LMFDB - Embedded newform 225.4.k.b.124.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(49,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("225.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.303595776.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			124.3
Root			$1.26217 + 1.18614i$ of defining polynomial
Character	$\chi$	$=$	225.124
Dual form			225.4.k.b.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18843 + 0.686141i) q^{2} +(1.18843 + 5.05842i) q^{3} +(-3.05842 - 5.29734i) q^{4} +(-2.05842 + 6.82701i) q^{6} +(4.43132 + 2.55842i) q^{7} -19.3723i q^{8} +(-24.1753 + 12.0232i) q^{9} +O(q^{10})$	\(q+(1.18843 + 0.686141i) q^{2} +(1.18843 + 5.05842i) q^{3} +(-3.05842 - 5.29734i) q^{4} +(-2.05842 + 6.82701i) q^{6} +(4.43132 + 2.55842i) q^{7} -19.3723i q^{8} +(-24.1753 + 12.0232i) q^{9} +(-27.9891 + 48.4786i) q^{11} +(23.1615 - 21.7663i) q^{12} +(-32.5489 + 18.7921i) q^{13} +(3.51087 + 6.08101i) q^{14} +(-11.1753 + 19.3561i) q^{16} +23.6495i q^{17} +(-36.9802 - 2.29894i) q^{18} -39.0516 q^{19} +(-7.67527 + 25.4560i) q^{21} +(-66.5263 + 38.4090i) q^{22} +(-61.5513 + 35.5367i) q^{23} +(97.9932 - 23.0226i) q^{24} -51.5761 q^{26} +(-89.5489 - 108.000i) q^{27} -31.2989i q^{28} +(-14.1861 + 24.5711i) q^{29} +(-6.44158 - 11.1571i) q^{31} +(-160.777 + 92.8247i) q^{32} +(-278.488 - 83.9674i) q^{33} +(-16.2269 + 28.1057i) q^{34} +(137.629 + 91.2927i) q^{36} -180.103i q^{37} +(-46.4101 - 26.7949i) q^{38} +(-133.741 - 142.313i) q^{39} +(107.742 + 186.614i) q^{41} +(-26.5879 + 24.9863i) q^{42} +(53.0299 + 30.6168i) q^{43} +342.410 q^{44} -97.5326 q^{46} +(53.5876 + 30.9388i) q^{47} +(-111.192 - 33.5258i) q^{48} +(-158.409 - 274.372i) q^{49} +(-119.629 + 28.1057i) q^{51} +(199.096 + 114.948i) q^{52} -492.310i q^{53} +(-32.3194 - 189.794i) q^{54} +(49.5625 - 85.8447i) q^{56} +(-46.4101 - 197.539i) q^{57} +(-33.7185 + 19.4674i) q^{58} +(394.815 + 683.840i) q^{59} +(-260.545 + 451.277i) q^{61} -17.6793i q^{62} +(-137.889 - 8.57207i) q^{63} -75.9590 q^{64} +(-273.351 - 290.872i) q^{66} +(263.644 - 152.215i) q^{67} +(125.279 - 72.3301i) q^{68} +(-252.909 - 269.120i) q^{69} +270.391 q^{71} +(232.916 + 468.330i) q^{72} +925.464i q^{73} +(123.576 - 214.040i) q^{74} +(119.436 + 206.870i) q^{76} +(-248.057 + 143.216i) q^{77} +(-61.2946 - 260.894i) q^{78} +(-644.517 + 1116.34i) q^{79} +(439.887 - 581.326i) q^{81} +295.704i q^{82} +(618.198 + 356.917i) q^{83} +(158.323 - 37.1966i) q^{84} +(42.0149 + 72.7720i) q^{86} +(-141.150 - 42.5584i) q^{87} +(939.141 + 542.213i) q^{88} +404.804 q^{89} -192.313 q^{91} +(376.500 + 217.372i) q^{92} +(48.7822 - 45.8437i) q^{93} +(42.4567 + 73.5372i) q^{94} +(-660.619 - 702.963i) q^{96} +(-64.9756 - 37.5137i) q^{97} -434.763i q^{98} +(93.7785 - 1508.50i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 10 q^{4} + 18 q^{6} - 90 q^{9}+O(q^{10}) $ 8 * q + 10 * q^4 + 18 * q^6 - 90 * q^9	$ 8 q + 10 q^{4} + 18 q^{6} - 90 q^{9} - 132 q^{11} + 120 q^{14} + 14 q^{16} + 308 q^{19} + 42 q^{21} + 198 q^{24} - 1056 q^{26} - 102 q^{29} - 86 q^{31} + 594 q^{34} - 450 q^{36} - 1518 q^{39} - 264 q^{41} + 924 q^{44} - 1056 q^{46} - 1026 q^{49} + 594 q^{51} - 2430 q^{54} - 132 q^{56} + 1596 q^{59} - 878 q^{61} + 2908 q^{64} - 1980 q^{66} - 1782 q^{69} + 5472 q^{71} + 1632 q^{74} + 3058 q^{76} - 1606 q^{79} - 1134 q^{81} - 1284 q^{84} - 66 q^{86} + 1584 q^{89} - 3124 q^{91} + 4200 q^{94} + 2160 q^{96} - 594 q^{99}+O(q^{100}) $ 8 * q + 10 * q^4 + 18 * q^6 - 90 * q^9 - 132 * q^11 + 120 * q^14 + 14 * q^16 + 308 * q^19 + 42 * q^21 + 198 * q^24 - 1056 * q^26 - 102 * q^29 - 86 * q^31 + 594 * q^34 - 450 * q^36 - 1518 * q^39 - 264 * q^41 + 924 * q^44 - 1056 * q^46 - 1026 * q^49 + 594 * q^51 - 2430 * q^54 - 132 * q^56 + 1596 * q^59 - 878 * q^61 + 2908 * q^64 - 1980 * q^66 - 1782 * q^69 + 5472 * q^71 + 1632 * q^74 + 3058 * q^76 - 1606 * q^79 - 1134 * q^81 - 1284 * q^84 - 66 * q^86 + 1584 * q^89 - 3124 * q^91 + 4200 * q^94 + 2160 * q^96 - 594 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	1.18843	+	0.686141i	0.420174	+	0.242587i	0.695152	−	0.718863i	$-0.255337\pi$
$2$	1.18843	+	0.686141i	0.420174	+	0.242587i	−0.274978	+	0.961451i	$0.588671\pi$
$3$	1.18843	+	5.05842i	0.228714	+	0.973494i
$3$	1.18843	+	5.05842i	0.228714	+	0.973494i
$4$	−3.05842	−	5.29734i	−0.382303	−	0.662168i
$5$		0			0
$5$		0			0
$6$	−2.05842	+	6.82701i	−0.140058	+	0.464519i
$7$	4.43132	+	2.55842i	0.239269	+	0.138142i	0.614841	−	0.788651i	$-0.289220\pi$
$7$	4.43132	+	2.55842i	0.239269	+	0.138142i	−0.375572	+	0.926793i	$0.622554\pi$
$8$		−	19.3723i		−	0.856142i
$9$	−24.1753	+	12.0232i	−0.895380	+	0.445302i
$10$		0			0
$11$	−27.9891	+	48.4786i	−0.767185	+	1.32880i	0.171898	+	0.985115i	$0.445010\pi$
$11$	−27.9891	+	48.4786i	−0.767185	+	1.32880i	−0.939083	+	0.343689i	$0.888323\pi$
$12$	23.1615	−	21.7663i	0.557178	−	0.523616i
$13$	−32.5489	+	18.7921i	−0.694418	+	0.400923i	−0.805265	−	0.592915i	$-0.797977\pi$
$13$	−32.5489	+	18.7921i	−0.694418	+	0.400923i	0.110847	+	0.993838i	$0.464644\pi$
$14$	3.51087	+	6.08101i	0.0670229	+	0.116087i
$15$		0			0
$16$	−11.1753	+	19.3561i	−0.174614	+	0.302440i
$17$			23.6495i			0.337402i	0.985667	+	0.168701i	$0.0539573\pi$
$17$			23.6495i			0.337402i	−0.985667	+	0.168701i	$0.946043\pi$
$18$	−36.9802	−	2.29894i	−0.484240	−	0.0301036i
$19$	−39.0516			−0.471529			−0.235764	−	0.971810i	$-0.575759\pi$
$19$	−39.0516			−0.471529			−0.235764	+	0.971810i	$0.575759\pi$
$20$		0			0
$21$	−7.67527	+	25.4560i	−0.0797562	+	0.264521i
$22$	−66.5263	+	38.4090i	−0.644702	+	0.372219i
$23$	−61.5513	+	35.5367i	−0.558015	+	0.322170i	−0.752348	−	0.658766i	$-0.771079\pi$
$23$	−61.5513	+	35.5367i	−0.558015	+	0.322170i	0.194334	+	0.980936i	$0.437746\pi$
$24$	97.9932	−	23.0226i	0.833449	−	0.195811i
$25$		0			0
$26$	−51.5761			−0.389035
$27$	−89.5489	−	108.000i	−0.638285	−	0.769800i
$28$		−	31.2989i		−	0.211248i
$29$	−14.1861	+	24.5711i	−0.0908379	+	0.157336i	−0.907864	−	0.419265i	$-0.862288\pi$
$29$	−14.1861	+	24.5711i	−0.0908379	+	0.157336i	0.817026	+	0.576601i	$0.195621\pi$
$30$		0			0
$31$	−6.44158	−	11.1571i	−0.0373207	−	0.0646413i	0.846762	−	0.531972i	$-0.178549\pi$
$31$	−6.44158	−	11.1571i	−0.0373207	−	0.0646413i	−0.884082	+	0.467331i	$0.845216\pi$
$32$	−160.777	+	92.8247i	−0.888177	+	0.512789i
$33$	−278.488	−	83.9674i	−1.46905	−	0.442935i
$34$	−16.2269	+	28.1057i	−0.0818495	+	0.141768i
$35$		0			0
$36$	137.629	+	91.2927i	0.637171	+	0.422652i
$37$		−	180.103i		−	0.800237i	−0.916463	−	0.400119i	$-0.868969\pi$
$37$		−	180.103i		−	0.800237i	0.916463	−	0.400119i	$-0.131031\pi$
$38$	−46.4101	−	26.7949i	−0.198124	−	0.114387i
$39$	−133.741	−	142.313i	−0.549119	−	0.584315i
$40$		0			0
$41$	107.742	+	186.614i	0.410401	+	0.710835i	0.994934	−	0.100535i	$-0.0320554\pi$
$41$	107.742	+	186.614i	0.410401	+	0.710835i	−0.584533	+	0.811370i	$0.698722\pi$
$42$	−26.5879	+	24.9863i	−0.0976810	+	0.0917971i
$43$	53.0299	+	30.6168i	0.188069	+	0.108582i	0.591078	−	0.806614i	$-0.298702\pi$
$43$	53.0299	+	30.6168i	0.188069	+	0.108582i	−0.403009	+	0.915196i	$0.632036\pi$
$44$	342.410			1.17319
$45$		0			0
$46$	−97.5326			−0.312617
$47$	53.5876	+	30.9388i	0.166310	+	0.0960189i	0.580845	−	0.814014i	$-0.302722\pi$
$47$	53.5876	+	30.9388i	0.166310	+	0.0960189i	−0.414535	+	0.910033i	$0.636056\pi$
$48$	−111.192	−	33.5258i	−0.334359	−	0.100813i
$49$	−158.409	−	274.372i	−0.461834	−	0.799919i
$50$		0			0
$51$	−119.629	+	28.1057i	−0.328459	+	0.0771685i
$52$	199.096	+	114.948i	0.530956	+	0.306548i
$53$		−	492.310i		−	1.27592i	−0.770068	−	0.637962i	$-0.779778\pi$
$53$		−	492.310i		−	1.27592i	0.770068	−	0.637962i	$-0.220222\pi$
$54$	−32.3194	−	189.794i	−0.0814466	−	0.478290i
$55$		0			0
$56$	49.5625	−	85.8447i	0.118269	−	0.204848i
$57$	−46.4101	−	197.539i	−0.107845	−	0.459031i
$58$	−33.7185	+	19.4674i	−0.0763354	+	0.0440723i
$59$	394.815	+	683.840i	0.871196	+	1.50896i	0.860761	+	0.509010i	$0.169988\pi$
$59$	394.815	+	683.840i	0.871196	+	1.50896i	0.0104351	+	0.999946i	$0.496678\pi$
$60$		0			0
$61$	−260.545	+	451.277i	−0.546874	+	0.947214i	0.451612	+	0.892214i	$0.350849\pi$
$61$	−260.545	+	451.277i	−0.546874	+	0.947214i	−0.998486	+	0.0549998i	$0.982484\pi$
$62$		−	17.6793i		−	0.0362141i
