LMFDB - Embedded newform 180.7.c.b.91.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,7,Mod(91,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("180.91");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	180.c (of order $2$, degree $1$, 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:	$41.4097350516$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.2
Character	$\chi$	$=$	180.91
Dual form			180.7.c.b.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.99899 + 0.126876i) q^{2} +(63.9678 - 2.02976i) q^{4} +55.9017 q^{5} -335.195i q^{7} +(-511.421 + 24.3521i) q^{8} +O(q^{10})$	\(q+(-7.99899 + 0.126876i) q^{2} +(63.9678 - 2.02976i) q^{4} +55.9017 q^{5} -335.195i q^{7} +(-511.421 + 24.3521i) q^{8} +(-447.157 + 7.09260i) q^{10} +1644.57i q^{11} +1200.29 q^{13} +(42.5283 + 2681.22i) q^{14} +(4087.76 - 259.679i) q^{16} +3941.20 q^{17} -3733.41i q^{19} +(3575.91 - 113.467i) q^{20} +(-208.656 - 13154.9i) q^{22} +4917.71i q^{23} +3125.00 q^{25} +(-9601.13 + 152.288i) q^{26} +(-680.367 - 21441.7i) q^{28} -20383.8 q^{29} +38457.5i q^{31} +(-32665.0 + 2595.81i) q^{32} +(-31525.6 + 500.045i) q^{34} -18738.0i q^{35} +17613.9 q^{37} +(473.681 + 29863.5i) q^{38} +(-28589.3 + 1361.32i) q^{40} -54135.0 q^{41} +3927.72i q^{43} +(3338.08 + 105199. i) q^{44} +(-623.940 - 39336.7i) q^{46} -145724. i q^{47} +5293.27 q^{49} +(-24996.9 + 396.488i) q^{50} +(76780.0 - 2436.31i) q^{52} +223584. q^{53} +91934.0i q^{55} +(8162.69 + 171426. i) q^{56} +(163050. - 2586.22i) q^{58} -349304. i q^{59} +144957. q^{61} +(-4879.34 - 307621. i) q^{62} +(260958. - 24908.3i) q^{64} +67098.4 q^{65} +524780. i q^{67} +(252110. - 7999.71i) q^{68} +(2377.40 + 149885. i) q^{70} +202515. i q^{71} +674498. q^{73} +(-140893. + 2234.78i) q^{74} +(-7577.94 - 238818. i) q^{76} +551250. q^{77} -311497. i q^{79} +(228513. - 14516.5i) q^{80} +(433025. - 6868.44i) q^{82} +975431. i q^{83} +220320. q^{85} +(-498.335 - 31417.8i) q^{86} +(-40048.6 - 841065. i) q^{88} +1.14871e6 q^{89} -402332. i q^{91} +(9981.79 + 314575. i) q^{92} +(18488.9 + 1.16565e6i) q^{94} -208704. i q^{95} +573799. q^{97} +(-42340.8 + 671.589i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8}+O(q^{10}) $ 24 * q - 20 * q^2 - 246 * q^4 + 340 * q^8	$ 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8} - 750 q^{10} + 5040 q^{13} + 2596 q^{14} + 4194 q^{16} - 7000 q^{20} + 45780 q^{22} + 75000 q^{25} - 75852 q^{26} + 54300 q^{28} - 132800 q^{29} + 10700 q^{32} - 173484 q^{34} - 69840 q^{37} - 215800 q^{38} - 14250 q^{40} + 70448 q^{41} + 395668 q^{44} - 158760 q^{46} - 642984 q^{49} - 62500 q^{50} - 210240 q^{52} + 644320 q^{53} + 917708 q^{56} - 1345020 q^{58} - 222864 q^{61} - 1948520 q^{62} + 935922 q^{64} - 266000 q^{65} - 572680 q^{68} + 220500 q^{70} + 771120 q^{73} + 589164 q^{74} - 191544 q^{76} - 1383840 q^{77} + 946000 q^{80} + 2672520 q^{82} - 372000 q^{85} - 1781528 q^{86} + 956940 q^{88} + 1566224 q^{89} + 3040560 q^{92} - 3788352 q^{94} - 1666800 q^{97} + 2709660 q^{98}+O(q^{100}) $ 24 * q - 20 * q^2 - 246 * q^4 + 340 * q^8 - 750 * q^10 + 5040 * q^13 + 2596 * q^14 + 4194 * q^16 - 7000 * q^20 + 45780 * q^22 + 75000 * q^25 - 75852 * q^26 + 54300 * q^28 - 132800 * q^29 + 10700 * q^32 - 173484 * q^34 - 69840 * q^37 - 215800 * q^38 - 14250 * q^40 + 70448 * q^41 + 395668 * q^44 - 158760 * q^46 - 642984 * q^49 - 62500 * q^50 - 210240 * q^52 + 644320 * q^53 + 917708 * q^56 - 1345020 * q^58 - 222864 * q^61 - 1948520 * q^62 + 935922 * q^64 - 266000 * q^65 - 572680 * q^68 + 220500 * q^70 + 771120 * q^73 + 589164 * q^74 - 191544 * q^76 - 1383840 * q^77 + 946000 * q^80 + 2672520 * q^82 - 372000 * q^85 - 1781528 * q^86 + 956940 * q^88 + 1566224 * q^89 + 3040560 * q^92 - 3788352 * q^94 - 1666800 * q^97 + 2709660 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−7.99899	+	0.126876i	−0.999874	+	0.0158595i
$2$	−7.99899	+	0.126876i	−0.999874	+	0.0158595i
$3$		0			0
$3$		0			0
$4$	63.9678	−	2.02976i	0.999497	−	0.0317151i
$5$	55.9017			0.447214
$5$	55.9017			0.447214
$6$		0			0
$7$		−	335.195i		−	0.977245i	−0.872495	−	0.488623i	$-0.837500\pi$
$7$		−	335.195i		−	0.977245i	0.872495	−	0.488623i	$-0.162500\pi$
$8$	−511.421	+	24.3521i	−0.998868	+	0.0475626i
$9$		0			0
$10$	−447.157	+	7.09260i	−0.447157	+	0.00709260i
$11$			1644.57i			1.23559i	0.786340	+	0.617793i	$0.211973\pi$
$11$			1644.57i			1.23559i	−0.786340	+	0.617793i	$0.788027\pi$
$12$		0			0
$13$	1200.29			0.546332			0.273166	−	0.961967i	$-0.411929\pi$
$13$	1200.29			0.546332			0.273166	+	0.961967i	$0.411929\pi$
$14$	42.5283	+	2681.22i	0.0154986	+	0.977122i
$15$		0			0
$16$	4087.76	−	259.679i	0.997988	−	0.0633982i
$17$	3941.20			0.802199			0.401099	−	0.916035i	$-0.368628\pi$
$17$	3941.20			0.802199			0.401099	+	0.916035i	$0.368628\pi$
$18$		0			0
$19$		−	3733.41i		−	0.544308i	−0.962254	−	0.272154i	$-0.912264\pi$
$19$		−	3733.41i		−	0.544308i	0.962254	−	0.272154i	$-0.0877360\pi$
$20$	3575.91	−	113.467i	0.446989	−	0.0141834i
$21$		0			0
$22$	−208.656	−	13154.9i	−0.0195958	−	1.23543i
$23$			4917.71i			0.404184i	0.979367	+	0.202092i	$0.0647740\pi$
$23$			4917.71i			0.404184i	−0.979367	+	0.202092i	$0.935226\pi$
$24$		0			0
$25$	3125.00			0.200000
$26$	−9601.13	+	152.288i	−0.546263	+	0.00866457i
$27$		0			0
$28$	−680.367	−	21441.7i	−0.0309934	−	0.976753i
$29$	−20383.8			−0.835780			−0.417890	−	0.908498i	$-0.637230\pi$
$29$	−20383.8			−0.835780			−0.417890	+	0.908498i	$0.637230\pi$
$30$		0			0
$31$			38457.5i			1.29091i	0.763799	+	0.645454i	$0.223332\pi$
$31$			38457.5i			1.29091i	−0.763799	+	0.645454i	$0.776668\pi$
$32$	−32665.0	+	2595.81i	−0.996857	+	0.0792179i
$33$		0			0
$34$	−31525.6	+	500.045i	−0.802098	+	0.0127225i
$35$		−	18738.0i		−	0.437037i
$36$		0			0
$37$	17613.9			0.347736			0.173868	−	0.984769i	$-0.444373\pi$
$37$	17613.9			0.347736			0.173868	+	0.984769i	$0.444373\pi$
$38$	473.681	+	29863.5i	0.00863247	+	0.544240i
$39$		0			0
$40$	−28589.3	+	1361.32i	−0.446707	+	0.0212707i
$41$	−54135.0			−0.785464			−0.392732	−	0.919653i	$-0.628470\pi$
$41$	−54135.0			−0.785464			−0.392732	+	0.919653i	$0.628470\pi$
$42$		0			0
$43$			3927.72i			0.0494010i	0.999695	+	0.0247005i	$0.00786321\pi$
$43$			3927.72i			0.0494010i	−0.999695	+	0.0247005i	$0.992137\pi$
$44$	3338.08	+	105199.i	0.0391867	+	1.23497i
$45$		0			0
$46$	−623.940	−	39336.7i	−0.00641017	−	0.404133i
$47$		−	145724.i		−	1.40358i	−0.712382	−	0.701792i	$-0.752384\pi$
$47$		−	145724.i		−	1.40358i	0.712382	−	0.701792i	$-0.247616\pi$
$48$		0			0
$49$	5293.27			0.0449920
$50$	−24996.9	+	396.488i	−0.199975	+	0.00317191i
$51$		0			0
$52$	76780.0	−	2436.31i	0.546057	−	0.0173270i
$53$	223584.			1.50180			0.750902	−	0.660414i	$-0.229619\pi$
$53$	223584.			1.50180			0.750902	+	0.660414i	$0.229619\pi$
$54$		0			0
$55$			91934.0i			0.552571i
$56$	8162.69	+	171426.i	0.0464803	+	0.976139i
$57$		0			0
$58$	163050.	−	2586.22i	0.835675	−	0.0132551i
$59$		−	349304.i		−	1.70078i	−0.526156	−	0.850388i	$-0.676367\pi$
$59$		−	349304.i		−	1.70078i	0.526156	−	0.850388i	$-0.323633\pi$
$60$		0			0
