LMFDB - Embedded newform 304.6.i.b.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,6,Mod(49,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("304.49");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	304.i (of order $3$, 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:	$48.7566812231$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 386x^{6} + 3436x^{5} + 128708x^{4} + 568528x^{3} + 7340704x^{2} - 19430784x + 211527936 $ x^8 - 2x^7 + 386x^6 + 3436x^5 + 128708x^4 + 568528x^3 + 7340704x^2 - 19430784*x + 211527936
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.1
Root			$-6.34386 - 10.9879i$ of defining polynomial
Character	$\chi$	$=$	304.49
Dual form			304.6.i.b.273.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.84386 + 8.38982i) q^{3} +(-23.1201 + 40.0451i) q^{5} -177.800 q^{7} +(74.5740 + 129.166i) q^{9} -5.50017 q^{11} +(515.695 + 893.211i) q^{13} +(-223.981 - 387.946i) q^{15} +(-466.501 + 808.003i) q^{17} +(-1046.56 + 1175.08i) q^{19} +(861.238 - 1491.71i) q^{21} +(1770.58 + 3066.73i) q^{23} +(493.425 + 854.637i) q^{25} -3799.02 q^{27} +(-2089.31 - 3618.79i) q^{29} -3762.40 q^{31} +(26.6421 - 46.1454i) q^{33} +(4110.74 - 7120.02i) q^{35} -7922.43 q^{37} -9991.83 q^{39} +(2497.50 - 4325.80i) q^{41} +(7272.70 - 12596.7i) q^{43} -6896.62 q^{45} +(7679.23 + 13300.8i) q^{47} +14805.8 q^{49} +(-4519.33 - 7827.71i) q^{51} +(10286.1 + 17816.1i) q^{53} +(127.164 - 220.255i) q^{55} +(-4789.36 - 14472.4i) q^{57} +(6119.91 - 10600.0i) q^{59} +(-9096.89 - 15756.3i) q^{61} +(-13259.2 - 22965.7i) q^{63} -47691.7 q^{65} +(11387.1 + 19723.0i) q^{67} -34305.8 q^{69} +(33788.2 - 58522.8i) q^{71} +(40463.9 - 70085.6i) q^{73} -9560.33 q^{75} +977.929 q^{77} +(-43313.1 + 75020.6i) q^{79} +(280.475 - 485.798i) q^{81} -29466.9 q^{83} +(-21571.1 - 37362.2i) q^{85} +40481.4 q^{87} +(-23045.4 - 39915.7i) q^{89} +(-91690.6 - 158813. i) q^{91} +(18224.5 - 31565.8i) q^{93} +(-22859.9 - 69077.5i) q^{95} +(-2229.77 + 3862.07i) q^{97} +(-410.169 - 710.434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 14 q^{3} - 36 q^{5} - 76 q^{7} + 156 q^{9} - 144 q^{11} - 674 q^{13} + 20 q^{15} + 522 q^{17} - 320 q^{19} - 770 q^{21} + 204 q^{23} - 2158 q^{25} - 13156 q^{27} - 5712 q^{29} + 2324 q^{31} - 15650 q^{33}+ \cdots + 138328 q^{99}+O(q^{100}) $ 8 * q + 14 * q^3 - 36 * q^5 - 76 * q^7 + 156 * q^9 - 144 * q^11 - 674 * q^13 + 20 * q^15 + 522 * q^17 - 320 * q^19 - 770 * q^21 + 204 * q^23 - 2158 * q^25 - 13156 * q^27 - 5712 * q^29 + 2324 * q^31 - 15650 * q^33 + 4188 * q^35 - 25508 * q^37 - 44156 * q^39 - 3480 * q^41 - 4066 * q^43 + 51560 * q^45 + 45768 * q^47 + 1416 * q^49 - 1506 * q^51 + 45654 * q^53 - 36570 * q^55 - 66702 * q^57 + 84006 * q^59 - 14012 * q^61 + 15128 * q^63 - 4020 * q^65 + 19046 * q^67 + 111592 * q^69 + 53274 * q^71 - 41084 * q^73 - 153216 * q^75 + 271524 * q^77 + 54170 * q^79 - 9528 * q^81 - 52392 * q^83 - 221850 * q^85 + 457120 * q^87 - 137862 * q^89 - 308516 * q^91 + 112746 * q^93 - 153078 * q^95 - 292388 * q^97 + 138328 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−4.84386	+	8.38982i	−0.310734	+	0.538207i	−0.978521	−	0.206145i	$-0.933908\pi$
$3$	−4.84386	+	8.38982i	−0.310734	+	0.538207i	0.667787	+	0.744352i	$0.267242\pi$
$4$		0			0
$5$	−23.1201	+	40.0451i	−0.413584	+	0.716349i	−0.995279	−	0.0970584i	$-0.969057\pi$
$5$	−23.1201	+	40.0451i	−0.413584	+	0.716349i	0.581694	+	0.813407i	$0.302390\pi$
$6$		0			0
$7$	−177.800			−1.37147			−0.685735	−	0.727851i	$-0.740519\pi$
$7$	−177.800			−1.37147			−0.685735	+	0.727851i	$0.740519\pi$
$8$		0			0
$9$	74.5740	+	129.166i	0.306889	+	0.531547i
$10$		0			0
$11$	−5.50017			−0.0137055			−0.00685274	−	0.999977i	$-0.502181\pi$
$11$	−5.50017			−0.0137055			−0.00685274	+	0.999977i	$0.502181\pi$
$12$		0			0
$13$	515.695	+	893.211i	0.846321	+	1.46587i	0.884469	+	0.466598i	$0.154521\pi$
$13$	515.695	+	893.211i	0.846321	+	1.46587i	−0.0381488	+	0.999272i	$0.512146\pi$
$14$		0			0
$15$	−223.981	−	387.946i	−0.257029	−	0.445188i
$16$		0			0
$17$	−466.501	+	808.003i	−0.391498	+	0.678095i	−0.992647	−	0.121042i	$-0.961377\pi$
$17$	−466.501	+	808.003i	−0.391498	+	0.678095i	0.601149	+	0.799137i	$0.294710\pi$
$18$		0			0
$19$	−1046.56	+	1175.08i	−0.665087	+	0.746766i
$19$	−1046.56	+	1175.08i	−0.665087	+	0.746766i
$20$		0			0
$21$	861.238	−	1491.71i	0.426162	−	0.738135i
$22$		0			0
$23$	1770.58	+	3066.73i	0.697904	+	1.20881i	0.969192	+	0.246307i	$0.0792172\pi$
$23$	1770.58	+	3066.73i	0.697904	+	1.20881i	−0.271288	+	0.962498i	$0.587449\pi$
$24$		0			0
$25$	493.425	+	854.637i	0.157896	+	0.273484i
$26$		0			0
$27$	−3799.02			−1.00291
$28$		0			0
$29$	−2089.31	−	3618.79i	−0.461326	−	0.799041i	0.537701	−	0.843136i	$-0.319293\pi$
$29$	−2089.31	−	3618.79i	−0.461326	−	0.799041i	−0.999027	+	0.0440948i	$0.985960\pi$
$30$		0			0
$31$	−3762.40			−0.703170			−0.351585	−	0.936156i	$-0.614357\pi$
$31$	−3762.40			−0.703170			−0.351585	+	0.936156i	$0.614357\pi$
$32$		0			0
$33$	26.6421	−	46.1454i	0.00425876	−	0.00737639i
$34$		0			0
$35$	4110.74	−	7120.02i	0.567218	−	0.982451i
$36$		0			0
$37$	−7922.43			−0.951380			−0.475690	−	0.879613i	$-0.657802\pi$
$37$	−7922.43			−0.951380			−0.475690	+	0.879613i	$0.657802\pi$
$38$		0			0
$39$	−9991.83			−1.05192
$40$		0			0
$41$	2497.50	−	4325.80i	0.232031	−	0.401889i	−0.726375	−	0.687299i	$-0.758796\pi$
$41$	2497.50	−	4325.80i	0.232031	−	0.401889i	0.958406	+	0.285409i	$0.0921296\pi$
$42$		0			0
$43$	7272.70	−	12596.7i	0.599825	−	1.03893i	−0.393022	−	0.919529i	$-0.628570\pi$
$43$	7272.70	−	12596.7i	0.599825	−	1.03893i	0.992847	−	0.119398i	$-0.0380964\pi$
$44$		0			0
$45$	−6896.62			−0.507697
$46$		0			0
$47$	7679.23	+	13300.8i	0.507076	+	0.878281i	0.999966	+	0.00818981i	$0.00260693\pi$
$47$	7679.23	+	13300.8i	0.507076	+	0.878281i	−0.492891	+	0.870091i	$0.664060\pi$
$48$		0			0
$49$	14805.8			0.880930
$50$		0			0
$51$	−4519.33	−	7827.71i	−0.243304	−	0.421415i
$52$		0			0
$53$	10286.1	+	17816.1i	0.502994	+	0.871211i	0.999994	+	0.00346060i	$0.00110155\pi$
$53$	10286.1	+	17816.1i	0.502994	+	0.871211i	−0.497000	+	0.867751i	$0.665565\pi$
$54$		0			0
$55$	127.164	−	220.255i	0.00566837	−	0.00981791i
$56$		0			0
$57$	−4789.36	−	14472.4i	−0.195250	−	0.590000i
$58$		0			0
$59$	6119.91	−	10600.0i	0.228884	−	0.396438i	−0.728594	−	0.684946i	$-0.759826\pi$
$59$	6119.91	−	10600.0i	0.228884	−	0.396438i	0.957478	+	0.288508i	$0.0931591\pi$
$60$		0			0
$61$	−9096.89	−	15756.3i	−0.313017	−	0.542162i	0.665997	−	0.745955i	$-0.268006\pi$
$61$	−9096.89	−	15756.3i	−0.313017	−	0.542162i	−0.979014	+	0.203793i	$0.934673\pi$
$62$		0			0
$63$	−13259.2	−	22965.7i	−0.420889	−	0.729001i
$64$		0			0
$65$	−47691.7			−1.40010
$66$		0			0
