LMFDB - Embedded newform 6035.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.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:	$48.1897176198$
Analytic rank:	$0$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69755 q^{2} +3.18040 q^{3} +5.27679 q^{4} -1.00000 q^{5} -8.57929 q^{6} +2.84577 q^{7} -8.83933 q^{8} +7.11493 q^{9} +O(q^{10})$	\(q-2.69755 q^{2} +3.18040 q^{3} +5.27679 q^{4} -1.00000 q^{5} -8.57929 q^{6} +2.84577 q^{7} -8.83933 q^{8} +7.11493 q^{9} +2.69755 q^{10} +0.275530 q^{11} +16.7823 q^{12} -4.71319 q^{13} -7.67662 q^{14} -3.18040 q^{15} +13.2910 q^{16} +1.00000 q^{17} -19.1929 q^{18} +0.349365 q^{19} -5.27679 q^{20} +9.05069 q^{21} -0.743256 q^{22} -0.891742 q^{23} -28.1126 q^{24} +1.00000 q^{25} +12.7141 q^{26} +13.0871 q^{27} +15.0166 q^{28} -5.91246 q^{29} +8.57929 q^{30} +4.83127 q^{31} -18.1744 q^{32} +0.876294 q^{33} -2.69755 q^{34} -2.84577 q^{35} +37.5440 q^{36} +6.79832 q^{37} -0.942430 q^{38} -14.9898 q^{39} +8.83933 q^{40} -6.30778 q^{41} -24.4147 q^{42} -1.15455 q^{43} +1.45391 q^{44} -7.11493 q^{45} +2.40552 q^{46} +3.91305 q^{47} +42.2706 q^{48} +1.09842 q^{49} -2.69755 q^{50} +3.18040 q^{51} -24.8705 q^{52} +11.4633 q^{53} -35.3032 q^{54} -0.275530 q^{55} -25.1547 q^{56} +1.11112 q^{57} +15.9492 q^{58} -2.92255 q^{59} -16.7823 q^{60} +7.18124 q^{61} -13.0326 q^{62} +20.2475 q^{63} +22.4446 q^{64} +4.71319 q^{65} -2.36385 q^{66} +8.62627 q^{67} +5.27679 q^{68} -2.83610 q^{69} +7.67662 q^{70} -1.00000 q^{71} -62.8912 q^{72} +4.10662 q^{73} -18.3388 q^{74} +3.18040 q^{75} +1.84353 q^{76} +0.784095 q^{77} +40.4359 q^{78} +6.59513 q^{79} -13.2910 q^{80} +20.2774 q^{81} +17.0156 q^{82} -4.36368 q^{83} +47.7586 q^{84} -1.00000 q^{85} +3.11445 q^{86} -18.8040 q^{87} -2.43550 q^{88} +8.64674 q^{89} +19.1929 q^{90} -13.4127 q^{91} -4.70554 q^{92} +15.3654 q^{93} -10.5556 q^{94} -0.349365 q^{95} -57.8020 q^{96} +7.93741 q^{97} -2.96304 q^{98} +1.96037 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q + q^{2} + 10 q^{3} + 55 q^{4} - 49 q^{5} + 2 q^{6} + 15 q^{7} + 3 q^{8} + 43 q^{9}+O(q^{10}) $ 49 * q + q^2 + 10 * q^3 + 55 * q^4 - 49 * q^5 + 2 * q^6 + 15 * q^7 + 3 * q^8 + 43 * q^9	\( 49 q + q^{2} + 10 q^{3} + 55 q^{4} - 49 q^{5} + 2 q^{6} + 15 q^{7} + 3 q^{8} + 43 q^{9} - q^{10} - 4 q^{11} + 32 q^{12} + 21 q^{13} + 8 q^{14} - 10 q^{15} + 63 q^{16} + 49 q^{17} + 12 q^{18} + 19 q^{19} - 55 q^{20} + 5 q^{21} + 10 q^{22} + 10 q^{23} + 7 q^{24} + 49 q^{25} - 20 q^{26} + 37 q^{27} + 48 q^{28} + 30 q^{29} - 2 q^{30} + 23 q^{31} + 2 q^{32} - q^{33} + q^{34} - 15 q^{35} + 39 q^{36} + 60 q^{37} + 13 q^{38} + 3 q^{39} - 3 q^{40} - 29 q^{41} + 32 q^{42} + 23 q^{43} + 11 q^{44} - 43 q^{45} + 6 q^{46} - 8 q^{47} + 96 q^{48} + 82 q^{49} + q^{50} + 10 q^{51} + 11 q^{52} + 15 q^{53} - 4 q^{54} + 4 q^{55} - 18 q^{56} + 44 q^{57} + 38 q^{58} - 28 q^{59} - 32 q^{60} + 107 q^{61} + 37 q^{62} + 54 q^{63} + 77 q^{64} - 21 q^{65} + 23 q^{66} + 11 q^{67} + 55 q^{68} + 27 q^{69} - 8 q^{70} - 49 q^{71} - 53 q^{72} + 97 q^{73} + 27 q^{74} + 10 q^{75} + 66 q^{76} + 19 q^{77} + 48 q^{78} + 31 q^{79} - 63 q^{80} - 7 q^{81} + 61 q^{82} + 6 q^{83} + 46 q^{84} - 49 q^{85} - 89 q^{86} + 36 q^{87} + 63 q^{88} - 20 q^{89} - 12 q^{90} + 35 q^{91} - 2 q^{92} + 47 q^{93} - 4 q^{94} - 19 q^{95} + 73 q^{96} + 92 q^{97} + 3 q^{98} + 5 q^{99}+O(q^{100}) \) 49 * q + q^2 + 10 * q^3 + 55 * q^4 - 49 * q^5 + 2 * q^6 + 15 * q^7 + 3 * q^8 + 43 * q^9 - q^10 - 4 * q^11 + 32 * q^12 + 21 * q^13 + 8 * q^14 - 10 * q^15 + 63 * q^16 + 49 * q^17 + 12 * q^18 + 19 * q^19 - 55 * q^20 + 5 * q^21 + 10 * q^22 + 10 * q^23 + 7 * q^24 + 49 * q^25 - 20 * q^26 + 37 * q^27 + 48 * q^28 + 30 * q^29 - 2 * q^30 + 23 * q^31 + 2 * q^32 - q^33 + q^34 - 15 * q^35 + 39 * q^36 + 60 * q^37 + 13 * q^38 + 3 * q^39 - 3 * q^40 - 29 * q^41 + 32 * q^42 + 23 * q^43 + 11 * q^44 - 43 * q^45 + 6 * q^46 - 8 * q^47 + 96 * q^48 + 82 * q^49 + q^50 + 10 * q^51 + 11 * q^52 + 15 * q^53 - 4 * q^54 + 4 * q^55 - 18 * q^56 + 44 * q^57 + 38 * q^58 - 28 * q^59 - 32 * q^60 + 107 * q^61 + 37 * q^62 + 54 * q^63 + 77 * q^64 - 21 * q^65 + 23 * q^66 + 11 * q^67 + 55 * q^68 + 27 * q^69 - 8 * q^70 - 49 * q^71 - 53 * q^72 + 97 * q^73 + 27 * q^74 + 10 * q^75 + 66 * q^76 + 19 * q^77 + 48 * q^78 + 31 * q^79 - 63 * q^80 - 7 * q^81 + 61 * q^82 + 6 * q^83 + 46 * q^84 - 49 * q^85 - 89 * q^86 + 36 * q^87 + 63 * q^88 - 20 * q^89 - 12 * q^90 + 35 * q^91 - 2 * q^92 + 47 * q^93 - 4 * q^94 - 19 * q^95 + 73 * q^96 + 92 * q^97 + 3 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.69755	−1.90746	−0.953729	−	0.300667i	$-0.902791\pi$
$2$	−2.69755	−1.90746	−0.953729	+	0.300667i	$0.902791\pi$
$3$	3.18040	1.83620	0.918102	−	0.396345i	$-0.129722\pi$
$3$	3.18040	1.83620	0.918102	+	0.396345i	$0.129722\pi$
$4$	5.27679	2.63840
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−8.57929	−3.50248
$7$	2.84577	1.07560	0.537800	−	0.843072i	$-0.319255\pi$
$7$	2.84577	1.07560	0.537800	+	0.843072i	$0.319255\pi$
$8$	−8.83933	−3.12517
$9$	7.11493	2.37164
$10$	2.69755	0.853041
$11$	0.275530	0.0830753	0.0415377	−	0.999137i	$-0.486774\pi$
$11$	0.275530	0.0830753	0.0415377	+	0.999137i	$0.486774\pi$
$12$	16.7823	4.84463
$13$	−4.71319	−1.30720	−0.653602	−	0.756838i	$-0.726743\pi$
$13$	−4.71319	−1.30720	−0.653602	+	0.756838i	$0.726743\pi$
$14$	−7.67662	−2.05166
$15$	−3.18040	−0.821175
$16$	13.2910	3.32274
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−19.1929	−4.52381
$19$	0.349365	0.0801498	0.0400749	−	0.999197i	$-0.487240\pi$
$19$	0.349365	0.0801498	0.0400749	+	0.999197i	$0.487240\pi$
$20$	−5.27679	−1.17993
$21$	9.05069	1.97502
$22$	−0.743256	−0.158463
$23$	−0.891742	−0.185941	−0.0929706	−	0.995669i	$-0.529636\pi$
$23$	−0.891742	−0.185941	−0.0929706	+	0.995669i	$0.529636\pi$
$24$	−28.1126	−5.73846
$25$	1.00000	0.200000
$26$	12.7141	2.49344
$27$	13.0871	2.51862
$28$	15.0166	2.83786
$29$	−5.91246	−1.09792	−0.548959	−	0.835850i	$-0.684976\pi$
$29$	−5.91246	−1.09792	−0.548959	+	0.835850i	$0.684976\pi$
$30$	8.57929	1.56636
$31$	4.83127	0.867722	0.433861	−	0.900980i	$-0.357151\pi$
$31$	4.83127	0.867722	0.433861	+	0.900980i	$0.357151\pi$
