LMFDB - Embedded newform 684.5.y.d.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,5,Mod(145,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("684.145");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	684.y (of order $6$, degree $2$, 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:	$70.7050547493$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 2826 x^{12} + 21668 x^{11} + 6144398 x^{10} + 32400228 x^{9} + 4476099452 x^{8} + \cdots + 21\!\cdots\!16 $ x^14 - 2x^13 + 2826x^12 + 21668x^11 + 6144398x^10 + 32400228x^9 + 4476099452x^8 + 1249545344x^7 + 2308151528484x^6 - 2140142598776x^5 + 625358881541536x^4 - 2569874136887808x^3 + 115090576468624800x^2 - 159892348486261824*x + 219826226298839616
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.2
Root			$-11.7951 - 20.4296i$ of defining polynomial
Character	$\chi$	$=$	684.145
Dual form			684.5.y.d.217.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-12.7951 - 22.1617i) q^{5} -23.8271 q^{7} +O(q^{10})$	$q+(-12.7951 - 22.1617i) q^{5} -23.8271 q^{7} +198.174 q^{11} +(-233.363 - 134.732i) q^{13} +(59.9242 + 103.792i) q^{17} +(278.153 - 230.113i) q^{19} +(-25.4643 + 44.1055i) q^{23} +(-14.9272 + 25.8546i) q^{25} +(318.713 + 184.009i) q^{29} -1891.53i q^{31} +(304.870 + 528.050i) q^{35} +1056.38i q^{37} +(171.147 - 98.8118i) q^{41} +(259.789 + 449.968i) q^{43} +(422.697 - 732.132i) q^{47} -1833.27 q^{49} +(-382.627 - 220.910i) q^{53} +(-2535.65 - 4391.88i) q^{55} +(5342.37 - 3084.42i) q^{59} +(-2017.55 + 3494.50i) q^{61} +6895.62i q^{65} +(-5125.30 - 2959.09i) q^{67} +(-7735.72 + 4466.22i) q^{71} +(47.6060 + 82.4560i) q^{73} -4721.93 q^{77} +(-5170.11 + 2984.97i) q^{79} -7203.41 q^{83} +(1533.47 - 2656.04i) q^{85} +(-261.478 - 150.964i) q^{89} +(5560.37 + 3210.28i) q^{91} +(-8658.67 - 3220.04i) q^{95} +(-10239.1 + 5911.53i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 12 q^{5} - 110 q^{7}+O(q^{10}) $ 14 * q - 12 * q^5 - 110 * q^7	$ 14 q - 12 q^{5} - 110 q^{7} + 84 q^{11} + 21 q^{13} - 282 q^{17} + 62 q^{19} + 678 q^{23} - 1293 q^{25} + 774 q^{29} - 228 q^{35} - 5268 q^{41} + 2239 q^{43} - 1674 q^{47} - 1080 q^{49} + 1806 q^{53} + 2204 q^{55} + 11496 q^{59} - 1661 q^{61} + 6957 q^{67} + 11784 q^{71} - 8129 q^{73} - 996 q^{77} - 5907 q^{79} - 24444 q^{83} + 3956 q^{85} - 21648 q^{89} + 13995 q^{91} + 28884 q^{95} - 9408 q^{97}+O(q^{100}) $ 14 * q - 12 * q^5 - 110 * q^7 + 84 * q^11 + 21 * q^13 - 282 * q^17 + 62 * q^19 + 678 * q^23 - 1293 * q^25 + 774 * q^29 - 228 * q^35 - 5268 * q^41 + 2239 * q^43 - 1674 * q^47 - 1080 * q^49 + 1806 * q^53 + 2204 * q^55 + 11496 * q^59 - 1661 * q^61 + 6957 * q^67 + 11784 * q^71 - 8129 * q^73 - 996 * q^77 - 5907 * q^79 - 24444 * q^83 + 3956 * q^85 - 21648 * q^89 + 13995 * q^91 + 28884 * q^95 - 9408 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−12.7951	−	22.1617i	−0.511802	−	0.886468i	−0.999906	−	0.0136823i	$-0.995645\pi$
$5$	−12.7951	−	22.1617i	−0.511802	−	0.886468i	0.488104	−	0.872785i	$-0.337689\pi$
$6$		0			0
$7$	−23.8271			−0.486268			−0.243134	−	0.969993i	$-0.578175\pi$
$7$	−23.8271			−0.486268			−0.243134	+	0.969993i	$0.578175\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	198.174			1.63780			0.818902	−	0.573933i	$-0.194583\pi$
$11$	198.174			1.63780			0.818902	+	0.573933i	$0.194583\pi$
$12$		0			0
$13$	−233.363	−	134.732i	−1.38084	−	0.797231i	−0.388585	−	0.921413i	$-0.627036\pi$
$13$	−233.363	−	134.732i	−1.38084	−	0.797231i	−0.992260	+	0.124182i	$0.960369\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	59.9242	+	103.792i	0.207350	+	0.359141i	0.950879	−	0.309563i	$-0.100183\pi$
$17$	59.9242	+	103.792i	0.207350	+	0.359141i	−0.743529	+	0.668704i	$0.766849\pi$
$18$		0			0
$19$	278.153	−	230.113i	0.770507	−	0.637431i
$19$	278.153	−	230.113i	0.770507	−	0.637431i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−25.4643	+	44.1055i	−0.0481367	+	0.0833753i	−0.889090	−	0.457733i	$-0.848662\pi$
$23$	−25.4643	+	44.1055i	−0.0481367	+	0.0833753i	0.840953	+	0.541108i	$0.181995\pi$
$24$		0			0
$25$	−14.9272	+	25.8546i	−0.0238834	+	0.0413673i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	318.713	+	184.009i	0.378969	+	0.218798i	0.677370	−	0.735643i	$-0.263120\pi$
$29$	318.713	+	184.009i	0.378969	+	0.218798i	−0.298401	+	0.954441i	$0.596453\pi$
$30$		0			0
$31$		−	1891.53i		−	1.96829i	−0.177358	−	0.984146i	$-0.556755\pi$
$31$		−	1891.53i		−	1.96829i	0.177358	−	0.984146i	$-0.443245\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	304.870	+	528.050i	0.248873	+	0.431061i
$36$		0			0
$37$			1056.38i			0.771645i	0.922573	+	0.385823i	$0.126082\pi$
$37$			1056.38i			0.771645i	−0.922573	+	0.385823i	$0.873918\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	171.147	−	98.8118i	0.101813	−	0.0587816i	−0.448229	−	0.893919i	$-0.647945\pi$
$41$	171.147	−	98.8118i	0.101813	−	0.0587816i	0.550042	+	0.835137i	$0.314612\pi$
$42$		0			0
$43$	259.789	+	449.968i	0.140503	+	0.243358i	0.927686	−	0.373361i	$-0.121795\pi$
$43$	259.789	+	449.968i	0.140503	+	0.243358i	−0.787183	+	0.616719i	$0.788462\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	422.697	−	732.132i	0.191352	−	0.331431i	−0.754346	−	0.656476i	$-0.772046\pi$
$47$	422.697	−	732.132i	0.191352	−	0.331431i	0.945699	+	0.325045i	$0.105379\pi$
$48$		0			0
$49$	−1833.27			−0.763543
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−382.627	−	220.910i	−0.136215	−	0.0786435i	0.430344	−	0.902665i	$-0.358392\pi$
$53$	−382.627	−	220.910i	−0.136215	−	0.0786435i	−0.566559	+	0.824021i	$0.691726\pi$
$54$		0			0
$55$	−2535.65	−	4391.88i	−0.838232	−	1.45186i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5342.37	−	3084.42i	1.53472	−	0.886073i	0.535588	−	0.844479i	$-0.320090\pi$
$59$	5342.37	−	3084.42i	1.53472	−	0.886073i	0.999135	−	0.0415936i	$-0.0132435\pi$
$60$		0			0
$61$	−2017.55	+	3494.50i	−0.542206	+	0.939129i	0.456571	+	0.889687i	$0.349078\pi$
