LMFDB - Embedded newform 1050.3.c.c.449.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(449,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1050.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			449.18
Character	$\chi$	$=$	1050.449
Dual form			1050.3.c.c.449.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +(-2.59182 + 1.51079i) q^{3} +2.00000 q^{4} +(-3.66538 + 2.13658i) q^{6} -2.64575i q^{7} +2.82843 q^{8} +(4.43502 - 7.83139i) q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +(-2.59182 + 1.51079i) q^{3} +2.00000 q^{4} +(-3.66538 + 2.13658i) q^{6} -2.64575i q^{7} +2.82843 q^{8} +(4.43502 - 7.83139i) q^{9} -14.6732i q^{11} +(-5.18363 + 3.02158i) q^{12} +19.1112i q^{13} -3.74166i q^{14} +4.00000 q^{16} -29.7911 q^{17} +(6.27207 - 11.0753i) q^{18} -14.7237 q^{19} +(3.99718 + 6.85730i) q^{21} -20.7510i q^{22} +22.7912 q^{23} +(-7.33076 + 4.27316i) q^{24} +27.0273i q^{26} +(0.336829 + 26.9979i) q^{27} -5.29150i q^{28} +51.5923i q^{29} -38.6980 q^{31} +5.65685 q^{32} +(22.1681 + 38.0302i) q^{33} -42.1310 q^{34} +(8.87004 - 15.6628i) q^{36} -29.2081i q^{37} -20.8224 q^{38} +(-28.8731 - 49.5328i) q^{39} -28.6850i q^{41} +(5.65286 + 9.69769i) q^{42} +40.4802i q^{43} -29.3464i q^{44} +32.2317 q^{46} +10.5901 q^{47} +(-10.3673 + 6.04316i) q^{48} -7.00000 q^{49} +(77.2131 - 45.0082i) q^{51} +38.2224i q^{52} -95.5975 q^{53} +(0.476348 + 38.1808i) q^{54} -7.48331i q^{56} +(38.1611 - 22.2444i) q^{57} +72.9625i q^{58} -11.1354i q^{59} -104.131 q^{61} -54.7273 q^{62} +(-20.7199 - 11.7340i) q^{63} +8.00000 q^{64} +(31.3504 + 53.7828i) q^{66} +45.2575i q^{67} -59.5823 q^{68} +(-59.0707 + 34.4328i) q^{69} -93.7964i q^{71} +(12.5441 - 22.1505i) q^{72} +62.8141i q^{73} -41.3066i q^{74} -29.4474 q^{76} -38.8216 q^{77} +(-40.8327 - 70.0499i) q^{78} -122.486 q^{79} +(-41.6612 - 69.4647i) q^{81} -40.5668i q^{82} -68.2772 q^{83} +(7.99435 + 13.7146i) q^{84} +57.2477i q^{86} +(-77.9452 - 133.718i) q^{87} -41.5020i q^{88} -79.4213i q^{89} +50.5635 q^{91} +45.5825 q^{92} +(100.298 - 58.4647i) q^{93} +14.9766 q^{94} +(-14.6615 + 8.54632i) q^{96} -28.2049i q^{97} -9.89949 q^{98} +(-114.911 - 65.0759i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9}+O(q^{10}) $ 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9	$ 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9} + 128 q^{16} - 96 q^{19} + 56 q^{21} + 64 q^{24} - 320 q^{34} + 16 q^{36} - 312 q^{39} + 64 q^{46} - 224 q^{49} + 168 q^{51} + 64 q^{54} + 224 q^{61} + 256 q^{64} - 16 q^{69} - 192 q^{76} - 16 q^{79} - 248 q^{81} + 112 q^{84} - 112 q^{91} - 64 q^{94} + 128 q^{96} + 104 q^{99}+O(q^{100}) $ 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9 + 128 * q^16 - 96 * q^19 + 56 * q^21 + 64 * q^24 - 320 * q^34 + 16 * q^36 - 312 * q^39 + 64 * q^46 - 224 * q^49 + 168 * q^51 + 64 * q^54 + 224 * q^61 + 256 * q^64 - 16 * q^69 - 192 * q^76 - 16 * q^79 - 248 * q^81 + 112 * q^84 - 112 * q^91 - 64 * q^94 + 128 * q^96 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.41421			0.707107
$2$	1.41421			0.707107
$3$	−2.59182	+	1.51079i	−0.863939	+	0.503597i
$3$	−2.59182	+	1.51079i	−0.863939	+	0.503597i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	−3.66538	+	2.13658i	−0.610897	+	0.356097i
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	2.82843			0.353553
$9$	4.43502	−	7.83139i	0.492780	−	0.870154i
$10$		0			0
$11$		−	14.6732i		−	1.33393i	−0.745091	−	0.666963i	$-0.767594\pi$
$11$		−	14.6732i		−	1.33393i	0.745091	−	0.666963i	$-0.232406\pi$
$12$	−5.18363	+	3.02158i	−0.431969	+	0.251799i
$13$			19.1112i			1.47009i	0.678016	+	0.735047i	$0.262840\pi$
$13$			19.1112i			1.47009i	−0.678016	+	0.735047i	$0.737160\pi$
$14$		−	3.74166i		−	0.267261i
$15$		0			0
$16$	4.00000			0.250000
$17$	−29.7911			−1.75242			−0.876210	−	0.481930i	$-0.839936\pi$
$17$	−29.7911			−1.75242			−0.876210	+	0.481930i	$0.839936\pi$
$18$	6.27207	−	11.0753i	0.348448	−	0.615292i
$19$	−14.7237			−0.774930			−0.387465	−	0.921884i	$-0.626649\pi$
$19$	−14.7237			−0.774930			−0.387465	+	0.921884i	$0.626649\pi$
$20$		0			0
$21$	3.99718	+	6.85730i	0.190342	+	0.326538i
$22$		−	20.7510i		−	0.943228i
$23$	22.7912			0.990924			0.495462	−	0.868630i	$-0.334999\pi$
$23$	22.7912			0.990924			0.495462	+	0.868630i	$0.334999\pi$
$24$	−7.33076	+	4.27316i	−0.305448	+	0.178048i
$25$		0			0
$26$			27.0273i			1.03951i
$27$	0.336829	+	26.9979i	0.0124751	+	0.999922i
$28$		−	5.29150i		−	0.188982i
$29$			51.5923i			1.77904i	0.456891	+	0.889522i	$0.348963\pi$
$29$			51.5923i			1.77904i	−0.456891	+	0.889522i	$0.651037\pi$
$30$		0			0
$31$	−38.6980			−1.24832			−0.624162	−	0.781295i	$-0.714560\pi$
$31$	−38.6980			−1.24832			−0.624162	+	0.781295i	$0.714560\pi$
$32$	5.65685			0.176777
$33$	22.1681	+	38.0302i	0.671761	+	1.15243i
$34$	−42.1310			−1.23915
$35$		0			0
$36$	8.87004	−	15.6628i	0.246390	−	0.435077i
$37$		−	29.2081i		−	0.789409i	−0.918808	−	0.394705i	$-0.870847\pi$
$37$		−	29.2081i		−	0.789409i	0.918808	−	0.394705i	$-0.129153\pi$
$38$	−20.8224			−0.547959
$39$	−28.8731	−	49.5328i	−0.740335	−	1.27007i
$40$		0			0
$41$		−	28.6850i		−	0.699635i	−0.936818	−	0.349817i	$-0.886244\pi$
$41$		−	28.6850i		−	0.699635i	0.936818	−	0.349817i	$-0.113756\pi$
$42$	5.65286	+	9.69769i	0.134592	+	0.230897i
$43$			40.4802i			0.941400i	0.882293	+	0.470700i	$0.155999\pi$
$43$			40.4802i			0.941400i	−0.882293	+	0.470700i	$0.844001\pi$
$44$		−	29.3464i		−	0.666963i
$45$		0			0
$46$	32.2317			0.700689
$47$	10.5901			0.225321			0.112660	−	0.993634i	$-0.464063\pi$
$47$	10.5901			0.225321			0.112660	+	0.993634i	$0.464063\pi$
$48$	−10.3673	+	6.04316i	−0.215985	+	0.125899i
$49$	−7.00000			−0.142857
$50$		0			0
$51$	77.2131	−	45.0082i	1.51398	−	0.882513i
$52$			38.2224i			0.735047i
$53$	−95.5975			−1.80373			−0.901863	−	0.432022i	$-0.857800\pi$
$53$	−95.5975			−1.80373			−0.901863	+	0.432022i	$0.857800\pi$
$54$	0.476348	+	38.1808i	0.00882126	+	0.707052i
$55$		0			0
$56$		−	7.48331i		−	0.133631i
$57$	38.1611	−	22.2444i	0.669492	−	0.390253i
$58$			72.9625i			1.25797i
$59$		−	11.1354i		−	0.188735i	−0.995537	−	0.0943675i	$-0.969917\pi$
$59$		−	11.1354i		−	0.188735i	0.995537	−	0.0943675i	$-0.0300829\pi$
$60$		0			0
$61$	−104.131			−1.70707			−0.853533	−	0.521038i	$-0.825545\pi$
$61$	−104.131			−1.70707			−0.853533	+	0.521038i	$0.825545\pi$
$62$	−54.7273			−0.882698
$63$	−20.7199	−	11.7340i	−0.328887	−	0.186253i
$64$	8.00000			0.125000
$65$		0			0
$66$	31.3504	+	53.7828i	0.475007	+	0.814891i
$67$			45.2575i			0.675486i	0.941238	+	0.337743i	$0.109663\pi$
$67$			45.2575i			0.675486i	−0.941238	+	0.337743i	$0.890337\pi$
$68$	−59.5823			−0.876210
$69$	−59.0707	+	34.4328i	−0.856097	+	0.499026i
$70$		0			0
$71$		−	93.7964i		−	1.32108i	−0.750792	−	0.660538i	$-0.770328\pi$
