# Properties

 Label 3150.2.m.j.2843.2 Level 3150 Weight 2 Character 3150.2843 Analytic conductor 25.153 Analytic rank 0 Dimension 8 CM no Inner twists 2

# Related objects

## Newspace parameters

 Level: $$N$$ = $$3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 3150.m (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$25.1528766367$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(i)$$ Coefficient field: 8.0.1698758656.6 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 630) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 2843.2 Root $$-0.692297i$$ Character $$\chi$$ = 3150.2843 Dual form 3150.2.m.j.1457.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$$ $$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.77786i q^{11} +(-0.692297 - 0.692297i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(-2.39327 - 2.39327i) q^{17} +(1.25714 - 1.25714i) q^{22} +(3.38459 - 3.38459i) q^{23} +0.979056i q^{26} +(-0.707107 - 0.707107i) q^{28} +4.42289 q^{29} -5.77786 q^{31} +(0.707107 + 0.707107i) q^{32} +3.38459i q^{34} +(-5.91399 + 5.91399i) q^{37} -0.807922i q^{41} +(4.64173 + 4.64173i) q^{43} -1.77786 q^{44} -4.78654 q^{46} +(-7.47016 - 7.47016i) q^{47} -1.00000i q^{49} +(0.692297 - 0.692297i) q^{52} +(3.56484 - 3.56484i) q^{53} +1.00000i q^{56} +(-3.12745 - 3.12745i) q^{58} +5.89887 q^{59} +2.39327 q^{61} +(4.08557 + 4.08557i) q^{62} -1.00000i q^{64} +(0.641735 - 0.641735i) q^{67} +(2.39327 - 2.39327i) q^{68} -10.6854i q^{71} +(-5.70097 - 5.70097i) q^{73} +8.36365 q^{74} +(-1.25714 - 1.25714i) q^{77} -16.3423i q^{79} +(-0.571287 + 0.571287i) q^{82} +(-0.171134 + 0.171134i) q^{83} -6.56440i q^{86} +(1.25714 + 1.25714i) q^{88} +13.2340 q^{89} +0.979056 q^{91} +(3.38459 + 3.38459i) q^{92} +10.5644i q^{94} +(-12.6413 + 12.6413i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + O(q^{10})$$ $$8q + 4q^{13} + 8q^{14} - 8q^{16} + 4q^{22} + 8q^{23} + 24q^{29} - 8q^{31} + 4q^{37} + 12q^{43} + 24q^{44} - 12q^{47} - 4q^{52} + 32q^{53} - 12q^{58} + 16q^{59} + 4q^{62} - 20q^{67} - 36q^{73} + 40q^{74} - 4q^{77} + 12q^{82} + 56q^{83} + 4q^{88} + 72q^{89} + 8q^{92} + 4q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$451$$ $$2801$$ $$\chi(n)$$ $$e\left(\frac{3}{4}\right)$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.707107 0.707107i −0.500000 0.500000i
$$3$$ 0 0
$$4$$ 1.00000i 0.500000i
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −0.707107 + 0.707107i −0.267261 + 0.267261i
$$8$$ 0.707107 0.707107i 0.250000 0.250000i
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 1.77786i 0.536046i 0.963412 + 0.268023i $$0.0863704\pi$$
−0.963412 + 0.268023i $$0.913630\pi$$
$$12$$ 0 0
$$13$$ −0.692297 0.692297i −0.192009 0.192009i 0.604555 0.796564i $$-0.293351\pi$$
−0.796564 + 0.604555i $$0.793351\pi$$
$$14$$ 1.00000 0.267261
$$15$$ 0 0
$$16$$ −1.00000 −0.250000
$$17$$ −2.39327 2.39327i −0.580453 0.580453i 0.354575 0.935028i $$-0.384626\pi$$
−0.935028 + 0.354575i $$0.884626\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 1.25714 1.25714i 0.268023 0.268023i
$$23$$ 3.38459 3.38459i 0.705737 0.705737i −0.259899 0.965636i $$-0.583689\pi$$
0.965636 + 0.259899i $$0.0836893\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0.979056i 0.192009i
$$27$$ 0 0
$$28$$ −0.707107 0.707107i −0.133631 0.133631i
$$29$$ 4.42289 0.821310 0.410655 0.911791i $$-0.365300\pi$$
0.410655 + 0.911791i $$0.365300\pi$$
$$30$$ 0 0
$$31$$ −5.77786 −1.03774 −0.518868 0.854855i $$-0.673646\pi$$
−0.518868 + 0.854855i $$0.673646\pi$$
$$32$$ 0.707107 + 0.707107i 0.125000 + 0.125000i
$$33$$ 0 0
$$34$$ 3.38459i 0.580453i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −5.91399 + 5.91399i −0.972255 + 0.972255i −0.999625 0.0273707i $$-0.991287\pi$$
0.0273707 + 0.999625i $$0.491287\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0.807922i 0.126176i −0.998008 0.0630881i $$-0.979905\pi$$
0.998008 0.0630881i $$-0.0200949\pi$$
$$42$$ 0 0
$$43$$ 4.64173 + 4.64173i 0.707858 + 0.707858i 0.966084 0.258227i $$-0.0831381\pi$$
−0.258227 + 0.966084i $$0.583138\pi$$
$$44$$ −1.77786 −0.268023
$$45$$ 0 0
$$46$$ −4.78654 −0.705737
$$47$$ −7.47016 7.47016i −1.08964 1.08964i −0.995566 0.0940694i $$-0.970012\pi$$
−0.0940694 0.995566i $$-0.529988\pi$$
$$48$$ 0 0