$63$	−137.889	−	8.57207i	−0.275751	−	0.0171425i
$64$	−75.9590			−0.148358
$65$		0			0
$66$	−273.351	−	290.872i	−0.509805	−	0.542482i
$67$	263.644	−	152.215i	0.480734	−	0.277552i	−0.239988	−	0.970776i	$-0.577144\pi$
$67$	263.644	−	152.215i	0.480734	−	0.277552i	0.720722	+	0.693224i	$0.243810\pi$
$68$	125.279	−	72.3301i	0.223417	−	0.128990i
$69$	−252.909	−	269.120i	−0.441256	−	0.469539i
$70$		0			0
$71$	270.391			0.451966			0.225983	−	0.974131i	$-0.427441\pi$
$71$	270.391			0.451966			0.225983	+	0.974131i	$0.427441\pi$
$72$	232.916	+	468.330i	0.381242	+	0.766573i
$73$			925.464i			1.48380i	0.670510	+	0.741900i	$0.266075\pi$
$73$			925.464i			1.48380i	−0.670510	+	0.741900i	$0.733925\pi$
$74$	123.576	−	214.040i	0.194127	−	0.336239i
$75$		0			0
$76$	119.436	+	206.870i	0.180267	+	0.312231i
$77$	−248.057	+	143.216i	−0.367127	+	0.211961i
$78$	−61.2946	−	260.894i	−0.0889776	−	0.378723i
$79$	−644.517	+	1116.34i	−0.917897	+	1.58984i	−0.115294	+	0.993331i	$0.536781\pi$
$79$	−644.517	+	1116.34i	−0.917897	+	1.58984i	−0.802603	+	0.596513i	$0.796552\pi$
$80$		0			0
$81$	439.887	−	581.326i	0.603411	−	0.797430i
$82$			295.704i			0.398232i
$83$	618.198	+	356.917i	0.817543	+	0.472009i	0.849569	−	0.527478i	$-0.176862\pi$
$83$	618.198	+	356.917i	0.817543	+	0.472009i	−0.0320252	+	0.999487i	$0.510196\pi$
$84$	158.323	−	37.1966i	0.205649	−	0.0483153i
$85$		0			0
$86$	42.0149	+	72.7720i	0.0526812	+	0.0912466i
$87$	−141.150	−	42.5584i	−0.173941	−	0.0524453i
$88$	939.141	+	542.213i	1.13764	+	0.656820i
$89$	404.804			0.482125			0.241063	−	0.970510i	$-0.422504\pi$
$89$	404.804			0.482125			0.241063	+	0.970510i	$0.422504\pi$
$90$		0			0
$91$	−192.313			−0.221537
$92$	376.500	+	217.372i	0.426661	+	0.246333i
$93$	48.7822	−	45.8437i	0.0543922	−	0.0511158i
$94$	42.4567	+	73.5372i	0.0465859	+	0.0806892i
$95$		0			0
$96$	−660.619	−	702.963i	−0.702335	−	0.747353i
$97$	−64.9756	−	37.5137i	−0.0680131	−	0.0392674i	0.465608	−	0.884991i	$-0.345836\pi$
$97$	−64.9756	−	37.5137i	−0.0680131	−	0.0392674i	−0.533621	+	0.845724i	$0.679169\pi$
$98$		−	434.763i		−	0.448140i
$99$	93.7785	−	1508.50i	0.0952029	−	1.53141i
$100$		0			0
$101$	543.939	−	942.130i	0.535881	−	0.928172i	−0.463240	−	0.886233i	$-0.653313\pi$
$101$	543.939	−	942.130i	0.535881	−	0.928172i	0.999120	−	0.0419392i	$-0.0133536\pi$
$102$	−161.455	−	48.6806i	−0.156730	−	0.0472558i
$103$	945.542	−	545.909i	0.904534	−	0.522233i	0.0258657	−	0.999665i	$-0.491766\pi$
$103$	945.542	−	545.909i	0.904534	−	0.522233i	0.878669	+	0.477432i	$0.158432\pi$
$104$	364.046	+	630.546i	0.343247	+	0.594521i
$105$		0			0
$106$	337.794	−	585.076i	0.309523	−	0.536109i
$107$		−	1029.15i		−	0.929833i	−0.885354	−	0.464917i	$-0.846084\pi$
$107$		−	1029.15i		−	0.929833i	0.885354	−	0.464917i	$-0.153916\pi$
$108$	−298.235	+	804.681i	−0.265719	+	0.716948i
$109$	−1776.52			−1.56110			−0.780548	−	0.625096i	$-0.785060\pi$
$109$	−1776.52			−1.56110			−0.780548	+	0.625096i	$0.785060\pi$
$110$		0			0
$111$	911.038	−	214.040i	0.779026	−	0.183025i
$112$	−99.0423	+	57.1821i	−0.0835591	+	0.0482429i
$113$	1399.44	−	807.969i	1.16503	−	0.672631i	0.212526	−	0.977155i	$-0.431831\pi$
$113$	1399.44	−	807.969i	1.16503	−	0.672631i	0.952505	+	0.304524i	$0.0984975\pi$
$114$	80.3847	−	266.606i	0.0660413	−	0.219034i
$115$		0			0
$116$	173.549			0.138910
$117$	560.937	−	845.645i	0.443237	−	0.668204i
$118$			1083.59i			0.845364i
$119$	−60.5053	+	104.798i	−0.0466094	+	0.0807298i
$120$		0			0
$121$	−901.282	−	1561.07i	−0.677147	−	1.17285i
$122$	−619.279	+	357.541i	−0.459564	+	0.265330i
$123$	−815.930	+	766.781i	−0.598130	+	0.562100i
$124$	−39.4021	+	68.2465i	−0.0285356	+	0.0494251i
$125$		0			0
$126$	−157.989	−	104.798i	−0.111705	−	0.0740966i
$127$		−	1206.10i		−	0.842711i	−0.906895	−	0.421356i	$-0.861554\pi$
$127$		−	1206.10i		−	0.842711i	0.906895	−	0.421356i	$-0.138446\pi$
$128$	1195.95	+	690.479i	0.825841	+	0.476799i
$129$	−91.8505	+	304.634i	−0.0626898	+	0.207919i
$130$		0			0
$131$	513.928	+	890.149i	0.342764	+	0.593684i	0.984945	−	0.172869i	$-0.0553036\pi$
$131$	513.928	+	890.149i	0.342764	+	0.593684i	−0.642181	+	0.766553i	$0.721970\pi$
$132$	406.931	+	1732.06i	0.268324	+	1.14209i
$133$	−173.050	−	99.9105i	−0.112822	−	0.0651379i
$134$	417.763			0.269322
$135$		0			0
$136$	458.144			0.288864
$137$	1091.98	+	630.454i	0.680978	+	0.393163i	0.800223	−	0.599702i	$-0.204714\pi$
$137$	1091.98	+	630.454i	0.680978	+	0.393163i	−0.119245	+	0.992865i	$0.538048\pi$
$138$	−115.911	−	493.361i	−0.0714998	−	0.304331i
$139$	230.916	+	399.958i	0.140907	+	0.244057i	0.927838	−	0.372983i	$-0.121665\pi$
$139$	230.916	+	399.958i	0.140907	+	0.244057i	−0.786932	+	0.617040i	$0.788332\pi$
$140$		0			0
$141$	−92.8164	+	307.837i	−0.0554365	+	0.183862i
$142$	321.341	+	185.527i	0.189904	+	0.109641i
$143$		−	2103.90i		−	1.23033i
$144$	37.4431	−	602.302i	0.0216685	−	0.348554i
$145$		0			0
$146$	−634.999	+	1099.85i	−0.359951	+	0.623454i
$147$	1199.63	−	1127.37i	0.673089	−	0.632545i
$148$	−954.068	+	550.832i	−0.529891	+	0.305933i
$149$	729.661	+	1263.81i	0.401182	+	0.694868i	0.993869	−	0.110565i	$-0.0352660\pi$
$149$	729.661	+	1263.81i	0.401182	+	0.694868i	−0.592687	+	0.805433i	$0.701933\pi$
$150$		0			0
$151$	−770.659	+	1334.82i	−0.415333	+	0.719378i	−0.995463	−	0.0951456i	$-0.969668\pi$
$151$	−770.659	+	1334.82i	−0.415333	+	0.719378i	0.580130	+	0.814524i	$0.303002\pi$
$152$			756.518i			0.403696i
$153$	−284.341	−	571.732i	−0.150246	−	0.302103i
$154$	−393.065			−0.205676
$155$		0			0
$156$	−344.845	+	1143.72i	−0.176985	+	0.586994i
$157$	−2784.77	+	1607.79i	−1.41560	+	0.817295i	−0.995908	−	0.0903734i	$-0.971194\pi$
$157$	−2784.77	+	1607.79i	−1.41560	+	0.817295i	−0.419688	+	0.907668i	$0.637861\pi$
$158$	−1531.93	+	884.459i	−0.771352	+	0.445341i
$159$	2490.31	−	585.076i	1.24210	−	0.291821i
$160$		0			0
$161$	−363.671			−0.178021
$162$	921.647	−	389.042i	0.446984	−	0.188679i
$163$		−	947.587i		−	0.455342i	−0.973738	−	0.227671i	$-0.926889\pi$
$163$		−	947.587i		−	0.455342i	0.973738	−	0.227671i	$-0.0731111\pi$
$164$	659.040	−	1141.49i	0.313795	−	0.543509i
$165$		0			0
$166$	489.791	+	848.342i	0.229007	+	0.396651i
$167$	594.058	−	342.980i	0.275267	−	0.158926i	−0.356012	−	0.934481i	$-0.615864\pi$
$167$	594.058	−	342.980i	0.275267	−	0.158926i	0.631279	+	0.775556i	$0.282530\pi$
$168$	493.140	+	148.687i	0.226468	+	0.0682826i
$169$	−392.213	+	679.333i	−0.178522	+	0.309209i
$170$		0			0
$171$	944.083	−	469.524i	0.422198	−	0.209973i
$172$		−	374.557i		−	0.166045i
$173$	−1916.36	−	1106.41i	−0.842188	−	0.486237i	0.0158193	−	0.999875i	$-0.494964\pi$
$173$	−1916.36	−	1106.41i	−0.842188	−	0.486237i	−0.858007	+	0.513637i	$0.828298\pi$
$174$	−138.546	−	147.427i	−0.0603630	−	0.0642321i
$175$		0			0
$176$	−625.572	−	1083.52i	−0.267922	−	0.464054i
$177$	−2989.94	+	2809.84i	−1.26970	+	1.19322i
$178$	481.082	+	277.753i	0.202576	+	0.116958i
$179$	−3023.22			−1.26238			−0.631190	−	0.775629i	$-0.717433\pi$
$179$	−3023.22			−1.26238			−0.631190	+	0.775629i	$0.717433\pi$
$180$		0			0
$181$	391.445			0.160751			0.0803753	−	0.996765i	$-0.474388\pi$
$181$	391.445			0.160751			0.0803753	+	0.996765i	$0.474388\pi$
$182$	−228.550	−	131.953i	−0.0930839	−	0.0537420i
$183$	−2592.39	−	781.634i	−1.04718	−	0.315738i
$184$	688.426	+	1192.39i	0.275823	+	0.477740i
$185$		0			0
$186$	89.4294	−	21.0106i	0.0352542	−	0.00828266i
$187$	−1146.49	−	661.928i	−0.448341	−	0.258850i
$188$		−	378.496i		−	0.146833i
$189$	−120.510	−	707.686i	−0.0463799	−	0.272363i
$190$		0			0
$191$	−1742.79	+	3018.61i	−0.660231	+	1.14355i	0.320324	+	0.947308i	$0.396208\pi$
$191$	−1742.79	+	3018.61i	−0.660231	+	1.14355i	−0.980555	+	0.196246i	$0.937125\pi$
$192$	−90.2720	−	384.233i	−0.0339314	−	0.144425i
$193$	−1918.31	+	1107.53i	−0.715455	+	0.413068i	−0.813077	−	0.582156i	$-0.802209\pi$
$193$	−1918.31	+	1107.53i	−0.715455	+	0.413068i	0.0976228	+	0.995223i	$0.468876\pi$
$194$	−51.4793	−	89.1647i	−0.0190515	−	0.0329982i
$195$		0			0
$196$	−968.963	+	1678.29i	−0.353121	+	0.611623i
$197$		−	3975.11i		−	1.43764i	−0.695196	−	0.718820i	$-0.744682\pi$
$197$		−	3975.11i		−	1.43764i	0.695196	−	0.718820i	$-0.255318\pi$
$198$	1146.49	−	1728.40i	0.411504	−	0.620365i
$199$	1555.34			0.554046			0.277023	−	0.960863i	$-0.410652\pi$
