LMFDB - Embedded newform 108.6.i.a.13.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,6,Mod(13,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("108.13");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	108.i (of order $9$, degree $6$, 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:	$17.3214525398$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$15$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			13.11
Character	$\chi$	$=$	108.13
Dual form			108.6.i.a.25.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.06551 - 12.6813i) q^{3} +(40.6723 + 34.1282i) q^{5} +(234.829 + 85.4708i) q^{7} +(-78.6332 - 229.926i) q^{9} +O(q^{10})$	\(q+(9.06551 - 12.6813i) q^{3} +(40.6723 + 34.1282i) q^{5} +(234.829 + 85.4708i) q^{7} +(-78.6332 - 229.926i) q^{9} +(-179.848 + 150.910i) q^{11} +(-163.977 + 929.960i) q^{13} +(801.506 - 206.391i) q^{15} +(-593.121 + 1027.32i) q^{17} +(225.775 + 391.053i) q^{19} +(3212.73 - 2203.11i) q^{21} +(4157.57 - 1513.23i) q^{23} +(-53.1415 - 301.380i) q^{25} +(-3628.62 - 1087.22i) q^{27} +(-463.328 - 2627.66i) q^{29} +(2371.55 - 863.175i) q^{31} +(283.334 + 3648.79i) q^{33} +(6634.09 + 11490.6i) q^{35} +(4553.67 - 7887.18i) q^{37} +(10306.6 + 10510.0i) q^{39} +(2395.05 - 13583.0i) q^{41} +(-6436.49 + 5400.86i) q^{43} +(4648.74 - 12035.2i) q^{45} +(692.039 + 251.882i) q^{47} +(34964.5 + 29338.7i) q^{49} +(7650.80 + 16834.7i) q^{51} -33102.1 q^{53} -12465.1 q^{55} +(7005.85 + 681.968i) q^{57} +(-25183.9 - 21131.8i) q^{59} +(8431.07 + 3068.66i) q^{61} +(1186.56 - 60714.1i) q^{63} +(-38407.2 + 32227.4i) q^{65} +(-4677.88 + 26529.6i) q^{67} +(18500.7 - 66441.8i) q^{69} +(3951.61 - 6844.40i) q^{71} +(-906.632 - 1570.33i) q^{73} +(-4303.66 - 2058.26i) q^{75} +(-55131.9 + 20066.4i) q^{77} +(-1934.75 - 10972.5i) q^{79} +(-46682.6 + 36159.6i) q^{81} +(-13283.4 - 75334.1i) q^{83} +(-59184.0 + 21541.2i) q^{85} +(-37522.6 - 17945.5i) q^{87} +(-17595.1 - 30475.5i) q^{89} +(-117991. + 204366. i) q^{91} +(10553.1 - 37899.6i) q^{93} +(-4163.14 + 23610.3i) q^{95} +(35234.4 - 29565.2i) q^{97} +(48840.1 + 29485.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 87 q^{5} + 330 q^{9}+O(q^{10}) $ 90 * q - 87 * q^5 + 330 * q^9	$ 90 q - 87 q^{5} + 330 q^{9} - 1257 q^{11} + 531 q^{15} - 3468 q^{17} + 12894 q^{21} + 8106 q^{23} + 4959 q^{25} - 17415 q^{27} + 3468 q^{29} - 6651 q^{31} + 33624 q^{33} - 8229 q^{35} - 10545 q^{39} + 68673 q^{41} + 9459 q^{43} - 53469 q^{45} - 57087 q^{47} - 5490 q^{49} + 42831 q^{51} - 4146 q^{53} + 24624 q^{57} + 5388 q^{59} + 70110 q^{61} - 98115 q^{63} - 172425 q^{65} - 15039 q^{67} + 251037 q^{69} + 67812 q^{71} - 27009 q^{73} - 75273 q^{75} + 23991 q^{77} - 216180 q^{79} + 177822 q^{81} - 76725 q^{83} - 53100 q^{85} - 201483 q^{87} - 98814 q^{89} - 90999 q^{91} + 21765 q^{93} - 143490 q^{95} - 71739 q^{97} + 13635 q^{99}+O(q^{100}) $ 90 * q - 87 * q^5 + 330 * q^9 - 1257 * q^11 + 531 * q^15 - 3468 * q^17 + 12894 * q^21 + 8106 * q^23 + 4959 * q^25 - 17415 * q^27 + 3468 * q^29 - 6651 * q^31 + 33624 * q^33 - 8229 * q^35 - 10545 * q^39 + 68673 * q^41 + 9459 * q^43 - 53469 * q^45 - 57087 * q^47 - 5490 * q^49 + 42831 * q^51 - 4146 * q^53 + 24624 * q^57 + 5388 * q^59 + 70110 * q^61 - 98115 * q^63 - 172425 * q^65 - 15039 * q^67 + 251037 * q^69 + 67812 * q^71 - 27009 * q^73 - 75273 * q^75 + 23991 * q^77 - 216180 * q^79 + 177822 * q^81 - 76725 * q^83 - 53100 * q^85 - 201483 * q^87 - 98814 * q^89 - 90999 * q^91 + 21765 * q^93 - 143490 * q^95 - 71739 * q^97 + 13635 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

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
$3$	9.06551	−	12.6813i	0.581552	−	0.813509i
$3$	9.06551	−	12.6813i	0.581552	−	0.813509i
$4$		0			0
$5$	40.6723	+	34.1282i	0.727569	+	0.610503i	0.929468	−	0.368904i	$-0.120267\pi$
$5$	40.6723	+	34.1282i	0.727569	+	0.610503i	−0.201899	+	0.979406i	$0.564711\pi$
$6$		0			0
$7$	234.829	+	85.4708i	1.81137	+	0.659284i	0.996865	+	0.0791245i	$0.0252125\pi$
$7$	234.829	+	85.4708i	1.81137	+	0.659284i	0.814503	+	0.580159i	$0.197010\pi$
$8$		0			0
$9$	−78.6332	−	229.926i	−0.323593	−	0.946196i
$10$		0			0
$11$	−179.848	+	150.910i	−0.448150	+	0.376043i	−0.838749	−	0.544518i	$-0.816712\pi$
$11$	−179.848	+	150.910i	−0.448150	+	0.376043i	0.390599	+	0.920561i	$0.372268\pi$
$12$		0			0
$13$	−163.977	+	929.960i	−0.269107	+	1.52618i	0.487973	+	0.872859i	$0.337736\pi$
$13$	−163.977	+	929.960i	−0.269107	+	1.52618i	−0.757080	+	0.653322i	$0.773375\pi$
$14$		0			0
$15$	801.506	−	206.391i	0.919769	−	0.236844i
$16$		0			0
$17$	−593.121	+	1027.32i	−0.497761	+	0.862147i	−0.999997	−	0.00258353i	$-0.999178\pi$
$17$	−593.121	+	1027.32i	−0.497761	+	0.862147i	0.502236	+	0.864731i	$0.332511\pi$
$18$		0			0
$19$	225.775	+	391.053i	0.143480	+	0.248515i	0.928805	−	0.370569i	$-0.120837\pi$
$19$	225.775	+	391.053i	0.143480	+	0.248515i	−0.785325	+	0.619084i	$0.787504\pi$
$20$		0			0
$21$	3212.73	−	2203.11i	1.58974	−	1.09016i
$22$		0			0
$23$	4157.57	−	1513.23i	1.63878	−	0.596467i	0.651954	−	0.758259i	$-0.273950\pi$
$23$	4157.57	−	1513.23i	1.63878	−	0.596467i	0.986825	+	0.161792i	$0.0517274\pi$
$24$		0			0
$25$	−53.1415	−	301.380i	−0.0170053	−	0.0964417i
$26$		0			0
$27$	−3628.62	−	1087.22i	−0.957926	−	0.287017i
$28$		0			0
$29$	−463.328	−	2627.66i	−0.102304	−	0.580196i	−0.992263	−	0.124155i	$-0.960378\pi$
$29$	−463.328	−	2627.66i	−0.102304	−	0.580196i	0.889959	−	0.456041i	$-0.150733\pi$
$30$		0			0
$31$	2371.55	−	863.175i	0.443230	−	0.161322i	−0.110758	−	0.993847i	$-0.535328\pi$
$31$	2371.55	−	863.175i	0.443230	−	0.161322i	0.553987	+	0.832525i	$0.313106\pi$
$32$		0			0
$33$	283.334	+	3648.79i	0.0452912	+	0.583262i
$34$		0			0
$35$	6634.09	+	11490.6i	0.915400	+	1.58552i
$36$		0			0
$37$	4553.67	−	7887.18i	0.546836	−	0.947147i	−0.451653	−	0.892194i	$-0.649166\pi$
$37$	4553.67	−	7887.18i	0.546836	−	0.947147i	0.998489	−	0.0549538i	$-0.0175011\pi$
$38$		0			0
$39$	10306.6	+	10510.0i	1.08506	+	1.10648i
$40$		0			0
$41$	2395.05	−	13583.0i	0.222513	−	1.26193i	−0.644871	−	0.764292i	$-0.723089\pi$
$41$	2395.05	−	13583.0i	0.222513	−	1.26193i	0.867383	−	0.497640i	$-0.165800\pi$
$42$		0			0
$43$	−6436.49	+	5400.86i	−0.530857	+	0.445442i	−0.868397	−	0.495869i	$-0.834850\pi$
$43$	−6436.49	+	5400.86i	−0.530857	+	0.445442i	0.337540	+	0.941311i	$0.390405\pi$
$44$		0			0
$45$	4648.74	−	12035.2i	0.342219	−	0.885978i
$46$		0			0
$47$	692.039	+	251.882i	0.0456968	+	0.0166323i	0.364767	−	0.931099i	$-0.381148\pi$
$47$	692.039	+	251.882i	0.0456968	+	0.0166323i	−0.319071	+	0.947731i	$0.603371\pi$
$48$		0			0
$49$	34964.5	+	29338.7i	2.08035	+	1.74562i
$50$		0			0
$51$	7650.80	+	16834.7i	0.411890	+	0.906317i
$52$		0			0
$53$	−33102.1			−1.61870			−0.809349	−	0.587328i	$-0.800180\pi$
$53$	−33102.1			−1.61870			−0.809349	+	0.587328i	$0.800180\pi$
$54$		0			0
$55$	−12465.1			−0.555635
$56$		0			0
$57$	7005.85	+	681.968i	0.285610	+	0.0278021i
$58$		0			0
$59$	−25183.9	−	21131.8i	−0.941873	−	0.790325i	0.0360376	−	0.999350i	$-0.488526\pi$
$59$	−25183.9	−	21131.8i	−0.941873	−	0.790325i	−0.977910	+	0.209025i	$0.932971\pi$
$60$		0			0
$61$	8431.07	+	3068.66i	0.290107	+	0.105590i	0.482974	−	0.875635i	$-0.339556\pi$
