LMFDB - Embedded newform 700.5.o.c.649.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,5,Mod(549,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("700.549");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	700.o (of order $6$, degree $2$, 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:	$72.3589741587$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			649.3
Character	$\chi$	$=$	700.649
Dual form			700.5.o.c.549.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.85023 - 11.8650i) q^{3} +(-45.7788 + 17.4728i) q^{7} +(-53.3514 + 92.4073i) q^{9} +(57.7250 + 99.9826i) q^{11} -84.0756 q^{13} +(117.198 + 202.993i) q^{17} +(159.006 + 91.8023i) q^{19} +(520.910 + 423.470i) q^{21} +(-281.615 - 162.590i) q^{23} +352.140 q^{27} +254.642 q^{29} +(355.041 - 204.983i) q^{31} +(790.859 - 1369.81i) q^{33} +(64.0352 + 36.9707i) q^{37} +(575.937 + 997.553i) q^{39} +586.885i q^{41} -3340.46i q^{43} +(-805.694 + 1395.50i) q^{47} +(1790.40 - 1599.77i) q^{49} +(1605.67 - 2781.10i) q^{51} +(3106.46 - 1793.51i) q^{53} -2515.47i q^{57} +(-225.232 + 130.038i) q^{59} +(801.042 + 462.482i) q^{61} +(827.746 - 5162.50i) q^{63} +(-5117.03 + 2954.32i) q^{67} +4455.12i q^{69} +8572.53 q^{71} +(-1180.22 - 2044.20i) q^{73} +(-4389.56 - 3568.47i) q^{77} +(-2574.66 + 4459.44i) q^{79} +(1909.22 + 3306.87i) q^{81} -7546.38 q^{83} +(-1744.35 - 3021.31i) q^{87} +(-10498.9 - 6061.52i) q^{89} +(3848.88 - 1469.04i) q^{91} +(-4864.22 - 2808.36i) q^{93} +14875.4 q^{97} -12318.8 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 684 q^{9} - 300 q^{11} + 540 q^{19} - 190 q^{21} - 528 q^{29} - 2334 q^{31} - 852 q^{39} + 4092 q^{49} - 3902 q^{51} + 9414 q^{59} - 23598 q^{61} + 32820 q^{71} - 4890 q^{79} - 23710 q^{81} - 37764 q^{89}+ \cdots + 168180 q^{99}+O(q^{100}) $ 44 * q - 684 * q^9 - 300 * q^11 + 540 * q^19 - 190 * q^21 - 528 * q^29 - 2334 * q^31 - 852 * q^39 + 4092 * q^49 - 3902 * q^51 + 9414 * q^59 - 23598 * q^61 + 32820 * q^71 - 4890 * q^79 - 23710 * q^81 - 37764 * q^89 + 6418 * q^91 + 168180 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−6.85023	−	11.8650i	−0.761137	−	1.31833i	−0.942265	−	0.334868i	$-0.891308\pi$
$3$	−6.85023	−	11.8650i	−0.761137	−	1.31833i	0.181128	−	0.983460i	$-0.442025\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−45.7788	+	17.4728i	−0.934262	+	0.356588i
$7$	−45.7788	+	17.4728i	−0.934262	+	0.356588i
$8$		0			0
$9$	−53.3514	+	92.4073i	−0.658659	+	1.14083i
$10$		0			0
$11$	57.7250	+	99.9826i	0.477066	+	0.826303i	0.999655	−	0.0262824i	$-0.00836690\pi$
$11$	57.7250	+	99.9826i	0.477066	+	0.826303i	−0.522588	+	0.852585i	$0.675034\pi$
$12$		0			0
$13$	−84.0756			−0.497489			−0.248744	−	0.968569i	$-0.580018\pi$
$13$	−84.0756			−0.497489			−0.248744	+	0.968569i	$0.580018\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	117.198	+	202.993i	0.405530	+	0.702398i	0.994383	−	0.105842i	$-0.0337537\pi$
$17$	117.198	+	202.993i	0.405530	+	0.702398i	−0.588853	+	0.808240i	$0.700420\pi$
$18$		0			0
$19$	159.006	+	91.8023i	0.440460	+	0.254300i	0.703793	−	0.710405i	$-0.251488\pi$
$19$	159.006	+	91.8023i	0.440460	+	0.254300i	−0.263333	+	0.964705i	$0.584822\pi$
$20$		0			0
$21$	520.910	+	423.470i	1.18120	+	0.960250i
$22$		0			0
$23$	−281.615	−	162.590i	−0.532353	−	0.307354i	0.209621	−	0.977783i	$-0.432777\pi$
$23$	−281.615	−	162.590i	−0.532353	−	0.307354i	−0.741974	+	0.670429i	$0.766110\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	352.140			0.483045
$28$		0			0
$29$	254.642			0.302784			0.151392	−	0.988474i	$-0.451624\pi$
$29$	254.642			0.302784			0.151392	+	0.988474i	$0.451624\pi$
$30$		0			0
$31$	355.041	−	204.983i	0.369449	−	0.213302i	−0.303769	−	0.952746i	$-0.598245\pi$
$31$	355.041	−	204.983i	0.369449	−	0.213302i	0.673218	+	0.739444i	$0.264912\pi$
$32$		0			0
$33$	790.859	−	1369.81i	0.726225	−	1.25786i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	64.0352	+	36.9707i	0.0467752	+	0.0270057i	0.523205	−	0.852207i	$-0.324736\pi$
$37$	64.0352	+	36.9707i	0.0467752	+	0.0270057i	−0.476430	+	0.879212i	$0.658069\pi$
$38$		0			0
$39$	575.937	+	997.553i	0.378657	+	0.655853i
$40$		0			0
$41$			586.885i			0.349128i	0.984646	+	0.174564i	$0.0558516\pi$
$41$			586.885i			0.349128i	−0.984646	+	0.174564i	$0.944148\pi$
$42$		0			0
$43$		−	3340.46i		−	1.80663i	−0.428976	−	0.903316i	$-0.641125\pi$
$43$		−	3340.46i		−	1.80663i	0.428976	−	0.903316i	$-0.358875\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−805.694	+	1395.50i	−0.364732	+	0.631735i	−0.988733	−	0.149689i	$-0.952173\pi$
$47$	−805.694	+	1395.50i	−0.364732	+	0.631735i	0.624001	+	0.781424i	$0.285506\pi$
$48$		0			0
$49$	1790.40	−	1599.77i	0.745689	−	0.666294i
$50$		0			0
$51$	1605.67	−	2781.10i	0.617328	−	1.06924i
$52$		0			0
$53$	3106.46	−	1793.51i	1.10589	−	0.638489i	0.168132	−	0.985765i	$-0.446227\pi$
$53$	3106.46	−	1793.51i	1.10589	−	0.638489i	0.937763	+	0.347276i	$0.112893\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	2515.47i		−	0.774228i
$58$		0			0
$59$	−225.232	+	130.038i	−0.0647033	+	0.0373564i	−0.532003	−	0.846743i	$-0.678560\pi$
$59$	−225.232	+	130.038i	−0.0647033	+	0.0373564i	0.467299	+	0.884099i	$0.345227\pi$
$60$		0			0
$61$	801.042	+	462.482i	0.215276	+	0.124290i	0.603761	−	0.797165i	$-0.293668\pi$
$61$	801.042	+	462.482i	0.215276	+	0.124290i	−0.388485	+	0.921455i	$0.627001\pi$
$62$		0			0
$63$	827.746	−	5162.50i	0.208553	−	1.30070i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−5117.03	+	2954.32i	−1.13990	+	0.658124i	−0.946407	−	0.322977i	$-0.895316\pi$
$67$	−5117.03	+	2954.32i	−1.13990	+	0.658124i	−0.193497	+	0.981101i	$0.561983\pi$
$68$		0			0
$69$			4455.12i			0.935754i
$70$		0			0
$71$	8572.53			1.70056			0.850280	−	0.526330i	$-0.176432\pi$
$71$	8572.53			1.70056			0.850280	+	0.526330i	$0.176432\pi$
$72$		0			0
$73$	−1180.22	−	2044.20i	−0.221471	−	0.383599i	0.733784	−	0.679383i	$-0.237752\pi$
$73$	−1180.22	−	2044.20i	−0.221471	−	0.383599i	−0.955255	+	0.295784i	$0.904419\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4389.56	−	3568.47i	−0.740355	−	0.601867i
$78$		0			0