$$49$$ 1.00000i 0.142857i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0.692297 0.692297i 0.0960044 0.0960044i
$$53$$ 3.56484 3.56484i 0.489669 0.489669i −0.418533 0.908202i $$-0.637456\pi$$
0.908202 + 0.418533i $$0.137456\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 1.00000i 0.133631i
$$57$$ 0 0
$$58$$ −3.12745 3.12745i −0.410655 0.410655i
$$59$$ 5.89887 0.767968 0.383984 0.923340i $$-0.374552\pi$$
0.383984 + 0.923340i $$0.374552\pi$$
$$60$$ 0 0
$$61$$ 2.39327 0.306427 0.153213 0.988193i $$-0.451038\pi$$
0.153213 + 0.988193i $$0.451038\pi$$
$$62$$ 4.08557 + 4.08557i 0.518868 + 0.518868i
$$63$$ 0 0
$$64$$ 1.00000i 0.125000i
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0.641735 0.641735i 0.0784004 0.0784004i −0.666819 0.745220i $$-0.732345\pi$$
0.745220 + 0.666819i $$0.232345\pi$$
$$68$$ 2.39327 2.39327i 0.290227 0.290227i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 10.6854i 1.26813i −0.773282 0.634063i $$-0.781386\pi$$
0.773282 0.634063i $$-0.218614\pi$$
$$72$$ 0 0
$$73$$ −5.70097 5.70097i −0.667248 0.667248i 0.289830 0.957078i $$-0.406401\pi$$
−0.957078 + 0.289830i $$0.906401\pi$$
$$74$$ 8.36365 0.972255
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −1.25714 1.25714i −0.143264 0.143264i
$$78$$ 0 0
$$79$$ 16.3423i 1.83865i −0.393500 0.919324i $$-0.628736\pi$$
0.393500 0.919324i $$-0.371264\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ −0.571287 + 0.571287i −0.0630881 + 0.0630881i
$$83$$ −0.171134 + 0.171134i −0.0187844 + 0.0187844i −0.716437 0.697652i $$-0.754228\pi$$
0.697652 + 0.716437i $$0.254228\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 6.56440i 0.707858i
$$87$$ 0 0
$$88$$ 1.25714 + 1.25714i 0.134012 + 0.134012i
$$89$$ 13.2340 1.40280 0.701399 0.712769i $$-0.252559\pi$$
0.701399 + 0.712769i $$0.252559\pi$$
$$90$$ 0 0
$$91$$ 0.979056 0.102633
$$92$$ 3.38459 + 3.38459i 0.352868 + 0.352868i
$$93$$ 0 0
$$94$$ 10.5644i 1.08964i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −12.6413 + 12.6413i −1.28353 + 1.28353i −0.344884 + 0.938645i $$0.612082\pi$$
−0.938645 + 0.344884i $$0.887918\pi$$
$$98$$ −0.707107 + 0.707107i −0.0714286 + 0.0714286i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 12.6778i 1.26149i −0.775991 0.630744i $$-0.782750\pi$$
0.775991 0.630744i $$-0.217250\pi$$
$$102$$ 0 0
$$103$$ −7.43472 7.43472i −0.732565 0.732565i 0.238563 0.971127i $$-0.423324\pi$$
−0.971127 + 0.238563i $$0.923324\pi$$
$$104$$ −0.979056 −0.0960044
$$105$$ 0 0
$$106$$ −5.04145 −0.489669
$$107$$ 13.5138 + 13.5138i 1.30643 + 1.30643i 0.923972 + 0.382461i $$0.124923\pi$$
0.382461 + 0.923972i $$0.375077\pi$$
$$108$$ 0 0
$$109$$ 3.30082i 0.316161i 0.987426 + 0.158081i $$0.0505306\pi$$
−0.987426 + 0.158081i $$0.949469\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0.707107 0.707107i 0.0668153 0.0668153i
$$113$$ 5.84937 5.84937i 0.550263 0.550263i −0.376254 0.926517i $$-0.622788\pi$$
0.926517 + 0.376254i $$0.122788\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 4.42289i 0.410655i
$$117$$ 0 0
$$118$$ −4.17113 4.17113i −0.383984 0.383984i
$$119$$ 3.38459 0.310265
$$120$$ 0 0
$$121$$ 7.83920 0.712654
$$122$$ −1.69230 1.69230i −0.153213 0.153213i
$$123$$ 0 0
$$124$$ 5.77786i 0.518868i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0.615405 0.615405i 0.0546084 0.0546084i −0.679275 0.733884i $$-0.737706\pi$$
0.733884 + 0.679275i $$0.237706\pi$$
$$128$$ −0.707107 + 0.707107i −0.0625000 + 0.0625000i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 6.52717i 0.570281i −0.958486 0.285141i $$-0.907960\pi$$
0.958486 0.285141i $$-0.0920403\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −0.907550 −0.0784004
$$135$$ 0 0
$$136$$ −3.38459 −0.290227
$$137$$ −0.192517 0.192517i −0.0164478 0.0164478i 0.698835 0.715283i $$-0.253702\pi$$
−0.715283 + 0.698835i $$0.753702\pi$$
$$138$$ 0 0
$$139$$ 14.8694i 1.26121i −0.776104 0.630605i $$-0.782807\pi$$
0.776104 0.630605i $$-0.217193\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −7.55573 + 7.55573i −0.634063 + 0.634063i
$$143$$ 1.23081 1.23081i 0.102926 0.102926i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 8.06239i 0.667248i
$$147$$ 0 0
$$148$$ −5.91399 5.91399i −0.486127 0.486127i
$$149$$ −20.6467 −1.69144 −0.845721 0.533625i $$-0.820829\pi$$
−0.845721 + 0.533625i $$0.820829\pi$$
$$150$$ 0 0