$61$	8431.07	+	3068.66i	0.290107	+	0.105590i	−0.192867	+	0.981225i	$0.561779\pi$
$62$		0			0
$63$	1186.56	−	60714.1i	0.0376652	−	1.92725i
$64$		0			0
$65$	−38407.2	+	32227.4i	−1.12753	+	0.946111i
$66$		0			0
$67$	−4677.88	+	26529.6i	−0.127310	+	0.722010i	0.852599	+	0.522565i	$0.175025\pi$
$67$	−4677.88	+	26529.6i	−0.127310	+	0.722010i	−0.979909	+	0.199445i	$0.936086\pi$
$68$		0			0
$69$	18500.7	−	66441.8i	0.467805	−	1.68004i
$70$		0			0
$71$	3951.61	−	6844.40i	0.0930312	−	0.161135i	−0.815754	−	0.578399i	$-0.803678\pi$
$71$	3951.61	−	6844.40i	0.0930312	−	0.161135i	0.908785	+	0.417264i	$0.137011\pi$
$72$		0			0
$73$	−906.632	−	1570.33i	−0.0199124	−	0.0344893i	0.855897	−	0.517146i	$-0.173005\pi$
$73$	−906.632	−	1570.33i	−0.0199124	−	0.0344893i	−0.875810	+	0.482656i	$0.839672\pi$
$74$		0			0
$75$	−4303.66	−	2058.26i	−0.0883457	−	0.0422520i
$76$		0			0
$77$	−55131.9	+	20066.4i	−1.05968	+	0.385693i
$78$		0			0
$79$	−1934.75	−	10972.5i	−0.0348784	−	0.197805i	0.962390	−	0.271673i	$-0.0875769\pi$
$79$	−1934.75	−	10972.5i	−0.0348784	−	0.197805i	−0.997268	+	0.0738676i	$0.976466\pi$
$80$		0			0
$81$	−46682.6	+	36159.6i	−0.790575	+	0.612366i
$82$		0			0
$83$	−13283.4	−	75334.1i	−0.211648	−	1.20032i	−0.886629	−	0.462482i	$-0.846959\pi$
$83$	−13283.4	−	75334.1i	−0.211648	−	1.20032i	0.674980	−	0.737836i	$-0.264152\pi$
$84$		0			0
$85$	−59184.0	+	21541.2i	−0.888499	+	0.323387i
$86$		0			0
$87$	−37522.6	−	17945.5i	−0.531490	−	0.254189i
$88$		0			0
$89$	−17595.1	−	30475.5i	−0.235459	−	0.407827i	0.723947	−	0.689856i	$-0.242326\pi$
$89$	−17595.1	−	30475.5i	−0.235459	−	0.407827i	−0.959406	+	0.282028i	$0.908993\pi$
$90$		0			0
$91$	−117991.	+	204366.i	−1.49364	+	2.58706i
$92$		0			0
$93$	10553.1	−	37899.6i	0.126524	−	0.454389i
$94$		0			0
$95$	−4163.14	+	23610.3i	−0.0473273	+	0.268407i
$96$		0			0
$97$	35234.4	−	29565.2i	0.380223	−	0.319045i	−0.432567	−	0.901602i	$-0.642392\pi$
$97$	35234.4	−	29565.2i	0.380223	−	0.319045i	0.812790	+	0.582557i	$0.197948\pi$
$98$		0			0
$99$	48840.1	+	29485.1i	0.500828	+	0.302353i
$100$		0			0
$101$	133642.	+	48641.7i	1.30359	+	0.474466i	0.898163	−	0.439663i	$-0.144902\pi$
$101$	133642.	+	48641.7i	1.30359	+	0.474466i	0.405423	+	0.914129i	$0.367124\pi$
$102$		0			0
$103$	−118174.	−	99159.7i	−1.09756	−	0.920963i	−0.100302	−	0.994957i	$-0.531981\pi$
$103$	−118174.	−	99159.7i	−1.09756	−	0.920963i	−0.997259	+	0.0739945i	$0.976425\pi$
$104$		0			0
$105$	205857.	+	20038.7i	1.82219	+	0.177377i
$106$		0			0
$107$	−157056.			−1.32616			−0.663079	−	0.748550i	$-0.730750\pi$
$107$	−157056.			−1.32616			−0.663079	+	0.748550i	$0.730750\pi$
$108$		0			0
$109$	239194.			1.92834			0.964171	−	0.265282i	$-0.0854650\pi$
$109$	239194.			1.92834			0.964171	+	0.265282i	$0.0854650\pi$
$110$		0			0
$111$	−58738.8	−	129248.i	−0.452499	−	0.995672i
$112$		0			0
$113$	−105312.	−	88367.1i	−0.775855	−	0.651020i	0.166346	−	0.986067i	$-0.446803\pi$
$113$	−105312.	−	88367.1i	−0.775855	−	0.651020i	−0.942201	+	0.335047i	$0.891248\pi$
$114$		0			0
$115$	220742.	+	80343.5i	1.55647	+	0.566508i
$116$		0			0
$117$	226716.	−	35423.2i	1.53115	−	0.239234i
$118$		0			0
$119$	−227087.	+	190549.i	−1.47003	+	1.23350i
$120$		0			0
$121$	−18394.9	+	104323.i	−0.114218	+	0.647761i
$122$		0			0
$123$	−150538.	−	153509.i	−0.897190	−	0.914896i
$124$		0			0
$125$	91083.5	−	157761.i	0.521392	−	0.903078i
$126$		0			0
$127$	114710.	+	198684.i	0.631091	+	1.09308i	0.987329	+	0.158687i	$0.0507261\pi$
$127$	114710.	+	198684.i	0.631091	+	1.09308i	−0.356238	+	0.934395i	$0.615941\pi$
$128$		0			0
$129$	10140.1	+	130585.i	0.0536498	+	0.690905i
$130$		0			0
$131$	−232413.	+	84591.2i	−1.18326	+	0.430673i	−0.857353	−	0.514728i	$-0.827893\pi$
$131$	−232413.	+	84591.2i	−1.18326	+	0.430673i	−0.325910	+	0.945401i	$0.605671\pi$
$132$		0			0
$133$	19594.8	+	111128.i	0.0960534	+	0.544746i
$134$		0			0
$135$	−110480.	−	168058.i	−0.521733	−	0.793641i
$136$		0			0
$137$	−32464.1	−	184113.i	−0.147775	−	0.838076i	−0.965097	−	0.261894i	$-0.915653\pi$
$137$	−32464.1	−	184113.i	−0.147775	−	0.838076i	0.817321	−	0.576182i	$-0.195458\pi$
$138$		0			0
$139$	96387.0	−	35082.0i	0.423138	−	0.154009i	−0.121670	−	0.992571i	$-0.538825\pi$
$139$	96387.0	−	35082.0i	0.423138	−	0.154009i	0.544807	+	0.838561i	$0.316603\pi$
$140$		0			0
$141$	9467.89	−	6492.56i	0.0401056	−	0.0275022i
$142$		0			0
$143$	−110850.	−	191997.i	−0.453309	−	0.785154i
$144$		0			0
$145$	70832.7	−	122686.i	0.279778	−	0.484590i
$146$		0			0
$147$	689025.	−	177427.i	2.62991	−	0.677214i
$148$		0			0
$149$	5283.11	−	29962.0i	0.0194950	−	0.110562i	−0.973507	−	0.228655i	$-0.926567\pi$
$149$	5283.11	−	29962.0i	0.0194950	−	0.110562i	0.993002	+	0.118094i	$0.0376783\pi$
$150$		0			0
$151$	−71790.4	+	60239.3i	−0.256227	+	0.215000i	−0.761848	−	0.647756i	$-0.775708\pi$
$151$	−71790.4	+	60239.3i	−0.256227	+	0.215000i	0.505621	+	0.862755i	$0.331263\pi$
$152$		0			0
$153$	282845.	+	55592.6i	0.976833	+	0.191994i
$154$		0			0
$155$	125915.	+	45829.4i	0.420968	+	0.153220i
$156$		0			0
$157$	101755.	+	85382.4i	0.329462	+	0.276452i	0.792481	−	0.609897i	$-0.208789\pi$
$157$	101755.	+	85382.4i	0.329462	+	0.276452i	−0.463019	+	0.886349i	$0.653234\pi$
$158$		0			0
$159$	−300087.	+	419779.i	−0.941358	+	1.31683i
$160$		0			0
$161$	1.10566e6			3.36167
$162$		0			0
$163$	232064.			0.684130			0.342065	−	0.939676i	$-0.388874\pi$
$163$	232064.			0.684130			0.342065	+	0.939676i	$0.388874\pi$
$164$		0			0
$165$	−113003.	+	158075.i	−0.323131	+	0.452014i
$166$		0			0
$167$	144857.	+	121549.i	0.401927	+	0.337257i	0.821238	−	0.570586i	$-0.193284\pi$
$167$	144857.	+	121549.i	0.401927	+	0.337257i	−0.419311	+	0.907843i	$0.637728\pi$
$168$		0			0
$169$	−489036.	−	177995.i	−1.31712	−	0.479391i
$170$		0			0
$171$	72159.8	−	82661.2i	0.188714	−	0.216178i
$172$		0			0
$173$	−538121.	+	451537.i	−1.36699	+	1.14704i	−0.393234	+	0.919439i	$0.628644\pi$
$173$	−538121.	+	451537.i	−1.36699	+	1.14704i	−0.973755	+	0.227601i	$0.926912\pi$
$174$		0			0
$175$	13280.0	−	75314.9i	0.0327797	−	0.185903i
$176$		0			0
$177$	−496284.	+	127795.i	−1.19068	+	0.306606i
$178$		0			0
$179$	−190441.	+	329853.i	−0.444250	+	0.769464i	−0.998000	−	0.0632194i	$-0.979863\pi$
$179$	−190441.	+	329853.i	−0.444250	+	0.769464i	0.553749	+	0.832683i	$0.313197\pi$
$180$		0			0
$181$	−206686.	−	357991.i	−0.468937	−	0.812223i	0.530432	−	0.847727i	$-0.322030\pi$
$181$	−206686.	−	357991.i	−0.468937	−	0.812223i	−0.999370	+	0.0355042i	$0.988696\pi$
$182$		0			0
$183$	115347.	−	79098.4i	0.254611	−	0.174598i
$184$		0			0
$185$	454383.	−	165382.i	0.976097	−	0.355270i
$186$		0			0
$187$	−48360.9	−	274268.i	−0.101132	−	0.573551i
$188$		0			0
$189$	−759179.	−	565451.i	−1.54593	−	1.15144i
$190$		0			0
$191$	−11933.3	−	67677.3i	−0.0236689	−	0.134233i	0.970684	−	0.240361i	$-0.0772658\pi$
$191$	−11933.3	−	67677.3i	−0.0236689	−	0.134233i	−0.994352	+	0.106128i	$0.966155\pi$
$192$		0			0
$193$	−775500.	+	282259.i	−1.49861	+	0.545449i	−0.955700	−	0.294342i	$-0.904899\pi$
$193$	−775500.	+	282259.i	−1.49861	+	0.545449i	−0.542909	+	0.839792i	$0.682677\pi$
$194$		0			0
$195$	60507.0	+	779213.i	0.113951	+	1.46747i
$196$		0			0
$197$	248473.	+	430367.i	0.456156	+	0.790085i	0.998754	−	0.0499076i	$-0.0158927\pi$
