# Properties

 Label 192.5.e.c.65.1 Level $192$ Weight $5$ Character 192.65 Analytic conductor $19.847$ Analytic rank $0$ Dimension $2$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,5,Mod(65,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("192.65");

S:= CuspForms(chi, 5);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$192 = 2^{6} \cdot 3$$ Weight: $$k$$ $$=$$ $$5$$ Character orbit: $$[\chi]$$ $$=$$ 192.e (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: $$19.8470329121$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{-2})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} + 2$$ x^2 + 2 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2\cdot 3$$ Twist minimal: no (minimal twist has level 6) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 65.1 Root $$-1.41421i$$ of defining polynomial Character $$\chi$$ $$=$$ 192.65 Dual form 192.5.e.c.65.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-3.00000 - 8.48528i) q^{3} -16.9706i q^{5} -26.0000 q^{7} +(-63.0000 + 50.9117i) q^{9} +O(q^{10})$$ $$q+(-3.00000 - 8.48528i) q^{3} -16.9706i q^{5} -26.0000 q^{7} +(-63.0000 + 50.9117i) q^{9} -118.794i q^{11} -50.0000 q^{13} +(-144.000 + 50.9117i) q^{15} +203.647i q^{17} -358.000 q^{19} +(78.0000 + 220.617i) q^{21} -373.352i q^{23} +337.000 q^{25} +(621.000 + 381.838i) q^{27} +1442.50i q^{29} +742.000 q^{31} +(-1008.00 + 356.382i) q^{33} +441.235i q^{35} -1874.00 q^{37} +(150.000 + 424.264i) q^{39} +2409.82i q^{41} -262.000 q^{43} +(864.000 + 1069.15i) q^{45} +1697.06i q^{47} -1725.00 q^{49} +(1728.00 - 610.940i) q^{51} +458.205i q^{53} -2016.00 q^{55} +(1074.00 + 3037.73i) q^{57} -1815.85i q^{59} +1486.00 q^{61} +(1638.00 - 1323.70i) q^{63} +848.528i q^{65} -4486.00 q^{67} +(-3168.00 + 1120.06i) q^{69} -3563.82i q^{71} +290.000 q^{73} +(-1011.00 - 2859.54i) q^{75} +3088.64i q^{77} -9818.00 q^{79} +(1377.00 - 6414.87i) q^{81} +7110.67i q^{83} +3456.00 q^{85} +(12240.0 - 4327.49i) q^{87} -7840.40i q^{89} +1300.00 q^{91} +(-2226.00 - 6296.08i) q^{93} +6075.46i q^{95} -478.000 q^{97} +(6048.00 + 7484.02i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 6 q^{3} - 52 q^{7} - 126 q^{9}+O(q^{10})$$ 2 * q - 6 * q^3 - 52 * q^7 - 126 * q^9 $$2 q - 6 q^{3} - 52 q^{7} - 126 q^{9} - 100 q^{13} - 288 q^{15} - 716 q^{19} + 156 q^{21} + 674 q^{25} + 1242 q^{27} + 1484 q^{31} - 2016 q^{33} - 3748 q^{37} + 300 q^{39} - 524 q^{43} + 1728 q^{45} - 3450 q^{49} + 3456 q^{51} - 4032 q^{55} + 2148 q^{57} + 2972 q^{61} + 3276 q^{63} - 8972 q^{67} - 6336 q^{69} + 580 q^{73} - 2022 q^{75} - 19636 q^{79} + 2754 q^{81} + 6912 q^{85} + 24480 q^{87} + 2600 q^{91} - 4452 q^{93} - 956 q^{97} + 12096 q^{99}+O(q^{100})$$ 2 * q - 6 * q^3 - 52 * q^7 - 126 * q^9 - 100 * q^13 - 288 * q^15 - 716 * q^19 + 156 * q^21 + 674 * q^25 + 1242 * q^27 + 1484 * q^31 - 2016 * q^33 - 3748 * q^37 + 300 * q^39 - 524 * q^43 + 1728 * q^45 - 3450 * q^49 + 3456 * q^51 - 4032 * q^55 + 2148 * q^57 + 2972 * q^61 + 3276 * q^63 - 8972 * q^67 - 6336 * q^69 + 580 * q^73 - 2022 * q^75 - 19636 * q^79 + 2754 * q^81 + 6912 * q^85 + 24480 * q^87 + 2600 * q^91 - 4452 * q^93 - 956 * q^97 + 12096 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$$.

 $$n$$ $$65$$ $$127$$ $$133$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −3.00000 8.48528i −0.333333 0.942809i
$$4$$ 0 0
$$5$$ 16.9706i 0.678823i −0.940638 0.339411i $$-0.889772\pi$$
0.940638 0.339411i $$-0.110228\pi$$
$$6$$ 0 0
$$7$$ −26.0000 −0.530612 −0.265306 0.964164i $$-0.585473\pi$$
−0.265306 + 0.964164i $$0.585473\pi$$
$$8$$ 0 0
$$9$$ −63.0000 + 50.9117i −0.777778 + 0.628539i
$$10$$ 0 0
$$11$$ 118.794i 0.981768i −0.871225 0.490884i $$-0.836674\pi$$
0.871225 0.490884i $$-0.163326\pi$$
$$12$$ 0 0
$$13$$ −50.0000 −0.295858 −0.147929 0.988998i $$-0.547261\pi$$
−0.147929 + 0.988998i $$0.547261\pi$$
$$14$$ 0 0
$$15$$ −144.000 + 50.9117i −0.640000 + 0.226274i
$$16$$ 0 0