$61$	−2017.55	+	3494.50i	−0.542206	+	0.939129i	−0.998777	+	0.0494419i	$0.984256\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			6895.62i			1.63210i
$66$		0			0
$67$	−5125.30	−	2959.09i	−1.14175	−	0.659187i	−0.194883	−	0.980826i	$-0.562433\pi$
$67$	−5125.30	−	2959.09i	−1.14175	−	0.659187i	−0.946862	+	0.321639i	$0.895766\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−7735.72	+	4466.22i	−1.53456	+	0.885979i	−0.535418	+	0.844587i	$0.679846\pi$
$71$	−7735.72	+	4466.22i	−1.53456	+	0.885979i	−0.999143	+	0.0413917i	$0.986821\pi$
$72$		0			0
$73$	47.6060	+	82.4560i	0.00893338	+	0.0154731i	0.870458	−	0.492244i	$-0.163823\pi$
$73$	47.6060	+	82.4560i	0.00893338	+	0.0154731i	−0.861524	+	0.507717i	$0.830490\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4721.93			−0.796412
$78$		0			0
$79$	−5170.11	+	2984.97i	−0.828411	+	0.478283i	−0.853308	−	0.521407i	$-0.825407\pi$
$79$	−5170.11	+	2984.97i	−0.828411	+	0.478283i	0.0248975	+	0.999690i	$0.492074\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7203.41			−1.04564			−0.522820	−	0.852443i	$-0.675120\pi$
$83$	−7203.41			−1.04564			−0.522820	+	0.852443i	$0.675120\pi$
$84$		0			0
$85$	1533.47	−	2656.04i	0.212244	−	0.367618i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−261.478	−	150.964i	−0.0330107	−	0.0190587i	0.483404	−	0.875397i	$-0.339400\pi$
$89$	−261.478	−	150.964i	−0.0330107	−	0.0190587i	−0.516415	+	0.856339i	$0.672734\pi$
$90$		0			0
$91$	5560.37	+	3210.28i	0.671461	+	0.387668i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−8658.67	−	3220.04i	−0.959410	−	0.356791i
$96$		0			0
$97$	−10239.1	+	5911.53i	−1.08822	+	0.628285i	−0.933102	−	0.359611i	$-0.882909\pi$
$97$	−10239.1	+	5911.53i	−1.08822	+	0.628285i	−0.155119	+	0.987896i	$0.549576\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4846.00	−	8393.51i	0.475051	−	0.822813i	−0.524540	−	0.851386i	$-0.675763\pi$
$101$	4846.00	−	8393.51i	0.475051	−	0.822813i	0.999592	+	0.0285726i	$0.00909617\pi$
$102$		0			0
$103$		−	1440.73i		−	0.135802i	−0.997692	−	0.0679011i	$-0.978370\pi$
$103$		−	1440.73i		−	0.135802i	0.997692	−	0.0679011i	$-0.0216302\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			18295.1i			1.59797i	0.601353	+	0.798983i	$0.294629\pi$
$107$			18295.1i			1.59797i	−0.601353	+	0.798983i	$0.705371\pi$
$108$		0			0
$109$	−2874.22	+	1659.43i	−0.241918	+	0.139671i	−0.616058	−	0.787701i	$-0.711271\pi$
$109$	−2874.22	+	1659.43i	−0.241918	+	0.139671i	0.374140	+	0.927372i	$0.377938\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	11712.2i		−	0.917237i	−0.888633	−	0.458618i	$-0.848344\pi$
$113$		−	11712.2i		−	0.917237i	0.888633	−	0.458618i	$-0.151656\pi$
$114$		0			0
$115$	1303.27			0.0985460
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1427.82	−	2473.06i	−0.100828	−	0.174639i
$120$		0			0
$121$	24632.1			1.68240
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−15229.9			−0.974710
$126$		0			0
$127$	14915.4	+	8611.40i	0.924755	+	0.533908i	0.885149	−	0.465308i	$-0.154056\pi$
$127$	14915.4	+	8611.40i	0.924755	+	0.533908i	0.0396062	+	0.999215i	$0.487390\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−9356.21	−	16205.4i	−0.545202	−	0.944317i	−0.998594	−	0.0530060i	$-0.983120\pi$
$131$	−9356.21	−	16205.4i	−0.545202	−	0.944317i	0.453393	−	0.891311i	$-0.350214\pi$
$132$		0			0
$133$	−6627.59	+	5482.93i	−0.374673	+	0.309962i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5787.06	−	10023.5i	0.308331	−	0.534044i	−0.669667	−	0.742662i	$-0.733563\pi$
$137$	5787.06	−	10023.5i	0.308331	−	0.534044i	0.977997	+	0.208617i	$0.0668963\pi$
$138$		0			0
$139$	−5357.79	+	9279.97i	−0.277304	+	0.480305i	−0.970714	−	0.240239i	$-0.922774\pi$
$139$	−5357.79	+	9279.97i	−0.277304	+	0.480305i	0.693410	+	0.720543i	$0.256108\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−46246.5	−	26700.4i	−2.26155	−	1.30571i
$144$		0			0
$145$		−	9417.62i		−	0.447925i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−8457.06	−	14648.1i	−0.380931	−	0.659793i	0.610264	−	0.792198i	$-0.291063\pi$
$149$	−8457.06	−	14648.1i	−0.380931	−	0.659793i	−0.991196	+	0.132405i	$0.957730\pi$
$150$		0			0
$151$		−	25055.7i		−	1.09889i	−0.835531	−	0.549444i	$-0.814840\pi$
$151$		−	25055.7i		−	1.09889i	0.835531	−	0.549444i	$-0.185160\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−41919.5	+	24202.2i	−1.74483	+	1.00738i
$156$		0			0
$157$	−14367.9	−	24886.0i	−0.582901	−	1.00961i	−0.995134	−	0.0985353i	$-0.968584\pi$
$157$	−14367.9	−	24886.0i	−0.582901	−	1.00961i	0.412233	−	0.911079i	$-0.364749\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	606.742	−	1050.91i	0.0234074	−	0.0405427i
$162$		0			0
$163$	−24463.1			−0.920738			−0.460369	−	0.887728i	$-0.652283\pi$
$163$	−24463.1			−0.920738			−0.460369	+	0.887728i	$0.652283\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−21318.9	−	12308.5i	−0.764418	−	0.441337i	0.0664615	−	0.997789i	$-0.478829\pi$
$167$	−21318.9	−	12308.5i	−0.764418	−	0.441337i	−0.830880	+	0.556452i	$0.812162\pi$
$168$		0			0
$169$	22025.0	+	38148.4i	0.771155	+	1.33568i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−33456.4	+	19316.1i	−1.11786	+	0.645397i	−0.940854	−	0.338813i	$-0.889975\pi$
$173$	−33456.4	+	19316.1i	−1.11786	+	0.645397i	−0.177007	+	0.984210i	$0.556641\pi$
$174$		0			0
$175$	355.671	−	616.041i	0.0116138	−	0.0201156i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			55123.3i			1.72040i	0.509958	+	0.860199i	$0.329661\pi$
$179$			55123.3i			1.72040i	−0.509958	+	0.860199i	$0.670339\pi$
$180$		0			0
$181$	−37473.8	−	21635.5i	−1.14385	−	0.660405i	−0.196473	−	0.980509i	$-0.562949\pi$
$181$	−37473.8	−	21635.5i	−1.14385	−	0.660405i	−0.947382	+	0.320104i	$0.896282\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	23411.2	−	13516.5i	0.684039	−	0.394930i
$186$		0			0
$187$	11875.4	+	20568.8i	0.339599	+	0.588202i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	21863.2			0.599304			0.299652	−	0.954049i	$-0.403129\pi$
$191$	21863.2			0.599304			0.299652	+	0.954049i	$0.403129\pi$
$192$		0			0