$79$	−2574.66	+	4459.44i	−0.412539	+	0.714539i	−0.995167	−	0.0982004i	$-0.968691\pi$
$79$	−2574.66	+	4459.44i	−0.412539	+	0.714539i	0.582627	+	0.812739i	$0.302025\pi$
$80$		0			0
$81$	1909.22	+	3306.87i	0.290995	+	0.504019i
$82$		0			0
$83$	−7546.38			−1.09542			−0.547712	−	0.836667i	$-0.684501\pi$
$83$	−7546.38			−1.09542			−0.547712	+	0.836667i	$0.684501\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1744.35	−	3021.31i	−0.230460	−	0.399169i
$88$		0			0
$89$	−10498.9	−	6061.52i	−1.32545	−	0.765247i	−0.340855	−	0.940116i	$-0.610716\pi$
$89$	−10498.9	−	6061.52i	−1.32545	−	0.765247i	−0.984592	+	0.174869i	$0.944050\pi$
$90$		0			0
$91$	3848.88	−	1469.04i	0.464785	−	0.177399i
$92$		0			0
$93$	−4864.22	−	2808.36i	−0.562403	−	0.324704i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	14875.4			1.58097			0.790487	−	0.612479i	$-0.209827\pi$
$97$	14875.4			1.58097			0.790487	+	0.612479i	$0.209827\pi$
$98$		0			0
$99$	−12318.8			−1.25690
$100$		0			0
$101$	−9645.68	+	5568.94i	−0.945562	+	0.545921i	−0.891700	−	0.452628i	$-0.850487\pi$
$101$	−9645.68	+	5568.94i	−0.945562	+	0.545921i	−0.0538628	+	0.998548i	$0.517153\pi$
$102$		0			0
$103$	2912.09	−	5043.89i	0.274493	−	0.475435i	−0.695514	−	0.718512i	$-0.744823\pi$
$103$	2912.09	−	5043.89i	0.274493	−	0.475435i	0.970007	+	0.243077i	$0.0781567\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1767.65	−	1020.55i	−0.154393	−	0.0891389i	0.420813	−	0.907147i	$-0.361745\pi$
$107$	−1767.65	−	1020.55i	−0.154393	−	0.0891389i	−0.575206	+	0.818008i	$0.695078\pi$
$108$		0			0
$109$	1362.91	+	2360.63i	0.114713	+	0.198689i	0.917665	−	0.397355i	$-0.130072\pi$
$109$	1362.91	+	2360.63i	0.114713	+	0.198689i	−0.802952	+	0.596044i	$0.796738\pi$
$110$		0			0
$111$		−	1013.03i		−	0.0822200i
$112$		0			0
$113$			18326.3i			1.43522i	0.696445	+	0.717610i	$0.254764\pi$
$113$			18326.3i			1.43522i	−0.696445	+	0.717610i	$0.745236\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	4485.55	−	7769.20i	0.327675	−	0.567551i
$118$		0			0
$119$	−8912.06	−	7245.00i	−0.629338	−	0.511616i
$120$		0			0
$121$	656.150	−	1136.48i	0.0448159	−	0.0776235i
$122$		0			0
$123$	6963.36	−	4020.30i	0.460266	−	0.265734i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	30138.9i		−	1.86861i	−0.356471	−	0.934306i	$-0.616020\pi$
$127$		−	30138.9i		−	1.86861i	0.356471	−	0.934306i	$-0.383980\pi$
$128$		0			0
$129$	−39634.4	+	22882.9i	−2.38173	+	1.37509i
$130$		0			0
$131$	−22213.6	−	12825.0i	−1.29442	−	0.747335i	−0.314988	−	0.949096i	$-0.602001\pi$
$131$	−22213.6	−	12825.0i	−1.29442	−	0.747335i	−0.979435	+	0.201760i	$0.935334\pi$
$132$		0			0
$133$	−8883.16	−	1424.31i	−0.502186	−	0.0805195i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	19199.4	−	11084.8i	1.02293	−	0.590590i	0.107980	−	0.994153i	$-0.465562\pi$
$137$	19199.4	−	11084.8i	1.02293	−	0.590590i	0.914952	+	0.403563i	$0.132228\pi$
$138$		0			0
$139$			3866.98i			0.200144i	0.994980	+	0.100072i	$0.0319073\pi$
$139$			3866.98i			0.200144i	−0.994980	+	0.100072i	$0.968093\pi$
$140$		0			0
$141$	22076.8			1.11045
$142$		0			0
$143$	−4853.26	−	8406.10i	−0.237335	−	0.411076i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−31245.9	−	10284.2i	−1.44597	−	0.475922i
$148$		0			0
$149$	−14945.8	+	25886.8i	−0.673202	+	1.16602i	0.303789	+	0.952739i	$0.401748\pi$
$149$	−14945.8	+	25886.8i	−0.673202	+	1.16602i	−0.976991	+	0.213281i	$0.931585\pi$
$150$		0			0
$151$	−19053.4	−	33001.5i	−0.835639	−	1.44737i	−0.893509	−	0.449045i	$-0.851764\pi$
$151$	−19053.4	−	33001.5i	−0.835639	−	1.44737i	0.0578701	−	0.998324i	$-0.481569\pi$
$152$		0			0
$153$	−25010.7			−1.06842
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−18873.8	−	32690.4i	−0.765703	−	1.32624i	−0.939874	−	0.341521i	$-0.889058\pi$
$157$	−18873.8	−	32690.4i	−0.765703	−	1.32624i	0.174171	−	0.984715i	$-0.444275\pi$
$158$		0			0
$159$	−42559.9	−	24572.0i	−1.68347	−	0.971955i
$160$		0			0
$161$	15732.9	+	2522.58i	0.606956	+	0.0973182i
$162$		0			0
$163$	7591.32	+	4382.85i	0.285721	+	0.164961i	0.636011	−	0.771680i	$-0.280583\pi$
$163$	7591.32	+	4382.85i	0.285721	+	0.164961i	−0.350290	+	0.936641i	$0.613917\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−19123.9			−0.685714			−0.342857	−	0.939388i	$-0.611395\pi$
$167$	−19123.9			−0.685714			−0.342857	+	0.939388i	$0.611395\pi$
$168$		0			0
$169$	−21492.3			−0.752505
$170$		0			0
$171$	−16966.4	+	9795.56i	−0.580226	+	0.334994i
$172$		0			0
$173$	−14573.2	+	25241.6i	−0.486926	+	0.843381i	−0.999887	−	0.0150309i	$-0.995215\pi$
$173$	−14573.2	+	25241.6i	−0.486926	+	0.843381i	0.512961	+	0.858412i	$0.328549\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3085.78	+	1781.58i	0.0984961	+	0.0568668i
$178$		0			0
$179$	−19220.2	−	33290.3i	−0.599861	−	1.03899i	−0.992841	−	0.119443i	$-0.961889\pi$
$179$	−19220.2	−	33290.3i	−0.599861	−	1.03899i	0.392980	−	0.919547i	$-0.371444\pi$
$180$		0			0
$181$			9245.61i			0.282214i	0.989994	+	0.141107i	$0.0450661\pi$
$181$			9245.61i			0.282214i	−0.989994	+	0.141107i	$0.954934\pi$
$182$		0			0
$183$		−	12672.4i		−	0.378406i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−13530.5	+	23435.6i	−0.386929	+	0.670181i
$188$		0			0
$189$	−16120.6	+	6152.89i	−0.451291	+	0.172248i
$190$		0			0
$191$	17059.5	−	29548.0i	0.467628	−	0.809955i	−0.531688	−	0.846940i	$-0.678442\pi$
$191$	17059.5	−	29548.0i	0.467628	−	0.809955i	0.999316	+	0.0369852i	$0.0117754\pi$
$192$		0			0
$193$	32770.5	−	18920.0i	0.879768	−	0.507934i	0.00918593	−	0.999958i	$-0.497076\pi$
$193$	32770.5	−	18920.0i	0.879768	−	0.507934i	0.870582	+	0.492024i	$0.163743\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	5128.01i		−	0.132135i	−0.997815	−	0.0660673i	$-0.978955\pi$
$197$		−	5128.01i		−	0.132135i	0.997815	−	0.0660673i	$-0.0210452\pi$
$198$		0			0
$199$	12391.4	−	7154.17i	0.312906	−	0.180656i	−0.335320	−	0.942104i	$-0.608845\pi$
$199$	12391.4	−	7154.17i	0.312906	−	0.180656i	0.648226	+	0.761448i	$0.275511\pi$
$200$		0			0
$201$	70105.7	+	40475.5i	1.73525	+	1.00184i
$202$		0			0
$203$	−11657.2	+	4449.31i	−0.282880	+	0.107969i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	30049.1	−	17348.8i	0.701278	−	0.404883i