$$151$$ 6.01735 0.489685 0.244843 0.969563i $$-0.421264\pi$$
0.244843 + 0.969563i $$0.421264\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 1.77786i 0.143264i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0.608522 0.608522i 0.0485654 0.0485654i −0.682407 0.730972i $$-0.739067\pi$$
0.730972 + 0.682407i $$0.239067\pi$$
$$158$$ −11.5557 + 11.5557i −0.919324 + 0.919324i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 4.78654i 0.377232i
$$162$$ 0 0
$$163$$ −6.12745 6.12745i −0.479939 0.479939i 0.425173 0.905112i $$-0.360213\pi$$
−0.905112 + 0.425173i $$0.860213\pi$$
$$164$$ 0.807922 0.0630881
$$165$$ 0 0
$$166$$ 0.242020 0.0187844
$$167$$ −6.18669 6.18669i −0.478741 0.478741i 0.425988 0.904729i $$-0.359927\pi$$
−0.904729 + 0.425988i $$0.859927\pi$$
$$168$$ 0 0
$$169$$ 12.0414i 0.926265i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −4.64173 + 4.64173i −0.353929 + 0.353929i
$$173$$ 15.7720 15.7720i 1.19913 1.19913i 0.224697 0.974429i $$-0.427861\pi$$
0.974429 0.224697i $$-0.0721394\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 1.77786i 0.134012i
$$177$$ 0 0
$$178$$ −9.35783 9.35783i −0.701399 0.701399i
$$179$$ −3.87899 −0.289929 −0.144965 0.989437i $$-0.546307\pi$$
−0.144965 + 0.989437i $$0.546307\pi$$
$$180$$ 0 0
$$181$$ 23.6896 1.76084 0.880418 0.474198i $$-0.157262\pi$$
0.880418 + 0.474198i $$0.157262\pi$$
$$182$$ −0.692297 0.692297i −0.0513165 0.0513165i
$$183$$ 0 0
$$184$$ 4.78654i 0.352868i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 4.25491 4.25491i 0.311150 0.311150i
$$188$$ 7.47016 7.47016i 0.544818 0.544818i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 23.4720i 1.69837i −0.528095 0.849185i $$-0.677093\pi$$
0.528095 0.849185i $$-0.322907\pi$$
$$192$$ 0 0
$$193$$ −18.1288 18.1288i −1.30494 1.30494i −0.925019 0.379921i $$-0.875951\pi$$
−0.379921 0.925019i $$-0.624049\pi$$
$$194$$ 17.8775 1.28353
$$195$$ 0 0
$$196$$ 1.00000 0.0714286
$$197$$ 9.58535 + 9.58535i 0.682928 + 0.682928i 0.960659 0.277731i $$-0.0895824\pi$$
−0.277731 + 0.960659i $$0.589582\pi$$
$$198$$ 0 0
$$199$$ 2.46416i 0.174679i 0.996179 + 0.0873397i $$0.0278366\pi$$
−0.996179 + 0.0873397i $$0.972163\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ −8.96456 + 8.96456i −0.630744 + 0.630744i
$$203$$ −3.12745 + 3.12745i −0.219504 + 0.219504i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 10.5143i 0.732565i
$$207$$ 0 0
$$208$$ 0.692297 + 0.692297i 0.0480022 + 0.0480022i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −5.57308 −0.383667 −0.191833 0.981428i $$-0.561443\pi$$
−0.191833 + 0.981428i $$0.561443\pi$$
$$212$$ 3.56484 + 3.56484i 0.244834 + 0.244834i
$$213$$ 0 0
$$214$$ 19.1115i 1.30643i
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 4.08557 4.08557i 0.277346 0.277346i
$$218$$ 2.33403 2.33403i 0.158081 0.158081i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 3.31371i 0.222904i
$$222$$ 0 0
$$223$$ 14.6854 + 14.6854i 0.983408 + 0.983408i 0.999865 0.0164565i $$-0.00523851\pi$$
−0.0164565 + 0.999865i $$0.505239\pi$$
$$224$$ −1.00000 −0.0668153
$$225$$ 0 0
$$226$$ −8.27226 −0.550263
$$227$$ −19.5557 19.5557i −1.29796 1.29796i −0.929738 0.368221i $$-0.879967\pi$$
−0.368221 0.929738i $$-0.620033\pi$$
$$228$$ 0 0
$$229$$ 24.3622i 1.60990i 0.593345 + 0.804948i $$0.297807\pi$$
−0.593345 + 0.804948i $$0.702193\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 3.12745 3.12745i 0.205327 0.205327i
$$233$$ 14.7692 14.7692i 0.967562 0.967562i −0.0319284 0.999490i $$-0.510165\pi$$
0.999490 + 0.0319284i $$0.0101649\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 5.89887i 0.383984i
$$237$$ 0 0
$$238$$ −2.39327 2.39327i −0.155133 0.155133i
$$239$$ −1.47283 −0.0952695 −0.0476348 0.998865i $$-0.515168\pi$$
−0.0476348 + 0.998865i $$0.515168\pi$$
$$240$$ 0 0
$$241$$ −21.5557 −1.38853 −0.694263 0.719721i $$-0.744270\pi$$
−0.694263 + 0.719721i $$0.744270\pi$$
$$242$$ −5.54315 5.54315i −0.356327 0.356327i
$$243$$ 0 0
$$244$$ 2.39327i 0.153213i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ −4.08557 + 4.08557i −0.259434 + 0.259434i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 2.68541i 0.169502i −0.996402 0.0847509i $$-0.972991\pi$$
0.996402 0.0847509i $$-0.0270095\pi$$
$$252$$ 0 0
$$253$$ 6.01735 + 6.01735i 0.378308 + 0.378308i
$$254$$ −0.870315 −0.0546084
