LMFDB - Embedded newform 224.6.p.a.31.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,6,Mod(31,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("224.31");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	224.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$35.9259756381$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.10
Character	$\chi$	$=$	224.31
Dual form			224.6.p.a.159.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.95676 + 15.5136i) q^{3} +(-94.4708 + 54.5427i) q^{5} +(65.8412 - 111.678i) q^{7} +(-38.9472 - 67.4586i) q^{9} +(-97.3073 - 56.1804i) q^{11} -345.316i q^{13} -1954.11i q^{15} +(-1624.18 - 937.724i) q^{17} +(87.2532 + 151.127i) q^{19} +(1142.80 + 2021.70i) q^{21} +(-2885.78 + 1666.11i) q^{23} +(4387.32 - 7599.06i) q^{25} -2957.62 q^{27} +7434.99 q^{29} +(2448.61 - 4241.11i) q^{31} +(1743.12 - 1006.39i) q^{33} +(-128.851 + 14141.4i) q^{35} +(1965.25 + 3403.91i) q^{37} +(5357.08 + 3092.91i) q^{39} +9615.48i q^{41} +20590.9i q^{43} +(7358.75 + 4248.58i) q^{45} +(4736.43 + 8203.74i) q^{47} +(-8136.88 - 14706.0i) q^{49} +(29094.9 - 16797.9i) q^{51} +(6818.03 - 11809.2i) q^{53} +12256.9 q^{55} -3126.02 q^{57} +(-4510.30 + 7812.08i) q^{59} +(-16227.8 + 9369.11i) q^{61} +(-10098.0 - 92.0087i) q^{63} +(18834.5 + 32622.2i) q^{65} +(-19019.3 - 10980.8i) q^{67} -59691.7i q^{69} +21401.3i q^{71} +(24471.4 + 14128.5i) q^{73} +(78592.3 + 136126. i) q^{75} +(-12680.9 + 7168.08i) q^{77} +(82812.6 - 47811.9i) q^{79} +(35954.9 - 62275.7i) q^{81} -73730.0 q^{83} +204584. q^{85} +(-66593.4 + 115343. i) q^{87} +(14912.9 - 8609.95i) q^{89} +(-38564.1 - 22736.0i) q^{91} +(43863.2 + 75973.2i) q^{93} +(-16485.8 - 9518.05i) q^{95} -72000.9i q^{97} +8752.28i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 3240 q^{9} + 6856 q^{21} + 27728 q^{25} - 15920 q^{29} - 28296 q^{33} - 2152 q^{37} + 35400 q^{45} + 29280 q^{49} - 17512 q^{53} - 108368 q^{57} + 37704 q^{61} + 18216 q^{65} + 157704 q^{73} + 28224 q^{77}+ \cdots + 39400 q^{93}+O(q^{100}) $ 80 * q - 3240 * q^9 + 6856 * q^21 + 27728 * q^25 - 15920 * q^29 - 28296 * q^33 - 2152 * q^37 + 35400 * q^45 + 29280 * q^49 - 17512 * q^53 - 108368 * q^57 + 37704 * q^61 + 18216 * q^65 + 157704 * q^73 + 28224 * q^77 - 273136 * q^81 + 230704 * q^85 + 28440 * q^89 + 39400 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−8.95676	+	15.5136i	−0.574577	+	0.995196i	0.421511	+	0.906823i	$0.361500\pi$
$3$	−8.95676	+	15.5136i	−0.574577	+	0.995196i	−0.996087	+	0.0883726i	$0.971833\pi$
$4$		0			0
$5$	−94.4708	+	54.5427i	−1.68994	+	0.975690i	−0.735394	+	0.677639i	$0.763003\pi$
$5$	−94.4708	+	54.5427i	−1.68994	+	0.975690i	−0.954550	+	0.298051i	$0.903664\pi$
$6$		0			0
$7$	65.8412	−	111.678i	0.507870	−	0.861434i
$7$	65.8412	−	111.678i	0.507870	−	0.861434i
$8$		0			0
$9$	−38.9472	−	67.4586i	−0.160277	−	0.277607i
$10$		0			0
$11$	−97.3073	−	56.1804i	−0.242473	−	0.139992i	0.373840	−	0.927493i	$-0.378041\pi$
$11$	−97.3073	−	56.1804i	−0.242473	−	0.139992i	−0.616313	+	0.787501i	$0.711374\pi$
$12$		0			0
$13$		−	345.316i		−	0.566706i	−0.959016	−	0.283353i	$-0.908553\pi$
$13$		−	345.316i		−	0.566706i	0.959016	−	0.283353i	$-0.0914468\pi$
$14$		0			0
$15$		−	1954.11i		−	2.24243i
$16$		0			0
$17$	−1624.18	−	937.724i	−1.36305	−	0.786960i	−0.373025	−	0.927821i	$-0.621679\pi$
$17$	−1624.18	−	937.724i	−1.36305	−	0.786960i	−0.990029	+	0.140862i	$0.955013\pi$
$18$		0			0
$19$	87.2532	+	151.127i	0.0554495	+	0.0960413i	0.892418	−	0.451210i	$-0.149007\pi$
$19$	87.2532	+	151.127i	0.0554495	+	0.0960413i	−0.836968	+	0.547251i	$0.815674\pi$
$20$		0			0
$21$	1142.80	+	2021.70i	0.565485	+	1.00039i
$22$		0			0
$23$	−2885.78	+	1666.11i	−1.13748	+	0.656724i	−0.945805	−	0.324734i	$-0.894725\pi$
$23$	−2885.78	+	1666.11i	−1.13748	+	0.656724i	−0.191674	+	0.981459i	$0.561392\pi$
$24$		0			0
$25$	4387.32	−	7599.06i	1.40394	−	2.43170i
$26$		0			0
$27$	−2957.62			−0.780788
$28$		0			0
$29$	7434.99			1.64167			0.820834	−	0.571167i	$-0.193509\pi$
$29$	7434.99			1.64167			0.820834	+	0.571167i	$0.193509\pi$
$30$		0			0
$31$	2448.61	−	4241.11i	0.457630	−	0.792639i	−0.541205	−	0.840891i	$-0.682032\pi$
$31$	2448.61	−	4241.11i	0.457630	−	0.792639i	0.998835	+	0.0482519i	$0.0153650\pi$
$32$		0			0
$33$	1743.12	−	1006.39i	0.278639	−	0.160872i
$34$		0			0
$35$	−128.851	+	14141.4i	−0.0177795	+	1.95130i
$36$		0			0
$37$	1965.25	+	3403.91i	0.236001	+	0.408765i	0.959563	−	0.281494i	$-0.0908299\pi$
$37$	1965.25	+	3403.91i	0.236001	+	0.408765i	−0.723562	+	0.690259i	$0.757497\pi$
$38$		0			0
$39$	5357.08	+	3092.91i	0.563984	+	0.325616i
$40$		0			0
$41$			9615.48i			0.893329i	0.894702	+	0.446664i	$0.147388\pi$
$41$			9615.48i			0.893329i	−0.894702	+	0.446664i	$0.852612\pi$
$42$		0			0
$43$			20590.9i			1.69826i	0.528183	+	0.849130i	$0.322873\pi$
$43$			20590.9i			1.69826i	−0.528183	+	0.849130i	$0.677127\pi$
$44$		0			0
$45$	7358.75	+	4248.58i	0.541717	+	0.312761i
$46$		0			0
$47$	4736.43	+	8203.74i	0.312757	+	0.541711i	0.978958	−	0.204061i	$-0.0654142\pi$
$47$	4736.43	+	8203.74i	0.312757	+	0.541711i	−0.666201	+	0.745772i	$0.732081\pi$
$48$		0			0
$49$	−8136.88	−	14706.0i	−0.484137	−	0.874992i
$50$		0			0
$51$	29094.9	−	16797.9i	1.56636	−	0.904337i
$52$		0			0
$53$	6818.03	−	11809.2i	0.333403	−	0.577470i	−0.649774	−	0.760127i	$-0.725136\pi$
$53$	6818.03	−	11809.2i	0.333403	−	0.577470i	0.983177	+	0.182657i	$0.0584698\pi$
$54$		0			0
$55$	12256.9			0.546355
$56$		0			0
$57$	−3126.02			−0.127440
$58$		0			0
$59$	−4510.30	+	7812.08i	−0.168685	+	0.292171i	−0.937958	−	0.346750i	$-0.887285\pi$
$59$	−4510.30	+	7812.08i	−0.168685	+	0.292171i	0.769273	+	0.638920i	$0.220619\pi$
$60$		0			0
$61$	−16227.8	+	9369.11i	−0.558386	+	0.322384i	−0.752497	−	0.658595i	$-0.771151\pi$
$61$	−16227.8	+	9369.11i	−0.558386	+	0.322384i	0.194111	+	0.980979i	$0.437818\pi$
$62$		0			0
$63$	−10098.0	−	92.0087i	−0.320540	−	0.00292064i
$64$		0			0
$65$	18834.5	+	32622.2i	0.552929	+	0.957702i
$66$		0			0
$67$	−19019.3	−	10980.8i	−0.517616	−	0.298846i	0.218343	−	0.975872i	$-0.429935\pi$
$67$	−19019.3	−	10980.8i	−0.517616	−	0.298846i	−0.735959	+	0.677027i	$0.763268\pi$
$68$		0			0
$69$		−	59691.7i		−	1.50935i
$70$		0			0
$71$			21401.3i			0.503842i	0.967748	+	0.251921i	$0.0810623\pi$
$71$			21401.3i			0.503842i	−0.967748	+	0.251921i	$0.918938\pi$
$72$		0			0
$73$	24471.4	+	14128.5i	0.537466	+	0.310306i	0.744051	−	0.668122i	$-0.232902\pi$
$73$	24471.4	+	14128.5i	0.537466	+	0.310306i	−0.206585	+	0.978429i	$0.566235\pi$
$74$		0			0
$75$	78592.3	+	136126.i	1.61334	+	2.79439i
$76$		0			0
$77$	−12680.9	+	7168.08i	−0.243739	+	0.137777i
