LMFDB - Embedded newform 76.6.i.a.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,Mod(5,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("76.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	76.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:	$12.1891703058$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			9.2
Character	$\chi$	$=$	76.9
Dual form			76.6.i.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-15.3348 + 12.8674i) q^{3} +(-87.8167 - 31.9627i) q^{5} +(31.3213 - 54.2501i) q^{7} +(27.3887 - 155.329i) q^{9} +O(q^{10})$	\(q+(-15.3348 + 12.8674i) q^{3} +(-87.8167 - 31.9627i) q^{5} +(31.3213 - 54.2501i) q^{7} +(27.3887 - 155.329i) q^{9} +(-93.1468 - 161.335i) q^{11} +(738.094 + 619.334i) q^{13} +(1757.93 - 639.833i) q^{15} +(71.8544 + 407.506i) q^{17} +(-1226.86 + 985.349i) q^{19} +(217.753 + 1234.94i) q^{21} +(3924.87 - 1428.53i) q^{23} +(4296.28 + 3605.01i) q^{25} +(-853.518 - 1478.34i) q^{27} +(1459.00 - 8274.38i) q^{29} +(625.573 - 1083.52i) q^{31} +(3504.35 + 1275.48i) q^{33} +(-4484.51 + 3762.95i) q^{35} +5213.39 q^{37} -19287.7 q^{39} +(9165.91 - 7691.11i) q^{41} +(-9270.60 - 3374.22i) q^{43} +(-7369.93 + 12765.1i) q^{45} +(-1463.23 + 8298.40i) q^{47} +(6441.45 + 11156.9i) q^{49} +(-6345.42 - 5324.44i) q^{51} +(9230.86 - 3359.76i) q^{53} +(3023.15 + 17145.1i) q^{55} +(6134.74 - 30896.6i) q^{57} +(2087.31 + 11837.7i) q^{59} +(-25838.3 + 9404.37i) q^{61} +(-7568.77 - 6350.96i) q^{63} +(-45021.4 - 77979.4i) q^{65} +(-3508.65 + 19898.6i) q^{67} +(-41805.4 + 72409.1i) q^{69} +(-17992.5 - 6548.74i) q^{71} +(33349.7 - 27983.7i) q^{73} -112270. q^{75} -11669.9 q^{77} +(47925.8 - 40214.5i) q^{79} +(68126.7 + 24796.1i) q^{81} +(31884.6 - 55225.8i) q^{83} +(6714.98 - 38082.5i) q^{85} +(84096.4 + 145659. i) q^{87} +(68817.4 + 57744.6i) q^{89} +(56717.0 - 20643.3i) q^{91} +(4349.12 + 24665.1i) q^{93} +(139233. - 47316.4i) q^{95} +(-9585.78 - 54363.6i) q^{97} +(-27611.2 + 10049.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9}+O(q^{10}) $ 48 * q + 33 * q^3 - 177 * q^7 + 33 * q^9	$ 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9} - 237 q^{11} + 2049 q^{13} + 2085 q^{15} - 609 q^{17} - 6012 q^{19} + 3591 q^{21} + 14100 q^{23} + 11802 q^{25} - 861 q^{27} - 10575 q^{29} - 6546 q^{31} - 21234 q^{33} - 231 q^{35} + 20052 q^{37} + 72204 q^{39} - 3249 q^{41} - 34677 q^{43} - 34956 q^{45} + 4461 q^{47} - 41139 q^{49} + 12099 q^{51} - 24291 q^{53} - 61767 q^{55} - 64470 q^{57} - 20100 q^{59} + 95490 q^{61} + 86403 q^{63} - 57915 q^{65} - 64452 q^{67} - 99315 q^{69} - 115536 q^{71} - 16362 q^{73} + 236250 q^{75} + 26688 q^{77} + 29799 q^{79} + 180327 q^{81} + 52347 q^{83} + 204618 q^{85} + 69414 q^{87} + 47394 q^{89} - 249384 q^{91} - 462126 q^{93} + 412869 q^{95} - 229974 q^{97} - 692274 q^{99}+O(q^{100}) $ 48 * q + 33 * q^3 - 177 * q^7 + 33 * q^9 - 237 * q^11 + 2049 * q^13 + 2085 * q^15 - 609 * q^17 - 6012 * q^19 + 3591 * q^21 + 14100 * q^23 + 11802 * q^25 - 861 * q^27 - 10575 * q^29 - 6546 * q^31 - 21234 * q^33 - 231 * q^35 + 20052 * q^37 + 72204 * q^39 - 3249 * q^41 - 34677 * q^43 - 34956 * q^45 + 4461 * q^47 - 41139 * q^49 + 12099 * q^51 - 24291 * q^53 - 61767 * q^55 - 64470 * q^57 - 20100 * q^59 + 95490 * q^61 + 86403 * q^63 - 57915 * q^65 - 64452 * q^67 - 99315 * q^69 - 115536 * q^71 - 16362 * q^73 + 236250 * q^75 + 26688 * q^77 + 29799 * q^79 + 180327 * q^81 + 52347 * q^83 + 204618 * q^85 + 69414 * q^87 + 47394 * q^89 - 249384 * q^91 - 462126 * q^93 + 412869 * q^95 - 229974 * q^97 - 692274 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

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
$3$	−15.3348	+	12.8674i	−0.983726	+	0.825444i	−0.984647	−	0.174555i	$-0.944151\pi$
$3$	−15.3348	+	12.8674i	−0.983726	+	0.825444i	0.000921000		1.00000i	$0.499707\pi$
$4$		0			0
$5$	−87.8167	−	31.9627i	−1.57091	−	0.571766i	−0.597710	−	0.801712i	$-0.703923\pi$
$5$	−87.8167	−	31.9627i	−1.57091	−	0.571766i	−0.973203	+	0.229946i	$0.926145\pi$
$6$		0			0
$7$	31.3213	−	54.2501i	0.241599	−	0.418461i	−0.719571	−	0.694419i	$-0.755662\pi$
$7$	31.3213	−	54.2501i	0.241599	−	0.418461i	0.961170	+	0.275958i	$0.0889949\pi$
$8$		0			0
$9$	27.3887	−	155.329i	0.112711	−	0.639215i
$10$		0			0
$11$	−93.1468	−	161.335i	−0.232106	−	0.402019i	0.726322	−	0.687355i	$-0.241228\pi$
$11$	−93.1468	−	161.335i	−0.232106	−	0.402019i	−0.958428	+	0.285336i	$0.907895\pi$
$12$		0			0
$13$	738.094	+	619.334i	1.21130	+	1.01641i	0.999233	+	0.0391509i	$0.0124653\pi$
$13$	738.094	+	619.334i	1.21130	+	1.01641i	0.212071	+	0.977254i	$0.431979\pi$
$14$		0			0
$15$	1757.93	−	639.833i	2.01731	−	0.734241i
$16$		0			0
$17$	71.8544	+	407.506i	0.0603019	+	0.341989i	1.00000		1.60712e-5i	$-5.11563e-6\pi$
$17$	71.8544	+	407.506i	0.0603019	+	0.341989i	−0.939698	+	0.342005i	$0.888894\pi$
$18$		0			0
$19$	−1226.86	+	985.349i	−0.779670	+	0.626190i
$19$	−1226.86	+	985.349i	−0.779670	+	0.626190i
$20$		0			0
$21$	217.753	+	1234.94i	0.107749	+	0.611078i
$22$		0			0
$23$	3924.87	−	1428.53i	1.54705	−	0.563082i	0.579330	−	0.815093i	$-0.303314\pi$
$23$	3924.87	−	1428.53i	1.54705	−	0.563082i	0.967724	+	0.252012i	$0.0810922\pi$
$24$		0			0
$25$	4296.28	+	3605.01i	1.37481	+	1.15360i
$26$		0			0
$27$	−853.518	−	1478.34i	−0.225322	−	0.390269i
$28$		0			0
$29$	1459.00	−	8274.38i	0.322151	−	1.82701i	−0.206834	−	0.978376i	$-0.566316\pi$
$29$	1459.00	−	8274.38i	0.322151	−	1.82701i	0.528985	−	0.848631i	$-0.322573\pi$
$30$		0			0
$31$	625.573	−	1083.52i	0.116916	−	0.202504i	−0.801628	−	0.597823i	$-0.796033\pi$
$31$	625.573	−	1083.52i	0.116916	−	0.202504i	0.918544	+	0.395319i	$0.129366\pi$
$32$		0			0
$33$	3504.35	+	1275.48i	0.560174	+	0.203887i
$34$		0			0
$35$	−4484.51	+	3762.95i	−0.618792	+	0.519228i
$36$		0			0
$37$	5213.39			0.626059			0.313030	−	0.949743i	$-0.398656\pi$
$37$	5213.39			0.626059			0.313030	+	0.949743i	$0.398656\pi$
$38$		0			0
$39$	−19287.7			−2.03058
$40$		0			0
$41$	9165.91	−	7691.11i	0.851561	−	0.714545i	−0.108572	−	0.994089i	$-0.534628\pi$
$41$	9165.91	−	7691.11i	0.851561	−	0.714545i	0.960133	+	0.279544i	$0.0901832\pi$
$42$		0			0
$43$	−9270.60	−	3374.22i	−0.764604	−	0.278293i	−0.0698664	−	0.997556i	$-0.522257\pi$
$43$	−9270.60	−	3374.22i	−0.764604	−	0.278293i	−0.694738	+	0.719263i	$0.744480\pi$
$44$		0			0
$45$	−7369.93	+	12765.1i	−0.542540	+	0.939708i
$46$		0			0
$47$	−1463.23	+	8298.40i	−0.0966204	+	0.547961i	0.897618	+	0.440773i	$0.145296\pi$
$47$	−1463.23	+	8298.40i	−0.0966204	+	0.547961i	−0.994239	+	0.107188i	$0.965815\pi$
$48$		0			0
$49$	6441.45	+	11156.9i	0.383260	+	0.663826i
$50$		0			0
$51$	−6345.42	−	5324.44i	−0.341613	−	0.286648i
$52$		0			0
$53$	9230.86	−	3359.76i	0.451391	−	0.164293i	−0.106313	−	0.994333i	$-0.533905\pi$
$53$	9230.86	−	3359.76i	0.451391	−	0.164293i	0.557704	+	0.830040i	$0.311682\pi$
$54$		0			0
$55$	3023.15	+	17145.1i	0.134758	+	0.764248i
$56$		0			0
$57$	6134.74	−	30896.6i	0.250097	−	1.25957i
$58$		0			0
$59$	2087.31	+	11837.7i	0.0780652	+	0.442730i	0.998639	+	0.0521605i	$0.0166107\pi$
$59$	2087.31	+	11837.7i	0.0780652	+	0.442730i	−0.920574	+	0.390569i	$0.872278\pi$
$60$		0			0
$61$	−25838.3	+	9404.37i	−0.889077	+	0.323598i	−0.745867	−	0.666095i	$-0.767965\pi$