$67$	11387.1	+	19723.0i	0.309903	+	0.536768i	0.978341	−	0.207000i	$-0.0663700\pi$
$67$	11387.1	+	19723.0i	0.309903	+	0.536768i	−0.668438	+	0.743768i	$0.733037\pi$
$68$		0			0
$69$	−34305.8			−0.867450
$70$		0			0
$71$	33788.2	−	58522.8i	0.795461	−	1.37778i	−0.127086	−	0.991892i	$-0.540562\pi$
$71$	33788.2	−	58522.8i	0.795461	−	1.37778i	0.922546	−	0.385886i	$-0.126104\pi$
$72$		0			0
$73$	40463.9	−	70085.6i	0.888711	−	1.53929i	0.0473118	−	0.998880i	$-0.484935\pi$
$73$	40463.9	−	70085.6i	0.888711	−	1.53929i	0.841400	−	0.540413i	$-0.181732\pi$
$74$		0			0
$75$	−9560.33			−0.196255
$76$		0			0
$77$	977.929			0.0187966
$78$		0			0
$79$	−43313.1	+	75020.6i	−0.780822	+	1.35242i	0.150642	+	0.988588i	$0.451866\pi$
$79$	−43313.1	+	75020.6i	−0.780822	+	1.35242i	−0.931464	+	0.363835i	$0.881467\pi$
$80$		0			0
$81$	280.475	−	485.798i	0.00474988	−	0.00822703i
$82$		0			0
$83$	−29466.9			−0.469504			−0.234752	−	0.972055i	$-0.575428\pi$
$83$	−29466.9			−0.469504			−0.234752	+	0.972055i	$0.575428\pi$
$84$		0			0
$85$	−21571.1	−	37362.2i	−0.323835	−	0.560899i
$86$		0			0
$87$	40481.4			0.573399
$88$		0			0
$89$	−23045.4	−	39915.7i	−0.308396	−	0.534157i	0.669616	−	0.742708i	$-0.266459\pi$
$89$	−23045.4	−	39915.7i	−0.308396	−	0.534157i	−0.978012	+	0.208550i	$0.933125\pi$
$90$		0			0
$91$	−91690.6	−	158813.i	−1.16070	−	2.01040i
$92$		0			0
$93$	18224.5	−	31565.8i	0.218499	−	0.378451i
$94$		0			0
$95$	−22859.9	−	69077.5i	−0.259876	−	0.785285i
$96$		0			0
$97$	−2229.77	+	3862.07i	−0.0240619	+	0.0416765i	−0.877806	−	0.479017i	$-0.840993\pi$
$97$	−2229.77	+	3862.07i	−0.0240619	+	0.0416765i	0.853744	+	0.520693i	$0.174327\pi$
$98$		0			0
$99$	−410.169	−	710.434i	−0.00420606	−	0.00728510i
$100$		0			0
$101$	−44061.3	−	76316.3i	−0.429787	−	0.744413i	0.567067	−	0.823672i	$-0.308078\pi$
$101$	−44061.3	−	76316.3i	−0.429787	−	0.744413i	−0.996854	+	0.0792585i	$0.974745\pi$
$102$		0			0
$103$	−50601.9			−0.469974			−0.234987	−	0.971998i	$-0.575505\pi$
$103$	−50601.9			−0.469974			−0.234987	+	0.971998i	$0.575505\pi$
$104$		0			0
$105$	39823.8	+	68976.8i	0.352508	+	0.610562i
$106$		0			0
$107$	−63576.1			−0.536827			−0.268414	−	0.963304i	$-0.586499\pi$
$107$	−63576.1			−0.536827			−0.268414	+	0.963304i	$0.586499\pi$
$108$		0			0
$109$	15795.7	−	27358.9i	0.127342	−	0.220563i	−0.795304	−	0.606211i	$-0.792689\pi$
$109$	15795.7	−	27358.9i	0.127342	−	0.220563i	0.922646	+	0.385648i	$0.126022\pi$
$110$		0			0
$111$	38375.2	−	66467.8i	0.295626	−	0.512040i
$112$		0			0
$113$	236103.			1.73942			0.869711	−	0.493561i	$-0.164305\pi$
$113$	236103.			1.73942			0.869711	+	0.493561i	$0.164305\pi$
$114$		0			0
$115$	−163744.			−1.15457
$116$		0			0
$117$	−76914.9	+	133221.i	−0.519453	+	0.899718i
$118$		0			0
$119$	82943.8	−	143663.i	0.536928	−	0.929987i
$120$		0			0
$121$	−161021.			−0.999812
$122$		0			0
$123$	24195.1	+	41907.2i	0.144200	+	0.249761i
$124$		0			0
$125$	−190132.			−1.08838
$126$		0			0
$127$	75478.8	+	130733.i	0.415256	+	0.719244i	0.995455	−	0.0952305i	$-0.0303588\pi$
$127$	75478.8	+	130733.i	0.415256	+	0.719244i	−0.580200	+	0.814474i	$0.697025\pi$
$128$		0			0
$129$	70455.9	+	122033.i	0.372772	+	0.645660i
$130$		0			0
$131$	−42728.8	+	74008.4i	−0.217542	+	0.376793i	−0.954056	−	0.299629i	$-0.903137\pi$
$131$	−42728.8	+	74008.4i	−0.217542	+	0.376793i	0.736514	+	0.676422i	$0.236470\pi$
$132$		0			0
$133$	186077.	−	208930.i	0.912147	−	1.02417i
$134$		0			0
$135$	87833.7	−	152132.i	0.414788	−	0.718434i
$136$		0			0
$137$	−152559.	−	264240.i	−0.694443	−	1.20281i	−0.970368	−	0.241632i	$-0.922317\pi$
$137$	−152559.	−	264240.i	−0.694443	−	1.20281i	0.275924	−	0.961179i	$-0.411016\pi$
$138$		0			0
$139$	150373.	+	260453.i	0.660134	+	1.14339i	0.980580	+	0.196118i	$0.0628337\pi$
$139$	150373.	+	260453.i	0.660134	+	1.14339i	−0.320447	+	0.947267i	$0.603833\pi$
$140$		0			0
$141$	−148789.			−0.630263
$142$		0			0
$143$	−2836.41	−	4912.81i	−0.0115992	−	0.0200905i
$144$		0			0
$145$	193220.			0.763190
$146$		0			0
$147$	−71717.2	+	124218.i	−0.273735	+	0.474123i
$148$		0			0
$149$	9608.88	−	16643.1i	0.0354574	−	0.0614140i	−0.847752	−	0.530393i	$-0.822045\pi$
$149$	9608.88	−	16643.1i	0.0354574	−	0.0614140i	0.883210	+	0.468979i	$0.155378\pi$
$150$		0			0
$151$	187140.			0.667920			0.333960	−	0.942587i	$-0.391615\pi$
$151$	187140.			0.667920			0.333960	+	0.942587i	$0.391615\pi$
$152$		0			0
$153$	−139155.			−0.480586
$154$		0			0
$155$	86986.9	−	150666.i	0.290820	−	0.503715i
$156$		0			0
$157$	−42664.9	+	73897.8i	−0.138141	+	0.239267i	−0.926793	−	0.375573i	$-0.877446\pi$
$157$	−42664.9	+	73897.8i	−0.138141	+	0.239267i	0.788652	+	0.614840i	$0.210779\pi$
$158$		0			0
$159$	−199299.			−0.625189
$160$		0			0
$161$	−314809.	−	545265.i	−0.957155	−	1.65784i
$162$		0			0
$163$	47671.9			0.140538			0.0702689	−	0.997528i	$-0.477614\pi$
$163$	47671.9			0.140538			0.0702689	+	0.997528i	$0.477614\pi$
$164$		0			0
$165$	1231.93	+	2133.77i	0.00352271	+	0.00610151i
$166$		0			0
$167$	−9863.67	−	17084.4i	−0.0273683	−	0.0474032i	0.852017	−	0.523514i	$-0.175379\pi$
$167$	−9863.67	−	17084.4i	−0.0273683	−	0.0474032i	−0.879385	+	0.476111i	$0.842046\pi$
$168$		0			0
$169$	−346237.	+	599700.i	−0.932517	+	1.61517i
$170$		0			0
$171$	−229826.	−	47548.7i	−0.601049	−	0.124351i
$172$		0			0
$173$	−361533.	+	626194.i	−0.918402	+	1.59072i	−0.116559	+	0.993184i	$0.537187\pi$
$173$	−361533.	+	626194.i	−0.918402	+	1.59072i	−0.801843	+	0.597535i	$0.796147\pi$
$174$		0			0
$175$	−87730.9	−	151954.i	−0.216550	−	0.375075i
$176$		0			0
$177$	59288.0	+	102690.i	0.142244	+	0.246374i
$178$		0			0
$179$	−553218.			−1.29052			−0.645259	−	0.763964i	$-0.723250\pi$
$179$	−553218.			−1.29052			−0.645259	+	0.763964i	$0.723250\pi$
$180$		0			0
$181$	332593.	+	576068.i	0.754599	+	1.30700i	0.945573	+	0.325409i	$0.105502\pi$
$181$	332593.	+	576068.i	0.754599	+	1.30700i	−0.190974	+	0.981595i	$0.561165\pi$
$182$		0			0
$183$	176256.			0.389060
$184$		0			0
$185$	183167.	−	317255.i	0.393476	−	0.681520i
$186$		0			0
$187$	2565.83	−	4444.15i	0.00536567	−	0.00929362i
$188$		0			0
$189$	675466.			1.37546
$190$		0			0
$191$	144263.			0.286135			0.143068	−	0.989713i	$-0.454303\pi$
$191$	144263.			0.286135			0.143068	+	0.989713i	$0.454303\pi$
$192$		0			0
$193$	360326.	−	624104.i	0.696310	−	1.20604i	−0.273427	−	0.961893i	$-0.588157\pi$
$193$	360326.	−	624104.i	0.696310	−	1.20604i	0.969737	−	0.244152i	$-0.0785096\pi$
$194$		0			0
$195$	231012.	−	400124.i	0.435059	−	0.753544i
$196$		0			0
$197$	1.00249e6			1.84041			0.920207	−	0.391432i	$-0.128020\pi$
$197$	1.00249e6			1.84041			0.920207	+	0.391432i	$0.128020\pi$
$198$		0			0
$199$	318120.	+	551000.i	0.569454	+	0.986323i	0.996620	+	0.0821495i	$0.0261785\pi$