$71$		−	93.7964i		−	1.32108i	0.750792	−	0.660538i	$-0.229672\pi$
$72$	12.5441	−	22.1505i	0.174224	−	0.307646i
$73$			62.8141i			0.860468i	0.902717	+	0.430234i	$0.141569\pi$
$73$			62.8141i			0.860468i	−0.902717	+	0.430234i	$0.858431\pi$
$74$		−	41.3066i		−	0.558197i
$75$		0			0
$76$	−29.4474			−0.387465
$77$	−38.8216			−0.504176
$78$	−40.8327	−	70.0499i	−0.523496	−	0.898076i
$79$	−122.486			−1.55046			−0.775231	−	0.631678i	$-0.782366\pi$
$79$	−122.486			−1.55046			−0.775231	+	0.631678i	$0.782366\pi$
$80$		0			0
$81$	−41.6612	−	69.4647i	−0.514336	−	0.857589i
$82$		−	40.5668i		−	0.494717i
$83$	−68.2772			−0.822617			−0.411309	−	0.911496i	$-0.634928\pi$
$83$	−68.2772			−0.822617			−0.411309	+	0.911496i	$0.634928\pi$
$84$	7.99435	+	13.7146i	0.0951709	+	0.163269i
$85$		0			0
$86$			57.2477i			0.665671i
$87$	−77.9452	−	133.718i	−0.895922	−	1.53699i
$88$		−	41.5020i		−	0.471614i
$89$		−	79.4213i		−	0.892374i	−0.894940	−	0.446187i	$-0.852782\pi$
$89$		−	79.4213i		−	0.892374i	0.894940	−	0.446187i	$-0.147218\pi$
$90$		0			0
$91$	50.5635			0.555643
$92$	45.5825			0.495462
$93$	100.298	−	58.4647i	1.07848	−	0.628652i
$94$	14.9766			0.159326
$95$		0			0
$96$	−14.6615	+	8.54632i	−0.152724	+	0.0890242i
$97$		−	28.2049i		−	0.290773i	−0.989375	−	0.145386i	$-0.953558\pi$
$97$		−	28.2049i		−	0.290773i	0.989375	−	0.145386i	$-0.0464425\pi$
$98$	−9.89949			−0.101015
$99$	−114.911	−	65.0759i	−1.16072	−	0.657332i
$100$		0			0
$101$		−	10.6769i		−	0.105712i	−0.998602	−	0.0528561i	$-0.983168\pi$
$101$		−	10.6769i		−	0.105712i	0.998602	−	0.0528561i	$-0.0168324\pi$
$102$	109.196	−	63.6512i	1.07055	−	0.624031i
$103$		−	34.1042i		−	0.331109i	−0.986201	−	0.165554i	$-0.947059\pi$
$103$		−	34.1042i		−	0.331109i	0.986201	−	0.165554i	$-0.0529414\pi$
$104$			54.0547i			0.519757i
$105$		0			0
$106$	−135.195			−1.27543
$107$	15.4338			0.144241			0.0721205	−	0.997396i	$-0.477023\pi$
$107$	15.4338			0.144241			0.0721205	+	0.997396i	$0.477023\pi$
$108$	0.673658	+	53.9958i	0.00623757	+	0.499961i
$109$	31.7494			0.291278			0.145639	−	0.989338i	$-0.453476\pi$
$109$	31.7494			0.291278			0.145639	+	0.989338i	$0.453476\pi$
$110$		0			0
$111$	44.1274	+	75.7021i	0.397544	+	0.682001i
$112$		−	10.5830i		−	0.0944911i
$113$	−26.1742			−0.231630			−0.115815	−	0.993271i	$-0.536948\pi$
$113$	−26.1742			−0.231630			−0.115815	+	0.993271i	$0.536948\pi$
$114$	53.9679	−	31.4583i	0.473403	−	0.275950i
$115$		0			0
$116$			103.185i			0.889522i
$117$	149.667	+	84.7587i	1.27921	+	0.724433i
$118$		−	15.7478i		−	0.133456i
$119$			78.8199i			0.662352i
$120$		0			0
$121$	−94.3023			−0.779358
$122$	−147.264			−1.20708
$123$	43.3371	+	74.3463i	0.352334	+	0.604442i
$124$	−77.3961			−0.624162
$125$		0			0
$126$	−29.3024	−	16.5943i	−0.232558	−	0.131701i
$127$			155.334i			1.22311i	0.791204	+	0.611553i	$0.209455\pi$
$127$			155.334i			1.22311i	−0.791204	+	0.611553i	$0.790545\pi$
$128$	11.3137			0.0883883
$129$	−61.1572	−	104.917i	−0.474086	−	0.813312i
$130$		0			0
$131$			100.859i			0.769912i	0.922935	+	0.384956i	$0.125783\pi$
$131$			100.859i			0.769912i	−0.922935	+	0.384956i	$0.874217\pi$
$132$	44.3362	+	76.0604i	0.335880	+	0.576215i
$133$			38.9552i			0.292896i
$134$			64.0038i			0.477640i
$135$		0			0
$136$	−84.2620			−0.619574
$137$	−117.672			−0.858920			−0.429460	−	0.903086i	$-0.641296\pi$
$137$	−117.672			−0.858920			−0.429460	+	0.903086i	$0.641296\pi$
$138$	−83.5386	+	48.6953i	−0.605352	+	0.352865i
$139$	74.8843			0.538736			0.269368	−	0.963037i	$-0.413185\pi$
$139$	74.8843			0.538736			0.269368	+	0.963037i	$0.413185\pi$
$140$		0			0
$141$	−27.4475	+	15.9994i	−0.194663	+	0.113471i
$142$		−	132.648i		−	0.934142i
$143$	280.422			1.96100
$144$	17.7401	−	31.3255i	0.123195	−	0.217538i
$145$		0			0
$146$			88.8326i			0.608443i
$147$	18.1427	−	10.5755i	0.123420	−	0.0719424i
$148$		−	58.4163i		−	0.394705i
$149$		−	149.584i		−	1.00392i	−0.864891	−	0.501960i	$-0.832612\pi$
$149$		−	149.584i		−	1.00392i	0.864891	−	0.501960i	$-0.167388\pi$
$150$		0			0
$151$	202.607			1.34177			0.670884	−	0.741562i	$-0.265915\pi$
$151$	202.607			1.34177			0.670884	+	0.741562i	$0.265915\pi$
$152$	−41.6449			−0.273979
$153$	−132.124	+	233.306i	−0.863557	+	1.52487i
$154$	−54.9020			−0.356507
$155$		0			0
$156$	−57.7461	−	99.0655i	−0.370167	−	0.635036i
$157$		−	79.2891i		−	0.505026i	−0.967594	−	0.252513i	$-0.918743\pi$
$157$		−	79.2891i		−	0.505026i	0.967594	−	0.252513i	$-0.0812570\pi$
$158$	−173.222			−1.09634
$159$	247.771	−	144.428i	1.55831	−	0.908351i
$160$		0			0
$161$		−	60.3000i		−	0.374534i
$162$	−58.9178	−	98.2379i	−0.363690	−	0.606407i
$163$			72.9838i			0.447753i	0.974617	+	0.223877i	$0.0718713\pi$
$163$			72.9838i			0.447753i	−0.974617	+	0.223877i	$0.928129\pi$
$164$		−	57.3701i		−	0.349817i
$165$		0			0
$166$	−96.5586			−0.581678
$167$	113.145			0.677512			0.338756	−	0.940874i	$-0.389994\pi$
$167$	113.145			0.677512			0.338756	+	0.940874i	$0.389994\pi$
$168$	11.3057	+	19.3954i	0.0672960	+	0.115449i
$169$	−196.239			−1.16118
$170$		0			0
$171$	−65.2998	+	115.307i	−0.381870	+	0.674309i
$172$			80.9604i			0.470700i
$173$	−115.843			−0.669611			−0.334806	−	0.942287i	$-0.608671\pi$
$173$	−115.843			−0.669611			−0.334806	+	0.942287i	$0.608671\pi$
$174$	−110.231	−	189.105i	−0.633512	−	1.08681i
$175$		0			0
$176$		−	58.6927i		−	0.333481i
$177$	16.8232	+	28.8608i	0.0950463	+	0.163055i
$178$		−	112.319i		−	0.631004i
$179$			76.5353i			0.427572i	0.976881	+	0.213786i	$0.0685794\pi$
$179$			76.5353i			0.427572i	−0.976881	+	0.213786i	$0.931421\pi$
$180$		0			0
$181$	38.3458			0.211855			0.105928	−	0.994374i	$-0.466219\pi$
$181$	38.3458			0.211855			0.105928	+	0.994374i	$0.466219\pi$
$182$	71.5076			0.392899
$183$	269.889	−	157.320i	1.47480	−	0.859674i
$184$	64.4634			0.350344
$185$		0			0
$186$	141.843	−	82.6815i	0.762597	−	0.444524i
$187$			437.131i			2.33760i
$188$	21.1802			0.112660
$189$	71.4297	−	0.891165i	0.377935	−	0.00471516i
$190$		0			0
$191$			0.0103646i			5.42648e-5i	1.00000		2.71324e-5i	$8.63652e-6\pi$
$191$			0.0103646i			5.42648e-5i	−1.00000		2.71324e-5i	$0.999991\pi$
$192$	−20.7345	+	12.0863i	−0.107992	+	0.0629496i
$193$		−	14.2760i		−	0.0739689i	−0.999316	−	0.0369844i	$-0.988225\pi$
$193$		−	14.2760i		−	0.0739689i	0.999316	−	0.0369844i	$-0.0117752\pi$
$194$		−	39.8878i		−	0.205607i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	123.543			0.627120			0.313560	−	0.949568i	$-0.398478\pi$
$197$	123.543			0.627120			0.313560	+	0.949568i	$0.398478\pi$
$198$	−162.509	−	92.0312i	−0.820753	−	0.464804i
$199$	187.525			0.942335			0.471167	−	0.882044i	$-0.343833\pi$
$199$	187.525			0.942335			0.471167	+	0.882044i	$0.343833\pi$
$200$		0			0
$201$	−68.3747	−	117.299i	−0.340173	−	0.583578i
$202$		−	15.0995i		−	0.0747498i
$203$	136.500			0.672416