$208$		0			0
$209$			21197.1i			0.485271i
$210$		0			0
$211$	49201.5			1.10513			0.552566	−	0.833469i	$-0.313649\pi$
$211$	49201.5			1.10513			0.552566	+	0.833469i	$0.313649\pi$
$212$		0			0
$213$	−58723.8	−	101713.i	−1.29436	−	2.24190i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−12671.7	+	15587.4i	−0.269101	+	0.331021i
$218$		0			0
$219$	−16169.5	+	28006.4i	−0.337139	+	0.583942i
$220$		0			0
$221$	−9853.50	−	17066.8i	−0.201746	−	0.349435i
$222$		0			0
$223$	68066.0			1.36874			0.684369	−	0.729136i	$-0.260078\pi$
$223$	68066.0			1.36874			0.684369	+	0.729136i	$0.260078\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−26245.4	−	45458.4i	−0.509333	−	0.882190i	−0.999942	−	0.0108100i	$-0.996559\pi$
$227$	−26245.4	−	45458.4i	−0.509333	−	0.882190i	0.490609	−	0.871380i	$-0.336774\pi$
$228$		0			0
$229$	28295.0	+	16336.1i	0.539559	+	0.311515i	0.744900	−	0.667176i	$-0.232497\pi$
$229$	28295.0	+	16336.1i	0.539559	+	0.311515i	−0.205341	+	0.978690i	$0.565830\pi$
$230$		0			0
$231$	−12270.2	+	76526.8i	−0.229946	+	1.43413i
$232$		0			0
$233$	−20250.3	−	11691.5i	−0.373010	−	0.215357i	0.301763	−	0.953383i	$-0.402425\pi$
$233$	−20250.3	−	11691.5i	−0.373010	−	0.215357i	−0.674772	+	0.738026i	$0.735758\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	70548.0			1.25600
$238$		0			0
$239$	−18183.9			−0.318340			−0.159170	−	0.987251i	$-0.550882\pi$
$239$	−18183.9			−0.318340			−0.159170	+	0.987251i	$0.550882\pi$
$240$		0			0
$241$	−13051.0	+	7534.99i	−0.224703	+	0.129732i	−0.608126	−	0.793840i	$-0.708078\pi$
$241$	−13051.0	+	7534.99i	−0.224703	+	0.129732i	0.383423	+	0.923573i	$0.374745\pi$
$242$		0			0
$243$	40418.9	−	70007.6i	0.684497	−	1.18558i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−13368.5	−	7718.33i	−0.219124	−	0.126511i
$248$		0			0
$249$	51694.5	+	89537.4i	0.833768	+	1.44413i
$250$		0			0
$251$		−	84203.4i		−	1.33654i	−0.743919	−	0.668270i	$-0.767035\pi$
$251$		−	84203.4i		−	1.33654i	0.743919	−	0.668270i	$-0.232965\pi$
$252$		0			0
$253$		−	37542.1i		−	0.586513i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6634.61	−	11491.5i	0.100450	−	0.173984i	−0.811420	−	0.584463i	$-0.801305\pi$
$257$	6634.61	−	11491.5i	0.100450	−	0.173984i	0.911870	+	0.410479i	$0.134638\pi$
$258$		0			0
$259$	−3577.44	−	573.600i	−0.0533302	−	0.00855086i
$260$		0			0
$261$	−13585.5	+	23530.7i	−0.199432	+	0.345426i
$262$		0			0
$263$	33534.6	−	19361.2i	0.484821	−	0.279912i	−0.237602	−	0.971363i	$-0.576362\pi$
$263$	33534.6	−	19361.2i	0.484821	−	0.279912i	0.722423	+	0.691451i	$0.243028\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			166091.i			2.32983i
$268$		0			0
$269$	105667.	−	61006.6i	1.46027	−	0.843087i	0.461247	−	0.887272i	$-0.347402\pi$
$269$	105667.	−	61006.6i	1.46027	−	0.843087i	0.999023	+	0.0441847i	$0.0140690\pi$
$270$		0			0
$271$	36617.3	+	21141.0i	0.498594	+	0.287864i	0.728133	−	0.685436i	$-0.240388\pi$
$271$	36617.3	+	21141.0i	0.498594	+	0.287864i	−0.229539	+	0.973300i	$0.573722\pi$
$272$		0			0
$273$	−43795.8	−	35603.5i	−0.587634	−	0.477714i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	57086.9	−	32959.1i	0.744007	−	0.429553i	−0.0795174	−	0.996833i	$-0.525338\pi$
$277$	57086.9	−	32959.1i	0.744007	−	0.429553i	0.823524	+	0.567281i	$0.192005\pi$
$278$		0			0
$279$			43744.5i			0.561972i
$280$		0			0
$281$	103798.			1.31455			0.657276	−	0.753650i	$-0.271709\pi$
$281$	103798.			1.31455			0.657276	+	0.753650i	$0.271709\pi$
$282$		0			0
$283$	−63652.1	−	110249.i	−0.794767	−	1.37658i	−0.922987	−	0.384831i	$-0.874260\pi$
$283$	−63652.1	−	110249.i	−0.794767	−	1.37658i	0.128220	−	0.991746i	$-0.459074\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−10254.5	−	26866.9i	−0.124495	−	0.326177i
$288$		0			0
$289$	14289.7	−	24750.5i	0.171091	−	0.296338i
$290$		0			0
$291$	−101900.	−	176496.i	−1.20334	−	2.08424i
$292$		0			0
$293$	41164.2			0.479496			0.239748	−	0.970835i	$-0.422935\pi$
$293$	41164.2			0.479496			0.239748	+	0.970835i	$0.422935\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	20327.3	+	35207.9i	0.230445	+	0.399142i
$298$		0			0
$299$	23676.9	+	13669.9i	0.264839	+	0.152905i
$300$		0			0
$301$	58367.4	+	152922.i	0.644224	+	1.68787i
$302$		0			0
$303$	132150.	+	76297.0i	1.43941	+	0.831041i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−172731.			−1.83270			−0.916352	−	0.400374i	$-0.868880\pi$
$307$	−172731.			−1.83270			−0.916352	+	0.400374i	$0.868880\pi$
$308$		0			0
$309$	−79794.1			−0.835706
$310$		0			0
$311$	−62526.6	+	36099.7i	−0.646463	+	0.373236i	−0.787100	−	0.616826i	$-0.788418\pi$
$311$	−62526.6	+	36099.7i	−0.646463	+	0.373236i	0.140637	+	0.990061i	$0.455085\pi$
$312$		0			0
$313$	−88093.6	+	152583.i	−0.899198	+	1.55746i	−0.0706772	+	0.997499i	$0.522516\pi$
$313$	−88093.6	+	152583.i	−0.899198	+	1.55746i	−0.828521	+	0.559958i	$0.810817\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−47855.8	−	27629.6i	−0.476230	−	0.274951i	0.242614	−	0.970123i	$-0.421995\pi$
$317$	−47855.8	−	27629.6i	−0.476230	−	0.274951i	−0.718844	+	0.695172i	$0.755328\pi$
$318$		0			0
$319$	14699.2	+	25459.7i	0.144448	+	0.250191i
$320$		0			0
$321$			27964.1i			0.271388i
$322$		0			0
$323$			43036.2i			0.412505i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	18672.5	−	32341.7i	0.174625	−	0.302459i
$328$		0			0
$329$	12500.3	−	77962.2i	0.115486	−	0.720265i
$330$		0			0
$331$	39669.5	−	68709.5i	0.362077	−	0.627135i	−0.626226	−	0.779642i	$-0.715401\pi$
$331$	39669.5	−	68709.5i	0.362077	−	0.627135i	0.988302	+	0.152507i	$0.0487345\pi$
$332$		0			0
$333$	−6832.74	+	3944.88i	−0.0616178	+	0.0355750i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			187217.i			1.64849i	0.566233	+	0.824245i	$0.308400\pi$
$337$			187217.i			1.64849i	−0.566233	+	0.824245i	$0.691600\pi$
$338$		0			0
$339$	217441.	−	125540.i	1.89209	−	1.09240i
$340$		0			0
$341$	40989.5	+	23665.3i	0.352504	+	0.203518i
$342$		0			0
$343$	−54009.8	+	104519.i	−0.459076	+	0.888397i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	107946.	−	62322.7i	0.896494	−	0.517591i	0.0204332	−	0.999791i	$-0.493495\pi$