$$17$$ 203.647i 0.704660i 0.935876 + 0.352330i $$0.114611\pi$$
−0.935876 + 0.352330i $$0.885389\pi$$
$$18$$ 0 0
$$19$$ −358.000 −0.991690 −0.495845 0.868411i $$-0.665142\pi$$
−0.495845 + 0.868411i $$0.665142\pi$$
$$20$$ 0 0
$$21$$ 78.0000 + 220.617i 0.176871 + 0.500266i
$$22$$ 0 0
$$23$$ 373.352i 0.705770i −0.935667 0.352885i $$-0.885201\pi$$
0.935667 0.352885i $$-0.114799\pi$$
$$24$$ 0 0
$$25$$ 337.000 0.539200
$$26$$ 0 0
$$27$$ 621.000 + 381.838i 0.851852 + 0.523783i
$$28$$ 0 0
$$29$$ 1442.50i 1.71522i 0.514303 + 0.857609i $$0.328051\pi$$
−0.514303 + 0.857609i $$0.671949\pi$$
$$30$$ 0 0
$$31$$ 742.000 0.772112 0.386056 0.922475i $$-0.373837\pi$$
0.386056 + 0.922475i $$0.373837\pi$$
$$32$$ 0 0
$$33$$ −1008.00 + 356.382i −0.925620 + 0.327256i
$$34$$ 0 0
$$35$$ 441.235i 0.360192i
$$36$$ 0 0
$$37$$ −1874.00 −1.36888 −0.684441 0.729068i $$-0.739954\pi$$
−0.684441 + 0.729068i $$0.739954\pi$$
$$38$$ 0 0
$$39$$ 150.000 + 424.264i 0.0986193 + 0.278938i
$$40$$ 0 0
$$41$$ 2409.82i 1.43356i 0.697298 + 0.716782i $$0.254386\pi$$
−0.697298 + 0.716782i $$0.745614\pi$$
$$42$$ 0 0
$$43$$ −262.000 −0.141698 −0.0708491 0.997487i $$-0.522571\pi$$
−0.0708491 + 0.997487i $$0.522571\pi$$
$$44$$ 0 0
$$45$$ 864.000 + 1069.15i 0.426667 + 0.527973i
$$46$$ 0 0
$$47$$ 1697.06i 0.768246i 0.923282 + 0.384123i $$0.125496\pi$$
−0.923282 + 0.384123i $$0.874504\pi$$
$$48$$ 0 0
$$49$$ −1725.00 −0.718451
$$50$$ 0 0
$$51$$ 1728.00 610.940i 0.664360 0.234887i
$$52$$ 0 0
$$53$$ 458.205i 0.163120i 0.996668 + 0.0815602i $$0.0259903\pi$$
−0.996668 + 0.0815602i $$0.974010\pi$$
$$54$$ 0 0
$$55$$ −2016.00 −0.666446
$$56$$ 0 0
$$57$$ 1074.00 + 3037.73i 0.330563 + 0.934974i
$$58$$ 0 0
$$59$$ 1815.85i 0.521646i −0.965387 0.260823i $$-0.916006\pi$$
0.965387 0.260823i $$-0.0839939\pi$$
$$60$$ 0 0
$$61$$ 1486.00 0.399355 0.199678 0.979862i $$-0.436011\pi$$
0.199678 + 0.979862i $$0.436011\pi$$
$$62$$ 0 0
$$63$$ 1638.00 1323.70i 0.412698 0.333511i
$$64$$ 0 0
$$65$$ 848.528i 0.200835i
$$66$$ 0 0
$$67$$ −4486.00 −0.999332 −0.499666 0.866218i $$-0.666544\pi$$
−0.499666 + 0.866218i $$0.666544\pi$$
$$68$$ 0 0
$$69$$ −3168.00 + 1120.06i −0.665406 + 0.235257i
$$70$$ 0 0
$$71$$ 3563.82i 0.706967i −0.935441 0.353483i $$-0.884997\pi$$
0.935441 0.353483i $$-0.115003\pi$$
$$72$$ 0 0
$$73$$ 290.000 0.0544192 0.0272096 0.999630i $$-0.491338\pi$$
0.0272096 + 0.999630i $$0.491338\pi$$
$$74$$ 0 0
$$75$$ −1011.00 2859.54i −0.179733 0.508363i
$$76$$ 0 0
$$77$$ 3088.64i 0.520938i
$$78$$ 0 0
$$79$$ −9818.00 −1.57315 −0.786573 0.617498i $$-0.788146\pi$$
−0.786573 + 0.617498i $$0.788146\pi$$
$$80$$ 0 0
$$81$$ 1377.00 6414.87i 0.209877 0.977728i
$$82$$ 0 0
$$83$$ 7110.67i 1.03218i 0.856535 + 0.516088i $$0.172612\pi$$
−0.856535 + 0.516088i $$0.827388\pi$$
$$84$$ 0 0
$$85$$ 3456.00 0.478339
$$86$$ 0 0
$$87$$ 12240.0 4327.49i 1.61712 0.571739i
$$88$$ 0 0
$$89$$ 7840.40i 0.989825i −0.868943 0.494912i $$-0.835200\pi$$
0.868943 0.494912i $$-0.164800\pi$$
$$90$$ 0 0
$$91$$ 1300.00 0.156986
$$92$$ 0 0
$$93$$ −2226.00 6296.08i −0.257371 0.727955i
$$94$$ 0 0
$$95$$ 6075.46i 0.673181i
$$96$$ 0 0
$$97$$ −478.000 −0.0508024 −0.0254012 0.999677i $$-0.508086\pi$$
−0.0254012 + 0.999677i $$0.508086\pi$$
$$98$$ 0 0
$$99$$ 6048.00 + 7484.02i 0.617080 + 0.763597i
$$100$$ 0 0
$$101$$ 13729.2i 1.34587i −0.739703 0.672933i $$-0.765034\pi$$
0.739703 0.672933i $$-0.234966\pi$$
$$102$$ 0 0
$$103$$ −2138.00 −0.201527 −0.100764 0.994910i $$-0.532129\pi$$
−0.100764 + 0.994910i $$0.532129\pi$$
$$104$$ 0 0
$$105$$ 3744.00 1323.70i 0.339592 0.120064i
$$106$$ 0 0
$$107$$ 10844.2i 0.947174i −0.880747 0.473587i $$-0.842959\pi$$
0.880747 0.473587i $$-0.157041\pi$$
$$108$$ 0 0
$$109$$ 4750.00 0.399798 0.199899 0.979817i $$-0.435939\pi$$
0.199899 + 0.979817i $$0.435939\pi$$
$$110$$ 0 0
$$111$$ 5622.00 + 15901.4i 0.456294 + 1.29059i
$$112$$ 0 0
$$113$$ 3190.47i 0.249860i −0.992166 0.124930i $$-0.960129\pi$$
0.992166 0.124930i $$-0.0398707\pi$$
