LMFDB - Embedded newform 175.4.k.d.149.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(74,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("175.74");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.k (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:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 75 x^{18} + 3638 x^{16} - 105775 x^{14} + 2246038 x^{12} - 30934571 x^{10} + 307864753 x^{8} + \cdots + 16777216 $ x^20 - 75x^18 + 3638x^16 - 105775x^14 + 2246038x^12 - 30934571x^10 + 307864753x^8 - 1719258496x^6 + 6352449536x^4 - 328728576*x^2 + 16777216
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.10
Root			$4.50647 - 2.60181i$ of defining polynomial
Character	$\chi$	$=$	175.149
Dual form			175.4.k.d.74.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.50647 + 2.60181i) q^{2} +(4.24917 - 2.45326i) q^{3} +(9.53885 + 16.5218i) q^{4} +25.5317 q^{6} +(4.23212 + 18.0302i) q^{7} +57.6442i q^{8} +(-1.46305 + 2.53407i) q^{9} +O(q^{10})$	\(q+(4.50647 + 2.60181i) q^{2} +(4.24917 - 2.45326i) q^{3} +(9.53885 + 16.5218i) q^{4} +25.5317 q^{6} +(4.23212 + 18.0302i) q^{7} +57.6442i q^{8} +(-1.46305 + 2.53407i) q^{9} +(-28.3386 - 49.0839i) q^{11} +(81.0644 + 46.8025i) q^{12} -43.4297i q^{13} +(-27.8393 + 92.2639i) q^{14} +(-73.6685 + 127.598i) q^{16} +(34.5013 - 19.9193i) q^{17} +(-13.1864 + 7.61315i) q^{18} +(26.1940 - 45.3693i) q^{19} +(62.2158 + 66.2310i) q^{21} -294.927i q^{22} +(46.3460 + 26.7579i) q^{23} +(141.416 + 244.940i) q^{24} +(112.996 - 195.715i) q^{26} +146.833i q^{27} +(-257.522 + 241.910i) q^{28} -49.6376 q^{29} +(36.8930 + 63.9006i) q^{31} +(-264.599 + 152.767i) q^{32} +(-240.831 - 139.044i) q^{33} +207.305 q^{34} -55.8231 q^{36} +(-265.938 - 153.540i) q^{37} +(236.085 - 136.304i) q^{38} +(-106.544 - 184.540i) q^{39} +292.064 q^{41} +(108.053 + 460.342i) q^{42} -365.956i q^{43} +(540.635 - 936.407i) q^{44} +(139.238 + 241.167i) q^{46} +(-383.175 - 221.226i) q^{47} +722.912i q^{48} +(-307.178 + 152.612i) q^{49} +(97.7346 - 169.281i) q^{51} +(717.536 - 414.269i) q^{52} +(22.3185 - 12.8856i) q^{53} +(-382.032 + 661.698i) q^{54} +(-1039.34 + 243.957i) q^{56} -257.043i q^{57} +(-223.690 - 129.148i) q^{58} +(188.300 + 326.146i) q^{59} +(-316.287 + 547.826i) q^{61} +383.955i q^{62} +(-51.8817 - 15.6546i) q^{63} -411.183 q^{64} +(-723.531 - 1253.19i) q^{66} +(-442.624 + 255.549i) q^{67} +(658.206 + 380.015i) q^{68} +262.576 q^{69} +134.881 q^{71} +(-146.075 - 84.3362i) q^{72} +(354.564 - 204.708i) q^{73} +(-798.962 - 1383.84i) q^{74} +999.443 q^{76} +(765.061 - 718.680i) q^{77} -1108.83i q^{78} +(-463.424 + 802.674i) q^{79} +(320.717 + 555.498i) q^{81} +(1316.18 + 759.897i) q^{82} +296.372i q^{83} +(-500.786 + 1659.68i) q^{84} +(952.150 - 1649.17i) q^{86} +(-210.918 + 121.774i) q^{87} +(2829.40 - 1633.55i) q^{88} +(244.391 - 423.297i) q^{89} +(783.047 - 183.800i) q^{91} +1020.96i q^{92} +(313.529 + 181.016i) q^{93} +(-1151.18 - 1993.90i) q^{94} +(-749.552 + 1298.26i) q^{96} +475.907i q^{97} +(-1781.36 - 111.477i) q^{98} +165.843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 70 q^{4} + 64 q^{6} + 162 q^{9}+O(q^{10}) $ 20 * q + 70 * q^4 + 64 * q^6 + 162 * q^9	$ 20 q + 70 q^{4} + 64 q^{6} + 162 q^{9} - 94 q^{11} - 14 q^{14} - 342 q^{16} - 42 q^{19} + 356 q^{21} + 1696 q^{24} + 94 q^{26} - 760 q^{29} - 776 q^{31} - 520 q^{34} + 4916 q^{36} + 28 q^{39} - 1124 q^{41} + 2182 q^{44} - 674 q^{46} - 1996 q^{49} - 1464 q^{51} - 1548 q^{54} - 2676 q^{56} + 1416 q^{59} - 3888 q^{61} + 500 q^{64} - 2964 q^{66} - 1496 q^{69} + 3456 q^{71} - 6570 q^{74} + 2764 q^{76} + 436 q^{79} + 910 q^{81} + 1468 q^{84} + 8528 q^{86} + 4644 q^{89} + 1048 q^{91} - 5354 q^{94} - 9184 q^{96} - 140 q^{99}+O(q^{100}) $ 20 * q + 70 * q^4 + 64 * q^6 + 162 * q^9 - 94 * q^11 - 14 * q^14 - 342 * q^16 - 42 * q^19 + 356 * q^21 + 1696 * q^24 + 94 * q^26 - 760 * q^29 - 776 * q^31 - 520 * q^34 + 4916 * q^36 + 28 * q^39 - 1124 * q^41 + 2182 * q^44 - 674 * q^46 - 1996 * q^49 - 1464 * q^51 - 1548 * q^54 - 2676 * q^56 + 1416 * q^59 - 3888 * q^61 + 500 * q^64 - 2964 * q^66 - 1496 * q^69 + 3456 * q^71 - 6570 * q^74 + 2764 * q^76 + 436 * q^79 + 910 * q^81 + 1468 * q^84 + 8528 * q^86 + 4644 * q^89 + 1048 * q^91 - 5354 * q^94 - 9184 * q^96 - 140 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	4.50647	+	2.60181i	1.59328	+	0.919879i	0.992740	+	0.120283i	$0.0383803\pi$
$2$	4.50647	+	2.60181i	1.59328	+	0.919879i	0.600538	+	0.799596i	$0.294953\pi$
$3$	4.24917	−	2.45326i	0.817753	−	0.472130i	−0.0318881	−	0.999491i	$-0.510152\pi$
$3$	4.24917	−	2.45326i	0.817753	−	0.472130i	0.849641	+	0.527362i	$0.176819\pi$
$4$	9.53885	+	16.5218i	1.19236	+	2.06522i
$5$		0			0
$5$		0			0
$6$	25.5317			1.73721
$7$	4.23212	+	18.0302i	0.228513	+	0.973541i
$7$	4.23212	+	18.0302i	0.228513	+	0.973541i
$8$			57.6442i			2.54754i
$9$	−1.46305	+	2.53407i	−0.0541869	+	0.0938545i
$10$		0			0
$11$	−28.3386	−	49.0839i	−0.776764	−	1.34539i	−0.933798	−	0.357802i	$-0.883526\pi$
$11$	−28.3386	−	49.0839i	−0.776764	−	1.34539i	0.157034	−	0.987593i	$-0.449807\pi$
$12$	81.0644	+	46.8025i	1.95011	+	1.12589i
$13$		−	43.4297i		−	0.926556i	−0.886213	−	0.463278i	$-0.846673\pi$
$13$		−	43.4297i		−	0.926556i	0.886213	−	0.463278i	$-0.153327\pi$
$14$	−27.8393	+	92.2639i	−0.531455	+	1.76133i
$15$		0			0
$16$	−73.6685	+	127.598i	−1.15107	+	1.99371i
$17$	34.5013	−	19.9193i	0.492223	−	0.284185i	−0.233273	−	0.972411i	$-0.574944\pi$
$17$	34.5013	−	19.9193i	0.492223	−	0.284185i	0.725496	+	0.688226i	$0.241610\pi$
$18$	−13.1864	+	7.61315i	−0.172670	+	0.0996909i
$19$	26.1940	−	45.3693i	0.316280	−	0.547813i	−0.663429	−	0.748239i	$-0.730899\pi$
$19$	26.1940	−	45.3693i	0.316280	−	0.547813i	0.979709	+	0.200427i	$0.0642328\pi$
$20$		0			0
$21$	62.2158	+	66.2310i	0.646505	+	0.688228i
$22$		−	294.927i		−	2.85812i
$23$	46.3460	+	26.7579i	0.420166	+	0.242583i	0.695148	−	0.718866i	$-0.255339\pi$
$23$	46.3460	+	26.7579i	0.420166	+	0.242583i	−0.274982	+	0.961449i	$0.588672\pi$
$24$	141.416	+	244.940i	1.20277	+	2.08326i
$25$		0			0
$26$	112.996	−	195.715i	0.852320	−	1.47626i
$27$			146.833i			1.04659i
$28$	−257.522	+	241.910i	−1.73811	+	1.63274i
$29$	−49.6376			−0.317844			−0.158922	−	0.987291i	$-0.550802\pi$
$29$	−49.6376			−0.317844			−0.158922	+	0.987291i	$0.550802\pi$
$30$		0			0
$31$	36.8930	+	63.9006i	0.213748	+	0.370222i	0.952884	−	0.303333i	$-0.0980996\pi$
$31$	36.8930	+	63.9006i	0.213748	+	0.370222i	−0.739137	+	0.673555i	$0.764766\pi$
$32$	−264.599	+	152.767i	−1.46172	+	0.843924i
$33$	−240.831	−	139.044i	−1.27040	−	0.733467i
$34$	207.305			1.04566
$35$		0			0
$36$	−55.8231			−0.258440
$37$	−265.938	−	153.540i	−1.18162	−	0.682210i	−0.225232	−	0.974305i	$-0.572314\pi$
$37$	−265.938	−	153.540i	−1.18162	−	0.682210i	−0.956389	+	0.292096i	$0.905647\pi$
$38$	236.085	−	136.304i	1.00784	−	0.581879i
$39$	−106.544	−	184.540i	−0.437455	−	0.757694i
$40$		0			0
$41$	292.064			1.11251			0.556254	−	0.831012i	$-0.312238\pi$
$41$	292.064			1.11251			0.556254	+	0.831012i	$0.312238\pi$
$42$	108.053	+	460.342i	0.396975	+	1.69124i
$43$		−	365.956i		−	1.29786i	−0.760850	−	0.648928i	$-0.775217\pi$
$43$		−	365.956i		−	1.29786i	0.760850	−	0.648928i	$-0.224783\pi$
$44$	540.635	−	936.407i	1.85236	−	3.20838i
$45$		0			0
$46$	139.238	+	241.167i	0.446294	+	0.773004i
$47$	−383.175	−	221.226i	−1.18919	−	0.686577i	−0.231065	−	0.972938i	$-0.574221\pi$
$47$	−383.175	−	221.226i	−1.18919	−	0.686577i	−0.958122	+	0.286361i	$0.907554\pi$
$48$			722.912i			2.17382i
$49$	−307.178	+	152.612i	−0.895563	+	0.444934i
$50$		0			0
$51$	97.7346	−	169.281i	0.268345	−	0.464787i
$52$	717.536	−	414.269i	1.91354	−	1.10479i
$53$	22.3185	−	12.8856i	0.0578430	−	0.0333957i	−0.470800	−	0.882240i	$-0.656035\pi$
$53$	22.3185	−	12.8856i	0.0578430	−	0.0333957i	0.528643	+	0.848845i	$0.322701\pi$
$54$	−382.032	+	661.698i	−0.962739	+	1.66751i
$55$		0			0
$56$	−1039.34	+	243.957i	−2.48013	+	0.582146i
$57$		−	257.043i		−	0.597300i
$58$	−223.690	−	129.148i	−0.506413	−	0.292378i
$59$	188.300	+	326.146i	0.415502	+	0.719670i	0.995481	−	0.0949609i	$-0.0302726\pi$