$61$	−25838.3	+	9404.37i	−0.889077	+	0.323598i	−0.143210	+	0.989692i	$0.545742\pi$
$62$		0			0
$63$	−7568.77	−	6350.96i	−0.240256	−	0.201599i
$64$		0			0
$65$	−45021.4	−	77979.4i	−1.32171	−	2.28927i
$66$		0			0
$67$	−3508.65	+	19898.6i	−0.0954890	+	0.541545i	0.899107	+	0.437728i	$0.144217\pi$
$67$	−3508.65	+	19898.6i	−0.0954890	+	0.541545i	−0.994596	+	0.103817i	$0.966894\pi$
$68$		0			0
$69$	−41805.4	+	72409.1i	−1.05709	+	1.83093i
$70$		0			0
$71$	−17992.5	−	6548.74i	−0.423590	−	0.154174i	0.121425	−	0.992601i	$-0.461254\pi$
$71$	−17992.5	−	6548.74i	−0.423590	−	0.154174i	−0.545015	+	0.838426i	$0.683476\pi$
$72$		0			0
$73$	33349.7	−	27983.7i	0.732462	−	0.614608i	−0.198340	−	0.980133i	$-0.563555\pi$
$73$	33349.7	−	27983.7i	0.732462	−	0.614608i	0.930802	+	0.365525i	$0.119111\pi$
$74$		0			0
$75$	−112270.			−2.30467
$76$		0			0
$77$	−11669.9			−0.224306
$78$		0			0
$79$	47925.8	−	40214.5i	0.863976	−	0.724962i	−0.0988447	−	0.995103i	$-0.531515\pi$
$79$	47925.8	−	40214.5i	0.863976	−	0.724962i	0.962821	+	0.270141i	$0.0870703\pi$
$80$		0			0
$81$	68126.7	+	24796.1i	1.15373	+	0.419924i
$82$		0			0
$83$	31884.6	−	55225.8i	0.508026	−	0.879927i	−0.491931	−	0.870634i	$-0.663709\pi$
$83$	31884.6	−	55225.8i	0.508026	−	0.879927i	0.999957	−	0.00929236i	$-0.00295789\pi$
$84$		0			0
$85$	6714.98	−	38082.5i	0.100809	−	0.571714i
$86$		0			0
$87$	84096.4	+	145659.i	1.19118	+	2.06319i
$88$		0			0
$89$	68817.4	+	57744.6i	0.920922	+	0.772746i	0.974165	−	0.225836i	$-0.0725113\pi$
$89$	68817.4	+	57744.6i	0.920922	+	0.772746i	−0.0532430	+	0.998582i	$0.516956\pi$
$90$		0			0
$91$	56717.0	−	20643.3i	0.717976	−	0.261322i
$92$		0			0
$93$	4349.12	+	24665.1i	0.0521428	+	0.295716i
$94$		0			0
$95$	139233.	−	47316.4i	1.58283	−	0.537902i
$96$		0			0
$97$	−9585.78	−	54363.6i	−0.103442	−	0.586650i	−0.991831	−	0.127558i	$-0.959286\pi$
$97$	−9585.78	−	54363.6i	−0.103442	−	0.586650i	0.888389	−	0.459092i	$-0.151825\pi$
$98$		0			0
$99$	−27611.2	+	10049.7i	−0.283138	+	0.103054i
$100$		0			0
$101$	72719.0	+	61018.5i	0.709324	+	0.595193i	0.924409	−	0.381402i	$-0.124559\pi$
$101$	72719.0	+	61018.5i	0.709324	+	0.595193i	−0.215086	+	0.976595i	$0.569003\pi$
$102$		0			0
$103$	−38513.6	−	66707.6i	−0.357702	−	0.619558i	0.629874	−	0.776697i	$-0.283106\pi$
$103$	−38513.6	−	66707.6i	−0.357702	−	0.619558i	−0.987577	+	0.157139i	$0.949773\pi$
$104$		0			0
$105$	20349.5	−	115408.i	0.180128	−	1.02156i
$106$		0			0
$107$	−70215.5	+	121617.i	−0.592889	+	1.02691i	0.400952	+	0.916099i	$0.368680\pi$
$107$	−70215.5	+	121617.i	−0.592889	+	1.02691i	−0.993841	+	0.110815i	$0.964654\pi$
$108$		0			0
$109$	219514.	+	79896.7i	1.76969	+	0.644113i	0.999984	+	0.00571187i	$0.00181816\pi$
$109$	219514.	+	79896.7i	1.76969	+	0.644113i	0.769703	+	0.638402i	$0.220404\pi$
$110$		0			0
$111$	−79946.1	+	67082.8i	−0.615871	+	0.516777i
$112$		0			0
$113$	7577.33			0.0558239			0.0279120	−	0.999610i	$-0.491114\pi$
$113$	7577.33			0.0558239			0.0279120	+	0.999610i	$0.491114\pi$
$114$		0			0
$115$	−390329.			−2.75224
$116$		0			0
$117$	116416.	−	97684.8i	0.786229	−	0.659724i
$118$		0			0
$119$	24357.8	+	8865.52i	0.157678	+	0.0573901i
$120$		0			0
$121$	63172.8	−	109419.i	0.392254	−	0.679403i
$122$		0			0
$123$	−41592.5	+	235883.i	−0.247886	+	1.40583i
$124$		0			0
$125$	−116040.	−	200987.i	−0.664250	−	1.15052i
$126$		0			0
$127$	−163672.	−	137337.i	−0.900460	−	0.755576i	0.0698203	−	0.997560i	$-0.477757\pi$
$127$	−163672.	−	137337.i	−0.900460	−	0.755576i	−0.970280	+	0.241984i	$0.922202\pi$
$128$		0			0
$129$	185580.	−	67545.6i	0.981877	−	0.357374i
$130$		0			0
$131$	−53888.9	−	305619.i	−0.274360	−	1.55597i	−0.740987	−	0.671519i	$-0.765642\pi$
$131$	−53888.9	−	305619.i	−0.274360	−	1.55597i	0.466627	−	0.884454i	$-0.345469\pi$
$132$		0			0
$133$	15028.4	+	97419.6i	0.0736689	+	0.477548i
$134$		0			0
$135$	27701.6	+	157103.i	0.130819	+	0.741910i
$136$		0			0
$137$	147216.	−	53582.2i	0.670121	−	0.243904i	0.0155211	−	0.999880i	$-0.495059\pi$
$137$	147216.	−	53582.2i	0.670121	−	0.243904i	0.654600	+	0.755975i	$0.272837\pi$
$138$		0			0
$139$	236862.	+	198751.i	1.03982	+	0.872514i	0.991987	−	0.126341i	$-0.0403234\pi$
$139$	236862.	+	198751.i	1.03982	+	0.872514i	0.0478350	+	0.998855i	$0.484768\pi$
$140$		0			0
$141$	−84340.6	−	146082.i	−0.357264	−	0.618799i
$142$		0			0
$143$	31169.2	−	176770.i	0.127464	−	0.722882i
$144$		0			0
$145$	−392595.	+	679995.i	−1.55069	+	2.68588i
$146$		0			0
$147$	−242339.	−	88204.2i	−0.924975	−	0.336663i
$148$		0			0
$149$	−283618.	+	237984.i	−1.04657	+	0.878175i	−0.992729	−	0.120374i	$-0.961591\pi$
$149$	−283618.	+	237984.i	−1.04657	+	0.878175i	−0.0538402	+	0.998550i	$0.517146\pi$
$150$		0			0
$151$	−105209.			−0.375499			−0.187750	−	0.982217i	$-0.560119\pi$
$151$	−105209.			−0.375499			−0.187750	+	0.982217i	$0.560119\pi$
$152$		0			0
$153$	65265.7			0.225401
$154$		0			0
$155$	−89568.1	+	75156.5i	−0.299450	+	0.251268i
$156$		0			0
$157$	221039.	+	80451.8i	0.715683	+	0.260487i	0.674092	−	0.738647i	$-0.264535\pi$
$157$	221039.	+	80451.8i	0.715683	+	0.260487i	0.0415909	+	0.999135i	$0.486757\pi$
$158$		0			0
$159$	−98321.8	+	170298.i	−0.308430	+	0.534217i
$160$		0			0
$161$	45433.8	−	257668.i	0.138138	−	0.783422i
$162$		0			0
$163$	−194941.	−	337648.i	−0.574691	−	0.995393i	−0.996075	−	0.0885113i	$-0.971789\pi$
$163$	−194941.	−	337648.i	−0.574691	−	0.995393i	0.421385	−	0.906882i	$-0.361544\pi$
$164$		0			0
$165$	−266973.	−	224017.i	−0.763409	−	0.640576i
$166$		0			0
$167$	−25840.0	+	9405.00i	−0.0716971	+	0.0260956i	−0.377620	−	0.925961i	$-0.623257\pi$
$167$	−25840.0	+	9405.00i	−0.0716971	+	0.0260956i	0.305923	+	0.952056i	$0.401035\pi$
$168$		0			0
$169$	96733.3	+	548602.i	0.260531	+	1.47754i
$170$		0			0
$171$	119451.	+	217555.i	0.312393	+	0.568956i
$172$		0			0
$173$	−92808.6	−	526344.i	−0.235762	−	1.33707i	−0.841004	−	0.541029i	$-0.818035\pi$
$173$	−92808.6	−	526344.i	−0.235762	−	1.33707i	0.605242	−	0.796041i	$-0.293076\pi$
$174$		0			0
$175$	330137.	−	120160.i	0.814889	−	0.296595i
$176$		0			0
$177$	−184329.	−	154671.i	−0.442244	−	0.371087i
$178$		0			0
$179$	−262045.	−	453876.i	−0.611285	−	1.05878i	−0.991024	−	0.133683i	$-0.957320\pi$
$179$	−262045.	−	453876.i	−0.611285	−	1.05878i	0.379739	−	0.925094i	$-0.376014\pi$
$180$		0			0
$181$	−96463.5	+	547071.i	−0.218860	+	1.24122i	0.655221	+	0.755437i	$0.272575\pi$
$181$	−96463.5	+	547071.i	−0.218860	+	1.24122i	−0.874081	+	0.485780i	$0.838536\pi$
$182$		0			0
$183$	275215.	−	476686.i	0.607497	−	1.05222i
$184$		0			0
$185$	−457823.	−	166634.i	−0.983485	−	0.357959i
$186$		0			0
$187$	59052.1	−	49550.6i	0.123490	−	0.103620i
$188$		0			0
$189$	−106933.			−0.217750
$190$		0			0
$191$	728209.			1.44435			0.722176	−	0.691710i	$-0.243142\pi$
$191$	728209.			1.44435			0.722176	+	0.691710i	$0.243142\pi$
$192$		0			0
$193$	−54896.9	+	46063.9i	−0.106085	+	0.0890159i	−0.694287	−	0.719698i	$-0.744280\pi$
$193$	−54896.9	+	46063.9i	−0.106085	+	0.0890159i	0.588202	+	0.808714i	$0.299836\pi$
$194$		0			0
$195$	1.69379e6	+	616488.i	3.18986	+	1.16102i
$196$		0			0
$197$	180679.	−	312945.i	0.331698	−	0.574517i	−0.651147	−	0.758951i	$-0.725712\pi$
$197$	180679.	−	312945.i	0.331698	−	0.574517i	0.982845	+	0.184434i	$0.0590453\pi$