$197$	248473.	+	430367.i	0.456156	+	0.790085i	−0.542598	+	0.839992i	$0.682559\pi$
$198$		0			0
$199$	−287425.	+	497835.i	−0.514508	+	0.891155i	0.485350	+	0.874320i	$0.338692\pi$
$199$	−287425.	+	497835.i	−0.514508	+	0.891155i	−0.999858	+	0.0168346i	$0.994641\pi$
$200$		0			0
$201$	294023.	+	299826.i	0.513324	+	0.523454i
$202$		0			0
$203$	115786.	−	656653.i	0.197203	−	1.11840i
$204$		0			0
$205$	560975.	−	470714.i	0.932307	−	0.782298i
$206$		0			0
$207$	−674854.	−	836942.i	−1.09467	−	1.35759i
$208$		0			0
$209$	−99619.1	−	36258.4i	−0.157753	−	0.0574173i
$210$		0			0
$211$	−470570.	−	394855.i	−0.727642	−	0.610565i	0.201845	−	0.979417i	$-0.435306\pi$
$211$	−470570.	−	394855.i	−0.727642	−	0.610565i	−0.929488	+	0.368853i	$0.879751\pi$
$212$		0			0
$213$	−50972.8	−	112160.i	−0.0769820	−	0.169390i
$214$		0			0
$215$	−446108.			−0.658179
$216$		0			0
$217$	630686.			0.909209
$218$		0			0
$219$	−28133.0	−	2738.54i	−0.0396375	−	0.00385842i
$220$		0			0
$221$	−858104.	−	720035.i	−1.18184	−	0.991683i
$222$		0			0
$223$	−203103.	−	73923.6i	−0.273499	−	0.0995454i	0.201630	−	0.979462i	$-0.435376\pi$
$223$	−203103.	−	73923.6i	−0.273499	−	0.0995454i	−0.475128	+	0.879916i	$0.657598\pi$
$224$		0			0
$225$	−65116.4	+	35917.1i	−0.0857500	+	0.0472982i
$226$		0			0
$227$	246379.	−	206737.i	0.317350	−	0.266289i	−0.470172	−	0.882575i	$-0.655808\pi$
$227$	246379.	−	206737.i	0.317350	−	0.266289i	0.787522	+	0.616286i	$0.211364\pi$
$228$		0			0
$229$	39026.1	−	221328.i	0.0491775	−	0.278900i	−0.950296	−	0.311348i	$-0.899219\pi$
$229$	39026.1	−	221328.i	0.0491775	−	0.278900i	0.999473	+	0.0324486i	$0.0103305\pi$
$230$		0			0
$231$	−245330.	+	881059.i	−0.302497	+	1.08636i
$232$		0			0
$233$	391091.	−	677390.i	0.471941	−	0.817426i	−0.527543	−	0.849528i	$-0.676887\pi$
$233$	391091.	−	677390.i	0.471941	−	0.817426i	0.999485	+	0.0321017i	$0.0102201\pi$
$234$		0			0
$235$	19550.6	+	33862.6i	0.0230935	+	0.0399992i
$236$		0			0
$237$	−156686.	−	74936.1i	−0.181200	−	0.0866603i
$238$		0			0
$239$	−841577.	+	306309.i	−0.953013	+	0.346868i	−0.771292	−	0.636482i	$-0.780389\pi$
$239$	−841577.	+	306309.i	−0.953013	+	0.346868i	−0.181721	+	0.983350i	$0.558167\pi$
$240$		0			0
$241$	−270419.	−	1.53362e6i	−0.299912	−	1.70089i	−0.646536	−	0.762883i	$-0.723783\pi$
$241$	−270419.	−	1.53362e6i	−0.299912	−	1.70089i	0.346624	−	0.938004i	$-0.387328\pi$
$242$		0			0
$243$	35350.7	+	919804.i	0.0384045	+	0.999262i
$244$		0			0
$245$	420813.	+	2.38655e6i	0.447892	+	2.54012i
$246$		0			0
$247$	−400686.	+	145838.i	−0.417890	+	0.152099i
$248$		0			0
$249$	−1.07576e6	−	514490.i	−1.09955	−	0.525870i
$250$		0			0
$251$	107029.	+	185379.i	0.107230	+	0.185728i	0.914647	−	0.404253i	$-0.132469\pi$
$251$	107029.	+	185379.i	0.107230	+	0.185728i	−0.807417	+	0.589981i	$0.799135\pi$
$252$		0			0
$253$	−519368.	+	899572.i	−0.510122	+	0.883557i
$254$		0			0
$255$	−263361.	+	945815.i	−0.253630	+	0.910868i
$256$		0			0
$257$	25431.3	−	144228.i	0.0240180	−	0.136213i	−0.970441	−	0.241339i	$-0.922414\pi$
$257$	25431.3	−	144228.i	0.0240180	−	0.136213i	0.994459	+	0.105126i	$0.0335246\pi$
$258$		0			0
$259$	1.74346e6	−	1.46293e6i	1.61496	−	1.35511i
$260$		0			0
$261$	−567735.	+	313153.i	−0.515875	+	0.284548i
$262$		0			0
$263$	1.67810e6	+	610778.i	1.49599	+	0.544495i	0.955018	−	0.296547i	$-0.0958351\pi$
$263$	1.67810e6	+	610778.i	1.49599	+	0.544495i	0.540970	+	0.841042i	$0.318057\pi$
$264$		0			0
$265$	−1.34634e6	−	1.12971e6i	−1.17771	−	0.988220i
$266$		0			0
$267$	−545979.	−	53147.1i	−0.468703	−	0.0456248i
$268$		0			0
$269$	2.02800e6			1.70878			0.854392	−	0.519629i	$-0.173930\pi$
$269$	2.02800e6			1.70878			0.854392	+	0.519629i	$0.173930\pi$
$270$		0			0
$271$	240302.			0.198762			0.0993810	−	0.995049i	$-0.468314\pi$
$271$	240302.			0.198762			0.0993810	+	0.995049i	$0.468314\pi$
$272$		0			0
$273$	1.52199e6	+	3.34897e6i	1.23597	+	2.71960i
$274$		0			0
$275$	55038.8	+	46183.0i	0.0438871	+	0.0368257i
$276$		0			0
$277$	934883.	+	340270.i	0.732079	+	0.266455i	0.681045	−	0.732242i	$-0.261526\pi$
$277$	934883.	+	340270.i	0.732079	+	0.266455i	0.0510343	+	0.998697i	$0.483748\pi$
$278$		0			0
$279$	−384949.	−	477407.i	−0.296069	−	0.367179i
$280$		0			0
$281$	1.60816e6	−	1.34940e6i	1.21496	−	1.01947i	0.215890	−	0.976418i	$-0.430735\pi$
$281$	1.60816e6	−	1.34940e6i	1.21496	−	1.01947i	0.999073	−	0.0430568i	$-0.0137096\pi$
$282$		0			0
$283$	8932.44	−	50658.4i	0.00662985	−	0.0375998i	−0.981313	−	0.192416i	$-0.938368\pi$
$283$	8932.44	−	50658.4i	0.00662985	−	0.0375998i	0.987943	+	0.154817i	$0.0494787\pi$
$284$		0			0
$285$	261670.	+	266834.i	0.190828	+	0.194594i
$286$		0			0
$287$	1.72338e6	−	2.98497e6i	1.23502	−	2.13912i
$288$		0			0
$289$	6344.09	+	10988.3i	0.00446812	+	0.00773901i
$290$		0			0
$291$	−55508.7	−	714844.i	−0.0384263	−	0.494856i
$292$		0			0
$293$	−1.15454e6	+	420218.i	−0.785670	+	0.285960i	−0.703535	−	0.710661i	$-0.748396\pi$
$293$	−1.15454e6	+	420218.i	−0.785670	+	0.285960i	−0.0821349	+	0.996621i	$0.526174\pi$
$294$		0			0
$295$	−303098.	−	1.71896e6i	−0.202782	−	1.15003i
$296$		0			0
$297$	816671.	−	352062.i	0.537225	−	0.231594i
$298$		0			0
$299$	725500.	+	4.11451e6i	0.469309	+	2.66159i
$300$		0			0
$301$	−1.97309e6	+	718146.i	−1.25525	+	0.456874i
$302$		0			0
$303$	1.82838e6	−	1.25380e6i	1.14409	−	0.784552i
$304$		0			0
$305$	238184.	+	412546.i	0.146610	+	0.253935i
$306$		0			0
$307$	−435991.	+	755158.i	−0.264017	+	0.457290i	−0.967305	−	0.253614i	$-0.918381\pi$
$307$	−435991.	+	755158.i	−0.264017	+	0.457290i	0.703289	+	0.710904i	$0.251714\pi$
$308$		0			0
$309$	−2.32878e6	+	599672.i	−1.38750	+	0.357287i
$310$		0			0
$311$	337085.	−	1.91170e6i	0.197623	−	1.12078i	−0.711010	−	0.703182i	$-0.751762\pi$
$311$	337085.	−	1.91170e6i	0.197623	−	1.12078i	0.908633	−	0.417595i	$-0.137127\pi$
$312$		0			0
$313$	564147.	−	473376.i	0.325486	−	0.273115i	−0.465372	−	0.885115i	$-0.654079\pi$
$313$	564147.	−	473376.i	0.325486	−	0.273115i	0.790857	+	0.612000i	$0.209635\pi$
$314$		0			0
$315$	2.12032e6	−	2.42889e6i	1.20400	−	1.37921i
$316$		0			0
$317$	−966879.	−	351915.i	−0.540411	−	0.196693i	0.0573700	−	0.998353i	$-0.481729\pi$
$317$	−966879.	−	351915.i	−0.540411	−	0.196693i	−0.597781	+	0.801659i	$0.703951\pi$
$318$		0			0
$319$	479870.	+	402659.i	0.264026	+	0.221544i
$320$		0			0
$321$	−1.42379e6	+	1.99168e6i	−0.771230	+	1.07884i
$322$		0			0
$323$	−535647.			−0.285675
$324$		0			0
$325$	288986.			0.151764
$326$		0			0
$327$	2.16841e6	−	3.03330e6i	1.12143	−	1.56872i
$328$		0			0
$329$	140982.	+	118298.i	0.0718084	+	0.0602544i
$330$		0			0
$331$	1.18910e6	+	432799.i	0.596554	+	0.217128i	0.622610	−	0.782532i	$-0.286072\pi$
$331$	1.18910e6	+	432799.i	0.596554	+	0.217128i	−0.0260554	+	0.999661i	$0.508295\pi$
$332$		0			0
$333$	−2.17154e6	−	426810.i	−1.07314	−	0.210923i
$334$		0			0
$335$	−1.09567e6	+	919373.i	−0.533416	+	0.447589i
$336$		0			0
$337$	20082.7	−	113895.i	0.00963267	−	0.0546296i	−0.979613	−	0.200896i	$-0.935615\pi$
$337$	20082.7	−	113895.i	0.00963267	−	0.0546296i	0.989245	+	0.146267i	$0.0467257\pi$
$338$		0			0
$339$	−2.07532e6	+	534403.i	−0.980811	+	0.252563i
$340$		0			0
$341$	−296257.	+	513132.i	−0.137969	+	0.238970i
$342$		0			0
$343$	3.60304e6	+	6.24065e6i	1.65361	+	2.86414i
$344$		0			0