$59$	188.300	+	326.146i	0.415502	+	0.719670i	−0.579979	+	0.814631i	$0.696939\pi$
$60$		0			0
$61$	−316.287	+	547.826i	−0.663876	+	1.14987i	0.315713	+	0.948855i	$0.397756\pi$
$61$	−316.287	+	547.826i	−0.663876	+	1.14987i	−0.979589	+	0.201012i	$0.935577\pi$
$62$			383.955i			0.786489i
$63$	−51.8817	−	15.6546i	−0.103754	−	0.0313062i
$64$	−411.183			−0.803092
$65$		0			0
$66$	−723.531	−	1253.19i	−1.34940	−	2.33723i
$67$	−442.624	+	255.549i	−0.807091	+	0.465974i	−0.845945	−	0.533271i	$-0.820963\pi$
$67$	−442.624	+	255.549i	−0.807091	+	0.465974i	0.0388534	+	0.999245i	$0.487629\pi$
$68$	658.206	+	380.015i	1.17381	+	0.677700i
$69$	262.576			0.458123
$70$		0			0
$71$	134.881			0.225457			0.112728	−	0.993626i	$-0.464041\pi$
$71$	134.881			0.225457			0.112728	+	0.993626i	$0.464041\pi$
$72$	−146.075	−	84.3362i	−0.239098	−	0.138043i
$73$	354.564	−	204.708i	0.568474	−	0.328208i	−0.188066	−	0.982156i	$-0.560222\pi$
$73$	354.564	−	204.708i	0.568474	−	0.328208i	0.756540	+	0.653948i	$0.226888\pi$
$74$	−798.962	−	1383.84i	−1.25510	−	2.17390i
$75$		0			0
$76$	999.443			1.50847
$77$	765.061	−	718.680i	1.13230	−	1.06365i
$78$		−	1108.83i		−	1.60962i
$79$	−463.424	+	802.674i	−0.659991	+	1.14314i	0.320627	+	0.947206i	$0.396106\pi$
$79$	−463.424	+	802.674i	−0.659991	+	1.14314i	−0.980618	+	0.195932i	$0.937227\pi$
$80$		0			0
$81$	320.717	+	555.498i	0.439941	+	0.762000i
$82$	1316.18	+	759.897i	1.77253	+	1.02337i
$83$			296.372i			0.391940i	0.980610	+	0.195970i	$0.0627856\pi$
$83$			296.372i			0.391940i	−0.980610	+	0.195970i	$0.937214\pi$
$84$	−500.786	+	1659.68i	−0.650479	+	2.15579i
$85$		0			0
$86$	952.150	−	1649.17i	1.19387	−	2.06785i
$87$	−210.918	+	121.774i	−0.259918	+	0.150063i
$88$	2829.40	−	1633.55i	3.42744	−	1.97884i
$89$	244.391	−	423.297i	0.291071	−	0.504150i	−0.682992	−	0.730426i	$-0.739322\pi$
$89$	244.391	−	423.297i	0.291071	−	0.504150i	0.974063	+	0.226275i	$0.0726550\pi$
$90$		0			0
$91$	783.047	−	183.800i	0.902040	−	0.211730i
$92$			1020.96i			1.15698i
$93$	313.529	+	181.016i	0.349586	+	0.201833i
$94$	−1151.18	−	1993.90i	−1.26314	−	2.18782i
$95$		0			0
$96$	−749.552	+	1298.26i	−0.796883	+	1.38024i
$97$			475.907i			0.498155i	0.968484	+	0.249077i	$0.0801274\pi$
$97$			475.907i			0.498155i	−0.968484	+	0.249077i	$0.919873\pi$
$98$	−1781.36	−	111.477i	−1.83617	−	0.114907i
$99$	165.843			0.168362
$100$		0			0
$101$	−38.7904	−	67.1870i	−0.0382158	−	0.0661917i	0.846285	−	0.532731i	$-0.178834\pi$
$101$	−38.7904	−	67.1870i	−0.0382158	−	0.0661917i	−0.884501	+	0.466539i	$0.845501\pi$
$102$	880.876	−	508.574i	0.855095	−	0.493689i
$103$	−985.340	−	568.886i	−0.942606	−	0.544214i	−0.0518297	−	0.998656i	$-0.516505\pi$
$103$	−985.340	−	568.886i	−0.942606	−	0.544214i	−0.890776	+	0.454442i	$0.849839\pi$
$104$	2503.47			2.36044
$105$		0			0
$106$	134.103			0.122880
$107$	65.0735	+	37.5702i	0.0587934	+	0.0339444i	0.529109	−	0.848554i	$-0.322526\pi$
$107$	65.0735	+	37.5702i	0.0587934	+	0.0339444i	−0.470315	+	0.882499i	$0.655860\pi$
$108$	−2425.94	+	1400.62i	−2.16145	+	1.24791i
$109$	41.4673	+	71.8235i	0.0364390	+	0.0631142i	0.883670	−	0.468111i	$-0.155065\pi$
$109$	41.4673	+	71.8235i	0.0364390	+	0.0631142i	−0.847231	+	0.531225i	$0.821732\pi$
$110$		0			0
$111$	−1506.69			−1.28837
$112$	−2612.39	−	788.251i	−2.20400	−	0.665024i
$113$			714.602i			0.594903i	0.954737	+	0.297452i	$0.0961367\pi$
$113$			714.602i			0.594903i	−0.954737	+	0.297452i	$0.903863\pi$
$114$	668.777	−	1158.35i	0.549444	−	0.951666i
$115$		0			0
$116$	−473.485	−	820.101i	−0.378983	−	0.656418i
$117$	110.054	+	63.5397i	0.0869615	+	0.0502072i
$118$			1959.69i			1.52885i
$119$	505.164	+	537.765i	0.389145	+	0.414259i
$120$		0			0
$121$	−940.651	+	1629.26i	−0.706725	+	1.22408i
$122$	−2850.68	+	1645.84i	−2.11548	+	1.22137i
$123$	1241.03	−	716.510i	0.909756	−	0.525248i
$124$	−703.834	+	1219.08i	−0.509727	+	0.882873i
$125$		0			0
$126$	−193.073	−	205.533i	−0.136510	−	0.145320i
$127$		−	1881.66i		−	1.31473i	−0.753574	−	0.657363i	$-0.771672\pi$
$127$		−	1881.66i		−	1.31473i	0.753574	−	0.657363i	$-0.228328\pi$
$128$	263.812	+	152.312i	0.182171	+	0.105177i
$129$	−897.786	−	1555.01i	−0.612757	−	1.06133i
$130$		0			0
$131$	−91.9544	+	159.270i	−0.0613289	+	0.106225i	−0.895060	−	0.445946i	$-0.852867\pi$
$131$	−91.9544	+	159.270i	−0.0613289	+	0.106225i	0.833731	+	0.552171i	$0.186201\pi$
$132$		−	5305.27i		−	3.49822i
$133$	928.876	+	280.275i	0.605592	+	0.182729i
$134$	−2659.56			−1.71456
$135$		0			0
$136$	1148.23	+	1988.80i	0.723972	+	1.25396i
$137$	−768.812	+	443.874i	−0.479445	+	0.276808i	−0.720185	−	0.693782i	$-0.755943\pi$
$137$	−768.812	+	443.874i	−0.479445	+	0.276808i	0.240740	+	0.970590i	$0.422610\pi$
$138$	1183.29	+	683.174i	0.729917	+	0.421417i
$139$	2335.25			1.42499			0.712495	−	0.701678i	$-0.247565\pi$
$139$	2335.25			1.42499			0.712495	+	0.701678i	$0.247565\pi$
$140$		0			0
$141$	−2170.90			−1.29661
$142$	607.837	+	350.935i	0.359215	+	0.207393i
$143$	−2131.70	+	1230.74i	−1.24658	+	0.719716i
$144$	−215.561	−	373.363i	−0.124746	−	0.216066i
$145$		0			0
$146$	2130.44			1.20765
$147$	−930.854	+	1402.06i	−0.522283	+	0.786668i
$148$		−	5858.36i		−	3.25375i
$149$	−1201.54	+	2081.12i	−0.660629	+	1.14424i	0.319821	+	0.947478i	$0.396377\pi$
$149$	−1201.54	+	2081.12i	−0.660629	+	1.14424i	−0.980451	+	0.196766i	$0.936956\pi$
$150$		0			0
$151$	−617.188	−	1069.00i	−0.332623	−	0.576120i	0.650402	−	0.759590i	$-0.274600\pi$
$151$	−617.188	−	1069.00i	−0.332623	−	0.576120i	−0.983025	+	0.183470i	$0.941267\pi$
$152$	2615.28	+	1509.93i	1.39557	+	0.805735i
$153$			116.572i			0.0615965i
$154$	5317.60	−	1248.17i	2.78249	−	0.653118i
$155$		0			0
$156$	2032.62	−	3520.60i	1.04320	−	1.80688i
$157$	−1240.57	+	716.244i	−0.630627	+	0.364092i	−0.780995	−	0.624538i	$-0.785287\pi$
$157$	−1240.57	+	716.244i	−0.630627	+	0.364092i	0.150368	+	0.988630i	$0.451954\pi$
$158$	−4176.81	+	2411.48i	−2.10310	+	1.21422i
$159$	63.2233	−	109.506i	0.0315342	−	0.0546188i
$160$		0			0
$161$	−286.309	+	948.872i	−0.140151	+	0.464482i
$162$			3337.78i			1.61877i
$163$	745.500	+	430.415i	0.358234	+	0.206826i	0.668306	−	0.743887i	$-0.267020\pi$
$163$	745.500	+	430.415i	0.358234	+	0.206826i	−0.310072	+	0.950713i	$0.600353\pi$
$164$	2785.96	+	4825.42i	1.32651	+	2.29757i
$165$		0			0
$166$	−771.104	+	1335.59i	−0.360538	+	0.624470i
$167$			1346.77i			0.624049i	0.950074	+	0.312024i	$0.101007\pi$
$167$			1346.77i			0.624049i	−0.950074	+	0.312024i	$0.898993\pi$
$168$	−3817.83	+	3586.38i	−1.75329	+	1.64700i
$169$	310.861			0.141493
$170$		0			0
$171$	76.6461	+	132.755i	0.0342765	+	0.0593686i
$172$	6046.25	−	3490.80i	2.68036	−	1.54751i
$173$	2260.75	+	1305.25i	0.993536	+	0.573618i	0.906329	−	0.422572i	$-0.138873\pi$
$173$	2260.75	+	1305.25i	0.993536	+	0.573618i	0.0872067	+	0.996190i	$0.472206\pi$
$174$	−1267.33			−0.552161
$175$		0			0
$176$	8350.65			3.57644
$177$	1600.24	+	923.899i	0.679556	+	0.392342i
$178$	2202.68	−	1271.72i	0.927515	−	0.535501i
$179$	675.224	+	1169.52i	0.281947	+	0.488347i	0.971864	−	0.235541i	$-0.0756863\pi$
$179$	675.224	+	1169.52i	0.281947	+	0.488347i	−0.689917	+	0.723889i	$0.742353\pi$
$180$		0			0
$181$	2846.61			1.16899			0.584493	−	0.811399i	$-0.301293\pi$
$181$	2846.61			1.16899			0.584493	+	0.811399i	$0.301293\pi$
$182$	4006.99	+	1209.05i	1.63197	+	0.492423i
$183$			3103.74i			1.25374i
$184$	−1542.44	+	2671.58i	−0.617989	+	1.07039i
$185$		0			0
$186$	941.940	+	1631.49i	0.371325	+	0.643154i
$187$	−1955.44	−	1128.97i	−0.764683	−	0.441490i
$188$		−	8440.97i		−	3.27458i
$189$	−2647.43	+	621.415i	−1.01890	+	0.239160i
$190$		0			0
$191$	−2101.75	+	3640.33i	−0.796215	+	1.37909i	0.125849	+	0.992049i	$0.459834\pi$
$191$	−2101.75	+	3640.33i	−0.796215	+	1.37909i	−0.922065	+	0.387036i	$0.873499\pi$
$192$	−1747.19	+	1008.74i	−0.656730	+	0.379163i
$193$	120.018	−	69.2923i	0.0447620	−	0.0258434i	−0.477452	−	0.878658i	$-0.658440\pi$
$193$	120.018	−	69.2923i	0.0447620	−	0.0258434i	0.522214	+	0.852814i	$0.325106\pi$
$194$	−1238.22	+	2144.66i	−0.458242	+	0.793699i
$195$		0			0