$199$	318120.	+	551000.i	0.569454	+	0.986323i	−0.427166	+	0.904173i	$0.640488\pi$
$200$		0			0
$201$	−220630.			−0.385190
$202$		0			0
$203$	371479.	+	643421.i	0.632695	+	1.09586i
$204$		0			0
$205$	115485.	+	200025.i	0.191929	+	0.332430i
$206$		0			0
$207$	−264078.	+	457397.i	−0.428358	+	0.741938i
$208$		0			0
$209$	5756.23	−	6463.15i	0.00911533	−	0.0102348i
$210$		0			0
$211$	528520.	−	915424.i	0.817251	−	1.41552i	−0.0904485	−	0.995901i	$-0.528830\pi$
$211$	528520.	−	915424.i	0.817251	−	1.41552i	0.907700	−	0.419620i	$-0.137837\pi$
$212$		0			0
$213$	327330.	+	566953.i	0.494353	+	0.856245i
$214$		0			0
$215$	336291.	+	582472.i	0.496156	+	0.859368i
$216$		0			0
$217$	668954.			0.964377
$218$		0			0
$219$	392003.	+	678970.i	0.552306	+	0.956622i
$220$		0			0
$221$	−962289.			−1.32533
$222$		0			0
$223$	−81135.2	+	140530.i	−0.109256	+	0.189238i	−0.915469	−	0.402388i	$-0.868180\pi$
$223$	−81135.2	+	140530.i	−0.109256	+	0.189238i	0.806213	+	0.591626i	$0.201514\pi$
$224$		0			0
$225$	−73593.3	+	127467.i	−0.0969130	+	0.167858i
$226$		0			0
$227$	280544.			0.361357			0.180678	−	0.983542i	$-0.442171\pi$
$227$	280544.			0.361357			0.180678	+	0.983542i	$0.442171\pi$
$228$		0			0
$229$	−555296.			−0.699738			−0.349869	−	0.936799i	$-0.613774\pi$
$229$	−555296.			−0.699738			−0.349869	+	0.936799i	$0.613774\pi$
$230$		0			0
$231$	−4736.95	+	8204.64i	−0.00584076	+	0.0101165i
$232$		0			0
$233$	416075.	−	720664.i	0.502091	−	0.869647i	−0.497906	−	0.867231i	$-0.665898\pi$
$233$	416075.	−	720664.i	0.502091	−	0.869647i	0.999997	−	0.00241578i	$-0.000768967\pi$
$234$		0			0
$235$	−710177.			−0.838874
$236$		0			0
$237$	−419606.	−	726779.i	−0.485256	−	0.840488i
$238$		0			0
$239$	−61445.3			−0.0695815			−0.0347907	−	0.999395i	$-0.511076\pi$
$239$	−61445.3			−0.0695815			−0.0347907	+	0.999395i	$0.511076\pi$
$240$		0			0
$241$	559423.	+	968950.i	0.620437	+	1.07463i	0.989404	+	0.145187i	$0.0463783\pi$
$241$	559423.	+	968950.i	0.620437	+	1.07463i	−0.368967	+	0.929443i	$0.620288\pi$
$242$		0			0
$243$	−458864.	−	794776.i	−0.498504	−	0.863434i
$244$		0			0
$245$	−342311.	+	592899.i	−0.364339	+	0.631053i
$246$		0			0
$247$	−1.58930e6	−	328810.i	−1.65754	−	0.342928i
$248$		0			0
$249$	142734.	−	247222.i	0.145891	−	0.252691i
$250$		0			0
$251$	604896.	+	1.04771e6i	0.606033	+	1.04968i	0.991887	+	0.127120i	$0.0405733\pi$
$251$	604896.	+	1.04771e6i	0.606033	+	1.04968i	−0.385855	+	0.922560i	$0.626093\pi$
$252$		0			0
$253$	−9738.48	−	16867.5i	−0.00956511	−	0.0165673i
$254$		0			0
$255$	417949.			0.402507
$256$		0			0
$257$	27061.0	+	46871.1i	0.0255571	+	0.0442662i	0.878521	−	0.477704i	$-0.158531\pi$
$257$	27061.0	+	46871.1i	0.0255571	+	0.0442662i	−0.852964	+	0.521970i	$0.825197\pi$
$258$		0			0
$259$	1.40861e6			1.30479
$260$		0			0
$261$	311617.	−	539736.i	0.283152	−	0.490433i
$262$		0			0
$263$	−1.07965e6	+	1.87002e6i	−0.962489	+	1.66708i	−0.246272	+	0.969201i	$0.579206\pi$
$263$	−1.07965e6	+	1.87002e6i	−0.962489	+	1.66708i	−0.716216	+	0.697878i	$0.754128\pi$
$264$		0			0
$265$	−951265.			−0.832122
$266$		0			0
$267$	446514.			0.383316
$268$		0			0
$269$	−1.02660e6	+	1.77812e6i	−0.865006	+	1.49823i	0.00203447	+	0.999998i	$0.499352\pi$
$269$	−1.02660e6	+	1.77812e6i	−0.865006	+	1.49823i	−0.867041	+	0.498237i	$0.833981\pi$
$270$		0			0
$271$	945648.	−	1.63791e6i	0.782179	−	1.35477i	−0.148491	−	0.988914i	$-0.547442\pi$
$271$	945648.	−	1.63791e6i	0.782179	−	1.35477i	0.930670	−	0.365860i	$-0.119225\pi$
$272$		0			0
$273$	1.77655e6			1.44268
$274$		0			0
$275$	−2713.92	−	4700.65i	−0.00216404	−	0.00374823i
$276$		0			0
$277$	48008.8			0.0375943			0.0187971	−	0.999823i	$-0.494016\pi$
$277$	48008.8			0.0375943			0.0187971	+	0.999823i	$0.494016\pi$
$278$		0			0
$279$	−280577.	−	485974.i	−0.215795	−	0.373768i
$280$		0			0
$281$	715331.	+	1.23899e6i	0.540432	+	0.936056i	0.998879	+	0.0473339i	$0.0150725\pi$
$281$	715331.	+	1.23899e6i	0.540432	+	0.936056i	−0.458447	+	0.888722i	$0.651594\pi$
$282$		0			0
$283$	874446.	−	1.51459e6i	0.649033	−	1.12416i	−0.334321	−	0.942459i	$-0.608507\pi$
$283$	874446.	−	1.51459e6i	0.649033	−	1.12416i	0.983354	−	0.181699i	$-0.0581598\pi$
$284$		0			0
$285$	690278.	+	142811.i	0.503398	+	0.104148i
$286$		0			0
$287$	−444055.	+	769126.i	−0.318223	+	0.551179i
$288$		0			0
$289$	274683.	+	475764.i	0.193458	+	0.335079i
$290$		0			0
$291$	−21601.4	−	37414.7i	−0.0149537	−	0.0259006i
$292$		0			0
$293$	−2.57086e6			−1.74948			−0.874741	−	0.484591i	$-0.838968\pi$
$293$	−2.57086e6			−1.74948			−0.874741	+	0.484591i	$0.838968\pi$
$294$		0			0
$295$	282985.	+	490145.i	0.189325	+	0.327921i
$296$		0			0
$297$	20895.3			0.0137454
$298$		0			0
$299$	−1.82616e6	+	3.16300e6i	−1.18130	+	2.04607i
$300$		0			0
$301$	−1.29308e6	+	2.23969e6i	−0.822642	+	1.42486i
$302$		0			0
$303$	853707.			0.534198
$304$		0			0
$305$	841283.			0.517836
$306$		0			0
$307$	−453293.	+	785126.i	−0.274494	+	0.475438i	−0.970007	−	0.243076i	$-0.921844\pi$
$307$	−453293.	+	785126.i	−0.274494	+	0.475438i	0.695513	+	0.718513i	$0.255177\pi$
$308$		0			0
$309$	245109.	−	424541.i	0.146037	−	0.252944i
$310$		0			0
$311$	1.35970e6			0.797157			0.398578	−	0.917134i	$-0.369504\pi$
$311$	1.35970e6			0.797157			0.398578	+	0.917134i	$0.369504\pi$
$312$		0			0
$313$	−1.10408e6	−	1.91231e6i	−0.636998	−	1.10331i	−0.986088	−	0.166223i	$-0.946843\pi$
$313$	−1.10408e6	−	1.91231e6i	−0.636998	−	1.10331i	0.349090	−	0.937089i	$-0.386491\pi$
$314$		0			0
$315$	1.22622e6			0.696292
$316$		0			0
$317$	514679.	+	891451.i	0.287666	+	0.498252i	0.973252	−	0.229739i	$-0.0737873\pi$
$317$	514679.	+	891451.i	0.287666	+	0.498252i	−0.685586	+	0.727992i	$0.740454\pi$
$318$		0			0
$319$	11491.6	+	19904.0i	0.00632270	+	0.0109512i
$320$		0			0
$321$	307954.	−	533392.i	0.166810	−	0.288924i
$322$		0			0
$323$	−461252.	−	1.39380e6i	−0.245998	−	0.743350i
$324$		0			0
$325$	−508914.	+	881465.i	−0.267261	+	0.462910i
$326$		0			0
$327$	153024.	+	265046.i	0.0791390	+	0.137073i
$328$		0			0
$329$	−1.36537e6	−	2.36488e6i	−0.695439	−	1.20454i
$330$		0			0
$331$	−1.31278e6			−0.658601			−0.329300	−	0.944225i	$-0.606813\pi$
$331$	−1.31278e6			−0.658601			−0.329300	+	0.944225i	$0.606813\pi$
$332$		0			0
$333$	−590807.	−	1.02331e6i	−0.291968	−	0.505703i
$334$		0			0
$335$	−1.05308e6			−0.512685
$336$		0			0
$337$	1.55929e6	−	2.70077e6i	0.747915	−	1.29543i	−0.200906	−	0.979611i	$-0.564389\pi$
$337$	1.55929e6	−	2.70077e6i	0.747915	−	1.29543i	0.948821	−	0.315816i	$-0.102278\pi$
$338$		0			0
$339$	−1.14365e6	+	1.98086e6i	−0.540498	+	0.936170i
$340$		0			0
$341$	20693.8			0.00963728
$342$		0			0
$343$	355816.			0.163302
$344$		0			0
$345$	793152.	−	1.37378e6i	0.358764	−	0.621397i
$346$		0			0