$198$		0			0
$199$	−162915.	+	923937.i	−0.291628	+	1.65390i	0.388974	+	0.921249i	$0.372830\pi$
$199$	−162915.	+	923937.i	−0.291628	+	1.65390i	−0.680602	+	0.732654i	$0.738282\pi$
$200$		0			0
$201$	−202238.	−	350287.i	−0.353080	−	0.611553i
$202$		0			0
$203$	−403188.	−	338315.i	−0.686700	−	0.576210i
$204$		0			0
$205$	−1.05075e6	+	382441.i	−1.74628	+	0.635595i
$206$		0			0
$207$	−114396.	−	648773.i	−0.185560	−	1.05237i
$208$		0			0
$209$	273250.	+	106153.i	0.432707	+	0.168100i
$210$		0			0
$211$	−46804.4	−	265441.i	−0.0723737	−	0.410452i	−0.999374	−	0.0353901i	$-0.988733\pi$
$211$	−46804.4	−	265441.i	−0.0723737	−	0.410452i	0.927000	−	0.375062i	$-0.122378\pi$
$212$		0			0
$213$	360176.	−	131093.i	0.543959	−	0.197985i
$214$		0			0
$215$	706264.	+	592626.i	1.04201	+	0.874349i
$216$		0			0
$217$	−39187.5	−	67874.7i	−0.0564934	−	0.0978495i
$218$		0			0
$219$	−151332.	+	858249.i	−0.213217	+	1.20921i
$220$		0			0
$221$	−199347.	+	345280.i	−0.274555	+	0.475544i
$222$		0			0
$223$	1.28553e6	+	467894.i	1.73109	+	0.630065i	0.998707	−	0.0508299i	$-0.0161866\pi$
$223$	1.28553e6	+	467894.i	1.73109	+	0.630065i	0.732381	+	0.680895i	$0.238409\pi$
$224$		0			0
$225$	677633.	−	568601.i	0.892356	−	0.748775i
$226$		0			0
$227$	696235.			0.896791			0.448395	−	0.893835i	$-0.351996\pi$
$227$	696235.			0.896791			0.448395	+	0.893835i	$0.351996\pi$
$228$		0			0
$229$	1.27070e6			1.60123			0.800616	−	0.599177i	$-0.204506\pi$
$229$	1.27070e6			1.60123			0.800616	+	0.599177i	$0.204506\pi$
$230$		0			0
$231$	178956.	−	150162.i	0.220656	−	0.185152i
$232$		0			0
$233$	146997.	+	53502.5i	0.177386	+	0.0645631i	0.429186	−	0.903216i	$-0.358800\pi$
$233$	146997.	+	53502.5i	0.177386	+	0.0645631i	−0.251800	+	0.967779i	$0.581023\pi$
$234$		0			0
$235$	393736.	−	681970.i	0.465088	−	0.805556i
$236$		0			0
$237$	−217475.	+	1.23336e6i	−0.251500	+	1.42633i
$238$		0			0
$239$	−672411.	−	1.16465e6i	−0.761447	−	1.31887i	−0.942105	−	0.335319i	$-0.891156\pi$
$239$	−672411.	−	1.16465e6i	−0.761447	−	1.31887i	0.180658	−	0.983546i	$-0.442177\pi$
$240$		0			0
$241$	17262.4	+	14484.8i	0.0191451	+	0.0160646i	0.652310	−	0.757952i	$-0.273800\pi$
$241$	17262.4	+	14484.8i	0.0191451	+	0.0160646i	−0.633165	+	0.774017i	$0.718244\pi$
$242$		0			0
$243$	−973976.	+	354498.i	−1.05811	+	0.385122i
$244$		0			0
$245$	−209062.	−	1.18565e6i	−0.222516	−	1.26195i
$246$		0			0
$247$	−1.51580e6	−	32556.4i	−1.58088	−	0.0339543i
$248$		0			0
$249$	221669.	+	1.25715e6i	0.226572	+	1.28495i
$250$		0			0
$251$	425765.	−	154966.i	0.426566	−	0.155257i	−0.119811	−	0.992797i	$-0.538229\pi$
$251$	425765.	−	154966.i	0.426566	−	0.155257i	0.546377	+	0.837539i	$0.316007\pi$
$252$		0			0
$253$	−596062.	−	500155.i	−0.585450	−	0.491251i
$254$		0			0
$255$	387051.	+	670392.i	0.372750	+	0.645622i
$256$		0			0
$257$	289754.	−	1.64328e6i	0.273651	−	1.55195i	−0.469563	−	0.882899i	$-0.655589\pi$
$257$	289754.	−	1.64328e6i	0.273651	−	1.55195i	0.743214	−	0.669053i	$-0.233300\pi$
$258$		0			0
$259$	163290.	−	282826.i	0.151255	−	0.261982i
$260$		0			0
$261$	−1.24529e6	−	453250.i	−1.13154	−	0.411847i
$262$		0			0
$263$	292876.	−	245752.i	0.261092	−	0.219083i	−0.502839	−	0.864380i	$-0.667711\pi$
$263$	292876.	−	245752.i	0.261092	−	0.219083i	0.763931	+	0.645298i	$0.223267\pi$
$264$		0			0
$265$	−918011.			−0.803033
$266$		0			0
$267$	−1.79832e6			−1.54379
$268$		0			0
$269$	−1.62679e6	+	1.36504e6i	−1.37073	+	1.15018i	−0.398228	+	0.917286i	$0.630375\pi$
$269$	−1.62679e6	+	1.36504e6i	−1.37073	+	1.15018i	−0.972502	+	0.232893i	$0.925181\pi$
$270$		0			0
$271$	−1.19283e6	−	434156.i	−0.986635	−	0.359106i	−0.202219	−	0.979340i	$-0.564815\pi$
$271$	−1.19283e6	−	434156.i	−0.986635	−	0.359106i	−0.784416	+	0.620235i	$0.787037\pi$
$272$		0			0
$273$	−604117.	+	1.04636e6i	−0.490585	+	0.849718i
$274$		0			0
$275$	181429.	−	1.02894e6i	0.144669	−	0.820458i
$276$		0			0
$277$	470252.	+	814500.i	0.368240	+	0.637810i	0.989290	−	0.145960i	$-0.0466272\pi$
$277$	470252.	+	814500.i	0.368240	+	0.637810i	−0.621051	+	0.783771i	$0.713294\pi$
$278$		0			0
$279$	−151169.	−	126846.i	−0.116266	−	0.0975589i
$280$		0			0
$281$	−85671.6	+	31181.9i	−0.0647248	+	0.0235579i	−0.374180	−	0.927356i	$-0.622076\pi$
$281$	−85671.6	+	31181.9i	−0.0647248	+	0.0235579i	0.309455	+	0.950914i	$0.399853\pi$
$282$		0			0
$283$	−97681.9	−	553981.i	−0.0725017	−	0.411177i	−0.999360	−	0.0357665i	$-0.988613\pi$
$283$	−97681.9	−	553981.i	−0.0725017	−	0.411177i	0.926859	−	0.375411i	$-0.122498\pi$
$284$		0			0
$285$	−1.52627e6	+	2.51716e6i	−1.11306	+	1.83569i
$286$		0			0
$287$	−130155.	−	738147.i	−0.0932732	−	0.528978i
$288$		0			0
$289$	1.17333e6	−	427057.i	0.826372	−	0.300775i
$290$		0			0
$291$	846515.	+	710310.i	0.586006	+	0.491717i
$292$		0			0
$293$	−556802.	−	964410.i	−0.378907	−	0.656285i	0.611997	−	0.790860i	$-0.290366\pi$
$293$	−556802.	−	964410.i	−0.378907	−	0.656285i	−0.990903	+	0.134575i	$0.957033\pi$
$294$		0			0
$295$	195065.	−	1.10627e6i	0.130504	−	0.740125i
$296$		0			0
$297$	−159005.	+	275405.i	−0.104597	+	0.181167i
$298$		0			0
$299$	3.78166e6	+	1.37641e6i	2.44627	+	0.890370i
$300$		0			0
$301$	−473419.	+	397246.i	−0.301182	+	0.252722i
$302$		0			0
$303$	−1.90028e6			−1.18908
$304$		0			0
$305$	2.56962e6			1.58169
$306$		0			0
$307$	1.82451e6	−	1.53094e6i	1.10484	−	0.927072i	0.107100	−	0.994248i	$-0.465843\pi$
$307$	1.82451e6	−	1.53094e6i	1.10484	−	0.927072i	0.997741	+	0.0671762i	$0.0213990\pi$
$308$		0			0
$309$	1.44895e6	+	527375.i	0.863292	+	0.314213i
$310$		0			0
$311$	−1.54632e6	+	2.67830e6i	−0.906561	+	1.57021i	−0.0877531	+	0.996142i	$0.527969\pi$
$311$	−1.54632e6	+	2.67830e6i	−0.906561	+	1.57021i	−0.818808	+	0.574068i	$0.805365\pi$
$312$		0			0
$313$	511985.	−	2.90361e6i	0.295390	−	1.67524i	−0.370222	−	0.928943i	$-0.620718\pi$
$313$	511985.	−	2.90361e6i	0.295390	−	1.67524i	0.665612	−	0.746298i	$-0.268171\pi$
$314$		0			0
$315$	461671.	+	799638.i	0.262154	+	0.454064i
$316$		0			0
$317$	−1.16109e6	−	974269.i	−0.648959	−	0.544541i	0.257796	−	0.966199i	$-0.417004\pi$
$317$	−1.16109e6	−	974269.i	−0.648959	−	0.544541i	−0.906755	+	0.421658i	$0.861448\pi$
$318$		0			0
$319$	−1.47085e6	+	535345.i	−0.809265	+	0.294549i
$320$		0			0
$321$	−488154.	−	2.76846e6i	−0.264420	−	1.49960i
$322$		0			0
$323$	−489691.	−	429152.i	−0.261166	−	0.228878i
$324$		0			0
$325$	938353.	+	5.32167e6i	0.492786	+	2.79473i
$326$		0			0
$327$	−4.39426e6	+	1.59938e6i	−2.27257	+	0.827147i
$328$		0			0
$329$	404359.	+	339297.i	0.205957	+	0.172819i
$330$		0			0
$331$	−21374.0	−	37020.9i	−0.0107230	−	0.0185728i	0.860614	−	0.509258i	$-0.170080\pi$
$331$	−21374.0	−	37020.9i	−0.0107230	−	0.0185728i	−0.871337	+	0.490685i	$0.836747\pi$
$332$		0			0
$333$	142788.	−	809792.i	0.0705637	−	0.400187i
$334$		0			0
$335$	944130.	−	1.63528e6i	0.459642	−	0.796123i
$336$		0			0
$337$	−2.51604e6	−	915764.i	−1.20682	−	0.439247i	−0.341222	−	0.939983i	$-0.610841\pi$
$337$	−2.51604e6	−	915764.i	−1.20682	−	0.439247i	−0.865600	+	0.500736i	$0.833063\pi$
$338$		0			0
$339$	−116197.	+	97500.6i	−0.0549155	+	0.0460795i
$340$		0			0
$341$	−233080.			−0.108548
$342$		0			0
$343$	1.85985e6			0.853578
$344$		0			0