$196$	−5451.55	−	3619.38i	−1.98672	−	1.31902i
$197$		−	1473.76i		−	0.532998i	−0.963835	−	0.266499i	$-0.914133\pi$
$197$		−	1473.76i		−	0.532998i	0.963835	−	0.266499i	$-0.0858670\pi$
$198$	747.365	+	431.492i	0.268247	+	0.154873i
$199$	−1804.80	−	3126.00i	−0.642909	−	1.11355i	−0.984780	−	0.173804i	$-0.944394\pi$
$199$	−1804.80	−	3126.00i	−0.642909	−	1.11355i	0.341872	−	0.939747i	$-0.388939\pi$
$200$		0			0
$201$	−1253.86	+	2171.74i	−0.440001	+	0.762104i
$202$		−	403.702i		−	0.140616i
$203$	−210.072	−	894.977i	−0.0726315	−	0.309434i
$204$	3729.10			1.27985
$205$		0			0
$206$	−2960.27	−	5127.34i	−1.00122	−	1.73417i
$207$	−135.613	+	78.2961i	−0.0455350	+	0.0262896i
$208$	5541.53	+	3199.40i	1.84729	+	1.06653i
$209$	−2969.20			−0.982699
$210$		0			0
$211$	1782.00			0.581412			0.290706	−	0.956812i	$-0.406110\pi$
$211$	1782.00			0.581412			0.290706	+	0.956812i	$0.406110\pi$
$212$	425.785	+	245.827i	0.137939	+	0.0796390i
$213$	573.132	−	330.898i	0.184368	−	0.106445i
$214$	195.501	+	338.618i	0.0624495	+	0.108166i
$215$		0			0
$216$	−8464.06			−2.66623
$217$	−996.006	+	935.625i	−0.311582	+	0.292693i
$218$			431.561i			0.134078i
$219$	1004.40	−	1739.67i	0.309914	−	0.536787i
$220$		0			0
$221$	−865.091	−	1498.38i	−0.263314	−	0.456073i
$222$	−6789.85	−	3920.12i	−2.05272	−	1.18514i
$223$			5258.44i			1.57906i	0.613709	+	0.789532i	$0.289677\pi$
$223$			5258.44i			1.57906i	−0.613709	+	0.789532i	$0.710323\pi$
$224$	−3874.23	−	4124.26i	−1.15562	−	1.23020i
$225$		0			0
$226$	−1859.26	+	3220.33i	−0.547239	+	0.947846i
$227$	5809.18	−	3353.93i	1.69854	−	0.980652i	0.751391	−	0.659857i	$-0.229383\pi$
$227$	5809.18	−	3353.93i	1.69854	−	0.980652i	0.947149	−	0.320795i	$-0.103950\pi$
$228$	4246.80	−	2451.89i	1.23356	−	0.712195i
$229$	600.126	−	1039.45i	0.173177	−	0.299951i	−0.766352	−	0.642421i	$-0.777930\pi$
$229$	600.126	−	1039.45i	0.173177	−	0.299951i	0.939529	+	0.342470i	$0.111264\pi$
$230$		0			0
$231$	1487.76	−	4930.69i	0.423756	−	1.40440i
$232$		−	2861.32i		−	0.809719i
$233$	−5500.49	−	3175.71i	−1.54656	−	0.892909i	−0.998400	−	0.0565373i	$-0.981994\pi$
$233$	−5500.49	−	3175.71i	−1.54656	−	0.892909i	−0.548163	−	0.836372i	$-0.684673\pi$
$234$	330.637	+	572.680i	0.0923692	+	0.159988i
$235$		0			0
$236$	−3592.34	+	6222.11i	−0.990853	+	1.71621i
$237$			4547.59i			1.24640i
$238$	877.343	+	3737.76i	0.238948	+	1.01800i
$239$	3003.73			0.812951			0.406475	−	0.913662i	$-0.366758\pi$
$239$	3003.73			0.812951			0.406475	+	0.913662i	$0.366758\pi$
$240$		0			0
$241$	−2846.16	−	4929.70i	−0.760736	−	1.31763i	−0.942472	−	0.334286i	$-0.891505\pi$
$241$	−2846.16	−	4929.70i	−0.760736	−	1.31763i	0.181736	−	0.983347i	$-0.441828\pi$
$242$	−8478.03	+	4894.79i	−2.25202	+	1.30020i
$243$	−707.789	−	408.642i	−0.186850	−	0.107878i
$244$	−12068.1			−3.16631
$245$		0			0
$246$	7456.89			1.93266
$247$	−1970.38	−	1137.60i	−0.507579	−	0.293051i
$248$	−3683.50	+	2126.67i	−0.943155	+	0.544531i
$249$	727.077	+	1259.33i	0.185047	+	0.320510i
$250$		0			0
$251$	6973.37			1.75361			0.876803	−	0.480850i	$-0.159672\pi$
$251$	6973.37			1.75361			0.876803	+	0.480850i	$0.159672\pi$
$252$	−236.251	−	1006.50i	−0.0590571	−	0.251602i
$253$		−	3033.12i		−	0.753719i
$254$	4895.72	−	8479.64i	1.20939	−	2.09472i
$255$		0			0
$256$	2437.31	+	4221.54i	0.595045	+	1.03065i
$257$	2677.59	+	1545.90i	0.649896	+	0.375217i	0.788416	−	0.615142i	$-0.210901\pi$
$257$	2677.59	+	1545.90i	0.649896	+	0.375217i	−0.138521	+	0.990360i	$0.544235\pi$
$258$		−	9343.48i		−	2.25465i
$259$	1642.87	−	5444.73i	0.394143	−	1.30625i
$260$		0			0
$261$	72.6221	−	125.785i	0.0172230	−	0.0298311i
$262$	−828.779	+	478.496i	−0.195428	+	0.112830i
$263$	1718.91	−	992.413i	0.403013	−	0.232680i	−0.284770	−	0.958596i	$-0.591917\pi$
$263$	1718.91	−	992.413i	0.403013	−	0.232680i	0.687783	+	0.725916i	$0.258584\pi$
$264$	8015.06	−	13882.5i	1.86853	−	3.23640i
$265$		0			0
$266$	3456.73	+	3679.81i	0.796788	+	0.848210i
$267$		−	2398.21i		−	0.549694i
$268$	−8444.25	−	4875.29i	−1.92468	−	1.11121i
$269$	3090.37	+	5352.68i	0.700458	+	1.21323i	0.968306	+	0.249767i	$0.0803540\pi$
$269$	3090.37	+	5352.68i	0.700458	+	1.21323i	−0.267848	+	0.963461i	$0.586313\pi$
$270$		0			0
$271$	3059.49	−	5299.20i	0.685797	−	1.18784i	−0.287388	−	0.957814i	$-0.592787\pi$
$271$	3059.49	−	5299.20i	0.685797	−	1.18784i	0.973186	−	0.230022i	$-0.0738797\pi$
$272$			5869.71i			1.30847i
$273$	2876.39	−	2702.01i	0.637682	−	0.599023i
$274$	−4619.50			−1.01852
$275$		0			0
$276$	2504.67	+	4338.22i	0.546245	+	0.946125i
$277$	−2853.41	+	1647.42i	−0.618935	+	0.357342i	−0.776454	−	0.630174i	$-0.782984\pi$
$277$	−2853.41	+	1647.42i	−0.618935	+	0.357342i	0.157519	+	0.987516i	$0.449650\pi$
$278$	10523.7	+	6075.89i	2.27040	+	1.31082i
$279$	−215.905			−0.0463294
$280$		0			0
$281$	−4604.53			−0.977521			−0.488760	−	0.872418i	$-0.662551\pi$
$281$	−4604.53			−0.977521			−0.488760	+	0.872418i	$0.662551\pi$
$282$	−9783.09	−	5648.27i	−2.06587	−	1.19273i
$283$	−1056.16	+	609.776i	−0.221846	+	0.128083i	−0.606805	−	0.794851i	$-0.707549\pi$
$283$	−1056.16	+	609.776i	−0.221846	+	0.128083i	0.384959	+	0.922934i	$0.374216\pi$
$284$	1286.61	+	2228.47i	0.268825	+	0.465618i
$285$		0			0
$286$	−12808.6			−2.64821
$287$	1236.05	+	5265.99i	0.254223	+	1.08307i
$288$		−	894.019i		−	0.182919i
$289$	−1662.94	+	2880.30i	−0.338478	+	0.586260i
$290$		0			0
$291$	1167.52	+	2022.21i	0.235194	+	0.407368i
$292$	6764.27	+	3905.35i	1.35565	+	0.782683i
$293$		−	8434.81i		−	1.68180i	−0.541192	−	0.840899i	$-0.682027\pi$
$293$		−	8434.81i		−	1.68180i	0.541192	−	0.840899i	$-0.317973\pi$
$294$	−7842.77	+	3896.45i	−1.55578	+	0.772944i
$295$		0			0
$296$	8850.66	−	15329.8i	1.73795	−	3.01022i
$297$	7207.13	−	4161.04i	1.40808	−	0.812956i
$298$	−10829.4	+	6252.35i	−2.10513	+	1.21540i
$299$	1162.09	−	2012.79i	0.224767	−	0.389307i
$300$		0			0
$301$	6598.28	−	1548.77i	1.26352	−	0.296577i
$302$		−	6423.23i		−	1.22389i
$303$	−329.654	−	190.326i	−0.0625021	−	0.0360856i
$304$	3859.35	+	6684.58i	0.728121	+	1.26114i
$305$		0			0
$306$	−303.298	+	525.327i	−0.0566613	+	0.0981403i
$307$		−	846.546i		−	0.157378i	−0.996899	−	0.0786888i	$-0.974927\pi$
$307$		−	846.546i		−	0.157378i	0.996899	−	0.0786888i	$-0.0250734\pi$
$308$	19171.7	+	5784.78i	3.54678	+	1.07019i
$309$	−5582.50			−1.02776
$310$		0			0
$311$	−980.793	−	1698.78i	−0.178829	−	0.309740i	0.762651	−	0.646810i	$-0.223897\pi$
$311$	−980.793	−	1698.78i	−0.178829	−	0.309740i	−0.941480	+	0.337070i	$0.890564\pi$
$312$	10637.7	−	6141.66i	1.93025	−	1.11443i
$313$	−5655.11	−	3264.98i	−1.02123	−	0.589609i	−0.106772	−	0.994284i	$-0.534052\pi$
$313$	−5655.11	−	3264.98i	−1.02123	−	0.589609i	−0.914461	+	0.404674i	$0.867385\pi$
$314$	−7454.13			−1.33968
$315$		0			0
$316$	−17682.1			−3.14778
$317$	−6660.19	−	3845.26i	−1.18004	−	0.681298i	−0.224019	−	0.974585i	$-0.571918\pi$
$317$	−6660.19	−	3845.26i	−1.18004	−	0.681298i	−0.956025	+	0.293287i	$0.905251\pi$
$318$	569.828	−	328.990i	0.100485	−	0.0580153i
$319$	1406.66	+	2436.40i	0.246890	+	0.427625i
$320$		0			0
$321$	368.678			0.0641047
$322$	−3759.03	+	3531.14i	−0.650567	+	0.611127i
$323$		−	2087.07i		−	0.359528i
$324$	−6118.54	+	10597.6i	−1.04913	+	1.81715i
$325$		0			0
$326$	2239.72	+	3879.30i	0.380511	+	0.659064i
$327$	352.403	+	203.460i	0.0595962	+	0.0344079i
$328$			16835.8i			2.83415i
$329$	2367.11	−	7844.98i	0.396666	−	1.31461i
$330$		0			0
$331$	−3263.13	+	5651.92i	−0.541867	+	0.938542i	0.456929	+	0.889503i	$0.348949\pi$
$331$	−3263.13	+	5651.92i	−0.541867	+	0.938542i	−0.998797	+	0.0490389i	$0.984384\pi$
$332$	−4896.59	+	2827.05i	−0.809444	+	0.467332i
$333$	778.161	−	449.271i	0.128057	−	0.0739337i
$334$	−3504.04	+	6069.18i	−0.574050	+	0.994283i
$335$		0			0
$336$	−13034.3	+	3059.45i	−2.11630	+	0.496746i
$337$		−	1217.56i		−	0.196809i	−0.995146	−	0.0984047i	$-0.968626\pi$
$337$		−	1217.56i		−	0.196809i	0.995146	−	0.0984047i	$-0.0313740\pi$
$338$	1400.89	+	808.802i	0.225438	+	0.130157i
$339$	1753.10	+	3036.46i	0.280872	+	0.486484i
$340$		0			0
$341$	2090.99	−	3621.70i	0.332063	−	0.575150i
$342$			797.675i			0.126121i
