LMFDB - Embedded newform 105.4.d.b.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(64,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("105.64");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.d (of order $2$, degree $1$, 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:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 37x^{8} + 398x^{6} + 1149x^{4} + 1040x^{2} + 100 $ x^10 + 37x^8 + 398x^6 + 1149x^4 + 1040x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.1
Root			$3.71490i$ of defining polynomial
Character	$\chi$	$=$	105.64
Dual form			105.4.d.b.64.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.18660i q^{2} -3.00000i q^{3} -18.9008 q^{4} +(-4.24321 + 10.3438i) q^{5} -15.5598 q^{6} -7.00000i q^{7} +56.5383i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-5.18660i q^{2} -3.00000i q^{3} -18.9008 q^{4} +(-4.24321 + 10.3438i) q^{5} -15.5598 q^{6} -7.00000i q^{7} +56.5383i q^{8} -9.00000 q^{9} +(53.6494 + 22.0078i) q^{10} -35.9555 q^{11} +56.7025i q^{12} +45.2622i q^{13} -36.3062 q^{14} +(31.0315 + 12.7296i) q^{15} +142.035 q^{16} -113.154i q^{17} +46.6794i q^{18} -61.5906 q^{19} +(80.2001 - 195.507i) q^{20} -21.0000 q^{21} +186.487i q^{22} -30.6108i q^{23} +169.615 q^{24} +(-88.9904 - 87.7822i) q^{25} +234.757 q^{26} +27.0000i q^{27} +132.306i q^{28} -214.989 q^{29} +(66.0235 - 160.948i) q^{30} +164.206 q^{31} -284.372i q^{32} +107.866i q^{33} -586.882 q^{34} +(72.4069 + 29.7024i) q^{35} +170.107 q^{36} +410.533i q^{37} +319.446i q^{38} +135.787 q^{39} +(-584.823 - 239.904i) q^{40} -309.310 q^{41} +108.919i q^{42} -29.9519i q^{43} +679.589 q^{44} +(38.1889 - 93.0946i) q^{45} -158.766 q^{46} -483.790i q^{47} -426.104i q^{48} -49.0000 q^{49} +(-455.291 + 461.558i) q^{50} -339.461 q^{51} -855.493i q^{52} -295.582i q^{53} +140.038 q^{54} +(152.567 - 371.918i) q^{55} +395.768 q^{56} +184.772i q^{57} +1115.06i q^{58} -416.191 q^{59} +(-586.522 - 240.600i) q^{60} -151.196 q^{61} -851.670i q^{62} +63.0000i q^{63} -338.644 q^{64} +(-468.185 - 192.057i) q^{65} +559.460 q^{66} -89.5253i q^{67} +2138.70i q^{68} -91.8324 q^{69} +(154.055 - 375.546i) q^{70} +714.265 q^{71} -508.844i q^{72} -1135.58i q^{73} +2129.27 q^{74} +(-263.347 + 266.971i) q^{75} +1164.11 q^{76} +251.688i q^{77} -704.271i q^{78} +323.347 q^{79} +(-602.683 + 1469.19i) q^{80} +81.0000 q^{81} +1604.27i q^{82} +297.898i q^{83} +396.917 q^{84} +(1170.44 + 480.134i) q^{85} -155.348 q^{86} +644.966i q^{87} -2032.86i q^{88} +90.2097 q^{89} +(-482.845 - 198.070i) q^{90} +316.835 q^{91} +578.570i q^{92} -492.617i q^{93} -2509.23 q^{94} +(261.342 - 637.084i) q^{95} -853.115 q^{96} +492.101i q^{97} +254.143i q^{98} +323.599 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 54 q^{4} - 14 q^{5} - 6 q^{6} - 90 q^{9}+O(q^{10}) $ 10 * q - 54 * q^4 - 14 * q^5 - 6 * q^6 - 90 * q^9	$ 10 q - 54 q^{4} - 14 q^{5} - 6 q^{6} - 90 q^{9} + 92 q^{10} + 132 q^{11} - 14 q^{14} + 310 q^{16} - 348 q^{19} + 366 q^{20} - 210 q^{21} + 198 q^{24} - 374 q^{25} + 892 q^{26} - 740 q^{29} - 378 q^{30} + 684 q^{31} - 224 q^{34} + 486 q^{36} - 12 q^{39} - 2156 q^{40} + 1604 q^{41} - 580 q^{44} + 126 q^{45} + 1280 q^{46} - 490 q^{49} - 2504 q^{50} - 648 q^{51} + 54 q^{54} - 452 q^{55} + 462 q^{56} - 1408 q^{59} - 852 q^{60} + 1300 q^{61} - 150 q^{64} - 3296 q^{65} + 3036 q^{66} - 696 q^{69} - 882 q^{70} + 2940 q^{71} + 2624 q^{74} - 408 q^{75} + 8740 q^{76} + 1640 q^{79} - 4126 q^{80} + 810 q^{81} + 1134 q^{84} - 1704 q^{85} + 1664 q^{86} - 572 q^{89} - 828 q^{90} - 28 q^{91} - 5080 q^{94} + 1268 q^{95} + 330 q^{96} - 1188 q^{99}+O(q^{100}) $ 10 * q - 54 * q^4 - 14 * q^5 - 6 * q^6 - 90 * q^9 + 92 * q^10 + 132 * q^11 - 14 * q^14 + 310 * q^16 - 348 * q^19 + 366 * q^20 - 210 * q^21 + 198 * q^24 - 374 * q^25 + 892 * q^26 - 740 * q^29 - 378 * q^30 + 684 * q^31 - 224 * q^34 + 486 * q^36 - 12 * q^39 - 2156 * q^40 + 1604 * q^41 - 580 * q^44 + 126 * q^45 + 1280 * q^46 - 490 * q^49 - 2504 * q^50 - 648 * q^51 + 54 * q^54 - 452 * q^55 + 462 * q^56 - 1408 * q^59 - 852 * q^60 + 1300 * q^61 - 150 * q^64 - 3296 * q^65 + 3036 * q^66 - 696 * q^69 - 882 * q^70 + 2940 * q^71 + 2624 * q^74 - 408 * q^75 + 8740 * q^76 + 1640 * q^79 - 4126 * q^80 + 810 * q^81 + 1134 * q^84 - 1704 * q^85 + 1664 * q^86 - 572 * q^89 - 828 * q^90 - 28 * q^91 - 5080 * q^94 + 1268 * q^95 + 330 * q^96 - 1188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	5.18660i		−	1.83374i	−0.399185	−	0.916870i	$-0.630707\pi$
$2$		−	5.18660i		−	1.83374i	0.399185	−	0.916870i	$-0.369293\pi$
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	−18.9008			−2.36260
$5$	−4.24321	+	10.3438i	−0.379524	+	0.925182i
$5$	−4.24321	+	10.3438i	−0.379524	+	0.925182i
$6$	−15.5598			−1.05871
$7$		−	7.00000i		−	0.377964i
$7$		−	7.00000i		−	0.377964i
$8$			56.5383i			2.49866i
$9$	−9.00000			−0.333333
$10$	53.6494	+	22.0078i	1.69654	+	0.695948i
$11$	−35.9555			−0.985545			−0.492772	−	0.870158i	$-0.664016\pi$
$11$	−35.9555			−0.985545			−0.492772	+	0.870158i	$0.664016\pi$
$12$			56.7025i			1.36405i
$13$			45.2622i			0.965652i	0.875716	+	0.482826i	$0.160390\pi$
$13$			45.2622i			0.965652i	−0.875716	+	0.482826i	$0.839610\pi$
$14$	−36.3062			−0.693089
$15$	31.0315	+	12.7296i	0.534154	+	0.219118i
$16$	142.035			2.21929
$17$		−	113.154i		−	1.61434i	−0.590319	−	0.807170i	$-0.700998\pi$
$17$		−	113.154i		−	1.61434i	0.590319	−	0.807170i	$-0.299002\pi$
$18$			46.6794i			0.611247i
$19$	−61.5906			−0.743677			−0.371838	−	0.928297i	$-0.621272\pi$
$19$	−61.5906			−0.743677			−0.371838	+	0.928297i	$0.621272\pi$
$20$	80.2001	−	195.507i	0.896665	−	2.18584i
$21$	−21.0000			−0.218218
$22$			186.487i			1.80723i
$23$		−	30.6108i		−	0.277513i	−0.990327	−	0.138756i	$-0.955690\pi$
$23$		−	30.6108i		−	0.277513i	0.990327	−	0.138756i	$-0.0443105\pi$
$24$	169.615			1.44260
$25$	−88.9904	−	87.7822i	−0.711923	−	0.702257i
$26$	234.757			1.77075
$27$			27.0000i			0.192450i
$28$			132.306i			0.892980i
$29$	−214.989			−1.37663			−0.688317	−	0.725410i	$-0.741650\pi$
$29$	−214.989			−1.37663			−0.688317	+	0.725410i	$0.741650\pi$
$30$	66.0235	−	160.948i	0.401806	−	0.979500i
$31$	164.206			0.951362			0.475681	−	0.879618i	$-0.342202\pi$
$31$	164.206			0.951362			0.475681	+	0.879618i	$0.342202\pi$
$32$		−	284.372i		−	1.57095i
$33$			107.866i			0.569004i
$34$	−586.882			−2.96028
$35$	72.4069	+	29.7024i	0.349686	+	0.143447i
$36$	170.107			0.787535
$37$			410.533i			1.82409i	0.410095	+	0.912043i	$0.365496\pi$
$37$			410.533i			1.82409i	−0.410095	+	0.912043i	$0.634504\pi$
$38$			319.446i			1.36371i
$39$	135.787			0.557519
$40$	−584.823	−	239.904i	−2.31172	−	0.948302i
$41$	−309.310			−1.17820			−0.589100	−	0.808060i	$-0.700517\pi$
$41$	−309.310			−1.17820			−0.589100	+	0.808060i	$0.700517\pi$
$42$			108.919i			0.400155i
$43$		−	29.9519i		−	0.106224i	−0.998589	−	0.0531118i	$-0.983086\pi$
$43$		−	29.9519i		−	0.106224i	0.998589	−	0.0531118i	$-0.0169140\pi$
$44$	679.589			2.32845
$45$	38.1889	−	93.0946i	0.126508	−	0.308394i
$46$	−158.766			−0.508886
$47$		−	483.790i		−	1.50145i	−0.660616	−	0.750724i	$-0.729705\pi$
$47$		−	483.790i		−	1.50145i	0.660616	−	0.750724i	$-0.270295\pi$
$48$		−	426.104i		−	1.28131i
$49$	−49.0000			−0.142857
$50$	−455.291	+	461.558i	−1.28776	+	1.30548i