$204$	154.426	−	90.0164i	0.756992	−	0.441257i
$205$		0			0
$206$		−	48.2307i		−	0.234129i
$207$	101.080	−	178.487i	0.488307	−	0.862256i
$208$			76.4449i			0.367523i
$209$			216.043i			1.03370i
$210$		0			0
$211$	−280.253			−1.32821			−0.664106	−	0.747638i	$-0.731188\pi$
$211$	−280.253			−1.32821			−0.664106	+	0.747638i	$0.731188\pi$
$212$	−191.195			−0.901863
$213$	141.707	+	243.103i	0.665290	+	1.14133i
$214$	21.8267			0.101994
$215$		0			0
$216$	0.952696	+	76.3616i	0.00441063	+	0.353526i
$217$			102.385i			0.471822i
$218$	44.9004			0.205965
$219$	−94.8990	−	162.803i	−0.433329	−	0.743391i
$220$		0			0
$221$		−	569.345i		−	2.57622i
$222$	62.4056	+	107.059i	0.281106	+	0.482248i
$223$			100.764i			0.451858i	0.974144	+	0.225929i	$0.0725418\pi$
$223$			100.764i			0.451858i	−0.974144	+	0.225929i	$0.927458\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	−37.0159			−0.163787
$227$	154.057			0.678664			0.339332	−	0.940667i	$-0.389799\pi$
$227$	154.057			0.678664			0.339332	+	0.940667i	$0.389799\pi$
$228$	76.3221	−	44.4888i	0.334746	−	0.195126i
$229$	−395.080			−1.72524			−0.862621	−	0.505852i	$-0.831178\pi$
$229$	−395.080			−1.72524			−0.862621	+	0.505852i	$0.831178\pi$
$230$		0			0
$231$	100.618	−	58.6513i	0.435578	−	0.253902i
$232$			145.925i			0.628987i
$233$	−192.917			−0.827972			−0.413986	−	0.910283i	$-0.635864\pi$
$233$	−192.917			−0.827972			−0.413986	+	0.910283i	$0.635864\pi$
$234$	211.662	+	119.867i	0.904537	+	0.512251i
$235$		0			0
$236$		−	22.2707i		−	0.0943675i
$237$	317.462	−	185.051i	1.33950	−	0.780808i
$238$			111.468i			0.468354i
$239$			312.840i			1.30896i	0.756081	+	0.654478i	$0.227112\pi$
$239$			312.840i			1.30896i	−0.756081	+	0.654478i	$0.772888\pi$
$240$		0			0
$241$	328.130			1.36153			0.680767	−	0.732500i	$-0.261647\pi$
$241$	328.130			1.36153			0.680767	+	0.732500i	$0.261647\pi$
$242$	−133.364			−0.551089
$243$	212.925	+	117.098i	0.876234	+	0.481886i
$244$	−208.262			−0.853533
$245$		0			0
$246$	61.2879	+	105.142i	0.249138	+	0.427405i
$247$		−	281.387i		−	1.13922i
$248$	−109.455			−0.441349
$249$	176.962	−	103.153i	0.710691	−	0.414268i
$250$		0			0
$251$			146.160i			0.582310i	0.956676	+	0.291155i	$0.0940396\pi$
$251$			146.160i			0.582310i	−0.956676	+	0.291155i	$0.905960\pi$
$252$	−41.4398	−	23.4679i	−0.164444	−	0.0931267i
$253$		−	334.420i		−	1.32182i
$254$			219.676i			0.864866i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−306.185			−1.19138			−0.595691	−	0.803214i	$-0.703122\pi$
$257$	−306.185			−1.19138			−0.595691	+	0.803214i	$0.703122\pi$
$258$	−86.4893	−	148.375i	−0.335230	−	0.575099i
$259$	−77.2775			−0.298369
$260$		0			0
$261$	404.039	+	228.813i	1.54804	+	0.876678i
$262$			142.635i			0.544410i
$263$	−158.182			−0.601452			−0.300726	−	0.953711i	$-0.597229\pi$
$263$	−158.182			−0.601452			−0.300726	+	0.953711i	$0.597229\pi$
$264$	62.7009	+	107.566i	0.237503	+	0.407446i
$265$		0			0
$266$			55.0910i			0.207109i
$267$	119.989	+	205.845i	0.449397	+	0.770956i
$268$			90.5151i			0.337743i
$269$			158.158i			0.587948i	0.955813	+	0.293974i	$0.0949779\pi$
$269$			158.158i			0.587948i	−0.955813	+	0.293974i	$0.905022\pi$
$270$		0			0
$271$	361.490			1.33391			0.666956	−	0.745097i	$-0.267597\pi$
$271$	361.490			1.33391			0.666956	+	0.745097i	$0.267597\pi$
$272$	−119.165			−0.438105
$273$	−131.051	+	76.3909i	−0.480042	+	0.279820i
$274$	−166.413			−0.607348
$275$		0			0
$276$	−118.141	+	68.8656i	−0.428049	+	0.249513i
$277$		−	77.1087i		−	0.278371i	−0.990266	−	0.139185i	$-0.955552\pi$
$277$		−	77.1087i		−	0.278371i	0.990266	−	0.139185i	$-0.0444484\pi$
$278$	105.902			0.380944
$279$	−171.627	+	303.059i	−0.615149	+	1.08623i
$280$		0			0
$281$			96.2437i			0.342504i	0.985227	+	0.171252i	$0.0547813\pi$
$281$			96.2437i			0.342504i	−0.985227	+	0.171252i	$0.945219\pi$
$282$	−38.8167	+	22.6266i	−0.137648	+	0.0802361i
$283$		−	210.868i		−	0.745118i	−0.928008	−	0.372559i	$-0.878480\pi$
$283$		−	210.868i		−	0.745118i	0.928008	−	0.372559i	$-0.121520\pi$
$284$		−	187.593i		−	0.660538i
$285$		0			0
$286$	396.577			1.38663
$287$	−75.8935			−0.264437
$288$	25.0883	−	44.3010i	0.0871120	−	0.153823i
$289$	598.512			2.07097
$290$		0			0
$291$	42.6118	+	73.1020i	0.146432	+	0.251210i
$292$			125.628i			0.430234i
$293$	441.017			1.50518			0.752588	−	0.658491i	$-0.228805\pi$
$293$	441.017			1.50518			0.752588	+	0.658491i	$0.228805\pi$
$294$	25.6577	−	14.9561i	0.0872710	−	0.0508710i
$295$		0			0
$296$		−	82.6131i		−	0.279098i
$297$	396.145	−	4.94235i	1.33382	−	0.0166409i
$298$		−	211.544i		−	0.709879i
$299$			435.569i			1.45675i
$300$		0			0
$301$	107.101			0.355816
$302$	286.529			0.948773
$303$	16.1306	+	27.6726i	0.0532363	+	0.0913288i
$304$	−58.8947			−0.193733
$305$		0			0
$306$	−186.852	+	329.944i	−0.610627	+	1.07825i
$307$			253.872i			0.826944i	0.910517	+	0.413472i	$0.135684\pi$
$307$			253.872i			0.826944i	−0.910517	+	0.413472i	$0.864316\pi$
$308$	−77.6432			−0.252088
$309$	51.5244	+	88.3919i	0.166745	+	0.286058i
$310$		0			0
$311$		−	402.715i		−	1.29490i	−0.762106	−	0.647452i	$-0.775835\pi$
$311$		−	402.715i		−	1.29490i	0.762106	−	0.647452i	$-0.224165\pi$
$312$	−81.6654	−	140.100i	−0.261748	−	0.449038i
$313$		−	58.4446i		−	0.186724i	−0.995632	−	0.0933620i	$-0.970239\pi$
$313$		−	58.4446i		−	0.186724i	0.995632	−	0.0933620i	$-0.0297614\pi$
$314$		−	112.132i		−	0.357107i
$315$		0			0
$316$	−244.973			−0.775231
$317$	−181.889			−0.573783			−0.286891	−	0.957963i	$-0.592622\pi$
$317$	−181.889			−0.573783			−0.286891	+	0.957963i	$0.592622\pi$
$318$	350.401	−	204.252i	1.10189	−	0.642301i
$319$	757.023			2.37311
$320$		0			0
$321$	−40.0015	+	23.3172i	−0.124615	+	0.0726393i
$322$		−	85.2770i		−	0.264835i
$323$	438.635			1.35800
$324$	−83.3224	−	138.929i	−0.257168	−	0.428795i
$325$		0			0
$326$			103.215i			0.316609i
$327$	−82.2885	+	47.9666i	−0.251647	+	0.146687i
$328$		−	81.1335i		−	0.247358i
$329$		−	28.0187i		−	0.0851633i
$330$		0			0
$331$	359.994			1.08760			0.543798	−	0.839216i	$-0.316986\pi$
$331$	359.994			1.08760			0.543798	+	0.839216i	$0.316986\pi$
$332$	−136.554			−0.411309
$333$	−228.740	−	129.539i	−0.686908	−	0.389005i
$334$	160.010			0.479073
$335$		0			0
$336$	15.9887	+	27.4292i	0.0475854	+	0.0816345i
$337$		−	637.901i		−	1.89288i	−0.322878	−	0.946441i	$-0.604650\pi$
$337$		−	637.901i		−	1.89288i	0.322878	−	0.946441i	$-0.395350\pi$
$338$	−277.524			−0.821076
$339$	67.8388	−	39.5438i	0.200114	−	0.116648i
$340$		0			0
$341$			567.823i			1.66517i
$342$	−92.3479	+	163.068i	−0.270023	+	0.476808i
$343$			18.5203i			0.0539949i
$344$			114.495i			0.332835i
$345$		0			0
$346$	−163.826			−0.473487
$347$	−131.343			−0.378509			−0.189255	−	0.981928i	$-0.560607\pi$
$347$	−131.343			−0.378509			−0.189255	+	0.981928i	$0.560607\pi$