$343$	−4051.65	−	4892.62i	−0.637809	−	0.770194i
$344$	21095.3			3.30634
$345$		0			0
$346$	6792.01	+	11764.1i	1.05532	+	1.82787i
$347$	7299.98	−	4214.64i	1.12935	−	0.652029i	0.185576	−	0.982630i	$-0.440585\pi$
$347$	7299.98	−	4214.64i	1.12935	−	0.652029i	0.943771	+	0.330601i	$0.107251\pi$
$348$	−4023.84	−	2323.16i	−0.619829	−	0.357858i
$349$	135.644			0.0208047			0.0104023	−	0.999946i	$-0.496689\pi$
$349$	135.644			0.0208047			0.0104023	+	0.999946i	$0.496689\pi$
$350$		0			0
$351$	6376.91			0.969727
$352$	14996.7	+	8658.38i	2.27082	+	1.31106i
$353$	2012.77	−	1162.07i	0.303481	−	0.175215i	−0.340525	−	0.940236i	$-0.610605\pi$
$353$	2012.77	−	1162.07i	0.303481	−	0.175215i	0.644005	+	0.765021i	$0.277271\pi$
$354$	4807.62	+	8327.04i	0.721814	+	1.25022i
$355$		0			0
$356$	9324.82			1.38824
$357$	3465.80	+	1045.76i	0.513809	+	0.155035i
$358$			7027.22i			1.03743i
$359$	−2663.65	+	4613.58i	−0.391594	+	0.678260i	−0.992660	−	0.120939i	$-0.961409\pi$
$359$	−2663.65	+	4613.58i	−0.391594	+	0.678260i	0.601066	+	0.799199i	$0.294743\pi$
$360$		0			0
$361$	2057.25	+	3563.26i	0.299934	+	0.519501i
$362$	12828.1	+	7406.33i	1.86252	+	1.07533i
$363$			9230.64i			1.33466i
$364$	10506.1	+	11184.1i	1.51282	+	1.61046i
$365$		0			0
$366$	−8075.34	+	13986.9i	−1.15329	+	1.99756i
$367$	6314.73	−	3645.81i	0.898164	−	0.518555i	0.0215599	−	0.999768i	$-0.493137\pi$
$367$	6314.73	−	3645.81i	0.898164	−	0.518555i	0.876604	+	0.481212i	$0.159803\pi$
$368$	−6828.49	+	3942.43i	−0.967282	+	0.558460i
$369$	−427.304	+	740.112i	−0.0602834	+	0.104414i
$370$		0			0
$371$	326.784	+	347.874i	0.0457299	+	0.0486811i
$372$			6906.75i			0.962629i
$373$	1438.90	+	830.751i	0.199742	+	0.115321i	0.596535	−	0.802587i	$-0.296544\pi$
$373$	1438.90	+	830.751i	0.199742	+	0.115321i	−0.396793	+	0.917908i	$0.629877\pi$
$374$	−5874.74	−	10175.4i	−0.812235	−	1.40683i
$375$		0			0
$376$	12752.4	−	22087.8i	1.74908	−	3.02950i
$377$			2155.75i			0.294500i
$378$	−13547.4	−	4087.73i	−1.84339	−	0.556217i
$379$	−409.820			−0.0555436			−0.0277718	−	0.999614i	$-0.508841\pi$
$379$	−409.820			−0.0555436			−0.0277718	+	0.999614i	$0.508841\pi$
$380$		0			0
$381$	−4616.19	−	7995.48i	−0.620721	−	1.07512i
$382$	−18942.9	+	10936.7i	−2.53718	+	1.46484i
$383$	9475.33	+	5470.58i	1.26414	+	0.729853i	0.973873	−	0.227092i	$-0.0729217\pi$
$383$	9475.33	+	5470.58i	1.26414	+	0.729853i	0.290269	+	0.956945i	$0.406255\pi$
$384$	1494.64			0.198628
$385$		0			0
$386$	721.142			0.0950911
$387$	927.360	+	535.411i	0.121810	+	0.0703269i
$388$	−7862.83	+	4539.60i	−1.02880	+	0.593978i
$389$	−3118.40	−	5401.23i	−0.406450	−	0.703992i	0.588039	−	0.808833i	$-0.299900\pi$
$389$	−3118.40	−	5401.23i	−0.406450	−	0.703992i	−0.994489	+	0.104840i	$0.966567\pi$
$390$		0			0
$391$	2132.00			0.275754
$392$	−8797.21	−	17707.0i	−1.13349	−	2.28148i
$393$			902.351i			0.115821i
$394$	3834.43	−	6641.43i	0.490294	−	0.849215i
$395$		0			0
$396$	1581.95	+	2740.02i	0.200747	+	0.347705i
$397$	−9914.10	−	5723.91i	−1.25334	−	0.723614i	−0.281565	−	0.959542i	$-0.590854\pi$
$397$	−9914.10	−	5723.91i	−1.25334	−	0.723614i	−0.971771	+	0.235928i	$0.924187\pi$
$398$		−	18783.0i		−	2.36559i
$399$	4634.54	−	1087.84i	0.581496	−	0.136491i
$400$		0			0
$401$	4616.74	−	7996.42i	0.574935	−	0.995816i	−0.421114	−	0.907008i	$-0.638361\pi$
$401$	4616.74	−	7996.42i	0.574935	−	0.995816i	0.996049	−	0.0888085i	$-0.0283059\pi$
$402$	−11300.9	+	6524.59i	−1.40209	+	0.809495i
$403$	2775.18	−	1602.25i	0.343032	−	0.198049i
$404$	740.032	−	1281.77i	0.0911336	−	0.157848i
$405$		0			0
$406$	1381.88	−	4579.76i	0.168920	−	0.559826i
$407$			17404.4i			2.11966i
$408$	9758.08	+	5633.83i	1.18406	+	0.683618i
$409$	−2217.57	−	3840.95i	−0.268097	−	0.464358i	0.700273	−	0.713875i	$-0.253062\pi$
$409$	−2217.57	−	3840.95i	−0.268097	−	0.464358i	−0.968370	+	0.249517i	$0.919728\pi$
$410$		0			0
$411$	−2177.87	+	3772.19i	−0.261379	+	0.452721i
$412$		−	21706.1i		−	2.59559i
$413$	−5083.57	+	4775.39i	−0.605681	+	0.568962i
$414$	−814.847			−0.0967332
$415$		0			0
$416$	6634.61	+	11491.5i	0.781943	+	1.35437i
$417$	9922.88	−	5728.98i	1.16529	−	0.672780i
$418$	−13380.6	−	7725.31i	−1.56571	−	0.903965i
$419$	6434.23			0.750197			0.375099	−	0.926985i	$-0.377609\pi$
$419$	6434.23			0.750197			0.375099	+	0.926985i	$0.377609\pi$
$420$		0			0
$421$	−9442.51			−1.09311			−0.546556	−	0.837423i	$-0.684061\pi$
$421$	−9442.51			−1.09311			−0.546556	+	0.837423i	$0.684061\pi$
$422$	8030.53	+	4636.43i	0.926351	+	0.534829i
$423$	1121.21	−	647.328i	0.128877	−	0.0744070i
$424$	742.778	+	1286.53i	0.0850767	+	0.147357i
$425$		0			0
$426$	3443.74			0.391666
$427$	−11216.0	−	3384.27i	−1.27115	−	0.383551i
$428$			1433.51i			0.161895i
$429$	−6038.63	+	10459.2i	−0.679598	+	1.17710i
$430$		0			0
$431$	1120.60	+	1940.94i	0.125238	+	0.216918i	0.921826	−	0.387604i	$-0.126697\pi$
$431$	1120.60	+	1940.94i	0.125238	+	0.216918i	−0.796588	+	0.604522i	$0.793364\pi$
$432$	−18735.5	−	10817.0i	−2.08661	−	1.20470i
$433$		−	14181.1i		−	1.57391i	−0.617012	−	0.786954i	$-0.711657\pi$
$433$		−	14181.1i		−	1.57391i	0.617012	−	0.786954i	$-0.288343\pi$
$434$	−6922.79	+	1624.94i	−0.765679	+	0.179723i
$435$		0			0
$436$	−791.101	+	1370.23i	−0.0868965	+	0.150509i
$437$	2427.98	−	1401.79i	0.265780	−	0.153448i
$438$	9052.61	−	5226.53i	0.987558	−	0.570167i
$439$	4346.32	−	7528.05i	0.472525	−	0.818438i	−0.526980	−	0.849878i	$-0.676676\pi$
$439$	4346.32	−	7528.05i	0.472525	−	0.818438i	0.999506	+	0.0314396i	$0.0100092\pi$
$440$		0			0
$441$	62.6856	−	1001.69i	0.00676877	−	0.108162i
$442$		−	9003.22i		−	0.968867i
$443$	8135.18	+	4696.85i	0.872492	+	0.503734i	0.868176	−	0.496257i	$-0.165293\pi$
$443$	8135.18	+	4696.85i	0.872492	+	0.503734i	0.00431671	+	0.999991i	$0.498626\pi$
$444$	−14372.1	−	24893.2i	−1.53619	−	2.66076i
$445$		0			0
$446$	−13681.5	+	23697.0i	−1.45255	+	2.51589i
$447$			11790.7i			1.24761i
$448$	−1740.18	−	7413.72i	−0.183517	−	0.781842i
$449$	−9511.86			−0.999761			−0.499880	−	0.866094i	$-0.666623\pi$
$449$	−9511.86			−0.999761			−0.499880	+	0.866094i	$0.666623\pi$
$450$		0			0
$451$	−8276.69	−	14335.7i	−0.864156	−	1.49676i
$452$	−11806.5	+	6816.48i	−1.22861	+	0.709337i
$453$	−5245.08	−	3028.25i	−0.544007	−	0.314083i
$454$	34905.2			3.60833
$455$		0			0
$456$	14817.0			1.52165
$457$	−1184.04	−	683.607i	−0.121197	−	0.0699732i	0.438176	−	0.898889i	$-0.355625\pi$
$457$	−1184.04	−	683.607i	−0.121197	−	0.0699732i	−0.559373	+	0.828916i	$0.688958\pi$
$458$	5408.90	−	3122.83i	0.551837	−	0.318603i
$459$	2924.81	+	5065.93i	0.297426	+	0.515157i
$460$		0			0
$461$	8760.60			0.885080			0.442540	−	0.896749i	$-0.354078\pi$
$461$	8760.60			0.885080			0.442540	+	0.896749i	$0.354078\pi$
$462$	19533.3	−	18349.1i	1.96704	−	1.84779i
$463$			10357.4i			1.03963i	0.854278	+	0.519817i	$0.174000\pi$
$463$			10357.4i			1.03963i	−0.854278	+	0.519817i	$0.826000\pi$
$464$	3656.73	−	6333.64i	0.365861	−	0.633689i
$465$		0			0
$466$	−16525.2	−	28622.5i	−1.64274	−	2.84530i
$467$	−7360.99	−	4249.87i	−0.729392	−	0.421115i	0.0888078	−	0.996049i	$-0.471694\pi$
$467$	−7360.99	−	4249.87i	−0.729392	−	0.421115i	−0.818200	+	0.574934i	$0.805028\pi$
$468$			2424.38i			0.239460i
$469$	−6480.85	−	6899.09i	−0.638076	−	0.679255i
$470$		0			0
$471$	−3514.26	+	6086.88i	−0.343798	+	0.595475i
$472$	−18800.4	+	10854.4i	−1.83339	+	1.05851i
$473$	−17962.6	+	10370.7i	−1.74613	+	1.00813i
$474$	−11832.0	+	20493.6i	−1.14654	+	1.98587i
$475$		0			0
$476$	−4066.15	+	13475.9i	−0.391537	+	1.29762i
$477$			75.4088i			0.00723843i
$478$	13536.2	+	7815.15i	1.29526	+	0.747817i
$479$	−361.486	−	626.113i	−0.0344817	−	0.0597240i	0.848270	−	0.529565i	$-0.177645\pi$
$479$	−361.486	−	626.113i	−0.0344817	−	0.0597240i	−0.882751	+	0.469841i	$0.844311\pi$
$480$		0			0
$481$	−6668.18	+	11549.6i	−0.632106	+	1.09484i
$482$		−	29620.7i		−	2.79914i
$483$	1111.26	+	4734.31i	0.104687	+	0.446001i
$484$	−35890.9			−3.37067
$485$		0			0
$486$	−2126.42	−	3683.07i	−0.198470	−	0.343760i
$487$	−1998.19	+	1153.66i	−0.185927	+	0.107345i	−0.590075	−	0.807349i	$-0.700902\pi$