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −10.9873 10.9873i −0.685368 0.685368i 0.275836 0.961205i $$-0.411045\pi$$
−0.961205 + 0.275836i $$0.911045\pi$$
$$258$$ 0 0
$$259$$ 8.36365i 0.519692i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −4.61541 + 4.61541i −0.285141 + 0.285141i
$$263$$ −7.92911 + 7.92911i −0.488930 + 0.488930i −0.907969 0.419038i $$-0.862367\pi$$
0.419038 + 0.907969i $$0.362367\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0.641735 + 0.641735i 0.0392002 + 0.0392002i
$$269$$ −7.26420 −0.442906 −0.221453 0.975171i $$-0.571080\pi$$
−0.221453 + 0.975171i $$0.571080\pi$$
$$270$$ 0 0
$$271$$ −17.5756 −1.06764 −0.533821 0.845597i $$-0.679244\pi$$
−0.533821 + 0.845597i $$0.679244\pi$$
$$272$$ 2.39327 + 2.39327i 0.145113 + 0.145113i
$$273$$ 0 0
$$274$$ 0.272260i 0.0164478i
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 9.81287 9.81287i 0.589598 0.589598i −0.347924 0.937523i $$-0.613113\pi$$
0.937523 + 0.347924i $$0.113113\pi$$
$$278$$ −10.5143 + 10.5143i −0.630605 + 0.630605i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 12.5849i 0.750753i 0.926872 + 0.375376i $$0.122487\pi$$
−0.926872 + 0.375376i $$0.877513\pi$$
$$282$$ 0 0
$$283$$ −4.69918 4.69918i −0.279337 0.279337i 0.553507 0.832844i $$-0.313289\pi$$
−0.832844 + 0.553507i $$0.813289\pi$$
$$284$$ 10.6854 0.634063
$$285$$ 0 0
$$286$$ −1.74063 −0.102926
$$287$$ 0.571287 + 0.571287i 0.0337220 + 0.0337220i
$$288$$ 0 0
$$289$$ 5.54452i 0.326148i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 5.70097 5.70097i 0.333624 0.333624i
$$293$$ 3.39866 3.39866i 0.198552 0.198552i −0.600827 0.799379i $$-0.705162\pi$$
0.799379 + 0.600827i $$0.205162\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 8.36365i 0.486127i
$$297$$ 0 0
$$298$$ 14.5994 + 14.5994i 0.845721 + 0.845721i
$$299$$ −4.68629 −0.271015
$$300$$ 0 0
$$301$$ −6.56440 −0.378366
$$302$$ −4.25491 4.25491i −0.244843 0.244843i
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 15.5557 15.5557i 0.887812 0.887812i −0.106500 0.994313i $$-0.533965\pi$$
0.994313 + 0.106500i $$0.0339645\pi$$
$$308$$ 1.25714 1.25714i 0.0716322 0.0716322i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0.773651i 0.0438697i 0.999759 + 0.0219349i $$0.00698264\pi$$
−0.999759 + 0.0219349i $$0.993017\pi$$
$$312$$ 0 0
$$313$$ 11.8548 + 11.8548i 0.670070 + 0.670070i 0.957732 0.287662i $$-0.0928779\pi$$
−0.287662 + 0.957732i $$0.592878\pi$$
$$314$$ −0.860580 −0.0485654
$$315$$ 0 0
$$316$$ 16.3423 0.919324
$$317$$ −0.00911383 0.00911383i −0.000511884 0.000511884i 0.706851 0.707363i $$-0.250115\pi$$
−0.707363 + 0.706851i $$0.750115\pi$$
$$318$$ 0 0
$$319$$ 7.86330i 0.440260i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 3.38459 3.38459i 0.188616 0.188616i
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 8.66553i 0.479939i
$$327$$ 0 0
$$328$$ −0.571287 0.571287i −0.0315441 0.0315441i
$$329$$ 10.5644 0.582434
$$330$$ 0 0
$$331$$ −23.7977 −1.30804 −0.654021 0.756476i $$-0.726919\pi$$
−0.654021 + 0.756476i $$0.726919\pi$$
$$332$$ −0.171134 0.171134i −0.00939221 0.00939221i
$$333$$ 0 0
$$334$$ 8.74930i 0.478741i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0.828866 0.828866i 0.0451512 0.0451512i −0.684171 0.729322i $$-0.739836\pi$$
0.729322 + 0.684171i $$0.239836\pi$$
$$338$$ −8.51459 + 8.51459i −0.463133 + 0.463133i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 10.2723i 0.556274i
$$342$$ 0 0
$$343$$ 0.707107 + 0.707107i 0.0381802 + 0.0381802i
$$344$$ 6.56440 0.353929
$$345$$ 0 0
$$346$$ −22.3050 −1.19913
$$347$$ −5.17157 5.17157i −0.277625 0.277625i 0.554535 0.832160i $$-0.312896\pi$$
−0.832160 + 0.554535i $$0.812896\pi$$
$$348$$ 0 0
$$349$$ 4.20837i 0.225269i −0.993636 0.112634i $$-0.964071\pi$$
0.993636 0.112634i $$-0.0359289\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −1.25714 + 1.25714i −0.0670058 + 0.0670058i
$$353$$ −2.22214 + 2.22214i −0.118272 + 0.118272i −0.763766 0.645493i $$-0.776652\pi$$
0.645493 + 0.763766i $$0.276652\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 13.2340i 0.701399i
$$357$$ 0 0
$$358$$ 2.74286 + 2.74286i 0.144965 + 0.144965i
$$359$$ −22.7692 −1.20171 −0.600856 0.799357i $$-0.705173\pi$$
−0.600856 + 0.799357i $$0.705173\pi$$
$$360$$ 0 0
$$361$$ 19.0000 1.00000
$$362$$ −16.7511 16.7511i −0.880418 0.880418i