$345$	3.02000e6	−	2.07095e6i	1.36603	−	0.936747i
$346$		0			0
$347$	−1.71685e6	+	624881.i	−0.765433	+	0.278595i	−0.695085	−	0.718927i	$-0.744633\pi$
$347$	−1.71685e6	+	624881.i	−0.765433	+	0.278595i	−0.0703484	+	0.997522i	$0.522411\pi$
$348$		0			0
$349$	−86622.8	−	491262.i	−0.0380688	−	0.215899i	0.959839	−	0.280551i	$-0.0905172\pi$
$349$	−86622.8	−	491262.i	−0.0380688	−	0.215899i	−0.997908	+	0.0646525i	$0.979406\pi$
$350$		0			0
$351$	1.60608e6	−	3.19619e6i	0.695824	−	1.38473i
$352$		0			0
$353$	−248142.	−	1.40729e6i	−0.105990	−	0.601098i	−0.990820	−	0.135185i	$-0.956837\pi$
$353$	−248142.	−	1.40729e6i	−0.105990	−	0.601098i	0.884831	−	0.465913i	$-0.154274\pi$
$354$		0			0
$355$	394308.	−	143516.i	0.166060	−	0.0604408i
$356$		0			0
$357$	357756.	+	4.60720e6i	0.148565	+	1.91323i
$358$		0			0
$359$	1.67811e6	+	2.90657e6i	0.687202	+	1.19027i	0.972739	+	0.231901i	$0.0744945\pi$
$359$	1.67811e6	+	2.90657e6i	0.687202	+	1.19027i	−0.285538	+	0.958368i	$0.592172\pi$
$360$		0			0
$361$	1.13610e6	−	1.96778e6i	0.458827	−	0.794712i
$362$		0			0
$363$	1.15619e6	+	1.17901e6i	0.460536	+	0.469624i
$364$		0			0
$365$	16717.7	−	94810.8i	0.00656817	−	0.0372500i
$366$		0			0
$367$	−1.00317e6	+	841759.i	−0.388785	+	0.326229i	−0.816140	−	0.577855i	$-0.803890\pi$
$367$	−1.00317e6	+	841759.i	−0.388785	+	0.326229i	0.427355	+	0.904084i	$0.359446\pi$
$368$		0			0
$369$	−3.31141e6	+	517392.i	−1.26604	+	0.197812i
$370$		0			0
$371$	−7.77333e6	−	2.82926e6i	−2.93206	−	1.06718i
$372$		0			0
$373$	−3.11712e6	−	2.61558e6i	−1.16006	−	0.973409i	−0.160157	−	0.987092i	$-0.551200\pi$
$373$	−3.11712e6	−	2.61558e6i	−1.16006	−	0.973409i	−0.999906	+	0.0136829i	$0.995644\pi$
$374$		0			0
$375$	−1.17491e6	−	2.58525e6i	−0.431445	−	0.949345i
$376$		0			0
$377$	2.51960e6			0.913015
$378$		0			0
$379$	1.01902e6			0.364407			0.182204	−	0.983261i	$-0.441677\pi$
$379$	1.01902e6			0.364407			0.182204	+	0.983261i	$0.441677\pi$
$380$		0			0
$381$	3.55948e6	+	346490.i	1.25625	+	0.122286i
$382$		0			0
$383$	−2.61207e6	−	2.19179e6i	−0.909889	−	0.763488i	0.0622089	−	0.998063i	$-0.480186\pi$
$383$	−2.61207e6	−	2.19179e6i	−0.909889	−	0.763488i	−0.972098	+	0.234576i	$0.924630\pi$
$384$		0			0
$385$	−2.92717e6	−	1.06540e6i	−1.00646	−	0.366321i
$386$		0			0
$387$	1.74792e6	+	1.05523e6i	0.593258	+	0.358153i
$388$		0			0
$389$	−1.52601e6	+	1.28048e6i	−0.511309	+	0.429039i	−0.861590	−	0.507605i	$-0.830531\pi$
$389$	−1.52601e6	+	1.28048e6i	−0.511309	+	0.429039i	0.350280	+	0.936645i	$0.386086\pi$
$390$		0			0
$391$	−911376.	+	5.16867e6i	−0.301478	+	1.70977i
$392$		0			0
$393$	−1.03421e6	+	3.71417e6i	−0.337774	+	1.21305i
$394$		0			0
$395$	295781.	−	512307.i	0.0953843	−	0.165210i
$396$		0			0
$397$	−476926.	−	826060.i	−0.151871	−	0.263048i	0.780044	−	0.625724i	$-0.215197\pi$
$397$	−476926.	−	826060.i	−0.151871	−	0.263048i	−0.931915	+	0.362676i	$0.881863\pi$
$398$		0			0
$399$	1.58689e6	+	758941.i	0.499016	+	0.238658i
$400$		0			0
$401$	963530.	−	350696.i	0.299229	−	0.108911i	−0.188043	−	0.982161i	$-0.560214\pi$
$401$	963530.	−	350696.i	0.299229	−	0.108911i	0.487272	+	0.873250i	$0.337992\pi$
$402$		0			0
$403$	413838.	+	2.34699e6i	0.126931	+	0.719862i
$404$		0			0
$405$	−3.13275e6	−	122497.i	−0.949049	−	0.0371096i
$406$		0			0
$407$	371290.	+	2.10569e6i	0.111103	+	0.630098i
$408$		0			0
$409$	−199701.	+	72685.2i	−0.0590299	+	0.0214851i	−0.371366	−	0.928486i	$-0.621111\pi$
$409$	−199701.	+	72685.2i	−0.0590299	+	0.0214851i	0.312336	+	0.949972i	$0.398888\pi$
$410$		0			0
$411$	−2.62911e6	−	1.25739e6i	−0.767721	−	0.367168i
$412$		0			0
$413$	−4.10775e6	−	7.11483e6i	−1.18503	−	2.05253i
$414$		0			0
$415$	2.03074e6	−	3.51735e6i	0.578809	−	1.00253i
$416$		0			0
$417$	428910.	−	1.54035e6i	0.120789	−	0.433791i
$418$		0			0
$419$	768117.	−	4.35621e6i	0.213743	−	1.21220i	−0.669331	−	0.742964i	$-0.733419\pi$
$419$	768117.	−	4.35621e6i	0.213743	−	1.21220i	0.883074	−	0.469233i	$-0.155470\pi$
$420$		0			0
$421$	−1.61446e6	+	1.35469e6i	−0.443937	+	0.372507i	−0.837180	−	0.546927i	$-0.815797\pi$
$421$	−1.61446e6	+	1.35469e6i	−0.443937	+	0.372507i	0.393243	+	0.919434i	$0.371353\pi$
$422$		0			0
$423$	3496.79	−	178924.i	0.000950209	−	0.0486203i
$424$		0			0
$425$	341132.	+	124162.i	0.0916115	+	0.0333439i
$426$		0			0
$427$	1.71758e6	+	1.44122e6i	0.455876	+	0.382526i
$428$		0			0
$429$	−3.43969e6	−	334829.i	−0.902352	−	0.0878374i
$430$		0			0
$431$	654474.			0.169707			0.0848534	−	0.996393i	$-0.472958\pi$
$431$	654474.			0.169707			0.0848534	+	0.996393i	$0.472958\pi$
$432$		0			0
$433$	−3.22891e6			−0.827629			−0.413815	−	0.910361i	$-0.635804\pi$
$433$	−3.22891e6			−0.827629			−0.413815	+	0.910361i	$0.635804\pi$
$434$		0			0
$435$	−913687.	−	2.01046e6i	−0.231513	−	0.509416i
$436$		0			0
$437$	1.53043e6	+	1.28418e6i	0.383363	+	0.321680i
$438$		0			0
$439$	3.07078e6	+	1.11767e6i	0.760480	+	0.276792i	0.693009	−	0.720929i	$-0.256285\pi$
$439$	3.07078e6	+	1.11767e6i	0.760480	+	0.276792i	0.0674712	+	0.997721i	$0.478507\pi$
$440$		0			0
$441$	3.99635e6	−	1.03462e7i	0.978514	−	2.53329i
$442$		0			0
$443$	−4.58920e6	+	3.85079e6i	−1.11103	+	0.932268i	−0.998117	−	0.0613365i	$-0.980464\pi$
$443$	−4.58920e6	+	3.85079e6i	−1.11103	+	0.932268i	−0.112917	+	0.993604i	$0.536019\pi$
$444$		0			0
$445$	324441.	−	1.84000e6i	0.0776669	−	0.440471i
$446$		0			0
$447$	−332064.	−	338617.i	−0.0786056	−	0.0801568i
$448$		0			0
$449$	−2.61981e6	+	4.53765e6i	−0.613274	+	1.06222i	0.377410	+	0.926046i	$0.376815\pi$
$449$	−2.61981e6	+	4.53765e6i	−0.613274	+	1.06222i	−0.990685	+	0.136176i	$0.956519\pi$
$450$		0			0
$451$	1.61907e6	+	2.80431e6i	0.374821	+	0.649209i
$452$		0			0
$453$	113099.	+	1.45650e6i	0.0258949	+	0.333476i
$454$		0			0
$455$	−1.17736e7	+	4.28525e6i	−2.66613	+	0.970392i
$456$		0			0
$457$	246801.	+	1.39968e6i	0.0552785	+	0.313500i	0.999892	−	0.0146846i	$-0.00467441\pi$
$457$	246801.	+	1.39968e6i	0.0552785	+	0.313500i	−0.944614	+	0.328184i	$0.893563\pi$
$458$		0			0
$459$	3.26912e6	−	3.08288e6i	0.724268	−	0.683007i
$460$		0			0
$461$	−200528.	−	1.13725e6i	−0.0439464	−	0.249233i	0.954918	−	0.296869i	$-0.0959423\pi$
$461$	−200528.	−	1.13725e6i	−0.0439464	−	0.249233i	−0.998865	+	0.0476360i	$0.984831\pi$
$462$		0			0
$463$	−5.20819e6	+	1.89563e6i	−1.12910	+	0.410960i	−0.837967	−	0.545721i	$-0.816256\pi$
$463$	−5.20819e6	+	1.89563e6i	−1.12910	+	0.410960i	−0.291137	+	0.956681i	$0.594034\pi$
$464$		0			0
$465$	1.72266e6	−	1.18131e6i	0.369461	−	0.253356i
$466$		0			0
$467$	−69036.9	−	119575.i	−0.0146484	−	0.0253717i	0.858608	−	0.512632i	$-0.171330\pi$
$467$	−69036.9	−	119575.i	−0.0146484	−	0.0253717i	−0.873257	+	0.487261i	$0.837996\pi$
$468$		0			0
$469$	−3.36600e6	+	5.83009e6i	−0.706615	+	1.22389i
$470$		0			0
$471$	2.00522e6	−	516353.i	0.416495	−	0.107249i
$472$		0			0
$473$	342544.	−	1.94266e6i	0.0703985	−	0.399250i
$474$		0			0
$475$	105858.	−	88825.3i	0.0215273	−	0.0180635i
$476$		0			0
$477$	2.60292e6	+	7.61102e6i	0.523800	+	1.53161i
$478$		0			0
$479$	8.37247e6	+	3.04733e6i	1.66730	+	0.606849i	0.991485	−	0.130220i	$-0.0415682\pi$
$479$	8.37247e6	+	3.04733e6i	1.66730	+	0.606849i	0.675818	+	0.737068i	$0.263790\pi$
$480$		0			0
$481$	6.58807e6	+	5.52805e6i	1.29836	+	1.08945i
$482$		0			0
$483$	1.00233e7	−	1.40212e7i	1.95499	−	2.73475i