$32$	−18.1744	−3.21282
$33$	0.876294	0.152543
$34$	−2.69755	−0.462627
$35$	−2.84577	−0.481023
$36$	37.5440	6.25734
$37$	6.79832	1.11764	0.558819	−	0.829290i	$-0.311255\pi$
$37$	6.79832	1.11764	0.558819	+	0.829290i	$0.311255\pi$
$38$	−0.942430	−0.152882
$39$	−14.9898	−2.40029
$40$	8.83933	1.39762
$41$	−6.30778	−0.985110	−0.492555	−	0.870281i	$-0.663937\pi$
$41$	−6.30778	−0.985110	−0.492555	+	0.870281i	$0.663937\pi$
$42$	−24.4147	−3.76727
$43$	−1.15455	−0.176067	−0.0880333	−	0.996118i	$-0.528058\pi$
$43$	−1.15455	−0.176067	−0.0880333	+	0.996118i	$0.528058\pi$
$44$	1.45391	0.219186
$45$	−7.11493	−1.06063
$46$	2.40552	0.354675
$47$	3.91305	0.570776	0.285388	−	0.958412i	$-0.407877\pi$
$47$	3.91305	0.570776	0.285388	+	0.958412i	$0.407877\pi$
$48$	42.2706	6.10123
$49$	1.09842	0.156917
$50$	−2.69755	−0.381492
$51$	3.18040	0.445345
$52$	−24.8705	−3.44892
$53$	11.4633	1.57461	0.787305	−	0.616563i	$-0.211475\pi$
$53$	11.4633	1.57461	0.787305	+	0.616563i	$0.211475\pi$
$54$	−35.3032	−4.80415
$55$	−0.275530	−0.0371524
$56$	−25.1547	−3.36144
$57$	1.11112	0.147171
$58$	15.9492	2.09423
$59$	−2.92255	−0.380483	−0.190242	−	0.981737i	$-0.560927\pi$
$59$	−2.92255	−0.380483	−0.190242	+	0.981737i	$0.560927\pi$
$60$	−16.7823	−2.16659
$61$	7.18124	0.919464	0.459732	−	0.888058i	$-0.347946\pi$
$61$	7.18124	0.919464	0.459732	+	0.888058i	$0.347946\pi$
$62$	−13.0326	−1.65514
$63$	20.2475	2.55094
$64$	22.4446	2.80557
$65$	4.71319	0.584600
$66$	−2.36385	−0.290970
$67$	8.62627	1.05387	0.526933	−	0.849907i	$-0.323342\pi$
$67$	8.62627	1.05387	0.526933	+	0.849907i	$0.323342\pi$
$68$	5.27679	0.639905
$69$	−2.83610	−0.341426
$70$	7.67662	0.917532
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−62.8912	−7.41180
$73$	4.10662	0.480644	0.240322	−	0.970693i	$-0.422747\pi$
$73$	4.10662	0.480644	0.240322	+	0.970693i	$0.422747\pi$
$74$	−18.3388	−2.13185
$75$	3.18040	0.367241
$76$	1.84353	0.211467
$77$	0.784095	0.0893559
$78$	40.4359	4.57846
$79$	6.59513	0.742010	0.371005	−	0.928631i	$-0.379013\pi$
$79$	6.59513	0.742010	0.371005	+	0.928631i	$0.379013\pi$
$80$	−13.2910	−1.48598
$81$	20.2774	2.25305
$82$	17.0156	1.87906
$83$	−4.36368	−0.478976	−0.239488	−	0.970899i	$-0.576980\pi$
$83$	−4.36368	−0.478976	−0.239488	+	0.970899i	$0.576980\pi$
$84$	47.7586	5.21089
$85$	−1.00000	−0.108465
$86$	3.11445	0.335840
$87$	−18.8040	−2.01600
$88$	−2.43550	−0.259625
$89$	8.64674	0.916553	0.458276	−	0.888810i	$-0.348467\pi$
$89$	8.64674	0.916553	0.458276	+	0.888810i	$0.348467\pi$
$90$	19.1929	2.02311
$91$	−13.4127	−1.40603
$92$	−4.70554	−0.490587
$93$	15.3654	1.59331
$94$	−10.5556	−1.08873
$95$	−0.349365	−0.0358441
$96$	−57.8020	−5.89939
$97$	7.93741	0.805922	0.402961	−	0.915217i	$-0.367981\pi$
$97$	7.93741	0.805922	0.402961	+	0.915217i	$0.367981\pi$
$98$	−2.96304	−0.299313
$99$	1.96037	0.197025
$100$	5.27679	0.527679
$101$	9.09860	0.905345	0.452672	−	0.891677i	$-0.350471\pi$
$101$	9.09860	0.905345	0.452672	+	0.891677i	$0.350471\pi$
$102$	−8.57929	−0.849477
$103$	1.80476	0.177828	0.0889141	−	0.996039i	$-0.471660\pi$
$103$	1.80476	0.177828	0.0889141	+	0.996039i	$0.471660\pi$
$104$	41.6615	4.08524
$105$	−9.05069	−0.883257
$106$	−30.9230	−3.00350
$107$	10.3112	0.996824	0.498412	−	0.866940i	$-0.333917\pi$
$107$	10.3112	0.996824	0.498412	+	0.866940i	$0.333917\pi$
$108$	69.0580	6.64511
$109$	3.33893	0.319811	0.159906	−	0.987132i	$-0.448881\pi$
$109$	3.33893	0.319811	0.159906	+	0.987132i	$0.448881\pi$
$110$	0.743256	0.0708667
$111$	21.6214	2.05221
$112$	37.8231	3.57394
$113$	−9.35353	−0.879906	−0.439953	−	0.898021i	$-0.645005\pi$
$113$	−9.35353	−0.879906	−0.439953	+	0.898021i	$0.645005\pi$
$114$	−2.99730	−0.280723
$115$	0.891742	0.0831554
$116$	−31.1989	−2.89674
$117$	−33.5340	−3.10022
$118$	7.88373	0.725756
$119$	2.84577	0.260872
$120$	28.1126	2.56632
$121$	−10.9241	−0.993098
$122$	−19.3718	−1.75384
$123$	−20.0613	−1.80886
$124$	25.4936	2.28939
$125$	−1.00000	−0.0894427
$126$	−54.6186	−4.86581
$127$	13.7774	1.22255	0.611274	−	0.791419i	$-0.290657\pi$
$127$	13.7774	1.22255	0.611274	+	0.791419i	$0.290657\pi$
$128$	−24.1966	−2.13870
$129$	−3.67192	−0.323294
$130$	−12.7141	−1.11510
$131$	−10.4835	−0.915949	−0.457974	−	0.888965i	$-0.651425\pi$
$131$	−10.4835	−0.915949	−0.457974	+	0.888965i	$0.651425\pi$
$132$	4.62402	0.402469
$133$	0.994213	0.0862092
$134$	−23.2698	−2.01021
$135$	−13.0871	−1.12636
$136$	−8.83933	−0.757966
$137$	7.23089	0.617776	0.308888	−	0.951098i	$-0.400043\pi$
$137$	7.23089	0.617776	0.308888	+	0.951098i	$0.400043\pi$
$138$	7.65052	0.651255
$139$	10.0191	0.849809	0.424904	−	0.905238i	$-0.360308\pi$
$139$	10.0191	0.849809	0.424904	+	0.905238i	$0.360308\pi$
$140$	−15.0166	−1.26913
$141$	12.4450	1.04806
$142$	2.69755	0.226374
$143$	−1.29862	−0.108596
$144$	94.5643	7.88036
$145$	5.91246	0.491003
$146$	−11.0778	−0.916808
$147$	3.49341	0.288132
$148$	35.8734	2.94877
$149$	−12.1565	−0.995897	−0.497949	−	0.867207i	$-0.665913\pi$
$149$	−12.1565	−0.995897	−0.497949	+	0.867207i	$0.665913\pi$
$150$	−8.57929	−0.700496
$151$	−14.6494	−1.19215	−0.596074	−	0.802929i	$-0.703274\pi$
$151$	−14.6494	−1.19215	−0.596074	+	0.802929i	$0.703274\pi$
$152$	−3.08815	−0.250482
$153$	7.11493	0.575208
$154$	−2.11514	−0.170443
$155$	−4.83127	−0.388057
$156$	−79.0982	−6.33293
$157$	5.57332	0.444799	0.222400	−	0.974956i	$-0.428611\pi$
$157$	5.57332	0.444799	0.222400	+	0.974956i	$0.428611\pi$
$158$	−17.7907	−1.41535
$159$	36.4580	2.89131
$160$	18.1744	1.43682
$161$	−2.53770	−0.199998
$162$	−54.6994	−4.29759
$163$	−0.683516	−0.0535371	−0.0267685	−	0.999642i	$-0.508522\pi$
$163$	−0.683516	−0.0535371	−0.0267685	+	0.999642i	$0.508522\pi$
$164$	−33.2849	−2.59911
$165$	−0.876294	−0.0682194
$166$	11.7713	0.913627
$167$	−19.9279	−1.54207	−0.771035	−	0.636793i	$-0.780260\pi$
$167$	−19.9279	−1.54207	−0.771035	+	0.636793i	$0.780260\pi$
$168$	−80.0020	−6.17229
$169$	9.21419	0.708784
$170$	2.69755	0.206893
$171$	2.48571	0.190087
$172$	−6.09230	−0.464534
$173$	23.4532	1.78311	0.891556	−	0.452910i	$-0.149614\pi$
$173$	23.4532	1.78311	0.891556	+	0.452910i	$0.149614\pi$
$174$	50.7248	3.84543
$175$	2.84577	0.215120