$345$	5.98561e6	−	5.02252e6i	2.70745	−	2.27182i
$346$		0			0
$347$	−1.88456e6	−	685925.i	−0.840209	−	0.305811i	−0.114167	−	0.993462i	$-0.536420\pi$
$347$	−1.88456e6	−	685925.i	−0.840209	−	0.305811i	−0.726042	+	0.687650i	$0.758642\pi$
$348$		0			0
$349$	−1.16369e6	+	2.01557e6i	−0.511415	+	0.885797i	0.488498	+	0.872565i	$0.337545\pi$
$349$	−1.16369e6	+	2.01557e6i	−0.511415	+	0.885797i	−0.999912	+	0.0132314i	$0.995788\pi$
$350$		0			0
$351$	285608.	−	1.61976e6i	0.123738	−	0.701753i
$352$		0			0
$353$	1.72975e6	+	2.99602e6i	0.738835	+	1.27970i	0.953020	+	0.302907i	$0.0979573\pi$
$353$	1.72975e6	+	2.99602e6i	0.738835	+	1.27970i	−0.214185	+	0.976793i	$0.568709\pi$
$354$		0			0
$355$	1.37073e6	+	1.15018e6i	0.577272	+	0.484389i
$356$		0			0
$357$	−487598.	+	177471.i	−0.202484	+	0.0736982i
$358$		0			0
$359$	−419102.	−	2.37685e6i	−0.171626	−	0.973342i	−0.941966	−	0.335708i	$-0.891024\pi$
$359$	−419102.	−	2.37685e6i	−0.171626	−	0.973342i	0.770340	−	0.637634i	$-0.220087\pi$
$360$		0			0
$361$	534273.	−	2.41777e6i	0.215772	−	0.976444i
$362$		0			0
$363$	439192.	+	2.49078e6i	0.174939	+	0.992130i
$364$		0			0
$365$	−3.82310e6	+	1.39149e6i	−1.50205	+	0.546700i
$366$		0			0
$367$	1.68838e6	+	1.41672e6i	0.654341	+	0.549057i	0.908385	−	0.418136i	$-0.137316\pi$
$367$	1.68838e6	+	1.41672e6i	0.654341	+	0.549057i	−0.254044	+	0.967193i	$0.581761\pi$
$368$		0			0
$369$	−943612.	−	1.63438e6i	−0.360768	−	0.624868i
$370$		0			0
$371$	106855.	−	606007.i	0.0403052	−	0.228582i
$372$		0			0
$373$	−854783.	+	1.48053e6i	−0.318115	+	0.550991i	−0.980095	−	0.198531i	$-0.936383\pi$
$373$	−854783.	+	1.48053e6i	−0.318115	+	0.550991i	0.661980	+	0.749522i	$0.269716\pi$
$374$		0			0
$375$	4.36562e6	+	1.58896e6i	1.60313	+	0.583491i
$376$		0			0
$377$	6.20148e6	−	5.20366e6i	2.24720	−	1.88563i
$378$		0			0
$379$	2.38091e6			0.851424			0.425712	−	0.904859i	$-0.360024\pi$
$379$	2.38091e6			0.851424			0.425712	+	0.904859i	$0.360024\pi$
$380$		0			0
$381$	4.27704e6			1.50949
$382$		0			0
$383$	−872081.	+	731763.i	−0.303781	+	0.254902i	−0.781916	−	0.623384i	$-0.785757\pi$
$383$	−872081.	+	731763.i	−0.303781	+	0.254902i	0.478135	+	0.878286i	$0.341313\pi$
$384$		0			0
$385$	1.02481e6	+	373002.i	0.352365	+	0.128251i
$386$		0			0
$387$	−778026.	+	1.34758e6i	−0.264068	+	0.457380i
$388$		0			0
$389$	487539.	−	2.76497e6i	0.163356	−	0.926439i	−0.787387	−	0.616459i	$-0.788567\pi$
$389$	487539.	−	2.76497e6i	0.163356	−	0.926439i	0.950743	−	0.309980i	$-0.100322\pi$
$390$		0			0
$391$	864156.	+	1.49676e6i	0.285858	+	0.495120i
$392$		0			0
$393$	4.75890e6	+	3.99319e6i	1.55426	+	1.30418i
$394$		0			0
$395$	−5.49405e6	+	1.99967e6i	−1.77174	+	0.644861i
$396$		0			0
$397$	−5636.15	−	31964.2i	−0.00179476	−	0.0101786i	0.983897	−	0.178735i	$-0.0572005\pi$
$397$	−5636.15	−	31964.2i	−0.00179476	−	0.0101786i	−0.985692	+	0.168557i	$0.946089\pi$
$398$		0			0
$399$	−1.48400e6	−	1.30053e6i	−0.466660	−	0.408967i
$400$		0			0
$401$	654010.	+	3.70907e6i	0.203106	+	1.15187i	0.900392	+	0.435079i	$0.143280\pi$
$401$	654010.	+	3.70907e6i	0.203106	+	1.15187i	−0.697286	+	0.716793i	$0.745609\pi$
$402$		0			0
$403$	1.13279e6	−	412304.i	0.347447	−	0.126460i
$404$		0			0
$405$	−5.19012e6	−	4.35503e6i	−1.57232	−	1.31933i
$406$		0			0
$407$	−485610.	−	841102.i	−0.145312	−	0.251688i
$408$		0			0
$409$	348947.	−	1.97898e6i	0.103146	−	0.584968i	−0.888799	−	0.458297i	$-0.848460\pi$
$409$	348947.	−	1.97898e6i	0.103146	−	0.584968i	0.991945	−	0.126671i	$-0.0404293\pi$
$410$		0			0
$411$	−1.56806e6	+	2.71596e6i	−0.457887	+	0.793083i
$412$		0			0
$413$	707575.	+	257536.i	0.204126	+	0.0742957i
$414$		0			0
$415$	−4.56516e6	+	3.83063e6i	−1.30118	+	1.09182i
$416$		0			0
$417$	−6.18964e6			−1.74311
$418$		0			0
$419$	−1.48192e6			−0.412373			−0.206187	−	0.978513i	$-0.566105\pi$
$419$	−1.48192e6			−0.412373			−0.206187	+	0.978513i	$0.566105\pi$
$420$		0			0
$421$	3.40538e6	−	2.85745e6i	0.936397	−	0.785730i	−0.0405580	−	0.999177i	$-0.512914\pi$
$421$	3.40538e6	−	2.85745e6i	0.936397	−	0.785730i	0.976955	+	0.213447i	$0.0684691\pi$
$422$		0			0
$423$	1.24891e6	+	454566.i	0.339375	+	0.123522i
$424$		0			0
$425$	−1.16036e6	+	2.00980e6i	−0.311615	+	0.539734i
$426$		0			0
$427$	−299101.	+	1.69629e6i	−0.0793868	+	0.450225i
$428$		0			0
$429$	1.79659e6	+	3.11179e6i	0.471309	+	0.816332i
$430$		0			0
$431$	2.56741e6	+	2.15432e6i	0.665737	+	0.558620i	0.911800	−	0.410634i	$-0.134693\pi$
$431$	2.56741e6	+	2.15432e6i	0.665737	+	0.558620i	−0.246063	+	0.969254i	$0.579137\pi$
$432$		0			0
$433$	−5.30481e6	+	1.93079e6i	−1.35972	+	0.494899i	−0.915969	−	0.401250i	$-0.868576\pi$
$433$	−5.30481e6	+	1.93079e6i	−1.35972	+	0.494899i	−0.443754	+	0.896149i	$0.646354\pi$
$434$		0			0
$435$	−2.72941e6	−	1.54793e7i	−0.691585	−	3.92218i
$436$		0			0
$437$	−3.40766e6	+	5.61998e6i	−0.853596	+	1.40777i
$438$		0			0
$439$	−133634.	−	757875.i	−0.0330944	−	0.187688i	0.963779	−	0.266702i	$-0.0859339\pi$
$439$	−133634.	−	757875.i	−0.0330944	−	0.187688i	−0.996874	+	0.0790141i	$0.974823\pi$
$440$		0			0
$441$	1.90942e6	−	694972.i	0.467525	−	0.170165i
$442$		0			0
$443$	4.54967e6	+	3.81762e6i	1.10146	+	0.924238i	0.997523	−	0.0703452i	$-0.0224101\pi$
$443$	4.54967e6	+	3.81762e6i	1.10146	+	0.924238i	0.103941	+	0.994583i	$0.466855\pi$
$444$		0			0
$445$	−4.19764e6	−	7.27053e6i	−1.00486	−	1.74047i
$446$		0			0
$447$	1.28698e6	−	7.29885e6i	0.304652	−	1.72777i
$448$		0			0
$449$	−1.27749e6	+	2.21268e6i	−0.299049	+	0.517968i	−0.975919	−	0.218135i	$-0.930003\pi$
$449$	−1.27749e6	+	2.21268e6i	−0.299049	+	0.517968i	0.676870	+	0.736103i	$0.263336\pi$
$450$		0			0
$451$	−2.09462e6	−	762380.i	−0.484913	−	0.176494i
$452$		0			0
$453$	1.61335e6	−	1.35376e6i	0.369389	−	0.309954i
$454$		0			0
$455$	−5.64052e6			−1.27729
$456$		0			0
$457$	−1.51914e6			−0.340258			−0.170129	−	0.985422i	$-0.554418\pi$
$457$	−1.51914e6			−0.340258			−0.170129	+	0.985422i	$0.554418\pi$
$458$		0			0
$459$	541102.	−	454039.i	0.119880	−	0.100592i
$460$		0			0
$461$	−798796.	−	290738.i	−0.175059	−	0.0637161i	0.253004	−	0.967465i	$-0.418581\pi$
$461$	−798796.	−	290738.i	−0.175059	−	0.0637161i	−0.428062	+	0.903749i	$0.640804\pi$
$462$		0			0
$463$	−1.22400e6	+	2.12003e6i	−0.265356	+	0.459610i	−0.967657	−	0.252270i	$-0.918823\pi$
$463$	−1.22400e6	+	2.12003e6i	−0.265356	+	0.459610i	0.702301	+	0.711880i	$0.252156\pi$
$464$		0			0
$465$	406437.	−	2.30502e6i	0.0871687	−	0.494358i
$466$		0			0
$467$	−681551.	−	1.18048e6i	−0.144613	−	0.250477i	0.784616	−	0.619982i	$-0.212860\pi$
$467$	−681551.	−	1.18048e6i	−0.144613	−	0.250477i	−0.929228	+	0.369506i	$0.879527\pi$
$468$		0			0
$469$	969603.	+	813593.i	0.203546	+	0.170795i
$470$		0			0
$471$	−4.42480e6	+	1.61049e6i	−0.919054	+	0.334508i
$472$		0			0
$473$	319147.	+	1.80997e6i	0.0655900	+	0.371979i
$474$		0			0
$475$	−8.82312e6	−	189504.i	−1.79427	−	0.0385375i
$476$		0			0
$477$	−269047.	−	1.52584e6i	−0.0541418	−	0.307053i
$478$		0			0
$479$	1.35169e6	−	491976.i	0.269178	−	0.0979726i	−0.203905	−	0.978991i	$-0.565363\pi$
$479$	1.35169e6	−	491976.i	0.269178	−	0.0979726i	0.473083	+	0.881018i	$0.343141\pi$
$480$		0			0
$481$	3.84797e6	+	3.22883e6i	0.758349	+	0.636330i
$482$		0			0
$483$	2.61880e6	+	4.53589e6i	0.510781	+	0.884698i