$348$	−155.890	−	267.436i	−0.447961	−	0.768493i
$349$	462.012			1.32382			0.661908	−	0.749585i	$-0.269747\pi$
$349$	462.012			1.32382			0.661908	+	0.749585i	$0.269747\pi$
$350$		0			0
$351$	−515.963	+	6.43721i	−1.46998	+	0.0183396i
$352$		−	83.0041i		−	0.235807i
$353$	43.9668			0.124552			0.0622759	−	0.998059i	$-0.480164\pi$
$353$	43.9668			0.124552			0.0622759	+	0.998059i	$0.480164\pi$
$354$	23.7916	+	40.8153i	0.0672079	+	0.115298i
$355$		0			0
$356$		−	158.843i		−	0.446187i
$357$	−119.080	−	204.287i	−0.333559	−	0.572232i
$358$			108.237i			0.302339i
$359$		−	106.165i		−	0.295724i	−0.989008	−	0.147862i	$-0.952761\pi$
$359$		−	106.165i		−	0.295724i	0.989008	−	0.147862i	$-0.0472392\pi$
$360$		0			0
$361$	−144.213			−0.399483
$362$	54.2291			0.149804
$363$	244.414	−	142.471i	0.673317	−	0.392482i
$364$	101.127			0.277822
$365$		0			0
$366$	381.680	−	222.484i	1.04284	−	0.607881i
$367$		−	181.497i		−	0.494543i	−0.968946	−	0.247272i	$-0.920466\pi$
$367$		−	181.497i		−	0.494543i	0.968946	−	0.247272i	$-0.0795340\pi$
$368$	91.1650			0.247731
$369$	−224.644	−	127.219i	−0.608790	−	0.344766i
$370$		0			0
$371$			252.927i			0.681744i
$372$	200.596	−	116.929i	0.539238	−	0.314326i
$373$			12.3681i			0.0331585i	0.999863	+	0.0165792i	$0.00527757\pi$
$373$			12.3681i			0.0331585i	−0.999863	+	0.0165792i	$0.994722\pi$
$374$			618.196i			1.65293i
$375$		0			0
$376$	29.9533			0.0796630
$377$	−985.992			−2.61536
$378$	101.017	−	1.26030i	0.267240	−	0.00333412i
$379$	423.772			1.11813			0.559067	−	0.829123i	$-0.311160\pi$
$379$	423.772			1.11813			0.559067	+	0.829123i	$0.311160\pi$
$380$		0			0
$381$	−234.678	−	402.598i	−0.615952	−	1.05669i
$382$			0.0146577i			3.83710e-5i
$383$	−485.717			−1.26819			−0.634096	−	0.773255i	$-0.718627\pi$
$383$	−485.717			−1.26819			−0.634096	+	0.773255i	$0.718627\pi$
$384$	−29.3231	+	17.0926i	−0.0763621	+	0.0445121i
$385$		0			0
$386$		−	20.1893i		−	0.0523039i
$387$	317.016	+	179.531i	0.819163	+	0.463903i
$388$		−	56.4099i		−	0.145386i
$389$			205.829i			0.529123i	0.964369	+	0.264562i	$0.0852273\pi$
$389$			205.829i			0.529123i	−0.964369	+	0.264562i	$0.914773\pi$
$390$		0			0
$391$	−678.977			−1.73651
$392$	−19.7990			−0.0505076
$393$	−152.376	−	261.407i	−0.387726	−	0.665157i
$394$	174.716			0.443441
$395$		0			0
$396$	−229.823	−	130.152i	−0.580360	−	0.328666i
$397$		−	266.721i		−	0.671842i	−0.941890	−	0.335921i	$-0.890952\pi$
$397$		−	266.721i		−	0.671842i	0.941890	−	0.335921i	$-0.109048\pi$
$398$	265.200			0.666331
$399$	−58.8532	−	100.965i	−0.147502	−	0.253044i
$400$		0			0
$401$			251.023i			0.625991i	0.949755	+	0.312996i	$0.101333\pi$
$401$			251.023i			0.625991i	−0.949755	+	0.312996i	$0.898667\pi$
$402$	−96.6964	−	165.886i	−0.240538	−	0.412652i
$403$		−	739.567i		−	1.83515i
$404$		−	21.3538i		−	0.0528561i
$405$		0			0
$406$	193.041			0.475470
$407$	−428.576			−1.05301
$408$	218.392	−	127.302i	0.535274	−	0.312016i
$409$	−588.064			−1.43781			−0.718905	−	0.695109i	$-0.755356\pi$
$409$	−588.064			−1.43781			−0.718905	+	0.695109i	$0.755356\pi$
$410$		0			0
$411$	304.984	−	177.778i	0.742054	−	0.432550i
$412$		−	68.2084i		−	0.165554i
$413$	−29.4614			−0.0713351
$414$	142.948	−	252.419i	0.345285	−	0.609707i
$415$		0			0
$416$			108.109i			0.259878i
$417$	−194.086	+	113.135i	−0.465435	+	0.271306i
$418$			305.531i			0.730936i
$419$			21.3662i			0.0509934i	0.999675	+	0.0254967i	$0.00811673\pi$
$419$			21.3662i			0.0509934i	−0.999675	+	0.0254967i	$0.991883\pi$
$420$		0			0
$421$	29.7516			0.0706688			0.0353344	−	0.999376i	$-0.488750\pi$
$421$	29.7516			0.0706688			0.0353344	+	0.999376i	$0.488750\pi$
$422$	−396.337			−0.939188
$423$	46.9672	−	82.9350i	0.111034	−	0.196064i
$424$	−270.390			−0.637713
$425$		0			0
$426$	200.404	+	343.800i	0.470431	+	0.807041i
$427$			275.505i			0.645210i
$428$	30.8676			0.0721205
$429$	−726.803	+	423.660i	−1.69418	+	0.987552i
$430$		0			0
$431$			44.2977i			0.102779i	0.998679	+	0.0513894i	$0.0163650\pi$
$431$			44.2977i			0.102779i	−0.998679	+	0.0513894i	$0.983635\pi$
$432$	1.34732	+	107.992i	0.00311879	+	0.249981i
$433$			742.259i			1.71422i	0.515131	+	0.857112i	$0.327743\pi$
$433$			742.259i			1.71422i	−0.515131	+	0.857112i	$0.672257\pi$
$434$			144.795i			0.333629i
$435$		0			0
$436$	63.4987			0.145639
$437$	−335.571			−0.767897
$438$	−134.208	−	230.238i	−0.306410	−	0.525657i
$439$	339.668			0.773732			0.386866	−	0.922136i	$-0.373558\pi$
$439$	339.668			0.773732			0.386866	+	0.922136i	$0.373558\pi$
$440$		0			0
$441$	−31.0451	+	54.8197i	−0.0703972	+	0.124308i
$442$		−	805.175i		−	1.82166i
$443$	7.56065			0.0170669			0.00853347	−	0.999964i	$-0.497284\pi$
$443$	7.56065			0.0170669			0.00853347	+	0.999964i	$0.497284\pi$
$444$	88.2548	+	151.404i	0.198772	+	0.341001i
$445$		0			0
$446$			142.502i			0.319512i
$447$	225.990	+	387.695i	0.505571	+	0.867326i
$448$		−	21.1660i		−	0.0472456i
$449$			480.937i			1.07113i	0.844494	+	0.535564i	$0.179901\pi$
$449$			480.937i			1.07113i	−0.844494	+	0.535564i	$0.820099\pi$
$450$		0			0
$451$	−420.901			−0.933261
$452$	−52.3484			−0.115815
$453$	−525.120	+	306.097i	−1.15921	+	0.675710i
$454$	217.869			0.479888
$455$		0			0
$456$	107.936	−	62.9167i	0.236701	−	0.137975i
$457$			593.531i			1.29876i	0.760466	+	0.649378i	$0.224970\pi$
$457$			593.531i			1.29876i	−0.760466	+	0.649378i	$0.775030\pi$
$458$	−558.728			−1.21993
$459$	−10.0345	−	804.298i	−0.0218617	−	1.75228i
$460$		0			0
$461$		−	211.732i		−	0.459289i	−0.973275	−	0.229645i	$-0.926244\pi$
$461$		−	211.732i		−	0.459289i	0.973275	−	0.229645i	$-0.0737564\pi$
$462$	142.296	−	82.9455i	0.308000	−	0.179536i
$463$		−	618.360i		−	1.33555i	−0.744363	−	0.667776i	$-0.767247\pi$
$463$		−	618.360i		−	1.33555i	0.744363	−	0.667776i	$-0.232753\pi$
$464$			206.369i			0.444761i
$465$		0			0
$466$	−272.827			−0.585465
$467$	365.286			0.782197			0.391099	−	0.920349i	$-0.372095\pi$
$467$	365.286			0.782197			0.391099	+	0.920349i	$0.372095\pi$
$468$	299.335	+	169.517i	0.639604	+	0.362217i
$469$	119.740			0.255310
$470$		0			0
$471$	119.789	+	205.503i	0.254330	+	0.436311i
$472$		−	31.4956i		−	0.0667279i
$473$	593.974			1.25576
$474$	448.959	−	261.702i	0.947172	−	0.552114i
$475$		0			0
$476$			157.640i			0.331176i
$477$	−423.977	+	748.661i	−0.888840	+	1.56952i
$478$			442.423i			0.925571i
$479$		−	167.464i		−	0.349611i	−0.984603	−	0.174805i	$-0.944070\pi$
$479$		−	167.464i		−	0.349611i	0.984603	−	0.174805i	$-0.0559296\pi$
$480$		0			0
$481$	558.203			1.16051
$482$	464.046			0.962750
$483$	91.1006	+	156.286i	0.188614	+	0.323574i
$484$	−188.605			−0.389679
$485$		0			0
$486$	301.121	+	165.602i	0.619591	+	0.340745i
$487$		−	239.295i		−	0.491366i	−0.969350	−	0.245683i	$-0.920988\pi$
$487$		−	239.295i		−	0.491366i	0.969350	−	0.245683i	$-0.0790122\pi$