$484$		0			0
$485$	2.44207e6			0.471416
$486$		0			0
$487$	4.99941e6			0.955204			0.477602	−	0.878576i	$-0.341506\pi$
$487$	4.99941e6			0.955204			0.477602	+	0.878576i	$0.341506\pi$
$488$		0			0
$489$	2.10378e6	−	2.94288e6i	0.397857	−	0.556546i
$490$		0			0
$491$	−197576.	−	165786.i	−0.0369854	−	0.0310344i	0.624108	−	0.781338i	$-0.285463\pi$
$491$	−197576.	−	165786.i	−0.0369854	−	0.0310344i	−0.661093	+	0.750304i	$0.729907\pi$
$492$		0			0
$493$	2.97425e6	+	1.08254e6i	0.551138	+	0.200598i
$494$		0			0
$495$	980172.	+	2.86605e6i	0.179800	+	0.525740i
$496$		0			0
$497$	1.51295e6	−	1.26952e6i	0.274747	−	0.230540i
$498$		0			0
$499$	726410.	−	4.11967e6i	0.130596	−	0.740648i	−0.847230	−	0.531227i	$-0.821731\pi$
$499$	726410.	−	4.11967e6i	0.130596	−	0.740648i	0.977826	−	0.209421i	$-0.0671578\pi$
$500$		0			0
$501$	2.85460e6	−	735072.i	0.508103	−	0.130839i
$502$		0			0
$503$	3.27004e6	−	5.66388e6i	0.576280	−	0.998146i	−0.419621	−	0.907699i	$-0.637837\pi$
$503$	3.27004e6	−	5.66388e6i	0.576280	−	0.998146i	0.995901	−	0.0904468i	$-0.0288295\pi$
$504$		0			0
$505$	3.77548e6	+	6.53933e6i	0.658785	+	1.14105i
$506$		0			0
$507$	−6.69057e6	+	4.58803e6i	−1.15596	+	0.792695i
$508$		0			0
$509$	939494.	−	341948.i	0.160731	−	0.0585013i	−0.260402	−	0.965500i	$-0.583855\pi$
$509$	939494.	−	341948.i	0.160731	−	0.0585013i	0.421133	+	0.906999i	$0.361633\pi$
$510$		0			0
$511$	−78686.0	−	446250.i	−0.0133305	−	0.0756008i
$512$		0			0
$513$	−394090.	−	1.66445e6i	−0.0661154	−	0.279240i
$514$		0			0
$515$	−1.42227e6	−	8.06611e6i	−0.236301	−	1.34013i
$516$		0			0
$517$	−162473.	+	59135.4i	−0.0267335	+	0.00973019i
$518$		0			0
$519$	847761.	+	1.09175e7i	0.138151	+	1.77912i
$520$		0			0
$521$	686495.	+	1.18904e6i	0.110801	+	0.191913i	0.916093	−	0.400965i	$-0.131325\pi$
$521$	686495.	+	1.18904e6i	0.110801	+	0.191913i	−0.805293	+	0.592878i	$0.797992\pi$
$522$		0			0
$523$	−2.89660e6	+	5.01706e6i	−0.463057	+	0.802038i	−0.999111	−	0.0421453i	$-0.986581\pi$
$523$	−2.89660e6	+	5.01706e6i	−0.463057	+	0.802038i	0.536055	+	0.844183i	$0.319914\pi$
$524$		0			0
$525$	−834704.	−	851177.i	−0.132170	−	0.134779i
$526$		0			0
$527$	−519865.	+	2.94830e6i	−0.0815388	+	0.462429i
$528$		0			0
$529$	1.00650e7	−	8.44555e6i	1.56378	−	1.31217i
$530$		0			0
$531$	−2.87845e6	+	7.45207e6i	−0.443019	+	1.14694i
$532$		0			0
$533$	1.22389e7	+	4.45460e6i	1.86606	+	0.679189i
$534$		0			0
$535$	−6.38783e6	−	5.36003e6i	−0.964871	−	0.809623i
$536$		0			0
$537$	2.45654e6	+	5.40533e6i	0.367611	+	0.808885i
$538$		0			0
$539$	−1.07158e7			−1.58874
$540$		0			0
$541$	−6.90272e6			−1.01397			−0.506987	−	0.861954i	$-0.669241\pi$
$541$	−6.90272e6			−1.01397			−0.506987	+	0.861954i	$0.669241\pi$
$542$		0			0
$543$	−6.41352e6	−	624309.i	−0.933462	−	0.0908657i
$544$		0			0
$545$	9.72858e6	+	8.16325e6i	1.40300	+	1.17726i
$546$		0			0
$547$	−2.79865e6	−	1.01863e6i	−0.399927	−	0.145562i	0.134223	−	0.990951i	$-0.457146\pi$
$547$	−2.79865e6	−	1.01863e6i	−0.399927	−	0.145562i	−0.534150	+	0.845390i	$0.679368\pi$
$548$		0			0
$549$	42601.2	−	2.17982e6i	0.00603241	−	0.308666i
$550$		0			0
$551$	922950.	−	774447.i	0.129509	−	0.108671i
$552$		0			0
$553$	483493.	−	2.74203e6i	0.0672322	−	0.381293i
$554$		0			0
$555$	2.02195e6	−	7.26146e6i	0.278636	−	1.00067i
$556$		0			0
$557$	−2.96376e6	+	5.13339e6i	−0.404767	+	0.701077i	−0.994294	−	0.106671i	$-0.965981\pi$
$557$	−2.96376e6	+	5.13339e6i	−0.404767	+	0.701077i	0.589527	+	0.807749i	$0.299314\pi$
$558$		0			0
$559$	−3.96714e6	−	6.87130e6i	−0.536968	−	0.930056i
$560$		0			0
$561$	−3.91651e6	−	1.87310e6i	−0.525402	−	0.251278i
$562$		0			0
$563$	1114.70	−	405.719i	0.000148214	−	5.39454e-5i	−0.341946	−	0.939720i	$-0.611086\pi$
$563$	1114.70	−	405.719i	0.000148214	−	5.39454e-5i	0.342094	+	0.939666i	$0.388864\pi$
$564$		0			0
$565$	−1.26747e6	−	7.18819e6i	−0.167039	−	0.947324i
$566$		0			0
$567$	−1.40530e7	+	4.50132e6i	−1.83574	+	0.588007i
$568$		0			0
$569$	−721446.	−	4.09153e6i	−0.0934164	−	0.529791i	−0.995221	−	0.0976471i	$-0.968868\pi$
$569$	−721446.	−	4.09153e6i	−0.0934164	−	0.529791i	0.901805	−	0.432144i	$-0.142243\pi$
$570$		0			0
$571$	8.88019e6	−	3.23213e6i	1.13981	−	0.414857i	0.297965	−	0.954577i	$-0.403692\pi$
$571$	8.88019e6	−	3.23213e6i	1.13981	−	0.414857i	0.841844	+	0.539720i	$0.181470\pi$
$572$		0			0
$573$	−966422.	−	462198.i	−0.122965	−	0.0588088i
$574$		0			0
$575$	−676998.	−	1.17260e6i	−0.0853922	−	0.147904i
$576$		0			0
$577$	6.95682e6	−	1.20496e7i	0.869903	−	1.50672i	0.00780863	−	0.999970i	$-0.497514\pi$
$577$	6.95682e6	−	1.20496e7i	0.869903	−	1.50672i	0.862095	−	0.506747i	$-0.169152\pi$
$578$		0			0
$579$	−3.45087e6	+	1.23932e7i	−0.427792	+	1.53634i
$580$		0			0
$581$	3.31953e6	−	1.88260e7i	0.407977	−	2.31375i
$582$		0			0
$583$	5.95334e6	−	4.99544e6i	0.725420	−	0.608699i
$584$		0			0
$585$	1.04300e7	+	6.29664e6i	1.26007	+	0.760711i
$586$		0			0
$587$	644050.	+	234415.i	0.0771479	+	0.0280796i	0.380306	−	0.924861i	$-0.375819\pi$
$587$	644050.	+	234415.i	0.0771479	+	0.0280796i	−0.303158	+	0.952940i	$0.598041\pi$
$588$		0			0
$589$	872985.	+	732521.i	0.103686	+	0.0870026i
$590$		0			0
$591$	7.71017e6	+	750528.i	0.908019	+	0.0883890i
$592$		0			0
$593$	4.65049e6			0.543078			0.271539	−	0.962427i	$-0.412467\pi$
$593$	4.65049e6			0.543078			0.271539	+	0.962427i	$0.412467\pi$
$594$		0			0
$595$	−1.57393e7			−1.82260
$596$		0			0
$597$	3.70757e6	+	8.15807e6i	0.425749	+	0.936810i
$598$		0			0
$599$	6.12586e6	+	5.14021e6i	0.697590	+	0.585347i	0.921087	−	0.389357i	$-0.127303\pi$
$599$	6.12586e6	+	5.14021e6i	0.697590	+	0.585347i	−0.223497	+	0.974705i	$0.571747\pi$
$600$		0			0
$601$	−1.34432e6	−	489292.i	−0.151815	−	0.0552563i	0.264995	−	0.964250i	$-0.414630\pi$
$601$	−1.34432e6	−	489292.i	−0.151815	−	0.0552563i	−0.416810	+	0.908994i	$0.636852\pi$
$602$		0			0
$603$	6.46767e6	−	1.01054e6i	0.724360	−	0.113178i
$604$		0			0
$605$	−4.30850e6	+	3.61526e6i	−0.478561	+	0.401560i
$606$		0			0
$607$	−2.98251e6	+	1.69147e7i	−0.328557	+	1.86334i	0.154845	+	0.987939i	$0.450512\pi$
$607$	−2.98251e6	+	1.69147e7i	−0.328557	+	1.86334i	−0.483402	+	0.875399i	$0.660599\pi$
$608$		0			0
$609$	−7.27759e6	−	7.42121e6i	−0.795141	−	0.810833i
$610$		0			0
$611$	−347719.	+	602266.i	−0.0376812	+	0.0652658i
$612$		0			0
$613$	−6.20607e6	−	1.07492e7i	−0.667061	−	1.15538i	−0.978722	−	0.205190i	$-0.934219\pi$
$613$	−6.20607e6	−	1.07492e7i	−0.667061	−	1.15538i	0.311662	−	0.950193i	$-0.399114\pi$
$614$		0			0
$615$	−883765.	−	1.13812e7i	−0.0942213	−	1.21339i
$616$		0			0
$617$	−1.82640e6	+	664754.i	−0.193144	+	0.0702988i	−0.436781	−	0.899568i	$-0.643882\pi$
$617$	−1.82640e6	+	664754.i	−0.193144	+	0.0702988i	0.243637	+	0.969866i	$0.421659\pi$
$618$		0			0
$619$	2.27754e6	+	1.29166e7i	0.238913	+	1.35494i	0.834214	+	0.551441i	$0.185922\pi$
$619$	2.27754e6	+	1.29166e7i	0.238913	+	1.35494i	−0.595301	+	0.803503i	$0.702967\pi$
$620$		0			0
$621$	−1.67315e7	+	970758.i	−1.74102	+	0.101014i
$622$		0			0
$623$	−1.52706e6	−	8.66040e6i	−0.157629	−	0.893960i
$624$		0			0
$625$	8.19001e6	−	2.98092e6i	0.838657	−	0.305246i
$626$		0			0
$627$	−1.36290e6	+	934604.i	−0.138451	+	0.0949421i
$628$		0			0
$629$	5.40175e6	+	9.35610e6i	0.544387	+	0.942906i