$484$		0			0
$485$	−895816.	+	5.08042e6i	−0.172928	+	0.980721i
$486$		0			0
$487$	2.95258e6	−	5.11402e6i	0.564130	−	0.977102i	−0.433000	−	0.901394i	$-0.642545\pi$
$487$	2.95258e6	−	5.11402e6i	0.564130	−	0.977102i	0.997130	−	0.0757082i	$-0.0241217\pi$
$488$		0			0
$489$	7.33403e6	+	2.66937e6i	1.38698	+	0.504820i
$490$		0			0
$491$	−4.20142e6	+	3.52541e6i	−0.786489	+	0.659943i	−0.944874	−	0.327435i	$-0.893816\pi$
$491$	−4.20142e6	+	3.52541e6i	−0.786489	+	0.659943i	0.158385	+	0.987377i	$0.449371\pi$
$492$		0			0
$493$	3.47670e6			0.644243
$494$		0			0
$495$	2.74594e6			0.503708
$496$		0			0
$497$	−918818.	+	770980.i	−0.166855	+	0.140008i
$498$		0			0
$499$	509797.	+	185551.i	0.0916528	+	0.0333589i	0.387440	−	0.921895i	$-0.373360\pi$
$499$	509797.	+	185551.i	0.0916528	+	0.0333589i	−0.295787	+	0.955254i	$0.595582\pi$
$500$		0			0
$501$	275233.	−	476718.i	0.0489899	−	0.0848529i
$502$		0			0
$503$	−1.71893e6	+	9.74856e6i	−0.302928	+	1.71799i	0.330173	+	0.943921i	$0.392893\pi$
$503$	−1.71893e6	+	9.74856e6i	−0.302928	+	1.71799i	−0.633101	+	0.774069i	$0.718218\pi$
$504$		0			0
$505$	−4.43563e6	−	7.68274e6i	−0.773975	−	1.34056i
$506$		0			0
$507$	−8.54247e6	−	7.16798e6i	−1.47592	−	1.23845i
$508$		0			0
$509$	2.69204e6	−	979823.i	0.460561	−	0.167631i	−0.101311	−	0.994855i	$-0.532304\pi$
$509$	2.69204e6	−	979823.i	0.460561	−	0.167631i	0.561872	+	0.827224i	$0.310081\pi$
$510$		0			0
$511$	−473563.	−	2.68571e6i	−0.0802279	−	0.454995i
$512$		0			0
$513$	2.50382e6	+	972699.i	0.420059	+	0.163187i
$514$		0			0
$515$	1.24999e6	+	7.08904e6i	0.207677	+	1.17779i
$516$		0			0
$517$	1.47512e6	−	536899.i	0.242717	−	0.0883419i
$518$		0			0
$519$	8.19588e6	+	6.87716e6i	1.33560	+	1.12070i
$520$		0			0
$521$	1.05438e6	+	1.82625e6i	0.170179	+	0.294758i	0.938482	−	0.345328i	$-0.112232\pi$
$521$	1.05438e6	+	1.82625e6i	0.170179	+	0.294758i	−0.768304	+	0.640086i	$0.778899\pi$
$522$		0			0
$523$	−153029.	+	867871.i	−0.0244636	+	0.138740i	−0.994593	−	0.103847i	$-0.966885\pi$
$523$	−153029.	+	867871.i	−0.0244636	+	0.138740i	0.970130	+	0.242587i	$0.0779959\pi$
$524$		0			0
$525$	−3.51643e6	+	6.09063e6i	−0.556805	+	0.964415i
$526$		0			0
$527$	486493.	+	177069.i	0.0763045	+	0.0277726i
$528$		0			0
$529$	8.43335e6	−	7.07642e6i	1.31027	−	1.09945i
$530$		0			0
$531$	1.89592e6			0.291798
$532$		0			0
$533$	1.15287e7			1.75777
$534$		0			0
$535$	1.00533e7	−	8.43572e6i	1.51853	−	1.27420i
$536$		0			0
$537$	9.85861e6	+	3.58824e6i	1.47530	+	0.536965i
$538$		0			0
$539$	1.20000e6	−	2.07846e6i	0.177914	−	0.308156i
$540$		0			0
$541$	67304.5	−	381703.i	0.00988669	−	0.0560702i	−0.979465	−	0.201613i	$-0.935382\pi$
$541$	67304.5	−	381703.i	0.00988669	−	0.0560702i	0.989352	+	0.145543i	$0.0464928\pi$
$542$		0			0
$543$	−5.56014e6	−	9.63045e6i	−0.809257	−	1.40167i
$544$		0			0
$545$	−1.67233e7	−	1.40325e7i	−2.41174	−	2.02369i
$546$		0			0
$547$	−967427.	+	352114.i	−0.138245	+	0.0503171i	−0.410216	−	0.911988i	$-0.634547\pi$
$547$	−967427.	+	352114.i	−0.138245	+	0.0503171i	0.271971	+	0.962305i	$0.412325\pi$
$548$		0			0
$549$	753096.	+	4.27102e6i	0.106640	+	0.604785i
$550$		0			0
$551$	6.36317e6	+	1.15891e7i	0.892882	+	1.62619i
$552$		0			0
$553$	−680543.	−	3.85955e6i	−0.0946330	−	0.536690i
$554$		0			0
$555$	9.16475e6	−	3.33570e6i	1.26296	−	0.459678i
$556$		0			0
$557$	−5.19610e6	−	4.36005e6i	−0.709643	−	0.595461i	0.214856	−	0.976646i	$-0.431072\pi$
$557$	−5.19610e6	−	4.36005e6i	−0.709643	−	0.595461i	−0.924499	+	0.381185i	$0.875516\pi$
$558$		0			0
$559$	−4.75280e6	−	8.23209e6i	−0.643310	−	1.11425i
$560$		0			0
$561$	−267963.	+	1.51969e6i	−0.0359474	+	0.203868i
$562$		0			0
$563$	−2.56459e6	+	4.44200e6i	−0.340994	+	0.590619i	−0.984618	−	0.174723i	$-0.944097\pi$
$563$	−2.56459e6	+	4.44200e6i	−0.340994	+	0.590619i	0.643624	+	0.765342i	$0.277430\pi$
$564$		0			0
$565$	−665417.	−	242192.i	−0.0876946	−	0.0319182i
$566$		0			0
$567$	3.47901e6	−	2.91923e6i	0.454462	−	0.381339i
$568$		0			0
$569$	2.26988e6			0.293916			0.146958	−	0.989143i	$-0.453052\pi$
$569$	2.26988e6			0.293916			0.146958	+	0.989143i	$0.453052\pi$
$570$		0			0
$571$	4.02673e6			0.516848			0.258424	−	0.966032i	$-0.416797\pi$
$571$	4.02673e6			0.516848			0.258424	+	0.966032i	$0.416797\pi$
$572$		0			0
$573$	−1.11669e7	+	9.37016e6i	−1.42085	+	1.19223i
$574$		0			0
$575$	2.20122e7	+	8.01178e6i	2.77647	+	1.01055i
$576$		0			0
$577$	−6.34302e6	+	1.09864e7i	−0.793153	+	1.37378i	0.130853	+	0.991402i	$0.458228\pi$
$577$	−6.34302e6	+	1.09864e7i	−0.793153	+	1.37378i	−0.924006	+	0.382379i	$0.875105\pi$
$578$		0			0
$579$	249108.	−	1.41276e6i	0.0308810	−	0.175135i
$580$		0			0
$581$	−1.99733e6	−	3.45948e6i	−0.245477	−	0.425178i
$582$		0			0
$583$	−1.40187e6	−	1.17631e6i	−0.170819	−	0.143334i
$584$		0			0
$585$	−1.33456e7	+	4.85739e6i	−1.61231	+	0.586831i
$586$		0			0
$587$	−1.45790e6	−	8.26816e6i	−0.174636	−	0.990407i	−0.938564	−	0.345106i	$-0.887843\pi$
$587$	−1.45790e6	−	8.26816e6i	−0.174636	−	0.990407i	0.763928	−	0.645301i	$-0.223268\pi$
$588$		0			0
$589$	300159.	+	1.94574e6i	0.0356503	+	0.231098i
$590$		0			0
$591$	1.25612e6	+	7.12382e6i	0.147932	+	0.838966i
$592$		0			0
$593$	−1.30381e6	+	474549.i	−0.152258	+	0.0554172i	−0.417025	−	0.908895i	$-0.636927\pi$
$593$	−1.30381e6	+	474549.i	−0.152258	+	0.0554172i	0.264767	+	0.964312i	$0.414705\pi$
$594$		0			0
$595$	−1.85566e6	−	1.55708e6i	−0.214885	−	0.180310i
$596$		0			0
$597$	−9.39041e6	−	1.62647e7i	−1.07832	−	1.86771i
$598$		0			0
$599$	551434.	−	3.12734e6i	0.0627953	−	0.356130i	−0.937178	−	0.348851i	$-0.886572\pi$
$599$	551434.	−	3.12734e6i	0.0627953	−	0.356130i	0.999974	−	0.00727875i	$-0.00231692\pi$
$600$		0			0
$601$	−1.91573e6	+	3.31815e6i	−0.216346	+	0.374722i	−0.953688	−	0.300797i	$-0.902747\pi$
$601$	−1.91573e6	+	3.31815e6i	−0.216346	+	0.374722i	0.737342	+	0.675520i	$0.236081\pi$
$602$		0			0
$603$	2.99473e6	+	1.08999e6i	0.335401	+	0.122076i
$604$		0			0
$605$	−9.04494e6	+	7.58961e6i	−1.00466	+	0.843006i
$606$		0			0
$607$	−2.21271e6			−0.243754			−0.121877	−	0.992545i	$-0.538891\pi$
$607$	−2.21271e6			−0.243754			−0.121877	+	0.992545i	$0.538891\pi$
$608$		0			0
$609$	1.05360e7			1.15115
$610$		0			0
$611$	−6.21949e6	+	5.21877e6i	−0.673987	+	0.565543i
$612$		0			0
$613$	1.36365e7	+	4.96330e6i	1.46573	+	0.533481i	0.946937	−	0.321420i	$-0.104160\pi$
$613$	1.36365e7	+	4.96330e6i	1.46573	+	0.533481i	0.518790	+	0.854901i	$0.326382\pi$
$614$		0			0
$615$	1.11920e7	−	1.93851e7i	1.19322	−	2.06671i
$616$		0			0
$617$	484607.	−	2.74834e6i	0.0512480	−	0.290642i	−0.948403	−	0.317068i	$-0.897302\pi$
$617$	484607.	−	2.74834e6i	0.0512480	−	0.290642i	0.999651	+	0.0264263i	$0.00841274\pi$
$618$		0			0
$619$	2.40971e6	+	4.17374e6i	0.252777	+	0.437823i	0.964289	−	0.264851i	$-0.0853226\pi$
$619$	2.40971e6	+	4.17374e6i	0.252777	+	0.437823i	−0.711512	+	0.702674i	$0.751989\pi$
$620$		0			0
$621$	−5.46180e6	−	4.58299e6i	−0.568338	−	0.476892i
$622$		0			0
$623$	5.28810e6	−	1.92471e6i	0.545858	−	0.198676i
$624$		0			0
$625$	722761.	+	4.09898e6i	0.0740107	+	0.419735i
$626$		0			0
$627$	−5.55614e6	+	1.88817e6i	−0.564422	+	0.191811i
$628$		0			0
$629$	374605.	+	2.12449e6i	0.0377526	+	0.214105i
$630$		0			0