$347$	107946.	−	62322.7i	0.896494	−	0.517591i	0.876061	+	0.482200i	$0.160162\pi$
$348$		0			0
$349$		−	202080.i		−	1.65910i	−0.558433	−	0.829550i	$-0.688597\pi$
$349$		−	202080.i		−	1.65910i	0.558433	−	0.829550i	$-0.311403\pi$
$350$		0			0
$351$	−29606.4			−0.240310
$352$		0			0
$353$	67949.5	+	117692.i	0.545302	+	0.944490i	0.998588	+	0.0531253i	$0.0169183\pi$
$353$	67949.5	+	117692.i	0.545302	+	0.944490i	−0.453286	+	0.891365i	$0.649748\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−24911.9	+	155371.i	−0.195466	+	1.21908i
$358$		0			0
$359$	−4598.65	+	7965.09i	−0.0356813	+	0.0618019i	−0.883315	−	0.468781i	$-0.844693\pi$
$359$	−4598.65	+	7965.09i	−0.0356813	+	0.0618019i	0.847633	+	0.530583i	$0.178027\pi$
$360$		0			0
$361$	−48305.2	−	83667.0i	−0.370663	−	0.642007i
$362$		0			0
$363$	−17979.1			−0.136444
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−96089.5	−	166432.i	−0.713418	−	1.23568i	−0.963567	−	0.267469i	$-0.913813\pi$
$367$	−96089.5	−	166432.i	−0.713418	−	1.23568i	0.250149	−	0.968207i	$-0.419521\pi$
$368$		0			0
$369$	−54232.4	−	31311.1i	−0.398296	−	0.229957i
$370$		0			0
$371$	−110872.	+	136384.i	−0.805517	+	0.990865i
$372$		0			0
$373$	180100.	+	103981.i	1.29448	+	0.747371i	0.979446	−	0.201708i	$-0.0646491\pi$
$373$	180100.	+	103981.i	1.29448	+	0.747371i	0.315039	+	0.949079i	$0.397982\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−21409.1			−0.150632
$378$		0			0
$379$	28606.8			0.199155			0.0995775	−	0.995030i	$-0.468251\pi$
$379$	28606.8			0.199155			0.0995775	+	0.995030i	$0.468251\pi$
$380$		0			0
$381$	−357596.	+	206458.i	−2.46344	+	1.42227i
$382$		0			0
$383$	−73689.5	+	127634.i	−0.502352	+	0.870099i	0.497644	+	0.867381i	$0.334199\pi$
$383$	−73689.5	+	127634.i	−0.502352	+	0.870099i	−0.999996	+	0.00271817i	$0.999135\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	308683.	+	178218.i	2.06106	+	1.18995i
$388$		0			0
$389$	42740.4	+	74028.6i	0.282449	+	0.489216i	0.971987	−	0.235033i	$-0.0755199\pi$
$389$	42740.4	+	74028.6i	0.282449	+	0.489216i	−0.689538	+	0.724249i	$0.742187\pi$
$390$		0			0
$391$		−	76221.1i		−	0.498565i
$392$		0			0
$393$			351418.i			2.27530i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	13665.2	−	23668.9i	0.0867033	−	0.150175i	−0.819412	−	0.573204i	$-0.805700\pi$
$397$	13665.2	−	23668.9i	0.0867033	−	0.150175i	0.906116	+	0.423030i	$0.139033\pi$
$398$		0			0
$399$	43952.4	+	115155.i	0.276081	+	0.723332i
$400$		0			0
$401$	86434.4	−	149709.i	0.537524	−	0.931019i	−0.461512	−	0.887134i	$-0.652693\pi$
$401$	86434.4	−	149709.i	0.537524	−	0.931019i	0.999037	−	0.0438855i	$-0.0139737\pi$
$402$		0			0
$403$	−29850.3	+	17234.1i	−0.183797	+	0.106115i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			8536.54i			0.0515339i
$408$		0			0
$409$	32575.4	−	18807.4i	0.194734	−	0.112430i	−0.399463	−	0.916749i	$-0.630803\pi$
$409$	32575.4	−	18807.4i	0.194734	−	0.112430i	0.594197	+	0.804320i	$0.297470\pi$
$410$		0			0
$411$	−263041.	−	151867.i	−1.55718	−	0.899040i
$412$		0			0
$413$	8038.73	−	9888.42i	0.0471289	−	0.0579731i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	45881.6	−	26489.7i	0.263855	−	0.152337i
$418$		0			0
$419$		−	38894.4i		−	0.221544i	−0.993846	−	0.110772i	$-0.964668\pi$
$419$		−	38894.4i		−	0.221544i	0.993846	−	0.110772i	$-0.0353323\pi$
$420$		0			0
$421$	25003.0			0.141068			0.0705340	−	0.997509i	$-0.477530\pi$
$421$	25003.0			0.141068			0.0705340	+	0.997509i	$0.477530\pi$
$422$		0			0
$423$	−85969.8	−	148904.i	−0.480469	−	0.832196i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−44751.6	−	7175.40i	−0.245444	−	0.0393541i
$428$		0			0
$429$	−66492.0	+	115167.i	−0.361289	+	0.625771i
$430$		0			0
$431$	−152326.	−	263836.i	−0.820008	−	1.42030i	−0.905675	−	0.423972i	$-0.860636\pi$
$431$	−152326.	−	263836.i	−0.820008	−	1.42030i	0.0856672	−	0.996324i	$-0.472698\pi$
$432$		0			0
$433$	−198456.			−1.05849			−0.529246	−	0.848468i	$-0.677525\pi$
$433$	−198456.			−1.05849			−0.529246	+	0.848468i	$0.677525\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−29852.3	−	51705.7i	−0.156320	−	0.270754i
$438$		0			0
$439$	115497.	+	66682.1i	0.599295	+	0.346003i	0.768764	−	0.639532i	$-0.220872\pi$
$439$	115497.	+	66682.1i	0.599295	+	0.346003i	−0.169469	+	0.985535i	$0.554205\pi$
$440$		0			0
$441$	52310.3	+	250796.i	0.268974	+	1.28957i
$442$		0			0
$443$	154408.	+	89147.4i	0.786795	+	0.454256i	0.838833	−	0.544389i	$-0.183238\pi$
$443$	154408.	+	89147.4i	0.786795	+	0.454256i	−0.0520380	+	0.998645i	$0.516572\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	409528.			2.04960
$448$		0			0
$449$	82383.4			0.408646			0.204323	−	0.978904i	$-0.434501\pi$
$449$	82383.4			0.408646			0.204323	+	0.978904i	$0.434501\pi$
$450$		0			0
$451$	−58678.3	+	33877.9i	−0.288486	+	0.166557i
$452$		0			0
$453$	−261041.	+	452135.i	−1.27207	+	2.20329i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−137001.	−	79097.8i	−0.655983	−	0.378732i	0.134762	−	0.990878i	$-0.456973\pi$
$457$	−137001.	−	79097.8i	−0.655983	−	0.378732i	−0.790745	+	0.612146i	$0.790306\pi$
$458$		0			0
$459$	41270.2	+	71482.0i	0.195889	+	0.339290i
$460$		0			0
$461$		−	215810.i		−	1.01548i	−0.861511	−	0.507739i	$-0.830481\pi$
$461$		−	215810.i		−	1.01548i	0.861511	−	0.507739i	$-0.169519\pi$
$462$		0			0
$463$			200095.i			0.933415i	0.884412	+	0.466708i	$0.154560\pi$
$463$			200095.i			0.933415i	−0.884412	+	0.466708i	$0.845440\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3718.76	−	6441.08i	0.0170516	−	0.0295342i	−0.857374	−	0.514694i	$-0.827905\pi$
$467$	3718.76	−	6441.08i	0.0170516	−	0.0295342i	0.874425	+	0.485160i	$0.161239\pi$
$468$		0			0
$469$	182631.	−	224654.i	0.830289	−	1.02134i
$470$		0			0
$471$	−258580.	+	447874.i	−1.16561	+	2.01890i
$472$		0			0
$473$	333988.	−	192828.i	1.49282	−	0.861883i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			382746.i			1.68219i
$478$		0			0
$479$	185843.	−	107296.i	0.809981	−	0.467643i	−0.0369682	−	0.999316i	$-0.511770\pi$
$479$	185843.	−	107296.i	0.809981	−	0.467643i	0.846949	+	0.531674i	$0.178437\pi$
$480$		0			0