$$114$$ 0 0
$$115$$ −6336.00 −0.479093
$$116$$ 0 0
$$117$$ 3150.00 2545.58i 0.230112 0.185958i
$$118$$ 0 0
$$119$$ 5294.82i 0.373901i
$$120$$ 0 0
$$121$$ 529.000 0.0361314
$$122$$ 0 0
$$123$$ 20448.0 7229.46i 1.35158 0.477854i
$$124$$ 0 0
$$125$$ 16325.7i 1.04484i
$$126$$ 0 0
$$127$$ −8282.00 −0.513485 −0.256743 0.966480i $$-0.582649\pi$$
−0.256743 + 0.966480i $$0.582649\pi$$
$$128$$ 0 0
$$129$$ 786.000 + 2223.14i 0.0472327 + 0.133594i
$$130$$ 0 0
$$131$$ 5413.61i 0.315460i 0.987482 + 0.157730i $$0.0504176\pi$$
−0.987482 + 0.157730i $$0.949582\pi$$
$$132$$ 0 0
$$133$$ 9308.00 0.526203
$$134$$ 0 0
$$135$$ 6480.00 10538.7i 0.355556 0.578256i
$$136$$ 0 0
$$137$$ 18090.6i 0.963856i −0.876211 0.481928i $$-0.839937\pi$$
0.876211 0.481928i $$-0.160063\pi$$
$$138$$ 0 0
$$139$$ −23206.0 −1.20108 −0.600538 0.799596i $$-0.705047\pi$$
−0.600538 + 0.799596i $$0.705047\pi$$
$$140$$ 0 0
$$141$$ 14400.0 5091.17i 0.724310 0.256082i
$$142$$ 0 0
$$143$$ 5939.70i 0.290464i
$$144$$ 0 0
$$145$$ 24480.0 1.16433
$$146$$ 0 0
$$147$$ 5175.00 + 14637.1i 0.239484 + 0.677362i
$$148$$ 0 0
$$149$$ 11183.6i 0.503743i 0.967761 + 0.251872i $$0.0810460\pi$$
−0.967761 + 0.251872i $$0.918954\pi$$
$$150$$ 0 0
$$151$$ −14426.0 −0.632692 −0.316346 0.948644i $$-0.602456\pi$$
−0.316346 + 0.948644i $$0.602456\pi$$
$$152$$ 0 0
$$153$$ −10368.0 12829.7i −0.442907 0.548069i
$$154$$ 0 0
$$155$$ 12592.2i 0.524127i
$$156$$ 0 0
$$157$$ −49010.0 −1.98832 −0.994158 0.107935i $$-0.965576\pi$$
−0.994158 + 0.107935i $$0.965576\pi$$
$$158$$ 0 0
$$159$$ 3888.00 1374.62i 0.153791 0.0543735i
$$160$$ 0 0
$$161$$ 9707.16i 0.374490i
$$162$$ 0 0
$$163$$ −42982.0 −1.61775 −0.808875 0.587981i $$-0.799923\pi$$
−0.808875 + 0.587981i $$0.799923\pi$$
$$164$$ 0 0
$$165$$ 6048.00 + 17106.3i 0.222149 + 0.628332i
$$166$$ 0 0
$$167$$ 44157.4i 1.58333i −0.610957 0.791663i $$-0.709215\pi$$
0.610957 0.791663i $$-0.290785\pi$$
$$168$$ 0 0
$$169$$ −26061.0 −0.912468
$$170$$ 0 0
$$171$$ 22554.0 18226.4i 0.771314 0.623316i
$$172$$ 0 0
$$173$$ 22418.1i 0.749043i 0.927218 + 0.374522i $$0.122193\pi$$
−0.927218 + 0.374522i $$0.877807\pi$$
$$174$$ 0 0
$$175$$ −8762.00 −0.286106
$$176$$ 0 0
$$177$$ −15408.0 + 5447.55i −0.491813 + 0.173882i
$$178$$ 0 0
$$179$$ 30597.9i 0.954962i 0.878642 + 0.477481i $$0.158450\pi$$
−0.878642 + 0.477481i $$0.841550\pi$$
$$180$$ 0 0
$$181$$ 13102.0 0.399927 0.199963 0.979803i $$-0.435918\pi$$
0.199963 + 0.979803i $$0.435918\pi$$
$$182$$ 0 0
$$183$$ −4458.00 12609.1i −0.133118 0.376516i
$$184$$ 0 0
$$185$$ 31802.8i 0.929228i
$$186$$ 0 0
$$187$$ 24192.0 0.691813
$$188$$ 0 0
$$189$$ −16146.0 9927.78i −0.452003 0.277926i
$$190$$ 0 0
$$191$$ 70326.0i 1.92774i 0.266367 + 0.963872i $$0.414177\pi$$
−0.266367 + 0.963872i $$0.585823\pi$$
$$192$$ 0 0
$$193$$ 18050.0 0.484577 0.242288 0.970204i $$-0.422102\pi$$
0.242288 + 0.970204i $$0.422102\pi$$
$$194$$ 0 0
$$195$$ 7200.00 2545.58i 0.189349 0.0669450i
$$196$$ 0 0
$$197$$ 26321.3i 0.678228i 0.940745 + 0.339114i $$0.110127\pi$$
−0.940745 + 0.339114i $$0.889873\pi$$
$$198$$ 0 0
$$199$$ 37222.0 0.939926 0.469963 0.882686i $$-0.344267\pi$$
0.469963 + 0.882686i $$0.344267\pi$$
$$200$$ 0 0
$$201$$ 13458.0 + 38065.0i 0.333111 + 0.942179i
$$202$$ 0 0
$$203$$ 37504.9i 0.910115i
$$204$$ 0 0
$$205$$ 40896.0 0.973135
$$206$$ 0 0
$$207$$ 19008.0 + 23521.2i 0.443604 + 0.548932i
$$208$$ 0 0
$$209$$ 42528.2i 0.973609i
$$210$$ 0 0
$$211$$ 15098.0 0.339121 0.169560 0.985520i $$-0.445765\pi$$
0.169560 + 0.985520i $$0.445765\pi$$
$$212$$ 0 0
$$213$$ −30240.0 + 10691.5i −0.666534 + 0.235656i
$$214$$ 0 0
$$215$$ 4446.29i 0.0961879i
$$216$$ 0 0
$$217$$ −19292.0 −0.409692
$$218$$ 0 0
$$219$$ −870.000 2460.73i −0.0181397 0.0513069i
$$220$$ 0 0
$$221$$ 10182.3i 0.208479i
$$222$$ 0 0
$$223$$ −58778.0 −1.18197 −0.590983 0.806684i $$-0.701260\pi$$
−0.590983 + 0.806684i $$0.701260\pi$$
$$224$$ 0 0
$$225$$ −21231.0 + 17157.2i −0.419378 + 0.338908i