$488$	−294.527			−0.603539
$489$	−110.263	−	189.161i	−0.225487	−	0.386831i
$490$		0			0
$491$			255.880i			0.521140i	0.965455	+	0.260570i	$0.0839105\pi$
$491$			255.880i			0.521140i	−0.965455	+	0.260570i	$0.916090\pi$
$492$	86.6742	+	148.693i	0.176167	+	0.302221i
$493$		−	1536.99i		−	3.11763i
$494$		−	397.942i		−	0.805551i
$495$		0			0
$496$	−154.792			−0.312081
$497$	−248.162			−0.499320
$498$	250.262	−	145.880i	0.502534	−	0.292931i
$499$	78.1567			0.156627			0.0783133	−	0.996929i	$-0.475047\pi$
$499$	78.1567			0.156627			0.0783133	+	0.996929i	$0.475047\pi$
$500$		0			0
$501$	−293.250	+	170.938i	−0.585329	+	0.341193i
$502$			206.701i			0.411755i
$503$	−756.325			−1.50363			−0.751814	−	0.659375i	$-0.770821\pi$
$503$	−756.325			−1.50363			−0.751814	+	0.659375i	$0.770821\pi$
$504$	−58.6047	−	33.1887i	−0.116279	−	0.0658505i
$505$		0			0
$506$		−	472.941i		−	0.934667i
$507$	508.615	−	296.476i	1.00319	−	0.584765i
$508$			310.669i			0.611553i
$509$		−	797.969i		−	1.56772i	−0.620938	−	0.783859i	$-0.713248\pi$
$509$		−	797.969i		−	1.56772i	0.620938	−	0.783859i	$-0.286752\pi$
$510$		0			0
$511$	166.191			0.325226
$512$	22.6274			0.0441942
$513$	−4.95936	−	397.508i	−0.00966737	−	0.774870i
$514$	−433.011			−0.842434
$515$		0			0
$516$	−122.314	−	209.835i	−0.237043	−	0.406656i
$517$		−	155.390i		−	0.300561i
$518$	−109.287			−0.210979
$519$	300.243	−	175.014i	0.578503	−	0.337214i
$520$		0			0
$521$			22.5301i			0.0432440i	0.999766	+	0.0216220i	$0.00688303\pi$
$521$			22.5301i			0.0432440i	−0.999766	+	0.0216220i	$0.993117\pi$
$522$	571.398	+	323.590i	1.09463	+	0.619905i
$523$		−	250.580i		−	0.479121i	−0.970881	−	0.239560i	$-0.922997\pi$
$523$		−	250.580i		−	0.479121i	0.970881	−	0.239560i	$-0.0770033\pi$
$524$			201.717i			0.384956i
$525$		0			0
$526$	−223.703			−0.425291
$527$	1152.86			2.18759
$528$	88.6724	+	152.121i	0.167940	+	0.288107i
$529$	−9.55921			−0.0180703
$530$		0			0
$531$	−87.2053	−	49.3856i	−0.164228	−	0.0930048i
$532$			77.9104i			0.146448i
$533$	548.206			1.02853
$534$	169.690	+	291.109i	0.317772	+	0.545149i
$535$		0			0
$536$			128.008i			0.238820i
$537$	−115.629	−	198.365i	−0.215324	−	0.369396i
$538$			223.669i			0.415742i
$539$			102.712i			0.190561i
$540$		0			0
$541$	−438.380			−0.810314			−0.405157	−	0.914247i	$-0.632783\pi$
$541$	−438.380			−0.810314			−0.405157	+	0.914247i	$0.632783\pi$
$542$	511.224			0.943218
$543$	−99.3851	+	57.9324i	−0.183030	+	0.106690i
$544$	−168.524			−0.309787
$545$		0			0
$546$	−185.335	+	108.033i	−0.339441	+	0.197863i
$547$		−	212.261i		−	0.388045i	−0.980997	−	0.194023i	$-0.937846\pi$
$547$		−	212.261i		−	0.388045i	0.980997	−	0.194023i	$-0.0621535\pi$
$548$	−235.344			−0.429460
$549$	−461.823	+	815.490i	−0.841208	+	1.48541i
$550$		0			0
$551$		−	759.628i		−	1.37864i
$552$	−167.077	+	97.3907i	−0.302676	+	0.176432i
$553$			324.069i			0.586019i
$554$		−	109.048i		−	0.196838i
$555$		0			0
$556$	149.769			0.269368
$557$	303.846			0.545504			0.272752	−	0.962084i	$-0.412066\pi$
$557$	303.846			0.545504			0.272752	+	0.962084i	$0.412066\pi$
$558$	−242.717	+	428.591i	−0.434976	+	0.768083i
$559$	−773.626			−1.38395
$560$		0			0
$561$	−660.413	−	1132.96i	−1.17721	−	2.01954i
$562$			136.109i			0.242187i
$563$	−59.7131			−0.106062			−0.0530312	−	0.998593i	$-0.516888\pi$
$563$	−59.7131			−0.106062			−0.0530312	+	0.998593i	$0.516888\pi$
$564$	−54.8951	+	31.9988i	−0.0973317	+	0.0567355i
$565$		0			0
$566$		−	298.213i		−	0.526878i
$567$	−183.786	+	110.225i	−0.324138	+	0.194401i
$568$		−	265.296i		−	0.467071i
$569$			125.358i			0.220313i	0.993914	+	0.110157i	$0.0351352\pi$
$569$			125.358i			0.220313i	−0.993914	+	0.110157i	$0.964865\pi$
$570$		0			0
$571$	865.616			1.51597			0.757983	−	0.652275i	$-0.226185\pi$
$571$	865.616			1.51597			0.757983	+	0.652275i	$0.226185\pi$
$572$	560.845			0.980498
$573$	−0.0156587	−	0.0268631i	−2.73276e−5	−	4.68815e-5i
$574$	−107.330			−0.186985
$575$		0			0
$576$	35.4802	−	62.6511i	0.0615975	−	0.108769i
$577$			176.822i			0.306451i	0.988191	+	0.153225i	$0.0489660\pi$
$577$			176.822i			0.306451i	−0.988191	+	0.153225i	$0.951034\pi$
$578$	846.423			1.46440
$579$	21.5680	+	37.0007i	0.0372505	+	0.0639046i
$580$		0			0
$581$			180.645i			0.310920i
$582$	60.2621	+	103.382i	0.103543	+	0.177632i
$583$			1402.72i			2.40604i
$584$			177.665i			0.304221i
$585$		0			0
$586$	623.692			1.06432
$587$	−330.200			−0.562521			−0.281260	−	0.959631i	$-0.590752\pi$
$587$	−330.200			−0.562521			−0.281260	+	0.959631i	$0.590752\pi$
$588$	36.2854	−	21.1511i	0.0617099	−	0.0359712i
$589$	569.778			0.967364
$590$		0			0
$591$	−320.200	+	186.647i	−0.541793	+	0.315816i
$592$		−	116.833i		−	0.197352i
$593$	−996.327			−1.68015			−0.840073	−	0.542473i	$-0.817488\pi$
$593$	−996.327			−1.68015			−0.840073	+	0.542473i	$0.817488\pi$
$594$	560.234	−	6.98954i	0.943154	−	0.0117669i
$595$		0			0
$596$		−	299.168i		−	0.501960i
$597$	−486.029	+	283.311i	−0.814119	+	0.474557i
$598$			615.987i			1.03008i
$599$		−	416.236i		−	0.694885i	−0.937701	−	0.347443i	$-0.887050\pi$
$599$		−	416.236i		−	0.694885i	0.937701	−	0.347443i	$-0.112950\pi$
$600$		0			0
$601$	1141.63			1.89955			0.949777	−	0.312929i	$-0.101310\pi$
$601$	1141.63			1.89955			0.949777	+	0.312929i	$0.101310\pi$
$602$	151.463			0.251600
$603$	354.429	+	200.718i	0.587776	+	0.332866i
$604$	405.214			0.670884
$605$		0			0
$606$	22.8121	+	39.1350i	0.0376438	+	0.0645792i
$607$		−	664.913i		−	1.09541i	−0.836672	−	0.547704i	$-0.815502\pi$
$607$		−	664.913i		−	1.09541i	0.836672	−	0.547704i	$-0.184498\pi$
$608$	−83.2897			−0.136990
$609$	−353.784	+	206.224i	−0.580926	+	0.338627i
$610$		0			0
$611$			202.389i			0.331243i
$612$	−264.249	+	466.612i	−0.431779	+	0.762437i
$613$			588.435i			0.959927i	0.877289	+	0.479963i	$0.159350\pi$
$613$			588.435i			0.959927i	−0.877289	+	0.479963i	$0.840650\pi$
$614$			359.029i			0.584738i
$615$		0			0
$616$	−109.804			−0.178253
$617$	−631.416			−1.02336			−0.511682	−	0.859175i	$-0.670978\pi$
$617$	−631.416			−1.02336			−0.511682	+	0.859175i	$0.670978\pi$
$618$	72.8664	+	125.005i	0.117907	+	0.202273i
$619$	335.858			0.542582			0.271291	−	0.962497i	$-0.412549\pi$
$619$	335.858			0.542582			0.271291	+	0.962497i	$0.412549\pi$
$620$		0			0
$621$	7.67675	+	615.316i	0.0123619	+	0.990847i
$622$		−	569.525i		−	0.915635i
$623$	−210.129			−0.337286
$624$	−115.492	−	198.131i	−0.185084	−	0.317518i
$625$		0			0
$626$		−	82.6532i		−	0.132034i
$627$	−326.396	−	559.944i	−0.520568	−	0.893053i
$628$		−	158.578i		−	0.252513i
$629$			870.144i			1.38338i
$630$		0			0
$631$	−641.185			−1.01614			−0.508070	−	0.861316i	$-0.669641\pi$
$631$	−641.185			−1.01614			−0.508070	+	0.861316i	$0.669641\pi$
$632$	−346.444			−0.548171
$633$	726.364	−	423.403i	1.14749	−	0.668884i