$51$	−339.461			−0.932039
$52$		−	855.493i		−	2.28145i
$53$		−	295.582i		−	0.766063i	−0.923735	−	0.383031i	$-0.874880\pi$
$53$		−	295.582i		−	0.766063i	0.923735	−	0.383031i	$-0.125120\pi$
$54$	140.038			0.352904
$55$	152.567	−	371.918i	0.374038	−	0.911808i
$56$	395.768			0.944405
$57$			184.772i			0.429362i
$58$			1115.06i			2.52439i
$59$	−416.191			−0.918364			−0.459182	−	0.888342i	$-0.651857\pi$
$59$	−416.191			−0.918364			−0.459182	+	0.888342i	$0.651857\pi$
$60$	−586.522	−	240.600i	−1.26199	−	0.517690i
$61$	−151.196			−0.317355			−0.158677	−	0.987330i	$-0.550723\pi$
$61$	−151.196			−0.317355			−0.158677	+	0.987330i	$0.550723\pi$
$62$		−	851.670i		−	1.74455i
$63$			63.0000i			0.125988i
$64$	−338.644			−0.661415
$65$	−468.185	−	192.057i	−0.893403	−	0.366488i
$66$	559.460			1.04341
$67$		−	89.5253i		−	0.163243i	−0.996663	−	0.0816213i	$-0.973990\pi$
$67$		−	89.5253i		−	0.163243i	0.996663	−	0.0816213i	$-0.0260098\pi$
$68$			2138.70i			3.81404i
$69$	−91.8324			−0.160222
$70$	154.055	−	375.546i	0.263044	−	0.641233i
$71$	714.265			1.19391			0.596955	−	0.802274i	$-0.296377\pi$
$71$	714.265			1.19391			0.596955	+	0.802274i	$0.296377\pi$
$72$		−	508.844i		−	0.832887i
$73$		−	1135.58i		−	1.82068i	−0.413861	−	0.910340i	$-0.635820\pi$
$73$		−	1135.58i		−	1.82068i	0.413861	−	0.910340i	$-0.364180\pi$
$74$	2129.27			3.34490
$75$	−263.347	+	266.971i	−0.405448	+	0.411029i
$76$	1164.11			1.75701
$77$			251.688i			0.372501i
$78$		−	704.271i		−	1.02235i
$79$	323.347			0.460498			0.230249	−	0.973132i	$-0.426046\pi$
$79$	323.347			0.460498			0.230249	+	0.973132i	$0.426046\pi$
$80$	−602.683	+	1469.19i	−0.842275	+	2.05325i
$81$	81.0000			0.111111
$82$			1604.27i			2.16051i
$83$			297.898i			0.393959i	0.980408	+	0.196979i	$0.0631132\pi$
$83$			297.898i			0.393959i	−0.980408	+	0.196979i	$0.936887\pi$
$84$	396.917			0.515562
$85$	1170.44	+	480.134i	1.49356	+	0.612680i
$86$	−155.348			−0.194787
$87$			644.966i			0.794800i
$88$		−	2032.86i		−	2.46254i
$89$	90.2097			0.107441			0.0537203	−	0.998556i	$-0.482892\pi$
$89$	90.2097			0.107441			0.0537203	+	0.998556i	$0.482892\pi$
$90$	−482.845	−	198.070i	−0.565515	−	0.231983i
$91$	316.835			0.364982
$92$			578.570i			0.655653i
$93$		−	492.617i		−	0.549269i
$94$	−2509.23			−2.75326
$95$	261.342	−	637.084i	0.282243	−	0.688036i
$96$	−853.115			−0.906986
$97$			492.101i			0.515106i	0.966264	+	0.257553i	$0.0829162\pi$
$97$			492.101i			0.515106i	−0.966264	+	0.257553i	$0.917084\pi$
$98$			254.143i			0.261963i
$99$	323.599			0.328515
$100$	1681.99	+	1659.16i	1.68199	+	1.65916i
$101$	−272.636			−0.268597			−0.134299	−	0.990941i	$-0.542878\pi$
$101$	−272.636			−0.268597			−0.134299	+	0.990941i	$0.542878\pi$
$102$			1760.65i			1.70912i
$103$		−	628.179i		−	0.600936i	−0.953792	−	0.300468i	$-0.902857\pi$
$103$		−	628.179i		−	0.600936i	0.953792	−	0.300468i	$-0.0971428\pi$
$104$	−2559.05			−2.41284
$105$	89.1073	−	217.221i	0.0828189	−	0.201891i
$106$	−1533.07			−1.40476
$107$		−	908.469i		−	0.820794i	−0.911907	−	0.410397i	$-0.865390\pi$
$107$		−	908.469i		−	0.820794i	0.911907	−	0.410397i	$-0.134610\pi$
$108$		−	510.322i		−	0.454683i
$109$	−984.306			−0.864948			−0.432474	−	0.901646i	$-0.642359\pi$
$109$	−984.306			−0.864948			−0.432474	+	0.901646i	$0.642359\pi$
$110$	−1928.99	−	791.302i	−1.67202	−	0.685888i
$111$	1231.60			1.05314
$112$		−	994.244i		−	0.838814i
$113$		−	2228.79i		−	1.85546i	−0.373251	−	0.927730i	$-0.621757\pi$
$113$		−	2228.79i		−	1.85546i	0.373251	−	0.927730i	$-0.378243\pi$
$114$	958.338			0.787339
$115$	316.633	+	129.888i	0.256750	+	0.105323i
$116$	4063.47			3.25244
$117$		−	407.360i		−	0.321884i
$118$			2158.62i			1.68404i
$119$	−792.075			−0.610163
$120$	−719.711	+	1754.47i	−0.547502	+	1.33467i
$121$	−38.2023			−0.0287019
$122$			784.193i			0.581946i
$123$			927.931i			0.680234i
$124$	−3103.63			−2.24769
$125$	1285.61	−	548.025i	0.919908	−	0.392135i
$126$	326.756			0.231030
$127$			2860.78i			1.99885i	0.0339770	+	0.999423i	$0.489183\pi$
$127$			2860.78i			1.99885i	−0.0339770	+	0.999423i	$0.510817\pi$
$128$		−	518.561i		−	0.358084i
$129$	−89.8556			−0.0613283
$130$	−996.122	+	2428.29i	−0.672044	+	1.63827i
$131$	−524.971			−0.350130			−0.175065	−	0.984557i	$-0.556013\pi$
$131$	−524.971			−0.350130			−0.175065	+	0.984557i	$0.556013\pi$
$132$		−	2038.77i		−	1.34433i
$133$			431.134i			0.281083i
$134$	−464.332			−0.299344
$135$	−279.284	−	114.567i	−0.178051	−	0.0730394i
$136$	6397.51			4.03369
$137$			2149.03i			1.34017i	0.742282	+	0.670087i	$0.233743\pi$
$137$			2149.03i			1.34017i	−0.742282	+	0.670087i	$0.766257\pi$
$138$			476.298i			0.293806i
$139$	1507.78			0.920060			0.460030	−	0.887903i	$-0.347839\pi$
$139$	1507.78			0.920060			0.460030	+	0.887903i	$0.347839\pi$
$140$	−1368.55	−	561.401i	−0.826169	−	0.338907i
$141$	−1451.37			−0.866861
$142$		−	3704.61i		−	2.18932i
$143$		−	1627.42i		−	0.951693i
$144$	−1278.31			−0.739765
$145$	912.242	−	2223.81i	0.522466	−	1.27364i
$146$	−5889.80			−3.33865
$147$			147.000i			0.0824786i
$148$		−	7759.41i		−	4.30959i
$149$	1013.61			0.557304			0.278652	−	0.960392i	$-0.410112\pi$
$149$	1013.61			0.557304			0.278652	+	0.960392i	$0.410112\pi$
$150$	1384.67	+	1365.87i	0.753721	+	0.743487i
$151$	1663.70			0.896623			0.448312	−	0.893877i	$-0.352025\pi$
$151$	1663.70			0.896623			0.448312	+	0.893877i	$0.352025\pi$
$152$		−	3482.23i		−	1.85820i
$153$			1018.38i			0.538113i
$154$	1305.41			0.683070
$155$	−696.759	+	1698.52i	−0.361065	+	0.880183i
$156$	−2566.48			−1.31720
$157$		−	2399.48i		−	1.21974i	−0.792500	−	0.609872i	$-0.791221\pi$
$157$		−	2399.48i		−	1.21974i	0.792500	−	0.609872i	$-0.208779\pi$
$158$		−	1677.07i		−	0.844434i
$159$	−886.746			−0.442286
$160$	2941.50	+	1206.65i	1.45341	+	0.596212i
$161$	−214.276			−0.104890
$162$		−	420.115i		−	0.203749i
$163$			1415.81i			0.680337i	0.940365	+	0.340168i	$0.110484\pi$
$163$			1415.81i			0.680337i	−0.940365	+	0.340168i	$0.889516\pi$
$164$	5846.22			2.78362
$165$	−1115.75	−	457.700i	−0.526433	−	0.215951i
$166$	1545.08			0.722418
$167$			3543.86i			1.64211i	0.570850	+	0.821055i	$0.306614\pi$
$167$			3543.86i			1.64211i	−0.570850	+	0.821055i	$0.693386\pi$
$168$		−	1187.30i		−	0.545253i
$169$	148.335			0.0675170
$170$	2490.26	−	6070.62i	1.12350	−	2.73880i
$171$	554.316			0.247892
$172$			566.115i			0.250964i
$173$		−	95.6649i		−	0.0420420i	−0.999779	−	0.0210210i	$-0.993308\pi$
$173$		−	95.6649i		−	0.0420420i	0.999779	−	0.0210210i	$-0.00669169\pi$
$174$	3345.18			1.45746
$175$	−614.475	+	622.933i	−0.265428	+	0.269082i
$176$	−5106.93			−2.18721
$177$			1248.57i			0.530218i
$178$		−	467.882i		−	0.197018i
$179$	−2166.13			−0.904491			−0.452245	−	0.891894i	$-0.649377\pi$
$179$	−2166.13			−0.904491			−0.452245	+	0.891894i	$0.649377\pi$
$180$	−721.801	+	1759.57i	−0.298888	+	0.728613i
$181$	−1859.24			−0.763514			−0.381757	−	0.924263i	$-0.624681\pi$
$181$	−1859.24			−0.763514			−0.381757	+	0.924263i	$0.624681\pi$
$182$		−	1643.30i		−	0.669282i
$183$			453.588i			0.183225i
$184$	1730.68			0.693411
$185$	−4246.49	−	1741.98i	−1.68761	−	0.692284i
$186$	−2555.01			−1.00722
$187$			4068.49i			1.59100i
$188$			9144.03i			3.54733i
$189$	189.000			0.0727393
$190$	−3304.30	−	1355.48i	−1.26168	−	0.517561i