$$226$$ 0 0
$$227$$ 68001.0i 1.31967i 0.751412 + 0.659833i $$0.229373\pi$$
−0.751412 + 0.659833i $$0.770627\pi$$
$$228$$ 0 0
$$229$$ −28562.0 −0.544650 −0.272325 0.962205i $$-0.587793\pi$$
−0.272325 + 0.962205i $$0.587793\pi$$
$$230$$ 0 0
$$231$$ 26208.0 9265.93i 0.491145 0.173646i
$$232$$ 0 0
$$233$$ 22503.0i 0.414503i 0.978288 + 0.207252i $$0.0664519\pi$$
−0.978288 + 0.207252i $$0.933548\pi$$
$$234$$ 0 0
$$235$$ 28800.0 0.521503
$$236$$ 0 0
$$237$$ 29454.0 + 83308.5i 0.524382 + 1.48318i
$$238$$ 0 0
$$239$$ 1289.76i 0.0225795i −0.999936 0.0112897i $$-0.996406\pi$$
0.999936 0.0112897i $$-0.00359371\pi$$
$$240$$ 0 0
$$241$$ −61246.0 −1.05449 −0.527246 0.849712i $$-0.676776\pi$$
−0.527246 + 0.849712i $$0.676776\pi$$
$$242$$ 0 0
$$243$$ −58563.0 + 7560.39i −0.991770 + 0.128036i
$$244$$ 0 0
$$245$$ 29274.2i 0.487700i
$$246$$ 0 0
$$247$$ 17900.0 0.293399
$$248$$ 0 0
$$249$$ 60336.0 21332.0i 0.973146 0.344059i
$$250$$ 0 0
$$251$$ 45260.5i 0.718409i −0.933259 0.359205i $$-0.883048\pi$$
0.933259 0.359205i $$-0.116952\pi$$
$$252$$ 0 0
$$253$$ −44352.0 −0.692903
$$254$$ 0 0
$$255$$ −10368.0 29325.1i −0.159446 0.450982i
$$256$$ 0 0
$$257$$ 85260.1i 1.29086i −0.763819 0.645431i $$-0.776678\pi$$
0.763819 0.645431i $$-0.223322\pi$$
$$258$$ 0 0
$$259$$ 48724.0 0.726346
$$260$$ 0 0
$$261$$ −73440.0 90877.4i −1.07808 1.33406i
$$262$$ 0 0
$$263$$ 84751.0i 1.22527i −0.790364 0.612637i $$-0.790109\pi$$
0.790364 0.612637i $$-0.209891\pi$$
$$264$$ 0 0
$$265$$ 7776.00 0.110730
$$266$$ 0 0
$$267$$ −66528.0 + 23521.2i −0.933216 + 0.329942i
$$268$$ 0 0
$$269$$ 42918.6i 0.593117i 0.955015 + 0.296559i $$0.0958390\pi$$
−0.955015 + 0.296559i $$0.904161\pi$$
$$270$$ 0 0
$$271$$ 27430.0 0.373497 0.186749 0.982408i $$-0.440205\pi$$
0.186749 + 0.982408i $$0.440205\pi$$
$$272$$ 0 0
$$273$$ −3900.00 11030.9i −0.0523286 0.148008i
$$274$$ 0 0
$$275$$ 40033.6i 0.529369i
$$276$$ 0 0
$$277$$ 93934.0 1.22423 0.612115 0.790768i $$-0.290319\pi$$
0.612115 + 0.790768i $$0.290319\pi$$
$$278$$ 0 0
$$279$$ −46746.0 + 37776.5i −0.600532 + 0.485303i
$$280$$ 0 0
$$281$$ 24471.6i 0.309919i 0.987921 + 0.154960i $$0.0495248\pi$$
−0.987921 + 0.154960i $$0.950475\pi$$
$$282$$ 0 0
$$283$$ −65830.0 −0.821961 −0.410980 0.911644i $$-0.634813\pi$$
−0.410980 + 0.911644i $$0.634813\pi$$
$$284$$ 0 0
$$285$$ 51552.0 18226.4i 0.634681 0.224394i
$$286$$ 0 0
$$287$$ 62655.3i 0.760666i
$$288$$ 0 0
$$289$$ 42049.0 0.503454
$$290$$ 0 0
$$291$$ 1434.00 + 4055.96i 0.0169341 + 0.0478970i
$$292$$ 0 0
$$293$$ 90028.8i 1.04869i −0.851506 0.524344i $$-0.824311\pi$$
0.851506 0.524344i $$-0.175689\pi$$
$$294$$ 0 0
$$295$$ −30816.0 −0.354105
$$296$$ 0 0
$$297$$ 45360.0 73771.0i 0.514233 0.836321i
$$298$$ 0 0
$$299$$ 18667.6i 0.208808i
$$300$$ 0 0
$$301$$ 6812.00 0.0751868
$$302$$ 0 0
$$303$$ −116496. + 41187.6i −1.26890 + 0.448622i
$$304$$ 0 0
$$305$$ 25218.3i 0.271091i
$$306$$ 0 0
$$307$$ 67322.0 0.714299 0.357150 0.934047i $$-0.383749\pi$$
0.357150 + 0.934047i $$0.383749\pi$$
$$308$$ 0 0
$$309$$ 6414.00 + 18141.5i 0.0671757 + 0.190001i
$$310$$ 0 0
$$311$$ 131997.i 1.36472i 0.731017 + 0.682360i $$0.239046\pi$$
−0.731017 + 0.682360i $$0.760954\pi$$
$$312$$ 0 0
$$313$$ −22078.0 −0.225357 −0.112679 0.993631i $$-0.535943\pi$$
−0.112679 + 0.993631i $$0.535943\pi$$
$$314$$ 0 0
$$315$$ −22464.0 27797.8i −0.226395 0.280149i
$$316$$ 0 0
$$317$$ 117894.i 1.17321i −0.809874 0.586604i $$-0.800465\pi$$
0.809874 0.586604i $$-0.199535\pi$$
$$318$$ 0 0
$$319$$ 171360. 1.68395
$$320$$ 0 0
$$321$$ −92016.0 + 32532.6i −0.893004 + 0.315725i
$$322$$ 0 0
$$323$$ 72905.5i 0.698804i
$$324$$ 0 0
$$325$$ −16850.0 −0.159527
$$326$$ 0 0
$$327$$ −14250.0 40305.1i −0.133266 0.376933i
$$328$$ 0 0
$$329$$ 44123.5i 0.407641i
$$330$$ 0 0
$$331$$ 167642. 1.53012 0.765062 0.643956i $$-0.222708\pi$$
0.765062 + 0.643956i $$0.222708\pi$$
$$332$$ 0 0
$$333$$ 118062. 95408.5i 1.06469 0.860396i
$$334$$ 0 0