$631$	1.42928e7	−	5.20216e6i	1.42904	−	0.520129i	0.492385	−	0.870378i	$-0.336125\pi$
$631$	1.42928e7	−	5.20216e6i	1.42904	−	0.520129i	0.936657	+	0.350249i	$0.113903\pi$
$632$		0			0
$633$	4.13328e6	+	3.46823e6i	0.410001	+	0.344032i
$634$		0			0
$635$	9.98346e6	+	1.72919e7i	0.982532	+	1.70180i
$636$		0			0
$637$	−2.15547e6	+	1.22243e7i	−0.210471	+	1.19364i
$638$		0			0
$639$	−1.51000e6	+	2.61540e6i	−0.146294	+	0.253388i
$640$		0			0
$641$	−1.01407e7	−	3.69091e6i	−0.974816	−	0.354804i	−0.194994	−	0.980805i	$-0.562469\pi$
$641$	−1.01407e7	−	3.69091e6i	−0.974816	−	0.354804i	−0.779823	+	0.626000i	$0.784691\pi$
$642$		0			0
$643$	7.67163e6	−	6.43727e6i	0.731746	−	0.614008i	−0.198861	−	0.980028i	$-0.563724\pi$
$643$	7.67163e6	−	6.43727e6i	0.731746	−	0.614008i	0.930607	+	0.366020i	$0.119280\pi$
$644$		0			0
$645$	−1.84560e7			−1.74678
$646$		0			0
$647$	−1.91791e7			−1.80122			−0.900610	−	0.434629i	$-0.856880\pi$
$647$	−1.91791e7			−1.80122			−0.900610	+	0.434629i	$0.856880\pi$
$648$		0			0
$649$	1.71542e6	−	1.43940e6i	0.159867	−	0.134144i
$650$		0			0
$651$	1.47430e6	+	536602.i	0.136343	+	0.0496249i
$652$		0			0
$653$	3.52031e6	−	6.09736e6i	0.323071	−	0.559576i	−0.658049	−	0.752975i	$-0.728618\pi$
$653$	3.52031e6	−	6.09736e6i	0.323071	−	0.559576i	0.981120	+	0.193399i	$0.0619513\pi$
$654$		0			0
$655$	−5.03606e6	+	2.85609e7i	−0.458656	+	2.60117i
$656$		0			0
$657$	−3.43329e6	−	5.94663e6i	−0.310311	−	0.537474i
$658$		0			0
$659$	3.72688e6	+	3.12722e6i	0.334296	+	0.280508i	0.794448	−	0.607332i	$-0.207760\pi$
$659$	3.72688e6	+	3.12722e6i	0.334296	+	0.280508i	−0.460151	+	0.887840i	$0.652205\pi$
$660$		0			0
$661$	−48768.9	+	17750.4i	−0.00434150	+	0.00158018i	−0.344190	−	0.938900i	$-0.611846\pi$
$661$	−48768.9	+	17750.4i	−0.00434150	+	0.00158018i	0.339848	+	0.940480i	$0.389624\pi$
$662$		0			0
$663$	−1.38591e6	−	7.85987e6i	−0.122448	−	0.694435i
$664$		0			0
$665$	1.79405e6	−	9.03542e6i	0.157318	−	0.792309i
$666$		0			0
$667$	−6.09387e6	−	3.45601e7i	−0.530370	−	3.00788i
$668$		0			0
$669$	−2.57339e7	+	9.36636e6i	−2.22300	+	0.809106i
$670$		0			0
$671$	3.92401e6	+	3.29264e6i	0.336453	+	0.282317i
$672$		0			0
$673$	−7.47505e6	−	1.29472e7i	−0.636175	−	1.10189i	−0.986265	−	0.165171i	$-0.947182\pi$
$673$	−7.47505e6	−	1.29472e7i	−0.636175	−	1.10189i	0.350090	−	0.936716i	$-0.386151\pi$
$674$		0			0
$675$	1.66246e6	−	9.42828e6i	0.140440	−	0.796477i
$676$		0			0
$677$	−2.76757e6	+	4.79356e6i	−0.232074	+	0.401964i	−0.958418	−	0.285367i	$-0.907884\pi$
$677$	−2.76757e6	+	4.79356e6i	−0.232074	+	0.401964i	0.726344	+	0.687331i	$0.241218\pi$
$678$		0			0
$679$	−3.24947e6	−	1.18271e6i	−0.270482	−	0.0984473i
$680$		0			0
$681$	−1.06766e7	+	8.95873e6i	−0.882197	+	0.740251i
$682$		0			0
$683$	1.93157e6			0.158437			0.0792187	−	0.996857i	$-0.474757\pi$
$683$	1.93157e6			0.158437			0.0792187	+	0.996857i	$0.474757\pi$
$684$		0			0
$685$	−1.46407e7			−1.19216
$686$		0			0
$687$	−1.94859e7	+	1.63506e7i	−1.57517	+	1.32173i
$688$		0			0
$689$	8.89406e6	+	3.23717e6i	0.713759	+	0.259787i
$690$		0			0
$691$	−62105.2	+	107569.i	−0.00494804	+	0.00857025i	−0.868489	−	0.495709i	$-0.834908\pi$
$691$	−62105.2	+	107569.i	−0.00494804	+	0.00857025i	0.863541	+	0.504279i	$0.168242\pi$
$692$		0			0
$693$	−319624.	+	1.81268e6i	−0.0252817	+	0.143380i
$694$		0			0
$695$	−1.44479e7	−	2.50244e7i	−1.13460	−	1.96518i
$696$		0			0
$697$	3.79279e6	+	3.18253e6i	0.295717	+	0.248136i
$698$		0			0
$699$	−2.94260e6	+	1.07102e6i	−0.227792	+	0.0829096i
$700$		0			0
$701$	−3.80268e6	−	2.15661e7i	−0.292277	−	1.65758i	−0.678069	−	0.734998i	$-0.737183\pi$
$701$	−3.80268e6	−	2.15661e7i	−0.292277	−	1.65758i	0.385792	−	0.922586i	$-0.373928\pi$
$702$		0			0
$703$	−6.39610e6	+	5.13701e6i	−0.488120	+	0.392032i
$704$		0			0
$705$	2.73734e6	+	1.55242e7i	0.207422	+	1.17635i
$706$		0			0
$707$	5.58791e6	−	2.03383e6i	0.420437	−	0.153027i
$708$		0			0
$709$	1.81335e7	+	1.52158e7i	1.35477	+	1.13679i	0.977559	+	0.210663i	$0.0675623\pi$
$709$	1.81335e7	+	1.52158e7i	1.35477	+	1.13679i	0.377214	+	0.926126i	$0.376882\pi$
$710$		0			0
$711$	−4.93387e6	−	8.54571e6i	−0.366027	−	0.633978i
$712$		0			0
$713$	907438.	−	5.14634e6i	0.0668488	−	0.379118i
$714$		0			0
$715$	−8.38721e6	+	1.45271e7i	−0.613553	+	1.06271i
$716$		0			0
$717$	2.52973e7	+	9.20746e6i	1.83771	+	0.668870i
$718$		0			0
$719$	−9.73072e6	+	8.16504e6i	−0.701977	+	0.589029i	−0.922335	−	0.386390i	$-0.873722\pi$
$719$	−9.73072e6	+	8.16504e6i	−0.701977	+	0.589029i	0.220358	+	0.975419i	$0.429277\pi$
$720$		0			0
$721$	−4.82519e6			−0.345681
$722$		0			0
$723$	−451097.			−0.0320940
$724$		0			0
$725$	3.60974e7	−	3.02893e7i	2.55053	−	2.14015i
$726$		0			0
$727$	−2.38343e7	−	8.67499e6i	−1.67250	−	0.608741i	−0.680251	−	0.732980i	$-0.738129\pi$
$727$	−2.38343e7	−	8.67499e6i	−1.67250	−	0.608741i	−0.992252	+	0.124238i	$0.960351\pi$
$728$		0			0
$729$	1.56561e6	−	2.71172e6i	0.109110	−	0.188984i
$730$		0			0
$731$	708884.	−	4.02028e6i	0.0490661	−	0.278268i
$732$		0			0
$733$	1.10906e7	+	1.92096e7i	0.762424	+	1.32056i	0.941598	+	0.336740i	$0.109324\pi$
$733$	1.10906e7	+	1.92096e7i	0.762424	+	1.32056i	−0.179174	+	0.983817i	$0.557342\pi$
$734$		0			0
$735$	1.84622e7	+	1.54916e7i	1.26056	+	1.05774i
$736$		0			0
$737$	3.53716e6	−	1.28742e6i	0.239875	−	0.0873075i
$738$		0			0
$739$	3.26064e6	+	1.84920e7i	0.219630	+	1.24558i	0.872689	+	0.488276i	$0.162374\pi$
$739$	3.26064e6	+	1.84920e7i	0.219630	+	1.24558i	−0.653059	+	0.757307i	$0.726515\pi$
$740$		0			0
$741$	2.36634e7	−	1.90052e7i	1.58318	−	1.27153i
$742$		0			0
$743$	1.52527e6	+	8.65025e6i	0.101362	+	0.574853i	0.992611	+	0.121339i	$0.0387187\pi$
$743$	1.52527e6	+	8.65025e6i	0.101362	+	0.574853i	−0.891249	+	0.453514i	$0.850170\pi$
$744$		0			0
$745$	3.25130e7	−	1.18338e7i	2.14618	−	0.781146i
$746$		0			0
$747$	−7.70490e6	−	6.46518e6i	−0.505202	−	0.423915i
$748$		0			0
$749$	4.39848e6	+	7.61839e6i	0.286483	+	0.496202i
$750$		0			0
$751$	3.24746e6	−	1.84173e7i	0.210109	−	1.19159i	−0.679087	−	0.734058i	$-0.737624\pi$
$751$	3.24746e6	−	1.84173e7i	0.210109	−	1.19159i	0.889195	−	0.457528i	$-0.151265\pi$
$752$		0			0
$753$	−4.53501e6	+	7.85486e6i	−0.291468	+	0.504837i
$754$		0			0
$755$	9.23908e6	+	3.36275e6i	0.589877	+	0.214698i
$756$		0			0
$757$	3.48906e6	−	2.92767e6i	0.221294	−	0.185687i	−0.525400	−	0.850855i	$-0.676084\pi$
$757$	3.48906e6	−	2.92767e6i	0.221294	−	0.185687i	0.746694	+	0.665168i	$0.231640\pi$
$758$		0			0
$759$	1.55762e7			0.981423
$760$		0			0
$761$	1.49314e6			0.0934627			0.0467313	−	0.998907i	$-0.485120\pi$
$761$	1.49314e6			0.0934627			0.0467313	+	0.998907i	$0.485120\pi$
$762$		0			0
$763$	1.12099e7	−	9.40620e6i	0.697090	−	0.584928i
$764$		0			0
$765$	−5.73142e6	−	2.08607e6i	−0.354086	−	0.128877i
$766$		0			0
$767$	−5.79089e6	+	1.00301e7i	−0.355432	+	0.615627i
$768$		0			0
$769$	−1.84111e6	+	1.04415e7i	−0.112270	+	0.636715i	0.875796	+	0.482682i	$0.160337\pi$
$769$	−1.84111e6	+	1.04415e7i	−0.112270	+	0.636715i	−0.988066	+	0.154033i	$0.950774\pi$
$770$		0			0
$771$	1.67014e7	+	2.89277e7i	1.01185	+	1.75258i
$772$		0			0
$773$	−7.12915e6	−	5.98207e6i	−0.429130	−	0.360083i	0.402493	−	0.915423i	$-0.368144\pi$
$773$	−7.12915e6	−	5.98207e6i	−0.429130	−	0.360083i	−0.831623	+	0.555340i	$0.812588\pi$