$199$	1555.34			0.554046			0.277023	+	0.960863i	$0.410652\pi$
$200$		0			0
$201$	1083.29	+	1152.72i	0.380146	+	0.404512i
$202$	1292.87	−	746.437i	0.450326	−	0.259996i
$203$	−125.727	+	72.5883i	−0.0434693	+	0.0250970i
$204$	514.762	+	547.756i	0.176669	+	0.187993i
$205$		0			0
$206$	1498.28			0.506749
$207$	1060.76	−	1599.15i	0.356172	−	0.536950i
$208$		−	840.027i		−	0.280026i
$209$	1093.02	−	1893.17i	0.361750	−	0.626570i
$210$		0			0
$211$	−873.865	−	1513.58i	−0.285115	−	0.493834i	0.687522	−	0.726164i	$-0.258699\pi$
$211$	−873.865	−	1513.58i	−0.285115	−	0.493834i	−0.972637	+	0.232329i	$0.925365\pi$
$212$	−2607.93	+	1505.69i	−0.844875	+	0.487789i
$213$	321.341	+	1367.75i	0.103371	+	0.439986i
$214$	706.145	−	1223.08i	0.225566	−	0.390691i
$215$		0			0
$216$	−2092.21	+	1734.77i	−0.659058	+	0.546462i
$217$		−	65.9211i		−	0.0206222i
$218$	−2111.27	−	1218.94i	−0.655931	−	0.378702i
$219$	−4681.39	+	1099.85i	−1.44447	+	0.339365i
$220$		0			0
$221$	−444.423	−	769.764i	−0.135272	−	0.234298i
$222$	1229.57	+	370.728i	0.371726	+	0.112080i
$223$	−2201.39	−	1270.97i	−0.661057	−	0.381662i	0.131622	−	0.991300i	$-0.457981\pi$
$223$	−2201.39	−	1270.97i	−0.661057	−	0.381662i	−0.792680	+	0.609638i	$0.791315\pi$
$224$	−949.939			−0.283350
$225$		0			0
$226$	2217.52			0.652687
$227$	2592.24	+	1496.63i	0.757943	+	0.437598i	0.828557	−	0.559905i	$-0.189163\pi$
$227$	2592.24	+	1496.63i	0.757943	+	0.437598i	−0.0706140	+	0.997504i	$0.522496\pi$
$228$	−904.492	+	850.009i	−0.262726	+	0.246900i
$229$	−2152.65	−	3728.50i	−0.621185	−	1.07592i	−0.989265	−	0.146130i	$-0.953318\pi$
$229$	−2152.65	−	3728.50i	−0.621185	−	1.07592i	0.368081	−	0.929794i	$-0.380015\pi$
$230$		0			0
$231$	−1019.25	−	1084.58i	−0.290309	−	0.308917i
$232$	475.999	+	274.818i	0.134702	+	0.0777702i
$233$			5581.34i			1.56930i	0.619942	+	0.784648i	$0.287156\pi$
$233$			5581.34i			1.56930i	−0.619942	+	0.784648i	$0.712844\pi$
$234$	1246.87	−	620.108i	0.348334	−	0.173238i
$235$		0			0
$236$	2415.02	−	4182.94i	0.666121	−	1.15376i
$237$	−6412.87	−	1933.55i	−1.75764	−	0.529948i
$238$	−143.813	+	83.0303i	−0.0391680	+	0.0226137i
$239$	704.814	+	1220.77i	0.190756	+	0.330399i	0.945501	−	0.325619i	$-0.105573\pi$
$239$	704.814	+	1220.77i	0.190756	+	0.330399i	−0.754745	+	0.656018i	$0.772239\pi$
$240$		0			0
$241$	−313.286	+	542.627i	−0.0837366	+	0.145036i	−0.904852	−	0.425726i	$-0.860019\pi$
$241$	−313.286	+	542.627i	−0.0837366	+	0.145036i	0.821116	+	0.570762i	$0.193352\pi$
$242$		−	2473.63i		−	0.657069i
$243$	3463.37	+	1534.27i	0.914302	+	0.405034i
$244$	3187.42			0.836286
$245$		0			0
$246$	−1495.80	+	351.424i	−0.387677	+	0.0910811i
$247$	1271.09	−	733.862i	0.327438	−	0.189047i
$248$	−216.139	+	124.788i	−0.0553422	+	0.0319518i
$249$	−1070.75	+	3551.28i	−0.272514	+	0.903828i
$250$		0			0
$251$	1705.53			0.428892			0.214446	−	0.976736i	$-0.431205\pi$
$251$	1705.53			0.428892			0.214446	+	0.976736i	$0.431205\pi$
$252$	376.312	+	756.660i	0.0940692	+	0.189147i
$253$		−	3978.56i		−	0.988656i
$254$	827.556	−	1433.37i	0.204431	−	0.354085i
$255$		0			0
$256$	1251.37	+	2167.43i	0.305510	+	0.529158i
$257$	−3115.42	+	1798.69i	−0.756166	+	0.436573i	−0.827918	−	0.560850i	$-0.810475\pi$
$257$	−3115.42	+	1798.69i	−0.756166	+	0.436573i	0.0717513	+	0.997423i	$0.477141\pi$
$258$	−318.180	+	299.014i	−0.0767791	+	0.0721542i
$259$	460.780	−	798.094i	0.110546	−	0.191472i
$260$		0			0
$261$	47.5311	−	764.576i	0.0112724	−	0.181326i
$262$			1410.51i			0.332601i
$263$	3583.18	+	2068.75i	0.840108	+	0.485037i	0.857301	−	0.514815i	$-0.172140\pi$
$263$	3583.18	+	2068.75i	0.840108	+	0.485037i	−0.0171926	+	0.999852i	$0.505473\pi$
$264$	−1626.64	+	5394.95i	−0.379215	+	1.25771i
$265$		0			0
$266$	−137.105	−	237.473i	−0.0316032	−	0.0547384i
$267$	481.082	+	2047.67i	0.110269	+	0.469346i
$268$	−1612.67	−	931.074i	−0.367572	−	0.212218i
$269$	−6090.99			−1.38057			−0.690287	−	0.723536i	$-0.742516\pi$
$269$	−6090.99			−1.38057			−0.690287	+	0.723536i	$0.742516\pi$
$270$		0			0
$271$	−3196.62			−0.716534			−0.358267	−	0.933619i	$-0.616632\pi$
$271$	−3196.62			−0.716534			−0.358267	+	0.933619i	$0.616632\pi$
$272$	−457.762	−	264.289i	−0.102044	−	0.0589150i
$273$	−228.550	−	972.798i	−0.0506684	−	0.215665i
$274$	865.160	+	1498.50i	0.190753	+	0.330393i
$275$		0			0
$276$	−652.117	+	2162.83i	−0.142220	+	0.471692i
$277$	2701.45	+	1559.68i	0.585972	+	0.338311i	0.763503	−	0.645804i	$-0.223478\pi$
$277$	2701.45	+	1559.68i	0.585972	+	0.338311i	−0.177531	+	0.984115i	$0.556811\pi$
$278$			633.763i			0.136729i
$279$	289.871	+	192.279i	0.0622012	+	0.0412596i
$280$		0			0
$281$	−2474.17	+	4285.38i	−0.525254	+	0.909767i	0.474313	+	0.880356i	$0.342696\pi$
$281$	−2474.17	+	4285.38i	−0.525254	+	0.909767i	−0.999567	+	0.0294105i	$0.990637\pi$
$282$	−321.525	+	302.158i	−0.0678956	+	0.0638058i
$283$	3936.03	−	2272.47i	0.826758	−	0.477329i	−0.0259834	−	0.999662i	$-0.508272\pi$
$283$	3936.03	−	2272.47i	0.826758	−	0.477329i	0.852741	+	0.522333i	$0.174938\pi$
$284$	−826.971	−	1432.36i	−0.172788	−	0.299277i
$285$		0			0
$286$	1443.57	−	2500.34i	0.298462	−	0.516951i
$287$			1102.60i			0.226774i
$288$	2770.78	−	4177.11i	0.566910	−	0.854648i
$289$	4353.70			0.886160
$290$		0			0
$291$	112.541	−	373.256i	0.0226710	−	0.0751913i
$292$	4902.50	−	2830.46i	0.982525	−	0.567261i
$293$	−5941.03	+	3430.05i	−1.18457	+	0.683911i	−0.957067	−	0.289867i	$-0.906389\pi$
$293$	−5941.03	+	3430.05i	−1.18457	+	0.683911i	−0.227501	+	0.973778i	$0.573056\pi$
$294$	2199.22	−	516.686i	0.436262	−	0.102496i
$295$		0			0
$296$	−3489.01			−0.685117
$297$	7742.08	−	1318.38i	1.51260	−	0.257576i
$298$			2002.60i			0.389287i
$299$	1335.62	−	2313.36i	0.258330	−	0.447441i
$300$		0			0
$301$	156.662	+	271.346i	0.0299994	+	0.0519605i
$302$	−1831.75	+	1057.56i	−0.349024	+	0.201509i
$303$	5412.12	+	1631.82i	1.02613	+	0.309391i
$304$	436.412	−	755.888i	0.0823353	−	0.142609i
$305$		0			0
$306$	54.3686	−	874.562i	0.0101570	−	0.163384i
$307$			6332.25i			1.17720i	0.808424	+	0.588600i	$0.200321\pi$
$307$			6332.25i			1.17720i	−0.808424	+	0.588600i	$0.799679\pi$
$308$	1517.33	+	876.030i	0.280707	+	0.162066i
$309$	3885.15	+	4134.18i	0.715270	+	0.761117i
$310$		0			0
$311$	−3538.84	−	6129.44i	−0.645238	−	1.11758i	−0.984247	−	0.176801i	$-0.943425\pi$
$311$	−3538.84	−	6129.44i	−0.645238	−	1.11758i	0.339009	−	0.940783i	$-0.389908\pi$
$312$	−2756.93	+	2590.86i	−0.500257	+	0.470123i
$313$	1196.24	+	690.649i	0.216024	+	0.124721i	0.604108	−	0.796903i	$-0.293530\pi$
$313$	1196.24	+	690.649i	0.216024	+	0.124721i	−0.388084	+	0.921624i	$0.626863\pi$
$314$	−4412.67			−0.793062
$315$		0			0
$316$	7884.83			1.40366
$317$	7079.70	+	4087.47i	1.25437	+	0.724211i	0.971974	−	0.235086i	$-0.0755373\pi$
$317$	7079.70	+	4087.47i	1.25437	+	0.724211i	0.282396	+	0.959298i	$0.408871\pi$
$318$	3361.00	+	1013.38i	0.592691	+	0.178703i
$319$	−794.115	−	1375.45i	−0.139379	−	0.241412i
$320$		0			0
$321$	5205.90	−	1223.08i	0.905187	−	0.212665i
$322$	−432.198	−	249.530i	−0.0747995	−	0.0431855i
$323$		−	923.549i		−	0.159095i
$324$	−4424.85	−	552.290i	−0.758718	−	0.0947000i
$325$		0			0
$326$	650.178	−	1126.14i	0.110460	−	0.191323i
$327$	−2111.27	−	8986.37i	−0.357044	−	1.51972i
$328$	3615.14	−	2087.20i	0.608576	−	0.351361i
$329$	158.309	+	274.199i	0.0265284	+	0.0459486i
$330$		0			0
$331$	4830.64	−	8366.92i	0.802163	−	1.38939i	−0.116026	−	0.993246i	$-0.537016\pi$
$331$	4830.64	−	8366.92i	0.802163	−	1.38939i	0.918189	−	0.396142i	$-0.129651\pi$
$332$		−	4366.41i		−	0.721801i
$333$	2165.41	+	4354.04i	0.356348	+	0.716517i
$334$	941.329			0.154213
$335$		0			0
$336$	−406.956	−	433.041i	−0.0660752	−	0.0703104i
$337$	−4292.04	+	2478.01i	−0.693776	+	0.400552i	−0.805025	−	0.593241i	$-0.797848\pi$
$337$	−4292.04	+	2478.01i	−0.693776	+	0.400552i	0.111249	+	0.993793i	$0.464515\pi$
$338$	−932.236	+	538.227i	−0.150021	+	0.0866144i
$339$	5750.19	+	6118.76i	0.921260	+	0.980311i
$340$		0			0
$341$	721.177			0.114528
$342$	1444.14	+	89.7771i	0.228333	+	0.0141947i
$343$		−	3376.19i		−	0.531478i
$344$	593.118	−	1027.31i	0.0929616	−	0.161014i
$345$		0			0
$346$	−1518.31	−	2629.79i	−0.235910	−	0.408608i
$347$	−879.540	+	507.802i	−0.136070	+	0.0785598i	−0.566490	−	0.824069i	$-0.691699\pi$