$630$		0			0
$631$	5.09558e6	−	8.82580e6i	0.509471	−	0.882430i	−0.490468	−	0.871459i	$-0.663174\pi$
$631$	5.09558e6	−	8.82580e6i	0.509471	−	0.882430i	0.999940	−	0.0109714i	$-0.00349239\pi$
$632$		0			0
$633$	−9.27325e6	+	2.38790e6i	−0.919862	+	0.236868i
$634$		0			0
$635$	−2.11518e6	+	1.19958e7i	−0.208167	+	1.18058i
$636$		0			0
$637$	−3.30172e7	+	2.77047e7i	−3.22397	+	2.70524i
$638$		0			0
$639$	−1.88443e6	−	370381.i	−0.182569	−	0.0358836i
$640$		0			0
$641$	−4.65907e6	−	1.69576e6i	−0.447872	−	0.163012i	0.108230	−	0.994126i	$-0.465482\pi$
$641$	−4.65907e6	−	1.69576e6i	−0.447872	−	0.163012i	−0.556102	+	0.831114i	$0.687704\pi$
$642$		0			0
$643$	613528.	+	514811.i	0.0585203	+	0.0491044i	0.671579	−	0.740933i	$-0.265617\pi$
$643$	613528.	+	514811.i	0.0585203	+	0.0491044i	−0.613058	+	0.790038i	$0.710061\pi$
$644$		0			0
$645$	−4.04420e6	+	5.65726e6i	−0.382766	+	0.535435i
$646$		0			0
$647$	−1.56281e7			−1.46773			−0.733863	−	0.679298i	$-0.762285\pi$
$647$	−1.56281e7			−1.46773			−0.733863	+	0.679298i	$0.762285\pi$
$648$		0			0
$649$	7.71826e6			0.719296
$650$		0			0
$651$	5.71749e6	−	7.99795e6i	0.528753	−	0.739650i
$652$		0			0
$653$	1.24980e7	+	1.04871e7i	1.14699	+	0.962438i	0.999645	−	0.0266475i	$-0.00848318\pi$
$653$	1.24980e7	+	1.04871e7i	1.14699	+	0.962438i	0.147344	+	0.989085i	$0.452928\pi$
$654$		0			0
$655$	−1.23397e7	−	4.49129e6i	−1.12383	−	0.409042i
$656$		0			0
$657$	−289769.	+	331938.i	−0.0261901	+	0.0300016i
$658$		0			0
$659$	3.68179e6	−	3.08939e6i	0.330252	−	0.277115i	−0.462550	−	0.886593i	$-0.653066\pi$
$659$	3.68179e6	−	3.08939e6i	0.330252	−	0.277115i	0.792803	+	0.609478i	$0.208621\pi$
$660$		0			0
$661$	3.45628e6	−	1.96015e7i	0.307684	−	1.74496i	−0.302909	−	0.953019i	$-0.597958\pi$
$661$	3.45628e6	−	1.96015e7i	0.307684	−	1.74496i	0.610593	−	0.791944i	$-0.290931\pi$
$662$		0			0
$663$	−1.69102e7	+	4.35444e6i	−1.49405	+	0.384723i
$664$		0			0
$665$	−2.99562e6	+	5.18857e6i	−0.262683	+	0.454981i
$666$		0			0
$667$	−5.90259e6	−	1.02236e7i	−0.513722	−	0.889792i
$668$		0			0
$669$	−2.77869e6	+	1.90547e6i	−0.240035	+	0.164603i
$670$		0			0
$671$	−1.97940e6	+	720443.i	−0.169718	+	0.0617722i
$672$		0			0
$673$	156871.	+	889659.i	0.0133507	+	0.0757157i	0.990755	−	0.135662i	$-0.0433161\pi$
$673$	156871.	+	889659.i	0.0133507	+	0.0757157i	−0.977404	+	0.211378i	$0.932205\pi$
$674$		0			0
$675$	−134836.	+	1.15137e6i	−0.0113906	+	0.0972648i
$676$		0			0
$677$	−429605.	−	2.43641e6i	−0.0360245	−	0.204305i	0.961483	−	0.274864i	$-0.0886328\pi$
$677$	−429605.	−	2.43641e6i	−0.0360245	−	0.204305i	−0.997508	+	0.0705590i	$0.977522\pi$
$678$		0			0
$679$	1.08010e7	−	3.93125e6i	0.899064	−	0.327233i
$680$		0			0
$681$	−388148.	−	4.99859e6i	−0.0320723	−	0.413028i
$682$		0			0
$683$	9.02576e6	+	1.56331e7i	0.740341	+	1.28231i	0.952340	+	0.305039i	$0.0986694\pi$
$683$	9.02576e6	+	1.56331e7i	0.740341	+	1.28231i	−0.211999	+	0.977270i	$0.567997\pi$
$684$		0			0
$685$	4.96305e6	−	8.59625e6i	0.404131	−	0.699975i
$686$		0			0
$687$	−2.45295e6	−	2.50136e6i	−0.198288	−	0.202201i
$688$		0			0
$689$	5.42799e6	−	3.07836e7i	0.435603	−	2.47043i
$690$		0			0
$691$	−3.04958e6	+	2.55890e6i	−0.242966	+	0.203872i	−0.756136	−	0.654414i	$-0.772915\pi$
$691$	−3.04958e6	+	2.55890e6i	−0.242966	+	0.203872i	0.513171	+	0.858287i	$0.328471\pi$
$692$		0			0
$693$	8.94897e6	+	1.10984e7i	0.707848	+	0.877860i
$694$		0			0
$695$	5.11757e6	+	1.86264e6i	0.401885	+	0.146274i
$696$		0			0
$697$	1.25335e7	+	1.05168e7i	0.977213	+	0.819979i
$698$		0			0
$699$	−5.04478e6	−	1.11004e7i	−0.390525	−	0.859305i
$700$		0			0
$701$	4.32695e6			0.332573			0.166286	−	0.986078i	$-0.446822\pi$
$701$	4.32695e6			0.332573			0.166286	+	0.986078i	$0.446822\pi$
$702$		0			0
$703$	4.11241e6			0.313840
$704$		0			0
$705$	606660.	+	59053.9i	0.0459698	+	0.00447482i
$706$		0			0
$707$	2.72256e7	+	2.28450e7i	2.04846	+	1.71887i
$708$		0			0
$709$	−2.18118e7	−	7.93886e6i	−1.62958	−	0.593120i	−0.644410	−	0.764680i	$-0.722897\pi$
$709$	−2.18118e7	−	7.93886e6i	−1.62958	−	0.593120i	−0.985174	+	0.171561i	$0.945119\pi$
$710$		0			0
$711$	−2.37073e6	+	1.30765e6i	−0.175876	+	0.0970104i
$712$		0			0
$713$	8.55373e6	−	7.17743e6i	0.630132	−	0.528744i
$714$		0			0
$715$	2.04399e6	−	1.15921e7i	0.149525	−	0.848000i
$716$		0			0
$717$	−3.74491e6	+	1.34492e7i	−0.272047	+	0.977007i
$718$		0			0
$719$	6.89038e6	−	1.19345e7i	0.497074	−	0.860958i	−0.502920	−	0.864333i	$-0.667741\pi$
$719$	6.89038e6	−	1.19345e7i	0.497074	−	0.860958i	0.999994	+	0.00337520i	$0.00107436\pi$
$720$		0			0
$721$	−1.92754e7	−	3.33860e7i	−1.38091	−	2.39181i
$722$		0			0
$723$	−2.18999e7	−	1.04738e7i	−1.55810	−	0.745174i
$724$		0			0
$725$	−767305.	+	279276.i	−0.0542154	+	0.0197328i
$726$		0			0
$727$	21312.4	+	120869.i	0.00149554	+	0.00848161i	0.985546	−	0.169406i	$-0.0541848\pi$
$727$	21312.4	+	120869.i	0.00149554	+	0.00848161i	−0.984051	+	0.177887i	$0.943074\pi$
$728$		0			0
$729$	1.19848e7	+	7.89019e6i	0.835243	+	0.549881i
$730$		0			0
$731$	−1.73077e6	−	9.81566e6i	−0.119797	−	0.679401i
$732$		0			0
$733$	−7.06772e6	+	2.57244e6i	−0.485869	+	0.176842i	−0.573327	−	0.819326i	$-0.694348\pi$
$733$	−7.06772e6	+	2.57244e6i	−0.485869	+	0.176842i	0.0874584	+	0.996168i	$0.472125\pi$
$734$		0			0
$735$	3.40795e7	+	1.62988e7i	2.32689	+	1.11285i
$736$		0			0
$737$	−3.16228e6	−	5.47723e6i	−0.214453	−	0.371443i
$738$		0			0
$739$	−1.18476e7	+	2.05207e7i	−0.798032	+	1.38223i	0.122864	+	0.992423i	$0.460792\pi$
$739$	−1.18476e7	+	2.05207e7i	−0.798032	+	1.38223i	−0.920896	+	0.389808i	$0.872541\pi$
$740$		0			0
$741$	−1.78300e6	+	6.40333e6i	−0.119291	+	0.428411i
$742$		0			0
$743$	−2.12952e6	+	1.20771e7i	−0.141517	+	0.802585i	0.828580	+	0.559870i	$0.189149\pi$
$743$	−2.12952e6	+	1.20771e7i	−0.141517	+	0.802585i	−0.970098	+	0.242715i	$0.921962\pi$
$744$		0			0
$745$	1.23742e6	−	1.03832e6i	0.0816822	−	0.0685395i
$746$		0			0
$747$	−1.62767e7	+	8.97796e6i	−1.06725	+	0.588676i
$748$		0			0
$749$	−3.68813e7	−	1.34237e7i	−2.40216	−	0.874314i
$750$		0			0
$751$	−2.16460e7	−	1.81631e7i	−1.40048	−	1.17514i	−0.960885	−	0.276949i	$-0.910677\pi$
$751$	−2.16460e7	−	1.81631e7i	−1.40048	−	1.17514i	−0.439597	−	0.898195i	$-0.644879\pi$
$752$		0			0
$753$	3.32112e6	+	323287.i	0.213451	+	0.0207779i
$754$		0			0
$755$	−4.97574e6			−0.317680
$756$		0			0
$757$	2.15937e7			1.36958			0.684789	−	0.728742i	$-0.259894\pi$
$757$	2.15937e7			1.36958			0.684789	+	0.728742i	$0.259894\pi$
$758$		0			0
$759$	6.69945e6	+	1.47414e7i	0.422119	+	0.928823i
$760$		0			0
$761$	1.58430e7	+	1.32938e7i	0.991689	+	0.832126i	0.985811	−	0.167857i	$-0.0536847\pi$
$761$	1.58430e7	+	1.32938e7i	0.991689	+	0.832126i	0.00587740	+	0.999983i	$0.498129\pi$
$762$		0			0
$763$	5.61697e7	+	2.04441e7i	3.49294	+	1.27132i
$764$		0			0
$765$	9.60670e6	+	1.19141e7i	0.593500	+	0.736048i
$766$		0			0
$767$	2.37813e7	−	1.99549e7i	1.45964	−	1.22479i
$768$		0			0
$769$	−1.90664e6	+	1.08131e7i	−0.116266	+	0.659377i	0.869850	+	0.493317i	$0.164216\pi$
$769$	−1.90664e6	+	1.08131e7i	−0.116266	+	0.659377i	−0.986116	+	0.166060i	$0.946895\pi$
$770$		0			0
$771$	−1.59846e6	−	1.63001e6i	−0.0968425	−	0.0987536i
$772$		0			0
$773$	−1.09395e7	+	1.89478e7i	−0.658492	+	1.14054i	0.322515	+	0.946564i	$0.395472\pi$