$481$	−5383.80	−	3108.34i	−0.0232701	−	0.0134350i
$482$		0			0
$483$	−77843.7	−	203950.i	−0.333679	−	0.874239i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	199761.	−	115332.i	0.842273	−	0.486286i	−0.0157633	−	0.999876i	$-0.505018\pi$
$487$	199761.	−	115332.i	0.842273	−	0.486286i	0.858036	+	0.513589i	$0.171684\pi$
$488$		0			0
$489$		−	120094.i		−	0.502232i
$490$		0			0
$491$	370672.			1.53754			0.768772	−	0.639524i	$-0.220868\pi$
$491$	370672.			1.53754			0.768772	+	0.639524i	$0.220868\pi$
$492$		0			0
$493$	29843.5	+	51690.5i	0.122788	+	0.212675i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−392440.	+	149786.i	−1.58877	+	0.606400i
$498$		0			0
$499$	77084.8	−	133515.i	0.309576	−	0.536202i	−0.668694	−	0.743538i	$-0.733146\pi$
$499$	77084.8	−	133515.i	0.309576	−	0.536202i	0.978270	+	0.207337i	$0.0664795\pi$
$500$		0			0
$501$	131003.	+	226904.i	0.521922	+	0.903996i
$502$		0			0
$503$	303483.			1.19950			0.599748	−	0.800189i	$-0.295267\pi$
$503$	303483.			1.19950			0.599748	+	0.800189i	$0.295267\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	147227.	+	255005.i	0.572759	+	0.992048i
$508$		0			0
$509$	−96738.5	−	55852.0i	−0.373391	−	0.215577i	0.301548	−	0.953451i	$-0.402497\pi$
$509$	−96738.5	−	55852.0i	−0.373391	−	0.215577i	−0.674939	+	0.737874i	$0.735830\pi$
$510$		0			0
$511$	89746.9	+	72959.1i	0.343698	+	0.279407i
$512$		0			0
$513$	55992.5	+	32327.3i	0.212762	+	0.122838i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−186035.			−0.696006
$518$		0			0
$519$	399320.			1.48247
$520$		0			0
$521$	21518.1	−	12423.5i	0.0792737	−	0.0457687i	−0.459839	−	0.888002i	$-0.652093\pi$
$521$	21518.1	−	12423.5i	0.0792737	−	0.0457687i	0.539113	+	0.842234i	$0.318760\pi$
$522$		0			0
$523$	93223.4	−	161468.i	0.340817	−	0.590313i	−0.643767	−	0.765221i	$-0.722630\pi$
$523$	93223.4	−	161468.i	0.340817	−	0.590313i	0.984585	+	0.174908i	$0.0559629\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	83220.2	+	48047.2i	0.299645	+	0.173000i
$528$		0			0
$529$	−87049.3	−	150774.i	−0.311067	−	0.538784i
$530$		0			0
$531$		−	27750.8i		−	0.0984207i
$532$		0			0
$533$		−	49342.7i		−	0.173687i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−263325.	+	456093.i	−0.913153	+	1.58163i
$538$		0			0
$539$	263300.	+	86662.1i	0.906303	+	0.298299i
$540$		0			0
$541$	119924.	−	207715.i	0.409745	−	0.709699i	−0.585116	−	0.810949i	$-0.698951\pi$
$541$	119924.	−	207715.i	0.409745	−	0.709699i	0.994861	+	0.101251i	$0.0322844\pi$
$542$		0			0
$543$	109699.	−	63334.6i	0.372050	−	0.214803i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	251032.i		−	0.838987i	−0.907758	−	0.419493i	$-0.862208\pi$
$547$		−	251032.i		−	0.838987i	0.907758	−	0.419493i	$-0.137792\pi$
$548$		0			0
$549$	−85473.5	+	49348.1i	−0.283587	+	0.163729i
$550$		0			0
$551$	40489.6	+	23376.7i	0.133364	+	0.0769980i
$552$		0			0
$553$	39945.8	−	249134.i	0.130623	−	0.814673i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−384536.	+	222012.i	−1.23944	+	0.715592i	−0.968980	−	0.247138i	$-0.920510\pi$
$557$	−384536.	+	222012.i	−1.23944	+	0.715592i	−0.270462	+	0.962731i	$0.587177\pi$
$558$		0			0
$559$			280851.i			0.898779i
$560$		0			0
$561$	370749.			1.17802
$562$		0			0
$563$	−303557.	−	525776.i	−0.957686	−	1.65876i	−0.728098	−	0.685473i	$-0.759595\pi$
$563$	−303557.	−	525776.i	−0.957686	−	1.65876i	−0.229588	−	0.973288i	$-0.573738\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−145182.	−	118025.i	−0.451593	−	0.367120i
$568$		0			0
$569$	32647.7	−	56547.5i	0.100839	−	0.174658i	−0.811192	−	0.584780i	$-0.801181\pi$
$569$	32647.7	−	56547.5i	0.100839	−	0.174658i	0.912031	+	0.410122i	$0.134514\pi$
$570$		0			0
$571$	−136687.	−	236748.i	−0.419231	−	0.726130i	0.576631	−	0.817005i	$-0.304367\pi$
$571$	−136687.	−	236748.i	−0.419231	−	0.726130i	−0.995862	+	0.0908746i	$0.971034\pi$
$572$		0			0
$573$	−467447.			−1.42372
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−75358.6	−	130525.i	−0.226350	−	0.392050i	0.730373	−	0.683048i	$-0.239346\pi$
$577$	−75358.6	−	130525.i	−0.226350	−	0.392050i	−0.956724	+	0.290998i	$0.906013\pi$
$578$		0			0
$579$	−448971.	−	259213.i	−1.33925	−	0.773215i
$580$		0			0
$581$	345464.	−	131857.i	1.02341	−	0.390616i
$582$		0			0
$583$	358641.	+	207061.i	1.05517	+	0.609202i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	555555.			1.61232			0.806159	−	0.591699i	$-0.201543\pi$
$587$	555555.			1.61232			0.806159	+	0.591699i	$0.201543\pi$
$588$		0			0
$589$	75271.6			0.216970
$590$		0			0
$591$	−60843.6	+	35128.1i	−0.174197	+	0.100572i
$592$		0			0
$593$	30216.6	−	52336.7i	0.0859283	−	0.148832i	−0.819858	−	0.572567i	$-0.805948\pi$
$593$	30216.6	−	52336.7i	0.0859283	−	0.148832i	0.905786	+	0.423735i	$0.139281\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−169768.	−	98015.5i	−0.476328	−	0.275008i
$598$		0			0
$599$	340752.	+	590201.i	0.949698	+	1.64492i	0.746060	+	0.665878i	$0.231943\pi$
$599$	340752.	+	590201.i	0.949698	+	1.64492i	0.203637	+	0.979046i	$0.434724\pi$
$600$		0			0
$601$			271491.i			0.751634i	0.926694	+	0.375817i	$0.122638\pi$
$601$			271491.i			0.751634i	−0.926694	+	0.375817i	$0.877362\pi$
$602$		0			0
$603$		−	630468.i		−	1.73392i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	154906.	−	268305.i	0.420426	−	0.728200i	−0.575555	−	0.817763i	$-0.695214\pi$
$607$	154906.	−	268305.i	0.420426	−	0.728200i	0.995981	+	0.0895633i	$0.0285471\pi$
$608$		0			0
$609$	132645.	+	107833.i	0.357649	+	0.290749i
$610$		0			0
$611$	67739.2	−	117328.i	0.181450	−	0.314281i
$612$		0			0
$613$	156332.	−	90258.5i	0.416033	−	0.240197i	−0.277346	−	0.960770i	$-0.589455\pi$
$613$	156332.	−	90258.5i	0.416033	−	0.240197i	0.693379	+	0.720573i	$0.256121\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	273351.i		−	0.718042i	−0.933330	−	0.359021i	$-0.883111\pi$
$617$		−	273351.i		−	0.718042i	0.933330	−	0.359021i	$-0.116889\pi$
$618$		0			0
$619$	381531.	−	220277.i	0.995747	−	0.574895i	0.0887596	−	0.996053i	$-0.471710\pi$
$619$	381531.	−	220277.i	0.995747	−	0.574895i	0.906987	+	0.421158i	$0.138376\pi$
$620$		0			0
$621$	−99167.8	−	57254.6i	−0.257151	−	0.148466i