$487$	−1998.19	+	1153.66i	−0.185927	+	0.107345i	0.404147	+	0.914694i	$0.367568\pi$
$488$	−31579.0	−	18232.1i	−2.92933	−	1.69125i
$489$	4223.67			0.390595
$490$		0			0
$491$	−8668.77			−0.796774			−0.398387	−	0.917217i	$-0.630430\pi$
$491$	−8668.77			−0.796774			−0.398387	+	0.917217i	$0.630430\pi$
$492$	23676.0	+	13669.4i	2.16951	+	1.25257i
$493$	−1712.56	+	988.748i	−0.156450	+	0.0903265i
$494$	−5919.63	−	10253.1i	−0.539143	−	0.933823i
$495$		0			0
$496$	−10871.4			−0.984155
$497$	570.833	+	2431.93i	0.0515198	+	0.219491i
$498$			7566.87i			0.680883i
$499$	9960.86	−	17252.7i	0.893606	−	1.54777i	0.0580860	−	0.998312i	$-0.481500\pi$
$499$	9960.86	−	17252.7i	0.893606	−	1.54777i	0.835520	−	0.549460i	$-0.185166\pi$
$500$		0			0
$501$	3303.97	+	5722.65i	0.294632	+	0.510318i
$502$	31425.3	+	18143.4i	2.79398	+	1.61311i
$503$			17007.8i			1.50763i	0.657084	+	0.753817i	$0.271790\pi$
$503$			17007.8i			1.50763i	−0.657084	+	0.753817i	$0.728210\pi$
$504$	902.395	−	2990.68i	0.0797537	−	0.264316i
$505$		0			0
$506$	7891.62	−	13668.7i	0.693330	−	1.20088i
$507$	1320.90	−	762.622i	0.115707	−	0.0668032i
$508$	31088.3	−	17948.9i	2.71520	−	1.56762i
$509$	−9232.52	+	15991.2i	−0.803977	+	1.39253i	0.113003	+	0.993595i	$0.463953\pi$
$509$	−9232.52	+	15991.2i	−0.803977	+	1.39253i	−0.916980	+	0.398934i	$0.869380\pi$
$510$		0			0
$511$	5191.48	+	5526.52i	0.449428	+	0.478432i
$512$			22928.6i			1.97913i
$513$	6661.71	+	3846.14i	0.573337	+	0.331016i
$514$	8044.31	+	13933.1i	0.690310	+	1.19565i
$515$		0			0
$516$	17127.7	−	29666.0i	1.46125	−	2.53096i
$517$			25076.9i			2.13323i
$518$	21569.7	−	20262.1i	1.82957	−	1.71866i
$519$	12808.4			1.08329
$520$		0			0
$521$	2167.92	+	3754.95i	0.182300	+	0.315753i	0.942663	−	0.333745i	$-0.108312\pi$
$521$	2167.92	+	3754.95i	0.182300	+	0.315753i	−0.760363	+	0.649498i	$0.774979\pi$
$522$	654.539	−	377.898i	0.0548820	−	0.0316861i
$523$	7251.40	+	4186.60i	0.606275	+	0.350033i	0.771506	−	0.636222i	$-0.219504\pi$
$523$	7251.40	+	4186.60i	0.606275	+	0.350033i	−0.165231	+	0.986255i	$0.552837\pi$
$524$	−3508.56			−0.292504
$525$		0			0
$526$	10328.3			0.856150
$527$	2545.71	+	1469.77i	0.210423	+	0.121488i
$528$	35483.3	−	20486.3i	2.92465	−	1.68854i
$529$	−4651.53	−	8056.69i	−0.382307	−	0.662175i
$530$		0			0
$531$	−1101.97			−0.0900591
$532$	4229.77	+	18020.2i	0.344706	+	1.46856i
$533$		−	12684.3i		−	1.03080i
$534$	6239.70	−	10807.5i	0.505652	−	0.875815i
$535$		0			0
$536$	−14730.9	−	25514.7i	−1.18709	−	2.05610i
$537$	5738.28	+	3313.00i	0.461126	+	0.266231i
$538$			32162.2i			2.57735i
$539$	16195.8	+	10752.7i	1.29425	+	0.859278i
$540$		0			0
$541$	−5937.49	+	10284.0i	−0.471853	+	0.817274i	−0.999481	−	0.0322016i	$-0.989748\pi$
$541$	−5937.49	+	10284.0i	−0.471853	+	0.817274i	0.527628	+	0.849475i	$0.323081\pi$
$542$	27575.0	−	15920.5i	2.18533	−	1.26170i
$543$	12095.7	−	6983.46i	0.955942	−	0.551913i
$544$	−6086.02	+	10541.3i	−0.479661	+	0.830798i
$545$		0			0
$546$	19992.5	−	4692.72i	1.56703	−	0.367820i
$547$		−	25018.5i		−	1.95560i	−0.209532	−	0.977802i	$-0.567194\pi$
$547$		−	25018.5i		−	1.95560i	0.209532	−	0.977802i	$-0.432806\pi$
$548$	−14667.2	−	8468.09i	−1.14334	−	0.660107i
$549$	−925.486	−	1602.99i	−0.0719468	−	0.124616i
$550$		0			0
$551$	−1300.21	+	2252.02i	−0.100528	+	0.174119i
$552$			15136.0i			1.16708i
$553$	−16433.7	−	4958.62i	−1.26371	−	0.381306i
$554$	−17145.1			−1.31485
$555$		0			0
$556$	22275.6	+	38582.5i	1.69909	+	2.94292i
$557$	3422.69	−	1976.09i	0.260366	−	0.150323i	−0.364135	−	0.931346i	$-0.618635\pi$
$557$	3422.69	−	1976.09i	0.260366	−	0.150323i	0.624502	+	0.781023i	$0.285302\pi$
$558$	−972.969	−	561.744i	−0.0738155	−	0.0426174i
$559$	−15893.4			−1.20254
$560$		0			0
$561$	−11078.6			−0.833762
$562$	−20750.2	−	11980.1i	−1.55746	−	0.899201i
$563$	276.666	−	159.733i	0.0207106	−	0.0119573i	−0.489609	−	0.871942i	$-0.662860\pi$
$563$	276.666	−	159.733i	0.0207106	−	0.0119573i	0.510320	+	0.859985i	$0.329527\pi$
$564$	−20707.9	−	35867.1i	−1.54603	−	2.67780i
$565$		0			0
$566$	−6346.09			−0.471283
$567$	−8658.44	+	8133.53i	−0.641305	+	0.602427i
$568$			7775.10i			0.574359i
$569$	−12125.5	+	21001.9i	−0.893366	+	1.54736i	−0.0575529	+	0.998342i	$0.518330\pi$
$569$	−12125.5	+	21001.9i	−0.893366	+	1.54736i	−0.835813	+	0.549014i	$0.815004\pi$
$570$		0			0
$571$	1413.73	+	2448.66i	0.103613	+	0.179463i	0.913171	−	0.407578i	$-0.133626\pi$
$571$	1413.73	+	2448.66i	0.103613	+	0.179463i	−0.809558	+	0.587040i	$0.800293\pi$
$572$	−40667.9	−	23479.6i	−2.97274	−	1.71632i
$573$			20624.5i			1.50367i
$574$	−8130.88	+	26947.0i	−0.591248	+	1.95949i
$575$		0			0
$576$	601.580	−	1041.97i	0.0435171	−	0.0753738i
$577$	−15813.8	+	9130.11i	−1.14097	+	0.658738i	−0.946670	−	0.322205i	$-0.895576\pi$
$577$	−15813.8	+	9130.11i	−1.14097	+	0.658738i	−0.194297	+	0.980943i	$0.562243\pi$
$578$	−14988.0	+	8653.31i	−1.07858	+	0.622717i
$579$	339.984	−	588.869i	0.0244028	−	0.0422669i
$580$		0			0
$581$	−5343.65	+	1254.28i	−0.381570	+	0.0895636i
$582$			12150.7i			0.865400i
$583$	−1264.95	−	730.318i	−0.0898607	−	0.0518811i
$584$	11800.2	+	20438.6i	0.836123	+	1.44821i
$585$		0			0
$586$	21945.8	−	38011.2i	1.54705	−	2.67957i
$587$		−	7749.13i		−	0.544873i	−0.962174	−	0.272437i	$-0.912170\pi$
$587$		−	7749.13i		−	0.544873i	0.962174	−	0.272437i	$-0.0878295\pi$
$588$	−32043.8	−	2005.30i	−2.24739	−	0.140641i
$589$	3865.50			0.270416
$590$		0			0
$591$	−3615.50	−	6262.23i	−0.251644	−	0.435861i
$592$	39182.6	−	22622.1i	2.72026	−	1.57054i
$593$	549.634	+	317.332i	0.0380620	+	0.0219751i	0.518910	−	0.854829i	$-0.326338\pi$
$593$	549.634	+	317.332i	0.0380620	+	0.0219751i	−0.480848	+	0.876804i	$0.659671\pi$
$594$	43304.9			2.99128
$595$		0			0
$596$	−45845.1			−3.15082
$597$	−15337.8	−	8855.28i	−1.05148	−	0.607073i
$598$	10473.8	−	6047.07i	0.716232	−	0.413517i
$599$	4318.74	+	7480.27i	0.294589	+	0.510243i	0.974889	−	0.222690i	$-0.0714839\pi$
$599$	4318.74	+	7480.27i	0.294589	+	0.510243i	−0.680300	+	0.732934i	$0.738151\pi$
$600$		0			0
$601$	−19947.7			−1.35388			−0.676941	−	0.736037i	$-0.736695\pi$
$601$	−19947.7			−1.35388			−0.676941	+	0.736037i	$0.736695\pi$
$602$	33764.6	+	10188.0i	2.28595	+	0.689752i
$603$		−	1495.52i		−	0.100999i
$604$	11774.5	−	20394.1i	0.793210	−	1.37388i
$605$		0			0
$606$	−990.385	−	1715.40i	−0.0663888	−	0.114989i
$607$	1071.42	+	618.585i	0.0716435	+	0.0413634i	0.535394	−	0.844603i	$-0.320163\pi$
$607$	1071.42	+	618.585i	0.0716435	+	0.0413634i	−0.463750	+	0.885966i	$0.653497\pi$
$608$			16006.3i			1.06766i
$609$	−3088.24	−	3287.55i	−0.205488	−	0.218749i
$610$		0			0
$611$	−9607.78	+	16641.2i	−0.636152	+	1.10185i
$612$	−1925.97	+	1111.96i	−0.127210	+	0.0734450i
$613$	15179.4	−	8763.81i	1.00014	−	0.577434i	0.0918535	−	0.995773i	$-0.470721\pi$
$613$	15179.4	−	8763.81i	1.00014	−	0.577434i	0.908291	+	0.418339i	$0.137388\pi$
$614$	2202.55	−	3814.94i	0.144768	−	0.250746i
$615$		0			0
$616$	41427.7	+	44101.3i	2.70969	+	2.88457i
$617$		−	18508.3i		−	1.20764i	−0.797120	−	0.603821i	$-0.793644\pi$
$617$		−	18508.3i		−	1.20764i	0.797120	−	0.603821i	$-0.206356\pi$
$618$	−25157.4	−	14524.6i	−1.63750	−	0.945414i
$619$	−3014.92	−	5221.99i	−0.195767	−	0.339079i	0.751385	−	0.659865i	$-0.229386\pi$
$619$	−3014.92	−	5221.99i	−0.195767	−	0.339079i	−0.947152	+	0.320786i	$0.896053\pi$
$620$		0			0
$621$	−3928.94	+	6805.12i	−0.253886	+	0.439743i
$622$		−	10207.4i		−	0.658003i
$623$	8666.43	+	2614.97i	0.557325	+	0.168165i
$624$	31395.8			2.01417
$625$		0			0
$626$	−16989.7	−	29427.1i	−1.08474	−	1.87882i
$627$	−12616.6	+	7284.22i	−0.803605	+	0.463962i
$628$	−23667.2	−	13664.3i	−1.50386	−	0.868256i
$629$	−12233.6			−0.775495
$630$		0			0
$631$	5728.80			0.361426			0.180713	−	0.983536i	$-0.442160\pi$
$631$	5728.80			0.361426			0.180713	+	0.983536i	$0.442160\pi$
$632$	−46269.5	−	26713.7i	−2.91218	−	1.68135i
$633$	7572.02	−	4371.71i	0.475451	−	0.274502i
$634$	−20009.3	−	34657.1i	−1.25342	−	2.17099i
$635$		0			0
$636$	2412.31			0.150400
$637$	6627.91	+	13340.7i	0.412256	+	0.829790i
$638$			14639.4i			0.908434i
$639$	−197.337	+	341.798i	−0.0122168	+	0.0211601i