$634$	−257.230			−0.405726
$635$		0			0
$636$	495.542	−	288.856i	0.779154	−	0.454175i
$637$		−	133.779i		−	0.210013i
$638$	1070.59			1.67804
$639$	−734.556	−	415.989i	−1.14954	−	0.651000i
$640$		0			0
$641$		−	358.234i		−	0.558867i	−0.960165	−	0.279433i	$-0.909853\pi$
$641$		−	358.234i		−	0.558867i	0.960165	−	0.279433i	$-0.0901466\pi$
$642$	−56.5707	+	32.9755i	−0.0881164	+	0.0513638i
$643$			1218.12i			1.89443i	0.320606	+	0.947213i	$0.396114\pi$
$643$			1218.12i			1.89443i	−0.320606	+	0.947213i	$0.603886\pi$
$644$		−	120.600i		−	0.187267i
$645$		0			0
$646$	620.324			0.960253
$647$	706.621			1.09215			0.546075	−	0.837737i	$-0.316121\pi$
$647$	706.621			1.09215			0.546075	+	0.837737i	$0.316121\pi$
$648$	−117.836	−	196.476i	−0.181845	−	0.303204i
$649$	−163.391			−0.251758
$650$		0			0
$651$	−154.683	−	265.364i	−0.237608	−	0.407625i
$652$			145.968i			0.223877i
$653$	−647.469			−0.991531			−0.495765	−	0.868457i	$-0.665112\pi$
$653$	−647.469			−0.991531			−0.495765	+	0.868457i	$0.665112\pi$
$654$	−116.373	+	67.8351i	−0.177941	+	0.103723i
$655$		0			0
$656$		−	114.740i		−	0.174909i
$657$	491.922	+	278.582i	0.748739	+	0.424021i
$658$		−	39.6245i		−	0.0602196i
$659$		−	925.263i		−	1.40404i	−0.712157	−	0.702020i	$-0.752282\pi$
$659$		−	925.263i		−	1.40404i	0.712157	−	0.702020i	$-0.247718\pi$
$660$		0			0
$661$	516.011			0.780652			0.390326	−	0.920677i	$-0.372362\pi$
$661$	516.011			0.780652			0.390326	+	0.920677i	$0.372362\pi$
$662$	509.109			0.769047
$663$	860.161	+	1475.64i	1.29738	+	2.22570i
$664$	−193.117			−0.290839
$665$		0			0
$666$	−323.488	−	183.195i	−0.485717	−	0.275068i
$667$			1175.85i			1.76290i
$668$	226.289			0.338756
$669$	−152.234	−	261.163i	−0.227555	−	0.390378i
$670$		0			0
$671$			1527.93i			2.27710i
$672$	22.6115	+	38.7908i	0.0336480	+	0.0577243i
$673$		−	1260.47i		−	1.87291i	−0.350782	−	0.936457i	$-0.614084\pi$
$673$		−	1260.47i		−	1.87291i	0.350782	−	0.936457i	$-0.385916\pi$
$674$		−	902.128i		−	1.33847i
$675$		0			0
$676$	−392.478			−0.580588
$677$	−364.477			−0.538370			−0.269185	−	0.963088i	$-0.586754\pi$
$677$	−364.477			−0.538370			−0.269185	+	0.963088i	$0.586754\pi$
$678$	95.9385	−	55.9233i	0.141502	−	0.0824828i
$679$	−74.6232			−0.109902
$680$		0			0
$681$	−399.286	+	232.747i	−0.586324	+	0.341773i
$682$			803.024i			1.17745i
$683$	−335.908			−0.491813			−0.245906	−	0.969294i	$-0.579086\pi$
$683$	−335.908			−0.491813			−0.245906	+	0.969294i	$0.579086\pi$
$684$	−130.600	+	230.614i	−0.190935	+	0.337154i
$685$		0			0
$686$			26.1916i			0.0381802i
$687$	1023.98	−	596.884i	1.49050	−	0.868826i
$688$			161.921i			0.235350i
$689$		−	1826.98i		−	2.65165i
$690$		0			0
$691$	56.3269			0.0815150			0.0407575	−	0.999169i	$-0.487023\pi$
$691$	56.3269			0.0815150			0.0407575	+	0.999169i	$0.487023\pi$
$692$	−231.686			−0.334806
$693$	−172.175	+	304.027i	−0.248448	+	0.438711i
$694$	−185.747			−0.267647
$695$		0			0
$696$	−220.462	−	378.211i	−0.316756	−	0.543407i
$697$			854.560i			1.22605i
$698$	653.383			0.936079
$699$	500.007	−	291.458i	0.715317	−	0.416964i
$700$		0			0
$701$			795.844i			1.13530i	0.823270	+	0.567649i	$0.192147\pi$
$701$			795.844i			1.13530i	−0.823270	+	0.567649i	$0.807853\pi$
$702$	−729.682	+	9.10359i	−1.03943	+	0.0129681i
$703$			430.051i			0.611737i
$704$		−	117.385i		−	0.166741i
$705$		0			0
$706$	62.1784			0.0880714
$707$	−28.2485			−0.0399554
$708$	33.6464	+	57.7216i	0.0475232	+	0.0815277i
$709$	−127.721			−0.180142			−0.0900712	−	0.995935i	$-0.528709\pi$
$709$	−127.721			−0.180142			−0.0900712	+	0.995935i	$0.528709\pi$
$710$		0			0
$711$	−543.230	+	959.238i	−0.764036	+	1.34914i
$712$		−	224.637i		−	0.315502i
$713$	−881.977			−1.23699
$714$	−168.405	−	288.905i	−0.235862	−	0.404629i
$715$		0			0
$716$			153.071i			0.213786i
$717$	−472.637	−	810.825i	−0.659186	−	1.13086i
$718$		−	150.140i		−	0.209108i
$719$		−	652.748i		−	0.907855i	−0.891039	−	0.453927i	$-0.850023\pi$
$719$		−	652.748i		−	0.907855i	0.891039	−	0.453927i	$-0.149977\pi$
$720$		0			0
$721$	−90.2313			−0.125147
$722$	−203.948			−0.282477
$723$	−850.452	+	495.736i	−1.17628	+	0.685665i
$724$	76.6915			0.105928
$725$		0			0
$726$	345.654	−	201.484i	0.476107	−	0.277527i
$727$			181.338i			0.249433i	0.992192	+	0.124717i	$0.0398022\pi$
$727$			181.338i			0.249433i	−0.992192	+	0.124717i	$0.960198\pi$
$728$	143.015			0.196450
$729$	−728.773	+	18.1873i	−0.999689	+	0.0249483i
$730$		0			0
$731$		−	1205.95i		−	1.64973i
$732$	539.777	−	314.641i	0.737400	−	0.429837i
$733$			980.665i			1.33788i	0.743317	+	0.668939i	$0.233251\pi$
$733$			980.665i			1.33788i	−0.743317	+	0.668939i	$0.766749\pi$
$734$		−	256.676i		−	0.349695i
$735$		0			0
$736$	128.927			0.175172
$737$	664.072			0.901047
$738$	−317.694	−	179.914i	−0.430480	−	0.243786i
$739$	−115.426			−0.156193			−0.0780963	−	0.996946i	$-0.524884\pi$
$739$	−115.426			−0.156193			−0.0780963	+	0.996946i	$0.524884\pi$
$740$		0			0
$741$	425.118	+	729.305i	0.573708	+	0.984217i
$742$			357.693i			0.482066i
$743$	131.260			0.176662			0.0883311	−	0.996091i	$-0.471847\pi$
$743$	131.260			0.176662			0.0883311	+	0.996091i	$0.471847\pi$
$744$	283.686	−	165.363i	0.381299	−	0.222262i
$745$		0			0
$746$			17.4911i			0.0234466i
$747$	−302.811	+	534.705i	−0.405369	+	0.715804i
$748$			874.261i			1.16880i
$749$		−	40.8340i		−	0.0545180i
$750$		0			0
$751$	−1088.21			−1.44902			−0.724508	−	0.689266i	$-0.757933\pi$
$751$	−1088.21			−1.44902			−0.724508	+	0.689266i	$0.757933\pi$
$752$	42.3603			0.0563302
$753$	−220.817	−	378.819i	−0.293250	−	0.503080i
$754$	−1394.40			−1.84934
$755$		0			0
$756$	142.859	−	1.78233i	0.188968	−	0.00235758i
$757$		−	1115.02i		−	1.47295i	−0.676467	−	0.736473i	$-0.736490\pi$
$757$		−	1115.02i		−	1.47295i	0.676467	−	0.736473i	$-0.263510\pi$
$758$	599.305			0.790639
$759$	505.239	+	866.755i	0.665664	+	1.14197i
$760$		0			0
$761$		−	632.008i		−	0.830497i	−0.909708	−	0.415249i	$-0.863695\pi$
$761$		−	632.008i		−	0.830497i	0.909708	−	0.415249i	$-0.136305\pi$
$762$	−331.885	−	569.360i	−0.435544	−	0.747191i
$763$		−	84.0009i		−	0.110093i
$764$			0.0207292i			2.71324e-5i
$765$		0			0
$766$	−686.908			−0.896746
$767$	212.810			0.277458
$768$	−41.4691	+	24.1727i	−0.0539962	+	0.0314748i
$769$	−183.616			−0.238773			−0.119386	−	0.992848i	$-0.538093\pi$
$769$	−183.616			−0.238773			−0.119386	+	0.992848i	$0.538093\pi$
$770$		0			0
$771$	793.575	−	462.582i	1.02928	−	0.599976i
$772$		−	28.5520i		−	0.0369844i
$773$	−239.771			−0.310182			−0.155091	−	0.987900i	$-0.549567\pi$
$773$	−239.771			−0.310182			−0.155091	+	0.987900i	$0.549567\pi$
$774$	448.329	+	253.895i	0.579236	+	0.328029i
$775$		0			0
$776$		−	79.7756i		−	0.102804i
$777$	200.289	−	116.750i	0.257772	−	0.150258i
$778$			291.086i			0.374147i
$779$			422.349i			0.542168i