$191$	−2661.60			−1.00831			−0.504154	−	0.863614i	$-0.668195\pi$
$191$	−2661.60			−1.00831			−0.504154	+	0.863614i	$0.668195\pi$
$192$			1015.93i			0.381868i
$193$			1952.03i			0.728033i	0.931393	+	0.364016i	$0.118595\pi$
$193$			1952.03i			0.728033i	−0.931393	+	0.364016i	$0.881405\pi$
$194$	2552.33			0.944570
$195$	−576.170	+	1404.56i	−0.211592	+	0.515807i
$196$	926.141			0.337515
$197$			3587.80i			1.29757i	0.760974	+	0.648783i	$0.224722\pi$
$197$			3587.80i			1.29757i	−0.760974	+	0.648783i	$0.775278\pi$
$198$		−	1678.38i		−	0.602411i
$199$	767.691			0.273468			0.136734	−	0.990608i	$-0.456339\pi$
$199$	767.691			0.273468			0.136734	+	0.990608i	$0.456339\pi$
$200$	4963.05	−	5031.36i	1.75470	−	1.77886i
$201$	−268.576			−0.0942481
$202$			1414.06i			0.492538i
$203$			1504.92i			0.520319i
$204$	6416.09			2.20204
$205$	1312.47	−	3199.46i	0.447155	−	1.09005i
$206$	−3258.12			−1.10196
$207$			275.497i			0.0925042i
$208$			6428.81i			2.14306i
$209$	2214.52			0.732927
$210$	−1126.64	−	462.164i	−0.370216	−	0.151868i
$211$	−1199.84			−0.391472			−0.195736	−	0.980657i	$-0.562710\pi$
$211$	−1199.84			−0.391472			−0.195736	+	0.980657i	$0.562710\pi$
$212$			5586.75i			1.80990i
$213$		−	2142.79i		−	0.689305i
$214$	−4711.87			−1.50512
$215$	309.818	+	127.092i	0.0982762	+	0.0403144i
$216$	−1526.53			−0.480868
$217$		−	1149.44i		−	0.359581i
$218$			5105.20i			1.58609i
$219$	−3406.74			−1.05117
$220$	−2883.64	+	7029.56i	−0.883703	+	2.15424i
$221$	5121.58			1.55889
$222$		−	6387.81i		−	1.93118i
$223$		−	2917.84i		−	0.876203i	−0.898926	−	0.438101i	$-0.855651\pi$
$223$		−	2917.84i		−	0.876203i	0.898926	−	0.438101i	$-0.144349\pi$
$224$	−1990.60			−0.593762
$225$	800.914	+	790.040i	0.237308	+	0.234086i
$226$	−11559.9			−3.40243
$227$			612.679i			0.179141i	0.995981	+	0.0895703i	$0.0285494\pi$
$227$			612.679i			0.179141i	−0.995981	+	0.0895703i	$0.971451\pi$
$228$		−	3492.34i		−	1.01441i
$229$	−2641.51			−0.762253			−0.381126	−	0.924523i	$-0.624464\pi$
$229$	−2641.51			−0.762253			−0.381126	+	0.924523i	$0.624464\pi$
$230$	673.677	−	1642.25i	0.193135	−	0.470812i
$231$	755.065			0.215063
$232$		−	12155.1i		−	3.43974i
$233$			2322.87i			0.653117i	0.945177	+	0.326558i	$0.105889\pi$
$233$			2322.87i			0.653117i	−0.945177	+	0.326558i	$0.894111\pi$
$234$	−2112.81			−0.590251
$235$	5004.25	+	2052.82i	1.38911	+	0.569835i
$236$	7866.36			2.16973
$237$		−	970.041i		−	0.265869i
$238$			4108.18i			1.11888i
$239$	−5372.54			−1.45406			−0.727030	−	0.686605i	$-0.759100\pi$
$239$	−5372.54			−1.45406			−0.727030	+	0.686605i	$0.759100\pi$
$240$	4407.56	+	1808.05i	1.18544	+	0.486288i
$241$	−1412.33			−0.377494			−0.188747	−	0.982026i	$-0.560443\pi$
$241$	−1412.33			−0.377494			−0.188747	+	0.982026i	$0.560443\pi$
$242$			198.140i			0.0526319i
$243$		−	243.000i		−	0.0641500i
$244$	2857.73			0.749784
$245$	207.917	−	506.849i	0.0542177	−	0.132169i
$246$	4812.81			1.24737
$247$		−	2787.73i		−	0.718133i
$248$			9283.91i			2.37713i
$249$	893.694			0.227452
$250$	−2842.39	−	6667.95i	−0.719074	−	1.68687i
$251$	5676.06			1.42737			0.713684	−	0.700467i	$-0.247025\pi$
$251$	5676.06			1.42737			0.713684	+	0.700467i	$0.247025\pi$
$252$		−	1190.75i		−	0.297660i
$253$			1100.63i			0.273501i
$254$	14837.7			3.66536
$255$	1440.40	−	3511.33i	0.353731	−	0.862306i
$256$	−5398.72			−1.31805
$257$		−	3939.60i		−	0.956207i	−0.878303	−	0.478104i	$-0.841324\pi$
$257$		−	3939.60i		−	0.956207i	0.878303	−	0.478104i	$-0.158676\pi$
$258$			466.045i			0.112460i
$259$	2873.73			0.689440
$260$	8849.09	+	3630.03i	2.11076	+	0.865866i
$261$	1934.90			0.458878
$262$			2722.82i			0.642047i
$263$			5397.68i			1.26553i	0.774343	+	0.632766i	$0.218081\pi$
$263$			5397.68i			1.26553i	−0.774343	+	0.632766i	$0.781919\pi$
$264$	−6098.58			−1.42175
$265$	3057.46	+	1254.22i	0.708747	+	0.290739i
$266$	2236.12			0.515434
$267$		−	270.629i		−	0.0620308i
$268$			1692.10i			0.385678i
$269$	−4973.60			−1.12731			−0.563654	−	0.826011i	$-0.690605\pi$
$269$	−4973.60			−1.12731			−0.563654	+	0.826011i	$0.690605\pi$
$270$	−594.211	+	1448.53i	−0.133935	+	0.326500i
$271$	4147.48			0.929672			0.464836	−	0.885397i	$-0.346113\pi$
$271$	4147.48			0.929672			0.464836	+	0.885397i	$0.346113\pi$
$272$		−	16071.7i		−	3.58269i
$273$		−	950.506i		−	0.210722i
$274$	11146.2			2.45753
$275$	3199.69	+	3156.25i	0.701632	+	0.692106i
$276$	1735.71			0.378541
$277$		−	2616.79i		−	0.567609i	−0.958882	−	0.283805i	$-0.908403\pi$
$277$		−	2616.79i		−	0.567609i	0.958882	−	0.283805i	$-0.0915968\pi$
$278$		−	7820.26i		−	1.68715i
$279$	−1477.85			−0.317121
$280$	−1679.32	+	4093.76i	−0.358424	+	0.873747i
$281$	2866.89			0.608628			0.304314	−	0.952572i	$-0.401573\pi$
$281$	2866.89			0.608628			0.304314	+	0.952572i	$0.401573\pi$
$282$			7527.68i			1.58960i
$283$		−	3015.40i		−	0.633381i	−0.948529	−	0.316691i	$-0.897428\pi$
$283$		−	3015.40i		−	0.633381i	0.948529	−	0.316691i	$-0.102572\pi$
$284$	−13500.2			−2.82074
$285$	−1911.25	−	784.025i	−0.397238	−	0.162953i
$286$	−8440.80			−1.74516
$287$			2165.17i			0.445318i
$288$			2559.35i			0.523649i
$289$	−7890.73			−1.60609
$290$	−11534.0	−	4731.43i	−2.33552	−	0.958067i
$291$	1476.30			0.297396
$292$			21463.4i			4.30155i
$293$		−	3580.41i		−	0.713890i	−0.934125	−	0.356945i	$-0.883818\pi$
$293$		−	3580.41i		−	0.713890i	0.934125	−	0.356945i	$-0.116182\pi$
$294$	762.430			0.151244
$295$	1765.98	−	4305.02i	0.348541	−	0.849653i
$296$	−23210.8			−4.55777
$297$		−	970.798i		−	0.189668i
$298$		−	5257.20i		−	1.02195i
$299$	1385.51			0.267981
$300$	4977.47	−	5045.98i	0.957914	−	0.971099i
$301$	−209.663			−0.0401488
$302$		−	8628.96i		−	1.64417i
$303$			817.909i			0.155075i
$304$	−8748.01			−1.65044
$305$	641.555	−	1563.95i	0.120444	−	0.293611i
$306$	5281.94			0.986760
$307$		−	1432.92i		−	0.266389i	−0.991090	−	0.133194i	$-0.957477\pi$
$307$		−	1432.92i		−	0.266389i	0.991090	−	0.133194i	$-0.0425234\pi$
$308$		−	4757.12i		−	0.880072i
$309$	−1884.54			−0.346950
$310$	8809.54	+	3613.81i	1.61403	+	0.662099i
$311$	5488.33			1.00069			0.500345	−	0.865826i	$-0.333206\pi$
$311$	5488.33			1.00069			0.500345	+	0.865826i	$0.333206\pi$
$312$			7677.14i			1.39305i
$313$		−	2461.68i		−	0.444545i	−0.974985	−	0.222272i	$-0.928653\pi$
$313$		−	2461.68i		−	0.444545i	0.974985	−	0.222272i	$-0.0713474\pi$
$314$	−12445.2			−2.23669
$315$	−651.662	−	267.322i	−0.116562	−	0.0478155i
$316$	−6111.53			−1.08798
$317$		−	3113.12i		−	0.551579i	−0.961218	−	0.275789i	$-0.911061\pi$
$317$		−	3113.12i		−	0.551579i	0.961218	−	0.275789i	$-0.0889393\pi$
$318$			4599.20i			0.811038i
$319$	7730.03			1.35673
$320$	1436.94	−	3502.88i	0.251023	−	0.611929i
$321$	−2725.41			−0.473886
$322$			1111.36i			0.192341i
$323$			6969.20i			1.20055i
$324$	−1530.97			−0.262512
$325$	3973.21	−	4027.90i	0.678136	−	0.687470i
$326$	7343.25			1.24756
$327$			2952.92i			0.499378i
$328$		−	17487.9i		−	2.94392i
$329$	−3386.53			−0.567494
$330$	−2373.91	+	5786.97i	−0.395998	+	0.965341i
$331$	−6364.21			−1.05682			−0.528411	−	0.848988i	$-0.677212\pi$
$331$	−6364.21			−1.05682			−0.528411	+	0.848988i	$0.677212\pi$
$332$		−	5630.52i		−	0.930768i
$333$		−	3694.79i		−	0.608029i
$334$	18380.6			3.01120
$335$	926.036	+	379.874i	0.151029	+	0.0619545i
$336$	−2982.73			−0.484290