$773$	−1.09395e7	+	1.89478e7i	−0.658492	+	1.14054i	−0.981006	+	0.193976i	$0.937861\pi$
$774$		0			0
$775$	−386172.	−	668870.i	−0.0230955	−	0.0400025i
$776$		0			0
$777$	−2.74666e6	−	3.53716e7i	−0.163212	−	2.10185i
$778$		0			0
$779$	5.85242e6	−	2.13011e6i	0.345535	−	0.125764i
$780$		0			0
$781$	322200.	+	1.82729e6i	0.0189016	+	0.107196i
$782$		0			0
$783$	−1.17560e6	+	1.00385e7i	−0.0685261	+	0.585148i
$784$		0			0
$785$	1.22466e6	+	6.94540e6i	0.0709320	+	0.402275i
$786$		0			0
$787$	1.08910e7	−	3.96398e6i	0.626800	−	0.228137i	−0.00903787	−	0.999959i	$-0.502877\pi$
$787$	1.08910e7	−	3.96398e6i	0.626800	−	0.228137i	0.635838	+	0.771823i	$0.280655\pi$
$788$		0			0
$789$	2.29583e7	−	1.57435e7i	1.31295	−	0.900347i
$790$		0			0
$791$	−1.71775e7	−	2.97522e7i	−0.976152	−	1.69075i
$792$		0			0
$793$	−4.23623e6	+	7.33737e6i	−0.239220	+	0.414341i
$794$		0			0
$795$	−2.65315e7	+	6.83198e6i	−1.48883	+	0.383380i
$796$		0			0
$797$	−3.40548e6	+	1.93134e7i	−0.189903	+	1.07699i	0.729589	+	0.683886i	$0.239711\pi$
$797$	−3.40548e6	+	1.93134e7i	−0.189903	+	1.07699i	−0.919492	+	0.393108i	$0.871400\pi$
$798$		0			0
$799$	−669225.	+	561546.i	−0.0370856	+	0.0311185i
$800$		0			0
$801$	−5.62355e6	+	6.44195e6i	−0.309692	+	0.354761i
$802$		0			0
$803$	400035.	+	145601.i	0.0218932	+	0.00796847i
$804$		0			0
$805$	4.49696e7	+	3.77340e7i	2.44585	+	2.05231i
$806$		0			0
$807$	1.83848e7	−	2.57178e7i	0.993748	−	1.39011i
$808$		0			0
$809$	4.17145e6			0.224087			0.112043	−	0.993703i	$-0.464260\pi$
$809$	4.17145e6			0.224087			0.112043	+	0.993703i	$0.464260\pi$
$810$		0			0
$811$	1.32047e7			0.704981			0.352490	−	0.935815i	$-0.385335\pi$
$811$	1.32047e7			0.704981			0.352490	+	0.935815i	$0.385335\pi$
$812$		0			0
$813$	2.17846e6	−	3.04735e6i	0.115591	−	0.161695i
$814$		0			0
$815$	9.43858e6	+	7.91991e6i	0.497752	+	0.417663i
$816$		0			0
$817$	−3.56522e6	−	1.29763e6i	−0.186866	−	0.0680138i
$818$		0			0
$819$	5.62671e7	+	1.10592e7i	2.93120	+	0.576120i
$820$		0			0
$821$	862864.	−	724029.i	0.0446771	−	0.0374885i	−0.620176	−	0.784463i	$-0.712939\pi$
$821$	862864.	−	724029.i	0.0446771	−	0.0374885i	0.664853	+	0.746974i	$0.268494\pi$
$822$		0			0
$823$	4.22082e6	−	2.39375e7i	0.217219	−	1.23191i	−0.659795	−	0.751445i	$-0.729357\pi$
$823$	4.22082e6	−	2.39375e7i	0.217219	−	1.23191i	0.877014	−	0.480464i	$-0.159532\pi$
$824$		0			0
$825$	1.08462e6	−	279293.i	0.0554807	−	0.0142865i
$826$		0			0
$827$	−1.12696e7	+	1.95194e7i	−0.572985	+	0.992439i	0.423272	+	0.906002i	$0.360881\pi$
$827$	−1.12696e7	+	1.95194e7i	−0.572985	+	0.992439i	−0.996257	+	0.0864365i	$0.972452\pi$
$828$		0			0
$829$	1.74525e7	+	3.02287e7i	0.882007	+	1.52768i	0.849106	+	0.528222i	$0.177141\pi$
$829$	1.74525e7	+	3.02287e7i	0.882007	+	1.52768i	0.0329004	+	0.999459i	$0.489526\pi$
$830$		0			0
$831$	1.27903e7	−	8.77086e6i	0.642506	−	0.440595i
$832$		0			0
$833$	−5.08783e7	+	1.85182e7i	−2.54050	+	0.924667i
$834$		0			0
$835$	1.74341e6	+	9.88737e6i	0.0865333	+	0.490755i
$836$		0			0
$837$	−9.54392e6	+	553738.i	−0.470883	+	0.0273206i
$838$		0			0
$839$	3.60784e6	+	2.04611e7i	0.176946	+	1.00351i	0.935873	+	0.352337i	$0.114613\pi$
$839$	3.60784e6	+	2.04611e7i	0.176946	+	1.00351i	−0.758927	+	0.651176i	$0.774276\pi$
$840$		0			0
$841$	1.25842e7	−	4.58028e6i	0.613531	−	0.223307i
$842$		0			0
$843$	−2.53351e6	−	3.26266e7i	−0.122787	−	1.58126i
$844$		0			0
$845$	−1.38156e7	−	2.39294e7i	−0.665624	−	1.15289i
$846$		0			0
$847$	−1.32362e7	+	2.29257e7i	−0.633949	+	1.09803i
$848$		0			0
$849$	−561439.	−	572519.i	−0.0267321	−	0.0272597i
$850$		0			0
$851$	6.99706e6	−	3.96823e7i	0.331201	−	1.87833i
$852$		0			0
$853$	−383816.	+	322060.i	−0.0180613	+	0.0151553i	−0.651774	−	0.758414i	$-0.725975\pi$
$853$	−383816.	+	322060.i	−0.0180613	+	0.0151553i	0.633712	+	0.773569i	$0.281530\pi$
$854$		0			0
$855$	5.75598e6	−	899344.i	0.269280	−	0.0420737i
$856$		0			0
$857$	−9.41404e6	−	3.42643e6i	−0.437849	−	0.159364i	0.113684	−	0.993517i	$-0.463735\pi$
$857$	−9.41404e6	−	3.42643e6i	−0.437849	−	0.159364i	−0.551533	+	0.834153i	$0.685957\pi$
$858$		0			0
$859$	−2.65464e7	−	2.22751e7i	−1.22750	−	1.03000i	−0.998397	−	0.0565956i	$-0.981975\pi$
$859$	−2.65464e7	−	2.22751e7i	−1.22750	−	1.03000i	−0.229106	−	0.973402i	$-0.573580\pi$
$860$		0			0
$861$	−2.22302e7	−	4.89150e7i	−1.02197	−	2.24872i
$862$		0			0
$863$	5.65742e6			0.258578			0.129289	−	0.991607i	$-0.458730\pi$
$863$	5.65742e6			0.258578			0.129289	+	0.991607i	$0.458730\pi$
$864$		0			0
$865$	−3.72968e7			−1.69485
$866$		0			0
$867$	196859.	+	19162.8i	0.00889420	+	0.000865785i
$868$		0			0
$869$	2.00382e6	+	1.68141e6i	0.0900140	+	0.0755307i
$870$		0			0
$871$	−2.39044e7	−	8.70048e6i	−1.06766	−	0.388596i
$872$		0			0
$873$	−9.56840e6	−	5.77650e6i	−0.424917	−	0.256525i
$874$		0			0
$875$	3.48730e7	−	2.92619e7i	1.53982	−	1.29206i
$876$		0			0
$877$	−4.40149e6	+	2.49621e7i	−0.193242	+	1.09593i	0.721659	+	0.692248i	$0.243380\pi$
$877$	−4.40149e6	+	2.49621e7i	−0.193242	+	1.09593i	−0.914901	+	0.403679i	$0.867731\pi$
$878$		0			0
$879$	−5.13756e6	+	1.84506e7i	−0.224277	+	0.805450i
$880$		0			0
$881$	−4.36165e6	+	7.55460e6i	−0.189326	+	0.327923i	−0.945026	−	0.326996i	$-0.893964\pi$
$881$	−4.36165e6	+	7.55460e6i	−0.189326	+	0.327923i	0.755699	+	0.654919i	$0.227297\pi$
$882$		0			0
$883$	−7.93896e6	−	1.37507e7i	−0.342659	−	0.593502i	0.642267	−	0.766481i	$-0.277994\pi$
$883$	−7.93896e6	−	1.37507e7i	−0.342659	−	0.593502i	−0.984926	+	0.172979i	$0.944661\pi$
$884$		0			0
$885$	−2.45464e7	−	1.17395e7i	−1.05349	−	0.503839i
$886$		0			0
$887$	−4.19102e7	+	1.52541e7i	−1.78859	+	0.650993i	−0.789272	+	0.614044i	$0.789542\pi$
$887$	−4.19102e7	+	1.52541e7i	−1.78859	+	0.650993i	−0.999317	+	0.0369494i	$0.988236\pi$
$888$		0			0
$889$	9.95561e6	+	5.64610e7i	0.422487	+	2.39604i
$890$		0			0
$891$	2.93892e6	−	1.35481e7i	0.124020	−	0.571721i
$892$		0			0
$893$	57745.8	+	327493.i	0.00242322	+	0.0137427i
$894$		0			0
$895$	−1.90030e7	+	6.91651e6i	−0.792983	+	0.288622i
$896$		0			0
$897$	5.87546e7	+	2.80998e7i	2.43815	+	1.16606i
$898$		0			0
$899$	−3.36694e6	−	5.83172e6i	−0.138943	−	0.240656i
$900$		0			0
$901$	1.96335e7	−	3.40063e7i	0.805725	−	1.39556i
$902$		0			0
$903$	−8.78000e6	+	3.15318e7i	−0.358323	+	1.28685i
$904$		0			0
$905$	3.81116e6	−	2.16141e7i	0.154680	−	0.877236i
$906$		0			0
$907$	−4.72125e6	+	3.96160e6i	−0.190563	+	0.159902i	−0.733078	−	0.680145i	$-0.761917\pi$
$907$	−4.72125e6	+	3.96160e6i	−0.190563	+	0.159902i	0.542514	+	0.840046i	$0.317472\pi$
$908$		0			0
$909$	675278.	−	3.45526e7i	0.0271065	−	1.38698i
$910$		0			0
$911$	1.87563e7	+	6.82674e6i	0.748776	+	0.272532i	0.688091	−	0.725625i	$-0.258449\pi$
$911$	1.87563e7	+	6.82674e6i	0.748776	+	0.272532i	0.0606853	+	0.998157i	$0.480671\pi$
$912$		0			0
$913$	1.37577e7	+	1.15441e7i	0.546221	+	0.458334i
$914$		0			0
$915$	7.39090e6	+	719450.i	0.291840	+	0.0284085i
$916$		0			0
$917$	−6.18073e7			−2.42726
$918$		0			0
$919$	−3.20033e7			−1.24999			−0.624995	−	0.780629i	$-0.714899\pi$
$919$	−3.20033e7			−1.24999			−0.624995	+	0.780629i	$0.714899\pi$
$920$		0			0
$921$	5.62394e6	+	1.23748e7i	0.218470	+	0.480718i
$922$		0			0
$923$	5.71704e6	+	4.79717e6i	0.220885	+	0.185345i
$924$		0			0
$925$	−2.61903e6	−	953249.i	−0.100644	−	0.0366313i