$193$	−59575.2	+	34395.7i	−1.59938	+	0.923400i	−0.607769	+	0.794114i	$0.707935\pi$
$193$	−59575.2	+	34395.7i	−1.59938	+	0.923400i	−0.991607	+	0.129287i	$0.958731\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−16472.3			−0.424445			−0.212223	−	0.977221i	$-0.568070\pi$
$197$	−16472.3			−0.424445			−0.212223	+	0.977221i	$0.568070\pi$
$198$		0			0
$199$	29569.8	−	51216.3i	0.746692	−	1.29331i	−0.202708	−	0.979239i	$-0.564974\pi$
$199$	29569.8	−	51216.3i	0.746692	−	1.29331i	0.949400	−	0.314070i	$-0.101693\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−7594.01	−	4384.40i	−0.184280	−	0.106394i
$204$		0			0
$205$	−4379.68	−	2528.61i	−0.104216	−	0.0601691i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	55122.8	−	45602.4i	1.26194	−	1.04399i
$210$		0			0
$211$	13809.4	−	7972.84i	0.310176	−	0.179080i	−0.336829	−	0.941566i	$-0.609354\pi$
$211$	13809.4	−	7972.84i	0.310176	−	0.179080i	0.647005	+	0.762485i	$0.276021\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	6648.04	−	11514.7i	0.143819	−	0.249102i
$216$		0			0
$217$			45069.7i			0.957118i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		−	32294.8i		−	0.661224i
$222$		0			0
$223$	47738.8	−	27562.0i	0.959978	−	0.554244i	0.0638120	−	0.997962i	$-0.479674\pi$
$223$	47738.8	−	27562.0i	0.959978	−	0.554244i	0.896166	+	0.443718i	$0.146341\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			68371.4i			1.32685i	0.748241	+	0.663427i	$0.230899\pi$
$227$			68371.4i			1.32685i	−0.748241	+	0.663427i	$0.769101\pi$
$228$		0			0
$229$	−26782.6			−0.510718			−0.255359	−	0.966846i	$-0.582194\pi$
$229$	−26782.6			−0.510718			−0.255359	+	0.966846i	$0.582194\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	44604.8	+	77257.8i	0.821618	+	1.42308i	0.904477	+	0.426522i	$0.140261\pi$
$233$	44604.8	+	77257.8i	0.821618	+	1.42308i	−0.0828594	+	0.996561i	$0.526405\pi$
$234$		0			0
$235$	−21633.7			−0.391738
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−106866.			−1.87087			−0.935437	−	0.353492i	$-0.884994\pi$
$239$	−106866.			−1.87087			−0.935437	+	0.353492i	$0.884994\pi$
$240$		0			0
$241$	−38268.5	−	22094.3i	−0.658882	−	0.380406i	0.132969	−	0.991120i	$-0.457549\pi$
$241$	−38268.5	−	22094.3i	−0.658882	−	0.380406i	−0.791851	+	0.610714i	$0.790882\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	23456.8	+	40628.3i	0.390783	+	0.676857i
$246$		0			0
$247$	−95914.1	+	16223.6i	−1.57213	+	0.265921i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	40074.2	−	69410.6i	0.636088	−	1.10174i	−0.350195	−	0.936677i	$-0.613885\pi$
$251$	40074.2	−	69410.6i	0.636088	−	1.10174i	0.986283	−	0.165061i	$-0.0527820\pi$
$252$		0			0
$253$	−5046.38	+	8740.58i	−0.0788386	+	0.136552i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	12820.4	+	7401.84i	0.194104	+	0.112066i	0.593902	−	0.804537i	$-0.297587\pi$
$257$	12820.4	+	7401.84i	0.194104	+	0.112066i	−0.399799	+	0.916603i	$0.630920\pi$
$258$		0			0
$259$		−	25170.6i		−	0.375226i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	19159.9	+	33185.9i	0.277001	+	0.479779i	0.970638	−	0.240545i	$-0.0773262\pi$
$263$	19159.9	+	33185.9i	0.277001	+	0.479779i	−0.693637	+	0.720325i	$0.743993\pi$
$264$		0			0
$265$			11306.2i			0.161000i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−9913.04	+	5723.29i	−0.136994	+	0.0790936i	−0.566931	−	0.823766i	$-0.691869\pi$
$269$	−9913.04	+	5723.29i	−0.136994	+	0.0790936i	0.429937	+	0.902859i	$0.358536\pi$
$270$		0			0
$271$	−4159.81	−	7205.00i	−0.0566415	−	0.0981060i	0.836314	−	0.548250i	$-0.184706\pi$
$271$	−4159.81	−	7205.00i	−0.0566415	−	0.0981060i	−0.892956	+	0.450144i	$0.851373\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2958.18	+	5123.72i	−0.0391164	+	0.0677516i
$276$		0			0
$277$	−83913.7			−1.09364			−0.546818	−	0.837251i	$-0.684161\pi$
$277$	−83913.7			−1.09364			−0.546818	+	0.837251i	$0.684161\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−66715.1	−	38518.0i	−0.844912	−	0.487810i	0.0140191	−	0.999902i	$-0.495537\pi$
$281$	−66715.1	−	38518.0i	−0.844912	−	0.487810i	−0.858931	+	0.512092i	$0.828871\pi$
$282$		0			0
$283$	75373.4	+	130551.i	0.941120	+	1.63007i	0.763339	+	0.645998i	$0.223559\pi$
$283$	75373.4	+	130551.i	0.941120	+	1.63007i	0.177781	+	0.984070i	$0.443108\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4077.95	+	2354.40i	−0.0495083	+	0.0285836i
$288$		0			0
$289$	34578.7	−	59892.1i	0.414012	−	0.717090i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			33947.1i			0.395428i	0.980260	+	0.197714i	$0.0633517\pi$
$293$			33947.1i			0.395428i	−0.980260	+	0.197714i	$0.936648\pi$
$294$		0			0
$295$	−136712.	−	78930.7i	−1.57095	−	0.906988i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	11884.9	−	6861.72i	0.132939	−	0.0767522i
$300$		0			0
$301$	−6190.03	−	10721.4i	−0.0683219	−	0.118337i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	103259.			1.11001
$306$		0			0
$307$	67410.0	−	38919.2i	0.715233	−	0.412940i	−0.0977625	−	0.995210i	$-0.531169\pi$
$307$	67410.0	−	38919.2i	0.715233	−	0.412940i	0.812996	+	0.582270i	$0.197835\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	100145.			1.03540			0.517700	−	0.855562i	$-0.326788\pi$
$311$	100145.			1.03540			0.517700	+	0.855562i	$0.326788\pi$
$312$		0			0
$313$	23712.7	−	41071.6i	0.242043	−	0.419230i	−0.719253	−	0.694748i	$-0.755516\pi$
$313$	23712.7	−	41071.6i	0.242043	−	0.419230i	0.961296	+	0.275518i	$0.0888493\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	66668.0	+	38490.8i	0.663436	+	0.383035i	0.793585	−	0.608460i	$-0.208212\pi$
$317$	66668.0	+	38490.8i	0.663436	+	0.383035i	−0.130149	+	0.991494i	$0.541546\pi$
$318$		0			0
$319$	63160.7	+	36465.8i	0.620677	+	0.358348i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	40551.9	+	15080.7i	0.388692	+	0.144549i
$324$		0			0
$325$	6966.88	−	4022.33i	0.0659587	−	0.0380813i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−10071.7	+	17444.6i	−0.0930484	+	0.161165i
$330$		0			0
$331$			1537.36i			0.0140320i	0.999975	+	0.00701601i	$0.00223328\pi$