$337$			5163.25i			0.834600i	0.908769	+	0.417300i	$0.137024\pi$
$337$			5163.25i			0.834600i	−0.908769	+	0.417300i	$0.862976\pi$
$338$		−	769.353i		−	0.123809i
$339$	−6686.37			−1.07125
$340$	−22122.4	−	9074.93i	−3.52869	−	1.44752i
$341$	−5904.10			−0.937610
$342$		−	2875.01i		−	0.454570i
$343$			343.000i			0.0539949i
$344$	1693.43			0.265417
$345$	389.664	−	949.900i	0.0608081	−	0.148235i
$346$	−496.176			−0.0770941
$347$		−	305.000i		−	0.0471851i	−0.999722	−	0.0235926i	$-0.992490\pi$
$347$		−	305.000i		−	0.0471851i	0.999722	−	0.0235926i	$-0.00751044\pi$
$348$		−	12190.4i		−	1.87780i
$349$	8233.50			1.26283			0.631417	−	0.775443i	$-0.282474\pi$
$349$	8233.50			1.26283			0.631417	+	0.775443i	$0.282474\pi$
$350$	3230.90	+	3187.04i	0.493426	+	0.486727i
$351$	−1222.08			−0.185840
$352$			10224.7i			1.54824i
$353$		−	1064.37i		−	0.160483i	−0.996775	−	0.0802415i	$-0.974431\pi$
$353$		−	1064.37i		−	0.160483i	0.996775	−	0.0802415i	$-0.0255692\pi$
$354$	6475.85			0.972281
$355$	−3030.77	+	7388.25i	−0.453118	+	1.10458i
$356$	−1705.04			−0.253839
$357$			2376.22i			0.352278i
$358$			11234.8i			1.65860i
$359$	3915.59			0.575646			0.287823	−	0.957684i	$-0.407069\pi$
$359$	3915.59			0.575646			0.287823	+	0.957684i	$0.407069\pi$
$360$	5263.41	+	2159.13i	0.770572	+	0.316101i
$361$	−3065.59			−0.446945
$362$			9643.13i			1.40009i
$363$			114.607i			0.0165711i
$364$	−5988.45			−0.862308
$365$	11746.3	+	4818.50i	1.68446	+	0.690992i
$366$	2352.58			0.335987
$367$		−	7430.70i		−	1.05689i	−0.848967	−	0.528446i	$-0.822775\pi$
$367$		−	7430.70i		−	1.05689i	0.848967	−	0.528446i	$-0.177225\pi$
$368$		−	4347.80i		−	0.615882i
$369$	2783.79			0.392733
$370$	−9034.93	+	22024.8i	−1.26947	+	3.09464i
$371$	−2069.07			−0.289544
$372$			9310.88i			1.29771i
$373$		−	3275.71i		−	0.454718i	−0.973811	−	0.227359i	$-0.926991\pi$
$373$		−	3275.71i		−	0.454718i	0.973811	−	0.227359i	$-0.0730090\pi$
$374$	21101.6			2.91749
$375$	−1644.08	−	3856.83i	−0.226399	−	0.531109i
$376$	27352.7			3.75161
$377$		−	9730.86i		−	1.32935i
$378$		−	980.268i		−	0.133385i
$379$	−5745.18			−0.778655			−0.389327	−	0.921099i	$-0.627293\pi$
$379$	−5745.18			−0.778655			−0.389327	+	0.921099i	$0.627293\pi$
$380$	−4939.58	+	12041.4i	−0.666829	+	1.62556i
$381$	8582.35			1.15403
$382$			13804.7i			1.84897i
$383$			101.844i			0.0135874i	0.999977	+	0.00679372i	$0.00216252\pi$
$383$			101.844i			0.0135874i	−0.999977	+	0.00679372i	$0.997837\pi$
$384$	−1555.68			−0.206740
$385$	−2603.43	−	1067.97i	−0.344631	−	0.141373i
$386$	10124.4			1.33502
$387$			269.567i			0.0354079i
$388$		−	9301.11i		−	1.21699i
$389$	−3047.72			−0.397237			−0.198619	−	0.980077i	$-0.563646\pi$
$389$	−3047.72			−0.397237			−0.198619	+	0.980077i	$0.563646\pi$
$390$	7284.87	+	2988.37i	0.945856	+	0.388005i
$391$	−3463.72			−0.448000
$392$		−	2770.38i		−	0.356952i
$393$			1574.91i			0.202147i
$394$	18608.5			2.37940
$395$	−1372.03	+	3344.65i	−0.174770	+	0.426045i
$396$	−6116.30			−0.776151
$397$		−	9830.23i		−	1.24273i	−0.783520	−	0.621367i	$-0.786578\pi$
$397$		−	9830.23i		−	1.24273i	0.783520	−	0.621367i	$-0.213422\pi$
$398$		−	3981.71i		−	0.501470i
$399$	1293.40			0.162284
$400$	−12639.7	−	12468.1i	−1.57997	−	1.55852i
$401$	3693.01			0.459900			0.229950	−	0.973202i	$-0.426144\pi$
$401$	3693.01			0.459900			0.229950	+	0.973202i	$0.426144\pi$
$402$			1393.00i			0.172827i
$403$			7432.31i			0.918684i
$404$	5153.06			0.634589
$405$	−343.700	+	837.852i	−0.0421693	+	0.102798i
$406$	7805.43			0.954130
$407$		−	14760.9i		−	1.79772i
$408$		−	19192.5i		−	2.32885i
$409$	−8815.07			−1.06571			−0.532857	−	0.846205i	$-0.678882\pi$
$409$	−8815.07			−1.06571			−0.532857	+	0.846205i	$0.678882\pi$
$410$	−16594.3	−	6807.25i	−1.99887	−	0.819966i
$411$	6447.09			0.773750
$412$			11873.1i			1.41977i
$413$			2913.34i			0.347109i
$414$	1428.89			0.169629
$415$	−3081.41	−	1264.04i	−0.364483	−	0.149517i
$416$	12871.3			1.51699
$417$		−	4523.35i		−	0.531197i
$418$		−	11485.8i		−	1.34400i
$419$	−3746.84			−0.436862			−0.218431	−	0.975852i	$-0.570094\pi$
$419$	−3746.84			−0.436862			−0.218431	+	0.975852i	$0.570094\pi$
$420$	−1684.20	+	4105.65i	−0.195668	+	0.476989i
$421$	−10554.5			−1.22184			−0.610922	−	0.791690i	$-0.709201\pi$
$421$	−10554.5			−1.22184			−0.610922	+	0.791690i	$0.709201\pi$
$422$			6223.10i			0.717858i
$423$			4354.11i			0.500482i
$424$	16711.7			1.91413
$425$	−9932.87	+	10069.6i	−1.13368	+	1.14929i
$426$	−11113.8			−1.26401
$427$			1058.37i			0.119949i
$428$			17170.8i			1.93921i
$429$	−4882.27			−0.549460
$430$	659.175	−	1606.90i	0.0739262	−	0.180213i
$431$	−14029.9			−1.56797			−0.783986	−	0.620778i	$-0.786817\pi$
$431$	−14029.9			−1.56797			−0.783986	+	0.620778i	$0.786817\pi$
$432$			3834.94i			0.427103i
$433$		−	9639.08i		−	1.06980i	−0.844915	−	0.534901i	$-0.820349\pi$
$433$		−	9639.08i		−	1.06980i	0.844915	−	0.534901i	$-0.179651\pi$
$434$	−5961.69			−0.659378
$435$	−6671.43	−	2736.72i	−0.735335	−	0.301646i
$436$	18604.2			2.04353
$437$			1885.34i			0.206380i
$438$			17669.4i			1.92757i
$439$	−3936.53			−0.427974			−0.213987	−	0.976837i	$-0.568645\pi$
$439$	−3936.53			−0.427974			−0.213987	+	0.976837i	$0.568645\pi$
$440$	21027.6	+	8625.85i	2.27830	+	0.934594i
$441$	441.000			0.0476190
$442$		−	26563.6i		−	2.85860i
$443$		−	10812.5i		−	1.15963i	−0.814746	−	0.579817i	$-0.803124\pi$
$443$		−	10812.5i		−	1.15963i	0.814746	−	0.579817i	$-0.196876\pi$
$444$	−23278.2			−2.48814
$445$	−382.778	+	933.115i	−0.0407762	+	0.0994020i
$446$	−15133.7			−1.60673
$447$		−	3040.84i		−	0.321760i
$448$			2370.51i			0.249991i
$449$	−8154.86			−0.857131			−0.428565	−	0.903511i	$-0.640981\pi$
$449$	−8154.86			−0.857131			−0.428565	+	0.903511i	$0.640981\pi$
$450$	4097.62	−	4154.02i	0.429253	−	0.435161i
$451$	11121.4			1.16117
$452$			42126.0i			4.38372i
$453$		−	4991.11i		−	0.517666i
$454$	3177.72			0.328497
$455$	−1344.40	+	3277.30i	−0.138519	+	0.337675i
$456$	−10446.7			−1.07283
$457$			17787.5i			1.82071i	0.413833	+	0.910353i	$0.364190\pi$
$457$			17787.5i			1.82071i	−0.413833	+	0.910353i	$0.635810\pi$
$458$			13700.5i			1.39777i
$459$	3055.15			0.310680
$460$	−5984.64	−	2454.99i	−0.606598	−	0.248836i
$461$	13192.1			1.33280			0.666398	−	0.745596i	$-0.267835\pi$
$461$	13192.1			1.33280			0.666398	+	0.745596i	$0.267835\pi$
$462$		−	3916.22i		−	0.394371i
$463$		−	542.568i		−	0.0544607i	−0.999629	−	0.0272303i	$-0.991331\pi$
$463$		−	542.568i		−	0.0544607i	0.999629	−	0.0272303i	$-0.00866876\pi$
$464$	−30535.9			−3.05516
$465$	5095.56	+	2090.28i	0.508174	+	0.208461i
$466$	12047.8			1.19765
$467$			5962.51i			0.590818i	0.955371	+	0.295409i	$0.0954559\pi$
$467$			5962.51i			0.590818i	−0.955371	+	0.295409i	$0.904544\pi$
$468$			7699.44i			0.760484i
$469$	−626.677			−0.0616999
$470$	10647.2	−	25955.1i	1.04493	−	2.54727i
$471$	−7198.45			−0.704219
$472$		−	23530.7i		−	2.29468i
$473$			1076.93i			0.104688i
$474$	−5031.21			−0.487534
$475$	5480.98	+	5406.56i	0.529441	+	0.522253i
$476$	14970.9			1.44157
$477$			2660.24i			0.255354i
$478$			27865.2i			2.66637i
$479$	1317.66			0.125690			0.0628451	−	0.998023i	$-0.479983\pi$
$479$	1317.66			0.125690			0.0628451	+	0.998023i	$0.479983\pi$
$480$	3619.94	−	8824.49i	0.344223	−	0.839127i