$61$	144957.			0.638631			0.319316	−	0.947648i	$-0.396547\pi$
$61$	144957.			0.638631			0.319316	+	0.947648i	$0.396547\pi$
$62$	−4879.34	−	307621.i	−0.0204732	−	1.29075i
$63$		0			0
$64$	260958.	−	24908.3i	0.995476	−	0.0950176i
$65$	67098.4			0.244327
$66$		0			0
$67$			524780.i			1.74483i	0.488766	+	0.872415i	$0.337447\pi$
$67$			524780.i			1.74483i	−0.488766	+	0.872415i	$0.662553\pi$
$68$	252110.	−	7999.71i	0.801795	−	0.0254418i
$69$		0			0
$70$	2377.40	+	149885.i	0.00693121	+	0.436982i
$71$			202515.i			0.565825i	0.959146	+	0.282913i	$0.0913006\pi$
$71$			202515.i			0.565825i	−0.959146	+	0.282913i	$0.908699\pi$
$72$		0			0
$73$	674498.			1.73385			0.866927	−	0.498436i	$-0.166092\pi$
$73$	674498.			1.73385			0.866927	+	0.498436i	$0.166092\pi$
$74$	−140893.	+	2234.78i	−0.347692	+	0.00551493i
$75$		0			0
$76$	−7577.94	−	238818.i	−0.0172628	−	0.544034i
$77$	551250.			1.20747
$78$		0			0
$79$		−	311497.i		−	0.631789i	−0.948794	−	0.315894i	$-0.897695\pi$
$79$		−	311497.i		−	0.631789i	0.948794	−	0.315894i	$-0.102305\pi$
$80$	228513.	−	14516.5i	0.446314	−	0.0283525i
$81$		0			0
$82$	433025.	−	6868.44i	0.785365	−	0.0124571i
$83$			975431.i			1.70593i	0.521965	+	0.852967i	$0.325199\pi$
$83$			975431.i			1.70593i	−0.521965	+	0.852967i	$0.674801\pi$
$84$		0			0
$85$	220320.			0.358754
$86$	−498.335	−	31417.8i	−0.000783476	−	0.0493948i
$87$		0			0
$88$	−40048.6	−	841065.i	−0.0587678	−	1.23419i
$89$	1.14871e6			1.62944			0.814722	−	0.579852i	$-0.196890\pi$
$89$	1.14871e6			1.62944			0.814722	+	0.579852i	$0.196890\pi$
$90$		0			0
$91$		−	402332.i		−	0.533900i
$92$	9981.79	+	314575.i	0.0128187	+	0.403981i
$93$		0			0
$94$	18488.9	+	1.16565e6i	0.0222602	+	1.40341i
$95$		−	208704.i		−	0.243422i
$96$		0			0
$97$	573799.			0.628702			0.314351	−	0.949307i	$-0.398213\pi$
$97$	573799.			0.628702			0.314351	+	0.949307i	$0.398213\pi$
$98$	−42340.8	+	671.589i	−0.0449864	+	0.000713552i
$99$		0			0
$100$	199899.	−	6343.01i	0.199899	−	0.00634301i
$101$	−376616.			−0.365540			−0.182770	−	0.983156i	$-0.558506\pi$
$101$	−376616.			−0.365540			−0.182770	+	0.983156i	$0.558506\pi$
$102$		0			0
$103$		−	2.16630e6i		−	1.98247i	−0.132097	−	0.991237i	$-0.542171\pi$
$103$		−	2.16630e6i		−	1.98247i	0.132097	−	0.991237i	$-0.457829\pi$
$104$	−613854.	+	29229.6i	−0.545714	+	0.0259850i
$105$		0			0
$106$	−1.78845e6	+	28367.5i	−1.50161	+	0.0238179i
$107$			1.67749e6i			1.36933i	0.728858	+	0.684664i	$0.240051\pi$
$107$			1.67749e6i			1.36933i	−0.728858	+	0.684664i	$0.759949\pi$
$108$		0			0
$109$	1.58805e6			1.22626			0.613132	−	0.789981i	$-0.289910\pi$
$109$	1.58805e6			1.22626			0.613132	+	0.789981i	$0.289910\pi$
$110$	−11664.2	−	735380.i	−0.00876352	−	0.552502i
$111$		0			0
$112$	−87043.2	−	1.37020e6i	−0.0619556	−	0.975279i
$113$	1.75946e6			1.21940			0.609699	−	0.792633i	$-0.291290\pi$
$113$	1.75946e6			1.21940			0.609699	+	0.792633i	$0.291290\pi$
$114$		0			0
$115$			274908.i			0.180757i
$116$	−1.30391e6	+	41374.4i	−0.835360	+	0.0265068i
$117$		0			0
$118$	44318.3	+	2.79408e6i	0.0269735	+	1.70056i
$119$		−	1.32107e6i		−	0.783945i
$120$		0			0
$121$	−933037.			−0.526675
$122$	−1.15951e6	+	18391.6i	−0.638551	+	0.0101284i
$123$		0			0
$124$	78059.6	+	2.46004e6i	0.0409413	+	1.29026i
$125$	174693.			0.0894427
$126$		0			0
$127$		−	705905.i		−	0.344616i	−0.985043	−	0.172308i	$-0.944878\pi$
$127$		−	705905.i		−	0.344616i	0.985043	−	0.172308i	$-0.0551224\pi$
$128$	−2.08424e6	+	232351.i	−0.993843	+	0.110793i
$129$		0			0
$130$	−536719.	+	8513.19i	−0.244296	+	0.00387491i
$131$		−	1.87952e6i		−	0.836052i	−0.908435	−	0.418026i	$-0.862722\pi$
$131$		−	1.87952e6i		−	0.836052i	0.908435	−	0.418026i	$-0.137278\pi$
$132$		0			0
$133$	−1.25142e6			−0.531922
$134$	−66582.1	−	4.19771e6i	−0.0276722	−	1.74461i
$135$		0			0
$136$	−2.01561e6	+	95976.4i	−0.801291	+	0.0381547i
$137$	2.33412e6			0.907740			0.453870	−	0.891068i	$-0.350043\pi$
$137$	2.33412e6			0.907740			0.453870	+	0.891068i	$0.350043\pi$
$138$		0			0
$139$			4.70664e6i			1.75253i	0.481827	+	0.876267i	$0.339974\pi$
$139$			4.70664e6i			1.75253i	−0.481827	+	0.876267i	$0.660026\pi$
$140$	−38033.7	−	1.19863e6i	−0.0138607	−	0.436817i
$141$		0			0
$142$	−25694.3	−	1.61992e6i	−0.00897372	−	0.565754i
$143$			1.97396e6i			0.675041i
$144$		0			0
$145$	−1.13949e6			−0.373772
$146$	−5.39531e6	+	85577.8i	−1.73364	+	0.0274981i
$147$		0			0
$148$	1.12672e6	−	35752.0i	0.347561	−	0.0110285i
$149$	−1.58358e6			−0.478718			−0.239359	−	0.970931i	$-0.576937\pi$
$149$	−1.58358e6			−0.478718			−0.239359	+	0.970931i	$0.576937\pi$
$150$		0			0
$151$			1.08810e6i			0.316036i	0.987436	+	0.158018i	$0.0505105\pi$
$151$			1.08810e6i			0.316036i	−0.987436	+	0.158018i	$0.949490\pi$
$152$	90916.2	+	1.90934e6i	0.0258887	+	0.543692i
$153$		0			0
$154$	−4.40945e6	+	69940.6i	−1.20732	+	0.0191499i
$155$			2.14984e6i			0.577312i
$156$		0			0
$157$	5.02586e6			1.29871			0.649354	−	0.760486i	$-0.275039\pi$
$157$	5.02586e6			1.29871			0.649354	+	0.760486i	$0.275039\pi$
$158$	39521.5	+	2.49166e6i	0.0100199	+	0.631709i
$159$		0			0
$160$	−1.82603e6	+	145110.i	−0.445808	+	0.0354273i
$161$	1.64839e6			0.394987
$162$		0			0
$163$		−	4.60727e6i		−	1.06385i	−0.846791	−	0.531926i	$-0.821468\pi$
$163$		−	4.60727e6i		−	1.06385i	0.846791	−	0.531926i	$-0.178532\pi$
$164$	−3.46289e6	+	109881.i	−0.785069	+	0.0249110i
$165$		0			0
$166$	−123759.	−	7.80246e6i	−0.0270553	−	1.70572i
$167$		−	2.82376e6i		−	0.606287i	−0.952945	−	0.303143i	$-0.901964\pi$
$167$		−	2.82376e6i		−	0.606287i	0.952945	−	0.303143i	$-0.0980361\pi$
$168$		0			0
$169$	−3.38611e6			−0.701521
$170$	−1.76234e6	+	27953.3i	−0.358709	+	0.00568967i
$171$		0			0
$172$	7972.35	+	251248.i	0.00156675	+	0.0493761i
$173$	−2.40352e6			−0.464205			−0.232102	−	0.972691i	$-0.574560\pi$
$173$	−2.40352e6			−0.464205			−0.232102	+	0.972691i	$0.574560\pi$
$174$		0			0
$175$		−	1.04748e6i		−	0.195449i
$176$	427059.	+	6.72259e6i	0.0783340	+	1.23310i
$177$		0			0
$178$	−9.18850e6	+	145744.i	−1.62924	+	0.0258422i
$179$		−	3.86839e6i		−	0.674484i	−0.941418	−	0.337242i	$-0.890506\pi$
$179$		−	3.86839e6i		−	0.674484i	0.941418	−	0.337242i	$-0.109494\pi$
$180$		0			0
$181$	−8.08086e6			−1.36277			−0.681384	−	0.731926i	$-0.738622\pi$
$181$	−8.08086e6			−1.36277			−0.681384	+	0.731926i	$0.738622\pi$
$182$	51046.4	+	3.21825e6i	0.00846741	+	0.533833i
$183$		0			0
$184$	−119756.	−	2.51502e6i	−0.0192241	−	0.403727i
$185$	984645.			0.155512
$186$		0			0
$187$			6.48157e6i			0.991186i
$188$	−295786.	−	9.32166e6i	−0.0445148	−	1.40288i
$189$		0			0
$190$	26479.6	+	1.66942e6i	0.00386056	+	0.243391i
$191$		−	3.72445e6i		−	0.534518i	−0.963625	−	0.267259i	$-0.913882\pi$
$191$		−	3.72445e6i		−	0.534518i	0.963625	−	0.267259i	$-0.0861179\pi$
$192$		0			0
$193$	2.55172e6			0.354945			0.177473	−	0.984126i	$-0.443208\pi$
$193$	2.55172e6			0.354945			0.177473	+	0.984126i	$0.443208\pi$
$194$	−4.58982e6	+	72801.5i	−0.628623	+	0.00997092i
$195$		0			0
$196$	338599.	−	10744.1i	0.0449694	−	0.00142692i
$197$	1.25901e7			1.64675			0.823377	−	0.567495i	$-0.192087\pi$
$197$	1.25901e7			1.64675			0.823377	+	0.567495i	$0.192087\pi$