$$363$$ 0 0
$$364$$ 0.979056i 0.0513165i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −2.13836 + 2.13836i −0.111622 + 0.111622i −0.760712 0.649090i $$-0.775150\pi$$
0.649090 + 0.760712i $$0.275150\pi$$
$$368$$ −3.38459 + 3.38459i −0.176434 + 0.176434i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 5.04145i 0.261739i
$$372$$ 0 0
$$373$$ −13.0263 13.0263i −0.674478 0.674478i 0.284267 0.958745i $$-0.408250\pi$$
−0.958745 + 0.284267i $$0.908250\pi$$
$$374$$ −6.01735 −0.311150
$$375$$ 0 0
$$376$$ −10.5644 −0.544818
$$377$$ −3.06195 3.06195i −0.157699 0.157699i
$$378$$ 0 0
$$379$$ 27.4011i 1.40750i −0.710449 0.703749i $$-0.751508\pi$$
0.710449 0.703749i $$-0.248492\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −16.5972 + 16.5972i −0.849185 + 0.849185i
$$383$$ 17.6715 17.6715i 0.902973 0.902973i −0.0927190 0.995692i $$-0.529556\pi$$
0.995692 + 0.0927190i $$0.0295558\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 25.6380i 1.30494i
$$387$$ 0 0
$$388$$ −12.6413 12.6413i −0.641765 0.641765i
$$389$$ −15.8356 −0.802897 −0.401449 0.915882i $$-0.631493\pi$$
−0.401449 + 0.915882i $$0.631493\pi$$
$$390$$ 0 0
$$391$$ −16.2005 −0.819294
$$392$$ −0.707107 0.707107i −0.0357143 0.0357143i
$$393$$ 0 0
$$394$$ 13.5557i 0.682928i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 14.5575 14.5575i 0.730621 0.730621i −0.240122 0.970743i $$-0.577187\pi$$
0.970743 + 0.240122i $$0.0771874\pi$$
$$398$$ 1.74242 1.74242i 0.0873397 0.0873397i
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 9.78102i 0.488441i 0.969720 + 0.244220i $$0.0785320\pi$$
−0.969720 + 0.244220i $$0.921468\pi$$
$$402$$ 0 0
$$403$$ 4.00000 + 4.00000i 0.199254 + 0.199254i
$$404$$ 12.6778 0.630744
$$405$$ 0 0
$$406$$ 4.42289 0.219504
$$407$$ −10.5143 10.5143i −0.521174 0.521174i
$$408$$ 0 0
$$409$$ 10.3907i 0.513789i 0.966439 + 0.256894i $$0.0826993\pi$$
−0.966439 + 0.256894i $$0.917301\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 7.43472 7.43472i 0.366282 0.366282i
$$413$$ −4.17113 + 4.17113i −0.205248 + 0.205248i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0.979056i 0.0480022i
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −32.8521 −1.60493 −0.802465 0.596700i $$-0.796478\pi$$
−0.802465 + 0.596700i $$0.796478\pi$$
$$420$$ 0 0
$$421$$ 33.6560 1.64029 0.820146 0.572154i $$-0.193892\pi$$
0.820146 + 0.572154i $$0.193892\pi$$
$$422$$ 3.94076 + 3.94076i 0.191833 + 0.191833i
$$423$$ 0 0
$$424$$ 5.04145i 0.244834i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −1.69230 + 1.69230i −0.0818960 + 0.0818960i
$$428$$ −13.5138 + 13.5138i −0.653216 + 0.653216i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 28.4260i 1.36923i 0.728903 + 0.684617i $$0.240031\pi$$
−0.728903 + 0.684617i $$0.759969\pi$$
$$432$$ 0 0
$$433$$ 8.84355 + 8.84355i 0.424994 + 0.424994i 0.886919 0.461925i $$-0.152841\pi$$
−0.461925 + 0.886919i $$0.652841\pi$$
$$434$$ −5.77786 −0.277346
$$435$$ 0 0
$$436$$ −3.30082 −0.158081
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0.481506i 0.0229810i 0.999934 + 0.0114905i $$0.00365763\pi$$
−0.999934 + 0.0114905i $$0.996342\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 2.34315 2.34315i 0.111452 0.111452i
$$443$$ −15.8570 + 15.8570i −0.753388 + 0.753388i −0.975110 0.221722i $$-0.928832\pi$$
0.221722 + 0.975110i $$0.428832\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 20.7683i 0.983408i
$$447$$ 0 0
$$448$$ 0.707107 + 0.707107i 0.0334077 + 0.0334077i
$$449$$ 31.8986 1.50539 0.752694 0.658370i $$-0.228754\pi$$
0.752694 + 0.658370i $$0.228754\pi$$
$$450$$ 0 0
$$451$$ 1.43638 0.0676363
$$452$$ 5.84937 + 5.84937i 0.275131 + 0.275131i
$$453$$ 0 0
$$454$$ 27.6560i 1.29796i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −20.5557 + 20.5557i −0.961556 + 0.961556i −0.999288 0.0377315i $$-0.987987\pi$$
0.0377315 + 0.999288i $$0.487987\pi$$
$$458$$ 17.2266 17.2266i 0.804948 0.804948i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 35.9849i 1.67599i −0.545682 0.837993i $$-0.683729\pi$$
0.545682 0.837993i $$-0.316271\pi$$
$$462$$ 0 0
$$463$$ 12.8703 + 12.8703i 0.598134 + 0.598134i 0.939816 0.341682i $$-0.110996\pi$$
−0.341682 + 0.939816i $$0.610996\pi$$
$$464$$ −4.42289 −0.205327
$$465$$ 0 0
$$466$$ −20.8868 −0.967562
$$467$$ 0.531630 + 0.531630i 0.0246009 + 0.0246009i 0.719300 0.694699i $$-0.244463\pi$$