$347$	−879.540	+	507.802i	−0.136070	+	0.0785598i	0.430420	+	0.902629i	$0.358365\pi$
$348$	206.251	+	877.883i	0.0317707	+	0.135228i
$349$	6079.29	−	10529.6i	0.932426	−	1.61501i	0.153267	−	0.988185i	$-0.451021\pi$
$349$	6079.29	−	10529.6i	0.932426	−	1.61501i	0.779160	−	0.626825i	$-0.215646\pi$
$350$		0			0
$351$	4944.26	+	1832.47i	0.751867	+	0.278661i
$352$		−	10392.3i		−	1.57362i
$353$	3668.56	+	2118.04i	0.553138	+	0.319354i	0.750387	−	0.660999i	$-0.229867\pi$
$353$	3668.56	+	2118.04i	0.553138	+	0.319354i	−0.197249	+	0.980353i	$0.563201\pi$
$354$	−5481.28	+	1287.78i	−0.822957	+	0.193346i
$355$		0			0
$356$	−1238.06	−	2144.39i	−0.184318	−	0.319248i
$357$	−602.020	−	181.516i	−0.0892501	−	0.0269099i
$358$	−3592.88	−	2074.35i	−0.530418	−	0.306237i
$359$	517.939			0.0761443			0.0380721	−	0.999275i	$-0.487878\pi$
$359$	517.939			0.0761443			0.0380721	+	0.999275i	$0.487878\pi$
$360$		0			0
$361$	−5333.97			−0.777660
$362$	465.205	+	268.586i	0.0675432	+	0.0389961i
$363$	6825.42	−	6414.29i	0.986892	−	0.927445i
$364$	588.173	+	1018.75i	0.0846941	+	0.146694i
$365$		0			0
$366$	−2544.56	−	2707.66i	−0.363405	−	0.386699i
$367$	3997.83	+	2308.15i	0.568624	+	0.328295i	0.756600	−	0.653879i	$-0.226859\pi$
$367$	3997.83	+	2308.15i	0.568624	+	0.328295i	−0.187976	+	0.982174i	$0.560193\pi$
$368$		−	1588.53i		−	0.225021i
$369$	−4848.38	−	3216.05i	−0.684002	−	0.453715i
$370$		0			0
$371$	1259.54	−	2181.58i	0.176258	−	0.305288i
$372$	−392.046	−	118.206i	−0.0546415	−	0.0164750i
$373$	−4126.98	+	2382.71i	−0.572887	+	0.330756i	−0.758301	−	0.651904i	$-0.773970\pi$
$373$	−4126.98	+	2382.71i	−0.572887	+	0.330756i	0.185415	+	0.982660i	$0.440637\pi$
$374$	−908.351	−	1573.31i	−0.125588	−	0.217524i
$375$		0			0
$376$	599.355	−	1038.11i	0.0822058	−	0.142385i
$377$		−	1066.35i		−	0.145676i
$378$	342.355	−	923.722i	0.0465842	−	0.125691i
$379$	2000.33			0.271108			0.135554	−	0.990770i	$-0.456719\pi$
$379$	2000.33			0.271108			0.135554	+	0.990770i	$0.456719\pi$
$380$		0			0
$381$	6100.98	−	1433.37i	0.820374	−	0.192740i
$382$	−4142.38	+	2391.60i	−0.554823	+	0.320327i
$383$	−857.619	+	495.147i	−0.114419	+	0.0660596i	−0.556117	−	0.831104i	$-0.687709\pi$
$383$	−857.619	+	495.147i	−0.114419	+	0.0660596i	0.441699	+	0.897164i	$0.354376\pi$
$384$	−2071.44	+	6870.18i	−0.275280	+	0.913001i
$385$		0			0
$386$	−3039.70			−0.400820
$387$	−1650.12	−	102.583i	−0.216746	−	0.0134743i
$388$			458.930i			0.0600481i
$389$	202.205	−	350.230i	0.0263553	−	0.0456487i	−0.852547	−	0.522651i	$-0.824943\pi$
$389$	202.205	−	350.230i	0.0263553	−	0.0456487i	0.878902	+	0.477002i	$0.158277\pi$
$390$		0			0
$391$	−840.423	−	1455.66i	−0.108701	−	0.188275i
$392$	−5315.22	+	3068.74i	−0.684845	+	0.395395i
$393$	−3891.98	+	3657.54i	−0.499553	+	0.469462i
$394$	2727.49	−	4724.15i	0.348753	−	0.604059i
$395$		0			0
$396$	−8277.86	+	4116.85i	−1.05045	+	0.522424i
$397$			2919.61i			0.369096i	0.982824	+	0.184548i	$0.0590821\pi$
$397$			2919.61i			0.369096i	−0.982824	+	0.184548i	$0.940918\pi$
$398$	1848.42	+	1067.18i	0.232796	+	0.134405i
$399$	299.731	−	994.097i	0.0376074	−	0.124730i
$400$		0			0
$401$	5093.10	+	8821.52i	0.634258	+	1.09857i	0.986672	+	0.162723i	$0.0520277\pi$
$401$	5093.10	+	8821.52i	0.634258	+	1.09857i	−0.352414	+	0.935844i	$0.614639\pi$
$402$	496.482	+	2113.22i	0.0615977	+	0.262184i
$403$	419.332	+	242.102i	0.0518323	+	0.0299254i
$404$	−6654.38			−0.819474
$405$		0			0
$406$	−199.223			−0.0243529
$407$	8731.15	+	5040.93i	1.06336	+	0.613930i
$408$	544.472	+	2317.49i	0.0660672	+	0.281208i
$409$	3457.12	+	5987.91i	0.417955	+	0.723920i	0.995734	−	0.0922740i	$-0.0294136\pi$
$409$	3457.12	+	5987.91i	0.417955	+	0.723920i	−0.577778	+	0.816194i	$0.696080\pi$
$410$		0			0
$411$	−1891.36	+	6272.94i	−0.226993	+	0.752850i
$412$	−5783.73	−	3339.24i	−0.691612	−	0.399302i
$413$			4040.41i			0.481394i
$414$	2357.88	−	1172.65i	0.279911	−	0.139209i
$415$		0			0
$416$	3488.75	−	6042.68i	0.411177	−	0.712180i
$417$	−1748.73	+	1643.39i	−0.205361	+	0.192991i
$418$	2597.96	−	1499.93i	0.303996	−	0.175512i
$419$	2560.16	+	4434.32i	0.298501	+	0.517019i	0.975793	−	0.218695i	$-0.0701801\pi$
$419$	2560.16	+	4434.32i	0.298501	+	0.517019i	−0.677292	+	0.735714i	$0.736847\pi$
$420$		0			0
$421$	−933.246	+	1616.43i	−0.108037	+	0.187126i	−0.914975	−	0.403511i	$-0.867790\pi$
$421$	−933.246	+	1616.43i	−0.108037	+	0.187126i	0.806938	+	0.590636i	$0.201123\pi$
$422$		−	2398.38i		−	0.276662i
$423$	−1667.48	−	103.661i	−0.191668	−	0.0119153i
$424$	−9537.16			−1.09237
$425$		0			0
$426$	−556.580	+	1845.97i	−0.0633014	+	0.209947i
$427$	−2309.11	+	1333.17i	−0.261700	+	0.151092i
$428$	−5451.79	+	3147.59i	−0.615706	+	0.355478i
$429$	10642.4	−	2500.34i	1.19772	−	0.281393i
$430$		0			0
$431$	−4090.64			−0.457168			−0.228584	−	0.973524i	$-0.573410\pi$
$431$	−4090.64			−0.457168			−0.228584	+	0.973524i	$0.573410\pi$
$432$	3091.19	−	526.391i	0.344271	−	0.0586250i
$433$		−	633.052i		−	0.0702599i	−0.999383	−	0.0351299i	$-0.988815\pi$
$433$		−	633.052i		−	0.0702599i	0.999383	−	0.0351299i	$-0.0111845\pi$
$434$	45.2311	−	78.3426i	0.00500268	−	0.00866490i
$435$		0			0
$436$	5433.34	+	9410.81i	0.596811	+	1.03371i
$437$	2403.68	−	1387.76i	0.263120	−	0.151912i
$438$	−6318.16	−	1905.00i	−0.689254	−	0.207818i
$439$	−5653.26	+	9791.74i	−0.614614	+	1.06454i	0.375838	+	0.926685i	$0.377355\pi$
$439$	−5653.26	+	9791.74i	−0.614614	+	1.06454i	−0.990452	+	0.137857i	$0.955979\pi$
$440$		0			0
$441$	7128.40	+	4728.45i	0.769723	+	0.510576i
$442$		−	1219.75i		−	0.131261i
$443$	−7171.82	−	4140.65i	−0.769172	−	0.444082i	0.0634071	−	0.997988i	$-0.479803\pi$
$443$	−7171.82	−	4140.65i	−0.769172	−	0.444082i	−0.832579	+	0.553906i	$0.813137\pi$
$444$	−3920.18	−	4171.45i	−0.419017	−	0.445875i
$445$		0			0
$446$	−1744.13	−	3020.92i	−0.185173	−	0.320728i
$447$	−5525.73	+	5192.88i	−0.584694	+	0.549474i
$448$	−336.599	−	194.335i	−0.0354973	−	0.0204944i
$449$	−6888.40			−0.724017			−0.362008	−	0.932175i	$-0.617909\pi$
$449$	−6888.40			−0.724017			−0.362008	+	0.932175i	$0.617909\pi$
$450$		0			0
$451$	−12062.4			−1.25941
$452$	−8560.17	−	4942.22i	−0.890789	−	0.514297i
$453$	−7667.96	−	2311.98i	−0.795302	−	0.239793i
$454$	2053.80	+	3557.28i	0.212312	+	0.367735i
$455$		0			0
$456$	−3826.79	+	899.070i	−0.392995	+	0.0923307i
$457$	−3709.71	−	2141.80i	−0.379722	−	0.219233i	0.297975	−	0.954574i	$-0.403689\pi$
$457$	−3709.71	−	2141.80i	−0.379722	−	0.219233i	−0.677697	+	0.735341i	$0.737022\pi$
$458$		−	5908.09i		−	0.602766i
$459$	2554.14	−	2117.78i	0.259732	−	0.215359i
$460$		0			0
$461$	−6889.16	+	11932.4i	−0.696009	+	1.20552i	0.273831	+	0.961778i	$0.411709\pi$
$461$	−6889.16	+	11932.4i	−0.696009	+	1.20552i	−0.969840	+	0.243744i	$0.921624\pi$
$462$	−467.131	−	1988.29i	−0.0470409	−	0.200224i
$463$	−4966.25	+	2867.27i	−0.498491	+	0.287804i	−0.728090	−	0.685481i	$-0.759592\pi$
$463$	−4966.25	+	2867.27i	−0.498491	+	0.287804i	0.229599	+	0.973285i	$0.426258\pi$
$464$	−317.068	−	549.178i	−0.0317231	−	0.0549460i
$465$		0			0
$466$	−3829.59	+	6633.04i	−0.380691	+	0.659377i
$467$		−	8950.97i		−	0.886941i	−0.896289	−	0.443470i	$-0.853747\pi$
$467$		−	8950.97i		−	0.886941i	0.896289	−	0.443470i	$-0.146253\pi$
$468$	−6195.25	−	385.138i	−0.611914	−	0.0380406i
$469$	1557.72			0.153366
$470$		0			0
$471$	−11442.4	−	12175.8i	−1.11940	−	1.19115i
$472$	13247.5	−	7648.47i	1.29188	−	0.745867i
$473$	−2968.52	+	1713.88i	−0.288568	+	0.166605i
$474$	−6294.56	−	6698.02i	−0.609955	−	0.649051i
$475$		0			0
$476$	740.203			0.0712755
$477$	5919.12	+	11901.7i	0.568172	+	1.14244i
$478$			1934.41i			0.185100i
$479$	4840.51	−	8384.00i	0.461729	−	0.799739i	−0.537318	−	0.843380i	$-0.680562\pi$
$479$	4840.51	−	8384.00i	0.461729	−	0.799739i	0.999047	+	0.0436411i	$0.0138958\pi$
$480$		0			0
$481$	3384.52	+	5862.16i	0.320833	+	0.555699i
$482$	−744.637	+	429.917i	−0.0703678	+	0.0406269i
$483$	−432.198	−	1839.60i	−0.0407157	−	0.173302i
$484$	−5513.00	+	9548.80i	−0.517750	+	0.896769i
$485$		0			0
$486$	3063.25	+	4199.73i	0.285909	+	0.391983i
$487$			8704.66i			0.809950i	0.914328	+	0.404975i	$0.132720\pi$
$487$			8704.66i			0.809950i	−0.914328	+	0.404975i	$0.867280\pi$
$488$	8742.26	+	5047.35i	0.810950	+	0.468202i