$198$		0			0
$199$		−	2.07688e6i		−	0.263544i	−0.991280	−	0.131772i	$-0.957933\pi$
$199$		−	2.07688e6i		−	0.263544i	0.991280	−	0.131772i	$-0.0420667\pi$
$200$	−1.59819e6	+	76100.2i	−0.199774	+	0.00951253i
$201$		0			0
$202$	3.01255e6	−	47783.6i	0.365494	−	0.00579729i
$203$			6.83256e6i			0.816762i
$204$		0			0
$205$	−3.02624e6			−0.351270
$206$	274852.	+	1.73282e7i	0.0314411	+	1.98222i
$207$		0			0
$208$	4.90651e6	−	311691.i	0.545233	−	0.0346365i
$209$	6.13984e6			0.672540
$210$		0			0
$211$			1.47283e7i			1.56786i	0.620851	+	0.783929i	$0.286787\pi$
$211$			1.47283e7i			1.56786i	−0.620851	+	0.783929i	$0.713213\pi$
$212$	1.43022e7	−	453823.i	1.50105	−	0.0476298i
$213$		0			0
$214$	−212833.	−	1.34182e7i	−0.0217169	−	1.36916i
$215$			219566.i			0.0220928i
$216$		0			0
$217$	1.28908e7			1.26153
$218$	−1.27028e7	+	201485.i	−1.22611	+	0.0194480i
$219$		0			0
$220$	186604.	+	5.88082e6i	0.0175248	+	0.552293i
$221$	4.73059e6			0.438267
$222$		0			0
$223$		−	7.72762e6i		−	0.696837i	−0.937339	−	0.348418i	$-0.886719\pi$
$223$		−	7.72762e6i		−	0.696837i	0.937339	−	0.348418i	$-0.113281\pi$
$224$	870103.	+	1.09492e7i	0.0774153	+	0.974174i
$225$		0			0
$226$	−1.40739e7	+	223234.i	−1.21924	+	0.0193391i
$227$		−	1.85645e7i		−	1.58711i	−0.608500	−	0.793554i	$-0.708229\pi$
$227$		−	1.85645e7i		−	1.58711i	0.608500	−	0.793554i	$-0.291771\pi$
$228$		0			0
$229$	1.55847e7			1.29775			0.648877	−	0.760893i	$-0.275239\pi$
$229$	1.55847e7			1.29775			0.648877	+	0.760893i	$0.275239\pi$
$230$	−34879.3	−	2.19899e6i	−0.00286672	−	0.180734i
$231$		0			0
$232$	1.04247e7	−	496389.i	0.834834	−	0.0397519i
$233$	−6.64517e6			−0.525338			−0.262669	−	0.964886i	$-0.584603\pi$
$233$	−6.64517e6			−0.525338			−0.262669	+	0.964886i	$0.584603\pi$
$234$		0			0
$235$		−	8.14624e6i		−	0.627702i
$236$	−709004.	−	2.23442e7i	−0.0539402	−	1.69992i
$237$		0			0
$238$	167613.	+	1.05672e7i	0.0124330	+	0.783846i
$239$			1.66721e7i			1.22122i	0.791930	+	0.610612i	$0.209076\pi$
$239$			1.66721e7i			1.22122i	−0.791930	+	0.610612i	$0.790924\pi$
$240$		0			0
$241$	−4.37877e6			−0.312825			−0.156412	−	0.987692i	$-0.549993\pi$
$241$	−4.37877e6			−0.312825			−0.156412	+	0.987692i	$0.549993\pi$
$242$	7.46335e6	−	118380.i	0.526609	−	0.00835281i
$243$		0			0
$244$	9.27259e6	−	294229.i	0.638310	−	0.0202542i
$245$	295903.			0.0201210
$246$		0			0
$247$		−	4.48118e6i		−	0.297373i
$248$	−936518.	−	1.96679e7i	−0.0613990	−	1.28945i
$249$		0			0
$250$	−1.39737e6	+	22164.4i	−0.0894315	+	0.00141852i
$251$		−	1.83077e7i		−	1.15774i	−0.815419	−	0.578871i	$-0.803494\pi$
$251$		−	1.83077e7i		−	1.15774i	0.815419	−	0.578871i	$-0.196506\pi$
$252$		0			0
$253$	−8.08750e6			−0.499405
$254$	89562.6	+	5.64653e6i	0.00546545	+	0.344573i
$255$		0			0
$256$	1.66423e7	−	2.12301e6i	0.991961	−	0.126541i
$257$	5.00298e6			0.294734			0.147367	−	0.989082i	$-0.452920\pi$
$257$	5.00298e6			0.294734			0.147367	+	0.989082i	$0.452920\pi$
$258$		0			0
$259$		−	5.90408e6i		−	0.339823i
$260$	4.29213e6	−	136194.i	0.244204	−	0.00774885i
$261$		0			0
$262$	238466.	+	1.50343e7i	0.0132594	+	0.835947i
$263$			2.92331e7i			1.60697i	0.595324	+	0.803485i	$0.297024\pi$
$263$			2.92331e7i			1.60697i	−0.595324	+	0.803485i	$0.702976\pi$
$264$		0			0
$265$	1.24987e7			0.671627
$266$	1.00101e7	−	158775.i	0.531856	−	0.00843604i
$267$		0			0
$268$	1.06518e6	+	3.35690e7i	0.0553374	+	1.74395i
$269$	−2.26722e7			−1.16476			−0.582380	−	0.812917i	$-0.697879\pi$
$269$	−2.26722e7			−1.16476			−0.582380	+	0.812917i	$0.697879\pi$
$270$		0			0
$271$			1.03314e7i			0.519102i	0.965729	+	0.259551i	$0.0835746\pi$
$271$			1.03314e7i			0.519102i	−0.965729	+	0.259551i	$0.916425\pi$
$272$	1.61107e7	−	1.02345e6i	0.800585	−	0.0508580i
$273$		0			0
$274$	−1.86706e7	+	296144.i	−0.907626	+	0.0143963i
$275$			5.13927e6i			0.247117i
$276$		0			0
$277$	−1.17712e6			−0.0553836			−0.0276918	−	0.999617i	$-0.508816\pi$
$277$	−1.17712e6			−0.0553836			−0.0276918	+	0.999617i	$0.508816\pi$
$278$	−597160.	−	3.76484e7i	−0.0277943	−	1.75231i
$279$		0			0
$280$	456308.	+	9.58298e6i	0.0207866	+	0.436543i
$281$	−2.16145e7			−0.974152			−0.487076	−	0.873360i	$-0.661937\pi$
$281$	−2.16145e7			−0.974152			−0.487076	+	0.873360i	$0.661937\pi$
$282$		0			0
$283$			4.25888e6i			0.187904i	0.995577	+	0.0939520i	$0.0299500\pi$
$283$			4.25888e6i			0.187904i	−0.995577	+	0.0939520i	$0.970050\pi$
$284$	411058.	+	1.29544e7i	0.0179452	+	0.565540i
$285$		0			0
$286$	−250448.	−	1.57897e7i	−0.0107058	−	0.674956i
$287$			1.81458e7i			0.767591i
$288$		0			0
$289$	−8.60450e6			−0.356478
$290$	9.11478e6	−	144574.i	0.373725	−	0.00592785i
$291$		0			0
$292$	4.31462e7	−	1.36907e6i	1.73298	−	0.0549893i
$293$	−2.44860e7			−0.973452			−0.486726	−	0.873555i	$-0.661809\pi$
$293$	−2.44860e7			−0.973452			−0.486726	+	0.873555i	$0.661809\pi$
$294$		0			0
$295$		−	1.95267e7i		−	0.760610i
$296$	−9.00810e6	+	428934.i	−0.347342	+	0.0165392i
$297$		0			0
$298$	1.26670e7	−	200918.i	0.478658	−	0.00759224i
$299$			5.90269e6i			0.220819i
$300$		0			0
$301$	1.31655e6			0.0482769
$302$	−138054.	−	8.70369e6i	−0.00501219	−	0.315997i
$303$		0			0
$304$	−969488.	−	1.52613e7i	−0.0345082	−	0.543213i
$305$	8.10335e6			0.285605
$306$		0			0
$307$			372143.i			0.0128616i	0.999979	+	0.00643079i	$0.00204700\pi$
$307$			372143.i			0.0128616i	−0.999979	+	0.00643079i	$0.997953\pi$
$308$	3.52623e7	−	1.11891e6i	1.20686	−	0.0382950i
$309$		0			0
$310$	−272763.	−	1.71965e7i	−0.00915589	−	0.577239i
$311$		−	4.61051e6i		−	0.153274i	−0.997059	−	0.0766368i	$-0.975582\pi$
$311$		−	4.61051e6i		−	0.153274i	0.997059	−	0.0766368i	$-0.0244182\pi$
$312$		0			0
$313$	−3.54207e7			−1.15511			−0.577557	−	0.816351i	$-0.695994\pi$
$313$	−3.54207e7			−1.15511			−0.577557	+	0.816351i	$0.695994\pi$
$314$	−4.02018e7	+	637663.i	−1.29855	+	0.0205969i
$315$		0			0
$316$	−632264.	−	1.99257e7i	−0.0200372	−	0.631471i
$317$	3.61574e7			1.13506			0.567531	−	0.823352i	$-0.307899\pi$
$317$	3.61574e7			1.13506			0.567531	+	0.823352i	$0.307899\pi$
$318$		0			0
$319$		−	3.35226e7i		−	1.03268i
$320$	1.45880e7	−	1.39242e6i	0.445190	−	0.0424932i
$321$		0			0
$322$	−1.31855e7	+	209142.i	−0.394937	+	0.00626431i
$323$		−	1.47141e7i		−	0.436643i
$324$		0			0
$325$	3.75091e6			0.109266
$326$	584553.	+	3.68535e7i	0.0168722	+	1.06372i
$327$		0			0
$328$	2.76857e7	−	1.31830e6i	0.784575	−	0.0373587i
$329$	−4.88461e7			−1.37165
$330$		0			0
$331$			1.43002e7i			0.394328i	0.980371	+	0.197164i	$0.0631731\pi$
$331$			1.43002e7i			0.394328i	−0.980371	+	0.197164i	$0.936827\pi$
$332$	1.97989e6	+	6.23962e7i	0.0541038	+	1.70508i
$333$		0			0
$334$	358268.	+	2.25872e7i	0.00961543	+	0.606211i
$335$			2.93361e7i			0.780312i
$336$		0			0
$337$	5.11693e6			0.133696			0.0668482	−	0.997763i	$-0.478706\pi$
$337$	5.11693e6			0.133696			0.0668482	+	0.997763i	$0.478706\pi$
$338$	2.70855e7	−	429617.i	0.701433	−	0.0111258i
$339$		0			0
$340$	1.40934e7	−	447197.i	0.358574	−	0.0113779i
$341$	−6.32458e7			−1.59503
$342$		0			0
$343$		−	4.12096e7i		−	1.02121i
$344$	−95648.2	−	2.00872e6i	−0.00234964	−	0.0493451i