−0.694699 + 0.719300i $$0.744463\pi$$
$$468$$ 0 0
$$469$$ 0.907550i 0.0419068i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 4.17113 4.17113i 0.191992 0.191992i
$$473$$ −8.25237 + 8.25237i −0.379445 + 0.379445i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 3.38459i 0.155133i
$$477$$ 0 0
$$478$$ 1.04145 + 1.04145i 0.0476348 + 0.0476348i
$$479$$ −23.0588 −1.05358 −0.526792 0.849994i $$-0.676605\pi$$
−0.526792 + 0.849994i $$0.676605\pi$$
$$480$$ 0 0
$$481$$ 8.18848 0.373363
$$482$$ 15.2422 + 15.2422i 0.694263 + 0.694263i
$$483$$ 0 0
$$484$$ 7.83920i 0.356327i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 15.9291 15.9291i 0.721817 0.721817i −0.247158 0.968975i $$-0.579497\pi$$
0.968975 + 0.247158i $$0.0794967\pi$$
$$488$$ 1.69230 1.69230i 0.0766067 0.0766067i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 11.3509i 0.512261i 0.966642 + 0.256130i $$0.0824477\pi$$
−0.966642 + 0.256130i $$0.917552\pi$$
$$492$$ 0 0
$$493$$ −10.5852 10.5852i −0.476732 0.476732i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 5.77786 0.259434
$$497$$ 7.55573 + 7.55573i 0.338921 + 0.338921i
$$498$$ 0 0
$$499$$ 20.6319i 0.923610i 0.886982 + 0.461805i $$0.152798\pi$$
−0.886982 + 0.461805i $$0.847202\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −1.89887 + 1.89887i −0.0847509 + 0.0847509i
$$503$$ −21.2982 + 21.2982i −0.949638 + 0.949638i −0.998791 0.0491536i $$-0.984348\pi$$
0.0491536 + 0.998791i $$0.484348\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 8.50982i 0.378308i
$$507$$ 0 0
$$508$$ 0.615405 + 0.615405i 0.0273042 + 0.0273042i
$$509$$ −8.13328 −0.360501 −0.180251 0.983621i $$-0.557691\pi$$
−0.180251 + 0.983621i $$0.557691\pi$$
$$510$$ 0 0
$$511$$ 8.06239 0.356659
$$512$$ −0.707107 0.707107i −0.0312500 0.0312500i
$$513$$ 0 0
$$514$$ 15.5384i 0.685368i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 13.2809 13.2809i 0.584095 0.584095i
$$518$$ −5.91399 + 5.91399i −0.259846 + 0.259846i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 19.2331i 0.842617i −0.906917 0.421308i $$-0.861571\pi$$
0.906917 0.421308i $$-0.138429\pi$$
$$522$$ 0 0
$$523$$ 3.22635 + 3.22635i 0.141078 + 0.141078i 0.774119 0.633040i $$-0.218193\pi$$
−0.633040 + 0.774119i $$0.718193\pi$$
$$524$$ 6.52717 0.285141
$$525$$ 0 0
$$526$$ 11.2135 0.488930
$$527$$ 13.8280 + 13.8280i 0.602357 + 0.602357i
$$528$$ 0 0
$$529$$ 0.0890385i 0.00387124i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −0.559322 + 0.559322i −0.0242269 + 0.0242269i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0.907550i 0.0392002i
$$537$$ 0 0
$$538$$ 5.13657 + 5.13657i 0.221453 + 0.221453i
$$539$$ 1.77786 0.0765780
$$540$$ 0 0
$$541$$ −12.9412 −0.556386 −0.278193 0.960525i $$-0.589735\pi$$
−0.278193 + 0.960525i $$0.589735\pi$$
$$542$$ 12.4278 + 12.4278i 0.533821 + 0.533821i
$$543$$ 0 0
$$544$$ 3.38459i 0.145113i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −7.15601 + 7.15601i −0.305969 + 0.305969i −0.843344 0.537375i $$-0.819416\pi$$
0.537375 + 0.843344i $$0.319416\pi$$
$$548$$ 0.192517 0.192517i 0.00822390 0.00822390i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 11.5557 + 11.5557i 0.491400 + 0.491400i
$$554$$ −13.8775 −0.589598
$$555$$ 0 0
$$556$$ 14.8694 0.630605
$$557$$ 19.5648 + 19.5648i 0.828989 + 0.828989i 0.987377 0.158388i $$-0.0506297\pi$$
−0.158388 + 0.987377i $$0.550630\pi$$
$$558$$ 0 0
$$559$$ 6.42692i 0.271830i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 8.89887 8.89887i 0.375376 0.375376i
$$563$$ −0.0708861 + 0.0708861i −0.00298749 + 0.00298749i −0.708599 0.705611i $$-0.750672\pi$$
0.705611 + 0.708599i $$0.250672\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 6.64564i 0.279337i
$$567$$ 0 0
$$568$$ −7.55573 7.55573i −0.317031 0.317031i
$$569$$ 20.2232 0.847799 0.423900 0.905709i $$-0.360661\pi$$
0.423900 + 0.905709i $$0.360661\pi$$
$$570$$ 0 0
$$571$$ 34.9439 1.46236 0.731179 0.682186i $$-0.238971\pi$$
0.731179 + 0.682186i $$0.238971\pi$$
$$572$$ 1.23081 + 1.23081i 0.0514628 + 0.0514628i
$$573$$ 0 0
$$574$$ 0.807922i 0.0337220i
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −32.2853 + 32.2853i −1.34405 + 1.34405i −0.452071 + 0.891982i $$0.649315\pi$$
−0.891982 + 0.452071i $$0.850685\pi$$