$331$			1537.36i			0.0140320i	−0.999975	+	0.00701601i	$0.997767\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			151447.i			1.34949i
$336$		0			0
$337$	81351.6	−	46968.4i	0.716319	−	0.413567i	−0.0970776	−	0.995277i	$-0.530949\pi$
$337$	81351.6	−	46968.4i	0.716319	−	0.413567i	0.813396	+	0.581710i	$0.197616\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	374853.i		−	3.22368i
$342$		0			0
$343$	100890.			0.857555
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−58126.7	−	100678.i	−0.482744	−	0.836137i	0.517060	−	0.855949i	$-0.327026\pi$
$347$	−58126.7	−	100678.i	−0.482744	−	0.836137i	−0.999804	+	0.0198122i	$0.993693\pi$
$348$		0			0
$349$	179283.			1.47193			0.735966	−	0.677019i	$-0.236728\pi$
$349$	179283.			1.47193			0.735966	+	0.677019i	$0.236728\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	62622.8			0.502554			0.251277	−	0.967915i	$-0.419149\pi$
$353$	62622.8			0.502554			0.251277	+	0.967915i	$0.419149\pi$
$354$		0			0
$355$	197958.	+	114291.i	1.57078	+	0.906892i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	64386.3	+	111520.i	0.499580	+	0.865297i	1.00000		0.000485445i	$-0.000154522\pi$
$359$	64386.3	+	111520.i	0.499580	+	0.865297i	−0.500420	+	0.865783i	$0.666821\pi$
$360$		0			0
$361$	24417.3	−	128013.i	0.187363	−	0.982291i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1218.24	−	2110.06i	0.00914425	−	0.0158383i
$366$		0			0
$367$	36488.6	−	63200.2i	0.270910	−	0.469230i	−0.698185	−	0.715917i	$-0.746009\pi$
$367$	36488.6	−	63200.2i	0.270910	−	0.469230i	0.969095	+	0.246687i	$0.0793420\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	9116.90	+	5263.64i	0.0662368	+	0.0382418i
$372$		0			0
$373$		−	92758.1i		−	0.666706i	−0.942802	−	0.333353i	$-0.891820\pi$
$373$		−	92758.1i		−	0.666706i	0.942802	−	0.333353i	$-0.108180\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−49583.8	−	85881.7i	−0.348865	−	0.604251i
$378$		0			0
$379$			66692.4i			0.464299i	0.972680	+	0.232149i	$0.0745759\pi$
$379$			66692.4i			0.464299i	−0.972680	+	0.232149i	$0.925424\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−85893.3	+	49590.5i	−0.585547	+	0.338066i	−0.763335	−	0.646003i	$-0.776439\pi$
$383$	−85893.3	+	49590.5i	−0.585547	+	0.338066i	0.177788	+	0.984069i	$0.443106\pi$
$384$		0			0
$385$	60417.3	+	104646.i	0.407606	+	0.705994i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	95064.0	−	164656.i	0.628228	−	1.08812i	−0.359680	−	0.933076i	$-0.617114\pi$
$389$	95064.0	−	164656.i	0.628228	−	1.08812i	0.987907	−	0.155046i	$-0.0495526\pi$
$390$		0			0
$391$	−6103.71			−0.0399246
$392$		0			0
$393$		0			0
$394$		0			0
$395$	132304.	+	76385.6i	0.847965	+	0.489573i
$396$		0			0
$397$	−6002.67	−	10396.9i	−0.0380859	−	0.0659666i	0.846354	−	0.532621i	$-0.178793\pi$
$397$	−6002.67	−	10396.9i	−0.0380859	−	0.0659666i	−0.884440	+	0.466654i	$0.845459\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	101016.	−	58321.7i	0.628206	−	0.362695i	−0.151851	−	0.988403i	$-0.548523\pi$
$401$	101016.	−	58321.7i	0.628206	−	0.362695i	0.780057	+	0.625708i	$0.215190\pi$
$402$		0			0
$403$	−254850.	+	441413.i	−1.56918	+	2.71791i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			209348.i			1.26380i
$408$		0			0
$409$	11755.3	+	6786.90i	0.0702725	+	0.0405718i	0.534725	−	0.845026i	$-0.320415\pi$
$409$	11755.3	+	6786.90i	0.0702725	+	0.0405718i	−0.464452	+	0.885598i	$0.653749\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−127293.	+	73492.9i	−0.746287	+	0.430869i
$414$		0			0
$415$	92168.1	+	159640.i	0.535161	+	0.926926i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−188771.			−1.07524			−0.537622	−	0.843186i	$-0.680677\pi$
$419$	−188771.			−1.07524			−0.537622	+	0.843186i	$0.680677\pi$
$420$		0			0
$421$	54800.0	−	31638.8i	0.309184	−	0.178507i	−0.337378	−	0.941369i	$-0.609540\pi$
$421$	54800.0	−	31638.8i	0.309184	−	0.178507i	0.646561	+	0.762862i	$0.276207\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3577.99			−0.0198089
$426$		0			0
$427$	48072.4	−	83263.9i	0.263658	−	0.456668i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	27485.9	+	15869.0i	0.147964	+	0.0854268i	0.572154	−	0.820146i	$-0.306108\pi$
$431$	27485.9	+	15869.0i	0.147964	+	0.0854268i	−0.424190	+	0.905573i	$0.639441\pi$
$432$		0			0
$433$	−1556.42	−	898.600i	−0.00830139	−	0.00479281i	0.495844	−	0.868412i	$-0.334859\pi$
$433$	−1556.42	−	898.600i	−0.00830139	−	0.00479281i	−0.504145	+	0.863619i	$0.668192\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3066.25	+	18127.8i	0.0160563	+	0.0949251i
$438$		0			0
$439$	−125576.	+	72501.1i	−0.651593	+	0.376197i	−0.789066	−	0.614308i	$-0.789435\pi$
$439$	−125576.	+	72501.1i	−0.651593	+	0.376197i	0.137473	+	0.990505i	$0.456102\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	76280.5	−	132122.i	0.388693	−	0.673235i	−0.603581	−	0.797301i	$-0.706260\pi$
$443$	76280.5	−	132122.i	0.388693	−	0.673235i	0.992274	+	0.124066i	$0.0395935\pi$
$444$		0			0
$445$			7726.38i			0.0390172i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	269219.i		−	1.33540i	−0.744429	−	0.667702i	$-0.767278\pi$
$449$		−	269219.i		−	1.33540i	0.744429	−	0.667702i	$-0.232722\pi$
$450$		0			0
$451$	33917.0	−	19582.0i	0.166749	−	0.0962727i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		−	164303.i		−	0.793638i
$456$		0			0
$457$	407841.			1.95280			0.976401	−	0.215966i	$-0.0692901\pi$
$457$	407841.			1.95280			0.976401	+	0.215966i	$0.0692901\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	63070.7	+	109242.i	0.296774	+	0.514028i	0.975396	−	0.220460i	$-0.0707558\pi$
$461$	63070.7	+	109242.i	0.296774	+	0.514028i	−0.678622	+	0.734488i	$0.737423\pi$
$462$		0			0
$463$	−420328.			−1.96077			−0.980385	−	0.197093i	$-0.936850\pi$
$463$	−420328.			−1.96077			−0.980385	+	0.197093i	$0.936850\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	284175.			1.30302			0.651512	−	0.758639i	$-0.274135\pi$
$467$	284175.			1.30302			0.651512	+	0.758639i	$0.274135\pi$