$347$	803660.	−	1.39198e6i	0.358301	−	0.620596i	−0.629376	−	0.777101i	$-0.716689\pi$
$347$	803660.	−	1.39198e6i	0.358301	−	0.620596i	0.987677	+	0.156505i	$0.0500227\pi$
$348$		0			0
$349$	−724001.			−0.318182			−0.159091	−	0.987264i	$-0.550856\pi$
$349$	−724001.			−0.318182			−0.159091	+	0.987264i	$0.550856\pi$
$350$		0			0
$351$	−1.95914e6	−	3.39333e6i	−0.848784	−	1.47014i
$352$		0			0
$353$	724652.			0.309523			0.154761	−	0.987952i	$-0.450539\pi$
$353$	724652.			0.309523			0.154761	+	0.987952i	$0.450539\pi$
$354$		0			0
$355$	1.56237e6	+	2.70610e6i	0.657980	+	1.13965i
$356$		0			0
$357$	803537.	+	1.39177e6i	0.333684	+	0.577957i
$358$		0			0
$359$	361869.	−	626775.i	0.148189	−	0.256670i	−0.782369	−	0.622815i	$-0.785989\pi$
$359$	361869.	−	626775.i	0.148189	−	0.256670i	0.930558	+	0.366144i	$0.119322\pi$
$360$		0			0
$361$	−285541.	−	2.45958e6i	−0.115319	−	0.993329i
$362$		0			0
$363$	779963.	−	1.35093e6i	0.310676	−	0.538106i
$364$		0			0
$365$	1.87106e6	+	3.24077e6i	0.735114	+	1.27326i
$366$		0			0
$367$	−2.43800e6	−	4.22274e6i	−0.944863	−	1.63655i	−0.756025	−	0.654543i	$-0.772861\pi$
$367$	−2.43800e6	−	4.22274e6i	−0.944863	−	1.63655i	−0.188838	−	0.982008i	$-0.560472\pi$
$368$		0			0
$369$	744994.			0.284831
$370$		0			0
$371$	−1.82887e6	−	3.16770e6i	−0.689841	−	1.19484i
$372$		0			0
$373$	−1.30910e6			−0.487194			−0.243597	−	0.969877i	$-0.578327\pi$
$373$	−1.30910e6			−0.487194			−0.243597	+	0.969877i	$0.578327\pi$
$374$		0			0
$375$	920976.	−	1.59518e6i	0.338197	−	0.585775i
$376$		0			0
$377$	2.15490e6	−	3.73239e6i	0.780860	−	1.35249i
$378$		0			0
$379$	−60313.7			−0.0215684			−0.0107842	−	0.999942i	$-0.503433\pi$
$379$	−60313.7			−0.0215684			−0.0107842	+	0.999942i	$0.503433\pi$
$380$		0			0
$381$	−1.46244e6			−0.516136
$382$		0			0
$383$	510882.	−	884873.i	0.177960	−	0.308236i	−0.763221	−	0.646137i	$-0.776383\pi$
$383$	510882.	−	884873.i	0.177960	−	0.308236i	0.941182	+	0.337901i	$0.109717\pi$
$384$		0			0
$385$	−22609.8	+	39161.3i	−0.00777400	+	0.0134650i
$386$		0			0
$387$	2.16942e6			0.736318
$388$		0			0
$389$	−1.16397e6	−	2.01606e6i	−0.390004	−	0.675506i	0.602446	−	0.798160i	$-0.294193\pi$
$389$	−1.16397e6	−	2.01606e6i	−0.390004	−	0.675506i	−0.992450	+	0.122654i	$0.960860\pi$
$390$		0			0
$391$	−3.30391e6			−1.09291
$392$		0			0
$393$	−413945.	−	716973.i	−0.135195	−	0.234165i
$394$		0			0
$395$	−2.00281e6	−	3.46896e6i	−0.645871	−	1.11868i
$396$		0			0
$397$	1.75278e6	−	3.03591e6i	0.558152	−	0.966747i	−0.439499	−	0.898243i	$-0.644844\pi$
$397$	1.75278e6	−	3.03591e6i	0.558152	−	0.966747i	0.997651	−	0.0685040i	$-0.0218226\pi$
$398$		0			0
$399$	851547.	+	2.57318e6i	0.267779	+	0.809167i
$400$		0			0
$401$	318265.	−	551251.i	0.0988389	−	0.171194i	−0.812365	−	0.583149i	$-0.801820\pi$
$401$	318265.	−	551251.i	0.0988389	−	0.171194i	0.911204	+	0.411955i	$0.135154\pi$
$402$		0			0
$403$	−1.94025e6	−	3.36061e6i	−0.595108	−	1.03076i
$404$		0			0
$405$	12969.2	+	22463.4i	0.00392895	+	0.00680514i
$406$		0			0
$407$	43574.7			0.0130391
$408$		0			0
$409$	844535.	+	1.46278e6i	0.249637	+	0.432384i	0.963425	−	0.267978i	$-0.0863553\pi$
$409$	844535.	+	1.46278e6i	0.249637	+	0.432384i	−0.713788	+	0.700362i	$0.753022\pi$
$410$		0			0
$411$	2.95590e6			0.863149
$412$		0			0
$413$	−1.08812e6	+	1.88468e6i	−0.313907	+	0.543703i
$414$		0			0
$415$	681277.	−	1.18001e6i	0.194180	−	0.336329i
$416$		0			0
$417$	−2.91354e6			−0.820504
$418$		0			0
$419$	−3.97406e6			−1.10586			−0.552929	−	0.833228i	$-0.686490\pi$
$419$	−3.97406e6			−1.10586			−0.552929	+	0.833228i	$0.686490\pi$
$420$		0			0
$421$	−1.71438e6	+	2.96939e6i	−0.471413	+	0.816511i	−0.999465	−	0.0327009i	$-0.989589\pi$
$421$	−1.71438e6	+	2.96939e6i	−0.471413	+	0.816511i	0.528052	+	0.849212i	$0.322922\pi$
$422$		0			0
$423$	−1.14534e6	+	1.98379e6i	−0.311232	+	0.539069i
$424$		0			0
$425$	−920733.			−0.247264
$426$		0			0
$427$	1.61742e6	+	2.80146e6i	0.429294	+	0.743558i
$428$		0			0
$429$	54956.8			0.0144171
$430$		0			0
$431$	420749.	+	728758.i	0.109101	+	0.188969i	0.915406	−	0.402531i	$-0.131869\pi$
$431$	420749.	+	728758.i	0.109101	+	0.188969i	−0.806305	+	0.591500i	$0.798536\pi$
$432$		0			0
$433$	−3.16621e6	−	5.48403e6i	−0.811558	−	1.40566i	−0.911774	−	0.410693i	$-0.865287\pi$
$433$	−3.16621e6	−	5.48403e6i	−0.811558	−	1.40566i	0.100216	−	0.994966i	$-0.468047\pi$
$434$		0			0
$435$	−935932.	+	1.62108e6i	−0.237149	+	0.410754i
$436$		0			0
$437$	−5.45668e6	−	1.12893e6i	−1.36686	−	0.282789i
$438$		0			0
$439$	−2.56854e6	+	4.44884e6i	−0.636099	+	1.10176i	0.350182	+	0.936682i	$0.386120\pi$
$439$	−2.56854e6	+	4.44884e6i	−0.636099	+	1.10176i	−0.986281	+	0.165074i	$0.947214\pi$
$440$		0			0
$441$	1.10413e6	+	1.91240e6i	0.270347	+	0.468255i
$442$		0			0
$443$	1.35968e6	+	2.35504e6i	0.329175	+	0.570149i	0.982348	−	0.187060i	$-0.0598959\pi$
$443$	1.35968e6	+	2.35504e6i	0.329175	+	0.570149i	−0.653173	+	0.757209i	$0.726563\pi$
$444$		0			0
$445$	2.13124e6			0.510191
$446$		0			0
$447$	93088.2	+	161234.i	0.0220356	+	0.0381669i
$448$		0			0
$449$	2.65490e6			0.621488			0.310744	−	0.950494i	$-0.399422\pi$
$449$	2.65490e6			0.621488			0.310744	+	0.950494i	$0.399422\pi$
$450$		0			0
$451$	−13736.7	+	23792.6i	−0.00318010	+	0.00550809i
$452$		0			0
$453$	−906481.	+	1.57007e6i	−0.207545	+	0.359479i
$454$		0			0
$455$	8.47957e6			1.92019
$456$		0			0
$457$	2.65356e6			0.594345			0.297172	−	0.954824i	$-0.403956\pi$
$457$	2.65356e6			0.594345			0.297172	+	0.954824i	$0.403956\pi$
$458$		0			0
$459$	1.77225e6	−	3.06962e6i	0.392638	−	0.680069i
$460$		0			0
$461$	−1.76886e6	+	3.06376e6i	−0.387652	+	0.671432i	−0.992133	−	0.125187i	$-0.960047\pi$
$461$	−1.76886e6	+	3.06376e6i	−0.387652	+	0.671432i	0.604481	+	0.796619i	$0.293380\pi$
$462$		0			0
$463$	5.93347e6			1.28634			0.643171	−	0.765723i	$-0.277619\pi$
$463$	5.93347e6			1.28634			0.643171	+	0.765723i	$0.277619\pi$
$464$		0			0
$465$	842705.	+	1.45961e6i	0.180735	+	0.313043i
$466$		0			0
$467$	−5.23855e6			−1.11152			−0.555762	−	0.831341i	$-0.687573\pi$
$467$	−5.23855e6			−1.11152			−0.555762	+	0.831341i	$0.687573\pi$
$468$		0			0
$469$	−2.02463e6	−	3.50675e6i	−0.425023	−	0.736162i
$470$		0			0
$471$	−413326.	−	715902.i	−0.0858501	−	0.148697i
$472$		0			0
$473$	−40001.0	+	69283.8i	−0.00822088	+	0.0142390i
$474$		0			0
$475$	−1.52067e6	−	314610.i	−0.309243	−	0.0639792i
$476$		0			0
$477$	−1.53416e6	+	2.65724e6i	−0.308726	+	0.534730i
$478$		0			0
$479$	−857165.	−	1.48465e6i	−0.170697	−	0.295656i	0.767967	−	0.640490i	$-0.221269\pi$
$479$	−857165.	−	1.48465e6i	−0.170697	−	0.295656i	−0.938664	+	0.344834i	$0.887935\pi$
$480$		0			0
$481$	−4.08556e6	−	7.07640e6i	−0.805173	−	1.39460i
$482$		0			0
$483$	6.09956e6			1.18968
$484$		0			0