$345$		0			0
$346$	1.92257e7	−	304949.i	0.464146	−	0.00736206i
$347$		−	1.37663e7i		−	0.329480i	−0.986337	−	0.164740i	$-0.947321\pi$
$347$		−	1.37663e7i		−	0.329480i	0.986337	−	0.164740i	$-0.0526785\pi$
$348$		0			0
$349$	−3.42645e7			−0.806062			−0.403031	−	0.915186i	$-0.632043\pi$
$349$	−3.42645e7			−0.806062			−0.403031	+	0.915186i	$0.632043\pi$
$350$	132901.	+	8.37882e6i	0.00309973	+	0.195424i
$351$		0			0
$352$	−4.26898e6	−	5.37198e7i	−0.0978806	−	1.23170i
$353$	3.92759e6			0.0892899			0.0446449	−	0.999003i	$-0.485784\pi$
$353$	3.92759e6			0.0892899			0.0446449	+	0.999003i	$0.485784\pi$
$354$		0			0
$355$			1.13209e7i			0.253045i
$356$	7.34803e7	−	2.33160e6i	1.62862	−	0.0516779i
$357$		0			0
$358$	490807.	+	3.09433e7i	0.0106970	+	0.674399i
$359$		−	2.26847e7i		−	0.490287i	−0.969487	−	0.245143i	$-0.921165\pi$
$359$		−	2.26847e7i		−	0.490287i	0.969487	−	0.245143i	$-0.0788351\pi$
$360$		0			0
$361$	3.31075e7			0.703729
$362$	6.46388e7	−	1.02527e6i	1.36260	−	0.0216129i
$363$		0			0
$364$	−816639.	−	2.57363e7i	−0.0169327	−	0.533632i
$365$	3.77056e7			0.775403
$366$		0			0
$367$			5.14521e7i			1.04089i	0.853895	+	0.520445i	$0.174234\pi$
$367$			5.14521e7i			1.04089i	−0.853895	+	0.520445i	$0.825766\pi$
$368$	1.27703e6	+	2.01024e7i	0.0256246	+	0.403371i
$369$		0			0
$370$	−7.87617e6	+	124928.i	−0.155493	+	0.00246635i
$371$		−	7.49442e7i		−	1.46763i
$372$		0			0
$373$	1.23981e7			0.238907			0.119453	−	0.992840i	$-0.461886\pi$
$373$	1.23981e7			0.238907			0.119453	+	0.992840i	$0.461886\pi$
$374$	−822357.	−	5.18460e7i	−0.0157197	−	0.991061i
$375$		0			0
$376$	3.54869e6	+	7.45264e7i	0.0667581	+	1.40200i
$377$	−2.44666e7			−0.456614
$378$		0			0
$379$			1.00801e8i			1.85160i	0.378018	+	0.925798i	$0.376606\pi$
$379$			1.00801e8i			1.85160i	−0.378018	+	0.925798i	$0.623394\pi$
$380$	−423620.	−	1.33503e7i	−0.00772014	−	0.243300i
$381$		0			0
$382$	472544.	+	2.97919e7i	0.00847720	+	0.534450i
$383$		−	5.39003e7i		−	0.959389i	−0.877436	−	0.479695i	$-0.840747\pi$
$383$		−	5.39003e7i		−	0.959389i	0.877436	−	0.479695i	$-0.159253\pi$
$384$		0			0
$385$	3.08158e7			0.539998
$386$	−2.04112e7	+	323753.i	−0.354901	+	0.00562927i
$387$		0			0
$388$	3.67047e7	−	1.16468e6i	0.628386	−	0.0199393i
$389$	1.63608e6			0.0277943			0.0138971	−	0.999903i	$-0.495576\pi$
$389$	1.63608e6			0.0277943			0.0138971	+	0.999903i	$0.495576\pi$
$390$		0			0
$391$			1.93817e7i			0.324236i
$392$	−2.70708e6	+	128902.i	−0.0449411	+	0.00213994i
$393$		0			0
$394$	−1.00708e8	+	1.59738e6i	−1.64655	+	0.0261167i
$395$		−	1.74132e7i		−	0.282545i
$396$		0			0
$397$	−5.15268e7			−0.823496			−0.411748	−	0.911298i	$-0.635082\pi$
$397$	−5.15268e7			−0.823496			−0.411748	+	0.911298i	$0.635082\pi$
$398$	263507.	+	1.66130e7i	0.00417968	+	0.263511i
$399$		0			0
$400$	1.27743e7	−	811497.i	0.199598	−	0.0126796i
$401$	4.97131e7			0.770970			0.385485	−	0.922714i	$-0.374034\pi$
$401$	4.97131e7			0.770970			0.385485	+	0.922714i	$0.374034\pi$
$402$		0			0
$403$			4.61602e7i			0.705265i
$404$	−2.40913e7	+	764441.i	−0.365356	+	0.0115931i
$405$		0			0
$406$	−866890.	−	5.46536e7i	−0.0129535	−	0.816659i
$407$			2.89672e7i			0.429658i
$408$		0			0
$409$	−3.25227e7			−0.475354			−0.237677	−	0.971344i	$-0.576386\pi$
$409$	−3.25227e7			−0.475354			−0.237677	+	0.971344i	$0.576386\pi$
$410$	2.42068e7	−	383957.i	0.351226	−	0.00557098i
$411$		0			0
$412$	−4.39708e6	−	1.38574e8i	−0.0628743	−	1.98148i
$413$	−1.17085e8			−1.66208
$414$		0			0
$415$			5.45282e7i			0.762917i
$416$	−3.92076e7	+	3.11573e6i	−0.544615	+	0.0432793i
$417$		0			0
$418$	−4.91125e7	+	778999.i	−0.672455	+	0.0106662i
$419$		−	2.90909e7i		−	0.395471i	−0.980255	−	0.197736i	$-0.936641\pi$
$419$		−	2.90909e7i		−	0.395471i	0.980255	−	0.197736i	$-0.0633587\pi$
$420$		0			0
$421$	−1.08942e8			−1.45998			−0.729991	−	0.683457i	$-0.760476\pi$
$421$	−1.08942e8			−1.45998			−0.729991	+	0.683457i	$0.760476\pi$
$422$	−1.86868e6	−	1.17812e8i	−0.0248655	−	1.56766i
$423$		0			0
$424$	−1.14345e8	+	5.44473e6i	−1.50010	+	0.0714297i
$425$	1.23163e7			0.160440
$426$		0			0
$427$		−	4.85889e7i		−	0.624099i
$428$	3.40490e6	+	1.07305e8i	0.0434284	+	1.36864i
$429$		0			0
$430$	−27857.8	−	1.75631e6i	−0.000350381	−	0.0220900i
$431$			1.42434e8i			1.77902i	0.456913	+	0.889511i	$0.348955\pi$
$431$			1.42434e8i			1.77902i	−0.456913	+	0.889511i	$0.651045\pi$
$432$		0			0
$433$	−1.44746e8			−1.78296			−0.891481	−	0.453059i	$-0.850333\pi$
$433$	−1.44746e8			−1.78296			−0.891481	+	0.453059i	$0.850333\pi$
$434$	−1.03113e8	+	1.63553e6i	−1.26138	+	0.0200073i
$435$		0			0
$436$	1.01584e8	−	3.22336e6i	1.22565	−	0.0388910i
$437$	1.83598e7			0.220001
$438$		0			0
$439$		−	1.01787e8i		−	1.20309i	−0.798837	−	0.601547i	$-0.794551\pi$
$439$		−	1.01787e8i		−	1.20309i	0.798837	−	0.601547i	$-0.205449\pi$
$440$	−2.23878e6	−	4.70170e7i	−0.0262817	−	0.551946i
$441$		0			0
$442$	−3.78400e7	+	600200.i	−0.438212	+	0.00695071i
$443$			5.44035e7i			0.625771i	0.949791	+	0.312885i	$0.101296\pi$
$443$			5.44035e7i			0.625771i	−0.949791	+	0.312885i	$0.898704\pi$
$444$		0			0
$445$	6.42147e7			0.728709
$446$	980451.	+	6.18132e7i	0.0110515	+	0.696749i
$447$		0			0
$448$	−8.34914e6	−	8.74718e7i	−0.0928555	−	0.972824i
$449$	−1.40905e8			−1.55664			−0.778319	−	0.627869i	$-0.783927\pi$
$449$	−1.40905e8			−1.55664			−0.778319	+	0.627869i	$0.783927\pi$
$450$		0			0
$451$		−	8.90285e7i		−	0.970509i
$452$	1.12549e8	−	3.57130e6i	1.21878	−	0.0386733i
$453$		0			0
$454$	2.35540e6	+	1.48498e8i	0.0251708	+	1.58691i
$455$		−	2.24910e7i		−	0.238768i
$456$		0			0
$457$	−6.44034e7			−0.674777			−0.337388	−	0.941366i	$-0.609544\pi$
$457$	−6.44034e7			−0.674777			−0.337388	+	0.941366i	$0.609544\pi$
$458$	−1.24662e8	+	1.97733e6i	−1.29759	+	0.0205818i
$459$		0			0
$460$	557999.	+	1.75853e7i	0.00573271	+	0.180666i
$461$	3.82834e7			0.390758			0.195379	−	0.980728i	$-0.437406\pi$
$461$	3.82834e7			0.390758			0.195379	+	0.980728i	$0.437406\pi$
$462$		0			0
$463$		−	1.02023e8i		−	1.02791i	−0.857818	−	0.513953i	$-0.828181\pi$
$463$		−	1.02023e8i		−	1.02791i	0.857818	−	0.513953i	$-0.171819\pi$
$464$	−8.33242e7	+	5.29326e6i	−0.834099	+	0.0529870i
$465$		0			0
$466$	5.31547e7	−	843115.i	0.525272	−	0.00833161i
$467$		−	4.70326e7i		−	0.461794i	−0.972978	−	0.230897i	$-0.925834\pi$
$467$		−	4.70326e7i		−	0.461794i	0.972978	−	0.230897i	$-0.0741660\pi$
$468$		0			0
$469$	1.75904e8			1.70513
$470$	1.03356e6	+	6.51617e7i	0.00995505	+	0.627623i
$471$		0			0
$472$	8.50627e6	+	1.78641e8i	0.0808934	+	1.69885i
$473$	−6.45940e6			−0.0610392
$474$		0			0
$475$		−	1.16669e7i		−	0.108862i
$476$	−2.68146e6	−	8.45060e7i	−0.0248629	−	0.783550i
$477$		0			0
$478$	−2.11529e6	−	1.33360e8i	−0.0193680	−	1.22107i
$479$		−	3.86857e7i		−	0.352001i	−0.984390	−	0.176001i	$-0.943684\pi$
$479$		−	3.86857e7i		−	0.352001i	0.984390	−	0.176001i	$-0.0563161\pi$
$480$		0			0
$481$	2.11418e7			0.189979
$482$	3.50258e7	−	555562.i	0.312785	−	0.00496125i
$483$		0			0
$484$	−5.96843e7	+	1.89384e6i	−0.526410	+	0.0167035i
$485$	3.20764e7			0.281164
$486$		0			0
$487$			2.57826e7i			0.223224i	0.993752	+	0.111612i	$0.0356013\pi$