$481$	−18581.6			−1.76143
$482$			7325.19i			0.692227i
$483$			642.827i			0.0605582i
$484$	722.054			0.0678113
$485$	−5090.22	−	2088.08i	−0.476567	−	0.195495i
$486$	−1260.34			−0.117635
$487$		−	5976.21i		−	0.556074i	−0.960570	−	0.278037i	$-0.910316\pi$
$487$		−	5976.21i		−	0.556074i	0.960570	−	0.278037i	$-0.0896837\pi$
$488$		−	8548.35i		−	0.792962i
$489$	4247.43			0.392793
$490$	−2628.82	−	1078.38i	−0.242363	−	0.0994212i
$491$	10338.9			0.950285			0.475143	−	0.879909i	$-0.342396\pi$
$491$	10338.9			0.950285			0.475143	+	0.879909i	$0.342396\pi$
$492$		−	17538.7i		−	1.60712i
$493$			24326.7i			2.22236i
$494$	−14458.8			−1.31687
$495$	−1373.10	+	3347.26i	−0.124679	+	0.303936i
$496$	23322.9			2.11135
$497$		−	4999.85i		−	0.451256i
$498$		−	4635.24i		−	0.417088i
$499$	4161.74			0.373357			0.186678	−	0.982421i	$-0.440228\pi$
$499$	4161.74			0.373357			0.186678	+	0.982421i	$0.440228\pi$
$500$	−24299.1	+	10358.1i	−2.17338	+	0.926460i
$501$	10631.6			0.948072
$502$		−	29439.4i		−	2.61742i
$503$			7556.24i			0.669813i	0.942251	+	0.334907i	$0.108705\pi$
$503$			7556.24i			0.669813i	−0.942251	+	0.334907i	$0.891295\pi$
$504$	−3561.91			−0.314802
$505$	1156.85	−	2820.11i	0.101939	−	0.248501i
$506$	5708.51			0.501530
$507$		−	445.004i		−	0.0389809i
$508$		−	54071.2i		−	4.72248i
$509$	−7231.12			−0.629693			−0.314847	−	0.949143i	$-0.601953\pi$
$509$	−7231.12			−0.629693			−0.314847	+	0.949143i	$0.601953\pi$
$510$	−18211.9	−	7470.79i	−1.58125	−	0.648651i
$511$	−7949.06			−0.688152
$512$			23852.5i			2.05887i
$513$		−	1662.95i		−	0.143121i
$514$	−20433.1			−1.75344
$515$	6497.79	+	2665.50i	0.555975	+	0.228069i
$516$	1698.35			0.144894
$517$			17394.9i			1.47974i
$518$		−	14904.9i		−	1.26425i
$519$	−286.995			−0.0242730
$520$	10858.6	−	26470.4i	0.915729	−	2.23231i
$521$	−7378.54			−0.620460			−0.310230	−	0.950661i	$-0.600406\pi$
$521$	−7378.54			−0.620460			−0.310230	+	0.950661i	$0.600406\pi$
$522$		−	10035.5i		−	0.841464i
$523$			2200.53i			0.183982i	0.995760	+	0.0919909i	$0.0293231\pi$
$523$			2200.53i			0.183982i	−0.995760	+	0.0919909i	$0.970677\pi$
$524$	9922.40			0.827217
$525$	1868.80	+	1843.43i	0.155354	+	0.153245i
$526$	27995.6			2.32066
$527$		−	18580.5i		−	1.53582i
$528$			15320.8i			1.26279i
$529$	11230.0			0.922987
$530$	6505.12	−	15857.8i	0.533140	−	1.29966i
$531$	3745.72			0.306121
$532$		−	8148.80i		−	0.664089i
$533$		−	14000.1i		−	1.13773i
$534$	−1403.64			−0.113748
$535$	9397.06	+	3854.82i	0.759384	+	0.311511i
$536$	5061.60			0.407888
$537$			6498.38i			0.522208i
$538$			25796.1i			2.06719i
$539$	1761.82			0.140792
$540$	5278.70	+	2165.40i	0.420665	+	0.172563i
$541$	−23797.3			−1.89118			−0.945588	−	0.325365i	$-0.894513\pi$
$541$	−23797.3			−1.89118			−0.945588	+	0.325365i	$0.894513\pi$
$542$		−	21511.3i		−	1.70478i
$543$			5577.72i			0.440815i
$544$	−32177.7			−2.53604
$545$	4176.61	−	10181.5i	0.328269	−	0.800235i
$546$	−4929.89			−0.386410
$547$		−	6586.46i		−	0.514839i	−0.966300	−	0.257419i	$-0.917128\pi$
$547$		−	6586.46i		−	0.514839i	0.966300	−	0.257419i	$-0.0828721\pi$
$548$		−	40618.4i		−	3.16630i
$549$	1360.76			0.105785
$550$	16370.2	−	16595.5i	1.26914	−	1.28661i
$551$	13241.3			1.02377
$552$		−	5192.04i		−	0.400341i
$553$		−	2263.43i		−	0.174052i
$554$	−13572.3			−1.04085
$555$	−5225.93	+	12739.5i	−0.399690	+	0.974343i
$556$	−28498.3			−2.17374
$557$		−	23522.6i		−	1.78938i	−0.446686	−	0.894691i	$-0.647396\pi$
$557$		−	23522.6i		−	1.78938i	0.446686	−	0.894691i	$-0.352604\pi$
$558$			7665.03i			0.581517i
$559$	1355.69			0.102575
$560$	10284.3	+	4218.78i	0.776056	+	0.318350i
$561$	12205.5			0.918566
$562$		−	14869.4i		−	1.11607i
$563$			17654.3i			1.32156i	0.750578	+	0.660782i	$0.229775\pi$
$563$			17654.3i			1.32156i	−0.750578	+	0.660782i	$0.770225\pi$
$564$	27432.1			2.04805
$565$	23054.3	+	9457.22i	1.71664	+	0.704192i
$566$	−15639.7			−1.16146
$567$		−	567.000i		−	0.0419961i
$568$			40383.3i			2.98318i
$569$	13453.6			0.991223			0.495611	−	0.868544i	$-0.334944\pi$
$569$	13453.6			0.991223			0.495611	+	0.868544i	$0.334944\pi$
$570$	−4066.43	+	9912.91i	−0.298814	+	0.728431i
$571$	9019.88			0.661069			0.330534	−	0.943794i	$-0.392771\pi$
$571$	9019.88			0.661069			0.330534	+	0.943794i	$0.392771\pi$
$572$			30759.7i			2.24847i
$573$			7984.80i			0.582146i
$574$	11229.9			0.816597
$575$	−2687.08	+	2724.07i	−0.194885	+	0.197568i
$576$	3047.80			0.220472
$577$		−	1328.73i		−	0.0958680i	−0.998851	−	0.0479340i	$-0.984736\pi$
$577$		−	1328.73i		−	0.0958680i	0.998851	−	0.0479340i	$-0.0152637\pi$
$578$			40926.1i			2.94516i
$579$	5856.09			0.420330
$580$	−17242.1	+	42031.9i	−1.23438	+	3.00910i
$581$	2085.29			0.148902
$582$		−	7656.99i		−	0.545348i
$583$			10627.8i			0.754989i
$584$	64203.8			4.54926
$585$	4213.67	+	1728.51i	0.297801	+	0.122163i
$586$	−18570.2			−1.30909
$587$		−	13927.3i		−	0.979283i	−0.871924	−	0.489642i	$-0.837128\pi$
$587$		−	13927.3i		−	0.979283i	0.871924	−	0.489642i	$-0.162872\pi$
$588$		−	2778.42i		−	0.194864i
$589$	−10113.5			−0.707506
$590$	−22328.4	−	9159.46i	−1.55804	−	0.639134i
$591$	10763.4			0.749150
$592$			58309.9i			4.04818i
$593$		−	5684.69i		−	0.393663i	−0.980437	−	0.196831i	$-0.936935\pi$
$593$		−	5684.69i		−	0.393663i	0.980437	−	0.196831i	$-0.0630652\pi$
$594$	−5035.14			−0.347802
$595$	3360.94	−	8193.10i	0.231571	−	0.564512i
$596$	−19158.1			−1.31669
$597$		−	2303.07i		−	0.157887i
$598$		−	7186.10i		−	0.491407i
$599$	−27961.5			−1.90730			−0.953651	−	0.300914i	$-0.902708\pi$
$599$	−27961.5			−1.90730			−0.953651	+	0.300914i	$0.902708\pi$
$600$	−15094.1	−	14889.2i	−1.02702	−	1.01308i
$601$	−12396.7			−0.841386			−0.420693	−	0.907203i	$-0.638213\pi$
$601$	−12396.7			−0.841386			−0.420693	+	0.907203i	$0.638213\pi$
$602$			1087.44i			0.0736224i
$603$			805.727i			0.0544142i
$604$	−31445.3			−2.11837
$605$	162.100	−	395.158i	0.0108931	−	0.0265545i
$606$	4242.17			0.284367
$607$		−	3124.52i		−	0.208930i	−0.994529	−	0.104465i	$-0.966687\pi$
$607$		−	3124.52i		−	0.208930i	0.994529	−	0.104465i	$-0.0333130\pi$
$608$			17514.6i			1.16828i
$609$	4514.76			0.300406
$610$	−8111.57	−	3327.49i	−0.538406	−	0.220863i
$611$	21897.4			1.44988
$612$		−	19248.3i		−	1.27135i
$613$		−	9531.29i		−	0.628002i	−0.949423	−	0.314001i	$-0.898330\pi$
$613$		−	9531.29i		−	0.628002i	0.949423	−	0.314001i	$-0.101670\pi$
$614$	−7432.01			−0.488488
$615$	−9598.38	−	3937.40i	−0.629340	−	0.258165i
$616$	−14230.0			−0.930754
$617$			5410.37i			0.353020i	0.984299	+	0.176510i	$0.0564808\pi$
$617$			5410.37i			0.353020i	−0.984299	+	0.176510i	$0.943519\pi$
$618$			9774.35i			0.636217i
$619$	10244.9			0.665228			0.332614	−	0.943063i	$-0.392069\pi$
$619$	10244.9			0.665228			0.332614	+	0.943063i	$0.392069\pi$
$620$	13169.3	−	32103.4i	0.853053	−	2.07952i
$621$	826.492			0.0534074
$622$		−	28465.8i		−	1.83501i
$623$		−	631.468i		−	0.0406087i
$624$	19286.4			1.23730
$625$	213.582	+	15623.5i	0.0136693	+	0.999907i
$626$	−12767.8			−0.815180
$627$		−	6643.57i		−	0.423155i
$628$			45352.3i			2.88177i
$629$	46453.2			2.94469
$630$	−1386.49	+	3379.91i	−0.0876813	+	0.213744i
$631$	−10342.8			−0.652522			−0.326261	−	0.945280i	$-0.605789\pi$
$631$	−10342.8			−0.652522			−0.326261	+	0.945280i	$0.605789\pi$
$632$			18281.5i			1.15063i