$78$		0			0
$79$	82812.6	−	47811.9i	1.49289	−	0.861923i	0.492927	−	0.870071i	$-0.335927\pi$
$79$	82812.6	−	47811.9i	1.49289	−	0.861923i	0.999967	+	0.00814818i	$0.00259367\pi$
$80$		0			0
$81$	35954.9	−	62275.7i	0.608899	−	1.05464i
$82$		0			0
$83$	−73730.0			−1.17476			−0.587379	−	0.809312i	$-0.699840\pi$
$83$	−73730.0			−1.17476			−0.587379	+	0.809312i	$0.699840\pi$
$84$		0			0
$85$	204584.			3.07131
$86$		0			0
$87$	−66593.4	+	115343.i	−0.943264	+	1.63378i
$88$		0			0
$89$	14912.9	−	8609.95i	0.199566	−	0.115219i	−0.396887	−	0.917867i	$-0.629910\pi$
$89$	14912.9	−	8609.95i	0.199566	−	0.115219i	0.596453	+	0.802648i	$0.296576\pi$
$90$		0			0
$91$	−38564.1	−	22736.0i	−0.488180	−	0.287813i
$92$		0			0
$93$	43863.2	+	75973.2i	0.525887	+	0.910863i
$94$		0			0
$95$	−16485.8	−	9518.05i	−0.187413	−	0.108203i
$96$		0			0
$97$		−	72000.9i		−	0.776977i	−0.921454	−	0.388489i	$-0.872997\pi$
$97$		−	72000.9i		−	0.776977i	0.921454	−	0.388489i	$-0.127003\pi$
$98$		0			0
$99$			8752.28i			0.0897497i
$100$		0			0
$101$	63961.9	+	36928.4i	0.623905	+	0.360211i	0.778388	−	0.627784i	$-0.216038\pi$
$101$	63961.9	+	36928.4i	0.623905	+	0.360211i	−0.154483	+	0.987995i	$0.549371\pi$
$102$		0			0
$103$	54075.3	+	93661.1i	0.502234	+	0.869894i	0.999997	+	0.00258097i	$0.000821550\pi$
$103$	54075.3	+	93661.1i	0.502234	+	0.869894i	−0.497763	+	0.867313i	$0.665845\pi$
$104$		0			0
$105$	−218230.	−	128661.i	−1.93171	−	1.13886i
$106$		0			0
$107$	39326.1	−	22705.0i	0.332064	−	0.191717i	−0.324693	−	0.945819i	$-0.605261\pi$
$107$	39326.1	−	22705.0i	0.332064	−	0.191717i	0.656757	+	0.754102i	$0.271928\pi$
$108$		0			0
$109$	74472.4	−	128990.i	0.600384	−	1.03990i	−0.392378	−	0.919804i	$-0.628348\pi$
$109$	74472.4	−	128990.i	0.600384	−	1.03990i	0.992763	−	0.120092i	$-0.0383191\pi$
$110$		0			0
$111$	−70409.0			−0.542402
$112$		0			0
$113$	67572.9			0.497824			0.248912	−	0.968526i	$-0.419927\pi$
$113$	67572.9			0.497824			0.248912	+	0.968526i	$0.419927\pi$
$114$		0			0
$115$	181748.	−	314797.i	1.28152	−	2.21965i
$116$		0			0
$117$	−23294.5	+	13449.1i	−0.157322	+	0.0908298i
$118$		0			0
$119$	−211661.	+	119645.i	−1.37017	+	0.774508i
$120$		0			0
$121$	−74213.0	−	128541.i	−0.460805	−	0.798137i
$122$		0			0
$123$	−149170.	−	86123.6i	−0.889037	−	0.513286i
$124$		0			0
$125$			616293.i			3.52787i
$126$		0			0
$127$		−	136321.i		−	0.749987i	−0.927027	−	0.374994i	$-0.877645\pi$
$127$		−	136321.i		−	0.749987i	0.927027	−	0.374994i	$-0.122355\pi$
$128$		0			0
$129$	−319438.	−	184428.i	−1.69010	−	0.975781i
$130$		0			0
$131$	−97247.5	−	168438.i	−0.495108	−	0.857552i	0.504876	−	0.863192i	$-0.331538\pi$
$131$	−97247.5	−	168438.i	−0.495108	−	0.857552i	−0.999984	+	0.00563953i	$0.998205\pi$
$132$		0			0
$133$	22622.4	+	206.126i	0.110894	+	0.00101043i
$134$		0			0
$135$	279409.	−	161317.i	1.31949	−	0.761807i
$136$		0			0
$137$	153703.	−	266221.i	0.699650	−	1.21183i	−0.268938	−	0.963157i	$-0.586673\pi$
$137$	153703.	−	266221.i	0.699650	−	1.21183i	0.968588	−	0.248671i	$-0.0799938\pi$
$138$		0			0
$139$	−104735.			−0.459786			−0.229893	−	0.973216i	$-0.573838\pi$
$139$	−104735.			−0.459786			−0.229893	+	0.973216i	$0.573838\pi$
$140$		0			0
$141$	−169692.			−0.718811
$142$		0			0
$143$	−19400.0	+	33601.7i	−0.0793343	+	0.137411i
$144$		0			0
$145$	−702389.	+	405524.i	−2.77433	+	1.60176i
$146$		0			0
$147$	301023.	+	5486.06i	1.14896	+	0.0209395i
$148$		0			0
$149$	23920.8	+	41432.1i	0.0882695	+	0.152887i	0.906780	−	0.421605i	$-0.138533\pi$
$149$	23920.8	+	41432.1i	0.0882695	+	0.152887i	−0.818510	+	0.574492i	$0.805200\pi$
$150$		0			0
$151$	262478.	+	151542.i	0.936806	+	0.540865i	0.888958	−	0.457989i	$-0.151430\pi$
$151$	262478.	+	151542.i	0.936806	+	0.540865i	0.0478487	+	0.998855i	$0.484763\pi$
$152$		0			0
$153$			146087.i			0.504525i
$154$		0			0
$155$			534215.i			1.78602i
$156$		0			0
$157$	67560.0	+	39005.8i	0.218746	+	0.126293i	0.605370	−	0.795945i	$-0.293025\pi$
$157$	67560.0	+	39005.8i	0.218746	+	0.126293i	−0.386623	+	0.922238i	$0.626359\pi$
$158$		0			0
$159$	122135.	+	211544.i	0.383131	+	0.663602i
$160$		0			0
$161$	−3936.00	+	431976.i	−0.0119671	+	1.31339i
$162$		0			0
$163$	−5708.73	+	3295.94i	−0.0168295	+	0.00971651i	−0.508391	−	0.861126i	$-0.669760\pi$
$163$	−5708.73	+	3295.94i	−0.0168295	+	0.00971651i	0.491562	+	0.870843i	$0.336426\pi$
$164$		0			0
$165$	−109782.	+	190149.i	−0.313923	+	0.543730i
$166$		0			0
$167$	−364752.			−1.01206			−0.506030	−	0.862516i	$-0.668888\pi$
$167$	−364752.			−1.01206			−0.506030	+	0.862516i	$0.668888\pi$
$168$		0			0
$169$	252050.			0.678844
$170$		0			0
$171$	6796.54	−	11772.0i	0.0177745	−	0.0307863i
$172$		0			0
$173$	432813.	−	249885.i	1.09947	−	0.634782i	0.163391	−	0.986561i	$-0.447757\pi$
$173$	432813.	−	249885.i	1.09947	−	0.634782i	0.936083	+	0.351780i	$0.114423\pi$
$174$		0			0
$175$	−559780.	−	990297.i	−1.38173	−	2.44439i
$176$		0			0
$177$	−80795.5	−	139942.i	−0.193845	−	0.335749i
$178$		0			0
$179$	−398662.	−	230168.i	−0.929977	−	0.536923i	−0.0431730	−	0.999068i	$-0.513747\pi$
$179$	−398662.	−	230168.i	−0.929977	−	0.536923i	−0.886804	+	0.462145i	$0.847080\pi$
$180$		0			0
$181$		−	170705.i		−	0.387301i	−0.981071	−	0.193651i	$-0.937967\pi$
$181$		−	170705.i		−	0.387301i	0.981071	−	0.193651i	$-0.0620328\pi$
$182$		0			0
$183$		−	335668.i		−	0.740938i
$184$		0			0
$185$	−371317.	−	214380.i	−0.797656	−	0.460527i
$186$		0			0
$187$	105363.	+	182495.i	0.220336	+	0.381633i
$188$		0			0
$189$	−194733.	+	330301.i	−0.396539	+	0.672598i
$190$		0			0
$191$	201998.	−	116623.i	0.400648	−	0.231314i	−0.286116	−	0.958195i	$-0.592364\pi$
$191$	201998.	−	116623.i	0.400648	−	0.231314i	0.686763	+	0.726881i	$0.259031\pi$
$192$		0			0
$193$	−196663.	+	340631.i	−0.380041	+	0.658249i	−0.991068	−	0.133360i	$-0.957423\pi$
$193$	−196663.	+	340631.i	−0.380041	+	0.658249i	0.611027	+	0.791610i	$0.290757\pi$
$194$		0			0
$195$	−674783.			−1.27080
$196$		0			0
$197$	19420.7			0.0356533			0.0178266	−	0.999841i	$-0.494325\pi$
$197$	19420.7			0.0356533			0.0178266	+	0.999841i	$0.494325\pi$
$198$		0			0
$199$	−51142.5	+	88581.4i	−0.0915481	+	0.158566i	−0.908163	−	0.418617i	$-0.862515\pi$
$199$	−51142.5	+	88581.4i	−0.0915481	+	0.158566i	0.816615	+	0.577183i	$0.195848\pi$
$200$		0			0
$201$	340703.	−	196705.i	0.594820	−	0.343419i
$202$		0			0
$203$	489528.	−	830323.i	0.833753	−	1.41419i
$204$		0			0
$205$	−524455.	−	908382.i	−0.871612	−	1.50968i
$206$		0			0
$207$	224786.	+	129780.i	0.364623	+	0.210515i
$208$		0			0
$209$		−	19607.7i		−	0.0310499i
$210$		0			0
$211$			644172.i			0.996083i	0.867153	+	0.498042i	$0.165947\pi$