$489$	4793.30	−	1126.14i	0.443273	−	0.104143i
$490$		0			0
$491$	7797.85	+	13506.3i	0.716725	+	1.24140i	0.962290	+	0.272024i	$0.0876930\pi$
$491$	7797.85	+	13506.3i	0.716725	+	1.24140i	−0.245565	+	0.969380i	$0.578974\pi$
$492$	6557.36	+	1977.12i	0.600871	+	0.181170i
$493$	−581.094	−	335.495i	−0.0530855	−	0.0306489i
$494$	2014.13			0.183441
$495$		0			0
$496$	287.945			0.0260668
$497$	1198.19	+	691.776i	0.108141	+	0.0624354i
$498$	−3709.19	+	3485.76i	−0.333761	+	0.313656i
$499$	−4848.14	−	8397.22i	−0.434935	−	0.753329i	0.562355	−	0.826896i	$-0.309895\pi$
$499$	−4848.14	−	8397.22i	−0.434935	−	0.753329i	−0.997290	+	0.0735663i	$0.976562\pi$
$500$		0			0
$501$	2440.93	+	2597.39i	0.217670	+	0.231622i
$502$	2026.90	+	1170.23i	0.180209	+	0.104044i
$503$		−	20949.7i		−	1.85706i	−0.371253	−	0.928532i	$-0.621072\pi$
$503$		−	20949.7i		−	1.85706i	0.371253	−	0.928532i	$-0.378928\pi$
$504$	−166.061	+	2671.22i	−0.0146764	+	0.236082i
$505$		0			0
$506$	2729.85	−	4728.24i	0.239835	−	0.415407i
$507$	−3902.47	−	1176.64i	−0.341844	−	0.103070i
$508$	−6389.14	+	3688.77i	−0.558016	+	0.322171i
$509$	5637.37	+	9764.22i	0.490908	+	0.850278i	0.999945	−	0.0104668i	$-0.00333174\pi$
$509$	5637.37	+	9764.22i	0.490908	+	0.850278i	−0.509037	+	0.860745i	$0.669998\pi$
$510$		0			0
$511$	−2367.73	+	4101.03i	−0.204975	+	0.355027i
$512$		−	7613.21i		−	0.657148i
$513$	3497.03	+	4217.57i	0.300970	+	0.362983i
$514$	−4936.62			−0.423628
$515$		0			0
$516$	1894.67	−	445.135i	0.161644	−	0.0379767i
$517$	−2999.74	+	1731.90i	−0.255181	+	0.147329i
$518$	1095.21	−	632.320i	0.0928972	−	0.0536342i
$519$	3319.24	−	11008.7i	0.280729	−	0.931074i
$520$		0			0
$521$	8675.49			0.729520			0.364760	−	0.931102i	$-0.381151\pi$
$521$	8675.49			0.729520			0.364760	+	0.931102i	$0.381151\pi$
$522$	581.094	−	876.032i	0.0487237	−	0.0734538i
$523$			4226.14i			0.353339i	0.984270	+	0.176670i	$0.0565324\pi$
$523$			4226.14i			0.353339i	−0.984270	+	0.176670i	$0.943468\pi$
$524$	3143.62	−	5444.90i	0.262079	−	0.453934i
$525$		0			0
$526$	2838.91	+	4917.14i	0.235328	+	0.407599i
$527$	263.860	−	152.340i	0.0218101	−	0.0125921i
$528$	4737.46	−	4452.10i	0.390477	−	0.366956i
$529$	−3557.79	+	6162.27i	−0.292413	+	0.506474i
$530$		0			0
$531$	−17766.7	−	11785.1i	−1.45199	−	0.963143i
$532$			1222.27i			0.0996095i
$533$	−7013.75	−	4049.39i	−0.569980	−	0.329078i
$534$	−833.258	+	2763.60i	−0.0675255	+	0.223957i
$535$		0			0
$536$	−2948.75	−	5107.38i	−0.237624	−	0.411577i
$537$	−3592.88	−	15292.7i	−0.288723	−	1.22892i
$538$	−7238.72	−	4179.28i	−0.580081	−	0.334910i
$539$	17734.9			1.41725
$540$		0			0
$541$	13357.8			1.06154			0.530771	−	0.847515i	$-0.321902\pi$
$541$	13357.8			1.06154			0.530771	+	0.847515i	$0.321902\pi$
$542$	−3798.96	−	2193.33i	−0.301069	−	0.173822i
$543$	465.205	+	1980.09i	0.0367658	+	0.156490i
$544$	−2195.26	−	3802.29i	−0.173016	−	0.299673i
$545$		0			0
$546$	395.860	−	1312.92i	0.0310280	−	0.102908i
$547$	−18767.7	−	10835.6i	−1.46700	−	0.846974i	−0.467684	−	0.883896i	$-0.654911\pi$
$547$	−18767.7	−	10835.6i	−1.46700	−	0.846974i	−0.999318	+	0.0369219i	$0.988245\pi$
$548$		−	7712.78i		−	0.601229i
$549$	872.964	−	14042.3i	0.0678637	−	1.09164i
$550$		0			0
$551$	553.991	−	959.541i	0.0428327	−	0.0741884i
$552$	−5213.46	+	4899.42i	−0.401992	+	0.377778i
$553$	−5712.12	+	3297.90i	−0.439248	+	0.253600i
$554$	2140.32	+	3707.15i	0.164140	+	0.284299i
$555$		0			0
$556$	1412.48	−	2446.48i	0.107738	−	0.186608i
$557$			7477.63i			0.568828i	0.958702	+	0.284414i	$0.0917991\pi$
$557$			7477.63i			0.568828i	−0.958702	+	0.284414i	$0.908201\pi$
$558$	212.561	+	427.402i	0.0161262	+	0.0324254i
$559$	−2301.42			−0.174132
$560$		0			0
$561$	1985.78	−	6586.10i	0.149447	−	0.495660i
$562$	−5880.75	+	3395.25i	−0.441396	+	0.254840i
$563$	20182.4	−	11652.3i	1.51082	−	0.872269i	0.510895	−	0.859643i	$-0.329314\pi$
$563$	20182.4	−	11652.3i	1.51082	−	0.872269i	0.999920	−	0.0126262i	$-0.00401914\pi$
$564$	1914.59	−	449.816i	0.142941	−	0.0335827i
$565$		0			0
$566$	6236.92			0.463176
$567$	3436.56	−	1450.63i	0.254536	−	0.107444i
$568$		−	5238.10i		−	0.386947i
$569$	−7324.54	+	12686.5i	−0.539650	+	0.934701i	0.459273	+	0.888295i	$0.348110\pi$
$569$	−7324.54	+	12686.5i	−0.539650	+	0.934701i	−0.998923	+	0.0464057i	$0.985223\pi$
$570$		0			0
$571$	−11582.0	−	20060.6i	−0.848846	−	1.47025i	−0.882239	−	0.470803i	$-0.843964\pi$
$571$	−11582.0	−	20060.6i	−0.848846	−	1.47025i	0.0333922	−	0.999442i	$-0.489369\pi$
$572$	−11145.1	+	6434.61i	−0.814683	+	0.470358i
$573$	−17340.6	−	5228.38i	−1.26425	−	0.381185i
$574$	−756.536	+	1310.36i	−0.0550125	+	0.0952845i
$575$		0			0
$576$	1836.33	−	913.268i	0.132836	−	0.0660640i
$577$			7865.97i			0.567529i	0.958894	+	0.283765i	$0.0915834\pi$
$577$			7865.97i			0.567529i	−0.958894	+	0.283765i	$0.908417\pi$
$578$	5174.07	+	2987.25i	0.372341	+	0.214971i
$579$	−7882.15	−	8387.38i	−0.565753	−	0.602016i
$580$		0			0
$581$	1826.29	+	3163.23i	0.130408	+	0.225874i
$582$	389.853	−	366.370i	0.0277662	−	0.0260937i
$583$	23866.5	+	13779.3i	1.69545	+	0.978869i
$584$	17928.4			1.27034
$585$		0			0
$586$	−9413.99			−0.663632
$587$	828.078	+	478.091i	0.0582256	+	0.0336166i	0.528830	−	0.848728i	$-0.322631\pi$
$587$	828.078	+	478.091i	0.0582256	+	0.0336166i	−0.470605	+	0.882344i	$0.655964\pi$
$588$	−9641.06	−	2906.89i	−0.676174	−	0.203874i
$589$	251.554	+	435.704i	0.0175978	+	0.0304803i
$590$		0			0
$591$	20107.8	−	4724.15i	1.39953	−	0.328808i
$592$	3486.10	+	2012.70i	0.242023	+	0.139732i
$593$			16966.0i			1.17489i	0.809265	+	0.587444i	$0.199866\pi$
$593$			16966.0i			1.17489i	−0.809265	+	0.587444i	$0.800134\pi$
$594$	10105.5	+	3745.36i	0.698038	+	0.258710i
$595$		0			0
$596$	4463.22	−	7730.53i	0.306746	−	0.531300i
$597$	1848.42	+	7867.57i	0.126718	+	0.539361i
$598$	3174.58	−	1832.84i	0.217087	−	0.125335i
$599$	−3095.70	−	5361.92i	−0.211164	−	0.365746i	0.740915	−	0.671598i	$-0.234392\pi$
$599$	−3095.70	−	5361.92i	−0.211164	−	0.365746i	−0.952079	+	0.305852i	$0.901059\pi$
$600$		0			0
$601$	1359.27	−	2354.33i	0.0922559	−	0.159792i	−0.816204	−	0.577764i	$-0.803926\pi$
$601$	1359.27	−	2354.33i	0.0922559	−	0.159792i	0.908460	+	0.417972i	$0.137259\pi$
$602$			429.968i			0.0291099i
$603$	−4543.55	+	6849.66i	−0.306845	+	0.462587i
$604$	9428.00			0.635132
$605$		0			0
$606$	5312.28	+	5652.78i	0.356100	+	0.378925i
$607$	14570.9	−	8412.49i	0.974321	−	0.562524i	0.0737701	−	0.997275i	$-0.476497\pi$
$607$	14570.9	−	8412.49i	0.974321	−	0.562524i	0.900551	+	0.434751i	$0.143164\pi$
$608$	6278.60	−	3624.95i	0.418801	−	0.241795i
$609$	−516.599	−	549.712i	−0.0343738	−	0.0365771i
$610$		0			0
$611$	−2325.62			−0.153985
$612$	−2159.02	+	3254.85i	−0.142604	+	0.214983i
$613$			20175.1i			1.32930i	0.747153	+	0.664652i	$0.231420\pi$
$613$			20175.1i			1.32930i	−0.747153	+	0.664652i	$0.768580\pi$
$614$	−4344.81	+	7525.44i	−0.285574	+	0.494629i
$615$		0			0
$616$	2774.42	+	4805.44i	0.181468	+	0.314313i
$617$	9795.29	−	5655.31i	0.639130	−	0.369002i	−0.145149	−	0.989410i	$-0.546366\pi$
$617$	9795.29	−	5655.31i	0.639130	−	0.369002i	0.784280	+	0.620408i	$0.213033\pi$
$618$	1780.60	+	7578.94i	0.115900	+	0.493317i
$619$	−8529.94	+	14774.3i	−0.553873	+	0.959336i	0.444117	+	0.895969i	$0.353517\pi$
$619$	−8529.94	+	14774.3i	−0.553873	+	0.959336i	−0.997990	+	0.0633676i	$0.979816\pi$
$620$		0			0
$621$	9349.81	+	3465.27i	0.604179	+	0.223924i
$622$		−	9712.56i		−	0.626106i
$623$	1793.82	+	1035.66i	0.115357	+	0.0666017i
$624$	4249.21	−	998.314i	0.272604	−	0.0640457i
$625$		0			0
$626$	947.764	+	1641.58i	0.0605116	+	0.104809i
$627$	10875.4	+	3279.06i	0.692699	+	0.208857i
$628$	17034.0	+	9834.58i	1.08237	+	0.624908i
$629$	4259.34			0.270002
$630$		0			0
$631$	−13186.3			−0.831916			−0.415958	−	0.909384i	$-0.636554\pi$
$631$	−13186.3			−0.831916			−0.415958	+	0.909384i	$0.636554\pi$
$632$	21626.0	+	12485.8i	1.36113	+	0.785850i
$633$	6617.79	−	6219.16i	0.415535	−	0.390505i
$634$	5609.15	+	9715.34i	0.351369	+	0.608589i
$635$		0			0
$636$	−10715.8	−	11402.6i	−0.668094	−	0.710917i
$637$	10312.1	+	5953.68i	0.641412	+	0.370319i
$638$		−	2179.50i		−	0.135246i
$639$	−6536.79	+	3250.96i	−0.404681	+	0.201261i
$640$		0			0
$641$	−8180.99	+	14169.9i	−0.504102	+	0.873131i	0.495886	+	0.868387i	$0.334843\pi$