$176$	3.66206	0.276038
$177$	−9.29487	−0.698645
$178$	−23.3250	−1.74829
$179$	22.3842	1.67308	0.836538	−	0.547909i	$-0.184576\pi$
$179$	22.3842	1.67308	0.836538	+	0.547909i	$0.184576\pi$
$180$	−37.5440	−2.79837
$181$	−1.07690	−0.0800455	−0.0400228	−	0.999199i	$-0.512743\pi$
$181$	−1.07690	−0.0800455	−0.0400228	+	0.999199i	$0.512743\pi$
$182$	36.1814	2.68194
$183$	22.8392	1.68832
$184$	7.88240	0.581098
$185$	−6.79832	−0.499823
$186$	−41.4489	−3.03918
$187$	0.275530	0.0201487
$188$	20.6483	1.50593
$189$	37.2429	2.70902
$190$	0.942430	0.0683711
$191$	22.6457	1.63858	0.819291	−	0.573378i	$-0.194367\pi$
$191$	22.6457	1.63858	0.819291	+	0.573378i	$0.194367\pi$
$192$	71.3827	5.15160
$193$	−15.8763	−1.14280	−0.571401	−	0.820671i	$-0.693600\pi$
$193$	−15.8763	−1.14280	−0.571401	+	0.820671i	$0.693600\pi$
$194$	−21.4116	−1.53726
$195$	14.9898	1.07344
$196$	5.79613	0.414009
$197$	22.4421	1.59893	0.799466	−	0.600712i	$-0.205116\pi$
$197$	22.4421	1.59893	0.799466	+	0.600712i	$0.205116\pi$
$198$	−5.28821	−0.375817
$199$	−13.1416	−0.931584	−0.465792	−	0.884894i	$-0.654231\pi$
$199$	−13.1416	−0.931584	−0.465792	+	0.884894i	$0.654231\pi$
$200$	−8.83933	−0.625035
$201$	27.4350	1.93511
$202$	−24.5440	−1.72691
$203$	−16.8255	−1.18092
$204$	16.7823	1.17500
$205$	6.30778	0.440555
$206$	−4.86844	−0.339200
$207$	−6.34468	−0.440986
$208$	−62.6429	−4.34350
$209$	0.0962604	0.00665847
$210$	24.4147	1.68478
$211$	24.0232	1.65382	0.826912	−	0.562331i	$-0.190095\pi$
$211$	24.0232	1.65382	0.826912	+	0.562331i	$0.190095\pi$
$212$	60.4897	4.15445
$213$	−3.18040	−0.217917
$214$	−27.8151	−1.90140
$215$	1.15455	0.0787394
$216$	−115.681	−7.87111
$217$	13.7487	0.933322
$218$	−9.00693	−0.610026
$219$	13.0607	0.882560
$220$	−1.45391	−0.0980228
$221$	−4.71319	−0.317044
$222$	−58.3248	−3.91450
$223$	27.0459	1.81113	0.905563	−	0.424212i	$-0.139449\pi$
$223$	27.0459	1.81113	0.905563	+	0.424212i	$0.139449\pi$
$224$	−51.7203	−3.45571
$225$	7.11493	0.474329
$226$	25.2317	1.67838
$227$	−12.5839	−0.835224	−0.417612	−	0.908625i	$-0.637133\pi$
$227$	−12.5839	−0.835224	−0.417612	+	0.908625i	$0.637133\pi$
$228$	5.86315	0.388296
$229$	−17.5124	−1.15725	−0.578626	−	0.815593i	$-0.696411\pi$
$229$	−17.5124	−1.15725	−0.578626	+	0.815593i	$0.696411\pi$
$230$	−2.40552	−0.158615
$231$	2.49373	0.164076
$232$	52.2622	3.43118
$233$	25.6469	1.68019	0.840093	−	0.542443i	$-0.182501\pi$
$233$	25.6469	1.68019	0.840093	+	0.542443i	$0.182501\pi$
$234$	90.4598	5.91354
$235$	−3.91305	−0.255259
$236$	−15.4217	−1.00387
$237$	20.9751	1.36248
$238$	−7.67662	−0.497602
$239$	24.5864	1.59036	0.795182	−	0.606370i	$-0.207375\pi$
$239$	24.5864	1.59036	0.795182	+	0.606370i	$0.207375\pi$
$240$	−42.2706	−2.72855
$241$	−1.04985	−0.0676267	−0.0338134	−	0.999428i	$-0.510765\pi$
$241$	−1.04985	−0.0676267	−0.0338134	+	0.999428i	$0.510765\pi$
$242$	29.4683	1.89429
$243$	25.2289	1.61844
$244$	37.8939	2.42591
$245$	−1.09842	−0.0701754
$246$	54.1163	3.45033
$247$	−1.64662	−0.104772
$248$	−42.7052	−2.71178
$249$	−13.8782	−0.879498
$250$	2.69755	0.170608
$251$	12.2072	0.770512	0.385256	−	0.922810i	$-0.374113\pi$
$251$	12.2072	0.770512	0.385256	+	0.922810i	$0.374113\pi$
$252$	106.842	6.73040
$253$	−0.245701	−0.0154471
$254$	−37.1653	−2.33196
$255$	−3.18040	−0.199164
$256$	20.3824	1.27390
$257$	−15.0162	−0.936688	−0.468344	−	0.883546i	$-0.655149\pi$
$257$	−15.0162	−0.936688	−0.468344	+	0.883546i	$0.655149\pi$
$258$	9.90519	0.616670
$259$	19.3465	1.20213
$260$	24.8705	1.54241
$261$	−42.0668	−2.60387
$262$	28.2798	1.74713
$263$	−26.7620	−1.65022	−0.825109	−	0.564974i	$-0.808886\pi$
$263$	−26.7620	−1.65022	−0.825109	+	0.564974i	$0.808886\pi$
$264$	−7.74585	−0.476724
$265$	−11.4633	−0.704187
$266$	−2.68194	−0.164440
$267$	27.5001	1.68298
$268$	45.5191	2.78052
$269$	8.86467	0.540489	0.270244	−	0.962792i	$-0.412896\pi$
$269$	8.86467	0.540489	0.270244	+	0.962792i	$0.412896\pi$
$270$	35.3032	2.14848
$271$	8.80664	0.534965	0.267483	−	0.963563i	$-0.413808\pi$
$271$	8.80664	0.534965	0.267483	+	0.963563i	$0.413808\pi$
$272$	13.2910	0.805883
$273$	−42.6576	−2.58176
$274$	−19.5057	−1.17838
$275$	0.275530	0.0166151
$276$	−14.9655	−0.900817
$277$	28.8769	1.73505	0.867523	−	0.497397i	$-0.165711\pi$
$277$	28.8769	1.73505	0.867523	+	0.497397i	$0.165711\pi$
$278$	−27.0271	−1.62097
$279$	34.3741	2.05793
$280$	25.1547	1.50328
$281$	−28.1362	−1.67847	−0.839233	−	0.543772i	$-0.816996\pi$
$281$	−28.1362	−1.67847	−0.839233	+	0.543772i	$0.816996\pi$
$282$	−33.5712	−1.99913
$283$	−2.24734	−0.133590	−0.0667951	−	0.997767i	$-0.521277\pi$
$283$	−2.24734	−0.133590	−0.0667951	+	0.997767i	$0.521277\pi$
$284$	−5.27679	−0.313120
$285$	−1.11112	−0.0658170
$286$	3.50311	0.207143
$287$	−17.9505	−1.05958
$288$	−129.310	−7.61966
$289$	1.00000	0.0588235
$290$	−15.9492	−0.936569
$291$	25.2441	1.47984
$292$	21.6698	1.26813
$293$	−21.9119	−1.28011	−0.640055	−	0.768329i	$-0.721088\pi$
$293$	−21.9119	−1.28011	−0.640055	+	0.768329i	$0.721088\pi$
$294$	−9.42366	−0.549599
$295$	2.92255	0.170157
$296$	−60.0926	−3.49281
$297$	3.60589	0.209235
$298$	32.7927	1.89963
$299$	4.20295	0.243063
$300$	16.7823	0.968927
$301$	−3.28557	−0.189377
$302$	39.5175	2.27397
$303$	28.9372	1.66240
$304$	4.64340	0.266317
$305$	−7.18124	−0.411197
$306$	−19.1929	−1.09719
$307$	−13.6355	−0.778220	−0.389110	−	0.921191i	$-0.627217\pi$
$307$	−13.6355	−0.778220	−0.389110	+	0.921191i	$0.627217\pi$
$308$	4.13751	0.235756
$309$	5.73985	0.326529
$310$	13.0326	0.740202
$311$	−18.9255	−1.07317	−0.536584	−	0.843847i	$-0.680286\pi$
$311$	−18.9255	−1.07317	−0.536584	+	0.843847i	$0.680286\pi$
$312$	132.500	7.50133
$313$	13.1890	0.745487	0.372744	−	0.927934i	$-0.378417\pi$
$313$	13.1890	0.745487	0.372744	+	0.927934i	$0.378417\pi$
$314$	−15.0343	−0.848436
$315$	−20.2475	−1.14082
$316$	34.8011	1.95772
$317$	−26.2470	−1.47418	−0.737089	−	0.675796i	$-0.763800\pi$
$317$	−26.2470	−1.47418	−0.737089	+	0.675796i	$0.763800\pi$
$318$	−98.3473	−5.51505
$319$	−1.62906	−0.0912098
$320$	−22.4446	−1.25469
$321$	32.7938	1.83037
$322$	6.84557	0.381489
$323$	0.349365	0.0194392
$324$	107.000	5.94443
$325$	−4.71319	−0.261441