$640$		0			0
$641$	937.912	+	1624.51i	0.0577930	+	0.100100i	0.893474	−	0.449114i	$-0.148260\pi$
$641$	937.912	+	1624.51i	0.0577930	+	0.100100i	−0.835681	+	0.549214i	$0.814927\pi$
$642$	1661.44	+	959.231i	0.102137	+	0.0589686i
$643$		−	20619.9i		−	1.26465i	−0.774703	−	0.632325i	$-0.782101\pi$
$643$		−	20619.9i		−	1.26465i	0.774703	−	0.632325i	$-0.217899\pi$
$644$	−18408.1	+	4320.82i	−1.12637	+	0.264386i
$645$		0			0
$646$	5430.16	−	9405.31i	0.330723	−	0.572828i
$647$	9982.80	−	5763.57i	0.606591	−	0.350216i	−0.165039	−	0.986287i	$-0.552775\pi$
$647$	9982.80	−	5763.57i	0.606591	−	0.350216i	0.771630	+	0.636072i	$0.219442\pi$
$648$	−32021.2	+	18487.5i	−1.94122	+	1.12077i
$649$	10672.3	−	18485.0i	0.645494	−	1.11803i
$650$		0			0
$651$	−1936.87	+	6419.09i	−0.116608	+	0.386458i
$652$			16422.6i			0.986443i
$653$	3911.15	+	2258.11i	0.234388	+	0.135324i	0.612595	−	0.790397i	$-0.290126\pi$
$653$	3911.15	+	2258.11i	0.234388	+	0.135324i	−0.378207	+	0.925721i	$0.623459\pi$
$654$	1058.73	+	1833.77i	0.0633022	+	0.109643i
$655$		0			0
$656$	−21516.0	+	37266.7i	−1.28057	+	2.21802i
$657$			1197.99i			0.0711384i
$658$	31078.5	−	29194.4i	1.84129	−	1.72966i
$659$	27663.5			1.63523			0.817615	−	0.575766i	$-0.195296\pi$
$659$	27663.5			1.63523			0.817615	+	0.575766i	$0.195296\pi$
$660$		0			0
$661$	15755.4	+	27289.2i	0.927103	+	1.60579i	0.788144	+	0.615491i	$0.211042\pi$
$661$	15755.4	+	27289.2i	0.927103	+	1.60579i	0.138959	+	0.990298i	$0.455624\pi$
$662$	−29410.4	+	16980.1i	−1.72669	+	0.996905i
$663$	−7351.83	−	4244.58i	−0.430651	−	0.248636i
$664$	−17084.1			−0.998482
$665$		0			0
$666$	4675.68			0.272040
$667$	−2300.51	−	1328.20i	−0.133547	−	0.0771035i
$668$	−22251.0	+	12846.6i	−1.28880	+	0.744089i
$669$	12900.3	+	22344.0i	0.745523	+	1.29128i
$670$		0			0
$671$	35852.5			2.06270
$672$	−26580.1	−	8020.18i	−1.52582	−	0.460395i
$673$		−	9072.58i		−	0.519647i	−0.965656	−	0.259823i	$-0.916336\pi$
$673$		−	9072.58i		−	0.519647i	0.965656	−	0.259823i	$-0.0836643\pi$
$674$	3167.86	−	5486.90i	0.181041	−	0.313572i
$675$		0			0
$676$	2965.26	+	5135.97i	0.168710	+	0.292215i
$677$	−21648.6	−	12498.9i	−1.22899	−	0.709557i	−0.262170	−	0.965022i	$-0.584438\pi$
$677$	−21648.6	−	12498.9i	−1.22899	−	0.709557i	−0.966818	+	0.255465i	$0.917771\pi$
$678$			18245.0i			1.03347i
$679$	−8580.71	+	2014.10i	−0.484974	+	0.113835i
$680$		0			0
$681$	16456.1	−	28502.8i	0.925990	−	1.60386i
$682$	18846.0	−	10880.7i	1.05814	−	0.610916i
$683$	−11485.0	+	6630.90i	−0.643431	+	0.371485i	−0.785935	−	0.618309i	$-0.787818\pi$
$683$	−11485.0	+	6630.90i	−0.643431	+	0.371485i	0.142504	+	0.989794i	$0.454485\pi$
$684$	−1462.23	+	2532.66i	−0.0817395	+	0.141577i
$685$		0			0
$686$	−5528.98	−	32590.1i	−0.307722	−	1.81384i
$687$		−	5889.06i		−	0.327047i
$688$	46695.2	+	26959.5i	2.58755	+	1.49392i
$689$	−559.617	−	969.284i	−0.0309430	−	0.0535948i
$690$		0			0
$691$	12321.8	−	21341.9i	0.678353	−	1.17494i	−0.297123	−	0.954839i	$-0.596027\pi$
$691$	12321.8	−	21341.9i	0.678353	−	1.17494i	0.975477	−	0.220103i	$-0.0706395\pi$
$692$			49802.2i			2.73583i
$693$	701.867	+	2990.18i	0.0384729	+	0.163907i
$694$	43862.8			2.39915
$695$		0			0
$696$	−7019.55	−	12158.2i	−0.382292	−	0.662150i
$697$	10076.6	−	5817.73i	0.547602	−	0.316158i
$698$	611.274	+	352.919i	0.0331476	+	0.0191378i
$699$	−31163.4			−1.68628
$700$		0			0
$701$	20723.2			1.11656			0.558278	−	0.829654i	$-0.311462\pi$
$701$	20723.2			1.11656			0.558278	+	0.829654i	$0.311462\pi$
$702$	28737.3	+	16591.5i	1.54504	+	0.892032i
$703$	−13932.0	+	8043.63i	−0.747446	+	0.431538i
$704$	11652.3	+	20182.4i	0.623813	+	1.08048i
$705$		0			0
$706$	12094.0			0.644705
$707$	1047.23	−	983.744i	0.0557075	−	0.0523303i
$708$			35251.7i			1.87124i
$709$	12967.9	−	22461.0i	0.686910	−	1.18976i	−0.285923	−	0.958253i	$-0.592300\pi$
$709$	12967.9	−	22461.0i	0.686910	−	1.18976i	0.972833	−	0.231510i	$-0.0743665\pi$
$710$		0			0
$711$	−1356.02	−	2348.70i	−0.0715257	−	0.123886i
$712$	24400.6	+	14087.7i	1.28434	+	0.741515i
$713$			3948.72i			0.207406i
$714$	12897.7	+	13730.0i	0.676027	+	0.719655i
$715$		0			0
$716$	−12881.7	+	22311.8i	−0.672363	+	1.16457i
$717$	12763.4	−	7368.93i	0.664793	−	0.383818i
$718$	−24007.3	+	13860.6i	−1.24784	+	0.720438i
$719$	−6826.85	+	11824.4i	−0.354101	+	0.613320i	−0.986964	−	0.160943i	$-0.948546\pi$
$719$	−6826.85	+	11824.4i	−0.354101	+	0.613320i	0.632863	+	0.774264i	$0.281880\pi$
$720$		0			0
$721$	6087.07	−	20173.5i	0.314416	−	1.04203i
$722$			21410.3i			1.10361i
$723$	−24187.6	−	13964.7i	−1.24419	−	0.718332i
$724$	27153.3	+	47031.0i	1.39385	+	2.41422i
$725$		0			0
$726$	−24016.4	+	41597.6i	−1.22773	+	2.12649i
$727$		−	17709.4i		−	0.903448i	−0.892158	−	0.451724i	$-0.850809\pi$
$727$		−	17709.4i		−	0.903448i	0.892158	−	0.451724i	$-0.149191\pi$
$728$	10595.0	+	45138.1i	0.539391	+	2.29798i
$729$	−21328.7			−1.08361
$730$		0			0
$731$	−7289.61	−	12626.0i	−0.368832	−	0.638835i
$732$	−51279.3	+	29606.1i	−2.58926	+	1.49491i
$733$	−10282.7	−	5936.73i	−0.518146	−	0.299152i	0.218030	−	0.975942i	$-0.430037\pi$
$733$	−10282.7	−	5936.73i	−0.518146	−	0.299152i	−0.736176	+	0.676790i	$0.763370\pi$
$734$	37942.9			1.90803
$735$		0			0
$736$	−16350.8			−0.818886
$737$	25086.7	+	14483.8i	1.25384	+	0.723904i
$738$	−3851.27	+	2223.53i	−0.192096	+	0.110907i
$739$	15651.4	+	27109.0i	0.779087	+	1.34942i	0.932469	+	0.361250i	$0.117650\pi$
$739$	15651.4	+	27109.0i	0.779087	+	1.34942i	−0.153382	+	0.988167i	$0.549017\pi$
$740$		0			0
$741$	−11163.3			−0.553433
$742$	567.542	+	2417.91i	0.0280797	+	0.119629i
$743$		−	10385.8i		−	0.512808i	−0.966570	−	0.256404i	$-0.917462\pi$
$743$		−	10385.8i		−	0.512808i	0.966570	−	0.256404i	$-0.0825378\pi$
$744$	−10434.5	+	18073.1i	−0.514178	+	0.890583i
$745$		0			0
$746$	4322.92	+	7487.51i	0.212163	+	0.367476i
$747$	−751.028	−	433.606i	−0.0367854	−	0.0212380i
$748$		−	43076.4i		−	2.10565i
$749$	−402.000	+	1332.29i	−0.0196112	+	0.0649946i
$750$		0			0
$751$	−8285.63	+	14351.1i	−0.402593	+	0.697311i	−0.994038	−	0.109034i	$-0.965224\pi$
$751$	−8285.63	+	14351.1i	−0.402593	+	0.697311i	0.591445	+	0.806345i	$0.298558\pi$
$752$	56455.8	−	32594.8i	2.73768	−	1.58060i
$753$	29631.0	−	17107.5i	1.43402	−	0.827929i
$754$	−5608.84	+	9714.80i	−0.270905	+	0.469220i
$755$		0			0
$756$	−35520.3	−	37812.7i	−1.70881	−	1.81909i
$757$		−	16463.8i		−	0.790473i	−0.918579	−	0.395236i	$-0.870663\pi$
$757$		−	16463.8i		−	0.790473i	0.918579	−	0.395236i	$-0.129337\pi$
$758$	−1846.84	−	1066.27i	−0.0884964	−	0.0510934i
$759$	−7441.04	−	12888.3i	−0.355853	−	0.616356i
$760$		0			0
$761$	−8210.95	+	14221.8i	−0.391126	+	0.677449i	−0.992598	−	0.121444i	$-0.961248\pi$
$761$	−8210.95	+	14221.8i	−0.391126	+	0.677449i	0.601473	+	0.798893i	$0.294581\pi$
$762$		−	48041.9i		−	2.28395i
$763$	−1119.50	+	1051.63i	−0.0531174	+	0.0498973i
$764$	−80193.0			−3.79749
$765$		0			0
$766$	28466.9	+	49306.0i	1.34275	+	2.32572i
$767$	14164.4	−	8177.83i	0.666815	−	0.384986i
$768$	20713.0	+	11958.7i	0.973200	+	0.561877i
$769$	−17603.4			−0.825479			−0.412739	−	0.910849i	$-0.635428\pi$
$769$	−17603.4			−0.825479			−0.412739	+	0.910849i	$0.635428\pi$
$770$		0			0
$771$	15170.0			0.708605
$772$	2289.66	+	1321.94i	0.106744	+	0.0616290i
$773$	13777.0	−	7954.16i	0.641041	−	0.370105i	−0.143975	−	0.989581i	$-0.545988\pi$
$773$	13777.0	−	7954.16i	0.641041	−	0.370105i	0.785015	+	0.619476i	$0.212655\pi$
$774$	2786.08	+	4825.63i	0.129384	+	0.224100i
$775$		0			0
$776$	−27433.3			−1.26907
$777$	−6376.50	−	27165.9i	−0.294409	−	1.25428i
$778$		−	32454.0i		−	1.49554i
$779$	7650.34	−	13250.8i	0.351864	−	0.609446i
$780$		0			0
$781$	−3822.34	−	6620.48i	−0.175127	−	0.303328i
$782$	9607.79	+	5547.06i	0.439353	+	0.253660i
$783$		−	7288.43i		−	0.332653i
$784$	3156.39	−	50437.9i	0.143786	−	2.29765i
$785$		0			0
$786$	−2347.75	+	4066.42i	−0.106541	+	0.184535i
$787$	−16444.8	+	9494.43i	−0.744847	+	0.430038i	−0.823829	−	0.566838i	$-0.808166\pi$
$787$	−16444.8	+	9494.43i	−0.744847	+	0.430038i	0.0789818	+	0.996876i	$0.474833\pi$
$788$	24349.0	−	14057.9i	1.10076	−	0.635524i