$780$		0			0
$781$	−1376.29			−1.76222
$782$	−960.218			−1.22790
$783$	−1392.88	+	17.3778i	−1.77891	+	0.0221938i
$784$	−28.0000			−0.0357143
$785$		0			0
$786$	−215.492	−	369.685i	−0.274163	−	0.470337i
$787$		−	430.055i		−	0.546449i	−0.961950	−	0.273224i	$-0.911910\pi$
$787$		−	430.055i		−	0.546449i	0.961950	−	0.273224i	$-0.0880902\pi$
$788$	247.085			0.313560
$789$	409.978	−	238.980i	0.519618	−	0.302889i
$790$		0			0
$791$			69.2505i			0.0875480i
$792$	−325.018	−	184.062i	−0.410377	−	0.232402i
$793$		−	1990.07i		−	2.50955i
$794$		−	377.201i		−	0.475064i
$795$		0			0
$796$	375.049			0.471167
$797$	454.406			0.570146			0.285073	−	0.958506i	$-0.407982\pi$
$797$	454.406			0.570146			0.285073	+	0.958506i	$0.407982\pi$
$798$	−83.2309	−	142.786i	−0.104299	−	0.178929i
$799$	−315.491			−0.394857
$800$		0			0
$801$	−621.979	−	352.235i	−0.776503	−	0.439744i
$802$			354.999i			0.442643i
$803$	921.683			1.14780
$804$	−136.749	−	234.598i	−0.170086	−	0.291789i
$805$		0			0
$806$		−	1045.91i		−	1.29765i
$807$	−238.944	−	409.916i	−0.296089	−	0.507951i
$808$		−	30.1989i		−	0.0373749i
$809$			1016.61i			1.25662i	0.777963	+	0.628310i	$0.216253\pi$
$809$			1016.61i			1.25662i	−0.777963	+	0.628310i	$0.783747\pi$
$810$		0			0
$811$	756.253			0.932494			0.466247	−	0.884654i	$-0.345606\pi$
$811$	756.253			0.932494			0.466247	+	0.884654i	$0.345606\pi$
$812$	273.001			0.336208
$813$	−936.916	+	546.136i	−1.15242	+	0.671754i
$814$	−606.099			−0.744593
$815$		0			0
$816$	308.853	−	180.033i	0.378496	−	0.220628i
$817$		−	596.018i		−	0.729520i
$818$	−831.648			−1.01668
$819$	224.250	−	395.983i	0.273810	−	0.483495i
$820$		0			0
$821$			1207.04i			1.47021i	0.677955	+	0.735104i	$0.262866\pi$
$821$			1207.04i			1.47021i	−0.677955	+	0.735104i	$0.737134\pi$
$822$	431.313	−	251.416i	0.524712	−	0.305859i
$823$		−	169.449i		−	0.205891i	−0.994687	−	0.102946i	$-0.967173\pi$
$823$		−	169.449i		−	0.205891i	0.994687	−	0.102946i	$-0.0328268\pi$
$824$		−	96.4613i		−	0.117065i
$825$		0			0
$826$	−41.6647			−0.0504415
$827$	953.176			1.15257			0.576285	−	0.817248i	$-0.304502\pi$
$827$	953.176			1.15257			0.576285	+	0.817248i	$0.304502\pi$
$828$	202.159	−	356.974i	0.244154	−	0.431128i
$829$	6.32036			0.00762407			0.00381204	−	0.999993i	$-0.498787\pi$
$829$	6.32036			0.00762407			0.00381204	+	0.999993i	$0.498787\pi$
$830$		0			0
$831$	116.495	+	199.852i	0.140187	+	0.240495i
$832$			152.890i			0.183762i
$833$	208.538			0.250346
$834$	−274.480	+	159.996i	−0.329112	+	0.191842i
$835$		0			0
$836$			432.086i			0.516850i
$837$	−13.0346	−	1044.77i	−0.0155730	−	1.24823i
$838$			30.2164i			0.0360578i
$839$		−	1230.70i		−	1.46686i	−0.679764	−	0.733430i	$-0.737918\pi$
$839$		−	1230.70i		−	1.46686i	0.679764	−	0.733430i	$-0.262082\pi$
$840$		0			0
$841$	−1820.77			−2.16500
$842$	42.0751			0.0499704
$843$	−145.404	−	249.446i	−0.172484	−	0.295903i
$844$	−560.506			−0.664106
$845$		0			0
$846$	66.4217	−	117.288i	0.0785127	−	0.138638i
$847$			249.500i			0.294569i
$848$	−382.390			−0.450931
$849$	318.578	+	546.532i	0.375239	+	0.643737i
$850$		0			0
$851$		−	665.690i		−	0.782244i
$852$	283.414	+	486.206i	0.332645	+	0.570664i
$853$		−	759.822i		−	0.890764i	−0.895341	−	0.445382i	$-0.853068\pi$
$853$		−	759.822i		−	0.890764i	0.895341	−	0.445382i	$-0.146932\pi$
$854$			389.623i			0.456233i
$855$		0			0
$856$	43.6533			0.0509969
$857$	−531.002			−0.619606			−0.309803	−	0.950801i	$-0.600263\pi$
$857$	−531.002			−0.619606			−0.309803	+	0.950801i	$0.600263\pi$
$858$	−1027.86	+	599.145i	−1.19797	+	0.698305i
$859$	−765.291			−0.890910			−0.445455	−	0.895304i	$-0.646958\pi$
$859$	−765.291			−0.890910			−0.445455	+	0.895304i	$0.646958\pi$
$860$		0			0
$861$	196.702	−	114.659i	0.228457	−	0.133170i
$862$			62.6464i			0.0726756i
$863$	−1329.43			−1.54048			−0.770240	−	0.637754i	$-0.779864\pi$
$863$	−1329.43			−1.54048			−0.770240	+	0.637754i	$0.779864\pi$
$864$	1.90539	+	152.723i	0.00220531	+	0.176763i
$865$		0			0
$866$			1049.71i			1.21214i
$867$	−1551.23	+	904.226i	−1.78919	+	1.04294i
$868$			204.771i			0.235911i
$869$			1797.27i			2.06820i
$870$		0			0
$871$	−864.927			−0.993027
$872$	89.8007			0.102982
$873$	−220.884	−	125.089i	−0.253017	−	0.143287i
$874$	−474.569			−0.542985
$875$		0			0
$876$	−189.798	−	325.605i	−0.216664	−	0.371696i
$877$		−	919.329i		−	1.04827i	−0.851637	−	0.524133i	$-0.824390\pi$
$877$		−	919.329i		−	1.04827i	0.851637	−	0.524133i	$-0.175610\pi$
$878$	480.364			0.547111
$879$	−1143.03	+	666.284i	−1.30038	+	0.758002i
$880$		0			0
$881$			832.315i			0.944739i	0.881401	+	0.472369i	$0.156601\pi$
$881$			832.315i			0.944739i	−0.881401	+	0.472369i	$0.843399\pi$
$882$	−43.9045	+	77.5268i	−0.0497783	+	0.0878988i
$883$		−	1425.51i		−	1.61439i	−0.590284	−	0.807196i	$-0.700984\pi$
$883$		−	1425.51i		−	1.61439i	0.590284	−	0.807196i	$-0.299016\pi$
$884$		−	1138.69i		−	1.28811i
$885$		0			0
$886$	10.6924			0.0120681
$887$	641.162			0.722843			0.361422	−	0.932402i	$-0.382291\pi$
$887$	641.162			0.722843			0.361422	+	0.932402i	$0.382291\pi$
$888$	124.811	+	214.118i	0.140553	+	0.241124i
$889$	410.976			0.462290
$890$		0			0
$891$	−1019.27	+	611.302i	−1.14396	+	0.686085i
$892$			201.529i			0.225929i
$893$	−155.925			−0.174608
$894$	319.599	+	548.283i	0.357493	+	0.613292i
$895$		0			0
$896$		−	29.9333i		−	0.0334077i
$897$	−658.053	−	1128.91i	−0.733615	−	1.25854i
$898$			680.147i			0.757402i
$899$		−	1996.52i		−	2.22082i
$900$		0			0
$901$	2847.96			3.16088
$902$	−595.243			−0.659915
$903$	−277.585	+	161.807i	−0.307403	+	0.179188i
$904$	−74.0319			−0.0818937
$905$		0			0
$906$	−742.632	+	432.886i	−0.819682	+	0.477799i
$907$			1569.63i			1.73057i	0.501278	+	0.865287i	$0.332864\pi$
$907$			1569.63i			1.73057i	−0.501278	+	0.865287i	$0.667136\pi$
$908$	308.113			0.339332
$909$	−83.6151	−	47.3524i	−0.0919858	−	0.0520928i
$910$		0			0
$911$		−	1742.53i		−	1.91277i	−0.292108	−	0.956385i	$-0.594357\pi$
$911$		−	1742.53i		−	1.91277i	0.292108	−	0.956385i	$-0.405643\pi$
$912$	152.644	−	88.9776i	0.167373	−	0.0975632i
$913$			1001.84i			1.09731i
$914$			839.380i			0.918359i
$915$		0			0
$916$	−790.160			−0.862621
$917$	266.847			0.291000
$918$	−14.1909	−	1137.45i	−0.0154585	−	1.23905i
$919$	944.373			1.02761			0.513805	−	0.857907i	$-0.328236\pi$
$919$	944.373			1.02761			0.513805	+	0.857907i	$0.328236\pi$
$920$		0			0
$921$	−383.547	−	657.989i	−0.416447	−	0.714429i
$922$		−	299.435i		−	0.324767i
$923$	1792.56			1.94211
$924$	201.237	−	117.303i	0.217789	−	0.126951i
$925$		0			0
$926$		−	874.494i		−	0.944377i
$927$	−267.083	−	151.253i	−0.288116	−	0.163164i
$928$			291.850i			0.314494i
$929$			600.958i			0.646887i	0.946248	+	0.323443i	$0.104841\pi$
$929$			600.958i			0.646887i	−0.946248	+	0.323443i	$0.895159\pi$
$930$		0			0