$487$			2.57826e7i			0.223224i	−0.993752	+	0.111612i	$0.964399\pi$
$488$	−7.41341e7	+	3.53001e6i	−0.637909	+	0.0303750i
$489$		0			0
$490$	−2.36692e6	+	37543.0i	−0.0201185	+	0.000319110i
$491$			1.22519e8i			1.03504i	0.855671	+	0.517521i	$0.173145\pi$
$491$			1.22519e8i			1.03504i	−0.855671	+	0.517521i	$0.826855\pi$
$492$		0			0
$493$	−8.03368e7			−0.670462
$494$	568555.	+	3.58449e7i	0.00471620	+	0.297336i
$495$		0			0
$496$	9.98660e6	+	1.57205e8i	0.0818413	+	1.28831i
$497$	6.78820e7			0.552950
$498$		0			0
$499$			3.41531e7i			0.274871i	0.990511	+	0.137436i	$0.0438860\pi$
$499$			3.41531e7i			0.274871i	−0.990511	+	0.137436i	$0.956114\pi$
$500$	1.11747e7	−	354585.i	0.0893977	−	0.00283668i
$501$		0			0
$502$	2.32281e6	+	1.46443e8i	0.0183612	+	1.15760i
$503$			7.48857e7i			0.588430i	0.955739	+	0.294215i	$0.0950581\pi$
$503$			7.48857e7i			0.588430i	−0.955739	+	0.294215i	$0.904942\pi$
$504$		0			0
$505$	−2.10535e7			−0.163474
$506$	6.46918e7	−	1.02611e6i	0.499342	−	0.00792032i
$507$		0			0
$508$	−1.43282e6	−	4.51552e7i	−0.0109295	−	0.344443i
$509$	2.15746e8			1.63603			0.818013	−	0.575200i	$-0.195076\pi$
$509$	2.15746e8			1.63603			0.818013	+	0.575200i	$0.195076\pi$
$510$		0			0
$511$		−	2.26089e8i		−	1.69440i
$512$	−1.32853e8	+	1.90935e7i	−0.989830	+	0.142257i
$513$		0			0
$514$	−4.00188e7	+	634759.i	−0.294696	+	0.00467433i
$515$		−	1.21100e8i		−	0.886589i
$516$		0			0
$517$	2.39653e8			1.73425
$518$	749088.	+	4.72267e7i	0.00538944	+	0.339781i
$519$		0			0
$520$	−3.43155e7	+	1.63398e6i	−0.244051	+	0.0116208i
$521$	−1.33165e7			−0.0941625			−0.0470812	−	0.998891i	$-0.514992\pi$
$521$	−1.33165e7			−0.0941625			−0.0470812	+	0.998891i	$0.514992\pi$
$522$		0			0
$523$			1.01022e8i			0.706174i	0.935590	+	0.353087i	$0.114868\pi$
$523$			1.01022e8i			0.706174i	−0.935590	+	0.353087i	$0.885132\pi$
$524$	−3.81498e6	−	1.20229e8i	−0.0265154	−	0.835631i
$525$		0			0
$526$	−3.70899e6	−	2.33836e8i	−0.0254858	−	1.60677i
$527$			1.51569e8i			1.03556i
$528$		0			0
$529$	1.23852e8			0.836635
$530$	−9.99772e7	+	1.58579e6i	−0.671542	+	0.0106517i
$531$		0			0
$532$	−8.00506e7	+	2.54009e6i	−0.531655	+	0.0168700i
$533$	−6.49777e7			−0.429124
$534$		0			0
$535$			9.37744e7i			0.612382i
$536$	−1.27795e7	−	2.68383e8i	−0.0829887	−	1.74286i
$537$		0			0
$538$	1.81355e8	−	2.87656e6i	1.16461	−	0.0184726i
$539$			8.70512e6i			0.0555915i
$540$		0			0
$541$	2.05333e8			1.29678			0.648391	−	0.761307i	$-0.275442\pi$
$541$	2.05333e8			1.29678			0.648391	+	0.761307i	$0.275442\pi$
$542$	−1.31081e6	−	8.26411e7i	−0.00823271	−	0.519037i
$543$		0			0
$544$	−1.28739e8	+	1.02306e7i	−0.799677	+	0.0635485i
$545$	8.87745e7			0.548402
$546$		0			0
$547$		−	5.12695e7i		−	0.313254i	−0.987658	−	0.156627i	$-0.949938\pi$
$547$		−	5.12695e7i		−	0.313254i	0.987658	−	0.156627i	$-0.0500621\pi$
$548$	1.49309e8	−	4.73772e6i	0.907284	−	0.0287890i
$549$		0			0
$550$	−652051.	−	4.11090e7i	−0.00391916	−	0.247086i
$551$			7.61012e7i			0.454922i
$552$		0			0
$553$	−1.04412e8			−0.617412
$554$	9.41576e6	−	149348.i	0.0553766	−	0.000878357i
$555$		0			0
$556$	9.55336e6	+	3.01073e8i	0.0555817	+	1.75165i
$557$	1.88880e8			1.09300			0.546501	−	0.837458i	$-0.315959\pi$
$557$	1.88880e8			1.09300			0.546501	+	0.837458i	$0.315959\pi$
$558$		0			0
$559$			4.71441e6i			0.0269893i
$560$	−4.86586e6	−	7.65963e7i	−0.0277074	−	0.436158i
$561$		0			0
$562$	1.72894e8	−	2.74237e6i	0.974030	−	0.0154496i
$563$		−	2.01659e8i		−	1.13004i	−0.825078	−	0.565019i	$-0.808869\pi$
$563$		−	2.01659e8i		−	1.13004i	0.825078	−	0.565019i	$-0.191131\pi$
$564$		0			0
$565$	9.83571e7			0.545331
$566$	−540350.	−	3.40667e7i	−0.00298007	−	0.187880i
$567$		0			0
$568$	−4.93166e6	−	1.03570e8i	−0.0269121	−	0.565185i
$569$	2.69336e8			1.46204			0.731018	−	0.682359i	$-0.239046\pi$
$569$	2.69336e8			1.46204			0.731018	+	0.682359i	$0.239046\pi$
$570$		0			0
$571$			1.31483e8i			0.706256i	0.935575	+	0.353128i	$0.114882\pi$
$571$			1.31483e8i			0.706256i	−0.935575	+	0.353128i	$0.885118\pi$
$572$	4.00667e6	+	1.26270e8i	0.0214090	+	0.674701i
$573$		0			0
$574$	−2.30227e6	−	1.45148e8i	−0.0121736	−	0.767494i
$575$			1.53678e7i			0.0808368i
$576$		0			0
$577$	1.62328e7			0.0845017			0.0422509	−	0.999107i	$-0.486547\pi$
$577$	1.62328e7			0.0845017			0.0422509	+	0.999107i	$0.486547\pi$
$578$	6.88274e7	−	1.09171e6i	0.356433	−	0.00565357i
$579$		0			0
$580$	−7.28908e7	+	2.31290e6i	−0.373584	+	0.0118542i
$581$	3.26960e8			1.66712
$582$		0			0
$583$			3.67699e8i			1.85561i
$584$	−3.44952e8	+	1.64254e7i	−1.73189	+	0.0824666i
$585$		0			0
$586$	1.95863e8	−	3.10669e6i	0.973330	−	0.0154385i
$587$			1.10074e8i			0.544216i	0.962267	+	0.272108i	$0.0877209\pi$
$587$			1.10074e8i			0.544216i	−0.962267	+	0.272108i	$0.912279\pi$
$588$		0			0
$589$	1.43577e8			0.702652
$590$	2.47747e6	+	1.56194e8i	0.0120629	+	0.760515i
$591$		0			0
$592$	7.20013e7	−	4.57395e6i	0.347036	−	0.0220458i
$593$	−3.80047e7			−0.182253			−0.0911263	−	0.995839i	$-0.529047\pi$
$593$	−3.80047e7			−0.182253			−0.0911263	+	0.995839i	$0.529047\pi$
$594$		0			0
$595$		−	7.38501e7i		−	0.350591i
$596$	−1.01298e8	+	3.21428e6i	−0.478477	+	0.0151826i
$597$		0			0
$598$	−748911.	−	4.72156e7i	−0.00350208	−	0.220791i
$599$			1.46223e7i			0.0680356i	0.999421	+	0.0340178i	$0.0108303\pi$
$599$			1.46223e7i			0.0680356i	−0.999421	+	0.0340178i	$0.989170\pi$
$600$		0			0
$601$	−4.14917e7			−0.191134			−0.0955671	−	0.995423i	$-0.530466\pi$
$601$	−4.14917e7			−0.191134			−0.0955671	+	0.995423i	$0.530466\pi$
$602$	−1.05311e7	+	167039.i	−0.0482708	+	0.000765648i
$603$		0			0
$604$	2.20858e6	+	6.96032e7i	0.0100231	+	0.315877i
$605$	−5.21583e7			−0.235536
$606$		0			0
$607$		−	3.48530e8i		−	1.55838i	−0.626786	−	0.779191i	$-0.715630\pi$
$607$		−	3.48530e8i		−	1.55838i	0.626786	−	0.779191i	$-0.284370\pi$
$608$	9.69123e6	+	1.21952e8i	0.0431189	+	0.542598i
$609$		0			0
$610$	−6.48187e7	+	1.02812e6i	−0.285569	+	0.00452956i
$611$		−	1.74912e8i		−	0.766823i
$612$		0			0
$613$	1.70343e8			0.739509			0.369755	−	0.929129i	$-0.379442\pi$
$613$	1.70343e8			0.739509			0.369755	+	0.929129i	$0.379442\pi$
$614$	−47216.1	−	2.97677e6i	−0.000203979	−	0.0128600i
$615$		0			0
$616$	−2.81921e8	+	1.34241e7i	−1.20610	+	0.0574305i
$617$	2.59449e8			1.10458			0.552289	−	0.833653i	$-0.313755\pi$
$617$	2.59449e8			1.10458			0.552289	+	0.833653i	$0.313755\pi$
$618$		0			0
$619$			2.78639e8i			1.17482i	0.809291	+	0.587408i	$0.199851\pi$
$619$			2.78639e8i			1.17482i	−0.809291	+	0.587408i	$0.800149\pi$
$620$	4.36366e6	+	1.37520e8i	0.0183095	+	0.577021i
$621$		0			0
$622$	584964.	+	3.68794e7i	0.00243085	+	0.153254i
$623$		−	3.85041e8i		−	1.59237i
$624$		0			0
$625$	9.76562e6			0.0400000
$626$	2.83330e8	−	4.49405e6i	1.15497	−	0.0183195i
$627$		0			0
$628$	3.21493e8	−	1.02013e7i	1.29806	−	0.0411886i
$629$	6.94198e7			0.278953
$630$		0			0
$631$		−	2.72427e7i		−	0.108433i	−0.998529	−	0.0542165i	$-0.982734\pi$
$631$		−	2.72427e7i		−	0.108433i	0.998529	−	0.0542165i	$-0.0172661\pi$
$632$	7.58558e6	+	1.59306e8i	0.0300495	+	0.631074i
$633$		0			0