$641$	−8180.99	+	14169.9i	−0.504102	+	0.873131i	−0.999989	+	0.00474343i	$0.998490\pi$
$642$	7026.05	+	2118.43i	0.431926	+	0.130230i
$643$	24287.6	−	14022.5i	1.48960	−	0.860019i	0.489667	−	0.871910i	$-0.337118\pi$
$643$	24287.6	−	14022.5i	1.48960	−	0.860019i	0.999929	+	0.0118907i	$0.00378502\pi$
$644$	1112.26	+	1926.49i	0.0680577	+	0.117879i
$645$		0			0
$646$	633.685	−	1097.57i	0.0385944	−	0.0668475i
$647$			21247.7i			1.29109i	0.763724	+	0.645543i	$0.223369\pi$
$647$			21247.7i			1.29109i	−0.763724	+	0.645543i	$0.776631\pi$
$648$	−11261.6	−	8521.61i	−0.682713	−	0.516606i
$649$	−44202.1			−2.67347
$650$		0			0
$651$	333.457	−	78.3426i	0.0200756	−	0.00471657i
$652$	−5019.69	+	2898.12i	−0.301513	+	0.174079i
$653$	−1091.07	+	629.928i	−0.0653856	+	0.0377504i	−0.532336	−	0.846533i	$-0.678686\pi$
$653$	−1091.07	+	629.928i	−0.0653856	+	0.0377504i	0.466951	+	0.884283i	$0.345353\pi$
$654$	3656.82	−	12128.3i	0.218644	−	0.725159i
$655$		0			0
$656$	−4816.17			−0.286646
$657$	−11127.0	−	22373.3i	−0.660740	−	1.32857i
$658$			434.489i			0.0257419i
$659$	−6023.35	+	10432.7i	−0.356049	+	0.616695i	−0.987297	−	0.158886i	$-0.949210\pi$
$659$	−6023.35	+	10432.7i	−0.356049	+	0.616695i	0.631248	+	0.775581i	$0.282543\pi$
$660$		0			0
$661$	−6554.04	−	11351.9i	−0.385662	−	0.667986i	0.606199	−	0.795313i	$-0.292693\pi$
$661$	−6554.04	−	11351.9i	−0.385662	−	0.667986i	−0.991861	+	0.127327i	$0.959360\pi$
$662$	11481.8	−	6629.00i	0.674096	−	0.389189i
$663$	3365.62	−	3162.89i	0.197149	−	0.185274i
$664$	6914.30	−	11975.9i	0.404107	−	0.699933i
$665$		0			0
$666$	−414.046	+	6660.25i	−0.0240900	+	0.387507i
$667$		−	2016.51i		−	0.117061i
$668$	−3633.76	−	2097.95i	−0.210471	−	0.121515i
$669$	3812.91	−	12646.0i	0.220352	−	0.730826i
$670$		0			0
$671$	−14584.8	−	25261.7i	−0.839108	−	1.45338i
$672$	−1128.94	−	4805.19i	−0.0648061	−	0.275840i
$673$	2376.07	+	1371.82i	0.136093	+	0.0785734i	0.566501	−	0.824061i	$-0.308297\pi$
$673$	2376.07	+	1371.82i	0.136093	+	0.0785734i	−0.430408	+	0.902635i	$0.641630\pi$
$674$	−6801.06			−0.388675
$675$		0			0
$676$	4798.21			0.272998
$677$	−21654.1	−	12502.0i	−1.22930	−	0.709735i	−0.262415	−	0.964955i	$-0.584519\pi$
$677$	−21654.1	−	12502.0i	−1.22930	−	0.709735i	−0.966883	+	0.255220i	$0.917852\pi$
$678$	2635.37	+	11217.2i	0.149278	+	0.635387i
$679$	−191.952	−	332.470i	−0.0108489	−	0.0187909i
$680$		0			0
$681$	−4489.89	+	14891.3i	−0.252648	+	0.837937i
$682$	857.068	+	494.829i	0.0481215	+	0.0277829i
$683$			4846.23i			0.271502i	0.990743	+	0.135751i	$0.0433447\pi$
$683$			4846.23i			0.271502i	−0.990743	+	0.135751i	$0.956655\pi$
$684$	−5374.63	−	3565.13i	−0.300445	−	0.199292i
$685$		0			0
$686$	2316.54	−	4012.36i	0.128930	−	0.223313i
$687$	16302.1	−	15320.1i	0.905331	−	0.850798i
$688$	−1185.25	+	684.303i	−0.0656790	+	0.0379198i
$689$	9251.54	+	16024.1i	0.511546	+	0.886024i
$690$		0			0
$691$	−1742.29	+	3017.73i	−0.0959187	+	0.166136i	−0.909992	−	0.414627i	$-0.863912\pi$
$691$	−1742.29	+	3017.73i	−0.0959187	+	0.166136i	0.814073	+	0.580763i	$0.197246\pi$
$692$			13535.5i			0.743560i
$693$	4274.94	−	6444.72i	0.234331	−	0.353268i
$694$	−1393.70			−0.0762305
$695$		0			0
$696$	−824.454	+	2734.40i	−0.0449006	+	0.148919i
$697$	−4413.33	+	2548.04i	−0.239837	+	0.138470i
$698$	14449.6	−	8342.49i	0.783562	−	0.452390i
$699$	−28232.8	+	6633.04i	−1.52770	+	0.358919i
$700$		0			0
$701$	15701.4			0.845981			0.422991	−	0.906134i	$-0.360980\pi$
$701$	15701.4			0.845981			0.422991	+	0.906134i	$0.360980\pi$
$702$	4618.58	+	5570.22i	0.248315	+	0.299479i
$703$			7033.32i			0.377335i
$704$	2126.03	−	3682.39i	0.113818	−	0.197138i
$705$		0			0
$706$	2906.55	+	5034.29i	0.154943	+	0.268368i
$707$	4820.73	−	2783.25i	0.256439	−	0.148055i
$708$	24029.2	+	7245.07i	1.27552	+	0.384585i
$709$	7821.72	−	13547.6i	0.414317	−	0.717618i	−0.581039	−	0.813875i	$-0.697354\pi$
$709$	7821.72	−	13547.6i	0.414317	−	0.717618i	0.995356	+	0.0962572i	$0.0306871\pi$
$710$		0			0
$711$	2159.48	−	34736.9i	0.113905	−	1.83226i
$712$		−	7841.98i		−	0.412768i
$713$	792.975	+	457.824i	0.0416510	+	0.0240472i
$714$	−590.914	−	628.790i	−0.0309725	−	0.0329578i
$715$		0			0
$716$	9246.27	+	16015.0i	0.482611	+	0.835907i
$717$	−5337.57	+	5016.05i	−0.278013	+	0.261266i
$718$	615.535	+	355.379i	0.0319938	+	0.0184716i
$719$	6964.13			0.361222			0.180611	−	0.983555i	$-0.442193\pi$
$719$	6964.13			0.361222			0.180611	+	0.983555i	$0.442193\pi$
$720$		0			0
$721$	5586.66			0.288569
$722$	−6339.06	−	3659.86i	−0.326752	−	0.188651i
$723$	−3117.16	−	939.858i	−0.160343	−	0.0483454i
$724$	−1197.20	−	2073.62i	−0.0614554	−	0.106444i
$725$		0			0
$726$	12512.6	−	2939.73i	0.639652	−	0.150281i
$727$	12303.8	+	7103.61i	0.627680	+	0.362391i	0.779853	−	0.625963i	$-0.215294\pi$
$727$	12303.8	+	7103.61i	0.627680	+	0.362391i	−0.152173	+	0.988354i	$0.548627\pi$
$728$			3725.53i			0.189667i
$729$	−3645.00	+	19342.6i	−0.185185	+	0.982704i
$730$		0			0
$731$	−724.072	+	1254.13i	−0.0366358	+	0.0634551i
$732$	3788.03	+	16123.3i	0.191270	+	0.814120i
$733$	−22976.1	+	13265.3i	−1.15777	+	0.668437i	−0.950768	−	0.309905i	$-0.899703\pi$
$733$	−22976.1	+	13265.3i	−1.15777	+	0.668437i	−0.206998	+	0.978341i	$0.566370\pi$
$734$	3167.43	+	5486.15i	0.159280	+	0.275882i
$735$		0			0
$736$	6597.36	−	11427.0i	0.330410	−	0.572288i
$737$			17041.4i			0.851735i
$738$	−3555.30	−	7148.72i	−0.177334	−	0.356569i
$739$	5683.47			0.282909			0.141455	−	0.989945i	$-0.454822\pi$
$739$	5683.47			0.282909			0.141455	+	0.989945i	$0.454822\pi$
$740$		0			0
$741$	5222.78	+	5557.55i	0.258925	+	0.275522i
$742$	2993.74	−	1728.44i	0.148118	−	0.0855161i
$743$	13482.8	−	7784.28i	0.665727	−	0.384358i	−0.128729	−	0.991680i	$-0.541090\pi$
$743$	13482.8	−	7784.28i	0.665727	−	0.384358i	0.794456	+	0.607322i	$0.207756\pi$
$744$	−888.097	−	945.022i	−0.0437624	−	0.0465674i
$745$		0			0
$746$	−6539.50			−0.320949
$747$	−19236.4	−	1195.86i	−0.942199	−	0.0585734i
$748$			8097.82i			0.395836i
$749$	2633.01	−	4560.51i	0.128449	−	0.222480i
$750$		0			0
$751$	4130.82	+	7154.79i	0.200713	+	0.347646i	0.948758	−	0.316002i	$-0.102341\pi$
$751$	4130.82	+	7154.79i	0.200713	+	0.347646i	−0.748045	+	0.663648i	$0.769007\pi$
$752$	−1197.71	+	691.499i	−0.0580798	+	0.0335324i
$753$	2026.90	+	8627.27i	0.0980933	+	0.417523i
$754$	731.666	−	1267.28i	0.0353391	−	0.0612092i
$755$		0			0
$756$	−3380.29	+	2802.78i	−0.162619	+	0.134836i
$757$		−	13381.5i		−	0.642481i	−0.946998	−	0.321240i	$-0.895900\pi$
$757$		−	13381.5i		−	0.642481i	0.946998	−	0.321240i	$-0.104100\pi$
$758$	2377.25	+	1372.51i	0.113913	+	0.0657674i
$759$	20125.2	−	4728.24i	0.962451	−	0.226119i
$760$		0			0
$761$	−2724.92	−	4719.70i	−0.129801	−	0.224821i	0.793799	−	0.608181i	$-0.208100\pi$
$761$	−2724.92	−	4719.70i	−0.129801	−	0.224821i	−0.923599	+	0.383359i	$0.874767\pi$
$762$	8234.08	+	2482.67i	0.391456	+	0.118028i
$763$	−7872.31	−	4545.08i	−0.373521	−	0.215652i
$764$	21320.8			1.00963
$765$		0			0
$766$	−1358.96			−0.0641009
$767$	−25701.6	−	14838.8i	−1.20995	−	0.698564i
$768$	−9476.63	+	8905.79i	−0.445258	+	0.418438i
$769$	−9681.98	−	16769.7i	−0.454020	−	0.786385i	0.544612	−	0.838688i	$-0.316677\pi$
$769$	−9681.98	−	16769.7i	−0.454020	−	0.786385i	−0.998631	+	0.0523033i	$0.983344\pi$
$770$		0			0
$771$	−12801.0	−	13621.5i	−0.597946	−	0.636273i
$772$	11734.0	+	6774.62i	0.547041	+	0.315834i
$773$			1865.54i			0.0868033i	0.999058	+	0.0434017i	$0.0138195\pi$
$773$			1865.54i			0.0868033i	−0.999058	+	0.0434017i	$0.986180\pi$
$774$	−1890.67	−	1254.13i	−0.0878020	−	0.0582413i
$775$		0			0
$776$	−726.725	+	1258.72i	−0.0336184	+	0.0582288i
$777$	4584.70	+	1382.34i	0.211680	+	0.0638239i
$778$	480.614	−	277.483i	0.0221476	−	0.0127869i
$779$	−4207.49	−	7287.58i	−0.193516	−	0.335179i
$780$		0			0
$781$	−7568.02	+	13108.2i	−0.346741	+	0.600574i
$782$		−	2306.59i		−	0.105478i
$783$	3924.03	−	668.212i	0.179098	−	0.0304980i
$784$	7081.05			0.322570
$785$		0			0
$786$	−7134.94	+	1676.29i	−0.323785	+	0.0760703i
$787$	−16634.0	+	9603.65i	−0.753416	+	0.434985i	−0.826927	−	0.562310i	$-0.809913\pi$
$787$	−16634.0	+	9603.65i	−0.753416	+	0.434985i	0.0735110	+	0.997294i	$0.476580\pi$
$788$	−21057.5	+	12157.6i	−0.951959	+	0.549614i