$468$		0			0
$469$	122121.	+	70506.7i	0.555194	+	0.320542i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	51483.6	+	89172.1i	0.230116	+	0.398572i
$474$		0			0
$475$	1797.43	+	10626.5i	0.00796646	+	0.0470979i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−82749.4	+	143326.i	−0.360656	+	0.624675i	−0.988069	−	0.154012i	$-0.950781\pi$
$479$	−82749.4	+	143326.i	−0.360656	+	0.624675i	0.627413	+	0.778687i	$0.284114\pi$
$480$		0			0
$481$	142329.	−	246520.i	0.615180	−	1.06552i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	262019.	+	151277.i	1.11391	+	0.643115i
$486$		0			0
$487$		−	1407.58i		−	0.00593491i	−0.999996	−	0.00296746i	$-0.999055\pi$
$487$		−	1407.58i		−	0.00593491i	0.999996	−	0.00296746i	$-0.000944572\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	94752.5	+	164116.i	0.393032	+	0.680751i	0.992848	−	0.119387i	$-0.0380928\pi$
$491$	94752.5	+	164116.i	0.393032	+	0.680751i	−0.599816	+	0.800138i	$0.704759\pi$
$492$		0			0
$493$			44106.3i			0.181471i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	184320.	−	106417.i	0.746208	−	0.430823i
$498$		0			0
$499$	−90126.8	−	156104.i	−0.361954	−	0.626922i	0.626329	−	0.779559i	$-0.284557\pi$
$499$	−90126.8	−	156104.i	−0.361954	−	0.626922i	−0.988282	+	0.152637i	$0.951224\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−120328.	+	208414.i	−0.475588	+	0.823742i	−0.999609	−	0.0279631i	$-0.991098\pi$
$503$	−120328.	+	208414.i	−0.475588	+	0.823742i	0.524021	+	0.851705i	$0.324431\pi$
$504$		0			0
$505$	−248019.			−0.972530
$506$		0			0
$507$		0			0
$508$		0			0
$509$	327004.	+	188796.i	1.26217	+	0.728715i	0.973494	−	0.228712i	$-0.0734515\pi$
$509$	327004.	+	188796.i	1.26217	+	0.728715i	0.288676	+	0.957427i	$0.406785\pi$
$510$		0			0
$511$	−1134.31	−	1964.69i	−0.00434402	−	0.00752406i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−31928.9	+	18434.2i	−0.120384	+	0.0695039i
$516$		0			0
$517$	83767.6	−	145090.i	0.313397	−	0.542820i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			35419.0i			0.130485i	0.997869	+	0.0652426i	$0.0207821\pi$
$521$			35419.0i			0.130485i	−0.997869	+	0.0652426i	$0.979218\pi$
$522$		0			0
$523$	80341.8	+	46385.4i	0.293723	+	0.169581i	0.639620	−	0.768691i	$-0.279092\pi$
$523$	80341.8	+	46385.4i	0.293723	+	0.169581i	−0.345897	+	0.938273i	$0.612425\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	196325.	−	113348.i	0.706894	−	0.408126i
$528$		0			0
$529$	138624.	+	240103.i	0.495366	+	0.857999i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−53252.5			−0.187450
$534$		0			0
$535$	405451.	−	234087.i	1.41655	−	0.817843i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−363307.			−1.25053
$540$		0			0
$541$	22722.0	−	39355.6i	0.0776339	−	0.134466i	−0.824595	−	0.565724i	$-0.808597\pi$
$541$	22722.0	−	39355.6i	0.0776339	−	0.134466i	0.902229	+	0.431258i	$0.141930\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	73551.7	+	42465.1i	0.247628	+	0.142968i
$546$		0			0
$547$	−334404.	−	193068.i	−1.11763	−	0.645263i	−0.176833	−	0.984241i	$-0.556585\pi$
$547$	−334404.	−	193068.i	−1.11763	−	0.645263i	−0.940794	+	0.338978i	$0.889919\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	130994.	−	22157.2i	0.431467	−	0.0729813i
$552$		0			0
$553$	123189.	−	71123.2i	0.402830	−	0.232574i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−213583.	+	369936.i	−0.688423	+	1.19238i	0.283924	+	0.958847i	$0.408364\pi$
$557$	−213583.	+	369936.i	−0.688423	+	1.19238i	−0.972348	+	0.233538i	$0.924970\pi$
$558$		0			0
$559$		−	140008.i		−	0.448052i
$560$		0			0
$561$		0			0
$562$		0			0
$563$		−	469742.i		−	1.48198i	−0.671516	−	0.740990i	$-0.734357\pi$
$563$		−	469742.i		−	1.48198i	0.671516	−	0.740990i	$-0.265643\pi$
$564$		0			0
$565$	−259562.	+	149858.i	−0.813101	+	0.469444i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	362298.i		−	1.11903i	−0.828820	−	0.559515i	$-0.810988\pi$
$569$		−	362298.i		−	1.11903i	0.828820	−	0.559515i	$-0.189012\pi$
$570$		0			0
$571$	−315619.			−0.968033			−0.484017	−	0.875059i	$-0.660823\pi$
$571$	−315619.			−0.968033			−0.484017	+	0.875059i	$0.660823\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−760.220	−	1316.74i	−0.00229934	−	0.00398258i
$576$		0			0
$577$	−524244.			−1.57464			−0.787321	−	0.616543i	$-0.788533\pi$
$577$	−524244.			−1.57464			−0.787321	+	0.616543i	$0.788533\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	171637.			0.508461
$582$		0			0
$583$	−75826.8	−	43778.6i	−0.223093	−	0.128803i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	109894.	+	190342.i	0.318932	+	0.552406i	0.980265	−	0.197686i	$-0.0633426\pi$
$587$	109894.	+	190342.i	0.318932	+	0.552406i	−0.661334	+	0.750092i	$0.730009\pi$
$588$		0			0
$589$	−435265.	−	526135.i	−1.25465	−	1.51658i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−177018.	+	306604.i	−0.503394	+	0.871903i	0.496599	+	0.867980i	$0.334582\pi$
$593$	−177018.	+	306604.i	−0.503394	+	0.871903i	−0.999992	+	0.00392292i	$0.998751\pi$
$594$		0			0
$595$	−36538.1	+	63285.9i	−0.103208	+	0.178761i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	324831.	+	187541.i	0.905322	+	0.522688i	0.878923	−	0.476963i	$-0.158263\pi$
$599$	324831.	+	187541.i	0.905322	+	0.522688i	0.0263993	+	0.999651i	$0.491596\pi$
$600$		0			0
$601$			362226.i			1.00284i	0.865205	+	0.501419i	$0.167188\pi$
$601$			362226.i			1.00284i	−0.865205	+	0.501419i	$0.832812\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−315169.	−	545889.i	−0.861058	−	1.49140i
$606$		0			0
$607$		−	255846.i		−	0.694385i	−0.937794	−	0.347193i	$-0.887135\pi$
$607$		−	255846.i		−	0.694385i	0.937794	−	0.347193i	$-0.112865\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−197283.	+	113902.i	−0.528455	+	0.305104i
$612$		0			0
$613$	−198064.	−	343057.i	−0.527089	−	0.912945i	−0.999502	−	0.0315677i	$-0.989950\pi$
$613$	−198064.	−	343057.i	−0.527089	−	0.912945i	0.472412	−	0.881378i	$-0.343383\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−27150.7	+	47026.3i	−0.0713198	+	0.123529i	−0.899480	−	0.436962i	$-0.856054\pi$