$485$	−103105.	−	178583.i	−0.0199033	−	0.0344735i
$486$		0			0
$487$	−5.46940e6			−1.04500			−0.522501	−	0.852639i	$-0.675001\pi$
$487$	−5.46940e6			−1.04500			−0.522501	+	0.852639i	$0.675001\pi$
$488$		0			0
$489$	−230916.	+	399959.i	−0.0436699	+	0.0756385i
$490$		0			0
$491$	570104.	−	987449.i	0.106721	−	0.184846i	−0.807719	−	0.589568i	$-0.799298\pi$
$491$	570104.	−	987449.i	0.106721	−	0.184846i	0.914440	+	0.404721i	$0.132631\pi$
$492$		0			0
$493$	3.89866e6			0.722434
$494$		0			0
$495$	37932.6			0.00695824
$496$		0			0
$497$	−6.00753e6	+	1.04053e7i	−1.09095	+	1.88958i
$498$		0			0
$499$	−2.55058e6	+	4.41773e6i	−0.458550	+	0.794232i	−0.998885	−	0.0472181i	$-0.984964\pi$
$499$	−2.55058e6	+	4.41773e6i	−0.458550	+	0.794232i	0.540334	+	0.841450i	$0.318298\pi$
$500$		0			0
$501$	191113.			0.0340170
$502$		0			0
$503$	−22139.7	−	38347.0i	−0.00390168	−	0.00675790i	0.864068	−	0.503375i	$-0.167909\pi$
$503$	−22139.7	−	38347.0i	−0.00390168	−	0.00675790i	−0.867970	+	0.496617i	$0.834575\pi$
$504$		0			0
$505$	4.07480e6			0.711013
$506$		0			0
$507$	−3.35425e6	−	5.80973e6i	−0.579530	−	1.00377i
$508$		0			0
$509$	−1.99430e6	−	3.45423e6i	−0.341190	−	0.590958i	0.643464	−	0.765476i	$-0.277497\pi$
$509$	−1.99430e6	−	3.45423e6i	−0.341190	−	0.590958i	−0.984654	+	0.174518i	$0.944163\pi$
$510$		0			0
$511$	−7.19448e6	+	1.24612e7i	−1.21884	+	2.11109i
$512$		0			0
$513$	3.97589e6	−	4.46417e6i	0.667023	−	0.748940i
$514$		0			0
$515$	1.16992e6	−	2.02636e6i	0.194374	−	0.336666i
$516$		0			0
$517$	−42237.0	−	73156.7i	−0.00694972	−	0.0120373i
$518$		0			0
$519$	−3.50243e6	−	6.06639e6i	−0.570758	−	0.988581i
$520$		0			0
$521$	−791816.			−0.127800			−0.0638998	−	0.997956i	$-0.520354\pi$
$521$	−791816.			−0.127800			−0.0638998	+	0.997956i	$0.520354\pi$
$522$		0			0
$523$	−318050.	−	550879.i	−0.0508442	−	0.0880648i	0.839483	−	0.543386i	$-0.182858\pi$
$523$	−318050.	−	550879.i	−0.0508442	−	0.0880648i	−0.890327	+	0.455321i	$0.849525\pi$
$524$		0			0
$525$	1.69983e6			0.269157
$526$		0			0
$527$	1.75516e6	−	3.04003e6i	0.275290	−	0.476816i
$528$		0			0
$529$	−3.05173e6	+	5.28575e6i	−0.474140	+	0.821235i
$530$		0			0
$531$	1.82554e6			0.280967
$532$		0			0
$533$	5.15180e6			0.785490
$534$		0			0
$535$	1.46988e6	−	2.54591e6i	0.222023	−	0.384556i
$536$		0			0
$537$	2.67971e6	−	4.64140e6i	0.401008	−	0.694566i
$538$		0			0
$539$	−81434.3			−0.0120736
$540$		0			0
$541$	4.33594e6	+	7.51007e6i	0.636928	+	1.10319i	0.986103	+	0.166134i	$0.0531285\pi$
$541$	4.33594e6	+	7.51007e6i	0.636928	+	1.10319i	−0.349175	+	0.937057i	$0.613538\pi$
$542$		0			0
$543$	−6.44414e6			−0.937919
$544$		0			0
$545$	730394.	+	1.26508e6i	0.105333	+	0.182443i
$546$		0			0
$547$	−4.16293e6	−	7.21041e6i	−0.594883	−	1.03037i	−0.993563	−	0.113277i	$-0.963865\pi$
$547$	−4.16293e6	−	7.21041e6i	−0.594883	−	1.03037i	0.398681	−	0.917090i	$-0.369468\pi$
$548$		0			0
$549$	1.35678e6	−	2.35001e6i	0.192123	−	0.332767i
$550$		0			0
$551$	6.43897e6	+	1.33216e6i	0.903519	+	0.186929i
$552$		0			0
$553$	7.70107e6	−	1.33386e7i	1.07087	−	1.85481i
$554$		0			0
$555$	1.77447e6	+	3.07348e6i	0.244533	+	0.423543i
$556$		0			0
$557$	7.17085e6	+	1.24203e7i	0.979338	+	1.69626i	0.664804	+	0.747018i	$0.268515\pi$
$557$	7.17085e6	+	1.24203e7i	0.979338	+	1.69626i	0.314534	+	0.949246i	$0.398152\pi$
$558$		0			0
$559$	1.50020e7			2.03058
$560$		0			0
$561$	24857.1	+	43053.7i	0.00333459	+	0.00577569i
$562$		0			0
$563$	−6.18370e6			−0.822201			−0.411100	−	0.911590i	$-0.634855\pi$
$563$	−6.18370e6			−0.822201			−0.411100	+	0.911590i	$0.634855\pi$
$564$		0			0
$565$	−5.45871e6	+	9.45477e6i	−0.719398	+	1.24603i
$566$		0			0
$567$	−49868.5	+	86374.8i	−0.00651431	+	0.0112831i
$568$		0			0
$569$	−42487.1			−0.00550144			−0.00275072	−	0.999996i	$-0.500876\pi$
$569$	−42487.1			−0.00550144			−0.00275072	+	0.999996i	$0.500876\pi$
$570$		0			0
$571$	1.07342e7			1.37778			0.688889	−	0.724867i	$-0.258099\pi$
$571$	1.07342e7			1.37778			0.688889	+	0.724867i	$0.258099\pi$
$572$		0			0
$573$	−698790.	+	1.21034e6i	−0.0889120	+	0.154000i
$574$		0			0
$575$	−1.74730e6	+	3.02641e6i	−0.220393	+	0.381731i
$576$		0			0
$577$	1.19721e6			0.149703			0.0748516	−	0.997195i	$-0.476152\pi$
$577$	1.19721e6			0.149703			0.0748516	+	0.997195i	$0.476152\pi$
$578$		0			0
$579$	3.49074e6	+	6.04615e6i	0.432735	+	0.749518i
$580$		0			0
$581$	5.23921e6			0.643911
$582$		0			0
$583$	−56575.5	−	97991.6i	−0.00689377	−	0.0119404i
$584$		0			0
$585$	−3.55656e6	−	6.16013e6i	−0.429675	−	0.744219i
$586$		0			0
$587$	−2.84952e6	+	4.93552e6i	−0.341332	+	0.591204i	−0.984680	−	0.174369i	$-0.944211\pi$
$587$	−2.84952e6	+	4.93552e6i	−0.341332	+	0.591204i	0.643348	+	0.765574i	$0.277545\pi$
$588$		0			0
$589$	3.93756e6	−	4.42113e6i	0.467669	−	0.525104i
$590$		0			0
$591$	−4.85594e6	+	8.41073e6i	−0.571879	+	0.990524i
$592$		0			0
$593$	6.90700e6	+	1.19633e7i	0.806590	+	1.39705i	0.915213	+	0.402971i	$0.132023\pi$
$593$	6.90700e6	+	1.19633e7i	0.806590	+	1.39705i	−0.108623	+	0.994083i	$0.534644\pi$
$594$		0			0
$595$	3.83533e6	+	6.64299e6i	0.444130	+	0.769256i
$596$		0			0
$597$	−6.16372e6			−0.707794
$598$		0			0
$599$	1.30413e6	+	2.25882e6i	0.148509	+	0.257226i	0.930677	−	0.365843i	$-0.119219\pi$
$599$	1.30413e6	+	2.25882e6i	0.148509	+	0.257226i	−0.782167	+	0.623068i	$0.785886\pi$
$600$		0			0
$601$	−1.09276e7			−1.23407			−0.617035	−	0.786935i	$-0.711666\pi$
$601$	−1.09276e7			−1.23407			−0.617035	+	0.786935i	$0.711666\pi$
$602$		0			0
$603$	−1.69836e6	+	2.94165e6i	−0.190212	+	0.329456i
$604$		0			0
$605$	3.72281e6	−	6.44810e6i	0.413507	−	0.716215i
$606$		0			0
$607$	1.12925e7			1.24400			0.621998	−	0.783019i	$-0.286321\pi$
$607$	1.12925e7			1.24400			0.621998	+	0.783019i	$0.286321\pi$
$608$		0			0
$609$	−7.19758e6			−0.786400
$610$		0			0
$611$	−7.92029e6	+	1.37183e7i	−0.858297	+	1.48661i
$612$		0			0
$613$	−6.37503e6	+	1.10419e7i	−0.685221	+	1.18684i	0.288146	+	0.957587i	$0.406961\pi$
$613$	−6.37503e6	+	1.10419e7i	−0.685221	+	1.18684i	−0.973367	+	0.229252i	$0.926372\pi$
$614$		0			0
$615$	−2.23757e6			−0.238555
$616$		0			0
$617$	4.94864e6	+	8.57129e6i	0.523326	+	0.906428i	0.999631	+	0.0271479i	$0.00864249\pi$
$617$	4.94864e6	+	8.57129e6i	0.523326	+	0.906428i	−0.476305	+	0.879280i	$0.658024\pi$
$618$		0			0
$619$	757549.			0.0794665			0.0397332	−	0.999210i	$-0.487349\pi$
$619$	757549.			0.0794665			0.0397332	+	0.999210i	$0.487349\pi$
$620$		0			0
$621$	−6.72647e6	−	1.16506e7i	−0.699936	−	1.21232i
$622$		0			0
$623$	4.09746e6	+	7.09701e6i	0.422956	+	0.732581i
$624$		0			0
$625$	2.85392e6	−	4.94314e6i	0.292242	−	0.506177i
$626$		0			0
$627$	26342.3	+	79600.4i	0.00267599	+	0.00808623i
$628$		0			0
$629$	3.69582e6	−	6.40135e6i	0.372464	−	0.645127i