$211$			644172.i			0.996083i	−0.867153	+	0.498042i	$0.834053\pi$
$212$		0			0
$213$	−332010.	−	191686.i	−0.501421	−	0.289496i
$214$		0			0
$215$	−1.12308e6	−	1.94524e6i	−1.65698	−	2.86997i
$216$		0			0
$217$	−312419.	−	552695.i	−0.450389	−	0.796775i
$218$		0			0
$219$	−438368.	+	253092.i	−0.617631	+	0.356589i
$220$		0			0
$221$	−323811.	+	560857.i	−0.445975	+	0.772451i
$222$		0			0
$223$	1.33868e6			1.80266			0.901329	−	0.433135i	$-0.142593\pi$
$223$	1.33868e6			1.80266			0.901329	+	0.433135i	$0.142593\pi$
$224$		0			0
$225$	−683495.			−0.900076
$226$		0			0
$227$	181618.	−	314572.i	0.233934	−	0.405186i	−0.725028	−	0.688719i	$-0.758173\pi$
$227$	181618.	−	314572.i	0.233934	−	0.405186i	0.958962	+	0.283533i	$0.0915066\pi$
$228$		0			0
$229$	855044.	−	493660.i	1.07746	−	0.622070i	0.147248	−	0.989100i	$-0.452959\pi$
$229$	855044.	−	493660.i	1.07746	−	0.622070i	0.930209	+	0.367030i	$0.119625\pi$
$230$		0			0
$231$	2377.49	−	260929.i	0.00293149	−	0.321731i
$232$		0			0
$233$	−163704.	−	283544.i	−0.197547	−	0.342162i	0.750185	−	0.661227i	$-0.229964\pi$
$233$	−163704.	−	283544.i	−0.197547	−	0.342162i	−0.947733	+	0.319066i	$0.896631\pi$
$234$		0			0
$235$	−894909.	−	516676.i	−1.05708	−	0.610307i
$236$		0			0
$237$			1.71296e6i			1.98096i
$238$		0			0
$239$			1.19235e6i			1.35024i	0.737709	+	0.675119i	$0.235908\pi$
$239$			1.19235e6i			1.35024i	−0.737709	+	0.675119i	$0.764092\pi$
$240$		0			0
$241$	229100.	+	132271.i	0.254087	+	0.146697i	0.621634	−	0.783308i	$-0.286469\pi$
$241$	229100.	+	132271.i	0.254087	+	0.146697i	−0.367547	+	0.930005i	$0.619802\pi$
$242$		0			0
$243$	284728.	+	493163.i	0.309325	+	0.535766i
$244$		0			0
$245$	1.57080e6	+	945479.i	1.67189	+	1.00632i
$246$		0			0
$247$	52186.5	−	30129.9i	0.0544272	−	0.0314235i
$248$		0			0
$249$	660382.	−	1.14381e6i	0.674989	−	1.16912i
$250$		0			0
$251$	1.74704e6			1.75033			0.875163	−	0.483827i	$-0.160754\pi$
$251$	1.74704e6			1.75033			0.875163	+	0.483827i	$0.160754\pi$
$252$		0			0
$253$	374410.			0.367744
$254$		0			0
$255$	−1.83241e6	+	3.17383e6i	−1.76471	+	3.05656i
$256$		0			0
$257$	637606.	−	368122.i	0.602170	−	0.347663i	−0.167725	−	0.985834i	$-0.553642\pi$
$257$	637606.	−	368122.i	0.602170	−	0.347663i	0.769895	+	0.638171i	$0.220309\pi$
$258$		0			0
$259$	509535.	+	4642.69i	0.471982	+	0.00430051i
$260$		0			0
$261$	−289572.	−	501554.i	−0.263121	−	0.455739i
$262$		0			0
$263$	1.87847e6	+	1.08453e6i	1.67461	+	0.966837i	0.965003	+	0.262240i	$0.0844613\pi$
$263$	1.87847e6	+	1.08453e6i	1.67461	+	0.966837i	0.709608	+	0.704597i	$0.248872\pi$
$264$		0			0
$265$			1.48750e6i			1.30119i
$266$		0			0
$267$			308469.i			0.264809i
$268$		0			0
$269$	−1.47091e6	−	849230.i	−1.23938	−	0.715558i	−0.270414	−	0.962744i	$-0.587161\pi$
$269$	−1.47091e6	−	849230.i	−1.23938	−	0.715558i	−0.968968	+	0.247186i	$0.920494\pi$
$270$		0			0
$271$	379291.	+	656952.i	0.313725	+	0.543388i	0.979166	−	0.203063i	$-0.0650895\pi$
$271$	379291.	+	656952.i	0.313725	+	0.543388i	−0.665440	+	0.746451i	$0.731756\pi$
$272$		0			0
$273$	698126.	−	394626.i	0.566927	−	0.320464i
$274$		0			0
$275$	−853836.	+	492962.i	−0.680836	+	0.393081i
$276$		0			0
$277$	302000.	−	523080.i	0.236487	−	0.409608i	−0.723217	−	0.690621i	$-0.757337\pi$
$277$	302000.	−	523080.i	0.236487	−	0.409608i	0.959704	+	0.281013i	$0.0906705\pi$
$278$		0			0
$279$	−381466.			−0.293390
$280$		0			0
$281$	1.66382e6			1.25701			0.628506	−	0.777805i	$-0.283667\pi$
$281$	1.66382e6			1.25701			0.628506	+	0.777805i	$0.283667\pi$
$282$		0			0
$283$	−124987.	+	216484.i	−0.0927682	+	0.160679i	−0.908675	−	0.417504i	$-0.862905\pi$
$283$	−124987.	+	216484.i	−0.0927682	+	0.160679i	0.815907	+	0.578184i	$0.196238\pi$
$284$		0			0
$285$	295318.	−	170502.i	0.215366	−	0.124342i
$286$		0			0
$287$	1.07384e6	+	633094.i	0.769544	+	0.453695i
$288$		0			0
$289$	1.04872e6	+	1.81644e6i	0.738611	+	1.27931i
$290$		0			0
$291$	1.11699e6	+	644895.i	0.773245	+	0.446433i
$292$		0			0
$293$		−	1.02182e6i		−	0.695356i	−0.937614	−	0.347678i	$-0.886970\pi$
$293$		−	1.02182e6i		−	0.695356i	0.937614	−	0.347678i	$-0.113030\pi$
$294$		0			0
$295$		−	984017.i		−	0.658336i
$296$		0			0
$297$	287798.	+	166160.i	0.189320	+	0.109304i
$298$		0			0
$299$	575333.	+	996505.i	0.372170	+	0.644617i
$300$		0			0
$301$	2.29955e6	+	1.35573e6i	1.46294	+	0.862495i
$302$		0			0
$303$	−1.14578e6	+	661519.i	−0.716962	+	0.413938i
$304$		0			0
$305$	1.02203e6	−	1.77021e6i	0.629094	−	1.08962i
$306$		0			0
$307$	−1.09185e6			−0.661174			−0.330587	−	0.943776i	$-0.607247\pi$
$307$	−1.09185e6			−0.661174			−0.330587	+	0.943776i	$0.607247\pi$
$308$		0			0
$309$	−1.93736e6			−1.15429
$310$		0			0
$311$	1.16890e6	−	2.02459e6i	0.685290	−	1.18696i	−0.288055	−	0.957614i	$-0.593009\pi$
$311$	1.16890e6	−	2.02459e6i	0.685290	−	1.18696i	0.973345	−	0.229344i	$-0.0736580\pi$
$312$		0			0
$313$	−1.96546e6	+	1.13476e6i	−1.13398	+	0.654701i	−0.944932	−	0.327268i	$-0.893872\pi$
$313$	−1.96546e6	+	1.13476e6i	−1.13398	+	0.654701i	−0.189044	+	0.981969i	$0.560539\pi$
$314$		0			0
$315$	958980.	−	542078.i	0.544544	−	0.307812i
$316$		0			0
$317$	−1.45783e6	−	2.52504e6i	−0.814816	−	1.41130i	−0.909460	−	0.415791i	$-0.863505\pi$
$317$	−1.45783e6	−	2.52504e6i	−0.814816	−	1.41130i	0.0946448	−	0.995511i	$-0.469828\pi$
$318$		0			0
$319$	−723478.	−	417700.i	−0.398060	−	0.229820i
$320$		0			0
$321$			813452.i			0.440625i
$322$		0			0
$323$		−	327277.i		−	0.174546i
$324$		0			0
$325$	−2.62407e6	−	1.51501e6i	−1.37806	−	0.795622i
$326$		0			0
$327$	1.33406e6	+	2.31067e6i	0.689934	+	1.19500i
$328$		0			0
$329$	1.22803e6	+	11189.3i	0.625488	+	0.00569920i
$330$		0			0
$331$	1.71806e6	−	991925.i	0.861925	−	0.497632i	−0.00273173	−	0.999996i	$-0.500870\pi$
$331$	1.71806e6	−	991925.i	0.861925	−	0.497632i	0.864656	+	0.502364i	$0.167536\pi$
$332$		0			0
$333$	153082.	−	265146.i	0.0756508	−	0.131031i
$334$		0			0
$335$	2.39569e6			1.16632
$336$		0			0
$337$	−1.18224e6			−0.567062			−0.283531	−	0.958963i	$-0.591506\pi$
$337$	−1.18224e6			−0.567062			−0.283531	+	0.958963i	$0.591506\pi$
$338$		0			0
$339$	−605234.	+	1.04830e6i	−0.286038	+	0.495433i
$340$		0			0
$341$	−476534.	+	275127.i	−0.221926	+	0.128129i
$342$		0			0
$343$	−2.17808e6	−	59550.6i	−0.999626	−	0.0273307i
$344$		0			0
$345$	3.25575e6	+	5.63912e6i	1.47266	+	2.55072i
$346$		0			0
$347$	−2.91868e6	−	1.68510e6i	−1.30126	−	0.751280i	−0.320636	−	0.947203i	$-0.603897\pi$
$347$	−2.91868e6	−	1.68510e6i	−1.30126	−	0.751280i	−0.980619	+	0.195923i	$0.937230\pi$
$348$		0			0
$349$		−	4.34253e6i		−	1.90844i	−0.299101	−	0.954222i	$-0.596687\pi$