$774$		0			0
$775$	6.59374e6	−	2.39993e6i	0.394346	−	0.143530i
$776$		0			0
$777$	1.13523e6	+	6.43820e6i	0.0674576	+	0.382571i
$778$		0			0
$779$	−3.66686e6	+	1.84675e7i	−0.216496	+	1.09035i
$780$		0			0
$781$	619404.	+	3.51282e6i	0.0363368	+	0.206076i
$782$		0			0
$783$	−1.34776e7	+	4.90544e6i	−0.785611	+	0.285939i
$784$		0			0
$785$	−1.68395e7	−	1.41300e7i	−0.975338	−	0.818406i
$786$		0			0
$787$	−1.12853e7	−	1.95466e7i	−0.649493	−	1.12495i	−0.983244	−	0.182294i	$-0.941648\pi$
$787$	−1.12853e7	−	1.95466e7i	−0.649493	−	1.12495i	0.333751	−	0.942661i	$-0.391686\pi$
$788$		0			0
$789$	−1.32900e6	+	7.53711e6i	−0.0760030	+	0.431035i
$790$		0			0
$791$	237332.	−	411071.i	0.0134870	−	0.0233601i
$792$		0			0
$793$	−2.48956e7	−	9.06124e6i	−1.40585	−	0.511687i
$794$		0			0
$795$	1.40775e7	−	1.18124e7i	0.789964	−	0.662859i
$796$		0			0
$797$	4.60306e6			0.256685			0.128343	−	0.991730i	$-0.459034\pi$
$797$	4.60306e6			0.256685			0.128343	+	0.991730i	$0.459034\pi$
$798$		0			0
$799$	−3.48679e6			−0.193223
$800$		0			0
$801$	1.08543e7	−	9.10780e6i	0.597749	−	0.501571i
$802$		0			0
$803$	−7.62118e6	−	2.77388e6i	−0.417093	−	0.151810i
$804$		0			0
$805$	−1.22256e7	+	2.11754e7i	−0.664937	+	1.15170i
$806$		0			0
$807$	7.38198e6	−	4.18653e7i	0.399015	−	2.26292i
$808$		0			0
$809$	1.10030e7	+	1.90578e7i	0.591072	+	1.02377i	0.994088	+	0.108574i	$0.0346285\pi$
$809$	1.10030e7	+	1.90578e7i	0.591072	+	1.02377i	−0.403016	+	0.915193i	$0.632038\pi$
$810$		0			0
$811$	−271515.	−	227828.i	−0.0144958	−	0.0121634i	0.635511	−	0.772092i	$-0.280789\pi$
$811$	−271515.	−	227828.i	−0.0144958	−	0.0121634i	−0.650007	+	0.759928i	$0.725234\pi$
$812$		0			0
$813$	2.38783e7	−	8.69099e6i	1.26700	−	0.461151i
$814$		0			0
$815$	6.32696e6	+	3.58820e7i	0.333657	+	1.89227i
$816$		0			0
$817$	1.46985e7	−	4.99508e6i	0.770404	−	0.261811i
$818$		0			0
$819$	−1.65310e6	−	9.37520e6i	−0.0861172	−	0.488395i
$820$		0			0
$821$	−1.65080e7	+	6.00843e6i	−0.854747	+	0.311102i	−0.731974	−	0.681333i	$-0.761401\pi$
$821$	−1.65080e7	+	6.00843e6i	−0.854747	+	0.311102i	−0.122773	+	0.992435i	$0.539179\pi$
$822$		0			0
$823$	−4.15493e6	−	3.48640e6i	−0.213828	−	0.179423i	0.529583	−	0.848258i	$-0.322349\pi$
$823$	−4.15493e6	−	3.48640e6i	−0.213828	−	0.179423i	−0.743410	+	0.668836i	$0.766793\pi$
$824$		0			0
$825$	1.04576e7	+	1.81130e7i	0.534928	+	0.926522i
$826$		0			0
$827$	−951873.	+	5.39834e6i	−0.0483966	+	0.274471i	−0.999397	−	0.0347184i	$-0.988947\pi$
$827$	−951873.	+	5.39834e6i	−0.0483966	+	0.274471i	0.951000	+	0.309189i	$0.100058\pi$
$828$		0			0
$829$	1.19151e7	−	2.06376e7i	0.602160	−	1.04297i	−0.390334	−	0.920673i	$-0.627640\pi$
$829$	1.19151e7	−	2.06376e7i	0.602160	−	1.04297i	0.992493	−	0.122298i	$-0.0390263\pi$
$830$		0			0
$831$	−1.76917e7	−	6.43925e6i	−0.888724	−	0.323469i
$832$		0			0
$833$	−4.08367e6	+	3.42661e6i	−0.203910	+	0.171101i
$834$		0			0
$835$	2.56980e6			0.127551
$836$		0			0
$837$	−2.13575e6			−0.105375
$838$		0			0
$839$	−7.75435e6	+	6.50668e6i	−0.380313	+	0.319120i	−0.812825	−	0.582508i	$-0.802072\pi$
$839$	−7.75435e6	+	6.50668e6i	−0.380313	+	0.319120i	0.432513	+	0.901628i	$0.357627\pi$
$840$		0			0
$841$	−4.70624e7	−	1.71293e7i	−2.29448	−	0.835123i
$842$		0			0
$843$	912524.	−	1.58054e6i	0.0442258	−	0.0766013i
$844$		0			0
$845$	9.03998e6	−	5.12683e7i	0.435538	−	2.47006i
$846$		0			0
$847$	−3.95731e6	−	6.85426e6i	−0.189536	−	0.328286i
$848$		0			0
$849$	8.62623e6	+	7.23827e6i	0.410726	+	0.344640i
$850$		0			0
$851$	2.04618e7	−	7.44750e6i	0.968548	−	0.352522i
$852$		0			0
$853$	390874.	+	2.21675e6i	0.0183935	+	0.104315i	0.992622	−	0.121247i	$-0.0386894\pi$
$853$	390874.	+	2.21675e6i	0.0183935	+	0.104315i	−0.974229	+	0.225562i	$0.927578\pi$
$854$		0			0
$855$	−3.53620e6	−	2.29229e7i	−0.165433	−	1.07240i
$856$		0			0
$857$	−675433.	−	3.83057e6i	−0.0314145	−	0.178161i	0.965063	−	0.262017i	$-0.0843875\pi$
$857$	−675433.	−	3.83057e6i	−0.0314145	−	0.178161i	−0.996478	+	0.0838561i	$0.973276\pi$
$858$		0			0
$859$	6.38183e6	−	2.32280e6i	0.295095	−	0.107406i	−0.190230	−	0.981740i	$-0.560923\pi$
$859$	6.38183e6	−	2.32280e6i	0.295095	−	0.107406i	0.485325	+	0.874334i	$0.338701\pi$
$860$		0			0
$861$	1.14939e7	+	9.64456e6i	0.528398	+	0.443378i
$862$		0			0
$863$	−1.97133e6	−	3.41444e6i	−0.0901014	−	0.156060i	0.817452	−	0.575996i	$-0.195386\pi$
$863$	−1.97133e6	−	3.41444e6i	−0.0901014	−	0.156060i	−0.907554	+	0.419936i	$0.862052\pi$
$864$		0			0
$865$	−8.67321e6	+	4.91882e7i	−0.394130	+	2.23522i
$866$		0			0
$867$	−1.24976e7	+	2.16466e7i	−0.564651	+	0.978005i
$868$		0			0
$869$	−1.09522e7	−	3.98626e6i	−0.491983	−	0.179067i
$870$		0			0
$871$	−1.49136e7	+	1.25140e7i	−0.666096	+	0.558921i
$872$		0			0
$873$	−8.70681e6			−0.386655
$874$		0			0
$875$	−1.45381e7			−0.641928
$876$		0			0
$877$	2.12407e7	−	1.78231e7i	0.932546	−	0.782499i	−0.0437266	−	0.999044i	$-0.513923\pi$
$877$	2.12407e7	−	1.78231e7i	0.932546	−	0.782499i	0.976273	+	0.216544i	$0.0694786\pi$
$878$		0			0
$879$	2.09479e7	+	7.62441e6i	0.914467	+	0.332839i
$880$		0			0
$881$	6.14896e6	−	1.06503e7i	0.266908	−	0.462299i	−0.701154	−	0.713010i	$-0.747331\pi$
$881$	6.14896e6	−	1.06503e7i	0.266908	−	0.462299i	0.968062	+	0.250712i	$0.0806646\pi$
$882$		0			0
$883$	−789907.	+	4.47978e6i	−0.0340937	+	0.193355i	−0.997098	−	0.0761319i	$-0.975743\pi$
$883$	−789907.	+	4.47978e6i	−0.0340937	+	0.193355i	0.963004	+	0.269487i	$0.0868541\pi$
$884$		0			0
$885$	1.12435e7	+	1.94744e7i	0.482552	+	0.835805i
$886$		0			0
$887$	4.30646e6	+	3.61355e6i	0.183785	+	0.154214i	0.730039	−	0.683406i	$-0.239502\pi$
$887$	4.30646e6	+	3.61355e6i	0.183785	+	0.154214i	−0.546253	+	0.837620i	$0.683946\pi$
$888$		0			0
$889$	−1.25769e7	+	4.57763e6i	−0.533729	+	0.194261i
$890$		0			0
$891$	−2.34531e6	−	1.33009e7i	−0.0989705	−	0.561290i
$892$		0			0
$893$	−6.38164e6	−	1.16228e7i	−0.267796	−	0.487732i
$894$		0			0
$895$	8.50487e6	+	4.82335e7i	0.354904	+	2.01276i
$896$		0			0
$897$	−7.57018e7	+	2.75532e7i	−3.14141	+	1.14338i
$898$		0			0
$899$	−8.05277e6	−	6.75708e6i	−0.332312	−	0.278843i
$900$		0			0
$901$	2.03240e6	+	3.52022e6i	0.0834060	+	0.144463i
$902$		0			0
$903$	2.14825e6	−	1.21833e7i	0.0876730	−	0.497218i
$904$		0			0
$905$	2.59570e7	−	4.49588e7i	1.05350	−	1.82471i
$906$		0			0
$907$	1.27637e7	+	4.64560e6i	0.515178	+	0.187510i	0.586508	−	0.809943i	$-0.300502\pi$
$907$	1.27637e7	+	4.64560e6i	0.515178	+	0.187510i	−0.0713300	+	0.997453i	$0.522724\pi$
$908$		0			0
$909$	1.14696e7	−	9.62417e6i	0.460405	−	0.386326i
$910$		0			0
$911$	−2.04315e7			−0.815651			−0.407825	−	0.913060i	$-0.633713\pi$
$911$	−2.04315e7			−0.815651			−0.407825	+	0.913060i	$0.633713\pi$
$912$		0			0
$913$	−1.18798e7			−0.471663
$914$		0			0
$915$	−3.94046e7	+	3.30644e7i	−1.55595	+	1.30559i
$916$		0			0
$917$	−1.82677e7	−	6.64891e6i	−0.717399	−	0.261112i
$918$		0			0
$919$	−1.94877e7	+	3.37536e7i	−0.761151	+	1.31835i	0.181106	+	0.983464i	$0.442032\pi$
$919$	−1.94877e7	+	3.37536e7i	−0.761151	+	1.31835i	−0.942258	+	0.334889i	$0.891301\pi$
$920$		0			0
$921$	−8.27915e6	+	4.69534e7i	−0.321615	+	1.82397i
$922$		0			0
$923$	−9.22430e6	−	1.59770e7i	−0.356393	−	0.617291i
$924$		0			0