$617$	−27150.7	+	47026.3i	−0.0713198	+	0.123529i	0.828160	+	0.560491i	$0.189388\pi$
$618$		0			0
$619$	−383463.			−1.00079			−0.500394	−	0.865798i	$-0.666812\pi$
$619$	−383463.			−1.00079			−0.500394	+	0.865798i	$0.666812\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	6230.26	+	3597.04i	0.0160520	+	0.00926765i
$624$		0			0
$625$	204196.	+	353678.i	0.522743	+	0.905417i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−109644.	+	63302.8i	−0.277129	+	0.160001i
$630$		0			0
$631$	−73499.0	+	127304.i	−0.184596	+	0.319730i	−0.943440	−	0.331542i	$-0.892431\pi$
$631$	−73499.0	+	127304.i	−0.184596	+	0.319730i	0.758844	+	0.651272i	$0.225764\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		−	440733.i		−	1.09302i
$636$		0			0
$637$	427816.	+	247000.i	1.05434	+	0.608721i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−265359.	+	153205.i	−0.645828	+	0.372869i	−0.786856	−	0.617136i	$-0.788293\pi$
$641$	−265359.	+	153205.i	−0.645828	+	0.372869i	0.141028	+	0.990006i	$0.454959\pi$
$642$		0			0
$643$	118008.	+	204396.i	0.285424	+	0.494369i	0.972712	−	0.232016i	$-0.0745322\pi$
$643$	118008.	+	204396.i	0.285424	+	0.494369i	−0.687288	+	0.726385i	$0.741199\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	431473.			1.03073			0.515365	−	0.856971i	$-0.327656\pi$
$647$	431473.			1.03073			0.515365	+	0.856971i	$0.327656\pi$
$648$		0			0
$649$	1.05872e6	−	611253.i	2.51358	−	1.45121i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−319604.			−0.749526			−0.374763	−	0.927121i	$-0.622276\pi$
$653$	−319604.			−0.749526			−0.374763	+	0.927121i	$0.622276\pi$
$654$		0			0
$655$	−239426.	+	414699.i	−0.558071	+	0.966607i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−552993.	−	319271.i	−1.27335	−	0.735171i	−0.297736	−	0.954648i	$-0.596231\pi$
$659$	−552993.	−	319271.i	−1.27335	−	0.735171i	−0.975618	+	0.219478i	$0.929565\pi$
$660$		0			0
$661$	351472.	+	202923.i	0.804430	+	0.464438i	0.845018	−	0.534738i	$-0.179590\pi$
$661$	351472.	+	202923.i	0.804430	+	0.464438i	−0.0405878	+	0.999176i	$0.512923\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	206311.	+	76724.3i	0.466530	+	0.173496i
$666$		0			0
$667$	−16231.6	+	9371.33i	−0.0364846	+	0.0210644i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−399827.	+	692520.i	−0.888028	+	1.53811i
$672$		0			0
$673$		−	648976.i		−	1.43284i	−0.697668	−	0.716421i	$-0.745779\pi$
$673$		−	648976.i		−	1.43284i	0.697668	−	0.716421i	$-0.254221\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	336961.i		−	0.735194i	−0.929985	−	0.367597i	$-0.880181\pi$
$677$		−	336961.i		−	0.735194i	0.929985	−	0.367597i	$-0.119819\pi$
$678$		0			0
$679$	243968.	−	140855.i	0.529167	−	0.305515i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	175345.i		−	0.375883i	−0.982180	−	0.187942i	$-0.939818\pi$
$683$		−	175345.i		−	0.375883i	0.982180	−	0.187942i	$-0.0601816\pi$
$684$		0			0
$685$	−296183.			−0.631218
$686$		0			0
$687$		0			0
$688$		0			0
$689$	59527.2	+	103104.i	0.125394	+	0.217189i
$690$		0			0
$691$	−109382.			−0.229082			−0.114541	−	0.993419i	$-0.536540\pi$
$691$	−109382.			−0.229082			−0.114541	+	0.993419i	$0.536540\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	274213.			0.567700
$696$		0			0
$697$	20511.7	+	11842.4i	0.0422217	+	0.0243767i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−95740.8	−	165828.i	−0.194832	−	0.337460i	0.752013	−	0.659148i	$-0.229083\pi$
$701$	−95740.8	−	165828.i	−0.194832	−	0.337460i	−0.946846	+	0.321689i	$0.895750\pi$
$702$		0			0
$703$	243087.	+	293836.i	0.491871	+	0.594558i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−115466.	+	199993.i	−0.231002	+	0.400108i
$708$		0			0
$709$	−21977.2	+	38065.7i	−0.0437201	+	0.0757254i	−0.887057	−	0.461659i	$-0.847254\pi$
$709$	−21977.2	+	38065.7i	−0.0437201	+	0.0757254i	0.843337	+	0.537385i	$0.180588\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	83426.9	+	48166.5i	0.164107	+	0.0947472i
$714$		0			0
$715$			1.36654e6i			2.67306i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−30121.3	−	52171.5i	−0.0582660	−	0.100920i	0.835421	−	0.549610i	$-0.185224\pi$
$719$	−30121.3	−	52171.5i	−0.0582660	−	0.100920i	−0.893687	+	0.448691i	$0.851890\pi$
$720$		0			0
$721$			34328.4i			0.0660363i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−9514.95	+	5493.46i	−0.0181022	+	0.0104513i
$726$		0			0
$727$	−297399.	−	515110.i	−0.562691	−	0.974610i	−0.997260	−	0.0739713i	$-0.976433\pi$
$727$	−297399.	−	515110.i	−0.562691	−	0.974610i	0.434569	−	0.900638i	$-0.356901\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−31135.3	+	53927.9i	−0.0582664	+	0.100920i
$732$		0			0
$733$	−3477.27			−0.00647187			−0.00323594	−	0.999995i	$-0.501030\pi$
$733$	−3477.27			−0.00647187			−0.00323594	+	0.999995i	$0.501030\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.01570e6	−	586416.i	−1.86996	−	1.07962i
$738$		0			0
$739$	−274999.	−	476312.i	−0.503549	−	0.872173i	−0.999992	−	0.00410347i	$-0.998694\pi$
$739$	−274999.	−	476312.i	−0.503549	−	0.872173i	0.496442	−	0.868070i	$-0.334640\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−756525.	+	436780.i	−1.37040	+	0.791198i	−0.990978	−	0.134028i	$-0.957209\pi$
$743$	−756525.	+	436780.i	−1.37040	+	0.791198i	−0.379418	+	0.925226i	$0.623876\pi$
$744$		0			0
$745$	−216417.	+	374846.i	−0.389923	+	0.675367i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	435920.i		−	0.777040i
$750$		0			0
$751$	−589668.	−	340445.i	−1.04551	−	0.603625i	−0.124120	−	0.992267i	$-0.539611\pi$
$751$	−589668.	−	340445.i	−1.04551	−	0.603625i	−0.921389	+	0.388643i	$0.872944\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−555278.	+	320590.i	−0.974129	+	0.562414i
$756$		0			0
$757$	252342.	+	437069.i	0.440350	+	0.762709i	0.997715	−	0.0675588i	$-0.0215210\pi$
$757$	252342.	+	437069.i	0.440350	+	0.762709i	−0.557365	+	0.830267i	$0.688188\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	384656.			0.664206			0.332103	−	0.943243i	$-0.392242\pi$