$326$	1.84382	0.102120
$327$	10.6191	0.587238
$328$	55.7565	3.07864
$329$	11.1356	0.613927
$330$	2.36385	0.130126
$331$	−23.7360	−1.30465	−0.652323	−	0.757941i	$-0.726206\pi$
$331$	−23.7360	−1.30465	−0.652323	+	0.757941i	$0.726206\pi$
$332$	−23.0262	−1.26373
$333$	48.3696	2.65064
$334$	53.7566	2.94143
$335$	−8.62627	−0.471304
$336$	120.292	6.56249
$337$	23.8976	1.30178	0.650892	−	0.759170i	$-0.274395\pi$
$337$	23.8976	1.30178	0.650892	+	0.759170i	$0.274395\pi$
$338$	−24.8558	−1.35198
$339$	−29.7480	−1.61569
$340$	−5.27679	−0.286174
$341$	1.33116	0.0720862
$342$	−6.70532	−0.362582
$343$	−16.7946	−0.906821
$344$	10.2054	0.550239
$345$	2.83610	0.152690
$346$	−63.2662	−3.40121
$347$	−10.5200	−0.564743	−0.282372	−	0.959305i	$-0.591121\pi$
$347$	−10.5200	−0.564743	−0.282372	+	0.959305i	$0.591121\pi$
$348$	−99.2248	−5.31901
$349$	−2.16415	−0.115845	−0.0579223	−	0.998321i	$-0.518448\pi$
$349$	−2.16415	−0.115845	−0.0579223	+	0.998321i	$0.518448\pi$
$350$	−7.67662	−0.410333
$351$	−61.6821	−3.29235
$352$	−5.00760	−0.266906
$353$	16.6761	0.887581	0.443791	−	0.896130i	$-0.353633\pi$
$353$	16.6761	0.887581	0.443791	+	0.896130i	$0.353633\pi$
$354$	25.0734	1.33264
$355$	1.00000	0.0530745
$356$	45.6271	2.41823
$357$	9.05069	0.479013
$358$	−60.3826	−3.19132
$359$	−3.71358	−0.195996	−0.0979978	−	0.995187i	$-0.531244\pi$
$359$	−3.71358	−0.195996	−0.0979978	+	0.995187i	$0.531244\pi$
$360$	62.8912	3.31466
$361$	−18.8779	−0.993576
$362$	2.90500	0.152684
$363$	−34.7429	−1.82353
$364$	−70.7759	−3.70967
$365$	−4.10662	−0.214950
$366$	−61.6100	−3.22040
$367$	−21.6802	−1.13170	−0.565849	−	0.824509i	$-0.691452\pi$
$367$	−21.6802	−1.13170	−0.565849	+	0.824509i	$0.691452\pi$
$368$	−11.8521	−0.617834
$369$	−44.8794	−2.33633
$370$	18.3388	0.953391
$371$	32.6221	1.69365
$372$	81.0798	4.20379
$373$	−29.5737	−1.53127	−0.765635	−	0.643276i	$-0.777575\pi$
$373$	−29.5737	−1.53127	−0.765635	+	0.643276i	$0.777575\pi$
$374$	−0.743256	−0.0384328
$375$	−3.18040	−0.164235
$376$	−34.5887	−1.78378
$377$	27.8666	1.43520
$378$	−100.465	−5.16735
$379$	−0.690475	−0.0354673	−0.0177337	−	0.999843i	$-0.505645\pi$
$379$	−0.690475	−0.0354673	−0.0177337	+	0.999843i	$0.505645\pi$
$380$	−1.84353	−0.0945709
$381$	43.8176	2.24485
$382$	−61.0879	−3.12553
$383$	16.2407	0.829863	0.414931	−	0.909853i	$-0.363806\pi$
$383$	16.2407	0.829863	0.414931	+	0.909853i	$0.363806\pi$
$384$	−76.9548	−3.92708
$385$	−0.784095	−0.0399612
$386$	42.8272	2.17985
$387$	−8.21451	−0.417567
$388$	41.8841	2.12634
$389$	15.0464	0.762883	0.381442	−	0.924393i	$-0.375428\pi$
$389$	15.0464	0.762883	0.381442	+	0.924393i	$0.375428\pi$
$390$	−40.4359	−2.04755
$391$	−0.891742	−0.0450973
$392$	−9.70929	−0.490393
$393$	−33.3417	−1.68187
$394$	−60.5387	−3.04990
$395$	−6.59513	−0.331837
$396$	10.3445	0.519830
$397$	4.08645	0.205093	0.102547	−	0.994728i	$-0.467301\pi$
$397$	4.08645	0.205093	0.102547	+	0.994728i	$0.467301\pi$
$398$	35.4502	1.77696
$399$	3.16199	0.158298
$400$	13.2910	0.664548
$401$	−28.4296	−1.41971	−0.709853	−	0.704350i	$-0.751239\pi$
$401$	−28.4296	−1.41971	−0.709853	+	0.704350i	$0.751239\pi$
$402$	−74.0073	−3.69115
$403$	−22.7707	−1.13429
$404$	48.0114	2.38866
$405$	−20.2774	−1.00759
$406$	45.3878	2.25256
$407$	1.87314	0.0928481
$408$	−28.1126	−1.39178
$409$	21.8152	1.07869	0.539345	−	0.842085i	$-0.318672\pi$
$409$	21.8152	1.07869	0.539345	+	0.842085i	$0.318672\pi$
$410$	−17.0156	−0.840339
$411$	22.9971	1.13436
$412$	9.52335	0.469182
$413$	−8.31691	−0.409248
$414$	17.1151	0.841162
$415$	4.36368	0.214205
$416$	85.6597	4.19981
$417$	31.8647	1.56042
$418$	−0.259667	−0.0127008
$419$	−6.93235	−0.338667	−0.169334	−	0.985559i	$-0.554162\pi$
$419$	−6.93235	−0.338667	−0.169334	+	0.985559i	$0.554162\pi$
$420$	−47.7586	−2.33038
$421$	−12.6176	−0.614943	−0.307471	−	0.951557i	$-0.599483\pi$
$421$	−12.6176	−0.614943	−0.307471	+	0.951557i	$0.599483\pi$
$422$	−64.8038	−3.15460
$423$	27.8410	1.35368
$424$	−101.328	−4.92093
$425$	1.00000	0.0485071
$426$	8.57929	0.415668
$427$	20.4362	0.988976
$428$	54.4102	2.63002
$429$	−4.13014	−0.199405
$430$	−3.11445	−0.150192
$431$	−37.1830	−1.79104	−0.895522	−	0.445018i	$-0.853197\pi$
$431$	−37.1830	−1.79104	−0.895522	+	0.445018i	$0.853197\pi$
$432$	173.940	8.36871
$433$	15.9716	0.767548	0.383774	−	0.923427i	$-0.374624\pi$
$433$	15.9716	0.767548	0.383774	+	0.923427i	$0.374624\pi$
$434$	−37.0878	−1.78027
$435$	18.8040	0.901582
$436$	17.6188	0.843789
$437$	−0.311543	−0.0149031
$438$	−35.2319	−1.68345
$439$	21.9530	1.04776	0.523879	−	0.851792i	$-0.324484\pi$
$439$	21.9530	1.04776	0.523879	+	0.851792i	$0.324484\pi$
$440$	2.43550	0.116108
$441$	7.81518	0.372151
$442$	12.7141	0.604748
$443$	−28.2099	−1.34029	−0.670147	−	0.742228i	$-0.733769\pi$
$443$	−28.2099	−1.34029	−0.670147	+	0.742228i	$0.733769\pi$
$444$	114.092	5.41454
$445$	−8.64674	−0.409895
$446$	−72.9577	−3.45465
$447$	−38.6624	−1.82867
$448$	63.8722	3.01768
$449$	−33.6137	−1.58633	−0.793164	−	0.609008i	$-0.791568\pi$
$449$	−33.6137	−1.58633	−0.793164	+	0.609008i	$0.791568\pi$
$450$	−19.1929	−0.904762
$451$	−1.73798	−0.0818383
$452$	−49.3567	−2.32154
$453$	−46.5908	−2.18903
$454$	33.9458	1.59315
$455$	13.4127	0.628796
$456$	−9.82155	−0.459936
$457$	−26.9946	−1.26276	−0.631378	−	0.775475i	$-0.717510\pi$
$457$	−26.9946	−1.26276	−0.631378	+	0.775475i	$0.717510\pi$
$458$	47.2406	2.20741
$459$	13.0871	0.610854
$460$	4.70554	0.219397
$461$	−19.7885	−0.921644	−0.460822	−	0.887493i	$-0.652445\pi$
$461$	−19.7885	−0.921644	−0.460822	+	0.887493i	$0.652445\pi$
$462$	−6.72698	−0.312967
$463$	14.3452	0.666677	0.333339	−	0.942807i	$-0.391825\pi$
$463$	14.3452	0.666677	0.333339	+	0.942807i	$0.391825\pi$
$464$	−78.5824	−3.64810
$465$	−15.3654	−0.712551
$466$	−69.1839	−3.20488
$467$	−6.76080	−0.312853	−0.156426	−	0.987690i	$-0.549997\pi$
$467$	−6.76080	−0.312853	−0.156426	+	0.987690i	$0.549997\pi$
$468$	−176.952	−8.17962
$469$	24.5484	1.13354
$470$	10.5556	0.486896
$471$	17.7254	0.816742
$472$	25.8334	1.18908
$473$	−0.318112	−0.0146268
$474$	−56.5815	−2.59887
$475$	0.349365	0.0160300
$476$	15.0166	0.688283
$477$	81.5609	3.73441
$478$	−66.3232	−3.03355