$$335$$ 76129.9i 0.678369i
$$336$$ 0 0
$$337$$ 162914. 1.43449 0.717247 0.696819i $$-0.245402\pi$$
0.717247 + 0.696819i $$0.245402\pi$$
$$338$$ 0 0
$$339$$ −27072.0 + 9571.40i −0.235571 + 0.0832868i
$$340$$ 0 0
$$341$$ 88145.1i 0.758035i
$$342$$ 0 0
$$343$$ 107276. 0.911831
$$344$$ 0 0
$$345$$ 19008.0 + 53762.7i 0.159698 + 0.451693i
$$346$$ 0 0
$$347$$ 132184.i 1.09779i 0.835892 + 0.548895i $$0.184951\pi$$
−0.835892 + 0.548895i $$0.815049\pi$$
$$348$$ 0 0
$$349$$ −53234.0 −0.437057 −0.218529 0.975831i $$-0.570126\pi$$
−0.218529 + 0.975831i $$0.570126\pi$$
$$350$$ 0 0
$$351$$ −31050.0 19091.9i −0.252027 0.154965i
$$352$$ 0 0
$$353$$ 144861.i 1.16252i −0.813717 0.581261i $$-0.802560\pi$$
0.813717 0.581261i $$-0.197440\pi$$
$$354$$ 0 0
$$355$$ −60480.0 −0.479905
$$356$$ 0 0
$$357$$ −44928.0 + 15884.4i −0.352517 + 0.124634i
$$358$$ 0 0
$$359$$ 12931.6i 0.100337i −0.998741 0.0501686i $$-0.984024\pi$$
0.998741 0.0501686i $$-0.0159759\pi$$
$$360$$ 0 0
$$361$$ −2157.00 −0.0165514
$$362$$ 0 0
$$363$$ −1587.00 4488.71i −0.0120438 0.0340650i
$$364$$ 0 0
$$365$$ 4921.46i 0.0369410i
$$366$$ 0 0
$$367$$ 44326.0 0.329099 0.164549 0.986369i $$-0.447383\pi$$
0.164549 + 0.986369i $$0.447383\pi$$
$$368$$ 0 0
$$369$$ −122688. 151819.i −0.901051 1.11499i
$$370$$ 0 0
$$371$$ 11913.3i 0.0865537i
$$372$$ 0 0
$$373$$ 60718.0 0.436415 0.218208 0.975902i $$-0.429979\pi$$
0.218208 + 0.975902i $$0.429979\pi$$
$$374$$ 0 0
$$375$$ −138528. + 48977.0i −0.985088 + 0.348281i
$$376$$ 0 0
$$377$$ 72124.9i 0.507461i
$$378$$ 0 0
$$379$$ 30458.0 0.212043 0.106021 0.994364i $$-0.466189\pi$$
0.106021 + 0.994364i $$0.466189\pi$$
$$380$$ 0 0
$$381$$ 24846.0 + 70275.1i 0.171162 + 0.484118i
$$382$$ 0 0
$$383$$ 235687.i 1.60671i −0.595498 0.803357i $$-0.703045\pi$$
0.595498 0.803357i $$-0.296955\pi$$
$$384$$ 0 0
$$385$$ 52416.0 0.353625
$$386$$ 0 0
$$387$$ 16506.0 13338.9i 0.110210 0.0890629i
$$388$$ 0 0
$$389$$ 150410.i 0.993980i 0.867756 + 0.496990i $$0.165561\pi$$
−0.867756 + 0.496990i $$0.834439\pi$$
$$390$$ 0 0
$$391$$ 76032.0 0.497328
$$392$$ 0 0
$$393$$ 45936.0 16240.8i 0.297419 0.105153i
$$394$$ 0 0
$$395$$ 166617.i 1.06789i
$$396$$ 0 0
$$397$$ −172658. −1.09548 −0.547742 0.836648i $$-0.684512\pi$$
−0.547742 + 0.836648i $$0.684512\pi$$
$$398$$ 0 0
$$399$$ −27924.0 78981.0i −0.175401 0.496109i
$$400$$ 0 0
$$401$$ 167466.i 1.04145i 0.853726 + 0.520723i $$0.174338\pi$$
−0.853726 + 0.520723i $$0.825662\pi$$
$$402$$ 0 0
$$403$$ −37100.0 −0.228436
$$404$$ 0 0
$$405$$ −108864. 23368.5i −0.663704 0.142469i
$$406$$ 0 0
$$407$$ 222620.i 1.34393i
$$408$$ 0 0
$$409$$ −150430. −0.899265 −0.449633 0.893214i $$-0.648445\pi$$
−0.449633 + 0.893214i $$0.648445\pi$$
$$410$$ 0 0
$$411$$ −153504. + 54271.9i −0.908732 + 0.321285i
$$412$$ 0 0
$$413$$ 47212.1i 0.276792i
$$414$$ 0 0
$$415$$ 120672. 0.700665
$$416$$ 0 0
$$417$$ 69618.0 + 196909.i 0.400359 + 1.13239i
$$418$$ 0 0
$$419$$ 178276.i 1.01546i −0.861515 0.507732i $$-0.830484\pi$$
0.861515 0.507732i $$-0.169516\pi$$
$$420$$ 0 0
$$421$$ 216046. 1.21894 0.609470 0.792809i $$-0.291382\pi$$
0.609470 + 0.792809i $$0.291382\pi$$
$$422$$ 0 0
$$423$$ −86400.0 106915.i −0.482873 0.597525i
$$424$$ 0 0
$$425$$ 68629.0i 0.379953i
$$426$$ 0 0
$$427$$ −38636.0 −0.211903
$$428$$ 0 0
$$429$$ 50400.0 17819.1i 0.273852 0.0968213i
$$430$$ 0 0
$$431$$ 5498.46i 0.0295997i 0.999890 + 0.0147998i $$0.00471110\pi$$
−0.999890 + 0.0147998i $$0.995289\pi$$
$$432$$ 0 0
$$433$$ 108002. 0.576044 0.288022 0.957624i $$-0.407002\pi$$
0.288022 + 0.957624i $$0.407002\pi$$
$$434$$ 0 0
$$435$$ −73440.0 207720.i −0.388109 1.09774i
$$436$$ 0 0
$$437$$ 133660.i 0.699905i
$$438$$ 0 0
$$439$$ −357722. −1.85617 −0.928083 0.372374i $$-0.878544\pi$$
−0.928083 + 0.372374i $$0.878544\pi$$
$$440$$ 0 0
$$441$$ 108675. 87822.7i 0.558795 0.451575i
$$442$$ 0 0
$$443$$ 86261.4i 0.439551i −0.975551 0.219775i $$-0.929468\pi$$
0.975551 0.219775i $$-0.0705324\pi$$
$$444$$ 0 0