$$578$$ −3.92057 + 3.92057i −0.163074 + 0.163074i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0.242020i 0.0100407i
$$582$$ 0 0
$$583$$ 6.33781 + 6.33781i 0.262485 + 0.262485i
$$584$$ −8.06239 −0.333624
$$585$$ 0 0
$$586$$ −4.80642 −0.198552
$$587$$ −9.40194 9.40194i −0.388060 0.388060i 0.485935 0.873995i $$-0.338479\pi$$
−0.873995 + 0.485935i $$0.838479\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 5.91399 5.91399i 0.243064 0.243064i
$$593$$ 0.326416 0.326416i 0.0134043 0.0134043i −0.700373 0.713777i $$-0.746983\pi$$
0.713777 + 0.700373i $$0.246983\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 20.6467i 0.845721i
$$597$$ 0 0
$$598$$ 3.31371 + 3.31371i 0.135508 + 0.135508i
$$599$$ −29.1288 −1.19017 −0.595085 0.803662i $$-0.702882\pi$$
−0.595085 + 0.803662i $$0.702882\pi$$
$$600$$ 0 0
$$601$$ 45.0579 1.83795 0.918975 0.394315i $$-0.129018\pi$$
0.918975 + 0.394315i $$0.129018\pi$$
$$602$$ 4.64173 + 4.64173i 0.189183 + 0.189183i
$$603$$ 0 0
$$604$$ 6.01735i 0.244843i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −6.68541 + 6.68541i −0.271353 + 0.271353i −0.829645 0.558292i $$-0.811457\pi$$
0.558292 + 0.829645i $$0.311457\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 10.3431i 0.418439i
$$612$$ 0 0
$$613$$ 20.5112 + 20.5112i 0.828438 + 0.828438i 0.987301 0.158862i $$-0.0507826\pi$$
−0.158862 + 0.987301i $$0.550783\pi$$
$$614$$ −21.9991 −0.887812
$$615$$ 0 0
$$616$$ −1.77786 −0.0716322
$$617$$ −4.29214 4.29214i −0.172795 0.172795i 0.615411 0.788206i $$-0.288990\pi$$
−0.788206 + 0.615411i $$0.788990\pi$$
$$618$$ 0 0
$$619$$ 8.16755i 0.328282i 0.986437 + 0.164141i $$0.0524851\pi$$
−0.986437 + 0.164141i $$0.947515\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0.547054 0.547054i 0.0219349 0.0219349i
$$623$$ −9.35783 + 9.35783i −0.374913 + 0.374913i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 16.7652i 0.670070i
$$627$$ 0 0
$$628$$ 0.608522 + 0.608522i 0.0242827 + 0.0242827i
$$629$$ 28.3076 1.12870
$$630$$ 0 0
$$631$$ 38.8694 1.54737 0.773684 0.633572i $$-0.218412\pi$$
0.773684 + 0.633572i $$0.218412\pi$$
$$632$$ −11.5557 11.5557i −0.459662 0.459662i
$$633$$ 0 0
$$634$$ 0.0128889i 0.000511884i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −0.692297 + 0.692297i −0.0274298 + 0.0274298i
$$638$$ 5.56019 5.56019i 0.220130 0.220130i
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 20.0751i 0.792918i −0.918052 0.396459i $$-0.870239\pi$$
0.918052 0.396459i $$-0.129761\pi$$
$$642$$ 0 0
$$643$$ 13.6257 + 13.6257i 0.537347 + 0.537347i 0.922749 0.385402i $$-0.125937\pi$$
−0.385402 + 0.922749i $$0.625937\pi$$
$$644$$ −4.78654 −0.188616
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 1.47104 + 1.47104i 0.0578325 + 0.0578325i 0.735432 0.677599i $$-0.236979\pi$$
−0.677599 + 0.735432i $$0.736979\pi$$
$$648$$ 0 0
$$649$$ 10.4874i 0.411666i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 6.12745 6.12745i 0.239970 0.239970i
$$653$$ 4.09647 4.09647i 0.160307 0.160307i −0.622396 0.782703i $$-0.713840\pi$$
0.782703 + 0.622396i $$0.213840\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0.807922i 0.0315441i
$$657$$ 0 0
$$658$$ −7.47016 7.47016i −0.291217 0.291217i
$$659$$ −0.683757 −0.0266354 −0.0133177 0.999911i $$-0.504239\pi$$
−0.0133177 + 0.999911i $$0.504239\pi$$
$$660$$ 0 0
$$661$$ −42.9776 −1.67163 −0.835817 0.549009i $$-0.815005\pi$$
−0.835817 + 0.549009i $$0.815005\pi$$
$$662$$ 16.8275 + 16.8275i 0.654021 + 0.654021i
$$663$$ 0 0
$$664$$ 0.242020i 0.00939221i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 14.9697 14.9697i 0.579629 0.579629i
$$668$$ 6.18669 6.18669i 0.239370 0.239370i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 4.25491i 0.164259i
$$672$$ 0 0
$$673$$ 24.6569 + 24.6569i 0.950452 + 0.950452i 0.998829 0.0483773i $$-0.0154050\pi$$
−0.0483773 + 0.998829i $$0.515405\pi$$
$$674$$ −1.17219 −0.0451512
$$675$$ 0 0
$$676$$ 12.0414 0.463133
$$677$$ 31.2343 + 31.2343i 1.20043 + 1.20043i 0.974036 + 0.226394i $$0.0726938\pi$$
0.226394 + 0.974036i $$0.427306\pi$$
$$678$$ 0 0
$$679$$ 17.8775i 0.686075i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ −7.26358 + 7.26358i −0.278137 + 0.278137i
$$683$$ −7.92000 + 7.92000i −0.303050 + 0.303050i −0.842206 0.539156i $$-0.818743\pi$$
0.539156 + 0.842206i $$0.318743\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 1.00000i 0.0381802i