$630$		0			0
$631$	−6.41621e6	−	1.11132e7i	−0.641512	−	1.11113i	−0.985095	−	0.172010i	$-0.944974\pi$
$631$	−6.41621e6	−	1.11132e7i	−0.641512	−	1.11113i	0.343583	−	0.939122i	$-0.388359\pi$
$632$		0			0
$633$	5.12016e6	+	8.86838e6i	0.507896	+	0.879701i
$634$		0			0
$635$	−6.98030e6			−0.686973
$636$		0			0
$637$	7.63527e6	+	1.32247e7i	0.745549	+	1.29133i
$638$		0			0
$639$	1.00789e7			0.976472
$640$		0			0
$641$	3.63523e6	−	6.29640e6i	0.349451	−	0.605267i	−0.636701	−	0.771111i	$-0.719701\pi$
$641$	3.63523e6	−	6.29640e6i	0.349451	−	0.605267i	0.986152	+	0.165844i	$0.0530347\pi$
$642$		0			0
$643$	1.06040e6	−	1.83666e6i	0.101144	−	0.175187i	−0.811012	−	0.585029i	$-0.801083\pi$
$643$	1.06040e6	−	1.83666e6i	0.101144	−	0.175187i	0.912156	+	0.409842i	$0.134416\pi$
$644$		0			0
$645$	−6.51578e6			−0.616690
$646$		0			0
$647$	1.14421e7			1.07460			0.537300	−	0.843391i	$-0.319444\pi$
$647$	1.14421e7			1.07460			0.537300	+	0.843391i	$0.319444\pi$
$648$		0			0
$649$	−33660.5	+	58301.7i	−0.00313696	+	0.00543338i
$650$		0			0
$651$	−3.24032e6	+	5.61240e6i	−0.299665	+	0.519034i
$652$		0			0
$653$	−1.73747e7			−1.59454			−0.797270	−	0.603623i	$-0.793723\pi$
$653$	−1.73747e7			−1.59454			−0.797270	+	0.603623i	$0.793723\pi$
$654$		0			0
$655$	−1.97578e6	−	3.42216e6i	−0.179944	−	0.311671i
$656$		0			0
$657$	1.20702e7			1.09094
$658$		0			0
$659$	−3.32289e6	−	5.75541e6i	−0.298059	−	0.516253i	0.677633	−	0.735400i	$-0.263006\pi$
$659$	−3.32289e6	−	5.75541e6i	−0.298059	−	0.516253i	−0.975692	+	0.219147i	$0.929672\pi$
$660$		0			0
$661$	−1.18645e6	−	2.05499e6i	−0.105620	−	0.182939i	0.808371	−	0.588673i	$-0.200349\pi$
$661$	−1.18645e6	−	2.05499e6i	−0.105620	−	0.182939i	−0.913991	+	0.405734i	$0.867016\pi$
$662$		0			0
$663$	4.66120e6	−	8.07343e6i	0.411826	−	0.713304i
$664$		0			0
$665$	4.06449e6	+	1.22820e7i	0.356412	+	1.07699i
$666$		0			0
$667$	7.39859e6	−	1.28147e7i	0.643923	−	1.11531i
$668$		0			0
$669$	−786015.	−	1.36142e6i	−0.0678994	−	0.117605i
$670$		0			0
$671$	50034.4	+	86662.1i	0.00429005	+	0.00743058i
$672$		0			0
$673$	−1.92310e6			−0.163668			−0.0818340	−	0.996646i	$-0.526078\pi$
$673$	−1.92310e6			−0.163668			−0.0818340	+	0.996646i	$0.526078\pi$
$674$		0			0
$675$	−1.87453e6	−	3.24679e6i	−0.158356	−	0.274280i
$676$		0			0
$677$	−525794.			−0.0440904			−0.0220452	−	0.999757i	$-0.507018\pi$
$677$	−525794.			−0.0440904			−0.0220452	+	0.999757i	$0.507018\pi$
$678$		0			0
$679$	396453.	−	686676.i	0.0330002	−	0.0571581i
$680$		0			0
$681$	−1.35892e6	+	2.35371e6i	−0.112286	+	0.194485i
$682$		0			0
$683$	−3.81145e6			−0.312635			−0.156318	−	0.987707i	$-0.549962\pi$
$683$	−3.81145e6			−0.312635			−0.156318	+	0.987707i	$0.549962\pi$
$684$		0			0
$685$	1.41087e7			1.14884
$686$		0			0
$687$	2.68978e6	−	4.65883e6i	0.217433	−	0.376604i
$688$		0			0
$689$	−1.06090e7	+	1.83754e7i	−0.851388	+	1.47465i
$690$		0			0
$691$	8.54562e6			0.680845			0.340423	−	0.940273i	$-0.389430\pi$
$691$	8.54562e6			0.680845			0.340423	+	0.940273i	$0.389430\pi$
$692$		0			0
$693$	72928.0	+	126315.i	0.00576848	+	0.00999130i
$694$		0			0
$695$	−1.39065e7			−1.09208
$696$		0			0
$697$	2.33017e6	+	4.03598e6i	0.181680	+	0.314678i
$698$		0			0
$699$	4.03082e6	+	6.98159e6i	0.312033	+	0.540458i
$700$		0			0
$701$	−2.37669e6	+	4.11655e6i	−0.182675	+	0.316402i	−0.942790	−	0.333386i	$-0.891809\pi$
$701$	−2.37669e6	+	4.11655e6i	−0.182675	+	0.316402i	0.760116	+	0.649788i	$0.225142\pi$
$702$		0			0
$703$	8.29127e6	−	9.30952e6i	0.632751	−	0.710459i
$704$		0			0
$705$	3.44000e6	−	5.95826e6i	0.260667	−	0.451488i
$706$		0			0
$707$	7.83408e6	+	1.35690e7i	0.589440	+	1.02094i
$708$		0			0
$709$	−1.06627e7	−	1.84683e7i	−0.796619	−	1.37978i	−0.921806	−	0.387651i	$-0.873287\pi$
$709$	−1.06627e7	−	1.84683e7i	−0.796619	−	1.37978i	0.125187	−	0.992133i	$-0.460047\pi$
$710$		0			0
$711$	−1.29201e7			−0.958502
$712$		0			0
$713$	−6.66162e6	−	1.15383e7i	−0.490745	−	0.849996i
$714$		0			0
$715$	262312.			0.0191890
$716$		0			0
$717$	297633.	−	515515.i	0.0216213	−	0.0374492i
$718$		0			0
$719$	−5.44618e6	+	9.43307e6i	−0.392889	+	0.680504i	−0.992829	−	0.119541i	$-0.961858\pi$
$719$	−5.44618e6	+	9.43307e6i	−0.392889	+	0.680504i	0.599940	+	0.800045i	$0.295191\pi$
$720$		0			0
$721$	8.99702e6			0.644556
$722$		0			0
$723$	−1.08391e7			−0.771164
$724$		0			0
$725$	2.06184e6	−	3.57121e6i	0.145683	−	0.252331i
$726$		0			0
$727$	−5.05507e6	+	8.75563e6i	−0.354724	+	0.614400i	−0.987071	−	0.160285i	$-0.948759\pi$
$727$	−5.05507e6	+	8.75563e6i	−0.354724	+	0.614400i	0.632347	+	0.774686i	$0.282092\pi$
$728$		0			0
$729$	9.02701e6			0.629108
$730$		0			0
$731$	6.78544e6	+	1.17527e7i	0.469661	+	0.813477i
$732$		0			0
$733$	−5.75940e6			−0.395929			−0.197965	−	0.980209i	$-0.563433\pi$
$733$	−5.75940e6			−0.395929			−0.197965	+	0.980209i	$0.563433\pi$
$734$		0			0
$735$	−3.31621e6	−	5.74385e6i	−0.226425	−	0.392179i
$736$		0			0
$737$	−62631.0	−	108480.i	−0.00424737	−	0.00735667i
$738$		0			0
$739$	1.21044e7	−	2.09654e7i	0.815326	−	1.41219i	−0.0937672	−	0.995594i	$-0.529891\pi$
$739$	1.21044e7	−	2.09654e7i	0.815326	−	1.41219i	0.909093	−	0.416592i	$-0.136776\pi$
$740$		0			0
$741$	1.04570e7	−	1.17412e7i	0.699620	−	0.785540i
$742$		0			0
$743$	−7.10772e6	+	1.23109e7i	−0.472344	+	0.818123i	−0.999499	−	0.0316458i	$-0.989925\pi$
$743$	−7.10772e6	+	1.23109e7i	−0.472344	+	0.818123i	0.527156	+	0.849769i	$0.323258\pi$
$744$		0			0
$745$	444316.	+	769578.i	0.0293293	+	0.0507998i
$746$		0			0
$747$	−2.19746e6	−	3.80612e6i	−0.144086	−	0.249563i
$748$		0			0
$749$	1.13038e7			0.736242
$750$		0			0
$751$	−4.15307e6	−	7.19333e6i	−0.268701	−	0.465404i	0.699826	−	0.714314i	$-0.253261\pi$
$751$	−4.15307e6	−	7.19333e6i	−0.268701	−	0.465404i	−0.968527	+	0.248910i	$0.919928\pi$
$752$		0			0
$753$	−1.17201e7			−0.753260
$754$		0			0
$755$	−4.32669e6	+	7.49405e6i	−0.276241	+	0.478464i
$756$		0			0
$757$	−1.95684e6	+	3.38935e6i	−0.124113	+	0.214969i	−0.921386	−	0.388649i	$-0.872942\pi$
$757$	−1.95684e6	+	3.38935e6i	−0.124113	+	0.214969i	0.797273	+	0.603619i	$0.206275\pi$
$758$		0			0
$759$	188688.			0.0118888
$760$		0			0
$761$	−2.93013e7			−1.83411			−0.917056	−	0.398758i	$-0.869441\pi$
$761$	−2.93013e7			−1.83411			−0.917056	+	0.398758i	$0.869441\pi$
$762$		0			0
$763$	−2.80847e6	+	4.86441e6i	−0.174646	+	0.302495i
$764$		0			0
$765$	3.21728e6	−	5.57249e6i	0.198763	−	0.344267i
$766$		0			0
$767$	1.26240e7			0.774836
$768$		0			0
$769$	3.04723e6	+	5.27795e6i	0.185818	+	0.321847i	0.943852	−	0.330369i	$-0.107173\pi$
$769$	3.04723e6	+	5.27795e6i	0.185818	+	0.321847i	−0.758034	+	0.652216i	$0.773840\pi$
$770$		0			0
$771$	−524320.			−0.0317658
$772$		0			0