$479$	−16.9620	−0.775015	−0.387507	−	0.921867i	$-0.626664\pi$
$479$	−16.9620	−0.775015	−0.387507	+	0.921867i	$0.626664\pi$
$480$	57.8020	2.63829
$481$	−32.0418	−1.46098
$482$	2.83202	0.128995
$483$	−8.07088	−0.367238
$484$	−57.6441	−2.62019
$485$	−7.93741	−0.360419
$486$	−68.0564	−3.08710
$487$	−14.8598	−0.673362	−0.336681	−	0.941619i	$-0.609304\pi$
$487$	−14.8598	−0.673362	−0.336681	+	0.941619i	$0.609304\pi$
$488$	−63.4773	−2.87348
$489$	−2.17385	−0.0983050
$490$	2.96304	0.133857
$491$	−35.8231	−1.61667	−0.808337	−	0.588720i	$-0.799632\pi$
$491$	−35.8231	−1.61667	−0.808337	+	0.588720i	$0.799632\pi$
$492$	−105.859	−4.77250
$493$	−5.91246	−0.266284
$494$	4.44186	0.199849
$495$	−1.96037	−0.0881122
$496$	64.2122	2.88321
$497$	−2.84577	−0.127650
$498$	37.4373	1.67760
$499$	−18.9121	−0.846620	−0.423310	−	0.905985i	$-0.639132\pi$
$499$	−18.9121	−0.846620	−0.423310	+	0.905985i	$0.639132\pi$
$500$	−5.27679	−0.235985
$501$	−63.3787	−2.83155
$502$	−32.9296	−1.46972
$503$	21.5673	0.961637	0.480818	−	0.876820i	$-0.340340\pi$
$503$	21.5673	0.961637	0.480818	+	0.876820i	$0.340340\pi$
$504$	−178.974	−7.97213
$505$	−9.09860	−0.404882
$506$	0.662793	0.0294647
$507$	29.3048	1.30147
$508$	72.7006	3.22557
$509$	−31.0862	−1.37787	−0.688935	−	0.724823i	$-0.741922\pi$
$509$	−31.0862	−1.37787	−0.688935	+	0.724823i	$0.741922\pi$
$510$	8.57929	0.379897
$511$	11.6865	0.516981
$512$	−6.58950	−0.291218
$513$	4.57218	0.201867
$514$	40.5071	1.78669
$515$	−1.80476	−0.0795272
$516$	−19.3759	−0.852978
$517$	1.07816	0.0474174
$518$	−52.1882	−2.29302
$519$	74.5904	3.27416
$520$	−41.6615	−1.82698
$521$	−6.12307	−0.268256	−0.134128	−	0.990964i	$-0.542823\pi$
$521$	−6.12307	−0.268256	−0.134128	+	0.990964i	$0.542823\pi$
$522$	113.477	4.96677
$523$	−9.45477	−0.413428	−0.206714	−	0.978401i	$-0.566277\pi$
$523$	−9.45477	−0.413428	−0.206714	+	0.978401i	$0.566277\pi$
$524$	−55.3193	−2.41664
$525$	9.05069	0.395004
$526$	72.1920	3.14772
$527$	4.83127	0.210453
$528$	11.6468	0.506862
$529$	−22.2048	−0.965426
$530$	30.9230	1.34321
$531$	−20.7937	−0.902371
$532$	5.24626	0.227454
$533$	29.7298	1.28774
$534$	−74.1829	−3.21021
$535$	−10.3112	−0.445793
$536$	−76.2504	−3.29352
$537$	71.1907	3.07211
$538$	−23.9129	−1.03096
$539$	0.302647	0.0130359
$540$	−69.0580	−2.97178
$541$	16.2666	0.699354	0.349677	−	0.936870i	$-0.386291\pi$
$541$	16.2666	0.699354	0.349677	+	0.936870i	$0.386291\pi$
$542$	−23.7564	−1.02042
$543$	−3.42498	−0.146980
$544$	−18.1744	−0.779223
$545$	−3.33893	−0.143024
$546$	115.071	4.92459
$547$	26.6935	1.14133	0.570665	−	0.821183i	$-0.306685\pi$
$547$	26.6935	1.14133	0.570665	+	0.821183i	$0.306685\pi$
$548$	38.1559	1.62994
$549$	51.0940	2.18064
$550$	−0.743256	−0.0316925
$551$	−2.06561	−0.0879978
$552$	25.0692	1.06701
$553$	18.7682	0.798106
$554$	−77.8970	−3.30953
$555$	−21.6214	−0.917776
$556$	52.8687	2.24213
$557$	28.4151	1.20399	0.601994	−	0.798501i	$-0.294373\pi$
$557$	28.4151	1.20399	0.601994	+	0.798501i	$0.294373\pi$
$558$	−92.7261	−3.92541
$559$	5.44160	0.230155
$560$	−37.8231	−1.59832
$561$	0.876294	0.0369972
$562$	75.8989	3.20160
$563$	34.1107	1.43759	0.718797	−	0.695220i	$-0.244693\pi$
$563$	34.1107	1.43759	0.718797	+	0.695220i	$0.244693\pi$
$564$	65.6699	2.76520
$565$	9.35353	0.393506
$566$	6.06231	0.254818
$567$	57.7049	2.42338
$568$	8.83933	0.370890
$569$	1.18662	0.0497457	0.0248729	−	0.999691i	$-0.492082\pi$
$569$	1.18662	0.0497457	0.0248729	+	0.999691i	$0.492082\pi$
$570$	2.99730	0.125543
$571$	23.0551	0.964824	0.482412	−	0.875944i	$-0.339761\pi$
$571$	23.0551	0.964824	0.482412	+	0.875944i	$0.339761\pi$
$572$	−6.85257	−0.286520
$573$	72.0222	3.00877
$574$	48.4225	2.02111
$575$	−0.891742	−0.0371882
$576$	159.692	6.65382
$577$	−45.5096	−1.89459	−0.947295	−	0.320363i	$-0.896195\pi$
$577$	−45.5096	−1.89459	−0.947295	+	0.320363i	$0.896195\pi$
$578$	−2.69755	−0.112203
$579$	−50.4930	−2.09842
$580$	31.1989	1.29546
$581$	−12.4180	−0.515187
$582$	−68.0974	−2.82273
$583$	3.15849	0.130811
$584$	−36.2998	−1.50210
$585$	33.5340	1.38646
$586$	59.1086	2.44175
$587$	−10.3440	−0.426943	−0.213471	−	0.976949i	$-0.568477\pi$
$587$	−10.3440	−0.426943	−0.213471	+	0.976949i	$0.568477\pi$
$588$	18.4340	0.760206
$589$	1.68788	0.0695477
$590$	−7.88373	−0.324568
$591$	71.3747	2.93596
$592$	90.3563	3.71362
$593$	13.6977	0.562499	0.281249	−	0.959635i	$-0.409251\pi$
$593$	13.6977	0.562499	0.281249	+	0.959635i	$0.409251\pi$
$594$	−9.72707	−0.399107
$595$	−2.84577	−0.116665
$596$	−64.1472	−2.62757
$597$	−41.7956	−1.71058
$598$	−11.3377	−0.463633
$599$	7.43921	0.303958	0.151979	−	0.988384i	$-0.451435\pi$
$599$	7.43921	0.303958	0.151979	+	0.988384i	$0.451435\pi$
$600$	−28.1126	−1.14769
$601$	−9.77905	−0.398896	−0.199448	−	0.979908i	$-0.563915\pi$
$601$	−9.77905	−0.398896	−0.199448	+	0.979908i	$0.563915\pi$
$602$	8.86301	0.361229
$603$	61.3753	2.49940
$604$	−77.3017	−3.14536
$605$	10.9241	0.444127
$606$	−78.0596	−3.17095
$607$	32.1885	1.30649	0.653246	−	0.757146i	$-0.273407\pi$
$607$	32.1885	1.30649	0.653246	+	0.757146i	$0.273407\pi$
$608$	−6.34951	−0.257507
$609$	−53.5119	−2.16841
$610$	19.3718	0.784341
$611$	−18.4429	−0.746121
$612$	37.5440	1.51763
$613$	25.4165	1.02656	0.513282	−	0.858220i	$-0.328429\pi$
$613$	25.4165	1.02656	0.513282	+	0.858220i	$0.328429\pi$
$614$	36.7825	1.48442
$615$	20.0613	0.808948
$616$	−6.93087	−0.279253
$617$	37.2621	1.50012	0.750058	−	0.661372i	$-0.230025\pi$
$617$	37.2621	1.50012	0.750058	+	0.661372i	$0.230025\pi$
$618$	−15.4836	−0.622840
$619$	−2.65749	−0.106813	−0.0534067	−	0.998573i	$-0.517008\pi$
$619$	−2.65749	−0.106813	−0.0534067	+	0.998573i	$0.517008\pi$
$620$	−25.4936	−1.02385
$621$	−11.6703	−0.468314
$622$	51.0526	2.04702
$623$	24.6067	0.985845
$624$	−199.229	−7.97556
$625$	1.00000	0.0400000
$626$	−35.5781	−1.42199
$627$	0.306146	0.0122263
$628$	29.4093	1.17356
$629$	6.79832	0.271067
$630$	54.6186	2.17606
$631$	−8.12025	−0.323262	−0.161631	−	0.986851i	$-0.551675\pi$
$631$	−8.12025	−0.323262	−0.161631	+	0.986851i	$0.551675\pi$
$632$	−58.2965	−2.31891
$633$	76.4033	3.03676
$634$	70.8027	2.81193
$635$	−13.7774	−0.546740
$636$	192.381	7.62841