$633$			3599.53i			0.226016i
$634$	−16146.5			−1.01145
$635$	−29591.5	−	12138.9i	−1.84930	−	0.758610i
$636$	16760.2			1.04495
$637$		−	2217.85i		−	0.137950i
$638$		−	40092.6i		−	2.48790i
$639$	−6428.38			−0.397970
$640$	5363.92	+	2200.36i	0.331293	+	0.135901i
$641$	−981.309			−0.0604671			−0.0302335	−	0.999543i	$-0.509625\pi$
$641$	−981.309			−0.0604671			−0.0302335	+	0.999543i	$0.509625\pi$
$642$			14135.6i			0.868984i
$643$		−	16289.5i		−	0.999062i	−0.866296	−	0.499531i	$-0.833506\pi$
$643$		−	16289.5i		−	0.999062i	0.866296	−	0.499531i	$-0.166494\pi$
$644$	4049.99			0.247813
$645$	381.276	−	929.453i	0.0232755	−	0.0567398i
$646$	36146.5			2.20149
$647$			11349.5i			0.689634i	0.938670	+	0.344817i	$0.112059\pi$
$647$			11349.5i			0.689634i	−0.938670	+	0.344817i	$0.887941\pi$
$648$			4579.60i			0.277629i
$649$	14964.4			0.905088
$650$	−20891.1	−	20607.5i	−1.26064	−	1.24353i
$651$	−3448.32			−0.207604
$652$		−	26760.0i		−	1.60737i
$653$			20510.7i			1.22917i	0.788852	+	0.614583i	$0.210676\pi$
$653$			20510.7i			1.22917i	−0.788852	+	0.614583i	$0.789324\pi$
$654$	15315.6			0.915730
$655$	2227.56	−	5430.22i	0.132883	−	0.323934i
$656$	−43932.8			−2.61477
$657$			10220.2i			0.606893i
$658$			17564.6i			1.04064i
$659$	−15480.4			−0.915070			−0.457535	−	0.889191i	$-0.651268\pi$
$659$	−15480.4			−0.915070			−0.457535	+	0.889191i	$0.651268\pi$
$660$	21088.7	+	8650.91i	1.24375	+	0.510206i
$661$	3720.51			0.218928			0.109464	−	0.993991i	$-0.465087\pi$
$661$	3720.51			0.218928			0.109464	+	0.993991i	$0.465087\pi$
$662$			33008.6i			1.93794i
$663$		−	15364.7i		−	0.900025i
$664$	−16842.6			−0.984369
$665$	−4459.59	−	1829.39i	−0.260053	−	0.106678i
$666$	−19163.4			−1.11497
$667$			6580.98i			0.382034i
$668$		−	66981.9i		−	3.87965i
$669$	−8753.53			−0.505876
$670$	1970.26	−	4802.98i	0.113608	−	0.276948i
$671$	5436.32			0.312767
$672$			5971.81i			0.342809i
$673$			17977.2i			1.02967i	0.857288	+	0.514837i	$0.172147\pi$
$673$			17977.2i			1.02967i	−0.857288	+	0.514837i	$0.827853\pi$
$674$	26779.7			1.53044
$675$	2370.12	−	2402.74i	0.135149	−	0.137010i
$676$	−2803.65			−0.159516
$677$			13079.2i			0.742505i	0.928532	+	0.371253i	$0.121072\pi$
$677$			13079.2i			0.742505i	−0.928532	+	0.371253i	$0.878928\pi$
$678$			34679.6i			1.96440i
$679$	3444.70			0.194692
$680$	−27145.9	+	66174.8i	−1.53088	+	3.73190i
$681$	1838.04			0.103427
$682$			30622.2i			1.71933i
$683$		−	22608.2i		−	1.26659i	−0.773912	−	0.633293i	$-0.781703\pi$
$683$		−	22608.2i		−	1.26659i	0.773912	−	0.633293i	$-0.218297\pi$
$684$	−10477.0			−0.585671
$685$	−22229.2	−	9118.77i	−1.23991	−	0.508628i
$686$	1779.00			0.0990127
$687$			7924.53i			0.440087i
$688$		−	4254.21i		−	0.235742i
$689$	13378.7			0.739749
$690$	−4926.75	−	2021.03i	−0.271824	−	0.111506i
$691$	26262.2			1.44582			0.722910	−	0.690942i	$-0.242804\pi$
$691$	26262.2			1.44582			0.722910	+	0.690942i	$0.242804\pi$
$692$			1808.15i			0.0993286i
$693$		−	2265.20i		−	0.124167i
$694$	−1581.91			−0.0865253
$695$	−6397.83	+	15596.3i	−0.349185	+	0.851223i
$696$	−36465.3			−1.98594
$697$			34999.6i			1.90201i
$698$		−	42703.9i		−	2.31571i
$699$	6968.61			0.377077
$700$	11614.1	−	11773.9i	0.627102	−	0.635733i
$701$	−15831.3			−0.852982			−0.426491	−	0.904492i	$-0.640250\pi$
$701$	−15831.3			−0.852982			−0.426491	+	0.904492i	$0.640250\pi$
$702$			6338.44i			0.340782i
$703$		−	25285.0i		−	1.35653i
$704$	12176.1			0.651853
$705$	6158.46	−	15012.8i	0.328995	−	0.802004i
$706$	−5520.44			−0.294284
$707$			1908.46i			0.101520i
$708$		−	23599.1i		−	1.25269i
$709$	874.284			0.0463109			0.0231554	−	0.999732i	$-0.492629\pi$
$709$	874.284			0.0463109			0.0231554	+	0.999732i	$0.492629\pi$
$710$	38319.9	+	15719.4i	2.02552	+	0.830900i
$711$	−2910.12			−0.153499
$712$			5100.30i			0.268458i
$713$		−	5026.47i		−	0.264015i
$714$	12324.5			0.645986
$715$	16833.8	+	6905.50i	0.880489	+	0.361190i
$716$	40941.6			2.13695
$717$			16117.6i			0.839502i
$718$		−	20308.6i		−	1.05559i
$719$	−103.934			−0.00539091			−0.00269546	−	0.999996i	$-0.500858\pi$
$719$	−103.934			−0.00539091			−0.00269546	+	0.999996i	$0.500858\pi$
$720$	5424.15	−	13222.7i	0.280758	−	0.684417i
$721$	−4397.26			−0.227132
$722$			15900.0i			0.819580i
$723$			4236.99i			0.217946i
$724$	35141.2			1.80388
$725$	19131.9	+	18872.2i	0.980058	+	0.966752i
$726$	594.420			0.0303870
$727$		−	20972.0i		−	1.06989i	−0.844887	−	0.534945i	$-0.820332\pi$
$727$		−	20972.0i		−	1.06989i	0.844887	−	0.534945i	$-0.179668\pi$
$728$			17913.3i			0.911967i
$729$	−729.000			−0.0370370
$730$	24991.7	−	60923.2i	1.26710	−	3.08886i
$731$	−3389.16			−0.171481
$732$		−	8573.18i		−	0.432888i
$733$			32298.2i			1.62750i	0.581213	+	0.813751i	$0.302578\pi$
$733$			32298.2i			1.62750i	−0.581213	+	0.813751i	$0.697422\pi$
$734$	−38540.1			−1.93807
$735$	−1520.55	−	623.751i	−0.0763077	−	0.0313026i
$736$	−8704.85			−0.435958
$737$			3218.93i			0.160883i
$738$		−	14438.4i		−	0.720171i
$739$	−19402.4			−0.965804			−0.482902	−	0.875674i	$-0.660417\pi$
$739$	−19402.4			−0.965804			−0.482902	+	0.875674i	$0.660417\pi$
$740$	80262.2	+	32924.8i	3.98716	+	1.63559i
$741$	−8363.18			−0.414614
$742$			10731.5i			0.530949i
$743$		−	28784.0i		−	1.42124i	−0.703575	−	0.710621i	$-0.748414\pi$
$743$		−	28784.0i		−	1.42124i	0.703575	−	0.710621i	$-0.251586\pi$
$744$	27851.7			1.37244
$745$	−4300.97	+	10484.7i	−0.211510	+	0.515608i
$746$	−16989.8			−0.833834
$747$		−	2681.08i		−	0.131320i
$748$		−	76897.9i		−	3.75891i
$749$	−6359.28			−0.310231
$750$	−20003.8	+	8527.17i	−0.973916	+	0.415157i
$751$	4382.70			0.212952			0.106476	−	0.994315i	$-0.466043\pi$
$751$	4382.70			0.212952			0.106476	+	0.994315i	$0.466043\pi$
$752$		−	68715.0i		−	3.33215i
$753$		−	17028.2i		−	0.824092i
$754$	−50470.1			−2.43768
$755$	−7059.43	+	17209.1i	−0.340290	+	0.829540i
$756$	−3572.26			−0.171854
$757$		−	13669.8i		−	0.656326i	−0.944621	−	0.328163i	$-0.893570\pi$
$757$		−	13669.8i		−	0.656326i	0.944621	−	0.328163i	$-0.106430\pi$
$758$			29798.0i			1.42785i
$759$	3301.88			0.157906
$760$	36019.6	+	14775.8i	1.71917	+	0.705230i
$761$	−25216.4			−1.20117			−0.600586	−	0.799560i	$-0.705066\pi$
$761$	−25216.4			−1.20117			−0.600586	+	0.799560i	$0.705066\pi$
$762$		−	44513.2i		−	2.11620i
$763$			6890.14i			0.326920i
$764$	50306.5			2.38223
$765$	−10534.0	−	4321.21i	−0.497853	−	0.204227i
$766$	528.225			0.0249158
$767$		−	18837.7i		−	0.886819i
$768$			16196.2i			0.760975i
$769$	−15930.6			−0.747038			−0.373519	−	0.927622i	$-0.621849\pi$
$769$	−15930.6			−0.747038			−0.373519	+	0.927622i	$0.621849\pi$
$770$	−5539.11	+	13502.9i	−0.259241	+	0.631964i
$771$	−11818.8			−0.552066
$772$		−	36895.0i		−	1.72005i
$773$			28154.5i			1.31002i	0.755618	+	0.655012i	$0.227336\pi$
$773$			28154.5i			1.31002i	−0.755618	+	0.655012i	$0.772664\pi$
$774$	1398.14			0.0649289
$775$	−14612.7	−	14414.3i	−0.677297	−	0.668101i
$776$	−27822.5			−1.28708
$777$		−	8621.19i		−	0.398048i
$778$			15807.3i			0.728430i
$779$	19050.6			0.876200
$780$	10890.1	−	26547.3i	0.499908	−	1.21865i
$781$	−25681.8			−1.17665
$782$			17964.9i			0.821515i
$783$		−	5804.70i		−	0.264933i
$784$	−6959.71			−0.317042
$785$	24819.9	+	10181.5i	1.12848	+	0.462922i
$786$	8168.45			0.370686