$622$		0			0
$623$	586537.	+	94044.4i	1.51119	+	0.242302i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	251503.	−	145205.i	0.639747	−	0.369358i
$628$		0			0
$629$			17331.6i			0.0438064i
$630$		0			0
$631$	−468914.			−1.17770			−0.588850	−	0.808242i	$-0.700419\pi$
$631$	−468914.			−1.17770			−0.588850	+	0.808242i	$0.700419\pi$
$632$		0			0
$633$	−337042.	−	583774.i	−0.841156	−	1.45693i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−150529.	+	134502.i	−0.370972	+	0.331474i
$638$		0			0
$639$	−457356.	+	792164.i	−1.12009	+	1.94005i
$640$		0			0
$641$	−17539.6	−	30379.5i	−0.0426879	−	0.0739376i	0.843892	−	0.536513i	$-0.180259\pi$
$641$	−17539.6	−	30379.5i	−0.0426879	−	0.0739376i	−0.886580	+	0.462575i	$0.846925\pi$
$642$		0			0
$643$	−399854.			−0.967117			−0.483559	−	0.875312i	$-0.660656\pi$
$643$	−399854.			−0.967117			−0.483559	+	0.875312i	$0.660656\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	128249.	+	222134.i	0.306370	+	0.530649i	0.977565	−	0.210632i	$-0.0675521\pi$
$647$	128249.	+	222134.i	0.306370	+	0.530649i	−0.671195	+	0.741281i	$0.734219\pi$
$648$		0			0
$649$	−26003.0	−	15012.9i	−0.0617355	−	0.0356430i
$650$		0			0
$651$	271749.	+	43571.7i	0.641217	+	0.102812i
$652$		0			0
$653$	42156.1	+	24338.8i	0.0988630	+	0.0570786i	0.548616	−	0.836074i	$-0.315155\pi$
$653$	42156.1	+	24338.8i	0.0988630	+	0.0570786i	−0.449753	+	0.893153i	$0.648488\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	251865.			0.583495
$658$		0			0
$659$	−22126.0			−0.0509487			−0.0254743	−	0.999675i	$-0.508110\pi$
$659$	−22126.0			−0.0509487			−0.0254743	+	0.999675i	$0.508110\pi$
$660$		0			0
$661$	406573.	−	234735.i	0.930541	−	0.537248i	0.0435586	−	0.999051i	$-0.486130\pi$
$661$	406573.	−	234735.i	0.930541	−	0.537248i	0.886983	+	0.461803i	$0.152797\pi$
$662$		0			0
$663$	−134998.	+	233823.i	−0.307113	+	0.531936i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−71710.8	−	41402.2i	−0.161188	−	0.0930620i
$668$		0			0
$669$	−466268.	−	807600.i	−1.04180	−	1.80445i
$670$		0			0
$671$			106787.i			0.237178i
$672$		0			0
$673$		−	307662.i		−	0.679272i	−0.940557	−	0.339636i	$-0.889696\pi$
$673$		−	307662.i		−	0.679272i	0.940557	−	0.339636i	$-0.110304\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	24910.8	−	43146.8i	0.0543514	−	0.0941394i	−0.837570	−	0.546331i	$-0.816024\pi$
$677$	24910.8	−	43146.8i	0.0543514	−	0.0941394i	0.891921	+	0.452191i	$0.149358\pi$
$678$		0			0
$679$	−680978.	+	259915.i	−1.47704	+	0.563757i
$680$		0			0
$681$	−359574.	+	622801.i	−0.775344	+	1.34293i
$682$		0			0
$683$	−446877.	+	258004.i	−0.957958	+	0.553077i	−0.895544	−	0.444973i	$-0.853213\pi$
$683$	−446877.	+	258004.i	−0.957958	+	0.553077i	−0.0624138	+	0.998050i	$0.519880\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	447626.i		−	0.948422i
$688$		0			0
$689$	−261177.	+	150791.i	−0.550170	+	0.317641i
$690$		0			0
$691$	−177161.	−	102284.i	−0.371034	−	0.214216i	0.302876	−	0.953030i	$-0.402053\pi$
$691$	−177161.	−	102284.i	−0.371034	−	0.214216i	−0.673910	+	0.738814i	$0.735386\pi$
$692$		0			0
$693$	563942.	−	215245.i	1.17427	−	0.448195i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−119134.	+	68781.8i	−0.245227	+	0.141582i
$698$		0			0
$699$			320359.i			0.655665i
$700$		0			0
$701$	666111.			1.35553			0.677767	−	0.735276i	$-0.262948\pi$
$701$	666111.			1.35553			0.677767	+	0.735276i	$0.262948\pi$
$702$		0			0
$703$	6788.00	+	11757.2i	0.0137351	+	0.0237898i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	344263.	−	423477.i	0.688734	−	0.847209i
$708$		0			0
$709$	−227965.	+	394847.i	−0.453498	+	0.785482i	−0.998600	−	0.0528874i	$-0.983158\pi$
$709$	−227965.	+	394847.i	−0.453498	+	0.785482i	0.545102	+	0.838370i	$0.316491\pi$
$710$		0			0
$711$	−274723.	−	475834.i	−0.543446	−	0.941275i
$712$		0			0
$713$	−133313.			−0.262236
$714$		0			0
$715$		0			0
$716$		0			0
$717$	124564.	+	215751.i	0.242300	+	0.419676i
$718$		0			0
$719$	−830790.	−	479657.i	−1.60706	−	0.927839i	−0.990023	−	0.140909i	$-0.954998\pi$
$719$	−830790.	−	479657.i	−1.60706	−	0.927839i	−0.617042	−	0.786930i	$-0.711669\pi$
$720$		0			0
$721$	−45181.1	+	281786.i	−0.0869132	+	0.542062i
$722$		0			0
$723$	178805.	+	103233.i	0.342060	+	0.197488i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−631745.			−1.19529			−0.597645	−	0.801761i	$-0.703897\pi$
$727$	−631745.			−1.19529			−0.597645	+	0.801761i	$0.703897\pi$
$728$		0			0
$729$	−798222.			−1.50199
$730$		0			0
$731$	678091.	−	391496.i	1.26898	−	0.732643i
$732$		0			0
$733$	−383825.	+	664804.i	−0.714373	+	1.23733i	0.248828	+	0.968548i	$0.419954\pi$
$733$	−383825.	+	664804.i	−0.714373	+	1.23733i	−0.963201	+	0.268782i	$0.913379\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−590761.	−	341076.i	−1.08762	−	0.627937i
$738$		0			0
$739$	−97266.2	−	168470.i	−0.178104	−	0.308485i	0.763127	−	0.646248i	$-0.223663\pi$
$739$	−97266.2	−	168470.i	−0.178104	−	0.308485i	−0.941231	+	0.337763i	$0.890330\pi$
$740$		0			0
$741$			211489.i			0.385170i
$742$		0			0
$743$			175567.i			0.318028i	0.987276	+	0.159014i	$0.0508315\pi$
$743$			175567.i			0.318028i	−0.987276	+	0.159014i	$0.949168\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	402610.	−	697341.i	0.721511	−	1.24969i
$748$		0			0
$749$	98752.7	+	15833.8i	0.176029	+	0.0282243i
$750$		0			0
$751$	−411668.	+	713030.i	−0.729907	+	1.26424i	0.227015	+	0.973891i	$0.427103\pi$
$751$	−411668.	+	713030.i	−0.729907	+	1.26424i	−0.956922	+	0.290345i	$0.906230\pi$
$752$		0			0
$753$	−999069.	+	576813.i	−1.76200	+	1.01729i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	189062.i		−	0.329923i	−0.986300	−	0.164961i	$-0.947250\pi$
$757$		−	189062.i		−	0.329923i	0.986300	−	0.164961i	$-0.0527499\pi$
$758$		0			0
$759$	−445435.	+	257172.i	−0.773216	+	0.446416i
$760$		0			0
$761$	−686765.	−	396504.i	−1.18588	−	0.684666i	−0.228509	−	0.973542i	$-0.573385\pi$
$761$	−686765.	−	396504.i	−1.18588	−	0.684666i	−0.957366	+	0.288876i	$0.906718\pi$
$762$		0			0
$763$	−103639.	−	84252.8i	−0.178022	−	0.144722i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	18936.5	−	10933.0i	0.0321891	−	0.0185844i