$349$		−	4.34253e6i		−	1.90844i	0.299101	−	0.954222i	$-0.403313\pi$
$350$		0			0
$351$			1.02131e6i			0.442478i
$352$		0			0
$353$	2.92996e6	+	1.69162e6i	1.25148	+	0.722545i	0.971404	−	0.237431i	$-0.0763055\pi$
$353$	2.92996e6	+	1.69162e6i	1.25148	+	0.722545i	0.280081	+	0.959977i	$0.409639\pi$
$354$		0			0
$355$	−1.16728e6	−	2.02180e6i	−0.491593	−	0.851465i
$356$		0			0
$357$	39683.4	−	4.35525e6i	0.0164793	−	1.80860i
$358$		0			0
$359$	−884270.	+	510534.i	−0.362117	+	0.209068i	−0.670009	−	0.742353i	$-0.733710\pi$
$359$	−884270.	+	510534.i	−0.362117	+	0.209068i	0.307892	+	0.951421i	$0.400376\pi$
$360$		0			0
$361$	1.22282e6	−	2.11799e6i	0.493851	−	0.855375i
$362$		0			0
$363$	2.65883e6			1.05907
$364$		0			0
$365$	−3.08244e6			−1.21105
$366$		0			0
$367$	−374851.	+	649260.i	−0.145276	+	0.251625i	−0.929476	−	0.368883i	$-0.879740\pi$
$367$	−374851.	+	649260.i	−0.145276	+	0.251625i	0.784200	+	0.620508i	$0.213074\pi$
$368$		0			0
$369$	648647.	−	374496.i	0.247995	−	0.143180i
$370$		0			0
$371$	−869916.	−	1.53895e6i	−0.328127	−	0.580484i
$372$		0			0
$373$	1.43465e6	+	2.48489e6i	0.533918	+	0.924773i	0.999215	+	0.0396180i	$0.0126141\pi$
$373$	1.43465e6	+	2.48489e6i	0.533918	+	0.924773i	−0.465297	+	0.885155i	$0.654053\pi$
$374$		0			0
$375$	−9.56090e6	−	5.51999e6i	−3.51092	−	2.02703i
$376$		0			0
$377$		−	2.56742e6i		−	0.930343i
$378$		0			0
$379$		−	480759.i		−	0.171921i	−0.996299	−	0.0859606i	$-0.972604\pi$
$379$		−	480759.i		−	0.171921i	0.996299	−	0.0859606i	$-0.0273959\pi$
$380$		0			0
$381$	2.11483e6	+	1.22100e6i	0.746384	+	0.430925i
$382$		0			0
$383$	1.52591e6	+	2.64295e6i	0.531534	+	0.920645i	0.999323	+	0.0368040i	$0.0117177\pi$
$383$	1.52591e6	+	2.64295e6i	0.531534	+	0.920645i	−0.467788	+	0.883841i	$0.654949\pi$
$384$		0			0
$385$	807010.	−	1.36883e6i	0.277477	−	0.470648i
$386$		0			0
$387$	1.38903e6	−	801959.i	0.471450	−	0.272192i
$388$		0			0
$389$	684217.	−	1.18510e6i	0.229255	−	0.397082i	−0.728332	−	0.685224i	$-0.759704\pi$
$389$	684217.	−	1.18510e6i	0.229255	−	0.397082i	0.957588	+	0.288142i	$0.0930376\pi$
$390$		0			0
$391$	6.24939e6			2.06726
$392$		0			0
$393$	3.48409e6			1.13791
$394$		0			0
$395$	−5.21558e6	+	9.03365e6i	−1.68194	+	2.91320i
$396$		0			0
$397$	−749567.	+	432763.i	−0.238690	+	0.137808i	−0.614574	−	0.788859i	$-0.710672\pi$
$397$	−749567.	+	432763.i	−0.238690	+	0.137808i	0.375885	+	0.926667i	$0.377339\pi$
$398$		0			0
$399$	−205821.	+	349108.i	−0.0647229	+	0.109781i
$400$		0			0
$401$	687837.	+	1.19137e6i	0.213611	+	0.369986i	0.952842	−	0.303466i	$-0.0981440\pi$
$401$	687837.	+	1.19137e6i	0.213611	+	0.369986i	−0.739231	+	0.673452i	$0.764811\pi$
$402$		0			0
$403$	−1.46452e6	−	845542.i	−0.449193	−	0.259342i
$404$		0			0
$405$			7.84431e6i			2.37639i
$406$		0			0
$407$		−	441633.i		−	0.132153i
$408$		0			0
$409$	−4.62914e6	−	2.67263e6i	−1.36833	−	0.790007i	−0.377618	−	0.925962i	$-0.623257\pi$
$409$	−4.62914e6	−	2.67263e6i	−1.36833	−	0.790007i	−0.990715	+	0.135954i	$0.956590\pi$
$410$		0			0
$411$	2.75336e6	+	4.76896e6i	0.804005	+	1.39258i
$412$		0			0
$413$	575472.	+	1.01806e6i	0.166016	+	0.293695i
$414$		0			0
$415$	6.96533e6	−	4.02143e6i	1.98528	−	1.14620i
$416$		0			0
$417$	938089.	−	1.62482e6i	0.264182	−	0.457577i
$418$		0			0
$419$	1.31536e6			0.366025			0.183012	−	0.983111i	$-0.441415\pi$
$419$	1.31536e6			0.366025			0.183012	+	0.983111i	$0.441415\pi$
$420$		0			0
$421$	−4.02114e6			−1.10572			−0.552859	−	0.833275i	$-0.686463\pi$
$421$	−4.02114e6			−1.10572			−0.552859	+	0.833275i	$0.686463\pi$
$422$		0			0
$423$	368942.	−	639026.i	0.100255	−	0.173647i
$424$		0			0
$425$	−1.42516e7	+	8.22818e6i	−3.82730	+	2.20969i
$426$		0			0
$427$	−22133.5	+	2.42916e6i	−0.00587464	+	0.644742i
$428$		0			0
$429$	−347522.	−	601925.i	−0.0911672	−	0.157906i
$430$		0			0
$431$	−6.21627e6	−	3.58897e6i	−1.61190	−	0.930628i	−0.988931	−	0.148378i	$-0.952595\pi$
$431$	−6.21627e6	−	3.58897e6i	−1.61190	−	0.930628i	−0.622964	−	0.782250i	$-0.714072\pi$
$432$		0			0
$433$		−	2.47219e6i		−	0.633669i	−0.948481	−	0.316835i	$-0.897380\pi$
$433$		−	2.47219e6i		−	0.633669i	0.948481	−	0.316835i	$-0.102620\pi$
$434$		0			0
$435$		−	1.45287e7i		−	3.68133i
$436$		0			0
$437$	−503587.	−	290746.i	−0.126145	−	0.0728300i
$438$		0			0
$439$	−2.56382e6	−	4.44067e6i	−0.634931	−	1.09973i	−0.986530	−	0.163582i	$-0.947695\pi$
$439$	−2.56382e6	−	4.44067e6i	−0.634931	−	1.09973i	0.351599	−	0.936151i	$-0.385638\pi$
$440$		0			0
$441$	−675137.	+	1.12166e6i	−0.165309	+	0.274641i
$442$		0			0
$443$	−2.65605e6	+	1.53347e6i	−0.643023	+	0.371249i	−0.785778	−	0.618509i	$-0.787737\pi$
$443$	−2.65605e6	+	1.53347e6i	−0.643023	+	0.371249i	0.142755	+	0.989758i	$0.454404\pi$
$444$		0			0
$445$	−939220.	+	1.62678e6i	−0.224837	+	0.389429i
$446$		0			0
$447$	−857013.			−0.202870
$448$		0			0
$449$	−102904.			−0.0240888			−0.0120444	−	0.999927i	$-0.503834\pi$
$449$	−102904.			−0.0240888			−0.0120444	+	0.999927i	$0.503834\pi$
$450$		0			0
$451$	540201.	−	935656.i	0.125059	−	0.216608i
$452$		0			0
$453$	−4.70190e6	+	2.71464e6i	−1.07653	+	0.621537i
$454$		0			0
$455$	4.88326e6	+	44494.4i	1.10581	+	0.0100757i
$456$		0			0
$457$	2.27448e6	+	3.93952e6i	0.509439	+	0.882374i	0.999940	+	0.0109339i	$0.00348044\pi$
$457$	2.27448e6	+	3.93952e6i	0.509439	+	0.882374i	−0.490501	+	0.871441i	$0.663186\pi$
$458$		0			0
$459$	4.80373e6	+	2.77343e6i	1.06426	+	0.614449i
$460$		0			0
$461$			2.90746e6i			0.637179i	0.947893	+	0.318590i	$0.103209\pi$
$461$			2.90746e6i			0.637179i	−0.947893	+	0.318590i	$0.896791\pi$
$462$		0			0
$463$			258727.i			0.0560904i	0.999607	+	0.0280452i	$0.00892824\pi$
$463$			258727.i			0.0560904i	−0.999607	+	0.0280452i	$0.991072\pi$
$464$		0			0
$465$	−8.28757e6	−	4.78483e6i	−1.77744	−	1.02621i
$466$		0			0
$467$	2.24507e6	+	3.88858e6i	0.476363	+	0.825084i	0.999633	−	0.0270823i	$-0.00862161\pi$
$467$	2.24507e6	+	3.88858e6i	0.476363	+	0.825084i	−0.523271	+	0.852167i	$0.675288\pi$
$468$		0			0
$469$	−2.47856e6	+	1.40105e6i	−0.520317	+	0.294117i
$470$		0			0
$471$	−1.21024e6	+	698731.i	−0.251373	+	0.145130i
$472$		0			0
$473$	1.15680e6	−	2.00364e6i	0.237743	−	0.411782i
$474$		0			0
$475$	1.53123e6			0.311391
$476$		0			0
$477$	−1.06217e6			−0.213747
$478$		0			0
$479$	2.39572e6	−	4.14951e6i	0.477086	−	0.826338i	−0.522569	−	0.852597i	$-0.675026\pi$
$479$	2.39572e6	−	4.14951e6i	0.477086	−	0.826338i	0.999655	+	0.0262593i	$0.00835955\pi$
$480$		0			0
$481$	1.17542e6	−	678631.i	0.231650	−	0.133743i
$482$		0			0
$483$	−6.66624e6	−	3.93017e6i	−1.30021	−	0.766555i
$484$		0			0
$485$	3.92712e6	+	6.80198e6i	0.758089	+	1.31305i
$486$		0			0