$787$			16392.1i			0.742461i	0.928541	+	0.371231i	$0.121064\pi$
$787$			16392.1i			0.742461i	−0.928541	+	0.371231i	$0.878936\pi$
$788$		−	67812.5i		−	3.06563i
$789$	16193.0			0.730656
$790$	17347.4	+	7116.16i	0.781255	+	0.320483i
$791$	−15601.5			−0.701298
$792$			18295.8i			0.820848i
$793$		−	6843.45i		−	0.306454i
$794$	−50985.5			−2.27885
$795$	3762.65	−	9172.37i	0.167858	−	0.409195i
$796$	−14510.0			−0.646097
$797$		−	2966.12i		−	0.131826i	−0.997825	−	0.0659129i	$-0.979004\pi$
$797$		−	2966.12i		−	0.131826i	0.997825	−	0.0659129i	$-0.0209960\pi$
$798$		−	6708.37i		−	0.297586i
$799$	−54742.6			−2.42385
$800$	−24962.8	+	25306.4i	−1.10321	+	1.11839i
$801$	−811.887			−0.0358135
$802$		−	19154.2i		−	0.843338i
$803$			40830.4i			1.79436i
$804$	5076.31			0.222671
$805$	909.216	−	2216.43i	0.0398082	−	0.0970423i
$806$	38548.4			1.68463
$807$			14920.8i			0.650851i
$808$		−	15414.4i		−	0.671134i
$809$	14712.3			0.639378			0.319689	−	0.947523i	$-0.396422\pi$
$809$	14712.3			0.639378			0.319689	+	0.947523i	$0.396422\pi$
$810$	4345.60	+	1782.63i	0.188505	+	0.0773276i
$811$	5794.69			0.250899			0.125450	−	0.992100i	$-0.459963\pi$
$811$	5794.69			0.250899			0.125450	+	0.992100i	$0.459963\pi$
$812$		−	28444.3i		−	1.22931i
$813$		−	12442.4i		−	0.536747i
$814$	−76559.0			−3.29655
$815$	−14644.9	−	6007.58i	−0.629435	−	0.258204i
$816$	−48215.2			−2.06847
$817$			1844.75i			0.0789961i
$818$			45720.3i			1.95424i
$819$	−2851.52			−0.121661
$820$	−24806.7	+	60472.5i	−1.05645	+	2.57535i
$821$	34345.7			1.46002			0.730009	−	0.683438i	$-0.239516\pi$
$821$	34345.7			1.46002			0.730009	+	0.683438i	$0.239516\pi$
$822$		−	33438.5i		−	1.41886i
$823$		−	17454.4i		−	0.739274i	−0.929176	−	0.369637i	$-0.879482\pi$
$823$		−	17454.4i		−	0.739274i	0.929176	−	0.369637i	$-0.120518\pi$
$824$	35516.2			1.50153
$825$	9468.75	−	9599.08i	0.399588	−	0.405087i
$826$	15110.3			0.636508
$827$			1378.54i			0.0579645i	0.999580	+	0.0289822i	$0.00922663\pi$
$827$			1378.54i			0.0579645i	−0.999580	+	0.0289822i	$0.990773\pi$
$828$		−	5207.13i		−	0.218551i
$829$	−36714.7			−1.53818			−0.769092	−	0.639138i	$-0.779291\pi$
$829$	−36714.7			−1.53818			−0.769092	+	0.639138i	$0.779291\pi$
$830$	−6556.09	+	15982.1i	−0.274175	+	0.668368i
$831$	−7850.38			−0.327709
$832$		−	15327.8i		−	0.638696i
$833$			5544.52i			0.230620i
$834$	−23460.8			−0.974078
$835$	−36657.2	−	15037.3i	−1.51925	−	0.623220i
$836$	−41856.3			−1.73162
$837$			4433.55i			0.183090i
$838$			19433.4i			0.801091i
$839$	−3191.34			−0.131320			−0.0656598	−	0.997842i	$-0.520915\pi$
$839$	−3191.34			−0.131320			−0.0656598	+	0.997842i	$0.520915\pi$
$840$	12281.3	+	5037.97i	0.504458	+	0.206936i
$841$	21831.2			0.895123
$842$			54742.2i			2.24055i
$843$		−	8600.68i		−	0.351392i
$844$	22678.0			0.924893
$845$	−629.415	+	1534.35i	−0.0256243	+	0.0624655i
$846$	22583.0			0.917755
$847$			267.416i			0.0108483i
$848$		−	41982.9i		−	1.70012i
$849$	−9046.20			−0.365683
$850$	52226.9	+	51517.8i	2.10749	+	2.07888i
$851$	12566.7			0.506207
$852$			40500.6i			1.62855i
$853$		−	42221.5i		−	1.69477i	−0.530980	−	0.847384i	$-0.678176\pi$
$853$		−	42221.5i		−	1.69477i	0.530980	−	0.847384i	$-0.321824\pi$
$854$	5489.35			0.219955
$855$	−2352.08	+	5733.76i	−0.0940811	+	0.229345i
$856$	51363.3			2.05089
$857$			5849.17i			0.233143i	0.993182	+	0.116572i	$0.0371904\pi$
$857$			5849.17i			0.233143i	−0.993182	+	0.116572i	$0.962810\pi$
$858$			25322.4i			1.00757i
$859$	45756.1			1.81744			0.908719	−	0.417409i	$-0.137062\pi$
$859$	45756.1			1.81744			0.908719	+	0.417409i	$0.137062\pi$
$860$	−5855.81	−	2402.14i	−0.232188	−	0.0952470i
$861$	6495.52			0.257104
$862$			72767.5i			2.87526i
$863$		−	33012.0i		−	1.30213i	−0.759020	−	0.651067i	$-0.774322\pi$
$863$		−	33012.0i		−	1.30213i	0.759020	−	0.651067i	$-0.225678\pi$
$864$	7678.04			0.302329
$865$	989.543	+	405.926i	0.0388965	+	0.0159559i
$866$	−49994.1			−1.96174
$867$			23672.2i			0.927278i
$868$			21725.4i			0.849548i
$869$	−11626.1			−0.453842
$870$	−14194.3	+	34602.1i	−0.553140	+	1.34841i
$871$	4052.11			0.157635
$872$		−	55650.9i		−	2.16121i
$873$		−	4428.91i		−	0.171702i
$874$	9778.50			0.378447
$875$	−3836.18	−	8999.27i	−0.148213	−	0.347692i
$876$	64390.3			2.48350
$877$			20709.9i			0.797404i	0.917080	+	0.398702i	$0.130539\pi$
$877$			20709.9i			0.797404i	−0.917080	+	0.398702i	$0.869461\pi$
$878$			20417.2i			0.784793i
$879$	−10741.2			−0.412164
$880$	21669.8	−	52825.3i	0.830100	−	2.02357i
$881$	−13604.5			−0.520258			−0.260129	−	0.965574i	$-0.583765\pi$
$881$	−13604.5			−0.520258			−0.260129	+	0.965574i	$0.583765\pi$
$882$		−	2287.29i		−	0.0873210i
$883$		−	47582.7i		−	1.81346i	−0.421713	−	0.906729i	$-0.638571\pi$
$883$		−	47582.7i		−	1.81346i	0.421713	−	0.906729i	$-0.361429\pi$
$884$	−96802.1			−3.68304
$885$	−12915.1	−	5297.95i	−0.490548	−	0.201230i
$886$	−56080.2			−2.12647
$887$		−	25132.9i		−	0.951386i	−0.879611	−	0.475693i	$-0.842197\pi$
$887$		−	25132.9i		−	0.951386i	0.879611	−	0.475693i	$-0.157803\pi$
$888$			69632.4i			2.63143i
$889$	20025.5			0.755492
$890$	4839.70	+	1985.32i	0.182278	+	0.0747731i
$891$	−2912.40			−0.109505
$892$			55149.7i			2.07012i
$893$			29796.9i			1.11659i
$894$	−15771.6			−0.590024
$895$	9191.32	−	22406.1i	0.343276	−	0.836819i
$896$	−3629.93			−0.135343
$897$		−	4156.53i		−	0.154719i
$898$			42296.0i			1.57176i
$899$	−35302.4			−1.30968
$900$	−15137.9	−	14932.4i	−0.560664	−	0.553052i
$901$	−33446.2			−1.23668
$902$		−	57682.3i		−	2.12928i
$903$			628.989i			0.0231799i
$904$	126012.			4.63617
$905$	7889.13	−	19231.7i	0.289772	−	0.706390i
$906$	−25886.9			−0.949265
$907$			36233.4i			1.32647i	0.748411	+	0.663235i	$0.230817\pi$
$907$			36233.4i			1.32647i	−0.748411	+	0.663235i	$0.769183\pi$
$908$		−	11580.1i		−	0.423238i
$909$	2453.73			0.0895325
$910$	16998.0	+	6972.85i	0.619208	+	0.254009i
$911$	16912.4			0.615076			0.307538	−	0.951536i	$-0.400495\pi$
$911$	16912.4			0.615076			0.307538	+	0.951536i	$0.400495\pi$
$912$			26244.0i			0.952881i
$913$		−	10711.1i		−	0.388264i
$914$	92256.5			3.33870
$915$	−4691.84	−	1924.67i	−0.169516	−	0.0695382i
$916$	49926.7			1.80090
$917$			3674.80i			0.132337i
$918$		−	15845.8i		−	0.569706i
$919$	49589.9			1.78000			0.890001	−	0.455959i	$-0.150704\pi$
$919$	49589.9			1.78000			0.890001	+	0.455959i	$0.150704\pi$
$920$	−7343.64	+	17901.9i	−0.263166	+	0.641531i
$921$	−4298.77			−0.153800
$922$		−	68422.4i		−	2.44400i
$923$			32329.2i			1.15290i
$924$	−14271.4			−0.508110
$925$	36037.5	−	36533.5i	1.28098	−	1.29861i
$926$	−2814.09			−0.0998668
$927$			5653.62i			0.200312i
$928$			61136.7i			2.16262i
$929$	40649.1			1.43558			0.717789	−	0.696261i	$-0.245154\pi$
$929$	40649.1			1.43558			0.717789	+	0.696261i	$0.245154\pi$
$930$	10841.4	−	26428.6i	0.382263	−	0.931859i
$931$	3017.94			0.106240
$932$		−	43904.2i		−	1.54306i
$933$		−	16465.0i		−	0.577749i
$934$	30925.1			1.08341
$935$	−42083.9	−	17263.5i	−1.47197	−	0.603824i
$936$	23031.4			0.804279
$937$			3678.18i			0.128240i	0.997942	+	0.0641200i	$0.0204240\pi$
$937$			3678.18i			0.128240i	−0.997942	+	0.0641200i	$0.979576\pi$
$938$			3250.32i			0.113142i
$939$	−7385.05			−0.256658
$940$	−94584.5	−	38800.0i	−3.28192	−	1.34629i
$941$	−4835.12			−0.167503			−0.0837516	−	0.996487i	$-0.526690\pi$