$789$	4869.29	−	8433.86i	0.219710	−	0.380549i
$790$		0			0
$791$	−12884.4	+	3024.28i	−0.579163	+	0.135943i
$792$			9559.87i			0.428908i
$793$	23791.9	+	13736.3i	1.06542	+	0.615119i
$794$	−29785.1	−	51589.2i	−1.33128	−	2.30584i
$795$		0			0
$796$	34431.4	−	59637.0i	1.53315	−	2.65550i
$797$			33731.8i			1.49917i	0.661906	+	0.749586i	$0.269748\pi$
$797$			33731.8i			1.49917i	−0.661906	+	0.749586i	$0.730252\pi$
$798$	23715.7	+	7155.89i	1.05204	+	0.317438i
$799$	−17626.7			−0.780460
$800$		0			0
$801$	715.110	+	1238.61i	0.0315445	+	0.0546367i
$802$	41610.4	−	24023.8i	1.83206	−	1.05774i
$803$	−20095.7	−	11602.2i	−0.883140	−	0.509881i
$804$	−47841.4			−2.09855
$805$		0			0
$806$	16675.0			0.728726
$807$	26263.0	+	15162.9i	1.14560	+	0.661414i
$808$	3872.94	−	2236.04i	0.168626	−	0.0973561i
$809$	13321.8	+	23074.1i	0.578950	+	1.00277i	0.995600	+	0.0937039i	$0.0298707\pi$
$809$	13321.8	+	23074.1i	0.578950	+	1.00277i	−0.416650	+	0.909067i	$0.636796\pi$
$810$		0			0
$811$	15678.2			0.678835			0.339418	−	0.940636i	$-0.389770\pi$
$811$	15678.2			0.678835			0.339418	+	0.940636i	$0.389770\pi$
$812$	12782.8	−	12007.8i	0.552447	−	0.518955i
$813$		−	30022.9i		−	1.29514i
$814$	−45282.9	+	78432.3i	−1.94983	+	3.37721i
$815$		0			0
$816$	14399.9	+	24941.4i	0.617767	+	1.07000i
$817$	−16603.2	−	9585.86i	−0.710982	−	0.410486i
$818$		−	23078.8i		−	0.986469i
$819$	−679.873	+	2253.21i	−0.0290069	+	0.0961336i
$820$		0			0
$821$	5066.92	−	8776.17i	0.215392	−	0.373070i	−0.738002	−	0.674799i	$-0.764230\pi$
$821$	5066.92	−	8776.17i	0.215392	−	0.373070i	0.953394	+	0.301729i	$0.0975637\pi$
$822$	−19629.0	+	11332.8i	−0.832897	+	0.480873i
$823$	−12178.6	+	7031.33i	−0.515820	+	0.297809i	−0.735223	−	0.677826i	$-0.762922\pi$
$823$	−12178.6	+	7031.33i	−0.515820	+	0.297809i	0.219403	+	0.975634i	$0.429589\pi$
$824$	32793.0	−	56799.1i	1.38640	−	2.40132i
$825$		0			0
$826$	−35333.6	+	8293.64i	−1.48839	+	0.349362i
$827$			13697.4i			0.575942i	0.957639	+	0.287971i	$0.0929807\pi$
$827$			13697.4i			0.575942i	−0.957639	+	0.287971i	$0.907019\pi$
$828$	−2587.18	−	1493.71i	−0.108588	−	0.0626933i
$829$	8777.47	+	15203.0i	0.367737	+	0.636940i	0.989211	−	0.146495i	$-0.0467992\pi$
$829$	8777.47	+	15203.0i	0.367737	+	0.636940i	−0.621474	+	0.783435i	$0.713466\pi$
$830$		0			0
$831$	−8083.09	+	14000.3i	−0.337424	+	0.584436i
$832$			17857.6i			0.744110i
$833$	−7558.11	+	11384.1i	−0.314373	+	0.473513i
$834$	59622.9			2.47551
$835$		0			0
$836$	−28322.8	−	49056.5i	−1.17173	−	2.02949i
$837$	−9382.71	+	5417.11i	−0.387472	+	0.223707i
$838$	28995.7	+	16740.7i	1.19527	+	0.690091i
$839$	−1415.03			−0.0582268			−0.0291134	−	0.999576i	$-0.509268\pi$
$839$	−1415.03			−0.0582268			−0.0291134	+	0.999576i	$0.509268\pi$
$840$		0			0
$841$	−21925.1			−0.898975
$842$	−42552.4	−	24567.6i	−1.74163	−	1.00553i
$843$	−19565.4	+	11296.1i	−0.799370	+	0.461517i
$844$	16998.2	+	29441.8i	0.693250	+	1.20074i
$845$		0			0
$846$	6736.90			0.273782
$847$	−33356.8	−	10064.9i	−1.35319	−	0.408306i
$848$			3797.05i			0.153763i
$849$	−2991.88	+	5182.08i	−0.120943	+	0.209480i
$850$		0			0
$851$	−8216.79	−	14231.9i	−0.330985	−	0.573282i
$852$	10934.0	+	6312.77i	0.439664	+	0.253840i
$853$		−	16014.1i		−	0.642804i	−0.946943	−	0.321402i	$-0.895846\pi$
$853$		−	16014.1i		−	0.642804i	0.946943	−	0.321402i	$-0.104154\pi$
$854$	−41739.3	−	44433.0i	−1.67247	−	1.78040i
$855$		0			0
$856$	−2165.71	+	3751.11i	−0.0864746	+	0.149778i
$857$	−37669.9	+	21748.7i	−1.50149	+	0.866886i	−0.501492	+	0.865162i	$0.667215\pi$
$857$	−37669.9	+	21748.7i	−1.50149	+	0.866886i	−0.999999	+	0.00172420i	$0.999451\pi$
$858$	−54425.8	+	31422.8i	−2.16558	+	1.25030i
$859$	12639.3	−	21891.9i	0.502034	−	0.869548i	−0.497963	−	0.867198i	$-0.665919\pi$
$859$	12639.3	−	21891.9i	0.502034	−	0.869548i	0.999997	−	0.00235021i	$-0.000748096\pi$
$860$		0			0
$861$	18171.0	+	19343.7i	0.719242	+	0.765659i
$862$			11662.4i			0.460814i
$863$	13343.5	+	7703.88i	0.526325	+	0.303874i	0.739519	−	0.673136i	$-0.235053\pi$
$863$	13343.5	+	7703.88i	0.526325	+	0.303874i	−0.213194	+	0.977010i	$0.568387\pi$
$864$	−22431.2	−	38851.9i	−0.883245	−	1.52982i
$865$		0			0
$866$	36896.7	−	63906.9i	1.44781	−	2.50767i
$867$			16318.5i			0.639221i
$868$	−24958.9	−	7531.01i	−0.975993	−	0.294492i
$869$	52531.1			2.05063
$870$		0			0
$871$	11098.4	+	19223.0i	0.431752	+	0.747816i
$872$	−4140.21	+	2390.35i	−0.160786	+	0.0928297i
$873$	−1205.98	−	696.274i	−0.0467541	−	0.0269935i
$874$	14588.8			0.564615
$875$		0			0
$876$	38323.3			1.47811
$877$	28395.7	+	16394.3i	1.09334	+	0.631238i	0.934463	−	0.356061i	$-0.115880\pi$
$877$	28395.7	+	16394.3i	1.09334	+	0.631238i	0.158874	+	0.987299i	$0.449214\pi$
$878$	39173.1	−	22616.6i	1.50573	−	0.869333i
$879$	−20692.8	−	35840.9i	−0.794027	−	1.37530i
$880$		0			0
$881$	−30457.9			−1.16476			−0.582379	−	0.812918i	$-0.697878\pi$
$881$	−30457.9			−1.16476			−0.582379	+	0.812918i	$0.697878\pi$
$882$	2888.70	−	4350.99i	0.110281	−	0.166106i
$883$			37997.3i			1.44814i	0.689725	+	0.724071i	$0.257731\pi$
$883$			37997.3i			1.44814i	−0.689725	+	0.724071i	$0.742269\pi$
$884$	16503.9	−	28585.7i	0.627927	−	1.08760i
$885$		0			0
$886$	24440.6	+	42332.4i	0.926749	+	1.60518i
$887$	4.84633	+	2.79803i	0.000183454	+	0.000105917i	0.500092	−	0.865972i	$-0.333300\pi$
$887$	4.84633	+	2.79803i	0.000183454	+	0.000105917i	−0.499908	+	0.866078i	$0.666633\pi$
$888$		−	86851.9i		−	3.28216i
$889$	33926.7	−	7963.41i	1.27994	−	0.300432i
$890$		0			0
$891$	18177.3	−	31484.0i	0.683460	−	1.18379i
$892$	−86878.8	+	50159.5i	−3.26112	+	1.88281i
$893$	−20073.8	+	11589.6i	−0.752231	+	0.434301i
$894$	−30677.3	+	53134.6i	−1.14765	+	1.98779i
$895$		0			0
$896$	−1629.73	+	5401.19i	−0.0607651	+	0.201385i
$897$		−	11403.6i		−	0.424476i
$898$	−42864.9	−	24748.1i	−1.59290	−	0.919659i
$899$	−1831.28	−	3171.87i	−0.0679384	−	0.117673i
$900$		0			0
$901$	513.344	−	889.138i	0.0189811	−	0.0328762i
$902$		−	86137.6i		−	3.17968i
$903$	24237.7	−	22768.3i	0.893221	−	0.839071i
$904$	−41192.6			−1.51554
$905$		0			0
$906$	−15757.9	−	27293.4i	−0.577836	−	1.00084i
$907$	6688.58	−	3861.66i	0.244863	−	0.141372i	−0.372547	−	0.928013i	$-0.621515\pi$
$907$	6688.58	−	3861.66i	0.244863	−	0.141372i	0.617410	+	0.786642i	$0.288182\pi$
$908$	110826.	+	63985.2i	4.05053	+	2.33857i
$909$	227.009			0.00828318
$910$		0			0
$911$	6805.43			0.247502			0.123751	−	0.992313i	$-0.460508\pi$
$911$	6805.43			0.247502			0.123751	+	0.992313i	$0.460508\pi$
$912$	32798.0	+	18936.0i	1.19085	+	0.687535i
$913$	14547.1	−	8398.76i	0.527314	−	0.304445i
$914$	−3557.23	−	6161.30i	−0.128734	−	0.222974i
$915$		0			0
$916$	22898.0			0.825953
$917$	−3260.83	−	983.909i	−0.117429	−	0.0354324i
$918$			30439.3i			1.09438i
$919$	−22590.1	+	39127.2i	−0.810858	+	1.40445i	0.101406	+	0.994845i	$0.467666\pi$
$919$	−22590.1	+	39127.2i	−0.810858	+	1.40445i	−0.912264	+	0.409602i	$0.865667\pi$
$920$		0			0
$921$	−2076.80	−	3597.12i	−0.0743027	−	0.128696i
$922$	39479.4	+	22793.4i	1.41018	+	0.814167i
$923$		−	5857.84i		−	0.208898i
$924$	95655.2	−	22452.6i	3.40566	−	0.799389i
$925$		0			0
$926$	−26948.1	+	46675.4i	−0.956337	+	1.65643i
$927$	2883.20	−	1664.61i	0.102154	−	0.0589785i
$928$	13134.1	−	7582.96i	0.464598	−	0.268236i
$929$	2596.11	−	4496.59i	0.0916852	−	0.158803i	−0.816535	−	0.577296i	$-0.804108\pi$
$929$	2596.11	−	4496.59i	0.0916852	−	0.158803i	0.908220	+	0.418492i	$0.137441\pi$
$930$		0			0
$931$	−1122.31	+	17934.0i	−0.0395081	+	0.631325i
$932$		−	121171.i		−	4.25866i
$933$	−8335.11	−	4812.28i	−0.292475	−	0.168861i
$934$	−22114.7	−	38303.8i	−0.774749	−	1.34191i
$935$		0			0
$936$	−3662.69	+	6343.97i	−0.127905	+	0.221538i
$937$			7107.58i			0.247806i	0.992294	+	0.123903i	$0.0395412\pi$
$937$			7107.58i			0.247806i	−0.992294	+	0.123903i	$0.960459\pi$
$938$	−11255.6	−	47952.5i	−0.391800	−	1.66920i
$939$	−32039.4			−1.11349
$940$		0			0
$941$	21831.5	+	37813.3i	0.756309	+	1.30997i	0.944721	+	0.327876i	$0.106333\pi$
$941$	21831.5	+	37813.3i	0.756309	+	1.30997i	−0.188411	+	0.982090i	$0.560334\pi$
$942$	−31673.9	+	18286.9i	−1.09553	+	0.632505i