$487$	−3.76123e6	−	2.17155e6i	−0.718634	−	0.414903i	0.0956159	−	0.995418i	$-0.469518\pi$
$487$	−3.76123e6	−	2.17155e6i	−0.718634	−	0.414903i	−0.814250	+	0.580515i	$0.802851\pi$
$488$		0			0
$489$		−	118084.i		−	0.0223315i
$490$		0			0
$491$		−	2.25468e6i		−	0.422067i	−0.977479	−	0.211034i	$-0.932317\pi$
$491$		−	2.25468e6i		−	0.422067i	0.977479	−	0.211034i	$-0.0676830\pi$
$492$		0			0
$493$	−1.20758e7	−	6.97196e6i	−2.23768	−	1.29193i
$494$		0			0
$495$	−477373.	−	826835.i	−0.0875679	−	0.151672i
$496$		0			0
$497$	2.39005e6	+	1.40909e6i	0.434026	+	0.255886i
$498$		0			0
$499$	3.84962e6	−	2.22258e6i	0.692096	−	0.399582i	−0.112301	−	0.993674i	$-0.535822\pi$
$499$	3.84962e6	−	2.22258e6i	0.692096	−	0.399582i	0.804397	+	0.594092i	$0.202489\pi$
$500$		0			0
$501$	3.26700e6	−	5.65861e6i	0.581507	−	1.00720i
$502$		0			0
$503$	−839314.			−0.147912			−0.0739562	−	0.997261i	$-0.523563\pi$
$503$	−839314.			−0.147912			−0.0739562	+	0.997261i	$0.523563\pi$
$504$		0			0
$505$	−8.05671e6			−1.40582
$506$		0			0
$507$	−2.25755e6	+	3.91020e6i	−0.390048	+	0.675583i
$508$		0			0
$509$	6.08923e6	−	3.51562e6i	1.04176	−	0.601461i	0.121430	−	0.992600i	$-0.461252\pi$
$509$	6.08923e6	−	3.51562e6i	1.04176	−	0.601461i	0.920332	+	0.391139i	$0.127919\pi$
$510$		0			0
$511$	3.18907e6	−	1.80267e6i	0.540271	−	0.305396i
$512$		0			0
$513$	−258062.	−	446976.i	−0.0432943	−	0.0749879i
$514$		0			0
$515$	−1.02171e7	−	5.89883e6i	−1.69749	−	0.980048i
$516$		0			0
$517$		−	1.06438e6i		−	0.175134i
$518$		0			0
$519$			8.95263e6i			1.45892i
$520$		0			0
$521$	8.36211e6	+	4.82787e6i	1.34965	+	0.779222i	0.988200	−	0.153169i	$-0.0489479\pi$
$521$	8.36211e6	+	4.82787e6i	1.34965	+	0.779222i	0.361452	+	0.932391i	$0.382281\pi$
$522$		0			0
$523$	−1.30041e6	−	2.25237e6i	−0.207886	−	0.360069i	0.743163	−	0.669111i	$-0.233325\pi$
$523$	−1.30041e6	−	2.25237e6i	−0.207886	−	0.360069i	−0.951048	+	0.309042i	$0.899992\pi$
$524$		0			0
$525$	2.03769e7	+	185666.i	3.22655	+	0.0293991i
$526$		0			0
$527$	−7.95398e6	+	4.59223e6i	−1.24755	+	0.720273i
$528$		0			0
$529$	2.33365e6	−	4.04199e6i	0.362573	−	0.627995i
$530$		0			0
$531$	702655.			0.108145
$532$		0			0
$533$	3.32038e6			0.506255
$534$		0			0
$535$	−2.47678e6	+	4.28991e6i	−0.374113	+	0.647983i
$536$		0			0
$537$	7.14144e6	−	4.12311e6i	1.06869	−	0.617006i
$538$		0			0
$539$	−34410.7	+	1.88813e6i	−0.00510179	+	0.279937i
$540$		0			0
$541$	−944463.	−	1.63586e6i	−0.138737	−	0.240299i	0.788282	−	0.615314i	$-0.210971\pi$
$541$	−944463.	−	1.63586e6i	−0.138737	−	0.240299i	−0.927019	+	0.375015i	$0.877638\pi$
$542$		0			0
$543$	2.64824e6	+	1.52896e6i	0.385440	+	0.222534i
$544$		0			0
$545$			1.62477e7i			2.34316i
$546$		0			0
$547$		−	1.52035e6i		−	0.217257i	−0.994082	−	0.108629i	$-0.965354\pi$
$547$		−	1.52035e6i		−	0.217257i	0.994082	−	0.108629i	$-0.0346459\pi$
$548$		0			0
$549$	1.26405e6	+	729802.i	0.178992	+	0.103341i
$550$		0			0
$551$	648726.	+	1.12363e6i	0.0910296	+	0.157668i
$552$		0			0
$553$	112951.	−	1.23963e7i	0.0157064	−	1.72377i
$554$		0			0
$555$	6.65160e6	−	3.84030e6i	0.916629	−	0.529216i
$556$		0			0
$557$	5.45065e6	−	9.44080e6i	0.744407	−	1.28935i	−0.206065	−	0.978538i	$-0.566066\pi$
$557$	5.45065e6	−	9.44080e6i	0.744407	−	1.28935i	0.950471	−	0.310812i	$-0.100601\pi$
$558$		0			0
$559$	7.11036e6			0.962415
$560$		0			0
$561$	−3.77486e6			−0.506400
$562$		0			0
$563$	−4.74213e6	+	8.21361e6i	−0.630525	+	1.09210i	0.356919	+	0.934135i	$0.383827\pi$
$563$	−4.74213e6	+	8.21361e6i	−0.630525	+	1.09210i	−0.987444	+	0.157967i	$0.949506\pi$
$564$		0			0
$565$	−6.38366e6	+	3.68561e6i	−0.841296	+	0.485722i
$566$		0			0
$567$	−4.58751e6	−	8.11567e6i	−0.599265	−	1.06015i
$568$		0			0
$569$	−1.31313e6	−	2.27441e6i	−0.170031	−	0.294503i	0.768399	−	0.639971i	$-0.221053\pi$
$569$	−1.31313e6	−	2.27441e6i	−0.170031	−	0.294503i	−0.938431	+	0.345468i	$0.887720\pi$
$570$		0			0
$571$	1.22829e7	+	7.09152e6i	1.57656	+	0.910226i	0.995335	+	0.0964809i	$0.0307587\pi$
$571$	1.22829e7	+	7.09152e6i	1.57656	+	0.910226i	0.581222	+	0.813745i	$0.302575\pi$
$572$		0			0
$573$			4.17827e6i			0.531631i
$574$		0			0
$575$			2.92389e7i			3.68801i
$576$		0			0
$577$	−1.00950e7	−	5.82832e6i	−1.26231	−	0.728793i	−0.288786	−	0.957394i	$-0.593252\pi$
$577$	−1.00950e7	−	5.82832e6i	−1.26231	−	0.728793i	−0.973520	+	0.228601i	$0.926585\pi$
$578$		0			0
$579$	−3.52293e6	−	6.10190e6i	−0.436725	−	0.756430i
$580$		0			0
$581$	−4.85447e6	+	8.23400e6i	−0.596625	+	1.01198i
$582$		0			0
$583$	−1.32689e6	+	766079.i	−0.161682	+	0.0933474i
$584$		0			0
$585$	1.46710e6	−	2.54109e6i	0.177243	−	0.306995i
$586$		0			0
$587$	−7.03901e6			−0.843172			−0.421586	−	0.906788i	$-0.638526\pi$
$587$	−7.03901e6			−0.843172			−0.421586	+	0.906788i	$0.638526\pi$
$588$		0			0
$589$	854595.			0.101501
$590$		0			0
$591$	−173947.	+	301284.i	−0.0204855	+	0.0354820i
$592$		0			0
$593$	7.16544e6	−	4.13697e6i	0.836770	−	0.483109i	−0.0193950	−	0.999812i	$-0.506174\pi$
$593$	7.16544e6	−	4.13697e6i	0.836770	−	0.483109i	0.856165	+	0.516703i	$0.172841\pi$
$594$		0			0
$595$	1.34700e7	−	2.28475e7i	1.55983	−	2.64573i
$596$		0			0
$597$	−916143.	−	1.58681e6i	−0.105203	−	0.182217i
$598$		0			0
$599$	−1.23503e7	−	7.13046e6i	−1.40641	−	0.811989i	−0.411367	−	0.911470i	$-0.634949\pi$
$599$	−1.23503e7	−	7.13046e6i	−1.40641	−	0.811989i	−0.995040	+	0.0994803i	$0.968282\pi$
$600$		0			0
$601$		−	259247.i		−	0.0292771i	−0.999893	−	0.0146385i	$-0.995340\pi$
$601$		−	259247.i		−	0.0292771i	0.999893	−	0.0146385i	$-0.00465976\pi$
$602$		0			0
$603$			1.71069e6i			0.191592i
$604$		0			0
$605$	1.40219e7	+	8.09556e6i	1.55747	+	0.899205i
$606$		0			0
$607$	3.45193e6	+	5.97892e6i	0.380268	+	0.658644i	0.991100	−	0.133116i	$-0.0424983\pi$
$607$	3.45193e6	+	5.97892e6i	0.380268	+	0.658644i	−0.610832	+	0.791760i	$0.709165\pi$
$608$		0			0
$609$	8.49669e6	+	1.50313e7i	0.928339	+	1.64231i
$610$		0			0
$611$	2.83288e6	−	1.63556e6i	0.306991	−	0.177241i
$612$		0			0
$613$	−3.64405e6	+	6.31168e6i	−0.391682	+	0.678413i	−0.992672	−	0.120844i	$-0.961440\pi$
$613$	−3.64405e6	+	6.31168e6i	−0.391682	+	0.678413i	0.600990	+	0.799257i	$0.294773\pi$
$614$		0			0
$615$	1.87897e7			2.00323
$616$		0			0
$617$	−7.54372e6			−0.797761			−0.398881	−	0.917003i	$-0.630601\pi$
$617$	−7.54372e6			−0.797761			−0.398881	+	0.917003i	$0.630601\pi$
$618$		0			0
$619$	−4.28788e6	+	7.42682e6i	−0.449796	+	0.779070i	−0.998372	−	0.0570306i	$-0.981837\pi$
$619$	−4.28788e6	+	7.42682e6i	−0.449796	+	0.779070i	0.548576	+	0.836101i	$0.315170\pi$
$620$		0			0
$621$	8.53505e6	−	4.92771e6i	0.888131	−	0.512763i
$622$		0			0
$623$	20340.1	−	2.23233e6i	0.00209958	−	0.230429i