$$687$$ 0 0
$$688$$ −4.64173 4.64173i −0.176964 0.176964i
$$689$$ −4.93586 −0.188041
$$690$$ 0 0
$$691$$ 22.1227 0.841586 0.420793 0.907157i $$-0.361752\pi$$
0.420793 + 0.907157i $$0.361752\pi$$
$$692$$ 15.7720 + 15.7720i 0.599563 + 0.599563i
$$693$$ 0 0
$$694$$ 7.31371i 0.277625i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −1.93358 + 1.93358i −0.0732394 + 0.0732394i
$$698$$ −2.97577 + 2.97577i −0.112634 + 0.112634i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 6.16352i 0.232793i 0.993203 + 0.116396i $$0.0371343\pi$$
−0.993203 + 0.116396i $$0.962866\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 1.77786 0.0670058
$$705$$ 0 0
$$706$$ 3.14257 0.118272
$$707$$ 8.96456 + 8.96456i 0.337147 + 0.337147i
$$708$$ 0 0
$$709$$ 49.7215i 1.86733i 0.358146 + 0.933666i $$0.383409\pi$$
−0.358146 + 0.933666i $$0.616591\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 9.35783 9.35783i 0.350699 0.350699i
$$713$$ −19.5557 + 19.5557i −0.732368 + 0.732368i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 3.87899i 0.144965i
$$717$$ 0 0
$$718$$ 16.1002 + 16.1002i 0.600856 + 0.600856i
$$719$$ 16.9706 0.632895 0.316448 0.948610i $$-0.397510\pi$$
0.316448 + 0.948610i $$0.397510\pi$$
$$720$$ 0 0
$$721$$ 10.5143 0.391572
$$722$$ −13.4350 13.4350i −0.500000 0.500000i
$$723$$ 0 0
$$724$$ 23.6896i 0.880418i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 15.9162 15.9162i 0.590300 0.590300i −0.347412 0.937712i $$-0.612940\pi$$
0.937712 + 0.347412i $$0.112940\pi$$
$$728$$ 0.692297 0.692297i 0.0256582 0.0256582i
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 22.2178i 0.821757i
$$732$$ 0 0
$$733$$ 15.3578 + 15.3578i 0.567254 + 0.567254i 0.931358 0.364104i $$-0.118625\pi$$
−0.364104 + 0.931358i $$0.618625\pi$$
$$734$$ 3.02410 0.111622
$$735$$ 0 0
$$736$$ 4.78654 0.176434
$$737$$ 1.14092 + 1.14092i 0.0420262 + 0.0420262i
$$738$$ 0 0
$$739$$ 45.6515i 1.67932i −0.543114 0.839659i $$-0.682755\pi$$
0.543114 0.839659i $$-0.317245\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 3.56484 3.56484i 0.130869 0.130869i
$$743$$ −5.67508 + 5.67508i −0.208199 + 0.208199i −0.803501 0.595303i $$-0.797032\pi$$
0.595303 + 0.803501i $$0.297032\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 18.4220i 0.674478i
$$747$$ 0 0
$$748$$ 4.25491 + 4.25491i 0.155575 + 0.155575i
$$749$$ −19.1115 −0.698317
$$750$$ 0 0
$$751$$ −41.4364 −1.51203 −0.756017 0.654552i $$-0.772857\pi$$
−0.756017 + 0.654552i $$0.772857\pi$$
$$752$$ 7.47016 + 7.47016i 0.272409 + 0.272409i
$$753$$ 0 0
$$754$$ 4.33026i 0.157699i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 22.4109 22.4109i 0.814539 0.814539i −0.170772 0.985311i $$-0.554626\pi$$
0.985311 + 0.170772i $$0.0546261\pi$$
$$758$$ −19.3755 + 19.3755i −0.703749 + 0.703749i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 15.1675i 0.549823i −0.961470 0.274911i $$-0.911351\pi$$
0.961470 0.274911i $$-0.0886485\pi$$
$$762$$ 0 0
$$763$$ −2.33403 2.33403i −0.0844976 0.0844976i
$$764$$ 23.4720 0.849185
$$765$$ 0 0
$$766$$ −24.9913 −0.902973
$$767$$ −4.08378 4.08378i −0.147457 0.147457i
$$768$$ 0 0
$$769$$ 19.8686i 0.716481i −0.933629 0.358241i $$-0.883377\pi$$
0.933629 0.358241i $$-0.116623\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 18.1288 18.1288i 0.652470 0.652470i
$$773$$ −0.293937 + 0.293937i −0.0105722 + 0.0105722i −0.712373 0.701801i $$-0.752380\pi$$
0.701801 + 0.712373i $$0.252380\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 17.8775i 0.641765i
$$777$$ 0 0
$$778$$ 11.1975 + 11.1975i 0.401449 + 0.401449i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 18.9972 0.679774
$$782$$ 11.4555 + 11.4555i 0.409647 + 0.409647i
$$783$$ 0 0
$$784$$ 1.00000i 0.0357143i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −16.3076 + 16.3076i −0.581302 + 0.581302i −0.935261 0.353959i $$-0.884835\pi$$
0.353959 + 0.935261i $$0.384835\pi$$
$$788$$ −9.58535 + 9.58535i −0.341464 + 0.341464i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 8.27226i 0.294128i
$$792$$ 0 0
$$793$$ −1.65685 1.65685i −0.0588366 0.0588366i
$$794$$ −20.5874 −0.730621
$$795$$ 0 0
$$796$$ −2.46416 −0.0873397
$$797$$ −22.1562 22.1562i −0.784813 0.784813i 0.195826 0.980639i $$-0.437261\pi$$
−0.980639 + 0.195826i $$0.937261\pi$$
$$798$$ 0 0
$$799$$ 35.7562i 1.26496i