$931$	103.066			0.110704
$932$	−385.835			−0.413986
$933$	608.418	+	1043.76i	0.652110	+	1.11872i
$934$	516.593			0.553097
$935$		0			0
$936$	423.323	+	239.734i	0.452268	+	0.256126i
$937$		−	19.4399i		−	0.0207470i	−0.999946	−	0.0103735i	$-0.996698\pi$
$937$		−	19.4399i		−	0.0207470i	0.999946	−	0.0103735i	$-0.00330204\pi$
$938$	169.338			0.180531
$939$	88.2976	+	151.478i	0.0940336	+	0.161318i
$940$		0			0
$941$			709.230i			0.753698i	0.926275	+	0.376849i	$0.122992\pi$
$941$			709.230i			0.753698i	−0.926275	+	0.376849i	$0.877008\pi$
$942$	169.408	+	290.625i	0.179838	+	0.308519i
$943$		−	653.768i		−	0.693285i
$944$		−	44.5414i		−	0.0471837i
$945$		0			0
$946$	840.006			0.887955
$947$	−228.266			−0.241041			−0.120521	−	0.992711i	$-0.538456\pi$
$947$	−228.266			−0.241041			−0.120521	+	0.992711i	$0.538456\pi$
$948$	634.925	−	370.103i	0.669752	−	0.390404i
$949$	−1200.45			−1.26497
$950$		0			0
$951$	471.423	−	274.796i	0.495713	−	0.288955i
$952$			222.936i			0.234177i
$953$	830.703			0.871672			0.435836	−	0.900026i	$-0.356453\pi$
$953$	830.703			0.871672			0.435836	+	0.900026i	$0.356453\pi$
$954$	−599.594	+	1058.77i	−0.628505	+	1.10982i
$955$		0			0
$956$			625.681i			0.654478i
$957$	−1962.06	+	1143.70i	−2.05022	+	1.19509i
$958$		−	236.829i		−	0.247212i
$959$			311.331i			0.324641i
$960$		0			0
$961$	536.539			0.558313
$962$	789.419			0.820602
$963$	68.4491	−	120.868i	0.0710791	−	0.125512i
$964$	656.260			0.680767
$965$		0			0
$966$	128.836	+	221.022i	0.133370	+	0.228802i
$967$			1120.26i			1.15849i	0.815153	+	0.579246i	$0.196653\pi$
$967$			1120.26i			1.15849i	−0.815153	+	0.579246i	$0.803347\pi$
$968$	−266.727			−0.275544
$969$	−1136.86	+	662.686i	−1.17323	+	0.683886i
$970$		0			0
$971$		−	533.802i		−	0.549745i	−0.961481	−	0.274872i	$-0.911364\pi$
$971$		−	533.802i		−	0.549745i	0.961481	−	0.274872i	$-0.0886356\pi$
$972$	425.850	+	234.197i	0.438117	+	0.240943i
$973$		−	198.125i		−	0.203623i
$974$		−	338.414i		−	0.347448i
$975$		0			0
$976$	−416.524			−0.426767
$977$	−1232.14			−1.26115			−0.630575	−	0.776129i	$-0.717181\pi$
$977$	−1232.14			−1.26115			−0.630575	+	0.776129i	$0.717181\pi$
$978$	−155.936	−	267.513i	−0.159444	−	0.273531i
$979$	−1165.36			−1.19036
$980$		0			0
$981$	140.809	−	248.641i	0.143536	−	0.253457i
$982$			361.868i			0.368502i
$983$	−1098.64			−1.11764			−0.558820	−	0.829289i	$-0.688746\pi$
$983$	−1098.64			−1.11764			−0.558820	+	0.829289i	$0.688746\pi$
$984$	122.576	+	210.283i	0.124569	+	0.213702i
$985$		0			0
$986$		−	2173.64i		−	2.20450i
$987$	42.3304	+	72.6194i	0.0428880	+	0.0735759i
$988$		−	562.775i		−	0.569610i
$989$			922.595i			0.932856i
$990$		0			0
$991$	−1388.10			−1.40070			−0.700352	−	0.713798i	$-0.746973\pi$
$991$	−1388.10			−1.40070			−0.700352	+	0.713798i	$0.746973\pi$
$992$	−218.909			−0.220675
$993$	−933.039	+	543.876i	−0.939617	+	0.547710i
$994$	−350.954			−0.353073
$995$		0			0
$996$	353.924	−	206.305i	0.355345	−	0.207134i
$997$		−	818.089i		−	0.820551i	−0.911962	−	0.410275i	$-0.865433\pi$
$997$		−	818.089i		−	0.820551i	0.911962	−	0.410275i	$-0.134567\pi$
$998$	110.530			0.110752
$999$	788.558	−	9.83814i	0.789348	−	0.00984799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.c.c.449.18		32
3.2	odd	2	inner	1050.3.c.c.449.16		32
5.2	odd	4		1050.3.e.d.701.13		16
5.3	odd	4		210.3.e.a.71.4	✓	16
5.4	even	2	inner	1050.3.c.c.449.15		32
15.2	even	4		1050.3.e.d.701.5		16
15.8	even	4		210.3.e.a.71.12	yes	16
15.14	odd	2	inner	1050.3.c.c.449.17		32
20.3	even	4		1680.3.l.c.1121.10		16
60.23	odd	4		1680.3.l.c.1121.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.e.a.71.4	✓	16	5.3	odd	4
210.3.e.a.71.12	yes	16	15.8	even	4
1050.3.c.c.449.15		32	5.4	even	2	inner
1050.3.c.c.449.16		32	3.2	odd	2	inner
1050.3.c.c.449.17		32	15.14	odd	2	inner
1050.3.c.c.449.18		32	1.1	even	1	trivial
1050.3.e.d.701.5		16	15.2	even	4
1050.3.e.d.701.13		16	5.2	odd	4
1680.3.l.c.1121.9		16	60.23	odd	4
1680.3.l.c.1121.10		16	20.3	even	4

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +(-2.59182 + 1.51079i) q^{3} +2.00000 q^{4} +(-3.66538 + 2.13658i) q^{6} -2.64575i q^{7} +2.82843 q^{8} +(4.43502 - 7.83139i) q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +(-2.59182 + 1.51079i) q^{3} +2.00000 q^{4} +(-3.66538 + 2.13658i) q^{6} -2.64575i q^{7} +2.82843 q^{8} +(4.43502 - 7.83139i) q^{9} -14.6732i q^{11} +(-5.18363 + 3.02158i) q^{12} +19.1112i q^{13} -3.74166i q^{14} +4.00000 q^{16} -29.7911 q^{17} +(6.27207 - 11.0753i) q^{18} -14.7237 q^{19} +(3.99718 + 6.85730i) q^{21} -20.7510i q^{22} +22.7912 q^{23} +(-7.33076 + 4.27316i) q^{24} +27.0273i q^{26} +(0.336829 + 26.9979i) q^{27} -5.29150i q^{28} +51.5923i q^{29} -38.6980 q^{31} +5.65685 q^{32} +(22.1681 + 38.0302i) q^{33} -42.1310 q^{34} +(8.87004 - 15.6628i) q^{36} -29.2081i q^{37} -20.8224 q^{38} +(-28.8731 - 49.5328i) q^{39} -28.6850i q^{41} +(5.65286 + 9.69769i) q^{42} +40.4802i q^{43} -29.3464i q^{44} +32.2317 q^{46} +10.5901 q^{47} +(-10.3673 + 6.04316i) q^{48} -7.00000 q^{49} +(77.2131 - 45.0082i) q^{51} +38.2224i q^{52} -95.5975 q^{53} +(0.476348 + 38.1808i) q^{54} -7.48331i q^{56} +(38.1611 - 22.2444i) q^{57} +72.9625i q^{58} -11.1354i q^{59} -104.131 q^{61} -54.7273 q^{62} +(-20.7199 - 11.7340i) q^{63} +8.00000 q^{64} +(31.3504 + 53.7828i) q^{66} +45.2575i q^{67} -59.5823 q^{68} +(-59.0707 + 34.4328i) q^{69} -93.7964i q^{71} +(12.5441 - 22.1505i) q^{72} +62.8141i q^{73} -41.3066i q^{74} -29.4474 q^{76} -38.8216 q^{77} +(-40.8327 - 70.0499i) q^{78} -122.486 q^{79} +(-41.6612 - 69.4647i) q^{81} -40.5668i q^{82} -68.2772 q^{83} +(7.99435 + 13.7146i) q^{84} +57.2477i q^{86} +(-77.9452 - 133.718i) q^{87} -41.5020i q^{88} -79.4213i q^{89} +50.5635 q^{91} +45.5825 q^{92} +(100.298 - 58.4647i) q^{93} +14.9766 q^{94} +(-14.6615 + 8.54632i) q^{96} -28.2049i q^{97} -9.89949 q^{98} +(-114.911 - 65.0759i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9}+O(q^{10}) \) 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9	\( 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9} + 128 q^{16} - 96 q^{19} + 56 q^{21} + 64 q^{24} - 320 q^{34} + 16 q^{36} - 312 q^{39} + 64 q^{46} - 224 q^{49} + 168 q^{51} + 64 q^{54} + 224 q^{61} + 256 q^{64} - 16 q^{69} - 192 q^{76} - 16 q^{79} - 248 q^{81} + 112 q^{84} - 112 q^{91} - 64 q^{94} + 128 q^{96} + 104 q^{99}+O(q^{100}) \) 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9 + 128 * q^16 - 96 * q^19 + 56 * q^21 + 64 * q^24 - 320 * q^34 + 16 * q^36 - 312 * q^39 + 64 * q^46 - 224 * q^49 + 168 * q^51 + 64 * q^54 + 224 * q^61 + 256 * q^64 - 16 * q^69 - 192 * q^76 - 16 * q^79 - 248 * q^81 + 112 * q^84 - 112 * q^91 - 64 * q^94 + 128 * q^96 + 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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