$768$		0			0
$769$		−	745465.i		−	1.26059i	−0.776355	−	0.630296i	$-0.782934\pi$
$769$		−	745465.i		−	1.26059i	0.776355	−	0.630296i	$-0.217066\pi$
$770$		0			0
$771$	−181795.			−0.305824
$772$		0			0
$773$	228288.	+	395406.i	0.382053	+	0.661735i	0.991356	−	0.131203i	$-0.0418838\pi$
$773$	228288.	+	395406.i	0.382053	+	0.661735i	−0.609303	+	0.792938i	$0.708551\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	17700.6	+	46375.4i	0.0293187	+	0.0768150i
$778$		0			0
$779$	−53877.3	+	93318.3i	−0.0887833	+	0.153777i
$780$		0			0
$781$	494849.	+	857104.i	0.811280	+	1.40518i
$782$		0			0
$783$	89669.5			0.146259
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−96039.4	−	166345.i	−0.155060	−	0.268572i	0.778021	−	0.628238i	$-0.216224\pi$
$787$	−96039.4	−	166345.i	−0.155060	−	0.268572i	−0.933081	+	0.359667i	$0.882890\pi$
$788$		0			0
$789$	−459440.	−	265258.i	−0.738031	−	0.426102i
$790$		0			0
$791$	−320213.	−	838957.i	−0.511783	−	1.34087i
$792$		0			0
$793$	−67348.1	−	38883.4i	−0.107097	−	0.0618327i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−89958.3			−0.141620			−0.0708100	−	0.997490i	$-0.522558\pi$
$797$	−89958.3			−0.141620			−0.0708100	+	0.997490i	$0.522558\pi$
$798$		0			0
$799$	−377703.			−0.591640
$800$		0			0
$801$	1.12026e6	−	646781.i	1.74604	−	1.00807i
$802$		0			0
$803$	136256.	−	236002.i	0.211312	−	0.366004i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.44768e6	−	835819.i	−2.22293	−	1.28341i
$808$		0			0
$809$	−324104.	−	561365.i	−0.495208	−	0.857725i	0.504777	−	0.863250i	$-0.331575\pi$
$809$	−324104.	−	561365.i	−0.495208	−	0.857725i	−0.999985	+	0.00552475i	$0.998241\pi$
$810$		0			0
$811$		−	988449.i		−	1.50284i	−0.659824	−	0.751420i	$-0.729369\pi$
$811$		−	988449.i		−	1.50284i	0.659824	−	0.751420i	$-0.270631\pi$
$812$		0			0
$813$		−	579283.i		−	0.876414i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	306662.	−	531154.i	0.459426	−	0.795750i
$818$		0			0
$819$	−69593.2	+	434040.i	−0.103753	+	0.647086i
$820$		0			0
$821$	−78251.6	+	135536.i	−0.116093	+	0.201079i	−0.918216	−	0.396080i	$-0.870370\pi$
$821$	−78251.6	+	135536.i	−0.116093	+	0.201079i	0.802123	+	0.597159i	$0.203704\pi$
$822$		0			0
$823$	−558679.	+	322553.i	−0.824826	+	0.476214i	−0.852078	−	0.523415i	$-0.824658\pi$
$823$	−558679.	+	322553.i	−0.824826	+	0.476214i	0.0272517	+	0.999629i	$0.491324\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	246758.i		−	0.360795i	−0.983594	−	0.180398i	$-0.942262\pi$
$827$		−	246758.i		−	0.360795i	0.983594	−	0.180398i	$-0.0577385\pi$
$828$		0			0
$829$	−62262.5	+	35947.3i	−0.0905978	+	0.0523067i	−0.544614	−	0.838687i	$-0.683324\pi$
$829$	−62262.5	+	35947.3i	−0.0905978	+	0.0523067i	0.454017	+	0.890993i	$0.349991\pi$
$830$		0			0
$831$	−782117.	−	451556.i	−1.13258	−	0.653897i
$832$		0			0
$833$	534574.	+	175949.i	0.770403	+	0.253569i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	125024.	−	72182.7i	0.178461	−	0.103034i
$838$		0			0
$839$			528527.i			0.750833i	0.926856	+	0.375416i	$0.122500\pi$
$839$			528527.i			0.750833i	−0.926856	+	0.375416i	$0.877500\pi$
$840$		0			0
$841$	−642439.			−0.908322
$842$		0			0
$843$	−711043.	−	1.23156e6i	−1.00055	−	1.73301i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−10180.2	+	63491.7i	−0.0141902	+	0.0885014i
$848$		0			0
$849$	−872063.	+	1.51046e6i	−1.20985	+	2.09553i
$850$		0			0
$851$	−12022.2	−	20823.0i	−0.0166006	−	0.0287531i
$852$		0			0
$853$	151069.			0.207624			0.103812	−	0.994597i	$-0.466896\pi$
$853$	151069.			0.207624			0.103812	+	0.994597i	$0.466896\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	290582.	+	503303.i	0.395646	+	0.685280i	0.993183	−	0.116562i	$-0.0371873\pi$
$857$	290582.	+	503303.i	0.395646	+	0.685280i	−0.597537	+	0.801841i	$0.703854\pi$
$858$		0			0
$859$	−295935.	−	170858.i	−0.401061	−	0.231553i	0.285881	−	0.958265i	$-0.407714\pi$
$859$	−295935.	−	170858.i	−0.401061	−	0.231553i	−0.686942	+	0.726712i	$0.741047\pi$
$860$		0			0
$861$	−248528.	+	305714.i	−0.335251	+	0.412391i
$862$		0			0
$863$	1.14349e6	+	660195.i	1.53536	+	0.886443i	0.999101	+	0.0423920i	$0.0134978\pi$
$863$	1.14349e6	+	660195.i	1.53536	+	0.886443i	0.536263	+	0.844051i	$0.319836\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−391551.			−0.520895
$868$		0			0
$869$	−594488.			−0.787234
$870$		0			0
$871$	430217.	−	248386.i	0.567089	−	0.327409i
$872$		0			0
$873$	−793623.	+	1.37459e6i	−1.04132	+	1.80362i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	197974.	+	114301.i	0.257401	+	0.148610i	0.623148	−	0.782104i	$-0.285853\pi$
$877$	197974.	+	114301.i	0.257401	+	0.148610i	−0.365748	+	0.930714i	$0.619187\pi$
$878$		0			0
$879$	−281985.	−	488412.i	−0.364962	−	0.632133i
$880$		0			0
$881$		−	1.08126e6i		−	1.39309i	−0.717514	−	0.696544i	$-0.754720\pi$
$881$		−	1.08126e6i		−	1.39309i	0.717514	−	0.696544i	$-0.245280\pi$
$882$		0			0
$883$		−	1.23295e6i		−	1.58133i	−0.612246	−	0.790667i	$-0.709734\pi$
$883$		−	1.23295e6i		−	1.58133i	0.612246	−	0.790667i	$-0.290266\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	535072.	−	926773.i	0.680088	−	1.17795i	−0.294865	−	0.955539i	$-0.595275\pi$
$887$	535072.	−	926773.i	0.680088	−	1.17795i	0.974954	−	0.222409i	$-0.0713919\pi$
$888$		0			0
$889$	526611.	+	1.37972e6i	0.666326	+	1.74577i
$890$		0			0
$891$	−220420.	+	381778.i	−0.277648	+	0.480901i
$892$		0			0
$893$	−256221.	+	147929.i	−0.321300	+	0.185503i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	374567.i		−	0.465527i
$898$		0			0
$899$	90408.2	−	52197.2i	0.111863	−	0.0645844i
$900$		0			0
$901$	728142.	+	420393.i	0.896947	+	0.517852i
$902$		0			0
$903$	1.41459e6	−	1.74008e6i	1.73482	−	2.13400i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−634840.	+	366525.i	−0.771702	+	0.445542i	−0.833481	−	0.552548i	$-0.813656\pi$
$907$	−634840.	+	366525.i	−0.771702	+	0.445542i	0.0617795	+	0.998090i	$0.480322\pi$
$908$		0			0
$909$		−	1.18844e6i		−	1.43830i
$910$		0			0
$911$	−1.42804e6			−1.72069			−0.860345	−	0.509713i	$-0.829752\pi$
$911$	−1.42804e6			−1.72069			−0.860345	+	0.509713i	$0.829752\pi$