$943$	13536.0	+	7815.03i	0.467438	+	0.269875i
$944$	−55487.2			−1.91309
$945$		0			0
$946$	−107930.			−3.70943
$947$	13373.2	+	7721.04i	0.458893	+	0.264942i	0.711579	−	0.702606i	$-0.247980\pi$
$947$	13373.2	+	7721.04i	0.458893	+	0.264942i	−0.252686	+	0.967548i	$0.581314\pi$
$948$	−75134.3	+	43378.8i	−2.57410	+	1.48616i
$949$	−8890.39	−	15398.6i	−0.304104	−	0.526723i
$950$		0			0
$951$	−37733.7			−1.28664
$952$	−30999.0	+	29119.8i	−1.05534	+	0.991363i
$953$			44561.5i			1.51468i	0.653022	+	0.757339i	$0.273501\pi$
$953$			44561.5i			1.51468i	−0.653022	+	0.757339i	$0.726499\pi$
$954$	−196.200	+	339.828i	−0.00665848	+	0.0115328i
$955$		0			0
$956$	28652.1	+	49627.0i	0.969327	+	1.67892i
$957$	11954.3	+	6901.79i	0.403789	+	0.233128i
$958$		−	3762.08i		−	0.126876i
$959$	−11256.8	−	11983.3i	−0.379043	−	0.403505i
$960$		0			0
$961$	12173.3	−	21084.8i	0.408624	−	0.707757i
$962$	−60099.9	+	34698.7i	−2.01424	+	1.16292i
$963$	−190.411	+	109.934i	−0.00637167	+	0.00367869i
$964$	54298.2	−	94047.2i	1.81414	−	3.14218i
$965$		0			0
$966$	−7309.94	+	24226.3i	−0.243472	+	0.806903i
$967$			34733.3i			1.15506i	0.816368	+	0.577532i	$0.195984\pi$
$967$			34733.3i			1.15506i	−0.816368	+	0.577532i	$0.804016\pi$
$968$	−93917.1	−	54223.1i	−3.11840	−	1.80041i
$969$	−5120.12	−	8868.31i	−0.169744	−	0.294005i
$970$		0			0
$971$	8855.15	−	15337.6i	0.292662	−	0.506906i	−0.681776	−	0.731561i	$-0.738792\pi$
$971$	8855.15	−	15337.6i	0.292662	−	0.506906i	0.974438	+	0.224655i	$0.0721255\pi$
$972$		−	15591.9i		−	0.514517i
$973$	9883.08	+	42105.1i	0.325629	+	1.38729i
$974$	−12006.4			−0.394979
$975$		0			0
$976$	−46600.8	−	80715.0i	−1.52834	−	2.64716i
$977$	49846.2	−	28778.7i	1.63226	−	0.942387i	0.648870	−	0.760900i	$-0.275242\pi$
$977$	49846.2	−	28778.7i	1.63226	−	0.942387i	0.983393	−	0.181488i	$-0.0580912\pi$
$978$	19033.9	+	10989.2i	0.622327	+	0.359301i
$979$	−27702.7			−0.904375
$980$		0			0
$981$	−242.675			−0.00789806
$982$	−39065.5	−	22554.5i	−1.26948	−	0.732936i
$983$	−21640.9	+	12494.4i	−0.702175	+	0.405401i	−0.808157	−	0.588967i	$-0.799535\pi$
$983$	−21640.9	+	12494.4i	−0.702175	+	0.405401i	0.105982	+	0.994368i	$0.466202\pi$
$984$	41302.6	+	71538.2i	1.33809	+	2.31764i
$985$		0			0
$986$	−10290.1			−0.332358
$987$	−9187.51	−	39141.8i	−0.296294	−	1.26231i
$988$		−	43405.5i		−	1.39769i
$989$	9792.23	−	16960.6i	0.314838	−	0.545315i
$990$		0			0
$991$	−30786.6	−	53324.0i	−0.986850	−	1.70927i	−0.633407	−	0.773819i	$-0.718344\pi$
$991$	−30786.6	−	53324.0i	−0.986850	−	1.70927i	−0.353443	−	0.935456i	$-0.614989\pi$
$992$	−19523.7	−	11272.0i	−0.624879	−	0.360774i
$993$			32021.2i			1.02333i
$994$	−3754.99	+	12444.6i	−0.119820	+	0.397103i
$995$		0			0
$996$	−13871.0	+	24025.2i	−0.441283	+	0.764325i
$997$	8134.74	−	4696.60i	0.258405	−	0.149190i	−0.365202	−	0.930928i	$-0.619000\pi$
$997$	8134.74	−	4696.60i	0.258405	−	0.149190i	0.623607	+	0.781738i	$0.285667\pi$
$998$	89776.7	−	51832.6i	2.84753	−	1.64402i
$999$	22544.7	−	39048.5i	0.713995	−	1.23668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.k.d.149.10		20
5.2	odd	4		35.4.e.c.16.1	yes	10
5.3	odd	4		175.4.e.d.51.5		10
5.4	even	2	inner	175.4.k.d.149.1		20
7.4	even	3	inner	175.4.k.d.74.1		20
15.2	even	4		315.4.j.g.226.5		10
20.7	even	4		560.4.q.n.401.4		10
35.2	odd	12		245.4.a.m.1.5		5
35.4	even	6	inner	175.4.k.d.74.10		20
35.12	even	12		245.4.a.n.1.5		5
35.17	even	12		245.4.e.o.116.1		10
35.18	odd	12		175.4.e.d.151.5		10
35.23	odd	12		1225.4.a.bg.1.1		5
35.27	even	4		245.4.e.o.226.1		10
35.32	odd	12		35.4.e.c.11.1	✓	10
35.33	even	12		1225.4.a.bf.1.1		5
105.2	even	12		2205.4.a.bu.1.1		5
105.32	even	12		315.4.j.g.46.5		10
105.47	odd	12		2205.4.a.bt.1.1		5
140.67	even	12		560.4.q.n.81.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.e.c.11.1	✓	10	35.32	odd	12
35.4.e.c.16.1	yes	10	5.2	odd	4
175.4.e.d.51.5		10	5.3	odd	4
175.4.e.d.151.5		10	35.18	odd	12
175.4.k.d.74.1		20	7.4	even	3	inner
175.4.k.d.74.10		20	35.4	even	6	inner
175.4.k.d.149.1		20	5.4	even	2	inner
175.4.k.d.149.10		20	1.1	even	1	trivial
245.4.a.m.1.5		5	35.2	odd	12
245.4.a.n.1.5		5	35.12	even	12
245.4.e.o.116.1		10	35.17	even	12
245.4.e.o.226.1		10	35.27	even	4
315.4.j.g.46.5		10	105.32	even	12
315.4.j.g.226.5		10	15.2	even	4
560.4.q.n.81.4		10	140.67	even	12
560.4.q.n.401.4		10	20.7	even	4
1225.4.a.bf.1.1		5	35.33	even	12
1225.4.a.bg.1.1		5	35.23	odd	12
2205.4.a.bt.1.1		5	105.47	odd	12
2205.4.a.bu.1.1		5	105.2	even	12

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.50647 + 2.60181i) q^{2} +(4.24917 - 2.45326i) q^{3} +(9.53885 + 16.5218i) q^{4} +25.5317 q^{6} +(4.23212 + 18.0302i) q^{7} +57.6442i q^{8} +(-1.46305 + 2.53407i) q^{9} +O(q^{10})\)	\(q+(4.50647 + 2.60181i) q^{2} +(4.24917 - 2.45326i) q^{3} +(9.53885 + 16.5218i) q^{4} +25.5317 q^{6} +(4.23212 + 18.0302i) q^{7} +57.6442i q^{8} +(-1.46305 + 2.53407i) q^{9} +(-28.3386 - 49.0839i) q^{11} +(81.0644 + 46.8025i) q^{12} -43.4297i q^{13} +(-27.8393 + 92.2639i) q^{14} +(-73.6685 + 127.598i) q^{16} +(34.5013 - 19.9193i) q^{17} +(-13.1864 + 7.61315i) q^{18} +(26.1940 - 45.3693i) q^{19} +(62.2158 + 66.2310i) q^{21} -294.927i q^{22} +(46.3460 + 26.7579i) q^{23} +(141.416 + 244.940i) q^{24} +(112.996 - 195.715i) q^{26} +146.833i q^{27} +(-257.522 + 241.910i) q^{28} -49.6376 q^{29} +(36.8930 + 63.9006i) q^{31} +(-264.599 + 152.767i) q^{32} +(-240.831 - 139.044i) q^{33} +207.305 q^{34} -55.8231 q^{36} +(-265.938 - 153.540i) q^{37} +(236.085 - 136.304i) q^{38} +(-106.544 - 184.540i) q^{39} +292.064 q^{41} +(108.053 + 460.342i) q^{42} -365.956i q^{43} +(540.635 - 936.407i) q^{44} +(139.238 + 241.167i) q^{46} +(-383.175 - 221.226i) q^{47} +722.912i q^{48} +(-307.178 + 152.612i) q^{49} +(97.7346 - 169.281i) q^{51} +(717.536 - 414.269i) q^{52} +(22.3185 - 12.8856i) q^{53} +(-382.032 + 661.698i) q^{54} +(-1039.34 + 243.957i) q^{56} -257.043i q^{57} +(-223.690 - 129.148i) q^{58} +(188.300 + 326.146i) q^{59} +(-316.287 + 547.826i) q^{61} +383.955i q^{62} +(-51.8817 - 15.6546i) q^{63} -411.183 q^{64} +(-723.531 - 1253.19i) q^{66} +(-442.624 + 255.549i) q^{67} +(658.206 + 380.015i) q^{68} +262.576 q^{69} +134.881 q^{71} +(-146.075 - 84.3362i) q^{72} +(354.564 - 204.708i) q^{73} +(-798.962 - 1383.84i) q^{74} +999.443 q^{76} +(765.061 - 718.680i) q^{77} -1108.83i q^{78} +(-463.424 + 802.674i) q^{79} +(320.717 + 555.498i) q^{81} +(1316.18 + 759.897i) q^{82} +296.372i q^{83} +(-500.786 + 1659.68i) q^{84} +(952.150 - 1649.17i) q^{86} +(-210.918 + 121.774i) q^{87} +(2829.40 - 1633.55i) q^{88} +(244.391 - 423.297i) q^{89} +(783.047 - 183.800i) q^{91} +1020.96i q^{92} +(313.529 + 181.016i) q^{93} +(-1151.18 - 1993.90i) q^{94} +(-749.552 + 1298.26i) q^{96} +475.907i q^{97} +(-1781.36 - 111.477i) q^{98} +165.843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 70 q^{4} + 64 q^{6} + 162 q^{9}+O(q^{10}) \) 20 * q + 70 * q^4 + 64 * q^6 + 162 * q^9	\( 20 q + 70 q^{4} + 64 q^{6} + 162 q^{9} - 94 q^{11} - 14 q^{14} - 342 q^{16} - 42 q^{19} + 356 q^{21} + 1696 q^{24} + 94 q^{26} - 760 q^{29} - 776 q^{31} - 520 q^{34} + 4916 q^{36} + 28 q^{39} - 1124 q^{41} + 2182 q^{44} - 674 q^{46} - 1996 q^{49} - 1464 q^{51} - 1548 q^{54} - 2676 q^{56} + 1416 q^{59} - 3888 q^{61} + 500 q^{64} - 2964 q^{66} - 1496 q^{69} + 3456 q^{71} - 6570 q^{74} + 2764 q^{76} + 436 q^{79} + 910 q^{81} + 1468 q^{84} + 8528 q^{86} + 4644 q^{89} + 1048 q^{91} - 5354 q^{94} - 9184 q^{96} - 140 q^{99}+O(q^{100}) \) 20 * q + 70 * q^4 + 64 * q^6 + 162 * q^9 - 94 * q^11 - 14 * q^14 - 342 * q^16 - 42 * q^19 + 356 * q^21 + 1696 * q^24 + 94 * q^26 - 760 * q^29 - 776 * q^31 - 520 * q^34 + 4916 * q^36 + 28 * q^39 - 1124 * q^41 + 2182 * q^44 - 674 * q^46 - 1996 * q^49 - 1464 * q^51 - 1548 * q^54 - 2676 * q^56 + 1416 * q^59 - 3888 * q^61 + 500 * q^64 - 2964 * q^66 - 1496 * q^69 + 3456 * q^71 - 6570 * q^74 + 2764 * q^76 + 436 * q^79 + 910 * q^81 + 1468 * q^84 + 8528 * q^86 + 4644 * q^89 + 1048 * q^91 - 5354 * q^94 - 9184 * q^96 - 140 * q^99

Introduction

L-functions

Modular forms

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