$634$	−2.89223e8	+	4.58751e6i	−1.13492	+	0.0180015i
$635$		−	3.94613e7i		−	0.154117i
$636$		0			0
$637$	6.35346e6			0.0245806
$638$	4.25322e6	+	2.68147e8i	0.0163778	+	1.03255i
$639$		0			0
$640$	−1.16513e8	+	1.29888e7i	−0.444460	+	0.0495483i
$641$	−4.19674e8			−1.59345			−0.796725	−	0.604342i	$-0.793436\pi$
$641$	−4.19674e8			−1.59345			−0.796725	+	0.604342i	$0.793436\pi$
$642$		0			0
$643$			2.92348e8i			1.09968i	0.835269	+	0.549841i	$0.185312\pi$
$643$			2.92348e8i			1.09968i	−0.835269	+	0.549841i	$0.814688\pi$
$644$	1.05444e8	−	3.34585e6i	0.394788	−	0.0125270i
$645$		0			0
$646$	1.86687e6	+	1.17698e8i	0.00692495	+	0.436588i
$647$		−	2.76931e8i		−	1.02249i	−0.859435	−	0.511245i	$-0.829185\pi$
$647$		−	2.76931e8i		−	1.02249i	0.859435	−	0.511245i	$-0.170815\pi$
$648$		0			0
$649$	5.74453e8			2.10146
$650$	−3.00035e7	+	475902.i	−0.109253	+	0.00173291i
$651$		0			0
$652$	−9.35168e6	−	2.94717e8i	−0.0337401	−	1.06332i
$653$	3.17212e8			1.13923			0.569613	−	0.821913i	$-0.307093\pi$
$653$	3.17212e8			1.13923			0.569613	+	0.821913i	$0.307093\pi$
$654$		0			0
$655$		−	1.05068e8i		−	0.373894i
$656$	−2.21291e8	+	1.40577e7i	−0.783884	+	0.0497970i
$657$		0			0
$658$	3.90719e8	−	6.19740e6i	1.37147	−	0.0217537i
$659$			2.32598e8i			0.812737i	0.913709	+	0.406368i	$0.133205\pi$
$659$			2.32598e8i			0.812737i	−0.913709	+	0.406368i	$0.866795\pi$
$660$		0			0
$661$	−4.50526e8			−1.55997			−0.779983	−	0.625801i	$-0.784772\pi$
$661$	−4.50526e8			−1.55997			−0.779983	+	0.625801i	$0.784772\pi$
$662$	−1.81435e6	−	1.14387e8i	−0.00625385	−	0.394278i
$663$		0			0
$664$	−2.37537e7	−	4.98855e8i	−0.0811387	−	1.70400i
$665$	−6.99565e7			−0.237883
$666$		0			0
$667$		−	1.00242e8i		−	0.337809i
$668$	−5.73157e6	−	1.80630e8i	−0.0192284	−	0.605982i
$669$		0			0
$670$	−3.72205e6	−	2.34659e8i	−0.0123754	−	0.780213i
$671$			2.38392e8i			0.789085i
$672$		0			0
$673$	−4.17718e8			−1.37037			−0.685185	−	0.728369i	$-0.740279\pi$
$673$	−4.17718e8			−1.37037			−0.685185	+	0.728369i	$0.740279\pi$
$674$	−4.09303e7	+	649217.i	−0.133680	+	0.00212036i
$675$		0			0
$676$	−2.16602e8	+	6.87300e6i	−0.701168	+	0.0222488i
$677$	−4.19200e8			−1.35100			−0.675500	−	0.737360i	$-0.736072\pi$
$677$	−4.19200e8			−1.35100			−0.675500	+	0.737360i	$0.736072\pi$
$678$		0			0
$679$		−	1.92335e8i		−	0.614396i
$680$	−1.12676e8	+	5.36524e6i	−0.358348	+	0.0170633i
$681$		0			0
$682$	5.05903e8	−	8.02439e6i	1.59483	−	0.0252964i
$683$		−	1.90249e8i		−	0.597119i	−0.954391	−	0.298560i	$-0.903494\pi$
$683$		−	1.90249e8i		−	0.597119i	0.954391	−	0.298560i	$-0.0965062\pi$
$684$		0			0
$685$	1.30481e8			0.405954
$686$	5.22852e6	+	3.29636e8i	0.0161960	+	1.02108i
$687$		0			0
$688$	1.01995e6	+	1.60556e7i	0.00313193	+	0.0493016i
$689$	2.68366e8			0.820483
$690$		0			0
$691$		−	2.14772e8i		−	0.650945i	−0.945551	−	0.325473i	$-0.894477\pi$
$691$		−	2.14772e8i		−	0.650945i	0.945551	−	0.325473i	$-0.105523\pi$
$692$	−1.53748e8	+	4.87858e6i	−0.463971	+	0.0147223i
$693$		0			0
$694$	1.74662e6	+	1.10117e8i	0.00522540	+	0.329439i
$695$			2.63109e8i			0.783757i
$696$		0			0
$697$	−2.13357e8			−0.630098
$698$	2.74082e8	−	4.34735e6i	0.805961	−	0.0127838i
$699$		0			0
$700$	−2.12615e6	−	6.70053e7i	−0.00619868	−	0.195351i
$701$	−4.63107e8			−1.34440			−0.672199	−	0.740371i	$-0.734650\pi$
$701$	−4.63107e8			−1.34440			−0.672199	+	0.740371i	$0.734650\pi$
$702$		0			0
$703$		−	6.57598e7i		−	0.189276i
$704$	4.09633e7	+	4.29163e8i	0.117402	+	1.23000i
$705$		0			0
$706$	−3.14168e7	+	498318.i	−0.0892786	+	0.00141610i
$707$			1.26240e8i			0.357222i
$708$		0			0
$709$	3.96583e8			1.11275			0.556373	−	0.830933i	$-0.312193\pi$
$709$	3.96583e8			1.11275			0.556373	+	0.830933i	$0.312193\pi$
$710$	−1.43636e6	−	9.05561e7i	−0.00401317	−	0.253013i
$711$		0			0
$712$	−5.87472e8	+	2.79734e7i	−1.62760	+	0.0775006i
$713$	−1.89123e8			−0.521765
$714$		0			0
$715$			1.10348e8i			0.301887i
$716$	−7.85193e6	−	2.47453e8i	−0.0213913	−	0.674145i
$717$		0			0
$718$	2.87815e6	+	1.81455e8i	0.00777572	+	0.490225i
$719$			3.04978e8i			0.820507i	0.911971	+	0.410254i	$0.134560\pi$
$719$			3.04978e8i			0.820507i	−0.911971	+	0.410254i	$0.865440\pi$
$720$		0			0
$721$	−7.26134e8			−1.93736
$722$	−2.64827e8	+	4.20056e6i	−0.703640	+	0.0111608i
$723$		0			0
$724$	−5.16915e8	+	1.64022e7i	−1.36208	+	0.0432203i
$725$	−6.36995e7			−0.167156
$726$		0			0
$727$			5.25666e8i			1.36807i	0.729451	+	0.684033i	$0.239775\pi$
$727$			5.25666e8i			1.36807i	−0.729451	+	0.684033i	$0.760225\pi$
$728$	9.79761e6	+	2.05761e8i	0.0253937	+	0.533296i
$729$		0			0
$730$	−3.01607e8	+	4.78395e6i	−0.775305	+	0.0122975i
$731$			1.54799e7i			0.0396294i
$732$		0			0
$733$	−6.44853e8			−1.63738			−0.818689	−	0.574237i	$-0.805299\pi$
$733$	−6.44853e8			−1.63738			−0.818689	+	0.574237i	$0.805299\pi$
$734$	−6.52805e6	−	4.11565e8i	−0.0165080	−	1.04076i
$735$		0			0
$736$	−1.27654e7	−	1.60637e8i	−0.0320186	−	0.402914i
$737$	−8.63036e8			−2.15589
$738$		0			0
$739$		−	3.90307e8i		−	0.967104i	−0.875316	−	0.483552i	$-0.839346\pi$
$739$		−	3.90307e8i		−	0.967104i	0.875316	−	0.483552i	$-0.160654\pi$
$740$	6.29856e7	−	1.99860e6i	0.155434	−	0.00493208i
$741$		0			0
$742$	9.50864e6	+	5.99479e8i	0.0232759	+	1.46745i
$743$		−	2.19194e8i		−	0.534395i	−0.963642	−	0.267197i	$-0.913902\pi$
$743$		−	2.19194e8i		−	0.534395i	0.963642	−	0.267197i	$-0.0860976\pi$
$744$		0			0
$745$	−8.85245e7			−0.214089
$746$	−9.91722e7	+	1.57302e6i	−0.238877	+	0.00378895i
$747$		0			0
$748$	1.31561e7	+	4.14612e8i	0.0314355	+	0.990687i
$749$	5.62285e8			1.33817
$750$		0			0
$751$			4.78886e8i			1.13061i	0.824883	+	0.565304i	$0.191241\pi$
$751$			4.78886e8i			1.13061i	−0.824883	+	0.565304i	$0.808759\pi$
$752$	−3.78416e7	−	5.95686e8i	−0.0889847	−	1.40076i
$753$		0			0
$754$	1.95708e8	−	3.10422e6i	0.456556	−	0.00724168i
$755$			6.08265e7i			0.141336i
$756$		0			0
$757$	−4.57136e8			−1.05380			−0.526900	−	0.849927i	$-0.676646\pi$
$757$	−4.57136e8			−1.05380			−0.526900	+	0.849927i	$0.676646\pi$
$758$	−1.27892e7	−	8.06305e8i	−0.0293654	−	1.85136i
$759$		0			0
$760$	5.08237e6	+	1.06735e8i	0.0115778	+	0.243146i
$761$	−5.21113e8			−1.18244			−0.591218	−	0.806512i	$-0.701353\pi$
$761$	−5.21113e8			−1.18244			−0.591218	+	0.806512i	$0.701353\pi$
$762$		0			0
$763$		−	5.32305e8i		−	1.19836i
$764$	−7.55976e6	−	2.38245e8i	−0.0169523	−	0.534249i
$765$		0			0
$766$	6.83867e6	+	4.31148e8i	0.0152155	+	0.959269i
$767$		−	4.19267e8i		−	0.929189i
$768$		0			0
$769$	4.13541e7			0.0909367			0.0454683	−	0.998966i	$-0.485522\pi$
$769$	4.13541e7			0.0909367			0.0454683	+	0.998966i	$0.485522\pi$
$770$	−2.46496e8	+	3.90980e6i	−0.539930	+	0.00856411i
$771$		0			0
$772$	1.63228e8	−	5.17940e6i	0.354767	−	0.0112571i
$773$	−4.87592e8			−1.05565			−0.527823	−	0.849354i	$-0.676992\pi$
$773$	−4.87592e8			−1.05565			−0.527823	+	0.849354i	$0.676992\pi$
$774$		0			0
$775$			1.20180e8i			0.258182i
$776$	−2.93453e8	+	1.39732e7i	−0.627991	+	0.0299027i
$777$		0			0
$778$	−1.30870e7	+	207580.i	−0.0277908	+	0.000440804i
$779$			2.02108e8i			0.427534i
$780$		0			0
$781$	−3.33049e8			−0.699126