$637$	−5.17706	−0.205123
$638$	4.39447	0.173979
$639$	−7.11493	−0.281462
$640$	24.1966	0.956455
$641$	−12.7338	−0.502955	−0.251477	−	0.967863i	$-0.580916\pi$
$641$	−12.7338	−0.502955	−0.251477	+	0.967863i	$0.580916\pi$
$642$	−88.4630	−3.49136
$643$	−43.5384	−1.71699	−0.858494	−	0.512824i	$-0.828600\pi$
$643$	−43.5384	−1.71699	−0.858494	+	0.512824i	$0.828600\pi$
$644$	−13.3909	−0.527675
$645$	3.67192	0.144582
$646$	−0.942430	−0.0370794
$647$	41.1993	1.61971	0.809856	−	0.586628i	$-0.199545\pi$
$647$	41.1993	1.61971	0.809856	+	0.586628i	$0.199545\pi$
$648$	−179.239	−7.04116
$649$	−0.805249	−0.0316088
$650$	12.7141	0.498688
$651$	43.7263	1.71377
$652$	−3.60677	−0.141252
$653$	10.4815	0.410172	0.205086	−	0.978744i	$-0.434253\pi$
$653$	10.4815	0.410172	0.205086	+	0.978744i	$0.434253\pi$
$654$	−28.6456	−1.12013
$655$	10.4835	0.409625
$656$	−83.8365	−3.27327
$657$	29.2183	1.13992
$658$	−30.0390	−1.17104
$659$	−27.4712	−1.07013	−0.535063	−	0.844812i	$-0.679712\pi$
$659$	−27.4712	−1.07013	−0.535063	+	0.844812i	$0.679712\pi$
$660$	−4.62402	−0.179990
$661$	−10.7306	−0.417373	−0.208686	−	0.977983i	$-0.566919\pi$
$661$	−10.7306	−0.417373	−0.208686	+	0.977983i	$0.566919\pi$
$662$	64.0290	2.48856
$663$	−14.9898	−0.582157
$664$	38.5720	1.49688
$665$	−0.994213	−0.0385539
$666$	−130.480	−5.05598
$667$	5.27240	0.204148
$668$	−105.156	−4.06859
$669$	86.0166	3.32560
$670$	23.2698	0.898992
$671$	1.97864	0.0763847
$672$	−164.491	−6.34539
$673$	−30.2186	−1.16484	−0.582420	−	0.812888i	$-0.697894\pi$
$673$	−30.2186	−1.16484	−0.582420	+	0.812888i	$0.697894\pi$
$674$	−64.4650	−2.48310
$675$	13.0871	0.503723
$676$	48.6214	1.87005
$677$	−30.7449	−1.18162	−0.590811	−	0.806810i	$-0.701192\pi$
$677$	−30.7449	−1.18162	−0.590811	+	0.806810i	$0.701192\pi$
$678$	80.2467	3.08186
$679$	22.5881	0.866851
$680$	8.83933	0.338973
$681$	−40.0219	−1.53364
$682$	−3.59087	−0.137501
$683$	2.68269	0.102650	0.0513251	−	0.998682i	$-0.483656\pi$
$683$	2.68269	0.102650	0.0513251	+	0.998682i	$0.483656\pi$
$684$	13.1166	0.501524
$685$	−7.23089	−0.276278
$686$	45.3042	1.72972
$687$	−55.6964	−2.12495
$688$	−15.3450	−0.585024
$689$	−54.0289	−2.05834
$690$	−7.65052	−0.291250
$691$	25.0297	0.952175	0.476087	−	0.879398i	$-0.342055\pi$
$691$	25.0297	0.952175	0.476087	+	0.879398i	$0.342055\pi$
$692$	123.758	4.70456
$693$	5.57878	0.211920
$694$	28.3783	1.07722
$695$	−10.0191	−0.380046
$696$	166.215	6.30035
$697$	−6.30778	−0.238924
$698$	5.83792	0.220969
$699$	81.5674	3.08516
$700$	15.0166	0.567572
$701$	28.3282	1.06994	0.534971	−	0.844871i	$-0.320323\pi$
$701$	28.3282	1.06994	0.534971	+	0.844871i	$0.320323\pi$
$702$	166.391	6.28001
$703$	2.37510	0.0895784
$704$	6.18415	0.233074
$705$	−12.4450	−0.468707
$706$	−44.9848	−1.69302
$707$	25.8925	0.973789
$708$	−49.0471	−1.84330
$709$	−18.0703	−0.678645	−0.339323	−	0.940670i	$-0.610198\pi$
$709$	−18.0703	−0.678645	−0.339323	+	0.940670i	$0.610198\pi$
$710$	−2.69755	−0.101237
$711$	46.9239	1.75978
$712$	−76.4314	−2.86439
$713$	−4.30825	−0.161345
$714$	−24.4147	−0.913698
$715$	1.29862	0.0485658
$716$	118.117	4.41424
$717$	78.1947	2.92023
$718$	10.0176	0.373853
$719$	19.8558	0.740497	0.370249	−	0.928933i	$-0.379272\pi$
$719$	19.8558	0.740497	0.370249	+	0.928933i	$0.379272\pi$
$720$	−94.5643	−3.52420
$721$	5.13594	0.191272
$722$	50.9243	1.89520
$723$	−3.33894	−0.124176
$724$	−5.68259	−0.211192
$725$	−5.91246	−0.219583
$726$	93.7209	3.47831
$727$	27.0586	1.00355	0.501774	−	0.864999i	$-0.332681\pi$
$727$	27.0586	1.00355	0.501774	+	0.864999i	$0.332681\pi$
$728$	118.559	4.39409
$729$	19.4058	0.718733
$730$	11.0778	0.410009
$731$	−1.15455	−0.0427024
$732$	120.518	4.45447
$733$	44.5826	1.64669	0.823347	−	0.567538i	$-0.192104\pi$
$733$	44.5826	1.64669	0.823347	+	0.567538i	$0.192104\pi$
$734$	58.4836	2.15867
$735$	−3.49341	−0.128856
$736$	16.2069	0.597395
$737$	2.37679	0.0875503
$738$	121.065	4.45645
$739$	−53.4844	−1.96746	−0.983728	−	0.179666i	$-0.942498\pi$
$739$	−53.4844	−1.96746	−0.983728	+	0.179666i	$0.942498\pi$
$740$	−35.8734	−1.31873
$741$	−5.23692	−0.192383
$742$	−87.9997	−3.23057
$743$	26.1739	0.960228	0.480114	−	0.877206i	$-0.340595\pi$
$743$	26.1739	0.960228	0.480114	+	0.877206i	$0.340595\pi$
$744$	−135.819	−4.97938
$745$	12.1565	0.445379
$746$	79.7767	2.92083
$747$	−31.0473	−1.13596
$748$	1.45391	0.0531603
$749$	29.3434	1.07218
$750$	8.57929	0.313271
$751$	−1.81809	−0.0663432	−0.0331716	−	0.999450i	$-0.510561\pi$
$751$	−1.81809	−0.0663432	−0.0331716	+	0.999450i	$0.510561\pi$
$752$	52.0082	1.89654
$753$	38.8238	1.41482
$754$	−75.1716	−2.73759
$755$	14.6494	0.533145
$756$	196.523	7.14748
$757$	−29.1732	−1.06032	−0.530158	−	0.847899i	$-0.677868\pi$
$757$	−29.1732	−1.06032	−0.530158	+	0.847899i	$0.677868\pi$
$758$	1.86259	0.0676524
$759$	−0.781428	−0.0283641
$760$	3.08815	0.112019
$761$	−4.63249	−0.167928	−0.0839638	−	0.996469i	$-0.526758\pi$
$761$	−4.63249	−0.167928	−0.0839638	+	0.996469i	$0.526758\pi$
$762$	−118.200	−4.28195
$763$	9.50182	0.343989
$764$	119.496	4.32323
$765$	−7.11493	−0.257241
$766$	−43.8102	−1.58293
$767$	13.7745	0.497370
$768$	64.8242	2.33914
$769$	41.7295	1.50480	0.752402	−	0.658704i	$-0.228895\pi$
$769$	41.7295	1.50480	0.752402	+	0.658704i	$0.228895\pi$
$770$	2.11514	0.0762242
$771$	−47.7576	−1.71995
$772$	−83.7760	−3.01516
$773$	−8.42708	−0.303101	−0.151550	−	0.988450i	$-0.548427\pi$
$773$	−8.42708	−0.303101	−0.151550	+	0.988450i	$0.548427\pi$
$774$	22.1591	0.796492
$775$	4.83127	0.173544
$776$	−70.1614	−2.51865
$777$	61.5295	2.20736
$778$	−40.5885	−1.45517
$779$	−2.20372	−0.0789564
$780$	79.0982	2.83217
$781$	−0.275530	−0.00985923
$782$	2.40552	0.0860213
$783$	−77.3771	−2.76523
$784$	14.5991	0.521395
$785$	−5.57332	−0.198920
$786$	89.9411	3.20809
$787$	33.9509	1.21022	0.605110	−	0.796142i	$-0.293129\pi$
$787$	33.9509	1.21022	0.605110	+	0.796142i	$0.293129\pi$
$788$	118.422	4.21862
$789$	−85.1139	−3.03013
$790$	17.7907	0.632965
$791$	−26.6180	−0.946428
$792$	−17.3284	−0.615737
$793$	−33.8466	−1.20193
$794$	−11.0234	−0.391207
$795$	−36.4580	−1.29303
$796$	−69.3456	−2.45789
$797$	−25.9801	−0.920263	−0.460132	−	0.887851i	$-0.652198\pi$