$761$	384656.			0.664206			0.332103	+	0.943243i	$0.392242\pi$
$762$		0			0
$763$	68484.5	−	39539.5i	0.117637	−	0.0679176i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.66228e6			−2.82562
$768$		0			0
$769$	−273765.	+	474174.i	−0.462940	+	0.801835i	−0.999106	−	0.0422773i	$-0.986539\pi$
$769$	−273765.	+	474174.i	−0.462940	+	0.801835i	0.536166	+	0.844112i	$0.319872\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−832567.	−	480683.i	−1.39335	−	0.804451i	−0.399665	−	0.916661i	$-0.630874\pi$
$773$	−832567.	−	480683.i	−1.39335	−	0.804451i	−0.993684	+	0.112210i	$0.964207\pi$
$774$		0			0
$775$	48904.7	+	28235.1i	0.0814230	+	0.0470096i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	24867.3	−	66867.9i	0.0409782	−	0.110190i
$780$		0			0
$781$	−1.53302e6	+	885090.i	−2.51331	+	1.45106i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−367677.	+	636835.i	−0.596660	+	1.03345i
$786$		0			0
$787$			353236.i			0.570316i	0.958481	+	0.285158i	$0.0920461\pi$
$787$			353236.i			0.570316i	−0.958481	+	0.285158i	$0.907954\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			279068.i			0.446023i
$792$		0			0
$793$	941642.	−	543657.i	1.49741	−	0.864528i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	588453.i		−	0.926393i	−0.886256	−	0.463197i	$-0.846702\pi$
$797$		−	588453.i		−	0.926393i	0.886256	−	0.463197i	$-0.153298\pi$
$798$		0			0
$799$	101319.			0.158707
$800$		0			0
$801$		0			0
$802$		0			0
$803$	9434.29	+	16340.7i	0.0146311	+	0.0253419i
$804$		0			0
$805$	−31053.2			−0.0479198
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−23210.1			−0.0354634			−0.0177317	−	0.999843i	$-0.505644\pi$
$809$	−23210.1			−0.0354634			−0.0177317	+	0.999843i	$0.505644\pi$
$810$		0			0
$811$	−251094.	−	144969.i	−0.381764	−	0.220412i	0.296821	−	0.954933i	$-0.404073\pi$
$811$	−251094.	−	144969.i	−0.381764	−	0.220412i	−0.678586	+	0.734521i	$0.737407\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	313007.	+	542143.i	0.471236	+	0.816205i
$816$		0			0
$817$	175805.	+	65379.3i	0.263382	+	0.0979481i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	555768.	−	962618.i	0.824531	−	1.42813i	−0.0777467	−	0.996973i	$-0.524773\pi$
$821$	555768.	−	962618.i	0.824531	−	1.42813i	0.902277	−	0.431156i	$-0.141894\pi$
$822$		0			0
$823$	36885.4	−	63887.3i	0.0544571	−	0.0943224i	−0.837512	−	0.546419i	$-0.815991\pi$
$823$	36885.4	−	63887.3i	0.0544571	−	0.0943224i	0.891969	+	0.452097i	$0.149324\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−629791.	−	363610.i	−0.920843	−	0.531649i	−0.0369393	−	0.999318i	$-0.511761\pi$
$827$	−629791.	−	363610.i	−0.920843	−	0.531649i	−0.883904	+	0.467668i	$0.845094\pi$
$828$		0			0
$829$		−	1.15093e6i		−	1.67471i	−0.546661	−	0.837354i	$-0.684101\pi$
$829$		−	1.15093e6i		−	1.67471i	0.546661	−	0.837354i	$-0.315899\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−109857.	−	190278.i	−0.158321	−	0.274220i
$834$		0			0
$835$			629949.i			0.903510i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−894965.	+	516708.i	−1.27140	+	0.734043i	−0.975251	−	0.221099i	$-0.929036\pi$
$839$	−894965.	+	516708.i	−1.27140	+	0.734043i	−0.296148	+	0.955142i	$0.595702\pi$
$840$		0			0
$841$	−285922.	−	495231.i	−0.404255	−	0.700190i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	563621.	−	976221.i	0.789358	−	1.36721i
$846$		0			0
$847$	−586912.			−0.818099
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−46592.3	−	26900.1i	−0.0643361	−	0.0371445i
$852$		0			0
$853$	−140017.	−	242516.i	−0.192434	−	0.333306i	0.753622	−	0.657308i	$-0.228305\pi$
$853$	−140017.	−	242516.i	−0.192434	−	0.333306i	−0.946056	+	0.324002i	$0.894972\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	425690.	−	245772.i	0.579604	−	0.334635i	−0.181372	−	0.983415i	$-0.558054\pi$
$857$	425690.	−	245772.i	0.579604	−	0.334635i	0.760976	+	0.648780i	$0.224720\pi$
$858$		0			0
$859$	−342269.	+	592827.i	−0.463853	+	0.803418i	−0.999149	−	0.0412471i	$-0.986867\pi$
$859$	−342269.	+	592827.i	−0.463853	+	0.803418i	0.535296	+	0.844665i	$0.320200\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			1.05721e6i			1.41951i	0.704447	+	0.709756i	$0.251195\pi$
$863$			1.05721e6i			1.41951i	−0.704447	+	0.709756i	$0.748805\pi$
$864$		0			0
$865$	856154.	+	494301.i	1.14425	+	0.660632i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.02458e6	+	591544.i	−1.35677	+	0.783334i
$870$		0			0
$871$	797369.	+	1.38108e6i	1.05105	+	1.82047i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	362884.			0.473971
$876$		0			0
$877$	941289.	−	543454.i	1.22384	−	0.706583i	0.258104	−	0.966117i	$-0.416902\pi$
$877$	941289.	−	543454.i	1.22384	−	0.706583i	0.965734	+	0.259534i	$0.0835689\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.30487e6			1.68118			0.840590	−	0.541672i	$-0.182208\pi$
$881$	1.30487e6			1.68118			0.840590	+	0.541672i	$0.182208\pi$
$882$		0			0
$883$	614758.	−	1.06479e6i	0.788465	−	1.36566i	−0.138442	−	0.990371i	$-0.544209\pi$
$883$	614758.	−	1.06479e6i	0.788465	−	1.36566i	0.926907	−	0.375291i	$-0.122457\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−519691.	−	300044.i	−0.660538	−	0.381362i	0.131944	−	0.991257i	$-0.457878\pi$
$887$	−519691.	−	300044.i	−0.660538	−	0.381362i	−0.792482	+	0.609895i	$0.791212\pi$
$888$		0			0
$889$	−355391.	−	205185.i	−0.449679	−	0.259622i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−50898.5	−	300913.i	−0.0638266	−	0.377344i
$894$		0			0
$895$	1.22163e6	−	705306.i	1.52508	−	0.880504i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	348058.	−	602854.i	0.430658	−	0.745921i
$900$		0			0
$901$		−	52951.3i		−	0.0652269i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			1.10731e6i			1.35199i
$906$		0			0
$907$	622480.	−	359389.i	0.756678	−	0.436868i	−0.0714239	−	0.997446i	$-0.522754\pi$
$907$	622480.	−	359389.i	0.756678	−	0.436868i	0.828102	+	0.560578i	$0.189421\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	701653.i		−	0.845445i	−0.906259	−	0.422723i	$-0.861074\pi$