$912$		0			0
$913$	−435615.	−	754507.i	−0.522590	−	0.905152i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.24100e6	+	198980.i	1.47582	+	0.236630i
$918$		0			0
$919$	572769.	−	992065.i	0.678186	−	1.17465i	−0.297341	−	0.954771i	$-0.596100\pi$
$919$	572769.	−	992065.i	0.678186	−	1.17465i	0.975527	−	0.219881i	$-0.0705668\pi$
$920$		0			0
$921$	1.18324e6	+	2.04944e6i	1.39494	+	2.41611i
$922$		0			0
$923$	−720740.			−0.846010
$924$		0			0
$925$		0			0
$926$		0			0
$927$	310728.	+	538197.i	0.361594	+	0.626300i
$928$		0			0
$929$	662079.	+	382251.i	0.767146	+	0.442912i	0.831856	−	0.554992i	$-0.187279\pi$
$929$	662079.	+	382251.i	0.767146	+	0.442912i	−0.0647092	+	0.997904i	$0.520612\pi$
$930$		0			0
$931$	431547.	−	90010.8i	0.497885	−	0.103847i
$932$		0			0
$933$	856643.	+	494583.i	0.984094	+	0.568167i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−885472.			−1.00855			−0.504273	−	0.863544i	$-0.668240\pi$
$937$	−885472.			−1.00855			−0.504273	+	0.863544i	$0.668240\pi$
$938$		0			0
$939$	2.41385e6			2.73765
$940$		0			0
$941$	1.44718e6	−	835532.i	1.63435	−	0.943591i	0.651618	−	0.758548i	$-0.274091\pi$
$941$	1.44718e6	−	835532.i	1.63435	−	0.943591i	0.982730	−	0.185043i	$-0.0592426\pi$
$942$		0			0
$943$	95421.7	−	165275.i	0.107306	−	0.185859i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.41490e6	+	816891.i	1.57770	+	0.910886i	0.995179	+	0.0980707i	$0.0312671\pi$
$947$	1.41490e6	+	816891.i	1.57770	+	0.910886i	0.582521	+	0.812815i	$0.302066\pi$
$948$		0			0
$949$	99227.5	+	171867.i	0.110179	+	0.190836i
$950$		0			0
$951$			757076.i			0.837102i
$952$		0			0
$953$		−	1.14167e6i		−	1.25706i	−0.777785	−	0.628531i	$-0.783657\pi$
$953$		−	1.14167e6i		−	1.25706i	0.777785	−	0.628531i	$-0.216343\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	201386.	−	348810.i	0.219890	−	0.380860i
$958$		0			0
$959$	−685244.	+	842917.i	−0.745089	+	0.916531i
$960$		0			0
$961$	−377725.	+	654238.i	−0.409005	+	0.708417i
$962$		0			0
$963$	188613.	−	108896.i	0.203385	−	0.117424i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			1.47251e6i			1.57473i	0.616487	+	0.787365i	$0.288555\pi$
$967$			1.47251e6i			1.57473i	−0.616487	+	0.787365i	$0.711445\pi$
$968$		0			0
$969$	510623.	−	294808.i	0.543817	−	0.313973i
$970$		0			0
$971$	−250048.	−	144366.i	−0.265207	−	0.153118i	0.361500	−	0.932372i	$-0.382265\pi$
$971$	−250048.	−	144366.i	−0.265207	−	0.153118i	−0.626708	+	0.779254i	$0.715598\pi$
$972$		0			0
$973$	−67567.2	−	177026.i	−0.0713691	−	0.186987i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	385218.	−	222406.i	0.403568	−	0.233000i	−0.284454	−	0.958690i	$-0.591812\pi$
$977$	385218.	−	222406.i	0.403568	−	0.233000i	0.688022	+	0.725689i	$0.258479\pi$
$978$		0			0
$979$		−	1.39961e6i		−	1.46029i
$980$		0			0
$981$	−290852.			−0.302228
$982$		0			0
$983$	752776.	+	1.30385e6i	0.779038	+	1.34933i	0.932496	+	0.361179i	$0.117626\pi$
$983$	752776.	+	1.30385e6i	0.779038	+	1.34933i	−0.153458	+	0.988155i	$0.549041\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−1.01065e6	+	385744.i	−1.03745	+	0.395972i
$988$		0			0
$989$	−543127.	+	940723.i	−0.555276	+	0.961766i
$990$		0			0
$991$	736806.	+	1.27619e6i	0.750250	+	1.29947i	0.947702	+	0.319158i	$0.103400\pi$
$991$	736806.	+	1.27619e6i	0.750250	+	1.29947i	−0.197452	+	0.980313i	$0.563267\pi$
$992$		0			0
$993$	−1.08698e6			−1.10236
$994$		0			0
$995$		0			0
$996$		0			0
$997$	289881.	+	502088.i	0.291628	+	0.505114i	0.974195	−	0.225709i	$-0.0724698\pi$
$997$	289881.	+	502088.i	0.291628	+	0.505114i	−0.682567	+	0.730823i	$0.739136\pi$
$998$		0			0
$999$	22549.4	+	13018.9i	0.0225945	+	0.0130450i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.5.o.c.649.3		44
5.2	odd	4		700.5.s.d.201.2	yes	22
5.3	odd	4		700.5.s.c.201.10	yes	22
5.4	even	2	inner	700.5.o.c.649.20		44
7.3	odd	6	inner	700.5.o.c.549.20		44
35.3	even	12		700.5.s.c.101.10	✓	22
35.17	even	12		700.5.s.d.101.2	yes	22
35.24	odd	6	inner	700.5.o.c.549.3		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.5.o.c.549.3		44	35.24	odd	6	inner
700.5.o.c.549.20		44	7.3	odd	6	inner
700.5.o.c.649.3		44	1.1	even	1	trivial
700.5.o.c.649.20		44	5.4	even	2	inner
700.5.s.c.101.10	✓	22	35.3	even	12
700.5.s.c.201.10	yes	22	5.3	odd	4
700.5.s.d.101.2	yes	22	35.17	even	12
700.5.s.d.201.2	yes	22	5.2	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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	700.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-6.85023 - 11.8650i) q^{3} +(-45.7788 + 17.4728i) q^{7} +(-53.3514 + 92.4073i) q^{9} +(57.7250 + 99.9826i) q^{11} -84.0756 q^{13} +(117.198 + 202.993i) q^{17} +(159.006 + 91.8023i) q^{19} +(520.910 + 423.470i) q^{21} +(-281.615 - 162.590i) q^{23} +352.140 q^{27} +254.642 q^{29} +(355.041 - 204.983i) q^{31} +(790.859 - 1369.81i) q^{33} +(64.0352 + 36.9707i) q^{37} +(575.937 + 997.553i) q^{39} +586.885i q^{41} -3340.46i q^{43} +(-805.694 + 1395.50i) q^{47} +(1790.40 - 1599.77i) q^{49} +(1605.67 - 2781.10i) q^{51} +(3106.46 - 1793.51i) q^{53} -2515.47i q^{57} +(-225.232 + 130.038i) q^{59} +(801.042 + 462.482i) q^{61} +(827.746 - 5162.50i) q^{63} +(-5117.03 + 2954.32i) q^{67} +4455.12i q^{69} +8572.53 q^{71} +(-1180.22 - 2044.20i) q^{73} +(-4389.56 - 3568.47i) q^{77} +(-2574.66 + 4459.44i) q^{79} +(1909.22 + 3306.87i) q^{81} -7546.38 q^{83} +(-1744.35 - 3021.31i) q^{87} +(-10498.9 - 6061.52i) q^{89} +(3848.88 - 1469.04i) q^{91} +(-4864.22 - 2808.36i) q^{93} +14875.4 q^{97} -12318.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 684 q^{9} - 300 q^{11} + 540 q^{19} - 190 q^{21} - 528 q^{29} - 2334 q^{31} - 852 q^{39} + 4092 q^{49} - 3902 q^{51} + 9414 q^{59} - 23598 q^{61} + 32820 q^{71} - 4890 q^{79} - 23710 q^{81} - 37764 q^{89}+ \cdots + 168180 q^{99}+O(q^{100}) \) 44 * q - 684 * q^9 - 300 * q^11 + 540 * q^19 - 190 * q^21 - 528 * q^29 - 2334 * q^31 - 852 * q^39 + 4092 * q^49 - 3902 * q^51 + 9414 * q^59 - 23598 * q^61 + 32820 * q^71 - 4890 * q^79 - 23710 * q^81 - 37764 * q^89 + 6418 * q^91 + 168180 * q^99

Introduction

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