$624$		0			0
$625$	−1.99039e7	−	3.44746e7i	−2.03816	−	3.53020i
$626$		0			0
$627$	304185.	+	175621.i	0.0309007	+	0.0178405i
$628$		0			0
$629$		−	7.37144e6i		−	0.742892i
$630$		0			0
$631$		−	1.35500e7i		−	1.35477i	−0.735626	−	0.677387i	$-0.763112\pi$
$631$		−	1.35500e7i		−	1.35477i	0.735626	−	0.677387i	$-0.236888\pi$
$632$		0			0
$633$	−9.99341e6	−	5.76970e6i	−0.991298	−	0.572326i
$634$		0			0
$635$	7.43533e6	+	1.28784e7i	0.731755	+	1.26744i
$636$		0			0
$637$	−5.07821e6	+	2.80979e6i	−0.495864	+	0.274363i
$638$		0			0
$639$	1.44370e6	−	833521.i	0.139870	−	0.0807541i
$640$		0			0
$641$	−3.26859e6	+	5.66136e6i	−0.314206	+	0.544221i	−0.979268	−	0.202567i	$-0.935072\pi$
$641$	−3.26859e6	+	5.66136e6i	−0.314206	+	0.544221i	0.665062	+	0.746788i	$0.268405\pi$
$642$		0			0
$643$	−3.58363e6			−0.341818			−0.170909	−	0.985287i	$-0.554670\pi$
$643$	−3.58363e6			−0.341818			−0.170909	+	0.985287i	$0.554670\pi$
$644$		0			0
$645$	4.02368e7			3.80824
$646$		0			0
$647$	−41305.0	+	71542.3i	−0.00387919	+	0.00671896i	−0.867958	−	0.496637i	$-0.834568\pi$
$647$	−41305.0	+	71542.3i	−0.00387919	+	0.00671896i	0.864079	+	0.503356i	$0.167901\pi$
$648$		0			0
$649$	877771.	−	506781.i	0.0818030	−	0.0472290i
$650$		0			0
$651$	1.13725e7	+	103622.i	1.05173	+	0.00958297i
$652$		0			0
$653$	631564.	+	1.09390e6i	0.0579608	+	0.100391i	0.893550	−	0.448964i	$-0.148207\pi$
$653$	631564.	+	1.09390e6i	0.0579608	+	0.100391i	−0.835589	+	0.549355i	$0.814873\pi$
$654$		0			0
$655$	1.83741e7	+	1.06083e7i	1.67341	+	0.966144i
$656$		0			0
$657$		−	2.20107e6i		−	0.198939i
$658$		0			0
$659$			1.56513e7i			1.40390i	0.712226	+	0.701950i	$0.247687\pi$
$659$			1.56513e7i			1.40390i	−0.712226	+	0.701950i	$0.752313\pi$
$660$		0			0
$661$	−149987.	−	86595.2i	−0.0133521	−	0.00770886i	0.493309	−	0.869854i	$-0.335787\pi$
$661$	−149987.	−	86595.2i	−0.0133521	−	0.00770886i	−0.506661	+	0.862145i	$0.669120\pi$
$662$		0			0
$663$	−5.80059e6	−	1.00469e7i	−0.512494	−	0.887665i
$664$		0			0
$665$	−2.14840e6	+	1.21441e6i	−0.188391	+	0.106491i
$666$		0			0
$667$	−2.14557e7	+	1.23875e7i	−1.86736	+	1.07812i
$668$		0			0
$669$	−1.19902e7	+	2.07676e7i	−1.03577	+	1.79400i
$670$		0			0
$671$	2.10544e6			0.180525
$672$		0			0
$673$	9.86699e6			0.839745			0.419872	−	0.907583i	$-0.362075\pi$
$673$	9.86699e6			0.839745			0.419872	+	0.907583i	$0.362075\pi$
$674$		0			0
$675$	−1.29760e7	+	2.24751e7i	−1.09618	+	1.89864i
$676$		0			0
$677$	−453371.	+	261754.i	−0.0380174	+	0.0219493i	−0.518888	−	0.854842i	$-0.673654\pi$
$677$	−453371.	+	261754.i	−0.0380174	+	0.0219493i	0.480871	+	0.876791i	$0.340321\pi$
$678$		0			0
$679$	−8.04090e6	−	4.74062e6i	−0.669315	−	0.394603i
$680$		0			0
$681$	3.25342e6	+	5.63509e6i	0.268827	+	0.465621i
$682$		0			0
$683$	7.47205e6	+	4.31399e6i	0.612898	+	0.353857i	0.774099	−	0.633065i	$-0.218203\pi$
$683$	7.47205e6	+	4.31399e6i	0.612898	+	0.353857i	−0.161201	+	0.986922i	$0.551537\pi$
$684$		0			0
$685$			3.35335e7i			2.73056i
$686$		0			0
$687$			1.76864e7i			1.42971i
$688$		0			0
$689$	−4.07789e6	−	2.35437e6i	−0.327256	−	0.188941i
$690$		0			0
$691$	7.71534e6	+	1.33634e7i	0.614696	+	1.06468i	0.990438	+	0.137960i	$0.0440545\pi$
$691$	7.71534e6	+	1.33634e7i	0.614696	+	1.06468i	−0.375742	+	0.926724i	$0.622612\pi$
$692$		0			0
$693$	977436.	+	576260.i	0.0773135	+	0.0455812i
$694$		0			0
$695$	9.89442e6	−	5.71254e6i	0.777013	−	0.448609i
$696$		0			0
$697$	9.01666e6	−	1.56173e7i	0.703014	−	1.21766i
$698$		0			0
$699$	5.86505e6			0.454024
$700$		0			0
$701$	−1.53187e7			−1.17741			−0.588705	−	0.808348i	$-0.700362\pi$
$701$	−1.53187e7			−1.17741			−0.588705	+	0.808348i	$0.700362\pi$
$702$		0			0
$703$	−342948.	+	594004.i	−0.0261722	+	0.0453316i
$704$		0			0
$705$	1.60310e7	−	9.25549e6i	1.21475	−	0.701337i
$706$		0			0
$707$	8.33542e6	−	4.71172e6i	0.627161	−	0.354512i
$708$		0			0
$709$	5.40716e6	+	9.36548e6i	0.403974	+	0.699704i	0.994201	−	0.107533i	$-0.0342952\pi$
$709$	5.40716e6	+	9.36548e6i	0.403974	+	0.699704i	−0.590227	+	0.807237i	$0.700962\pi$
$710$		0			0
$711$	−6.45065e6	−	3.72428e6i	−0.478552	−	0.276292i
$712$		0			0
$713$			1.63185e7i			1.20215i
$714$		0			0
$715$		−	4.23251e6i		−	0.309623i
$716$		0			0
$717$	−1.84977e7	−	1.06796e7i	−1.34375	−	0.775815i
$718$		0			0
$719$	−3.79124e6	−	6.56663e6i	−0.273501	−	0.473718i	0.696255	−	0.717795i	$-0.254848\pi$
$719$	−3.79124e6	−	6.56663e6i	−0.273501	−	0.473718i	−0.969756	+	0.244077i	$0.921515\pi$
$720$		0			0
$721$	1.40203e7	+	127747.i	1.00443	+	0.00915194i
$722$		0			0
$723$	−4.10399e6	+	2.36944e6i	−0.291985	+	0.168578i
$724$		0			0
$725$	3.26196e7	−	5.64989e7i	2.30480	−	3.99204i
$726$		0			0
$727$	9.49468e6			0.666261			0.333131	−	0.942881i	$-0.391895\pi$
$727$	9.49468e6			0.666261			0.333131	+	0.942881i	$0.391895\pi$
$728$		0			0
$729$	7.27312e6			0.506876
$730$		0			0
$731$	1.93086e7	−	3.34434e7i	1.33646	−	2.31482i
$732$		0			0
$733$	6.59858e6	−	3.80969e6i	0.453618	−	0.261897i	−0.255739	−	0.966746i	$-0.582319\pi$
$733$	6.59858e6	−	3.80969e6i	0.453618	−	0.261897i	0.709357	+	0.704849i	$0.248985\pi$
$734$		0			0
$735$	−2.87371e7	+	1.59003e7i	−1.96211	+	1.08564i
$736$		0			0
$737$	1.23381e6	+	2.13702e6i	0.0836719	+	0.144924i
$738$		0			0
$739$	−4.14096e6	−	2.39079e6i	−0.278927	−	0.161038i	0.354011	−	0.935241i	$-0.384818\pi$
$739$	−4.14096e6	−	2.39079e6i	−0.278927	−	0.161038i	−0.632937	+	0.774203i	$0.718151\pi$
$740$		0			0
$741$			1.07947e6i			0.0722209i
$742$		0			0
$743$		−	1.56274e6i		−	0.103852i	−0.998651	−	0.0519259i	$-0.983464\pi$
$743$		−	1.56274e6i		−	0.103852i	0.998651	−	0.0519259i	$-0.0165360\pi$
$744$		0			0
$745$	−4.51964e6	−	2.60941e6i	−0.298341	−	0.172247i
$746$		0			0
$747$	2.87158e6	+	4.97372e6i	0.188286	+	0.326122i
$748$		0			0
$749$	53638.1	−	5.88678e6i	0.00349356	−	0.383419i
$750$		0			0
$751$	1.69979e7	−	9.81372e6i	1.09975	−	0.634942i	0.163595	−	0.986528i	$-0.447691\pi$
$751$	1.69979e7	−	9.81372e6i	1.09975	−	0.634942i	0.936156	+	0.351586i	$0.114358\pi$
$752$		0			0
$753$	−1.56478e7	+	2.71029e7i	−1.00570	+	1.74192i
$754$		0			0
$755$	−3.30619e7			−2.11087
$756$		0			0
$757$	−1.54356e7			−0.979003			−0.489501	−	0.872002i	$-0.662821\pi$
$757$	−1.54356e7			−0.979003			−0.489501	+	0.872002i	$0.662821\pi$
$758$		0			0
$759$	−3.35350e6	+	5.80843e6i	−0.211297	+	0.365978i
$760$		0			0
$761$	−1.34280e7	+	7.75267e6i	−0.840524	+	0.485277i	−0.857442	−	0.514580i	$-0.827948\pi$
$761$	−1.34280e7	+	7.75267e6i	−0.840524	+	0.485277i	0.0169180	+	0.999857i	$0.494615\pi$
$762$		0			0
$763$	−9.50198e6	−	1.68098e7i	−0.590885	−	1.04532i
$764$		0			0
