
$905$	0	0
$906$	−2729.70	−0.100097
$907$	− 32998.6i	− 1.20805i	−0.796966	−	0.604024i	$-0.793563\pi$
$907$	− 32998.6i	− 1.20805i	0.796966	−	0.604024i	$-0.206437\pi$
$908$	5064.62i	0.185105i
$909$	3043.29	0.111045
$910$	0	0
$911$	33446.3	1.21638	0.608192	−	0.793790i	$-0.291895\pi$
$911$	33446.3	1.21638	0.608192	+	0.793790i	$0.291895\pi$
$912$	− 474.225i	− 0.0172184i
$913$	− 14106.6i	− 0.511347i
$914$	12576.6	0.455139
$915$	0	0
$916$	32728.2	1.18053
$917$	4525.59i	0.162975i
$918$	2683.88i	0.0964939i
$919$	−41708.7	−1.49711	−0.748554	−	0.663074i	$-0.769252\pi$
$919$	−41708.7	−1.49711	−0.748554	+	0.663074i	$0.769252\pi$
$920$	0	0
$921$	−14398.9	−0.515158
$922$	12137.8i	0.433556i
$923$	3491.58i	0.124514i
$924$	4009.56	0.142754
$925$	0	0
$926$	−24607.7	−0.873283
$927$	− 5100.30i	− 0.180707i
$928$	25220.6i	0.892140i
$929$	−49024.6	−1.73137	−0.865686	−	0.500587i	$-0.833117\pi$
$929$	−49024.6	−1.73137	−0.865686	+	0.500587i	$0.833117\pi$
$930$	0	0
$931$	−2675.25	−0.0941758
$932$	11609.9i	0.408040i
$933$	− 1740.34i	− 0.0610677i
$934$	−27894.6	−0.977235
$935$	0	0
$936$	5823.03	0.203346
$937$	− 5447.58i	− 0.189930i	−0.995481	−	0.0949651i	$-0.969726\pi$
$937$	− 5447.58i	− 0.189930i	0.995481	−	0.0949651i	$-0.0302739\pi$
$938$	6574.31i	0.228848i
$939$	18344.4	0.637535
$940$	0	0
$941$	4125.75	0.142928	0.0714642	−	0.997443i	$-0.477233\pi$
$941$	4125.75	0.142928	0.0714642	+	0.997443i	$0.477233\pi$
$942$	− 7987.60i	− 0.276274i
$943$	− 57195.5i	− 1.97513i
$944$	−42.5069	−0.00146555
$945$	0	0
$946$	32977.4	1.13339
$947$	17332.3i	0.594747i	0.954761	+	0.297374i	$0.0961107\pi$
$947$	17332.3i	0.594747i	−0.954761	+	0.297374i	$0.903889\pi$
$948$	14419.9i	0.494026i
$949$	−8259.57	−0.282526
$950$	0	0
$951$	−12901.9	−0.439929
$952$	9118.53i	0.310434i
$953$	− 56839.4i	− 1.93201i	−0.258517	−	0.966007i	$-0.583234\pi$
$953$	− 56839.4i	− 1.93201i	0.258517	−	0.966007i	$-0.416766\pi$
$954$	4675.53	0.158675
$955$	0	0
$956$	−14615.3	−0.494449
$957$	15437.9i	0.521459i
$958$	− 22105.7i	− 0.745515i
$959$	6272.07	0.211195
$960$	0	0
$961$	−5871.48	−0.197089
$962$	17286.3i	0.579349i
$963$	5062.78i	0.169414i
$964$	−27382.7	−0.914873
$965$	0	0
$966$	−5777.10	−0.192417
$967$	− 13284.2i	− 0.441769i	−0.975300	−	0.220884i	$-0.929106\pi$
$967$	− 13284.2i	− 0.441769i	0.975300	−	0.220884i	$-0.0708943\pi$
$968$	− 1516.15i	− 0.0503420i
$969$	9568.44	0.317216
$970$	0	0
$971$	12153.0	0.401658	0.200829	−	0.979626i	$-0.435636\pi$
$971$	12153.0	0.401658	0.200829	+	0.979626i	$0.435636\pi$
$972$	− 1240.44i	− 0.0409332i
$973$	16195.3i	0.533604i
$974$	−21888.1	−0.720060
$975$	0	0
$976$	−495.298	−0.0162440
$977$	− 37999.3i	− 1.24433i	−0.782888	−	0.622163i	$-0.786254\pi$
$977$	− 37999.3i	− 1.24433i	0.782888	−	0.622163i	$-0.213746\pi$
$978$	− 5688.18i	− 0.185980i
$979$	25349.0	0.827537
$980$	0	0
$981$	16477.1	0.536264
$982$	8334.42i	0.270837i
$983$	− 22375.0i	− 0.725993i	−0.931791	−	0.362996i	$-0.881754\pi$
$983$	− 22375.0i	− 0.725993i	0.931791	−	0.362996i	$-0.118246\pi$
$984$	−23665.5	−0.766695
$985$	0	0
$986$	−13676.0	−0.441717
$987$	− 11386.6i	− 0.367213i
$988$	− 8086.65i	− 0.260395i
$989$	83772.9	2.69345
$990$	0	0
$991$	18985.3	0.608564	0.304282	−	0.952582i	$-0.401583\pi$
$991$	18985.3	0.608564	0.304282	+	0.952582i	$0.401583\pi$
$992$	− 28351.2i	− 0.907412i
$993$	20062.6i	0.641156i
$994$	−1433.29	−0.0457358
$995$	0	0
$996$	−5775.70	−0.183745
$997$	− 56476.5i	− 1.79401i	−0.442019	−	0.897006i	$-0.645738\pi$
$997$	− 56476.5i	− 1.79401i	0.442019	−	0.897006i	$-0.354262\pi$