$$445$$ −133056. −0.671915
$$446$$ 0 0
$$447$$ 94896.0 33550.8i 0.474934 0.167914i
$$448$$ 0 0
$$449$$ 301397.i 1.49502i 0.664251 + 0.747509i $$0.268750\pi$$
−0.664251 + 0.747509i $$0.731250\pi$$
$$450$$ 0 0
$$451$$ 286272. 1.40743
$$452$$ 0 0
$$453$$ 43278.0 + 122409.i 0.210897 + 0.596507i
$$454$$ 0 0
$$455$$ 22061.7i 0.106566i
$$456$$ 0 0
$$457$$ −399070. −1.91081 −0.955403 0.295305i $$-0.904579\pi$$
−0.955403 + 0.295305i $$0.904579\pi$$
$$458$$ 0 0
$$459$$ −77760.0 + 126465.i −0.369089 + 0.600266i
$$460$$ 0 0
$$461$$ 38268.6i 0.180070i −0.995939 0.0900349i $$-0.971302\pi$$
0.995939 0.0900349i $$-0.0286979\pi$$
$$462$$ 0 0
$$463$$ −144410. −0.673652 −0.336826 0.941567i $$-0.609353\pi$$
−0.336826 + 0.941567i $$0.609353\pi$$
$$464$$ 0 0
$$465$$ −106848. + 37776.5i −0.494152 + 0.174709i
$$466$$ 0 0
$$467$$ 148204.i 0.679557i −0.940505 0.339779i $$-0.889648\pi$$
0.940505 0.339779i $$-0.110352\pi$$
$$468$$ 0 0
$$469$$ 116636. 0.530258
$$470$$ 0 0
$$471$$ 147030. + 415864.i 0.662772 + 1.87460i
$$472$$ 0 0
$$473$$ 31124.0i 0.139115i
$$474$$ 0 0
$$475$$ −120646. −0.534719
$$476$$ 0 0
$$477$$ −23328.0 28866.9i −0.102528 0.126871i
$$478$$ 0 0
$$479$$ 305606.i 1.33196i −0.745970 0.665979i $$-0.768014\pi$$
0.745970 0.665979i $$-0.231986\pi$$
$$480$$ 0 0
$$481$$ 93700.0 0.404995
$$482$$ 0 0
$$483$$ 82368.0 29121.5i 0.353073 0.124830i
$$484$$ 0 0
$$485$$ 8111.93i 0.0344858i
$$486$$ 0 0
$$487$$ 196774. 0.829678 0.414839 0.909895i $$-0.363838\pi$$
0.414839 + 0.909895i $$0.363838\pi$$
$$488$$ 0 0
$$489$$ 128946. + 364714.i 0.539250 + 1.52523i
$$490$$ 0 0
$$491$$ 166193.i 0.689365i 0.938719 + 0.344682i $$0.112013\pi$$
−0.938719 + 0.344682i $$0.887987\pi$$
$$492$$ 0 0
$$493$$ −293760. −1.20865
$$494$$ 0 0
$$495$$ 127008. 102638.i 0.518347 0.418888i
$$496$$ 0 0
$$497$$ 92659.3i 0.375125i
$$498$$ 0 0
$$499$$ 189050. 0.759234 0.379617 0.925144i $$-0.376056\pi$$
0.379617 + 0.925144i $$0.376056\pi$$
$$500$$ 0 0
$$501$$ −374688. + 132472.i −1.49277 + 0.527776i
$$502$$ 0 0
$$503$$ 344061.i 1.35988i 0.733269 + 0.679939i $$0.237994\pi$$
−0.733269 + 0.679939i $$0.762006\pi$$
$$504$$ 0 0
$$505$$ −232992. −0.913605
$$506$$ 0 0
$$507$$ 78183.0 + 221135.i 0.304156 + 0.860283i
$$508$$ 0 0
$$509$$ 353208.i 1.36331i 0.731673 + 0.681656i $$0.238740\pi$$
−0.731673 + 0.681656i $$0.761260\pi$$
$$510$$ 0 0
$$511$$ −7540.00 −0.0288755
$$512$$ 0 0
$$513$$ −222318. 136698.i −0.844773 0.519430i
$$514$$ 0 0
$$515$$ 36283.1i 0.136801i
$$516$$ 0 0
$$517$$ 201600. 0.754240
$$518$$ 0 0
$$519$$ 190224. 67254.3i 0.706205 0.249681i
$$520$$ 0 0
$$521$$ 276043.i 1.01695i −0.861075 0.508477i $$-0.830209\pi$$
0.861075 0.508477i $$-0.169791\pi$$
$$522$$ 0 0
$$523$$ −146950. −0.537237 −0.268619 0.963247i $$-0.586567\pi$$
−0.268619 + 0.963247i $$0.586567\pi$$
$$524$$ 0 0
$$525$$ 26286.0 + 74348.0i 0.0953687 + 0.269743i
$$526$$ 0 0
$$527$$ 151106.i 0.544077i
$$528$$ 0 0
$$529$$ 140449. 0.501889
$$530$$ 0 0
$$531$$ 92448.0 + 114399.i 0.327875 + 0.405725i
$$532$$ 0 0
$$533$$ 120491.i 0.424131i
$$534$$ 0 0
$$535$$ −184032. −0.642963
$$536$$ 0 0
$$537$$ 259632. 91793.8i 0.900346 0.318321i
$$538$$ 0 0
$$539$$ 204920.i 0.705352i
$$540$$ 0 0
$$541$$ 244942. 0.836891 0.418445 0.908242i $$-0.362575\pi$$
0.418445 + 0.908242i $$0.362575\pi$$
$$542$$ 0 0
$$543$$ −39306.0 111174.i −0.133309 0.377055i
$$544$$ 0 0
$$545$$ 80610.2i 0.271392i
$$546$$ 0 0
$$547$$ −283366. −0.947050 −0.473525 0.880780i $$-0.657019\pi$$
−0.473525 + 0.880780i $$0.657019\pi$$
$$548$$ 0 0
$$549$$ −93618.0 + 75654.8i −0.310609 + 0.251010i
$$550$$ 0 0
$$551$$ 516414.i 1.70096i
$$552$$ 0 0
$$553$$ 255268. 0.834730
$$554$$ 0 0
$$555$$ 269856. 95408.5i 0.876085 0.309743i
$$556$$ 0 0
$$557$$ 47093.3i 0.151792i −0.997116 0.0758960i $$-0.975818\pi$$
0.997116 0.0758960i $$-0.0241817\pi$$
$$558$$ 0 0
$$559$$ 13100.0 0.0419225
$$560$$ 0 0
$$561$$ −72576.0 205276.i −0.230604 0.652247i
$$562$$ 0 0