$765$	−7.96798e6	−	1.38009e7i	−0.492260	−	0.852619i
$766$		0			0
$767$	2.69763e6	+	1.55748e6i	0.165575	+	0.0955947i
$768$		0			0
$769$			9.54849e6i			0.582263i	0.956683	+	0.291131i	$0.0940317\pi$
$769$			9.54849e6i			0.582263i	−0.956683	+	0.291131i	$0.905968\pi$
$770$		0			0
$771$			1.31887e7i			0.799036i
$772$		0			0
$773$	−2.47123e6	−	1.42677e6i	−0.148753	−	0.0858824i	0.423776	−	0.905767i	$-0.360704\pi$
$773$	−2.47123e6	−	1.42677e6i	−0.148753	−	0.0858824i	−0.572529	+	0.819884i	$0.694038\pi$
$774$		0			0
$775$	−2.14856e7	−	3.72142e7i	−1.28497	−	2.22564i
$776$		0			0
$777$	−4.63581e6	+	7.86313e6i	−0.275469	+	0.467243i
$778$		0			0
$779$	−1.45316e6	+	838981.i	−0.0857964	+	0.0495346i
$780$		0			0
$781$	1.20233e6	−	2.08250e6i	0.0705338	−	0.122168i
$782$		0			0
$783$	−2.19899e7			−1.28179
$784$		0			0
$785$	−8.50992e6			−0.492892
$786$		0			0
$787$	1.60873e7	−	2.78639e7i	0.925860	−	1.60364i	0.135687	−	0.990752i	$-0.456676\pi$
$787$	1.60873e7	−	2.78639e7i	0.925860	−	1.60364i	0.790173	−	0.612884i	$-0.209991\pi$
$788$		0			0
$789$	−3.36499e7	+	1.94278e7i	−1.92438	+	1.11104i
$790$		0			0
$791$	4.44908e6	−	7.54639e6i	0.252830	−	0.428843i
$792$		0			0
$793$	3.23530e6	+	5.60371e6i	0.182697	+	0.316441i
$794$		0			0
$795$	−2.30764e7	−	1.33231e7i	−1.29494	−	0.747634i
$796$		0			0
$797$		−	1.34199e7i		−	0.748346i	−0.927359	−	0.374173i	$-0.877927\pi$
$797$		−	1.34199e7i		−	0.748346i	0.927359	−	0.374173i	$-0.122073\pi$
$798$		0			0
$799$		−	1.77659e7i		−	0.984508i
$800$		0			0
$801$	−1.16163e6	−	670667.i	−0.0639715	−	0.0369339i
$802$		0			0
$803$	−1.58749e6	−	2.74962e6i	−0.0868807	−	0.150482i
$804$		0			0
$805$	−2.31893e7	−	4.10238e7i	−1.26124	−	2.23124i
$806$		0			0
$807$	2.63492e7	−	1.52127e7i	1.42424	−	0.822286i
$808$		0			0
$809$	9.65010e6	−	1.67145e7i	0.518394	−	0.897886i	−0.481377	−	0.876514i	$-0.659863\pi$
$809$	9.65010e6	−	1.67145e7i	0.518394	−	0.897886i	0.999772	−	0.0213720i	$-0.00680343\pi$
$810$		0			0
$811$	−1.53616e7			−0.820132			−0.410066	−	0.912056i	$-0.634494\pi$
$811$	−1.53616e7			−0.820132			−0.410066	+	0.912056i	$0.634494\pi$
$812$		0			0
$813$	−1.35889e7			−0.721037
$814$		0			0
$815$	359539.	−	622740.i	0.0189606	−	0.0328407i
$816$		0			0
$817$	−3.11184e6	+	1.79662e6i	−0.163103	+	0.0941676i
$818$		0			0
$819$	−31772.1	+	3.48698e6i	−0.00165514	+	0.181652i
$820$		0			0
$821$	9.36444e6	+	1.62197e7i	0.484868	+	0.839817i	0.999849	−	0.0173853i	$-0.00553419\pi$
$821$	9.36444e6	+	1.62197e7i	0.484868	+	0.839817i	−0.514981	+	0.857202i	$0.672201\pi$
$822$		0			0
$823$	4.12115e6	+	2.37935e6i	0.212089	+	0.122450i	0.602282	−	0.798283i	$-0.294258\pi$
$823$	4.12115e6	+	2.37935e6i	0.212089	+	0.122450i	−0.390193	+	0.920733i	$0.627592\pi$
$824$		0			0
$825$		−	1.76614e7i		−	0.903420i
$826$		0			0
$827$		−	3.00137e7i		−	1.52600i	−0.646397	−	0.763001i	$-0.723725\pi$
$827$		−	3.00137e7i		−	1.52600i	0.646397	−	0.763001i	$-0.276275\pi$
$828$		0			0
$829$	400389.	+	231164.i	0.0202346	+	0.0116825i	0.510083	−	0.860125i	$-0.329615\pi$
$829$	400389.	+	231164.i	0.0202346	+	0.0116825i	−0.489849	+	0.871808i	$0.662948\pi$
$830$		0			0
$831$	5.40989e6	+	9.37020e6i	0.271760	+	0.470702i
$832$		0			0
$833$	−574360.	+	3.15154e7i	−0.0286795	+	1.57366i
$834$		0			0
$835$	3.44584e7	−	1.98946e7i	1.71033	−	0.987458i
$836$		0			0
$837$	−7.24205e6	+	1.25436e7i	−0.357312	+	0.618883i
$838$		0			0
$839$	−3.09749e6			−0.151917			−0.0759583	−	0.997111i	$-0.524202\pi$
$839$	−3.09749e6			−0.151917			−0.0759583	+	0.997111i	$0.524202\pi$
$840$		0			0
$841$	3.47679e7			1.69507
$842$		0			0
$843$	−1.49024e7	+	2.58117e7i	−0.722250	+	1.25097i
$844$		0			0
$845$	−2.38114e7	+	1.37475e7i	−1.14721	+	0.662341i
$846$		0			0
$847$	−1.92414e7	−	175320.i	−0.921571	−	0.00839700i
$848$		0			0
$849$	−2.23896e6	−	3.87799e6i	−0.106605	−	0.184645i
$850$		0			0
$851$	−1.13425e7	−	6.54862e6i	−0.536892	−	0.309975i
$852$		0			0
$853$		−	1.42277e7i		−	0.669516i	−0.942304	−	0.334758i	$-0.891346\pi$
$853$		−	1.42277e7i		−	0.669516i	0.942304	−	0.334758i	$-0.108654\pi$
$854$		0			0
$855$			1.48281e6i			0.0693696i
$856$		0			0
$857$	2.49770e7	+	1.44205e7i	1.16168	+	0.670698i	0.951707	−	0.307008i	$-0.0993279\pi$
$857$	2.49770e7	+	1.44205e7i	1.16168	+	0.670698i	0.209977	+	0.977706i	$0.432661\pi$
$858$		0			0
$859$	1.59301e7	+	2.75917e7i	0.736606	+	1.27584i	0.954015	+	0.299759i	$0.0969062\pi$
$859$	1.59301e7	+	2.75917e7i	0.736606	+	1.27584i	−0.217409	+	0.976081i	$0.569760\pi$
$860$		0			0
$861$	−1.94397e7	+	1.09886e7i	−0.893677	+	0.505164i
$862$		0			0
$863$	−1.00725e7	+	5.81537e6i	−0.460374	+	0.265797i	−0.712202	−	0.701975i	$-0.752302\pi$
$863$	−1.00725e7	+	5.81537e6i	−0.460374	+	0.265797i	0.251827	+	0.967772i	$0.418968\pi$
$864$		0			0
$865$	−2.72588e7	+	4.72136e7i	−1.23870	+	2.14549i
$866$		0			0
$867$	−3.75726e7			−1.69756
$868$		0			0
$869$	−1.07444e7			−0.482649
$870$		0			0
$871$	−3.79184e6	+	6.56766e6i	−0.169358	+	0.293336i
$872$		0			0
$873$	−4.85708e6	+	2.80423e6i	−0.215695	+	0.124531i
$874$		0			0
$875$	6.88263e7	+	4.05774e7i	3.03902	+	1.79170i
$876$		0			0
$877$	8.59482e6	+	1.48867e7i	0.377344	+	0.653579i	0.990675	−	0.136247i	$-0.0435041\pi$
$877$	8.59482e6	+	1.48867e7i	0.377344	+	0.653579i	−0.613331	+	0.789826i	$0.710171\pi$
$878$		0			0
$879$	1.58521e7	+	9.15223e6i	0.692015	+	0.399535i
$880$		0			0
$881$		−	1.01520e7i		−	0.440670i	−0.975424	−	0.220335i	$-0.929285\pi$
$881$		−	1.01520e7i		−	0.440670i	0.975424	−	0.220335i	$-0.0707151\pi$
$882$		0			0
$883$		−	3.46326e7i		−	1.49480i	−0.664373	−	0.747401i	$-0.731301\pi$
$883$		−	3.46326e7i		−	1.49480i	0.664373	−	0.747401i	$-0.268699\pi$
$884$		0			0
$885$	1.52656e7	+	8.81361e6i	0.655173	+	0.378265i
$886$		0			0
$887$	1.42911e7	+	2.47529e7i	0.609896	+	1.05637i	0.991257	+	0.131945i	$0.0421222\pi$
$887$	1.42911e7	+	2.47529e7i	0.609896	+	1.05637i	−0.381361	+	0.924426i	$0.624544\pi$
$888$		0			0
$889$	−1.52241e7	−	8.97554e6i	−0.646065	−	0.380896i
$890$		0			0
$891$	−6.99735e6	+	4.03992e6i	−0.295283	+	0.170482i
$892$		0			0
$893$	−826538.	+	1.43161e6i	−0.0346844	+	0.0600751i
$894$		0			0
$895$	5.02159e7			2.09548
$896$		0			0
$897$	−2.06125e7			−0.855360
$898$		0			0
$899$	1.82053e7	−	3.15326e7i	0.751276	−	1.30125i
$900$		0			0
$901$	−2.21475e7	+	1.27869e7i	−0.908892	+	0.524749i
$902$		0			0
$903$	−4.16287e7	+	2.35313e7i	−1.69892	+	0.960341i
$904$		0			0
$905$	9.31069e6	+	1.61266e7i	0.377886	+	0.654517i
$906$		0			0
$907$	−3.07337e7	−	1.77441e7i	−1.24050	−	0.716203i	−0.271303	−	0.962494i	$-0.587455\pi$
$907$	−3.07337e7	−	1.77441e7i	−1.24050	−	0.716203i	−0.969196	+	0.246291i	$0.920788\pi$
$908$		0			0
$909$		−	5.75304e6i		−	0.230934i