$797$	−25.9801	−0.920263	−0.460132	+	0.887851i	$0.652198\pi$
$798$	−8.52964	−0.301946
$799$	3.91305	0.138434
$800$	−18.1744	−0.642564
$801$	61.5210	2.17374
$802$	76.6904	2.70803
$803$	1.13150	0.0399296
$804$	144.769	5.10560
$805$	2.53770	0.0894420
$806$	61.4252	2.16361
$807$	28.1932	0.992447
$808$	−80.4255	−2.82936
$809$	−0.983893	−0.0345919	−0.0172959	−	0.999850i	$-0.505506\pi$
$809$	−0.983893	−0.0345919	−0.0172959	+	0.999850i	$0.505506\pi$
$810$	54.6994	1.92194
$811$	−11.3003	−0.396808	−0.198404	−	0.980120i	$-0.563576\pi$
$811$	−11.3003	−0.396808	−0.198404	+	0.980120i	$0.563576\pi$
$812$	−88.7848	−3.11574
$813$	28.0086	0.982305
$814$	−5.05289	−0.177104
$815$	0.683516	0.0239425
$816$	42.2706	1.47977
$817$	−0.403358	−0.0141117
$818$	−58.8476	−2.05756
$819$	−95.4302	−3.33460
$820$	33.2849	1.16236
$821$	3.89470	0.135926	0.0679631	−	0.997688i	$-0.478350\pi$
$821$	3.89470	0.135926	0.0679631	+	0.997688i	$0.478350\pi$
$822$	−62.0359	−2.16375
$823$	−46.1921	−1.61016	−0.805079	−	0.593168i	$-0.797877\pi$
$823$	−46.1921	−1.61016	−0.805079	+	0.593168i	$0.797877\pi$
$824$	−15.9529	−0.555744
$825$	0.876294	0.0305086
$826$	22.4353	0.780624
$827$	−39.4933	−1.37332	−0.686658	−	0.726981i	$-0.740923\pi$
$827$	−39.4933	−1.37332	−0.686658	+	0.726981i	$0.740923\pi$
$828$	−33.4796	−1.16350
$829$	−2.83430	−0.0984392	−0.0492196	−	0.998788i	$-0.515673\pi$
$829$	−2.83430	−0.0984392	−0.0492196	+	0.998788i	$0.515673\pi$
$830$	−11.7713	−0.408586
$831$	91.8401	3.18590
$832$	−105.786	−3.66746
$833$	1.09842	0.0380580
$834$	−85.9568	−2.97644
$835$	19.9279	0.689634
$836$	0.507946	0.0175677
$837$	63.2273	2.18546
$838$	18.7004	0.645994
$839$	27.9202	0.963912	0.481956	−	0.876195i	$-0.339926\pi$
$839$	27.9202	0.963912	0.481956	+	0.876195i	$0.339926\pi$
$840$	80.0020	2.76033
$841$	5.95724	0.205422
$842$	34.0366	1.17298
$843$	−89.4843	−3.08200
$844$	126.765	4.36345
$845$	−9.21419	−0.316978
$846$	−75.1027	−2.58208
$847$	−31.0875	−1.06818
$848$	152.359	5.23203
$849$	−7.14742	−0.245299
$850$	−2.69755	−0.0925253
$851$	−6.06235	−0.207815
$852$	−16.7823	−0.574952
$853$	5.08937	0.174257	0.0871284	−	0.996197i	$-0.472231\pi$
$853$	5.08937	0.174257	0.0871284	+	0.996197i	$0.472231\pi$
$854$	−55.1277	−1.88643
$855$	−2.48571	−0.0850094
$856$	−91.1443	−3.11525
$857$	−24.7556	−0.845635	−0.422818	−	0.906215i	$-0.638959\pi$
$857$	−24.7556	−0.845635	−0.422818	+	0.906215i	$0.638959\pi$
$858$	11.1413	0.380357
$859$	−18.0133	−0.614607	−0.307304	−	0.951612i	$-0.599427\pi$
$859$	−18.0133	−0.614607	−0.307304	+	0.951612i	$0.599427\pi$
$860$	6.09230	0.207746
$861$	−57.0898	−1.94561
$862$	100.303	3.41634
$863$	37.0240	1.26031	0.630156	−	0.776468i	$-0.282991\pi$
$863$	37.0240	1.26031	0.630156	+	0.776468i	$0.282991\pi$
$864$	−237.851	−8.09185
$865$	−23.4532	−0.797432
$866$	−43.0843	−1.46407
$867$	3.18040	0.108012
$868$	72.5490	2.46247
$869$	1.81715	0.0616427
$870$	−50.7248	−1.71973
$871$	−40.6573	−1.37762
$872$	−29.5139	−0.999465
$873$	56.4741	1.91136
$874$	0.840405	0.0284271
$875$	−2.84577	−0.0962047
$876$	68.9186	2.32854
$877$	28.7289	0.970107	0.485054	−	0.874484i	$-0.338800\pi$
$877$	28.7289	0.970107	0.485054	+	0.874484i	$0.338800\pi$
$878$	−59.2193	−1.99856
$879$	−69.6887	−2.35054
$880$	−3.66206	−0.123448
$881$	2.30441	0.0776375	0.0388188	−	0.999246i	$-0.487640\pi$
$881$	2.30441	0.0776375	0.0388188	+	0.999246i	$0.487640\pi$
$882$	−21.0819	−0.709863
$883$	36.0110	1.21187	0.605933	−	0.795516i	$-0.292800\pi$
$883$	36.0110	1.21187	0.605933	+	0.795516i	$0.292800\pi$
$884$	−24.8705	−0.836487
$885$	9.29487	0.312444
$886$	76.0978	2.55656
$887$	−58.6613	−1.96965	−0.984826	−	0.173542i	$-0.944479\pi$
$887$	−58.6613	−1.96965	−0.984826	+	0.173542i	$0.944479\pi$
$888$	−191.118	−6.41351
$889$	39.2074	1.31497
$890$	23.3250	0.781857
$891$	5.58703	0.187173
$892$	142.716	4.77847
$893$	1.36708	0.0457476
$894$	104.294	3.48811
$895$	−22.3842	−0.748222
$896$	−68.8580	−2.30038
$897$	13.3671	0.446313
$898$	90.6747	3.02585
$899$	−28.5647	−0.952686
$900$	37.5440	1.25147
$901$	11.4633	0.381899
$902$	4.68830	0.156103
$903$	−10.4494	−0.347735
$904$	82.6789	2.74986
$905$	1.07690	0.0357975
$906$	125.681	4.17548
$907$	−15.8605	−0.526638	−0.263319	−	0.964709i	$-0.584817\pi$
$907$	−15.8605	−0.526638	−0.263319	+	0.964709i	$0.584817\pi$
$908$	−66.4027	−2.20365
$909$	64.7359	2.14715
$910$	−36.1814	−1.19940
$911$	39.1938	1.29855	0.649274	−	0.760555i	$-0.275073\pi$
$911$	39.1938	1.29855	0.649274	+	0.760555i	$0.275073\pi$
$912$	14.7678	0.489012
$913$	−1.20232	−0.0397911
$914$	72.8195	2.40865
$915$	−22.8392	−0.755041
$916$	−92.4093	−3.05329
$917$	−29.8337	−0.985195
$918$	−35.3032	−1.16518
$919$	46.5033	1.53400	0.767001	−	0.641646i	$-0.221748\pi$
$919$	46.5033	1.53400	0.767001	+	0.641646i	$0.221748\pi$
$920$	−7.88240	−0.259875
$921$	−43.3664	−1.42897
$922$	53.3806	1.75800
$923$	4.71319	0.155137
$924$	13.1589	0.432896
$925$	6.79832	0.223528
$926$	−38.6969	−1.27166
$927$	12.8407	0.421745
$928$	107.456	3.52741
$929$	−0.460171	−0.0150977	−0.00754886	−	0.999972i	$-0.502403\pi$
$929$	−0.460171	−0.0150977	−0.00754886	+	0.999972i	$0.502403\pi$
$930$	41.4489	1.35916
$931$	0.383749	0.0125769
$932$	135.333	4.43300
$933$	−60.1907	−1.97056
$934$	18.2376	0.596753
$935$	−0.275530	−0.00901078
$936$	296.418	9.68873
$937$	−58.7929	−1.92068	−0.960339	−	0.278834i	$-0.910052\pi$
$937$	−58.7929	−1.92068	−0.960339	+	0.278834i	$0.910052\pi$
$938$	−66.2206	−2.16218
$939$	41.9463	1.36887
$940$	−20.6483	−0.673474
$941$	−49.2885	−1.60676	−0.803379	−	0.595468i	$-0.796967\pi$
$941$	−49.2885	−1.60676	−0.803379	+	0.595468i	$0.796967\pi$
$942$	−47.8151	−1.55790
$943$	5.62492	0.183172
$944$	−38.8435	−1.26425
$945$	−37.2429	−1.21151
$946$	0.858123	0.0279000
$947$	25.3430	0.823537	0.411768	−	0.911289i	$-0.364911\pi$
$947$	25.3430	0.823537	0.411768	+	0.911289i	$0.364911\pi$
$948$	110.681	3.59476
$949$	−19.3553	−0.628300
$950$	−0.942430	−0.0305765
$951$	−83.4759	−2.70689
$952$	−25.1547	−0.815269
$953$	−8.93054	−0.289288	−0.144644	−	0.989484i	$-0.546204\pi$
$953$	−8.93054	−0.289288	−0.144644	+	0.989484i	$0.546204\pi$
$954$	−220.015	−7.12324
$955$	−22.6457	−0.732796