$773$	212714.	+	368431.i	0.0128040	+	0.0221773i	0.872356	−	0.488870i	$-0.162591\pi$
$773$	212714.	+	368431.i	0.0128040	+	0.0221773i	−0.859552	+	0.511048i	$0.829258\pi$
$774$		0			0
$775$	−1.85646e6	−	3.21549e6i	−0.111028	−	0.192306i
$776$		0			0
$777$	−6.82310e6	+	1.18180e7i	−0.405443	+	0.702247i
$778$		0			0
$779$	2.46940e6	+	7.46196e6i	0.145797	+	0.440564i
$780$		0			0
$781$	−185841.	+	321885.i	−0.0109022	+	0.0188831i
$782$		0			0
$783$	7.93734e6	+	1.37479e7i	0.462669	+	0.801367i
$784$		0			0
$785$	−1.97283e6	−	3.41704e6i	−0.114266	−	0.197914i
$786$		0			0
$787$	1.02091e7			0.587556			0.293778	−	0.955874i	$-0.405087\pi$
$787$	1.02091e7			0.587556			0.293778	+	0.955874i	$0.405087\pi$
$788$		0			0
$789$	−1.04594e7	−	1.81162e7i	−0.598156	−	1.03604i
$790$		0			0
$791$	−4.19790e7			−2.38557
$792$		0			0
$793$	9.38245e6	−	1.62509e7i	0.529826	−	0.917685i
$794$		0			0
$795$	4.60780e6	−	7.98094e6i	0.258569	−	0.447854i
$796$		0			0
$797$	−6.53033e6			−0.364157			−0.182079	−	0.983284i	$-0.558283\pi$
$797$	−6.53033e6			−0.364157			−0.182079	+	0.983284i	$0.558283\pi$
$798$		0			0
$799$	−1.43295e7			−0.794078
$800$		0			0
$801$	3.43717e6	−	5.95335e6i	0.189286	−	0.327854i
$802$		0			0
$803$	−222558.	+	385482.i	−0.0121802	+	0.0210968i
$804$		0			0
$805$	2.91136e7			1.58346
$806$		0			0
$807$	−9.94539e6	−	1.72259e7i	−0.537574	−	0.931105i
$808$		0			0
$809$	−1.81878e7			−0.977032			−0.488516	−	0.872555i	$-0.662462\pi$
$809$	−1.81878e7			−0.977032			−0.488516	+	0.872555i	$0.662462\pi$
$810$		0			0
$811$	−2.30613e6	−	3.99433e6i	−0.123121	−	0.213251i	0.797876	−	0.602822i	$-0.205957\pi$
$811$	−2.30613e6	−	3.99433e6i	−0.123121	−	0.213251i	−0.920997	+	0.389570i	$0.872624\pi$
$812$		0			0
$813$	9.16118e6	+	1.58676e7i	0.486099	+	0.841948i
$814$		0			0
$815$	−1.10218e6	+	1.90903e6i	−0.0581243	+	0.100674i
$816$		0			0
$817$	7.19086e6	+	2.17292e7i	0.376900	+	1.13891i
$818$		0			0
$819$	1.36755e7	−	2.36866e7i	0.712413	−	1.23394i
$820$		0			0
$821$	2.86812e6	+	4.96773e6i	0.148504	+	0.257217i	0.930675	−	0.365847i	$-0.119221\pi$
$821$	2.86812e6	+	4.96773e6i	0.148504	+	0.257217i	−0.782170	+	0.623065i	$0.785887\pi$
$822$		0			0
$823$	1.08809e7	+	1.88463e7i	0.559972	+	0.969900i	0.997498	+	0.0706943i	$0.0225215\pi$
$823$	1.08809e7	+	1.88463e7i	0.559972	+	0.969900i	−0.437526	+	0.899206i	$0.644145\pi$
$824$		0			0
$825$	52583.4			0.00268976
$826$		0			0
$827$	−1.33891e7	−	2.31907e7i	−0.680751	−	1.17910i	−0.974752	−	0.223291i	$-0.928320\pi$
$827$	−1.33891e7	−	2.31907e7i	−0.680751	−	1.17910i	0.294000	−	0.955805i	$-0.405013\pi$
$828$		0			0
$829$	310674.			0.0157007			0.00785035	−	0.999969i	$-0.497501\pi$
$829$	310674.			0.0157007			0.00785035	+	0.999969i	$0.497501\pi$
$830$		0			0
$831$	−232548.	+	402785.i	−0.0116818	+	0.0202335i
$832$		0			0
$833$	−6.90691e6	+	1.19631e7i	−0.344883	+	0.597354i
$834$		0			0
$835$	912195.			0.0452763
$836$		0			0
$837$	1.42934e7			0.705217
$838$		0			0
$839$	4.18809e6	−	7.25399e6i	0.205405	−	0.355772i	−0.744857	−	0.667225i	$-0.767482\pi$
$839$	4.18809e6	−	7.25399e6i	0.205405	−	0.355772i	0.950262	+	0.311452i	$0.100815\pi$
$840$		0			0
$841$	1.52512e6	−	2.64159e6i	0.0743558	−	0.128788i
$842$		0			0
$843$	−1.38599e7			−0.671722
$844$		0			0
$845$	−1.60100e7	−	2.77302e7i	−0.771349	−	1.33602i
$846$		0			0
$847$	2.86295e7			1.37121
$848$		0			0
$849$	8.47140e6	+	1.46729e7i	0.403353	+	0.698629i
$850$		0			0
$851$	−1.40273e7	−	2.42960e7i	−0.663972	−	1.15003i
$852$		0			0
$853$	1.80296e7	−	3.12283e7i	0.848427	−	1.46952i	−0.0341843	−	0.999416i	$-0.510883\pi$
$853$	1.80296e7	−	3.12283e7i	0.848427	−	1.46952i	0.882611	−	0.470103i	$-0.155783\pi$
$854$		0			0
$855$	7.21770e6	−	8.10410e6i	0.337663	−	0.379131i
$856$		0			0
$857$	−1.53061e7	+	2.65109e7i	−0.711889	+	1.23303i	0.252258	+	0.967660i	$0.418827\pi$
$857$	−1.53061e7	+	2.65109e7i	−0.711889	+	1.23303i	−0.964147	+	0.265368i	$0.914507\pi$
$858$		0			0
$859$	−1.53666e7	−	2.66158e7i	−0.710551	−	1.23071i	−0.964651	−	0.263532i	$-0.915112\pi$
$859$	−1.53666e7	−	2.66158e7i	−0.710551	−	1.23071i	0.254100	−	0.967178i	$-0.418221\pi$
$860$		0			0
$861$	−4.30189e6	−	7.45109e6i	−0.197766	−	0.342540i
$862$		0			0
$863$	−3.77643e7			−1.72605			−0.863026	−	0.505159i	$-0.831434\pi$
$863$	−3.77643e7			−1.72605			−0.863026	+	0.505159i	$0.831434\pi$
$864$		0			0
$865$	−1.67173e7	−	2.89553e7i	−0.759673	−	1.31579i
$866$		0			0
$867$	−5.32210e6			−0.240456
$868$		0			0
$869$	238229.	−	412626.i	0.0107015	−	0.0185356i
$870$		0			0
$871$	−1.17446e7	+	2.03422e7i	−0.524555	+	0.908556i
$872$		0			0
$873$	−665131.			−0.0295373
$874$		0			0
$875$	3.38055e7			1.49268
$876$		0			0
$877$	4.12280e6	−	7.14090e6i	0.181006	−	0.313512i	−0.761217	−	0.648497i	$-0.775398\pi$
$877$	4.12280e6	−	7.14090e6i	0.181006	−	0.313512i	0.942223	+	0.334985i	$0.108731\pi$
$878$		0			0
$879$	1.24529e7	−	2.15690e7i	0.543623	−	0.941583i
$880$		0			0
$881$	1.71534e7			0.744579			0.372289	−	0.928117i	$-0.378573\pi$
$881$	1.71534e7			0.744579			0.372289	+	0.928117i	$0.378573\pi$
$882$		0			0
$883$	−8.33139e6	−	1.44304e7i	−0.359597	−	0.622839i	0.628297	−	0.777974i	$-0.283752\pi$
$883$	−8.33139e6	−	1.44304e7i	−0.359597	−	0.622839i	−0.987893	+	0.155134i	$0.950419\pi$
$884$		0			0
$885$	−5.48297e6			−0.235319
$886$		0			0
$887$	1.47463e7	+	2.55413e7i	0.629322	+	1.09002i	0.987688	+	0.156436i	$0.0500005\pi$
$887$	1.47463e7	+	2.55413e7i	0.629322	+	1.09002i	−0.358366	+	0.933581i	$0.616666\pi$
$888$		0			0
$889$	−1.34201e7	−	2.32443e7i	−0.569510	−	0.986421i
$890$		0			0
$891$	−1542.66	+	2671.97i	−6.50993e−5	+	0.000112755i
$892$		0			0
$893$	−2.36663e7	−	4.89631e6i	−0.993120	−	0.205466i
$894$		0			0
$895$	1.27904e7	−	2.21537e7i	0.533738	−	0.924461i
$896$		0			0
$897$	−1.76913e7	−	3.06423e7i	−0.734141	−	1.27157i
$898$		0			0
$899$	7.86082e6	+	1.36153e7i	0.324391	+	0.561862i
$900$		0			0
$901$	−1.91940e7			−0.787685
$902$		0			0
$903$	−1.25271e7	−	2.16975e7i	−0.511245	−	0.885503i
$904$		0			0
$905$	−3.07583e7			−1.24836
$906$		0			0
$907$	−3.47306e6	+	6.01551e6i	−0.140182	+	0.242803i	−0.927565	−	0.373661i	$-0.878102\pi$
$907$	−3.47306e6	+	6.01551e6i	−0.140182	+	0.242803i	0.787383	+	0.616464i	$0.211436\pi$
$908$		0			0
$909$	6.57164e6	−	1.13824e7i	0.263794	−	0.456904i
$910$		0			0
$911$	−1.26026e7			−0.503113			−0.251556	−	0.967843i	$-0.580942\pi$
$911$	−1.26026e7			−0.503113			−0.251556	+	0.967843i	$0.580942\pi$
$912$		0			0
$913$	162073.			0.00643478
$914$		0			0
$915$	−4.07506e6	+	7.05821e6i	−0.160909	+	0.278703i
$916$		0			0
$917$	7.59717e6	−	1.31587e7i	0.298352	−	0.516760i
$918$		0			0
$919$	−2.84869e7			−1.11264			−0.556321	−	0.830967i	$-0.687788\pi$
$919$	−2.84869e7			−1.11264			−0.556321	+	0.830967i	$0.687788\pi$
$920$		0			0