$910$		0			0
$911$			3.81040e7i			1.52116i	0.649245	+	0.760579i	$0.275085\pi$
$911$			3.81040e7i			1.52116i	−0.649245	+	0.760579i	$0.724915\pi$
$912$		0			0
$913$	7.17446e6	+	4.14218e6i	0.284847	+	0.164457i
$914$		0			0
$915$	1.83082e7	+	3.17108e7i	0.722926	+	1.25214i
$916$		0			0
$917$	−2.52136e7	−	229737.i	−0.990175	−	0.00902209i
$918$		0			0
$919$	−3.56154e7	+	2.05626e7i	−1.39107	+	0.803134i	−0.993434	−	0.114409i	$-0.963503\pi$
$919$	−3.56154e7	+	2.05626e7i	−1.39107	+	0.803134i	−0.397636	+	0.917543i	$0.630169\pi$
$920$		0			0
$921$	9.77942e6	−	1.69384e7i	0.379895	−	0.657998i
$922$		0			0
$923$	7.39020e6			0.285530
$924$		0			0
$925$	3.44887e7			1.32532
$926$		0			0
$927$	4.21216e6	−	7.29568e6i	0.160993	−	0.278847i
$928$		0			0
$929$	2.89633e7	−	1.67220e7i	1.10105	−	0.635693i	0.164556	−	0.986368i	$-0.447381\pi$
$929$	2.89633e7	−	1.67220e7i	1.10105	−	0.635693i	0.936497	+	0.350674i	$0.114048\pi$
$930$		0			0
$931$	1.51250e6	−	2.51285e6i	0.0571903	−	0.0950149i
$932$		0			0
$933$	2.09390e7	+	3.62675e7i	0.787504	+	1.36400i
$934$		0			0
$935$	−1.99075e7	−	1.14936e7i	−0.744711	−	0.429959i
$936$		0			0
$937$		−	3.56831e6i		−	0.132774i	−0.997794	−	0.0663870i	$-0.978853\pi$
$937$		−	3.56831e6i		−	0.132774i	0.997794	−	0.0663870i	$-0.0211472\pi$
$938$		0			0
$939$		−	4.06551e7i		−	1.50470i
$940$		0			0
$941$	197534.	+	114046.i	0.00727223	+	0.00419862i	0.503632	−	0.863918i	$-0.331997\pi$
$941$	197534.	+	114046.i	0.00727223	+	0.00419862i	−0.496359	+	0.868117i	$0.665330\pi$
$942$		0			0
$943$	−1.60204e7	−	2.77482e7i	−0.586671	−	1.01614i
$944$		0			0
$945$	381094.	−	4.18251e7i	0.0138820	−	1.52355i
$946$		0			0
$947$	−2.22643e7	+	1.28543e7i	−0.806741	+	0.465772i	−0.845823	−	0.533464i	$-0.820890\pi$
$947$	−2.22643e7	+	1.28543e7i	−0.806741	+	0.465772i	0.0390820	+	0.999236i	$0.487557\pi$
$948$		0			0
$949$	4.87881e6	−	8.45035e6i	0.175852	−	0.304585i
$950$		0			0
$951$	5.22298e7			1.87270
$952$		0			0
$953$	−9.70879e6			−0.346284			−0.173142	−	0.984897i	$-0.555392\pi$
$953$	−9.70879e6			−0.346284			−0.173142	+	0.984897i	$0.555392\pi$
$954$		0			0
$955$	−1.27219e7	+	2.20350e7i	−0.451382	+	0.781816i
$956$		0			0
$957$	1.29600e7	−	7.48249e6i	0.457432	−	0.264099i
$958$		0			0
$959$	−1.96110e7	−	3.46935e7i	−0.688579	−	1.21815i
$960$		0			0
$961$	2.32323e6	+	4.02396e6i	0.0811492	+	0.140555i
$962$		0			0
$963$	−3.06329e6	−	1.76859e6i	−0.106444	−	0.0614556i
$964$		0			0
$965$		−	4.29062e7i		−	1.48321i
$966$		0			0
$967$		−	7.88773e6i		−	0.271260i	−0.990760	−	0.135630i	$-0.956694\pi$
$967$		−	7.88773e6i		−	0.271260i	0.990760	−	0.135630i	$-0.0433059\pi$
$968$		0			0
$969$	5.07724e6	+	2.93135e6i	0.173707	+	0.100290i
$970$		0			0
$971$	−5.09217e6	−	8.81989e6i	−0.173322	−	0.300203i	0.766257	−	0.642534i	$-0.222117\pi$
$971$	−5.09217e6	−	8.81989e6i	−0.173322	−	0.300203i	−0.939579	+	0.342331i	$0.888784\pi$
$972$		0			0
$973$	−6.89589e6	+	1.16966e7i	−0.233511	+	0.396075i
$974$		0			0
$975$	4.70064e7	−	2.71392e7i	1.58360	−	0.914292i
$976$		0			0
$977$	4.56804e6	−	7.91208e6i	0.153107	−	0.265188i	−0.779261	−	0.626699i	$-0.784406\pi$
$977$	4.56804e6	−	7.91208e6i	0.153107	−	0.265188i	0.932368	+	0.361511i	$0.117739\pi$
$978$		0			0
$979$	−1.93484e6			−0.0645191
$980$		0			0
$981$	−1.16020e7			−0.384910
$982$		0			0
$983$	9.27209e6	−	1.60597e7i	0.306051	−	0.530096i	−0.671444	−	0.741056i	$-0.734326\pi$
$983$	9.27209e6	−	1.60597e7i	0.306051	−	0.530096i	0.977495	+	0.210960i	$0.0676588\pi$
$984$		0			0
$985$	−1.83469e6	+	1.05926e6i	−0.0602520	+	0.0347865i
$986$		0			0
$987$	−1.11727e7	+	1.89509e7i	−0.365062	+	0.619208i
$988$		0			0
$989$	−3.43066e7	−	5.94208e7i	−1.11529	−	1.93174i
$990$		0			0
$991$	−2.13699e7	−	1.23379e7i	−0.691222	−	0.399077i	0.112848	−	0.993612i	$-0.464003\pi$
$991$	−2.13699e7	−	1.23379e7i	−0.691222	−	0.399077i	−0.804070	+	0.594535i	$0.797336\pi$
$992$		0			0
$993$			3.55377e7i			1.14371i
$994$		0			0
$995$		−	1.11578e7i		−	0.357290i
$996$		0			0
$997$	3.35140e6	+	1.93493e6i	0.106780	+	0.0616492i	0.552439	−	0.833554i	$-0.313697\pi$
$997$	3.35140e6	+	1.93493e6i	0.106780	+	0.0616492i	−0.445659	+	0.895203i	$0.647031\pi$
$998$		0			0
$999$	−5.81246e6	−	1.00675e7i	−0.184266	−	0.319159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.6.p.a.31.10	✓	80
4.3	odd	2	inner	224.6.p.a.31.31	yes	80
7.5	odd	6	inner	224.6.p.a.159.31	yes	80
28.19	even	6	inner	224.6.p.a.159.10	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.6.p.a.31.10	✓	80	1.1	even	1	trivial
224.6.p.a.31.31	yes	80	4.3	odd	2	inner
224.6.p.a.159.10	yes	80	28.19	even	6	inner
224.6.p.a.159.31	yes	80	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	224.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.95676 + 15.5136i) q^{3} +(-94.4708 + 54.5427i) q^{5} +(65.8412 - 111.678i) q^{7} +(-38.9472 - 67.4586i) q^{9} +(-97.3073 - 56.1804i) q^{11} -345.316i q^{13} -1954.11i q^{15} +(-1624.18 - 937.724i) q^{17} +(87.2532 + 151.127i) q^{19} +(1142.80 + 2021.70i) q^{21} +(-2885.78 + 1666.11i) q^{23} +(4387.32 - 7599.06i) q^{25} -2957.62 q^{27} +7434.99 q^{29} +(2448.61 - 4241.11i) q^{31} +(1743.12 - 1006.39i) q^{33} +(-128.851 + 14141.4i) q^{35} +(1965.25 + 3403.91i) q^{37} +(5357.08 + 3092.91i) q^{39} +9615.48i q^{41} +20590.9i q^{43} +(7358.75 + 4248.58i) q^{45} +(4736.43 + 8203.74i) q^{47} +(-8136.88 - 14706.0i) q^{49} +(29094.9 - 16797.9i) q^{51} +(6818.03 - 11809.2i) q^{53} +12256.9 q^{55} -3126.02 q^{57} +(-4510.30 + 7812.08i) q^{59} +(-16227.8 + 9369.11i) q^{61} +(-10098.0 - 92.0087i) q^{63} +(18834.5 + 32622.2i) q^{65} +(-19019.3 - 10980.8i) q^{67} -59691.7i q^{69} +21401.3i q^{71} +(24471.4 + 14128.5i) q^{73} +(78592.3 + 136126. i) q^{75} +(-12680.9 + 7168.08i) q^{77} +(82812.6 - 47811.9i) q^{79} +(35954.9 - 62275.7i) q^{81} -73730.0 q^{83} +204584. q^{85} +(-66593.4 + 115343. i) q^{87} +(14912.9 - 8609.95i) q^{89} +(-38564.1 - 22736.0i) q^{91} +(43863.2 + 75973.2i) q^{93} +(-16485.8 - 9518.05i) q^{95} -72000.9i q^{97} +8752.28i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 3240 q^{9} + 6856 q^{21} + 27728 q^{25} - 15920 q^{29} - 28296 q^{33} - 2152 q^{37} + 35400 q^{45} + 29280 q^{49} - 17512 q^{53} - 108368 q^{57} + 37704 q^{61} + 18216 q^{65} + 157704 q^{73} + 28224 q^{77}+ \cdots + 39400 q^{93}+O(q^{100}) \) 80 * q - 3240 * q^9 + 6856 * q^21 + 27728 * q^25 - 15920 * q^29 - 28296 * q^33 - 2152 * q^37 + 35400 * q^45 + 29280 * q^49 - 17512 * q^53 - 108368 * q^57 + 37704 * q^61 + 18216 * q^65 + 157704 * q^73 + 28224 * q^77 - 273136 * q^81 + 230704 * q^85 + 28440 * q^89 + 39400 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more