$998$	17539.6i	0.556321i
$999$	9453.37	0.299391

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.d.j.274.2		4
5.2	odd	4		525.4.a.i.1.2		2
5.3	odd	4		105.4.a.g.1.1	✓	2
5.4	even	2	inner	525.4.d.j.274.3		4
15.2	even	4		1575.4.a.y.1.1		2
15.8	even	4		315.4.a.g.1.2		2
20.3	even	4		1680.4.a.y.1.1		2
35.13	even	4		735.4.a.q.1.1		2
105.83	odd	4		2205.4.a.v.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.a.g.1.1	✓	2	5.3	odd	4
315.4.a.g.1.2		2	15.8	even	4
525.4.a.i.1.2		2	5.2	odd	4
525.4.d.j.274.2		4	1.1	even	1	trivial
525.4.d.j.274.3		4	5.4	even	2	inner
735.4.a.q.1.1		2	35.13	even	4
1575.4.a.y.1.1		2	15.2	even	4
1680.4.a.y.1.1		2	20.3	even	4
2205.4.a.v.1.2		2	105.83	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.70156i q^{2} -3.00000i q^{3} +5.10469 q^{4} -5.10469 q^{6} +7.00000i q^{7} -22.2984i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-1.70156i q^{2} -3.00000i q^{3} +5.10469 q^{4} -5.10469 q^{6} +7.00000i q^{7} -22.2984i q^{8} -9.00000 q^{9} +37.4031 q^{11} -15.3141i q^{12} -29.0156i q^{13} +11.9109 q^{14} +2.89531 q^{16} +58.4187i q^{17} +15.3141i q^{18} +54.5969 q^{19} +21.0000 q^{21} -63.6437i q^{22} -161.675i q^{23} -66.8953 q^{24} -49.3719 q^{26} +27.0000i q^{27} +35.7328i q^{28} -137.581 q^{29} +154.659 q^{31} -183.314i q^{32} -112.209i q^{33} +99.4031 q^{34} -45.9422 q^{36} -350.125i q^{37} -92.9000i q^{38} -87.0469 q^{39} +353.769 q^{41} -35.7328i q^{42} +518.156i q^{43} +190.931 q^{44} -275.100 q^{46} -542.219i q^{47} -8.68594i q^{48} -49.0000 q^{49} +175.256 q^{51} -148.116i q^{52} -305.309i q^{53} +45.9422 q^{54} +156.089 q^{56} -163.791i q^{57} +234.103i q^{58} -14.6813 q^{59} -171.069 q^{61} -263.163i q^{62} -63.0000i q^{63} -288.758 q^{64} -190.931 q^{66} +551.956i q^{67} +298.209i q^{68} -485.025 q^{69} -120.334 q^{71} +200.686i q^{72} -284.659i q^{73} -595.759 q^{74} +278.700 q^{76} +261.822i q^{77} +148.116i q^{78} -941.612 q^{79} +81.0000 q^{81} -601.959i q^{82} -377.150i q^{83} +107.198 q^{84} +881.675 q^{86} +412.744i q^{87} -834.031i q^{88} +677.725 q^{89} +203.109 q^{91} -825.300i q^{92} -463.978i q^{93} -922.619 q^{94} -549.942 q^{96} -1225.03i q^{97} +83.3765i q^{98} -336.628 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 18 q^{4} + 18 q^{6} - 36 q^{9}+O(q^{10}) \) 4 * q - 18 * q^4 + 18 * q^6 - 36 * q^9	\( 4 q - 18 q^{4} + 18 q^{6} - 36 q^{9} + 124 q^{11} - 42 q^{14} + 50 q^{16} + 244 q^{19} + 84 q^{21} - 306 q^{24} - 428 q^{26} - 704 q^{29} + 132 q^{31} + 372 q^{34} + 162 q^{36} + 36 q^{39} + 32 q^{41} - 312 q^{44} - 1920 q^{46} - 196 q^{49} + 240 q^{51} - 162 q^{54} + 714 q^{56} - 1032 q^{59} - 1760 q^{61} + 958 q^{64} + 312 q^{66} - 96 q^{69} + 620 q^{71} - 2716 q^{74} - 1344 q^{76} - 3664 q^{79} + 324 q^{81} - 378 q^{84} + 2912 q^{86} - 1592 q^{89} - 84 q^{91} - 5176 q^{94} - 1854 q^{96} - 1116 q^{99}+O(q^{100}) \) 4 * q - 18 * q^4 + 18 * q^6 - 36 * q^9 + 124 * q^11 - 42 * q^14 + 50 * q^16 + 244 * q^19 + 84 * q^21 - 306 * q^24 - 428 * q^26 - 704 * q^29 + 132 * q^31 + 372 * q^34 + 162 * q^36 + 36 * q^39 + 32 * q^41 - 312 * q^44 - 1920 * q^46 - 196 * q^49 + 240 * q^51 - 162 * q^54 + 714 * q^56 - 1032 * q^59 - 1760 * q^61 + 958 * q^64 + 312 * q^66 - 96 * q^69 + 620 * q^71 - 2716 * q^74 - 1344 * q^76 - 3664 * q^79 + 324 * q^81 - 378 * q^84 + 2912 * q^86 - 1592 * q^89 - 84 * q^91 - 5176 * q^94 - 1854 * q^96 - 1116 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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