$921$	−4.39138e6	−	7.60609e6i	−0.170589	−	0.295469i
$922$		0			0
$923$	6.96976e7			2.69286
$924$		0			0
$925$	−3.90913e6	−	6.77080e6i	−0.150219	−	0.260187i
$926$		0			0
$927$	−3.77359e6	−	6.53604e6i	−0.144230	−	0.249813i
$928$		0			0
$929$	−1.50033e7	+	2.59864e7i	−0.570357	+	0.987888i	0.426172	+	0.904642i	$0.359862\pi$
$929$	−1.50033e7	+	2.59864e7i	−0.570357	+	0.987888i	−0.996529	+	0.0832453i	$0.973471\pi$
$930$		0			0
$931$	−1.54951e7	+	1.73980e7i	−0.585895	+	0.657848i
$932$		0			0
$933$	−6.58622e6	+	1.14077e7i	−0.247704	+	0.429035i
$934$		0			0
$935$	118644.	+	205498.i	0.00443832	+	0.00768739i
$936$		0			0
$937$	1.83152e7	+	3.17229e7i	0.681495	+	1.18038i	0.974525	+	0.224281i	$0.0720034\pi$
$937$	1.83152e7	+	3.17229e7i	0.681495	+	1.18038i	−0.293029	+	0.956103i	$0.594663\pi$
$938$		0			0
$939$	2.13920e7			0.791748
$940$		0			0
$941$	−1.98334e7	−	3.43524e7i	−0.730167	−	1.26469i	−0.956811	−	0.290709i	$-0.906109\pi$
$941$	−1.98334e7	−	3.43524e7i	−0.730167	−	1.26469i	0.226644	−	0.973978i	$-0.427225\pi$
$942$		0			0
$943$	1.76881e7			0.647742
$944$		0			0
$945$	−1.56168e7	+	2.70491e7i	−0.568870	+	0.985311i
$946$		0			0
$947$	−1.96508e7	+	3.40362e7i	−0.712041	+	1.23329i	0.252049	+	0.967714i	$0.418896\pi$
$947$	−1.96508e7	+	3.40362e7i	−0.712041	+	1.23329i	−0.964090	+	0.265576i	$0.914438\pi$
$948$		0			0
$949$	8.34682e7			3.00854
$950$		0			0
$951$	−9.97215e6			−0.357551
$952$		0			0
$953$	3.63675e6	−	6.29904e6i	0.129712	−	0.224669i	−0.793853	−	0.608110i	$-0.791928\pi$
$953$	3.63675e6	−	6.29904e6i	0.129712	−	0.224669i	0.923565	+	0.383442i	$0.125261\pi$
$954$		0			0
$955$	−3.33537e6	+	5.77703e6i	−0.118341	+	0.204973i
$956$		0			0
$957$	−222654.			−0.00785871
$958$		0			0
$959$	2.71250e7	+	4.69819e7i	0.952408	+	1.64962i
$960$		0			0
$961$	−1.44735e7			−0.505552
$962$		0			0
$963$	−4.74112e6	−	8.21186e6i	−0.164746	−	0.285349i
$964$		0			0
$965$	1.66615e7	+	2.88586e7i	0.575966	+	0.997602i
$966$		0			0
$967$	2.26883e7	−	3.92972e7i	0.780253	−	1.35144i	−0.151542	−	0.988451i	$-0.548424\pi$
$967$	2.26883e7	−	3.92972e7i	0.780253	−	1.35144i	0.931794	−	0.362986i	$-0.118243\pi$
$968$		0			0
$969$	1.39279e7	+	2.88155e6i	0.476516	+	0.0985862i
$970$		0			0
$971$	−4.87437e6	+	8.44266e6i	−0.165909	+	0.287363i	−0.936978	−	0.349389i	$-0.886389\pi$
$971$	−4.87437e6	+	8.44266e6i	−0.165909	+	0.287363i	0.771069	+	0.636752i	$0.219723\pi$
$972$		0			0
$973$	−2.67362e7	−	4.63085e7i	−0.905353	−	1.56812i
$974$		0			0
$975$	−4.93022e6	−	8.53939e6i	−0.166094	−	0.287684i
$976$		0			0
$977$	1.80142e7			0.603779			0.301890	−	0.953343i	$-0.402383\pi$
$977$	1.80142e7			0.603779			0.301890	+	0.953343i	$0.402383\pi$
$978$		0			0
$979$	126753.	+	219543.i	0.00422671	+	0.00732088i
$980$		0			0
$981$	4.71178e6			0.156319
$982$		0			0
$983$	1.74891e7	−	3.02920e7i	0.577277	−	0.999872i	−0.418514	−	0.908211i	$-0.637449\pi$
$983$	1.74891e7	−	3.02920e7i	0.577277	−	0.999872i	0.995790	−	0.0916618i	$-0.0292179\pi$
$984$		0			0
$985$	−2.31777e7	+	4.01449e7i	−0.761166	+	1.31838i
$986$		0			0
$987$	2.64546e7			0.864386
$988$		0			0
$989$	5.15076e7			1.67448
$990$		0			0
$991$	1.59799e6	−	2.76780e6i	0.0516880	−	0.0895262i	−0.839024	−	0.544095i	$-0.816873\pi$
$991$	1.59799e6	−	2.76780e6i	0.0516880	−	0.0895262i	0.890712	+	0.454569i	$0.150207\pi$
$992$		0			0
$993$	6.35893e6	−	1.10140e7i	0.204650	−	0.354464i
$994$		0			0
$995$	−2.94198e7			−0.942068
$996$		0			0
$997$	−2.30696e7	−	3.99577e7i	−0.735025	−	1.27310i	−0.954712	−	0.297530i	$-0.903837\pi$
$997$	−2.30696e7	−	3.99577e7i	−0.735025	−	1.27310i	0.219687	−	0.975570i	$-0.429496\pi$
$998$		0			0
$999$	3.00975e7			0.954150

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.6.i.b.49.1		8
4.3	odd	2		38.6.c.b.11.4	yes	8
12.11	even	2		342.6.g.d.163.3		8
19.7	even	3	inner	304.6.i.b.273.1		8
76.7	odd	6		38.6.c.b.7.4	✓	8
76.11	odd	6		722.6.a.j.1.1		4
76.27	even	6		722.6.a.g.1.4		4
228.83	even	6		342.6.g.d.235.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.c.b.7.4	✓	8	76.7	odd	6
38.6.c.b.11.4	yes	8	4.3	odd	2
304.6.i.b.49.1		8	1.1	even	1	trivial
304.6.i.b.273.1		8	19.7	even	3	inner
342.6.g.d.163.3		8	12.11	even	2
342.6.g.d.235.3		8	228.83	even	6
722.6.a.g.1.4		4	76.27	even	6
722.6.a.j.1.1		4	76.11	odd	6

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	304.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.84386 + 8.38982i) q^{3} +(-23.1201 + 40.0451i) q^{5} -177.800 q^{7} +(74.5740 + 129.166i) q^{9} -5.50017 q^{11} +(515.695 + 893.211i) q^{13} +(-223.981 - 387.946i) q^{15} +(-466.501 + 808.003i) q^{17} +(-1046.56 + 1175.08i) q^{19} +(861.238 - 1491.71i) q^{21} +(1770.58 + 3066.73i) q^{23} +(493.425 + 854.637i) q^{25} -3799.02 q^{27} +(-2089.31 - 3618.79i) q^{29} -3762.40 q^{31} +(26.6421 - 46.1454i) q^{33} +(4110.74 - 7120.02i) q^{35} -7922.43 q^{37} -9991.83 q^{39} +(2497.50 - 4325.80i) q^{41} +(7272.70 - 12596.7i) q^{43} -6896.62 q^{45} +(7679.23 + 13300.8i) q^{47} +14805.8 q^{49} +(-4519.33 - 7827.71i) q^{51} +(10286.1 + 17816.1i) q^{53} +(127.164 - 220.255i) q^{55} +(-4789.36 - 14472.4i) q^{57} +(6119.91 - 10600.0i) q^{59} +(-9096.89 - 15756.3i) q^{61} +(-13259.2 - 22965.7i) q^{63} -47691.7 q^{65} +(11387.1 + 19723.0i) q^{67} -34305.8 q^{69} +(33788.2 - 58522.8i) q^{71} +(40463.9 - 70085.6i) q^{73} -9560.33 q^{75} +977.929 q^{77} +(-43313.1 + 75020.6i) q^{79} +(280.475 - 485.798i) q^{81} -29466.9 q^{83} +(-21571.1 - 37362.2i) q^{85} +40481.4 q^{87} +(-23045.4 - 39915.7i) q^{89} +(-91690.6 - 158813. i) q^{91} +(18224.5 - 31565.8i) q^{93} +(-22859.9 - 69077.5i) q^{95} +(-2229.77 + 3862.07i) q^{97} +(-410.169 - 710.434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 14 q^{3} - 36 q^{5} - 76 q^{7} + 156 q^{9} - 144 q^{11} - 674 q^{13} + 20 q^{15} + 522 q^{17} - 320 q^{19} - 770 q^{21} + 204 q^{23} - 2158 q^{25} - 13156 q^{27} - 5712 q^{29} + 2324 q^{31} - 15650 q^{33}+ \cdots + 138328 q^{99}+O(q^{100}) \) 8 * q + 14 * q^3 - 36 * q^5 - 76 * q^7 + 156 * q^9 - 144 * q^11 - 674 * q^13 + 20 * q^15 + 522 * q^17 - 320 * q^19 - 770 * q^21 + 204 * q^23 - 2158 * q^25 - 13156 * q^27 - 5712 * q^29 + 2324 * q^31 - 15650 * q^33 + 4188 * q^35 - 25508 * q^37 - 44156 * q^39 - 3480 * q^41 - 4066 * q^43 + 51560 * q^45 + 45768 * q^47 + 1416 * q^49 - 1506 * q^51 + 45654 * q^53 - 36570 * q^55 - 66702 * q^57 + 84006 * q^59 - 14012 * q^61 + 15128 * q^63 - 4020 * q^65 + 19046 * q^67 + 111592 * q^69 + 53274 * q^71 - 41084 * q^73 - 153216 * q^75 + 271524 * q^77 + 54170 * q^79 - 9528 * q^81 - 52392 * q^83 - 221850 * q^85 + 457120 * q^87 - 137862 * q^89 - 308516 * q^91 + 112746 * q^93 - 153078 * q^95 - 292388 * q^97 + 138328 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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