$782$	−2.45907e6	−	1.55034e8i	−0.00514223	−	0.324195i
$783$		0			0
$784$	2.16376e7	−	1.37455e6i	0.0449015	−	0.00285241i
$785$	2.80954e8			0.580800
$786$		0			0
$787$			2.13319e8i			0.437628i	0.975767	+	0.218814i	$0.0702188\pi$
$787$			2.13319e8i			0.437628i	−0.975767	+	0.218814i	$0.929781\pi$
$788$	8.05358e8	−	2.55548e7i	1.64593	−	0.0522269i
$789$		0			0
$790$	2.20932e6	+	1.39288e8i	0.00448102	+	0.282509i
$791$		−	5.89764e8i		−	1.19165i
$792$		0			0
$793$	1.73991e8			0.348905
$794$	4.12162e8	−	6.53752e6i	0.823392	−	0.0130603i
$795$		0			0
$796$	−4.21559e6	−	1.32854e8i	−0.00835832	−	0.263411i
$797$	−1.05081e8			−0.207563			−0.103782	−	0.994600i	$-0.533094\pi$
$797$	−1.05081e8			−0.207563			−0.103782	+	0.994600i	$0.533094\pi$
$798$		0			0
$799$		−	5.74329e8i		−	1.12595i
$800$	−1.02078e8	+	8.11191e6i	−0.199371	+	0.0158436i
$801$		0			0
$802$	−3.97654e8	+	6.30740e6i	−0.770873	+	0.0122272i
$803$			1.10926e9i			2.14233i
$804$		0			0
$805$	9.21479e7			0.176644
$806$	−5.85663e6	−	3.69235e8i	−0.0111852	−	0.705176i
$807$		0			0
$808$	1.92609e8	−	9.17137e6i	0.365126	−	0.0173860i
$809$	−2.69036e8			−0.508119			−0.254059	−	0.967189i	$-0.581766\pi$
$809$	−2.69036e8			−0.508119			−0.254059	+	0.967189i	$0.581766\pi$
$810$		0			0
$811$		−	4.49639e8i		−	0.842950i	−0.906840	−	0.421475i	$-0.861513\pi$
$811$		−	4.49639e8i		−	0.842950i	0.906840	−	0.421475i	$-0.138487\pi$
$812$	1.38685e7	+	4.37064e8i	0.0259037	+	0.816351i
$813$		0			0
$814$	−3.67525e6	−	2.31708e8i	−0.00681417	−	0.429604i
$815$		−	2.57554e8i		−	0.475769i
$816$		0			0
$817$	1.46638e7			0.0268893
$818$	2.60149e8	−	4.12636e6i	0.475294	−	0.00753889i
$819$		0			0
$820$	−1.93582e8	+	6.14255e6i	−0.351093	+	0.0111406i
$821$	4.85361e8			0.877073			0.438536	−	0.898713i	$-0.355497\pi$
$821$	4.85361e8			0.877073			0.438536	+	0.898713i	$0.355497\pi$
$822$		0			0
$823$		−	1.54487e8i		−	0.277135i	−0.990353	−	0.138568i	$-0.955750\pi$
$823$		−	1.54487e8i		−	0.277135i	0.990353	−	0.138568i	$-0.0442498\pi$
$824$	5.27539e7	+	1.10789e9i	0.0942917	+	1.98023i
$825$		0			0
$826$	9.36562e8	−	1.48553e7i	1.66187	−	0.0263597i
$827$			8.90923e8i			1.57516i	0.616215	+	0.787578i	$0.288665\pi$
$827$			8.90923e8i			1.57516i	−0.616215	+	0.787578i	$0.711335\pi$
$828$		0			0
$829$	1.13467e9			1.99162			0.995809	−	0.0914624i	$-0.0291541\pi$
$829$	1.13467e9			1.99162			0.995809	+	0.0914624i	$0.0291541\pi$
$830$	−6.91834e6	−	4.36171e8i	−0.0120995	−	0.762821i
$831$		0			0
$832$	3.13226e8	−	2.98972e7i	0.543860	−	0.0519112i
$833$	2.08618e7			0.0360925
$834$		0			0
$835$		−	1.57853e8i		−	0.271140i
$836$	3.92752e8	−	1.24624e7i	0.672202	−	0.0213296i
$837$		0			0
$838$	3.69094e6	+	2.32698e8i	0.00627198	+	0.395421i
$839$		−	5.96120e8i		−	1.00936i	−0.863306	−	0.504682i	$-0.831610\pi$
$839$		−	5.96120e8i		−	1.00936i	0.863306	−	0.504682i	$-0.168390\pi$
$840$		0			0
$841$	−1.79322e8			−0.301472
$842$	8.71423e8	−	1.38221e7i	1.45980	−	0.0231546i
$843$		0			0
$844$	2.98951e7	+	9.42140e8i	0.0497247	+	1.56707i
$845$	−1.89289e8			−0.313730
$846$		0			0
$847$			3.12749e8i			0.514690i
$848$	9.13958e8	−	5.80601e7i	1.49878	−	0.0952117i
$849$		0			0
$850$	−9.85176e7	+	1.56264e6i	−0.160420	+	0.00254450i
$851$			8.66199e7i			0.140549i
$852$		0			0
$853$	−2.27412e8			−0.366409			−0.183204	−	0.983075i	$-0.558647\pi$
$853$	−2.27412e8			−0.366409			−0.183204	+	0.983075i	$0.558647\pi$
$854$	6.16478e6	+	3.88663e8i	0.00989792	+	0.624021i
$855$		0			0
$856$	−4.08503e7	−	8.57901e8i	−0.0651289	−	1.36778i
$857$	−4.29555e8			−0.682459			−0.341230	−	0.939980i	$-0.610843\pi$
$857$	−4.29555e8			−0.682459			−0.341230	+	0.939980i	$0.610843\pi$
$858$		0			0
$859$		−	1.64716e7i		−	0.0259870i	−0.999916	−	0.0129935i	$-0.995864\pi$
$859$		−	1.64716e7i		−	0.0259870i	0.999916	−	0.0129935i	$-0.00413607\pi$
$860$	445668.	+	1.40452e7i	0.000700674	+	0.0220817i
$861$		0			0
$862$	−1.80715e7	−	1.13933e9i	−0.0282145	−	1.77880i
$863$			6.68021e8i			1.03934i	0.854367	+	0.519670i	$0.173945\pi$
$863$			6.68021e8i			1.03934i	−0.854367	+	0.519670i	$0.826055\pi$
$864$		0			0
$865$	−1.34361e8			−0.207599
$866$	1.15782e9	−	1.83648e7i	1.78274	−	0.0282769i
$867$		0			0
$868$	8.24593e8	−	2.61652e7i	1.26090	−	0.0400096i
$869$	5.12277e8			0.780630
$870$		0			0
$871$			6.29889e8i			0.953257i
$872$	−8.12160e8	+	3.86722e7i	−1.22488	+	0.0583243i
$873$		0			0
$874$	−1.46860e8	+	2.32942e6i	−0.219973	+	0.00348911i
$875$		−	5.85562e7i		−	0.0874075i
$876$		0			0
$877$	5.13857e8			0.761805			0.380902	−	0.924615i	$-0.375613\pi$
$877$	5.13857e8			0.761805			0.380902	+	0.924615i	$0.375613\pi$
$878$	1.29144e7	+	8.14195e8i	0.0190805	+	1.20294i
$879$		0			0
$880$	2.38734e7	+	3.75804e8i	0.0350320	+	0.551460i
$881$	9.06780e7			0.132609			0.0663047	−	0.997799i	$-0.478879\pi$
$881$	9.06780e7			0.132609			0.0663047	+	0.997799i	$0.478879\pi$
$882$		0			0
$883$		−	6.91985e8i		−	1.00511i	−0.864545	−	0.502556i	$-0.832393\pi$
$883$		−	6.91985e8i		−	1.00511i	0.864545	−	0.502556i	$-0.167607\pi$
$884$	3.02606e8	−	9.60199e6i	0.438046	−	0.0138997i
$885$		0			0
$886$	−6.90251e6	−	4.35173e8i	−0.00992443	−	0.625692i
$887$		−	4.18647e8i		−	0.599898i	−0.953955	−	0.299949i	$-0.903030\pi$
$887$		−	4.18647e8i		−	0.599898i	0.953955	−	0.299949i	$-0.0969697\pi$
$888$		0			0
$889$	−2.36616e8			−0.336774
$890$	−5.13653e8	+	8.14732e6i	−0.728618	+	0.0115570i
$891$		0			0
$892$	−1.56852e7	−	4.94319e8i	−0.0221002	−	0.696486i
$893$	−5.44048e8			−0.763982
$894$		0			0
$895$		−	2.16250e8i		−	0.301638i
$896$	7.78828e7	+	6.98627e8i	0.108272	+	0.971229i
$897$		0			0
$898$	1.12710e9	−	1.78775e7i	1.55644	−	0.0246875i
$899$		−	7.83911e8i		−	1.07892i
$900$		0			0
$901$	8.81189e8			1.20474
$902$	1.12956e7	+	7.12139e8i	0.0153918	+	0.970387i
$903$		0			0
$904$	−8.99826e8	+	4.28466e7i	−1.21802	+	0.0579977i
$905$	−4.51734e8			−0.609448
$906$		0			0
$907$			2.05308e7i			0.0275159i	0.999905	+	0.0137579i	$0.00437943\pi$
$907$			2.05308e7i			0.0275159i	−0.999905	+	0.0137579i	$0.995621\pi$
$908$	−3.76816e7	−	1.18753e9i	−0.0503352	−	1.58631i
$909$		0			0
$910$	2.85358e6	+	1.79906e8i	0.00378674	+	0.238738i
$911$		−	4.59638e8i		−	0.607940i	−0.952682	−	0.303970i	$-0.901688\pi$
$911$		−	4.59638e8i		−	0.607940i	0.952682	−	0.303970i	$-0.0983123\pi$
$912$		0			0
$913$	−1.60416e9			−2.10783
$914$	5.15162e8	−	8.17126e6i	0.674692	−	0.0107016i
$915$		0			0
$916$	9.96920e8	−	3.16333e7i	1.29710	−	0.0411584i
$917$	−6.30006e8			−0.817027
$918$		0			0
$919$			1.30912e9i			1.68669i	0.537375	+	0.843344i	$0.319416\pi$
$919$			1.30912e9i			1.68669i	−0.537375	+	0.843344i	$0.680584\pi$
$920$	−6.69459e6	−	1.40594e8i	−0.00859726	−	0.180552i
$921$		0			0
$922$	−3.06229e8	+	4.85725e6i	−0.390709	+	0.00619724i
$923$			2.43077e8i			0.309128i
$924$		0			0
$925$	5.50434e7			0.0695472
$926$	1.29442e7	+	8.16078e8i	0.0163021	+	1.02778i
$927$		0			0
$928$	6.65839e8	−	5.29126e7i	0.833153	−	0.0662087i
$929$	7.99235e8			0.996845			0.498422	−	0.866934i	$-0.333913\pi$
$929$	7.99235e8			0.996845			0.498422	+	0.866934i	$0.333913\pi$
$930$		0			0
$931$		−	1.97619e7i		−	0.0244895i
$932$	−4.25077e8	+	1.34881e7i	−0.525073	+	0.0166611i