$925$	2.23982e7	+	1.87943e7i	0.860712	+	0.722223i
$926$		0			0
$927$	−1.14165e7	+	4.15526e6i	−0.436348	+	0.158818i
$928$		0			0
$929$	−1.32755e6	−	7.52890e6i	−0.0504674	−	0.286215i	0.949121	−	0.314912i	$-0.101975\pi$
$929$	−1.32755e6	−	7.52890e6i	−0.0504674	−	0.286215i	−0.999588	+	0.0286975i	$0.990864\pi$
$930$		0			0
$931$	−1.88962e7	−	7.34091e6i	−0.714498	−	0.277572i
$932$		0			0
$933$	−1.07503e7	−	6.09681e7i	−0.404313	−	2.29297i
$934$		0			0
$935$	−6.76953e6	+	2.46391e6i	−0.253238	+	0.0921712i
$936$		0			0
$937$	−446002.	−	374240.i	−0.0165954	−	0.0139252i	0.634452	−	0.772962i	$-0.281226\pi$
$937$	−446002.	−	374240.i	−0.0165954	−	0.0139252i	−0.651048	+	0.759037i	$0.725670\pi$
$938$		0			0
$939$	2.95108e7	+	5.11141e7i	1.09224	+	1.89181i
$940$		0			0
$941$	7.50164e6	−	4.25439e7i	0.276174	−	1.56626i	−0.459035	−	0.888418i	$-0.651805\pi$
$941$	7.50164e6	−	4.25439e7i	0.276174	−	1.56626i	0.735209	−	0.677840i	$-0.237084\pi$
$942$		0			0
$943$	2.49880e7	−	4.32804e7i	0.915064	−	1.58494i
$944$		0			0
$945$	9.39052e6	+	3.41787e6i	0.342066	+	0.124502i
$946$		0			0
$947$	1.71355e7	−	1.43784e7i	0.620902	−	0.520998i	−0.277185	−	0.960816i	$-0.589402\pi$
$947$	1.71355e7	−	1.43784e7i	0.620902	−	0.520998i	0.898087	+	0.439818i	$0.144957\pi$
$948$		0			0
$949$	4.19465e7			1.51193
$950$		0			0
$951$	3.03414e7			1.08789
$952$		0			0
$953$	−2.96980e7	+	2.49196e7i	−1.05924	+	0.888809i	−0.994035	−	0.109063i	$-0.965215\pi$
$953$	−2.96980e7	+	2.49196e7i	−1.05924	+	0.888809i	−0.0652064	+	0.997872i	$0.520771\pi$
$954$		0			0
$955$	−6.39490e7	−	2.32755e7i	−2.26895	−	0.825830i
$956$		0			0
$957$	1.56666e7	−	2.71354e7i	0.552962	−	0.957759i
$958$		0			0
$959$	1.70415e6	−	9.66474e6i	0.0598360	−	0.339347i
$960$		0			0
$961$	1.35319e7	+	2.34379e7i	0.472661	+	0.818673i
$962$		0			0
$963$	1.69675e7	+	1.42375e7i	0.589594	+	0.494729i
$964$		0			0
$965$	6.29319e6	−	2.29053e6i	0.217547	−	0.0791805i
$966$		0			0
$967$	4.06535e6	+	2.30557e7i	0.139808	+	0.792890i	0.971390	+	0.237488i	$0.0763242\pi$
$967$	4.06535e6	+	2.30557e7i	0.139808	+	0.792890i	−0.831583	+	0.555401i	$0.812565\pi$
$968$		0			0
$969$	1.30314e7	+	279889.i	0.445842	+	0.00957582i
$970$		0			0
$971$	4.28381e6	+	2.42947e7i	0.145808	+	0.826920i	0.966715	+	0.255857i	$0.0823576\pi$
$971$	4.28381e6	+	2.42947e7i	0.145808	+	0.826920i	−0.820906	+	0.571063i	$0.806531\pi$
$972$		0			0
$973$	1.82011e7	−	6.62465e6i	0.616333	−	0.224327i
$974$		0			0
$975$	−8.28655e7	−	6.95324e7i	−2.79166	−	2.34248i
$976$		0			0
$977$	1.65604e7	+	2.86834e7i	0.555053	+	0.961379i	0.997899	+	0.0647819i	$0.0206352\pi$
$977$	1.65604e7	+	2.86834e7i	0.555053	+	0.961379i	−0.442847	+	0.896597i	$0.646031\pi$
$978$		0			0
$979$	2.90611e6	−	1.64814e7i	0.0969071	−	0.549588i
$980$		0			0
$981$	1.84225e7	−	3.19087e7i	0.611190	−	1.05861i
$982$		0			0
$983$	1.55133e7	+	5.64638e6i	0.512060	+	0.186374i	0.585110	−	0.810954i	$-0.301051\pi$
$983$	1.55133e7	+	5.64638e6i	0.512060	+	0.186374i	−0.0730507	+	0.997328i	$0.523273\pi$
$984$		0			0
$985$	−2.58692e7	+	2.17069e7i	−0.849557	+	0.712863i
$986$		0			0
$987$	−1.05666e7			−0.345258
$988$		0			0
$989$	−4.12061e7			−1.33959
$990$		0			0
$991$	−4.51841e7	+	3.79140e7i	−1.46151	+	1.22635i	−0.537904	+	0.843006i	$0.680784\pi$
$991$	−4.51841e7	+	3.79140e7i	−1.46151	+	1.22635i	−0.923605	+	0.383346i	$0.874772\pi$
$992$		0			0
$993$	804128.	+	292679.i	0.0258793	+	0.00941929i
$994$		0			0
$995$	4.38382e7	−	7.59300e7i	1.40377	−	2.43139i
$996$		0			0
$997$	2.87991e6	−	1.63328e7i	0.0917575	−	0.520383i	−0.903935	−	0.427669i	$-0.859335\pi$
$997$	2.87991e6	−	1.63328e7i	0.0917575	−	0.520383i	0.995693	−	0.0927134i	$-0.0295540\pi$
$998$		0			0
$999$	−4.44972e6	−	7.70714e6i	−0.141065	−	0.244331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.i.a.9.2	✓	48
19.17	even	9	inner	76.6.i.a.17.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.i.a.9.2	✓	48	1.1	even	1	trivial
76.6.i.a.17.2	yes	48	19.17	even	9	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	76.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-15.3348 + 12.8674i) q^{3} +(-87.8167 - 31.9627i) q^{5} +(31.3213 - 54.2501i) q^{7} +(27.3887 - 155.329i) q^{9} +O(q^{10})\)	\(q+(-15.3348 + 12.8674i) q^{3} +(-87.8167 - 31.9627i) q^{5} +(31.3213 - 54.2501i) q^{7} +(27.3887 - 155.329i) q^{9} +(-93.1468 - 161.335i) q^{11} +(738.094 + 619.334i) q^{13} +(1757.93 - 639.833i) q^{15} +(71.8544 + 407.506i) q^{17} +(-1226.86 + 985.349i) q^{19} +(217.753 + 1234.94i) q^{21} +(3924.87 - 1428.53i) q^{23} +(4296.28 + 3605.01i) q^{25} +(-853.518 - 1478.34i) q^{27} +(1459.00 - 8274.38i) q^{29} +(625.573 - 1083.52i) q^{31} +(3504.35 + 1275.48i) q^{33} +(-4484.51 + 3762.95i) q^{35} +5213.39 q^{37} -19287.7 q^{39} +(9165.91 - 7691.11i) q^{41} +(-9270.60 - 3374.22i) q^{43} +(-7369.93 + 12765.1i) q^{45} +(-1463.23 + 8298.40i) q^{47} +(6441.45 + 11156.9i) q^{49} +(-6345.42 - 5324.44i) q^{51} +(9230.86 - 3359.76i) q^{53} +(3023.15 + 17145.1i) q^{55} +(6134.74 - 30896.6i) q^{57} +(2087.31 + 11837.7i) q^{59} +(-25838.3 + 9404.37i) q^{61} +(-7568.77 - 6350.96i) q^{63} +(-45021.4 - 77979.4i) q^{65} +(-3508.65 + 19898.6i) q^{67} +(-41805.4 + 72409.1i) q^{69} +(-17992.5 - 6548.74i) q^{71} +(33349.7 - 27983.7i) q^{73} -112270. q^{75} -11669.9 q^{77} +(47925.8 - 40214.5i) q^{79} +(68126.7 + 24796.1i) q^{81} +(31884.6 - 55225.8i) q^{83} +(6714.98 - 38082.5i) q^{85} +(84096.4 + 145659. i) q^{87} +(68817.4 + 57744.6i) q^{89} +(56717.0 - 20643.3i) q^{91} +(4349.12 + 24665.1i) q^{93} +(139233. - 47316.4i) q^{95} +(-9585.78 - 54363.6i) q^{97} +(-27611.2 + 10049.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9}+O(q^{10}) \) 48 * q + 33 * q^3 - 177 * q^7 + 33 * q^9	\( 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9} - 237 q^{11} + 2049 q^{13} + 2085 q^{15} - 609 q^{17} - 6012 q^{19} + 3591 q^{21} + 14100 q^{23} + 11802 q^{25} - 861 q^{27} - 10575 q^{29} - 6546 q^{31} - 21234 q^{33} - 231 q^{35} + 20052 q^{37} + 72204 q^{39} - 3249 q^{41} - 34677 q^{43} - 34956 q^{45} + 4461 q^{47} - 41139 q^{49} + 12099 q^{51} - 24291 q^{53} - 61767 q^{55} - 64470 q^{57} - 20100 q^{59} + 95490 q^{61} + 86403 q^{63} - 57915 q^{65} - 64452 q^{67} - 99315 q^{69} - 115536 q^{71} - 16362 q^{73} + 236250 q^{75} + 26688 q^{77} + 29799 q^{79} + 180327 q^{81} + 52347 q^{83} + 204618 q^{85} + 69414 q^{87} + 47394 q^{89} - 249384 q^{91} - 462126 q^{93} + 412869 q^{95} - 229974 q^{97} - 692274 q^{99}+O(q^{100}) \) 48 * q + 33 * q^3 - 177 * q^7 + 33 * q^9 - 237 * q^11 + 2049 * q^13 + 2085 * q^15 - 609 * q^17 - 6012 * q^19 + 3591 * q^21 + 14100 * q^23 + 11802 * q^25 - 861 * q^27 - 10575 * q^29 - 6546 * q^31 - 21234 * q^33 - 231 * q^35 + 20052 * q^37 + 72204 * q^39 - 3249 * q^41 - 34677 * q^43 - 34956 * q^45 + 4461 * q^47 - 41139 * q^49 + 12099 * q^51 - 24291 * q^53 - 61767 * q^55 - 64470 * q^57 - 20100 * q^59 + 95490 * q^61 + 86403 * q^63 - 57915 * q^65 - 64452 * q^67 - 99315 * q^69 - 115536 * q^71 - 16362 * q^73 + 236250 * q^75 + 26688 * q^77 + 29799 * q^79 + 180327 * q^81 + 52347 * q^83 + 204618 * q^85 + 69414 * q^87 + 47394 * q^89 - 249384 * q^91 - 462126 * q^93 + 412869 * q^95 - 229974 * q^97 - 692274 * q^99

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