$789$	−6206.25	+	20583.8i	−0.280036	+	0.928775i
$790$		0			0
$791$	8268.50			0.371674
$792$	−29223.1	−	1816.70i	−1.31111	−	0.0815072i
$793$		−	19584.7i		−	0.877017i
$794$	−2003.26	+	3469.76i	−0.0895380	+	0.155084i
$795$		0			0
$796$	−4756.89	−	8239.18i	−0.211813	−	0.366872i
$797$	161.145	−	93.0372i	0.00716193	−	0.00413494i	−0.496415	−	0.868085i	$-0.665350\pi$
$797$	161.145	−	93.0372i	0.00716193	−	0.00413494i	0.503577	+	0.863951i	$0.332017\pi$
$798$	1038.30	−	975.757i	0.0460594	−	0.0432850i
$799$	−731.686	+	1267.32i	−0.0323970	+	0.0561132i
$800$		0			0
$801$	−9786.25	+	4867.03i	−0.431686	+	0.214692i
$802$			13978.3i			0.615452i
$803$	−44865.2	−	25902.9i	−1.97168	−	1.13835i
$804$	2793.22	−	9264.07i	0.122524	−	0.406366i
$805$		0			0
$806$	332.232	+	575.442i	0.0145191	+	0.0251477i
$807$	−7238.72	−	30810.8i	−0.315756	−	1.34398i
$808$	−18251.2	−	10537.3i	−0.794647	−	0.458790i
$809$	−5903.09			−0.256541			−0.128270	−	0.991739i	$-0.540943\pi$
$809$	−5903.09			−0.256541			−0.128270	+	0.991739i	$0.540943\pi$
$810$		0			0
$811$	23111.0			1.00066			0.500331	−	0.865834i	$-0.333212\pi$
$811$	23111.0			1.00066			0.500331	+	0.865834i	$0.333212\pi$
$812$	769.050	+	444.011i	0.0332369	+	0.0191893i
$813$	−3798.96	−	16169.8i	−0.163881	−	0.697542i
$814$	6917.58	+	11981.6i	0.297863	+	0.515915i
$815$		0			0
$816$	792.867	−	2629.64i	0.0340146	−	0.112814i
$817$	−2070.90	−	1195.64i	−0.0886802	−	0.0511995i
$818$			9488.29i			0.405563i
$819$	4649.21	−	2312.21i	0.198360	−	0.0986508i
$820$		0			0
$821$	4822.14	−	8352.20i	0.204987	−	0.355047i	−0.745142	−	0.666906i	$-0.767618\pi$
$821$	4822.14	−	8352.20i	0.204987	−	0.355047i	0.950128	+	0.311859i	$0.100952\pi$
$822$	−6551.87	+	6157.21i	−0.278008	+	0.261262i
$823$	29075.5	−	16786.7i	1.23148	−	0.710994i	0.264140	−	0.964484i	$-0.414912\pi$
$823$	29075.5	−	16786.7i	1.23148	−	0.710994i	0.967338	+	0.253490i	$0.0815785\pi$
$824$	−10575.5	−	18317.3i	−0.447106	−	0.774410i
$825$		0			0
$826$	−2772.29	+	4801.75i	−0.116780	+	0.202269i
$827$		−	25916.1i		−	1.08971i	−0.838530	−	0.544855i	$-0.816585\pi$
$827$		−	25916.1i		−	1.08971i	0.838530	−	0.544855i	$-0.183415\pi$
$828$	−11715.5	−	728.313i	−0.491717	−	0.0305684i
$829$	28650.6			1.20033			0.600166	−	0.799876i	$-0.295101\pi$
$829$	28650.6			1.20033			0.600166	+	0.799876i	$0.295101\pi$
$830$		0			0
$831$	−4679.04	+	15518.6i	−0.195324	+	0.647816i
$832$	2472.38	−	1427.43i	0.103022	−	0.0594799i
$833$	6488.76	−	3746.29i	0.269895	−	0.155824i
$834$	−3205.84	+	753.183i	−0.133105	+	0.0312717i
$835$		0			0
$836$	−13371.7			−0.553192
$837$	−628.135	+	1694.80i	−0.0259397	+	0.0699891i
$838$			7026.51i			0.289650i
$839$	356.480	−	617.441i	0.0146687	−	0.0254070i	−0.858598	−	0.512650i	$-0.828664\pi$
$839$	356.480	−	617.441i	0.0146687	−	0.0254070i	0.873267	+	0.487243i	$0.161997\pi$
$840$		0			0
$841$	11792.0	+	20424.4i	0.483497	+	0.837441i
$842$	−2218.20	+	1280.68i	−0.0907887	+	0.0524169i
$843$	−24617.6	−	7422.50i	−1.00578	−	0.303256i
$844$	−5345.30	+	9258.32i	−0.218001	+	0.377588i
$845$		0			0
$846$	−1910.55	−	1267.32i	−0.0776432	−	0.0515027i
$847$		−	9223.44i		−	0.374169i
$848$	9529.21	+	5501.69i	0.385890	+	0.222793i
$849$	16172.8	+	17209.4i	0.653767	+	0.695672i
$850$		0			0
$851$	6400.27	+	11085.6i	0.257812	+	0.446544i
$852$	6262.66	−	5885.43i	0.251826	−	0.236657i
$853$	−26298.8	−	15183.6i	−1.05563	−	0.609469i	−0.131411	−	0.991328i	$-0.541951\pi$
$853$	−26298.8	−	15183.6i	−1.05563	−	0.609469i	−0.924221	+	0.381859i	$0.875284\pi$
$854$	−3658.96			−0.146612
$855$		0			0
$856$	−19937.1			−0.796069
$857$	−7864.12	−	4540.35i	−0.313458	−	0.180975i	0.335015	−	0.942213i	$-0.391259\pi$
$857$	−7864.12	−	4540.35i	−0.313458	−	0.180975i	−0.648473	+	0.761238i	$0.724592\pi$
$858$	14363.3	+	4330.71i	0.571511	+	0.172317i
$859$	13080.1	+	22655.4i	0.519543	+	0.899874i	0.999742	+	0.0227150i	$0.00723102\pi$
$859$	13080.1	+	22655.4i	0.519543	+	0.899874i	−0.480199	+	0.877159i	$0.659436\pi$
$860$		0			0
$861$	−5577.39	+	1310.36i	−0.220763	+	0.0518663i
$862$	−4861.45	−	2806.76i	−0.192090	−	0.110903i
$863$			40102.0i			1.58180i	0.611949	+	0.790898i	$0.290386\pi$
$863$			40102.0i			1.58180i	−0.611949	+	0.790898i	$0.709614\pi$
$864$	24422.5	+	9051.58i	0.961655	+	0.356413i
$865$		0			0
$866$	434.362	−	752.338i	0.0170442	−	0.0295213i
$867$	5174.07	+	22022.9i	0.202677	+	0.862671i
$868$	−349.207	+	201.615i	−0.0136554	+	0.00788392i
$869$	−36079.0	−	62490.6i	−1.40839	−	2.43941i
$870$		0			0
$871$	−5720.87	+	9908.84i	−0.222554	+	0.385474i
$872$			34415.2i			1.33652i
$873$	2021.83	+	125.691i	0.0783834	+	0.00487284i
$874$	3808.80			0.147408
$875$		0			0
$876$	20143.9	+	21435.1i	0.776942	+	0.826741i
$877$	21869.0	−	12626.1i	0.842036	−	0.486149i	−0.0159201	−	0.999873i	$-0.505068\pi$
$877$	21869.0	−	12626.1i	0.842036	−	0.486149i	0.857956	+	0.513724i	$0.171734\pi$
$878$	−13437.0	+	7757.86i	−0.516489	+	0.298195i
$879$	−24411.1	−	25975.8i	−0.936709	−	0.996750i
$880$		0			0
$881$	−2049.26			−0.0783670			−0.0391835	−	0.999232i	$-0.512476\pi$
$881$	−2049.26			−0.0783670			−0.0391835	+	0.999232i	$0.512476\pi$
$882$	5227.23	+	10510.5i	0.199558	+	0.401256i
$883$		−	39413.4i		−	1.50211i	−0.660237	−	0.751057i	$-0.729544\pi$
$883$		−	39413.4i		−	1.50211i	0.660237	−	0.751057i	$-0.270456\pi$
$884$	−2718.47	+	4708.53i	−0.103430	+	0.179146i
$885$		0			0
$886$	−5682.14	−	9841.75i	−0.215457	−	0.373183i
$887$	32015.6	−	18484.2i	1.21193	−	0.699707i	0.248749	−	0.968568i	$-0.419981\pi$
$887$	32015.6	−	18484.2i	1.21193	−	0.699707i	0.963179	+	0.268861i	$0.0866473\pi$
$888$	−4146.45	−	17648.9i	−0.156695	−	0.666957i
$889$	3085.72	−	5344.63i	0.116414	−	0.201634i
$890$		0			0
$891$	15869.8	+	37595.9i	0.596700	+	1.41359i
$892$			15548.7i			0.583641i
$893$	−2092.68	−	1208.21i	−0.0784198	−	0.0452757i
$894$	−10130.0	+	2379.95i	−0.378969	+	0.0890352i
$895$		0			0
$896$	3533.07	+	6119.46i	0.131732	+	0.228166i
$897$	13289.2	+	4006.85i	0.494665	+	0.149147i
$898$	−8186.38	−	4726.41i	−0.304213	−	0.175637i
$899$	365.525			0.0135605
$900$		0			0
$901$	11642.9			0.430499
$902$	−14335.3	−	8276.50i	−0.529173	−	0.305518i
$903$	−1186.40	+	1114.94i	−0.0437220	+	0.0410883i
$904$	−15652.2	−	27110.4i	−0.575868	−	0.997432i
$905$		0			0
$906$	−7526.49	−	8008.92i	−0.275994	−	0.293685i
$907$	−2347.47	−	1355.31i	−0.0859386	−	0.0496167i	0.456415	−	0.889767i	$-0.349133\pi$
$907$	−2347.47	−	1355.31i	−0.0859386	−	0.0496167i	−0.542353	+	0.840150i	$0.682467\pi$
$908$		−	18309.3i		−	0.669180i
$909$	−1822.48	+	29316.1i	−0.0664994	+	1.06970i
$910$		0			0
$911$	−11498.3	+	19915.6i	−0.418172	+	0.724296i	−0.995756	−	0.0920360i	$-0.970663\pi$
$911$	−11498.3	+	19915.6i	−0.418172	+	0.724296i	0.577583	+	0.816332i	$0.303996\pi$
$912$	4342.24	+	1309.24i	0.157660	+	0.0475363i
$913$	−34605.7	+	19979.6i	−1.25441	+	0.724237i
$914$	−2939.15	−	5090.77i	−0.106366	−	0.184231i
$915$		0			0
$916$	−13167.4	+	22806.7i	−0.474961	+	0.822657i
$917$			5259.38i			0.189400i
$918$	4488.52	−	764.337i	0.161376	−	0.0274803i
$919$	39103.8			1.40361			0.701804	−	0.712370i	$-0.252378\pi$
$919$	39103.8			1.40361			0.701804	+	0.712370i	$0.252378\pi$
$920$		0			0
$921$	−32031.2	+	7525.44i	−1.14600	+	0.269242i
$922$	−16374.6	+	9453.86i	−0.584889	+	0.337686i
$923$	−8800.94	+	5081.23i	−0.313853	+	0.181203i
$924$	−2628.09	+	8716.39i	−0.0935690	+	0.310333i
$925$		0			0
$926$	−7869.39			−0.279270
$927$	−16295.2	+	24565.9i	−0.577350	+	0.870388i
$928$		−	5267.30i		−	0.186323i
$929$	−17977.3	+	31137.6i	−0.634894	+	1.09967i	0.351644	+	0.936134i	$0.385623\pi$
$929$	−17977.3	+	31137.6i	−0.634894	+	1.09967i	−0.986538	+	0.163534i	$0.947711\pi$
$930$		0			0
$931$	6186.12	+	10714.7i	0.217768	+	0.377185i
$932$	29566.3	−	17070.1i	1.03914	−	0.599946i
$933$	26799.6	−	25185.3i	0.940387	−	0.883742i
$934$	6141.62	−	10637.6i	0.215161	−	0.372669i
$935$		0			0
$936$	−16382.1	−	10866.6i	−0.572078	−	0.379473i
$937$		−	7263.94i		−	0.253258i	−0.991950	−	0.126629i	$-0.959584\pi$
$937$		−	7263.94i		−	0.253258i	0.991950	−	0.126629i	$-0.0404157\pi$
$938$	1851.24	+	1068.81i	0.0644404	+	0.0372047i
$939$	−2071.95	+	6871.87i	−0.0720079	+	0.238823i
$940$		0			0
$941$	−3739.45	−	6476.92i	−0.129546	−	0.224380i	0.793955	−	0.607977i	$-0.208019\pi$
$941$	−3739.45	−	6476.92i	−0.129546	−	0.224380i	−0.923501	+	0.383597i	$0.874685\pi$