$933$		0			0
$934$	5.96731e6	+	3.76213e8i	0.00732383	+	0.461736i
$935$			3.62331e8i			0.443272i
$936$		0			0
$937$	−9.78066e8			−1.18891			−0.594456	−	0.804128i	$-0.702633\pi$
$937$	−9.78066e8			−1.18891			−0.594456	+	0.804128i	$0.702633\pi$
$938$	−1.40705e9	+	2.23180e7i	−1.70491	+	0.0270425i
$939$		0			0
$940$	−1.65349e7	−	5.21097e8i	−0.0199076	−	0.627386i
$941$	2.94969e8			0.354004			0.177002	−	0.984210i	$-0.443360\pi$
$941$	2.94969e8			0.354004			0.177002	+	0.984210i	$0.443360\pi$
$942$		0			0
$943$		−	2.66220e8i		−	0.317472i
$944$	−9.07069e7	−	1.42787e9i	−0.107826	−	1.69736i
$945$		0			0
$946$	5.16687e7	−	819544.i	0.0610315	−	0.000968053i
$947$		−	5.93617e8i		−	0.698966i	−0.936943	−	0.349483i	$-0.886357\pi$
$947$		−	5.93617e8i		−	0.698966i	0.936943	−	0.349483i	$-0.113643\pi$
$948$		0			0
$949$	8.09595e8			0.947260
$950$	1.48025e6	+	9.33235e7i	0.00172649	+	0.108848i
$951$		0			0
$952$	3.21708e7	+	6.75623e8i	0.0372865	+	0.783057i
$953$	−9.10574e7			−0.105205			−0.0526025	−	0.998616i	$-0.516752\pi$
$953$	−9.10574e7			−0.105205			−0.0526025	+	0.998616i	$0.516752\pi$
$954$		0			0
$955$		−	2.08203e8i		−	0.239044i
$956$	3.38403e7	+	1.06647e9i	0.0387312	+	1.22061i
$957$		0			0
$958$	4.90830e6	+	3.09447e8i	0.00558257	+	0.351957i
$959$		−	7.82386e8i		−	0.887085i
$960$		0			0
$961$	−5.91472e8			−0.666445
$962$	−1.69113e8	+	2.68239e6i	−0.189955	+	0.00301298i
$963$		0			0
$964$	−2.80100e8	+	8.88787e6i	−0.312667	+	0.00992126i
$965$	1.42646e8			0.158736
$966$		0			0
$967$			4.80655e7i			0.0531562i	0.999647	+	0.0265781i	$0.00846107\pi$
$967$			4.80655e7i			0.0531562i	−0.999647	+	0.0265781i	$0.991539\pi$
$968$	4.77174e8	−	2.27214e7i	0.526079	−	0.0250500i
$969$		0			0
$970$	−2.56579e8	+	4.06973e6i	−0.281129	+	0.00445913i
$971$		−	2.29463e8i		−	0.250643i	−0.992116	−	0.125321i	$-0.960004\pi$
$971$		−	2.29463e8i		−	0.250643i	0.992116	−	0.125321i	$-0.0399962\pi$
$972$		0			0
$973$	1.57764e9			1.71265
$974$	−3.27120e6	−	2.06235e8i	−0.00354022	−	0.223196i
$975$		0			0
$976$	5.92550e8	−	3.76424e7i	0.637347	−	0.0404881i
$977$	−4.93252e8			−0.528915			−0.264457	−	0.964397i	$-0.585193\pi$
$977$	−4.93252e8			−0.528915			−0.264457	+	0.964397i	$0.585193\pi$
$978$		0			0
$979$			1.88912e9i			2.01332i
$980$	1.89282e7	−	600612.i	0.0201109	−	0.000638140i
$981$		0			0
$982$	−1.55447e7	−	9.80026e8i	−0.0164153	−	1.03491i
$983$			4.15036e8i			0.436944i	0.975843	+	0.218472i	$0.0701072\pi$
$983$			4.15036e8i			0.436944i	−0.975843	+	0.218472i	$0.929893\pi$
$984$		0			0
$985$	7.03805e8			0.736451
$986$	6.42614e8	−	1.01928e7i	0.670377	−	0.0106332i
$987$		0			0
$988$	−9.09574e6	−	2.86651e8i	−0.00943121	−	0.297223i
$989$	−1.93154e7			−0.0199671
$990$		0			0
$991$			1.69893e9i			1.74564i	0.488039	+	0.872822i	$0.337713\pi$
$991$			1.69893e9i			1.74564i	−0.488039	+	0.872822i	$0.662287\pi$
$992$	−9.98283e7	−	1.25621e9i	−0.102263	−	1.28685i
$993$		0			0
$994$	−5.42988e8	+	8.61262e6i	−0.552880	+	0.00876952i
$995$		−	1.16101e8i		−	0.117860i
$996$		0			0
$997$	−1.43910e9			−1.45213			−0.726066	−	0.687625i	$-0.758653\pi$
$997$	−1.43910e9			−1.45213			−0.726066	+	0.687625i	$0.758653\pi$
$998$	−4.33322e6	−	2.73191e8i	−0.00435933	−	0.274837i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.7.c.b.91.2		24
3.2	odd	2		60.7.c.a.31.23	✓	24
4.3	odd	2	inner	180.7.c.b.91.1		24
12.11	even	2		60.7.c.a.31.24	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.c.a.31.23	✓	24	3.2	odd	2
60.7.c.a.31.24	yes	24	12.11	even	2
180.7.c.b.91.1		24	4.3	odd	2	inner
180.7.c.b.91.2		24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	180.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.99899 + 0.126876i) q^{2} +(63.9678 - 2.02976i) q^{4} +55.9017 q^{5} -335.195i q^{7} +(-511.421 + 24.3521i) q^{8} +O(q^{10})\)	\(q+(-7.99899 + 0.126876i) q^{2} +(63.9678 - 2.02976i) q^{4} +55.9017 q^{5} -335.195i q^{7} +(-511.421 + 24.3521i) q^{8} +(-447.157 + 7.09260i) q^{10} +1644.57i q^{11} +1200.29 q^{13} +(42.5283 + 2681.22i) q^{14} +(4087.76 - 259.679i) q^{16} +3941.20 q^{17} -3733.41i q^{19} +(3575.91 - 113.467i) q^{20} +(-208.656 - 13154.9i) q^{22} +4917.71i q^{23} +3125.00 q^{25} +(-9601.13 + 152.288i) q^{26} +(-680.367 - 21441.7i) q^{28} -20383.8 q^{29} +38457.5i q^{31} +(-32665.0 + 2595.81i) q^{32} +(-31525.6 + 500.045i) q^{34} -18738.0i q^{35} +17613.9 q^{37} +(473.681 + 29863.5i) q^{38} +(-28589.3 + 1361.32i) q^{40} -54135.0 q^{41} +3927.72i q^{43} +(3338.08 + 105199. i) q^{44} +(-623.940 - 39336.7i) q^{46} -145724. i q^{47} +5293.27 q^{49} +(-24996.9 + 396.488i) q^{50} +(76780.0 - 2436.31i) q^{52} +223584. q^{53} +91934.0i q^{55} +(8162.69 + 171426. i) q^{56} +(163050. - 2586.22i) q^{58} -349304. i q^{59} +144957. q^{61} +(-4879.34 - 307621. i) q^{62} +(260958. - 24908.3i) q^{64} +67098.4 q^{65} +524780. i q^{67} +(252110. - 7999.71i) q^{68} +(2377.40 + 149885. i) q^{70} +202515. i q^{71} +674498. q^{73} +(-140893. + 2234.78i) q^{74} +(-7577.94 - 238818. i) q^{76} +551250. q^{77} -311497. i q^{79} +(228513. - 14516.5i) q^{80} +(433025. - 6868.44i) q^{82} +975431. i q^{83} +220320. q^{85} +(-498.335 - 31417.8i) q^{86} +(-40048.6 - 841065. i) q^{88} +1.14871e6 q^{89} -402332. i q^{91} +(9981.79 + 314575. i) q^{92} +(18488.9 + 1.16565e6i) q^{94} -208704. i q^{95} +573799. q^{97} +(-42340.8 + 671.589i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8}+O(q^{10}) \) 24 * q - 20 * q^2 - 246 * q^4 + 340 * q^8	\( 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8} - 750 q^{10} + 5040 q^{13} + 2596 q^{14} + 4194 q^{16} - 7000 q^{20} + 45780 q^{22} + 75000 q^{25} - 75852 q^{26} + 54300 q^{28} - 132800 q^{29} + 10700 q^{32} - 173484 q^{34} - 69840 q^{37} - 215800 q^{38} - 14250 q^{40} + 70448 q^{41} + 395668 q^{44} - 158760 q^{46} - 642984 q^{49} - 62500 q^{50} - 210240 q^{52} + 644320 q^{53} + 917708 q^{56} - 1345020 q^{58} - 222864 q^{61} - 1948520 q^{62} + 935922 q^{64} - 266000 q^{65} - 572680 q^{68} + 220500 q^{70} + 771120 q^{73} + 589164 q^{74} - 191544 q^{76} - 1383840 q^{77} + 946000 q^{80} + 2672520 q^{82} - 372000 q^{85} - 1781528 q^{86} + 956940 q^{88} + 1566224 q^{89} + 3040560 q^{92} - 3788352 q^{94} - 1666800 q^{97} + 2709660 q^{98}+O(q^{100}) \) 24 * q - 20 * q^2 - 246 * q^4 + 340 * q^8 - 750 * q^10 + 5040 * q^13 + 2596 * q^14 + 4194 * q^16 - 7000 * q^20 + 45780 * q^22 + 75000 * q^25 - 75852 * q^26 + 54300 * q^28 - 132800 * q^29 + 10700 * q^32 - 173484 * q^34 - 69840 * q^37 - 215800 * q^38 - 14250 * q^40 + 70448 * q^41 + 395668 * q^44 - 158760 * q^46 - 642984 * q^49 - 62500 * q^50 - 210240 * q^52 + 644320 * q^53 + 917708 * q^56 - 1345020 * q^58 - 222864 * q^61 - 1948520 * q^62 + 935922 * q^64 - 266000 * q^65 - 572680 * q^68 + 220500 * q^70 + 771120 * q^73 + 589164 * q^74 - 191544 * q^76 - 1383840 * q^77 + 946000 * q^80 + 2672520 * q^82 - 372000 * q^85 - 1781528 * q^86 + 956940 * q^88 + 1566224 * q^89 + 3040560 * q^92 - 3788352 * q^94 - 1666800 * q^97 + 2709660 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

Properties

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