$956$	129.738	4.19601
$957$	−5.18106	−0.167480
$958$	45.7560	1.47831
$959$	20.5775	0.664481
$960$	−71.3827	−2.30387
$961$	−7.65884	−0.247059
$962$	86.4345	2.78676
$963$	73.3637	2.36411
$964$	−5.53984	−0.178426
$965$	15.8763	0.511076
$966$	21.7716	0.700491
$967$	11.3677	0.365559	0.182779	−	0.983154i	$-0.441491\pi$
$967$	11.3677	0.365559	0.182779	+	0.983154i	$0.441491\pi$
$968$	96.5615	3.10361
$969$	1.11112	0.0356943
$970$	21.4116	0.687485
$971$	40.0192	1.28428	0.642139	−	0.766588i	$-0.278047\pi$
$971$	40.0192	1.28428	0.642139	+	0.766588i	$0.278047\pi$
$972$	133.128	4.27008
$973$	28.5121	0.914055
$974$	40.0851	1.28441
$975$	−14.9898	−0.480059
$976$	95.4457	3.05514
$977$	35.0625	1.12175	0.560874	−	0.827901i	$-0.310465\pi$
$977$	35.0625	1.12175	0.560874	+	0.827901i	$0.310465\pi$
$978$	5.86408	0.187513
$979$	2.38243	0.0761429
$980$	−5.79613	−0.185151
$981$	23.7562	0.758478
$982$	96.6347	3.08374
$983$	19.3763	0.618008	0.309004	−	0.951061i	$-0.400004\pi$
$983$	19.3763	0.618008	0.309004	+	0.951061i	$0.400004\pi$
$984$	177.328	5.65301
$985$	−22.4421	−0.715064
$986$	15.9492	0.507926
$987$	35.4157	1.12730
$988$	−8.68890	−0.276431
$989$	1.02956	0.0327380
$990$	5.28821	0.168070
$991$	−43.0845	−1.36863	−0.684313	−	0.729189i	$-0.739898\pi$
$991$	−43.0845	−1.36863	−0.684313	+	0.729189i	$0.739898\pi$
$992$	−87.8056	−2.78783
$993$	−75.4898	−2.39560
$994$	7.67662	0.243488
$995$	13.1416	0.416617
$996$	−73.2326	−2.32046
$997$	−21.0303	−0.666035	−0.333018	−	0.942921i	$-0.608067\pi$
$997$	−21.0303	−0.666035	−0.333018	+	0.942921i	$0.608067\pi$
$998$	51.0163	1.61489
$999$	88.9704	2.81490

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.e.1.2	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.e.1.2	✓	49	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69755 q^{2} +3.18040 q^{3} +5.27679 q^{4} -1.00000 q^{5} -8.57929 q^{6} +2.84577 q^{7} -8.83933 q^{8} +7.11493 q^{9} +O(q^{10})\)	\(q-2.69755 q^{2} +3.18040 q^{3} +5.27679 q^{4} -1.00000 q^{5} -8.57929 q^{6} +2.84577 q^{7} -8.83933 q^{8} +7.11493 q^{9} +2.69755 q^{10} +0.275530 q^{11} +16.7823 q^{12} -4.71319 q^{13} -7.67662 q^{14} -3.18040 q^{15} +13.2910 q^{16} +1.00000 q^{17} -19.1929 q^{18} +0.349365 q^{19} -5.27679 q^{20} +9.05069 q^{21} -0.743256 q^{22} -0.891742 q^{23} -28.1126 q^{24} +1.00000 q^{25} +12.7141 q^{26} +13.0871 q^{27} +15.0166 q^{28} -5.91246 q^{29} +8.57929 q^{30} +4.83127 q^{31} -18.1744 q^{32} +0.876294 q^{33} -2.69755 q^{34} -2.84577 q^{35} +37.5440 q^{36} +6.79832 q^{37} -0.942430 q^{38} -14.9898 q^{39} +8.83933 q^{40} -6.30778 q^{41} -24.4147 q^{42} -1.15455 q^{43} +1.45391 q^{44} -7.11493 q^{45} +2.40552 q^{46} +3.91305 q^{47} +42.2706 q^{48} +1.09842 q^{49} -2.69755 q^{50} +3.18040 q^{51} -24.8705 q^{52} +11.4633 q^{53} -35.3032 q^{54} -0.275530 q^{55} -25.1547 q^{56} +1.11112 q^{57} +15.9492 q^{58} -2.92255 q^{59} -16.7823 q^{60} +7.18124 q^{61} -13.0326 q^{62} +20.2475 q^{63} +22.4446 q^{64} +4.71319 q^{65} -2.36385 q^{66} +8.62627 q^{67} +5.27679 q^{68} -2.83610 q^{69} +7.67662 q^{70} -1.00000 q^{71} -62.8912 q^{72} +4.10662 q^{73} -18.3388 q^{74} +3.18040 q^{75} +1.84353 q^{76} +0.784095 q^{77} +40.4359 q^{78} +6.59513 q^{79} -13.2910 q^{80} +20.2774 q^{81} +17.0156 q^{82} -4.36368 q^{83} +47.7586 q^{84} -1.00000 q^{85} +3.11445 q^{86} -18.8040 q^{87} -2.43550 q^{88} +8.64674 q^{89} +19.1929 q^{90} -13.4127 q^{91} -4.70554 q^{92} +15.3654 q^{93} -10.5556 q^{94} -0.349365 q^{95} -57.8020 q^{96} +7.93741 q^{97} -2.96304 q^{98} +1.96037 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q + q^{2} + 10 q^{3} + 55 q^{4} - 49 q^{5} + 2 q^{6} + 15 q^{7} + 3 q^{8} + 43 q^{9}+O(q^{10}) \) 49 * q + q^2 + 10 * q^3 + 55 * q^4 - 49 * q^5 + 2 * q^6 + 15 * q^7 + 3 * q^8 + 43 * q^9	\( 49 q + q^{2} + 10 q^{3} + 55 q^{4} - 49 q^{5} + 2 q^{6} + 15 q^{7} + 3 q^{8} + 43 q^{9} - q^{10} - 4 q^{11} + 32 q^{12} + 21 q^{13} + 8 q^{14} - 10 q^{15} + 63 q^{16} + 49 q^{17} + 12 q^{18} + 19 q^{19} - 55 q^{20} + 5 q^{21} + 10 q^{22} + 10 q^{23} + 7 q^{24} + 49 q^{25} - 20 q^{26} + 37 q^{27} + 48 q^{28} + 30 q^{29} - 2 q^{30} + 23 q^{31} + 2 q^{32} - q^{33} + q^{34} - 15 q^{35} + 39 q^{36} + 60 q^{37} + 13 q^{38} + 3 q^{39} - 3 q^{40} - 29 q^{41} + 32 q^{42} + 23 q^{43} + 11 q^{44} - 43 q^{45} + 6 q^{46} - 8 q^{47} + 96 q^{48} + 82 q^{49} + q^{50} + 10 q^{51} + 11 q^{52} + 15 q^{53} - 4 q^{54} + 4 q^{55} - 18 q^{56} + 44 q^{57} + 38 q^{58} - 28 q^{59} - 32 q^{60} + 107 q^{61} + 37 q^{62} + 54 q^{63} + 77 q^{64} - 21 q^{65} + 23 q^{66} + 11 q^{67} + 55 q^{68} + 27 q^{69} - 8 q^{70} - 49 q^{71} - 53 q^{72} + 97 q^{73} + 27 q^{74} + 10 q^{75} + 66 q^{76} + 19 q^{77} + 48 q^{78} + 31 q^{79} - 63 q^{80} - 7 q^{81} + 61 q^{82} + 6 q^{83} + 46 q^{84} - 49 q^{85} - 89 q^{86} + 36 q^{87} + 63 q^{88} - 20 q^{89} - 12 q^{90} + 35 q^{91} - 2 q^{92} + 47 q^{93} - 4 q^{94} - 19 q^{95} + 73 q^{96} + 92 q^{97} + 3 q^{98} + 5 q^{99}+O(q^{100}) \) 49 * q + q^2 + 10 * q^3 + 55 * q^4 - 49 * q^5 + 2 * q^6 + 15 * q^7 + 3 * q^8 + 43 * q^9 - q^10 - 4 * q^11 + 32 * q^12 + 21 * q^13 + 8 * q^14 - 10 * q^15 + 63 * q^16 + 49 * q^17 + 12 * q^18 + 19 * q^19 - 55 * q^20 + 5 * q^21 + 10 * q^22 + 10 * q^23 + 7 * q^24 + 49 * q^25 - 20 * q^26 + 37 * q^27 + 48 * q^28 + 30 * q^29 - 2 * q^30 + 23 * q^31 + 2 * q^32 - q^33 + q^34 - 15 * q^35 + 39 * q^36 + 60 * q^37 + 13 * q^38 + 3 * q^39 - 3 * q^40 - 29 * q^41 + 32 * q^42 + 23 * q^43 + 11 * q^44 - 43 * q^45 + 6 * q^46 - 8 * q^47 + 96 * q^48 + 82 * q^49 + q^50 + 10 * q^51 + 11 * q^52 + 15 * q^53 - 4 * q^54 + 4 * q^55 - 18 * q^56 + 44 * q^57 + 38 * q^58 - 28 * q^59 - 32 * q^60 + 107 * q^61 + 37 * q^62 + 54 * q^63 + 77 * q^64 - 21 * q^65 + 23 * q^66 + 11 * q^67 + 55 * q^68 + 27 * q^69 - 8 * q^70 - 49 * q^71 - 53 * q^72 + 97 * q^73 + 27 * q^74 + 10 * q^75 + 66 * q^76 + 19 * q^77 + 48 * q^78 + 31 * q^79 - 63 * q^80 - 7 * q^81 + 61 * q^82 + 6 * q^83 + 46 * q^84 - 49 * q^85 - 89 * q^86 + 36 * q^87 + 63 * q^88 - 20 * q^89 - 12 * q^90 + 35 * q^91 - 2 * q^92 + 47 * q^93 - 4 * q^94 - 19 * q^95 + 73 * q^96 + 92 * q^97 + 3 * q^98 + 5 * q^99

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