$911$		−	701653.i		−	0.845445i	0.906259	−	0.422723i	$-0.138926\pi$
$912$		0			0
$913$	−1.42753e6			−1.71255
$914$		0			0
$915$		0			0
$916$		0			0
$917$	222932.	+	386129.i	0.265114	+	0.459191i
$918$		0			0
$919$	308448.			0.365217			0.182609	−	0.983186i	$-0.441546\pi$
$919$	308448.			0.365217			0.182609	+	0.983186i	$0.441546\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	2.40697e6			2.82532
$924$		0			0
$925$	−27312.3	−	15768.8i	−0.0319209	−	0.0184295i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	114058.	+	197554.i	0.132158	+	0.228904i	0.924508	−	0.381162i	$-0.124476\pi$
$929$	114058.	+	197554.i	0.132158	+	0.228904i	−0.792350	+	0.610066i	$0.791143\pi$
$930$		0			0
$931$	−509929.	+	421858.i	−0.588316	+	0.486706i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	303894.	−	526359.i	0.347615	−	0.602087i
$936$		0			0
$937$	710133.	−	1.22999e6i	0.808836	−	1.40095i	−0.104834	−	0.994490i	$-0.533431\pi$
$937$	710133.	−	1.22999e6i	0.808836	−	1.40095i	0.913670	−	0.406456i	$-0.133236\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−484707.	−	279846.i	−0.547395	−	0.316038i	0.200676	−	0.979658i	$-0.435686\pi$
$941$	−484707.	−	279846.i	−0.547395	−	0.316038i	−0.748070	+	0.663619i	$0.769020\pi$
$942$		0			0
$943$			10064.7i			0.0113182i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	202257.	+	350319.i	0.225529	+	0.390628i	0.956478	−	0.291804i	$-0.0942556\pi$
$947$	202257.	+	350319.i	0.225529	+	0.390628i	−0.730949	+	0.682432i	$0.760922\pi$
$948$		0			0
$949$		−	25656.2i		−	0.0284879i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1.10903e6	−	640300.i	1.22112	−	0.705013i	0.255963	−	0.966687i	$-0.417608\pi$
$953$	1.10903e6	−	640300.i	1.22112	−	0.705013i	0.965157	+	0.261673i	$0.0842743\pi$
$954$		0			0
$955$	−279741.	−	484526.i	−0.306725	−	0.531263i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−137889.	+	238831.i	−0.149931	+	0.259689i
$960$		0			0
$961$	−2.65436e6			−2.87418
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.52454e6	+	880191.i	1.63713	+	0.945197i
$966$		0			0
$967$	−888059.	−	1.53816e6i	−0.949706	−	1.64494i	−0.746044	−	0.665897i	$-0.768049\pi$
$967$	−888059.	−	1.53816e6i	−0.949706	−	1.64494i	−0.203662	−	0.979041i	$-0.565284\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	585681.	−	338143.i	0.621187	−	0.358642i	−0.156144	−	0.987734i	$-0.549906\pi$
$971$	585681.	−	338143.i	0.621187	−	0.358642i	0.777331	+	0.629092i	$0.216573\pi$
$972$		0			0
$973$	127661.	−	221115.i	0.134844	−	0.233557i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			991515.i			1.03875i	0.854547	+	0.519374i	$0.173835\pi$
$977$			991515.i			1.03875i	−0.854547	+	0.519374i	$0.826165\pi$
$978$		0			0
$979$	−51818.1	−	29917.2i	−0.0540650	−	0.0312145i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1.05199e6	+	607364.i	−1.08869	+	0.628553i	−0.933226	−	0.359289i	$-0.883019\pi$
$983$	−1.05199e6	+	607364.i	−1.08869	+	0.628553i	−0.155460	+	0.987842i	$0.549686\pi$
$984$		0			0
$985$	210764.	+	365054.i	0.217232	+	0.376257i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−26461.4			−0.0270533
$990$		0			0
$991$	−647155.	+	373635.i	−0.658963	+	0.380453i	−0.791882	−	0.610674i	$-0.790898\pi$
$991$	−647155.	+	373635.i	−0.658963	+	0.380453i	0.132919	+	0.991127i	$0.457565\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.51339e6			−1.52864
$996$		0			0
$997$	−108672.	+	188225.i	−0.109327	+	0.189360i	−0.915498	−	0.402323i	$-0.868203\pi$
$997$	−108672.	+	188225.i	−0.109327	+	0.189360i	0.806171	+	0.591683i	$0.201536\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.5.y.d.145.2		14
3.2	odd	2		228.5.l.b.145.6	✓	14
19.8	odd	6	inner	684.5.y.d.217.2		14
57.8	even	6		228.5.l.b.217.6	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.5.l.b.145.6	✓	14	3.2	odd	2
228.5.l.b.217.6	yes	14	57.8	even	6
684.5.y.d.145.2		14	1.1	even	1	trivial
684.5.y.d.217.2		14	19.8	odd	6	inner

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	684.y (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-12.7951 - 22.1617i) q^{5} -23.8271 q^{7} +O(q^{10})\)	\(q+(-12.7951 - 22.1617i) q^{5} -23.8271 q^{7} +198.174 q^{11} +(-233.363 - 134.732i) q^{13} +(59.9242 + 103.792i) q^{17} +(278.153 - 230.113i) q^{19} +(-25.4643 + 44.1055i) q^{23} +(-14.9272 + 25.8546i) q^{25} +(318.713 + 184.009i) q^{29} -1891.53i q^{31} +(304.870 + 528.050i) q^{35} +1056.38i q^{37} +(171.147 - 98.8118i) q^{41} +(259.789 + 449.968i) q^{43} +(422.697 - 732.132i) q^{47} -1833.27 q^{49} +(-382.627 - 220.910i) q^{53} +(-2535.65 - 4391.88i) q^{55} +(5342.37 - 3084.42i) q^{59} +(-2017.55 + 3494.50i) q^{61} +6895.62i q^{65} +(-5125.30 - 2959.09i) q^{67} +(-7735.72 + 4466.22i) q^{71} +(47.6060 + 82.4560i) q^{73} -4721.93 q^{77} +(-5170.11 + 2984.97i) q^{79} -7203.41 q^{83} +(1533.47 - 2656.04i) q^{85} +(-261.478 - 150.964i) q^{89} +(5560.37 + 3210.28i) q^{91} +(-8658.67 - 3220.04i) q^{95} +(-10239.1 + 5911.53i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 12 q^{5} - 110 q^{7}+O(q^{10}) \) 14 * q - 12 * q^5 - 110 * q^7	\( 14 q - 12 q^{5} - 110 q^{7} + 84 q^{11} + 21 q^{13} - 282 q^{17} + 62 q^{19} + 678 q^{23} - 1293 q^{25} + 774 q^{29} - 228 q^{35} - 5268 q^{41} + 2239 q^{43} - 1674 q^{47} - 1080 q^{49} + 1806 q^{53} + 2204 q^{55} + 11496 q^{59} - 1661 q^{61} + 6957 q^{67} + 11784 q^{71} - 8129 q^{73} - 996 q^{77} - 5907 q^{79} - 24444 q^{83} + 3956 q^{85} - 21648 q^{89} + 13995 q^{91} + 28884 q^{95} - 9408 q^{97}+O(q^{100}) \) 14 * q - 12 * q^5 - 110 * q^7 + 84 * q^11 + 21 * q^13 - 282 * q^17 + 62 * q^19 + 678 * q^23 - 1293 * q^25 + 774 * q^29 - 228 * q^35 - 5268 * q^41 + 2239 * q^43 - 1674 * q^47 - 1080 * q^49 + 1806 * q^53 + 2204 * q^55 + 11496 * q^59 - 1661 * q^61 + 6957 * q^67 + 11784 * q^71 - 8129 * q^73 - 996 * q^77 - 5907 * q^79 - 24444 * q^83 + 3956 * q^85 - 21648 * q^89 + 13995 * q^91 + 28884 * q^95 - 9408 * q^97

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