$941$	−4835.12			−0.167503			−0.0837516	+	0.996487i	$0.526690\pi$
$942$			37335.5i			1.29136i
$943$			9468.24i			0.326965i
$944$	−59113.6			−2.03812
$945$	−801.966	+	1954.99i	−0.0276063	+	0.0672971i
$946$	5585.63			0.191971
$947$			31497.4i			1.08081i	0.841405	+	0.540405i	$0.181729\pi$
$947$			31497.4i			1.08081i	−0.841405	+	0.540405i	$0.818271\pi$
$948$			18334.6i			0.628143i
$949$	51398.9			1.75814
$950$	28041.7	−	28427.6i	0.957676	−	0.970857i
$951$	−9339.37			−0.318454
$952$		−	44782.5i		−	1.52459i
$953$			26365.5i			0.896183i	0.893988	+	0.448092i	$0.147896\pi$
$953$			26365.5i			0.896183i	−0.893988	+	0.448092i	$0.852104\pi$
$954$	13797.6			0.468253
$955$	11293.7	−	27531.2i	0.382677	−	0.932868i
$956$	101545.			3.43537
$957$		−	23190.1i		−	0.783311i
$958$		−	6834.20i		−	0.230483i
$959$	15043.2			0.506538
$960$	−10508.7	−	4310.81i	−0.353297	−	0.144928i
$961$	−2827.48			−0.0949104
$962$			96375.4i			3.23001i
$963$			8176.22i			0.273598i
$964$	26694.2			0.891870
$965$	−20191.5	−	8282.87i	−0.673563	−	0.276306i
$966$	3334.09			0.111048
$967$			2307.07i			0.0767221i	0.999264	+	0.0383611i	$0.0122137\pi$
$967$			2307.07i			0.0767221i	−0.999264	+	0.0383611i	$0.987786\pi$
$968$		−	2159.89i		−	0.0717164i
$969$	20907.6			0.693136
$970$	−10830.1	+	26400.9i	−0.358487	+	0.873899i
$971$	−48345.5			−1.59782			−0.798909	−	0.601452i	$-0.794589\pi$
$971$	−48345.5			−1.59782			−0.798909	+	0.601452i	$0.794589\pi$
$972$			4592.90i			0.151561i
$973$		−	10554.5i		−	0.347750i
$974$	−30996.2			−1.01969
$975$	−12083.7	−	11919.6i	−0.396911	−	0.391522i
$976$	−21475.1			−0.704304
$977$		−	25534.5i		−	0.836153i	−0.908412	−	0.418076i	$-0.862704\pi$
$977$		−	25534.5i		−	0.836153i	0.908412	−	0.418076i	$-0.137296\pi$
$978$		−	22029.7i		−	0.720280i
$979$	−3243.53			−0.105887
$980$	−3929.81	+	9579.86i	−0.128095	+	0.312263i
$981$	8858.75			0.288316
$982$		−	53624.0i		−	1.74258i
$983$		−	41611.3i		−	1.35015i	−0.737750	−	0.675074i	$-0.764112\pi$
$983$		−	41611.3i		−	1.35015i	0.737750	−	0.675074i	$-0.235888\pi$
$984$	−52463.6			−1.69967
$985$	−37111.7	−	15223.8i	−1.20048	−	0.492457i
$986$	126173.			4.07522
$987$			10159.6i			0.327643i
$988$			52690.4i			1.69666i
$989$	−916.851			−0.0294784
$990$	17360.9	+	7121.72i	0.557340	+	0.228629i
$991$	9963.65			0.319380			0.159690	−	0.987167i	$-0.448950\pi$
$991$	9963.65			0.319380			0.159690	+	0.987167i	$0.448950\pi$
$992$		−	46695.5i		−	1.49454i
$993$			19092.6i			0.610157i
$994$	−25932.3			−0.827486
$995$	−3257.47	+	7940.88i	−0.103788	+	0.253008i
$996$	−16891.6			−0.537379
$997$		−	15960.8i		−	0.507005i	−0.967335	−	0.253502i	$-0.918417\pi$
$997$		−	15960.8i		−	0.507005i	0.967335	−	0.253502i	$-0.0815825\pi$
$998$		−	21585.3i		−	0.684639i
$999$	−11084.4			−0.351045

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.d.b.64.1	✓	10
3.2	odd	2		315.4.d.b.64.10		10
5.2	odd	4		525.4.a.x.1.5		5
5.3	odd	4		525.4.a.w.1.1		5
5.4	even	2	inner	105.4.d.b.64.10	yes	10
15.2	even	4		1575.4.a.bo.1.1		5
15.8	even	4		1575.4.a.bp.1.5		5
15.14	odd	2		315.4.d.b.64.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.d.b.64.1	✓	10	1.1	even	1	trivial
105.4.d.b.64.10	yes	10	5.4	even	2	inner
315.4.d.b.64.1		10	15.14	odd	2
315.4.d.b.64.10		10	3.2	odd	2
525.4.a.w.1.1		5	5.3	odd	4
525.4.a.x.1.5		5	5.2	odd	4
1575.4.a.bo.1.1		5	15.2	even	4
1575.4.a.bp.1.5		5	15.8	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.18660i q^{2} -3.00000i q^{3} -18.9008 q^{4} +(-4.24321 + 10.3438i) q^{5} -15.5598 q^{6} -7.00000i q^{7} +56.5383i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-5.18660i q^{2} -3.00000i q^{3} -18.9008 q^{4} +(-4.24321 + 10.3438i) q^{5} -15.5598 q^{6} -7.00000i q^{7} +56.5383i q^{8} -9.00000 q^{9} +(53.6494 + 22.0078i) q^{10} -35.9555 q^{11} +56.7025i q^{12} +45.2622i q^{13} -36.3062 q^{14} +(31.0315 + 12.7296i) q^{15} +142.035 q^{16} -113.154i q^{17} +46.6794i q^{18} -61.5906 q^{19} +(80.2001 - 195.507i) q^{20} -21.0000 q^{21} +186.487i q^{22} -30.6108i q^{23} +169.615 q^{24} +(-88.9904 - 87.7822i) q^{25} +234.757 q^{26} +27.0000i q^{27} +132.306i q^{28} -214.989 q^{29} +(66.0235 - 160.948i) q^{30} +164.206 q^{31} -284.372i q^{32} +107.866i q^{33} -586.882 q^{34} +(72.4069 + 29.7024i) q^{35} +170.107 q^{36} +410.533i q^{37} +319.446i q^{38} +135.787 q^{39} +(-584.823 - 239.904i) q^{40} -309.310 q^{41} +108.919i q^{42} -29.9519i q^{43} +679.589 q^{44} +(38.1889 - 93.0946i) q^{45} -158.766 q^{46} -483.790i q^{47} -426.104i q^{48} -49.0000 q^{49} +(-455.291 + 461.558i) q^{50} -339.461 q^{51} -855.493i q^{52} -295.582i q^{53} +140.038 q^{54} +(152.567 - 371.918i) q^{55} +395.768 q^{56} +184.772i q^{57} +1115.06i q^{58} -416.191 q^{59} +(-586.522 - 240.600i) q^{60} -151.196 q^{61} -851.670i q^{62} +63.0000i q^{63} -338.644 q^{64} +(-468.185 - 192.057i) q^{65} +559.460 q^{66} -89.5253i q^{67} +2138.70i q^{68} -91.8324 q^{69} +(154.055 - 375.546i) q^{70} +714.265 q^{71} -508.844i q^{72} -1135.58i q^{73} +2129.27 q^{74} +(-263.347 + 266.971i) q^{75} +1164.11 q^{76} +251.688i q^{77} -704.271i q^{78} +323.347 q^{79} +(-602.683 + 1469.19i) q^{80} +81.0000 q^{81} +1604.27i q^{82} +297.898i q^{83} +396.917 q^{84} +(1170.44 + 480.134i) q^{85} -155.348 q^{86} +644.966i q^{87} -2032.86i q^{88} +90.2097 q^{89} +(-482.845 - 198.070i) q^{90} +316.835 q^{91} +578.570i q^{92} -492.617i q^{93} -2509.23 q^{94} +(261.342 - 637.084i) q^{95} -853.115 q^{96} +492.101i q^{97} +254.143i q^{98} +323.599 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 54 q^{4} - 14 q^{5} - 6 q^{6} - 90 q^{9}+O(q^{10}) \) 10 * q - 54 * q^4 - 14 * q^5 - 6 * q^6 - 90 * q^9	\( 10 q - 54 q^{4} - 14 q^{5} - 6 q^{6} - 90 q^{9} + 92 q^{10} + 132 q^{11} - 14 q^{14} + 310 q^{16} - 348 q^{19} + 366 q^{20} - 210 q^{21} + 198 q^{24} - 374 q^{25} + 892 q^{26} - 740 q^{29} - 378 q^{30} + 684 q^{31} - 224 q^{34} + 486 q^{36} - 12 q^{39} - 2156 q^{40} + 1604 q^{41} - 580 q^{44} + 126 q^{45} + 1280 q^{46} - 490 q^{49} - 2504 q^{50} - 648 q^{51} + 54 q^{54} - 452 q^{55} + 462 q^{56} - 1408 q^{59} - 852 q^{60} + 1300 q^{61} - 150 q^{64} - 3296 q^{65} + 3036 q^{66} - 696 q^{69} - 882 q^{70} + 2940 q^{71} + 2624 q^{74} - 408 q^{75} + 8740 q^{76} + 1640 q^{79} - 4126 q^{80} + 810 q^{81} + 1134 q^{84} - 1704 q^{85} + 1664 q^{86} - 572 q^{89} - 828 q^{90} - 28 q^{91} - 5080 q^{94} + 1268 q^{95} + 330 q^{96} - 1188 q^{99}+O(q^{100}) \) 10 * q - 54 * q^4 - 14 * q^5 - 6 * q^6 - 90 * q^9 + 92 * q^10 + 132 * q^11 - 14 * q^14 + 310 * q^16 - 348 * q^19 + 366 * q^20 - 210 * q^21 + 198 * q^24 - 374 * q^25 + 892 * q^26 - 740 * q^29 - 378 * q^30 + 684 * q^31 - 224 * q^34 + 486 * q^36 - 12 * q^39 - 2156 * q^40 + 1604 * q^41 - 580 * q^44 + 126 * q^45 + 1280 * q^46 - 490 * q^49 - 2504 * q^50 - 648 * q^51 + 54 * q^54 - 452 * q^55 + 462 * q^56 - 1408 * q^59 - 852 * q^60 + 1300 * q^61 - 150 * q^64 - 3296 * q^65 + 3036 * q^66 - 696 * q^69 - 882 * q^70 + 2940 * q^71 + 2624 * q^74 - 408 * q^75 + 8740 * q^76 + 1640 * q^79 - 4126 * q^80 + 810 * q^81 + 1134 * q^84 - 1704 * q^85 + 1664 * q^86 - 572 * q^89 - 828 * q^90 - 28 * q^91 - 5080 * q^94 + 1268 * q^95 + 330 * q^96 - 1188 * q^99

Introduction

L-functions

Modular forms

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