$$563$$ 84.8528i 0.000267701i −1.00000 0.000133850i $$-0.999957\pi$$
1.00000 0.000133850i $$-4.26059e-5\pi$$
$$564$$ 0 0
$$565$$ −54144.0 −0.169611
$$566$$ 0 0
$$567$$ −35802.0 + 166787.i −0.111363 + 0.518794i
$$568$$ 0 0
$$569$$ 239115.i 0.738555i 0.929319 + 0.369277i $$0.120395\pi$$
−0.929319 + 0.369277i $$0.879605\pi$$
$$570$$ 0 0
$$571$$ −140710. −0.431571 −0.215786 0.976441i $$-0.569231\pi$$
−0.215786 + 0.976441i $$0.569231\pi$$
$$572$$ 0 0
$$573$$ 596736. 210978.i 1.81749 0.642581i
$$574$$ 0 0
$$575$$ 125820.i 0.380551i
$$576$$ 0 0
$$577$$ 36002.0 0.108137 0.0540686 0.998537i $$-0.482781\pi$$
0.0540686 + 0.998537i $$0.482781\pi$$
$$578$$ 0 0
$$579$$ −54150.0 153159.i −0.161526 0.456863i
$$580$$ 0 0
$$581$$ 184877.i 0.547686i
$$582$$ 0 0
$$583$$ 54432.0 0.160146
$$584$$ 0 0
$$585$$ −43200.0 53457.3i −0.126233 0.156205i
$$586$$ 0 0
$$587$$ 316179.i 0.917606i −0.888538 0.458803i $$-0.848278\pi$$
0.888538 0.458803i $$-0.151722\pi$$
$$588$$ 0 0
$$589$$ −265636. −0.765696
$$590$$ 0 0
$$591$$ 223344. 78964.0i 0.639439 0.226076i
$$592$$ 0 0
$$593$$ 262093.i 0.745327i −0.927967 0.372663i $$-0.878445\pi$$
0.927967 0.372663i $$-0.121555\pi$$
$$594$$ 0 0
$$595$$ −89856.0 −0.253813
$$596$$ 0 0
$$597$$ −111666. 315839.i −0.313309 0.886171i
$$598$$ 0 0
$$599$$ 606494.i 1.69034i 0.534501 + 0.845168i $$0.320499\pi$$
−0.534501 + 0.845168i $$0.679501\pi$$
$$600$$ 0 0
$$601$$ 306530. 0.848641 0.424321 0.905512i $$-0.360513\pi$$
0.424321 + 0.905512i $$0.360513\pi$$
$$602$$ 0 0
$$603$$ 282618. 228390.i 0.777258 0.628119i
$$604$$ 0 0
$$605$$ 8977.43i 0.0245268i
$$606$$ 0 0
$$607$$ −563162. −1.52847 −0.764233 0.644940i $$-0.776882\pi$$
−0.764233 + 0.644940i $$0.776882\pi$$
$$608$$ 0 0
$$609$$ −318240. + 112515.i −0.858065 + 0.303372i
$$610$$ 0 0
$$611$$ 84852.8i 0.227292i
$$612$$ 0 0
$$613$$ −111314. −0.296230 −0.148115 0.988970i $$-0.547321\pi$$
−0.148115 + 0.988970i $$0.547321\pi$$
$$614$$ 0 0
$$615$$ −122688. 347014.i −0.324378 0.917481i
$$616$$ 0 0
$$617$$ 121340.i 0.318737i 0.987219 + 0.159368i $$0.0509457\pi$$
−0.987219 + 0.159368i $$0.949054\pi$$
$$618$$ 0 0
$$619$$ −581158. −1.51675 −0.758373 0.651821i $$-0.774005\pi$$
−0.758373 + 0.651821i $$0.774005\pi$$
$$620$$ 0 0
$$621$$ 142560. 231852.i 0.369670 0.601212i
$$622$$ 0 0
$$623$$ 203850.i 0.525213i
$$624$$ 0 0
$$625$$ −66431.0 −0.170063
$$626$$ 0 0
$$627$$ 360864. 127585.i 0.917928 0.324536i
$$628$$ 0 0
$$629$$ 381634.i 0.964597i
$$630$$ 0 0
$$631$$ −232346. −0.583548 −0.291774 0.956487i $$-0.594245\pi$$
−0.291774 + 0.956487i $$0.594245\pi$$
$$632$$ 0 0
$$633$$ −45294.0 128111.i −0.113040 0.319726i
$$634$$ 0 0
$$635$$ 140550.i 0.348565i
$$636$$ 0 0
$$637$$ 86250.0 0.212559
$$638$$ 0 0
$$639$$ 181440. + 224521.i 0.444356 + 0.549863i
$$640$$ 0 0
$$641$$ 653570.i 1.59066i −0.606179 0.795328i $$-0.707299\pi$$
0.606179 0.795328i $$-0.292701\pi$$
$$642$$ 0 0
$$643$$ −424678. −1.02716 −0.513580 0.858042i $$-0.671681\pi$$
−0.513580 + 0.858042i $$0.671681\pi$$
$$644$$ 0 0
$$645$$ 37728.0 13338.9i 0.0906869 0.0320626i
$$646$$ 0 0
$$647$$ 427964.i 1.02235i −0.859478 0.511173i $$-0.829211\pi$$
0.859478 0.511173i $$-0.170789\pi$$
$$648$$ 0 0
$$649$$ −215712. −0.512136
$$650$$ 0 0
$$651$$ 57876.0 + 163698.i 0.136564 + 0.386262i
$$652$$ 0 0
$$653$$ 720621.i 1.68998i −0.534785 0.844988i $$-0.679607\pi$$
0.534785 0.844988i $$-0.320393\pi$$
$$654$$ 0 0
$$655$$ 91872.0 0.214141
$$656$$ 0 0
$$657$$ −18270.0 + 14764.4i −0.0423261 + 0.0342046i
$$658$$ 0 0
$$659$$ 40135.4i 0.0924180i −0.998932 0.0462090i $$-0.985286\pi$$
0.998932 0.0462090i $$-0.0147140\pi$$
$$660$$ 0 0
$$661$$ 358510. 0.820537 0.410269 0.911965i $$-0.365435\pi$$
0.410269 + 0.911965i $$0.365435\pi$$
$$662$$ 0 0
$$663$$ −86400.0 + 30547.0i −0.196556 + 0.0694931i
$$664$$ 0 0
$$665$$ 157962.i 0.357198i
$$666$$ 0 0
$$667$$ 538560. 1.21055
$$668$$ 0 0
$$669$$ 176334. + 498748.i 0.393989 + 1.11437i
$$670$$ 0 0
$$671$$ 176528.i 0.392074i