$926$		0			0
$927$	−1.35070e7	+	3.49685e7i	−0.516248	+	1.33653i
$928$		0			0
$929$	−1.55873e7	+	1.30793e7i	−0.592560	+	0.497217i	−0.889045	−	0.457821i	$-0.848630\pi$
$929$	−1.55873e7	+	1.30793e7i	−0.592560	+	0.497217i	0.296484	+	0.955038i	$0.404186\pi$
$930$		0			0
$931$	−3.57890e6	+	2.02969e7i	−0.135324	+	0.767461i
$932$		0			0
$933$	−2.11871e7	−	2.16052e7i	−0.796834	−	0.812559i
$934$		0			0
$935$	7.39332e6	−	1.28056e7i	0.276573	−	0.479039i
$936$		0			0
$937$	−1.32523e7	−	2.29537e7i	−0.493109	−	0.854091i	0.506859	−	0.862029i	$-0.330806\pi$
$937$	−1.32523e7	−	2.29537e7i	−0.493109	−	0.854091i	−0.999968	+	0.00793833i	$0.997473\pi$
$938$		0			0
$939$	−888763.	−	1.14455e7i	−0.0328944	−	0.423616i
$940$		0			0
$941$	2.15255e7	−	7.83462e6i	0.792462	−	0.288432i	0.0861026	−	0.996286i	$-0.472559\pi$
$941$	2.15255e7	−	7.83462e6i	0.792462	−	0.288432i	0.706359	+	0.707854i	$0.250336\pi$
$942$		0			0
$943$	−1.05966e7	−	6.00966e7i	−0.388051	−	2.20075i
$944$		0			0
$945$	−1.15798e7	−	4.89076e7i	−0.421815	−	1.78155i
$946$		0			0
$947$	4.08340e6	+	2.31581e7i	0.147961	+	0.839127i	0.964942	+	0.262463i	$0.0845347\pi$
$947$	4.08340e6	+	2.31581e7i	0.147961	+	0.839127i	−0.816981	+	0.576664i	$0.804354\pi$
$948$		0			0
$949$	1.60901e6	−	585633.i	0.0579955	−	0.0211086i
$950$		0			0
$951$	−1.32280e7	+	9.07104e6i	−0.474289	+	0.325242i
$952$		0			0
$953$	2.57865e7	+	4.46636e7i	0.919731	+	1.59302i	0.799824	+	0.600235i	$0.204926\pi$
$953$	2.57865e7	+	4.46636e7i	0.919731	+	1.59302i	0.119907	+	0.992785i	$0.461740\pi$
$954$		0			0
$955$	1.82435e6	−	3.15986e6i	0.0647290	−	0.112114i
$956$		0			0
$957$	9.45652e6	−	2.43509e6i	0.333773	−	0.0859480i
$958$		0			0
$959$	8.11277e6	−	4.60098e7i	0.284854	−	1.61549i
$960$		0			0
$961$	−1.70520e7	+	1.43083e7i	−0.595617	+	0.499782i
$962$		0			0
$963$	1.23498e7	+	3.61112e7i	0.429136	+	1.25480i
$964$		0			0
$965$	−4.11744e7	−	1.49862e7i	−1.42334	−	0.518053i
$966$		0			0
$967$	3.96880e7	+	3.33022e7i	1.36488	+	1.14527i	0.974443	+	0.224635i	$0.0721190\pi$
$967$	3.96880e7	+	3.33022e7i	1.36488	+	1.14527i	0.390433	+	0.920632i	$0.372325\pi$
$968$		0			0
$969$	−4.85591e6	+	6.79273e6i	−0.166135	+	0.232399i
$970$		0			0
$971$	−8.62427e6			−0.293545			−0.146772	−	0.989170i	$-0.546888\pi$
$971$	−8.62427e6			−0.293545			−0.146772	+	0.989170i	$0.546888\pi$
$972$		0			0
$973$	2.56330e7			0.867994
$974$		0			0
$975$	2.61980e6	−	3.66473e6i	0.0882586	−	0.123461i
$976$		0			0
$977$	1.65502e6	+	1.38873e6i	0.0554712	+	0.0465459i	0.670102	−	0.742269i	$-0.266250\pi$
$977$	1.65502e6	+	1.38873e6i	0.0554712	+	0.0465459i	−0.614631	+	0.788815i	$0.710695\pi$
$978$		0			0
$979$	7.76350e6	+	2.82568e6i	0.258881	+	0.0942252i
$980$		0			0
$981$	−1.88086e7	−	5.49968e7i	−0.623999	−	1.82459i
$982$		0			0
$983$	−3.05155e7	+	2.56055e7i	−1.00725	+	0.845182i	−0.987972	−	0.154632i	$-0.950581\pi$
$983$	−3.05155e7	+	2.56055e7i	−1.00725	+	0.845182i	−0.0192766	+	0.999814i	$0.506136\pi$
$984$		0			0
$985$	−4.58167e6	+	2.59840e7i	−0.150464	+	0.853326i
$986$		0			0
$987$	2.77826e6	−	715413.i	0.0907778	−	0.0233757i
$988$		0			0
$989$	−1.85874e7	+	3.21944e7i	−0.604266	+	1.04662i
$990$		0			0
$991$	1.96649e7	+	3.40607e7i	0.636075	+	1.10171i	0.986286	+	0.165043i	$0.0527764\pi$
$991$	1.96649e7	+	3.40607e7i	0.636075	+	1.10171i	−0.350212	+	0.936671i	$0.613890\pi$
$992$		0			0
$993$	1.62683e7	−	1.11559e7i	0.523563	−	0.359031i
$994$		0			0
$995$	−2.86805e7	+	1.04388e7i	−0.918393	+	0.334268i
$996$		0			0
$997$	7.02123e6	+	3.98194e7i	0.223705	+	1.26869i	0.865146	+	0.501520i	$0.167226\pi$
$997$	7.02123e6	+	3.98194e7i	0.223705	+	1.26869i	−0.641441	+	0.767172i	$0.721663\pi$
$998$		0			0
$999$	−2.50986e7	+	2.36687e7i	−0.795675	+	0.750346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.i.a.13.11	✓	90
3.2	odd	2		324.6.i.a.253.4		90
27.2	odd	18		324.6.i.a.73.4		90
27.25	even	9	inner	108.6.i.a.25.11	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.6.i.a.13.11	✓	90	1.1	even	1	trivial
108.6.i.a.25.11	yes	90	27.25	even	9	inner
324.6.i.a.73.4		90	27.2	odd	18
324.6.i.a.253.4		90	3.2	odd	2

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	108.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(9.06551 - 12.6813i) q^{3} +(40.6723 + 34.1282i) q^{5} +(234.829 + 85.4708i) q^{7} +(-78.6332 - 229.926i) q^{9} +O(q^{10})\)	\(q+(9.06551 - 12.6813i) q^{3} +(40.6723 + 34.1282i) q^{5} +(234.829 + 85.4708i) q^{7} +(-78.6332 - 229.926i) q^{9} +(-179.848 + 150.910i) q^{11} +(-163.977 + 929.960i) q^{13} +(801.506 - 206.391i) q^{15} +(-593.121 + 1027.32i) q^{17} +(225.775 + 391.053i) q^{19} +(3212.73 - 2203.11i) q^{21} +(4157.57 - 1513.23i) q^{23} +(-53.1415 - 301.380i) q^{25} +(-3628.62 - 1087.22i) q^{27} +(-463.328 - 2627.66i) q^{29} +(2371.55 - 863.175i) q^{31} +(283.334 + 3648.79i) q^{33} +(6634.09 + 11490.6i) q^{35} +(4553.67 - 7887.18i) q^{37} +(10306.6 + 10510.0i) q^{39} +(2395.05 - 13583.0i) q^{41} +(-6436.49 + 5400.86i) q^{43} +(4648.74 - 12035.2i) q^{45} +(692.039 + 251.882i) q^{47} +(34964.5 + 29338.7i) q^{49} +(7650.80 + 16834.7i) q^{51} -33102.1 q^{53} -12465.1 q^{55} +(7005.85 + 681.968i) q^{57} +(-25183.9 - 21131.8i) q^{59} +(8431.07 + 3068.66i) q^{61} +(1186.56 - 60714.1i) q^{63} +(-38407.2 + 32227.4i) q^{65} +(-4677.88 + 26529.6i) q^{67} +(18500.7 - 66441.8i) q^{69} +(3951.61 - 6844.40i) q^{71} +(-906.632 - 1570.33i) q^{73} +(-4303.66 - 2058.26i) q^{75} +(-55131.9 + 20066.4i) q^{77} +(-1934.75 - 10972.5i) q^{79} +(-46682.6 + 36159.6i) q^{81} +(-13283.4 - 75334.1i) q^{83} +(-59184.0 + 21541.2i) q^{85} +(-37522.6 - 17945.5i) q^{87} +(-17595.1 - 30475.5i) q^{89} +(-117991. + 204366. i) q^{91} +(10553.1 - 37899.6i) q^{93} +(-4163.14 + 23610.3i) q^{95} +(35234.4 - 29565.2i) q^{97} +(48840.1 + 29485.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 87 q^{5} + 330 q^{9}+O(q^{10}) \) 90 * q - 87 * q^5 + 330 * q^9	\( 90 q - 87 q^{5} + 330 q^{9} - 1257 q^{11} + 531 q^{15} - 3468 q^{17} + 12894 q^{21} + 8106 q^{23} + 4959 q^{25} - 17415 q^{27} + 3468 q^{29} - 6651 q^{31} + 33624 q^{33} - 8229 q^{35} - 10545 q^{39} + 68673 q^{41} + 9459 q^{43} - 53469 q^{45} - 57087 q^{47} - 5490 q^{49} + 42831 q^{51} - 4146 q^{53} + 24624 q^{57} + 5388 q^{59} + 70110 q^{61} - 98115 q^{63} - 172425 q^{65} - 15039 q^{67} + 251037 q^{69} + 67812 q^{71} - 27009 q^{73} - 75273 q^{75} + 23991 q^{77} - 216180 q^{79} + 177822 q^{81} - 76725 q^{83} - 53100 q^{85} - 201483 q^{87} - 98814 q^{89} - 90999 q^{91} + 21765 q^{93} - 143490 q^{95} - 71739 q^{97} + 13635 q^{99}+O(q^{100}) \) 90 * q - 87 * q^5 + 330 * q^9 - 1257 * q^11 + 531 * q^15 - 3468 * q^17 + 12894 * q^21 + 8106 * q^23 + 4959 * q^25 - 17415 * q^27 + 3468 * q^29 - 6651 * q^31 + 33624 * q^33 - 8229 * q^35 - 10545 * q^39 + 68673 * q^41 + 9459 * q^43 - 53469 * q^45 - 57087 * q^47 - 5490 * q^49 + 42831 * q^51 - 4146 * q^53 + 24624 * q^57 + 5388 * q^59 + 70110 * q^61 - 98115 * q^63 - 172425 * q^65 - 15039 * q^67 + 251037 * q^69 + 67812 * q^71 - 27009 * q^73 - 75273 * q^75 + 23991 * q^77 - 216180 * q^79 + 177822 * q^81 - 76725 * q^83 - 53100 * q^85 - 201483 * q^87 - 98814 * q^89 - 90999 * q^91 + 21765 * q^93 - 143490 * q^95 - 71739 * q^97 + 13635 * q^99

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