$942$	−5244.15	−	22321.1i	−0.181384	−	0.772041i
$943$	−13263.3	−	7657.57i	−0.458020	−	0.264438i
$944$	−17648.7			−0.608490
$945$		0			0
$946$	−4703.84			−0.161665
$947$	−11683.9	−	6745.68i	−0.400923	−	0.231473i	0.285959	−	0.958242i	$-0.407688\pi$
$947$	−11683.9	−	6745.68i	−0.400923	−	0.231473i	−0.686882	+	0.726769i	$0.741021\pi$
$948$	9370.57	+	39884.8i	0.321036	+	1.36645i
$949$	−17391.4	−	30122.8i	−0.594889	−	1.03038i
$950$		0			0
$951$	−12262.4	+	40669.8i	−0.418124	+	1.38676i
$952$	2030.18	+	1172.13i	0.0691161	+	0.0399042i
$953$			13981.6i			0.475246i	0.971357	+	0.237623i	$0.0763682\pi$
$953$			13981.6i			0.475246i	−0.971357	+	0.237623i	$0.923632\pi$
$954$	−1131.79	+	18205.7i	−0.0384099	+	0.617853i
$955$		0			0
$956$	4311.24	−	7467.29i	0.145853	−	0.252625i
$957$	6013.85	−	5651.59i	0.203135	−	0.190899i
$958$	11505.2	−	6642.54i	0.388013	−	0.224019i
$959$	3225.93	+	5587.48i	0.108624	+	0.188143i
$960$		0			0
$961$	14812.5	−	25656.0i	0.497214	−	0.861200i
$962$			9289.02i			0.311320i
$963$	12373.7	+	24880.1i	0.414057	+	0.832554i
$964$	3832.64			0.128051
$965$		0			0
$966$	748.589	−	2482.79i	0.0249332	−	0.0826940i
$967$	−7864.78	+	4540.73i	−0.261545	+	0.151003i	−0.625039	−	0.780593i	$-0.714917\pi$
$967$	−7864.78	+	4540.73i	−0.261545	+	0.151003i	0.363494	+	0.931597i	$0.381584\pi$
$968$	−30241.4	+	17459.9i	−1.00413	+	0.579734i
$969$	4671.70	−	1097.57i	0.154878	−	0.0363872i
$970$		0			0
$971$	−9709.13			−0.320887			−0.160443	−	0.987045i	$-0.551292\pi$
$971$	−9709.13			−0.320887			−0.160443	+	0.987045i	$0.551292\pi$
$972$	−2464.90	−	23039.1i	−0.0813393	−	0.760267i
$973$			2363.12i			0.0778604i
$974$	−5972.62	+	10344.9i	−0.196484	+	0.340320i
$975$		0			0
$976$	−5823.31	−	10086.3i	−0.190983	−	0.330793i
$977$	9400.63	−	5427.45i	0.307833	−	0.177727i	−0.338123	−	0.941102i	$-0.609792\pi$
$977$	9400.63	−	5427.45i	0.307833	−	0.177727i	0.645956	+	0.763374i	$0.276459\pi$
$978$	6469.19	+	1950.53i	0.211515	+	0.0637742i
$979$	−11330.1	+	19624.3i	−0.369880	+	0.640650i
$980$		0			0
$981$	42947.7	−	21359.3i	1.39777	−	0.695159i
$982$			21401.7i			0.695474i
$983$	−6503.94	−	3755.05i	−0.211031	−	0.121839i	0.390759	−	0.920493i	$-0.372212\pi$
$983$	−6503.94	−	3755.05i	−0.211031	−	0.121839i	−0.601790	+	0.798654i	$0.705546\pi$
$984$	14854.3	+	15806.4i	0.481238	+	0.512084i
$985$		0			0
$986$	−460.393	−	797.424i	−0.0148701	−	0.0257557i
$987$	−1198.88	+	1126.66i	−0.0386633	+	0.0363343i
$988$	−7775.04	−	4488.92i	−0.250361	−	0.144546i
$989$	−4352.08			−0.139927
$990$		0			0
$991$	46125.6			1.47854			0.739268	−	0.673412i	$-0.235172\pi$
$991$	46125.6			1.47854			0.739268	+	0.673412i	$0.235172\pi$
$992$	2071.32	+	1195.88i	0.0662947	+	0.0382753i
$993$	48064.3	+	14491.9i	1.53603	+	0.463129i
$994$	949.311	+	1644.25i	0.0302921	+	0.0524674i
$995$		0			0
$996$	22087.2	−	5189.18i	0.702669	−	0.165086i
$997$	−39274.3	−	22675.0i	−1.24757	−	0.720287i	−0.276948	−	0.960885i	$-0.589323\pi$
$997$	−39274.3	−	22675.0i	−1.24757	−	0.720287i	−0.970625	+	0.240598i	$0.922656\pi$
$998$		−	13306.0i		−	0.422039i
$999$	−19451.1	+	16128.0i	−0.616023	+	0.510779i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.k.b.124.3		8
5.2	odd	4		225.4.e.b.151.1		4
5.3	odd	4		9.4.c.a.7.2	yes	4
5.4	even	2	inner	225.4.k.b.124.2		8
9.4	even	3	inner	225.4.k.b.49.2		8
15.8	even	4		27.4.c.a.19.1		4
20.3	even	4		144.4.i.c.97.2		4
45.2	even	12		2025.4.a.n.1.1		2
45.4	even	6	inner	225.4.k.b.49.3		8
45.7	odd	12		2025.4.a.g.1.2		2
45.13	odd	12		9.4.c.a.4.2	✓	4
45.22	odd	12		225.4.e.b.76.1		4
45.23	even	12		27.4.c.a.10.1		4
45.38	even	12		81.4.a.a.1.2		2
45.43	odd	12		81.4.a.d.1.1		2
60.23	odd	4		432.4.i.c.289.2		4
180.23	odd	12		432.4.i.c.145.2		4
180.43	even	12		1296.4.a.u.1.2		2
180.83	odd	12		1296.4.a.i.1.1		2
180.103	even	12		144.4.i.c.49.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.4.c.a.4.2	✓	4	45.13	odd	12
9.4.c.a.7.2	yes	4	5.3	odd	4
27.4.c.a.10.1		4	45.23	even	12
27.4.c.a.19.1		4	15.8	even	4
81.4.a.a.1.2		2	45.38	even	12
81.4.a.d.1.1		2	45.43	odd	12
144.4.i.c.49.2		4	180.103	even	12
144.4.i.c.97.2		4	20.3	even	4
225.4.e.b.76.1		4	45.22	odd	12
225.4.e.b.151.1		4	5.2	odd	4
225.4.k.b.49.2		8	9.4	even	3	inner
225.4.k.b.49.3		8	45.4	even	6	inner
225.4.k.b.124.2		8	5.4	even	2	inner
225.4.k.b.124.3		8	1.1	even	1	trivial
432.4.i.c.145.2		4	180.23	odd	12
432.4.i.c.289.2		4	60.23	odd	4
1296.4.a.i.1.1		2	180.83	odd	12
1296.4.a.u.1.2		2	180.43	even	12
2025.4.a.g.1.2		2	45.7	odd	12
2025.4.a.n.1.1		2	45.2	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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.18843 + 0.686141i) q^{2} +(1.18843 + 5.05842i) q^{3} +(-3.05842 - 5.29734i) q^{4} +(-2.05842 + 6.82701i) q^{6} +(4.43132 + 2.55842i) q^{7} -19.3723i q^{8} +(-24.1753 + 12.0232i) q^{9} +O(q^{10})\)	\(q+(1.18843 + 0.686141i) q^{2} +(1.18843 + 5.05842i) q^{3} +(-3.05842 - 5.29734i) q^{4} +(-2.05842 + 6.82701i) q^{6} +(4.43132 + 2.55842i) q^{7} -19.3723i q^{8} +(-24.1753 + 12.0232i) q^{9} +(-27.9891 + 48.4786i) q^{11} +(23.1615 - 21.7663i) q^{12} +(-32.5489 + 18.7921i) q^{13} +(3.51087 + 6.08101i) q^{14} +(-11.1753 + 19.3561i) q^{16} +23.6495i q^{17} +(-36.9802 - 2.29894i) q^{18} -39.0516 q^{19} +(-7.67527 + 25.4560i) q^{21} +(-66.5263 + 38.4090i) q^{22} +(-61.5513 + 35.5367i) q^{23} +(97.9932 - 23.0226i) q^{24} -51.5761 q^{26} +(-89.5489 - 108.000i) q^{27} -31.2989i q^{28} +(-14.1861 + 24.5711i) q^{29} +(-6.44158 - 11.1571i) q^{31} +(-160.777 + 92.8247i) q^{32} +(-278.488 - 83.9674i) q^{33} +(-16.2269 + 28.1057i) q^{34} +(137.629 + 91.2927i) q^{36} -180.103i q^{37} +(-46.4101 - 26.7949i) q^{38} +(-133.741 - 142.313i) q^{39} +(107.742 + 186.614i) q^{41} +(-26.5879 + 24.9863i) q^{42} +(53.0299 + 30.6168i) q^{43} +342.410 q^{44} -97.5326 q^{46} +(53.5876 + 30.9388i) q^{47} +(-111.192 - 33.5258i) q^{48} +(-158.409 - 274.372i) q^{49} +(-119.629 + 28.1057i) q^{51} +(199.096 + 114.948i) q^{52} -492.310i q^{53} +(-32.3194 - 189.794i) q^{54} +(49.5625 - 85.8447i) q^{56} +(-46.4101 - 197.539i) q^{57} +(-33.7185 + 19.4674i) q^{58} +(394.815 + 683.840i) q^{59} +(-260.545 + 451.277i) q^{61} -17.6793i q^{62} +(-137.889 - 8.57207i) q^{63} -75.9590 q^{64} +(-273.351 - 290.872i) q^{66} +(263.644 - 152.215i) q^{67} +(125.279 - 72.3301i) q^{68} +(-252.909 - 269.120i) q^{69} +270.391 q^{71} +(232.916 + 468.330i) q^{72} +925.464i q^{73} +(123.576 - 214.040i) q^{74} +(119.436 + 206.870i) q^{76} +(-248.057 + 143.216i) q^{77} +(-61.2946 - 260.894i) q^{78} +(-644.517 + 1116.34i) q^{79} +(439.887 - 581.326i) q^{81} +295.704i q^{82} +(618.198 + 356.917i) q^{83} +(158.323 - 37.1966i) q^{84} +(42.0149 + 72.7720i) q^{86} +(-141.150 - 42.5584i) q^{87} +(939.141 + 542.213i) q^{88} +404.804 q^{89} -192.313 q^{91} +(376.500 + 217.372i) q^{92} +(48.7822 - 45.8437i) q^{93} +(42.4567 + 73.5372i) q^{94} +(-660.619 - 702.963i) q^{96} +(-64.9756 - 37.5137i) q^{97} -434.763i q^{98} +(93.7785 - 1508.50i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{4} + 18 q^{6} - 90 q^{9}+O(q^{10}) \) 8 * q + 10 * q^4 + 18 * q^6 - 90 * q^9	\( 8 q + 10 q^{4} + 18 q^{6} - 90 q^{9} - 132 q^{11} + 120 q^{14} + 14 q^{16} + 308 q^{19} + 42 q^{21} + 198 q^{24} - 1056 q^{26} - 102 q^{29} - 86 q^{31} + 594 q^{34} - 450 q^{36} - 1518 q^{39} - 264 q^{41} + 924 q^{44} - 1056 q^{46} - 1026 q^{49} + 594 q^{51} - 2430 q^{54} - 132 q^{56} + 1596 q^{59} - 878 q^{61} + 2908 q^{64} - 1980 q^{66} - 1782 q^{69} + 5472 q^{71} + 1632 q^{74} + 3058 q^{76} - 1606 q^{79} - 1134 q^{81} - 1284 q^{84} - 66 q^{86} + 1584 q^{89} - 3124 q^{91} + 4200 q^{94} + 2160 q^{96} - 594 q^{99}+O(q^{100}) \) 8 * q + 10 * q^4 + 18 * q^6 - 90 * q^9 - 132 * q^11 + 120 * q^14 + 14 * q^16 + 308 * q^19 + 42 * q^21 + 198 * q^24 - 1056 * q^26 - 102 * q^29 - 86 * q^31 + 594 * q^34 - 450 * q^36 - 1518 * q^39 - 264 * q^41 + 924 * q^44 - 1056 * q^46 - 1026 * q^49 + 594 * q^51 - 2430 * q^54 - 132 * q^56 + 1596 * q^59 - 878 * q^61 + 2908 * q^64 - 1980 * q^66 - 1782 * q^69 + 5472 * q^71 + 1632 * q^74 + 3058 * q^76 - 1606 * q^79 - 1134 * q^81 - 1284 * q^84 - 66 * q^86 + 1584 * q^89 - 3124 * q^91 + 4200 * q^94 + 2160 * q^96 - 594 * q^99

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