$$672$$ 0 0
$$673$$ 582434. 1.28593 0.642964 0.765896i $$-0.277705\pi$$
0.642964 + 0.765896i $$0.277705\pi$$
$$674$$ 0 0
$$675$$ 209277. + 128679.i 0.459319 + 0.282424i
$$676$$ 0 0
$$677$$ 37352.2i 0.0814965i −0.999169 0.0407482i $$-0.987026\pi$$
0.999169 0.0407482i $$-0.0129742\pi$$
$$678$$ 0 0
$$679$$ 12428.0 0.0269564
$$680$$ 0 0
$$681$$ 577008. 204003.i 1.24419 0.439889i
$$682$$ 0 0
$$683$$ 161848.i 0.346950i 0.984838 + 0.173475i $$0.0554995\pi$$
−0.984838 + 0.173475i $$0.944500\pi$$
$$684$$ 0 0
$$685$$ −307008. −0.654287
$$686$$ 0 0
$$687$$ 85686.0 + 242357.i 0.181550 + 0.513501i
$$688$$ 0 0
$$689$$ 22910.3i 0.0482605i
$$690$$ 0 0
$$691$$ −630118. −1.31967 −0.659836 0.751410i $$-0.729374\pi$$
−0.659836 + 0.751410i $$0.729374\pi$$
$$692$$ 0 0
$$693$$ −157248. 194584.i −0.327430 0.405174i
$$694$$ 0 0
$$695$$ 393819.i 0.815318i
$$696$$ 0 0
$$697$$ −490752. −1.01017
$$698$$ 0 0
$$699$$ 190944. 67508.9i 0.390797 0.138168i
$$700$$ 0 0
$$701$$ 457747.i 0.931514i 0.884913 + 0.465757i $$0.154218\pi$$
−0.884913 + 0.465757i $$0.845782\pi$$
$$702$$ 0 0
$$703$$ 670892. 1.35751
$$704$$ 0 0
$$705$$ −86400.0 244376.i −0.173834 0.491678i
$$706$$ 0 0
$$707$$ 356959.i 0.714133i
$$708$$ 0 0
$$709$$ −274130. −0.545336 −0.272668 0.962108i $$-0.587906\pi$$
−0.272668 + 0.962108i $$0.587906\pi$$
$$710$$ 0 0
$$711$$ 618534. 499851.i 1.22356 0.988784i
$$712$$ 0 0
$$713$$ 277027.i 0.544934i
$$714$$ 0 0
$$715$$ 100800. 0.197173
$$716$$ 0 0
$$717$$ −10944.0 + 3869.29i −0.0212881 + 0.00752650i
$$718$$ 0 0
$$719$$ 304045.i 0.588138i 0.955784 + 0.294069i $$0.0950096\pi$$
−0.955784 + 0.294069i $$0.904990\pi$$
$$720$$ 0 0
$$721$$ 55588.0 0.106933
$$722$$ 0 0
$$723$$ 183738. + 519690.i 0.351498 + 0.994185i
$$724$$ 0 0
$$725$$ 486122.i 0.924845i
$$726$$ 0 0
$$727$$ −364058. −0.688814 −0.344407 0.938821i $$-0.611920\pi$$
−0.344407 + 0.938821i $$0.611920\pi$$
$$728$$ 0 0
$$729$$ 239841. + 474242.i 0.451303 + 0.892371i
$$730$$ 0 0
$$731$$ 53355.4i 0.0998491i
$$732$$ 0 0
$$733$$ 301198. 0.560588 0.280294 0.959914i $$-0.409568\pi$$
0.280294 + 0.959914i $$0.409568\pi$$
$$734$$ 0 0
$$735$$ 248400. 87822.7i 0.459808 0.162567i
$$736$$ 0 0
$$737$$ 532910.i 0.981112i
$$738$$ 0 0
$$739$$ 872570. 1.59776 0.798880 0.601491i $$-0.205426\pi$$
0.798880 + 0.601491i $$0.205426\pi$$
$$740$$ 0 0
$$741$$ −53700.0 151887.i −0.0977998 0.276620i
$$742$$ 0 0
$$743$$ 874222.i 1.58359i −0.610784 0.791797i $$-0.709146\pi$$
0.610784 0.791797i $$-0.290854\pi$$
$$744$$ 0 0
$$745$$ 189792. 0.341952
$$746$$ 0 0
$$747$$ −362016. 447972.i −0.648764 0.802804i
$$748$$ 0 0
$$749$$ 281949.i 0.502582i
$$750$$ 0 0
$$751$$ −916250. −1.62455 −0.812277 0.583272i $$-0.801772\pi$$
−0.812277 + 0.583272i $$0.801772\pi$$
$$752$$ 0 0
$$753$$ −384048. + 135781.i −0.677323 + 0.239470i
$$754$$ 0 0
$$755$$ 244817.i 0.429485i
$$756$$ 0 0
$$757$$ 691630. 1.20693 0.603465 0.797390i $$-0.293786\pi$$
0.603465 + 0.797390i $$0.293786\pi$$
$$758$$ 0 0
$$759$$ 133056. + 376339.i 0.230968 + 0.653275i
$$760$$ 0 0
$$761$$ 90249.5i 0.155839i −0.996960 0.0779193i $$-0.975172\pi$$
0.996960 0.0779193i $$-0.0248277\pi$$
$$762$$ 0 0
$$763$$ −123500. −0.212138
$$764$$ 0 0
$$765$$ −217728. + 175951.i −0.372042 + 0.300655i
$$766$$ 0 0
$$767$$ 90792.5i 0.154333i
$$768$$ 0 0
$$769$$ −515326. −0.871424 −0.435712 0.900086i $$-0.643503\pi$$
−0.435712 + 0.900086i $$0.643503\pi$$
$$770$$ 0 0
$$771$$ −723456. + 255780.i −1.21704 + 0.430287i
$$772$$ 0 0
$$773$$ 100449.i 0.168107i 0.996461 + 0.0840535i $$0.0267867\pi$$
−0.996461 + 0.0840535i $$0.973213\pi$$
$$774$$ 0 0
$$775$$ 250054. 0.416323
$$776$$ 0 0
$$777$$ −146172. 413437.i −0.242115 0.684805i
$$778$$ 0 0
$$779$$ 862716.i 1.42165i
$$780$$ 0 0
$$781$$ −423360. −0.694077
$$782$$ 0 0
$$783$$ −550800. + 895791.i −0.898401 + 1.46111i
$$784$$ 0 0
$$785$$ 831727.i 1.34971i
$$786$$ 0 0
$$787$$ −107878. −0.174174 −0.0870870 0.996201i $$-0.527756\pi$$
−0.0870870 + 0.996201i